LMFDB - Embedded newform 5929.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.91223$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.656620 q^{2} +1.91223 q^{3} -1.56885 q^{4} -3.56885 q^{5} -1.25561 q^{6} +2.34338 q^{8} +0.656620 q^{9} +O(q^{10})$	\(q-0.656620 q^{2} +1.91223 q^{3} -1.56885 q^{4} -3.56885 q^{5} -1.25561 q^{6} +2.34338 q^{8} +0.656620 q^{9} +2.34338 q^{10} -3.00000 q^{12} +5.91223 q^{13} -6.82446 q^{15} +1.59899 q^{16} +1.65662 q^{17} -0.431150 q^{18} -1.48108 q^{19} +5.59899 q^{20} +3.34338 q^{23} +4.48108 q^{24} +7.73669 q^{25} -3.88209 q^{26} -4.48108 q^{27} -3.08007 q^{29} +4.48108 q^{30} -7.08007 q^{31} -5.73669 q^{32} -1.08777 q^{34} -1.03014 q^{36} -4.51122 q^{37} +0.972507 q^{38} +11.3055 q^{39} -8.36317 q^{40} +1.28575 q^{41} -1.59899 q^{43} -2.34338 q^{45} -2.19533 q^{46} -1.65662 q^{47} +3.05763 q^{48} -5.08007 q^{50} +3.16784 q^{51} -9.27540 q^{52} +9.22547 q^{53} +2.94237 q^{54} -2.83216 q^{57} +2.02243 q^{58} +8.85195 q^{59} +10.7065 q^{60} +6.68676 q^{61} +4.64892 q^{62} +0.568850 q^{64} -21.0999 q^{65} -9.82446 q^{67} -2.59899 q^{68} +6.39331 q^{69} -8.61878 q^{71} +1.53871 q^{72} -4.56115 q^{73} +2.96216 q^{74} +14.7943 q^{75} +2.32359 q^{76} -7.42345 q^{78} +6.39331 q^{79} -5.70655 q^{80} -10.5387 q^{81} -0.844248 q^{82} -0.167838 q^{83} -5.91223 q^{85} +1.04993 q^{86} -5.88979 q^{87} -2.56885 q^{89} +1.53871 q^{90} -5.24526 q^{92} -13.5387 q^{93} +1.08777 q^{94} +5.28575 q^{95} -10.9699 q^{96} +9.73669 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{3} + 4 q^{4} - 2 q^{5} + q^{6} + 9 q^{8}+O(q^{10}) $ 3 * q - q^3 + 4 * q^4 - 2 * q^5 + q^6 + 9 * q^8	$ 3 q - q^{3} + 4 q^{4} - 2 q^{5} + q^{6} + 9 q^{8} + 9 q^{10} - 9 q^{12} + 11 q^{13} - 7 q^{15} + 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} + 14 q^{20} + 12 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} + 2 q^{27} + 9 q^{29} - 2 q^{30} - 3 q^{31} + 3 q^{32} - 10 q^{34} - 9 q^{36} - 4 q^{37} + 8 q^{38} + 5 q^{39} + 3 q^{40} + 5 q^{41} - 2 q^{43} - 9 q^{45} + 10 q^{46} - 3 q^{47} + 10 q^{48} + 3 q^{50} - 2 q^{51} + 7 q^{52} + 17 q^{53} + 8 q^{54} - 20 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} + 24 q^{61} - 13 q^{62} - 7 q^{64} - 15 q^{65} - 16 q^{67} - 5 q^{68} - 3 q^{69} + 7 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} + 25 q^{75} + 39 q^{76} - 6 q^{78} - 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 11 q^{83} - 11 q^{85} - 21 q^{86} - 30 q^{87} + q^{89} - 10 q^{90} + 25 q^{92} - 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} + 9 q^{97}+O(q^{100}) $ 3 * q - q^3 + 4 * q^4 - 2 * q^5 + q^6 + 9 * q^8 + 9 * q^10 - 9 * q^12 + 11 * q^13 - 7 * q^15 + 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 + 14 * q^20 + 12 * q^23 - 2 * q^24 + 3 * q^25 + q^26 + 2 * q^27 + 9 * q^29 - 2 * q^30 - 3 * q^31 + 3 * q^32 - 10 * q^34 - 9 * q^36 - 4 * q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 + 5 * q^41 - 2 * q^43 - 9 * q^45 + 10 * q^46 - 3 * q^47 + 10 * q^48 + 3 * q^50 - 2 * q^51 + 7 * q^52 + 17 * q^53 + 8 * q^54 - 20 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 + 24 * q^61 - 13 * q^62 - 7 * q^64 - 15 * q^65 - 16 * q^67 - 5 * q^68 - 3 * q^69 + 7 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 + 25 * q^75 + 39 * q^76 - 6 * q^78 - 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 11 * q^83 - 11 * q^85 - 21 * q^86 - 30 * q^87 + q^89 - 10 * q^90 + 25 * q^92 - 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 + 9 * q^97

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 $

$2$	−0.656620	−0.464301	−0.232150	−	0.972680i	$-0.574576\pi$
$2$	−0.656620	−0.464301	−0.232150	+	0.972680i	$0.574576\pi$
$3$	1.91223	1.10403	0.552013	−	0.833835i	$-0.313860\pi$
$3$	1.91223	1.10403	0.552013	+	0.833835i	$0.313860\pi$
$4$	−1.56885	−0.784425
$5$	−3.56885	−1.59604	−0.798019	−	0.602632i	$-0.794119\pi$
$5$	−3.56885	−1.59604	−0.798019	+	0.602632i	$0.794119\pi$
$6$	−1.25561	−0.512600
$7$	0	0
$7$	0	0
$8$	2.34338	0.828510
$9$	0.656620	0.218873
$10$	2.34338	0.741042
$11$	0	0
$11$	0	0
$12$	−3.00000	−0.866025
$13$	5.91223	1.63976	0.819879	−	0.572537i	$-0.194041\pi$
$13$	5.91223	1.63976	0.819879	+	0.572537i	$0.194041\pi$
$14$	0	0
$15$	−6.82446	−1.76207
$16$	1.59899	0.399747
$17$	1.65662	0.401789	0.200895	−	0.979613i	$-0.435615\pi$
$17$	1.65662	0.401789	0.200895	+	0.979613i	$0.435615\pi$
$18$	−0.431150	−0.101623
$19$	−1.48108	−0.339783	−0.169891	−	0.985463i	$-0.554342\pi$
$19$	−1.48108	−0.339783	−0.169891	+	0.985463i	$0.554342\pi$
$20$	5.59899	1.25197
$21$	0	0
$22$	0	0
$23$	3.34338	0.697143	0.348571	−	0.937282i	$-0.386667\pi$
$23$	3.34338	0.697143	0.348571	+	0.937282i	$0.386667\pi$
$24$	4.48108	0.914696
$25$	7.73669	1.54734
$26$	−3.88209	−0.761341
$27$	−4.48108	−0.862384
$28$	0	0
$29$	−3.08007	−0.571954	−0.285977	−	0.958236i	$-0.592318\pi$
$29$	−3.08007	−0.571954	−0.285977	+	0.958236i	$0.592318\pi$
$30$	4.48108	0.818129
$31$	−7.08007	−1.27162	−0.635809	−	0.771847i	$-0.719333\pi$
$31$	−7.08007	−1.27162	−0.635809	+	0.771847i	$0.719333\pi$
$32$	−5.73669	−1.01411
$33$	0	0
$34$	−1.08777	−0.186551
$35$	0	0
$36$	−1.03014	−0.171690
$37$	−4.51122	−0.741640	−0.370820	−	0.928705i	$-0.620923\pi$
$37$	−4.51122	−0.741640	−0.370820	+	0.928705i	$0.620923\pi$
$38$	0.972507	0.157761
$39$	11.3055	1.81033
$40$	−8.36317	−1.32233
$41$	1.28575	0.200800	0.100400	−	0.994947i	$-0.467988\pi$
$41$	1.28575	0.200800	0.100400	+	0.994947i	$0.467988\pi$
$42$	0	0
$43$	−1.59899	−0.243843	−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−1.59899	−0.243843	−0.121922	+	0.992540i	$0.538906\pi$
$44$	0	0
$45$	−2.34338	−0.349330
$46$	−2.19533	−0.323684
$47$	−1.65662	−0.241643	−0.120821	−	0.992674i	$-0.538553\pi$
$47$	−1.65662	−0.241643	−0.120821	+	0.992674i	$0.538553\pi$
$48$	3.05763	0.441331
$49$	0	0
$50$	−5.08007	−0.718430
$51$	3.16784	0.443586
$52$	−9.27540	−1.28627
$53$	9.22547	1.26722	0.633608	−	0.773654i	$-0.281573\pi$
$53$	9.22547	1.26722	0.633608	+	0.773654i	$0.281573\pi$
$54$	2.94237	0.400406
$55$	0	0
$56$	0	0
$57$	−2.83216	−0.375129
$58$	2.02243	0.265559
$59$	8.85195	1.15243	0.576213	−	0.817300i	$-0.304530\pi$
$59$	8.85195	1.15243	0.576213	+	0.817300i	$0.304530\pi$
$60$	10.7065	1.38221
$61$	6.68676	0.856152	0.428076	−	0.903743i	$-0.359192\pi$
$61$	6.68676	0.856152	0.428076	+	0.903743i	$0.359192\pi$
$62$	4.64892	0.590413
$63$	0	0
$64$	0.568850	0.0711062
$65$	−21.0999	−2.61712
$66$	0	0
$67$	−9.82446	−1.20025	−0.600124	−	0.799907i	$-0.704882\pi$
$67$	−9.82446	−1.20025	−0.600124	+	0.799907i	$0.704882\pi$
$68$	−2.59899	−0.315174
$69$	6.39331	0.769664
$70$	0	0
$71$	−8.61878	−1.02286	−0.511430	−	0.859325i	$-0.670884\pi$
$71$	−8.61878	−1.02286	−0.511430	+	0.859325i	$0.670884\pi$
$72$	1.53871	0.181339
$73$	−4.56115	−0.533842	−0.266921	−	0.963718i	$-0.586006\pi$
$73$	−4.56115	−0.533842	−0.266921	+	0.963718i	$0.586006\pi$
$74$	2.96216	0.344344
$75$	14.7943	1.70830
$76$	2.32359	0.266534
$77$	0	0
$78$	−7.42345	−0.840540
$79$	6.39331	0.719303	0.359652	−	0.933087i	$-0.382896\pi$
$79$	6.39331	0.719303	0.359652	+	0.933087i	$0.382896\pi$
$80$	−5.70655	−0.638012
$81$	−10.5387	−1.17097
$82$	−0.844248	−0.0932316
$83$	−0.167838	−0.0184226	−0.00921130	−	0.999958i	$-0.502932\pi$
$83$	−0.167838	−0.0184226	−0.00921130	+	0.999958i	$0.502932\pi$
$84$	0	0
$85$	−5.91223	−0.641271
$86$	1.04993	0.113217
$87$	−5.88979	−0.631452
$88$	0	0
$89$	−2.56885	−0.272298	−0.136149	−	0.990688i	$-0.543473\pi$
$89$	−2.56885	−0.272298	−0.136149	+	0.990688i	$0.543473\pi$
$90$	1.53871	0.162194
$91$	0	0
$92$	−5.24526	−0.546856
$93$	−13.5387	−1.40390
$94$	1.08777	0.112195
$95$	5.28575	0.542306
$96$	−10.9699	−1.11961
$97$	9.73669	0.988611	0.494305	−	0.869288i	$-0.335422\pi$
$97$	9.73669	0.988611	0.494305	+	0.869288i	$0.335422\pi$
$98$	0	0
$99$	0	0
$100$	−12.1377	−1.21377
$101$	−1.85460	−0.184539	−0.0922697	−	0.995734i	$-0.529412\pi$
$101$	−1.85460	−0.184539	−0.0922697	+	0.995734i	$0.529412\pi$
$102$	−2.08007	−0.205957
$103$	−3.16784	−0.312136	−0.156068	−	0.987746i	$-0.549882\pi$
$103$	−3.16784	−0.312136	−0.156068	+	0.987746i	$0.549882\pi$
$104$	13.8546	1.35856
$105$	0	0
$106$	−6.05763	−0.588369
$107$	4.76683	0.460826	0.230413	−	0.973093i	$-0.425992\pi$
$107$	4.76683	0.460826	0.230413	+	0.973093i	$0.425992\pi$
$108$	7.03014	0.676475
$109$	14.8821	1.42545	0.712723	−	0.701446i	$-0.247462\pi$
$109$	14.8821	1.42545	0.712723	+	0.701446i	$0.247462\pi$
$110$	0	0
$111$	−8.62648	−0.818789
$112$	0	0
$113$	12.4432	1.17056	0.585281	−	0.810831i	$-0.300984\pi$
$113$	12.4432	1.17056	0.585281	+	0.810831i	$0.300984\pi$
$114$	1.85966	0.174173
$115$	−11.9320	−1.11267
$116$	4.83216	0.448655
$117$	3.88209	0.358899
$118$	−5.81237	−0.535072
$119$	0	0
$120$	−15.9923	−1.45989
$121$	0	0
$122$	−4.39066	−0.397512
$123$	2.45864	0.221688
$124$	11.1076	0.997488
$125$	−9.76683	−0.873571
$126$	0	0
$127$	6.62142	0.587556	0.293778	−	0.955874i	$-0.405087\pi$
$127$	6.62142	0.587556	0.293778	+	0.955874i	$0.405087\pi$
$128$	11.0999	0.981098
$129$	−3.05763	−0.269209
$130$	13.8546	1.21513
$131$	6.05763	0.529258	0.264629	−	0.964350i	$-0.414751\pi$
$131$	6.05763	0.529258	0.264629	+	0.964350i	$0.414751\pi$
$132$	0	0
$133$	0	0
$134$	6.45094	0.557276
$135$	15.9923	1.37640
$136$	3.88209	0.332887
$137$	−7.42345	−0.634228	−0.317114	−	0.948387i	$-0.602714\pi$
$137$	−7.42345	−0.634228	−0.317114	+	0.948387i	$0.602714\pi$
$138$	−4.19798	−0.357356
$139$	10.8245	0.918119	0.459059	−	0.888406i	$-0.348187\pi$
$139$	10.8245	0.918119	0.459059	+	0.888406i	$0.348187\pi$
$140$	0	0
$141$	−3.16784	−0.266780
$142$	5.65927	0.474915
$143$	0	0
$144$	1.04993	0.0874940
$145$	10.9923	0.912861
$146$	2.99494	0.247863
$147$	0	0
$148$	7.07742	0.581760
$149$	1.00000	0.0819232	0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000	0.0819232	0.0409616	+	0.999161i	$0.486958\pi$
$150$	−9.71425	−0.793165
$151$	−16.4234	−1.33652	−0.668261	−	0.743927i	$-0.732961\pi$
$151$	−16.4234	−1.33652	−0.668261	+	0.743927i	$0.732961\pi$
$152$	−3.47073	−0.281513
$153$	1.08777	0.0879411
$154$	0	0
$155$	25.2677	2.02955
$156$	−17.7367	−1.42007
$157$	−11.4509	−0.913885	−0.456942	−	0.889496i	$-0.651055\pi$
$157$	−11.4509	−0.913885	−0.456942	+	0.889496i	$0.651055\pi$
$158$	−4.19798	−0.333973
$159$	17.6412	1.39904
$160$	20.4734	1.61856
$161$	0	0
$162$	6.91993	0.543681
$163$	−8.93972	−0.700213	−0.350107	−	0.936710i	$-0.613855\pi$
$163$	−8.93972	−0.700213	−0.350107	+	0.936710i	$0.613855\pi$
$164$	−2.01714	−0.157513
$165$	0	0
$166$	0.110206	0.00855363
$167$	18.2178	1.40973	0.704867	−	0.709340i	$-0.251007\pi$
$167$	18.2178	1.40973	0.704867	+	0.709340i	$0.251007\pi$
$168$	0	0
$169$	21.9545	1.68880
$170$	3.88209	0.297743
$171$	−0.972507	−0.0743694
$172$	2.50857	0.191277
$173$	−19.5611	−1.48721	−0.743603	−	0.668621i	$-0.766885\pi$
$173$	−19.5611	−1.48721	−0.743603	+	0.668621i	$0.766885\pi$
$174$	3.86736	0.293184
$175$	0	0
$176$	0	0
$177$	16.9270	1.27231
$178$	1.68676	0.126428
$179$	3.24791	0.242760	0.121380	−	0.992606i	$-0.461268\pi$
$179$	3.24791	0.242760	0.121380	+	0.992606i	$0.461268\pi$
$180$	3.67641	0.274023
$181$	−10.3407	−0.768621	−0.384310	−	0.923204i	$-0.625561\pi$
$181$	−10.3407	−0.768621	−0.384310	+	0.923204i	$0.625561\pi$
$182$	0	0
$183$	12.7866	0.945214
$184$	7.83481	0.577590
$185$	16.0999	1.18369
$186$	8.88979	0.651831
$187$	0	0
$188$	2.59899	0.189551
$189$	0	0
$190$	−3.47073	−0.251793
$191$	10.0224	0.725198	0.362599	−	0.931945i	$-0.381889\pi$
$191$	10.0224	0.725198	0.362599	+	0.931945i	$0.381889\pi$
$192$	1.08777	0.0785031
$193$	−25.3253	−1.82296	−0.911478	−	0.411348i	$-0.865058\pi$
$193$	−25.3253	−1.82296	−0.911478	+	0.411348i	$0.865058\pi$
$194$	−6.39331	−0.459013
$195$	−40.3478	−2.88936
$196$	0	0
$197$	24.5809	1.75132	0.875660	−	0.482929i	$-0.160427\pi$
$197$	24.5809	1.75132	0.875660	+	0.482929i	$0.160427\pi$
$198$	0	0
$199$	5.59128	0.396356	0.198178	−	0.980166i	$-0.436498\pi$
$199$	5.59128	0.396356	0.198178	+	0.980166i	$0.436498\pi$
$200$	18.1300	1.28198
$201$	−18.7866	−1.32511
$202$	1.21777	0.0856817
$203$	0	0
$204$	−4.96986	−0.347960
$205$	−4.58864	−0.320484
$206$	2.08007	0.144925
$207$	2.19533	0.152586
$208$	9.45359	0.655488
$209$	0	0
$210$	0	0
$211$	−12.0999	−0.832988	−0.416494	−	0.909138i	$-0.636741\pi$
$211$	−12.0999	−0.832988	−0.416494	+	0.909138i	$0.636741\pi$
$212$	−14.4734	−0.994035
$213$	−16.4811	−1.12926
$214$	−3.13000	−0.213962
$215$	5.70655	0.389183
$216$	−10.5009	−0.714494
$217$	0	0
$218$	−9.77188	−0.661836
$219$	−8.72196	−0.589375
$220$	0	0
$221$	9.79432	0.658837
$222$	5.66432	0.380165
$223$	15.6265	1.04643	0.523213	−	0.852202i	$-0.324733\pi$
$223$	15.6265	1.04643	0.523213	+	0.852202i	$0.324733\pi$
$224$	0	0
$225$	5.08007	0.338671
$226$	−8.17048	−0.543492
$227$	15.6687	1.03997	0.519984	−	0.854176i	$-0.325938\pi$
$227$	15.6687	1.03997	0.519984	+	0.854176i	$0.325938\pi$
$228$	4.44324	0.294261
$229$	−5.57149	−0.368175	−0.184087	−	0.982910i	$-0.558933\pi$
$229$	−5.57149	−0.368175	−0.184087	+	0.982910i	$0.558933\pi$
$230$	7.83481	0.516612
$231$	0	0
$232$	−7.21777	−0.473870
$233$	19.2754	1.26277	0.631387	−	0.775468i	$-0.282486\pi$
$233$	19.2754	1.26277	0.631387	+	0.775468i	$0.282486\pi$
$234$	−2.54906	−0.166637
$235$	5.91223	0.385671
$236$	−13.8874	−0.903992
$237$	12.2255	0.794130
$238$	0	0
$239$	22.1575	1.43325	0.716624	−	0.697459i	$-0.245686\pi$
$239$	22.1575	1.43325	0.716624	+	0.697459i	$0.245686\pi$
$240$	−10.9122	−0.704381
$241$	19.8744	1.28022	0.640111	−	0.768283i	$-0.278888\pi$
$241$	19.8744	1.28022	0.640111	+	0.768283i	$0.278888\pi$
$242$	0	0
$243$	−6.70919	−0.430395
$244$	−10.4905	−0.671587
$245$	0	0
$246$	−1.61440	−0.102930
$247$	−8.75648	−0.557161
$248$	−16.5913	−1.05355
$249$	−0.320945	−0.0203390
$250$	6.41310	0.405600
$251$	22.1076	1.39542	0.697708	−	0.716382i	$-0.254203\pi$
$251$	22.1076	1.39542	0.697708	+	0.716382i	$0.254203\pi$
$252$	0	0
$253$	0	0
$254$	−4.34776	−0.272803
$255$	−11.3055	−0.707980
$256$	−8.42609	−0.526631
$257$	29.1196	1.81643	0.908217	−	0.418500i	$-0.137444\pi$
$257$	29.1196	1.81643	0.908217	+	0.418500i	$0.137444\pi$
$258$	2.00770	0.124994
$259$	0	0
$260$	33.1025	2.05293
$261$	−2.02243	−0.125186
$262$	−3.97757	−0.245735
$263$	15.5035	0.955988	0.477994	−	0.878363i	$-0.341364\pi$
$263$	15.5035	0.955988	0.477994	+	0.878363i	$0.341364\pi$
$264$	0	0
$265$	−32.9243	−2.02252
$266$	0	0
$267$	−4.91223	−0.300624
$268$	15.4131	0.941505
$269$	1.70655	0.104050	0.0520251	−	0.998646i	$-0.483432\pi$
$269$	1.70655	0.104050	0.0520251	+	0.998646i	$0.483432\pi$
$270$	−10.5009	−0.639063
$271$	20.5284	1.24701	0.623505	−	0.781820i	$-0.285708\pi$
$271$	20.5284	1.24701	0.623505	+	0.781820i	$0.285708\pi$
$272$	2.64892	0.160614
$273$	0	0
$274$	4.87439	0.294472
$275$	0	0
$276$	−10.0301	−0.603743
$277$	26.6610	1.60190	0.800952	−	0.598728i	$-0.204327\pi$
$277$	26.6610	1.60190	0.800952	+	0.598728i	$0.204327\pi$
$278$	−7.10756	−0.426283
$279$	−4.64892	−0.278323
$280$	0	0
$281$	−15.7444	−0.939232	−0.469616	−	0.882871i	$-0.655608\pi$
$281$	−15.7444	−0.939232	−0.469616	+	0.882871i	$0.655608\pi$
$282$	2.08007	0.123866
$283$	16.0697	0.955246	0.477623	−	0.878565i	$-0.341499\pi$
$283$	16.0697	0.955246	0.477623	+	0.878565i	$0.341499\pi$
$284$	13.5216	0.802357
$285$	10.1076	0.598720
$286$	0	0
$287$	0	0
$288$	−3.76683	−0.221962
$289$	−14.2556	−0.838565
$290$	−7.21777	−0.423842
$291$	18.6188	1.09145
$292$	7.15575	0.418759
$293$	−15.3357	−0.895920	−0.447960	−	0.894054i	$-0.647849\pi$
$293$	−15.3357	−0.895920	−0.447960	+	0.894054i	$0.647849\pi$
$294$	0	0
$295$	−31.5913	−1.83932
$296$	−10.5715	−0.614456
$297$	0	0
$298$	−0.656620	−0.0380370
$299$	19.7668	1.14315
$300$	−23.2101	−1.34003
$301$	0	0
$302$	10.7840	0.620548
$303$	−3.54641	−0.203736
$304$	−2.36823	−0.135827
$305$	−23.8640	−1.36645
$306$	−0.714253	−0.0408311
$307$	16.4707	0.940034	0.470017	−	0.882657i	$-0.344248\pi$
$307$	16.4707	0.940034	0.470017	+	0.882657i	$0.344248\pi$
$308$	0	0
$309$	−6.05763	−0.344607
$310$	−16.5913	−0.942322
$311$	21.6291	1.22648	0.613238	−	0.789898i	$-0.289867\pi$
$311$	21.6291	1.22648	0.613238	+	0.789898i	$0.289867\pi$
$312$	26.4932	1.49988
$313$	16.3882	0.926319	0.463159	−	0.886275i	$-0.346716\pi$
$313$	16.3882	0.926319	0.463159	+	0.886275i	$0.346716\pi$
$314$	7.51892	0.424317
$315$	0	0
$316$	−10.0301	−0.564239
$317$	4.46129	0.250571	0.125285	−	0.992121i	$-0.460015\pi$
$317$	4.46129	0.250571	0.125285	+	0.992121i	$0.460015\pi$
$318$	−11.5836	−0.649575
$319$	0	0
$320$	−2.03014	−0.113488
$321$	9.11526	0.508764
$322$	0	0
$323$	−2.45359	−0.136521
$324$	16.5337	0.918536
$325$	45.7411	2.53726
$326$	5.87000	0.325109
$327$	28.4580	1.57373
$328$	3.01299	0.166365
$329$	0	0
$330$	0	0
$331$	19.0396	1.04651	0.523255	−	0.852176i	$-0.324718\pi$
$331$	19.0396	1.04651	0.523255	+	0.852176i	$0.324718\pi$
$332$	0.263312	0.0144511
$333$	−2.96216	−0.162325
$334$	−11.9622	−0.654540
$335$	35.0620	1.91564
$336$	0	0
$337$	−27.0147	−1.47159	−0.735793	−	0.677206i	$-0.763190\pi$
$337$	−27.0147	−1.47159	−0.735793	+	0.677206i	$0.763190\pi$
$338$	−14.4157	−0.784113
$339$	23.7943	1.29233
$340$	9.27540	0.503029
$341$	0	0
$342$	0.638568	0.0345298
$343$	0	0
$344$	−3.74704	−0.202027
$345$	−22.8168	−1.22841
$346$	12.8442	0.690511
$347$	20.2178	1.08535	0.542673	−	0.839944i	$-0.317412\pi$
$347$	20.2178	1.08535	0.542673	+	0.839944i	$0.317412\pi$
$348$	9.24020	0.495327
$349$	12.0224	0.643546	0.321773	−	0.946817i	$-0.395721\pi$
$349$	12.0224	0.643546	0.321773	+	0.946817i	$0.395721\pi$
$350$	0	0
$351$	−26.4932	−1.41410
$352$	0	0
$353$	−10.7591	−0.572650	−0.286325	−	0.958133i	$-0.592434\pi$
$353$	−10.7591	−0.572650	−0.286325	+	0.958133i	$0.592434\pi$
$354$	−11.1146	−0.590734
$355$	30.7591	1.63252
$356$	4.03014	0.213597
$357$	0	0
$358$	−2.13264	−0.112714
$359$	−24.2901	−1.28198	−0.640992	−	0.767548i	$-0.721477\pi$
$359$	−24.2901	−1.28198	−0.640992	+	0.767548i	$0.721477\pi$
$360$	−5.49143	−0.289424
$361$	−16.8064	−0.884548
$362$	6.78994	0.356871
$363$	0	0
$364$	0	0
$365$	16.2780	0.852032
$366$	−8.39595	−0.438864
$367$	10.8442	0.566065	0.283033	−	0.959110i	$-0.408660\pi$
$367$	10.8442	0.566065	0.283033	+	0.959110i	$0.408660\pi$
$368$	5.34602	0.278681
$369$	0.844248	0.0439498
$370$	−10.5715	−0.549586
$371$	0	0
$372$	21.2402	1.10125
$373$	33.0242	1.70993	0.854963	−	0.518688i	$-0.173579\pi$
$373$	33.0242	1.70993	0.854963	+	0.518688i	$0.173579\pi$
$374$	0	0
$375$	−18.6764	−0.964446
$376$	−3.88209	−0.200204
$377$	−18.2101	−0.937866
$378$	0	0
$379$	−21.9320	−1.12657	−0.563286	−	0.826262i	$-0.690463\pi$
$379$	−21.9320	−1.12657	−0.563286	+	0.826262i	$0.690463\pi$
$380$	−8.29254	−0.425398
$381$	12.6617	0.648677
$382$	−6.58094	−0.336710
$383$	36.4630	1.86317	0.931587	−	0.363519i	$-0.118425\pi$
$383$	36.4630	1.86317	0.931587	+	0.363519i	$0.118425\pi$
$384$	21.2255	1.08316
$385$	0	0
$386$	16.6291	0.846400
$387$	−1.04993	−0.0533709
$388$	−15.2754	−0.775491
$389$	19.4760	0.987473	0.493737	−	0.869611i	$-0.335631\pi$
$389$	19.4760	0.987473	0.493737	+	0.869611i	$0.335631\pi$
$390$	26.4932	1.34153
$391$	5.53871	0.280105
$392$	0	0
$393$	11.5836	0.584314
$394$	−16.1403	−0.813139
$395$	−22.8168	−1.14804
$396$	0	0
$397$	−7.83987	−0.393472	−0.196736	−	0.980457i	$-0.563034\pi$
$397$	−7.83987	−0.393472	−0.196736	+	0.980457i	$0.563034\pi$
$398$	−3.67135	−0.184028
$399$	0	0
$400$	12.3709	0.618544
$401$	−24.4459	−1.22077	−0.610385	−	0.792105i	$-0.708985\pi$
$401$	−24.4459	−1.22077	−0.610385	+	0.792105i	$0.708985\pi$
$402$	12.3357	0.615248
$403$	−41.8590	−2.08514
$404$	2.90958	0.144757
$405$	37.6111	1.86891
$406$	0	0
$407$	0	0
$408$	7.42345	0.367515
$409$	2.35373	0.116384	0.0581922	−	0.998305i	$-0.481466\pi$
$409$	2.35373	0.116384	0.0581922	+	0.998305i	$0.481466\pi$
$410$	3.01299	0.148801
$411$	−14.1953	−0.700204
$412$	4.96986	0.244847
$413$	0	0
$414$	−1.44150	−0.0708458
$415$	0.598988	0.0294032
$416$	−33.9166	−1.66290
$417$	20.6988	1.01363
$418$	0	0
$419$	9.29081	0.453886	0.226943	−	0.973908i	$-0.427127\pi$
$419$	9.29081	0.453886	0.226943	+	0.973908i	$0.427127\pi$
$420$	0	0
$421$	−39.0319	−1.90230	−0.951149	−	0.308733i	$-0.900095\pi$
$421$	−39.0319	−1.90230	−0.951149	+	0.308733i	$0.900095\pi$
$422$	7.94501	0.386757
$423$	−1.08777	−0.0528892
$424$	21.6188	1.04990
$425$	12.8168	0.621704
$426$	10.8218	0.524319
$427$	0	0
$428$	−7.47843	−0.361484
$429$	0	0
$430$	−3.74704	−0.180698
$431$	3.80202	0.183137	0.0915685	−	0.995799i	$-0.470812\pi$
$431$	3.80202	0.183137	0.0915685	+	0.995799i	$0.470812\pi$
$432$	−7.16519	−0.344735
$433$	8.22041	0.395048	0.197524	−	0.980298i	$-0.436710\pi$
$433$	8.22041	0.395048	0.197524	+	0.980298i	$0.436710\pi$
$434$	0	0
$435$	21.0198	1.00782
$436$	−23.3478	−1.11815
$437$	−4.95181	−0.236877
$438$	5.72701	0.273647
$439$	−4.54136	−0.216747	−0.108374	−	0.994110i	$-0.534564\pi$
$439$	−4.54136	−0.216747	−0.108374	+	0.994110i	$0.534564\pi$
$440$	0	0
$441$	0	0
$442$	−6.43115	−0.305899
$443$	13.7444	0.653016	0.326508	−	0.945194i	$-0.394128\pi$
$443$	13.7444	0.653016	0.326508	+	0.945194i	$0.394128\pi$
$444$	13.5337	0.642279
$445$	9.16784	0.434597
$446$	−10.2607	−0.485857
$447$	1.91223	0.0904453
$448$	0	0
$449$	21.5662	1.01777	0.508886	−	0.860834i	$-0.330057\pi$
$449$	21.5662	1.01777	0.508886	+	0.860834i	$0.330057\pi$
$450$	−3.33568	−0.157245
$451$	0	0
$452$	−19.5216	−0.918217
$453$	−31.4054	−1.47555
$454$	−10.2884	−0.482858
$455$	0	0
$456$	−6.63683	−0.310798
$457$	3.30554	0.154627	0.0773133	−	0.997007i	$-0.475366\pi$
$457$	3.30554	0.154627	0.0773133	+	0.997007i	$0.475366\pi$
$458$	3.65836	0.170944
$459$	−7.42345	−0.346497
$460$	18.7195	0.872803
$461$	32.1524	1.49749	0.748744	−	0.662859i	$-0.230657\pi$
$461$	32.1524	1.49749	0.748744	+	0.662859i	$0.230657\pi$
$462$	0	0
$463$	5.82181	0.270563	0.135281	−	0.990807i	$-0.456806\pi$
$463$	5.82181	0.270563	0.135281	+	0.990807i	$0.456806\pi$
$464$	−4.92499	−0.228637
$465$	48.3176	2.24068
$466$	−12.6566	−0.586307
$467$	−6.01473	−0.278329	−0.139164	−	0.990269i	$-0.544442\pi$
$467$	−6.01473	−0.278329	−0.139164	+	0.990269i	$0.544442\pi$
$468$	−6.09042	−0.281530
$469$	0	0
$470$	−3.88209	−0.179067
$471$	−21.8968	−1.00895
$472$	20.7435	0.954796
$473$	0	0
$474$	−8.02749	−0.368715
$475$	−11.4586	−0.525759
$476$	0	0
$477$	6.05763	0.277360
$478$	−14.5491	−0.665459
$479$	−17.1351	−0.782921	−0.391460	−	0.920195i	$-0.628030\pi$
$479$	−17.1351	−0.782921	−0.391460	+	0.920195i	$0.628030\pi$
$480$	39.1498	1.78694
$481$	−26.6714	−1.21611
$482$	−13.0499	−0.594408
$483$	0	0
$484$	0	0
$485$	−34.7488	−1.57786
$486$	4.40539	0.199833
$487$	5.71425	0.258937	0.129469	−	0.991584i	$-0.458673\pi$
$487$	5.71425	0.258937	0.129469	+	0.991584i	$0.458673\pi$
$488$	15.6696	0.709330
$489$	−17.0948	−0.773054
$490$	0	0
$491$	−24.0673	−1.08614	−0.543071	−	0.839687i	$-0.682739\pi$
$491$	−24.0673	−1.08614	−0.543071	+	0.839687i	$0.682739\pi$
$492$	−3.85724	−0.173898
$493$	−5.10250	−0.229805
$494$	5.74968	0.258690
$495$	0	0
$496$	−11.3209	−0.508325
$497$	0	0
$498$	0.210739	0.00944343
$499$	10.7893	0.482994	0.241497	−	0.970402i	$-0.422362\pi$
$499$	10.7893	0.482994	0.241497	+	0.970402i	$0.422362\pi$
$500$	15.3227	0.685251
$501$	34.8365	1.55638
$502$	−14.5163	−0.647893
$503$	−28.0121	−1.24900	−0.624499	−	0.781026i	$-0.714697\pi$
$503$	−28.0121	−1.24900	−0.624499	+	0.781026i	$0.714697\pi$
$504$	0	0
$505$	6.61878	0.294532
$506$	0	0
$507$	41.9819	1.86448
$508$	−10.3880	−0.460894
$509$	−1.91487	−0.0848753	−0.0424377	−	0.999099i	$-0.513512\pi$
$509$	−1.91487	−0.0848753	−0.0424377	+	0.999099i	$0.513512\pi$
$510$	7.42345	0.328716
$511$	0	0
$512$	−16.6670	−0.736583
$513$	6.63683	0.293023
$514$	−19.1206	−0.843372
$515$	11.3055	0.498181
$516$	4.79696	0.211175
$517$	0	0
$518$	0	0
$519$	−37.4054	−1.64191
$520$	−49.4450	−2.16831
$521$	1.57920	0.0691859	0.0345930	−	0.999401i	$-0.488987\pi$
$521$	1.57920	0.0691859	0.0345930	+	0.999401i	$0.488987\pi$
$522$	1.32797	0.0581238
$523$	8.96986	0.392225	0.196112	−	0.980581i	$-0.437168\pi$
$523$	8.96986	0.392225	0.196112	+	0.980581i	$0.437168\pi$
$524$	−9.50351	−0.415163
$525$	0	0
$526$	−10.1799	−0.443866
$527$	−11.7290	−0.510923
$528$	0	0
$529$	−11.8218	−0.513992
$530$	21.6188	0.939060
$531$	5.81237	0.252235
$532$	0	0
$533$	7.60163	0.329263
$534$	3.22547	0.139580
$535$	−17.0121	−0.735497
$536$	−23.0224	−0.994418
$537$	6.21074	0.268013
$538$	−1.12055	−0.0483105
$539$	0	0
$540$	−25.0895	−1.07968
$541$	−18.1025	−0.778287	−0.389144	−	0.921177i	$-0.627229\pi$
$541$	−18.1025	−0.778287	−0.389144	+	0.921177i	$0.627229\pi$
$542$	−13.4793	−0.578987
$543$	−19.7739	−0.848577
$544$	−9.50351	−0.407460
$545$	−53.1119	−2.27507
$546$	0	0
$547$	−22.6885	−0.970090	−0.485045	−	0.874489i	$-0.661197\pi$
$547$	−22.6885	−0.970090	−0.485045	+	0.874489i	$0.661197\pi$
$548$	11.6463	0.497504
$549$	4.39066	0.187389
$550$	0	0
$551$	4.56182	0.194340
$552$	14.9819	0.637674
$553$	0	0
$554$	−17.5062	−0.743765
$555$	30.7866	1.30682
$556$	−16.9819	−0.720195
$557$	−38.3555	−1.62517	−0.812587	−	0.582840i	$-0.801941\pi$
$557$	−38.3555	−1.62517	−0.812587	+	0.582840i	$0.801941\pi$
$558$	3.05257	0.129226
$559$	−9.45359	−0.399844
$560$	0	0
$561$	0	0
$562$	10.3381	0.436086
$563$	41.7739	1.76056	0.880279	−	0.474456i	$-0.157355\pi$
$563$	41.7739	1.76056	0.880279	+	0.474456i	$0.157355\pi$
$564$	4.96986	0.209269
$565$	−44.4080	−1.86826
$566$	−10.5517	−0.443521
$567$	0	0
$568$	−20.1971	−0.847450
$569$	11.8700	0.497616	0.248808	−	0.968553i	$-0.419961\pi$
$569$	11.8700	0.497616	0.248808	+	0.968553i	$0.419961\pi$
$570$	−6.63683	−0.277986
$571$	−19.8013	−0.828661	−0.414330	−	0.910127i	$-0.635984\pi$
$571$	−19.8013	−0.828661	−0.414330	+	0.910127i	$0.635984\pi$
$572$	0	0
$573$	19.1652	0.800637
$574$	0	0
$575$	25.8667	1.07872
$576$	0.373518	0.0155633
$577$	28.6791	1.19392	0.596962	−	0.802269i	$-0.296374\pi$
$577$	28.6791	1.19392	0.596962	+	0.802269i	$0.296374\pi$
$578$	9.36052	0.389346
$579$	−48.4278	−2.01259
$580$	−17.2453	−0.716070
$581$	0	0
$582$	−12.2255	−0.506762
$583$	0	0
$584$	−10.6885	−0.442293
$585$	−13.8546	−0.572817
$586$	10.0697	0.415976
$587$	1.01209	0.0417733	0.0208866	−	0.999782i	$-0.493351\pi$
$587$	1.01209	0.0417733	0.0208866	+	0.999782i	$0.493351\pi$
$588$	0	0
$589$	10.4861	0.432074
$590$	20.7435	0.853996
$591$	47.0044	1.93350
$592$	−7.21338	−0.296468
$593$	−14.2332	−0.584486	−0.292243	−	0.956344i	$-0.594402\pi$
$593$	−14.2332	−0.584486	−0.292243	+	0.956344i	$0.594402\pi$
$594$	0	0
$595$	0	0
$596$	−1.56885	−0.0642626
$597$	10.6918	0.437587
$598$	−12.9793	−0.530763
$599$	−26.5457	−1.08463	−0.542315	−	0.840175i	$-0.682452\pi$
$599$	−26.5457	−1.08463	−0.542315	+	0.840175i	$0.682452\pi$
$600$	34.6687	1.41534
$601$	12.1558	0.495843	0.247922	−	0.968780i	$-0.420252\pi$
$601$	12.1558	0.495843	0.247922	+	0.968780i	$0.420252\pi$
$602$	0	0
$603$	−6.45094	−0.262703
$604$	25.7659	1.04840
$605$	0	0
$606$	2.32865	0.0945949
$607$	−13.9672	−0.566912	−0.283456	−	0.958985i	$-0.591481\pi$
$607$	−13.9672	−0.566912	−0.283456	+	0.958985i	$0.591481\pi$
$608$	8.49649	0.344578
$609$	0	0
$610$	15.6696	0.634444
$611$	−9.79432	−0.396236
$612$	−1.70655	−0.0689831
$613$	−4.64189	−0.187484	−0.0937421	−	0.995597i	$-0.529883\pi$
$613$	−4.64189	−0.187484	−0.0937421	+	0.995597i	$0.529883\pi$
$614$	−10.8150	−0.436459
$615$	−8.77453	−0.353823
$616$	0	0
$617$	−26.3960	−1.06266	−0.531331	−	0.847165i	$-0.678308\pi$
$617$	−26.3960	−1.06266	−0.531331	+	0.847165i	$0.678308\pi$
$618$	3.97757	0.160001
$619$	14.6815	0.590098	0.295049	−	0.955482i	$-0.404664\pi$
$619$	14.6815	0.590098	0.295049	+	0.955482i	$0.404664\pi$
$620$	−39.6412	−1.59203
$621$	−14.9819	−0.601205
$622$	−14.2021	−0.569453
$623$	0	0
$624$	18.0774	0.723676
$625$	−3.82710	−0.153084
$626$	−10.7609	−0.430090
$627$	0	0
$628$	17.9648	0.716874
$629$	−7.47338	−0.297983
$630$	0	0
$631$	−30.1498	−1.20024	−0.600122	−	0.799908i	$-0.704881\pi$
$631$	−30.1498	−1.20024	−0.600122	+	0.799908i	$0.704881\pi$
$632$	14.9819	0.595950
$633$	−23.1377	−0.919641
$634$	−2.92937	−0.116340
$635$	−23.6309	−0.937762
$636$	−27.6764	−1.09744
$637$	0	0
$638$	0	0
$639$	−5.65927	−0.223877
$640$	−39.6137	−1.56587
$641$	−16.1782	−0.639000	−0.319500	−	0.947586i	$-0.603515\pi$
$641$	−16.1782	−0.639000	−0.319500	+	0.947586i	$0.603515\pi$
$642$	−5.98527	−0.236220
$643$	−2.33568	−0.0921101	−0.0460550	−	0.998939i	$-0.514665\pi$
$643$	−2.33568	−0.0921101	−0.0460550	+	0.998939i	$0.514665\pi$
$644$	0	0
$645$	10.9122	0.429669
$646$	1.61107	0.0633869
$647$	14.9622	0.588223	0.294112	−	0.955771i	$-0.404976\pi$
$647$	14.9622	0.588223	0.294112	+	0.955771i	$0.404976\pi$
$648$	−24.6962	−0.970158
$649$	0	0
$650$	−30.0345	−1.17805
$651$	0	0
$652$	14.0251	0.549265
$653$	−22.8898	−0.895747	−0.447873	−	0.894097i	$-0.647818\pi$
$653$	−22.8898	−0.895747	−0.447873	+	0.894097i	$0.647818\pi$
$654$	−18.6861	−0.730684
$655$	−21.6188	−0.844716
$656$	2.05590	0.0802692
$657$	−2.99494	−0.116844
$658$	0	0
$659$	2.20568	0.0859211	0.0429606	−	0.999077i	$-0.486321\pi$
$659$	2.20568	0.0859211	0.0429606	+	0.999077i	$0.486321\pi$
$660$	0	0
$661$	−0.682377	−0.0265414	−0.0132707	−	0.999912i	$-0.504224\pi$
$661$	−0.682377	−0.0265414	−0.0132707	+	0.999912i	$0.504224\pi$
$662$	−12.5018	−0.485895
$663$	18.7290	0.727373
$664$	−0.393308	−0.0152633
$665$	0	0
$666$	1.94501	0.0753677
$667$	−10.2978	−0.398734
$668$	−28.5809	−1.10583
$669$	29.8814	1.15528
$670$	−23.0224	−0.889434
$671$	0	0
$672$	0	0
$673$	10.8865	0.419643	0.209821	−	0.977740i	$-0.432712\pi$
$673$	10.8865	0.419643	0.209821	+	0.977740i	$0.432712\pi$
$674$	17.7384	0.683259
$675$	−34.6687	−1.33440
$676$	−34.4432	−1.32474
$677$	−45.6654	−1.75506	−0.877532	−	0.479519i	$-0.840811\pi$
$677$	−45.6654	−1.75506	−0.877532	+	0.479519i	$0.840811\pi$
$678$	−15.6238	−0.600030
$679$	0	0
$680$	−13.8546	−0.531300
$681$	29.9622	1.14815
$682$	0	0
$683$	6.48372	0.248093	0.124046	−	0.992276i	$-0.460413\pi$
$683$	6.48372	0.248093	0.124046	+	0.992276i	$0.460413\pi$
$684$	1.52572	0.0583372
$685$	26.4932	1.01225
$686$	0	0
$687$	−10.6540	−0.406475
$688$	−2.55676	−0.0974757
$689$	54.5431	2.07793
$690$	14.9819	0.570353
$691$	10.9468	0.416434	0.208217	−	0.978083i	$-0.433234\pi$
$691$	10.9468	0.416434	0.208217	+	0.978083i	$0.433234\pi$
$692$	30.6885	1.16660
$693$	0	0
$694$	−13.2754	−0.503927
$695$	−38.6309	−1.46535
$696$	−13.8020	−0.523164
$697$	2.13000	0.0806793
$698$	−7.89418	−0.298799
$699$	36.8590	1.39413
$700$	0	0
$701$	0.914874	0.0345543	0.0172772	−	0.999851i	$-0.494500\pi$
$701$	0.914874	0.0345543	0.0172772	+	0.999851i	$0.494500\pi$
$702$	17.3960	0.656568
$703$	6.68147	0.251996
$704$	0	0
$705$	11.3055	0.425791
$706$	7.06466	0.265882
$707$	0	0
$708$	−26.5559	−0.998030
$709$	44.3123	1.66418	0.832092	−	0.554637i	$-0.187143\pi$
$709$	44.3123	1.66418	0.832092	+	0.554637i	$0.187143\pi$
$710$	−20.1971	−0.757982
$711$	4.19798	0.157436
$712$	−6.01979	−0.225601
$713$	−23.6714	−0.886499
$714$	0	0
$715$	0	0
$716$	−5.09547	−0.190427
$717$	42.3702	1.58234
$718$	15.9494	0.595226
$719$	−5.20236	−0.194015	−0.0970076	−	0.995284i	$-0.530927\pi$
$719$	−5.20236	−0.194015	−0.0970076	+	0.995284i	$0.530927\pi$
$720$	−3.74704	−0.139644
$721$	0	0
$722$	11.0354	0.410696
$723$	38.0044	1.41340
$724$	16.2231	0.602925
$725$	−23.8295	−0.885006
$726$	0	0
$727$	50.0871	1.85763	0.928814	−	0.370547i	$-0.120830\pi$
$727$	50.0871	1.85763	0.928814	+	0.370547i	$0.120830\pi$
$728$	0	0
$729$	18.7866	0.695801
$730$	−10.6885	−0.395599
$731$	−2.64892	−0.0979737
$732$	−20.0603	−0.741449
$733$	47.0697	1.73856	0.869280	−	0.494320i	$-0.164583\pi$
$733$	47.0697	1.73856	0.869280	+	0.494320i	$0.164583\pi$
$734$	−7.12055	−0.262824
$735$	0	0
$736$	−19.1799	−0.706981
$737$	0	0
$738$	−0.554351	−0.0204059
$739$	−46.9914	−1.72861	−0.864303	−	0.502971i	$-0.832240\pi$
$739$	−46.9914	−1.72861	−0.864303	+	0.502971i	$0.832240\pi$
$740$	−25.2583	−0.928512
$741$	−16.7444	−0.615121
$742$	0	0
$743$	5.19533	0.190598	0.0952991	−	0.995449i	$-0.469619\pi$
$743$	5.19533	0.190598	0.0952991	+	0.995449i	$0.469619\pi$
$744$	−31.7263	−1.16314
$745$	−3.56885	−0.130753
$746$	−21.6843	−0.793920
$747$	−0.110206	−0.00403222
$748$	0	0
$749$	0	0
$750$	12.2633	0.447793
$751$	33.4536	1.22074	0.610369	−	0.792117i	$-0.291021\pi$
$751$	33.4536	1.22074	0.610369	+	0.792117i	$0.291021\pi$
$752$	−2.64892	−0.0965961
$753$	42.2747	1.54058
$754$	11.9571	0.435452
$755$	58.6128	2.13314
$756$	0	0
$757$	40.0440	1.45542	0.727711	−	0.685884i	$-0.240584\pi$
$757$	40.0440	1.45542	0.727711	+	0.685884i	$0.240584\pi$
$758$	14.4010	0.523068
$759$	0	0
$760$	12.3865	0.449306
$761$	7.55850	0.273995	0.136998	−	0.990571i	$-0.456255\pi$
$761$	7.55850	0.273995	0.136998	+	0.990571i	$0.456255\pi$
$762$	−8.31392	−0.301181
$763$	0	0
$764$	−15.7237	−0.568863
$765$	−3.88209	−0.140357
$766$	−23.9424	−0.865073
$767$	52.3348	1.88970
$768$	−16.1126	−0.581414
$769$	−51.5407	−1.85860	−0.929302	−	0.369320i	$-0.879591\pi$
$769$	−51.5407	−1.85860	−0.929302	+	0.369320i	$0.879591\pi$
$770$	0	0
$771$	55.6834	2.00539
$772$	39.7316	1.42997
$773$	−15.4657	−0.556262	−0.278131	−	0.960543i	$-0.589715\pi$
$773$	−15.4657	−0.556262	−0.278131	+	0.960543i	$0.589715\pi$
$774$	0.689404	0.0247801
$775$	−54.7763	−1.96762
$776$	22.8168	0.819074
$777$	0	0
$778$	−12.7884	−0.458485
$779$	−1.90429	−0.0682284
$780$	63.2996	2.26649
$781$	0	0
$782$	−3.63683	−0.130053
$783$	13.8020	0.493244
$784$	0	0
$785$	40.8667	1.45859
$786$	−7.60602	−0.271298
$787$	−21.9518	−0.782497	−0.391249	−	0.920285i	$-0.627957\pi$
$787$	−21.9518	−0.782497	−0.391249	+	0.920285i	$0.627957\pi$
$788$	−38.5638	−1.37378
$789$	29.6463	1.05544
$790$	14.9819	0.533034
$791$	0	0
$792$	0	0
$793$	39.5337	1.40388
$794$	5.14782	0.182689
$795$	−62.9588	−2.23292
$796$	−8.77188	−0.310911
$797$	42.6258	1.50988	0.754942	−	0.655792i	$-0.227665\pi$
$797$	42.6258	1.50988	0.754942	+	0.655792i	$0.227665\pi$
$798$	0	0
$799$	−2.74439	−0.0970896
$800$	−44.3830	−1.56917
$801$	−1.68676	−0.0595987
$802$	16.0517	0.566804
$803$	0	0
$804$	29.4734	1.03945
$805$	0	0
$806$	27.4855	0.968134
$807$	3.26331	0.114874
$808$	−4.34602	−0.152893
$809$	−3.96745	−0.139488	−0.0697440	−	0.997565i	$-0.522218\pi$
$809$	−3.96745	−0.139488	−0.0697440	+	0.997565i	$0.522218\pi$
$810$	−24.6962	−0.867736
$811$	46.9217	1.64764	0.823821	−	0.566850i	$-0.191838\pi$
$811$	46.9217	1.64764	0.823821	+	0.566850i	$0.191838\pi$
$812$	0	0
$813$	39.2549	1.37673
$814$	0	0
$815$	31.9045	1.11757
$816$	5.06534	0.177322
$817$	2.36823	0.0828538
$818$	−1.54551	−0.0540374
$819$	0	0
$820$	7.19888	0.251396
$821$	50.6000	1.76595	0.882977	−	0.469416i	$-0.155536\pi$
$821$	50.6000	1.76595	0.882977	+	0.469416i	$0.155536\pi$
$822$	9.32094	0.325105
$823$	0.398599	0.0138943	0.00694714	−	0.999976i	$-0.497789\pi$
$823$	0.398599	0.0138943	0.00694714	+	0.999976i	$0.497789\pi$
$824$	−7.42345	−0.258608
$825$	0	0
$826$	0	0
$827$	20.4234	0.710193	0.355096	−	0.934830i	$-0.384448\pi$
$827$	20.4234	0.710193	0.355096	+	0.934830i	$0.384448\pi$
$828$	−3.44414	−0.119692
$829$	−23.2633	−0.807968	−0.403984	−	0.914766i	$-0.632375\pi$
$829$	−23.2633	−0.807968	−0.403984	+	0.914766i	$0.632375\pi$
$830$	−0.393308	−0.0136519
$831$	50.9819	1.76854
$832$	3.36317	0.116597
$833$	0	0
$834$	−13.5913	−0.470628
$835$	−65.0165	−2.24999
$836$	0	0
$837$	31.7263	1.09662
$838$	−6.10053	−0.210739
$839$	−16.4861	−0.569165	−0.284582	−	0.958652i	$-0.591855\pi$
$839$	−16.4861	−0.569165	−0.284582	+	0.958652i	$0.591855\pi$
$840$	0	0
$841$	−19.5132	−0.672869
$842$	25.6291	0.883238
$843$	−30.1069	−1.03694
$844$	18.9829	0.653417
$845$	−78.3521	−2.69540
$846$	0.714253	0.0245565
$847$	0	0
$848$	14.7514	0.506566
$849$	30.7290	1.05462
$850$	−8.41574	−0.288658
$851$	−15.0827	−0.517029
$852$	25.8563	0.885823
$853$	14.8315	0.507820	0.253910	−	0.967228i	$-0.418283\pi$
$853$	14.8315	0.507820	0.253910	+	0.967228i	$0.418283\pi$
$854$	0	0
$855$	3.47073	0.118696
$856$	11.1705	0.381799
$857$	5.03188	0.171886	0.0859428	−	0.996300i	$-0.472610\pi$
$857$	5.03188	0.171886	0.0859428	+	0.996300i	$0.472610\pi$
$858$	0	0
$859$	−56.0363	−1.91193	−0.955966	−	0.293477i	$-0.905188\pi$
$859$	−56.0363	−1.91193	−0.955966	+	0.293477i	$0.905188\pi$
$860$	−8.95272	−0.305285
$861$	0	0
$862$	−2.49649	−0.0850307
$863$	−36.4760	−1.24166	−0.620829	−	0.783946i	$-0.713204\pi$
$863$	−36.4760	−1.24166	−0.620829	+	0.783946i	$0.713204\pi$
$864$	25.7065	0.874555
$865$	69.8108	2.37364
$866$	−5.39769	−0.183421
$867$	−27.2600	−0.925798
$868$	0	0
$869$	0	0
$870$	−13.8020	−0.467932
$871$	−58.0844	−1.96812
$872$	34.8744	1.18100
$873$	6.39331	0.216381
$874$	3.25146	0.109982
$875$	0	0
$876$	13.6834	0.462321
$877$	6.61613	0.223411	0.111705	−	0.993741i	$-0.464369\pi$
$877$	6.61613	0.223411	0.111705	+	0.993741i	$0.464369\pi$
$878$	2.98195	0.100636
$879$	−29.3253	−0.989119
$880$	0	0
$881$	−22.5286	−0.759008	−0.379504	−	0.925190i	$-0.623905\pi$
$881$	−22.5286	−0.759008	−0.379504	+	0.925190i	$0.623905\pi$
$882$	0	0
$883$	−51.1652	−1.72185	−0.860923	−	0.508735i	$-0.830113\pi$
$883$	−51.1652	−1.72185	−0.860923	+	0.508735i	$0.830113\pi$
$884$	−15.3658	−0.516808
$885$	−60.4098	−2.03065
$886$	−9.02485	−0.303196
$887$	6.33809	0.212812	0.106406	−	0.994323i	$-0.466066\pi$
$887$	6.33809	0.212812	0.106406	+	0.994323i	$0.466066\pi$
$888$	−20.2151	−0.678375
$889$	0	0
$890$	−6.01979	−0.201784
$891$	0	0
$892$	−24.5156	−0.820843
$893$	2.45359	0.0821061
$894$	−1.25561	−0.0419938
$895$	−11.5913	−0.387454
$896$	0	0
$897$	37.7987	1.26206
$898$	−14.1608	−0.472552
$899$	21.8071	0.727307
$900$	−7.96986	−0.265662
$901$	15.2831	0.509154
$902$	0	0
$903$	0	0
$904$	29.1592	0.969821
$905$	36.9045	1.22675
$906$	20.6214	0.685101
$907$	−6.88474	−0.228604	−0.114302	−	0.993446i	$-0.536463\pi$
$907$	−6.88474	−0.228604	−0.114302	+	0.993446i	$0.536463\pi$
$908$	−24.5818	−0.815777
$909$	−1.21777	−0.0403908
$910$	0	0
$911$	−41.0818	−1.36110	−0.680550	−	0.732701i	$-0.738259\pi$
$911$	−41.0818	−1.36110	−0.680550	+	0.732701i	$0.738259\pi$
$912$	−4.52859	−0.149957
$913$	0	0
$914$	−2.17048	−0.0717932
$915$	−45.6335	−1.50860
$916$	8.74084	0.288805
$917$	0	0
$918$	4.87439	0.160879
$919$	11.6265	0.383522	0.191761	−	0.981442i	$-0.438580\pi$
$919$	11.6265	0.383522	0.191761	+	0.981442i	$0.438580\pi$
$920$	−27.9612	−0.921855
$921$	31.4958	1.03782
$922$	−21.1119	−0.695285
$923$	−50.9562	−1.67724
$924$	0	0
$925$	−34.9019	−1.14757
$926$	−3.82272	−0.125622
$927$	−2.08007	−0.0683184
$928$	17.6694	0.580026
$929$	24.7668	0.812573	0.406287	−	0.913746i	$-0.366823\pi$
$929$	24.7668	0.812573	0.406287	+	0.913746i	$0.366823\pi$
$930$	−31.7263	−1.04035
$931$	0	0
$932$	−30.2402	−0.990551
$933$	41.3598	1.35406
$934$	3.94940	0.129228
$935$	0	0
$936$	9.09721	0.297352
$937$	−1.15046	−0.0375839	−0.0187920	−	0.999823i	$-0.505982\pi$
$937$	−1.15046	−0.0375839	−0.0187920	+	0.999823i	$0.505982\pi$
$938$	0	0
$939$	31.3381	1.02268
$940$	−9.27540	−0.302530
$941$	−10.1102	−0.329583	−0.164792	−	0.986328i	$-0.552695\pi$
$941$	−10.1102	−0.329583	−0.164792	+	0.986328i	$0.552695\pi$
$942$	14.3779	0.468457
$943$	4.29874	0.139986
$944$	14.1542	0.460679
$945$	0	0
$946$	0	0
$947$	−24.4553	−0.794691	−0.397346	−	0.917669i	$-0.630069\pi$
$947$	−24.4553	−0.794691	−0.397346	+	0.917669i	$0.630069\pi$
$948$	−19.1799	−0.622935
$949$	−26.9665	−0.875371
$950$	7.52398	0.244110
$951$	8.53101	0.276637
$952$	0	0
$953$	16.1696	0.523784	0.261892	−	0.965097i	$-0.415654\pi$
$953$	16.1696	0.523784	0.261892	+	0.965097i	$0.415654\pi$
$954$	−3.97757	−0.128778
$955$	−35.7686	−1.15744
$956$	−34.7618	−1.12428
$957$	0	0
$958$	11.2512	0.363511
$959$	0	0
$960$	−3.88209	−0.125294
$961$	19.1274	0.617011
$962$	17.5130	0.564640
$963$	3.13000	0.100863
$964$	−31.1799	−1.00424
$965$	90.3823	2.90951
$966$	0	0
$967$	1.55941	0.0501472	0.0250736	−	0.999686i	$-0.492018\pi$
$967$	1.55941	0.0501472	0.0250736	+	0.999686i	$0.492018\pi$
$968$	0	0
$969$	−4.69182	−0.150723
$970$	22.8168	0.732602
$971$	−9.04728	−0.290341	−0.145171	−	0.989407i	$-0.546373\pi$
$971$	−9.04728	−0.290341	−0.145171	+	0.989407i	$0.546373\pi$
$972$	10.5257	0.337613
$973$	0	0
$974$	−3.75209	−0.120225
$975$	87.4674	2.80120
$976$	10.6920	0.342244
$977$	−6.75648	−0.216159	−0.108079	−	0.994142i	$-0.534470\pi$
$977$	−6.75648	−0.216159	−0.108079	+	0.994142i	$0.534470\pi$
$978$	11.2248	0.358929
$979$	0	0
$980$	0	0
$981$	9.77188	0.311992
$982$	15.8031	0.504297
$983$	26.4305	0.843001	0.421501	−	0.906828i	$-0.361504\pi$
$983$	26.4305	0.843001	0.421501	+	0.906828i	$0.361504\pi$
$984$	5.76154	0.183671
$985$	−87.7257	−2.79517
$986$	3.35041	0.106699
$987$	0	0
$988$	13.7376	0.437051
$989$	−5.34602	−0.169994
$990$	0	0
$991$	−0.634185	−0.0201456	−0.0100728	−	0.999949i	$-0.503206\pi$
$991$	−0.634185	−0.0201456	−0.0100728	+	0.999949i	$0.503206\pi$
$992$	40.6161	1.28956
$993$	36.4080	1.15537
$994$	0	0
$995$	−19.9545	−0.632599
$996$	0.503514	0.0159544
$997$	−10.1274	−0.320736	−0.160368	−	0.987057i	$-0.551268\pi$
$997$	−10.1274	−0.320736	−0.160368	+	0.987057i	$0.551268\pi$
$998$	−7.08445	−0.224254
$999$	20.2151	0.639578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.v.1.2		3
7.2	even	3		847.2.e.d.606.2		6
7.4	even	3		847.2.e.d.485.2		6
7.6	odd	2		5929.2.a.w.1.2		3
11.10	odd	2		539.2.a.h.1.2		3
33.32	even	2		4851.2.a.bo.1.2		3
44.43	even	2		8624.2.a.cl.1.1		3
77.2	odd	30		847.2.n.e.81.2		24
77.4	even	15		847.2.n.d.632.2		24
77.9	even	15		847.2.n.d.81.2		24
77.10	even	6		539.2.e.l.177.2		6
77.16	even	15		847.2.n.d.487.2		24
77.18	odd	30		847.2.n.e.632.2		24
77.25	even	15		847.2.n.d.9.2		24
77.30	odd	30		847.2.n.e.130.2		24
77.32	odd	6		77.2.e.b.23.2	✓	6
77.37	even	15		847.2.n.d.753.2		24
77.39	odd	30		847.2.n.e.366.2		24
77.46	odd	30		847.2.n.e.807.2		24
77.51	odd	30		847.2.n.e.753.2		24
77.53	even	15		847.2.n.d.807.2		24
77.54	even	6		539.2.e.l.67.2		6
77.58	even	15		847.2.n.d.130.2		24
77.60	even	15		847.2.n.d.366.2		24
77.65	odd	6		77.2.e.b.67.2	yes	6
77.72	odd	30		847.2.n.e.487.2		24
77.74	odd	30		847.2.n.e.9.2		24
77.76	even	2		539.2.a.i.1.2		3
231.32	even	6		693.2.i.g.100.2		6
231.65	even	6		693.2.i.g.298.2		6
231.230	odd	2		4851.2.a.bn.1.2		3
308.219	even	6		1232.2.q.k.529.3		6
308.263	even	6		1232.2.q.k.177.3		6
308.307	odd	2		8624.2.a.ck.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.2	✓	6	77.32	odd	6
77.2.e.b.67.2	yes	6	77.65	odd	6
539.2.a.h.1.2		3	11.10	odd	2
539.2.a.i.1.2		3	77.76	even	2
539.2.e.l.67.2		6	77.54	even	6
539.2.e.l.177.2		6	77.10	even	6
693.2.i.g.100.2		6	231.32	even	6
693.2.i.g.298.2		6	231.65	even	6
847.2.e.d.485.2		6	7.4	even	3
847.2.e.d.606.2		6	7.2	even	3
847.2.n.d.9.2		24	77.25	even	15
847.2.n.d.81.2		24	77.9	even	15
847.2.n.d.130.2		24	77.58	even	15
847.2.n.d.366.2		24	77.60	even	15
847.2.n.d.487.2		24	77.16	even	15
847.2.n.d.632.2		24	77.4	even	15
847.2.n.d.753.2		24	77.37	even	15
847.2.n.d.807.2		24	77.53	even	15
847.2.n.e.9.2		24	77.74	odd	30
847.2.n.e.81.2		24	77.2	odd	30
847.2.n.e.130.2		24	77.30	odd	30
847.2.n.e.366.2		24	77.39	odd	30
847.2.n.e.487.2		24	77.72	odd	30
847.2.n.e.632.2		24	77.18	odd	30
847.2.n.e.753.2		24	77.51	odd	30
847.2.n.e.807.2		24	77.46	odd	30
1232.2.q.k.177.3		6	308.263	even	6
1232.2.q.k.529.3		6	308.219	even	6
4851.2.a.bn.1.2		3	231.230	odd	2
4851.2.a.bo.1.2		3	33.32	even	2
5929.2.a.v.1.2		3	1.1	even	1	trivial
5929.2.a.w.1.2		3	7.6	odd	2
8624.2.a.ck.1.3		3	308.307	odd	2
8624.2.a.cl.1.1		3	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q-0.656620 q^{2} +1.91223 q^{3} -1.56885 q^{4} -3.56885 q^{5} -1.25561 q^{6} +2.34338 q^{8} +0.656620 q^{9} +O(q^{10})\)	\(q-0.656620 q^{2} +1.91223 q^{3} -1.56885 q^{4} -3.56885 q^{5} -1.25561 q^{6} +2.34338 q^{8} +0.656620 q^{9} +2.34338 q^{10} -3.00000 q^{12} +5.91223 q^{13} -6.82446 q^{15} +1.59899 q^{16} +1.65662 q^{17} -0.431150 q^{18} -1.48108 q^{19} +5.59899 q^{20} +3.34338 q^{23} +4.48108 q^{24} +7.73669 q^{25} -3.88209 q^{26} -4.48108 q^{27} -3.08007 q^{29} +4.48108 q^{30} -7.08007 q^{31} -5.73669 q^{32} -1.08777 q^{34} -1.03014 q^{36} -4.51122 q^{37} +0.972507 q^{38} +11.3055 q^{39} -8.36317 q^{40} +1.28575 q^{41} -1.59899 q^{43} -2.34338 q^{45} -2.19533 q^{46} -1.65662 q^{47} +3.05763 q^{48} -5.08007 q^{50} +3.16784 q^{51} -9.27540 q^{52} +9.22547 q^{53} +2.94237 q^{54} -2.83216 q^{57} +2.02243 q^{58} +8.85195 q^{59} +10.7065 q^{60} +6.68676 q^{61} +4.64892 q^{62} +0.568850 q^{64} -21.0999 q^{65} -9.82446 q^{67} -2.59899 q^{68} +6.39331 q^{69} -8.61878 q^{71} +1.53871 q^{72} -4.56115 q^{73} +2.96216 q^{74} +14.7943 q^{75} +2.32359 q^{76} -7.42345 q^{78} +6.39331 q^{79} -5.70655 q^{80} -10.5387 q^{81} -0.844248 q^{82} -0.167838 q^{83} -5.91223 q^{85} +1.04993 q^{86} -5.88979 q^{87} -2.56885 q^{89} +1.53871 q^{90} -5.24526 q^{92} -13.5387 q^{93} +1.08777 q^{94} +5.28575 q^{95} -10.9699 q^{96} +9.73669 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{3} + 4 q^{4} - 2 q^{5} + q^{6} + 9 q^{8}+O(q^{10}) \) 3 * q - q^3 + 4 * q^4 - 2 * q^5 + q^6 + 9 * q^8	\( 3 q - q^{3} + 4 q^{4} - 2 q^{5} + q^{6} + 9 q^{8} + 9 q^{10} - 9 q^{12} + 11 q^{13} - 7 q^{15} + 2 q^{16} + 3 q^{17} - 10 q^{18} + 11 q^{19} + 14 q^{20} + 12 q^{23} - 2 q^{24} + 3 q^{25} + q^{26} + 2 q^{27} + 9 q^{29} - 2 q^{30} - 3 q^{31} + 3 q^{32} - 10 q^{34} - 9 q^{36} - 4 q^{37} + 8 q^{38} + 5 q^{39} + 3 q^{40} + 5 q^{41} - 2 q^{43} - 9 q^{45} + 10 q^{46} - 3 q^{47} + 10 q^{48} + 3 q^{50} - 2 q^{51} + 7 q^{52} + 17 q^{53} + 8 q^{54} - 20 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} + 24 q^{61} - 13 q^{62} - 7 q^{64} - 15 q^{65} - 16 q^{67} - 5 q^{68} - 3 q^{69} + 7 q^{71} - 10 q^{72} + 20 q^{73} - 22 q^{74} + 25 q^{75} + 39 q^{76} - 6 q^{78} - 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 11 q^{83} - 11 q^{85} - 21 q^{86} - 30 q^{87} + q^{89} - 10 q^{90} + 25 q^{92} - 26 q^{93} + 10 q^{94} + 17 q^{95} - 27 q^{96} + 9 q^{97}+O(q^{100}) \) 3 * q - q^3 + 4 * q^4 - 2 * q^5 + q^6 + 9 * q^8 + 9 * q^10 - 9 * q^12 + 11 * q^13 - 7 * q^15 + 2 * q^16 + 3 * q^17 - 10 * q^18 + 11 * q^19 + 14 * q^20 + 12 * q^23 - 2 * q^24 + 3 * q^25 + q^26 + 2 * q^27 + 9 * q^29 - 2 * q^30 - 3 * q^31 + 3 * q^32 - 10 * q^34 - 9 * q^36 - 4 * q^37 + 8 * q^38 + 5 * q^39 + 3 * q^40 + 5 * q^41 - 2 * q^43 - 9 * q^45 + 10 * q^46 - 3 * q^47 + 10 * q^48 + 3 * q^50 - 2 * q^51 + 7 * q^52 + 17 * q^53 + 8 * q^54 - 20 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 + 24 * q^61 - 13 * q^62 - 7 * q^64 - 15 * q^65 - 16 * q^67 - 5 * q^68 - 3 * q^69 + 7 * q^71 - 10 * q^72 + 20 * q^73 - 22 * q^74 + 25 * q^75 + 39 * q^76 - 6 * q^78 - 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 11 * q^83 - 11 * q^85 - 21 * q^86 - 30 * q^87 + q^89 - 10 * q^90 + 25 * q^92 - 26 * q^93 + 10 * q^94 + 17 * q^95 - 27 * q^96 + 9 * q^97

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