LMFDB - Embedded newform 961.2.a.l.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(1,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,-8,0,8,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.67362363425$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 24x^{14} + 220x^{12} - 992x^{10} + 2366x^{8} - 2944x^{6} + 1688x^{4} - 288x^{2} + 4 $ x^16 - 24x^14 + 220x^12 - 992x^10 + 2366x^8 - 2944x^6 + 1688x^4 - 288*x^2 + 4
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			1.7
Root			$-1.23447$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.31607 q^{2} -1.23447 q^{3} -0.267953 q^{4} +0.00727825 q^{5} +1.62465 q^{6} -0.794917 q^{7} +2.98479 q^{8} -1.47609 q^{9} -0.00957870 q^{10} +3.97765 q^{11} +0.330779 q^{12} -6.30973 q^{13} +1.04617 q^{14} -0.00898475 q^{15} -3.39229 q^{16} +6.28085 q^{17} +1.94265 q^{18} +3.73460 q^{19} -0.00195023 q^{20} +0.981298 q^{21} -5.23488 q^{22} +0.483672 q^{23} -3.68462 q^{24} -4.99995 q^{25} +8.30406 q^{26} +5.52559 q^{27} +0.213001 q^{28} -1.62052 q^{29} +0.0118246 q^{30} -1.50508 q^{32} -4.91028 q^{33} -8.26605 q^{34} -0.00578561 q^{35} +0.395524 q^{36} +7.49037 q^{37} -4.91500 q^{38} +7.78915 q^{39} +0.0217241 q^{40} -4.02886 q^{41} -1.29146 q^{42} +0.701504 q^{43} -1.06583 q^{44} -0.0107434 q^{45} -0.636548 q^{46} +4.30532 q^{47} +4.18767 q^{48} -6.36811 q^{49} +6.58029 q^{50} -7.75350 q^{51} +1.69071 q^{52} -4.07969 q^{53} -7.27207 q^{54} +0.0289504 q^{55} -2.37266 q^{56} -4.61023 q^{57} +2.13272 q^{58} -13.7036 q^{59} +0.00240749 q^{60} -5.02369 q^{61} +1.17337 q^{63} +8.76538 q^{64} -0.0459238 q^{65} +6.46228 q^{66} -14.5255 q^{67} -1.68297 q^{68} -0.597077 q^{69} +0.00761428 q^{70} -9.41325 q^{71} -4.40583 q^{72} +4.42318 q^{73} -9.85787 q^{74} +6.17226 q^{75} -1.00070 q^{76} -3.16191 q^{77} -10.2511 q^{78} -10.4589 q^{79} -0.0246900 q^{80} -2.39286 q^{81} +5.30227 q^{82} -2.00812 q^{83} -0.262942 q^{84} +0.0457136 q^{85} -0.923230 q^{86} +2.00047 q^{87} +11.8725 q^{88} -1.12238 q^{89} +0.0141391 q^{90} +5.01572 q^{91} -0.129602 q^{92} -5.66611 q^{94} +0.0271813 q^{95} +1.85797 q^{96} +7.27529 q^{97} +8.38089 q^{98} -5.87139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 8 q^{4} - 16 q^{5} - 16 q^{7} + 8 q^{10} - 8 q^{14} - 8 q^{16} - 24 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{28} - 8 q^{32} - 32 q^{33} - 16 q^{35} - 40 q^{36} - 24 q^{38} - 32 q^{39} - 32 q^{41}+ \cdots + 16 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 8 * q^4 - 16 * q^5 - 16 * q^7 + 8 * q^10 - 8 * q^14 - 8 * q^16 - 24 * q^18 - 32 * q^19 - 24 * q^20 - 8 * q^28 - 8 * q^32 - 32 * q^33 - 16 * q^35 - 40 * q^36 - 24 * q^38 - 32 * q^39 - 32 * q^41 - 16 * q^45 - 32 * q^47 - 16 * q^49 - 32 * q^50 - 32 * q^51 - 48 * q^56 - 64 * q^59 - 16 * q^63 - 16 * q^64 + 16 * q^67 - 32 * q^69 + 88 * q^70 - 48 * q^71 + 48 * q^72 + 40 * q^76 + 32 * q^78 - 40 * q^80 - 16 * q^81 + 88 * q^82 - 32 * q^87 + 40 * q^90 - 32 * q^94 - 48 * q^95 + 16 * q^98

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 $

$2$	−1.31607	−0.930604	−0.465302	−	0.885152i	$-0.654054\pi$
$2$	−1.31607	−0.930604	−0.465302	+	0.885152i	$0.654054\pi$
$3$	−1.23447	−0.712719	−0.356360	−	0.934349i	$-0.615982\pi$
$3$	−1.23447	−0.712719	−0.356360	+	0.934349i	$0.615982\pi$
$4$	−0.267953	−0.133977
$5$	0.00727825	0.00325493	0.00162747	−	0.999999i	$-0.499482\pi$
$5$	0.00727825	0.00325493	0.00162747	+	0.999999i	$0.499482\pi$
$6$	1.62465	0.663259
$7$	−0.794917	−0.300451	−0.150225	−	0.988652i	$-0.548000\pi$
$7$	−0.794917	−0.300451	−0.150225	+	0.988652i	$0.548000\pi$
$8$	2.98479	1.05528
$9$	−1.47609	−0.492031
$10$	−0.00957870	−0.00302905
$11$	3.97765	1.19931	0.599654	−	0.800260i	$-0.295305\pi$
$11$	3.97765	1.19931	0.599654	+	0.800260i	$0.295305\pi$
$12$	0.330779	0.0954877
$13$	−6.30973	−1.75000	−0.875002	−	0.484119i	$-0.839140\pi$
$13$	−6.30973	−1.75000	−0.875002	+	0.484119i	$0.839140\pi$
$14$	1.04617	0.279600
$15$	−0.00898475	−0.00231985
$16$	−3.39229	−0.848074
$17$	6.28085	1.52333	0.761665	−	0.647971i	$-0.224382\pi$
$17$	6.28085	1.52333	0.761665	+	0.647971i	$0.224382\pi$
$18$	1.94265	0.457886
$19$	3.73460	0.856776	0.428388	−	0.903595i	$-0.359082\pi$
$19$	3.73460	0.856776	0.428388	+	0.903595i	$0.359082\pi$
$20$	−0.00195023	−0.000436085 0
$21$	0.981298	0.214137
$22$	−5.23488	−1.11608
$23$	0.483672	0.100853	0.0504263	−	0.998728i	$-0.483942\pi$
$23$	0.483672	0.100853	0.0504263	+	0.998728i	$0.483942\pi$
$24$	−3.68462	−0.752120
$25$	−4.99995	−0.999989
$26$	8.30406	1.62856
$27$	5.52559	1.06340
$28$	0.213001	0.0402534
$29$	−1.62052	−0.300922	−0.150461	−	0.988616i	$-0.548076\pi$
$29$	−1.62052	−0.300922	−0.150461	+	0.988616i	$0.548076\pi$
$30$	0.0118246	0.00215886
$31$	0	0
$31$	0	0
$32$	−1.50508	−0.266062
$33$	−4.91028	−0.854769
$34$	−8.26605	−1.41762
$35$	−0.00578561	−0.000977946 0
$36$	0.395524	0.0659207
$37$	7.49037	1.23141	0.615705	−	0.787977i	$-0.288871\pi$
$37$	7.49037	1.23141	0.615705	+	0.787977i	$0.288871\pi$
$38$	−4.91500	−0.797319
$39$	7.78915	1.24726
$40$	0.0217241	0.00343487
$41$	−4.02886	−0.629202	−0.314601	−	0.949224i	$-0.601871\pi$
$41$	−4.02886	−0.629202	−0.314601	+	0.949224i	$0.601871\pi$
$42$	−1.29146	−0.199277
$43$	0.701504	0.106978	0.0534892	−	0.998568i	$-0.482966\pi$
$43$	0.701504	0.106978	0.0534892	+	0.998568i	$0.482966\pi$
$44$	−1.06583	−0.160679
$45$	−0.0107434	−0.00160153
$46$	−0.636548	−0.0938538
$47$	4.30532	0.627995	0.313997	−	0.949424i	$-0.398332\pi$
$47$	4.30532	0.627995	0.313997	+	0.949424i	$0.398332\pi$
$48$	4.18767	0.604438
$49$	−6.36811	−0.909729
$50$	6.58029	0.930594
$51$	−7.75350	−1.08571
$52$	1.69071	0.234460
$53$	−4.07969	−0.560388	−0.280194	−	0.959943i	$-0.590399\pi$
$53$	−4.07969	−0.560388	−0.280194	+	0.959943i	$0.590399\pi$
$54$	−7.27207	−0.989603
$55$	0.0289504	0.00390366
$56$	−2.37266	−0.317060
$57$	−4.61023	−0.610640
$58$	2.13272	0.280039
$59$	−13.7036	−1.78406	−0.892028	−	0.451979i	$-0.850718\pi$
$59$	−13.7036	−1.78406	−0.892028	+	0.451979i	$0.850718\pi$
$60$	0.00240749	0.000310806 0
$61$	−5.02369	−0.643218	−0.321609	−	0.946873i	$-0.604224\pi$
$61$	−5.02369	−0.643218	−0.321609	+	0.946873i	$0.604224\pi$
$62$	0	0
$63$	1.17337	0.147831
$64$	8.76538	1.09567
$65$	−0.0459238	−0.00569615
$66$	6.46228	0.795452
$67$	−14.5255	−1.77457	−0.887287	−	0.461217i	$-0.847413\pi$
$67$	−14.5255	−1.77457	−0.887287	+	0.461217i	$0.847413\pi$
$68$	−1.68297	−0.204091
$69$	−0.597077	−0.0718796
$70$	0.00761428	0.000910080 0
$71$	−9.41325	−1.11715	−0.558574	−	0.829455i	$-0.688651\pi$
$71$	−9.41325	−1.11715	−0.558574	+	0.829455i	$0.688651\pi$
$72$	−4.40583	−0.519232
$73$	4.42318	0.517695	0.258847	−	0.965918i	$-0.416657\pi$
$73$	4.42318	0.517695	0.258847	+	0.965918i	$0.416657\pi$
$74$	−9.85787	−1.14595
$75$	6.17226	0.712712
$76$	−1.00070	−0.114788
$77$	−3.16191	−0.360333
$78$	−10.2511	−1.16071
$79$	−10.4589	−1.17671	−0.588356	−	0.808602i	$-0.700225\pi$
$79$	−10.4589	−1.17671	−0.588356	+	0.808602i	$0.700225\pi$
$80$	−0.0246900	−0.00276042
$81$	−2.39286	−0.265874
$82$	5.30227	0.585538
$83$	−2.00812	−0.220420	−0.110210	−	0.993908i	$-0.535152\pi$
$83$	−2.00812	−0.220420	−0.110210	+	0.993908i	$0.535152\pi$
$84$	−0.262942	−0.0286893
$85$	0.0457136	0.00495834
$86$	−0.923230	−0.0995545
$87$	2.00047	0.214473
$88$	11.8725	1.26561
$89$	−1.12238	−0.118972	−0.0594859	−	0.998229i	$-0.518946\pi$
$89$	−1.12238	−0.118972	−0.0594859	+	0.998229i	$0.518946\pi$
$90$	0.0141391	0.00149039
$91$	5.01572	0.525790
$92$	−0.129602	−0.0135119
$93$	0	0
$94$	−5.66611	−0.584414
$95$	0.0271813	0.00278875
$96$	1.85797	0.189628
$97$	7.27529	0.738694	0.369347	−	0.929292i	$-0.379581\pi$
$97$	7.27529	0.738694	0.369347	+	0.929292i	$0.379581\pi$
$98$	8.38089	0.846598
$99$	−5.87139	−0.590097
$100$	1.33975	0.133975
$101$	−6.43242	−0.640050	−0.320025	−	0.947409i	$-0.603691\pi$
$101$	−6.43242	−0.640050	−0.320025	+	0.947409i	$0.603691\pi$
$102$	10.2042	1.01036
$103$	−8.53543	−0.841021	−0.420510	−	0.907288i	$-0.638149\pi$
$103$	−8.53543	−0.841021	−0.420510	+	0.907288i	$0.638149\pi$
$104$	−18.8332	−1.84675
$105$	0.00714213	0.000697001 0
$106$	5.36916	0.521499
$107$	−13.5147	−1.30652	−0.653259	−	0.757134i	$-0.726599\pi$
$107$	−13.5147	−1.30652	−0.653259	+	0.757134i	$0.726599\pi$
$108$	−1.48060	−0.142471
$109$	10.2309	0.979944	0.489972	−	0.871738i	$-0.337007\pi$
$109$	10.2309	0.979944	0.489972	+	0.871738i	$0.337007\pi$
$110$	−0.0381008	−0.00363276
$111$	−9.24661	−0.877649
$112$	2.69659	0.254804
$113$	−8.32437	−0.783091	−0.391546	−	0.920159i	$-0.628059\pi$
$113$	−8.32437	−0.783091	−0.391546	+	0.920159i	$0.628059\pi$
$114$	6.06740	0.568264
$115$	0.00352029	0.000328268 0
$116$	0.434223	0.0403166
$117$	9.31376	0.861057
$118$	18.0349	1.66025
$119$	−4.99276	−0.457685
$120$	−0.0268176	−0.00244810
$121$	4.82172	0.438338
$122$	6.61154	0.598581
$123$	4.97349	0.448445
$124$	0	0
$125$	−0.0727821	−0.00650983
$126$	−1.54424	−0.137572
$127$	11.2464	0.997953	0.498976	−	0.866616i	$-0.333709\pi$
$127$	11.2464	0.997953	0.498976	+	0.866616i	$0.333709\pi$
$128$	−8.52572	−0.753574
$129$	−0.865983	−0.0762455
$130$	0.0604390	0.00530086
$131$	0.645577	0.0564044	0.0282022	−	0.999602i	$-0.491022\pi$
$131$	0.645577	0.0564044	0.0282022	+	0.999602i	$0.491022\pi$
$132$	1.31572	0.114519
$133$	−2.96870	−0.257419
$134$	19.1166	1.65143
$135$	0.0402166	0.00346129
$136$	18.7470	1.60754
$137$	2.88395	0.246393	0.123196	−	0.992382i	$-0.460685\pi$
$137$	2.88395	0.246393	0.123196	+	0.992382i	$0.460685\pi$
$138$	0.785796	0.0668914
$139$	3.37884	0.286589	0.143295	−	0.989680i	$-0.454230\pi$
$139$	3.37884	0.286589	0.143295	+	0.989680i	$0.454230\pi$
$140$	0.00155027	0.000131022 0
$141$	−5.31477	−0.447584
$142$	12.3885	1.03962
$143$	−25.0979	−2.09879
$144$	5.00735	0.417279
$145$	−0.0117945	−0.000979482 0
$146$	−5.82123	−0.481768
$147$	7.86121	0.648382
$148$	−2.00707	−0.164980
$149$	−11.7699	−0.964230	−0.482115	−	0.876108i	$-0.660131\pi$
$149$	−11.7699	−0.964230	−0.482115	+	0.876108i	$0.660131\pi$
$150$	−8.12315	−0.663252
$151$	−17.8685	−1.45412	−0.727061	−	0.686573i	$-0.759114\pi$
$151$	−17.8685	−1.45412	−0.727061	+	0.686573i	$0.759114\pi$
$152$	11.1470	0.904141
$153$	−9.27113	−0.749526
$154$	4.16130	0.335327
$155$	0	0
$156$	−2.08713	−0.167104
$157$	2.66095	0.212367	0.106184	−	0.994347i	$-0.466137\pi$
$157$	2.66095	0.212367	0.106184	+	0.994347i	$0.466137\pi$
$158$	13.7646	1.09505
$159$	5.03623	0.399399
$160$	−0.0109543	−0.000866015 0
$161$	−0.384479	−0.0303012
$162$	3.14918	0.247423
$163$	−16.9049	−1.32410	−0.662048	−	0.749461i	$-0.730312\pi$
$163$	−16.9049	−1.32410	−0.662048	+	0.749461i	$0.730312\pi$
$164$	1.07955	0.0842984
$165$	−0.0357382	−0.00278222
$166$	2.64283	0.205123
$167$	−15.4826	−1.19808	−0.599039	−	0.800720i	$-0.704450\pi$
$167$	−15.4826	−1.19808	−0.599039	+	0.800720i	$0.704450\pi$
$168$	2.92897	0.225975
$169$	26.8127	2.06252
$170$	−0.0601624	−0.00461425
$171$	−5.51262	−0.421560
$172$	−0.187970	−0.0143326
$173$	6.91064	0.525406	0.262703	−	0.964877i	$-0.415386\pi$
$173$	6.91064	0.525406	0.262703	+	0.964877i	$0.415386\pi$
$174$	−2.63277	−0.199590
$175$	3.97455	0.300447
$176$	−13.4934	−1.01710
$177$	16.9166	1.27153
$178$	1.47713	0.110716
$179$	14.4811	1.08237	0.541184	−	0.840904i	$-0.317976\pi$
$179$	14.4811	1.08237	0.541184	+	0.840904i	$0.317976\pi$
$180$	0.00287872	0.000214567 0
$181$	−17.3533	−1.28986	−0.644932	−	0.764240i	$-0.723114\pi$
$181$	−17.3533	−1.28986	−0.644932	+	0.764240i	$0.723114\pi$
$182$	−6.60104	−0.489302
$183$	6.20158	0.458434
$184$	1.44366	0.106428
$185$	0.0545168	0.00400815
$186$	0	0
$187$	24.9830	1.82694
$188$	−1.15362	−0.0841367
$189$	−4.39238	−0.319499
$190$	−0.0357726	−0.00259522
$191$	14.9051	1.07850	0.539248	−	0.842147i	$-0.318709\pi$
$191$	14.9051	1.07850	0.539248	+	0.842147i	$0.318709\pi$
$192$	−10.8206	−0.780907
$193$	10.2755	0.739647	0.369824	−	0.929102i	$-0.379418\pi$
$193$	10.2755	0.739647	0.369824	+	0.929102i	$0.379418\pi$
$194$	−9.57481	−0.687432
$195$	0.0566914	0.00405975
$196$	1.70636	0.121883
$197$	14.6052	1.04058	0.520289	−	0.853990i	$-0.325824\pi$
$197$	14.6052	1.04058	0.520289	+	0.853990i	$0.325824\pi$
$198$	7.72717	0.549146
$199$	−10.5918	−0.750831	−0.375415	−	0.926857i	$-0.622500\pi$
$199$	−10.5918	−0.750831	−0.375415	+	0.926857i	$0.622500\pi$
$200$	−14.9238	−1.05527
$201$	17.9313	1.26477
$202$	8.46553	0.595633
$203$	1.28818	0.0904123
$204$	2.07757	0.145459
$205$	−0.0293231	−0.00204801
$206$	11.2332	0.782657
$207$	−0.713946	−0.0496227
$208$	21.4045	1.48413
$209$	14.8549	1.02754
$210$	−0.00939957	−0.000648632 0
$211$	16.5603	1.14006	0.570030	−	0.821624i	$-0.306931\pi$
$211$	16.5603	1.14006	0.570030	+	0.821624i	$0.306931\pi$
$212$	1.09317	0.0750789
$213$	11.6203	0.796212
$214$	17.7864	1.21585
$215$	0.00510572	0.000348207 0
$216$	16.4927	1.12219
$217$	0	0
$218$	−13.4646	−0.911940
$219$	−5.46027	−0.368971
$220$	−0.00775734	−0.000523000 0
$221$	−39.6305	−2.66583
$222$	12.1692	0.816744
$223$	−0.805193	−0.0539197	−0.0269599	−	0.999637i	$-0.508583\pi$
$223$	−0.805193	−0.0539197	−0.0269599	+	0.999637i	$0.508583\pi$
$224$	1.19641	0.0799386
$225$	7.38039	0.492026
$226$	10.9555	0.728748
$227$	13.4746	0.894341	0.447171	−	0.894449i	$-0.352432\pi$
$227$	13.4746	0.894341	0.447171	+	0.894449i	$0.352432\pi$
$228$	1.23533	0.0818116
$229$	12.9495	0.855728	0.427864	−	0.903843i	$-0.359266\pi$
$229$	12.9495	0.855728	0.427864	+	0.903843i	$0.359266\pi$
$230$	−0.00463295	−0.000305488 0
$231$	3.90326	0.256816
$232$	−4.83690	−0.317558
$233$	12.3559	0.809465	0.404732	−	0.914435i	$-0.367365\pi$
$233$	12.3559	0.809465	0.404732	+	0.914435i	$0.367365\pi$
$234$	−12.2576	−0.801303
$235$	0.0313352	0.00204408
$236$	3.67192	0.239022
$237$	12.9111	0.838666
$238$	6.57083	0.425924
$239$	15.9331	1.03063	0.515314	−	0.857001i	$-0.327675\pi$
$239$	15.9331	1.03063	0.515314	+	0.857001i	$0.327675\pi$
$240$	0.0304789	0.00196741
$241$	−20.5217	−1.32192	−0.660961	−	0.750421i	$-0.729851\pi$
$241$	−20.5217	−1.32192	−0.660961	+	0.750421i	$0.729851\pi$
$242$	−6.34574	−0.407919
$243$	−13.6228	−0.873906
$244$	1.34612	0.0861762
$245$	−0.0463487	−0.00296111
$246$	−6.54548	−0.417324
$247$	−23.5643	−1.49936
$248$	0	0
$249$	2.47896	0.157097
$250$	0.0957865	0.00605807
$251$	−4.22944	−0.266960	−0.133480	−	0.991052i	$-0.542615\pi$
$251$	−4.22944	−0.266960	−0.133480	+	0.991052i	$0.542615\pi$
$252$	−0.314409	−0.0198059
$253$	1.92388	0.120953
$254$	−14.8010	−0.928698
$255$	−0.0564319	−0.00353390
$256$	−6.31029	−0.394393
$257$	18.5477	1.15697	0.578486	−	0.815692i	$-0.303644\pi$
$257$	18.5477	1.15697	0.578486	+	0.815692i	$0.303644\pi$
$258$	1.13970	0.0709544
$259$	−5.95423	−0.369978
$260$	0.0123054	0.000763151 0
$261$	2.39204	0.148063
$262$	−0.849627	−0.0524901
$263$	−14.4865	−0.893278	−0.446639	−	0.894714i	$-0.647379\pi$
$263$	−14.4865	−0.893278	−0.446639	+	0.894714i	$0.647379\pi$
$264$	−14.6561	−0.902024
$265$	−0.0296930	−0.00182403
$266$	3.90702	0.239555
$267$	1.38554	0.0847935
$268$	3.89216	0.237752
$269$	−15.0412	−0.917078	−0.458539	−	0.888674i	$-0.651627\pi$
$269$	−15.0412	−0.917078	−0.458539	+	0.888674i	$0.651627\pi$
$270$	−0.0529279	−0.00322109
$271$	−22.9151	−1.39199	−0.695996	−	0.718046i	$-0.745037\pi$
$271$	−22.9151	−1.39199	−0.695996	+	0.718046i	$0.745037\pi$
$272$	−21.3065	−1.29190
$273$	−6.19173	−0.374741
$274$	−3.79549	−0.229294
$275$	−19.8881	−1.19929
$276$	0.159989	0.00963019
$277$	−14.4506	−0.868255	−0.434127	−	0.900851i	$-0.642943\pi$
$277$	−14.4506	−0.868255	−0.434127	+	0.900851i	$0.642943\pi$
$278$	−4.44679	−0.266701
$279$	0	0
$280$	−0.0172688	−0.00103201
$281$	−5.81764	−0.347051	−0.173526	−	0.984829i	$-0.555516\pi$
$281$	−5.81764	−0.347051	−0.173526	+	0.984829i	$0.555516\pi$
$282$	6.99462	0.416523
$283$	2.58301	0.153544	0.0767721	−	0.997049i	$-0.475539\pi$
$283$	2.58301	0.153544	0.0767721	+	0.997049i	$0.475539\pi$
$284$	2.52231	0.149672
$285$	−0.0335544	−0.00198759
$286$	33.0307	1.95315
$287$	3.20261	0.189044
$288$	2.22163	0.130911
$289$	22.4491	1.32053
$290$	0.0155224	0.000911510 0
$291$	−8.98110	−0.526481
$292$	−1.18521	−0.0693590
$293$	18.4503	1.07788	0.538940	−	0.842344i	$-0.318825\pi$
$293$	18.4503	1.07788	0.538940	+	0.842344i	$0.318825\pi$
$294$	−10.3459	−0.603386
$295$	−0.0997382	−0.00580698
$296$	22.3572	1.29949
$297$	21.9789	1.27534
$298$	15.4901	0.897316
$299$	−3.05184	−0.176493
$300$	−1.65388	−0.0954867
$301$	−0.557638	−0.0321417
$302$	23.5163	1.35321
$303$	7.94061	0.456176
$304$	−12.6689	−0.726609
$305$	−0.0365637	−0.00209363
$306$	12.2015	0.697512
$307$	1.64574	0.0939276	0.0469638	−	0.998897i	$-0.485045\pi$
$307$	1.64574	0.0939276	0.0469638	+	0.998897i	$0.485045\pi$
$308$	0.847243	0.0482762
$309$	10.5367	0.599412
$310$	0	0
$311$	−19.2427	−1.09115	−0.545576	−	0.838061i	$-0.683689\pi$
$311$	−19.2427	−1.09115	−0.545576	+	0.838061i	$0.683689\pi$
$312$	23.2490	1.31621
$313$	−15.4030	−0.870630	−0.435315	−	0.900278i	$-0.643363\pi$
$313$	−15.4030	−0.870630	−0.435315	+	0.900278i	$0.643363\pi$
$314$	−3.50201	−0.197630
$315$	0.00854010	0.000481180 0
$316$	2.80248	0.157652
$317$	−28.9259	−1.62464	−0.812319	−	0.583214i	$-0.801795\pi$
$317$	−28.9259	−1.62464	−0.812319	+	0.583214i	$0.801795\pi$
$318$	−6.62805	−0.371683
$319$	−6.44585	−0.360898
$320$	0.0637966	0.00356634
$321$	16.6835	0.931181
$322$	0.506003	0.0281984
$323$	23.4565	1.30515
$324$	0.641176	0.0356209
$325$	31.5483	1.74999
$326$	22.2481	1.23221
$327$	−12.6297	−0.698425
$328$	−12.0253	−0.663987
$329$	−3.42237	−0.188681
$330$	0.0470341	0.00258914
$331$	1.84711	0.101526	0.0507631	−	0.998711i	$-0.483835\pi$
$331$	1.84711	0.101526	0.0507631	+	0.998711i	$0.483835\pi$
$332$	0.538082	0.0295311
$333$	−11.0565	−0.605892
$334$	20.3762	1.11494
$335$	−0.105720	−0.00577612
$336$	−3.32885	−0.181604
$337$	18.4735	1.00632	0.503158	−	0.864194i	$-0.332171\pi$
$337$	18.4735	1.00632	0.503158	+	0.864194i	$0.332171\pi$
$338$	−35.2875	−1.91939
$339$	10.2762	0.558124
$340$	−0.0122491	−0.000664301 0
$341$	0	0
$342$	7.25501	0.392306
$343$	10.6265	0.573779
$344$	2.09384	0.112892
$345$	−0.00434567	−0.000233963 0
$346$	−9.09490	−0.488945
$347$	12.1294	0.651142	0.325571	−	0.945518i	$-0.394444\pi$
$347$	12.1294	0.651142	0.325571	+	0.945518i	$0.394444\pi$
$348$	−0.536033	−0.0287344
$349$	1.08075	0.0578512	0.0289256	−	0.999582i	$-0.490791\pi$
$349$	1.08075	0.0578512	0.0289256	+	0.999582i	$0.490791\pi$
$350$	−5.23079	−0.279597
$351$	−34.8650	−1.86095
$352$	−5.98667	−0.319091
$353$	−18.3736	−0.977926	−0.488963	−	0.872305i	$-0.662625\pi$
$353$	−18.3736	−0.977926	−0.488963	+	0.872305i	$0.662625\pi$
$354$	−22.2635	−1.18329
$355$	−0.0685120	−0.00363624
$356$	0.300745	0.0159394
$357$	6.16339	0.326201
$358$	−19.0582	−1.00726
$359$	−27.6937	−1.46162	−0.730810	−	0.682581i	$-0.760857\pi$
$359$	−27.6937	−1.46162	−0.730810	+	0.682581i	$0.760857\pi$
$360$	−0.0320667	−0.00169007
$361$	−5.05278	−0.265936
$362$	22.8383	1.20035
$363$	−5.95225	−0.312412
$364$	−1.34398	−0.0704436
$365$	0.0321930	0.00168506
$366$	−8.16173	−0.426620
$367$	5.52561	0.288434	0.144217	−	0.989546i	$-0.453934\pi$
$367$	5.52561	0.288434	0.144217	+	0.989546i	$0.453934\pi$
$368$	−1.64076	−0.0855304
$369$	5.94698	0.309587
$370$	−0.0717481	−0.00373000
$371$	3.24301	0.168369
$372$	0	0
$373$	5.64476	0.292274	0.146137	−	0.989264i	$-0.453316\pi$
$373$	5.64476	0.292274	0.146137	+	0.989264i	$0.453316\pi$
$374$	−32.8795	−1.70016
$375$	0.0898470	0.00463968
$376$	12.8505	0.662712
$377$	10.2250	0.526616
$378$	5.78070	0.297327
$379$	−11.1725	−0.573895	−0.286947	−	0.957946i	$-0.592640\pi$
$379$	−11.1725	−0.573895	−0.286947	+	0.957946i	$0.592640\pi$
$380$	−0.00728333	−0.000373627 0
$381$	−13.8832	−0.711260
$382$	−19.6162	−1.00365
$383$	−18.5205	−0.946354	−0.473177	−	0.880967i	$-0.656893\pi$
$383$	−18.5205	−0.946354	−0.473177	+	0.880967i	$0.656893\pi$
$384$	10.5247	0.537087
$385$	−0.0230131	−0.00117286
$386$	−13.5233	−0.688319
$387$	−1.03549	−0.0526367
$388$	−1.94944	−0.0989678
$389$	23.5859	1.19585	0.597926	−	0.801551i	$-0.295992\pi$
$389$	23.5859	1.19585	0.597926	+	0.801551i	$0.295992\pi$
$390$	−0.0746099	−0.00377802
$391$	3.03787	0.153632
$392$	−19.0075	−0.960022
$393$	−0.796943	−0.0402005
$394$	−19.2215	−0.968366
$395$	−0.0761221	−0.00383012
$396$	1.57326	0.0790592
$397$	10.9091	0.547514	0.273757	−	0.961799i	$-0.411734\pi$
$397$	10.9091	0.547514	0.273757	+	0.961799i	$0.411734\pi$
$398$	13.9395	0.698726
$399$	3.66476	0.183467
$400$	16.9613	0.848065
$401$	10.6709	0.532879	0.266440	−	0.963852i	$-0.414153\pi$
$401$	10.6709	0.532879	0.266440	+	0.963852i	$0.414153\pi$
$402$	−23.5988	−1.17700
$403$	0	0
$404$	1.72359	0.0857517
$405$	−0.0174159	−0.000865401 0
$406$	−1.69533	−0.0841380
$407$	29.7941	1.47684
$408$	−23.1426	−1.14573
$409$	9.42592	0.466082	0.233041	−	0.972467i	$-0.425132\pi$
$409$	9.42592	0.466082	0.233041	+	0.972467i	$0.425132\pi$
$410$	0.0385913	0.00190589
$411$	−3.56014	−0.175609
$412$	2.28710	0.112677
$413$	10.8932	0.536021
$414$	0.939604	0.0461790
$415$	−0.0146156	−0.000717451 0
$416$	9.49663	0.465610
$417$	−4.17106	−0.204258
$418$	−19.5502	−0.956230
$419$	−29.2065	−1.42683	−0.713416	−	0.700740i	$-0.752853\pi$
$419$	−29.2065	−1.42683	−0.713416	+	0.700740i	$0.752853\pi$
$420$	−0.00191376	−9.33819e−5 0
$421$	0.596656	0.0290792	0.0145396	−	0.999894i	$-0.495372\pi$
$421$	0.596656	0.0290792	0.0145396	+	0.999894i	$0.495372\pi$
$422$	−21.7946	−1.06094
$423$	−6.35505	−0.308993
$424$	−12.1770	−0.591368
$425$	−31.4039	−1.52331
$426$	−15.2932	−0.740958
$427$	3.99342	0.193255
$428$	3.62132	0.175043
$429$	30.9825	1.49585
$430$	−0.00671950	−0.000324043 0
$431$	−24.0044	−1.15625	−0.578127	−	0.815947i	$-0.696216\pi$
$431$	−24.0044	−1.15625	−0.578127	+	0.815947i	$0.696216\pi$
$432$	−18.7444	−0.901841
$433$	12.5443	0.602840	0.301420	−	0.953492i	$-0.402539\pi$
$433$	12.5443	0.602840	0.301420	+	0.953492i	$0.402539\pi$
$434$	0	0
$435$	0.0145599	0.000698096 0
$436$	−2.74141	−0.131290
$437$	1.80632	0.0864081
$438$	7.18611	0.343366
$439$	−39.1172	−1.86696	−0.933482	−	0.358625i	$-0.883246\pi$
$439$	−39.1172	−1.86696	−0.933482	+	0.358625i	$0.883246\pi$
$440$	0.0864107	0.00411947
$441$	9.39992	0.447615
$442$	52.1566	2.48084
$443$	−7.49207	−0.355959	−0.177979	−	0.984034i	$-0.556956\pi$
$443$	−7.49207	−0.355959	−0.177979	+	0.984034i	$0.556956\pi$
$444$	2.47766	0.117585
$445$	−0.00816894	−0.000387245 0
$446$	1.05969	0.0501779
$447$	14.5296	0.687225
$448$	−6.96775	−0.329195
$449$	−17.5141	−0.826541	−0.413271	−	0.910608i	$-0.635614\pi$
$449$	−17.5141	−0.826541	−0.413271	+	0.910608i	$0.635614\pi$
$450$	−9.71313	−0.457881
$451$	−16.0254	−0.754607
$452$	2.23054	0.104916
$453$	22.0581	1.03638
$454$	−17.7336	−0.832277
$455$	0.0365056	0.00171141
$456$	−13.7606	−0.644398
$457$	4.89406	0.228934	0.114467	−	0.993427i	$-0.463484\pi$
$457$	4.89406	0.228934	0.114467	+	0.993427i	$0.463484\pi$
$458$	−17.0425	−0.796344
$459$	34.7054	1.61991
$460$	−0.000943272 0	−4.39803e−5 0
$461$	−20.2773	−0.944406	−0.472203	−	0.881490i	$-0.656541\pi$
$461$	−20.2773	−0.944406	−0.472203	+	0.881490i	$0.656541\pi$
$462$	−5.13698	−0.238994
$463$	22.9558	1.06685	0.533423	−	0.845848i	$-0.320905\pi$
$463$	22.9558	1.06685	0.533423	+	0.845848i	$0.320905\pi$
$464$	5.49727	0.255204
$465$	0	0
$466$	−16.2613	−0.753291
$467$	27.2874	1.26271	0.631355	−	0.775494i	$-0.282499\pi$
$467$	27.2874	1.26271	0.631355	+	0.775494i	$0.282499\pi$
$468$	−2.49565	−0.115362
$469$	11.5466	0.533172
$470$	−0.0412394	−0.00190223
$471$	−3.28486	−0.151358
$472$	−40.9024	−1.88268
$473$	2.79034	0.128300
$474$	−16.9919	−0.780465
$475$	−18.6728	−0.856767
$476$	1.33783	0.0613191
$477$	6.02200	0.275729
$478$	−20.9691	−0.959107
$479$	−34.3921	−1.57142	−0.785708	−	0.618597i	$-0.787701\pi$
$479$	−34.3921	−1.57142	−0.785708	+	0.618597i	$0.787701\pi$
$480$	0.0135227	0.000617226 0
$481$	−47.2622	−2.15497
$482$	27.0081	1.23019
$483$	0.474627	0.0215963
$484$	−1.29200	−0.0587271
$485$	0.0529514	0.00240440
$486$	17.9287	0.813260
$487$	−27.3078	−1.23743	−0.618717	−	0.785614i	$-0.712347\pi$
$487$	−27.3078	−1.23743	−0.618717	+	0.785614i	$0.712347\pi$
$488$	−14.9947	−0.678777
$489$	20.8686	0.943709
$490$	0.0609982	0.00275562
$491$	35.5025	1.60221	0.801103	−	0.598526i	$-0.204247\pi$
$491$	35.5025	1.60221	0.801103	+	0.598526i	$0.204247\pi$
$492$	−1.33266	−0.0600811
$493$	−10.1782	−0.458404
$494$	31.0123	1.39531
$495$	−0.0427334	−0.00192073
$496$	0	0
$497$	7.48275	0.335647
$498$	−3.26248	−0.146195
$499$	11.2078	0.501728	0.250864	−	0.968022i	$-0.419285\pi$
$499$	11.2078	0.501728	0.250864	+	0.968022i	$0.419285\pi$
$500$	0.0195022	0.000872165 0
$501$	19.1127	0.853892
$502$	5.56625	0.248434
$503$	−1.69935	−0.0757701	−0.0378851	−	0.999282i	$-0.512062\pi$
$503$	−1.69935	−0.0757701	−0.0378851	+	0.999282i	$0.512062\pi$
$504$	3.50227	0.156004
$505$	−0.0468168	−0.00208332
$506$	−2.53197	−0.112560
$507$	−33.0994	−1.46999
$508$	−3.01350	−0.133702
$509$	−41.5080	−1.83981	−0.919905	−	0.392141i	$-0.871734\pi$
$509$	−41.5080	−1.83981	−0.919905	+	0.392141i	$0.871734\pi$
$510$	0.0742684	0.00328866
$511$	−3.51607	−0.155542
$512$	25.3562	1.12060
$513$	20.6358	0.911095
$514$	−24.4101	−1.07668
$515$	−0.0621230	−0.00273747
$516$	0.232043	0.0102151
$517$	17.1251	0.753159
$518$	7.83619	0.344303
$519$	−8.53095	−0.374467
$520$	−0.137073	−0.00601105
$521$	−32.5673	−1.42680	−0.713399	−	0.700758i	$-0.752845\pi$
$521$	−32.5673	−1.42680	−0.713399	+	0.700758i	$0.752845\pi$
$522$	−3.14809	−0.137788
$523$	14.5341	0.635533	0.317766	−	0.948169i	$-0.397067\pi$
$523$	14.5341	0.635533	0.317766	+	0.948169i	$0.397067\pi$
$524$	−0.172985	−0.00755687
$525$	−4.90644	−0.214135
$526$	19.0653	0.831288
$527$	0	0
$528$	16.6571	0.724907
$529$	−22.7661	−0.989829
$530$	0.0390781	0.00169745
$531$	20.2278	0.877812
$532$	0.795472	0.0344881
$533$	25.4210	1.10111
$534$	−1.82347	−0.0789091
$535$	−0.0983636	−0.00425263
$536$	−43.3556	−1.87268
$537$	−17.8764	−0.771424
$538$	19.7953	0.853436
$539$	−25.3301	−1.09105
$540$	−0.0107762	−0.000463732 0
$541$	−8.39816	−0.361065	−0.180532	−	0.983569i	$-0.557782\pi$
$541$	−8.39816	−0.361065	−0.180532	+	0.983569i	$0.557782\pi$
$542$	30.1579	1.29539
$543$	21.4221	0.919311
$544$	−9.45316	−0.405301
$545$	0.0744632	0.00318965
$546$	8.14876	0.348735
$547$	12.4927	0.534150	0.267075	−	0.963676i	$-0.413943\pi$
$547$	12.4927	0.534150	0.267075	+	0.963676i	$0.413943\pi$
$548$	−0.772765	−0.0330109
$549$	7.41544	0.316483
$550$	26.1741	1.11607
$551$	−6.05198	−0.257823
$552$	−1.78215	−0.0758533
$553$	8.31392	0.353544
$554$	19.0181	0.808001
$555$	−0.0672991	−0.00285669
$556$	−0.905370	−0.0383962
$557$	−16.8308	−0.713144	−0.356572	−	0.934268i	$-0.616054\pi$
$557$	−16.8308	−0.713144	−0.356572	+	0.934268i	$0.616054\pi$
$558$	0	0
$559$	−4.42630	−0.187213
$560$	0.0196265	0.000829370 0
$561$	−30.8407	−1.30210
$562$	7.65644	0.322967
$563$	−16.7349	−0.705291	−0.352645	−	0.935757i	$-0.614718\pi$
$563$	−16.7349	−0.705291	−0.352645	+	0.935757i	$0.614718\pi$
$564$	1.42411	0.0599658
$565$	−0.0605869	−0.00254891
$566$	−3.39943	−0.142889
$567$	1.90213	0.0798819
$568$	−28.0966	−1.17891
$569$	5.33828	0.223792	0.111896	−	0.993720i	$-0.464308\pi$
$569$	5.33828	0.223792	0.111896	+	0.993720i	$0.464308\pi$
$570$	0.0441601	0.00184966
$571$	36.0006	1.50658	0.753290	−	0.657689i	$-0.228466\pi$
$571$	36.0006	1.50658	0.753290	+	0.657689i	$0.228466\pi$
$572$	6.72507	0.281189
$573$	−18.3998	−0.768665
$574$	−4.21487	−0.175925
$575$	−2.41834	−0.100852
$576$	−12.9385	−0.539105
$577$	2.28925	0.0953029	0.0476514	−	0.998864i	$-0.484826\pi$
$577$	2.28925	0.0953029	0.0476514	+	0.998864i	$0.484826\pi$
$578$	−29.5446	−1.22889
$579$	−12.6848	−0.527161
$580$	0.00316038	0.000131228 0
$581$	1.59629	0.0662252
$582$	11.8198	0.489946
$583$	−16.2276	−0.672078
$584$	13.2023	0.546314
$585$	0.0677879	0.00280268
$586$	−24.2820	−1.00308
$587$	2.09767	0.0865799	0.0432900	−	0.999063i	$-0.486216\pi$
$587$	2.09767	0.0865799	0.0432900	+	0.999063i	$0.486216\pi$
$588$	−2.10644	−0.0868680
$589$	0	0
$590$	0.131263	0.00540400
$591$	−18.0296	−0.741640
$592$	−25.4095	−1.04433
$593$	−6.64085	−0.272707	−0.136354	−	0.990660i	$-0.543538\pi$
$593$	−6.64085	−0.272707	−0.136354	+	0.990660i	$0.543538\pi$
$594$	−28.9258	−1.18684
$595$	−0.0363385	−0.00148973
$596$	3.15379	0.129184
$597$	13.0752	0.535132
$598$	4.01644	0.164245
$599$	30.7228	1.25530	0.627650	−	0.778495i	$-0.284017\pi$
$599$	30.7228	1.25530	0.627650	+	0.778495i	$0.284017\pi$
$600$	18.4229	0.752112
$601$	16.9603	0.691825	0.345913	−	0.938267i	$-0.387569\pi$
$601$	16.9603	0.691825	0.345913	+	0.938267i	$0.387569\pi$
$602$	0.733892	0.0299112
$603$	21.4410	0.873146
$604$	4.78793	0.194818
$605$	0.0350937	0.00142676
$606$	−10.4504	−0.424519
$607$	17.9166	0.727213	0.363606	−	0.931553i	$-0.381545\pi$
$607$	17.9166	0.727213	0.363606	+	0.931553i	$0.381545\pi$
$608$	−5.62086	−0.227956
$609$	−1.59021	−0.0644386
$610$	0.0481205	0.00194834
$611$	−27.1654	−1.09899
$612$	2.48423	0.100419
$613$	−17.6545	−0.713057	−0.356529	−	0.934284i	$-0.616040\pi$
$613$	−17.6545	−0.713057	−0.356529	+	0.934284i	$0.616040\pi$
$614$	−2.16592	−0.0874093
$615$	0.0361983	0.00145966
$616$	−9.43763	−0.380253
$617$	20.3423	0.818949	0.409474	−	0.912322i	$-0.365712\pi$
$617$	20.3423	0.818949	0.409474	+	0.912322i	$0.365712\pi$
$618$	−13.8671	−0.557815
$619$	16.4294	0.660354	0.330177	−	0.943919i	$-0.392892\pi$
$619$	16.4294	0.660354	0.330177	+	0.943919i	$0.392892\pi$
$620$	0	0
$621$	2.67257	0.107247
$622$	25.3247	1.01543
$623$	0.892197	0.0357451
$624$	−26.4231	−1.05777
$625$	24.9992	0.999968
$626$	20.2715	0.810211
$627$	−18.3379	−0.732346
$628$	−0.713012	−0.0284523
$629$	47.0459	1.87584
$630$	−0.0112394	−0.000447788 0
$631$	10.4159	0.414651	0.207326	−	0.978272i	$-0.433524\pi$
$631$	10.4159	0.414651	0.207326	+	0.978272i	$0.433524\pi$
$632$	−31.2175	−1.24176
$633$	−20.4432	−0.812543
$634$	38.0685	1.51189
$635$	0.0818538	0.00324827
$636$	−1.34948	−0.0535102
$637$	40.1810	1.59203
$638$	8.48321	0.335853
$639$	13.8948	0.549671
$640$	−0.0620523	−0.00245283
$641$	−22.8137	−0.901087	−0.450543	−	0.892755i	$-0.648770\pi$
$641$	−22.8137	−0.901087	−0.450543	+	0.892755i	$0.648770\pi$
$642$	−21.9567	−0.866561
$643$	−23.9877	−0.945982	−0.472991	−	0.881067i	$-0.656826\pi$
$643$	−23.9877	−0.945982	−0.472991	+	0.881067i	$0.656826\pi$
$644$	0.103023	0.00405966
$645$	−0.00630284	−0.000248174 0
$646$	−30.8704	−1.21458
$647$	19.6935	0.774232	0.387116	−	0.922031i	$-0.373471\pi$
$647$	19.6935	0.774232	0.387116	+	0.922031i	$0.373471\pi$
$648$	−7.14220	−0.280572
$649$	−54.5082	−2.13963
$650$	−41.5199	−1.62854
$651$	0	0
$652$	4.52973	0.177398
$653$	−4.96806	−0.194415	−0.0972076	−	0.995264i	$-0.530991\pi$
$653$	−4.96806	−0.194415	−0.0972076	+	0.995264i	$0.530991\pi$
$654$	16.6216	0.649957
$655$	0.00469867	0.000183592 0
$656$	13.6671	0.533610
$657$	−6.52904	−0.254722
$658$	4.50409	0.175588
$659$	1.54371	0.0601343	0.0300671	−	0.999548i	$-0.490428\pi$
$659$	1.54371	0.0601343	0.0300671	+	0.999548i	$0.490428\pi$
$660$	0.00957617	0.000372752 0
$661$	16.0367	0.623754	0.311877	−	0.950122i	$-0.399042\pi$
$661$	16.0367	0.623754	0.311877	+	0.950122i	$0.399042\pi$
$662$	−2.43093	−0.0944807
$663$	48.9225	1.89999
$664$	−5.99382	−0.232605
$665$	−0.0216069	−0.000837880 0
$666$	14.5511	0.563846
$667$	−0.783799	−0.0303488
$668$	4.14860	0.160514
$669$	0.993984	0.0384296
$670$	0.139136	0.00537528
$671$	−19.9825	−0.771416
$672$	−1.47693	−0.0569738
$673$	40.0730	1.54470	0.772351	−	0.635196i	$-0.219081\pi$
$673$	40.0730	1.54470	0.772351	+	0.635196i	$0.219081\pi$
$674$	−24.3125	−0.936482
$675$	−27.6276	−1.06339
$676$	−7.18455	−0.276329
$677$	−36.5467	−1.40461	−0.702303	−	0.711879i	$-0.747845\pi$
$677$	−36.5467	−1.40461	−0.702303	+	0.711879i	$0.747845\pi$
$678$	−13.5242	−0.519392
$679$	−5.78326	−0.221941
$680$	0.136446	0.00523245
$681$	−16.6339	−0.637414
$682$	0	0
$683$	−37.5447	−1.43661	−0.718303	−	0.695730i	$-0.755081\pi$
$683$	−37.5447	−1.43661	−0.718303	+	0.695730i	$0.755081\pi$
$684$	1.47712	0.0564793
$685$	0.0209901	0.000801992 0
$686$	−13.9853	−0.533961
$687$	−15.9857	−0.609894
$688$	−2.37971	−0.0907255
$689$	25.7417	0.980682
$690$	0.00571922	0.000217727 0
$691$	1.85926	0.0707296	0.0353648	−	0.999374i	$-0.488741\pi$
$691$	1.85926	0.0707296	0.0353648	+	0.999374i	$0.488741\pi$
$692$	−1.85173	−0.0703922
$693$	4.66727	0.177295
$694$	−15.9632	−0.605955
$695$	0.0245920	0.000932828 0
$696$	5.97099	0.226330
$697$	−25.3047	−0.958483
$698$	−1.42234	−0.0538365
$699$	−15.2530	−0.576921
$700$	−1.06499	−0.0402529
$701$	43.1920	1.63134	0.815670	−	0.578517i	$-0.196368\pi$
$701$	43.1920	1.63134	0.815670	+	0.578517i	$0.196368\pi$
$702$	45.8848	1.73181
$703$	27.9735	1.05504
$704$	34.8656	1.31405
$705$	−0.0386822	−0.00145686
$706$	24.1809	0.910061
$707$	5.11324	0.192303
$708$	−4.53287	−0.170356
$709$	48.5108	1.82186	0.910930	−	0.412561i	$-0.135366\pi$
$709$	48.5108	1.82186	0.910930	+	0.412561i	$0.135366\pi$
$710$	0.0901667	0.00338390
$711$	15.4382	0.578980
$712$	−3.35006	−0.125549
$713$	0	0
$714$	−8.11147	−0.303564
$715$	−0.182669	−0.00683143
$716$	−3.88026	−0.145012
$717$	−19.6689	−0.734549
$718$	36.4470	1.36019
$719$	−26.6658	−0.994466	−0.497233	−	0.867617i	$-0.665651\pi$
$719$	−26.6658	−0.994466	−0.497233	+	0.867617i	$0.665651\pi$
$720$	0.0364447	0.00135821
$721$	6.78496	0.252685
$722$	6.64982	0.247481
$723$	25.3334	0.942159
$724$	4.64989	0.172812
$725$	8.10250	0.300919
$726$	7.83359	0.290732
$727$	−36.7670	−1.36361	−0.681807	−	0.731532i	$-0.738806\pi$
$727$	−36.7670	−1.36361	−0.681807	+	0.731532i	$0.738806\pi$
$728$	14.9709	0.554857
$729$	23.9955	0.888723
$730$	−0.0423684	−0.00156812
$731$	4.40604	0.162963
$732$	−1.66173	−0.0614194
$733$	49.5889	1.83161	0.915803	−	0.401628i	$-0.131555\pi$
$733$	49.5889	1.83161	0.915803	+	0.401628i	$0.131555\pi$
$734$	−7.27210	−0.268418
$735$	0.0572158	0.00211044
$736$	−0.727964	−0.0268331
$737$	−57.7775	−2.12826
$738$	−7.82666	−0.288103
$739$	30.9679	1.13917	0.569587	−	0.821931i	$-0.307103\pi$
$739$	30.9679	1.13917	0.569587	+	0.821931i	$0.307103\pi$
$740$	−0.0146080	−0.000536999 0
$741$	29.0893	1.06862
$742$	−4.26804	−0.156685
$743$	45.6267	1.67388	0.836940	−	0.547294i	$-0.184342\pi$
$743$	45.6267	1.67388	0.836940	+	0.547294i	$0.184342\pi$
$744$	0	0
$745$	−0.0856644	−0.00313850
$746$	−7.42891	−0.271992
$747$	2.96417	0.108453
$748$	−6.69429	−0.244767
$749$	10.7431	0.392544
$750$	−0.118245	−0.00431770
$751$	28.5894	1.04324	0.521621	−	0.853177i	$-0.325327\pi$
$751$	28.5894	1.04324	0.521621	+	0.853177i	$0.325327\pi$
$752$	−14.6049	−0.532586
$753$	5.22110	0.190267
$754$	−13.4569	−0.490070
$755$	−0.130052	−0.00473307
$756$	1.17695	0.0428054
$757$	−7.91417	−0.287645	−0.143823	−	0.989603i	$-0.545939\pi$
$757$	−7.91417	−0.287645	−0.143823	+	0.989603i	$0.545939\pi$
$758$	14.7039	0.534069
$759$	−2.37496	−0.0862057
$760$	0.0811306	0.00294292
$761$	−22.8705	−0.829056	−0.414528	−	0.910036i	$-0.636053\pi$
$761$	−22.8705	−0.829056	−0.414528	+	0.910036i	$0.636053\pi$
$762$	18.2713	0.661901
$763$	−8.13274	−0.294425
$764$	−3.99387	−0.144493
$765$	−0.0674776	−0.00243966
$766$	24.3743	0.880680
$767$	86.4660	3.12211
$768$	7.78984	0.281092
$769$	−23.2138	−0.837110	−0.418555	−	0.908191i	$-0.637463\pi$
$769$	−23.2138	−0.837110	−0.418555	+	0.908191i	$0.637463\pi$
$770$	0.0302870	0.00109147
$771$	−22.8965	−0.824596
$772$	−2.75336	−0.0990955
$773$	22.3694	0.804572	0.402286	−	0.915514i	$-0.368216\pi$
$773$	22.3694	0.804572	0.402286	+	0.915514i	$0.368216\pi$
$774$	1.36277	0.0489839
$775$	0	0
$776$	21.7152	0.779531
$777$	7.35029	0.263690
$778$	−31.0407	−1.11286
$779$	−15.0462	−0.539085
$780$	−0.0151906	−0.000543912 0
$781$	−37.4426	−1.33980
$782$	−3.99806	−0.142970
$783$	−8.95430	−0.320001
$784$	21.6025	0.771518
$785$	0.0193671	0.000691241 0
$786$	1.04884	0.0374107
$787$	−11.4632	−0.408618	−0.204309	−	0.978906i	$-0.565495\pi$
$787$	−11.4632	−0.408618	−0.204309	+	0.978906i	$0.565495\pi$
$788$	−3.91351	−0.139413
$789$	17.8831	0.636657
$790$	0.100182	0.00356432
$791$	6.61719	0.235280
$792$	−17.5249	−0.622719
$793$	31.6982	1.12563
$794$	−14.3572	−0.509518
$795$	0.0366550	0.00130002
$796$	2.83810	0.100594
$797$	35.3903	1.25359	0.626794	−	0.779185i	$-0.284367\pi$
$797$	35.3903	1.25359	0.626794	+	0.779185i	$0.284367\pi$
$798$	−4.82308	−0.170735
$799$	27.0410	0.956644
$800$	7.52530	0.266060
$801$	1.65673	0.0585378
$802$	−14.0437	−0.495900
$803$	17.5939	0.620875
$804$	−4.80474	−0.169450
$805$	−0.00279834	−9.86284e−5 0
$806$	0	0
$807$	18.5678	0.653619
$808$	−19.1994	−0.675434
$809$	−10.8601	−0.381820	−0.190910	−	0.981608i	$-0.561144\pi$
$809$	−10.8601	−0.381820	−0.190910	+	0.981608i	$0.561144\pi$
$810$	0.0229205	0.000805345 0
$811$	41.2607	1.44886	0.724429	−	0.689349i	$-0.242103\pi$
$811$	41.2607	1.44886	0.724429	+	0.689349i	$0.242103\pi$
$812$	−0.345171	−0.0121131
$813$	28.2879	0.992099
$814$	−39.2112	−1.37435
$815$	−0.123038	−0.00430984
$816$	26.3021	0.920759
$817$	2.61984	0.0916565
$818$	−12.4052	−0.433737
$819$	−7.40367	−0.258705
$820$	0.00785721	0.000274386 0
$821$	5.91019	0.206267	0.103134	−	0.994668i	$-0.467113\pi$
$821$	5.91019	0.206267	0.103134	+	0.994668i	$0.467113\pi$
$822$	4.68541	0.163422
$823$	11.1079	0.387198	0.193599	−	0.981081i	$-0.437984\pi$
$823$	11.1079	0.387198	0.193599	+	0.981081i	$0.437984\pi$
$824$	−25.4765	−0.887515
$825$	24.5511	0.854760
$826$	−14.3363	−0.498823
$827$	−5.48482	−0.190726	−0.0953629	−	0.995443i	$-0.530401\pi$
$827$	−5.48482	−0.190726	−0.0953629	+	0.995443i	$0.530401\pi$
$828$	0.191304	0.00664828
$829$	−37.1412	−1.28997	−0.644983	−	0.764197i	$-0.723136\pi$
$829$	−37.1412	−1.28997	−0.644983	+	0.764197i	$0.723136\pi$
$830$	0.0192352	0.000667663 0
$831$	17.8388	0.618822
$832$	−55.3072	−1.91743
$833$	−39.9971	−1.38582
$834$	5.48941	0.190083
$835$	−0.112686	−0.00389966
$836$	−3.98043	−0.137666
$837$	0	0
$838$	38.4379	1.32782
$839$	36.2002	1.24977	0.624886	−	0.780716i	$-0.285146\pi$
$839$	36.2002	1.24977	0.624886	+	0.780716i	$0.285146\pi$
$840$	0.0213178	0.000735533 0
$841$	−26.3739	−0.909446
$842$	−0.785242	−0.0270612
$843$	7.18168	0.247350
$844$	−4.43740	−0.152742
$845$	0.195150	0.00671335
$846$	8.36371	0.287550
$847$	−3.83287	−0.131699
$848$	13.8395	0.475250
$849$	−3.18864	−0.109434
$850$	41.3298	1.41760
$851$	3.62288	0.124191
$852$	−3.11371	−0.106674
$853$	−11.1741	−0.382593	−0.191296	−	0.981532i	$-0.561269\pi$
$853$	−11.1741	−0.382593	−0.191296	+	0.981532i	$0.561269\pi$
$854$	−5.25563	−0.179844
$855$	−0.0401222	−0.00137215
$856$	−40.3387	−1.37875
$857$	54.8661	1.87419	0.937095	−	0.349075i	$-0.113504\pi$
$857$	54.8661	1.87419	0.937095	+	0.349075i	$0.113504\pi$
$858$	−40.7752	−1.39204
$859$	19.9109	0.679350	0.339675	−	0.940543i	$-0.389683\pi$
$859$	19.9109	0.679350	0.339675	+	0.940543i	$0.389683\pi$
$860$	−0.00136810	−4.66517e−5 0
$861$	−3.95352	−0.134735
$862$	31.5916	1.07601
$863$	−11.1772	−0.380477	−0.190238	−	0.981738i	$-0.560926\pi$
$863$	−11.1772	−0.380477	−0.190238	+	0.981738i	$0.560926\pi$
$864$	−8.31643	−0.282931
$865$	0.0502974	0.00171016
$866$	−16.5092	−0.561005
$867$	−27.7126	−0.941170
$868$	0	0
$869$	−41.6017	−1.41124
$870$	−0.0191619	−0.000649650 0
$871$	91.6521	3.10551
$872$	30.5372	1.03412
$873$	−10.7390	−0.363461
$874$	−2.37725	−0.0804117
$875$	0.0578558	0.00195588
$876$	1.46310	0.0494335
$877$	−27.5485	−0.930248	−0.465124	−	0.885246i	$-0.653990\pi$
$877$	−27.5485	−0.930248	−0.465124	+	0.885246i	$0.653990\pi$
$878$	51.4811	1.73740
$879$	−22.7763	−0.768225
$880$	−0.0982081	−0.00331059
$881$	−14.2624	−0.480514	−0.240257	−	0.970709i	$-0.577232\pi$
$881$	−14.2624	−0.480514	−0.240257	+	0.970709i	$0.577232\pi$
$882$	−12.3710	−0.416553
$883$	18.6749	0.628459	0.314229	−	0.949347i	$-0.398254\pi$
$883$	18.6749	0.628459	0.314229	+	0.949347i	$0.398254\pi$
$884$	10.6191	0.357160
$885$	0.123123	0.00413875
$886$	9.86011	0.331257
$887$	−34.7385	−1.16640	−0.583202	−	0.812327i	$-0.698200\pi$
$887$	−34.7385	−1.16640	−0.583202	+	0.812327i	$0.698200\pi$
$888$	−27.5992	−0.926168
$889$	−8.93992	−0.299835
$890$	0.0107509	0.000360372 0
$891$	−9.51798	−0.318864
$892$	0.215754	0.00722398
$893$	16.0786	0.538051
$894$	−19.1220	−0.639534
$895$	0.105397	0.00352303
$896$	6.77724	0.226412
$897$	3.76739	0.125790
$898$	23.0498	0.769183
$899$	0	0
$900$	−1.97760	−0.0659200
$901$	−25.6239	−0.853656
$902$	21.0906	0.702240
$903$	0.688385	0.0229080
$904$	−24.8465	−0.826383
$905$	−0.126302	−0.00419842
$906$	−29.0301	−0.964459
$907$	−6.36985	−0.211507	−0.105754	−	0.994392i	$-0.533725\pi$
$907$	−6.36985	−0.211507	−0.105754	+	0.994392i	$0.533725\pi$
$908$	−3.61057	−0.119821
$909$	9.49486	0.314925
$910$	−0.0480441	−0.00159264
$911$	54.3419	1.80043	0.900214	−	0.435447i	$-0.143410\pi$
$911$	54.3419	1.80043	0.900214	+	0.435447i	$0.143410\pi$
$912$	15.6393	0.517868
$913$	−7.98760	−0.264351
$914$	−6.44093	−0.213047
$915$	0.0451366	0.00149217
$916$	−3.46986	−0.114648
$917$	−0.513181	−0.0169467
$918$	−45.6748	−1.50749
$919$	−44.6967	−1.47441	−0.737204	−	0.675670i	$-0.763854\pi$
$919$	−44.6967	−1.47441	−0.737204	+	0.675670i	$0.763854\pi$
$920$	0.0105073	0.000346416 0
$921$	−2.03161	−0.0669440
$922$	26.6863	0.878868
$923$	59.3951	1.95501
$924$	−1.04589	−0.0344073
$925$	−37.4515	−1.23140
$926$	−30.2115	−0.992812
$927$	12.5991	0.413809
$928$	2.43900	0.0800641
$929$	15.4573	0.507139	0.253569	−	0.967317i	$-0.418395\pi$
$929$	15.4573	0.507139	0.253569	+	0.967317i	$0.418395\pi$
$930$	0	0
$931$	−23.7823	−0.779434
$932$	−3.31082	−0.108449
$933$	23.7544	0.777685
$934$	−35.9122	−1.17508
$935$	0.181833	0.00594657
$936$	27.7996	0.908659
$937$	−5.31792	−0.173729	−0.0868645	−	0.996220i	$-0.527685\pi$
$937$	−5.31792	−0.173729	−0.0868645	+	0.996220i	$0.527685\pi$
$938$	−15.1961	−0.496172
$939$	19.0145	0.620514
$940$	−0.00839636	−0.000273859 0
$941$	13.3788	0.436137	0.218069	−	0.975933i	$-0.430024\pi$
$941$	13.3788	0.436137	0.218069	+	0.975933i	$0.430024\pi$
$942$	4.32311	0.140855
$943$	−1.94865	−0.0634567
$944$	46.4866	1.51301
$945$	−0.0319689	−0.00103995
$946$	−3.67229	−0.119396
$947$	−6.71768	−0.218295	−0.109148	−	0.994026i	$-0.534812\pi$
$947$	−6.71768	−0.218295	−0.109148	+	0.994026i	$0.534812\pi$
$948$	−3.45957	−0.112362
$949$	−27.9091	−0.905968
$950$	24.5747	0.797310
$951$	35.7080	1.15791
$952$	−14.9023	−0.482988
$953$	20.6118	0.667682	0.333841	−	0.942629i	$-0.391655\pi$
$953$	20.6118	0.667682	0.333841	+	0.942629i	$0.391655\pi$
$954$	−7.92539	−0.256594
$955$	0.108483	0.00351043
$956$	−4.26933	−0.138080
$957$	7.95718	0.257219
$958$	45.2625	1.46237
$959$	−2.29251	−0.0740289
$960$	−0.0787547	−0.00254180
$961$	0	0
$962$	62.2005	2.00543
$963$	19.9490	0.642848
$964$	5.49887	0.177107
$965$	0.0747877	0.00240750
$966$	−0.624643	−0.0200976
$967$	−59.1290	−1.90146	−0.950731	−	0.310018i	$-0.899665\pi$
$967$	−59.1290	−1.90146	−0.950731	+	0.310018i	$0.899665\pi$
$968$	14.3918	0.462571
$969$	−28.9562	−0.930207
$970$	−0.0696879	−0.00223754
$971$	−45.7817	−1.46920	−0.734602	−	0.678498i	$-0.762631\pi$
$971$	−45.7817	−1.46920	−0.734602	+	0.678498i	$0.762631\pi$
$972$	3.65029	0.117083
$973$	−2.68590	−0.0861059
$974$	35.9390	1.15156
$975$	−38.9453	−1.24725
$976$	17.0418	0.545496
$977$	7.43684	0.237926	0.118963	−	0.992899i	$-0.462043\pi$
$977$	7.43684	0.237926	0.118963	+	0.992899i	$0.462043\pi$
$978$	−27.4645	−0.878219
$979$	−4.46443	−0.142684
$980$	0.0124193	0.000396719 0
$981$	−15.1018	−0.482163
$982$	−46.7239	−1.49102
$983$	−27.2101	−0.867867	−0.433934	−	0.900945i	$-0.642875\pi$
$983$	−27.2101	−0.867867	−0.433934	+	0.900945i	$0.642875\pi$
$984$	14.8448	0.473236
$985$	0.106300	0.00338701
$986$	13.3953	0.426593
$987$	4.22480	0.134477
$988$	6.31414	0.200879
$989$	0.339298	0.0107891
$990$	0.0562403	0.00178743
$991$	17.2059	0.546563	0.273282	−	0.961934i	$-0.411891\pi$
$991$	17.2059	0.546563	0.273282	+	0.961934i	$0.411891\pi$
$992$	0	0
$993$	−2.28019	−0.0723597
$994$	−9.84785	−0.312355
$995$	−0.0770896	−0.00244390
$996$	−0.664244	−0.0210474
$997$	29.5057	0.934454	0.467227	−	0.884137i	$-0.345253\pi$
$997$	29.5057	0.934454	0.467227	+	0.884137i	$0.345253\pi$
$998$	−14.7502	−0.466910
$999$	41.3887	1.30948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.l.1.7	✓	16
3.2	odd	2		8649.2.a.bs.1.9		16
31.2	even	5		961.2.d.s.531.7		64
31.3	odd	30		961.2.g.w.846.7		128
31.4	even	5		961.2.d.s.388.10		64
31.5	even	3		961.2.c.l.521.8		32
31.6	odd	6		961.2.c.l.439.7		32
31.7	even	15		961.2.g.w.235.9		128
31.8	even	5		961.2.d.s.374.10		64
31.9	even	15		961.2.g.w.732.9		128
31.10	even	15		961.2.g.w.844.8		128
31.11	odd	30		961.2.g.w.338.9		128
31.12	odd	30		961.2.g.w.547.8		128
31.13	odd	30		961.2.g.w.448.8		128
31.14	even	15		961.2.g.w.816.10		128
31.15	odd	10		961.2.d.s.628.8		64
31.16	even	5		961.2.d.s.628.7		64
31.17	odd	30		961.2.g.w.816.9		128
31.18	even	15		961.2.g.w.448.7		128
31.19	even	15		961.2.g.w.547.7		128
31.20	even	15		961.2.g.w.338.10		128
31.21	odd	30		961.2.g.w.844.7		128
31.22	odd	30		961.2.g.w.732.10		128
31.23	odd	10		961.2.d.s.374.9		64
31.24	odd	30		961.2.g.w.235.10		128
31.25	even	3		961.2.c.l.439.8		32
31.26	odd	6		961.2.c.l.521.7		32
31.27	odd	10		961.2.d.s.388.9		64
31.28	even	15		961.2.g.w.846.8		128
31.29	odd	10		961.2.d.s.531.8		64
31.30	odd	2	inner	961.2.a.l.1.8	yes	16
93.92	even	2		8649.2.a.bs.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.7	✓	16	1.1	even	1	trivial
961.2.a.l.1.8	yes	16	31.30	odd	2	inner
961.2.c.l.439.7		32	31.6	odd	6
961.2.c.l.439.8		32	31.25	even	3
961.2.c.l.521.7		32	31.26	odd	6
961.2.c.l.521.8		32	31.5	even	3
961.2.d.s.374.9		64	31.23	odd	10
961.2.d.s.374.10		64	31.8	even	5
961.2.d.s.388.9		64	31.27	odd	10
961.2.d.s.388.10		64	31.4	even	5
961.2.d.s.531.7		64	31.2	even	5
961.2.d.s.531.8		64	31.29	odd	10
961.2.d.s.628.7		64	31.16	even	5
961.2.d.s.628.8		64	31.15	odd	10
961.2.g.w.235.9		128	31.7	even	15
961.2.g.w.235.10		128	31.24	odd	30
961.2.g.w.338.9		128	31.11	odd	30
961.2.g.w.338.10		128	31.20	even	15
961.2.g.w.448.7		128	31.18	even	15
961.2.g.w.448.8		128	31.13	odd	30
961.2.g.w.547.7		128	31.19	even	15
961.2.g.w.547.8		128	31.12	odd	30
961.2.g.w.732.9		128	31.9	even	15
961.2.g.w.732.10		128	31.22	odd	30
961.2.g.w.816.9		128	31.17	odd	30
961.2.g.w.816.10		128	31.14	even	15
961.2.g.w.844.7		128	31.21	odd	30
961.2.g.w.844.8		128	31.10	even	15
961.2.g.w.846.7		128	31.3	odd	30
961.2.g.w.846.8		128	31.28	even	15
8649.2.a.bs.1.9		16	3.2	odd	2
8649.2.a.bs.1.10		16	93.92	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31607 q^{2} -1.23447 q^{3} -0.267953 q^{4} +0.00727825 q^{5} +1.62465 q^{6} -0.794917 q^{7} +2.98479 q^{8} -1.47609 q^{9} -0.00957870 q^{10} +3.97765 q^{11} +0.330779 q^{12} -6.30973 q^{13} +1.04617 q^{14} -0.00898475 q^{15} -3.39229 q^{16} +6.28085 q^{17} +1.94265 q^{18} +3.73460 q^{19} -0.00195023 q^{20} +0.981298 q^{21} -5.23488 q^{22} +0.483672 q^{23} -3.68462 q^{24} -4.99995 q^{25} +8.30406 q^{26} +5.52559 q^{27} +0.213001 q^{28} -1.62052 q^{29} +0.0118246 q^{30} -1.50508 q^{32} -4.91028 q^{33} -8.26605 q^{34} -0.00578561 q^{35} +0.395524 q^{36} +7.49037 q^{37} -4.91500 q^{38} +7.78915 q^{39} +0.0217241 q^{40} -4.02886 q^{41} -1.29146 q^{42} +0.701504 q^{43} -1.06583 q^{44} -0.0107434 q^{45} -0.636548 q^{46} +4.30532 q^{47} +4.18767 q^{48} -6.36811 q^{49} +6.58029 q^{50} -7.75350 q^{51} +1.69071 q^{52} -4.07969 q^{53} -7.27207 q^{54} +0.0289504 q^{55} -2.37266 q^{56} -4.61023 q^{57} +2.13272 q^{58} -13.7036 q^{59} +0.00240749 q^{60} -5.02369 q^{61} +1.17337 q^{63} +8.76538 q^{64} -0.0459238 q^{65} +6.46228 q^{66} -14.5255 q^{67} -1.68297 q^{68} -0.597077 q^{69} +0.00761428 q^{70} -9.41325 q^{71} -4.40583 q^{72} +4.42318 q^{73} -9.85787 q^{74} +6.17226 q^{75} -1.00070 q^{76} -3.16191 q^{77} -10.2511 q^{78} -10.4589 q^{79} -0.0246900 q^{80} -2.39286 q^{81} +5.30227 q^{82} -2.00812 q^{83} -0.262942 q^{84} +0.0457136 q^{85} -0.923230 q^{86} +2.00047 q^{87} +11.8725 q^{88} -1.12238 q^{89} +0.0141391 q^{90} +5.01572 q^{91} -0.129602 q^{92} -5.66611 q^{94} +0.0271813 q^{95} +1.85797 q^{96} +7.27529 q^{97} +8.38089 q^{98} -5.87139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 8 q^{4} - 16 q^{5} - 16 q^{7} + 8 q^{10} - 8 q^{14} - 8 q^{16} - 24 q^{18} - 32 q^{19} - 24 q^{20} - 8 q^{28} - 8 q^{32} - 32 q^{33} - 16 q^{35} - 40 q^{36} - 24 q^{38} - 32 q^{39} - 32 q^{41}+ \cdots + 16 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 8 * q^4 - 16 * q^5 - 16 * q^7 + 8 * q^10 - 8 * q^14 - 8 * q^16 - 24 * q^18 - 32 * q^19 - 24 * q^20 - 8 * q^28 - 8 * q^32 - 32 * q^33 - 16 * q^35 - 40 * q^36 - 24 * q^38 - 32 * q^39 - 32 * q^41 - 16 * q^45 - 32 * q^47 - 16 * q^49 - 32 * q^50 - 32 * q^51 - 48 * q^56 - 64 * q^59 - 16 * q^63 - 16 * q^64 + 16 * q^67 - 32 * q^69 + 88 * q^70 - 48 * q^71 + 48 * q^72 + 40 * q^76 + 32 * q^78 - 40 * q^80 - 16 * q^81 + 88 * q^82 - 32 * q^87 + 40 * q^90 - 32 * q^94 - 48 * q^95 + 16 * q^98

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