LMFDB - Embedded newform 3024.2.bf.e.2287.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1711,3024)]

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([3, 0, 2, 1]))

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

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

chi := DirichletCharacter("3024.1711");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2287.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	3024.2287
Dual form			3024.2.bf.e.1711.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.18154i q^{5} +(-2.62132 + 0.358719i) q^{7} -1.73205i q^{11} +(-0.621320 + 0.358719i) q^{13} +(-5.74264 + 3.31552i) q^{17} +(0.500000 - 0.866025i) q^{19} +7.64564i q^{23} -12.4853 q^{25} +(3.62132 - 6.27231i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(1.50000 + 10.9612i) q^{35} +(-2.62132 + 4.54026i) q^{37} +(-0.257359 + 0.148586i) q^{41} +(2.74264 + 1.58346i) q^{43} +(4.24264 + 7.34847i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-3.62132 - 6.27231i) q^{53} -7.24264 q^{55} +(3.00000 - 5.19615i) q^{59} +(6.00000 - 3.46410i) q^{61} +(1.50000 + 2.59808i) q^{65} +6.33386i q^{71} +(-7.50000 + 4.33013i) q^{73} +(0.621320 + 4.54026i) q^{77} +(10.2426 - 5.91359i) q^{79} +(-2.74264 + 4.75039i) q^{83} +(13.8640 + 24.0131i) q^{85} +(-11.2279 - 6.48244i) q^{89} +(1.50000 - 1.16320i) q^{91} +(-3.62132 - 2.09077i) q^{95} +(-2.74264 - 1.58346i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{7} + 6 q^{13} - 6 q^{17} + 2 q^{19} - 16 q^{25} + 6 q^{29} - 8 q^{31} + 6 q^{35} - 2 q^{37} - 18 q^{41} - 6 q^{43} + 10 q^{49} - 6 q^{53} - 12 q^{55} + 12 q^{59} + 24 q^{61} + 6 q^{65} - 30 q^{73}+ \cdots + 6 q^{97}+O(q^{100}) $ 4 * q - 2 * q^7 + 6 * q^13 - 6 * q^17 + 2 * q^19 - 16 * q^25 + 6 * q^29 - 8 * q^31 + 6 * q^35 - 2 * q^37 - 18 * q^41 - 6 * q^43 + 10 * q^49 - 6 * q^53 - 12 * q^55 + 12 * q^59 + 24 * q^61 + 6 * q^65 - 30 * q^73 - 6 * q^77 + 24 * q^79 + 6 * q^83 + 30 * q^85 + 6 * q^89 + 6 * q^91 - 6 * q^95 + 6 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$		−	4.18154i		−	1.87004i	−0.354593	−	0.935021i	$-0.615380\pi$
$5$		−	4.18154i		−	1.87004i	0.354593	−	0.935021i	$-0.384620\pi$
$6$		0			0
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	1.73205i		−	0.522233i	−0.965307	−	0.261116i	$-0.915909\pi$
$11$		−	1.73205i		−	0.522233i	0.965307	−	0.261116i	$-0.0840907\pi$
$12$		0			0
$13$	−0.621320	+	0.358719i	−0.172323	+	0.0994909i	−0.583681	−	0.811983i	$-0.698388\pi$
$13$	−0.621320	+	0.358719i	−0.172323	+	0.0994909i	0.411358	+	0.911474i	$0.365055\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.74264	+	3.31552i	−1.39279	+	0.804131i	−0.993624	−	0.112746i	$-0.964035\pi$
$17$	−5.74264	+	3.31552i	−1.39279	+	0.804131i	−0.399171	+	0.916876i	$0.630702\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			7.64564i			1.59423i	0.603830	+	0.797113i	$0.293641\pi$
$23$			7.64564i			1.59423i	−0.603830	+	0.797113i	$0.706359\pi$
$24$		0			0
$25$	−12.4853			−2.49706
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.62132	−	6.27231i	0.672462	−	1.16474i	−0.304741	−	0.952435i	$-0.598570\pi$
$29$	3.62132	−	6.27231i	0.672462	−	1.16474i	0.977204	−	0.212304i	$-0.0680966\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	+	10.9612i	0.253546	+	1.85277i
$36$		0			0
$37$	−2.62132	+	4.54026i	−0.430942	+	0.746414i	−0.996955	−	0.0779826i	$-0.975152\pi$
$37$	−2.62132	+	4.54026i	−0.430942	+	0.746414i	0.566012	+	0.824397i	$0.308485\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.257359	+	0.148586i	−0.0401928	+	0.0232053i	−0.519962	−	0.854190i	$-0.674054\pi$
$41$	−0.257359	+	0.148586i	−0.0401928	+	0.0232053i	0.479769	+	0.877395i	$0.340720\pi$
$42$		0			0
$43$	2.74264	+	1.58346i	0.418249	+	0.241476i	0.694328	−	0.719659i	$-0.255702\pi$
$43$	2.74264	+	1.58346i	0.418249	+	0.241476i	−0.276079	+	0.961135i	$0.589035\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.24264	+	7.34847i	0.618853	+	1.07188i	0.989695	+	0.143189i	$0.0457356\pi$
$47$	4.24264	+	7.34847i	0.618853	+	1.07188i	−0.370843	+	0.928696i	$0.620931\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.62132	−	6.27231i	−0.497427	−	0.861568i	0.502569	−	0.864537i	$-0.332388\pi$
$53$	−3.62132	−	6.27231i	−0.497427	−	0.861568i	−0.999996	+	0.00296896i	$0.999055\pi$
$54$		0			0
$55$	−7.24264			−0.976597
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	0.832240	+	0.554416i	$0.187058\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.50000	+	2.59808i	0.186052	+	0.322252i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			6.33386i			0.751691i	0.926682	+	0.375845i	$0.122648\pi$
$71$			6.33386i			0.751691i	−0.926682	+	0.375845i	$0.877352\pi$
$72$		0			0
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.869935	−	0.493166i	$-0.835840\pi$
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.00787336	+	0.999969i	$0.502506\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.621320	+	4.54026i	0.0708060	+	0.517411i
$78$		0			0
$79$	10.2426	−	5.91359i	1.15239	−	0.665331i	0.202919	−	0.979195i	$-0.434957\pi$
$79$	10.2426	−	5.91359i	1.15239	−	0.665331i	0.949468	+	0.313864i	$0.101624\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.74264	+	4.75039i	−0.301044	+	0.521423i	−0.976373	−	0.216093i	$-0.930668\pi$
$83$	−2.74264	+	4.75039i	−0.301044	+	0.521423i	0.675329	+	0.737517i	$0.264002\pi$
$84$		0			0
$85$	13.8640	+	24.0131i	1.50376	+	2.60458i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.2279	−	6.48244i	−1.19016	−	0.687138i	−0.231815	−	0.972760i	$-0.574466\pi$
$89$	−11.2279	−	6.48244i	−1.19016	−	0.687138i	−0.958342	+	0.285622i	$0.907800\pi$
$90$		0			0
$91$	1.50000	−	1.16320i	0.157243	−	0.121936i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.62132	−	2.09077i	−0.371540	−	0.214509i
$96$		0			0
$97$	−2.74264	−	1.58346i	−0.278473	−	0.160776i	0.354259	−	0.935147i	$-0.384733\pi$
$97$	−2.74264	−	1.58346i	−0.278473	−	0.160776i	−0.632732	+	0.774371i	$0.718066\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	0.717439i		−	0.0713878i	−0.999363	−	0.0356939i	$-0.988636\pi$
$101$		−	0.717439i		−	0.0713878i	0.999363	−	0.0356939i	$-0.0113641\pi$
$102$		0			0
$103$	13.7279			1.35265			0.676326	−	0.736602i	$-0.263571\pi$
$103$	13.7279			1.35265			0.676326	+	0.736602i	$0.263571\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.98528	−	4.03295i	−0.675293	−	0.389880i	0.122786	−	0.992433i	$-0.460817\pi$
$107$	−6.98528	−	4.03295i	−0.675293	−	0.389880i	−0.798079	+	0.602553i	$0.794150\pi$
$108$		0			0
$109$	8.62132	+	14.9326i	0.825773	+	1.43028i	0.901327	+	0.433139i	$0.142594\pi$
$109$	8.62132	+	14.9326i	0.825773	+	1.43028i	−0.0755546	+	0.997142i	$0.524073\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.74264	+	4.75039i	0.258006	+	0.446879i	0.965708	−	0.259632i	$-0.0836013\pi$
$113$	2.74264	+	4.75039i	0.258006	+	0.446879i	−0.707702	+	0.706511i	$0.750268\pi$
$114$		0			0
$115$	31.9706			2.98127
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.8640	−	10.7510i	1.27091	−	0.985545i
$120$		0			0
$121$	8.00000			0.727273
$122$		0			0
$123$		0			0
$124$		0			0
$125$			31.3000i			2.79956i
$126$		0			0
$127$			20.1903i			1.79160i	0.444461	+	0.895798i	$0.353395\pi$
$127$			20.1903i			1.79160i	−0.444461	+	0.895798i	$0.646605\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.514719			0.0449712			0.0224856	−	0.999747i	$-0.492842\pi$
$131$	0.514719			0.0449712			0.0224856	+	0.999747i	$0.492842\pi$
$132$		0			0
$133$	−1.00000	+	2.44949i	−0.0867110	+	0.212398i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$		0			0
$139$	−6.50000	−	11.2583i	−0.551323	−	0.954919i	−0.998179	−	0.0603135i	$-0.980790\pi$
$139$	−6.50000	−	11.2583i	−0.551323	−	0.954919i	0.446857	−	0.894606i	$-0.352543\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.621320	+	1.07616i	0.0519574	+	0.0899929i
$144$		0			0
$145$	−26.2279	−	15.1427i	−2.17811	−	1.25753i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.7574			0.881277			0.440639	−	0.897685i	$-0.354752\pi$
$149$	10.7574			0.881277			0.440639	+	0.897685i	$0.354752\pi$
$150$		0			0
$151$			20.3134i			1.65308i	0.562880	+	0.826539i	$0.309693\pi$
$151$			20.3134i			1.65308i	−0.562880	+	0.826539i	$0.690307\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	14.4853	+	8.36308i	1.16349	+	0.671739i
$156$		0			0
$157$	−10.2426	−	5.91359i	−0.817452	−	0.471956i	0.0320852	−	0.999485i	$-0.489785\pi$
$157$	−10.2426	−	5.91359i	−0.817452	−	0.471956i	−0.849537	+	0.527529i	$0.823119\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.74264	−	20.0417i	−0.216150	−	1.57951i
$162$		0			0
$163$	−8.74264	−	5.04757i	−0.684776	−	0.395356i	0.116876	−	0.993147i	$-0.462712\pi$
$163$	−8.74264	−	5.04757i	−0.684776	−	0.395356i	−0.801652	+	0.597791i	$0.796045\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.86396	−	8.42463i	−0.376385	−	0.651917i	0.614149	−	0.789190i	$-0.289500\pi$
$167$	−4.86396	−	8.42463i	−0.376385	−	0.651917i	−0.990533	+	0.137273i	$0.956166\pi$
$168$		0			0
$169$	−6.24264	+	10.8126i	−0.480203	+	0.831736i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.48528	+	4.89898i	−0.645124	+	0.372463i	−0.786586	−	0.617481i	$-0.788153\pi$
$173$	−8.48528	+	4.89898i	−0.645124	+	0.372463i	0.141462	+	0.989944i	$0.454820\pi$
$174$		0			0
$175$	32.7279	−	4.47871i	2.47400	−	0.338559i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−15.9853	+	9.22911i	−1.19480	+	0.689816i	−0.959390	−	0.282081i	$-0.908975\pi$
$179$	−15.9853	+	9.22911i	−1.19480	+	0.689816i	−0.235406	+	0.971897i	$0.575642\pi$
$180$		0			0
$181$			6.33386i			0.470792i	0.971900	+	0.235396i	$0.0756387\pi$
$181$			6.33386i			0.470792i	−0.971900	+	0.235396i	$0.924361\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.9853	+	10.9612i	1.39583	+	0.805880i
$186$		0			0
$187$	5.74264	+	9.94655i	0.419943	+	0.727363i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.72792	−	5.61642i	0.703888	−	0.406390i	−0.104906	−	0.994482i	$-0.533454\pi$
$191$	9.72792	−	5.61642i	0.703888	−	0.406390i	0.808794	+	0.588092i	$0.200121\pi$
$192$		0			0
$193$	6.48528	−	11.2328i	0.466821	−	0.808557i	−0.532461	−	0.846455i	$-0.678733\pi$
$193$	6.48528	−	11.2328i	0.466821	−	0.808557i	0.999282	+	0.0378973i	$0.0120660\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.48528			−0.177069			−0.0885345	−	0.996073i	$-0.528218\pi$
$197$	−2.48528			−0.177069			−0.0885345	+	0.996073i	$0.528218\pi$
$198$		0			0
$199$	−2.86396	−	4.96053i	−0.203021	−	0.351642i	0.746480	−	0.665408i	$-0.231743\pi$
$199$	−2.86396	−	4.96053i	−0.203021	−	0.351642i	−0.949500	+	0.313766i	$0.898409\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.24264	+	17.7408i	−0.508334	+	1.24516i
$204$		0			0
$205$	0.621320	+	1.07616i	0.0433949	+	0.0751622i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.50000	−	0.866025i	−0.103757	−	0.0599042i
$210$		0			0
$211$	−6.25736	+	3.61269i	−0.430774	+	0.248708i	−0.699676	−	0.714460i	$-0.746673\pi$
$211$	−6.25736	+	3.61269i	−0.430774	+	0.248708i	0.268902	+	0.963168i	$0.413339\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.62132	−	11.4685i	0.451570	−	0.782143i
$216$		0			0
$217$	4.00000	−	9.79796i	0.271538	−	0.665129i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.37868	−	4.11999i	0.160007	−	0.277141i
$222$		0			0
$223$	−1.62132	+	2.80821i	−0.108572	+	0.188052i	−0.915192	−	0.403019i	$-0.867961\pi$
$223$	−1.62132	+	2.80821i	−0.108572	+	0.188052i	0.806620	+	0.591070i	$0.201294\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.514719			−0.0341631			−0.0170815	−	0.999854i	$-0.505437\pi$
$227$	−0.514719			−0.0341631			−0.0170815	+	0.999854i	$0.505437\pi$
$228$		0			0
$229$		−	24.9662i		−	1.64981i	−0.565272	−	0.824905i	$-0.691229\pi$
$229$		−	24.9662i		−	1.64981i	0.565272	−	0.824905i	$-0.308771\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.7426	+	25.5350i	−0.965823	+	1.67285i	−0.258434	+	0.966029i	$0.583206\pi$
$233$	−14.7426	+	25.5350i	−0.965823	+	1.67285i	−0.707389	+	0.706825i	$0.750127\pi$
$234$		0			0
$235$	30.7279	−	17.7408i	2.00447	−	1.15728i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−21.1066	+	12.1859i	−1.36527	+	0.788240i	−0.990320	−	0.138803i	$-0.955674\pi$
$239$	−21.1066	+	12.1859i	−1.36527	+	0.788240i	−0.374953	+	0.927044i	$0.622341\pi$
$240$		0			0
$241$			10.0951i			0.650285i	0.945665	+	0.325142i	$0.105412\pi$
$241$			10.0951i			0.650285i	−0.945665	+	0.325142i	$0.894588\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.86396	−	28.1946i	−0.502410	−	1.80129i
$246$		0			0
$247$			0.717439i			0.0456495i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.51472			0.600564			0.300282	−	0.953851i	$-0.402919\pi$
$251$	9.51472			0.600564			0.300282	+	0.953851i	$0.402919\pi$
$252$		0			0
$253$	13.2426			0.832558
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	5.79050i		−	0.361201i	−0.983557	−	0.180601i	$-0.942196\pi$
$257$		−	5.79050i		−	0.361201i	0.983557	−	0.180601i	$-0.0578042\pi$
$258$		0			0
$259$	5.24264	−	12.8418i	0.325762	−	0.797950i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			10.5154i			0.648407i	0.945987	+	0.324204i	$0.105096\pi$
$263$			10.5154i			0.648407i	−0.945987	+	0.324204i	$0.894904\pi$
$264$		0			0
$265$	−26.2279	+	15.1427i	−1.61117	+	0.930209i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.3492	+	5.97514i	−0.631004	+	0.364311i	−0.781141	−	0.624355i	$-0.785362\pi$
$269$	−10.3492	+	5.97514i	−0.631004	+	0.364311i	0.150137	+	0.988665i	$0.452029\pi$
$270$		0			0
$271$	−6.86396	+	11.8887i	−0.416956	+	0.722189i	−0.995632	−	0.0933689i	$-0.970236\pi$
$271$	−6.86396	+	11.8887i	−0.416956	+	0.722189i	0.578676	+	0.815558i	$0.303570\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			21.6251i			1.30405i
$276$		0			0
$277$	13.7279			0.824831			0.412415	−	0.910996i	$-0.364685\pi$
$277$	13.7279			0.824831			0.412415	+	0.910996i	$0.364685\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.985281	−	1.70656i	0.0587770	−	0.101805i	−0.835140	−	0.550038i	$-0.814613\pi$
$281$	0.985281	−	1.70656i	0.0587770	−	0.101805i	0.893917	+	0.448233i	$0.147947\pi$
$282$		0			0
$283$	−11.2426	+	19.4728i	−0.668306	+	1.15754i	0.310072	+	0.950713i	$0.399647\pi$
$283$	−11.2426	+	19.4728i	−0.668306	+	1.15754i	−0.978378	+	0.206826i	$0.933687\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.621320	−	0.481813i	0.0366754	−	0.0284405i
$288$		0			0
$289$	13.4853	−	23.3572i	0.793252	−	1.37395i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−23.5919	+	13.6208i	−1.37825	+	0.795734i	−0.991949	−	0.126637i	$-0.959582\pi$
$293$	−23.5919	+	13.6208i	−1.37825	+	0.795734i	−0.386303	+	0.922372i	$0.626248\pi$
$294$		0			0
$295$	−21.7279	−	12.5446i	−1.26505	−	0.730376i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.74264	−	4.75039i	−0.158611	−	0.274722i
$300$		0			0
$301$	−7.75736	−	3.16693i	−0.447127	−	0.182539i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.4853	−	25.0892i	−0.829425	−	1.43661i
$306$		0			0
$307$	−1.51472			−0.0864496			−0.0432248	−	0.999065i	$-0.513763\pi$
$307$	−1.51472			−0.0864496			−0.0432248	+	0.999065i	$0.513763\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.48528	+	9.50079i	−0.311042	+	0.538740i	−0.978588	−	0.205828i	$-0.934011\pi$
$311$	−5.48528	+	9.50079i	−0.311042	+	0.538740i	0.667546	+	0.744568i	$0.267345\pi$
$312$		0			0
$313$	7.24264	−	4.18154i	0.409378	−	0.236355i	−0.281144	−	0.959666i	$-0.590714\pi$
$313$	7.24264	−	4.18154i	0.409378	−	0.236355i	0.690523	+	0.723311i	$0.257381\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	−10.8640	−	6.27231i	−0.608265	−	0.351182i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			6.63103i			0.368960i
$324$		0			0
$325$	7.75736	−	4.47871i	0.430301	−	0.248434i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.7574	−	17.7408i	−0.758468	−	0.978081i
$330$		0			0
$331$	−26.4853	+	15.2913i	−1.45576	+	0.840485i	−0.998799	−	0.0490002i	$-0.984396\pi$
$331$	−26.4853	+	15.2913i	−1.45576	+	0.840485i	−0.456964	+	0.889485i	$0.651063\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	0.789865	−	0.613280i	$-0.210150\pi$
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	−0.926049	+	0.377403i	$0.876817\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	+	3.46410i	0.324918	+	0.187592i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−24.0000	−	13.8564i	−1.28839	−	0.743851i	−0.310021	−	0.950730i	$-0.600336\pi$
$347$	−24.0000	−	13.8564i	−1.28839	−	0.743851i	−0.978367	+	0.206879i	$0.933669\pi$
$348$		0			0
$349$	−6.62132	−	3.82282i	−0.354431	−	0.204631i	0.312204	−	0.950015i	$-0.398933\pi$
$349$	−6.62132	−	3.82282i	−0.354431	−	0.204631i	−0.666635	+	0.745384i	$0.732266\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	3.16693i		−	0.168559i	−0.996442	−	0.0842793i	$-0.973141\pi$
$353$		−	3.16693i		−	0.168559i	0.996442	−	0.0842793i	$-0.0268588\pi$
$354$		0			0
$355$	26.4853			1.40569
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.62132	+	5.55487i	0.507794	+	0.293175i	0.731926	−	0.681384i	$-0.238621\pi$
$359$	9.62132	+	5.55487i	0.507794	+	0.293175i	−0.224132	+	0.974559i	$0.571955\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	18.1066	+	31.3616i	0.947743	+	1.64154i
$366$		0			0
$367$	−31.7279			−1.65618			−0.828092	−	0.560592i	$-0.810574\pi$
$367$	−31.7279			−1.65618			−0.828092	+	0.560592i	$0.810574\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	11.7426	+	15.1427i	0.609648	+	0.786170i
$372$		0			0
$373$	10.2721			0.531868			0.265934	−	0.963991i	$-0.414320\pi$
$373$	10.2721			0.531868			0.265934	+	0.963991i	$0.414320\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.19615i			0.267615i
$378$		0			0
$379$			11.8272i			0.607522i	0.952748	+	0.303761i	$0.0982424\pi$
$379$			11.8272i			0.607522i	−0.952748	+	0.303761i	$0.901758\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.7574			0.549675			0.274838	−	0.961491i	$-0.411376\pi$
$383$	10.7574			0.549675			0.274838	+	0.961491i	$0.411376\pi$
$384$		0			0
$385$	18.9853	−	2.59808i	0.967580	−	0.132410i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−37.2426			−1.88828			−0.944138	−	0.329549i	$-0.893103\pi$
$389$	−37.2426			−1.88828			−0.944138	+	0.329549i	$0.893103\pi$
$390$		0			0
$391$	−25.3492	−	43.9062i	−1.28197	−	2.22043i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−24.7279	−	42.8300i	−1.24420	−	2.15501i
$396$		0			0
$397$	−11.8934	−	6.86666i	−0.596913	−	0.344628i	0.170913	−	0.985286i	$-0.445328\pi$
$397$	−11.8934	−	6.86666i	−0.596913	−	0.344628i	−0.767826	+	0.640658i	$0.778661\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.4558			0.821766			0.410883	−	0.911688i	$-0.365221\pi$
$401$	16.4558			0.821766			0.410883	+	0.911688i	$0.365221\pi$
$402$		0			0
$403$		−	2.86976i		−	0.142953i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.86396	+	4.54026i	0.389802	+	0.225052i
$408$		0			0
$409$	−19.2426	−	11.1097i	−0.951487	−	0.549341i	−0.0579447	−	0.998320i	$-0.518455\pi$
$409$	−19.2426	−	11.1097i	−0.951487	−	0.549341i	−0.893543	+	0.448978i	$0.851788\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.00000	+	14.6969i	−0.295241	+	0.723189i
$414$		0			0
$415$	19.8640	+	11.4685i	0.975083	+	0.562965i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.9853	+	22.4912i	0.634373	+	1.09877i	0.986648	+	0.162869i	$0.0520748\pi$
$419$	12.9853	+	22.4912i	0.634373	+	1.09877i	−0.352275	+	0.935896i	$0.614592\pi$
$420$		0			0
$421$	5.86396	−	10.1567i	0.285792	−	0.495006i	−0.687009	−	0.726649i	$-0.741077\pi$
$421$	5.86396	−	10.1567i	0.285792	−	0.495006i	0.972801	+	0.231643i	$0.0744100\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	71.6985	−	41.3951i	3.47789	−	2.00796i
$426$		0			0
$427$	−14.4853	+	11.2328i	−0.700992	+	0.543595i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.8345	−	7.41002i	0.618217	−	0.356928i	−0.157957	−	0.987446i	$-0.550491\pi$
$431$	12.8345	−	7.41002i	0.618217	−	0.356928i	0.776175	+	0.630518i	$0.217158\pi$
$432$		0			0
$433$		−	6.33386i		−	0.304386i	−0.988351	−	0.152193i	$-0.951367\pi$
$433$		−	6.33386i		−	0.304386i	0.988351	−	0.152193i	$-0.0486335\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.62132	+	3.82282i	0.316741	+	0.182870i
$438$		0			0
$439$	−3.48528	−	6.03668i	−0.166343	−	0.288115i	0.770788	−	0.637092i	$-0.219863\pi$
$439$	−3.48528	−	6.03668i	−0.166343	−	0.288115i	−0.937132	+	0.348976i	$0.886529\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−16.2426	+	9.37769i	−0.771711	+	0.445548i	−0.833485	−	0.552543i	$-0.813658\pi$
$443$	−16.2426	+	9.37769i	−0.771711	+	0.445548i	0.0617735	+	0.998090i	$0.480324\pi$
$444$		0			0
$445$	−27.1066	+	46.9500i	−1.28498	+	2.22564i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$		0			0
$451$	0.257359	+	0.445759i	0.0121186	+	0.0209900i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.86396	−	6.27231i	−0.228026	−	0.294050i
$456$		0			0
$457$	2.51472	+	4.35562i	0.117634	+	0.203747i	0.918829	−	0.394655i	$-0.129136\pi$
$457$	2.51472	+	4.35562i	0.117634	+	0.203747i	−0.801196	+	0.598402i	$0.795803\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1360	−	5.85204i	−0.472082	−	0.272557i	0.245029	−	0.969516i	$-0.421203\pi$
$461$	−10.1360	−	5.85204i	−0.472082	−	0.272557i	−0.717111	+	0.696959i	$0.754536\pi$
$462$		0			0
$463$	15.6213	−	9.01897i	0.725984	−	0.419147i	−0.0909670	−	0.995854i	$-0.528996\pi$
$463$	15.6213	−	9.01897i	0.725984	−	0.419147i	0.816951	+	0.576707i	$0.195662\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.25736	+	5.64191i	−0.150733	+	0.261077i	−0.931497	−	0.363749i	$-0.881497\pi$
$467$	−3.25736	+	5.64191i	−0.150733	+	0.261077i	0.780764	+	0.624826i	$0.214830\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.74264	−	4.75039i	0.126107	−	0.218423i
$474$		0			0
$475$	−6.24264	+	10.8126i	−0.286432	+	0.496115i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.24264			0.0567777			0.0283889	−	0.999597i	$-0.490962\pi$
$479$	1.24264			0.0567777			0.0283889	+	0.999597i	$0.490962\pi$
$480$		0			0
$481$		−	3.76127i		−	0.171499i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.62132	+	11.4685i	−0.300659	+	0.520756i
$486$		0			0
$487$	33.1066	−	19.1141i	1.50020	−	0.866143i	0.500203	−	0.865908i	$-0.333259\pi$
$487$	33.1066	−	19.1141i	1.50020	−	0.866143i	1.00000		0.000234827i	$-7.47477e-5\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.98528	−	2.30090i	0.179853	−	0.103838i	−0.407370	−	0.913263i	$-0.633554\pi$
$491$	3.98528	−	2.30090i	0.179853	−	0.103838i	0.587224	+	0.809425i	$0.300221\pi$
$492$		0			0
$493$			48.0262i			2.16299i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.27208	−	16.6031i	−0.101917	−	0.744749i
$498$		0			0
$499$			4.35562i			0.194984i	0.995236	+	0.0974922i	$0.0310821\pi$
$499$			4.35562i			0.194984i	−0.995236	+	0.0974922i	$0.968918\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$		0			0
$507$		0			0
$508$		0			0
$509$			25.8067i			1.14386i	0.820302	+	0.571931i	$0.193805\pi$
$509$			25.8067i			1.14386i	−0.820302	+	0.571931i	$0.806195\pi$
$510$		0			0
$511$	18.1066	−	14.0410i	0.800989	−	0.621139i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	57.4039i		−	2.52952i
$516$		0			0
$517$	12.7279	−	7.34847i	0.559773	−	0.323185i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.50000	+	4.33013i	−0.328581	+	0.189706i	−0.655211	−	0.755446i	$-0.727420\pi$
$521$	−7.50000	+	4.33013i	−0.328581	+	0.189706i	0.326630	+	0.945152i	$0.394087\pi$
$522$		0			0
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	−0.876750	−	0.480946i	$-0.840293\pi$
$523$	−0.500000	+	0.866025i	−0.0218635	+	0.0378686i	0.854887	+	0.518815i	$0.173627\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	26.5241i		−	1.15541i
$528$		0			0
$529$	−35.4558			−1.54156
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.106602	−	0.184640i	0.00461743	−	0.00799763i
$534$		0			0
$535$	−16.8640	+	29.2092i	−0.729093	+	1.26283i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.25736	−	11.6786i	−0.140304	−	0.503033i
$540$		0			0
$541$	0.893398	−	1.54741i	0.0384102	−	0.0665284i	−0.846181	−	0.532895i	$-0.821104\pi$
$541$	0.893398	−	1.54741i	0.0384102	−	0.0665284i	0.884591	+	0.466367i	$0.154437\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	62.4411	−	36.0504i	2.67468	−	1.54423i
$546$		0			0
$547$	−2.22792	−	1.28629i	−0.0952591	−	0.0549978i	0.451614	−	0.892214i	$-0.350849\pi$
$547$	−2.22792	−	1.28629i	−0.0952591	−	0.0549978i	−0.546873	+	0.837216i	$0.684182\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.62132	−	6.27231i	−0.154273	−	0.267209i
$552$		0			0
$553$	−24.7279	+	19.1757i	−1.05154	+	0.815432i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.1066	+	20.9692i	0.512973	+	0.888496i	0.999887	+	0.0150455i	$0.00478931\pi$
$557$	12.1066	+	20.9692i	0.512973	+	0.888496i	−0.486914	+	0.873450i	$0.661877\pi$
$558$		0			0
$559$	−2.27208			−0.0960987
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.4853	−	30.2854i	0.736917	−	1.27638i	−0.216961	−	0.976180i	$-0.569614\pi$
$563$	17.4853	−	30.2854i	0.736917	−	1.27638i	0.953877	−	0.300197i	$-0.0970524\pi$
$564$		0			0
$565$	19.8640	−	11.4685i	0.835683	−	0.482482i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.48528	−	9.50079i	−0.229955	−	0.398294i	0.727840	−	0.685747i	$-0.240525\pi$
$569$	−5.48528	−	9.50079i	−0.229955	−	0.398294i	−0.957795	+	0.287454i	$0.907191\pi$
$570$		0			0
$571$	−39.9411	−	23.0600i	−1.67148	−	0.965032i	−0.966808	−	0.255502i	$-0.917759\pi$
$571$	−39.9411	−	23.0600i	−1.67148	−	0.965032i	−0.704676	−	0.709530i	$-0.748907\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	95.4580i		−	3.98087i
$576$		0			0
$577$	38.9558	−	22.4912i	1.62175	−	0.936320i	0.635302	−	0.772264i	$-0.280876\pi$
$577$	38.9558	−	22.4912i	1.62175	−	0.936320i	0.986451	−	0.164056i	$-0.0524577\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.48528	−	13.4361i	0.227568	−	0.557425i
$582$		0			0
$583$	−10.8640	+	6.27231i	−0.449939	+	0.259773i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.98528	−	12.0989i	0.288313	−	0.499373i	−0.685094	−	0.728455i	$-0.740239\pi$
$587$	6.98528	−	12.0989i	0.288313	−	0.499373i	0.973407	+	0.229081i	$0.0735722\pi$
$588$		0			0
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.2279	−	8.21449i	−0.584271	−	0.337329i	0.178558	−	0.983929i	$-0.442857\pi$
$593$	−14.2279	−	8.21449i	−0.584271	−	0.337329i	−0.762829	+	0.646601i	$0.776190\pi$
$594$		0			0
$595$	−44.9558	−	57.9727i	−1.84301	−	2.37665i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.4853	+	13.5592i	0.959583	+	0.554015i	0.896045	−	0.443964i	$-0.146428\pi$
$599$	23.4853	+	13.5592i	0.959583	+	0.554015i	0.0635380	+	0.997979i	$0.479762\pi$
$600$		0			0
$601$	−5.01472	−	2.89525i	−0.204555	−	0.118100i	0.394224	−	0.919015i	$-0.371014\pi$
$601$	−5.01472	−	2.89525i	−0.204555	−	0.118100i	−0.598778	+	0.800915i	$0.704347\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		−	33.4523i		−	1.36003i
$606$		0			0
$607$	−24.6985			−1.00248			−0.501240	−	0.865308i	$-0.667123\pi$
$607$	−24.6985			−1.00248			−0.501240	+	0.865308i	$0.667123\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.27208	−	3.04384i	−0.213285	−	0.123140i
$612$		0			0
$613$	2.62132	+	4.54026i	0.105874	+	0.183379i	0.914095	−	0.405500i	$-0.132903\pi$
$613$	2.62132	+	4.54026i	0.105874	+	0.183379i	−0.808221	+	0.588879i	$0.799569\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.74264	−	9.94655i	−0.231190	−	0.400433i	0.726969	−	0.686671i	$-0.240929\pi$
$617$	−5.74264	−	9.94655i	−0.231190	−	0.400433i	−0.958159	+	0.286238i	$0.907595\pi$
$618$		0			0
$619$	35.9706			1.44578			0.722889	−	0.690964i	$-0.242814\pi$
$619$	35.9706			1.44578			0.722889	+	0.690964i	$0.242814\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	31.7574	+	12.9649i	1.27233	+	0.519427i
$624$		0			0
$625$	68.4558			2.73823
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	34.7641i		−	1.38614i
$630$		0			0
$631$			5.49333i			0.218686i	0.994004	+	0.109343i	$0.0348747\pi$
$631$			5.49333i			0.218686i	−0.994004	+	0.109343i	$0.965125\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	84.4264			3.35036
$636$		0			0
$637$	−3.51472	+	3.58719i	−0.139258	+	0.142130i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	30.9411			1.22210			0.611050	−	0.791592i	$-0.290747\pi$
$641$	30.9411			1.22210			0.611050	+	0.791592i	$0.290747\pi$
$642$		0			0
$643$	13.2279	+	22.9114i	0.521658	+	0.903539i	0.999683	+	0.0251921i	$0.00801975\pi$
$643$	13.2279	+	22.9114i	0.521658	+	0.903539i	−0.478024	+	0.878347i	$0.658647\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.86396	−	8.42463i	−0.191222	−	0.331206i	0.754433	−	0.656377i	$-0.227912\pi$
$647$	−4.86396	−	8.42463i	−0.191222	−	0.331206i	−0.945655	+	0.325170i	$0.894578\pi$
$648$		0			0
$649$	−9.00000	−	5.19615i	−0.353281	−	0.203967i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	34.7574			1.36016			0.680080	−	0.733138i	$-0.261945\pi$
$653$	34.7574			1.36016			0.680080	+	0.733138i	$0.261945\pi$
$654$		0			0
$655$		−	2.15232i		−	0.0840980i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.4706	−	7.19988i	−0.485784	−	0.280468i	0.237040	−	0.971500i	$-0.423823\pi$
$659$	−12.4706	−	7.19988i	−0.485784	−	0.280468i	−0.722824	+	0.691032i	$0.757156\pi$
$660$		0			0
$661$	−13.4558	−	7.76874i	−0.523372	−	0.302169i	0.214941	−	0.976627i	$-0.431044\pi$
$661$	−13.4558	−	7.76874i	−0.523372	−	0.302169i	−0.738313	+	0.674458i	$0.764377\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.2426	+	4.18154i	0.397193	+	0.162153i
$666$		0			0
$667$	47.9558	+	27.6873i	1.85686	+	1.07206i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.00000	−	10.3923i	−0.231627	−	0.401190i
$672$		0			0
$673$	4.98528	−	8.63476i	0.192168	−	0.332846i	−0.753800	−	0.657104i	$-0.771781\pi$
$673$	4.98528	−	8.63476i	0.192168	−	0.332846i	0.945969	+	0.324258i	$0.105115\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.7279	−	10.8126i	0.719773	−	0.415561i	−0.0948964	−	0.995487i	$-0.530252\pi$
$677$	18.7279	−	10.8126i	0.719773	−	0.415561i	0.814669	+	0.579926i	$0.196919\pi$
$678$		0			0
$679$	7.75736	+	3.16693i	0.297700	+	0.121536i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−30.9853	+	17.8894i	−1.18562	+	0.684517i	−0.957308	−	0.289071i	$-0.906654\pi$
$683$	−30.9853	+	17.8894i	−1.18562	+	0.684517i	−0.228311	+	0.973588i	$0.573320\pi$
$684$		0			0
$685$			37.6339i			1.43792i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.50000	+	2.59808i	0.171436	+	0.0989788i
$690$		0			0
$691$	−21.9706	−	38.0541i	−0.835800	−	1.44765i	−0.893378	−	0.449306i	$-0.851671\pi$
$691$	−21.9706	−	38.0541i	−0.835800	−	1.44765i	0.0575781	−	0.998341i	$-0.481662\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−47.0772	+	27.1800i	−1.78574	+	1.03100i
$696$		0			0
$697$	0.985281	−	1.70656i	0.0373202	−	0.0646405i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−34.9706			−1.32082			−0.660410	−	0.750905i	$-0.729617\pi$
$701$	−34.9706			−1.32082			−0.660410	+	0.750905i	$0.729617\pi$
$702$		0			0
$703$	2.62132	+	4.54026i	0.0988650	+	0.171239i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.257359	+	1.88064i	0.00967899	+	0.0707286i
$708$		0			0
$709$	−5.75736	−	9.97204i	−0.216222	−	0.374508i	0.737428	−	0.675426i	$-0.236040\pi$
$709$	−5.75736	−	9.97204i	−0.216222	−	0.374508i	−0.953650	+	0.300918i	$0.902707\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−26.4853	−	15.2913i	−0.991882	−	0.572663i
$714$		0			0
$715$	4.50000	−	2.59808i	0.168290	−	0.0971625i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.3787	+	35.2969i	−0.759997	+	1.31635i	0.182855	+	0.983140i	$0.441466\pi$
$719$	−20.3787	+	35.2969i	−0.759997	+	1.31635i	−0.942852	+	0.333213i	$0.891867\pi$
$720$		0			0
$721$	−35.9853	+	4.92447i	−1.34016	+	0.183397i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−45.2132	+	78.3116i	−1.67918	+	2.90842i
$726$		0			0
$727$	8.34924	−	14.4613i	0.309656	−	0.536340i	−0.668631	−	0.743594i	$-0.733119\pi$
$727$	8.34924	−	14.4613i	0.309656	−	0.536340i	0.978287	+	0.207254i	$0.0664527\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.0000			−0.776713
$732$		0			0
$733$		−	49.2149i		−	1.81779i	−0.417022	−	0.908896i	$-0.636926\pi$
$733$		−	49.2149i		−	1.81779i	0.417022	−	0.908896i	$-0.363074\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−35.7426	+	20.6360i	−1.31481	+	0.759108i	−0.982889	−	0.184197i	$-0.941031\pi$
$739$	−35.7426	+	20.6360i	−1.31481	+	0.759108i	−0.331925	+	0.943306i	$0.607698\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.8640	+	14.9326i	−0.948857	+	0.547823i	−0.892726	−	0.450601i	$-0.851210\pi$
$743$	−25.8640	+	14.9326i	−0.948857	+	0.547823i	−0.0561311	+	0.998423i	$0.517876\pi$
$744$		0			0
$745$		−	44.9823i		−	1.64803i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	19.7574	+	8.06591i	0.721918	+	0.294722i
$750$		0			0
$751$			1.90613i			0.0695557i	0.999395	+	0.0347778i	$0.0110724\pi$
$751$			1.90613i			0.0695557i	−0.999395	+	0.0347778i	$0.988928\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	84.9411			3.09132
$756$		0			0
$757$	−43.9411			−1.59707			−0.798534	−	0.601950i	$-0.794391\pi$
$757$	−43.9411			−1.59707			−0.798534	+	0.601950i	$0.794391\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	14.1536i		−	0.513067i	−0.966535	−	0.256533i	$-0.917420\pi$
$761$		−	14.1536i		−	0.513067i	0.966535	−	0.256533i	$-0.0825804\pi$
$762$		0			0
$763$	−27.9558	−	36.0504i	−1.01207	−	1.30511i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			4.30463i			0.155431i
$768$		0			0
$769$	34.1985	−	19.7445i	1.23323	−	0.712005i	0.265527	−	0.964103i	$-0.414454\pi$
$769$	34.1985	−	19.7445i	1.23323	−	0.712005i	0.967702	+	0.252098i	$0.0811206\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	28.3492	−	16.3674i	1.01965	−	0.588696i	0.105648	−	0.994404i	$-0.466308\pi$
$773$	28.3492	−	16.3674i	1.01965	−	0.588696i	0.914003	+	0.405708i	$0.132975\pi$
$774$		0			0
$775$	24.9706	−	43.2503i	0.896969	−	1.55360i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			0.297173i			0.0106473i
$780$		0			0
$781$	10.9706			0.392558
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−24.7279	+	42.8300i	−0.882577	+	1.52867i
$786$		0			0
$787$	−3.24264	+	5.61642i	−0.115588	+	0.200204i	−0.918015	−	0.396547i	$-0.870208\pi$
$787$	−3.24264	+	5.61642i	−0.115588	+	0.200204i	0.802427	+	0.596750i	$0.203542\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.89340	−	11.4685i	−0.316213	−	0.407772i
$792$		0			0
$793$	−2.48528	+	4.30463i	−0.0882549	+	0.152862i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.1066	+	8.72180i	−0.535103	+	0.308942i	−0.743092	−	0.669189i	$-0.766642\pi$
$797$	−15.1066	+	8.72180i	−0.535103	+	0.308942i	0.207989	+	0.978131i	$0.433308\pi$
$798$		0			0
$799$	−48.7279	−	28.1331i	−1.72387	−	0.995277i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.50000	+	12.9904i	0.264669	+	0.458421i
$804$		0			0
$805$	−83.8051	+	11.4685i	−2.95374	+	0.404210i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.985281	+	1.70656i	0.0346406	+	0.0599994i	0.882826	−	0.469700i	$-0.155638\pi$
$809$	0.985281	+	1.70656i	0.0346406	+	0.0599994i	−0.848185	+	0.529700i	$0.822305\pi$
$810$		0			0
$811$	−29.9411			−1.05138			−0.525688	−	0.850678i	$-0.676192\pi$
$811$	−29.9411			−1.05138			−0.525688	+	0.850678i	$0.676192\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−21.1066	+	36.5577i	−0.739332	+	1.28056i
$816$		0			0
$817$	2.74264	−	1.58346i	0.0959529	−	0.0553984i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.727922	−	1.26080i	−0.0254047	−	0.0440022i	0.853044	−	0.521840i	$-0.174754\pi$
$821$	−0.727922	−	1.26080i	−0.0254047	−	0.0440022i	−0.878448	+	0.477838i	$0.841421\pi$
$822$		0			0
$823$	0.213203	+	0.123093i	0.00743180	+	0.00429075i	0.503711	−	0.863872i	$-0.331968\pi$
$823$	0.213203	+	0.123093i	0.00743180	+	0.00429075i	−0.496279	+	0.868163i	$0.665301\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	7.76874i		−	0.270145i	−0.990836	−	0.135073i	$-0.956873\pi$
$827$		−	7.76874i		−	0.270145i	0.990836	−	0.135073i	$-0.0431268\pi$
$828$		0			0
$829$	27.8345	−	16.0703i	0.966733	−	0.558144i	0.0684943	−	0.997652i	$-0.478181\pi$
$829$	27.8345	−	16.0703i	0.966733	−	0.558144i	0.898239	+	0.439508i	$0.144847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−32.4853	+	33.1552i	−1.12555	+	1.14876i
$834$		0			0
$835$	−35.2279	+	20.3389i	−1.21911	+	0.703855i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.37868	+	9.31615i	−0.185693	+	0.321629i	−0.943810	−	0.330489i	$-0.892786\pi$
$839$	−5.37868	+	9.31615i	−0.185693	+	0.321629i	0.758117	+	0.652118i	$0.226120\pi$
$840$		0			0
$841$	−11.7279	−	20.3134i	−0.404411	−	0.700461i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	45.2132	+	26.1039i	1.55538	+	0.898000i
$846$		0			0
$847$	−20.9706	+	2.86976i	−0.720557	+	0.0986060i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−34.7132	−	20.0417i	−1.18995	−	0.687020i
$852$		0			0
$853$	4.86396	+	2.80821i	0.166539	+	0.0961513i	0.580953	−	0.813937i	$-0.302680\pi$
$853$	4.86396	+	2.80821i	0.166539	+	0.0961513i	−0.414414	+	0.910089i	$0.636013\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	14.9941i		−	0.512189i	−0.966652	−	0.256095i	$-0.917564\pi$
$857$		−	14.9941i		−	0.512189i	0.966652	−	0.256095i	$-0.0824358\pi$
$858$		0			0
$859$	0.0294373			0.00100439			0.000502193	−	1.00000i	$-0.499840\pi$
$859$	0.0294373			0.00100439			0.000502193		1.00000i	$0.499840\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.5919	−	18.8169i	−1.10944	−	0.640536i	−0.170756	−	0.985313i	$-0.554621\pi$
$863$	−32.5919	−	18.8169i	−1.10944	−	0.640536i	−0.938684	+	0.344777i	$0.887954\pi$
$864$		0			0
$865$	20.4853	+	35.4815i	0.696520	+	1.20641i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−10.2426	−	17.7408i	−0.347458	−	0.601815i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.2279	−	82.0473i	−0.379573	−	2.77371i
$876$		0			0
$877$	46.6985			1.57690			0.788448	−	0.615102i	$-0.210885\pi$
$877$	46.6985			1.57690			0.788448	+	0.615102i	$0.210885\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			12.4215i			0.418492i	0.977863	+	0.209246i	$0.0671009\pi$
$881$			12.4215i			0.418492i	−0.977863	+	0.209246i	$0.932899\pi$
$882$		0			0
$883$			4.89898i			0.164864i	0.996597	+	0.0824319i	$0.0262687\pi$
$883$			4.89898i			0.164864i	−0.996597	+	0.0824319i	$0.973731\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−49.6690			−1.66772			−0.833862	−	0.551973i	$-0.813875\pi$
$887$	−49.6690			−1.66772			−0.833862	+	0.551973i	$0.813875\pi$
$888$		0			0
$889$	−7.24264	−	52.9251i	−0.242910	−	1.77505i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.48528			0.283949
$894$		0			0
$895$	38.5919	+	66.8431i	1.28998	+	2.23432i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	14.4853	+	25.0892i	0.483111	+	0.836773i
$900$		0			0
$901$	41.5919	+	24.0131i	1.38563	+	0.799992i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	26.4853			0.880401
$906$		0			0
$907$			18.4582i			0.612895i	0.951888	+	0.306447i	$0.0991404\pi$
$907$			18.4582i			0.612895i	−0.951888	+	0.306447i	$0.900860\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−28.8640	−	16.6646i	−0.956306	−	0.552123i	−0.0612716	−	0.998121i	$-0.519516\pi$
$911$	−28.8640	−	16.6646i	−0.956306	−	0.552123i	−0.895034	+	0.445998i	$0.852849\pi$
$912$		0			0
$913$	8.22792	+	4.75039i	0.272304	+	0.157215i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.34924	+	0.184640i	−0.0445559	+	0.00609734i
$918$		0			0
$919$	−16.8640	−	9.73641i	−0.556291	−	0.321175i	0.195365	−	0.980731i	$-0.437411\pi$
$919$	−16.8640	−	9.73641i	−0.556291	−	0.321175i	−0.751655	+	0.659556i	$0.770744\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.27208	−	3.93535i	−0.0747864	−	0.129534i
$924$		0			0
$925$	32.7279	−	56.6864i	1.07609	−	1.86384i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.5147	−	14.1536i	0.804302	−	0.464364i	−0.0406713	−	0.999173i	$-0.512950\pi$
$929$	24.5147	−	14.1536i	0.804302	−	0.464364i	0.844973	+	0.534809i	$0.179616\pi$
$930$		0			0
$931$	1.74264	−	6.77962i	0.0571127	−	0.222193i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	41.5919	−	24.0131i	1.36020	−	0.785312i
$936$		0			0
$937$		−	45.5257i		−	1.48726i	−0.668592	−	0.743630i	$-0.733103\pi$
$937$		−	45.5257i		−	1.48726i	0.668592	−	0.743630i	$-0.266897\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.4558	+	11.2328i	0.634242	+	0.366180i	0.782393	−	0.622785i	$-0.213999\pi$
$941$	19.4558	+	11.2328i	0.634242	+	0.366180i	−0.148151	+	0.988965i	$0.547332\pi$
$942$		0			0
$943$	−1.13604	−	1.96768i	−0.0369945	−	0.0640764i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.0294	+	9.25460i	−0.520887	+	0.300734i	−0.737297	−	0.675568i	$-0.763898\pi$
$947$	−16.0294	+	9.25460i	−0.520887	+	0.300734i	0.216411	+	0.976302i	$0.430565\pi$
$948$		0			0
$949$	3.10660	−	5.38079i	0.100845	−	0.174668i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−44.4853			−1.44102			−0.720510	−	0.693445i	$-0.756092\pi$
$953$	−44.4853			−1.44102			−0.720510	+	0.693445i	$0.756092\pi$
$954$		0			0
$955$	−23.4853	−	40.6777i	−0.759966	−	1.31630i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	23.5919	−	3.22848i	0.761822	−	0.104253i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−46.9706	−	27.1185i	−1.51204	−	0.872974i
$966$		0			0
$967$	5.59188	−	3.22848i	0.179823	−	0.103821i	−0.407387	−	0.913256i	$-0.633560\pi$
$967$	5.59188	−	3.22848i	0.179823	−	0.103821i	0.587209	+	0.809435i	$0.300227\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.7426	+	25.5350i	−0.473114	+	0.819457i	−0.999526	−	0.0307720i	$-0.990203\pi$
$971$	−14.7426	+	25.5350i	−0.473114	+	0.819457i	0.526413	+	0.850229i	$0.323537\pi$
$972$		0			0
$973$	21.0772	+	27.1800i	0.675703	+	0.871351i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.48528	−	14.6969i	0.271468	−	0.470197i	−0.697770	−	0.716322i	$-0.745824\pi$
$977$	8.48528	−	14.6969i	0.271468	−	0.470197i	0.969238	+	0.246125i	$0.0791575\pi$
$978$		0			0
$979$	−11.2279	+	19.4473i	−0.358846	+	0.621539i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.7574			0.534477			0.267238	−	0.963630i	$-0.413889\pi$
$983$	16.7574			0.534477			0.267238	+	0.963630i	$0.413889\pi$
$984$		0			0
$985$			10.3923i			0.331126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−12.1066	+	20.9692i	−0.384968	+	0.666783i
$990$		0			0
$991$	−37.8640	+	21.8608i	−1.20279	+	0.694430i	−0.961174	−	0.275942i	$-0.911010\pi$
$991$	−37.8640	+	21.8608i	−1.20279	+	0.694430i	−0.241614	+	0.970372i	$0.577677\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.7426	+	11.9758i	−0.657586	+	0.379657i
$996$		0			0
$997$		−	5.61642i		−	0.177874i	−0.996037	−	0.0889369i	$-0.971653\pi$
$997$		−	5.61642i		−	0.177874i	0.996037	−	0.0889369i	$-0.0283469\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bf.e.2287.1		4
3.2	odd	2		1008.2.bf.f.943.2	yes	4
4.3	odd	2		3024.2.bf.f.2287.1		4
7.3	odd	6		3024.2.cz.e.2719.1		4
9.4	even	3		3024.2.cz.f.1279.1		4
9.5	odd	6		1008.2.cz.f.607.2	yes	4
12.11	even	2		1008.2.bf.e.943.2	yes	4
21.17	even	6		1008.2.cz.e.367.2	yes	4
28.3	even	6		3024.2.cz.f.2719.1		4
36.23	even	6		1008.2.cz.e.607.2	yes	4
36.31	odd	6		3024.2.cz.e.1279.1		4
63.31	odd	6		3024.2.bf.f.1711.2		4
63.59	even	6		1008.2.bf.e.31.1	✓	4
84.59	odd	6		1008.2.cz.f.367.2	yes	4
252.31	even	6	inner	3024.2.bf.e.1711.2		4
252.59	odd	6		1008.2.bf.f.31.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.e.31.1	✓	4	63.59	even	6
1008.2.bf.e.943.2	yes	4	12.11	even	2
1008.2.bf.f.31.1	yes	4	252.59	odd	6
1008.2.bf.f.943.2	yes	4	3.2	odd	2
1008.2.cz.e.367.2	yes	4	21.17	even	6
1008.2.cz.e.607.2	yes	4	36.23	even	6
1008.2.cz.f.367.2	yes	4	84.59	odd	6
1008.2.cz.f.607.2	yes	4	9.5	odd	6
3024.2.bf.e.1711.2		4	252.31	even	6	inner
3024.2.bf.e.2287.1		4	1.1	even	1	trivial
3024.2.bf.f.1711.2		4	63.31	odd	6
3024.2.bf.f.2287.1		4	4.3	odd	2
3024.2.cz.e.1279.1		4	36.31	odd	6
3024.2.cz.e.2719.1		4	7.3	odd	6
3024.2.cz.f.1279.1		4	9.4	even	3
3024.2.cz.f.2719.1		4	28.3	even	6

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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.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-4.18154i q^{5} +(-2.62132 + 0.358719i) q^{7} -1.73205i q^{11} +(-0.621320 + 0.358719i) q^{13} +(-5.74264 + 3.31552i) q^{17} +(0.500000 - 0.866025i) q^{19} +7.64564i q^{23} -12.4853 q^{25} +(3.62132 - 6.27231i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(1.50000 + 10.9612i) q^{35} +(-2.62132 + 4.54026i) q^{37} +(-0.257359 + 0.148586i) q^{41} +(2.74264 + 1.58346i) q^{43} +(4.24264 + 7.34847i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-3.62132 - 6.27231i) q^{53} -7.24264 q^{55} +(3.00000 - 5.19615i) q^{59} +(6.00000 - 3.46410i) q^{61} +(1.50000 + 2.59808i) q^{65} +6.33386i q^{71} +(-7.50000 + 4.33013i) q^{73} +(0.621320 + 4.54026i) q^{77} +(10.2426 - 5.91359i) q^{79} +(-2.74264 + 4.75039i) q^{83} +(13.8640 + 24.0131i) q^{85} +(-11.2279 - 6.48244i) q^{89} +(1.50000 - 1.16320i) q^{91} +(-3.62132 - 2.09077i) q^{95} +(-2.74264 - 1.58346i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{7} + 6 q^{13} - 6 q^{17} + 2 q^{19} - 16 q^{25} + 6 q^{29} - 8 q^{31} + 6 q^{35} - 2 q^{37} - 18 q^{41} - 6 q^{43} + 10 q^{49} - 6 q^{53} - 12 q^{55} + 12 q^{59} + 24 q^{61} + 6 q^{65} - 30 q^{73}+ \cdots + 6 q^{97}+O(q^{100}) \) 4 * q - 2 * q^7 + 6 * q^13 - 6 * q^17 + 2 * q^19 - 16 * q^25 + 6 * q^29 - 8 * q^31 + 6 * q^35 - 2 * q^37 - 18 * q^41 - 6 * q^43 + 10 * q^49 - 6 * q^53 - 12 * q^55 + 12 * q^59 + 24 * q^61 + 6 * q^65 - 30 * q^73 - 6 * q^77 + 24 * q^79 + 6 * q^83 + 30 * q^85 + 6 * q^89 + 6 * q^91 - 6 * q^95 + 6 * q^97

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