LMFDB - Embedded newform 60.7.g.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(41,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.8032450172$
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} - 4x^{7} - 202x^{6} + 620x^{5} + 12167x^{4} - 25372x^{3} - 177926x^{2} + 190716x + 977814 $ x^8 - 4x^7 - 202x^6 + 620x^5 + 12167x^4 - 25372x^3 - 177926x^2 + 190716*x + 977814
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{7}\cdot 5^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.5
Root			$3.67163 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	60.41
Dual form			60.7.g.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.2485 - 24.5453i) q^{3} +55.9017i q^{5} -414.697 q^{7} +(-475.944 - 552.194i) q^{9} +O(q^{10})$	\(q+(11.2485 - 24.5453i) q^{3} +55.9017i q^{5} -414.697 q^{7} +(-475.944 - 552.194i) q^{9} -61.5283i q^{11} -1379.66 q^{13} +(1372.12 + 628.809i) q^{15} +6808.58i q^{17} -7822.89 q^{19} +(-4664.71 + 10178.9i) q^{21} -7459.40i q^{23} -3125.00 q^{25} +(-18907.4 + 5470.84i) q^{27} -424.303i q^{29} -49671.1 q^{31} +(-1510.23 - 692.099i) q^{33} -23182.3i q^{35} +2272.15 q^{37} +(-15519.1 + 33864.3i) q^{39} +56271.8i q^{41} +131325. q^{43} +(30868.6 - 26606.1i) q^{45} -84752.1i q^{47} +54324.8 q^{49} +(167119. + 76586.2i) q^{51} -166720. i q^{53} +3439.53 q^{55} +(-87995.5 + 192015. i) q^{57} -400288. i q^{59} -83666.7 q^{61} +(197373. + 228993. i) q^{63} -77125.5i q^{65} +425271. q^{67} +(-183093. - 83906.8i) q^{69} -346163. i q^{71} -171712. q^{73} +(-35151.5 + 76704.1i) q^{75} +25515.6i q^{77} -266214. q^{79} +(-78396.2 + 525627. i) q^{81} +1.01555e6i q^{83} -380611. q^{85} +(-10414.6 - 4772.76i) q^{87} -955706. i q^{89} +572143. q^{91} +(-558724. + 1.21919e6i) q^{93} -437313. i q^{95} -1.19431e6 q^{97} +(-33975.6 + 29284.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9}+O(q^{10}) $ 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9	$ 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9} - 6440 q^{13} + 2000 q^{15} - 15272 q^{19} - 868 q^{21} - 25000 q^{25} - 18620 q^{27} + 35032 q^{31} - 111120 q^{33} + 99880 q^{37} + 39608 q^{39} - 161000 q^{43} - 5500 q^{45} + 202560 q^{49} + 429120 q^{51} - 33000 q^{55} - 27160 q^{57} - 135608 q^{61} + 377240 q^{63} + 404920 q^{67} - 254940 q^{69} - 356960 q^{73} + 62500 q^{75} + 707704 q^{79} - 1198112 q^{81} + 828000 q^{85} - 1528440 q^{87} - 2004112 q^{91} - 467920 q^{93} - 1326320 q^{97} + 2650080 q^{99}+O(q^{100}) $ 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9 - 6440 * q^13 + 2000 * q^15 - 15272 * q^19 - 868 * q^21 - 25000 * q^25 - 18620 * q^27 + 35032 * q^31 - 111120 * q^33 + 99880 * q^37 + 39608 * q^39 - 161000 * q^43 - 5500 * q^45 + 202560 * q^49 + 429120 * q^51 - 33000 * q^55 - 27160 * q^57 - 135608 * q^61 + 377240 * q^63 + 404920 * q^67 - 254940 * q^69 - 356960 * q^73 + 62500 * q^75 + 707704 * q^79 - 1198112 * q^81 + 828000 * q^85 - 1528440 * q^87 - 2004112 * q^91 - 467920 * q^93 - 1326320 * q^97 + 2650080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	11.2485	−	24.5453i	0.416610	−	0.909085i
$3$	11.2485	−	24.5453i	0.416610	−	0.909085i
$4$		0			0
$5$			55.9017i			0.447214i
$5$			55.9017i			0.447214i
$6$		0			0
$7$	−414.697			−1.20903			−0.604515	−	0.796594i	$-0.706633\pi$
$7$	−414.697			−1.20903			−0.604515	+	0.796594i	$0.706633\pi$
$8$		0			0
$9$	−475.944	−	552.194i	−0.652872	−	0.757468i
$10$		0			0
$11$		−	61.5283i		−	0.0462271i	−0.999733	−	0.0231135i	$-0.992642\pi$
$11$		−	61.5283i		−	0.0462271i	0.999733	−	0.0231135i	$-0.00735792\pi$
$12$		0			0
$13$	−1379.66			−0.627976			−0.313988	−	0.949427i	$-0.601665\pi$
$13$	−1379.66			−0.627976			−0.313988	+	0.949427i	$0.601665\pi$
$14$		0			0
$15$	1372.12	+	628.809i	0.406555	+	0.186314i
$16$		0			0
$17$			6808.58i			1.38583i	0.721019	+	0.692915i	$0.243674\pi$
$17$			6808.58i			1.38583i	−0.721019	+	0.692915i	$0.756326\pi$
$18$		0			0
$19$	−7822.89			−1.14053			−0.570264	−	0.821461i	$-0.693159\pi$
$19$	−7822.89			−1.14053			−0.570264	+	0.821461i	$0.693159\pi$
$20$		0			0
$21$	−4664.71	+	10178.9i	−0.503694	+	1.09911i
$22$		0			0
$23$		−	7459.40i		−	0.613084i	−0.951857	−	0.306542i	$-0.900828\pi$
$23$		−	7459.40i		−	0.613084i	0.951857	−	0.306542i	$-0.0991721\pi$
$24$		0			0
$25$	−3125.00			−0.200000
$26$		0			0
$27$	−18907.4	+	5470.84i	−0.960596	+	0.277947i
$28$		0			0
$29$		−	424.303i		−	0.0173973i	−0.999962	−	0.00869865i	$-0.997231\pi$
$29$		−	424.303i		−	0.0173973i	0.999962	−	0.00869865i	$-0.00276890\pi$
$30$		0			0
$31$	−49671.1			−1.66732			−0.833660	−	0.552279i	$-0.813758\pi$
$31$	−49671.1			−1.66732			−0.833660	+	0.552279i	$0.813758\pi$
$32$		0			0
$33$	−1510.23	−	692.099i	−0.0420244	−	0.0192587i
$34$		0			0
$35$		−	23182.3i		−	0.540695i
$36$		0			0
$37$	2272.15			0.0448572			0.0224286	−	0.999748i	$-0.492860\pi$
$37$	2272.15			0.0448572			0.0224286	+	0.999748i	$0.492860\pi$
$38$		0			0
$39$	−15519.1	+	33864.3i	−0.261621	+	0.570884i
$40$		0			0
$41$			56271.8i			0.816469i	0.912877	+	0.408234i	$0.133855\pi$
$41$			56271.8i			0.816469i	−0.912877	+	0.408234i	$0.866145\pi$
$42$		0			0
$43$	131325.			1.65174			0.825872	−	0.563858i	$-0.190684\pi$
$43$	131325.			1.65174			0.825872	+	0.563858i	$0.190684\pi$
$44$		0			0
$45$	30868.6	−	26606.1i	0.338750	−	0.291973i
$46$		0			0
$47$		−	84752.1i		−	0.816313i	−0.912912	−	0.408157i	$-0.866172\pi$
$47$		−	84752.1i		−	0.816313i	0.912912	−	0.408157i	$-0.133828\pi$
$48$		0			0
$49$	54324.8			0.461754
$50$		0			0
$51$	167119.	+	76586.2i	1.25984	+	0.577351i
$52$		0			0
$53$		−	166720.i		−	1.11985i	−0.828544	−	0.559924i	$-0.810830\pi$
$53$		−	166720.i		−	1.11985i	0.828544	−	0.559924i	$-0.189170\pi$
$54$		0			0
$55$	3439.53			0.0206734
$56$		0			0
$57$	−87995.5	+	192015.i	−0.475156	+	1.03684i
$58$		0			0
$59$		−	400288.i		−	1.94902i	−0.224342	−	0.974511i	$-0.572023\pi$
$59$		−	400288.i		−	1.94902i	0.224342	−	0.974511i	$-0.427977\pi$
$60$		0			0
$61$	−83666.7			−0.368607			−0.184303	−	0.982869i	$-0.559003\pi$
$61$	−83666.7			−0.368607			−0.184303	+	0.982869i	$0.559003\pi$
$62$		0			0
$63$	197373.	+	228993.i	0.789342	+	0.915802i
$64$		0			0
$65$		−	77125.5i		−	0.280839i
$66$		0			0
$67$	425271.			1.41397			0.706986	−	0.707227i	$-0.250054\pi$
$67$	425271.			1.41397			0.706986	+	0.707227i	$0.250054\pi$
$68$		0			0
$69$	−183093.	−	83906.8i	−0.557346	−	0.255417i
$70$		0			0
$71$		−	346163.i		−	0.967175i	−0.875296	−	0.483587i	$-0.839334\pi$
$71$		−	346163.i		−	0.967175i	0.875296	−	0.483587i	$-0.160666\pi$
$72$		0			0
$73$	−171712.			−0.441401			−0.220700	−	0.975342i	$-0.570834\pi$
$73$	−171712.			−0.441401			−0.220700	+	0.975342i	$0.570834\pi$
$74$		0			0
$75$	−35151.5	+	76704.1i	−0.0833220	+	0.181817i
$76$		0			0
$77$			25515.6i			0.0558899i
$78$		0			0
$79$	−266214.			−0.539944			−0.269972	−	0.962868i	$-0.587015\pi$
$79$	−266214.			−0.539944			−0.269972	+	0.962868i	$0.587015\pi$
$80$		0			0
$81$	−78396.2	+	525627.i	−0.147516	+	0.989060i
$82$		0			0
$83$			1.01555e6i			1.77610i	0.459751	+	0.888048i	$0.347939\pi$
$83$			1.01555e6i			1.77610i	−0.459751	+	0.888048i	$0.652061\pi$
$84$		0			0
$85$	−380611.			−0.619762
$86$		0			0
$87$	−10414.6	−	4772.76i	−0.0158156	−	0.00724789i
$88$		0			0
$89$		−	955706.i		−	1.35567i	−0.735214	−	0.677835i	$-0.762918\pi$
$89$		−	955706.i		−	1.35567i	0.735214	−	0.677835i	$-0.237082\pi$
$90$		0			0
$91$	572143.			0.759242
$92$		0			0
$93$	−558724.	+	1.21919e6i	−0.694622	+	1.51574i
$94$		0			0
$95$		−	437313.i		−	0.510060i
$96$		0			0
$97$	−1.19431e6			−1.30859			−0.654294	−	0.756240i	$-0.727034\pi$
$97$	−1.19431e6			−1.30859			−0.654294	+	0.756240i	$0.727034\pi$
$98$		0			0
$99$	−33975.6	+	29284.0i	−0.0350155	+	0.0301804i
$100$		0			0
$101$			173920.i			0.168805i	0.996432	+	0.0844025i	$0.0268981\pi$
$101$			173920.i			0.168805i	−0.996432	+	0.0844025i	$0.973102\pi$
$102$		0			0
$103$	−32602.0			−0.0298355			−0.0149177	−	0.999889i	$-0.504749\pi$
$103$	−32602.0			−0.0298355			−0.0149177	+	0.999889i	$0.504749\pi$
$104$		0			0
$105$	−569016.	−	260765.i	−0.491538	−	0.225259i
$106$		0			0
$107$		−	1.24930e6i		−	1.01980i	−0.860233	−	0.509902i	$-0.829682\pi$
$107$		−	1.24930e6i		−	1.01980i	0.860233	−	0.509902i	$-0.170318\pi$
$108$		0			0
$109$	−2.29804e6			−1.77451			−0.887255	−	0.461279i	$-0.847391\pi$
$109$	−2.29804e6			−1.77451			−0.887255	+	0.461279i	$0.847391\pi$
$110$		0			0
$111$	25558.2	−	55770.6i	0.0186879	−	0.0407790i
$112$		0			0
$113$			1.94978e6i			1.35130i	0.737224	+	0.675648i	$0.236136\pi$
$113$			1.94978e6i			1.35130i	−0.737224	+	0.675648i	$0.763864\pi$
$114$		0			0
$115$	416993.			0.274180
$116$		0			0
$117$	656642.	+	761842.i	0.409988	+	0.475672i
$118$		0			0
$119$		−	2.82350e6i		−	1.67551i
$120$		0			0
$121$	1.76778e6			0.997863
$122$		0			0
$123$	1.38121e6	+	632972.i	0.742240	+	0.340149i
$124$		0			0
$125$		−	174693.i		−	0.0894427i
$126$		0			0
$127$	2.24490e6			1.09594			0.547969	−	0.836498i	$-0.315401\pi$
$127$	2.24490e6			1.09594			0.547969	+	0.836498i	$0.315401\pi$
$128$		0			0
$129$	1.47721e6	−	3.22342e6i	0.688133	−	1.50158i
$130$		0			0
$131$			2.73023e6i			1.21446i	0.794524	+	0.607232i	$0.207720\pi$
$131$			2.73023e6i			1.21446i	−0.794524	+	0.607232i	$0.792280\pi$
$132$		0			0
$133$	3.24413e6			1.37893
$134$		0			0
$135$	−305829.	−	1.05696e6i	−0.124302	−	0.429592i
$136$		0			0
$137$			4.34993e6i			1.69169i	0.533429	+	0.845845i	$0.320903\pi$
$137$			4.34993e6i			1.69169i	−0.533429	+	0.845845i	$0.679097\pi$
$138$		0			0
$139$	53660.9			0.0199808			0.00999041	−	0.999950i	$-0.496820\pi$
$139$	53660.9			0.0199808			0.00999041	+	0.999950i	$0.496820\pi$
$140$		0			0
$141$	−2.08027e6	−	953332.i	−0.742098	−	0.340084i
$142$		0			0
$143$			84888.3i			0.0290295i
$144$		0			0
$145$	23719.2			0.00778031
$146$		0			0
$147$	611071.	−	1.33342e6i	0.192371	−	0.419773i
$148$		0			0
$149$		−	2.96446e6i		−	0.896163i	−0.893993	−	0.448081i	$-0.852107\pi$
$149$		−	2.96446e6i		−	0.896163i	0.893993	−	0.448081i	$-0.147893\pi$
$150$		0			0
$151$	−129392.			−0.0375817			−0.0187909	−	0.999823i	$-0.505982\pi$
$151$	−129392.			−0.0375817			−0.0187909	+	0.999823i	$0.505982\pi$
$152$		0			0
$153$	3.75966e6	−	3.24050e6i	1.04972	−	0.904770i
$154$		0			0
$155$		−	2.77670e6i		−	0.745648i
$156$		0			0
$157$	−38136.7			−0.00985472			−0.00492736	−	0.999988i	$-0.501568\pi$
$157$	−38136.7			−0.00985472			−0.00492736	+	0.999988i	$0.501568\pi$
$158$		0			0
$159$	−4.09218e6	−	1.87534e6i	−1.01804	−	0.466540i
$160$		0			0
$161$			3.09339e6i			0.741238i
$162$		0			0
$163$	−879856.			−0.203165			−0.101582	−	0.994827i	$-0.532391\pi$
$163$	−879856.			−0.203165			−0.101582	+	0.994827i	$0.532391\pi$
$164$		0			0
$165$	38689.5	−	84424.4i	0.00861274	−	0.0187939i
$166$		0			0
$167$		−	682306.i		−	0.146497i	−0.997314	−	0.0732487i	$-0.976663\pi$
$167$		−	682306.i		−	0.146497i	0.997314	−	0.0732487i	$-0.0233367\pi$
$168$		0			0
$169$	−2.92334e6			−0.605646
$170$		0			0
$171$	3.72325e6	+	4.31975e6i	0.744619	+	0.863914i
$172$		0			0
$173$			6.54016e6i			1.26314i	0.775321	+	0.631568i	$0.217588\pi$
$173$			6.54016e6i			1.26314i	−0.775321	+	0.631568i	$0.782412\pi$
$174$		0			0
$175$	1.29593e6			0.241806
$176$		0			0
$177$	−9.82519e6	−	4.50263e6i	−1.77183	−	0.811982i
$178$		0			0
$179$			7.06827e6i			1.23241i	0.787587	+	0.616203i	$0.211330\pi$
$179$			7.06827e6i			1.23241i	−0.787587	+	0.616203i	$0.788670\pi$
$180$		0			0
$181$	−6.16556e6			−1.03977			−0.519885	−	0.854237i	$-0.674025\pi$
$181$	−6.16556e6			−1.03977			−0.519885	+	0.854237i	$0.674025\pi$
$182$		0			0
$183$	−941123.	+	2.05363e6i	−0.153565	+	0.335095i
$184$		0			0
$185$			127017.i			0.0200607i
$186$		0			0
$187$	418920.			0.0640629
$188$		0			0
$189$	7.84085e6	−	2.26874e6i	1.16139	−	0.336047i
$190$		0			0
$191$			4.08743e6i			0.586611i	0.956019	+	0.293306i	$0.0947554\pi$
$191$			4.08743e6i			0.586611i	−0.956019	+	0.293306i	$0.905245\pi$
$192$		0			0
$193$	56701.9			0.00788725			0.00394363	−	0.999992i	$-0.498745\pi$
$193$	56701.9			0.00788725			0.00394363	+	0.999992i	$0.498745\pi$
$194$		0			0
$195$	−1.89307e6	−	867545.i	−0.255307	−	0.117001i
$196$		0			0
$197$			6.15117e6i			0.804561i	0.915516	+	0.402281i	$0.131782\pi$
$197$			6.15117e6i			0.804561i	−0.915516	+	0.402281i	$0.868218\pi$
$198$		0			0
$199$	−8.00172e6			−1.01537			−0.507685	−	0.861543i	$-0.669499\pi$
$199$	−8.00172e6			−1.01537			−0.507685	+	0.861543i	$0.669499\pi$
$200$		0			0
$201$	4.78365e6	−	1.04384e7i	0.589075	−	1.28542i
$202$		0			0
$203$			175957.i			0.0210339i
$204$		0			0
$205$	−3.14569e6			−0.365136
$206$		0			0
$207$	−4.11904e6	+	3.55025e6i	−0.464392	+	0.400266i
$208$		0			0
$209$			481328.i			0.0527233i
$210$		0			0
$211$	−8.73879e6			−0.930259			−0.465130	−	0.885243i	$-0.653992\pi$
$211$	−8.73879e6			−0.930259			−0.465130	+	0.885243i	$0.653992\pi$
$212$		0			0
$213$	−8.49666e6	−	3.89380e6i	−0.879244	−	0.402935i
$214$		0			0
$215$			7.34130e6i			0.738682i
$216$		0			0
$217$	2.05985e7			2.01584
$218$		0			0
$219$	−1.93150e6	+	4.21473e6i	−0.183892	+	0.401271i
$220$		0			0
$221$		−	9.39355e6i		−	0.870268i
$222$		0			0
$223$	−1.51154e7			−1.36302			−0.681512	−	0.731807i	$-0.738677\pi$
$223$	−1.51154e7			−1.36302			−0.681512	+	0.731807i	$0.738677\pi$
$224$		0			0
$225$	1.48732e6	+	1.72561e6i	0.130574	+	0.151494i
$226$		0			0
$227$		−	1.32527e7i		−	1.13299i	−0.824064	−	0.566497i	$-0.808298\pi$
$227$		−	1.32527e7i		−	1.13299i	0.824064	−	0.566497i	$-0.191702\pi$
$228$		0			0
$229$	8.97752e6			0.747567			0.373783	−	0.927516i	$-0.378060\pi$
$229$	8.97752e6			0.747567			0.373783	+	0.927516i	$0.378060\pi$
$230$		0			0
$231$	626288.	+	287012.i	0.0508087	+	0.0232843i
$232$		0			0
$233$		−	1.05430e7i		−	0.833479i	−0.909026	−	0.416739i	$-0.863173\pi$
$233$		−	1.05430e7i		−	0.833479i	0.909026	−	0.416739i	$-0.136827\pi$
$234$		0			0
$235$	4.73779e6			0.365066
$236$		0			0
$237$	−2.99450e6	+	6.53429e6i	−0.224946	+	0.490855i
$238$		0			0
$239$		−	4.63239e6i		−	0.339322i	−0.985503	−	0.169661i	$-0.945733\pi$
$239$		−	4.63239e6i		−	0.339322i	0.985503	−	0.169661i	$-0.0542672\pi$
$240$		0			0
$241$	2.14836e7			1.53481			0.767407	−	0.641161i	$-0.221547\pi$
$241$	2.14836e7			1.53481			0.767407	+	0.641161i	$0.221547\pi$
$242$		0			0
$243$	1.20198e7	+	7.83676e6i	0.837683	+	0.546157i
$244$		0			0
$245$			3.03685e6i			0.206502i
$246$		0			0
$247$	1.07929e7			0.716225
$248$		0			0
$249$	2.49269e7	+	1.14234e7i	1.61462	+	0.739939i
$250$		0			0
$251$		−	2.26878e7i		−	1.43473i	−0.696697	−	0.717366i	$-0.745348\pi$
$251$		−	2.26878e7i		−	1.43473i	0.696697	−	0.717366i	$-0.254652\pi$
$252$		0			0
$253$	−458964.			−0.0283411
$254$		0			0
$255$	−4.28130e6	+	9.34222e6i	−0.258199	+	0.563417i
$256$		0			0
$257$		−	3.52158e6i		−	0.207462i	−0.994605	−	0.103731i	$-0.966922\pi$
$257$		−	3.52158e6i		−	0.207462i	0.994605	−	0.103731i	$-0.0330781\pi$
$258$		0			0
$259$	−942254.			−0.0542337
$260$		0			0
$261$	−234298.	+	201944.i	−0.0131779	+	0.0113582i
$262$		0			0
$263$		−	1.73580e7i		−	0.954185i	−0.878853	−	0.477093i	$-0.841691\pi$
$263$		−	1.73580e7i		−	0.954185i	0.878853	−	0.477093i	$-0.158309\pi$
$264$		0			0
$265$	9.31991e6			0.500811
$266$		0			0
$267$	−2.34581e7	−	1.07502e7i	−1.23242	−	0.564786i
$268$		0			0
$269$			3.42910e7i			1.76167i	0.473428	+	0.880833i	$0.343016\pi$
$269$			3.42910e7i			1.76167i	−0.473428	+	0.880833i	$0.656984\pi$
$270$		0			0
$271$	7.75571e6			0.389685			0.194843	−	0.980835i	$-0.437580\pi$
$271$	7.75571e6			0.389685			0.194843	+	0.980835i	$0.437580\pi$
$272$		0			0
$273$	6.43573e6	−	1.40434e7i	0.316308	−	0.690216i
$274$		0			0
$275$			192276.i			0.00924542i
$276$		0			0
$277$	2.75252e6			0.129507			0.0647533	−	0.997901i	$-0.479374\pi$
$277$	2.75252e6			0.129507			0.0647533	+	0.997901i	$0.479374\pi$
$278$		0			0
$279$	2.36406e7	+	2.74281e7i	1.08855	+	1.26294i
$280$		0			0
$281$		−	9.11525e6i		−	0.410818i	−0.978676	−	0.205409i	$-0.934148\pi$
$281$		−	9.11525e6i		−	0.410818i	0.978676	−	0.205409i	$-0.0658525\pi$
$282$		0			0
$283$	−2.81125e7			−1.24034			−0.620169	−	0.784468i	$-0.712936\pi$
$283$	−2.81125e7			−1.24034			−0.620169	+	0.784468i	$0.712936\pi$
$284$		0			0
$285$	−1.07340e7	−	4.91910e6i	−0.463688	−	0.212496i
$286$		0			0
$287$		−	2.33358e7i		−	0.987135i
$288$		0			0
$289$	−2.22192e7			−0.920525
$290$		0			0
$291$	−1.34342e7	+	2.93148e7i	−0.545171	+	1.18962i
$292$		0			0
$293$		−	3.34576e7i		−	1.33012i	−0.746788	−	0.665062i	$-0.768405\pi$
$293$		−	3.34576e7i		−	1.33012i	0.746788	−	0.665062i	$-0.231595\pi$
$294$		0			0
$295$	2.23768e7			0.871629
$296$		0			0
$297$	336611.	+	1.16334e6i	0.0128487	+	0.0444056i
$298$		0			0
$299$			1.02915e7i			0.385002i
$300$		0			0
$301$	−5.44602e7			−1.99701
$302$		0			0
$303$	4.26892e6	+	1.95633e6i	0.153458	+	0.0703259i
$304$		0			0
$305$		−	4.67711e6i		−	0.164846i
$306$		0			0
$307$	−1.57467e7			−0.544219			−0.272110	−	0.962266i	$-0.587721\pi$
$307$	−1.57467e7			−0.544219			−0.272110	+	0.962266i	$0.587721\pi$
$308$		0			0
$309$	−366723.	+	800226.i	−0.0124298	+	0.0271230i
$310$		0			0
$311$			7.00699e6i			0.232943i	0.993194	+	0.116472i	$0.0371584\pi$
$311$			7.00699e6i			0.232943i	−0.993194	+	0.116472i	$0.962842\pi$
$312$		0			0
$313$	−5.79389e6			−0.188946			−0.0944728	−	0.995527i	$-0.530117\pi$
$313$	−5.79389e6			−0.188946			−0.0944728	+	0.995527i	$0.530117\pi$
$314$		0			0
$315$	−1.28011e7	+	1.10335e7i	−0.409559	+	0.353004i
$316$		0			0
$317$			3.96429e7i			1.24448i	0.782827	+	0.622239i	$0.213777\pi$
$317$			3.96429e7i			1.24448i	−0.782827	+	0.622239i	$0.786223\pi$
$318$		0			0
$319$	−26106.6			−0.000804227
$320$		0			0
$321$	−3.06645e7	−	1.40528e7i	−0.927089	−	0.424861i
$322$		0			0
$323$		−	5.32628e7i		−	1.58058i
$324$		0			0
$325$	4.31145e6			0.125595
$326$		0			0
$327$	−2.58495e7	+	5.64061e7i	−0.739279	+	1.61318i
$328$		0			0
$329$			3.51465e7i			0.986947i
$330$		0			0
$331$	3.49643e6			0.0964142			0.0482071	−	0.998837i	$-0.484649\pi$
$331$	3.49643e6			0.0964142			0.0482071	+	0.998837i	$0.484649\pi$
$332$		0			0
$333$	−1.08142e6	−	1.25467e6i	−0.0292860	−	0.0339779i
$334$		0			0
$335$			2.37734e7i			0.632348i
$336$		0			0
$337$	4.53770e7			1.18562			0.592811	−	0.805342i	$-0.298018\pi$
$337$	4.53770e7			1.18562			0.592811	+	0.805342i	$0.298018\pi$
$338$		0			0
$339$	4.78580e7	+	2.19321e7i	1.22844	+	0.562964i
$340$		0			0
$341$			3.05618e6i			0.0770753i
$342$		0			0
$343$	2.62604e7			0.650756
$344$		0			0
$345$	4.69054e6	−	1.02352e7i	0.114226	−	0.249253i
$346$		0			0
$347$		−	1.83908e7i		−	0.440162i	−0.975482	−	0.220081i	$-0.929368\pi$
$347$		−	1.83908e7i		−	0.440162i	0.975482	−	0.220081i	$-0.0706321\pi$
$348$		0			0
$349$	−7.74052e7			−1.82093			−0.910467	−	0.413583i	$-0.864277\pi$
$349$	−7.74052e7			−1.82093			−0.910467	+	0.413583i	$0.864277\pi$
$350$		0			0
$351$	2.60859e7	−	7.54792e6i	0.603232	−	0.174544i
$352$		0			0
$353$			4.76509e7i			1.08330i	0.840605	+	0.541648i	$0.182199\pi$
$353$			4.76509e7i			1.08330i	−0.840605	+	0.541648i	$0.817801\pi$
$354$		0			0
$355$	1.93511e7			0.432534
$356$		0			0
$357$	−6.93037e7	−	3.17601e7i	−1.52318	−	0.698034i
$358$		0			0
$359$		−	8.95438e7i		−	1.93532i	−0.252262	−	0.967659i	$-0.581174\pi$
$359$		−	8.95438e7i		−	1.93532i	0.252262	−	0.967659i	$-0.418826\pi$
$360$		0			0
$361$	1.41516e7			0.300805
$362$		0			0
$363$	1.98848e7	−	4.33906e7i	0.415720	−	0.907143i
$364$		0			0
$365$		−	9.59902e6i		−	0.197400i
$366$		0			0
$367$	7.10716e7			1.43780			0.718899	−	0.695115i	$-0.244647\pi$
$367$	7.10716e7			1.43780			0.718899	+	0.695115i	$0.244647\pi$
$368$		0			0
$369$	3.10730e7	−	2.67822e7i	0.618449	−	0.533049i
$370$		0			0
$371$			6.91382e7i			1.35393i
$372$		0			0
$373$	−9.06999e7			−1.74775			−0.873877	−	0.486146i	$-0.838402\pi$
$373$	−9.06999e7			−1.74775			−0.873877	+	0.486146i	$0.838402\pi$
$374$		0			0
$375$	−4.28789e6	−	1.96503e6i	−0.0813111	−	0.0372627i
$376$		0			0
$377$			585395.i			0.0109251i
$378$		0			0
$379$	−1.66542e7			−0.305918			−0.152959	−	0.988233i	$-0.548880\pi$
$379$	−1.66542e7			−0.305918			−0.152959	+	0.988233i	$0.548880\pi$
$380$		0			0
$381$	2.52517e7	−	5.51018e7i	0.456579	−	0.996302i
$382$		0			0
$383$			1.04612e7i			0.186202i	0.995657	+	0.0931010i	$0.0296779\pi$
$383$			1.04612e7i			0.186202i	−0.995657	+	0.0931010i	$0.970322\pi$
$384$		0			0
$385$	−1.42637e6			−0.0249947
$386$		0			0
$387$	−6.25034e7	−	7.25170e7i	−1.07838	−	1.25114i
$388$		0			0
$389$			1.01213e8i			1.71945i	0.510758	+	0.859724i	$0.329365\pi$
$389$			1.01213e8i			1.71945i	−0.510758	+	0.859724i	$0.670635\pi$
$390$		0			0
$391$	5.07879e7			0.849631
$392$		0			0
$393$	6.70143e7	+	3.07109e7i	1.10405	+	0.505958i
$394$		0			0
$395$		−	1.48818e7i		−	0.241470i
$396$		0			0
$397$	1.01774e8			1.62655			0.813273	−	0.581883i	$-0.197684\pi$
$397$	1.01774e8			1.62655			0.813273	+	0.581883i	$0.197684\pi$
$398$		0			0
$399$	3.64915e7	−	7.96281e7i	0.574478	−	1.25357i
$400$		0			0
$401$		−	1.02772e8i		−	1.59382i	−0.604095	−	0.796912i	$-0.706465\pi$
$401$		−	1.02772e8i		−	1.59382i	0.604095	−	0.796912i	$-0.293535\pi$
$402$		0			0
$403$	6.85294e7			1.04704
$404$		0			0
$405$	−2.93834e7	−	4.38248e6i	−0.442321	−	0.0659713i
$406$		0			0
$407$		−	139801.i		−	0.00207362i
$408$		0			0
$409$	6.56844e7			0.960047			0.480023	−	0.877256i	$-0.340628\pi$
$409$	6.56844e7			0.960047			0.480023	+	0.877256i	$0.340628\pi$
$410$		0			0
$411$	1.06770e8	+	4.89301e7i	1.53789	+	0.704775i
$412$		0			0
$413$			1.65998e8i			2.35642i
$414$		0			0
$415$	−5.67709e7			−0.794294
$416$		0			0
$417$	603603.	−	1.31712e6i	0.00832421	−	0.0181643i
$418$		0			0
$419$		−	6.34334e7i		−	0.862334i	−0.902272	−	0.431167i	$-0.858102\pi$
$419$		−	6.34334e7i		−	0.862334i	0.902272	−	0.431167i	$-0.141898\pi$
$420$		0			0
$421$	−9.10207e7			−1.21981			−0.609907	−	0.792473i	$-0.708793\pi$
$421$	−9.10207e7			−1.21981			−0.609907	+	0.792473i	$0.708793\pi$
$422$		0			0
$423$	−4.67996e7	+	4.03372e7i	−0.618331	+	0.532948i
$424$		0			0
$425$		−	2.12768e7i		−	0.277166i
$426$		0			0
$427$	3.46964e7			0.445657
$428$		0			0
$429$	2.08361e6	+	954864.i	0.0263903	+	0.0120940i
$430$		0			0
$431$			4.20911e7i			0.525725i	0.964833	+	0.262862i	$0.0846666\pi$
$431$			4.20911e7i			0.525725i	−0.964833	+	0.262862i	$0.915333\pi$
$432$		0			0
$433$	−92285.8			−0.00113677			−0.000568383	−	1.00000i	$-0.500181\pi$
$433$	−92285.8			−0.00113677			−0.000568383		1.00000i	$0.500181\pi$
$434$		0			0
$435$	266805.	−	582196.i	0.00324136	−	0.00707297i
$436$		0			0
$437$			5.83540e7i			0.699240i
$438$		0			0
$439$	−1.42372e8			−1.68280			−0.841398	−	0.540416i	$-0.818267\pi$
$439$	−1.42372e8			−1.68280			−0.841398	+	0.540416i	$0.818267\pi$
$440$		0			0
$441$	−2.58556e7	−	2.99979e7i	−0.301466	−	0.349764i
$442$		0			0
$443$			8.16658e7i			0.939354i	0.882838	+	0.469677i	$0.155630\pi$
$443$			8.16658e7i			0.939354i	−0.882838	+	0.469677i	$0.844370\pi$
$444$		0			0
$445$	5.34256e7			0.606274
$446$		0			0
$447$	−7.27636e7	−	3.33457e7i	−0.814688	−	0.373350i
$448$		0			0
$449$		−	1.31510e8i		−	1.45284i	−0.687250	−	0.726421i	$-0.741183\pi$
$449$		−	1.31510e8i		−	1.45284i	0.687250	−	0.726421i	$-0.258817\pi$
$450$		0			0
$451$	3.46231e6			0.0377430
$452$		0			0
$453$	−1.45546e6	+	3.17597e6i	−0.0156569	+	0.0341650i
$454$		0			0
$455$			3.19837e7i			0.339543i
$456$		0			0
$457$	8.80615e7			0.922651			0.461326	−	0.887231i	$-0.347374\pi$
$457$	8.80615e7			0.922651			0.461326	+	0.887231i	$0.347374\pi$
$458$		0			0
$459$	−3.72487e7	−	1.28733e8i	−0.385188	−	1.33122i
$460$		0			0
$461$			7.89270e7i			0.805606i	0.915287	+	0.402803i	$0.131964\pi$
$461$			7.89270e7i			0.805606i	−0.915287	+	0.402803i	$0.868036\pi$
$462$		0			0
$463$	−1.04058e8			−1.04841			−0.524205	−	0.851592i	$-0.675637\pi$
$463$	−1.04058e8			−1.04841			−0.524205	+	0.851592i	$0.675637\pi$
$464$		0			0
$465$	−6.81549e7	−	3.12336e7i	−0.677857	−	0.310644i
$466$		0			0
$467$			2.93827e7i			0.288497i	0.989542	+	0.144248i	$0.0460765\pi$
$467$			2.93827e7i			0.288497i	−0.989542	+	0.144248i	$0.953924\pi$
$468$		0			0
$469$	−1.76359e8			−1.70954
$470$		0			0
$471$	−428980.	+	936077.i	−0.00410558	+	0.00895878i
$472$		0			0
$473$		−	8.08021e6i		−	0.0763553i
$474$		0			0
$475$	2.44465e7			0.228106
$476$		0			0
$477$	−9.20617e7	+	7.93492e7i	−0.848250	+	0.731118i
$478$		0			0
$479$		−	1.71918e7i		−	0.156429i	−0.996937	−	0.0782143i	$-0.975078\pi$
$479$		−	1.71918e7i		−	0.156429i	0.996937	−	0.0782143i	$-0.0249218\pi$
$480$		0			0
$481$	−3.13480e6			−0.0281692
$482$		0			0
$483$	7.59283e7	+	3.47959e7i	0.673848	+	0.308807i
$484$		0			0
$485$		−	6.67641e7i		−	0.585218i
$486$		0			0
$487$	−8.72586e7			−0.755477			−0.377739	−	0.925912i	$-0.623298\pi$
$487$	−8.72586e7			−0.755477			−0.377739	+	0.925912i	$0.623298\pi$
$488$		0			0
$489$	−9.89704e6	+	2.15963e7i	−0.0846406	+	0.184694i
$490$		0			0
$491$			1.79828e8i			1.51919i	0.650396	+	0.759596i	$0.274603\pi$
$491$			1.79828e8i			1.51919i	−0.650396	+	0.759596i	$0.725397\pi$
$492$		0			0
$493$	2.88890e6			0.0241097
$494$		0			0
$495$	−1.63702e6	−	1.89929e6i	−0.0134971	−	0.0156594i
$496$		0			0
$497$			1.43553e8i			1.16934i
$498$		0			0
$499$	−8.70160e7			−0.700321			−0.350161	−	0.936690i	$-0.613873\pi$
$499$	−8.70160e7			−0.700321			−0.350161	+	0.936690i	$0.613873\pi$
$500$		0			0
$501$	−1.67474e7	−	7.67490e6i	−0.133179	−	0.0610323i
$502$		0			0
$503$			4.25009e7i			0.333960i	0.985960	+	0.166980i	$0.0534016\pi$
$503$			4.25009e7i			0.333960i	−0.985960	+	0.166980i	$0.946598\pi$
$504$		0			0
$505$	−9.72242e6			−0.0754919
$506$		0			0
$507$	−3.28831e7	+	7.17542e7i	−0.252318	+	0.550584i
$508$		0			0
$509$		−	1.86035e8i		−	1.41072i	−0.708850	−	0.705359i	$-0.750786\pi$
$509$		−	1.86035e8i		−	1.41072i	0.708850	−	0.705359i	$-0.249214\pi$
$510$		0			0
$511$	7.12087e7			0.533667
$512$		0			0
$513$	1.47911e8	−	4.27977e7i	1.09559	−	0.317007i
$514$		0			0
$515$		−	1.82251e6i		−	0.0133428i
$516$		0			0
$517$	−5.21465e6			−0.0377358
$518$		0			0
$519$	1.60530e8	+	7.35668e7i	1.14830	+	0.526235i
$520$		0			0
$521$		−	5.95626e7i		−	0.421173i	−0.977575	−	0.210587i	$-0.932463\pi$
$521$		−	5.95626e7i		−	0.421173i	0.977575	−	0.210587i	$-0.0675374\pi$
$522$		0			0
$523$	1.77836e8			1.24313			0.621563	−	0.783364i	$-0.286498\pi$
$523$	1.77836e8			1.24313			0.621563	+	0.783364i	$0.286498\pi$
$524$		0			0
$525$	1.45772e7	−	3.18090e7i	0.100739	−	0.219822i
$526$		0			0
$527$		−	3.38190e8i		−	2.31062i
$528$		0			0
$529$	9.23933e7			0.624127
$530$		0			0
$531$	−2.21037e8	+	1.90515e8i	−1.47632	+	1.27246i
$532$		0			0
$533$		−	7.76362e7i		−	0.512723i
$534$		0			0
$535$	6.98382e7			0.456070
$536$		0			0
$537$	1.73493e8	+	7.95072e7i	1.12036	+	0.513433i
$538$		0			0
$539$		−	3.34251e6i		−	0.0213455i
$540$		0			0
$541$	1.08545e8			0.685519			0.342760	−	0.939423i	$-0.388638\pi$
$541$	1.08545e8			0.685519			0.342760	+	0.939423i	$0.388638\pi$
$542$		0			0
$543$	−6.93532e7	+	1.51336e8i	−0.433178	+	0.945239i
$544$		0			0
$545$		−	1.28464e8i		−	0.793585i
$546$		0			0
$547$	−1.25572e7			−0.0767241			−0.0383620	−	0.999264i	$-0.512214\pi$
$547$	−1.25572e7			−0.0767241			−0.0383620	+	0.999264i	$0.512214\pi$
$548$		0			0
$549$	3.98207e7	+	4.62003e7i	0.240653	+	0.279208i
$550$		0			0
$551$			3.31927e6i			0.0198421i
$552$		0			0
$553$	1.10398e8			0.652809
$554$		0			0
$555$	3.11767e6	+	1.42875e6i	0.0182369	+	0.00835750i
$556$		0			0
$557$		−	2.86738e7i		−	0.165928i	−0.996553	−	0.0829641i	$-0.973561\pi$
$557$		−	2.86738e7i		−	0.165928i	0.996553	−	0.0829641i	$-0.0264387\pi$
$558$		0			0
$559$	−1.81185e8			−1.03726
$560$		0			0
$561$	4.71221e6	−	1.02825e7i	0.0266892	−	0.0582386i
$562$		0			0
$563$		−	1.61064e8i		−	0.902555i	−0.892384	−	0.451278i	$-0.850968\pi$
$563$		−	1.61064e8i		−	0.902555i	0.892384	−	0.451278i	$-0.149032\pi$
$564$		0			0
$565$	−1.08996e8			−0.604318
$566$		0			0
$567$	3.25107e7	−	2.17976e8i	0.178352	−	1.19580i
$568$		0			0
$569$			1.14947e8i			0.623965i	0.950088	+	0.311982i	$0.100993\pi$
$569$			1.14947e8i			0.623965i	−0.950088	+	0.311982i	$0.899007\pi$
$570$		0			0
$571$	−8.55993e7			−0.459792			−0.229896	−	0.973215i	$-0.573839\pi$
$571$	−8.55993e7			−0.459792			−0.229896	+	0.973215i	$0.573839\pi$
$572$		0			0
$573$	1.00327e8	+	4.59774e7i	0.533280	+	0.244388i
$574$		0			0
$575$			2.33106e7i			0.122617i
$576$		0			0
$577$	8.75149e7			0.455569			0.227785	−	0.973712i	$-0.426852\pi$
$577$	8.75149e7			0.455569			0.227785	+	0.973712i	$0.426852\pi$
$578$		0			0
$579$	637810.	−	1.39177e6i	0.00328591	−	0.00717019i
$580$		0			0
$581$		−	4.21145e8i		−	2.14735i
$582$		0			0
$583$	−1.02580e7			−0.0517673
$584$		0			0
$585$	−4.25883e7	+	3.67074e7i	−0.212727	+	0.183352i
$586$		0			0
$587$			1.61940e8i			0.800646i	0.916374	+	0.400323i	$0.131102\pi$
$587$			1.61940e8i			0.800646i	−0.916374	+	0.400323i	$0.868898\pi$
$588$		0			0
$589$	3.88571e8			1.90163
$590$		0			0
$591$	1.50982e8	+	6.91913e7i	0.731415	+	0.335188i
$592$		0			0
$593$		−	2.85726e8i		−	1.37021i	−0.728446	−	0.685104i	$-0.759757\pi$
$593$		−	2.85726e8i		−	1.37021i	0.728446	−	0.685104i	$-0.240243\pi$
$594$		0			0
$595$	1.57839e8			0.749311
$596$		0			0
$597$	−9.00071e7	+	1.96405e8i	−0.423013	+	0.923058i
$598$		0			0
$599$		−	4.98255e7i		−	0.231831i	−0.993259	−	0.115916i	$-0.963020\pi$
$599$		−	4.98255e7i		−	0.231831i	0.993259	−	0.115916i	$-0.0369802\pi$
$600$		0			0
$601$	7.73983e7			0.356540			0.178270	−	0.983982i	$-0.442950\pi$
$601$	7.73983e7			0.356540			0.178270	+	0.983982i	$0.442950\pi$
$602$		0			0
$603$	−2.02405e8	−	2.34832e8i	−0.923143	−	1.07104i
$604$		0			0
$605$			9.88216e7i			0.446258i
$606$		0			0
$607$	−4.82366e7			−0.215680			−0.107840	−	0.994168i	$-0.534393\pi$
$607$	−4.82366e7			−0.215680			−0.107840	+	0.994168i	$0.534393\pi$
$608$		0			0
$609$	4.31892e6	+	1.97925e6i	0.0191216	+	0.00876292i
$610$		0			0
$611$			1.16929e8i			0.512625i
$612$		0			0
$613$	−1.34171e8			−0.582474			−0.291237	−	0.956651i	$-0.594067\pi$
$613$	−1.34171e8			−0.582474			−0.291237	+	0.956651i	$0.594067\pi$
$614$		0			0
$615$	−3.53842e7	+	7.72119e7i	−0.152119	+	0.331940i
$616$		0			0
$617$			4.66923e7i			0.198788i	0.995048	+	0.0993939i	$0.0316904\pi$
$617$			4.66923e7i			0.198788i	−0.995048	+	0.0993939i	$0.968310\pi$
$618$		0			0
$619$	−1.05294e8			−0.443948			−0.221974	−	0.975053i	$-0.571250\pi$
$619$	−1.05294e8			−0.443948			−0.221974	+	0.975053i	$0.571250\pi$
$620$		0			0
$621$	4.08092e7	+	1.41038e8i	0.170405	+	0.588927i
$622$		0			0
$623$			3.96329e8i			1.63905i
$624$		0			0
$625$	9.76562e6			0.0400000
$626$		0			0
$627$	1.18144e7	+	5.41421e6i	0.0479300	+	0.0219651i
$628$		0			0
$629$			1.54701e7i			0.0621644i
$630$		0			0
$631$	2.38661e7			0.0949936			0.0474968	−	0.998871i	$-0.484876\pi$
$631$	2.38661e7			0.0949936			0.0474968	+	0.998871i	$0.484876\pi$
$632$		0			0
$633$	−9.82981e7	+	2.14496e8i	−0.387555	+	0.845685i
$634$		0			0
$635$			1.25494e8i			0.490119i
$636$		0			0
$637$	−7.49500e7			−0.289970
$638$		0			0
$639$	−1.91149e8	+	1.64754e8i	−0.732604	+	0.631441i
$640$		0			0
$641$		−	8.49890e7i		−	0.322692i	−0.986898	−	0.161346i	$-0.948416\pi$
$641$		−	8.49890e7i		−	0.322692i	0.986898	−	0.161346i	$-0.0515836\pi$
$642$		0			0
$643$	−3.40735e8			−1.28169			−0.640845	−	0.767670i	$-0.721416\pi$
$643$	−3.40735e8			−1.28169			−0.640845	+	0.767670i	$0.721416\pi$
$644$		0			0
$645$	1.80194e8	+	8.25784e7i	0.671525	+	0.307742i
$646$		0			0
$647$		−	3.26674e8i		−	1.20615i	−0.797684	−	0.603076i	$-0.793942\pi$
$647$		−	3.26674e8i		−	1.20615i	0.797684	−	0.603076i	$-0.206058\pi$
$648$		0			0
$649$	−2.46290e7			−0.0900976
$650$		0			0
$651$	2.31701e8	−	5.05596e8i	0.839819	−	1.83257i
$652$		0			0
$653$		−	2.15329e8i		−	0.773326i	−0.922221	−	0.386663i	$-0.873628\pi$
$653$		−	2.15329e8i		−	0.773326i	0.922221	−	0.386663i	$-0.126372\pi$
$654$		0			0
$655$	−1.52624e8			−0.543125
$656$		0			0
$657$	8.17254e7	+	9.48186e7i	0.288178	+	0.334347i
$658$		0			0
$659$			3.75646e8i			1.31257i	0.754513	+	0.656285i	$0.227873\pi$
$659$			3.75646e8i			1.31257i	−0.754513	+	0.656285i	$0.772127\pi$
$660$		0			0
$661$	−3.65705e8			−1.26627			−0.633135	−	0.774041i	$-0.718232\pi$
$661$	−3.65705e8			−1.26627			−0.633135	+	0.774041i	$0.718232\pi$
$662$		0			0
$663$	−2.30568e8	−	1.05663e8i	−0.791148	−	0.362563i
$664$		0			0
$665$			1.81352e8i			0.616678i
$666$		0			0
$667$	−3.16504e6			−0.0106660
$668$		0			0
$669$	−1.70025e8	+	3.71011e8i	−0.567850	+	1.23911i
$670$		0			0
$671$			5.14787e6i			0.0170396i
$672$		0			0
$673$	−2.47794e8			−0.812917			−0.406459	−	0.913669i	$-0.633236\pi$
$673$	−2.47794e8			−0.812917			−0.406459	+	0.913669i	$0.633236\pi$
$674$		0			0
$675$	5.90857e7	−	1.70964e7i	0.192119	−	0.0555895i
$676$		0			0
$677$			1.27016e8i			0.409347i	0.978830	+	0.204674i	$0.0656133\pi$
$677$			1.27016e8i			0.409347i	−0.978830	+	0.204674i	$0.934387\pi$
$678$		0			0
$679$	4.95278e8			1.58212
$680$		0			0
$681$	−3.25292e8	−	1.49073e8i	−1.02999	−	0.472017i
$682$		0			0
$683$		−	3.06787e8i		−	0.962884i	−0.876478	−	0.481442i	$-0.840113\pi$
$683$		−	3.06787e8i		−	0.962884i	0.876478	−	0.481442i	$-0.159887\pi$
$684$		0			0
$685$	−2.43169e8			−0.756547
$686$		0			0
$687$	1.00983e8	−	2.20356e8i	0.311444	−	0.679602i
$688$		0			0
$689$			2.30017e8i			0.703238i
$690$		0			0
$691$	−1.85102e8			−0.561017			−0.280509	−	0.959852i	$-0.590503\pi$
$691$	−1.85102e8			−0.561017			−0.280509	+	0.959852i	$0.590503\pi$
$692$		0			0
$693$	1.40896e7	−	1.21440e7i	0.0423348	−	0.0364890i
$694$		0			0
$695$			2.99973e6i			0.00893569i
$696$		0			0
$697$	−3.83131e8			−1.13149
$698$		0			0
$699$	−2.58780e8	−	1.18592e8i	−0.757703	−	0.347236i
$700$		0			0
$701$		−	4.66462e8i		−	1.35414i	−0.735920	−	0.677068i	$-0.763250\pi$
$701$		−	4.66462e8i		−	1.35414i	0.735920	−	0.677068i	$-0.236750\pi$
$702$		0			0
$703$	−1.77748e7			−0.0511609
$704$		0			0
$705$	5.32929e7	−	1.16290e8i	0.152090	−	0.331876i
$706$		0			0
$707$		−	7.21241e7i		−	0.204090i
$708$		0			0
$709$	5.51189e8			1.54654			0.773271	−	0.634076i	$-0.218619\pi$
$709$	5.51189e8			1.54654			0.773271	+	0.634076i	$0.218619\pi$
$710$		0			0
$711$	1.26703e8	+	1.47002e8i	0.352515	+	0.408991i
$712$		0			0
$713$			3.70517e8i			1.02221i
$714$		0			0
$715$	−4.74540e6			−0.0129824
$716$		0			0
$717$	−1.13703e8	−	5.21073e7i	−0.308472	−	0.141365i
$718$		0			0
$719$			6.52168e8i			1.75458i	0.479963	+	0.877289i	$0.340650\pi$
$719$			6.52168e8i			1.75458i	−0.479963	+	0.877289i	$0.659350\pi$
$720$		0			0
$721$	1.35200e7			0.0360720
$722$		0			0
$723$	2.41657e8	−	5.27321e8i	0.639419	−	1.39528i
$724$		0			0
$725$			1.32595e6i			0.00347946i
$726$		0			0
$727$	2.30050e7			0.0598713			0.0299357	−	0.999552i	$-0.490470\pi$
$727$	2.30050e7			0.0598713			0.0299357	+	0.999552i	$0.490470\pi$
$728$		0			0
$729$	3.27560e8	−	2.06879e8i	0.845490	−	0.533990i
$730$		0			0
$731$			8.94138e8i			2.28904i
$732$		0			0
$733$	2.39083e8			0.607068			0.303534	−	0.952821i	$-0.401833\pi$
$733$	2.39083e8			0.607068			0.303534	+	0.952821i	$0.401833\pi$
$734$		0			0
$735$	7.45404e7	+	3.41599e7i	0.187728	+	0.0860310i
$736$		0			0
$737$		−	2.61662e7i		−	0.0653638i
$738$		0			0
$739$	4.07576e8			1.00989			0.504946	−	0.863151i	$-0.331512\pi$
$739$	4.07576e8			1.00989			0.504946	+	0.863151i	$0.331512\pi$
$740$		0			0
$741$	1.21404e8	−	2.64916e8i	0.298386	−	0.651109i
$742$		0			0
$743$		−	2.87465e8i		−	0.700841i	−0.936593	−	0.350420i	$-0.886039\pi$
$743$		−	2.87465e8i		−	0.700841i	0.936593	−	0.350420i	$-0.113961\pi$
$744$		0			0
$745$	1.65718e8			0.400776
$746$		0			0
$747$	5.60780e8	−	4.83344e8i	1.34534	−	1.15956i
$748$		0			0
$749$			5.18083e8i			1.23297i
$750$		0			0
$751$	4.86133e8			1.14772			0.573859	−	0.818954i	$-0.305446\pi$
$751$	4.86133e8			1.14772			0.573859	+	0.818954i	$0.305446\pi$
$752$		0			0
$753$	−5.56878e8	−	2.55203e8i	−1.30429	−	0.597724i
$754$		0			0
$755$		−	7.23323e6i		−	0.0168071i
$756$		0			0
$757$	2.22098e8			0.511986			0.255993	−	0.966679i	$-0.417598\pi$
$757$	2.22098e8			0.511986			0.255993	+	0.966679i	$0.417598\pi$
$758$		0			0
$759$	−5.16264e6	+	1.12654e7i	−0.0118072	+	0.0257645i
$760$		0			0
$761$		−	1.36605e8i		−	0.309964i	−0.987917	−	0.154982i	$-0.950468\pi$
$761$		−	1.36605e8i		−	0.309964i	0.987917	−	0.154982i	$-0.0495320\pi$
$762$		0			0
$763$	9.52992e8			2.14544
$764$		0			0
$765$	1.81150e8	+	2.10171e8i	0.404625	+	0.469450i
$766$		0			0
$767$			5.52263e8i			1.22394i
$768$		0			0
$769$	−6.76897e8			−1.48848			−0.744241	−	0.667911i	$-0.767189\pi$
$769$	−6.76897e8			−1.48848			−0.744241	+	0.667911i	$0.767189\pi$
$770$		0			0
$771$	−8.64383e7	−	3.96124e7i	−0.188601	−	0.0864308i
$772$		0			0
$773$		−	6.32394e8i		−	1.36914i	−0.728945	−	0.684572i	$-0.759989\pi$
$773$		−	6.32394e8i		−	1.36914i	0.728945	−	0.684572i	$-0.240011\pi$
$774$		0			0
$775$	1.55222e8			0.333464
$776$		0			0
$777$	−1.05989e7	+	2.31279e7i	−0.0225943	+	0.0493030i
$778$		0			0
$779$		−	4.40208e8i		−	0.931206i
$780$		0			0
$781$	−2.12988e7			−0.0447097
$782$		0			0
$783$	2.32129e6	+	8.02247e6i	0.00483553	+	0.0167118i
$784$		0			0
$785$		−	2.13191e6i		−	0.00440717i
$786$		0			0
$787$	−7.43145e8			−1.52458			−0.762288	−	0.647238i	$-0.775924\pi$
$787$	−7.43145e8			−1.52458			−0.762288	+	0.647238i	$0.775924\pi$
$788$		0			0
$789$	−4.26058e8	−	1.95251e8i	−0.867436	−	0.397523i
$790$		0			0
$791$		−	8.08569e8i		−	1.63376i
$792$		0			0
$793$	1.15432e8			0.231476
$794$		0			0
$795$	1.04835e8	−	2.28760e8i	0.208643	−	0.455280i
$796$		0			0
$797$			4.32008e7i			0.0853329i	0.999089	+	0.0426664i	$0.0135853\pi$
$797$			4.32008e7i			0.0853329i	−0.999089	+	0.0426664i	$0.986415\pi$
$798$		0			0
$799$	5.77042e8			1.13127
$800$		0			0
$801$	−5.27735e8	+	4.54862e8i	−1.02688	+	0.885079i
$802$		0			0
$803$			1.05652e7i			0.0204047i
$804$		0			0
$805$	−1.72926e8			−0.331492
$806$		0			0
$807$	8.41683e8	+	3.85721e8i	1.60150	+	0.733927i
$808$		0			0
$809$		−	4.44561e8i		−	0.839627i	−0.907610	−	0.419813i	$-0.862096\pi$
$809$		−	4.44561e8i		−	0.839627i	0.907610	−	0.419813i	$-0.137904\pi$
$810$		0			0
$811$	−3.11585e8			−0.584136			−0.292068	−	0.956398i	$-0.594343\pi$
$811$	−3.11585e8			−0.584136			−0.292068	+	0.956398i	$0.594343\pi$
$812$		0			0
$813$	8.72399e7	−	1.90366e8i	0.162347	−	0.354257i
$814$		0			0
$815$		−	4.91854e7i		−	0.0908581i
$816$		0			0
$817$	−1.02734e9			−1.88386
$818$		0			0
$819$	−2.72308e8	−	3.15934e8i	−0.495688	−	0.575102i
$820$		0			0
$821$			1.06060e9i			1.91656i	0.285833	+	0.958280i	$0.407730\pi$
$821$			1.06060e9i			1.91656i	−0.285833	+	0.958280i	$0.592270\pi$
$822$		0			0
$823$	4.65269e7			0.0834651			0.0417325	−	0.999129i	$-0.486712\pi$
$823$	4.65269e7			0.0834651			0.0417325	+	0.999129i	$0.486712\pi$
$824$		0			0
$825$	4.71947e6	+	2.16281e6i	0.00840487	+	0.00385173i
$826$		0			0
$827$			4.51328e8i			0.797951i	0.916962	+	0.398975i	$0.130634\pi$
$827$			4.51328e8i			0.797951i	−0.916962	+	0.398975i	$0.869366\pi$
$828$		0			0
$829$	3.04859e8			0.535100			0.267550	−	0.963544i	$-0.413786\pi$
$829$	3.04859e8			0.535100			0.267550	+	0.963544i	$0.413786\pi$
$830$		0			0
$831$	3.09617e7	−	6.75616e7i	0.0539538	−	0.117733i
$832$		0			0
$833$			3.69875e8i			0.639912i
$834$		0			0
$835$	3.81421e7			0.0655156
$836$		0			0
$837$	9.39152e8	−	2.71743e8i	1.60162	−	0.463427i
$838$		0			0
$839$		−	2.25607e8i		−	0.382003i	−0.981590	−	0.191001i	$-0.938827\pi$
$839$		−	2.25607e8i		−	0.382003i	0.981590	−	0.191001i	$-0.0611735\pi$
$840$		0			0
$841$	5.94643e8			0.999697
$842$		0			0
$843$	−2.23737e8	−	1.02533e8i	−0.373469	−	0.171151i
$844$		0			0
$845$		−	1.63420e8i		−	0.270853i
$846$		0			0
$847$	−7.33092e8			−1.20645
$848$		0			0
$849$	−3.16222e8	+	6.90029e8i	−0.516737	+	1.12757i
$850$		0			0
$851$		−	1.69489e7i		−	0.0275012i
$852$		0			0
$853$	−2.50662e8			−0.403869			−0.201935	−	0.979399i	$-0.564723\pi$
$853$	−2.50662e8			−0.403869			−0.201935	+	0.979399i	$0.564723\pi$
$854$		0			0
$855$	−2.41482e8	+	2.08136e8i	−0.386354	+	0.333004i
$856$		0			0
$857$		−	2.24351e8i		−	0.356440i	−0.983991	−	0.178220i	$-0.942966\pi$
$857$		−	2.24351e8i		−	0.356440i	0.983991	−	0.178220i	$-0.0570339\pi$
$858$		0			0
$859$	1.58303e8			0.249753			0.124876	−	0.992172i	$-0.460147\pi$
$859$	1.58303e8			0.249753			0.124876	+	0.992172i	$0.460147\pi$
$860$		0			0
$861$	−5.72784e8	−	2.62492e8i	−0.897390	−	0.411250i
$862$		0			0
$863$			4.43360e8i			0.689801i	0.938639	+	0.344900i	$0.112087\pi$
$863$			4.43360e8i			0.689801i	−0.938639	+	0.344900i	$0.887913\pi$
$864$		0			0
$865$	−3.65606e8			−0.564892
$866$		0			0
$867$	−2.49932e8	+	5.45378e8i	−0.383500	+	0.836836i
$868$		0			0
$869$			1.63797e7i			0.0249601i
$870$		0			0
$871$	−5.86730e8			−0.887941
$872$		0			0
$873$	5.68426e8	+	6.59493e8i	0.854340	+	0.991214i
$874$		0			0
$875$			7.24446e7i			0.108139i
$876$		0			0
$877$	7.04336e8			1.04419			0.522097	−	0.852886i	$-0.325150\pi$
$877$	7.04336e8			1.04419			0.522097	+	0.852886i	$0.325150\pi$
$878$		0			0
$879$	−8.21227e8	−	3.76347e8i	−1.20920	−	0.554143i
$880$		0			0
$881$			1.02359e9i			1.49692i	0.663181	+	0.748459i	$0.269206\pi$
$881$			1.02359e9i			1.49692i	−0.663181	+	0.748459i	$0.730794\pi$
$882$		0			0
$883$	−3.14880e8			−0.457365			−0.228682	−	0.973501i	$-0.573442\pi$
$883$	−3.14880e8			−0.457365			−0.228682	+	0.973501i	$0.573442\pi$
$884$		0			0
$885$	2.51705e8	−	5.49245e8i	0.363129	−	0.792385i
$886$		0			0
$887$		−	6.28597e8i		−	0.900744i	−0.892841	−	0.450372i	$-0.851291\pi$
$887$		−	6.28597e8i		−	0.900744i	0.892841	−	0.450372i	$-0.148709\pi$
$888$		0			0
$889$	−9.30955e8			−1.32502
$890$		0			0
$891$	3.23409e7	+	4.82358e6i	0.0457213	+	0.00681925i
$892$		0			0
$893$			6.63006e8i			0.931029i
$894$		0			0
$895$	−3.95128e8			−0.551149
$896$		0			0
$897$	2.52607e8	+	1.15763e8i	0.350000	+	0.160396i
$898$		0			0
$899$			2.10756e7i			0.0290069i
$900$		0			0
$901$	1.13512e9			1.55192
$902$		0			0
$903$	−6.12594e8	+	1.33674e9i	−0.831973	+	1.81545i
$904$		0			0
$905$		−	3.44665e8i		−	0.464999i
$906$		0			0
$907$	−6.20458e8			−0.831555			−0.415777	−	0.909466i	$-0.636490\pi$
$907$	−6.20458e8			−0.831555			−0.415777	+	0.909466i	$0.636490\pi$
$908$		0			0
$909$	9.60376e7	−	8.27761e7i	0.127864	−	0.110208i
$910$		0			0
$911$		−	1.24142e9i		−	1.64197i	−0.570953	−	0.820983i	$-0.693426\pi$
$911$		−	1.24142e9i		−	1.64197i	0.570953	−	0.820983i	$-0.306574\pi$
$912$		0			0
$913$	6.24849e7			0.0821037
$914$		0			0
$915$	−1.14801e8	−	5.26104e7i	−0.149859	−	0.0686765i
$916$		0			0
$917$		−	1.13222e9i		−	1.46832i
$918$		0			0
$919$	6.59663e8			0.849916			0.424958	−	0.905213i	$-0.360289\pi$
$919$	6.59663e8			0.849916			0.424958	+	0.905213i	$0.360289\pi$
$920$		0			0
$921$	−1.77126e8	+	3.86507e8i	−0.226727	+	0.494741i
$922$		0			0
$923$			4.77588e8i			0.607363i
$924$		0			0
$925$	−7.10047e6			−0.00897143
$926$		0			0
$927$	1.55167e7	+	1.80027e7i	0.0194787	+	0.0225994i
$928$		0			0
$929$		−	1.38845e9i		−	1.73174i	−0.500270	−	0.865870i	$-0.666766\pi$
$929$		−	1.38845e9i		−	1.73174i	0.500270	−	0.865870i	$-0.333234\pi$
$930$		0			0
$931$	−4.24977e8			−0.526643
$932$		0			0
$933$	1.71989e8	+	7.88179e7i	0.211765	+	0.0970466i
$934$		0			0
$935$			2.34184e7i			0.0286498i
$936$		0			0
$937$	−9.75190e8			−1.18541			−0.592707	−	0.805418i	$-0.701941\pi$
$937$	−9.75190e8			−1.18541			−0.592707	+	0.805418i	$0.701941\pi$
$938$		0			0
$939$	−6.51724e7	+	1.42213e8i	−0.0787167	+	0.171768i
$940$		0			0
$941$		−	7.89692e8i		−	0.947739i	−0.880595	−	0.473870i	$-0.842857\pi$
$941$		−	7.89692e8i		−	0.947739i	0.880595	−	0.473870i	$-0.157143\pi$
$942$		0			0
$943$	4.19754e8			0.500564
$944$		0			0
$945$	1.26827e8	+	4.38317e8i	0.150285	+	0.519389i
$946$		0			0
$947$			5.10202e8i			0.600747i	0.953822	+	0.300374i	$0.0971114\pi$
$947$			5.10202e8i			0.600747i	−0.953822	+	0.300374i	$0.902889\pi$
$948$		0			0
$949$	2.36905e8			0.277189
$950$		0			0
$951$	9.73047e8	+	4.45922e8i	1.13134	+	0.518462i
$952$		0			0
$953$			6.26272e8i			0.723576i	0.932260	+	0.361788i	$0.117834\pi$
$953$			6.26272e8i			0.723576i	−0.932260	+	0.361788i	$0.882166\pi$
$954$		0			0
$955$	−2.28494e8			−0.262341
$956$		0			0
$957$	−293659.	+	640795.i	−0.000335049	+	0.000731111i
$958$		0			0
$959$		−	1.80390e9i		−	2.04530i
$960$		0			0
$961$	1.57971e9			1.77995
$962$		0			0
$963$	−6.89858e8	+	5.94598e8i	−0.772469	+	0.665801i
$964$		0			0
$965$			3.16973e6i			0.00352729i
$966$		0			0
$967$	4.99324e8			0.552209			0.276104	−	0.961128i	$-0.410956\pi$
$967$	4.99324e8			0.552209			0.276104	+	0.961128i	$0.410956\pi$
$968$		0			0
$969$	−1.30735e9	−	5.99125e8i	−1.43688	−	0.658485i
$970$		0			0
$971$			4.94342e7i			0.0539970i	0.999635	+	0.0269985i	$0.00859494\pi$
$971$			4.94342e7i			0.0539970i	−0.999635	+	0.0269985i	$0.991405\pi$
$972$		0			0
$973$	−2.22530e7			−0.0241574
$974$		0			0
$975$	4.84972e7	−	1.05826e8i	0.0523242	−	0.114177i
$976$		0			0
$977$		−	4.90224e7i		−	0.0525667i	−0.999655	−	0.0262834i	$-0.991633\pi$
$977$		−	4.90224e7i		−	0.0525667i	0.999655	−	0.0262834i	$-0.00836722\pi$
$978$		0			0
$979$	−5.88029e7			−0.0626687
$980$		0			0
$981$	1.09374e9	+	1.26897e9i	1.15853	+	1.34414i
$982$		0			0
$983$		−	2.97397e8i		−	0.313095i	−0.987670	−	0.156548i	$-0.949964\pi$
$983$		−	2.97397e8i		−	0.313095i	0.987670	−	0.156548i	$-0.0500364\pi$
$984$		0			0
$985$	−3.43861e8			−0.359811
$986$		0			0
$987$	8.62681e8	+	3.95344e8i	0.897219	+	0.411172i
$988$		0			0
$989$		−	9.79607e8i		−	1.01266i
$990$		0			0
$991$	−8.08393e8			−0.830619			−0.415309	−	0.909680i	$-0.636327\pi$
$991$	−8.08393e8			−0.830619			−0.415309	+	0.909680i	$0.636327\pi$
$992$		0			0
$993$	3.93295e7	−	8.58210e7i	0.0401671	−	0.0876488i
$994$		0			0
$995$		−	4.47310e8i		−	0.454087i
$996$		0			0
$997$	1.39077e9			1.40336			0.701680	−	0.712493i	$-0.252434\pi$
$997$	1.39077e9			1.40336			0.701680	+	0.712493i	$0.252434\pi$
$998$		0			0
$999$	−4.29605e7	+	1.24306e7i	−0.0430896	+	0.0124679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.g.a.41.5	✓	8
3.2	odd	2	inner	60.7.g.a.41.6	yes	8
4.3	odd	2		240.7.l.c.161.4		8
5.2	odd	4		300.7.b.e.149.1		16
5.3	odd	4		300.7.b.e.149.16		16
5.4	even	2		300.7.g.h.101.4		8
12.11	even	2		240.7.l.c.161.3		8
15.2	even	4		300.7.b.e.149.15		16
15.8	even	4		300.7.b.e.149.2		16
15.14	odd	2		300.7.g.h.101.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.g.a.41.5	✓	8	1.1	even	1	trivial
60.7.g.a.41.6	yes	8	3.2	odd	2	inner
240.7.l.c.161.3		8	12.11	even	2
240.7.l.c.161.4		8	4.3	odd	2
300.7.b.e.149.1		16	5.2	odd	4
300.7.b.e.149.2		16	15.8	even	4
300.7.b.e.149.15		16	15.2	even	4
300.7.b.e.149.16		16	5.3	odd	4
300.7.g.h.101.3		8	15.14	odd	2
300.7.g.h.101.4		8	5.4	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(11.2485 - 24.5453i) q^{3} +55.9017i q^{5} -414.697 q^{7} +(-475.944 - 552.194i) q^{9} +O(q^{10})\)	\(q+(11.2485 - 24.5453i) q^{3} +55.9017i q^{5} -414.697 q^{7} +(-475.944 - 552.194i) q^{9} -61.5283i q^{11} -1379.66 q^{13} +(1372.12 + 628.809i) q^{15} +6808.58i q^{17} -7822.89 q^{19} +(-4664.71 + 10178.9i) q^{21} -7459.40i q^{23} -3125.00 q^{25} +(-18907.4 + 5470.84i) q^{27} -424.303i q^{29} -49671.1 q^{31} +(-1510.23 - 692.099i) q^{33} -23182.3i q^{35} +2272.15 q^{37} +(-15519.1 + 33864.3i) q^{39} +56271.8i q^{41} +131325. q^{43} +(30868.6 - 26606.1i) q^{45} -84752.1i q^{47} +54324.8 q^{49} +(167119. + 76586.2i) q^{51} -166720. i q^{53} +3439.53 q^{55} +(-87995.5 + 192015. i) q^{57} -400288. i q^{59} -83666.7 q^{61} +(197373. + 228993. i) q^{63} -77125.5i q^{65} +425271. q^{67} +(-183093. - 83906.8i) q^{69} -346163. i q^{71} -171712. q^{73} +(-35151.5 + 76704.1i) q^{75} +25515.6i q^{77} -266214. q^{79} +(-78396.2 + 525627. i) q^{81} +1.01555e6i q^{83} -380611. q^{85} +(-10414.6 - 4772.76i) q^{87} -955706. i q^{89} +572143. q^{91} +(-558724. + 1.21919e6i) q^{93} -437313. i q^{95} -1.19431e6 q^{97} +(-33975.6 + 29284.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9}+O(q^{10}) \) 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9	\( 8 q - 20 q^{3} - 560 q^{7} + 1492 q^{9} - 6440 q^{13} + 2000 q^{15} - 15272 q^{19} - 868 q^{21} - 25000 q^{25} - 18620 q^{27} + 35032 q^{31} - 111120 q^{33} + 99880 q^{37} + 39608 q^{39} - 161000 q^{43} - 5500 q^{45} + 202560 q^{49} + 429120 q^{51} - 33000 q^{55} - 27160 q^{57} - 135608 q^{61} + 377240 q^{63} + 404920 q^{67} - 254940 q^{69} - 356960 q^{73} + 62500 q^{75} + 707704 q^{79} - 1198112 q^{81} + 828000 q^{85} - 1528440 q^{87} - 2004112 q^{91} - 467920 q^{93} - 1326320 q^{97} + 2650080 q^{99}+O(q^{100}) \) 8 * q - 20 * q^3 - 560 * q^7 + 1492 * q^9 - 6440 * q^13 + 2000 * q^15 - 15272 * q^19 - 868 * q^21 - 25000 * q^25 - 18620 * q^27 + 35032 * q^31 - 111120 * q^33 + 99880 * q^37 + 39608 * q^39 - 161000 * q^43 - 5500 * q^45 + 202560 * q^49 + 429120 * q^51 - 33000 * q^55 - 27160 * q^57 - 135608 * q^61 + 377240 * q^63 + 404920 * q^67 - 254940 * q^69 - 356960 * q^73 + 62500 * q^75 + 707704 * q^79 - 1198112 * q^81 + 828000 * q^85 - 1528440 * q^87 - 2004112 * q^91 - 467920 * q^93 - 1326320 * q^97 + 2650080 * q^99

Introduction

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