LMFDB - Embedded newform 3024.2.r.g.1009.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1009,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1009"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-5,0,-3,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1009.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	3024.1009
Dual form			3024.2.r.g.2017.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79418 + 3.10761i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.40545 + 2.43430i) q^{11} +(-0.500000 + 0.866025i) q^{13} +4.11126 q^{17} +0.888736 q^{19} +(-2.93818 + 5.08907i) q^{23} +(-3.93818 - 6.82112i) q^{25} +(-0.849814 - 1.47192i) q^{29} +(-3.49381 + 6.05146i) q^{31} +3.58836 q^{35} +4.76509 q^{37} +(-2.70582 + 4.68661i) q^{41} +(2.60507 + 4.51212i) q^{43} +(1.33310 + 2.30900i) q^{47} +(-0.500000 + 0.866025i) q^{49} +0.123644 q^{53} -10.0865 q^{55} +(4.43818 - 7.68715i) q^{59} +(-1.93818 - 3.35702i) q^{61} +(-1.79418 - 3.10761i) q^{65} +(6.15452 - 10.6599i) q^{67} -2.87636 q^{71} -10.6414 q^{73} +(1.40545 - 2.43430i) q^{77} +(-3.54325 - 6.13709i) q^{79} +(2.05563 + 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} -9.60940 q^{89} +1.00000 q^{91} +(-1.59455 + 2.76185i) q^{95} +(-3.66071 - 6.34053i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59}+ \cdots - 3 q^{97}+O(q^{100}) $ 6 * q - 5 * q^5 - 3 * q^7 + 2 * q^11 - 3 * q^13 + 24 * q^17 + 6 * q^19 - 6 * q^25 + q^29 - 3 * q^31 + 10 * q^35 - 6 * q^37 - 22 * q^41 - 3 * q^43 + 9 * q^47 - 3 * q^49 + 36 * q^53 + 12 * q^55 + 9 * q^59 + 6 * q^61 - 5 * q^65 + 18 * q^71 + 6 * q^73 + 2 * q^77 + 15 * q^79 + 12 * q^83 - 9 * q^85 + 4 * q^89 + 6 * q^91 - 16 * q^95 - 3 * q^97

Character values

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

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

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
$5$	−1.79418	+	3.10761i	−0.802383	+	1.38977i	0.115661	+	0.993289i	$0.463101\pi$
$5$	−1.79418	+	3.10761i	−0.802383	+	1.38977i	−0.918044	+	0.396479i	$0.870232\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.40545	+	2.43430i	0.423758	+	0.733970i	0.996304	−	0.0859026i	$-0.0273774\pi$
$11$	1.40545	+	2.43430i	0.423758	+	0.733970i	−0.572546	+	0.819873i	$0.694044\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.11126			0.997128			0.498564	−	0.866853i	$-0.333861\pi$
$17$	4.11126			0.997128			0.498564	+	0.866853i	$0.333861\pi$
$18$		0			0
$19$	0.888736			0.203890			0.101945	−	0.994790i	$-0.467493\pi$
$19$	0.888736			0.203890			0.101945	+	0.994790i	$0.467493\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.93818	+	5.08907i	−0.612652	+	1.06115i	0.378139	+	0.925749i	$0.376564\pi$
$23$	−2.93818	+	5.08907i	−0.612652	+	1.06115i	−0.990792	+	0.135396i	$0.956769\pi$
$24$		0			0
$25$	−3.93818	−	6.82112i	−0.787636	−	1.36422i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.849814	−	1.47192i	−0.157807	−	0.273329i	0.776271	−	0.630399i	$-0.217109\pi$
$29$	−0.849814	−	1.47192i	−0.157807	−	0.273329i	−0.934077	+	0.357071i	$0.883776\pi$
$30$		0			0
$31$	−3.49381	+	6.05146i	−0.627507	+	1.08687i	0.360544	+	0.932742i	$0.382591\pi$
$31$	−3.49381	+	6.05146i	−0.627507	+	1.08687i	−0.988050	+	0.154131i	$0.950742\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.58836			0.606544
$36$		0			0
$37$	4.76509			0.783376			0.391688	−	0.920098i	$-0.371891\pi$
$37$	4.76509			0.783376			0.391688	+	0.920098i	$0.371891\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.70582	+	4.68661i	−0.422578	+	0.731926i	−0.996191	−	0.0872002i	$-0.972208\pi$
$41$	−2.70582	+	4.68661i	−0.422578	+	0.731926i	0.573613	+	0.819126i	$0.305541\pi$
$42$		0			0
$43$	2.60507	+	4.51212i	0.397270	+	0.688092i	0.993388	−	0.114805i	$-0.0366243\pi$
$43$	2.60507	+	4.51212i	0.397270	+	0.688092i	−0.596118	+	0.802897i	$0.703291\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.33310	+	2.30900i	0.194453	+	0.336803i	0.946721	−	0.322055i	$-0.104373\pi$
$47$	1.33310	+	2.30900i	0.194453	+	0.336803i	−0.752268	+	0.658857i	$0.771040\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.123644			0.0169838			0.00849190	−	0.999964i	$-0.497297\pi$
$53$	0.123644			0.0169838			0.00849190	+	0.999964i	$0.497297\pi$
$54$		0			0
$55$	−10.0865			−1.36006
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.43818	−	7.68715i	0.577802	−	1.00078i	−0.417929	−	0.908479i	$-0.637244\pi$
$59$	4.43818	−	7.68715i	0.577802	−	1.00078i	0.995731	−	0.0923022i	$-0.0294226\pi$
$60$		0			0
$61$	−1.93818	−	3.35702i	−0.248158	−	0.429823i	0.714857	−	0.699271i	$-0.246492\pi$
$61$	−1.93818	−	3.35702i	−0.248158	−	0.429823i	−0.963015	+	0.269448i	$0.913159\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.79418	−	3.10761i	−0.222541	−	0.385452i
$66$		0			0
$67$	6.15452	−	10.6599i	0.751894	−	1.30232i	−0.195010	−	0.980801i	$-0.562474\pi$
$67$	6.15452	−	10.6599i	0.751894	−	1.30232i	0.946904	−	0.321517i	$-0.104193\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.87636			−0.341361			−0.170680	−	0.985326i	$-0.554597\pi$
$71$	−2.87636			−0.341361			−0.170680	+	0.985326i	$0.554597\pi$
$72$		0			0
$73$	−10.6414			−1.24549			−0.622744	−	0.782426i	$-0.713982\pi$
$73$	−10.6414			−1.24549			−0.622744	+	0.782426i	$0.713982\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.40545	−	2.43430i	0.160165	−	0.277415i
$78$		0			0
$79$	−3.54325	−	6.13709i	−0.398647	−	0.690477i	0.594912	−	0.803791i	$-0.297187\pi$
$79$	−3.54325	−	6.13709i	−0.398647	−	0.690477i	−0.993559	+	0.113314i	$0.963853\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.05563	+	3.56046i	0.225635	+	0.390811i	0.956510	−	0.291700i	$-0.0942210\pi$
$83$	2.05563	+	3.56046i	0.225635	+	0.390811i	−0.730875	+	0.682512i	$0.760888\pi$
$84$		0			0
$85$	−7.37636	+	12.7762i	−0.800078	+	1.38578i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.60940			−1.01859			−0.509297	−	0.860591i	$-0.670095\pi$
$89$	−9.60940			−1.01859			−0.509297	+	0.860591i	$0.670095\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.59455	+	2.76185i	−0.163598	+	0.283360i
$96$		0			0
$97$	−3.66071	−	6.34053i	−0.371688	−	0.643783i	0.618137	−	0.786070i	$-0.287888\pi$
$97$	−3.66071	−	6.34053i	−0.371688	−	0.643783i	−0.989825	+	0.142287i	$0.954554\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.73236	+	3.00054i	0.172376	+	0.298564i	0.939250	−	0.343233i	$-0.111522\pi$
$101$	1.73236	+	3.00054i	0.172376	+	0.298564i	−0.766874	+	0.641798i	$0.778189\pi$
$102$		0			0
$103$	−7.93818	+	13.7493i	−0.782172	+	1.35476i	0.148502	+	0.988912i	$0.452555\pi$
$103$	−7.93818	+	13.7493i	−0.782172	+	1.35476i	−0.930674	+	0.365849i	$0.880779\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.35346			−0.517538			−0.258769	−	0.965939i	$-0.583317\pi$
$107$	−5.35346			−0.517538			−0.258769	+	0.965939i	$0.583317\pi$
$108$		0			0
$109$	−18.8640			−1.80684			−0.903421	−	0.428755i	$-0.858952\pi$
$109$	−18.8640			−1.80684			−0.903421	+	0.428755i	$0.858952\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.27561	+	16.0658i	−0.872576	+	1.51135i	−0.0132538	+	0.999912i	$0.504219\pi$
$113$	−9.27561	+	16.0658i	−0.872576	+	1.51135i	−0.859322	+	0.511434i	$0.829114\pi$
$114$		0			0
$115$	−10.5433	−	18.2614i	−0.983163	−	1.70289i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.05563	−	3.56046i	−0.188439	−	0.326387i
$120$		0			0
$121$	1.54944	−	2.68371i	0.140858	−	0.243974i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.3214			0.923175
$126$		0			0
$127$	−9.98762			−0.886258			−0.443129	−	0.896458i	$-0.646132\pi$
$127$	−9.98762			−0.886258			−0.443129	+	0.896458i	$0.646132\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.02654	+	13.9024i	−0.701282	+	1.21466i	0.266734	+	0.963770i	$0.414055\pi$
$131$	−8.02654	+	13.9024i	−0.701282	+	1.21466i	−0.968017	+	0.250886i	$0.919278\pi$
$132$		0			0
$133$	−0.444368	−	0.769668i	−0.0385316	−	0.0667387i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.49381	−	11.2476i	−0.554804	−	0.960948i	−0.997919	−	0.0644834i	$-0.979460\pi$
$137$	−6.49381	−	11.2476i	−0.554804	−	0.960948i	0.443115	−	0.896465i	$-0.353873\pi$
$138$		0			0
$139$	0.555632	−	0.962383i	0.0471281	−	0.0816283i	−0.841499	−	0.540259i	$-0.818326\pi$
$139$	0.555632	−	0.962383i	0.0471281	−	0.0816283i	0.888627	+	0.458630i	$0.151660\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.81089			−0.235059
$144$		0			0
$145$	6.09888			0.506485
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.21634	−	7.30291i	0.345416	−	0.598278i	−0.640013	−	0.768364i	$-0.721071\pi$
$149$	4.21634	−	7.30291i	0.345416	−	0.598278i	0.985429	+	0.170086i	$0.0544045\pi$
$150$		0			0
$151$	−7.42580	−	12.8619i	−0.604303	−	1.04668i	−0.992161	−	0.124964i	$-0.960118\pi$
$151$	−7.42580	−	12.8619i	−0.604303	−	1.04668i	0.387858	−	0.921719i	$-0.373215\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.5371	−	21.7148i	−1.00700	−	1.74418i
$156$		0			0
$157$	−1.44437	+	2.50172i	−0.115273	+	0.199659i	−0.917889	−	0.396837i	$-0.870108\pi$
$157$	−1.44437	+	2.50172i	−0.115273	+	0.199659i	0.802616	+	0.596496i	$0.203441\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.87636			0.463122
$162$		0			0
$163$	10.3090			0.807466			0.403733	−	0.914877i	$-0.367713\pi$
$163$	10.3090			0.807466			0.403733	+	0.914877i	$0.367713\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.07598	+	10.5239i	−0.470174	+	0.814365i	−0.999418	−	0.0341045i	$-0.989142\pi$
$167$	−6.07598	+	10.5239i	−0.470174	+	0.814365i	0.529244	+	0.848469i	$0.322475\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.30470	−	5.72391i	−0.251252	−	0.435181i	0.712619	−	0.701551i	$-0.247509\pi$
$173$	−3.30470	−	5.72391i	−0.251252	−	0.435181i	−0.963871	+	0.266370i	$0.914176\pi$
$174$		0			0
$175$	−3.93818	+	6.82112i	−0.297698	+	0.515629i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.84294			−0.287234			−0.143617	−	0.989633i	$-0.545873\pi$
$179$	−3.84294			−0.287234			−0.143617	+	0.989633i	$0.545873\pi$
$180$		0			0
$181$	18.5426			1.37826			0.689129	−	0.724639i	$-0.257993\pi$
$181$	18.5426			1.37826			0.689129	+	0.724639i	$0.257993\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.54944	+	14.8081i	−0.628567	+	1.08871i
$186$		0			0
$187$	5.77816	+	10.0081i	0.422541	+	0.731862i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.31708	−	4.01330i	−0.167658	−	0.290392i	0.769938	−	0.638119i	$-0.220287\pi$
$191$	−2.31708	−	4.01330i	−0.167658	−	0.290392i	−0.937596	+	0.347726i	$0.886954\pi$
$192$		0			0
$193$	12.6483	−	21.9075i	0.910446	−	1.57694i	0.0970118	−	0.995283i	$-0.469072\pi$
$193$	12.6483	−	21.9075i	0.910446	−	1.57694i	0.813435	−	0.581656i	$-0.197595\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.7207			−0.763816			−0.381908	−	0.924200i	$-0.624733\pi$
$197$	−10.7207			−0.763816			−0.381908	+	0.924200i	$0.624733\pi$
$198$		0			0
$199$	8.76647			0.621439			0.310719	−	0.950502i	$-0.399430\pi$
$199$	8.76647			0.621439			0.310719	+	0.950502i	$0.399430\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.849814	+	1.47192i	−0.0596453	+	0.103309i
$204$		0			0
$205$	−9.70946	−	16.8173i	−0.678138	−	1.17457i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.24907	+	2.16345i	0.0864000	+	0.149649i
$210$		0			0
$211$	5.26509	−	9.11941i	0.362464	−	0.627806i	−0.625902	−	0.779902i	$-0.715269\pi$
$211$	5.26509	−	9.11941i	0.362464	−	0.627806i	0.988366	+	0.152096i	$0.0486023\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−18.6959			−1.27505
$216$		0			0
$217$	6.98762			0.474351
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.05563	+	3.56046i	−0.138277	+	0.239502i
$222$		0			0
$223$	−2.83379	−	4.90827i	−0.189765	−	0.328682i	0.755407	−	0.655256i	$-0.227439\pi$
$223$	−2.83379	−	4.90827i	−0.189765	−	0.328682i	−0.945172	+	0.326574i	$0.894106\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.54944	+	9.61192i	0.368329	+	0.637965i	0.989304	−	0.145865i	$-0.0465965\pi$
$227$	5.54944	+	9.61192i	0.368329	+	0.637965i	−0.620975	+	0.783830i	$0.713263\pi$
$228$		0			0
$229$	−9.82141	+	17.0112i	−0.649017	+	1.12413i	0.334341	+	0.942452i	$0.391486\pi$
$229$	−9.82141	+	17.0112i	−0.649017	+	1.12413i	−0.983358	+	0.181679i	$0.941847\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.96286			−0.587177			−0.293588	−	0.955932i	$-0.594849\pi$
$233$	−8.96286			−0.587177			−0.293588	+	0.955932i	$0.594849\pi$
$234$		0			0
$235$	−9.56732			−0.624103
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.61126	+	9.71899i	−0.362963	+	0.628670i	−0.988447	−	0.151567i	$-0.951568\pi$
$239$	−5.61126	+	9.71899i	−0.362963	+	0.628670i	0.625484	+	0.780237i	$0.284901\pi$
$240$		0			0
$241$	3.49312	+	6.05026i	0.225012	+	0.389732i	0.956323	−	0.292312i	$-0.0944246\pi$
$241$	3.49312	+	6.05026i	0.225012	+	0.389732i	−0.731311	+	0.682044i	$0.761091\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.79418	−	3.10761i	−0.114626	−	0.198538i
$246$		0			0
$247$	−0.444368	+	0.769668i	−0.0282745	+	0.0489728i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.62041			0.291638			0.145819	−	0.989311i	$-0.453418\pi$
$251$	4.62041			0.291638			0.145819	+	0.989311i	$0.453418\pi$
$252$		0			0
$253$	−16.5178			−1.03847
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.712008	+	1.23323i	−0.0444138	+	0.0769270i	−0.887378	−	0.461043i	$-0.847475\pi$
$257$	−0.712008	+	1.23323i	−0.0444138	+	0.0769270i	0.842964	+	0.537970i	$0.180809\pi$
$258$		0			0
$259$	−2.38255	−	4.12669i	−0.148044	−	0.256420i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.13162	−	14.0844i	−0.501417	−	0.868480i	−0.999999	−	0.00163692i	$-0.999479\pi$
$263$	−8.13162	−	14.0844i	−0.501417	−	0.868480i	0.498582	−	0.866843i	$-0.333854\pi$
$264$		0			0
$265$	−0.221840	+	0.384237i	−0.0136275	+	0.0236035i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.6538			1.13734			0.568672	−	0.822564i	$-0.307457\pi$
$269$	18.6538			1.13734			0.568672	+	0.822564i	$0.307457\pi$
$270$		0			0
$271$	−3.96286			−0.240727			−0.120363	−	0.992730i	$-0.538406\pi$
$271$	−3.96286			−0.240727			−0.120363	+	0.992730i	$0.538406\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.0698	−	19.1734i	0.667534	−	1.15620i
$276$		0			0
$277$	1.16690	+	2.02112i	0.0701120	+	0.121438i	0.898950	−	0.438051i	$-0.144331\pi$
$277$	1.16690	+	2.02112i	0.0701120	+	0.121438i	−0.828838	+	0.559488i	$0.810998\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.9975	+	24.2443i	0.835018	+	1.44629i	0.894016	+	0.448035i	$0.147876\pi$
$281$	13.9975	+	24.2443i	0.835018	+	1.44629i	−0.0589978	+	0.998258i	$0.518790\pi$
$282$		0			0
$283$	5.16002	−	8.93741i	0.306731	−	0.531274i	−0.670914	−	0.741535i	$-0.734098\pi$
$283$	5.16002	−	8.93741i	0.306731	−	0.531274i	0.977645	+	0.210261i	$0.0674314\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.41164			0.319439
$288$		0			0
$289$	−0.0975070			−0.00573571
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.3480	+	26.5834i	−0.896637	+	1.55302i	−0.0648718	+	0.997894i	$0.520664\pi$
$293$	−15.3480	+	26.5834i	−0.896637	+	1.55302i	−0.831765	+	0.555127i	$0.812670\pi$
$294$		0			0
$295$	15.9258	+	27.5843i	0.927236	+	1.60602i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.93818	−	5.08907i	−0.169919	−	0.294309i
$300$		0			0
$301$	2.60507	−	4.51212i	0.150154	−	0.260074i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	13.9098			0.796471
$306$		0			0
$307$	11.4437			0.653125			0.326563	−	0.945176i	$-0.394110\pi$
$307$	11.4437			0.653125			0.326563	+	0.945176i	$0.394110\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.98143	+	10.3601i	−0.339176	+	0.587470i	−0.984278	−	0.176627i	$-0.943481\pi$
$311$	−5.98143	+	10.3601i	−0.339176	+	0.587470i	0.645102	+	0.764096i	$0.276815\pi$
$312$		0			0
$313$	6.77197	+	11.7294i	0.382774	+	0.662985i	0.991458	−	0.130429i	$-0.0416353\pi$
$313$	6.77197	+	11.7294i	0.382774	+	0.662985i	−0.608683	+	0.793413i	$0.708302\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.9814	−	25.9486i	−0.841441	−	1.45742i	−0.888676	−	0.458535i	$-0.848374\pi$
$317$	−14.9814	−	25.9486i	−0.841441	−	1.45742i	0.0472355	−	0.998884i	$-0.484959\pi$
$318$		0			0
$319$	2.38874	−	4.13741i	0.133744	−	0.231651i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.65383			0.203304
$324$		0			0
$325$	7.87636			0.436902
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.33310	−	2.30900i	0.0734964	−	0.127299i
$330$		0			0
$331$	1.04325	+	1.80697i	0.0573423	+	0.0993198i	0.893272	−	0.449517i	$-0.148404\pi$
$331$	1.04325	+	1.80697i	0.0573423	+	0.0993198i	−0.835929	+	0.548837i	$0.815071\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	22.0846	+	38.2517i	1.20661	+	2.08992i
$336$		0			0
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	−0.556325	−	0.830965i	$-0.687789\pi$
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	0.997799	+	0.0663093i	$0.0211224\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−19.6414			−1.06364
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.63348	+	9.75747i	−0.302421	+	0.523808i	−0.976684	−	0.214683i	$-0.931128\pi$
$347$	−5.63348	+	9.75747i	−0.302421	+	0.523808i	0.674263	+	0.738491i	$0.264461\pi$
$348$		0			0
$349$	0.0988844	+	0.171273i	0.00529316	+	0.00916803i	0.868660	−	0.495409i	$-0.164982\pi$
$349$	0.0988844	+	0.171273i	0.00529316	+	0.00916803i	−0.863367	+	0.504577i	$0.831648\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.25093	−	10.8269i	−0.332703	−	0.576259i	0.650338	−	0.759645i	$-0.274627\pi$
$353$	−6.25093	−	10.8269i	−0.332703	−	0.576259i	−0.983041	+	0.183386i	$0.941294\pi$
$354$		0			0
$355$	5.16071	−	8.93861i	0.273902	−	0.474412i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	20.0197			1.05660			0.528299	−	0.849059i	$-0.322830\pi$
$359$	20.0197			1.05660			0.528299	+	0.849059i	$0.322830\pi$
$360$		0			0
$361$	−18.2101			−0.958429
$362$		0			0
$363$		0			0
$364$		0			0
$365$	19.0927	−	33.0695i	0.999357	−	1.73094i
$366$		0			0
$367$	15.0364	+	26.0438i	0.784892	+	1.35947i	0.929063	+	0.369921i	$0.120615\pi$
$367$	15.0364	+	26.0438i	0.784892	+	1.35947i	−0.144171	+	0.989553i	$0.546052\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0618219	−	0.107079i	−0.00320963	−	0.00555925i
$372$		0			0
$373$	−3.50619	+	6.07290i	−0.181544	+	0.314443i	−0.942406	−	0.334470i	$-0.891443\pi$
$373$	−3.50619	+	6.07290i	−0.181544	+	0.314443i	0.760863	+	0.648913i	$0.224776\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.69963			0.0875353
$378$		0			0
$379$	19.0741			0.979772			0.489886	−	0.871787i	$-0.337038\pi$
$379$	19.0741			0.979772			0.489886	+	0.871787i	$0.337038\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.60507	+	2.78007i	−0.0820155	+	0.142055i	−0.904116	−	0.427288i	$-0.859469\pi$
$383$	−1.60507	+	2.78007i	−0.0820155	+	0.142055i	0.822100	+	0.569343i	$0.192802\pi$
$384$		0			0
$385$	5.04325	+	8.73517i	0.257028	+	0.445185i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.56801	+	4.44793i	0.130203	+	0.225519i	0.923755	−	0.382984i	$-0.125104\pi$
$389$	2.56801	+	4.44793i	0.130203	+	0.225519i	−0.793552	+	0.608503i	$0.791770\pi$
$390$		0			0
$391$	−12.0796	+	20.9225i	−0.610893	+	1.05810i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	25.4290			1.27947
$396$		0			0
$397$	22.9381			1.15123			0.575615	−	0.817721i	$-0.304763\pi$
$397$	22.9381			1.15123			0.575615	+	0.817721i	$0.304763\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.10507	+	15.7705i	−0.454686	+	0.787539i	−0.998670	−	0.0515566i	$-0.983582\pi$
$401$	−9.10507	+	15.7705i	−0.454686	+	0.787539i	0.543984	+	0.839095i	$0.316915\pi$
$402$		0			0
$403$	−3.49381	−	6.05146i	−0.174039	−	0.301445i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.69708	+	11.5997i	0.331962	+	0.574975i
$408$		0			0
$409$	7.66621	−	13.2783i	0.379070	−	0.656568i	−0.611858	−	0.790968i	$-0.709577\pi$
$409$	7.66621	−	13.2783i	0.379070	−	0.656568i	0.990927	+	0.134400i	$0.0429108\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.87636			−0.436777
$414$		0			0
$415$	−14.7527			−0.724182
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.28435	+	9.15276i	−0.258157	+	0.447142i	−0.965748	−	0.259481i	$-0.916449\pi$
$419$	−5.28435	+	9.15276i	−0.258157	+	0.447142i	0.707591	+	0.706622i	$0.249782\pi$
$420$		0			0
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.849731	+	0.527217i	$0.176765\pi$
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.0317181	+	0.999497i	$0.489902\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−16.1909	−	28.0434i	−0.785374	−	1.36031i
$426$		0			0
$427$	−1.93818	+	3.35702i	−0.0937950	+	0.162458i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	35.0989			1.69065			0.845327	−	0.534249i	$-0.179406\pi$
$431$	35.0989			1.69065			0.845327	+	0.534249i	$0.179406\pi$
$432$		0			0
$433$	−41.1730			−1.97865			−0.989324	−	0.145731i	$-0.953447\pi$
$433$	−41.1730			−1.97865			−0.989324	+	0.145731i	$0.953447\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.61126	+	4.52284i	−0.124914	+	0.216357i
$438$		0			0
$439$	−2.33929	−	4.05178i	−0.111648	−	0.193381i	0.804787	−	0.593564i	$-0.202280\pi$
$439$	−2.33929	−	4.05178i	−0.111648	−	0.193381i	−0.916435	+	0.400184i	$0.868946\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.0865	−	26.1306i	−0.716781	−	1.24150i	−0.962268	−	0.272102i	$-0.912281\pi$
$443$	−15.0865	−	26.1306i	−0.716781	−	1.24150i	0.245487	−	0.969400i	$-0.421052\pi$
$444$		0			0
$445$	17.2410	−	29.8623i	0.817303	−	1.41561i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.333792			−0.0157526			−0.00787632	−	0.999969i	$-0.502507\pi$
$449$	−0.333792			−0.0157526			−0.00787632	+	0.999969i	$0.502507\pi$
$450$		0			0
$451$	−15.2115			−0.716283
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.79418	+	3.10761i	−0.0841125	+	0.145687i
$456$		0			0
$457$	9.65452	+	16.7221i	0.451619	+	0.782227i	0.998487	−	0.0549917i	$-0.0175132\pi$
$457$	9.65452	+	16.7221i	0.451619	+	0.782227i	−0.546868	+	0.837219i	$0.684180\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	19.5538	+	33.8681i	0.910710	+	1.57740i	0.813064	+	0.582175i	$0.197798\pi$
$461$	19.5538	+	33.8681i	0.910710	+	1.57740i	0.0976463	+	0.995221i	$0.468869\pi$
$462$		0			0
$463$	10.9382	−	18.9455i	0.508340	−	0.880471i	−0.491613	−	0.870814i	$-0.663593\pi$
$463$	10.9382	−	18.9455i	0.508340	−	0.880471i	0.999953	−	0.00965741i	$-0.00307410\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.3200			−0.570103			−0.285052	−	0.958512i	$-0.592011\pi$
$467$	−12.3200			−0.570103			−0.285052	+	0.958512i	$0.592011\pi$
$468$		0			0
$469$	−12.3090			−0.568378
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.32258	+	12.6831i	−0.336693	+	0.583169i
$474$		0			0
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.74474	−	11.6822i	−0.308175	−	0.533775i	0.669788	−	0.742552i	$-0.266385\pi$
$479$	−6.74474	−	11.6822i	−0.308175	−	0.533775i	−0.977963	+	0.208777i	$0.933052\pi$
$480$		0			0
$481$	−2.38255	+	4.12669i	−0.108635	+	0.188161i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	26.2719			1.19295
$486$		0			0
$487$	−7.54394			−0.341849			−0.170924	−	0.985284i	$-0.554675\pi$
$487$	−7.54394			−0.341849			−0.170924	+	0.985284i	$0.554675\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.06979	−	13.9773i	0.364185	−	0.630786i	−0.624460	−	0.781057i	$-0.714681\pi$
$491$	8.06979	−	13.9773i	0.364185	−	0.630786i	0.988645	+	0.150270i	$0.0480143\pi$
$492$		0			0
$493$	−3.49381	−	6.05146i	−0.157353	−	0.272544i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.43818	+	2.49100i	0.0645111	+	0.111737i
$498$		0			0
$499$	−15.4327	+	26.7302i	−0.690862	+	1.19661i	0.280694	+	0.959797i	$0.409435\pi$
$499$	−15.4327	+	26.7302i	−0.690862	+	1.19661i	−0.971556	+	0.236810i	$0.923898\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.6304			1.09822			0.549109	−	0.835751i	$-0.314967\pi$
$503$	24.6304			1.09822			0.549109	+	0.835751i	$0.314967\pi$
$504$		0			0
$505$	−12.4327			−0.553247
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.79487	−	11.7691i	0.301177	−	0.521654i	−0.675226	−	0.737611i	$-0.735954\pi$
$509$	6.79487	−	11.7691i	0.301177	−	0.521654i	0.976403	+	0.215957i	$0.0692870\pi$
$510$		0			0
$511$	5.32072	+	9.21576i	0.235375	+	0.407681i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−28.4851	−	49.3376i	−1.25520	−	2.17407i
$516$		0			0
$517$	−3.74721	+	6.49036i	−0.164802	+	0.285446i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	39.1730			1.71620			0.858100	−	0.513482i	$-0.171645\pi$
$521$	39.1730			1.71620			0.858100	+	0.513482i	$0.171645\pi$
$522$		0			0
$523$	−19.1236			−0.836219			−0.418109	−	0.908397i	$-0.637307\pi$
$523$	−19.1236			−0.836219			−0.418109	+	0.908397i	$0.637307\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.3640	+	24.8791i	−0.625705	+	1.08375i
$528$		0			0
$529$	−5.76578	−	9.98663i	−0.250686	−	0.434201i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.70582	−	4.68661i	−0.117202	−	0.203000i
$534$		0			0
$535$	9.60507	−	16.6365i	0.415264	−	0.719258i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.81089			−0.121074
$540$		0			0
$541$	2.53018			0.108781			0.0543906	−	0.998520i	$-0.482678\pi$
$541$	2.53018			0.108781			0.0543906	+	0.998520i	$0.482678\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	33.8454	−	58.6220i	1.44978	−	2.51109i
$546$		0			0
$547$	8.92580	+	15.4599i	0.381640	+	0.661019i	0.991297	−	0.131646i	$-0.0420262\pi$
$547$	8.92580	+	15.4599i	0.381640	+	0.661019i	−0.609657	+	0.792665i	$0.708693\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.755260	−	1.30815i	−0.0321752	−	0.0557290i
$552$		0			0
$553$	−3.54325	+	6.13709i	−0.150674	+	0.260976i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−41.3607			−1.75251			−0.876255	−	0.481847i	$-0.839966\pi$
$557$	−41.3607			−1.75251			−0.876255	+	0.481847i	$0.839966\pi$
$558$		0			0
$559$	−5.21015			−0.220366
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.3683	−	17.9584i	0.436972	−	0.756858i	−0.560482	−	0.828166i	$-0.689384\pi$
$563$	10.3683	−	17.9584i	0.436972	−	0.756858i	0.997454	+	0.0713087i	$0.0227175\pi$
$564$		0			0
$565$	−33.2843	−	57.6501i	−1.40028	−	2.42536i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.134164	−	0.232379i	−0.00562446	−	0.00974185i	0.863199	−	0.504863i	$-0.168457\pi$
$569$	−0.134164	−	0.232379i	−0.00562446	−	0.00974185i	−0.868824	+	0.495121i	$0.835124\pi$
$570$		0			0
$571$	17.9684	−	31.1221i	0.751953	−	1.30242i	−0.194923	−	0.980819i	$-0.562446\pi$
$571$	17.9684	−	31.1221i	0.751953	−	1.30242i	0.946875	−	0.321601i	$-0.104221\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	46.2843			1.93019
$576$		0			0
$577$	5.43130			0.226108			0.113054	−	0.993589i	$-0.463937\pi$
$577$	5.43130			0.226108			0.113054	+	0.993589i	$0.463937\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.05563	−	3.56046i	0.0852820	−	0.147713i
$582$		0			0
$583$	0.173775	+	0.300987i	0.00719702	+	0.0124656i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.5822	−	30.4532i	−0.725694	−	1.25694i	−0.958688	−	0.284461i	$-0.908185\pi$
$587$	−17.5822	−	30.4532i	−0.725694	−	1.25694i	0.232994	−	0.972478i	$-0.425148\pi$
$588$		0			0
$589$	−3.10507	+	5.37815i	−0.127942	+	0.221603i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	33.5068			1.37596			0.687980	−	0.725730i	$-0.258498\pi$
$593$	33.5068			1.37596			0.687980	+	0.725730i	$0.258498\pi$
$594$		0			0
$595$	14.7527			0.604802
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.12364	+	5.41031i	−0.127629	+	0.221059i	−0.922757	−	0.385381i	$-0.874070\pi$
$599$	−3.12364	+	5.41031i	−0.127629	+	0.221059i	0.795129	+	0.606441i	$0.207403\pi$
$600$		0			0
$601$	−11.2040	−	19.4058i	−0.457019	−	0.791580i	0.541783	−	0.840519i	$-0.317750\pi$
$601$	−11.2040	−	19.4058i	−0.457019	−	0.791580i	−0.998802	+	0.0489384i	$0.984416\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.55996	+	9.63014i	0.226045	+	0.391521i
$606$		0			0
$607$	7.47524	−	12.9475i	0.303411	−	0.525523i	−0.673496	−	0.739191i	$-0.735208\pi$
$607$	7.47524	−	12.9475i	0.303411	−	0.525523i	0.976906	+	0.213669i	$0.0685413\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.66621			−0.107863
$612$		0			0
$613$	35.1978			1.42162			0.710812	−	0.703382i	$-0.248328\pi$
$613$	35.1978			1.42162			0.710812	+	0.703382i	$0.248328\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.00619	+	1.74277i	−0.0405077	+	0.0701614i	−0.885568	−	0.464509i	$-0.846231\pi$
$617$	−1.00619	+	1.74277i	−0.0405077	+	0.0701614i	0.845061	+	0.534670i	$0.179564\pi$
$618$		0			0
$619$	19.6909	+	34.1056i	0.791444	+	1.37082i	0.925073	+	0.379789i	$0.124004\pi$
$619$	19.6909	+	34.1056i	0.791444	+	1.37082i	−0.133629	+	0.991031i	$0.542663\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.80470	+	8.32199i	0.192496	+	0.333413i
$624$		0			0
$625$	1.17240	−	2.03065i	0.0468959	−	0.0812261i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.5906			0.781126
$630$		0			0
$631$	−44.3832			−1.76687			−0.883433	−	0.468558i	$-0.844774\pi$
$631$	−44.3832			−1.76687			−0.883433	+	0.468558i	$0.844774\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	17.9196	−	31.0377i	0.711118	−	1.23169i
$636$		0			0
$637$	−0.500000	−	0.866025i	−0.0198107	−	0.0343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.49312	−	12.9785i	−0.295961	−	0.512619i	0.679247	−	0.733909i	$-0.262306\pi$
$641$	−7.49312	−	12.9785i	−0.295961	−	0.512619i	−0.975208	+	0.221291i	$0.928973\pi$
$642$		0			0
$643$	−5.32691	+	9.22649i	−0.210073	+	0.363857i	−0.951737	−	0.306914i	$-0.900703\pi$
$643$	−5.32691	+	9.22649i	−0.210073	+	0.363857i	0.741664	+	0.670771i	$0.234037\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.12955			0.0837213			0.0418606	−	0.999123i	$-0.486671\pi$
$647$	2.12955			0.0837213			0.0418606	+	0.999123i	$0.486671\pi$
$648$		0			0
$649$	24.9505			0.979392
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.58582	−	9.67492i	0.218590	−	0.378609i	−0.735787	−	0.677213i	$-0.763188\pi$
$653$	5.58582	−	9.67492i	0.218590	−	0.378609i	0.954377	+	0.298604i	$0.0965210\pi$
$654$		0			0
$655$	−28.8022	−	49.8868i	−1.12539	−	1.94924i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.65452	+	9.79391i	0.220269	+	0.381517i	0.954890	−	0.296961i	$-0.0959733\pi$
$659$	5.65452	+	9.79391i	0.220269	+	0.381517i	−0.734621	+	0.678478i	$0.762640\pi$
$660$		0			0
$661$	−16.1785	+	28.0220i	−0.629271	+	1.08993i	0.358427	+	0.933558i	$0.383313\pi$
$661$	−16.1785	+	28.0220i	−0.629271	+	1.08993i	−0.987698	+	0.156372i	$0.950020\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.18911			0.123668
$666$		0			0
$667$	9.98762			0.386722
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.44801	−	9.43623i	0.210318	−	0.364282i
$672$		0			0
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	0.999231	−	0.0392063i	$-0.0124830\pi$
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	−0.533569	+	0.845756i	$0.679150\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.5371	+	21.7148i	0.481838	+	0.834569i	0.999783	−	0.0208457i	$-0.00663587\pi$
$677$	12.5371	+	21.7148i	0.481838	+	0.834569i	−0.517944	+	0.855414i	$0.673303\pi$
$678$		0			0
$679$	−3.66071	+	6.34053i	−0.140485	+	0.243327i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−47.6784			−1.82436			−0.912182	−	0.409785i	$-0.865604\pi$
$683$	−47.6784			−1.82436			−0.912182	+	0.409785i	$0.865604\pi$
$684$		0			0
$685$	46.6043			1.78066
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0618219	+	0.107079i	−0.00235523	+	0.00407937i
$690$		0			0
$691$	−12.3400	−	21.3735i	−0.469435	−	0.813085i	0.529954	−	0.848026i	$-0.322209\pi$
$691$	−12.3400	−	21.3735i	−0.469435	−	0.813085i	−0.999389	+	0.0349408i	$0.988876\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.99381	+	3.45338i	0.0756295	+	0.130994i
$696$		0			0
$697$	−11.1243	+	19.2679i	−0.421364	+	0.729824i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	29.6784			1.12094			0.560469	−	0.828175i	$-0.310621\pi$
$701$	29.6784			1.12094			0.560469	+	0.828175i	$0.310621\pi$
$702$		0			0
$703$	4.23491			0.159723
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.73236	−	3.00054i	0.0651521	−	0.112847i
$708$		0			0
$709$	14.6291	+	25.3383i	0.549406	+	0.951599i	0.998315	+	0.0580220i	$0.0184794\pi$
$709$	14.6291	+	25.3383i	0.549406	+	0.951599i	−0.448909	+	0.893577i	$0.648187\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.5309	−	35.5605i	−0.768887	−	1.33175i
$714$		0			0
$715$	5.04325	−	8.73517i	0.188607	−	0.326677i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.07413			0.0400581			0.0200291	−	0.999799i	$-0.493624\pi$
$719$	1.07413			0.0400581			0.0200291	+	0.999799i	$0.493624\pi$
$720$		0			0
$721$	15.8764			0.591266
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.69344	+	11.5934i	−0.248588	+	0.430567i
$726$		0			0
$727$	12.7163	+	22.0253i	0.471623	+	0.816875i	0.999473	−	0.0324628i	$-0.0103350\pi$
$727$	12.7163	+	22.0253i	0.471623	+	0.816875i	−0.527850	+	0.849338i	$0.677002\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.7101	+	18.5505i	0.396129	+	0.686116i
$732$		0			0
$733$	5.69777	−	9.86883i	0.210452	−	0.364513i	−0.741404	−	0.671059i	$-0.765840\pi$
$733$	5.69777	−	9.86883i	0.210452	−	0.364513i	0.951856	+	0.306545i	$0.0991731\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	34.5994			1.27448
$738$		0			0
$739$	29.9395			1.10134			0.550671	−	0.834723i	$-0.314372\pi$
$739$	29.9395			1.10134			0.550671	+	0.834723i	$0.314372\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.50069	−	16.4557i	0.348546	−	0.603700i	−0.637445	−	0.770496i	$-0.720009\pi$
$743$	9.50069	−	16.4557i	0.348546	−	0.603700i	0.985991	+	0.166796i	$0.0533420\pi$
$744$		0			0
$745$	15.1298	+	26.2055i	0.554311	+	0.960096i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.67673	+	4.63623i	0.0978055	+	0.169404i
$750$		0			0
$751$	0.0130684	−	0.0226352i	0.000476873	−	0.000825969i	−0.865787	−	0.500413i	$-0.833182\pi$
$751$	0.0130684	−	0.0226352i	0.000476873	−	0.000825969i	0.866264	+	0.499587i	$0.166515\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	53.2929			1.93953
$756$		0			0
$757$	−13.6910			−0.497607			−0.248803	−	0.968554i	$-0.580037\pi$
$757$	−13.6910			−0.497607			−0.248803	+	0.968554i	$0.580037\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.32141	+	12.6811i	−0.265401	+	0.459688i	−0.967669	−	0.252225i	$-0.918838\pi$
$761$	−7.32141	+	12.6811i	−0.265401	+	0.459688i	0.702268	+	0.711913i	$0.252171\pi$
$762$		0			0
$763$	9.43199	+	16.3367i	0.341461	+	0.591428i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.43818	+	7.68715i	0.160253	+	0.277567i
$768$		0			0
$769$	−24.5672	+	42.5517i	−0.885918	+	1.53445i	−0.0412592	+	0.999148i	$0.513137\pi$
$769$	−24.5672	+	42.5517i	−0.885918	+	1.53445i	−0.844658	+	0.535306i	$0.820196\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.4413			−0.447484			−0.223742	−	0.974648i	$-0.571827\pi$
$773$	−12.4413			−0.447484			−0.223742	+	0.974648i	$0.571827\pi$
$774$		0			0
$775$	55.0370			1.97699
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.40476	+	4.16516i	−0.0861594	+	0.149232i
$780$		0			0
$781$	−4.04256	−	7.00193i	−0.144654	−	0.250549i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.18292	−	8.97708i	−0.184986	−	0.320406i
$786$		0			0
$787$	−16.4567	+	28.5038i	−0.586617	+	1.01605i	0.408055	+	0.912957i	$0.366207\pi$
$787$	−16.4567	+	28.5038i	−0.586617	+	1.01605i	−0.994672	+	0.103093i	$0.967126\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	18.5512			0.659606
$792$		0			0
$793$	3.87636			0.137653
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.1989	−	22.8612i	0.467530	−	0.809786i	−0.531781	−	0.846882i	$-0.678477\pi$
$797$	13.1989	−	22.8612i	0.467530	−	0.809786i	0.999312	+	0.0370953i	$0.0118105\pi$
$798$		0			0
$799$	5.48074	+	9.49292i	0.193895	+	0.335835i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−14.9560	−	25.9045i	−0.527785	−	0.914151i
$804$		0			0
$805$	−10.5433	+	18.2614i	−0.371601	+	0.643631i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−35.5919			−1.25135			−0.625673	−	0.780086i	$-0.715175\pi$
$809$	−35.5919			−1.25135			−0.625673	+	0.780086i	$0.715175\pi$
$810$		0			0
$811$	37.8268			1.32828			0.664140	−	0.747608i	$-0.268798\pi$
$811$	37.8268			1.32828			0.664140	+	0.747608i	$0.268798\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−18.4963	+	32.0365i	−0.647896	+	1.12219i
$816$		0			0
$817$	2.31522	+	4.01008i	0.0809994	+	0.140295i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.15638	−	15.8593i	−0.319560	−	0.553494i	0.660836	−	0.750530i	$-0.270202\pi$
$821$	−9.15638	−	15.8593i	−0.319560	−	0.553494i	−0.980396	+	0.197036i	$0.936868\pi$
$822$		0			0
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	0.360623	+	0.932712i	$0.382564\pi$
$823$	−18.0000	+	31.1769i	−0.627441	+	1.08676i	−0.988063	+	0.154047i	$0.950769\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.2115			−0.981011			−0.490505	−	0.871438i	$-0.663188\pi$
$827$	−28.2115			−0.981011			−0.490505	+	0.871438i	$0.663188\pi$
$828$		0			0
$829$	−11.2843			−0.391919			−0.195960	−	0.980612i	$-0.562782\pi$
$829$	−11.2843			−0.391919			−0.195960	+	0.980612i	$0.562782\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.05563	+	3.56046i	−0.0712234	+	0.123363i
$834$		0			0
$835$	−21.8028	−	37.7636i	−0.754519	−	1.30686i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.02152	+	1.76933i	0.0352669	+	0.0610840i	0.883120	−	0.469147i	$-0.155439\pi$
$839$	1.02152	+	1.76933i	0.0352669	+	0.0610840i	−0.847853	+	0.530231i	$0.822105\pi$
$840$		0			0
$841$	13.0556	−	22.6130i	0.450194	−	0.779759i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−43.0604			−1.48132
$846$		0			0
$847$	−3.09888			−0.106479
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.0007	+	24.2499i	−0.479937	+	0.831276i
$852$		0			0
$853$	24.2960	+	42.0818i	0.831878	+	1.44085i	0.896547	+	0.442948i	$0.146067\pi$
$853$	24.2960	+	42.0818i	0.831878	+	1.44085i	−0.0646692	+	0.997907i	$0.520599\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.4487	−	38.8823i	−0.766833	−	1.32819i	−0.939272	−	0.343173i	$-0.888498\pi$
$857$	−22.4487	−	38.8823i	−0.766833	−	1.32819i	0.172439	−	0.985020i	$-0.444835\pi$
$858$		0			0
$859$	14.9065	−	25.8189i	0.508605	−	0.880929i	−0.491346	−	0.870965i	$-0.663495\pi$
$859$	14.9065	−	25.8189i	0.508605	−	0.880929i	0.999950	−	0.00996438i	$-0.00317181\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−42.2595			−1.43853			−0.719265	−	0.694736i	$-0.755521\pi$
$863$	−42.2595			−1.43853			−0.719265	+	0.694736i	$0.755521\pi$
$864$		0			0
$865$	23.7170			0.806401
$866$		0			0
$867$		0			0
$868$		0			0
$869$	9.95970	−	17.2507i	0.337860	−	0.585190i
$870$		0			0
$871$	6.15452	+	10.6599i	0.208538	+	0.361198i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.16071	−	8.93861i	−0.174464	−	0.302180i
$876$		0			0
$877$	15.2658	−	26.4411i	0.515489	−	0.892853i	−0.484350	−	0.874875i	$-0.660944\pi$
$877$	15.2658	−	26.4411i	0.515489	−	0.892853i	0.999838	−	0.0179782i	$-0.00572295\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.4079			0.451724			0.225862	−	0.974159i	$-0.427480\pi$
$881$	13.4079			0.451724			0.225862	+	0.974159i	$0.427480\pi$
$882$		0			0
$883$	14.1250			0.475345			0.237672	−	0.971345i	$-0.423616\pi$
$883$	14.1250			0.475345			0.237672	+	0.971345i	$0.423616\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.9716	−	34.5918i	0.670581	−	1.16148i	−0.307159	−	0.951658i	$-0.599378\pi$
$887$	19.9716	−	34.5918i	0.670581	−	1.16148i	0.977740	−	0.209822i	$-0.0672883\pi$
$888$		0			0
$889$	4.99381	+	8.64953i	0.167487	+	0.290096i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.18478	+	2.05209i	0.0396471	+	0.0686707i
$894$		0			0
$895$	6.89493	−	11.9424i	0.230472	−	0.399189i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	11.8764			0.396099
$900$		0			0
$901$	0.508333			0.0169350
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−33.2687	+	57.6231i	−1.10589	+	1.91546i
$906$		0			0
$907$	20.7101	+	35.8710i	0.687669	+	1.19108i	0.972590	+	0.232527i	$0.0746994\pi$
$907$	20.7101	+	35.8710i	0.687669	+	1.19108i	−0.284921	+	0.958551i	$0.591967\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.894237	−	1.54886i	−0.0296274	−	0.0513162i	0.850832	−	0.525439i	$-0.176099\pi$
$911$	−0.894237	−	1.54886i	−0.0296274	−	0.0513162i	−0.880459	+	0.474122i	$0.842765\pi$
$912$		0			0
$913$	−5.77816	+	10.0081i	−0.191229	+	0.331219i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	16.0531			0.530120
$918$		0			0
$919$	57.4683			1.89570			0.947852	−	0.318711i	$-0.103250\pi$
$919$	57.4683			1.89570			0.947852	+	0.318711i	$0.103250\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.43818	−	2.49100i	0.0473382	−	0.0819922i
$924$		0			0
$925$	−18.7658	−	32.5033i	−0.617015	−	1.06870i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.3676	+	30.0816i	0.569813	+	0.986945i	0.996584	+	0.0825854i	$0.0263177\pi$
$929$	17.3676	+	30.0816i	0.569813	+	0.986945i	−0.426771	+	0.904360i	$0.640349\pi$
$930$		0			0
$931$	−0.444368	+	0.769668i	−0.0145636	+	0.0252248i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−41.4683			−1.35616
$936$		0			0
$937$	11.6662			0.381118			0.190559	−	0.981676i	$-0.438970\pi$
$937$	11.6662			0.381118			0.190559	+	0.981676i	$0.438970\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−25.1687	+	43.5934i	−0.820475	+	1.42111i	0.0848531	+	0.996393i	$0.472958\pi$
$941$	−25.1687	+	43.5934i	−0.820475	+	1.42111i	−0.905329	+	0.424712i	$0.860375\pi$
$942$		0			0
$943$	−15.9004	−	27.5402i	−0.517787	−	0.896833i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.1941	+	28.0491i	0.526238	+	0.911472i	0.999533	+	0.0305673i	$0.00973139\pi$
$947$	16.1941	+	28.0491i	0.526238	+	0.911472i	−0.473294	+	0.880904i	$0.656935\pi$
$948$		0			0
$949$	5.32072	−	9.21576i	0.172718	−	0.299156i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	12.5367			0.406102			0.203051	−	0.979168i	$-0.434914\pi$
$953$	12.5367			0.406102			0.203051	+	0.979168i	$0.434914\pi$
$954$		0			0
$955$	16.6291			0.538104
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.49381	+	11.2476i	−0.209696	+	0.363204i
$960$		0			0
$961$	−8.91342	−	15.4385i	−0.287530	−	0.498016i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	45.3868	+	78.6122i	1.46105	+	2.53062i
$966$		0			0
$967$	−28.9937	+	50.2186i	−0.932376	+	1.61492i	−0.153127	+	0.988206i	$0.548935\pi$
$967$	−28.9937	+	50.2186i	−0.932376	+	1.61492i	−0.779248	+	0.626715i	$0.784399\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.0370			0.899750			0.449875	−	0.893092i	$-0.351469\pi$
$971$	28.0370			0.899750			0.449875	+	0.893092i	$0.351469\pi$
$972$		0			0
$973$	−1.11126			−0.0356255
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.92030	−	8.52220i	0.157414	−	0.272649i	−0.776521	−	0.630091i	$-0.783018\pi$
$977$	4.92030	−	8.52220i	0.157414	−	0.272649i	0.933935	+	0.357442i	$0.116351\pi$
$978$		0			0
$979$	−13.5055	−	23.3922i	−0.431638	−	0.747618i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.3447	+	42.1663i	0.776476	+	1.34490i	0.933961	+	0.357374i	$0.116328\pi$
$983$	24.3447	+	42.1663i	0.776476	+	1.34490i	−0.157485	+	0.987521i	$0.550339\pi$
$984$		0			0
$985$	19.2348	−	33.3157i	0.612873	−	1.06153i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.6167			−0.973554
$990$		0			0
$991$	−2.86398			−0.0909772			−0.0454886	−	0.998965i	$-0.514484\pi$
$991$	−2.86398			−0.0909772			−0.0454886	+	0.998965i	$0.514484\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−15.7286	+	27.2428i	−0.498631	+	0.863655i
$996$		0			0
$997$	25.4203	+	44.0292i	0.805069	+	1.39442i	0.916245	+	0.400619i	$0.131205\pi$
$997$	25.4203	+	44.0292i	0.805069	+	1.39442i	−0.111176	+	0.993801i	$0.535462\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.g.1009.1		6
3.2	odd	2		1008.2.r.k.337.1		6
4.3	odd	2		189.2.f.a.64.3		6
9.2	odd	6		1008.2.r.k.673.1		6
9.4	even	3		9072.2.a.cd.1.3		3
9.5	odd	6		9072.2.a.bq.1.1		3
9.7	even	3	inner	3024.2.r.g.2017.1		6
12.11	even	2		63.2.f.b.22.1	✓	6
28.3	even	6		1323.2.h.e.226.1		6
28.11	odd	6		1323.2.h.d.226.1		6
28.19	even	6		1323.2.g.b.361.3		6
28.23	odd	6		1323.2.g.c.361.3		6
28.27	even	2		1323.2.f.c.442.3		6
36.7	odd	6		189.2.f.a.127.3		6
36.11	even	6		63.2.f.b.43.1	yes	6
36.23	even	6		567.2.a.d.1.3		3
36.31	odd	6		567.2.a.g.1.1		3
84.11	even	6		441.2.h.c.373.3		6
84.23	even	6		441.2.g.e.67.1		6
84.47	odd	6		441.2.g.d.67.1		6
84.59	odd	6		441.2.h.b.373.3		6
84.83	odd	2		441.2.f.d.148.1		6
252.11	even	6		441.2.g.e.79.1		6
252.47	odd	6		441.2.h.b.214.3		6
252.79	odd	6		1323.2.h.d.802.1		6
252.83	odd	6		441.2.f.d.295.1		6
252.115	even	6		1323.2.g.b.667.3		6
252.139	even	6		3969.2.a.p.1.1		3
252.151	odd	6		1323.2.g.c.667.3		6
252.167	odd	6		3969.2.a.m.1.3		3
252.187	even	6		1323.2.h.e.802.1		6
252.191	even	6		441.2.h.c.214.3		6
252.223	even	6		1323.2.f.c.883.3		6
252.227	odd	6		441.2.g.d.79.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	12.11	even	2
63.2.f.b.43.1	yes	6	36.11	even	6
189.2.f.a.64.3		6	4.3	odd	2
189.2.f.a.127.3		6	36.7	odd	6
441.2.f.d.148.1		6	84.83	odd	2
441.2.f.d.295.1		6	252.83	odd	6
441.2.g.d.67.1		6	84.47	odd	6
441.2.g.d.79.1		6	252.227	odd	6
441.2.g.e.67.1		6	84.23	even	6
441.2.g.e.79.1		6	252.11	even	6
441.2.h.b.214.3		6	252.47	odd	6
441.2.h.b.373.3		6	84.59	odd	6
441.2.h.c.214.3		6	252.191	even	6
441.2.h.c.373.3		6	84.11	even	6
567.2.a.d.1.3		3	36.23	even	6
567.2.a.g.1.1		3	36.31	odd	6
1008.2.r.k.337.1		6	3.2	odd	2
1008.2.r.k.673.1		6	9.2	odd	6
1323.2.f.c.442.3		6	28.27	even	2
1323.2.f.c.883.3		6	252.223	even	6
1323.2.g.b.361.3		6	28.19	even	6
1323.2.g.b.667.3		6	252.115	even	6
1323.2.g.c.361.3		6	28.23	odd	6
1323.2.g.c.667.3		6	252.151	odd	6
1323.2.h.d.226.1		6	28.11	odd	6
1323.2.h.d.802.1		6	252.79	odd	6
1323.2.h.e.226.1		6	28.3	even	6
1323.2.h.e.802.1		6	252.187	even	6
3024.2.r.g.1009.1		6	1.1	even	1	trivial
3024.2.r.g.2017.1		6	9.7	even	3	inner
3969.2.a.m.1.3		3	252.167	odd	6
3969.2.a.p.1.1		3	252.139	even	6
9072.2.a.bq.1.1		3	9.5	odd	6
9072.2.a.cd.1.3		3	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.79418 + 3.10761i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.40545 + 2.43430i) q^{11} +(-0.500000 + 0.866025i) q^{13} +4.11126 q^{17} +0.888736 q^{19} +(-2.93818 + 5.08907i) q^{23} +(-3.93818 - 6.82112i) q^{25} +(-0.849814 - 1.47192i) q^{29} +(-3.49381 + 6.05146i) q^{31} +3.58836 q^{35} +4.76509 q^{37} +(-2.70582 + 4.68661i) q^{41} +(2.60507 + 4.51212i) q^{43} +(1.33310 + 2.30900i) q^{47} +(-0.500000 + 0.866025i) q^{49} +0.123644 q^{53} -10.0865 q^{55} +(4.43818 - 7.68715i) q^{59} +(-1.93818 - 3.35702i) q^{61} +(-1.79418 - 3.10761i) q^{65} +(6.15452 - 10.6599i) q^{67} -2.87636 q^{71} -10.6414 q^{73} +(1.40545 - 2.43430i) q^{77} +(-3.54325 - 6.13709i) q^{79} +(2.05563 + 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} -9.60940 q^{89} +1.00000 q^{91} +(-1.59455 + 2.76185i) q^{95} +(-3.66071 - 6.34053i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{5} - 3 q^{7} + 2 q^{11} - 3 q^{13} + 24 q^{17} + 6 q^{19} - 6 q^{25} + q^{29} - 3 q^{31} + 10 q^{35} - 6 q^{37} - 22 q^{41} - 3 q^{43} + 9 q^{47} - 3 q^{49} + 36 q^{53} + 12 q^{55} + 9 q^{59}+ \cdots - 3 q^{97}+O(q^{100}) \) 6 * q - 5 * q^5 - 3 * q^7 + 2 * q^11 - 3 * q^13 + 24 * q^17 + 6 * q^19 - 6 * q^25 + q^29 - 3 * q^31 + 10 * q^35 - 6 * q^37 - 22 * q^41 - 3 * q^43 + 9 * q^47 - 3 * q^49 + 36 * q^53 + 12 * q^55 + 9 * q^59 + 6 * q^61 - 5 * q^65 + 18 * q^71 + 6 * q^73 + 2 * q^77 + 15 * q^79 + 12 * q^83 - 9 * q^85 + 4 * q^89 + 6 * q^91 - 16 * q^95 - 3 * q^97

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