LMFDB - Embedded newform 3024.2.bf.f.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.f.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	$0.0840907\pi$
$11$			1.73205i			0.522233i	−0.965307	+	0.261116i	$0.915909\pi$
$12$		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	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	7.64564i		−	1.59423i	−0.603830	−	0.797113i	$-0.706359\pi$
$23$		−	7.64564i		−	1.59423i	0.603830	−	0.797113i	$-0.293641\pi$
$24$		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	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		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	0.276079	−	0.961135i	$-0.410965\pi$
$43$	−2.74264	−	1.58346i	−0.418249	−	0.241476i	−0.694328	+	0.719659i	$0.744298\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.24264	−	7.34847i	−0.618853	−	1.07188i	−0.989695	−	0.143189i	$-0.954264\pi$
$47$	−4.24264	−	7.34847i	−0.618853	−	1.07188i	0.370843	−	0.928696i	$-0.379069\pi$
$48$		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	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		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	$-0.877352\pi$
$71$		−	6.33386i		−	0.751691i	0.926682	−	0.375845i	$-0.122648\pi$
$72$		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	−0.949468	−	0.313864i	$-0.898376\pi$
$79$	−10.2426	+	5.91359i	−1.15239	+	0.665331i	−0.202919	+	0.979195i	$0.565043\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.74264	−	4.75039i	0.301044	−	0.521423i	−0.675329	−	0.737517i	$-0.735998\pi$
$83$	2.74264	−	4.75039i	0.301044	−	0.521423i	0.976373	+	0.216093i	$0.0693316\pi$
$84$		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	$-0.736429\pi$
$103$	−13.7279			−1.35265			−0.676326	+	0.736602i	$0.736429\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.98528	+	4.03295i	0.675293	+	0.389880i	0.798079	−	0.602553i	$-0.205850\pi$
$107$	6.98528	+	4.03295i	0.675293	+	0.389880i	−0.122786	+	0.992433i	$0.539183\pi$
$108$		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	$-0.646605\pi$
$127$		−	20.1903i		−	1.79160i	0.444461	−	0.895798i	$-0.353395\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.514719			−0.0449712			−0.0224856	−	0.999747i	$-0.507158\pi$
$131$	−0.514719			−0.0449712			−0.0224856	+	0.999747i	$0.507158\pi$
$132$		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	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$		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	$-0.690307\pi$
$151$		−	20.3134i		−	1.65308i	0.562880	−	0.826539i	$-0.309693\pi$
$152$		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	0.801652	−	0.597791i	$-0.203955\pi$
$163$	8.74264	+	5.04757i	0.684776	+	0.395356i	−0.116876	+	0.993147i	$0.537288\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.86396	+	8.42463i	0.376385	+	0.651917i	0.990533	−	0.137273i	$-0.0438338\pi$
$167$	4.86396	+	8.42463i	0.376385	+	0.651917i	−0.614149	+	0.789190i	$0.710500\pi$
$168$		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	0.235406	−	0.971897i	$-0.424358\pi$
$179$	15.9853	−	9.22911i	1.19480	−	0.689816i	0.959390	+	0.282081i	$0.0910248\pi$
$180$		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	−0.808794	−	0.588092i	$-0.799879\pi$
$191$	−9.72792	+	5.61642i	−0.703888	+	0.406390i	0.104906	+	0.994482i	$0.466546\pi$
$192$		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	0.949500	−	0.313766i	$-0.101591\pi$
$199$	2.86396	+	4.96053i	0.203021	+	0.351642i	−0.746480	+	0.665408i	$0.768257\pi$
$200$		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	−0.268902	−	0.963168i	$-0.586661\pi$
$211$	6.25736	−	3.61269i	0.430774	−	0.248708i	0.699676	+	0.714460i	$0.253327\pi$
$212$		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	−0.806620	−	0.591070i	$-0.798706\pi$
$223$	1.62132	−	2.80821i	0.108572	−	0.188052i	0.915192	+	0.403019i	$0.132039\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.514719			0.0341631			0.0170815	−	0.999854i	$-0.494563\pi$
$227$	0.514719			0.0341631			0.0170815	+	0.999854i	$0.494563\pi$
$228$		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	0.374953	−	0.927044i	$-0.377659\pi$
$239$	21.1066	−	12.1859i	1.36527	−	0.788240i	0.990320	+	0.138803i	$0.0443256\pi$
$240$		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	$-0.597081\pi$
$251$	−9.51472			−0.600564			−0.300282	+	0.953851i	$0.597081\pi$
$252$		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	$-0.894904\pi$
$263$		−	10.5154i		−	0.648407i	0.945987	−	0.324204i	$-0.105096\pi$
$264$		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	−0.578676	−	0.815558i	$-0.696430\pi$
$271$	6.86396	−	11.8887i	0.416956	−	0.722189i	0.995632	+	0.0933689i	$0.0297636\pi$
$272$		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	$-0.600353\pi$
$283$	11.2426	−	19.4728i	0.668306	−	1.15754i	0.978378	−	0.206826i	$-0.0663135\pi$
$284$		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	$-0.486237\pi$
$307$	1.51472			0.0864496			0.0432248	+	0.999065i	$0.486237\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.48528	−	9.50079i	0.311042	−	0.538740i	−0.667546	−	0.744568i	$-0.732655\pi$
$311$	5.48528	−	9.50079i	0.311042	−	0.538740i	0.978588	+	0.205828i	$0.0659888\pi$
$312$		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	0.456964	−	0.889485i	$-0.348937\pi$
$331$	26.4853	−	15.2913i	1.45576	−	0.840485i	0.998799	+	0.0490002i	$0.0156035\pi$
$332$		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	0.978367	−	0.206879i	$-0.0663306\pi$
$347$	24.0000	+	13.8564i	1.28839	+	0.743851i	0.310021	+	0.950730i	$0.399664\pi$
$348$		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	0.224132	−	0.974559i	$-0.428045\pi$
$359$	−9.62132	−	5.55487i	−0.507794	−	0.293175i	−0.731926	+	0.681384i	$0.761379\pi$
$360$		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	$-0.189426\pi$
$367$	31.7279			1.65618			0.828092	+	0.560592i	$0.189426\pi$
$368$		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	$-0.901758\pi$
$379$		−	11.8272i		−	0.607522i	0.952748	−	0.303761i	$-0.0982424\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.7574			−0.549675			−0.274838	−	0.961491i	$-0.588624\pi$
$383$	−10.7574			−0.549675			−0.274838	+	0.961491i	$0.588624\pi$
$384$		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	$-0.947925\pi$
$419$	−12.9853	−	22.4912i	−0.634373	−	1.09877i	0.352275	−	0.935896i	$-0.385408\pi$
$420$		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	−0.776175	−	0.630518i	$-0.782842\pi$
$431$	−12.8345	+	7.41002i	−0.618217	+	0.356928i	0.157957	+	0.987446i	$0.449509\pi$
$432$		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	0.937132	−	0.348976i	$-0.113471\pi$
$439$	3.48528	+	6.03668i	0.166343	+	0.288115i	−0.770788	+	0.637092i	$0.780137\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.2426	−	9.37769i	0.771711	−	0.445548i	−0.0617735	−	0.998090i	$-0.519676\pi$
$443$	16.2426	−	9.37769i	0.771711	−	0.445548i	0.833485	+	0.552543i	$0.186342\pi$
$444$		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	−0.816951	−	0.576707i	$-0.804338\pi$
$463$	−15.6213	+	9.01897i	−0.725984	+	0.419147i	0.0909670	+	0.995854i	$0.471004\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.25736	−	5.64191i	0.150733	−	0.261077i	−0.780764	−	0.624826i	$-0.785170\pi$
$467$	3.25736	−	5.64191i	0.150733	−	0.261077i	0.931497	+	0.363749i	$0.118503\pi$
$468$		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	$-0.509038\pi$
$479$	−1.24264			−0.0567777			−0.0283889	+	0.999597i	$0.509038\pi$
$480$		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	$0.666741\pi$
$487$	−33.1066	+	19.1141i	−1.50020	+	0.866143i	−1.00000		0.000234827i	$0.999925\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.98528	+	2.30090i	−0.179853	+	0.103838i	−0.587224	−	0.809425i	$-0.699779\pi$
$491$	−3.98528	+	2.30090i	−0.179853	+	0.103838i	0.407370	+	0.913263i	$0.366446\pi$
$492$		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	$-0.968918\pi$
$499$		−	4.35562i		−	0.194984i	0.995236	−	0.0974922i	$-0.0310821\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		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	−0.854887	−	0.518815i	$-0.826373\pi$
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	0.876750	+	0.480946i	$0.159707\pi$
$524$		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	0.546873	−	0.837216i	$-0.315818\pi$
$547$	2.22792	+	1.28629i	0.0952591	+	0.0549978i	−0.451614	+	0.892214i	$0.649151\pi$
$548$		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	$0.430386\pi$
$563$	−17.4853	+	30.2854i	−0.736917	+	1.27638i	−0.953877	+	0.300197i	$0.902948\pi$
$564$		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	$0.0822408\pi$
$571$	39.9411	+	23.0600i	1.67148	+	0.965032i	0.704676	+	0.709530i	$0.251093\pi$
$572$		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	−0.973407	−	0.229081i	$-0.926428\pi$
$587$	−6.98528	+	12.0989i	−0.288313	+	0.499373i	0.685094	+	0.728455i	$0.259761\pi$
$588$		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	−0.0635380	−	0.997979i	$-0.520238\pi$
$599$	−23.4853	−	13.5592i	−0.959583	−	0.554015i	−0.896045	+	0.443964i	$0.853572\pi$
$600$		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	$-0.332877\pi$
$607$	24.6985			1.00248			0.501240	+	0.865308i	$0.332877\pi$
$608$		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	$-0.757186\pi$
$619$	−35.9706			−1.44578			−0.722889	+	0.690964i	$0.757186\pi$
$620$		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	$-0.965125\pi$
$631$		−	5.49333i		−	0.218686i	0.994004	−	0.109343i	$-0.0348747\pi$
$632$		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	$-0.991980\pi$
$643$	−13.2279	−	22.9114i	−0.521658	−	0.903539i	0.478024	−	0.878347i	$-0.341353\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.86396	+	8.42463i	0.191222	+	0.331206i	0.945655	−	0.325170i	$-0.105422\pi$
$647$	4.86396	+	8.42463i	0.191222	+	0.331206i	−0.754433	+	0.656377i	$0.772088\pi$
$648$		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	0.722824	−	0.691032i	$-0.242844\pi$
$659$	12.4706	+	7.19988i	0.485784	+	0.280468i	−0.237040	+	0.971500i	$0.576177\pi$
$660$		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	0.228311	−	0.973588i	$-0.426680\pi$
$683$	30.9853	−	17.8894i	1.18562	−	0.684517i	0.957308	+	0.289071i	$0.0933463\pi$
$684$		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	$0.148329\pi$
$691$	21.9706	+	38.0541i	0.835800	+	1.44765i	−0.0575781	+	0.998341i	$0.518338\pi$
$692$		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	$-0.558534\pi$
$719$	20.3787	−	35.2969i	0.759997	−	1.31635i	0.942852	−	0.333213i	$-0.108133\pi$
$720$		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	−0.978287	−	0.207254i	$-0.933547\pi$
$727$	−8.34924	+	14.4613i	−0.309656	+	0.536340i	0.668631	+	0.743594i	$0.266881\pi$
$728$		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	0.331925	−	0.943306i	$-0.392302\pi$
$739$	35.7426	−	20.6360i	1.31481	−	0.759108i	0.982889	+	0.184197i	$0.0589686\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.8640	−	14.9326i	0.948857	−	0.547823i	0.0561311	−	0.998423i	$-0.482124\pi$
$743$	25.8640	−	14.9326i	0.948857	−	0.547823i	0.892726	+	0.450601i	$0.148790\pi$
$744$		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	$-0.988928\pi$
$751$		−	1.90613i		−	0.0695557i	0.999395	−	0.0347778i	$-0.0110724\pi$
$752$		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	−0.802427	−	0.596750i	$-0.796458\pi$
$787$	3.24264	−	5.61642i	0.115588	−	0.200204i	0.918015	+	0.396547i	$0.129792\pi$
$788$		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	$-0.323808\pi$
$811$	29.9411			1.05138			0.525688	+	0.850678i	$0.323808\pi$
$812$		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	0.496279	−	0.868163i	$-0.334699\pi$
$823$	−0.213203	−	0.123093i	−0.00743180	−	0.00429075i	−0.503711	+	0.863872i	$0.668032\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			7.76874i			0.270145i	0.990836	+	0.135073i	$0.0431268\pi$
$827$			7.76874i			0.270145i	−0.990836	+	0.135073i	$0.956873\pi$
$828$		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	−0.758117	−	0.652118i	$-0.773880\pi$
$839$	5.37868	−	9.31615i	0.185693	−	0.321629i	0.943810	+	0.330489i	$0.107214\pi$
$840$		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	$-0.500160\pi$
$859$	−0.0294373			−0.00100439			−0.000502193		1.00000i	$0.500160\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.5919	+	18.8169i	1.10944	+	0.640536i	0.938684	−	0.344777i	$-0.112046\pi$
$863$	32.5919	+	18.8169i	1.10944	+	0.640536i	0.170756	+	0.985313i	$0.445379\pi$
$864$		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	$-0.973731\pi$
$883$		−	4.89898i		−	0.164864i	0.996597	−	0.0824319i	$-0.0262687\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	49.6690			1.66772			0.833862	−	0.551973i	$-0.186125\pi$
$887$	49.6690			1.66772			0.833862	+	0.551973i	$0.186125\pi$
$888$		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	$-0.900860\pi$
$907$		−	18.4582i		−	0.612895i	0.951888	−	0.306447i	$-0.0991404\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	28.8640	+	16.6646i	0.956306	+	0.552123i	0.895034	−	0.445998i	$-0.147151\pi$
$911$	28.8640	+	16.6646i	0.956306	+	0.552123i	0.0612716	+	0.998121i	$0.480484\pi$
$912$		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	0.751655	−	0.659556i	$-0.229256\pi$
$919$	16.8640	+	9.73641i	0.556291	+	0.321175i	−0.195365	+	0.980731i	$0.562589\pi$
$920$		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	−0.216411	−	0.976302i	$-0.569435\pi$
$947$	16.0294	−	9.25460i	0.520887	−	0.300734i	0.737297	+	0.675568i	$0.236102\pi$
$948$		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	−0.587209	−	0.809435i	$-0.699773\pi$
$967$	−5.59188	+	3.22848i	−0.179823	+	0.103821i	0.407387	+	0.913256i	$0.366440\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.7426	−	25.5350i	0.473114	−	0.819457i	−0.526413	−	0.850229i	$-0.676463\pi$
$971$	14.7426	−	25.5350i	0.473114	−	0.819457i	0.999526	+	0.0307720i	$0.00979659\pi$
$972$		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	$-0.586111\pi$
$983$	−16.7574			−0.534477			−0.267238	+	0.963630i	$0.586111\pi$
$984$		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	0.241614	−	0.970372i	$-0.422323\pi$
$991$	37.8640	−	21.8608i	1.20279	−	0.694430i	0.961174	+	0.275942i	$0.0889898\pi$
$992$		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.f.2287.1		4
3.2	odd	2		1008.2.bf.e.943.2	yes	4
4.3	odd	2		3024.2.bf.e.2287.1		4
7.3	odd	6		3024.2.cz.f.2719.1		4
9.4	even	3		3024.2.cz.e.1279.1		4
9.5	odd	6		1008.2.cz.e.607.2	yes	4
12.11	even	2		1008.2.bf.f.943.2	yes	4
21.17	even	6		1008.2.cz.f.367.2	yes	4
28.3	even	6		3024.2.cz.e.2719.1		4
36.23	even	6		1008.2.cz.f.607.2	yes	4
36.31	odd	6		3024.2.cz.f.1279.1		4
63.31	odd	6		3024.2.bf.e.1711.2		4
63.59	even	6		1008.2.bf.f.31.1	yes	4
84.59	odd	6		1008.2.cz.e.367.2	yes	4
252.31	even	6	inner	3024.2.bf.f.1711.2		4
252.59	odd	6		1008.2.bf.e.31.1	✓	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more