LMFDB - Embedded newform 6027.2.a.bi.1.9

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:	$1$
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			1.9
Root			$-0.558375$ 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)

$f(q)$	$=$	$q+0.558375 q^{2} +1.00000 q^{3} -1.68822 q^{4} -0.297196 q^{5} +0.558375 q^{6} -2.05941 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.558375 q^{2} +1.00000 q^{3} -1.68822 q^{4} -0.297196 q^{5} +0.558375 q^{6} -2.05941 q^{8} +1.00000 q^{9} -0.165947 q^{10} +1.45967 q^{11} -1.68822 q^{12} -5.31713 q^{13} -0.297196 q^{15} +2.22651 q^{16} -6.78493 q^{17} +0.558375 q^{18} +4.21478 q^{19} +0.501732 q^{20} +0.815044 q^{22} +9.21603 q^{23} -2.05941 q^{24} -4.91167 q^{25} -2.96896 q^{26} +1.00000 q^{27} +7.74267 q^{29} -0.165947 q^{30} +7.15968 q^{31} +5.36205 q^{32} +1.45967 q^{33} -3.78854 q^{34} -1.68822 q^{36} +1.91642 q^{37} +2.35343 q^{38} -5.31713 q^{39} +0.612049 q^{40} +1.00000 q^{41} -12.3476 q^{43} -2.46424 q^{44} -0.297196 q^{45} +5.14600 q^{46} +0.223629 q^{47} +2.22651 q^{48} -2.74256 q^{50} -6.78493 q^{51} +8.97647 q^{52} -3.99794 q^{53} +0.558375 q^{54} -0.433809 q^{55} +4.21478 q^{57} +4.32332 q^{58} -5.57298 q^{59} +0.501732 q^{60} -5.08551 q^{61} +3.99779 q^{62} -1.45899 q^{64} +1.58023 q^{65} +0.815044 q^{66} -12.8143 q^{67} +11.4544 q^{68} +9.21603 q^{69} -9.53578 q^{71} -2.05941 q^{72} +7.16392 q^{73} +1.07008 q^{74} -4.91167 q^{75} -7.11546 q^{76} -2.96896 q^{78} +2.54442 q^{79} -0.661711 q^{80} +1.00000 q^{81} +0.558375 q^{82} -5.99018 q^{83} +2.01646 q^{85} -6.89461 q^{86} +7.74267 q^{87} -3.00606 q^{88} -15.5513 q^{89} -0.165947 q^{90} -15.5587 q^{92} +7.15968 q^{93} +0.124869 q^{94} -1.25262 q^{95} +5.36205 q^{96} -10.7127 q^{97} +1.45967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.558375	0.394831	0.197415	−	0.980320i	$-0.436745\pi$
$2$	0.558375	0.394831	0.197415	+	0.980320i	$0.436745\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.68822	−0.844108
$5$	−0.297196	−0.132910	−0.0664551	−	0.997789i	$-0.521169\pi$
$5$	−0.297196	−0.132910	−0.0664551	+	0.997789i	$0.521169\pi$
$6$	0.558375	0.227956
$7$	0	0
$7$	0	0
$8$	−2.05941	−0.728111
$9$	1.00000	0.333333
$10$	−0.165947	−0.0524771
$11$	1.45967	0.440107	0.220054	−	0.975488i	$-0.429377\pi$
$11$	1.45967	0.440107	0.220054	+	0.975488i	$0.429377\pi$
$12$	−1.68822	−0.487346
$13$	−5.31713	−1.47471	−0.737354	−	0.675507i	$-0.763925\pi$
$13$	−5.31713	−1.47471	−0.737354	+	0.675507i	$0.763925\pi$
$14$	0	0
$15$	−0.297196	−0.0767358
$16$	2.22651	0.556628
$17$	−6.78493	−1.64559	−0.822793	−	0.568341i	$-0.807586\pi$
$17$	−6.78493	−1.64559	−0.822793	+	0.568341i	$0.807586\pi$
$18$	0.558375	0.131610
$19$	4.21478	0.966937	0.483468	−	0.875362i	$-0.339377\pi$
$19$	4.21478	0.966937	0.483468	+	0.875362i	$0.339377\pi$
$20$	0.501732	0.112191
$21$	0	0
$22$	0.815044	0.173768
$23$	9.21603	1.92168	0.960838	−	0.277112i	$-0.0893774\pi$
$23$	9.21603	1.92168	0.960838	+	0.277112i	$0.0893774\pi$
$24$	−2.05941	−0.420375
$25$	−4.91167	−0.982335
$26$	−2.96896	−0.582260
$27$	1.00000	0.192450
$28$	0	0
$29$	7.74267	1.43778	0.718889	−	0.695125i	$-0.244651\pi$
$29$	7.74267	1.43778	0.718889	+	0.695125i	$0.244651\pi$
$30$	−0.165947	−0.0302977
$31$	7.15968	1.28592	0.642958	−	0.765901i	$-0.277707\pi$
$31$	7.15968	1.28592	0.642958	+	0.765901i	$0.277707\pi$
$32$	5.36205	0.947885
$33$	1.45967	0.254096
$34$	−3.78854	−0.649729
$35$	0	0
$36$	−1.68822	−0.281369
$37$	1.91642	0.315058	0.157529	−	0.987514i	$-0.449647\pi$
$37$	1.91642	0.315058	0.157529	+	0.987514i	$0.449647\pi$
$38$	2.35343	0.381777
$39$	−5.31713	−0.851423
$40$	0.612049	0.0967735
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−12.3476	−1.88299	−0.941497	−	0.337020i	$-0.890581\pi$
$43$	−12.3476	−1.88299	−0.941497	+	0.337020i	$0.890581\pi$
$44$	−2.46424	−0.371498
$45$	−0.297196	−0.0443034
$46$	5.14600	0.758737
$47$	0.223629	0.0326197	0.0163098	−	0.999867i	$-0.494808\pi$
$47$	0.223629	0.0326197	0.0163098	+	0.999867i	$0.494808\pi$
$48$	2.22651	0.321369
$49$	0	0
$50$	−2.74256	−0.387856
$51$	−6.78493	−0.950080
$52$	8.97647	1.24481
$53$	−3.99794	−0.549160	−0.274580	−	0.961564i	$-0.588539\pi$
$53$	−3.99794	−0.549160	−0.274580	+	0.961564i	$0.588539\pi$
$54$	0.558375	0.0759853
$55$	−0.433809	−0.0584948
$56$	0	0
$57$	4.21478	0.558261
$58$	4.32332	0.567680
$59$	−5.57298	−0.725541	−0.362770	−	0.931879i	$-0.618169\pi$
$59$	−5.57298	−0.725541	−0.362770	+	0.931879i	$0.618169\pi$
$60$	0.501732	0.0647733
$61$	−5.08551	−0.651133	−0.325567	−	0.945519i	$-0.605555\pi$
$61$	−5.08551	−0.651133	−0.325567	+	0.945519i	$0.605555\pi$
$62$	3.99779	0.507720
$63$	0	0
$64$	−1.45899	−0.182373
$65$	1.58023	0.196004
$66$	0.815044	0.100325
$67$	−12.8143	−1.56551	−0.782757	−	0.622328i	$-0.786187\pi$
$67$	−12.8143	−1.56551	−0.782757	+	0.622328i	$0.786187\pi$
$68$	11.4544	1.38905
$69$	9.21603	1.10948
$70$	0	0
$71$	−9.53578	−1.13169	−0.565845	−	0.824512i	$-0.691450\pi$
$71$	−9.53578	−1.13169	−0.565845	+	0.824512i	$0.691450\pi$
$72$	−2.05941	−0.242704
$73$	7.16392	0.838474	0.419237	−	0.907877i	$-0.362298\pi$
$73$	7.16392	0.838474	0.419237	+	0.907877i	$0.362298\pi$
$74$	1.07008	0.124395
$75$	−4.91167	−0.567151
$76$	−7.11546	−0.816199
$77$	0	0
$78$	−2.96896	−0.336168
$79$	2.54442	0.286270	0.143135	−	0.989703i	$-0.454282\pi$
$79$	2.54442	0.286270	0.143135	+	0.989703i	$0.454282\pi$
$80$	−0.661711	−0.0739815
$81$	1.00000	0.111111
$82$	0.558375	0.0616622
$83$	−5.99018	−0.657507	−0.328754	−	0.944416i	$-0.606629\pi$
$83$	−5.99018	−0.657507	−0.328754	+	0.944416i	$0.606629\pi$
$84$	0	0
$85$	2.01646	0.218715
$86$	−6.89461	−0.743465
$87$	7.74267	0.830102
$88$	−3.00606	−0.320447
$89$	−15.5513	−1.64843	−0.824215	−	0.566276i	$-0.808383\pi$
$89$	−15.5513	−1.64843	−0.824215	+	0.566276i	$0.808383\pi$
$90$	−0.165947	−0.0174924
$91$	0	0
$92$	−15.5587	−1.62210
$93$	7.15968	0.742424
$94$	0.124869	0.0128793
$95$	−1.25262	−0.128516
$96$	5.36205	0.547262
$97$	−10.7127	−1.08771	−0.543854	−	0.839180i	$-0.683035\pi$
$97$	−10.7127	−1.08771	−0.543854	+	0.839180i	$0.683035\pi$
$98$	0	0
$99$	1.45967	0.146702
$100$	8.29197	0.829197
$101$	−7.00779	−0.697301	−0.348650	−	0.937253i	$-0.613360\pi$
$101$	−7.00779	−0.697301	−0.348650	+	0.937253i	$0.613360\pi$
$102$	−3.78854	−0.375121
$103$	−18.9625	−1.86843	−0.934214	−	0.356714i	$-0.883897\pi$
$103$	−18.9625	−1.86843	−0.934214	+	0.356714i	$0.883897\pi$
$104$	10.9502	1.07375
$105$	0	0
$106$	−2.23235	−0.216825
$107$	11.6090	1.12228	0.561141	−	0.827720i	$-0.310363\pi$
$107$	11.6090	1.12228	0.561141	+	0.827720i	$0.310363\pi$
$108$	−1.68822	−0.162449
$109$	1.63148	0.156267	0.0781335	−	0.996943i	$-0.475104\pi$
$109$	1.63148	0.156267	0.0781335	+	0.996943i	$0.475104\pi$
$110$	−0.242228	−0.0230956
$111$	1.91642	0.181899
$112$	0	0
$113$	−4.44890	−0.418517	−0.209259	−	0.977860i	$-0.567105\pi$
$113$	−4.44890	−0.418517	−0.209259	+	0.977860i	$0.567105\pi$
$114$	2.35343	0.220419
$115$	−2.73897	−0.255410
$116$	−13.0713	−1.21364
$117$	−5.31713	−0.491569
$118$	−3.11182	−0.286466
$119$	0	0
$120$	0.612049	0.0558722
$121$	−8.86936	−0.806306
$122$	−2.83962	−0.257088
$123$	1.00000	0.0901670
$124$	−12.0871	−1.08545
$125$	2.94571	0.263473
$126$	0	0
$127$	−7.10513	−0.630478	−0.315239	−	0.949012i	$-0.602085\pi$
$127$	−7.10513	−0.630478	−0.315239	+	0.949012i	$0.602085\pi$
$128$	−11.5388	−1.01989
$129$	−12.3476	−1.08715
$130$	0.882363	0.0773884
$131$	−4.48115	−0.391520	−0.195760	−	0.980652i	$-0.562717\pi$
$131$	−4.48115	−0.391520	−0.195760	+	0.980652i	$0.562717\pi$
$132$	−2.46424	−0.214485
$133$	0	0
$134$	−7.15518	−0.618113
$135$	−0.297196	−0.0255786
$136$	13.9729	1.19817
$137$	−0.900588	−0.0769424	−0.0384712	−	0.999260i	$-0.512249\pi$
$137$	−0.900588	−0.0769424	−0.0384712	+	0.999260i	$0.512249\pi$
$138$	5.14600	0.438057
$139$	−8.49710	−0.720714	−0.360357	−	0.932814i	$-0.617345\pi$
$139$	−8.49710	−0.720714	−0.360357	+	0.932814i	$0.617345\pi$
$140$	0	0
$141$	0.223629	0.0188330
$142$	−5.32455	−0.446826
$143$	−7.76126	−0.649029
$144$	2.22651	0.185543
$145$	−2.30110	−0.191096
$146$	4.00016	0.331055
$147$	0	0
$148$	−3.23534	−0.265943
$149$	6.02077	0.493241	0.246620	−	0.969112i	$-0.420680\pi$
$149$	6.02077	0.493241	0.246620	+	0.969112i	$0.420680\pi$
$150$	−2.74256	−0.223929
$151$	13.9321	1.13378	0.566890	−	0.823794i	$-0.308147\pi$
$151$	13.9321	1.13378	0.566890	+	0.823794i	$0.308147\pi$
$152$	−8.67996	−0.704037
$153$	−6.78493	−0.548529
$154$	0	0
$155$	−2.12783	−0.170911
$156$	8.97647	0.718693
$157$	−3.69661	−0.295022	−0.147511	−	0.989060i	$-0.547126\pi$
$157$	−3.69661	−0.295022	−0.147511	+	0.989060i	$0.547126\pi$
$158$	1.42074	0.113028
$159$	−3.99794	−0.317057
$160$	−1.59358	−0.125984
$161$	0	0
$162$	0.558375	0.0438701
$163$	13.7262	1.07512	0.537560	−	0.843225i	$-0.319346\pi$
$163$	13.7262	1.07512	0.537560	+	0.843225i	$0.319346\pi$
$164$	−1.68822	−0.131828
$165$	−0.433809	−0.0337720
$166$	−3.34477	−0.259604
$167$	0.949295	0.0734587	0.0367293	−	0.999325i	$-0.488306\pi$
$167$	0.949295	0.0734587	0.0367293	+	0.999325i	$0.488306\pi$
$168$	0	0
$169$	15.2719	1.17476
$170$	1.12594	0.0863556
$171$	4.21478	0.322312
$172$	20.8455	1.58945
$173$	−2.70402	−0.205582	−0.102791	−	0.994703i	$-0.532777\pi$
$173$	−2.70402	−0.205582	−0.102791	+	0.994703i	$0.532777\pi$
$174$	4.32332	0.327750
$175$	0	0
$176$	3.24997	0.244976
$177$	−5.57298	−0.418891
$178$	−8.68344	−0.650852
$179$	−21.5598	−1.61145	−0.805726	−	0.592288i	$-0.798225\pi$
$179$	−21.5598	−1.61145	−0.805726	+	0.592288i	$0.798225\pi$
$180$	0.501732	0.0373969
$181$	0.117037	0.00869929	0.00434964	−	0.999991i	$-0.498615\pi$
$181$	0.117037	0.00869929	0.00434964	+	0.999991i	$0.498615\pi$
$182$	0	0
$183$	−5.08551	−0.375932
$184$	−18.9796	−1.39919
$185$	−0.569554	−0.0418745
$186$	3.99779	0.293132
$187$	−9.90376	−0.724235
$188$	−0.377535	−0.0275345
$189$	0	0
$190$	−0.699431	−0.0507420
$191$	−25.0818	−1.81485	−0.907427	−	0.420209i	$-0.861957\pi$
$191$	−25.0818	−1.81485	−0.907427	+	0.420209i	$0.861957\pi$
$192$	−1.45899	−0.105293
$193$	6.82223	0.491075	0.245538	−	0.969387i	$-0.421036\pi$
$193$	6.82223	0.491075	0.245538	+	0.969387i	$0.421036\pi$
$194$	−5.98169	−0.429461
$195$	1.58023	0.113163
$196$	0	0
$197$	18.8073	1.33996	0.669981	−	0.742379i	$-0.266302\pi$
$197$	18.8073	1.33996	0.669981	+	0.742379i	$0.266302\pi$
$198$	0.815044	0.0579227
$199$	0.595593	0.0422205	0.0211102	−	0.999777i	$-0.493280\pi$
$199$	0.595593	0.0422205	0.0211102	+	0.999777i	$0.493280\pi$
$200$	10.1151	0.715249
$201$	−12.8143	−0.903849
$202$	−3.91298	−0.275316
$203$	0	0
$204$	11.4544	0.801971
$205$	−0.297196	−0.0207571
$206$	−10.5882	−0.737713
$207$	9.21603	0.640558
$208$	−11.8387	−0.820863
$209$	6.15219	0.425556
$210$	0	0
$211$	−0.700374	−0.0482157	−0.0241079	−	0.999709i	$-0.507675\pi$
$211$	−0.700374	−0.0482157	−0.0241079	+	0.999709i	$0.507675\pi$
$212$	6.74939	0.463550
$213$	−9.53578	−0.653381
$214$	6.48217	0.443112
$215$	3.66967	0.250269
$216$	−2.05941	−0.140125
$217$	0	0
$218$	0.910976	0.0616991
$219$	7.16392	0.484093
$220$	0.732364	0.0493759
$221$	36.0764	2.42676
$222$	1.07008	0.0718193
$223$	21.0088	1.40685	0.703426	−	0.710768i	$-0.251652\pi$
$223$	21.0088	1.40685	0.703426	+	0.710768i	$0.251652\pi$
$224$	0	0
$225$	−4.91167	−0.327445
$226$	−2.48416	−0.165244
$227$	20.9063	1.38760	0.693800	−	0.720168i	$-0.255935\pi$
$227$	20.9063	1.38760	0.693800	+	0.720168i	$0.255935\pi$
$228$	−7.11546	−0.471233
$229$	12.0293	0.794920	0.397460	−	0.917619i	$-0.369892\pi$
$229$	12.0293	0.794920	0.397460	+	0.917619i	$0.369892\pi$
$230$	−1.52937	−0.100844
$231$	0	0
$232$	−15.9453	−1.04686
$233$	24.9061	1.63165	0.815825	−	0.578299i	$-0.196283\pi$
$233$	24.9061	1.63165	0.815825	+	0.578299i	$0.196283\pi$
$234$	−2.96896	−0.194087
$235$	−0.0664618	−0.00433549
$236$	9.40841	0.612435
$237$	2.54442	0.165278
$238$	0	0
$239$	−9.05767	−0.585892	−0.292946	−	0.956129i	$-0.594636\pi$
$239$	−9.05767	−0.585892	−0.292946	+	0.956129i	$0.594636\pi$
$240$	−0.661711	−0.0427133
$241$	−25.6281	−1.65085	−0.825424	−	0.564513i	$-0.809064\pi$
$241$	−25.6281	−1.65085	−0.825424	+	0.564513i	$0.809064\pi$
$242$	−4.95243	−0.318354
$243$	1.00000	0.0641500
$244$	8.58545	0.549627
$245$	0	0
$246$	0.558375	0.0356007
$247$	−22.4105	−1.42595
$248$	−14.7447	−0.936290
$249$	−5.99018	−0.379612
$250$	1.64481	0.104027
$251$	9.37294	0.591614	0.295807	−	0.955248i	$-0.404411\pi$
$251$	9.37294	0.591614	0.295807	+	0.955248i	$0.404411\pi$
$252$	0	0
$253$	13.4524	0.845743
$254$	−3.96733	−0.248932
$255$	2.01646	0.126275
$256$	−3.52499	−0.220312
$257$	4.73910	0.295617	0.147809	−	0.989016i	$-0.452778\pi$
$257$	4.73910	0.295617	0.147809	+	0.989016i	$0.452778\pi$
$258$	−6.89461	−0.429240
$259$	0	0
$260$	−2.66778	−0.165448
$261$	7.74267	0.479260
$262$	−2.50217	−0.154584
$263$	−9.78415	−0.603316	−0.301658	−	0.953416i	$-0.597540\pi$
$263$	−9.78415	−0.603316	−0.301658	+	0.953416i	$0.597540\pi$
$264$	−3.00606	−0.185010
$265$	1.18817	0.0729890
$266$	0	0
$267$	−15.5513	−0.951722
$268$	21.6333	1.32146
$269$	−4.51836	−0.275489	−0.137745	−	0.990468i	$-0.543985\pi$
$269$	−4.51836	−0.275489	−0.137745	+	0.990468i	$0.543985\pi$
$270$	−0.165947	−0.0100992
$271$	−22.4459	−1.36349	−0.681746	−	0.731589i	$-0.738779\pi$
$271$	−22.4459	−1.36349	−0.681746	+	0.731589i	$0.738779\pi$
$272$	−15.1067	−0.915979
$273$	0	0
$274$	−0.502866	−0.0303793
$275$	−7.16943	−0.432333
$276$	−15.5587	−0.936521
$277$	−21.6884	−1.30313	−0.651566	−	0.758592i	$-0.725887\pi$
$277$	−21.6884	−1.30313	−0.651566	+	0.758592i	$0.725887\pi$
$278$	−4.74457	−0.284560
$279$	7.15968	0.428639
$280$	0	0
$281$	27.1574	1.62007	0.810037	−	0.586379i	$-0.199447\pi$
$281$	27.1574	1.62007	0.810037	+	0.586379i	$0.199447\pi$
$282$	0.124869	0.00743584
$283$	−24.0760	−1.43117	−0.715585	−	0.698526i	$-0.753840\pi$
$283$	−24.0760	−1.43117	−0.715585	+	0.698526i	$0.753840\pi$
$284$	16.0985	0.955268
$285$	−1.25262	−0.0741986
$286$	−4.33370	−0.256257
$287$	0	0
$288$	5.36205	0.315962
$289$	29.0352	1.70796
$290$	−1.28487	−0.0754504
$291$	−10.7127	−0.627988
$292$	−12.0943	−0.707763
$293$	−22.3277	−1.30440	−0.652198	−	0.758049i	$-0.726153\pi$
$293$	−22.3277	−1.30440	−0.652198	+	0.758049i	$0.726153\pi$
$294$	0	0
$295$	1.65627	0.0964318
$296$	−3.94670	−0.229397
$297$	1.45967	0.0846987
$298$	3.36185	0.194747
$299$	−49.0029	−2.83391
$300$	8.29197	0.478737
$301$	0	0
$302$	7.77935	0.447651
$303$	−7.00779	−0.402587
$304$	9.38425	0.538224
$305$	1.51140	0.0865423
$306$	−3.78854	−0.216576
$307$	−27.2615	−1.55590	−0.777949	−	0.628327i	$-0.783740\pi$
$307$	−27.2615	−1.55590	−0.777949	+	0.628327i	$0.783740\pi$
$308$	0	0
$309$	−18.9625	−1.07874
$310$	−1.18813	−0.0674812
$311$	−31.0565	−1.76106	−0.880528	−	0.473995i	$-0.842811\pi$
$311$	−31.0565	−1.76106	−0.880528	+	0.473995i	$0.842811\pi$
$312$	10.9502	0.619930
$313$	12.0765	0.682607	0.341303	−	0.939953i	$-0.389132\pi$
$313$	12.0765	0.682607	0.341303	+	0.939953i	$0.389132\pi$
$314$	−2.06410	−0.116484
$315$	0	0
$316$	−4.29553	−0.241643
$317$	1.47604	0.0829026	0.0414513	−	0.999141i	$-0.486802\pi$
$317$	1.47604	0.0829026	0.0414513	+	0.999141i	$0.486802\pi$
$318$	−2.23235	−0.125184
$319$	11.3018	0.632777
$320$	0.433605	0.0242393
$321$	11.6090	0.647950
$322$	0	0
$323$	−28.5970	−1.59118
$324$	−1.68822	−0.0937898
$325$	26.1160	1.44866
$326$	7.66438	0.424491
$327$	1.63148	0.0902208
$328$	−2.05941	−0.113712
$329$	0	0
$330$	−0.242228	−0.0133342
$331$	0.783978	0.0430913	0.0215457	−	0.999768i	$-0.493141\pi$
$331$	0.783978	0.0430913	0.0215457	+	0.999768i	$0.493141\pi$
$332$	10.1127	0.555007
$333$	1.91642	0.105019
$334$	0.530063	0.0290038
$335$	3.80836	0.208073
$336$	0	0
$337$	1.19157	0.0649090	0.0324545	−	0.999473i	$-0.489668\pi$
$337$	1.19157	0.0649090	0.0324545	+	0.999473i	$0.489668\pi$
$338$	8.52745	0.463832
$339$	−4.44890	−0.241631
$340$	−3.40422	−0.184620
$341$	10.4508	0.565941
$342$	2.35343	0.127259
$343$	0	0
$344$	25.4288	1.37103
$345$	−2.73897	−0.147461
$346$	−1.50986	−0.0811703
$347$	5.75582	0.308989	0.154494	−	0.987994i	$-0.450625\pi$
$347$	5.75582	0.308989	0.154494	+	0.987994i	$0.450625\pi$
$348$	−13.0713	−0.700696
$349$	13.9938	0.749069	0.374534	−	0.927213i	$-0.377803\pi$
$349$	13.9938	0.749069	0.374534	+	0.927213i	$0.377803\pi$
$350$	0	0
$351$	−5.31713	−0.283808
$352$	7.82682	0.417171
$353$	0.452113	0.0240636	0.0120318	−	0.999928i	$-0.496170\pi$
$353$	0.452113	0.0240636	0.0120318	+	0.999928i	$0.496170\pi$
$354$	−3.11182	−0.165391
$355$	2.83400	0.150413
$356$	26.2539	1.39145
$357$	0	0
$358$	−12.0384	−0.636251
$359$	−5.40535	−0.285283	−0.142642	−	0.989774i	$-0.545560\pi$
$359$	−5.40535	−0.285283	−0.142642	+	0.989774i	$0.545560\pi$
$360$	0.612049	0.0322578
$361$	−1.23564	−0.0650337
$362$	0.0653506	0.00343475
$363$	−8.86936	−0.465521
$364$	0	0
$365$	−2.12909	−0.111442
$366$	−2.83962	−0.148430
$367$	6.86693	0.358451	0.179225	−	0.983808i	$-0.442641\pi$
$367$	6.86693	0.358451	0.179225	+	0.983808i	$0.442641\pi$
$368$	20.5196	1.06966
$369$	1.00000	0.0520579
$370$	−0.318025	−0.0165333
$371$	0	0
$372$	−12.0871	−0.626686
$373$	−25.7371	−1.33261	−0.666307	−	0.745677i	$-0.732126\pi$
$373$	−25.7371	−1.33261	−0.666307	+	0.745677i	$0.732126\pi$
$374$	−5.53002	−0.285950
$375$	2.94571	0.152116
$376$	−0.460544	−0.0237507
$377$	−41.1688	−2.12030
$378$	0	0
$379$	4.80138	0.246631	0.123315	−	0.992368i	$-0.460647\pi$
$379$	4.80138	0.246631	0.123315	+	0.992368i	$0.460647\pi$
$380$	2.11469	0.108481
$381$	−7.10513	−0.364007
$382$	−14.0051	−0.716561
$383$	2.08567	0.106573	0.0532863	−	0.998579i	$-0.483030\pi$
$383$	2.08567	0.106573	0.0532863	+	0.998579i	$0.483030\pi$
$384$	−11.5388	−0.588835
$385$	0	0
$386$	3.80937	0.193892
$387$	−12.3476	−0.627665
$388$	18.0853	0.918143
$389$	2.04279	0.103573	0.0517867	−	0.998658i	$-0.483508\pi$
$389$	2.04279	0.103573	0.0517867	+	0.998658i	$0.483508\pi$
$390$	0.882363	0.0446802
$391$	−62.5301	−3.16228
$392$	0	0
$393$	−4.48115	−0.226044
$394$	10.5015	0.529058
$395$	−0.756192	−0.0380482
$396$	−2.46424	−0.123833
$397$	22.2895	1.11868	0.559338	−	0.828940i	$-0.311055\pi$
$397$	22.2895	1.11868	0.559338	+	0.828940i	$0.311055\pi$
$398$	0.332564	0.0166699
$399$	0	0
$400$	−10.9359	−0.546795
$401$	14.5064	0.724414	0.362207	−	0.932098i	$-0.382023\pi$
$401$	14.5064	0.724414	0.362207	+	0.932098i	$0.382023\pi$
$402$	−7.15518	−0.356868
$403$	−38.0690	−1.89635
$404$	11.8307	0.588598
$405$	−0.297196	−0.0147678
$406$	0	0
$407$	2.79735	0.138659
$408$	13.9729	0.691764
$409$	18.8610	0.932614	0.466307	−	0.884623i	$-0.345584\pi$
$409$	18.8610	0.932614	0.466307	+	0.884623i	$0.345584\pi$
$410$	−0.165947	−0.00819555
$411$	−0.900588	−0.0444227
$412$	32.0128	1.57716
$413$	0	0
$414$	5.14600	0.252912
$415$	1.78026	0.0873895
$416$	−28.5107	−1.39785
$417$	−8.49710	−0.416105
$418$	3.43523	0.168023
$419$	−28.1776	−1.37657	−0.688283	−	0.725442i	$-0.741635\pi$
$419$	−28.1776	−1.37657	−0.688283	+	0.725442i	$0.741635\pi$
$420$	0	0
$421$	0.752196	0.0366598	0.0183299	−	0.999832i	$-0.494165\pi$
$421$	0.752196	0.0366598	0.0183299	+	0.999832i	$0.494165\pi$
$422$	−0.391071	−0.0190371
$423$	0.223629	0.0108732
$424$	8.23340	0.399849
$425$	33.3254	1.61652
$426$	−5.32455	−0.257975
$427$	0	0
$428$	−19.5985	−0.947328
$429$	−7.76126	−0.374717
$430$	2.04905	0.0988141
$431$	31.0617	1.49619	0.748095	−	0.663591i	$-0.230969\pi$
$431$	31.0617	1.49619	0.748095	+	0.663591i	$0.230969\pi$
$432$	2.22651	0.107123
$433$	−12.1837	−0.585511	−0.292755	−	0.956187i	$-0.594572\pi$
$433$	−12.1837	−0.585511	−0.292755	+	0.956187i	$0.594572\pi$
$434$	0	0
$435$	−2.30110	−0.110329
$436$	−2.75428	−0.131906
$437$	38.8435	1.85814
$438$	4.00016	0.191135
$439$	26.7934	1.27878	0.639389	−	0.768883i	$-0.279187\pi$
$439$	26.7934	1.27878	0.639389	+	0.768883i	$0.279187\pi$
$440$	0.893390	0.0425907
$441$	0	0
$442$	20.1441	0.958159
$443$	−16.8725	−0.801638	−0.400819	−	0.916157i	$-0.631274\pi$
$443$	−16.8725	−0.801638	−0.400819	+	0.916157i	$0.631274\pi$
$444$	−3.23534	−0.153542
$445$	4.62178	0.219093
$446$	11.7308	0.555469
$447$	6.02077	0.284773
$448$	0	0
$449$	−28.1355	−1.32779	−0.663897	−	0.747824i	$-0.731099\pi$
$449$	−28.1355	−1.32779	−0.663897	+	0.747824i	$0.731099\pi$
$450$	−2.74256	−0.129285
$451$	1.45967	0.0687332
$452$	7.51071	0.353274
$453$	13.9321	0.654588
$454$	11.6736	0.547868
$455$	0	0
$456$	−8.67996	−0.406476
$457$	−38.4409	−1.79819	−0.899094	−	0.437756i	$-0.855773\pi$
$457$	−38.4409	−1.79819	−0.899094	+	0.437756i	$0.855773\pi$
$458$	6.71688	0.313859
$459$	−6.78493	−0.316693
$460$	4.62398	0.215594
$461$	−23.1788	−1.07954	−0.539771	−	0.841812i	$-0.681489\pi$
$461$	−23.1788	−1.07954	−0.539771	+	0.841812i	$0.681489\pi$
$462$	0	0
$463$	15.1968	0.706253	0.353126	−	0.935576i	$-0.385119\pi$
$463$	15.1968	0.706253	0.353126	+	0.935576i	$0.385119\pi$
$464$	17.2391	0.800307
$465$	−2.12783	−0.0986758
$466$	13.9069	0.644226
$467$	−12.0228	−0.556348	−0.278174	−	0.960531i	$-0.589729\pi$
$467$	−12.0228	−0.556348	−0.278174	+	0.960531i	$0.589729\pi$
$468$	8.97647	0.414938
$469$	0	0
$470$	−0.0371106	−0.00171179
$471$	−3.69661	−0.170331
$472$	11.4771	0.528274
$473$	−18.0235	−0.828720
$474$	1.42074	0.0652568
$475$	−20.7016	−0.949856
$476$	0	0
$477$	−3.99794	−0.183053
$478$	−5.05758	−0.231328
$479$	−9.04799	−0.413413	−0.206707	−	0.978403i	$-0.566275\pi$
$479$	−9.04799	−0.413413	−0.206707	+	0.978403i	$0.566275\pi$
$480$	−1.59358	−0.0727367
$481$	−10.1899	−0.464618
$482$	−14.3101	−0.651806
$483$	0	0
$484$	14.9734	0.680609
$485$	3.18377	0.144567
$486$	0.558375	0.0253284
$487$	−15.6700	−0.710075	−0.355038	−	0.934852i	$-0.615532\pi$
$487$	−15.6700	−0.710075	−0.355038	+	0.934852i	$0.615532\pi$
$488$	10.4732	0.474097
$489$	13.7262	0.620721
$490$	0	0
$491$	−21.7635	−0.982174	−0.491087	−	0.871110i	$-0.663400\pi$
$491$	−21.7635	−0.982174	−0.491087	+	0.871110i	$0.663400\pi$
$492$	−1.68822	−0.0761107
$493$	−52.5335	−2.36599
$494$	−12.5135	−0.563009
$495$	−0.433809	−0.0194983
$496$	15.9411	0.715776
$497$	0	0
$498$	−3.34477	−0.149883
$499$	42.3789	1.89714	0.948570	−	0.316567i	$-0.102530\pi$
$499$	42.3789	1.89714	0.948570	+	0.316567i	$0.102530\pi$
$500$	−4.97300	−0.222400
$501$	0.949295	0.0424114
$502$	5.23362	0.233588
$503$	10.1587	0.452956	0.226478	−	0.974016i	$-0.427279\pi$
$503$	10.1587	0.452956	0.226478	+	0.974016i	$0.427279\pi$
$504$	0	0
$505$	2.08269	0.0926784
$506$	7.51147	0.333926
$507$	15.2719	0.678249
$508$	11.9950	0.532192
$509$	10.5288	0.466681	0.233340	−	0.972395i	$-0.425034\pi$
$509$	10.5288	0.466681	0.233340	+	0.972395i	$0.425034\pi$
$510$	1.12594	0.0498574
$511$	0	0
$512$	21.1092	0.932906
$513$	4.21478	0.186087
$514$	2.64620	0.116719
$515$	5.63558	0.248333
$516$	20.8455	0.917670
$517$	0.326425	0.0143562
$518$	0	0
$519$	−2.70402	−0.118693
$520$	−3.25435	−0.142713
$521$	−23.6607	−1.03659	−0.518297	−	0.855201i	$-0.673434\pi$
$521$	−23.6607	−1.03659	−0.518297	+	0.855201i	$0.673434\pi$
$522$	4.32332	0.189227
$523$	−33.8712	−1.48108	−0.740542	−	0.672010i	$-0.765431\pi$
$523$	−33.8712	−1.48108	−0.740542	+	0.672010i	$0.765431\pi$
$524$	7.56516	0.330486
$525$	0	0
$526$	−5.46323	−0.238208
$527$	−48.5779	−2.11609
$528$	3.24997	0.141437
$529$	61.9352	2.69284
$530$	0.663447	0.0288183
$531$	−5.57298	−0.241847
$532$	0	0
$533$	−5.31713	−0.230311
$534$	−8.68344	−0.375769
$535$	−3.45015	−0.149163
$536$	26.3898	1.13987
$537$	−21.5598	−0.930373
$538$	−2.52294	−0.108772
$539$	0	0
$540$	0.501732	0.0215911
$541$	36.7522	1.58010	0.790050	−	0.613042i	$-0.210054\pi$
$541$	36.7522	1.58010	0.790050	+	0.613042i	$0.210054\pi$
$542$	−12.5333	−0.538349
$543$	0.117037	0.00502254
$544$	−36.3811	−1.55983
$545$	−0.484869	−0.0207695
$546$	0	0
$547$	−3.16326	−0.135251	−0.0676255	−	0.997711i	$-0.521542\pi$
$547$	−3.16326	−0.135251	−0.0676255	+	0.997711i	$0.521542\pi$
$548$	1.52039	0.0649478
$549$	−5.08551	−0.217044
$550$	−4.00323	−0.170698
$551$	32.6337	1.39024
$552$	−18.9796	−0.807825
$553$	0	0
$554$	−12.1103	−0.514517
$555$	−0.569554	−0.0241762
$556$	14.3449	0.608361
$557$	−13.8532	−0.586980	−0.293490	−	0.955962i	$-0.594817\pi$
$557$	−13.8532	−0.586980	−0.293490	+	0.955962i	$0.594817\pi$
$558$	3.99779	0.169240
$559$	65.6539	2.77687
$560$	0	0
$561$	−9.90376	−0.418137
$562$	15.1640	0.639655
$563$	−18.3422	−0.773031	−0.386515	−	0.922283i	$-0.626321\pi$
$563$	−18.3422	−0.773031	−0.386515	+	0.922283i	$0.626321\pi$
$564$	−0.377535	−0.0158971
$565$	1.32220	0.0556253
$566$	−13.4434	−0.565070
$567$	0	0
$568$	19.6381	0.823996
$569$	7.22740	0.302988	0.151494	−	0.988458i	$-0.451592\pi$
$569$	7.22740	0.302988	0.151494	+	0.988458i	$0.451592\pi$
$570$	−0.699431	−0.0292959
$571$	−11.5485	−0.483292	−0.241646	−	0.970365i	$-0.577687\pi$
$571$	−11.5485	−0.483292	−0.241646	+	0.970365i	$0.577687\pi$
$572$	13.1027	0.547851
$573$	−25.0818	−1.04781
$574$	0	0
$575$	−45.2661	−1.88773
$576$	−1.45899	−0.0607911
$577$	22.9622	0.955930	0.477965	−	0.878379i	$-0.341375\pi$
$577$	22.9622	0.955930	0.477965	+	0.878379i	$0.341375\pi$
$578$	16.2126	0.674354
$579$	6.82223	0.283522
$580$	3.88475	0.161305
$581$	0	0
$582$	−5.98169	−0.247949
$583$	−5.83568	−0.241689
$584$	−14.7535	−0.610502
$585$	1.58023	0.0653346
$586$	−12.4672	−0.515016
$587$	4.87577	0.201245	0.100622	−	0.994925i	$-0.467917\pi$
$587$	4.87577	0.201245	0.100622	+	0.994925i	$0.467917\pi$
$588$	0	0
$589$	30.1765	1.24340
$590$	0.924821	0.0380743
$591$	18.8073	0.773627
$592$	4.26694	0.175370
$593$	−34.7229	−1.42590	−0.712949	−	0.701215i	$-0.752641\pi$
$593$	−34.7229	−1.42590	−0.712949	+	0.701215i	$0.752641\pi$
$594$	0.815044	0.0334417
$595$	0	0
$596$	−10.1644	−0.416349
$597$	0.595593	0.0243760
$598$	−27.3620	−1.11891
$599$	7.26176	0.296707	0.148354	−	0.988934i	$-0.452603\pi$
$599$	7.26176	0.296707	0.148354	+	0.988934i	$0.452603\pi$
$600$	10.1151	0.412949
$601$	34.0886	1.39050	0.695252	−	0.718766i	$-0.255293\pi$
$601$	34.0886	1.39050	0.695252	+	0.718766i	$0.255293\pi$
$602$	0	0
$603$	−12.8143	−0.521838
$604$	−23.5204	−0.957033
$605$	2.63594	0.107166
$606$	−3.91298	−0.158954
$607$	17.8489	0.724464	0.362232	−	0.932088i	$-0.382015\pi$
$607$	17.8489	0.724464	0.362232	+	0.932088i	$0.382015\pi$
$608$	22.5998	0.916545
$609$	0	0
$610$	0.843926	0.0341696
$611$	−1.18907	−0.0481045
$612$	11.4544	0.463018
$613$	−8.70810	−0.351717	−0.175858	−	0.984415i	$-0.556270\pi$
$613$	−8.70810	−0.351717	−0.175858	+	0.984415i	$0.556270\pi$
$614$	−15.2222	−0.614317
$615$	−0.297196	−0.0119841
$616$	0	0
$617$	−22.4277	−0.902904	−0.451452	−	0.892295i	$-0.649094\pi$
$617$	−22.4277	−0.902904	−0.451452	+	0.892295i	$0.649094\pi$
$618$	−10.5882	−0.425919
$619$	−15.2107	−0.611368	−0.305684	−	0.952133i	$-0.598885\pi$
$619$	−15.2107	−0.611368	−0.305684	+	0.952133i	$0.598885\pi$
$620$	3.59224	0.144268
$621$	9.21603	0.369827
$622$	−17.3412	−0.695319
$623$	0	0
$624$	−11.8387	−0.473925
$625$	23.6829	0.947317
$626$	6.74325	0.269514
$627$	6.15219	0.245695
$628$	6.24068	0.249030
$629$	−13.0028	−0.518455
$630$	0	0
$631$	33.6465	1.33945	0.669723	−	0.742611i	$-0.266413\pi$
$631$	33.6465	1.33945	0.669723	+	0.742611i	$0.266413\pi$
$632$	−5.24000	−0.208436
$633$	−0.700374	−0.0278374
$634$	0.824183	0.0327325
$635$	2.11162	0.0837971
$636$	6.74939	0.267631
$637$	0	0
$638$	6.31062	0.249840
$639$	−9.53578	−0.377230
$640$	3.42928	0.135554
$641$	−22.8787	−0.903656	−0.451828	−	0.892105i	$-0.649228\pi$
$641$	−22.8787	−0.903656	−0.451828	+	0.892105i	$0.649228\pi$
$642$	6.48217	0.255831
$643$	16.1298	0.636095	0.318048	−	0.948075i	$-0.396973\pi$
$643$	16.1298	0.636095	0.318048	+	0.948075i	$0.396973\pi$
$644$	0	0
$645$	3.66967	0.144493
$646$	−15.9678	−0.628246
$647$	13.5777	0.533795	0.266898	−	0.963725i	$-0.414001\pi$
$647$	13.5777	0.533795	0.266898	+	0.963725i	$0.414001\pi$
$648$	−2.05941	−0.0809012
$649$	−8.13472	−0.319316
$650$	14.5825	0.571974
$651$	0	0
$652$	−23.1728	−0.907518
$653$	15.8684	0.620978	0.310489	−	0.950577i	$-0.399507\pi$
$653$	15.8684	0.620978	0.310489	+	0.950577i	$0.399507\pi$
$654$	0.910976	0.0356220
$655$	1.33178	0.0520371
$656$	2.22651	0.0869306
$657$	7.16392	0.279491
$658$	0	0
$659$	44.8002	1.74517	0.872584	−	0.488464i	$-0.162443\pi$
$659$	44.8002	1.74517	0.872584	+	0.488464i	$0.162443\pi$
$660$	0.732364	0.0285072
$661$	9.82114	0.381998	0.190999	−	0.981590i	$-0.438827\pi$
$661$	9.82114	0.381998	0.190999	+	0.981590i	$0.438827\pi$
$662$	0.437754	0.0170138
$663$	36.0764	1.40109
$664$	12.3362	0.478738
$665$	0	0
$666$	1.07008	0.0414649
$667$	71.3567	2.76294
$668$	−1.60262	−0.0620071
$669$	21.0088	0.812247
$670$	2.12649	0.0821536
$671$	−7.42317	−0.286568
$672$	0	0
$673$	46.6958	1.79999	0.899996	−	0.435899i	$-0.143569\pi$
$673$	46.6958	1.79999	0.899996	+	0.435899i	$0.143569\pi$
$674$	0.665344	0.0256281
$675$	−4.91167	−0.189050
$676$	−25.7823	−0.991626
$677$	−18.3825	−0.706495	−0.353248	−	0.935530i	$-0.614923\pi$
$677$	−18.3825	−0.706495	−0.353248	+	0.935530i	$0.614923\pi$
$678$	−2.48416	−0.0954034
$679$	0	0
$680$	−4.15271	−0.159249
$681$	20.9063	0.801131
$682$	5.83545	0.223451
$683$	−7.31673	−0.279967	−0.139983	−	0.990154i	$-0.544705\pi$
$683$	−7.31673	−0.279967	−0.139983	+	0.990154i	$0.544705\pi$
$684$	−7.11546	−0.272066
$685$	0.267652	0.0102264
$686$	0	0
$687$	12.0293	0.458948
$688$	−27.4921	−1.04813
$689$	21.2576	0.809850
$690$	−1.52937	−0.0582223
$691$	−29.5844	−1.12545	−0.562723	−	0.826646i	$-0.690246\pi$
$691$	−29.5844	−1.12545	−0.562723	+	0.826646i	$0.690246\pi$
$692$	4.56496	0.173534
$693$	0	0
$694$	3.21391	0.121998
$695$	2.52531	0.0957903
$696$	−15.9453	−0.604406
$697$	−6.78493	−0.256997
$698$	7.81377	0.295756
$699$	24.9061	0.942033
$700$	0	0
$701$	−34.7837	−1.31376	−0.656880	−	0.753995i	$-0.728124\pi$
$701$	−34.7837	−1.31376	−0.656880	+	0.753995i	$0.728124\pi$
$702$	−2.96896	−0.112056
$703$	8.07730	0.304641
$704$	−2.12964	−0.0802638
$705$	−0.0664618	−0.00250310
$706$	0.252449	0.00950104
$707$	0	0
$708$	9.40841	0.353590
$709$	22.6688	0.851345	0.425673	−	0.904877i	$-0.360038\pi$
$709$	22.6688	0.851345	0.425673	+	0.904877i	$0.360038\pi$
$710$	1.58244	0.0593878
$711$	2.54442	0.0954232
$712$	32.0264	1.20024
$713$	65.9838	2.47111
$714$	0	0
$715$	2.30662	0.0862627
$716$	36.3976	1.36024
$717$	−9.05767	−0.338265
$718$	−3.01821	−0.112639
$719$	15.3765	0.573445	0.286722	−	0.958014i	$-0.407434\pi$
$719$	15.3765	0.573445	0.286722	+	0.958014i	$0.407434\pi$
$720$	−0.661711	−0.0246605
$721$	0	0
$722$	−0.689951	−0.0256773
$723$	−25.6281	−0.953118
$724$	−0.197584	−0.00734314
$725$	−38.0295	−1.41238
$726$	−4.95243	−0.183802
$727$	−28.6575	−1.06285	−0.531424	−	0.847106i	$-0.678343\pi$
$727$	−28.6575	−1.06285	−0.531424	+	0.847106i	$0.678343\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.18883	−0.0440007
$731$	83.7777	3.09863
$732$	8.58545	0.317327
$733$	−3.16521	−0.116910	−0.0584549	−	0.998290i	$-0.518617\pi$
$733$	−3.16521	−0.116910	−0.0584549	+	0.998290i	$0.518617\pi$
$734$	3.83432	0.141527
$735$	0	0
$736$	49.4168	1.82153
$737$	−18.7046	−0.688994
$738$	0.558375	0.0205541
$739$	25.1392	0.924760	0.462380	−	0.886682i	$-0.346996\pi$
$739$	25.1392	0.924760	0.462380	+	0.886682i	$0.346996\pi$
$740$	0.961531	0.0353466
$741$	−22.4105	−0.823272
$742$	0	0
$743$	−12.2882	−0.450811	−0.225406	−	0.974265i	$-0.572371\pi$
$743$	−12.2882	−0.450811	−0.225406	+	0.974265i	$0.572371\pi$
$744$	−14.7447	−0.540567
$745$	−1.78935	−0.0655568
$746$	−14.3709	−0.526158
$747$	−5.99018	−0.219169
$748$	16.7197	0.611333
$749$	0	0
$750$	1.64481	0.0600601
$751$	39.2342	1.43168	0.715838	−	0.698267i	$-0.246045\pi$
$751$	39.2342	1.43168	0.715838	+	0.698267i	$0.246045\pi$
$752$	0.497913	0.0181570
$753$	9.37294	0.341569
$754$	−22.9877	−0.837161
$755$	−4.14057	−0.150691
$756$	0	0
$757$	−23.8360	−0.866333	−0.433166	−	0.901314i	$-0.642604\pi$
$757$	−23.8360	−0.866333	−0.433166	+	0.901314i	$0.642604\pi$
$758$	2.68097	0.0973774
$759$	13.4524	0.488290
$760$	2.57965	0.0935738
$761$	−14.9892	−0.543358	−0.271679	−	0.962388i	$-0.587579\pi$
$761$	−14.9892	−0.543358	−0.271679	+	0.962388i	$0.587579\pi$
$762$	−3.96733	−0.143721
$763$	0	0
$764$	42.3435	1.53193
$765$	2.01646	0.0729051
$766$	1.16459	0.0420782
$767$	29.6323	1.06996
$768$	−3.52499	−0.127197
$769$	−10.1121	−0.364652	−0.182326	−	0.983238i	$-0.558363\pi$
$769$	−10.1121	−0.364652	−0.182326	+	0.983238i	$0.558363\pi$
$770$	0	0
$771$	4.73910	0.170675
$772$	−11.5174	−0.414521
$773$	−7.67006	−0.275873	−0.137937	−	0.990441i	$-0.544047\pi$
$773$	−7.67006	−0.275873	−0.137937	+	0.990441i	$0.544047\pi$
$774$	−6.89461	−0.247822
$775$	−35.1660	−1.26320
$776$	22.0618	0.791972
$777$	0	0
$778$	1.14064	0.0408940
$779$	4.21478	0.151010
$780$	−2.66778	−0.0955217
$781$	−13.9191	−0.498065
$782$	−34.9153	−1.24857
$783$	7.74267	0.276701
$784$	0	0
$785$	1.09862	0.0392114
$786$	−2.50217	−0.0892493
$787$	6.04269	0.215399	0.107699	−	0.994184i	$-0.465652\pi$
$787$	6.04269	0.215399	0.107699	+	0.994184i	$0.465652\pi$
$788$	−31.7507	−1.13107
$789$	−9.78415	−0.348325
$790$	−0.422239	−0.0150226
$791$	0	0
$792$	−3.00606	−0.106816
$793$	27.0403	0.960231
$794$	12.4459	0.441688
$795$	1.18817	0.0421402
$796$	−1.00549	−0.0356386
$797$	1.19201	0.0422231	0.0211115	−	0.999777i	$-0.493279\pi$
$797$	1.19201	0.0422231	0.0211115	+	0.999777i	$0.493279\pi$
$798$	0	0
$799$	−1.51731	−0.0536785
$800$	−26.3366	−0.931140
$801$	−15.5513	−0.549477
$802$	8.10000	0.286021
$803$	10.4570	0.369019
$804$	21.6333	0.762947
$805$	0	0
$806$	−21.2568	−0.748738
$807$	−4.51836	−0.159054
$808$	14.4319	0.507713
$809$	30.9790	1.08917	0.544583	−	0.838707i	$-0.316688\pi$
$809$	30.9790	1.08917	0.544583	+	0.838707i	$0.316688\pi$
$810$	−0.165947	−0.00583079
$811$	−39.8799	−1.40037	−0.700186	−	0.713960i	$-0.746900\pi$
$811$	−39.8799	−1.40037	−0.700186	+	0.713960i	$0.746900\pi$
$812$	0	0
$813$	−22.4459	−0.787213
$814$	1.56197	0.0547470
$815$	−4.07938	−0.142895
$816$	−15.1067	−0.528841
$817$	−52.0425	−1.82074
$818$	10.5315	0.368225
$819$	0	0
$820$	0.501732	0.0175212
$821$	43.3471	1.51282	0.756411	−	0.654096i	$-0.226951\pi$
$821$	43.3471	1.51282	0.756411	+	0.654096i	$0.226951\pi$
$822$	−0.502866	−0.0175395
$823$	−11.3966	−0.397261	−0.198630	−	0.980074i	$-0.563649\pi$
$823$	−11.3966	−0.397261	−0.198630	+	0.980074i	$0.563649\pi$
$824$	39.0515	1.36042
$825$	−7.16943	−0.249607
$826$	0	0
$827$	13.6912	0.476090	0.238045	−	0.971254i	$-0.423493\pi$
$827$	13.6912	0.476090	0.238045	+	0.971254i	$0.423493\pi$
$828$	−15.5587	−0.540701
$829$	−10.1163	−0.351352	−0.175676	−	0.984448i	$-0.556211\pi$
$829$	−10.1163	−0.351352	−0.175676	+	0.984448i	$0.556211\pi$
$830$	0.994053	0.0345041
$831$	−21.6884	−0.752363
$832$	7.75762	0.268947
$833$	0	0
$834$	−4.74457	−0.164291
$835$	−0.282127	−0.00976341
$836$	−10.3862	−0.359215
$837$	7.15968	0.247475
$838$	−15.7337	−0.543511
$839$	35.3736	1.22123	0.610616	−	0.791927i	$-0.290922\pi$
$839$	35.3736	1.22123	0.610616	+	0.791927i	$0.290922\pi$
$840$	0	0
$841$	30.9490	1.06721
$842$	0.420008	0.0144744
$843$	27.1574	0.935350
$844$	1.18238	0.0406993
$845$	−4.53875	−0.156138
$846$	0.124869	0.00429309
$847$	0	0
$848$	−8.90146	−0.305677
$849$	−24.0760	−0.826287
$850$	18.6081	0.638251
$851$	17.6618	0.605439
$852$	16.0985	0.551524
$853$	−32.4957	−1.11263	−0.556315	−	0.830971i	$-0.687785\pi$
$853$	−32.4957	−1.11263	−0.556315	+	0.830971i	$0.687785\pi$
$854$	0	0
$855$	−1.25262	−0.0428386
$856$	−23.9076	−0.817146
$857$	−33.9980	−1.16135	−0.580674	−	0.814136i	$-0.697211\pi$
$857$	−33.9980	−1.16135	−0.580674	+	0.814136i	$0.697211\pi$
$858$	−4.33370	−0.147950
$859$	29.5637	1.00870	0.504350	−	0.863500i	$-0.331732\pi$
$859$	29.5637	1.00870	0.504350	+	0.863500i	$0.331732\pi$
$860$	−6.19520	−0.211254
$861$	0	0
$862$	17.3441	0.590742
$863$	−2.54014	−0.0864673	−0.0432337	−	0.999065i	$-0.513766\pi$
$863$	−2.54014	−0.0864673	−0.0432337	+	0.999065i	$0.513766\pi$
$864$	5.36205	0.182421
$865$	0.803624	0.0273240
$866$	−6.80307	−0.231178
$867$	29.0352	0.986089
$868$	0	0
$869$	3.71402	0.125989
$870$	−1.28487	−0.0435613
$871$	68.1352	2.30867
$872$	−3.35988	−0.113780
$873$	−10.7127	−0.362569
$874$	21.6893	0.733650
$875$	0	0
$876$	−12.0943	−0.408627
$877$	−49.8096	−1.68195	−0.840975	−	0.541075i	$-0.818018\pi$
$877$	−49.8096	−1.68195	−0.840975	+	0.541075i	$0.818018\pi$
$878$	14.9608	0.504901
$879$	−22.3277	−0.753093
$880$	−0.965880	−0.0325598
$881$	29.6662	0.999480	0.499740	−	0.866175i	$-0.333429\pi$
$881$	29.6662	0.999480	0.499740	+	0.866175i	$0.333429\pi$
$882$	0	0
$883$	−20.5138	−0.690345	−0.345172	−	0.938539i	$-0.612180\pi$
$883$	−20.5138	−0.690345	−0.345172	+	0.938539i	$0.612180\pi$
$884$	−60.9047	−2.04845
$885$	1.65627	0.0556749
$886$	−9.42120	−0.316511
$887$	6.70324	0.225073	0.112536	−	0.993648i	$-0.464103\pi$
$887$	6.70324	0.225073	0.112536	+	0.993648i	$0.464103\pi$
$888$	−3.94670	−0.132443
$889$	0	0
$890$	2.58069	0.0865049
$891$	1.45967	0.0489008
$892$	−35.4674	−1.18754
$893$	0.942548	0.0315412
$894$	3.36185	0.112437
$895$	6.40749	0.214179
$896$	0	0
$897$	−49.0029	−1.63616
$898$	−15.7101	−0.524254
$899$	55.4351	1.84886
$900$	8.29197	0.276399
$901$	27.1258	0.903690
$902$	0.815044	0.0271380
$903$	0	0
$904$	9.16211	0.304727
$905$	−0.0347830	−0.00115622
$906$	7.77935	0.258451
$907$	13.7161	0.455435	0.227718	−	0.973727i	$-0.426874\pi$
$907$	13.7161	0.455435	0.227718	+	0.973727i	$0.426874\pi$
$908$	−35.2944	−1.17129
$909$	−7.00779	−0.232434
$910$	0	0
$911$	39.3560	1.30392	0.651962	−	0.758252i	$-0.273946\pi$
$911$	39.3560	1.30392	0.651962	+	0.758252i	$0.273946\pi$
$912$	9.38425	0.310744
$913$	−8.74369	−0.289374
$914$	−21.4644	−0.709980
$915$	1.51140	0.0499652
$916$	−20.3081	−0.670999
$917$	0	0
$918$	−3.78854	−0.125040
$919$	−30.0321	−0.990668	−0.495334	−	0.868703i	$-0.664954\pi$
$919$	−30.0321	−0.990668	−0.495334	+	0.868703i	$0.664954\pi$
$920$	5.64066	0.185967
$921$	−27.2615	−0.898298
$922$	−12.9424	−0.426237
$923$	50.7030	1.66891
$924$	0	0
$925$	−9.41285	−0.309492
$926$	8.48549	0.278851
$927$	−18.9625	−0.622809
$928$	41.5166	1.36285
$929$	26.8972	0.882469	0.441234	−	0.897392i	$-0.354541\pi$
$929$	26.8972	0.882469	0.441234	+	0.897392i	$0.354541\pi$
$930$	−1.18813	−0.0389603
$931$	0	0
$932$	−42.0468	−1.37729
$933$	−31.0565	−1.01675
$934$	−6.71323	−0.219663
$935$	2.94336	0.0962582
$936$	10.9502	0.357917
$937$	12.8652	0.420287	0.210144	−	0.977671i	$-0.432607\pi$
$937$	12.8652	0.420287	0.210144	+	0.977671i	$0.432607\pi$
$938$	0	0
$939$	12.0765	0.394103
$940$	0.112202	0.00365962
$941$	−7.46024	−0.243197	−0.121598	−	0.992579i	$-0.538802\pi$
$941$	−7.46024	−0.243197	−0.121598	+	0.992579i	$0.538802\pi$
$942$	−2.06410	−0.0672519
$943$	9.21603	0.300115
$944$	−12.4083	−0.403856
$945$	0	0
$946$	−10.0639	−0.327204
$947$	−32.8317	−1.06689	−0.533443	−	0.845836i	$-0.679102\pi$
$947$	−32.8317	−1.06689	−0.533443	+	0.845836i	$0.679102\pi$
$948$	−4.29553	−0.139512
$949$	−38.0915	−1.23650
$950$	−11.5593	−0.375032
$951$	1.47604	0.0478638
$952$	0	0
$953$	−39.3987	−1.27625	−0.638125	−	0.769933i	$-0.720290\pi$
$953$	−39.3987	−1.27625	−0.638125	+	0.769933i	$0.720290\pi$
$954$	−2.23235	−0.0722751
$955$	7.45422	0.241213
$956$	15.2913	0.494557
$957$	11.3018	0.365334
$958$	−5.05218	−0.163228
$959$	0	0
$960$	0.433605	0.0139946
$961$	20.2610	0.653580
$962$	−5.68978	−0.183446
$963$	11.6090	0.374094
$964$	43.2657	1.39350
$965$	−2.02754	−0.0652689
$966$	0	0
$967$	27.5183	0.884929	0.442465	−	0.896786i	$-0.354104\pi$
$967$	27.5183	0.884929	0.442465	+	0.896786i	$0.354104\pi$
$968$	18.2656	0.587080
$969$	−28.5970	−0.918667
$970$	1.77774	0.0570797
$971$	4.43144	0.142212	0.0711058	−	0.997469i	$-0.477347\pi$
$971$	4.43144	0.142212	0.0711058	+	0.997469i	$0.477347\pi$
$972$	−1.68822	−0.0541496
$973$	0	0
$974$	−8.74974	−0.280360
$975$	26.1160	0.836382
$976$	−11.3229	−0.362439
$977$	−24.1449	−0.772463	−0.386231	−	0.922402i	$-0.626223\pi$
$977$	−24.1449	−0.772463	−0.386231	+	0.922402i	$0.626223\pi$
$978$	7.66438	0.245080
$979$	−22.6997	−0.725486
$980$	0	0
$981$	1.63148	0.0520890
$982$	−12.1522	−0.387793
$983$	−33.5286	−1.06940	−0.534698	−	0.845043i	$-0.679575\pi$
$983$	−33.5286	−1.06940	−0.534698	+	0.845043i	$0.679575\pi$
$984$	−2.05941	−0.0656516
$985$	−5.58945	−0.178095
$986$	−29.3334	−0.934166
$987$	0	0
$988$	37.8339	1.20366
$989$	−113.796	−3.61850
$990$	−0.242228	−0.00769852
$991$	−25.0274	−0.795021	−0.397510	−	0.917598i	$-0.630126\pi$
$991$	−25.0274	−0.795021	−0.397510	+	0.917598i	$0.630126\pi$
$992$	38.3905	1.21890
$993$	0.783978	0.0248788
$994$	0	0
$995$	−0.177008	−0.00561153
$996$	10.1127	0.320434
$997$	47.6306	1.50848	0.754238	−	0.656602i	$-0.228007\pi$
$997$	47.6306	1.50848	0.754238	+	0.656602i	$0.228007\pi$
$998$	23.6633	0.749050
$999$	1.91642	0.0606329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bi.1.9		13
7.2	even	3		861.2.i.f.739.5	yes	26
7.4	even	3		861.2.i.f.247.5	✓	26
7.6	odd	2		6027.2.a.bh.1.9		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.5	✓	26	7.4	even	3
861.2.i.f.739.5	yes	26	7.2	even	3
6027.2.a.bh.1.9		13	7.6	odd	2
6027.2.a.bi.1.9		13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.558375 q^{2} +1.00000 q^{3} -1.68822 q^{4} -0.297196 q^{5} +0.558375 q^{6} -2.05941 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.558375 q^{2} +1.00000 q^{3} -1.68822 q^{4} -0.297196 q^{5} +0.558375 q^{6} -2.05941 q^{8} +1.00000 q^{9} -0.165947 q^{10} +1.45967 q^{11} -1.68822 q^{12} -5.31713 q^{13} -0.297196 q^{15} +2.22651 q^{16} -6.78493 q^{17} +0.558375 q^{18} +4.21478 q^{19} +0.501732 q^{20} +0.815044 q^{22} +9.21603 q^{23} -2.05941 q^{24} -4.91167 q^{25} -2.96896 q^{26} +1.00000 q^{27} +7.74267 q^{29} -0.165947 q^{30} +7.15968 q^{31} +5.36205 q^{32} +1.45967 q^{33} -3.78854 q^{34} -1.68822 q^{36} +1.91642 q^{37} +2.35343 q^{38} -5.31713 q^{39} +0.612049 q^{40} +1.00000 q^{41} -12.3476 q^{43} -2.46424 q^{44} -0.297196 q^{45} +5.14600 q^{46} +0.223629 q^{47} +2.22651 q^{48} -2.74256 q^{50} -6.78493 q^{51} +8.97647 q^{52} -3.99794 q^{53} +0.558375 q^{54} -0.433809 q^{55} +4.21478 q^{57} +4.32332 q^{58} -5.57298 q^{59} +0.501732 q^{60} -5.08551 q^{61} +3.99779 q^{62} -1.45899 q^{64} +1.58023 q^{65} +0.815044 q^{66} -12.8143 q^{67} +11.4544 q^{68} +9.21603 q^{69} -9.53578 q^{71} -2.05941 q^{72} +7.16392 q^{73} +1.07008 q^{74} -4.91167 q^{75} -7.11546 q^{76} -2.96896 q^{78} +2.54442 q^{79} -0.661711 q^{80} +1.00000 q^{81} +0.558375 q^{82} -5.99018 q^{83} +2.01646 q^{85} -6.89461 q^{86} +7.74267 q^{87} -3.00606 q^{88} -15.5513 q^{89} -0.165947 q^{90} -15.5587 q^{92} +7.15968 q^{93} +0.124869 q^{94} -1.25262 q^{95} +5.36205 q^{96} -10.7127 q^{97} +1.45967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 4 q^{2} + 13 q^{3} + 12 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 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

Introduction

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Modular forms

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