LMFDB - Embedded newform 3024.2.t.l.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.l.1873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.84095 q^{5} +(-0.676469 - 2.55781i) q^{7} +O(q^{10})$	$q-3.84095 q^{5} +(-0.676469 - 2.55781i) q^{7} +1.80663 q^{11} +(-0.692713 - 1.19981i) q^{13} +(0.833405 + 1.44350i) q^{17} +(0.0802084 - 0.138925i) q^{19} +3.20038 q^{23} +9.75291 q^{25} +(3.78000 - 6.54716i) q^{29} +(1.61011 - 2.78879i) q^{31} +(2.59829 + 9.82442i) q^{35} +(1.58395 - 2.74348i) q^{37} +(-6.00329 - 10.3980i) q^{41} +(-3.45480 + 5.98389i) q^{43} +(-5.71921 - 9.90595i) q^{47} +(-6.08478 + 3.46056i) q^{49} +(-1.37450 - 2.38071i) q^{53} -6.93918 q^{55} +(-7.53527 + 13.0515i) q^{59} +(4.60143 + 7.96990i) q^{61} +(2.66068 + 4.60843i) q^{65} +(-6.16830 + 10.6838i) q^{67} -6.93289 q^{71} +(-6.22457 - 10.7813i) q^{73} +(-1.22213 - 4.62102i) q^{77} +(8.03716 + 13.9208i) q^{79} +(-1.45280 + 2.51633i) q^{83} +(-3.20107 - 5.54441i) q^{85} +(-5.04034 + 8.73012i) q^{89} +(-2.60030 + 2.58347i) q^{91} +(-0.308077 + 0.533604i) q^{95} +(4.18830 - 7.25435i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 - 7 * q^7	$ 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−3.84095			−1.71773			−0.858863	−	0.512205i	$-0.828829\pi$
$5$	−3.84095			−1.71773			−0.858863	+	0.512205i	$0.828829\pi$
$6$		0			0
$7$	−0.676469	−	2.55781i	−0.255681	−	0.966761i
$7$	−0.676469	−	2.55781i	−0.255681	−	0.966761i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.80663			0.544720			0.272360	−	0.962195i	$-0.412196\pi$
$11$	1.80663			0.544720			0.272360	+	0.962195i	$0.412196\pi$
$12$		0			0
$13$	−0.692713	−	1.19981i	−0.192124	−	0.332769i	0.753830	−	0.657070i	$-0.228204\pi$
$13$	−0.692713	−	1.19981i	−0.192124	−	0.332769i	−0.945954	+	0.324301i	$0.894871\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.833405	+	1.44350i	0.202130	+	0.350100i	0.949215	−	0.314629i	$-0.101880\pi$
$17$	0.833405	+	1.44350i	0.202130	+	0.350100i	−0.747084	+	0.664729i	$0.768547\pi$
$18$		0			0
$19$	0.0802084	−	0.138925i	0.0184011	−	0.0318716i	−0.856678	−	0.515851i	$-0.827476\pi$
$19$	0.0802084	−	0.138925i	0.0184011	−	0.0318716i	0.875079	+	0.483980i	$0.160809\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.20038			0.667326			0.333663	−	0.942692i	$-0.391715\pi$
$23$	3.20038			0.667326			0.333663	+	0.942692i	$0.391715\pi$
$24$		0			0
$25$	9.75291			1.95058
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.78000	−	6.54716i	0.701929	−	1.21578i	−0.265859	−	0.964012i	$-0.585656\pi$
$29$	3.78000	−	6.54716i	0.701929	−	1.21578i	0.967788	−	0.251765i	$-0.0810110\pi$
$30$		0			0
$31$	1.61011	−	2.78879i	0.289184	−	0.500881i	−0.684431	−	0.729077i	$-0.739949\pi$
$31$	1.61011	−	2.78879i	0.289184	−	0.500881i	0.973615	+	0.228196i	$0.0732828\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.59829	+	9.82442i	0.439190	+	1.66063i
$36$		0			0
$37$	1.58395	−	2.74348i	0.260399	−	0.451025i	−0.705949	−	0.708263i	$-0.749479\pi$
$37$	1.58395	−	2.74348i	0.260399	−	0.451025i	0.966348	+	0.257238i	$0.0828124\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.00329	−	10.3980i	−0.937556	−	1.62389i	−0.770011	−	0.638030i	$-0.779750\pi$
$41$	−6.00329	−	10.3980i	−0.937556	−	1.62389i	−0.167545	−	0.985864i	$-0.553584\pi$
$42$		0			0
$43$	−3.45480	+	5.98389i	−0.526852	+	0.912535i	0.472658	+	0.881246i	$0.343295\pi$
$43$	−3.45480	+	5.98389i	−0.526852	+	0.912535i	−0.999510	+	0.0312891i	$0.990039\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.71921	−	9.90595i	−0.834232	−	1.44493i	−0.894654	−	0.446759i	$-0.852578\pi$
$47$	−5.71921	−	9.90595i	−0.834232	−	1.44493i	0.0604225	−	0.998173i	$-0.480755\pi$
$48$		0			0
$49$	−6.08478	+	3.46056i	−0.869254	+	0.494366i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.37450	−	2.38071i	−0.188802	−	0.327015i	0.756049	−	0.654515i	$-0.227127\pi$
$53$	−1.37450	−	2.38071i	−0.188802	−	0.327015i	−0.944851	+	0.327500i	$0.893794\pi$
$54$		0			0
$55$	−6.93918			−0.935679
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.53527	+	13.0515i	−0.981009	+	1.69916i	−0.322527	+	0.946560i	$0.604532\pi$
$59$	−7.53527	+	13.0515i	−0.981009	+	1.69916i	−0.658482	+	0.752597i	$0.728801\pi$
$60$		0			0
$61$	4.60143	+	7.96990i	0.589152	+	1.02044i	0.994344	+	0.106210i	$0.0338715\pi$
$61$	4.60143	+	7.96990i	0.589152	+	1.02044i	−0.405192	+	0.914232i	$0.632795\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.66068	+	4.60843i	0.330016	+	0.571605i
$66$		0			0
$67$	−6.16830	+	10.6838i	−0.753578	+	1.30523i	0.192501	+	0.981297i	$0.438340\pi$
$67$	−6.16830	+	10.6838i	−0.753578	+	1.30523i	−0.946078	+	0.323938i	$0.894993\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.93289			−0.822783			−0.411391	−	0.911459i	$-0.634957\pi$
$71$	−6.93289			−0.822783			−0.411391	+	0.911459i	$0.634957\pi$
$72$		0			0
$73$	−6.22457	−	10.7813i	−0.728531	−	1.26185i	−0.957504	−	0.288420i	$-0.906870\pi$
$73$	−6.22457	−	10.7813i	−0.728531	−	1.26185i	0.228973	−	0.973433i	$-0.426463\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.22213	−	4.62102i	−0.139275	−	0.526614i
$78$		0			0
$79$	8.03716	+	13.9208i	0.904251	+	1.56621i	0.821920	+	0.569604i	$0.192903\pi$
$79$	8.03716	+	13.9208i	0.904251	+	1.56621i	0.0823313	+	0.996605i	$0.473763\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.45280	+	2.51633i	−0.159466	+	0.276203i	−0.934676	−	0.355500i	$-0.884311\pi$
$83$	−1.45280	+	2.51633i	−0.159466	+	0.276203i	0.775210	+	0.631703i	$0.217644\pi$
$84$		0			0
$85$	−3.20107	−	5.54441i	−0.347205	−	0.601376i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.04034	+	8.73012i	−0.534275	+	0.925391i	0.464923	+	0.885351i	$0.346082\pi$
$89$	−5.04034	+	8.73012i	−0.534275	+	0.925391i	−0.999198	+	0.0400399i	$0.987251\pi$
$90$		0			0
$91$	−2.60030	+	2.58347i	−0.272585	+	0.270821i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.308077	+	0.533604i	−0.0316080	+	0.0547466i
$96$		0			0
$97$	4.18830	−	7.25435i	0.425257	−	0.736567i	−0.571187	−	0.820820i	$-0.693517\pi$
$97$	4.18830	−	7.25435i	0.425257	−	0.736567i	0.996444	+	0.0842527i	$0.0268503\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.11500			−0.807473			−0.403736	−	0.914875i	$-0.632289\pi$
$101$	−8.11500			−0.807473			−0.403736	+	0.914875i	$0.632289\pi$
$102$		0			0
$103$	7.53782			0.742723			0.371362	−	0.928488i	$-0.378891\pi$
$103$	7.53782			0.742723			0.371362	+	0.928488i	$0.378891\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.95731	+	5.12221i	−0.285894	+	0.495183i	−0.972826	−	0.231539i	$-0.925624\pi$
$107$	−2.95731	+	5.12221i	−0.285894	+	0.495183i	0.686932	+	0.726722i	$0.258957\pi$
$108$		0			0
$109$	−4.48409	−	7.76668i	−0.429498	−	0.743913i	0.567331	−	0.823490i	$-0.307976\pi$
$109$	−4.48409	−	7.76668i	−0.429498	−	0.743913i	−0.996829	+	0.0795776i	$0.974643\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.98131	+	13.8240i	0.750819	+	1.30046i	0.947426	+	0.319974i	$0.103674\pi$
$113$	7.98131	+	13.8240i	0.750819	+	1.30046i	−0.196608	+	0.980482i	$0.562993\pi$
$114$		0			0
$115$	−12.2925			−1.14628
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.12842	−	3.10817i	0.286782	−	0.284926i
$120$		0			0
$121$	−7.73608			−0.703280
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−18.2557			−1.63284
$126$		0			0
$127$	−8.60913			−0.763937			−0.381968	−	0.924175i	$-0.624754\pi$
$127$	−8.60913			−0.763937			−0.381968	+	0.924175i	$0.624754\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.92966			−0.168595			−0.0842976	−	0.996441i	$-0.526865\pi$
$131$	−1.92966			−0.168595			−0.0842976	+	0.996441i	$0.526865\pi$
$132$		0			0
$133$	−0.409602	−	0.111179i	−0.0355170	−	0.00964047i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.70885			0.316868			0.158434	−	0.987370i	$-0.449355\pi$
$137$	3.70885			0.316868			0.158434	+	0.987370i	$0.449355\pi$
$138$		0			0
$139$	−0.134568	−	0.233079i	−0.0114139	−	0.0197695i	0.860262	−	0.509852i	$-0.170300\pi$
$139$	−0.134568	−	0.233079i	−0.0114139	−	0.0197695i	−0.871676	+	0.490083i	$0.836967\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.25148	−	2.16762i	−0.104654	−	0.181266i
$144$		0			0
$145$	−14.5188	+	25.1473i	−1.20572	+	2.08837i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.31760			−0.681404			−0.340702	−	0.940171i	$-0.610665\pi$
$149$	−8.31760			−0.681404			−0.340702	+	0.940171i	$0.610665\pi$
$150$		0			0
$151$	−9.74138			−0.792742			−0.396371	−	0.918090i	$-0.629731\pi$
$151$	−9.74138			−0.792742			−0.396371	+	0.918090i	$0.629731\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.18434	+	10.7116i	−0.496738	+	0.860376i
$156$		0			0
$157$	−12.1290	+	21.0081i	−0.968001	+	1.67663i	−0.266674	+	0.963787i	$0.585925\pi$
$157$	−12.1290	+	21.0081i	−0.968001	+	1.67663i	−0.701327	+	0.712840i	$0.747409\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.16496	−	8.18597i	−0.170623	−	0.645145i
$162$		0			0
$163$	−3.91401	+	6.77927i	−0.306569	+	0.530993i	−0.977609	−	0.210428i	$-0.932514\pi$
$163$	−3.91401	+	6.77927i	−0.306569	+	0.530993i	0.671040	+	0.741421i	$0.265848\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.15395	−	3.73076i	−0.166678	−	0.288695i	0.770572	−	0.637353i	$-0.219971\pi$
$167$	−2.15395	−	3.73076i	−0.166678	−	0.288695i	−0.937250	+	0.348658i	$0.886637\pi$
$168$		0			0
$169$	5.54030	−	9.59608i	0.426177	−	0.738160i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.66797	−	15.0134i	−0.659014	−	1.14144i	−0.980871	−	0.194657i	$-0.937641\pi$
$173$	−8.66797	−	15.0134i	−0.659014	−	1.14144i	0.321858	−	0.946788i	$-0.395693\pi$
$174$		0			0
$175$	−6.59754	−	24.9461i	−0.498728	−	1.88575i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.68644	−	16.7774i	−0.723998	−	1.25400i	−0.959385	−	0.282100i	$-0.908969\pi$
$179$	−9.68644	−	16.7774i	−0.723998	−	1.25400i	0.235387	−	0.971902i	$-0.424364\pi$
$180$		0			0
$181$	2.89036			0.214839			0.107420	−	0.994214i	$-0.465741\pi$
$181$	2.89036			0.214839			0.107420	+	0.994214i	$0.465741\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.08387	+	10.5376i	−0.447295	+	0.774737i
$186$		0			0
$187$	1.50566	+	2.60787i	0.110104	+	0.190706i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.85022	−	3.20468i	−0.133877	−	0.231882i	0.791291	−	0.611440i	$-0.209409\pi$
$191$	−1.85022	−	3.20468i	−0.133877	−	0.231882i	−0.925168	+	0.379558i	$0.876076\pi$
$192$		0			0
$193$	6.38351	−	11.0566i	0.459495	−	0.795869i	−0.539439	−	0.842025i	$-0.681364\pi$
$193$	6.38351	−	11.0566i	0.459495	−	0.795869i	0.998934	+	0.0461554i	$0.0146970\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.44715			−0.174352			−0.0871762	−	0.996193i	$-0.527784\pi$
$197$	−2.44715			−0.174352			−0.0871762	+	0.996193i	$0.527784\pi$
$198$		0			0
$199$	−2.24829	−	3.89415i	−0.159377	−	0.276049i	0.775267	−	0.631633i	$-0.217615\pi$
$199$	−2.24829	−	3.89415i	−0.159377	−	0.276049i	−0.934644	+	0.355584i	$0.884282\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−19.3034	−	5.23958i	−1.35484	−	0.367746i
$204$		0			0
$205$	23.0583	+	39.9382i	1.61046	+	2.78941i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.144907	−	0.250986i	0.0100234	−	0.0173611i
$210$		0			0
$211$	−1.09087	−	1.88945i	−0.0750987	−	0.130075i	0.826030	−	0.563625i	$-0.190594\pi$
$211$	−1.09087	−	1.88945i	−0.0750987	−	0.130075i	−0.901129	+	0.433551i	$0.857261\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.2697	−	22.9838i	0.904988	−	1.56749i
$216$		0			0
$217$	−8.22237	−	2.23182i	−0.558171	−	0.151506i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.15462	−	1.99986i	0.0776682	−	0.134525i
$222$		0			0
$223$	2.87967	−	4.98773i	0.192837	−	0.334003i	−0.753352	−	0.657617i	$-0.771564\pi$
$223$	2.87967	−	4.98773i	0.192837	−	0.334003i	0.946189	+	0.323614i	$0.104898\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.5827			1.10063			0.550316	−	0.834956i	$-0.314507\pi$
$227$	16.5827			1.10063			0.550316	+	0.834956i	$0.314507\pi$
$228$		0			0
$229$	−14.5938			−0.964382			−0.482191	−	0.876066i	$-0.660159\pi$
$229$	−14.5938			−0.964382			−0.482191	+	0.876066i	$0.660159\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.949438	+	1.64448i	−0.0621998	+	0.107733i	−0.895448	−	0.445165i	$-0.853145\pi$
$233$	−0.949438	+	1.64448i	−0.0621998	+	0.107733i	0.833249	+	0.552898i	$0.186478\pi$
$234$		0			0
$235$	21.9672	+	38.0483i	1.43298	+	2.48200i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.46351	−	7.73103i	−0.288721	−	0.500079i	0.684784	−	0.728746i	$-0.259897\pi$
$239$	−4.46351	−	7.73103i	−0.288721	−	0.500079i	−0.973505	+	0.228667i	$0.926563\pi$
$240$		0			0
$241$	−24.2929			−1.56485			−0.782423	−	0.622748i	$-0.786016\pi$
$241$	−24.2929			−1.56485			−0.782423	+	0.622748i	$0.786016\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	23.3713	−	13.2918i	1.49314	−	0.849185i
$246$		0			0
$247$	−0.222246			−0.0141411
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.64873			−0.356545			−0.178272	−	0.983981i	$-0.557051\pi$
$251$	−5.64873			−0.356545			−0.178272	+	0.983981i	$0.557051\pi$
$252$		0			0
$253$	5.78191			0.363506
$254$		0			0
$255$		0			0
$256$		0			0
$257$	23.5711			1.47033			0.735163	−	0.677891i	$-0.237106\pi$
$257$	23.5711			1.47033			0.735163	+	0.677891i	$0.237106\pi$
$258$		0			0
$259$	−8.08879	−	2.19556i	−0.502613	−	0.136425i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	25.6405			1.58106			0.790531	−	0.612422i	$-0.209805\pi$
$263$	25.6405			1.58106			0.790531	+	0.612422i	$0.209805\pi$
$264$		0			0
$265$	5.27940	+	9.14419i	0.324311	+	0.561723i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.27239	+	14.3282i	0.504376	+	0.873606i	0.999987	+	0.00506090i	$0.00161094\pi$
$269$	8.27239	+	14.3282i	0.504376	+	0.873606i	−0.495611	+	0.868545i	$0.665056\pi$
$270$		0			0
$271$	−8.90748	+	15.4282i	−0.541091	+	0.937197i	0.457751	+	0.889081i	$0.348655\pi$
$271$	−8.90748	+	15.4282i	−0.541091	+	0.937197i	−0.998842	+	0.0481166i	$0.984678\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	17.6199			1.06252
$276$		0			0
$277$	−5.84382			−0.351121			−0.175560	−	0.984469i	$-0.556174\pi$
$277$	−5.84382			−0.351121			−0.175560	+	0.984469i	$0.556174\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.5591	−	18.2889i	0.629905	−	1.09103i	−0.357666	−	0.933850i	$-0.616427\pi$
$281$	10.5591	−	18.2889i	0.629905	−	1.09103i	0.987570	−	0.157177i	$-0.0502394\pi$
$282$		0			0
$283$	−6.38811	+	11.0645i	−0.379734	+	0.657718i	−0.991023	−	0.133689i	$-0.957318\pi$
$283$	−6.38811	+	11.0645i	−0.379734	+	0.657718i	0.611289	+	0.791407i	$0.290651\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.5351	+	22.3892i	−1.33020	+	1.32159i
$288$		0			0
$289$	7.11087	−	12.3164i	0.418287	−	0.724494i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.93828	−	10.2854i	−0.346918	−	0.600880i	0.638782	−	0.769388i	$-0.279439\pi$
$293$	−5.93828	−	10.2854i	−0.346918	−	0.600880i	−0.985700	+	0.168508i	$0.946105\pi$
$294$		0			0
$295$	28.9426	−	50.1301i	1.68510	−	2.91869i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.21695	−	3.83986i	−0.128209	−	0.222065i
$300$		0			0
$301$	17.6427	+	4.78881i	1.01691	+	0.276022i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−17.6739	−	30.6120i	−1.01200	−	1.75284i
$306$		0			0
$307$	3.93298			0.224467			0.112234	−	0.993682i	$-0.464200\pi$
$307$	3.93298			0.224467			0.112234	+	0.993682i	$0.464200\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.991107	+	1.71665i	−0.0562005	+	0.0973422i	−0.892757	−	0.450539i	$-0.851232\pi$
$311$	−0.991107	+	1.71665i	−0.0562005	+	0.0973422i	0.836556	+	0.547881i	$0.184565\pi$
$312$		0			0
$313$	−10.2497	−	17.7530i	−0.579349	−	1.00346i	−0.995554	−	0.0941908i	$-0.969974\pi$
$313$	−10.2497	−	17.7530i	−0.579349	−	1.00346i	0.416205	−	0.909271i	$-0.363360\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.75708	+	8.23951i	0.267184	+	0.462777i	0.968134	−	0.250434i	$-0.0805734\pi$
$317$	4.75708	+	8.23951i	0.267184	+	0.462777i	−0.700949	+	0.713211i	$0.747240\pi$
$318$		0			0
$319$	6.82907	−	11.8283i	0.382355	−	0.662258i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.267384			0.0148777
$324$		0			0
$325$	−6.75597	−	11.7017i	−0.374754	−	0.649093i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−21.4687	+	21.3297i	−1.18361	+	1.17595i
$330$		0			0
$331$	0.764929	+	1.32490i	0.0420443	+	0.0728228i	0.886282	−	0.463146i	$-0.153280\pi$
$331$	0.764929	+	1.32490i	0.0420443	+	0.0728228i	−0.844237	+	0.535969i	$0.819946\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	23.6921	−	41.0360i	1.29444	−	2.24204i
$336$		0			0
$337$	10.6972	+	18.5281i	0.582714	+	1.00929i	0.995156	+	0.0983063i	$0.0313425\pi$
$337$	10.6972	+	18.5281i	0.582714	+	1.00929i	−0.412442	+	0.910984i	$0.635324\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.90887	−	5.03831i	0.157524	−	0.272840i
$342$		0			0
$343$	12.9676	+	13.2227i	0.700185	+	0.713961i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.57191	+	4.45467i	−0.138067	+	0.239139i	−0.926765	−	0.375642i	$-0.877422\pi$
$347$	−2.57191	+	4.45467i	−0.138067	+	0.239139i	0.788698	+	0.614781i	$0.210756\pi$
$348$		0			0
$349$	0.207526	−	0.359446i	0.0111086	−	0.0192407i	−0.860418	−	0.509590i	$-0.829797\pi$
$349$	0.207526	−	0.359446i	0.0111086	−	0.0192407i	0.871526	+	0.490349i	$0.163131\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.0824			0.643083			0.321542	−	0.946895i	$-0.395799\pi$
$353$	12.0824			0.643083			0.321542	+	0.946895i	$0.395799\pi$
$354$		0			0
$355$	26.6289			1.41332
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.14926	+	14.1149i	−0.430102	+	0.744958i	−0.996882	−	0.0789113i	$-0.974856\pi$
$359$	−8.14926	+	14.1149i	−0.430102	+	0.744958i	0.566780	+	0.823869i	$0.308189\pi$
$360$		0			0
$361$	9.48713	+	16.4322i	0.499323	+	0.864852i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	23.9083	+	41.4104i	1.25142	+	2.16752i
$366$		0			0
$367$	−34.7000			−1.81133			−0.905664	−	0.423996i	$-0.860627\pi$
$367$	−34.7000			−1.81133			−0.905664	+	0.423996i	$0.860627\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.15959	+	5.12619i	−0.267873	+	0.266139i
$372$		0			0
$373$	−15.5066			−0.802900			−0.401450	−	0.915881i	$-0.631494\pi$
$373$	−15.5066			−0.802900			−0.401450	+	0.915881i	$0.631494\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.4738			−0.539430
$378$		0			0
$379$	16.1820			0.831214			0.415607	−	0.909544i	$-0.363569\pi$
$379$	16.1820			0.831214			0.415607	+	0.909544i	$0.363569\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.34054			0.221791			0.110896	−	0.993832i	$-0.464628\pi$
$383$	4.34054			0.221791			0.110896	+	0.993832i	$0.464628\pi$
$384$		0			0
$385$	4.69414	+	17.7491i	0.239236	+	0.904578i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−25.5463			−1.29525			−0.647624	−	0.761960i	$-0.724237\pi$
$389$	−25.5463			−1.29525			−0.647624	+	0.761960i	$0.724237\pi$
$390$		0			0
$391$	2.66722	+	4.61975i	0.134887	+	0.233631i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−30.8703	−	53.4690i	−1.55326	−	2.69032i
$396$		0			0
$397$	2.28225	−	3.95297i	0.114543	−	0.198394i	−0.803054	−	0.595906i	$-0.796793\pi$
$397$	2.28225	−	3.95297i	0.114543	−	0.198394i	0.917597	+	0.397512i	$0.130126\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.33626			−0.0667294			−0.0333647	−	0.999443i	$-0.510622\pi$
$401$	−1.33626			−0.0667294			−0.0333647	+	0.999443i	$0.510622\pi$
$402$		0			0
$403$	−4.46137			−0.222237
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.86161	−	4.95645i	0.141845	−	0.245682i
$408$		0			0
$409$	−10.3332	+	17.8976i	−0.510944	+	0.884981i	0.488976	+	0.872297i	$0.337371\pi$
$409$	−10.3332	+	17.8976i	−0.510944	+	0.884981i	−0.999920	+	0.0126832i	$0.995963\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	38.4806	+	10.4449i	1.89350	+	0.513958i
$414$		0			0
$415$	5.58015	−	9.66510i	0.273919	−	0.474441i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.5227	+	18.2259i	0.514069	+	0.890394i	0.999867	+	0.0163228i	$0.00519594\pi$
$419$	10.5227	+	18.2259i	0.514069	+	0.890394i	−0.485797	+	0.874071i	$0.661471\pi$
$420$		0			0
$421$	−8.51630	+	14.7507i	−0.415059	+	0.718903i	−0.995435	−	0.0954456i	$-0.969572\pi$
$421$	−8.51630	+	14.7507i	−0.415059	+	0.718903i	0.580376	+	0.814349i	$0.302906\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	8.12813	+	14.0783i	0.394272	+	0.682899i
$426$		0			0
$427$	17.2728	−	17.1610i	0.835888	−	0.830477i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.2925	+	31.6836i	0.881121	+	1.52615i	0.850096	+	0.526627i	$0.176544\pi$
$431$	18.2925	+	31.6836i	0.881121	+	1.52615i	0.0310244	+	0.999519i	$0.490123\pi$
$432$		0			0
$433$	−23.6571			−1.13689			−0.568444	−	0.822722i	$-0.692454\pi$
$433$	−23.6571			−1.13689			−0.568444	+	0.822722i	$0.692454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.256698	−	0.444613i	0.0122795	−	0.0212687i
$438$		0			0
$439$	10.3932	+	18.0016i	0.496041	+	0.859168i	0.999990	−	0.00456551i	$-0.00145325\pi$
$439$	10.3932	+	18.0016i	0.496041	+	0.859168i	−0.503949	+	0.863734i	$0.668120\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.71404	−	6.43290i	−0.176459	−	0.305636i	0.764206	−	0.644972i	$-0.223131\pi$
$443$	−3.71404	−	6.43290i	−0.176459	−	0.305636i	−0.940665	+	0.339336i	$0.889798\pi$
$444$		0			0
$445$	19.3597	−	33.5320i	0.917737	−	1.58957i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.15800			0.385000			0.192500	−	0.981297i	$-0.438340\pi$
$449$	8.15800			0.385000			0.192500	+	0.981297i	$0.438340\pi$
$450$		0			0
$451$	−10.8457	−	18.7854i	−0.510705	−	0.884568i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.98762	−	9.92297i	0.468227	−	0.465196i
$456$		0			0
$457$	−7.15292	−	12.3892i	−0.334600	−	0.579544i	0.648808	−	0.760952i	$-0.275268\pi$
$457$	−7.15292	−	12.3892i	−0.334600	−	0.579544i	−0.983408	+	0.181408i	$0.941934\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.71961	+	13.3708i	−0.359538	+	0.622738i	−0.987884	−	0.155196i	$-0.950399\pi$
$461$	−7.71961	+	13.3708i	−0.359538	+	0.622738i	0.628346	+	0.777934i	$0.283732\pi$
$462$		0			0
$463$	−10.5531	−	18.2785i	−0.490444	−	0.849474i	0.509496	−	0.860473i	$-0.329832\pi$
$463$	−10.5531	−	18.2785i	−0.490444	−	0.849474i	−0.999940	+	0.0109995i	$0.996499\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.49896	−	6.06037i	0.161912	−	0.280440i	−0.773642	−	0.633623i	$-0.781567\pi$
$467$	3.49896	−	6.06037i	0.161912	−	0.280440i	0.935555	+	0.353182i	$0.114900\pi$
$468$		0			0
$469$	31.4998	+	8.55007i	1.45453	+	0.394805i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.24155	+	10.8107i	−0.286987	+	0.497076i
$474$		0			0
$475$	0.782265	−	1.35492i	0.0358928	−	0.0621681i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.08813			0.141100			0.0705500	−	0.997508i	$-0.477525\pi$
$479$	3.08813			0.141100			0.0705500	+	0.997508i	$0.477525\pi$
$480$		0			0
$481$	−4.38888			−0.200116
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.0871	+	27.8636i	−0.730475	+	1.26522i
$486$		0			0
$487$	−4.90011	−	8.48725i	−0.222045	−	0.384594i	0.733384	−	0.679815i	$-0.237940\pi$
$487$	−4.90011	−	8.48725i	−0.222045	−	0.384594i	−0.955429	+	0.295221i	$0.904607\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.98641	+	17.2970i	0.450680	+	0.780601i	0.998428	−	0.0560419i	$-0.0178481\pi$
$491$	9.98641	+	17.2970i	0.450680	+	0.780601i	−0.547748	+	0.836643i	$0.684515\pi$
$492$		0			0
$493$	12.6011			0.567525
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.68989	+	17.7330i	0.210370	+	0.795435i
$498$		0			0
$499$	20.3299			0.910092			0.455046	−	0.890468i	$-0.349623\pi$
$499$	20.3299			0.910092			0.455046	+	0.890468i	$0.349623\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−23.9595			−1.06830			−0.534151	−	0.845389i	$-0.679369\pi$
$503$	−23.9595			−1.06830			−0.534151	+	0.845389i	$0.679369\pi$
$504$		0			0
$505$	31.1693			1.38702
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.0609			−0.445943			−0.222971	−	0.974825i	$-0.571576\pi$
$509$	−10.0609			−0.445943			−0.222971	+	0.974825i	$0.571576\pi$
$510$		0			0
$511$	−23.3657	+	23.2145i	−1.03364	+	1.02695i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−28.9524			−1.27580
$516$		0			0
$517$	−10.3325	−	17.8964i	−0.454423	−	0.787083i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.99821	−	13.8533i	−0.350408	−	0.606924i	0.635913	−	0.771761i	$-0.280624\pi$
$521$	−7.99821	−	13.8533i	−0.350408	−	0.606924i	−0.986321	+	0.164836i	$0.947290\pi$
$522$		0			0
$523$	18.7103	−	32.4072i	0.818146	−	1.41707i	−0.0889016	−	0.996040i	$-0.528336\pi$
$523$	18.7103	−	32.4072i	0.818146	−	1.41707i	0.907047	−	0.421029i	$-0.138331\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.36748			0.233811
$528$		0			0
$529$	−12.7575			−0.554676
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.31711	+	14.4057i	−0.360254	+	0.623978i
$534$		0			0
$535$	11.3589	−	19.6742i	0.491087	−	0.850588i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.9930	+	6.25195i	−0.473500	+	0.269291i
$540$		0			0
$541$	0.229159	−	0.396916i	0.00985233	−	0.0170647i	−0.861057	−	0.508508i	$-0.830197\pi$
$541$	0.229159	−	0.396916i	0.00985233	−	0.0170647i	0.870910	+	0.491443i	$0.163531\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.2232	+	29.8314i	0.737760	+	1.27784i
$546$		0			0
$547$	11.2013	−	19.4011i	0.478931	−	0.829533i	−0.520777	−	0.853693i	$-0.674358\pi$
$547$	11.2013	−	19.4011i	0.478931	−	0.829533i	0.999708	+	0.0241596i	$0.00769098\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.606376	−	1.05027i	−0.0258325	−	0.0447432i
$552$		0			0
$553$	30.1698	−	29.9745i	1.28295	−	1.27464i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.4155	−	18.0401i	−0.441317	−	0.764383i	0.556471	−	0.830867i	$-0.312155\pi$
$557$	−10.4155	−	18.0401i	−0.441317	−	0.764383i	−0.997787	+	0.0664841i	$0.978822\pi$
$558$		0			0
$559$	9.57275			0.404884
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.40302	+	7.62626i	−0.185565	+	0.321409i	−0.943767	−	0.330612i	$-0.892745\pi$
$563$	−4.40302	+	7.62626i	−0.185565	+	0.321409i	0.758202	+	0.652020i	$0.226078\pi$
$564$		0			0
$565$	−30.6558	−	53.0975i	−1.28970	−	2.23383i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.49287	+	16.4421i	0.397962	+	0.689290i	0.993474	−	0.114056i	$-0.0363844\pi$
$569$	9.49287	+	16.4421i	0.397962	+	0.689290i	−0.595513	+	0.803346i	$0.703051\pi$
$570$		0			0
$571$	−7.87986	+	13.6483i	−0.329762	+	0.571164i	−0.982464	−	0.186450i	$-0.940302\pi$
$571$	−7.87986	+	13.6483i	−0.329762	+	0.571164i	0.652703	+	0.757614i	$0.273635\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	31.2131			1.30167
$576$		0			0
$577$	−15.9306	−	27.5927i	−0.663201	−	1.14870i	−0.979770	−	0.200128i	$-0.935864\pi$
$577$	−15.9306	−	27.5927i	−0.663201	−	1.14870i	0.316569	−	0.948570i	$-0.397469\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.41907	+	2.01377i	0.307795	+	0.0835454i
$582$		0			0
$583$	−2.48322	−	4.30106i	−0.102844	−	0.178132i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.3597	+	35.2640i	−0.840333	+	1.45550i	0.0492799	+	0.998785i	$0.484307\pi$
$587$	−20.3597	+	35.2640i	−0.840333	+	1.45550i	−0.889613	+	0.456715i	$0.849026\pi$
$588$		0			0
$589$	−0.258288	−	0.447368i	−0.0106426	−	0.0184335i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.0693	−	24.3688i	0.577759	−	1.00071i	−0.417977	−	0.908458i	$-0.637261\pi$
$593$	14.0693	−	24.3688i	0.577759	−	1.00071i	0.995736	−	0.0922500i	$-0.0294059\pi$
$594$		0			0
$595$	−12.0161	+	11.9383i	−0.492613	+	0.489425i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.4963	+	28.5724i	−0.674020	+	1.16744i	0.302735	+	0.953075i	$0.402100\pi$
$599$	−16.4963	+	28.5724i	−0.674020	+	1.16744i	−0.976754	+	0.214361i	$0.931233\pi$
$600$		0			0
$601$	−1.98103	+	3.43124i	−0.0808079	+	0.139963i	−0.903597	−	0.428383i	$-0.859083\pi$
$601$	−1.98103	+	3.43124i	−0.0808079	+	0.139963i	0.822789	+	0.568347i	$0.192417\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	29.7139			1.20804
$606$		0			0
$607$	−34.0263			−1.38109			−0.690543	−	0.723292i	$-0.742628\pi$
$607$	−34.0263			−1.38109			−0.690543	+	0.723292i	$0.742628\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.92354	+	13.7240i	−0.320552	+	0.555212i
$612$		0			0
$613$	−15.2967	−	26.4946i	−0.617827	−	1.07011i	−0.989881	−	0.141897i	$-0.954680\pi$
$613$	−15.2967	−	26.4946i	−0.617827	−	1.07011i	0.372054	−	0.928211i	$-0.378654\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.7646	−	32.5013i	−0.755435	−	1.30845i	−0.945158	−	0.326614i	$-0.894092\pi$
$617$	−18.7646	−	32.5013i	−0.755435	−	1.30845i	0.189723	−	0.981838i	$-0.439241\pi$
$618$		0			0
$619$	5.84604			0.234972			0.117486	−	0.993075i	$-0.462516\pi$
$619$	5.84604			0.234972			0.117486	+	0.993075i	$0.462516\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	25.7396	+	6.98656i	1.03124	+	0.279911i
$624$		0			0
$625$	21.3547			0.854189
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.28028			0.210539
$630$		0			0
$631$	−25.6347			−1.02050			−0.510251	−	0.860025i	$-0.670448\pi$
$631$	−25.6347			−1.02050			−0.510251	+	0.860025i	$0.670448\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	33.0673			1.31223
$636$		0			0
$637$	8.36703	+	4.90343i	0.331514	+	0.194281i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−25.9647			−1.02554			−0.512772	−	0.858525i	$-0.671381\pi$
$641$	−25.9647			−1.02554			−0.512772	+	0.858525i	$0.671381\pi$
$642$		0			0
$643$	22.5634	+	39.0809i	0.889812	+	1.54120i	0.840097	+	0.542436i	$0.182498\pi$
$643$	22.5634	+	39.0809i	0.889812	+	1.54120i	0.0497151	+	0.998763i	$0.484169\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.70324	+	4.68215i	0.106275	+	0.184074i	0.914259	−	0.405131i	$-0.132774\pi$
$647$	2.70324	+	4.68215i	0.106275	+	0.184074i	−0.807983	+	0.589206i	$0.799441\pi$
$648$		0			0
$649$	−13.6135	+	23.5792i	−0.534375	+	0.925564i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	31.9030			1.24846			0.624231	−	0.781240i	$-0.285412\pi$
$653$	31.9030			1.24846			0.624231	+	0.781240i	$0.285412\pi$
$654$		0			0
$655$	7.41174			0.289600
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.50215	−	4.33385i	0.0974699	−	0.168823i	−0.813167	−	0.582031i	$-0.802258\pi$
$659$	2.50215	−	4.33385i	0.0974699	−	0.168823i	0.910637	+	0.413208i	$0.135592\pi$
$660$		0			0
$661$	−4.81703	+	8.34334i	−0.187361	+	0.324518i	−0.944369	−	0.328887i	$-0.893327\pi$
$661$	−4.81703	+	8.34334i	−0.187361	+	0.324518i	0.757009	+	0.653405i	$0.226660\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.57326	+	0.427034i	0.0610085	+	0.0165597i
$666$		0			0
$667$	12.0975	−	20.9534i	0.468415	−	0.811319i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	8.31308	+	14.3987i	0.320923	+	0.555855i
$672$		0			0
$673$	13.5885	−	23.5359i	0.523797	−	0.907243i	−0.475819	−	0.879543i	$-0.657848\pi$
$673$	13.5885	−	23.5359i	0.523797	−	0.907243i	0.999616	−	0.0276998i	$-0.00881825\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.0251	−	32.9525i	−0.731194	−	1.26647i	−0.956373	−	0.292148i	$-0.905630\pi$
$677$	−19.0251	−	32.9525i	−0.731194	−	1.26647i	0.225179	−	0.974318i	$-0.427703\pi$
$678$		0			0
$679$	−21.3885	−	5.80553i	−0.820815	−	0.222796i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.0571	+	26.0797i	0.576146	+	0.997913i	0.995916	+	0.0902831i	$0.0287772\pi$
$683$	15.0571	+	26.0797i	0.576146	+	0.997913i	−0.419771	+	0.907630i	$0.637889\pi$
$684$		0			0
$685$	−14.2455			−0.544293
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.90427	+	3.29830i	−0.0725470	+	0.125655i
$690$		0			0
$691$	7.19510	+	12.4623i	0.273714	+	0.474087i	0.969810	−	0.243862i	$-0.0784143\pi$
$691$	7.19510	+	12.4623i	0.273714	+	0.474087i	−0.696096	+	0.717949i	$0.745081\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.516871	+	0.895246i	0.0196060	+	0.0339586i
$696$		0			0
$697$	10.0063	−	17.3315i	0.379017	−	0.656477i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.4170			−0.544521			−0.272261	−	0.962224i	$-0.587771\pi$
$701$	−14.4170			−0.544521			−0.272261	+	0.962224i	$0.587771\pi$
$702$		0			0
$703$	−0.254092	−	0.440100i	−0.00958325	−	0.0165987i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.48955	+	20.7566i	0.206456	+	0.780633i
$708$		0			0
$709$	−5.74410	−	9.94907i	−0.215724	−	0.373645i	0.737772	−	0.675050i	$-0.235878\pi$
$709$	−5.74410	−	9.94907i	−0.215724	−	0.373645i	−0.953496	+	0.301405i	$0.902545\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.15296	−	8.92519i	0.192980	−	0.334251i
$714$		0			0
$715$	4.80686	+	8.32573i	0.179766	+	0.311365i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	17.9451	−	31.0818i	0.669240	−	1.15916i	−0.308877	−	0.951102i	$-0.599953\pi$
$719$	17.9451	−	31.0818i	0.669240	−	1.15916i	0.978117	−	0.208055i	$-0.0667134\pi$
$720$		0			0
$721$	−5.09910	−	19.2803i	−0.189901	−	0.718036i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	36.8660	−	63.8539i	1.36917	−	2.37147i
$726$		0			0
$727$	5.03060	−	8.71326i	0.186575	−	0.323157i	−0.757531	−	0.652799i	$-0.773595\pi$
$727$	5.03060	−	8.71326i	0.186575	−	0.323157i	0.944106	+	0.329642i	$0.106928\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−11.5170			−0.425972
$732$		0			0
$733$	33.1381			1.22398			0.611992	−	0.790864i	$-0.290369\pi$
$733$	33.1381			1.22398			0.611992	+	0.790864i	$0.290369\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.1438	+	19.3017i	−0.410489	+	0.710987i
$738$		0			0
$739$	−21.9237	−	37.9729i	−0.806475	−	1.39686i	−0.915291	−	0.402793i	$-0.868039\pi$
$739$	−21.9237	−	37.9729i	−0.806475	−	1.39686i	0.108816	−	0.994062i	$-0.465294\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.50115	+	7.79622i	0.165131	+	0.286016i	0.936702	−	0.350128i	$-0.113862\pi$
$743$	4.50115	+	7.79622i	0.165131	+	0.286016i	−0.771571	+	0.636144i	$0.780529\pi$
$744$		0			0
$745$	31.9475			1.17047
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.1022	+	4.09922i	0.551821	+	0.149782i
$750$		0			0
$751$	−11.1828			−0.408067			−0.204033	−	0.978964i	$-0.565405\pi$
$751$	−11.1828			−0.408067			−0.204033	+	0.978964i	$0.565405\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	37.4162			1.36171
$756$		0			0
$757$	42.1431			1.53172			0.765859	−	0.643009i	$-0.222314\pi$
$757$	42.1431			1.53172			0.765859	+	0.643009i	$0.222314\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.28309			−0.0827620			−0.0413810	−	0.999143i	$-0.513176\pi$
$761$	−2.28309			−0.0827620			−0.0413810	+	0.999143i	$0.513176\pi$
$762$		0			0
$763$	−16.8323	+	16.7234i	−0.609371	+	0.605427i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	20.8791			0.753901
$768$		0			0
$769$	8.96676	+	15.5309i	0.323350	+	0.560058i	0.981177	−	0.193111i	$-0.0618577\pi$
$769$	8.96676	+	15.5309i	0.323350	+	0.560058i	−0.657827	+	0.753169i	$0.728524\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.4807	−	30.2775i	−0.628737	−	1.08901i	−0.987805	−	0.155694i	$-0.950239\pi$
$773$	−17.4807	−	30.2775i	−0.628737	−	1.08901i	0.359068	−	0.933311i	$-0.383095\pi$
$774$		0			0
$775$	15.7032	−	27.1988i	0.564077	−	0.977009i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.92606			−0.0690081
$780$		0			0
$781$	−12.5252			−0.448186
$782$		0			0
$783$		0			0
$784$		0			0
$785$	46.5870	−	80.6910i	1.66276	−	2.87998i
$786$		0			0
$787$	−14.1782	+	24.5573i	−0.505397	+	0.875374i	0.494583	+	0.869130i	$0.335321\pi$
$787$	−14.1782	+	24.5573i	−0.505397	+	0.875374i	−0.999981	+	0.00624370i	$0.998013\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	29.9601	−	29.7662i	1.06526	−	1.05836i
$792$		0			0
$793$	6.37494	−	11.0417i	0.226381	−	0.392103i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.51922	+	16.4878i	0.337188	+	0.584027i	0.983903	−	0.178705i	$-0.0571908\pi$
$797$	9.51922	+	16.4878i	0.337188	+	0.584027i	−0.646715	+	0.762732i	$0.723857\pi$
$798$		0			0
$799$	9.53283	−	16.5113i	0.337247	−	0.584129i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.2455	−	19.4778i	−0.396845	−	0.687356i
$804$		0			0
$805$	8.31551	+	31.4419i	0.293083	+	1.10818i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.4529	+	18.1050i	0.367505	+	0.636538i	0.989175	−	0.146742i	$-0.0468787\pi$
$809$	10.4529	+	18.1050i	0.367505	+	0.636538i	−0.621670	+	0.783280i	$0.713545\pi$
$810$		0			0
$811$	−17.5392			−0.615884			−0.307942	−	0.951405i	$-0.599640\pi$
$811$	−17.5392			−0.615884			−0.307942	+	0.951405i	$0.599640\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.0335	−	26.0388i	0.526601	−	0.912101i
$816$		0			0
$817$	0.554208	+	0.959917i	0.0193893	+	0.0335832i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.4881	−	30.2903i	−0.610339	−	1.05714i	−0.991183	−	0.132499i	$-0.957700\pi$
$821$	−17.4881	−	30.2903i	−0.610339	−	1.05714i	0.380844	−	0.924639i	$-0.375634\pi$
$822$		0			0
$823$	−15.2118	+	26.3475i	−0.530249	+	0.918418i	0.469128	+	0.883130i	$0.344568\pi$
$823$	−15.2118	+	26.3475i	−0.530249	+	0.918418i	−0.999377	+	0.0352878i	$0.988765\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.6276			−0.891158			−0.445579	−	0.895243i	$-0.647002\pi$
$827$	−25.6276			−0.891158			−0.445579	+	0.895243i	$0.647002\pi$
$828$		0			0
$829$	23.9403	+	41.4658i	0.831481	+	1.44017i	0.896864	+	0.442307i	$0.145840\pi$
$829$	23.9403	+	41.4658i	0.831481	+	1.44017i	−0.0653833	+	0.997860i	$0.520827\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.0664	−	5.89933i	−0.348780	−	0.204400i
$834$		0			0
$835$	8.27323	+	14.3297i	0.286307	+	0.495898i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.8466	+	37.8394i	−0.754227	+	1.30636i	0.191530	+	0.981487i	$0.438655\pi$
$839$	−21.8466	+	37.8394i	−0.754227	+	1.30636i	−0.945758	+	0.324873i	$0.894678\pi$
$840$		0			0
$841$	−14.0769	−	24.3818i	−0.485409	−	0.840753i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−21.2800	+	36.8581i	−0.732055	+	1.26796i
$846$		0			0
$847$	5.23322	+	19.7874i	0.179816	+	0.679904i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.06924	−	8.78018i	0.173771	−	0.300981i
$852$		0			0
$853$	8.33994	−	14.4452i	0.285554	−	0.494594i	−0.687189	−	0.726478i	$-0.741156\pi$
$853$	8.33994	−	14.4452i	0.285554	−	0.494594i	0.972743	+	0.231884i	$0.0744890\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.4290			−0.492887			−0.246443	−	0.969157i	$-0.579262\pi$
$857$	−14.4290			−0.492887			−0.246443	+	0.969157i	$0.579262\pi$
$858$		0			0
$859$	−22.7733			−0.777016			−0.388508	−	0.921445i	$-0.627009\pi$
$859$	−22.7733			−0.777016			−0.388508	+	0.921445i	$0.627009\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.97266	+	10.3450i	−0.203312	+	0.352146i	−0.949594	−	0.313484i	$-0.898504\pi$
$863$	−5.97266	+	10.3450i	−0.203312	+	0.352146i	0.746282	+	0.665630i	$0.231837\pi$
$864$		0			0
$865$	33.2933	+	57.6656i	1.13200	+	1.96069i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.5202	+	25.1497i	0.492563	+	0.853145i
$870$		0			0
$871$	17.0914			0.579122
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.3494	+	46.6946i	0.417487	+	1.57857i
$876$		0			0
$877$	−56.6198			−1.91191			−0.955957	−	0.293507i	$-0.905178\pi$
$877$	−56.6198			−1.91191			−0.955957	+	0.293507i	$0.905178\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.41130			0.216002			0.108001	−	0.994151i	$-0.465555\pi$
$881$	6.41130			0.216002			0.108001	+	0.994151i	$0.465555\pi$
$882$		0			0
$883$	25.7180			0.865481			0.432741	−	0.901518i	$-0.357547\pi$
$883$	25.7180			0.865481			0.432741	+	0.901518i	$0.357547\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.9894			0.671180			0.335590	−	0.942008i	$-0.391064\pi$
$887$	19.9894			0.671180			0.335590	+	0.942008i	$0.391064\pi$
$888$		0			0
$889$	5.82381	+	22.0205i	0.195324	+	0.738545i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.83491			−0.0614030
$894$		0			0
$895$	37.2051	+	64.4412i	1.24363	+	2.15403i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.1724	−	21.0832i	−0.405973	−	0.703166i
$900$		0			0
$901$	2.29104	−	3.96819i	0.0763254	−	0.132200i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.1017			−0.369035
$906$		0			0
$907$	−24.3034			−0.806981			−0.403491	−	0.914984i	$-0.632203\pi$
$907$	−24.3034			−0.806981			−0.403491	+	0.914984i	$0.632203\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	19.7871	−	34.2723i	0.655577	−	1.13549i	−0.326171	−	0.945311i	$-0.605759\pi$
$911$	19.7871	−	34.2723i	0.655577	−	1.13549i	0.981749	−	0.190183i	$-0.0609080\pi$
$912$		0			0
$913$	−2.62468	+	4.54608i	−0.0868642	+	0.150453i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.30536	+	4.93571i	0.0431067	+	0.162991i
$918$		0			0
$919$	12.9220	−	22.3815i	0.426257	−	0.738298i	−0.570280	−	0.821450i	$-0.693165\pi$
$919$	12.9220	−	22.3815i	0.426257	−	0.738298i	0.996537	+	0.0831519i	$0.0264987\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.80251	+	8.31818i	0.158076	+	0.273796i
$924$		0			0
$925$	15.4481	−	26.7569i	0.507930	−	0.879761i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.4253	+	44.0379i	0.834178	+	1.44484i	0.894698	+	0.446671i	$0.147391\pi$
$929$	25.4253	+	44.0379i	0.834178	+	1.44484i	−0.0605205	+	0.998167i	$0.519276\pi$
$930$		0			0
$931$	−0.00729213	+	1.12289i	−0.000238990	+	0.0368014i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.78315	−	10.0167i	−0.189129	−	0.327581i
$936$		0			0
$937$	32.7623			1.07030			0.535149	−	0.844758i	$-0.320256\pi$
$937$	32.7623			1.07030			0.535149	+	0.844758i	$0.320256\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	25.3396	−	43.8895i	0.826048	−	1.43076i	−0.0750670	−	0.997178i	$-0.523917\pi$
$941$	25.3396	−	43.8895i	0.826048	−	1.43076i	0.901115	−	0.433579i	$-0.142750\pi$
$942$		0			0
$943$	−19.2128	−	33.2776i	−0.625655	−	1.08367i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.76277	+	9.98140i	0.187265	+	0.324352i	0.944337	−	0.328979i	$-0.106704\pi$
$947$	5.76277	+	9.98140i	0.187265	+	0.324352i	−0.757073	+	0.653331i	$0.773371\pi$
$948$		0			0
$949$	−8.62369	+	14.9367i	−0.279937	+	0.484865i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	45.7747			1.48279			0.741395	−	0.671069i	$-0.234165\pi$
$953$	45.7747			1.48279			0.741395	+	0.671069i	$0.234165\pi$
$954$		0			0
$955$	7.10661	+	12.3090i	0.229965	+	0.398310i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.50892	−	9.48652i	−0.0810173	−	0.306336i
$960$		0			0
$961$	10.3151	+	17.8663i	0.332746	+	0.576332i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−24.5188	+	42.4678i	−0.789287	+	1.36709i
$966$		0			0
$967$	4.07666	+	7.06098i	0.131097	+	0.227066i	0.924100	−	0.382152i	$-0.124817\pi$
$967$	4.07666	+	7.06098i	0.131097	+	0.227066i	−0.793003	+	0.609218i	$0.791484\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.1137	−	24.4457i	0.452932	−	0.784501i	−0.545635	−	0.838023i	$-0.683712\pi$
$971$	14.1137	−	24.4457i	0.452932	−	0.784501i	0.998567	+	0.0535223i	$0.0170448\pi$
$972$		0			0
$973$	−0.505141	+	0.501871i	−0.0161941	+	0.0160893i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.82510	+	13.5535i	−0.250347	+	0.433614i	−0.963621	−	0.267271i	$-0.913878\pi$
$977$	−7.82510	+	13.5535i	−0.250347	+	0.433614i	0.713274	+	0.700885i	$0.247211\pi$
$978$		0			0
$979$	−9.10603	+	15.7721i	−0.291030	+	0.504079i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.95162			0.0941419			0.0470710	−	0.998892i	$-0.485011\pi$
$983$	2.95162			0.0941419			0.0470710	+	0.998892i	$0.485011\pi$
$984$		0			0
$985$	9.39940			0.299490
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.0567	+	19.1507i	−0.351582	+	0.608958i
$990$		0			0
$991$	−15.8182	−	27.3979i	−0.502482	−	0.870324i	−0.999996	−	0.00286819i	$-0.999087\pi$
$991$	−15.8182	−	27.3979i	−0.502482	−	0.870324i	0.497514	−	0.867456i	$-0.334246\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.63557	+	14.9572i	0.273766	+	0.474176i
$996$		0			0
$997$	−1.58522			−0.0502043			−0.0251021	−	0.999685i	$-0.507991\pi$
$997$	−1.58522			−0.0502043			−0.0251021	+	0.999685i	$0.507991\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.l.289.1		22
3.2	odd	2		1008.2.t.k.961.10		22
4.3	odd	2		1512.2.t.d.289.1		22
7.4	even	3		3024.2.q.k.2881.11		22
9.4	even	3		3024.2.q.k.2305.11		22
9.5	odd	6		1008.2.q.k.625.2		22
12.11	even	2		504.2.t.d.457.2	yes	22
21.11	odd	6		1008.2.q.k.529.2		22
28.11	odd	6		1512.2.q.c.1369.11		22
36.23	even	6		504.2.q.d.121.10	yes	22
36.31	odd	6		1512.2.q.c.793.11		22
63.4	even	3	inner	3024.2.t.l.1873.1		22
63.32	odd	6		1008.2.t.k.193.10		22
84.11	even	6		504.2.q.d.25.10	✓	22
252.67	odd	6		1512.2.t.d.361.1		22
252.95	even	6		504.2.t.d.193.2	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.10	✓	22	84.11	even	6
504.2.q.d.121.10	yes	22	36.23	even	6
504.2.t.d.193.2	yes	22	252.95	even	6
504.2.t.d.457.2	yes	22	12.11	even	2
1008.2.q.k.529.2		22	21.11	odd	6
1008.2.q.k.625.2		22	9.5	odd	6
1008.2.t.k.193.10		22	63.32	odd	6
1008.2.t.k.961.10		22	3.2	odd	2
1512.2.q.c.793.11		22	36.31	odd	6
1512.2.q.c.1369.11		22	28.11	odd	6
1512.2.t.d.289.1		22	4.3	odd	2
1512.2.t.d.361.1		22	252.67	odd	6
3024.2.q.k.2305.11		22	9.4	even	3
3024.2.q.k.2881.11		22	7.4	even	3
3024.2.t.l.289.1		22	1.1	even	1	trivial
3024.2.t.l.1873.1		22	63.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-3.84095 q^{5} +(-0.676469 - 2.55781i) q^{7} +O(q^{10})\)	\(q-3.84095 q^{5} +(-0.676469 - 2.55781i) q^{7} +1.80663 q^{11} +(-0.692713 - 1.19981i) q^{13} +(0.833405 + 1.44350i) q^{17} +(0.0802084 - 0.138925i) q^{19} +3.20038 q^{23} +9.75291 q^{25} +(3.78000 - 6.54716i) q^{29} +(1.61011 - 2.78879i) q^{31} +(2.59829 + 9.82442i) q^{35} +(1.58395 - 2.74348i) q^{37} +(-6.00329 - 10.3980i) q^{41} +(-3.45480 + 5.98389i) q^{43} +(-5.71921 - 9.90595i) q^{47} +(-6.08478 + 3.46056i) q^{49} +(-1.37450 - 2.38071i) q^{53} -6.93918 q^{55} +(-7.53527 + 13.0515i) q^{59} +(4.60143 + 7.96990i) q^{61} +(2.66068 + 4.60843i) q^{65} +(-6.16830 + 10.6838i) q^{67} -6.93289 q^{71} +(-6.22457 - 10.7813i) q^{73} +(-1.22213 - 4.62102i) q^{77} +(8.03716 + 13.9208i) q^{79} +(-1.45280 + 2.51633i) q^{83} +(-3.20107 - 5.54441i) q^{85} +(-5.04034 + 8.73012i) q^{89} +(-2.60030 + 2.58347i) q^{91} +(-0.308077 + 0.533604i) q^{95} +(4.18830 - 7.25435i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 - 7 * q^7	\( 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

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