LMFDB - Embedded newform 3024.2.cc.d.881.9

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			881.9
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422480 + 0.731757i) q^{5} +(-0.327684 - 2.62538i) q^{7} +O(q^{10})$	$q+(-0.422480 + 0.731757i) q^{5} +(-0.327684 - 2.62538i) q^{7} +(-0.791371 + 0.456898i) q^{11} +(-0.472651 - 0.272885i) q^{13} -4.77352 q^{17} -3.15579i q^{19} +(1.39291 + 0.804196i) q^{23} +(2.14302 + 3.71182i) q^{25} +(-5.56478 + 3.21283i) q^{29} +(-1.57351 - 0.908468i) q^{31} +(2.05958 + 0.869387i) q^{35} +7.14037 q^{37} +(-2.82322 + 4.88995i) q^{41} +(1.84576 + 3.19695i) q^{43} +(6.75196 + 11.6947i) q^{47} +(-6.78525 + 1.72059i) q^{49} -2.49672i q^{53} -0.772122i q^{55} +(0.279096 - 0.483409i) q^{59} +(-10.9926 + 6.34661i) q^{61} +(0.399372 - 0.230577i) q^{65} +(3.06545 - 5.30951i) q^{67} -9.24488i q^{71} +8.87479i q^{73} +(1.45885 + 1.92793i) q^{77} +(5.58581 + 9.67491i) q^{79} +(0.122120 + 0.211518i) q^{83} +(2.01672 - 3.49306i) q^{85} -6.19322 q^{89} +(-0.561548 + 1.33031i) q^{91} +(2.30927 + 1.33326i) q^{95} +(-12.2408 + 7.06722i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.422480	+	0.731757i	−0.188939	+	0.327252i	−0.944897	−	0.327368i	$-0.893838\pi$
$5$	−0.422480	+	0.731757i	−0.188939	+	0.327252i	0.755958	+	0.654620i	$0.227171\pi$
$6$		0			0
$7$	−0.327684	−	2.62538i	−0.123853	−	0.992301i
$7$	−0.327684	−	2.62538i	−0.123853	−	0.992301i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.791371	+	0.456898i	−0.238607	+	0.137760i	−0.614537	−	0.788888i	$-0.710657\pi$
$11$	−0.791371	+	0.456898i	−0.238607	+	0.137760i	0.375929	+	0.926648i	$0.377324\pi$
$12$		0			0
$13$	−0.472651	−	0.272885i	−0.131090	−	0.0756848i	0.433021	−	0.901384i	$-0.357448\pi$
$13$	−0.472651	−	0.272885i	−0.131090	−	0.0756848i	−0.564111	+	0.825699i	$0.690781\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.77352			−1.15775			−0.578874	−	0.815417i	$-0.696508\pi$
$17$	−4.77352			−1.15775			−0.578874	+	0.815417i	$0.696508\pi$
$18$		0			0
$19$		−	3.15579i		−	0.723988i	−0.932180	−	0.361994i	$-0.882096\pi$
$19$		−	3.15579i		−	0.723988i	0.932180	−	0.361994i	$-0.117904\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.39291	+	0.804196i	0.290441	+	0.167686i	0.638141	−	0.769920i	$-0.279704\pi$
$23$	1.39291	+	0.804196i	0.290441	+	0.167686i	−0.347699	+	0.937606i	$0.613037\pi$
$24$		0			0
$25$	2.14302	+	3.71182i	0.428604	+	0.742364i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.56478	+	3.21283i	−1.03335	+	0.596607i	−0.917944	−	0.396711i	$-0.870152\pi$
$29$	−5.56478	+	3.21283i	−1.03335	+	0.596607i	−0.115410	+	0.993318i	$0.536818\pi$
$30$		0			0
$31$	−1.57351	−	0.908468i	−0.282611	−	0.163166i	0.351994	−	0.936002i	$-0.385504\pi$
$31$	−1.57351	−	0.908468i	−0.282611	−	0.163166i	−0.634605	+	0.772837i	$0.718837\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.05958	+	0.869387i	0.348133	+	0.146953i
$36$		0			0
$37$	7.14037			1.17387			0.586935	−	0.809634i	$-0.300334\pi$
$37$	7.14037			1.17387			0.586935	+	0.809634i	$0.300334\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.82322	+	4.88995i	−0.440912	+	0.763683i	−0.997757	−	0.0669338i	$-0.978678\pi$
$41$	−2.82322	+	4.88995i	−0.440912	+	0.763683i	0.556845	+	0.830616i	$0.312012\pi$
$42$		0			0
$43$	1.84576	+	3.19695i	0.281476	+	0.487531i	0.971748	−	0.236019i	$-0.0758427\pi$
$43$	1.84576	+	3.19695i	0.281476	+	0.487531i	−0.690273	+	0.723549i	$0.742509\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.75196	+	11.6947i	0.984874	+	1.70585i	0.642494	+	0.766291i	$0.277900\pi$
$47$	6.75196	+	11.6947i	0.984874	+	1.70585i	0.342381	+	0.939561i	$0.388767\pi$
$48$		0			0
$49$	−6.78525	+	1.72059i	−0.969321	+	0.245798i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.49672i		−	0.342951i	−0.985188	−	0.171476i	$-0.945147\pi$
$53$		−	2.49672i		−	0.342951i	0.985188	−	0.171476i	$-0.0548535\pi$
$54$		0			0
$55$		−	0.772122i		−	0.104113i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.279096	−	0.483409i	0.0363353	−	0.0629345i	−0.847286	−	0.531137i	$-0.821765\pi$
$59$	0.279096	−	0.483409i	0.0363353	−	0.0629345i	0.883621	+	0.468203i	$0.155098\pi$
$60$		0			0
$61$	−10.9926	+	6.34661i	−1.40746	+	0.812600i	−0.995143	−	0.0984388i	$-0.968615\pi$
$61$	−10.9926	+	6.34661i	−1.40746	+	0.812600i	−0.412321	+	0.911039i	$0.635282\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.399372	−	0.230577i	0.0495360	−	0.0285996i
$66$		0			0
$67$	3.06545	−	5.30951i	0.374504	−	0.648660i	−0.615748	−	0.787943i	$-0.711146\pi$
$67$	3.06545	−	5.30951i	0.374504	−	0.648660i	0.990253	+	0.139282i	$0.0444796\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	9.24488i		−	1.09717i	−0.836096	−	0.548583i	$-0.815168\pi$
$71$		−	9.24488i		−	1.09717i	0.836096	−	0.548583i	$-0.184832\pi$
$72$		0			0
$73$			8.87479i			1.03872i	0.854557	+	0.519358i	$0.173829\pi$
$73$			8.87479i			1.03872i	−0.854557	+	0.519358i	$0.826171\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.45885	+	1.92793i	0.166252	+	0.219708i
$78$		0			0
$79$	5.58581	+	9.67491i	0.628453	+	1.08851i	0.987862	+	0.155332i	$0.0496448\pi$
$79$	5.58581	+	9.67491i	0.628453	+	1.08851i	−0.359410	+	0.933180i	$0.617022\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.122120	+	0.211518i	0.0134044	+	0.0232171i	0.872650	−	0.488347i	$-0.162400\pi$
$83$	0.122120	+	0.211518i	0.0134044	+	0.0232171i	−0.859245	+	0.511564i	$0.829066\pi$
$84$		0			0
$85$	2.01672	−	3.49306i	0.218744	−	0.378875i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.19322			−0.656480			−0.328240	−	0.944594i	$-0.606455\pi$
$89$	−6.19322			−0.656480			−0.328240	+	0.944594i	$0.606455\pi$
$90$		0			0
$91$	−0.561548	+	1.33031i	−0.0588662	+	0.139454i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.30927	+	1.33326i	0.236926	+	0.136790i
$96$		0			0
$97$	−12.2408	+	7.06722i	−1.24286	+	0.717568i	−0.969676	−	0.244393i	$-0.921411\pi$
$97$	−12.2408	+	7.06722i	−1.24286	+	0.717568i	−0.273187	+	0.961961i	$0.588078\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.62446	+	9.74186i	0.559655	+	0.969351i	0.997525	+	0.0703128i	$0.0223997\pi$
$101$	5.62446	+	9.74186i	0.559655	+	0.969351i	−0.437870	+	0.899038i	$0.644267\pi$
$102$		0			0
$103$	−1.97803	−	1.14202i	−0.194901	−	0.112526i	0.399374	−	0.916788i	$-0.369228\pi$
$103$	−1.97803	−	1.14202i	−0.194901	−	0.112526i	−0.594275	+	0.804262i	$0.702561\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	10.9749i		−	1.06098i	−0.847690	−	0.530492i	$-0.822007\pi$
$107$		−	10.9749i		−	1.06098i	0.847690	−	0.530492i	$-0.177993\pi$
$108$		0			0
$109$	6.21135			0.594939			0.297470	−	0.954731i	$-0.403857\pi$
$109$	6.21135			0.594939			0.297470	+	0.954731i	$0.403857\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.1205	+	8.72980i	1.42241	+	0.821230i	0.996505	−	0.0835364i	$-0.0266215\pi$
$113$	15.1205	+	8.72980i	1.42241	+	0.821230i	0.425908	+	0.904767i	$0.359955\pi$
$114$		0			0
$115$	−1.17695	+	0.679514i	−0.109751	+	0.0633650i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.56420	+	12.5323i	0.143390	+	1.14883i
$120$		0			0
$121$	−5.08249	+	8.80313i	−0.462044	+	0.800284i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.84634			−0.701798
$126$		0			0
$127$	−7.19234			−0.638217			−0.319109	−	0.947718i	$-0.603383\pi$
$127$	−7.19234			−0.638217			−0.319109	+	0.947718i	$0.603383\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.51594	+	4.35773i	−0.219819	+	0.380737i	−0.954752	−	0.297402i	$-0.903880\pi$
$131$	−2.51594	+	4.35773i	−0.219819	+	0.380737i	0.734934	+	0.678139i	$0.237213\pi$
$132$		0			0
$133$	−8.28515	+	1.03410i	−0.718414	+	0.0896679i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.61383	−	0.931746i	0.137879	−	0.0796044i	−0.429474	−	0.903079i	$-0.641301\pi$
$137$	1.61383	−	0.931746i	0.137879	−	0.0796044i	0.567353	+	0.823475i	$0.307968\pi$
$138$		0			0
$139$	−9.90462	−	5.71843i	−0.840098	−	0.485031i	0.0171992	−	0.999852i	$-0.494525\pi$
$139$	−9.90462	−	5.71843i	−0.840098	−	0.485031i	−0.857298	+	0.514821i	$0.827858\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.498724			0.0417054
$144$		0			0
$145$		−	5.42943i		−	0.450889i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.443690	−	0.256164i	−0.0363485	−	0.0209858i	0.481716	−	0.876328i	$-0.340014\pi$
$149$	−0.443690	−	0.256164i	−0.0363485	−	0.0209858i	−0.518064	+	0.855342i	$0.673347\pi$
$150$		0			0
$151$	5.74808	+	9.95597i	0.467772	+	0.810205i	0.999322	−	0.0368219i	$-0.0117234\pi$
$151$	5.74808	+	9.95597i	0.467772	+	0.810205i	−0.531550	+	0.847027i	$0.678390\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.32956	−	0.767619i	0.106793	−	0.0616567i
$156$		0			0
$157$	14.9187	+	8.61334i	1.19065	+	0.687419i	0.958453	−	0.285250i	$-0.0920768\pi$
$157$	14.9187	+	8.61334i	1.19065	+	0.687419i	0.232192	+	0.972670i	$0.425410\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.65489	−	3.92044i	0.130423	−	0.308974i
$162$		0			0
$163$	−12.7474			−0.998450			−0.499225	−	0.866473i	$-0.666382\pi$
$163$	−12.7474			−0.998450			−0.499225	+	0.866473i	$0.666382\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.92213	+	6.79333i	−0.303503	+	0.525683i	−0.976927	−	0.213573i	$-0.931490\pi$
$167$	−3.92213	+	6.79333i	−0.303503	+	0.525683i	0.673424	+	0.739257i	$0.264823\pi$
$168$		0			0
$169$	−6.35107	−	11.0004i	−0.488544	−	0.846182i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.00420	+	1.73933i	0.0763482	+	0.132239i	0.901672	−	0.432421i	$-0.142341\pi$
$173$	1.00420	+	1.73933i	0.0763482	+	0.132239i	−0.825324	+	0.564660i	$0.809007\pi$
$174$		0			0
$175$	9.04271	−	6.84255i	0.683565	−	0.517248i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			11.8357i			0.884641i	0.896857	+	0.442320i	$0.145845\pi$
$179$			11.8357i			0.884641i	−0.896857	+	0.442320i	$0.854155\pi$
$180$		0			0
$181$		−	10.7449i		−	0.798660i	−0.916807	−	0.399330i	$-0.869243\pi$
$181$		−	10.7449i		−	0.798660i	0.916807	−	0.399330i	$-0.130757\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.01667	+	5.22502i	−0.221790	+	0.384151i
$186$		0			0
$187$	3.77762	−	2.18101i	0.276247	−	0.159491i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.86793	−	1.65580i	0.207516	−	0.119809i	−0.392640	−	0.919692i	$-0.628438\pi$
$191$	2.86793	−	1.65580i	0.207516	−	0.119809i	0.600156	+	0.799883i	$0.295105\pi$
$192$		0			0
$193$	−11.7223	+	20.3036i	−0.843788	+	1.46148i	0.0428821	+	0.999080i	$0.486346\pi$
$193$	−11.7223	+	20.3036i	−0.843788	+	1.46148i	−0.886670	+	0.462403i	$0.846987\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			17.9144i			1.27635i	0.769893	+	0.638173i	$0.220310\pi$
$197$			17.9144i			1.27635i	−0.769893	+	0.638173i	$0.779690\pi$
$198$		0			0
$199$			16.0924i			1.14076i	0.821381	+	0.570380i	$0.193204\pi$
$199$			16.0924i			1.14076i	−0.821381	+	0.570380i	$0.806796\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.2584	+	13.5569i	0.719997	+	0.951506i
$204$		0			0
$205$	−2.38551	−	4.13182i	−0.166611	−	0.288579i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.44188	+	2.49740i	0.0997367	+	0.172749i
$210$		0			0
$211$	−1.95748	+	3.39046i	−0.134759	+	0.233409i	−0.925505	−	0.378735i	$-0.876359\pi$
$211$	−1.95748	+	3.39046i	−0.134759	+	0.233409i	0.790747	+	0.612144i	$0.209693\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.11919			−0.212727
$216$		0			0
$217$	−1.86946	+	4.42876i	−0.126907	+	0.300644i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.25621	+	1.30262i	0.151769	+	0.0876239i
$222$		0			0
$223$	−21.6047	+	12.4735i	−1.44676	+	0.835288i	−0.998287	−	0.0585082i	$-0.981366\pi$
$223$	−21.6047	+	12.4735i	−1.44676	+	0.835288i	−0.448474	+	0.893796i	$0.648032\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.3878	−	19.7243i	−0.755838	−	1.30915i	−0.944957	−	0.327195i	$-0.893897\pi$
$227$	−11.3878	−	19.7243i	−0.755838	−	1.30915i	0.189119	−	0.981954i	$-0.439437\pi$
$228$		0			0
$229$	−22.3549	−	12.9066i	−1.47725	−	0.852891i	−0.477581	−	0.878588i	$-0.658486\pi$
$229$	−22.3549	−	12.9066i	−1.47725	−	0.852891i	−0.999670	+	0.0256966i	$0.991820\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	28.7072i		−	1.88067i	−0.340245	−	0.940337i	$-0.610510\pi$
$233$		−	28.7072i		−	1.88067i	0.340245	−	0.940337i	$-0.389490\pi$
$234$		0			0
$235$	−11.4103			−0.744325
$236$		0			0
$237$		0			0
$238$		0			0
$239$	20.7087	+	11.9562i	1.33954	+	0.773381i	0.986738	−	0.162318i	$-0.0518971\pi$
$239$	20.7087	+	11.9562i	1.33954	+	0.773381i	0.352797	+	0.935700i	$0.385230\pi$
$240$		0			0
$241$	12.7991	−	7.38955i	0.824461	−	0.476003i	−0.0274914	−	0.999622i	$-0.508752\pi$
$241$	12.7991	−	7.38955i	0.824461	−	0.476003i	0.851952	+	0.523619i	$0.175419\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.60758	−	5.69207i	0.102705	−	0.363653i
$246$		0			0
$247$	−0.861169	+	1.49159i	−0.0547949	+	0.0949075i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.5524			−1.61285			−0.806426	−	0.591334i	$-0.798601\pi$
$251$	−25.5524			−1.61285			−0.806426	+	0.591334i	$0.798601\pi$
$252$		0			0
$253$	−1.46974			−0.0924020
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.67566	−	4.63438i	0.166903	−	0.289085i	−0.770426	−	0.637529i	$-0.779957\pi$
$257$	2.67566	−	4.63438i	0.166903	−	0.289085i	0.937330	+	0.348444i	$0.113290\pi$
$258$		0			0
$259$	−2.33978	−	18.7462i	−0.145387	−	1.16483i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.09220	+	2.36263i	−0.252336	+	0.145686i	−0.620833	−	0.783943i	$-0.713206\pi$
$263$	−4.09220	+	2.36263i	−0.252336	+	0.145686i	0.368497	+	0.929629i	$0.379872\pi$
$264$		0			0
$265$	1.82700	+	1.05482i	0.112231	+	0.0647969i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	22.4749			1.37032			0.685161	−	0.728392i	$-0.259732\pi$
$269$	22.4749			1.37032			0.685161	+	0.728392i	$0.259732\pi$
$270$		0			0
$271$			26.2752i			1.59611i	0.602588	+	0.798053i	$0.294136\pi$
$271$			26.2752i			1.59611i	−0.602588	+	0.798053i	$0.705864\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.39185	−	1.95829i	−0.204536	−	0.118089i
$276$		0			0
$277$	−1.43859	−	2.49171i	−0.0864365	−	0.149712i	0.819566	−	0.572985i	$-0.194215\pi$
$277$	−1.43859	−	2.49171i	−0.0864365	−	0.149712i	−0.906002	+	0.423272i	$0.860881\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.15735	+	1.82290i	−0.188352	+	0.108745i	−0.591211	−	0.806517i	$-0.701350\pi$
$281$	−3.15735	+	1.82290i	−0.188352	+	0.108745i	0.402859	+	0.915262i	$0.368017\pi$
$282$		0			0
$283$	−22.9147	−	13.2298i	−1.36214	−	0.786431i	−0.372231	−	0.928140i	$-0.621407\pi$
$283$	−22.9147	−	13.2298i	−1.36214	−	0.786431i	−0.989908	+	0.141709i	$0.954740\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.7631	+	5.80966i	0.812411	+	0.342933i
$288$		0			0
$289$	5.78646			0.340380
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.80499	+	15.2507i	−0.514393	+	0.890955i	0.485468	+	0.874255i	$0.338649\pi$
$293$	−8.80499	+	15.2507i	−0.514393	+	0.890955i	−0.999861	+	0.0167000i	$0.994684\pi$
$294$		0			0
$295$	0.235826	+	0.408462i	0.0137303	+	0.0237816i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.438907	−	0.760209i	−0.0253826	−	0.0439640i
$300$		0			0
$301$	7.78839	−	5.89341i	0.448915	−	0.339691i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	10.7253i		−	0.614127i
$306$		0			0
$307$		−	19.7066i		−	1.12472i	−0.826894	−	0.562358i	$-0.809894\pi$
$307$		−	19.7066i		−	1.12472i	0.826894	−	0.562358i	$-0.190106\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.9357	−	20.6733i	0.676812	−	1.17227i	−0.299124	−	0.954214i	$-0.596694\pi$
$311$	11.9357	−	20.6733i	0.676812	−	1.17227i	0.975936	−	0.218058i	$-0.0699723\pi$
$312$		0			0
$313$	6.86688	−	3.96459i	0.388139	−	0.224092i	−0.293215	−	0.956047i	$-0.594725\pi$
$313$	6.86688	−	3.96459i	0.388139	−	0.224092i	0.681353	+	0.731955i	$0.261392\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.42664	+	4.86513i	−0.473287	+	0.273253i	−0.717615	−	0.696440i	$-0.754766\pi$
$317$	−8.42664	+	4.86513i	−0.473287	+	0.273253i	0.244327	+	0.969693i	$0.421433\pi$
$318$		0			0
$319$	2.93587	−	5.08508i	0.164377	−	0.284710i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			15.0642i			0.838196i
$324$		0			0
$325$		−	2.33920i		−	0.129755i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	28.4906	−	21.5586i	1.57074	−	1.18857i
$330$		0			0
$331$	15.2451	+	26.4053i	0.837947	+	1.45137i	0.891609	+	0.452807i	$0.149577\pi$
$331$	15.2451	+	26.4053i	0.837947	+	1.45137i	−0.0536621	+	0.998559i	$0.517089\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.59018	+	4.48633i	0.141517	+	0.245114i
$336$		0			0
$337$	9.31669	−	16.1370i	0.507512	−	0.879037i	−0.492450	−	0.870341i	$-0.663899\pi$
$337$	9.31669	−	16.1370i	0.507512	−	0.879037i	0.999962	−	0.00869629i	$-0.00276815\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.66031			0.0899108
$342$		0			0
$343$	6.74061	+	17.2500i	0.363959	+	0.931415i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.95873	+	1.70822i	0.158833	+	0.0917022i	0.577310	−	0.816525i	$-0.304103\pi$
$347$	2.95873	+	1.70822i	0.158833	+	0.0917022i	−0.418477	+	0.908227i	$0.637436\pi$
$348$		0			0
$349$	11.0696	−	6.39102i	0.592541	−	0.342104i	−0.173561	−	0.984823i	$-0.555527\pi$
$349$	11.0696	−	6.39102i	0.592541	−	0.342104i	0.766101	+	0.642720i	$0.222194\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.3612	+	31.8025i	0.977268	+	1.69268i	0.672237	+	0.740336i	$0.265334\pi$
$353$	18.3612	+	31.8025i	0.977268	+	1.69268i	0.305031	+	0.952342i	$0.401333\pi$
$354$		0			0
$355$	6.76501	+	3.90578i	0.359049	+	0.207297i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	31.9790i		−	1.68779i	−0.536510	−	0.843894i	$-0.680258\pi$
$359$		−	31.9790i		−	1.68779i	0.536510	−	0.843894i	$-0.319742\pi$
$360$		0			0
$361$	9.04098			0.475841
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.49419	−	3.74943i	−0.339922	−	0.196254i
$366$		0			0
$367$	−24.6434	+	14.2279i	−1.28638	+	0.742689i	−0.978006	−	0.208577i	$-0.933117\pi$
$367$	−24.6434	+	14.2279i	−1.28638	+	0.742689i	−0.308370	+	0.951267i	$0.599783\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.55485	+	0.818135i	−0.340311	+	0.0424755i
$372$		0			0
$373$	−11.7350	+	20.3257i	−0.607618	+	1.05242i	0.384014	+	0.923327i	$0.374541\pi$
$373$	−11.7350	+	20.3257i	−0.607618	+	1.05242i	−0.991632	+	0.129098i	$0.958792\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.50694			0.180616
$378$		0			0
$379$	12.5179			0.643003			0.321502	−	0.946909i	$-0.395812\pi$
$379$	12.5179			0.643003			0.321502	+	0.946909i	$0.395812\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.71492	+	11.6306i	−0.343116	+	0.594295i	−0.985010	−	0.172499i	$-0.944816\pi$
$383$	−6.71492	+	11.6306i	−0.343116	+	0.594295i	0.641893	+	0.766794i	$0.278149\pi$
$384$		0			0
$385$	−2.02712	+	0.253012i	−0.103311	+	0.0128947i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.38955	−	2.53431i	0.222559	−	0.128495i	−0.384576	−	0.923094i	$-0.625652\pi$
$389$	4.38955	−	2.53431i	0.222559	−	0.128495i	0.607135	+	0.794599i	$0.292319\pi$
$390$		0			0
$391$	−6.64907	−	3.83884i	−0.336258	−	0.194139i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.43958			−0.474957
$396$		0			0
$397$			1.08699i			0.0545543i	0.999628	+	0.0272771i	$0.00868366\pi$
$397$			1.08699i			0.0545543i	−0.999628	+	0.0272771i	$0.991316\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.72547	+	2.72825i	0.235979	+	0.136242i	0.613327	−	0.789829i	$-0.289831\pi$
$401$	4.72547	+	2.72825i	0.235979	+	0.136242i	−0.377348	+	0.926071i	$0.623164\pi$
$402$		0			0
$403$	0.495815	+	0.858777i	0.0246983	+	0.0427787i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.65069	+	3.26243i	−0.280094	+	0.161712i
$408$		0			0
$409$	21.4739	+	12.3979i	1.06181	+	0.613039i	0.925934	−	0.377686i	$-0.123280\pi$
$409$	21.4739	+	12.3979i	1.06181	+	0.613039i	0.135881	+	0.990725i	$0.456614\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.36059	−	0.574329i	−0.0669502	−	0.0282609i
$414$		0			0
$415$	−0.206373			−0.0101305
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.145143	+	0.251394i	−0.00709068	+	0.0122814i	−0.869549	−	0.493847i	$-0.835590\pi$
$419$	−0.145143	+	0.251394i	−0.00709068	+	0.0122814i	0.862458	+	0.506128i	$0.168924\pi$
$420$		0			0
$421$	−2.47275	−	4.28293i	−0.120515	−	0.208737i	0.799456	−	0.600724i	$-0.205121\pi$
$421$	−2.47275	−	4.28293i	−0.120515	−	0.208737i	−0.919971	+	0.391987i	$0.871788\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−10.2297	−	17.7184i	−0.496215	−	0.859470i
$426$		0			0
$427$	20.2644	+	26.7802i	0.980662	+	1.29598i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	15.4421i		−	0.743818i	−0.928269	−	0.371909i	$-0.878703\pi$
$431$		−	15.4421i		−	0.743818i	0.928269	−	0.371909i	$-0.121297\pi$
$432$		0			0
$433$		−	20.5683i		−	0.988451i	−0.869334	−	0.494225i	$-0.835452\pi$
$433$		−	20.5683i		−	0.988451i	0.869334	−	0.494225i	$-0.164548\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.53787	−	4.39573i	0.121403	−	0.210276i
$438$		0			0
$439$	16.1823	−	9.34286i	0.772339	−	0.445910i	−0.0613693	−	0.998115i	$-0.519547\pi$
$439$	16.1823	−	9.34286i	0.772339	−	0.445910i	0.833708	+	0.552205i	$0.186213\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−29.4963	+	17.0297i	−1.40141	+	0.809104i	−0.994537	−	0.104380i	$-0.966714\pi$
$443$	−29.4963	+	17.0297i	−1.40141	+	0.809104i	−0.406873	+	0.913485i	$0.633381\pi$
$444$		0			0
$445$	2.61651	−	4.53193i	0.124035	−	0.214834i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	12.7995i		−	0.604045i	−0.953301	−	0.302023i	$-0.902338\pi$
$449$		−	12.7995i		−	0.604045i	0.953301	−	0.302023i	$-0.0976618\pi$
$450$		0			0
$451$		−	5.15969i		−	0.242960i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.736221	−	0.972947i	−0.0345146	−	0.0456124i
$456$		0			0
$457$	−1.55034	−	2.68526i	−0.0725217	−	0.125611i	0.827484	−	0.561489i	$-0.189771\pi$
$457$	−1.55034	−	2.68526i	−0.0725217	−	0.125611i	−0.900006	+	0.435878i	$0.856438\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.78519	+	4.82409i	0.129719	+	0.224680i	0.923568	−	0.383435i	$-0.125259\pi$
$461$	2.78519	+	4.82409i	0.129719	+	0.224680i	−0.793849	+	0.608115i	$0.791926\pi$
$462$		0			0
$463$	3.87498	−	6.71166i	0.180086	−	0.311917i	−0.761824	−	0.647784i	$-0.775696\pi$
$463$	3.87498	−	6.71166i	0.180086	−	0.311917i	0.941909	+	0.335867i	$0.109029\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.7545			−0.821579			−0.410789	−	0.911730i	$-0.634747\pi$
$467$	−17.7545			−0.821579			−0.410789	+	0.911730i	$0.634747\pi$
$468$		0			0
$469$	−14.9440	−	6.30813i	−0.690050	−	0.291282i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.92136	−	1.68665i	−0.134325	−	0.0775523i
$474$		0			0
$475$	11.7137	−	6.76293i	0.537463	−	0.310304i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.03903	+	3.53171i	0.0931658	+	0.161368i	0.908842	−	0.417141i	$-0.136968\pi$
$479$	2.03903	+	3.53171i	0.0931658	+	0.161368i	−0.815676	+	0.578509i	$0.803635\pi$
$480$		0			0
$481$	−3.37491	−	1.94850i	−0.153882	−	0.0888441i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	11.9430i		−	0.542306i
$486$		0			0
$487$	29.6103			1.34177			0.670885	−	0.741561i	$-0.265914\pi$
$487$	29.6103			1.34177			0.670885	+	0.741561i	$0.265914\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−24.9656	−	14.4139i	−1.12668	−	0.650491i	−0.183584	−	0.983004i	$-0.558770\pi$
$491$	−24.9656	−	14.4139i	−1.12668	−	0.650491i	−0.943099	+	0.332513i	$0.892103\pi$
$492$		0			0
$493$	26.5636	−	15.3365i	1.19636	−	0.690721i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−24.2713	+	3.02940i	−1.08872	+	0.135887i
$498$		0			0
$499$	13.9354	−	24.1367i	0.623832	−	1.08051i	−0.364933	−	0.931034i	$-0.618908\pi$
$499$	13.9354	−	24.1367i	0.623832	−	1.08051i	0.988765	−	0.149475i	$-0.0477585\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.6312			−0.919901			−0.459950	−	0.887945i	$-0.652133\pi$
$503$	−20.6312			−0.919901			−0.459950	+	0.887945i	$0.652133\pi$
$504$		0			0
$505$	−9.50490			−0.422963
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.4163	−	21.5056i	0.550341	−	0.953219i	−0.447908	−	0.894079i	$-0.647831\pi$
$509$	12.4163	−	21.5056i	0.550341	−	0.953219i	0.998250	−	0.0591396i	$-0.0188357\pi$
$510$		0			0
$511$	23.2997	−	2.90812i	1.03072	−	0.128648i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.67136	−	0.964960i	0.0736489	−	0.0425212i
$516$		0			0
$517$	−10.6866	−	6.16992i	−0.469997	−	0.271353i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	25.5525			1.11947			0.559737	−	0.828670i	$-0.310902\pi$
$521$	25.5525			1.11947			0.559737	+	0.828670i	$0.310902\pi$
$522$		0			0
$523$		−	25.0505i		−	1.09538i	−0.836681	−	0.547691i	$-0.815507\pi$
$523$		−	25.0505i		−	1.09538i	0.836681	−	0.547691i	$-0.184493\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.51119	+	4.33659i	0.327192	+	0.188905i
$528$		0			0
$529$	−10.2065	−	17.6782i	−0.443762	−	0.768619i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.66879	−	1.54083i	0.115598	−	0.0667407i
$534$		0			0
$535$	8.03097	+	4.63668i	0.347209	+	0.200461i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.58352	−	4.46179i	0.197426	−	0.192183i
$540$		0			0
$541$	23.6313			1.01599			0.507995	−	0.861360i	$-0.330387\pi$
$541$	23.6313			1.01599			0.507995	+	0.861360i	$0.330387\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.62417	+	4.54520i	−0.112407	+	0.194695i
$546$		0			0
$547$	−14.0512	−	24.3375i	−0.600788	−	1.04060i	−0.992702	−	0.120593i	$-0.961520\pi$
$547$	−14.0512	−	24.3375i	−0.600788	−	1.04060i	0.391914	−	0.920002i	$-0.371813\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.1390	+	17.5613i	0.431937	+	0.748136i
$552$		0			0
$553$	23.5699	−	17.8352i	1.00230	−	0.758429i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			14.3227i			0.606871i	0.952852	+	0.303436i	$0.0981338\pi$
$557$			14.3227i			0.606871i	−0.952852	+	0.303436i	$0.901866\pi$
$558$		0			0
$559$		−	2.01472i		−	0.0852138i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.2183	−	33.2871i	0.809955	−	1.40288i	−0.102940	−	0.994688i	$-0.532825\pi$
$563$	19.2183	−	33.2871i	0.809955	−	1.40288i	0.912895	−	0.408196i	$-0.133842\pi$
$564$		0			0
$565$	−12.7762	+	7.37634i	−0.537498	+	0.310325i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.5883	+	13.0414i	−0.946951	+	0.546722i	−0.892132	−	0.451774i	$-0.850791\pi$
$569$	−22.5883	+	13.0414i	−0.946951	+	0.546722i	−0.0548183	+	0.998496i	$0.517458\pi$
$570$		0			0
$571$	−9.74336	+	16.8760i	−0.407747	+	0.706238i	−0.994637	−	0.103428i	$-0.967019\pi$
$571$	−9.74336	+	16.8760i	−0.407747	+	0.706238i	0.586890	+	0.809667i	$0.300352\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			6.89364i			0.287484i
$576$		0			0
$577$			8.07209i			0.336045i	0.985783	+	0.168023i	$0.0537382\pi$
$577$			8.07209i			0.336045i	−0.985783	+	0.168023i	$0.946262\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.515298	−	0.389922i	0.0213782	−	0.0161767i
$582$		0			0
$583$	1.14075	+	1.97584i	0.0472450	+	0.0818307i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.1825	−	28.0289i	−0.667923	−	1.15688i	−0.978484	−	0.206323i	$-0.933850\pi$
$587$	−16.1825	−	28.0289i	−0.667923	−	1.15688i	0.310561	−	0.950554i	$-0.399483\pi$
$588$		0			0
$589$	−2.86693	+	4.96568i	−0.118130	+	0.204607i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−43.7169			−1.79524			−0.897619	−	0.440772i	$-0.854705\pi$
$593$	−43.7169			−1.79524			−0.897619	+	0.440772i	$0.854705\pi$
$594$		0			0
$595$	−9.83145	−	4.15003i	−0.403050	−	0.170135i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.4061	−	11.7814i	−0.833769	−	0.481377i	0.0213724	−	0.999772i	$-0.493196\pi$
$599$	−20.4061	−	11.7814i	−0.833769	−	0.481377i	−0.855141	+	0.518395i	$0.826530\pi$
$600$		0			0
$601$	3.85990	−	2.22851i	0.157449	−	0.0909030i	−0.419206	−	0.907891i	$-0.637691\pi$
$601$	3.85990	−	2.22851i	0.157449	−	0.0909030i	0.576654	+	0.816988i	$0.304358\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.29450	−	7.43830i	−0.174596	−	0.302410i
$606$		0			0
$607$	8.95483	+	5.17007i	0.363465	+	0.209847i	0.670600	−	0.741819i	$-0.266037\pi$
$607$	8.95483	+	5.17007i	0.363465	+	0.209847i	−0.307134	+	0.951666i	$0.599370\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	7.37004i		−	0.298160i
$612$		0			0
$613$	2.30558			0.0931214			0.0465607	−	0.998915i	$-0.485174\pi$
$613$	2.30558			0.0931214			0.0465607	+	0.998915i	$0.485174\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.725847	+	0.419068i	0.0292215	+	0.0168710i	0.514540	−	0.857467i	$-0.327963\pi$
$617$	0.725847	+	0.419068i	0.0292215	+	0.0168710i	−0.485318	+	0.874338i	$0.661296\pi$
$618$		0			0
$619$	21.8761	−	12.6302i	0.879274	−	0.507649i	0.00885512	−	0.999961i	$-0.497181\pi$
$619$	21.8761	−	12.6302i	0.879274	−	0.507649i	0.870419	+	0.492312i	$0.163848\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.02942	+	16.2596i	0.0813068	+	0.651425i
$624$		0			0
$625$	−7.40018	+	12.8175i	−0.296007	+	0.512699i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−34.0847			−1.35905
$630$		0			0
$631$	−8.42854			−0.335535			−0.167768	−	0.985827i	$-0.553656\pi$
$631$	−8.42854			−0.335535			−0.167768	+	0.985827i	$0.553656\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.03862	−	5.26305i	0.120584	−	0.208858i
$636$		0			0
$637$	3.67658	+	1.03836i	0.145671	+	0.0411412i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−28.3658	+	16.3770i	−1.12038	+	0.646853i	−0.941498	−	0.337017i	$-0.890582\pi$
$641$	−28.3658	+	16.3770i	−1.12038	+	0.646853i	−0.178884	+	0.983870i	$0.557249\pi$
$642$		0			0
$643$	−33.5703	−	19.3818i	−1.32388	−	0.764344i	−0.339537	−	0.940593i	$-0.610270\pi$
$643$	−33.5703	−	19.3818i	−1.32388	−	0.764344i	−0.984346	+	0.176249i	$0.943604\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	33.9121			1.33322			0.666611	−	0.745405i	$-0.267744\pi$
$647$	33.9121			1.33322			0.666611	+	0.745405i	$0.267744\pi$
$648$		0			0
$649$			0.510075i			0.0200222i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.48007	+	4.89597i	0.331851	+	0.191594i	0.656663	−	0.754185i	$-0.271968\pi$
$653$	8.48007	+	4.89597i	0.331851	+	0.191594i	−0.324812	+	0.945779i	$0.605301\pi$
$654$		0			0
$655$	−2.12587	−	3.68211i	−0.0830646	−	0.143872i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−28.8977	+	16.6841i	−1.12569	+	0.649920i	−0.942849	−	0.333221i	$-0.891864\pi$
$659$	−28.8977	+	16.6841i	−1.12569	+	0.649920i	−0.182846	+	0.983142i	$0.558531\pi$
$660$		0			0
$661$	36.8160	+	21.2558i	1.43198	+	0.826753i	0.997272	−	0.0738194i	$-0.0235188\pi$
$661$	36.8160	+	21.2558i	1.43198	+	0.826753i	0.434706	+	0.900572i	$0.356852\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.74360	−	6.49961i	0.106392	−	0.252044i
$666$		0			0
$667$	−10.3350			−0.400172
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.79951	−	10.0450i	0.223888	−	0.387785i
$672$		0			0
$673$	22.7186	+	39.3498i	0.875739	+	1.51682i	0.855974	+	0.517019i	$0.172958\pi$
$673$	22.7186	+	39.3498i	0.875739	+	1.51682i	0.0197649	+	0.999805i	$0.493708\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.2542	−	28.1532i	−0.624701	−	1.08201i	−0.988599	−	0.150575i	$-0.951888\pi$
$677$	−16.2542	−	28.1532i	−0.624701	−	1.08201i	0.363898	−	0.931439i	$-0.381446\pi$
$678$		0			0
$679$	22.5653	+	29.8209i	0.865975	+	1.14442i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	24.3776i		−	0.932781i	−0.884579	−	0.466391i	$-0.845554\pi$
$683$		−	24.3776i		−	0.932781i	0.884579	−	0.466391i	$-0.154446\pi$
$684$		0			0
$685$			1.57458i			0.0601615i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.681319	+	1.18008i	−0.0259562	+	0.0449575i
$690$		0			0
$691$	23.5773	−	13.6123i	0.896922	−	0.517838i	0.0207214	−	0.999785i	$-0.493404\pi$
$691$	23.5773	−	13.6123i	0.896922	−	0.517838i	0.876200	+	0.481947i	$0.160070\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.36901	−	4.83185i	0.317455	−	0.183283i
$696$		0			0
$697$	13.4767	−	23.3423i	0.510465	−	0.884152i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	32.8777i		−	1.24177i	−0.783900	−	0.620887i	$-0.786773\pi$
$701$		−	32.8777i		−	1.24177i	0.783900	−	0.620887i	$-0.213227\pi$
$702$		0			0
$703$		−	22.5335i		−	0.849868i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	23.7330	−	17.9586i	0.892573	−	0.675403i
$708$		0			0
$709$	2.02639	+	3.50981i	0.0761026	+	0.131814i	0.901565	−	0.432643i	$-0.142419\pi$
$709$	2.02639	+	3.50981i	0.0761026	+	0.131814i	−0.825463	+	0.564457i	$0.809086\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.46117	−	2.53082i	−0.0547213	−	0.0947801i
$714$		0			0
$715$	−0.210701	+	0.364945i	−0.00787977	+	0.0136482i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	35.0419			1.30684			0.653420	−	0.756995i	$-0.273333\pi$
$719$	35.0419			1.30684			0.653420	+	0.756995i	$0.273333\pi$
$720$		0			0
$721$	−2.35006	+	5.56731i	−0.0875209	+	0.207337i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.8509	−	13.7703i	−0.885800	−	0.511417i
$726$		0			0
$727$	−0.292512	+	0.168882i	−0.0108487	+	0.00626349i	−0.505415	−	0.862877i	$-0.668660\pi$
$727$	−0.292512	+	0.168882i	−0.0108487	+	0.00626349i	0.494566	+	0.869140i	$0.335327\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.81077	−	15.2607i	−0.325878	−	0.564437i
$732$		0			0
$733$	−2.16404	−	1.24941i	−0.0799306	−	0.0461479i	0.459502	−	0.888177i	$-0.348028\pi$
$733$	−2.16404	−	1.24941i	−0.0799306	−	0.0461479i	−0.539433	+	0.842029i	$0.681361\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			5.60240i			0.206367i
$738$		0			0
$739$	−34.0147			−1.25125			−0.625625	−	0.780124i	$-0.715156\pi$
$739$	−34.0147			−1.25125			−0.625625	+	0.780124i	$0.715156\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	30.1013	+	17.3790i	1.10431	+	0.637573i	0.937350	−	0.348390i	$-0.113272\pi$
$743$	30.1013	+	17.3790i	1.10431	+	0.637573i	0.166960	+	0.985964i	$0.446605\pi$
$744$		0			0
$745$	0.374900	−	0.216449i	0.0137353	−	0.00793007i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−28.8133	+	3.59630i	−1.05281	+	0.131406i
$750$		0			0
$751$	5.46861	−	9.47191i	0.199552	−	0.345635i	−0.748831	−	0.662761i	$-0.769385\pi$
$751$	5.46861	−	9.47191i	0.199552	−	0.345635i	0.948383	+	0.317126i	$0.102718\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−9.71381			−0.353522
$756$		0			0
$757$	−37.5008			−1.36299			−0.681496	−	0.731822i	$-0.738670\pi$
$757$	−37.5008			−1.36299			−0.681496	+	0.731822i	$0.738670\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.94575	−	15.4945i	0.324283	−	0.561675i	−0.657084	−	0.753818i	$-0.728210\pi$
$761$	8.94575	−	15.4945i	0.324283	−	0.561675i	0.981367	+	0.192143i	$0.0615436\pi$
$762$		0			0
$763$	−2.03536	−	16.3072i	−0.0736849	−	0.590359i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.263831	+	0.152323i	−0.00952637	+	0.00550005i
$768$		0			0
$769$	−47.0913	−	27.1882i	−1.69816	−	0.980431i	−0.947510	−	0.319727i	$-0.896409\pi$
$769$	−47.0913	−	27.1882i	−1.69816	−	0.980431i	−0.750647	−	0.660704i	$-0.770258\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.26464			0.0814533			0.0407266	−	0.999170i	$-0.487033\pi$
$773$	2.26464			0.0814533			0.0407266	+	0.999170i	$0.487033\pi$
$774$		0			0
$775$		−	7.78746i		−	0.279734i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	15.4317	+	8.90948i	0.552897	+	0.319215i
$780$		0			0
$781$	4.22397	+	7.31613i	0.151146	+	0.261792i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.6058	+	7.27793i	−0.449919	+	0.259761i
$786$		0			0
$787$	12.2816	+	7.09078i	0.437792	+	0.252759i	0.702660	−	0.711525i	$-0.251995\pi$
$787$	12.2816	+	7.09078i	0.437792	+	0.252759i	−0.264869	+	0.964284i	$0.585329\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	17.9643	−	42.5576i	0.638738	−	1.51317i
$792$		0			0
$793$	6.92759			0.246006
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.56607	−	2.71252i	0.0554731	−	0.0960823i	−0.836955	−	0.547271i	$-0.815667\pi$
$797$	1.56607	−	2.71252i	0.0554731	−	0.0960823i	0.892428	+	0.451189i	$0.149000\pi$
$798$		0			0
$799$	−32.2306	−	55.8250i	−1.14024	−	1.97495i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.05488	−	7.02326i	−0.143094	−	0.247845i
$804$		0			0
$805$	2.16965	+	2.86728i	0.0764702	+	0.101058i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			8.37975i			0.294616i	0.989091	+	0.147308i	$0.0470609\pi$
$809$			8.37975i			0.294616i	−0.989091	+	0.147308i	$0.952939\pi$
$810$		0			0
$811$		−	21.1311i		−	0.742013i	−0.928630	−	0.371006i	$-0.879013\pi$
$811$		−	21.1311i		−	0.742013i	0.928630	−	0.371006i	$-0.120987\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.38551	−	9.32797i	0.188646	−	0.326744i
$816$		0			0
$817$	10.0889	−	5.82484i	0.352966	−	0.203785i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.9473	−	13.2486i	0.800867	−	0.462381i	−0.0429075	−	0.999079i	$-0.513662\pi$
$821$	22.9473	−	13.2486i	0.800867	−	0.462381i	0.843774	+	0.536699i	$0.180329\pi$
$822$		0			0
$823$	3.00916	−	5.21202i	0.104893	−	0.181679i	−0.808802	−	0.588082i	$-0.799883\pi$
$823$	3.00916	−	5.21202i	0.104893	−	0.181679i	0.913694	+	0.406402i	$0.133217\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.447159i			0.0155492i	0.999970	+	0.00777462i	$0.00247476\pi$
$827$			0.447159i			0.0155492i	−0.999970	+	0.00777462i	$0.997525\pi$
$828$		0			0
$829$			23.3395i			0.810614i	0.914181	+	0.405307i	$0.132835\pi$
$829$			23.3395i			0.810614i	−0.914181	+	0.405307i	$0.867165\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	32.3895	−	8.21326i	1.12223	−	0.284572i
$834$		0			0
$835$	−3.31404	−	5.74009i	−0.114687	−	0.198644i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.0244	+	19.0948i	0.380603	+	0.659224i	0.991149	−	0.132757i	$-0.0423830\pi$
$839$	11.0244	+	19.0948i	0.380603	+	0.659224i	−0.610545	+	0.791981i	$0.709050\pi$
$840$		0			0
$841$	6.14453	−	10.6426i	0.211880	−	0.366987i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.7328			0.369220
$846$		0			0
$847$	24.7770	+	10.4588i	0.851348	+	0.359369i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.94589	+	5.74226i	0.340941	+	0.196842i
$852$		0			0
$853$	−9.94613	+	5.74240i	−0.340549	+	0.196616i	−0.660515	−	0.750813i	$-0.729662\pi$
$853$	−9.94613	+	5.74240i	−0.340549	+	0.196616i	0.319966	+	0.947429i	$0.396329\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.1891	+	34.9686i	0.689648	+	1.19451i	0.971952	+	0.235180i	$0.0755681\pi$
$857$	20.1891	+	34.9686i	0.689648	+	1.19451i	−0.282304	+	0.959325i	$0.591099\pi$
$858$		0			0
$859$	22.7331	+	13.1250i	0.775643	+	0.447818i	0.834884	−	0.550426i	$-0.185535\pi$
$859$	22.7331	+	13.1250i	0.775643	+	0.447818i	−0.0592409	+	0.998244i	$0.518868\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			39.2987i			1.33774i	0.743378	+	0.668871i	$0.233222\pi$
$863$			39.2987i			1.33774i	−0.743378	+	0.668871i	$0.766778\pi$
$864$		0			0
$865$	−1.69702			−0.0577006
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.84090	−	5.10430i	−0.299907	−	0.173151i
$870$		0			0
$871$	−2.89778	+	1.67303i	−0.0981875	+	0.0566886i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.57112	+	20.5996i	0.0869196	+	0.696395i
$876$		0			0
$877$	7.40252	−	12.8215i	0.249965	−	0.432952i	−0.713551	−	0.700604i	$-0.752914\pi$
$877$	7.40252	−	12.8215i	0.249965	−	0.432952i	0.963516	+	0.267651i	$0.0862475\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−47.2029			−1.59031			−0.795153	−	0.606409i	$-0.792610\pi$
$881$	−47.2029			−1.59031			−0.795153	+	0.606409i	$0.792610\pi$
$882$		0			0
$883$	50.0235			1.68343			0.841713	−	0.539925i	$-0.181548\pi$
$883$	50.0235			1.68343			0.841713	+	0.539925i	$0.181548\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.91871	−	3.32330i	0.0644239	−	0.111585i	−0.832014	−	0.554754i	$-0.812812\pi$
$887$	1.91871	−	3.32330i	0.0644239	−	0.111585i	0.896438	+	0.443169i	$0.146146\pi$
$888$		0			0
$889$	2.35681	+	18.8826i	0.0790450	+	0.633303i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	36.9061	−	21.3078i	1.23502	−	0.713037i
$894$		0			0
$895$	−8.66085	−	5.00034i	−0.289500	−	0.167143i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.6750			0.389383
$900$		0			0
$901$			11.9181i			0.397051i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.86264	+	4.53950i	0.261363	+	0.150898i
$906$		0			0
$907$	−12.9009	−	22.3450i	−0.428367	−	0.741954i	0.568361	−	0.822779i	$-0.307578\pi$
$907$	−12.9009	−	22.3450i	−0.428367	−	0.741954i	−0.996728	+	0.0808252i	$0.974244\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	38.0894	−	21.9909i	1.26196	−	0.728592i	0.288505	−	0.957478i	$-0.406842\pi$
$911$	38.0894	−	21.9909i	1.26196	−	0.728592i	0.973453	+	0.228886i	$0.0735084\pi$
$912$		0			0
$913$	−0.193284	−	0.111593i	−0.00639678	−	0.00369318i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.2651	+	5.17734i	0.405031	+	0.170971i
$918$		0			0
$919$	−13.8634			−0.457312			−0.228656	−	0.973507i	$-0.573433\pi$
$919$	−13.8634			−0.457312			−0.228656	+	0.973507i	$0.573433\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.52279	+	4.36960i	−0.0830387	+	0.143827i
$924$		0			0
$925$	15.3020	+	26.5038i	0.503126	+	0.871439i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.0022	−	22.5204i	−0.426588	−	0.738872i	0.569979	−	0.821659i	$-0.306951\pi$
$929$	−13.0022	−	22.5204i	−0.426588	−	0.738872i	−0.996567	+	0.0827871i	$0.973618\pi$
$930$		0			0
$931$	5.42982	+	21.4128i	0.177955	+	0.701777i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			3.68574i			0.120537i
$936$		0			0
$937$			12.2999i			0.401819i	0.979610	+	0.200910i	$0.0643898\pi$
$937$			12.2999i			0.401819i	−0.979610	+	0.200910i	$0.935610\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.4720	−	33.7264i	0.634768	−	1.09945i	−0.351797	−	0.936076i	$-0.614429\pi$
$941$	19.4720	−	33.7264i	0.634768	−	1.09945i	0.986564	−	0.163374i	$-0.0522376\pi$
$942$		0			0
$943$	−7.86496	+	4.54084i	−0.256118	+	0.147870i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.79744	+	4.50186i	−0.253383	+	0.146291i	−0.621312	−	0.783563i	$-0.713400\pi$
$947$	−7.79744	+	4.50186i	−0.253383	+	0.146291i	0.367929	+	0.929854i	$0.380067\pi$
$948$		0			0
$949$	2.42180	−	4.19468i	0.0786150	−	0.136165i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			12.2826i			0.397873i	0.980012	+	0.198937i	$0.0637488\pi$
$953$			12.2826i			0.397873i	−0.980012	+	0.198937i	$0.936251\pi$
$954$		0			0
$955$			2.79817i			0.0905466i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.97501	−	3.93160i	−0.0960682	−	0.126958i
$960$		0			0
$961$	−13.8494	−	23.9878i	−0.446754	−	0.773801i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.90486	−	17.1557i	−0.318849	−	0.552262i
$966$		0			0
$967$	−19.6853	+	34.0960i	−0.633037	+	1.09645i	0.353890	+	0.935287i	$0.384859\pi$
$967$	−19.6853	+	34.0960i	−0.633037	+	1.09645i	−0.986927	+	0.161166i	$0.948475\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.59421			−0.0511608			−0.0255804	−	0.999673i	$-0.508143\pi$
$971$	−1.59421			−0.0511608			−0.0255804	+	0.999673i	$0.508143\pi$
$972$		0			0
$973$	−11.7675	+	27.8772i	−0.377248	+	0.893703i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	35.5341	+	20.5156i	1.13684	+	0.656353i	0.945646	−	0.325199i	$-0.105431\pi$
$977$	35.5341	+	20.5156i	1.13684	+	0.656353i	0.191192	+	0.981553i	$0.438765\pi$
$978$		0			0
$979$	4.90114	−	2.82967i	0.156641	−	0.0904367i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.72534	−	13.3807i	−0.246400	−	0.426778i	0.716124	−	0.697973i	$-0.245914\pi$
$983$	−7.72534	−	13.3807i	−0.246400	−	0.426778i	−0.962524	+	0.271195i	$0.912581\pi$
$984$		0			0
$985$	−13.1090	−	7.56847i	−0.417687	−	0.241152i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			5.93742i			0.188799i
$990$		0			0
$991$	−1.86113			−0.0591207			−0.0295604	−	0.999563i	$-0.509411\pi$
$991$	−1.86113			−0.0591207			−0.0295604	+	0.999563i	$0.509411\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.7757	−	6.79872i	−0.373316	−	0.215534i
$996$		0			0
$997$	35.7835	−	20.6596i	1.13328	−	0.654297i	0.188519	−	0.982070i	$-0.439631\pi$
$997$	35.7835	−	20.6596i	1.13328	−	0.654297i	0.944757	+	0.327773i	$0.106298\pi$
$998$		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.881.9		48
3.2	odd	2		1008.2.cc.d.545.21		48
4.3	odd	2		1512.2.bu.a.881.9		48
7.6	odd	2	inner	3024.2.cc.d.881.16		48
9.2	odd	6	inner	3024.2.cc.d.2897.16		48
9.7	even	3		1008.2.cc.d.209.4		48
12.11	even	2		504.2.bu.a.41.4	✓	48
21.20	even	2		1008.2.cc.d.545.4		48
28.27	even	2		1512.2.bu.a.881.16		48
36.7	odd	6		504.2.bu.a.209.21	yes	48
36.11	even	6		1512.2.bu.a.1385.16		48
36.23	even	6		4536.2.k.a.3401.18		48
36.31	odd	6		4536.2.k.a.3401.31		48
63.20	even	6	inner	3024.2.cc.d.2897.9		48
63.34	odd	6		1008.2.cc.d.209.21		48
84.83	odd	2		504.2.bu.a.41.21	yes	48
252.83	odd	6		1512.2.bu.a.1385.9		48
252.139	even	6		4536.2.k.a.3401.17		48
252.167	odd	6		4536.2.k.a.3401.32		48
252.223	even	6		504.2.bu.a.209.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.4	✓	48	12.11	even	2
504.2.bu.a.41.21	yes	48	84.83	odd	2
504.2.bu.a.209.4	yes	48	252.223	even	6
504.2.bu.a.209.21	yes	48	36.7	odd	6
1008.2.cc.d.209.4		48	9.7	even	3
1008.2.cc.d.209.21		48	63.34	odd	6
1008.2.cc.d.545.4		48	21.20	even	2
1008.2.cc.d.545.21		48	3.2	odd	2
1512.2.bu.a.881.9		48	4.3	odd	2
1512.2.bu.a.881.16		48	28.27	even	2
1512.2.bu.a.1385.9		48	252.83	odd	6
1512.2.bu.a.1385.16		48	36.11	even	6
3024.2.cc.d.881.9		48	1.1	even	1	trivial
3024.2.cc.d.881.16		48	7.6	odd	2	inner
3024.2.cc.d.2897.9		48	63.20	even	6	inner
3024.2.cc.d.2897.16		48	9.2	odd	6	inner
4536.2.k.a.3401.17		48	252.139	even	6
4536.2.k.a.3401.18		48	36.23	even	6
4536.2.k.a.3401.31		48	36.31	odd	6
4536.2.k.a.3401.32		48	252.167	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)

\(f(q)\)	\(=\)	\(q+(-0.422480 + 0.731757i) q^{5} +(-0.327684 - 2.62538i) q^{7} +O(q^{10})\)	\(q+(-0.422480 + 0.731757i) q^{5} +(-0.327684 - 2.62538i) q^{7} +(-0.791371 + 0.456898i) q^{11} +(-0.472651 - 0.272885i) q^{13} -4.77352 q^{17} -3.15579i q^{19} +(1.39291 + 0.804196i) q^{23} +(2.14302 + 3.71182i) q^{25} +(-5.56478 + 3.21283i) q^{29} +(-1.57351 - 0.908468i) q^{31} +(2.05958 + 0.869387i) q^{35} +7.14037 q^{37} +(-2.82322 + 4.88995i) q^{41} +(1.84576 + 3.19695i) q^{43} +(6.75196 + 11.6947i) q^{47} +(-6.78525 + 1.72059i) q^{49} -2.49672i q^{53} -0.772122i q^{55} +(0.279096 - 0.483409i) q^{59} +(-10.9926 + 6.34661i) q^{61} +(0.399372 - 0.230577i) q^{65} +(3.06545 - 5.30951i) q^{67} -9.24488i q^{71} +8.87479i q^{73} +(1.45885 + 1.92793i) q^{77} +(5.58581 + 9.67491i) q^{79} +(0.122120 + 0.211518i) q^{83} +(2.01672 - 3.49306i) q^{85} -6.19322 q^{89} +(-0.561548 + 1.33031i) q^{91} +(2.30927 + 1.33326i) q^{95} +(-12.2408 + 7.06722i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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