LMFDB - Embedded newform 5390.2.a.bs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5390,2,Mod(1,5390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5390, 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("5390.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5390.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:	$43.0393666895$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	5390.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.73205 q^{6} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.73205 q^{6} +1.00000 q^{8} +4.46410 q^{9} +1.00000 q^{10} +1.00000 q^{11} -2.73205 q^{12} +1.46410 q^{13} -2.73205 q^{15} +1.00000 q^{16} +3.46410 q^{17} +4.46410 q^{18} -6.73205 q^{19} +1.00000 q^{20} +1.00000 q^{22} -8.19615 q^{23} -2.73205 q^{24} +1.00000 q^{25} +1.46410 q^{26} -4.00000 q^{27} -4.73205 q^{29} -2.73205 q^{30} -2.00000 q^{31} +1.00000 q^{32} -2.73205 q^{33} +3.46410 q^{34} +4.46410 q^{36} +0.732051 q^{37} -6.73205 q^{38} -4.00000 q^{39} +1.00000 q^{40} +2.19615 q^{41} +2.00000 q^{43} +1.00000 q^{44} +4.46410 q^{45} -8.19615 q^{46} -6.92820 q^{47} -2.73205 q^{48} +1.00000 q^{50} -9.46410 q^{51} +1.46410 q^{52} -7.26795 q^{53} -4.00000 q^{54} +1.00000 q^{55} +18.3923 q^{57} -4.73205 q^{58} -6.92820 q^{59} -2.73205 q^{60} +4.92820 q^{61} -2.00000 q^{62} +1.00000 q^{64} +1.46410 q^{65} -2.73205 q^{66} -4.00000 q^{67} +3.46410 q^{68} +22.3923 q^{69} +9.46410 q^{71} +4.46410 q^{72} +14.3923 q^{73} +0.732051 q^{74} -2.73205 q^{75} -6.73205 q^{76} -4.00000 q^{78} -12.1962 q^{79} +1.00000 q^{80} -2.46410 q^{81} +2.19615 q^{82} +16.3923 q^{83} +3.46410 q^{85} +2.00000 q^{86} +12.9282 q^{87} +1.00000 q^{88} -3.46410 q^{89} +4.46410 q^{90} -8.19615 q^{92} +5.46410 q^{93} -6.92820 q^{94} -6.73205 q^{95} -2.73205 q^{96} -14.5885 q^{97} +4.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 4 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{18} - 10 q^{19} + 2 q^{20} + 2 q^{22} - 6 q^{23} - 2 q^{24} + 2 q^{25} - 4 q^{26} - 8 q^{27} - 6 q^{29} - 2 q^{30} - 4 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{36} - 2 q^{37} - 10 q^{38} - 8 q^{39} + 2 q^{40} - 6 q^{41} + 4 q^{43} + 2 q^{44} + 2 q^{45} - 6 q^{46} - 2 q^{48} + 2 q^{50} - 12 q^{51} - 4 q^{52} - 18 q^{53} - 8 q^{54} + 2 q^{55} + 16 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 4 q^{62} + 2 q^{64} - 4 q^{65} - 2 q^{66} - 8 q^{67} + 24 q^{69} + 12 q^{71} + 2 q^{72} + 8 q^{73} - 2 q^{74} - 2 q^{75} - 10 q^{76} - 8 q^{78} - 14 q^{79} + 2 q^{80} + 2 q^{81} - 6 q^{82} + 12 q^{83} + 4 q^{86} + 12 q^{87} + 2 q^{88} + 2 q^{90} - 6 q^{92} + 4 q^{93} - 10 q^{95} - 2 q^{96} + 2 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 4 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^18 - 10 * q^19 + 2 * q^20 + 2 * q^22 - 6 * q^23 - 2 * q^24 + 2 * q^25 - 4 * q^26 - 8 * q^27 - 6 * q^29 - 2 * q^30 - 4 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^36 - 2 * q^37 - 10 * q^38 - 8 * q^39 + 2 * q^40 - 6 * q^41 + 4 * q^43 + 2 * q^44 + 2 * q^45 - 6 * q^46 - 2 * q^48 + 2 * q^50 - 12 * q^51 - 4 * q^52 - 18 * q^53 - 8 * q^54 + 2 * q^55 + 16 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 4 * q^62 + 2 * q^64 - 4 * q^65 - 2 * q^66 - 8 * q^67 + 24 * q^69 + 12 * q^71 + 2 * q^72 + 8 * q^73 - 2 * q^74 - 2 * q^75 - 10 * q^76 - 8 * q^78 - 14 * q^79 + 2 * q^80 + 2 * q^81 - 6 * q^82 + 12 * q^83 + 4 * q^86 + 12 * q^87 + 2 * q^88 + 2 * q^90 - 6 * q^92 + 4 * q^93 - 10 * q^95 - 2 * q^96 + 2 * q^97 + 2 * 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
$3$	−2.73205	−1.57735	−0.788675	−	0.614810i	$-0.789233\pi$
$3$	−2.73205	−1.57735	−0.788675	+	0.614810i	$0.789233\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.73205	−1.11536
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	4.46410	1.48803
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.73205	−0.788675
$13$	1.46410	0.406069	0.203034	−	0.979172i	$-0.434920\pi$
$13$	1.46410	0.406069	0.203034	+	0.979172i	$0.434920\pi$
$14$	0	0
$15$	−2.73205	−0.705412
$16$	1.00000	0.250000
$17$	3.46410	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$18$	4.46410	1.05220
$19$	−6.73205	−1.54444	−0.772219	−	0.635356i	$-0.780853\pi$
$19$	−6.73205	−1.54444	−0.772219	+	0.635356i	$0.780853\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	1.00000	0.213201
$23$	−8.19615	−1.70902	−0.854508	−	0.519438i	$-0.826141\pi$
$23$	−8.19615	−1.70902	−0.854508	+	0.519438i	$0.826141\pi$
$24$	−2.73205	−0.557678
$25$	1.00000	0.200000
$26$	1.46410	0.287134
$27$	−4.00000	−0.769800
$28$	0	0
$29$	−4.73205	−0.878720	−0.439360	−	0.898311i	$-0.644795\pi$
$29$	−4.73205	−0.878720	−0.439360	+	0.898311i	$0.644795\pi$
$30$	−2.73205	−0.498802
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	−2.73205	−0.475589
$34$	3.46410	0.594089
$35$	0	0
$36$	4.46410	0.744017
$37$	0.732051	0.120348	0.0601742	−	0.998188i	$-0.480834\pi$
$37$	0.732051	0.120348	0.0601742	+	0.998188i	$0.480834\pi$
$38$	−6.73205	−1.09208
$39$	−4.00000	−0.640513
$40$	1.00000	0.158114
$41$	2.19615	0.342981	0.171491	−	0.985186i	$-0.445142\pi$
$41$	2.19615	0.342981	0.171491	+	0.985186i	$0.445142\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	1.00000	0.150756
$45$	4.46410	0.665469
$46$	−8.19615	−1.20846
$47$	−6.92820	−1.01058	−0.505291	−	0.862949i	$-0.668615\pi$
$47$	−6.92820	−1.01058	−0.505291	+	0.862949i	$0.668615\pi$
$48$	−2.73205	−0.394338
$49$	0	0
$50$	1.00000	0.141421
$51$	−9.46410	−1.32524
$52$	1.46410	0.203034
$53$	−7.26795	−0.998330	−0.499165	−	0.866507i	$-0.666360\pi$
$53$	−7.26795	−0.998330	−0.499165	+	0.866507i	$0.666360\pi$
$54$	−4.00000	−0.544331
$55$	1.00000	0.134840
$56$	0	0
$57$	18.3923	2.43612
$58$	−4.73205	−0.621349
$59$	−6.92820	−0.901975	−0.450988	−	0.892530i	$-0.648928\pi$
$59$	−6.92820	−0.901975	−0.450988	+	0.892530i	$0.648928\pi$
$60$	−2.73205	−0.352706
$61$	4.92820	0.630992	0.315496	−	0.948927i	$-0.397829\pi$
$61$	4.92820	0.630992	0.315496	+	0.948927i	$0.397829\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	1.46410	0.181599
$66$	−2.73205	−0.336292
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	3.46410	0.420084
$69$	22.3923	2.69572
$70$	0	0
$71$	9.46410	1.12318	0.561591	−	0.827415i	$-0.310189\pi$
$71$	9.46410	1.12318	0.561591	+	0.827415i	$0.310189\pi$
$72$	4.46410	0.526099
$73$	14.3923	1.68449	0.842246	−	0.539093i	$-0.181233\pi$
$73$	14.3923	1.68449	0.842246	+	0.539093i	$0.181233\pi$
$74$	0.732051	0.0850992
$75$	−2.73205	−0.315470
$76$	−6.73205	−0.772219
$77$	0	0
$78$	−4.00000	−0.452911
$79$	−12.1962	−1.37217	−0.686087	−	0.727519i	$-0.740673\pi$
$79$	−12.1962	−1.37217	−0.686087	+	0.727519i	$0.740673\pi$
$80$	1.00000	0.111803
$81$	−2.46410	−0.273789
$82$	2.19615	0.242524
$83$	16.3923	1.79929	0.899645	−	0.436623i	$-0.143826\pi$
$83$	16.3923	1.79929	0.899645	+	0.436623i	$0.143826\pi$
$84$	0	0
$85$	3.46410	0.375735
$86$	2.00000	0.215666
$87$	12.9282	1.38605
$88$	1.00000	0.106600
$89$	−3.46410	−0.367194	−0.183597	−	0.983002i	$-0.558774\pi$
$89$	−3.46410	−0.367194	−0.183597	+	0.983002i	$0.558774\pi$
$90$	4.46410	0.470558
$91$	0	0
$92$	−8.19615	−0.854508
$93$	5.46410	0.566601
$94$	−6.92820	−0.714590
$95$	−6.73205	−0.690694
$96$	−2.73205	−0.278839
$97$	−14.5885	−1.48123	−0.740617	−	0.671928i	$-0.765467\pi$
$97$	−14.5885	−1.48123	−0.740617	+	0.671928i	$0.765467\pi$
$98$	0	0
$99$	4.46410	0.448659
$100$	1.00000	0.100000
$101$	7.85641	0.781742	0.390871	−	0.920446i	$-0.372174\pi$
$101$	7.85641	0.781742	0.390871	+	0.920446i	$0.372174\pi$
$102$	−9.46410	−0.937086
$103$	−12.3923	−1.22105	−0.610525	−	0.791997i	$-0.709042\pi$
$103$	−12.3923	−1.22105	−0.610525	+	0.791997i	$0.709042\pi$
$104$	1.46410	0.143567
$105$	0	0
$106$	−7.26795	−0.705926
$107$	7.85641	0.759507	0.379754	−	0.925088i	$-0.376009\pi$
$107$	7.85641	0.759507	0.379754	+	0.925088i	$0.376009\pi$
$108$	−4.00000	−0.384900
$109$	−15.6603	−1.49998	−0.749990	−	0.661449i	$-0.769942\pi$
$109$	−15.6603	−1.49998	−0.749990	+	0.661449i	$0.769942\pi$
$110$	1.00000	0.0953463
$111$	−2.00000	−0.189832
$112$	0	0
$113$	7.85641	0.739069	0.369534	−	0.929217i	$-0.379517\pi$
$113$	7.85641	0.739069	0.369534	+	0.929217i	$0.379517\pi$
$114$	18.3923	1.72260
$115$	−8.19615	−0.764295
$116$	−4.73205	−0.439360
$117$	6.53590	0.604244
$118$	−6.92820	−0.637793
$119$	0	0
$120$	−2.73205	−0.249401
$121$	1.00000	0.0909091
$122$	4.92820	0.446179
$123$	−6.00000	−0.541002
$124$	−2.00000	−0.179605
$125$	1.00000	0.0894427
$126$	0	0
$127$	1.07180	0.0951066	0.0475533	−	0.998869i	$-0.484858\pi$
$127$	1.07180	0.0951066	0.0475533	+	0.998869i	$0.484858\pi$
$128$	1.00000	0.0883883
$129$	−5.46410	−0.481087
$130$	1.46410	0.128410
$131$	−5.66025	−0.494539	−0.247269	−	0.968947i	$-0.579533\pi$
$131$	−5.66025	−0.494539	−0.247269	+	0.968947i	$0.579533\pi$
$132$	−2.73205	−0.237795
$133$	0	0
$134$	−4.00000	−0.345547
$135$	−4.00000	−0.344265
$136$	3.46410	0.297044
$137$	−0.928203	−0.0793018	−0.0396509	−	0.999214i	$-0.512625\pi$
$137$	−0.928203	−0.0793018	−0.0396509	+	0.999214i	$0.512625\pi$
$138$	22.3923	1.90616
$139$	−13.6603	−1.15865	−0.579324	−	0.815097i	$-0.696683\pi$
$139$	−13.6603	−1.15865	−0.579324	+	0.815097i	$0.696683\pi$
$140$	0	0
$141$	18.9282	1.59404
$142$	9.46410	0.794210
$143$	1.46410	0.122434
$144$	4.46410	0.372008
$145$	−4.73205	−0.392975
$146$	14.3923	1.19112
$147$	0	0
$148$	0.732051	0.0601742
$149$	−7.26795	−0.595414	−0.297707	−	0.954657i	$-0.596222\pi$
$149$	−7.26795	−0.595414	−0.297707	+	0.954657i	$0.596222\pi$
$150$	−2.73205	−0.223071
$151$	11.1244	0.905287	0.452644	−	0.891692i	$-0.350481\pi$
$151$	11.1244	0.905287	0.452644	+	0.891692i	$0.350481\pi$
$152$	−6.73205	−0.546041
$153$	15.4641	1.25020
$154$	0	0
$155$	−2.00000	−0.160644
$156$	−4.00000	−0.320256
$157$	−4.53590	−0.362004	−0.181002	−	0.983483i	$-0.557934\pi$
$157$	−4.53590	−0.362004	−0.181002	+	0.983483i	$0.557934\pi$
$158$	−12.1962	−0.970274
$159$	19.8564	1.57472
$160$	1.00000	0.0790569
$161$	0	0
$162$	−2.46410	−0.193598
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.19615	0.171491
$165$	−2.73205	−0.212690
$166$	16.3923	1.27229
$167$	−13.8564	−1.07224	−0.536120	−	0.844141i	$-0.680111\pi$
$167$	−13.8564	−1.07224	−0.536120	+	0.844141i	$0.680111\pi$
$168$	0	0
$169$	−10.8564	−0.835108
$170$	3.46410	0.265684
$171$	−30.0526	−2.29818
$172$	2.00000	0.152499
$173$	−0.928203	−0.0705700	−0.0352850	−	0.999377i	$-0.511234\pi$
$173$	−0.928203	−0.0705700	−0.0352850	+	0.999377i	$0.511234\pi$
$174$	12.9282	0.980085
$175$	0	0
$176$	1.00000	0.0753778
$177$	18.9282	1.42273
$178$	−3.46410	−0.259645
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	4.46410	0.332734
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	0	0
$183$	−13.4641	−0.995295
$184$	−8.19615	−0.604228
$185$	0.732051	0.0538214
$186$	5.46410	0.400647
$187$	3.46410	0.253320
$188$	−6.92820	−0.505291
$189$	0	0
$190$	−6.73205	−0.488394
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	−2.73205	−0.197169
$193$	12.3923	0.892018	0.446009	−	0.895029i	$-0.352845\pi$
$193$	12.3923	0.892018	0.446009	+	0.895029i	$0.352845\pi$
$194$	−14.5885	−1.04739
$195$	−4.00000	−0.286446
$196$	0	0
$197$	−24.2487	−1.72765	−0.863825	−	0.503793i	$-0.831938\pi$
$197$	−24.2487	−1.72765	−0.863825	+	0.503793i	$0.831938\pi$
$198$	4.46410	0.317250
$199$	−2.92820	−0.207575	−0.103787	−	0.994600i	$-0.533096\pi$
$199$	−2.92820	−0.207575	−0.103787	+	0.994600i	$0.533096\pi$
$200$	1.00000	0.0707107
$201$	10.9282	0.770816
$202$	7.85641	0.552775
$203$	0	0
$204$	−9.46410	−0.662620
$205$	2.19615	0.153386
$206$	−12.3923	−0.863413
$207$	−36.5885	−2.54307
$208$	1.46410	0.101517
$209$	−6.73205	−0.465666
$210$	0	0
$211$	26.9282	1.85381	0.926907	−	0.375291i	$-0.122457\pi$
$211$	26.9282	1.85381	0.926907	+	0.375291i	$0.122457\pi$
$212$	−7.26795	−0.499165
$213$	−25.8564	−1.77165
$214$	7.85641	0.537053
$215$	2.00000	0.136399
$216$	−4.00000	−0.272166
$217$	0	0
$218$	−15.6603	−1.06065
$219$	−39.3205	−2.65703
$220$	1.00000	0.0674200
$221$	5.07180	0.341166
$222$	−2.00000	−0.134231
$223$	25.4641	1.70520	0.852601	−	0.522562i	$-0.175024\pi$
$223$	25.4641	1.70520	0.852601	+	0.522562i	$0.175024\pi$
$224$	0	0
$225$	4.46410	0.297607
$226$	7.85641	0.522600
$227$	−6.92820	−0.459841	−0.229920	−	0.973209i	$-0.573847\pi$
$227$	−6.92820	−0.459841	−0.229920	+	0.973209i	$0.573847\pi$
$228$	18.3923	1.21806
$229$	−24.3923	−1.61189	−0.805944	−	0.591991i	$-0.798342\pi$
$229$	−24.3923	−1.61189	−0.805944	+	0.591991i	$0.798342\pi$
$230$	−8.19615	−0.540438
$231$	0	0
$232$	−4.73205	−0.310674
$233$	−7.85641	−0.514690	−0.257345	−	0.966320i	$-0.582848\pi$
$233$	−7.85641	−0.514690	−0.257345	+	0.966320i	$0.582848\pi$
$234$	6.53590	0.427265
$235$	−6.92820	−0.451946
$236$	−6.92820	−0.450988
$237$	33.3205	2.16440
$238$	0	0
$239$	1.26795	0.0820168	0.0410084	−	0.999159i	$-0.486943\pi$
$239$	1.26795	0.0820168	0.0410084	+	0.999159i	$0.486943\pi$
$240$	−2.73205	−0.176353
$241$	−3.26795	−0.210507	−0.105254	−	0.994445i	$-0.533565\pi$
$241$	−3.26795	−0.210507	−0.105254	+	0.994445i	$0.533565\pi$
$242$	1.00000	0.0642824
$243$	18.7321	1.20166
$244$	4.92820	0.315496
$245$	0	0
$246$	−6.00000	−0.382546
$247$	−9.85641	−0.627148
$248$	−2.00000	−0.127000
$249$	−44.7846	−2.83811
$250$	1.00000	0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	−8.19615	−0.515288
$254$	1.07180	0.0672505
$255$	−9.46410	−0.592665
$256$	1.00000	0.0625000
$257$	23.6603	1.47589	0.737943	−	0.674863i	$-0.235797\pi$
$257$	23.6603	1.47589	0.737943	+	0.674863i	$0.235797\pi$
$258$	−5.46410	−0.340180
$259$	0	0
$260$	1.46410	0.0907997
$261$	−21.1244	−1.30756
$262$	−5.66025	−0.349692
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−2.73205	−0.168146
$265$	−7.26795	−0.446467
$266$	0	0
$267$	9.46410	0.579194
$268$	−4.00000	−0.244339
$269$	−28.3923	−1.73111	−0.865555	−	0.500814i	$-0.833034\pi$
$269$	−28.3923	−1.73111	−0.865555	+	0.500814i	$0.833034\pi$
$270$	−4.00000	−0.243432
$271$	−0.392305	−0.0238308	−0.0119154	−	0.999929i	$-0.503793\pi$
$271$	−0.392305	−0.0238308	−0.0119154	+	0.999929i	$0.503793\pi$
$272$	3.46410	0.210042
$273$	0	0
$274$	−0.928203	−0.0560748
$275$	1.00000	0.0603023
$276$	22.3923	1.34786
$277$	7.07180	0.424903	0.212452	−	0.977172i	$-0.431855\pi$
$277$	7.07180	0.424903	0.212452	+	0.977172i	$0.431855\pi$
$278$	−13.6603	−0.819288
$279$	−8.92820	−0.534518
$280$	0	0
$281$	22.3923	1.33581	0.667906	−	0.744245i	$-0.267191\pi$
$281$	22.3923	1.33581	0.667906	+	0.744245i	$0.267191\pi$
$282$	18.9282	1.12716
$283$	31.7128	1.88513	0.942566	−	0.334021i	$-0.108406\pi$
$283$	31.7128	1.88513	0.942566	+	0.334021i	$0.108406\pi$
$284$	9.46410	0.561591
$285$	18.3923	1.08947
$286$	1.46410	0.0865741
$287$	0	0
$288$	4.46410	0.263050
$289$	−5.00000	−0.294118
$290$	−4.73205	−0.277876
$291$	39.8564	2.33642
$292$	14.3923	0.842246
$293$	−21.4641	−1.25395	−0.626973	−	0.779041i	$-0.715706\pi$
$293$	−21.4641	−1.25395	−0.626973	+	0.779041i	$0.715706\pi$
$294$	0	0
$295$	−6.92820	−0.403376
$296$	0.732051	0.0425496
$297$	−4.00000	−0.232104
$298$	−7.26795	−0.421021
$299$	−12.0000	−0.693978
$300$	−2.73205	−0.157735
$301$	0	0
$302$	11.1244	0.640135
$303$	−21.4641	−1.23308
$304$	−6.73205	−0.386110
$305$	4.92820	0.282188
$306$	15.4641	0.884024
$307$	−24.3923	−1.39214	−0.696071	−	0.717973i	$-0.745070\pi$
$307$	−24.3923	−1.39214	−0.696071	+	0.717973i	$0.745070\pi$
$308$	0	0
$309$	33.8564	1.92602
$310$	−2.00000	−0.113592
$311$	−24.9282	−1.41355	−0.706774	−	0.707439i	$-0.749850\pi$
$311$	−24.9282	−1.41355	−0.706774	+	0.707439i	$0.749850\pi$
$312$	−4.00000	−0.226455
$313$	−22.1962	−1.25460	−0.627300	−	0.778777i	$-0.715840\pi$
$313$	−22.1962	−1.25460	−0.627300	+	0.778777i	$0.715840\pi$
$314$	−4.53590	−0.255976
$315$	0	0
$316$	−12.1962	−0.686087
$317$	30.5885	1.71802	0.859009	−	0.511960i	$-0.171080\pi$
$317$	30.5885	1.71802	0.859009	+	0.511960i	$0.171080\pi$
$318$	19.8564	1.11349
$319$	−4.73205	−0.264944
$320$	1.00000	0.0559017
$321$	−21.4641	−1.19801
$322$	0	0
$323$	−23.3205	−1.29759
$324$	−2.46410	−0.136895
$325$	1.46410	0.0812137
$326$	−4.00000	−0.221540
$327$	42.7846	2.36599
$328$	2.19615	0.121262
$329$	0	0
$330$	−2.73205	−0.150394
$331$	−18.7846	−1.03250	−0.516248	−	0.856439i	$-0.672672\pi$
$331$	−18.7846	−1.03250	−0.516248	+	0.856439i	$0.672672\pi$
$332$	16.3923	0.899645
$333$	3.26795	0.179083
$334$	−13.8564	−0.758189
$335$	−4.00000	−0.218543
$336$	0	0
$337$	22.7846	1.24116	0.620578	−	0.784144i	$-0.286898\pi$
$337$	22.7846	1.24116	0.620578	+	0.784144i	$0.286898\pi$
$338$	−10.8564	−0.590511
$339$	−21.4641	−1.16577
$340$	3.46410	0.187867
$341$	−2.00000	−0.108306
$342$	−30.0526	−1.62506
$343$	0	0
$344$	2.00000	0.107833
$345$	22.3923	1.20556
$346$	−0.928203	−0.0499005
$347$	−23.0718	−1.23856	−0.619279	−	0.785171i	$-0.712575\pi$
$347$	−23.0718	−1.23856	−0.619279	+	0.785171i	$0.712575\pi$
$348$	12.9282	0.693024
$349$	5.60770	0.300173	0.150087	−	0.988673i	$-0.452045\pi$
$349$	5.60770	0.300173	0.150087	+	0.988673i	$0.452045\pi$
$350$	0	0
$351$	−5.85641	−0.312592
$352$	1.00000	0.0533002
$353$	−14.1962	−0.755585	−0.377792	−	0.925890i	$-0.623317\pi$
$353$	−14.1962	−0.755585	−0.377792	+	0.925890i	$0.623317\pi$
$354$	18.9282	1.00602
$355$	9.46410	0.502302
$356$	−3.46410	−0.183597
$357$	0	0
$358$	−6.00000	−0.317110
$359$	−34.0526	−1.79723	−0.898613	−	0.438743i	$-0.855424\pi$
$359$	−34.0526	−1.79723	−0.898613	+	0.438743i	$0.855424\pi$
$360$	4.46410	0.235279
$361$	26.3205	1.38529
$362$	−14.0000	−0.735824
$363$	−2.73205	−0.143395
$364$	0	0
$365$	14.3923	0.753328
$366$	−13.4641	−0.703780
$367$	−12.3923	−0.646873	−0.323437	−	0.946250i	$-0.604838\pi$
$367$	−12.3923	−0.646873	−0.323437	+	0.946250i	$0.604838\pi$
$368$	−8.19615	−0.427254
$369$	9.80385	0.510368
$370$	0.732051	0.0380575
$371$	0	0
$372$	5.46410	0.283300
$373$	18.3923	0.952317	0.476159	−	0.879359i	$-0.342029\pi$
$373$	18.3923	0.952317	0.476159	+	0.879359i	$0.342029\pi$
$374$	3.46410	0.179124
$375$	−2.73205	−0.141082
$376$	−6.92820	−0.357295
$377$	−6.92820	−0.356821
$378$	0	0
$379$	6.14359	0.315575	0.157788	−	0.987473i	$-0.449564\pi$
$379$	6.14359	0.315575	0.157788	+	0.987473i	$0.449564\pi$
$380$	−6.73205	−0.345347
$381$	−2.92820	−0.150016
$382$	−12.0000	−0.613973
$383$	33.4641	1.70994	0.854968	−	0.518681i	$-0.173577\pi$
$383$	33.4641	1.70994	0.854968	+	0.518681i	$0.173577\pi$
$384$	−2.73205	−0.139419
$385$	0	0
$386$	12.3923	0.630752
$387$	8.92820	0.453846
$388$	−14.5885	−0.740617
$389$	−1.60770	−0.0815134	−0.0407567	−	0.999169i	$-0.512977\pi$
$389$	−1.60770	−0.0815134	−0.0407567	+	0.999169i	$0.512977\pi$
$390$	−4.00000	−0.202548
$391$	−28.3923	−1.43586
$392$	0	0
$393$	15.4641	0.780061
$394$	−24.2487	−1.22163
$395$	−12.1962	−0.613655
$396$	4.46410	0.224330
$397$	−30.3923	−1.52535	−0.762673	−	0.646784i	$-0.776113\pi$
$397$	−30.3923	−1.52535	−0.762673	+	0.646784i	$0.776113\pi$
$398$	−2.92820	−0.146778
$399$	0	0
$400$	1.00000	0.0500000
$401$	2.53590	0.126637	0.0633184	−	0.997993i	$-0.479832\pi$
$401$	2.53590	0.126637	0.0633184	+	0.997993i	$0.479832\pi$
$402$	10.9282	0.545049
$403$	−2.92820	−0.145864
$404$	7.85641	0.390871
$405$	−2.46410	−0.122442
$406$	0	0
$407$	0.732051	0.0362864
$408$	−9.46410	−0.468543
$409$	−10.8756	−0.537766	−0.268883	−	0.963173i	$-0.586654\pi$
$409$	−10.8756	−0.537766	−0.268883	+	0.963173i	$0.586654\pi$
$410$	2.19615	0.108460
$411$	2.53590	0.125087
$412$	−12.3923	−0.610525
$413$	0	0
$414$	−36.5885	−1.79822
$415$	16.3923	0.804667
$416$	1.46410	0.0717835
$417$	37.3205	1.82759
$418$	−6.73205	−0.329275
$419$	−30.9282	−1.51094	−0.755471	−	0.655182i	$-0.772592\pi$
$419$	−30.9282	−1.51094	−0.755471	+	0.655182i	$0.772592\pi$
$420$	0	0
$421$	−35.8564	−1.74753	−0.873767	−	0.486344i	$-0.838330\pi$
$421$	−35.8564	−1.74753	−0.873767	+	0.486344i	$0.838330\pi$
$422$	26.9282	1.31084
$423$	−30.9282	−1.50378
$424$	−7.26795	−0.352963
$425$	3.46410	0.168034
$426$	−25.8564	−1.25275
$427$	0	0
$428$	7.85641	0.379754
$429$	−4.00000	−0.193122
$430$	2.00000	0.0964486
$431$	3.12436	0.150495	0.0752475	−	0.997165i	$-0.476025\pi$
$431$	3.12436	0.150495	0.0752475	+	0.997165i	$0.476025\pi$
$432$	−4.00000	−0.192450
$433$	18.1962	0.874451	0.437226	−	0.899352i	$-0.355961\pi$
$433$	18.1962	0.874451	0.437226	+	0.899352i	$0.355961\pi$
$434$	0	0
$435$	12.9282	0.619860
$436$	−15.6603	−0.749990
$437$	55.1769	2.63947
$438$	−39.3205	−1.87881
$439$	−26.2487	−1.25278	−0.626391	−	0.779509i	$-0.715469\pi$
$439$	−26.2487	−1.25278	−0.626391	+	0.779509i	$0.715469\pi$
$440$	1.00000	0.0476731
$441$	0	0
$442$	5.07180	0.241241
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	−2.00000	−0.0949158
$445$	−3.46410	−0.164214
$446$	25.4641	1.20576
$447$	19.8564	0.939176
$448$	0	0
$449$	40.3923	1.90623	0.953115	−	0.302607i	$-0.0978570\pi$
$449$	40.3923	1.90623	0.953115	+	0.302607i	$0.0978570\pi$
$450$	4.46410	0.210440
$451$	2.19615	0.103413
$452$	7.85641	0.369534
$453$	−30.3923	−1.42796
$454$	−6.92820	−0.325157
$455$	0	0
$456$	18.3923	0.861299
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	−24.3923	−1.13978
$459$	−13.8564	−0.646762
$460$	−8.19615	−0.382148
$461$	−22.3923	−1.04291	−0.521457	−	0.853278i	$-0.674611\pi$
$461$	−22.3923	−1.04291	−0.521457	+	0.853278i	$0.674611\pi$
$462$	0	0
$463$	27.5167	1.27881	0.639404	−	0.768871i	$-0.279181\pi$
$463$	27.5167	1.27881	0.639404	+	0.768871i	$0.279181\pi$
$464$	−4.73205	−0.219680
$465$	5.46410	0.253392
$466$	−7.85641	−0.363941
$467$	34.0526	1.57576	0.787882	−	0.615826i	$-0.211178\pi$
$467$	34.0526	1.57576	0.787882	+	0.615826i	$0.211178\pi$
$468$	6.53590	0.302122
$469$	0	0
$470$	−6.92820	−0.319574
$471$	12.3923	0.571007
$472$	−6.92820	−0.318896
$473$	2.00000	0.0919601
$474$	33.3205	1.53046
$475$	−6.73205	−0.308888
$476$	0	0
$477$	−32.4449	−1.48555
$478$	1.26795	0.0579946
$479$	32.7846	1.49797	0.748984	−	0.662589i	$-0.230542\pi$
$479$	32.7846	1.49797	0.748984	+	0.662589i	$0.230542\pi$
$480$	−2.73205	−0.124700
$481$	1.07180	0.0488697
$482$	−3.26795	−0.148851
$483$	0	0
$484$	1.00000	0.0454545
$485$	−14.5885	−0.662428
$486$	18.7321	0.849703
$487$	4.19615	0.190146	0.0950729	−	0.995470i	$-0.469692\pi$
$487$	4.19615	0.190146	0.0950729	+	0.995470i	$0.469692\pi$
$488$	4.92820	0.223089
$489$	10.9282	0.494190
$490$	0	0
$491$	−27.7128	−1.25066	−0.625331	−	0.780360i	$-0.715036\pi$
$491$	−27.7128	−1.25066	−0.625331	+	0.780360i	$0.715036\pi$
$492$	−6.00000	−0.270501
$493$	−16.3923	−0.738272
$494$	−9.85641	−0.443461
$495$	4.46410	0.200646
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−44.7846	−2.00685
$499$	12.1436	0.543622	0.271811	−	0.962351i	$-0.412377\pi$
$499$	12.1436	0.543622	0.271811	+	0.962351i	$0.412377\pi$
$500$	1.00000	0.0447214
$501$	37.8564	1.69130
$502$	−12.0000	−0.535586
$503$	−8.78461	−0.391686	−0.195843	−	0.980635i	$-0.562744\pi$
$503$	−8.78461	−0.391686	−0.195843	+	0.980635i	$0.562744\pi$
$504$	0	0
$505$	7.85641	0.349605
$506$	−8.19615	−0.364363
$507$	29.6603	1.31726
$508$	1.07180	0.0475533
$509$	−11.0718	−0.490749	−0.245374	−	0.969428i	$-0.578911\pi$
$509$	−11.0718	−0.490749	−0.245374	+	0.969428i	$0.578911\pi$
$510$	−9.46410	−0.419077
$511$	0	0
$512$	1.00000	0.0441942
$513$	26.9282	1.18891
$514$	23.6603	1.04361
$515$	−12.3923	−0.546070
$516$	−5.46410	−0.240544
$517$	−6.92820	−0.304702
$518$	0	0
$519$	2.53590	0.111314
$520$	1.46410	0.0642051
$521$	−10.3923	−0.455295	−0.227648	−	0.973744i	$-0.573103\pi$
$521$	−10.3923	−0.455295	−0.227648	+	0.973744i	$0.573103\pi$
$522$	−21.1244	−0.924588
$523$	29.1769	1.27582	0.637909	−	0.770112i	$-0.279800\pi$
$523$	29.1769	1.27582	0.637909	+	0.770112i	$0.279800\pi$
$524$	−5.66025	−0.247269
$525$	0	0
$526$	−24.0000	−1.04645
$527$	−6.92820	−0.301797
$528$	−2.73205	−0.118897
$529$	44.1769	1.92074
$530$	−7.26795	−0.315700
$531$	−30.9282	−1.34217
$532$	0	0
$533$	3.21539	0.139274
$534$	9.46410	0.409552
$535$	7.85641	0.339662
$536$	−4.00000	−0.172774
$537$	16.3923	0.707380
$538$	−28.3923	−1.22408
$539$	0	0
$540$	−4.00000	−0.172133
$541$	−20.7321	−0.891340	−0.445670	−	0.895197i	$-0.647035\pi$
$541$	−20.7321	−0.891340	−0.445670	+	0.895197i	$0.647035\pi$
$542$	−0.392305	−0.0168509
$543$	38.2487	1.64141
$544$	3.46410	0.148522
$545$	−15.6603	−0.670812
$546$	0	0
$547$	28.7846	1.23074	0.615371	−	0.788238i	$-0.289006\pi$
$547$	28.7846	1.23074	0.615371	+	0.788238i	$0.289006\pi$
$548$	−0.928203	−0.0396509
$549$	22.0000	0.938937
$550$	1.00000	0.0426401
$551$	31.8564	1.35713
$552$	22.3923	0.953080
$553$	0	0
$554$	7.07180	0.300452
$555$	−2.00000	−0.0848953
$556$	−13.6603	−0.579324
$557$	−25.6077	−1.08503	−0.542516	−	0.840045i	$-0.682528\pi$
$557$	−25.6077	−1.08503	−0.542516	+	0.840045i	$0.682528\pi$
$558$	−8.92820	−0.377961
$559$	2.92820	0.123850
$560$	0	0
$561$	−9.46410	−0.399575
$562$	22.3923	0.944562
$563$	−5.07180	−0.213751	−0.106875	−	0.994272i	$-0.534085\pi$
$563$	−5.07180	−0.213751	−0.106875	+	0.994272i	$0.534085\pi$
$564$	18.9282	0.797021
$565$	7.85641	0.330522
$566$	31.7128	1.33299
$567$	0	0
$568$	9.46410	0.397105
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	18.3923	0.770369
$571$	3.60770	0.150977	0.0754887	−	0.997147i	$-0.475948\pi$
$571$	3.60770	0.150977	0.0754887	+	0.997147i	$0.475948\pi$
$572$	1.46410	0.0612172
$573$	32.7846	1.36960
$574$	0	0
$575$	−8.19615	−0.341803
$576$	4.46410	0.186004
$577$	34.5885	1.43994	0.719968	−	0.694007i	$-0.244156\pi$
$577$	34.5885	1.43994	0.719968	+	0.694007i	$0.244156\pi$
$578$	−5.00000	−0.207973
$579$	−33.8564	−1.40702
$580$	−4.73205	−0.196488
$581$	0	0
$582$	39.8564	1.65210
$583$	−7.26795	−0.301008
$584$	14.3923	0.595558
$585$	6.53590	0.270226
$586$	−21.4641	−0.886674
$587$	11.4115	0.471005	0.235502	−	0.971874i	$-0.424326\pi$
$587$	11.4115	0.471005	0.235502	+	0.971874i	$0.424326\pi$
$588$	0	0
$589$	13.4641	0.554779
$590$	−6.92820	−0.285230
$591$	66.2487	2.72511
$592$	0.732051	0.0300871
$593$	−0.248711	−0.0102133	−0.00510667	−	0.999987i	$-0.501626\pi$
$593$	−0.248711	−0.0102133	−0.00510667	+	0.999987i	$0.501626\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−7.26795	−0.297707
$597$	8.00000	0.327418
$598$	−12.0000	−0.490716
$599$	37.1769	1.51901	0.759504	−	0.650503i	$-0.225442\pi$
$599$	37.1769	1.51901	0.759504	+	0.650503i	$0.225442\pi$
$600$	−2.73205	−0.111536
$601$	5.51666	0.225029	0.112515	−	0.993650i	$-0.464109\pi$
$601$	5.51666	0.225029	0.112515	+	0.993650i	$0.464109\pi$
$602$	0	0
$603$	−17.8564	−0.727169
$604$	11.1244	0.452644
$605$	1.00000	0.0406558
$606$	−21.4641	−0.871920
$607$	−20.9282	−0.849450	−0.424725	−	0.905323i	$-0.639629\pi$
$607$	−20.9282	−0.849450	−0.424725	+	0.905323i	$0.639629\pi$
$608$	−6.73205	−0.273021
$609$	0	0
$610$	4.92820	0.199537
$611$	−10.1436	−0.410366
$612$	15.4641	0.625099
$613$	−35.1769	−1.42078	−0.710391	−	0.703807i	$-0.751482\pi$
$613$	−35.1769	−1.42078	−0.710391	+	0.703807i	$0.751482\pi$
$614$	−24.3923	−0.984393
$615$	−6.00000	−0.241943
$616$	0	0
$617$	17.3205	0.697297	0.348649	−	0.937253i	$-0.386641\pi$
$617$	17.3205	0.697297	0.348649	+	0.937253i	$0.386641\pi$
$618$	33.8564	1.36190
$619$	−28.7846	−1.15695	−0.578476	−	0.815700i	$-0.696352\pi$
$619$	−28.7846	−1.15695	−0.578476	+	0.815700i	$0.696352\pi$
$620$	−2.00000	−0.0803219
$621$	32.7846	1.31560
$622$	−24.9282	−0.999530
$623$	0	0
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−22.1962	−0.887137
$627$	18.3923	0.734518
$628$	−4.53590	−0.181002
$629$	2.53590	0.101113
$630$	0	0
$631$	−46.9282	−1.86818	−0.934091	−	0.357035i	$-0.883788\pi$
$631$	−46.9282	−1.86818	−0.934091	+	0.357035i	$0.883788\pi$
$632$	−12.1962	−0.485137
$633$	−73.5692	−2.92411
$634$	30.5885	1.21482
$635$	1.07180	0.0425330
$636$	19.8564	0.787358
$637$	0	0
$638$	−4.73205	−0.187344
$639$	42.2487	1.67133
$640$	1.00000	0.0395285
$641$	−35.5692	−1.40490	−0.702450	−	0.711733i	$-0.747910\pi$
$641$	−35.5692	−1.40490	−0.702450	+	0.711733i	$0.747910\pi$
$642$	−21.4641	−0.847121
$643$	−33.2679	−1.31196	−0.655980	−	0.754778i	$-0.727744\pi$
$643$	−33.2679	−1.31196	−0.655980	+	0.754778i	$0.727744\pi$
$644$	0	0
$645$	−5.46410	−0.215149
$646$	−23.3205	−0.917533
$647$	26.5359	1.04323	0.521617	−	0.853180i	$-0.325329\pi$
$647$	26.5359	1.04323	0.521617	+	0.853180i	$0.325329\pi$
$648$	−2.46410	−0.0967991
$649$	−6.92820	−0.271956
$650$	1.46410	0.0574268
$651$	0	0
$652$	−4.00000	−0.156652
$653$	11.6603	0.456301	0.228151	−	0.973626i	$-0.426732\pi$
$653$	11.6603	0.456301	0.228151	+	0.973626i	$0.426732\pi$
$654$	42.7846	1.67301
$655$	−5.66025	−0.221164
$656$	2.19615	0.0857453
$657$	64.2487	2.50658
$658$	0	0
$659$	30.2487	1.17832	0.589161	−	0.808015i	$-0.299458\pi$
$659$	30.2487	1.17832	0.589161	+	0.808015i	$0.299458\pi$
$660$	−2.73205	−0.106345
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	−18.7846	−0.730085
$663$	−13.8564	−0.538138
$664$	16.3923	0.636145
$665$	0	0
$666$	3.26795	0.126630
$667$	38.7846	1.50175
$668$	−13.8564	−0.536120
$669$	−69.5692	−2.68970
$670$	−4.00000	−0.154533
$671$	4.92820	0.190251
$672$	0	0
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	22.7846	0.877630
$675$	−4.00000	−0.153960
$676$	−10.8564	−0.417554
$677$	4.14359	0.159251	0.0796256	−	0.996825i	$-0.474628\pi$
$677$	4.14359	0.159251	0.0796256	+	0.996825i	$0.474628\pi$
$678$	−21.4641	−0.824324
$679$	0	0
$680$	3.46410	0.132842
$681$	18.9282	0.725330
$682$	−2.00000	−0.0765840
$683$	6.24871	0.239100	0.119550	−	0.992828i	$-0.461855\pi$
$683$	6.24871	0.239100	0.119550	+	0.992828i	$0.461855\pi$
$684$	−30.0526	−1.14909
$685$	−0.928203	−0.0354648
$686$	0	0
$687$	66.6410	2.54251
$688$	2.00000	0.0762493
$689$	−10.6410	−0.405390
$690$	22.3923	0.852460
$691$	13.4641	0.512199	0.256099	−	0.966650i	$-0.417563\pi$
$691$	13.4641	0.512199	0.256099	+	0.966650i	$0.417563\pi$
$692$	−0.928203	−0.0352850
$693$	0	0
$694$	−23.0718	−0.875793
$695$	−13.6603	−0.518163
$696$	12.9282	0.490042
$697$	7.60770	0.288162
$698$	5.60770	0.212254
$699$	21.4641	0.811847
$700$	0	0
$701$	41.9090	1.58288	0.791440	−	0.611247i	$-0.209332\pi$
$701$	41.9090	1.58288	0.791440	+	0.611247i	$0.209332\pi$
$702$	−5.85641	−0.221036
$703$	−4.92820	−0.185871
$704$	1.00000	0.0376889
$705$	18.9282	0.712877
$706$	−14.1962	−0.534279
$707$	0	0
$708$	18.9282	0.711365
$709$	25.3205	0.950932	0.475466	−	0.879734i	$-0.342280\pi$
$709$	25.3205	0.950932	0.475466	+	0.879734i	$0.342280\pi$
$710$	9.46410	0.355181
$711$	−54.4449	−2.04184
$712$	−3.46410	−0.129823
$713$	16.3923	0.613897
$714$	0	0
$715$	1.46410	0.0547543
$716$	−6.00000	−0.224231
$717$	−3.46410	−0.129369
$718$	−34.0526	−1.27083
$719$	27.7128	1.03351	0.516757	−	0.856132i	$-0.327139\pi$
$719$	27.7128	1.03351	0.516757	+	0.856132i	$0.327139\pi$
$720$	4.46410	0.166367
$721$	0	0
$722$	26.3205	0.979548
$723$	8.92820	0.332043
$724$	−14.0000	−0.520306
$725$	−4.73205	−0.175744
$726$	−2.73205	−0.101396
$727$	4.00000	0.148352	0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000	0.148352	0.0741759	+	0.997245i	$0.476367\pi$
$728$	0	0
$729$	−43.7846	−1.62165
$730$	14.3923	0.532683
$731$	6.92820	0.256249
$732$	−13.4641	−0.497648
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	−12.3923	−0.457408
$735$	0	0
$736$	−8.19615	−0.302114
$737$	−4.00000	−0.147342
$738$	9.80385	0.360885
$739$	11.7128	0.430863	0.215431	−	0.976519i	$-0.430884\pi$
$739$	11.7128	0.430863	0.215431	+	0.976519i	$0.430884\pi$
$740$	0.732051	0.0269107
$741$	26.9282	0.989232
$742$	0	0
$743$	−32.7846	−1.20275	−0.601375	−	0.798967i	$-0.705380\pi$
$743$	−32.7846	−1.20275	−0.601375	+	0.798967i	$0.705380\pi$
$744$	5.46410	0.200324
$745$	−7.26795	−0.266277
$746$	18.3923	0.673390
$747$	73.1769	2.67740
$748$	3.46410	0.126660
$749$	0	0
$750$	−2.73205	−0.0997604
$751$	−11.6077	−0.423571	−0.211785	−	0.977316i	$-0.567928\pi$
$751$	−11.6077	−0.423571	−0.211785	+	0.977316i	$0.567928\pi$
$752$	−6.92820	−0.252646
$753$	32.7846	1.19474
$754$	−6.92820	−0.252310
$755$	11.1244	0.404857
$756$	0	0
$757$	−43.3731	−1.57642	−0.788210	−	0.615406i	$-0.788992\pi$
$757$	−43.3731	−1.57642	−0.788210	+	0.615406i	$0.788992\pi$
$758$	6.14359	0.223145
$759$	22.3923	0.812789
$760$	−6.73205	−0.244197
$761$	12.3397	0.447315	0.223658	−	0.974668i	$-0.428200\pi$
$761$	12.3397	0.447315	0.223658	+	0.974668i	$0.428200\pi$
$762$	−2.92820	−0.106078
$763$	0	0
$764$	−12.0000	−0.434145
$765$	15.4641	0.559106
$766$	33.4641	1.20911
$767$	−10.1436	−0.366264
$768$	−2.73205	−0.0985844
$769$	18.1962	0.656170	0.328085	−	0.944648i	$-0.393597\pi$
$769$	18.1962	0.656170	0.328085	+	0.944648i	$0.393597\pi$
$770$	0	0
$771$	−64.6410	−2.32799
$772$	12.3923	0.446009
$773$	0.928203	0.0333851	0.0166926	−	0.999861i	$-0.494686\pi$
$773$	0.928203	0.0333851	0.0166926	+	0.999861i	$0.494686\pi$
$774$	8.92820	0.320918
$775$	−2.00000	−0.0718421
$776$	−14.5885	−0.523695
$777$	0	0
$778$	−1.60770	−0.0576387
$779$	−14.7846	−0.529714
$780$	−4.00000	−0.143223
$781$	9.46410	0.338652
$782$	−28.3923	−1.01531
$783$	18.9282	0.676439
$784$	0	0
$785$	−4.53590	−0.161893
$786$	15.4641	0.551586
$787$	−18.1436	−0.646749	−0.323375	−	0.946271i	$-0.604817\pi$
$787$	−18.1436	−0.646749	−0.323375	+	0.946271i	$0.604817\pi$
$788$	−24.2487	−0.863825
$789$	65.5692	2.33433
$790$	−12.1962	−0.433920
$791$	0	0
$792$	4.46410	0.158625
$793$	7.21539	0.256226
$794$	−30.3923	−1.07858
$795$	19.8564	0.704234
$796$	−2.92820	−0.103787
$797$	25.6077	0.907071	0.453536	−	0.891238i	$-0.350163\pi$
$797$	25.6077	0.907071	0.453536	+	0.891238i	$0.350163\pi$
$798$	0	0
$799$	−24.0000	−0.849059
$800$	1.00000	0.0353553
$801$	−15.4641	−0.546397
$802$	2.53590	0.0895457
$803$	14.3923	0.507893
$804$	10.9282	0.385408
$805$	0	0
$806$	−2.92820	−0.103142
$807$	77.5692	2.73057
$808$	7.85641	0.276387
$809$	−31.1769	−1.09612	−0.548061	−	0.836438i	$-0.684634\pi$
$809$	−31.1769	−1.09612	−0.548061	+	0.836438i	$0.684634\pi$
$810$	−2.46410	−0.0865797
$811$	43.1244	1.51430	0.757150	−	0.653241i	$-0.226591\pi$
$811$	43.1244	1.51430	0.757150	+	0.653241i	$0.226591\pi$
$812$	0	0
$813$	1.07180	0.0375896
$814$	0.732051	0.0256584
$815$	−4.00000	−0.140114
$816$	−9.46410	−0.331310
$817$	−13.4641	−0.471049
$818$	−10.8756	−0.380258
$819$	0	0
$820$	2.19615	0.0766930
$821$	17.9090	0.625027	0.312514	−	0.949913i	$-0.398829\pi$
$821$	17.9090	0.625027	0.312514	+	0.949913i	$0.398829\pi$
$822$	2.53590	0.0884496
$823$	−0.875644	−0.0305230	−0.0152615	−	0.999884i	$-0.504858\pi$
$823$	−0.875644	−0.0305230	−0.0152615	+	0.999884i	$0.504858\pi$
$824$	−12.3923	−0.431706
$825$	−2.73205	−0.0951178
$826$	0	0
$827$	−25.8564	−0.899115	−0.449558	−	0.893251i	$-0.648418\pi$
$827$	−25.8564	−0.899115	−0.449558	+	0.893251i	$0.648418\pi$
$828$	−36.5885	−1.27154
$829$	−2.24871	−0.0781010	−0.0390505	−	0.999237i	$-0.512433\pi$
$829$	−2.24871	−0.0781010	−0.0390505	+	0.999237i	$0.512433\pi$
$830$	16.3923	0.568985
$831$	−19.3205	−0.670221
$832$	1.46410	0.0507586
$833$	0	0
$834$	37.3205	1.29230
$835$	−13.8564	−0.479521
$836$	−6.73205	−0.232833
$837$	8.00000	0.276520
$838$	−30.9282	−1.06840
$839$	31.8564	1.09981	0.549903	−	0.835229i	$-0.314665\pi$
$839$	31.8564	1.09981	0.549903	+	0.835229i	$0.314665\pi$
$840$	0	0
$841$	−6.60770	−0.227852
$842$	−35.8564	−1.23569
$843$	−61.1769	−2.10704
$844$	26.9282	0.926907
$845$	−10.8564	−0.373472
$846$	−30.9282	−1.06333
$847$	0	0
$848$	−7.26795	−0.249582
$849$	−86.6410	−2.97351
$850$	3.46410	0.118818
$851$	−6.00000	−0.205677
$852$	−25.8564	−0.885826
$853$	54.7846	1.87579	0.937895	−	0.346920i	$-0.112773\pi$
$853$	54.7846	1.87579	0.937895	+	0.346920i	$0.112773\pi$
$854$	0	0
$855$	−30.0526	−1.02778
$856$	7.85641	0.268526
$857$	27.4641	0.938156	0.469078	−	0.883157i	$-0.344586\pi$
$857$	27.4641	0.938156	0.469078	+	0.883157i	$0.344586\pi$
$858$	−4.00000	−0.136558
$859$	12.7846	0.436205	0.218103	−	0.975926i	$-0.430013\pi$
$859$	12.7846	0.436205	0.218103	+	0.975926i	$0.430013\pi$
$860$	2.00000	0.0681994
$861$	0	0
$862$	3.12436	0.106416
$863$	−7.51666	−0.255870	−0.127935	−	0.991783i	$-0.540835\pi$
$863$	−7.51666	−0.255870	−0.127935	+	0.991783i	$0.540835\pi$
$864$	−4.00000	−0.136083
$865$	−0.928203	−0.0315599
$866$	18.1962	0.618330
$867$	13.6603	0.463927
$868$	0	0
$869$	−12.1962	−0.413726
$870$	12.9282	0.438307
$871$	−5.85641	−0.198437
$872$	−15.6603	−0.530323
$873$	−65.1244	−2.20413
$874$	55.1769	1.86639
$875$	0	0
$876$	−39.3205	−1.32852
$877$	−21.3205	−0.719942	−0.359971	−	0.932963i	$-0.617213\pi$
$877$	−21.3205	−0.719942	−0.359971	+	0.932963i	$0.617213\pi$
$878$	−26.2487	−0.885851
$879$	58.6410	1.97791
$880$	1.00000	0.0337100
$881$	−11.0718	−0.373018	−0.186509	−	0.982453i	$-0.559717\pi$
$881$	−11.0718	−0.373018	−0.186509	+	0.982453i	$0.559717\pi$
$882$	0	0
$883$	−35.6077	−1.19829	−0.599147	−	0.800639i	$-0.704494\pi$
$883$	−35.6077	−1.19829	−0.599147	+	0.800639i	$0.704494\pi$
$884$	5.07180	0.170583
$885$	18.9282	0.636265
$886$	0	0
$887$	−13.8564	−0.465253	−0.232626	−	0.972566i	$-0.574732\pi$
$887$	−13.8564	−0.465253	−0.232626	+	0.972566i	$0.574732\pi$
$888$	−2.00000	−0.0671156
$889$	0	0
$890$	−3.46410	−0.116117
$891$	−2.46410	−0.0825505
$892$	25.4641	0.852601
$893$	46.6410	1.56078
$894$	19.8564	0.664098
$895$	−6.00000	−0.200558
$896$	0	0
$897$	32.7846	1.09465
$898$	40.3923	1.34791
$899$	9.46410	0.315645
$900$	4.46410	0.148803
$901$	−25.1769	−0.838765
$902$	2.19615	0.0731239
$903$	0	0
$904$	7.85641	0.261300
$905$	−14.0000	−0.465376
$906$	−30.3923	−1.00972
$907$	−31.0333	−1.03044	−0.515222	−	0.857057i	$-0.672291\pi$
$907$	−31.0333	−1.03044	−0.515222	+	0.857057i	$0.672291\pi$
$908$	−6.92820	−0.229920
$909$	35.0718	1.16326
$910$	0	0
$911$	9.46410	0.313560	0.156780	−	0.987634i	$-0.449889\pi$
$911$	9.46410	0.313560	0.156780	+	0.987634i	$0.449889\pi$
$912$	18.3923	0.609030
$913$	16.3923	0.542506
$914$	2.00000	0.0661541
$915$	−13.4641	−0.445109
$916$	−24.3923	−0.805944
$917$	0	0
$918$	−13.8564	−0.457330
$919$	−25.3731	−0.836980	−0.418490	−	0.908221i	$-0.637441\pi$
$919$	−25.3731	−0.836980	−0.418490	+	0.908221i	$0.637441\pi$
$920$	−8.19615	−0.270219
$921$	66.6410	2.19590
$922$	−22.3923	−0.737451
$923$	13.8564	0.456089
$924$	0	0
$925$	0.732051	0.0240697
$926$	27.5167	0.904254
$927$	−55.3205	−1.81696
$928$	−4.73205	−0.155337
$929$	25.6077	0.840161	0.420081	−	0.907487i	$-0.362002\pi$
$929$	25.6077	0.840161	0.420081	+	0.907487i	$0.362002\pi$
$930$	5.46410	0.179175
$931$	0	0
$932$	−7.85641	−0.257345
$933$	68.1051	2.22966
$934$	34.0526	1.11423
$935$	3.46410	0.113288
$936$	6.53590	0.213633
$937$	1.21539	0.0397051	0.0198525	−	0.999803i	$-0.493680\pi$
$937$	1.21539	0.0397051	0.0198525	+	0.999803i	$0.493680\pi$
$938$	0	0
$939$	60.6410	1.97894
$940$	−6.92820	−0.225973
$941$	14.7846	0.481965	0.240982	−	0.970530i	$-0.422530\pi$
$941$	14.7846	0.481965	0.240982	+	0.970530i	$0.422530\pi$
$942$	12.3923	0.403763
$943$	−18.0000	−0.586161
$944$	−6.92820	−0.225494
$945$	0	0
$946$	2.00000	0.0650256
$947$	47.3205	1.53771	0.768855	−	0.639423i	$-0.220827\pi$
$947$	47.3205	1.53771	0.768855	+	0.639423i	$0.220827\pi$
$948$	33.3205	1.08220
$949$	21.0718	0.684019
$950$	−6.73205	−0.218417
$951$	−83.5692	−2.70992
$952$	0	0
$953$	26.5359	0.859582	0.429791	−	0.902928i	$-0.358587\pi$
$953$	26.5359	0.859582	0.429791	+	0.902928i	$0.358587\pi$
$954$	−32.4449	−1.05044
$955$	−12.0000	−0.388311
$956$	1.26795	0.0410084
$957$	12.9282	0.417909
$958$	32.7846	1.05922
$959$	0	0
$960$	−2.73205	−0.0881766
$961$	−27.0000	−0.870968
$962$	1.07180	0.0345561
$963$	35.0718	1.13017
$964$	−3.26795	−0.105254
$965$	12.3923	0.398922
$966$	0	0
$967$	26.9282	0.865953	0.432976	−	0.901405i	$-0.357463\pi$
$967$	26.9282	0.865953	0.432976	+	0.901405i	$0.357463\pi$
$968$	1.00000	0.0321412
$969$	63.7128	2.04675
$970$	−14.5885	−0.468407
$971$	−42.9282	−1.37763	−0.688816	−	0.724936i	$-0.741869\pi$
$971$	−42.9282	−1.37763	−0.688816	+	0.724936i	$0.741869\pi$
$972$	18.7321	0.600831
$973$	0	0
$974$	4.19615	0.134453
$975$	−4.00000	−0.128103
$976$	4.92820	0.157748
$977$	−33.7128	−1.07857	−0.539284	−	0.842124i	$-0.681305\pi$
$977$	−33.7128	−1.07857	−0.539284	+	0.842124i	$0.681305\pi$
$978$	10.9282	0.349445
$979$	−3.46410	−0.110713
$980$	0	0
$981$	−69.9090	−2.23202
$982$	−27.7128	−0.884351
$983$	37.1769	1.18576	0.592880	−	0.805291i	$-0.297991\pi$
$983$	37.1769	1.18576	0.592880	+	0.805291i	$0.297991\pi$
$984$	−6.00000	−0.191273
$985$	−24.2487	−0.772628
$986$	−16.3923	−0.522037
$987$	0	0
$988$	−9.85641	−0.313574
$989$	−16.3923	−0.521245
$990$	4.46410	0.141878
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−2.00000	−0.0635001
$993$	51.3205	1.62861
$994$	0	0
$995$	−2.92820	−0.0928303
$996$	−44.7846	−1.41905
$997$	−17.7128	−0.560970	−0.280485	−	0.959858i	$-0.590495\pi$
$997$	−17.7128	−0.560970	−0.280485	+	0.959858i	$0.590495\pi$
$998$	12.1436	0.384399
$999$	−2.92820	−0.0926443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5390.2.a.bs.1.1		2
7.6	odd	2		770.2.a.j.1.2	✓	2
21.20	even	2		6930.2.a.bv.1.1		2
28.27	even	2		6160.2.a.t.1.1		2
35.13	even	4		3850.2.c.x.1849.2		4
35.27	even	4		3850.2.c.x.1849.3		4
35.34	odd	2		3850.2.a.bd.1.1		2
77.76	even	2		8470.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.j.1.2	✓	2	7.6	odd	2
3850.2.a.bd.1.1		2	35.34	odd	2
3850.2.c.x.1849.2		4	35.13	even	4
3850.2.c.x.1849.3		4	35.27	even	4
5390.2.a.bs.1.1		2	1.1	even	1	trivial
6160.2.a.t.1.1		2	28.27	even	2
6930.2.a.bv.1.1		2	21.20	even	2
8470.2.a.br.1.2		2	77.76	even	2

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:	\( N \)	\(=\)	\( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5390.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.73205 q^{6} +1.00000 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73205 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.73205 q^{6} +1.00000 q^{8} +4.46410 q^{9} +1.00000 q^{10} +1.00000 q^{11} -2.73205 q^{12} +1.46410 q^{13} -2.73205 q^{15} +1.00000 q^{16} +3.46410 q^{17} +4.46410 q^{18} -6.73205 q^{19} +1.00000 q^{20} +1.00000 q^{22} -8.19615 q^{23} -2.73205 q^{24} +1.00000 q^{25} +1.46410 q^{26} -4.00000 q^{27} -4.73205 q^{29} -2.73205 q^{30} -2.00000 q^{31} +1.00000 q^{32} -2.73205 q^{33} +3.46410 q^{34} +4.46410 q^{36} +0.732051 q^{37} -6.73205 q^{38} -4.00000 q^{39} +1.00000 q^{40} +2.19615 q^{41} +2.00000 q^{43} +1.00000 q^{44} +4.46410 q^{45} -8.19615 q^{46} -6.92820 q^{47} -2.73205 q^{48} +1.00000 q^{50} -9.46410 q^{51} +1.46410 q^{52} -7.26795 q^{53} -4.00000 q^{54} +1.00000 q^{55} +18.3923 q^{57} -4.73205 q^{58} -6.92820 q^{59} -2.73205 q^{60} +4.92820 q^{61} -2.00000 q^{62} +1.00000 q^{64} +1.46410 q^{65} -2.73205 q^{66} -4.00000 q^{67} +3.46410 q^{68} +22.3923 q^{69} +9.46410 q^{71} +4.46410 q^{72} +14.3923 q^{73} +0.732051 q^{74} -2.73205 q^{75} -6.73205 q^{76} -4.00000 q^{78} -12.1962 q^{79} +1.00000 q^{80} -2.46410 q^{81} +2.19615 q^{82} +16.3923 q^{83} +3.46410 q^{85} +2.00000 q^{86} +12.9282 q^{87} +1.00000 q^{88} -3.46410 q^{89} +4.46410 q^{90} -8.19615 q^{92} +5.46410 q^{93} -6.92820 q^{94} -6.73205 q^{95} -2.73205 q^{96} -14.5885 q^{97} +4.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 4 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{18} - 10 q^{19} + 2 q^{20} + 2 q^{22} - 6 q^{23} - 2 q^{24} + 2 q^{25} - 4 q^{26} - 8 q^{27} - 6 q^{29} - 2 q^{30} - 4 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{36} - 2 q^{37} - 10 q^{38} - 8 q^{39} + 2 q^{40} - 6 q^{41} + 4 q^{43} + 2 q^{44} + 2 q^{45} - 6 q^{46} - 2 q^{48} + 2 q^{50} - 12 q^{51} - 4 q^{52} - 18 q^{53} - 8 q^{54} + 2 q^{55} + 16 q^{57} - 6 q^{58} - 2 q^{60} - 4 q^{61} - 4 q^{62} + 2 q^{64} - 4 q^{65} - 2 q^{66} - 8 q^{67} + 24 q^{69} + 12 q^{71} + 2 q^{72} + 8 q^{73} - 2 q^{74} - 2 q^{75} - 10 q^{76} - 8 q^{78} - 14 q^{79} + 2 q^{80} + 2 q^{81} - 6 q^{82} + 12 q^{83} + 4 q^{86} + 12 q^{87} + 2 q^{88} + 2 q^{90} - 6 q^{92} + 4 q^{93} - 10 q^{95} - 2 q^{96} + 2 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 4 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^18 - 10 * q^19 + 2 * q^20 + 2 * q^22 - 6 * q^23 - 2 * q^24 + 2 * q^25 - 4 * q^26 - 8 * q^27 - 6 * q^29 - 2 * q^30 - 4 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^36 - 2 * q^37 - 10 * q^38 - 8 * q^39 + 2 * q^40 - 6 * q^41 + 4 * q^43 + 2 * q^44 + 2 * q^45 - 6 * q^46 - 2 * q^48 + 2 * q^50 - 12 * q^51 - 4 * q^52 - 18 * q^53 - 8 * q^54 + 2 * q^55 + 16 * q^57 - 6 * q^58 - 2 * q^60 - 4 * q^61 - 4 * q^62 + 2 * q^64 - 4 * q^65 - 2 * q^66 - 8 * q^67 + 24 * q^69 + 12 * q^71 + 2 * q^72 + 8 * q^73 - 2 * q^74 - 2 * q^75 - 10 * q^76 - 8 * q^78 - 14 * q^79 + 2 * q^80 + 2 * q^81 - 6 * q^82 + 12 * q^83 + 4 * q^86 + 12 * q^87 + 2 * q^88 + 2 * q^90 - 6 * q^92 + 4 * q^93 - 10 * q^95 - 2 * q^96 + 2 * q^97 + 2 * q^99

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