LMFDB - Embedded newform 931.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 57x^6 - 98x^5 - 93x^4 + 152x^3 + 39x^2 - 58*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.58984$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58984 q^{2} -1.33784 q^{3} +0.527606 q^{4} -0.921074 q^{5} +2.12696 q^{6} +2.34088 q^{8} -1.21017 q^{9} +O(q^{10})$	\(q-1.58984 q^{2} -1.33784 q^{3} +0.527606 q^{4} -0.921074 q^{5} +2.12696 q^{6} +2.34088 q^{8} -1.21017 q^{9} +1.46436 q^{10} -4.89445 q^{11} -0.705855 q^{12} -2.00945 q^{13} +1.23225 q^{15} -4.77684 q^{16} +4.36499 q^{17} +1.92399 q^{18} +1.00000 q^{19} -0.485964 q^{20} +7.78141 q^{22} -2.75694 q^{23} -3.13173 q^{24} -4.15162 q^{25} +3.19471 q^{26} +5.63256 q^{27} -1.04504 q^{29} -1.95909 q^{30} -7.63918 q^{31} +2.91269 q^{32} +6.54800 q^{33} -6.93965 q^{34} -0.638496 q^{36} -4.59760 q^{37} -1.58984 q^{38} +2.68833 q^{39} -2.15612 q^{40} -1.06899 q^{41} -3.09076 q^{43} -2.58234 q^{44} +1.11466 q^{45} +4.38311 q^{46} +2.37859 q^{47} +6.39067 q^{48} +6.60044 q^{50} -5.83967 q^{51} -1.06020 q^{52} +11.3241 q^{53} -8.95489 q^{54} +4.50815 q^{55} -1.33784 q^{57} +1.66145 q^{58} +8.49491 q^{59} +0.650145 q^{60} +9.80934 q^{61} +12.1451 q^{62} +4.92297 q^{64} +1.85085 q^{65} -10.4103 q^{66} -1.77700 q^{67} +2.30300 q^{68} +3.68836 q^{69} +4.03345 q^{71} -2.83287 q^{72} +8.39827 q^{73} +7.30947 q^{74} +5.55422 q^{75} +0.527606 q^{76} -4.27402 q^{78} +12.0311 q^{79} +4.39983 q^{80} -3.90496 q^{81} +1.69953 q^{82} +5.56817 q^{83} -4.02048 q^{85} +4.91383 q^{86} +1.39810 q^{87} -11.4573 q^{88} +5.54181 q^{89} -1.77214 q^{90} -1.45458 q^{92} +10.2200 q^{93} -3.78159 q^{94} -0.921074 q^{95} -3.89672 q^{96} +3.89678 q^{97} +5.92313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.58984	−1.12419	−0.562095	−	0.827073i	$-0.690004\pi$
$2$	−1.58984	−1.12419	−0.562095	+	0.827073i	$0.690004\pi$
$3$	−1.33784	−0.772404	−0.386202	−	0.922414i	$-0.626213\pi$
$3$	−1.33784	−0.772404	−0.386202	+	0.922414i	$0.626213\pi$
$4$	0.527606	0.263803
$5$	−0.921074	−0.411917	−0.205958	−	0.978561i	$-0.566031\pi$
$5$	−0.921074	−0.411917	−0.205958	+	0.978561i	$0.566031\pi$
$6$	2.12696	0.868329
$7$	0	0
$7$	0	0
$8$	2.34088	0.827625
$9$	−1.21017	−0.403391
$10$	1.46436	0.463073
$11$	−4.89445	−1.47573	−0.737865	−	0.674948i	$-0.764166\pi$
$11$	−4.89445	−1.47573	−0.737865	+	0.674948i	$0.764166\pi$
$12$	−0.705855	−0.203763
$13$	−2.00945	−0.557321	−0.278660	−	0.960390i	$-0.589890\pi$
$13$	−2.00945	−0.557321	−0.278660	+	0.960390i	$0.589890\pi$
$14$	0	0
$15$	1.23225	0.318166
$16$	−4.77684	−1.19421
$17$	4.36499	1.05866	0.529332	−	0.848415i	$-0.322442\pi$
$17$	4.36499	1.05866	0.529332	+	0.848415i	$0.322442\pi$
$18$	1.92399	0.453489
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.485964	−0.108665
$21$	0	0
$22$	7.78141	1.65900
$23$	−2.75694	−0.574862	−0.287431	−	0.957801i	$-0.592801\pi$
$23$	−2.75694	−0.574862	−0.287431	+	0.957801i	$0.592801\pi$
$24$	−3.13173	−0.639261
$25$	−4.15162	−0.830325
$26$	3.19471	0.626534
$27$	5.63256	1.08399
$28$	0	0
$29$	−1.04504	−0.194059	−0.0970296	−	0.995281i	$-0.530934\pi$
$29$	−1.04504	−0.194059	−0.0970296	+	0.995281i	$0.530934\pi$
$30$	−1.95909	−0.357679
$31$	−7.63918	−1.37204	−0.686019	−	0.727584i	$-0.740643\pi$
$31$	−7.63918	−1.37204	−0.686019	+	0.727584i	$0.740643\pi$
$32$	2.91269	0.514895
$33$	6.54800	1.13986
$34$	−6.93965	−1.19014
$35$	0	0
$36$	−0.638496	−0.106416
$37$	−4.59760	−0.755841	−0.377920	−	0.925838i	$-0.623361\pi$
$37$	−4.59760	−0.755841	−0.377920	+	0.925838i	$0.623361\pi$
$38$	−1.58984	−0.257907
$39$	2.68833	0.430477
$40$	−2.15612	−0.340913
$41$	−1.06899	−0.166948	−0.0834742	−	0.996510i	$-0.526602\pi$
$41$	−1.06899	−0.166948	−0.0834742	+	0.996510i	$0.526602\pi$
$42$	0	0
$43$	−3.09076	−0.471337	−0.235668	−	0.971834i	$-0.575728\pi$
$43$	−3.09076	−0.471337	−0.235668	+	0.971834i	$0.575728\pi$
$44$	−2.58234	−0.389303
$45$	1.11466	0.166164
$46$	4.38311	0.646254
$47$	2.37859	0.346953	0.173477	−	0.984838i	$-0.444500\pi$
$47$	2.37859	0.346953	0.173477	+	0.984838i	$0.444500\pi$
$48$	6.39067	0.922414
$49$	0	0
$50$	6.60044	0.933443
$51$	−5.83967	−0.817717
$52$	−1.06020	−0.147023
$53$	11.3241	1.55549	0.777745	−	0.628579i	$-0.216363\pi$
$53$	11.3241	1.55549	0.777745	+	0.628579i	$0.216363\pi$
$54$	−8.95489	−1.21861
$55$	4.50815	0.607878
$56$	0	0
$57$	−1.33784	−0.177202
$58$	1.66145	0.218159
$59$	8.49491	1.10594	0.552972	−	0.833200i	$-0.313494\pi$
$59$	8.49491	1.10594	0.552972	+	0.833200i	$0.313494\pi$
$60$	0.650145	0.0839333
$61$	9.80934	1.25596	0.627979	−	0.778230i	$-0.283882\pi$
$61$	9.80934	1.25596	0.627979	+	0.778230i	$0.283882\pi$
$62$	12.1451	1.54243
$63$	0	0
$64$	4.92297	0.615371
$65$	1.85085	0.229570
$66$	−10.4103	−1.28142
$67$	−1.77700	−0.217095	−0.108548	−	0.994091i	$-0.534620\pi$
$67$	−1.77700	−0.217095	−0.108548	+	0.994091i	$0.534620\pi$
$68$	2.30300	0.279279
$69$	3.68836	0.444026
$70$	0	0
$71$	4.03345	0.478683	0.239341	−	0.970935i	$-0.423068\pi$
$71$	4.03345	0.478683	0.239341	+	0.970935i	$0.423068\pi$
$72$	−2.83287	−0.333857
$73$	8.39827	0.982943	0.491472	−	0.870894i	$-0.336459\pi$
$73$	8.39827	0.982943	0.491472	+	0.870894i	$0.336459\pi$
$74$	7.30947	0.849709
$75$	5.55422	0.641346
$76$	0.527606	0.0605206
$77$	0	0
$78$	−4.27402	−0.483938
$79$	12.0311	1.35361	0.676804	−	0.736163i	$-0.263364\pi$
$79$	12.0311	1.35361	0.676804	+	0.736163i	$0.263364\pi$
$80$	4.39983	0.491916
$81$	−3.90496	−0.433884
$82$	1.69953	0.187682
$83$	5.56817	0.611186	0.305593	−	0.952162i	$-0.401145\pi$
$83$	5.56817	0.611186	0.305593	+	0.952162i	$0.401145\pi$
$84$	0	0
$85$	−4.02048	−0.436082
$86$	4.91383	0.529872
$87$	1.39810	0.149892
$88$	−11.4573	−1.22135
$89$	5.54181	0.587431	0.293715	−	0.955893i	$-0.405108\pi$
$89$	5.54181	0.587431	0.293715	+	0.955893i	$0.405108\pi$
$90$	−1.77214	−0.186800
$91$	0	0
$92$	−1.45458	−0.151650
$93$	10.2200	1.05977
$94$	−3.78159	−0.390041
$95$	−0.921074	−0.0945002
$96$	−3.89672	−0.397707
$97$	3.89678	0.395658	0.197829	−	0.980237i	$-0.436611\pi$
$97$	3.89678	0.395658	0.197829	+	0.980237i	$0.436611\pi$
$98$	0	0
$99$	5.92313	0.595297
$100$	−2.19042	−0.219042
$101$	13.7798	1.37114	0.685569	−	0.728008i	$-0.259554\pi$
$101$	13.7798	1.37114	0.685569	+	0.728008i	$0.259554\pi$
$102$	9.28417	0.919270
$103$	−15.4644	−1.52375	−0.761876	−	0.647723i	$-0.775721\pi$
$103$	−15.4644	−1.52375	−0.761876	+	0.647723i	$0.775721\pi$
$104$	−4.70387	−0.461252
$105$	0	0
$106$	−18.0036	−1.74867
$107$	−5.43108	−0.525043	−0.262521	−	0.964926i	$-0.584554\pi$
$107$	−5.43108	−0.525043	−0.262521	+	0.964926i	$0.584554\pi$
$108$	2.97177	0.285959
$109$	5.66759	0.542856	0.271428	−	0.962459i	$-0.412504\pi$
$109$	5.66759	0.542856	0.271428	+	0.962459i	$0.412504\pi$
$110$	−7.16725	−0.683371
$111$	6.15087	0.583815
$112$	0	0
$113$	−16.4755	−1.54988	−0.774941	−	0.632034i	$-0.782220\pi$
$113$	−16.4755	−1.54988	−0.774941	+	0.632034i	$0.782220\pi$
$114$	2.12696	0.199208
$115$	2.53935	0.236795
$116$	−0.551370	−0.0511934
$117$	2.43178	0.224818
$118$	−13.5056	−1.24329
$119$	0	0
$120$	2.88455	0.263322
$121$	12.9556	1.17778
$122$	−15.5953	−1.41194
$123$	1.43014	0.128952
$124$	−4.03048	−0.361948
$125$	8.42932	0.753941
$126$	0	0
$127$	−16.6318	−1.47583	−0.737916	−	0.674893i	$-0.764190\pi$
$127$	−16.6318	−1.47583	−0.737916	+	0.674893i	$0.764190\pi$
$128$	−13.6521	−1.20669
$129$	4.13496	0.364063
$130$	−2.94256	−0.258080
$131$	19.2102	1.67840	0.839201	−	0.543821i	$-0.183023\pi$
$131$	19.2102	1.67840	0.839201	+	0.543821i	$0.183023\pi$
$132$	3.45477	0.300699
$133$	0	0
$134$	2.82515	0.244056
$135$	−5.18800	−0.446512
$136$	10.2179	0.876178
$137$	−13.7573	−1.17537	−0.587685	−	0.809090i	$-0.699960\pi$
$137$	−13.7573	−1.17537	−0.587685	+	0.809090i	$0.699960\pi$
$138$	−5.86391	−0.499170
$139$	−14.4092	−1.22217	−0.611085	−	0.791565i	$-0.709267\pi$
$139$	−14.4092	−1.22217	−0.611085	+	0.791565i	$0.709267\pi$
$140$	0	0
$141$	−3.18218	−0.267988
$142$	−6.41256	−0.538130
$143$	9.83513	0.822455
$144$	5.78081	0.481734
$145$	0.962560	0.0799362
$146$	−13.3519	−1.10502
$147$	0	0
$148$	−2.42572	−0.199393
$149$	16.6987	1.36801	0.684004	−	0.729478i	$-0.260237\pi$
$149$	16.6987	1.36801	0.684004	+	0.729478i	$0.260237\pi$
$150$	−8.83035	−0.720995
$151$	15.0737	1.22668	0.613339	−	0.789820i	$-0.289826\pi$
$151$	15.0737	1.22668	0.613339	+	0.789820i	$0.289826\pi$
$152$	2.34088	0.189870
$153$	−5.28239	−0.427056
$154$	0	0
$155$	7.03625	0.565165
$156$	1.41838	0.113561
$157$	−0.866746	−0.0691739	−0.0345869	−	0.999402i	$-0.511012\pi$
$157$	−0.866746	−0.0691739	−0.0345869	+	0.999402i	$0.511012\pi$
$158$	−19.1276	−1.52171
$159$	−15.1499	−1.20147
$160$	−2.68280	−0.212094
$161$	0	0
$162$	6.20827	0.487768
$163$	21.5909	1.69113	0.845563	−	0.533876i	$-0.179265\pi$
$163$	21.5909	1.69113	0.845563	+	0.533876i	$0.179265\pi$
$164$	−0.564007	−0.0440415
$165$	−6.03119	−0.469528
$166$	−8.85253	−0.687090
$167$	−1.10594	−0.0855800	−0.0427900	−	0.999084i	$-0.513625\pi$
$167$	−1.10594	−0.0855800	−0.0427900	+	0.999084i	$0.513625\pi$
$168$	0	0
$169$	−8.96212	−0.689394
$170$	6.39193	0.490239
$171$	−1.21017	−0.0925443
$172$	−1.63071	−0.124340
$173$	19.9412	1.51610	0.758051	−	0.652195i	$-0.226152\pi$
$173$	19.9412	1.51610	0.758051	+	0.652195i	$0.226152\pi$
$174$	−2.22276	−0.168507
$175$	0	0
$176$	23.3800	1.76233
$177$	−11.3649	−0.854235
$178$	−8.81062	−0.660384
$179$	−6.83473	−0.510852	−0.255426	−	0.966829i	$-0.582216\pi$
$179$	−6.83473	−0.510852	−0.255426	+	0.966829i	$0.582216\pi$
$180$	0.588102	0.0438345
$181$	−11.4381	−0.850190	−0.425095	−	0.905149i	$-0.639759\pi$
$181$	−11.4381	−0.850190	−0.425095	+	0.905149i	$0.639759\pi$
$182$	0	0
$183$	−13.1234	−0.970107
$184$	−6.45366	−0.475770
$185$	4.23473	0.311343
$186$	−16.2483	−1.19138
$187$	−21.3642	−1.56230
$188$	1.25496	0.0915274
$189$	0	0
$190$	1.46436	0.106236
$191$	−7.66755	−0.554804	−0.277402	−	0.960754i	$-0.589473\pi$
$191$	−7.66755	−0.554804	−0.277402	+	0.960754i	$0.589473\pi$
$192$	−6.58616	−0.475315
$193$	10.4449	0.751837	0.375919	−	0.926653i	$-0.377327\pi$
$193$	10.4449	0.751837	0.375919	+	0.926653i	$0.377327\pi$
$194$	−6.19527	−0.444794
$195$	−2.47615	−0.177321
$196$	0	0
$197$	24.5993	1.75263	0.876313	−	0.481743i	$-0.159996\pi$
$197$	24.5993	1.75263	0.876313	+	0.481743i	$0.159996\pi$
$198$	−9.41686	−0.669227
$199$	−1.73370	−0.122899	−0.0614494	−	0.998110i	$-0.519572\pi$
$199$	−1.73370	−0.122899	−0.0614494	+	0.998110i	$0.519572\pi$
$200$	−9.71844	−0.687197
$201$	2.37735	0.167685
$202$	−21.9077	−1.54142
$203$	0	0
$204$	−3.08105	−0.215716
$205$	0.984620	0.0687688
$206$	24.5860	1.71299
$207$	3.33638	0.231894
$208$	9.59882	0.665558
$209$	−4.89445	−0.338556
$210$	0	0
$211$	−14.5700	−1.00304	−0.501522	−	0.865145i	$-0.667226\pi$
$211$	−14.5700	−1.00304	−0.501522	+	0.865145i	$0.667226\pi$
$212$	5.97469	0.410343
$213$	−5.39613	−0.369737
$214$	8.63458	0.590248
$215$	2.84682	0.194152
$216$	13.1851	0.897134
$217$	0	0
$218$	−9.01058	−0.610274
$219$	−11.2356	−0.759230
$220$	2.37853	0.160360
$221$	−8.77121	−0.590016
$222$	−9.77893	−0.656319
$223$	−11.0288	−0.738546	−0.369273	−	0.929321i	$-0.620393\pi$
$223$	−11.0288	−0.738546	−0.369273	+	0.929321i	$0.620393\pi$
$224$	0	0
$225$	5.02419	0.334946
$226$	26.1934	1.74236
$227$	−23.9276	−1.58813	−0.794064	−	0.607834i	$-0.792039\pi$
$227$	−23.9276	−1.58813	−0.794064	+	0.607834i	$0.792039\pi$
$228$	−0.705855	−0.0467464
$229$	−25.2326	−1.66741	−0.833707	−	0.552207i	$-0.813786\pi$
$229$	−25.2326	−1.66741	−0.833707	+	0.552207i	$0.813786\pi$
$230$	−4.03717	−0.266203
$231$	0	0
$232$	−2.44631	−0.160608
$233$	17.5991	1.15296	0.576478	−	0.817113i	$-0.304427\pi$
$233$	17.5991	1.15296	0.576478	+	0.817113i	$0.304427\pi$
$234$	−3.86616	−0.252739
$235$	−2.19086	−0.142916
$236$	4.48197	0.291751
$237$	−16.0958	−1.04553
$238$	0	0
$239$	−5.01140	−0.324160	−0.162080	−	0.986778i	$-0.551820\pi$
$239$	−5.01140	−0.324160	−0.162080	+	0.986778i	$0.551820\pi$
$240$	−5.88628	−0.379958
$241$	3.06702	0.197564	0.0987819	−	0.995109i	$-0.468505\pi$
$241$	3.06702	0.197564	0.0987819	+	0.995109i	$0.468505\pi$
$242$	−20.5974	−1.32405
$243$	−11.6734	−0.748852
$244$	5.17547	0.331326
$245$	0	0
$246$	−2.27371	−0.144966
$247$	−2.00945	−0.127858
$248$	−17.8824	−1.13553
$249$	−7.44934	−0.472083
$250$	−13.4013	−0.847573
$251$	24.4585	1.54381	0.771903	−	0.635740i	$-0.219305\pi$
$251$	24.4585	1.54381	0.771903	+	0.635740i	$0.219305\pi$
$252$	0	0
$253$	13.4937	0.848342
$254$	26.4419	1.65912
$255$	5.37877	0.336831
$256$	11.8588	0.741177
$257$	−23.1609	−1.44474	−0.722369	−	0.691507i	$-0.756947\pi$
$257$	−23.1609	−1.44474	−0.722369	+	0.691507i	$0.756947\pi$
$258$	−6.57394	−0.409276
$259$	0	0
$260$	0.976520	0.0605612
$261$	1.26468	0.0782818
$262$	−30.5412	−1.88684
$263$	20.2172	1.24664	0.623322	−	0.781965i	$-0.285783\pi$
$263$	20.2172	1.24664	0.623322	+	0.781965i	$0.285783\pi$
$264$	15.3281	0.943377
$265$	−10.4304	−0.640733
$266$	0	0
$267$	−7.41408	−0.453734
$268$	−0.937557	−0.0572704
$269$	−11.0749	−0.675248	−0.337624	−	0.941281i	$-0.609623\pi$
$269$	−11.0749	−0.675248	−0.337624	+	0.941281i	$0.609623\pi$
$270$	8.24811	0.501964
$271$	−16.7966	−1.02032	−0.510160	−	0.860079i	$-0.670414\pi$
$271$	−16.7966	−1.02032	−0.510160	+	0.860079i	$0.670414\pi$
$272$	−20.8509	−1.26427
$273$	0	0
$274$	21.8720	1.32134
$275$	20.3199	1.22534
$276$	1.94600	0.117135
$277$	2.97484	0.178741	0.0893704	−	0.995998i	$-0.471515\pi$
$277$	2.97484	0.178741	0.0893704	+	0.995998i	$0.471515\pi$
$278$	22.9084	1.37395
$279$	9.24474	0.553468
$280$	0	0
$281$	20.4781	1.22162	0.610810	−	0.791777i	$-0.290844\pi$
$281$	20.4781	1.22162	0.610810	+	0.791777i	$0.290844\pi$
$282$	5.05918	0.301270
$283$	−15.3609	−0.913113	−0.456557	−	0.889694i	$-0.650917\pi$
$283$	−15.3609	−0.913113	−0.456557	+	0.889694i	$0.650917\pi$
$284$	2.12808	0.126278
$285$	1.23225	0.0729924
$286$	−15.6363	−0.924596
$287$	0	0
$288$	−3.52486	−0.207704
$289$	2.05311	0.120771
$290$	−1.53032	−0.0898635
$291$	−5.21328	−0.305608
$292$	4.43098	0.259304
$293$	−0.713696	−0.0416946	−0.0208473	−	0.999783i	$-0.506636\pi$
$293$	−0.713696	−0.0416946	−0.0208473	+	0.999783i	$0.506636\pi$
$294$	0	0
$295$	−7.82444	−0.455556
$296$	−10.7624	−0.625553
$297$	−27.5682	−1.59967
$298$	−26.5483	−1.53790
$299$	5.53993	0.320382
$300$	2.93044	0.169189
$301$	0	0
$302$	−23.9648	−1.37902
$303$	−18.4352	−1.05907
$304$	−4.77684	−0.273971
$305$	−9.03513	−0.517350
$306$	8.39819	0.480092
$307$	26.2825	1.50002	0.750012	−	0.661425i	$-0.230048\pi$
$307$	26.2825	1.50002	0.750012	+	0.661425i	$0.230048\pi$
$308$	0	0
$309$	20.6889	1.17695
$310$	−11.1865	−0.635353
$311$	15.7868	0.895189	0.447594	−	0.894237i	$-0.352281\pi$
$311$	15.7868	0.895189	0.447594	+	0.894237i	$0.352281\pi$
$312$	6.29304	0.356273
$313$	28.8711	1.63189	0.815946	−	0.578128i	$-0.196217\pi$
$313$	28.8711	1.63189	0.815946	+	0.578128i	$0.196217\pi$
$314$	1.37799	0.0777646
$315$	0	0
$316$	6.34771	0.357086
$317$	−28.9077	−1.62362	−0.811809	−	0.583922i	$-0.801517\pi$
$317$	−28.9077	−1.62362	−0.811809	+	0.583922i	$0.801517\pi$
$318$	24.0860	1.35068
$319$	5.11489	0.286379
$320$	−4.53442	−0.253482
$321$	7.26594	0.405545
$322$	0	0
$323$	4.36499	0.242874
$324$	−2.06028	−0.114460
$325$	8.34247	0.462757
$326$	−34.3261	−1.90115
$327$	−7.58234	−0.419305
$328$	−2.50238	−0.138171
$329$	0	0
$330$	9.58866	0.527838
$331$	16.3394	0.898096	0.449048	−	0.893508i	$-0.351763\pi$
$331$	16.3394	0.898096	0.449048	+	0.893508i	$0.351763\pi$
$332$	2.93780	0.161233
$333$	5.56390	0.304900
$334$	1.75827	0.0962082
$335$	1.63675	0.0894251
$336$	0	0
$337$	−7.75609	−0.422501	−0.211251	−	0.977432i	$-0.567754\pi$
$337$	−7.75609	−0.422501	−0.211251	+	0.977432i	$0.567754\pi$
$338$	14.2484	0.775010
$339$	22.0416	1.19713
$340$	−2.12123	−0.115040
$341$	37.3895	2.02476
$342$	1.92399	0.104037
$343$	0	0
$344$	−7.23510	−0.390090
$345$	−3.39725	−0.182902
$346$	−31.7034	−1.70439
$347$	24.5341	1.31706	0.658530	−	0.752554i	$-0.271178\pi$
$347$	24.5341	1.31706	0.658530	+	0.752554i	$0.271178\pi$
$348$	0.737647	0.0395420
$349$	30.5639	1.63605	0.818023	−	0.575185i	$-0.195070\pi$
$349$	30.5639	1.63605	0.818023	+	0.575185i	$0.195070\pi$
$350$	0	0
$351$	−11.3183	−0.604128
$352$	−14.2560	−0.759847
$353$	16.2887	0.866960	0.433480	−	0.901163i	$-0.357285\pi$
$353$	16.2887	0.866960	0.433480	+	0.901163i	$0.357285\pi$
$354$	18.0684	0.960323
$355$	−3.71511	−0.197177
$356$	2.92390	0.154966
$357$	0	0
$358$	10.8662	0.574295
$359$	−9.90106	−0.522558	−0.261279	−	0.965263i	$-0.584144\pi$
$359$	−9.90106	−0.522558	−0.261279	+	0.965263i	$0.584144\pi$
$360$	2.60928	0.137521
$361$	1.00000	0.0526316
$362$	18.1849	0.955775
$363$	−17.3326	−0.909723
$364$	0	0
$365$	−7.73543	−0.404891
$366$	20.8641	1.09058
$367$	−11.7221	−0.611888	−0.305944	−	0.952050i	$-0.598972\pi$
$367$	−11.7221	−0.611888	−0.305944	+	0.952050i	$0.598972\pi$
$368$	13.1695	0.686507
$369$	1.29367	0.0673455
$370$	−6.73256	−0.350009
$371$	0	0
$372$	5.39215	0.279570
$373$	18.7553	0.971114	0.485557	−	0.874205i	$-0.338617\pi$
$373$	18.7553	0.971114	0.485557	+	0.874205i	$0.338617\pi$
$374$	33.9657	1.75633
$375$	−11.2771	−0.582348
$376$	5.56799	0.287147
$377$	2.09996	0.108153
$378$	0	0
$379$	−37.9305	−1.94836	−0.974179	−	0.225779i	$-0.927507\pi$
$379$	−37.9305	−1.94836	−0.974179	+	0.225779i	$0.927507\pi$
$380$	−0.485964	−0.0249295
$381$	22.2507	1.13994
$382$	12.1902	0.623705
$383$	−23.0865	−1.17966	−0.589832	−	0.807526i	$-0.700806\pi$
$383$	−23.0865	−1.17966	−0.589832	+	0.807526i	$0.700806\pi$
$384$	18.2644	0.932052
$385$	0	0
$386$	−16.6057	−0.845208
$387$	3.74036	0.190133
$388$	2.05596	0.104376
$389$	−6.18005	−0.313341	−0.156670	−	0.987651i	$-0.550076\pi$
$389$	−6.18005	−0.313341	−0.156670	+	0.987651i	$0.550076\pi$
$390$	3.93669	0.199342
$391$	−12.0340	−0.608586
$392$	0	0
$393$	−25.7002	−1.29641
$394$	−39.1090	−1.97028
$395$	−11.0816	−0.557574
$396$	3.12508	0.157041
$397$	−6.16132	−0.309228	−0.154614	−	0.987975i	$-0.549413\pi$
$397$	−6.16132	−0.309228	−0.154614	+	0.987975i	$0.549413\pi$
$398$	2.75631	0.138162
$399$	0	0
$400$	19.8317	0.991583
$401$	−11.9645	−0.597478	−0.298739	−	0.954335i	$-0.596566\pi$
$401$	−11.9645	−0.597478	−0.298739	+	0.954335i	$0.596566\pi$
$402$	−3.77961	−0.188510
$403$	15.3505	0.764664
$404$	7.27029	0.361711
$405$	3.59675	0.178724
$406$	0	0
$407$	22.5027	1.11542
$408$	−13.6700	−0.676763
$409$	36.0597	1.78304	0.891518	−	0.452986i	$-0.149641\pi$
$409$	36.0597	1.78304	0.891518	+	0.452986i	$0.149641\pi$
$410$	−1.56539	−0.0773092
$411$	18.4052	0.907860
$412$	−8.15911	−0.401971
$413$	0	0
$414$	−5.30433	−0.260693
$415$	−5.12870	−0.251758
$416$	−5.85289	−0.286962
$417$	19.2772	0.944010
$418$	7.78141	0.380601
$419$	26.6207	1.30051	0.650253	−	0.759717i	$-0.274663\pi$
$419$	26.6207	1.30051	0.650253	+	0.759717i	$0.274663\pi$
$420$	0	0
$421$	27.3357	1.33226	0.666130	−	0.745836i	$-0.267950\pi$
$421$	27.3357	1.33226	0.666130	+	0.745836i	$0.267950\pi$
$422$	23.1641	1.12761
$423$	−2.87851	−0.139958
$424$	26.5084	1.28736
$425$	−18.1218	−0.879035
$426$	8.57901	0.415654
$427$	0	0
$428$	−2.86547	−0.138508
$429$	−13.1579	−0.635268
$430$	−4.52600	−0.218263
$431$	−18.5449	−0.893276	−0.446638	−	0.894715i	$-0.647379\pi$
$431$	−18.5449	−0.893276	−0.446638	+	0.894715i	$0.647379\pi$
$432$	−26.9058	−1.29451
$433$	16.8498	0.809748	0.404874	−	0.914372i	$-0.367315\pi$
$433$	16.8498	0.809748	0.404874	+	0.914372i	$0.367315\pi$
$434$	0	0
$435$	−1.28775	−0.0617431
$436$	2.99026	0.143207
$437$	−2.75694	−0.131882
$438$	17.8628	0.853518
$439$	−19.6943	−0.939959	−0.469980	−	0.882677i	$-0.655739\pi$
$439$	−19.6943	−0.939959	−0.469980	+	0.882677i	$0.655739\pi$
$440$	10.5530	0.503095
$441$	0	0
$442$	13.9449	0.663290
$443$	−25.0222	−1.18884	−0.594421	−	0.804154i	$-0.702619\pi$
$443$	−25.0222	−1.18884	−0.594421	+	0.804154i	$0.702619\pi$
$444$	3.24524	0.154012
$445$	−5.10442	−0.241973
$446$	17.5341	0.830266
$447$	−22.3402	−1.05666
$448$	0	0
$449$	2.86818	0.135358	0.0676788	−	0.997707i	$-0.478441\pi$
$449$	2.86818	0.135358	0.0676788	+	0.997707i	$0.478441\pi$
$450$	−7.98768	−0.376543
$451$	5.23212	0.246371
$452$	−8.69256	−0.408864
$453$	−20.1662	−0.947491
$454$	38.0411	1.78536
$455$	0	0
$456$	−3.13173	−0.146657
$457$	−0.343243	−0.0160562	−0.00802811	−	0.999968i	$-0.502555\pi$
$457$	−0.343243	−0.0160562	−0.00802811	+	0.999968i	$0.502555\pi$
$458$	40.1158	1.87449
$459$	24.5860	1.14758
$460$	1.33978	0.0624674
$461$	14.4944	0.675072	0.337536	−	0.941313i	$-0.390407\pi$
$461$	14.4944	0.675072	0.337536	+	0.941313i	$0.390407\pi$
$462$	0	0
$463$	−30.0295	−1.39559	−0.697795	−	0.716297i	$-0.745835\pi$
$463$	−30.0295	−1.39559	−0.697795	+	0.716297i	$0.745835\pi$
$464$	4.99200	0.231748
$465$	−9.41340	−0.436536
$466$	−27.9798	−1.29614
$467$	−13.2015	−0.610894	−0.305447	−	0.952209i	$-0.598806\pi$
$467$	−13.2015	−0.610894	−0.305447	+	0.952209i	$0.598806\pi$
$468$	1.28302	0.0593078
$469$	0	0
$470$	3.48312	0.160665
$471$	1.15957	0.0534302
$472$	19.8855	0.915306
$473$	15.1276	0.695566
$474$	25.5898	1.17538
$475$	−4.15162	−0.190490
$476$	0	0
$477$	−13.7042	−0.627472
$478$	7.96735	0.364418
$479$	−17.0291	−0.778080	−0.389040	−	0.921221i	$-0.627193\pi$
$479$	−17.0291	−0.778080	−0.389040	+	0.921221i	$0.627193\pi$
$480$	3.58917	0.163822
$481$	9.23864	0.421246
$482$	−4.87608	−0.222099
$483$	0	0
$484$	6.83545	0.310702
$485$	−3.58922	−0.162978
$486$	18.5590	0.841852
$487$	11.0041	0.498644	0.249322	−	0.968421i	$-0.419792\pi$
$487$	11.0041	0.498644	0.249322	+	0.968421i	$0.419792\pi$
$488$	22.9625	1.03946
$489$	−28.8852	−1.30623
$490$	0	0
$491$	32.1415	1.45053	0.725264	−	0.688471i	$-0.241718\pi$
$491$	32.1415	1.45053	0.725264	+	0.688471i	$0.241718\pi$
$492$	0.754553	0.0340179
$493$	−4.56159	−0.205444
$494$	3.19471	0.143737
$495$	−5.45564	−0.245213
$496$	36.4912	1.63850
$497$	0	0
$498$	11.8433	0.530711
$499$	10.0670	0.450659	0.225329	−	0.974283i	$-0.427654\pi$
$499$	10.0670	0.450659	0.225329	+	0.974283i	$0.427654\pi$
$500$	4.44736	0.198892
$501$	1.47957	0.0661024
$502$	−38.8852	−1.73553
$503$	12.2667	0.546944	0.273472	−	0.961880i	$-0.411828\pi$
$503$	12.2667	0.546944	0.273472	+	0.961880i	$0.411828\pi$
$504$	0	0
$505$	−12.6922	−0.564794
$506$	−21.4529	−0.953697
$507$	11.9899	0.532491
$508$	−8.77503	−0.389329
$509$	41.5323	1.84089	0.920444	−	0.390874i	$-0.127827\pi$
$509$	41.5323	1.84089	0.920444	+	0.390874i	$0.127827\pi$
$510$	−8.55141	−0.378663
$511$	0	0
$512$	8.45056	0.373466
$513$	5.63256	0.248683
$514$	36.8223	1.62416
$515$	14.2438	0.627659
$516$	2.18163	0.0960409
$517$	−11.6419	−0.512009
$518$	0	0
$519$	−26.6782	−1.17104
$520$	4.33261	0.189998
$521$	16.5432	0.724773	0.362386	−	0.932028i	$-0.381962\pi$
$521$	16.5432	0.724773	0.362386	+	0.932028i	$0.381962\pi$
$522$	−2.01065	−0.0880036
$523$	−16.5511	−0.723728	−0.361864	−	0.932231i	$-0.617859\pi$
$523$	−16.5511	−0.723728	−0.361864	+	0.932231i	$0.617859\pi$
$524$	10.1354	0.442768
$525$	0	0
$526$	−32.1422	−1.40147
$527$	−33.3449	−1.45253
$528$	−31.2788	−1.36123
$529$	−15.3993	−0.669534
$530$	16.5827	0.720305
$531$	−10.2803	−0.446128
$532$	0	0
$533$	2.14808	0.0930438
$534$	11.7872	0.510084
$535$	5.00243	0.216274
$536$	−4.15974	−0.179673
$537$	9.14380	0.394584
$538$	17.6074	0.759107
$539$	0	0
$540$	−2.73722	−0.117791
$541$	−23.2230	−0.998435	−0.499217	−	0.866477i	$-0.666379\pi$
$541$	−23.2230	−0.998435	−0.499217	+	0.866477i	$0.666379\pi$
$542$	26.7040	1.14703
$543$	15.3024	0.656691
$544$	12.7138	0.545101
$545$	−5.22027	−0.223612
$546$	0	0
$547$	18.8730	0.806953	0.403476	−	0.914990i	$-0.367802\pi$
$547$	18.8730	0.806953	0.403476	+	0.914990i	$0.367802\pi$
$548$	−7.25846	−0.310066
$549$	−11.8710	−0.506643
$550$	−32.3055	−1.37751
$551$	−1.04504	−0.0445202
$552$	8.63399	0.367487
$553$	0	0
$554$	−4.72954	−0.200939
$555$	−5.66541	−0.240483
$556$	−7.60238	−0.322413
$557$	−25.0658	−1.06207	−0.531037	−	0.847349i	$-0.678197\pi$
$557$	−25.0658	−1.06207	−0.531037	+	0.847349i	$0.678197\pi$
$558$	−14.6977	−0.622203
$559$	6.21073	0.262686
$560$	0	0
$561$	28.5819	1.20673
$562$	−32.5570	−1.37333
$563$	−38.5050	−1.62279	−0.811396	−	0.584497i	$-0.801292\pi$
$563$	−38.5050	−1.62279	−0.811396	+	0.584497i	$0.801292\pi$
$564$	−1.67894	−0.0706961
$565$	15.1751	0.638422
$566$	24.4215	1.02651
$567$	0	0
$568$	9.44182	0.396170
$569$	38.6595	1.62069	0.810345	−	0.585953i	$-0.199280\pi$
$569$	38.6595	1.62069	0.810345	+	0.585953i	$0.199280\pi$
$570$	−1.95909	−0.0820573
$571$	−10.0910	−0.422295	−0.211147	−	0.977454i	$-0.567720\pi$
$571$	−10.0910	−0.422295	−0.211147	+	0.977454i	$0.567720\pi$
$572$	5.18908	0.216966
$573$	10.2580	0.428533
$574$	0	0
$575$	11.4458	0.477322
$576$	−5.95765	−0.248235
$577$	−31.9815	−1.33141	−0.665705	−	0.746215i	$-0.731869\pi$
$577$	−31.9815	−1.33141	−0.665705	+	0.746215i	$0.731869\pi$
$578$	−3.26413	−0.135770
$579$	−13.9736	−0.580722
$580$	0.507853	0.0210874
$581$	0	0
$582$	8.28830	0.343561
$583$	−55.4254	−2.29549
$584$	19.6593	0.813508
$585$	−2.23985	−0.0926064
$586$	1.13467	0.0468726
$587$	−20.3512	−0.839984	−0.419992	−	0.907528i	$-0.637967\pi$
$587$	−20.3512	−0.839984	−0.419992	+	0.907528i	$0.637967\pi$
$588$	0	0
$589$	−7.63918	−0.314767
$590$	12.4396	0.512132
$591$	−32.9100	−1.35374
$592$	21.9620	0.902633
$593$	32.2562	1.32460	0.662302	−	0.749237i	$-0.269580\pi$
$593$	32.2562	1.32460	0.662302	+	0.749237i	$0.269580\pi$
$594$	43.8292	1.79833
$595$	0	0
$596$	8.81032	0.360885
$597$	2.31942	0.0949275
$598$	−8.80763	−0.360171
$599$	17.7020	0.723285	0.361643	−	0.932317i	$-0.382216\pi$
$599$	17.7020	0.723285	0.361643	+	0.932317i	$0.382216\pi$
$600$	13.0018	0.530794
$601$	−17.5840	−0.717266	−0.358633	−	0.933479i	$-0.616757\pi$
$601$	−17.5840	−0.717266	−0.358633	+	0.933479i	$0.616757\pi$
$602$	0	0
$603$	2.15048	0.0875743
$604$	7.95296	0.323601
$605$	−11.9331	−0.485148
$606$	29.3091	1.19060
$607$	38.2578	1.55284	0.776418	−	0.630218i	$-0.217034\pi$
$607$	38.2578	1.55284	0.776418	+	0.630218i	$0.217034\pi$
$608$	2.91269	0.118125
$609$	0	0
$610$	14.3645	0.581600
$611$	−4.77965	−0.193364
$612$	−2.78703	−0.112659
$613$	8.36322	0.337787	0.168894	−	0.985634i	$-0.445981\pi$
$613$	8.36322	0.337787	0.168894	+	0.985634i	$0.445981\pi$
$614$	−41.7851	−1.68631
$615$	−1.31727	−0.0531173
$616$	0	0
$617$	−6.16193	−0.248070	−0.124035	−	0.992278i	$-0.539584\pi$
$617$	−6.16193	−0.248070	−0.124035	+	0.992278i	$0.539584\pi$
$618$	−32.8922	−1.32312
$619$	−20.0432	−0.805603	−0.402801	−	0.915287i	$-0.631963\pi$
$619$	−20.0432	−0.805603	−0.402801	+	0.915287i	$0.631963\pi$
$620$	3.71237	0.149092
$621$	−15.5286	−0.623142
$622$	−25.0986	−1.00636
$623$	0	0
$624$	−12.8417	−0.514080
$625$	12.9941	0.519764
$626$	−45.9006	−1.83456
$627$	6.54800	0.261502
$628$	−0.457301	−0.0182483
$629$	−20.0685	−0.800182
$630$	0	0
$631$	6.98034	0.277883	0.138941	−	0.990301i	$-0.455630\pi$
$631$	6.98034	0.277883	0.138941	+	0.990301i	$0.455630\pi$
$632$	28.1634	1.12028
$633$	19.4924	0.774755
$634$	45.9588	1.82526
$635$	15.3191	0.607920
$636$	−7.99320	−0.316951
$637$	0	0
$638$	−8.13189	−0.321945
$639$	−4.88118	−0.193097
$640$	12.5746	0.497055
$641$	−27.4849	−1.08559	−0.542794	−	0.839866i	$-0.682634\pi$
$641$	−27.4849	−1.08559	−0.542794	+	0.839866i	$0.682634\pi$
$642$	−11.5517	−0.455910
$643$	34.2026	1.34882	0.674409	−	0.738358i	$-0.264398\pi$
$643$	34.2026	1.34882	0.674409	+	0.738358i	$0.264398\pi$
$644$	0	0
$645$	−3.80860	−0.149964
$646$	−6.93965	−0.273037
$647$	6.01536	0.236488	0.118244	−	0.992985i	$-0.462273\pi$
$647$	6.01536	0.236488	0.118244	+	0.992985i	$0.462273\pi$
$648$	−9.14102	−0.359093
$649$	−41.5779	−1.63207
$650$	−13.2632	−0.520227
$651$	0	0
$652$	11.3915	0.446125
$653$	−2.90207	−0.113567	−0.0567833	−	0.998387i	$-0.518084\pi$
$653$	−2.90207	−0.113567	−0.0567833	+	0.998387i	$0.518084\pi$
$654$	12.0548	0.471378
$655$	−17.6940	−0.691362
$656$	5.10640	0.199372
$657$	−10.1634	−0.396511
$658$	0	0
$659$	7.29792	0.284287	0.142143	−	0.989846i	$-0.454601\pi$
$659$	7.29792	0.284287	0.142143	+	0.989846i	$0.454601\pi$
$660$	−3.18210	−0.123863
$661$	49.1630	1.91222	0.956110	−	0.293008i	$-0.0946562\pi$
$661$	49.1630	1.91222	0.956110	+	0.293008i	$0.0946562\pi$
$662$	−25.9771	−1.00963
$663$	11.7345	0.455731
$664$	13.0344	0.505833
$665$	0	0
$666$	−8.84573	−0.342765
$667$	2.88112	0.111557
$668$	−0.583500	−0.0225763
$669$	14.7549	0.570456
$670$	−2.60218	−0.100531
$671$	−48.0113	−1.85346
$672$	0	0
$673$	25.3470	0.977054	0.488527	−	0.872549i	$-0.337534\pi$
$673$	25.3470	0.977054	0.488527	+	0.872549i	$0.337534\pi$
$674$	12.3310	0.474971
$675$	−23.3842	−0.900060
$676$	−4.72847	−0.181864
$677$	−12.4843	−0.479809	−0.239905	−	0.970796i	$-0.577116\pi$
$677$	−12.4843	−0.479809	−0.239905	+	0.970796i	$0.577116\pi$
$678$	−35.0427	−1.34581
$679$	0	0
$680$	−9.41144	−0.360912
$681$	32.0114	1.22668
$682$	−59.4436	−2.27621
$683$	−27.9149	−1.06813	−0.534066	−	0.845443i	$-0.679337\pi$
$683$	−27.9149	−1.06813	−0.534066	+	0.845443i	$0.679337\pi$
$684$	−0.638496	−0.0244135
$685$	12.6715	0.484154
$686$	0	0
$687$	33.7572	1.28792
$688$	14.7641	0.562876
$689$	−22.7553	−0.866907
$690$	5.40110	0.205616
$691$	42.3271	1.61020	0.805100	−	0.593140i	$-0.202112\pi$
$691$	42.3271	1.61020	0.805100	+	0.593140i	$0.202112\pi$
$692$	10.5211	0.399953
$693$	0	0
$694$	−39.0054	−1.48063
$695$	13.2719	0.503433
$696$	3.27278	0.124055
$697$	−4.66613	−0.176742
$698$	−48.5918	−1.83923
$699$	−23.5448	−0.890548
$700$	0	0
$701$	24.3827	0.920921	0.460460	−	0.887680i	$-0.347684\pi$
$701$	24.3827	0.920921	0.460460	+	0.887680i	$0.347684\pi$
$702$	17.9944	0.679154
$703$	−4.59760	−0.173402
$704$	−24.0952	−0.908122
$705$	2.93103	0.110389
$706$	−25.8965	−0.974628
$707$	0	0
$708$	−5.99617	−0.225350
$709$	−1.94001	−0.0728588	−0.0364294	−	0.999336i	$-0.511598\pi$
$709$	−1.94001	−0.0728588	−0.0364294	+	0.999336i	$0.511598\pi$
$710$	5.90645	0.221665
$711$	−14.5598	−0.546034
$712$	12.9727	0.486173
$713$	21.0608	0.788732
$714$	0	0
$715$	−9.05888	−0.338783
$716$	−3.60605	−0.134764
$717$	6.70447	0.250383
$718$	15.7411	0.587454
$719$	−27.4622	−1.02417	−0.512084	−	0.858935i	$-0.671126\pi$
$719$	−27.4622	−1.02417	−0.512084	+	0.858935i	$0.671126\pi$
$720$	−5.32456	−0.198434
$721$	0	0
$722$	−1.58984	−0.0591679
$723$	−4.10319	−0.152599
$724$	−6.03484	−0.224283
$725$	4.33862	0.161132
$726$	27.5561	1.02270
$727$	−18.7684	−0.696081	−0.348041	−	0.937479i	$-0.613153\pi$
$727$	−18.7684	−0.696081	−0.348041	+	0.937479i	$0.613153\pi$
$728$	0	0
$729$	27.3321	1.01230
$730$	12.2981	0.455174
$731$	−13.4911	−0.498988
$732$	−6.92397	−0.255917
$733$	38.2534	1.41292	0.706461	−	0.707752i	$-0.250290\pi$
$733$	38.2534	1.41292	0.706461	+	0.707752i	$0.250290\pi$
$734$	18.6363	0.687878
$735$	0	0
$736$	−8.03011	−0.295994
$737$	8.69743	0.320374
$738$	−2.05673	−0.0757092
$739$	43.0751	1.58454	0.792272	−	0.610168i	$-0.208898\pi$
$739$	43.0751	1.58454	0.792272	+	0.610168i	$0.208898\pi$
$740$	2.23427	0.0821334
$741$	2.68833	0.0987582
$742$	0	0
$743$	3.03951	0.111509	0.0557545	−	0.998445i	$-0.482244\pi$
$743$	3.03951	0.111509	0.0557545	+	0.998445i	$0.482244\pi$
$744$	23.9238	0.877090
$745$	−15.3807	−0.563505
$746$	−29.8181	−1.09172
$747$	−6.73846	−0.246547
$748$	−11.2719	−0.412141
$749$	0	0
$750$	17.9289	0.654669
$751$	−16.8163	−0.613634	−0.306817	−	0.951768i	$-0.599264\pi$
$751$	−16.8163	−0.613634	−0.306817	+	0.951768i	$0.599264\pi$
$752$	−11.3622	−0.414335
$753$	−32.7216	−1.19244
$754$	−3.33860	−0.121585
$755$	−13.8840	−0.505289
$756$	0	0
$757$	8.98576	0.326593	0.163296	−	0.986577i	$-0.447787\pi$
$757$	8.98576	0.326593	0.163296	+	0.986577i	$0.447787\pi$
$758$	60.3036	2.19032
$759$	−18.0525	−0.655263
$760$	−2.15612	−0.0782107
$761$	−15.5631	−0.564161	−0.282081	−	0.959391i	$-0.591025\pi$
$761$	−15.5631	−0.564161	−0.282081	+	0.959391i	$0.591025\pi$
$762$	−35.3752	−1.28151
$763$	0	0
$764$	−4.04545	−0.146359
$765$	4.86548	0.175912
$766$	36.7039	1.32617
$767$	−17.0701	−0.616365
$768$	−15.8653	−0.572488
$769$	51.5950	1.86056	0.930282	−	0.366844i	$-0.119562\pi$
$769$	51.5950	1.86056	0.930282	+	0.366844i	$0.119562\pi$
$770$	0	0
$771$	30.9857	1.11592
$772$	5.51077	0.198337
$773$	5.73561	0.206295	0.103148	−	0.994666i	$-0.467109\pi$
$773$	5.73561	0.206295	0.103148	+	0.994666i	$0.467109\pi$
$774$	−5.94660	−0.213746
$775$	31.7150	1.13924
$776$	9.12187	0.327456
$777$	0	0
$778$	9.82531	0.352255
$779$	−1.06899	−0.0383006
$780$	−1.30643	−0.0467778
$781$	−19.7415	−0.706407
$782$	19.1322	0.684167
$783$	−5.88625	−0.210357
$784$	0	0
$785$	0.798337	0.0284939
$786$	40.8594	1.45741
$787$	−5.15928	−0.183909	−0.0919543	−	0.995763i	$-0.529311\pi$
$787$	−5.15928	−0.183909	−0.0919543	+	0.995763i	$0.529311\pi$
$788$	12.9787	0.462348
$789$	−27.0474	−0.962914
$790$	17.6180	0.626819
$791$	0	0
$792$	13.8653	0.492683
$793$	−19.7114	−0.699971
$794$	9.79554	0.347631
$795$	13.9542	0.494905
$796$	−0.914711	−0.0324211
$797$	−3.73501	−0.132301	−0.0661505	−	0.997810i	$-0.521072\pi$
$797$	−3.73501	−0.132301	−0.0661505	+	0.997810i	$0.521072\pi$
$798$	0	0
$799$	10.3825	0.367307
$800$	−12.0924	−0.427530
$801$	−6.70656	−0.236965
$802$	19.0217	0.671679
$803$	−41.1049	−1.45056
$804$	1.25430	0.0442359
$805$	0	0
$806$	−24.4050	−0.859628
$807$	14.8165	0.521565
$808$	32.2567	1.13479
$809$	−37.9348	−1.33372	−0.666858	−	0.745185i	$-0.732361\pi$
$809$	−37.9348	−1.33372	−0.666858	+	0.745185i	$0.732361\pi$
$810$	−5.71828	−0.200920
$811$	−38.2521	−1.34321	−0.671606	−	0.740908i	$-0.734395\pi$
$811$	−38.2521	−1.34321	−0.671606	+	0.740908i	$0.734395\pi$
$812$	0	0
$813$	22.4712	0.788100
$814$	−35.7758	−1.25394
$815$	−19.8868	−0.696603
$816$	27.8952	0.976527
$817$	−3.09076	−0.108132
$818$	−57.3293	−2.00447
$819$	0	0
$820$	0.519492	0.0181414
$821$	−7.72337	−0.269547	−0.134774	−	0.990876i	$-0.543031\pi$
$821$	−7.72337	−0.269547	−0.134774	+	0.990876i	$0.543031\pi$
$822$	−29.2614	−1.02061
$823$	−20.4419	−0.712561	−0.356281	−	0.934379i	$-0.615955\pi$
$823$	−20.4419	−0.712561	−0.356281	+	0.934379i	$0.615955\pi$
$824$	−36.2002	−1.26110
$825$	−27.1848	−0.946455
$826$	0	0
$827$	−3.63691	−0.126468	−0.0632340	−	0.997999i	$-0.520141\pi$
$827$	−3.63691	−0.126468	−0.0632340	+	0.997999i	$0.520141\pi$
$828$	1.76030	0.0611745
$829$	33.4020	1.16010	0.580049	−	0.814582i	$-0.303033\pi$
$829$	33.4020	1.16010	0.580049	+	0.814582i	$0.303033\pi$
$830$	8.15383	0.283024
$831$	−3.97987	−0.138060
$832$	−9.89245	−0.342959
$833$	0	0
$834$	−30.6478	−1.06125
$835$	1.01865	0.0352518
$836$	−2.58234	−0.0893121
$837$	−43.0281	−1.48727
$838$	−42.3228	−1.46202
$839$	−7.32368	−0.252842	−0.126421	−	0.991977i	$-0.540349\pi$
$839$	−7.32368	−0.252842	−0.126421	+	0.991977i	$0.540349\pi$
$840$	0	0
$841$	−27.9079	−0.962341
$842$	−43.4595	−1.49771
$843$	−27.3965	−0.943585
$844$	−7.68725	−0.264606
$845$	8.25477	0.283973
$846$	4.57638	0.157339
$847$	0	0
$848$	−54.0937	−1.85758
$849$	20.5505	0.705293
$850$	28.8108	0.988203
$851$	12.6753	0.434504
$852$	−2.84703	−0.0975377
$853$	11.8322	0.405127	0.202563	−	0.979269i	$-0.435073\pi$
$853$	11.8322	0.405127	0.202563	+	0.979269i	$0.435073\pi$
$854$	0	0
$855$	1.11466	0.0381206
$856$	−12.7135	−0.434538
$857$	−32.6270	−1.11452	−0.557258	−	0.830340i	$-0.688146\pi$
$857$	−32.6270	−1.11452	−0.557258	+	0.830340i	$0.688146\pi$
$858$	20.9190	0.714162
$859$	−26.2072	−0.894180	−0.447090	−	0.894489i	$-0.647540\pi$
$859$	−26.2072	−0.894180	−0.447090	+	0.894489i	$0.647540\pi$
$860$	1.50200	0.0512178
$861$	0	0
$862$	29.4835	1.00421
$863$	−2.83616	−0.0965440	−0.0482720	−	0.998834i	$-0.515371\pi$
$863$	−2.83616	−0.0965440	−0.0482720	+	0.998834i	$0.515371\pi$
$864$	16.4059	0.558139
$865$	−18.3673	−0.624508
$866$	−26.7885	−0.910311
$867$	−2.74674	−0.0932842
$868$	0	0
$869$	−58.8857	−1.99756
$870$	2.04733	0.0694110
$871$	3.57079	0.120992
$872$	13.2671	0.449281
$873$	−4.71578	−0.159605
$874$	4.38311	0.148261
$875$	0	0
$876$	−5.92796	−0.200287
$877$	−12.6963	−0.428725	−0.214363	−	0.976754i	$-0.568767\pi$
$877$	−12.6963	−0.428725	−0.214363	+	0.976754i	$0.568767\pi$
$878$	31.3109	1.05669
$879$	0.954814	0.0322051
$880$	−21.5347	−0.725935
$881$	23.3775	0.787607	0.393804	−	0.919195i	$-0.371159\pi$
$881$	23.3775	0.787607	0.393804	+	0.919195i	$0.371159\pi$
$882$	0	0
$883$	−17.5254	−0.589777	−0.294889	−	0.955532i	$-0.595283\pi$
$883$	−17.5254	−0.589777	−0.294889	+	0.955532i	$0.595283\pi$
$884$	−4.62775	−0.155648
$885$	10.4679	0.351874
$886$	39.7814	1.33648
$887$	−21.3712	−0.717575	−0.358787	−	0.933419i	$-0.616810\pi$
$887$	−21.3712	−0.717575	−0.358787	+	0.933419i	$0.616810\pi$
$888$	14.3984	0.483180
$889$	0	0
$890$	8.11523	0.272023
$891$	19.1126	0.640296
$892$	−5.81889	−0.194831
$893$	2.37859	0.0795965
$894$	35.5175	1.18788
$895$	6.29529	0.210428
$896$	0	0
$897$	−7.41156	−0.247465
$898$	−4.55995	−0.152168
$899$	7.98325	0.266256
$900$	2.65079	0.0883598
$901$	49.4297	1.64674
$902$	−8.31826	−0.276968
$903$	0	0
$904$	−38.5670	−1.28272
$905$	10.5354	0.350208
$906$	32.0611	1.06516
$907$	4.73336	0.157169	0.0785844	−	0.996907i	$-0.474960\pi$
$907$	4.73336	0.157169	0.0785844	+	0.996907i	$0.474960\pi$
$908$	−12.6243	−0.418954
$909$	−16.6759	−0.553105
$910$	0	0
$911$	8.71101	0.288609	0.144304	−	0.989533i	$-0.453906\pi$
$911$	8.71101	0.288609	0.144304	+	0.989533i	$0.453906\pi$
$912$	6.39067	0.211616
$913$	−27.2531	−0.901946
$914$	0.545703	0.0180502
$915$	12.0876	0.399603
$916$	−13.3129	−0.439869
$917$	0	0
$918$	−39.0880	−1.29010
$919$	26.5863	0.877001	0.438501	−	0.898731i	$-0.355510\pi$
$919$	26.5863	0.877001	0.438501	+	0.898731i	$0.355510\pi$
$920$	5.94430	0.195978
$921$	−35.1619	−1.15862
$922$	−23.0439	−0.758909
$923$	−8.10501	−0.266780
$924$	0	0
$925$	19.0875	0.627593
$926$	47.7423	1.56891
$927$	18.7146	0.614668
$928$	−3.04388	−0.0999201
$929$	31.3999	1.03020	0.515098	−	0.857131i	$-0.327756\pi$
$929$	31.3999	1.03020	0.515098	+	0.857131i	$0.327756\pi$
$930$	14.9658	0.490749
$931$	0	0
$932$	9.28540	0.304153
$933$	−21.1203	−0.691448
$934$	20.9884	0.686761
$935$	19.6780	0.643539
$936$	5.69250	0.186065
$937$	13.6016	0.444346	0.222173	−	0.975007i	$-0.428685\pi$
$937$	13.6016	0.444346	0.222173	+	0.975007i	$0.428685\pi$
$938$	0	0
$939$	−38.6250	−1.26048
$940$	−1.15591	−0.0377017
$941$	31.8478	1.03821	0.519105	−	0.854710i	$-0.326265\pi$
$941$	31.8478	1.03821	0.519105	+	0.854710i	$0.326265\pi$
$942$	−1.84354	−0.0600657
$943$	2.94715	0.0959723
$944$	−40.5789	−1.32073
$945$	0	0
$946$	−24.0505	−0.781949
$947$	−32.2423	−1.04774	−0.523868	−	0.851800i	$-0.675511\pi$
$947$	−32.2423	−1.04774	−0.523868	+	0.851800i	$0.675511\pi$
$948$	−8.49224	−0.275815
$949$	−16.8759	−0.547815
$950$	6.60044	0.214146
$951$	38.6740	1.25409
$952$	0	0
$953$	−29.4552	−0.954146	−0.477073	−	0.878864i	$-0.658302\pi$
$953$	−29.4552	−0.954146	−0.477073	+	0.878864i	$0.658302\pi$
$954$	21.7875	0.705397
$955$	7.06238	0.228533
$956$	−2.64405	−0.0855146
$957$	−6.84293	−0.221201
$958$	27.0737	0.874710
$959$	0	0
$960$	6.06634	0.195790
$961$	27.3571	0.882486
$962$	−14.6880	−0.473560
$963$	6.57256	0.211798
$964$	1.61818	0.0521180
$965$	−9.62048	−0.309694
$966$	0	0
$967$	44.6199	1.43488	0.717440	−	0.696621i	$-0.245314\pi$
$967$	44.6199	1.43488	0.717440	+	0.696621i	$0.245314\pi$
$968$	30.3275	0.974761
$969$	−5.83967	−0.187597
$970$	5.70630	0.183218
$971$	25.7414	0.826082	0.413041	−	0.910712i	$-0.364467\pi$
$971$	25.7414	0.826082	0.413041	+	0.910712i	$0.364467\pi$
$972$	−6.15898	−0.197550
$973$	0	0
$974$	−17.4948	−0.560570
$975$	−11.1609	−0.357436
$976$	−46.8577	−1.49988
$977$	16.8590	0.539366	0.269683	−	0.962949i	$-0.413081\pi$
$977$	16.8590	0.539366	0.269683	+	0.962949i	$0.413081\pi$
$978$	45.9230	1.46845
$979$	−27.1241	−0.866890
$980$	0	0
$981$	−6.85877	−0.218984
$982$	−51.1001	−1.63067
$983$	53.4576	1.70503	0.852516	−	0.522700i	$-0.175075\pi$
$983$	53.4576	1.70503	0.852516	+	0.522700i	$0.175075\pi$
$984$	3.34779	0.106724
$985$	−22.6577	−0.721936
$986$	7.25222	0.230958
$987$	0	0
$988$	−1.06020	−0.0337294
$989$	8.52105	0.270954
$990$	8.67362	0.275666
$991$	4.94618	0.157120	0.0785602	−	0.996909i	$-0.474968\pi$
$991$	4.94618	0.157120	0.0785602	+	0.996909i	$0.474968\pi$
$992$	−22.2505	−0.706455
$993$	−21.8596	−0.693693
$994$	0	0
$995$	1.59687	0.0506240
$996$	−3.93032	−0.124537
$997$	−17.2528	−0.546402	−0.273201	−	0.961957i	$-0.588082\pi$
$997$	−17.2528	−0.546402	−0.273201	+	0.961957i	$0.588082\pi$
$998$	−16.0049	−0.506626
$999$	−25.8962	−0.819321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.q.1.3	yes	10
3.2	odd	2		8379.2.a.cs.1.8		10
7.2	even	3		931.2.f.q.704.8		20
7.3	odd	6		931.2.f.r.324.8		20
7.4	even	3		931.2.f.q.324.8		20
7.5	odd	6		931.2.f.r.704.8		20
7.6	odd	2		931.2.a.p.1.3	✓	10
21.20	even	2		8379.2.a.ct.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.3	✓	10	7.6	odd	2
931.2.a.q.1.3	yes	10	1.1	even	1	trivial
931.2.f.q.324.8		20	7.4	even	3
931.2.f.q.704.8		20	7.2	even	3
931.2.f.r.324.8		20	7.3	odd	6
931.2.f.r.704.8		20	7.5	odd	6
8379.2.a.cs.1.8		10	3.2	odd	2
8379.2.a.ct.1.8		10	21.20	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-1.58984 q^{2} -1.33784 q^{3} +0.527606 q^{4} -0.921074 q^{5} +2.12696 q^{6} +2.34088 q^{8} -1.21017 q^{9} +O(q^{10})\)	\(q-1.58984 q^{2} -1.33784 q^{3} +0.527606 q^{4} -0.921074 q^{5} +2.12696 q^{6} +2.34088 q^{8} -1.21017 q^{9} +1.46436 q^{10} -4.89445 q^{11} -0.705855 q^{12} -2.00945 q^{13} +1.23225 q^{15} -4.77684 q^{16} +4.36499 q^{17} +1.92399 q^{18} +1.00000 q^{19} -0.485964 q^{20} +7.78141 q^{22} -2.75694 q^{23} -3.13173 q^{24} -4.15162 q^{25} +3.19471 q^{26} +5.63256 q^{27} -1.04504 q^{29} -1.95909 q^{30} -7.63918 q^{31} +2.91269 q^{32} +6.54800 q^{33} -6.93965 q^{34} -0.638496 q^{36} -4.59760 q^{37} -1.58984 q^{38} +2.68833 q^{39} -2.15612 q^{40} -1.06899 q^{41} -3.09076 q^{43} -2.58234 q^{44} +1.11466 q^{45} +4.38311 q^{46} +2.37859 q^{47} +6.39067 q^{48} +6.60044 q^{50} -5.83967 q^{51} -1.06020 q^{52} +11.3241 q^{53} -8.95489 q^{54} +4.50815 q^{55} -1.33784 q^{57} +1.66145 q^{58} +8.49491 q^{59} +0.650145 q^{60} +9.80934 q^{61} +12.1451 q^{62} +4.92297 q^{64} +1.85085 q^{65} -10.4103 q^{66} -1.77700 q^{67} +2.30300 q^{68} +3.68836 q^{69} +4.03345 q^{71} -2.83287 q^{72} +8.39827 q^{73} +7.30947 q^{74} +5.55422 q^{75} +0.527606 q^{76} -4.27402 q^{78} +12.0311 q^{79} +4.39983 q^{80} -3.90496 q^{81} +1.69953 q^{82} +5.56817 q^{83} -4.02048 q^{85} +4.91383 q^{86} +1.39810 q^{87} -11.4573 q^{88} +5.54181 q^{89} -1.77214 q^{90} -1.45458 q^{92} +10.2200 q^{93} -3.78159 q^{94} -0.921074 q^{95} -3.89672 q^{96} +3.89678 q^{97} +5.92313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

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