LMFDB - Embedded newform 592.2.i.c.417.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(417,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("592.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			417.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	592.417
Dual form			592.2.i.c.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{17} +(-3.00000 - 5.19615i) q^{19} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +9.00000 q^{29} +10.0000 q^{31} +(1.00000 - 1.73205i) q^{35} +(-5.50000 - 2.59808i) q^{37} +(4.50000 + 7.79423i) q^{41} -2.00000 q^{43} -3.00000 q^{45} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{61} +6.00000 q^{63} +(1.00000 - 1.73205i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(3.00000 + 5.19615i) q^{71} -10.0000 q^{73} +(2.00000 + 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +3.00000 q^{85} +(-3.50000 + 6.06218i) q^{89} +(-2.00000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(3.00000 - 5.19615i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - q^5 + 2 * q^7 + 3 * q^9	$ 2 q - q^{5} + 2 q^{7} + 3 q^{9} + 4 q^{11} + 2 q^{13} - 3 q^{17} - 6 q^{19} + 8 q^{23} + 4 q^{25} + 18 q^{29} + 20 q^{31} + 2 q^{35} - 11 q^{37} + 9 q^{41} - 4 q^{43} - 6 q^{45} - 12 q^{47} + 3 q^{49} + 2 q^{53} - 2 q^{55} - 4 q^{59} - q^{61} + 12 q^{63} + 2 q^{65} - 10 q^{67} + 6 q^{71} - 20 q^{73} + 4 q^{77} + 10 q^{79} - 9 q^{81} - 12 q^{83} + 6 q^{85} - 7 q^{89} - 4 q^{91} - 6 q^{95} + 14 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q - q^5 + 2 * q^7 + 3 * q^9 + 4 * q^11 + 2 * q^13 - 3 * q^17 - 6 * q^19 + 8 * q^23 + 4 * q^25 + 18 * q^29 + 20 * q^31 + 2 * q^35 - 11 * q^37 + 9 * q^41 - 4 * q^43 - 6 * q^45 - 12 * q^47 + 3 * q^49 + 2 * q^53 - 2 * q^55 - 4 * q^59 - q^61 + 12 * q^63 + 2 * q^65 - 10 * q^67 + 6 * q^71 - 20 * q^73 + 4 * q^77 + 10 * q^79 - 9 * q^81 - 12 * q^83 + 6 * q^85 - 7 * q^89 - 4 * q^91 - 6 * q^95 + 14 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$		0			0
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$		0			0
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	6.00000			0.755929
$64$		0			0
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.00000	+	3.46410i	0.227921	+	0.394771i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$		0			0
$91$	−2.00000	+	3.46410i	−0.209657	+	0.363137i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$		0			0
$99$	3.00000	−	5.19615i	0.301511	−	0.522233i
$100$		0			0
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	6.00000			0.554700
$118$		0			0
$119$	−6.00000			−0.550019
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	−0.987108	−	0.160055i	$-0.948833\pi$
$127$	−4.00000	+	6.92820i	−0.354943	+	0.614779i	0.632166	+	0.774833i	$0.282166\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$		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
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.0000			−0.901155			−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000			−0.901155			−0.450578	+	0.892737i	$0.648782\pi$
$150$		0			0
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	0.935857	−	0.352381i	$-0.114628\pi$
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	−0.773099	+	0.634285i	$0.781294\pi$
$152$		0			0
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$	−5.00000	−	8.66025i	−0.401610	−	0.695608i
$156$		0			0
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.00000	+	6.92820i	0.315244	+	0.546019i
$162$		0			0
$163$	−3.00000	+	5.19615i	−0.234978	+	0.406994i	−0.959266	−	0.282503i	$-0.908835\pi$
$163$	−3.00000	+	5.19615i	−0.234978	+	0.406994i	0.724288	+	0.689497i	$0.242169\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−18.0000			−1.37649
$172$		0			0
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$		0			0
$175$	8.00000			0.604743
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	0.758030	−	0.652219i	$-0.226162\pi$
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	−0.943854	+	0.330364i	$0.892829\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.500000	+	6.06218i	0.0367607	+	0.445700i
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$		0			0
$193$	19.0000			1.36765			0.683825	−	0.729646i	$-0.260315\pi$
$193$	19.0000			1.36765			0.683825	+	0.729646i	$0.260315\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	−0.464841	−	0.885394i	$-0.653889\pi$
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	0.999194	−	0.0401324i	$-0.0127780\pi$
$198$		0			0
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	9.00000	+	15.5885i	0.631676	+	1.09410i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$		0			0
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$		0			0
$209$	−6.00000	−	10.3923i	−0.415029	−	0.718851i
$210$		0			0
$211$	−2.00000			−0.137686			−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$	10.0000	+	17.3205i	0.678844	+	1.17579i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.00000			−0.403604
$222$		0			0
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$	−6.00000	−	10.3923i	−0.400000	−	0.692820i
$226$		0			0
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	0.999184	−	0.0403978i	$-0.0128625\pi$
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	−0.534577	+	0.845120i	$0.679529\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	−0.752536	−	0.658551i	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.00000			−0.191663
$246$		0			0
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	14.0000			0.883672			0.441836	−	0.897096i	$-0.354327\pi$
$251$	14.0000			0.883672			0.441836	+	0.897096i	$0.354327\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$		0			0
$259$	−1.00000	−	12.1244i	−0.0621370	−	0.753371i
$260$		0			0
$261$	13.5000	−	23.3827i	0.835629	−	1.44735i
$262$		0			0
$263$	2.00000	+	3.46410i	0.123325	+	0.213606i	0.921077	−	0.389380i	$-0.127311\pi$
$263$	2.00000	+	3.46410i	0.123325	+	0.213606i	−0.797752	+	0.602986i	$0.793977\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	−0.571221	−	0.820796i	$-0.693530\pi$
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	0.996441	+	0.0842940i	$0.0268635\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.00000	−	6.92820i	0.241209	−	0.417786i
$276$		0			0
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	0.907564	−	0.419914i	$-0.137940\pi$
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	−0.817438	+	0.576017i	$0.804606\pi$
$278$		0			0
$279$	15.0000	−	25.9808i	0.898027	−	1.55543i
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.00000	+	15.5885i	−0.531253	+	0.920158i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	11.5000	+	19.9186i	0.671837	+	1.16366i	0.977383	+	0.211479i	$0.0678279\pi$
$293$	11.5000	+	19.9186i	0.671837	+	1.16366i	−0.305545	+	0.952177i	$0.598839\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$		0			0
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	−0.947825	−	0.318791i	$-0.896723\pi$
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	0.749993	+	0.661445i	$0.230057\pi$
$314$		0			0
$315$	−3.00000	−	5.19615i	−0.169031	−	0.292770i
$316$		0			0
$317$	−0.500000	+	0.866025i	−0.0280828	+	0.0486408i	−0.879725	−	0.475482i	$-0.842274\pi$
$317$	−0.500000	+	0.866025i	−0.0280828	+	0.0486408i	0.851642	+	0.524123i	$0.175607\pi$
$318$		0			0
$319$	18.0000			1.00781
$320$		0			0
$321$		0			0
$322$		0			0
$323$	18.0000			1.00155
$324$		0			0
$325$	8.00000			0.443760
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$		0			0
$333$	−15.0000	+	10.3923i	−0.821995	+	0.569495i
$334$		0			0
$335$	−5.00000	+	8.66025i	−0.273179	+	0.473160i
$336$		0			0
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	20.0000			1.08306
$342$		0			0
$343$	20.0000			1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.0000			0.858925			0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000			0.858925			0.429463	+	0.903085i	$0.358703\pi$
$348$		0			0
$349$	−4.50000	+	7.79423i	−0.240879	+	0.417215i	−0.960965	−	0.276670i	$-0.910769\pi$
$349$	−4.50000	+	7.79423i	−0.240879	+	0.417215i	0.720086	+	0.693885i	$0.244103\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	−0.313894	−	0.949458i	$-0.601634\pi$
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	0.979202	−	0.202889i	$-0.0650330\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.00000	+	8.66025i	0.261712	+	0.453298i
$366$		0			0
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$		0			0
$369$	27.0000			1.40556
$370$		0			0
$371$	4.00000			0.207670
$372$		0			0
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	0.557584	−	0.830120i	$-0.311728\pi$
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	−0.997697	+	0.0678218i	$0.978395\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.00000	+	15.5885i	0.463524	+	0.802846i
$378$		0			0
$379$	3.00000	−	5.19615i	0.154100	−	0.266908i	−0.778631	−	0.627482i	$-0.784086\pi$
$379$	3.00000	−	5.19615i	0.154100	−	0.266908i	0.932731	+	0.360573i	$0.117419\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	2.00000	−	3.46410i	0.101929	−	0.176547i
$386$		0			0
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$		0			0
$389$	−12.5000	−	21.6506i	−0.633775	−	1.09773i	−0.986773	−	0.162107i	$-0.948171\pi$
$389$	−12.5000	−	21.6506i	−0.633775	−	1.09773i	0.352998	−	0.935624i	$-0.385162\pi$
$390$		0			0
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.00000	−	8.66025i	0.251577	−	0.435745i
$396$		0			0
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$		0			0
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$		0			0
$407$	−11.0000	−	5.19615i	−0.545250	−	0.257564i
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.00000			−0.393654
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	0.351404	+	0.936224i	$0.385704\pi$
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	−0.986496	+	0.163787i	$0.947629\pi$
$420$		0			0
$421$	9.00000			0.438633			0.219317	−	0.975654i	$-0.429617\pi$
$421$	9.00000			0.438633			0.219317	+	0.975654i	$0.429617\pi$
$422$		0			0
$423$	−9.00000	+	15.5885i	−0.437595	+	0.757937i
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$	−21.0000			−1.00920			−0.504598	−	0.863355i	$-0.668359\pi$
$433$	−21.0000			−1.00920			−0.504598	+	0.863355i	$0.668359\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$		0			0
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	0.522387	−	0.852709i	$-0.325042\pi$
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	−0.999661	+	0.0260459i	$0.991708\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	32.0000			1.52037			0.760183	−	0.649709i	$-0.225109\pi$
$443$	32.0000			1.52037			0.760183	+	0.649709i	$0.225109\pi$
$444$		0			0
$445$	7.00000			0.331832
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	0.786513	−	0.617574i	$-0.211885\pi$
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	−0.928091	+	0.372353i	$0.878551\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.00000			0.187523
$456$		0			0
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	0.828807	−	0.559534i	$-0.189020\pi$
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	−0.898974	+	0.438001i	$0.855687\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	−11.0000	−	19.0526i	−0.511213	−	0.885448i	−0.999916	−	0.0129968i	$-0.995863\pi$
$463$	−11.0000	−	19.0526i	−0.511213	−	0.885448i	0.488702	−	0.872451i	$-0.337470\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	10.0000	−	17.3205i	0.461757	−	0.799787i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.00000			−0.183920
$474$		0			0
$475$	−24.0000			−1.10120
$476$		0			0
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$		0			0
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		0			0
$481$	−1.00000	−	12.1244i	−0.0455961	−	0.552823i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$		0			0
$487$	−12.0000			−0.543772			−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.00000			−0.0902587			−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000			−0.0902587			−0.0451294	+	0.998981i	$0.514370\pi$
$492$		0			0
$493$	−13.5000	+	23.3827i	−0.608009	+	1.05310i
$494$		0			0
$495$	−6.00000			−0.269680
$496$		0			0
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	−9.00000	−	15.5885i	−0.402895	−	0.697835i	0.591179	−	0.806541i	$-0.298663\pi$
$499$	−9.00000	−	15.5885i	−0.402895	−	0.697835i	−0.994074	+	0.108705i	$0.965329\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−13.0000	+	22.5167i	−0.579641	+	1.00397i	0.415879	+	0.909420i	$0.363474\pi$
$503$	−13.0000	+	22.5167i	−0.579641	+	1.00397i	−0.995520	+	0.0945483i	$0.969859\pi$
$504$		0			0
$505$	1.50000	+	2.59808i	0.0667491	+	0.115613i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	−0.777973	−	0.628297i	$-0.783752\pi$
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	0.933108	+	0.359596i	$0.117085\pi$
$510$		0			0
$511$	−10.0000	−	17.3205i	−0.442374	−	0.766214i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.00000	+	5.19615i	0.132196	+	0.228970i
$516$		0			0
$517$	−12.0000			−0.527759
$518$		0			0
$519$		0			0
$520$		0			0
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$		0			0
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	0.940129	−	0.340818i	$-0.110704\pi$
$523$	4.00000	+	6.92820i	0.174908	+	0.302949i	−0.765222	+	0.643767i	$0.777371\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.0000	+	25.9808i	−0.653410	+	1.13174i
$528$		0			0
$529$	−7.00000			−0.304348
$530$		0			0
$531$	6.00000	+	10.3923i	0.260378	+	0.450988i
$532$		0			0
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	−9.00000	+	15.5885i	−0.389104	+	0.673948i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.00000			0.214176
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$	−3.00000			−0.128037
$550$		0			0
$551$	−27.0000	−	46.7654i	−1.15024	−	1.99227i
$552$		0			0
$553$	−10.0000	+	17.3205i	−0.425243	+	0.736543i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	0.269642	+	0.962961i	$0.413095\pi$
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	−0.968769	+	0.247964i	$0.920239\pi$
$558$		0			0
$559$	−2.00000	−	3.46410i	−0.0845910	−	0.146516i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	24.0000			1.01148			0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000			1.01148			0.505740	+	0.862686i	$0.331220\pi$
$564$		0			0
$565$	6.00000			0.252422
$566$		0			0
$567$	9.00000	−	15.5885i	0.377964	−	0.654654i
$568$		0			0
$569$	3.00000			0.125767			0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000			0.125767			0.0628833	+	0.998021i	$0.479970\pi$
$570$		0			0
$571$	−22.0000	+	38.1051i	−0.920671	+	1.59465i	−0.122292	+	0.992494i	$0.539025\pi$
$571$	−22.0000	+	38.1051i	−0.920671	+	1.59465i	−0.798379	+	0.602155i	$0.794309\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$		0			0
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.0000			−0.995688
$582$		0			0
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$		0			0
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$		0			0
$587$	20.0000	+	34.6410i	0.825488	+	1.42979i	0.901546	+	0.432684i	$0.142434\pi$
$587$	20.0000	+	34.6410i	0.825488	+	1.42979i	−0.0760572	+	0.997103i	$0.524233\pi$
$588$		0			0
$589$	−30.0000	−	51.9615i	−1.23613	−	2.14104i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−29.0000			−1.19089			−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000			−1.19089			−0.595444	+	0.803397i	$0.703024\pi$
$594$		0			0
$595$	3.00000	+	5.19615i	0.122988	+	0.213021i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−19.0000	−	32.9090i	−0.776319	−	1.34462i	−0.934050	−	0.357142i	$-0.883751\pi$
$599$	−19.0000	−	32.9090i	−0.776319	−	1.34462i	0.157731	−	0.987482i	$-0.449582\pi$
$600$		0			0
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	−30.0000			−1.22169
$604$		0			0
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.00000	−	10.3923i	−0.242734	−	0.420428i
$612$		0			0
$613$	−16.5000	+	28.5788i	−0.666429	+	1.15429i	0.312467	+	0.949929i	$0.398845\pi$
$613$	−16.5000	+	28.5788i	−0.666429	+	1.15429i	−0.978896	+	0.204360i	$0.934489\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	−0.555056	−	0.831813i	$-0.687303\pi$
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	0.997899	+	0.0647859i	$0.0206365\pi$
$618$		0			0
$619$	10.0000			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.0000			−0.560898
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	15.0000	−	10.3923i	0.598089	−	0.414368i
$630$		0			0
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	−0.595397	−	0.803432i	$-0.703005\pi$
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	0.993491	+	0.113913i	$0.0363385\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.00000			0.317470
$636$		0			0
$637$	6.00000			0.237729
$638$		0			0
$639$	18.0000			0.712069
$640$		0			0
$641$	18.5000	−	32.0429i	0.730706	−	1.26562i	−0.225876	−	0.974156i	$-0.572524\pi$
$641$	18.5000	−	32.0429i	0.730706	−	1.26562i	0.956582	−	0.291464i	$-0.0941423\pi$
$642$		0			0
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	0.694987	−	0.719023i	$-0.255410\pi$
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	−0.970185	+	0.242365i	$0.922077\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−15.0000	+	25.9808i	−0.585206	+	1.01361i
$658$		0			0
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	−0.968052	−	0.250748i	$-0.919323\pi$
$659$	−18.0000	−	31.1769i	−0.701180	−	1.21448i	0.266872	−	0.963732i	$-0.414010\pi$
$660$		0			0
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	0.926030	−	0.377450i	$-0.123199\pi$
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	−0.789896	+	0.613241i	$0.789865\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.0000			−0.465340
$666$		0			0
$667$	36.0000			1.39393
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.00000	−	1.73205i	−0.0386046	−	0.0668651i
$672$		0			0
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	0.802395	−	0.596794i	$-0.203559\pi$
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	−0.918036	+	0.396497i	$0.870226\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.0000			0.499631			0.249815	−	0.968294i	$-0.419630\pi$
$677$	13.0000			0.499631			0.249815	+	0.968294i	$0.419630\pi$
$678$		0			0
$679$	7.00000	+	12.1244i	0.268635	+	0.465290i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.0000	+	25.9808i	−0.573959	+	0.994126i	0.422195	+	0.906505i	$0.361260\pi$
$683$	−15.0000	+	25.9808i	−0.573959	+	0.994126i	−0.996154	+	0.0876211i	$0.972074\pi$
$684$		0			0
$685$	4.50000	+	7.79423i	0.171936	+	0.297802i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.00000			0.152388
$690$		0			0
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	−0.967901	−	0.251330i	$-0.919132\pi$
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	0.701609	+	0.712562i	$0.252465\pi$
$692$		0			0
$693$	12.0000			0.455842
$694$		0			0
$695$	−16.0000			−0.606915
$696$		0			0
$697$	−27.0000			−1.02270
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$	3.00000	+	36.3731i	0.113147	+	1.37184i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$		0			0
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$		0			0
$711$	30.0000			1.12509
$712$		0			0
$713$	40.0000			1.49801
$714$		0			0
$715$	2.00000	−	3.46410i	0.0747958	−	0.129550i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	−6.00000	−	10.3923i	−0.223452	−	0.387030i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	0.951694	+	0.307049i	$0.0993415\pi$
$727$	20.0000	+	34.6410i	0.741759	+	1.28476i	−0.209935	+	0.977715i	$0.567325\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.0000	−	17.3205i	−0.368355	−	0.638009i
$738$		0			0
$739$	−12.0000			−0.441427			−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000			−0.441427			−0.220714	+	0.975339i	$0.570839\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		0			0
$745$	5.50000	+	9.52628i	0.201504	+	0.349016i
$746$		0			0
$747$	18.0000	+	31.1769i	0.658586	+	1.14070i
$748$		0			0
$749$	18.0000	−	31.1769i	0.657706	−	1.13918i
$750$		0			0
$751$	−10.0000			−0.364905			−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000			−0.364905			−0.182453	+	0.983215i	$0.558404\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.00000	−	3.46410i	0.0727875	−	0.126072i
$756$		0			0
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	−0.922464	−	0.386082i	$-0.873828\pi$
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	0.795589	+	0.605836i	$0.207161\pi$
$762$		0			0
$763$	−10.0000			−0.362024
$764$		0			0
$765$	4.50000	−	7.79423i	0.162698	−	0.281801i
$766$		0			0
$767$	−8.00000			−0.288863
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$		0			0
$775$	20.0000	−	34.6410i	0.718421	−	1.24434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	27.0000	−	46.7654i	0.967375	−	1.67554i
$780$		0			0
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.0000			0.606756
$786$		0			0
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.0000	−	22.5167i	0.460484	−	0.797581i	−0.538501	−	0.842625i	$-0.681009\pi$
$797$	13.0000	−	22.5167i	0.460484	−	0.797581i	0.998985	+	0.0450436i	$0.0143427\pi$
$798$		0			0
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$		0			0
$801$	10.5000	+	18.1865i	0.370999	+	0.642590i
$802$		0			0
$803$	−20.0000			−0.705785
$804$		0			0
$805$	4.00000	−	6.92820i	0.140981	−	0.244187i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	0.940435	−	0.339975i	$-0.110418\pi$
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	−0.764644	+	0.644453i	$0.777085\pi$
$810$		0			0
$811$	−8.00000	−	13.8564i	−0.280918	−	0.486564i	0.690693	−	0.723148i	$-0.257306\pi$
$811$	−8.00000	−	13.8564i	−0.280918	−	0.486564i	−0.971611	+	0.236584i	$0.923972\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.00000			0.210171
$816$		0			0
$817$	6.00000	+	10.3923i	0.209913	+	0.363581i
$818$		0			0
$819$	6.00000	+	10.3923i	0.209657	+	0.363137i
$820$		0			0
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	0.765487	−	0.643451i	$-0.222498\pi$
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	−0.939989	+	0.341206i	$0.889165\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.00000	−	6.92820i	−0.139094	−	0.240917i	0.788060	−	0.615598i	$-0.211086\pi$
$827$	−4.00000	−	6.92820i	−0.139094	−	0.240917i	−0.927154	+	0.374681i	$0.877752\pi$
$828$		0			0
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.50000	+	7.79423i	0.155916	+	0.270054i
$834$		0			0
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	0.281205	+	0.959648i	$0.409266\pi$
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	−0.971682	+	0.236293i	$0.924067\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.00000			−0.309609
$846$		0			0
$847$	−7.00000	−	12.1244i	−0.240523	−	0.416598i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−22.0000	−	10.3923i	−0.754150	−	0.356244i
$852$		0			0
$853$	9.50000	−	16.4545i	0.325274	−	0.563391i	−0.656294	−	0.754505i	$-0.727877\pi$
$853$	9.50000	−	16.4545i	0.325274	−	0.563391i	0.981568	+	0.191115i	$0.0612102\pi$
$854$		0			0
$855$	9.00000	+	15.5885i	0.307794	+	0.533114i
$856$		0			0
$857$	−45.0000			−1.53717			−0.768585	−	0.639747i	$-0.779039\pi$
$857$	−45.0000			−1.53717			−0.768585	+	0.639747i	$0.779039\pi$
$858$		0			0
$859$	50.0000			1.70598			0.852989	−	0.521929i	$-0.174787\pi$
$859$	50.0000			1.70598			0.852989	+	0.521929i	$0.174787\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	−0.378052	−	0.925785i	$-0.623406\pi$
$863$	18.0000	−	31.1769i	0.612727	−	1.06127i	0.990779	−	0.135490i	$-0.0432609\pi$
$864$		0			0
$865$	21.0000			0.714021
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.0000	+	17.3205i	0.339227	+	0.587558i
$870$		0			0
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$		0			0
$873$	10.5000	−	18.1865i	0.355371	−	0.615521i
$874$		0			0
$875$	−9.00000	−	15.5885i	−0.304256	−	0.526986i
$876$		0			0
$877$	17.0000			0.574049			0.287025	−	0.957923i	$-0.407334\pi$
$877$	17.0000			0.574049			0.287025	+	0.957923i	$0.407334\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	0.660438	−	0.750881i	$-0.270371\pi$
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	−0.980501	+	0.196515i	$0.937037\pi$
$882$		0			0
$883$	24.0000	+	41.5692i	0.807664	+	1.39892i	0.914478	+	0.404637i	$0.132602\pi$
$883$	24.0000	+	41.5692i	0.807664	+	1.39892i	−0.106813	+	0.994279i	$0.534065\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.00000			0.268614			0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$		0			0
$889$	−16.0000			−0.536623
$890$		0			0
$891$	−9.00000	−	15.5885i	−0.301511	−	0.522233i
$892$		0			0
$893$	18.0000	+	31.1769i	0.602347	+	1.04330i
$894$		0			0
$895$	6.00000	+	10.3923i	0.200558	+	0.347376i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	90.0000			3.00167
$900$		0			0
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.50000	+	4.33013i	−0.0831028	+	0.143938i
$906$		0			0
$907$	−19.0000	−	32.9090i	−0.630885	−	1.09272i	−0.987371	−	0.158424i	$-0.949359\pi$
$907$	−19.0000	−	32.9090i	−0.630885	−	1.09272i	0.356487	−	0.934300i	$-0.383975\pi$
$908$		0			0
$909$	−4.50000	+	7.79423i	−0.149256	+	0.258518i
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.00000	+	10.3923i	−0.197492	+	0.342067i
$924$		0			0
$925$	−20.0000	+	13.8564i	−0.657596	+	0.455596i
$926$		0			0
$927$	−9.00000	+	15.5885i	−0.295599	+	0.511992i
$928$		0			0
$929$	−7.50000	−	12.9904i	−0.246067	−	0.426201i	0.716364	−	0.697727i	$-0.245805\pi$
$929$	−7.50000	−	12.9904i	−0.246067	−	0.426201i	−0.962431	+	0.271526i	$0.912472\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.00000			0.196221
$936$		0			0
$937$	2.50000	−	4.33013i	0.0816714	−	0.141459i	−0.822297	−	0.569059i	$-0.807308\pi$
$937$	2.50000	−	4.33013i	0.0816714	−	0.141459i	0.903968	+	0.427600i	$0.140641\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	−0.970661	−	0.240453i	$-0.922704\pi$
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	0.693569	+	0.720390i	$0.256037\pi$
$942$		0			0
$943$	18.0000	+	31.1769i	0.586161	+	1.01526i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$		0			0
$949$	−10.0000	−	17.3205i	−0.324614	−	0.562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	25.0000	−	43.3013i	0.809829	−	1.40267i	−0.103152	−	0.994666i	$-0.532893\pi$
$953$	25.0000	−	43.3013i	0.809829	−	1.40267i	0.912982	−	0.408000i	$-0.133774\pi$
$954$		0			0
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.00000	−	15.5885i	−0.290625	−	0.503378i
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	−54.0000			−1.74013
$964$		0			0
$965$	−9.50000	−	16.4545i	−0.305816	−	0.529689i
$966$		0			0
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	0.794515	−	0.607244i	$-0.207725\pi$
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	−0.923147	+	0.384448i	$0.874392\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	−0.549058	−	0.835784i	$-0.685013\pi$
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	0.998339	+	0.0576061i	$0.0183467\pi$
$972$		0			0
$973$	32.0000			1.02587
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	−0.849586	−	0.527451i	$-0.823148\pi$
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	0.881579	+	0.472037i	$0.156481\pi$
$978$		0			0
$979$	−7.00000	+	12.1244i	−0.223721	+	0.387496i
$980$		0			0
$981$	7.50000	+	12.9904i	0.239457	+	0.414751i
$982$		0			0
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	−0.973106	−	0.230360i	$-0.926010\pi$
$983$	−9.00000	+	15.5885i	−0.287055	+	0.497195i	0.686050	+	0.727554i	$0.259343\pi$
$984$		0			0
$985$	−15.0000			−0.477940
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.00000			−0.254385
$990$		0			0
$991$	30.0000			0.952981			0.476491	−	0.879180i	$-0.341909\pi$
$991$	30.0000			0.952981			0.476491	+	0.879180i	$0.341909\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.00000	−	8.66025i	−0.158511	−	0.274549i
$996$		0			0
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	−0.687584	−	0.726105i	$-0.741329\pi$
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	0.972617	+	0.232413i	$0.0746622\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.i.c.417.1		2
4.3	odd	2		37.2.c.a.10.1	✓	2
12.11	even	2		333.2.f.a.10.1		2
20.3	even	4		925.2.o.a.824.2		4
20.7	even	4		925.2.o.a.824.1		4
20.19	odd	2		925.2.e.a.676.1		2
37.26	even	3	inner	592.2.i.c.433.1		2
148.23	even	12		1369.2.b.b.1368.1		2
148.27	odd	6		1369.2.a.b.1.1		1
148.47	odd	6		1369.2.a.d.1.1		1
148.51	even	12		1369.2.b.b.1368.2		2
148.63	odd	6		37.2.c.a.26.1	yes	2
444.359	even	6		333.2.f.a.100.1		2
740.63	even	12		925.2.o.a.174.1		4
740.359	odd	6		925.2.e.a.26.1		2
740.507	even	12		925.2.o.a.174.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.c.a.10.1	✓	2	4.3	odd	2
37.2.c.a.26.1	yes	2	148.63	odd	6
333.2.f.a.10.1		2	12.11	even	2
333.2.f.a.100.1		2	444.359	even	6
592.2.i.c.417.1		2	1.1	even	1	trivial
592.2.i.c.433.1		2	37.26	even	3	inner
925.2.e.a.26.1		2	740.359	odd	6
925.2.e.a.676.1		2	20.19	odd	2
925.2.o.a.174.1		4	740.63	even	12
925.2.o.a.174.2		4	740.507	even	12
925.2.o.a.824.1		4	20.7	even	4
925.2.o.a.824.2		4	20.3	even	4
1369.2.a.b.1.1		1	148.27	odd	6
1369.2.a.d.1.1		1	148.47	odd	6
1369.2.b.b.1368.1		2	148.23	even	12
1369.2.b.b.1368.2		2	148.51	even	12

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{7} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{17} +(-3.00000 - 5.19615i) q^{19} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +9.00000 q^{29} +10.0000 q^{31} +(1.00000 - 1.73205i) q^{35} +(-5.50000 - 2.59808i) q^{37} +(4.50000 + 7.79423i) q^{41} -2.00000 q^{43} -3.00000 q^{45} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{61} +6.00000 q^{63} +(1.00000 - 1.73205i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(3.00000 + 5.19615i) q^{71} -10.0000 q^{73} +(2.00000 + 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +3.00000 q^{85} +(-3.50000 + 6.06218i) q^{89} +(-2.00000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - q^5 + 2 * q^7 + 3 * q^9	\( 2 q - q^{5} + 2 q^{7} + 3 q^{9} + 4 q^{11} + 2 q^{13} - 3 q^{17} - 6 q^{19} + 8 q^{23} + 4 q^{25} + 18 q^{29} + 20 q^{31} + 2 q^{35} - 11 q^{37} + 9 q^{41} - 4 q^{43} - 6 q^{45} - 12 q^{47} + 3 q^{49} + 2 q^{53} - 2 q^{55} - 4 q^{59} - q^{61} + 12 q^{63} + 2 q^{65} - 10 q^{67} + 6 q^{71} - 20 q^{73} + 4 q^{77} + 10 q^{79} - 9 q^{81} - 12 q^{83} + 6 q^{85} - 7 q^{89} - 4 q^{91} - 6 q^{95} + 14 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q - q^5 + 2 * q^7 + 3 * q^9 + 4 * q^11 + 2 * q^13 - 3 * q^17 - 6 * q^19 + 8 * q^23 + 4 * q^25 + 18 * q^29 + 20 * q^31 + 2 * q^35 - 11 * q^37 + 9 * q^41 - 4 * q^43 - 6 * q^45 - 12 * q^47 + 3 * q^49 + 2 * q^53 - 2 * q^55 - 4 * q^59 - q^61 + 12 * q^63 + 2 * q^65 - 10 * q^67 + 6 * q^71 - 20 * q^73 + 4 * q^77 + 10 * q^79 - 9 * q^81 - 12 * q^83 + 6 * q^85 - 7 * q^89 - 4 * q^91 - 6 * q^95 + 14 * q^97 + 6 * q^99

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