LMFDB - Embedded newform 931.2.a.p.1.5

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:	$1$
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			1.5
Root			$0.897685$ 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)

$f(q)$	$=$	$q-0.897685 q^{2} -0.315265 q^{3} -1.19416 q^{4} -1.27247 q^{5} +0.283008 q^{6} +2.86735 q^{8} -2.90061 q^{9} +O(q^{10})$	\(q-0.897685 q^{2} -0.315265 q^{3} -1.19416 q^{4} -1.27247 q^{5} +0.283008 q^{6} +2.86735 q^{8} -2.90061 q^{9} +1.14227 q^{10} +5.80955 q^{11} +0.376477 q^{12} -2.74233 q^{13} +0.401164 q^{15} -0.185651 q^{16} +6.46541 q^{17} +2.60383 q^{18} -1.00000 q^{19} +1.51953 q^{20} -5.21514 q^{22} -4.75742 q^{23} -0.903975 q^{24} -3.38083 q^{25} +2.46175 q^{26} +1.86025 q^{27} +7.81421 q^{29} -0.360118 q^{30} -9.97990 q^{31} -5.56804 q^{32} -1.83155 q^{33} -5.80389 q^{34} +3.46380 q^{36} +2.10180 q^{37} +0.897685 q^{38} +0.864560 q^{39} -3.64860 q^{40} -11.5648 q^{41} +3.55962 q^{43} -6.93755 q^{44} +3.69092 q^{45} +4.27066 q^{46} -7.39563 q^{47} +0.0585294 q^{48} +3.03492 q^{50} -2.03831 q^{51} +3.27479 q^{52} -7.83543 q^{53} -1.66992 q^{54} -7.39245 q^{55} +0.315265 q^{57} -7.01469 q^{58} -1.70440 q^{59} -0.479054 q^{60} +2.36493 q^{61} +8.95880 q^{62} +5.36965 q^{64} +3.48952 q^{65} +1.64415 q^{66} +5.33754 q^{67} -7.72074 q^{68} +1.49985 q^{69} -9.02074 q^{71} -8.31706 q^{72} -14.6748 q^{73} -1.88676 q^{74} +1.06586 q^{75} +1.19416 q^{76} -0.776102 q^{78} +2.32738 q^{79} +0.236235 q^{80} +8.11535 q^{81} +10.3815 q^{82} -11.3760 q^{83} -8.22700 q^{85} -3.19541 q^{86} -2.46354 q^{87} +16.6580 q^{88} -4.53762 q^{89} -3.31328 q^{90} +5.68113 q^{92} +3.14631 q^{93} +6.63894 q^{94} +1.27247 q^{95} +1.75541 q^{96} +14.4796 q^{97} -16.8512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.897685	−0.634759	−0.317379	−	0.948299i	$-0.602803\pi$
$2$	−0.897685	−0.634759	−0.317379	+	0.948299i	$0.602803\pi$
$3$	−0.315265	−0.182018	−0.0910091	−	0.995850i	$-0.529009\pi$
$3$	−0.315265	−0.182018	−0.0910091	+	0.995850i	$0.529009\pi$
$4$	−1.19416	−0.597081
$5$	−1.27247	−0.569064	−0.284532	−	0.958667i	$-0.591838\pi$
$5$	−1.27247	−0.569064	−0.284532	+	0.958667i	$0.591838\pi$
$6$	0.283008	0.115538
$7$	0	0
$7$	0	0
$8$	2.86735	1.01376
$9$	−2.90061	−0.966869
$10$	1.14227	0.361218
$11$	5.80955	1.75165	0.875823	−	0.482633i	$-0.160319\pi$
$11$	5.80955	1.75165	0.875823	+	0.482633i	$0.160319\pi$
$12$	0.376477	0.108680
$13$	−2.74233	−0.760585	−0.380293	−	0.924866i	$-0.624177\pi$
$13$	−2.74233	−0.760585	−0.380293	+	0.924866i	$0.624177\pi$
$14$	0	0
$15$	0.401164	0.103580
$16$	−0.185651	−0.0464129
$17$	6.46541	1.56809	0.784046	−	0.620703i	$-0.213153\pi$
$17$	6.46541	1.56809	0.784046	+	0.620703i	$0.213153\pi$
$18$	2.60383	0.613729
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.51953	0.339777
$21$	0	0
$22$	−5.21514	−1.11187
$23$	−4.75742	−0.991990	−0.495995	−	0.868325i	$-0.665197\pi$
$23$	−4.75742	−0.991990	−0.495995	+	0.868325i	$0.665197\pi$
$24$	−0.903975	−0.184523
$25$	−3.38083	−0.676167
$26$	2.46175	0.482788
$27$	1.86025	0.358006
$28$	0	0
$29$	7.81421	1.45106	0.725531	−	0.688190i	$-0.241594\pi$
$29$	7.81421	1.45106	0.725531	+	0.688190i	$0.241594\pi$
$30$	−0.360118	−0.0657483
$31$	−9.97990	−1.79244	−0.896222	−	0.443607i	$-0.853699\pi$
$31$	−9.97990	−1.79244	−0.896222	+	0.443607i	$0.853699\pi$
$32$	−5.56804	−0.984300
$33$	−1.83155	−0.318831
$34$	−5.80389	−0.995360
$35$	0	0
$36$	3.46380	0.577300
$37$	2.10180	0.345534	0.172767	−	0.984963i	$-0.444729\pi$
$37$	2.10180	0.345534	0.172767	+	0.984963i	$0.444729\pi$
$38$	0.897685	0.145624
$39$	0.864560	0.138440
$40$	−3.64860	−0.576895
$41$	−11.5648	−1.80612	−0.903058	−	0.429520i	$-0.858683\pi$
$41$	−11.5648	−1.80612	−0.903058	+	0.429520i	$0.858683\pi$
$42$	0	0
$43$	3.55962	0.542836	0.271418	−	0.962462i	$-0.412507\pi$
$43$	3.55962	0.542836	0.271418	+	0.962462i	$0.412507\pi$
$44$	−6.93755	−1.04587
$45$	3.69092	0.550210
$46$	4.27066	0.629674
$47$	−7.39563	−1.07876	−0.539382	−	0.842061i	$-0.681342\pi$
$47$	−7.39563	−1.07876	−0.539382	+	0.842061i	$0.681342\pi$
$48$	0.0585294	0.00844799
$49$	0	0
$50$	3.03492	0.429203
$51$	−2.03831	−0.285421
$52$	3.27479	0.454131
$53$	−7.83543	−1.07628	−0.538140	−	0.842856i	$-0.680873\pi$
$53$	−7.83543	−1.07628	−0.538140	+	0.842856i	$0.680873\pi$
$54$	−1.66992	−0.227248
$55$	−7.39245	−0.996798
$56$	0	0
$57$	0.315265	0.0417578
$58$	−7.01469	−0.921074
$59$	−1.70440	−0.221894	−0.110947	−	0.993826i	$-0.535388\pi$
$59$	−1.70440	−0.221894	−0.110947	+	0.993826i	$0.535388\pi$
$60$	−0.479054	−0.0618457
$61$	2.36493	0.302799	0.151399	−	0.988473i	$-0.451622\pi$
$61$	2.36493	0.302799	0.151399	+	0.988473i	$0.451622\pi$
$62$	8.95880	1.13777
$63$	0	0
$64$	5.36965	0.671206
$65$	3.48952	0.432822
$66$	1.64415	0.202381
$67$	5.33754	0.652084	0.326042	−	0.945355i	$-0.394285\pi$
$67$	5.33754	0.652084	0.326042	+	0.945355i	$0.394285\pi$
$68$	−7.72074	−0.936278
$69$	1.49985	0.180560
$70$	0	0
$71$	−9.02074	−1.07056	−0.535282	−	0.844673i	$-0.679795\pi$
$71$	−9.02074	−1.07056	−0.535282	+	0.844673i	$0.679795\pi$
$72$	−8.31706	−0.980175
$73$	−14.6748	−1.71756	−0.858779	−	0.512346i	$-0.828777\pi$
$73$	−14.6748	−1.71756	−0.858779	+	0.512346i	$0.828777\pi$
$74$	−1.88676	−0.219331
$75$	1.06586	0.123075
$76$	1.19416	0.136980
$77$	0	0
$78$	−0.776102	−0.0878763
$79$	2.32738	0.261850	0.130925	−	0.991392i	$-0.458205\pi$
$79$	2.32738	0.261850	0.130925	+	0.991392i	$0.458205\pi$
$80$	0.236235	0.0264119
$81$	8.11535	0.901706
$82$	10.3815	1.14645
$83$	−11.3760	−1.24868	−0.624341	−	0.781152i	$-0.714632\pi$
$83$	−11.3760	−1.24868	−0.624341	+	0.781152i	$0.714632\pi$
$84$	0	0
$85$	−8.22700	−0.892344
$86$	−3.19541	−0.344570
$87$	−2.46354	−0.264120
$88$	16.6580	1.77575
$89$	−4.53762	−0.480986	−0.240493	−	0.970651i	$-0.577309\pi$
$89$	−4.53762	−0.480986	−0.240493	+	0.970651i	$0.577309\pi$
$90$	−3.31328	−0.349251
$91$	0	0
$92$	5.68113	0.592298
$93$	3.14631	0.326257
$94$	6.63894	0.684755
$95$	1.27247	0.130552
$96$	1.75541	0.179161
$97$	14.4796	1.47018	0.735089	−	0.677971i	$-0.237140\pi$
$97$	14.4796	1.47018	0.735089	+	0.677971i	$0.237140\pi$
$98$	0	0
$99$	−16.8512	−1.69361
$100$	4.03726	0.403726
$101$	−10.0259	−0.997611	−0.498805	−	0.866714i	$-0.666228\pi$
$101$	−10.0259	−0.997611	−0.498805	+	0.866714i	$0.666228\pi$
$102$	1.82976	0.181174
$103$	−7.57772	−0.746655	−0.373328	−	0.927700i	$-0.621783\pi$
$103$	−7.57772	−0.746655	−0.373328	+	0.927700i	$0.621783\pi$
$104$	−7.86322	−0.771052
$105$	0	0
$106$	7.03375	0.683178
$107$	6.22774	0.602058	0.301029	−	0.953615i	$-0.402670\pi$
$107$	6.22774	0.602058	0.301029	+	0.953615i	$0.402670\pi$
$108$	−2.22145	−0.213759
$109$	−4.99391	−0.478330	−0.239165	−	0.970979i	$-0.576874\pi$
$109$	−4.99391	−0.478330	−0.239165	+	0.970979i	$0.576874\pi$
$110$	6.63609	0.632726
$111$	−0.662625	−0.0628935
$112$	0	0
$113$	−3.60310	−0.338951	−0.169475	−	0.985534i	$-0.554207\pi$
$113$	−3.60310	−0.338951	−0.169475	+	0.985534i	$0.554207\pi$
$114$	−0.283008	−0.0265062
$115$	6.05364	0.564505
$116$	−9.33143	−0.866402
$117$	7.95442	0.735387
$118$	1.53001	0.140849
$119$	0	0
$120$	1.15028	0.105005
$121$	22.7509	2.06826
$122$	−2.12296	−0.192204
$123$	3.64597	0.328746
$124$	11.9176	1.07023
$125$	10.6643	0.953845
$126$	0	0
$127$	−6.12402	−0.543419	−0.271710	−	0.962379i	$-0.587589\pi$
$127$	−6.12402	−0.543419	−0.271710	+	0.962379i	$0.587589\pi$
$128$	6.31584	0.558246
$129$	−1.12222	−0.0988061
$130$	−3.13249	−0.274737
$131$	−6.71633	−0.586809	−0.293404	−	0.955988i	$-0.594788\pi$
$131$	−6.71633	−0.586809	−0.293404	+	0.955988i	$0.594788\pi$
$132$	2.18716	0.190368
$133$	0	0
$134$	−4.79143	−0.413916
$135$	−2.36711	−0.203728
$136$	18.5386	1.58967
$137$	0.530329	0.0453091	0.0226545	−	0.999743i	$-0.492788\pi$
$137$	0.530329	0.0453091	0.0226545	+	0.999743i	$0.492788\pi$
$138$	−1.34639	−0.114612
$139$	5.37877	0.456222	0.228111	−	0.973635i	$-0.426745\pi$
$139$	5.37877	0.456222	0.228111	+	0.973635i	$0.426745\pi$
$140$	0	0
$141$	2.33158	0.196355
$142$	8.09778	0.679551
$143$	−15.9317	−1.33228
$144$	0.538502	0.0448752
$145$	−9.94330	−0.825746
$146$	13.1734	1.09024
$147$	0	0
$148$	−2.50989	−0.206312
$149$	−12.3232	−1.00956	−0.504778	−	0.863249i	$-0.668426\pi$
$149$	−12.3232	−1.00956	−0.504778	+	0.863249i	$0.668426\pi$
$150$	−0.956804	−0.0781227
$151$	−13.4836	−1.09728	−0.548638	−	0.836060i	$-0.684853\pi$
$151$	−13.4836	−1.09728	−0.548638	+	0.836060i	$0.684853\pi$
$152$	−2.86735	−0.232573
$153$	−18.7536	−1.51614
$154$	0	0
$155$	12.6991	1.02001
$156$	−1.03243	−0.0826602
$157$	−0.939590	−0.0749874	−0.0374937	−	0.999297i	$-0.511937\pi$
$157$	−0.939590	−0.0749874	−0.0374937	+	0.999297i	$0.511937\pi$
$158$	−2.08925	−0.166212
$159$	2.47024	0.195903
$160$	7.08514	0.560130
$161$	0	0
$162$	−7.28503	−0.572366
$163$	−14.6413	−1.14680	−0.573398	−	0.819277i	$-0.694375\pi$
$163$	−14.6413	−1.14680	−0.573398	+	0.819277i	$0.694375\pi$
$164$	13.8102	1.07840
$165$	2.33058	0.181435
$166$	10.2121	0.792612
$167$	−5.23757	−0.405295	−0.202648	−	0.979252i	$-0.564955\pi$
$167$	−5.23757	−0.405295	−0.202648	+	0.979252i	$0.564955\pi$
$168$	0	0
$169$	−5.47963	−0.421510
$170$	7.38525	0.566423
$171$	2.90061	0.221815
$172$	−4.25076	−0.324117
$173$	6.75692	0.513719	0.256859	−	0.966449i	$-0.417312\pi$
$173$	6.75692	0.513719	0.256859	+	0.966449i	$0.417312\pi$
$174$	2.21149	0.167652
$175$	0	0
$176$	−1.07855	−0.0812989
$177$	0.537336	0.0403887
$178$	4.07335	0.305310
$179$	6.39275	0.477816	0.238908	−	0.971042i	$-0.423211\pi$
$179$	6.39275	0.477816	0.238908	+	0.971042i	$0.423211\pi$
$180$	−4.40756	−0.328520
$181$	3.34289	0.248475	0.124238	−	0.992252i	$-0.460351\pi$
$181$	3.34289	0.248475	0.124238	+	0.992252i	$0.460351\pi$
$182$	0	0
$183$	−0.745580	−0.0551149
$184$	−13.6412	−1.00564
$185$	−2.67447	−0.196631
$186$	−2.82440	−0.207095
$187$	37.5611	2.74674
$188$	8.83158	0.644109
$189$	0	0
$190$	−1.14227	−0.0828691
$191$	12.1447	0.878759	0.439379	−	0.898302i	$-0.355198\pi$
$191$	12.1447	0.878759	0.439379	+	0.898302i	$0.355198\pi$
$192$	−1.69286	−0.122172
$193$	−1.11046	−0.0799325	−0.0399662	−	0.999201i	$-0.512725\pi$
$193$	−1.11046	−0.0799325	−0.0399662	+	0.999201i	$0.512725\pi$
$194$	−12.9981	−0.933208
$195$	−1.10012	−0.0787814
$196$	0	0
$197$	1.07408	0.0765254	0.0382627	−	0.999268i	$-0.487818\pi$
$197$	1.07408	0.0765254	0.0382627	+	0.999268i	$0.487818\pi$
$198$	15.1271	1.07504
$199$	12.5299	0.888222	0.444111	−	0.895972i	$-0.353520\pi$
$199$	12.5299	0.888222	0.444111	+	0.895972i	$0.353520\pi$
$200$	−9.69403	−0.685472
$201$	−1.68274	−0.118691
$202$	9.00006	0.633242
$203$	0	0
$204$	2.43408	0.170420
$205$	14.7158	1.02779
$206$	6.80241	0.473946
$207$	13.7994	0.959124
$208$	0.509117	0.0353009
$209$	−5.80955	−0.401855
$210$	0	0
$211$	−20.6433	−1.42114	−0.710572	−	0.703624i	$-0.751564\pi$
$211$	−20.6433	−1.42114	−0.710572	+	0.703624i	$0.751564\pi$
$212$	9.35678	0.642626
$213$	2.84392	0.194862
$214$	−5.59054	−0.382162
$215$	−4.52949	−0.308908
$216$	5.33400	0.362933
$217$	0	0
$218$	4.48295	0.303624
$219$	4.62646	0.312627
$220$	8.82779	0.595169
$221$	−17.7303	−1.19267
$222$	0.594828	0.0399222
$223$	17.7398	1.18794	0.593972	−	0.804486i	$-0.297559\pi$
$223$	17.7398	1.18794	0.593972	+	0.804486i	$0.297559\pi$
$224$	0	0
$225$	9.80647	0.653765
$226$	3.23444	0.215152
$227$	12.1340	0.805361	0.402681	−	0.915341i	$-0.368079\pi$
$227$	12.1340	0.805361	0.402681	+	0.915341i	$0.368079\pi$
$228$	−0.376477	−0.0249328
$229$	1.49447	0.0987572	0.0493786	−	0.998780i	$-0.484276\pi$
$229$	1.49447	0.0987572	0.0493786	+	0.998780i	$0.484276\pi$
$230$	−5.43426	−0.358325
$231$	0	0
$232$	22.4061	1.47103
$233$	27.6620	1.81220	0.906099	−	0.423066i	$-0.139046\pi$
$233$	27.6620	1.81220	0.906099	+	0.423066i	$0.139046\pi$
$234$	−7.14056	−0.466793
$235$	9.41068	0.613885
$236$	2.03533	0.132488
$237$	−0.733740	−0.0476615
$238$	0	0
$239$	0.834497	0.0539792	0.0269896	−	0.999636i	$-0.491408\pi$
$239$	0.834497	0.0539792	0.0269896	+	0.999636i	$0.491408\pi$
$240$	−0.0744766	−0.00480744
$241$	−18.1728	−1.17061	−0.585305	−	0.810813i	$-0.699025\pi$
$241$	−18.1728	−1.17061	−0.585305	+	0.810813i	$0.699025\pi$
$242$	−20.4231	−1.31285
$243$	−8.13925	−0.522133
$244$	−2.82411	−0.180795
$245$	0	0
$246$	−3.27293	−0.208674
$247$	2.74233	0.174490
$248$	−28.6159	−1.81711
$249$	3.58646	0.227283
$250$	−9.57319	−0.605462
$251$	14.9619	0.944385	0.472192	−	0.881495i	$-0.343463\pi$
$251$	14.9619	0.944385	0.472192	+	0.881495i	$0.343463\pi$
$252$	0	0
$253$	−27.6384	−1.73761
$254$	5.49744	0.344940
$255$	2.59368	0.162423
$256$	−16.4089	−1.02556
$257$	−4.81183	−0.300154	−0.150077	−	0.988674i	$-0.547952\pi$
$257$	−4.81183	−0.300154	−0.150077	+	0.988674i	$0.547952\pi$
$258$	1.00740	0.0627181
$259$	0	0
$260$	−4.16705	−0.258430
$261$	−22.6659	−1.40299
$262$	6.02915	0.372482
$263$	−26.4482	−1.63087	−0.815434	−	0.578849i	$-0.803502\pi$
$263$	−26.4482	−1.63087	−0.815434	+	0.578849i	$0.803502\pi$
$264$	−5.25169	−0.323219
$265$	9.97032	0.612472
$266$	0	0
$267$	1.43055	0.0875483
$268$	−6.37389	−0.389347
$269$	−27.4070	−1.67103	−0.835516	−	0.549466i	$-0.814831\pi$
$269$	−27.4070	−1.67103	−0.835516	+	0.549466i	$0.814831\pi$
$270$	2.12492	0.129318
$271$	12.2941	0.746811	0.373406	−	0.927668i	$-0.378190\pi$
$271$	12.2941	0.746811	0.373406	+	0.927668i	$0.378190\pi$
$272$	−1.20031	−0.0727796
$273$	0	0
$274$	−0.476068	−0.0287603
$275$	−19.6411	−1.18440
$276$	−1.79106	−0.107809
$277$	−4.49759	−0.270234	−0.135117	−	0.990830i	$-0.543141\pi$
$277$	−4.49759	−0.270234	−0.135117	+	0.990830i	$0.543141\pi$
$278$	−4.82844	−0.289591
$279$	28.9478	1.73306
$280$	0	0
$281$	9.99749	0.596401	0.298200	−	0.954503i	$-0.403614\pi$
$281$	9.99749	0.596401	0.298200	+	0.954503i	$0.403614\pi$
$282$	−2.09303	−0.124638
$283$	32.5419	1.93442	0.967208	−	0.253987i	$-0.0817420\pi$
$283$	32.5419	1.93442	0.967208	+	0.253987i	$0.0817420\pi$
$284$	10.7722	0.639214
$285$	−0.401164	−0.0237629
$286$	14.3016	0.845674
$287$	0	0
$288$	16.1507	0.951690
$289$	24.8015	1.45891
$290$	8.92595	0.524150
$291$	−4.56490	−0.267599
$292$	17.5241	1.02552
$293$	−9.14458	−0.534232	−0.267116	−	0.963664i	$-0.586071\pi$
$293$	−9.14458	−0.534232	−0.267116	+	0.963664i	$0.586071\pi$
$294$	0	0
$295$	2.16878	0.126272
$296$	6.02661	0.350289
$297$	10.8072	0.627100
$298$	11.0623	0.640825
$299$	13.0464	0.754493
$300$	−1.27281	−0.0734856
$301$	0	0
$302$	12.1040	0.696506
$303$	3.16080	0.181583
$304$	0.185651	0.0106478
$305$	−3.00929	−0.172312
$306$	16.8348	0.962383
$307$	12.4962	0.713197	0.356599	−	0.934258i	$-0.383936\pi$
$307$	12.4962	0.713197	0.356599	+	0.934258i	$0.383936\pi$
$308$	0	0
$309$	2.38899	0.135905
$310$	−11.3998	−0.647463
$311$	6.20982	0.352126	0.176063	−	0.984379i	$-0.443664\pi$
$311$	6.20982	0.352126	0.176063	+	0.984379i	$0.443664\pi$
$312$	2.47900	0.140346
$313$	10.2769	0.580885	0.290442	−	0.956893i	$-0.406198\pi$
$313$	10.2769	0.580885	0.290442	+	0.956893i	$0.406198\pi$
$314$	0.843455	0.0475989
$315$	0	0
$316$	−2.77927	−0.156346
$317$	−19.2160	−1.07928	−0.539638	−	0.841897i	$-0.681439\pi$
$317$	−19.2160	−1.07928	−0.539638	+	0.841897i	$0.681439\pi$
$318$	−2.21749	−0.124351
$319$	45.3970	2.54175
$320$	−6.83269	−0.381959
$321$	−1.96339	−0.109586
$322$	0	0
$323$	−6.46541	−0.359745
$324$	−9.69105	−0.538392
$325$	9.27136	0.514282
$326$	13.1433	0.727939
$327$	1.57440	0.0870647
$328$	−33.1603	−1.83097
$329$	0	0
$330$	−2.09213	−0.115168
$331$	−6.91456	−0.380059	−0.190029	−	0.981778i	$-0.560858\pi$
$331$	−6.91456	−0.380059	−0.190029	+	0.981778i	$0.560858\pi$
$332$	13.5848	0.745564
$333$	−6.09651	−0.334087
$334$	4.70168	0.257265
$335$	−6.79183	−0.371078
$336$	0	0
$337$	−9.14183	−0.497987	−0.248993	−	0.968505i	$-0.580100\pi$
$337$	−9.14183	−0.497987	−0.248993	+	0.968505i	$0.580100\pi$
$338$	4.91898	0.267557
$339$	1.13593	0.0616952
$340$	9.82438	0.532802
$341$	−57.9787	−3.13973
$342$	−2.60383	−0.140799
$343$	0	0
$344$	10.2067	0.550307
$345$	−1.90850	−0.102750
$346$	−6.06558	−0.326088
$347$	7.79889	0.418666	0.209333	−	0.977844i	$-0.432871\pi$
$347$	7.79889	0.418666	0.209333	+	0.977844i	$0.432871\pi$
$348$	2.94187	0.157701
$349$	−17.3327	−0.927801	−0.463900	−	0.885887i	$-0.653550\pi$
$349$	−17.3327	−0.927801	−0.463900	+	0.885887i	$0.653550\pi$
$350$	0	0
$351$	−5.10143	−0.272294
$352$	−32.3478	−1.72415
$353$	−15.7557	−0.838593	−0.419296	−	0.907849i	$-0.637723\pi$
$353$	−15.7557	−0.838593	−0.419296	+	0.907849i	$0.637723\pi$
$354$	−0.482359	−0.0256371
$355$	11.4786	0.609220
$356$	5.41865	0.287188
$357$	0	0
$358$	−5.73867	−0.303298
$359$	33.3839	1.76193	0.880967	−	0.473178i	$-0.156893\pi$
$359$	33.3839	1.76193	0.880967	+	0.473178i	$0.156893\pi$
$360$	10.5832	0.557782
$361$	1.00000	0.0526316
$362$	−3.00086	−0.157722
$363$	−7.17255	−0.376461
$364$	0	0
$365$	18.6732	0.977400
$366$	0.669296	0.0349846
$367$	1.98897	0.103823	0.0519117	−	0.998652i	$-0.483469\pi$
$367$	1.98897	0.103823	0.0519117	+	0.998652i	$0.483469\pi$
$368$	0.883221	0.0460411
$369$	33.5449	1.74628
$370$	2.40083	0.124813
$371$	0	0
$372$	−3.75721	−0.194802
$373$	−26.5140	−1.37284	−0.686420	−	0.727205i	$-0.740819\pi$
$373$	−26.5140	−1.37284	−0.686420	+	0.727205i	$0.740819\pi$
$374$	−33.7180	−1.74352
$375$	−3.36208	−0.173617
$376$	−21.2059	−1.09361
$377$	−21.4291	−1.10366
$378$	0	0
$379$	−22.9628	−1.17952	−0.589760	−	0.807579i	$-0.700778\pi$
$379$	−22.9628	−1.17952	−0.589760	+	0.807579i	$0.700778\pi$
$380$	−1.51953	−0.0779502
$381$	1.93069	0.0989122
$382$	−10.9021	−0.557800
$383$	16.1098	0.823172	0.411586	−	0.911371i	$-0.364975\pi$
$383$	16.1098	0.823172	0.411586	+	0.911371i	$0.364975\pi$
$384$	−1.99116	−0.101611
$385$	0	0
$386$	0.996841	0.0507378
$387$	−10.3251	−0.524852
$388$	−17.2910	−0.877815
$389$	−6.17203	−0.312934	−0.156467	−	0.987683i	$-0.550011\pi$
$389$	−6.17203	−0.312934	−0.156467	+	0.987683i	$0.550011\pi$
$390$	0.987563	0.0500072
$391$	−30.7586	−1.55553
$392$	0	0
$393$	2.11742	0.106810
$394$	−0.964189	−0.0485752
$395$	−2.96150	−0.149009
$396$	20.1231	1.01122
$397$	−31.6486	−1.58840	−0.794199	−	0.607658i	$-0.792109\pi$
$397$	−31.6486	−1.58840	−0.794199	+	0.607658i	$0.792109\pi$
$398$	−11.2479	−0.563807
$399$	0	0
$400$	0.627657	0.0313828
$401$	5.37936	0.268632	0.134316	−	0.990939i	$-0.457116\pi$
$401$	5.37936	0.268632	0.134316	+	0.990939i	$0.457116\pi$
$402$	1.51057	0.0753403
$403$	27.3682	1.36331
$404$	11.9725	0.595655
$405$	−10.3265	−0.513128
$406$	0	0
$407$	12.2105	0.605254
$408$	−5.84456	−0.289349
$409$	−25.8724	−1.27931	−0.639654	−	0.768663i	$-0.720922\pi$
$409$	−25.8724	−1.27931	−0.639654	+	0.768663i	$0.720922\pi$
$410$	−13.2101	−0.652402
$411$	−0.167194	−0.00824708
$412$	9.04903	0.445814
$413$	0	0
$414$	−12.3875	−0.608813
$415$	14.4756	0.710579
$416$	15.2694	0.748645
$417$	−1.69574	−0.0830407
$418$	5.21514	0.255081
$419$	2.47109	0.120721	0.0603604	−	0.998177i	$-0.480775\pi$
$419$	2.47109	0.120721	0.0603604	+	0.998177i	$0.480775\pi$
$420$	0	0
$421$	−6.28643	−0.306382	−0.153191	−	0.988197i	$-0.548955\pi$
$421$	−6.28643	−0.306382	−0.153191	+	0.988197i	$0.548955\pi$
$422$	18.5312	0.902084
$423$	21.4518	1.04302
$424$	−22.4669	−1.09109
$425$	−21.8585	−1.06029
$426$	−2.55295	−0.123691
$427$	0	0
$428$	−7.43693	−0.359478
$429$	5.02271	0.242499
$430$	4.06605	0.196082
$431$	−20.1942	−0.972718	−0.486359	−	0.873759i	$-0.661675\pi$
$431$	−20.1942	−0.972718	−0.486359	+	0.873759i	$0.661675\pi$
$432$	−0.345359	−0.0166161
$433$	28.8237	1.38518	0.692590	−	0.721331i	$-0.256470\pi$
$433$	28.8237	1.38518	0.692590	+	0.721331i	$0.256470\pi$
$434$	0	0
$435$	3.13477	0.150301
$436$	5.96354	0.285602
$437$	4.75742	0.227578
$438$	−4.15310	−0.198443
$439$	−37.2484	−1.77777	−0.888886	−	0.458129i	$-0.848520\pi$
$439$	−37.2484	−1.77777	−0.888886	+	0.458129i	$0.848520\pi$
$440$	−21.1967	−1.01052
$441$	0	0
$442$	15.9162	0.757056
$443$	−20.0463	−0.952427	−0.476213	−	0.879330i	$-0.657991\pi$
$443$	−20.0463	−0.952427	−0.476213	+	0.879330i	$0.657991\pi$
$444$	0.791281	0.0375526
$445$	5.77396	0.273712
$446$	−15.9247	−0.754058
$447$	3.88507	0.183758
$448$	0	0
$449$	−39.6134	−1.86947	−0.934735	−	0.355344i	$-0.884364\pi$
$449$	−39.6134	−1.86947	−0.934735	+	0.355344i	$0.884364\pi$
$450$	−8.80312	−0.414983
$451$	−67.1862	−3.16367
$452$	4.30268	0.202381
$453$	4.25089	0.199724
$454$	−10.8925	−0.511210
$455$	0	0
$456$	0.903975	0.0423325
$457$	−15.0401	−0.703547	−0.351774	−	0.936085i	$-0.614421\pi$
$457$	−15.0401	−0.703547	−0.351774	+	0.936085i	$0.614421\pi$
$458$	−1.34156	−0.0626870
$459$	12.0273	0.561386
$460$	−7.22903	−0.337055
$461$	−29.2313	−1.36144	−0.680719	−	0.732545i	$-0.738332\pi$
$461$	−29.2313	−1.36144	−0.680719	+	0.732545i	$0.738332\pi$
$462$	0	0
$463$	31.5867	1.46796	0.733980	−	0.679171i	$-0.237660\pi$
$463$	31.5867	1.46796	0.733980	+	0.679171i	$0.237660\pi$
$464$	−1.45072	−0.0673479
$465$	−4.00357	−0.185661
$466$	−24.8317	−1.15031
$467$	−0.374229	−0.0173173	−0.00865863	−	0.999963i	$-0.502756\pi$
$467$	−0.374229	−0.0173173	−0.00865863	+	0.999963i	$0.502756\pi$
$468$	−9.49887	−0.439086
$469$	0	0
$470$	−8.44782	−0.389669
$471$	0.296220	0.0136491
$472$	−4.88710	−0.224947
$473$	20.6798	0.950857
$474$	0.658667	0.0302536
$475$	3.38083	0.155123
$476$	0	0
$477$	22.7275	1.04062
$478$	−0.749115	−0.0342637
$479$	17.2317	0.787334	0.393667	−	0.919253i	$-0.371206\pi$
$479$	17.2317	0.787334	0.393667	+	0.919253i	$0.371206\pi$
$480$	−2.23370	−0.101954
$481$	−5.76384	−0.262808
$482$	16.3134	0.743055
$483$	0	0
$484$	−27.1683	−1.23492
$485$	−18.4247	−0.836625
$486$	7.30648	0.331429
$487$	31.7164	1.43721	0.718604	−	0.695419i	$-0.244781\pi$
$487$	31.7164	1.43721	0.718604	+	0.695419i	$0.244781\pi$
$488$	6.78109	0.306965
$489$	4.61589	0.208738
$490$	0	0
$491$	3.22837	0.145694	0.0728472	−	0.997343i	$-0.476791\pi$
$491$	3.22837	0.145694	0.0728472	+	0.997343i	$0.476791\pi$
$492$	−4.35388	−0.196288
$493$	50.5220	2.27540
$494$	−2.46175	−0.110759
$495$	21.4426	0.963773
$496$	1.85278	0.0831924
$497$	0	0
$498$	−3.21951	−0.144270
$499$	5.55879	0.248845	0.124423	−	0.992229i	$-0.460292\pi$
$499$	5.55879	0.248845	0.124423	+	0.992229i	$0.460292\pi$
$500$	−12.7349	−0.569523
$501$	1.65122	0.0737711
$502$	−13.4310	−0.599457
$503$	−15.2311	−0.679123	−0.339562	−	0.940584i	$-0.610279\pi$
$503$	−15.2311	−0.679123	−0.339562	+	0.940584i	$0.610279\pi$
$504$	0	0
$505$	12.7576	0.567704
$506$	24.8106	1.10297
$507$	1.72753	0.0767225
$508$	7.31308	0.324465
$509$	−1.10202	−0.0488461	−0.0244230	−	0.999702i	$-0.507775\pi$
$509$	−1.10202	−0.0488461	−0.0244230	+	0.999702i	$0.507775\pi$
$510$	−2.32831	−0.103099
$511$	0	0
$512$	2.09837	0.0927358
$513$	−1.86025	−0.0821322
$514$	4.31950	0.190525
$515$	9.64239	0.424894
$516$	1.34012	0.0589953
$517$	−42.9653	−1.88961
$518$	0	0
$519$	−2.13022	−0.0935062
$520$	10.0057	0.438778
$521$	−12.6547	−0.554413	−0.277206	−	0.960810i	$-0.589409\pi$
$521$	−12.6547	−0.554413	−0.277206	+	0.960810i	$0.589409\pi$
$522$	20.3469	0.890558
$523$	28.3846	1.24117	0.620585	−	0.784139i	$-0.286895\pi$
$523$	28.3846	1.24117	0.620585	+	0.784139i	$0.286895\pi$
$524$	8.02039	0.350373
$525$	0	0
$526$	23.7422	1.03521
$527$	−64.5241	−2.81071
$528$	0.340029	0.0147979
$529$	−0.367002	−0.0159566
$530$	−8.95020	−0.388772
$531$	4.94379	0.214542
$532$	0	0
$533$	31.7144	1.37370
$534$	−1.28418	−0.0555720
$535$	−7.92458	−0.342609
$536$	15.3046	0.661058
$537$	−2.01541	−0.0869713
$538$	24.6028	1.06070
$539$	0	0
$540$	2.82671	0.121642
$541$	29.0546	1.24915	0.624577	−	0.780963i	$-0.285271\pi$
$541$	29.0546	1.24915	0.624577	+	0.780963i	$0.285271\pi$
$542$	−11.0362	−0.474045
$543$	−1.05390	−0.0452270
$544$	−35.9997	−1.54347
$545$	6.35457	0.272200
$546$	0	0
$547$	26.7331	1.14302	0.571511	−	0.820594i	$-0.306357\pi$
$547$	26.7331	1.14302	0.571511	+	0.820594i	$0.306357\pi$
$548$	−0.633299	−0.0270532
$549$	−6.85974	−0.292767
$550$	17.6315	0.751811
$551$	−7.81421	−0.332896
$552$	4.30058	0.183045
$553$	0	0
$554$	4.03741	0.171533
$555$	0.843167	0.0357904
$556$	−6.42313	−0.272401
$557$	−13.7325	−0.581864	−0.290932	−	0.956744i	$-0.593965\pi$
$557$	−13.7325	−0.581864	−0.290932	+	0.956744i	$0.593965\pi$
$558$	−25.9860	−1.10007
$559$	−9.76164	−0.412873
$560$	0	0
$561$	−11.8417	−0.499957
$562$	−8.97460	−0.378571
$563$	13.2968	0.560393	0.280197	−	0.959943i	$-0.409600\pi$
$563$	13.2968	0.560393	0.280197	+	0.959943i	$0.409600\pi$
$564$	−2.78429	−0.117240
$565$	4.58481	0.192885
$566$	−29.2124	−1.22789
$567$	0	0
$568$	−25.8656	−1.08530
$569$	−19.6630	−0.824316	−0.412158	−	0.911112i	$-0.635225\pi$
$569$	−19.6630	−0.824316	−0.412158	+	0.911112i	$0.635225\pi$
$570$	0.360118	0.0150837
$571$	−14.5792	−0.610122	−0.305061	−	0.952333i	$-0.598677\pi$
$571$	−14.5792	−0.610122	−0.305061	+	0.952333i	$0.598677\pi$
$572$	19.0250	0.795477
$573$	−3.82879	−0.159950
$574$	0	0
$575$	16.0840	0.670750
$576$	−15.5753	−0.648969
$577$	34.2488	1.42580	0.712898	−	0.701267i	$-0.247382\pi$
$577$	34.2488	1.42580	0.712898	+	0.701267i	$0.247382\pi$
$578$	−22.2639	−0.926056
$579$	0.350088	0.0145492
$580$	11.8739	0.493038
$581$	0	0
$582$	4.09784	0.169861
$583$	−45.5204	−1.88526
$584$	−42.0779	−1.74119
$585$	−10.1217	−0.418482
$586$	8.20895	0.339109
$587$	−6.33114	−0.261314	−0.130657	−	0.991428i	$-0.541709\pi$
$587$	−6.33114	−0.261314	−0.130657	+	0.991428i	$0.541709\pi$
$588$	0	0
$589$	9.97990	0.411215
$590$	−1.94688	−0.0801520
$591$	−0.338621	−0.0139290
$592$	−0.390203	−0.0160372
$593$	−6.35383	−0.260921	−0.130460	−	0.991454i	$-0.541646\pi$
$593$	−6.35383	−0.260921	−0.130460	+	0.991454i	$0.541646\pi$
$594$	−9.70150	−0.398057
$595$	0	0
$596$	14.7159	0.602787
$597$	−3.95024	−0.161673
$598$	−11.7116	−0.478921
$599$	−3.36695	−0.137570	−0.0687850	−	0.997632i	$-0.521912\pi$
$599$	−3.36695	−0.137570	−0.0687850	+	0.997632i	$0.521912\pi$
$600$	3.05619	0.124768
$601$	6.23608	0.254375	0.127188	−	0.991879i	$-0.459405\pi$
$601$	6.23608	0.254375	0.127188	+	0.991879i	$0.459405\pi$
$602$	0	0
$603$	−15.4821	−0.630480
$604$	16.1015	0.655163
$605$	−28.9497	−1.17697
$606$	−2.83740	−0.115262
$607$	−3.18937	−0.129452	−0.0647262	−	0.997903i	$-0.520617\pi$
$607$	−3.18937	−0.129452	−0.0647262	+	0.997903i	$0.520617\pi$
$608$	5.56804	0.225814
$609$	0	0
$610$	2.70140	0.109376
$611$	20.2813	0.820492
$612$	22.3949	0.905258
$613$	19.1641	0.774031	0.387016	−	0.922073i	$-0.373506\pi$
$613$	19.1641	0.774031	0.387016	+	0.922073i	$0.373506\pi$
$614$	−11.2177	−0.452708
$615$	−4.63937	−0.187077
$616$	0	0
$617$	23.0381	0.927479	0.463740	−	0.885971i	$-0.346507\pi$
$617$	23.0381	0.927479	0.463740	+	0.885971i	$0.346507\pi$
$618$	−2.14456	−0.0862668
$619$	−11.1582	−0.448487	−0.224243	−	0.974533i	$-0.571991\pi$
$619$	−11.1582	−0.448487	−0.224243	+	0.974533i	$0.571991\pi$
$620$	−15.1648	−0.609031
$621$	−8.85000	−0.355138
$622$	−5.57446	−0.223515
$623$	0	0
$624$	−0.160507	−0.00642542
$625$	3.33419	0.133368
$626$	−9.22541	−0.368722
$627$	1.83155	0.0731450
$628$	1.12202	0.0447736
$629$	13.5890	0.541829
$630$	0	0
$631$	−9.50456	−0.378370	−0.189185	−	0.981941i	$-0.560585\pi$
$631$	−9.50456	−0.378370	−0.189185	+	0.981941i	$0.560585\pi$
$632$	6.67340	0.265454
$633$	6.50811	0.258674
$634$	17.2499	0.685080
$635$	7.79261	0.309240
$636$	−2.94986	−0.116970
$637$	0	0
$638$	−40.7522	−1.61340
$639$	26.1656	1.03510
$640$	−8.03668	−0.317678
$641$	−30.9079	−1.22079	−0.610394	−	0.792098i	$-0.708989\pi$
$641$	−30.9079	−1.22079	−0.610394	+	0.792098i	$0.708989\pi$
$642$	1.76250	0.0695604
$643$	6.22986	0.245682	0.122841	−	0.992426i	$-0.460800\pi$
$643$	6.22986	0.245682	0.122841	+	0.992426i	$0.460800\pi$
$644$	0	0
$645$	1.42799	0.0562270
$646$	5.80389	0.228351
$647$	19.0641	0.749486	0.374743	−	0.927129i	$-0.377731\pi$
$647$	19.0641	0.749486	0.374743	+	0.927129i	$0.377731\pi$
$648$	23.2696	0.914114
$649$	−9.90178	−0.388679
$650$	−8.32275	−0.326445
$651$	0	0
$652$	17.4841	0.684730
$653$	26.5922	1.04063	0.520317	−	0.853973i	$-0.325814\pi$
$653$	26.5922	1.04063	0.520317	+	0.853973i	$0.325814\pi$
$654$	−1.41332	−0.0552651
$655$	8.54630	0.333932
$656$	2.14702	0.0838270
$657$	42.5659	1.66065
$658$	0	0
$659$	−39.2379	−1.52849	−0.764246	−	0.644925i	$-0.776889\pi$
$659$	−39.2379	−1.52849	−0.764246	+	0.644925i	$0.776889\pi$
$660$	−2.78309	−0.108332
$661$	28.6258	1.11341	0.556707	−	0.830709i	$-0.312065\pi$
$661$	28.6258	1.11341	0.556707	+	0.830709i	$0.312065\pi$
$662$	6.20710	0.241246
$663$	5.58973	0.217087
$664$	−32.6191	−1.26587
$665$	0	0
$666$	5.47274	0.212064
$667$	−37.1754	−1.43944
$668$	6.25450	0.241994
$669$	−5.59273	−0.216227
$670$	6.09692	0.235545
$671$	13.7392	0.530396
$672$	0	0
$673$	8.13581	0.313612	0.156806	−	0.987629i	$-0.449880\pi$
$673$	8.13581	0.313612	0.156806	+	0.987629i	$0.449880\pi$
$674$	8.20648	0.316102
$675$	−6.28921	−0.242072
$676$	6.54357	0.251676
$677$	−26.0175	−0.999933	−0.499967	−	0.866045i	$-0.666654\pi$
$677$	−26.0175	−0.999933	−0.499967	+	0.866045i	$0.666654\pi$
$678$	−1.01971	−0.0391616
$679$	0	0
$680$	−23.5897	−0.904624
$681$	−3.82542	−0.146590
$682$	52.0466	1.99297
$683$	22.4051	0.857307	0.428654	−	0.903469i	$-0.358988\pi$
$683$	22.4051	0.857307	0.428654	+	0.903469i	$0.358988\pi$
$684$	−3.46380	−0.132442
$685$	−0.674825	−0.0257837
$686$	0	0
$687$	−0.471153	−0.0179756
$688$	−0.660848	−0.0251946
$689$	21.4873	0.818603
$690$	1.71323	0.0652216
$691$	44.5197	1.69361	0.846804	−	0.531905i	$-0.178524\pi$
$691$	44.5197	1.69361	0.846804	+	0.531905i	$0.178524\pi$
$692$	−8.06886	−0.306732
$693$	0	0
$694$	−7.00094	−0.265752
$695$	−6.84430	−0.259619
$696$	−7.06384	−0.267754
$697$	−74.7710	−2.83215
$698$	15.5593	0.588930
$699$	−8.72085	−0.329853
$700$	0	0
$701$	34.7917	1.31406	0.657032	−	0.753863i	$-0.271812\pi$
$701$	34.7917	1.31406	0.657032	+	0.753863i	$0.271812\pi$
$702$	4.57948	0.172841
$703$	−2.10180	−0.0792710
$704$	31.1953	1.17572
$705$	−2.96686	−0.111738
$706$	14.1437	0.532304
$707$	0	0
$708$	−0.641667	−0.0241153
$709$	−9.13112	−0.342926	−0.171463	−	0.985191i	$-0.554849\pi$
$709$	−9.13112	−0.342926	−0.171463	+	0.985191i	$0.554849\pi$
$710$	−10.3041	−0.386708
$711$	−6.75081	−0.253175
$712$	−13.0109	−0.487605
$713$	47.4785	1.77809
$714$	0	0
$715$	20.2725	0.758150
$716$	−7.63398	−0.285295
$717$	−0.263088	−0.00982519
$718$	−29.9682	−1.11840
$719$	24.2568	0.904626	0.452313	−	0.891859i	$-0.350599\pi$
$719$	24.2568	0.904626	0.452313	+	0.891859i	$0.350599\pi$
$720$	−0.685225	−0.0255368
$721$	0	0
$722$	−0.897685	−0.0334084
$723$	5.72923	0.213072
$724$	−3.99196	−0.148360
$725$	−26.4185	−0.981159
$726$	6.43869	0.238962
$727$	37.7041	1.39837	0.699183	−	0.714943i	$-0.253547\pi$
$727$	37.7041	1.39837	0.699183	+	0.714943i	$0.253547\pi$
$728$	0	0
$729$	−21.7800	−0.806668
$730$	−16.7626	−0.620413
$731$	23.0144	0.851217
$732$	0.890344	0.0329080
$733$	38.8444	1.43475	0.717376	−	0.696686i	$-0.245343\pi$
$733$	38.8444	1.43475	0.717376	+	0.696686i	$0.245343\pi$
$734$	−1.78547	−0.0659028
$735$	0	0
$736$	26.4895	0.976416
$737$	31.0087	1.14222
$738$	−30.1127	−1.10846
$739$	−3.49371	−0.128518	−0.0642592	−	0.997933i	$-0.520468\pi$
$739$	−3.49371	−0.128518	−0.0642592	+	0.997933i	$0.520468\pi$
$740$	3.19375	0.117405
$741$	−0.864560	−0.0317604
$742$	0	0
$743$	−15.8531	−0.581594	−0.290797	−	0.956785i	$-0.593920\pi$
$743$	−15.8531	−0.581594	−0.290797	+	0.956785i	$0.593920\pi$
$744$	9.02158	0.330747
$745$	15.6808	0.574502
$746$	23.8012	0.871423
$747$	32.9974	1.20731
$748$	−44.8541	−1.64003
$749$	0	0
$750$	3.01809	0.110205
$751$	−30.3469	−1.10737	−0.553687	−	0.832725i	$-0.686779\pi$
$751$	−30.3469	−1.10737	−0.553687	+	0.832725i	$0.686779\pi$
$752$	1.37301	0.0500685
$753$	−4.71695	−0.171895
$754$	19.2366	0.700556
$755$	17.1573	0.624420
$756$	0	0
$757$	26.2877	0.955444	0.477722	−	0.878511i	$-0.341463\pi$
$757$	26.2877	0.955444	0.477722	+	0.878511i	$0.341463\pi$
$758$	20.6134	0.748711
$759$	8.71343	0.316277
$760$	3.64860	0.132349
$761$	25.3152	0.917674	0.458837	−	0.888521i	$-0.348266\pi$
$761$	25.3152	0.917674	0.458837	+	0.888521i	$0.348266\pi$
$762$	−1.73315	−0.0627854
$763$	0	0
$764$	−14.5027	−0.524690
$765$	23.8633	0.862780
$766$	−14.4615	−0.522516
$767$	4.67402	0.168769
$768$	5.17316	0.186670
$769$	39.3637	1.41949	0.709746	−	0.704458i	$-0.248810\pi$
$769$	39.3637	1.41949	0.709746	+	0.704458i	$0.248810\pi$
$770$	0	0
$771$	1.51700	0.0546334
$772$	1.32607	0.0477262
$773$	−22.9656	−0.826015	−0.413007	−	0.910728i	$-0.635522\pi$
$773$	−22.9656	−0.826015	−0.413007	+	0.910728i	$0.635522\pi$
$774$	9.26864	0.333154
$775$	33.7404	1.21199
$776$	41.5180	1.49041
$777$	0	0
$778$	5.54053	0.198638
$779$	11.5648	0.414351
$780$	1.31372	0.0470389
$781$	−52.4065	−1.87525
$782$	27.6115	0.987386
$783$	14.5364	0.519489
$784$	0	0
$785$	1.19560	0.0426726
$786$	−1.90078	−0.0677985
$787$	49.8568	1.77720	0.888602	−	0.458679i	$-0.151677\pi$
$787$	49.8568	1.77720	0.888602	+	0.458679i	$0.151677\pi$
$788$	−1.28263	−0.0456919
$789$	8.33820	0.296848
$790$	2.65850	0.0945851
$791$	0	0
$792$	−48.3184	−1.71692
$793$	−6.48542	−0.230304
$794$	28.4105	1.00825
$795$	−3.14329	−0.111481
$796$	−14.9627	−0.530340
$797$	17.5366	0.621177	0.310588	−	0.950545i	$-0.399474\pi$
$797$	17.5366	0.621177	0.310588	+	0.950545i	$0.399474\pi$
$798$	0	0
$799$	−47.8158	−1.69160
$800$	18.8246	0.665551
$801$	13.1618	0.465051
$802$	−4.82897	−0.170517
$803$	−85.2542	−3.00855
$804$	2.00946	0.0708683
$805$	0	0
$806$	−24.5680	−0.865371
$807$	8.64045	0.304158
$808$	−28.7477	−1.01134
$809$	−0.241469	−0.00848960	−0.00424480	−	0.999991i	$-0.501351\pi$
$809$	−0.241469	−0.00848960	−0.00424480	+	0.999991i	$0.501351\pi$
$810$	9.26994	0.325713
$811$	−21.5761	−0.757641	−0.378820	−	0.925470i	$-0.623670\pi$
$811$	−21.5761	−0.757641	−0.378820	+	0.925470i	$0.623670\pi$
$812$	0	0
$813$	−3.87589	−0.135933
$814$	−10.9612	−0.384190
$815$	18.6305	0.652600
$816$	0.378416	0.0132472
$817$	−3.55962	−0.124535
$818$	23.2253	0.812052
$819$	0	0
$820$	−17.5730	−0.613677
$821$	4.78428	0.166973	0.0834863	−	0.996509i	$-0.473395\pi$
$821$	4.78428	0.166973	0.0834863	+	0.996509i	$0.473395\pi$
$822$	0.150088	0.00523490
$823$	48.8506	1.70283	0.851413	−	0.524496i	$-0.175746\pi$
$823$	48.8506	1.70283	0.851413	+	0.524496i	$0.175746\pi$
$824$	−21.7280	−0.756930
$825$	6.19215	0.215583
$826$	0	0
$827$	41.4198	1.44031	0.720155	−	0.693814i	$-0.244071\pi$
$827$	41.4198	1.44031	0.720155	+	0.693814i	$0.244071\pi$
$828$	−16.4787	−0.572675
$829$	27.3755	0.950789	0.475395	−	0.879773i	$-0.342305\pi$
$829$	27.3755	0.950789	0.475395	+	0.879773i	$0.342305\pi$
$830$	−12.9945	−0.451047
$831$	1.41793	0.0491875
$832$	−14.7254	−0.510510
$833$	0	0
$834$	1.52224	0.0527108
$835$	6.66462	0.230639
$836$	6.93755	0.239940
$837$	−18.5652	−0.641706
$838$	−2.21826	−0.0766286
$839$	−40.5455	−1.39979	−0.699894	−	0.714247i	$-0.746769\pi$
$839$	−40.5455	−1.39979	−0.699894	+	0.714247i	$0.746769\pi$
$840$	0	0
$841$	32.0618	1.10558
$842$	5.64323	0.194479
$843$	−3.15186	−0.108556
$844$	24.6515	0.848539
$845$	6.97264	0.239866
$846$	−19.2570	−0.662068
$847$	0	0
$848$	1.45466	0.0499532
$849$	−10.2593	−0.352099
$850$	19.6220	0.673029
$851$	−9.99915	−0.342766
$852$	−3.39611	−0.116349
$853$	−18.7751	−0.642847	−0.321423	−	0.946936i	$-0.604161\pi$
$853$	−18.7751	−0.642847	−0.321423	+	0.946936i	$0.604161\pi$
$854$	0	0
$855$	−3.69092	−0.126227
$856$	17.8571	0.610343
$857$	−49.9885	−1.70757	−0.853787	−	0.520623i	$-0.825700\pi$
$857$	−49.9885	−1.70757	−0.853787	+	0.520623i	$0.825700\pi$
$858$	−4.50881	−0.153928
$859$	−32.8565	−1.12105	−0.560525	−	0.828138i	$-0.689401\pi$
$859$	−32.8565	−1.12105	−0.560525	+	0.828138i	$0.689401\pi$
$860$	5.40894	0.184443
$861$	0	0
$862$	18.1280	0.617442
$863$	35.3419	1.20305	0.601527	−	0.798853i	$-0.294559\pi$
$863$	35.3419	1.20305	0.601527	+	0.798853i	$0.294559\pi$
$864$	−10.3580	−0.352386
$865$	−8.59794	−0.292339
$866$	−25.8746	−0.879255
$867$	−7.81903	−0.265548
$868$	0	0
$869$	13.5210	0.458669
$870$	−2.81404	−0.0954048
$871$	−14.6373	−0.495966
$872$	−14.3193	−0.484912
$873$	−41.9996	−1.42147
$874$	−4.27066	−0.144457
$875$	0	0
$876$	−5.52474	−0.186664
$877$	12.8075	0.432480	0.216240	−	0.976340i	$-0.430621\pi$
$877$	12.8075	0.432480	0.216240	+	0.976340i	$0.430621\pi$
$878$	33.4374	1.12846
$879$	2.88296	0.0972400
$880$	1.37242	0.0462642
$881$	−12.9759	−0.437170	−0.218585	−	0.975818i	$-0.570144\pi$
$881$	−12.9759	−0.437170	−0.218585	+	0.975818i	$0.570144\pi$
$882$	0	0
$883$	16.2295	0.546167	0.273084	−	0.961990i	$-0.411956\pi$
$883$	16.2295	0.546167	0.273084	+	0.961990i	$0.411956\pi$
$884$	21.1728	0.712119
$885$	−0.683742	−0.0229837
$886$	17.9952	0.604561
$887$	38.1665	1.28151	0.640754	−	0.767747i	$-0.278622\pi$
$887$	38.1665	1.28151	0.640754	+	0.767747i	$0.278622\pi$
$888$	−1.89998	−0.0637590
$889$	0	0
$890$	−5.18319	−0.173741
$891$	47.1465	1.57947
$892$	−21.1842	−0.709299
$893$	7.39563	0.247485
$894$	−3.48757	−0.116642
$895$	−8.13455	−0.271908
$896$	0	0
$897$	−4.11307	−0.137331
$898$	35.5603	1.18666
$899$	−77.9850	−2.60095
$900$	−11.7105	−0.390351
$901$	−50.6593	−1.68770
$902$	60.3120	2.00817
$903$	0	0
$904$	−10.3313	−0.343615
$905$	−4.25371	−0.141398
$906$	−3.81596	−0.126777
$907$	−10.6315	−0.353013	−0.176506	−	0.984300i	$-0.556480\pi$
$907$	−10.6315	−0.353013	−0.176506	+	0.984300i	$0.556480\pi$
$908$	−14.4900	−0.480866
$909$	29.0811	0.964559
$910$	0	0
$911$	8.97251	0.297273	0.148636	−	0.988892i	$-0.452512\pi$
$911$	8.97251	0.297273	0.148636	+	0.988892i	$0.452512\pi$
$912$	−0.0585294	−0.00193810
$913$	−66.0896	−2.18725
$914$	13.5013	0.446583
$915$	0.948725	0.0313639
$916$	−1.78464	−0.0589661
$917$	0	0
$918$	−10.7967	−0.356345
$919$	24.2004	0.798296	0.399148	−	0.916886i	$-0.369306\pi$
$919$	24.2004	0.798296	0.399148	+	0.916886i	$0.369306\pi$
$920$	17.3579	0.572274
$921$	−3.93962	−0.129815
$922$	26.2405	0.864184
$923$	24.7378	0.814256
$924$	0	0
$925$	−7.10584	−0.233639
$926$	−28.3549	−0.931801
$927$	21.9800	0.721918
$928$	−43.5098	−1.42828
$929$	−7.96584	−0.261351	−0.130675	−	0.991425i	$-0.541715\pi$
$929$	−7.96584	−0.261351	−0.130675	+	0.991425i	$0.541715\pi$
$930$	3.59395	0.117850
$931$	0	0
$932$	−33.0329	−1.08203
$933$	−1.95774	−0.0640934
$934$	0.335940	0.0109923
$935$	−47.7952	−1.56307
$936$	22.8081	0.745507
$937$	34.7177	1.13418	0.567088	−	0.823657i	$-0.308070\pi$
$937$	34.7177	1.13418	0.567088	+	0.823657i	$0.308070\pi$
$938$	0	0
$939$	−3.23994	−0.105732
$940$	−11.2379	−0.366539
$941$	−4.64089	−0.151289	−0.0756443	−	0.997135i	$-0.524101\pi$
$941$	−4.64089	−0.151289	−0.0756443	+	0.997135i	$0.524101\pi$
$942$	−0.265912	−0.00866387
$943$	55.0185	1.79165
$944$	0.316424	0.0102987
$945$	0	0
$946$	−18.5639	−0.603565
$947$	−6.56768	−0.213421	−0.106710	−	0.994290i	$-0.534032\pi$
$947$	−6.56768	−0.213421	−0.106710	+	0.994290i	$0.534032\pi$
$948$	0.876205	0.0284578
$949$	40.2432	1.30635
$950$	−3.03492	−0.0984659
$951$	6.05812	0.196448
$952$	0	0
$953$	7.94480	0.257357	0.128679	−	0.991686i	$-0.458926\pi$
$953$	7.94480	0.257357	0.128679	+	0.991686i	$0.458926\pi$
$954$	−20.4021	−0.660544
$955$	−15.4537	−0.500070
$956$	−0.996525	−0.0322299
$957$	−14.3121	−0.462644
$958$	−15.4686	−0.499767
$959$	0	0
$960$	2.15411	0.0695235
$961$	68.5984	2.21285
$962$	5.17411	0.166820
$963$	−18.0642	−0.582112
$964$	21.7012	0.698949
$965$	1.41302	0.0454867
$966$	0	0
$967$	−38.7543	−1.24625	−0.623127	−	0.782121i	$-0.714138\pi$
$967$	−38.7543	−1.24625	−0.623127	+	0.782121i	$0.714138\pi$
$968$	65.2348	2.09672
$969$	2.03831	0.0654801
$970$	16.5396	0.531055
$971$	−22.6607	−0.727215	−0.363608	−	0.931552i	$-0.618455\pi$
$971$	−22.6607	−0.727215	−0.363608	+	0.931552i	$0.618455\pi$
$972$	9.71958	0.311756
$973$	0	0
$974$	−28.4714	−0.912281
$975$	−2.92293	−0.0936088
$976$	−0.439053	−0.0140537
$977$	−1.43989	−0.0460662	−0.0230331	−	0.999735i	$-0.507332\pi$
$977$	−1.43989	−0.0460662	−0.0230331	+	0.999735i	$0.507332\pi$
$978$	−4.14361	−0.132498
$979$	−26.3615	−0.842518
$980$	0	0
$981$	14.4854	0.462482
$982$	−2.89806	−0.0924808
$983$	47.0907	1.50196	0.750980	−	0.660325i	$-0.229581\pi$
$983$	47.0907	1.50196	0.750980	+	0.660325i	$0.229581\pi$
$984$	10.4543	0.333270
$985$	−1.36674	−0.0435478
$986$	−45.3528	−1.44433
$987$	0	0
$988$	−3.27479	−0.104185
$989$	−16.9346	−0.538488
$990$	−19.2487	−0.611764
$991$	21.6261	0.686976	0.343488	−	0.939157i	$-0.388392\pi$
$991$	21.6261	0.686976	0.343488	+	0.939157i	$0.388392\pi$
$992$	55.5685	1.76430
$993$	2.17992	0.0691776
$994$	0	0
$995$	−15.9439	−0.505455
$996$	−4.28282	−0.135706
$997$	−0.181803	−0.00575777	−0.00287888	−	0.999996i	$-0.500916\pi$
$997$	−0.181803	−0.00575777	−0.00287888	+	0.999996i	$0.500916\pi$
$998$	−4.99004	−0.157957
$999$	3.90989	0.123703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.p.1.5	✓	10
3.2	odd	2		8379.2.a.ct.1.6		10
7.2	even	3		931.2.f.r.704.6		20
7.3	odd	6		931.2.f.q.324.6		20
7.4	even	3		931.2.f.r.324.6		20
7.5	odd	6		931.2.f.q.704.6		20
7.6	odd	2		931.2.a.q.1.5	yes	10
21.20	even	2		8379.2.a.cs.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.5	✓	10	1.1	even	1	trivial
931.2.a.q.1.5	yes	10	7.6	odd	2
931.2.f.q.324.6		20	7.3	odd	6
931.2.f.q.704.6		20	7.5	odd	6
931.2.f.r.324.6		20	7.4	even	3
931.2.f.r.704.6		20	7.2	even	3
8379.2.a.cs.1.6		10	21.20	even	2
8379.2.a.ct.1.6		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-0.897685 q^{2} -0.315265 q^{3} -1.19416 q^{4} -1.27247 q^{5} +0.283008 q^{6} +2.86735 q^{8} -2.90061 q^{9} +O(q^{10})\)	\(q-0.897685 q^{2} -0.315265 q^{3} -1.19416 q^{4} -1.27247 q^{5} +0.283008 q^{6} +2.86735 q^{8} -2.90061 q^{9} +1.14227 q^{10} +5.80955 q^{11} +0.376477 q^{12} -2.74233 q^{13} +0.401164 q^{15} -0.185651 q^{16} +6.46541 q^{17} +2.60383 q^{18} -1.00000 q^{19} +1.51953 q^{20} -5.21514 q^{22} -4.75742 q^{23} -0.903975 q^{24} -3.38083 q^{25} +2.46175 q^{26} +1.86025 q^{27} +7.81421 q^{29} -0.360118 q^{30} -9.97990 q^{31} -5.56804 q^{32} -1.83155 q^{33} -5.80389 q^{34} +3.46380 q^{36} +2.10180 q^{37} +0.897685 q^{38} +0.864560 q^{39} -3.64860 q^{40} -11.5648 q^{41} +3.55962 q^{43} -6.93755 q^{44} +3.69092 q^{45} +4.27066 q^{46} -7.39563 q^{47} +0.0585294 q^{48} +3.03492 q^{50} -2.03831 q^{51} +3.27479 q^{52} -7.83543 q^{53} -1.66992 q^{54} -7.39245 q^{55} +0.315265 q^{57} -7.01469 q^{58} -1.70440 q^{59} -0.479054 q^{60} +2.36493 q^{61} +8.95880 q^{62} +5.36965 q^{64} +3.48952 q^{65} +1.64415 q^{66} +5.33754 q^{67} -7.72074 q^{68} +1.49985 q^{69} -9.02074 q^{71} -8.31706 q^{72} -14.6748 q^{73} -1.88676 q^{74} +1.06586 q^{75} +1.19416 q^{76} -0.776102 q^{78} +2.32738 q^{79} +0.236235 q^{80} +8.11535 q^{81} +10.3815 q^{82} -11.3760 q^{83} -8.22700 q^{85} -3.19541 q^{86} -2.46354 q^{87} +16.6580 q^{88} -4.53762 q^{89} -3.31328 q^{90} +5.68113 q^{92} +3.14631 q^{93} +6.63894 q^{94} +1.27247 q^{95} +1.75541 q^{96} +14.4796 q^{97} -16.8512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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