LMFDB - Embedded newform 3024.2.bf.f.1711.2

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			1711.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	3024.1711
Dual form			3024.2.bf.f.2287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.18154i q^{5} +(2.62132 + 0.358719i) q^{7} -1.73205i q^{11} +(-0.621320 - 0.358719i) q^{13} +(-5.74264 - 3.31552i) q^{17} +(-0.500000 - 0.866025i) q^{19} +7.64564i q^{23} -12.4853 q^{25} +(3.62132 + 6.27231i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-1.50000 + 10.9612i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(-0.257359 - 0.148586i) q^{41} +(-2.74264 + 1.58346i) q^{43} +(-4.24264 + 7.34847i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-3.62132 + 6.27231i) q^{53} +7.24264 q^{55} +(-3.00000 - 5.19615i) q^{59} +(6.00000 + 3.46410i) q^{61} +(1.50000 - 2.59808i) q^{65} +6.33386i q^{71} +(-7.50000 - 4.33013i) q^{73} +(0.621320 - 4.54026i) q^{77} +(-10.2426 - 5.91359i) q^{79} +(2.74264 + 4.75039i) q^{83} +(13.8640 - 24.0131i) q^{85} +(-11.2279 + 6.48244i) q^{89} +(-1.50000 - 1.16320i) q^{91} +(3.62132 - 2.09077i) q^{95} +(-2.74264 + 1.58346i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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	$0.384620\pi$
$5$			4.18154i			1.87004i	−0.354593	+	0.935021i	$0.615380\pi$
$6$		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	0.411358	−	0.911474i	$-0.365055\pi$
$13$	−0.621320	−	0.358719i	−0.172323	−	0.0994909i	−0.583681	+	0.811983i	$0.698388\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.74264	−	3.31552i	−1.39279	−	0.804131i	−0.399171	−	0.916876i	$-0.630702\pi$
$17$	−5.74264	−	3.31552i	−1.39279	−	0.804131i	−0.993624	+	0.112746i	$0.964035\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		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	0.977204	+	0.212304i	$0.0680966\pi$
$29$	3.62132	+	6.27231i	0.672462	+	1.16474i	−0.304741	+	0.952435i	$0.598570\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		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	0.566012	−	0.824397i	$-0.308485\pi$
$37$	−2.62132	−	4.54026i	−0.430942	−	0.746414i	−0.996955	+	0.0779826i	$0.975152\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.257359	−	0.148586i	−0.0401928	−	0.0232053i	0.479769	−	0.877395i	$-0.340720\pi$
$41$	−0.257359	−	0.148586i	−0.0401928	−	0.0232053i	−0.519962	+	0.854190i	$0.674054\pi$
$42$		0			0
$43$	−2.74264	+	1.58346i	−0.418249	+	0.241476i	−0.694328	−	0.719659i	$-0.744298\pi$
$43$	−2.74264	+	1.58346i	−0.418249	+	0.241476i	0.276079	+	0.961135i	$0.410965\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.24264	+	7.34847i	−0.618853	+	1.07188i	0.370843	+	0.928696i	$0.379069\pi$
$47$	−4.24264	+	7.34847i	−0.618853	+	1.07188i	−0.989695	+	0.143189i	$0.954264\pi$
$48$		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	−0.999996	−	0.00296896i	$-0.999055\pi$
$53$	−3.62132	+	6.27231i	−0.497427	+	0.861568i	0.502569	+	0.864537i	$0.332388\pi$
$54$		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	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		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	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		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	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$		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	$-0.565043\pi$
$79$	−10.2426	−	5.91359i	−1.15239	−	0.665331i	−0.949468	+	0.313864i	$0.898376\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.74264	+	4.75039i	0.301044	+	0.521423i	0.976373	−	0.216093i	$-0.0693316\pi$
$83$	2.74264	+	4.75039i	0.301044	+	0.521423i	−0.675329	+	0.737517i	$0.735998\pi$
$84$		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	−0.958342	−	0.285622i	$-0.907800\pi$
$89$	−11.2279	+	6.48244i	−1.19016	+	0.687138i	−0.231815	+	0.972760i	$0.574466\pi$
$90$		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	−0.632732	−	0.774371i	$-0.718066\pi$
$97$	−2.74264	+	1.58346i	−0.278473	+	0.160776i	0.354259	+	0.935147i	$0.384733\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			0.717439i			0.0713878i	0.999363	+	0.0356939i	$0.0113641\pi$
$101$			0.717439i			0.0713878i	−0.999363	+	0.0356939i	$0.988636\pi$
$102$		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	−0.122786	−	0.992433i	$-0.539183\pi$
$107$	6.98528	−	4.03295i	0.675293	−	0.389880i	0.798079	+	0.602553i	$0.205850\pi$
$108$		0			0
$109$	8.62132	−	14.9326i	0.825773	−	1.43028i	−0.0755546	−	0.997142i	$-0.524073\pi$
$109$	8.62132	−	14.9326i	0.825773	−	1.43028i	0.901327	−	0.433139i	$-0.142594\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.74264	−	4.75039i	0.258006	−	0.446879i	−0.707702	−	0.706511i	$-0.750268\pi$
$113$	2.74264	−	4.75039i	0.258006	−	0.446879i	0.965708	+	0.259632i	$0.0836013\pi$
$114$		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	$-0.507158\pi$
$131$	−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	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$		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	−0.849537	−	0.527529i	$-0.823119\pi$
$157$	−10.2426	+	5.91359i	−0.817452	+	0.471956i	0.0320852	+	0.999485i	$0.489785\pi$
$158$		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	$-0.537288\pi$
$163$	8.74264	−	5.04757i	0.684776	−	0.395356i	0.801652	+	0.597791i	$0.203955\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.86396	−	8.42463i	0.376385	−	0.651917i	−0.614149	−	0.789190i	$-0.710500\pi$
$167$	4.86396	−	8.42463i	0.376385	−	0.651917i	0.990533	+	0.137273i	$0.0438338\pi$
$168$		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	0.141462	−	0.989944i	$-0.454820\pi$
$173$	−8.48528	−	4.89898i	−0.645124	−	0.372463i	−0.786586	+	0.617481i	$0.788153\pi$
$174$		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	$-0.0910248\pi$
$179$	15.9853	+	9.22911i	1.19480	+	0.689816i	0.235406	+	0.971897i	$0.424358\pi$
$180$		0			0
$181$		−	6.33386i		−	0.470792i	−0.971900	−	0.235396i	$-0.924361\pi$
$181$		−	6.33386i		−	0.470792i	0.971900	−	0.235396i	$-0.0756387\pi$
$182$		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	$-0.466546\pi$
$191$	−9.72792	−	5.61642i	−0.703888	−	0.406390i	−0.808794	+	0.588092i	$0.799879\pi$
$192$		0			0
$193$	6.48528	+	11.2328i	0.466821	+	0.808557i	0.999282	−	0.0378973i	$-0.0120660\pi$
$193$	6.48528	+	11.2328i	0.466821	+	0.808557i	−0.532461	+	0.846455i	$0.678733\pi$
$194$		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	$-0.768257\pi$
$199$	2.86396	−	4.96053i	0.203021	−	0.351642i	0.949500	+	0.313766i	$0.101591\pi$
$200$		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	$-0.253327\pi$
$211$	6.25736	+	3.61269i	0.430774	+	0.248708i	−0.268902	+	0.963168i	$0.586661\pi$
$212$		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	$-0.132039\pi$
$223$	1.62132	+	2.80821i	0.108572	+	0.188052i	−0.806620	+	0.591070i	$0.798706\pi$
$224$		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	$0.308771\pi$
$229$			24.9662i			1.64981i	−0.565272	+	0.824905i	$0.691229\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.7426	−	25.5350i	−0.965823	−	1.67285i	−0.707389	−	0.706825i	$-0.750127\pi$
$233$	−14.7426	−	25.5350i	−0.965823	−	1.67285i	−0.258434	−	0.966029i	$-0.583206\pi$
$234$		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	$-0.0443256\pi$
$239$	21.1066	+	12.1859i	1.36527	+	0.788240i	0.374953	+	0.927044i	$0.377659\pi$
$240$		0			0
$241$		−	10.0951i		−	0.650285i	−0.945665	−	0.325142i	$-0.894588\pi$
$241$		−	10.0951i		−	0.650285i	0.945665	−	0.325142i	$-0.105412\pi$
$242$		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	$0.0578042\pi$
$257$			5.79050i			0.361201i	−0.983557	+	0.180601i	$0.942196\pi$
$258$		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	0.150137	−	0.988665i	$-0.452029\pi$
$269$	−10.3492	−	5.97514i	−0.631004	−	0.364311i	−0.781141	+	0.624355i	$0.785362\pi$
$270$		0			0
$271$	6.86396	+	11.8887i	0.416956	+	0.722189i	0.995632	−	0.0933689i	$-0.0297636\pi$
$271$	6.86396	+	11.8887i	0.416956	+	0.722189i	−0.578676	+	0.815558i	$0.696430\pi$
$272$		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	0.893917	−	0.448233i	$-0.147947\pi$
$281$	0.985281	+	1.70656i	0.0587770	+	0.101805i	−0.835140	+	0.550038i	$0.814613\pi$
$282$		0			0
$283$	11.2426	+	19.4728i	0.668306	+	1.15754i	0.978378	+	0.206826i	$0.0663135\pi$
$283$	11.2426	+	19.4728i	0.668306	+	1.15754i	−0.310072	+	0.950713i	$0.600353\pi$
$284$		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	−0.386303	−	0.922372i	$-0.626248\pi$
$293$	−23.5919	−	13.6208i	−1.37825	−	0.795734i	−0.991949	+	0.126637i	$0.959582\pi$
$294$		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	0.978588	−	0.205828i	$-0.0659888\pi$
$311$	5.48528	+	9.50079i	0.311042	+	0.538740i	−0.667546	+	0.744568i	$0.732655\pi$
$312$		0			0
$313$	7.24264	+	4.18154i	0.409378	+	0.236355i	0.690523	−	0.723311i	$-0.257381\pi$
$313$	7.24264	+	4.18154i	0.409378	+	0.236355i	−0.281144	+	0.959666i	$0.590714\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		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	$-0.0156035\pi$
$331$	26.4853	+	15.2913i	1.45576	+	0.840485i	0.456964	+	0.889485i	$0.348937\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	0.789865	+	0.613280i	$0.210150\pi$
$338$		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	$-0.399664\pi$
$347$	24.0000	−	13.8564i	1.28839	−	0.743851i	0.978367	+	0.206879i	$0.0663306\pi$
$348$		0			0
$349$	−6.62132	+	3.82282i	−0.354431	+	0.204631i	−0.666635	−	0.745384i	$-0.732266\pi$
$349$	−6.62132	+	3.82282i	−0.354431	+	0.204631i	0.312204	+	0.950015i	$0.398933\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			3.16693i			0.168559i	0.996442	+	0.0842793i	$0.0268588\pi$
$353$			3.16693i			0.168559i	−0.996442	+	0.0842793i	$0.973141\pi$
$354$		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	$-0.761379\pi$
$359$	−9.62132	+	5.55487i	−0.507794	+	0.293175i	0.224132	+	0.974559i	$0.428045\pi$
$360$		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	$0.0982424\pi$
$379$			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	$-0.588624\pi$
$383$	−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	−0.767826	−	0.640658i	$-0.778661\pi$
$397$	−11.8934	+	6.86666i	−0.596913	+	0.344628i	0.170913	+	0.985286i	$0.445328\pi$
$398$		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	−0.893543	−	0.448978i	$-0.851788\pi$
$409$	−19.2426	+	11.1097i	−0.951487	+	0.549341i	−0.0579447	+	0.998320i	$0.518455\pi$
$410$		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	0.352275	+	0.935896i	$0.385408\pi$
$419$	−12.9853	+	22.4912i	−0.634373	+	1.09877i	−0.986648	+	0.162869i	$0.947925\pi$
$420$		0			0
$421$	5.86396	+	10.1567i	0.285792	+	0.495006i	0.972801	−	0.231643i	$-0.0744100\pi$
$421$	5.86396	+	10.1567i	0.285792	+	0.495006i	−0.687009	+	0.726649i	$0.741077\pi$
$422$		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	$-0.449509\pi$
$431$	−12.8345	−	7.41002i	−0.618217	−	0.356928i	−0.776175	+	0.630518i	$0.782842\pi$
$432$		0			0
$433$			6.33386i			0.304386i	0.988351	+	0.152193i	$0.0486335\pi$
$433$			6.33386i			0.304386i	−0.988351	+	0.152193i	$0.951367\pi$
$434$		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	$-0.780137\pi$
$439$	3.48528	−	6.03668i	0.166343	−	0.288115i	0.937132	+	0.348976i	$0.113471\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.2426	+	9.37769i	0.771711	+	0.445548i	0.833485	−	0.552543i	$-0.186342\pi$
$443$	16.2426	+	9.37769i	0.771711	+	0.445548i	−0.0617735	+	0.998090i	$0.519676\pi$
$444$		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	−0.801196	−	0.598402i	$-0.795803\pi$
$457$	2.51472	−	4.35562i	0.117634	−	0.203747i	0.918829	+	0.394655i	$0.129136\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.1360	+	5.85204i	−0.472082	+	0.272557i	−0.717111	−	0.696959i	$-0.754536\pi$
$461$	−10.1360	+	5.85204i	−0.472082	+	0.272557i	0.245029	+	0.969516i	$0.421203\pi$
$462$		0			0
$463$	−15.6213	−	9.01897i	−0.725984	−	0.419147i	0.0909670	−	0.995854i	$-0.471004\pi$
$463$	−15.6213	−	9.01897i	−0.725984	−	0.419147i	−0.816951	+	0.576707i	$0.804338\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.25736	+	5.64191i	0.150733	+	0.261077i	0.931497	−	0.363749i	$-0.118503\pi$
$467$	3.25736	+	5.64191i	0.150733	+	0.261077i	−0.780764	+	0.624826i	$0.785170\pi$
$468$		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	−1.00000		0.000234827i	$-0.999925\pi$
$487$	−33.1066	−	19.1141i	−1.50020	−	0.866143i	−0.500203	−	0.865908i	$-0.666741\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.98528	−	2.30090i	−0.179853	−	0.103838i	0.407370	−	0.913263i	$-0.366446\pi$
$491$	−3.98528	−	2.30090i	−0.179853	−	0.103838i	−0.587224	+	0.809425i	$0.699779\pi$
$492$		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	$-0.413794\pi$
$503$	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	$-0.806195\pi$
$509$		−	25.8067i		−	1.14386i	0.820302	−	0.571931i	$-0.193805\pi$
$510$		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	0.326630	−	0.945152i	$-0.394087\pi$
$521$	−7.50000	−	4.33013i	−0.328581	−	0.189706i	−0.655211	+	0.755446i	$0.727420\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		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	0.884591	−	0.466367i	$-0.154437\pi$
$541$	0.893398	+	1.54741i	0.0384102	+	0.0665284i	−0.846181	+	0.532895i	$0.821104\pi$
$542$		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	$-0.649151\pi$
$547$	2.22792	−	1.28629i	0.0952591	−	0.0549978i	0.546873	+	0.837216i	$0.315818\pi$
$548$		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	−0.486914	−	0.873450i	$-0.661877\pi$
$557$	12.1066	−	20.9692i	0.512973	−	0.888496i	0.999887	−	0.0150455i	$-0.00478931\pi$
$558$		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	−0.953877	−	0.300197i	$-0.902948\pi$
$563$	−17.4853	−	30.2854i	−0.736917	−	1.27638i	0.216961	−	0.976180i	$-0.430386\pi$
$564$		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	−0.957795	−	0.287454i	$-0.907191\pi$
$569$	−5.48528	+	9.50079i	−0.229955	+	0.398294i	0.727840	+	0.685747i	$0.240525\pi$
$570$		0			0
$571$	39.9411	−	23.0600i	1.67148	−	0.965032i	0.704676	−	0.709530i	$-0.251093\pi$
$571$	39.9411	−	23.0600i	1.67148	−	0.965032i	0.966808	−	0.255502i	$-0.0822408\pi$
$572$		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	0.986451	+	0.164056i	$0.0524577\pi$
$577$	38.9558	+	22.4912i	1.62175	+	0.936320i	0.635302	+	0.772264i	$0.280876\pi$
$578$		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	$-0.259761\pi$
$587$	−6.98528	−	12.0989i	−0.288313	−	0.499373i	−0.973407	+	0.229081i	$0.926428\pi$
$588$		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	−0.762829	−	0.646601i	$-0.776190\pi$
$593$	−14.2279	+	8.21449i	−0.584271	+	0.337329i	0.178558	+	0.983929i	$0.442857\pi$
$594$		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	$-0.853572\pi$
$599$	−23.4853	+	13.5592i	−0.959583	+	0.554015i	−0.0635380	+	0.997979i	$0.520238\pi$
$600$		0			0
$601$	−5.01472	+	2.89525i	−0.204555	+	0.118100i	−0.598778	−	0.800915i	$-0.704347\pi$
$601$	−5.01472	+	2.89525i	−0.204555	+	0.118100i	0.394224	+	0.919015i	$0.371014\pi$
$602$		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	−0.808221	−	0.588879i	$-0.799569\pi$
$613$	2.62132	−	4.54026i	0.105874	−	0.183379i	0.914095	+	0.405500i	$0.132903\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.74264	+	9.94655i	−0.231190	+	0.400433i	−0.958159	−	0.286238i	$-0.907595\pi$
$617$	−5.74264	+	9.94655i	−0.231190	+	0.400433i	0.726969	+	0.686671i	$0.240929\pi$
$618$		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	$0.0348747\pi$
$631$			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	0.478024	+	0.878347i	$0.341353\pi$
$643$	−13.2279	+	22.9114i	−0.521658	+	0.903539i	−0.999683	+	0.0251921i	$0.991980\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.86396	−	8.42463i	0.191222	−	0.331206i	−0.754433	−	0.656377i	$-0.772088\pi$
$647$	4.86396	−	8.42463i	0.191222	−	0.331206i	0.945655	+	0.325170i	$0.105422\pi$
$648$		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	$-0.576177\pi$
$659$	12.4706	−	7.19988i	0.485784	−	0.280468i	0.722824	+	0.691032i	$0.242844\pi$
$660$		0			0
$661$	−13.4558	+	7.76874i	−0.523372	+	0.302169i	−0.738313	−	0.674458i	$-0.764377\pi$
$661$	−13.4558	+	7.76874i	−0.523372	+	0.302169i	0.214941	+	0.976627i	$0.431044\pi$
$662$		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	0.945969	−	0.324258i	$-0.105115\pi$
$673$	4.98528	+	8.63476i	0.192168	+	0.332846i	−0.753800	+	0.657104i	$0.771781\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.7279	+	10.8126i	0.719773	+	0.415561i	0.814669	−	0.579926i	$-0.196919\pi$
$677$	18.7279	+	10.8126i	0.719773	+	0.415561i	−0.0948964	+	0.995487i	$0.530252\pi$
$678$		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	$-0.0933463\pi$
$683$	30.9853	+	17.8894i	1.18562	+	0.684517i	0.228311	+	0.973588i	$0.426680\pi$
$684$		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	−0.0575781	−	0.998341i	$-0.518338\pi$
$691$	21.9706	−	38.0541i	0.835800	−	1.44765i	0.893378	−	0.449306i	$-0.148329\pi$
$692$		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	−0.953650	−	0.300918i	$-0.902707\pi$
$709$	−5.75736	+	9.97204i	−0.216222	+	0.374508i	0.737428	+	0.675426i	$0.236040\pi$
$710$		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	0.942852	+	0.333213i	$0.108133\pi$
$719$	20.3787	+	35.2969i	0.759997	+	1.31635i	−0.182855	+	0.983140i	$0.558534\pi$
$720$		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	$-0.266881\pi$
$727$	−8.34924	−	14.4613i	−0.309656	−	0.536340i	−0.978287	+	0.207254i	$0.933547\pi$
$728$		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	$0.363074\pi$
$733$			49.2149i			1.81779i	−0.417022	+	0.908896i	$0.636926\pi$
$734$		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	$-0.0589686\pi$
$739$	35.7426	+	20.6360i	1.31481	+	0.759108i	0.331925	+	0.943306i	$0.392302\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.8640	+	14.9326i	0.948857	+	0.547823i	0.892726	−	0.450601i	$-0.148790\pi$
$743$	25.8640	+	14.9326i	0.948857	+	0.547823i	0.0561311	+	0.998423i	$0.482124\pi$
$744$		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	$0.0825804\pi$
$761$			14.1536i			0.513067i	−0.966535	+	0.256533i	$0.917420\pi$
$762$		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	0.967702	−	0.252098i	$-0.0811206\pi$
$769$	34.1985	+	19.7445i	1.23323	+	0.712005i	0.265527	+	0.964103i	$0.414454\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	28.3492	+	16.3674i	1.01965	+	0.588696i	0.914003	−	0.405708i	$-0.132975\pi$
$773$	28.3492	+	16.3674i	1.01965	+	0.588696i	0.105648	+	0.994404i	$0.466308\pi$
$774$		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	$-0.129792\pi$
$787$	3.24264	+	5.61642i	0.115588	+	0.200204i	−0.802427	+	0.596750i	$0.796458\pi$
$788$		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	0.207989	−	0.978131i	$-0.433308\pi$
$797$	−15.1066	−	8.72180i	−0.535103	−	0.308942i	−0.743092	+	0.669189i	$0.766642\pi$
$798$		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	−0.848185	−	0.529700i	$-0.822305\pi$
$809$	0.985281	−	1.70656i	0.0346406	−	0.0599994i	0.882826	+	0.469700i	$0.155638\pi$
$810$		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	−0.878448	−	0.477838i	$-0.841421\pi$
$821$	−0.727922	+	1.26080i	−0.0254047	+	0.0440022i	0.853044	+	0.521840i	$0.174754\pi$
$822$		0			0
$823$	−0.213203	+	0.123093i	−0.00743180	+	0.00429075i	−0.503711	−	0.863872i	$-0.668032\pi$
$823$	−0.213203	+	0.123093i	−0.00743180	+	0.00429075i	0.496279	+	0.868163i	$0.334699\pi$
$824$		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	0.898239	−	0.439508i	$-0.144847\pi$
$829$	27.8345	+	16.0703i	0.966733	+	0.558144i	0.0684943	+	0.997652i	$0.478181\pi$
$830$		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	$-0.107214\pi$
$839$	5.37868	+	9.31615i	0.185693	+	0.321629i	−0.758117	+	0.652118i	$0.773880\pi$
$840$		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	−0.414414	−	0.910089i	$-0.636013\pi$
$853$	4.86396	−	2.80821i	0.166539	−	0.0961513i	0.580953	+	0.813937i	$0.302680\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			14.9941i			0.512189i	0.966652	+	0.256095i	$0.0824358\pi$
$857$			14.9941i			0.512189i	−0.966652	+	0.256095i	$0.917564\pi$
$858$		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	0.170756	−	0.985313i	$-0.445379\pi$
$863$	32.5919	−	18.8169i	1.10944	−	0.640536i	0.938684	+	0.344777i	$0.112046\pi$
$864$		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	$-0.932899\pi$
$881$		−	12.4215i		−	0.418492i	0.977863	−	0.209246i	$-0.0671009\pi$
$882$		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	$-0.186125\pi$
$887$	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	$0.0991404\pi$
$907$			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	$-0.480484\pi$
$911$	28.8640	−	16.6646i	0.956306	−	0.552123i	0.895034	+	0.445998i	$0.147151\pi$
$912$		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	$-0.562589\pi$
$919$	16.8640	−	9.73641i	0.556291	−	0.321175i	0.751655	+	0.659556i	$0.229256\pi$
$920$		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	0.844973	−	0.534809i	$-0.179616\pi$
$929$	24.5147	+	14.1536i	0.804302	+	0.464364i	−0.0406713	+	0.999173i	$0.512950\pi$
$930$		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	$0.266897\pi$
$937$			45.5257i			1.48726i	−0.668592	+	0.743630i	$0.733103\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.4558	−	11.2328i	0.634242	−	0.366180i	−0.148151	−	0.988965i	$-0.547332\pi$
$941$	19.4558	−	11.2328i	0.634242	−	0.366180i	0.782393	+	0.622785i	$0.213999\pi$
$942$		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	$-0.236102\pi$
$947$	16.0294	+	9.25460i	0.520887	+	0.300734i	−0.216411	+	0.976302i	$0.569435\pi$
$948$		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	$-0.366440\pi$
$967$	−5.59188	−	3.22848i	−0.179823	−	0.103821i	−0.587209	+	0.809435i	$0.699773\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.7426	+	25.5350i	0.473114	+	0.819457i	0.999526	−	0.0307720i	$-0.00979659\pi$
$971$	14.7426	+	25.5350i	0.473114	+	0.819457i	−0.526413	+	0.850229i	$0.676463\pi$
$972$		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	0.969238	−	0.246125i	$-0.0791575\pi$
$977$	8.48528	+	14.6969i	0.271468	+	0.470197i	−0.697770	+	0.716322i	$0.745824\pi$
$978$		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	0.961174	−	0.275942i	$-0.0889898\pi$
$991$	37.8640	+	21.8608i	1.20279	+	0.694430i	0.241614	+	0.970372i	$0.422323\pi$
$992$		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	$0.0283469\pi$
$997$			5.61642i			0.177874i	−0.996037	+	0.0889369i	$0.971653\pi$
$998$		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.1711.2		4
3.2	odd	2		1008.2.bf.e.31.1	✓	4
4.3	odd	2		3024.2.bf.e.1711.2		4
7.5	odd	6		3024.2.cz.f.1279.1		4
9.2	odd	6		1008.2.cz.e.367.2	yes	4
9.7	even	3		3024.2.cz.e.2719.1		4
12.11	even	2		1008.2.bf.f.31.1	yes	4
21.5	even	6		1008.2.cz.f.607.2	yes	4
28.19	even	6		3024.2.cz.e.1279.1		4
36.7	odd	6		3024.2.cz.f.2719.1		4
36.11	even	6		1008.2.cz.f.367.2	yes	4
63.47	even	6		1008.2.bf.f.943.2	yes	4
63.61	odd	6		3024.2.bf.e.2287.1		4
84.47	odd	6		1008.2.cz.e.607.2	yes	4
252.47	odd	6		1008.2.bf.e.943.2	yes	4
252.187	even	6	inner	3024.2.bf.f.2287.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.e.31.1	✓	4	3.2	odd	2
1008.2.bf.e.943.2	yes	4	252.47	odd	6
1008.2.bf.f.31.1	yes	4	12.11	even	2
1008.2.bf.f.943.2	yes	4	63.47	even	6
1008.2.cz.e.367.2	yes	4	9.2	odd	6
1008.2.cz.e.607.2	yes	4	84.47	odd	6
1008.2.cz.f.367.2	yes	4	36.11	even	6
1008.2.cz.f.607.2	yes	4	21.5	even	6
3024.2.bf.e.1711.2		4	4.3	odd	2
3024.2.bf.e.2287.1		4	63.61	odd	6
3024.2.bf.f.1711.2		4	1.1	even	1	trivial
3024.2.bf.f.2287.1		4	252.187	even	6	inner
3024.2.cz.e.1279.1		4	28.19	even	6
3024.2.cz.e.2719.1		4	9.7	even	3
3024.2.cz.f.1279.1		4	7.5	odd	6
3024.2.cz.f.2719.1		4	36.7	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