LMFDB - Embedded newform 983.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.55013 q^{2} -0.251970 q^{3} +0.402914 q^{4} -1.29975 q^{5} +0.390586 q^{6} -4.11447 q^{7} +2.47570 q^{8} -2.93651 q^{9} +O(q^{10})$	\(q-1.55013 q^{2} -0.251970 q^{3} +0.402914 q^{4} -1.29975 q^{5} +0.390586 q^{6} -4.11447 q^{7} +2.47570 q^{8} -2.93651 q^{9} +2.01479 q^{10} +4.84302 q^{11} -0.101522 q^{12} -3.12205 q^{13} +6.37798 q^{14} +0.327498 q^{15} -4.64349 q^{16} -7.50605 q^{17} +4.55198 q^{18} -1.93890 q^{19} -0.523688 q^{20} +1.03672 q^{21} -7.50732 q^{22} +8.18959 q^{23} -0.623800 q^{24} -3.31065 q^{25} +4.83959 q^{26} +1.49582 q^{27} -1.65778 q^{28} -5.11845 q^{29} -0.507665 q^{30} -4.55536 q^{31} +2.24663 q^{32} -1.22029 q^{33} +11.6354 q^{34} +5.34779 q^{35} -1.18316 q^{36} +6.16137 q^{37} +3.00556 q^{38} +0.786661 q^{39} -3.21779 q^{40} +0.788014 q^{41} -1.60706 q^{42} +11.7031 q^{43} +1.95132 q^{44} +3.81673 q^{45} -12.6950 q^{46} +2.85520 q^{47} +1.17002 q^{48} +9.92890 q^{49} +5.13195 q^{50} +1.89130 q^{51} -1.25792 q^{52} +1.08026 q^{53} -2.31872 q^{54} -6.29471 q^{55} -10.1862 q^{56} +0.488544 q^{57} +7.93428 q^{58} -6.50914 q^{59} +0.131953 q^{60} -5.31690 q^{61} +7.06142 q^{62} +12.0822 q^{63} +5.80439 q^{64} +4.05789 q^{65} +1.89162 q^{66} +10.0684 q^{67} -3.02429 q^{68} -2.06353 q^{69} -8.28979 q^{70} -12.1102 q^{71} -7.26991 q^{72} +12.7299 q^{73} -9.55094 q^{74} +0.834182 q^{75} -0.781210 q^{76} -19.9265 q^{77} -1.21943 q^{78} +6.95224 q^{79} +6.03538 q^{80} +8.43263 q^{81} -1.22153 q^{82} +11.1614 q^{83} +0.417710 q^{84} +9.75600 q^{85} -18.1414 q^{86} +1.28969 q^{87} +11.9898 q^{88} -9.97547 q^{89} -5.91645 q^{90} +12.8456 q^{91} +3.29970 q^{92} +1.14781 q^{93} -4.42593 q^{94} +2.52009 q^{95} -0.566083 q^{96} -1.74802 q^{97} -15.3911 q^{98} -14.2216 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.55013	−1.09611	−0.548055	−	0.836442i	$-0.684632\pi$
$2$	−1.55013	−1.09611	−0.548055	+	0.836442i	$0.684632\pi$
$3$	−0.251970	−0.145475	−0.0727373	−	0.997351i	$-0.523173\pi$
$3$	−0.251970	−0.145475	−0.0727373	+	0.997351i	$0.523173\pi$
$4$	0.402914	0.201457
$5$	−1.29975	−0.581266	−0.290633	−	0.956835i	$-0.593866\pi$
$5$	−1.29975	−0.581266	−0.290633	+	0.956835i	$0.593866\pi$
$6$	0.390586	0.159456
$7$	−4.11447	−1.55513	−0.777563	−	0.628806i	$-0.783544\pi$
$7$	−4.11447	−1.55513	−0.777563	+	0.628806i	$0.783544\pi$
$8$	2.47570	0.875291
$9$	−2.93651	−0.978837
$10$	2.01479	0.637132
$11$	4.84302	1.46022	0.730112	−	0.683327i	$-0.239468\pi$
$11$	4.84302	1.46022	0.730112	+	0.683327i	$0.239468\pi$
$12$	−0.101522	−0.0293069
$13$	−3.12205	−0.865901	−0.432950	−	0.901418i	$-0.642527\pi$
$13$	−3.12205	−0.865901	−0.432950	+	0.901418i	$0.642527\pi$
$14$	6.37798	1.70459
$15$	0.327498	0.0845595
$16$	−4.64349	−1.16087
$17$	−7.50605	−1.82048	−0.910242	−	0.414076i	$-0.864105\pi$
$17$	−7.50605	−1.82048	−0.910242	+	0.414076i	$0.864105\pi$
$18$	4.55198	1.07291
$19$	−1.93890	−0.444814	−0.222407	−	0.974954i	$-0.571391\pi$
$19$	−1.93890	−0.444814	−0.222407	+	0.974954i	$0.571391\pi$
$20$	−0.523688	−0.117100
$21$	1.03672	0.226231
$22$	−7.50732	−1.60057
$23$	8.18959	1.70765	0.853824	−	0.520562i	$-0.174278\pi$
$23$	8.18959	1.70765	0.853824	+	0.520562i	$0.174278\pi$
$24$	−0.623800	−0.127333
$25$	−3.31065	−0.662130
$26$	4.83959	0.949122
$27$	1.49582	0.287871
$28$	−1.65778	−0.313291
$29$	−5.11845	−0.950472	−0.475236	−	0.879858i	$-0.657637\pi$
$29$	−5.11845	−0.950472	−0.475236	+	0.879858i	$0.657637\pi$
$30$	−0.507665	−0.0926865
$31$	−4.55536	−0.818167	−0.409084	−	0.912497i	$-0.634152\pi$
$31$	−4.55536	−0.818167	−0.409084	+	0.912497i	$0.634152\pi$
$32$	2.24663	0.397152
$33$	−1.22029	−0.212426
$34$	11.6354	1.99545
$35$	5.34779	0.903942
$36$	−1.18316	−0.197194
$37$	6.16137	1.01292	0.506461	−	0.862263i	$-0.330953\pi$
$37$	6.16137	1.01292	0.506461	+	0.862263i	$0.330953\pi$
$38$	3.00556	0.487566
$39$	0.786661	0.125967
$40$	−3.21779	−0.508777
$41$	0.788014	0.123067	0.0615335	−	0.998105i	$-0.480401\pi$
$41$	0.788014	0.123067	0.0615335	+	0.998105i	$0.480401\pi$
$42$	−1.60706	−0.247974
$43$	11.7031	1.78471	0.892356	−	0.451333i	$-0.149051\pi$
$43$	11.7031	1.78471	0.892356	+	0.451333i	$0.149051\pi$
$44$	1.95132	0.294172
$45$	3.81673	0.568965
$46$	−12.6950	−1.87177
$47$	2.85520	0.416473	0.208237	−	0.978078i	$-0.433228\pi$
$47$	2.85520	0.416473	0.208237	+	0.978078i	$0.433228\pi$
$48$	1.17002	0.168877
$49$	9.92890	1.41841
$50$	5.13195	0.725767
$51$	1.89130	0.264834
$52$	−1.25792	−0.174442
$53$	1.08026	0.148384	0.0741922	−	0.997244i	$-0.476362\pi$
$53$	1.08026	0.148384	0.0741922	+	0.997244i	$0.476362\pi$
$54$	−2.31872	−0.315538
$55$	−6.29471	−0.848779
$56$	−10.1862	−1.36119
$57$	0.488544	0.0647092
$58$	7.93428	1.04182
$59$	−6.50914	−0.847418	−0.423709	−	0.905798i	$-0.639272\pi$
$59$	−6.50914	−0.847418	−0.423709	+	0.905798i	$0.639272\pi$
$60$	0.131953	0.0170351
$61$	−5.31690	−0.680759	−0.340379	−	0.940288i	$-0.610555\pi$
$61$	−5.31690	−0.680759	−0.340379	+	0.940288i	$0.610555\pi$
$62$	7.06142	0.896801
$63$	12.0822	1.52221
$64$	5.80439	0.725549
$65$	4.05789	0.503319
$66$	1.89162	0.232842
$67$	10.0684	1.23005	0.615024	−	0.788508i	$-0.289146\pi$
$67$	10.0684	1.23005	0.615024	+	0.788508i	$0.289146\pi$
$68$	−3.02429	−0.366749
$69$	−2.06353	−0.248419
$70$	−8.28979	−0.990820
$71$	−12.1102	−1.43721	−0.718607	−	0.695417i	$-0.755220\pi$
$71$	−12.1102	−1.43721	−0.718607	+	0.695417i	$0.755220\pi$
$72$	−7.26991	−0.856767
$73$	12.7299	1.48992	0.744961	−	0.667108i	$-0.232468\pi$
$73$	12.7299	1.48992	0.744961	+	0.667108i	$0.232468\pi$
$74$	−9.55094	−1.11027
$75$	0.834182	0.0963231
$76$	−0.781210	−0.0896110
$77$	−19.9265	−2.27083
$78$	−1.21943	−0.138073
$79$	6.95224	0.782188	0.391094	−	0.920351i	$-0.372097\pi$
$79$	6.95224	0.782188	0.391094	+	0.920351i	$0.372097\pi$
$80$	6.03538	0.674776
$81$	8.43263	0.936959
$82$	−1.22153	−0.134895
$83$	11.1614	1.22512	0.612560	−	0.790424i	$-0.290140\pi$
$83$	11.1614	1.22512	0.612560	+	0.790424i	$0.290140\pi$
$84$	0.417710	0.0455759
$85$	9.75600	1.05819
$86$	−18.1414	−1.95624
$87$	1.28969	0.138270
$88$	11.9898	1.27812
$89$	−9.97547	−1.05740	−0.528699	−	0.848810i	$-0.677320\pi$
$89$	−9.97547	−1.05740	−0.528699	+	0.848810i	$0.677320\pi$
$90$	−5.91645	−0.623648
$91$	12.8456	1.34658
$92$	3.29970	0.344017
$93$	1.14781	0.119023
$94$	−4.42593	−0.456500
$95$	2.52009	0.258556
$96$	−0.566083	−0.0577756
$97$	−1.74802	−0.177485	−0.0887423	−	0.996055i	$-0.528285\pi$
$97$	−1.74802	−0.177485	−0.0887423	+	0.996055i	$0.528285\pi$
$98$	−15.3911	−1.55474
$99$	−14.2216	−1.42932
$100$	−1.33391	−0.133391
$101$	8.21268	0.817192	0.408596	−	0.912715i	$-0.366019\pi$
$101$	8.21268	0.817192	0.408596	+	0.912715i	$0.366019\pi$
$102$	−2.93176	−0.290288
$103$	−16.1337	−1.58970	−0.794852	−	0.606803i	$-0.792452\pi$
$103$	−16.1337	−1.58970	−0.794852	+	0.606803i	$0.792452\pi$
$104$	−7.72925	−0.757915
$105$	−1.34748	−0.131501
$106$	−1.67454	−0.162646
$107$	12.2686	1.18605	0.593026	−	0.805183i	$-0.297933\pi$
$107$	12.2686	1.18605	0.593026	+	0.805183i	$0.297933\pi$
$108$	0.602687	0.0579936
$109$	4.07852	0.390651	0.195326	−	0.980738i	$-0.437424\pi$
$109$	4.07852	0.390651	0.195326	+	0.980738i	$0.437424\pi$
$110$	9.75765	0.930355
$111$	−1.55248	−0.147355
$112$	19.1055	1.80530
$113$	14.4754	1.36173	0.680867	−	0.732407i	$-0.261603\pi$
$113$	14.4754	1.36173	0.680867	+	0.732407i	$0.261603\pi$
$114$	−0.757308	−0.0709284
$115$	−10.6444	−0.992598
$116$	−2.06229	−0.191479
$117$	9.16793	0.847576
$118$	10.0900	0.928864
$119$	30.8835	2.83108
$120$	0.810785	0.0740142
$121$	12.4548	1.13225
$122$	8.24190	0.746186
$123$	−0.198555	−0.0179031
$124$	−1.83542	−0.164825
$125$	10.8018	0.966140
$126$	−18.7290	−1.66851
$127$	11.5864	1.02813	0.514064	−	0.857752i	$-0.328139\pi$
$127$	11.5864	1.02813	0.514064	+	0.857752i	$0.328139\pi$
$128$	−13.4909	−1.19243
$129$	−2.94883	−0.259630
$130$	−6.29026	−0.551693
$131$	−3.05084	−0.266553	−0.133277	−	0.991079i	$-0.542550\pi$
$131$	−3.05084	−0.266553	−0.133277	+	0.991079i	$0.542550\pi$
$132$	−0.491673	−0.0427946
$133$	7.97756	0.691742
$134$	−15.6073	−1.34827
$135$	−1.94419	−0.167330
$136$	−18.5827	−1.59345
$137$	−10.9212	−0.933065	−0.466533	−	0.884504i	$-0.654497\pi$
$137$	−10.9212	−0.933065	−0.466533	+	0.884504i	$0.654497\pi$
$138$	3.19874	0.272295
$139$	14.6896	1.24596	0.622978	−	0.782240i	$-0.285923\pi$
$139$	14.6896	1.24596	0.622978	+	0.782240i	$0.285923\pi$
$140$	2.15470	0.182105
$141$	−0.719422	−0.0605863
$142$	18.7724	1.57534
$143$	−15.1201	−1.26441
$144$	13.6357	1.13630
$145$	6.65271	0.552477
$146$	−19.7331	−1.63312
$147$	−2.50178	−0.206343
$148$	2.48250	0.204060
$149$	21.9969	1.80206	0.901028	−	0.433761i	$-0.142814\pi$
$149$	21.9969	1.80206	0.901028	+	0.433761i	$0.142814\pi$
$150$	−1.29309	−0.105581
$151$	−19.0814	−1.55282	−0.776412	−	0.630226i	$-0.782962\pi$
$151$	−19.0814	−1.55282	−0.776412	+	0.630226i	$0.782962\pi$
$152$	−4.80013	−0.389342
$153$	22.0416	1.78196
$154$	30.8887	2.48908
$155$	5.92084	0.475573
$156$	0.316957	0.0253768
$157$	21.6953	1.73147	0.865737	−	0.500500i	$-0.166850\pi$
$157$	21.6953	1.73147	0.865737	+	0.500500i	$0.166850\pi$
$158$	−10.7769	−0.857364
$159$	−0.272191	−0.0215862
$160$	−2.92006	−0.230851
$161$	−33.6959	−2.65561
$162$	−13.0717	−1.02701
$163$	−13.5796	−1.06364	−0.531820	−	0.846858i	$-0.678492\pi$
$163$	−13.5796	−1.06364	−0.531820	+	0.846858i	$0.678492\pi$
$164$	0.317502	0.0247927
$165$	1.58608	0.123476
$166$	−17.3016	−1.34287
$167$	−22.4079	−1.73398	−0.866988	−	0.498328i	$-0.833947\pi$
$167$	−22.4079	−1.73398	−0.866988	+	0.498328i	$0.833947\pi$
$168$	2.56661	0.198018
$169$	−3.25281	−0.250216
$170$	−15.1231	−1.15989
$171$	5.69361	0.435401
$172$	4.71536	0.359543
$173$	−5.33843	−0.405873	−0.202936	−	0.979192i	$-0.565048\pi$
$173$	−5.33843	−0.405873	−0.202936	+	0.979192i	$0.565048\pi$
$174$	−1.99920	−0.151559
$175$	13.6216	1.02969
$176$	−22.4885	−1.69513
$177$	1.64011	0.123278
$178$	15.4633	1.15902
$179$	−19.6350	−1.46759	−0.733793	−	0.679373i	$-0.762252\pi$
$179$	−19.6350	−1.46759	−0.733793	+	0.679373i	$0.762252\pi$
$180$	1.53782	0.114622
$181$	−4.54533	−0.337852	−0.168926	−	0.985629i	$-0.554030\pi$
$181$	−4.54533	−0.337852	−0.168926	+	0.985629i	$0.554030\pi$
$182$	−19.9124	−1.47600
$183$	1.33970	0.0990331
$184$	20.2749	1.49469
$185$	−8.00824	−0.588778
$186$	−1.77926	−0.130462
$187$	−36.3519	−2.65832
$188$	1.15040	0.0839014
$189$	−6.15451	−0.447675
$190$	−3.90647	−0.283405
$191$	−4.23397	−0.306359	−0.153180	−	0.988198i	$-0.548951\pi$
$191$	−4.23397	−0.306359	−0.153180	+	0.988198i	$0.548951\pi$
$192$	−1.46253	−0.105549
$193$	−6.06037	−0.436235	−0.218117	−	0.975923i	$-0.569992\pi$
$193$	−6.06037	−0.436235	−0.218117	+	0.975923i	$0.569992\pi$
$194$	2.70967	0.194543
$195$	−1.02246	−0.0732201
$196$	4.00049	0.285749
$197$	15.4689	1.10211	0.551055	−	0.834469i	$-0.314225\pi$
$197$	15.4689	1.10211	0.551055	+	0.834469i	$0.314225\pi$
$198$	22.0453	1.56669
$199$	−19.3895	−1.37449	−0.687244	−	0.726427i	$-0.741180\pi$
$199$	−19.3895	−1.37449	−0.687244	+	0.726427i	$0.741180\pi$
$200$	−8.19616	−0.579556
$201$	−2.53692	−0.178941
$202$	−12.7307	−0.895732
$203$	21.0597	1.47810
$204$	0.762030	0.0533527
$205$	−1.02422	−0.0715347
$206$	25.0094	1.74249
$207$	−24.0488	−1.67151
$208$	14.4972	1.00520
$209$	−9.39013	−0.649529
$210$	2.08877	0.144139
$211$	25.6172	1.76356	0.881782	−	0.471658i	$-0.156344\pi$
$211$	25.6172	1.76356	0.881782	+	0.471658i	$0.156344\pi$
$212$	0.435250	0.0298931
$213$	3.05140	0.209078
$214$	−19.0180	−1.30004
$215$	−15.2112	−1.03739
$216$	3.70320	0.251971
$217$	18.7429	1.27235
$218$	−6.32225	−0.428197
$219$	−3.20755	−0.216746
$220$	−2.53623	−0.170992
$221$	23.4343	1.57636
$222$	2.40655	0.161517
$223$	−10.1778	−0.681558	−0.340779	−	0.940143i	$-0.610691\pi$
$223$	−10.1778	−0.681558	−0.340779	+	0.940143i	$0.610691\pi$
$224$	−9.24372	−0.617622
$225$	9.72175	0.648117
$226$	−22.4389	−1.49261
$227$	−3.65676	−0.242708	−0.121354	−	0.992609i	$-0.538724\pi$
$227$	−3.65676	−0.242708	−0.121354	+	0.992609i	$0.538724\pi$
$228$	0.196841	0.0130361
$229$	2.93773	0.194131	0.0970654	−	0.995278i	$-0.469054\pi$
$229$	2.93773	0.194131	0.0970654	+	0.995278i	$0.469054\pi$
$230$	16.5003	1.08800
$231$	5.02086	0.330348
$232$	−12.6717	−0.831939
$233$	−11.7201	−0.767808	−0.383904	−	0.923373i	$-0.625421\pi$
$233$	−11.7201	−0.767808	−0.383904	+	0.923373i	$0.625421\pi$
$234$	−14.2115	−0.929036
$235$	−3.71104	−0.242082
$236$	−2.62263	−0.170718
$237$	−1.75175	−0.113789
$238$	−47.8735	−3.10318
$239$	−1.88895	−0.122186	−0.0610929	−	0.998132i	$-0.519459\pi$
$239$	−1.88895	−0.122186	−0.0610929	+	0.998132i	$0.519459\pi$
$240$	−1.52073	−0.0981628
$241$	−7.89184	−0.508358	−0.254179	−	0.967157i	$-0.581805\pi$
$241$	−7.89184	−0.508358	−0.254179	+	0.967157i	$0.581805\pi$
$242$	−19.3066	−1.24108
$243$	−6.61223	−0.424175
$244$	−2.14225	−0.137144
$245$	−12.9051	−0.824476
$246$	0.307787	0.0196238
$247$	6.05334	0.385165
$248$	−11.2777	−0.716134
$249$	−2.81232	−0.178224
$250$	−16.7442	−1.05900
$251$	18.9320	1.19498	0.597488	−	0.801878i	$-0.296165\pi$
$251$	18.9320	1.19498	0.597488	+	0.801878i	$0.296165\pi$
$252$	4.86809	0.306661
$253$	39.6623	2.49355
$254$	−17.9605	−1.12694
$255$	−2.45821	−0.153939
$256$	9.30384	0.581490
$257$	−17.1995	−1.07288	−0.536439	−	0.843939i	$-0.680231\pi$
$257$	−17.1995	−1.07288	−0.536439	+	0.843939i	$0.680231\pi$
$258$	4.57109	0.284583
$259$	−25.3508	−1.57522
$260$	1.63498	0.101397
$261$	15.0304	0.930357
$262$	4.72921	0.292171
$263$	7.52065	0.463743	0.231872	−	0.972746i	$-0.425515\pi$
$263$	7.52065	0.463743	0.231872	+	0.972746i	$0.425515\pi$
$264$	−3.02107	−0.185934
$265$	−1.40406	−0.0862509
$266$	−12.3663	−0.758225
$267$	2.51351	0.153825
$268$	4.05669	0.247802
$269$	−20.8540	−1.27149	−0.635746	−	0.771898i	$-0.719308\pi$
$269$	−20.8540	−1.27149	−0.635746	+	0.771898i	$0.719308\pi$
$270$	3.01376	0.183412
$271$	17.1101	1.03937	0.519683	−	0.854359i	$-0.326050\pi$
$271$	17.1101	1.03937	0.519683	+	0.854359i	$0.326050\pi$
$272$	34.8543	2.11335
$273$	−3.23670	−0.195894
$274$	16.9294	1.02274
$275$	−16.0335	−0.966858
$276$	−0.831424	−0.0500458
$277$	−19.0930	−1.14719	−0.573593	−	0.819141i	$-0.694451\pi$
$277$	−19.0930	−1.14719	−0.573593	+	0.819141i	$0.694451\pi$
$278$	−22.7708	−1.36570
$279$	13.3769	0.800852
$280$	13.2395	0.791212
$281$	−1.86310	−0.111143	−0.0555715	−	0.998455i	$-0.517698\pi$
$281$	−1.86310	−0.111143	−0.0555715	+	0.998455i	$0.517698\pi$
$282$	1.11520	0.0664092
$283$	0.757646	0.0450374	0.0225187	−	0.999746i	$-0.492831\pi$
$283$	0.757646	0.0450374	0.0225187	+	0.999746i	$0.492831\pi$
$284$	−4.87936	−0.289537
$285$	−0.634985	−0.0376133
$286$	23.4382	1.38593
$287$	−3.24226	−0.191385
$288$	−6.59727	−0.388748
$289$	39.3408	2.31416
$290$	−10.3126	−0.605576
$291$	0.440448	0.0258195
$292$	5.12906	0.300155
$293$	18.3904	1.07438	0.537190	−	0.843461i	$-0.319486\pi$
$293$	18.3904	1.07438	0.537190	+	0.843461i	$0.319486\pi$
$294$	3.87809	0.226175
$295$	8.46027	0.492576
$296$	15.2537	0.886602
$297$	7.24428	0.420356
$298$	−34.0981	−1.97525
$299$	−25.5683	−1.47865
$300$	0.336104	0.0194050
$301$	−48.1523	−2.77545
$302$	29.5788	1.70207
$303$	−2.06934	−0.118881
$304$	9.00327	0.516373
$305$	6.91064	0.395702
$306$	−34.1674	−1.95322
$307$	−2.29317	−0.130878	−0.0654391	−	0.997857i	$-0.520845\pi$
$307$	−2.29317	−0.130878	−0.0654391	+	0.997857i	$0.520845\pi$
$308$	−8.02865	−0.457475
$309$	4.06521	0.231262
$310$	−9.17809	−0.521280
$311$	9.16682	0.519803	0.259901	−	0.965635i	$-0.416310\pi$
$311$	9.16682	0.519803	0.259901	+	0.965635i	$0.416310\pi$
$312$	1.94753	0.110257
$313$	−3.51493	−0.198676	−0.0993378	−	0.995054i	$-0.531672\pi$
$313$	−3.51493	−0.198676	−0.0993378	+	0.995054i	$0.531672\pi$
$314$	−33.6306	−1.89788
$315$	−15.7039	−0.884812
$316$	2.80116	0.157577
$317$	−10.7833	−0.605653	−0.302826	−	0.953046i	$-0.597930\pi$
$317$	−10.7833	−0.605653	−0.302826	+	0.953046i	$0.597930\pi$
$318$	0.421933	0.0236608
$319$	−24.7887	−1.38790
$320$	−7.54427	−0.421737
$321$	−3.09132	−0.172541
$322$	52.2331	2.91084
$323$	14.5535	0.809778
$324$	3.39763	0.188757
$325$	10.3360	0.573338
$326$	21.0502	1.16587
$327$	−1.02766	−0.0568299
$328$	1.95088	0.107719
$329$	−11.7476	−0.647668
$330$	−2.45863	−0.135343
$331$	4.49378	0.247001	0.123500	−	0.992345i	$-0.460588\pi$
$331$	4.49378	0.247001	0.123500	+	0.992345i	$0.460588\pi$
$332$	4.49707	0.246809
$333$	−18.0929	−0.991486
$334$	34.7353	1.90063
$335$	−13.0864	−0.714986
$336$	−4.81401	−0.262626
$337$	23.8159	1.29733	0.648667	−	0.761072i	$-0.275327\pi$
$337$	23.8159	1.29733	0.648667	+	0.761072i	$0.275327\pi$
$338$	5.04229	0.274265
$339$	−3.64737	−0.198098
$340$	3.93083	0.213179
$341$	−22.0617	−1.19471
$342$	−8.82585	−0.477247
$343$	−12.0509	−0.650687
$344$	28.9734	1.56214
$345$	2.68207	0.144398
$346$	8.27527	0.444881
$347$	2.60844	0.140028	0.0700142	−	0.997546i	$-0.477696\pi$
$347$	2.60844	0.140028	0.0700142	+	0.997546i	$0.477696\pi$
$348$	0.519635	0.0278554
$349$	8.58796	0.459703	0.229851	−	0.973226i	$-0.426176\pi$
$349$	8.58796	0.459703	0.229851	+	0.973226i	$0.426176\pi$
$350$	−21.1153	−1.12866
$351$	−4.67002	−0.249267
$352$	10.8805	0.579932
$353$	−11.6607	−0.620636	−0.310318	−	0.950633i	$-0.600436\pi$
$353$	−11.6607	−0.620636	−0.310318	+	0.950633i	$0.600436\pi$
$354$	−2.54238	−0.135126
$355$	15.7402	0.835404
$356$	−4.01926	−0.213020
$357$	−7.78169	−0.411851
$358$	30.4368	1.60864
$359$	2.31932	0.122409	0.0612044	−	0.998125i	$-0.480506\pi$
$359$	2.31932	0.122409	0.0612044	+	0.998125i	$0.480506\pi$
$360$	9.44907	0.498010
$361$	−15.2407	−0.802140
$362$	7.04587	0.370323
$363$	−3.13823	−0.164714
$364$	5.17567	0.271279
$365$	−16.5457	−0.866042
$366$	−2.07671	−0.108551
$367$	−17.1912	−0.897372	−0.448686	−	0.893689i	$-0.648108\pi$
$367$	−17.1912	−0.897372	−0.448686	+	0.893689i	$0.648108\pi$
$368$	−38.0283	−1.98236
$369$	−2.31401	−0.120463
$370$	12.4138	0.645365
$371$	−4.44468	−0.230756
$372$	0.462470	0.0239779
$373$	−12.1129	−0.627181	−0.313590	−	0.949558i	$-0.601532\pi$
$373$	−12.1129	−0.627181	−0.313590	+	0.949558i	$0.601532\pi$
$374$	56.3503	2.91381
$375$	−2.72172	−0.140549
$376$	7.06860	0.364535
$377$	15.9800	0.823014
$378$	9.54032	0.490701
$379$	21.8983	1.12484	0.562419	−	0.826852i	$-0.309871\pi$
$379$	21.8983	1.12484	0.562419	+	0.826852i	$0.309871\pi$
$380$	1.01538	0.0520878
$381$	−2.91942	−0.149567
$382$	6.56322	0.335804
$383$	15.4079	0.787308	0.393654	−	0.919259i	$-0.371211\pi$
$383$	15.4079	0.787308	0.393654	+	0.919259i	$0.371211\pi$
$384$	3.39928	0.173469
$385$	25.8994	1.31996
$386$	9.39438	0.478161
$387$	−34.3664	−1.74694
$388$	−0.704302	−0.0357555
$389$	−20.5740	−1.04314	−0.521571	−	0.853208i	$-0.674654\pi$
$389$	−20.5740	−1.04314	−0.521571	+	0.853208i	$0.674654\pi$
$390$	1.58495	0.0802573
$391$	−61.4715	−3.10875
$392$	24.5809	1.24153
$393$	0.768718	0.0387767
$394$	−23.9788	−1.20803
$395$	−9.03618	−0.454660
$396$	−5.73007	−0.287947
$397$	36.3091	1.82230	0.911151	−	0.412073i	$-0.135195\pi$
$397$	36.3091	1.82230	0.911151	+	0.412073i	$0.135195\pi$
$398$	30.0564	1.50659
$399$	−2.01010	−0.100631
$400$	15.3730	0.768648
$401$	13.1352	0.655940	0.327970	−	0.944688i	$-0.393636\pi$
$401$	13.1352	0.655940	0.327970	+	0.944688i	$0.393636\pi$
$402$	3.93257	0.196139
$403$	14.2221	0.708451
$404$	3.30900	0.164629
$405$	−10.9603	−0.544623
$406$	−32.6454	−1.62016
$407$	29.8396	1.47909
$408$	4.68227	0.231807
$409$	−1.21990	−0.0603200	−0.0301600	−	0.999545i	$-0.509602\pi$
$409$	−1.21990	−0.0603200	−0.0301600	+	0.999545i	$0.509602\pi$
$410$	1.58768	0.0784099
$411$	2.75182	0.135737
$412$	−6.50051	−0.320257
$413$	26.7817	1.31784
$414$	37.2789	1.83216
$415$	−14.5070	−0.712120
$416$	−7.01410	−0.343895
$417$	−3.70133	−0.181255
$418$	14.5560	0.711955
$419$	30.8389	1.50658	0.753289	−	0.657689i	$-0.228466\pi$
$419$	30.8389	1.50658	0.753289	+	0.657689i	$0.228466\pi$
$420$	−0.542919	−0.0264917
$421$	21.3148	1.03882	0.519411	−	0.854525i	$-0.326152\pi$
$421$	21.3148	1.03882	0.519411	+	0.854525i	$0.326152\pi$
$422$	−39.7101	−1.93306
$423$	−8.38431	−0.407659
$424$	2.67438	0.129880
$425$	24.8499	1.20540
$426$	−4.73007	−0.229173
$427$	21.8762	1.05866
$428$	4.94320	0.238938
$429$	3.80981	0.183939
$430$	23.5793	1.13710
$431$	27.8409	1.34105	0.670525	−	0.741887i	$-0.266069\pi$
$431$	27.8409	1.34105	0.670525	+	0.741887i	$0.266069\pi$
$432$	−6.94582	−0.334181
$433$	−1.77283	−0.0851970	−0.0425985	−	0.999092i	$-0.513564\pi$
$433$	−1.77283	−0.0851970	−0.0425985	+	0.999092i	$0.513564\pi$
$434$	−29.0540	−1.39464
$435$	−1.67628	−0.0803714
$436$	1.64329	0.0786995
$437$	−15.8788	−0.759586
$438$	4.97213	0.237577
$439$	8.41790	0.401764	0.200882	−	0.979615i	$-0.435619\pi$
$439$	8.41790	0.401764	0.200882	+	0.979615i	$0.435619\pi$
$440$	−15.5838	−0.742929
$441$	−29.1563	−1.38840
$442$	−36.3262	−1.72786
$443$	−3.12666	−0.148552	−0.0742761	−	0.997238i	$-0.523665\pi$
$443$	−3.12666	−0.148552	−0.0742761	+	0.997238i	$0.523665\pi$
$444$	−0.625514	−0.0296856
$445$	12.9656	0.614630
$446$	15.7770	0.747062
$447$	−5.54255	−0.262154
$448$	−23.8820	−1.12832
$449$	−16.7062	−0.788413	−0.394207	−	0.919022i	$-0.628981\pi$
$449$	−16.7062	−0.788413	−0.394207	+	0.919022i	$0.628981\pi$
$450$	−15.0700	−0.710407
$451$	3.81636	0.179705
$452$	5.83235	0.274331
$453$	4.80794	0.225897
$454$	5.66847	0.266035
$455$	−16.6961	−0.782724
$456$	1.20949	0.0566394
$457$	30.8677	1.44393	0.721964	−	0.691930i	$-0.243240\pi$
$457$	30.8677	1.44393	0.721964	+	0.691930i	$0.243240\pi$
$458$	−4.55388	−0.212789
$459$	−11.2277	−0.524064
$460$	−4.28879	−0.199966
$461$	0.317249	0.0147757	0.00738787	−	0.999973i	$-0.497648\pi$
$461$	0.317249	0.0147757	0.00738787	+	0.999973i	$0.497648\pi$
$462$	−7.78301	−0.362098
$463$	21.3813	0.993675	0.496838	−	0.867844i	$-0.334494\pi$
$463$	21.3813	0.993675	0.496838	+	0.867844i	$0.334494\pi$
$464$	23.7674	1.10338
$465$	−1.49187	−0.0691838
$466$	18.1677	0.841602
$467$	−15.9956	−0.740190	−0.370095	−	0.928994i	$-0.620675\pi$
$467$	−15.9956	−0.740190	−0.370095	+	0.928994i	$0.620675\pi$
$468$	3.69389	0.170750
$469$	−41.4261	−1.91288
$470$	5.75261	0.265348
$471$	−5.46655	−0.251885
$472$	−16.1147	−0.741738
$473$	56.6785	2.60608
$474$	2.71545	0.124725
$475$	6.41902	0.294525
$476$	12.4434	0.570341
$477$	−3.17218	−0.145244
$478$	2.92812	0.133929
$479$	−6.01704	−0.274926	−0.137463	−	0.990507i	$-0.543895\pi$
$479$	−6.01704	−0.274926	−0.137463	+	0.990507i	$0.543895\pi$
$480$	0.735767	0.0335830
$481$	−19.2361	−0.877090
$482$	12.2334	0.557217
$483$	8.49033	0.386323
$484$	5.01821	0.228101
$485$	2.27199	0.103166
$486$	10.2498	0.464942
$487$	16.2714	0.737326	0.368663	−	0.929563i	$-0.379816\pi$
$487$	16.2714	0.737326	0.368663	+	0.929563i	$0.379816\pi$
$488$	−13.1630	−0.595862
$489$	3.42165	0.154733
$490$	20.0046	0.903717
$491$	41.8759	1.88983	0.944916	−	0.327312i	$-0.106143\pi$
$491$	41.8759	1.88983	0.944916	+	0.327312i	$0.106143\pi$
$492$	−0.0800008	−0.00360671
$493$	38.4193	1.73032
$494$	−9.38349	−0.422183
$495$	18.4845	0.830816
$496$	21.1528	0.949787
$497$	49.8270	2.23505
$498$	4.35948	0.195353
$499$	−18.1711	−0.813449	−0.406724	−	0.913551i	$-0.633329\pi$
$499$	−18.1711	−0.813449	−0.406724	+	0.913551i	$0.633329\pi$
$500$	4.35218	0.194636
$501$	5.64611	0.252250
$502$	−29.3471	−1.30983
$503$	−30.0050	−1.33786	−0.668929	−	0.743327i	$-0.733247\pi$
$503$	−30.0050	−1.33786	−0.668929	+	0.743327i	$0.733247\pi$
$504$	29.9119	1.33238
$505$	−10.6744	−0.475006
$506$	−61.4819	−2.73320
$507$	0.819609	0.0364001
$508$	4.66833	0.207124
$509$	−32.2779	−1.43069	−0.715346	−	0.698770i	$-0.753731\pi$
$509$	−32.2779	−1.43069	−0.715346	+	0.698770i	$0.753731\pi$
$510$	3.81056	0.168734
$511$	−52.3769	−2.31702
$512$	12.5595	0.555058
$513$	−2.90025	−0.128049
$514$	26.6616	1.17599
$515$	20.9698	0.924041
$516$	−1.18813	−0.0523043
$517$	13.8278	0.608144
$518$	39.2971	1.72662
$519$	1.34512	0.0590442
$520$	10.0461	0.440550
$521$	30.0927	1.31838	0.659192	−	0.751975i	$-0.270898\pi$
$521$	30.0927	1.31838	0.659192	+	0.751975i	$0.270898\pi$
$522$	−23.2991	−1.01977
$523$	5.72992	0.250552	0.125276	−	0.992122i	$-0.460018\pi$
$523$	5.72992	0.250552	0.125276	+	0.992122i	$0.460018\pi$
$524$	−1.22923	−0.0536990
$525$	−3.43222	−0.149794
$526$	−11.6580	−0.508313
$527$	34.1928	1.48946
$528$	5.66641	0.246599
$529$	44.0694	1.91606
$530$	2.17648	0.0945405
$531$	19.1142	0.829485
$532$	3.21427	0.139356
$533$	−2.46022	−0.106564
$534$	−3.89628	−0.168609
$535$	−15.9461	−0.689412
$536$	24.9263	1.07665
$537$	4.94742	0.213497
$538$	32.3265	1.39370
$539$	48.0858	2.07120
$540$	−0.783343	−0.0337097
$541$	−18.7752	−0.807208	−0.403604	−	0.914934i	$-0.632243\pi$
$541$	−18.7752	−0.807208	−0.403604	+	0.914934i	$0.632243\pi$
$542$	−26.5230	−1.13926
$543$	1.14529	0.0491489
$544$	−16.8633	−0.723010
$545$	−5.30106	−0.227073
$546$	5.01731	0.214721
$547$	1.81153	0.0774554	0.0387277	−	0.999250i	$-0.487670\pi$
$547$	1.81153	0.0774554	0.0387277	+	0.999250i	$0.487670\pi$
$548$	−4.40032	−0.187973
$549$	15.6131	0.666352
$550$	24.8541	1.05978
$551$	9.92416	0.422784
$552$	−5.10867	−0.217439
$553$	−28.6048	−1.21640
$554$	29.5967	1.25744
$555$	2.01783	0.0856522
$556$	5.91864	0.251006
$557$	−9.15745	−0.388013	−0.194007	−	0.981000i	$-0.562148\pi$
$557$	−9.15745	−0.388013	−0.194007	+	0.981000i	$0.562148\pi$
$558$	−20.7359	−0.877822
$559$	−36.5378	−1.54538
$560$	−24.8324	−1.04936
$561$	9.15958	0.386718
$562$	2.88805	0.121825
$563$	28.7795	1.21291	0.606456	−	0.795117i	$-0.292591\pi$
$563$	28.7795	1.21291	0.606456	+	0.795117i	$0.292591\pi$
$564$	−0.289865	−0.0122055
$565$	−18.8145	−0.791530
$566$	−1.17445	−0.0493659
$567$	−34.6959	−1.45709
$568$	−29.9811	−1.25798
$569$	−28.9546	−1.21384	−0.606919	−	0.794764i	$-0.707595\pi$
$569$	−28.9546	−1.21384	−0.606919	+	0.794764i	$0.707595\pi$
$570$	0.984312	0.0412283
$571$	31.1010	1.30154	0.650769	−	0.759276i	$-0.274447\pi$
$571$	31.1010	1.30154	0.650769	+	0.759276i	$0.274447\pi$
$572$	−6.09211	−0.254724
$573$	1.06683	0.0445675
$574$	5.02594	0.209779
$575$	−27.1128	−1.13068
$576$	−17.0447	−0.710195
$577$	36.8683	1.53485	0.767424	−	0.641139i	$-0.221538\pi$
$577$	36.8683	1.53485	0.767424	+	0.641139i	$0.221538\pi$
$578$	−60.9835	−2.53658
$579$	1.52703	0.0634611
$580$	2.68047	0.111300
$581$	−45.9232	−1.90521
$582$	−0.682753	−0.0283010
$583$	5.23169	0.216675
$584$	31.5154	1.30412
$585$	−11.9160	−0.492667
$586$	−28.5076	−1.17764
$587$	−16.9507	−0.699629	−0.349814	−	0.936819i	$-0.613755\pi$
$587$	−16.9507	−0.699629	−0.349814	+	0.936819i	$0.613755\pi$
$588$	−1.00800	−0.0415693
$589$	8.83240	0.363933
$590$	−13.1145	−0.539917
$591$	−3.89768	−0.160329
$592$	−28.6102	−1.17587
$593$	40.2549	1.65307	0.826535	−	0.562886i	$-0.190309\pi$
$593$	40.2549	1.65307	0.826535	+	0.562886i	$0.190309\pi$
$594$	−11.2296	−0.460756
$595$	−40.1408	−1.64561
$596$	8.86286	0.363037
$597$	4.88557	0.199953
$598$	39.6343	1.62077
$599$	44.2113	1.80643	0.903213	−	0.429193i	$-0.141202\pi$
$599$	44.2113	1.80643	0.903213	+	0.429193i	$0.141202\pi$
$600$	2.06518	0.0843107
$601$	32.1764	1.31250	0.656251	−	0.754543i	$-0.272141\pi$
$601$	32.1764	1.31250	0.656251	+	0.754543i	$0.272141\pi$
$602$	74.6424	3.04220
$603$	−29.5659	−1.20402
$604$	−7.68817	−0.312827
$605$	−16.1881	−0.658141
$606$	3.20776	0.130306
$607$	−13.1486	−0.533686	−0.266843	−	0.963740i	$-0.585981\pi$
$607$	−13.1486	−0.533686	−0.266843	+	0.963740i	$0.585981\pi$
$608$	−4.35600	−0.176659
$609$	−5.30641	−0.215026
$610$	−10.7124	−0.433733
$611$	−8.91406	−0.360624
$612$	8.88087	0.358988
$613$	−43.8360	−1.77052	−0.885260	−	0.465096i	$-0.846020\pi$
$613$	−43.8360	−1.77052	−0.885260	+	0.465096i	$0.846020\pi$
$614$	3.55472	0.143457
$615$	0.258073	0.0104065
$616$	−49.3319	−1.98764
$617$	0.445157	0.0179214	0.00896068	−	0.999960i	$-0.497148\pi$
$617$	0.445157	0.0179214	0.00896068	+	0.999960i	$0.497148\pi$
$618$	−6.30162	−0.253488
$619$	6.09057	0.244801	0.122400	−	0.992481i	$-0.460941\pi$
$619$	6.09057	0.244801	0.122400	+	0.992481i	$0.460941\pi$
$620$	2.38559	0.0958075
$621$	12.2502	0.491582
$622$	−14.2098	−0.569761
$623$	41.0438	1.64439
$624$	−3.65285	−0.146231
$625$	2.51363	0.100545
$626$	5.44861	0.217770
$627$	2.36603	0.0944900
$628$	8.74134	0.348817
$629$	−46.2475	−1.84401
$630$	24.3431	0.969851
$631$	−8.71918	−0.347105	−0.173553	−	0.984825i	$-0.555525\pi$
$631$	−8.71918	−0.347105	−0.173553	+	0.984825i	$0.555525\pi$
$632$	17.2116	0.684642
$633$	−6.45476	−0.256554
$634$	16.7156	0.663862
$635$	−15.0595	−0.597616
$636$	−0.109670	−0.00434869
$637$	−30.9985	−1.22821
$638$	38.4258	1.52129
$639$	35.5617	1.40680
$640$	17.5347	0.693122
$641$	−14.7912	−0.584216	−0.292108	−	0.956385i	$-0.594357\pi$
$641$	−14.7912	−0.584216	−0.292108	+	0.956385i	$0.594357\pi$
$642$	4.79196	0.189123
$643$	38.7890	1.52969	0.764845	−	0.644214i	$-0.222816\pi$
$643$	38.7890	1.52969	0.764845	+	0.644214i	$0.222816\pi$
$644$	−13.5765	−0.534990
$645$	3.83275	0.150914
$646$	−22.5599	−0.887606
$647$	19.7178	0.775189	0.387594	−	0.921830i	$-0.373306\pi$
$647$	19.7178	0.775189	0.387594	+	0.921830i	$0.373306\pi$
$648$	20.8766	0.820112
$649$	−31.5239	−1.23742
$650$	−16.0222	−0.628442
$651$	−4.72264	−0.185095
$652$	−5.47143	−0.214278
$653$	−14.6449	−0.573100	−0.286550	−	0.958065i	$-0.592508\pi$
$653$	−14.6449	−0.573100	−0.286550	+	0.958065i	$0.592508\pi$
$654$	1.59301	0.0622918
$655$	3.96533	0.154938
$656$	−3.65913	−0.142865
$657$	−37.3815	−1.45839
$658$	18.2104	0.709915
$659$	−0.272548	−0.0106170	−0.00530848	−	0.999986i	$-0.501690\pi$
$659$	−0.272548	−0.0106170	−0.00530848	+	0.999986i	$0.501690\pi$
$660$	0.639052	0.0248751
$661$	11.1999	0.435627	0.217814	−	0.975990i	$-0.430107\pi$
$661$	11.1999	0.435627	0.217814	+	0.975990i	$0.430107\pi$
$662$	−6.96596	−0.270740
$663$	−5.90472	−0.229320
$664$	27.6322	1.07234
$665$	−10.3688	−0.402086
$666$	28.0464	1.08678
$667$	−41.9180	−1.62307
$668$	−9.02846	−0.349322
$669$	2.56450	0.0991494
$670$	20.2856	0.783703
$671$	−25.7498	−0.994060
$672$	2.32913	0.0898483
$673$	−15.1817	−0.585212	−0.292606	−	0.956233i	$-0.594522\pi$
$673$	−15.1817	−0.585212	−0.292606	+	0.956233i	$0.594522\pi$
$674$	−36.9178	−1.42202
$675$	−4.95213	−0.190608
$676$	−1.31060	−0.0504078
$677$	14.8084	0.569133	0.284567	−	0.958656i	$-0.408150\pi$
$677$	14.8084	0.569133	0.284567	+	0.958656i	$0.408150\pi$
$678$	5.65391	0.217137
$679$	7.19219	0.276011
$680$	24.1529	0.926221
$681$	0.921393	0.0353079
$682$	34.1986	1.30953
$683$	−16.9531	−0.648693	−0.324347	−	0.945938i	$-0.605144\pi$
$683$	−16.9531	−0.648693	−0.324347	+	0.945938i	$0.605144\pi$
$684$	2.29403	0.0877146
$685$	14.1949	0.542359
$686$	18.6805	0.713224
$687$	−0.740219	−0.0282411
$688$	−54.3434	−2.07182
$689$	−3.37261	−0.128486
$690$	−4.15757	−0.158276
$691$	14.1412	0.537958	0.268979	−	0.963146i	$-0.413314\pi$
$691$	14.1412	0.537958	0.268979	+	0.963146i	$0.413314\pi$
$692$	−2.15093	−0.0817659
$693$	58.5143	2.22277
$694$	−4.04343	−0.153487
$695$	−19.0928	−0.724232
$696$	3.19289	0.121026
$697$	−5.91487	−0.224042
$698$	−13.3125	−0.503885
$699$	2.95310	0.111697
$700$	5.48832	0.207439
$701$	−25.1032	−0.948135	−0.474068	−	0.880488i	$-0.657215\pi$
$701$	−25.1032	−0.948135	−0.474068	+	0.880488i	$0.657215\pi$
$702$	7.23916	0.273224
$703$	−11.9463	−0.450563
$704$	28.1108	1.05946
$705$	0.935070	0.0352168
$706$	18.0756	0.680285
$707$	−33.7908	−1.27084
$708$	0.660822	0.0248352
$709$	24.6978	0.927547	0.463774	−	0.885954i	$-0.346495\pi$
$709$	24.6978	0.927547	0.463774	+	0.885954i	$0.346495\pi$
$710$	−24.3994	−0.915694
$711$	−20.4153	−0.765635
$712$	−24.6962	−0.925531
$713$	−37.3065	−1.39714
$714$	12.0627	0.451434
$715$	19.6524	0.734958
$716$	−7.91121	−0.295656
$717$	0.475957	0.0177749
$718$	−3.59525	−0.134173
$719$	−36.6730	−1.36767	−0.683837	−	0.729635i	$-0.739690\pi$
$719$	−36.6730	−1.36767	−0.683837	+	0.729635i	$0.739690\pi$
$720$	−17.7230	−0.660496
$721$	66.3818	2.47219
$722$	23.6251	0.879234
$723$	1.98850	0.0739533
$724$	−1.83138	−0.0680626
$725$	16.9454	0.629335
$726$	4.86468	0.180545
$727$	1.32972	0.0493167	0.0246584	−	0.999696i	$-0.492150\pi$
$727$	1.32972	0.0493167	0.0246584	+	0.999696i	$0.492150\pi$
$728$	31.8018	1.17865
$729$	−23.6318	−0.875253
$730$	25.6481	0.949277
$731$	−87.8443	−3.24904
$732$	0.539782	0.0199509
$733$	40.9464	1.51239	0.756195	−	0.654347i	$-0.227056\pi$
$733$	40.9464	1.51239	0.756195	+	0.654347i	$0.227056\pi$
$734$	26.6486	0.983618
$735$	3.25169	0.119940
$736$	18.3990	0.678196
$737$	48.7613	1.79615
$738$	3.58703	0.132040
$739$	−27.6605	−1.01751	−0.508754	−	0.860912i	$-0.669894\pi$
$739$	−27.6605	−1.01751	−0.508754	+	0.860912i	$0.669894\pi$
$740$	−3.22663	−0.118613
$741$	−1.52526	−0.0560318
$742$	6.88985	0.252934
$743$	27.1682	0.996704	0.498352	−	0.866975i	$-0.333939\pi$
$743$	27.1682	0.996704	0.498352	+	0.866975i	$0.333939\pi$
$744$	2.84164	0.104179
$745$	−28.5905	−1.04747
$746$	18.7766	0.687459
$747$	−32.7755	−1.19919
$748$	−14.6467	−0.535536
$749$	−50.4789	−1.84446
$750$	4.21903	0.154057
$751$	−10.0249	−0.365813	−0.182907	−	0.983130i	$-0.558551\pi$
$751$	−10.0249	−0.365813	−0.182907	+	0.983130i	$0.558551\pi$
$752$	−13.2581	−0.483472
$753$	−4.77029	−0.173839
$754$	−24.7712	−0.902114
$755$	24.8011	0.902604
$756$	−2.47974	−0.0901872
$757$	−5.02644	−0.182689	−0.0913446	−	0.995819i	$-0.529116\pi$
$757$	−5.02644	−0.182689	−0.0913446	+	0.995819i	$0.529116\pi$
$758$	−33.9452	−1.23295
$759$	−9.99369	−0.362748
$760$	6.23897	0.226311
$761$	24.6638	0.894063	0.447032	−	0.894518i	$-0.352481\pi$
$761$	24.6638	0.894063	0.447032	+	0.894518i	$0.352481\pi$
$762$	4.52550	0.163941
$763$	−16.7810	−0.607512
$764$	−1.70593	−0.0617183
$765$	−28.6486	−1.03579
$766$	−23.8843	−0.862976
$767$	20.3219	0.733780
$768$	−2.34428	−0.0845920
$769$	7.47047	0.269392	0.134696	−	0.990887i	$-0.456994\pi$
$769$	7.47047	0.269392	0.134696	+	0.990887i	$0.456994\pi$
$770$	−40.1476	−1.44682
$771$	4.33376	0.156077
$772$	−2.44181	−0.0878825
$773$	−7.16519	−0.257714	−0.128857	−	0.991663i	$-0.541131\pi$
$773$	−7.16519	−0.257714	−0.128857	+	0.991663i	$0.541131\pi$
$774$	53.2725	1.91484
$775$	15.0812	0.541733
$776$	−4.32757	−0.155351
$777$	6.38763	0.229155
$778$	31.8924	1.14340
$779$	−1.52788	−0.0547420
$780$	−0.411965	−0.0147507
$781$	−58.6498	−2.09865
$782$	95.2890	3.40753
$783$	−7.65628	−0.273613
$784$	−46.1047	−1.64660
$785$	−28.1985	−1.00645
$786$	−1.19162	−0.0425035
$787$	36.2462	1.29204	0.646018	−	0.763322i	$-0.276433\pi$
$787$	36.2462	1.29204	0.646018	+	0.763322i	$0.276433\pi$
$788$	6.23262	0.222028
$789$	−1.89497	−0.0674629
$790$	14.0073	0.498357
$791$	−59.5588	−2.11767
$792$	−35.2083	−1.25107
$793$	16.5996	0.589469
$794$	−56.2840	−1.99744
$795$	0.353781	0.0125473
$796$	−7.81231	−0.276900
$797$	−6.14021	−0.217497	−0.108749	−	0.994069i	$-0.534684\pi$
$797$	−6.14021	−0.217497	−0.108749	+	0.994069i	$0.534684\pi$
$798$	3.11593	0.110303
$799$	−21.4312	−0.758183
$800$	−7.43781	−0.262966
$801$	29.2931	1.03502
$802$	−20.3613	−0.718982
$803$	61.6511	2.17562
$804$	−1.02216	−0.0360489
$805$	43.7962	1.54361
$806$	−22.0461	−0.776541
$807$	5.25458	0.184970
$808$	20.3321	0.715281
$809$	−32.0997	−1.12857	−0.564283	−	0.825581i	$-0.690847\pi$
$809$	−32.0997	−1.12857	−0.564283	+	0.825581i	$0.690847\pi$
$810$	16.9900	0.596966
$811$	−3.62218	−0.127192	−0.0635959	−	0.997976i	$-0.520257\pi$
$811$	−3.62218	−0.127192	−0.0635959	+	0.997976i	$0.520257\pi$
$812$	8.48526	0.297774
$813$	−4.31123	−0.151201
$814$	−46.2554	−1.62125
$815$	17.6501	0.618258
$816$	−8.78221	−0.307439
$817$	−22.6912	−0.793865
$818$	1.89100	0.0661173
$819$	−37.7212	−1.31809
$820$	−0.412673	−0.0144112
$821$	−8.81047	−0.307488	−0.153744	−	0.988111i	$-0.549133\pi$
$821$	−8.81047	−0.307488	−0.153744	+	0.988111i	$0.549133\pi$
$822$	−4.26569	−0.148783
$823$	−50.0940	−1.74617	−0.873083	−	0.487572i	$-0.837883\pi$
$823$	−50.0940	−1.74617	−0.873083	+	0.487572i	$0.837883\pi$
$824$	−39.9422	−1.39145
$825$	4.03996	0.140653
$826$	−41.5152	−1.44450
$827$	−39.7305	−1.38157	−0.690783	−	0.723062i	$-0.742734\pi$
$827$	−39.7305	−1.38157	−0.690783	+	0.723062i	$0.742734\pi$
$828$	−9.68961	−0.336737
$829$	4.35900	0.151394	0.0756972	−	0.997131i	$-0.475882\pi$
$829$	4.35900	0.151394	0.0756972	+	0.997131i	$0.475882\pi$
$830$	22.4878	0.780562
$831$	4.81085	0.166886
$832$	−18.1216	−0.628254
$833$	−74.5268	−2.58220
$834$	5.73756	0.198675
$835$	29.1247	1.00790
$836$	−3.78341	−0.130852
$837$	−6.81400	−0.235526
$838$	−47.8044	−1.65138
$839$	38.3553	1.32417	0.662086	−	0.749428i	$-0.269671\pi$
$839$	38.3553	1.32417	0.662086	+	0.749428i	$0.269671\pi$
$840$	−3.33595	−0.115101
$841$	−2.80150	−0.0966034
$842$	−33.0408	−1.13866
$843$	0.469443	0.0161685
$844$	10.3215	0.355282
$845$	4.22784	0.145442
$846$	12.9968	0.446839
$847$	−51.2450	−1.76080
$848$	−5.01615	−0.172255
$849$	−0.190904	−0.00655179
$850$	−38.5206	−1.32125
$851$	50.4591	1.72971
$852$	1.22945	0.0421203
$853$	47.4750	1.62551	0.812756	−	0.582604i	$-0.197966\pi$
$853$	47.4750	1.62551	0.812756	+	0.582604i	$0.197966\pi$
$854$	−33.9111	−1.16041
$855$	−7.40027	−0.253084
$856$	30.3734	1.03814
$857$	32.7067	1.11724	0.558619	−	0.829424i	$-0.311331\pi$
$857$	32.7067	1.11724	0.558619	+	0.829424i	$0.311331\pi$
$858$	−5.90572	−0.201618
$859$	19.1447	0.653208	0.326604	−	0.945161i	$-0.394096\pi$
$859$	19.1447	0.653208	0.326604	+	0.945161i	$0.394096\pi$
$860$	−6.12879	−0.208990
$861$	0.816951	0.0278416
$862$	−43.1571	−1.46994
$863$	−12.4931	−0.425268	−0.212634	−	0.977132i	$-0.568204\pi$
$863$	−12.4931	−0.425268	−0.212634	+	0.977132i	$0.568204\pi$
$864$	3.36056	0.114329
$865$	6.93862	0.235920
$866$	2.74813	0.0933852
$867$	−9.91268	−0.336652
$868$	7.55178	0.256324
$869$	33.6698	1.14217
$870$	2.59846	0.0880959
$871$	−31.4340	−1.06510
$872$	10.0972	0.341934
$873$	5.13309	0.173729
$874$	24.6143	0.832590
$875$	−44.4436	−1.50247
$876$	−1.29237	−0.0436650
$877$	−15.9441	−0.538395	−0.269198	−	0.963085i	$-0.586758\pi$
$877$	−15.9441	−0.538395	−0.269198	+	0.963085i	$0.586758\pi$
$878$	−13.0489	−0.440378
$879$	−4.63383	−0.156295
$880$	29.2294	0.985324
$881$	32.6872	1.10126	0.550629	−	0.834750i	$-0.314388\pi$
$881$	32.6872	1.10126	0.550629	+	0.834750i	$0.314388\pi$
$882$	45.1962	1.52184
$883$	24.6543	0.829684	0.414842	−	0.909894i	$-0.363837\pi$
$883$	24.6543	0.829684	0.414842	+	0.909894i	$0.363837\pi$
$884$	9.44199	0.317568
$885$	−2.13173	−0.0716573
$886$	4.84674	0.162830
$887$	−40.5624	−1.36195	−0.680976	−	0.732306i	$-0.738444\pi$
$887$	−40.5624	−1.36195	−0.680976	+	0.732306i	$0.738444\pi$
$888$	−3.84346	−0.128978
$889$	−47.6720	−1.59887
$890$	−20.0984	−0.673702
$891$	40.8394	1.36817
$892$	−4.10079	−0.137305
$893$	−5.53594	−0.185253
$894$	8.59169	0.287349
$895$	25.5206	0.853059
$896$	55.5078	1.85438
$897$	6.44243	0.215107
$898$	25.8968	0.864187
$899$	23.3164	0.777645
$900$	3.91703	0.130568
$901$	−8.10845	−0.270132
$902$	−5.91587	−0.196977
$903$	12.1329	0.403758
$904$	35.8368	1.19191
$905$	5.90780	0.196382
$906$	−7.45294	−0.247607
$907$	24.2976	0.806789	0.403395	−	0.915026i	$-0.367830\pi$
$907$	24.2976	0.806789	0.403395	+	0.915026i	$0.367830\pi$
$908$	−1.47336	−0.0488952
$909$	−24.1166	−0.799898
$910$	25.8811	0.857951
$911$	−34.4492	−1.14135	−0.570677	−	0.821175i	$-0.693319\pi$
$911$	−34.4492	−1.14135	−0.570677	+	0.821175i	$0.693319\pi$
$912$	−2.26855	−0.0751191
$913$	54.0547	1.78895
$914$	−47.8490	−1.58270
$915$	−1.74127	−0.0575646
$916$	1.18365	0.0391090
$917$	12.5526	0.414523
$918$	17.4044	0.574432
$919$	−3.22637	−0.106428	−0.0532140	−	0.998583i	$-0.516947\pi$
$919$	−3.22637	−0.106428	−0.0532140	+	0.998583i	$0.516947\pi$
$920$	−26.3524	−0.868812
$921$	0.577809	0.0190395
$922$	−0.491778	−0.0161958
$923$	37.8086	1.24448
$924$	2.02298	0.0665510
$925$	−20.3981	−0.670686
$926$	−33.1439	−1.08918
$927$	47.3769	1.55606
$928$	−11.4993	−0.377482
$929$	−21.8182	−0.715831	−0.357915	−	0.933754i	$-0.616512\pi$
$929$	−21.8182	−0.715831	−0.357915	+	0.933754i	$0.616512\pi$
$930$	2.31260	0.0758331
$931$	−19.2512	−0.630931
$932$	−4.72218	−0.154680
$933$	−2.30976	−0.0756181
$934$	24.7954	0.811330
$935$	47.2484	1.54519
$936$	22.6970	0.741875
$937$	47.7881	1.56117	0.780584	−	0.625051i	$-0.214922\pi$
$937$	47.7881	1.56117	0.780584	+	0.625051i	$0.214922\pi$
$938$	64.2160	2.09673
$939$	0.885655	0.0289023
$940$	−1.49523	−0.0487691
$941$	−25.9536	−0.846062	−0.423031	−	0.906115i	$-0.639034\pi$
$941$	−25.9536	−0.846062	−0.423031	+	0.906115i	$0.639034\pi$
$942$	8.47389	0.276094
$943$	6.45351	0.210155
$944$	30.2251	0.983744
$945$	7.99933	0.260218
$946$	−87.8592	−2.85655
$947$	−13.3473	−0.433730	−0.216865	−	0.976202i	$-0.569583\pi$
$947$	−13.3473	−0.433730	−0.216865	+	0.976202i	$0.569583\pi$
$948$	−0.705806	−0.0229235
$949$	−39.7434	−1.29012
$950$	−9.95034	−0.322832
$951$	2.71707	0.0881071
$952$	76.4581	2.47802
$953$	10.7810	0.349230	0.174615	−	0.984637i	$-0.444132\pi$
$953$	10.7810	0.349230	0.174615	+	0.984637i	$0.444132\pi$
$954$	4.91731	0.159204
$955$	5.50311	0.178076
$956$	−0.761083	−0.0246152
$957$	6.24600	0.201905
$958$	9.32722	0.301349
$959$	44.9352	1.45103
$960$	1.90093	0.0613521
$961$	−10.2487	−0.330602
$962$	29.8185	0.961387
$963$	−36.0269	−1.16095
$964$	−3.17973	−0.102412
$965$	7.87697	0.253569
$966$	−13.1611	−0.423453
$967$	−5.74128	−0.184627	−0.0923135	−	0.995730i	$-0.529426\pi$
$967$	−5.74128	−0.184627	−0.0923135	+	0.995730i	$0.529426\pi$
$968$	30.8343	0.991052
$969$	−3.66704	−0.117802
$970$	−3.52189	−0.113081
$971$	−45.4019	−1.45702	−0.728508	−	0.685037i	$-0.759786\pi$
$971$	−45.4019	−1.45702	−0.728508	+	0.685037i	$0.759786\pi$
$972$	−2.66416	−0.0854529
$973$	−60.4400	−1.93762
$974$	−25.2228	−0.808191
$975$	−2.60436	−0.0834062
$976$	24.6889	0.790274
$977$	25.1149	0.803497	0.401748	−	0.915750i	$-0.368403\pi$
$977$	25.1149	0.803497	0.401748	+	0.915750i	$0.368403\pi$
$978$	−5.30402	−0.169604
$979$	−48.3114	−1.54404
$980$	−5.19964	−0.166097
$981$	−11.9766	−0.382384
$982$	−64.9132	−2.07146
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−0.491563	−0.0156705
$985$	−20.1057	−0.640619
$986$	−59.5551	−1.89662
$987$	2.96004	0.0942193
$988$	2.43898	0.0775942
$989$	95.8439	3.04766
$990$	−28.6534	−0.910666
$991$	−5.34753	−0.169870	−0.0849349	−	0.996386i	$-0.527068\pi$
$991$	−5.34753	−0.169870	−0.0849349	+	0.996386i	$0.527068\pi$
$992$	−10.2342	−0.324937
$993$	−1.13230	−0.0359323
$994$	−77.2385	−2.44986
$995$	25.2016	0.798943
$996$	−1.13312	−0.0359044
$997$	−42.1964	−1.33637	−0.668186	−	0.743994i	$-0.732929\pi$
$997$	−42.1964	−1.33637	−0.668186	+	0.743994i	$0.732929\pi$
$998$	28.1676	0.891629
$999$	9.21629	0.291591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.13	✓	54
3.2	odd	2		8847.2.a.g.1.42		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.13	✓	54	1.1	even	1	trivial
8847.2.a.g.1.42		54	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-1.55013 q^{2} -0.251970 q^{3} +0.402914 q^{4} -1.29975 q^{5} +0.390586 q^{6} -4.11447 q^{7} +2.47570 q^{8} -2.93651 q^{9} +O(q^{10})\)	\(q-1.55013 q^{2} -0.251970 q^{3} +0.402914 q^{4} -1.29975 q^{5} +0.390586 q^{6} -4.11447 q^{7} +2.47570 q^{8} -2.93651 q^{9} +2.01479 q^{10} +4.84302 q^{11} -0.101522 q^{12} -3.12205 q^{13} +6.37798 q^{14} +0.327498 q^{15} -4.64349 q^{16} -7.50605 q^{17} +4.55198 q^{18} -1.93890 q^{19} -0.523688 q^{20} +1.03672 q^{21} -7.50732 q^{22} +8.18959 q^{23} -0.623800 q^{24} -3.31065 q^{25} +4.83959 q^{26} +1.49582 q^{27} -1.65778 q^{28} -5.11845 q^{29} -0.507665 q^{30} -4.55536 q^{31} +2.24663 q^{32} -1.22029 q^{33} +11.6354 q^{34} +5.34779 q^{35} -1.18316 q^{36} +6.16137 q^{37} +3.00556 q^{38} +0.786661 q^{39} -3.21779 q^{40} +0.788014 q^{41} -1.60706 q^{42} +11.7031 q^{43} +1.95132 q^{44} +3.81673 q^{45} -12.6950 q^{46} +2.85520 q^{47} +1.17002 q^{48} +9.92890 q^{49} +5.13195 q^{50} +1.89130 q^{51} -1.25792 q^{52} +1.08026 q^{53} -2.31872 q^{54} -6.29471 q^{55} -10.1862 q^{56} +0.488544 q^{57} +7.93428 q^{58} -6.50914 q^{59} +0.131953 q^{60} -5.31690 q^{61} +7.06142 q^{62} +12.0822 q^{63} +5.80439 q^{64} +4.05789 q^{65} +1.89162 q^{66} +10.0684 q^{67} -3.02429 q^{68} -2.06353 q^{69} -8.28979 q^{70} -12.1102 q^{71} -7.26991 q^{72} +12.7299 q^{73} -9.55094 q^{74} +0.834182 q^{75} -0.781210 q^{76} -19.9265 q^{77} -1.21943 q^{78} +6.95224 q^{79} +6.03538 q^{80} +8.43263 q^{81} -1.22153 q^{82} +11.1614 q^{83} +0.417710 q^{84} +9.75600 q^{85} -18.1414 q^{86} +1.28969 q^{87} +11.9898 q^{88} -9.97547 q^{89} -5.91645 q^{90} +12.8456 q^{91} +3.29970 q^{92} +1.14781 q^{93} -4.42593 q^{94} +2.52009 q^{95} -0.566083 q^{96} -1.74802 q^{97} -15.3911 q^{98} -14.2216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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