LMFDB - Embedded newform 3024.2.r.e.1009.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1009,3024)]

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, 2, 0]))

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

//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);

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: 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1009.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	3024.1009
Dual form			3024.2.r.e.2017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.724745 + 1.25529i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-0.724745 + 1.25529i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{13} -2.00000 q^{17} -2.55051 q^{19} +(0.500000 - 0.866025i) q^{23} +(1.44949 + 2.51059i) q^{25} +(-3.44949 - 5.97469i) q^{29} +(3.00000 - 5.19615i) q^{31} +1.44949 q^{35} +11.7980 q^{37} +(4.89898 - 8.48528i) q^{41} +(3.44949 + 5.97469i) q^{43} +(-4.89898 - 8.48528i) q^{47} +(-0.500000 + 0.866025i) q^{49} +10.8990 q^{53} +2.89898 q^{55} +(1.00000 - 1.73205i) q^{59} +(-3.27526 - 5.67291i) q^{61} +(-3.55051 - 6.14966i) q^{65} +(-6.44949 + 11.1708i) q^{67} +0.101021 q^{71} -6.89898 q^{73} +(-1.00000 + 1.73205i) q^{77} +(-0.949490 - 1.64456i) q^{79} +(-1.00000 - 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +16.8990 q^{89} +4.89898 q^{91} +(1.84847 - 3.20164i) q^{95} +(-1.44949 - 2.51059i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{5} - 2 q^{7} - 4 q^{11} - 8 q^{17} - 20 q^{19} + 2 q^{23} - 4 q^{25} - 4 q^{29} + 12 q^{31} - 4 q^{35} + 8 q^{37} + 4 q^{43} - 2 q^{49} + 24 q^{53} - 8 q^{55} + 4 q^{59} - 18 q^{61} - 24 q^{65} - 16 q^{67} + 20 q^{71} - 8 q^{73} - 4 q^{77} + 6 q^{79} - 4 q^{83} - 4 q^{85} + 48 q^{89} - 22 q^{95} + 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^11 - 8 * q^17 - 20 * q^19 + 2 * q^23 - 4 * q^25 - 4 * q^29 + 12 * q^31 - 4 * q^35 + 8 * q^37 + 4 * q^43 - 2 * q^49 + 24 * q^53 - 8 * q^55 + 4 * q^59 - 18 * q^61 - 24 * q^65 - 16 * q^67 + 20 * q^71 - 8 * q^73 - 4 * q^77 + 6 * q^79 - 4 * q^83 - 4 * q^85 + 48 * q^89 - 22 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.724745	+	1.25529i	−0.324116	+	0.561385i	−0.981333	−	0.192316i	$-0.938400\pi$
$5$	−0.724745	+	1.25529i	−0.324116	+	0.561385i	0.657217	+	0.753701i	$0.271733\pi$
$6$		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
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	0.295806	+	0.955248i	$0.404412\pi$
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	−0.975172	+	0.221449i	$0.928921\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	−2.55051			−0.585127			−0.292564	−	0.956246i	$-0.594508\pi$
$19$	−2.55051			−0.585127			−0.292564	+	0.956246i	$0.594508\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	1.44949	+	2.51059i	0.289898	+	0.502118i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.44949	−	5.97469i	−0.640554	−	1.10947i	−0.985309	−	0.170780i	$-0.945371\pi$
$29$	−3.44949	−	5.97469i	−0.640554	−	1.10947i	0.344755	−	0.938693i	$-0.387962\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.44949			0.245008
$36$		0			0
$37$	11.7980			1.93957			0.969786	−	0.243956i	$-0.0784453\pi$
$37$	11.7980			1.93957			0.969786	+	0.243956i	$0.0784453\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	−0.175106	−	0.984550i	$-0.556027\pi$
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	0.940198	−	0.340629i	$-0.110640\pi$
$42$		0			0
$43$	3.44949	+	5.97469i	0.526042	+	0.911132i	0.999540	+	0.0303367i	$0.00965797\pi$
$43$	3.44949	+	5.97469i	0.526042	+	0.911132i	−0.473497	+	0.880795i	$0.657009\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	−0.963118	−	0.269081i	$-0.913280\pi$
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	0.248528	−	0.968625i	$-0.420053\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.8990			1.49709			0.748545	−	0.663084i	$-0.230753\pi$
$53$	10.8990			1.49709			0.748545	+	0.663084i	$0.230753\pi$
$54$		0			0
$55$	2.89898			0.390898
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	−0.793560	−	0.608492i	$-0.791775\pi$
$59$	1.00000	−	1.73205i	0.130189	−	0.225494i	0.923749	+	0.382998i	$0.125108\pi$
$60$		0			0
$61$	−3.27526	−	5.67291i	−0.419353	−	0.726341i	0.576521	−	0.817082i	$-0.304410\pi$
$61$	−3.27526	−	5.67291i	−0.419353	−	0.726341i	−0.995875	+	0.0907408i	$0.971077\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.55051	−	6.14966i	−0.440387	−	0.762772i
$66$		0			0
$67$	−6.44949	+	11.1708i	−0.787931	+	1.36474i	0.139302	+	0.990250i	$0.455514\pi$
$67$	−6.44949	+	11.1708i	−0.787931	+	1.36474i	−0.927233	+	0.374486i	$0.877819\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.101021			0.0119889			0.00599446	−	0.999982i	$-0.498092\pi$
$71$	0.101021			0.0119889			0.00599446	+	0.999982i	$0.498092\pi$
$72$		0			0
$73$	−6.89898			−0.807464			−0.403732	−	0.914877i	$-0.632287\pi$
$73$	−6.89898			−0.807464			−0.403732	+	0.914877i	$0.632287\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.00000	+	1.73205i	−0.113961	+	0.197386i
$78$		0			0
$79$	−0.949490	−	1.64456i	−0.106826	−	0.185028i	0.807657	−	0.589653i	$-0.200735\pi$
$79$	−0.949490	−	1.64456i	−0.106826	−	0.185028i	−0.914483	+	0.404625i	$0.867402\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$		0			0
$85$	1.44949	−	2.51059i	0.157219	−	0.272312i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	16.8990			1.79129			0.895644	−	0.444771i	$-0.146715\pi$
$89$	16.8990			1.79129			0.895644	+	0.444771i	$0.146715\pi$
$90$		0			0
$91$	4.89898			0.513553
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.84847	−	3.20164i	0.189649	−	0.328482i
$96$		0			0
$97$	−1.44949	−	2.51059i	−0.147173	−	0.254912i	0.783008	−	0.622011i	$-0.213684\pi$
$97$	−1.44949	−	2.51059i	−0.147173	−	0.254912i	−0.930182	+	0.367099i	$0.880351\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.62372	−	14.9367i	−0.858093	−	1.48626i	−0.873746	−	0.486383i	$-0.838316\pi$
$101$	−8.62372	−	14.9367i	−0.858093	−	1.48626i	0.0156533	−	0.999877i	$-0.495017\pi$
$102$		0			0
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	12.6969			1.21615			0.608073	−	0.793881i	$-0.291943\pi$
$109$	12.6969			1.21615			0.608073	+	0.793881i	$0.291943\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.05051	+	5.28364i	−0.286968	+	0.497043i	−0.973084	−	0.230449i	$-0.925981\pi$
$113$	−3.05051	+	5.28364i	−0.286968	+	0.497043i	0.686117	+	0.727492i	$0.259314\pi$
$114$		0			0
$115$	0.724745	+	1.25529i	0.0675828	+	0.117057i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.00000	+	1.73205i	0.0916698	+	0.158777i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.4495			−1.02407
$126$		0			0
$127$	3.00000			0.266207			0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000			0.266207			0.133103	+	0.991102i	$0.457506\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.27526	−	7.40496i	0.373531	−	0.646974i	−0.616575	−	0.787296i	$-0.711480\pi$
$131$	4.27526	−	7.40496i	0.373531	−	0.646974i	0.990106	+	0.140322i	$0.0448137\pi$
$132$		0			0
$133$	1.27526	+	2.20881i	0.110579	+	0.191528i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.89898	+	6.75323i	0.333112	+	0.576967i	0.983120	−	0.182960i	$-0.0585678\pi$
$137$	3.89898	+	6.75323i	0.333112	+	0.576967i	−0.650008	+	0.759927i	$0.725235\pi$
$138$		0			0
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	−0.753253	−	0.657730i	$-0.771517\pi$
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	0.946238	+	0.323471i	$0.104850\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.79796			0.819346
$144$		0			0
$145$	10.0000			0.830455
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.34847	+	7.53177i	0.349277	+	0.604966i
$156$		0			0
$157$	4.17423	−	7.22999i	0.333140	−	0.577016i	−0.649986	−	0.759947i	$-0.725225\pi$
$157$	4.17423	−	7.22999i	0.333140	−	0.577016i	0.983126	+	0.182931i	$0.0585584\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.00000			−0.0788110
$162$		0			0
$163$	19.7980			1.55070			0.775348	−	0.631534i	$-0.217575\pi$
$163$	19.7980			1.55070			0.775348	+	0.631534i	$0.217575\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	−0.581433	−	0.813594i	$-0.697508\pi$
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	0.995310	+	0.0967384i	$0.0308410\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.55051	−	2.68556i	−0.117883	−	0.204180i	0.801045	−	0.598604i	$-0.204277\pi$
$173$	−1.55051	−	2.68556i	−0.117883	−	0.204180i	−0.918929	+	0.394424i	$0.870944\pi$
$174$		0			0
$175$	1.44949	−	2.51059i	0.109571	−	0.189783i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	20.6969			1.54696			0.773481	−	0.633820i	$-0.218514\pi$
$179$	20.6969			1.54696			0.773481	+	0.633820i	$0.218514\pi$
$180$		0			0
$181$	−10.3485			−0.769196			−0.384598	−	0.923084i	$-0.625660\pi$
$181$	−10.3485			−0.769196			−0.384598	+	0.923084i	$0.625660\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.55051	+	14.8099i	−0.628646	+	1.08885i
$186$		0			0
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.05051	−	3.55159i	−0.148370	−	0.256984i	0.782255	−	0.622958i	$-0.214069\pi$
$191$	−2.05051	−	3.55159i	−0.148370	−	0.256984i	−0.930625	+	0.365974i	$0.880736\pi$
$192$		0			0
$193$	8.94949	−	15.5010i	0.644198	−	1.11578i	−0.340288	−	0.940321i	$-0.610524\pi$
$193$	8.94949	−	15.5010i	0.644198	−	1.11578i	0.984486	−	0.175463i	$-0.0561422\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.6969			−1.18961			−0.594804	−	0.803871i	$-0.702770\pi$
$197$	−16.6969			−1.18961			−0.594804	+	0.803871i	$0.702770\pi$
$198$		0			0
$199$	2.89898			0.205503			0.102752	−	0.994707i	$-0.467235\pi$
$199$	2.89898			0.205503			0.102752	+	0.994707i	$0.467235\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.44949	+	5.97469i	−0.242107	+	0.419341i
$204$		0			0
$205$	7.10102	+	12.2993i	0.495957	+	0.859022i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.55051	+	4.41761i	0.176422	+	0.305573i
$210$		0			0
$211$	6.44949	−	11.1708i	0.444001	−	0.769033i	−0.553981	−	0.832529i	$-0.686892\pi$
$211$	6.44949	−	11.1708i	0.444001	−	0.769033i	0.997982	+	0.0634968i	$0.0202253\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.0000			−0.681994
$216$		0			0
$217$	−6.00000			−0.407307
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.89898	−	8.48528i	0.329541	−	0.570782i
$222$		0			0
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	0.618136	−	0.786071i	$-0.287888\pi$
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	−0.989826	+	0.142286i	$0.954555\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.72474	+	4.71940i	0.180848	+	0.313237i	0.942169	−	0.335137i	$-0.108783\pi$
$227$	2.72474	+	4.71940i	0.180848	+	0.313237i	−0.761322	+	0.648374i	$0.775449\pi$
$228$		0			0
$229$	−0.623724	+	1.08032i	−0.0412169	+	0.0713897i	−0.885898	−	0.463880i	$-0.846457\pi$
$229$	−0.623724	+	1.08032i	−0.0412169	+	0.0713897i	0.844681	+	0.535270i	$0.179790\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.00000			0.458585			0.229293	−	0.973358i	$-0.426359\pi$
$233$	7.00000			0.458585			0.229293	+	0.973358i	$0.426359\pi$
$234$		0			0
$235$	14.2020			0.926439
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.39898	+	5.88721i	−0.219862	+	0.380812i	−0.954766	−	0.297360i	$-0.903894\pi$
$239$	−3.39898	+	5.88721i	−0.219862	+	0.380812i	0.734904	+	0.678171i	$0.237227\pi$
$240$		0			0
$241$	−0.449490	−	0.778539i	−0.0289542	−	0.0501501i	0.851185	−	0.524865i	$-0.175884\pi$
$241$	−0.449490	−	0.778539i	−0.0289542	−	0.0501501i	−0.880139	+	0.474715i	$0.842551\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.724745	−	1.25529i	−0.0463023	−	0.0801979i
$246$		0			0
$247$	6.24745	−	10.8209i	0.397516	−	0.688517i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	17.4495			1.10140			0.550701	−	0.834703i	$-0.314360\pi$
$251$	17.4495			1.10140			0.550701	+	0.834703i	$0.314360\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.10102	−	7.10318i	0.255815	−	0.443084i	−0.709302	−	0.704905i	$-0.750990\pi$
$257$	4.10102	−	7.10318i	0.255815	−	0.443084i	0.965116	+	0.261821i	$0.0843230\pi$
$258$		0			0
$259$	−5.89898	−	10.2173i	−0.366545	−	0.634874i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.9495	−	22.4292i	−0.798500	−	1.38304i	−0.920593	−	0.390523i	$-0.872294\pi$
$263$	−12.9495	−	22.4292i	−0.798500	−	1.38304i	0.122093	−	0.992519i	$-0.461039\pi$
$264$		0			0
$265$	−7.89898	+	13.6814i	−0.485230	+	0.840444i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.3485			1.11873			0.559363	−	0.828923i	$-0.311046\pi$
$269$	18.3485			1.11873			0.559363	+	0.828923i	$0.311046\pi$
$270$		0			0
$271$	−7.10102			−0.431356			−0.215678	−	0.976465i	$-0.569196\pi$
$271$	−7.10102			−0.431356			−0.215678	+	0.976465i	$0.569196\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.89898	−	5.02118i	0.174815	−	0.302789i
$276$		0			0
$277$	9.34847	+	16.1920i	0.561695	+	0.972884i	0.997349	+	0.0727700i	$0.0231839\pi$
$277$	9.34847	+	16.1920i	0.561695	+	0.972884i	−0.435654	+	0.900114i	$0.643483\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	−0.996887	−	0.0788417i	$-0.974878\pi$
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	0.430165	−	0.902750i	$-0.358455\pi$
$282$		0			0
$283$	−12.7247	+	22.0399i	−0.756408	+	1.31014i	0.188264	+	0.982118i	$0.439714\pi$
$283$	−12.7247	+	22.0399i	−0.756408	+	1.31014i	−0.944672	+	0.328018i	$0.893619\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.79796			−0.578355
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.37628	−	2.38378i	0.0804029	−	0.139262i	−0.823020	−	0.568012i	$-0.807713\pi$
$293$	1.37628	−	2.38378i	0.0804029	−	0.139262i	0.903423	+	0.428750i	$0.141046\pi$
$294$		0			0
$295$	1.44949	+	2.51059i	0.0843926	+	0.146172i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.44949	+	4.24264i	0.141658	+	0.245358i
$300$		0			0
$301$	3.44949	−	5.97469i	0.198825	−	0.344375i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.49490			0.543676
$306$		0			0
$307$	−25.2474			−1.44095			−0.720474	−	0.693482i	$-0.756076\pi$
$307$	−25.2474			−1.44095			−0.720474	+	0.693482i	$0.756076\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.3485	+	26.5843i	−0.870332	+	1.50746i	−0.00867810	+	0.999962i	$0.502762\pi$
$311$	−15.3485	+	26.5843i	−0.870332	+	1.50746i	−0.861654	+	0.507497i	$0.830571\pi$
$312$		0			0
$313$	2.34847	+	4.06767i	0.132743	+	0.229918i	0.924733	−	0.380616i	$-0.124288\pi$
$313$	2.34847	+	4.06767i	0.132743	+	0.229918i	−0.791990	+	0.610534i	$0.790955\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.3485	+	17.9241i	0.581228	+	1.00672i	0.995334	+	0.0964878i	$0.0307609\pi$
$317$	10.3485	+	17.9241i	0.581228	+	1.00672i	−0.414106	+	0.910229i	$0.635906\pi$
$318$		0			0
$319$	−6.89898	+	11.9494i	−0.386269	+	0.669037i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	5.10102			0.283828
$324$		0			0
$325$	−14.2020			−0.787787
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4.89898	+	8.48528i	−0.270089	+	0.467809i
$330$		0			0
$331$	2.34847	+	4.06767i	0.129084	+	0.223579i	0.923322	−	0.384027i	$-0.125463\pi$
$331$	2.34847	+	4.06767i	0.129084	+	0.223579i	−0.794238	+	0.607606i	$0.792130\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.34847	−	16.1920i	−0.510761	−	0.884665i
$336$		0			0
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	−0.348877	−	0.937168i	$-0.613437\pi$
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	0.986050	−	0.166447i	$-0.0532296\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.0000			−0.649836
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.79796	+	16.9706i	−0.525982	+	0.911028i	0.473560	+	0.880762i	$0.342969\pi$
$347$	−9.79796	+	16.9706i	−0.525982	+	0.911028i	−0.999542	+	0.0302659i	$0.990365\pi$
$348$		0			0
$349$	−5.55051	−	9.61377i	−0.297112	−	0.514613i	0.678362	−	0.734728i	$-0.262690\pi$
$349$	−5.55051	−	9.61377i	−0.297112	−	0.514613i	−0.975474	+	0.220115i	$0.929357\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$	−0.0732141	+	0.126811i	−0.00388580	+	0.00673040i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.79796			−0.464339			−0.232169	−	0.972675i	$-0.574582\pi$
$359$	−8.79796			−0.464339			−0.232169	+	0.972675i	$0.574582\pi$
$360$		0			0
$361$	−12.4949			−0.657626
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.00000	−	8.66025i	0.261712	−	0.453298i
$366$		0			0
$367$	−6.89898	−	11.9494i	−0.360124	−	0.623753i	0.627857	−	0.778329i	$-0.283932\pi$
$367$	−6.89898	−	11.9494i	−0.360124	−	0.623753i	−0.987981	+	0.154576i	$0.950599\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.44949	−	9.43879i	−0.282923	−	0.490038i
$372$		0			0
$373$	3.44949	−	5.97469i	0.178608	−	0.309358i	−0.762796	−	0.646639i	$-0.776174\pi$
$373$	3.44949	−	5.97469i	0.178608	−	0.309358i	0.941404	+	0.337281i	$0.109507\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	33.7980			1.74068
$378$		0			0
$379$	−22.4949			−1.15549			−0.577743	−	0.816219i	$-0.696066\pi$
$379$	−22.4949			−1.15549			−0.577743	+	0.816219i	$0.696066\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.44949	−	2.51059i	0.0740655	−	0.128285i	−0.826614	−	0.562769i	$-0.809736\pi$
$383$	1.44949	−	2.51059i	0.0740655	−	0.128285i	0.900679	+	0.434484i	$0.143069\pi$
$384$		0			0
$385$	−1.44949	−	2.51059i	−0.0738728	−	0.127952i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.4495	−	21.5631i	−0.631214	−	1.09330i	−0.987304	−	0.158843i	$-0.949224\pi$
$389$	−12.4495	−	21.5631i	−0.631214	−	1.09330i	0.356090	−	0.934452i	$-0.384110\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.75255			0.138496
$396$		0			0
$397$	38.6969			1.94214			0.971072	−	0.238788i	$-0.0767500\pi$
$397$	38.6969			1.94214			0.971072	+	0.238788i	$0.0767500\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.94949	+	17.2330i	−0.496854	+	0.860576i	−0.999993	−	0.00362911i	$-0.998845\pi$
$401$	−9.94949	+	17.2330i	−0.496854	+	0.860576i	0.503140	+	0.864205i	$0.332178\pi$
$402$		0			0
$403$	14.6969	+	25.4558i	0.732107	+	1.26805i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.7980	−	20.4347i	−0.584803	−	1.01291i
$408$		0			0
$409$	6.89898	−	11.9494i	0.341133	−	0.590859i	−0.643511	−	0.765437i	$-0.722523\pi$
$409$	6.89898	−	11.9494i	0.341133	−	0.590859i	0.984643	+	0.174578i	$0.0558562\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.00000			−0.0984136
$414$		0			0
$415$	2.89898			0.142305
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	0.241906	+	0.970300i	$0.422227\pi$
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	−0.961257	+	0.275653i	$0.911106\pi$
$420$		0			0
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	−0.997662	−	0.0683385i	$-0.978230\pi$
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	0.439648	−	0.898170i	$-0.355103\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.89898	−	5.02118i	−0.140621	−	0.243563i
$426$		0			0
$427$	−3.27526	+	5.67291i	−0.158501	+	0.274531i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	31.5959			1.52192			0.760961	−	0.648798i	$-0.224728\pi$
$431$	31.5959			1.52192			0.760961	+	0.648798i	$0.224728\pi$
$432$		0			0
$433$	−7.79796			−0.374746			−0.187373	−	0.982289i	$-0.559997\pi$
$433$	−7.79796			−0.374746			−0.187373	+	0.982289i	$0.559997\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.27526	+	2.20881i	−0.0610037	+	0.105662i
$438$		0			0
$439$	1.10102	+	1.90702i	0.0525488	+	0.0910173i	0.891103	−	0.453801i	$-0.149932\pi$
$439$	1.10102	+	1.90702i	0.0525488	+	0.0910173i	−0.838554	+	0.544818i	$0.816599\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.44949	+	12.9029i	0.353936	+	0.613035i	0.986935	−	0.161117i	$-0.0515098\pi$
$443$	7.44949	+	12.9029i	0.353936	+	0.613035i	−0.632999	+	0.774152i	$0.718176\pi$
$444$		0			0
$445$	−12.2474	+	21.2132i	−0.580585	+	1.00560i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.5959			−0.971981			−0.485991	−	0.873964i	$-0.661541\pi$
$449$	−20.5959			−0.971981			−0.485991	+	0.873964i	$0.661541\pi$
$450$		0			0
$451$	−19.5959			−0.922736
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.55051	+	6.14966i	−0.166450	+	0.288301i
$456$		0			0
$457$	8.74745	+	15.1510i	0.409188	+	0.708735i	0.994799	−	0.101857i	$-0.0324785\pi$
$457$	8.74745	+	15.1510i	0.409188	+	0.708735i	−0.585611	+	0.810593i	$0.699145\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.82577	+	4.89437i	0.131609	+	0.227954i	0.924297	−	0.381674i	$-0.124652\pi$
$461$	2.82577	+	4.89437i	0.131609	+	0.227954i	−0.792688	+	0.609628i	$0.791319\pi$
$462$		0			0
$463$	1.84847	−	3.20164i	0.0859057	−	0.148793i	−0.819871	−	0.572548i	$-0.805955\pi$
$463$	1.84847	−	3.20164i	0.0859057	−	0.148793i	0.905777	+	0.423755i	$0.139288\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.0000			0.462745			0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000			0.462745			0.231372	+	0.972865i	$0.425678\pi$
$468$		0			0
$469$	12.8990			0.595620
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.89898	−	11.9494i	0.317215	−	0.549433i
$474$		0			0
$475$	−3.69694	−	6.40329i	−0.169627	−	0.293803i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.79796	−	8.31031i	−0.219224	−	0.379708i	0.735347	−	0.677691i	$-0.237019\pi$
$479$	−4.79796	−	8.31031i	−0.219224	−	0.379708i	−0.954571	+	0.297983i	$0.903686\pi$
$480$		0			0
$481$	−28.8990	+	50.0545i	−1.31768	+	2.28229i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.20204			0.190805
$486$		0			0
$487$	36.3939			1.64916			0.824582	−	0.565742i	$-0.191410\pi$
$487$	36.3939			1.64916			0.824582	+	0.565742i	$0.191410\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.89898	+	13.6814i	−0.356476	+	0.617434i	−0.987369	−	0.158435i	$-0.949355\pi$
$491$	−7.89898	+	13.6814i	−0.356476	+	0.617434i	0.630893	+	0.775869i	$0.282688\pi$
$492$		0			0
$493$	6.89898	+	11.9494i	0.310714	+	0.538173i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.0505103	−	0.0874863i	−0.00226569	−	0.00392430i
$498$		0			0
$499$	−12.6969	+	21.9917i	−0.568393	+	0.984486i	0.428332	+	0.903621i	$0.359101\pi$
$499$	−12.6969	+	21.9917i	−0.568393	+	0.984486i	−0.996725	+	0.0808642i	$0.974232\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.55051	+	6.14966i	−0.157374	+	0.272579i	−0.933921	−	0.357480i	$-0.883636\pi$
$509$	−3.55051	+	6.14966i	−0.157374	+	0.272579i	0.776547	+	0.630059i	$0.216969\pi$
$510$		0			0
$511$	3.44949	+	5.97469i	0.152596	+	0.264305i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.1464	+	17.5741i	0.447105	+	0.774409i
$516$		0			0
$517$	−9.79796	+	16.9706i	−0.430914	+	0.746364i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.30306			0.407575			0.203787	−	0.979015i	$-0.434675\pi$
$521$	9.30306			0.407575			0.203787	+	0.979015i	$0.434675\pi$
$522$		0			0
$523$	14.3485			0.627415			0.313707	−	0.949520i	$-0.398429\pi$
$523$	14.3485			0.627415			0.313707	+	0.949520i	$0.398429\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.0000	+	41.5692i	1.03956	+	1.80056i
$534$		0			0
$535$	8.69694	−	15.0635i	0.376001	−	0.651254i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.00000			0.0861461
$540$		0			0
$541$	−18.4949			−0.795158			−0.397579	−	0.917568i	$-0.630149\pi$
$541$	−18.4949			−0.795158			−0.397579	+	0.917568i	$0.630149\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.20204	+	15.9384i	−0.394172	+	0.682726i
$546$		0			0
$547$	−3.79796	−	6.57826i	−0.162389	−	0.281266i	0.773336	−	0.633996i	$-0.218587\pi$
$547$	−3.79796	−	6.57826i	−0.162389	−	0.281266i	−0.935725	+	0.352730i	$0.885253\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.79796	+	15.2385i	0.374806	+	0.649182i
$552$		0			0
$553$	−0.949490	+	1.64456i	−0.0403764	+	0.0699340i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.8990			0.546547			0.273274	−	0.961936i	$-0.411894\pi$
$557$	12.8990			0.546547			0.273274	+	0.961936i	$0.411894\pi$
$558$		0			0
$559$	−33.7980			−1.42950
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.9722	−	34.5929i	0.841728	−	1.45791i	−0.0467054	−	0.998909i	$-0.514872\pi$
$563$	19.9722	−	34.5929i	0.841728	−	1.45791i	0.888433	−	0.459006i	$-0.151794\pi$
$564$		0			0
$565$	−4.42168	−	7.65858i	−0.186022	−	0.322199i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$	16.8990	−	29.2699i	0.707200	−	1.22491i	−0.258691	−	0.965960i	$-0.583291\pi$
$571$	16.8990	−	29.2699i	0.707200	−	1.22491i	0.965892	−	0.258947i	$-0.0833754\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.89898			0.120896
$576$		0			0
$577$	−15.5959			−0.649267			−0.324633	−	0.945840i	$-0.605241\pi$
$577$	−15.5959			−0.649267			−0.324633	+	0.945840i	$0.605241\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.00000	+	1.73205i	−0.0414870	+	0.0718576i
$582$		0			0
$583$	−10.8990	−	18.8776i	−0.451390	−	0.781830i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	0.649924	−	0.760000i	$-0.274801\pi$
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	−0.983141	+	0.182850i	$0.941468\pi$
$588$		0			0
$589$	−7.65153	+	13.2528i	−0.315276	+	0.546074i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.6969			−0.603531			−0.301765	−	0.953382i	$-0.597576\pi$
$593$	−14.6969			−0.603531			−0.301765	+	0.953382i	$0.597576\pi$
$594$		0			0
$595$	−2.89898			−0.118847
$596$		0			0
$597$		0			0
$598$		0			0
$599$	16.8990	−	29.2699i	0.690474	−	1.19594i	−0.281209	−	0.959646i	$-0.590736\pi$
$599$	16.8990	−	29.2699i	0.690474	−	1.19594i	0.971683	−	0.236289i	$-0.0759312\pi$
$600$		0			0
$601$	−8.34847	−	14.4600i	−0.340541	−	0.589835i	0.643992	−	0.765032i	$-0.277277\pi$
$601$	−8.34847	−	14.4600i	−0.340541	−	0.589835i	−0.984533	+	0.175198i	$0.943944\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.07321	+	8.78706i	0.206255	+	0.357245i
$606$		0			0
$607$	10.3485	−	17.9241i	0.420031	−	0.727516i	−0.575911	−	0.817513i	$-0.695352\pi$
$607$	10.3485	−	17.9241i	0.420031	−	0.727516i	0.995942	+	0.0899969i	$0.0286857\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	48.0000			1.94187
$612$		0			0
$613$	−14.6969			−0.593604			−0.296802	−	0.954939i	$-0.595920\pi$
$613$	−14.6969			−0.593604			−0.296802	+	0.954939i	$0.595920\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.69694	+	13.3315i	−0.309867	+	0.536706i	−0.978333	−	0.207037i	$-0.933618\pi$
$617$	−7.69694	+	13.3315i	−0.309867	+	0.536706i	0.668466	+	0.743743i	$0.266951\pi$
$618$		0			0
$619$	15.0732	+	26.1076i	0.605844	+	1.04935i	0.991918	+	0.126884i	$0.0404976\pi$
$619$	15.0732	+	26.1076i	0.605844	+	1.04935i	−0.386074	+	0.922468i	$0.626169\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.44949	−	14.6349i	−0.338522	−	0.586337i
$624$		0			0
$625$	1.05051	−	1.81954i	0.0420204	−	0.0727815i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−23.5959			−0.940831
$630$		0			0
$631$	−27.8990			−1.11064			−0.555320	−	0.831636i	$-0.687404\pi$
$631$	−27.8990			−1.11064			−0.555320	+	0.831636i	$0.687404\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.17423	+	3.76588i	−0.0862819	+	0.149445i
$636$		0			0
$637$	−2.44949	−	4.24264i	−0.0970523	−	0.168100i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.74745	−	6.49077i	−0.148015	−	0.256370i	0.782479	−	0.622678i	$-0.213955\pi$
$641$	−3.74745	−	6.49077i	−0.148015	−	0.256370i	−0.930494	+	0.366308i	$0.880622\pi$
$642$		0			0
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	0.157022	+	0.987595i	$0.449811\pi$
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	−0.933793	+	0.357812i	$0.883523\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−50.6969			−1.99310			−0.996551	−	0.0829807i	$-0.973556\pi$
$647$	−50.6969			−1.99310			−0.996551	+	0.0829807i	$0.973556\pi$
$648$		0			0
$649$	−4.00000			−0.157014
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.89898	−	8.48528i	0.191712	−	0.332055i	−0.754106	−	0.656753i	$-0.771929\pi$
$653$	4.89898	−	8.48528i	0.191712	−	0.332055i	0.945818	+	0.324698i	$0.105263\pi$
$654$		0			0
$655$	6.19694	+	10.7334i	0.242134	+	0.419389i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.3485	+	21.3882i	0.481028	+	0.833165i	0.999763	−	0.0217701i	$-0.00693018\pi$
$659$	12.3485	+	21.3882i	0.481028	+	0.833165i	−0.518735	+	0.854935i	$0.673597\pi$
$660$		0			0
$661$	−2.27526	+	3.94086i	−0.0884972	+	0.153282i	−0.906876	−	0.421397i	$-0.861540\pi$
$661$	−2.27526	+	3.94086i	−0.0884972	+	0.153282i	0.818379	+	0.574679i	$0.194873\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.69694			−0.143361
$666$		0			0
$667$	−6.89898			−0.267130
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.55051	+	11.3458i	−0.252880	+	0.438000i
$672$		0			0
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	0.936894	−	0.349612i	$-0.113687\pi$
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	−0.771220	+	0.636568i	$0.780353\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.34847	+	12.7279i	0.282425	+	0.489174i	0.971981	−	0.235058i	$-0.0755280\pi$
$677$	7.34847	+	12.7279i	0.282425	+	0.489174i	−0.689557	+	0.724232i	$0.742195\pi$
$678$		0			0
$679$	−1.44949	+	2.51059i	−0.0556263	+	0.0963476i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	51.7980			1.98199			0.990997	−	0.133885i	$-0.0427452\pi$
$683$	51.7980			1.98199			0.990997	+	0.133885i	$0.0427452\pi$
$684$		0			0
$685$	−11.3031			−0.431868
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−26.6969	+	46.2405i	−1.01707	+	1.76162i
$690$		0			0
$691$	25.5227	+	44.2066i	0.970929	+	1.68170i	0.692762	+	0.721167i	$0.256394\pi$
$691$	25.5227	+	44.2066i	0.970929	+	1.68170i	0.278168	+	0.960533i	$0.410273\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.29796	+	5.71223i	0.125099	+	0.216677i
$696$		0			0
$697$	−9.79796	+	16.9706i	−0.371124	+	0.642806i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	7.39388			0.279263			0.139631	−	0.990204i	$-0.455408\pi$
$701$	7.39388			0.279263			0.139631	+	0.990204i	$0.455408\pi$
$702$		0			0
$703$	−30.0908			−1.13490
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.62372	+	14.9367i	−0.324329	+	0.561754i
$708$		0			0
$709$	−13.7980	−	23.8988i	−0.518193	−	0.897537i	−0.999777	−	0.0211367i	$-0.993271\pi$
$709$	−13.7980	−	23.8988i	−0.518193	−	0.897537i	0.481583	−	0.876400i	$-0.340062\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.00000	−	5.19615i	−0.112351	−	0.194597i
$714$		0			0
$715$	−7.10102	+	12.2993i	−0.265563	+	0.459969i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.79796			0.365402			0.182701	−	0.983169i	$-0.441516\pi$
$719$	9.79796			0.365402			0.182701	+	0.983169i	$0.441516\pi$
$720$		0			0
$721$	−14.0000			−0.521387
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.0000	−	17.3205i	0.371391	−	0.643268i
$726$		0			0
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	0.776448	−	0.630181i	$-0.217019\pi$
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	−0.933977	+	0.357333i	$0.883686\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.89898	−	11.9494i	−0.255168	−	0.441964i
$732$		0			0
$733$	8.72474	−	15.1117i	0.322256	−	0.558163i	−0.658697	−	0.752408i	$-0.728892\pi$
$733$	8.72474	−	15.1117i	0.322256	−	0.558163i	0.980953	+	0.194245i	$0.0622255\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.7980			0.950280
$738$		0			0
$739$	−13.5959			−0.500134			−0.250067	−	0.968229i	$-0.580453\pi$
$739$	−13.5959			−0.500134			−0.250067	+	0.968229i	$0.580453\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$		0			0
$745$	−4.34847	−	7.53177i	−0.159316	−	0.275943i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$		0			0
$751$	0.702041	−	1.21597i	0.0256178	−	0.0443714i	−0.852932	−	0.522022i	$-0.825178\pi$
$751$	0.702041	−	1.21597i	0.0256178	−	0.0443714i	0.878550	+	0.477650i	$0.158511\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.24745			0.263762
$756$		0			0
$757$	−35.3939			−1.28641			−0.643206	−	0.765693i	$-0.722396\pi$
$757$	−35.3939			−1.28641			−0.643206	+	0.765693i	$0.722396\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	−0.847331	−	0.531065i	$-0.821792\pi$
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	0.883581	+	0.468278i	$0.155125\pi$
$762$		0			0
$763$	−6.34847	−	10.9959i	−0.229830	−	0.398077i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.89898	+	8.48528i	0.176892	+	0.306386i
$768$		0			0
$769$	17.0454	−	29.5235i	0.614673	−	1.06465i	−0.375769	−	0.926714i	$-0.622621\pi$
$769$	17.0454	−	29.5235i	0.614673	−	1.06465i	0.990442	−	0.137932i	$-0.0440454\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−33.9444			−1.22089			−0.610447	−	0.792057i	$-0.709010\pi$
$773$	−33.9444			−1.22089			−0.610447	+	0.792057i	$0.709010\pi$
$774$		0			0
$775$	17.3939			0.624807
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.4949	+	21.6418i	−0.447676	+	0.775398i
$780$		0			0
$781$	−0.101021	−	0.174973i	−0.00361480	−	0.00626101i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.05051	+	10.4798i	0.215952	+	0.374040i
$786$		0			0
$787$	−5.69694	+	9.86739i	−0.203074	+	0.351734i	−0.949517	−	0.313715i	$-0.898427\pi$
$787$	−5.69694	+	9.86739i	−0.203074	+	0.351734i	0.746443	+	0.665449i	$0.231760\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.10102			0.216927
$792$		0			0
$793$	32.0908			1.13958
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.97219	+	15.5403i	−0.317811	+	0.550465i	−0.980031	−	0.198844i	$-0.936281\pi$
$797$	−8.97219	+	15.5403i	−0.317811	+	0.550465i	0.662220	+	0.749310i	$0.269615\pi$
$798$		0			0
$799$	9.79796	+	16.9706i	0.346627	+	0.600375i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.89898	+	11.9494i	0.243460	+	0.421685i
$804$		0			0
$805$	0.724745	−	1.25529i	0.0255439	−	0.0442433i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16.2020			0.569633			0.284817	−	0.958582i	$-0.408067\pi$
$809$	16.2020			0.569633			0.284817	+	0.958582i	$0.408067\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.3485	+	24.8523i	−0.502605	+	0.870537i
$816$		0			0
$817$	−8.79796	−	15.2385i	−0.307802	−	0.533128i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.202041	+	0.349945i	0.00705128	+	0.0122132i	0.869530	−	0.493881i	$-0.164422\pi$
$821$	0.202041	+	0.349945i	0.00705128	+	0.0122132i	−0.862478	+	0.506094i	$0.831089\pi$
$822$		0			0
$823$	−6.69694	+	11.5994i	−0.233441	+	0.404331i	−0.958818	−	0.284020i	$-0.908332\pi$
$823$	−6.69694	+	11.5994i	−0.233441	+	0.404331i	0.725378	+	0.688351i	$0.241665\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−36.4949			−1.26905			−0.634526	−	0.772902i	$-0.718805\pi$
$827$	−36.4949			−1.26905			−0.634526	+	0.772902i	$0.718805\pi$
$828$		0			0
$829$	1.30306			0.0452572			0.0226286	−	0.999744i	$-0.492796\pi$
$829$	1.30306			0.0452572			0.0226286	+	0.999744i	$0.492796\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.00000	−	1.73205i	0.0346479	−	0.0600120i
$834$		0			0
$835$	7.75255	+	13.4278i	0.268288	+	0.464689i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	0.991907	+	0.126968i	$0.0405245\pi$
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	−0.385996	+	0.922500i	$0.626142\pi$
$840$		0			0
$841$	−9.29796	+	16.1045i	−0.320619	+	0.555329i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	15.9444			0.548504
$846$		0			0
$847$	−7.00000			−0.240523
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.89898	−	10.2173i	0.202214	−	0.350246i
$852$		0			0
$853$	−12.4217	−	21.5150i	−0.425310	−	0.736659i	0.571139	−	0.820853i	$-0.306502\pi$
$853$	−12.4217	−	21.5150i	−0.425310	−	0.736659i	−0.996449	+	0.0841942i	$0.973168\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.4495	−	30.2234i	−0.596063	−	1.03241i	−0.993396	−	0.114737i	$-0.963397\pi$
$857$	−17.4495	−	30.2234i	−0.596063	−	1.03241i	0.397333	−	0.917675i	$-0.369936\pi$
$858$		0			0
$859$	−5.00000	+	8.66025i	−0.170598	+	0.295484i	−0.938629	−	0.344928i	$-0.887903\pi$
$859$	−5.00000	+	8.66025i	−0.170598	+	0.295484i	0.768031	+	0.640412i	$0.221237\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	11.8990			0.405046			0.202523	−	0.979278i	$-0.435086\pi$
$863$	11.8990			0.405046			0.202523	+	0.979278i	$0.435086\pi$
$864$		0			0
$865$	4.49490			0.152831
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.89898	+	3.28913i	−0.0644185	+	0.111576i
$870$		0			0
$871$	−31.5959	−	54.7257i	−1.07059	−	1.85431i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.72474	+	9.91555i	0.193532	+	0.335207i
$876$		0			0
$877$	−11.2474	+	19.4812i	−0.379799	+	0.657832i	−0.991033	−	0.133619i	$-0.957340\pi$
$877$	−11.2474	+	19.4812i	−0.379799	+	0.657832i	0.611233	+	0.791450i	$0.290674\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.5959			−0.660203			−0.330102	−	0.943945i	$-0.607083\pi$
$881$	−19.5959			−0.660203			−0.330102	+	0.943945i	$0.607083\pi$
$882$		0			0
$883$	19.7980			0.666254			0.333127	−	0.942882i	$-0.391896\pi$
$883$	19.7980			0.666254			0.333127	+	0.942882i	$0.391896\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.10102	−	12.2993i	0.238429	−	0.412971i	−0.721835	−	0.692065i	$-0.756701\pi$
$887$	7.10102	−	12.2993i	0.238429	−	0.412971i	0.960264	+	0.279094i	$0.0900343\pi$
$888$		0			0
$889$	−1.50000	−	2.59808i	−0.0503084	−	0.0871367i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	12.4949	+	21.6418i	0.418126	+	0.724215i
$894$		0			0
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−41.3939			−1.38056
$900$		0			0
$901$	−21.7980			−0.726195
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.50000	−	12.9904i	0.249308	−	0.431815i
$906$		0			0
$907$	1.34847	+	2.33562i	0.0447752	+	0.0775529i	0.887544	−	0.460722i	$-0.152410\pi$
$907$	1.34847	+	2.33562i	0.0447752	+	0.0775529i	−0.842769	+	0.538275i	$0.819076\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.9949	−	45.0245i	−0.861249	−	1.49173i	−0.870724	−	0.491773i	$-0.836349\pi$
$911$	−25.9949	−	45.0245i	−0.861249	−	1.49173i	0.00947432	−	0.999955i	$-0.496984\pi$
$912$		0			0
$913$	−2.00000	+	3.46410i	−0.0661903	+	0.114645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.55051			−0.282363
$918$		0			0
$919$	25.6969			0.847664			0.423832	−	0.905741i	$-0.360685\pi$
$919$	25.6969			0.847664			0.423832	+	0.905741i	$0.360685\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.247449	+	0.428594i	−0.00814487	+	0.0141073i
$924$		0			0
$925$	17.1010	+	29.6198i	0.562278	+	0.973894i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.1464	+	29.6985i	0.562556	+	0.974376i	0.997272	+	0.0738083i	$0.0235153\pi$
$929$	17.1464	+	29.6985i	0.562556	+	0.974376i	−0.434716	+	0.900567i	$0.643151\pi$
$930$		0			0
$931$	1.27526	−	2.20881i	0.0417948	−	0.0723907i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.79796			−0.189614
$936$		0			0
$937$	45.5959			1.48955			0.744777	−	0.667314i	$-0.232556\pi$
$937$	45.5959			1.48955			0.744777	+	0.667314i	$0.232556\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.724745	+	1.25529i	−0.0236260	+	0.0409214i	−0.877597	−	0.479400i	$-0.840854\pi$
$941$	−0.724745	+	1.25529i	−0.0236260	+	0.0409214i	0.853971	+	0.520321i	$0.174188\pi$
$942$		0			0
$943$	−4.89898	−	8.48528i	−0.159533	−	0.276319i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26.2474	−	45.4619i	−0.852927	−	1.47731i	−0.878554	−	0.477642i	$-0.841492\pi$
$947$	−26.2474	−	45.4619i	−0.852927	−	1.47731i	0.0256270	−	0.999672i	$-0.491842\pi$
$948$		0			0
$949$	16.8990	−	29.2699i	0.548564	−	0.950141i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	3.39388			0.109938			0.0549692	−	0.998488i	$-0.482494\pi$
$953$	3.39388			0.109938			0.0549692	+	0.998488i	$0.482494\pi$
$954$		0			0
$955$	5.94439			0.192356
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.89898	−	6.75323i	0.125905	−	0.218073i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	12.9722	+	22.4685i	0.417590	+	0.723287i
$966$		0			0
$967$	12.2980	−	21.3007i	0.395476	−	0.684984i	−0.597686	−	0.801730i	$-0.703913\pi$
$967$	12.2980	−	21.3007i	0.395476	−	0.684984i	0.993162	+	0.116746i	$0.0372464\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.0556128			−0.00178470			−0.000892350	−	1.00000i	$-0.500284\pi$
$971$	−0.0556128			−0.00178470			−0.000892350		1.00000i	$0.500284\pi$
$972$		0			0
$973$	−4.55051			−0.145883
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.7980	+	32.5590i	−0.601400	+	1.04166i	0.391209	+	0.920302i	$0.372057\pi$
$977$	−18.7980	+	32.5590i	−0.601400	+	1.04166i	−0.992609	+	0.121354i	$0.961276\pi$
$978$		0			0
$979$	−16.8990	−	29.2699i	−0.540094	−	0.935470i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.5959	+	28.7450i	0.529328	+	0.916822i	0.999415	+	0.0342024i	$0.0108891\pi$
$983$	16.5959	+	28.7450i	0.529328	+	0.916822i	−0.470087	+	0.882620i	$0.655778\pi$
$984$		0			0
$985$	12.1010	−	20.9596i	0.385571	−	0.667828i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	6.89898			0.219375
$990$		0			0
$991$	1.79796			0.0571140			0.0285570	−	0.999592i	$-0.490909\pi$
$991$	1.79796			0.0571140			0.0285570	+	0.999592i	$0.490909\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.10102	+	3.63907i	−0.0666068	+	0.115366i
$996$		0			0
$997$	−26.0732	−	45.1601i	−0.825747	−	1.43024i	−0.901347	−	0.433097i	$-0.857421\pi$
$997$	−26.0732	−	45.1601i	−0.825747	−	1.43024i	0.0756001	−	0.997138i	$-0.475913\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.r.e.1009.1		4
3.2	odd	2		1008.2.r.e.337.2		4
4.3	odd	2		378.2.f.d.253.1		4
9.2	odd	6		1008.2.r.e.673.1		4
9.4	even	3		9072.2.a.bd.1.2		2
9.5	odd	6		9072.2.a.bk.1.1		2
9.7	even	3	inner	3024.2.r.e.2017.1		4
12.11	even	2		126.2.f.c.85.1	yes	4
28.3	even	6		2646.2.e.k.1549.2		4
28.11	odd	6		2646.2.e.l.1549.1		4
28.19	even	6		2646.2.h.n.361.1		4
28.23	odd	6		2646.2.h.m.361.2		4
28.27	even	2		2646.2.f.k.1765.2		4
36.7	odd	6		378.2.f.d.127.1		4
36.11	even	6		126.2.f.c.43.2	✓	4
36.23	even	6		1134.2.a.p.1.1		2
36.31	odd	6		1134.2.a.i.1.2		2
84.11	even	6		882.2.e.m.373.1		4
84.23	even	6		882.2.h.k.67.2		4
84.47	odd	6		882.2.h.l.67.1		4
84.59	odd	6		882.2.e.n.373.2		4
84.83	odd	2		882.2.f.j.589.2		4
252.11	even	6		882.2.h.k.79.2		4
252.47	odd	6		882.2.e.n.655.2		4
252.79	odd	6		2646.2.e.l.2125.1		4
252.83	odd	6		882.2.f.j.295.1		4
252.115	even	6		2646.2.h.n.667.1		4
252.139	even	6		7938.2.a.bm.1.1		2
252.151	odd	6		2646.2.h.m.667.2		4
252.167	odd	6		7938.2.a.bn.1.2		2
252.187	even	6		2646.2.e.k.2125.2		4
252.191	even	6		882.2.e.m.655.1		4
252.223	even	6		2646.2.f.k.883.2		4
252.227	odd	6		882.2.h.l.79.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	36.11	even	6
126.2.f.c.85.1	yes	4	12.11	even	2
378.2.f.d.127.1		4	36.7	odd	6
378.2.f.d.253.1		4	4.3	odd	2
882.2.e.m.373.1		4	84.11	even	6
882.2.e.m.655.1		4	252.191	even	6
882.2.e.n.373.2		4	84.59	odd	6
882.2.e.n.655.2		4	252.47	odd	6
882.2.f.j.295.1		4	252.83	odd	6
882.2.f.j.589.2		4	84.83	odd	2
882.2.h.k.67.2		4	84.23	even	6
882.2.h.k.79.2		4	252.11	even	6
882.2.h.l.67.1		4	84.47	odd	6
882.2.h.l.79.1		4	252.227	odd	6
1008.2.r.e.337.2		4	3.2	odd	2
1008.2.r.e.673.1		4	9.2	odd	6
1134.2.a.i.1.2		2	36.31	odd	6
1134.2.a.p.1.1		2	36.23	even	6
2646.2.e.k.1549.2		4	28.3	even	6
2646.2.e.k.2125.2		4	252.187	even	6
2646.2.e.l.1549.1		4	28.11	odd	6
2646.2.e.l.2125.1		4	252.79	odd	6
2646.2.f.k.883.2		4	252.223	even	6
2646.2.f.k.1765.2		4	28.27	even	2
2646.2.h.m.361.2		4	28.23	odd	6
2646.2.h.m.667.2		4	252.151	odd	6
2646.2.h.n.361.1		4	28.19	even	6
2646.2.h.n.667.1		4	252.115	even	6
3024.2.r.e.1009.1		4	1.1	even	1	trivial
3024.2.r.e.2017.1		4	9.7	even	3	inner
7938.2.a.bm.1.1		2	252.139	even	6
7938.2.a.bn.1.2		2	252.167	odd	6
9072.2.a.bd.1.2		2	9.4	even	3
9072.2.a.bk.1.1		2	9.5	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.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.724745 + 1.25529i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-0.724745 + 1.25529i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{13} -2.00000 q^{17} -2.55051 q^{19} +(0.500000 - 0.866025i) q^{23} +(1.44949 + 2.51059i) q^{25} +(-3.44949 - 5.97469i) q^{29} +(3.00000 - 5.19615i) q^{31} +1.44949 q^{35} +11.7980 q^{37} +(4.89898 - 8.48528i) q^{41} +(3.44949 + 5.97469i) q^{43} +(-4.89898 - 8.48528i) q^{47} +(-0.500000 + 0.866025i) q^{49} +10.8990 q^{53} +2.89898 q^{55} +(1.00000 - 1.73205i) q^{59} +(-3.27526 - 5.67291i) q^{61} +(-3.55051 - 6.14966i) q^{65} +(-6.44949 + 11.1708i) q^{67} +0.101021 q^{71} -6.89898 q^{73} +(-1.00000 + 1.73205i) q^{77} +(-0.949490 - 1.64456i) q^{79} +(-1.00000 - 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +16.8990 q^{89} +4.89898 q^{91} +(1.84847 - 3.20164i) q^{95} +(-1.44949 - 2.51059i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{5} - 2 q^{7} - 4 q^{11} - 8 q^{17} - 20 q^{19} + 2 q^{23} - 4 q^{25} - 4 q^{29} + 12 q^{31} - 4 q^{35} + 8 q^{37} + 4 q^{43} - 2 q^{49} + 24 q^{53} - 8 q^{55} + 4 q^{59} - 18 q^{61} - 24 q^{65} - 16 q^{67} + 20 q^{71} - 8 q^{73} - 4 q^{77} + 6 q^{79} - 4 q^{83} - 4 q^{85} + 48 q^{89} - 22 q^{95} + 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^11 - 8 * q^17 - 20 * q^19 + 2 * q^23 - 4 * q^25 - 4 * q^29 + 12 * q^31 - 4 * q^35 + 8 * q^37 + 4 * q^43 - 2 * q^49 + 24 * q^53 - 8 * q^55 + 4 * q^59 - 18 * q^61 - 24 * q^65 - 16 * q^67 + 20 * q^71 - 8 * q^73 - 4 * q^77 + 6 * q^79 - 4 * q^83 - 4 * q^85 + 48 * q^89 - 22 * q^95 + 4 * q^97

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