LMFDB - Embedded newform 5586.2.a.cf.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 22x^{6} + 60x^{5} + 87x^{4} - 176x^{3} - 40x^{2} + 64x + 16 $ x^8 - 4x^7 - 22x^6 + 60x^5 + 87x^4 - 176x^3 - 40x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.35228$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05440 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05440 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.05440 q^{10} +0.0875857 q^{11} +1.00000 q^{12} -2.29213 q^{13} -3.05440 q^{15} +1.00000 q^{16} -6.83496 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.05440 q^{20} +0.0875857 q^{22} -0.451414 q^{23} +1.00000 q^{24} +4.32934 q^{25} -2.29213 q^{26} +1.00000 q^{27} +9.78639 q^{29} -3.05440 q^{30} +6.48513 q^{31} +1.00000 q^{32} +0.0875857 q^{33} -6.83496 q^{34} +1.00000 q^{36} -2.85857 q^{37} +1.00000 q^{38} -2.29213 q^{39} -3.05440 q^{40} +0.960987 q^{41} +5.57707 q^{43} +0.0875857 q^{44} -3.05440 q^{45} -0.451414 q^{46} +11.3254 q^{47} +1.00000 q^{48} +4.32934 q^{50} -6.83496 q^{51} -2.29213 q^{52} +11.9336 q^{53} +1.00000 q^{54} -0.267522 q^{55} +1.00000 q^{57} +9.78639 q^{58} +3.07976 q^{59} -3.05440 q^{60} -4.54501 q^{61} +6.48513 q^{62} +1.00000 q^{64} +7.00109 q^{65} +0.0875857 q^{66} -15.2354 q^{67} -6.83496 q^{68} -0.451414 q^{69} +14.3896 q^{71} +1.00000 q^{72} +1.76605 q^{73} -2.85857 q^{74} +4.32934 q^{75} +1.00000 q^{76} -2.29213 q^{78} -1.62682 q^{79} -3.05440 q^{80} +1.00000 q^{81} +0.960987 q^{82} +11.0116 q^{83} +20.8767 q^{85} +5.57707 q^{86} +9.78639 q^{87} +0.0875857 q^{88} +2.34189 q^{89} -3.05440 q^{90} -0.451414 q^{92} +6.48513 q^{93} +11.3254 q^{94} -3.05440 q^{95} +1.00000 q^{96} +0.176657 q^{97} +0.0875857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9} + 4 q^{10} + 8 q^{11} + 8 q^{12} - 4 q^{13} + 4 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 8 q^{19} + 4 q^{20} + 8 q^{22} + 4 q^{23} + 8 q^{24} + 24 q^{25} - 4 q^{26} + 8 q^{27} + 16 q^{29} + 4 q^{30} + 4 q^{31} + 8 q^{32} + 8 q^{33} + 8 q^{34} + 8 q^{36} + 12 q^{37} + 8 q^{38} - 4 q^{39} + 4 q^{40} + 16 q^{43} + 8 q^{44} + 4 q^{45} + 4 q^{46} + 12 q^{47} + 8 q^{48} + 24 q^{50} + 8 q^{51} - 4 q^{52} + 24 q^{53} + 8 q^{54} - 8 q^{55} + 8 q^{57} + 16 q^{58} - 8 q^{59} + 4 q^{60} + 4 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{66} + 8 q^{67} + 8 q^{68} + 4 q^{69} + 24 q^{71} + 8 q^{72} - 16 q^{73} + 12 q^{74} + 24 q^{75} + 8 q^{76} - 4 q^{78} + 20 q^{79} + 4 q^{80} + 8 q^{81} + 16 q^{83} + 48 q^{85} + 16 q^{86} + 16 q^{87} + 8 q^{88} + 4 q^{90} + 4 q^{92} + 4 q^{93} + 12 q^{94} + 4 q^{95} + 8 q^{96} - 8 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9 + 4 * q^10 + 8 * q^11 + 8 * q^12 - 4 * q^13 + 4 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 8 * q^19 + 4 * q^20 + 8 * q^22 + 4 * q^23 + 8 * q^24 + 24 * q^25 - 4 * q^26 + 8 * q^27 + 16 * q^29 + 4 * q^30 + 4 * q^31 + 8 * q^32 + 8 * q^33 + 8 * q^34 + 8 * q^36 + 12 * q^37 + 8 * q^38 - 4 * q^39 + 4 * q^40 + 16 * q^43 + 8 * q^44 + 4 * q^45 + 4 * q^46 + 12 * q^47 + 8 * q^48 + 24 * q^50 + 8 * q^51 - 4 * q^52 + 24 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 - 8 * q^59 + 4 * q^60 + 4 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^66 + 8 * q^67 + 8 * q^68 + 4 * q^69 + 24 * q^71 + 8 * q^72 - 16 * q^73 + 12 * q^74 + 24 * q^75 + 8 * q^76 - 4 * q^78 + 20 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^83 + 48 * q^85 + 16 * q^86 + 16 * q^87 + 8 * q^88 + 4 * q^90 + 4 * q^92 + 4 * q^93 + 12 * q^94 + 4 * q^95 + 8 * q^96 - 8 * q^97 + 8 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.05440	−1.36597	−0.682984	−	0.730434i	$-0.739318\pi$
$5$	−3.05440	−1.36597	−0.682984	+	0.730434i	$0.739318\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.05440	−0.965885
$11$	0.0875857	0.0264081	0.0132040	−	0.999913i	$-0.495797\pi$
$11$	0.0875857	0.0264081	0.0132040	+	0.999913i	$0.495797\pi$
$12$	1.00000	0.288675
$13$	−2.29213	−0.635724	−0.317862	−	0.948137i	$-0.602965\pi$
$13$	−2.29213	−0.635724	−0.317862	+	0.948137i	$0.602965\pi$
$14$	0	0
$15$	−3.05440	−0.788642
$16$	1.00000	0.250000
$17$	−6.83496	−1.65772	−0.828861	−	0.559454i	$-0.811011\pi$
$17$	−6.83496	−1.65772	−0.828861	+	0.559454i	$0.811011\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.05440	−0.682984
$21$	0	0
$22$	0.0875857	0.0186733
$23$	−0.451414	−0.0941264	−0.0470632	−	0.998892i	$-0.514986\pi$
$23$	−0.451414	−0.0941264	−0.0470632	+	0.998892i	$0.514986\pi$
$24$	1.00000	0.204124
$25$	4.32934	0.865867
$26$	−2.29213	−0.449525
$27$	1.00000	0.192450
$28$	0	0
$29$	9.78639	1.81729	0.908644	−	0.417572i	$-0.137119\pi$
$29$	9.78639	1.81729	0.908644	+	0.417572i	$0.137119\pi$
$30$	−3.05440	−0.557654
$31$	6.48513	1.16476	0.582382	−	0.812915i	$-0.302121\pi$
$31$	6.48513	1.16476	0.582382	+	0.812915i	$0.302121\pi$
$32$	1.00000	0.176777
$33$	0.0875857	0.0152467
$34$	−6.83496	−1.17219
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.85857	−0.469946	−0.234973	−	0.972002i	$-0.575500\pi$
$37$	−2.85857	−0.469946	−0.234973	+	0.972002i	$0.575500\pi$
$38$	1.00000	0.162221
$39$	−2.29213	−0.367035
$40$	−3.05440	−0.482942
$41$	0.960987	0.150081	0.0750404	−	0.997180i	$-0.476091\pi$
$41$	0.960987	0.150081	0.0750404	+	0.997180i	$0.476091\pi$
$42$	0	0
$43$	5.57707	0.850495	0.425247	−	0.905077i	$-0.360187\pi$
$43$	5.57707	0.850495	0.425247	+	0.905077i	$0.360187\pi$
$44$	0.0875857	0.0132040
$45$	−3.05440	−0.455322
$46$	−0.451414	−0.0665574
$47$	11.3254	1.65197	0.825987	−	0.563689i	$-0.190618\pi$
$47$	11.3254	1.65197	0.825987	+	0.563689i	$0.190618\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.32934	0.612261
$51$	−6.83496	−0.957086
$52$	−2.29213	−0.317862
$53$	11.9336	1.63921	0.819604	−	0.572930i	$-0.194193\pi$
$53$	11.9336	1.63921	0.819604	+	0.572930i	$0.194193\pi$
$54$	1.00000	0.136083
$55$	−0.267522	−0.0360726
$56$	0	0
$57$	1.00000	0.132453
$58$	9.78639	1.28502
$59$	3.07976	0.400951	0.200475	−	0.979699i	$-0.435751\pi$
$59$	3.07976	0.400951	0.200475	+	0.979699i	$0.435751\pi$
$60$	−3.05440	−0.394321
$61$	−4.54501	−0.581929	−0.290965	−	0.956734i	$-0.593976\pi$
$61$	−4.54501	−0.581929	−0.290965	+	0.956734i	$0.593976\pi$
$62$	6.48513	0.823612
$63$	0	0
$64$	1.00000	0.125000
$65$	7.00109	0.868378
$66$	0.0875857	0.0107811
$67$	−15.2354	−1.86130	−0.930648	−	0.365915i	$-0.880756\pi$
$67$	−15.2354	−1.86130	−0.930648	+	0.365915i	$0.880756\pi$
$68$	−6.83496	−0.828861
$69$	−0.451414	−0.0543439
$70$	0	0
$71$	14.3896	1.70773	0.853863	−	0.520497i	$-0.174253\pi$
$71$	14.3896	1.70773	0.853863	+	0.520497i	$0.174253\pi$
$72$	1.00000	0.117851
$73$	1.76605	0.206701	0.103350	−	0.994645i	$-0.467044\pi$
$73$	1.76605	0.206701	0.103350	+	0.994645i	$0.467044\pi$
$74$	−2.85857	−0.332302
$75$	4.32934	0.499909
$76$	1.00000	0.114708
$77$	0	0
$78$	−2.29213	−0.259533
$79$	−1.62682	−0.183031	−0.0915156	−	0.995804i	$-0.529171\pi$
$79$	−1.62682	−0.183031	−0.0915156	+	0.995804i	$0.529171\pi$
$80$	−3.05440	−0.341492
$81$	1.00000	0.111111
$82$	0.960987	0.106123
$83$	11.0116	1.20868	0.604341	−	0.796726i	$-0.293436\pi$
$83$	11.0116	1.20868	0.604341	+	0.796726i	$0.293436\pi$
$84$	0	0
$85$	20.8767	2.26439
$86$	5.57707	0.601390
$87$	9.78639	1.04921
$88$	0.0875857	0.00933667
$89$	2.34189	0.248239	0.124120	−	0.992267i	$-0.460389\pi$
$89$	2.34189	0.248239	0.124120	+	0.992267i	$0.460389\pi$
$90$	−3.05440	−0.321962
$91$	0	0
$92$	−0.451414	−0.0470632
$93$	6.48513	0.672477
$94$	11.3254	1.16812
$95$	−3.05440	−0.313374
$96$	1.00000	0.102062
$97$	0.176657	0.0179368	0.00896840	−	0.999960i	$-0.497145\pi$
$97$	0.176657	0.0179368	0.00896840	+	0.999960i	$0.497145\pi$
$98$	0	0
$99$	0.0875857	0.00880270
$100$	4.32934	0.432934
$101$	−4.95868	−0.493407	−0.246703	−	0.969091i	$-0.579347\pi$
$101$	−4.95868	−0.493407	−0.246703	+	0.969091i	$0.579347\pi$
$102$	−6.83496	−0.676762
$103$	−4.04500	−0.398566	−0.199283	−	0.979942i	$-0.563861\pi$
$103$	−4.04500	−0.398566	−0.199283	+	0.979942i	$0.563861\pi$
$104$	−2.29213	−0.224762
$105$	0	0
$106$	11.9336	1.15910
$107$	13.0668	1.26321	0.631606	−	0.775290i	$-0.282396\pi$
$107$	13.0668	1.26321	0.631606	+	0.775290i	$0.282396\pi$
$108$	1.00000	0.0962250
$109$	−15.3865	−1.47376	−0.736879	−	0.676025i	$-0.763701\pi$
$109$	−15.3865	−1.47376	−0.736879	+	0.676025i	$0.763701\pi$
$110$	−0.267522	−0.0255072
$111$	−2.85857	−0.271323
$112$	0	0
$113$	11.6322	1.09427	0.547133	−	0.837046i	$-0.315719\pi$
$113$	11.6322	1.09427	0.547133	+	0.837046i	$0.315719\pi$
$114$	1.00000	0.0936586
$115$	1.37880	0.128574
$116$	9.78639	0.908644
$117$	−2.29213	−0.211908
$118$	3.07976	0.283515
$119$	0	0
$120$	−3.05440	−0.278827
$121$	−10.9923	−0.999303
$122$	−4.54501	−0.411486
$123$	0.960987	0.0866492
$124$	6.48513	0.582382
$125$	2.04847	0.183221
$126$	0	0
$127$	11.7900	1.04619	0.523095	−	0.852274i	$-0.324777\pi$
$127$	11.7900	1.04619	0.523095	+	0.852274i	$0.324777\pi$
$128$	1.00000	0.0883883
$129$	5.57707	0.491033
$130$	7.00109	0.614036
$131$	9.72124	0.849348	0.424674	−	0.905346i	$-0.360389\pi$
$131$	9.72124	0.849348	0.424674	+	0.905346i	$0.360389\pi$
$132$	0.0875857	0.00762336
$133$	0	0
$134$	−15.2354	−1.31614
$135$	−3.05440	−0.262881
$136$	−6.83496	−0.586093
$137$	5.62949	0.480959	0.240480	−	0.970654i	$-0.422695\pi$
$137$	5.62949	0.480959	0.240480	+	0.970654i	$0.422695\pi$
$138$	−0.451414	−0.0384270
$139$	1.45730	0.123606	0.0618032	−	0.998088i	$-0.480315\pi$
$139$	1.45730	0.123606	0.0618032	+	0.998088i	$0.480315\pi$
$140$	0	0
$141$	11.3254	0.953768
$142$	14.3896	1.20755
$143$	−0.200758	−0.0167883
$144$	1.00000	0.0833333
$145$	−29.8915	−2.48236
$146$	1.76605	0.146159
$147$	0	0
$148$	−2.85857	−0.234973
$149$	−11.3010	−0.925818	−0.462909	−	0.886406i	$-0.653194\pi$
$149$	−11.3010	−0.925818	−0.462909	+	0.886406i	$0.653194\pi$
$150$	4.32934	0.353489
$151$	19.3648	1.57588	0.787941	−	0.615751i	$-0.211147\pi$
$151$	19.3648	1.57588	0.787941	+	0.615751i	$0.211147\pi$
$152$	1.00000	0.0811107
$153$	−6.83496	−0.552574
$154$	0	0
$155$	−19.8082	−1.59103
$156$	−2.29213	−0.183518
$157$	10.5602	0.842798	0.421399	−	0.906875i	$-0.361539\pi$
$157$	10.5602	0.842798	0.421399	+	0.906875i	$0.361539\pi$
$158$	−1.62682	−0.129423
$159$	11.9336	0.946398
$160$	−3.05440	−0.241471
$161$	0	0
$162$	1.00000	0.0785674
$163$	9.73483	0.762491	0.381245	−	0.924474i	$-0.375495\pi$
$163$	9.73483	0.762491	0.381245	+	0.924474i	$0.375495\pi$
$164$	0.960987	0.0750404
$165$	−0.267522	−0.0208265
$166$	11.0116	0.854668
$167$	−21.1337	−1.63537	−0.817686	−	0.575665i	$-0.804743\pi$
$167$	−21.1337	−1.63537	−0.817686	+	0.575665i	$0.804743\pi$
$168$	0	0
$169$	−7.74612	−0.595855
$170$	20.8767	1.60117
$171$	1.00000	0.0764719
$172$	5.57707	0.425247
$173$	−7.41960	−0.564102	−0.282051	−	0.959399i	$-0.591015\pi$
$173$	−7.41960	−0.564102	−0.282051	+	0.959399i	$0.591015\pi$
$174$	9.78639	0.741904
$175$	0	0
$176$	0.0875857	0.00660202
$177$	3.07976	0.231489
$178$	2.34189	0.175532
$179$	13.6445	1.01984	0.509919	−	0.860223i	$-0.329675\pi$
$179$	13.6445	1.01984	0.509919	+	0.860223i	$0.329675\pi$
$180$	−3.05440	−0.227661
$181$	0.865106	0.0643028	0.0321514	−	0.999483i	$-0.489764\pi$
$181$	0.865106	0.0643028	0.0321514	+	0.999483i	$0.489764\pi$
$182$	0	0
$183$	−4.54501	−0.335977
$184$	−0.451414	−0.0332787
$185$	8.73120	0.641931
$186$	6.48513	0.475513
$187$	−0.598645	−0.0437773
$188$	11.3254	0.825987
$189$	0	0
$190$	−3.05440	−0.221589
$191$	−15.8346	−1.14575	−0.572874	−	0.819643i	$-0.694172\pi$
$191$	−15.8346	−1.14575	−0.572874	+	0.819643i	$0.694172\pi$
$192$	1.00000	0.0721688
$193$	−10.7620	−0.774669	−0.387335	−	0.921939i	$-0.626604\pi$
$193$	−10.7620	−0.774669	−0.387335	+	0.921939i	$0.626604\pi$
$194$	0.176657	0.0126832
$195$	7.00109	0.501358
$196$	0	0
$197$	−15.2333	−1.08533	−0.542665	−	0.839949i	$-0.682585\pi$
$197$	−15.2333	−1.08533	−0.542665	+	0.839949i	$0.682585\pi$
$198$	0.0875857	0.00622445
$199$	−7.70575	−0.546246	−0.273123	−	0.961979i	$-0.588057\pi$
$199$	−7.70575	−0.546246	−0.273123	+	0.961979i	$0.588057\pi$
$200$	4.32934	0.306130
$201$	−15.2354	−1.07462
$202$	−4.95868	−0.348891
$203$	0	0
$204$	−6.83496	−0.478543
$205$	−2.93523	−0.205006
$206$	−4.04500	−0.281829
$207$	−0.451414	−0.0313755
$208$	−2.29213	−0.158931
$209$	0.0875857	0.00605843
$210$	0	0
$211$	9.01556	0.620657	0.310328	−	0.950629i	$-0.399561\pi$
$211$	9.01556	0.620657	0.310328	+	0.950629i	$0.399561\pi$
$212$	11.9336	0.819604
$213$	14.3896	0.985957
$214$	13.0668	0.893225
$215$	−17.0346	−1.16175
$216$	1.00000	0.0680414
$217$	0	0
$218$	−15.3865	−1.04210
$219$	1.76605	0.119339
$220$	−0.267522	−0.0180363
$221$	15.6667	1.05385
$222$	−2.85857	−0.191855
$223$	3.82319	0.256020	0.128010	−	0.991773i	$-0.459141\pi$
$223$	3.82319	0.256020	0.128010	+	0.991773i	$0.459141\pi$
$224$	0	0
$225$	4.32934	0.288622
$226$	11.6322	0.773763
$227$	18.0509	1.19808	0.599039	−	0.800719i	$-0.295549\pi$
$227$	18.0509	1.19808	0.599039	+	0.800719i	$0.295549\pi$
$228$	1.00000	0.0662266
$229$	−15.8467	−1.04718	−0.523590	−	0.851971i	$-0.675407\pi$
$229$	−15.8467	−1.04718	−0.523590	+	0.851971i	$0.675407\pi$
$230$	1.37880	0.0909153
$231$	0	0
$232$	9.78639	0.642508
$233$	−16.4699	−1.07898	−0.539491	−	0.841991i	$-0.681383\pi$
$233$	−16.4699	−1.07898	−0.539491	+	0.841991i	$0.681383\pi$
$234$	−2.29213	−0.149842
$235$	−34.5922	−2.25654
$236$	3.07976	0.200475
$237$	−1.62682	−0.105673
$238$	0	0
$239$	−2.91375	−0.188475	−0.0942374	−	0.995550i	$-0.530041\pi$
$239$	−2.91375	−0.188475	−0.0942374	+	0.995550i	$0.530041\pi$
$240$	−3.05440	−0.197160
$241$	16.0515	1.03397	0.516985	−	0.855995i	$-0.327054\pi$
$241$	16.0515	1.03397	0.516985	+	0.855995i	$0.327054\pi$
$242$	−10.9923	−0.706614
$243$	1.00000	0.0641500
$244$	−4.54501	−0.290965
$245$	0	0
$246$	0.960987	0.0612703
$247$	−2.29213	−0.145845
$248$	6.48513	0.411806
$249$	11.0116	0.697833
$250$	2.04847	0.129557
$251$	−1.15331	−0.0727961	−0.0363981	−	0.999337i	$-0.511588\pi$
$251$	−1.15331	−0.0727961	−0.0363981	+	0.999337i	$0.511588\pi$
$252$	0	0
$253$	−0.0395375	−0.00248570
$254$	11.7900	0.739768
$255$	20.8767	1.30735
$256$	1.00000	0.0625000
$257$	−24.8428	−1.54965	−0.774825	−	0.632176i	$-0.782162\pi$
$257$	−24.8428	−1.54965	−0.774825	+	0.632176i	$0.782162\pi$
$258$	5.57707	0.347213
$259$	0	0
$260$	7.00109	0.434189
$261$	9.78639	0.605762
$262$	9.72124	0.600580
$263$	12.9557	0.798883	0.399441	−	0.916759i	$-0.369204\pi$
$263$	12.9557	0.798883	0.399441	+	0.916759i	$0.369204\pi$
$264$	0.0875857	0.00539053
$265$	−36.4500	−2.23911
$266$	0	0
$267$	2.34189	0.143321
$268$	−15.2354	−0.930648
$269$	−4.06356	−0.247760	−0.123880	−	0.992297i	$-0.539534\pi$
$269$	−4.06356	−0.247760	−0.123880	+	0.992297i	$0.539534\pi$
$270$	−3.05440	−0.185885
$271$	−3.62966	−0.220486	−0.110243	−	0.993905i	$-0.535163\pi$
$271$	−3.62966	−0.220486	−0.110243	+	0.993905i	$0.535163\pi$
$272$	−6.83496	−0.414431
$273$	0	0
$274$	5.62949	0.340090
$275$	0.379188	0.0228659
$276$	−0.451414	−0.0271720
$277$	−11.6912	−0.702459	−0.351229	−	0.936289i	$-0.614236\pi$
$277$	−11.6912	−0.702459	−0.351229	+	0.936289i	$0.614236\pi$
$278$	1.45730	0.0874029
$279$	6.48513	0.388255
$280$	0	0
$281$	26.4512	1.57795	0.788974	−	0.614427i	$-0.210613\pi$
$281$	26.4512	1.57795	0.788974	+	0.614427i	$0.210613\pi$
$282$	11.3254	0.674416
$283$	2.15554	0.128134	0.0640668	−	0.997946i	$-0.479593\pi$
$283$	2.15554	0.128134	0.0640668	+	0.997946i	$0.479593\pi$
$284$	14.3896	0.853863
$285$	−3.05440	−0.180927
$286$	−0.200758	−0.0118711
$287$	0	0
$288$	1.00000	0.0589256
$289$	29.7167	1.74804
$290$	−29.8915	−1.75529
$291$	0.176657	0.0103558
$292$	1.76605	0.103350
$293$	30.1462	1.76116	0.880580	−	0.473897i	$-0.157153\pi$
$293$	30.1462	1.76116	0.880580	+	0.473897i	$0.157153\pi$
$294$	0	0
$295$	−9.40681	−0.547686
$296$	−2.85857	−0.166151
$297$	0.0875857	0.00508224
$298$	−11.3010	−0.654652
$299$	1.03470	0.0598384
$300$	4.32934	0.249954
$301$	0	0
$302$	19.3648	1.11432
$303$	−4.95868	−0.284869
$304$	1.00000	0.0573539
$305$	13.8823	0.794897
$306$	−6.83496	−0.390729
$307$	15.3955	0.878669	0.439335	−	0.898323i	$-0.355214\pi$
$307$	15.3955	0.878669	0.439335	+	0.898323i	$0.355214\pi$
$308$	0	0
$309$	−4.04500	−0.230112
$310$	−19.8082	−1.12503
$311$	19.1805	1.08763	0.543813	−	0.839207i	$-0.316980\pi$
$311$	19.1805	1.08763	0.543813	+	0.839207i	$0.316980\pi$
$312$	−2.29213	−0.129767
$313$	28.4089	1.60576	0.802882	−	0.596138i	$-0.203299\pi$
$313$	28.4089	1.60576	0.802882	+	0.596138i	$0.203299\pi$
$314$	10.5602	0.595948
$315$	0	0
$316$	−1.62682	−0.0915156
$317$	20.3097	1.14071	0.570353	−	0.821400i	$-0.306806\pi$
$317$	20.3097	1.14071	0.570353	+	0.821400i	$0.306806\pi$
$318$	11.9336	0.669204
$319$	0.857148	0.0479911
$320$	−3.05440	−0.170746
$321$	13.0668	0.729315
$322$	0	0
$323$	−6.83496	−0.380308
$324$	1.00000	0.0555556
$325$	−9.92342	−0.550452
$326$	9.73483	0.539162
$327$	−15.3865	−0.850874
$328$	0.960987	0.0530616
$329$	0	0
$330$	−0.267522	−0.0147266
$331$	23.9122	1.31433	0.657167	−	0.753745i	$-0.271755\pi$
$331$	23.9122	1.31433	0.657167	+	0.753745i	$0.271755\pi$
$332$	11.0116	0.604341
$333$	−2.85857	−0.156649
$334$	−21.1337	−1.15638
$335$	46.5348	2.54247
$336$	0	0
$337$	−7.07270	−0.385274	−0.192637	−	0.981270i	$-0.561704\pi$
$337$	−7.07270	−0.385274	−0.192637	+	0.981270i	$0.561704\pi$
$338$	−7.74612	−0.421333
$339$	11.6322	0.631774
$340$	20.8767	1.13220
$341$	0.568005	0.0307592
$342$	1.00000	0.0540738
$343$	0	0
$344$	5.57707	0.300695
$345$	1.37880	0.0742320
$346$	−7.41960	−0.398880
$347$	24.1469	1.29628	0.648138	−	0.761523i	$-0.275548\pi$
$347$	24.1469	1.29628	0.648138	+	0.761523i	$0.275548\pi$
$348$	9.78639	0.524606
$349$	8.18361	0.438059	0.219029	−	0.975718i	$-0.429711\pi$
$349$	8.18361	0.438059	0.219029	+	0.975718i	$0.429711\pi$
$350$	0	0
$351$	−2.29213	−0.122345
$352$	0.0875857	0.00466834
$353$	−4.20569	−0.223846	−0.111923	−	0.993717i	$-0.535701\pi$
$353$	−4.20569	−0.223846	−0.111923	+	0.993717i	$0.535701\pi$
$354$	3.07976	0.163688
$355$	−43.9514	−2.33270
$356$	2.34189	0.124120
$357$	0	0
$358$	13.6445	0.721134
$359$	9.49044	0.500886	0.250443	−	0.968131i	$-0.419424\pi$
$359$	9.49044	0.500886	0.250443	+	0.968131i	$0.419424\pi$
$360$	−3.05440	−0.160981
$361$	1.00000	0.0526316
$362$	0.865106	0.0454690
$363$	−10.9923	−0.576948
$364$	0	0
$365$	−5.39422	−0.282346
$366$	−4.54501	−0.237572
$367$	−14.8745	−0.776445	−0.388222	−	0.921566i	$-0.626911\pi$
$367$	−14.8745	−0.776445	−0.388222	+	0.921566i	$0.626911\pi$
$368$	−0.451414	−0.0235316
$369$	0.960987	0.0500270
$370$	8.73120	0.453914
$371$	0	0
$372$	6.48513	0.336238
$373$	−14.2951	−0.740170	−0.370085	−	0.928998i	$-0.620671\pi$
$373$	−14.2951	−0.740170	−0.370085	+	0.928998i	$0.620671\pi$
$374$	−0.598645	−0.0309552
$375$	2.04847	0.105783
$376$	11.3254	0.584061
$377$	−22.4317	−1.15529
$378$	0	0
$379$	−0.874477	−0.0449189	−0.0224594	−	0.999748i	$-0.507150\pi$
$379$	−0.874477	−0.0449189	−0.0224594	+	0.999748i	$0.507150\pi$
$380$	−3.05440	−0.156687
$381$	11.7900	0.604018
$382$	−15.8346	−0.810167
$383$	−36.8911	−1.88505	−0.942524	−	0.334139i	$-0.891555\pi$
$383$	−36.8911	−1.88505	−0.942524	+	0.334139i	$0.891555\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−10.7620	−0.547774
$387$	5.57707	0.283498
$388$	0.176657	0.00896840
$389$	−13.3849	−0.678642	−0.339321	−	0.940671i	$-0.610197\pi$
$389$	−13.3849	−0.678642	−0.339321	+	0.940671i	$0.610197\pi$
$390$	7.00109	0.354514
$391$	3.08540	0.156035
$392$	0	0
$393$	9.72124	0.490371
$394$	−15.2333	−0.767444
$395$	4.96894	0.250015
$396$	0.0875857	0.00440135
$397$	−16.2033	−0.813223	−0.406611	−	0.913601i	$-0.633290\pi$
$397$	−16.2033	−0.813223	−0.406611	+	0.913601i	$0.633290\pi$
$398$	−7.70575	−0.386254
$399$	0	0
$400$	4.32934	0.216467
$401$	−35.9549	−1.79550	−0.897752	−	0.440502i	$-0.854801\pi$
$401$	−35.9549	−1.79550	−0.897752	+	0.440502i	$0.854801\pi$
$402$	−15.2354	−0.759871
$403$	−14.8648	−0.740468
$404$	−4.95868	−0.246703
$405$	−3.05440	−0.151774
$406$	0	0
$407$	−0.250370	−0.0124104
$408$	−6.83496	−0.338381
$409$	18.5672	0.918089	0.459044	−	0.888413i	$-0.348192\pi$
$409$	18.5672	0.918089	0.459044	+	0.888413i	$0.348192\pi$
$410$	−2.93523	−0.144961
$411$	5.62949	0.277682
$412$	−4.04500	−0.199283
$413$	0	0
$414$	−0.451414	−0.0221858
$415$	−33.6339	−1.65102
$416$	−2.29213	−0.112381
$417$	1.45730	0.0713642
$418$	0.0875857	0.00428396
$419$	−14.7725	−0.721684	−0.360842	−	0.932627i	$-0.617511\pi$
$419$	−14.7725	−0.721684	−0.360842	+	0.932627i	$0.617511\pi$
$420$	0	0
$421$	12.1993	0.594560	0.297280	−	0.954790i	$-0.403921\pi$
$421$	12.1993	0.594560	0.297280	+	0.954790i	$0.403921\pi$
$422$	9.01556	0.438871
$423$	11.3254	0.550658
$424$	11.9336	0.579548
$425$	−29.5909	−1.43537
$426$	14.3896	0.697177
$427$	0	0
$428$	13.0668	0.631606
$429$	−0.200758	−0.00969270
$430$	−17.0346	−0.821480
$431$	7.49328	0.360938	0.180469	−	0.983581i	$-0.442238\pi$
$431$	7.49328	0.360938	0.180469	+	0.983581i	$0.442238\pi$
$432$	1.00000	0.0481125
$433$	−25.9789	−1.24847	−0.624234	−	0.781238i	$-0.714589\pi$
$433$	−25.9789	−1.24847	−0.624234	+	0.781238i	$0.714589\pi$
$434$	0	0
$435$	−29.8915	−1.43319
$436$	−15.3865	−0.736879
$437$	−0.451414	−0.0215941
$438$	1.76605	0.0843851
$439$	10.3947	0.496110	0.248055	−	0.968746i	$-0.420209\pi$
$439$	10.3947	0.496110	0.248055	+	0.968746i	$0.420209\pi$
$440$	−0.267522	−0.0127536
$441$	0	0
$442$	15.6667	0.745187
$443$	15.7006	0.745956	0.372978	−	0.927840i	$-0.378337\pi$
$443$	15.7006	0.745956	0.372978	+	0.927840i	$0.378337\pi$
$444$	−2.85857	−0.135662
$445$	−7.15305	−0.339087
$446$	3.82319	0.181034
$447$	−11.3010	−0.534521
$448$	0	0
$449$	33.9994	1.60453	0.802264	−	0.596969i	$-0.203628\pi$
$449$	33.9994	1.60453	0.802264	+	0.596969i	$0.203628\pi$
$450$	4.32934	0.204087
$451$	0.0841687	0.00396335
$452$	11.6322	0.547133
$453$	19.3648	0.909836
$454$	18.0509	0.847170
$455$	0	0
$456$	1.00000	0.0468293
$457$	−6.93327	−0.324325	−0.162162	−	0.986764i	$-0.551847\pi$
$457$	−6.93327	−0.324325	−0.162162	+	0.986764i	$0.551847\pi$
$458$	−15.8467	−0.740467
$459$	−6.83496	−0.319029
$460$	1.37880	0.0642868
$461$	−28.4600	−1.32552	−0.662758	−	0.748834i	$-0.730614\pi$
$461$	−28.4600	−1.32552	−0.662758	+	0.748834i	$0.730614\pi$
$462$	0	0
$463$	−2.21623	−0.102997	−0.0514985	−	0.998673i	$-0.516400\pi$
$463$	−2.21623	−0.102997	−0.0514985	+	0.998673i	$0.516400\pi$
$464$	9.78639	0.454322
$465$	−19.8082	−0.918581
$466$	−16.4699	−0.762955
$467$	8.88235	0.411026	0.205513	−	0.978654i	$-0.434114\pi$
$467$	8.88235	0.411026	0.205513	+	0.978654i	$0.434114\pi$
$468$	−2.29213	−0.105954
$469$	0	0
$470$	−34.5922	−1.59562
$471$	10.5602	0.486590
$472$	3.07976	0.141758
$473$	0.488471	0.0224599
$474$	−1.62682	−0.0747222
$475$	4.32934	0.198644
$476$	0	0
$477$	11.9336	0.546403
$478$	−2.91375	−0.133272
$479$	35.0507	1.60151	0.800753	−	0.598994i	$-0.204433\pi$
$479$	35.0507	1.60151	0.800753	+	0.598994i	$0.204433\pi$
$480$	−3.05440	−0.139413
$481$	6.55222	0.298756
$482$	16.0515	0.731127
$483$	0	0
$484$	−10.9923	−0.499651
$485$	−0.539580	−0.0245011
$486$	1.00000	0.0453609
$487$	−9.22262	−0.417917	−0.208959	−	0.977925i	$-0.567007\pi$
$487$	−9.22262	−0.417917	−0.208959	+	0.977925i	$0.567007\pi$
$488$	−4.54501	−0.205743
$489$	9.73483	0.440224
$490$	0	0
$491$	−23.9656	−1.08155	−0.540776	−	0.841167i	$-0.681869\pi$
$491$	−23.9656	−1.08155	−0.540776	+	0.841167i	$0.681869\pi$
$492$	0.960987	0.0433246
$493$	−66.8896	−3.01256
$494$	−2.29213	−0.103128
$495$	−0.267522	−0.0120242
$496$	6.48513	0.291191
$497$	0	0
$498$	11.0116	0.493443
$499$	21.6579	0.969542	0.484771	−	0.874641i	$-0.338903\pi$
$499$	21.6579	0.969542	0.484771	+	0.874641i	$0.338903\pi$
$500$	2.04847	0.0916106
$501$	−21.1337	−0.944182
$502$	−1.15331	−0.0514746
$503$	−3.96376	−0.176735	−0.0883677	−	0.996088i	$-0.528165\pi$
$503$	−3.96376	−0.176735	−0.0883677	+	0.996088i	$0.528165\pi$
$504$	0	0
$505$	15.1458	0.673978
$506$	−0.0395375	−0.00175766
$507$	−7.74612	−0.344017
$508$	11.7900	0.523095
$509$	−13.6394	−0.604556	−0.302278	−	0.953220i	$-0.597747\pi$
$509$	−13.6394	−0.604556	−0.302278	+	0.953220i	$0.597747\pi$
$510$	20.8767	0.924435
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−24.8428	−1.09577
$515$	12.3550	0.544428
$516$	5.57707	0.245517
$517$	0.991941	0.0436255
$518$	0	0
$519$	−7.41960	−0.325684
$520$	7.00109	0.307018
$521$	21.5566	0.944412	0.472206	−	0.881488i	$-0.343458\pi$
$521$	21.5566	0.944412	0.472206	+	0.881488i	$0.343458\pi$
$522$	9.78639	0.428339
$523$	3.45859	0.151233	0.0756167	−	0.997137i	$-0.475907\pi$
$523$	3.45859	0.151233	0.0756167	+	0.997137i	$0.475907\pi$
$524$	9.72124	0.424674
$525$	0	0
$526$	12.9557	0.564895
$527$	−44.3256	−1.93085
$528$	0.0875857	0.00381168
$529$	−22.7962	−0.991140
$530$	−36.4500	−1.58329
$531$	3.07976	0.133650
$532$	0	0
$533$	−2.20271	−0.0954100
$534$	2.34189	0.101343
$535$	−39.9111	−1.72551
$536$	−15.2354	−0.658068
$537$	13.6445	0.588804
$538$	−4.06356	−0.175193
$539$	0	0
$540$	−3.05440	−0.131440
$541$	−38.0384	−1.63540	−0.817700	−	0.575645i	$-0.804751\pi$
$541$	−38.0384	−1.63540	−0.817700	+	0.575645i	$0.804751\pi$
$542$	−3.62966	−0.155907
$543$	0.865106	0.0371252
$544$	−6.83496	−0.293047
$545$	46.9964	2.01310
$546$	0	0
$547$	22.8731	0.977981	0.488991	−	0.872289i	$-0.337365\pi$
$547$	22.8731	0.977981	0.488991	+	0.872289i	$0.337365\pi$
$548$	5.62949	0.240480
$549$	−4.54501	−0.193976
$550$	0.379188	0.0161686
$551$	9.78639	0.416914
$552$	−0.451414	−0.0192135
$553$	0	0
$554$	−11.6912	−0.496713
$555$	8.73120	0.370619
$556$	1.45730	0.0618032
$557$	−19.8296	−0.840208	−0.420104	−	0.907476i	$-0.638006\pi$
$557$	−19.8296	−0.840208	−0.420104	+	0.907476i	$0.638006\pi$
$558$	6.48513	0.274537
$559$	−12.7834	−0.540680
$560$	0	0
$561$	−0.598645	−0.0252748
$562$	26.4512	1.11578
$563$	34.0658	1.43570	0.717850	−	0.696198i	$-0.245126\pi$
$563$	34.0658	1.43570	0.717850	+	0.696198i	$0.245126\pi$
$564$	11.3254	0.476884
$565$	−35.5294	−1.49473
$566$	2.15554	0.0906041
$567$	0	0
$568$	14.3896	0.603773
$569$	29.4120	1.23301	0.616507	−	0.787350i	$-0.288547\pi$
$569$	29.4120	1.23301	0.616507	+	0.787350i	$0.288547\pi$
$570$	−3.05440	−0.127935
$571$	−4.29818	−0.179873	−0.0899366	−	0.995947i	$-0.528666\pi$
$571$	−4.29818	−0.179873	−0.0899366	+	0.995947i	$0.528666\pi$
$572$	−0.200758	−0.00839413
$573$	−15.8346	−0.661498
$574$	0	0
$575$	−1.95432	−0.0815010
$576$	1.00000	0.0416667
$577$	−38.3859	−1.59802	−0.799012	−	0.601314i	$-0.794644\pi$
$577$	−38.3859	−1.59802	−0.799012	+	0.601314i	$0.794644\pi$
$578$	29.7167	1.23605
$579$	−10.7620	−0.447255
$580$	−29.8915	−1.24118
$581$	0	0
$582$	0.176657	0.00732267
$583$	1.04522	0.0432884
$584$	1.76605	0.0730797
$585$	7.00109	0.289459
$586$	30.1462	1.24533
$587$	4.82449	0.199128	0.0995640	−	0.995031i	$-0.468255\pi$
$587$	4.82449	0.199128	0.0995640	+	0.995031i	$0.468255\pi$
$588$	0	0
$589$	6.48513	0.267215
$590$	−9.40681	−0.387272
$591$	−15.2333	−0.626615
$592$	−2.85857	−0.117486
$593$	7.21405	0.296246	0.148123	−	0.988969i	$-0.452677\pi$
$593$	7.21405	0.296246	0.148123	+	0.988969i	$0.452677\pi$
$594$	0.0875857	0.00359369
$595$	0	0
$596$	−11.3010	−0.462909
$597$	−7.70575	−0.315375
$598$	1.03470	0.0423121
$599$	−23.2770	−0.951071	−0.475536	−	0.879697i	$-0.657746\pi$
$599$	−23.2770	−0.951071	−0.475536	+	0.879697i	$0.657746\pi$
$600$	4.32934	0.176744
$601$	19.3297	0.788474	0.394237	−	0.919009i	$-0.371009\pi$
$601$	19.3297	0.788474	0.394237	+	0.919009i	$0.371009\pi$
$602$	0	0
$603$	−15.2354	−0.620432
$604$	19.3648	0.787941
$605$	33.5749	1.36501
$606$	−4.95868	−0.201433
$607$	2.04520	0.0830122	0.0415061	−	0.999138i	$-0.486784\pi$
$607$	2.04520	0.0830122	0.0415061	+	0.999138i	$0.486784\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	13.8823	0.562077
$611$	−25.9593	−1.05020
$612$	−6.83496	−0.276287
$613$	−31.4857	−1.27169	−0.635847	−	0.771815i	$-0.719349\pi$
$613$	−31.4857	−1.27169	−0.635847	+	0.771815i	$0.719349\pi$
$614$	15.3955	0.621313
$615$	−2.93523	−0.118360
$616$	0	0
$617$	−39.2185	−1.57888	−0.789439	−	0.613828i	$-0.789629\pi$
$617$	−39.2185	−1.57888	−0.789439	+	0.613828i	$0.789629\pi$
$618$	−4.04500	−0.162714
$619$	−10.0887	−0.405498	−0.202749	−	0.979231i	$-0.564988\pi$
$619$	−10.0887	−0.405498	−0.202749	+	0.979231i	$0.564988\pi$
$620$	−19.8082	−0.795515
$621$	−0.451414	−0.0181146
$622$	19.1805	0.769067
$623$	0	0
$624$	−2.29213	−0.0917588
$625$	−27.9035	−1.11614
$626$	28.4089	1.13545
$627$	0.0875857	0.00349784
$628$	10.5602	0.421399
$629$	19.5382	0.779040
$630$	0	0
$631$	29.0863	1.15791	0.578954	−	0.815360i	$-0.303461\pi$
$631$	29.0863	1.15791	0.578954	+	0.815360i	$0.303461\pi$
$632$	−1.62682	−0.0647113
$633$	9.01556	0.358336
$634$	20.3097	0.806601
$635$	−36.0112	−1.42906
$636$	11.9336	0.473199
$637$	0	0
$638$	0.857148	0.0339348
$639$	14.3896	0.569242
$640$	−3.05440	−0.120736
$641$	−23.7457	−0.937899	−0.468949	−	0.883225i	$-0.655367\pi$
$641$	−23.7457	−0.937899	−0.468949	+	0.883225i	$0.655367\pi$
$642$	13.0668	0.515704
$643$	−26.7571	−1.05520	−0.527599	−	0.849493i	$-0.676908\pi$
$643$	−26.7571	−1.05520	−0.527599	+	0.849493i	$0.676908\pi$
$644$	0	0
$645$	−17.0346	−0.670735
$646$	−6.83496	−0.268918
$647$	−33.1089	−1.30165	−0.650823	−	0.759230i	$-0.725576\pi$
$647$	−33.1089	−1.30165	−0.650823	+	0.759230i	$0.725576\pi$
$648$	1.00000	0.0392837
$649$	0.269743	0.0105883
$650$	−9.92342	−0.389229
$651$	0	0
$652$	9.73483	0.381245
$653$	−24.8959	−0.974253	−0.487127	−	0.873331i	$-0.661955\pi$
$653$	−24.8959	−0.974253	−0.487127	+	0.873331i	$0.661955\pi$
$654$	−15.3865	−0.601659
$655$	−29.6925	−1.16018
$656$	0.960987	0.0375202
$657$	1.76605	0.0689002
$658$	0	0
$659$	18.5712	0.723429	0.361715	−	0.932289i	$-0.382191\pi$
$659$	18.5712	0.723429	0.361715	+	0.932289i	$0.382191\pi$
$660$	−0.267522	−0.0104133
$661$	14.5296	0.565137	0.282568	−	0.959247i	$-0.408814\pi$
$661$	14.5296	0.565137	0.282568	+	0.959247i	$0.408814\pi$
$662$	23.9122	0.929375
$663$	15.6667	0.608443
$664$	11.0116	0.427334
$665$	0	0
$666$	−2.85857	−0.110767
$667$	−4.41772	−0.171055
$668$	−21.1337	−0.817686
$669$	3.82319	0.147813
$670$	46.5348	1.79780
$671$	−0.398078	−0.0153676
$672$	0	0
$673$	41.3408	1.59357	0.796784	−	0.604264i	$-0.206533\pi$
$673$	41.3408	1.59357	0.796784	+	0.604264i	$0.206533\pi$
$674$	−7.07270	−0.272430
$675$	4.32934	0.166636
$676$	−7.74612	−0.297928
$677$	−27.6982	−1.06453	−0.532264	−	0.846578i	$-0.678659\pi$
$677$	−27.6982	−1.06453	−0.532264	+	0.846578i	$0.678659\pi$
$678$	11.6322	0.446732
$679$	0	0
$680$	20.8767	0.800584
$681$	18.0509	0.691711
$682$	0.568005	0.0217500
$683$	−47.0270	−1.79944	−0.899720	−	0.436468i	$-0.856229\pi$
$683$	−47.0270	−1.79944	−0.899720	+	0.436468i	$0.856229\pi$
$684$	1.00000	0.0382360
$685$	−17.1947	−0.656975
$686$	0	0
$687$	−15.8467	−0.604589
$688$	5.57707	0.212624
$689$	−27.3535	−1.04208
$690$	1.37880	0.0524900
$691$	34.2350	1.30236	0.651181	−	0.758923i	$-0.274274\pi$
$691$	34.2350	1.30236	0.651181	+	0.758923i	$0.274274\pi$
$692$	−7.41960	−0.282051
$693$	0	0
$694$	24.1469	0.916605
$695$	−4.45117	−0.168842
$696$	9.78639	0.370952
$697$	−6.56831	−0.248792
$698$	8.18361	0.309754
$699$	−16.4699	−0.622950
$700$	0	0
$701$	−6.28753	−0.237477	−0.118738	−	0.992926i	$-0.537885\pi$
$701$	−6.28753	−0.237477	−0.118738	+	0.992926i	$0.537885\pi$
$702$	−2.29213	−0.0865110
$703$	−2.85857	−0.107813
$704$	0.0875857	0.00330101
$705$	−34.5922	−1.30282
$706$	−4.20569	−0.158283
$707$	0	0
$708$	3.07976	0.115745
$709$	−1.08351	−0.0406922	−0.0203461	−	0.999793i	$-0.506477\pi$
$709$	−1.08351	−0.0406922	−0.0203461	+	0.999793i	$0.506477\pi$
$710$	−43.9514	−1.64947
$711$	−1.62682	−0.0610104
$712$	2.34189	0.0877659
$713$	−2.92748	−0.109635
$714$	0	0
$715$	0.613195	0.0229322
$716$	13.6445	0.509919
$717$	−2.91375	−0.108816
$718$	9.49044	0.354180
$719$	53.0916	1.97998	0.989991	−	0.141130i	$-0.0450734\pi$
$719$	53.0916	1.97998	0.989991	+	0.141130i	$0.0450734\pi$
$720$	−3.05440	−0.113831
$721$	0	0
$722$	1.00000	0.0372161
$723$	16.0515	0.596963
$724$	0.865106	0.0321514
$725$	42.3686	1.57353
$726$	−10.9923	−0.407964
$727$	15.1879	0.563288	0.281644	−	0.959519i	$-0.409120\pi$
$727$	15.1879	0.563288	0.281644	+	0.959519i	$0.409120\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.39422	−0.199649
$731$	−38.1190	−1.40988
$732$	−4.54501	−0.167989
$733$	4.46425	0.164891	0.0824455	−	0.996596i	$-0.473727\pi$
$733$	4.46425	0.164891	0.0824455	+	0.996596i	$0.473727\pi$
$734$	−14.8745	−0.549029
$735$	0	0
$736$	−0.451414	−0.0166394
$737$	−1.33440	−0.0491533
$738$	0.960987	0.0353744
$739$	21.0986	0.776126	0.388063	−	0.921633i	$-0.373144\pi$
$739$	21.0986	0.776126	0.388063	+	0.921633i	$0.373144\pi$
$740$	8.73120	0.320965
$741$	−2.29213	−0.0842037
$742$	0	0
$743$	−32.5823	−1.19533	−0.597664	−	0.801747i	$-0.703904\pi$
$743$	−32.5823	−1.19533	−0.597664	+	0.801747i	$0.703904\pi$
$744$	6.48513	0.237756
$745$	34.5179	1.26464
$746$	−14.2951	−0.523379
$747$	11.0116	0.402894
$748$	−0.598645	−0.0218886
$749$	0	0
$750$	2.04847	0.0747997
$751$	−15.9699	−0.582749	−0.291374	−	0.956609i	$-0.594113\pi$
$751$	−15.9699	−0.582749	−0.291374	+	0.956609i	$0.594113\pi$
$752$	11.3254	0.412994
$753$	−1.15331	−0.0420289
$754$	−22.4317	−0.816915
$755$	−59.1476	−2.15260
$756$	0	0
$757$	−31.7558	−1.15419	−0.577093	−	0.816679i	$-0.695813\pi$
$757$	−31.7558	−1.15419	−0.577093	+	0.816679i	$0.695813\pi$
$758$	−0.874477	−0.0317624
$759$	−0.0395375	−0.00143512
$760$	−3.05440	−0.110795
$761$	−19.6721	−0.713113	−0.356556	−	0.934274i	$-0.616049\pi$
$761$	−19.6721	−0.713113	−0.356556	+	0.934274i	$0.616049\pi$
$762$	11.7900	0.427105
$763$	0	0
$764$	−15.8346	−0.572874
$765$	20.8767	0.754798
$766$	−36.8911	−1.33293
$767$	−7.05923	−0.254894
$768$	1.00000	0.0360844
$769$	−4.26815	−0.153913	−0.0769567	−	0.997034i	$-0.524520\pi$
$769$	−4.26815	−0.153913	−0.0769567	+	0.997034i	$0.524520\pi$
$770$	0	0
$771$	−24.8428	−0.894690
$772$	−10.7620	−0.387335
$773$	37.5800	1.35166	0.675829	−	0.737058i	$-0.263786\pi$
$773$	37.5800	1.35166	0.675829	+	0.737058i	$0.263786\pi$
$774$	5.57707	0.200463
$775$	28.0763	1.00853
$776$	0.176657	0.00634161
$777$	0	0
$778$	−13.3849	−0.479872
$779$	0.960987	0.0344309
$780$	7.00109	0.250679
$781$	1.26032	0.0450978
$782$	3.08540	0.110334
$783$	9.78639	0.349737
$784$	0	0
$785$	−32.2551	−1.15124
$786$	9.72124	0.346745
$787$	−1.20610	−0.0429929	−0.0214965	−	0.999769i	$-0.506843\pi$
$787$	−1.20610	−0.0429929	−0.0214965	+	0.999769i	$0.506843\pi$
$788$	−15.2333	−0.542665
$789$	12.9557	0.461235
$790$	4.96894	0.176787
$791$	0	0
$792$	0.0875857	0.00311222
$793$	10.4178	0.369946
$794$	−16.2033	−0.575035
$795$	−36.4500	−1.29275
$796$	−7.70575	−0.273123
$797$	35.2298	1.24790	0.623952	−	0.781462i	$-0.285526\pi$
$797$	35.2298	1.24790	0.623952	+	0.781462i	$0.285526\pi$
$798$	0	0
$799$	−77.4085	−2.73851
$800$	4.32934	0.153065
$801$	2.34189	0.0827465
$802$	−35.9549	−1.26961
$803$	0.154681	0.00545857
$804$	−15.2354	−0.537310
$805$	0	0
$806$	−14.8648	−0.523590
$807$	−4.06356	−0.143044
$808$	−4.95868	−0.174446
$809$	−12.8748	−0.452655	−0.226328	−	0.974051i	$-0.572672\pi$
$809$	−12.8748	−0.452655	−0.226328	+	0.974051i	$0.572672\pi$
$810$	−3.05440	−0.107321
$811$	45.5828	1.60063	0.800314	−	0.599581i	$-0.204666\pi$
$811$	45.5828	1.60063	0.800314	+	0.599581i	$0.204666\pi$
$812$	0	0
$813$	−3.62966	−0.127298
$814$	−0.250370	−0.00877546
$815$	−29.7340	−1.04154
$816$	−6.83496	−0.239272
$817$	5.57707	0.195117
$818$	18.5672	0.649187
$819$	0	0
$820$	−2.93523	−0.102503
$821$	34.6989	1.21100	0.605500	−	0.795845i	$-0.292973\pi$
$821$	34.6989	1.21100	0.605500	+	0.795845i	$0.292973\pi$
$822$	5.62949	0.196351
$823$	46.8803	1.63414	0.817072	−	0.576536i	$-0.195596\pi$
$823$	46.8803	1.63414	0.817072	+	0.576536i	$0.195596\pi$
$824$	−4.04500	−0.140914
$825$	0.379188	0.0132016
$826$	0	0
$827$	−16.3888	−0.569896	−0.284948	−	0.958543i	$-0.591976\pi$
$827$	−16.3888	−0.569896	−0.284948	+	0.958543i	$0.591976\pi$
$828$	−0.451414	−0.0156877
$829$	−33.8476	−1.17558	−0.587789	−	0.809015i	$-0.700001\pi$
$829$	−33.8476	−1.17558	−0.587789	+	0.809015i	$0.700001\pi$
$830$	−33.6339	−1.16745
$831$	−11.6912	−0.405565
$832$	−2.29213	−0.0794655
$833$	0	0
$834$	1.45730	0.0504621
$835$	64.5506	2.23386
$836$	0.0875857	0.00302922
$837$	6.48513	0.224159
$838$	−14.7725	−0.510308
$839$	−20.5591	−0.709778	−0.354889	−	0.934909i	$-0.615481\pi$
$839$	−20.5591	−0.709778	−0.354889	+	0.934909i	$0.615481\pi$
$840$	0	0
$841$	66.7735	2.30253
$842$	12.1993	0.420417
$843$	26.4512	0.911029
$844$	9.01556	0.310328
$845$	23.6597	0.813919
$846$	11.3254	0.389374
$847$	0	0
$848$	11.9336	0.409802
$849$	2.15554	0.0739779
$850$	−29.5909	−1.01496
$851$	1.29040	0.0442343
$852$	14.3896	0.492978
$853$	−34.9704	−1.19736	−0.598682	−	0.800986i	$-0.704309\pi$
$853$	−34.9704	−1.19736	−0.598682	+	0.800986i	$0.704309\pi$
$854$	0	0
$855$	−3.05440	−0.104458
$856$	13.0668	0.446613
$857$	13.5961	0.464434	0.232217	−	0.972664i	$-0.425402\pi$
$857$	13.5961	0.464434	0.232217	+	0.972664i	$0.425402\pi$
$858$	−0.200758	−0.00685378
$859$	32.5162	1.10944	0.554720	−	0.832037i	$-0.312825\pi$
$859$	32.5162	1.10944	0.554720	+	0.832037i	$0.312825\pi$
$860$	−17.0346	−0.580874
$861$	0	0
$862$	7.49328	0.255222
$863$	−58.4402	−1.98933	−0.994664	−	0.103165i	$-0.967103\pi$
$863$	−58.4402	−1.98933	−0.994664	+	0.103165i	$0.967103\pi$
$864$	1.00000	0.0340207
$865$	22.6624	0.770545
$866$	−25.9789	−0.882800
$867$	29.7167	1.00923
$868$	0	0
$869$	−0.142486	−0.00483350
$870$	−29.8915	−1.01342
$871$	34.9215	1.18327
$872$	−15.3865	−0.521052
$873$	0.176657	0.00597893
$874$	−0.451414	−0.0152693
$875$	0	0
$876$	1.76605	0.0596693
$877$	−25.3836	−0.857144	−0.428572	−	0.903508i	$-0.640983\pi$
$877$	−25.3836	−0.857144	−0.428572	+	0.903508i	$0.640983\pi$
$878$	10.3947	0.350803
$879$	30.1462	1.01681
$880$	−0.267522	−0.00901815
$881$	29.2400	0.985122	0.492561	−	0.870278i	$-0.336061\pi$
$881$	29.2400	0.985122	0.492561	+	0.870278i	$0.336061\pi$
$882$	0	0
$883$	0.941987	0.0317004	0.0158502	−	0.999874i	$-0.494955\pi$
$883$	0.941987	0.0317004	0.0158502	+	0.999874i	$0.494955\pi$
$884$	15.6667	0.526927
$885$	−9.40681	−0.316207
$886$	15.7006	0.527470
$887$	13.9593	0.468706	0.234353	−	0.972152i	$-0.424703\pi$
$887$	13.9593	0.468706	0.234353	+	0.972152i	$0.424703\pi$
$888$	−2.85857	−0.0959273
$889$	0	0
$890$	−7.15305	−0.239771
$891$	0.0875857	0.00293423
$892$	3.82319	0.128010
$893$	11.3254	0.378989
$894$	−11.3010	−0.377964
$895$	−41.6757	−1.39306
$896$	0	0
$897$	1.03470	0.0345477
$898$	33.9994	1.13457
$899$	63.4660	2.11671
$900$	4.32934	0.144311
$901$	−81.5659	−2.71735
$902$	0.0841687	0.00280251
$903$	0	0
$904$	11.6322	0.386881
$905$	−2.64238	−0.0878355
$906$	19.3648	0.643351
$907$	3.32141	0.110286	0.0551428	−	0.998478i	$-0.482439\pi$
$907$	3.32141	0.110286	0.0551428	+	0.998478i	$0.482439\pi$
$908$	18.0509	0.599039
$909$	−4.95868	−0.164469
$910$	0	0
$911$	−31.7935	−1.05337	−0.526683	−	0.850062i	$-0.676564\pi$
$911$	−31.7935	−1.05337	−0.526683	+	0.850062i	$0.676564\pi$
$912$	1.00000	0.0331133
$913$	0.964461	0.0319190
$914$	−6.93327	−0.229332
$915$	13.8823	0.458934
$916$	−15.8467	−0.523590
$917$	0	0
$918$	−6.83496	−0.225587
$919$	−16.7180	−0.551476	−0.275738	−	0.961233i	$-0.588922\pi$
$919$	−16.7180	−0.551476	−0.275738	+	0.961233i	$0.588922\pi$
$920$	1.37880	0.0454576
$921$	15.3955	0.507300
$922$	−28.4600	−0.937281
$923$	−32.9828	−1.08564
$924$	0	0
$925$	−12.3757	−0.406911
$926$	−2.21623	−0.0728298
$927$	−4.04500	−0.132855
$928$	9.78639	0.321254
$929$	−1.38431	−0.0454176	−0.0227088	−	0.999742i	$-0.507229\pi$
$929$	−1.38431	−0.0454176	−0.0227088	+	0.999742i	$0.507229\pi$
$930$	−19.8082	−0.649535
$931$	0	0
$932$	−16.4699	−0.539491
$933$	19.1805	0.627941
$934$	8.88235	0.290639
$935$	1.82850	0.0597984
$936$	−2.29213	−0.0749208
$937$	31.4054	1.02597	0.512984	−	0.858398i	$-0.328540\pi$
$937$	31.4054	1.02597	0.512984	+	0.858398i	$0.328540\pi$
$938$	0	0
$939$	28.4089	0.927088
$940$	−34.5922	−1.12827
$941$	39.2723	1.28024	0.640121	−	0.768274i	$-0.278884\pi$
$941$	39.2723	1.28024	0.640121	+	0.768274i	$0.278884\pi$
$942$	10.5602	0.344071
$943$	−0.433803	−0.0141266
$944$	3.07976	0.100238
$945$	0	0
$946$	0.488471	0.0158816
$947$	−39.6954	−1.28993	−0.644963	−	0.764214i	$-0.723127\pi$
$947$	−39.6954	−1.28993	−0.644963	+	0.764214i	$0.723127\pi$
$948$	−1.62682	−0.0528366
$949$	−4.04802	−0.131404
$950$	4.32934	0.140462
$951$	20.3097	0.658587
$952$	0	0
$953$	−42.1863	−1.36655	−0.683275	−	0.730162i	$-0.739445\pi$
$953$	−42.1863	−1.36655	−0.683275	+	0.730162i	$0.739445\pi$
$954$	11.9336	0.386365
$955$	48.3650	1.56506
$956$	−2.91375	−0.0942374
$957$	0.857148	0.0277077
$958$	35.0507	1.13244
$959$	0	0
$960$	−3.05440	−0.0985802
$961$	11.0569	0.356675
$962$	6.55222	0.211252
$963$	13.0668	0.421070
$964$	16.0515	0.516985
$965$	32.8716	1.05817
$966$	0	0
$967$	10.2502	0.329624	0.164812	−	0.986325i	$-0.447298\pi$
$967$	10.2502	0.329624	0.164812	+	0.986325i	$0.447298\pi$
$968$	−10.9923	−0.353307
$969$	−6.83496	−0.219571
$970$	−0.539580	−0.0173249
$971$	37.1803	1.19317	0.596586	−	0.802549i	$-0.296523\pi$
$971$	37.1803	1.19317	0.596586	+	0.802549i	$0.296523\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−9.22262	−0.295512
$975$	−9.92342	−0.317804
$976$	−4.54501	−0.145482
$977$	30.7935	0.985172	0.492586	−	0.870264i	$-0.336052\pi$
$977$	30.7935	0.985172	0.492586	+	0.870264i	$0.336052\pi$
$978$	9.73483	0.311285
$979$	0.205116	0.00655553
$980$	0	0
$981$	−15.3865	−0.491252
$982$	−23.9656	−0.764773
$983$	−56.4971	−1.80198	−0.900988	−	0.433844i	$-0.857157\pi$
$983$	−56.4971	−1.80198	−0.900988	+	0.433844i	$0.857157\pi$
$984$	0.960987	0.0306351
$985$	46.5286	1.48253
$986$	−66.8896	−2.13020
$987$	0	0
$988$	−2.29213	−0.0729225
$989$	−2.51757	−0.0800540
$990$	−0.267522	−0.00850239
$991$	−16.0311	−0.509244	−0.254622	−	0.967041i	$-0.581951\pi$
$991$	−16.0311	−0.509244	−0.254622	+	0.967041i	$0.581951\pi$
$992$	6.48513	0.205903
$993$	23.9122	0.758831
$994$	0	0
$995$	23.5364	0.746154
$996$	11.0116	0.348917
$997$	−54.6963	−1.73225	−0.866124	−	0.499829i	$-0.833396\pi$
$997$	−54.6963	−1.73225	−0.866124	+	0.499829i	$0.833396\pi$
$998$	21.6579	0.685570
$999$	−2.85857	−0.0904411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.cf.1.2	yes	8
7.6	odd	2		5586.2.a.ce.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.ce.1.7	✓	8	7.6	odd	2
5586.2.a.cf.1.2	yes	8	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05440 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.05440 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.05440 q^{10} +0.0875857 q^{11} +1.00000 q^{12} -2.29213 q^{13} -3.05440 q^{15} +1.00000 q^{16} -6.83496 q^{17} +1.00000 q^{18} +1.00000 q^{19} -3.05440 q^{20} +0.0875857 q^{22} -0.451414 q^{23} +1.00000 q^{24} +4.32934 q^{25} -2.29213 q^{26} +1.00000 q^{27} +9.78639 q^{29} -3.05440 q^{30} +6.48513 q^{31} +1.00000 q^{32} +0.0875857 q^{33} -6.83496 q^{34} +1.00000 q^{36} -2.85857 q^{37} +1.00000 q^{38} -2.29213 q^{39} -3.05440 q^{40} +0.960987 q^{41} +5.57707 q^{43} +0.0875857 q^{44} -3.05440 q^{45} -0.451414 q^{46} +11.3254 q^{47} +1.00000 q^{48} +4.32934 q^{50} -6.83496 q^{51} -2.29213 q^{52} +11.9336 q^{53} +1.00000 q^{54} -0.267522 q^{55} +1.00000 q^{57} +9.78639 q^{58} +3.07976 q^{59} -3.05440 q^{60} -4.54501 q^{61} +6.48513 q^{62} +1.00000 q^{64} +7.00109 q^{65} +0.0875857 q^{66} -15.2354 q^{67} -6.83496 q^{68} -0.451414 q^{69} +14.3896 q^{71} +1.00000 q^{72} +1.76605 q^{73} -2.85857 q^{74} +4.32934 q^{75} +1.00000 q^{76} -2.29213 q^{78} -1.62682 q^{79} -3.05440 q^{80} +1.00000 q^{81} +0.960987 q^{82} +11.0116 q^{83} +20.8767 q^{85} +5.57707 q^{86} +9.78639 q^{87} +0.0875857 q^{88} +2.34189 q^{89} -3.05440 q^{90} -0.451414 q^{92} +6.48513 q^{93} +11.3254 q^{94} -3.05440 q^{95} +1.00000 q^{96} +0.176657 q^{97} +0.0875857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} + 8 q^{9} + 4 q^{10} + 8 q^{11} + 8 q^{12} - 4 q^{13} + 4 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 8 q^{19} + 4 q^{20} + 8 q^{22} + 4 q^{23} + 8 q^{24} + 24 q^{25} - 4 q^{26} + 8 q^{27} + 16 q^{29} + 4 q^{30} + 4 q^{31} + 8 q^{32} + 8 q^{33} + 8 q^{34} + 8 q^{36} + 12 q^{37} + 8 q^{38} - 4 q^{39} + 4 q^{40} + 16 q^{43} + 8 q^{44} + 4 q^{45} + 4 q^{46} + 12 q^{47} + 8 q^{48} + 24 q^{50} + 8 q^{51} - 4 q^{52} + 24 q^{53} + 8 q^{54} - 8 q^{55} + 8 q^{57} + 16 q^{58} - 8 q^{59} + 4 q^{60} + 4 q^{62} + 8 q^{64} + 8 q^{65} + 8 q^{66} + 8 q^{67} + 8 q^{68} + 4 q^{69} + 24 q^{71} + 8 q^{72} - 16 q^{73} + 12 q^{74} + 24 q^{75} + 8 q^{76} - 4 q^{78} + 20 q^{79} + 4 q^{80} + 8 q^{81} + 16 q^{83} + 48 q^{85} + 16 q^{86} + 16 q^{87} + 8 q^{88} + 4 q^{90} + 4 q^{92} + 4 q^{93} + 12 q^{94} + 4 q^{95} + 8 q^{96} - 8 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 + 8 * q^9 + 4 * q^10 + 8 * q^11 + 8 * q^12 - 4 * q^13 + 4 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 8 * q^19 + 4 * q^20 + 8 * q^22 + 4 * q^23 + 8 * q^24 + 24 * q^25 - 4 * q^26 + 8 * q^27 + 16 * q^29 + 4 * q^30 + 4 * q^31 + 8 * q^32 + 8 * q^33 + 8 * q^34 + 8 * q^36 + 12 * q^37 + 8 * q^38 - 4 * q^39 + 4 * q^40 + 16 * q^43 + 8 * q^44 + 4 * q^45 + 4 * q^46 + 12 * q^47 + 8 * q^48 + 24 * q^50 + 8 * q^51 - 4 * q^52 + 24 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 - 8 * q^59 + 4 * q^60 + 4 * q^62 + 8 * q^64 + 8 * q^65 + 8 * q^66 + 8 * q^67 + 8 * q^68 + 4 * q^69 + 24 * q^71 + 8 * q^72 - 16 * q^73 + 12 * q^74 + 24 * q^75 + 8 * q^76 - 4 * q^78 + 20 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^83 + 48 * q^85 + 16 * q^86 + 16 * q^87 + 8 * q^88 + 4 * q^90 + 4 * q^92 + 4 * q^93 + 12 * q^94 + 4 * q^95 + 8 * q^96 - 8 * q^97 + 8 * q^99

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