LMFDB - Embedded newform 3024.2.r.e.2017.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1009,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("3024.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2017.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	3024.2017
Dual form			3024.2.r.e.1009.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72474 + 2.98735i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})$	$q+(1.72474 + 2.98735i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.00000 + 1.73205i) q^{11} +(2.44949 + 4.24264i) q^{13} -2.00000 q^{17} -7.44949 q^{19} +(0.500000 + 0.866025i) q^{23} +(-3.44949 + 5.97469i) q^{25} +(1.44949 - 2.51059i) q^{29} +(3.00000 + 5.19615i) q^{31} -3.44949 q^{35} -7.79796 q^{37} +(-4.89898 - 8.48528i) q^{41} +(-1.44949 + 2.51059i) q^{43} +(4.89898 - 8.48528i) q^{47} +(-0.500000 - 0.866025i) q^{49} +1.10102 q^{53} -6.89898 q^{55} +(1.00000 + 1.73205i) q^{59} +(-5.72474 + 9.91555i) q^{61} +(-8.44949 + 14.6349i) q^{65} +(-1.55051 - 2.68556i) q^{67} +9.89898 q^{71} +2.89898 q^{73} +(-1.00000 - 1.73205i) q^{77} +(3.94949 - 6.84072i) q^{79} +(-1.00000 + 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} +7.10102 q^{89} -4.89898 q^{91} +(-12.8485 - 22.2542i) q^{95} +(3.44949 - 5.97469i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{5} - 2 q^{7} - 4 q^{11} - 8 q^{17} - 20 q^{19} + 2 q^{23} - 4 q^{25} - 4 q^{29} + 12 q^{31} - 4 q^{35} + 8 q^{37} + 4 q^{43} - 2 q^{49} + 24 q^{53} - 8 q^{55} + 4 q^{59} - 18 q^{61} - 24 q^{65} - 16 q^{67} + 20 q^{71} - 8 q^{73} - 4 q^{77} + 6 q^{79} - 4 q^{83} - 4 q^{85} + 48 q^{89} - 22 q^{95} + 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^11 - 8 * q^17 - 20 * q^19 + 2 * q^23 - 4 * q^25 - 4 * q^29 + 12 * q^31 - 4 * q^35 + 8 * q^37 + 4 * q^43 - 2 * q^49 + 24 * q^53 - 8 * q^55 + 4 * q^59 - 18 * q^61 - 24 * q^65 - 16 * q^67 + 20 * q^71 - 8 * q^73 - 4 * q^77 + 6 * q^79 - 4 * q^83 - 4 * q^85 + 48 * q^89 - 22 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.72474	+	2.98735i	0.771329	+	1.33598i	0.936835	+	0.349773i	$0.113741\pi$
$5$	1.72474	+	2.98735i	0.771329	+	1.33598i	−0.165505	+	0.986209i	$0.552925\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	2.44949	+	4.24264i	0.679366	+	1.17670i	0.975172	+	0.221449i	$0.0710785\pi$
$13$	2.44949	+	4.24264i	0.679366	+	1.17670i	−0.295806	+	0.955248i	$0.595588\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	−7.44949			−1.70903			−0.854515	−	0.519427i	$-0.826146\pi$
$19$	−7.44949			−1.70903			−0.854515	+	0.519427i	$0.826146\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		0			0
$25$	−3.44949	+	5.97469i	−0.689898	+	1.19494i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.44949	−	2.51059i	0.269163	−	0.466205i	−0.699483	−	0.714650i	$-0.746586\pi$
$29$	1.44949	−	2.51059i	0.269163	−	0.466205i	0.968646	+	0.248445i	$0.0799195\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.44949			−0.583070
$36$		0			0
$37$	−7.79796			−1.28198			−0.640988	−	0.767551i	$-0.721475\pi$
$37$	−7.79796			−1.28198			−0.640988	+	0.767551i	$0.721475\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.89898	−	8.48528i	−0.765092	−	1.32518i	−0.940198	−	0.340629i	$-0.889360\pi$
$41$	−4.89898	−	8.48528i	−0.765092	−	1.32518i	0.175106	−	0.984550i	$-0.443973\pi$
$42$		0			0
$43$	−1.44949	+	2.51059i	−0.221045	+	0.382861i	−0.955126	−	0.296201i	$-0.904280\pi$
$43$	−1.44949	+	2.51059i	−0.221045	+	0.382861i	0.734080	+	0.679062i	$0.237613\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	−0.248528	−	0.968625i	$-0.579947\pi$
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	0.963118	−	0.269081i	$-0.0867199\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.10102			0.151237			0.0756184	−	0.997137i	$-0.475907\pi$
$53$	1.10102			0.151237			0.0756184	+	0.997137i	$0.475907\pi$
$54$		0			0
$55$	−6.89898			−0.930258
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$		0			0
$61$	−5.72474	+	9.91555i	−0.732978	+	1.26956i	0.222626	+	0.974904i	$0.428537\pi$
$61$	−5.72474	+	9.91555i	−0.732978	+	1.26956i	−0.955605	+	0.294652i	$0.904796\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.44949	+	14.6349i	−1.04803	+	1.81524i
$66$		0			0
$67$	−1.55051	−	2.68556i	−0.189425	−	0.328094i	0.755634	−	0.654994i	$-0.227329\pi$
$67$	−1.55051	−	2.68556i	−0.189425	−	0.328094i	−0.945059	+	0.326901i	$0.893996\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.89898			1.17479			0.587396	−	0.809299i	$-0.300153\pi$
$71$	9.89898			1.17479			0.587396	+	0.809299i	$0.300153\pi$
$72$		0			0
$73$	2.89898			0.339300			0.169650	−	0.985504i	$-0.445736\pi$
$73$	2.89898			0.339300			0.169650	+	0.985504i	$0.445736\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.00000	−	1.73205i	−0.113961	−	0.197386i
$78$		0			0
$79$	3.94949	−	6.84072i	0.444352	−	0.769641i	−0.553655	−	0.832746i	$-0.686767\pi$
$79$	3.94949	−	6.84072i	0.444352	−	0.769641i	0.998007	+	0.0631057i	$0.0201005\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$		0			0
$85$	−3.44949	−	5.97469i	−0.374150	−	0.648046i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.10102			0.752707			0.376353	−	0.926476i	$-0.377178\pi$
$89$	7.10102			0.752707			0.376353	+	0.926476i	$0.377178\pi$
$90$		0			0
$91$	−4.89898			−0.513553
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−12.8485	−	22.2542i	−1.31823	−	2.28323i
$96$		0			0
$97$	3.44949	−	5.97469i	0.350243	−	0.606638i	−0.636049	−	0.771649i	$-0.719432\pi$
$97$	3.44949	−	5.97469i	0.350243	−	0.606638i	0.986292	+	0.165011i	$0.0527658\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.62372	−	6.27647i	0.360574	−	0.624533i	−0.627481	−	0.778632i	$-0.715914\pi$
$101$	3.62372	−	6.27647i	0.360574	−	0.624533i	0.988055	+	0.154099i	$0.0492475\pi$
$102$		0			0
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−16.6969			−1.59928			−0.799638	−	0.600482i	$-0.794975\pi$
$109$	−16.6969			−1.59928			−0.799638	+	0.600482i	$0.794975\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.94949	−	13.7689i	−0.747825	−	1.29527i	−0.948863	−	0.315688i	$-0.897765\pi$
$113$	−7.94949	−	13.7689i	−0.747825	−	1.29527i	0.201038	−	0.979583i	$-0.435569\pi$
$114$		0			0
$115$	−1.72474	+	2.98735i	−0.160833	+	0.278571i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.00000	−	1.73205i	0.0916698	−	0.158777i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.55051			−0.585895
$126$		0			0
$127$	3.00000			0.266207			0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000			0.266207			0.133103	+	0.991102i	$0.457506\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.72474	+	11.6476i	0.587544	+	1.01766i	0.994553	+	0.104232i	$0.0332383\pi$
$131$	6.72474	+	11.6476i	0.587544	+	1.01766i	−0.407009	+	0.913424i	$0.633428\pi$
$132$		0			0
$133$	3.72474	−	6.45145i	0.322976	−	0.559411i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.89898	+	10.2173i	−0.503984	+	0.872926i	0.496006	+	0.868319i	$0.334800\pi$
$137$	−5.89898	+	10.2173i	−0.503984	+	0.872926i	−0.999989	+	0.00460626i	$0.998534\pi$
$138$		0			0
$139$	4.72474	+	8.18350i	0.400748	+	0.694115i	0.993816	−	0.111037i	$-0.0354171\pi$
$139$	4.72474	+	8.18350i	0.400748	+	0.694115i	−0.593069	+	0.805152i	$0.702084\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−9.79796			−0.819346
$144$		0			0
$145$	10.0000			0.830455
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.3485	+	17.9241i	−0.831209	+	1.43970i
$156$		0			0
$157$	−3.17423	−	5.49794i	−0.253332	−	0.438783i	0.711109	−	0.703081i	$-0.248193\pi$
$157$	−3.17423	−	5.49794i	−0.253332	−	0.438783i	−0.964441	+	0.264298i	$0.914860\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.00000			−0.0788110
$162$		0			0
$163$	0.202041			0.0158251			0.00791254	−	0.999969i	$-0.497481\pi$
$163$	0.202041			0.0158251			0.00791254	+	0.999969i	$0.497481\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.34847	−	16.1920i	−0.723406	−	1.25298i	−0.959627	−	0.281277i	$-0.909242\pi$
$167$	−9.34847	−	16.1920i	−0.723406	−	1.25298i	0.236220	−	0.971700i	$-0.424091\pi$
$168$		0			0
$169$	−5.50000	+	9.52628i	−0.423077	+	0.732791i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.44949	+	11.1708i	−0.490346	+	0.849304i	−0.999938	−	0.0111123i	$-0.996463\pi$
$173$	−6.44949	+	11.1708i	−0.490346	+	0.849304i	0.509593	+	0.860416i	$0.329796\pi$
$174$		0			0
$175$	−3.44949	−	5.97469i	−0.260757	−	0.451644i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.69694			−0.650040			−0.325020	−	0.945707i	$-0.605371\pi$
$179$	−8.69694			−0.650040			−0.325020	+	0.945707i	$0.605371\pi$
$180$		0			0
$181$	4.34847			0.323219			0.161610	−	0.986855i	$-0.448331\pi$
$181$	4.34847			0.323219			0.161610	+	0.986855i	$0.448331\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−13.4495	−	23.2952i	−0.988826	−	1.71270i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.94949	+	12.0369i	−0.502847	+	0.870957i	0.497147	+	0.867666i	$0.334381\pi$
$191$	−6.94949	+	12.0369i	−0.502847	+	0.870957i	−0.999995	+	0.00329106i	$0.998952\pi$
$192$		0			0
$193$	4.05051	+	7.01569i	0.291562	+	0.505000i	0.974179	−	0.225776i	$-0.0724917\pi$
$193$	4.05051	+	7.01569i	0.291562	+	0.505000i	−0.682617	+	0.730776i	$0.739158\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.6969			0.904619			0.452310	−	0.891861i	$-0.350600\pi$
$197$	12.6969			0.904619			0.452310	+	0.891861i	$0.350600\pi$
$198$		0			0
$199$	−6.89898			−0.489056			−0.244528	−	0.969642i	$-0.578633\pi$
$199$	−6.89898			−0.489056			−0.244528	+	0.969642i	$0.578633\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.44949	+	2.51059i	0.101734	+	0.176209i
$204$		0			0
$205$	16.8990	−	29.2699i	1.18028	−	2.04430i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.44949	−	12.9029i	0.515292	−	0.892512i
$210$		0			0
$211$	1.55051	+	2.68556i	0.106742	+	0.184882i	0.914448	−	0.404703i	$-0.132625\pi$
$211$	1.55051	+	2.68556i	0.106742	+	0.184882i	−0.807707	+	0.589584i	$0.799292\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.0000			−0.681994
$216$		0			0
$217$	−6.00000			−0.407307
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.89898	−	8.48528i	−0.329541	−	0.570782i
$222$		0			0
$223$	−10.4495	+	18.0990i	−0.699750	+	1.21200i	0.268804	+	0.963195i	$0.413372\pi$
$223$	−10.4495	+	18.0990i	−0.699750	+	1.21200i	−0.968553	+	0.248807i	$0.919962\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.275255	−	0.476756i	0.0182693	−	0.0316434i	−0.856746	−	0.515738i	$-0.827518\pi$
$227$	0.275255	−	0.476756i	0.0182693	−	0.0316434i	0.875016	+	0.484095i	$0.160851\pi$
$228$		0			0
$229$	11.6237	+	20.1329i	0.768117	+	1.33042i	0.938583	+	0.345055i	$0.112140\pi$
$229$	11.6237	+	20.1329i	0.768117	+	1.33042i	−0.170465	+	0.985364i	$0.554527\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.00000			0.458585			0.229293	−	0.973358i	$-0.426359\pi$
$233$	7.00000			0.458585			0.229293	+	0.973358i	$0.426359\pi$
$234$		0			0
$235$	33.7980			2.20474
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.39898	+	11.0834i	0.413916	+	0.716923i	0.995314	−	0.0966962i	$-0.0308275\pi$
$239$	6.39898	+	11.0834i	0.413916	+	0.716923i	−0.581398	+	0.813619i	$0.697494\pi$
$240$		0			0
$241$	4.44949	−	7.70674i	0.286617	−	0.496435i	−0.686383	−	0.727240i	$-0.740803\pi$
$241$	4.44949	−	7.70674i	0.286617	−	0.496435i	0.973000	+	0.230805i	$0.0741360\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.72474	−	2.98735i	0.110190	−	0.190855i
$246$		0			0
$247$	−18.2474	−	31.6055i	−1.16106	−	2.01101i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.5505			0.792181			0.396091	−	0.918211i	$-0.370367\pi$
$251$	12.5505			0.792181			0.396091	+	0.918211i	$0.370367\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.8990	+	24.0737i	0.866995	+	1.50168i	0.865053	+	0.501680i	$0.167285\pi$
$257$	13.8990	+	24.0737i	0.866995	+	1.50168i	0.00194150	+	0.999998i	$0.499382\pi$
$258$		0			0
$259$	3.89898	−	6.75323i	0.242271	−	0.419625i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.05051	+	13.9439i	−0.496416	+	0.859817i	−0.999991	−	0.00413383i	$-0.998684\pi$
$263$	−8.05051	+	13.9439i	−0.496416	+	0.859817i	0.503576	+	0.863951i	$0.332017\pi$
$264$		0			0
$265$	1.89898	+	3.28913i	0.116653	+	0.202050i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.65153			0.222638			0.111319	−	0.993785i	$-0.464493\pi$
$269$	3.65153			0.222638			0.111319	+	0.993785i	$0.464493\pi$
$270$		0			0
$271$	−16.8990			−1.02654			−0.513270	−	0.858227i	$-0.671566\pi$
$271$	−16.8990			−1.02654			−0.513270	+	0.858227i	$0.671566\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.89898	−	11.9494i	−0.416024	−	0.720575i
$276$		0			0
$277$	−5.34847	+	9.26382i	−0.321358	+	0.556609i	−0.980769	−	0.195174i	$-0.937473\pi$
$277$	−5.34847	+	9.26382i	−0.321358	+	0.556609i	0.659410	+	0.751783i	$0.270806\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	0.430165	+	0.902750i	$0.358455\pi$
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	−0.996887	+	0.0788417i	$0.974878\pi$
$282$		0			0
$283$	−10.2753	−	17.7973i	−0.610801	−	1.05794i	−0.991106	−	0.133077i	$-0.957514\pi$
$283$	−10.2753	−	17.7973i	−0.610801	−	1.05794i	0.380305	−	0.924861i	$-0.375819\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.79796			0.578355
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.6237	+	23.5970i	0.795906	+	1.37855i	0.922262	+	0.386565i	$0.126339\pi$
$293$	13.6237	+	23.5970i	0.795906	+	1.37855i	−0.126356	+	0.991985i	$0.540328\pi$
$294$		0			0
$295$	−3.44949	+	5.97469i	−0.200837	+	0.347860i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.44949	+	4.24264i	−0.141658	+	0.245358i
$300$		0			0
$301$	−1.44949	−	2.51059i	−0.0835472	−	0.144708i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−39.4949			−2.26147
$306$		0			0
$307$	−0.752551			−0.0429504			−0.0214752	−	0.999769i	$-0.506836\pi$
$307$	−0.752551			−0.0429504			−0.0214752	+	0.999769i	$0.506836\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.651531	−	1.12848i	−0.0369449	−	0.0639905i	0.846962	−	0.531654i	$-0.178429\pi$
$311$	−0.651531	−	1.12848i	−0.0369449	−	0.0639905i	−0.883907	+	0.467663i	$0.845096\pi$
$312$		0			0
$313$	−12.3485	+	21.3882i	−0.697977	+	1.20893i	0.271190	+	0.962526i	$0.412583\pi$
$313$	−12.3485	+	21.3882i	−0.697977	+	1.20893i	−0.969167	+	0.246405i	$0.920751\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.34847	+	7.53177i	−0.244234	+	0.423026i	−0.961916	−	0.273345i	$-0.911870\pi$
$317$	−4.34847	+	7.53177i	−0.244234	+	0.423026i	0.717682	+	0.696371i	$0.245203\pi$
$318$		0			0
$319$	2.89898	+	5.02118i	0.162312	+	0.281132i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	14.8990			0.829001
$324$		0			0
$325$	−33.7980			−1.87477
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.89898	+	8.48528i	0.270089	+	0.467809i
$330$		0			0
$331$	−12.3485	+	21.3882i	−0.678733	+	1.17560i	0.296629	+	0.954993i	$0.404137\pi$
$331$	−12.3485	+	21.3882i	−0.678733	+	1.17560i	−0.975363	+	0.220608i	$0.929196\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.34847	−	9.26382i	0.292218	−	0.506137i
$336$		0			0
$337$	−17.6969	−	30.6520i	−0.964014	−	1.66972i	−0.712242	−	0.701934i	$-0.752320\pi$
$337$	−17.6969	−	30.6520i	−0.964014	−	1.66972i	−0.251772	−	0.967787i	$-0.581013\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.0000			−0.649836
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.79796	+	16.9706i	0.525982	+	0.911028i	0.999542	+	0.0302659i	$0.00963541\pi$
$347$	9.79796	+	16.9706i	0.525982	+	0.911028i	−0.473560	+	0.880762i	$0.657031\pi$
$348$		0			0
$349$	−10.4495	+	18.0990i	−0.559348	+	0.968820i	0.438203	+	0.898876i	$0.355615\pi$
$349$	−10.4495	+	18.0990i	−0.559348	+	0.968820i	−0.997551	+	0.0699435i	$0.977718\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$	17.0732	+	29.5717i	0.906152	+	1.56950i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.7980			0.569894			0.284947	−	0.958543i	$-0.408024\pi$
$359$	10.7980			0.569894			0.284947	+	0.958543i	$0.408024\pi$
$360$		0			0
$361$	36.4949			1.92078
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.00000	+	8.66025i	0.261712	+	0.453298i
$366$		0			0
$367$	2.89898	−	5.02118i	0.151325	−	0.262103i	−0.780389	−	0.625294i	$-0.784979\pi$
$367$	2.89898	−	5.02118i	0.151325	−	0.262103i	0.931715	+	0.363190i	$0.118313\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.550510	+	0.953512i	−0.0285811	+	0.0495039i
$372$		0			0
$373$	−1.44949	−	2.51059i	−0.0750517	−	0.129993i	0.826057	−	0.563587i	$-0.190579\pi$
$373$	−1.44949	−	2.51059i	−0.0750517	−	0.129993i	−0.901109	+	0.433593i	$0.857246\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.2020			0.731442
$378$		0			0
$379$	26.4949			1.36095			0.680476	−	0.732771i	$-0.261773\pi$
$379$	26.4949			1.36095			0.680476	+	0.732771i	$0.261773\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.44949	−	5.97469i	−0.176261	−	0.305292i	0.764336	−	0.644818i	$-0.223067\pi$
$383$	−3.44949	−	5.97469i	−0.176261	−	0.305292i	−0.940597	+	0.339526i	$0.889734\pi$
$384$		0			0
$385$	3.44949	−	5.97469i	0.175802	−	0.304498i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.55051	+	13.0779i	−0.382826	+	0.663074i	−0.991465	−	0.130373i	$-0.958382\pi$
$389$	−7.55051	+	13.0779i	−0.382826	+	0.663074i	0.608639	+	0.793447i	$0.291716\pi$
$390$		0			0
$391$	−1.00000	−	1.73205i	−0.0505722	−	0.0875936i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	27.2474			1.37097
$396$		0			0
$397$	9.30306			0.466907			0.233454	−	0.972368i	$-0.424997\pi$
$397$	9.30306			0.466907			0.233454	+	0.972368i	$0.424997\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.05051	−	8.74774i	−0.252210	−	0.436841i	0.711924	−	0.702257i	$-0.247824\pi$
$401$	−5.05051	−	8.74774i	−0.252210	−	0.436841i	−0.964134	+	0.265416i	$0.914491\pi$
$402$		0			0
$403$	−14.6969	+	25.4558i	−0.732107	+	1.26805i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.79796	−	13.5065i	0.386530	−	0.669490i
$408$		0			0
$409$	−2.89898	−	5.02118i	−0.143345	−	0.248281i	0.785409	−	0.618977i	$-0.212453\pi$
$409$	−2.89898	−	5.02118i	−0.143345	−	0.248281i	−0.928754	+	0.370696i	$0.879119\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.00000			−0.0984136
$414$		0			0
$415$	−6.89898			−0.338658
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.2753	−	21.2614i	−0.599685	−	1.03869i	−0.992867	−	0.119225i	$-0.961959\pi$
$419$	−12.2753	−	21.2614i	−0.599685	−	1.03869i	0.393182	−	0.919461i	$-0.371374\pi$
$420$		0			0
$421$	−6.55051	+	11.3458i	−0.319252	+	0.552961i	−0.980332	−	0.197354i	$-0.936765\pi$
$421$	−6.55051	+	11.3458i	−0.319252	+	0.552961i	0.661080	+	0.750316i	$0.270098\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.89898	−	11.9494i	0.334650	−	0.579630i
$426$		0			0
$427$	−5.72474	−	9.91555i	−0.277040	−	0.479847i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.59592			−0.365882			−0.182941	−	0.983124i	$-0.558562\pi$
$431$	−7.59592			−0.365882			−0.182941	+	0.983124i	$0.558562\pi$
$432$		0			0
$433$	11.7980			0.566974			0.283487	−	0.958976i	$-0.408509\pi$
$433$	11.7980			0.566974			0.283487	+	0.958976i	$0.408509\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.72474	−	6.45145i	−0.178179	−	0.308615i
$438$		0			0
$439$	10.8990	−	18.8776i	0.520180	−	0.900978i	−0.479545	−	0.877517i	$-0.659198\pi$
$439$	10.8990	−	18.8776i	0.520180	−	0.900978i	0.999725	−	0.0234607i	$-0.00746845\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.55051	−	4.41761i	0.121178	−	0.209887i	−0.799054	−	0.601259i	$-0.794666\pi$
$443$	2.55051	−	4.41761i	0.121178	−	0.209887i	0.920233	+	0.391372i	$0.127999\pi$
$444$		0			0
$445$	12.2474	+	21.2132i	0.580585	+	1.00560i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.5959			0.877596			0.438798	−	0.898586i	$-0.355404\pi$
$449$	18.5959			0.877596			0.438798	+	0.898586i	$0.355404\pi$
$450$		0			0
$451$	19.5959			0.922736
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.44949	−	14.6349i	−0.396118	−	0.686097i
$456$		0			0
$457$	−15.7474	+	27.2754i	−0.736635	+	1.27589i	0.217368	+	0.976090i	$0.430253\pi$
$457$	−15.7474	+	27.2754i	−0.736635	+	1.27589i	−0.954002	+	0.299799i	$0.903080\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.1742	−	17.6223i	0.473861	−	0.820752i	−0.525691	−	0.850676i	$-0.676193\pi$
$461$	10.1742	−	17.6223i	0.473861	−	0.820752i	0.999552	+	0.0299238i	$0.00952645\pi$
$462$		0			0
$463$	−12.8485	−	22.2542i	−0.597119	−	1.03424i	−0.993244	−	0.116044i	$-0.962979\pi$
$463$	−12.8485	−	22.2542i	−0.597119	−	1.03424i	0.396125	−	0.918197i	$-0.370355\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.0000			0.462745			0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000			0.462745			0.231372	+	0.972865i	$0.425678\pi$
$468$		0			0
$469$	3.10102			0.143192
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.89898	−	5.02118i	−0.133295	−	0.230874i
$474$		0			0
$475$	25.6969	−	44.5084i	1.17906	−	2.04219i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.7980	−	25.6308i	0.676136	−	1.17110i	−0.299999	−	0.953939i	$-0.596987\pi$
$479$	14.7980	−	25.6308i	0.676136	−	1.17110i	0.976135	−	0.217163i	$-0.0696802\pi$
$480$		0			0
$481$	−19.1010	−	33.0839i	−0.870932	−	1.50850i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	23.7980			1.08061
$486$		0			0
$487$	−22.3939			−1.01476			−0.507382	−	0.861721i	$-0.669387\pi$
$487$	−22.3939			−1.01476			−0.507382	+	0.861721i	$0.669387\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.89898	+	3.28913i	0.0856997	+	0.148436i	0.905689	−	0.423942i	$-0.139354\pi$
$491$	1.89898	+	3.28913i	0.0856997	+	0.148436i	−0.819989	+	0.572379i	$0.806021\pi$
$492$		0			0
$493$	−2.89898	+	5.02118i	−0.130563	+	0.226143i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.94949	+	8.57277i	−0.222015	+	0.384541i
$498$		0			0
$499$	16.6969	+	28.9199i	0.747458	+	1.29463i	0.949038	+	0.315163i	$0.102059\pi$
$499$	16.6969	+	28.9199i	0.747458	+	1.29463i	−0.201580	+	0.979472i	$0.564608\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.4949			1.09217			0.546087	−	0.837729i	$-0.316117\pi$
$503$	24.4949			1.09217			0.546087	+	0.837729i	$0.316117\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.44949	−	14.6349i	−0.374517	−	0.648683i	0.615738	−	0.787951i	$-0.288858\pi$
$509$	−8.44949	−	14.6349i	−0.374517	−	0.648683i	−0.990255	+	0.139269i	$0.955525\pi$
$510$		0			0
$511$	−1.44949	+	2.51059i	−0.0641217	+	0.111062i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−24.1464	+	41.8228i	−1.06402	+	1.84293i
$516$		0			0
$517$	9.79796	+	16.9706i	0.430914	+	0.746364i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	38.6969			1.69534			0.847672	−	0.530521i	$-0.178004\pi$
$521$	38.6969			1.69534			0.847672	+	0.530521i	$0.178004\pi$
$522$		0			0
$523$	−0.348469			−0.0152375			−0.00761875	−	0.999971i	$-0.502425\pi$
$523$	−0.348469			−0.0152375			−0.00761875	+	0.999971i	$0.502425\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.0000	−	41.5692i	1.03956	−	1.80056i
$534$		0			0
$535$	−20.6969	−	35.8481i	−0.894807	−	1.54985i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.00000			0.0861461
$540$		0			0
$541$	30.4949			1.31108			0.655539	−	0.755161i	$-0.272441\pi$
$541$	30.4949			1.31108			0.655539	+	0.755161i	$0.272441\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−28.7980	−	49.8795i	−1.23357	−	2.13660i
$546$		0			0
$547$	15.7980	−	27.3629i	0.675472	−	1.16995i	−0.300859	−	0.953669i	$-0.597273\pi$
$547$	15.7980	−	27.3629i	0.675472	−	1.16995i	0.976331	−	0.216283i	$-0.0693934\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.7980	+	18.7026i	−0.460009	+	0.796758i
$552$		0			0
$553$	3.94949	+	6.84072i	0.167949	+	0.290897i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.10102			0.131394			0.0656972	−	0.997840i	$-0.479073\pi$
$557$	3.10102			0.131394			0.0656972	+	0.997840i	$0.479073\pi$
$558$		0			0
$559$	−14.2020			−0.600682
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.97219	−	12.0762i	−0.293843	−	0.508951i	0.680872	−	0.732402i	$-0.261601\pi$
$563$	−6.97219	−	12.0762i	−0.293843	−	0.508951i	−0.974715	+	0.223451i	$0.928268\pi$
$564$		0			0
$565$	27.4217	−	47.4957i	1.15364	−	1.99816i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	7.10102	+	12.2993i	0.297168	+	0.514711i	0.975487	−	0.220057i	$-0.0706244\pi$
$571$	7.10102	+	12.2993i	0.297168	+	0.514711i	−0.678319	+	0.734768i	$0.737291\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.89898			−0.287707
$576$		0			0
$577$	23.5959			0.982311			0.491155	−	0.871072i	$-0.336575\pi$
$577$	23.5959			0.982311			0.491155	+	0.871072i	$0.336575\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.00000	−	1.73205i	−0.0414870	−	0.0718576i
$582$		0			0
$583$	−1.10102	+	1.90702i	−0.0455996	+	0.0789808i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.07321	−	15.7153i	0.374492	−	0.648639i	−0.615759	−	0.787934i	$-0.711151\pi$
$587$	9.07321	−	15.7153i	0.374492	−	0.648639i	0.990251	+	0.139296i	$0.0444839\pi$
$588$		0			0
$589$	−22.3485	−	38.7087i	−0.920853	−	1.59496i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.6969			0.603531			0.301765	−	0.953382i	$-0.402424\pi$
$593$	14.6969			0.603531			0.301765	+	0.953382i	$0.402424\pi$
$594$		0			0
$595$	6.89898			0.282831
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.10102	+	12.2993i	0.290140	+	0.502537i	0.973843	−	0.227224i	$-0.0729648\pi$
$599$	7.10102	+	12.2993i	0.290140	+	0.502537i	−0.683703	+	0.729761i	$0.739632\pi$
$600$		0			0
$601$	6.34847	−	10.9959i	0.258959	−	0.448531i	−0.707004	−	0.707210i	$-0.749954\pi$
$601$	6.34847	−	10.9959i	0.258959	−	0.448531i	0.965963	+	0.258679i	$0.0832871\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−12.0732	+	20.9114i	−0.490846	+	0.850170i
$606$		0			0
$607$	−4.34847	−	7.53177i	−0.176499	−	0.305705i	0.764180	−	0.645003i	$-0.223144\pi$
$607$	−4.34847	−	7.53177i	−0.176499	−	0.305705i	−0.940679	+	0.339298i	$0.889811\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	48.0000			1.94187
$612$		0			0
$613$	14.6969			0.593604			0.296802	−	0.954939i	$-0.404080\pi$
$613$	14.6969			0.593604			0.296802	+	0.954939i	$0.404080\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.6969	+	37.5802i	0.873486	+	1.51292i	0.858367	+	0.513036i	$0.171479\pi$
$617$	21.6969	+	37.5802i	0.873486	+	1.51292i	0.0151189	+	0.999886i	$0.495187\pi$
$618$		0			0
$619$	−2.07321	+	3.59091i	−0.0833295	+	0.144331i	−0.904678	−	0.426096i	$-0.859889\pi$
$619$	−2.07321	+	3.59091i	−0.0833295	+	0.144331i	0.821349	+	0.570426i	$0.193222\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.55051	+	6.14966i	−0.142248	+	0.246381i
$624$		0			0
$625$	5.94949	+	10.3048i	0.237980	+	0.412193i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.5959			0.621850
$630$		0			0
$631$	−18.1010			−0.720590			−0.360295	−	0.932838i	$-0.617324\pi$
$631$	−18.1010			−0.720590			−0.360295	+	0.932838i	$0.617324\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.17423	+	8.96204i	0.205333	+	0.355648i
$636$		0			0
$637$	2.44949	−	4.24264i	0.0970523	−	0.168100i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.7474	−	35.9356i	0.819475	−	1.41937i	−0.0865947	−	0.996244i	$-0.527599\pi$
$641$	20.7474	−	35.9356i	0.819475	−	1.41937i	0.906070	−	0.423129i	$-0.139068\pi$
$642$		0			0
$643$	9.69694	+	16.7956i	0.382410	+	0.662353i	0.991406	−	0.130820i	$-0.0417609\pi$
$643$	9.69694	+	16.7956i	0.382410	+	0.662353i	−0.608996	+	0.793173i	$0.708428\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.3031			−0.837510			−0.418755	−	0.908099i	$-0.637533\pi$
$647$	−21.3031			−0.837510			−0.418755	+	0.908099i	$0.637533\pi$
$648$		0			0
$649$	−4.00000			−0.157014
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.89898	−	8.48528i	−0.191712	−	0.332055i	0.754106	−	0.656753i	$-0.228071\pi$
$653$	−4.89898	−	8.48528i	−0.191712	−	0.332055i	−0.945818	+	0.324698i	$0.894737\pi$
$654$		0			0
$655$	−23.1969	+	40.1783i	−0.906379	+	1.56990i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.34847	+	4.06767i	−0.0914834	+	0.158454i	−0.908136	−	0.418676i	$-0.862494\pi$
$659$	−2.34847	+	4.06767i	−0.0914834	+	0.158454i	0.816652	+	0.577130i	$0.195828\pi$
$660$		0			0
$661$	−4.72474	−	8.18350i	−0.183771	−	0.318301i	0.759391	−	0.650635i	$-0.225497\pi$
$661$	−4.72474	−	8.18350i	−0.183771	−	0.318301i	−0.943162	+	0.332334i	$0.892164\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	25.6969			0.996485
$666$		0			0
$667$	2.89898			0.112249
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.4495	−	19.8311i	−0.442003	−	0.765571i
$672$		0			0
$673$	−15.2980	+	26.4968i	−0.589693	+	1.02138i	0.404579	+	0.914503i	$0.367418\pi$
$673$	−15.2980	+	26.4968i	−0.589693	+	1.02138i	−0.994272	+	0.106875i	$0.965915\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	−0.971981	−	0.235058i	$-0.924472\pi$
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	0.689557	+	0.724232i	$0.257805\pi$
$678$		0			0
$679$	3.44949	+	5.97469i	0.132379	+	0.229288i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	32.2020			1.23218			0.616088	−	0.787677i	$-0.288716\pi$
$683$	32.2020			1.23218			0.616088	+	0.787677i	$0.288716\pi$
$684$		0			0
$685$	−40.6969			−1.55495
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.69694	+	4.67123i	0.102745	+	0.177960i
$690$		0			0
$691$	3.47730	−	6.02285i	0.132283	−	0.229120i	−0.792274	−	0.610166i	$-0.791103\pi$
$691$	3.47730	−	6.02285i	0.132283	−	0.229120i	0.924556	+	0.381046i	$0.124436\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.2980	+	28.2289i	−0.618217	+	1.07078i
$696$		0			0
$697$	9.79796	+	16.9706i	0.371124	+	0.642806i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−51.3939			−1.94112			−0.970560	−	0.240860i	$-0.922571\pi$
$701$	−51.3939			−1.94112			−0.970560	+	0.240860i	$0.922571\pi$
$702$		0			0
$703$	58.0908			2.19094
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.62372	+	6.27647i	0.136284	+	0.236051i
$708$		0			0
$709$	5.79796	−	10.0424i	0.217747	−	0.377149i	−0.736372	−	0.676577i	$-0.763463\pi$
$709$	5.79796	−	10.0424i	0.217747	−	0.377149i	0.954119	+	0.299428i	$0.0967959\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	−16.8990	−	29.2699i	−0.631986	−	1.09463i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.79796			−0.365402			−0.182701	−	0.983169i	$-0.558484\pi$
$719$	−9.79796			−0.365402			−0.182701	+	0.983169i	$0.558484\pi$
$720$		0			0
$721$	−14.0000			−0.521387
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.0000	+	17.3205i	0.371391	+	0.643268i
$726$		0			0
$727$	20.2474	−	35.0696i	0.750936	−	1.30066i	−0.196433	−	0.980517i	$-0.562936\pi$
$727$	20.2474	−	35.0696i	0.750936	−	1.30066i	0.947369	−	0.320143i	$-0.103731\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.89898	−	5.02118i	0.107223	−	0.185715i
$732$		0			0
$733$	6.27526	+	10.8691i	0.231782	+	0.401458i	0.958333	−	0.285655i	$-0.0922111\pi$
$733$	6.27526	+	10.8691i	0.231782	+	0.401458i	−0.726551	+	0.687113i	$0.758878\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.20204			0.228455
$738$		0			0
$739$	25.5959			0.941561			0.470781	−	0.882250i	$-0.343972\pi$
$739$	25.5959			0.941561			0.470781	+	0.882250i	$0.343972\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$		0			0
$745$	10.3485	−	17.9241i	0.379139	−	0.656687i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	−	10.3923i	0.219235	−	0.379727i
$750$		0			0
$751$	20.2980	+	35.1571i	0.740683	+	1.28290i	0.952185	+	0.305523i	$0.0988313\pi$
$751$	20.2980	+	35.1571i	0.740683	+	1.28290i	−0.211502	+	0.977378i	$0.567835\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.2474			−0.627699
$756$		0			0
$757$	23.3939			0.850265			0.425132	−	0.905131i	$-0.360228\pi$
$757$	23.3939			0.850265			0.425132	+	0.905131i	$0.360228\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	0.883581	−	0.468278i	$-0.155125\pi$
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	−0.847331	+	0.531065i	$0.821792\pi$
$762$		0			0
$763$	8.34847	−	14.4600i	0.302235	−	0.523486i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.89898	+	8.48528i	−0.176892	+	0.306386i
$768$		0			0
$769$	−27.0454	−	46.8440i	−0.975282	−	1.68924i	−0.679000	−	0.734138i	$-0.737586\pi$
$769$	−27.0454	−	46.8440i	−0.975282	−	1.68924i	−0.296282	−	0.955100i	$-0.595747\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.9444			0.717350			0.358675	−	0.933463i	$-0.383229\pi$
$773$	19.9444			0.717350			0.358675	+	0.933463i	$0.383229\pi$
$774$		0			0
$775$	−41.3939			−1.48691
$776$		0			0
$777$		0			0
$778$		0			0
$779$	36.4949	+	63.2110i	1.30757	+	2.26477i
$780$		0			0
$781$	−9.89898	+	17.1455i	−0.354213	+	0.613515i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.9495	−	18.9651i	0.390804	−	0.676892i
$786$		0			0
$787$	23.6969	+	41.0443i	0.844705	+	1.46307i	0.885877	+	0.463919i	$0.153557\pi$
$787$	23.6969	+	41.0443i	0.844705	+	1.46307i	−0.0411728	+	0.999152i	$0.513109\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.8990			0.565303
$792$		0			0
$793$	−56.0908			−1.99184
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.9722	+	31.1288i	0.636608	+	1.10264i	0.986172	+	0.165725i	$0.0529963\pi$
$797$	17.9722	+	31.1288i	0.636608	+	1.10264i	−0.349564	+	0.936912i	$0.613670\pi$
$798$		0			0
$799$	−9.79796	+	16.9706i	−0.346627	+	0.600375i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.89898	+	5.02118i	−0.102303	+	0.177194i
$804$		0			0
$805$	−1.72474	−	2.98735i	−0.0607893	−	0.105290i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	35.7980			1.25859			0.629295	−	0.777167i	$-0.283344\pi$
$809$	35.7980			1.25859			0.629295	+	0.777167i	$0.283344\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.348469	+	0.603566i	0.0122063	+	0.0211420i
$816$		0			0
$817$	10.7980	−	18.7026i	0.377773	−	0.654322i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.7980	−	34.2911i	0.690954	−	1.19677i	−0.280572	−	0.959833i	$-0.590524\pi$
$821$	19.7980	−	34.2911i	0.690954	−	1.19677i	0.971526	−	0.236934i	$-0.0761424\pi$
$822$		0			0
$823$	22.6969	+	39.3123i	0.791166	+	1.37034i	0.925246	+	0.379368i	$0.123859\pi$
$823$	22.6969	+	39.3123i	0.791166	+	1.37034i	−0.134080	+	0.990970i	$0.542808\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.4949			0.434490			0.217245	−	0.976117i	$-0.430293\pi$
$827$	12.4949			0.434490			0.217245	+	0.976117i	$0.430293\pi$
$828$		0			0
$829$	30.6969			1.06615			0.533074	−	0.846068i	$-0.321037\pi$
$829$	30.6969			1.06615			0.533074	+	0.846068i	$0.321037\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.00000	+	1.73205i	0.0346479	+	0.0600120i
$834$		0			0
$835$	32.2474	−	55.8542i	1.11597	−	1.93291i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.4495	−	38.8837i	0.775042	−	1.34241i	−0.159728	−	0.987161i	$-0.551062\pi$
$839$	22.4495	−	38.8837i	0.775042	−	1.34241i	0.934771	−	0.355252i	$-0.115605\pi$
$840$		0			0
$841$	10.2980	+	17.8366i	0.355102	+	0.615055i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−37.9444			−1.30533
$846$		0			0
$847$	−7.00000			−0.240523
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.89898	−	6.75323i	−0.133655	−	0.231498i
$852$		0			0
$853$	19.4217	−	33.6393i	0.664986	−	1.15179i	−0.314303	−	0.949323i	$-0.601771\pi$
$853$	19.4217	−	33.6393i	0.664986	−	1.15179i	0.979289	−	0.202467i	$-0.0648957\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.5505	+	21.7381i	−0.428717	+	0.742560i	−0.996760	−	0.0804393i	$-0.974368\pi$
$857$	−12.5505	+	21.7381i	−0.428717	+	0.742560i	0.568042	+	0.822999i	$0.307701\pi$
$858$		0			0
$859$	−5.00000	−	8.66025i	−0.170598	−	0.295484i	0.768031	−	0.640412i	$-0.221237\pi$
$859$	−5.00000	−	8.66025i	−0.170598	−	0.295484i	−0.938629	+	0.344928i	$0.887903\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.10102			0.0715196			0.0357598	−	0.999360i	$-0.488615\pi$
$863$	2.10102			0.0715196			0.0357598	+	0.999360i	$0.488615\pi$
$864$		0			0
$865$	−44.4949			−1.51287
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.89898	+	13.6814i	0.267955	+	0.464111i
$870$		0			0
$871$	7.59592	−	13.1565i	0.257378	−	0.445792i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.27526	−	5.67291i	0.110724	−	0.191779i
$876$		0			0
$877$	13.2474	+	22.9453i	0.447335	+	0.774806i	0.998212	−	0.0597803i	$-0.0190400\pi$
$877$	13.2474	+	22.9453i	0.447335	+	0.774806i	−0.550877	+	0.834586i	$0.685707\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.5959			0.660203			0.330102	−	0.943945i	$-0.392917\pi$
$881$	19.5959			0.660203			0.330102	+	0.943945i	$0.392917\pi$
$882$		0			0
$883$	0.202041			0.00679922			0.00339961	−	0.999994i	$-0.498918\pi$
$883$	0.202041			0.00679922			0.00339961	+	0.999994i	$0.498918\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.8990	+	29.2699i	0.567412	+	0.982787i	0.996821	+	0.0796764i	$0.0253887\pi$
$887$	16.8990	+	29.2699i	0.567412	+	0.982787i	−0.429409	+	0.903110i	$0.641278\pi$
$888$		0			0
$889$	−1.50000	+	2.59808i	−0.0503084	+	0.0871367i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−36.4949	+	63.2110i	−1.22126	+	2.11528i
$894$		0			0
$895$	−15.0000	−	25.9808i	−0.501395	−	0.868441i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.3939			0.580118
$900$		0			0
$901$	−2.20204			−0.0733606
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.50000	+	12.9904i	0.249308	+	0.431815i
$906$		0			0
$907$	−13.3485	+	23.1202i	−0.443229	+	0.767695i	−0.997927	−	0.0643570i	$-0.979500\pi$
$907$	−13.3485	+	23.1202i	−0.443229	+	0.767695i	0.554698	+	0.832052i	$0.312834\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.9949	−	39.8283i	0.761855	−	1.31957i	−0.180038	−	0.983660i	$-0.557622\pi$
$911$	22.9949	−	39.8283i	0.761855	−	1.31957i	0.941893	−	0.335912i	$-0.109044\pi$
$912$		0			0
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.4495			−0.444141
$918$		0			0
$919$	−3.69694			−0.121951			−0.0609754	−	0.998139i	$-0.519421\pi$
$919$	−3.69694			−0.121951			−0.0609754	+	0.998139i	$0.519421\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.2474	+	41.9978i	0.798114	+	1.38237i
$924$		0			0
$925$	26.8990	−	46.5904i	0.884433	−	1.53188i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.1464	+	29.6985i	−0.562556	+	0.974376i	0.434716	+	0.900567i	$0.356849\pi$
$929$	−17.1464	+	29.6985i	−0.562556	+	0.974376i	−0.997272	+	0.0738083i	$0.976485\pi$
$930$		0			0
$931$	3.72474	+	6.45145i	0.122074	+	0.211438i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13.7980			0.451242
$936$		0			0
$937$	6.40408			0.209212			0.104606	−	0.994514i	$-0.466642\pi$
$937$	6.40408			0.209212			0.104606	+	0.994514i	$0.466642\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.72474	+	2.98735i	0.0562251	+	0.0973847i	0.892768	−	0.450517i	$-0.148760\pi$
$941$	1.72474	+	2.98735i	0.0562251	+	0.0973847i	−0.836543	+	0.547901i	$0.815427\pi$
$942$		0			0
$943$	4.89898	−	8.48528i	0.159533	−	0.276319i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.75255	+	3.03551i	−0.0569503	+	0.0986408i	−0.893095	−	0.449868i	$-0.851471\pi$
$947$	−1.75255	+	3.03551i	−0.0569503	+	0.0986408i	0.836145	+	0.548509i	$0.184804\pi$
$948$		0			0
$949$	7.10102	+	12.2993i	0.230509	+	0.399253i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−55.3939			−1.79438			−0.897192	−	0.441641i	$-0.854396\pi$
$953$	−55.3939			−1.79438			−0.897192	+	0.441641i	$0.854396\pi$
$954$		0			0
$955$	−47.9444			−1.55144
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.89898	−	10.2173i	−0.190488	−	0.329935i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.9722	+	24.2005i	−0.449781	+	0.779043i
$966$		0			0
$967$	−7.29796	−	12.6404i	−0.234687	−	0.406489i	0.724495	−	0.689280i	$-0.242073\pi$
$967$	−7.29796	−	12.6404i	−0.234687	−	0.406489i	−0.959182	+	0.282791i	$0.908740\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−53.9444			−1.73116			−0.865579	−	0.500773i	$-0.833049\pi$
$971$	−53.9444			−1.73116			−0.865579	+	0.500773i	$0.833049\pi$
$972$		0			0
$973$	−9.44949			−0.302937
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.797959	+	1.38211i	0.0255290	+	0.0442175i	0.878508	−	0.477728i	$-0.158540\pi$
$977$	0.797959	+	1.38211i	0.0255290	+	0.0442175i	−0.852979	+	0.521946i	$0.825206\pi$
$978$		0			0
$979$	−7.10102	+	12.2993i	−0.226950	+	0.393088i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.5959	+	39.1373i	−0.720698	+	1.24829i	0.240023	+	0.970767i	$0.422845\pi$
$983$	−22.5959	+	39.1373i	−0.720698	+	1.24829i	−0.960720	+	0.277518i	$0.910488\pi$
$984$		0			0
$985$	21.8990	+	37.9301i	0.697760	+	1.20855i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.89898			−0.0921822
$990$		0			0
$991$	−17.7980			−0.565371			−0.282685	−	0.959213i	$-0.591225\pi$
$991$	−17.7980			−0.565371			−0.282685	+	0.959213i	$0.591225\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.8990	−	20.6096i	−0.377223	−	0.653369i
$996$		0			0
$997$	−8.92679	+	15.4616i	−0.282714	+	0.489675i	−0.972052	−	0.234764i	$-0.924568\pi$
$997$	−8.92679	+	15.4616i	−0.282714	+	0.489675i	0.689338	+	0.724440i	$0.257901\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.e.2017.2		4
3.2	odd	2		1008.2.r.e.673.2		4
4.3	odd	2		378.2.f.d.127.2		4
9.2	odd	6		9072.2.a.bk.1.2		2
9.4	even	3	inner	3024.2.r.e.1009.2		4
9.5	odd	6		1008.2.r.e.337.1		4
9.7	even	3		9072.2.a.bd.1.1		2
12.11	even	2		126.2.f.c.43.1	✓	4
28.3	even	6		2646.2.h.n.667.2		4
28.11	odd	6		2646.2.h.m.667.1		4
28.19	even	6		2646.2.e.k.2125.1		4
28.23	odd	6		2646.2.e.l.2125.2		4
28.27	even	2		2646.2.f.k.883.1		4
36.7	odd	6		1134.2.a.i.1.1		2
36.11	even	6		1134.2.a.p.1.2		2
36.23	even	6		126.2.f.c.85.2	yes	4
36.31	odd	6		378.2.f.d.253.2		4
84.11	even	6		882.2.h.k.79.1		4
84.23	even	6		882.2.e.m.655.2		4
84.47	odd	6		882.2.e.n.655.1		4
84.59	odd	6		882.2.h.l.79.2		4
84.83	odd	2		882.2.f.j.295.2		4
252.23	even	6		882.2.h.k.67.1		4
252.31	even	6		2646.2.e.k.1549.1		4
252.59	odd	6		882.2.e.n.373.1		4
252.67	odd	6		2646.2.e.l.1549.2		4
252.83	odd	6		7938.2.a.bn.1.1		2
252.95	even	6		882.2.e.m.373.2		4
252.103	even	6		2646.2.h.n.361.2		4
252.131	odd	6		882.2.h.l.67.2		4
252.139	even	6		2646.2.f.k.1765.1		4
252.167	odd	6		882.2.f.j.589.1		4
252.223	even	6		7938.2.a.bm.1.2		2
252.247	odd	6		2646.2.h.m.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.1	✓	4	12.11	even	2
126.2.f.c.85.2	yes	4	36.23	even	6
378.2.f.d.127.2		4	4.3	odd	2
378.2.f.d.253.2		4	36.31	odd	6
882.2.e.m.373.2		4	252.95	even	6
882.2.e.m.655.2		4	84.23	even	6
882.2.e.n.373.1		4	252.59	odd	6
882.2.e.n.655.1		4	84.47	odd	6
882.2.f.j.295.2		4	84.83	odd	2
882.2.f.j.589.1		4	252.167	odd	6
882.2.h.k.67.1		4	252.23	even	6
882.2.h.k.79.1		4	84.11	even	6
882.2.h.l.67.2		4	252.131	odd	6
882.2.h.l.79.2		4	84.59	odd	6
1008.2.r.e.337.1		4	9.5	odd	6
1008.2.r.e.673.2		4	3.2	odd	2
1134.2.a.i.1.1		2	36.7	odd	6
1134.2.a.p.1.2		2	36.11	even	6
2646.2.e.k.1549.1		4	252.31	even	6
2646.2.e.k.2125.1		4	28.19	even	6
2646.2.e.l.1549.2		4	252.67	odd	6
2646.2.e.l.2125.2		4	28.23	odd	6
2646.2.f.k.883.1		4	28.27	even	2
2646.2.f.k.1765.1		4	252.139	even	6
2646.2.h.m.361.1		4	252.247	odd	6
2646.2.h.m.667.1		4	28.11	odd	6
2646.2.h.n.361.2		4	252.103	even	6
2646.2.h.n.667.2		4	28.3	even	6
3024.2.r.e.1009.2		4	9.4	even	3	inner
3024.2.r.e.2017.2		4	1.1	even	1	trivial
7938.2.a.bm.1.2		2	252.223	even	6
7938.2.a.bn.1.1		2	252.83	odd	6
9072.2.a.bd.1.1		2	9.7	even	3
9072.2.a.bk.1.2		2	9.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72474 + 2.98735i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(1.72474 + 2.98735i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-1.00000 + 1.73205i) q^{11} +(2.44949 + 4.24264i) q^{13} -2.00000 q^{17} -7.44949 q^{19} +(0.500000 + 0.866025i) q^{23} +(-3.44949 + 5.97469i) q^{25} +(1.44949 - 2.51059i) q^{29} +(3.00000 + 5.19615i) q^{31} -3.44949 q^{35} -7.79796 q^{37} +(-4.89898 - 8.48528i) q^{41} +(-1.44949 + 2.51059i) q^{43} +(4.89898 - 8.48528i) q^{47} +(-0.500000 - 0.866025i) q^{49} +1.10102 q^{53} -6.89898 q^{55} +(1.00000 + 1.73205i) q^{59} +(-5.72474 + 9.91555i) q^{61} +(-8.44949 + 14.6349i) q^{65} +(-1.55051 - 2.68556i) q^{67} +9.89898 q^{71} +2.89898 q^{73} +(-1.00000 - 1.73205i) q^{77} +(3.94949 - 6.84072i) q^{79} +(-1.00000 + 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} +7.10102 q^{89} -4.89898 q^{91} +(-12.8485 - 22.2542i) q^{95} +(3.44949 - 5.97469i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{5} - 2 q^{7} - 4 q^{11} - 8 q^{17} - 20 q^{19} + 2 q^{23} - 4 q^{25} - 4 q^{29} + 12 q^{31} - 4 q^{35} + 8 q^{37} + 4 q^{43} - 2 q^{49} + 24 q^{53} - 8 q^{55} + 4 q^{59} - 18 q^{61} - 24 q^{65} - 16 q^{67} + 20 q^{71} - 8 q^{73} - 4 q^{77} + 6 q^{79} - 4 q^{83} - 4 q^{85} + 48 q^{89} - 22 q^{95} + 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^11 - 8 * q^17 - 20 * q^19 + 2 * q^23 - 4 * q^25 - 4 * q^29 + 12 * q^31 - 4 * q^35 + 8 * q^37 + 4 * q^43 - 2 * q^49 + 24 * q^53 - 8 * q^55 + 4 * q^59 - 18 * q^61 - 24 * q^65 - 16 * q^67 + 20 * q^71 - 8 * q^73 - 4 * q^77 + 6 * q^79 - 4 * q^83 - 4 * q^85 + 48 * q^89 - 22 * q^95 + 4 * q^97

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