LMFDB - Embedded newform 8029.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93012 q^{2} +2.98089 q^{3} +1.72535 q^{4} +0.211062 q^{5} -5.75346 q^{6} +1.00000 q^{7} +0.530105 q^{8} +5.88570 q^{9} +O(q^{10})$	\(q-1.93012 q^{2} +2.98089 q^{3} +1.72535 q^{4} +0.211062 q^{5} -5.75346 q^{6} +1.00000 q^{7} +0.530105 q^{8} +5.88570 q^{9} -0.407374 q^{10} -0.705745 q^{11} +5.14308 q^{12} +0.272573 q^{13} -1.93012 q^{14} +0.629152 q^{15} -4.47387 q^{16} +6.04726 q^{17} -11.3601 q^{18} -7.37232 q^{19} +0.364156 q^{20} +2.98089 q^{21} +1.36217 q^{22} -7.57537 q^{23} +1.58018 q^{24} -4.95545 q^{25} -0.526097 q^{26} +8.60196 q^{27} +1.72535 q^{28} -10.3053 q^{29} -1.21434 q^{30} +1.00000 q^{31} +7.57487 q^{32} -2.10375 q^{33} -11.6719 q^{34} +0.211062 q^{35} +10.1549 q^{36} -1.00000 q^{37} +14.2294 q^{38} +0.812509 q^{39} +0.111885 q^{40} +1.11727 q^{41} -5.75346 q^{42} +0.0871520 q^{43} -1.21766 q^{44} +1.24225 q^{45} +14.6214 q^{46} -4.35822 q^{47} -13.3361 q^{48} +1.00000 q^{49} +9.56460 q^{50} +18.0262 q^{51} +0.470283 q^{52} +6.61780 q^{53} -16.6028 q^{54} -0.148956 q^{55} +0.530105 q^{56} -21.9761 q^{57} +19.8904 q^{58} -11.4583 q^{59} +1.08551 q^{60} -11.8204 q^{61} -1.93012 q^{62} +5.88570 q^{63} -5.67266 q^{64} +0.0575297 q^{65} +4.06048 q^{66} +1.96890 q^{67} +10.4336 q^{68} -22.5813 q^{69} -0.407374 q^{70} +5.06737 q^{71} +3.12004 q^{72} -3.49228 q^{73} +1.93012 q^{74} -14.7717 q^{75} -12.7198 q^{76} -0.705745 q^{77} -1.56824 q^{78} +6.78781 q^{79} -0.944262 q^{80} +7.98438 q^{81} -2.15647 q^{82} -14.4937 q^{83} +5.14308 q^{84} +1.27635 q^{85} -0.168214 q^{86} -30.7189 q^{87} -0.374118 q^{88} -2.85496 q^{89} -2.39768 q^{90} +0.272573 q^{91} -13.0702 q^{92} +2.98089 q^{93} +8.41188 q^{94} -1.55602 q^{95} +22.5799 q^{96} -5.24758 q^{97} -1.93012 q^{98} -4.15380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−1.93012	−1.36480	−0.682399	−	0.730980i	$-0.739063\pi$
$2$	−1.93012	−1.36480	−0.682399	+	0.730980i	$0.739063\pi$
$3$	2.98089	1.72102	0.860509	−	0.509436i	$-0.170146\pi$
$3$	2.98089	1.72102	0.860509	+	0.509436i	$0.170146\pi$
$4$	1.72535	0.862676
$5$	0.211062	0.0943897	0.0471949	−	0.998886i	$-0.484972\pi$
$5$	0.211062	0.0943897	0.0471949	+	0.998886i	$0.484972\pi$
$6$	−5.75346	−2.34884
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.530105	0.187420
$9$	5.88570	1.96190
$10$	−0.407374	−0.128823
$11$	−0.705745	−0.212790	−0.106395	−	0.994324i	$-0.533931\pi$
$11$	−0.705745	−0.212790	−0.106395	+	0.994324i	$0.533931\pi$
$12$	5.14308	1.48468
$13$	0.272573	0.0755980	0.0377990	−	0.999285i	$-0.487965\pi$
$13$	0.272573	0.0755980	0.0377990	+	0.999285i	$0.487965\pi$
$14$	−1.93012	−0.515845
$15$	0.629152	0.162446
$16$	−4.47387	−1.11847
$17$	6.04726	1.46668	0.733338	−	0.679864i	$-0.237961\pi$
$17$	6.04726	1.46668	0.733338	+	0.679864i	$0.237961\pi$
$18$	−11.3601	−2.67760
$19$	−7.37232	−1.69133	−0.845663	−	0.533717i	$-0.820795\pi$
$19$	−7.37232	−1.69133	−0.845663	+	0.533717i	$0.820795\pi$
$20$	0.364156	0.0814277
$21$	2.98089	0.650483
$22$	1.36217	0.290415
$23$	−7.57537	−1.57957	−0.789787	−	0.613381i	$-0.789809\pi$
$23$	−7.57537	−1.57957	−0.789787	+	0.613381i	$0.789809\pi$
$24$	1.58018	0.322554
$25$	−4.95545	−0.991091
$26$	−0.526097	−0.103176
$27$	8.60196	1.65545
$28$	1.72535	0.326061
$29$	−10.3053	−1.91364	−0.956821	−	0.290679i	$-0.906119\pi$
$29$	−10.3053	−1.91364	−0.956821	+	0.290679i	$0.906119\pi$
$30$	−1.21434	−0.221707
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.57487	1.33906
$33$	−2.10375	−0.366215
$34$	−11.6719	−2.00172
$35$	0.211062	0.0356760
$36$	10.1549	1.69248
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	14.2294	2.30832
$39$	0.812509	0.130106
$40$	0.111885	0.0176905
$41$	1.11727	0.174489	0.0872445	−	0.996187i	$-0.472194\pi$
$41$	1.11727	0.174489	0.0872445	+	0.996187i	$0.472194\pi$
$42$	−5.75346	−0.887779
$43$	0.0871520	0.0132906	0.00664528	−	0.999978i	$-0.497885\pi$
$43$	0.0871520	0.0132906	0.00664528	+	0.999978i	$0.497885\pi$
$44$	−1.21766	−0.183569
$45$	1.24225	0.185183
$46$	14.6214	2.15580
$47$	−4.35822	−0.635712	−0.317856	−	0.948139i	$-0.602963\pi$
$47$	−4.35822	−0.635712	−0.317856	+	0.948139i	$0.602963\pi$
$48$	−13.3361	−1.92490
$49$	1.00000	0.142857
$50$	9.56460	1.35264
$51$	18.0262	2.52418
$52$	0.470283	0.0652166
$53$	6.61780	0.909025	0.454512	−	0.890740i	$-0.349814\pi$
$53$	6.61780	0.909025	0.454512	+	0.890740i	$0.349814\pi$
$54$	−16.6028	−2.25935
$55$	−0.148956	−0.0200852
$56$	0.530105	0.0708382
$57$	−21.9761	−2.91080
$58$	19.8904	2.61173
$59$	−11.4583	−1.49174	−0.745871	−	0.666090i	$-0.767967\pi$
$59$	−11.4583	−1.49174	−0.745871	+	0.666090i	$0.767967\pi$
$60$	1.08551	0.140138
$61$	−11.8204	−1.51345	−0.756723	−	0.653735i	$-0.773201\pi$
$61$	−11.8204	−1.51345	−0.756723	+	0.653735i	$0.773201\pi$
$62$	−1.93012	−0.245125
$63$	5.88570	0.741529
$64$	−5.67266	−0.709083
$65$	0.0575297	0.00713568
$66$	4.06048	0.499810
$67$	1.96890	0.240539	0.120270	−	0.992741i	$-0.461624\pi$
$67$	1.96890	0.240539	0.120270	+	0.992741i	$0.461624\pi$
$68$	10.4336	1.26527
$69$	−22.5813	−2.71847
$70$	−0.407374	−0.0486905
$71$	5.06737	0.601386	0.300693	−	0.953721i	$-0.402782\pi$
$71$	5.06737	0.601386	0.300693	+	0.953721i	$0.402782\pi$
$72$	3.12004	0.367700
$73$	−3.49228	−0.408740	−0.204370	−	0.978894i	$-0.565515\pi$
$73$	−3.49228	−0.408740	−0.204370	+	0.978894i	$0.565515\pi$
$74$	1.93012	0.224372
$75$	−14.7717	−1.70568
$76$	−12.7198	−1.45907
$77$	−0.705745	−0.0804271
$78$	−1.56824	−0.177568
$79$	6.78781	0.763689	0.381844	−	0.924227i	$-0.375289\pi$
$79$	6.78781	0.763689	0.381844	+	0.924227i	$0.375289\pi$
$80$	−0.944262	−0.105572
$81$	7.98438	0.887153
$82$	−2.15647	−0.238142
$83$	−14.4937	−1.59089	−0.795445	−	0.606026i	$-0.792763\pi$
$83$	−14.4937	−1.59089	−0.795445	+	0.606026i	$0.792763\pi$
$84$	5.14308	0.561156
$85$	1.27635	0.138439
$86$	−0.168214	−0.0181389
$87$	−30.7189	−3.29341
$88$	−0.374118	−0.0398812
$89$	−2.85496	−0.302625	−0.151312	−	0.988486i	$-0.548350\pi$
$89$	−2.85496	−0.302625	−0.151312	+	0.988486i	$0.548350\pi$
$90$	−2.39768	−0.252738
$91$	0.272573	0.0285734
$92$	−13.0702	−1.36266
$93$	2.98089	0.309104
$94$	8.41188	0.867619
$95$	−1.55602	−0.159644
$96$	22.5799	2.30455
$97$	−5.24758	−0.532811	−0.266406	−	0.963861i	$-0.585836\pi$
$97$	−5.24758	−0.532811	−0.266406	+	0.963861i	$0.585836\pi$
$98$	−1.93012	−0.194971
$99$	−4.15380	−0.417473
$100$	−8.54990	−0.854990
$101$	0.255738	0.0254469	0.0127235	−	0.999919i	$-0.495950\pi$
$101$	0.255738	0.0254469	0.0127235	+	0.999919i	$0.495950\pi$
$102$	−34.7927	−3.44499
$103$	−17.4868	−1.72302	−0.861511	−	0.507739i	$-0.830482\pi$
$103$	−17.4868	−1.72302	−0.861511	+	0.507739i	$0.830482\pi$
$104$	0.144492	0.0141686
$105$	0.629152	0.0613990
$106$	−12.7731	−1.24064
$107$	0.149784	0.0144801	0.00724007	−	0.999974i	$-0.497695\pi$
$107$	0.149784	0.0144801	0.00724007	+	0.999974i	$0.497695\pi$
$108$	14.8414	1.42811
$109$	−9.91232	−0.949428	−0.474714	−	0.880140i	$-0.657449\pi$
$109$	−9.91232	−0.949428	−0.474714	+	0.880140i	$0.657449\pi$
$110$	0.287502	0.0274122
$111$	−2.98089	−0.282934
$112$	−4.47387	−0.422741
$113$	9.82122	0.923903	0.461951	−	0.886905i	$-0.347149\pi$
$113$	9.82122	0.923903	0.461951	+	0.886905i	$0.347149\pi$
$114$	42.4164	3.97266
$115$	−1.59887	−0.149096
$116$	−17.7802	−1.65085
$117$	1.60428	0.148316
$118$	22.1158	2.03593
$119$	6.04726	0.554352
$120$	0.333516	0.0304457
$121$	−10.5019	−0.954720
$122$	22.8147	2.06555
$123$	3.33047	0.300299
$124$	1.72535	0.154941
$125$	−2.10122	−0.187939
$126$	−11.3601	−1.01204
$127$	−5.62017	−0.498709	−0.249355	−	0.968412i	$-0.580218\pi$
$127$	−5.62017	−0.498709	−0.249355	+	0.968412i	$0.580218\pi$
$128$	−4.20085	−0.371306
$129$	0.259790	0.0228733
$130$	−0.111039	−0.00973876
$131$	−17.0119	−1.48634	−0.743168	−	0.669105i	$-0.766678\pi$
$131$	−17.0119	−1.48634	−0.743168	+	0.669105i	$0.766678\pi$
$132$	−3.62970	−0.315925
$133$	−7.37232	−0.639261
$134$	−3.80021	−0.328288
$135$	1.81555	0.156257
$136$	3.20568	0.274885
$137$	−4.62783	−0.395383	−0.197691	−	0.980264i	$-0.563344\pi$
$137$	−4.62783	−0.395383	−0.197691	+	0.980264i	$0.563344\pi$
$138$	43.5846	3.71017
$139$	10.4010	0.882205	0.441103	−	0.897457i	$-0.354587\pi$
$139$	10.4010	0.882205	0.441103	+	0.897457i	$0.354587\pi$
$140$	0.364156	0.0307768
$141$	−12.9914	−1.09407
$142$	−9.78061	−0.820771
$143$	−0.192367	−0.0160865
$144$	−26.3318	−2.19432
$145$	−2.17505	−0.180628
$146$	6.74050	0.557848
$147$	2.98089	0.245860
$148$	−1.72535	−0.141823
$149$	−11.1298	−0.911786	−0.455893	−	0.890034i	$-0.650680\pi$
$149$	−11.1298	−0.911786	−0.455893	+	0.890034i	$0.650680\pi$
$150$	28.5110	2.32792
$151$	14.9867	1.21960	0.609798	−	0.792557i	$-0.291250\pi$
$151$	14.9867	1.21960	0.609798	+	0.792557i	$0.291250\pi$
$152$	−3.90810	−0.316989
$153$	35.5924	2.87747
$154$	1.36217	0.109767
$155$	0.211062	0.0169529
$156$	1.40186	0.112239
$157$	−5.48392	−0.437664	−0.218832	−	0.975763i	$-0.570225\pi$
$157$	−5.48392	−0.437664	−0.218832	+	0.975763i	$0.570225\pi$
$158$	−13.1013	−1.04228
$159$	19.7269	1.56445
$160$	1.59877	0.126394
$161$	−7.57537	−0.597023
$162$	−15.4108	−1.21079
$163$	12.7681	1.00008	0.500038	−	0.866003i	$-0.333319\pi$
$163$	12.7681	1.00008	0.500038	+	0.866003i	$0.333319\pi$
$164$	1.92769	0.150527
$165$	−0.444021	−0.0345670
$166$	27.9745	2.17124
$167$	16.1915	1.25294	0.626469	−	0.779446i	$-0.284499\pi$
$167$	16.1915	1.25294	0.626469	+	0.779446i	$0.284499\pi$
$168$	1.58018	0.121914
$169$	−12.9257	−0.994285
$170$	−2.46350	−0.188942
$171$	−43.3913	−3.31821
$172$	0.150368	0.0114654
$173$	−14.0813	−1.07058	−0.535291	−	0.844668i	$-0.679798\pi$
$173$	−14.0813	−1.07058	−0.535291	+	0.844668i	$0.679798\pi$
$174$	59.2910	4.49484
$175$	−4.95545	−0.374597
$176$	3.15741	0.237998
$177$	−34.1559	−2.56731
$178$	5.51040	0.413022
$179$	8.03359	0.600459	0.300229	−	0.953867i	$-0.402937\pi$
$179$	8.03359	0.600459	0.300229	+	0.953867i	$0.402937\pi$
$180$	2.14331	0.159753
$181$	25.6761	1.90849	0.954243	−	0.299031i	$-0.0966634\pi$
$181$	25.6761	1.90849	0.954243	+	0.299031i	$0.0966634\pi$
$182$	−0.526097	−0.0389969
$183$	−35.2353	−2.60467
$184$	−4.01574	−0.296044
$185$	−0.211062	−0.0155176
$186$	−5.75346	−0.421865
$187$	−4.26782	−0.312094
$188$	−7.51946	−0.548413
$189$	8.60196	0.625700
$190$	3.00329	0.217882
$191$	12.4478	0.900694	0.450347	−	0.892854i	$-0.351300\pi$
$191$	12.4478	0.900694	0.450347	+	0.892854i	$0.351300\pi$
$192$	−16.9096	−1.22034
$193$	8.85466	0.637373	0.318686	−	0.947860i	$-0.396758\pi$
$193$	8.85466	0.637373	0.318686	+	0.947860i	$0.396758\pi$
$194$	10.1284	0.727180
$195$	0.171490	0.0122806
$196$	1.72535	0.123239
$197$	17.9206	1.27679	0.638394	−	0.769710i	$-0.279599\pi$
$197$	17.9206	1.27679	0.638394	+	0.769710i	$0.279599\pi$
$198$	8.01732	0.569766
$199$	14.2668	1.01135	0.505674	−	0.862725i	$-0.331244\pi$
$199$	14.2668	1.01135	0.505674	+	0.862725i	$0.331244\pi$
$200$	−2.62691	−0.185750
$201$	5.86907	0.413972
$202$	−0.493605	−0.0347299
$203$	−10.3053	−0.723288
$204$	31.1016	2.17754
$205$	0.235814	0.0164700
$206$	33.7515	2.35158
$207$	−44.5864	−3.09897
$208$	−1.21945	−0.0845539
$209$	5.20297	0.359897
$210$	−1.21434	−0.0837972
$211$	−19.4042	−1.33584	−0.667922	−	0.744231i	$-0.732816\pi$
$211$	−19.4042	−1.33584	−0.667922	+	0.744231i	$0.732816\pi$
$212$	11.4180	0.784193
$213$	15.1053	1.03500
$214$	−0.289100	−0.0197625
$215$	0.0183945	0.00125449
$216$	4.55994	0.310264
$217$	1.00000	0.0678844
$218$	19.1319	1.29578
$219$	−10.4101	−0.703449
$220$	−0.257001	−0.0173270
$221$	1.64832	0.110878
$222$	5.75346	0.386147
$223$	−12.7692	−0.855086	−0.427543	−	0.903995i	$-0.640621\pi$
$223$	−12.7692	−0.855086	−0.427543	+	0.903995i	$0.640621\pi$
$224$	7.57487	0.506118
$225$	−29.1663	−1.94442
$226$	−18.9561	−1.26094
$227$	6.35697	0.421927	0.210964	−	0.977494i	$-0.432340\pi$
$227$	6.35697	0.421927	0.210964	+	0.977494i	$0.432340\pi$
$228$	−37.9164	−2.51108
$229$	4.21393	0.278464	0.139232	−	0.990260i	$-0.455537\pi$
$229$	4.21393	0.278464	0.139232	+	0.990260i	$0.455537\pi$
$230$	3.08601	0.203485
$231$	−2.10375	−0.138416
$232$	−5.46287	−0.358655
$233$	20.3771	1.33495	0.667476	−	0.744632i	$-0.267375\pi$
$233$	20.3771	1.33495	0.667476	+	0.744632i	$0.267375\pi$
$234$	−3.09645	−0.202421
$235$	−0.919854	−0.0600047
$236$	−19.7696	−1.28689
$237$	20.2337	1.31432
$238$	−11.6719	−0.756578
$239$	25.1072	1.62405	0.812024	−	0.583624i	$-0.198366\pi$
$239$	25.1072	1.62405	0.812024	+	0.583624i	$0.198366\pi$
$240$	−2.81474	−0.181691
$241$	11.1693	0.719475	0.359737	−	0.933054i	$-0.382866\pi$
$241$	11.1693	0.719475	0.359737	+	0.933054i	$0.382866\pi$
$242$	20.2699	1.30300
$243$	−2.00532	−0.128641
$244$	−20.3943	−1.30561
$245$	0.211062	0.0134842
$246$	−6.42820	−0.409847
$247$	−2.00949	−0.127861
$248$	0.530105	0.0336617
$249$	−43.2041	−2.73795
$250$	4.05559	0.256498
$251$	15.4423	0.974710	0.487355	−	0.873204i	$-0.337962\pi$
$251$	15.4423	0.974710	0.487355	+	0.873204i	$0.337962\pi$
$252$	10.1549	0.639699
$253$	5.34628	0.336118
$254$	10.8476	0.680638
$255$	3.80465	0.238256
$256$	19.4535	1.21584
$257$	−26.3369	−1.64285	−0.821427	−	0.570314i	$-0.806821\pi$
$257$	−26.3369	−1.64285	−0.821427	+	0.570314i	$0.806821\pi$
$258$	−0.501426	−0.0312174
$259$	−1.00000	−0.0621370
$260$	0.0992589	0.00615577
$261$	−60.6538	−3.75437
$262$	32.8350	2.02855
$263$	28.7645	1.77370	0.886848	−	0.462062i	$-0.152890\pi$
$263$	28.7645	1.77370	0.886848	+	0.462062i	$0.152890\pi$
$264$	−1.11521	−0.0686362
$265$	1.39676	0.0858026
$266$	14.2294	0.872463
$267$	−8.51032	−0.520823
$268$	3.39704	0.207507
$269$	15.0396	0.916980	0.458490	−	0.888700i	$-0.348391\pi$
$269$	15.0396	0.916980	0.458490	+	0.888700i	$0.348391\pi$
$270$	−3.50421	−0.213260
$271$	19.2214	1.16762	0.583810	−	0.811891i	$-0.301561\pi$
$271$	19.2214	1.16762	0.583810	+	0.811891i	$0.301561\pi$
$272$	−27.0546	−1.64043
$273$	0.812509	0.0491753
$274$	8.93226	0.539618
$275$	3.49728	0.210894
$276$	−38.9608	−2.34516
$277$	2.80008	0.168240	0.0841201	−	0.996456i	$-0.473192\pi$
$277$	2.80008	0.168240	0.0841201	+	0.996456i	$0.473192\pi$
$278$	−20.0752	−1.20403
$279$	5.88570	0.352368
$280$	0.111885	0.00668640
$281$	−13.2584	−0.790928	−0.395464	−	0.918481i	$-0.629416\pi$
$281$	−13.2584	−0.790928	−0.395464	+	0.918481i	$0.629416\pi$
$282$	25.0749	1.49319
$283$	22.5383	1.33976	0.669880	−	0.742469i	$-0.266346\pi$
$283$	22.5383	1.33976	0.669880	+	0.742469i	$0.266346\pi$
$284$	8.74299	0.518801
$285$	−4.63831	−0.274750
$286$	0.371290	0.0219548
$287$	1.11727	0.0659506
$288$	44.5835	2.62711
$289$	19.5694	1.15114
$290$	4.19810	0.246521
$291$	−15.6425	−0.916977
$292$	−6.02540	−0.352610
$293$	−30.1452	−1.76110	−0.880550	−	0.473953i	$-0.842827\pi$
$293$	−30.1452	−1.76110	−0.880550	+	0.473953i	$0.842827\pi$
$294$	−5.75346	−0.335549
$295$	−2.41841	−0.140805
$296$	−0.530105	−0.0308117
$297$	−6.07078	−0.352263
$298$	21.4818	1.24440
$299$	−2.06484	−0.119413
$300$	−25.4863	−1.47145
$301$	0.0871520	0.00502336
$302$	−28.9260	−1.66450
$303$	0.762328	0.0437946
$304$	32.9828	1.89169
$305$	−2.49483	−0.142854
$306$	−68.6974	−3.92717
$307$	−16.0205	−0.914337	−0.457169	−	0.889380i	$-0.651136\pi$
$307$	−16.0205	−0.914337	−0.457169	+	0.889380i	$0.651136\pi$
$308$	−1.21766	−0.0693824
$309$	−52.1261	−2.96535
$310$	−0.407374	−0.0231373
$311$	−16.4708	−0.933971	−0.466985	−	0.884265i	$-0.654660\pi$
$311$	−16.4708	−0.933971	−0.466985	+	0.884265i	$0.654660\pi$
$312$	0.430715	0.0243844
$313$	14.2241	0.803991	0.401996	−	0.915642i	$-0.368317\pi$
$313$	14.2241	0.803991	0.401996	+	0.915642i	$0.368317\pi$
$314$	10.5846	0.597324
$315$	1.24225	0.0699927
$316$	11.7114	0.658816
$317$	3.84420	0.215912	0.107956	−	0.994156i	$-0.465570\pi$
$317$	3.84420	0.215912	0.107956	+	0.994156i	$0.465570\pi$
$318$	−38.0753	−2.13516
$319$	7.27289	0.407204
$320$	−1.19728	−0.0669301
$321$	0.446489	0.0249206
$322$	14.6214	0.814816
$323$	−44.5823	−2.48063
$324$	13.7759	0.765325
$325$	−1.35072	−0.0749245
$326$	−24.6440	−1.36490
$327$	−29.5475	−1.63398
$328$	0.592272	0.0327028
$329$	−4.35822	−0.240277
$330$	0.857012	0.0471769
$331$	−23.1958	−1.27496	−0.637479	−	0.770467i	$-0.720023\pi$
$331$	−23.1958	−1.27496	−0.637479	+	0.770467i	$0.720023\pi$
$332$	−25.0067	−1.37242
$333$	−5.88570	−0.322534
$334$	−31.2516	−1.71001
$335$	0.415560	0.0227044
$336$	−13.3361	−0.727544
$337$	12.0060	0.654007	0.327003	−	0.945023i	$-0.393961\pi$
$337$	12.0060	0.654007	0.327003	+	0.945023i	$0.393961\pi$
$338$	24.9481	1.35700
$339$	29.2760	1.59005
$340$	2.20215	0.119428
$341$	−0.705745	−0.0382182
$342$	83.7502	4.52869
$343$	1.00000	0.0539949
$344$	0.0461997	0.00249092
$345$	−4.76606	−0.256596
$346$	27.1786	1.46113
$347$	−26.0267	−1.39719	−0.698593	−	0.715519i	$-0.746190\pi$
$347$	−26.0267	−1.39719	−0.698593	+	0.715519i	$0.746190\pi$
$348$	−53.0008	−2.84114
$349$	25.9392	1.38849	0.694246	−	0.719738i	$-0.255738\pi$
$349$	25.9392	1.38849	0.694246	+	0.719738i	$0.255738\pi$
$350$	9.56460	0.511250
$351$	2.34466	0.125149
$352$	−5.34593	−0.284939
$353$	−28.1312	−1.49727	−0.748636	−	0.662981i	$-0.769291\pi$
$353$	−28.1312	−1.49727	−0.748636	+	0.662981i	$0.769291\pi$
$354$	65.9249	3.50387
$355$	1.06953	0.0567646
$356$	−4.92581	−0.261067
$357$	18.0262	0.954049
$358$	−15.5058	−0.819505
$359$	13.9473	0.736109	0.368054	−	0.929804i	$-0.380024\pi$
$359$	13.9473	0.736109	0.368054	+	0.929804i	$0.380024\pi$
$360$	0.658521	0.0347071
$361$	35.3511	1.86058
$362$	−49.5578	−2.60470
$363$	−31.3051	−1.64309
$364$	0.470283	0.0246495
$365$	−0.737087	−0.0385809
$366$	68.0082	3.55485
$367$	3.83029	0.199939	0.0999697	−	0.994990i	$-0.468125\pi$
$367$	3.83029	0.199939	0.0999697	+	0.994990i	$0.468125\pi$
$368$	33.8912	1.76670
$369$	6.57595	0.342330
$370$	0.407374	0.0211784
$371$	6.61780	0.343579
$372$	5.14308	0.266656
$373$	−9.91424	−0.513340	−0.256670	−	0.966499i	$-0.582625\pi$
$373$	−9.91424	−0.513340	−0.256670	+	0.966499i	$0.582625\pi$
$374$	8.23739	0.425945
$375$	−6.26349	−0.323445
$376$	−2.31031	−0.119145
$377$	−2.80893	−0.144667
$378$	−16.6028	−0.853955
$379$	5.09401	0.261662	0.130831	−	0.991405i	$-0.458236\pi$
$379$	5.09401	0.261662	0.130831	+	0.991405i	$0.458236\pi$
$380$	−2.68467	−0.137721
$381$	−16.7531	−0.858287
$382$	−24.0258	−1.22927
$383$	−5.43558	−0.277745	−0.138873	−	0.990310i	$-0.544348\pi$
$383$	−5.43558	−0.277745	−0.138873	+	0.990310i	$0.544348\pi$
$384$	−12.5223	−0.639024
$385$	−0.148956	−0.00759149
$386$	−17.0905	−0.869885
$387$	0.512951	0.0260747
$388$	−9.05392	−0.459643
$389$	15.4531	0.783504	0.391752	−	0.920071i	$-0.371869\pi$
$389$	15.4531	0.783504	0.391752	+	0.920071i	$0.371869\pi$
$390$	−0.330995	−0.0167606
$391$	−45.8103	−2.31672
$392$	0.530105	0.0267743
$393$	−50.7106	−2.55801
$394$	−34.5888	−1.74256
$395$	1.43265	0.0720844
$396$	−7.16677	−0.360144
$397$	25.4339	1.27649	0.638245	−	0.769833i	$-0.279661\pi$
$397$	25.4339	1.27649	0.638245	+	0.769833i	$0.279661\pi$
$398$	−27.5366	−1.38029
$399$	−21.9761	−1.10018
$400$	22.1700	1.10850
$401$	−29.3961	−1.46797	−0.733985	−	0.679166i	$-0.762342\pi$
$401$	−29.3961	−1.46797	−0.733985	+	0.679166i	$0.762342\pi$
$402$	−11.3280	−0.564989
$403$	0.272573	0.0135778
$404$	0.441239	0.0219524
$405$	1.68520	0.0837382
$406$	19.8904	0.987143
$407$	0.705745	0.0349825
$408$	9.55578	0.473082
$409$	0.620445	0.0306791	0.0153395	−	0.999882i	$-0.495117\pi$
$409$	0.620445	0.0306791	0.0153395	+	0.999882i	$0.495117\pi$
$410$	−0.455149	−0.0224782
$411$	−13.7951	−0.680460
$412$	−30.1708	−1.48641
$413$	−11.4583	−0.563826
$414$	86.0569	4.22947
$415$	−3.05907	−0.150164
$416$	2.06470	0.101230
$417$	31.0044	1.51829
$418$	−10.0423	−0.491187
$419$	−20.2305	−0.988327	−0.494163	−	0.869369i	$-0.664526\pi$
$419$	−20.2305	−0.988327	−0.494163	+	0.869369i	$0.664526\pi$
$420$	1.08551	0.0529674
$421$	3.25017	0.158404	0.0792019	−	0.996859i	$-0.474763\pi$
$421$	3.25017	0.158404	0.0792019	+	0.996859i	$0.474763\pi$
$422$	37.4525	1.82316
$423$	−25.6512	−1.24720
$424$	3.50813	0.170370
$425$	−29.9669	−1.45361
$426$	−29.1549	−1.41256
$427$	−11.8204	−0.572029
$428$	0.258430	0.0124917
$429$	−0.573424	−0.0276851
$430$	−0.0355035	−0.00171213
$431$	−10.6933	−0.515076	−0.257538	−	0.966268i	$-0.582911\pi$
$431$	−10.6933	−0.515076	−0.257538	+	0.966268i	$0.582911\pi$
$432$	−38.4840	−1.85156
$433$	19.5164	0.937899	0.468949	−	0.883225i	$-0.344633\pi$
$433$	19.5164	0.937899	0.468949	+	0.883225i	$0.344633\pi$
$434$	−1.93012	−0.0926486
$435$	−6.48358	−0.310864
$436$	−17.1022	−0.819049
$437$	55.8481	2.67158
$438$	20.0927	0.960066
$439$	33.9663	1.62112	0.810561	−	0.585654i	$-0.199162\pi$
$439$	33.9663	1.62112	0.810561	+	0.585654i	$0.199162\pi$
$440$	−0.0789621	−0.00376437
$441$	5.88570	0.280272
$442$	−3.18145	−0.151326
$443$	23.5440	1.11861	0.559305	−	0.828962i	$-0.311068\pi$
$443$	23.5440	1.11861	0.559305	+	0.828962i	$0.311068\pi$
$444$	−5.14308	−0.244080
$445$	−0.602573	−0.0285647
$446$	24.6460	1.16702
$447$	−33.1766	−1.56920
$448$	−5.67266	−0.268008
$449$	13.2163	0.623718	0.311859	−	0.950128i	$-0.399048\pi$
$449$	13.2163	0.623718	0.311859	+	0.950128i	$0.399048\pi$
$450$	56.2944	2.65374
$451$	−0.788510	−0.0371295
$452$	16.9451	0.797028
$453$	44.6736	2.09895
$454$	−12.2697	−0.575846
$455$	0.0575297	0.00269703
$456$	−11.6496	−0.545543
$457$	−6.77992	−0.317151	−0.158576	−	0.987347i	$-0.550690\pi$
$457$	−6.77992	−0.317151	−0.158576	+	0.987347i	$0.550690\pi$
$458$	−8.13338	−0.380048
$459$	52.0183	2.42801
$460$	−2.75862	−0.128621
$461$	40.3709	1.88026	0.940130	−	0.340815i	$-0.110703\pi$
$461$	40.3709	1.88026	0.940130	+	0.340815i	$0.110703\pi$
$462$	4.06048	0.188910
$463$	1.50541	0.0699625	0.0349813	−	0.999388i	$-0.488863\pi$
$463$	1.50541	0.0699625	0.0349813	+	0.999388i	$0.488863\pi$
$464$	46.1044	2.14034
$465$	0.629152	0.0291762
$466$	−39.3303	−1.82194
$467$	−32.1373	−1.48714	−0.743568	−	0.668661i	$-0.766868\pi$
$467$	−32.1373	−1.48714	−0.743568	+	0.668661i	$0.766868\pi$
$468$	2.76795	0.127948
$469$	1.96890	0.0909153
$470$	1.77543	0.0818943
$471$	−16.3470	−0.753228
$472$	−6.07409	−0.279583
$473$	−0.0615070	−0.00282810
$474$	−39.0534	−1.79378
$475$	36.5332	1.67626
$476$	10.4336	0.478225
$477$	38.9504	1.78342
$478$	−48.4598	−2.21650
$479$	−20.3217	−0.928521	−0.464261	−	0.885699i	$-0.653680\pi$
$479$	−20.3217	−0.928521	−0.464261	+	0.885699i	$0.653680\pi$
$480$	4.76575	0.217526
$481$	−0.272573	−0.0124282
$482$	−21.5580	−0.981938
$483$	−22.5813	−1.02749
$484$	−18.1195	−0.823614
$485$	−1.10756	−0.0502919
$486$	3.87051	0.175570
$487$	−15.3700	−0.696479	−0.348240	−	0.937406i	$-0.613220\pi$
$487$	−15.3700	−0.696479	−0.348240	+	0.937406i	$0.613220\pi$
$488$	−6.26604	−0.283651
$489$	38.0604	1.72115
$490$	−0.407374	−0.0184033
$491$	−36.6718	−1.65498	−0.827488	−	0.561484i	$-0.810231\pi$
$491$	−36.6718	−1.65498	−0.827488	+	0.561484i	$0.810231\pi$
$492$	5.74623	0.259060
$493$	−62.3187	−2.80669
$494$	3.87855	0.174504
$495$	−0.876709	−0.0394051
$496$	−4.47387	−0.200883
$497$	5.06737	0.227302
$498$	83.3890	3.73675
$499$	−41.6874	−1.86619	−0.933093	−	0.359635i	$-0.882901\pi$
$499$	−41.6874	−1.86619	−0.933093	+	0.359635i	$0.882901\pi$
$500$	−3.62534	−0.162130
$501$	48.2652	2.15633
$502$	−29.8055	−1.33028
$503$	−26.0788	−1.16280	−0.581399	−	0.813618i	$-0.697495\pi$
$503$	−26.0788	−1.16280	−0.581399	+	0.813618i	$0.697495\pi$
$504$	3.12004	0.138978
$505$	0.0539766	0.00240193
$506$	−10.3189	−0.458733
$507$	−38.5301	−1.71118
$508$	−9.69677	−0.430224
$509$	1.57523	0.0698210	0.0349105	−	0.999390i	$-0.488885\pi$
$509$	1.57523	0.0698210	0.0349105	+	0.999390i	$0.488885\pi$
$510$	−7.34341	−0.325172
$511$	−3.49228	−0.154489
$512$	−29.1457	−1.28807
$513$	−63.4164	−2.79990
$514$	50.8334	2.24216
$515$	−3.69079	−0.162636
$516$	0.448230	0.0197322
$517$	3.07579	0.135273
$518$	1.93012	0.0848045
$519$	−41.9748	−1.84249
$520$	0.0304967	0.00133737
$521$	15.0609	0.659832	0.329916	−	0.944010i	$-0.392980\pi$
$521$	15.0609	0.659832	0.329916	+	0.944010i	$0.392980\pi$
$522$	117.069	5.12396
$523$	24.0247	1.05053	0.525264	−	0.850939i	$-0.323967\pi$
$523$	24.0247	1.05053	0.525264	+	0.850939i	$0.323967\pi$
$524$	−29.3515	−1.28223
$525$	−14.7717	−0.644688
$526$	−55.5189	−2.42074
$527$	6.04726	0.263423
$528$	9.41188	0.409599
$529$	34.3863	1.49505
$530$	−2.69592	−0.117103
$531$	−67.4401	−2.92665
$532$	−12.7198	−0.551475
$533$	0.304538	0.0131910
$534$	16.4259	0.710818
$535$	0.0316136	0.00136678
$536$	1.04372	0.0450819
$537$	23.9472	1.03340
$538$	−29.0282	−1.25149
$539$	−0.705745	−0.0303986
$540$	3.13245	0.134799
$541$	25.3356	1.08926	0.544631	−	0.838676i	$-0.316670\pi$
$541$	25.3356	1.08926	0.544631	+	0.838676i	$0.316670\pi$
$542$	−37.0996	−1.59357
$543$	76.5375	3.28454
$544$	45.8072	1.96397
$545$	−2.09211	−0.0896163
$546$	−1.56824	−0.0671143
$547$	−32.9033	−1.40684	−0.703422	−	0.710772i	$-0.748346\pi$
$547$	−32.9033	−1.40684	−0.703422	+	0.710772i	$0.748346\pi$
$548$	−7.98464	−0.341087
$549$	−69.5713	−2.96923
$550$	−6.75017	−0.287828
$551$	75.9738	3.23659
$552$	−11.9705	−0.509497
$553$	6.78781	0.288647
$554$	−5.40447	−0.229614
$555$	−0.629152	−0.0267060
$556$	17.9455	0.761057
$557$	9.26530	0.392583	0.196292	−	0.980546i	$-0.437110\pi$
$557$	9.26530	0.392583	0.196292	+	0.980546i	$0.437110\pi$
$558$	−11.3601	−0.480911
$559$	0.0237552	0.00100474
$560$	−0.944262	−0.0399024
$561$	−12.7219	−0.537119
$562$	25.5902	1.07946
$563$	−27.5496	−1.16108	−0.580539	−	0.814233i	$-0.697158\pi$
$563$	−27.5496	−1.16108	−0.580539	+	0.814233i	$0.697158\pi$
$564$	−22.4147	−0.943828
$565$	2.07288	0.0872069
$566$	−43.5015	−1.82850
$567$	7.98438	0.335312
$568$	2.68623	0.112712
$569$	7.08459	0.297001	0.148501	−	0.988912i	$-0.452555\pi$
$569$	7.08459	0.297001	0.148501	+	0.988912i	$0.452555\pi$
$570$	8.95248	0.374978
$571$	38.2155	1.59927	0.799634	−	0.600488i	$-0.205027\pi$
$571$	38.2155	1.59927	0.799634	+	0.600488i	$0.205027\pi$
$572$	−0.331900	−0.0138774
$573$	37.1056	1.55011
$574$	−2.15647	−0.0900093
$575$	37.5394	1.56550
$576$	−33.3876	−1.39115
$577$	33.2222	1.38306	0.691528	−	0.722349i	$-0.256938\pi$
$577$	33.2222	1.38306	0.691528	+	0.722349i	$0.256938\pi$
$578$	−37.7712	−1.57107
$579$	26.3948	1.09693
$580$	−3.75272	−0.155823
$581$	−14.4937	−0.601300
$582$	30.1918	1.25149
$583$	−4.67048	−0.193431
$584$	−1.85127	−0.0766062
$585$	0.338602	0.0139995
$586$	58.1837	2.40355
$587$	8.96423	0.369994	0.184997	−	0.982739i	$-0.440773\pi$
$587$	8.96423	0.369994	0.184997	+	0.982739i	$0.440773\pi$
$588$	5.14308	0.212097
$589$	−7.37232	−0.303771
$590$	4.66781	0.192171
$591$	53.4193	2.19737
$592$	4.47387	0.183875
$593$	−23.7261	−0.974313	−0.487157	−	0.873315i	$-0.661966\pi$
$593$	−23.7261	−0.974313	−0.487157	+	0.873315i	$0.661966\pi$
$594$	11.7173	0.480768
$595$	1.27635	0.0523251
$596$	−19.2028	−0.786576
$597$	42.5278	1.74055
$598$	3.98538	0.162974
$599$	−21.8300	−0.891948	−0.445974	−	0.895046i	$-0.647143\pi$
$599$	−21.8300	−0.891948	−0.445974	+	0.895046i	$0.647143\pi$
$600$	−7.83052	−0.319680
$601$	19.0288	0.776200	0.388100	−	0.921617i	$-0.373131\pi$
$601$	19.0288	0.776200	0.388100	+	0.921617i	$0.373131\pi$
$602$	−0.168214	−0.00685587
$603$	11.5884	0.471914
$604$	25.8572	1.05212
$605$	−2.21656	−0.0901158
$606$	−1.47138	−0.0597708
$607$	−33.3013	−1.35166	−0.675829	−	0.737059i	$-0.736214\pi$
$607$	−33.3013	−1.35166	−0.675829	+	0.737059i	$0.736214\pi$
$608$	−55.8444	−2.26479
$609$	−30.7189	−1.24479
$610$	4.81532	0.194967
$611$	−1.18793	−0.0480586
$612$	61.4093	2.48233
$613$	−28.2737	−1.14196	−0.570982	−	0.820963i	$-0.693437\pi$
$613$	−28.2737	−1.14196	−0.570982	+	0.820963i	$0.693437\pi$
$614$	30.9214	1.24789
$615$	0.702936	0.0283451
$616$	−0.374118	−0.0150737
$617$	−17.4242	−0.701471	−0.350735	−	0.936475i	$-0.614068\pi$
$617$	−17.4242	−0.701471	−0.350735	+	0.936475i	$0.614068\pi$
$618$	100.610	4.04711
$619$	33.8946	1.36234	0.681169	−	0.732127i	$-0.261472\pi$
$619$	33.8946	1.36234	0.681169	+	0.732127i	$0.261472\pi$
$620$	0.364156	0.0146248
$621$	−65.1630	−2.61490
$622$	31.7905	1.27468
$623$	−2.85496	−0.114381
$624$	−3.63505	−0.145519
$625$	24.3338	0.973351
$626$	−27.4541	−1.09729
$627$	15.5095	0.619389
$628$	−9.46168	−0.377562
$629$	−6.04726	−0.241120
$630$	−2.39768	−0.0955259
$631$	−19.8908	−0.791841	−0.395921	−	0.918285i	$-0.629574\pi$
$631$	−19.8908	−0.791841	−0.395921	+	0.918285i	$0.629574\pi$
$632$	3.59825	0.143131
$633$	−57.8419	−2.29901
$634$	−7.41975	−0.294676
$635$	−1.18620	−0.0470730
$636$	34.0359	1.34961
$637$	0.272573	0.0107997
$638$	−14.0375	−0.555751
$639$	29.8250	1.17986
$640$	−0.886639	−0.0350475
$641$	2.57764	0.101811	0.0509054	−	0.998703i	$-0.483789\pi$
$641$	2.57764	0.101811	0.0509054	+	0.998703i	$0.483789\pi$
$642$	−0.861776	−0.0340116
$643$	−0.0415885	−0.00164009	−0.000820045	−	1.00000i	$-0.500261\pi$
$643$	−0.0415885	−0.00164009	−0.000820045		1.00000i	$0.500261\pi$
$644$	−13.0702	−0.515037
$645$	0.0548319	0.00215900
$646$	86.0491	3.38556
$647$	31.4645	1.23700	0.618498	−	0.785787i	$-0.287742\pi$
$647$	31.4645	1.23700	0.618498	+	0.785787i	$0.287742\pi$
$648$	4.23256	0.166270
$649$	8.08662	0.317428
$650$	2.60705	0.102257
$651$	2.98089	0.116830
$652$	22.0295	0.862742
$653$	−30.7310	−1.20260	−0.601299	−	0.799024i	$-0.705350\pi$
$653$	−30.7310	−1.20260	−0.601299	+	0.799024i	$0.705350\pi$
$654$	57.0302	2.23006
$655$	−3.59056	−0.140295
$656$	−4.99854	−0.195160
$657$	−20.5545	−0.801908
$658$	8.41188	0.327929
$659$	−9.01945	−0.351348	−0.175674	−	0.984448i	$-0.556210\pi$
$659$	−9.01945	−0.351348	−0.175674	+	0.984448i	$0.556210\pi$
$660$	−0.766091	−0.0298201
$661$	33.5779	1.30603	0.653014	−	0.757345i	$-0.273504\pi$
$661$	33.5779	1.30603	0.653014	+	0.757345i	$0.273504\pi$
$662$	44.7707	1.74006
$663$	4.91345	0.190823
$664$	−7.68317	−0.298165
$665$	−1.55602	−0.0603397
$666$	11.3601	0.440195
$667$	78.0663	3.02274
$668$	27.9361	1.08088
$669$	−38.0635	−1.47162
$670$	−0.802078	−0.0309870
$671$	8.34218	0.322046
$672$	22.5799	0.871037
$673$	46.3946	1.78838	0.894190	−	0.447687i	$-0.147752\pi$
$673$	46.3946	1.78838	0.894190	+	0.447687i	$0.147752\pi$
$674$	−23.1729	−0.892588
$675$	−42.6266	−1.64070
$676$	−22.3014	−0.857745
$677$	32.2379	1.23900	0.619501	−	0.784996i	$-0.287335\pi$
$677$	32.2379	1.23900	0.619501	+	0.784996i	$0.287335\pi$
$678$	−56.5060	−2.17010
$679$	−5.24758	−0.201384
$680$	0.676597	0.0259463
$681$	18.9494	0.726144
$682$	1.36217	0.0521602
$683$	−41.9753	−1.60614	−0.803070	−	0.595885i	$-0.796801\pi$
$683$	−41.9753	−1.60614	−0.803070	+	0.595885i	$0.796801\pi$
$684$	−74.8652	−2.86254
$685$	−0.976759	−0.0373201
$686$	−1.93012	−0.0736922
$687$	12.5613	0.479242
$688$	−0.389906	−0.0148650
$689$	1.80383	0.0687205
$690$	9.19905	0.350202
$691$	−6.12895	−0.233156	−0.116578	−	0.993182i	$-0.537193\pi$
$691$	−6.12895	−0.233156	−0.116578	+	0.993182i	$0.537193\pi$
$692$	−24.2952	−0.923565
$693$	−4.15380	−0.157790
$694$	50.2346	1.90688
$695$	2.19526	0.0832711
$696$	−16.2842	−0.617252
$697$	6.75645	0.255919
$698$	−50.0656	−1.89501
$699$	60.7420	2.29747
$700$	−8.54990	−0.323156
$701$	−24.9262	−0.941449	−0.470724	−	0.882280i	$-0.656007\pi$
$701$	−24.9262	−0.941449	−0.470724	+	0.882280i	$0.656007\pi$
$702$	−4.52546	−0.170803
$703$	7.37232	0.278052
$704$	4.00345	0.150886
$705$	−2.74198	−0.103269
$706$	54.2965	2.04348
$707$	0.255738	0.00961803
$708$	−58.9309	−2.21476
$709$	−11.1645	−0.419290	−0.209645	−	0.977778i	$-0.567231\pi$
$709$	−11.1645	−0.419290	−0.209645	+	0.977778i	$0.567231\pi$
$710$	−2.06431	−0.0774723
$711$	39.9510	1.49828
$712$	−1.51343	−0.0567181
$713$	−7.57537	−0.283700
$714$	−34.7927	−1.30208
$715$	−0.0406012	−0.00151840
$716$	13.8608	0.518001
$717$	74.8417	2.79501
$718$	−26.9199	−1.00464
$719$	−43.8125	−1.63393	−0.816964	−	0.576688i	$-0.804345\pi$
$719$	−43.8125	−1.63393	−0.816964	+	0.576688i	$0.804345\pi$
$720$	−5.55765	−0.207121
$721$	−17.4868	−0.651241
$722$	−68.2318	−2.53932
$723$	33.2943	1.23823
$724$	44.3002	1.64640
$725$	51.0673	1.89659
$726$	60.4225	2.24249
$727$	14.3726	0.533049	0.266524	−	0.963828i	$-0.414125\pi$
$727$	14.3726	0.533049	0.266524	+	0.963828i	$0.414125\pi$
$728$	0.144492	0.00535523
$729$	−29.9308	−1.10855
$730$	1.42266	0.0526551
$731$	0.527031	0.0194929
$732$	−60.7932	−2.24698
$733$	6.57893	0.242998	0.121499	−	0.992592i	$-0.461230\pi$
$733$	6.57893	0.242998	0.121499	+	0.992592i	$0.461230\pi$
$734$	−7.39290	−0.272877
$735$	0.629152	0.0232066
$736$	−57.3825	−2.11515
$737$	−1.38954	−0.0511844
$738$	−12.6923	−0.467212
$739$	−14.1909	−0.522020	−0.261010	−	0.965336i	$-0.584056\pi$
$739$	−14.1909	−0.522020	−0.261010	+	0.965336i	$0.584056\pi$
$740$	−0.364156	−0.0133866
$741$	−5.99007	−0.220051
$742$	−12.7731	−0.468916
$743$	−39.3333	−1.44300	−0.721500	−	0.692414i	$-0.756547\pi$
$743$	−39.3333	−1.44300	−0.721500	+	0.692414i	$0.756547\pi$
$744$	1.58018	0.0579323
$745$	−2.34907	−0.0860633
$746$	19.1356	0.700605
$747$	−85.3056	−3.12117
$748$	−7.36349	−0.269236
$749$	0.149784	0.00547298
$750$	12.0893	0.441438
$751$	−13.5397	−0.494072	−0.247036	−	0.969006i	$-0.579457\pi$
$751$	−13.5397	−0.494072	−0.247036	+	0.969006i	$0.579457\pi$
$752$	19.4981	0.711022
$753$	46.0318	1.67749
$754$	5.42157	0.197442
$755$	3.16311	0.115117
$756$	14.8414	0.539776
$757$	39.0885	1.42070	0.710348	−	0.703850i	$-0.248538\pi$
$757$	39.0885	1.42070	0.710348	+	0.703850i	$0.248538\pi$
$758$	−9.83203	−0.357115
$759$	15.9367	0.578464
$760$	−0.824851	−0.0299205
$761$	4.04628	0.146677	0.0733387	−	0.997307i	$-0.476635\pi$
$761$	4.04628	0.146677	0.0733387	+	0.997307i	$0.476635\pi$
$762$	32.3354	1.17139
$763$	−9.91232	−0.358850
$764$	21.4769	0.777007
$765$	7.51219	0.271604
$766$	10.4913	0.379066
$767$	−3.12322	−0.112773
$768$	57.9886	2.09248
$769$	34.7747	1.25401	0.627003	−	0.779017i	$-0.284281\pi$
$769$	34.7747	1.25401	0.627003	+	0.779017i	$0.284281\pi$
$770$	0.287502	0.0103609
$771$	−78.5075	−2.82738
$772$	15.2774	0.549846
$773$	−39.7447	−1.42952	−0.714759	−	0.699371i	$-0.753464\pi$
$773$	−39.7447	−1.42952	−0.714759	+	0.699371i	$0.753464\pi$
$774$	−0.990055	−0.0355868
$775$	−4.95545	−0.178005
$776$	−2.78177	−0.0998596
$777$	−2.98089	−0.106939
$778$	−29.8263	−1.06933
$779$	−8.23691	−0.295118
$780$	0.295880	0.0105942
$781$	−3.57627	−0.127969
$782$	88.4191	3.16186
$783$	−88.6455	−3.16793
$784$	−4.47387	−0.159781
$785$	−1.15745	−0.0413110
$786$	97.8774	3.49117
$787$	−13.9121	−0.495913	−0.247957	−	0.968771i	$-0.579759\pi$
$787$	−13.9121	−0.495913	−0.247957	+	0.968771i	$0.579759\pi$
$788$	30.9193	1.10145
$789$	85.7438	3.05256
$790$	−2.76518	−0.0983807
$791$	9.82122	0.349202
$792$	−2.20195	−0.0782429
$793$	−3.22192	−0.114414
$794$	−49.0904	−1.74215
$795$	4.16360	0.147668
$796$	24.6153	0.872465
$797$	30.9682	1.09695	0.548475	−	0.836167i	$-0.315208\pi$
$797$	30.9682	1.09695	0.548475	+	0.836167i	$0.315208\pi$
$798$	42.4164	1.50152
$799$	−26.3553	−0.932383
$800$	−37.5369	−1.32713
$801$	−16.8034	−0.593720
$802$	56.7378	2.00348
$803$	2.46466	0.0869758
$804$	10.1262	0.357124
$805$	−1.59887	−0.0563528
$806$	−0.526097	−0.0185310
$807$	44.8313	1.57814
$808$	0.135568	0.00476927
$809$	−38.5206	−1.35431	−0.677156	−	0.735840i	$-0.736788\pi$
$809$	−38.5206	−1.35431	−0.677156	+	0.735840i	$0.736788\pi$
$810$	−3.25263	−0.114286
$811$	−29.1795	−1.02463	−0.512316	−	0.858797i	$-0.671212\pi$
$811$	−29.1795	−1.02463	−0.512316	+	0.858797i	$0.671212\pi$
$812$	−17.7802	−0.623963
$813$	57.2970	2.00949
$814$	−1.36217	−0.0477440
$815$	2.69486	0.0943970
$816$	−80.6469	−2.82321
$817$	−0.642512	−0.0224787
$818$	−1.19753	−0.0418707
$819$	1.60428	0.0560581
$820$	0.406862	0.0142082
$821$	3.93997	0.137506	0.0687530	−	0.997634i	$-0.478098\pi$
$821$	3.93997	0.137506	0.0687530	+	0.997634i	$0.478098\pi$
$822$	26.6261	0.928691
$823$	15.6322	0.544904	0.272452	−	0.962169i	$-0.412165\pi$
$823$	15.6322	0.544904	0.272452	+	0.962169i	$0.412165\pi$
$824$	−9.26982	−0.322929
$825$	10.4250	0.362952
$826$	22.1158	0.769508
$827$	52.7227	1.83335	0.916674	−	0.399635i	$-0.130863\pi$
$827$	52.7227	1.83335	0.916674	+	0.399635i	$0.130863\pi$
$828$	−76.9272	−2.67340
$829$	−21.5400	−0.748117	−0.374058	−	0.927405i	$-0.622034\pi$
$829$	−21.5400	−0.748117	−0.374058	+	0.927405i	$0.622034\pi$
$830$	5.90435	0.204943
$831$	8.34672	0.289544
$832$	−1.54621	−0.0536053
$833$	6.04726	0.209525
$834$	−59.8421	−2.07216
$835$	3.41742	0.118265
$836$	8.97696	0.310475
$837$	8.60196	0.297327
$838$	39.0473	1.34887
$839$	−26.2895	−0.907613	−0.453806	−	0.891100i	$-0.649934\pi$
$839$	−26.2895	−0.907613	−0.453806	+	0.891100i	$0.649934\pi$
$840$	0.333516	0.0115074
$841$	77.1986	2.66202
$842$	−6.27322	−0.216189
$843$	−39.5217	−1.36120
$844$	−33.4791	−1.15240
$845$	−2.72812	−0.0938503
$846$	49.5098	1.70218
$847$	−10.5019	−0.360850
$848$	−29.6071	−1.01671
$849$	67.1840	2.30575
$850$	57.8397	1.98388
$851$	7.57537	0.259680
$852$	26.0619	0.892865
$853$	−0.550931	−0.0188635	−0.00943177	−	0.999956i	$-0.503002\pi$
$853$	−0.550931	−0.0188635	−0.00943177	+	0.999956i	$0.503002\pi$
$854$	22.8147	0.780704
$855$	−9.15824	−0.313205
$856$	0.0794011	0.00271387
$857$	−32.0244	−1.09393	−0.546967	−	0.837154i	$-0.684218\pi$
$857$	−32.0244	−1.09393	−0.546967	+	0.837154i	$0.684218\pi$
$858$	1.10677	0.0377847
$859$	−50.5364	−1.72428	−0.862140	−	0.506670i	$-0.830876\pi$
$859$	−50.5364	−1.72428	−0.862140	+	0.506670i	$0.830876\pi$
$860$	0.0317369	0.00108222
$861$	3.33047	0.113502
$862$	20.6392	0.702976
$863$	30.3753	1.03399	0.516993	−	0.855990i	$-0.327051\pi$
$863$	30.3753	1.03399	0.516993	+	0.855990i	$0.327051\pi$
$864$	65.1588	2.21675
$865$	−2.97203	−0.101052
$866$	−37.6689	−1.28004
$867$	58.3341	1.98113
$868$	1.72535	0.0585622
$869$	−4.79046	−0.162505
$870$	12.5141	0.424267
$871$	0.536668	0.0181843
$872$	−5.25457	−0.177942
$873$	−30.8857	−1.04532
$874$	−107.793	−3.64616
$875$	−2.10122	−0.0710341
$876$	−17.9611	−0.606848
$877$	−11.8399	−0.399805	−0.199903	−	0.979816i	$-0.564063\pi$
$877$	−11.8399	−0.399805	−0.199903	+	0.979816i	$0.564063\pi$
$878$	−65.5589	−2.21251
$879$	−89.8594	−3.03088
$880$	0.666408	0.0224646
$881$	−22.4741	−0.757171	−0.378585	−	0.925566i	$-0.623589\pi$
$881$	−22.4741	−0.757171	−0.378585	+	0.925566i	$0.623589\pi$
$882$	−11.3601	−0.382514
$883$	−30.8948	−1.03969	−0.519846	−	0.854260i	$-0.674011\pi$
$883$	−30.8948	−1.03969	−0.519846	+	0.854260i	$0.674011\pi$
$884$	2.84393	0.0956516
$885$	−7.20901	−0.242328
$886$	−45.4427	−1.52668
$887$	46.6265	1.56556	0.782782	−	0.622296i	$-0.213800\pi$
$887$	46.6265	1.56556	0.782782	+	0.622296i	$0.213800\pi$
$888$	−1.58018	−0.0530275
$889$	−5.62017	−0.188494
$890$	1.16304	0.0389851
$891$	−5.63493	−0.188777
$892$	−22.0313	−0.737662
$893$	32.1302	1.07520
$894$	64.0348	2.14164
$895$	1.69558	0.0566771
$896$	−4.20085	−0.140341
$897$	−6.15506	−0.205511
$898$	−25.5091	−0.851249
$899$	−10.3053	−0.343700
$900$	−50.3221	−1.67740
$901$	40.0196	1.33324
$902$	1.52192	0.0506743
$903$	0.259790	0.00864529
$904$	5.20627	0.173158
$905$	5.41924	0.180142
$906$	−86.2252	−2.86464
$907$	11.0069	0.365477	0.182738	−	0.983162i	$-0.441504\pi$
$907$	11.0069	0.365477	0.182738	+	0.983162i	$0.441504\pi$
$908$	10.9680	0.363986
$909$	1.50520	0.0499243
$910$	−0.111039	−0.00368091
$911$	−0.198175	−0.00656583	−0.00328291	−	0.999995i	$-0.501045\pi$
$911$	−0.198175	−0.00656583	−0.00328291	+	0.999995i	$0.501045\pi$
$912$	98.3180	3.25563
$913$	10.2288	0.338525
$914$	13.0860	0.432847
$915$	−7.43683	−0.245854
$916$	7.27051	0.240224
$917$	−17.0119	−0.561782
$918$	−100.401	−3.31374
$919$	−24.1575	−0.796883	−0.398442	−	0.917194i	$-0.630449\pi$
$919$	−24.1575	−0.796883	−0.398442	+	0.917194i	$0.630449\pi$
$920$	−0.847569	−0.0279435
$921$	−47.7553	−1.57359
$922$	−77.9206	−2.56618
$923$	1.38123	0.0454636
$924$	−3.62970	−0.119408
$925$	4.95545	0.162934
$926$	−2.90562	−0.0954847
$927$	−102.922	−3.38040
$928$	−78.0611	−2.56248
$929$	−20.0848	−0.658962	−0.329481	−	0.944162i	$-0.606874\pi$
$929$	−20.0848	−0.658962	−0.329481	+	0.944162i	$0.606874\pi$
$930$	−1.21434	−0.0398197
$931$	−7.37232	−0.241618
$932$	35.1577	1.15163
$933$	−49.0975	−1.60738
$934$	62.0287	2.02964
$935$	−0.900774	−0.0294585
$936$	0.850437	0.0277974
$937$	31.6431	1.03374	0.516868	−	0.856065i	$-0.327098\pi$
$937$	31.6431	1.03374	0.516868	+	0.856065i	$0.327098\pi$
$938$	−3.80021	−0.124081
$939$	42.4003	1.38368
$940$	−1.58707	−0.0517646
$941$	6.42546	0.209464	0.104732	−	0.994500i	$-0.466602\pi$
$941$	6.42546	0.209464	0.104732	+	0.994500i	$0.466602\pi$
$942$	31.5515	1.02800
$943$	−8.46377	−0.275618
$944$	51.2628	1.66846
$945$	1.81555	0.0590597
$946$	0.118716	0.00385978
$947$	−21.2722	−0.691255	−0.345627	−	0.938372i	$-0.612334\pi$
$947$	−21.2722	−0.691255	−0.345627	+	0.938372i	$0.612334\pi$
$948$	34.9103	1.13383
$949$	−0.951899	−0.0308999
$950$	−70.5133	−2.28775
$951$	11.4591	0.371588
$952$	3.20568	0.103897
$953$	−21.3928	−0.692980	−0.346490	−	0.938054i	$-0.612627\pi$
$953$	−21.3928	−0.692980	−0.346490	+	0.938054i	$0.612627\pi$
$954$	−75.1788	−2.43400
$955$	2.62726	0.0850163
$956$	43.3187	1.40103
$957$	21.6797	0.700804
$958$	39.2232	1.26724
$959$	−4.62783	−0.149441
$960$	−3.56897	−0.115188
$961$	1.00000	0.0322581
$962$	0.526097	0.0169620
$963$	0.881583	0.0284086
$964$	19.2709	0.620673
$965$	1.86888	0.0601614
$966$	43.5846	1.40231
$967$	−32.8095	−1.05508	−0.527541	−	0.849529i	$-0.676886\pi$
$967$	−32.8095	−1.05508	−0.527541	+	0.849529i	$0.676886\pi$
$968$	−5.56712	−0.178934
$969$	−132.895	−4.26920
$970$	2.13773	0.0686383
$971$	59.7535	1.91758	0.958790	−	0.284114i	$-0.0916995\pi$
$971$	59.7535	1.91758	0.958790	+	0.284114i	$0.0916995\pi$
$972$	−3.45988	−0.110976
$973$	10.4010	0.333442
$974$	29.6658	0.950554
$975$	−4.02635	−0.128946
$976$	52.8829	1.69274
$977$	−24.6601	−0.788945	−0.394473	−	0.918908i	$-0.629073\pi$
$977$	−24.6601	−0.788945	−0.394473	+	0.918908i	$0.629073\pi$
$978$	−73.4610	−2.34902
$979$	2.01487	0.0643956
$980$	0.364156	0.0116325
$981$	−58.3410	−1.86268
$982$	70.7809	2.25871
$983$	−37.2469	−1.18799	−0.593996	−	0.804468i	$-0.702450\pi$
$983$	−37.2469	−1.18799	−0.593996	+	0.804468i	$0.702450\pi$
$984$	1.76550	0.0562820
$985$	3.78235	0.120516
$986$	120.282	3.83057
$987$	−12.9914	−0.413520
$988$	−3.46708	−0.110302
$989$	−0.660209	−0.0209934
$990$	1.69215	0.0537801
$991$	30.4554	0.967446	0.483723	−	0.875221i	$-0.339284\pi$
$991$	30.4554	0.967446	0.483723	+	0.875221i	$0.339284\pi$
$992$	7.57487	0.240503
$993$	−69.1442	−2.19423
$994$	−9.78061	−0.310222
$995$	3.01118	0.0954609
$996$	−74.5422	−2.36196
$997$	−20.3154	−0.643396	−0.321698	−	0.946842i	$-0.604254\pi$
$997$	−20.3154	−0.643396	−0.321698	+	0.946842i	$0.604254\pi$
$998$	80.4616	2.54697
$999$	−8.60196	−0.272154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.13	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.13	✓	66	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93012 q^{2} +2.98089 q^{3} +1.72535 q^{4} +0.211062 q^{5} -5.75346 q^{6} +1.00000 q^{7} +0.530105 q^{8} +5.88570 q^{9} +O(q^{10})\)	\(q-1.93012 q^{2} +2.98089 q^{3} +1.72535 q^{4} +0.211062 q^{5} -5.75346 q^{6} +1.00000 q^{7} +0.530105 q^{8} +5.88570 q^{9} -0.407374 q^{10} -0.705745 q^{11} +5.14308 q^{12} +0.272573 q^{13} -1.93012 q^{14} +0.629152 q^{15} -4.47387 q^{16} +6.04726 q^{17} -11.3601 q^{18} -7.37232 q^{19} +0.364156 q^{20} +2.98089 q^{21} +1.36217 q^{22} -7.57537 q^{23} +1.58018 q^{24} -4.95545 q^{25} -0.526097 q^{26} +8.60196 q^{27} +1.72535 q^{28} -10.3053 q^{29} -1.21434 q^{30} +1.00000 q^{31} +7.57487 q^{32} -2.10375 q^{33} -11.6719 q^{34} +0.211062 q^{35} +10.1549 q^{36} -1.00000 q^{37} +14.2294 q^{38} +0.812509 q^{39} +0.111885 q^{40} +1.11727 q^{41} -5.75346 q^{42} +0.0871520 q^{43} -1.21766 q^{44} +1.24225 q^{45} +14.6214 q^{46} -4.35822 q^{47} -13.3361 q^{48} +1.00000 q^{49} +9.56460 q^{50} +18.0262 q^{51} +0.470283 q^{52} +6.61780 q^{53} -16.6028 q^{54} -0.148956 q^{55} +0.530105 q^{56} -21.9761 q^{57} +19.8904 q^{58} -11.4583 q^{59} +1.08551 q^{60} -11.8204 q^{61} -1.93012 q^{62} +5.88570 q^{63} -5.67266 q^{64} +0.0575297 q^{65} +4.06048 q^{66} +1.96890 q^{67} +10.4336 q^{68} -22.5813 q^{69} -0.407374 q^{70} +5.06737 q^{71} +3.12004 q^{72} -3.49228 q^{73} +1.93012 q^{74} -14.7717 q^{75} -12.7198 q^{76} -0.705745 q^{77} -1.56824 q^{78} +6.78781 q^{79} -0.944262 q^{80} +7.98438 q^{81} -2.15647 q^{82} -14.4937 q^{83} +5.14308 q^{84} +1.27635 q^{85} -0.168214 q^{86} -30.7189 q^{87} -0.374118 q^{88} -2.85496 q^{89} -2.39768 q^{90} +0.272573 q^{91} -13.0702 q^{92} +2.98089 q^{93} +8.41188 q^{94} -1.55602 q^{95} +22.5799 q^{96} -5.24758 q^{97} -1.93012 q^{98} -4.15380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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