LMFDB - Embedded newform 504.2.bl.a.89.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(17,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("504.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bl (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.6
Root			$-0.587308 + 2.01725i$ of defining polynomial
Character	$\chi$	$=$	504.89
Dual form			504.2.bl.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587308 - 1.01725i) q^{5} +(2.35282 + 1.21006i) q^{7} +O(q^{10})$	$q+(0.587308 - 1.01725i) q^{5} +(2.35282 + 1.21006i) q^{7} +(1.44725 - 0.835571i) q^{11} +1.14525i q^{13} +(-2.07609 - 3.59589i) q^{17} +(1.83453 + 1.05917i) q^{19} +(4.22379 + 2.43860i) q^{23} +(1.81014 + 3.13525i) q^{25} -8.32591i q^{29} +(7.18124 - 4.14609i) q^{31} +(2.61276 - 1.68272i) q^{35} +(-2.19996 + 3.81045i) q^{37} -2.67577 q^{41} +4.08536 q^{43} +(-1.75282 + 3.03597i) q^{47} +(4.07150 + 5.69411i) q^{49} +(-1.59764 + 0.922398i) q^{53} -1.96295i q^{55} +(2.98667 + 5.17306i) q^{59} +(-12.8011 - 7.39071i) q^{61} +(1.16500 + 0.672614i) q^{65} +(-4.22435 - 7.31679i) q^{67} +5.48320i q^{71} +(0.846715 - 0.488851i) q^{73} +(4.41621 - 0.214682i) q^{77} +(-5.56097 + 9.63187i) q^{79} -10.2258 q^{83} -4.87721 q^{85} +(-6.29987 + 10.9117i) q^{89} +(-1.38582 + 2.69456i) q^{91} +(2.15487 - 1.24411i) q^{95} -9.52049i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 12 q^{19} + 12 q^{25} + 24 q^{31} + 4 q^{37} + 8 q^{43} + 32 q^{49} - 28 q^{67} - 60 q^{73} - 32 q^{79} - 32 q^{85} - 84 q^{91}+O(q^{100}) $ 16 * q - 8 * q^7 + 12 * q^19 + 12 * q^25 + 24 * q^31 + 4 * q^37 + 8 * q^43 + 32 * q^49 - 28 * q^67 - 60 * q^73 - 32 * q^79 - 32 * q^85 - 84 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

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
$5$	0.587308	−	1.01725i	0.262652	−	0.454926i	−0.704294	−	0.709909i	$-0.748736\pi$
$5$	0.587308	−	1.01725i	0.262652	−	0.454926i	0.966946	+	0.254982i	$0.0820696\pi$
$6$		0			0
$7$	2.35282	+	1.21006i	0.889281	+	0.457361i
$7$	2.35282	+	1.21006i	0.889281	+	0.457361i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.44725	−	0.835571i	0.436363	−	0.251934i	−0.265691	−	0.964058i	$-0.585600\pi$
$11$	1.44725	−	0.835571i	0.436363	−	0.251934i	0.702054	+	0.712124i	$0.252267\pi$
$12$		0			0
$13$			1.14525i			0.317635i	0.987308	+	0.158818i	$0.0507682\pi$
$13$			1.14525i			0.317635i	−0.987308	+	0.158818i	$0.949232\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.07609	−	3.59589i	−0.503525	−	0.872131i	−0.999992	−	0.00407535i	$-0.998703\pi$
$17$	−2.07609	−	3.59589i	−0.503525	−	0.872131i	0.496466	−	0.868056i	$-0.334631\pi$
$18$		0			0
$19$	1.83453	+	1.05917i	0.420870	+	0.242989i	0.695449	−	0.718575i	$-0.255205\pi$
$19$	1.83453	+	1.05917i	0.420870	+	0.242989i	−0.274579	+	0.961564i	$0.588539\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.22379	+	2.43860i	0.880720	+	0.508484i	0.870896	−	0.491468i	$-0.163539\pi$
$23$	4.22379	+	2.43860i	0.880720	+	0.508484i	0.00982439	+	0.999952i	$0.496873\pi$
$24$		0			0
$25$	1.81014	+	3.13525i	0.362028	+	0.627051i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	8.32591i		−	1.54608i	−0.634355	−	0.773042i	$-0.718734\pi$
$29$		−	8.32591i		−	1.54608i	0.634355	−	0.773042i	$-0.281266\pi$
$30$		0			0
$31$	7.18124	−	4.14609i	1.28979	−	0.744660i	0.311173	−	0.950353i	$-0.399278\pi$
$31$	7.18124	−	4.14609i	1.28979	−	0.744660i	0.978617	+	0.205693i	$0.0659448\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.61276	−	1.68272i	0.441637	−	0.284431i
$36$		0			0
$37$	−2.19996	+	3.81045i	−0.361672	+	0.626434i	−0.988236	−	0.152936i	$-0.951127\pi$
$37$	−2.19996	+	3.81045i	−0.361672	+	0.626434i	0.626564	+	0.779370i	$0.284461\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.67577			−0.417885			−0.208942	−	0.977928i	$-0.567002\pi$
$41$	−2.67577			−0.417885			−0.208942	+	0.977928i	$0.567002\pi$
$42$		0			0
$43$	4.08536			0.623011			0.311505	−	0.950244i	$-0.399167\pi$
$43$	4.08536			0.623011			0.311505	+	0.950244i	$0.399167\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.75282	+	3.03597i	−0.255674	+	0.442841i	−0.965078	−	0.261961i	$-0.915631\pi$
$47$	−1.75282	+	3.03597i	−0.255674	+	0.442841i	0.709404	+	0.704802i	$0.248964\pi$
$48$		0			0
$49$	4.07150	+	5.69411i	0.581643	+	0.813444i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.59764	+	0.922398i	−0.219453	+	0.126701i	−0.605697	−	0.795695i	$-0.707106\pi$
$53$	−1.59764	+	0.922398i	−0.219453	+	0.126701i	0.386244	+	0.922397i	$0.373772\pi$
$54$		0			0
$55$		−	1.96295i		−	0.264684i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.98667	+	5.17306i	0.388831	+	0.673475i	0.992293	−	0.123917i	$-0.0395457\pi$
$59$	2.98667	+	5.17306i	0.388831	+	0.673475i	−0.603462	+	0.797392i	$0.706212\pi$
$60$		0			0
$61$	−12.8011	−	7.39071i	−1.63901	−	0.946284i	−0.981174	−	0.193124i	$-0.938138\pi$
$61$	−12.8011	−	7.39071i	−1.63901	−	0.946284i	−0.657838	−	0.753160i	$-0.728529\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.16500	+	0.672614i	0.144501	+	0.0834275i
$66$		0			0
$67$	−4.22435	−	7.31679i	−0.516087	−	0.893889i	−0.999826	−	0.0186762i	$-0.994055\pi$
$67$	−4.22435	−	7.31679i	−0.516087	−	0.893889i	0.483739	−	0.875212i	$-0.339279\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.48320i			0.650736i	0.945587	+	0.325368i	$0.105488\pi$
$71$			5.48320i			0.650736i	−0.945587	+	0.325368i	$0.894512\pi$
$72$		0			0
$73$	0.846715	−	0.488851i	0.0991004	−	0.0572157i	−0.449631	−	0.893215i	$-0.648444\pi$
$73$	0.846715	−	0.488851i	0.0991004	−	0.0572157i	0.548731	+	0.835999i	$0.315111\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.41621	−	0.214682i	0.503274	−	0.0244652i
$78$		0			0
$79$	−5.56097	+	9.63187i	−0.625657	+	1.08367i	0.362756	+	0.931884i	$0.381836\pi$
$79$	−5.56097	+	9.63187i	−0.625657	+	1.08367i	−0.988413	+	0.151786i	$0.951497\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10.2258			−1.12242			−0.561212	−	0.827672i	$-0.689665\pi$
$83$	−10.2258			−1.12242			−0.561212	+	0.827672i	$0.689665\pi$
$84$		0			0
$85$	−4.87721			−0.529007
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.29987	+	10.9117i	−0.667785	+	1.15664i	0.310737	+	0.950496i	$0.399424\pi$
$89$	−6.29987	+	10.9117i	−0.667785	+	1.15664i	−0.978522	+	0.206142i	$0.933909\pi$
$90$		0			0
$91$	−1.38582	+	2.69456i	−0.145274	+	0.282467i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.15487	−	1.24411i	0.221085	−	0.127643i
$96$		0			0
$97$		−	9.52049i		−	0.966660i	−0.875438	−	0.483330i	$-0.839427\pi$
$97$		−	9.52049i		−	0.966660i	0.875438	−	0.483330i	$-0.160573\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.65944	−	16.7306i	−0.961150	−	1.66476i	−0.719621	−	0.694367i	$-0.755685\pi$
$101$	−9.65944	−	16.7306i	−0.961150	−	1.66476i	−0.241528	−	0.970394i	$-0.577649\pi$
$102$		0			0
$103$	−13.0730	−	7.54769i	−1.28812	−	0.743696i	−0.309801	−	0.950801i	$-0.600262\pi$
$103$	−13.0730	−	7.54769i	−1.28812	−	0.743696i	−0.978319	+	0.207105i	$0.933596\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.46986	+	5.46743i	0.915486	+	0.528556i	0.882192	−	0.470890i	$-0.156067\pi$
$107$	9.46986	+	5.46743i	0.915486	+	0.528556i	0.0332936	+	0.999446i	$0.489400\pi$
$108$		0			0
$109$	−3.25885	−	5.64449i	−0.312141	−	0.540644i	0.666685	−	0.745340i	$-0.267713\pi$
$109$	−3.25885	−	5.64449i	−0.312141	−	0.540644i	−0.978826	+	0.204696i	$0.934379\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			10.8743i			1.02296i	0.859294	+	0.511482i	$0.170903\pi$
$113$			10.8743i			1.02296i	−0.859294	+	0.511482i	$0.829097\pi$
$114$		0			0
$115$	4.96132	−	2.86442i	0.462646	−	0.267109i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.533405	−	10.9727i	−0.0488972	−	1.00586i
$120$		0			0
$121$	−4.10364	+	7.10772i	−0.373058	+	0.646156i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.1255			0.905653
$126$		0			0
$127$	−1.56264			−0.138662			−0.0693308	−	0.997594i	$-0.522086\pi$
$127$	−1.56264			−0.138662			−0.0693308	+	0.997594i	$0.522086\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.2969	+	17.8347i	−0.899642	+	1.55823i	−0.0716899	+	0.997427i	$0.522839\pi$
$131$	−10.2969	+	17.8347i	−0.899642	+	1.55823i	−0.827952	+	0.560799i	$0.810494\pi$
$132$		0			0
$133$	3.03466	+	4.71192i	0.263138	+	0.408575i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−18.4299	+	10.6405i	−1.57457	+	0.909078i	−0.578972	+	0.815348i	$0.696546\pi$
$137$	−18.4299	+	10.6405i	−1.57457	+	0.909078i	−0.995598	+	0.0937303i	$0.970121\pi$
$138$		0			0
$139$		−	6.50746i		−	0.551955i	−0.961164	−	0.275978i	$-0.910998\pi$
$139$		−	6.50746i		−	0.551955i	0.961164	−	0.275978i	$-0.0890016\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.956937	+	1.65746i	0.0800231	+	0.138604i
$144$		0			0
$145$	−8.46951	−	4.88987i	−0.703354	−	0.406082i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.4565	+	7.19178i	1.02048	+	0.589173i	0.914242	−	0.405168i	$-0.132787\pi$
$149$	12.4565	+	7.19178i	1.02048	+	0.589173i	0.106236	+	0.994341i	$0.466120\pi$
$150$		0			0
$151$	−5.12846	−	8.88276i	−0.417348	−	0.722869i	0.578323	−	0.815808i	$-0.303707\pi$
$151$	−5.12846	−	8.88276i	−0.417348	−	0.722869i	−0.995672	+	0.0929389i	$0.970374\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	9.74013i		−	0.782346i
$156$		0			0
$157$	0.399926	−	0.230897i	0.0319176	−	0.0184276i	−0.483956	−	0.875092i	$-0.660801\pi$
$157$	0.399926	−	0.230897i	0.0319176	−	0.0184276i	0.515874	+	0.856665i	$0.327467\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.98693	+	10.8486i	0.550648	+	0.854992i
$162$		0			0
$163$	−11.1644	+	19.3374i	−0.874467	+	1.51462i	−0.0171370	+	0.999853i	$0.505455\pi$
$163$	−11.1644	+	19.3374i	−0.874467	+	1.51462i	−0.857330	+	0.514768i	$0.827878\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.42604			−0.419879			−0.209940	−	0.977714i	$-0.567327\pi$
$167$	−5.42604			−0.419879			−0.209940	+	0.977714i	$0.567327\pi$
$168$		0			0
$169$	11.6884			0.899108
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.75719	−	8.23970i	0.361683	−	0.626453i	−0.626555	−	0.779377i	$-0.715536\pi$
$173$	4.75719	−	8.23970i	0.361683	−	0.626453i	0.988238	+	0.152924i	$0.0488691\pi$
$174$		0			0
$175$	0.465076	+	9.56706i	0.0351564	+	0.723202i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.95968	−	1.13142i	0.146474	−	0.0845665i	−0.424972	−	0.905206i	$-0.639716\pi$
$179$	1.95968	−	1.13142i	0.146474	−	0.0845665i	0.571446	+	0.820640i	$0.306383\pi$
$180$		0			0
$181$		−	21.7987i		−	1.62029i	−0.586231	−	0.810144i	$-0.699389\pi$
$181$		−	21.7987i		−	1.62029i	0.586231	−	0.810144i	$-0.300611\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.58411	+	4.47581i	0.189988	+	0.329068i
$186$		0			0
$187$	−6.00924	−	3.46944i	−0.439439	−	0.253710i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.8301	−	10.8716i	−1.36250	−	0.786638i	−0.372541	−	0.928016i	$-0.621513\pi$
$191$	−18.8301	−	10.8716i	−1.36250	−	0.786638i	−0.989956	+	0.141378i	$0.954847\pi$
$192$		0			0
$193$	10.8259	+	18.7510i	0.779266	+	1.34973i	0.932365	+	0.361518i	$0.117741\pi$
$193$	10.8259	+	18.7510i	0.779266	+	1.34973i	−0.153099	+	0.988211i	$0.548925\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.58787i		−	0.398119i	−0.979987	−	0.199060i	$-0.936211\pi$
$197$		−	5.58787i		−	0.398119i	0.979987	−	0.199060i	$-0.0637887\pi$
$198$		0			0
$199$	14.2081	−	8.20308i	1.00719	−	0.581501i	0.0968215	−	0.995302i	$-0.469132\pi$
$199$	14.2081	−	8.20308i	1.00719	−	0.581501i	0.910367	+	0.413801i	$0.135799\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.0749	−	19.5894i	0.707118	−	1.37490i
$204$		0			0
$205$	−1.57150	+	2.72192i	−0.109758	+	0.190107i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.54003			0.244869
$210$		0			0
$211$	8.11777			0.558850			0.279425	−	0.960168i	$-0.409856\pi$
$211$	8.11777			0.558850			0.279425	+	0.960168i	$0.409856\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.39936	−	4.15581i	0.163635	−	0.283424i
$216$		0			0
$217$	21.9132	−	1.06525i	1.48756	−	0.0723138i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.11819	−	2.37764i	0.277020	−	0.159937i
$222$		0			0
$223$			21.1486i			1.41621i	0.706105	+	0.708107i	$0.250451\pi$
$223$			21.1486i			1.41621i	−0.706105	+	0.708107i	$0.749549\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.7990	−	20.4365i	−0.783130	−	1.35642i	−0.930110	−	0.367281i	$-0.880289\pi$
$227$	−11.7990	−	20.4365i	−0.783130	−	1.35642i	0.146980	−	0.989139i	$-0.453045\pi$
$228$		0			0
$229$	−0.969507	−	0.559745i	−0.0640668	−	0.0369890i	0.467624	−	0.883927i	$-0.345110\pi$
$229$	−0.969507	−	0.559745i	−0.0640668	−	0.0369890i	−0.531691	+	0.846938i	$0.678443\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.9299	+	12.0839i	1.37116	+	0.791642i	0.991075	−	0.133309i	$-0.0425601\pi$
$233$	20.9299	+	12.0839i	1.37116	+	0.791642i	0.380089	+	0.924950i	$0.375893\pi$
$234$		0			0
$235$	2.05888	+	3.56609i	0.134307	+	0.232626i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	0.484062i		−	0.0313114i	−0.999877	−	0.0156557i	$-0.995016\pi$
$239$		−	0.484062i		−	0.0313114i	0.999877	−	0.0156557i	$-0.00498356\pi$
$240$		0			0
$241$	11.3783	−	6.56924i	0.732938	−	0.423162i	−0.0865578	−	0.996247i	$-0.527587\pi$
$241$	11.3783	−	6.56924i	0.732938	−	0.423162i	0.819496	+	0.573085i	$0.194253\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.18354	−	0.797524i	0.522827	−	0.0509519i
$246$		0			0
$247$	−1.21301	+	2.10099i	−0.0771820	+	0.133683i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−13.4221			−0.847193			−0.423597	−	0.905851i	$-0.639233\pi$
$251$	−13.4221			−0.847193			−0.423597	+	0.905851i	$0.639233\pi$
$252$		0			0
$253$	8.15051			0.512418
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.22980	+	9.05827i	−0.326226	+	0.565040i	−0.981760	−	0.190126i	$-0.939110\pi$
$257$	−5.22980	+	9.05827i	−0.326226	+	0.565040i	0.655534	+	0.755166i	$0.272444\pi$
$258$		0			0
$259$	−9.78699	+	6.30320i	−0.608134	+	0.391662i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.4998	−	11.8356i	1.26407	−	0.729813i	0.290214	−	0.956962i	$-0.406274\pi$
$263$	20.4998	−	11.8356i	1.26407	−	0.729813i	0.973860	+	0.227148i	$0.0729402\pi$
$264$		0			0
$265$			2.16693i			0.133113i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.05065	−	15.6762i	−0.551828	−	0.955794i	−0.998143	−	0.0609178i	$-0.980597\pi$
$269$	−9.05065	−	15.6762i	−0.551828	−	0.955794i	0.446315	−	0.894876i	$-0.352736\pi$
$270$		0			0
$271$	5.79002	+	3.34287i	0.351718	+	0.203065i	0.665442	−	0.746450i	$-0.268243\pi$
$271$	5.79002	+	3.34287i	0.351718	+	0.203065i	−0.313723	+	0.949514i	$0.601576\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.23945	+	3.02500i	0.315951	+	0.182414i
$276$		0			0
$277$	1.72478	+	2.98741i	0.103632	+	0.179496i	0.913179	−	0.407560i	$-0.133620\pi$
$277$	1.72478	+	2.98741i	0.103632	+	0.179496i	−0.809546	+	0.587056i	$0.800287\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	9.58198i		−	0.571613i	−0.958287	−	0.285807i	$-0.907739\pi$
$281$		−	9.58198i		−	0.571613i	0.958287	−	0.285807i	$-0.0922615\pi$
$282$		0			0
$283$	7.02161	−	4.05393i	0.417391	−	0.240981i	−0.276569	−	0.960994i	$-0.589198\pi$
$283$	7.02161	−	4.05393i	0.417391	−	0.240981i	0.693961	+	0.720013i	$0.255864\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.29559	−	3.23785i	−0.371617	−	0.191124i
$288$		0			0
$289$	−0.120279	+	0.208330i	−0.00707526	+	0.0122547i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.9122			0.754339			0.377170	−	0.926144i	$-0.376897\pi$
$293$	12.9122			0.754339			0.377170	+	0.926144i	$0.376897\pi$
$294$		0			0
$295$	7.01637			0.408509
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.79281	+	4.83729i	−0.161512	+	0.279748i
$300$		0			0
$301$	9.61209	+	4.94353i	0.554032	+	0.284941i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−15.0364	+	8.68124i	−0.860979	+	0.497087i
$306$		0			0
$307$			11.9163i			0.680099i	0.940408	+	0.340049i	$0.110444\pi$
$307$			11.9163i			0.680099i	−0.940408	+	0.340049i	$0.889556\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.3295	+	26.5516i	0.869259	+	1.50560i	0.862755	+	0.505622i	$0.168737\pi$
$311$	15.3295	+	26.5516i	0.869259	+	1.50560i	0.00650358	+	0.999979i	$0.497930\pi$
$312$		0			0
$313$	8.14799	+	4.70425i	0.460552	+	0.265900i	0.712276	−	0.701899i	$-0.247664\pi$
$313$	8.14799	+	4.70425i	0.460552	+	0.265900i	−0.251724	+	0.967799i	$0.580998\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.23712	+	0.714251i	0.0694835	+	0.0401163i	0.534339	−	0.845270i	$-0.320560\pi$
$317$	1.23712	+	0.714251i	0.0694835	+	0.0401163i	−0.464856	+	0.885386i	$0.653894\pi$
$318$		0			0
$319$	−6.95689	−	12.0497i	−0.389511	−	0.674653i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	8.79569i		−	0.489405i
$324$		0			0
$325$	−3.59065	+	2.07306i	−0.199173	+	0.114993i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.79776	+	5.02206i	−0.429904	+	0.276875i
$330$		0			0
$331$	7.20798	−	12.4846i	0.396187	−	0.686215i	−0.597065	−	0.802193i	$-0.703667\pi$
$331$	7.20798	−	12.4846i	0.396187	−	0.686215i	0.993252	+	0.115977i	$0.0370000\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.92398			−0.542205
$336$		0			0
$337$	3.62914			0.197692			0.0988460	−	0.995103i	$-0.468485\pi$
$337$	3.62914			0.197692			0.0988460	+	0.995103i	$0.468485\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.92871	−	12.0009i	0.375211	−	0.649884i
$342$		0			0
$343$	2.68927	+	18.3240i	0.145207	+	0.989401i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	25.7433	−	14.8629i	1.38197	−	0.797883i	0.389581	−	0.920992i	$-0.372620\pi$
$347$	25.7433	−	14.8629i	1.38197	−	0.797883i	0.992393	+	0.123109i	$0.0392864\pi$
$348$		0			0
$349$		−	5.41027i		−	0.289605i	−0.989461	−	0.144802i	$-0.953745\pi$
$349$		−	5.41027i		−	0.289605i	0.989461	−	0.144802i	$-0.0462547\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.02520	−	12.1680i	−0.373914	−	0.647637i	0.616250	−	0.787550i	$-0.288651\pi$
$353$	−7.02520	−	12.1680i	−0.373914	−	0.647637i	−0.990164	+	0.139913i	$0.955318\pi$
$354$		0			0
$355$	5.57777	+	3.22032i	0.296037	+	0.170917i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.69438	−	3.86500i	−0.353316	−	0.203987i	0.312829	−	0.949810i	$-0.398723\pi$
$359$	−6.69438	−	3.86500i	−0.353316	−	0.203987i	−0.666145	+	0.745823i	$0.732057\pi$
$360$		0			0
$361$	−7.25633	−	12.5683i	−0.381912	−	0.661491i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	1.14842i		−	0.0601112i
$366$		0			0
$367$	6.80239	−	3.92736i	0.355082	−	0.205006i	−0.311839	−	0.950135i	$-0.600945\pi$
$367$	6.80239	−	3.92736i	0.355082	−	0.205006i	0.666921	+	0.745128i	$0.267612\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.87512	+	0.236990i	−0.253103	+	0.0123039i
$372$		0			0
$373$	−3.94428	+	6.83169i	−0.204227	+	0.353731i	−0.949886	−	0.312596i	$-0.898801\pi$
$373$	−3.94428	+	6.83169i	−0.204227	+	0.353731i	0.745659	+	0.666327i	$0.232135\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.53525			0.491090
$378$		0			0
$379$	−11.9349			−0.613052			−0.306526	−	0.951862i	$-0.599167\pi$
$379$	−11.9349			−0.613052			−0.306526	+	0.951862i	$0.599167\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.35936	+	2.35449i	−0.0694603	+	0.120309i	−0.898664	−	0.438638i	$-0.855461\pi$
$383$	−1.35936	+	2.35449i	−0.0694603	+	0.120309i	0.829204	+	0.558947i	$0.188794\pi$
$384$		0			0
$385$	2.37529	−	4.61846i	0.121056	−	0.235378i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.2510	+	9.95985i	−0.874659	+	0.504984i	−0.868894	−	0.494999i	$-0.835168\pi$
$389$	−17.2510	+	9.95985i	−0.874659	+	0.504984i	−0.00576514	+	0.999983i	$0.501835\pi$
$390$		0			0
$391$		−	20.2510i		−	1.02414i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.53199	+	11.3137i	0.328660	+	0.569256i
$396$		0			0
$397$	−14.5532	−	8.40230i	−0.730405	−	0.421699i	0.0881655	−	0.996106i	$-0.471900\pi$
$397$	−14.5532	−	8.40230i	−0.730405	−	0.421699i	−0.818570	+	0.574406i	$0.805233\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.31347	−	4.22244i	−0.365217	−	0.210858i	0.306150	−	0.951983i	$-0.400959\pi$
$401$	−7.31347	−	4.22244i	−0.365217	−	0.210858i	−0.671367	+	0.741125i	$0.734293\pi$
$402$		0			0
$403$	4.74831	+	8.22432i	0.236530	+	0.409682i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			7.35290i			0.364470i
$408$		0			0
$409$	−21.5958	+	12.4684i	−1.06785	+	0.616521i	−0.927592	−	0.373595i	$-0.878125\pi$
$409$	−21.5958	+	12.4684i	−1.06785	+	0.616521i	−0.140253	+	0.990116i	$0.544792\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.767359	+	15.7853i	0.0377593	+	0.776745i
$414$		0			0
$415$	−6.00567	+	10.4021i	−0.294807	+	0.510620i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−32.2386			−1.57496			−0.787480	−	0.616340i	$-0.788615\pi$
$419$	−32.2386			−1.57496			−0.787480	+	0.616340i	$0.788615\pi$
$420$		0			0
$421$	−36.4958			−1.77869			−0.889347	−	0.457232i	$-0.848841\pi$
$421$	−36.4958			−1.77869			−0.889347	+	0.457232i	$0.848841\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.51602	−	13.0181i	0.364580	−	0.631472i
$426$		0			0
$427$	−21.1754	−	32.8791i	−1.02475	−	1.59113i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.1694	+	9.33541i	−0.778853	+	0.449671i	−0.836023	−	0.548694i	$-0.815125\pi$
$431$	−16.1694	+	9.33541i	−0.778853	+	0.449671i	0.0571709	+	0.998364i	$0.481792\pi$
$432$		0			0
$433$			12.4261i			0.597163i	0.954384	+	0.298581i	$0.0965134\pi$
$433$			12.4261i			0.597163i	−0.954384	+	0.298581i	$0.903487\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.16577	+	8.94738i	0.247112	+	0.428011i
$438$		0			0
$439$	−17.2673	−	9.96928i	−0.824123	−	0.475808i	0.0277131	−	0.999616i	$-0.491178\pi$
$439$	−17.2673	−	9.96928i	−0.824123	−	0.475808i	−0.851836	+	0.523808i	$0.824511\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.3854	+	14.6563i	1.20610	+	0.696340i	0.961904	−	0.273387i	$-0.0881440\pi$
$443$	25.3854	+	14.6563i	1.20610	+	0.696340i	0.244192	+	0.969727i	$0.421477\pi$
$444$		0			0
$445$	7.39993	+	12.8170i	0.350790	+	0.607586i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.58492i			0.169183i	0.996416	+	0.0845915i	$0.0269585\pi$
$449$			3.58492i			0.169183i	−0.996416	+	0.0845915i	$0.973041\pi$
$450$		0			0
$451$	−3.87251	+	2.23579i	−0.182349	+	0.105279i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.92713	+	2.99226i	0.0903453	+	0.140279i
$456$		0			0
$457$	8.39741	−	14.5447i	0.392814	−	0.680375i	−0.600005	−	0.799996i	$-0.704835\pi$
$457$	8.39741	−	14.5447i	0.392814	−	0.680375i	0.992820	+	0.119622i	$0.0381681\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.3775			−0.529903			−0.264951	−	0.964262i	$-0.585356\pi$
$461$	−11.3775			−0.529903			−0.264951	+	0.964262i	$0.585356\pi$
$462$		0			0
$463$	2.48145			0.115323			0.0576613	−	0.998336i	$-0.481636\pi$
$463$	2.48145			0.115323			0.0576613	+	0.998336i	$0.481636\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.9839	+	20.7568i	−0.554550	+	0.960508i	0.443389	+	0.896329i	$0.353776\pi$
$467$	−11.9839	+	20.7568i	−0.554550	+	0.960508i	−0.997938	+	0.0641788i	$0.979557\pi$
$468$		0			0
$469$	−1.08536	−	22.3268i	−0.0501171	−	1.03096i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.91254	−	3.41360i	0.271859	−	0.156958i
$474$		0			0
$475$			7.66896i			0.351876i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.2447	+	19.4764i	0.513784	+	0.889899i	0.999872	+	0.0159898i	$0.00508992\pi$
$479$	11.2447	+	19.4764i	0.513784	+	0.889899i	−0.486089	+	0.873910i	$0.661577\pi$
$480$		0			0
$481$	−4.36391	−	2.51951i	−0.198977	−	0.114880i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−9.68469	−	5.59146i	−0.439759	−	0.253895i
$486$		0			0
$487$	−10.9567	−	18.9776i	−0.496497	−	0.859958i	0.503495	−	0.863998i	$-0.332047\pi$
$487$	−10.9567	−	18.9776i	−0.496497	−	0.859958i	−0.999992	+	0.00404053i	$0.998714\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			22.5875i			1.01936i	0.860364	+	0.509681i	$0.170236\pi$
$491$			22.5875i			1.01936i	−0.860364	+	0.509681i	$0.829764\pi$
$492$		0			0
$493$	−29.9391	+	17.2853i	−1.34839	+	0.778492i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.63501	+	12.9010i	−0.297621	+	0.578687i
$498$		0			0
$499$	14.3299	−	24.8201i	0.641495	−	1.11110i	−0.343604	−	0.939115i	$-0.611648\pi$
$499$	14.3299	−	24.8201i	0.641495	−	1.11110i	0.985099	−	0.171987i	$-0.0550188\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	39.4762			1.76016			0.880078	−	0.474830i	$-0.157490\pi$
$503$	39.4762			1.76016			0.880078	+	0.474830i	$0.157490\pi$
$504$		0			0
$505$	−22.6922			−1.00979
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.73501	+	4.73717i	−0.121227	+	0.209971i	−0.920252	−	0.391327i	$-0.872016\pi$
$509$	−2.73501	+	4.73717i	−0.121227	+	0.209971i	0.799025	+	0.601298i	$0.205350\pi$
$510$		0			0
$511$	2.58370	−	0.125600i	0.114296	−	0.00555620i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.3557	+	8.86563i	−0.676654	+	0.390666i
$516$		0			0
$517$			5.85841i			0.257652i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.1796	−	26.2918i	−0.665029	−	1.15186i	−0.979277	−	0.202524i	$-0.935086\pi$
$521$	−15.1796	−	26.2918i	−0.665029	−	1.15186i	0.314248	−	0.949341i	$-0.398248\pi$
$522$		0			0
$523$	32.4905	+	18.7584i	1.42071	+	0.820248i	0.996360	−	0.0852494i	$-0.0271687\pi$
$523$	32.4905	+	18.7584i	1.42071	+	0.820248i	0.424352	+	0.905497i	$0.360502\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−29.8178	−	17.2153i	−1.29888	−	0.749911i
$528$		0			0
$529$	0.393577	+	0.681695i	0.0171120	+	0.0296389i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	3.06442i		−	0.132735i
$534$		0			0
$535$	11.1234	−	6.42212i	0.480908	−	0.277652i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.6503	+	4.83878i	0.458742	+	0.208421i
$540$		0			0
$541$	10.5259	−	18.2314i	0.452543	−	0.783827i	−0.546000	−	0.837785i	$-0.683850\pi$
$541$	10.5259	−	18.2314i	0.452543	−	0.783827i	0.998543	+	0.0539578i	$0.0171836\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.65578			−0.327938
$546$		0			0
$547$	2.57620			0.110150			0.0550751	−	0.998482i	$-0.482460\pi$
$547$	2.57620			0.110150			0.0550751	+	0.998482i	$0.482460\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.81853	−	15.2741i	0.375682	−	0.650700i
$552$		0			0
$553$	−24.7391	+	15.9329i	−1.05201	+	0.677537i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.7118	+	11.3806i	−0.835215	+	0.482211i	−0.855635	−	0.517580i	$-0.826833\pi$
$557$	−19.7118	+	11.3806i	−0.835215	+	0.482211i	0.0204201	+	0.999791i	$0.493500\pi$
$558$		0			0
$559$			4.67875i			0.197890i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.2404	+	22.9331i	0.558018	+	0.966516i	0.997662	+	0.0683439i	$0.0217715\pi$
$563$	13.2404	+	22.9331i	0.558018	+	0.966516i	−0.439643	+	0.898172i	$0.644895\pi$
$564$		0			0
$565$	11.0618	+	6.38654i	0.465374	+	0.268684i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.2254	−	8.79038i	−0.638281	−	0.368512i	0.145671	−	0.989333i	$-0.453466\pi$
$569$	−15.2254	−	8.79038i	−0.638281	−	0.368512i	−0.783952	+	0.620821i	$0.786799\pi$
$570$		0			0
$571$	−12.1117	−	20.9780i	−0.506857	−	0.877903i	−0.999969	−	0.00793637i	$-0.997474\pi$
$571$	−12.1117	−	20.9780i	−0.506857	−	0.877903i	0.493111	−	0.869966i	$-0.335860\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			17.6569i			0.736342i
$576$		0			0
$577$	−18.5934	+	10.7349i	−0.774052	+	0.446899i	−0.834318	−	0.551283i	$-0.814138\pi$
$577$	−18.5934	+	10.7349i	−0.774052	+	0.446899i	0.0602665	+	0.998182i	$0.480805\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.0594	−	12.3738i	−0.998151	−	0.513352i
$582$		0			0
$583$	−1.54146	+	2.66988i	−0.0638407	+	0.110575i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.2492			1.24852			0.624260	−	0.781217i	$-0.285401\pi$
$587$	30.2492			1.24852			0.624260	+	0.781217i	$0.285401\pi$
$588$		0			0
$589$	17.5656			0.723778
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16.9023	−	29.2757i	0.694095	−	1.20221i	−0.276390	−	0.961046i	$-0.589138\pi$
$593$	16.9023	−	29.2757i	0.694095	−	1.20221i	0.970485	−	0.241162i	$-0.0775285\pi$
$594$		0			0
$595$	−11.4752	−	5.90172i	−0.470436	−	0.241947i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	33.0568	−	19.0854i	1.35066	−	0.779806i	0.362322	−	0.932053i	$-0.381984\pi$
$599$	33.0568	−	19.0854i	1.35066	−	0.779806i	0.988343	+	0.152247i	$0.0486508\pi$
$600$		0			0
$601$		−	37.6195i		−	1.53453i	−0.641329	−	0.767266i	$-0.721616\pi$
$601$		−	37.6195i		−	1.53453i	0.641329	−	0.767266i	$-0.278384\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.82020	+	8.34883i	0.195969	+	0.339428i
$606$		0			0
$607$	−0.749770	−	0.432880i	−0.0304322	−	0.0175700i	0.484707	−	0.874677i	$-0.338926\pi$
$607$	−0.749770	−	0.432880i	−0.0304322	−	0.0175700i	−0.515139	+	0.857107i	$0.672260\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.47694	−	2.00741i	−0.140662	−	0.0812112i
$612$		0			0
$613$	10.5564	+	18.2842i	0.426368	+	0.738491i	0.996547	−	0.0830296i	$-0.0264596\pi$
$613$	10.5564	+	18.2842i	0.426368	+	0.738491i	−0.570179	+	0.821520i	$0.693126\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	10.6262i		−	0.427795i	−0.976856	−	0.213897i	$-0.931384\pi$
$617$		−	10.6262i		−	0.427795i	0.976856	−	0.213897i	$-0.0686158\pi$
$618$		0			0
$619$	−19.8636	+	11.4683i	−0.798385	+	0.460948i	−0.842906	−	0.538060i	$-0.819157\pi$
$619$	−19.8636	+	11.4683i	−0.798385	+	0.460948i	0.0445209	+	0.999008i	$0.485824\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−28.0263	+	18.0500i	−1.12285	+	0.723158i
$624$		0			0
$625$	−3.10391	+	5.37613i	−0.124156	+	0.215045i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.2693			0.728443
$630$		0			0
$631$	−4.19211			−0.166885			−0.0834425	−	0.996513i	$-0.526592\pi$
$631$	−4.19211			−0.166885			−0.0834425	+	0.996513i	$0.526592\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.917748	+	1.58959i	−0.0364197	+	0.0630808i
$636$		0			0
$637$	−6.52118	+	4.66288i	−0.258379	+	0.184750i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.4895	−	8.94287i	0.611799	−	0.353222i	−0.161870	−	0.986812i	$-0.551753\pi$
$641$	15.4895	−	8.94287i	0.611799	−	0.353222i	0.773669	+	0.633590i	$0.218419\pi$
$642$		0			0
$643$			30.8980i			1.21850i	0.792980	+	0.609248i	$0.208529\pi$
$643$			30.8980i			1.21850i	−0.792980	+	0.609248i	$0.791471\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.81704	+	6.61130i	0.150063	+	0.259917i	0.931250	−	0.364380i	$-0.118719\pi$
$647$	3.81704	+	6.61130i	0.150063	+	0.259917i	−0.781187	+	0.624297i	$0.785386\pi$
$648$		0			0
$649$	8.64492	+	4.99114i	0.339343	+	0.195920i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.2668	−	11.1237i	−0.753967	−	0.435303i	0.0731587	−	0.997320i	$-0.476692\pi$
$653$	−19.2668	−	11.1237i	−0.753967	−	0.435303i	−0.827125	+	0.562017i	$0.810025\pi$
$654$		0			0
$655$	12.0949	+	20.9489i	0.472585	+	0.818542i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			8.74939i			0.340828i	0.985373	+	0.170414i	$0.0545105\pi$
$659$			8.74939i			0.340828i	−0.985373	+	0.170414i	$0.945490\pi$
$660$		0			0
$661$	6.46910	−	3.73493i	0.251619	−	0.145272i	−0.368887	−	0.929474i	$-0.620261\pi$
$661$	6.46910	−	3.73493i	0.251619	−	0.145272i	0.620505	+	0.784202i	$0.286928\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.57546	−	0.319648i	0.254985	−	0.0123954i
$666$		0			0
$667$	20.3036	−	35.1669i	0.786159	−	1.36167i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−24.7019			−0.953605
$672$		0			0
$673$	−0.388583			−0.0149788			−0.00748938	−	0.999972i	$-0.502384\pi$
$673$	−0.388583			−0.0149788			−0.00748938	+	0.999972i	$0.502384\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.45942	+	16.3842i	−0.363555	+	0.629696i	−0.988543	−	0.150938i	$-0.951771\pi$
$677$	−9.45942	+	16.3842i	−0.363555	+	0.629696i	0.624988	+	0.780634i	$0.285104\pi$
$678$		0			0
$679$	11.5204	−	22.4000i	0.442112	−	0.859633i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.95105	−	2.85849i	0.189447	−	0.109377i	−0.402277	−	0.915518i	$-0.631781\pi$
$683$	4.95105	−	2.85849i	0.189447	−	0.109377i	0.591723	+	0.806141i	$0.298448\pi$
$684$		0			0
$685$			24.9969i			0.955084i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.05638	−	1.82970i	−0.0402447	−	0.0697059i
$690$		0			0
$691$	43.7605	+	25.2652i	1.66473	+	0.961132i	0.970410	+	0.241465i	$0.0776277\pi$
$691$	43.7605	+	25.2652i	1.66473	+	0.961132i	0.694319	+	0.719667i	$0.255706\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.61969	−	3.82188i	−0.251099	−	0.144972i
$696$		0			0
$697$	5.55513	+	9.62177i	0.210416	+	0.364450i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			14.5025i			0.547752i	0.961765	+	0.273876i	$0.0883058\pi$
$701$			14.5025i			0.547752i	−0.961765	+	0.273876i	$0.911694\pi$
$702$		0			0
$703$	−8.07180	+	4.66025i	−0.304434	+	0.175765i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.48178	−	51.0526i	−0.0933370	−	1.92003i
$708$		0			0
$709$	9.03657	−	15.6518i	0.339376	−	0.587816i	−0.644940	−	0.764233i	$-0.723118\pi$
$709$	9.03657	−	15.6518i	0.339376	−	0.587816i	0.984315	+	0.176417i	$0.0564509\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	40.4427			1.51459
$714$		0			0
$715$	2.24807			0.0840729
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25.3720	−	43.9456i	0.946216	−	1.63889i	0.192918	−	0.981215i	$-0.438205\pi$
$719$	25.3720	−	43.9456i	0.946216	−	1.63889i	0.753298	−	0.657679i	$-0.228462\pi$
$720$		0			0
$721$	−21.6252	−	33.5775i	−0.805363	−	1.25049i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	26.1039	−	15.0711i	0.969473	−	0.559725i
$726$		0			0
$727$			6.77139i			0.251137i	0.992085	+	0.125568i	$0.0400755\pi$
$727$			6.77139i			0.251137i	−0.992085	+	0.125568i	$0.959925\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.48156	−	14.6905i	−0.313702	−	0.543347i
$732$		0			0
$733$	43.8337	+	25.3074i	1.61903	+	0.934750i	0.987170	+	0.159671i	$0.0510433\pi$
$733$	43.8337	+	25.3074i	1.61903	+	0.934750i	0.631864	+	0.775079i	$0.282290\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.2274	−	7.05949i	−0.450402	−	0.260040i
$738$		0			0
$739$	15.3510	+	26.5887i	0.564695	+	0.978080i	0.997078	+	0.0763904i	$0.0243395\pi$
$739$	15.3510	+	26.5887i	0.564695	+	0.978080i	−0.432383	+	0.901690i	$0.642327\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	5.18883i		−	0.190360i	−0.995460	−	0.0951799i	$-0.969657\pi$
$743$		−	5.18883i		−	0.190360i	0.995460	−	0.0951799i	$-0.0303426\pi$
$744$		0			0
$745$	14.6316	−	8.44757i	0.536061	−	0.309495i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.6649	+	24.3230i	0.572384	+	0.888742i
$750$		0			0
$751$	0.618608	−	1.07146i	0.0225733	−	0.0390981i	−0.854518	−	0.519422i	$-0.826147\pi$
$751$	0.618608	−	1.07146i	0.0225733	−	0.0390981i	0.877091	+	0.480324i	$0.159481\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.0479			−0.438470
$756$		0			0
$757$	51.3970			1.86806			0.934028	−	0.357200i	$-0.116268\pi$
$757$	51.3970			1.86806			0.934028	+	0.357200i	$0.116268\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.8191	−	25.6674i	0.537190	−	0.930441i	−0.461864	−	0.886951i	$-0.652819\pi$
$761$	14.8191	−	25.6674i	0.537190	−	0.930441i	0.999054	−	0.0434899i	$-0.0138476\pi$
$762$		0			0
$763$	−0.837289	−	17.2239i	−0.0303119	−	0.623545i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.92445	+	3.42048i	−0.213919	+	0.123506i
$768$		0			0
$769$			28.1387i			1.01471i	0.861738	+	0.507354i	$0.169376\pi$
$769$			28.1387i			1.01471i	−0.861738	+	0.507354i	$0.830624\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.95227	+	10.3096i	0.214088	+	0.370812i	0.952990	−	0.303001i	$-0.0979886\pi$
$773$	5.95227	+	10.3096i	0.214088	+	0.370812i	−0.738902	+	0.673813i	$0.764655\pi$
$774$		0			0
$775$	25.9981	+	15.0100i	0.933880	+	0.539176i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.90878	−	2.83408i	−0.175875	−	0.101542i
$780$		0			0
$781$	4.58160	+	7.93557i	0.163943	+	0.283957i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	0.542431i		−	0.0193602i
$786$		0			0
$787$	−29.4945	+	17.0287i	−1.05137	+	0.607007i	−0.923031	−	0.384724i	$-0.874296\pi$
$787$	−29.4945	+	17.0287i	−1.05137	+	0.607007i	−0.128335	+	0.991731i	$0.540963\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−13.1585	+	25.5852i	−0.467864	+	0.909703i
$792$		0			0
$793$	8.46421	−	14.6604i	0.300573	−	0.520608i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−32.8088			−1.16215			−0.581074	−	0.813851i	$-0.697367\pi$
$797$	−32.8088			−1.16215			−0.581074	+	0.813851i	$0.697367\pi$
$798$		0			0
$799$	14.5560			0.514954
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.816939	−	1.41498i	0.0288292	−	0.0499336i
$804$		0			0
$805$	15.1392	−	0.735950i	0.533587	−	0.0259388i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.88851	+	3.97708i	−0.242187	+	0.139827i	−0.616182	−	0.787604i	$-0.711321\pi$
$809$	−6.88851	+	3.97708i	−0.242187	+	0.139827i	0.373994	+	0.927431i	$0.377988\pi$
$810$		0			0
$811$		−	22.4200i		−	0.787273i	−0.919266	−	0.393636i	$-0.871217\pi$
$811$		−	22.4200i		−	0.787273i	0.919266	−	0.393636i	$-0.128783\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.1139	+	22.7140i	0.459361	+	0.795636i
$816$		0			0
$817$	7.49471	+	4.32707i	0.262207	+	0.151385i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4.65642	+	2.68839i	0.162510	+	0.0938254i	0.579050	−	0.815292i	$-0.303424\pi$
$821$	4.65642	+	2.68839i	0.162510	+	0.0938254i	−0.416539	+	0.909118i	$0.636757\pi$
$822$		0			0
$823$	3.55129	+	6.15102i	0.123790	+	0.214411i	0.921259	−	0.388949i	$-0.127162\pi$
$823$	3.55129	+	6.15102i	0.123790	+	0.214411i	−0.797469	+	0.603360i	$0.793828\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	49.1228i		−	1.70817i	−0.520135	−	0.854084i	$-0.674118\pi$
$827$		−	49.1228i		−	1.70817i	0.520135	−	0.854084i	$-0.325882\pi$
$828$		0			0
$829$	−0.147346	+	0.0850705i	−0.00511755	+	0.00295462i	−0.502557	−	0.864544i	$-0.667607\pi$
$829$	−0.147346	+	0.0850705i	−0.00511755	+	0.00295462i	0.497439	+	0.867499i	$0.334274\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.0226	−	26.4621i	0.416558	−	0.916859i
$834$		0			0
$835$	−3.18675	+	5.51962i	−0.110282	+	0.191014i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	43.2416			1.49287			0.746434	−	0.665460i	$-0.231765\pi$
$839$	43.2416			1.49287			0.746434	+	0.665460i	$0.231765\pi$
$840$		0			0
$841$	−40.3208			−1.39037
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.86469	−	11.8900i	0.236152	−	0.409028i
$846$		0			0
$847$	−18.2559	+	11.7575i	−0.627280	+	0.403992i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.5843	+	10.7297i	−0.637063	+	0.367809i
$852$		0			0
$853$			19.3097i			0.661153i	0.943779	+	0.330577i	$0.107243\pi$
$853$			19.3097i			0.661153i	−0.943779	+	0.330577i	$0.892757\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.7997	+	46.4185i	0.915461	+	1.58562i	0.806225	+	0.591608i	$0.201507\pi$
$857$	26.7997	+	46.4185i	0.915461	+	1.58562i	0.109235	+	0.994016i	$0.465160\pi$
$858$		0			0
$859$	2.59883	+	1.50044i	0.0886710	+	0.0511943i	0.543680	−	0.839293i	$-0.317031\pi$
$859$	2.59883	+	1.50044i	0.0886710	+	0.0511943i	−0.455009	+	0.890487i	$0.650364\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−36.0064	−	20.7883i	−1.22567	−	0.707641i	−0.259549	−	0.965730i	$-0.583574\pi$
$863$	−36.0064	−	20.7883i	−1.22567	−	0.707641i	−0.966121	+	0.258089i	$0.916907\pi$
$864$		0			0
$865$	−5.58787	−	9.67847i	−0.189993	−	0.329078i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			18.5863i			0.630498i
$870$		0			0
$871$	8.37956	−	4.83794i	0.283930	−	0.163927i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23.8235	+	12.2525i	0.805380	+	0.414210i
$876$		0			0
$877$	17.7460	−	30.7371i	0.599241	−	1.03792i	−0.393692	−	0.919242i	$-0.628802\pi$
$877$	17.7460	−	30.7371i	0.599241	−	1.03792i	0.992933	−	0.118674i	$-0.0378644\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.7343			0.429030			0.214515	−	0.976721i	$-0.431183\pi$
$881$	12.7343			0.429030			0.214515	+	0.976721i	$0.431183\pi$
$882$		0			0
$883$	−29.0274			−0.976849			−0.488425	−	0.872606i	$-0.662428\pi$
$883$	−29.0274			−0.976849			−0.488425	+	0.872606i	$0.662428\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.3243	−	38.6668i	0.749575	−	1.29830i	−0.198451	−	0.980111i	$-0.563591\pi$
$887$	22.3243	−	38.6668i	0.749575	−	1.29830i	0.948026	−	0.318192i	$-0.103076\pi$
$888$		0			0
$889$	−3.67660	−	1.89089i	−0.123309	−	0.0634183i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.43118	+	3.71305i	−0.215211	+	0.124252i
$894$		0			0
$895$		−	2.65797i		−	0.0888462i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−34.5200	−	59.7904i	−1.15131	−	1.99412i
$900$		0			0
$901$	6.63368	+	3.82996i	0.221000	+	0.127594i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−22.1747	−	12.8026i	−0.737112	−	0.425572i
$906$		0			0
$907$	−14.8863	−	25.7838i	−0.494291	−	0.856137i	0.505687	−	0.862717i	$-0.331239\pi$
$907$	−14.8863	−	25.7838i	−0.494291	−	0.856137i	−0.999978	+	0.00657974i	$0.997906\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			33.4911i			1.10961i	0.831981	+	0.554804i	$0.187207\pi$
$911$			33.4911i			1.10961i	−0.831981	+	0.554804i	$0.812793\pi$
$912$		0			0
$913$	−14.7993	+	8.54436i	−0.489784	+	0.282777i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−45.8078	+	29.5020i	−1.51271	+	0.974240i
$918$		0			0
$919$	−6.79202	+	11.7641i	−0.224048	+	0.388062i	−0.956033	−	0.293258i	$-0.905261\pi$
$919$	−6.79202	+	11.7641i	−0.224048	+	0.388062i	0.731985	+	0.681320i	$0.238594\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.27963			−0.206697
$924$		0			0
$925$	−15.9290			−0.523741
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.0268156	+	0.0464460i	−0.000879793	+	0.00152385i	−0.866465	−	0.499238i	$-0.833613\pi$
$929$	−0.0268156	+	0.0464460i	−0.000879793	+	0.00152385i	0.865585	+	0.500762i	$0.166947\pi$
$930$		0			0
$931$	1.43828	+	14.7584i	0.0471376	+	0.483687i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.05854	+	4.07525i	−0.230839	+	0.133275i
$936$		0			0
$937$			14.3633i			0.469230i	0.972088	+	0.234615i	$0.0753829\pi$
$937$			14.3633i			0.469230i	−0.972088	+	0.234615i	$0.924617\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	16.9562	+	29.3690i	0.552757	+	0.957403i	0.998074	+	0.0620301i	$0.0197575\pi$
$941$	16.9562	+	29.3690i	0.552757	+	0.957403i	−0.445318	+	0.895373i	$0.646909\pi$
$942$		0			0
$943$	−11.3019	−	6.52514i	−0.368040	−	0.212488i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.3993	+	16.3964i	0.922854	+	0.532810i	0.884544	−	0.466456i	$-0.154469\pi$
$947$	28.3993	+	16.3964i	0.922854	+	0.532810i	0.0383093	+	0.999266i	$0.487803\pi$
$948$		0			0
$949$	0.559856	+	0.969700i	0.0181737	+	0.0314778i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	25.2186i		−	0.816912i	−0.912778	−	0.408456i	$-0.866067\pi$
$953$		−	25.2186i		−	0.816912i	0.912778	−	0.408456i	$-0.133933\pi$
$954$		0			0
$955$	−22.1181	+	12.7699i	−0.715725	+	0.413224i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−56.2377	+	2.73384i	−1.81601	+	0.0882803i
$960$		0			0
$961$	18.8802	−	32.7014i	0.609038	−	1.05488i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	25.4326			0.818703
$966$		0			0
$967$	−15.0565			−0.484183			−0.242091	−	0.970253i	$-0.577833\pi$
$967$	−15.0565			−0.484183			−0.242091	+	0.970253i	$0.577833\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.30245	+	10.9162i	−0.202255	+	0.350316i	−0.949255	−	0.314508i	$-0.898160\pi$
$971$	−6.30245	+	10.9162i	−0.202255	+	0.350316i	0.747000	+	0.664825i	$0.231494\pi$
$972$		0			0
$973$	7.87443	−	15.3109i	0.252443	−	0.490844i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	46.0439	−	26.5835i	1.47307	−	0.850480i	0.473534	−	0.880776i	$-0.342978\pi$
$977$	46.0439	−	26.5835i	1.47307	−	0.850480i	0.999541	+	0.0302958i	$0.00964493\pi$
$978$		0			0
$979$			21.0560i			0.672951i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.43065	+	7.67412i	0.141316	+	0.244766i	0.927992	−	0.372599i	$-0.121533\pi$
$983$	4.43065	+	7.67412i	0.141316	+	0.244766i	−0.786677	+	0.617365i	$0.788200\pi$
$984$		0			0
$985$	−5.68424	−	3.28180i	−0.181115	−	0.104567i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	17.2557	+	9.96256i	0.548698	+	0.316791i
$990$		0			0
$991$	14.9235	+	25.8482i	0.474059	+	0.821095i	0.999559	−	0.0296992i	$-0.00945495\pi$
$991$	14.9235	+	25.8482i	0.474059	+	0.821095i	−0.525500	+	0.850794i	$0.676122\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	19.2709i		−	0.610929i
$996$		0			0
$997$	11.0516	−	6.38062i	0.350006	−	0.202076i	−0.314682	−	0.949197i	$-0.601898\pi$
$997$	11.0516	−	6.38062i	0.350006	−	0.202076i	0.664688	+	0.747121i	$0.268564\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bl.a.89.6	yes	16
3.2	odd	2	inner	504.2.bl.a.89.3	yes	16
4.3	odd	2		1008.2.bt.d.593.6		16
7.2	even	3		3528.2.k.b.881.6		16
7.3	odd	6	inner	504.2.bl.a.17.3	✓	16
7.4	even	3		3528.2.bl.a.521.6		16
7.5	odd	6		3528.2.k.b.881.12		16
7.6	odd	2		3528.2.bl.a.1097.3		16
12.11	even	2		1008.2.bt.d.593.3		16
21.2	odd	6		3528.2.k.b.881.11		16
21.5	even	6		3528.2.k.b.881.5		16
21.11	odd	6		3528.2.bl.a.521.3		16
21.17	even	6	inner	504.2.bl.a.17.6	yes	16
21.20	even	2		3528.2.bl.a.1097.6		16
28.3	even	6		1008.2.bt.d.17.3		16
28.19	even	6		7056.2.k.h.881.11		16
28.23	odd	6		7056.2.k.h.881.5		16
84.23	even	6		7056.2.k.h.881.12		16
84.47	odd	6		7056.2.k.h.881.6		16
84.59	odd	6		1008.2.bt.d.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bl.a.17.3	✓	16	7.3	odd	6	inner
504.2.bl.a.17.6	yes	16	21.17	even	6	inner
504.2.bl.a.89.3	yes	16	3.2	odd	2	inner
504.2.bl.a.89.6	yes	16	1.1	even	1	trivial
1008.2.bt.d.17.3		16	28.3	even	6
1008.2.bt.d.17.6		16	84.59	odd	6
1008.2.bt.d.593.3		16	12.11	even	2
1008.2.bt.d.593.6		16	4.3	odd	2
3528.2.k.b.881.5		16	21.5	even	6
3528.2.k.b.881.6		16	7.2	even	3
3528.2.k.b.881.11		16	21.2	odd	6
3528.2.k.b.881.12		16	7.5	odd	6
3528.2.bl.a.521.3		16	21.11	odd	6
3528.2.bl.a.521.6		16	7.4	even	3
3528.2.bl.a.1097.3		16	7.6	odd	2
3528.2.bl.a.1097.6		16	21.20	even	2
7056.2.k.h.881.5		16	28.23	odd	6
7056.2.k.h.881.6		16	84.47	odd	6
7056.2.k.h.881.11		16	28.19	even	6
7056.2.k.h.881.12		16	84.23	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587308 - 1.01725i) q^{5} +(2.35282 + 1.21006i) q^{7} +O(q^{10})\)	\(q+(0.587308 - 1.01725i) q^{5} +(2.35282 + 1.21006i) q^{7} +(1.44725 - 0.835571i) q^{11} +1.14525i q^{13} +(-2.07609 - 3.59589i) q^{17} +(1.83453 + 1.05917i) q^{19} +(4.22379 + 2.43860i) q^{23} +(1.81014 + 3.13525i) q^{25} -8.32591i q^{29} +(7.18124 - 4.14609i) q^{31} +(2.61276 - 1.68272i) q^{35} +(-2.19996 + 3.81045i) q^{37} -2.67577 q^{41} +4.08536 q^{43} +(-1.75282 + 3.03597i) q^{47} +(4.07150 + 5.69411i) q^{49} +(-1.59764 + 0.922398i) q^{53} -1.96295i q^{55} +(2.98667 + 5.17306i) q^{59} +(-12.8011 - 7.39071i) q^{61} +(1.16500 + 0.672614i) q^{65} +(-4.22435 - 7.31679i) q^{67} +5.48320i q^{71} +(0.846715 - 0.488851i) q^{73} +(4.41621 - 0.214682i) q^{77} +(-5.56097 + 9.63187i) q^{79} -10.2258 q^{83} -4.87721 q^{85} +(-6.29987 + 10.9117i) q^{89} +(-1.38582 + 2.69456i) q^{91} +(2.15487 - 1.24411i) q^{95} -9.52049i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 12 q^{19} + 12 q^{25} + 24 q^{31} + 4 q^{37} + 8 q^{43} + 32 q^{49} - 28 q^{67} - 60 q^{73} - 32 q^{79} - 32 q^{85} - 84 q^{91}+O(q^{100}) \) 16 * q - 8 * q^7 + 12 * q^19 + 12 * q^25 + 24 * q^31 + 4 * q^37 + 8 * q^43 + 32 * q^49 - 28 * q^67 - 60 * q^73 - 32 * q^79 - 32 * q^85 - 84 * q^91

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