LMFDB - Embedded newform 7098.2.a.cd.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.69202 q^{10} -3.15883 q^{11} -1.00000 q^{12} -1.00000 q^{14} +1.69202 q^{15} +1.00000 q^{16} +7.74094 q^{17} -1.00000 q^{18} -3.15883 q^{19} -1.69202 q^{20} -1.00000 q^{21} +3.15883 q^{22} +7.89977 q^{23} +1.00000 q^{24} -2.13706 q^{25} -1.00000 q^{27} +1.00000 q^{28} -4.96077 q^{29} -1.69202 q^{30} -4.82908 q^{31} -1.00000 q^{32} +3.15883 q^{33} -7.74094 q^{34} -1.69202 q^{35} +1.00000 q^{36} +0.185981 q^{37} +3.15883 q^{38} +1.69202 q^{40} -0.978230 q^{41} +1.00000 q^{42} -8.19806 q^{43} -3.15883 q^{44} -1.69202 q^{45} -7.89977 q^{46} -2.78017 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.13706 q^{50} -7.74094 q^{51} -0.652793 q^{53} +1.00000 q^{54} +5.34481 q^{55} -1.00000 q^{56} +3.15883 q^{57} +4.96077 q^{58} +4.80194 q^{59} +1.69202 q^{60} +3.21983 q^{61} +4.82908 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.15883 q^{66} +4.52111 q^{67} +7.74094 q^{68} -7.89977 q^{69} +1.69202 q^{70} +1.20775 q^{71} -1.00000 q^{72} +14.1564 q^{73} -0.185981 q^{74} +2.13706 q^{75} -3.15883 q^{76} -3.15883 q^{77} -7.33944 q^{79} -1.69202 q^{80} +1.00000 q^{81} +0.978230 q^{82} +8.32304 q^{83} -1.00000 q^{84} -13.0978 q^{85} +8.19806 q^{86} +4.96077 q^{87} +3.15883 q^{88} -13.5526 q^{89} +1.69202 q^{90} +7.89977 q^{92} +4.82908 q^{93} +2.78017 q^{94} +5.34481 q^{95} +1.00000 q^{96} +7.83340 q^{97} -1.00000 q^{98} -3.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{16} + 9 q^{17} - 3 q^{18} - q^{19} - 3 q^{21} + q^{22} + q^{23} + 3 q^{24} - q^{25} - 3 q^{27} + 3 q^{28} - 2 q^{29} - 4 q^{31} - 3 q^{32} + q^{33} - 9 q^{34} + 3 q^{36} - 14 q^{37} + q^{38} - 6 q^{41} + 3 q^{42} - 29 q^{43} - q^{44} - q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} + q^{50} - 9 q^{51} + 16 q^{53} + 3 q^{54} - 7 q^{55} - 3 q^{56} + q^{57} + 2 q^{58} + 10 q^{59} + 11 q^{61} + 4 q^{62} + 3 q^{63} + 3 q^{64} - q^{66} - 2 q^{67} + 9 q^{68} - q^{69} - 14 q^{71} - 3 q^{72} - 7 q^{73} + 14 q^{74} + q^{75} - q^{76} - q^{77} - 2 q^{79} + 3 q^{81} + 6 q^{82} + 5 q^{83} - 3 q^{84} - 21 q^{85} + 29 q^{86} + 2 q^{87} + q^{88} + q^{92} + 4 q^{93} + 7 q^{94} - 7 q^{95} + 3 q^{96} - 6 q^{97} - 3 q^{98} - q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - q^11 - 3 * q^12 - 3 * q^14 + 3 * q^16 + 9 * q^17 - 3 * q^18 - q^19 - 3 * q^21 + q^22 + q^23 + 3 * q^24 - q^25 - 3 * q^27 + 3 * q^28 - 2 * q^29 - 4 * q^31 - 3 * q^32 + q^33 - 9 * q^34 + 3 * q^36 - 14 * q^37 + q^38 - 6 * q^41 + 3 * q^42 - 29 * q^43 - q^44 - q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 + q^50 - 9 * q^51 + 16 * q^53 + 3 * q^54 - 7 * q^55 - 3 * q^56 + q^57 + 2 * q^58 + 10 * q^59 + 11 * q^61 + 4 * q^62 + 3 * q^63 + 3 * q^64 - q^66 - 2 * q^67 + 9 * q^68 - q^69 - 14 * q^71 - 3 * q^72 - 7 * q^73 + 14 * q^74 + q^75 - q^76 - q^77 - 2 * q^79 + 3 * q^81 + 6 * q^82 + 5 * q^83 - 3 * q^84 - 21 * q^85 + 29 * q^86 + 2 * q^87 + q^88 + q^92 + 4 * q^93 + 7 * q^94 - 7 * q^95 + 3 * q^96 - 6 * q^97 - 3 * q^98 - 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
$5$	−1.69202	−0.756695	−0.378348	−	0.925664i	$-0.623508\pi$
$5$	−1.69202	−0.756695	−0.378348	+	0.925664i	$0.623508\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.69202	0.535064
$11$	−3.15883	−0.952424	−0.476212	−	0.879330i	$-0.657991\pi$
$11$	−3.15883	−0.952424	−0.476212	+	0.879330i	$0.657991\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	1.69202	0.436878
$16$	1.00000	0.250000
$17$	7.74094	1.87745	0.938727	−	0.344662i	$-0.112007\pi$
$17$	7.74094	1.87745	0.938727	+	0.344662i	$0.112007\pi$
$18$	−1.00000	−0.235702
$19$	−3.15883	−0.724686	−0.362343	−	0.932045i	$-0.618023\pi$
$19$	−3.15883	−0.724686	−0.362343	+	0.932045i	$0.618023\pi$
$20$	−1.69202	−0.378348
$21$	−1.00000	−0.218218
$22$	3.15883	0.673466
$23$	7.89977	1.64722	0.823608	−	0.567159i	$-0.191958\pi$
$23$	7.89977	1.64722	0.823608	+	0.567159i	$0.191958\pi$
$24$	1.00000	0.204124
$25$	−2.13706	−0.427413
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−4.96077	−0.921192	−0.460596	−	0.887610i	$-0.652364\pi$
$29$	−4.96077	−0.921192	−0.460596	+	0.887610i	$0.652364\pi$
$30$	−1.69202	−0.308919
$31$	−4.82908	−0.867329	−0.433665	−	0.901074i	$-0.642780\pi$
$31$	−4.82908	−0.867329	−0.433665	+	0.901074i	$0.642780\pi$
$32$	−1.00000	−0.176777
$33$	3.15883	0.549882
$34$	−7.74094	−1.32756
$35$	−1.69202	−0.286004
$36$	1.00000	0.166667
$37$	0.185981	0.0305750	0.0152875	−	0.999883i	$-0.495134\pi$
$37$	0.185981	0.0305750	0.0152875	+	0.999883i	$0.495134\pi$
$38$	3.15883	0.512430
$39$	0	0
$40$	1.69202	0.267532
$41$	−0.978230	−0.152774	−0.0763869	−	0.997078i	$-0.524338\pi$
$41$	−0.978230	−0.152774	−0.0763869	+	0.997078i	$0.524338\pi$
$42$	1.00000	0.154303
$43$	−8.19806	−1.25019	−0.625096	−	0.780548i	$-0.714940\pi$
$43$	−8.19806	−1.25019	−0.625096	+	0.780548i	$0.714940\pi$
$44$	−3.15883	−0.476212
$45$	−1.69202	−0.252232
$46$	−7.89977	−1.16476
$47$	−2.78017	−0.405529	−0.202765	−	0.979228i	$-0.564993\pi$
$47$	−2.78017	−0.405529	−0.202765	+	0.979228i	$0.564993\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	2.13706	0.302226
$51$	−7.74094	−1.08395
$52$	0	0
$53$	−0.652793	−0.0896680	−0.0448340	−	0.998994i	$-0.514276\pi$
$53$	−0.652793	−0.0896680	−0.0448340	+	0.998994i	$0.514276\pi$
$54$	1.00000	0.136083
$55$	5.34481	0.720695
$56$	−1.00000	−0.133631
$57$	3.15883	0.418398
$58$	4.96077	0.651381
$59$	4.80194	0.625159	0.312580	−	0.949892i	$-0.398807\pi$
$59$	4.80194	0.625159	0.312580	+	0.949892i	$0.398807\pi$
$60$	1.69202	0.218439
$61$	3.21983	0.412257	0.206129	−	0.978525i	$-0.433913\pi$
$61$	3.21983	0.412257	0.206129	+	0.978525i	$0.433913\pi$
$62$	4.82908	0.613294
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−3.15883	−0.388826
$67$	4.52111	0.552341	0.276171	−	0.961109i	$-0.410935\pi$
$67$	4.52111	0.552341	0.276171	+	0.961109i	$0.410935\pi$
$68$	7.74094	0.938727
$69$	−7.89977	−0.951021
$70$	1.69202	0.202235
$71$	1.20775	0.143334	0.0716668	−	0.997429i	$-0.477168\pi$
$71$	1.20775	0.143334	0.0716668	+	0.997429i	$0.477168\pi$
$72$	−1.00000	−0.117851
$73$	14.1564	1.65689	0.828443	−	0.560073i	$-0.189227\pi$
$73$	14.1564	1.65689	0.828443	+	0.560073i	$0.189227\pi$
$74$	−0.185981	−0.0216198
$75$	2.13706	0.246767
$76$	−3.15883	−0.362343
$77$	−3.15883	−0.359982
$78$	0	0
$79$	−7.33944	−0.825751	−0.412876	−	0.910787i	$-0.635476\pi$
$79$	−7.33944	−0.825751	−0.412876	+	0.910787i	$0.635476\pi$
$80$	−1.69202	−0.189174
$81$	1.00000	0.111111
$82$	0.978230	0.108027
$83$	8.32304	0.913573	0.456786	−	0.889576i	$-0.349000\pi$
$83$	8.32304	0.913573	0.456786	+	0.889576i	$0.349000\pi$
$84$	−1.00000	−0.109109
$85$	−13.0978	−1.42066
$86$	8.19806	0.884020
$87$	4.96077	0.531851
$88$	3.15883	0.336733
$89$	−13.5526	−1.43657	−0.718285	−	0.695749i	$-0.755072\pi$
$89$	−13.5526	−1.43657	−0.718285	+	0.695749i	$0.755072\pi$
$90$	1.69202	0.178355
$91$	0	0
$92$	7.89977	0.823608
$93$	4.82908	0.500753
$94$	2.78017	0.286752
$95$	5.34481	0.548366
$96$	1.00000	0.102062
$97$	7.83340	0.795361	0.397680	−	0.917524i	$-0.369815\pi$
$97$	7.83340	0.795361	0.397680	+	0.917524i	$0.369815\pi$
$98$	−1.00000	−0.101015
$99$	−3.15883	−0.317475
$100$	−2.13706	−0.213706
$101$	15.2228	1.51473	0.757363	−	0.652994i	$-0.226487\pi$
$101$	15.2228	1.51473	0.757363	+	0.652994i	$0.226487\pi$
$102$	7.74094	0.766467
$103$	−11.6528	−1.14818	−0.574092	−	0.818791i	$-0.694645\pi$
$103$	−11.6528	−1.14818	−0.574092	+	0.818791i	$0.694645\pi$
$104$	0	0
$105$	1.69202	0.165124
$106$	0.652793	0.0634048
$107$	14.5797	1.40947	0.704737	−	0.709469i	$-0.251065\pi$
$107$	14.5797	1.40947	0.704737	+	0.709469i	$0.251065\pi$
$108$	−1.00000	−0.0962250
$109$	−6.29590	−0.603038	−0.301519	−	0.953460i	$-0.597494\pi$
$109$	−6.29590	−0.603038	−0.301519	+	0.953460i	$0.597494\pi$
$110$	−5.34481	−0.509608
$111$	−0.185981	−0.0176525
$112$	1.00000	0.0944911
$113$	15.1860	1.42858	0.714288	−	0.699851i	$-0.246750\pi$
$113$	15.1860	1.42858	0.714288	+	0.699851i	$0.246750\pi$
$114$	−3.15883	−0.295852
$115$	−13.3666	−1.24644
$116$	−4.96077	−0.460596
$117$	0	0
$118$	−4.80194	−0.442054
$119$	7.74094	0.709611
$120$	−1.69202	−0.154460
$121$	−1.02177	−0.0928882
$122$	−3.21983	−0.291510
$123$	0.978230	0.0882040
$124$	−4.82908	−0.433665
$125$	12.0761	1.08012
$126$	−1.00000	−0.0890871
$127$	11.8629	1.05267	0.526333	−	0.850279i	$-0.323567\pi$
$127$	11.8629	1.05267	0.526333	+	0.850279i	$0.323567\pi$
$128$	−1.00000	−0.0883883
$129$	8.19806	0.721799
$130$	0	0
$131$	−1.56465	−0.136704	−0.0683519	−	0.997661i	$-0.521774\pi$
$131$	−1.56465	−0.136704	−0.0683519	+	0.997661i	$0.521774\pi$
$132$	3.15883	0.274941
$133$	−3.15883	−0.273906
$134$	−4.52111	−0.390564
$135$	1.69202	0.145626
$136$	−7.74094	−0.663780
$137$	−20.5700	−1.75742	−0.878708	−	0.477360i	$-0.841594\pi$
$137$	−20.5700	−1.75742	−0.878708	+	0.477360i	$0.841594\pi$
$138$	7.89977	0.672473
$139$	−22.5308	−1.91104	−0.955519	−	0.294931i	$-0.904703\pi$
$139$	−22.5308	−1.91104	−0.955519	+	0.294931i	$0.904703\pi$
$140$	−1.69202	−0.143002
$141$	2.78017	0.234132
$142$	−1.20775	−0.101352
$143$	0	0
$144$	1.00000	0.0833333
$145$	8.39373	0.697061
$146$	−14.1564	−1.17160
$147$	−1.00000	−0.0824786
$148$	0.185981	0.0152875
$149$	1.60925	0.131835	0.0659175	−	0.997825i	$-0.479003\pi$
$149$	1.60925	0.131835	0.0659175	+	0.997825i	$0.479003\pi$
$150$	−2.13706	−0.174490
$151$	−13.1709	−1.07183	−0.535917	−	0.844271i	$-0.680034\pi$
$151$	−13.1709	−1.07183	−0.535917	+	0.844271i	$0.680034\pi$
$152$	3.15883	0.256215
$153$	7.74094	0.625818
$154$	3.15883	0.254546
$155$	8.17092	0.656304
$156$	0	0
$157$	−2.61596	−0.208776	−0.104388	−	0.994537i	$-0.533288\pi$
$157$	−2.61596	−0.208776	−0.104388	+	0.994537i	$0.533288\pi$
$158$	7.33944	0.583894
$159$	0.652793	0.0517698
$160$	1.69202	0.133766
$161$	7.89977	0.622589
$162$	−1.00000	−0.0785674
$163$	−0.853248	−0.0668315	−0.0334158	−	0.999442i	$-0.510639\pi$
$163$	−0.853248	−0.0668315	−0.0334158	+	0.999442i	$0.510639\pi$
$164$	−0.978230	−0.0763869
$165$	−5.34481	−0.416093
$166$	−8.32304	−0.645993
$167$	−14.8944	−1.15256	−0.576281	−	0.817251i	$-0.695497\pi$
$167$	−14.8944	−1.15256	−0.576281	+	0.817251i	$0.695497\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	13.0978	1.00456
$171$	−3.15883	−0.241562
$172$	−8.19806	−0.625096
$173$	−7.28621	−0.553960	−0.276980	−	0.960876i	$-0.589334\pi$
$173$	−7.28621	−0.553960	−0.276980	+	0.960876i	$0.589334\pi$
$174$	−4.96077	−0.376075
$175$	−2.13706	−0.161547
$176$	−3.15883	−0.238106
$177$	−4.80194	−0.360936
$178$	13.5526	1.01581
$179$	−4.10992	−0.307190	−0.153595	−	0.988134i	$-0.549085\pi$
$179$	−4.10992	−0.307190	−0.153595	+	0.988134i	$0.549085\pi$
$180$	−1.69202	−0.126116
$181$	−8.63640	−0.641939	−0.320969	−	0.947090i	$-0.604009\pi$
$181$	−8.63640	−0.641939	−0.320969	+	0.947090i	$0.604009\pi$
$182$	0	0
$183$	−3.21983	−0.238017
$184$	−7.89977	−0.582379
$185$	−0.314683	−0.0231360
$186$	−4.82908	−0.354086
$187$	−24.4523	−1.78813
$188$	−2.78017	−0.202765
$189$	−1.00000	−0.0727393
$190$	−5.34481	−0.387754
$191$	26.9922	1.95309	0.976545	−	0.215315i	$-0.0690779\pi$
$191$	26.9922	1.95309	0.976545	+	0.215315i	$0.0690779\pi$
$192$	−1.00000	−0.0721688
$193$	−16.2174	−1.16736	−0.583678	−	0.811985i	$-0.698387\pi$
$193$	−16.2174	−1.16736	−0.583678	+	0.811985i	$0.698387\pi$
$194$	−7.83340	−0.562405
$195$	0	0
$196$	1.00000	0.0714286
$197$	21.6625	1.54339	0.771694	−	0.635994i	$-0.219410\pi$
$197$	21.6625	1.54339	0.771694	+	0.635994i	$0.219410\pi$
$198$	3.15883	0.224489
$199$	−8.81700	−0.625021	−0.312510	−	0.949914i	$-0.601170\pi$
$199$	−8.81700	−0.625021	−0.312510	+	0.949914i	$0.601170\pi$
$200$	2.13706	0.151113
$201$	−4.52111	−0.318894
$202$	−15.2228	−1.07107
$203$	−4.96077	−0.348178
$204$	−7.74094	−0.541974
$205$	1.65519	0.115603
$206$	11.6528	0.811889
$207$	7.89977	0.549072
$208$	0	0
$209$	9.97823	0.690209
$210$	−1.69202	−0.116761
$211$	0.753020	0.0518401	0.0259200	−	0.999664i	$-0.491748\pi$
$211$	0.753020	0.0518401	0.0259200	+	0.999664i	$0.491748\pi$
$212$	−0.652793	−0.0448340
$213$	−1.20775	−0.0827537
$214$	−14.5797	−0.996649
$215$	13.8713	0.946015
$216$	1.00000	0.0680414
$217$	−4.82908	−0.327820
$218$	6.29590	0.426412
$219$	−14.1564	−0.956604
$220$	5.34481	0.360347
$221$	0	0
$222$	0.185981	0.0124822
$223$	2.14377	0.143557	0.0717787	−	0.997421i	$-0.477132\pi$
$223$	2.14377	0.143557	0.0717787	+	0.997421i	$0.477132\pi$
$224$	−1.00000	−0.0668153
$225$	−2.13706	−0.142471
$226$	−15.1860	−1.01016
$227$	−21.3327	−1.41590	−0.707952	−	0.706261i	$-0.750381\pi$
$227$	−21.3327	−1.41590	−0.707952	+	0.706261i	$0.750381\pi$
$228$	3.15883	0.209199
$229$	15.3502	1.01437	0.507185	−	0.861837i	$-0.330686\pi$
$229$	15.3502	1.01437	0.507185	+	0.861837i	$0.330686\pi$
$230$	13.3666	0.881366
$231$	3.15883	0.207836
$232$	4.96077	0.325691
$233$	23.1468	1.51639	0.758197	−	0.652025i	$-0.226080\pi$
$233$	23.1468	1.51639	0.758197	+	0.652025i	$0.226080\pi$
$234$	0	0
$235$	4.70410	0.306862
$236$	4.80194	0.312580
$237$	7.33944	0.476748
$238$	−7.74094	−0.501771
$239$	17.8538	1.15487	0.577434	−	0.816437i	$-0.304054\pi$
$239$	17.8538	1.15487	0.577434	+	0.816437i	$0.304054\pi$
$240$	1.69202	0.109220
$241$	−16.4179	−1.05757	−0.528785	−	0.848756i	$-0.677352\pi$
$241$	−16.4179	−1.05757	−0.528785	+	0.848756i	$0.677352\pi$
$242$	1.02177	0.0656819
$243$	−1.00000	−0.0641500
$244$	3.21983	0.206129
$245$	−1.69202	−0.108099
$246$	−0.978230	−0.0623696
$247$	0	0
$248$	4.82908	0.306647
$249$	−8.32304	−0.527451
$250$	−12.0761	−0.763757
$251$	−23.9124	−1.50934	−0.754670	−	0.656104i	$-0.772203\pi$
$251$	−23.9124	−1.50934	−0.754670	+	0.656104i	$0.772203\pi$
$252$	1.00000	0.0629941
$253$	−24.9541	−1.56885
$254$	−11.8629	−0.744347
$255$	13.0978	0.820218
$256$	1.00000	0.0625000
$257$	8.77479	0.547356	0.273678	−	0.961821i	$-0.411760\pi$
$257$	8.77479	0.547356	0.273678	+	0.961821i	$0.411760\pi$
$258$	−8.19806	−0.510389
$259$	0.185981	0.0115563
$260$	0	0
$261$	−4.96077	−0.307064
$262$	1.56465	0.0966642
$263$	6.78448	0.418349	0.209174	−	0.977878i	$-0.432922\pi$
$263$	6.78448	0.418349	0.209174	+	0.977878i	$0.432922\pi$
$264$	−3.15883	−0.194413
$265$	1.10454	0.0678513
$266$	3.15883	0.193681
$267$	13.5526	0.829404
$268$	4.52111	0.276171
$269$	−5.13706	−0.313212	−0.156606	−	0.987661i	$-0.550055\pi$
$269$	−5.13706	−0.313212	−0.156606	+	0.987661i	$0.550055\pi$
$270$	−1.69202	−0.102973
$271$	25.7995	1.56721	0.783605	−	0.621259i	$-0.213378\pi$
$271$	25.7995	1.56721	0.783605	+	0.621259i	$0.213378\pi$
$272$	7.74094	0.469363
$273$	0	0
$274$	20.5700	1.24268
$275$	6.75063	0.407078
$276$	−7.89977	−0.475510
$277$	19.9976	1.20154	0.600770	−	0.799422i	$-0.294861\pi$
$277$	19.9976	1.20154	0.600770	+	0.799422i	$0.294861\pi$
$278$	22.5308	1.35131
$279$	−4.82908	−0.289110
$280$	1.69202	0.101118
$281$	−18.5851	−1.10869	−0.554347	−	0.832286i	$-0.687032\pi$
$281$	−18.5851	−1.10869	−0.554347	+	0.832286i	$0.687032\pi$
$282$	−2.78017	−0.165557
$283$	−4.35152	−0.258671	−0.129335	−	0.991601i	$-0.541284\pi$
$283$	−4.35152	−0.258671	−0.129335	+	0.991601i	$0.541284\pi$
$284$	1.20775	0.0716668
$285$	−5.34481	−0.316599
$286$	0	0
$287$	−0.978230	−0.0577431
$288$	−1.00000	−0.0589256
$289$	42.9221	2.52483
$290$	−8.39373	−0.492897
$291$	−7.83340	−0.459202
$292$	14.1564	0.828443
$293$	−7.14138	−0.417204	−0.208602	−	0.978001i	$-0.566891\pi$
$293$	−7.14138	−0.417204	−0.208602	+	0.978001i	$0.566891\pi$
$294$	1.00000	0.0583212
$295$	−8.12498	−0.473055
$296$	−0.185981	−0.0108099
$297$	3.15883	0.183294
$298$	−1.60925	−0.0932215
$299$	0	0
$300$	2.13706	0.123383
$301$	−8.19806	−0.472528
$302$	13.1709	0.757901
$303$	−15.2228	−0.874528
$304$	−3.15883	−0.181172
$305$	−5.44803	−0.311953
$306$	−7.74094	−0.442520
$307$	3.13467	0.178905	0.0894525	−	0.995991i	$-0.471488\pi$
$307$	3.13467	0.178905	0.0894525	+	0.995991i	$0.471488\pi$
$308$	−3.15883	−0.179991
$309$	11.6528	0.662904
$310$	−8.17092	−0.464077
$311$	−32.7875	−1.85921	−0.929603	−	0.368562i	$-0.879850\pi$
$311$	−32.7875	−1.85921	−0.929603	+	0.368562i	$0.879850\pi$
$312$	0	0
$313$	11.5985	0.655586	0.327793	−	0.944750i	$-0.393695\pi$
$313$	11.5985	0.655586	0.327793	+	0.944750i	$0.393695\pi$
$314$	2.61596	0.147627
$315$	−1.69202	−0.0953346
$316$	−7.33944	−0.412876
$317$	3.71810	0.208830	0.104415	−	0.994534i	$-0.466703\pi$
$317$	3.71810	0.208830	0.104415	+	0.994534i	$0.466703\pi$
$318$	−0.652793	−0.0366068
$319$	15.6703	0.877366
$320$	−1.69202	−0.0945869
$321$	−14.5797	−0.813760
$322$	−7.89977	−0.440237
$323$	−24.4523	−1.36056
$324$	1.00000	0.0555556
$325$	0	0
$326$	0.853248	0.0472570
$327$	6.29590	0.348164
$328$	0.978230	0.0540137
$329$	−2.78017	−0.153276
$330$	5.34481	0.294222
$331$	−15.8532	−0.871373	−0.435687	−	0.900098i	$-0.643494\pi$
$331$	−15.8532	−0.871373	−0.435687	+	0.900098i	$0.643494\pi$
$332$	8.32304	0.456786
$333$	0.185981	0.0101917
$334$	14.8944	0.814985
$335$	−7.64981	−0.417954
$336$	−1.00000	−0.0545545
$337$	−26.2597	−1.43045	−0.715227	−	0.698892i	$-0.753677\pi$
$337$	−26.2597	−1.43045	−0.715227	+	0.698892i	$0.753677\pi$
$338$	0	0
$339$	−15.1860	−0.824789
$340$	−13.0978	−0.710330
$341$	15.2543	0.826065
$342$	3.15883	0.170810
$343$	1.00000	0.0539949
$344$	8.19806	0.442010
$345$	13.3666	0.719633
$346$	7.28621	0.391709
$347$	−16.3099	−0.875561	−0.437781	−	0.899082i	$-0.644235\pi$
$347$	−16.3099	−0.875561	−0.437781	+	0.899082i	$0.644235\pi$
$348$	4.96077	0.265925
$349$	−34.3937	−1.84105	−0.920527	−	0.390679i	$-0.872240\pi$
$349$	−34.3937	−1.84105	−0.920527	+	0.390679i	$0.872240\pi$
$350$	2.13706	0.114231
$351$	0	0
$352$	3.15883	0.168366
$353$	−16.3284	−0.869074	−0.434537	−	0.900654i	$-0.643088\pi$
$353$	−16.3284	−0.869074	−0.434537	+	0.900654i	$0.643088\pi$
$354$	4.80194	0.255220
$355$	−2.04354	−0.108460
$356$	−13.5526	−0.718285
$357$	−7.74094	−0.409694
$358$	4.10992	0.217216
$359$	21.0248	1.10964	0.554822	−	0.831969i	$-0.312786\pi$
$359$	21.0248	1.10964	0.554822	+	0.831969i	$0.312786\pi$
$360$	1.69202	0.0891774
$361$	−9.02177	−0.474830
$362$	8.63640	0.453919
$363$	1.02177	0.0536290
$364$	0	0
$365$	−23.9530	−1.25376
$366$	3.21983	0.168303
$367$	−23.0858	−1.20507	−0.602533	−	0.798094i	$-0.705842\pi$
$367$	−23.0858	−1.20507	−0.602533	+	0.798094i	$0.705842\pi$
$368$	7.89977	0.411804
$369$	−0.978230	−0.0509246
$370$	0.314683	0.0163596
$371$	−0.652793	−0.0338913
$372$	4.82908	0.250376
$373$	−16.6189	−0.860496	−0.430248	−	0.902711i	$-0.641574\pi$
$373$	−16.6189	−0.860496	−0.430248	+	0.902711i	$0.641574\pi$
$374$	24.4523	1.26440
$375$	−12.0761	−0.623605
$376$	2.78017	0.143376
$377$	0	0
$378$	1.00000	0.0514344
$379$	16.4131	0.843085	0.421542	−	0.906809i	$-0.361489\pi$
$379$	16.4131	0.843085	0.421542	+	0.906809i	$0.361489\pi$
$380$	5.34481	0.274183
$381$	−11.8629	−0.607757
$382$	−26.9922	−1.38104
$383$	−0.241603	−0.0123453	−0.00617266	−	0.999981i	$-0.501965\pi$
$383$	−0.241603	−0.0123453	−0.00617266	+	0.999981i	$0.501965\pi$
$384$	1.00000	0.0510310
$385$	5.34481	0.272397
$386$	16.2174	0.825446
$387$	−8.19806	−0.416731
$388$	7.83340	0.397680
$389$	−28.5042	−1.44522	−0.722611	−	0.691255i	$-0.757058\pi$
$389$	−28.5042	−1.44522	−0.722611	+	0.691255i	$0.757058\pi$
$390$	0	0
$391$	61.1517	3.09257
$392$	−1.00000	−0.0505076
$393$	1.56465	0.0789260
$394$	−21.6625	−1.09134
$395$	12.4185	0.624842
$396$	−3.15883	−0.158737
$397$	−13.8009	−0.692646	−0.346323	−	0.938115i	$-0.612570\pi$
$397$	−13.8009	−0.692646	−0.346323	+	0.938115i	$0.612570\pi$
$398$	8.81700	0.441956
$399$	3.15883	0.158139
$400$	−2.13706	−0.106853
$401$	20.3134	1.01440	0.507200	−	0.861828i	$-0.330680\pi$
$401$	20.3134	1.01440	0.507200	+	0.861828i	$0.330680\pi$
$402$	4.52111	0.225492
$403$	0	0
$404$	15.2228	0.757363
$405$	−1.69202	−0.0840772
$406$	4.96077	0.246199
$407$	−0.587482	−0.0291204
$408$	7.74094	0.383234
$409$	21.0683	1.04176	0.520880	−	0.853630i	$-0.325604\pi$
$409$	21.0683	1.04176	0.520880	+	0.853630i	$0.325604\pi$
$410$	−1.65519	−0.0817438
$411$	20.5700	1.01464
$412$	−11.6528	−0.574092
$413$	4.80194	0.236288
$414$	−7.89977	−0.388253
$415$	−14.0828	−0.691296
$416$	0	0
$417$	22.5308	1.10334
$418$	−9.97823	−0.488051
$419$	−0.486663	−0.0237751	−0.0118875	−	0.999929i	$-0.503784\pi$
$419$	−0.486663	−0.0237751	−0.0118875	+	0.999929i	$0.503784\pi$
$420$	1.69202	0.0825622
$421$	−26.4644	−1.28980	−0.644898	−	0.764268i	$-0.723100\pi$
$421$	−26.4644	−1.28980	−0.644898	+	0.764268i	$0.723100\pi$
$422$	−0.753020	−0.0366565
$423$	−2.78017	−0.135176
$424$	0.652793	0.0317024
$425$	−16.5429	−0.802447
$426$	1.20775	0.0585157
$427$	3.21983	0.155819
$428$	14.5797	0.704737
$429$	0	0
$430$	−13.8713	−0.668933
$431$	−17.2476	−0.830786	−0.415393	−	0.909642i	$-0.636356\pi$
$431$	−17.2476	−0.830786	−0.415393	+	0.909642i	$0.636356\pi$
$432$	−1.00000	−0.0481125
$433$	2.78687	0.133929	0.0669643	−	0.997755i	$-0.478669\pi$
$433$	2.78687	0.133929	0.0669643	+	0.997755i	$0.478669\pi$
$434$	4.82908	0.231803
$435$	−8.39373	−0.402449
$436$	−6.29590	−0.301519
$437$	−24.9541	−1.19371
$438$	14.1564	0.676421
$439$	−21.4808	−1.02522	−0.512612	−	0.858621i	$-0.671322\pi$
$439$	−21.4808	−1.02522	−0.512612	+	0.858621i	$0.671322\pi$
$440$	−5.34481	−0.254804
$441$	1.00000	0.0476190
$442$	0	0
$443$	9.85623	0.468284	0.234142	−	0.972202i	$-0.424772\pi$
$443$	9.85623	0.468284	0.234142	+	0.972202i	$0.424772\pi$
$444$	−0.185981	−0.00882625
$445$	22.9312	1.08704
$446$	−2.14377	−0.101510
$447$	−1.60925	−0.0761150
$448$	1.00000	0.0472456
$449$	−10.8358	−0.511373	−0.255686	−	0.966760i	$-0.582301\pi$
$449$	−10.8358	−0.511373	−0.255686	+	0.966760i	$0.582301\pi$
$450$	2.13706	0.100742
$451$	3.09006	0.145505
$452$	15.1860	0.714288
$453$	13.1709	0.618824
$454$	21.3327	1.00119
$455$	0	0
$456$	−3.15883	−0.147926
$457$	15.5386	0.726863	0.363432	−	0.931621i	$-0.381605\pi$
$457$	15.5386	0.726863	0.363432	+	0.931621i	$0.381605\pi$
$458$	−15.3502	−0.717267
$459$	−7.74094	−0.361316
$460$	−13.3666	−0.623220
$461$	5.55389	0.258671	0.129335	−	0.991601i	$-0.458716\pi$
$461$	5.55389	0.258671	0.129335	+	0.991601i	$0.458716\pi$
$462$	−3.15883	−0.146962
$463$	−8.29291	−0.385404	−0.192702	−	0.981257i	$-0.561725\pi$
$463$	−8.29291	−0.385404	−0.192702	+	0.981257i	$0.561725\pi$
$464$	−4.96077	−0.230298
$465$	−8.17092	−0.378917
$466$	−23.1468	−1.07225
$467$	−22.7071	−1.05076	−0.525379	−	0.850868i	$-0.676077\pi$
$467$	−22.7071	−1.05076	−0.525379	+	0.850868i	$0.676077\pi$
$468$	0	0
$469$	4.52111	0.208765
$470$	−4.70410	−0.216984
$471$	2.61596	0.120537
$472$	−4.80194	−0.221027
$473$	25.8963	1.19071
$474$	−7.33944	−0.337112
$475$	6.75063	0.309740
$476$	7.74094	0.354805
$477$	−0.652793	−0.0298893
$478$	−17.8538	−0.816616
$479$	−22.9245	−1.04745	−0.523724	−	0.851888i	$-0.675458\pi$
$479$	−22.9245	−1.04745	−0.523724	+	0.851888i	$0.675458\pi$
$480$	−1.69202	−0.0772299
$481$	0	0
$482$	16.4179	0.747815
$483$	−7.89977	−0.359452
$484$	−1.02177	−0.0464441
$485$	−13.2543	−0.601846
$486$	1.00000	0.0453609
$487$	−7.97525	−0.361393	−0.180696	−	0.983539i	$-0.557835\pi$
$487$	−7.97525	−0.361393	−0.180696	+	0.983539i	$0.557835\pi$
$488$	−3.21983	−0.145755
$489$	0.853248	0.0385852
$490$	1.69202	0.0764377
$491$	−25.0116	−1.12876	−0.564379	−	0.825516i	$-0.690884\pi$
$491$	−25.0116	−1.12876	−0.564379	+	0.825516i	$0.690884\pi$
$492$	0.978230	0.0441020
$493$	−38.4010	−1.72950
$494$	0	0
$495$	5.34481	0.240232
$496$	−4.82908	−0.216832
$497$	1.20775	0.0541750
$498$	8.32304	0.372965
$499$	−11.7168	−0.524515	−0.262257	−	0.964998i	$-0.584467\pi$
$499$	−11.7168	−0.524515	−0.262257	+	0.964998i	$0.584467\pi$
$500$	12.0761	0.540058
$501$	14.8944	0.665433
$502$	23.9124	1.06726
$503$	6.62133	0.295231	0.147615	−	0.989045i	$-0.452840\pi$
$503$	6.62133	0.295231	0.147615	+	0.989045i	$0.452840\pi$
$504$	−1.00000	−0.0445435
$505$	−25.7573	−1.14619
$506$	24.9541	1.10934
$507$	0	0
$508$	11.8629	0.526333
$509$	−33.6728	−1.49252	−0.746259	−	0.665655i	$-0.768152\pi$
$509$	−33.6728	−1.49252	−0.746259	+	0.665655i	$0.768152\pi$
$510$	−13.0978	−0.579982
$511$	14.1564	0.626244
$512$	−1.00000	−0.0441942
$513$	3.15883	0.139466
$514$	−8.77479	−0.387039
$515$	19.7168	0.868825
$516$	8.19806	0.360900
$517$	8.78209	0.386236
$518$	−0.185981	−0.00817152
$519$	7.28621	0.319829
$520$	0	0
$521$	−6.73125	−0.294901	−0.147451	−	0.989069i	$-0.547107\pi$
$521$	−6.73125	−0.294901	−0.147451	+	0.989069i	$0.547107\pi$
$522$	4.96077	0.217127
$523$	4.01938	0.175755	0.0878776	−	0.996131i	$-0.471992\pi$
$523$	4.01938	0.175755	0.0878776	+	0.996131i	$0.471992\pi$
$524$	−1.56465	−0.0683519
$525$	2.13706	0.0932691
$526$	−6.78448	−0.295817
$527$	−37.3817	−1.62837
$528$	3.15883	0.137471
$529$	39.4064	1.71332
$530$	−1.10454	−0.0479781
$531$	4.80194	0.208386
$532$	−3.15883	−0.136953
$533$	0	0
$534$	−13.5526	−0.586477
$535$	−24.6692	−1.06654
$536$	−4.52111	−0.195282
$537$	4.10992	0.177356
$538$	5.13706	0.221475
$539$	−3.15883	−0.136061
$540$	1.69202	0.0728130
$541$	−44.8286	−1.92733	−0.963666	−	0.267109i	$-0.913932\pi$
$541$	−44.8286	−1.92733	−0.963666	+	0.267109i	$0.913932\pi$
$542$	−25.7995	−1.10819
$543$	8.63640	0.370623
$544$	−7.74094	−0.331890
$545$	10.6528	0.456316
$546$	0	0
$547$	−30.5603	−1.30667	−0.653333	−	0.757071i	$-0.726630\pi$
$547$	−30.5603	−1.30667	−0.653333	+	0.757071i	$0.726630\pi$
$548$	−20.5700	−0.878708
$549$	3.21983	0.137419
$550$	−6.75063	−0.287848
$551$	15.6703	0.667575
$552$	7.89977	0.336237
$553$	−7.33944	−0.312105
$554$	−19.9976	−0.849617
$555$	0.314683	0.0133576
$556$	−22.5308	−0.955519
$557$	−44.0277	−1.86552	−0.932758	−	0.360504i	$-0.882605\pi$
$557$	−44.0277	−1.86552	−0.932758	+	0.360504i	$0.882605\pi$
$558$	4.82908	0.204431
$559$	0	0
$560$	−1.69202	−0.0715010
$561$	24.4523	1.03238
$562$	18.5851	0.783965
$563$	−30.7138	−1.29443	−0.647216	−	0.762307i	$-0.724067\pi$
$563$	−30.7138	−1.29443	−0.647216	+	0.762307i	$0.724067\pi$
$564$	2.78017	0.117066
$565$	−25.6950	−1.08100
$566$	4.35152	0.182908
$567$	1.00000	0.0419961
$568$	−1.20775	−0.0506761
$569$	35.8963	1.50485	0.752426	−	0.658677i	$-0.228884\pi$
$569$	35.8963	1.50485	0.752426	+	0.658677i	$0.228884\pi$
$570$	5.34481	0.223870
$571$	−30.2218	−1.26474	−0.632370	−	0.774666i	$-0.717918\pi$
$571$	−30.2218	−1.26474	−0.632370	+	0.774666i	$0.717918\pi$
$572$	0	0
$573$	−26.9922	−1.12762
$574$	0.978230	0.0408305
$575$	−16.8823	−0.704041
$576$	1.00000	0.0416667
$577$	−10.6799	−0.444612	−0.222306	−	0.974977i	$-0.571358\pi$
$577$	−10.6799	−0.444612	−0.222306	+	0.974977i	$0.571358\pi$
$578$	−42.9221	−1.78533
$579$	16.2174	0.673974
$580$	8.39373	0.348531
$581$	8.32304	0.345298
$582$	7.83340	0.324705
$583$	2.06206	0.0854020
$584$	−14.1564	−0.585798
$585$	0	0
$586$	7.14138	0.295007
$587$	−5.42865	−0.224064	−0.112032	−	0.993705i	$-0.535736\pi$
$587$	−5.42865	−0.224064	−0.112032	+	0.993705i	$0.535736\pi$
$588$	−1.00000	−0.0412393
$589$	15.2543	0.628541
$590$	8.12498	0.334500
$591$	−21.6625	−0.891075
$592$	0.185981	0.00764376
$593$	−12.3037	−0.505251	−0.252626	−	0.967564i	$-0.581294\pi$
$593$	−12.3037	−0.505251	−0.252626	+	0.967564i	$0.581294\pi$
$594$	−3.15883	−0.129609
$595$	−13.0978	−0.536959
$596$	1.60925	0.0659175
$597$	8.81700	0.360856
$598$	0	0
$599$	−42.9487	−1.75484	−0.877418	−	0.479727i	$-0.840736\pi$
$599$	−42.9487	−1.75484	−0.877418	+	0.479727i	$0.840736\pi$
$600$	−2.13706	−0.0872452
$601$	6.95348	0.283638	0.141819	−	0.989893i	$-0.454705\pi$
$601$	6.95348	0.283638	0.141819	+	0.989893i	$0.454705\pi$
$602$	8.19806	0.334128
$603$	4.52111	0.184114
$604$	−13.1709	−0.535917
$605$	1.72886	0.0702880
$606$	15.2228	0.618385
$607$	4.25129	0.172555	0.0862773	−	0.996271i	$-0.472503\pi$
$607$	4.25129	0.172555	0.0862773	+	0.996271i	$0.472503\pi$
$608$	3.15883	0.128108
$609$	4.96077	0.201021
$610$	5.44803	0.220584
$611$	0	0
$612$	7.74094	0.312909
$613$	9.09113	0.367187	0.183594	−	0.983002i	$-0.441227\pi$
$613$	9.09113	0.367187	0.183594	+	0.983002i	$0.441227\pi$
$614$	−3.13467	−0.126505
$615$	−1.65519	−0.0667435
$616$	3.15883	0.127273
$617$	−12.2067	−0.491423	−0.245711	−	0.969343i	$-0.579022\pi$
$617$	−12.2067	−0.491423	−0.245711	+	0.969343i	$0.579022\pi$
$618$	−11.6528	−0.468744
$619$	−49.1183	−1.97423	−0.987115	−	0.160012i	$-0.948847\pi$
$619$	−49.1183	−1.97423	−0.987115	+	0.160012i	$0.948847\pi$
$620$	8.17092	0.328152
$621$	−7.89977	−0.317007
$622$	32.7875	1.31466
$623$	−13.5526	−0.542972
$624$	0	0
$625$	−9.74764	−0.389906
$626$	−11.5985	−0.463569
$627$	−9.97823	−0.398492
$628$	−2.61596	−0.104388
$629$	1.43967	0.0574032
$630$	1.69202	0.0674117
$631$	16.4620	0.655343	0.327671	−	0.944792i	$-0.393736\pi$
$631$	16.4620	0.655343	0.327671	+	0.944792i	$0.393736\pi$
$632$	7.33944	0.291947
$633$	−0.753020	−0.0299299
$634$	−3.71810	−0.147665
$635$	−20.0723	−0.796547
$636$	0.652793	0.0258849
$637$	0	0
$638$	−15.6703	−0.620391
$639$	1.20775	0.0477779
$640$	1.69202	0.0668830
$641$	43.0428	1.70009	0.850044	−	0.526711i	$-0.176575\pi$
$641$	43.0428	1.70009	0.850044	+	0.526711i	$0.176575\pi$
$642$	14.5797	0.575415
$643$	20.3220	0.801421	0.400710	−	0.916205i	$-0.368763\pi$
$643$	20.3220	0.801421	0.400710	+	0.916205i	$0.368763\pi$
$644$	7.89977	0.311295
$645$	−13.8713	−0.546182
$646$	24.4523	0.962064
$647$	11.0049	0.432647	0.216324	−	0.976322i	$-0.430593\pi$
$647$	11.0049	0.432647	0.216324	+	0.976322i	$0.430593\pi$
$648$	−1.00000	−0.0392837
$649$	−15.1685	−0.595417
$650$	0	0
$651$	4.82908	0.189267
$652$	−0.853248	−0.0334158
$653$	−17.9355	−0.701872	−0.350936	−	0.936399i	$-0.614137\pi$
$653$	−17.9355	−0.701872	−0.350936	+	0.936399i	$0.614137\pi$
$654$	−6.29590	−0.246189
$655$	2.64742	0.103443
$656$	−0.978230	−0.0381935
$657$	14.1564	0.552295
$658$	2.78017	0.108382
$659$	29.1594	1.13589	0.567945	−	0.823067i	$-0.307739\pi$
$659$	29.1594	1.13589	0.567945	+	0.823067i	$0.307739\pi$
$660$	−5.34481	−0.208047
$661$	34.5217	1.34274	0.671369	−	0.741123i	$-0.265707\pi$
$661$	34.5217	1.34274	0.671369	+	0.741123i	$0.265707\pi$
$662$	15.8532	0.616154
$663$	0	0
$664$	−8.32304	−0.322997
$665$	5.34481	0.207263
$666$	−0.185981	−0.00720660
$667$	−39.1890	−1.51740
$668$	−14.8944	−0.576281
$669$	−2.14377	−0.0828829
$670$	7.64981	0.295538
$671$	−10.1709	−0.392644
$672$	1.00000	0.0385758
$673$	−9.46203	−0.364734	−0.182367	−	0.983231i	$-0.558376\pi$
$673$	−9.46203	−0.364734	−0.182367	+	0.983231i	$0.558376\pi$
$674$	26.2597	1.01148
$675$	2.13706	0.0822556
$676$	0	0
$677$	−17.1438	−0.658889	−0.329444	−	0.944175i	$-0.606861\pi$
$677$	−17.1438	−0.658889	−0.329444	+	0.944175i	$0.606861\pi$
$678$	15.1860	0.583214
$679$	7.83340	0.300618
$680$	13.0978	0.502279
$681$	21.3327	0.817472
$682$	−15.2543	−0.584116
$683$	21.0339	0.804838	0.402419	−	0.915456i	$-0.368170\pi$
$683$	21.0339	0.804838	0.402419	+	0.915456i	$0.368170\pi$
$684$	−3.15883	−0.120781
$685$	34.8049	1.32983
$686$	−1.00000	−0.0381802
$687$	−15.3502	−0.585646
$688$	−8.19806	−0.312548
$689$	0	0
$690$	−13.3666	−0.508857
$691$	9.23490	0.351312	0.175656	−	0.984452i	$-0.443795\pi$
$691$	9.23490	0.351312	0.175656	+	0.984452i	$0.443795\pi$
$692$	−7.28621	−0.276980
$693$	−3.15883	−0.119994
$694$	16.3099	0.619115
$695$	38.1226	1.44607
$696$	−4.96077	−0.188038
$697$	−7.57242	−0.286826
$698$	34.3937	1.30182
$699$	−23.1468	−0.875491
$700$	−2.13706	−0.0807734
$701$	−17.2989	−0.653370	−0.326685	−	0.945133i	$-0.605932\pi$
$701$	−17.2989	−0.653370	−0.326685	+	0.945133i	$0.605932\pi$
$702$	0	0
$703$	−0.587482	−0.0221573
$704$	−3.15883	−0.119053
$705$	−4.70410	−0.177167
$706$	16.3284	0.614528
$707$	15.2228	0.572513
$708$	−4.80194	−0.180468
$709$	−19.2911	−0.724493	−0.362246	−	0.932082i	$-0.617990\pi$
$709$	−19.2911	−0.724493	−0.362246	+	0.932082i	$0.617990\pi$
$710$	2.04354	0.0766927
$711$	−7.33944	−0.275250
$712$	13.5526	0.507904
$713$	−38.1487	−1.42868
$714$	7.74094	0.289697
$715$	0	0
$716$	−4.10992	−0.153595
$717$	−17.8538	−0.666764
$718$	−21.0248	−0.784637
$719$	−3.61165	−0.134692	−0.0673458	−	0.997730i	$-0.521453\pi$
$719$	−3.61165	−0.134692	−0.0673458	+	0.997730i	$0.521453\pi$
$720$	−1.69202	−0.0630579
$721$	−11.6528	−0.433973
$722$	9.02177	0.335756
$723$	16.4179	0.610588
$724$	−8.63640	−0.320969
$725$	10.6015	0.393729
$726$	−1.02177	−0.0379215
$727$	−18.6614	−0.692114	−0.346057	−	0.938214i	$-0.612480\pi$
$727$	−18.6614	−0.692114	−0.346057	+	0.938214i	$0.612480\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	23.9530	0.886540
$731$	−63.4607	−2.34718
$732$	−3.21983	−0.119008
$733$	41.8872	1.54714	0.773570	−	0.633711i	$-0.218469\pi$
$733$	41.8872	1.54714	0.773570	+	0.633711i	$0.218469\pi$
$734$	23.0858	0.852111
$735$	1.69202	0.0624112
$736$	−7.89977	−0.291189
$737$	−14.2814	−0.526063
$738$	0.978230	0.0360091
$739$	46.7622	1.72018	0.860088	−	0.510145i	$-0.170408\pi$
$739$	46.7622	1.72018	0.860088	+	0.510145i	$0.170408\pi$
$740$	−0.314683	−0.0115680
$741$	0	0
$742$	0.652793	0.0239648
$743$	13.3260	0.488885	0.244442	−	0.969664i	$-0.421395\pi$
$743$	13.3260	0.488885	0.244442	+	0.969664i	$0.421395\pi$
$744$	−4.82908	−0.177043
$745$	−2.72289	−0.0997589
$746$	16.6189	0.608463
$747$	8.32304	0.304524
$748$	−24.4523	−0.894066
$749$	14.5797	0.532731
$750$	12.0761	0.440956
$751$	21.8888	0.798732	0.399366	−	0.916792i	$-0.369230\pi$
$751$	21.8888	0.798732	0.399366	+	0.916792i	$0.369230\pi$
$752$	−2.78017	−0.101382
$753$	23.9124	0.871418
$754$	0	0
$755$	22.2855	0.811051
$756$	−1.00000	−0.0363696
$757$	12.6974	0.461495	0.230747	−	0.973014i	$-0.425883\pi$
$757$	12.6974	0.461495	0.230747	+	0.973014i	$0.425883\pi$
$758$	−16.4131	−0.596151
$759$	24.9541	0.905775
$760$	−5.34481	−0.193877
$761$	53.5096	1.93972	0.969861	−	0.243659i	$-0.0783477\pi$
$761$	53.5096	1.93972	0.969861	+	0.243659i	$0.0783477\pi$
$762$	11.8629	0.429749
$763$	−6.29590	−0.227927
$764$	26.9922	0.976545
$765$	−13.0978	−0.473553
$766$	0.241603	0.00872946
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−22.2892	−0.803769	−0.401884	−	0.915690i	$-0.631645\pi$
$769$	−22.2892	−0.803769	−0.401884	+	0.915690i	$0.631645\pi$
$770$	−5.34481	−0.192614
$771$	−8.77479	−0.316016
$772$	−16.2174	−0.583678
$773$	32.3726	1.16436	0.582180	−	0.813060i	$-0.302200\pi$
$773$	32.3726	1.16436	0.582180	+	0.813060i	$0.302200\pi$
$774$	8.19806	0.294673
$775$	10.3201	0.370708
$776$	−7.83340	−0.281203
$777$	−0.185981	−0.00667202
$778$	28.5042	1.02193
$779$	3.09006	0.110713
$780$	0	0
$781$	−3.81508	−0.136514
$782$	−61.1517	−2.18678
$783$	4.96077	0.177284
$784$	1.00000	0.0357143
$785$	4.42626	0.157980
$786$	−1.56465	−0.0558091
$787$	−31.0984	−1.10854	−0.554270	−	0.832337i	$-0.687002\pi$
$787$	−31.0984	−1.10854	−0.554270	+	0.832337i	$0.687002\pi$
$788$	21.6625	0.771694
$789$	−6.78448	−0.241534
$790$	−12.4185	−0.441830
$791$	15.1860	0.539951
$792$	3.15883	0.112244
$793$	0	0
$794$	13.8009	0.489775
$795$	−1.10454	−0.0391740
$796$	−8.81700	−0.312510
$797$	−23.1997	−0.821776	−0.410888	−	0.911686i	$-0.634781\pi$
$797$	−23.1997	−0.821776	−0.410888	+	0.911686i	$0.634781\pi$
$798$	−3.15883	−0.111821
$799$	−21.5211	−0.761362
$800$	2.13706	0.0755566
$801$	−13.5526	−0.478856
$802$	−20.3134	−0.717290
$803$	−44.7178	−1.57806
$804$	−4.52111	−0.159447
$805$	−13.3666	−0.471110
$806$	0	0
$807$	5.13706	0.180833
$808$	−15.2228	−0.535537
$809$	−5.47948	−0.192648	−0.0963242	−	0.995350i	$-0.530709\pi$
$809$	−5.47948	−0.192648	−0.0963242	+	0.995350i	$0.530709\pi$
$810$	1.69202	0.0594516
$811$	−52.0592	−1.82805	−0.914023	−	0.405663i	$-0.867041\pi$
$811$	−52.0592	−1.82805	−0.914023	+	0.405663i	$0.867041\pi$
$812$	−4.96077	−0.174089
$813$	−25.7995	−0.904830
$814$	0.587482	0.0205912
$815$	1.44371	0.0505711
$816$	−7.74094	−0.270987
$817$	25.8963	0.905997
$818$	−21.0683	−0.736636
$819$	0	0
$820$	1.65519	0.0578016
$821$	−2.61655	−0.0913182	−0.0456591	−	0.998957i	$-0.514539\pi$
$821$	−2.61655	−0.0913182	−0.0456591	+	0.998957i	$0.514539\pi$
$822$	−20.5700	−0.717462
$823$	50.4596	1.75891	0.879456	−	0.475980i	$-0.157907\pi$
$823$	50.4596	1.75891	0.879456	+	0.475980i	$0.157907\pi$
$824$	11.6528	0.405944
$825$	−6.75063	−0.235027
$826$	−4.80194	−0.167081
$827$	−2.91079	−0.101218	−0.0506090	−	0.998719i	$-0.516116\pi$
$827$	−2.91079	−0.101218	−0.0506090	+	0.998719i	$0.516116\pi$
$828$	7.89977	0.274536
$829$	−6.09724	−0.211766	−0.105883	−	0.994379i	$-0.533767\pi$
$829$	−6.09724	−0.211766	−0.105883	+	0.994379i	$0.533767\pi$
$830$	14.0828	0.488820
$831$	−19.9976	−0.693709
$832$	0	0
$833$	7.74094	0.268208
$834$	−22.5308	−0.780178
$835$	25.2016	0.872139
$836$	9.97823	0.345104
$837$	4.82908	0.166918
$838$	0.486663	0.0168115
$839$	4.22654	0.145916	0.0729581	−	0.997335i	$-0.476756\pi$
$839$	4.22654	0.145916	0.0729581	+	0.997335i	$0.476756\pi$
$840$	−1.69202	−0.0583803
$841$	−4.39075	−0.151405
$842$	26.4644	0.912024
$843$	18.5851	0.640104
$844$	0.753020	0.0259200
$845$	0	0
$846$	2.78017	0.0955841
$847$	−1.02177	−0.0351084
$848$	−0.652793	−0.0224170
$849$	4.35152	0.149344
$850$	16.5429	0.567416
$851$	1.46921	0.0503637
$852$	−1.20775	−0.0413769
$853$	−42.0538	−1.43990	−0.719948	−	0.694028i	$-0.755834\pi$
$853$	−42.0538	−1.43990	−0.719948	+	0.694028i	$0.755834\pi$
$854$	−3.21983	−0.110180
$855$	5.34481	0.182789
$856$	−14.5797	−0.498324
$857$	−40.6039	−1.38700	−0.693501	−	0.720456i	$-0.743933\pi$
$857$	−40.6039	−1.38700	−0.693501	+	0.720456i	$0.743933\pi$
$858$	0	0
$859$	4.53643	0.154781	0.0773906	−	0.997001i	$-0.475341\pi$
$859$	4.53643	0.154781	0.0773906	+	0.997001i	$0.475341\pi$
$860$	13.8713	0.473007
$861$	0.978230	0.0333380
$862$	17.2476	0.587455
$863$	−27.8592	−0.948339	−0.474169	−	0.880434i	$-0.657252\pi$
$863$	−27.8592	−0.948339	−0.474169	+	0.880434i	$0.657252\pi$
$864$	1.00000	0.0340207
$865$	12.3284	0.419179
$866$	−2.78687	−0.0947018
$867$	−42.9221	−1.45771
$868$	−4.82908	−0.163910
$869$	23.1841	0.786465
$870$	8.39373	0.284574
$871$	0	0
$872$	6.29590	0.213206
$873$	7.83340	0.265120
$874$	24.9541	0.844084
$875$	12.0761	0.408245
$876$	−14.1564	−0.478302
$877$	45.6892	1.54281	0.771407	−	0.636343i	$-0.219554\pi$
$877$	45.6892	1.54281	0.771407	+	0.636343i	$0.219554\pi$
$878$	21.4808	0.724942
$879$	7.14138	0.240873
$880$	5.34481	0.180174
$881$	17.2935	0.582633	0.291316	−	0.956627i	$-0.405907\pi$
$881$	17.2935	0.582633	0.291316	+	0.956627i	$0.405907\pi$
$882$	−1.00000	−0.0336718
$883$	41.8179	1.40728	0.703641	−	0.710555i	$-0.251556\pi$
$883$	41.8179	1.40728	0.703641	+	0.710555i	$0.251556\pi$
$884$	0	0
$885$	8.12498	0.273118
$886$	−9.85623	−0.331127
$887$	−11.4196	−0.383431	−0.191715	−	0.981451i	$-0.561405\pi$
$887$	−11.4196	−0.383431	−0.191715	+	0.981451i	$0.561405\pi$
$888$	0.185981	0.00624110
$889$	11.8629	0.397870
$890$	−22.9312	−0.768657
$891$	−3.15883	−0.105825
$892$	2.14377	0.0717787
$893$	8.78209	0.293881
$894$	1.60925	0.0538214
$895$	6.95407	0.232449
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	10.8358	0.361595
$899$	23.9560	0.798977
$900$	−2.13706	−0.0712354
$901$	−5.05323	−0.168347
$902$	−3.09006	−0.102888
$903$	8.19806	0.272814
$904$	−15.1860	−0.505078
$905$	14.6130	0.485752
$906$	−13.1709	−0.437574
$907$	−31.6396	−1.05058	−0.525289	−	0.850924i	$-0.676043\pi$
$907$	−31.6396	−1.05058	−0.525289	+	0.850924i	$0.676043\pi$
$908$	−21.3327	−0.707952
$909$	15.2228	0.504909
$910$	0	0
$911$	14.5875	0.483305	0.241652	−	0.970363i	$-0.422311\pi$
$911$	14.5875	0.483305	0.241652	+	0.970363i	$0.422311\pi$
$912$	3.15883	0.104599
$913$	−26.2911	−0.870109
$914$	−15.5386	−0.513970
$915$	5.44803	0.180106
$916$	15.3502	0.507185
$917$	−1.56465	−0.0516692
$918$	7.74094	0.255489
$919$	−47.3019	−1.56034	−0.780172	−	0.625565i	$-0.784869\pi$
$919$	−47.3019	−1.56034	−0.780172	+	0.625565i	$0.784869\pi$
$920$	13.3666	0.440683
$921$	−3.13467	−0.103291
$922$	−5.55389	−0.182908
$923$	0	0
$924$	3.15883	0.103918
$925$	−0.397452	−0.0130682
$926$	8.29291	0.272522
$927$	−11.6528	−0.382728
$928$	4.96077	0.162845
$929$	40.5526	1.33049	0.665243	−	0.746627i	$-0.268328\pi$
$929$	40.5526	1.33049	0.665243	+	0.746627i	$0.268328\pi$
$930$	8.17092	0.267935
$931$	−3.15883	−0.103527
$932$	23.1468	0.758197
$933$	32.7875	1.07341
$934$	22.7071	0.742999
$935$	41.3739	1.35307
$936$	0	0
$937$	18.7186	0.611509	0.305755	−	0.952110i	$-0.401091\pi$
$937$	18.7186	0.611509	0.305755	+	0.952110i	$0.401091\pi$
$938$	−4.52111	−0.147619
$939$	−11.5985	−0.378503
$940$	4.70410	0.153431
$941$	−27.2285	−0.887622	−0.443811	−	0.896120i	$-0.646374\pi$
$941$	−27.2285	−0.887622	−0.443811	+	0.896120i	$0.646374\pi$
$942$	−2.61596	−0.0852325
$943$	−7.72779	−0.251652
$944$	4.80194	0.156290
$945$	1.69202	0.0550415
$946$	−25.8963	−0.841962
$947$	−51.9963	−1.68965	−0.844826	−	0.535041i	$-0.820296\pi$
$947$	−51.9963	−1.68965	−0.844826	+	0.535041i	$0.820296\pi$
$948$	7.33944	0.238374
$949$	0	0
$950$	−6.75063	−0.219019
$951$	−3.71810	−0.120568
$952$	−7.74094	−0.250885
$953$	−37.5265	−1.21560	−0.607801	−	0.794089i	$-0.707948\pi$
$953$	−37.5265	−1.21560	−0.607801	+	0.794089i	$0.707948\pi$
$954$	0.652793	0.0211349
$955$	−45.6714	−1.47789
$956$	17.8538	0.577434
$957$	−15.6703	−0.506547
$958$	22.9245	0.740658
$959$	−20.5700	−0.664241
$960$	1.69202	0.0546098
$961$	−7.67994	−0.247740
$962$	0	0
$963$	14.5797	0.469825
$964$	−16.4179	−0.528785
$965$	27.4403	0.883333
$966$	7.89977	0.254171
$967$	−49.0786	−1.57826	−0.789130	−	0.614226i	$-0.789468\pi$
$967$	−49.0786	−1.57826	−0.789130	+	0.614226i	$0.789468\pi$
$968$	1.02177	0.0328409
$969$	24.4523	0.785522
$970$	13.2543	0.425569
$971$	−37.6746	−1.20903	−0.604517	−	0.796592i	$-0.706634\pi$
$971$	−37.6746	−1.20903	−0.604517	+	0.796592i	$0.706634\pi$
$972$	−1.00000	−0.0320750
$973$	−22.5308	−0.722304
$974$	7.97525	0.255543
$975$	0	0
$976$	3.21983	0.103064
$977$	−10.0852	−0.322653	−0.161326	−	0.986901i	$-0.551577\pi$
$977$	−10.0852	−0.322653	−0.161326	+	0.986901i	$0.551577\pi$
$978$	−0.853248	−0.0272839
$979$	42.8103	1.36822
$980$	−1.69202	−0.0540496
$981$	−6.29590	−0.201013
$982$	25.0116	0.798152
$983$	24.1299	0.769624	0.384812	−	0.922995i	$-0.374266\pi$
$983$	24.1299	0.769624	0.384812	+	0.922995i	$0.374266\pi$
$984$	−0.978230	−0.0311848
$985$	−36.6534	−1.16787
$986$	38.4010	1.22294
$987$	2.78017	0.0884937
$988$	0	0
$989$	−64.7628	−2.05934
$990$	−5.34481	−0.169869
$991$	−39.6553	−1.25969	−0.629846	−	0.776720i	$-0.716882\pi$
$991$	−39.6553	−1.25969	−0.629846	+	0.776720i	$0.716882\pi$
$992$	4.82908	0.153324
$993$	15.8532	0.503088
$994$	−1.20775	−0.0383075
$995$	14.9186	0.472950
$996$	−8.32304	−0.263726
$997$	−29.5394	−0.935523	−0.467761	−	0.883855i	$-0.654939\pi$
$997$	−29.5394	−0.935523	−0.467761	+	0.883855i	$0.654939\pi$
$998$	11.7168	0.370888
$999$	−0.185981	−0.00588417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.cd.1.1	✓	3
13.12	even	2		7098.2.a.ci.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cd.1.1	✓	3	1.1	even	1	trivial
7098.2.a.ci.1.3	yes	3	13.12	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:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.69202 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.69202 q^{10} -3.15883 q^{11} -1.00000 q^{12} -1.00000 q^{14} +1.69202 q^{15} +1.00000 q^{16} +7.74094 q^{17} -1.00000 q^{18} -3.15883 q^{19} -1.69202 q^{20} -1.00000 q^{21} +3.15883 q^{22} +7.89977 q^{23} +1.00000 q^{24} -2.13706 q^{25} -1.00000 q^{27} +1.00000 q^{28} -4.96077 q^{29} -1.69202 q^{30} -4.82908 q^{31} -1.00000 q^{32} +3.15883 q^{33} -7.74094 q^{34} -1.69202 q^{35} +1.00000 q^{36} +0.185981 q^{37} +3.15883 q^{38} +1.69202 q^{40} -0.978230 q^{41} +1.00000 q^{42} -8.19806 q^{43} -3.15883 q^{44} -1.69202 q^{45} -7.89977 q^{46} -2.78017 q^{47} -1.00000 q^{48} +1.00000 q^{49} +2.13706 q^{50} -7.74094 q^{51} -0.652793 q^{53} +1.00000 q^{54} +5.34481 q^{55} -1.00000 q^{56} +3.15883 q^{57} +4.96077 q^{58} +4.80194 q^{59} +1.69202 q^{60} +3.21983 q^{61} +4.82908 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.15883 q^{66} +4.52111 q^{67} +7.74094 q^{68} -7.89977 q^{69} +1.69202 q^{70} +1.20775 q^{71} -1.00000 q^{72} +14.1564 q^{73} -0.185981 q^{74} +2.13706 q^{75} -3.15883 q^{76} -3.15883 q^{77} -7.33944 q^{79} -1.69202 q^{80} +1.00000 q^{81} +0.978230 q^{82} +8.32304 q^{83} -1.00000 q^{84} -13.0978 q^{85} +8.19806 q^{86} +4.96077 q^{87} +3.15883 q^{88} -13.5526 q^{89} +1.69202 q^{90} +7.89977 q^{92} +4.82908 q^{93} +2.78017 q^{94} +5.34481 q^{95} +1.00000 q^{96} +7.83340 q^{97} -1.00000 q^{98} -3.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - q^{11} - 3 q^{12} - 3 q^{14} + 3 q^{16} + 9 q^{17} - 3 q^{18} - q^{19} - 3 q^{21} + q^{22} + q^{23} + 3 q^{24} - q^{25} - 3 q^{27} + 3 q^{28} - 2 q^{29} - 4 q^{31} - 3 q^{32} + q^{33} - 9 q^{34} + 3 q^{36} - 14 q^{37} + q^{38} - 6 q^{41} + 3 q^{42} - 29 q^{43} - q^{44} - q^{46} - 7 q^{47} - 3 q^{48} + 3 q^{49} + q^{50} - 9 q^{51} + 16 q^{53} + 3 q^{54} - 7 q^{55} - 3 q^{56} + q^{57} + 2 q^{58} + 10 q^{59} + 11 q^{61} + 4 q^{62} + 3 q^{63} + 3 q^{64} - q^{66} - 2 q^{67} + 9 q^{68} - q^{69} - 14 q^{71} - 3 q^{72} - 7 q^{73} + 14 q^{74} + q^{75} - q^{76} - q^{77} - 2 q^{79} + 3 q^{81} + 6 q^{82} + 5 q^{83} - 3 q^{84} - 21 q^{85} + 29 q^{86} + 2 q^{87} + q^{88} + q^{92} + 4 q^{93} + 7 q^{94} - 7 q^{95} + 3 q^{96} - 6 q^{97} - 3 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - q^11 - 3 * q^12 - 3 * q^14 + 3 * q^16 + 9 * q^17 - 3 * q^18 - q^19 - 3 * q^21 + q^22 + q^23 + 3 * q^24 - q^25 - 3 * q^27 + 3 * q^28 - 2 * q^29 - 4 * q^31 - 3 * q^32 + q^33 - 9 * q^34 + 3 * q^36 - 14 * q^37 + q^38 - 6 * q^41 + 3 * q^42 - 29 * q^43 - q^44 - q^46 - 7 * q^47 - 3 * q^48 + 3 * q^49 + q^50 - 9 * q^51 + 16 * q^53 + 3 * q^54 - 7 * q^55 - 3 * q^56 + q^57 + 2 * q^58 + 10 * q^59 + 11 * q^61 + 4 * q^62 + 3 * q^63 + 3 * q^64 - q^66 - 2 * q^67 + 9 * q^68 - q^69 - 14 * q^71 - 3 * q^72 - 7 * q^73 + 14 * q^74 + q^75 - q^76 - q^77 - 2 * q^79 + 3 * q^81 + 6 * q^82 + 5 * q^83 - 3 * q^84 - 21 * q^85 + 29 * q^86 + 2 * q^87 + q^88 + q^92 + 4 * q^93 + 7 * q^94 - 7 * q^95 + 3 * q^96 - 6 * q^97 - 3 * q^98 - q^99

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