LMFDB - Embedded newform 72.2.l.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(11,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, 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:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			59.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	72.59
Dual form			72.2.l.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.224745 + 2.43916i) q^{6} -2.82843i q^{8} +(-1.94949 - 2.28024i) q^{9} +(-5.72474 + 3.30518i) q^{11} +(2.00000 + 2.82843i) q^{12} +(-2.00000 - 3.46410i) q^{16} -2.36773i q^{17} +(-4.00000 - 1.41421i) q^{18} +6.34847 q^{19} +(-4.67423 + 8.09601i) q^{22} +(4.44949 + 2.04989i) q^{24} +(2.50000 + 4.33013i) q^{25} +(5.00000 - 1.41421i) q^{27} +(-4.89898 - 2.82843i) q^{32} +(-1.05051 - 11.4012i) q^{33} +(-1.67423 - 2.89986i) q^{34} +(-5.89898 + 1.09638i) q^{36} +(7.77526 - 4.48905i) q^{38} +(9.39898 + 5.42650i) q^{41} +(-6.17423 - 10.6941i) q^{43} +13.2207i q^{44} +(6.89898 - 0.635674i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(6.12372 + 3.53553i) q^{50} +(3.72474 + 1.71600i) q^{51} +(5.12372 - 5.26758i) q^{54} +(-4.60102 + 9.98698i) q^{57} +(-1.62372 - 0.937458i) q^{59} -8.00000 q^{64} +(-9.34847 - 13.2207i) q^{66} +(-0.174235 + 0.301783i) q^{67} +(-4.10102 - 2.36773i) q^{68} +(-6.44949 + 5.51399i) q^{72} -15.6969 q^{73} +(-8.62372 + 0.794593i) q^{75} +(6.34847 - 10.9959i) q^{76} +(-1.39898 + 8.89060i) q^{81} +15.3485 q^{82} +(2.44949 - 1.41421i) q^{83} +(-15.1237 - 8.73169i) q^{86} +(9.34847 + 16.1920i) q^{88} -5.65685i q^{89} +(8.00000 - 5.65685i) q^{96} +(4.84847 + 8.39780i) q^{97} +9.89949i q^{98} +(18.6969 + 6.61037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 2 q^{9} - 18 q^{11} + 8 q^{12} - 8 q^{16} - 16 q^{18} - 4 q^{19} - 4 q^{22} + 8 q^{24} + 10 q^{25} + 20 q^{27} - 14 q^{33} + 8 q^{34} - 4 q^{36} + 36 q^{38} + 18 q^{41}+ \cdots + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^4 - 4 * q^6 + 2 * q^9 - 18 * q^11 + 8 * q^12 - 8 * q^16 - 16 * q^18 - 4 * q^19 - 4 * q^22 + 8 * q^24 + 10 * q^25 + 20 * q^27 - 14 * q^33 + 8 * q^34 - 4 * q^36 + 36 * q^38 + 18 * q^41 - 10 * q^43 + 8 * q^48 - 14 * q^49 + 10 * q^51 - 4 * q^54 - 38 * q^57 + 18 * q^59 - 32 * q^64 - 8 * q^66 + 14 * q^67 - 36 * q^68 - 16 * q^72 - 4 * q^73 - 10 * q^75 - 4 * q^76 + 14 * q^81 + 32 * q^82 - 36 * q^86 + 8 * q^88 + 32 * q^96 - 10 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	0.224745	+	2.43916i	0.0917517	+	0.995782i
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$		−	2.82843i		−	1.00000i
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$		0			0
$11$	−5.72474	+	3.30518i	−1.72608	+	0.996550i	−0.821541	+	0.570149i	$0.806886\pi$
$11$	−5.72474	+	3.30518i	−1.72608	+	0.996550i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	2.00000	+	2.82843i	0.577350	+	0.816497i
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		−	2.36773i		−	0.574258i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$		−	2.36773i		−	0.574258i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	−4.00000	−	1.41421i	−0.942809	−	0.333333i
$19$	6.34847			1.45644			0.728219	−	0.685344i	$-0.240348\pi$
$19$	6.34847			1.45644			0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$		0			0
$22$	−4.67423	+	8.09601i	−0.996550	+	1.72608i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	4.44949	+	2.04989i	0.908248	+	0.418432i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$		0			0
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$	−1.05051	−	11.4012i	−0.182870	−	1.98469i
$34$	−1.67423	−	2.89986i	−0.287129	−	0.497322i
$35$		0			0
$36$	−5.89898	+	1.09638i	−0.983163	+	0.182729i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	7.77526	−	4.48905i	1.26131	−	0.728219i
$39$		0			0
$40$		0			0
$41$	9.39898	+	5.42650i	1.46787	+	0.847477i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	9.39898	+	5.42650i	1.46787	+	0.847477i	0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−6.17423	−	10.6941i	−0.941562	−	1.63083i	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−6.17423	−	10.6941i	−0.941562	−	1.63083i	−0.179069	−	0.983836i	$-0.557309\pi$
$44$			13.2207i			1.99310i
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	6.89898	−	0.635674i	0.995782	−	0.0917517i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	6.12372	+	3.53553i	0.866025	+	0.500000i
$51$	3.72474	+	1.71600i	0.521569	+	0.240288i
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	5.12372	−	5.26758i	0.697251	−	0.716827i
$55$		0			0
$56$		0			0
$57$	−4.60102	+	9.98698i	−0.609420	+	1.32281i
$58$		0			0
$59$	−1.62372	−	0.937458i	−0.211391	−	0.122047i	0.390567	−	0.920575i	$-0.372279\pi$
$59$	−1.62372	−	0.937458i	−0.211391	−	0.122047i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$		0			0
$66$	−9.34847	−	13.2207i	−1.15072	−	1.62736i
$67$	−0.174235	+	0.301783i	−0.0212861	+	0.0368687i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−0.174235	+	0.301783i	−0.0212861	+	0.0368687i	0.855186	+	0.518321i	$0.173443\pi$
$68$	−4.10102	−	2.36773i	−0.497322	−	0.287129i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−6.44949	+	5.51399i	−0.760080	+	0.649830i
$73$	−15.6969			−1.83719			−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−15.6969			−1.83719			−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	−8.62372	+	0.794593i	−0.995782	+	0.0917517i
$76$	6.34847	−	10.9959i	0.728219	−	1.26131i
$77$		0			0
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$		0			0
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	15.3485			1.69495
$83$	2.44949	−	1.41421i	0.268866	−	0.155230i	−0.359506	−	0.933143i	$-0.617055\pi$
$83$	2.44949	−	1.41421i	0.268866	−	0.155230i	0.628372	+	0.777913i	$0.283721\pi$
$84$		0			0
$85$		0			0
$86$	−15.1237	−	8.73169i	−1.63083	−	0.941562i
$87$		0			0
$88$	9.34847	+	16.1920i	0.996550	+	1.72608i
$89$		−	5.65685i		−	0.599625i	−0.953998	−	0.299813i	$-0.903076\pi$
$89$		−	5.65685i		−	0.599625i	0.953998	−	0.299813i	$-0.0969242\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	8.00000	−	5.65685i	0.816497	−	0.577350i
$97$	4.84847	+	8.39780i	0.492287	+	0.852667i	0.999961	−	0.00888289i	$-0.00282755\pi$
$97$	4.84847	+	8.39780i	0.492287	+	0.852667i	−0.507673	+	0.861550i	$0.669494\pi$
$98$			9.89949i			1.00000i
$99$	18.6969	+	6.61037i	1.87911	+	0.664367i
$100$	10.0000			1.00000
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	5.77526	−	0.532134i	0.571835	−	0.0526891i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	15.0956i		−	1.45935i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$		−	15.0956i		−	1.45935i	0.683793	−	0.729676i	$-0.260329\pi$
$108$	2.55051	−	10.0745i	0.245423	−	0.969416i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.79796	−	5.65685i	−0.921714	−	0.532152i	−0.0375328	−	0.999295i	$-0.511950\pi$
$113$	−9.79796	−	5.65685i	−0.921714	−	0.532152i	−0.884182	+	0.467143i	$0.845283\pi$
$114$	1.42679	+	15.4849i	0.133631	+	1.45030i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−2.65153			−0.244093
$119$		0			0
$120$		0			0
$121$	16.3485	−	28.3164i	1.48622	−	2.57422i
$122$		0			0
$123$	−15.3485	+	10.8530i	−1.38392	+	0.978583i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$	21.2980	−	1.96240i	1.87518	−	0.172780i
$130$		0			0
$131$	12.2474	+	7.07107i	1.07006	+	0.617802i	0.928199	−	0.372084i	$-0.121357\pi$
$131$	12.2474	+	7.07107i	1.07006	+	0.617802i	0.141865	+	0.989886i	$0.454690\pi$
$132$	−20.7980	−	9.58166i	−1.81023	−	0.833976i
$133$		0			0
$134$			0.492810i			0.0425723i
$135$		0			0
$136$	−6.69694			−0.574258
$137$	5.29796	−	3.05878i	0.452635	−	0.261329i	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	5.29796	−	3.05878i	0.452635	−	0.261329i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−9.17423	+	15.8902i	−0.778148	+	1.34779i	0.154859	+	0.987937i	$0.450508\pi$
$139$	−9.17423	+	15.8902i	−0.778148	+	1.34779i	−0.933008	+	0.359856i	$0.882826\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−4.00000	+	11.3137i	−0.333333	+	0.942809i
$145$		0			0
$146$	−19.2247	+	11.0994i	−1.59105	+	0.918594i
$147$	−7.00000	−	9.89949i	−0.577350	−	0.816497i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	−10.0000	+	7.07107i	−0.816497	+	0.577350i
$151$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$151$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$152$		−	17.9562i		−	1.45644i
$153$	−5.39898	+	4.61586i	−0.436482	+	0.373170i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	4.57321	+	11.8780i	0.359306	+	0.933220i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	18.7980	−	10.8530i	1.46787	−	0.847477i
$165$		0			0
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$170$		0			0
$171$	−12.3763	−	14.4760i	−0.946437	−	1.10701i
$172$	−24.6969			−1.88312
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$		0			0
$176$	22.8990	+	13.2207i	1.72608	+	0.996550i
$177$	2.65153	−	1.87492i	0.199301	−	0.140927i
$178$	−4.00000	−	6.92820i	−0.299813	−	0.519291i
$179$			19.7990i			1.47985i	0.672692	+	0.739923i	$0.265138\pi$
$179$			19.7990i			1.47985i	−0.672692	+	0.739923i	$0.734862\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	7.82577	+	13.5546i	0.572277	+	0.991212i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	5.79796	−	12.5851i	0.418432	−	0.908248i
$193$	1.84847	−	3.20164i	0.133056	−	0.230459i	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	1.84847	−	3.20164i	0.133056	−	0.230459i	0.924853	+	0.380325i	$0.124188\pi$
$194$	11.8763	+	6.85677i	0.852667	+	0.492287i
$195$		0			0
$196$	7.00000	+	12.1244i	0.500000	+	0.866025i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	27.5732	−	5.12472i	1.95954	−	0.364198i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	12.2474	−	7.07107i	0.866025	−	0.500000i
$201$	−0.348469	−	0.492810i	−0.0245791	−	0.0347601i
$202$		0			0
$203$		0			0
$204$	6.69694	−	4.73545i	0.468879	−	0.331548i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−36.3434	+	20.9829i	−2.51392	+	1.45141i
$210$		0			0
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$		0			0
$213$		0			0
$214$	−10.6742	−	18.4883i	−0.729676	−	1.26384i
$215$		0			0
$216$	−4.00000	−	14.1421i	−0.272166	−	0.962250i
$217$		0			0
$218$		0			0
$219$	11.3763	−	24.6934i	0.768737	−	1.66862i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$		0			0
$225$	5.00000	−	14.1421i	0.333333	−	0.942809i
$226$	−16.0000			−1.06430
$227$	21.2753	−	12.2833i	1.41209	−	0.815270i	0.416503	−	0.909134i	$-0.363255\pi$
$227$	21.2753	−	12.2833i	1.41209	−	0.815270i	0.995585	+	0.0938647i	$0.0299221\pi$
$228$	12.6969	+	17.9562i	0.840875	+	1.18918i
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			28.8092i			1.88735i	0.330870	+	0.943676i	$0.392658\pi$
$233$			28.8092i			1.88735i	−0.330870	+	0.943676i	$0.607342\pi$
$234$		0			0
$235$		0			0
$236$	−3.24745	+	1.87492i	−0.211391	+	0.122047i
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	13.8485	+	23.9863i	0.892058	+	1.54509i	0.837404	+	0.546585i	$0.184072\pi$
$241$	13.8485	+	23.9863i	0.892058	+	1.54509i	0.0546547	+	0.998505i	$0.482594\pi$
$242$		−	46.2405i		−	2.97245i
$243$	−12.9722	−	8.64420i	−0.832167	−	0.554526i
$244$		0			0
$245$		0			0
$246$	−11.1237	+	24.1452i	−0.709223	+	1.53944i
$247$		0			0
$248$		0			0
$249$	0.449490	+	4.87832i	0.0284853	+	0.309151i
$250$		0			0
$251$			10.3602i			0.653930i	0.945036	+	0.326965i	$0.106026\pi$
$251$			10.3602i			0.653930i	−0.945036	+	0.326965i	$0.893974\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−17.6010	−	10.1620i	−1.09792	−	0.633885i	−0.162247	−	0.986750i	$-0.551874\pi$
$257$	−17.6010	−	10.1620i	−1.09792	−	0.633885i	−0.935674	+	0.352865i	$0.885208\pi$
$258$	24.6969	−	17.4634i	1.53756	−	1.08722i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	20.0000			1.23560
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	−32.2474	+	2.97129i	−1.98469	+	0.182870i
$265$		0			0
$266$		0			0
$267$	8.89898	+	4.09978i	0.544609	+	0.250902i
$268$	0.348469	+	0.603566i	0.0212861	+	0.0368687i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−8.20204	+	4.73545i	−0.497322	+	0.287129i
$273$		0			0
$274$	4.32577	−	7.49245i	0.261329	−	0.452635i
$275$	−28.6237	−	16.5259i	−1.72608	−	0.996550i
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$			25.9487i			1.55630i
$279$		0			0
$280$		0			0
$281$	24.4949	−	14.1421i	1.46124	−	0.843649i	0.462174	−	0.886789i	$-0.347070\pi$
$281$	24.4949	−	14.1421i	1.46124	−	0.843649i	0.999069	+	0.0431402i	$0.0137362\pi$
$282$		0			0
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	−0.328291	−	0.944577i	$-0.606473\pi$
$283$	11.0000	−	19.0526i	0.653882	−	1.13256i	0.982173	−	0.187980i	$-0.0601941\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	3.10102	+	16.6848i	0.182729	+	0.983163i
$289$	11.3939			0.670228
$290$		0			0
$291$	−16.7247	+	1.54102i	−0.980422	+	0.0903364i
$292$	−15.6969	+	27.1879i	−0.918594	+	1.59105i
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$	−15.5732	−	7.17461i	−0.908248	−	0.418432i
$295$		0			0
$296$		0			0
$297$	−23.9495	+	24.6219i	−1.38969	+	1.42871i
$298$		0			0
$299$		0			0
$300$	−7.24745	+	15.7313i	−0.418432	+	0.908248i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−12.6969	−	21.9917i	−0.728219	−	1.26131i
$305$		0			0
$306$	−3.34847	+	9.47090i	−0.191419	+	0.541415i
$307$	24.3485			1.38964			0.694820	−	0.719183i	$-0.255484\pi$
$307$	24.3485			1.38964			0.694820	+	0.719183i	$0.255484\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	−17.1969	−	29.7860i	−0.972028	−	1.68360i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	−17.1969	−	29.7860i	−0.972028	−	1.68360i	−0.282617	−	0.959233i	$-0.591202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	23.7474	+	10.9405i	1.32545	+	0.610639i
$322$		0			0
$323$		−	15.0314i		−	0.836371i
$324$	14.0000	+	11.3137i	0.777778	+	0.628539i
$325$		0			0
$326$	2.44949	−	1.41421i	0.135665	−	0.0783260i
$327$		0			0
$328$	15.3485	−	26.5843i	0.847477	−	1.46787i
$329$		0			0
$330$		0			0
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	−0.963135	−	0.269019i	$-0.913301\pi$
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	0.248590	−	0.968609i	$-0.420033\pi$
$332$		−	5.65685i		−	0.310460i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.1969	+	19.3937i	−0.609936	+	1.05644i	0.381314	+	0.924445i	$0.375472\pi$
$337$	−11.1969	+	19.3937i	−0.609936	+	1.05644i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	−15.9217	−	9.19239i	−0.866025	−	0.500000i
$339$	16.0000	−	11.3137i	0.869001	−	0.614476i
$340$		0			0
$341$		0			0
$342$	−25.3939	−	8.97809i	−1.37314	−	0.485480i
$343$		0			0
$344$	−30.2474	+	17.4634i	−1.63083	+	0.941562i
$345$		0			0
$346$		0			0
$347$	20.4217	+	11.7905i	1.09629	+	0.632945i	0.935245	−	0.354001i	$-0.115179\pi$
$347$	20.4217	+	11.7905i	1.09629	+	0.632945i	0.161048	+	0.986947i	$0.448512\pi$
$348$		0			0
$349$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$349$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$350$		0			0
$351$		0			0
$352$	37.3939			1.99310
$353$	32.2980	−	18.6472i	1.71905	−	0.992492i	0.798369	−	0.602168i	$-0.205696\pi$
$353$	32.2980	−	18.6472i	1.71905	−	0.992492i	0.920677	−	0.390324i	$-0.127637\pi$
$354$	1.92168	−	4.17121i	0.102136	−	0.221697i
$355$		0			0
$356$	−9.79796	−	5.65685i	−0.519291	−	0.299813i
$357$		0			0
$358$	14.0000	+	24.2487i	0.739923	+	1.28158i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	21.3031			1.12121
$362$		0			0
$363$	32.6969	+	46.2405i	1.71614	+	2.42699i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		0			0
$369$	−5.94949	−	32.0108i	−0.309718	−	1.66642i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$	19.1691	+	11.0673i	0.991212	+	0.572277i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−11.6515			−0.598499			−0.299249	−	0.954175i	$-0.596736\pi$
$379$	−11.6515			−0.598499			−0.299249	+	0.954175i	$0.596736\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	−1.79796	−	19.5133i	−0.0917517	−	0.995782i
$385$		0			0
$386$		−	5.22826i		−	0.266111i
$387$	−12.3485	+	34.9267i	−0.627708	+	1.77543i
$388$	19.3939			0.984575
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$		0			0
$392$	17.1464	+	9.89949i	0.866025	+	0.500000i
$393$	−20.0000	+	14.1421i	−1.00887	+	0.713376i
$394$		0			0
$395$		0			0
$396$	30.1464	−	25.7737i	1.51492	−	1.29518i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	10.0000	−	17.3205i	0.500000	−	0.866025i
$401$	−12.6464	−	7.30142i	−0.631532	−	0.364615i	0.149813	−	0.988714i	$-0.452133\pi$
$401$	−12.6464	−	7.30142i	−0.631532	−	0.364615i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	−0.775255	−	0.357161i	−0.0386662	−	0.0178136i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	4.85357	−	10.5352i	0.240288	−	0.521569i
$409$	−20.1969	+	34.9821i	−0.998674	+	1.72975i	−0.454759	+	0.890614i	$0.650275\pi$
$409$	−20.1969	+	34.9821i	−0.998674	+	1.72975i	−0.543915	+	0.839140i	$0.683059\pi$
$410$		0			0
$411$	0.972194	+	10.5512i	0.0479548	+	0.520453i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−18.3485	−	25.9487i	−0.898528	−	1.27071i
$418$	−29.6742	+	51.3973i	−1.45141	+	2.51392i
$419$	−31.8434	−	18.3848i	−1.55565	−	0.898155i	−0.997665	−	0.0683046i	$-0.978241\pi$
$419$	−31.8434	−	18.3848i	−1.55565	−	0.898155i	−0.557986	−	0.829851i	$-0.688426\pi$
$420$		0			0
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$			19.7990i			0.963800i
$423$		0			0
$424$		0			0
$425$	10.2526	−	5.91931i	0.497322	−	0.287129i
$426$		0			0
$427$		0			0
$428$	−26.1464	−	15.0956i	−1.26384	−	0.729676i
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−14.8990	−	14.4921i	−0.716827	−	0.697251i
$433$	−33.6969			−1.61937			−0.809686	−	0.586864i	$-0.800362\pi$
$433$	−33.6969			−1.61937			−0.809686	+	0.586864i	$0.800362\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−3.52781	−	38.2873i	−0.168565	−	1.82944i
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	20.6464	−	3.83732i	0.983163	−	0.182729i
$442$		0			0
$443$	−32.7247	+	18.8936i	−1.55480	+	0.897664i	−0.557059	+	0.830473i	$0.688070\pi$
$443$	−32.7247	+	18.8936i	−1.55480	+	0.897664i	−0.997740	+	0.0671913i	$0.978596\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	33.5446i		−	1.58307i	−0.611124	−	0.791535i	$-0.709282\pi$
$449$		−	33.5446i		−	1.58307i	0.611124	−	0.791535i	$-0.290718\pi$
$450$	−3.87628	−	20.8560i	−0.182729	−	0.983163i
$451$	−71.7423			−3.37822
$452$	−19.5959	+	11.3137i	−0.921714	+	0.532152i
$453$		0			0
$454$	17.3712	−	30.0878i	0.815270	−	1.41209i
$455$		0			0
$456$	28.2474	+	13.0137i	1.32281	+	0.609420i
$457$	−8.19694	−	14.1975i	−0.383437	−	0.664132i	0.608114	−	0.793849i	$-0.291926\pi$
$457$	−8.19694	−	14.1975i	−0.383437	−	0.664132i	−0.991551	+	0.129718i	$0.958593\pi$
$458$		0			0
$459$	−3.34847	−	11.8386i	−0.156293	−	0.552580i
$460$		0			0
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$	20.3712	+	35.2839i	0.943676	+	1.63450i
$467$			41.5371i			1.92211i	0.276360	+	0.961054i	$0.410872\pi$
$467$			41.5371i			1.92211i	−0.276360	+	0.961054i	$0.589128\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−2.65153	+	4.59259i	−0.122047	+	0.211391i
$473$	70.6918	+	40.8140i	3.25041	+	1.87663i
$474$		0			0
$475$	15.8712	+	27.4897i	0.728219	+	1.26131i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$		0			0
$482$	33.9217	+	19.5847i	1.54509	+	0.892058i
$483$		0			0
$484$	−32.6969	−	56.6328i	−1.48622	−	2.57422i
$485$		0			0
$486$	−22.0000	−	1.41421i	−0.997940	−	0.0641500i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	−1.44949	+	3.14626i	−0.0655482	+	0.142279i
$490$		0			0
$491$	25.3763	+	14.6510i	1.14522	+	0.661190i	0.947717	−	0.319113i	$-0.103385\pi$
$491$	25.3763	+	14.6510i	1.14522	+	0.661190i	0.197499	+	0.980303i	$0.436718\pi$
$492$	3.44949	+	37.4373i	0.155515	+	1.68781i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	4.00000	+	5.65685i	0.179244	+	0.253490i
$499$	21.8712	−	37.8820i	0.979088	−	1.69583i	0.313363	−	0.949633i	$-0.398544\pi$
$499$	21.8712	−	37.8820i	0.979088	−	1.69583i	0.665725	−	0.746197i	$-0.268122\pi$
$500$		0			0
$501$		0			0
$502$	7.32577	+	12.6886i	0.326965	+	0.566320i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.4217	−	2.06594i	0.995782	−	0.0917517i
$508$		0			0
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			1.00000i
$513$	31.7423	−	8.97809i	1.40146	−	0.396392i
$514$	−28.7423			−1.26777
$515$		0			0
$516$	17.8990	−	38.8515i	0.787959	−	1.71034i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	27.8236i		−	1.21897i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$		−	27.8236i		−	1.21897i	0.792797	−	0.609486i	$-0.208624\pi$
$522$		0			0
$523$	38.0000			1.66162			0.830812	−	0.556553i	$-0.187876\pi$
$523$	38.0000			1.66162			0.830812	+	0.556553i	$0.187876\pi$
$524$	24.4949	−	14.1421i	1.07006	−	0.617802i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−37.3939	+	26.4415i	−1.62736	+	1.15072i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	1.02781	+	5.53004i	0.0446030	+	0.239983i
$532$		0			0
$533$		0			0
$534$	13.7980	−	1.27135i	0.597096	−	0.0550167i
$535$		0			0
$536$	0.853572	+	0.492810i	0.0368687	+	0.0212861i
$537$	−31.1464	−	14.3492i	−1.34407	−	0.619214i
$538$		0			0
$539$		−	46.2726i		−	1.99310i
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$		0			0
$544$	−6.69694	+	11.5994i	−0.287129	+	0.497322i
$545$		0			0
$546$		0			0
$547$	−15.1742	−	26.2825i	−0.648803	−	1.12376i	−0.983409	−	0.181402i	$-0.941936\pi$
$547$	−15.1742	−	26.2825i	−0.648803	−	1.12376i	0.334606	−	0.942358i	$-0.391397\pi$
$548$		−	12.2351i		−	0.522658i
$549$		0			0
$550$	−46.7423			−1.99310
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	18.3485	+	31.7805i	0.778148	+	1.34779i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−26.9949	+	2.48732i	−1.13973	+	0.105015i
$562$	20.0000	−	34.6410i	0.843649	−	1.46124i
$563$	−6.57832	−	3.79799i	−0.277243	−	0.160066i	0.354932	−	0.934892i	$-0.384504\pi$
$563$	−6.57832	−	3.79799i	−0.277243	−	0.160066i	−0.632175	+	0.774826i	$0.717837\pi$
$564$		0			0
$565$		0			0
$566$		−	31.1127i		−	1.30776i
$567$		0			0
$568$		0			0
$569$	−21.7020	+	12.5297i	−0.909797	+	0.525271i	−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−21.7020	+	12.5297i	−0.909797	+	0.525271i	−0.0294311	+	0.999567i	$0.509370\pi$
$570$		0			0
$571$	12.8712	−	22.2935i	0.538642	−	0.932955i	−0.460336	−	0.887745i	$-0.652271\pi$
$571$	12.8712	−	22.2935i	0.538642	−	0.932955i	0.998978	−	0.0452101i	$-0.0143957\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	15.5959	+	18.2419i	0.649830	+	0.760080i
$577$	46.3939			1.93140			0.965701	−	0.259656i	$-0.0836092\pi$
$577$	46.3939			1.93140			0.965701	+	0.259656i	$0.0836092\pi$
$578$	13.9546	−	8.05669i	0.580435	−	0.335114i
$579$	3.69694	+	5.22826i	0.153640	+	0.217279i
$580$		0			0
$581$		0			0
$582$	−19.3939	+	13.7135i	−0.803902	+	0.568445i
$583$		0			0
$584$			44.3976i			1.83719i
$585$		0			0
$586$		0			0
$587$	16.3207	−	9.42274i	0.673626	−	0.388918i	−0.123823	−	0.992304i	$-0.539516\pi$
$587$	16.3207	−	9.42274i	0.673626	−	0.388918i	0.797449	+	0.603386i	$0.206182\pi$
$588$	−24.1464	+	2.22486i	−0.995782	+	0.0917517i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			45.2548i			1.85839i	0.369586	+	0.929197i	$0.379500\pi$
$593$			45.2548i			1.85839i	−0.369586	+	0.929197i	$0.620500\pi$
$594$	−11.9217	+	47.0904i	−0.489153	+	1.93214i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	2.24745	+	24.3916i	0.0917517	+	0.995782i
$601$	−4.15153	−	7.19066i	−0.169344	−	0.293313i	0.768845	−	0.639435i	$-0.220832\pi$
$601$	−4.15153	−	7.19066i	−0.169344	−	0.293313i	−0.938190	+	0.346122i	$0.887498\pi$
$602$		0			0
$603$	1.02781	−	0.191027i	0.0418555	−	0.00777921i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−31.1010	−	17.9562i	−1.26131	−	0.728219i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	2.59592	+	13.9672i	0.104934	+	0.564589i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	29.8207	−	17.2170i	1.20346	−	0.694820i
$615$		0			0
$616$		0			0
$617$	−39.6464	−	22.8899i	−1.59611	−	0.921512i	−0.992228	−	0.124434i	$-0.960288\pi$
$617$	−39.6464	−	22.8899i	−1.59611	−	0.921512i	−0.603877	−	0.797077i	$-0.706378\pi$
$618$		0			0
$619$	24.8712	+	43.0781i	0.999657	+	1.73146i	0.522514	+	0.852631i	$0.324994\pi$
$619$	24.8712	+	43.0781i	0.999657	+	1.73146i	0.477143	+	0.878826i	$0.341672\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−42.1237	−	24.3201i	−1.68360	−	0.972028i
$627$	−6.66913	−	72.3801i	−0.266339	−	2.89058i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	−14.0000	−	19.7990i	−0.556450	−	0.786939i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−43.7474	+	25.2576i	−1.72792	+	0.997615i	−0.829450	+	0.558581i	$0.811346\pi$
$641$	−43.7474	+	25.2576i	−1.72792	+	0.997615i	−0.898470	+	0.439034i	$0.855321\pi$
$642$	36.8207	−	3.39267i	1.45320	−	0.133898i
$643$	8.82577	−	15.2867i	0.348054	−	0.602848i	−0.637850	−	0.770161i	$-0.720176\pi$
$643$	8.82577	−	15.2867i	0.348054	−	0.602848i	0.985904	+	0.167313i	$0.0535092\pi$
$644$		0			0
$645$		0			0
$646$	−10.6288	−	18.4097i	−0.418186	−	0.724319i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	25.1464	+	3.95691i	0.987845	+	0.155442i
$649$	12.3939			0.486502
$650$		0			0
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$		0			0
$656$		−	43.4120i		−	1.69495i
$657$	30.6010	+	35.7928i	1.19386	+	1.39641i
$658$		0			0
$659$	−41.6413	+	24.0416i	−1.62212	+	0.936529i	−0.635763	+	0.771885i	$0.719314\pi$
$659$	−41.6413	+	24.0416i	−1.62212	+	0.936529i	−0.986353	+	0.164644i	$0.947352\pi$
$660$		0			0
$661$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$661$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$662$	−31.8434	−	18.3848i	−1.23763	−	0.714545i
$663$		0			0
$664$	−4.00000	−	6.92820i	−0.155230	−	0.268866i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$			31.6697i			1.21987i
$675$	18.6237	+	18.1151i	0.716827	+	0.697251i
$676$	−26.0000			−1.00000
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$	11.5959	−	25.1701i	0.445339	−	0.966652i
$679$		0			0
$680$		0			0
$681$	3.90408	+	42.3710i	0.149605	+	1.62366i
$682$		0			0
$683$		−	20.8167i		−	0.796530i	−0.917270	−	0.398265i	$-0.869613\pi$
$683$		−	20.8167i		−	0.796530i	0.917270	−	0.398265i	$-0.130387\pi$
$684$	−37.4495	+	6.96031i	−1.43192	+	0.266134i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−24.6969	+	42.7764i	−0.941562	+	1.63083i
$689$		0			0
$690$		0			0
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.856804	+	0.515642i	$0.172447\pi$
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.0181572	+	0.999835i	$0.494220\pi$
$692$		0			0
$693$		0			0
$694$	33.3485			1.26589
$695$		0			0
$696$		0			0
$697$	12.8485	−	22.2542i	0.486670	−	0.842938i
$698$		0			0
$699$	−45.3207	−	20.8793i	−1.71418	−	0.789728i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$	45.7980	−	26.4415i	1.72608	−	0.996550i
$705$		0			0
$706$	26.3712	−	45.6762i	0.992492	−	1.71905i
$707$		0			0
$708$	−0.595918	−	6.46750i	−0.0223960	−	0.243064i
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$		0			0
$711$		0			0
$712$	−16.0000			−0.599625
$713$		0			0
$714$		0			0
$715$		0			0
$716$	34.2929	+	19.7990i	1.28158	+	0.739923i
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$	26.0908	−	15.0635i	0.971000	−	0.560607i
$723$	−47.7702	+	4.40156i	−1.77659	+	0.163696i
$724$		0			0
$725$		0			0
$726$	72.7423	+	33.5125i	2.69972	+	1.24377i
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$		0			0
$731$	−25.3207	+	14.6189i	−0.936519	+	0.540699i
$732$		0			0
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2.30351i		−	0.0848508i
$738$	−29.9217	−	34.9982i	−1.10143	−	1.28830i
$739$	−19.7423			−0.726234			−0.363117	−	0.931744i	$-0.618287\pi$
$739$	−19.7423			−0.726234			−0.363117	+	0.931744i	$0.618287\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$743$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−8.00000	−	2.82843i	−0.292705	−	0.103487i
$748$	31.3031			1.14455
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	−16.2980	−	7.50850i	−0.593931	−	0.273625i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	−14.2702	+	8.23888i	−0.518315	+	0.299249i
$759$		0			0
$760$		0			0
$761$	−9.79796	−	5.65685i	−0.355176	−	0.205061i	0.311787	−	0.950152i	$-0.399073\pi$
$761$	−9.79796	−	5.65685i	−0.355176	−	0.205061i	−0.666962	+	0.745091i	$0.732406\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−16.0000	−	22.6274i	−0.577350	−	0.816497i
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$		0			0
$771$	28.7423	−	20.3239i	1.03513	−	0.731948i
$772$	−3.69694	−	6.40329i	−0.133056	−	0.230459i
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$	9.57321	+	51.5080i	0.344102	+	1.85142i
$775$		0			0
$776$	23.7526	−	13.7135i	0.852667	−	0.492287i
$777$		0			0
$778$		0			0
$779$	59.6691	+	34.4500i	2.13787	+	1.23430i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	28.0000			1.00000
$785$		0			0
$786$	−14.4949	+	31.4626i	−0.517016	+	1.12224i
$787$	−25.0000	+	43.3013i	−0.891154	+	1.54352i	−0.0526599	+	0.998613i	$0.516770\pi$
$787$	−25.0000	+	43.3013i	−0.891154	+	1.54352i	−0.838494	+	0.544911i	$0.816563\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	18.6969	−	52.8829i	0.664367	−	1.87911i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$		0			0
$800$		−	28.2843i		−	1.00000i
$801$	−12.8990	+	11.0280i	−0.455763	+	0.389654i
$802$	−20.6515			−0.729231
$803$	89.8610	−	51.8813i	3.17112	−	1.83085i
$804$	−1.20204	+	0.110756i	−0.0423927	+	0.00390608i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			23.0881i			0.811735i	0.913932	+	0.405868i	$0.133031\pi$
$809$			23.0881i			0.811735i	−0.913932	+	0.405868i	$0.866969\pi$
$810$		0			0
$811$	−55.7423			−1.95738			−0.978689	−	0.205347i	$-0.934168\pi$
$811$	−55.7423			−1.95738			−0.978689	+	0.205347i	$0.934168\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.50510	−	16.3349i	−0.0526891	−	0.571835i
$817$	−39.1969	−	67.8911i	−1.37133	−	2.37521i
$818$			57.1256i			1.99735i
$819$		0			0
$820$		0			0
$821$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$821$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$822$	8.65153	+	12.2351i	0.301757	+	0.426749i
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$	46.7423	−	33.0518i	1.62736	−	1.15072i
$826$		0			0
$827$			19.7990i			0.688478i	0.938882	+	0.344239i	$0.111863\pi$
$827$			19.7990i			0.688478i	−0.938882	+	0.344239i	$0.888137\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	14.3536	+	8.28704i	0.497322	+	0.287129i
$834$	−40.8207	−	18.8062i	−1.41350	−	0.651204i
$835$		0			0
$836$			83.9314i			2.90283i
$837$		0			0
$838$	−52.0000			−1.79631
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$		0			0
$843$	4.49490	+	48.7832i	0.154812	+	1.68018i
$844$	14.0000	+	24.2487i	0.481900	+	0.834675i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	22.0000	+	31.1127i	0.755038	+	1.06779i
$850$	8.37117	−	14.4993i	0.287129	−	0.497322i
$851$		0			0
$852$		0			0
$853$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$853$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$854$		0			0
$855$		0			0
$856$	−42.6969			−1.45935
$857$	−19.5959	+	11.3137i	−0.669384	+	0.386469i	−0.795843	−	0.605503i	$-0.792972\pi$
$857$	−19.5959	+	11.3137i	−0.669384	+	0.386469i	0.126459	+	0.991972i	$0.459639\pi$
$858$		0			0
$859$	−18.1742	+	31.4787i	−0.620097	+	1.07404i	0.369370	+	0.929282i	$0.379573\pi$
$859$	−18.1742	+	31.4787i	−0.620097	+	1.07404i	−0.989467	+	0.144757i	$0.953760\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	−28.4949	−	7.21393i	−0.969416	−	0.245423i
$865$		0			0
$866$	−41.2702	+	23.8273i	−1.40242	+	0.809686i
$867$	−8.25765	+	17.9241i	−0.280445	+	0.608733i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	9.69694	−	27.4271i	0.328192	−	0.928266i
$874$		0			0
$875$		0			0
$876$	−31.3939	−	44.3976i	−1.06070	−	1.50006i
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	56.5685i		−	1.90584i	−0.303218	−	0.952921i	$-0.598061\pi$
$881$		−	56.5685i		−	1.90584i	0.303218	−	0.952921i	$-0.401939\pi$
$882$	22.5732	−	19.2990i	0.760080	−	0.649830i
$883$	50.4393			1.69742			0.848709	−	0.528861i	$-0.177381\pi$
$883$	50.4393			1.69742			0.848709	+	0.528861i	$0.177381\pi$
$884$		0			0
$885$		0			0
$886$	−26.7196	+	46.2798i	−0.897664	+	1.55480i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−21.3763	−	55.5203i	−0.716132	−	1.86000i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−23.7196	−	41.0836i	−0.791535	−	1.37098i
$899$		0			0
$900$	−19.4949	−	22.8024i	−0.649830	−	0.760080i
$901$		0			0
$902$	−87.8661	+	50.7295i	−2.92562	+	1.68911i
$903$		0			0
$904$	−16.0000	+	27.7128i	−0.532152	+	0.921714i
$905$		0			0
$906$		0			0
$907$	−28.2196	−	48.8779i	−0.937018	−	1.62296i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	−28.2196	−	48.8779i	−0.937018	−	1.62296i	−0.166022	−	0.986122i	$-0.553092\pi$
$908$		−	49.1331i		−	1.63054i
$909$		0			0
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$	43.7980	−	4.03556i	1.45030	−	0.133631i
$913$	−9.34847	+	16.1920i	−0.309389	+	0.535878i
$914$	−20.0783	−	11.5922i	−0.664132	−	0.383437i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−12.4722	−	12.1316i	−0.411644	−	0.400402i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−17.6464	+	38.3034i	−0.581470	+	1.26214i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.4949	−	14.1421i	0.803652	−	0.463988i	−0.0410949	−	0.999155i	$-0.513085\pi$
$929$	24.4949	−	14.1421i	0.803652	−	0.463988i	0.844746	+	0.535167i	$0.179751\pi$
$930$		0			0
$931$	−22.2196	+	38.4855i	−0.728219	+	1.26131i
$932$	49.8990	+	28.8092i	1.63450	+	0.943676i
$933$		0			0
$934$	29.3712	+	50.8724i	0.961054	+	1.66459i
$935$		0			0
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	59.3207	−	5.46583i	1.93586	−	0.178371i
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$		0			0
$944$			7.49966i			0.244093i
$945$		0			0
$946$	115.439			3.75325
$947$	−0.770153	+	0.444648i	−0.0250266	+	0.0144491i	−0.512461	−	0.858710i	$-0.671266\pi$
$947$	−0.770153	+	0.444648i	−0.0250266	+	0.0144491i	0.487435	+	0.873160i	$0.337933\pi$
$948$		0			0
$949$		0			0
$950$	38.8763	+	22.4452i	1.26131	+	0.728219i
$951$		0			0
$952$		0			0
$953$		−	59.0005i		−	1.91121i	−0.294646	−	0.955607i	$-0.595202\pi$
$953$		−	59.0005i		−	1.91121i	0.294646	−	0.955607i	$-0.404798\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$		0			0
$963$	−34.4217	+	29.4288i	−1.10922	+	0.948330i
$964$	55.3939			1.78412
$965$		0			0
$966$		0			0
$967$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$967$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$968$	−80.0908	−	46.2405i	−2.57422	−	1.48622i
$969$	23.6464	+	10.8940i	0.759633	+	0.349964i
$970$		0			0
$971$		−	31.1127i		−	0.998454i	−0.866471	−	0.499227i	$-0.833617\pi$
$971$		−	31.1127i		−	0.998454i	0.866471	−	0.499227i	$-0.166383\pi$
$972$	−27.9444	+	13.8243i	−0.896317	+	0.443415i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	31.4444	+	18.1544i	1.00600	+	0.580812i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	31.4444	+	18.1544i	1.00600	+	0.580812i	0.0959785	+	0.995383i	$0.469402\pi$
$978$	0.449490	+	4.87832i	0.0143731	+	0.155991i
$979$	18.6969	+	32.3840i	0.597557	+	1.03500i
$980$		0			0
$981$		0			0
$982$	41.4393			1.32238
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	30.6969	+	43.4120i	0.978583	+	1.38392i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	44.8434	−	4.13188i	1.42306	−	0.131121i
$994$		0			0
$995$		0			0
$996$	8.89898	+	4.09978i	0.281975	+	0.129906i
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		−	61.8610i		−	1.95818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.l.a.59.2	yes	4
3.2	odd	2		216.2.l.a.179.1		4
4.3	odd	2		288.2.p.a.239.2		4
8.3	odd	2	CM	72.2.l.a.59.2	yes	4
8.5	even	2		288.2.p.a.239.2		4
9.2	odd	6	inner	72.2.l.a.11.2	✓	4
9.4	even	3		648.2.f.a.323.3		4
9.5	odd	6		648.2.f.a.323.2		4
9.7	even	3		216.2.l.a.35.1		4
12.11	even	2		864.2.p.a.719.1		4
24.5	odd	2		864.2.p.a.719.1		4
24.11	even	2		216.2.l.a.179.1		4
36.7	odd	6		864.2.p.a.143.1		4
36.11	even	6		288.2.p.a.47.2		4
36.23	even	6		2592.2.f.a.1295.1		4
36.31	odd	6		2592.2.f.a.1295.4		4
72.5	odd	6		2592.2.f.a.1295.1		4
72.11	even	6	inner	72.2.l.a.11.2	✓	4
72.13	even	6		2592.2.f.a.1295.4		4
72.29	odd	6		288.2.p.a.47.2		4
72.43	odd	6		216.2.l.a.35.1		4
72.59	even	6		648.2.f.a.323.2		4
72.61	even	6		864.2.p.a.143.1		4
72.67	odd	6		648.2.f.a.323.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.a.11.2	✓	4	9.2	odd	6	inner
72.2.l.a.11.2	✓	4	72.11	even	6	inner
72.2.l.a.59.2	yes	4	1.1	even	1	trivial
72.2.l.a.59.2	yes	4	8.3	odd	2	CM
216.2.l.a.35.1		4	9.7	even	3
216.2.l.a.35.1		4	72.43	odd	6
216.2.l.a.179.1		4	3.2	odd	2
216.2.l.a.179.1		4	24.11	even	2
288.2.p.a.47.2		4	36.11	even	6
288.2.p.a.47.2		4	72.29	odd	6
288.2.p.a.239.2		4	4.3	odd	2
288.2.p.a.239.2		4	8.5	even	2
648.2.f.a.323.2		4	9.5	odd	6
648.2.f.a.323.2		4	72.59	even	6
648.2.f.a.323.3		4	9.4	even	3
648.2.f.a.323.3		4	72.67	odd	6
864.2.p.a.143.1		4	36.7	odd	6
864.2.p.a.143.1		4	72.61	even	6
864.2.p.a.719.1		4	12.11	even	2
864.2.p.a.719.1		4	24.5	odd	2
2592.2.f.a.1295.1		4	36.23	even	6
2592.2.f.a.1295.1		4	72.5	odd	6
2592.2.f.a.1295.4		4	36.31	odd	6
2592.2.f.a.1295.4		4	72.13	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.224745 + 2.43916i) q^{6} -2.82843i q^{8} +(-1.94949 - 2.28024i) q^{9} +(-5.72474 + 3.30518i) q^{11} +(2.00000 + 2.82843i) q^{12} +(-2.00000 - 3.46410i) q^{16} -2.36773i q^{17} +(-4.00000 - 1.41421i) q^{18} +6.34847 q^{19} +(-4.67423 + 8.09601i) q^{22} +(4.44949 + 2.04989i) q^{24} +(2.50000 + 4.33013i) q^{25} +(5.00000 - 1.41421i) q^{27} +(-4.89898 - 2.82843i) q^{32} +(-1.05051 - 11.4012i) q^{33} +(-1.67423 - 2.89986i) q^{34} +(-5.89898 + 1.09638i) q^{36} +(7.77526 - 4.48905i) q^{38} +(9.39898 + 5.42650i) q^{41} +(-6.17423 - 10.6941i) q^{43} +13.2207i q^{44} +(6.89898 - 0.635674i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(6.12372 + 3.53553i) q^{50} +(3.72474 + 1.71600i) q^{51} +(5.12372 - 5.26758i) q^{54} +(-4.60102 + 9.98698i) q^{57} +(-1.62372 - 0.937458i) q^{59} -8.00000 q^{64} +(-9.34847 - 13.2207i) q^{66} +(-0.174235 + 0.301783i) q^{67} +(-4.10102 - 2.36773i) q^{68} +(-6.44949 + 5.51399i) q^{72} -15.6969 q^{73} +(-8.62372 + 0.794593i) q^{75} +(6.34847 - 10.9959i) q^{76} +(-1.39898 + 8.89060i) q^{81} +15.3485 q^{82} +(2.44949 - 1.41421i) q^{83} +(-15.1237 - 8.73169i) q^{86} +(9.34847 + 16.1920i) q^{88} -5.65685i q^{89} +(8.00000 - 5.65685i) q^{96} +(4.84847 + 8.39780i) q^{97} +9.89949i q^{98} +(18.6969 + 6.61037i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{4} - 4 q^{6} + 2 q^{9} - 18 q^{11} + 8 q^{12} - 8 q^{16} - 16 q^{18} - 4 q^{19} - 4 q^{22} + 8 q^{24} + 10 q^{25} + 20 q^{27} - 14 q^{33} + 8 q^{34} - 4 q^{36} + 36 q^{38} + 18 q^{41}+ \cdots + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^4 - 4 * q^6 + 2 * q^9 - 18 * q^11 + 8 * q^12 - 8 * q^16 - 16 * q^18 - 4 * q^19 - 4 * q^22 + 8 * q^24 + 10 * q^25 + 20 * q^27 - 14 * q^33 + 8 * q^34 - 4 * q^36 + 36 * q^38 + 18 * q^41 - 10 * q^43 + 8 * q^48 - 14 * q^49 + 10 * q^51 - 4 * q^54 - 38 * q^57 + 18 * q^59 - 32 * q^64 - 8 * q^66 + 14 * q^67 - 36 * q^68 - 16 * q^72 - 4 * q^73 - 10 * q^75 - 4 * q^76 + 14 * q^81 + 32 * q^82 - 36 * q^86 + 8 * q^88 + 32 * q^96 - 10 * q^97 + 16 * q^99

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