LMFDB - Embedded newform 3024.2.df.e.17.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(17,3024)]

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, 5, 1]))

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

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

chi := DirichletCharacter("3024.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.23
Character	$\chi$	$=$	3024.17
Dual form			3024.2.df.e.1601.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.64567 q^{5} +(-1.05524 - 2.42620i) q^{7} +O(q^{10})$	$q+3.64567 q^{5} +(-1.05524 - 2.42620i) q^{7} -1.39835i q^{11} +(-2.97474 - 1.71747i) q^{13} +(2.41670 - 4.18585i) q^{17} +(-7.23869 + 4.17926i) q^{19} -8.92741i q^{23} +8.29094 q^{25} +(-5.02182 + 2.89935i) q^{29} +(-5.29782 + 3.05870i) q^{31} +(-3.84708 - 8.84514i) q^{35} +(-2.89032 - 5.00617i) q^{37} +(-0.802159 + 1.38938i) q^{41} +(-2.22777 - 3.85862i) q^{43} +(1.51221 - 2.61923i) q^{47} +(-4.77292 + 5.12047i) q^{49} +(4.40240 + 2.54173i) q^{53} -5.09795i q^{55} +(3.21233 + 5.56392i) q^{59} +(-7.78670 - 4.49565i) q^{61} +(-10.8449 - 6.26133i) q^{65} +(-2.53496 - 4.39068i) q^{67} +4.20682i q^{71} +(-0.745839 - 0.430610i) q^{73} +(-3.39269 + 1.47561i) q^{77} +(1.31221 - 2.27282i) q^{79} +(-3.82295 - 6.62154i) q^{83} +(8.81051 - 15.2603i) q^{85} +(4.44212 + 7.69398i) q^{89} +(-1.02785 + 9.02968i) q^{91} +(-26.3899 + 15.2362i) q^{95} +(9.63985 - 5.56557i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.64567			1.63039			0.815197	−	0.579183i	$-0.196628\pi$
$5$	3.64567			1.63039			0.815197	+	0.579183i	$0.196628\pi$
$6$		0			0
$7$	−1.05524	−	2.42620i	−0.398845	−	0.917018i
$7$	−1.05524	−	2.42620i	−0.398845	−	0.917018i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	1.39835i		−	0.421620i	−0.977527	−	0.210810i	$-0.932390\pi$
$11$		−	1.39835i		−	0.421620i	0.977527	−	0.210810i	$-0.0676101\pi$
$12$		0			0
$13$	−2.97474	−	1.71747i	−0.825046	−	0.476340i	0.0271077	−	0.999633i	$-0.491370\pi$
$13$	−2.97474	−	1.71747i	−0.825046	−	0.476340i	−0.852153	+	0.523292i	$0.824704\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.41670	−	4.18585i	0.586137	−	1.01522i	−0.408596	−	0.912715i	$-0.633982\pi$
$17$	2.41670	−	4.18585i	0.586137	−	1.01522i	0.994733	−	0.102503i	$-0.0326852\pi$
$18$		0			0
$19$	−7.23869	+	4.17926i	−1.66067	+	0.958787i	−0.688272	+	0.725453i	$0.741630\pi$
$19$	−7.23869	+	4.17926i	−1.66067	+	0.958787i	−0.972397	+	0.233334i	$0.925036\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	8.92741i		−	1.86149i	−0.365665	−	0.930747i	$-0.619158\pi$
$23$		−	8.92741i		−	1.86149i	0.365665	−	0.930747i	$-0.380842\pi$
$24$		0			0
$25$	8.29094			1.65819
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.02182	+	2.89935i	−0.932529	+	0.538396i	−0.887611	−	0.460595i	$-0.847636\pi$
$29$	−5.02182	+	2.89935i	−0.932529	+	0.538396i	−0.0449185	+	0.998991i	$0.514303\pi$
$30$		0			0
$31$	−5.29782	+	3.05870i	−0.951516	+	0.549358i	−0.893552	−	0.448961i	$-0.851794\pi$
$31$	−5.29782	+	3.05870i	−0.951516	+	0.549358i	−0.0579644	+	0.998319i	$0.518461\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.84708	−	8.84514i	−0.650274	−	1.49510i
$36$		0			0
$37$	−2.89032	−	5.00617i	−0.475165	−	0.823010i	0.524431	−	0.851453i	$-0.324278\pi$
$37$	−2.89032	−	5.00617i	−0.475165	−	0.823010i	−0.999595	+	0.0284435i	$0.990945\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.802159	+	1.38938i	−0.125276	+	0.216985i	−0.921841	−	0.387569i	$-0.873315\pi$
$41$	−0.802159	+	1.38938i	−0.125276	+	0.216985i	0.796565	+	0.604553i	$0.206648\pi$
$42$		0			0
$43$	−2.22777	−	3.85862i	−0.339732	−	0.588434i	0.644650	−	0.764478i	$-0.277003\pi$
$43$	−2.22777	−	3.85862i	−0.339732	−	0.588434i	−0.984382	+	0.176044i	$0.943670\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.51221	−	2.61923i	0.220579	−	0.382053i	−0.734405	−	0.678711i	$-0.762539\pi$
$47$	1.51221	−	2.61923i	0.220579	−	0.382053i	0.954984	+	0.296658i	$0.0958721\pi$
$48$		0			0
$49$	−4.77292	+	5.12047i	−0.681846	+	0.731496i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.40240	+	2.54173i	0.604716	+	0.349133i	0.770895	−	0.636963i	$-0.219809\pi$
$53$	4.40240	+	2.54173i	0.604716	+	0.349133i	−0.166178	+	0.986096i	$0.553143\pi$
$54$		0			0
$55$		−	5.09795i		−	0.687407i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.21233	+	5.56392i	0.418210	+	0.724360i	0.995759	−	0.0919952i	$-0.0293244\pi$
$59$	3.21233	+	5.56392i	0.418210	+	0.724360i	−0.577550	+	0.816355i	$0.695991\pi$
$60$		0			0
$61$	−7.78670	−	4.49565i	−0.996985	−	0.575609i	−0.0896300	−	0.995975i	$-0.528568\pi$
$61$	−7.78670	−	4.49565i	−0.996985	−	0.575609i	−0.907355	+	0.420366i	$0.861902\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.8449	−	6.26133i	−1.34515	−	0.776623i
$66$		0			0
$67$	−2.53496	−	4.39068i	−0.309694	−	0.536407i	0.668601	−	0.743621i	$-0.266893\pi$
$67$	−2.53496	−	4.39068i	−0.309694	−	0.536407i	−0.978295	+	0.207215i	$0.933560\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			4.20682i			0.499258i	0.968342	+	0.249629i	$0.0803087\pi$
$71$			4.20682i			0.499258i	−0.968342	+	0.249629i	$0.919691\pi$
$72$		0			0
$73$	−0.745839	−	0.430610i	−0.0872938	−	0.0503991i	0.455718	−	0.890124i	$-0.349383\pi$
$73$	−0.745839	−	0.430610i	−0.0872938	−	0.0503991i	−0.543012	+	0.839725i	$0.682716\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.39269	+	1.47561i	−0.386633	+	0.168161i
$78$		0			0
$79$	1.31221	−	2.27282i	0.147636	−	0.255712i	−0.782718	−	0.622377i	$-0.786167\pi$
$79$	1.31221	−	2.27282i	0.147636	−	0.255712i	0.930353	+	0.366665i	$0.119500\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.82295	−	6.62154i	−0.419623	−	0.726808i	0.576278	−	0.817253i	$-0.304504\pi$
$83$	−3.82295	−	6.62154i	−0.419623	−	0.726808i	−0.995901	+	0.0904451i	$0.971171\pi$
$84$		0			0
$85$	8.81051	−	15.2603i	0.955634	−	1.65521i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.44212	+	7.69398i	0.470864	+	0.815560i	0.999445	−	0.0333231i	$-0.0106090\pi$
$89$	4.44212	+	7.69398i	0.470864	+	0.815560i	−0.528581	+	0.848883i	$0.677276\pi$
$90$		0			0
$91$	−1.02785	+	9.02968i	−0.107748	+	0.946568i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−26.3899	+	15.2362i	−2.70755	+	1.56320i
$96$		0			0
$97$	9.63985	−	5.56557i	0.978778	−	0.565098i	0.0768773	−	0.997041i	$-0.475505\pi$
$97$	9.63985	−	5.56557i	0.978778	−	0.565098i	0.901901	+	0.431943i	$0.142172\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.81086			−0.578203			−0.289101	−	0.957299i	$-0.593356\pi$
$101$	−5.81086			−0.578203			−0.289101	+	0.957299i	$0.593356\pi$
$102$		0			0
$103$			12.4310i			1.22486i	0.790523	+	0.612432i	$0.209809\pi$
$103$			12.4310i			1.22486i	−0.790523	+	0.612432i	$0.790191\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.1989	−	5.88835i	0.985968	−	0.569249i	0.0819012	−	0.996640i	$-0.473901\pi$
$107$	10.1989	−	5.88835i	0.985968	−	0.569249i	0.904067	+	0.427392i	$0.140567\pi$
$108$		0			0
$109$	−4.47772	+	7.75563i	−0.428887	+	0.742855i	−0.996775	−	0.0802516i	$-0.974428\pi$
$109$	−4.47772	+	7.75563i	−0.428887	+	0.742855i	0.567887	+	0.823106i	$0.307761\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.2381	+	5.91096i	0.963117	+	0.556056i	0.897131	−	0.441764i	$-0.145647\pi$
$113$	10.2381	+	5.91096i	0.963117	+	0.556056i	0.0659864	+	0.997821i	$0.478981\pi$
$114$		0			0
$115$		−	32.5464i		−	3.03497i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.7059	−	1.44632i	−1.16475	−	0.132584i
$120$		0			0
$121$	9.04460			0.822237
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.9977			1.07311
$126$		0			0
$127$	6.85247			0.608059			0.304029	−	0.952663i	$-0.401668\pi$
$127$	6.85247			0.608059			0.304029	+	0.952663i	$0.401668\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.689055			−0.0602030			−0.0301015	−	0.999547i	$-0.509583\pi$
$131$	−0.689055			−0.0602030			−0.0301015	+	0.999547i	$0.509583\pi$
$132$		0			0
$133$	17.7783	+	13.1524i	1.54157	+	1.14046i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	3.47292i		−	0.296712i	−0.988934	−	0.148356i	$-0.952602\pi$
$137$		−	3.47292i		−	0.296712i	0.988934	−	0.148356i	$-0.0473981\pi$
$138$		0			0
$139$	7.69570	+	4.44311i	0.652741	+	0.376860i	0.789505	−	0.613744i	$-0.210337\pi$
$139$	7.69570	+	4.44311i	0.652741	+	0.376860i	−0.136765	+	0.990604i	$0.543670\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.40163	+	4.15975i	−0.200835	+	0.347856i
$144$		0			0
$145$	−18.3079	+	10.5701i	−1.52039	+	0.877798i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			0.567607i			0.0465002i	0.999730	+	0.0232501i	$0.00740140\pi$
$149$			0.567607i			0.0465002i	−0.999730	+	0.0232501i	$0.992599\pi$
$150$		0			0
$151$	−0.206398			−0.0167964			−0.00839821	−	0.999965i	$-0.502673\pi$
$151$	−0.206398			−0.0167964			−0.00839821	+	0.999965i	$0.502673\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−19.3141	+	11.1510i	−1.55135	+	0.895671i
$156$		0			0
$157$	7.69254	−	4.44129i	0.613931	−	0.354453i	−0.160571	−	0.987024i	$-0.551334\pi$
$157$	7.69254	−	4.44129i	0.613931	−	0.354453i	0.774502	+	0.632571i	$0.218000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−21.6597	+	9.42060i	−1.70702	+	0.742447i
$162$		0			0
$163$	0.351149	+	0.608208i	0.0275041	+	0.0476386i	0.879450	−	0.475992i	$-0.157911\pi$
$163$	0.351149	+	0.608208i	0.0275041	+	0.0476386i	−0.851946	+	0.523630i	$0.824577\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.24845	−	14.2867i	0.638285	−	1.10554i	−0.347524	−	0.937671i	$-0.612978\pi$
$167$	8.24845	−	14.2867i	0.638285	−	1.10554i	0.985809	−	0.167870i	$-0.0536890\pi$
$168$		0			0
$169$	−0.600599	−	1.04027i	−0.0461999	−	0.0800206i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.14623	−	8.91353i	0.391261	−	0.677683i	−0.601355	−	0.798982i	$-0.705372\pi$
$173$	5.14623	−	8.91353i	0.391261	−	0.677683i	0.992616	+	0.121298i	$0.0387057\pi$
$174$		0			0
$175$	−8.74896	−	20.1155i	−0.661360	−	1.52059i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.02136	+	4.05378i	0.524801	+	0.302994i	0.738897	−	0.673819i	$-0.235347\pi$
$179$	7.02136	+	4.05378i	0.524801	+	0.302994i	−0.214096	+	0.976813i	$0.568680\pi$
$180$		0			0
$181$		−	15.1524i		−	1.12627i	−0.826365	−	0.563134i	$-0.809595\pi$
$181$		−	15.1524i		−	1.12627i	0.826365	−	0.563134i	$-0.190405\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.5371	−	18.2509i	−0.774706	−	1.34183i
$186$		0			0
$187$	−5.85331	−	3.37941i	−0.428036	−	0.247127i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.49394	+	1.43988i	0.180455	+	0.104186i	0.587506	−	0.809220i	$-0.300110\pi$
$191$	2.49394	+	1.43988i	0.180455	+	0.104186i	−0.407051	+	0.913405i	$0.633443\pi$
$192$		0			0
$193$	−8.03659	−	13.9198i	−0.578486	−	1.00197i	−0.995653	−	0.0931378i	$-0.970310\pi$
$193$	−8.03659	−	13.9198i	−0.578486	−	1.00197i	0.417167	−	0.908830i	$-0.363023\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	6.37179i		−	0.453972i	−0.973898	−	0.226986i	$-0.927113\pi$
$197$		−	6.37179i		−	0.453972i	0.973898	−	0.226986i	$-0.0728871\pi$
$198$		0			0
$199$	5.73328	+	3.31011i	0.406422	+	0.234648i	0.689251	−	0.724523i	$-0.257940\pi$
$199$	5.73328	+	3.31011i	0.406422	+	0.234648i	−0.282830	+	0.959170i	$0.591273\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.3337	+	9.12444i	0.865653	+	0.640410i
$204$		0			0
$205$	−2.92441	+	5.06522i	−0.204250	+	0.353771i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.84408	+	10.1223i	0.404244	+	0.700171i
$210$		0			0
$211$	−2.13230	+	3.69326i	−0.146794	+	0.254255i	−0.930041	−	0.367456i	$-0.880229\pi$
$211$	−2.13230	+	3.69326i	−0.146794	+	0.254255i	0.783247	+	0.621711i	$0.213562\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.12174	−	14.0673i	−0.553898	−	0.959380i
$216$		0			0
$217$	13.0115	+	9.62591i	0.883279	+	0.653449i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−14.3781	+	8.30123i	−0.967179	+	0.558401i
$222$		0			0
$223$	0.338403	−	0.195377i	0.0226611	−	0.0130834i	−0.488627	−	0.872493i	$-0.662502\pi$
$223$	0.338403	−	0.195377i	0.0226611	−	0.0130834i	0.511288	+	0.859410i	$0.329169\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.07487			−0.137714			−0.0688571	−	0.997627i	$-0.521935\pi$
$227$	−2.07487			−0.137714			−0.0688571	+	0.997627i	$0.521935\pi$
$228$		0			0
$229$		−	14.7152i		−	0.972411i	−0.873845	−	0.486205i	$-0.838381\pi$
$229$		−	14.7152i		−	0.972411i	0.873845	−	0.486205i	$-0.161619\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.8713	−	6.85389i	0.777713	−	0.449013i	−0.0579059	−	0.998322i	$-0.518442\pi$
$233$	11.8713	−	6.85389i	0.777713	−	0.449013i	0.835619	+	0.549309i	$0.185109\pi$
$234$		0			0
$235$	5.51303	−	9.54884i	0.359630	−	0.622898i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.08032	+	4.66517i	0.522672	+	0.301765i	0.738027	−	0.674771i	$-0.235758\pi$
$239$	8.08032	+	4.66517i	0.522672	+	0.301765i	−0.215355	+	0.976536i	$0.569091\pi$
$240$		0			0
$241$		−	17.1500i		−	1.10473i	−0.833604	−	0.552363i	$-0.813726\pi$
$241$		−	17.1500i		−	1.10473i	0.833604	−	0.552363i	$-0.186274\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.4005	+	18.6676i	−1.11168	+	1.19263i
$246$		0			0
$247$	28.7110			1.82684
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.53124			0.601606			0.300803	−	0.953686i	$-0.402745\pi$
$251$	9.53124			0.601606			0.300803	+	0.953686i	$0.402745\pi$
$252$		0			0
$253$	−12.4837			−0.784843
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−23.6663			−1.47626			−0.738131	−	0.674658i	$-0.764291\pi$
$257$	−23.6663			−1.47626			−0.738131	+	0.674658i	$0.764291\pi$
$258$		0			0
$259$	−9.09600	+	12.2952i	−0.565198	+	0.763988i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	18.8037i		−	1.15949i	−0.814799	−	0.579744i	$-0.803153\pi$
$263$		−	18.8037i		−	1.15949i	0.814799	−	0.579744i	$-0.196847\pi$
$264$		0			0
$265$	16.0497	+	9.26631i	0.985926	+	0.569225i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.16840	−	2.02372i	0.0712383	−	0.123388i	−0.828206	−	0.560424i	$-0.810638\pi$
$269$	1.16840	−	2.02372i	0.0712383	−	0.123388i	0.899444	+	0.437035i	$0.143972\pi$
$270$		0			0
$271$	19.9051	−	11.4922i	1.20915	−	0.698103i	0.246576	−	0.969123i	$-0.420694\pi$
$271$	19.9051	−	11.4922i	1.20915	−	0.698103i	0.962574	+	0.271021i	$0.0873612\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	11.5937i		−	0.699125i
$276$		0			0
$277$	−30.9918			−1.86211			−0.931057	−	0.364873i	$-0.881113\pi$
$277$	−30.9918			−1.86211			−0.931057	+	0.364873i	$0.881113\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.29924	−	4.21422i	0.435436	−	0.251399i	−0.266224	−	0.963911i	$-0.585776\pi$
$281$	7.29924	−	4.21422i	0.435436	−	0.251399i	0.701660	+	0.712512i	$0.252443\pi$
$282$		0			0
$283$	−18.6948	+	10.7935i	−1.11129	+	0.641604i	−0.939163	−	0.343471i	$-0.888397\pi$
$283$	−18.6948	+	10.7935i	−1.11129	+	0.641604i	−0.172128	+	0.985075i	$0.555064\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.21739	+	0.480065i	0.248945	+	0.0283373i
$288$		0			0
$289$	−3.18091	−	5.50950i	−0.187112	−	0.324088i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.7083	−	22.0114i	0.742427	−	1.28592i	−0.208960	−	0.977924i	$-0.567008\pi$
$293$	12.7083	−	22.0114i	0.742427	−	1.28592i	0.951387	−	0.307998i	$-0.0996589\pi$
$294$		0			0
$295$	11.7111	+	20.2842i	0.681847	+	1.18099i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.3326	+	26.5568i	−0.886704	+	1.53582i
$300$		0			0
$301$	−7.01095	+	9.47682i	−0.404104	+	0.546235i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−28.3878	−	16.3897i	−1.62548	−	0.938471i
$306$		0			0
$307$		−	9.44895i		−	0.539280i	−0.962961	−	0.269640i	$-0.913095\pi$
$307$		−	9.44895i		−	0.539280i	0.962961	−	0.269640i	$-0.0869047\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.73567	−	8.20242i	−0.268535	−	0.465117i	0.699949	−	0.714193i	$-0.253206\pi$
$311$	−4.73567	−	8.20242i	−0.268535	−	0.465117i	−0.968484	+	0.249077i	$0.919873\pi$
$312$		0			0
$313$	5.90654	+	3.41015i	0.333858	+	0.192753i	0.657552	−	0.753409i	$-0.271592\pi$
$313$	5.90654	+	3.41015i	0.333858	+	0.192753i	−0.323695	+	0.946162i	$0.604925\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.8540	−	14.3494i	−1.39594	−	0.805945i	−0.401974	−	0.915651i	$-0.631676\pi$
$317$	−24.8540	−	14.3494i	−1.39594	−	0.805945i	−0.993964	+	0.109706i	$0.965009\pi$
$318$		0			0
$319$	4.05432	+	7.02229i	0.226998	+	0.393173i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			40.4001i			2.24792i
$324$		0			0
$325$	−24.6634	−	14.2394i	−1.36808	−	0.789862i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.95052	−	0.905007i	−0.438327	−	0.0498947i
$330$		0			0
$331$	0.600666	−	1.04038i	0.0330156	−	0.0571847i	−0.849045	−	0.528320i	$-0.822822\pi$
$331$	0.600666	−	1.04038i	0.0330156	−	0.0571847i	0.882061	+	0.471135i	$0.156156\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.24163	−	16.0070i	−0.504924	−	0.874554i
$336$		0			0
$337$	3.34451	−	5.79285i	0.182187	−	0.315557i	−0.760438	−	0.649410i	$-0.775016\pi$
$337$	3.34451	−	5.79285i	0.182187	−	0.315557i	0.942625	+	0.333854i	$0.108349\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.27714	+	7.40823i	0.231620	+	0.401178i
$342$		0			0
$343$	17.4599	+	6.17672i	0.942746	+	0.333512i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.14577	+	0.661512i	−0.0615083	+	0.0355118i	−0.530439	−	0.847723i	$-0.677973\pi$
$347$	−1.14577	+	0.661512i	−0.0615083	+	0.0355118i	0.468930	+	0.883235i	$0.344639\pi$
$348$		0			0
$349$	−3.25327	+	1.87828i	−0.174144	+	0.100542i	−0.584538	−	0.811366i	$-0.698724\pi$
$349$	−3.25327	+	1.87828i	−0.174144	+	0.100542i	0.410395	+	0.911908i	$0.365391\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.7059			−0.623040			−0.311520	−	0.950240i	$-0.600838\pi$
$353$	−11.7059			−0.623040			−0.311520	+	0.950240i	$0.600838\pi$
$354$		0			0
$355$			15.3367i			0.813988i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	23.0847	−	13.3280i	1.21836	−	0.703423i	0.253797	−	0.967258i	$-0.418321\pi$
$359$	23.0847	−	13.3280i	1.21836	−	0.703423i	0.964568	+	0.263835i	$0.0849873\pi$
$360$		0			0
$361$	25.4324	−	44.0502i	1.33855	−	2.31843i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.71909	−	1.56986i	−0.142323	−	0.0821705i
$366$		0			0
$367$		−	27.0815i		−	1.41364i	−0.707392	−	0.706821i	$-0.750128\pi$
$367$		−	27.0815i		−	1.41364i	0.707392	−	0.706821i	$-0.249872\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.52114	−	13.3633i	0.0789736	−	0.693786i
$372$		0			0
$373$	8.60898			0.445756			0.222878	−	0.974846i	$-0.428455\pi$
$373$	8.60898			0.445756			0.222878	+	0.974846i	$0.428455\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.9182			1.02584
$378$		0			0
$379$	−2.49028			−0.127917			−0.0639585	−	0.997953i	$-0.520373\pi$
$379$	−2.49028			−0.127917			−0.0639585	+	0.997953i	$0.520373\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	20.2597			1.03522			0.517612	−	0.855616i	$-0.326821\pi$
$383$	20.2597			1.03522			0.517612	+	0.855616i	$0.326821\pi$
$384$		0			0
$385$	−12.3687	+	5.37958i	−0.630365	+	0.274169i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	3.60894i		−	0.182980i	−0.995806	−	0.0914902i	$-0.970837\pi$
$389$		−	3.60894i		−	0.182980i	0.995806	−	0.0914902i	$-0.0291630\pi$
$390$		0			0
$391$	−37.3688	−	21.5749i	−1.88982	−	1.09109i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.78390	−	8.28597i	0.240704	−	0.416912i
$396$		0			0
$397$	−16.3076	+	9.41521i	−0.818456	+	0.472536i	−0.849884	−	0.526970i	$-0.823328\pi$
$397$	−16.3076	+	9.41521i	−0.818456	+	0.472536i	0.0314275	+	0.999506i	$0.489995\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			14.3026i			0.714239i	0.934059	+	0.357119i	$0.116241\pi$
$401$			14.3026i			0.714239i	−0.934059	+	0.357119i	$0.883759\pi$
$402$		0			0
$403$	21.0129			1.04673
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.00041	+	4.04169i	−0.346997	+	0.200339i
$408$		0			0
$409$	−30.3685	+	17.5332i	−1.50162	+	0.866963i	−0.501626	+	0.865085i	$0.667265\pi$
$409$	−30.3685	+	17.5332i	−1.50162	+	0.866963i	−0.999998	+	0.00187827i	$0.999402\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.1094	−	13.6650i	0.497451	−	0.672413i
$414$		0			0
$415$	−13.9372	−	24.1400i	−0.684151	−	1.18498i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.83034	+	10.0984i	−0.284831	+	0.493341i	−0.972568	−	0.232618i	$-0.925271\pi$
$419$	−5.83034	+	10.0984i	−0.284831	+	0.493341i	0.687737	+	0.725959i	$0.258604\pi$
$420$		0			0
$421$	1.42981	+	2.47650i	0.0696845	+	0.120697i	0.898762	−	0.438436i	$-0.144467\pi$
$421$	1.42981	+	2.47650i	0.0696845	+	0.120697i	−0.829078	+	0.559133i	$0.811134\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	20.0367	−	34.7046i	0.971925	−	1.68342i
$426$		0			0
$427$	−2.69050	+	23.6361i	−0.130202	+	1.14383i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.720513	−	0.415989i	−0.0347059	−	0.0200375i	0.482547	−	0.875870i	$-0.339712\pi$
$431$	−0.720513	−	0.415989i	−0.0347059	−	0.0200375i	−0.517253	+	0.855833i	$0.673045\pi$
$432$		0			0
$433$			41.2560i			1.98264i	0.131479	+	0.991319i	$0.458027\pi$
$433$			41.2560i			1.98264i	−0.131479	+	0.991319i	$0.541973\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	37.3099	+	64.6227i	1.78478	+	3.09132i
$438$		0			0
$439$	3.72695	+	2.15175i	0.177877	+	0.102698i	0.586295	−	0.810098i	$-0.300586\pi$
$439$	3.72695	+	2.15175i	0.177877	+	0.102698i	−0.408418	+	0.912795i	$0.633919\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.98795	+	5.18919i	0.427030	+	0.246546i	0.698081	−	0.716019i	$-0.254038\pi$
$443$	8.98795	+	5.18919i	0.427030	+	0.246546i	−0.271050	+	0.962565i	$0.587371\pi$
$444$		0			0
$445$	16.1945	+	28.0497i	0.767694	+	1.32968i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	29.5119i		−	1.39275i	−0.717677	−	0.696376i	$-0.754795\pi$
$449$		−	29.5119i		−	1.39275i	0.717677	−	0.696376i	$-0.245205\pi$
$450$		0			0
$451$	1.94285	+	1.12170i	0.0914850	+	0.0528189i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.74720	+	32.9193i	−0.175671	+	1.54328i
$456$		0			0
$457$	−1.11805	+	1.93652i	−0.0523001	+	0.0905864i	−0.890990	−	0.454023i	$-0.849989\pi$
$457$	−1.11805	+	1.93652i	−0.0523001	+	0.0905864i	0.838690	+	0.544609i	$0.183322\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.62018	+	9.73443i	0.261758	+	0.453378i	0.966709	−	0.255878i	$-0.0823645\pi$
$461$	5.62018	+	9.73443i	0.261758	+	0.453378i	−0.704951	+	0.709256i	$0.749031\pi$
$462$		0			0
$463$	2.58576	−	4.47867i	0.120170	−	0.208141i	−0.799664	−	0.600447i	$-0.794989\pi$
$463$	2.58576	−	4.47867i	0.120170	−	0.208141i	0.919835	+	0.392306i	$0.128323\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.9873	+	25.9587i	0.693528	+	1.20123i	0.970674	+	0.240398i	$0.0772780\pi$
$467$	14.9873	+	25.9587i	0.693528	+	1.20123i	−0.277146	+	0.960828i	$0.589389\pi$
$468$		0			0
$469$	−7.97767	+	10.7836i	−0.368375	+	0.497938i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.39572	+	3.11522i	−0.248095	+	0.143238i
$474$		0			0
$475$	−60.0155	+	34.6500i	−2.75370	+	1.58985i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	35.2436			1.61032			0.805159	−	0.593058i	$-0.202080\pi$
$479$	35.2436			1.61032			0.805159	+	0.593058i	$0.202080\pi$
$480$		0			0
$481$			19.8561i			0.905361i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	35.1437	−	20.2903i	1.59580	−	0.921333i
$486$		0			0
$487$	12.3984	−	21.4747i	0.561826	−	0.973111i	−0.435511	−	0.900183i	$-0.643432\pi$
$487$	12.3984	−	21.4747i	0.561826	−	0.973111i	0.997337	−	0.0729280i	$-0.0232343\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.4696	−	10.0860i	−0.788390	−	0.455177i	0.0510056	−	0.998698i	$-0.483757\pi$
$491$	−17.4696	−	10.0860i	−0.788390	−	0.455177i	−0.839395	+	0.543521i	$0.817091\pi$
$492$		0			0
$493$			28.0275i			1.26229i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.2066	−	4.43922i	0.457829	−	0.199126i
$498$		0			0
$499$	27.5961			1.23537			0.617687	−	0.786424i	$-0.288070\pi$
$499$	27.5961			1.23537			0.617687	+	0.786424i	$0.288070\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.9512			−1.24628			−0.623142	−	0.782109i	$-0.714144\pi$
$503$	−27.9512			−1.24628			−0.623142	+	0.782109i	$0.714144\pi$
$504$		0			0
$505$	−21.1845			−0.942699
$506$		0			0
$507$		0			0
$508$		0			0
$509$	43.1118			1.91090			0.955448	−	0.295160i	$-0.0953730\pi$
$509$	43.1118			1.91090			0.955448	+	0.295160i	$0.0953730\pi$
$510$		0			0
$511$	−0.257706	+	2.26396i	−0.0114002	+	0.100151i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			45.3194i			1.99701i
$516$		0			0
$517$	−3.66261	−	2.11461i	−0.161081	−	0.0930003i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.06052	+	5.30098i	−0.134084	+	0.232240i	−0.925247	−	0.379365i	$-0.876143\pi$
$521$	−3.06052	+	5.30098i	−0.134084	+	0.232240i	0.791163	+	0.611605i	$0.209476\pi$
$522$		0			0
$523$	−13.1647	+	7.60065i	−0.575652	+	0.332353i	−0.759404	−	0.650620i	$-0.774509\pi$
$523$	−13.1647	+	7.60065i	−0.575652	+	0.332353i	0.183751	+	0.982973i	$0.441176\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			29.5678i			1.28800i
$528$		0			0
$529$	−56.6986			−2.46516
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.77243	−	2.75537i	0.206717	−	0.119348i
$534$		0			0
$535$	37.1820	−	21.4670i	1.60752	−	0.928100i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.16024	+	6.67424i	0.308413	+	0.287480i
$540$		0			0
$541$	12.9995	+	22.5159i	0.558894	+	0.968033i	0.997589	+	0.0693968i	$0.0221074\pi$
$541$	12.9995	+	22.5159i	0.558894	+	0.968033i	−0.438695	+	0.898636i	$0.644559\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−16.3243	+	28.2745i	−0.699256	+	1.21115i
$546$		0			0
$547$	15.7120	+	27.2139i	0.671794	+	1.16358i	0.977395	+	0.211422i	$0.0678095\pi$
$547$	15.7120	+	27.2139i	0.671794	+	1.16358i	−0.305600	+	0.952160i	$0.598857\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	24.2343	−	41.9750i	1.03241	−	1.78819i
$552$		0			0
$553$	−6.89903	−	0.785316i	−0.293377	−	0.0333950i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−33.8867	−	19.5645i	−1.43582	−	0.828974i	−0.438268	−	0.898844i	$-0.644408\pi$
$557$	−33.8867	−	19.5645i	−1.43582	−	0.828974i	−0.997556	+	0.0698707i	$0.977741\pi$
$558$		0			0
$559$			15.3045i			0.647313i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.6402	+	25.3576i	0.617012	+	1.06870i	0.990028	+	0.140871i	$0.0449902\pi$
$563$	14.6402	+	25.3576i	0.617012	+	1.06870i	−0.373016	+	0.927825i	$0.621676\pi$
$564$		0			0
$565$	37.3247	+	21.5494i	1.57026	+	0.906591i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−28.3754	−	16.3825i	−1.18956	−	0.686791i	−0.231351	−	0.972870i	$-0.574315\pi$
$569$	−28.3754	−	16.3825i	−1.18956	−	0.686791i	−0.958206	+	0.286079i	$0.907648\pi$
$570$		0			0
$571$	10.5170	+	18.2160i	0.440123	+	0.762315i	0.997698	−	0.0678114i	$-0.0216016\pi$
$571$	10.5170	+	18.2160i	0.440123	+	0.762315i	−0.557576	+	0.830126i	$0.688268\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	74.0166i		−	3.08671i
$576$		0			0
$577$	14.9926	+	8.65597i	0.624149	+	0.360353i	0.778483	−	0.627666i	$-0.215990\pi$
$577$	14.9926	+	8.65597i	0.624149	+	0.360353i	−0.154334	+	0.988019i	$0.549323\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−12.0311	+	16.2626i	−0.499132	+	0.674686i
$582$		0			0
$583$	3.55424	−	6.15612i	0.147201	−	0.254960i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.95712	−	15.5142i	−0.369700	−	0.640339i	0.619819	−	0.784745i	$-0.287206\pi$
$587$	−8.95712	−	15.5142i	−0.369700	−	0.640339i	−0.989518	+	0.144406i	$0.953873\pi$
$588$		0			0
$589$	25.5662	−	44.2819i	1.05343	−	1.82460i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	17.6799	+	30.6225i	0.726028	+	1.25752i	0.958550	+	0.284926i	$0.0919689\pi$
$593$	17.6799	+	30.6225i	0.726028	+	1.25752i	−0.232522	+	0.972591i	$0.574698\pi$
$594$		0			0
$595$	−46.3217	−	5.27280i	−1.89901	−	0.216164i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.773338	+	0.446487i	−0.0315977	+	0.0182430i	−0.515716	−	0.856760i	$-0.672474\pi$
$599$	−0.773338	+	0.446487i	−0.0315977	+	0.0182430i	0.484118	+	0.875003i	$0.339141\pi$
$600$		0			0
$601$	23.7713	−	13.7244i	0.969653	−	0.559829i	0.0705225	−	0.997510i	$-0.477533\pi$
$601$	23.7713	−	13.7244i	0.969653	−	0.559829i	0.899130	+	0.437681i	$0.144200\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	32.9737			1.34057
$606$		0			0
$607$			20.3891i			0.827568i	0.910375	+	0.413784i	$0.135793\pi$
$607$			20.3891i			0.827568i	−0.910375	+	0.413784i	$0.864207\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.99688	+	5.19435i	−0.363975	+	0.210141i
$612$		0			0
$613$	16.6541	−	28.8457i	0.672652	−	1.16507i	−0.304497	−	0.952513i	$-0.598488\pi$
$613$	16.6541	−	28.8457i	0.672652	−	1.16507i	0.977149	−	0.212554i	$-0.0681783\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.6812	+	15.9817i	1.11440	+	0.643401i	0.939966	−	0.341268i	$-0.110856\pi$
$617$	27.6812	+	15.9817i	1.11440	+	0.643401i	0.174437	+	0.984668i	$0.444190\pi$
$618$		0			0
$619$			4.39913i			0.176816i	0.996084	+	0.0884079i	$0.0281779\pi$
$619$			4.39913i			0.176816i	−0.996084	+	0.0884079i	$0.971822\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	13.9796	−	18.8965i	0.560082	−	0.757072i
$624$		0			0
$625$	2.28497			0.0913990
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−27.9401			−1.11405
$630$		0			0
$631$	18.0749			0.719549			0.359775	−	0.933039i	$-0.382854\pi$
$631$	18.0749			0.719549			0.359775	+	0.933039i	$0.382854\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.9819			0.991376
$636$		0			0
$637$	22.9925	−	7.03475i	0.910995	−	0.278727i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			4.10040i			0.161956i	0.996716	+	0.0809779i	$0.0258043\pi$
$641$			4.10040i			0.161956i	−0.996716	+	0.0809779i	$0.974196\pi$
$642$		0			0
$643$	−7.12890	−	4.11587i	−0.281136	−	0.162314i	0.352801	−	0.935698i	$-0.385229\pi$
$643$	−7.12890	−	4.11587i	−0.281136	−	0.162314i	−0.633938	+	0.773384i	$0.718562\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.07138	−	12.2480i	0.278004	−	0.481518i	−0.692884	−	0.721049i	$-0.743660\pi$
$647$	7.07138	−	12.2480i	0.278004	−	0.481518i	0.970889	+	0.239531i	$0.0769937\pi$
$648$		0			0
$649$	7.78033	−	4.49198i	0.305405	−	0.176325i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	23.0473i		−	0.901911i	−0.892546	−	0.450956i	$-0.851083\pi$
$653$		−	23.0473i		−	0.901911i	0.892546	−	0.450956i	$-0.148917\pi$
$654$		0			0
$655$	−2.51207			−0.0981547
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.09924	−	4.09875i	0.276547	−	0.159665i	−0.355312	−	0.934748i	$-0.615625\pi$
$659$	7.09924	−	4.09875i	0.276547	−	0.159665i	0.631859	+	0.775083i	$0.282292\pi$
$660$		0			0
$661$	26.3464	−	15.2111i	1.02476	−	0.591643i	0.109277	−	0.994011i	$-0.465146\pi$
$661$	26.3464	−	15.2111i	1.02476	−	0.591643i	0.915478	+	0.402369i	$0.131813\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	64.8139	+	47.9493i	2.51338	+	1.85939i
$666$		0			0
$667$	25.8837	+	44.8319i	1.00222	+	1.73590i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.28652	+	10.8886i	−0.242688	+	0.420349i
$672$		0			0
$673$	2.44406	+	4.23323i	0.0942115	+	0.163179i	0.909279	−	0.416187i	$-0.136634\pi$
$673$	2.44406	+	4.23323i	0.0942115	+	0.163179i	−0.815068	+	0.579366i	$0.803300\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.7121	+	18.5539i	−0.411699	+	0.713083i	−0.995076	−	0.0991185i	$-0.968398\pi$
$677$	−10.7121	+	18.5539i	−0.411699	+	0.713083i	0.583377	+	0.812202i	$0.301731\pi$
$678$		0			0
$679$	−23.6756	−	17.5152i	−0.908586	−	0.672171i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.49101	−	2.01553i	−0.133580	−	0.0771222i	0.431721	−	0.902007i	$-0.357906\pi$
$683$	−3.49101	−	2.01553i	−0.133580	−	0.0771222i	−0.565301	+	0.824885i	$0.691240\pi$
$684$		0			0
$685$		−	12.6611i		−	0.483757i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.73068	−	15.1220i	−0.332612	−	0.576101i
$690$		0			0
$691$	30.0272	+	17.3362i	1.14229	+	0.659500i	0.946996	−	0.321246i	$-0.104101\pi$
$691$	30.0272	+	17.3362i	1.14229	+	0.659500i	0.195291	+	0.980745i	$0.437435\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	28.0560	+	16.1981i	1.06422	+	0.614431i
$696$		0			0
$697$	3.87716	+	6.71544i	0.146858	+	0.254365i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	31.1575i		−	1.17680i	−0.808569	−	0.588401i	$-0.799758\pi$
$701$		−	31.1575i		−	1.17680i	0.808569	−	0.588401i	$-0.200242\pi$
$702$		0			0
$703$	41.8442	+	24.1587i	1.57818	+	0.911164i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.13188	+	14.0983i	0.230613	+	0.530222i
$708$		0			0
$709$	−14.1925	+	24.5821i	−0.533009	+	0.923199i	0.466248	+	0.884654i	$0.345606\pi$
$709$	−14.1925	+	24.5821i	−0.533009	+	0.923199i	−0.999257	+	0.0385448i	$0.987728\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	27.3062	+	47.2958i	1.02263	+	1.77124i
$714$		0			0
$715$	−8.75557	+	15.1651i	−0.327440	+	0.567142i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.8969	+	25.8022i	0.555561	+	0.962259i	0.997860	+	0.0653917i	$0.0208297\pi$
$719$	14.8969	+	25.8022i	0.555561	+	0.962259i	−0.442299	+	0.896868i	$0.645837\pi$
$720$		0			0
$721$	30.1602	−	13.1178i	1.12322	−	0.488531i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−41.6356	+	24.0383i	−1.54631	+	0.892762i
$726$		0			0
$727$	−36.8231	+	21.2598i	−1.36569	+	0.788484i	−0.990375	−	0.138411i	$-0.955800\pi$
$727$	−36.8231	+	21.2598i	−1.36569	+	0.788484i	−0.375320	+	0.926895i	$0.622467\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.5355			−0.796519
$732$		0			0
$733$			36.9920i			1.36633i	0.730263	+	0.683166i	$0.239398\pi$
$733$			36.9920i			1.36633i	−0.730263	+	0.683166i	$0.760602\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.13972	+	3.54477i	−0.226160	+	0.130573i
$738$		0			0
$739$	−17.3127	+	29.9864i	−0.636857	+	1.10307i	0.349261	+	0.937025i	$0.386433\pi$
$739$	−17.3127	+	29.9864i	−0.636857	+	1.10307i	−0.986118	+	0.166044i	$0.946901\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.1788	−	12.2276i	−0.776976	−	0.448587i	0.0583814	−	0.998294i	$-0.481406\pi$
$743$	−21.1788	−	12.2276i	−0.776976	−	0.448587i	−0.835358	+	0.549707i	$0.814739\pi$
$744$		0			0
$745$			2.06931i			0.0758136i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−25.0487	−	18.5310i	−0.915260	−	0.677109i
$750$		0			0
$751$	4.19662			0.153137			0.0765685	−	0.997064i	$-0.475604\pi$
$751$	4.19662			0.153137			0.0765685	+	0.997064i	$0.475604\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.752460			−0.0273848
$756$		0			0
$757$	19.3020			0.701545			0.350772	−	0.936461i	$-0.385919\pi$
$757$	19.3020			0.701545			0.350772	+	0.936461i	$0.385919\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.7261			0.533821			0.266910	−	0.963721i	$-0.413997\pi$
$761$	14.7261			0.533821			0.266910	+	0.963721i	$0.413997\pi$
$762$		0			0
$763$	23.5418	+	2.67976i	0.852271	+	0.0970139i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	22.0683i		−	0.796840i
$768$		0			0
$769$	−43.6719	−	25.2140i	−1.57485	−	0.909240i	−0.995561	−	0.0941181i	$-0.969997\pi$
$769$	−43.6719	−	25.2140i	−1.57485	−	0.909240i	−0.579289	−	0.815122i	$-0.696670\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.54706	+	16.5360i	−0.343384	+	0.594758i	−0.985059	−	0.172218i	$-0.944907\pi$
$773$	−9.54706	+	16.5360i	−0.343384	+	0.594758i	0.641675	+	0.766977i	$0.278240\pi$
$774$		0			0
$775$	−43.9239	+	25.3595i	−1.57779	+	0.910939i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	13.4097i		−	0.480453i
$780$		0			0
$781$	5.88263			0.210497
$782$		0			0
$783$		0			0
$784$		0			0
$785$	28.0445	−	16.1915i	1.00095	−	0.577899i
$786$		0			0
$787$	−43.0297	+	24.8432i	−1.53384	+	0.885566i	−0.534665	+	0.845064i	$0.679562\pi$
$787$	−43.0297	+	24.8432i	−1.53384	+	0.885566i	−0.999179	+	0.0405015i	$0.987104\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.53751	−	31.0772i	0.125779	−	1.10498i
$792$		0			0
$793$	15.4423	+	26.7468i	0.548372	+	0.949808i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.17665	−	8.96621i	0.183366	−	0.317600i	−0.759659	−	0.650322i	$-0.774634\pi$
$797$	5.17665	−	8.96621i	0.183366	−	0.317600i	0.943025	+	0.332723i	$0.107967\pi$
$798$		0			0
$799$	−7.30913	−	12.6598i	−0.258578	−	0.447871i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.602146	+	1.04295i	−0.0212493	+	0.0368048i
$804$		0			0
$805$	−78.9642	+	34.3444i	−2.78312	+	1.21048i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	41.5520	+	23.9901i	1.46089	+	0.843446i	0.999053	−	0.0435184i	$-0.0138567\pi$
$809$	41.5520	+	23.9901i	1.46089	+	0.843446i	0.461838	+	0.886964i	$0.347190\pi$
$810$		0			0
$811$		−	4.79426i		−	0.168349i	−0.996451	−	0.0841745i	$-0.973175\pi$
$811$		−	4.79426i		−	0.168349i	0.996451	−	0.0841745i	$-0.0268253\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.28018	+	2.21733i	0.0448426	+	0.0776697i
$816$		0			0
$817$	32.2523	+	18.6209i	1.12837	+	0.651462i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.3923	+	14.0829i	0.851296	+	0.491496i	0.861088	−	0.508456i	$-0.169784\pi$
$821$	24.3923	+	14.0829i	0.851296	+	0.491496i	−0.00979179	+	0.999952i	$0.503117\pi$
$822$		0			0
$823$	−28.6428	−	49.6107i	−0.998424	−	1.72932i	−0.547813	−	0.836601i	$-0.684540\pi$
$823$	−28.6428	−	49.6107i	−0.998424	−	1.72932i	−0.450611	−	0.892720i	$-0.648794\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	27.9805i		−	0.972976i	−0.873687	−	0.486488i	$-0.838278\pi$
$827$		−	27.9805i		−	0.972976i	0.873687	−	0.486488i	$-0.161722\pi$
$828$		0			0
$829$	44.6428	+	25.7745i	1.55051	+	0.895186i	0.998100	+	0.0616119i	$0.0196241\pi$
$829$	44.6428	+	25.7745i	1.55051	+	0.895186i	0.552408	+	0.833574i	$0.313709\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.89881	+	32.3534i	0.342973	+	1.12098i
$834$		0			0
$835$	30.0712	−	52.0848i	1.04066	−	1.80247i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.64286	+	8.04167i	0.160289	+	0.277629i	0.934972	−	0.354720i	$-0.115424\pi$
$839$	4.64286	+	8.04167i	0.160289	+	0.277629i	−0.774683	+	0.632350i	$0.782091\pi$
$840$		0			0
$841$	2.31247	−	4.00531i	0.0797403	−	0.138114i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.18959	−	3.79248i	−0.0753241	−	0.130465i
$846$		0			0
$847$	−9.54426	−	21.9440i	−0.327945	−	0.754006i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−44.6922	+	25.8030i	−1.53203	+	0.884516i
$852$		0			0
$853$	21.5591	−	12.4471i	0.738168	−	0.426181i	−0.0832349	−	0.996530i	$-0.526525\pi$
$853$	21.5591	−	12.4471i	0.738168	−	0.426181i	0.821403	+	0.570349i	$0.193192\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−33.4238			−1.14174			−0.570868	−	0.821042i	$-0.693393\pi$
$857$	−33.4238			−1.14174			−0.570868	+	0.821042i	$0.693393\pi$
$858$		0			0
$859$		−	33.7864i		−	1.15278i	−0.817175	−	0.576389i	$-0.804461\pi$
$859$		−	33.7864i		−	1.15278i	0.817175	−	0.576389i	$-0.195539\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.74739	−	5.62766i	0.331805	−	0.191568i	−0.324837	−	0.945770i	$-0.605309\pi$
$863$	9.74739	−	5.62766i	0.331805	−	0.191568i	0.656642	+	0.754202i	$0.271976\pi$
$864$		0			0
$865$	18.7615	−	32.4958i	0.637910	−	1.10489i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.17821	−	1.83494i	−0.107813	−	0.0622461i
$870$		0			0
$871$			17.4149i			0.590080i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−12.6605	−	29.1088i	−0.428003	−	0.984058i
$876$		0			0
$877$	−41.7801			−1.41081			−0.705407	−	0.708803i	$-0.749236\pi$
$877$	−41.7801			−1.41081			−0.705407	+	0.708803i	$0.749236\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.2845			−0.649710			−0.324855	−	0.945764i	$-0.605315\pi$
$881$	−19.2845			−0.649710			−0.324855	+	0.945764i	$0.605315\pi$
$882$		0			0
$883$	−55.1130			−1.85470			−0.927350	−	0.374195i	$-0.877919\pi$
$883$	−55.1130			−1.85470			−0.927350	+	0.374195i	$0.877919\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	24.9546			0.837892			0.418946	−	0.908011i	$-0.362400\pi$
$887$	24.9546			0.837892			0.418946	+	0.908011i	$0.362400\pi$
$888$		0			0
$889$	−7.23103	−	16.6255i	−0.242521	−	0.557601i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			25.2797i			0.845952i
$894$		0			0
$895$	25.5976	+	14.7788i	0.855633	+	0.494000i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.7365	−	30.7205i	0.591544	−	1.02458i
$900$		0			0
$901$	21.2786	−	12.2852i	0.708893	−	0.409279i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	55.2407i		−	1.83626i
$906$		0			0
$907$	−58.8709			−1.95478			−0.977388	−	0.211452i	$-0.932181\pi$
$907$	−58.8709			−1.95478			−0.977388	+	0.211452i	$0.932181\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−36.6533	+	21.1618i	−1.21438	+	0.701121i	−0.963710	−	0.266952i	$-0.913983\pi$
$911$	−36.6533	+	21.1618i	−1.21438	+	0.701121i	−0.250668	+	0.968073i	$0.580650\pi$
$912$		0			0
$913$	−9.25926	+	5.34584i	−0.306437	+	0.176921i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.727121	+	1.67179i	0.0240117	+	0.0552073i
$918$		0			0
$919$	−16.9879	−	29.4239i	−0.560379	−	0.970605i	−0.997463	−	0.0711842i	$-0.977322\pi$
$919$	−16.9879	−	29.4239i	−0.560379	−	0.970605i	0.437084	−	0.899421i	$-0.356011\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.22509	−	12.5142i	0.237817	−	0.411911i
$924$		0			0
$925$	−23.9634	−	41.5059i	−0.787913	−	1.36470i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.41930	−	11.1185i	0.210610	−	0.364788i	−0.741295	−	0.671179i	$-0.765788\pi$
$929$	6.41930	−	11.1185i	0.210610	−	0.364788i	0.951906	+	0.306391i	$0.0991216\pi$
$930$		0			0
$931$	13.1499	−	57.0127i	0.430970	−	1.86852i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−21.3393	−	12.3202i	−0.697868	−	0.402914i
$936$		0			0
$937$			28.2886i			0.924149i	0.886841	+	0.462075i	$0.152895\pi$
$937$			28.2886i			0.924149i	−0.886841	+	0.462075i	$0.847105\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−12.8901	−	22.3263i	−0.420205	−	0.727817i	0.575754	−	0.817623i	$-0.304709\pi$
$941$	−12.8901	−	22.3263i	−0.420205	−	0.727817i	−0.995959	+	0.0898059i	$0.971375\pi$
$942$		0			0
$943$	12.4036	+	7.16120i	0.403915	+	0.233201i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−52.3308	−	30.2132i	−1.70052	−	0.981798i	−0.945227	−	0.326415i	$-0.894159\pi$
$947$	−52.3308	−	30.2132i	−1.70052	−	0.981798i	−0.755297	−	0.655383i	$-0.772507\pi$
$948$		0			0
$949$	1.47912	+	2.56191i	0.0480143	+	0.0831631i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			3.83769i			0.124315i	0.998066	+	0.0621575i	$0.0197981\pi$
$953$			3.83769i			0.124315i	−0.998066	+	0.0621575i	$0.980202\pi$
$954$		0			0
$955$	9.09208	+	5.24932i	0.294213	+	0.169864i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−8.42601	+	3.66478i	−0.272090	+	0.118342i
$960$		0			0
$961$	3.21124	−	5.56203i	0.103588	−	0.179420i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−29.2988	−	50.7470i	−0.943161	−	1.63360i
$966$		0			0
$967$	3.68243	−	6.37816i	0.118419	−	0.205108i	−0.800722	−	0.599036i	$-0.795551\pi$
$967$	3.68243	−	6.37816i	0.118419	−	0.205108i	0.919141	+	0.393928i	$0.128884\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	26.6276	+	46.1204i	0.854521	+	1.48007i	0.877089	+	0.480328i	$0.159482\pi$
$971$	26.6276	+	46.1204i	0.854521	+	1.48007i	−0.0225686	+	0.999745i	$0.507184\pi$
$972$		0			0
$973$	2.65905	−	23.3599i	0.0852454	−	0.748884i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	50.5473	−	29.1835i	1.61715	−	0.933663i	0.629500	−	0.777001i	$-0.283260\pi$
$977$	50.5473	−	29.1835i	1.61715	−	0.933663i	0.987652	−	0.156662i	$-0.0500734\pi$
$978$		0			0
$979$	10.7589	−	6.21166i	0.343856	−	0.198525i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−56.9508			−1.81645			−0.908224	−	0.418485i	$-0.862561\pi$
$983$	−56.9508			−1.81645			−0.908224	+	0.418485i	$0.862561\pi$
$984$		0			0
$985$		−	23.2295i		−	0.740153i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−34.4475	+	19.8883i	−1.09537	+	0.632410i
$990$		0			0
$991$	7.39894	−	12.8153i	0.235035	−	0.407093i	−0.724248	−	0.689540i	$-0.757813\pi$
$991$	7.39894	−	12.8153i	0.235035	−	0.407093i	0.959283	+	0.282447i	$0.0911461\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	20.9017	+	12.0676i	0.662628	+	0.382568i
$996$		0			0
$997$		−	39.0440i		−	1.23654i	−0.785967	−	0.618268i	$-0.787835\pi$
$997$		−	39.0440i		−	1.23654i	0.785967	−	0.618268i	$-0.212165\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.17.23		48
3.2	odd	2		1008.2.df.e.689.23		48
4.3	odd	2		1512.2.cx.a.17.23		48
7.5	odd	6		3024.2.ca.e.2609.23		48
9.2	odd	6		3024.2.ca.e.2033.23		48
9.7	even	3		1008.2.ca.e.353.16		48
12.11	even	2		504.2.cx.a.185.2	yes	48
21.5	even	6		1008.2.ca.e.257.16		48
28.19	even	6		1512.2.bs.a.1097.23		48
36.7	odd	6		504.2.bs.a.353.9	yes	48
36.11	even	6		1512.2.bs.a.521.23		48
63.47	even	6	inner	3024.2.df.e.1601.23		48
63.61	odd	6		1008.2.df.e.929.23		48
84.47	odd	6		504.2.bs.a.257.9	✓	48
252.47	odd	6		1512.2.cx.a.89.23		48
252.187	even	6		504.2.cx.a.425.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.9	✓	48	84.47	odd	6
504.2.bs.a.353.9	yes	48	36.7	odd	6
504.2.cx.a.185.2	yes	48	12.11	even	2
504.2.cx.a.425.2	yes	48	252.187	even	6
1008.2.ca.e.257.16		48	21.5	even	6
1008.2.ca.e.353.16		48	9.7	even	3
1008.2.df.e.689.23		48	3.2	odd	2
1008.2.df.e.929.23		48	63.61	odd	6
1512.2.bs.a.521.23		48	36.11	even	6
1512.2.bs.a.1097.23		48	28.19	even	6
1512.2.cx.a.17.23		48	4.3	odd	2
1512.2.cx.a.89.23		48	252.47	odd	6
3024.2.ca.e.2033.23		48	9.2	odd	6
3024.2.ca.e.2609.23		48	7.5	odd	6
3024.2.df.e.17.23		48	1.1	even	1	trivial
3024.2.df.e.1601.23		48	63.47	even	6	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.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.64567 q^{5} +(-1.05524 - 2.42620i) q^{7} +O(q^{10})\)	\(q+3.64567 q^{5} +(-1.05524 - 2.42620i) q^{7} -1.39835i q^{11} +(-2.97474 - 1.71747i) q^{13} +(2.41670 - 4.18585i) q^{17} +(-7.23869 + 4.17926i) q^{19} -8.92741i q^{23} +8.29094 q^{25} +(-5.02182 + 2.89935i) q^{29} +(-5.29782 + 3.05870i) q^{31} +(-3.84708 - 8.84514i) q^{35} +(-2.89032 - 5.00617i) q^{37} +(-0.802159 + 1.38938i) q^{41} +(-2.22777 - 3.85862i) q^{43} +(1.51221 - 2.61923i) q^{47} +(-4.77292 + 5.12047i) q^{49} +(4.40240 + 2.54173i) q^{53} -5.09795i q^{55} +(3.21233 + 5.56392i) q^{59} +(-7.78670 - 4.49565i) q^{61} +(-10.8449 - 6.26133i) q^{65} +(-2.53496 - 4.39068i) q^{67} +4.20682i q^{71} +(-0.745839 - 0.430610i) q^{73} +(-3.39269 + 1.47561i) q^{77} +(1.31221 - 2.27282i) q^{79} +(-3.82295 - 6.62154i) q^{83} +(8.81051 - 15.2603i) q^{85} +(4.44212 + 7.69398i) q^{89} +(-1.02785 + 9.02968i) q^{91} +(-26.3899 + 15.2362i) q^{95} +(9.63985 - 5.56557i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

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