LMFDB - Embedded newform 6027.2.a.bh.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} + \cdots - 4 $ x^13 - 4x^12 - 11x^11 + 56x^10 + 26x^9 - 263x^8 + 50x^7 + 478x^6 - 174x^5 - 311x^4 + 84x^3 + 69x^2 - 12x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.58904$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58904 q^{2} -1.00000 q^{3} +4.70310 q^{4} +3.45213 q^{5} +2.58904 q^{6} -6.99843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58904 q^{2} -1.00000 q^{3} +4.70310 q^{4} +3.45213 q^{5} +2.58904 q^{6} -6.99843 q^{8} +1.00000 q^{9} -8.93769 q^{10} -2.74102 q^{11} -4.70310 q^{12} -1.59973 q^{13} -3.45213 q^{15} +8.71297 q^{16} +6.70489 q^{17} -2.58904 q^{18} +4.64493 q^{19} +16.2357 q^{20} +7.09661 q^{22} +0.175240 q^{23} +6.99843 q^{24} +6.91722 q^{25} +4.14177 q^{26} -1.00000 q^{27} +10.0992 q^{29} +8.93769 q^{30} +4.40039 q^{31} -8.56133 q^{32} +2.74102 q^{33} -17.3592 q^{34} +4.70310 q^{36} +8.43337 q^{37} -12.0259 q^{38} +1.59973 q^{39} -24.1595 q^{40} -1.00000 q^{41} +6.34977 q^{43} -12.8913 q^{44} +3.45213 q^{45} -0.453702 q^{46} -6.63881 q^{47} -8.71297 q^{48} -17.9089 q^{50} -6.70489 q^{51} -7.52372 q^{52} +6.35075 q^{53} +2.58904 q^{54} -9.46238 q^{55} -4.64493 q^{57} -26.1471 q^{58} -3.26935 q^{59} -16.2357 q^{60} -14.1988 q^{61} -11.3928 q^{62} +4.73965 q^{64} -5.52250 q^{65} -7.09661 q^{66} +6.37958 q^{67} +31.5338 q^{68} -0.175240 q^{69} -15.5181 q^{71} -6.99843 q^{72} +15.3176 q^{73} -21.8343 q^{74} -6.91722 q^{75} +21.8456 q^{76} -4.14177 q^{78} +2.95091 q^{79} +30.0783 q^{80} +1.00000 q^{81} +2.58904 q^{82} -0.195700 q^{83} +23.1462 q^{85} -16.4398 q^{86} -10.0992 q^{87} +19.1829 q^{88} -2.66652 q^{89} -8.93769 q^{90} +0.824170 q^{92} -4.40039 q^{93} +17.1881 q^{94} +16.0349 q^{95} +8.56133 q^{96} +8.38817 q^{97} -2.74102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9	$ 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9} + q^{10} - 10 q^{11} - 12 q^{12} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 12 q^{17} - 4 q^{18} + 11 q^{19} + 6 q^{20} + q^{22} - 15 q^{23} + 12 q^{24} + 15 q^{25} + 18 q^{26} - 13 q^{27} - 8 q^{29} - q^{30} + 9 q^{31} - 23 q^{32} + 10 q^{33} - 7 q^{34} + 12 q^{36} - 2 q^{37} + 20 q^{38} - 16 q^{39} + 49 q^{40} - 13 q^{41} - 7 q^{43} - 22 q^{44} + 8 q^{45} - 4 q^{46} + 26 q^{47} - 26 q^{48} - 15 q^{50} - 12 q^{51} + 24 q^{52} + 4 q^{53} + 4 q^{54} + q^{55} - 11 q^{57} + 39 q^{58} - 3 q^{59} - 6 q^{60} + 28 q^{61} + 7 q^{62} + 2 q^{64} - 20 q^{65} - q^{66} + 7 q^{67} + 55 q^{68} + 15 q^{69} - 40 q^{71} - 12 q^{72} - 2 q^{73} + q^{74} - 15 q^{75} - 26 q^{76} - 18 q^{78} + 13 q^{79} + 22 q^{80} + 13 q^{81} + 4 q^{82} + 14 q^{83} + 48 q^{85} - 49 q^{86} + 8 q^{87} + 20 q^{88} + 35 q^{89} + q^{90} - 105 q^{92} - 9 q^{93} - 2 q^{94} + 7 q^{95} + 23 q^{96} + 64 q^{97} - 10 q^{99}+O(q^{100}) $ 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9 + q^10 - 10 * q^11 - 12 * q^12 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 12 * q^17 - 4 * q^18 + 11 * q^19 + 6 * q^20 + q^22 - 15 * q^23 + 12 * q^24 + 15 * q^25 + 18 * q^26 - 13 * q^27 - 8 * q^29 - q^30 + 9 * q^31 - 23 * q^32 + 10 * q^33 - 7 * q^34 + 12 * q^36 - 2 * q^37 + 20 * q^38 - 16 * q^39 + 49 * q^40 - 13 * q^41 - 7 * q^43 - 22 * q^44 + 8 * q^45 - 4 * q^46 + 26 * q^47 - 26 * q^48 - 15 * q^50 - 12 * q^51 + 24 * q^52 + 4 * q^53 + 4 * q^54 + q^55 - 11 * q^57 + 39 * q^58 - 3 * q^59 - 6 * q^60 + 28 * q^61 + 7 * q^62 + 2 * q^64 - 20 * q^65 - q^66 + 7 * q^67 + 55 * q^68 + 15 * q^69 - 40 * q^71 - 12 * q^72 - 2 * q^73 + q^74 - 15 * q^75 - 26 * q^76 - 18 * q^78 + 13 * q^79 + 22 * q^80 + 13 * q^81 + 4 * q^82 + 14 * q^83 + 48 * q^85 - 49 * q^86 + 8 * q^87 + 20 * q^88 + 35 * q^89 + q^90 - 105 * q^92 - 9 * q^93 - 2 * q^94 + 7 * q^95 + 23 * q^96 + 64 * q^97 - 10 * 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 $

$2$	−2.58904	−1.83072	−0.915362	−	0.402631i	$-0.868096\pi$
$2$	−2.58904	−1.83072	−0.915362	+	0.402631i	$0.868096\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.70310	2.35155
$5$	3.45213	1.54384	0.771920	−	0.635719i	$-0.219296\pi$
$5$	3.45213	1.54384	0.771920	+	0.635719i	$0.219296\pi$
$6$	2.58904	1.05697
$7$	0	0
$7$	0	0
$8$	−6.99843	−2.47432
$9$	1.00000	0.333333
$10$	−8.93769	−2.82635
$11$	−2.74102	−0.826450	−0.413225	−	0.910629i	$-0.635598\pi$
$11$	−2.74102	−0.826450	−0.413225	+	0.910629i	$0.635598\pi$
$12$	−4.70310	−1.35767
$13$	−1.59973	−0.443686	−0.221843	−	0.975082i	$-0.571207\pi$
$13$	−1.59973	−0.443686	−0.221843	+	0.975082i	$0.571207\pi$
$14$	0	0
$15$	−3.45213	−0.891337
$16$	8.71297	2.17824
$17$	6.70489	1.62618	0.813088	−	0.582141i	$-0.197785\pi$
$17$	6.70489	1.62618	0.813088	+	0.582141i	$0.197785\pi$
$18$	−2.58904	−0.610241
$19$	4.64493	1.06562	0.532810	−	0.846235i	$-0.321136\pi$
$19$	4.64493	1.06562	0.532810	+	0.846235i	$0.321136\pi$
$20$	16.2357	3.63042
$21$	0	0
$22$	7.09661	1.51300
$23$	0.175240	0.0365400	0.0182700	−	0.999833i	$-0.494184\pi$
$23$	0.175240	0.0365400	0.0182700	+	0.999833i	$0.494184\pi$
$24$	6.99843	1.42855
$25$	6.91722	1.38344
$26$	4.14177	0.812268
$27$	−1.00000	−0.192450
$28$	0	0
$29$	10.0992	1.87537	0.937683	−	0.347492i	$-0.112967\pi$
$29$	10.0992	1.87537	0.937683	+	0.347492i	$0.112967\pi$
$30$	8.93769	1.63179
$31$	4.40039	0.790333	0.395167	−	0.918609i	$-0.370687\pi$
$31$	4.40039	0.790333	0.395167	+	0.918609i	$0.370687\pi$
$32$	−8.56133	−1.51344
$33$	2.74102	0.477151
$34$	−17.3592	−2.97708
$35$	0	0
$36$	4.70310	0.783851
$37$	8.43337	1.38644	0.693219	−	0.720727i	$-0.256192\pi$
$37$	8.43337	1.38644	0.693219	+	0.720727i	$0.256192\pi$
$38$	−12.0259	−1.95085
$39$	1.59973	0.256163
$40$	−24.1595	−3.81995
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	6.34977	0.968331	0.484165	−	0.874977i	$-0.339123\pi$
$43$	6.34977	0.968331	0.484165	+	0.874977i	$0.339123\pi$
$44$	−12.8913	−1.94344
$45$	3.45213	0.514614
$46$	−0.453702	−0.0668946
$47$	−6.63881	−0.968369	−0.484185	−	0.874966i	$-0.660884\pi$
$47$	−6.63881	−0.968369	−0.484185	+	0.874966i	$0.660884\pi$
$48$	−8.71297	−1.25761
$49$	0	0
$50$	−17.9089	−2.53271
$51$	−6.70489	−0.938873
$52$	−7.52372	−1.04335
$53$	6.35075	0.872343	0.436171	−	0.899864i	$-0.356334\pi$
$53$	6.35075	0.872343	0.436171	+	0.899864i	$0.356334\pi$
$54$	2.58904	0.352323
$55$	−9.46238	−1.27591
$56$	0	0
$57$	−4.64493	−0.615236
$58$	−26.1471	−3.43328
$59$	−3.26935	−0.425633	−0.212816	−	0.977092i	$-0.568264\pi$
$59$	−3.26935	−0.425633	−0.212816	+	0.977092i	$0.568264\pi$
$60$	−16.2357	−2.09602
$61$	−14.1988	−1.81797	−0.908987	−	0.416824i	$-0.863143\pi$
$61$	−14.1988	−1.81797	−0.908987	+	0.416824i	$0.863143\pi$
$62$	−11.3928	−1.44688
$63$	0	0
$64$	4.73965	0.592456
$65$	−5.52250	−0.684981
$66$	−7.09661	−0.873532
$67$	6.37958	0.779390	0.389695	−	0.920944i	$-0.372580\pi$
$67$	6.37958	0.779390	0.389695	+	0.920944i	$0.372580\pi$
$68$	31.5338	3.82403
$69$	−0.175240	−0.0210964
$70$	0	0
$71$	−15.5181	−1.84166	−0.920829	−	0.389966i	$-0.872487\pi$
$71$	−15.5181	−1.84166	−0.920829	+	0.389966i	$0.872487\pi$
$72$	−6.99843	−0.824773
$73$	15.3176	1.79279	0.896395	−	0.443256i	$-0.146177\pi$
$73$	15.3176	1.79279	0.896395	+	0.443256i	$0.146177\pi$
$74$	−21.8343	−2.53818
$75$	−6.91722	−0.798732
$76$	21.8456	2.50586
$77$	0	0
$78$	−4.14177	−0.468963
$79$	2.95091	0.332004	0.166002	−	0.986125i	$-0.446914\pi$
$79$	2.95091	0.332004	0.166002	+	0.986125i	$0.446914\pi$
$80$	30.0783	3.36286
$81$	1.00000	0.111111
$82$	2.58904	0.285911
$83$	−0.195700	−0.0214809	−0.0107405	−	0.999942i	$-0.503419\pi$
$83$	−0.195700	−0.0214809	−0.0107405	+	0.999942i	$0.503419\pi$
$84$	0	0
$85$	23.1462	2.51056
$86$	−16.4398	−1.77275
$87$	−10.0992	−1.08274
$88$	19.1829	2.04490
$89$	−2.66652	−0.282650	−0.141325	−	0.989963i	$-0.545136\pi$
$89$	−2.66652	−0.282650	−0.141325	+	0.989963i	$0.545136\pi$
$90$	−8.93769	−0.942116
$91$	0	0
$92$	0.824170	0.0859257
$93$	−4.40039	−0.456299
$94$	17.1881	1.77282
$95$	16.0349	1.64515
$96$	8.56133	0.873788
$97$	8.38817	0.851689	0.425845	−	0.904796i	$-0.359977\pi$
$97$	8.38817	0.851689	0.425845	+	0.904796i	$0.359977\pi$
$98$	0	0
$99$	−2.74102	−0.275483
$100$	32.5324	3.25324
$101$	0.0134570	0.00133902	0.000669510	−	1.00000i	$-0.499787\pi$
$101$	0.0134570	0.00133902	0.000669510		1.00000i	$0.499787\pi$
$102$	17.3592	1.71882
$103$	0.339443	0.0334463	0.0167231	−	0.999860i	$-0.494677\pi$
$103$	0.339443	0.0334463	0.0167231	+	0.999860i	$0.494677\pi$
$104$	11.1956	1.09782
$105$	0	0
$106$	−16.4423	−1.59702
$107$	−10.8832	−1.05212	−0.526061	−	0.850447i	$-0.676331\pi$
$107$	−10.8832	−1.05212	−0.526061	+	0.850447i	$0.676331\pi$
$108$	−4.70310	−0.452556
$109$	1.42527	0.136516	0.0682582	−	0.997668i	$-0.478256\pi$
$109$	1.42527	0.136516	0.0682582	+	0.997668i	$0.478256\pi$
$110$	24.4984	2.33583
$111$	−8.43337	−0.800460
$112$	0	0
$113$	−5.93916	−0.558709	−0.279354	−	0.960188i	$-0.590120\pi$
$113$	−5.93916	−0.558709	−0.279354	+	0.960188i	$0.590120\pi$
$114$	12.0259	1.12633
$115$	0.604951	0.0564119
$116$	47.4974	4.41002
$117$	−1.59973	−0.147895
$118$	8.46445	0.779216
$119$	0	0
$120$	24.1595	2.20545
$121$	−3.48678	−0.316980
$122$	36.7613	3.32821
$123$	1.00000	0.0901670
$124$	20.6955	1.85851
$125$	6.61852	0.591978
$126$	0	0
$127$	−1.42370	−0.126333	−0.0631666	−	0.998003i	$-0.520120\pi$
$127$	−1.42370	−0.126333	−0.0631666	+	0.998003i	$0.520120\pi$
$128$	4.85155	0.428820
$129$	−6.34977	−0.559066
$130$	14.2979	1.25401
$131$	−5.56414	−0.486141	−0.243070	−	0.970009i	$-0.578155\pi$
$131$	−5.56414	−0.486141	−0.243070	+	0.970009i	$0.578155\pi$
$132$	12.8913	1.12205
$133$	0	0
$134$	−16.5170	−1.42685
$135$	−3.45213	−0.297112
$136$	−46.9237	−4.02368
$137$	4.92410	0.420695	0.210347	−	0.977627i	$-0.432541\pi$
$137$	4.92410	0.420695	0.210347	+	0.977627i	$0.432541\pi$
$138$	0.453702	0.0386216
$139$	−12.6186	−1.07030	−0.535148	−	0.844759i	$-0.679744\pi$
$139$	−12.6186	−1.07030	−0.535148	+	0.844759i	$0.679744\pi$
$140$	0	0
$141$	6.63881	0.559088
$142$	40.1769	3.37157
$143$	4.38491	0.366685
$144$	8.71297	0.726081
$145$	34.8636	2.89527
$146$	−39.6578	−3.28210
$147$	0	0
$148$	39.6630	3.26028
$149$	−11.1341	−0.912139	−0.456070	−	0.889944i	$-0.650743\pi$
$149$	−11.1341	−0.912139	−0.456070	+	0.889944i	$0.650743\pi$
$150$	17.9089	1.46226
$151$	18.3055	1.48968	0.744842	−	0.667241i	$-0.232525\pi$
$151$	18.3055	1.48968	0.744842	+	0.667241i	$0.232525\pi$
$152$	−32.5072	−2.63668
$153$	6.70489	0.542058
$154$	0	0
$155$	15.1907	1.22015
$156$	7.52372	0.602379
$157$	8.55996	0.683159	0.341580	−	0.939853i	$-0.389038\pi$
$157$	8.55996	0.683159	0.341580	+	0.939853i	$0.389038\pi$
$158$	−7.64002	−0.607807
$159$	−6.35075	−0.503647
$160$	−29.5549	−2.33652
$161$	0	0
$162$	−2.58904	−0.203414
$163$	−1.84692	−0.144662	−0.0723311	−	0.997381i	$-0.523044\pi$
$163$	−1.84692	−0.144662	−0.0723311	+	0.997381i	$0.523044\pi$
$164$	−4.70310	−0.367251
$165$	9.46238	0.736645
$166$	0.506675	0.0393256
$167$	−16.0879	−1.24492	−0.622458	−	0.782653i	$-0.713866\pi$
$167$	−16.0879	−1.24492	−0.622458	+	0.782653i	$0.713866\pi$
$168$	0	0
$169$	−10.4408	−0.803142
$170$	−59.9263	−4.59614
$171$	4.64493	0.355206
$172$	29.8636	2.27708
$173$	13.2822	1.00983	0.504913	−	0.863170i	$-0.331525\pi$
$173$	13.2822	1.00983	0.504913	+	0.863170i	$0.331525\pi$
$174$	26.1471	1.98220
$175$	0	0
$176$	−23.8825	−1.80021
$177$	3.26935	0.245739
$178$	6.90370	0.517455
$179$	12.3614	0.923934	0.461967	−	0.886897i	$-0.347144\pi$
$179$	12.3614	0.923934	0.461967	+	0.886897i	$0.347144\pi$
$180$	16.2357	1.21014
$181$	17.0088	1.26425	0.632127	−	0.774865i	$-0.282182\pi$
$181$	17.0088	1.26425	0.632127	+	0.774865i	$0.282182\pi$
$182$	0	0
$183$	14.1988	1.04961
$184$	−1.22640	−0.0904116
$185$	29.1131	2.14044
$186$	11.3928	0.835358
$187$	−18.3783	−1.34395
$188$	−31.2230	−2.27717
$189$	0	0
$190$	−41.5149	−3.01181
$191$	−8.85782	−0.640930	−0.320465	−	0.947260i	$-0.603839\pi$
$191$	−8.85782	−0.640930	−0.320465	+	0.947260i	$0.603839\pi$
$192$	−4.73965	−0.342055
$193$	−27.1552	−1.95468	−0.977339	−	0.211681i	$-0.932106\pi$
$193$	−27.1552	−1.95468	−0.977339	+	0.211681i	$0.932106\pi$
$194$	−21.7173	−1.55921
$195$	5.52250	0.395474
$196$	0	0
$197$	−6.43515	−0.458485	−0.229243	−	0.973369i	$-0.573625\pi$
$197$	−6.43515	−0.458485	−0.229243	+	0.973369i	$0.573625\pi$
$198$	7.09661	0.504334
$199$	5.88649	0.417282	0.208641	−	0.977992i	$-0.433096\pi$
$199$	5.88649	0.417282	0.208641	+	0.977992i	$0.433096\pi$
$200$	−48.4097	−3.42308
$201$	−6.37958	−0.449981
$202$	−0.0348406	−0.00245138
$203$	0	0
$204$	−31.5338	−2.20781
$205$	−3.45213	−0.241107
$206$	−0.878829	−0.0612309
$207$	0.175240	0.0121800
$208$	−13.9384	−0.966457
$209$	−12.7319	−0.880681
$210$	0	0
$211$	−5.27109	−0.362877	−0.181438	−	0.983402i	$-0.558075\pi$
$211$	−5.27109	−0.362877	−0.181438	+	0.983402i	$0.558075\pi$
$212$	29.8682	2.05136
$213$	15.5181	1.06328
$214$	28.1771	1.92614
$215$	21.9203	1.49495
$216$	6.99843	0.476183
$217$	0	0
$218$	−3.69008	−0.249924
$219$	−15.3176	−1.03507
$220$	−44.5026	−3.00036
$221$	−10.7260	−0.721512
$222$	21.8343	1.46542
$223$	25.8347	1.73002	0.865010	−	0.501755i	$-0.167312\pi$
$223$	25.8347	1.73002	0.865010	+	0.501755i	$0.167312\pi$
$224$	0	0
$225$	6.91722	0.461148
$226$	15.3767	1.02284
$227$	21.8083	1.44747	0.723735	−	0.690078i	$-0.242424\pi$
$227$	21.8083	1.44747	0.723735	+	0.690078i	$0.242424\pi$
$228$	−21.8456	−1.44676
$229$	−0.621588	−0.0410757	−0.0205379	−	0.999789i	$-0.506538\pi$
$229$	−0.621588	−0.0410757	−0.0205379	+	0.999789i	$0.506538\pi$
$230$	−1.56624	−0.103275
$231$	0	0
$232$	−70.6782	−4.64025
$233$	19.5114	1.27823	0.639116	−	0.769111i	$-0.279300\pi$
$233$	19.5114	1.27823	0.639116	+	0.769111i	$0.279300\pi$
$234$	4.14177	0.270756
$235$	−22.9180	−1.49501
$236$	−15.3761	−1.00090
$237$	−2.95091	−0.191682
$238$	0	0
$239$	−12.6273	−0.816794	−0.408397	−	0.912804i	$-0.633912\pi$
$239$	−12.6273	−0.816794	−0.408397	+	0.912804i	$0.633912\pi$
$240$	−30.0783	−1.94155
$241$	9.78473	0.630290	0.315145	−	0.949044i	$-0.397947\pi$
$241$	9.78473	0.630290	0.315145	+	0.949044i	$0.397947\pi$
$242$	9.02741	0.580304
$243$	−1.00000	−0.0641500
$244$	−66.7786	−4.27506
$245$	0	0
$246$	−2.58904	−0.165071
$247$	−7.43065	−0.472801
$248$	−30.7958	−1.95554
$249$	0.195700	0.0124020
$250$	−17.1356	−1.08375
$251$	12.4957	0.788722	0.394361	−	0.918956i	$-0.370966\pi$
$251$	12.4957	0.788722	0.394361	+	0.918956i	$0.370966\pi$
$252$	0	0
$253$	−0.480336	−0.0301985
$254$	3.68602	0.231281
$255$	−23.1462	−1.44947
$256$	−22.0401	−1.37751
$257$	−24.1013	−1.50340	−0.751699	−	0.659507i	$-0.770765\pi$
$257$	−24.1013	−1.50340	−0.751699	+	0.659507i	$0.770765\pi$
$258$	16.4398	1.02350
$259$	0	0
$260$	−25.9729	−1.61077
$261$	10.0992	0.625122
$262$	14.4057	0.889990
$263$	14.2580	0.879187	0.439594	−	0.898197i	$-0.355122\pi$
$263$	14.2580	0.879187	0.439594	+	0.898197i	$0.355122\pi$
$264$	−19.1829	−1.18062
$265$	21.9236	1.34676
$266$	0	0
$267$	2.66652	0.163188
$268$	30.0038	1.83278
$269$	−24.6858	−1.50512	−0.752559	−	0.658525i	$-0.771181\pi$
$269$	−24.6858	−1.50512	−0.752559	+	0.658525i	$0.771181\pi$
$270$	8.93769	0.543931
$271$	−4.37245	−0.265608	−0.132804	−	0.991142i	$-0.542398\pi$
$271$	−4.37245	−0.265608	−0.132804	+	0.991142i	$0.542398\pi$
$272$	58.4195	3.54221
$273$	0	0
$274$	−12.7487	−0.770176
$275$	−18.9603	−1.14335
$276$	−0.824170	−0.0496092
$277$	−11.5344	−0.693036	−0.346518	−	0.938043i	$-0.612636\pi$
$277$	−11.5344	−0.693036	−0.346518	+	0.938043i	$0.612636\pi$
$278$	32.6700	1.95942
$279$	4.40039	0.263444
$280$	0	0
$281$	−0.964381	−0.0575302	−0.0287651	−	0.999586i	$-0.509157\pi$
$281$	−0.964381	−0.0575302	−0.0287651	+	0.999586i	$0.509157\pi$
$282$	−17.1881	−1.02354
$283$	−13.2929	−0.790183	−0.395091	−	0.918642i	$-0.629287\pi$
$283$	−13.2929	−0.790183	−0.395091	+	0.918642i	$0.629287\pi$
$284$	−72.9832	−4.33076
$285$	−16.0349	−0.949826
$286$	−11.3527	−0.671299
$287$	0	0
$288$	−8.56133	−0.504481
$289$	27.9556	1.64445
$290$	−90.2632	−5.30044
$291$	−8.38817	−0.491723
$292$	72.0403	4.21584
$293$	−11.3870	−0.665236	−0.332618	−	0.943062i	$-0.607932\pi$
$293$	−11.3870	−0.665236	−0.332618	+	0.943062i	$0.607932\pi$
$294$	0	0
$295$	−11.2862	−0.657109
$296$	−59.0203	−3.43049
$297$	2.74102	0.159050
$298$	28.8265	1.66988
$299$	−0.280337	−0.0162123
$300$	−32.5324	−1.87826
$301$	0	0
$302$	−47.3937	−2.72720
$303$	−0.0134570	−0.000773083 0
$304$	40.4711	2.32118
$305$	−49.0163	−2.80666
$306$	−17.3592	−0.992360
$307$	−11.8478	−0.676188	−0.338094	−	0.941112i	$-0.609782\pi$
$307$	−11.8478	−0.676188	−0.338094	+	0.941112i	$0.609782\pi$
$308$	0	0
$309$	−0.339443	−0.0193102
$310$	−39.3293	−2.23376
$311$	−23.9826	−1.35993	−0.679964	−	0.733246i	$-0.738004\pi$
$311$	−23.9826	−1.35993	−0.679964	+	0.733246i	$0.738004\pi$
$312$	−11.1956	−0.633828
$313$	25.6754	1.45126	0.725629	−	0.688086i	$-0.241549\pi$
$313$	25.6754	1.45126	0.725629	+	0.688086i	$0.241549\pi$
$314$	−22.1620	−1.25068
$315$	0	0
$316$	13.8784	0.780724
$317$	−27.8308	−1.56313	−0.781566	−	0.623822i	$-0.785579\pi$
$317$	−27.8308	−1.56313	−0.781566	+	0.623822i	$0.785579\pi$
$318$	16.4423	0.922039
$319$	−27.6820	−1.54990
$320$	16.3619	0.914659
$321$	10.8832	0.607442
$322$	0	0
$323$	31.1437	1.73288
$324$	4.70310	0.261284
$325$	−11.0657	−0.613816
$326$	4.78175	0.264836
$327$	−1.42527	−0.0788177
$328$	6.99843	0.386424
$329$	0	0
$330$	−24.4984	−1.34859
$331$	−1.19571	−0.0657223	−0.0328611	−	0.999460i	$-0.510462\pi$
$331$	−1.19571	−0.0657223	−0.0328611	+	0.999460i	$0.510462\pi$
$332$	−0.920399	−0.0505135
$333$	8.43337	0.462146
$334$	41.6520	2.27910
$335$	22.0232	1.20325
$336$	0	0
$337$	27.3445	1.48955	0.744774	−	0.667317i	$-0.232557\pi$
$337$	27.3445	1.48955	0.744774	+	0.667317i	$0.232557\pi$
$338$	27.0317	1.47033
$339$	5.93916	0.322571
$340$	108.859	5.90370
$341$	−12.0616	−0.653171
$342$	−12.0259	−0.650285
$343$	0	0
$344$	−44.4384	−2.39596
$345$	−0.604951	−0.0325694
$346$	−34.3880	−1.84871
$347$	−34.1646	−1.83405	−0.917026	−	0.398828i	$-0.869417\pi$
$347$	−34.1646	−1.83405	−0.917026	+	0.398828i	$0.869417\pi$
$348$	−47.4974	−2.54613
$349$	−1.78300	−0.0954420	−0.0477210	−	0.998861i	$-0.515196\pi$
$349$	−1.78300	−0.0954420	−0.0477210	+	0.998861i	$0.515196\pi$
$350$	0	0
$351$	1.59973	0.0853875
$352$	23.4668	1.25079
$353$	27.3366	1.45498	0.727489	−	0.686119i	$-0.240687\pi$
$353$	27.3366	1.45498	0.727489	+	0.686119i	$0.240687\pi$
$354$	−8.46445	−0.449881
$355$	−53.5705	−2.84323
$356$	−12.5409	−0.664666
$357$	0	0
$358$	−32.0041	−1.69147
$359$	11.7333	0.619258	0.309629	−	0.950858i	$-0.399795\pi$
$359$	11.7333	0.619258	0.309629	+	0.950858i	$0.399795\pi$
$360$	−24.1595	−1.27332
$361$	2.57534	0.135544
$362$	−44.0364	−2.31450
$363$	3.48678	0.183009
$364$	0	0
$365$	52.8784	2.76778
$366$	−36.7613	−1.92154
$367$	20.5750	1.07401	0.537003	−	0.843580i	$-0.319556\pi$
$367$	20.5750	1.07401	0.537003	+	0.843580i	$0.319556\pi$
$368$	1.52686	0.0795930
$369$	−1.00000	−0.0520579
$370$	−75.3749	−3.91855
$371$	0	0
$372$	−20.6955	−1.07301
$373$	6.45253	0.334099	0.167050	−	0.985948i	$-0.446576\pi$
$373$	6.45253	0.334099	0.167050	+	0.985948i	$0.446576\pi$
$374$	47.5820	2.46041
$375$	−6.61852	−0.341779
$376$	46.4612	2.39605
$377$	−16.1560	−0.832075
$378$	0	0
$379$	16.8280	0.864394	0.432197	−	0.901779i	$-0.357739\pi$
$379$	16.8280	0.864394	0.432197	+	0.901779i	$0.357739\pi$
$380$	75.4138	3.86865
$381$	1.42370	0.0729385
$382$	22.9332	1.17337
$383$	9.00819	0.460297	0.230148	−	0.973156i	$-0.426079\pi$
$383$	9.00819	0.460297	0.230148	+	0.973156i	$0.426079\pi$
$384$	−4.85155	−0.247579
$385$	0	0
$386$	70.3059	3.57848
$387$	6.34977	0.322777
$388$	39.4504	2.00279
$389$	14.4965	0.735004	0.367502	−	0.930023i	$-0.380213\pi$
$389$	14.4965	0.735004	0.367502	+	0.930023i	$0.380213\pi$
$390$	−14.2979	−0.724004
$391$	1.17496	0.0594204
$392$	0	0
$393$	5.56414	0.280674
$394$	16.6608	0.839360
$395$	10.1869	0.512561
$396$	−12.8913	−0.647813
$397$	−6.16787	−0.309557	−0.154778	−	0.987949i	$-0.549466\pi$
$397$	−6.16787	−0.309557	−0.154778	+	0.987949i	$0.549466\pi$
$398$	−15.2403	−0.763928
$399$	0	0
$400$	60.2696	3.01348
$401$	17.4520	0.871514	0.435757	−	0.900064i	$-0.356481\pi$
$401$	17.4520	0.871514	0.435757	+	0.900064i	$0.356481\pi$
$402$	16.5170	0.823791
$403$	−7.03945	−0.350660
$404$	0.0632896	0.00314877
$405$	3.45213	0.171538
$406$	0	0
$407$	−23.1161	−1.14582
$408$	46.9237	2.32307
$409$	16.6327	0.822432	0.411216	−	0.911538i	$-0.365104\pi$
$409$	16.6327	0.822432	0.411216	+	0.911538i	$0.365104\pi$
$410$	8.93769	0.441401
$411$	−4.92410	−0.242888
$412$	1.59643	0.0786507
$413$	0	0
$414$	−0.453702	−0.0222982
$415$	−0.675584	−0.0331631
$416$	13.6959	0.671495
$417$	12.6186	0.617935
$418$	32.9632	1.61228
$419$	7.83207	0.382621	0.191311	−	0.981530i	$-0.438726\pi$
$419$	7.83207	0.382621	0.191311	+	0.981530i	$0.438726\pi$
$420$	0	0
$421$	15.0345	0.732738	0.366369	−	0.930470i	$-0.380601\pi$
$421$	15.0345	0.732738	0.366369	+	0.930470i	$0.380601\pi$
$422$	13.6470	0.664328
$423$	−6.63881	−0.322790
$424$	−44.4453	−2.15845
$425$	46.3792	2.24972
$426$	−40.1769	−1.94658
$427$	0	0
$428$	−51.1849	−2.47412
$429$	−4.38491	−0.211706
$430$	−56.7523	−2.73684
$431$	29.6156	1.42653	0.713267	−	0.700892i	$-0.247215\pi$
$431$	29.6156	1.42653	0.713267	+	0.700892i	$0.247215\pi$
$432$	−8.71297	−0.419203
$433$	26.4153	1.26944	0.634720	−	0.772742i	$-0.281116\pi$
$433$	26.4153	1.26944	0.634720	+	0.772742i	$0.281116\pi$
$434$	0	0
$435$	−34.8636	−1.67158
$436$	6.70320	0.321025
$437$	0.813975	0.0389377
$438$	39.6578	1.89492
$439$	28.0524	1.33887	0.669435	−	0.742871i	$-0.266536\pi$
$439$	28.0524	1.33887	0.669435	+	0.742871i	$0.266536\pi$
$440$	66.2218	3.15700
$441$	0	0
$442$	27.7701	1.32089
$443$	−20.4826	−0.973158	−0.486579	−	0.873636i	$-0.661755\pi$
$443$	−20.4826	−0.973158	−0.486579	+	0.873636i	$0.661755\pi$
$444$	−39.6630	−1.88232
$445$	−9.20517	−0.436367
$446$	−66.8870	−3.16719
$447$	11.1341	0.526624
$448$	0	0
$449$	−11.3278	−0.534593	−0.267297	−	0.963614i	$-0.586130\pi$
$449$	−11.3278	−0.534593	−0.267297	+	0.963614i	$0.586130\pi$
$450$	−17.9089	−0.844235
$451$	2.74102	0.129070
$452$	−27.9325	−1.31383
$453$	−18.3055	−0.860069
$454$	−56.4626	−2.64992
$455$	0	0
$456$	32.5072	1.52229
$457$	−23.0312	−1.07736	−0.538678	−	0.842512i	$-0.681076\pi$
$457$	−23.0312	−1.07736	−0.538678	+	0.842512i	$0.681076\pi$
$458$	1.60931	0.0751983
$459$	−6.70489	−0.312958
$460$	2.84515	0.132656
$461$	−9.79452	−0.456176	−0.228088	−	0.973640i	$-0.573247\pi$
$461$	−9.79452	−0.456176	−0.228088	+	0.973640i	$0.573247\pi$
$462$	0	0
$463$	14.4771	0.672808	0.336404	−	0.941718i	$-0.390789\pi$
$463$	14.4771	0.672808	0.336404	+	0.941718i	$0.390789\pi$
$464$	87.9937	4.08500
$465$	−15.1907	−0.704453
$466$	−50.5156	−2.34009
$467$	36.0119	1.66643	0.833215	−	0.552948i	$-0.186497\pi$
$467$	36.0119	1.66643	0.833215	+	0.552948i	$0.186497\pi$
$468$	−7.52372	−0.347784
$469$	0	0
$470$	59.3356	2.73695
$471$	−8.55996	−0.394422
$472$	22.8803	1.05315
$473$	−17.4049	−0.800277
$474$	7.64002	0.350918
$475$	32.1300	1.47423
$476$	0	0
$477$	6.35075	0.290781
$478$	32.6926	1.49533
$479$	−34.0384	−1.55525	−0.777627	−	0.628726i	$-0.783577\pi$
$479$	−34.0384	−1.55525	−0.777627	+	0.628726i	$0.783577\pi$
$480$	29.5549	1.34899
$481$	−13.4911	−0.615143
$482$	−25.3330	−1.15389
$483$	0	0
$484$	−16.3987	−0.745396
$485$	28.9571	1.31487
$486$	2.58904	0.117441
$487$	30.2843	1.37231	0.686156	−	0.727454i	$-0.259297\pi$
$487$	30.2843	1.37231	0.686156	+	0.727454i	$0.259297\pi$
$488$	99.3695	4.49825
$489$	1.84692	0.0835207
$490$	0	0
$491$	−20.1672	−0.910135	−0.455067	−	0.890457i	$-0.650385\pi$
$491$	−20.1672	−0.910135	−0.455067	+	0.890457i	$0.650385\pi$
$492$	4.70310	0.212032
$493$	67.7137	3.04967
$494$	19.2382	0.865568
$495$	−9.46238	−0.425302
$496$	38.3405	1.72154
$497$	0	0
$498$	−0.506675	−0.0227047
$499$	28.9219	1.29472	0.647362	−	0.762183i	$-0.275872\pi$
$499$	28.9219	1.29472	0.647362	+	0.762183i	$0.275872\pi$
$500$	31.1276	1.39207
$501$	16.0879	0.718752
$502$	−32.3518	−1.44393
$503$	1.19798	0.0534153	0.0267077	−	0.999643i	$-0.491498\pi$
$503$	1.19798	0.0534153	0.0267077	+	0.999643i	$0.491498\pi$
$504$	0	0
$505$	0.0464553	0.00206723
$506$	1.24361	0.0552851
$507$	10.4408	0.463694
$508$	−6.69582	−0.297079
$509$	27.9597	1.23929	0.619647	−	0.784881i	$-0.287276\pi$
$509$	27.9597	1.23929	0.619647	+	0.784881i	$0.287276\pi$
$510$	59.9263	2.65358
$511$	0	0
$512$	47.3596	2.09302
$513$	−4.64493	−0.205079
$514$	62.3991	2.75231
$515$	1.17180	0.0516357
$516$	−29.8636	−1.31467
$517$	18.1971	0.800309
$518$	0	0
$519$	−13.2822	−0.583023
$520$	38.6488	1.69486
$521$	−12.1916	−0.534123	−0.267062	−	0.963679i	$-0.586053\pi$
$521$	−12.1916	−0.534123	−0.267062	+	0.963679i	$0.586053\pi$
$522$	−26.1471	−1.14443
$523$	−38.3554	−1.67716	−0.838581	−	0.544777i	$-0.816614\pi$
$523$	−38.3554	−1.67716	−0.838581	+	0.544777i	$0.816614\pi$
$524$	−26.1687	−1.14319
$525$	0	0
$526$	−36.9145	−1.60955
$527$	29.5041	1.28522
$528$	23.8825	1.03935
$529$	−22.9693	−0.998665
$530$	−56.7611	−2.46554
$531$	−3.26935	−0.141878
$532$	0	0
$533$	1.59973	0.0692922
$534$	−6.90370	−0.298753
$535$	−37.5703	−1.62431
$536$	−44.6471	−1.92846
$537$	−12.3614	−0.533433
$538$	63.9123	2.75546
$539$	0	0
$540$	−16.2357	−0.698675
$541$	−16.4918	−0.709038	−0.354519	−	0.935049i	$-0.615355\pi$
$541$	−16.4918	−0.709038	−0.354519	+	0.935049i	$0.615355\pi$
$542$	11.3204	0.486254
$543$	−17.0088	−0.729917
$544$	−57.4028	−2.46113
$545$	4.92023	0.210759
$546$	0	0
$547$	−5.75652	−0.246131	−0.123065	−	0.992399i	$-0.539272\pi$
$547$	−5.75652	−0.246131	−0.123065	+	0.992399i	$0.539272\pi$
$548$	23.1586	0.989285
$549$	−14.1988	−0.605992
$550$	49.0888	2.09316
$551$	46.9098	1.99843
$552$	1.22640	0.0521991
$553$	0	0
$554$	29.8630	1.26876
$555$	−29.1131	−1.23578
$556$	−59.3466	−2.51685
$557$	−1.25758	−0.0532852	−0.0266426	−	0.999645i	$-0.508482\pi$
$557$	−1.25758	−0.0532852	−0.0266426	+	0.999645i	$0.508482\pi$
$558$	−11.3928	−0.482294
$559$	−10.1579	−0.429635
$560$	0	0
$561$	18.3783	0.775931
$562$	2.49682	0.105322
$563$	13.2611	0.558890	0.279445	−	0.960162i	$-0.409850\pi$
$563$	13.2611	0.558890	0.279445	+	0.960162i	$0.409850\pi$
$564$	31.2230	1.31473
$565$	−20.5028	−0.862557
$566$	34.4159	1.44661
$567$	0	0
$568$	108.602	4.55685
$569$	−15.1716	−0.636027	−0.318014	−	0.948086i	$-0.603016\pi$
$569$	−15.1716	−0.636027	−0.318014	+	0.948086i	$0.603016\pi$
$570$	41.5149	1.73887
$571$	7.50483	0.314067	0.157034	−	0.987593i	$-0.449807\pi$
$571$	7.50483	0.314067	0.157034	+	0.987593i	$0.449807\pi$
$572$	20.6227	0.862278
$573$	8.85782	0.370041
$574$	0	0
$575$	1.21217	0.0505511
$576$	4.73965	0.197485
$577$	−13.6445	−0.568027	−0.284013	−	0.958820i	$-0.591666\pi$
$577$	−13.6445	−0.568027	−0.284013	+	0.958820i	$0.591666\pi$
$578$	−72.3780	−3.01053
$579$	27.1552	1.12853
$580$	163.967	6.80837
$581$	0	0
$582$	21.7173	0.900209
$583$	−17.4076	−0.720948
$584$	−107.199	−4.43593
$585$	−5.52250	−0.228327
$586$	29.4813	1.21786
$587$	−9.21302	−0.380262	−0.190131	−	0.981759i	$-0.560891\pi$
$587$	−9.21302	−0.380262	−0.190131	+	0.981759i	$0.560891\pi$
$588$	0	0
$589$	20.4395	0.842194
$590$	29.2204	1.20299
$591$	6.43515	0.264707
$592$	73.4797	3.02000
$593$	34.7421	1.42669	0.713344	−	0.700814i	$-0.247180\pi$
$593$	34.7421	1.42669	0.713344	+	0.700814i	$0.247180\pi$
$594$	−7.09661	−0.291177
$595$	0	0
$596$	−52.3647	−2.14494
$597$	−5.88649	−0.240918
$598$	0.725802	0.0296803
$599$	−3.50177	−0.143078	−0.0715392	−	0.997438i	$-0.522791\pi$
$599$	−3.50177	−0.143078	−0.0715392	+	0.997438i	$0.522791\pi$
$600$	48.4097	1.97632
$601$	5.26565	0.214791	0.107395	−	0.994216i	$-0.465749\pi$
$601$	5.26565	0.214791	0.107395	+	0.994216i	$0.465749\pi$
$602$	0	0
$603$	6.37958	0.259797
$604$	86.0928	3.50307
$605$	−12.0368	−0.489367
$606$	0.0348406	0.00141530
$607$	−45.4719	−1.84565	−0.922824	−	0.385223i	$-0.874125\pi$
$607$	−45.4719	−1.84565	−0.922824	+	0.385223i	$0.874125\pi$
$608$	−39.7668	−1.61276
$609$	0	0
$610$	126.905	5.13823
$611$	10.6203	0.429652
$612$	31.5338	1.27468
$613$	−7.24459	−0.292606	−0.146303	−	0.989240i	$-0.546738\pi$
$613$	−7.24459	−0.292606	−0.146303	+	0.989240i	$0.546738\pi$
$614$	30.6743	1.23791
$615$	3.45213	0.139203
$616$	0	0
$617$	−16.6007	−0.668319	−0.334159	−	0.942517i	$-0.608452\pi$
$617$	−16.6007	−0.668319	−0.334159	+	0.942517i	$0.608452\pi$
$618$	0.878829	0.0353517
$619$	−33.1322	−1.33169	−0.665847	−	0.746088i	$-0.731930\pi$
$619$	−33.1322	−1.33169	−0.665847	+	0.746088i	$0.731930\pi$
$620$	71.4436	2.86924
$621$	−0.175240	−0.00703212
$622$	62.0917	2.48965
$623$	0	0
$624$	13.9384	0.557984
$625$	−11.7381	−0.469525
$626$	−66.4745	−2.65685
$627$	12.7319	0.508461
$628$	40.2584	1.60648
$629$	56.5448	2.25459
$630$	0	0
$631$	−28.7045	−1.14271	−0.571354	−	0.820704i	$-0.693581\pi$
$631$	−28.7045	−1.14271	−0.571354	+	0.820704i	$0.693581\pi$
$632$	−20.6518	−0.821483
$633$	5.27109	0.209507
$634$	72.0549	2.86167
$635$	−4.91481	−0.195038
$636$	−29.8682	−1.18435
$637$	0	0
$638$	71.6698	2.83743
$639$	−15.5181	−0.613886
$640$	16.7482	0.662030
$641$	17.3816	0.686531	0.343266	−	0.939238i	$-0.388467\pi$
$641$	17.3816	0.686531	0.343266	+	0.939238i	$0.388467\pi$
$642$	−28.1771	−1.11206
$643$	44.5625	1.75737	0.878687	−	0.477398i	$-0.158420\pi$
$643$	44.5625	1.75737	0.878687	+	0.477398i	$0.158420\pi$
$644$	0	0
$645$	−21.9203	−0.863109
$646$	−80.6322	−3.17243
$647$	34.0479	1.33856	0.669281	−	0.743009i	$-0.266602\pi$
$647$	34.0479	1.33856	0.669281	+	0.743009i	$0.266602\pi$
$648$	−6.99843	−0.274924
$649$	8.96136	0.351764
$650$	28.6495	1.12373
$651$	0	0
$652$	−8.68627	−0.340180
$653$	−31.0579	−1.21539	−0.607694	−	0.794171i	$-0.707905\pi$
$653$	−31.0579	−1.21539	−0.607694	+	0.794171i	$0.707905\pi$
$654$	3.69008	0.144294
$655$	−19.2081	−0.750524
$656$	−8.71297	−0.340184
$657$	15.3176	0.597597
$658$	0	0
$659$	−42.8035	−1.66739	−0.833693	−	0.552228i	$-0.813778\pi$
$659$	−42.8035	−1.66739	−0.833693	+	0.552228i	$0.813778\pi$
$660$	44.5026	1.73226
$661$	35.6457	1.38646	0.693229	−	0.720717i	$-0.256187\pi$
$661$	35.6457	1.38646	0.693229	+	0.720717i	$0.256187\pi$
$662$	3.09574	0.120319
$663$	10.7260	0.416565
$664$	1.36960	0.0531506
$665$	0	0
$666$	−21.8343	−0.846061
$667$	1.76977	0.0685259
$668$	−75.6628	−2.92748
$669$	−25.8347	−0.998827
$670$	−57.0188	−2.20283
$671$	38.9194	1.50247
$672$	0	0
$673$	−23.6047	−0.909894	−0.454947	−	0.890519i	$-0.650342\pi$
$673$	−23.6047	−0.909894	−0.454947	+	0.890519i	$0.650342\pi$
$674$	−70.7958	−2.72695
$675$	−6.91722	−0.266244
$676$	−49.1044	−1.88863
$677$	13.8832	0.533574	0.266787	−	0.963756i	$-0.414038\pi$
$677$	13.8832	0.533574	0.266787	+	0.963756i	$0.414038\pi$
$678$	−15.3767	−0.590538
$679$	0	0
$680$	−161.987	−6.21191
$681$	−21.8083	−0.835697
$682$	31.2278	1.19578
$683$	37.7252	1.44352	0.721758	−	0.692145i	$-0.243334\pi$
$683$	37.7252	1.44352	0.721758	+	0.692145i	$0.243334\pi$
$684$	21.8456	0.835286
$685$	16.9987	0.649485
$686$	0	0
$687$	0.621588	0.0237151
$688$	55.3254	2.10926
$689$	−10.1595	−0.387047
$690$	1.56624	0.0596257
$691$	−10.9217	−0.415481	−0.207741	−	0.978184i	$-0.566611\pi$
$691$	−10.9217	−0.415481	−0.207741	+	0.978184i	$0.566611\pi$
$692$	62.4675	2.37466
$693$	0	0
$694$	88.4533	3.35764
$695$	−43.5611	−1.65237
$696$	70.6782	2.67905
$697$	−6.70489	−0.253966
$698$	4.61626	0.174728
$699$	−19.5114	−0.737987
$700$	0	0
$701$	−20.4003	−0.770508	−0.385254	−	0.922811i	$-0.625886\pi$
$701$	−20.4003	−0.770508	−0.385254	+	0.922811i	$0.625886\pi$
$702$	−4.14177	−0.156321
$703$	39.1724	1.47741
$704$	−12.9915	−0.489636
$705$	22.9180	0.863143
$706$	−70.7753	−2.66366
$707$	0	0
$708$	15.3761	0.577868
$709$	28.3393	1.06430	0.532152	−	0.846649i	$-0.321384\pi$
$709$	28.3393	1.06430	0.532152	+	0.846649i	$0.321384\pi$
$710$	138.696	5.20517
$711$	2.95091	0.110668
$712$	18.6614	0.699367
$713$	0.771123	0.0288788
$714$	0	0
$715$	15.1373	0.566103
$716$	58.1369	2.17268
$717$	12.6273	0.471576
$718$	−30.3778	−1.13369
$719$	20.8642	0.778103	0.389051	−	0.921216i	$-0.372803\pi$
$719$	20.8642	0.778103	0.389051	+	0.921216i	$0.372803\pi$
$720$	30.0783	1.12095
$721$	0	0
$722$	−6.66765	−0.248144
$723$	−9.78473	−0.363898
$724$	79.9941	2.97296
$725$	69.8581	2.59447
$726$	−9.02741	−0.335038
$727$	31.3456	1.16254	0.581272	−	0.813709i	$-0.302555\pi$
$727$	31.3456	1.16254	0.581272	+	0.813709i	$0.302555\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−136.904	−5.06705
$731$	42.5745	1.57468
$732$	66.7786	2.46821
$733$	−3.01937	−0.111523	−0.0557615	−	0.998444i	$-0.517759\pi$
$733$	−3.01937	−0.111523	−0.0557615	+	0.998444i	$0.517759\pi$
$734$	−53.2694	−1.96621
$735$	0	0
$736$	−1.50029	−0.0553012
$737$	−17.4866	−0.644127
$738$	2.58904	0.0953037
$739$	−9.31337	−0.342598	−0.171299	−	0.985219i	$-0.554796\pi$
$739$	−9.31337	−0.342598	−0.171299	+	0.985219i	$0.554796\pi$
$740$	136.922	5.03335
$741$	7.43065	0.272972
$742$	0	0
$743$	−13.9389	−0.511369	−0.255685	−	0.966760i	$-0.582301\pi$
$743$	−13.9389	−0.511369	−0.255685	+	0.966760i	$0.582301\pi$
$744$	30.7958	1.12903
$745$	−38.4363	−1.40820
$746$	−16.7058	−0.611643
$747$	−0.195700	−0.00716030
$748$	−86.4349	−3.16037
$749$	0	0
$750$	17.1356	0.625703
$751$	−11.9583	−0.436364	−0.218182	−	0.975908i	$-0.570013\pi$
$751$	−11.9583	−0.436364	−0.218182	+	0.975908i	$0.570013\pi$
$752$	−57.8437	−2.10934
$753$	−12.4957	−0.455369
$754$	41.8284	1.52330
$755$	63.1931	2.29983
$756$	0	0
$757$	−37.3787	−1.35855	−0.679276	−	0.733883i	$-0.737706\pi$
$757$	−37.3787	−1.35855	−0.679276	+	0.733883i	$0.737706\pi$
$758$	−43.5682	−1.58247
$759$	0.480336	0.0174351
$760$	−112.219	−4.07062
$761$	−22.9957	−0.833593	−0.416796	−	0.909000i	$-0.636847\pi$
$761$	−22.9957	−0.833593	−0.416796	+	0.909000i	$0.636847\pi$
$762$	−3.68602	−0.133530
$763$	0	0
$764$	−41.6593	−1.50718
$765$	23.1462	0.836852
$766$	−23.3225	−0.842676
$767$	5.23009	0.188847
$768$	22.0401	0.795304
$769$	−0.234077	−0.00844105	−0.00422052	−	0.999991i	$-0.501343\pi$
$769$	−0.234077	−0.00844105	−0.00422052	+	0.999991i	$0.501343\pi$
$770$	0	0
$771$	24.1013	0.867987
$772$	−127.714	−4.59652
$773$	36.0470	1.29652	0.648260	−	0.761419i	$-0.275497\pi$
$773$	36.0470	1.29652	0.648260	+	0.761419i	$0.275497\pi$
$774$	−16.4398	−0.590916
$775$	30.4385	1.09338
$776$	−58.7040	−2.10735
$777$	0	0
$778$	−37.5320	−1.34559
$779$	−4.64493	−0.166422
$780$	25.9729	0.929978
$781$	42.5355	1.52204
$782$	−3.04202	−0.108782
$783$	−10.0992	−0.360914
$784$	0	0
$785$	29.5501	1.05469
$786$	−14.4057	−0.513836
$787$	12.0696	0.430234	0.215117	−	0.976588i	$-0.430987\pi$
$787$	12.0696	0.430234	0.215117	+	0.976588i	$0.430987\pi$
$788$	−30.2652	−1.07815
$789$	−14.2580	−0.507599
$790$	−26.3744	−0.938358
$791$	0	0
$792$	19.1829	0.681633
$793$	22.7144	0.806611
$794$	15.9688	0.566713
$795$	−21.9236	−0.777551
$796$	27.6848	0.981260
$797$	−18.8615	−0.668110	−0.334055	−	0.942554i	$-0.608417\pi$
$797$	−18.8615	−0.668110	−0.334055	+	0.942554i	$0.608417\pi$
$798$	0	0
$799$	−44.5125	−1.57474
$800$	−59.2207	−2.09377
$801$	−2.66652	−0.0942167
$802$	−45.1840	−1.59550
$803$	−41.9859	−1.48165
$804$	−30.0038	−1.05815
$805$	0	0
$806$	18.2254	0.641962
$807$	24.6858	0.868980
$808$	−0.0941777	−0.00331316
$809$	5.41645	0.190432	0.0952162	−	0.995457i	$-0.469646\pi$
$809$	5.41645	0.190432	0.0952162	+	0.995457i	$0.469646\pi$
$810$	−8.93769	−0.314039
$811$	−30.2465	−1.06210	−0.531049	−	0.847341i	$-0.678202\pi$
$811$	−30.2465	−1.06210	−0.531049	+	0.847341i	$0.678202\pi$
$812$	0	0
$813$	4.37245	0.153349
$814$	59.8483	2.09768
$815$	−6.37582	−0.223335
$816$	−58.4195	−2.04509
$817$	29.4942	1.03187
$818$	−43.0626	−1.50565
$819$	0	0
$820$	−16.2357	−0.566977
$821$	49.6603	1.73316	0.866578	−	0.499041i	$-0.166314\pi$
$821$	49.6603	1.73316	0.866578	+	0.499041i	$0.166314\pi$
$822$	12.7487	0.444661
$823$	−39.3660	−1.37221	−0.686106	−	0.727502i	$-0.740681\pi$
$823$	−39.3660	−1.37221	−0.686106	+	0.727502i	$0.740681\pi$
$824$	−2.37557	−0.0827568
$825$	18.9603	0.660112
$826$	0	0
$827$	31.8660	1.10809	0.554045	−	0.832487i	$-0.313084\pi$
$827$	31.8660	1.10809	0.554045	+	0.832487i	$0.313084\pi$
$828$	0.824170	0.0286419
$829$	21.3189	0.740435	0.370218	−	0.928945i	$-0.379283\pi$
$829$	21.3189	0.740435	0.370218	+	0.928945i	$0.379283\pi$
$830$	1.74911	0.0607125
$831$	11.5344	0.400125
$832$	−7.58218	−0.262865
$833$	0	0
$834$	−32.6700	−1.13127
$835$	−55.5374	−1.92195
$836$	−59.8792	−2.07097
$837$	−4.40039	−0.152100
$838$	−20.2775	−0.700474
$839$	−28.0624	−0.968822	−0.484411	−	0.874841i	$-0.660966\pi$
$839$	−28.0624	−0.968822	−0.484411	+	0.874841i	$0.660966\pi$
$840$	0	0
$841$	72.9929	2.51700
$842$	−38.9249	−1.34144
$843$	0.964381	0.0332150
$844$	−24.7905	−0.853324
$845$	−36.0432	−1.23992
$846$	17.1881	0.590939
$847$	0	0
$848$	55.3339	1.90017
$849$	13.2929	0.456212
$850$	−120.077	−4.11862
$851$	1.47786	0.0506604
$852$	72.9832	2.50036
$853$	24.2830	0.831434	0.415717	−	0.909494i	$-0.363531\pi$
$853$	24.2830	0.831434	0.415717	+	0.909494i	$0.363531\pi$
$854$	0	0
$855$	16.0349	0.548382
$856$	76.1655	2.60328
$857$	−26.8481	−0.917114	−0.458557	−	0.888665i	$-0.651634\pi$
$857$	−26.8481	−0.917114	−0.458557	+	0.888665i	$0.651634\pi$
$858$	11.3527	0.387574
$859$	2.04240	0.0696860	0.0348430	−	0.999393i	$-0.488907\pi$
$859$	2.04240	0.0696860	0.0348430	+	0.999393i	$0.488907\pi$
$860$	103.093	3.51545
$861$	0	0
$862$	−76.6759	−2.61159
$863$	17.0331	0.579814	0.289907	−	0.957055i	$-0.406376\pi$
$863$	17.0331	0.579814	0.289907	+	0.957055i	$0.406376\pi$
$864$	8.56133	0.291263
$865$	45.8519	1.55901
$866$	−68.3902	−2.32399
$867$	−27.9556	−0.949421
$868$	0	0
$869$	−8.08852	−0.274384
$870$	90.2632	3.06021
$871$	−10.2056	−0.345805
$872$	−9.97467	−0.337785
$873$	8.38817	0.283896
$874$	−2.10741	−0.0712842
$875$	0	0
$876$	−72.0403	−2.43402
$877$	−12.5749	−0.424624	−0.212312	−	0.977202i	$-0.568099\pi$
$877$	−12.5749	−0.424624	−0.212312	+	0.977202i	$0.568099\pi$
$878$	−72.6287	−2.45110
$879$	11.3870	0.384074
$880$	−82.4455	−2.77924
$881$	−30.8768	−1.04027	−0.520134	−	0.854085i	$-0.674118\pi$
$881$	−30.8768	−1.04027	−0.520134	+	0.854085i	$0.674118\pi$
$882$	0	0
$883$	−12.2143	−0.411045	−0.205523	−	0.978652i	$-0.565889\pi$
$883$	−12.2143	−0.411045	−0.205523	+	0.978652i	$0.565889\pi$
$884$	−50.4457	−1.69667
$885$	11.2862	0.379382
$886$	53.0302	1.78158
$887$	25.4190	0.853485	0.426743	−	0.904373i	$-0.359661\pi$
$887$	25.4190	0.853485	0.426743	+	0.904373i	$0.359661\pi$
$888$	59.0203	1.98059
$889$	0	0
$890$	23.8325	0.798868
$891$	−2.74102	−0.0918278
$892$	121.503	4.06823
$893$	−30.8368	−1.03191
$894$	−28.8265	−0.964103
$895$	42.6732	1.42641
$896$	0	0
$897$	0.280337	0.00936018
$898$	29.3282	0.978693
$899$	44.4402	1.48216
$900$	32.5324	1.08441
$901$	42.5811	1.41858
$902$	−7.09661	−0.236291
$903$	0	0
$904$	41.5648	1.38242
$905$	58.7166	1.95181
$906$	47.3937	1.57455
$907$	−32.8472	−1.09067	−0.545336	−	0.838217i	$-0.683598\pi$
$907$	−32.8472	−1.09067	−0.545336	+	0.838217i	$0.683598\pi$
$908$	102.567	3.40380
$909$	0.0134570	0.000446340 0
$910$	0	0
$911$	13.8000	0.457214	0.228607	−	0.973519i	$-0.426583\pi$
$911$	13.8000	0.457214	0.228607	+	0.973519i	$0.426583\pi$
$912$	−40.4711	−1.34013
$913$	0.536420	0.0177529
$914$	59.6287	1.97234
$915$	49.0163	1.62043
$916$	−2.92339	−0.0965916
$917$	0	0
$918$	17.3592	0.572939
$919$	−30.4222	−1.00354	−0.501768	−	0.865002i	$-0.667317\pi$
$919$	−30.4222	−1.00354	−0.501768	+	0.865002i	$0.667317\pi$
$920$	−4.23370	−0.139581
$921$	11.8478	0.390397
$922$	25.3584	0.835133
$923$	24.8248	0.817119
$924$	0	0
$925$	58.3355	1.91806
$926$	−37.4817	−1.23173
$927$	0.339443	0.0111488
$928$	−86.4622	−2.83826
$929$	23.1916	0.760890	0.380445	−	0.924803i	$-0.375771\pi$
$929$	23.1916	0.760890	0.380445	+	0.924803i	$0.375771\pi$
$930$	39.3293	1.28966
$931$	0	0
$932$	91.7639	3.00583
$933$	23.9826	0.785154
$934$	−93.2360	−3.05078
$935$	−63.4443	−2.07485
$936$	11.1956	0.365941
$937$	−39.9010	−1.30351	−0.651754	−	0.758430i	$-0.725967\pi$
$937$	−39.9010	−1.30351	−0.651754	+	0.758430i	$0.725967\pi$
$938$	0	0
$939$	−25.6754	−0.837885
$940$	−107.786	−3.51559
$941$	−10.0743	−0.328413	−0.164207	−	0.986426i	$-0.552506\pi$
$941$	−10.0743	−0.328413	−0.164207	+	0.986426i	$0.552506\pi$
$942$	22.1620	0.722078
$943$	−0.175240	−0.00570659
$944$	−28.4857	−0.927132
$945$	0	0
$946$	45.0618	1.46509
$947$	−5.59874	−0.181935	−0.0909674	−	0.995854i	$-0.528996\pi$
$947$	−5.59874	−0.181935	−0.0909674	+	0.995854i	$0.528996\pi$
$948$	−13.8784	−0.450751
$949$	−24.5041	−0.795437
$950$	−83.1857	−2.69890
$951$	27.8308	0.902475
$952$	0	0
$953$	14.0059	0.453697	0.226848	−	0.973930i	$-0.427158\pi$
$953$	14.0059	0.453697	0.226848	+	0.973930i	$0.427158\pi$
$954$	−16.4423	−0.532340
$955$	−30.5784	−0.989493
$956$	−59.3876	−1.92073
$957$	27.6820	0.894833
$958$	88.1266	2.84724
$959$	0	0
$960$	−16.3619	−0.528078
$961$	−11.6366	−0.375373
$962$	34.9291	1.12616
$963$	−10.8832	−0.350707
$964$	46.0186	1.48216
$965$	−93.7435	−3.01771
$966$	0	0
$967$	58.1641	1.87043	0.935215	−	0.354079i	$-0.115206\pi$
$967$	58.1641	1.87043	0.935215	+	0.354079i	$0.115206\pi$
$968$	24.4020	0.784310
$969$	−31.1437	−1.00048
$970$	−74.9709	−2.40717
$971$	19.4572	0.624411	0.312205	−	0.950015i	$-0.398932\pi$
$971$	19.4572	0.624411	0.312205	+	0.950015i	$0.398932\pi$
$972$	−4.70310	−0.150852
$973$	0	0
$974$	−78.4071	−2.51233
$975$	11.0657	0.354387
$976$	−123.714	−3.95999
$977$	36.1881	1.15776	0.578881	−	0.815412i	$-0.303490\pi$
$977$	36.1881	1.15776	0.578881	+	0.815412i	$0.303490\pi$
$978$	−4.78175	−0.152903
$979$	7.30899	0.233596
$980$	0	0
$981$	1.42527	0.0455054
$982$	52.2137	1.66621
$983$	14.7043	0.468994	0.234497	−	0.972117i	$-0.424656\pi$
$983$	14.7043	0.468994	0.234497	+	0.972117i	$0.424656\pi$
$984$	−6.99843	−0.223102
$985$	−22.2150	−0.707828
$986$	−175.313	−5.58311
$987$	0	0
$988$	−34.9471	−1.11182
$989$	1.11273	0.0353828
$990$	24.4984	0.778612
$991$	43.0542	1.36766	0.683830	−	0.729641i	$-0.260313\pi$
$991$	43.0542	1.36766	0.683830	+	0.729641i	$0.260313\pi$
$992$	−37.6732	−1.19613
$993$	1.19571	0.0379448
$994$	0	0
$995$	20.3209	0.644217
$996$	0.920399	0.0291640
$997$	−13.3126	−0.421613	−0.210807	−	0.977528i	$-0.567609\pi$
$997$	−13.3126	−0.421613	−0.210807	+	0.977528i	$0.567609\pi$
$998$	−74.8799	−2.37028
$999$	−8.43337	−0.266820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bh.1.2		13
7.3	odd	6		861.2.i.f.247.12	✓	26
7.5	odd	6		861.2.i.f.739.12	yes	26
7.6	odd	2		6027.2.a.bi.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.12	✓	26	7.3	odd	6
861.2.i.f.739.12	yes	26	7.5	odd	6
6027.2.a.bh.1.2		13	1.1	even	1	trivial
6027.2.a.bi.1.2		13	7.6	odd	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58904 q^{2} -1.00000 q^{3} +4.70310 q^{4} +3.45213 q^{5} +2.58904 q^{6} -6.99843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58904 q^{2} -1.00000 q^{3} +4.70310 q^{4} +3.45213 q^{5} +2.58904 q^{6} -6.99843 q^{8} +1.00000 q^{9} -8.93769 q^{10} -2.74102 q^{11} -4.70310 q^{12} -1.59973 q^{13} -3.45213 q^{15} +8.71297 q^{16} +6.70489 q^{17} -2.58904 q^{18} +4.64493 q^{19} +16.2357 q^{20} +7.09661 q^{22} +0.175240 q^{23} +6.99843 q^{24} +6.91722 q^{25} +4.14177 q^{26} -1.00000 q^{27} +10.0992 q^{29} +8.93769 q^{30} +4.40039 q^{31} -8.56133 q^{32} +2.74102 q^{33} -17.3592 q^{34} +4.70310 q^{36} +8.43337 q^{37} -12.0259 q^{38} +1.59973 q^{39} -24.1595 q^{40} -1.00000 q^{41} +6.34977 q^{43} -12.8913 q^{44} +3.45213 q^{45} -0.453702 q^{46} -6.63881 q^{47} -8.71297 q^{48} -17.9089 q^{50} -6.70489 q^{51} -7.52372 q^{52} +6.35075 q^{53} +2.58904 q^{54} -9.46238 q^{55} -4.64493 q^{57} -26.1471 q^{58} -3.26935 q^{59} -16.2357 q^{60} -14.1988 q^{61} -11.3928 q^{62} +4.73965 q^{64} -5.52250 q^{65} -7.09661 q^{66} +6.37958 q^{67} +31.5338 q^{68} -0.175240 q^{69} -15.5181 q^{71} -6.99843 q^{72} +15.3176 q^{73} -21.8343 q^{74} -6.91722 q^{75} +21.8456 q^{76} -4.14177 q^{78} +2.95091 q^{79} +30.0783 q^{80} +1.00000 q^{81} +2.58904 q^{82} -0.195700 q^{83} +23.1462 q^{85} -16.4398 q^{86} -10.0992 q^{87} +19.1829 q^{88} -2.66652 q^{89} -8.93769 q^{90} +0.824170 q^{92} -4.40039 q^{93} +17.1881 q^{94} +16.0349 q^{95} +8.56133 q^{96} +8.38817 q^{97} -2.74102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9} + q^{10} - 10 q^{11} - 12 q^{12} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 12 q^{17} - 4 q^{18} + 11 q^{19} + 6 q^{20} + q^{22} - 15 q^{23} + 12 q^{24} + 15 q^{25} + 18 q^{26} - 13 q^{27} - 8 q^{29} - q^{30} + 9 q^{31} - 23 q^{32} + 10 q^{33} - 7 q^{34} + 12 q^{36} - 2 q^{37} + 20 q^{38} - 16 q^{39} + 49 q^{40} - 13 q^{41} - 7 q^{43} - 22 q^{44} + 8 q^{45} - 4 q^{46} + 26 q^{47} - 26 q^{48} - 15 q^{50} - 12 q^{51} + 24 q^{52} + 4 q^{53} + 4 q^{54} + q^{55} - 11 q^{57} + 39 q^{58} - 3 q^{59} - 6 q^{60} + 28 q^{61} + 7 q^{62} + 2 q^{64} - 20 q^{65} - q^{66} + 7 q^{67} + 55 q^{68} + 15 q^{69} - 40 q^{71} - 12 q^{72} - 2 q^{73} + q^{74} - 15 q^{75} - 26 q^{76} - 18 q^{78} + 13 q^{79} + 22 q^{80} + 13 q^{81} + 4 q^{82} + 14 q^{83} + 48 q^{85} - 49 q^{86} + 8 q^{87} + 20 q^{88} + 35 q^{89} + q^{90} - 105 q^{92} - 9 q^{93} - 2 q^{94} + 7 q^{95} + 23 q^{96} + 64 q^{97} - 10 q^{99}+O(q^{100}) \) 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9 + q^10 - 10 * q^11 - 12 * q^12 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 12 * q^17 - 4 * q^18 + 11 * q^19 + 6 * q^20 + q^22 - 15 * q^23 + 12 * q^24 + 15 * q^25 + 18 * q^26 - 13 * q^27 - 8 * q^29 - q^30 + 9 * q^31 - 23 * q^32 + 10 * q^33 - 7 * q^34 + 12 * q^36 - 2 * q^37 + 20 * q^38 - 16 * q^39 + 49 * q^40 - 13 * q^41 - 7 * q^43 - 22 * q^44 + 8 * q^45 - 4 * q^46 + 26 * q^47 - 26 * q^48 - 15 * q^50 - 12 * q^51 + 24 * q^52 + 4 * q^53 + 4 * q^54 + q^55 - 11 * q^57 + 39 * q^58 - 3 * q^59 - 6 * q^60 + 28 * q^61 + 7 * q^62 + 2 * q^64 - 20 * q^65 - q^66 + 7 * q^67 + 55 * q^68 + 15 * q^69 - 40 * q^71 - 12 * q^72 - 2 * q^73 + q^74 - 15 * q^75 - 26 * q^76 - 18 * q^78 + 13 * q^79 + 22 * q^80 + 13 * q^81 + 4 * q^82 + 14 * q^83 + 48 * q^85 - 49 * q^86 + 8 * q^87 + 20 * q^88 + 35 * q^89 + q^90 - 105 * q^92 - 9 * q^93 - 2 * q^94 + 7 * q^95 + 23 * q^96 + 64 * q^97 - 10 * q^99

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