LMFDB - Embedded newform 3024.2.cc.d.881.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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, 3]))

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (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			881.12
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00869840 + 0.0150661i) q^{5} +(0.514871 - 2.59517i) q^{7} +O(q^{10})$	$q+(-0.00869840 + 0.0150661i) q^{5} +(0.514871 - 2.59517i) q^{7} +(4.13424 - 2.38691i) q^{11} +(1.31594 + 0.759761i) q^{13} -1.91072 q^{17} +6.45989i q^{19} +(3.82432 + 2.20797i) q^{23} +(2.49985 + 4.32986i) q^{25} +(-1.73895 + 1.00399i) q^{29} +(6.51946 + 3.76401i) q^{31} +(0.0346205 + 0.0303309i) q^{35} -6.10467 q^{37} +(4.67759 - 8.10182i) q^{41} +(1.46638 + 2.53985i) q^{43} +(1.45659 + 2.52289i) q^{47} +(-6.46982 - 2.67235i) q^{49} -8.94416i q^{53} +0.0830491i q^{55} +(4.08337 - 7.07261i) q^{59} +(0.484917 - 0.279967i) q^{61} +(-0.0228932 + 0.0132174i) q^{65} +(3.69036 - 6.39189i) q^{67} -11.6825i q^{71} +12.8105i q^{73} +(-4.06583 - 11.9580i) q^{77} +(-4.75827 - 8.24157i) q^{79} +(6.67701 + 11.5649i) q^{83} +(0.0166202 - 0.0287871i) q^{85} +4.00356 q^{89} +(2.64925 - 3.02392i) q^{91} +(-0.0973252 - 0.0561907i) q^{95} +(-4.09514 + 2.36433i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.00869840	+	0.0150661i	−0.00389004	+	0.00673776i	−0.867964	−	0.496627i	$-0.834572\pi$
$5$	−0.00869840	+	0.0150661i	−0.00389004	+	0.00673776i	0.864074	+	0.503365i	$0.167905\pi$
$6$		0			0
$7$	0.514871	−	2.59517i	0.194603	−	0.980882i
$7$	0.514871	−	2.59517i	0.194603	−	0.980882i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.13424	−	2.38691i	1.24652	−	0.719679i	0.276107	−	0.961127i	$-0.410956\pi$
$11$	4.13424	−	2.38691i	1.24652	−	0.719679i	0.970414	+	0.241448i	$0.0776222\pi$
$12$		0			0
$13$	1.31594	+	0.759761i	0.364977	+	0.210720i	0.671262	−	0.741220i	$-0.265753\pi$
$13$	1.31594	+	0.759761i	0.364977	+	0.210720i	−0.306285	+	0.951940i	$0.599086\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.91072			−0.463418			−0.231709	−	0.972785i	$-0.574432\pi$
$17$	−1.91072			−0.463418			−0.231709	+	0.972785i	$0.574432\pi$
$18$		0			0
$19$			6.45989i			1.48200i	0.671505	+	0.741000i	$0.265648\pi$
$19$			6.45989i			1.48200i	−0.671505	+	0.741000i	$0.734352\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.82432	+	2.20797i	0.797426	+	0.460394i	0.842570	−	0.538586i	$-0.181041\pi$
$23$	3.82432	+	2.20797i	0.797426	+	0.460394i	−0.0451444	+	0.998980i	$0.514375\pi$
$24$		0			0
$25$	2.49985	+	4.32986i	0.499970	+	0.865973i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.73895	+	1.00399i	−0.322916	+	0.186435i	−0.652691	−	0.757624i	$-0.726360\pi$
$29$	−1.73895	+	1.00399i	−0.322916	+	0.186435i	0.329776	+	0.944059i	$0.393027\pi$
$30$		0			0
$31$	6.51946	+	3.76401i	1.17093	+	0.676036i	0.953899	−	0.300129i	$-0.0970297\pi$
$31$	6.51946	+	3.76401i	1.17093	+	0.676036i	0.217030	+	0.976165i	$0.430363\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.0346205	+	0.0303309i	0.00585193	+	0.00512686i
$36$		0			0
$37$	−6.10467			−1.00360			−0.501801	−	0.864983i	$-0.667329\pi$
$37$	−6.10467			−1.00360			−0.501801	+	0.864983i	$0.667329\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.67759	−	8.10182i	0.730516	−	1.26529i	−0.226146	−	0.974093i	$-0.572613\pi$
$41$	4.67759	−	8.10182i	0.730516	−	1.26529i	0.956663	−	0.291198i	$-0.0940539\pi$
$42$		0			0
$43$	1.46638	+	2.53985i	0.223621	+	0.387323i	0.955905	−	0.293677i	$-0.0948789\pi$
$43$	1.46638	+	2.53985i	0.223621	+	0.387323i	−0.732284	+	0.680999i	$0.761546\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.45659	+	2.52289i	0.212466	+	0.368001i	0.952486	−	0.304584i	$-0.0985173\pi$
$47$	1.45659	+	2.52289i	0.212466	+	0.368001i	−0.740020	+	0.672585i	$0.765184\pi$
$48$		0			0
$49$	−6.46982	−	2.67235i	−0.924259	−	0.381765i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	8.94416i		−	1.22858i	−0.789082	−	0.614288i	$-0.789443\pi$
$53$		−	8.94416i		−	1.22858i	0.789082	−	0.614288i	$-0.210557\pi$
$54$		0			0
$55$			0.0830491i			0.0111983i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.08337	−	7.07261i	0.531610	−	0.920776i	−0.467709	−	0.883882i	$-0.654921\pi$
$59$	4.08337	−	7.07261i	0.531610	−	0.920776i	0.999319	−	0.0368933i	$-0.0117462\pi$
$60$		0			0
$61$	0.484917	−	0.279967i	0.0620873	−	0.0358461i	−0.468635	−	0.883392i	$-0.655254\pi$
$61$	0.484917	−	0.279967i	0.0620873	−	0.0358461i	0.530722	+	0.847546i	$0.321921\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0228932	+	0.0132174i	−0.00283956	+	0.00163942i
$66$		0			0
$67$	3.69036	−	6.39189i	0.450849	−	0.780893i	−0.547590	−	0.836747i	$-0.684455\pi$
$67$	3.69036	−	6.39189i	0.450849	−	0.780893i	0.998439	+	0.0558536i	$0.0177880\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.6825i		−	1.38645i	−0.720719	−	0.693227i	$-0.756188\pi$
$71$		−	11.6825i		−	1.38645i	0.720719	−	0.693227i	$-0.243812\pi$
$72$		0			0
$73$			12.8105i			1.49936i	0.661801	+	0.749680i	$0.269792\pi$
$73$			12.8105i			1.49936i	−0.661801	+	0.749680i	$0.730208\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.06583	−	11.9580i	−0.463344	−	1.36274i
$78$		0			0
$79$	−4.75827	−	8.24157i	−0.535348	−	0.927249i	−0.999146	−	0.0413086i	$-0.986847\pi$
$79$	−4.75827	−	8.24157i	−0.535348	−	0.927249i	0.463799	−	0.885940i	$-0.346486\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.67701	+	11.5649i	0.732897	+	1.26942i	0.955640	+	0.294538i	$0.0951657\pi$
$83$	6.67701	+	11.5649i	0.732897	+	1.26942i	−0.222743	+	0.974877i	$0.571501\pi$
$84$		0			0
$85$	0.0166202	−	0.0287871i	0.00180272	−	0.00312240i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.00356			0.424376			0.212188	−	0.977229i	$-0.431941\pi$
$89$	4.00356			0.424376			0.212188	+	0.977229i	$0.431941\pi$
$90$		0			0
$91$	2.64925	−	3.02392i	0.277717	−	0.316993i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0973252	−	0.0561907i	−0.00998536	−	0.00576505i
$96$		0			0
$97$	−4.09514	+	2.36433i	−0.415799	+	0.240062i	−0.693278	−	0.720670i	$-0.743834\pi$
$97$	−4.09514	+	2.36433i	−0.415799	+	0.240062i	0.277479	+	0.960732i	$0.410501\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.98289	−	5.16652i	−0.296809	−	0.514088i	0.678595	−	0.734513i	$-0.262589\pi$
$101$	−2.98289	−	5.16652i	−0.296809	−	0.514088i	−0.975404	+	0.220424i	$0.929256\pi$
$102$		0			0
$103$	10.0607	+	5.80854i	0.991308	+	0.572332i	0.905665	−	0.423994i	$-0.139372\pi$
$103$	10.0607	+	5.80854i	0.991308	+	0.572332i	0.0856432	+	0.996326i	$0.472705\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	11.8633i		−	1.14687i	−0.819251	−	0.573434i	$-0.805611\pi$
$107$		−	11.8633i		−	1.14687i	0.819251	−	0.573434i	$-0.194389\pi$
$108$		0			0
$109$	−3.23313			−0.309677			−0.154839	−	0.987940i	$-0.549486\pi$
$109$	−3.23313			−0.309677			−0.154839	+	0.987940i	$0.549486\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.33701	+	1.92662i	0.313919	+	0.181241i	0.648679	−	0.761062i	$-0.275322\pi$
$113$	3.33701	+	1.92662i	0.313919	+	0.181241i	−0.334760	+	0.942304i	$0.608655\pi$
$114$		0			0
$115$	−0.0665310	+	0.0384117i	−0.00620404	+	0.00358191i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.983775	+	4.95865i	−0.0901825	+	0.454559i
$120$		0			0
$121$	5.89464	−	10.2098i	0.535876	−	0.928165i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.173963			−0.0155597
$126$		0			0
$127$	21.9600			1.94864			0.974318	−	0.225175i	$-0.0722955\pi$
$127$	21.9600			1.94864			0.974318	+	0.225175i	$0.0722955\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.11460	+	14.0549i	−0.708976	+	1.22798i	0.256261	+	0.966608i	$0.417509\pi$
$131$	−8.11460	+	14.0549i	−0.708976	+	1.22798i	−0.965237	+	0.261375i	$0.915824\pi$
$132$		0			0
$133$	16.7645	+	3.32601i	1.45367	+	0.288402i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.40456	+	3.12033i	−0.461743	+	0.266587i	−0.712777	−	0.701391i	$-0.752563\pi$
$137$	−5.40456	+	3.12033i	−0.461743	+	0.266587i	0.251034	+	0.967978i	$0.419229\pi$
$138$		0			0
$139$	9.14307	+	5.27875i	0.775505	+	0.447738i	0.834835	−	0.550500i	$-0.185563\pi$
$139$	9.14307	+	5.27875i	0.775505	+	0.447738i	−0.0593300	+	0.998238i	$0.518896\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.25391			0.606603
$144$		0			0
$145$		−	0.0349323i		−	0.00290097i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.13927	+	4.12186i	0.584872	+	0.337676i	0.763067	−	0.646319i	$-0.223693\pi$
$149$	7.13927	+	4.12186i	0.584872	+	0.337676i	−0.178195	+	0.983995i	$0.557026\pi$
$150$		0			0
$151$	−6.58096	−	11.3986i	−0.535551	−	0.927602i	−0.999136	−	0.0415494i	$-0.986771\pi$
$151$	−6.58096	−	11.3986i	−0.535551	−	0.927602i	0.463585	−	0.886052i	$-0.346563\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.113418	+	0.0654818i	−0.00910993	+	0.00525962i
$156$		0			0
$157$	7.30128	+	4.21540i	0.582705	+	0.336425i	0.762208	−	0.647332i	$-0.224115\pi$
$157$	7.30128	+	4.21540i	0.582705	+	0.336425i	−0.179502	+	0.983758i	$0.557449\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.69909	−	8.78794i	0.606774	−	0.692587i
$162$		0			0
$163$	8.15879			0.639046			0.319523	−	0.947579i	$-0.396477\pi$
$163$	8.15879			0.639046			0.319523	+	0.947579i	$0.396477\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.3487	−	19.6566i	0.878191	−	1.52107i	0.0248668	−	0.999691i	$-0.492084\pi$
$167$	11.3487	−	19.6566i	0.878191	−	1.52107i	0.853324	−	0.521381i	$-0.174583\pi$
$168$		0			0
$169$	−5.34553	−	9.25872i	−0.411194	−	0.712210i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.92866	+	5.07259i	0.222662	+	0.385662i	0.955615	−	0.294617i	$-0.0951921\pi$
$173$	2.92866	+	5.07259i	0.222662	+	0.385662i	−0.732953	+	0.680279i	$0.761859\pi$
$174$		0			0
$175$	12.5238	−	4.25821i	0.946713	−	0.321891i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			13.8391i			1.03438i	0.855869	+	0.517192i	$0.173023\pi$
$179$			13.8391i			1.03438i	−0.855869	+	0.517192i	$0.826977\pi$
$180$		0			0
$181$			16.7885i			1.24788i	0.781472	+	0.623940i	$0.214469\pi$
$181$			16.7885i			1.24788i	−0.781472	+	0.623940i	$0.785531\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0531009	−	0.0919735i	0.00390406	−	0.00676202i
$186$		0			0
$187$	−7.89939	+	4.56071i	−0.577660	+	0.333512i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.62396	+	3.24700i	−0.406935	+	0.234944i	−0.689472	−	0.724312i	$-0.742157\pi$
$191$	−5.62396	+	3.24700i	−0.406935	+	0.234944i	0.282537	+	0.959256i	$0.408824\pi$
$192$		0			0
$193$	8.37754	−	14.5103i	0.603028	−	1.04448i	−0.389331	−	0.921098i	$-0.627294\pi$
$193$	8.37754	−	14.5103i	0.603028	−	1.04448i	0.992360	−	0.123378i	$-0.0393728\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.89156i		−	0.419756i	−0.977728	−	0.209878i	$-0.932693\pi$
$197$		−	5.89156i		−	0.419756i	0.977728	−	0.209878i	$-0.0673067\pi$
$198$		0			0
$199$		−	18.7851i		−	1.33164i	−0.746113	−	0.665819i	$-0.768082\pi$
$199$		−	18.7851i		−	1.33164i	0.746113	−	0.665819i	$-0.231918\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.71018	+	5.02980i	0.120031	+	0.353023i
$204$		0			0
$205$	0.0813751	+	0.140946i	0.00568348	+	0.00984408i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.4191	+	26.7067i	1.06656	+	1.84734i
$210$		0			0
$211$	−10.9508	+	18.9674i	−0.753886	+	1.30577i	0.192040	+	0.981387i	$0.438490\pi$
$211$	−10.9508	+	18.9674i	−0.753886	+	1.30577i	−0.945926	+	0.324382i	$0.894844\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.0510207			−0.00347958
$216$		0			0
$217$	13.1249	−	14.9811i	0.890978	−	1.01698i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.51440	−	1.45169i	−0.169137	−	0.0976514i
$222$		0			0
$223$	−11.2455	+	6.49259i	−0.753054	+	0.434776i	−0.826796	−	0.562501i	$-0.809839\pi$
$223$	−11.2455	+	6.49259i	−0.753054	+	0.434776i	0.0737421	+	0.997277i	$0.476506\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.31567	−	7.47496i	−0.286441	−	0.496131i	0.686516	−	0.727114i	$-0.259139\pi$
$227$	−4.31567	−	7.47496i	−0.286441	−	0.496131i	−0.972958	+	0.230984i	$0.925806\pi$
$228$		0			0
$229$	−7.37873	−	4.26011i	−0.487600	−	0.281516i	0.235978	−	0.971758i	$-0.424171\pi$
$229$	−7.37873	−	4.26011i	−0.487600	−	0.281516i	−0.723578	+	0.690242i	$0.757504\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			0.246911i			0.0161757i	0.999967	+	0.00808783i	$0.00257447\pi$
$233$			0.246911i			0.0161757i	−0.999967	+	0.00808783i	$0.997426\pi$
$234$		0			0
$235$	−0.0506801			−0.00330600
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−23.5814	−	13.6147i	−1.52535	−	0.880664i	−0.999548	−	0.0300592i	$-0.990430\pi$
$239$	−23.5814	−	13.6147i	−1.52535	−	0.880664i	−0.525806	−	0.850604i	$-0.676236\pi$
$240$		0			0
$241$	5.71926	−	3.30201i	0.368410	−	0.212701i	−0.304354	−	0.952559i	$-0.598441\pi$
$241$	5.71926	−	3.30201i	0.368410	−	0.212701i	0.672763	+	0.739858i	$0.265107\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.0965390	−	0.0742295i	0.00616765	−	0.00474235i
$246$		0			0
$247$	−4.90797	+	8.50086i	−0.312287	+	0.540897i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.1930			0.706496			0.353248	−	0.935530i	$-0.385077\pi$
$251$	11.1930			0.706496			0.353248	+	0.935530i	$0.385077\pi$
$252$		0			0
$253$	21.0809			1.32534
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.85692	−	8.41243i	0.302966	−	0.524753i	−0.673840	−	0.738877i	$-0.735356\pi$
$257$	4.85692	−	8.41243i	0.302966	−	0.524753i	0.976806	+	0.214124i	$0.0686898\pi$
$258$		0			0
$259$	−3.14312	+	15.8427i	−0.195304	+	0.984415i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.18772	+	2.99513i	−0.319888	+	0.184688i	−0.651343	−	0.758784i	$-0.725794\pi$
$263$	−5.18772	+	2.99513i	−0.319888	+	0.184688i	0.331454	+	0.943471i	$0.392461\pi$
$264$		0			0
$265$	0.134753	+	0.0777999i	0.00827784	+	0.00477921i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−22.7332			−1.38607			−0.693034	−	0.720905i	$-0.743727\pi$
$269$	−22.7332			−1.38607			−0.693034	+	0.720905i	$0.743727\pi$
$270$		0			0
$271$		−	1.03859i		−	0.0630896i	−0.999502	−	0.0315448i	$-0.989957\pi$
$271$		−	1.03859i		−	0.0630896i	0.999502	−	0.0315448i	$-0.0100427\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	20.6700	+	11.9338i	1.24645	+	0.719636i
$276$		0			0
$277$	7.59222	+	13.1501i	0.456172	+	0.790113i	0.998755	−	0.0498891i	$-0.0158868\pi$
$277$	7.59222	+	13.1501i	0.456172	+	0.790113i	−0.542583	+	0.840002i	$0.682553\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.8641	+	7.42710i	−0.767408	+	0.443063i	−0.831949	−	0.554852i	$-0.812775\pi$
$281$	−12.8641	+	7.42710i	−0.767408	+	0.443063i	0.0645409	+	0.997915i	$0.479442\pi$
$282$		0			0
$283$	−28.6064	−	16.5159i	−1.70048	−	0.981770i	−0.945274	−	0.326277i	$-0.894206\pi$
$283$	−28.6064	−	16.5159i	−1.70048	−	0.981770i	−0.755202	−	0.655493i	$-0.772461\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.6172	−	16.3105i	−1.09894	−	0.962780i
$288$		0			0
$289$	−13.3491			−0.785244
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.7859	+	22.1459i	−0.746963	+	1.29378i	0.202309	+	0.979322i	$0.435155\pi$
$293$	−12.7859	+	22.1459i	−0.746963	+	1.29378i	−0.949272	+	0.314456i	$0.898178\pi$
$294$		0			0
$295$	0.0710377	+	0.123041i	0.00413597	+	0.00716372i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.35506	+	5.81114i	0.194028	+	0.336067i
$300$		0			0
$301$	7.34633	−	2.49781i	0.423435	−	0.143972i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			0.00974107i			0.000557772i
$306$		0			0
$307$			6.04267i			0.344873i	0.985021	+	0.172437i	$0.0551640\pi$
$307$			6.04267i			0.344873i	−0.985021	+	0.172437i	$0.944836\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	17.0708	−	29.5674i	0.967994	−	1.67661i	0.266648	−	0.963794i	$-0.414084\pi$
$311$	17.0708	−	29.5674i	0.967994	−	1.67661i	0.701346	−	0.712821i	$-0.252583\pi$
$312$		0			0
$313$	10.9506	−	6.32235i	0.618966	−	0.357360i	−0.157500	−	0.987519i	$-0.550343\pi$
$313$	10.9506	−	6.32235i	0.618966	−	0.357360i	0.776466	+	0.630159i	$0.217010\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.95447	−	2.86047i	0.278271	−	0.160660i	−0.354369	−	0.935105i	$-0.615304\pi$
$317$	4.95447	−	2.86047i	0.278271	−	0.160660i	0.632640	+	0.774446i	$0.281971\pi$
$318$		0			0
$319$	−4.79284	+	8.30144i	−0.268347	+	0.464791i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	12.3431i		−	0.686786i
$324$		0			0
$325$			7.59715i			0.421414i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.29729	−	2.48114i	0.402312	−	0.136790i
$330$		0			0
$331$	−7.18521	−	12.4452i	−0.394935	−	0.684047i	0.598158	−	0.801378i	$-0.295900\pi$
$331$	−7.18521	−	12.4452i	−0.394935	−	0.684047i	−0.993093	+	0.117331i	$0.962566\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.0642004	+	0.111198i	0.00350764	+	0.00607542i
$336$		0			0
$337$	2.20813	−	3.82460i	0.120285	−	0.208339i	−0.799595	−	0.600539i	$-0.794953\pi$
$337$	2.20813	−	3.82460i	0.120285	−	0.208339i	0.919880	+	0.392200i	$0.128286\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	35.9373			1.94612
$342$		0			0
$343$	−10.2663	+	15.4144i	−0.554330	+	0.832297i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.305641	+	0.176462i	0.0164077	+	0.00947298i	0.508181	−	0.861250i	$-0.330318\pi$
$347$	0.305641	+	0.176462i	0.0164077	+	0.00947298i	−0.491774	+	0.870723i	$0.663651\pi$
$348$		0			0
$349$	1.16292	−	0.671412i	0.0622497	−	0.0359399i	−0.468552	−	0.883436i	$-0.655224\pi$
$349$	1.16292	−	0.671412i	0.0622497	−	0.0359399i	0.530802	+	0.847496i	$0.321891\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.09184	+	14.0155i	0.430685	+	0.745968i	0.996932	−	0.0782669i	$-0.0249386\pi$
$353$	8.09184	+	14.0155i	0.430685	+	0.745968i	−0.566247	+	0.824235i	$0.691605\pi$
$354$		0			0
$355$	0.176009	+	0.101619i	0.00934159	+	0.00539337i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			13.1262i			0.692777i	0.938091	+	0.346388i	$0.112592\pi$
$359$			13.1262i			0.692777i	−0.938091	+	0.346388i	$0.887408\pi$
$360$		0			0
$361$	−22.7302			−1.19632
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.193004	−	0.111431i	−0.0101023	−	0.00583257i
$366$		0			0
$367$	27.4478	−	15.8470i	1.43276	−	0.827206i	0.435432	−	0.900222i	$-0.356596\pi$
$367$	27.4478	−	15.8470i	1.43276	−	0.827206i	0.997331	+	0.0730154i	$0.0232622\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−23.2116	−	4.60509i	−1.20509	−	0.239084i
$372$		0			0
$373$	8.85016	−	15.3289i	0.458244	−	0.793702i	−0.540624	−	0.841264i	$-0.681812\pi$
$373$	8.85016	−	15.3289i	0.458244	−	0.793702i	0.998868	+	0.0475622i	$0.0151452\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.05116			−0.157142
$378$		0			0
$379$	−5.09384			−0.261653			−0.130827	−	0.991405i	$-0.541763\pi$
$379$	−5.09384			−0.261653			−0.130827	+	0.991405i	$0.541763\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.84567	−	11.8571i	0.349798	−	0.605867i	−0.636416	−	0.771346i	$-0.719584\pi$
$383$	6.84567	−	11.8571i	0.349798	−	0.605867i	0.986213	+	0.165479i	$0.0529170\pi$
$384$		0			0
$385$	0.215527	+	0.0427596i	0.0109842	+	0.00217923i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.9566	−	9.21256i	0.809033	−	0.467095i	−0.0375873	−	0.999293i	$-0.511967\pi$
$389$	15.9566	−	9.21256i	0.809033	−	0.467095i	0.846620	+	0.532198i	$0.178634\pi$
$390$		0			0
$391$	−7.30721	−	4.21882i	−0.369542	−	0.213355i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.165558			0.00833010
$396$		0			0
$397$		−	7.04050i		−	0.353352i	−0.984269	−	0.176676i	$-0.943465\pi$
$397$		−	7.04050i		−	0.353352i	0.984269	−	0.176676i	$-0.0565345\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	31.0404	+	17.9212i	1.55008	+	0.894940i	0.998134	+	0.0610617i	$0.0194487\pi$
$401$	31.0404	+	17.9212i	1.55008	+	0.894940i	0.551948	+	0.833879i	$0.313885\pi$
$402$		0			0
$403$	5.71949	+	9.90646i	0.284908	+	0.493476i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−25.2382	+	14.5713i	−1.25101	+	0.722271i
$408$		0			0
$409$	11.5808	+	6.68621i	0.572636	+	0.330612i	0.758202	−	0.652020i	$-0.226078\pi$
$409$	11.5808	+	6.68621i	0.572636	+	0.330612i	−0.185565	+	0.982632i	$0.559412\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.2522	−	14.2385i	−0.799720	−	0.700632i
$414$		0			0
$415$	−0.232317			−0.0114040
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−20.1508	+	34.9023i	−0.984433	+	1.70509i	−0.340001	+	0.940425i	$0.610428\pi$
$419$	−20.1508	+	34.9023i	−0.984433	+	1.70509i	−0.644431	+	0.764662i	$0.722906\pi$
$420$		0			0
$421$	−6.04485	−	10.4700i	−0.294608	−	0.510276i	0.680286	−	0.732947i	$-0.261856\pi$
$421$	−6.04485	−	10.4700i	−0.294608	−	0.510276i	−0.974894	+	0.222671i	$0.928522\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.77652	−	8.27317i	−0.231695	−	0.401308i
$426$		0			0
$427$	−0.476892	−	1.40259i	−0.0230784	−	0.0678761i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	20.2652i		−	0.976140i	−0.872805	−	0.488070i	$-0.837701\pi$
$431$		−	20.2652i		−	0.976140i	0.872805	−	0.488070i	$-0.162299\pi$
$432$		0			0
$433$			33.6180i			1.61558i	0.589472	+	0.807789i	$0.299336\pi$
$433$			33.6180i			1.61558i	−0.589472	+	0.807789i	$0.700664\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.2633	+	24.7047i	−0.682304	+	1.18179i
$438$		0			0
$439$	−10.2274	+	5.90480i	−0.488128	+	0.281821i	−0.723797	−	0.690013i	$-0.757605\pi$
$439$	−10.2274	+	5.90480i	−0.488128	+	0.281821i	0.235670	+	0.971833i	$0.424272\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.0807550	−	0.0466239i	0.00383678	−	0.00221517i	−0.498080	−	0.867131i	$-0.665962\pi$
$443$	0.0807550	−	0.0466239i	0.00383678	−	0.00221517i	0.501917	+	0.864916i	$0.332628\pi$
$444$		0			0
$445$	−0.0348246	+	0.0603179i	−0.00165084	+	0.00285934i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	14.9759i		−	0.706755i	−0.935481	−	0.353378i	$-0.885033\pi$
$449$		−	14.9759i		−	0.706755i	0.935481	−	0.353378i	$-0.114967\pi$
$450$		0			0
$451$		−	44.6598i		−	2.10295i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0225144	+	0.0662171i	0.00105549	+	0.00310431i
$456$		0			0
$457$	−3.63391	−	6.29411i	−0.169987	−	0.294426i	0.768428	−	0.639936i	$-0.221039\pi$
$457$	−3.63391	−	6.29411i	−0.169987	−	0.294426i	−0.938415	+	0.345510i	$0.887706\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.63421	−	6.29464i	−0.169262	−	0.293170i	0.768899	−	0.639371i	$-0.220805\pi$
$461$	−3.63421	−	6.29464i	−0.169262	−	0.293170i	−0.938161	+	0.346200i	$0.887472\pi$
$462$		0			0
$463$	15.5092	−	26.8627i	0.720774	−	1.24842i	−0.239916	−	0.970794i	$-0.577120\pi$
$463$	15.5092	−	26.8627i	0.720774	−	1.24842i	0.960690	−	0.277624i	$-0.0895468\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−22.6887			−1.04991			−0.524954	−	0.851130i	$-0.675918\pi$
$467$	−22.6887			−1.04991			−0.524954	+	0.851130i	$0.675918\pi$
$468$		0			0
$469$	−14.6880	−	12.8681i	−0.678228	−	0.594194i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.1247	+	7.00022i	0.557496	+	0.321871i
$474$		0			0
$475$	−27.9704	+	16.1487i	−1.28337	+	0.740955i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.547354	−	0.948045i	−0.0250092	−	0.0433173i	0.853250	−	0.521502i	$-0.174628\pi$
$479$	−0.547354	−	0.948045i	−0.0250092	−	0.0433173i	−0.878259	+	0.478185i	$0.841295\pi$
$480$		0			0
$481$	−8.03341	−	4.63809i	−0.366292	−	0.211479i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	0.0822637i		−	0.00373540i
$486$		0			0
$487$	−12.3778			−0.560892			−0.280446	−	0.959870i	$-0.590482\pi$
$487$	−12.3778			−0.560892			−0.280446	+	0.959870i	$0.590482\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	27.1411	+	15.6700i	1.22486	+	0.707175i	0.965951	−	0.258726i	$-0.0833026\pi$
$491$	27.1411	+	15.6700i	1.22486	+	0.707175i	0.258912	+	0.965901i	$0.416636\pi$
$492$		0			0
$493$	3.32266	−	1.91834i	0.149645	−	0.0863975i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−30.3180	−	6.01496i	−1.35995	−	0.269808i
$498$		0			0
$499$	−16.9940	+	29.4345i	−0.760756	+	1.31767i	0.181706	+	0.983353i	$0.441838\pi$
$499$	−16.9940	+	29.4345i	−0.760756	+	1.31767i	−0.942462	+	0.334315i	$0.891495\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.16212			0.0518163			0.0259082	−	0.999664i	$-0.491752\pi$
$503$	1.16212			0.0518163			0.0259082	+	0.999664i	$0.491752\pi$
$504$		0			0
$505$	0.103786			0.00461840
$506$		0			0
$507$		0			0
$508$		0			0
$509$	18.3129	−	31.7189i	0.811705	−	1.40591i	−0.0999657	−	0.994991i	$-0.531873\pi$
$509$	18.3129	−	31.7189i	0.811705	−	1.40591i	0.911670	−	0.410923i	$-0.134793\pi$
$510$		0			0
$511$	33.2455	+	6.59577i	1.47069	+	0.291780i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.175024	+	0.101050i	−0.00771247	+	0.00445280i
$516$		0			0
$517$	12.0438	+	6.95349i	0.529686	+	0.305814i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−42.9713			−1.88261			−0.941303	−	0.337563i	$-0.890397\pi$
$521$	−42.9713			−1.88261			−0.941303	+	0.337563i	$0.890397\pi$
$522$		0			0
$523$			21.1229i			0.923639i	0.886974	+	0.461820i	$0.152803\pi$
$523$			21.1229i			0.923639i	−0.886974	+	0.461820i	$0.847197\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.4569	−	7.19197i	−0.542630	−	0.313287i
$528$		0			0
$529$	−1.74972	−	3.03060i	−0.0760746	−	0.131765i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.3109	−	7.10770i	0.533244	−	0.307868i
$534$		0			0
$535$	0.178733	+	0.103192i	0.00772732	+	0.00446137i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−33.1264	+	4.39468i	−1.42686	+	0.189292i
$540$		0			0
$541$	−32.2695			−1.38737			−0.693687	−	0.720277i	$-0.744015\pi$
$541$	−32.2695			−1.38737			−0.693687	+	0.720277i	$0.744015\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0281230	−	0.0487105i	0.00120466	−	0.00208653i
$546$		0			0
$547$	11.9637	+	20.7218i	0.511532	+	0.886000i	0.999911	+	0.0133677i	$0.00425520\pi$
$547$	11.9637	+	20.7218i	0.511532	+	0.886000i	−0.488379	+	0.872632i	$0.662411\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.48563	−	11.2334i	−0.276297	−	0.478561i
$552$		0			0
$553$	−23.8382	+	8.10518i	−1.01370	+	0.344667i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			34.1881i			1.44860i	0.689486	+	0.724299i	$0.257836\pi$
$557$			34.1881i			1.44860i	−0.689486	+	0.724299i	$0.742164\pi$
$558$		0			0
$559$			4.45639i			0.188485i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.79724	−	16.9693i	0.412904	−	0.715171i	−0.582302	−	0.812973i	$-0.697848\pi$
$563$	9.79724	−	16.9693i	0.412904	−	0.715171i	0.995206	+	0.0978016i	$0.0311810\pi$
$564$		0			0
$565$	−0.0580533	+	0.0335171i	−0.00244232	+	0.00141007i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.5347	+	12.4330i	−0.902780	+	0.521220i	−0.878101	−	0.478475i	$-0.841190\pi$
$569$	−21.5347	+	12.4330i	−0.902780	+	0.521220i	−0.0246790	+	0.999695i	$0.507856\pi$
$570$		0			0
$571$	−7.82182	+	13.5478i	−0.327333	+	0.566957i	−0.981982	−	0.188976i	$-0.939483\pi$
$571$	−7.82182	+	13.5478i	−0.327333	+	0.566957i	0.654649	+	0.755933i	$0.272817\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			22.0784i			0.920732i
$576$		0			0
$577$			0.540475i			0.0225003i	0.999937	+	0.0112501i	$0.00358110\pi$
$577$			0.540475i			0.0225003i	−0.999937	+	0.0112501i	$0.996419\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	33.4507	−	11.3735i	1.38777	−	0.471854i
$582$		0			0
$583$	−21.3489	−	36.9773i	−0.884180	−	1.53144i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.2822	+	31.6656i	0.754586	+	1.30698i	0.945580	+	0.325390i	$0.105496\pi$
$587$	18.2822	+	31.6656i	0.754586	+	1.30698i	−0.190994	+	0.981591i	$0.561171\pi$
$588$		0			0
$589$	−24.3151	+	42.1150i	−1.00189	+	1.73532i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−42.9714			−1.76462			−0.882312	−	0.470665i	$-0.844014\pi$
$593$	−42.9714			−1.76462			−0.882312	+	0.470665i	$0.844014\pi$
$594$		0			0
$595$	−0.0661501	−	0.0579540i	−0.00271189	−	0.00237588i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.7897	+	13.1576i	0.931161	+	0.537606i	0.887178	−	0.461426i	$-0.152662\pi$
$599$	22.7897	+	13.1576i	0.931161	+	0.537606i	0.0439823	+	0.999032i	$0.485995\pi$
$600$		0			0
$601$	−27.3703	+	15.8022i	−1.11646	+	0.644587i	−0.940494	−	0.339810i	$-0.889637\pi$
$601$	−27.3703	+	15.8022i	−1.11646	+	0.644587i	−0.175963	+	0.984397i	$0.556304\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.102548	+	0.177618i	0.00416917	+	0.00722121i
$606$		0			0
$607$	7.85286	+	4.53385i	0.318738	+	0.184023i	0.650830	−	0.759224i	$-0.274421\pi$
$607$	7.85286	+	4.53385i	0.318738	+	0.184023i	−0.332092	+	0.943247i	$0.607754\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			4.42665i			0.179083i
$612$		0			0
$613$	15.2630			0.616465			0.308233	−	0.951311i	$-0.400262\pi$
$613$	15.2630			0.616465			0.308233	+	0.951311i	$0.400262\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.1768	−	7.03028i	−0.490219	−	0.283028i	0.234446	−	0.972129i	$-0.424672\pi$
$617$	−12.1768	−	7.03028i	−0.490219	−	0.283028i	−0.724665	+	0.689101i	$0.758006\pi$
$618$		0			0
$619$	4.52202	−	2.61079i	0.181755	−	0.104936i	−0.406362	−	0.913712i	$-0.633203\pi$
$619$	4.52202	−	2.61079i	0.181755	−	0.104936i	0.588117	+	0.808776i	$0.299869\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.06132	−	10.3899i	0.0825849	−	0.416263i
$624$		0			0
$625$	−12.4977	+	21.6467i	−0.499909	+	0.865868i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	11.6643			0.465087
$630$		0			0
$631$	−34.8593			−1.38773			−0.693863	−	0.720107i	$-0.744093\pi$
$631$	−34.8593			−1.38773			−0.693863	+	0.720107i	$0.744093\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.191017	+	0.330851i	−0.00758028	+	0.0131294i
$636$		0			0
$637$	−6.48357	−	8.43218i	−0.256888	−	0.334095i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	5.33065	−	3.07765i	0.210548	−	0.121560i	−0.391018	−	0.920383i	$-0.627877\pi$
$641$	5.33065	−	3.07765i	0.210548	−	0.121560i	0.601566	+	0.798823i	$0.294544\pi$
$642$		0			0
$643$	−9.75081	−	5.62963i	−0.384534	−	0.222011i	0.295255	−	0.955419i	$-0.404595\pi$
$643$	−9.75081	−	5.62963i	−0.384534	−	0.222011i	−0.679789	+	0.733407i	$0.737929\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.33809			−0.288490			−0.144245	−	0.989542i	$-0.546075\pi$
$647$	−7.33809			−0.288490			−0.144245	+	0.989542i	$0.546075\pi$
$648$		0			0
$649$		−	38.9865i		−	1.53035i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.18110	−	0.681911i	−0.0462202	−	0.0266852i	0.476712	−	0.879060i	$-0.341829\pi$
$653$	−1.18110	−	0.681911i	−0.0462202	−	0.0266852i	−0.522932	+	0.852374i	$0.675162\pi$
$654$		0			0
$655$	−0.141168	−	0.244511i	−0.00551590	−	0.00955382i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	35.8162	−	20.6785i	1.39520	−	0.805519i	0.401314	−	0.915940i	$-0.368553\pi$
$659$	35.8162	−	20.6785i	1.39520	−	0.805519i	0.993885	+	0.110422i	$0.0352202\pi$
$660$		0			0
$661$	−36.0595	−	20.8190i	−1.40255	−	0.809763i	−0.407897	−	0.913028i	$-0.633738\pi$
$661$	−36.0595	−	20.8190i	−1.40255	−	0.809763i	−0.994654	+	0.103264i	$0.967071\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.195934	+	0.223644i	−0.00759801	+	0.00867256i
$666$		0			0
$667$	−8.86709			−0.343335
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.33651	−	2.31490i	0.0515954	−	0.0893658i
$672$		0			0
$673$	25.4080	+	44.0079i	0.979406	+	1.69638i	0.664555	+	0.747239i	$0.268621\pi$
$673$	25.4080	+	44.0079i	0.979406	+	1.69638i	0.314851	+	0.949141i	$0.398046\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.7278	+	18.5810i	0.412302	+	0.714128i	0.995141	−	0.0984599i	$-0.0313916\pi$
$677$	10.7278	+	18.5810i	0.412302	+	0.714128i	−0.582839	+	0.812587i	$0.698058\pi$
$678$		0			0
$679$	4.02738	+	11.8449i	0.154556	+	0.454566i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			5.66012i			0.216578i	0.994119	+	0.108289i	$0.0345373\pi$
$683$			5.66012i			0.216578i	−0.994119	+	0.108289i	$0.965463\pi$
$684$		0			0
$685$		−	0.108567i		−	0.00414815i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.79543	−	11.7700i	0.258885	−	0.448402i
$690$		0			0
$691$	−15.6444	+	9.03228i	−0.595140	+	0.343604i	−0.767127	−	0.641495i	$-0.778314\pi$
$691$	−15.6444	+	9.03228i	−0.595140	+	0.343604i	0.171988	+	0.985099i	$0.444981\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.159060	+	0.0918335i	−0.00603350	+	0.00348344i
$696$		0			0
$697$	−8.93757	+	15.4803i	−0.338535	+	0.586359i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			28.7091i			1.08433i	0.840273	+	0.542163i	$0.182395\pi$
$701$			28.7091i			1.08433i	−0.840273	+	0.542163i	$0.817605\pi$
$702$		0			0
$703$		−	39.4355i		−	1.48734i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.9438	+	5.08102i	−0.562020	+	0.191092i
$708$		0			0
$709$	13.3468	+	23.1174i	0.501251	+	0.868193i	0.999999	+	0.00144551i	$0.000460119\pi$
$709$	13.3468	+	23.1174i	0.501251	+	0.868193i	−0.498748	+	0.866747i	$0.666207\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.6217	+	28.7896i	0.622486	+	1.07818i
$714$		0			0
$715$	−0.0630975	+	0.109288i	−0.00235971	+	0.00408714i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−25.2381			−0.941224			−0.470612	−	0.882340i	$-0.655967\pi$
$719$	−25.2381			−0.941224			−0.470612	+	0.882340i	$0.655967\pi$
$720$		0			0
$721$	20.2541	−	23.1185i	0.754302	−	0.860979i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.69424	−	5.01962i	−0.322896	−	0.186424i
$726$		0			0
$727$	24.5712	−	14.1862i	0.911294	−	0.526136i	0.0304464	−	0.999536i	$-0.490307\pi$
$727$	24.5712	−	14.1862i	0.911294	−	0.526136i	0.880847	+	0.473401i	$0.156974\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.80185	−	4.85294i	−0.103630	−	0.179492i
$732$		0			0
$733$	−16.2190	−	9.36404i	−0.599062	−	0.345869i	0.169610	−	0.985511i	$-0.445749\pi$
$733$	−16.2190	−	9.36404i	−0.599062	−	0.345869i	−0.768673	+	0.639642i	$0.779082\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	35.2341i		−	1.29787i
$738$		0			0
$739$	31.3341			1.15265			0.576323	−	0.817222i	$-0.304487\pi$
$739$	31.3341			1.15265			0.576323	+	0.817222i	$0.304487\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.2784	+	9.39834i	0.597197	+	0.344792i	0.767938	−	0.640524i	$-0.221283\pi$
$743$	16.2784	+	9.39834i	0.597197	+	0.344792i	−0.170741	+	0.985316i	$0.554616\pi$
$744$		0			0
$745$	−0.124200	+	0.0717072i	−0.00455035	+	0.00262715i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−30.7873	−	6.10807i	−1.12494	−	0.223184i
$750$		0			0
$751$	7.34792	−	12.7270i	0.268129	−	0.464414i	−0.700249	−	0.713898i	$-0.746928\pi$
$751$	7.34792	−	12.7270i	0.268129	−	0.464414i	0.968379	+	0.249485i	$0.0802612\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.228975			0.00833327
$756$		0			0
$757$	15.4439			0.561318			0.280659	−	0.959808i	$-0.409447\pi$
$757$	15.4439			0.561318			0.280659	+	0.959808i	$0.409447\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.201785	−	0.349502i	0.00731470	−	0.0126694i	−0.862345	−	0.506321i	$-0.831005\pi$
$761$	0.201785	−	0.349502i	0.00731470	−	0.0126694i	0.869660	+	0.493652i	$0.164338\pi$
$762$		0			0
$763$	−1.66464	+	8.39051i	−0.0602641	+	0.303757i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.7470	−	6.20478i	0.388051	−	0.224042i
$768$		0			0
$769$	−10.4462	−	6.03109i	−0.376698	−	0.217487i	0.299682	−	0.954039i	$-0.403119\pi$
$769$	−10.4462	−	6.03109i	−0.376698	−	0.217487i	−0.676381	+	0.736552i	$0.736453\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−35.6215			−1.28122			−0.640608	−	0.767868i	$-0.721318\pi$
$773$	−35.6215			−1.28122			−0.640608	+	0.767868i	$0.721318\pi$
$774$		0			0
$775$			37.6378i			1.35199i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	52.3369	+	30.2167i	1.87516	+	1.08263i
$780$		0			0
$781$	−27.8850	−	48.2982i	−0.997802	−	1.72824i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.127019	+	0.0733344i	−0.00453350	+	0.00261742i
$786$		0			0
$787$	−16.7626	−	9.67792i	−0.597524	−	0.344981i	0.170543	−	0.985350i	$-0.445448\pi$
$787$	−16.7626	−	9.67792i	−0.597524	−	0.344981i	−0.768067	+	0.640370i	$0.778781\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.71804	−	7.66814i	0.238866	−	0.272648i
$792$		0			0
$793$	0.850832			0.0302139
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.71888	+	16.8336i	−0.344261	+	0.596277i	−0.985219	−	0.171299i	$-0.945204\pi$
$797$	−9.71888	+	16.8336i	−0.344261	+	0.596277i	0.640959	+	0.767575i	$0.278537\pi$
$798$		0			0
$799$	−2.78314	−	4.82054i	−0.0984605	−	0.170539i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	30.5775	+	52.9618i	1.07906	+	1.86898i
$804$		0			0
$805$	0.0654300	+	0.192436i	0.00230610	+	0.00678249i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			4.83109i			0.169852i	0.996387	+	0.0849261i	$0.0270654\pi$
$809$			4.83109i			0.169852i	−0.996387	+	0.0849261i	$0.972935\pi$
$810$		0			0
$811$			36.9933i			1.29901i	0.760358	+	0.649505i	$0.225024\pi$
$811$			36.9933i			1.29901i	−0.760358	+	0.649505i	$0.774976\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.0709684	+	0.122921i	−0.00248592	+	0.00430573i
$816$		0			0
$817$	−16.4071	+	9.47266i	−0.574012	+	0.331406i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−32.3478	+	18.6760i	−1.12895	+	0.651798i	−0.943670	−	0.330888i	$-0.892652\pi$
$821$	−32.3478	+	18.6760i	−1.12895	+	0.651798i	−0.185277	+	0.982686i	$0.559318\pi$
$822$		0			0
$823$	8.13705	−	14.0938i	0.283640	−	0.491279i	−0.688639	−	0.725105i	$-0.741791\pi$
$823$	8.13705	−	14.0938i	0.283640	−	0.491279i	0.972278	+	0.233826i	$0.0751247\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			19.0164i			0.661265i	0.943760	+	0.330633i	$0.107262\pi$
$827$			19.0164i			0.661265i	−0.943760	+	0.330633i	$0.892738\pi$
$828$		0			0
$829$		−	54.5471i		−	1.89450i	−0.320497	−	0.947250i	$-0.603850\pi$
$829$		−	54.5471i		−	1.89450i	0.320497	−	0.947250i	$-0.396150\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.3620	+	5.10613i	0.428319	+	0.176917i
$834$		0			0
$835$	0.197432	+	0.341962i	0.00683240	+	0.0118341i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.7950	+	20.4295i	0.407208	+	0.705305i	0.994576	−	0.104015i	$-0.0331691\pi$
$839$	11.7950	+	20.4295i	0.407208	+	0.705305i	−0.587368	+	0.809320i	$0.699836\pi$
$840$		0			0
$841$	−12.4840	+	21.6230i	−0.430484	+	0.745620i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.185990			0.00639826
$846$		0			0
$847$	−23.4612	−	20.5543i	−0.806137	−	0.706255i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−23.3462	−	13.4789i	−0.800298	−	0.462052i
$852$		0			0
$853$	−44.4097	+	25.6400i	−1.52056	+	0.877895i	−0.520853	+	0.853646i	$0.674386\pi$
$853$	−44.4097	+	25.6400i	−1.52056	+	0.877895i	−0.999706	+	0.0242489i	$0.992281\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−25.4437	−	44.0698i	−0.869141	−	1.50540i	−0.862875	−	0.505417i	$-0.831339\pi$
$857$	−25.4437	−	44.0698i	−0.869141	−	1.50540i	−0.00626618	−	0.999980i	$-0.501995\pi$
$858$		0			0
$859$	3.87842	+	2.23921i	0.132330	+	0.0764007i	0.564704	−	0.825294i	$-0.308991\pi$
$859$	3.87842	+	2.23921i	0.132330	+	0.0764007i	−0.432374	+	0.901695i	$0.642324\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	19.5957i		−	0.667046i	−0.942742	−	0.333523i	$-0.891763\pi$
$863$		−	19.5957i		−	0.667046i	0.942742	−	0.333523i	$-0.108237\pi$
$864$		0			0
$865$	−0.101899			−0.00346466
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−39.3437	−	22.7151i	−1.33464	−	0.770557i
$870$		0			0
$871$	9.71261	−	5.60758i	0.329099	−	0.190006i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.0895684	+	0.451463i	−0.00302796	+	0.0152622i
$876$		0			0
$877$	10.7024	−	18.5371i	0.361395	−	0.625954i	−0.626796	−	0.779183i	$-0.715634\pi$
$877$	10.7024	−	18.5371i	0.361395	−	0.625954i	0.988191	+	0.153230i	$0.0489674\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−9.43135			−0.317750			−0.158875	−	0.987299i	$-0.550787\pi$
$881$	−9.43135			−0.317750			−0.158875	+	0.987299i	$0.550787\pi$
$882$		0			0
$883$	−39.5587			−1.33126			−0.665628	−	0.746284i	$-0.731836\pi$
$883$	−39.5587			−1.33126			−0.665628	+	0.746284i	$0.731836\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.1249	+	34.8573i	−0.675727	+	1.17039i	0.300529	+	0.953773i	$0.402837\pi$
$887$	−20.1249	+	34.8573i	−0.675727	+	1.17039i	−0.976256	+	0.216620i	$0.930497\pi$
$888$		0			0
$889$	11.3066	−	56.9900i	0.379210	−	1.91138i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−16.2976	+	9.40942i	−0.545378	+	0.314874i
$894$		0			0
$895$	−0.208501	−	0.120378i	−0.00696943	−	0.00402380i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−15.1160			−0.504148
$900$		0			0
$901$			17.0898i			0.569344i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.252937	−	0.146033i	−0.00840791	−	0.00485431i
$906$		0			0
$907$	2.84241	+	4.92321i	0.0943808	+	0.163472i	0.909350	−	0.416032i	$-0.136580\pi$
$907$	2.84241	+	4.92321i	0.0943808	+	0.163472i	−0.814969	+	0.579504i	$0.803246\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−40.0431	+	23.1189i	−1.32669	+	0.765963i	−0.984786	−	0.173773i	$-0.944404\pi$
$911$	−40.0431	+	23.1189i	−1.32669	+	0.765963i	−0.341901	+	0.939736i	$0.611071\pi$
$912$		0			0
$913$	55.2088	+	31.8748i	1.82714	+	1.05490i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	32.2969	+	28.2952i	1.06654	+	0.934391i
$918$		0			0
$919$	50.9663			1.68122			0.840612	−	0.541637i	$-0.182195\pi$
$919$	50.9663			1.68122			0.840612	+	0.541637i	$0.182195\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.87589	−	15.3735i	0.292153	−	0.506024i
$924$		0			0
$925$	−15.2608	−	26.4324i	−0.501770	−	0.869092i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	14.4161	+	24.9694i	0.472977	+	0.819221i	0.999522	−	0.0309269i	$-0.00984590\pi$
$929$	14.4161	+	24.9694i	0.472977	+	0.819221i	−0.526544	+	0.850148i	$0.676513\pi$
$930$		0			0
$931$	17.2631	−	41.7943i	0.565776	−	1.36975i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	0.158684i		−	0.00518951i
$936$		0			0
$937$		−	21.8146i		−	0.712652i	−0.934362	−	0.356326i	$-0.884029\pi$
$937$		−	21.8146i		−	0.712652i	0.934362	−	0.356326i	$-0.115971\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.21225	+	9.02789i	−0.169915	+	0.294301i	−0.938390	−	0.345579i	$-0.887683\pi$
$941$	−5.21225	+	9.02789i	−0.169915	+	0.294301i	0.768475	+	0.639880i	$0.221016\pi$
$942$		0			0
$943$	35.7772	−	20.6560i	1.16507	−	0.672651i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.8197	+	10.8655i	−0.611557	+	0.353083i	−0.773575	−	0.633705i	$-0.781533\pi$
$947$	−18.8197	+	10.8655i	−0.611557	+	0.353083i	0.162018	+	0.986788i	$0.448200\pi$
$948$		0			0
$949$	−9.73294	+	16.8580i	−0.315945	+	0.547232i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	22.2100i		−	0.719453i	−0.933058	−	0.359726i	$-0.882870\pi$
$953$		−	22.2100i		−	0.719453i	0.933058	−	0.359726i	$-0.117130\pi$
$954$		0			0
$955$		−	0.112975i		−	0.00365578i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.31512	+	15.6323i	0.171634	+	0.504794i
$960$		0			0
$961$	12.8355	+	22.2318i	0.414049	+	0.717155i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.145742	+	0.252433i	0.00469162	+	0.00812612i
$966$		0			0
$967$	30.2262	−	52.3534i	0.972010	−	1.68357i	0.282541	−	0.959255i	$-0.408823\pi$
$967$	30.2262	−	52.3534i	0.972010	−	1.68357i	0.689469	−	0.724315i	$-0.257844\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24.7707			−0.794931			−0.397466	−	0.917617i	$-0.630110\pi$
$971$	−24.7707			−0.794931			−0.397466	+	0.917617i	$0.630110\pi$
$972$		0			0
$973$	18.4068	−	21.0099i	0.590094	−	0.673548i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.1210	−	10.4621i	−0.579741	−	0.334714i	0.181290	−	0.983430i	$-0.441973\pi$
$977$	−18.1210	−	10.4621i	−0.579741	−	0.334714i	−0.761030	+	0.648716i	$0.775306\pi$
$978$		0			0
$979$	16.5517	−	9.55612i	0.528994	−	0.305415i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.1275	−	33.1297i	−0.610071	−	1.05667i	−0.991228	−	0.132164i	$-0.957808\pi$
$983$	−19.1275	−	33.1297i	−0.610071	−	1.05667i	0.381157	−	0.924510i	$-0.375526\pi$
$984$		0			0
$985$	0.0887627	+	0.0512472i	0.00282821	+	0.00163287i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			12.9509i			0.411815i
$990$		0			0
$991$	−21.5607			−0.684898			−0.342449	−	0.939536i	$-0.611256\pi$
$991$	−21.5607			−0.684898			−0.342449	+	0.939536i	$0.611256\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.283017	+	0.163400i	0.00897225	+	0.00518013i
$996$		0			0
$997$	−23.2029	+	13.3962i	−0.734845	+	0.424263i	−0.820192	−	0.572089i	$-0.806133\pi$
$997$	−23.2029	+	13.3962i	−0.734845	+	0.424263i	0.0853473	+	0.996351i	$0.472800\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.d.881.12		48
3.2	odd	2		1008.2.cc.d.545.7		48
4.3	odd	2		1512.2.bu.a.881.12		48
7.6	odd	2	inner	3024.2.cc.d.881.13		48
9.2	odd	6	inner	3024.2.cc.d.2897.13		48
9.7	even	3		1008.2.cc.d.209.18		48
12.11	even	2		504.2.bu.a.41.18	yes	48
21.20	even	2		1008.2.cc.d.545.18		48
28.27	even	2		1512.2.bu.a.881.13		48
36.7	odd	6		504.2.bu.a.209.7	yes	48
36.11	even	6		1512.2.bu.a.1385.13		48
36.23	even	6		4536.2.k.a.3401.23		48
36.31	odd	6		4536.2.k.a.3401.26		48
63.20	even	6	inner	3024.2.cc.d.2897.12		48
63.34	odd	6		1008.2.cc.d.209.7		48
84.83	odd	2		504.2.bu.a.41.7	✓	48
252.83	odd	6		1512.2.bu.a.1385.12		48
252.139	even	6		4536.2.k.a.3401.24		48
252.167	odd	6		4536.2.k.a.3401.25		48
252.223	even	6		504.2.bu.a.209.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.7	✓	48	84.83	odd	2
504.2.bu.a.41.18	yes	48	12.11	even	2
504.2.bu.a.209.7	yes	48	36.7	odd	6
504.2.bu.a.209.18	yes	48	252.223	even	6
1008.2.cc.d.209.7		48	63.34	odd	6
1008.2.cc.d.209.18		48	9.7	even	3
1008.2.cc.d.545.7		48	3.2	odd	2
1008.2.cc.d.545.18		48	21.20	even	2
1512.2.bu.a.881.12		48	4.3	odd	2
1512.2.bu.a.881.13		48	28.27	even	2
1512.2.bu.a.1385.12		48	252.83	odd	6
1512.2.bu.a.1385.13		48	36.11	even	6
3024.2.cc.d.881.12		48	1.1	even	1	trivial
3024.2.cc.d.881.13		48	7.6	odd	2	inner
3024.2.cc.d.2897.12		48	63.20	even	6	inner
3024.2.cc.d.2897.13		48	9.2	odd	6	inner
4536.2.k.a.3401.23		48	36.23	even	6
4536.2.k.a.3401.24		48	252.139	even	6
4536.2.k.a.3401.25		48	252.167	odd	6
4536.2.k.a.3401.26		48	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.00869840 + 0.0150661i) q^{5} +(0.514871 - 2.59517i) q^{7} +O(q^{10})\)	\(q+(-0.00869840 + 0.0150661i) q^{5} +(0.514871 - 2.59517i) q^{7} +(4.13424 - 2.38691i) q^{11} +(1.31594 + 0.759761i) q^{13} -1.91072 q^{17} +6.45989i q^{19} +(3.82432 + 2.20797i) q^{23} +(2.49985 + 4.32986i) q^{25} +(-1.73895 + 1.00399i) q^{29} +(6.51946 + 3.76401i) q^{31} +(0.0346205 + 0.0303309i) q^{35} -6.10467 q^{37} +(4.67759 - 8.10182i) q^{41} +(1.46638 + 2.53985i) q^{43} +(1.45659 + 2.52289i) q^{47} +(-6.46982 - 2.67235i) q^{49} -8.94416i q^{53} +0.0830491i q^{55} +(4.08337 - 7.07261i) q^{59} +(0.484917 - 0.279967i) q^{61} +(-0.0228932 + 0.0132174i) q^{65} +(3.69036 - 6.39189i) q^{67} -11.6825i q^{71} +12.8105i q^{73} +(-4.06583 - 11.9580i) q^{77} +(-4.75827 - 8.24157i) q^{79} +(6.67701 + 11.5649i) q^{83} +(0.0166202 - 0.0287871i) q^{85} +4.00356 q^{89} +(2.64925 - 3.02392i) q^{91} +(-0.0973252 - 0.0561907i) q^{95} +(-4.09514 + 2.36433i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

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