LMFDB - Embedded newform 261.12.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,12,Mod(1,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("261.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	261.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:	$200.537570126$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 $ x^11 - x^10 - 15790x^9 + 14666x^8 + 87206462x^7 - 14008334x^6 - 203974096304x^5 - 388180519304x^4 + 193065378004825x^3 + 1279291654973975x^2 - 65244901875230266*x - 758324542468966858
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$65.2743$ of defining polynomial
Character	$\chi$	$=$	261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-62.2743 q^{2} +1830.09 q^{4} -1377.47 q^{5} +33050.3 q^{7} +13570.0 q^{8} +O(q^{10})$	\(q-62.2743 q^{2} +1830.09 q^{4} -1377.47 q^{5} +33050.3 q^{7} +13570.0 q^{8} +85780.8 q^{10} +800438. q^{11} +1.48554e6 q^{13} -2.05818e6 q^{14} -4.59309e6 q^{16} +1.13043e7 q^{17} -9.78812e6 q^{19} -2.52089e6 q^{20} -4.98468e7 q^{22} -546284. q^{23} -4.69307e7 q^{25} -9.25112e7 q^{26} +6.04851e7 q^{28} -2.05111e7 q^{29} +4.17817e6 q^{31} +2.58240e8 q^{32} -7.03969e8 q^{34} -4.55257e7 q^{35} +3.50598e8 q^{37} +6.09549e8 q^{38} -1.86923e7 q^{40} -7.34075e8 q^{41} -1.74203e9 q^{43} +1.46488e9 q^{44} +3.40195e7 q^{46} -1.70223e9 q^{47} -8.85005e8 q^{49} +2.92258e9 q^{50} +2.71868e9 q^{52} -2.30025e9 q^{53} -1.10258e9 q^{55} +4.48494e8 q^{56} +1.27732e9 q^{58} +2.84523e8 q^{59} +5.13866e9 q^{61} -2.60193e8 q^{62} -6.67509e9 q^{64} -2.04629e9 q^{65} -3.85315e9 q^{67} +2.06880e10 q^{68} +2.83508e9 q^{70} -2.82041e10 q^{71} -1.81192e10 q^{73} -2.18333e10 q^{74} -1.79132e10 q^{76} +2.64547e10 q^{77} -3.94609e10 q^{79} +6.32684e9 q^{80} +4.57140e10 q^{82} -1.27885e10 q^{83} -1.55713e10 q^{85} +1.08484e11 q^{86} +1.08620e10 q^{88} -4.46844e10 q^{89} +4.90976e10 q^{91} -9.99751e8 q^{92} +1.06005e11 q^{94} +1.34828e10 q^{95} -7.40280e10 q^{97} +5.51131e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) $ 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8} - 685834 q^{10} + 612246 q^{11} + 1510364 q^{13} - 3955400 q^{14} + 3024818 q^{16} + 3291098 q^{17} - 44121388 q^{19} + 49472662 q^{20} - 43435618 q^{22} + 88684076 q^{23} - 44195521 q^{25} + 324999762 q^{26} - 391274848 q^{28} - 225622639 q^{29} - 292235934 q^{31} + 632542514 q^{32} - 1113307936 q^{34} + 1312820120 q^{35} - 1380429338 q^{37} + 1222857284 q^{38} - 2713154106 q^{40} + 1062067494 q^{41} + 74588594 q^{43} - 52891466 q^{44} - 87670324 q^{46} + 1821239394 q^{47} + 4692522003 q^{49} - 9494259926 q^{50} + 3266669866 q^{52} - 7818635688 q^{53} - 191002682 q^{55} - 11263587512 q^{56} - 656356768 q^{58} - 1230002712 q^{59} - 18602654230 q^{61} - 22075953162 q^{62} + 11813658086 q^{64} - 32245789334 q^{65} + 27481284652 q^{67} - 29588811820 q^{68} + 42862666712 q^{70} + 20347168516 q^{71} - 57740010478 q^{73} + 2640709564 q^{74} - 33350650772 q^{76} - 871959792 q^{77} - 120245016462 q^{79} + 84319695274 q^{80} - 111495532412 q^{82} + 142463983824 q^{83} - 181628566552 q^{85} - 47870165542 q^{86} - 180608014462 q^{88} + 96700717270 q^{89} - 355162031176 q^{91} + 22429477796 q^{92} + 172608565078 q^{94} + 195922150708 q^{95} - 303190852014 q^{97} + 123776497136 q^{98}+O(q^{100}) \) 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8 - 685834 * q^10 + 612246 * q^11 + 1510364 * q^13 - 3955400 * q^14 + 3024818 * q^16 + 3291098 * q^17 - 44121388 * q^19 + 49472662 * q^20 - 43435618 * q^22 + 88684076 * q^23 - 44195521 * q^25 + 324999762 * q^26 - 391274848 * q^28 - 225622639 * q^29 - 292235934 * q^31 + 632542514 * q^32 - 1113307936 * q^34 + 1312820120 * q^35 - 1380429338 * q^37 + 1222857284 * q^38 - 2713154106 * q^40 + 1062067494 * q^41 + 74588594 * q^43 - 52891466 * q^44 - 87670324 * q^46 + 1821239394 * q^47 + 4692522003 * q^49 - 9494259926 * q^50 + 3266669866 * q^52 - 7818635688 * q^53 - 191002682 * q^55 - 11263587512 * q^56 - 656356768 * q^58 - 1230002712 * q^59 - 18602654230 * q^61 - 22075953162 * q^62 + 11813658086 * q^64 - 32245789334 * q^65 + 27481284652 * q^67 - 29588811820 * q^68 + 42862666712 * q^70 + 20347168516 * q^71 - 57740010478 * q^73 + 2640709564 * q^74 - 33350650772 * q^76 - 871959792 * q^77 - 120245016462 * q^79 + 84319695274 * q^80 - 111495532412 * q^82 + 142463983824 * q^83 - 181628566552 * q^85 - 47870165542 * q^86 - 180608014462 * q^88 + 96700717270 * q^89 - 355162031176 * q^91 + 22429477796 * q^92 + 172608565078 * q^94 + 195922150708 * q^95 - 303190852014 * q^97 + 123776497136 * q^98

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 $

$2$	−62.2743	−1.37608	−0.688041	−	0.725672i	$-0.741529\pi$
$2$	−62.2743	−1.37608	−0.688041	+	0.725672i	$0.741529\pi$
$3$	0	0
$3$	0	0
$4$	1830.09	0.893600
$5$	−1377.47	−0.197127	−0.0985635	−	0.995131i	$-0.531425\pi$
$5$	−1377.47	−0.197127	−0.0985635	+	0.995131i	$0.531425\pi$
$6$	0	0
$7$	33050.3	0.743252	0.371626	−	0.928383i	$-0.378800\pi$
$7$	33050.3	0.743252	0.371626	+	0.928383i	$0.378800\pi$
$8$	13570.0	0.146415
$9$	0	0
$10$	85780.8	0.271263
$11$	800438.	1.49854	0.749270	−	0.662265i	$-0.230405\pi$
$11$	800438.	1.49854	0.749270	+	0.662265i	$0.230405\pi$
$12$	0	0
$13$	1.48554e6	1.10968	0.554839	−	0.831958i	$-0.312780\pi$
$13$	1.48554e6	1.10968	0.554839	+	0.831958i	$0.312780\pi$
$14$	−2.05818e6	−1.02277
$15$	0	0
$16$	−4.59309e6	−1.09508
$17$	1.13043e7	1.93097	0.965485	−	0.260457i	$-0.0838733\pi$
$17$	1.13043e7	1.93097	0.965485	+	0.260457i	$0.0838733\pi$
$18$	0	0
$19$	−9.78812e6	−0.906890	−0.453445	−	0.891284i	$-0.649805\pi$
$19$	−9.78812e6	−0.906890	−0.453445	+	0.891284i	$0.649805\pi$
$20$	−2.52089e6	−0.176153
$21$	0	0
$22$	−4.98468e7	−2.06211
$23$	−546284.	−0.0176977	−0.00884883	−	0.999961i	$-0.502817\pi$
$23$	−546284.	−0.0176977	−0.00884883	+	0.999961i	$0.502817\pi$
$24$	0	0
$25$	−4.69307e7	−0.961141
$26$	−9.25112e7	−1.52701
$27$	0	0
$28$	6.04851e7	0.664170
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	0	0
$31$	4.17817e6	0.0262118	0.0131059	−	0.999914i	$-0.495828\pi$
$31$	4.17817e6	0.0262118	0.0131059	+	0.999914i	$0.495828\pi$
$32$	2.58240e8	1.36050
$33$	0	0
$34$	−7.03969e8	−2.65717
$35$	−4.55257e7	−0.146515
$36$	0	0
$37$	3.50598e8	0.831190	0.415595	−	0.909550i	$-0.363573\pi$
$37$	3.50598e8	0.831190	0.415595	+	0.909550i	$0.363573\pi$
$38$	6.09549e8	1.24795
$39$	0	0
$40$	−1.86923e7	−0.0288624
$41$	−7.34075e8	−0.989531	−0.494765	−	0.869027i	$-0.664746\pi$
$41$	−7.34075e8	−0.989531	−0.494765	+	0.869027i	$0.664746\pi$
$42$	0	0
$43$	−1.74203e9	−1.80709	−0.903545	−	0.428494i	$-0.859044\pi$
$43$	−1.74203e9	−1.80709	−0.903545	+	0.428494i	$0.859044\pi$
$44$	1.46488e9	1.33909
$45$	0	0
$46$	3.40195e7	0.0243534
$47$	−1.70223e9	−1.08263	−0.541315	−	0.840820i	$-0.682073\pi$
$47$	−1.70223e9	−1.08263	−0.541315	+	0.840820i	$0.682073\pi$
$48$	0	0
$49$	−8.85005e8	−0.447577
$50$	2.92258e9	1.32261
$51$	0	0
$52$	2.71868e9	0.991608
$53$	−2.30025e9	−0.755539	−0.377770	−	0.925900i	$-0.623309\pi$
$53$	−2.30025e9	−0.755539	−0.377770	+	0.925900i	$0.623309\pi$
$54$	0	0
$55$	−1.10258e9	−0.295403
$56$	4.48494e8	0.108823
$57$	0	0
$58$	1.27732e9	0.255532
$59$	2.84523e8	0.0518121	0.0259060	−	0.999664i	$-0.491753\pi$
$59$	2.84523e8	0.0518121	0.0259060	+	0.999664i	$0.491753\pi$
$60$	0	0
$61$	5.13866e9	0.778997	0.389499	−	0.921027i	$-0.372648\pi$
$61$	5.13866e9	0.778997	0.389499	+	0.921027i	$0.372648\pi$
$62$	−2.60193e8	−0.0360696
$63$	0	0
$64$	−6.67509e9	−0.777083
$65$	−2.04629e9	−0.218747
$66$	0	0
$67$	−3.85315e9	−0.348662	−0.174331	−	0.984687i	$-0.555776\pi$
$67$	−3.85315e9	−0.348662	−0.174331	+	0.984687i	$0.555776\pi$
$68$	2.06880e10	1.72552
$69$	0	0
$70$	2.83508e9	0.201617
$71$	−2.82041e10	−1.85520	−0.927602	−	0.373570i	$-0.878133\pi$
$71$	−2.82041e10	−1.85520	−0.927602	+	0.373570i	$0.878133\pi$
$72$	0	0
$73$	−1.81192e10	−1.02297	−0.511484	−	0.859293i	$-0.670904\pi$
$73$	−1.81192e10	−1.02297	−0.511484	+	0.859293i	$0.670904\pi$
$74$	−2.18333e10	−1.14378
$75$	0	0
$76$	−1.79132e10	−0.810396
$77$	2.64547e10	1.11379
$78$	0	0
$79$	−3.94609e10	−1.44284	−0.721419	−	0.692499i	$-0.756510\pi$
$79$	−3.94609e10	−1.44284	−0.721419	+	0.692499i	$0.756510\pi$
$80$	6.32684e9	0.215870
$81$	0	0
$82$	4.57140e10	1.36168
$83$	−1.27885e10	−0.356362	−0.178181	−	0.983998i	$-0.557021\pi$
$83$	−1.27885e10	−0.356362	−0.178181	+	0.983998i	$0.557021\pi$
$84$	0	0
$85$	−1.55713e10	−0.380646
$86$	1.08484e11	2.48670
$87$	0	0
$88$	1.08620e10	0.219409
$89$	−4.46844e10	−0.848225	−0.424112	−	0.905610i	$-0.639414\pi$
$89$	−4.46844e10	−0.848225	−0.424112	+	0.905610i	$0.639414\pi$
$90$	0	0
$91$	4.90976e10	0.824770
$92$	−9.99751e8	−0.0158146
$93$	0	0
$94$	1.06005e11	1.48979
$95$	1.34828e10	0.178772
$96$	0	0
$97$	−7.40280e10	−0.875289	−0.437644	−	0.899148i	$-0.644187\pi$
$97$	−7.40280e10	−0.875289	−0.437644	+	0.899148i	$0.644187\pi$
$98$	5.51131e10	0.615902
$99$	0	0
$100$	−8.58875e10	−0.858875
$101$	8.70065e10	0.823728	0.411864	−	0.911245i	$-0.364878\pi$
$101$	8.70065e10	0.823728	0.411864	+	0.911245i	$0.364878\pi$
$102$	0	0
$103$	−2.00277e11	−1.70227	−0.851133	−	0.524951i	$-0.824084\pi$
$103$	−2.00277e11	−1.70227	−0.851133	+	0.524951i	$0.824084\pi$
$104$	2.01589e10	0.162474
$105$	0	0
$106$	1.43246e11	1.03968
$107$	6.27684e10	0.432644	0.216322	−	0.976322i	$-0.430594\pi$
$107$	6.27684e10	0.432644	0.216322	+	0.976322i	$0.430594\pi$
$108$	0	0
$109$	1.65628e11	1.03107	0.515535	−	0.856868i	$-0.327593\pi$
$109$	1.65628e11	1.03107	0.515535	+	0.856868i	$0.327593\pi$
$110$	6.86623e10	0.406498
$111$	0	0
$112$	−1.51803e11	−0.813920
$113$	−1.11390e11	−0.568741	−0.284370	−	0.958714i	$-0.591785\pi$
$113$	−1.11390e11	−0.568741	−0.284370	+	0.958714i	$0.591785\pi$
$114$	0	0
$115$	7.52489e8	0.00348869
$116$	−3.75373e10	−0.165937
$117$	0	0
$118$	−1.77185e10	−0.0712977
$119$	3.73611e11	1.43520
$120$	0	0
$121$	3.55390e11	1.24562
$122$	−3.20007e11	−1.07196
$123$	0	0
$124$	7.64644e9	0.0234229
$125$	1.31905e11	0.386594
$126$	0	0
$127$	−4.11525e11	−1.10529	−0.552644	−	0.833417i	$-0.686381\pi$
$127$	−4.11525e11	−1.10529	−0.552644	+	0.833417i	$0.686381\pi$
$128$	−1.13189e11	−0.291173
$129$	0	0
$130$	1.27431e11	0.301014
$131$	9.62047e10	0.217873	0.108937	−	0.994049i	$-0.465255\pi$
$131$	9.62047e10	0.217873	0.108937	+	0.994049i	$0.465255\pi$
$132$	0	0
$133$	−3.23500e11	−0.674047
$134$	2.39952e11	0.479787
$135$	0	0
$136$	1.53400e11	0.282724
$137$	3.08367e11	0.545890	0.272945	−	0.962030i	$-0.412002\pi$
$137$	3.08367e11	0.545890	0.272945	+	0.962030i	$0.412002\pi$
$138$	0	0
$139$	6.03606e11	0.986671	0.493336	−	0.869839i	$-0.335777\pi$
$139$	6.03606e11	0.986671	0.493336	+	0.869839i	$0.335777\pi$
$140$	−8.33162e10	−0.130926
$141$	0	0
$142$	1.75639e12	2.55291
$143$	1.18909e12	1.66290
$144$	0	0
$145$	2.82534e10	0.0366056
$146$	1.12836e12	1.40769
$147$	0	0
$148$	6.41627e11	0.742751
$149$	1.18808e12	1.32532	0.662660	−	0.748920i	$-0.269427\pi$
$149$	1.18808e12	1.32532	0.662660	+	0.748920i	$0.269427\pi$
$150$	0	0
$151$	4.61543e11	0.478453	0.239226	−	0.970964i	$-0.423106\pi$
$151$	4.61543e11	0.478453	0.239226	+	0.970964i	$0.423106\pi$
$152$	−1.32825e11	−0.132782
$153$	0	0
$154$	−1.64745e12	−1.53267
$155$	−5.75529e9	−0.00516706
$156$	0	0
$157$	4.49681e11	0.376232	0.188116	−	0.982147i	$-0.439762\pi$
$157$	4.49681e11	0.376232	0.188116	+	0.982147i	$0.439762\pi$
$158$	2.45740e12	1.98546
$159$	0	0
$160$	−3.55718e11	−0.268192
$161$	−1.80549e10	−0.0131538
$162$	0	0
$163$	−1.77931e12	−1.21121	−0.605604	−	0.795766i	$-0.707068\pi$
$163$	−1.77931e12	−1.21121	−0.605604	+	0.795766i	$0.707068\pi$
$164$	−1.34343e12	−0.884245
$165$	0	0
$166$	7.96398e11	0.490383
$167$	−5.68373e11	−0.338604	−0.169302	−	0.985564i	$-0.554151\pi$
$167$	−5.68373e11	−0.338604	−0.169302	+	0.985564i	$0.554151\pi$
$168$	0	0
$169$	4.14679e11	0.231385
$170$	9.69695e11	0.523801
$171$	0	0
$172$	−3.18808e12	−1.61481
$173$	3.46675e11	0.170086	0.0850430	−	0.996377i	$-0.472897\pi$
$173$	3.46675e11	0.170086	0.0850430	+	0.996377i	$0.472897\pi$
$174$	0	0
$175$	−1.55107e12	−0.714370
$176$	−3.67649e12	−1.64102
$177$	0	0
$178$	2.78269e12	1.16723
$179$	1.84659e12	0.751068	0.375534	−	0.926809i	$-0.377459\pi$
$179$	1.84659e12	0.751068	0.375534	+	0.926809i	$0.377459\pi$
$180$	0	0
$181$	1.69842e12	0.649849	0.324925	−	0.945740i	$-0.394661\pi$
$181$	1.69842e12	0.649849	0.324925	+	0.945740i	$0.394661\pi$
$182$	−3.05752e12	−1.13495
$183$	0	0
$184$	−7.41310e9	−0.00259121
$185$	−4.82938e11	−0.163850
$186$	0	0
$187$	9.04842e12	2.89364
$188$	−3.11524e12	−0.967437
$189$	0	0
$190$	−8.39633e11	−0.246005
$191$	−6.53577e12	−1.86043	−0.930215	−	0.367016i	$-0.880379\pi$
$191$	−6.53577e12	−1.86043	−0.930215	+	0.367016i	$0.880379\pi$
$192$	0	0
$193$	2.24825e12	0.604338	0.302169	−	0.953254i	$-0.402289\pi$
$193$	2.24825e12	0.604338	0.302169	+	0.953254i	$0.402289\pi$
$194$	4.61004e12	1.20447
$195$	0	0
$196$	−1.61964e12	−0.399955
$197$	−4.50505e12	−1.08177	−0.540885	−	0.841097i	$-0.681911\pi$
$197$	−4.50505e12	−1.08177	−0.540885	+	0.841097i	$0.681911\pi$
$198$	0	0
$199$	−4.83401e12	−1.09803	−0.549017	−	0.835811i	$-0.684998\pi$
$199$	−4.83401e12	−1.09803	−0.549017	+	0.835811i	$0.684998\pi$
$200$	−6.36852e11	−0.140726
$201$	0	0
$202$	−5.41827e12	−1.13352
$203$	−6.77899e11	−0.138018
$204$	0	0
$205$	1.01116e12	0.195063
$206$	1.24721e13	2.34246
$207$	0	0
$208$	−6.82324e12	−1.21519
$209$	−7.83479e12	−1.35901
$210$	0	0
$211$	−1.10099e13	−1.81229	−0.906146	−	0.422964i	$-0.860990\pi$
$211$	−1.10099e13	−1.81229	−0.906146	+	0.422964i	$0.860990\pi$
$212$	−4.20966e12	−0.675150
$213$	0	0
$214$	−3.90886e12	−0.595353
$215$	2.39959e12	0.356226
$216$	0	0
$217$	1.38090e11	0.0194820
$218$	−1.03144e13	−1.41884
$219$	0	0
$220$	−2.01782e12	−0.263972
$221$	1.67931e13	2.14276
$222$	0	0
$223$	−5.53451e12	−0.672051	−0.336026	−	0.941853i	$-0.609083\pi$
$223$	−5.53451e12	−0.672051	−0.336026	+	0.941853i	$0.609083\pi$
$224$	8.53492e12	1.01120
$225$	0	0
$226$	6.93673e12	0.782634
$227$	4.70942e12	0.518592	0.259296	−	0.965798i	$-0.416510\pi$
$227$	4.70942e12	0.518592	0.259296	+	0.965798i	$0.416510\pi$
$228$	0	0
$229$	−4.06336e12	−0.426374	−0.213187	−	0.977011i	$-0.568384\pi$
$229$	−4.06336e12	−0.426374	−0.213187	+	0.977011i	$0.568384\pi$
$230$	−4.68607e10	−0.00480072
$231$	0	0
$232$	−2.78337e11	−0.0271886
$233$	−1.96315e13	−1.87282	−0.936411	−	0.350906i	$-0.885874\pi$
$233$	−1.96315e13	−1.87282	−0.936411	+	0.350906i	$0.885874\pi$
$234$	0	0
$235$	2.34476e12	0.213415
$236$	5.20703e11	0.0462993
$237$	0	0
$238$	−2.32664e13	−1.97495
$239$	−1.39900e13	−1.16046	−0.580231	−	0.814452i	$-0.697038\pi$
$239$	−1.39900e13	−1.16046	−0.580231	+	0.814452i	$0.697038\pi$
$240$	0	0
$241$	−1.44074e13	−1.14154	−0.570772	−	0.821109i	$-0.693356\pi$
$241$	−1.44074e13	−1.14154	−0.570772	+	0.821109i	$0.693356\pi$
$242$	−2.21317e13	−1.71408
$243$	0	0
$244$	9.40423e12	0.696112
$245$	1.21907e12	0.0882295
$246$	0	0
$247$	−1.45407e13	−1.00636
$248$	5.66980e10	0.00383781
$249$	0	0
$250$	−8.21427e12	−0.531985
$251$	2.15745e13	1.36689	0.683446	−	0.730001i	$-0.260480\pi$
$251$	2.15745e13	1.36689	0.683446	+	0.730001i	$0.260480\pi$
$252$	0	0
$253$	−4.37267e11	−0.0265206
$254$	2.56274e13	1.52097
$255$	0	0
$256$	2.07194e13	1.17776
$257$	−2.02393e13	−1.12607	−0.563034	−	0.826434i	$-0.690366\pi$
$257$	−2.02393e13	−1.12607	−0.563034	+	0.826434i	$0.690366\pi$
$258$	0	0
$259$	1.15874e13	0.617783
$260$	−3.74489e12	−0.195473
$261$	0	0
$262$	−5.99108e12	−0.299811
$263$	−1.12028e13	−0.548997	−0.274499	−	0.961587i	$-0.588512\pi$
$263$	−1.12028e13	−0.548997	−0.274499	+	0.961587i	$0.588512\pi$
$264$	0	0
$265$	3.16851e12	0.148937
$266$	2.01458e13	0.927544
$267$	0	0
$268$	−7.05162e12	−0.311564
$269$	1.31186e13	0.567871	0.283935	−	0.958843i	$-0.408360\pi$
$269$	1.31186e13	0.567871	0.283935	+	0.958843i	$0.408360\pi$
$270$	0	0
$271$	−1.61271e13	−0.670232	−0.335116	−	0.942177i	$-0.608775\pi$
$271$	−1.61271e13	−0.670232	−0.335116	+	0.942177i	$0.608775\pi$
$272$	−5.19219e13	−2.11457
$273$	0	0
$274$	−1.92034e13	−0.751189
$275$	−3.75651e13	−1.44031
$276$	0	0
$277$	3.78738e13	1.39540	0.697702	−	0.716388i	$-0.254206\pi$
$277$	3.78738e13	1.39540	0.697702	+	0.716388i	$0.254206\pi$
$278$	−3.75892e13	−1.35774
$279$	0	0
$280$	−6.17785e11	−0.0214520
$281$	5.07029e12	0.172643	0.0863214	−	0.996267i	$-0.472489\pi$
$281$	5.07029e12	0.172643	0.0863214	+	0.996267i	$0.472489\pi$
$282$	0	0
$283$	−5.45868e13	−1.78757	−0.893783	−	0.448500i	$-0.851958\pi$
$283$	−5.45868e13	−1.78757	−0.893783	+	0.448500i	$0.851958\pi$
$284$	−5.16161e13	−1.65781
$285$	0	0
$286$	−7.40495e13	−2.28828
$287$	−2.42614e13	−0.735471
$288$	0	0
$289$	9.35159e13	2.72865
$290$	−1.75946e12	−0.0503722
$291$	0	0
$292$	−3.31597e13	−0.914125
$293$	3.12899e13	0.846511	0.423256	−	0.906010i	$-0.360887\pi$
$293$	3.12899e13	0.846511	0.423256	+	0.906010i	$0.360887\pi$
$294$	0	0
$295$	−3.91921e11	−0.0102136
$296$	4.75763e12	0.121699
$297$	0	0
$298$	−7.39869e13	−1.82375
$299$	−8.11529e11	−0.0196387
$300$	0	0
$301$	−5.75746e13	−1.34312
$302$	−2.87423e13	−0.658390
$303$	0	0
$304$	4.49578e13	0.993116
$305$	−7.07834e12	−0.153561
$306$	0	0
$307$	−2.08032e12	−0.0435381	−0.0217691	−	0.999763i	$-0.506930\pi$
$307$	−2.08032e12	−0.0435381	−0.0217691	+	0.999763i	$0.506930\pi$
$308$	4.84146e13	0.995285
$309$	0	0
$310$	3.58407e11	0.00711029
$311$	−3.53426e13	−0.688837	−0.344418	−	0.938816i	$-0.611924\pi$
$311$	−3.53426e13	−0.688837	−0.344418	+	0.938816i	$0.611924\pi$
$312$	0	0
$313$	2.98830e13	0.562252	0.281126	−	0.959671i	$-0.409292\pi$
$313$	2.98830e13	0.562252	0.281126	+	0.959671i	$0.409292\pi$
$314$	−2.80036e13	−0.517726
$315$	0	0
$316$	−7.22170e13	−1.28932
$317$	4.25262e13	0.746157	0.373079	−	0.927800i	$-0.378302\pi$
$317$	4.25262e13	0.746157	0.373079	+	0.927800i	$0.378302\pi$
$318$	0	0
$319$	−1.64179e13	−0.278272
$320$	9.19472e12	0.153184
$321$	0	0
$322$	1.12435e12	0.0181007
$323$	−1.10648e14	−1.75118
$324$	0	0
$325$	−6.97176e13	−1.06656
$326$	1.10805e14	1.66672
$327$	0	0
$328$	−9.96143e12	−0.144882
$329$	−5.62592e13	−0.804666
$330$	0	0
$331$	3.15763e12	0.0436825	0.0218412	−	0.999761i	$-0.493047\pi$
$331$	3.15763e12	0.0436825	0.0218412	+	0.999761i	$0.493047\pi$
$332$	−2.34042e13	−0.318445
$333$	0	0
$334$	3.53950e13	0.465947
$335$	5.30758e12	0.0687307
$336$	0	0
$337$	−6.97371e13	−0.873976	−0.436988	−	0.899467i	$-0.643955\pi$
$337$	−6.97371e13	−0.873976	−0.436988	+	0.899467i	$0.643955\pi$
$338$	−2.58239e13	−0.318405
$339$	0	0
$340$	−2.84970e13	−0.340146
$341$	3.34437e12	0.0392794
$342$	0	0
$343$	−9.46009e13	−1.07591
$344$	−2.36394e13	−0.264585
$345$	0	0
$346$	−2.15889e13	−0.234052
$347$	1.18515e14	1.26462	0.632309	−	0.774716i	$-0.282107\pi$
$347$	1.18515e14	1.26462	0.632309	+	0.774716i	$0.282107\pi$
$348$	0	0
$349$	−3.54876e13	−0.366890	−0.183445	−	0.983030i	$-0.558725\pi$
$349$	−3.54876e13	−0.366890	−0.183445	+	0.983030i	$0.558725\pi$
$350$	9.65921e13	0.983031
$351$	0	0
$352$	2.06706e14	2.03877
$353$	1.48557e14	1.44256	0.721278	−	0.692645i	$-0.243555\pi$
$353$	1.48557e14	1.44256	0.721278	+	0.692645i	$0.243555\pi$
$354$	0	0
$355$	3.88502e13	0.365711
$356$	−8.17766e13	−0.757973
$357$	0	0
$358$	−1.14995e14	−1.03353
$359$	1.39595e14	1.23552	0.617760	−	0.786367i	$-0.288040\pi$
$359$	1.39595e14	1.23552	0.617760	+	0.786367i	$0.288040\pi$
$360$	0	0
$361$	−2.06830e13	−0.177551
$362$	−1.05768e14	−0.894246
$363$	0	0
$364$	8.98532e13	0.737014
$365$	2.49585e13	0.201655
$366$	0	0
$367$	−2.38895e14	−1.87303	−0.936514	−	0.350631i	$-0.885967\pi$
$367$	−2.38895e14	−1.87303	−0.936514	+	0.350631i	$0.885967\pi$
$368$	2.50914e12	0.0193803
$369$	0	0
$370$	3.00746e13	0.225471
$371$	−7.60238e13	−0.561556
$372$	0	0
$373$	−3.21648e13	−0.230665	−0.115333	−	0.993327i	$-0.536793\pi$
$373$	−3.21648e13	−0.230665	−0.115333	+	0.993327i	$0.536793\pi$
$374$	−5.63484e14	−3.98188
$375$	0	0
$376$	−2.30993e13	−0.158513
$377$	−3.04702e13	−0.206062
$378$	0	0
$379$	1.37788e14	0.905099	0.452550	−	0.891739i	$-0.350515\pi$
$379$	1.37788e14	0.905099	0.452550	+	0.891739i	$0.350515\pi$
$380$	2.46748e13	0.159751
$381$	0	0
$382$	4.07011e14	2.56010
$383$	1.73711e14	1.07704	0.538522	−	0.842611i	$-0.318983\pi$
$383$	1.73711e14	1.07704	0.538522	+	0.842611i	$0.318983\pi$
$384$	0	0
$385$	−3.64405e13	−0.219559
$386$	−1.40008e14	−0.831618
$387$	0	0
$388$	−1.35478e14	−0.782158
$389$	−2.34150e14	−1.33282	−0.666411	−	0.745585i	$-0.732170\pi$
$389$	−2.34150e14	−1.33282	−0.666411	+	0.745585i	$0.732170\pi$
$390$	0	0
$391$	−6.17538e12	−0.0341737
$392$	−1.20096e13	−0.0655321
$393$	0	0
$394$	2.80549e14	1.48860
$395$	5.43560e13	0.284422
$396$	0	0
$397$	−1.79333e14	−0.912669	−0.456334	−	0.889808i	$-0.650838\pi$
$397$	−1.79333e14	−0.912669	−0.456334	+	0.889808i	$0.650838\pi$
$398$	3.01035e14	1.51098
$399$	0	0
$400$	2.15557e14	1.05253
$401$	3.03065e14	1.45963	0.729813	−	0.683646i	$-0.239607\pi$
$401$	3.03065e14	1.45963	0.729813	+	0.683646i	$0.239607\pi$
$402$	0	0
$403$	6.20686e12	0.0290867
$404$	1.59230e14	0.736083
$405$	0	0
$406$	4.22157e13	0.189925
$407$	2.80632e14	1.24557
$408$	0	0
$409$	1.52684e14	0.659651	0.329825	−	0.944042i	$-0.393010\pi$
$409$	1.52684e14	0.659651	0.329825	+	0.944042i	$0.393010\pi$
$410$	−6.29696e13	−0.268423
$411$	0	0
$412$	−3.66526e14	−1.52114
$413$	9.40356e12	0.0385094
$414$	0	0
$415$	1.76158e13	0.0702486
$416$	3.83627e14	1.50972
$417$	0	0
$418$	4.87906e14	1.87011
$419$	2.74751e14	1.03935	0.519676	−	0.854363i	$-0.326053\pi$
$419$	2.74751e14	1.03935	0.519676	+	0.854363i	$0.326053\pi$
$420$	0	0
$421$	−9.97837e13	−0.367712	−0.183856	−	0.982953i	$-0.558858\pi$
$421$	−9.97837e13	−0.367712	−0.183856	+	0.982953i	$0.558858\pi$
$422$	6.85632e14	2.49386
$423$	0	0
$424$	−3.12144e13	−0.110622
$425$	−5.30520e14	−1.85593
$426$	0	0
$427$	1.69834e14	0.578991
$428$	1.14872e14	0.386610
$429$	0	0
$430$	−1.49433e14	−0.490196
$431$	9.82326e13	0.318149	0.159075	−	0.987267i	$-0.449149\pi$
$431$	9.82326e13	0.318149	0.159075	+	0.987267i	$0.449149\pi$
$432$	0	0
$433$	1.34165e14	0.423601	0.211800	−	0.977313i	$-0.432067\pi$
$433$	1.34165e14	0.423601	0.211800	+	0.977313i	$0.432067\pi$
$434$	−8.59945e12	−0.0268088
$435$	0	0
$436$	3.03115e14	0.921364
$437$	5.34710e12	0.0160498
$438$	0	0
$439$	1.46616e14	0.429168	0.214584	−	0.976705i	$-0.431160\pi$
$439$	1.46616e14	0.429168	0.214584	+	0.976705i	$0.431160\pi$
$440$	−1.49620e13	−0.0432514
$441$	0	0
$442$	−1.04578e15	−2.94861
$443$	1.21156e13	0.0337385	0.0168693	−	0.999858i	$-0.494630\pi$
$443$	1.21156e13	0.0337385	0.0168693	+	0.999858i	$0.494630\pi$
$444$	0	0
$445$	6.15513e13	0.167208
$446$	3.44658e14	0.924797
$447$	0	0
$448$	−2.20614e14	−0.577569
$449$	−4.14075e14	−1.07084	−0.535419	−	0.844586i	$-0.679846\pi$
$449$	−4.14075e14	−1.07084	−0.535419	+	0.844586i	$0.679846\pi$
$450$	0	0
$451$	−5.87582e14	−1.48285
$452$	−2.03854e14	−0.508227
$453$	0	0
$454$	−2.93276e14	−0.713624
$455$	−6.76304e13	−0.162584
$456$	0	0
$457$	6.86418e14	1.61083	0.805415	−	0.592711i	$-0.201942\pi$
$457$	6.86418e14	1.61083	0.805415	+	0.592711i	$0.201942\pi$
$458$	2.53043e14	0.586725
$459$	0	0
$460$	1.37712e12	0.00311749
$461$	−8.82601e14	−1.97428	−0.987142	−	0.159848i	$-0.948900\pi$
$461$	−8.82601e14	−1.97428	−0.987142	+	0.159848i	$0.948900\pi$
$462$	0	0
$463$	−3.93909e14	−0.860399	−0.430200	−	0.902734i	$-0.641557\pi$
$463$	−3.93909e14	−0.860399	−0.430200	+	0.902734i	$0.641557\pi$
$464$	9.42097e13	0.203351
$465$	0	0
$466$	1.22254e15	2.57715
$467$	4.51731e13	0.0941102	0.0470551	−	0.998892i	$-0.485016\pi$
$467$	4.51731e13	0.0941102	0.0470551	+	0.998892i	$0.485016\pi$
$468$	0	0
$469$	−1.27348e14	−0.259143
$470$	−1.46019e14	−0.293677
$471$	0	0
$472$	3.86099e12	0.00758608
$473$	−1.39439e15	−2.70799
$474$	0	0
$475$	4.59363e14	0.871649
$476$	6.83743e14	1.28249
$477$	0	0
$478$	8.71221e14	1.59689
$479$	4.93799e14	0.894756	0.447378	−	0.894345i	$-0.352358\pi$
$479$	4.93799e14	0.894756	0.447378	+	0.894345i	$0.352358\pi$
$480$	0	0
$481$	5.20829e14	0.922353
$482$	8.97213e14	1.57086
$483$	0	0
$484$	6.50397e14	1.11309
$485$	1.01971e14	0.172543
$486$	0	0
$487$	5.62413e14	0.930350	0.465175	−	0.885219i	$-0.345991\pi$
$487$	5.62413e14	0.930350	0.465175	+	0.885219i	$0.345991\pi$
$488$	6.97319e13	0.114057
$489$	0	0
$490$	−7.59165e13	−0.121411
$491$	6.06349e14	0.958902	0.479451	−	0.877569i	$-0.340836\pi$
$491$	6.06349e14	0.958902	0.479451	+	0.877569i	$0.340836\pi$
$492$	0	0
$493$	−2.31865e14	−0.358572
$494$	9.05511e14	1.38483
$495$	0	0
$496$	−1.91907e13	−0.0287040
$497$	−9.32154e14	−1.37888
$498$	0	0
$499$	−9.66448e14	−1.39838	−0.699191	−	0.714935i	$-0.746456\pi$
$499$	−9.66448e14	−1.39838	−0.699191	+	0.714935i	$0.746456\pi$
$500$	2.41398e14	0.345460
$501$	0	0
$502$	−1.34353e15	−1.88095
$503$	−5.10073e14	−0.706331	−0.353166	−	0.935561i	$-0.614895\pi$
$503$	−5.10073e14	−0.706331	−0.353166	+	0.935561i	$0.614895\pi$
$504$	0	0
$505$	−1.19849e14	−0.162379
$506$	2.72305e13	0.0364946
$507$	0	0
$508$	−7.53128e14	−0.987685
$509$	5.21410e12	0.00676443	0.00338222	−	0.999994i	$-0.498923\pi$
$509$	5.21410e12	0.00676443	0.00338222	+	0.999994i	$0.498923\pi$
$510$	0	0
$511$	−5.98843e14	−0.760323
$512$	−1.05847e15	−1.32952
$513$	0	0
$514$	1.26039e15	1.54956
$515$	2.75876e14	0.335562
$516$	0	0
$517$	−1.36253e15	−1.62236
$518$	−7.21596e14	−0.850120
$519$	0	0
$520$	−2.77682e13	−0.0320280
$521$	−4.21554e14	−0.481112	−0.240556	−	0.970635i	$-0.577330\pi$
$521$	−4.21554e14	−0.481112	−0.240556	+	0.970635i	$0.577330\pi$
$522$	0	0
$523$	8.60935e14	0.962080	0.481040	−	0.876699i	$-0.340259\pi$
$523$	8.60935e14	0.962080	0.481040	+	0.876699i	$0.340259\pi$
$524$	1.76064e14	0.194692
$525$	0	0
$526$	6.97648e14	0.755465
$527$	4.72314e13	0.0506142
$528$	0	0
$529$	−9.52511e14	−0.999687
$530$	−1.97317e14	−0.204950
$531$	0	0
$532$	−5.92035e14	−0.602329
$533$	−1.09050e15	−1.09806
$534$	0	0
$535$	−8.64614e13	−0.0852858
$536$	−5.22874e13	−0.0510494
$537$	0	0
$538$	−8.16951e14	−0.781436
$539$	−7.08392e14	−0.670711
$540$	0	0
$541$	−2.89790e14	−0.268842	−0.134421	−	0.990924i	$-0.542918\pi$
$541$	−2.89790e14	−0.268842	−0.134421	+	0.990924i	$0.542918\pi$
$542$	1.00430e15	0.922293
$543$	0	0
$544$	2.91923e15	2.62709
$545$	−2.28147e14	−0.203252
$546$	0	0
$547$	2.01239e15	1.75704	0.878520	−	0.477705i	$-0.158531\pi$
$547$	2.01239e15	1.75704	0.878520	+	0.477705i	$0.158531\pi$
$548$	5.64340e14	0.487807
$549$	0	0
$550$	2.33934e15	1.98198
$551$	2.00766e14	0.168405
$552$	0	0
$553$	−1.30419e15	−1.07239
$554$	−2.35857e15	−1.92019
$555$	0	0
$556$	1.10466e15	0.881689
$557$	−1.45243e15	−1.14787	−0.573933	−	0.818902i	$-0.694583\pi$
$557$	−1.45243e15	−1.14787	−0.573933	+	0.818902i	$0.694583\pi$
$558$	0	0
$559$	−2.58786e15	−2.00529
$560$	2.09104e14	0.160446
$561$	0	0
$562$	−3.15749e14	−0.237571
$563$	1.90166e15	1.41689	0.708447	−	0.705764i	$-0.249396\pi$
$563$	1.90166e15	1.41689	0.708447	+	0.705764i	$0.249396\pi$
$564$	0	0
$565$	1.53436e14	0.112114
$566$	3.39935e15	2.45984
$567$	0	0
$568$	−3.82731e14	−0.271630
$569$	−1.27765e15	−0.898041	−0.449020	−	0.893522i	$-0.648227\pi$
$569$	−1.27765e15	−0.898041	−0.449020	+	0.893522i	$0.648227\pi$
$570$	0	0
$571$	8.73926e14	0.602527	0.301263	−	0.953541i	$-0.402592\pi$
$571$	8.73926e14	0.602527	0.301263	+	0.953541i	$0.402592\pi$
$572$	2.17614e15	1.48596
$573$	0	0
$574$	1.51086e15	1.01207
$575$	2.56375e13	0.0170099
$576$	0	0
$577$	1.90100e15	1.23741	0.618706	−	0.785623i	$-0.287657\pi$
$577$	1.90100e15	1.23741	0.618706	+	0.785623i	$0.287657\pi$
$578$	−5.82364e15	−3.75484
$579$	0	0
$580$	5.17064e13	0.0327107
$581$	−4.22665e14	−0.264867
$582$	0	0
$583$	−1.84121e15	−1.13221
$584$	−2.45878e14	−0.149778
$585$	0	0
$586$	−1.94856e15	−1.16487
$587$	5.70371e14	0.337791	0.168895	−	0.985634i	$-0.445980\pi$
$587$	5.70371e14	0.337791	0.168895	+	0.985634i	$0.445980\pi$
$588$	0	0
$589$	−4.08964e13	−0.0237712
$590$	2.44066e13	0.0140547
$591$	0	0
$592$	−1.61033e15	−0.910219
$593$	−6.76252e14	−0.378711	−0.189355	−	0.981909i	$-0.560640\pi$
$593$	−6.76252e14	−0.378711	−0.189355	+	0.981909i	$0.560640\pi$
$594$	0	0
$595$	−5.14637e14	−0.282916
$596$	2.17430e15	1.18431
$597$	0	0
$598$	5.05375e13	0.0270244
$599$	5.41473e14	0.286899	0.143449	−	0.989658i	$-0.454181\pi$
$599$	5.41473e14	0.286899	0.143449	+	0.989658i	$0.454181\pi$
$600$	0	0
$601$	2.86332e15	1.48957	0.744785	−	0.667305i	$-0.232552\pi$
$601$	2.86332e15	1.48957	0.744785	+	0.667305i	$0.232552\pi$
$602$	3.58542e15	1.84825
$603$	0	0
$604$	8.44666e14	0.427545
$605$	−4.89538e14	−0.245545
$606$	0	0
$607$	2.24665e15	1.10662	0.553310	−	0.832976i	$-0.313365\pi$
$607$	2.24665e15	1.10662	0.553310	+	0.832976i	$0.313365\pi$
$608$	−2.52769e15	−1.23383
$609$	0	0
$610$	4.40799e14	0.211313
$611$	−2.52874e15	−1.20137
$612$	0	0
$613$	−1.37966e15	−0.643783	−0.321891	−	0.946777i	$-0.604319\pi$
$613$	−1.37966e15	−0.643783	−0.321891	+	0.946777i	$0.604319\pi$
$614$	1.29551e14	0.0599120
$615$	0	0
$616$	3.58992e14	0.163076
$617$	1.77458e15	0.798966	0.399483	−	0.916741i	$-0.369190\pi$
$617$	1.77458e15	0.798966	0.399483	+	0.916741i	$0.369190\pi$
$618$	0	0
$619$	−6.71770e14	−0.297113	−0.148557	−	0.988904i	$-0.547463\pi$
$619$	−6.71770e14	−0.297113	−0.148557	+	0.988904i	$0.547463\pi$
$620$	−1.05327e13	−0.00461728
$621$	0	0
$622$	2.20094e15	0.947895
$623$	−1.47683e15	−0.630445
$624$	0	0
$625$	2.10984e15	0.884933
$626$	−1.86095e15	−0.773705
$627$	0	0
$628$	8.22957e14	0.336201
$629$	3.96328e15	1.60500
$630$	0	0
$631$	3.94122e15	1.56845	0.784223	−	0.620479i	$-0.213062\pi$
$631$	3.94122e15	1.56845	0.784223	+	0.620479i	$0.213062\pi$
$632$	−5.35486e14	−0.211253
$633$	0	0
$634$	−2.64829e15	−1.02677
$635$	5.66862e14	0.217882
$636$	0	0
$637$	−1.31471e15	−0.496666
$638$	1.02241e15	0.382925
$639$	0	0
$640$	1.55915e14	0.0573980
$641$	2.71163e15	0.989716	0.494858	−	0.868974i	$-0.335220\pi$
$641$	2.71163e15	0.989716	0.494858	+	0.868974i	$0.335220\pi$
$642$	0	0
$643$	1.11976e15	0.401757	0.200879	−	0.979616i	$-0.435620\pi$
$643$	1.11976e15	0.401757	0.200879	+	0.979616i	$0.435620\pi$
$644$	−3.30421e13	−0.0117542
$645$	0	0
$646$	6.89054e15	2.40976
$647$	5.20369e14	0.180442	0.0902210	−	0.995922i	$-0.471243\pi$
$647$	5.20369e14	0.180442	0.0902210	+	0.995922i	$0.471243\pi$
$648$	0	0
$649$	2.27743e14	0.0776425
$650$	4.34162e15	1.46767
$651$	0	0
$652$	−3.25629e15	−1.08234
$653$	−6.45444e14	−0.212734	−0.106367	−	0.994327i	$-0.533922\pi$
$653$	−6.45444e14	−0.212734	−0.106367	+	0.994327i	$0.533922\pi$
$654$	0	0
$655$	−1.32519e14	−0.0429487
$656$	3.37168e15	1.08361
$657$	0	0
$658$	3.50350e15	1.10729
$659$	4.90862e14	0.153847	0.0769236	−	0.997037i	$-0.475490\pi$
$659$	4.90862e14	0.153847	0.0769236	+	0.997037i	$0.475490\pi$
$660$	0	0
$661$	−1.13195e15	−0.348915	−0.174458	−	0.984665i	$-0.555817\pi$
$661$	−1.13195e15	−0.348915	−0.174458	+	0.984665i	$0.555817\pi$
$662$	−1.96639e14	−0.0601106
$663$	0	0
$664$	−1.73541e14	−0.0521768
$665$	4.45611e14	0.132873
$666$	0	0
$667$	1.12049e13	0.00328637
$668$	−1.04017e15	−0.302577
$669$	0	0
$670$	−3.30526e14	−0.0945790
$671$	4.11318e15	1.16736
$672$	0	0
$673$	−1.66789e15	−0.465676	−0.232838	−	0.972516i	$-0.574801\pi$
$673$	−1.66789e15	−0.465676	−0.232838	+	0.972516i	$0.574801\pi$
$674$	4.34283e15	1.20266
$675$	0	0
$676$	7.58901e14	0.206766
$677$	−3.40687e15	−0.920699	−0.460349	−	0.887738i	$-0.652276\pi$
$677$	−3.40687e15	−0.920699	−0.460349	+	0.887738i	$0.652276\pi$
$678$	0	0
$679$	−2.44665e15	−0.650560
$680$	−2.11304e14	−0.0557324
$681$	0	0
$682$	−2.08268e14	−0.0540517
$683$	−1.01334e15	−0.260882	−0.130441	−	0.991456i	$-0.541639\pi$
$683$	−1.01334e15	−0.260882	−0.130441	+	0.991456i	$0.541639\pi$
$684$	0	0
$685$	−4.24765e14	−0.107610
$686$	5.89121e15	1.48055
$687$	0	0
$688$	8.00132e15	1.97891
$689$	−3.41712e15	−0.838405
$690$	0	0
$691$	−3.43978e15	−0.830618	−0.415309	−	0.909680i	$-0.636327\pi$
$691$	−3.43978e15	−0.830618	−0.415309	+	0.909680i	$0.636327\pi$
$692$	6.34447e14	0.151989
$693$	0	0
$694$	−7.38041e15	−1.74022
$695$	−8.31448e14	−0.194500
$696$	0	0
$697$	−8.29823e15	−1.91076
$698$	2.20996e15	0.504871
$699$	0	0
$700$	−2.83861e15	−0.638361
$701$	1.06049e15	0.236622	0.118311	−	0.992977i	$-0.462252\pi$
$701$	1.06049e15	0.236622	0.118311	+	0.992977i	$0.462252\pi$
$702$	0	0
$703$	−3.43170e15	−0.753797
$704$	−5.34300e15	−1.16449
$705$	0	0
$706$	−9.25130e15	−1.98507
$707$	2.87559e15	0.612237
$708$	0	0
$709$	2.55303e15	0.535181	0.267591	−	0.963533i	$-0.413773\pi$
$709$	2.55303e15	0.535181	0.267591	+	0.963533i	$0.413773\pi$
$710$	−2.41937e15	−0.503248
$711$	0	0
$712$	−6.06369e14	−0.124193
$713$	−2.28247e12	−0.000463888 0
$714$	0	0
$715$	−1.63793e15	−0.327802
$716$	3.37944e15	0.671155
$717$	0	0
$718$	−8.69317e15	−1.70018
$719$	−2.96226e15	−0.574929	−0.287464	−	0.957791i	$-0.592812\pi$
$719$	−2.96226e15	−0.574929	−0.287464	+	0.957791i	$0.592812\pi$
$720$	0	0
$721$	−6.61923e15	−1.26521
$722$	1.28802e15	0.244325
$723$	0	0
$724$	3.10826e15	0.580705
$725$	9.62603e14	0.178479
$726$	0	0
$727$	1.27741e15	0.233287	0.116643	−	0.993174i	$-0.462787\pi$
$727$	1.27741e15	0.233287	0.116643	+	0.993174i	$0.462787\pi$
$728$	6.66257e14	0.120759
$729$	0	0
$730$	−1.55428e15	−0.277493
$731$	−1.96925e16	−3.48944
$732$	0	0
$733$	7.57379e15	1.32203	0.661015	−	0.750372i	$-0.270126\pi$
$733$	7.57379e15	1.32203	0.661015	+	0.750372i	$0.270126\pi$
$734$	1.48770e16	2.57744
$735$	0	0
$736$	−1.41073e14	−0.0240777
$737$	−3.08421e15	−0.522483
$738$	0	0
$739$	−3.67278e15	−0.612986	−0.306493	−	0.951873i	$-0.599156\pi$
$739$	−3.67278e15	−0.612986	−0.306493	+	0.951873i	$0.599156\pi$
$740$	−8.83820e14	−0.146416
$741$	0	0
$742$	4.73433e15	0.772747
$743$	−7.23474e15	−1.17215	−0.586077	−	0.810256i	$-0.699328\pi$
$743$	−7.23474e15	−1.17215	−0.586077	+	0.810256i	$0.699328\pi$
$744$	0	0
$745$	−1.63654e15	−0.261257
$746$	2.00304e15	0.317414
$747$	0	0
$748$	1.65594e16	2.58575
$749$	2.07451e15	0.321563
$750$	0	0
$751$	−2.47237e15	−0.377654	−0.188827	−	0.982010i	$-0.560469\pi$
$751$	−2.47237e15	−0.377654	−0.188827	+	0.982010i	$0.560469\pi$
$752$	7.81850e15	1.18556
$753$	0	0
$754$	1.89751e15	0.283558
$755$	−6.35760e14	−0.0943159
$756$	0	0
$757$	1.07908e15	0.157771	0.0788854	−	0.996884i	$-0.474864\pi$
$757$	1.07908e15	0.157771	0.0788854	+	0.996884i	$0.474864\pi$
$758$	−8.58066e15	−1.24549
$759$	0	0
$760$	1.82962e14	0.0261750
$761$	−8.35973e15	−1.18734	−0.593672	−	0.804707i	$-0.702322\pi$
$761$	−8.35973e15	−1.18734	−0.593672	+	0.804707i	$0.702322\pi$
$762$	0	0
$763$	5.47406e15	0.766345
$764$	−1.19611e16	−1.66248
$765$	0	0
$766$	−1.08177e16	−1.48210
$767$	4.22671e14	0.0574947
$768$	0	0
$769$	8.47458e15	1.13638	0.568190	−	0.822898i	$-0.307644\pi$
$769$	8.47458e15	1.13638	0.568190	+	0.822898i	$0.307644\pi$
$770$	2.26931e15	0.302130
$771$	0	0
$772$	4.11451e15	0.540036
$773$	1.35997e16	1.77232	0.886159	−	0.463381i	$-0.153364\pi$
$773$	1.35997e16	1.77232	0.886159	+	0.463381i	$0.153364\pi$
$774$	0	0
$775$	−1.96085e14	−0.0251932
$776$	−1.00456e15	−0.128156
$777$	0	0
$778$	1.45816e16	1.83407
$779$	7.18522e15	0.897395
$780$	0	0
$781$	−2.25757e16	−2.78010
$782$	3.84568e14	0.0470257
$783$	0	0
$784$	4.06491e15	0.490132
$785$	−6.19420e14	−0.0741655
$786$	0	0
$787$	6.33252e15	0.747680	0.373840	−	0.927493i	$-0.378041\pi$
$787$	6.33252e15	0.747680	0.373840	+	0.927493i	$0.378041\pi$
$788$	−8.24465e15	−0.966670
$789$	0	0
$790$	−3.38499e15	−0.391388
$791$	−3.68147e15	−0.422718
$792$	0	0
$793$	7.63370e15	0.864436
$794$	1.11679e16	1.25591
$795$	0	0
$796$	−8.84669e15	−0.981203
$797$	1.53574e16	1.69159	0.845796	−	0.533507i	$-0.179126\pi$
$797$	1.53574e16	1.69159	0.845796	+	0.533507i	$0.179126\pi$
$798$	0	0
$799$	−1.92426e16	−2.09053
$800$	−1.21194e16	−1.30763
$801$	0	0
$802$	−1.88732e16	−2.00857
$803$	−1.45033e16	−1.53296
$804$	0	0
$805$	2.48700e13	0.00259297
$806$	−3.86528e14	−0.0400256
$807$	0	0
$808$	1.18068e15	0.120606
$809$	8.68168e15	0.880819	0.440410	−	0.897797i	$-0.354833\pi$
$809$	8.68168e15	0.880819	0.440410	+	0.897797i	$0.354833\pi$
$810$	0	0
$811$	−1.24520e16	−1.24630	−0.623151	−	0.782102i	$-0.714148\pi$
$811$	−1.24520e16	−1.24630	−0.623151	+	0.782102i	$0.714148\pi$
$812$	−1.24062e15	−0.123333
$813$	0	0
$814$	−1.74762e16	−1.71401
$815$	2.45093e15	0.238762
$816$	0	0
$817$	1.70512e16	1.63883
$818$	−9.50827e15	−0.907733
$819$	0	0
$820$	1.85052e15	0.174309
$821$	−1.60834e16	−1.50484	−0.752420	−	0.658684i	$-0.771113\pi$
$821$	−1.60834e16	−1.50484	−0.752420	+	0.658684i	$0.771113\pi$
$822$	0	0
$823$	9.49861e15	0.876922	0.438461	−	0.898750i	$-0.355524\pi$
$823$	9.49861e15	0.876922	0.438461	+	0.898750i	$0.355524\pi$
$824$	−2.71777e15	−0.249238
$825$	0	0
$826$	−5.85601e14	−0.0529921
$827$	−2.12819e15	−0.191306	−0.0956532	−	0.995415i	$-0.530494\pi$
$827$	−2.12819e15	−0.191306	−0.0956532	+	0.995415i	$0.530494\pi$
$828$	0	0
$829$	−1.90510e15	−0.168993	−0.0844965	−	0.996424i	$-0.526928\pi$
$829$	−1.90510e15	−0.168993	−0.0844965	+	0.996424i	$0.526928\pi$
$830$	−1.09701e15	−0.0966678
$831$	0	0
$832$	−9.91614e15	−0.862312
$833$	−1.00044e16	−0.864258
$834$	0	0
$835$	7.82914e14	0.0667481
$836$	−1.43384e16	−1.21441
$837$	0	0
$838$	−1.71100e16	−1.43023
$839$	−2.03621e15	−0.169095	−0.0845477	−	0.996419i	$-0.526945\pi$
$839$	−2.03621e15	−0.169095	−0.0845477	+	0.996419i	$0.526945\pi$
$840$	0	0
$841$	4.20707e14	0.0344828
$842$	6.21396e15	0.506002
$843$	0	0
$844$	−2.01491e16	−1.61946
$845$	−5.71207e14	−0.0456122
$846$	0	0
$847$	1.17457e16	0.925810
$848$	1.05652e16	0.827375
$849$	0	0
$850$	3.30378e16	2.55392
$851$	−1.91526e14	−0.0147101
$852$	0	0
$853$	−1.08461e16	−0.822343	−0.411172	−	0.911558i	$-0.634880\pi$
$853$	−1.08461e16	−0.822343	−0.411172	+	0.911558i	$0.634880\pi$
$854$	−1.05763e16	−0.796739
$855$	0	0
$856$	8.51770e14	0.0633456
$857$	−2.23715e16	−1.65311	−0.826553	−	0.562859i	$-0.809701\pi$
$857$	−2.23715e16	−1.65311	−0.826553	+	0.562859i	$0.809701\pi$
$858$	0	0
$859$	1.15245e16	0.840738	0.420369	−	0.907353i	$-0.361901\pi$
$859$	1.15245e16	0.840738	0.420369	+	0.907353i	$0.361901\pi$
$860$	4.39147e15	0.318324
$861$	0	0
$862$	−6.11737e15	−0.437799
$863$	6.38998e15	0.454402	0.227201	−	0.973848i	$-0.427043\pi$
$863$	6.38998e15	0.454402	0.227201	+	0.973848i	$0.427043\pi$
$864$	0	0
$865$	−4.77533e14	−0.0335286
$866$	−8.35505e15	−0.582909
$867$	0	0
$868$	2.52717e14	0.0174091
$869$	−3.15860e16	−2.16215
$870$	0	0
$871$	−5.72402e15	−0.386902
$872$	2.24758e15	0.150964
$873$	0	0
$874$	−3.32987e14	−0.0220859
$875$	4.35949e15	0.287337
$876$	0	0
$877$	−1.02607e16	−0.667849	−0.333924	−	0.942600i	$-0.608373\pi$
$877$	−1.02607e16	−0.667849	−0.333924	+	0.942600i	$0.608373\pi$
$878$	−9.13044e15	−0.590571
$879$	0	0
$880$	5.06424e15	0.323489
$881$	7.21654e15	0.458101	0.229051	−	0.973415i	$-0.426438\pi$
$881$	7.21654e15	0.458101	0.229051	+	0.973415i	$0.426438\pi$
$882$	0	0
$883$	8.51122e15	0.533591	0.266795	−	0.963753i	$-0.414035\pi$
$883$	8.51122e15	0.533591	0.266795	+	0.963753i	$0.414035\pi$
$884$	3.07329e16	1.91477
$885$	0	0
$886$	−7.54494e14	−0.0464269
$887$	1.37601e16	0.841477	0.420739	−	0.907182i	$-0.361771\pi$
$887$	1.37601e16	0.841477	0.420739	+	0.907182i	$0.361771\pi$
$888$	0	0
$889$	−1.36010e16	−0.821507
$890$	−3.83307e15	−0.230092
$891$	0	0
$892$	−1.01287e16	−0.600545
$893$	1.66616e16	0.981825
$894$	0	0
$895$	−2.54362e15	−0.148056
$896$	−3.74094e15	−0.216415
$897$	0	0
$898$	2.57862e16	1.47356
$899$	−8.56991e13	−0.00486741
$900$	0	0
$901$	−2.60027e16	−1.45892
$902$	3.65913e16	2.04052
$903$	0	0
$904$	−1.51157e15	−0.0832723
$905$	−2.33952e15	−0.128103
$906$	0	0
$907$	−1.86017e15	−0.100626	−0.0503132	−	0.998733i	$-0.516022\pi$
$907$	−1.86017e15	−0.100626	−0.0503132	+	0.998733i	$0.516022\pi$
$908$	8.61868e15	0.463413
$909$	0	0
$910$	4.21164e15	0.223729
$911$	−1.78581e15	−0.0942939	−0.0471469	−	0.998888i	$-0.515013\pi$
$911$	−1.78581e15	−0.0942939	−0.0471469	+	0.998888i	$0.515013\pi$
$912$	0	0
$913$	−1.02364e16	−0.534023
$914$	−4.27462e16	−2.21663
$915$	0	0
$916$	−7.43633e15	−0.381008
$917$	3.17959e15	0.161935
$918$	0	0
$919$	−1.41640e15	−0.0712770	−0.0356385	−	0.999365i	$-0.511346\pi$
$919$	−1.41640e15	−0.0712770	−0.0356385	+	0.999365i	$0.511346\pi$
$920$	1.02113e13	0.000510797 0
$921$	0	0
$922$	5.49634e16	2.71677
$923$	−4.18984e16	−2.05868
$924$	0	0
$925$	−1.64538e16	−0.798891
$926$	2.45304e16	1.18398
$927$	0	0
$928$	−5.29681e15	−0.252639
$929$	3.39995e16	1.61208	0.806039	−	0.591862i	$-0.201607\pi$
$929$	3.39995e16	1.61208	0.806039	+	0.591862i	$0.201607\pi$
$930$	0	0
$931$	8.66254e15	0.405903
$932$	−3.59275e16	−1.67355
$933$	0	0
$934$	−2.81312e15	−0.129503
$935$	−1.24639e16	−0.570414
$936$	0	0
$937$	−7.34935e14	−0.0332415	−0.0166208	−	0.999862i	$-0.505291\pi$
$937$	−7.34935e14	−0.0332415	−0.0166208	+	0.999862i	$0.505291\pi$
$938$	7.93049e15	0.356603
$939$	0	0
$940$	4.29114e15	0.190708
$941$	3.19965e16	1.41371	0.706854	−	0.707360i	$-0.250114\pi$
$941$	3.19965e16	1.41371	0.706854	+	0.707360i	$0.250114\pi$
$942$	0	0
$943$	4.01014e14	0.0175124
$944$	−1.30684e15	−0.0567383
$945$	0	0
$946$	8.68347e16	3.72642
$947$	−3.54537e16	−1.51264	−0.756321	−	0.654201i	$-0.773005\pi$
$947$	−3.54537e16	−1.51264	−0.756321	+	0.654201i	$0.773005\pi$
$948$	0	0
$949$	−2.69168e16	−1.13517
$950$	−2.86065e16	−1.19946
$951$	0	0
$952$	5.06992e15	0.210135
$953$	−1.61742e16	−0.666519	−0.333260	−	0.942835i	$-0.608149\pi$
$953$	−1.61742e16	−0.666519	−0.333260	+	0.942835i	$0.608149\pi$
$954$	0	0
$955$	9.00281e15	0.366741
$956$	−2.56031e16	−1.03699
$957$	0	0
$958$	−3.07510e16	−1.23126
$959$	1.01916e16	0.405733
$960$	0	0
$961$	−2.53910e16	−0.999313
$962$	−3.24343e16	−1.26923
$963$	0	0
$964$	−2.63669e16	−1.02008
$965$	−3.09689e15	−0.119131
$966$	0	0
$967$	2.66442e16	1.01335	0.506673	−	0.862138i	$-0.330875\pi$
$967$	2.66442e16	1.01335	0.506673	+	0.862138i	$0.330875\pi$
$968$	4.82266e15	0.182378
$969$	0	0
$970$	−6.35018e15	−0.237433
$971$	3.55781e16	1.32275	0.661374	−	0.750056i	$-0.269974\pi$
$971$	3.55781e16	1.32275	0.661374	+	0.750056i	$0.269974\pi$
$972$	0	0
$973$	1.99494e16	0.733345
$974$	−3.50239e16	−1.28024
$975$	0	0
$976$	−2.36024e16	−0.853064
$977$	−8.11999e15	−0.291834	−0.145917	−	0.989297i	$-0.546613\pi$
$977$	−8.11999e15	−0.291834	−0.145917	+	0.989297i	$0.546613\pi$
$978$	0	0
$979$	−3.57671e16	−1.27110
$980$	2.23100e15	0.0788418
$981$	0	0
$982$	−3.77600e16	−1.31953
$983$	−1.07762e15	−0.0374472	−0.0187236	−	0.999825i	$-0.505960\pi$
$983$	−1.07762e15	−0.0374472	−0.0187236	+	0.999825i	$0.505960\pi$
$984$	0	0
$985$	6.20555e15	0.213246
$986$	1.44392e16	0.493425
$987$	0	0
$988$	−2.66108e16	−0.899279
$989$	9.51645e14	0.0319812
$990$	0	0
$991$	1.71972e16	0.571547	0.285773	−	0.958297i	$-0.407750\pi$
$991$	1.71972e16	0.571547	0.285773	+	0.958297i	$0.407750\pi$
$992$	1.07897e15	0.0356612
$993$	0	0
$994$	5.80493e16	1.89746
$995$	6.65869e15	0.216452
$996$	0	0
$997$	3.20573e16	1.03063	0.515316	−	0.857000i	$-0.327674\pi$
$997$	3.20573e16	1.03063	0.515316	+	0.857000i	$0.327674\pi$
$998$	6.01849e16	1.92429
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.12.a.a.1.2		11
3.2	odd	2		29.12.a.a.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.10	✓	11	3.2	odd	2
261.12.a.a.1.2		11	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	261.a (trivial)

\(f(q)\)	\(=\)	\(q-62.2743 q^{2} +1830.09 q^{4} -1377.47 q^{5} +33050.3 q^{7} +13570.0 q^{8} +O(q^{10})\)	\(q-62.2743 q^{2} +1830.09 q^{4} -1377.47 q^{5} +33050.3 q^{7} +13570.0 q^{8} +85780.8 q^{10} +800438. q^{11} +1.48554e6 q^{13} -2.05818e6 q^{14} -4.59309e6 q^{16} +1.13043e7 q^{17} -9.78812e6 q^{19} -2.52089e6 q^{20} -4.98468e7 q^{22} -546284. q^{23} -4.69307e7 q^{25} -9.25112e7 q^{26} +6.04851e7 q^{28} -2.05111e7 q^{29} +4.17817e6 q^{31} +2.58240e8 q^{32} -7.03969e8 q^{34} -4.55257e7 q^{35} +3.50598e8 q^{37} +6.09549e8 q^{38} -1.86923e7 q^{40} -7.34075e8 q^{41} -1.74203e9 q^{43} +1.46488e9 q^{44} +3.40195e7 q^{46} -1.70223e9 q^{47} -8.85005e8 q^{49} +2.92258e9 q^{50} +2.71868e9 q^{52} -2.30025e9 q^{53} -1.10258e9 q^{55} +4.48494e8 q^{56} +1.27732e9 q^{58} +2.84523e8 q^{59} +5.13866e9 q^{61} -2.60193e8 q^{62} -6.67509e9 q^{64} -2.04629e9 q^{65} -3.85315e9 q^{67} +2.06880e10 q^{68} +2.83508e9 q^{70} -2.82041e10 q^{71} -1.81192e10 q^{73} -2.18333e10 q^{74} -1.79132e10 q^{76} +2.64547e10 q^{77} -3.94609e10 q^{79} +6.32684e9 q^{80} +4.57140e10 q^{82} -1.27885e10 q^{83} -1.55713e10 q^{85} +1.08484e11 q^{86} +1.08620e10 q^{88} -4.46844e10 q^{89} +4.90976e10 q^{91} -9.99751e8 q^{92} +1.06005e11 q^{94} +1.34828e10 q^{95} -7.40280e10 q^{97} +5.51131e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8}+O(q^{10}) \) 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8	\( 11 q + 32 q^{2} + 9146 q^{4} + 2740 q^{5} - 49432 q^{7} + 150054 q^{8} - 685834 q^{10} + 612246 q^{11} + 1510364 q^{13} - 3955400 q^{14} + 3024818 q^{16} + 3291098 q^{17} - 44121388 q^{19} + 49472662 q^{20} - 43435618 q^{22} + 88684076 q^{23} - 44195521 q^{25} + 324999762 q^{26} - 391274848 q^{28} - 225622639 q^{29} - 292235934 q^{31} + 632542514 q^{32} - 1113307936 q^{34} + 1312820120 q^{35} - 1380429338 q^{37} + 1222857284 q^{38} - 2713154106 q^{40} + 1062067494 q^{41} + 74588594 q^{43} - 52891466 q^{44} - 87670324 q^{46} + 1821239394 q^{47} + 4692522003 q^{49} - 9494259926 q^{50} + 3266669866 q^{52} - 7818635688 q^{53} - 191002682 q^{55} - 11263587512 q^{56} - 656356768 q^{58} - 1230002712 q^{59} - 18602654230 q^{61} - 22075953162 q^{62} + 11813658086 q^{64} - 32245789334 q^{65} + 27481284652 q^{67} - 29588811820 q^{68} + 42862666712 q^{70} + 20347168516 q^{71} - 57740010478 q^{73} + 2640709564 q^{74} - 33350650772 q^{76} - 871959792 q^{77} - 120245016462 q^{79} + 84319695274 q^{80} - 111495532412 q^{82} + 142463983824 q^{83} - 181628566552 q^{85} - 47870165542 q^{86} - 180608014462 q^{88} + 96700717270 q^{89} - 355162031176 q^{91} + 22429477796 q^{92} + 172608565078 q^{94} + 195922150708 q^{95} - 303190852014 q^{97} + 123776497136 q^{98}+O(q^{100}) \) 11 * q + 32 * q^2 + 9146 * q^4 + 2740 * q^5 - 49432 * q^7 + 150054 * q^8 - 685834 * q^10 + 612246 * q^11 + 1510364 * q^13 - 3955400 * q^14 + 3024818 * q^16 + 3291098 * q^17 - 44121388 * q^19 + 49472662 * q^20 - 43435618 * q^22 + 88684076 * q^23 - 44195521 * q^25 + 324999762 * q^26 - 391274848 * q^28 - 225622639 * q^29 - 292235934 * q^31 + 632542514 * q^32 - 1113307936 * q^34 + 1312820120 * q^35 - 1380429338 * q^37 + 1222857284 * q^38 - 2713154106 * q^40 + 1062067494 * q^41 + 74588594 * q^43 - 52891466 * q^44 - 87670324 * q^46 + 1821239394 * q^47 + 4692522003 * q^49 - 9494259926 * q^50 + 3266669866 * q^52 - 7818635688 * q^53 - 191002682 * q^55 - 11263587512 * q^56 - 656356768 * q^58 - 1230002712 * q^59 - 18602654230 * q^61 - 22075953162 * q^62 + 11813658086 * q^64 - 32245789334 * q^65 + 27481284652 * q^67 - 29588811820 * q^68 + 42862666712 * q^70 + 20347168516 * q^71 - 57740010478 * q^73 + 2640709564 * q^74 - 33350650772 * q^76 - 871959792 * q^77 - 120245016462 * q^79 + 84319695274 * q^80 - 111495532412 * q^82 + 142463983824 * q^83 - 181628566552 * q^85 - 47870165542 * q^86 - 180608014462 * q^88 + 96700717270 * q^89 - 355162031176 * q^91 + 22429477796 * q^92 + 172608565078 * q^94 + 195922150708 * q^95 - 303190852014 * q^97 + 123776497136 * q^98

Introduction

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