LMFDB - Embedded newform 6027.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.a (trivial)

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:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +1.00000 q^{5} -0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +1.00000 q^{5} -0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} +0.414214 q^{10} -2.00000 q^{11} +1.82843 q^{12} +4.41421 q^{13} -1.00000 q^{15} +3.00000 q^{16} +1.17157 q^{17} +0.414214 q^{18} +2.82843 q^{19} -1.82843 q^{20} -0.828427 q^{22} -3.24264 q^{23} +1.58579 q^{24} -4.00000 q^{25} +1.82843 q^{26} -1.00000 q^{27} -7.58579 q^{29} -0.414214 q^{30} -7.65685 q^{31} +4.41421 q^{32} +2.00000 q^{33} +0.485281 q^{34} -1.82843 q^{36} -2.17157 q^{37} +1.17157 q^{38} -4.41421 q^{39} -1.58579 q^{40} +1.00000 q^{41} -1.65685 q^{43} +3.65685 q^{44} +1.00000 q^{45} -1.34315 q^{46} +4.65685 q^{47} -3.00000 q^{48} -1.65685 q^{50} -1.17157 q^{51} -8.07107 q^{52} +2.41421 q^{53} -0.414214 q^{54} -2.00000 q^{55} -2.82843 q^{57} -3.14214 q^{58} +10.0000 q^{59} +1.82843 q^{60} +15.3137 q^{61} -3.17157 q^{62} -4.17157 q^{64} +4.41421 q^{65} +0.828427 q^{66} -0.171573 q^{67} -2.14214 q^{68} +3.24264 q^{69} +10.8284 q^{71} -1.58579 q^{72} -7.65685 q^{73} -0.899495 q^{74} +4.00000 q^{75} -5.17157 q^{76} -1.82843 q^{78} +1.48528 q^{79} +3.00000 q^{80} +1.00000 q^{81} +0.414214 q^{82} +8.82843 q^{83} +1.17157 q^{85} -0.686292 q^{86} +7.58579 q^{87} +3.17157 q^{88} +2.82843 q^{89} +0.414214 q^{90} +5.92893 q^{92} +7.65685 q^{93} +1.92893 q^{94} +2.82843 q^{95} -4.41421 q^{96} -16.8995 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{24} - 8 q^{25} - 2 q^{26} - 2 q^{27} - 18 q^{29} + 2 q^{30} - 4 q^{31} + 6 q^{32} + 4 q^{33} - 16 q^{34} + 2 q^{36} - 10 q^{37} + 8 q^{38} - 6 q^{39} - 6 q^{40} + 2 q^{41} + 8 q^{43} - 4 q^{44} + 2 q^{45} - 14 q^{46} - 2 q^{47} - 6 q^{48} + 8 q^{50} - 8 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} - 4 q^{55} + 22 q^{58} + 20 q^{59} - 2 q^{60} + 8 q^{61} - 12 q^{62} - 14 q^{64} + 6 q^{65} - 4 q^{66} - 6 q^{67} + 24 q^{68} - 2 q^{69} + 16 q^{71} - 6 q^{72} - 4 q^{73} + 18 q^{74} + 8 q^{75} - 16 q^{76} + 2 q^{78} - 14 q^{79} + 6 q^{80} + 2 q^{81} - 2 q^{82} + 12 q^{83} + 8 q^{85} - 24 q^{86} + 18 q^{87} + 12 q^{88} - 2 q^{90} + 26 q^{92} + 4 q^{93} + 18 q^{94} - 6 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^24 - 8 * q^25 - 2 * q^26 - 2 * q^27 - 18 * q^29 + 2 * q^30 - 4 * q^31 + 6 * q^32 + 4 * q^33 - 16 * q^34 + 2 * q^36 - 10 * q^37 + 8 * q^38 - 6 * q^39 - 6 * q^40 + 2 * q^41 + 8 * q^43 - 4 * q^44 + 2 * q^45 - 14 * q^46 - 2 * q^47 - 6 * q^48 + 8 * q^50 - 8 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 - 4 * q^55 + 22 * q^58 + 20 * q^59 - 2 * q^60 + 8 * q^61 - 12 * q^62 - 14 * q^64 + 6 * q^65 - 4 * q^66 - 6 * q^67 + 24 * q^68 - 2 * q^69 + 16 * q^71 - 6 * q^72 - 4 * q^73 + 18 * q^74 + 8 * q^75 - 16 * q^76 + 2 * q^78 - 14 * q^79 + 6 * q^80 + 2 * q^81 - 2 * q^82 + 12 * q^83 + 8 * q^85 - 24 * q^86 + 18 * q^87 + 12 * q^88 - 2 * q^90 + 26 * q^92 + 4 * q^93 + 18 * q^94 - 6 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82843	−0.914214
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.414214	−0.169102
$7$	0	0
$7$	0	0
$8$	−1.58579	−0.560660
$9$	1.00000	0.333333
$10$	0.414214	0.130986
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.82843	0.527821
$13$	4.41421	1.22428	0.612141	−	0.790748i	$-0.290308\pi$
$13$	4.41421	1.22428	0.612141	+	0.790748i	$0.290308\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	3.00000	0.750000
$17$	1.17157	0.284148	0.142074	−	0.989856i	$-0.454623\pi$
$17$	1.17157	0.284148	0.142074	+	0.989856i	$0.454623\pi$
$18$	0.414214	0.0976311
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	−1.82843	−0.408849
$21$	0	0
$22$	−0.828427	−0.176621
$23$	−3.24264	−0.676137	−0.338069	−	0.941121i	$-0.609774\pi$
$23$	−3.24264	−0.676137	−0.338069	+	0.941121i	$0.609774\pi$
$24$	1.58579	0.323697
$25$	−4.00000	−0.800000
$26$	1.82843	0.358584
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−7.58579	−1.40865	−0.704323	−	0.709880i	$-0.748749\pi$
$29$	−7.58579	−1.40865	−0.704323	+	0.709880i	$0.748749\pi$
$30$	−0.414214	−0.0756247
$31$	−7.65685	−1.37521	−0.687606	−	0.726084i	$-0.741338\pi$
$31$	−7.65685	−1.37521	−0.687606	+	0.726084i	$0.741338\pi$
$32$	4.41421	0.780330
$33$	2.00000	0.348155
$34$	0.485281	0.0832251
$35$	0	0
$36$	−1.82843	−0.304738
$37$	−2.17157	−0.357004	−0.178502	−	0.983940i	$-0.557125\pi$
$37$	−2.17157	−0.357004	−0.178502	+	0.983940i	$0.557125\pi$
$38$	1.17157	0.190054
$39$	−4.41421	−0.706840
$40$	−1.58579	−0.250735
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−1.65685	−0.252668	−0.126334	−	0.991988i	$-0.540321\pi$
$43$	−1.65685	−0.252668	−0.126334	+	0.991988i	$0.540321\pi$
$44$	3.65685	0.551292
$45$	1.00000	0.149071
$46$	−1.34315	−0.198036
$47$	4.65685	0.679272	0.339636	−	0.940557i	$-0.389696\pi$
$47$	4.65685	0.679272	0.339636	+	0.940557i	$0.389696\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	−1.65685	−0.234315
$51$	−1.17157	−0.164053
$52$	−8.07107	−1.11926
$53$	2.41421	0.331618	0.165809	−	0.986158i	$-0.446977\pi$
$53$	2.41421	0.331618	0.165809	+	0.986158i	$0.446977\pi$
$54$	−0.414214	−0.0563673
$55$	−2.00000	−0.269680
$56$	0	0
$57$	−2.82843	−0.374634
$58$	−3.14214	−0.412583
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	1.82843	0.236049
$61$	15.3137	1.96072	0.980360	−	0.197218i	$-0.0631906\pi$
$61$	15.3137	1.96072	0.980360	+	0.197218i	$0.0631906\pi$
$62$	−3.17157	−0.402790
$63$	0	0
$64$	−4.17157	−0.521447
$65$	4.41421	0.547516
$66$	0.828427	0.101972
$67$	−0.171573	−0.0209610	−0.0104805	−	0.999945i	$-0.503336\pi$
$67$	−0.171573	−0.0209610	−0.0104805	+	0.999945i	$0.503336\pi$
$68$	−2.14214	−0.259772
$69$	3.24264	0.390368
$70$	0	0
$71$	10.8284	1.28510	0.642549	−	0.766245i	$-0.277877\pi$
$71$	10.8284	1.28510	0.642549	+	0.766245i	$0.277877\pi$
$72$	−1.58579	−0.186887
$73$	−7.65685	−0.896167	−0.448084	−	0.893992i	$-0.647893\pi$
$73$	−7.65685	−0.896167	−0.448084	+	0.893992i	$0.647893\pi$
$74$	−0.899495	−0.104564
$75$	4.00000	0.461880
$76$	−5.17157	−0.593220
$77$	0	0
$78$	−1.82843	−0.207029
$79$	1.48528	0.167107	0.0835536	−	0.996503i	$-0.473373\pi$
$79$	1.48528	0.167107	0.0835536	+	0.996503i	$0.473373\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	0.414214	0.0457422
$83$	8.82843	0.969046	0.484523	−	0.874779i	$-0.338993\pi$
$83$	8.82843	0.969046	0.484523	+	0.874779i	$0.338993\pi$
$84$	0	0
$85$	1.17157	0.127075
$86$	−0.686292	−0.0740047
$87$	7.58579	0.813282
$88$	3.17157	0.338091
$89$	2.82843	0.299813	0.149906	−	0.988700i	$-0.452103\pi$
$89$	2.82843	0.299813	0.149906	+	0.988700i	$0.452103\pi$
$90$	0.414214	0.0436619
$91$	0	0
$92$	5.92893	0.618134
$93$	7.65685	0.793979
$94$	1.92893	0.198954
$95$	2.82843	0.290191
$96$	−4.41421	−0.450524
$97$	−16.8995	−1.71588	−0.857942	−	0.513747i	$-0.828257\pi$
$97$	−16.8995	−1.71588	−0.857942	+	0.513747i	$0.828257\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	7.31371	0.731371
$101$	−14.9706	−1.48963	−0.744813	−	0.667273i	$-0.767461\pi$
$101$	−14.9706	−1.48963	−0.744813	+	0.667273i	$0.767461\pi$
$102$	−0.485281	−0.0480500
$103$	−10.4142	−1.02614	−0.513071	−	0.858346i	$-0.671492\pi$
$103$	−10.4142	−1.02614	−0.513071	+	0.858346i	$0.671492\pi$
$104$	−7.00000	−0.686406
$105$	0	0
$106$	1.00000	0.0971286
$107$	7.72792	0.747086	0.373543	−	0.927613i	$-0.378143\pi$
$107$	7.72792	0.747086	0.373543	+	0.927613i	$0.378143\pi$
$108$	1.82843	0.175940
$109$	14.1421	1.35457	0.677285	−	0.735720i	$-0.263156\pi$
$109$	14.1421	1.35457	0.677285	+	0.735720i	$0.263156\pi$
$110$	−0.828427	−0.0789874
$111$	2.17157	0.206117
$112$	0	0
$113$	−6.82843	−0.642364	−0.321182	−	0.947017i	$-0.604080\pi$
$113$	−6.82843	−0.642364	−0.321182	+	0.947017i	$0.604080\pi$
$114$	−1.17157	−0.109728
$115$	−3.24264	−0.302378
$116$	13.8701	1.28780
$117$	4.41421	0.408094
$118$	4.14214	0.381314
$119$	0	0
$120$	1.58579	0.144762
$121$	−7.00000	−0.636364
$122$	6.34315	0.574281
$123$	−1.00000	−0.0901670
$124$	14.0000	1.25724
$125$	−9.00000	−0.804984
$126$	0	0
$127$	12.9706	1.15095	0.575476	−	0.817819i	$-0.304817\pi$
$127$	12.9706	1.15095	0.575476	+	0.817819i	$0.304817\pi$
$128$	−10.5563	−0.933058
$129$	1.65685	0.145878
$130$	1.82843	0.160364
$131$	15.3137	1.33796	0.668982	−	0.743278i	$-0.266730\pi$
$131$	15.3137	1.33796	0.668982	+	0.743278i	$0.266730\pi$
$132$	−3.65685	−0.318288
$133$	0	0
$134$	−0.0710678	−0.00613932
$135$	−1.00000	−0.0860663
$136$	−1.85786	−0.159311
$137$	−18.8995	−1.61469	−0.807346	−	0.590078i	$-0.799097\pi$
$137$	−18.8995	−1.61469	−0.807346	+	0.590078i	$0.799097\pi$
$138$	1.34315	0.114336
$139$	−20.5563	−1.74357	−0.871783	−	0.489892i	$-0.837036\pi$
$139$	−20.5563	−1.74357	−0.871783	+	0.489892i	$0.837036\pi$
$140$	0	0
$141$	−4.65685	−0.392178
$142$	4.48528	0.376396
$143$	−8.82843	−0.738270
$144$	3.00000	0.250000
$145$	−7.58579	−0.629965
$146$	−3.17157	−0.262481
$147$	0	0
$148$	3.97056	0.326378
$149$	−23.7990	−1.94969	−0.974845	−	0.222886i	$-0.928452\pi$
$149$	−23.7990	−1.94969	−0.974845	+	0.222886i	$0.928452\pi$
$150$	1.65685	0.135282
$151$	−5.65685	−0.460348	−0.230174	−	0.973149i	$-0.573930\pi$
$151$	−5.65685	−0.460348	−0.230174	+	0.973149i	$0.573930\pi$
$152$	−4.48528	−0.363804
$153$	1.17157	0.0947161
$154$	0	0
$155$	−7.65685	−0.615013
$156$	8.07107	0.646203
$157$	−9.17157	−0.731971	−0.365986	−	0.930621i	$-0.619268\pi$
$157$	−9.17157	−0.731971	−0.365986	+	0.930621i	$0.619268\pi$
$158$	0.615224	0.0489446
$159$	−2.41421	−0.191460
$160$	4.41421	0.348974
$161$	0	0
$162$	0.414214	0.0325437
$163$	−2.48528	−0.194662	−0.0973311	−	0.995252i	$-0.531031\pi$
$163$	−2.48528	−0.194662	−0.0973311	+	0.995252i	$0.531031\pi$
$164$	−1.82843	−0.142776
$165$	2.00000	0.155700
$166$	3.65685	0.283827
$167$	9.14214	0.707440	0.353720	−	0.935351i	$-0.384917\pi$
$167$	9.14214	0.707440	0.353720	+	0.935351i	$0.384917\pi$
$168$	0	0
$169$	6.48528	0.498868
$170$	0.485281	0.0372194
$171$	2.82843	0.216295
$172$	3.02944	0.230992
$173$	−7.82843	−0.595184	−0.297592	−	0.954693i	$-0.596184\pi$
$173$	−7.82843	−0.595184	−0.297592	+	0.954693i	$0.596184\pi$
$174$	3.14214	0.238205
$175$	0	0
$176$	−6.00000	−0.452267
$177$	−10.0000	−0.751646
$178$	1.17157	0.0878131
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.82843	−0.136283
$181$	−12.4853	−0.928024	−0.464012	−	0.885829i	$-0.653590\pi$
$181$	−12.4853	−0.928024	−0.464012	+	0.885829i	$0.653590\pi$
$182$	0	0
$183$	−15.3137	−1.13202
$184$	5.14214	0.379083
$185$	−2.17157	−0.159657
$186$	3.17157	0.232551
$187$	−2.34315	−0.171348
$188$	−8.51472	−0.621000
$189$	0	0
$190$	1.17157	0.0849948
$191$	1.17157	0.0847720	0.0423860	−	0.999101i	$-0.486504\pi$
$191$	1.17157	0.0847720	0.0423860	+	0.999101i	$0.486504\pi$
$192$	4.17157	0.301057
$193$	−5.65685	−0.407189	−0.203595	−	0.979055i	$-0.565262\pi$
$193$	−5.65685	−0.407189	−0.203595	+	0.979055i	$0.565262\pi$
$194$	−7.00000	−0.502571
$195$	−4.41421	−0.316108
$196$	0	0
$197$	−20.8284	−1.48396	−0.741982	−	0.670420i	$-0.766114\pi$
$197$	−20.8284	−1.48396	−0.741982	+	0.670420i	$0.766114\pi$
$198$	−0.828427	−0.0588738
$199$	−11.3137	−0.802008	−0.401004	−	0.916076i	$-0.631339\pi$
$199$	−11.3137	−0.802008	−0.401004	+	0.916076i	$0.631339\pi$
$200$	6.34315	0.448528
$201$	0.171573	0.0121018
$202$	−6.20101	−0.436302
$203$	0	0
$204$	2.14214	0.149979
$205$	1.00000	0.0698430
$206$	−4.31371	−0.300550
$207$	−3.24264	−0.225379
$208$	13.2426	0.918212
$209$	−5.65685	−0.391293
$210$	0	0
$211$	−17.4853	−1.20374	−0.601868	−	0.798595i	$-0.705577\pi$
$211$	−17.4853	−1.20374	−0.601868	+	0.798595i	$0.705577\pi$
$212$	−4.41421	−0.303169
$213$	−10.8284	−0.741952
$214$	3.20101	0.218817
$215$	−1.65685	−0.112997
$216$	1.58579	0.107899
$217$	0	0
$218$	5.85786	0.396745
$219$	7.65685	0.517402
$220$	3.65685	0.246545
$221$	5.17157	0.347878
$222$	0.899495	0.0603701
$223$	−5.92893	−0.397031	−0.198515	−	0.980098i	$-0.563612\pi$
$223$	−5.92893	−0.397031	−0.198515	+	0.980098i	$0.563612\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−2.82843	−0.188144
$227$	6.65685	0.441831	0.220915	−	0.975293i	$-0.429096\pi$
$227$	6.65685	0.441831	0.220915	+	0.975293i	$0.429096\pi$
$228$	5.17157	0.342496
$229$	7.24264	0.478607	0.239304	−	0.970945i	$-0.423081\pi$
$229$	7.24264	0.478607	0.239304	+	0.970945i	$0.423081\pi$
$230$	−1.34315	−0.0885644
$231$	0	0
$232$	12.0294	0.789771
$233$	−16.4853	−1.07999	−0.539993	−	0.841669i	$-0.681573\pi$
$233$	−16.4853	−1.07999	−0.539993	+	0.841669i	$0.681573\pi$
$234$	1.82843	0.119528
$235$	4.65685	0.303780
$236$	−18.2843	−1.19020
$237$	−1.48528	−0.0964794
$238$	0	0
$239$	−26.6274	−1.72238	−0.861192	−	0.508279i	$-0.830282\pi$
$239$	−26.6274	−1.72238	−0.861192	+	0.508279i	$0.830282\pi$
$240$	−3.00000	−0.193649
$241$	−20.1421	−1.29747	−0.648735	−	0.761015i	$-0.724701\pi$
$241$	−20.1421	−1.29747	−0.648735	+	0.761015i	$0.724701\pi$
$242$	−2.89949	−0.186387
$243$	−1.00000	−0.0641500
$244$	−28.0000	−1.79252
$245$	0	0
$246$	−0.414214	−0.0264093
$247$	12.4853	0.794419
$248$	12.1421	0.771026
$249$	−8.82843	−0.559479
$250$	−3.72792	−0.235774
$251$	−10.9706	−0.692456	−0.346228	−	0.938150i	$-0.612538\pi$
$251$	−10.9706	−0.692456	−0.346228	+	0.938150i	$0.612538\pi$
$252$	0	0
$253$	6.48528	0.407726
$254$	5.37258	0.337106
$255$	−1.17157	−0.0733667
$256$	3.97056	0.248160
$257$	−29.4558	−1.83741	−0.918703	−	0.394950i	$-0.870762\pi$
$257$	−29.4558	−1.83741	−0.918703	+	0.394950i	$0.870762\pi$
$258$	0.686292	0.0427266
$259$	0	0
$260$	−8.07107	−0.500546
$261$	−7.58579	−0.469548
$262$	6.34315	0.391881
$263$	3.17157	0.195568	0.0977838	−	0.995208i	$-0.468825\pi$
$263$	3.17157	0.195568	0.0977838	+	0.995208i	$0.468825\pi$
$264$	−3.17157	−0.195197
$265$	2.41421	0.148304
$266$	0	0
$267$	−2.82843	−0.173097
$268$	0.313708	0.0191628
$269$	5.14214	0.313522	0.156761	−	0.987637i	$-0.449895\pi$
$269$	5.14214	0.313522	0.156761	+	0.987637i	$0.449895\pi$
$270$	−0.414214	−0.0252082
$271$	5.10051	0.309834	0.154917	−	0.987928i	$-0.450489\pi$
$271$	5.10051	0.309834	0.154917	+	0.987928i	$0.450489\pi$
$272$	3.51472	0.213111
$273$	0	0
$274$	−7.82843	−0.472933
$275$	8.00000	0.482418
$276$	−5.92893	−0.356880
$277$	−12.6569	−0.760477	−0.380238	−	0.924889i	$-0.624158\pi$
$277$	−12.6569	−0.760477	−0.380238	+	0.924889i	$0.624158\pi$
$278$	−8.51472	−0.510679
$279$	−7.65685	−0.458404
$280$	0	0
$281$	−0.899495	−0.0536594	−0.0268297	−	0.999640i	$-0.508541\pi$
$281$	−0.899495	−0.0536594	−0.0268297	+	0.999640i	$0.508541\pi$
$282$	−1.92893	−0.114866
$283$	17.3137	1.02919	0.514597	−	0.857432i	$-0.327942\pi$
$283$	17.3137	1.02919	0.514597	+	0.857432i	$0.327942\pi$
$284$	−19.7990	−1.17485
$285$	−2.82843	−0.167542
$286$	−3.65685	−0.216234
$287$	0	0
$288$	4.41421	0.260110
$289$	−15.6274	−0.919260
$290$	−3.14214	−0.184513
$291$	16.8995	0.990666
$292$	14.0000	0.819288
$293$	12.4853	0.729398	0.364699	−	0.931125i	$-0.381172\pi$
$293$	12.4853	0.729398	0.364699	+	0.931125i	$0.381172\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	3.44365	0.200158
$297$	2.00000	0.116052
$298$	−9.85786	−0.571051
$299$	−14.3137	−0.827783
$300$	−7.31371	−0.422257
$301$	0	0
$302$	−2.34315	−0.134833
$303$	14.9706	0.860036
$304$	8.48528	0.486664
$305$	15.3137	0.876860
$306$	0.485281	0.0277417
$307$	16.8995	0.964505	0.482253	−	0.876032i	$-0.339819\pi$
$307$	16.8995	0.964505	0.482253	+	0.876032i	$0.339819\pi$
$308$	0	0
$309$	10.4142	0.592444
$310$	−3.17157	−0.180133
$311$	−11.0000	−0.623753	−0.311876	−	0.950123i	$-0.600957\pi$
$311$	−11.0000	−0.623753	−0.311876	+	0.950123i	$0.600957\pi$
$312$	7.00000	0.396297
$313$	18.2132	1.02947	0.514736	−	0.857349i	$-0.327890\pi$
$313$	18.2132	1.02947	0.514736	+	0.857349i	$0.327890\pi$
$314$	−3.79899	−0.214389
$315$	0	0
$316$	−2.71573	−0.152772
$317$	14.4142	0.809583	0.404791	−	0.914409i	$-0.367344\pi$
$317$	14.4142	0.809583	0.404791	+	0.914409i	$0.367344\pi$
$318$	−1.00000	−0.0560772
$319$	15.1716	0.849445
$320$	−4.17157	−0.233198
$321$	−7.72792	−0.431331
$322$	0	0
$323$	3.31371	0.184380
$324$	−1.82843	−0.101579
$325$	−17.6569	−0.979426
$326$	−1.02944	−0.0570153
$327$	−14.1421	−0.782062
$328$	−1.58579	−0.0875604
$329$	0	0
$330$	0.828427	0.0456034
$331$	−21.9706	−1.20761	−0.603806	−	0.797132i	$-0.706350\pi$
$331$	−21.9706	−1.20761	−0.603806	+	0.797132i	$0.706350\pi$
$332$	−16.1421	−0.885915
$333$	−2.17157	−0.119001
$334$	3.78680	0.207204
$335$	−0.171573	−0.00937403
$336$	0	0
$337$	31.8284	1.73380	0.866902	−	0.498478i	$-0.166107\pi$
$337$	31.8284	1.73380	0.866902	+	0.498478i	$0.166107\pi$
$338$	2.68629	0.146115
$339$	6.82843	0.370869
$340$	−2.14214	−0.116174
$341$	15.3137	0.829284
$342$	1.17157	0.0633514
$343$	0	0
$344$	2.62742	0.141661
$345$	3.24264	0.174578
$346$	−3.24264	−0.174325
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−13.8701	−0.743513
$349$	3.65685	0.195747	0.0978735	−	0.995199i	$-0.468796\pi$
$349$	3.65685	0.195747	0.0978735	+	0.995199i	$0.468796\pi$
$350$	0	0
$351$	−4.41421	−0.235613
$352$	−8.82843	−0.470557
$353$	17.3137	0.921516	0.460758	−	0.887526i	$-0.347578\pi$
$353$	17.3137	0.921516	0.460758	+	0.887526i	$0.347578\pi$
$354$	−4.14214	−0.220152
$355$	10.8284	0.574713
$356$	−5.17157	−0.274093
$357$	0	0
$358$	4.97056	0.262702
$359$	−26.0711	−1.37598	−0.687989	−	0.725721i	$-0.741506\pi$
$359$	−26.0711	−1.37598	−0.687989	+	0.725721i	$0.741506\pi$
$360$	−1.58579	−0.0835783
$361$	−11.0000	−0.578947
$362$	−5.17157	−0.271812
$363$	7.00000	0.367405
$364$	0	0
$365$	−7.65685	−0.400778
$366$	−6.34315	−0.331562
$367$	12.8995	0.673348	0.336674	−	0.941621i	$-0.390698\pi$
$367$	12.8995	0.673348	0.336674	+	0.941621i	$0.390698\pi$
$368$	−9.72792	−0.507103
$369$	1.00000	0.0520579
$370$	−0.899495	−0.0467625
$371$	0	0
$372$	−14.0000	−0.725866
$373$	−30.1716	−1.56222	−0.781112	−	0.624390i	$-0.785347\pi$
$373$	−30.1716	−1.56222	−0.781112	+	0.624390i	$0.785347\pi$
$374$	−0.970563	−0.0501866
$375$	9.00000	0.464758
$376$	−7.38478	−0.380841
$377$	−33.4853	−1.72458
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	−5.17157	−0.265296
$381$	−12.9706	−0.664502
$382$	0.485281	0.0248292
$383$	8.31371	0.424811	0.212405	−	0.977182i	$-0.431870\pi$
$383$	8.31371	0.424811	0.212405	+	0.977182i	$0.431870\pi$
$384$	10.5563	0.538701
$385$	0	0
$386$	−2.34315	−0.119263
$387$	−1.65685	−0.0842226
$388$	30.8995	1.56868
$389$	21.4558	1.08785	0.543927	−	0.839132i	$-0.316937\pi$
$389$	21.4558	1.08785	0.543927	+	0.839132i	$0.316937\pi$
$390$	−1.82843	−0.0925860
$391$	−3.79899	−0.192123
$392$	0	0
$393$	−15.3137	−0.772474
$394$	−8.62742	−0.434643
$395$	1.48528	0.0747326
$396$	3.65685	0.183764
$397$	−14.8284	−0.744217	−0.372109	−	0.928189i	$-0.621365\pi$
$397$	−14.8284	−0.744217	−0.372109	+	0.928189i	$0.621365\pi$
$398$	−4.68629	−0.234903
$399$	0	0
$400$	−12.0000	−0.600000
$401$	15.7990	0.788964	0.394482	−	0.918904i	$-0.370924\pi$
$401$	15.7990	0.788964	0.394482	+	0.918904i	$0.370924\pi$
$402$	0.0710678	0.00354454
$403$	−33.7990	−1.68365
$404$	27.3726	1.36184
$405$	1.00000	0.0496904
$406$	0	0
$407$	4.34315	0.215282
$408$	1.85786	0.0919780
$409$	−23.7990	−1.17678	−0.588392	−	0.808576i	$-0.700239\pi$
$409$	−23.7990	−1.17678	−0.588392	+	0.808576i	$0.700239\pi$
$410$	0.414214	0.0204565
$411$	18.8995	0.932243
$412$	19.0416	0.938114
$413$	0	0
$414$	−1.34315	−0.0660120
$415$	8.82843	0.433370
$416$	19.4853	0.955345
$417$	20.5563	1.00665
$418$	−2.34315	−0.114607
$419$	33.1716	1.62054	0.810269	−	0.586059i	$-0.199321\pi$
$419$	33.1716	1.62054	0.810269	+	0.586059i	$0.199321\pi$
$420$	0	0
$421$	23.3137	1.13624	0.568120	−	0.822946i	$-0.307671\pi$
$421$	23.3137	1.13624	0.568120	+	0.822946i	$0.307671\pi$
$422$	−7.24264	−0.352566
$423$	4.65685	0.226424
$424$	−3.82843	−0.185925
$425$	−4.68629	−0.227319
$426$	−4.48528	−0.217313
$427$	0	0
$428$	−14.1299	−0.682997
$429$	8.82843	0.426240
$430$	−0.686292	−0.0330959
$431$	5.31371	0.255952	0.127976	−	0.991777i	$-0.459152\pi$
$431$	5.31371	0.255952	0.127976	+	0.991777i	$0.459152\pi$
$432$	−3.00000	−0.144338
$433$	16.1421	0.775742	0.387871	−	0.921714i	$-0.373211\pi$
$433$	16.1421	0.775742	0.387871	+	0.921714i	$0.373211\pi$
$434$	0	0
$435$	7.58579	0.363711
$436$	−25.8579	−1.23837
$437$	−9.17157	−0.438736
$438$	3.17157	0.151544
$439$	18.9706	0.905416	0.452708	−	0.891659i	$-0.350458\pi$
$439$	18.9706	0.905416	0.452708	+	0.891659i	$0.350458\pi$
$440$	3.17157	0.151199
$441$	0	0
$442$	2.14214	0.101891
$443$	−32.6274	−1.55018	−0.775088	−	0.631854i	$-0.782294\pi$
$443$	−32.6274	−1.55018	−0.775088	+	0.631854i	$0.782294\pi$
$444$	−3.97056	−0.188435
$445$	2.82843	0.134080
$446$	−2.45584	−0.116288
$447$	23.7990	1.12565
$448$	0	0
$449$	−5.31371	−0.250769	−0.125385	−	0.992108i	$-0.540017\pi$
$449$	−5.31371	−0.250769	−0.125385	+	0.992108i	$0.540017\pi$
$450$	−1.65685	−0.0781049
$451$	−2.00000	−0.0941763
$452$	12.4853	0.587258
$453$	5.65685	0.265782
$454$	2.75736	0.129409
$455$	0	0
$456$	4.48528	0.210043
$457$	−11.3137	−0.529233	−0.264616	−	0.964354i	$-0.585245\pi$
$457$	−11.3137	−0.529233	−0.264616	+	0.964354i	$0.585245\pi$
$458$	3.00000	0.140181
$459$	−1.17157	−0.0546843
$460$	5.92893	0.276438
$461$	−1.20101	−0.0559366	−0.0279683	−	0.999609i	$-0.508904\pi$
$461$	−1.20101	−0.0559366	−0.0279683	+	0.999609i	$0.508904\pi$
$462$	0	0
$463$	−13.8284	−0.642662	−0.321331	−	0.946967i	$-0.604130\pi$
$463$	−13.8284	−0.642662	−0.321331	+	0.946967i	$0.604130\pi$
$464$	−22.7574	−1.05648
$465$	7.65685	0.355078
$466$	−6.82843	−0.316321
$467$	35.1127	1.62482	0.812411	−	0.583085i	$-0.198155\pi$
$467$	35.1127	1.62482	0.812411	+	0.583085i	$0.198155\pi$
$468$	−8.07107	−0.373085
$469$	0	0
$470$	1.92893	0.0889750
$471$	9.17157	0.422604
$472$	−15.8579	−0.729917
$473$	3.31371	0.152364
$474$	−0.615224	−0.0282582
$475$	−11.3137	−0.519109
$476$	0	0
$477$	2.41421	0.110539
$478$	−11.0294	−0.504475
$479$	−28.9706	−1.32370	−0.661849	−	0.749637i	$-0.730228\pi$
$479$	−28.9706	−1.32370	−0.661849	+	0.749637i	$0.730228\pi$
$480$	−4.41421	−0.201480
$481$	−9.58579	−0.437074
$482$	−8.34315	−0.380020
$483$	0	0
$484$	12.7990	0.581772
$485$	−16.8995	−0.767367
$486$	−0.414214	−0.0187891
$487$	−0.485281	−0.0219902	−0.0109951	−	0.999940i	$-0.503500\pi$
$487$	−0.485281	−0.0219902	−0.0109951	+	0.999940i	$0.503500\pi$
$488$	−24.2843	−1.09930
$489$	2.48528	0.112388
$490$	0	0
$491$	−8.34315	−0.376521	−0.188260	−	0.982119i	$-0.560285\pi$
$491$	−8.34315	−0.376521	−0.188260	+	0.982119i	$0.560285\pi$
$492$	1.82843	0.0824319
$493$	−8.88730	−0.400264
$494$	5.17157	0.232680
$495$	−2.00000	−0.0898933
$496$	−22.9706	−1.03141
$497$	0	0
$498$	−3.65685	−0.163868
$499$	−21.6569	−0.969494	−0.484747	−	0.874654i	$-0.661088\pi$
$499$	−21.6569	−0.969494	−0.484747	+	0.874654i	$0.661088\pi$
$500$	16.4558	0.735928
$501$	−9.14214	−0.408440
$502$	−4.54416	−0.202816
$503$	8.51472	0.379653	0.189826	−	0.981818i	$-0.439208\pi$
$503$	8.51472	0.379653	0.189826	+	0.981818i	$0.439208\pi$
$504$	0	0
$505$	−14.9706	−0.666181
$506$	2.68629	0.119420
$507$	−6.48528	−0.288021
$508$	−23.7157	−1.05222
$509$	−16.3431	−0.724397	−0.362199	−	0.932101i	$-0.617974\pi$
$509$	−16.3431	−0.724397	−0.362199	+	0.932101i	$0.617974\pi$
$510$	−0.485281	−0.0214886
$511$	0	0
$512$	22.7574	1.00574
$513$	−2.82843	−0.124878
$514$	−12.2010	−0.538163
$515$	−10.4142	−0.458905
$516$	−3.02944	−0.133364
$517$	−9.31371	−0.409616
$518$	0	0
$519$	7.82843	0.343630
$520$	−7.00000	−0.306970
$521$	15.1716	0.664679	0.332339	−	0.943160i	$-0.392162\pi$
$521$	15.1716	0.664679	0.332339	+	0.943160i	$0.392162\pi$
$522$	−3.14214	−0.137528
$523$	−13.3137	−0.582168	−0.291084	−	0.956698i	$-0.594016\pi$
$523$	−13.3137	−0.582168	−0.291084	+	0.956698i	$0.594016\pi$
$524$	−28.0000	−1.22319
$525$	0	0
$526$	1.31371	0.0572804
$527$	−8.97056	−0.390764
$528$	6.00000	0.261116
$529$	−12.4853	−0.542838
$530$	1.00000	0.0434372
$531$	10.0000	0.433963
$532$	0	0
$533$	4.41421	0.191201
$534$	−1.17157	−0.0506989
$535$	7.72792	0.334107
$536$	0.272078	0.0117520
$537$	−12.0000	−0.517838
$538$	2.12994	0.0918283
$539$	0	0
$540$	1.82843	0.0786830
$541$	8.79899	0.378298	0.189149	−	0.981948i	$-0.439427\pi$
$541$	8.79899	0.378298	0.189149	+	0.981948i	$0.439427\pi$
$542$	2.11270	0.0907482
$543$	12.4853	0.535795
$544$	5.17157	0.221729
$545$	14.1421	0.605783
$546$	0	0
$547$	12.6569	0.541168	0.270584	−	0.962696i	$-0.412783\pi$
$547$	12.6569	0.541168	0.270584	+	0.962696i	$0.412783\pi$
$548$	34.5563	1.47617
$549$	15.3137	0.653573
$550$	3.31371	0.141297
$551$	−21.4558	−0.914050
$552$	−5.14214	−0.218864
$553$	0	0
$554$	−5.24264	−0.222738
$555$	2.17157	0.0921781
$556$	37.5858	1.59399
$557$	3.79899	0.160968	0.0804842	−	0.996756i	$-0.474353\pi$
$557$	3.79899	0.160968	0.0804842	+	0.996756i	$0.474353\pi$
$558$	−3.17157	−0.134263
$559$	−7.31371	−0.309337
$560$	0	0
$561$	2.34315	0.0989277
$562$	−0.372583	−0.0157165
$563$	−20.4558	−0.862111	−0.431056	−	0.902325i	$-0.641859\pi$
$563$	−20.4558	−0.862111	−0.431056	+	0.902325i	$0.641859\pi$
$564$	8.51472	0.358534
$565$	−6.82843	−0.287274
$566$	7.17157	0.301444
$567$	0	0
$568$	−17.1716	−0.720503
$569$	15.1716	0.636025	0.318013	−	0.948086i	$-0.396985\pi$
$569$	15.1716	0.636025	0.318013	+	0.948086i	$0.396985\pi$
$570$	−1.17157	−0.0490718
$571$	−23.3137	−0.975648	−0.487824	−	0.872942i	$-0.662209\pi$
$571$	−23.3137	−0.975648	−0.487824	+	0.872942i	$0.662209\pi$
$572$	16.1421	0.674937
$573$	−1.17157	−0.0489432
$574$	0	0
$575$	12.9706	0.540910
$576$	−4.17157	−0.173816
$577$	−16.4853	−0.686291	−0.343146	−	0.939282i	$-0.611492\pi$
$577$	−16.4853	−0.686291	−0.343146	+	0.939282i	$0.611492\pi$
$578$	−6.47309	−0.269245
$579$	5.65685	0.235091
$580$	13.8701	0.575923
$581$	0	0
$582$	7.00000	0.290159
$583$	−4.82843	−0.199973
$584$	12.1421	0.502445
$585$	4.41421	0.182505
$586$	5.17157	0.213636
$587$	−3.02944	−0.125038	−0.0625191	−	0.998044i	$-0.519913\pi$
$587$	−3.02944	−0.125038	−0.0625191	+	0.998044i	$0.519913\pi$
$588$	0	0
$589$	−21.6569	−0.892355
$590$	4.14214	0.170529
$591$	20.8284	0.856767
$592$	−6.51472	−0.267753
$593$	−2.34315	−0.0962215	−0.0481107	−	0.998842i	$-0.515320\pi$
$593$	−2.34315	−0.0962215	−0.0481107	+	0.998842i	$0.515320\pi$
$594$	0.828427	0.0339908
$595$	0	0
$596$	43.5147	1.78243
$597$	11.3137	0.463039
$598$	−5.92893	−0.242452
$599$	−13.7279	−0.560908	−0.280454	−	0.959868i	$-0.590485\pi$
$599$	−13.7279	−0.560908	−0.280454	+	0.959868i	$0.590485\pi$
$600$	−6.34315	−0.258958
$601$	−18.4142	−0.751131	−0.375566	−	0.926796i	$-0.622552\pi$
$601$	−18.4142	−0.751131	−0.375566	+	0.926796i	$0.622552\pi$
$602$	0	0
$603$	−0.171573	−0.00698699
$604$	10.3431	0.420857
$605$	−7.00000	−0.284590
$606$	6.20101	0.251899
$607$	29.3137	1.18981	0.594903	−	0.803797i	$-0.297190\pi$
$607$	29.3137	1.18981	0.594903	+	0.803797i	$0.297190\pi$
$608$	12.4853	0.506345
$609$	0	0
$610$	6.34315	0.256826
$611$	20.5563	0.831621
$612$	−2.14214	−0.0865907
$613$	8.65685	0.349647	0.174824	−	0.984600i	$-0.444065\pi$
$613$	8.65685	0.349647	0.174824	+	0.984600i	$0.444065\pi$
$614$	7.00000	0.282497
$615$	−1.00000	−0.0403239
$616$	0	0
$617$	−12.0000	−0.483102	−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000	−0.483102	−0.241551	+	0.970388i	$0.577656\pi$
$618$	4.31371	0.173523
$619$	12.8995	0.518474	0.259237	−	0.965814i	$-0.416529\pi$
$619$	12.8995	0.518474	0.259237	+	0.965814i	$0.416529\pi$
$620$	14.0000	0.562254
$621$	3.24264	0.130123
$622$	−4.55635	−0.182693
$623$	0	0
$624$	−13.2426	−0.530130
$625$	11.0000	0.440000
$626$	7.54416	0.301525
$627$	5.65685	0.225913
$628$	16.7696	0.669178
$629$	−2.54416	−0.101442
$630$	0	0
$631$	−21.4558	−0.854144	−0.427072	−	0.904218i	$-0.640455\pi$
$631$	−21.4558	−0.854144	−0.427072	+	0.904218i	$0.640455\pi$
$632$	−2.35534	−0.0936904
$633$	17.4853	0.694978
$634$	5.97056	0.237121
$635$	12.9706	0.514721
$636$	4.41421	0.175035
$637$	0	0
$638$	6.28427	0.248797
$639$	10.8284	0.428366
$640$	−10.5563	−0.417276
$641$	−21.1716	−0.836227	−0.418113	−	0.908395i	$-0.637309\pi$
$641$	−21.1716	−0.836227	−0.418113	+	0.908395i	$0.637309\pi$
$642$	−3.20101	−0.126334
$643$	−5.79899	−0.228690	−0.114345	−	0.993441i	$-0.536477\pi$
$643$	−5.79899	−0.228690	−0.114345	+	0.993441i	$0.536477\pi$
$644$	0	0
$645$	1.65685	0.0652386
$646$	1.37258	0.0540036
$647$	−39.3137	−1.54558	−0.772791	−	0.634661i	$-0.781140\pi$
$647$	−39.3137	−1.54558	−0.772791	+	0.634661i	$0.781140\pi$
$648$	−1.58579	−0.0622956
$649$	−20.0000	−0.785069
$650$	−7.31371	−0.286867
$651$	0	0
$652$	4.54416	0.177963
$653$	1.17157	0.0458472	0.0229236	−	0.999737i	$-0.492703\pi$
$653$	1.17157	0.0458472	0.0229236	+	0.999737i	$0.492703\pi$
$654$	−5.85786	−0.229061
$655$	15.3137	0.598356
$656$	3.00000	0.117130
$657$	−7.65685	−0.298722
$658$	0	0
$659$	4.14214	0.161355	0.0806773	−	0.996740i	$-0.474292\pi$
$659$	4.14214	0.161355	0.0806773	+	0.996740i	$0.474292\pi$
$660$	−3.65685	−0.142343
$661$	−37.1716	−1.44581	−0.722903	−	0.690949i	$-0.757193\pi$
$661$	−37.1716	−1.44581	−0.722903	+	0.690949i	$0.757193\pi$
$662$	−9.10051	−0.353701
$663$	−5.17157	−0.200847
$664$	−14.0000	−0.543305
$665$	0	0
$666$	−0.899495	−0.0348547
$667$	24.5980	0.952438
$668$	−16.7157	−0.646751
$669$	5.92893	0.229226
$670$	−0.0710678	−0.00274559
$671$	−30.6274	−1.18236
$672$	0	0
$673$	−36.9706	−1.42511	−0.712555	−	0.701616i	$-0.752462\pi$
$673$	−36.9706	−1.42511	−0.712555	+	0.701616i	$0.752462\pi$
$674$	13.1838	0.507820
$675$	4.00000	0.153960
$676$	−11.8579	−0.456072
$677$	14.6863	0.564440	0.282220	−	0.959350i	$-0.408929\pi$
$677$	14.6863	0.564440	0.282220	+	0.959350i	$0.408929\pi$
$678$	2.82843	0.108625
$679$	0	0
$680$	−1.85786	−0.0712458
$681$	−6.65685	−0.255091
$682$	6.34315	0.242892
$683$	39.1127	1.49661	0.748303	−	0.663357i	$-0.230869\pi$
$683$	39.1127	1.49661	0.748303	+	0.663357i	$0.230869\pi$
$684$	−5.17157	−0.197740
$685$	−18.8995	−0.722113
$686$	0	0
$687$	−7.24264	−0.276324
$688$	−4.97056	−0.189501
$689$	10.6569	0.405994
$690$	1.34315	0.0511327
$691$	41.1716	1.56624	0.783120	−	0.621870i	$-0.213627\pi$
$691$	41.1716	1.56624	0.783120	+	0.621870i	$0.213627\pi$
$692$	14.3137	0.544126
$693$	0	0
$694$	4.97056	0.188680
$695$	−20.5563	−0.779747
$696$	−12.0294	−0.455975
$697$	1.17157	0.0443765
$698$	1.51472	0.0573329
$699$	16.4853	0.623531
$700$	0	0
$701$	2.62742	0.0992362	0.0496181	−	0.998768i	$-0.484200\pi$
$701$	2.62742	0.0992362	0.0496181	+	0.998768i	$0.484200\pi$
$702$	−1.82843	−0.0690095
$703$	−6.14214	−0.231655
$704$	8.34315	0.314444
$705$	−4.65685	−0.175387
$706$	7.17157	0.269906
$707$	0	0
$708$	18.2843	0.687165
$709$	−2.48528	−0.0933367	−0.0466684	−	0.998910i	$-0.514860\pi$
$709$	−2.48528	−0.0933367	−0.0466684	+	0.998910i	$0.514860\pi$
$710$	4.48528	0.168330
$711$	1.48528	0.0557024
$712$	−4.48528	−0.168093
$713$	24.8284	0.929832
$714$	0	0
$715$	−8.82843	−0.330164
$716$	−21.9411	−0.819978
$717$	26.6274	0.994419
$718$	−10.7990	−0.403015
$719$	−12.6863	−0.473119	−0.236559	−	0.971617i	$-0.576020\pi$
$719$	−12.6863	−0.473119	−0.236559	+	0.971617i	$0.576020\pi$
$720$	3.00000	0.111803
$721$	0	0
$722$	−4.55635	−0.169570
$723$	20.1421	0.749094
$724$	22.8284	0.848412
$725$	30.3431	1.12692
$726$	2.89949	0.107610
$727$	−8.20101	−0.304159	−0.152079	−	0.988368i	$-0.548597\pi$
$727$	−8.20101	−0.304159	−0.152079	+	0.988368i	$0.548597\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.17157	−0.117385
$731$	−1.94113	−0.0717951
$732$	28.0000	1.03491
$733$	−48.0000	−1.77292	−0.886460	−	0.462805i	$-0.846843\pi$
$733$	−48.0000	−1.77292	−0.886460	+	0.462805i	$0.846843\pi$
$734$	5.34315	0.197219
$735$	0	0
$736$	−14.3137	−0.527610
$737$	0.343146	0.0126399
$738$	0.414214	0.0152474
$739$	−51.3137	−1.88761	−0.943803	−	0.330510i	$-0.892779\pi$
$739$	−51.3137	−1.88761	−0.943803	+	0.330510i	$0.892779\pi$
$740$	3.97056	0.145961
$741$	−12.4853	−0.458658
$742$	0	0
$743$	−40.6274	−1.49048	−0.745238	−	0.666799i	$-0.767664\pi$
$743$	−40.6274	−1.49048	−0.745238	+	0.666799i	$0.767664\pi$
$744$	−12.1421	−0.445152
$745$	−23.7990	−0.871928
$746$	−12.4975	−0.457565
$747$	8.82843	0.323015
$748$	4.28427	0.156648
$749$	0	0
$750$	3.72792	0.136124
$751$	−16.7990	−0.613004	−0.306502	−	0.951870i	$-0.599159\pi$
$751$	−16.7990	−0.613004	−0.306502	+	0.951870i	$0.599159\pi$
$752$	13.9706	0.509454
$753$	10.9706	0.399790
$754$	−13.8701	−0.505118
$755$	−5.65685	−0.205874
$756$	0	0
$757$	−5.31371	−0.193130	−0.0965650	−	0.995327i	$-0.530786\pi$
$757$	−5.31371	−0.193130	−0.0965650	+	0.995327i	$0.530786\pi$
$758$	−4.97056	−0.180539
$759$	−6.48528	−0.235401
$760$	−4.48528	−0.162698
$761$	19.2843	0.699054	0.349527	−	0.936926i	$-0.386342\pi$
$761$	19.2843	0.699054	0.349527	+	0.936926i	$0.386342\pi$
$762$	−5.37258	−0.194628
$763$	0	0
$764$	−2.14214	−0.0774997
$765$	1.17157	0.0423583
$766$	3.44365	0.124424
$767$	44.1421	1.59388
$768$	−3.97056	−0.143275
$769$	9.45584	0.340986	0.170493	−	0.985359i	$-0.445464\pi$
$769$	9.45584	0.340986	0.170493	+	0.985359i	$0.445464\pi$
$770$	0	0
$771$	29.4558	1.06083
$772$	10.3431	0.372258
$773$	−9.17157	−0.329879	−0.164939	−	0.986304i	$-0.552743\pi$
$773$	−9.17157	−0.329879	−0.164939	+	0.986304i	$0.552743\pi$
$774$	−0.686292	−0.0246682
$775$	30.6274	1.10017
$776$	26.7990	0.962028
$777$	0	0
$778$	8.88730	0.318625
$779$	2.82843	0.101339
$780$	8.07107	0.288991
$781$	−21.6569	−0.774943
$782$	−1.57359	−0.0562716
$783$	7.58579	0.271094
$784$	0	0
$785$	−9.17157	−0.327347
$786$	−6.34315	−0.226253
$787$	−29.1005	−1.03732	−0.518660	−	0.854980i	$-0.673569\pi$
$787$	−29.1005	−1.03732	−0.518660	+	0.854980i	$0.673569\pi$
$788$	38.0833	1.35666
$789$	−3.17157	−0.112911
$790$	0.615224	0.0218887
$791$	0	0
$792$	3.17157	0.112697
$793$	67.5980	2.40047
$794$	−6.14214	−0.217976
$795$	−2.41421	−0.0856233
$796$	20.6863	0.733206
$797$	−38.9706	−1.38041	−0.690204	−	0.723615i	$-0.742479\pi$
$797$	−38.9706	−1.38041	−0.690204	+	0.723615i	$0.742479\pi$
$798$	0	0
$799$	5.45584	0.193014
$800$	−17.6569	−0.624264
$801$	2.82843	0.0999376
$802$	6.54416	0.231082
$803$	15.3137	0.540409
$804$	−0.313708	−0.0110636
$805$	0	0
$806$	−14.0000	−0.493129
$807$	−5.14214	−0.181012
$808$	23.7401	0.835174
$809$	24.3553	0.856288	0.428144	−	0.903710i	$-0.359168\pi$
$809$	24.3553	0.856288	0.428144	+	0.903710i	$0.359168\pi$
$810$	0.414214	0.0145540
$811$	−13.8701	−0.487044	−0.243522	−	0.969895i	$-0.578303\pi$
$811$	−13.8701	−0.487044	−0.243522	+	0.969895i	$0.578303\pi$
$812$	0	0
$813$	−5.10051	−0.178883
$814$	1.79899	0.0630546
$815$	−2.48528	−0.0870556
$816$	−3.51472	−0.123040
$817$	−4.68629	−0.163953
$818$	−9.85786	−0.344672
$819$	0	0
$820$	−1.82843	−0.0638514
$821$	30.4264	1.06189	0.530944	−	0.847407i	$-0.321837\pi$
$821$	30.4264	1.06189	0.530944	+	0.847407i	$0.321837\pi$
$822$	7.82843	0.273048
$823$	−5.65685	−0.197186	−0.0985928	−	0.995128i	$-0.531434\pi$
$823$	−5.65685	−0.197186	−0.0985928	+	0.995128i	$0.531434\pi$
$824$	16.5147	0.575317
$825$	−8.00000	−0.278524
$826$	0	0
$827$	56.4853	1.96419	0.982093	−	0.188398i	$-0.0603294\pi$
$827$	56.4853	1.96419	0.982093	+	0.188398i	$0.0603294\pi$
$828$	5.92893	0.206045
$829$	9.11270	0.316497	0.158249	−	0.987399i	$-0.449415\pi$
$829$	9.11270	0.316497	0.158249	+	0.987399i	$0.449415\pi$
$830$	3.65685	0.126931
$831$	12.6569	0.439061
$832$	−18.4142	−0.638398
$833$	0	0
$834$	8.51472	0.294841
$835$	9.14214	0.316377
$836$	10.3431	0.357725
$837$	7.65685	0.264660
$838$	13.7401	0.474644
$839$	45.0833	1.55645	0.778224	−	0.627987i	$-0.216121\pi$
$839$	45.0833	1.55645	0.778224	+	0.627987i	$0.216121\pi$
$840$	0	0
$841$	28.5442	0.984281
$842$	9.65685	0.332797
$843$	0.899495	0.0309803
$844$	31.9706	1.10047
$845$	6.48528	0.223100
$846$	1.92893	0.0663181
$847$	0	0
$848$	7.24264	0.248713
$849$	−17.3137	−0.594205
$850$	−1.94113	−0.0665801
$851$	7.04163	0.241384
$852$	19.7990	0.678302
$853$	−36.8284	−1.26098	−0.630491	−	0.776197i	$-0.717146\pi$
$853$	−36.8284	−1.26098	−0.630491	+	0.776197i	$0.717146\pi$
$854$	0	0
$855$	2.82843	0.0967302
$856$	−12.2548	−0.418862
$857$	−1.28427	−0.0438699	−0.0219349	−	0.999759i	$-0.506983\pi$
$857$	−1.28427	−0.0438699	−0.0219349	+	0.999759i	$0.506983\pi$
$858$	3.65685	0.124843
$859$	−3.72792	−0.127195	−0.0635975	−	0.997976i	$-0.520257\pi$
$859$	−3.72792	−0.127195	−0.0635975	+	0.997976i	$0.520257\pi$
$860$	3.02944	0.103303
$861$	0	0
$862$	2.20101	0.0749667
$863$	41.5269	1.41359	0.706796	−	0.707417i	$-0.250140\pi$
$863$	41.5269	1.41359	0.706796	+	0.707417i	$0.250140\pi$
$864$	−4.41421	−0.150175
$865$	−7.82843	−0.266175
$866$	6.68629	0.227209
$867$	15.6274	0.530735
$868$	0	0
$869$	−2.97056	−0.100769
$870$	3.14214	0.106528
$871$	−0.757359	−0.0256621
$872$	−22.4264	−0.759454
$873$	−16.8995	−0.571961
$874$	−3.79899	−0.128503
$875$	0	0
$876$	−14.0000	−0.473016
$877$	21.5980	0.729312	0.364656	−	0.931142i	$-0.381187\pi$
$877$	21.5980	0.729312	0.364656	+	0.931142i	$0.381187\pi$
$878$	7.85786	0.265190
$879$	−12.4853	−0.421118
$880$	−6.00000	−0.202260
$881$	−21.6274	−0.728646	−0.364323	−	0.931273i	$-0.618700\pi$
$881$	−21.6274	−0.728646	−0.364323	+	0.931273i	$0.618700\pi$
$882$	0	0
$883$	−22.0294	−0.741350	−0.370675	−	0.928763i	$-0.620874\pi$
$883$	−22.0294	−0.741350	−0.370675	+	0.928763i	$0.620874\pi$
$884$	−9.45584	−0.318034
$885$	−10.0000	−0.336146
$886$	−13.5147	−0.454036
$887$	20.1716	0.677295	0.338648	−	0.940913i	$-0.390031\pi$
$887$	20.1716	0.677295	0.338648	+	0.940913i	$0.390031\pi$
$888$	−3.44365	−0.115561
$889$	0	0
$890$	1.17157	0.0392712
$891$	−2.00000	−0.0670025
$892$	10.8406	0.362971
$893$	13.1716	0.440770
$894$	9.85786	0.329696
$895$	12.0000	0.401116
$896$	0	0
$897$	14.3137	0.477921
$898$	−2.20101	−0.0734487
$899$	58.0833	1.93719
$900$	7.31371	0.243790
$901$	2.82843	0.0942286
$902$	−0.828427	−0.0275836
$903$	0	0
$904$	10.8284	0.360148
$905$	−12.4853	−0.415025
$906$	2.34315	0.0778458
$907$	−10.2010	−0.338719	−0.169359	−	0.985554i	$-0.554170\pi$
$907$	−10.2010	−0.338719	−0.169359	+	0.985554i	$0.554170\pi$
$908$	−12.1716	−0.403928
$909$	−14.9706	−0.496542
$910$	0	0
$911$	2.00000	0.0662630	0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000	0.0662630	0.0331315	+	0.999451i	$0.489452\pi$
$912$	−8.48528	−0.280976
$913$	−17.6569	−0.584357
$914$	−4.68629	−0.155009
$915$	−15.3137	−0.506256
$916$	−13.2426	−0.437549
$917$	0	0
$918$	−0.485281	−0.0160167
$919$	−11.6274	−0.383553	−0.191777	−	0.981439i	$-0.561425\pi$
$919$	−11.6274	−0.383553	−0.191777	+	0.981439i	$0.561425\pi$
$920$	5.14214	0.169531
$921$	−16.8995	−0.556857
$922$	−0.497475	−0.0163835
$923$	47.7990	1.57332
$924$	0	0
$925$	8.68629	0.285604
$926$	−5.72792	−0.188231
$927$	−10.4142	−0.342048
$928$	−33.4853	−1.09921
$929$	−27.9411	−0.916719	−0.458359	−	0.888767i	$-0.651563\pi$
$929$	−27.9411	−0.916719	−0.458359	+	0.888767i	$0.651563\pi$
$930$	3.17157	0.104000
$931$	0	0
$932$	30.1421	0.987338
$933$	11.0000	0.360124
$934$	14.5442	0.475899
$935$	−2.34315	−0.0766291
$936$	−7.00000	−0.228802
$937$	40.4853	1.32260	0.661298	−	0.750123i	$-0.270006\pi$
$937$	40.4853	1.32260	0.661298	+	0.750123i	$0.270006\pi$
$938$	0	0
$939$	−18.2132	−0.594365
$940$	−8.51472	−0.277719
$941$	−23.4853	−0.765598	−0.382799	−	0.923832i	$-0.625040\pi$
$941$	−23.4853	−0.765598	−0.382799	+	0.923832i	$0.625040\pi$
$942$	3.79899	0.123778
$943$	−3.24264	−0.105595
$944$	30.0000	0.976417
$945$	0	0
$946$	1.37258	0.0446265
$947$	59.1838	1.92321	0.961607	−	0.274430i	$-0.0884893\pi$
$947$	59.1838	1.92321	0.961607	+	0.274430i	$0.0884893\pi$
$948$	2.71573	0.0882028
$949$	−33.7990	−1.09716
$950$	−4.68629	−0.152043
$951$	−14.4142	−0.467413
$952$	0	0
$953$	15.1127	0.489548	0.244774	−	0.969580i	$-0.421286\pi$
$953$	15.1127	0.489548	0.244774	+	0.969580i	$0.421286\pi$
$954$	1.00000	0.0323762
$955$	1.17157	0.0379112
$956$	48.6863	1.57463
$957$	−15.1716	−0.490427
$958$	−12.0000	−0.387702
$959$	0	0
$960$	4.17157	0.134637
$961$	27.6274	0.891207
$962$	−3.97056	−0.128016
$963$	7.72792	0.249029
$964$	36.8284	1.18616
$965$	−5.65685	−0.182101
$966$	0	0
$967$	29.6863	0.954647	0.477323	−	0.878728i	$-0.341607\pi$
$967$	29.6863	0.954647	0.477323	+	0.878728i	$0.341607\pi$
$968$	11.1005	0.356784
$969$	−3.31371	−0.106452
$970$	−7.00000	−0.224756
$971$	7.68629	0.246665	0.123332	−	0.992365i	$-0.460642\pi$
$971$	7.68629	0.246665	0.123332	+	0.992365i	$0.460642\pi$
$972$	1.82843	0.0586468
$973$	0	0
$974$	−0.201010	−0.00644078
$975$	17.6569	0.565472
$976$	45.9411	1.47054
$977$	−49.1716	−1.57314	−0.786569	−	0.617502i	$-0.788145\pi$
$977$	−49.1716	−1.57314	−0.786569	+	0.617502i	$0.788145\pi$
$978$	1.02944	0.0329178
$979$	−5.65685	−0.180794
$980$	0	0
$981$	14.1421	0.451524
$982$	−3.45584	−0.110280
$983$	−39.9411	−1.27392	−0.636962	−	0.770895i	$-0.719809\pi$
$983$	−39.9411	−1.27392	−0.636962	+	0.770895i	$0.719809\pi$
$984$	1.58579	0.0505530
$985$	−20.8284	−0.663649
$986$	−3.68124	−0.117235
$987$	0	0
$988$	−22.8284	−0.726269
$989$	5.37258	0.170838
$990$	−0.828427	−0.0263291
$991$	−19.9706	−0.634386	−0.317193	−	0.948361i	$-0.602740\pi$
$991$	−19.9706	−0.634386	−0.317193	+	0.948361i	$0.602740\pi$
$992$	−33.7990	−1.07312
$993$	21.9706	0.697215
$994$	0	0
$995$	−11.3137	−0.358669
$996$	16.1421	0.511483
$997$	−48.8995	−1.54866	−0.774331	−	0.632780i	$-0.781914\pi$
$997$	−48.8995	−1.54866	−0.774331	+	0.632780i	$0.781914\pi$
$998$	−8.97056	−0.283958
$999$	2.17157	0.0687055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.i.1.2		2
7.6	odd	2		861.2.a.e.1.2	✓	2
21.20	even	2		2583.2.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.e.1.2	✓	2	7.6	odd	2
2583.2.a.k.1.1		2	21.20	even	2
6027.2.a.i.1.2		2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +1.00000 q^{5} -0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +1.00000 q^{5} -0.414214 q^{6} -1.58579 q^{8} +1.00000 q^{9} +0.414214 q^{10} -2.00000 q^{11} +1.82843 q^{12} +4.41421 q^{13} -1.00000 q^{15} +3.00000 q^{16} +1.17157 q^{17} +0.414214 q^{18} +2.82843 q^{19} -1.82843 q^{20} -0.828427 q^{22} -3.24264 q^{23} +1.58579 q^{24} -4.00000 q^{25} +1.82843 q^{26} -1.00000 q^{27} -7.58579 q^{29} -0.414214 q^{30} -7.65685 q^{31} +4.41421 q^{32} +2.00000 q^{33} +0.485281 q^{34} -1.82843 q^{36} -2.17157 q^{37} +1.17157 q^{38} -4.41421 q^{39} -1.58579 q^{40} +1.00000 q^{41} -1.65685 q^{43} +3.65685 q^{44} +1.00000 q^{45} -1.34315 q^{46} +4.65685 q^{47} -3.00000 q^{48} -1.65685 q^{50} -1.17157 q^{51} -8.07107 q^{52} +2.41421 q^{53} -0.414214 q^{54} -2.00000 q^{55} -2.82843 q^{57} -3.14214 q^{58} +10.0000 q^{59} +1.82843 q^{60} +15.3137 q^{61} -3.17157 q^{62} -4.17157 q^{64} +4.41421 q^{65} +0.828427 q^{66} -0.171573 q^{67} -2.14214 q^{68} +3.24264 q^{69} +10.8284 q^{71} -1.58579 q^{72} -7.65685 q^{73} -0.899495 q^{74} +4.00000 q^{75} -5.17157 q^{76} -1.82843 q^{78} +1.48528 q^{79} +3.00000 q^{80} +1.00000 q^{81} +0.414214 q^{82} +8.82843 q^{83} +1.17157 q^{85} -0.686292 q^{86} +7.58579 q^{87} +3.17157 q^{88} +2.82843 q^{89} +0.414214 q^{90} +5.92893 q^{92} +7.65685 q^{93} +1.92893 q^{94} +2.82843 q^{95} -4.41421 q^{96} -16.8995 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{24} - 8 q^{25} - 2 q^{26} - 2 q^{27} - 18 q^{29} + 2 q^{30} - 4 q^{31} + 6 q^{32} + 4 q^{33} - 16 q^{34} + 2 q^{36} - 10 q^{37} + 8 q^{38} - 6 q^{39} - 6 q^{40} + 2 q^{41} + 8 q^{43} - 4 q^{44} + 2 q^{45} - 14 q^{46} - 2 q^{47} - 6 q^{48} + 8 q^{50} - 8 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} - 4 q^{55} + 22 q^{58} + 20 q^{59} - 2 q^{60} + 8 q^{61} - 12 q^{62} - 14 q^{64} + 6 q^{65} - 4 q^{66} - 6 q^{67} + 24 q^{68} - 2 q^{69} + 16 q^{71} - 6 q^{72} - 4 q^{73} + 18 q^{74} + 8 q^{75} - 16 q^{76} + 2 q^{78} - 14 q^{79} + 6 q^{80} + 2 q^{81} - 2 q^{82} + 12 q^{83} + 8 q^{85} - 24 q^{86} + 18 q^{87} + 12 q^{88} - 2 q^{90} + 26 q^{92} + 4 q^{93} + 18 q^{94} - 6 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^24 - 8 * q^25 - 2 * q^26 - 2 * q^27 - 18 * q^29 + 2 * q^30 - 4 * q^31 + 6 * q^32 + 4 * q^33 - 16 * q^34 + 2 * q^36 - 10 * q^37 + 8 * q^38 - 6 * q^39 - 6 * q^40 + 2 * q^41 + 8 * q^43 - 4 * q^44 + 2 * q^45 - 14 * q^46 - 2 * q^47 - 6 * q^48 + 8 * q^50 - 8 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 - 4 * q^55 + 22 * q^58 + 20 * q^59 - 2 * q^60 + 8 * q^61 - 12 * q^62 - 14 * q^64 + 6 * q^65 - 4 * q^66 - 6 * q^67 + 24 * q^68 - 2 * q^69 + 16 * q^71 - 6 * q^72 - 4 * q^73 + 18 * q^74 + 8 * q^75 - 16 * q^76 + 2 * q^78 - 14 * q^79 + 6 * q^80 + 2 * q^81 - 2 * q^82 + 12 * q^83 + 8 * q^85 - 24 * q^86 + 18 * q^87 + 12 * q^88 - 2 * q^90 + 26 * q^92 + 4 * q^93 + 18 * q^94 - 6 * q^96 - 14 * q^97 - 4 * q^99

Introduction

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