LMFDB - Embedded newform 3024.2.cc.d.881.2

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			881.2
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79302 + 3.10561i) q^{5} +(-2.25543 + 1.38312i) q^{7} +O(q^{10})$	$q+(-1.79302 + 3.10561i) q^{5} +(-2.25543 + 1.38312i) q^{7} +(-4.38785 + 2.53333i) q^{11} +(-5.48988 - 3.16959i) q^{13} -0.256659 q^{17} +6.71942i q^{19} +(0.138917 + 0.0802038i) q^{23} +(-3.92986 - 6.80672i) q^{25} +(1.17068 - 0.675891i) q^{29} +(-3.01592 - 1.74124i) q^{31} +(-0.251382 - 9.48445i) q^{35} +9.37941 q^{37} +(-2.31970 + 4.01783i) q^{41} +(2.70333 + 4.68230i) q^{43} +(-1.50565 - 2.60787i) q^{47} +(3.17396 - 6.23907i) q^{49} -4.35786i q^{53} -18.1693i q^{55} +(-2.32686 + 4.03024i) q^{59} +(2.50053 - 1.44368i) q^{61} +(19.6870 - 11.3663i) q^{65} +(-4.52009 + 7.82902i) q^{67} +1.74818i q^{71} +7.77127i q^{73} +(6.39262 - 11.7827i) q^{77} +(-6.10623 - 10.5763i) q^{79} +(1.90636 + 3.30191i) q^{83} +(0.460196 - 0.797083i) q^{85} +4.79259 q^{89} +(16.7660 - 0.444376i) q^{91} +(-20.8679 - 12.0481i) q^{95} +(11.0008 - 6.35132i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.79302	+	3.10561i	−0.801864	+	1.38887i	0.116524	+	0.993188i	$0.462825\pi$
$5$	−1.79302	+	3.10561i	−0.801864	+	1.38887i	−0.918388	+	0.395682i	$0.870508\pi$
$6$		0			0
$7$	−2.25543	+	1.38312i	−0.852474	+	0.522770i
$7$	−2.25543	+	1.38312i	−0.852474	+	0.522770i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.38785	+	2.53333i	−1.32299	+	0.763827i	−0.984204	−	0.177037i	$-0.943349\pi$
$11$	−4.38785	+	2.53333i	−1.32299	+	0.763827i	−0.338783	+	0.940864i	$0.610015\pi$
$12$		0			0
$13$	−5.48988	−	3.16959i	−1.52262	−	0.879085i	−0.999642	−	0.0267382i	$-0.991488\pi$
$13$	−5.48988	−	3.16959i	−1.52262	−	0.879085i	−0.522977	−	0.852347i	$-0.675179\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.256659			−0.0622490			−0.0311245	−	0.999516i	$-0.509909\pi$
$17$	−0.256659			−0.0622490			−0.0311245	+	0.999516i	$0.509909\pi$
$18$		0			0
$19$			6.71942i			1.54154i	0.637113	+	0.770771i	$0.280129\pi$
$19$			6.71942i			1.54154i	−0.637113	+	0.770771i	$0.719871\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.138917	+	0.0802038i	0.0289662	+	0.0167236i	0.514413	−	0.857542i	$-0.328010\pi$
$23$	0.138917	+	0.0802038i	0.0289662	+	0.0167236i	−0.485447	+	0.874266i	$0.661343\pi$
$24$		0			0
$25$	−3.92986	−	6.80672i	−0.785972	−	1.36134i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.17068	−	0.675891i	0.217389	−	0.125510i	−0.387351	−	0.921932i	$-0.626610\pi$
$29$	1.17068	−	0.675891i	0.217389	−	0.125510i	0.604741	+	0.796422i	$0.293277\pi$
$30$		0			0
$31$	−3.01592	−	1.74124i	−0.541676	−	0.312737i	0.204082	−	0.978954i	$-0.434579\pi$
$31$	−3.01592	−	1.74124i	−0.541676	−	0.312737i	−0.745758	+	0.666217i	$0.767912\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.251382	−	9.48445i	−0.0424913	−	1.60317i
$36$		0			0
$37$	9.37941			1.54197			0.770983	−	0.636856i	$-0.219765\pi$
$37$	9.37941			1.54197			0.770983	+	0.636856i	$0.219765\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.31970	+	4.01783i	−0.362276	+	0.627480i	−0.988335	−	0.152295i	$-0.951333\pi$
$41$	−2.31970	+	4.01783i	−0.362276	+	0.627480i	0.626059	+	0.779775i	$0.284667\pi$
$42$		0			0
$43$	2.70333	+	4.68230i	0.412254	+	0.714045i	0.995136	−	0.0985122i	$-0.0314083\pi$
$43$	2.70333	+	4.68230i	0.412254	+	0.714045i	−0.582882	+	0.812557i	$0.698075\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.50565	−	2.60787i	−0.219622	−	0.380396i	0.735070	−	0.677991i	$-0.237149\pi$
$47$	−1.50565	−	2.60787i	−0.219622	−	0.380396i	−0.954692	+	0.297594i	$0.903816\pi$
$48$		0			0
$49$	3.17396	−	6.23907i	0.453423	−	0.891296i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	4.35786i		−	0.598598i	−0.954159	−	0.299299i	$-0.903247\pi$
$53$		−	4.35786i		−	0.598598i	0.954159	−	0.299299i	$-0.0967527\pi$
$54$		0			0
$55$		−	18.1693i		−	2.44994i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.32686	+	4.03024i	−0.302931	+	0.524692i	−0.976799	−	0.214160i	$-0.931299\pi$
$59$	−2.32686	+	4.03024i	−0.302931	+	0.524692i	0.673867	+	0.738852i	$0.264632\pi$
$60$		0			0
$61$	2.50053	−	1.44368i	0.320160	−	0.184845i	−0.331304	−	0.943524i	$-0.607488\pi$
$61$	2.50053	−	1.44368i	0.320160	−	0.184845i	0.651464	+	0.758680i	$0.274155\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	19.6870	−	11.3663i	2.44187	−	1.40981i
$66$		0			0
$67$	−4.52009	+	7.82902i	−0.552217	+	0.956467i	0.445898	+	0.895084i	$0.352885\pi$
$67$	−4.52009	+	7.82902i	−0.552217	+	0.956467i	−0.998114	+	0.0613833i	$0.980449\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.74818i			0.207471i	0.994605	+	0.103735i	$0.0330795\pi$
$71$			1.74818i			0.207471i	−0.994605	+	0.103735i	$0.966920\pi$
$72$		0			0
$73$			7.77127i			0.909558i	0.890604	+	0.454779i	$0.150282\pi$
$73$			7.77127i			0.909558i	−0.890604	+	0.454779i	$0.849718\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.39262	−	11.7827i	0.728506	−	1.34276i
$78$		0			0
$79$	−6.10623	−	10.5763i	−0.687005	−	1.18993i	−0.972802	−	0.231637i	$-0.925592\pi$
$79$	−6.10623	−	10.5763i	−0.687005	−	1.18993i	0.285797	−	0.958290i	$-0.407742\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.90636	+	3.30191i	0.209250	+	0.362432i	0.951479	−	0.307715i	$-0.0995644\pi$
$83$	1.90636	+	3.30191i	0.209250	+	0.362432i	−0.742228	+	0.670147i	$0.766231\pi$
$84$		0			0
$85$	0.460196	−	0.797083i	0.0499153	−	0.0864558i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.79259			0.508013			0.254007	−	0.967202i	$-0.418252\pi$
$89$	4.79259			0.508013			0.254007	+	0.967202i	$0.418252\pi$
$90$		0			0
$91$	16.7660	−	0.444376i	1.75755	−	0.0465832i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−20.8679	−	12.0481i	−2.14100	−	1.23611i
$96$		0			0
$97$	11.0008	−	6.35132i	1.11696	−	0.644879i	0.176339	−	0.984330i	$-0.443575\pi$
$97$	11.0008	−	6.35132i	1.11696	−	0.644879i	0.940624	+	0.339451i	$0.110241\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.72407	+	4.71822i	0.271055	+	0.469480i	0.969132	−	0.246542i	$-0.0792943\pi$
$101$	2.72407	+	4.71822i	0.271055	+	0.469480i	−0.698078	+	0.716022i	$0.745961\pi$
$102$		0			0
$103$	3.62613	+	2.09355i	0.357293	+	0.206283i	0.667893	−	0.744258i	$-0.267197\pi$
$103$	3.62613	+	2.09355i	0.357293	+	0.206283i	−0.310600	+	0.950541i	$0.600530\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			4.44654i			0.429863i	0.976629	+	0.214932i	$0.0689529\pi$
$107$			4.44654i			0.429863i	−0.976629	+	0.214932i	$0.931047\pi$
$108$		0			0
$109$	8.53233			0.817249			0.408625	−	0.912702i	$-0.366008\pi$
$109$	8.53233			0.817249			0.408625	+	0.912702i	$0.366008\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−12.5720	−	7.25847i	−1.18268	−	0.682820i	−0.226046	−	0.974117i	$-0.572580\pi$
$113$	−12.5720	−	7.25847i	−1.18268	−	0.682820i	−0.956633	+	0.291297i	$0.905913\pi$
$114$		0			0
$115$	−0.498163	+	0.287614i	−0.0464539	+	0.0268202i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.578878	−	0.354990i	0.0530657	−	0.0325419i
$120$		0			0
$121$	7.33550	−	12.7055i	0.666864	−	1.15504i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.2551			0.917244
$126$		0			0
$127$	9.53109			0.845747			0.422874	−	0.906189i	$-0.361021\pi$
$127$	9.53109			0.845747			0.422874	+	0.906189i	$0.361021\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.56765	+	11.3755i	−0.573818	+	0.993882i	0.422351	+	0.906432i	$0.361205\pi$
$131$	−6.56765	+	11.3755i	−0.573818	+	0.993882i	−0.996169	+	0.0874496i	$0.972128\pi$
$132$		0			0
$133$	−9.29377	−	15.1552i	−0.805872	−	1.31412i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.0421	+	6.95253i	−1.02883	+	0.593995i	−0.916649	−	0.399693i	$-0.869117\pi$
$137$	−12.0421	+	6.95253i	−1.02883	+	0.593995i	−0.112180	+	0.993688i	$0.535783\pi$
$138$		0			0
$139$	9.85312	+	5.68870i	0.835730	+	0.482509i	0.855811	−	0.517289i	$-0.173059\pi$
$139$	9.85312	+	5.68870i	0.835730	+	0.482509i	−0.0200802	+	0.999798i	$0.506392\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	32.1184			2.68588
$144$		0			0
$145$			4.84755i			0.402567i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.94977	+	4.58980i	0.651271	+	0.376011i	0.788943	−	0.614466i	$-0.210629\pi$
$149$	7.94977	+	4.58980i	0.651271	+	0.376011i	−0.137672	+	0.990478i	$0.543962\pi$
$150$		0			0
$151$	0.781156	+	1.35300i	0.0635696	+	0.110106i	0.896059	−	0.443936i	$-0.146418\pi$
$151$	0.781156	+	1.35300i	0.0635696	+	0.110106i	−0.832489	+	0.554042i	$0.813085\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10.8152	−	6.24418i	0.868701	−	0.501545i
$156$		0			0
$157$	1.12561	+	0.649874i	0.0898339	+	0.0518656i	0.544244	−	0.838927i	$-0.316817\pi$
$157$	1.12561	+	0.649874i	0.0898339	+	0.0518656i	−0.454410	+	0.890793i	$0.650150\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.424249	+	0.0112446i	−0.0334355	+	0.000886196i
$162$		0			0
$163$	−14.0737			−1.10234			−0.551169	−	0.834394i	$-0.685818\pi$
$163$	−14.0737			−1.10234			−0.551169	+	0.834394i	$0.685818\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.44133	−	12.8888i	0.575828	−	0.997363i	−0.420124	−	0.907467i	$-0.638013\pi$
$167$	7.44133	−	12.8888i	0.575828	−	0.997363i	0.995951	−	0.0898958i	$-0.0286534\pi$
$168$		0			0
$169$	13.5925	+	23.5430i	1.04558	+	1.81100i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.77587	−	15.2002i	−0.667217	−	1.15565i	−0.978679	−	0.205395i	$-0.934152\pi$
$173$	−8.77587	−	15.2002i	−0.667217	−	1.15565i	0.311462	−	0.950258i	$-0.399181\pi$
$174$		0			0
$175$	18.2781	+	9.91664i	1.38169	+	0.749627i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	4.58589i		−	0.342765i	−0.985205	−	0.171383i	$-0.945177\pi$
$179$		−	4.58589i		−	0.342765i	0.985205	−	0.171383i	$-0.0548234\pi$
$180$		0			0
$181$		−	1.54234i		−	0.114642i	−0.998356	−	0.0573208i	$-0.981744\pi$
$181$		−	1.54234i		−	0.114642i	0.998356	−	0.0573208i	$-0.0182558\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−16.8175	+	29.1288i	−1.23645	+	2.14159i
$186$		0			0
$187$	1.12618	−	0.650202i	0.0823547	−	0.0475475i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.35637	−	0.783100i	0.0981434	−	0.0566631i	−0.450125	−	0.892966i	$-0.648621\pi$
$191$	1.35637	−	0.783100i	0.0981434	−	0.0566631i	0.548268	+	0.836302i	$0.315287\pi$
$192$		0			0
$193$	−5.33436	+	9.23938i	−0.383976	+	0.665065i	−0.991626	−	0.129139i	$-0.958779\pi$
$193$	−5.33436	+	9.23938i	−0.383976	+	0.665065i	0.607651	+	0.794204i	$0.292112\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	20.6011i		−	1.46777i	−0.679275	−	0.733883i	$-0.737706\pi$
$197$		−	20.6011i		−	1.46777i	0.679275	−	0.733883i	$-0.262294\pi$
$198$		0			0
$199$		−	15.4996i		−	1.09874i	−0.835579	−	0.549370i	$-0.814868\pi$
$199$		−	15.4996i		−	1.09874i	0.835579	−	0.549370i	$-0.185132\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.70555	+	3.14361i	−0.119706	+	0.220638i
$204$		0			0
$205$	−8.31854	−	14.4081i	−0.580992	−	1.00631i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−17.0225	−	29.4838i	−1.17747	−	2.03944i
$210$		0			0
$211$	3.96776	−	6.87236i	0.273152	−	0.473113i	−0.696515	−	0.717542i	$-0.745267\pi$
$211$	3.96776	−	6.87236i	0.273152	−	0.473113i	0.969667	+	0.244429i	$0.0786005\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−19.3885			−1.32229
$216$		0			0
$217$	9.21056	−	0.244122i	0.625254	−	0.0165721i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.40903	+	0.813504i	0.0947816	+	0.0547222i
$222$		0			0
$223$	−16.7059	+	9.64515i	−1.11871	+	0.645887i	−0.941071	−	0.338209i	$-0.890179\pi$
$223$	−16.7059	+	9.64515i	−1.11871	+	0.645887i	−0.177638	+	0.984096i	$0.556846\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.6591	−	25.3903i	−0.972958	−	1.68521i	−0.686514	−	0.727116i	$-0.740860\pi$
$227$	−14.6591	−	25.3903i	−0.972958	−	1.68521i	−0.286444	−	0.958097i	$-0.592473\pi$
$228$		0			0
$229$	−14.2571	−	8.23134i	−0.942136	−	0.543942i	−0.0515067	−	0.998673i	$-0.516402\pi$
$229$	−14.2571	−	8.23134i	−0.942136	−	0.543942i	−0.890629	+	0.454730i	$0.849736\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	13.0685i		−	0.856148i	−0.903744	−	0.428074i	$-0.859192\pi$
$233$		−	13.0685i		−	0.856148i	0.903744	−	0.428074i	$-0.140808\pi$
$234$		0			0
$235$	10.7987			0.704428
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.1535	−	8.17154i	−0.915515	−	0.528573i	−0.0333136	−	0.999445i	$-0.510606\pi$
$239$	−14.1535	−	8.17154i	−0.915515	−	0.528573i	−0.882202	+	0.470872i	$0.843939\pi$
$240$		0			0
$241$	−5.48896	+	3.16905i	−0.353575	+	0.204137i	−0.666259	−	0.745721i	$-0.732105\pi$
$241$	−5.48896	+	3.16905i	−0.353575	+	0.204137i	0.312684	+	0.949857i	$0.398772\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.6851	+	21.0439i	0.874310	+	1.34444i
$246$		0			0
$247$	21.2978	−	36.8888i	1.35515	−	2.34718i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14.5359			−0.917498			−0.458749	−	0.888566i	$-0.651702\pi$
$251$	−14.5359			−0.917498			−0.458749	+	0.888566i	$0.651702\pi$
$252$		0			0
$253$	−0.812730			−0.0510959
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.43647	−	16.3444i	0.588631	−	1.01954i	−0.405781	−	0.913970i	$-0.633001\pi$
$257$	9.43647	−	16.3444i	0.588631	−	1.01954i	0.994412	−	0.105568i	$-0.0336661\pi$
$258$		0			0
$259$	−21.1546	+	12.9728i	−1.31449	+	0.806094i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.1632	−	8.17711i	0.873339	−	0.504222i	0.00488231	−	0.999988i	$-0.498446\pi$
$263$	14.1632	−	8.17711i	0.873339	−	0.504222i	0.868456	+	0.495766i	$0.165113\pi$
$264$		0			0
$265$	13.5338	+	7.81374i	0.831374	+	0.479994i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.984016			−0.0599965			−0.0299983	−	0.999550i	$-0.509550\pi$
$269$	−0.984016			−0.0599965			−0.0299983	+	0.999550i	$0.509550\pi$
$270$		0			0
$271$			14.4953i			0.880529i	0.897868	+	0.440265i	$0.145115\pi$
$271$			14.4953i			0.880529i	−0.897868	+	0.440265i	$0.854885\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	34.4873	+	19.9113i	2.07966	+	1.20069i
$276$		0			0
$277$	7.53027	+	13.0428i	0.452450	+	0.783666i	0.998538	−	0.0540618i	$-0.0172168\pi$
$277$	7.53027	+	13.0428i	0.452450	+	0.783666i	−0.546088	+	0.837728i	$0.683883\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.3712	+	9.45194i	−0.976626	+	0.563855i	−0.901250	−	0.433300i	$-0.857349\pi$
$281$	−16.3712	+	9.45194i	−0.976626	+	0.563855i	−0.0753762	+	0.997155i	$0.524016\pi$
$282$		0			0
$283$	−1.30597	−	0.753999i	−0.0776316	−	0.0448206i	0.460682	−	0.887565i	$-0.347605\pi$
$283$	−1.30597	−	0.753999i	−0.0776316	−	0.0448206i	−0.538313	+	0.842745i	$0.680938\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.325221	−	12.2704i	−0.0191972	−	0.724297i
$288$		0			0
$289$	−16.9341			−0.996125
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.10635	+	14.0406i	−0.473578	+	0.820261i	−0.999543	−	0.0302454i	$-0.990371\pi$
$293$	−8.10635	+	14.0406i	−0.473578	+	0.820261i	0.525965	+	0.850506i	$0.323704\pi$
$294$		0			0
$295$	−8.34422	−	14.4526i	−0.485819	−	0.841463i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.508425	−	0.880619i	−0.0294030	−	0.0509275i
$300$		0			0
$301$	−12.5734	−	6.82160i	−0.724717	−	0.393190i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			10.3542i			0.592881i
$306$		0			0
$307$		−	4.75821i		−	0.271565i	−0.990739	−	0.135783i	$-0.956645\pi$
$307$		−	4.75821i		−	0.271565i	0.990739	−	0.135783i	$-0.0433549\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.4105	+	18.0316i	−0.590328	+	1.02248i	0.403860	+	0.914821i	$0.367668\pi$
$311$	−10.4105	+	18.0316i	−0.590328	+	1.02248i	−0.994188	+	0.107657i	$0.965665\pi$
$312$		0			0
$313$	23.5994	−	13.6251i	1.33391	−	0.770136i	0.348018	−	0.937488i	$-0.386855\pi$
$313$	23.5994	−	13.6251i	1.33391	−	0.770136i	0.985897	+	0.167352i	$0.0535216\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−27.3254	+	15.7763i	−1.53475	+	0.886087i	−0.535615	+	0.844462i	$0.679920\pi$
$317$	−27.3254	+	15.7763i	−1.53475	+	0.886087i	−0.999133	+	0.0416249i	$0.986747\pi$
$318$		0			0
$319$	−3.42451	+	5.93142i	−0.191736	+	0.332096i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.72460i		−	0.0959594i
$324$		0			0
$325$			49.8241i			2.76375i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.00289	+	3.79937i	0.386082	+	0.209466i
$330$		0			0
$331$	4.29733	+	7.44320i	0.236203	+	0.409115i	0.959622	−	0.281294i	$-0.0907637\pi$
$331$	4.29733	+	7.44320i	0.236203	+	0.409115i	−0.723419	+	0.690409i	$0.757430\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−16.2092	−	28.0752i	−0.885605	−	1.53391i
$336$		0			0
$337$	8.25998	−	14.3067i	0.449950	−	0.779336i	−0.548432	−	0.836195i	$-0.684775\pi$
$337$	8.25998	−	14.3067i	0.449950	−	0.779336i	0.998382	+	0.0568588i	$0.0181085\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	17.6446			0.955507
$342$		0			0
$343$	1.47072	+	18.4618i	0.0794115	+	0.996842i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	20.7345	+	11.9711i	1.11308	+	0.642640i	0.939627	−	0.342202i	$-0.111173\pi$
$347$	20.7345	+	11.9711i	1.11308	+	0.642640i	0.173458	+	0.984841i	$0.444506\pi$
$348$		0			0
$349$	−13.7319	+	7.92813i	−0.735053	+	0.424383i	−0.820268	−	0.571979i	$-0.806176\pi$
$349$	−13.7319	+	7.92813i	−0.735053	+	0.424383i	0.0852148	+	0.996363i	$0.472842\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.65270	−	9.79076i	−0.300863	−	0.521110i	0.675469	−	0.737389i	$-0.263941\pi$
$353$	−5.65270	−	9.79076i	−0.300863	−	0.521110i	−0.976332	+	0.216279i	$0.930608\pi$
$354$		0			0
$355$	−5.42916	−	3.13453i	−0.288150	−	0.166363i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	23.5925i		−	1.24517i	−0.782554	−	0.622583i	$-0.786083\pi$
$359$		−	23.5925i		−	1.24517i	0.782554	−	0.622583i	$-0.213917\pi$
$360$		0			0
$361$	−26.1506			−1.37635
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−24.1345	−	13.9341i	−1.26326	−	0.729342i
$366$		0			0
$367$	−0.105255	+	0.0607690i	−0.00549427	+	0.00317212i	−0.502745	−	0.864435i	$-0.667676\pi$
$367$	−0.105255	+	0.0607690i	−0.00549427	+	0.00317212i	0.497250	+	0.867607i	$0.334343\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.02744	+	9.82886i	0.312929	+	0.510289i
$372$		0			0
$373$	−16.1633	+	27.9956i	−0.836904	+	1.44956i	0.0555676	+	0.998455i	$0.482303\pi$
$373$	−16.1633	+	27.9956i	−0.836904	+	1.44956i	−0.892471	+	0.451105i	$0.851030\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.56918			−0.441335
$378$		0			0
$379$	−15.5708			−0.799819			−0.399910	−	0.916555i	$-0.630959\pi$
$379$	−15.5708			−0.799819			−0.399910	+	0.916555i	$0.630959\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.55021	−	7.88120i	0.232505	−	0.402711i	−0.726040	−	0.687653i	$-0.758641\pi$
$383$	4.55021	−	7.88120i	0.232505	−	0.402711i	0.958545	+	0.284942i	$0.0919745\pi$
$384$		0			0
$385$	25.1303	+	40.9796i	1.28076	+	2.08851i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.8896	−	6.86448i	0.602828	−	0.348043i	−0.167326	−	0.985902i	$-0.553513\pi$
$389$	11.8896	−	6.86448i	0.602828	−	0.348043i	0.770153	+	0.637859i	$0.220180\pi$
$390$		0			0
$391$	−0.0356543	−	0.0205850i	−0.00180312	−	0.00104103i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	43.7945			2.20354
$396$		0			0
$397$		−	7.95634i		−	0.399317i	−0.979866	−	0.199659i	$-0.936017\pi$
$397$		−	7.95634i		−	0.399317i	0.979866	−	0.199659i	$-0.0639833\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.7734	+	7.37472i	0.637872	+	0.368276i	0.783794	−	0.621020i	$-0.213282\pi$
$401$	12.7734	+	7.37472i	0.637872	+	0.368276i	−0.145922	+	0.989296i	$0.546615\pi$
$402$		0			0
$403$	11.0380	+	19.1185i	0.549844	+	0.952358i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−41.1555	+	23.7611i	−2.04000	+	1.17780i
$408$		0			0
$409$	0.310827	+	0.179456i	0.0153694	+	0.00887354i	0.507665	−	0.861555i	$-0.330509\pi$
$409$	0.310827	+	0.179456i	0.0153694	+	0.00887354i	−0.492296	+	0.870428i	$0.663842\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.326225	−	12.3083i	−0.0160525	−	0.605649i
$414$		0			0
$415$	−13.6726			−0.671161
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.08152	−	8.80146i	0.248249	−	0.429979i	−0.714791	−	0.699338i	$-0.753478\pi$
$419$	5.08152	−	8.80146i	0.248249	−	0.429979i	0.963040	+	0.269359i	$0.0868117\pi$
$420$		0			0
$421$	6.91893	+	11.9839i	0.337208	+	0.584062i	0.983906	−	0.178684i	$-0.0571840\pi$
$421$	6.91893	+	11.9839i	0.337208	+	0.584062i	−0.646698	+	0.762746i	$0.723851\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.00864	+	1.74701i	0.0489260	+	0.0847423i
$426$		0			0
$427$	−3.64300	+	6.71466i	−0.176297	+	0.324945i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			19.7667i			0.952127i	0.879411	+	0.476063i	$0.157937\pi$
$431$			19.7667i			0.952127i	−0.879411	+	0.476063i	$0.842063\pi$
$432$		0			0
$433$		−	17.8164i		−	0.856200i	−0.903731	−	0.428100i	$-0.859183\pi$
$433$		−	17.8164i		−	0.856200i	0.903731	−	0.428100i	$-0.140817\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.538923	+	0.933442i	−0.0257802	+	0.0446526i
$438$		0			0
$439$	10.3967	−	6.00252i	0.496206	−	0.286484i	−0.230940	−	0.972968i	$-0.574180\pi$
$439$	10.3967	−	6.00252i	0.496206	−	0.286484i	0.727145	+	0.686484i	$0.240847\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	29.4430	−	16.9989i	1.39888	−	0.807642i	0.404602	−	0.914493i	$-0.367410\pi$
$443$	29.4430	−	16.9989i	1.39888	−	0.807642i	0.994275	+	0.106851i	$0.0340767\pi$
$444$		0			0
$445$	−8.59322	+	14.8839i	−0.407358	+	0.705564i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			15.4292i			0.728150i	0.931370	+	0.364075i	$0.118615\pi$
$449$			15.4292i			0.728150i	−0.931370	+	0.364075i	$0.881385\pi$
$450$		0			0
$451$		−	23.5062i		−	1.10686i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−28.6817	+	52.8653i	−1.34462	+	2.47836i
$456$		0			0
$457$	−14.7489	−	25.5458i	−0.689924	−	1.19498i	−0.971862	−	0.235551i	$-0.924311\pi$
$457$	−14.7489	−	25.5458i	−0.689924	−	1.19498i	0.281938	−	0.959433i	$-0.409023\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−14.2621	−	24.7028i	−0.664254	−	1.15052i	−0.979487	−	0.201508i	$-0.935416\pi$
$461$	−14.2621	−	24.7028i	−0.664254	−	1.15052i	0.315233	−	0.949014i	$-0.397917\pi$
$462$		0			0
$463$	12.5381	−	21.7166i	0.582693	−	1.00925i	−0.412466	−	0.910973i	$-0.635332\pi$
$463$	12.5381	−	21.7166i	0.582693	−	1.00925i	0.995159	−	0.0982809i	$-0.0313344\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.6966			1.14282			0.571411	−	0.820664i	$-0.306396\pi$
$467$	24.6966			1.14282			0.571411	+	0.820664i	$0.306396\pi$
$468$		0			0
$469$	−0.633716	−	23.9097i	−0.0292623	−	1.10405i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−23.7236	−	13.6968i	−1.09081	−	0.629781i
$474$		0			0
$475$	45.7372	−	26.4064i	2.09857	−	1.21161i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.3263	+	17.8856i	0.471819	+	0.817215i	0.999480	−	0.0322405i	$-0.0102642\pi$
$479$	10.3263	+	17.8856i	0.471819	+	0.817215i	−0.527661	+	0.849455i	$0.676931\pi$
$480$		0			0
$481$	−51.4919	−	29.7288i	−2.34783	−	1.35552i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			45.5522i			2.06842i
$486$		0			0
$487$	−21.7426			−0.985250			−0.492625	−	0.870242i	$-0.663963\pi$
$487$	−21.7426			−0.985250			−0.492625	+	0.870242i	$0.663963\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.96621	+	5.17664i	0.404639	+	0.233619i	0.688484	−	0.725252i	$-0.258277\pi$
$491$	8.96621	+	5.17664i	0.404639	+	0.233619i	−0.283844	+	0.958870i	$0.591610\pi$
$492$		0			0
$493$	−0.300465	+	0.173474i	−0.0135323	+	0.00781286i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.41794	−	3.94291i	−0.108460	−	0.176863i
$498$		0			0
$499$	−5.78399	+	10.0182i	−0.258927	+	0.448475i	−0.965955	−	0.258711i	$-0.916702\pi$
$499$	−5.78399	+	10.0182i	−0.258927	+	0.448475i	0.707028	+	0.707186i	$0.250036\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.17373			−0.141509			−0.0707547	−	0.997494i	$-0.522541\pi$
$503$	−3.17373			−0.141509			−0.0707547	+	0.997494i	$0.522541\pi$
$504$		0			0
$505$	−19.5372			−0.869396
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.38218	−	4.12606i	0.105588	−	0.182884i	−0.808390	−	0.588647i	$-0.799661\pi$
$509$	2.38218	−	4.12606i	0.105588	−	0.182884i	0.913978	+	0.405763i	$0.132994\pi$
$510$		0			0
$511$	−10.7486	−	17.5276i	−0.475490	−	0.775374i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−13.0035	+	7.50755i	−0.573001	+	0.330822i
$516$		0			0
$517$	13.2132	+	7.62863i	0.581114	+	0.335507i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.74523			0.120271			0.0601353	−	0.998190i	$-0.480847\pi$
$521$	2.74523			0.120271			0.0601353	+	0.998190i	$0.480847\pi$
$522$		0			0
$523$		−	8.52554i		−	0.372796i	−0.982474	−	0.186398i	$-0.940319\pi$
$523$		−	8.52554i		−	0.372796i	0.982474	−	0.186398i	$-0.0596814\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.774065	+	0.446906i	0.0337188	+	0.0194676i
$528$		0			0
$529$	−11.4871	−	19.8963i	−0.499441	−	0.865057i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	25.4697	−	14.7050i	1.10322	−	0.636942i
$534$		0			0
$535$	−13.8092	−	7.97275i	−0.597024	−	0.344692i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.87874	+	35.4168i	0.0809229	+	1.52551i
$540$		0			0
$541$	0.382282			0.0164356			0.00821779	−	0.999966i	$-0.497384\pi$
$541$	0.382282			0.0164356			0.00821779	+	0.999966i	$0.497384\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−15.2987	+	26.4981i	−0.655323	+	1.13505i
$546$		0			0
$547$	13.7475	+	23.8113i	0.587799	+	1.01810i	0.994520	+	0.104545i	$0.0333387\pi$
$547$	13.7475	+	23.8113i	0.587799	+	1.01810i	−0.406721	+	0.913552i	$0.633328\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.54160	+	7.86628i	0.193479	+	0.335115i
$552$		0			0
$553$	28.4005	+	15.4085i	1.20771	+	0.655236i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			41.0055i			1.73746i	0.495285	+	0.868730i	$0.335064\pi$
$557$			41.0055i			1.73746i	−0.495285	+	0.868730i	$0.664936\pi$
$558$		0			0
$559$		−	34.2737i		−	1.44962i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.8631	−	30.9398i	0.752841	−	1.30396i	−0.193600	−	0.981081i	$-0.562016\pi$
$563$	17.8631	−	30.9398i	0.752841	−	1.30396i	0.946441	−	0.322878i	$-0.104650\pi$
$564$		0			0
$565$	45.0839	−	26.0292i	1.89669	−	1.09506i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.0598	+	5.80801i	−0.421728	+	0.243485i	−0.695816	−	0.718220i	$-0.744957\pi$
$569$	−10.0598	+	5.80801i	−0.421728	+	0.243485i	0.274089	+	0.961704i	$0.411624\pi$
$570$		0			0
$571$	2.99429	−	5.18626i	0.125307	−	0.217038i	−0.796546	−	0.604578i	$-0.793342\pi$
$571$	2.99429	−	5.18626i	0.125307	−	0.217038i	0.921853	+	0.387540i	$0.126675\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	1.26076i		−	0.0525773i
$576$		0			0
$577$			23.4017i			0.974225i	0.873339	+	0.487113i	$0.161950\pi$
$577$			23.4017i			0.974225i	−0.873339	+	0.487113i	$0.838050\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.86661	−	4.81052i	−0.367849	−	0.199574i
$582$		0			0
$583$	11.0399	+	19.1216i	0.457225	+	0.791937i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.60180	+	7.97055i	0.189937	+	0.328980i	0.945229	−	0.326408i	$-0.105838\pi$
$587$	4.60180	+	7.97055i	0.189937	+	0.328980i	−0.755292	+	0.655388i	$0.772505\pi$
$588$		0			0
$589$	11.7002	−	20.2653i	0.482097	−	0.835016i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	48.1037			1.97538			0.987690	−	0.156423i	$-0.0499963\pi$
$593$	48.1037			1.97538			0.987690	+	0.156423i	$0.0499963\pi$
$594$		0			0
$595$	0.0645195	+	2.43427i	0.00264504	+	0.0997955i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.07850	−	0.622673i	−0.0440664	−	0.0254417i	0.477805	−	0.878466i	$-0.341433\pi$
$599$	−1.07850	−	0.622673i	−0.0440664	−	0.0254417i	−0.521871	+	0.853024i	$0.674766\pi$
$600$		0			0
$601$	−10.4680	+	6.04372i	−0.427000	+	0.246528i	−0.698068	−	0.716032i	$-0.745957\pi$
$601$	−10.4680	+	6.04372i	−0.427000	+	0.246528i	0.271068	+	0.962560i	$0.412623\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	26.3055	+	45.5624i	1.06947	+	1.85237i
$606$		0			0
$607$	−5.71617	−	3.30023i	−0.232012	−	0.133952i	0.379488	−	0.925197i	$-0.376100\pi$
$607$	−5.71617	−	3.30023i	−0.232012	−	0.133952i	−0.611500	+	0.791245i	$0.709434\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			19.0892i			0.772266i
$612$		0			0
$613$	12.3737			0.499769			0.249885	−	0.968276i	$-0.419607\pi$
$613$	12.3737			0.499769			0.249885	+	0.968276i	$0.419607\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.8657	+	23.0165i	1.60493	+	0.926607i	0.990481	+	0.137652i	$0.0439556\pi$
$617$	39.8657	+	23.0165i	1.60493	+	0.926607i	0.614451	+	0.788955i	$0.289378\pi$
$618$		0			0
$619$	−26.2793	+	15.1724i	−1.05626	+	0.609830i	−0.924394	−	0.381438i	$-0.875429\pi$
$619$	−26.2793	+	15.1724i	−1.05626	+	0.609830i	−0.131862	+	0.991268i	$0.542096\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−10.8094	+	6.62872i	−0.433068	+	0.265574i
$624$		0			0
$625$	1.26168	−	2.18530i	0.0504673	−	0.0874119i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.40731			−0.0959859
$630$		0			0
$631$	2.59782			0.103418			0.0517088	−	0.998662i	$-0.483533\pi$
$631$	2.59782			0.103418			0.0517088	+	0.998662i	$0.483533\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.0895	+	29.5998i	−0.678175	+	1.17463i
$636$		0			0
$637$	−37.1999	+	24.1916i	−1.47392	+	0.958507i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	30.2365	−	17.4570i	1.19427	−	0.689511i	0.234997	−	0.971996i	$-0.424492\pi$
$641$	30.2365	−	17.4570i	1.19427	−	0.689511i	0.959272	+	0.282485i	$0.0911587\pi$
$642$		0			0
$643$	−16.6357	−	9.60463i	−0.656048	−	0.378769i	0.134722	−	0.990883i	$-0.456986\pi$
$643$	−16.6357	−	9.60463i	−0.656048	−	0.378769i	−0.790769	+	0.612114i	$0.790319\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.01178			0.0790914			0.0395457	−	0.999218i	$-0.487409\pi$
$647$	2.01178			0.0790914			0.0395457	+	0.999218i	$0.487409\pi$
$648$		0			0
$649$		−	23.5788i		−	0.925548i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.3877	+	11.1935i	0.758700	+	0.438036i	0.828829	−	0.559502i	$-0.189008\pi$
$653$	19.3877	+	11.1935i	0.758700	+	0.438036i	−0.0701288	+	0.997538i	$0.522341\pi$
$654$		0			0
$655$	−23.5519	−	40.7931i	−0.920248	−	1.59392i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	23.8449	−	13.7668i	0.928864	−	0.536280i	0.0424122	−	0.999100i	$-0.486496\pi$
$659$	23.8449	−	13.7668i	0.928864	−	0.536280i	0.886452	+	0.462820i	$0.153162\pi$
$660$		0			0
$661$	38.8235	+	22.4148i	1.51006	+	0.871833i	0.999931	+	0.0117349i	$0.00373543\pi$
$661$	38.8235	+	22.4148i	1.51006	+	0.871833i	0.510128	+	0.860098i	$0.329598\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	63.7301	−	1.68914i	2.47135	−	0.0655020i
$666$		0			0
$667$	0.216836			0.00839593
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.31464	+	12.6693i	−0.282379	+	0.489094i
$672$		0			0
$673$	8.44895	+	14.6340i	0.325683	+	0.564100i	0.981650	−	0.190690i	$-0.0610724\pi$
$673$	8.44895	+	14.6340i	0.325683	+	0.564100i	−0.655967	+	0.754789i	$0.727739\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.589425	+	1.02091i	0.0226534	+	0.0392369i	0.877130	−	0.480253i	$-0.159455\pi$
$677$	0.589425	+	1.02091i	0.0226534	+	0.0392369i	−0.854476	+	0.519490i	$0.826122\pi$
$678$		0			0
$679$	−16.0270	+	29.5404i	−0.615058	+	1.13366i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			22.6633i			0.867189i	0.901108	+	0.433594i	$0.142755\pi$
$683$			22.6633i			0.867189i	−0.901108	+	0.433594i	$0.857245\pi$
$684$		0			0
$685$		−	49.8642i		−	1.90521i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−13.8126	+	23.9241i	−0.526218	+	0.911437i
$690$		0			0
$691$	8.36568	−	4.82993i	0.318246	−	0.183739i	−0.332365	−	0.943151i	$-0.607846\pi$
$691$	8.36568	−	4.82993i	0.318246	−	0.183739i	0.650610	+	0.759412i	$0.274513\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−35.3337	+	20.3999i	−1.34028	+	0.773814i
$696$		0			0
$697$	0.595372	−	1.03121i	0.0225513	−	0.0390600i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			19.2571i			0.727331i	0.931530	+	0.363665i	$0.118475\pi$
$701$			19.2571i			0.727331i	−0.931530	+	0.363665i	$0.881525\pi$
$702$		0			0
$703$			63.0242i			2.37700i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.6698	−	6.87392i	−0.476497	−	0.258520i
$708$		0			0
$709$	−1.02264	−	1.77127i	−0.0384062	−	0.0665215i	0.846183	−	0.532892i	$-0.178895\pi$
$709$	−1.02264	−	1.77127i	−0.0384062	−	0.0665215i	−0.884590	+	0.466370i	$0.845561\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.279309	−	0.483777i	−0.0104602	−	0.0181176i
$714$		0			0
$715$	−57.5890	+	99.7471i	−2.15371	+	3.73033i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−36.3501			−1.35563			−0.677815	−	0.735232i	$-0.737073\pi$
$719$	−36.3501			−1.35563			−0.677815	+	0.735232i	$0.737073\pi$
$720$		0			0
$721$	−11.0741	+	0.293515i	−0.412421	+	0.0109311i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.20120	−	5.31232i	−0.341724	−	0.197294i
$726$		0			0
$727$	−1.30802	+	0.755186i	−0.0485118	+	0.0280083i	−0.524060	−	0.851681i	$-0.675583\pi$
$727$	−1.30802	+	0.755186i	−0.0485118	+	0.0280083i	0.475548	+	0.879690i	$0.342250\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.693835	−	1.20176i	−0.0256624	−	0.0444486i
$732$		0			0
$733$	−3.63585	−	2.09916i	−0.134293	−	0.0775342i	0.431348	−	0.902185i	$-0.358038\pi$
$733$	−3.63585	−	2.09916i	−0.134293	−	0.0775342i	−0.565641	+	0.824651i	$0.691371\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	45.8035i		−	1.68719i
$738$		0			0
$739$	−17.5346			−0.645022			−0.322511	−	0.946566i	$-0.604527\pi$
$739$	−17.5346			−0.645022			−0.322511	+	0.946566i	$0.604527\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−28.4191	−	16.4078i	−1.04260	−	0.601943i	−0.122028	−	0.992527i	$-0.538940\pi$
$743$	−28.4191	−	16.4078i	−1.04260	−	0.601943i	−0.920567	+	0.390584i	$0.872273\pi$
$744$		0			0
$745$	−28.5083	+	16.4592i	−1.04446	+	0.603020i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.15010	−	10.0289i	−0.224720	−	0.366447i
$750$		0			0
$751$	−19.6767	+	34.0811i	−0.718015	+	1.24364i	0.243770	+	0.969833i	$0.421616\pi$
$751$	−19.6767	+	34.0811i	−0.718015	+	1.24364i	−0.961785	+	0.273805i	$0.911718\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.60252			−0.203897
$756$		0			0
$757$	−26.1692			−0.951134			−0.475567	−	0.879679i	$-0.657757\pi$
$757$	−26.1692			−0.951134			−0.475567	+	0.879679i	$0.657757\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−10.1319	+	17.5489i	−0.367280	+	0.636148i	−0.989139	−	0.146981i	$-0.953044\pi$
$761$	−10.1319	+	17.5489i	−0.367280	+	0.636148i	0.621859	+	0.783129i	$0.286378\pi$
$762$		0			0
$763$	−19.2441	+	11.8012i	−0.696684	+	0.427234i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	25.5484	−	14.7503i	0.922498	−	0.532604i
$768$		0			0
$769$	−1.46947	−	0.848401i	−0.0529906	−	0.0305941i	0.473271	−	0.880917i	$-0.343073\pi$
$769$	−1.46947	−	0.848401i	−0.0529906	−	0.0305941i	−0.526261	+	0.850323i	$0.676407\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−45.7185			−1.64438			−0.822191	−	0.569212i	$-0.807248\pi$
$773$	−45.7185			−1.64438			−0.822191	+	0.569212i	$0.807248\pi$
$774$		0			0
$775$			27.3714i			0.983210i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−26.9975	−	15.5870i	−0.967286	−	0.558463i
$780$		0			0
$781$	−4.42872	−	7.67076i	−0.158472	−	0.274481i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.03651	+	2.33048i	−0.144069	+	0.0831783i
$786$		0			0
$787$	−7.90330	−	4.56297i	−0.281722	−	0.162652i	0.352481	−	0.935819i	$-0.385338\pi$
$787$	−7.90330	−	4.56297i	−0.281722	−	0.162652i	−0.634203	+	0.773167i	$0.718672\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	38.3947	−	1.01764i	1.36516	−	0.0361830i
$792$		0			0
$793$	−18.3035			−0.649976
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.9328	−	27.5965i	0.564370	−	0.977517i	−0.432738	−	0.901520i	$-0.642453\pi$
$797$	15.9328	−	27.5965i	0.564370	−	0.977517i	0.997108	−	0.0759972i	$-0.0242140\pi$
$798$		0			0
$799$	0.386440	+	0.669333i	0.0136713	+	0.0236793i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.6872	−	34.0992i	−0.694745	−	1.20333i
$804$		0			0
$805$	0.725768	−	1.33771i	0.0255800	−	0.0471482i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			11.6152i			0.408369i	0.978932	+	0.204184i	$0.0654542\pi$
$809$			11.6152i			0.408369i	−0.978932	+	0.204184i	$0.934546\pi$
$810$		0			0
$811$		−	34.2551i		−	1.20286i	−0.798926	−	0.601429i	$-0.794598\pi$
$811$		−	34.2551i		−	1.20286i	0.798926	−	0.601429i	$-0.205402\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	25.2345	−	43.7074i	0.883925	−	1.53100i
$816$		0			0
$817$	−31.4624	+	18.1648i	−1.10073	+	0.635506i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.66362	+	3.84724i	−0.232562	+	0.134270i	−0.611753	−	0.791049i	$-0.709536\pi$
$821$	−6.66362	+	3.84724i	−0.232562	+	0.134270i	0.379191	+	0.925318i	$0.376202\pi$
$822$		0			0
$823$	18.9632	−	32.8452i	0.661015	−	1.14491i	−0.319334	−	0.947642i	$-0.603459\pi$
$823$	18.9632	−	32.8452i	0.661015	−	1.14491i	0.980349	−	0.197270i	$-0.0632075\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.755724i			0.0262791i	0.999914	+	0.0131396i	$0.00418257\pi$
$827$			0.755724i			0.0262791i	−0.999914	+	0.0131396i	$0.995817\pi$
$828$		0			0
$829$			16.9707i			0.589417i	0.955587	+	0.294709i	$0.0952226\pi$
$829$			16.9707i			0.589417i	−0.955587	+	0.294709i	$0.904777\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.814626	+	1.60131i	−0.0282251	+	0.0554823i
$834$		0			0
$835$	26.6850	+	46.2197i	0.923471	+	1.59950i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.5075	−	44.1803i	−0.880617	−	1.52527i	−0.850656	−	0.525723i	$-0.823795\pi$
$839$	−25.5075	−	44.1803i	−0.880617	−	1.52527i	−0.0299611	−	0.999551i	$-0.509538\pi$
$840$		0			0
$841$	−13.5863	+	23.5322i	−0.468495	+	0.811456i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−97.4870			−3.35365
$846$		0			0
$847$	1.02844	+	38.8022i	0.0353375	+	1.33326i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.30296	+	0.752264i	0.0446649	+	0.0257873i
$852$		0			0
$853$	45.3128	−	26.1613i	1.55148	−	0.895747i	0.553458	−	0.832877i	$-0.313308\pi$
$853$	45.3128	−	26.1613i	1.55148	−	0.895747i	0.998022	−	0.0628701i	$-0.0200254\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.7217	−	23.7667i	−0.468725	−	0.811856i	0.530636	−	0.847600i	$-0.321953\pi$
$857$	−13.7217	−	23.7667i	−0.468725	−	0.811856i	−0.999361	+	0.0357438i	$0.988620\pi$
$858$		0			0
$859$	−2.13722	−	1.23393i	−0.0729211	−	0.0421010i	0.463096	−	0.886308i	$-0.346738\pi$
$859$	−2.13722	−	1.23393i	−0.0729211	−	0.0421010i	−0.536017	+	0.844207i	$0.680072\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			52.7336i			1.79507i	0.440940	+	0.897537i	$0.354645\pi$
$863$			52.7336i			1.79507i	−0.440940	+	0.897537i	$0.645355\pi$
$864$		0			0
$865$	62.9413			2.14007
$866$		0			0
$867$		0			0
$868$		0			0
$869$	53.5865	+	30.9382i	1.81780	+	1.04951i
$870$		0			0
$871$	49.6295	−	28.6536i	1.68163	−	0.970891i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−23.1297	+	14.1840i	−0.781926	+	0.479508i
$876$		0			0
$877$	−28.7085	+	49.7246i	−0.969418	+	1.67908i	−0.272173	+	0.962248i	$0.587742\pi$
$877$	−28.7085	+	49.7246i	−0.969418	+	1.67908i	−0.697245	+	0.716833i	$0.745591\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.9151			−0.637266			−0.318633	−	0.947878i	$-0.603224\pi$
$881$	−18.9151			−0.637266			−0.318633	+	0.947878i	$0.603224\pi$
$882$		0			0
$883$	40.4378			1.36084			0.680420	−	0.732822i	$-0.261797\pi$
$883$	40.4378			1.36084			0.680420	+	0.732822i	$0.261797\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.53242	+	9.58244i	−0.185761	+	0.321747i	−0.943833	−	0.330424i	$-0.892808\pi$
$887$	−5.53242	+	9.58244i	−0.185761	+	0.321747i	0.758072	+	0.652171i	$0.226142\pi$
$888$		0			0
$889$	−21.4967	+	13.1826i	−0.720977	+	0.442131i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.5234	−	10.1171i	0.586397	−	0.338556i
$894$		0			0
$895$	14.2420	+	8.22260i	0.476056	+	0.274851i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.70757			−0.157006
$900$		0			0
$901$			1.11848i			0.0372621i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.78992	+	2.76546i	0.159222	+	0.0919270i
$906$		0			0
$907$	−0.892111	−	1.54518i	−0.0296221	−	0.0513069i	0.850834	−	0.525434i	$-0.176097\pi$
$907$	−0.892111	−	1.54518i	−0.0296221	−	0.0513069i	−0.880456	+	0.474127i	$0.842764\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.470971	−	0.271915i	0.0156040	−	0.00900896i	−0.492178	−	0.870495i	$-0.663799\pi$
$911$	0.470971	−	0.271915i	0.0156040	−	0.00900896i	0.507782	+	0.861486i	$0.330466\pi$
$912$		0			0
$913$	−16.7297	−	9.65887i	−0.553671	−	0.319662i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.920784	−	34.7405i	−0.0304070	−	1.14723i
$918$		0			0
$919$	−48.0844			−1.58616			−0.793079	−	0.609119i	$-0.791523\pi$
$919$	−48.0844			−1.58616			−0.793079	+	0.609119i	$0.791523\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.54101	−	9.59731i	0.182385	−	0.315899i
$924$		0			0
$925$	−36.8598	−	63.8430i	−1.21194	−	2.09915i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.3459	−	21.3838i	−0.405056	−	0.701578i	0.589272	−	0.807935i	$-0.299415\pi$
$929$	−12.3459	−	21.3838i	−0.405056	−	0.701578i	−0.994328	+	0.106357i	$0.966081\pi$
$930$		0			0
$931$	41.9229	+	21.3272i	1.37397	+	0.698970i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			4.66331i			0.152507i
$936$		0			0
$937$		−	26.8110i		−	0.875876i	−0.899005	−	0.437938i	$-0.855709\pi$
$937$		−	26.8110i		−	0.875876i	0.899005	−	0.437938i	$-0.144291\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8.36236	−	14.4840i	0.272605	−	0.472166i	−0.696923	−	0.717146i	$-0.745448\pi$
$941$	8.36236	−	14.4840i	0.272605	−	0.472166i	0.969528	+	0.244980i	$0.0787814\pi$
$942$		0			0
$943$	−0.644491	+	0.372097i	−0.0209875	+	0.0121171i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.0864	+	18.5251i	−1.04267	+	0.601985i	−0.920588	−	0.390535i	$-0.872290\pi$
$947$	−32.0864	+	18.5251i	−1.04267	+	0.601985i	−0.122081	+	0.992520i	$0.538957\pi$
$948$		0			0
$949$	24.6317	−	42.6633i	0.799579	−	1.38491i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			37.8134i			1.22490i	0.790510	+	0.612449i	$0.209815\pi$
$953$			37.8134i			1.22490i	−0.790510	+	0.612449i	$0.790185\pi$
$954$		0			0
$955$			5.61646i			0.181745i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	17.5441	−	32.3367i	0.566527	−	1.04421i
$960$		0			0
$961$	−9.43614	−	16.3439i	−0.304392	−	0.527222i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−19.1293	−	33.1328i	−0.615792	−	1.06658i
$966$		0			0
$967$	−0.841655	+	1.45779i	−0.0270658	+	0.0468794i	−0.879241	−	0.476377i	$-0.841950\pi$
$967$	−0.841655	+	1.45779i	−0.0270658	+	0.0468794i	0.852175	+	0.523257i	$0.175283\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−35.4405			−1.13734			−0.568670	−	0.822566i	$-0.692542\pi$
$971$	−35.4405			−1.13734			−0.568670	+	0.822566i	$0.692542\pi$
$972$		0			0
$973$	−30.0912	+	0.797556i	−0.964680	+	0.0255685i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.4900	+	14.7167i	0.815499	+	0.470828i	0.848862	−	0.528615i	$-0.177288\pi$
$977$	25.4900	+	14.7167i	0.815499	+	0.470828i	−0.0333630	+	0.999443i	$0.510622\pi$
$978$		0			0
$979$	−21.0292	+	12.1412i	−0.672095	+	0.388034i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.90245	+	10.2233i	0.188259	+	0.326074i	0.944670	−	0.328023i	$-0.106382\pi$
$983$	5.90245	+	10.2233i	0.188259	+	0.326074i	−0.756411	+	0.654097i	$0.773049\pi$
$984$		0			0
$985$	63.9789	+	36.9382i	2.03854	+	1.17695i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			0.867269i			0.0275775i
$990$		0			0
$991$	−20.9777			−0.666378			−0.333189	−	0.942860i	$-0.608125\pi$
$991$	−20.9777			−0.666378			−0.333189	+	0.942860i	$0.608125\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	48.1358	+	27.7912i	1.52601	+	0.881041i
$996$		0			0
$997$	−51.1435	+	29.5277i	−1.61973	+	0.935152i	−0.632742	+	0.774363i	$0.718070\pi$
$997$	−51.1435	+	29.5277i	−1.61973	+	0.935152i	−0.986989	+	0.160789i	$0.948596\pi$
$998$		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.881.2		48
3.2	odd	2		1008.2.cc.d.545.19		48
4.3	odd	2		1512.2.bu.a.881.2		48
7.6	odd	2	inner	3024.2.cc.d.881.23		48
9.2	odd	6	inner	3024.2.cc.d.2897.23		48
9.7	even	3		1008.2.cc.d.209.6		48
12.11	even	2		504.2.bu.a.41.6	✓	48
21.20	even	2		1008.2.cc.d.545.6		48
28.27	even	2		1512.2.bu.a.881.23		48
36.7	odd	6		504.2.bu.a.209.19	yes	48
36.11	even	6		1512.2.bu.a.1385.23		48
36.23	even	6		4536.2.k.a.3401.3		48
36.31	odd	6		4536.2.k.a.3401.46		48
63.20	even	6	inner	3024.2.cc.d.2897.2		48
63.34	odd	6		1008.2.cc.d.209.19		48
84.83	odd	2		504.2.bu.a.41.19	yes	48
252.83	odd	6		1512.2.bu.a.1385.2		48
252.139	even	6		4536.2.k.a.3401.4		48
252.167	odd	6		4536.2.k.a.3401.45		48
252.223	even	6		504.2.bu.a.209.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.6	✓	48	12.11	even	2
504.2.bu.a.41.19	yes	48	84.83	odd	2
504.2.bu.a.209.6	yes	48	252.223	even	6
504.2.bu.a.209.19	yes	48	36.7	odd	6
1008.2.cc.d.209.6		48	9.7	even	3
1008.2.cc.d.209.19		48	63.34	odd	6
1008.2.cc.d.545.6		48	21.20	even	2
1008.2.cc.d.545.19		48	3.2	odd	2
1512.2.bu.a.881.2		48	4.3	odd	2
1512.2.bu.a.881.23		48	28.27	even	2
1512.2.bu.a.1385.2		48	252.83	odd	6
1512.2.bu.a.1385.23		48	36.11	even	6
3024.2.cc.d.881.2		48	1.1	even	1	trivial
3024.2.cc.d.881.23		48	7.6	odd	2	inner
3024.2.cc.d.2897.2		48	63.20	even	6	inner
3024.2.cc.d.2897.23		48	9.2	odd	6	inner
4536.2.k.a.3401.3		48	36.23	even	6
4536.2.k.a.3401.4		48	252.139	even	6
4536.2.k.a.3401.45		48	252.167	odd	6
4536.2.k.a.3401.46		48	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.79302 + 3.10561i) q^{5} +(-2.25543 + 1.38312i) q^{7} +O(q^{10})\)	\(q+(-1.79302 + 3.10561i) q^{5} +(-2.25543 + 1.38312i) q^{7} +(-4.38785 + 2.53333i) q^{11} +(-5.48988 - 3.16959i) q^{13} -0.256659 q^{17} +6.71942i q^{19} +(0.138917 + 0.0802038i) q^{23} +(-3.92986 - 6.80672i) q^{25} +(1.17068 - 0.675891i) q^{29} +(-3.01592 - 1.74124i) q^{31} +(-0.251382 - 9.48445i) q^{35} +9.37941 q^{37} +(-2.31970 + 4.01783i) q^{41} +(2.70333 + 4.68230i) q^{43} +(-1.50565 - 2.60787i) q^{47} +(3.17396 - 6.23907i) q^{49} -4.35786i q^{53} -18.1693i q^{55} +(-2.32686 + 4.03024i) q^{59} +(2.50053 - 1.44368i) q^{61} +(19.6870 - 11.3663i) q^{65} +(-4.52009 + 7.82902i) q^{67} +1.74818i q^{71} +7.77127i q^{73} +(6.39262 - 11.7827i) q^{77} +(-6.10623 - 10.5763i) q^{79} +(1.90636 + 3.30191i) q^{83} +(0.460196 - 0.797083i) q^{85} +4.79259 q^{89} +(16.7660 - 0.444376i) q^{91} +(-20.8679 - 12.0481i) q^{95} +(11.0008 - 6.35132i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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