LMFDB - Embedded newform 5586.2.a.bv.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:	$1$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.210756$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.21076 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.21076 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.21076 q^{10} +3.95558 q^{11} +1.00000 q^{12} -7.06814 q^{13} -2.21076 q^{15} +1.00000 q^{16} -5.21076 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.21076 q^{20} +3.95558 q^{22} +7.23448 q^{23} +1.00000 q^{24} -0.112558 q^{25} -7.06814 q^{26} +1.00000 q^{27} +1.11256 q^{29} -2.21076 q^{30} -2.57849 q^{31} +1.00000 q^{32} +3.95558 q^{33} -5.21076 q^{34} +1.00000 q^{36} -5.85738 q^{37} -1.00000 q^{38} -7.06814 q^{39} -2.21076 q^{40} -2.67669 q^{41} -9.76855 q^{43} +3.95558 q^{44} -2.21076 q^{45} +7.23448 q^{46} +12.5578 q^{47} +1.00000 q^{48} -0.112558 q^{50} -5.21076 q^{51} -7.06814 q^{52} -8.06814 q^{53} +1.00000 q^{54} -8.74483 q^{55} -1.00000 q^{57} +1.11256 q^{58} -4.32331 q^{59} -2.21076 q^{60} +4.42151 q^{61} -2.57849 q^{62} +1.00000 q^{64} +15.6259 q^{65} +3.95558 q^{66} +1.06814 q^{67} -5.21076 q^{68} +7.23448 q^{69} -13.7685 q^{71} +1.00000 q^{72} +8.02372 q^{73} -5.85738 q^{74} -0.112558 q^{75} -1.00000 q^{76} -7.06814 q^{78} -15.8667 q^{79} -2.21076 q^{80} +1.00000 q^{81} -2.67669 q^{82} -15.7542 q^{83} +11.5197 q^{85} -9.76855 q^{86} +1.11256 q^{87} +3.95558 q^{88} -2.67669 q^{89} -2.21076 q^{90} +7.23448 q^{92} -2.57849 q^{93} +12.5578 q^{94} +2.21076 q^{95} +1.00000 q^{96} -12.3233 q^{97} +3.95558 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 5 q^{10} + q^{11} + 3 q^{12} - 6 q^{13} - 5 q^{15} + 3 q^{16} - 14 q^{17} + 3 q^{18} - 3 q^{19} - 5 q^{20} + q^{22} - 6 q^{23} + 3 q^{24} + 4 q^{25} - 6 q^{26} + 3 q^{27} - q^{29} - 5 q^{30} - 11 q^{31} + 3 q^{32} + q^{33} - 14 q^{34} + 3 q^{36} - 4 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 14 q^{41} + 6 q^{43} + q^{44} - 5 q^{45} - 6 q^{46} + 4 q^{47} + 3 q^{48} + 4 q^{50} - 14 q^{51} - 6 q^{52} - 9 q^{53} + 3 q^{54} - 17 q^{55} - 3 q^{57} - q^{58} - 7 q^{59} - 5 q^{60} + 10 q^{61} - 11 q^{62} + 3 q^{64} - 2 q^{65} + q^{66} - 12 q^{67} - 14 q^{68} - 6 q^{69} - 6 q^{71} + 3 q^{72} - 2 q^{73} - 4 q^{74} + 4 q^{75} - 3 q^{76} - 6 q^{78} - 15 q^{79} - 5 q^{80} + 3 q^{81} - 14 q^{82} - 19 q^{83} + 34 q^{85} + 6 q^{86} - q^{87} + q^{88} - 14 q^{89} - 5 q^{90} - 6 q^{92} - 11 q^{93} + 4 q^{94} + 5 q^{95} + 3 q^{96} - 31 q^{97} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 5 * q^10 + q^11 + 3 * q^12 - 6 * q^13 - 5 * q^15 + 3 * q^16 - 14 * q^17 + 3 * q^18 - 3 * q^19 - 5 * q^20 + q^22 - 6 * q^23 + 3 * q^24 + 4 * q^25 - 6 * q^26 + 3 * q^27 - q^29 - 5 * q^30 - 11 * q^31 + 3 * q^32 + q^33 - 14 * q^34 + 3 * q^36 - 4 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 14 * q^41 + 6 * q^43 + q^44 - 5 * q^45 - 6 * q^46 + 4 * q^47 + 3 * q^48 + 4 * q^50 - 14 * q^51 - 6 * q^52 - 9 * q^53 + 3 * q^54 - 17 * q^55 - 3 * q^57 - q^58 - 7 * q^59 - 5 * q^60 + 10 * q^61 - 11 * q^62 + 3 * q^64 - 2 * q^65 + q^66 - 12 * q^67 - 14 * q^68 - 6 * q^69 - 6 * q^71 + 3 * q^72 - 2 * q^73 - 4 * q^74 + 4 * q^75 - 3 * q^76 - 6 * q^78 - 15 * q^79 - 5 * q^80 + 3 * q^81 - 14 * q^82 - 19 * q^83 + 34 * q^85 + 6 * q^86 - q^87 + q^88 - 14 * q^89 - 5 * q^90 - 6 * q^92 - 11 * q^93 + 4 * q^94 + 5 * q^95 + 3 * q^96 - 31 * q^97 + 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
$5$	−2.21076	−0.988680	−0.494340	−	0.869269i	$-0.664590\pi$
$5$	−2.21076	−0.988680	−0.494340	+	0.869269i	$0.664590\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.21076	−0.699102
$11$	3.95558	1.19265	0.596326	−	0.802742i	$-0.296626\pi$
$11$	3.95558	1.19265	0.596326	+	0.802742i	$0.296626\pi$
$12$	1.00000	0.288675
$13$	−7.06814	−1.96035	−0.980175	−	0.198135i	$-0.936512\pi$
$13$	−7.06814	−1.96035	−0.980175	+	0.198135i	$0.936512\pi$
$14$	0	0
$15$	−2.21076	−0.570815
$16$	1.00000	0.250000
$17$	−5.21076	−1.26379	−0.631897	−	0.775052i	$-0.717723\pi$
$17$	−5.21076	−1.26379	−0.631897	+	0.775052i	$0.717723\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.21076	−0.494340
$21$	0	0
$22$	3.95558	0.843333
$23$	7.23448	1.50849	0.754246	−	0.656591i	$-0.228002\pi$
$23$	7.23448	1.50849	0.754246	+	0.656591i	$0.228002\pi$
$24$	1.00000	0.204124
$25$	−0.112558	−0.0225117
$26$	−7.06814	−1.38618
$27$	1.00000	0.192450
$28$	0	0
$29$	1.11256	0.206597	0.103298	−	0.994650i	$-0.467060\pi$
$29$	1.11256	0.206597	0.103298	+	0.994650i	$0.467060\pi$
$30$	−2.21076	−0.403627
$31$	−2.57849	−0.463110	−0.231555	−	0.972822i	$-0.574381\pi$
$31$	−2.57849	−0.463110	−0.231555	+	0.972822i	$0.574381\pi$
$32$	1.00000	0.176777
$33$	3.95558	0.688578
$34$	−5.21076	−0.893637
$35$	0	0
$36$	1.00000	0.166667
$37$	−5.85738	−0.962948	−0.481474	−	0.876460i	$-0.659898\pi$
$37$	−5.85738	−0.962948	−0.481474	+	0.876460i	$0.659898\pi$
$38$	−1.00000	−0.162221
$39$	−7.06814	−1.13181
$40$	−2.21076	−0.349551
$41$	−2.67669	−0.418028	−0.209014	−	0.977913i	$-0.567025\pi$
$41$	−2.67669	−0.418028	−0.209014	+	0.977913i	$0.567025\pi$
$42$	0	0
$43$	−9.76855	−1.48969	−0.744845	−	0.667238i	$-0.767477\pi$
$43$	−9.76855	−1.48969	−0.744845	+	0.667238i	$0.767477\pi$
$44$	3.95558	0.596326
$45$	−2.21076	−0.329560
$46$	7.23448	1.06667
$47$	12.5578	1.83174	0.915871	−	0.401472i	$-0.131501\pi$
$47$	12.5578	1.83174	0.915871	+	0.401472i	$0.131501\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−0.112558	−0.0159182
$51$	−5.21076	−0.729652
$52$	−7.06814	−0.980175
$53$	−8.06814	−1.10824	−0.554122	−	0.832435i	$-0.686946\pi$
$53$	−8.06814	−1.10824	−0.554122	+	0.832435i	$0.686946\pi$
$54$	1.00000	0.136083
$55$	−8.74483	−1.17915
$56$	0	0
$57$	−1.00000	−0.132453
$58$	1.11256	0.146086
$59$	−4.32331	−0.562848	−0.281424	−	0.959584i	$-0.590807\pi$
$59$	−4.32331	−0.562848	−0.281424	+	0.959584i	$0.590807\pi$
$60$	−2.21076	−0.285407
$61$	4.42151	0.566117	0.283058	−	0.959103i	$-0.408651\pi$
$61$	4.42151	0.566117	0.283058	+	0.959103i	$0.408651\pi$
$62$	−2.57849	−0.327468
$63$	0	0
$64$	1.00000	0.125000
$65$	15.6259	1.93816
$66$	3.95558	0.486898
$67$	1.06814	0.130494	0.0652471	−	0.997869i	$-0.479216\pi$
$67$	1.06814	0.130494	0.0652471	+	0.997869i	$0.479216\pi$
$68$	−5.21076	−0.631897
$69$	7.23448	0.870929
$70$	0	0
$71$	−13.7685	−1.63403	−0.817013	−	0.576619i	$-0.804372\pi$
$71$	−13.7685	−1.63403	−0.817013	+	0.576619i	$0.804372\pi$
$72$	1.00000	0.117851
$73$	8.02372	0.939106	0.469553	−	0.882904i	$-0.344415\pi$
$73$	8.02372	0.939106	0.469553	+	0.882904i	$0.344415\pi$
$74$	−5.85738	−0.680907
$75$	−0.112558	−0.0129971
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−7.06814	−0.800309
$79$	−15.8667	−1.78515	−0.892574	−	0.450901i	$-0.851103\pi$
$79$	−15.8667	−1.78515	−0.892574	+	0.450901i	$0.851103\pi$
$80$	−2.21076	−0.247170
$81$	1.00000	0.111111
$82$	−2.67669	−0.295590
$83$	−15.7542	−1.72925	−0.864623	−	0.502421i	$-0.832443\pi$
$83$	−15.7542	−1.72925	−0.864623	+	0.502421i	$0.832443\pi$
$84$	0	0
$85$	11.5197	1.24949
$86$	−9.76855	−1.05337
$87$	1.11256	0.119279
$88$	3.95558	0.421666
$89$	−2.67669	−0.283728	−0.141864	−	0.989886i	$-0.545310\pi$
$89$	−2.67669	−0.283728	−0.141864	+	0.989886i	$0.545310\pi$
$90$	−2.21076	−0.233034
$91$	0	0
$92$	7.23448	0.754246
$93$	−2.57849	−0.267377
$94$	12.5578	1.29524
$95$	2.21076	0.226819
$96$	1.00000	0.102062
$97$	−12.3233	−1.25124	−0.625621	−	0.780127i	$-0.715155\pi$
$97$	−12.3233	−1.25124	−0.625621	+	0.780127i	$0.715155\pi$
$98$	0	0
$99$	3.95558	0.397551
$100$	−0.112558	−0.0112558
$101$	−2.51035	−0.249789	−0.124894	−	0.992170i	$-0.539859\pi$
$101$	−2.51035	−0.249789	−0.124894	+	0.992170i	$0.539859\pi$
$102$	−5.21076	−0.515942
$103$	15.6022	1.53733	0.768666	−	0.639651i	$-0.220921\pi$
$103$	15.6022	1.53733	0.768666	+	0.639651i	$0.220921\pi$
$104$	−7.06814	−0.693088
$105$	0	0
$106$	−8.06814	−0.783647
$107$	−19.4152	−1.87694	−0.938468	−	0.345366i	$-0.887755\pi$
$107$	−19.4152	−1.87694	−0.938468	+	0.345366i	$0.887755\pi$
$108$	1.00000	0.0962250
$109$	−2.47529	−0.237090	−0.118545	−	0.992949i	$-0.537823\pi$
$109$	−2.47529	−0.237090	−0.118545	+	0.992949i	$0.537823\pi$
$110$	−8.74483	−0.833786
$111$	−5.85738	−0.555958
$112$	0	0
$113$	11.8811	1.11768	0.558840	−	0.829275i	$-0.311246\pi$
$113$	11.8811	1.11768	0.558840	+	0.829275i	$0.311246\pi$
$114$	−1.00000	−0.0936586
$115$	−15.9937	−1.49142
$116$	1.11256	0.103298
$117$	−7.06814	−0.653450
$118$	−4.32331	−0.397993
$119$	0	0
$120$	−2.21076	−0.201813
$121$	4.64663	0.422421
$122$	4.42151	0.400305
$123$	−2.67669	−0.241349
$124$	−2.57849	−0.231555
$125$	11.3026	1.01094
$126$	0	0
$127$	5.22512	0.463654	0.231827	−	0.972757i	$-0.425530\pi$
$127$	5.22512	0.463654	0.231827	+	0.972757i	$0.425530\pi$
$128$	1.00000	0.0883883
$129$	−9.76855	−0.860073
$130$	15.6259	1.37048
$131$	−2.06814	−0.180694	−0.0903471	−	0.995910i	$-0.528798\pi$
$131$	−2.06814	−0.180694	−0.0903471	+	0.995910i	$0.528798\pi$
$132$	3.95558	0.344289
$133$	0	0
$134$	1.06814	0.0922733
$135$	−2.21076	−0.190272
$136$	−5.21076	−0.446819
$137$	−3.71477	−0.317374	−0.158687	−	0.987329i	$-0.550726\pi$
$137$	−3.71477	−0.317374	−0.158687	+	0.987329i	$0.550726\pi$
$138$	7.23448	0.615840
$139$	−22.1901	−1.88214	−0.941068	−	0.338217i	$-0.890176\pi$
$139$	−22.1901	−1.88214	−0.941068	+	0.338217i	$0.890176\pi$
$140$	0	0
$141$	12.5578	1.05756
$142$	−13.7685	−1.15543
$143$	−27.9586	−2.33802
$144$	1.00000	0.0833333
$145$	−2.45960	−0.204258
$146$	8.02372	0.664048
$147$	0	0
$148$	−5.85738	−0.481474
$149$	−2.55779	−0.209543	−0.104771	−	0.994496i	$-0.533411\pi$
$149$	−2.55779	−0.209543	−0.104771	+	0.994496i	$0.533411\pi$
$150$	−0.112558	−0.00919036
$151$	−9.84302	−0.801014	−0.400507	−	0.916294i	$-0.631166\pi$
$151$	−9.84302	−0.801014	−0.400507	+	0.916294i	$0.631166\pi$
$152$	−1.00000	−0.0811107
$153$	−5.21076	−0.421265
$154$	0	0
$155$	5.70041	0.457868
$156$	−7.06814	−0.565904
$157$	17.7148	1.41379	0.706896	−	0.707317i	$-0.250095\pi$
$157$	17.7148	1.41379	0.706896	+	0.707317i	$0.250095\pi$
$158$	−15.8667	−1.26229
$159$	−8.06814	−0.639845
$160$	−2.21076	−0.174776
$161$	0	0
$162$	1.00000	0.0785674
$163$	12.7829	1.00123	0.500617	−	0.865669i	$-0.333106\pi$
$163$	12.7829	1.00123	0.500617	+	0.865669i	$0.333106\pi$
$164$	−2.67669	−0.209014
$165$	−8.74483	−0.680784
$166$	−15.7542	−1.22276
$167$	11.6323	0.900132	0.450066	−	0.892995i	$-0.351400\pi$
$167$	11.6323	0.900132	0.450066	+	0.892995i	$0.351400\pi$
$168$	0	0
$169$	36.9586	2.84297
$170$	11.5197	0.883521
$171$	−1.00000	−0.0764719
$172$	−9.76855	−0.744845
$173$	−10.1126	−0.768844	−0.384422	−	0.923158i	$-0.625599\pi$
$173$	−10.1126	−0.768844	−0.384422	+	0.923158i	$0.625599\pi$
$174$	1.11256	0.0843428
$175$	0	0
$176$	3.95558	0.298163
$177$	−4.32331	−0.324960
$178$	−2.67669	−0.200626
$179$	−5.06814	−0.378811	−0.189405	−	0.981899i	$-0.560656\pi$
$179$	−5.06814	−0.378811	−0.189405	+	0.981899i	$0.560656\pi$
$180$	−2.21076	−0.164780
$181$	10.8905	0.809482	0.404741	−	0.914431i	$-0.367362\pi$
$181$	10.8905	0.809482	0.404741	+	0.914431i	$0.367362\pi$
$182$	0	0
$183$	4.42151	0.326848
$184$	7.23448	0.533333
$185$	12.9492	0.952048
$186$	−2.57849	−0.189064
$187$	−20.6116	−1.50727
$188$	12.5578	0.915871
$189$	0	0
$190$	2.21076	0.160385
$191$	5.40082	0.390789	0.195395	−	0.980725i	$-0.437401\pi$
$191$	5.40082	0.390789	0.195395	+	0.980725i	$0.437401\pi$
$192$	1.00000	0.0721688
$193$	0.857385	0.0617159	0.0308579	−	0.999524i	$-0.490176\pi$
$193$	0.857385	0.0617159	0.0308579	+	0.999524i	$0.490176\pi$
$194$	−12.3233	−0.884762
$195$	15.6259	1.11900
$196$	0	0
$197$	−5.51337	−0.392812	−0.196406	−	0.980523i	$-0.562927\pi$
$197$	−5.51337	−0.392812	−0.196406	+	0.980523i	$0.562927\pi$
$198$	3.95558	0.281111
$199$	17.0681	1.20993	0.604964	−	0.796253i	$-0.293187\pi$
$199$	17.0681	1.20993	0.604964	+	0.796253i	$0.293187\pi$
$200$	−0.112558	−0.00795908
$201$	1.06814	0.0753408
$202$	−2.51035	−0.176627
$203$	0	0
$204$	−5.21076	−0.364826
$205$	5.91750	0.413296
$206$	15.6022	1.08706
$207$	7.23448	0.502831
$208$	−7.06814	−0.490087
$209$	−3.95558	−0.273613
$210$	0	0
$211$	−17.7034	−1.21875	−0.609377	−	0.792880i	$-0.708581\pi$
$211$	−17.7034	−1.21875	−0.609377	+	0.792880i	$0.708581\pi$
$212$	−8.06814	−0.554122
$213$	−13.7685	−0.943405
$214$	−19.4152	−1.32719
$215$	21.5959	1.47283
$216$	1.00000	0.0680414
$217$	0	0
$218$	−2.47529	−0.167648
$219$	8.02372	0.542193
$220$	−8.74483	−0.589576
$221$	36.8304	2.47748
$222$	−5.85738	−0.393122
$223$	−3.62291	−0.242608	−0.121304	−	0.992615i	$-0.538708\pi$
$223$	−3.62291	−0.242608	−0.121304	+	0.992615i	$0.538708\pi$
$224$	0	0
$225$	−0.112558	−0.00750390
$226$	11.8811	0.790319
$227$	2.21076	0.146733	0.0733665	−	0.997305i	$-0.476626\pi$
$227$	2.21076	0.146733	0.0733665	+	0.997305i	$0.476626\pi$
$228$	−1.00000	−0.0662266
$229$	1.03942	0.0686867	0.0343434	−	0.999410i	$-0.489066\pi$
$229$	1.03942	0.0686867	0.0343434	+	0.999410i	$0.489066\pi$
$230$	−15.9937	−1.05459
$231$	0	0
$232$	1.11256	0.0730430
$233$	−9.82233	−0.643482	−0.321741	−	0.946828i	$-0.604268\pi$
$233$	−9.82233	−0.643482	−0.321741	+	0.946828i	$0.604268\pi$
$234$	−7.06814	−0.462059
$235$	−27.7622	−1.81101
$236$	−4.32331	−0.281424
$237$	−15.8667	−1.03066
$238$	0	0
$239$	0.225117	0.0145616	0.00728080	−	0.999973i	$-0.497682\pi$
$239$	0.225117	0.0145616	0.00728080	+	0.999973i	$0.497682\pi$
$240$	−2.21076	−0.142704
$241$	2.65599	0.171087	0.0855437	−	0.996334i	$-0.472737\pi$
$241$	2.65599	0.171087	0.0855437	+	0.996334i	$0.472737\pi$
$242$	4.64663	0.298697
$243$	1.00000	0.0641500
$244$	4.42151	0.283058
$245$	0	0
$246$	−2.67669	−0.170659
$247$	7.06814	0.449735
$248$	−2.57849	−0.163734
$249$	−15.7542	−0.998381
$250$	11.3026	0.714840
$251$	15.2201	0.960685	0.480343	−	0.877081i	$-0.340512\pi$
$251$	15.2201	0.960685	0.480343	+	0.877081i	$0.340512\pi$
$252$	0	0
$253$	28.6166	1.79911
$254$	5.22512	0.327853
$255$	11.5197	0.721392
$256$	1.00000	0.0625000
$257$	−19.2933	−1.20348	−0.601740	−	0.798692i	$-0.705526\pi$
$257$	−19.2933	−1.20348	−0.601740	+	0.798692i	$0.705526\pi$
$258$	−9.76855	−0.608163
$259$	0	0
$260$	15.6259	0.969079
$261$	1.11256	0.0688656
$262$	−2.06814	−0.127770
$263$	−7.60855	−0.469163	−0.234582	−	0.972096i	$-0.575372\pi$
$263$	−7.60855	−0.469163	−0.234582	+	0.972096i	$0.575372\pi$
$264$	3.95558	0.243449
$265$	17.8367	1.09570
$266$	0	0
$267$	−2.67669	−0.163811
$268$	1.06814	0.0652471
$269$	−6.99500	−0.426493	−0.213246	−	0.976998i	$-0.568404\pi$
$269$	−6.99500	−0.426493	−0.213246	+	0.976998i	$0.568404\pi$
$270$	−2.21076	−0.134542
$271$	2.52471	0.153365	0.0766826	−	0.997056i	$-0.475567\pi$
$271$	2.52471	0.153365	0.0766826	+	0.997056i	$0.475567\pi$
$272$	−5.21076	−0.315948
$273$	0	0
$274$	−3.71477	−0.224417
$275$	−0.445234	−0.0268486
$276$	7.23448	0.435464
$277$	18.2138	1.09436	0.547180	−	0.837015i	$-0.315701\pi$
$277$	18.2138	1.09436	0.547180	+	0.837015i	$0.315701\pi$
$278$	−22.1901	−1.33087
$279$	−2.57849	−0.154370
$280$	0	0
$281$	−22.0474	−1.31524	−0.657620	−	0.753350i	$-0.728437\pi$
$281$	−22.0474	−1.31524	−0.657620	+	0.753350i	$0.728437\pi$
$282$	12.5578	0.747806
$283$	19.5722	1.16344	0.581722	−	0.813388i	$-0.302379\pi$
$283$	19.5722	1.16344	0.581722	+	0.813388i	$0.302379\pi$
$284$	−13.7685	−0.817013
$285$	2.21076	0.130954
$286$	−27.9586	−1.65323
$287$	0	0
$288$	1.00000	0.0589256
$289$	10.1520	0.597175
$290$	−2.45960	−0.144432
$291$	−12.3233	−0.722405
$292$	8.02372	0.469553
$293$	−19.1600	−1.11934	−0.559670	−	0.828716i	$-0.689072\pi$
$293$	−19.1600	−1.11934	−0.559670	+	0.828716i	$0.689072\pi$
$294$	0	0
$295$	9.55779	0.556476
$296$	−5.85738	−0.340454
$297$	3.95558	0.229526
$298$	−2.55779	−0.148169
$299$	−51.1343	−2.95717
$300$	−0.112558	−0.00649856
$301$	0	0
$302$	−9.84302	−0.566402
$303$	−2.51035	−0.144216
$304$	−1.00000	−0.0573539
$305$	−9.77488	−0.559708
$306$	−5.21076	−0.297879
$307$	5.79227	0.330582	0.165291	−	0.986245i	$-0.447144\pi$
$307$	5.79227	0.330582	0.165291	+	0.986245i	$0.447144\pi$
$308$	0	0
$309$	15.6022	0.887579
$310$	5.70041	0.323761
$311$	−23.5484	−1.33531	−0.667655	−	0.744471i	$-0.732702\pi$
$311$	−23.5484	−1.33531	−0.667655	+	0.744471i	$0.732702\pi$
$312$	−7.06814	−0.400155
$313$	3.75919	0.212482	0.106241	−	0.994340i	$-0.466119\pi$
$313$	3.75919	0.212482	0.106241	+	0.994340i	$0.466119\pi$
$314$	17.7148	0.999702
$315$	0	0
$316$	−15.8667	−0.892574
$317$	4.66732	0.262143	0.131072	−	0.991373i	$-0.458158\pi$
$317$	4.66732	0.262143	0.131072	+	0.991373i	$0.458158\pi$
$318$	−8.06814	−0.452439
$319$	4.40082	0.246398
$320$	−2.21076	−0.123585
$321$	−19.4152	−1.08365
$322$	0	0
$323$	5.21076	0.289934
$324$	1.00000	0.0555556
$325$	0.795579	0.0441308
$326$	12.7829	0.707980
$327$	−2.47529	−0.136884
$328$	−2.67669	−0.147795
$329$	0	0
$330$	−8.74483	−0.481387
$331$	−13.5672	−0.745718	−0.372859	−	0.927888i	$-0.621623\pi$
$331$	−13.5672	−0.745718	−0.372859	+	0.927888i	$0.621623\pi$
$332$	−15.7542	−0.864623
$333$	−5.85738	−0.320983
$334$	11.6323	0.636489
$335$	−2.36140	−0.129017
$336$	0	0
$337$	34.8998	1.90111	0.950557	−	0.310549i	$-0.100513\pi$
$337$	34.8998	1.90111	0.950557	+	0.310549i	$0.100513\pi$
$338$	36.9586	2.01028
$339$	11.8811	0.645293
$340$	11.5197	0.624744
$341$	−10.1994	−0.552330
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−9.76855	−0.526685
$345$	−15.9937	−0.861070
$346$	−10.1126	−0.543655
$347$	−24.9556	−1.33969	−0.669843	−	0.742503i	$-0.733639\pi$
$347$	−24.9556	−1.33969	−0.669843	+	0.742503i	$0.733639\pi$
$348$	1.11256	0.0596394
$349$	−18.4990	−0.990229	−0.495115	−	0.868828i	$-0.664874\pi$
$349$	−18.4990	−0.990229	−0.495115	+	0.868828i	$0.664874\pi$
$350$	0	0
$351$	−7.06814	−0.377269
$352$	3.95558	0.210833
$353$	−13.4359	−0.715119	−0.357560	−	0.933890i	$-0.616391\pi$
$353$	−13.4359	−0.715119	−0.357560	+	0.933890i	$0.616391\pi$
$354$	−4.32331	−0.229782
$355$	30.4389	1.61553
$356$	−2.67669	−0.141864
$357$	0	0
$358$	−5.06814	−0.267860
$359$	5.82233	0.307291	0.153645	−	0.988126i	$-0.450899\pi$
$359$	5.82233	0.307291	0.153645	+	0.988126i	$0.450899\pi$
$360$	−2.21076	−0.116517
$361$	1.00000	0.0526316
$362$	10.8905	0.572390
$363$	4.64663	0.243885
$364$	0	0
$365$	−17.7385	−0.928475
$366$	4.42151	0.231116
$367$	9.47529	0.494606	0.247303	−	0.968938i	$-0.420456\pi$
$367$	9.47529	0.494606	0.247303	+	0.968938i	$0.420456\pi$
$368$	7.23448	0.377123
$369$	−2.67669	−0.139343
$370$	12.9492	0.673199
$371$	0	0
$372$	−2.57849	−0.133688
$373$	−25.1757	−1.30355	−0.651774	−	0.758413i	$-0.725975\pi$
$373$	−25.1757	−1.30355	−0.651774	+	0.758413i	$0.725975\pi$
$374$	−20.6116	−1.06580
$375$	11.3026	0.583665
$376$	12.5578	0.647619
$377$	−7.86372	−0.405002
$378$	0	0
$379$	−30.1837	−1.55043	−0.775217	−	0.631695i	$-0.782359\pi$
$379$	−30.1837	−1.55043	−0.775217	+	0.631695i	$0.782359\pi$
$380$	2.21076	0.113409
$381$	5.22512	0.267691
$382$	5.40082	0.276330
$383$	12.5103	0.639249	0.319624	−	0.947544i	$-0.396443\pi$
$383$	12.5103	0.639249	0.319624	+	0.947544i	$0.396443\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	0.857385	0.0436397
$387$	−9.76855	−0.496563
$388$	−12.3233	−0.625621
$389$	−15.8036	−0.801275	−0.400637	−	0.916237i	$-0.631211\pi$
$389$	−15.8036	−0.801275	−0.400637	+	0.916237i	$0.631211\pi$
$390$	15.6259	0.791250
$391$	−37.6971	−1.90642
$392$	0	0
$393$	−2.06814	−0.104324
$394$	−5.51337	−0.277760
$395$	35.0775	1.76494
$396$	3.95558	0.198775
$397$	17.2645	0.866482	0.433241	−	0.901278i	$-0.357370\pi$
$397$	17.2645	0.866482	0.433241	+	0.901278i	$0.357370\pi$
$398$	17.0681	0.855549
$399$	0	0
$400$	−0.112558	−0.00562792
$401$	2.96058	0.147844	0.0739222	−	0.997264i	$-0.476448\pi$
$401$	2.96058	0.147844	0.0739222	+	0.997264i	$0.476448\pi$
$402$	1.06814	0.0532740
$403$	18.2251	0.907858
$404$	−2.51035	−0.124894
$405$	−2.21076	−0.109853
$406$	0	0
$407$	−23.1694	−1.14846
$408$	−5.21076	−0.257971
$409$	−20.3708	−1.00727	−0.503635	−	0.863917i	$-0.668004\pi$
$409$	−20.3708	−1.00727	−0.503635	+	0.863917i	$0.668004\pi$
$410$	5.91750	0.292244
$411$	−3.71477	−0.183236
$412$	15.6022	0.768666
$413$	0	0
$414$	7.23448	0.355555
$415$	34.8287	1.70967
$416$	−7.06814	−0.346544
$417$	−22.1901	−1.08665
$418$	−3.95558	−0.193474
$419$	−11.1520	−0.544810	−0.272405	−	0.962183i	$-0.587819\pi$
$419$	−11.1520	−0.544810	−0.272405	+	0.962183i	$0.587819\pi$
$420$	0	0
$421$	14.3327	0.698532	0.349266	−	0.937024i	$-0.386431\pi$
$421$	14.3327	0.698532	0.349266	+	0.937024i	$0.386431\pi$
$422$	−17.7034	−0.861790
$423$	12.5578	0.610581
$424$	−8.06814	−0.391824
$425$	0.586515	0.0284501
$426$	−13.7685	−0.667088
$427$	0	0
$428$	−19.4152	−0.938468
$429$	−27.9586	−1.34985
$430$	21.5959	1.04145
$431$	24.1901	1.16519	0.582597	−	0.812761i	$-0.302037\pi$
$431$	24.1901	1.16519	0.582597	+	0.812761i	$0.302037\pi$
$432$	1.00000	0.0481125
$433$	−9.51337	−0.457184	−0.228592	−	0.973522i	$-0.573412\pi$
$433$	−9.51337	−0.457184	−0.228592	+	0.973522i	$0.573412\pi$
$434$	0	0
$435$	−2.45960	−0.117929
$436$	−2.47529	−0.118545
$437$	−7.23448	−0.346072
$438$	8.02372	0.383388
$439$	−9.11256	−0.434919	−0.217459	−	0.976069i	$-0.569777\pi$
$439$	−9.11256	−0.434919	−0.217459	+	0.976069i	$0.569777\pi$
$440$	−8.74483	−0.416893
$441$	0	0
$442$	36.8304	1.75184
$443$	12.0030	0.570281	0.285141	−	0.958486i	$-0.407960\pi$
$443$	12.0030	0.570281	0.285141	+	0.958486i	$0.407960\pi$
$444$	−5.85738	−0.277979
$445$	5.91750	0.280516
$446$	−3.62291	−0.171550
$447$	−2.55779	−0.120979
$448$	0	0
$449$	2.13762	0.100880	0.0504402	−	0.998727i	$-0.483938\pi$
$449$	2.13762	0.100880	0.0504402	+	0.998727i	$0.483938\pi$
$450$	−0.112558	−0.00530606
$451$	−10.5878	−0.498562
$452$	11.8811	0.558840
$453$	−9.84302	−0.462466
$454$	2.21076	0.103756
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	26.7572	1.25165	0.625825	−	0.779964i	$-0.284762\pi$
$457$	26.7572	1.25165	0.625825	+	0.779964i	$0.284762\pi$
$458$	1.03942	0.0485688
$459$	−5.21076	−0.243217
$460$	−15.9937	−0.745708
$461$	−13.4295	−0.625476	−0.312738	−	0.949839i	$-0.601246\pi$
$461$	−13.4295	−0.625476	−0.312738	+	0.949839i	$0.601246\pi$
$462$	0	0
$463$	5.24581	0.243794	0.121897	−	0.992543i	$-0.461102\pi$
$463$	5.24581	0.243794	0.121897	+	0.992543i	$0.461102\pi$
$464$	1.11256	0.0516492
$465$	5.70041	0.264350
$466$	−9.82233	−0.455011
$467$	25.1106	1.16198	0.580990	−	0.813911i	$-0.302666\pi$
$467$	25.1106	1.16198	0.580990	+	0.813911i	$0.302666\pi$
$468$	−7.06814	−0.326725
$469$	0	0
$470$	−27.7622	−1.28058
$471$	17.7148	0.816253
$472$	−4.32331	−0.198997
$473$	−38.6403	−1.77668
$474$	−15.8667	−0.728784
$475$	0.112558	0.00516454
$476$	0	0
$477$	−8.06814	−0.369415
$478$	0.225117	0.0102966
$479$	12.6654	0.578695	0.289347	−	0.957224i	$-0.406562\pi$
$479$	12.6654	0.578695	0.289347	+	0.957224i	$0.406562\pi$
$480$	−2.21076	−0.100907
$481$	41.4008	1.88771
$482$	2.65599	0.120977
$483$	0	0
$484$	4.64663	0.211210
$485$	27.2438	1.23708
$486$	1.00000	0.0453609
$487$	6.02070	0.272824	0.136412	−	0.990652i	$-0.456443\pi$
$487$	6.02070	0.272824	0.136412	+	0.990652i	$0.456443\pi$
$488$	4.42151	0.200152
$489$	12.7829	0.578063
$490$	0	0
$491$	37.0662	1.67277	0.836386	−	0.548140i	$-0.184664\pi$
$491$	37.0662	1.67277	0.836386	+	0.548140i	$0.184664\pi$
$492$	−2.67669	−0.120674
$493$	−5.79727	−0.261096
$494$	7.06814	0.318011
$495$	−8.74483	−0.393051
$496$	−2.57849	−0.115778
$497$	0	0
$498$	−15.7542	−0.705962
$499$	18.8905	0.845653	0.422827	−	0.906211i	$-0.361038\pi$
$499$	18.8905	0.845653	0.422827	+	0.906211i	$0.361038\pi$
$500$	11.3026	0.505468
$501$	11.6323	0.519691
$502$	15.2201	0.679307
$503$	8.48029	0.378117	0.189059	−	0.981966i	$-0.439456\pi$
$503$	8.48029	0.378117	0.189059	+	0.981966i	$0.439456\pi$
$504$	0	0
$505$	5.54977	0.246961
$506$	28.6166	1.27216
$507$	36.9586	1.64139
$508$	5.22512	0.231827
$509$	29.6002	1.31201	0.656004	−	0.754758i	$-0.272246\pi$
$509$	29.6002	1.31201	0.656004	+	0.754758i	$0.272246\pi$
$510$	11.5197	0.510101
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−19.2933	−0.850989
$515$	−34.4927	−1.51993
$516$	−9.76855	−0.430036
$517$	49.6734	2.18463
$518$	0	0
$519$	−10.1126	−0.443892
$520$	15.6259	0.685242
$521$	40.3200	1.76645	0.883226	−	0.468948i	$-0.155367\pi$
$521$	40.3200	1.76645	0.883226	+	0.468948i	$0.155367\pi$
$522$	1.11256	0.0486954
$523$	5.65599	0.247319	0.123660	−	0.992325i	$-0.460537\pi$
$523$	5.65599	0.247319	0.123660	+	0.992325i	$0.460537\pi$
$524$	−2.06814	−0.0903471
$525$	0	0
$526$	−7.60855	−0.331748
$527$	13.4359	0.585276
$528$	3.95558	0.172145
$529$	29.3377	1.27555
$530$	17.8367	0.774776
$531$	−4.32331	−0.187616
$532$	0	0
$533$	18.9192	0.819481
$534$	−2.67669	−0.115832
$535$	42.9222	1.85569
$536$	1.06814	0.0461366
$537$	−5.06814	−0.218706
$538$	−6.99500	−0.301576
$539$	0	0
$540$	−2.21076	−0.0951358
$541$	28.6066	1.22989	0.614946	−	0.788569i	$-0.289178\pi$
$541$	28.6066	1.22989	0.614946	+	0.788569i	$0.289178\pi$
$542$	2.52471	0.108446
$543$	10.8905	0.467355
$544$	−5.21076	−0.223409
$545$	5.47226	0.234406
$546$	0	0
$547$	−15.0094	−0.641754	−0.320877	−	0.947121i	$-0.603978\pi$
$547$	−15.0094	−0.641754	−0.320877	+	0.947121i	$0.603978\pi$
$548$	−3.71477	−0.158687
$549$	4.42151	0.188706
$550$	−0.445234	−0.0189848
$551$	−1.11256	−0.0473966
$552$	7.23448	0.307920
$553$	0	0
$554$	18.2138	0.773829
$555$	12.9492	0.549665
$556$	−22.1901	−0.941068
$557$	−12.8811	−0.545790	−0.272895	−	0.962044i	$-0.587981\pi$
$557$	−12.8811	−0.545790	−0.272895	+	0.962044i	$0.587981\pi$
$558$	−2.57849	−0.109156
$559$	69.0455	2.92031
$560$	0	0
$561$	−20.6116	−0.870221
$562$	−22.0474	−0.930015
$563$	14.3233	0.603656	0.301828	−	0.953362i	$-0.402403\pi$
$563$	14.3233	0.603656	0.301828	+	0.953362i	$0.402403\pi$
$564$	12.5578	0.528778
$565$	−26.2662	−1.10503
$566$	19.5722	0.822679
$567$	0	0
$568$	−13.7685	−0.577715
$569$	1.10953	0.0465140	0.0232570	−	0.999730i	$-0.492596\pi$
$569$	1.10953	0.0465140	0.0232570	+	0.999730i	$0.492596\pi$
$570$	2.21076	0.0925984
$571$	−7.66099	−0.320602	−0.160301	−	0.987068i	$-0.551247\pi$
$571$	−7.66099	−0.320602	−0.160301	+	0.987068i	$0.551247\pi$
$572$	−27.9586	−1.16901
$573$	5.40082	0.225622
$574$	0	0
$575$	−0.814302	−0.0339587
$576$	1.00000	0.0416667
$577$	−43.1837	−1.79776	−0.898881	−	0.438193i	$-0.855619\pi$
$577$	−43.1837	−1.79776	−0.898881	+	0.438193i	$0.855619\pi$
$578$	10.1520	0.422267
$579$	0.857385	0.0356317
$580$	−2.45960	−0.102129
$581$	0	0
$582$	−12.3233	−0.510818
$583$	−31.9142	−1.32175
$584$	8.02372	0.332024
$585$	15.6259	0.646053
$586$	−19.1600	−0.791492
$587$	−0.348372	−0.0143788	−0.00718942	−	0.999974i	$-0.502288\pi$
$587$	−0.348372	−0.0143788	−0.00718942	+	0.999974i	$0.502288\pi$
$588$	0	0
$589$	2.57849	0.106245
$590$	9.55779	0.393488
$591$	−5.51337	−0.226790
$592$	−5.85738	−0.240737
$593$	37.1757	1.52662	0.763311	−	0.646031i	$-0.223572\pi$
$593$	37.1757	1.52662	0.763311	+	0.646031i	$0.223572\pi$
$594$	3.95558	0.162299
$595$	0	0
$596$	−2.55779	−0.104771
$597$	17.0681	0.698552
$598$	−51.1343	−2.09104
$599$	−30.7766	−1.25750	−0.628748	−	0.777609i	$-0.716432\pi$
$599$	−30.7766	−1.25750	−0.628748	+	0.777609i	$0.716432\pi$
$600$	−0.112558	−0.00459518
$601$	−30.6847	−1.25166	−0.625828	−	0.779961i	$-0.715239\pi$
$601$	−30.6847	−1.25166	−0.625828	+	0.779961i	$0.715239\pi$
$602$	0	0
$603$	1.06814	0.0434980
$604$	−9.84302	−0.400507
$605$	−10.2726	−0.417639
$606$	−2.51035	−0.101976
$607$	37.6704	1.52899	0.764496	−	0.644628i	$-0.222988\pi$
$607$	37.6704	1.52899	0.764496	+	0.644628i	$0.222988\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−9.77488	−0.395773
$611$	−88.7602	−3.59085
$612$	−5.21076	−0.210632
$613$	8.11889	0.327919	0.163960	−	0.986467i	$-0.447573\pi$
$613$	8.11889	0.327919	0.163960	+	0.986467i	$0.447573\pi$
$614$	5.79227	0.233757
$615$	5.91750	0.238617
$616$	0	0
$617$	33.7873	1.36022	0.680112	−	0.733108i	$-0.261931\pi$
$617$	33.7873	1.36022	0.680112	+	0.733108i	$0.261931\pi$
$618$	15.6022	0.627613
$619$	10.7355	0.431495	0.215747	−	0.976449i	$-0.430781\pi$
$619$	10.7355	0.431495	0.215747	+	0.976449i	$0.430781\pi$
$620$	5.70041	0.228934
$621$	7.23448	0.290310
$622$	−23.5484	−0.944206
$623$	0	0
$624$	−7.06814	−0.282952
$625$	−24.4245	−0.976982
$626$	3.75919	0.150247
$627$	−3.95558	−0.157971
$628$	17.7148	0.706896
$629$	30.5214	1.21697
$630$	0	0
$631$	30.5308	1.21541	0.607705	−	0.794163i	$-0.292090\pi$
$631$	30.5308	1.21541	0.607705	+	0.794163i	$0.292090\pi$
$632$	−15.8667	−0.631145
$633$	−17.7034	−0.703648
$634$	4.66732	0.185363
$635$	−11.5515	−0.458406
$636$	−8.06814	−0.319923
$637$	0	0
$638$	4.40082	0.174230
$639$	−13.7685	−0.544675
$640$	−2.21076	−0.0873878
$641$	−2.85436	−0.112740	−0.0563702	−	0.998410i	$-0.517953\pi$
$641$	−2.85436	−0.112740	−0.0563702	+	0.998410i	$0.517953\pi$
$642$	−19.4152	−0.766256
$643$	−39.2582	−1.54819	−0.774096	−	0.633068i	$-0.781795\pi$
$643$	−39.2582	−1.54819	−0.774096	+	0.633068i	$0.781795\pi$
$644$	0	0
$645$	21.5959	0.850337
$646$	5.21076	0.205014
$647$	−50.8190	−1.99790	−0.998951	−	0.0457938i	$-0.985418\pi$
$647$	−50.8190	−1.99790	−0.998951	+	0.0457938i	$0.985418\pi$
$648$	1.00000	0.0392837
$649$	−17.1012	−0.671282
$650$	0.795579	0.0312052
$651$	0	0
$652$	12.7829	0.500617
$653$	20.3895	0.797902	0.398951	−	0.916972i	$-0.369374\pi$
$653$	20.3895	0.797902	0.398951	+	0.916972i	$0.369374\pi$
$654$	−2.47529	−0.0967915
$655$	4.57215	0.178649
$656$	−2.67669	−0.104507
$657$	8.02372	0.313035
$658$	0	0
$659$	5.04442	0.196503	0.0982513	−	0.995162i	$-0.468675\pi$
$659$	5.04442	0.196503	0.0982513	+	0.995162i	$0.468675\pi$
$660$	−8.74483	−0.340392
$661$	−4.41518	−0.171730	−0.0858652	−	0.996307i	$-0.527365\pi$
$661$	−4.41518	−0.171730	−0.0858652	+	0.996307i	$0.527365\pi$
$662$	−13.5672	−0.527302
$663$	36.8304	1.43037
$664$	−15.7542	−0.611381
$665$	0	0
$666$	−5.85738	−0.226969
$667$	8.04878	0.311650
$668$	11.6323	0.450066
$669$	−3.62291	−0.140070
$670$	−2.36140	−0.0912288
$671$	17.4897	0.675181
$672$	0	0
$673$	−6.18203	−0.238300	−0.119150	−	0.992876i	$-0.538017\pi$
$673$	−6.18203	−0.238300	−0.119150	+	0.992876i	$0.538017\pi$
$674$	34.8998	1.34429
$675$	−0.112558	−0.00433238
$676$	36.9586	1.42148
$677$	12.1757	0.467950	0.233975	−	0.972243i	$-0.424827\pi$
$677$	12.1757	0.467950	0.233975	+	0.972243i	$0.424827\pi$
$678$	11.8811	0.456291
$679$	0	0
$680$	11.5197	0.441761
$681$	2.21076	0.0847163
$682$	−10.1994	−0.390556
$683$	48.0017	1.83673	0.918367	−	0.395730i	$-0.129508\pi$
$683$	48.0017	1.83673	0.918367	+	0.395730i	$0.129508\pi$
$684$	−1.00000	−0.0382360
$685$	8.21245	0.313781
$686$	0	0
$687$	1.03942	0.0396563
$688$	−9.76855	−0.372422
$689$	57.0267	2.17255
$690$	−15.9937	−0.608868
$691$	−4.42785	−0.168443	−0.0842216	−	0.996447i	$-0.526840\pi$
$691$	−4.42785	−0.168443	−0.0842216	+	0.996447i	$0.526840\pi$
$692$	−10.1126	−0.384422
$693$	0	0
$694$	−24.9556	−0.947301
$695$	49.0568	1.86083
$696$	1.11256	0.0421714
$697$	13.9476	0.528301
$698$	−18.4990	−0.700198
$699$	−9.82233	−0.371515
$700$	0	0
$701$	−19.7241	−0.744970	−0.372485	−	0.928038i	$-0.621494\pi$
$701$	−19.7241	−0.744970	−0.372485	+	0.928038i	$0.621494\pi$
$702$	−7.06814	−0.266770
$703$	5.85738	0.220915
$704$	3.95558	0.149082
$705$	−27.7622	−1.04559
$706$	−13.4359	−0.505666
$707$	0	0
$708$	−4.32331	−0.162480
$709$	26.7529	1.00472	0.502362	−	0.864657i	$-0.332464\pi$
$709$	26.7529	1.00472	0.502362	+	0.864657i	$0.332464\pi$
$710$	30.4389	1.14235
$711$	−15.8667	−0.595049
$712$	−2.67669	−0.100313
$713$	−18.6540	−0.698598
$714$	0	0
$715$	61.8097	2.31155
$716$	−5.06814	−0.189405
$717$	0.225117	0.00840714
$718$	5.82233	0.217287
$719$	−29.1443	−1.08690	−0.543450	−	0.839442i	$-0.682882\pi$
$719$	−29.1443	−1.08690	−0.543450	+	0.839442i	$0.682882\pi$
$720$	−2.21076	−0.0823900
$721$	0	0
$722$	1.00000	0.0372161
$723$	2.65599	0.0987773
$724$	10.8905	0.404741
$725$	−0.125228	−0.00465085
$726$	4.64663	0.172453
$727$	40.7685	1.51202	0.756011	−	0.654559i	$-0.227146\pi$
$727$	40.7685	1.51202	0.756011	+	0.654559i	$0.227146\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−17.7385	−0.656531
$731$	50.9015	1.88266
$732$	4.42151	0.163424
$733$	−1.79227	−0.0661990	−0.0330995	−	0.999452i	$-0.510538\pi$
$733$	−1.79227	−0.0661990	−0.0330995	+	0.999452i	$0.510538\pi$
$734$	9.47529	0.349739
$735$	0	0
$736$	7.23448	0.266666
$737$	4.22512	0.155634
$738$	−2.67669	−0.0985302
$739$	7.79727	0.286827	0.143414	−	0.989663i	$-0.454192\pi$
$739$	7.79727	0.286827	0.143414	+	0.989663i	$0.454192\pi$
$740$	12.9492	0.476024
$741$	7.06814	0.259655
$742$	0	0
$743$	27.3594	1.00372	0.501860	−	0.864949i	$-0.332649\pi$
$743$	27.3594	1.00372	0.501860	+	0.864949i	$0.332649\pi$
$744$	−2.57849	−0.0945320
$745$	5.65465	0.207171
$746$	−25.1757	−0.921748
$747$	−15.7542	−0.576416
$748$	−20.6116	−0.753634
$749$	0	0
$750$	11.3026	0.412713
$751$	−23.3377	−0.851604	−0.425802	−	0.904816i	$-0.640008\pi$
$751$	−23.3377	−0.851604	−0.425802	+	0.904816i	$0.640008\pi$
$752$	12.5578	0.457936
$753$	15.2201	0.554652
$754$	−7.86372	−0.286380
$755$	21.7605	0.791946
$756$	0	0
$757$	6.43285	0.233806	0.116903	−	0.993143i	$-0.462703\pi$
$757$	6.43285	0.233806	0.116903	+	0.993143i	$0.462703\pi$
$758$	−30.1837	−1.09632
$759$	28.6166	1.03872
$760$	2.21076	0.0801925
$761$	−4.52907	−0.164179	−0.0820893	−	0.996625i	$-0.526159\pi$
$761$	−4.52907	−0.164179	−0.0820893	+	0.996625i	$0.526159\pi$
$762$	5.22512	0.189286
$763$	0	0
$764$	5.40082	0.195395
$765$	11.5197	0.416496
$766$	12.5103	0.452017
$767$	30.5578	1.10338
$768$	1.00000	0.0360844
$769$	−35.7305	−1.28847	−0.644237	−	0.764826i	$-0.722825\pi$
$769$	−35.7305	−1.28847	−0.644237	+	0.764826i	$0.722825\pi$
$770$	0	0
$771$	−19.2933	−0.694830
$772$	0.857385	0.0308579
$773$	5.55477	0.199791	0.0998955	−	0.994998i	$-0.468149\pi$
$773$	5.55477	0.199791	0.0998955	+	0.994998i	$0.468149\pi$
$774$	−9.76855	−0.351123
$775$	0.290231	0.0104254
$776$	−12.3233	−0.442381
$777$	0	0
$778$	−15.8036	−0.566587
$779$	2.67669	0.0959022
$780$	15.6259	0.559498
$781$	−54.4626	−1.94883
$782$	−37.6971	−1.34805
$783$	1.11256	0.0397596
$784$	0	0
$785$	−39.1630	−1.39779
$786$	−2.06814	−0.0737681
$787$	−32.2312	−1.14892	−0.574459	−	0.818534i	$-0.694787\pi$
$787$	−32.2312	−1.14892	−0.574459	+	0.818534i	$0.694787\pi$
$788$	−5.51337	−0.196406
$789$	−7.60855	−0.270871
$790$	35.0775	1.24800
$791$	0	0
$792$	3.95558	0.140555
$793$	−31.2519	−1.10979
$794$	17.2645	0.612695
$795$	17.8367	0.632602
$796$	17.0681	0.604964
$797$	29.4165	1.04199	0.520993	−	0.853561i	$-0.325562\pi$
$797$	29.4165	1.04199	0.520993	+	0.853561i	$0.325562\pi$
$798$	0	0
$799$	−65.4356	−2.31494
$800$	−0.112558	−0.00397954
$801$	−2.67669	−0.0945760
$802$	2.96058	0.104542
$803$	31.7385	1.12003
$804$	1.06814	0.0376704
$805$	0	0
$806$	18.2251	0.641952
$807$	−6.99500	−0.246236
$808$	−2.51035	−0.0883137
$809$	−19.5434	−0.687110	−0.343555	−	0.939132i	$-0.611631\pi$
$809$	−19.5434	−0.687110	−0.343555	+	0.939132i	$0.611631\pi$
$810$	−2.21076	−0.0776780
$811$	3.41215	0.119817	0.0599084	−	0.998204i	$-0.480919\pi$
$811$	3.41215	0.119817	0.0599084	+	0.998204i	$0.480919\pi$
$812$	0	0
$813$	2.52471	0.0885454
$814$	−23.1694	−0.812086
$815$	−28.2599	−0.989901
$816$	−5.21076	−0.182413
$817$	9.76855	0.341758
$818$	−20.3708	−0.712247
$819$	0	0
$820$	5.91750	0.206648
$821$	7.48029	0.261064	0.130532	−	0.991444i	$-0.458331\pi$
$821$	7.48029	0.261064	0.130532	+	0.991444i	$0.458331\pi$
$822$	−3.71477	−0.129567
$823$	52.6052	1.83370	0.916852	−	0.399228i	$-0.130722\pi$
$823$	52.6052	1.83370	0.916852	+	0.399228i	$0.130722\pi$
$824$	15.6022	0.543529
$825$	−0.445234	−0.0155011
$826$	0	0
$827$	5.12495	0.178212	0.0891059	−	0.996022i	$-0.471599\pi$
$827$	5.12495	0.178212	0.0891059	+	0.996022i	$0.471599\pi$
$828$	7.23448	0.251415
$829$	−24.0949	−0.836850	−0.418425	−	0.908251i	$-0.637418\pi$
$829$	−24.0949	−0.836850	−0.418425	+	0.908251i	$0.637418\pi$
$830$	34.8287	1.20892
$831$	18.2138	0.631829
$832$	−7.06814	−0.245044
$833$	0	0
$834$	−22.1901	−0.768379
$835$	−25.7161	−0.889942
$836$	−3.95558	−0.136807
$837$	−2.57849	−0.0891256
$838$	−11.1520	−0.385239
$839$	−31.4833	−1.08692	−0.543462	−	0.839434i	$-0.682887\pi$
$839$	−31.4833	−1.08692	−0.543462	+	0.839434i	$0.682887\pi$
$840$	0	0
$841$	−27.7622	−0.957318
$842$	14.3327	0.493937
$843$	−22.0474	−0.759354
$844$	−17.7034	−0.609377
$845$	−81.7065	−2.81079
$846$	12.5578	0.431746
$847$	0	0
$848$	−8.06814	−0.277061
$849$	19.5722	0.671715
$850$	0.586515	0.0201173
$851$	−42.3751	−1.45260
$852$	−13.7685	−0.471703
$853$	26.9680	0.923366	0.461683	−	0.887045i	$-0.347246\pi$
$853$	26.9680	0.923366	0.461683	+	0.887045i	$0.347246\pi$
$854$	0	0
$855$	2.21076	0.0756063
$856$	−19.4152	−0.663597
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	−27.9586	−0.954491
$859$	−53.2105	−1.81552	−0.907759	−	0.419492i	$-0.862208\pi$
$859$	−53.2105	−1.81552	−0.907759	+	0.419492i	$0.862208\pi$
$860$	21.5959	0.736413
$861$	0	0
$862$	24.1901	0.823917
$863$	−28.7892	−0.979997	−0.489999	−	0.871723i	$-0.663003\pi$
$863$	−28.7892	−0.979997	−0.489999	+	0.871723i	$0.663003\pi$
$864$	1.00000	0.0340207
$865$	22.3564	0.760140
$866$	−9.51337	−0.323278
$867$	10.1520	0.344779
$868$	0	0
$869$	−62.7622	−2.12906
$870$	−2.45960	−0.0833881
$871$	−7.54977	−0.255814
$872$	−2.47529	−0.0838239
$873$	−12.3233	−0.417081
$874$	−7.23448	−0.244710
$875$	0	0
$876$	8.02372	0.271096
$877$	40.6590	1.37296	0.686479	−	0.727150i	$-0.259155\pi$
$877$	40.6590	1.37296	0.686479	+	0.727150i	$0.259155\pi$
$878$	−9.11256	−0.307534
$879$	−19.1600	−0.646251
$880$	−8.74483	−0.294788
$881$	22.4690	0.756998	0.378499	−	0.925602i	$-0.376440\pi$
$881$	22.4690	0.756998	0.378499	+	0.925602i	$0.376440\pi$
$882$	0	0
$883$	44.9917	1.51409	0.757045	−	0.653362i	$-0.226642\pi$
$883$	44.9917	1.51409	0.757045	+	0.653362i	$0.226642\pi$
$884$	36.8304	1.23874
$885$	9.55779	0.321282
$886$	12.0030	0.403250
$887$	19.9362	0.669393	0.334696	−	0.942326i	$-0.391366\pi$
$887$	19.9362	0.669393	0.334696	+	0.942326i	$0.391366\pi$
$888$	−5.85738	−0.196561
$889$	0	0
$890$	5.91750	0.198355
$891$	3.95558	0.132517
$892$	−3.62291	−0.121304
$893$	−12.5578	−0.420231
$894$	−2.55779	−0.0855454
$895$	11.2044	0.374522
$896$	0	0
$897$	−51.1343	−1.70732
$898$	2.13762	0.0713332
$899$	−2.86872	−0.0956771
$900$	−0.112558	−0.00375195
$901$	42.0411	1.40059
$902$	−10.5878	−0.352537
$903$	0	0
$904$	11.8811	0.395160
$905$	−24.0762	−0.800319
$906$	−9.84302	−0.327013
$907$	−12.9680	−0.430594	−0.215297	−	0.976549i	$-0.569072\pi$
$907$	−12.9680	−0.430594	−0.215297	+	0.976549i	$0.569072\pi$
$908$	2.21076	0.0733665
$909$	−2.51035	−0.0832630
$910$	0	0
$911$	13.0394	0.432015	0.216008	−	0.976392i	$-0.430696\pi$
$911$	13.0394	0.432015	0.216008	+	0.976392i	$0.430696\pi$
$912$	−1.00000	−0.0331133
$913$	−62.3170	−2.06239
$914$	26.7572	0.885050
$915$	−9.77488	−0.323148
$916$	1.03942	0.0343434
$917$	0	0
$918$	−5.21076	−0.171981
$919$	29.9349	0.987461	0.493730	−	0.869615i	$-0.335633\pi$
$919$	29.9349	0.987461	0.493730	+	0.869615i	$0.335633\pi$
$920$	−15.9937	−0.527296
$921$	5.79227	0.190862
$922$	−13.4295	−0.442278
$923$	97.3180	3.20326
$924$	0	0
$925$	0.659298	0.0216776
$926$	5.24581	0.172388
$927$	15.6022	0.512444
$928$	1.11256	0.0365215
$929$	−6.58285	−0.215976	−0.107988	−	0.994152i	$-0.534441\pi$
$929$	−6.58285	−0.215976	−0.107988	+	0.994152i	$0.534441\pi$
$930$	5.70041	0.186924
$931$	0	0
$932$	−9.82233	−0.321741
$933$	−23.5484	−0.770941
$934$	25.1106	0.821643
$935$	45.5672	1.49021
$936$	−7.06814	−0.231029
$937$	−18.1156	−0.591810	−0.295905	−	0.955217i	$-0.595621\pi$
$937$	−18.1156	−0.591810	−0.295905	+	0.955217i	$0.595621\pi$
$938$	0	0
$939$	3.75919	0.122676
$940$	−27.7622	−0.905504
$941$	−7.53907	−0.245767	−0.122883	−	0.992421i	$-0.539214\pi$
$941$	−7.53907	−0.245767	−0.122883	+	0.992421i	$0.539214\pi$
$942$	17.7148	0.577178
$943$	−19.3644	−0.630592
$944$	−4.32331	−0.140712
$945$	0	0
$946$	−38.6403	−1.25630
$947$	3.26953	0.106246	0.0531228	−	0.998588i	$-0.483083\pi$
$947$	3.26953	0.106246	0.0531228	+	0.998588i	$0.483083\pi$
$948$	−15.8667	−0.515328
$949$	−56.7128	−1.84098
$950$	0.112558	0.00365188
$951$	4.66732	0.151348
$952$	0	0
$953$	−42.4215	−1.37417	−0.687084	−	0.726578i	$-0.741109\pi$
$953$	−42.4215	−1.37417	−0.687084	+	0.726578i	$0.741109\pi$
$954$	−8.06814	−0.261216
$955$	−11.9399	−0.386366
$956$	0.225117	0.00728080
$957$	4.40082	0.142258
$958$	12.6654	0.409199
$959$	0	0
$960$	−2.21076	−0.0713518
$961$	−24.3514	−0.785529
$962$	41.4008	1.33482
$963$	−19.4152	−0.625645
$964$	2.65599	0.0855437
$965$	−1.89547	−0.0610173
$966$	0	0
$967$	13.5277	0.435023	0.217511	−	0.976058i	$-0.430206\pi$
$967$	13.5277	0.435023	0.217511	+	0.976058i	$0.430206\pi$
$968$	4.64663	0.149348
$969$	5.21076	0.167394
$970$	27.2438	0.874747
$971$	54.6747	1.75460	0.877298	−	0.479947i	$-0.159344\pi$
$971$	54.6747	1.75460	0.877298	+	0.479947i	$0.159344\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	6.02070	0.192916
$975$	0.795579	0.0254789
$976$	4.42151	0.141529
$977$	38.2626	1.22413	0.612064	−	0.790808i	$-0.290340\pi$
$977$	38.2626	1.22413	0.612064	+	0.790808i	$0.290340\pi$
$978$	12.7829	0.408752
$979$	−10.5878	−0.338389
$980$	0	0
$981$	−2.47529	−0.0790300
$982$	37.0662	1.18283
$983$	18.9319	0.603833	0.301916	−	0.953334i	$-0.402374\pi$
$983$	18.9319	0.603833	0.301916	+	0.953334i	$0.402374\pi$
$984$	−2.67669	−0.0853296
$985$	12.1887	0.388365
$986$	−5.79727	−0.184623
$987$	0	0
$988$	7.06814	0.224868
$989$	−70.6704	−2.24719
$990$	−8.74483	−0.277929
$991$	28.7809	0.914257	0.457128	−	0.889401i	$-0.348878\pi$
$991$	28.7809	0.914257	0.457128	+	0.889401i	$0.348878\pi$
$992$	−2.57849	−0.0818671
$993$	−13.5672	−0.430541
$994$	0	0
$995$	−37.7335	−1.19623
$996$	−15.7542	−0.499191
$997$	16.3801	0.518764	0.259382	−	0.965775i	$-0.416481\pi$
$997$	16.3801	0.518764	0.259382	+	0.965775i	$0.416481\pi$
$998$	18.8905	0.597967
$999$	−5.85738	−0.185319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bv.1.2		3
7.2	even	3		798.2.j.i.571.2	yes	6
7.4	even	3		798.2.j.i.457.2	✓	6
7.6	odd	2		5586.2.a.bu.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.i.457.2	✓	6	7.4	even	3
798.2.j.i.571.2	yes	6	7.2	even	3
5586.2.a.bu.1.2		3	7.6	odd	2
5586.2.a.bv.1.2		3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.21076 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.21076 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.21076 q^{10} +3.95558 q^{11} +1.00000 q^{12} -7.06814 q^{13} -2.21076 q^{15} +1.00000 q^{16} -5.21076 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.21076 q^{20} +3.95558 q^{22} +7.23448 q^{23} +1.00000 q^{24} -0.112558 q^{25} -7.06814 q^{26} +1.00000 q^{27} +1.11256 q^{29} -2.21076 q^{30} -2.57849 q^{31} +1.00000 q^{32} +3.95558 q^{33} -5.21076 q^{34} +1.00000 q^{36} -5.85738 q^{37} -1.00000 q^{38} -7.06814 q^{39} -2.21076 q^{40} -2.67669 q^{41} -9.76855 q^{43} +3.95558 q^{44} -2.21076 q^{45} +7.23448 q^{46} +12.5578 q^{47} +1.00000 q^{48} -0.112558 q^{50} -5.21076 q^{51} -7.06814 q^{52} -8.06814 q^{53} +1.00000 q^{54} -8.74483 q^{55} -1.00000 q^{57} +1.11256 q^{58} -4.32331 q^{59} -2.21076 q^{60} +4.42151 q^{61} -2.57849 q^{62} +1.00000 q^{64} +15.6259 q^{65} +3.95558 q^{66} +1.06814 q^{67} -5.21076 q^{68} +7.23448 q^{69} -13.7685 q^{71} +1.00000 q^{72} +8.02372 q^{73} -5.85738 q^{74} -0.112558 q^{75} -1.00000 q^{76} -7.06814 q^{78} -15.8667 q^{79} -2.21076 q^{80} +1.00000 q^{81} -2.67669 q^{82} -15.7542 q^{83} +11.5197 q^{85} -9.76855 q^{86} +1.11256 q^{87} +3.95558 q^{88} -2.67669 q^{89} -2.21076 q^{90} +7.23448 q^{92} -2.57849 q^{93} +12.5578 q^{94} +2.21076 q^{95} +1.00000 q^{96} -12.3233 q^{97} +3.95558 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 5 q^{10} + q^{11} + 3 q^{12} - 6 q^{13} - 5 q^{15} + 3 q^{16} - 14 q^{17} + 3 q^{18} - 3 q^{19} - 5 q^{20} + q^{22} - 6 q^{23} + 3 q^{24} + 4 q^{25} - 6 q^{26} + 3 q^{27} - q^{29} - 5 q^{30} - 11 q^{31} + 3 q^{32} + q^{33} - 14 q^{34} + 3 q^{36} - 4 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 14 q^{41} + 6 q^{43} + q^{44} - 5 q^{45} - 6 q^{46} + 4 q^{47} + 3 q^{48} + 4 q^{50} - 14 q^{51} - 6 q^{52} - 9 q^{53} + 3 q^{54} - 17 q^{55} - 3 q^{57} - q^{58} - 7 q^{59} - 5 q^{60} + 10 q^{61} - 11 q^{62} + 3 q^{64} - 2 q^{65} + q^{66} - 12 q^{67} - 14 q^{68} - 6 q^{69} - 6 q^{71} + 3 q^{72} - 2 q^{73} - 4 q^{74} + 4 q^{75} - 3 q^{76} - 6 q^{78} - 15 q^{79} - 5 q^{80} + 3 q^{81} - 14 q^{82} - 19 q^{83} + 34 q^{85} + 6 q^{86} - q^{87} + q^{88} - 14 q^{89} - 5 q^{90} - 6 q^{92} - 11 q^{93} + 4 q^{94} + 5 q^{95} + 3 q^{96} - 31 q^{97} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 5 * q^10 + q^11 + 3 * q^12 - 6 * q^13 - 5 * q^15 + 3 * q^16 - 14 * q^17 + 3 * q^18 - 3 * q^19 - 5 * q^20 + q^22 - 6 * q^23 + 3 * q^24 + 4 * q^25 - 6 * q^26 + 3 * q^27 - q^29 - 5 * q^30 - 11 * q^31 + 3 * q^32 + q^33 - 14 * q^34 + 3 * q^36 - 4 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 14 * q^41 + 6 * q^43 + q^44 - 5 * q^45 - 6 * q^46 + 4 * q^47 + 3 * q^48 + 4 * q^50 - 14 * q^51 - 6 * q^52 - 9 * q^53 + 3 * q^54 - 17 * q^55 - 3 * q^57 - q^58 - 7 * q^59 - 5 * q^60 + 10 * q^61 - 11 * q^62 + 3 * q^64 - 2 * q^65 + q^66 - 12 * q^67 - 14 * q^68 - 6 * q^69 - 6 * q^71 + 3 * q^72 - 2 * q^73 - 4 * q^74 + 4 * q^75 - 3 * q^76 - 6 * q^78 - 15 * q^79 - 5 * q^80 + 3 * q^81 - 14 * q^82 - 19 * q^83 + 34 * q^85 + 6 * q^86 - q^87 + q^88 - 14 * q^89 - 5 * q^90 - 6 * q^92 - 11 * q^93 + 4 * q^94 + 5 * q^95 + 3 * q^96 - 31 * q^97 + q^99

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