LMFDB - Embedded newform 3024.2.bh.d.2447.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1871,3024)]

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([3, 0, 1, 2]))

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

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

chi := DirichletCharacter("3024.1871");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bh (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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2447.13
Character	$\chi$	$=$	3024.2447
Dual form			3024.2.bh.d.1871.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.71056i q^{5} +(1.81297 - 1.92695i) q^{7} +O(q^{10})$	$q+2.71056i q^{5} +(1.81297 - 1.92695i) q^{7} -1.42297 q^{11} +(2.56378 - 4.44059i) q^{13} +(-1.04103 - 0.601041i) q^{17} +(-6.15547 + 3.55386i) q^{19} -7.49622 q^{23} -2.34715 q^{25} +(-6.90901 + 3.98892i) q^{29} +(-6.36392 + 3.67421i) q^{31} +(5.22311 + 4.91418i) q^{35} +(-0.194581 - 0.337025i) q^{37} +(1.52819 + 0.882303i) q^{41} +(-0.214184 + 0.123659i) q^{43} +(-3.40171 + 5.89194i) q^{47} +(-0.426244 - 6.98701i) q^{49} +(10.7865 + 6.22758i) q^{53} -3.85704i q^{55} +(2.37824 + 4.11923i) q^{59} +(0.102313 - 0.177212i) q^{61} +(12.0365 + 6.94928i) q^{65} +(4.62294 - 2.66906i) q^{67} -2.22420 q^{71} +(-7.54731 + 13.0723i) q^{73} +(-2.57980 + 2.74198i) q^{77} +(-8.33242 - 4.81072i) q^{79} +(-2.59188 - 4.48927i) q^{83} +(1.62916 - 2.82179i) q^{85} +(-4.17410 + 2.40992i) q^{89} +(-3.90872 - 12.9910i) q^{91} +(-9.63297 - 16.6848i) q^{95} +(2.40373 + 4.16339i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{7}+O(q^{10}) $ 30 * q + 2 * q^7	$ 30 q + 2 q^{7} + 6 q^{11} - 12 q^{17} - 9 q^{19} - 24 q^{23} - 36 q^{25} - 27 q^{29} - 6 q^{31} - 6 q^{35} + 6 q^{37} - 9 q^{41} + 21 q^{43} + 12 q^{49} + 3 q^{53} + 3 q^{59} - 3 q^{61} + 39 q^{67} + 18 q^{71} + 21 q^{73} - 36 q^{77} + 33 q^{79} - 15 q^{83} - 3 q^{85} - 6 q^{89} + 26 q^{91} - 27 q^{95} - 6 q^{97}+O(q^{100}) $ 30 * q + 2 * q^7 + 6 * q^11 - 12 * q^17 - 9 * q^19 - 24 * q^23 - 36 * q^25 - 27 * q^29 - 6 * q^31 - 6 * q^35 + 6 * q^37 - 9 * q^41 + 21 * q^43 + 12 * q^49 + 3 * q^53 + 3 * q^59 - 3 * q^61 + 39 * q^67 + 18 * q^71 + 21 * q^73 - 36 * q^77 + 33 * q^79 - 15 * q^83 - 3 * q^85 - 6 * q^89 + 26 * q^91 - 27 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$			2.71056i			1.21220i	0.795388	+	0.606100i	$0.207267\pi$
$5$			2.71056i			1.21220i	−0.795388	+	0.606100i	$0.792733\pi$
$6$		0			0
$7$	1.81297	−	1.92695i	0.685240	−	0.728317i
$7$	1.81297	−	1.92695i	0.685240	−	0.728317i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.42297			−0.429040			−0.214520	−	0.976720i	$-0.568819\pi$
$11$	−1.42297			−0.429040			−0.214520	+	0.976720i	$0.568819\pi$
$12$		0			0
$13$	2.56378	−	4.44059i	0.711064	−	1.23160i	−0.253394	−	0.967363i	$-0.581547\pi$
$13$	2.56378	−	4.44059i	0.711064	−	1.23160i	0.964458	−	0.264236i	$-0.0851198\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.04103	−	0.601041i	−0.252488	−	0.145774i	0.368415	−	0.929661i	$-0.379901\pi$
$17$	−1.04103	−	0.601041i	−0.252488	−	0.145774i	−0.620903	+	0.783887i	$0.713234\pi$
$18$		0			0
$19$	−6.15547	+	3.55386i	−1.41216	+	0.815312i	−0.995592	−	0.0937915i	$-0.970101\pi$
$19$	−6.15547	+	3.55386i	−1.41216	+	0.815312i	−0.416570	+	0.909104i	$0.636768\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.49622			−1.56307			−0.781535	−	0.623861i	$-0.785563\pi$
$23$	−7.49622			−1.56307			−0.781535	+	0.623861i	$0.785563\pi$
$24$		0			0
$25$	−2.34715			−0.469430
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.90901	+	3.98892i	−1.28297	+	0.740724i	−0.977390	−	0.211443i	$-0.932184\pi$
$29$	−6.90901	+	3.98892i	−1.28297	+	0.740724i	−0.305581	+	0.952166i	$0.598851\pi$
$30$		0			0
$31$	−6.36392	+	3.67421i	−1.14299	+	0.659908i	−0.947170	−	0.320731i	$-0.896071\pi$
$31$	−6.36392	+	3.67421i	−1.14299	+	0.659908i	−0.195824	+	0.980639i	$0.562738\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.22311	+	4.91418i	0.882866	+	0.830648i
$36$		0			0
$37$	−0.194581	−	0.337025i	−0.0319890	−	0.0554065i	0.849588	−	0.527447i	$-0.176851\pi$
$37$	−0.194581	−	0.337025i	−0.0319890	−	0.0554065i	−0.881577	+	0.472041i	$0.843517\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.52819	+	0.882303i	0.238664	+	0.137793i	0.614562	−	0.788868i	$-0.289333\pi$
$41$	1.52819	+	0.882303i	0.238664	+	0.137793i	−0.375899	+	0.926661i	$0.622666\pi$
$42$		0			0
$43$	−0.214184	+	0.123659i	−0.0326628	+	0.0188579i	−0.516242	−	0.856442i	$-0.672670\pi$
$43$	−0.214184	+	0.123659i	−0.0326628	+	0.0188579i	0.483580	+	0.875300i	$0.339336\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.40171	+	5.89194i	−0.496191	+	0.859428i	−0.999990	−	0.00439269i	$-0.998602\pi$
$47$	−3.40171	+	5.89194i	−0.496191	+	0.859428i	0.503799	+	0.863821i	$0.331935\pi$
$48$		0			0
$49$	−0.426244	−	6.98701i	−0.0608920	−	0.998144i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.7865	+	6.22758i	1.48164	+	0.855423i	0.999783	−	0.0208286i	$-0.00663044\pi$
$53$	10.7865	+	6.22758i	1.48164	+	0.855423i	0.481853	+	0.876252i	$0.339964\pi$
$54$		0			0
$55$		−	3.85704i		−	0.520083i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.37824	+	4.11923i	0.309620	+	0.536278i	0.978279	−	0.207291i	$-0.0664648\pi$
$59$	2.37824	+	4.11923i	0.309620	+	0.536278i	−0.668659	+	0.743569i	$0.733131\pi$
$60$		0			0
$61$	0.102313	−	0.177212i	0.0130999	−	0.0226897i	−0.859401	−	0.511302i	$-0.829163\pi$
$61$	0.102313	−	0.177212i	0.0130999	−	0.0226897i	0.872501	+	0.488612i	$0.162497\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	12.0365	+	6.94928i	1.49295	+	0.861952i
$66$		0			0
$67$	4.62294	−	2.66906i	0.564783	−	0.326077i	−0.190280	−	0.981730i	$-0.560940\pi$
$67$	4.62294	−	2.66906i	0.564783	−	0.326077i	0.755063	+	0.655652i	$0.227606\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.22420			−0.263964			−0.131982	−	0.991252i	$-0.542134\pi$
$71$	−2.22420			−0.263964			−0.131982	+	0.991252i	$0.542134\pi$
$72$		0			0
$73$	−7.54731	+	13.0723i	−0.883345	+	1.53000i	−0.0357471	+	0.999361i	$0.511381\pi$
$73$	−7.54731	+	13.0723i	−0.883345	+	1.53000i	−0.847598	+	0.530638i	$0.821952\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.57980	+	2.74198i	−0.293996	+	0.312477i
$78$		0			0
$79$	−8.33242	−	4.81072i	−0.937470	−	0.541249i	−0.0483037	−	0.998833i	$-0.515382\pi$
$79$	−8.33242	−	4.81072i	−0.937470	−	0.541249i	−0.889166	+	0.457584i	$0.848715\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.59188	−	4.48927i	−0.284496	−	0.492761i	0.687991	−	0.725719i	$-0.258493\pi$
$83$	−2.59188	−	4.48927i	−0.284496	−	0.492761i	−0.972487	+	0.232958i	$0.925159\pi$
$84$		0			0
$85$	1.62916	−	2.82179i	0.176707	−	0.306066i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.17410	+	2.40992i	−0.442454	+	0.255451i	−0.704638	−	0.709567i	$-0.748891\pi$
$89$	−4.17410	+	2.40992i	−0.442454	+	0.255451i	0.262184	+	0.965018i	$0.415557\pi$
$90$		0			0
$91$	−3.90872	−	12.9910i	−0.409745	−	1.36182i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.63297	−	16.6848i	−0.988322	−	1.71182i
$96$		0			0
$97$	2.40373	+	4.16339i	0.244062	+	0.422728i	0.961868	−	0.273516i	$-0.0881865\pi$
$97$	2.40373	+	4.16339i	0.244062	+	0.422728i	−0.717805	+	0.696244i	$0.754853\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			3.88565i			0.386636i	0.981136	+	0.193318i	$0.0619250\pi$
$101$			3.88565i			0.386636i	−0.981136	+	0.193318i	$0.938075\pi$
$102$		0			0
$103$		−	12.7719i		−	1.25845i	−0.777222	−	0.629226i	$-0.783372\pi$
$103$		−	12.7719i		−	1.25845i	0.777222	−	0.629226i	$-0.216628\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.20389	+	10.7455i	0.599753	+	1.03880i	0.992857	+	0.119309i	$0.0380679\pi$
$107$	6.20389	+	10.7455i	0.599753	+	1.03880i	−0.393104	+	0.919494i	$0.628599\pi$
$108$		0			0
$109$	−6.14048	+	10.6356i	−0.588152	+	1.01871i	0.406323	+	0.913730i	$0.366811\pi$
$109$	−6.14048	+	10.6356i	−0.588152	+	1.01871i	−0.994474	+	0.104979i	$0.966523\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.2555	−	7.65305i	−1.24697	−	0.719938i	−0.276465	−	0.961024i	$-0.589163\pi$
$113$	−13.2555	−	7.65305i	−1.24697	−	0.719938i	−0.970504	+	0.241086i	$0.922496\pi$
$114$		0			0
$115$		−	20.3190i		−	1.89475i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.04554	+	0.916344i	−0.279185	+	0.0840011i
$120$		0			0
$121$	−8.97517			−0.815924
$122$		0			0
$123$		0			0
$124$		0			0
$125$			7.19072i			0.643158i
$126$		0			0
$127$			15.1494i			1.34429i	0.740418	+	0.672147i	$0.234628\pi$
$127$			15.1494i			1.34429i	−0.740418	+	0.672147i	$0.765372\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.24044			−0.807341			−0.403671	−	0.914904i	$-0.632266\pi$
$131$	−9.24044			−0.807341			−0.403671	+	0.914904i	$0.632266\pi$
$132$		0			0
$133$	−4.31161	+	18.3043i	−0.373864	+	1.58719i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	4.12231i		−	0.352193i	−0.984373	−	0.176096i	$-0.943653\pi$
$137$		−	4.12231i		−	0.352193i	0.984373	−	0.176096i	$-0.0563470\pi$
$138$		0			0
$139$	−3.87372	−	2.23649i	−0.328564	−	0.189697i	0.326639	−	0.945149i	$-0.394084\pi$
$139$	−3.87372	−	2.23649i	−0.328564	−	0.189697i	−0.655204	+	0.755452i	$0.727417\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.64817	+	6.31881i	−0.305075	+	0.528406i
$144$		0			0
$145$	−10.8122	−	18.7273i	−0.897905	−	1.55522i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	20.2640i		−	1.66009i	−0.557696	−	0.830045i	$-0.688314\pi$
$149$		−	20.2640i		−	1.66009i	0.557696	−	0.830045i	$-0.311686\pi$
$150$		0			0
$151$		−	7.44219i		−	0.605637i	−0.953048	−	0.302818i	$-0.902072\pi$
$151$		−	7.44219i		−	0.605637i	0.953048	−	0.302818i	$-0.0979275\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.95918	−	17.2498i	−0.799940	−	1.38554i
$156$		0			0
$157$	7.47069	+	12.9396i	0.596226	+	1.03269i	0.993373	+	0.114939i	$0.0366672\pi$
$157$	7.47069	+	12.9396i	0.596226	+	1.03269i	−0.397146	+	0.917755i	$0.629999\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−13.5905	+	14.4448i	−1.07108	+	1.13841i
$162$		0			0
$163$	−10.3855	+	5.99605i	−0.813453	+	0.469647i	−0.848153	−	0.529751i	$-0.822286\pi$
$163$	−10.3855	+	5.99605i	−0.813453	+	0.469647i	0.0347008	+	0.999398i	$0.488952\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.91245	−	15.4368i	0.689666	−	1.19454i	−0.282280	−	0.959332i	$-0.591091\pi$
$167$	8.91245	−	15.4368i	0.689666	−	1.19454i	0.971946	−	0.235205i	$-0.0755760\pi$
$168$		0			0
$169$	−6.64592	−	11.5111i	−0.511225	−	0.885467i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	21.8668	+	12.6248i	1.66250	+	0.959847i	0.971514	+	0.236981i	$0.0761579\pi$
$173$	21.8668	+	12.6248i	1.66250	+	0.959847i	0.690989	+	0.722866i	$0.257175\pi$
$174$		0			0
$175$	−4.25532	+	4.52283i	−0.321672	+	0.341894i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.16327	+	7.21099i	−0.311177	+	0.538975i	−0.978617	−	0.205689i	$-0.934057\pi$
$179$	−4.16327	+	7.21099i	−0.311177	+	0.538975i	0.667440	+	0.744663i	$0.267390\pi$
$180$		0			0
$181$	15.6017			1.15967			0.579833	−	0.814735i	$-0.303118\pi$
$181$	15.6017			1.15967			0.579833	+	0.814735i	$0.303118\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.913526	−	0.527424i	0.0671638	−	0.0387770i
$186$		0			0
$187$	1.48136	+	0.855261i	0.108327	+	0.0625429i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.42827	−	9.40204i	0.392776	−	0.680308i	−0.600039	−	0.799971i	$-0.704848\pi$
$191$	5.42827	−	9.40204i	0.392776	−	0.680308i	0.992815	+	0.119663i	$0.0381815\pi$
$192$		0			0
$193$	−2.60478	−	4.51161i	−0.187496	−	0.324753i	0.756919	−	0.653509i	$-0.226704\pi$
$193$	−2.60478	−	4.51161i	−0.187496	−	0.324753i	−0.944415	+	0.328756i	$0.893371\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	20.7479i		−	1.47823i	−0.673582	−	0.739113i	$-0.735245\pi$
$197$		−	20.7479i		−	1.47823i	0.673582	−	0.739113i	$-0.264755\pi$
$198$		0			0
$199$	−1.76108	−	1.01676i	−0.124839	−	0.0720760i	0.436280	−	0.899811i	$-0.356296\pi$
$199$	−1.76108	−	1.01676i	−0.124839	−	0.0720760i	−0.561119	+	0.827735i	$0.689629\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.83943	+	20.5451i	−0.339661	+	1.44198i
$204$		0			0
$205$	−2.39154	+	4.14226i	−0.167032	+	0.289308i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.75902	−	5.05702i	0.605874	−	0.349802i
$210$		0			0
$211$	−0.705274	−	0.407190i	−0.0485531	−	0.0280321i	0.475527	−	0.879701i	$-0.342257\pi$
$211$	−0.705274	−	0.407190i	−0.0485531	−	0.0280321i	−0.524080	+	0.851669i	$0.675591\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.335187	−	0.580560i	−0.0228595	−	0.0395939i
$216$		0			0
$217$	−4.45762	+	18.9242i	−0.302603	+	1.28466i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.33796	+	3.08187i	−0.359070	+	0.207309i
$222$		0			0
$223$	9.40736	−	5.43134i	0.629963	−	0.363709i	−0.150775	−	0.988568i	$-0.548177\pi$
$223$	9.40736	−	5.43134i	0.629963	−	0.363709i	0.780738	+	0.624859i	$0.214843\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−20.2988			−1.34728			−0.673638	−	0.739062i	$-0.735269\pi$
$227$	−20.2988			−1.34728			−0.673638	+	0.739062i	$0.735269\pi$
$228$		0			0
$229$	5.02282			0.331917			0.165959	−	0.986133i	$-0.446928\pi$
$229$	5.02282			0.331917			0.165959	+	0.986133i	$0.446928\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.4121	+	7.16616i	−0.813147	+	0.469470i	−0.848047	−	0.529920i	$-0.822222\pi$
$233$	−12.4121	+	7.16616i	−0.813147	+	0.469470i	0.0349007	+	0.999391i	$0.488889\pi$
$234$		0			0
$235$	−15.9705	−	9.22056i	−1.04180	−	0.601483i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.71239	+	16.8224i	−0.628242	+	1.08815i	0.359662	+	0.933083i	$0.382892\pi$
$239$	−9.71239	+	16.8224i	−0.628242	+	1.08815i	−0.987904	+	0.155065i	$0.950441\pi$
$240$		0			0
$241$	−6.11762			−0.394070			−0.197035	−	0.980396i	$-0.563131\pi$
$241$	−6.11762			−0.394070			−0.197035	+	0.980396i	$0.563131\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	18.9387	−	1.15536i	1.20995	−	0.0738133i
$246$		0			0
$247$			36.4453i			2.31896i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.54044			−0.160351			−0.0801757	−	0.996781i	$-0.525548\pi$
$251$	−2.54044			−0.160351			−0.0801757	+	0.996781i	$0.525548\pi$
$252$		0			0
$253$	10.6669			0.670620
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	18.5285i		−	1.15577i	−0.816117	−	0.577886i	$-0.803878\pi$
$257$		−	18.5285i		−	1.15577i	0.816117	−	0.577886i	$-0.196122\pi$
$258$		0			0
$259$	−1.00220	−	0.236069i	−0.0622736	−	0.0146686i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.4370			−0.766901			−0.383451	−	0.923561i	$-0.625264\pi$
$263$	−12.4370			−0.766901			−0.383451	+	0.923561i	$0.625264\pi$
$264$		0			0
$265$	−16.8802	+	29.2374i	−1.03694	+	1.79604i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−21.0139	−	12.1324i	−1.28124	−	0.739723i	−0.304163	−	0.952620i	$-0.598377\pi$
$269$	−21.0139	−	12.1324i	−1.28124	−	0.739723i	−0.977075	+	0.212897i	$0.931710\pi$
$270$		0			0
$271$	17.6964	−	10.2170i	1.07498	−	0.620638i	0.145440	−	0.989367i	$-0.453540\pi$
$271$	17.6964	−	10.2170i	1.07498	−	0.620638i	0.929537	+	0.368729i	$0.120207\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.33991			0.201404
$276$		0			0
$277$	13.2708			0.797366			0.398683	−	0.917089i	$-0.369467\pi$
$277$	13.2708			0.797366			0.398683	+	0.917089i	$0.369467\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.56448	+	0.903251i	−0.0933289	+	0.0538835i	−0.545938	−	0.837826i	$-0.683827\pi$
$281$	−1.56448	+	0.903251i	−0.0933289	+	0.0538835i	0.452609	+	0.891709i	$0.350493\pi$
$282$		0			0
$283$	24.4119	−	14.0942i	1.45114	−	0.837816i	0.452593	−	0.891717i	$-0.350499\pi$
$283$	24.4119	−	14.0942i	1.45114	−	0.837816i	0.998546	+	0.0539018i	$0.0171658\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.47073	−	1.34515i	0.263899	−	0.0794019i
$288$		0			0
$289$	−7.77750	−	13.4710i	−0.457500	−	0.792413i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.28005	+	4.78049i	0.483726	+	0.279279i	0.721968	−	0.691927i	$-0.243238\pi$
$293$	8.28005	+	4.78049i	0.483726	+	0.279279i	−0.238242	+	0.971206i	$0.576571\pi$
$294$		0			0
$295$	−11.1654	+	6.44636i	−0.650076	+	0.375322i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−19.2187	+	33.2877i	−1.11144	+	1.92508i
$300$		0			0
$301$	−0.150026	+	0.636913i	−0.00864735	+	0.0367111i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.480344	+	0.277327i	0.0275044	+	0.0158797i
$306$		0			0
$307$			19.8578i			1.13334i	0.823944	+	0.566671i	$0.191769\pi$
$307$			19.8578i			1.13334i	−0.823944	+	0.566671i	$0.808231\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.378886	−	0.656249i	−0.0214846	−	0.0372125i	0.855083	−	0.518491i	$-0.173506\pi$
$311$	−0.378886	−	0.656249i	−0.0214846	−	0.0372125i	−0.876568	+	0.481278i	$0.840173\pi$
$312$		0			0
$313$	3.97641	−	6.88735i	0.224760	−	0.389296i	−0.731487	−	0.681855i	$-0.761174\pi$
$313$	3.97641	−	6.88735i	0.224760	−	0.389296i	0.956247	+	0.292559i	$0.0945068\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.2839	+	7.09213i	0.689934	+	0.398334i	0.803587	−	0.595187i	$-0.202922\pi$
$317$	12.2839	+	7.09213i	0.689934	+	0.398334i	−0.113653	+	0.993520i	$0.536255\pi$
$318$		0			0
$319$	9.83128	−	5.67609i	0.550446	−	0.317800i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.54408			0.475405
$324$		0			0
$325$	−6.01757	+	10.4227i	−0.333795	+	0.578149i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	5.18623	+	17.2369i	0.285926	+	0.950299i
$330$		0			0
$331$	−7.30828	−	4.21944i	−0.401700	−	0.231921i	0.285518	−	0.958373i	$-0.407835\pi$
$331$	−7.30828	−	4.21944i	−0.401700	−	0.231921i	−0.687217	+	0.726452i	$0.741168\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.23465	+	12.5308i	0.395271	+	0.684630i
$336$		0			0
$337$	6.41921	−	11.1184i	0.349677	−	0.605658i	−0.636515	−	0.771264i	$-0.719625\pi$
$337$	6.41921	−	11.1184i	0.349677	−	0.605658i	0.986192	+	0.165606i	$0.0529582\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.05564	−	5.22828i	0.490390	−	0.283127i
$342$		0			0
$343$	−14.2364	−	11.8459i	−0.768691	−	0.639620i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.27698	−	9.14000i	−0.283283	−	0.490661i	0.688908	−	0.724849i	$-0.258090\pi$
$347$	−5.27698	−	9.14000i	−0.283283	−	0.490661i	−0.972191	+	0.234188i	$0.924757\pi$
$348$		0			0
$349$	−7.84572	−	13.5892i	−0.419972	−	0.727412i	0.575964	−	0.817475i	$-0.304627\pi$
$349$	−7.84572	−	13.5892i	−0.419972	−	0.727412i	−0.995936	+	0.0900624i	$0.971293\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			0.0215722i			0.00114817i	1.00000		0.000574087i	$0.000182738\pi$
$353$			0.0215722i			0.00114817i	−1.00000		0.000574087i	$0.999817\pi$
$354$		0			0
$355$		−	6.02883i		−	0.319977i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.41437	−	5.91386i	−0.180203	−	0.312121i	0.761746	−	0.647875i	$-0.224342\pi$
$359$	−3.41437	−	5.91386i	−0.180203	−	0.312121i	−0.941950	+	0.335754i	$0.891009\pi$
$360$		0			0
$361$	15.7599	−	27.2969i	0.829468	−	1.43668i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−35.4333	−	20.4574i	−1.85467	−	1.07079i
$366$		0			0
$367$			3.46331i			0.180783i	0.995906	+	0.0903916i	$0.0288119\pi$
$367$			3.46331i			0.180783i	−0.995906	+	0.0903916i	$0.971188\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	31.5558	−	9.49452i	1.63830	−	0.492931i
$372$		0			0
$373$	8.53539			0.441946			0.220973	−	0.975280i	$-0.429077\pi$
$373$	8.53539			0.441946			0.220973	+	0.975280i	$0.429077\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			40.9068i			2.10681i
$378$		0			0
$379$		−	6.38671i		−	0.328063i	−0.986455	−	0.164032i	$-0.947550\pi$
$379$		−	6.38671i		−	0.328063i	0.986455	−	0.164032i	$-0.0524499\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−26.5208			−1.35515			−0.677575	−	0.735454i	$-0.736969\pi$
$383$	−26.5208			−1.35515			−0.677575	+	0.735454i	$0.736969\pi$
$384$		0			0
$385$	−7.43230	−	6.99271i	−0.378785	−	0.356382i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			0.286122i			0.0145069i	0.999974	+	0.00725347i	$0.00230887\pi$
$389$			0.286122i			0.0145069i	−0.999974	+	0.00725347i	$0.997691\pi$
$390$		0			0
$391$	7.80382	+	4.50554i	0.394656	+	0.227855i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.0398	−	22.5855i	0.656102	−	1.13640i
$396$		0			0
$397$	15.6448	+	27.0975i	0.785188	+	1.35998i	0.928887	+	0.370363i	$0.120767\pi$
$397$	15.6448	+	27.0975i	0.785188	+	1.35998i	−0.143699	+	0.989621i	$0.545900\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			14.5305i			0.725621i	0.931863	+	0.362810i	$0.118183\pi$
$401$			14.5305i			0.725621i	−0.931863	+	0.362810i	$0.881817\pi$
$402$		0			0
$403$			37.6794i			1.87695i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.276882	+	0.479574i	0.0137245	+	0.0237716i
$408$		0			0
$409$	9.34916	+	16.1932i	0.462286	+	0.800704i	0.999074	−	0.0430136i	$-0.0136959\pi$
$409$	9.34916	+	16.1932i	0.462286	+	0.800704i	−0.536788	+	0.843717i	$0.680363\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.2492	+	2.88532i	0.602744	+	0.141977i
$414$		0			0
$415$	12.1684	−	7.02545i	0.597325	−	0.344866i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.0728005	−	0.126094i	0.00355653	−	0.00616010i	−0.864242	−	0.503077i	$-0.832201\pi$
$419$	0.0728005	−	0.126094i	0.00355653	−	0.00616010i	0.867798	+	0.496917i	$0.165535\pi$
$420$		0			0
$421$	−10.4460	−	18.0930i	−0.509107	−	0.881799i	−0.999944	−	0.0105480i	$-0.996642\pi$
$421$	−10.4460	−	18.0930i	−0.509107	−	0.881799i	0.490837	−	0.871251i	$-0.336691\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.44346	+	1.41073i	0.118525	+	0.0684306i
$426$		0			0
$427$	−0.155986	−	0.518433i	−0.00754870	−	0.0250887i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.5495	+	18.2723i	−0.508151	+	0.880144i	0.491804	+	0.870706i	$0.336338\pi$
$431$	−10.5495	+	18.2723i	−0.508151	+	0.880144i	−0.999955	+	0.00943786i	$0.996996\pi$
$432$		0			0
$433$	9.19616			0.441939			0.220970	−	0.975281i	$-0.429078\pi$
$433$	9.19616			0.441939			0.220970	+	0.975281i	$0.429078\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	46.1428	−	26.6405i	2.20731	−	1.27439i
$438$		0			0
$439$	9.80671	+	5.66190i	0.468049	+	0.270228i	0.715422	−	0.698692i	$-0.246234\pi$
$439$	9.80671	+	5.66190i	0.468049	+	0.270228i	−0.247374	+	0.968920i	$0.579568\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.4472	−	30.2194i	0.828940	−	1.43577i	−0.0699313	−	0.997552i	$-0.522278\pi$
$443$	17.4472	−	30.2194i	0.828940	−	1.43577i	0.898871	−	0.438214i	$-0.144389\pi$
$444$		0			0
$445$	−6.53223	−	11.3142i	−0.309657	−	0.536342i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			24.4981i			1.15614i	0.815988	+	0.578069i	$0.196194\pi$
$449$			24.4981i			1.15614i	−0.815988	+	0.578069i	$0.803806\pi$
$450$		0			0
$451$	−2.17457	−	1.25549i	−0.102396	−	0.0591186i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	35.2128	−	10.5948i	1.65080	−	0.496693i
$456$		0			0
$457$	−16.9258	+	29.3164i	−0.791756	+	1.37136i	0.133123	+	0.991100i	$0.457499\pi$
$457$	−16.9258	+	29.3164i	−0.791756	+	1.37136i	−0.924879	+	0.380262i	$0.875834\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.526552	+	0.304005i	−0.0245240	+	0.0141589i	−0.512212	−	0.858859i	$-0.671174\pi$
$461$	−0.526552	+	0.304005i	−0.0245240	+	0.0141589i	0.487688	+	0.873018i	$0.337840\pi$
$462$		0			0
$463$	−13.6357	−	7.87260i	−0.633707	−	0.365871i	0.148479	−	0.988915i	$-0.452562\pi$
$463$	−13.6357	−	7.87260i	−0.633707	−	0.365871i	−0.782186	+	0.623045i	$0.785895\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.73247	−	6.46483i	−0.172718	−	0.299156i	0.766651	−	0.642064i	$-0.221922\pi$
$467$	−3.73247	−	6.46483i	−0.172718	−	0.299156i	−0.939369	+	0.342907i	$0.888588\pi$
$468$		0			0
$469$	3.23815	−	13.7471i	0.149524	−	0.634782i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.304777	−	0.175963i	0.0140137	−	0.00809079i
$474$		0			0
$475$	14.4478	−	8.34144i	0.662910	−	0.382732i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	28.0935			1.28363			0.641813	−	0.766862i	$-0.278183\pi$
$479$	28.0935			1.28363			0.641813	+	0.766862i	$0.278183\pi$
$480$		0			0
$481$	−1.99545			−0.0909848
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.2851	+	6.51547i	−0.512431	+	0.295852i
$486$		0			0
$487$	23.2895	+	13.4462i	1.05535	+	0.609305i	0.924141	−	0.382051i	$-0.124782\pi$
$487$	23.2895	+	13.4462i	1.05535	+	0.609305i	0.131205	+	0.991355i	$0.458115\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.958840	+	1.66076i	−0.0432719	+	0.0749491i	−0.886850	−	0.462057i	$-0.847111\pi$
$491$	−0.958840	+	1.66076i	−0.0432719	+	0.0749491i	0.843578	+	0.537006i	$0.180445\pi$
$492$		0			0
$493$	9.59002			0.431913
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.03242	+	4.28591i	−0.180879	+	0.192249i
$498$		0			0
$499$			5.87095i			0.262820i	0.991328	+	0.131410i	$0.0419504\pi$
$499$			5.87095i			0.262820i	−0.991328	+	0.131410i	$0.958050\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	10.9558			0.488495			0.244248	−	0.969713i	$-0.421459\pi$
$503$	10.9558			0.488495			0.244248	+	0.969713i	$0.421459\pi$
$504$		0			0
$505$	−10.5323			−0.468681
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	38.5507i		−	1.70873i	−0.519675	−	0.854364i	$-0.673947\pi$
$509$		−	38.5507i		−	1.70873i	0.519675	−	0.854364i	$-0.326053\pi$
$510$		0			0
$511$	11.5066	+	38.2430i	0.509021	+	1.69177i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	34.6190			1.52550
$516$		0			0
$517$	4.84052	−	8.38403i	0.212886	−	0.368729i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	16.6259	+	9.59898i	0.728395	+	0.420539i	0.817835	−	0.575453i	$-0.195174\pi$
$521$	16.6259	+	9.59898i	0.728395	+	0.420539i	−0.0894400	+	0.995992i	$0.528508\pi$
$522$		0			0
$523$	12.6079	−	7.27919i	0.551306	−	0.318297i	−0.198343	−	0.980133i	$-0.563556\pi$
$523$	12.6079	−	7.27919i	0.551306	−	0.318297i	0.749649	+	0.661836i	$0.230222\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.83341			0.384789
$528$		0			0
$529$	33.1934			1.44319
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.83590	−	4.52406i	0.339410	−	0.195959i
$534$		0			0
$535$	−29.1262	+	16.8160i	−1.25924	+	0.727021i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.606531	+	9.94228i	0.0261251	+	0.428244i
$540$		0			0
$541$	−2.33531	−	4.04487i	−0.100403	−	0.173903i	0.811448	−	0.584425i	$-0.198680\pi$
$541$	−2.33531	−	4.04487i	−0.100403	−	0.173903i	−0.911851	+	0.410522i	$0.865346\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−28.8285	−	16.6442i	−1.23488	−	0.712957i
$546$		0			0
$547$	−30.6708	+	17.7078i	−1.31139	+	0.757130i	−0.982326	−	0.187178i	$-0.940066\pi$
$547$	−30.6708	+	17.7078i	−1.31139	+	0.757130i	−0.329062	+	0.944308i	$0.606733\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	28.3521	−	49.1073i	1.20784	−	2.09204i
$552$		0			0
$553$	−24.3765	+	7.33440i	−1.03659	+	0.311890i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.7408	−	11.3974i	−0.836446	−	0.482922i	0.0196089	−	0.999808i	$-0.493758\pi$
$557$	−19.7408	−	11.3974i	−0.836446	−	0.482922i	−0.856054	+	0.516886i	$0.827091\pi$
$558$		0			0
$559$			1.26814i			0.0536367i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.3460	+	26.5800i	0.646756	+	1.12021i	0.983893	+	0.178759i	$0.0572082\pi$
$563$	15.3460	+	26.5800i	0.646756	+	1.12021i	−0.337137	+	0.941456i	$0.609458\pi$
$564$		0			0
$565$	20.7441	−	35.9298i	0.872709	−	1.51158i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−33.9766	−	19.6164i	−1.42437	−	0.822362i	−0.427704	−	0.903919i	$-0.640677\pi$
$569$	−33.9766	−	19.6164i	−1.42437	−	0.822362i	−0.996669	+	0.0815573i	$0.974011\pi$
$570$		0			0
$571$	1.61803	−	0.934171i	0.0677125	−	0.0390938i	−0.465762	−	0.884910i	$-0.654220\pi$
$571$	1.61803	−	0.934171i	0.0677125	−	0.0390938i	0.533474	+	0.845816i	$0.320886\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	17.5947			0.733751
$576$		0			0
$577$	20.6560	−	35.7773i	0.859921	−	1.48943i	−0.0120819	−	0.999927i	$-0.503846\pi$
$577$	20.6560	−	35.7773i	0.859921	−	1.48943i	0.872003	−	0.489500i	$-0.162821\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.3496	−	3.14452i	−0.553834	−	0.130456i
$582$		0			0
$583$	−15.3488	−	8.86163i	−0.635682	−	0.367011i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.03460	−	12.1843i	−0.290349	−	0.502899i	0.683543	−	0.729910i	$-0.260438\pi$
$587$	−7.03460	−	12.1843i	−0.290349	−	0.502899i	−0.973892	+	0.227011i	$0.927105\pi$
$588$		0			0
$589$	26.1153	−	45.2330i	1.07606	−	1.86379i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−36.5014	+	21.0741i	−1.49893	+	0.865410i	−0.999999	−	0.00122942i	$-0.999609\pi$
$593$	−36.5014	+	21.0741i	−1.49893	+	0.865410i	−0.498935	+	0.866639i	$0.666275\pi$
$594$		0			0
$595$	−2.48381	−	8.25514i	−0.101826	−	0.338428i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.18506	+	14.1769i	0.334432	+	0.579254i	0.983376	−	0.181583i	$-0.0581221\pi$
$599$	8.18506	+	14.1769i	0.334432	+	0.579254i	−0.648943	+	0.760837i	$0.724789\pi$
$600$		0			0
$601$	3.42868	+	5.93864i	0.139859	+	0.242242i	0.927443	−	0.373965i	$-0.122002\pi$
$601$	3.42868	+	5.93864i	0.139859	+	0.242242i	−0.787584	+	0.616207i	$0.788669\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		−	24.3278i		−	0.989064i
$606$		0			0
$607$		−	42.2279i		−	1.71398i	−0.515334	−	0.856989i	$-0.672332\pi$
$607$		−	42.2279i		−	1.71398i	0.515334	−	0.856989i	$-0.327668\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.4425	+	30.2113i	0.705647	+	1.22222i
$612$		0			0
$613$	3.14051	−	5.43953i	0.126844	−	0.219700i	−0.795608	−	0.605812i	$-0.792849\pi$
$613$	3.14051	−	5.43953i	0.126844	−	0.219700i	0.922452	+	0.386111i	$0.126182\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.8749	−	13.2068i	−0.920910	−	0.531688i	−0.0369847	−	0.999316i	$-0.511775\pi$
$617$	−22.8749	−	13.2068i	−0.920910	−	0.531688i	−0.883925	+	0.467628i	$0.845109\pi$
$618$		0			0
$619$			7.98926i			0.321116i	0.987026	+	0.160558i	$0.0513293\pi$
$619$			7.98926i			0.321116i	−0.987026	+	0.160558i	$0.948671\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.92376	+	12.4124i	−0.117138	+	0.497292i
$624$		0			0
$625$	−31.2266			−1.24907
$626$		0			0
$627$		0			0
$628$		0			0
$629$			0.467805i			0.0186526i
$630$		0			0
$631$			28.8074i			1.14681i	0.819274	+	0.573403i	$0.194377\pi$
$631$			28.8074i			1.14681i	−0.819274	+	0.573403i	$0.805623\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−41.0635			−1.62955
$636$		0			0
$637$	−32.1193	−	16.0204i	−1.27261	−	0.634750i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			30.1334i			1.19020i	0.803653	+	0.595099i	$0.202887\pi$
$641$			30.1334i			1.19020i	−0.803653	+	0.595099i	$0.797113\pi$
$642$		0			0
$643$	−13.6075	−	7.85629i	−0.536627	−	0.309822i	0.207084	−	0.978323i	$-0.433603\pi$
$643$	−13.6075	−	7.85629i	−0.536627	−	0.309822i	−0.743711	+	0.668501i	$0.766936\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.3703	−	19.6939i	0.447012	−	0.774248i	−0.551177	−	0.834388i	$-0.685821\pi$
$647$	11.3703	−	19.6939i	0.447012	−	0.774248i	0.998190	+	0.0601397i	$0.0191546\pi$
$648$		0			0
$649$	−3.38415	−	5.86152i	−0.132839	−	0.230085i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			40.7387i			1.59423i	0.603829	+	0.797114i	$0.293641\pi$
$653$			40.7387i			1.59423i	−0.603829	+	0.797114i	$0.706359\pi$
$654$		0			0
$655$		−	25.0468i		−	0.978659i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.8968	−	27.5340i	−0.619251	−	1.07257i	−0.989623	−	0.143690i	$-0.954103\pi$
$659$	−15.8968	−	27.5340i	−0.619251	−	1.07257i	0.370372	−	0.928884i	$-0.379230\pi$
$660$		0			0
$661$	19.7459	+	34.2009i	0.768026	+	1.33026i	0.938632	+	0.344921i	$0.112094\pi$
$661$	19.7459	+	34.2009i	0.768026	+	1.33026i	−0.170606	+	0.985339i	$0.554572\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−49.6150	−	11.6869i	−1.92399	−	0.453198i
$666$		0			0
$667$	51.7915	−	29.9018i	2.00537	−	1.15780i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.145588	+	0.252166i	−0.00562038	+	0.00973478i
$672$		0			0
$673$	−6.03747	−	10.4572i	−0.232727	−	0.403095i	0.725883	−	0.687819i	$-0.241432\pi$
$673$	−6.03747	−	10.4572i	−0.232727	−	0.403095i	−0.958610	+	0.284723i	$0.908098\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.17385	−	4.71917i	−0.314146	−	0.181373i	0.334634	−	0.942348i	$-0.391387\pi$
$677$	−8.17385	−	4.71917i	−0.314146	−	0.181373i	−0.648780	+	0.760976i	$0.724721\pi$
$678$		0			0
$679$	12.3805	+	2.91625i	0.475121	+	0.111916i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	18.4219	−	31.9076i	0.704893	−	1.22091i	−0.261837	−	0.965112i	$-0.584328\pi$
$683$	18.4219	−	31.9076i	0.704893	−	1.22091i	0.966730	−	0.255799i	$-0.0823384\pi$
$684$		0			0
$685$	11.1738			0.426928
$686$		0			0
$687$		0			0
$688$		0			0
$689$	55.3083	−	31.9322i	2.10708	−	1.21652i
$690$		0			0
$691$	14.2544	+	8.22979i	0.542263	+	0.313076i	0.745996	−	0.665951i	$-0.231974\pi$
$691$	14.2544	+	8.22979i	0.542263	+	0.313076i	−0.203732	+	0.979027i	$0.565307\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.06215	−	10.4999i	0.229950	−	0.398286i
$696$		0			0
$697$	−1.06060	−	1.83702i	−0.0401731	−	0.0695819i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	23.7098i		−	0.895506i	−0.894157	−	0.447753i	$-0.852224\pi$
$701$		−	23.7098i		−	0.895506i	0.894157	−	0.447753i	$-0.147776\pi$
$702$		0			0
$703$	2.39548	+	1.38303i	0.0903472	+	0.0521620i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.48743	+	7.04458i	0.281594	+	0.264939i
$708$		0			0
$709$	−18.7824	+	32.5320i	−0.705387	+	1.22177i	0.261164	+	0.965294i	$0.415894\pi$
$709$	−18.7824	+	32.5320i	−0.705387	+	1.22177i	−0.966552	+	0.256472i	$0.917440\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	47.7054	−	27.5427i	1.78658	−	1.03148i
$714$		0			0
$715$	−17.1275	−	9.88859i	−0.640534	−	0.369812i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.5085	+	23.3975i	0.503783	+	0.872578i	0.999990	+	0.00437396i	$0.00139228\pi$
$719$	13.5085	+	23.3975i	0.503783	+	0.872578i	−0.496207	+	0.868204i	$0.665274\pi$
$720$		0			0
$721$	−24.6108	−	23.1551i	−0.916553	−	0.862342i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	16.2165	−	9.36258i	0.602264	−	0.347718i
$726$		0			0
$727$	6.96075	−	4.01879i	0.258160	−	0.149049i	−0.365335	−	0.930876i	$-0.619046\pi$
$727$	6.96075	−	4.01879i	0.258160	−	0.149049i	0.623495	+	0.781827i	$0.285712\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.297298			0.0109960
$732$		0			0
$733$	−9.75948			−0.360475			−0.180237	−	0.983623i	$-0.557687\pi$
$733$	−9.75948			−0.360475			−0.180237	+	0.983623i	$0.557687\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.57829	+	3.79798i	−0.242314	+	0.139900i
$738$		0			0
$739$	8.20806	+	4.73893i	0.301938	+	0.174324i	0.643313	−	0.765603i	$-0.277559\pi$
$739$	8.20806	+	4.73893i	0.301938	+	0.174324i	−0.341375	+	0.939927i	$0.610893\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.9246	+	41.4386i	−0.877709	+	1.52024i	−0.0238602	+	0.999715i	$0.507596\pi$
$743$	−23.9246	+	41.4386i	−0.877709	+	1.52024i	−0.853849	+	0.520521i	$0.825738\pi$
$744$		0			0
$745$	54.9268			2.01236
$746$		0			0
$747$		0			0
$748$		0			0
$749$	31.9534	+	7.52668i	1.16755	+	0.275019i
$750$		0			0
$751$			21.7520i			0.793740i	0.917875	+	0.396870i	$0.129904\pi$
$751$			21.7520i			0.793740i	−0.917875	+	0.396870i	$0.870096\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.1725			0.734153
$756$		0			0
$757$	18.2247			0.662390			0.331195	−	0.943562i	$-0.392548\pi$
$757$	18.2247			0.662390			0.331195	+	0.943562i	$0.392548\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			7.47676i			0.271032i	0.990775	+	0.135516i	$0.0432693\pi$
$761$			7.47676i			0.271032i	−0.990775	+	0.135516i	$0.956731\pi$
$762$		0			0
$763$	9.36174	+	31.1145i	0.338918	+	1.12642i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	24.3891			0.880639
$768$		0			0
$769$	−11.1663	+	19.3406i	−0.402666	+	0.697439i	−0.994047	−	0.108954i	$-0.965250\pi$
$769$	−11.1663	+	19.3406i	−0.402666	+	0.697439i	0.591380	+	0.806393i	$0.298583\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	41.7168	+	24.0852i	1.50045	+	0.866285i	1.00000		0.000519449i	$0.000165346\pi$
$773$	41.7168	+	24.0852i	1.50045	+	0.866285i	0.500450	+	0.865766i	$0.333168\pi$
$774$		0			0
$775$	14.9371	−	8.62391i	0.536555	−	0.309780i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.5423			−0.449376
$780$		0			0
$781$	3.16496			0.113251
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−35.0737	+	20.2498i	−1.25183	+	0.722746i
$786$		0			0
$787$	3.62124	−	2.09072i	0.129083	−	0.0745263i	−0.434068	−	0.900880i	$-0.642922\pi$
$787$	3.62124	−	2.09072i	0.129083	−	0.0745263i	0.563151	+	0.826354i	$0.309589\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−38.7788	+	11.6678i	−1.37882	+	0.414859i
$792$		0			0
$793$	−0.524617	−	0.908664i	−0.0186297	−	0.0322676i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−28.4260	−	16.4118i	−1.00690	−	0.581335i	−0.0966189	−	0.995321i	$-0.530803\pi$
$797$	−28.4260	−	16.4118i	−1.00690	−	0.581335i	−0.910283	+	0.413986i	$0.864136\pi$
$798$		0			0
$799$	7.08260	−	4.08914i	0.250564	−	0.144663i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.7396	−	18.6015i	0.378991	−	0.656431i
$804$		0			0
$805$	−39.1536	−	36.8378i	−1.37998	−	1.29836i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.93633	+	2.27264i	0.138394	+	0.0799018i	0.567598	−	0.823306i	$-0.307873\pi$
$809$	3.93633	+	2.27264i	0.138394	+	0.0799018i	−0.429204	+	0.903207i	$0.641206\pi$
$810$		0			0
$811$			31.5008i			1.10614i	0.833133	+	0.553072i	$0.186545\pi$
$811$			31.5008i			1.10614i	−0.833133	+	0.553072i	$0.813455\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.2527	−	28.1505i	−0.569306	−	0.986068i
$816$		0			0
$817$	0.878937	−	1.52236i	0.0307501	−	0.0532608i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.4725	+	14.1292i	0.854095	+	0.493112i	0.862030	−	0.506857i	$-0.169193\pi$
$821$	24.4725	+	14.1292i	0.854095	+	0.493112i	−0.00793570	+	0.999969i	$0.502526\pi$
$822$		0			0
$823$	12.9961	−	7.50328i	0.453014	−	0.261548i	−0.256088	−	0.966653i	$-0.582434\pi$
$823$	12.9961	−	7.50328i	0.453014	−	0.261548i	0.709102	+	0.705106i	$0.249100\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.7519			−0.860709			−0.430354	−	0.902660i	$-0.641611\pi$
$827$	−24.7519			−0.860709			−0.430354	+	0.902660i	$0.641611\pi$
$828$		0			0
$829$	−1.67861	+	2.90744i	−0.0583005	+	0.100979i	−0.893703	−	0.448660i	$-0.851901\pi$
$829$	−1.67861	+	2.90744i	−0.0583005	+	0.100979i	0.835402	+	0.549639i	$0.185235\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.75575	+	7.52991i	−0.130129	+	0.260896i
$834$		0			0
$835$	41.8425	+	24.1578i	1.44802	+	0.836013i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.54338	+	4.40526i	0.0878073	+	0.152087i	0.906584	−	0.422025i	$-0.138681\pi$
$839$	2.54338	+	4.40526i	0.0878073	+	0.152087i	−0.818777	+	0.574112i	$0.805347\pi$
$840$		0			0
$841$	17.3229	−	30.0042i	0.597343	−	1.03463i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	31.2015	−	18.0142i	1.07336	−	0.619707i
$846$		0			0
$847$	−16.2718	+	17.2947i	−0.559104	+	0.594252i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.45862	+	2.52641i	0.0500010	+	0.0866042i
$852$		0			0
$853$	20.5066	+	35.5185i	0.702134	+	1.21613i	0.967716	+	0.252043i	$0.0811024\pi$
$853$	20.5066	+	35.5185i	0.702134	+	1.21613i	−0.265582	+	0.964088i	$0.585564\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	31.3869i		−	1.07216i	−0.844168	−	0.536078i	$-0.819905\pi$
$857$		−	31.3869i		−	1.07216i	0.844168	−	0.536078i	$-0.180095\pi$
$858$		0			0
$859$			55.3235i			1.88761i	0.330496	+	0.943807i	$0.392784\pi$
$859$			55.3235i			1.88761i	−0.330496	+	0.943807i	$0.607216\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.18055	+	12.4371i	0.244429	+	0.423363i	0.961971	−	0.273152i	$-0.0880662\pi$
$863$	7.18055	+	12.4371i	0.244429	+	0.423363i	−0.717542	+	0.696515i	$0.754733\pi$
$864$		0			0
$865$	−34.2203	+	59.2714i	−1.16353	+	2.01529i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.8567	+	6.84549i	0.402212	+	0.232217i
$870$		0			0
$871$		−	27.3715i		−	0.927448i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.8561	+	13.0366i	0.468423	+	0.440717i
$876$		0			0
$877$	51.0736			1.72463			0.862316	−	0.506370i	$-0.169013\pi$
$877$	51.0736			1.72463			0.862316	+	0.506370i	$0.169013\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	38.4851i		−	1.29660i	−0.761387	−	0.648298i	$-0.775481\pi$
$881$		−	38.4851i		−	1.29660i	0.761387	−	0.648298i	$-0.224519\pi$
$882$		0			0
$883$			16.7854i			0.564872i	0.959286	+	0.282436i	$0.0911425\pi$
$883$			16.7854i			0.564872i	−0.959286	+	0.282436i	$0.908857\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	34.3127			1.15211			0.576054	−	0.817412i	$-0.304592\pi$
$887$	34.3127			1.15211			0.576054	+	0.817412i	$0.304592\pi$
$888$		0			0
$889$	29.1921	+	27.4655i	0.979073	+	0.921164i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	48.3569i		−	1.61820i
$894$		0			0
$895$	−19.5458	−	11.2848i	−0.653345	−	0.377209i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	29.3123	−	50.7703i	0.977618	−	1.69328i
$900$		0			0
$901$	−7.48606	−	12.9662i	−0.249397	−	0.431968i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			42.2894i			1.40575i
$906$		0			0
$907$			30.2567i			1.00466i	0.864677	+	0.502328i	$0.167523\pi$
$907$			30.2567i			1.00466i	−0.864677	+	0.502328i	$0.832477\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.9890	+	39.8181i	0.761660	+	1.31923i	0.941995	+	0.335628i	$0.108948\pi$
$911$	22.9890	+	39.8181i	0.761660	+	1.31923i	−0.180335	+	0.983605i	$0.557718\pi$
$912$		0			0
$913$	3.68816	+	6.38807i	0.122060	+	0.211414i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−16.7527	+	17.8058i	−0.553223	+	0.588001i
$918$		0			0
$919$	6.58006	−	3.79900i	0.217056	−	0.125317i	−0.387530	−	0.921857i	$-0.626672\pi$
$919$	6.58006	−	3.79900i	0.217056	−	0.125317i	0.604586	+	0.796540i	$0.293338\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.70235	+	9.87677i	−0.187695	+	0.325098i
$924$		0			0
$925$	0.456711	+	0.791046i	0.0150166	+	0.0260094i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−32.9192	−	19.0059i	−1.08004	−	0.623564i	−0.149136	−	0.988817i	$-0.547649\pi$
$929$	−32.9192	−	19.0059i	−1.08004	−	0.623564i	−0.930908	+	0.365253i	$0.880982\pi$
$930$		0			0
$931$	27.4546	+	41.4935i	0.899789	+	1.35990i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.31824	+	4.01531i	−0.0758145	+	0.131315i
$936$		0			0
$937$	−53.0882			−1.73431			−0.867157	−	0.498034i	$-0.834055\pi$
$937$	−53.0882			−1.73431			−0.867157	+	0.498034i	$0.834055\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.25032	+	4.76333i	−0.268953	+	0.155280i	−0.628412	−	0.777881i	$-0.716295\pi$
$941$	−8.25032	+	4.76333i	−0.268953	+	0.155280i	0.359459	+	0.933161i	$0.382961\pi$
$942$		0			0
$943$	−11.4557	−	6.61394i	−0.373048	−	0.215379i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.80505	−	6.59053i	0.123647	−	0.214164i	−0.797556	−	0.603245i	$-0.793874\pi$
$947$	3.80505	−	6.59053i	0.123647	−	0.214164i	0.921203	+	0.389081i	$0.127207\pi$
$948$		0			0
$949$	38.6992	+	67.0291i	1.25623	+	2.17586i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	8.51742i		−	0.275906i	−0.990439	−	0.137953i	$-0.955948\pi$
$953$		−	8.51742i		−	0.275906i	0.990439	−	0.137953i	$-0.0440524\pi$
$954$		0			0
$955$	25.4848	+	14.7137i	0.824669	+	0.476123i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.94347	−	7.47364i	−0.256508	−	0.241336i
$960$		0			0
$961$	11.4996	−	19.9180i	0.370956	−	0.642515i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	12.2290	−	7.06042i	0.393666	−	0.227283i
$966$		0			0
$967$	13.0326	+	7.52437i	0.419100	+	0.241967i	0.694692	−	0.719307i	$-0.255541\pi$
$967$	13.0326	+	7.52437i	0.419100	+	0.241967i	−0.275592	+	0.961275i	$0.588874\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.1706	+	22.8121i	0.422664	+	0.732076i	0.996199	−	0.0871050i	$-0.0277616\pi$
$971$	13.1706	+	22.8121i	0.422664	+	0.732076i	−0.573535	+	0.819181i	$0.694428\pi$
$972$		0			0
$973$	−11.3325	+	3.40974i	−0.363305	+	0.109311i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.5996	−	13.6252i	0.755017	−	0.435909i	−0.0724869	−	0.997369i	$-0.523094\pi$
$977$	23.5996	−	13.6252i	0.755017	−	0.435909i	0.827504	+	0.561460i	$0.189760\pi$
$978$		0			0
$979$	5.93960	−	3.42923i	0.189830	−	0.109599i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−40.3581			−1.28722			−0.643612	−	0.765352i	$-0.722565\pi$
$983$	−40.3581			−1.28722			−0.643612	+	0.765352i	$0.722565\pi$
$984$		0			0
$985$	56.2384			1.79191
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.60557	−	0.926979i	0.0510543	−	0.0294762i
$990$		0			0
$991$	−24.0823	−	13.9039i	−0.765000	−	0.441673i	0.0660879	−	0.997814i	$-0.478948\pi$
$991$	−24.0823	−	13.9039i	−0.765000	−	0.441673i	−0.831088	+	0.556141i	$0.812282\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.75598	−	4.77350i	0.0873706	−	0.151330i
$996$		0			0
$997$	46.2357			1.46430			0.732149	−	0.681144i	$-0.238517\pi$
$997$	46.2357			1.46430			0.732149	+	0.681144i	$0.238517\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bh.d.2447.13		30
3.2	odd	2		1008.2.bh.d.95.1	yes	30
4.3	odd	2		3024.2.bh.c.2447.13		30
7.2	even	3		3024.2.cj.d.2879.13		30
9.2	odd	6		3024.2.cj.c.1439.13		30
9.7	even	3		1008.2.cj.c.767.5	yes	30
12.11	even	2		1008.2.bh.c.95.15	✓	30
21.2	odd	6		1008.2.cj.d.527.11	yes	30
28.23	odd	6		3024.2.cj.c.2879.13		30
36.7	odd	6		1008.2.cj.d.767.11	yes	30
36.11	even	6		3024.2.cj.d.1439.13		30
63.2	odd	6		3024.2.bh.c.1871.3		30
63.16	even	3		1008.2.bh.c.191.15	yes	30
84.23	even	6		1008.2.cj.c.527.5	yes	30
252.79	odd	6		1008.2.bh.d.191.1	yes	30
252.191	even	6	inner	3024.2.bh.d.1871.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.15	✓	30	12.11	even	2
1008.2.bh.c.191.15	yes	30	63.16	even	3
1008.2.bh.d.95.1	yes	30	3.2	odd	2
1008.2.bh.d.191.1	yes	30	252.79	odd	6
1008.2.cj.c.527.5	yes	30	84.23	even	6
1008.2.cj.c.767.5	yes	30	9.7	even	3
1008.2.cj.d.527.11	yes	30	21.2	odd	6
1008.2.cj.d.767.11	yes	30	36.7	odd	6
3024.2.bh.c.1871.3		30	63.2	odd	6
3024.2.bh.c.2447.13		30	4.3	odd	2
3024.2.bh.d.1871.3		30	252.191	even	6	inner
3024.2.bh.d.2447.13		30	1.1	even	1	trivial
3024.2.cj.c.1439.13		30	9.2	odd	6
3024.2.cj.c.2879.13		30	28.23	odd	6
3024.2.cj.d.1439.13		30	36.11	even	6
3024.2.cj.d.2879.13		30	7.2	even	3

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.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.71056i q^{5} +(1.81297 - 1.92695i) q^{7} +O(q^{10})\)	\(q+2.71056i q^{5} +(1.81297 - 1.92695i) q^{7} -1.42297 q^{11} +(2.56378 - 4.44059i) q^{13} +(-1.04103 - 0.601041i) q^{17} +(-6.15547 + 3.55386i) q^{19} -7.49622 q^{23} -2.34715 q^{25} +(-6.90901 + 3.98892i) q^{29} +(-6.36392 + 3.67421i) q^{31} +(5.22311 + 4.91418i) q^{35} +(-0.194581 - 0.337025i) q^{37} +(1.52819 + 0.882303i) q^{41} +(-0.214184 + 0.123659i) q^{43} +(-3.40171 + 5.89194i) q^{47} +(-0.426244 - 6.98701i) q^{49} +(10.7865 + 6.22758i) q^{53} -3.85704i q^{55} +(2.37824 + 4.11923i) q^{59} +(0.102313 - 0.177212i) q^{61} +(12.0365 + 6.94928i) q^{65} +(4.62294 - 2.66906i) q^{67} -2.22420 q^{71} +(-7.54731 + 13.0723i) q^{73} +(-2.57980 + 2.74198i) q^{77} +(-8.33242 - 4.81072i) q^{79} +(-2.59188 - 4.48927i) q^{83} +(1.62916 - 2.82179i) q^{85} +(-4.17410 + 2.40992i) q^{89} +(-3.90872 - 12.9910i) q^{91} +(-9.63297 - 16.6848i) q^{95} +(2.40373 + 4.16339i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{7}+O(q^{10}) \) 30 * q + 2 * q^7	\( 30 q + 2 q^{7} + 6 q^{11} - 12 q^{17} - 9 q^{19} - 24 q^{23} - 36 q^{25} - 27 q^{29} - 6 q^{31} - 6 q^{35} + 6 q^{37} - 9 q^{41} + 21 q^{43} + 12 q^{49} + 3 q^{53} + 3 q^{59} - 3 q^{61} + 39 q^{67} + 18 q^{71} + 21 q^{73} - 36 q^{77} + 33 q^{79} - 15 q^{83} - 3 q^{85} - 6 q^{89} + 26 q^{91} - 27 q^{95} - 6 q^{97}+O(q^{100}) \) 30 * q + 2 * q^7 + 6 * q^11 - 12 * q^17 - 9 * q^19 - 24 * q^23 - 36 * q^25 - 27 * q^29 - 6 * q^31 - 6 * q^35 + 6 * q^37 - 9 * q^41 + 21 * q^43 + 12 * q^49 + 3 * q^53 + 3 * q^59 - 3 * q^61 + 39 * q^67 + 18 * q^71 + 21 * q^73 - 36 * q^77 + 33 * q^79 - 15 * q^83 - 3 * q^85 - 6 * q^89 + 26 * q^91 - 27 * q^95 - 6 * q^97

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