LMFDB - Embedded newform 80.16.c.c.49.2

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} + 8 x^{6} + 6172534 x^{5} + 23752924445 x^{4} + 1095295465934 x^{3} + \cdots + 59\!\cdots\!64 $ x^8 - 4x^7 + 8x^6 + 6172534x^5 + 23752924445x^4 + 1095295465934x^3 + 14478882731282x^2 - 41384481648202964*x + 59143904715457383364
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{2}\cdot 5^{11} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-249.000 - 249.000i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.16.c.c.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5042.00i q^{3} +(79524.6 + 155542. i) q^{5} -3.81841e6i q^{7} -1.10729e7 q^{9} +O(q^{10})$	\(q-5042.00i q^{3} +(79524.6 + 155542. i) q^{5} -3.81841e6i q^{7} -1.10729e7 q^{9} -6.58816e7 q^{11} -2.98243e7i q^{13} +(7.84245e8 - 4.00963e8i) q^{15} -2.71990e9i q^{17} +2.59055e8 q^{19} -1.92524e10 q^{21} +8.56893e9i q^{23} +(-1.78693e10 + 2.47389e10i) q^{25} -1.65177e10i q^{27} +1.46270e11 q^{29} -1.80940e11 q^{31} +3.32175e11i q^{33} +(5.93925e11 - 3.03658e11i) q^{35} +1.52555e11i q^{37} -1.50374e11 q^{39} -1.17421e12 q^{41} +8.75693e11i q^{43} +(-8.80567e11 - 1.72230e12i) q^{45} -5.72415e12i q^{47} -9.83271e12 q^{49} -1.37138e13 q^{51} -8.50996e12i q^{53} +(-5.23921e12 - 1.02474e13i) q^{55} -1.30616e12i q^{57} -7.18836e12 q^{59} +5.57263e12 q^{61} +4.22809e13i q^{63} +(4.63894e12 - 2.37176e12i) q^{65} -3.26451e12i q^{67} +4.32046e13 q^{69} +5.83158e13 q^{71} -6.27971e13i q^{73} +(1.24734e14 + 9.00968e13i) q^{75} +2.51563e14i q^{77} -1.09818e14 q^{79} -2.42166e14 q^{81} +2.82120e14i q^{83} +(4.23060e14 - 2.16299e14i) q^{85} -7.37491e14i q^{87} -6.26105e13 q^{89} -1.13881e14 q^{91} +9.12301e14i q^{93} +(2.06012e13 + 4.02940e13i) q^{95} +6.53097e14i q^{97} +7.29500e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 251400 q^{5} - 43491176 q^{9}+O(q^{10}) $ 8 * q + 251400 * q^5 - 43491176 * q^9	$ 8 q + 251400 q^{5} - 43491176 q^{9} - 95435616 q^{11} - 5448800 q^{15} - 6479216160 q^{19} - 14760325504 q^{21} - 2241855000 q^{25} - 244549636560 q^{29} - 522311705216 q^{31} + 1829607146400 q^{35} + 2307595824192 q^{39} + 6699117519216 q^{41} - 9090807477800 q^{45} - 15809163185544 q^{49} - 40555579650176 q^{51} + 39746288199200 q^{55} - 3791808509280 q^{59} + 57800629300816 q^{61} + 58028394892800 q^{65} + 59060996328448 q^{69} + 245426235422784 q^{71} - 226448486200000 q^{75} - 624094605411840 q^{79} - 13\!\cdots\!52 q^{81}+ \cdots - 16\!\cdots\!48 q^{99}+O(q^{100}) $ 8 * q + 251400 * q^5 - 43491176 * q^9 - 95435616 * q^11 - 5448800 * q^15 - 6479216160 * q^19 - 14760325504 * q^21 - 2241855000 * q^25 - 244549636560 * q^29 - 522311705216 * q^31 + 1829607146400 * q^35 + 2307595824192 * q^39 + 6699117519216 * q^41 - 9090807477800 * q^45 - 15809163185544 * q^49 - 40555579650176 * q^51 + 39746288199200 * q^55 - 3791808509280 * q^59 + 57800629300816 * q^61 + 58028394892800 * q^65 + 59060996328448 * q^69 + 245426235422784 * q^71 - 226448486200000 * q^75 - 624094605411840 * q^79 - 1376711600108152 * q^81 + 1092463762441600 * q^85 - 635249793637680 * q^89 + 976491706492224 * q^91 + 1859590136604000 * q^95 - 1626246829353248 * 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
$3$		−	5042.00i		−	1.33105i	−0.746376	−	0.665524i	$-0.768208\pi$
$3$		−	5042.00i		−	1.33105i	0.746376	−	0.665524i	$-0.231792\pi$
$4$		0			0
$5$	79524.6	+	155542.i	0.455225	+	0.890376i
$5$	79524.6	+	155542.i	0.455225	+	0.890376i
$6$		0			0
$7$		−	3.81841e6i		−	1.75246i	−0.481895	−	0.876229i	$-0.660052\pi$
$7$		−	3.81841e6i		−	1.75246i	0.481895	−	0.876229i	$-0.339948\pi$
$8$		0			0
$9$	−1.10729e7			−0.771689
$10$		0			0
$11$	−6.58816e7			−1.01934			−0.509670	−	0.860370i	$-0.670233\pi$
$11$	−6.58816e7			−1.01934			−0.509670	+	0.860370i	$0.670233\pi$
$12$		0			0
$13$		−	2.98243e7i		−	0.131824i	−0.997825	−	0.0659120i	$-0.979004\pi$
$13$		−	2.98243e7i		−	0.131824i	0.997825	−	0.0659120i	$-0.0209957\pi$
$14$		0			0
$15$	7.84245e8	−	4.00963e8i	1.18513	−	0.605927i
$16$		0			0
$17$		−	2.71990e9i		−	1.60763i	−0.594878	−	0.803816i	$-0.702800\pi$
$17$		−	2.71990e9i		−	1.60763i	0.594878	−	0.803816i	$-0.297200\pi$
$18$		0			0
$19$	2.59055e8			0.0664875			0.0332437	−	0.999447i	$-0.489416\pi$
$19$	2.59055e8			0.0664875			0.0332437	+	0.999447i	$0.489416\pi$
$20$		0			0
$21$	−1.92524e10			−2.33260
$22$		0			0
$23$			8.56893e9i			0.524769i	0.964963	+	0.262384i	$0.0845088\pi$
$23$			8.56893e9i			0.524769i	−0.964963	+	0.262384i	$0.915491\pi$
$24$		0			0
$25$	−1.78693e10	+	2.47389e10i	−0.585540	+	0.810644i
$26$		0			0
$27$		−	1.65177e10i		−	0.303893i
$28$		0			0
$29$	1.46270e11			1.57459			0.787297	−	0.616573i	$-0.211480\pi$
$29$	1.46270e11			1.57459			0.787297	+	0.616573i	$0.211480\pi$
$30$		0			0
$31$	−1.80940e11			−1.18120			−0.590598	−	0.806966i	$-0.701108\pi$
$31$	−1.80940e11			−1.18120			−0.590598	+	0.806966i	$0.701108\pi$
$32$		0			0
$33$			3.32175e11i			1.35679i
$34$		0			0
$35$	5.93925e11	−	3.03658e11i	1.56035	−	0.797763i
$36$		0			0
$37$			1.52555e11i			0.264188i	0.991237	+	0.132094i	$0.0421701\pi$
$37$			1.52555e11i			0.264188i	−0.991237	+	0.132094i	$0.957830\pi$
$38$		0			0
$39$	−1.50374e11			−0.175464
$40$		0			0
$41$	−1.17421e12			−0.941598			−0.470799	−	0.882240i	$-0.656034\pi$
$41$	−1.17421e12			−0.941598			−0.470799	+	0.882240i	$0.656034\pi$
$42$		0			0
$43$			8.75693e11i			0.491290i	0.969360	+	0.245645i	$0.0789998\pi$
$43$			8.75693e11i			0.491290i	−0.969360	+	0.245645i	$0.921000\pi$
$44$		0			0
$45$	−8.80567e11	−	1.72230e12i	−0.351292	−	0.687093i
$46$		0			0
$47$		−	5.72415e12i		−	1.64807i	−0.566536	−	0.824037i	$-0.691717\pi$
$47$		−	5.72415e12i		−	1.64807i	0.566536	−	0.824037i	$-0.308283\pi$
$48$		0			0
$49$	−9.83271e12			−2.07111
$50$		0			0
$51$	−1.37138e13			−2.13983
$52$		0			0
$53$		−	8.50996e12i		−	0.995081i	−0.867441	−	0.497541i	$-0.834237\pi$
$53$		−	8.50996e12i		−	0.995081i	0.867441	−	0.497541i	$-0.165763\pi$
$54$		0			0
$55$	−5.23921e12	−	1.02474e13i	−0.464030	−	0.907596i
$56$		0			0
$57$		−	1.30616e12i		−	0.0884980i
$58$		0			0
$59$	−7.18836e12			−0.376045			−0.188023	−	0.982165i	$-0.560208\pi$
$59$	−7.18836e12			−0.376045			−0.188023	+	0.982165i	$0.560208\pi$
$60$		0			0
$61$	5.57263e12			0.227032			0.113516	−	0.993536i	$-0.463789\pi$
$61$	5.57263e12			0.227032			0.113516	+	0.993536i	$0.463789\pi$
$62$		0			0
$63$			4.22809e13i			1.35235i
$64$		0			0
$65$	4.63894e12	−	2.37176e12i	0.117373	−	0.0600097i
$66$		0			0
$67$		−	3.26451e12i		−	0.0658046i	−0.999459	−	0.0329023i	$-0.989525\pi$
$67$		−	3.26451e12i		−	0.0658046i	0.999459	−	0.0329023i	$-0.0104750\pi$
$68$		0			0
$69$	4.32046e13			0.698493
$70$		0			0
$71$	5.83158e13			0.760937			0.380469	−	0.924794i	$-0.375763\pi$
$71$	5.83158e13			0.760937			0.380469	+	0.924794i	$0.375763\pi$
$72$		0			0
$73$		−	6.27971e13i		−	0.665301i	−0.943050	−	0.332650i	$-0.892057\pi$
$73$		−	6.27971e13i		−	0.665301i	0.943050	−	0.332650i	$-0.107943\pi$
$74$		0			0
$75$	1.24734e14	+	9.00968e13i	1.07901	+	0.779381i
$76$		0			0
$77$			2.51563e14i			1.78635i
$78$		0			0
$79$	−1.09818e14			−0.643384			−0.321692	−	0.946844i	$-0.604252\pi$
$79$	−1.09818e14			−0.643384			−0.321692	+	0.946844i	$0.604252\pi$
$80$		0			0
$81$	−2.42166e14			−1.17619
$82$		0			0
$83$			2.82120e14i			1.14116i	0.821241	+	0.570582i	$0.193282\pi$
$83$			2.82120e14i			1.14116i	−0.821241	+	0.570582i	$0.806718\pi$
$84$		0			0
$85$	4.23060e14	−	2.16299e14i	1.43140	−	0.731835i
$86$		0			0
$87$		−	7.37491e14i		−	2.09586i
$88$		0			0
$89$	−6.26105e13			−0.150045			−0.0750226	−	0.997182i	$-0.523903\pi$
$89$	−6.26105e13			−0.150045			−0.0750226	+	0.997182i	$0.523903\pi$
$90$		0			0
$91$	−1.13881e14			−0.231016
$92$		0			0
$93$			9.12301e14i			1.57223i
$94$		0			0
$95$	2.06012e13	+	4.02940e13i	0.0302668	+	0.0591989i
$96$		0			0
$97$			6.53097e14i			0.820710i	0.911926	+	0.410355i	$0.134595\pi$
$97$			6.53097e14i			0.820710i	−0.911926	+	0.410355i	$0.865405\pi$
$98$		0			0
$99$	7.29500e14			0.786613
$100$		0			0
$101$	1.04808e15			0.972712			0.486356	−	0.873761i	$-0.338326\pi$
$101$	1.04808e15			0.972712			0.486356	+	0.873761i	$0.338326\pi$
$102$		0			0
$103$			2.11702e15i			1.69608i	0.529932	+	0.848040i	$0.322217\pi$
$103$			2.11702e15i			1.69608i	−0.529932	+	0.848040i	$0.677783\pi$
$104$		0			0
$105$	−1.53104e15	−	2.99457e15i	−1.06186	−	2.07690i
$106$		0			0
$107$		−	4.25190e13i		−	0.0255980i	−0.999918	−	0.0127990i	$-0.995926\pi$
$107$		−	4.25190e13i		−	0.0255980i	0.999918	−	0.0127990i	$-0.00407415\pi$
$108$		0			0
$109$	−1.94135e15			−1.01720			−0.508598	−	0.861004i	$-0.669836\pi$
$109$	−1.94135e15			−1.01720			−0.508598	+	0.861004i	$0.669836\pi$
$110$		0			0
$111$	7.69183e14			0.351647
$112$		0			0
$113$			4.23147e15i			1.69201i	0.533176	+	0.846004i	$0.320998\pi$
$113$			4.23147e15i			1.69201i	−0.533176	+	0.846004i	$0.679002\pi$
$114$		0			0
$115$	−1.33283e15	+	6.81441e14i	−0.467242	+	0.238888i
$116$		0			0
$117$			3.30241e14i			0.101727i
$118$		0			0
$119$	−1.03857e16			−2.81731
$120$		0			0
$121$	1.63141e14			0.0390546
$122$		0			0
$123$			5.92035e15i			1.25331i
$124$		0			0
$125$	−5.26899e15	−	8.12075e14i	−0.988330	−	0.152325i
$126$		0			0
$127$		−	3.51641e15i		−	0.585560i	−0.956180	−	0.292780i	$-0.905420\pi$
$127$		−	3.51641e15i		−	0.585560i	0.956180	−	0.292780i	$-0.0945803\pi$
$128$		0			0
$129$	4.41525e15			0.653931
$130$		0			0
$131$	−6.86455e15			−0.905894			−0.452947	−	0.891537i	$-0.649627\pi$
$131$	−6.86455e15			−0.905894			−0.452947	+	0.891537i	$0.649627\pi$
$132$		0			0
$133$		−	9.89178e14i		−	0.116516i
$134$		0			0
$135$	2.56920e15	−	1.31356e15i	0.270579	−	0.138340i
$136$		0			0
$137$			9.66931e15i			0.911993i	0.889982	+	0.455996i	$0.150717\pi$
$137$			9.66931e15i			0.911993i	−0.889982	+	0.455996i	$0.849283\pi$
$138$		0			0
$139$	1.99151e16			1.68489			0.842444	−	0.538784i	$-0.181116\pi$
$139$	1.99151e16			1.68489			0.842444	+	0.538784i	$0.181116\pi$
$140$		0			0
$141$	−2.88612e16			−2.19367
$142$		0			0
$143$			1.96487e15i			0.134374i
$144$		0			0
$145$	1.16320e16	+	2.27511e16i	0.716796	+	1.40198i
$146$		0			0
$147$			4.95765e16i			2.75674i
$148$		0			0
$149$	5.69937e15			0.286372			0.143186	−	0.989696i	$-0.454265\pi$
$149$	5.69937e15			0.286372			0.143186	+	0.989696i	$0.454265\pi$
$150$		0			0
$151$	9.09809e15			0.413640			0.206820	−	0.978379i	$-0.433688\pi$
$151$	9.09809e15			0.413640			0.206820	+	0.978379i	$0.433688\pi$
$152$		0			0
$153$			3.01172e16i			1.24059i
$154$		0			0
$155$	−1.43892e16	−	2.81438e16i	−0.537711	−	1.05171i
$156$		0			0
$157$			6.96026e15i			0.236254i	0.992999	+	0.118127i	$0.0376889\pi$
$157$			6.96026e15i			0.236254i	−0.992999	+	0.118127i	$0.962311\pi$
$158$		0			0
$159$	−4.29072e16			−1.32450
$160$		0			0
$161$	3.27197e16			0.919635
$162$		0			0
$163$			1.50326e16i			0.385148i	0.981282	+	0.192574i	$0.0616836\pi$
$163$			1.50326e16i			0.385148i	−0.981282	+	0.192574i	$0.938316\pi$
$164$		0			0
$165$	−5.16673e16	+	2.64161e16i	−1.20805	+	0.617646i
$166$		0			0
$167$			5.36303e16i			1.14561i	0.819692	+	0.572805i	$0.194145\pi$
$167$			5.36303e16i			1.14561i	−0.819692	+	0.572805i	$0.805855\pi$
$168$		0			0
$169$	5.02964e16			0.982622
$170$		0			0
$171$	−2.86849e15			−0.0513076
$172$		0			0
$173$		−	1.73767e16i		−	0.284854i	−0.989805	−	0.142427i	$-0.954509\pi$
$173$		−	1.73767e16i		−	0.284854i	0.989805	−	0.142427i	$-0.0454906\pi$
$174$		0			0
$175$	9.44632e16	+	6.82322e16i	1.42062	+	1.02613i
$176$		0			0
$177$			3.62437e16i			0.500534i
$178$		0			0
$179$	−1.03346e17			−1.31189			−0.655944	−	0.754809i	$-0.727729\pi$
$179$	−1.03346e17			−1.31189			−0.655944	+	0.754809i	$0.727729\pi$
$180$		0			0
$181$	−9.41305e16			−1.09936			−0.549681	−	0.835374i	$-0.685251\pi$
$181$	−9.41305e16			−1.09936			−0.549681	+	0.835374i	$0.685251\pi$
$182$		0			0
$183$		−	2.80972e16i		−	0.302190i
$184$		0			0
$185$	−2.37288e16	+	1.21319e16i	−0.235227	+	0.120265i
$186$		0			0
$187$			1.79192e17i			1.63872i
$188$		0			0
$189$	−6.30714e16			−0.532560
$190$		0			0
$191$	−1.11137e17			−0.867178			−0.433589	−	0.901111i	$-0.642753\pi$
$191$	−1.11137e17			−0.867178			−0.433589	+	0.901111i	$0.642753\pi$
$192$		0			0
$193$		−	7.35343e16i		−	0.530653i	−0.964159	−	0.265326i	$-0.914520\pi$
$193$		−	7.35343e16i		−	0.530653i	0.964159	−	0.265326i	$-0.0854797\pi$
$194$		0			0
$195$	−1.19584e16	−	2.33895e16i	−0.0798757	−	0.156229i
$196$		0			0
$197$			1.15175e17i			0.712629i	0.934366	+	0.356314i	$0.115967\pi$
$197$			1.15175e17i			0.712629i	−0.934366	+	0.356314i	$0.884033\pi$
$198$		0			0
$199$	−7.91937e16			−0.454248			−0.227124	−	0.973866i	$-0.572932\pi$
$199$	−7.91937e16			−0.454248			−0.227124	+	0.973866i	$0.572932\pi$
$200$		0			0
$201$	−1.64596e16			−0.0875891
$202$		0			0
$203$		−	5.58517e17i		−	2.75941i
$204$		0			0
$205$	−9.33783e16	−	1.82639e17i	−0.428639	−	0.838377i
$206$		0			0
$207$		−	9.48829e16i		−	0.404958i
$208$		0			0
$209$	−1.70670e16			−0.0677734
$210$		0			0
$211$	1.72304e17			0.637056			0.318528	−	0.947913i	$-0.396812\pi$
$211$	1.72304e17			0.637056			0.318528	+	0.947913i	$0.396812\pi$
$212$		0			0
$213$		−	2.94029e17i		−	1.01284i
$214$		0			0
$215$	−1.36207e17	+	6.96391e16i	−0.437433	+	0.223648i
$216$		0			0
$217$			6.90904e17i			2.07000i
$218$		0			0
$219$	−3.16623e17			−0.885547
$220$		0			0
$221$	−8.11191e16			−0.211925
$222$		0			0
$223$			6.00876e17i			1.46723i	0.679565	+	0.733615i	$0.262168\pi$
$223$			6.00876e17i			1.46723i	−0.679565	+	0.733615i	$0.737832\pi$
$224$		0			0
$225$	1.97864e17	−	2.73931e17i	0.451854	−	0.625565i
$226$		0			0
$227$		−	1.13161e17i		−	0.241826i	−0.992663	−	0.120913i	$-0.961418\pi$
$227$		−	1.13161e17i		−	0.241826i	0.992663	−	0.120913i	$-0.0385821\pi$
$228$		0			0
$229$	5.81603e17			1.16375			0.581876	−	0.813277i	$-0.302319\pi$
$229$	5.81603e17			1.16375			0.581876	+	0.813277i	$0.302319\pi$
$230$		0			0
$231$	1.26838e18			2.37772
$232$		0			0
$233$		−	1.21206e17i		−	0.212988i	−0.994313	−	0.106494i	$-0.966038\pi$
$233$		−	1.21206e17i		−	0.212988i	0.994313	−	0.106494i	$-0.0339625\pi$
$234$		0			0
$235$	8.90347e17	−	4.55210e17i	1.46741	−	0.750245i
$236$		0			0
$237$			5.53703e17i			0.856375i
$238$		0			0
$239$	4.54537e17			0.660063			0.330031	−	0.943970i	$-0.392941\pi$
$239$	4.54537e17			0.660063			0.330031	+	0.943970i	$0.392941\pi$
$240$		0			0
$241$	1.15683e18			1.57813			0.789065	−	0.614310i	$-0.210566\pi$
$241$	1.15683e18			1.57813			0.789065	+	0.614310i	$0.210566\pi$
$242$		0			0
$243$			9.83991e17i			1.26167i
$244$		0			0
$245$	−7.81942e17	−	1.52940e18i	−0.942821	−	1.84406i
$246$		0			0
$247$		−	7.72613e15i		−	0.00876465i
$248$		0			0
$249$	1.42245e18			1.51894
$250$		0			0
$251$	−1.19328e18			−1.20003			−0.600013	−	0.799990i	$-0.704838\pi$
$251$	−1.19328e18			−1.20003			−0.600013	+	0.799990i	$0.704838\pi$
$252$		0			0
$253$		−	5.64535e17i		−	0.534918i
$254$		0			0
$255$	−1.09058e18	−	2.13307e18i	−0.974107	−	1.90526i
$256$		0			0
$257$		−	1.14545e18i		−	0.964890i	−0.875926	−	0.482445i	$-0.839749\pi$
$257$		−	1.14545e18i		−	0.964890i	0.875926	−	0.482445i	$-0.160251\pi$
$258$		0			0
$259$	5.82518e17			0.462979
$260$		0			0
$261$	−1.61963e18			−1.21510
$262$		0			0
$263$		−	2.25180e18i		−	1.59537i	−0.603076	−	0.797684i	$-0.706058\pi$
$263$		−	2.25180e18i		−	1.59537i	0.603076	−	0.797684i	$-0.293942\pi$
$264$		0			0
$265$	1.32366e18	−	6.76751e17i	0.885997	−	0.452986i
$266$		0			0
$267$			3.15683e17i			0.199717i
$268$		0			0
$269$	−1.61251e18			−0.964632			−0.482316	−	0.875997i	$-0.660204\pi$
$269$	−1.61251e18			−0.964632			−0.482316	+	0.875997i	$0.660204\pi$
$270$		0			0
$271$	−2.98675e18			−1.69016			−0.845082	−	0.534637i	$-0.820448\pi$
$271$	−2.98675e18			−1.69016			−0.845082	+	0.534637i	$0.820448\pi$
$272$		0			0
$273$			5.74190e17i			0.307493i
$274$		0			0
$275$	1.17726e18	−	1.62984e18i	0.596864	−	0.826322i
$276$		0			0
$277$		−	7.33903e17i		−	0.352404i	−0.984354	−	0.176202i	$-0.943619\pi$
$277$		−	7.33903e17i		−	0.352404i	0.984354	−	0.176202i	$-0.0563811\pi$
$278$		0			0
$279$	2.00353e18			0.911516
$280$		0			0
$281$	−1.80787e17			−0.0779598			−0.0389799	−	0.999240i	$-0.512411\pi$
$281$	−1.80787e17			−0.0779598			−0.0389799	+	0.999240i	$0.512411\pi$
$282$		0			0
$283$		−	1.81111e18i		−	0.740536i	−0.928925	−	0.370268i	$-0.879266\pi$
$283$		−	1.81111e18i		−	0.740536i	0.928925	−	0.370268i	$-0.120734\pi$
$284$		0			0
$285$	2.03163e17	−	1.03872e17i	0.0787965	−	0.0402865i
$286$		0			0
$287$			4.48360e18i			1.65011i
$288$		0			0
$289$	−4.53545e18			−1.58448
$290$		0			0
$291$	3.29292e18			1.09240
$292$		0			0
$293$		−	9.38285e17i		−	0.295684i	−0.989011	−	0.147842i	$-0.952767\pi$
$293$		−	9.38285e17i		−	0.295684i	0.989011	−	0.147842i	$-0.0472327\pi$
$294$		0			0
$295$	−5.71652e17	−	1.11809e18i	−0.171185	−	0.334822i
$296$		0			0
$297$			1.08821e18i			0.309771i
$298$		0			0
$299$	2.55562e17			0.0691772
$300$		0			0
$301$	3.34376e18			0.860966
$302$		0			0
$303$		−	5.28442e18i		−	1.29473i
$304$		0			0
$305$	4.43161e17	+	8.66779e17i	0.103351	+	0.202143i
$306$		0			0
$307$			3.30085e18i			0.732973i	0.930423	+	0.366487i	$0.119439\pi$
$307$			3.30085e18i			0.732973i	−0.930423	+	0.366487i	$0.880561\pi$
$308$		0			0
$309$	1.06740e19			2.25756
$310$		0			0
$311$	6.55235e18			1.32037			0.660183	−	0.751105i	$-0.270479\pi$
$311$	6.55235e18			1.32037			0.660183	+	0.751105i	$0.270479\pi$
$312$		0			0
$313$		−	1.25098e18i		−	0.240252i	−0.992759	−	0.120126i	$-0.961670\pi$
$313$		−	1.25098e18i		−	0.240252i	0.992759	−	0.120126i	$-0.0383298\pi$
$314$		0			0
$315$	−6.57646e18	+	3.36237e18i	−1.20410	+	0.615625i
$316$		0			0
$317$			8.16730e18i			1.42605i	0.701140	+	0.713024i	$0.252675\pi$
$317$			8.16730e18i			1.42605i	−0.701140	+	0.713024i	$0.747325\pi$
$318$		0			0
$319$	−9.63647e18			−1.60505
$320$		0			0
$321$	−2.14381e17			−0.0340721
$322$		0			0
$323$		−	7.04604e17i		−	0.106887i
$324$		0			0
$325$	7.37819e17	+	5.32937e17i	0.106862	+	0.0771882i
$326$		0			0
$327$			9.78828e18i			1.35394i
$328$		0			0
$329$	−2.18571e19			−2.88818
$330$		0			0
$331$	−8.19945e18			−1.03532			−0.517660	−	0.855586i	$-0.673197\pi$
$331$	−8.19945e18			−1.03532			−0.517660	+	0.855586i	$0.673197\pi$
$332$		0			0
$333$		−	1.68923e18i		−	0.203871i
$334$		0			0
$335$	5.07769e17	−	2.59609e17i	0.0585909	−	0.0299559i
$336$		0			0
$337$		−	1.33250e19i		−	1.47042i	−0.677838	−	0.735212i	$-0.737083\pi$
$337$		−	1.33250e19i		−	1.47042i	0.677838	−	0.735212i	$-0.262917\pi$
$338$		0			0
$339$	2.13351e19			2.25214
$340$		0			0
$341$	1.19206e19			1.20404
$342$		0			0
$343$			1.94172e19i			1.87707i
$344$		0			0
$345$	3.43583e18	+	6.72014e18i	0.317972	+	0.621921i
$346$		0			0
$347$		−	1.08670e19i		−	0.963027i	−0.876439	−	0.481513i	$-0.840087\pi$
$347$		−	1.08670e19i		−	0.963027i	0.876439	−	0.481513i	$-0.159913\pi$
$348$		0			0
$349$	−4.69536e18			−0.398546			−0.199273	−	0.979944i	$-0.563858\pi$
$349$	−4.69536e18			−0.398546			−0.199273	+	0.979944i	$0.563858\pi$
$350$		0			0
$351$	−4.92628e17			−0.0400605
$352$		0			0
$353$		−	3.69821e18i		−	0.288191i	−0.989564	−	0.144096i	$-0.953973\pi$
$353$		−	3.69821e18i		−	0.288191i	0.989564	−	0.144096i	$-0.0460273\pi$
$354$		0			0
$355$	4.63754e18	+	9.07058e18i	0.346398	+	0.677520i
$356$		0			0
$357$			5.23648e19i			3.74997i
$358$		0			0
$359$	−2.86790e18			−0.196950			−0.0984749	−	0.995140i	$-0.531396\pi$
$359$	−2.86790e18			−0.196950			−0.0984749	+	0.995140i	$0.531396\pi$
$360$		0			0
$361$	−1.51140e19			−0.995579
$362$		0			0
$363$		−	8.22555e17i		−	0.0519835i
$364$		0			0
$365$	9.76760e18	−	4.99391e18i	0.592368	−	0.302862i
$366$		0			0
$367$		−	1.62272e19i		−	0.944600i	−0.881438	−	0.472300i	$-0.843424\pi$
$367$		−	1.62272e19i		−	0.944600i	0.881438	−	0.472300i	$-0.156576\pi$
$368$		0			0
$369$	1.30019e19			0.726621
$370$		0			0
$371$	−3.24945e19			−1.74384
$372$		0			0
$373$		−	1.81528e18i		−	0.0935681i	−0.998905	−	0.0467841i	$-0.985103\pi$
$373$		−	1.81528e18i		−	0.0935681i	0.998905	−	0.0467841i	$-0.0148973\pi$
$374$		0			0
$375$	−4.09449e18	+	2.65663e19i	−0.202752	+	1.31552i
$376$		0			0
$377$		−	4.36238e18i		−	0.207570i
$378$		0			0
$379$	−2.29492e19			−1.04948			−0.524739	−	0.851263i	$-0.675837\pi$
$379$	−2.29492e19			−1.04948			−0.524739	+	0.851263i	$0.675837\pi$
$380$		0			0
$381$	−1.77297e19			−0.779408
$382$		0			0
$383$			3.26097e18i			0.137834i	0.997622	+	0.0689170i	$0.0219544\pi$
$383$			3.26097e18i			0.137834i	−0.997622	+	0.0689170i	$0.978046\pi$
$384$		0			0
$385$	−3.91287e19	+	2.00055e19i	−1.59052	+	0.813192i
$386$		0			0
$387$		−	9.69645e18i		−	0.379123i
$388$		0			0
$389$	−1.59231e19			−0.598971			−0.299485	−	0.954101i	$-0.596815\pi$
$389$	−1.59231e19			−0.598971			−0.299485	+	0.954101i	$0.596815\pi$
$390$		0			0
$391$	2.33067e19			0.843635
$392$		0			0
$393$			3.46111e19i			1.20579i
$394$		0			0
$395$	−8.73323e18	−	1.70813e19i	−0.292885	−	0.572854i
$396$		0			0
$397$		−	5.88909e19i		−	1.90160i	−0.309806	−	0.950800i	$-0.600264\pi$
$397$		−	5.88909e19i		−	1.90160i	0.309806	−	0.950800i	$-0.399736\pi$
$398$		0			0
$399$	−4.98744e18			−0.155089
$400$		0			0
$401$	−5.88679e18			−0.176318			−0.0881588	−	0.996106i	$-0.528098\pi$
$401$	−5.88679e18			−0.176318			−0.0881588	+	0.996106i	$0.528098\pi$
$402$		0			0
$403$			5.39641e18i			0.155710i
$404$		0			0
$405$	−1.92582e19	−	3.76671e19i	−0.535429	−	1.04725i
$406$		0			0
$407$		−	1.00506e19i		−	0.269298i
$408$		0			0
$409$	4.43754e19			1.14609			0.573044	−	0.819525i	$-0.305762\pi$
$409$	4.43754e19			1.14609			0.573044	+	0.819525i	$0.305762\pi$
$410$		0			0
$411$	4.87527e19			1.21391
$412$		0			0
$413$			2.74481e19i			0.659003i
$414$		0			0
$415$	−4.38816e19	+	2.24355e19i	−1.01607	+	0.519487i
$416$		0			0
$417$		−	1.00412e20i		−	2.24267i
$418$		0			0
$419$	5.09132e17			0.0109705			0.00548524	−	0.999985i	$-0.498254\pi$
$419$	5.09132e17			0.0109705			0.00548524	+	0.999985i	$0.498254\pi$
$420$		0			0
$421$	1.71471e19			0.356513			0.178256	−	0.983984i	$-0.442954\pi$
$421$	1.71471e19			0.356513			0.178256	+	0.983984i	$0.442954\pi$
$422$		0			0
$423$			6.33828e19i			1.27180i
$424$		0			0
$425$	6.72874e19	+	4.86026e19i	1.30322	+	0.941332i
$426$		0			0
$427$		−	2.12786e19i		−	0.397863i
$428$		0			0
$429$	9.90689e18			0.178858
$430$		0			0
$431$	−1.91150e19			−0.333269			−0.166635	−	0.986019i	$-0.553290\pi$
$431$	−1.91150e19			−0.333269			−0.166635	+	0.986019i	$0.553290\pi$
$432$		0			0
$433$			8.78686e19i			1.47970i	0.672770	+	0.739852i	$0.265104\pi$
$433$			8.78686e19i			1.47970i	−0.672770	+	0.739852i	$0.734896\pi$
$434$		0			0
$435$	1.14711e20	−	5.86487e19i	1.86611	−	0.954089i
$436$		0			0
$437$			2.21982e18i			0.0348906i
$438$		0			0
$439$	1.77525e19			0.269634			0.134817	−	0.990870i	$-0.456955\pi$
$439$	1.77525e19			0.269634			0.134817	+	0.990870i	$0.456955\pi$
$440$		0			0
$441$	1.08876e20			1.59825
$442$		0			0
$443$		−	1.61332e19i		−	0.228924i	−0.993428	−	0.114462i	$-0.963486\pi$
$443$		−	1.61332e19i		−	0.228924i	0.993428	−	0.114462i	$-0.0365145\pi$
$444$		0			0
$445$	−4.97908e18	−	9.73859e18i	−0.0683044	−	0.133597i
$446$		0			0
$447$		−	2.87363e19i		−	0.381174i
$448$		0			0
$449$	3.38252e19			0.433904			0.216952	−	0.976182i	$-0.430389\pi$
$449$	3.38252e19			0.433904			0.216952	+	0.976182i	$0.430389\pi$
$450$		0			0
$451$	7.73586e19			0.959809
$452$		0			0
$453$		−	4.58726e19i		−	0.550575i
$454$		0			0
$455$	−9.05637e18	−	1.77134e19i	−0.105164	−	0.205691i
$456$		0			0
$457$		−	1.55141e20i		−	1.74323i	−0.490195	−	0.871613i	$-0.663074\pi$
$457$		−	1.55141e20i		−	1.74323i	0.490195	−	0.871613i	$-0.336926\pi$
$458$		0			0
$459$	−4.49265e19			−0.488549
$460$		0			0
$461$	−4.95610e19			−0.521654			−0.260827	−	0.965386i	$-0.583995\pi$
$461$	−4.95610e19			−0.521654			−0.260827	+	0.965386i	$0.583995\pi$
$462$		0			0
$463$		−	5.11362e19i		−	0.521040i	−0.965468	−	0.260520i	$-0.916106\pi$
$463$		−	5.11362e19i		−	0.521040i	0.965468	−	0.260520i	$-0.0838940\pi$
$464$		0			0
$465$	−1.41901e20	+	7.25503e19i	−1.39988	+	0.715719i
$466$		0			0
$467$		−	3.72339e19i		−	0.355682i	−0.984059	−	0.177841i	$-0.943089\pi$
$467$		−	3.72339e19i		−	0.355682i	0.984059	−	0.177841i	$-0.0569113\pi$
$468$		0			0
$469$	−1.24652e19			−0.115320
$470$		0			0
$471$	3.50937e19			0.314465
$472$		0			0
$473$		−	5.76921e19i		−	0.500792i
$474$		0			0
$475$	−4.62912e18	+	6.40873e18i	−0.0389311	+	0.0538977i
$476$		0			0
$477$			9.42298e19i			0.767893i
$478$		0			0
$479$	−1.09530e20			−0.865001			−0.432500	−	0.901634i	$-0.642369\pi$
$479$	−1.09530e20			−0.865001			−0.432500	+	0.901634i	$0.642369\pi$
$480$		0			0
$481$	4.54984e18			0.0348264
$482$		0			0
$483$		−	1.64973e20i		−	1.22408i
$484$		0			0
$485$	−1.01584e20	+	5.19373e19i	−0.730741	+	0.373608i
$486$		0			0
$487$		−	8.59385e19i		−	0.599405i	−0.954033	−	0.299703i	$-0.903113\pi$
$487$		−	8.59385e19i		−	0.599405i	0.954033	−	0.299703i	$-0.0968874\pi$
$488$		0			0
$489$	7.57946e19			0.512651
$490$		0			0
$491$	1.91469e20			1.25599			0.627997	−	0.778215i	$-0.283875\pi$
$491$	1.91469e20			1.25599			0.627997	+	0.778215i	$0.283875\pi$
$492$		0			0
$493$		−	3.97839e20i		−	2.53137i
$494$		0			0
$495$	5.80132e19	+	1.13468e20i	0.358086	+	0.700382i
$496$		0			0
$497$		−	2.22674e20i		−	1.33351i
$498$		0			0
$499$	−6.42565e19			−0.373390			−0.186695	−	0.982418i	$-0.559778\pi$
$499$	−6.42565e19			−0.373390			−0.186695	+	0.982418i	$0.559778\pi$
$500$		0			0
$501$	2.70404e20			1.52486
$502$		0			0
$503$		−	1.44519e19i		−	0.0790977i	−0.999218	−	0.0395488i	$-0.987408\pi$
$503$		−	1.44519e19i		−	0.0790977i	0.999218	−	0.0395488i	$-0.0125921\pi$
$504$		0			0
$505$	8.33481e19	+	1.63021e20i	0.442803	+	0.866079i
$506$		0			0
$507$		−	2.53595e20i		−	1.30792i
$508$		0			0
$509$	−2.88288e20			−1.44359			−0.721793	−	0.692109i	$-0.756682\pi$
$509$	−2.88288e20			−1.44359			−0.721793	+	0.692109i	$0.756682\pi$
$510$		0			0
$511$	−2.39785e20			−1.16591
$512$		0			0
$513$		−	4.27899e18i		−	0.0202051i
$514$		0			0
$515$	−3.29287e20	+	1.68355e20i	−1.51015	+	0.772099i
$516$		0			0
$517$			3.77116e20i			1.67995i
$518$		0			0
$519$	−8.76134e19			−0.379154
$520$		0			0
$521$	−2.05016e20			−0.861997			−0.430999	−	0.902353i	$-0.641839\pi$
$521$	−2.05016e20			−0.861997			−0.430999	+	0.902353i	$0.641839\pi$
$522$		0			0
$523$		−	1.23440e20i		−	0.504307i	−0.967687	−	0.252153i	$-0.918861\pi$
$523$		−	1.23440e20i		−	0.504307i	0.967687	−	0.252153i	$-0.0811388\pi$
$524$		0			0
$525$	3.44027e20	−	4.76284e20i	1.36583	−	1.89091i
$526$		0			0
$527$			4.92140e20i			1.89893i
$528$		0			0
$529$	1.93209e20			0.724618
$530$		0			0
$531$	7.95959e19			0.290190
$532$		0			0
$533$			3.50199e19i			0.124125i
$534$		0			0
$535$	6.61351e18	−	3.38131e18i	0.0227918	−	0.0116528i
$536$		0			0
$537$			5.21072e20i			1.74619i
$538$		0			0
$539$	6.47795e20			2.11116
$540$		0			0
$541$	−4.82550e20			−1.52955			−0.764774	−	0.644299i	$-0.777149\pi$
$541$	−4.82550e20			−1.52955			−0.764774	+	0.644299i	$0.777149\pi$
$542$		0			0
$543$			4.74606e20i			1.46330i
$544$		0			0
$545$	−1.54385e20	−	3.01962e20i	−0.463053	−	0.905687i
$546$		0			0
$547$		−	3.26428e20i		−	0.952539i	−0.879299	−	0.476269i	$-0.841989\pi$
$547$		−	3.26428e20i		−	0.952539i	0.879299	−	0.476269i	$-0.158011\pi$
$548$		0			0
$549$	−6.17051e19			−0.175198
$550$		0			0
$551$	3.78918e19			0.104691
$552$		0			0
$553$			4.19330e20i			1.12750i
$554$		0			0
$555$	6.11690e19	+	1.19641e20i	0.160079	+	0.313098i
$556$		0			0
$557$			1.21694e20i			0.309995i	0.987915	+	0.154997i	$0.0495369\pi$
$557$			1.21694e20i			0.309995i	−0.987915	+	0.154997i	$0.950463\pi$
$558$		0			0
$559$	2.61169e19			0.0647639
$560$		0			0
$561$	9.03485e20			2.18122
$562$		0			0
$563$		−	3.47821e20i		−	0.817603i	−0.912623	−	0.408801i	$-0.865947\pi$
$563$		−	3.47821e20i		−	0.817603i	0.912623	−	0.408801i	$-0.134053\pi$
$564$		0			0
$565$	−6.58172e20	+	3.36506e20i	−1.50652	+	0.770245i
$566$		0			0
$567$			9.24690e20i			2.06121i
$568$		0			0
$569$	−1.09895e20			−0.238580			−0.119290	−	0.992859i	$-0.538062\pi$
$569$	−1.09895e20			−0.238580			−0.119290	+	0.992859i	$0.538062\pi$
$570$		0			0
$571$	2.43662e20			0.515249			0.257624	−	0.966245i	$-0.417060\pi$
$571$	2.43662e20			0.515249			0.257624	+	0.966245i	$0.417060\pi$
$572$		0			0
$573$			5.60353e20i			1.15426i
$574$		0			0
$575$	−2.11986e20	−	1.53120e20i	−0.425401	−	0.307273i
$576$		0			0
$577$			1.44534e20i			0.282587i	0.989968	+	0.141293i	$0.0451261\pi$
$577$			1.44534e20i			0.282587i	−0.989968	+	0.141293i	$0.954874\pi$
$578$		0			0
$579$	−3.70760e20			−0.706324
$580$		0			0
$581$	1.07725e21			1.99984
$582$		0			0
$583$			5.60650e20i			1.01433i
$584$		0			0
$585$	−5.13664e19	+	2.62623e19i	−0.0905754	+	0.0463088i
$586$		0			0
$587$		−	1.40670e19i		−	0.0241778i	−0.999927	−	0.0120889i	$-0.996152\pi$
$587$		−	1.40670e19i		−	0.0241778i	0.999927	−	0.0120889i	$-0.00384811\pi$
$588$		0			0
$589$	−4.68734e19			−0.0785348
$590$		0			0
$591$	5.80715e20			0.948543
$592$		0			0
$593$			2.23822e20i			0.356445i	0.983990	+	0.178223i	$0.0570347\pi$
$593$			2.23822e20i			0.356445i	−0.983990	+	0.178223i	$0.942965\pi$
$594$		0			0
$595$	−8.25920e20	−	1.61542e21i	−1.28251	−	2.50846i
$596$		0			0
$597$			3.99295e20i			0.604625i
$598$		0			0
$599$	−8.06304e20			−1.19069			−0.595343	−	0.803471i	$-0.702984\pi$
$599$	−8.06304e20			−1.19069			−0.595343	+	0.803471i	$0.702984\pi$
$600$		0			0
$601$	−4.18833e20			−0.603229			−0.301615	−	0.953430i	$-0.597526\pi$
$601$	−4.18833e20			−0.603229			−0.301615	+	0.953430i	$0.597526\pi$
$602$		0			0
$603$			3.61475e19i			0.0507807i
$604$		0			0
$605$	1.29737e19	+	2.53753e19i	0.0177786	+	0.0347733i
$606$		0			0
$607$			1.32503e21i			1.77138i	0.464277	+	0.885690i	$0.346314\pi$
$607$			1.32503e21i			1.77138i	−0.464277	+	0.885690i	$0.653686\pi$
$608$		0			0
$609$	−2.81605e21			−3.67291
$610$		0			0
$611$	−1.70719e20			−0.217256
$612$		0			0
$613$		−	8.57196e20i		−	1.06445i	−0.846602	−	0.532227i	$-0.821355\pi$
$613$		−	8.57196e20i		−	1.06445i	0.846602	−	0.532227i	$-0.178645\pi$
$614$		0			0
$615$	−9.20866e20	+	4.70814e20i	−1.11592	+	0.570540i
$616$		0			0
$617$		−	8.40232e20i		−	0.993712i	−0.867833	−	0.496856i	$-0.834488\pi$
$617$		−	8.40232e20i		−	0.993712i	0.867833	−	0.496856i	$-0.165512\pi$
$618$		0			0
$619$	8.53361e20			0.985038			0.492519	−	0.870302i	$-0.336076\pi$
$619$	8.53361e20			0.985038			0.492519	+	0.870302i	$0.336076\pi$
$620$		0			0
$621$	1.41539e20			0.159474
$622$		0			0
$623$			2.39073e20i			0.262948i
$624$		0			0
$625$	−2.92702e20	−	8.84131e20i	−0.314287	−	0.949328i
$626$		0			0
$627$			8.60517e19i			0.0902096i
$628$		0			0
$629$	4.14935e20			0.424718
$630$		0			0
$631$	−9.99690e20			−0.999184			−0.499592	−	0.866261i	$-0.666517\pi$
$631$	−9.99690e20			−0.999184			−0.499592	+	0.866261i	$0.666517\pi$
$632$		0			0
$633$		−	8.68759e20i		−	0.847952i
$634$		0			0
$635$	5.46950e20	−	2.79641e20i	0.521369	−	0.266562i
$636$		0			0
$637$			2.93253e20i			0.273022i
$638$		0			0
$639$	−6.45725e20			−0.587207
$640$		0			0
$641$	1.69488e20			0.150558			0.0752788	−	0.997163i	$-0.476015\pi$
$641$	1.69488e20			0.150558			0.0752788	+	0.997163i	$0.476015\pi$
$642$		0			0
$643$		−	4.61444e20i		−	0.400439i	−0.979751	−	0.200220i	$-0.935834\pi$
$643$		−	4.61444e20i		−	0.400439i	0.979751	−	0.200220i	$-0.0641656\pi$
$644$		0			0
$645$	3.51121e20	+	6.86758e20i	0.297686	+	0.582245i
$646$		0			0
$647$			4.81849e18i			0.00399144i	0.999998	+	0.00199572i	$0.000635257\pi$
$647$			4.81849e18i			0.00399144i	−0.999998	+	0.00199572i	$0.999365\pi$
$648$		0			0
$649$	4.73581e20			0.383318
$650$		0			0
$651$	3.48354e21			2.75526
$652$		0			0
$653$			2.12619e21i			1.64344i	0.569894	+	0.821718i	$0.306984\pi$
$653$			2.12619e21i			1.64344i	−0.569894	+	0.821718i	$0.693016\pi$
$654$		0			0
$655$	−5.45901e20	−	1.06773e21i	−0.412386	−	0.806587i
$656$		0			0
$657$			6.95345e20i			0.513405i
$658$		0			0
$659$	−1.96153e21			−1.41565			−0.707823	−	0.706390i	$-0.750322\pi$
$659$	−1.96153e21			−1.41565			−0.707823	+	0.706390i	$0.750322\pi$
$660$		0			0
$661$	1.73858e21			1.22654			0.613271	−	0.789872i	$-0.289853\pi$
$661$	1.73858e21			1.22654			0.613271	+	0.789872i	$0.289853\pi$
$662$		0			0
$663$			4.09003e20i			0.282082i
$664$		0			0
$665$	1.53859e20	−	7.86640e19i	0.103744	−	0.0530413i
$666$		0			0
$667$			1.25337e21i			0.826298i
$668$		0			0
$669$	3.02962e21			1.95295
$670$		0			0
$671$	−3.67134e20			−0.231422
$672$		0			0
$673$			3.18606e19i			0.0196400i	0.999952	+	0.00981998i	$0.00312585\pi$
$673$			3.18606e19i			0.0196400i	−0.999952	+	0.00981998i	$0.996874\pi$
$674$		0			0
$675$	4.08629e20	+	2.95159e20i	0.246349	+	0.177942i
$676$		0			0
$677$		−	1.90729e21i		−	1.12461i	−0.826930	−	0.562304i	$-0.809915\pi$
$677$		−	1.90729e21i		−	1.12461i	0.826930	−	0.562304i	$-0.190085\pi$
$678$		0			0
$679$	2.49379e21			1.43826
$680$		0			0
$681$	−5.70557e20			−0.321882
$682$		0			0
$683$		−	2.46776e21i		−	1.36191i	−0.732326	−	0.680955i	$-0.761565\pi$
$683$		−	2.46776e21i		−	1.36191i	0.732326	−	0.680955i	$-0.238435\pi$
$684$		0			0
$685$	−1.50399e21	+	7.68948e20i	−0.812017	+	0.415162i
$686$		0			0
$687$		−	2.93245e21i		−	1.54901i
$688$		0			0
$689$	−2.53803e20			−0.131176
$690$		0			0
$691$	2.73418e21			1.38274			0.691372	−	0.722499i	$-0.257007\pi$
$691$	2.73418e21			1.38274			0.691372	+	0.722499i	$0.257007\pi$
$692$		0			0
$693$		−	2.78553e21i		−	1.37851i
$694$		0			0
$695$	1.58374e21	+	3.09764e21i	0.767004	+	1.50018i
$696$		0			0
$697$			3.19373e21i			1.51374i
$698$		0			0
$699$	−6.11121e20			−0.283497
$700$		0			0
$701$	9.00624e20			0.408939			0.204469	−	0.978873i	$-0.434453\pi$
$701$	9.00624e20			0.408939			0.204469	+	0.978873i	$0.434453\pi$
$702$		0			0
$703$			3.95201e19i			0.0175652i
$704$		0			0
$705$	−2.29517e21	−	4.48913e21i	−0.998613	−	1.95319i
$706$		0			0
$707$		−	4.00200e21i		−	1.70464i
$708$		0			0
$709$	−2.98281e21			−1.24388			−0.621941	−	0.783064i	$-0.713656\pi$
$709$	−2.98281e21			−1.24388			−0.621941	+	0.783064i	$0.713656\pi$
$710$		0			0
$711$	1.21600e21			0.496492
$712$		0			0
$713$		−	1.55046e21i		−	0.619855i
$714$		0			0
$715$	−3.05621e20	+	1.56256e20i	−0.119643	+	0.0611703i
$716$		0			0
$717$		−	2.29178e21i		−	0.878575i
$718$		0			0
$719$	−3.34379e21			−1.25537			−0.627686	−	0.778467i	$-0.715998\pi$
$719$	−3.34379e21			−1.25537			−0.627686	+	0.778467i	$0.715998\pi$
$720$		0			0
$721$	8.08367e21			2.97231
$722$		0			0
$723$		−	5.83275e21i		−	2.10057i
$724$		0			0
$725$	−2.61373e21	+	3.61854e21i	−0.921988	+	1.27644i
$726$		0			0
$727$			5.56511e20i			0.192294i	0.995367	+	0.0961469i	$0.0306519\pi$
$727$			5.56511e20i			0.192294i	−0.995367	+	0.0961469i	$0.969348\pi$
$728$		0			0
$729$	1.48647e21			0.503152
$730$		0			0
$731$	2.38180e21			0.789814
$732$		0			0
$733$		−	5.77641e21i		−	1.87663i	−0.345782	−	0.938315i	$-0.612386\pi$
$733$		−	5.77641e21i		−	1.87663i	0.345782	−	0.938315i	$-0.387614\pi$
$734$		0			0
$735$	−7.71125e21	+	3.94256e21i	−2.45454	+	1.25494i
$736$		0			0
$737$			2.15071e20i			0.0670773i
$738$		0			0
$739$	1.90658e21			0.582670			0.291335	−	0.956621i	$-0.405901\pi$
$739$	1.90658e21			0.582670			0.291335	+	0.956621i	$0.405901\pi$
$740$		0			0
$741$	−3.89551e19			−0.0116662
$742$		0			0
$743$			3.50311e21i			1.02811i	0.857758	+	0.514053i	$0.171857\pi$
$743$			3.50311e21i			1.02811i	−0.857758	+	0.514053i	$0.828143\pi$
$744$		0			0
$745$	4.53240e20	+	8.86494e20i	0.130364	+	0.254979i
$746$		0			0
$747$		−	3.12388e21i		−	0.880623i
$748$		0			0
$749$	−1.62355e20			−0.0448593
$750$		0			0
$751$	3.96156e21			1.07292			0.536460	−	0.843926i	$-0.319761\pi$
$751$	3.96156e21			1.07292			0.536460	+	0.843926i	$0.319761\pi$
$752$		0			0
$753$			6.01654e21i			1.59729i
$754$		0			0
$755$	7.23522e20	+	1.41514e21i	0.188300	+	0.368296i
$756$		0			0
$757$		−	2.36000e21i		−	0.602133i	−0.953603	−	0.301067i	$-0.902657\pi$
$757$		−	2.36000e21i		−	0.602133i	0.953603	−	0.301067i	$-0.0973427\pi$
$758$		0			0
$759$	−2.84639e21			−0.712002
$760$		0			0
$761$	3.45546e20			0.0847463			0.0423731	−	0.999102i	$-0.486508\pi$
$761$	3.45546e20			0.0847463			0.0423731	+	0.999102i	$0.486508\pi$
$762$		0			0
$763$			7.41286e21i			1.78259i
$764$		0			0
$765$	−4.68450e21	+	2.39506e21i	−1.10459	+	0.564749i
$766$		0			0
$767$			2.14388e20i			0.0495718i
$768$		0			0
$769$	8.12285e21			1.84188			0.920939	−	0.389707i	$-0.127424\pi$
$769$	8.12285e21			1.84188			0.920939	+	0.389707i	$0.127424\pi$
$770$		0			0
$771$	−5.77536e21			−1.28431
$772$		0			0
$773$		−	1.01919e21i		−	0.222284i	−0.993805	−	0.111142i	$-0.964549\pi$
$773$		−	1.01919e21i		−	0.222284i	0.993805	−	0.111142i	$-0.0354508\pi$
$774$		0			0
$775$	3.23326e21	−	4.47626e21i	0.691637	−	0.957530i
$776$		0			0
$777$		−	2.93706e21i		−	0.616247i
$778$		0			0
$779$	−3.04184e20			−0.0626045
$780$		0			0
$781$	−3.84194e21			−0.775654
$782$		0			0
$783$		−	2.41604e21i		−	0.478509i
$784$		0			0
$785$	−1.08262e21	+	5.53512e20i	−0.210355	+	0.107549i
$786$		0			0
$787$		−	5.71362e21i		−	1.08918i	−0.838702	−	0.544591i	$-0.816685\pi$
$787$		−	5.71362e21i		−	1.08918i	0.838702	−	0.544591i	$-0.183315\pi$
$788$		0			0
$789$	−1.13536e22			−2.12351
$790$		0			0
$791$	1.61575e22			2.96517
$792$		0			0
$793$		−	1.66200e20i		−	0.0299282i
$794$		0			0
$795$	−3.41218e21	−	6.67389e21i	−0.602946	−	1.17930i
$796$		0			0
$797$		−	1.04166e22i		−	1.80630i	−0.429328	−	0.903149i	$-0.641250\pi$
$797$		−	1.04166e22i		−	1.80630i	0.429328	−	0.903149i	$-0.358750\pi$
$798$		0			0
$799$	−1.55691e22			−2.64950
$800$		0			0
$801$	6.93279e20			0.115788
$802$		0			0
$803$			4.13717e21i			0.678168i
$804$		0			0
$805$	2.60202e21	+	5.08930e21i	0.418641	+	0.818821i
$806$		0			0
$807$			8.13030e21i			1.28397i
$808$		0			0
$809$	−5.31828e21			−0.824437			−0.412218	−	0.911085i	$-0.635246\pi$
$809$	−5.31828e21			−0.824437			−0.412218	+	0.911085i	$0.635246\pi$
$810$		0			0
$811$	2.55694e21			0.389102			0.194551	−	0.980892i	$-0.437675\pi$
$811$	2.55694e21			0.389102			0.194551	+	0.980892i	$0.437675\pi$
$812$		0			0
$813$			1.50592e22i			2.24969i
$814$		0			0
$815$	−2.33821e21	+	1.19546e21i	−0.342927	+	0.175329i
$816$		0			0
$817$			2.26853e20i			0.0326647i
$818$		0			0
$819$	1.26100e21			0.178272
$820$		0			0
$821$	9.61860e21			1.33517			0.667587	−	0.744531i	$-0.267327\pi$
$821$	9.61860e21			1.33517			0.667587	+	0.744531i	$0.267327\pi$
$822$		0			0
$823$			1.02614e22i			1.39865i	0.714805	+	0.699324i	$0.246515\pi$
$823$			1.02614e22i			1.39865i	−0.714805	+	0.699324i	$0.753485\pi$
$824$		0			0
$825$	−8.21765e21	−	5.93573e21i	−1.09987	−	0.794455i
$826$		0			0
$827$		−	3.28610e21i		−	0.431906i	−0.976404	−	0.215953i	$-0.930714\pi$
$827$		−	3.28610e21i		−	0.431906i	0.976404	−	0.215953i	$-0.0692857\pi$
$828$		0			0
$829$	−2.32835e21			−0.300531			−0.150266	−	0.988646i	$-0.548013\pi$
$829$	−2.32835e21			−0.300531			−0.150266	+	0.988646i	$0.548013\pi$
$830$		0			0
$831$	−3.70034e21			−0.469066
$832$		0			0
$833$			2.67440e22i			3.32958i
$834$		0			0
$835$	−8.34178e21	+	4.26493e21i	−1.02002	+	0.521510i
$836$		0			0
$837$			2.98871e21i			0.358958i
$838$		0			0
$839$	1.52420e22			1.79816			0.899079	−	0.437786i	$-0.144237\pi$
$839$	1.52420e22			1.79816			0.899079	+	0.437786i	$0.144237\pi$
$840$		0			0
$841$	1.27656e22			1.47935
$842$		0			0
$843$			9.11531e20i			0.103768i
$844$		0			0
$845$	3.99980e21	+	7.82322e21i	0.447315	+	0.874904i
$846$		0			0
$847$		−	6.22938e20i		−	0.0684415i
$848$		0			0
$849$	−9.13162e21			−0.985689
$850$		0			0
$851$	−1.30723e21			−0.138638
$852$		0			0
$853$		−	1.69959e22i		−	1.77104i	−0.464605	−	0.885518i	$-0.653804\pi$
$853$		−	1.69959e22i		−	1.77104i	0.464605	−	0.885518i	$-0.346196\pi$
$854$		0			0
$855$	−2.28115e20	−	4.46171e20i	−0.0233565	−	0.0456831i
$856$		0			0
$857$		−	1.53882e21i		−	0.154821i	−0.996999	−	0.0774107i	$-0.975335\pi$
$857$		−	1.53882e21i		−	0.154821i	0.996999	−	0.0774107i	$-0.0246653\pi$
$858$		0			0
$859$	9.05890e21			0.895626			0.447813	−	0.894127i	$-0.352203\pi$
$859$	9.05890e21			0.895626			0.447813	+	0.894127i	$0.352203\pi$
$860$		0			0
$861$	2.26063e22			2.19638
$862$		0			0
$863$		−	5.29023e21i		−	0.505119i	−0.967581	−	0.252559i	$-0.918728\pi$
$863$		−	5.29023e21i		−	0.505119i	0.967581	−	0.252559i	$-0.0812723\pi$
$864$		0			0
$865$	2.70281e21	−	1.38188e21i	0.253627	−	0.129673i
$866$		0			0
$867$			2.28678e22i			2.10902i
$868$		0			0
$869$	7.23499e21			0.655827
$870$		0			0
$871$	−9.73615e19			−0.00867463
$872$		0			0
$873$		−	7.23167e21i		−	0.633333i
$874$		0			0
$875$	−3.10084e21	+	2.01192e22i	−0.266943	+	1.73201i
$876$		0			0
$877$			1.19812e22i			1.01392i	0.861970	+	0.506960i	$0.169231\pi$
$877$			1.19812e22i			1.01392i	−0.861970	+	0.506960i	$0.830769\pi$
$878$		0			0
$879$	−4.73083e21			−0.393569
$880$		0			0
$881$	−1.94299e22			−1.58910			−0.794549	−	0.607200i	$-0.792293\pi$
$881$	−1.94299e22			−1.58910			−0.794549	+	0.607200i	$0.792293\pi$
$882$		0			0
$883$			1.29139e21i			0.103837i	0.998651	+	0.0519184i	$0.0165336\pi$
$883$			1.29139e21i			0.103837i	−0.998651	+	0.0519184i	$0.983466\pi$
$884$		0			0
$885$	−5.63744e21	+	2.88227e21i	−0.445664	+	0.227856i
$886$		0			0
$887$			3.30690e21i			0.257036i	0.991707	+	0.128518i	$0.0410220\pi$
$887$			3.30690e21i			0.257036i	−0.991707	+	0.128518i	$0.958978\pi$
$888$		0			0
$889$	−1.34271e22			−1.02617
$890$		0			0
$891$	1.59543e22			1.19893
$892$		0			0
$893$		−	1.48287e21i		−	0.109576i
$894$		0			0
$895$	−8.21857e21	−	1.60747e22i	−0.597205	−	1.16807i
$896$		0			0
$897$		−	1.28855e21i		−	0.0920781i
$898$		0			0
$899$	−2.64660e22			−1.85991
$900$		0			0
$901$	−2.31463e22			−1.59972
$902$		0			0
$903$		−	1.68592e22i		−	1.14599i
$904$		0			0
$905$	−7.48569e21	−	1.46413e22i	−0.500458	−	0.978847i
$906$		0			0
$907$		−	2.53575e21i		−	0.166745i	−0.996518	−	0.0833723i	$-0.973431\pi$
$907$		−	2.53575e21i		−	0.166745i	0.996518	−	0.0833723i	$-0.0265691\pi$
$908$		0			0
$909$	−1.16053e22			−0.750631
$910$		0			0
$911$	−1.82827e22			−1.16319			−0.581597	−	0.813477i	$-0.697572\pi$
$911$	−1.82827e22			−1.16319			−0.581597	+	0.813477i	$0.697572\pi$
$912$		0			0
$913$		−	1.85865e22i		−	1.16323i
$914$		0			0
$915$	4.37030e21	−	2.23442e21i	0.269063	−	0.137564i
$916$		0			0
$917$			2.62117e22i			1.58754i
$918$		0			0
$919$	8.20865e21			0.489109			0.244554	−	0.969636i	$-0.421358\pi$
$919$	8.20865e21			0.489109			0.244554	+	0.969636i	$0.421358\pi$
$920$		0			0
$921$	1.66429e22			0.975622
$922$		0			0
$923$		−	1.73923e21i		−	0.100310i
$924$		0			0
$925$	−3.77404e21	−	2.72604e21i	−0.214163	−	0.154693i
$926$		0			0
$927$		−	2.34416e22i		−	1.30885i
$928$		0			0
$929$	1.31215e22			0.720887			0.360443	−	0.932781i	$-0.382625\pi$
$929$	1.31215e22			0.720887			0.360443	+	0.932781i	$0.382625\pi$
$930$		0			0
$931$	−2.54721e21			−0.137703
$932$		0			0
$933$		−	3.30370e22i		−	1.75747i
$934$		0			0
$935$	−2.78719e22	+	1.42501e22i	−1.45908	+	0.745989i
$936$		0			0
$937$			3.86691e21i			0.199213i	0.995027	+	0.0996065i	$0.0317584\pi$
$937$			3.86691e21i			0.199213i	−0.995027	+	0.0996065i	$0.968242\pi$
$938$		0			0
$939$	−6.30743e21			−0.319787
$940$		0			0
$941$	2.91264e22			1.45333			0.726665	−	0.686992i	$-0.241069\pi$
$941$	2.91264e22			1.45333			0.726665	+	0.686992i	$0.241069\pi$
$942$		0			0
$943$		−	1.00617e22i		−	0.494121i
$944$		0			0
$945$	−5.01572e21	−	9.81027e21i	−0.242435	−	0.474179i
$946$		0			0
$947$		−	1.76075e22i		−	0.837671i	−0.908062	−	0.418835i	$-0.862438\pi$
$947$		−	1.76075e22i		−	0.837671i	0.908062	−	0.418835i	$-0.137562\pi$
$948$		0			0
$949$	−1.87288e21			−0.0877026
$950$		0			0
$951$	4.11795e22			1.89814
$952$		0			0
$953$			3.28538e22i			1.49069i	0.666677	+	0.745347i	$0.267716\pi$
$953$			3.28538e22i			1.49069i	−0.666677	+	0.745347i	$0.732284\pi$
$954$		0			0
$955$	−8.83813e21	−	1.72865e22i	−0.394762	−	0.772115i
$956$		0			0
$957$			4.85871e22i			2.13640i
$958$		0			0
$959$	3.69214e22			1.59823
$960$		0			0
$961$	9.27406e21			0.395225
$962$		0			0
$963$			4.70809e20i			0.0197536i
$964$		0			0
$965$	1.14377e22	−	5.84779e21i	0.472481	−	0.241567i
$966$		0			0
$967$		−	2.77962e22i		−	1.13054i	−0.824905	−	0.565272i	$-0.808771\pi$
$967$		−	2.77962e22i		−	1.13054i	0.824905	−	0.565272i	$-0.191229\pi$
$968$		0			0
$969$	−3.55262e21			−0.142272
$970$		0			0
$971$	4.39922e22			1.73473			0.867365	−	0.497673i	$-0.165812\pi$
$971$	4.39922e22			1.73473			0.867365	+	0.497673i	$0.165812\pi$
$972$		0			0
$973$		−	7.60440e22i		−	2.95269i
$974$		0			0
$975$	2.68707e21	−	3.72009e21i	0.102741	−	0.142239i
$976$		0			0
$977$		−	5.03867e22i		−	1.89717i	−0.316520	−	0.948586i	$-0.602514\pi$
$977$		−	5.03867e22i		−	1.89717i	0.316520	−	0.948586i	$-0.397486\pi$
$978$		0			0
$979$	4.12488e21			0.152947
$980$		0			0
$981$	2.14963e22			0.784958
$982$		0			0
$983$		−	7.99986e21i		−	0.287694i	−0.989600	−	0.143847i	$-0.954053\pi$
$983$		−	7.99986e21i		−	0.287694i	0.989600	−	0.143847i	$-0.0459474\pi$
$984$		0			0
$985$	−1.79147e22	+	9.15929e21i	−0.634508	+	0.324407i
$986$		0			0
$987$			1.10204e23i			3.84431i
$988$		0			0
$989$	−7.50375e21			−0.257814
$990$		0			0
$991$	2.28991e22			0.774937			0.387469	−	0.921883i	$-0.373350\pi$
$991$	2.28991e22			0.774937			0.387469	+	0.921883i	$0.373350\pi$
$992$		0			0
$993$			4.13416e22i			1.37806i
$994$		0			0
$995$	−6.29785e21	−	1.23180e22i	−0.206785	−	0.404451i
$996$		0			0
$997$			2.70362e22i			0.874443i	0.899354	+	0.437222i	$0.144037\pi$
$997$			2.70362e22i			0.874443i	−0.899354	+	0.437222i	$0.855963\pi$
$998$		0			0
$999$	2.51986e21			0.0802851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.16.c.c.49.2		8
4.3	odd	2		10.16.b.a.9.8	yes	8
5.4	even	2	inner	80.16.c.c.49.7		8
12.11	even	2		90.16.c.c.19.2		8
20.3	even	4		50.16.a.k.1.1		4
20.7	even	4		50.16.a.j.1.4		4
20.19	odd	2		10.16.b.a.9.1	✓	8
60.59	even	2		90.16.c.c.19.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.b.a.9.1	✓	8	20.19	odd	2
10.16.b.a.9.8	yes	8	4.3	odd	2
50.16.a.j.1.4		4	20.7	even	4
50.16.a.k.1.1		4	20.3	even	4
80.16.c.c.49.2		8	1.1	even	1	trivial
80.16.c.c.49.7		8	5.4	even	2	inner
90.16.c.c.19.2		8	12.11	even	2
90.16.c.c.19.6		8	60.59	even	2

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)

\(f(q)\)	\(=\)	\(q-5042.00i q^{3} +(79524.6 + 155542. i) q^{5} -3.81841e6i q^{7} -1.10729e7 q^{9} +O(q^{10})\)	\(q-5042.00i q^{3} +(79524.6 + 155542. i) q^{5} -3.81841e6i q^{7} -1.10729e7 q^{9} -6.58816e7 q^{11} -2.98243e7i q^{13} +(7.84245e8 - 4.00963e8i) q^{15} -2.71990e9i q^{17} +2.59055e8 q^{19} -1.92524e10 q^{21} +8.56893e9i q^{23} +(-1.78693e10 + 2.47389e10i) q^{25} -1.65177e10i q^{27} +1.46270e11 q^{29} -1.80940e11 q^{31} +3.32175e11i q^{33} +(5.93925e11 - 3.03658e11i) q^{35} +1.52555e11i q^{37} -1.50374e11 q^{39} -1.17421e12 q^{41} +8.75693e11i q^{43} +(-8.80567e11 - 1.72230e12i) q^{45} -5.72415e12i q^{47} -9.83271e12 q^{49} -1.37138e13 q^{51} -8.50996e12i q^{53} +(-5.23921e12 - 1.02474e13i) q^{55} -1.30616e12i q^{57} -7.18836e12 q^{59} +5.57263e12 q^{61} +4.22809e13i q^{63} +(4.63894e12 - 2.37176e12i) q^{65} -3.26451e12i q^{67} +4.32046e13 q^{69} +5.83158e13 q^{71} -6.27971e13i q^{73} +(1.24734e14 + 9.00968e13i) q^{75} +2.51563e14i q^{77} -1.09818e14 q^{79} -2.42166e14 q^{81} +2.82120e14i q^{83} +(4.23060e14 - 2.16299e14i) q^{85} -7.37491e14i q^{87} -6.26105e13 q^{89} -1.13881e14 q^{91} +9.12301e14i q^{93} +(2.06012e13 + 4.02940e13i) q^{95} +6.53097e14i q^{97} +7.29500e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 251400 q^{5} - 43491176 q^{9}+O(q^{10}) \) 8 * q + 251400 * q^5 - 43491176 * q^9	\( 8 q + 251400 q^{5} - 43491176 q^{9} - 95435616 q^{11} - 5448800 q^{15} - 6479216160 q^{19} - 14760325504 q^{21} - 2241855000 q^{25} - 244549636560 q^{29} - 522311705216 q^{31} + 1829607146400 q^{35} + 2307595824192 q^{39} + 6699117519216 q^{41} - 9090807477800 q^{45} - 15809163185544 q^{49} - 40555579650176 q^{51} + 39746288199200 q^{55} - 3791808509280 q^{59} + 57800629300816 q^{61} + 58028394892800 q^{65} + 59060996328448 q^{69} + 245426235422784 q^{71} - 226448486200000 q^{75} - 624094605411840 q^{79} - 13\!\cdots\!52 q^{81}+ \cdots - 16\!\cdots\!48 q^{99}+O(q^{100}) \) 8 * q + 251400 * q^5 - 43491176 * q^9 - 95435616 * q^11 - 5448800 * q^15 - 6479216160 * q^19 - 14760325504 * q^21 - 2241855000 * q^25 - 244549636560 * q^29 - 522311705216 * q^31 + 1829607146400 * q^35 + 2307595824192 * q^39 + 6699117519216 * q^41 - 9090807477800 * q^45 - 15809163185544 * q^49 - 40555579650176 * q^51 + 39746288199200 * q^55 - 3791808509280 * q^59 + 57800629300816 * q^61 + 58028394892800 * q^65 + 59060996328448 * q^69 + 245426235422784 * q^71 - 226448486200000 * q^75 - 624094605411840 * q^79 - 1376711600108152 * q^81 + 1092463762441600 * q^85 - 635249793637680 * q^89 + 976491706492224 * q^91 + 1859590136604000 * q^95 - 1626246829353248 * q^99

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