LMFDB - Embedded newform 8045.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8045,2,Mod(1,8045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8045 = 5 \cdot 1609 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8045.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:	$64.2396484261$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25161 q^{2} -2.78948 q^{3} +3.06974 q^{4} -1.00000 q^{5} +6.28081 q^{6} +1.00140 q^{7} -2.40864 q^{8} +4.78119 q^{9} +O(q^{10})$	\(q-2.25161 q^{2} -2.78948 q^{3} +3.06974 q^{4} -1.00000 q^{5} +6.28081 q^{6} +1.00140 q^{7} -2.40864 q^{8} +4.78119 q^{9} +2.25161 q^{10} -2.17986 q^{11} -8.56298 q^{12} -3.97199 q^{13} -2.25477 q^{14} +2.78948 q^{15} -0.716165 q^{16} -4.37696 q^{17} -10.7654 q^{18} -7.45740 q^{19} -3.06974 q^{20} -2.79340 q^{21} +4.90820 q^{22} +9.35083 q^{23} +6.71885 q^{24} +1.00000 q^{25} +8.94336 q^{26} -4.96858 q^{27} +3.07406 q^{28} -10.1827 q^{29} -6.28081 q^{30} +9.43529 q^{31} +6.42981 q^{32} +6.08068 q^{33} +9.85520 q^{34} -1.00140 q^{35} +14.6770 q^{36} +1.61166 q^{37} +16.7911 q^{38} +11.0798 q^{39} +2.40864 q^{40} -10.5136 q^{41} +6.28964 q^{42} +0.624388 q^{43} -6.69161 q^{44} -4.78119 q^{45} -21.0544 q^{46} +3.84871 q^{47} +1.99773 q^{48} -5.99719 q^{49} -2.25161 q^{50} +12.2094 q^{51} -12.1930 q^{52} +11.5374 q^{53} +11.1873 q^{54} +2.17986 q^{55} -2.41203 q^{56} +20.8022 q^{57} +22.9275 q^{58} -2.03485 q^{59} +8.56298 q^{60} +1.58427 q^{61} -21.2446 q^{62} +4.78790 q^{63} -13.0451 q^{64} +3.97199 q^{65} -13.6913 q^{66} -1.36779 q^{67} -13.4361 q^{68} -26.0839 q^{69} +2.25477 q^{70} +13.0999 q^{71} -11.5162 q^{72} +7.17644 q^{73} -3.62883 q^{74} -2.78948 q^{75} -22.8923 q^{76} -2.18292 q^{77} -24.9473 q^{78} -4.83578 q^{79} +0.716165 q^{80} -0.483809 q^{81} +23.6725 q^{82} +2.38146 q^{83} -8.57501 q^{84} +4.37696 q^{85} -1.40588 q^{86} +28.4044 q^{87} +5.25051 q^{88} +9.48140 q^{89} +10.7654 q^{90} -3.97757 q^{91} +28.7046 q^{92} -26.3195 q^{93} -8.66580 q^{94} +7.45740 q^{95} -17.9358 q^{96} -9.60174 q^{97} +13.5033 q^{98} -10.4223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) $ 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * 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 $

$2$	−2.25161	−1.59213	−0.796064	−	0.605212i	$-0.793088\pi$
$2$	−2.25161	−1.59213	−0.796064	+	0.605212i	$0.793088\pi$
$3$	−2.78948	−1.61051	−0.805253	−	0.592931i	$-0.797970\pi$
$3$	−2.78948	−1.61051	−0.805253	+	0.592931i	$0.797970\pi$
$4$	3.06974	1.53487
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.28081	2.56413
$7$	1.00140	0.378496	0.189248	−	0.981929i	$-0.439395\pi$
$7$	1.00140	0.378496	0.189248	+	0.981929i	$0.439395\pi$
$8$	−2.40864	−0.851584
$9$	4.78119	1.59373
$10$	2.25161	0.712021
$11$	−2.17986	−0.657253	−0.328627	−	0.944460i	$-0.606586\pi$
$11$	−2.17986	−0.657253	−0.328627	+	0.944460i	$0.606586\pi$
$12$	−8.56298	−2.47192
$13$	−3.97199	−1.10163	−0.550816	−	0.834627i	$-0.685683\pi$
$13$	−3.97199	−1.10163	−0.550816	+	0.834627i	$0.685683\pi$
$14$	−2.25477	−0.602613
$15$	2.78948	0.720240
$16$	−0.716165	−0.179041
$17$	−4.37696	−1.06157	−0.530784	−	0.847507i	$-0.678103\pi$
$17$	−4.37696	−1.06157	−0.530784	+	0.847507i	$0.678103\pi$
$18$	−10.7654	−2.53742
$19$	−7.45740	−1.71084	−0.855422	−	0.517931i	$-0.826702\pi$
$19$	−7.45740	−1.71084	−0.855422	+	0.517931i	$0.826702\pi$
$20$	−3.06974	−0.686415
$21$	−2.79340	−0.609569
$22$	4.90820	1.04643
$23$	9.35083	1.94978	0.974891	−	0.222683i	$-0.0714814\pi$
$23$	9.35083	1.94978	0.974891	+	0.222683i	$0.0714814\pi$
$24$	6.71885	1.37148
$25$	1.00000	0.200000
$26$	8.94336	1.75394
$27$	−4.96858	−0.956204
$28$	3.07406	0.580942
$29$	−10.1827	−1.89088	−0.945440	−	0.325795i	$-0.894368\pi$
$29$	−10.1827	−1.89088	−0.945440	+	0.325795i	$0.894368\pi$
$30$	−6.28081	−1.14671
$31$	9.43529	1.69463	0.847314	−	0.531092i	$-0.178218\pi$
$31$	9.43529	1.69463	0.847314	+	0.531092i	$0.178218\pi$
$32$	6.42981	1.13664
$33$	6.08068	1.05851
$34$	9.85520	1.69015
$35$	−1.00140	−0.169268
$36$	14.6770	2.44617
$37$	1.61166	0.264955	0.132478	−	0.991186i	$-0.457707\pi$
$37$	1.61166	0.264955	0.132478	+	0.991186i	$0.457707\pi$
$38$	16.7911	2.72388
$39$	11.0798	1.77418
$40$	2.40864	0.380840
$41$	−10.5136	−1.64195	−0.820975	−	0.570965i	$-0.806569\pi$
$41$	−10.5136	−1.64195	−0.820975	+	0.570965i	$0.806569\pi$
$42$	6.28964	0.970512
$43$	0.624388	0.0952182	0.0476091	−	0.998866i	$-0.484840\pi$
$43$	0.624388	0.0952182	0.0476091	+	0.998866i	$0.484840\pi$
$44$	−6.69161	−1.00880
$45$	−4.78119	−0.712737
$46$	−21.0544	−3.10430
$47$	3.84871	0.561393	0.280696	−	0.959797i	$-0.409435\pi$
$47$	3.84871	0.561393	0.280696	+	0.959797i	$0.409435\pi$
$48$	1.99773	0.288347
$49$	−5.99719	−0.856741
$50$	−2.25161	−0.318426
$51$	12.2094	1.70966
$52$	−12.1930	−1.69086
$53$	11.5374	1.58478	0.792389	−	0.610016i	$-0.208837\pi$
$53$	11.5374	1.58478	0.792389	+	0.610016i	$0.208837\pi$
$54$	11.1873	1.52240
$55$	2.17986	0.293932
$56$	−2.41203	−0.322321
$57$	20.8022	2.75532
$58$	22.9275	3.01052
$59$	−2.03485	−0.264914	−0.132457	−	0.991189i	$-0.542287\pi$
$59$	−2.03485	−0.264914	−0.132457	+	0.991189i	$0.542287\pi$
$60$	8.56298	1.10548
$61$	1.58427	0.202845	0.101422	−	0.994843i	$-0.467661\pi$
$61$	1.58427	0.202845	0.101422	+	0.994843i	$0.467661\pi$
$62$	−21.2446	−2.69806
$63$	4.78790	0.603219
$64$	−13.0451	−1.63064
$65$	3.97199	0.492664
$66$	−13.6913	−1.68528
$67$	−1.36779	−0.167102	−0.0835509	−	0.996504i	$-0.526626\pi$
$67$	−1.36779	−0.167102	−0.0835509	+	0.996504i	$0.526626\pi$
$68$	−13.4361	−1.62937
$69$	−26.0839	−3.14014
$70$	2.25477	0.269497
$71$	13.0999	1.55467	0.777337	−	0.629085i	$-0.216570\pi$
$71$	13.0999	1.55467	0.777337	+	0.629085i	$0.216570\pi$
$72$	−11.5162	−1.35719
$73$	7.17644	0.839939	0.419970	−	0.907538i	$-0.362041\pi$
$73$	7.17644	0.839939	0.419970	+	0.907538i	$0.362041\pi$
$74$	−3.62883	−0.421842
$75$	−2.78948	−0.322101
$76$	−22.8923	−2.62593
$77$	−2.18292	−0.248767
$78$	−24.9473	−2.82473
$79$	−4.83578	−0.544067	−0.272034	−	0.962288i	$-0.587696\pi$
$79$	−4.83578	−0.544067	−0.272034	+	0.962288i	$0.587696\pi$
$80$	0.716165	0.0800697
$81$	−0.483809	−0.0537566
$82$	23.6725	2.61419
$83$	2.38146	0.261399	0.130700	−	0.991422i	$-0.458278\pi$
$83$	2.38146	0.261399	0.130700	+	0.991422i	$0.458278\pi$
$84$	−8.57501	−0.935610
$85$	4.37696	0.474748
$86$	−1.40588	−0.151600
$87$	28.4044	3.04527
$88$	5.25051	0.559706
$89$	9.48140	1.00503	0.502513	−	0.864570i	$-0.332409\pi$
$89$	9.48140	1.00503	0.502513	+	0.864570i	$0.332409\pi$
$90$	10.7654	1.13477
$91$	−3.97757	−0.416962
$92$	28.7046	2.99266
$93$	−26.3195	−2.72921
$94$	−8.66580	−0.893809
$95$	7.45740	0.765113
$96$	−17.9358	−1.83057
$97$	−9.60174	−0.974909	−0.487455	−	0.873148i	$-0.662075\pi$
$97$	−9.60174	−0.974909	−0.487455	+	0.873148i	$0.662075\pi$
$98$	13.5033	1.36404
$99$	−10.4223	−1.04748
$100$	3.06974	0.306974
$101$	−4.63202	−0.460904	−0.230452	−	0.973084i	$-0.574020\pi$
$101$	−4.63202	−0.460904	−0.230452	+	0.973084i	$0.574020\pi$
$102$	−27.4909	−2.72200
$103$	−14.0256	−1.38198	−0.690990	−	0.722864i	$-0.742825\pi$
$103$	−14.0256	−1.38198	−0.690990	+	0.722864i	$0.742825\pi$
$104$	9.56710	0.938131
$105$	2.79340	0.272608
$106$	−25.9776	−2.52317
$107$	12.2320	1.18251	0.591257	−	0.806483i	$-0.298632\pi$
$107$	12.2320	1.18251	0.591257	+	0.806483i	$0.298632\pi$
$108$	−15.2523	−1.46765
$109$	−5.45015	−0.522030	−0.261015	−	0.965335i	$-0.584057\pi$
$109$	−5.45015	−0.522030	−0.261015	+	0.965335i	$0.584057\pi$
$110$	−4.90820	−0.467978
$111$	−4.49569	−0.426712
$112$	−0.717171	−0.0677663
$113$	13.5765	1.27717	0.638586	−	0.769551i	$-0.279520\pi$
$113$	13.5765	1.27717	0.638586	+	0.769551i	$0.279520\pi$
$114$	−46.8385	−4.38683
$115$	−9.35083	−0.871969
$116$	−31.2583	−2.90226
$117$	−18.9908	−1.75570
$118$	4.58168	0.421778
$119$	−4.38311	−0.401799
$120$	−6.71885	−0.613345
$121$	−6.24820	−0.568018
$122$	−3.56716	−0.322955
$123$	29.3275	2.64437
$124$	28.9639	2.60104
$125$	−1.00000	−0.0894427
$126$	−10.7805	−0.960402
$127$	−18.7921	−1.66753	−0.833766	−	0.552118i	$-0.813820\pi$
$127$	−18.7921	−1.66753	−0.833766	+	0.552118i	$0.813820\pi$
$128$	16.5128	1.45954
$129$	−1.74172	−0.153350
$130$	−8.94336	−0.784385
$131$	−20.0518	−1.75193	−0.875966	−	0.482372i	$-0.839775\pi$
$131$	−20.0518	−1.75193	−0.875966	+	0.482372i	$0.839775\pi$
$132$	18.6661	1.62468
$133$	−7.46787	−0.647547
$134$	3.07972	0.266047
$135$	4.96858	0.427628
$136$	10.5425	0.904014
$137$	−1.61198	−0.137721	−0.0688603	−	0.997626i	$-0.521936\pi$
$137$	−1.61198	−0.137721	−0.0688603	+	0.997626i	$0.521936\pi$
$138$	58.7308	4.99950
$139$	8.50316	0.721228	0.360614	−	0.932715i	$-0.382567\pi$
$139$	8.50316	0.721228	0.360614	+	0.932715i	$0.382567\pi$
$140$	−3.07406	−0.259805
$141$	−10.7359	−0.904126
$142$	−29.4959	−2.47524
$143$	8.65838	0.724050
$144$	−3.42412	−0.285343
$145$	10.1827	0.845628
$146$	−16.1585	−1.33729
$147$	16.7290	1.37979
$148$	4.94738	0.406672
$149$	16.0970	1.31871	0.659357	−	0.751830i	$-0.270828\pi$
$149$	16.0970	1.31871	0.659357	+	0.751830i	$0.270828\pi$
$150$	6.28081	0.512826
$151$	18.8820	1.53659	0.768296	−	0.640095i	$-0.221105\pi$
$151$	18.8820	1.53659	0.768296	+	0.640095i	$0.221105\pi$
$152$	17.9622	1.45693
$153$	−20.9271	−1.69185
$154$	4.91509	0.396069
$155$	−9.43529	−0.757861
$156$	34.0121	2.72314
$157$	−14.7285	−1.17546	−0.587731	−	0.809057i	$-0.699978\pi$
$157$	−14.7285	−1.17546	−0.587731	+	0.809057i	$0.699978\pi$
$158$	10.8883	0.866225
$159$	−32.1832	−2.55229
$160$	−6.42981	−0.508321
$161$	9.36396	0.737984
$162$	1.08935	0.0855873
$163$	6.81299	0.533634	0.266817	−	0.963747i	$-0.414028\pi$
$163$	6.81299	0.533634	0.266817	+	0.963747i	$0.414028\pi$
$164$	−32.2741	−2.52018
$165$	−6.08068	−0.473380
$166$	−5.36212	−0.416181
$167$	3.89400	0.301326	0.150663	−	0.988585i	$-0.451859\pi$
$167$	3.89400	0.301326	0.150663	+	0.988585i	$0.451859\pi$
$168$	6.72829	0.519099
$169$	2.77669	0.213591
$170$	−9.85520	−0.755859
$171$	−35.6552	−2.72662
$172$	1.91671	0.146148
$173$	−0.859327	−0.0653334	−0.0326667	−	0.999466i	$-0.510400\pi$
$173$	−0.859327	−0.0653334	−0.0326667	+	0.999466i	$0.510400\pi$
$174$	−63.9557	−4.84847
$175$	1.00140	0.0756991
$176$	1.56114	0.117675
$177$	5.67616	0.426646
$178$	−21.3484	−1.60013
$179$	24.9193	1.86256	0.931279	−	0.364307i	$-0.118694\pi$
$179$	24.9193	1.86256	0.931279	+	0.364307i	$0.118694\pi$
$180$	−14.6770	−1.09396
$181$	19.0669	1.41723	0.708616	−	0.705594i	$-0.249320\pi$
$181$	19.0669	1.41723	0.708616	+	0.705594i	$0.249320\pi$
$182$	8.95593	0.663858
$183$	−4.41929	−0.326683
$184$	−22.5228	−1.66040
$185$	−1.61166	−0.118492
$186$	59.2613	4.34525
$187$	9.54116	0.697719
$188$	11.8146	0.861666
$189$	−4.97556	−0.361919
$190$	−16.7911	−1.21816
$191$	−21.6364	−1.56555	−0.782776	−	0.622303i	$-0.786197\pi$
$191$	−21.6364	−1.56555	−0.782776	+	0.622303i	$0.786197\pi$
$192$	36.3890	2.62615
$193$	10.5620	0.760272	0.380136	−	0.924931i	$-0.375877\pi$
$193$	10.5620	0.760272	0.380136	+	0.924931i	$0.375877\pi$
$194$	21.6194	1.55218
$195$	−11.0798	−0.793439
$196$	−18.4098	−1.31499
$197$	16.3299	1.16346	0.581728	−	0.813383i	$-0.302377\pi$
$197$	16.3299	1.16346	0.581728	+	0.813383i	$0.302377\pi$
$198$	23.4670	1.66773
$199$	19.8315	1.40582	0.702911	−	0.711278i	$-0.251883\pi$
$199$	19.8315	1.40582	0.702911	+	0.711278i	$0.251883\pi$
$200$	−2.40864	−0.170317
$201$	3.81541	0.269118
$202$	10.4295	0.733818
$203$	−10.1970	−0.715690
$204$	37.4798	2.62411
$205$	10.5136	0.734302
$206$	31.5801	2.20029
$207$	44.7081	3.10742
$208$	2.84460	0.197237
$209$	16.2561	1.12446
$210$	−6.28964	−0.434026
$211$	−2.43935	−0.167931	−0.0839657	−	0.996469i	$-0.526759\pi$
$211$	−2.43935	−0.167931	−0.0839657	+	0.996469i	$0.526759\pi$
$212$	35.4167	2.43243
$213$	−36.5419	−2.50381
$214$	−27.5417	−1.88271
$215$	−0.624388	−0.0425829
$216$	11.9675	0.814288
$217$	9.44855	0.641409
$218$	12.2716	0.831139
$219$	−20.0185	−1.35273
$220$	6.69161	0.451149
$221$	17.3852	1.16946
$222$	10.1225	0.679380
$223$	−5.58733	−0.374155	−0.187078	−	0.982345i	$-0.559902\pi$
$223$	−5.58733	−0.374155	−0.187078	+	0.982345i	$0.559902\pi$
$224$	6.43884	0.430213
$225$	4.78119	0.318746
$226$	−30.5690	−2.03342
$227$	12.3142	0.817321	0.408661	−	0.912686i	$-0.365996\pi$
$227$	12.3142	0.817321	0.408661	+	0.912686i	$0.365996\pi$
$228$	63.8575	4.22907
$229$	27.4902	1.81660	0.908301	−	0.418318i	$-0.137380\pi$
$229$	27.4902	1.81660	0.908301	+	0.418318i	$0.137380\pi$
$230$	21.0544	1.38829
$231$	6.08922	0.400641
$232$	24.5265	1.61024
$233$	−13.4487	−0.881055	−0.440527	−	0.897739i	$-0.645209\pi$
$233$	−13.4487	−0.881055	−0.440527	+	0.897739i	$0.645209\pi$
$234$	42.7599	2.79530
$235$	−3.84871	−0.251062
$236$	−6.24646	−0.406610
$237$	13.4893	0.876224
$238$	9.86905	0.639715
$239$	6.59981	0.426906	0.213453	−	0.976953i	$-0.431529\pi$
$239$	6.59981	0.426906	0.213453	+	0.976953i	$0.431529\pi$
$240$	−1.99773	−0.128953
$241$	7.00781	0.451413	0.225706	−	0.974195i	$-0.427531\pi$
$241$	7.00781	0.451413	0.225706	+	0.974195i	$0.427531\pi$
$242$	14.0685	0.904358
$243$	16.2553	1.04278
$244$	4.86330	0.311341
$245$	5.99719	0.383146
$246$	−66.0340	−4.21017
$247$	29.6207	1.88472
$248$	−22.7262	−1.44312
$249$	−6.64303	−0.420985
$250$	2.25161	0.142404
$251$	−2.63347	−0.166223	−0.0831116	−	0.996540i	$-0.526486\pi$
$251$	−2.63347	−0.166223	−0.0831116	+	0.996540i	$0.526486\pi$
$252$	14.6976	0.925864
$253$	−20.3835	−1.28150
$254$	42.3125	2.65492
$255$	−12.2094	−0.764584
$256$	−11.0902	−0.693139
$257$	−27.4572	−1.71273	−0.856366	−	0.516370i	$-0.827283\pi$
$257$	−27.4572	−1.71273	−0.856366	+	0.516370i	$0.827283\pi$
$258$	3.92166	0.244152
$259$	1.61392	0.100284
$260$	12.1930	0.756177
$261$	−48.6854	−3.01355
$262$	45.1488	2.78930
$263$	0.347078	0.0214017	0.0107009	−	0.999943i	$-0.496594\pi$
$263$	0.347078	0.0214017	0.0107009	+	0.999943i	$0.496594\pi$
$264$	−14.6462	−0.901410
$265$	−11.5374	−0.708734
$266$	16.8147	1.03098
$267$	−26.4482	−1.61860
$268$	−4.19875	−0.256480
$269$	−20.5086	−1.25043	−0.625217	−	0.780451i	$-0.714990\pi$
$269$	−20.5086	−1.25043	−0.625217	+	0.780451i	$0.714990\pi$
$270$	−11.1873	−0.680838
$271$	14.4196	0.875925	0.437963	−	0.898993i	$-0.355700\pi$
$271$	14.4196	0.875925	0.437963	+	0.898993i	$0.355700\pi$
$272$	3.13462	0.190064
$273$	11.0953	0.671520
$274$	3.62954	0.219269
$275$	−2.17986	−0.131451
$276$	−80.0709	−4.81970
$277$	2.48405	0.149252	0.0746259	−	0.997212i	$-0.476224\pi$
$277$	2.48405	0.149252	0.0746259	+	0.997212i	$0.476224\pi$
$278$	−19.1458	−1.14829
$279$	45.1119	2.70078
$280$	2.41203	0.144146
$281$	25.6551	1.53045	0.765227	−	0.643761i	$-0.222627\pi$
$281$	25.6551	1.53045	0.765227	+	0.643761i	$0.222627\pi$
$282$	24.1731	1.43948
$283$	−24.0128	−1.42742	−0.713708	−	0.700444i	$-0.752985\pi$
$283$	−24.0128	−1.42742	−0.713708	+	0.700444i	$0.752985\pi$
$284$	40.2134	2.38622
$285$	−20.8022	−1.23222
$286$	−19.4953	−1.15278
$287$	−10.5284	−0.621470
$288$	30.7421	1.81150
$289$	2.15777	0.126927
$290$	−22.9275	−1.34635
$291$	26.7839	1.57010
$292$	22.0298	1.28920
$293$	27.3800	1.59956	0.799779	−	0.600294i	$-0.204950\pi$
$293$	27.3800	1.59956	0.799779	+	0.600294i	$0.204950\pi$
$294$	−37.6672	−2.19680
$295$	2.03485	0.118473
$296$	−3.88191	−0.225631
$297$	10.8308	0.628468
$298$	−36.2441	−2.09956
$299$	−37.1414	−2.14794
$300$	−8.56298	−0.494384
$301$	0.625265	0.0360397
$302$	−42.5148	−2.44645
$303$	12.9209	0.742288
$304$	5.34073	0.306312
$305$	−1.58427	−0.0907150
$306$	47.1196	2.69365
$307$	−15.5633	−0.888246	−0.444123	−	0.895966i	$-0.646485\pi$
$307$	−15.5633	−0.888246	−0.444123	+	0.895966i	$0.646485\pi$
$308$	−6.70102	−0.381826
$309$	39.1240	2.22569
$310$	21.2446	1.20661
$311$	−15.7140	−0.891058	−0.445529	−	0.895268i	$-0.646984\pi$
$311$	−15.7140	−0.891058	−0.445529	+	0.895268i	$0.646984\pi$
$312$	−26.6872	−1.51087
$313$	24.5254	1.38626	0.693129	−	0.720813i	$-0.256232\pi$
$313$	24.5254	1.38626	0.693129	+	0.720813i	$0.256232\pi$
$314$	33.1628	1.87148
$315$	−4.78790	−0.269768
$316$	−14.8446	−0.835073
$317$	11.9125	0.669073	0.334536	−	0.942383i	$-0.391420\pi$
$317$	11.9125	0.669073	0.334536	+	0.942383i	$0.391420\pi$
$318$	72.4640	4.06358
$319$	22.1969	1.24279
$320$	13.0451	0.729242
$321$	−34.1210	−1.90445
$322$	−21.0840	−1.17496
$323$	32.6407	1.81618
$324$	−1.48517	−0.0825094
$325$	−3.97199	−0.220326
$326$	−15.3402	−0.849614
$327$	15.2031	0.840733
$328$	25.3235	1.39826
$329$	3.85412	0.212485
$330$	13.6913	0.753682
$331$	−12.2572	−0.673718	−0.336859	−	0.941555i	$-0.609365\pi$
$331$	−12.2572	−0.673718	−0.336859	+	0.941555i	$0.609365\pi$
$332$	7.31047	0.401214
$333$	7.70564	0.422267
$334$	−8.76776	−0.479750
$335$	1.36779	0.0747302
$336$	2.00053	0.109138
$337$	7.09642	0.386567	0.193283	−	0.981143i	$-0.438086\pi$
$337$	7.09642	0.386567	0.193283	+	0.981143i	$0.438086\pi$
$338$	−6.25201	−0.340065
$339$	−37.8714	−2.05689
$340$	13.4361	0.728677
$341$	−20.5676	−1.11380
$342$	80.2816	4.34113
$343$	−13.0154	−0.702768
$344$	−1.50393	−0.0810863
$345$	26.0839	1.40431
$346$	1.93487	0.104019
$347$	−14.6198	−0.784834	−0.392417	−	0.919787i	$-0.628361\pi$
$347$	−14.6198	−0.784834	−0.392417	+	0.919787i	$0.628361\pi$
$348$	87.1943	4.67410
$349$	27.0172	1.44620	0.723099	−	0.690744i	$-0.242717\pi$
$349$	27.0172	1.44620	0.723099	+	0.690744i	$0.242717\pi$
$350$	−2.25477	−0.120523
$351$	19.7352	1.05338
$352$	−14.0161	−0.747060
$353$	27.3060	1.45335	0.726675	−	0.686982i	$-0.241065\pi$
$353$	27.3060	1.45335	0.726675	+	0.686982i	$0.241065\pi$
$354$	−12.7805	−0.679275
$355$	−13.0999	−0.695271
$356$	29.1055	1.54259
$357$	12.2266	0.647099
$358$	−56.1086	−2.96543
$359$	29.9319	1.57975	0.789874	−	0.613269i	$-0.210146\pi$
$359$	29.9319	1.57975	0.789874	+	0.613269i	$0.210146\pi$
$360$	11.5162	0.606955
$361$	36.6128	1.92699
$362$	−42.9312	−2.25641
$363$	17.4292	0.914797
$364$	−12.2101	−0.639984
$365$	−7.17644	−0.375632
$366$	9.95050	0.520121
$367$	−15.8593	−0.827851	−0.413926	−	0.910311i	$-0.635843\pi$
$367$	−15.8593	−0.827851	−0.413926	+	0.910311i	$0.635843\pi$
$368$	−6.69673	−0.349091
$369$	−50.2675	−2.61682
$370$	3.62883	0.188654
$371$	11.5536	0.599831
$372$	−80.7942	−4.18898
$373$	−19.6892	−1.01947	−0.509734	−	0.860332i	$-0.670256\pi$
$373$	−19.6892	−1.01947	−0.509734	+	0.860332i	$0.670256\pi$
$374$	−21.4830	−1.11086
$375$	2.78948	0.144048
$376$	−9.27018	−0.478073
$377$	40.4456	2.08305
$378$	11.2030	0.576221
$379$	−26.2348	−1.34759	−0.673797	−	0.738917i	$-0.735338\pi$
$379$	−26.2348	−1.34759	−0.673797	+	0.738917i	$0.735338\pi$
$380$	22.8923	1.17435
$381$	52.4202	2.68557
$382$	48.7166	2.49256
$383$	27.2094	1.39034	0.695168	−	0.718847i	$-0.255330\pi$
$383$	27.2094	1.39034	0.695168	+	0.718847i	$0.255330\pi$
$384$	−46.0621	−2.35060
$385$	2.18292	0.111252
$386$	−23.7816	−1.21045
$387$	2.98531	0.151752
$388$	−29.4749	−1.49636
$389$	12.8621	0.652133	0.326067	−	0.945347i	$-0.394277\pi$
$389$	12.8621	0.652133	0.326067	+	0.945347i	$0.394277\pi$
$390$	24.9473	1.26326
$391$	−40.9282	−2.06983
$392$	14.4451	0.729587
$393$	55.9340	2.82150
$394$	−36.7685	−1.85237
$395$	4.83578	0.243314
$396$	−31.9939	−1.60775
$397$	−23.7569	−1.19232	−0.596161	−	0.802865i	$-0.703308\pi$
$397$	−23.7569	−1.19232	−0.596161	+	0.802865i	$0.703308\pi$
$398$	−44.6529	−2.23825
$399$	20.8315	1.04288
$400$	−0.716165	−0.0358082
$401$	−14.7395	−0.736054	−0.368027	−	0.929815i	$-0.619967\pi$
$401$	−14.7395	−0.736054	−0.368027	+	0.929815i	$0.619967\pi$
$402$	−8.59081	−0.428471
$403$	−37.4769	−1.86686
$404$	−14.2191	−0.707428
$405$	0.483809	0.0240407
$406$	22.9597	1.13947
$407$	−3.51319	−0.174143
$408$	−29.4081	−1.45592
$409$	−19.6003	−0.969174	−0.484587	−	0.874743i	$-0.661030\pi$
$409$	−19.6003	−0.969174	−0.484587	+	0.874743i	$0.661030\pi$
$410$	−23.6725	−1.16910
$411$	4.49658	0.221800
$412$	−43.0549	−2.12116
$413$	−2.03771	−0.100269
$414$	−100.665	−4.94742
$415$	−2.38146	−0.116901
$416$	−25.5391	−1.25216
$417$	−23.7194	−1.16154
$418$	−36.6024	−1.79028
$419$	−28.5212	−1.39335	−0.696676	−	0.717386i	$-0.745339\pi$
$419$	−28.5212	−1.39335	−0.696676	+	0.717386i	$0.745339\pi$
$420$	8.57501	0.418418
$421$	−16.1249	−0.785877	−0.392939	−	0.919565i	$-0.628542\pi$
$421$	−16.1249	−0.785877	−0.392939	+	0.919565i	$0.628542\pi$
$422$	5.49245	0.267368
$423$	18.4014	0.894708
$424$	−27.7894	−1.34957
$425$	−4.37696	−0.212314
$426$	82.2781	3.98639
$427$	1.58650	0.0767759
$428$	37.5492	1.81501
$429$	−24.1524	−1.16609
$430$	1.40588	0.0677974
$431$	−31.1445	−1.50018	−0.750089	−	0.661337i	$-0.769989\pi$
$431$	−31.1445	−1.50018	−0.750089	+	0.661337i	$0.769989\pi$
$432$	3.55832	0.171200
$433$	−0.204630	−0.00983390	−0.00491695	−	0.999988i	$-0.501565\pi$
$433$	−0.204630	−0.00983390	−0.00491695	+	0.999988i	$0.501565\pi$
$434$	−21.2744	−1.02121
$435$	−28.4044	−1.36189
$436$	−16.7306	−0.801249
$437$	−69.7328	−3.33577
$438$	45.0739	2.15371
$439$	17.8795	0.853340	0.426670	−	0.904407i	$-0.359687\pi$
$439$	17.8795	0.853340	0.426670	+	0.904407i	$0.359687\pi$
$440$	−5.25051	−0.250308
$441$	−28.6737	−1.36541
$442$	−39.1447	−1.86192
$443$	−11.8391	−0.562495	−0.281247	−	0.959635i	$-0.590748\pi$
$443$	−11.8391	−0.562495	−0.281247	+	0.959635i	$0.590748\pi$
$444$	−13.8006	−0.654948
$445$	−9.48140	−0.449461
$446$	12.5805	0.595703
$447$	−44.9021	−2.12380
$448$	−13.0634	−0.617188
$449$	12.3084	0.580869	0.290435	−	0.956895i	$-0.406200\pi$
$449$	12.3084	0.580869	0.290435	+	0.956895i	$0.406200\pi$
$450$	−10.7654	−0.507484
$451$	22.9182	1.07918
$452$	41.6764	1.96029
$453$	−52.6708	−2.47469
$454$	−27.7267	−1.30128
$455$	3.97757	0.186471
$456$	−50.1052	−2.34639
$457$	27.2373	1.27411	0.637053	−	0.770820i	$-0.280153\pi$
$457$	27.2373	1.27411	0.637053	+	0.770820i	$0.280153\pi$
$458$	−61.8971	−2.89226
$459$	21.7473	1.01508
$460$	−28.7046	−1.33836
$461$	16.0428	0.747186	0.373593	−	0.927593i	$-0.378126\pi$
$461$	16.0428	0.747186	0.373593	+	0.927593i	$0.378126\pi$
$462$	−13.7105	−0.637872
$463$	19.7007	0.915568	0.457784	−	0.889063i	$-0.348643\pi$
$463$	19.7007	0.915568	0.457784	+	0.889063i	$0.348643\pi$
$464$	7.29249	0.338546
$465$	26.3195	1.22054
$466$	30.2813	1.40275
$467$	13.1820	0.609992	0.304996	−	0.952354i	$-0.401345\pi$
$467$	13.1820	0.609992	0.304996	+	0.952354i	$0.401345\pi$
$468$	−58.2969	−2.69478
$469$	−1.36971	−0.0632473
$470$	8.66580	0.399724
$471$	41.0848	1.89309
$472$	4.90122	0.225597
$473$	−1.36108	−0.0625825
$474$	−30.3726	−1.39506
$475$	−7.45740	−0.342169
$476$	−13.4550	−0.616710
$477$	55.1623	2.52571
$478$	−14.8602	−0.679689
$479$	−29.0390	−1.32683	−0.663414	−	0.748253i	$-0.730893\pi$
$479$	−29.0390	−1.32683	−0.663414	+	0.748253i	$0.730893\pi$
$480$	17.9358	0.818654
$481$	−6.40149	−0.291883
$482$	−15.7789	−0.718707
$483$	−26.1206	−1.18853
$484$	−19.1804	−0.871835
$485$	9.60174	0.435993
$486$	−36.6006	−1.66024
$487$	9.27875	0.420460	0.210230	−	0.977652i	$-0.432579\pi$
$487$	9.27875	0.420460	0.210230	+	0.977652i	$0.432579\pi$
$488$	−3.81594	−0.172739
$489$	−19.0047	−0.859421
$490$	−13.5033	−0.610018
$491$	23.9799	1.08220	0.541098	−	0.840960i	$-0.318009\pi$
$491$	23.9799	1.08220	0.541098	+	0.840960i	$0.318009\pi$
$492$	90.0278	4.05877
$493$	44.5693	2.00730
$494$	−66.6942	−3.00071
$495$	10.4223	0.468449
$496$	−6.75722	−0.303408
$497$	13.1183	0.588437
$498$	14.9575	0.670262
$499$	−11.4901	−0.514367	−0.257184	−	0.966363i	$-0.582795\pi$
$499$	−11.4901	−0.514367	−0.257184	+	0.966363i	$0.582795\pi$
$500$	−3.06974	−0.137283
$501$	−10.8622	−0.485288
$502$	5.92954	0.264649
$503$	10.2989	0.459206	0.229603	−	0.973284i	$-0.426257\pi$
$503$	10.2989	0.459206	0.229603	+	0.973284i	$0.426257\pi$
$504$	−11.5324	−0.513692
$505$	4.63202	0.206122
$506$	45.8957	2.04031
$507$	−7.74550	−0.343990
$508$	−57.6870	−2.55945
$509$	2.95197	0.130844	0.0654219	−	0.997858i	$-0.479161\pi$
$509$	2.95197	0.130844	0.0654219	+	0.997858i	$0.479161\pi$
$510$	27.4909	1.21732
$511$	7.18653	0.317913
$512$	−8.05477	−0.355974
$513$	37.0527	1.63592
$514$	61.8228	2.72689
$515$	14.0256	0.618040
$516$	−5.34662	−0.235372
$517$	−8.38967	−0.368977
$518$	−3.63392	−0.159665
$519$	2.39707	0.105220
$520$	−9.56710	−0.419545
$521$	−2.49744	−0.109415	−0.0547074	−	0.998502i	$-0.517423\pi$
$521$	−2.49744	−0.109415	−0.0547074	+	0.998502i	$0.517423\pi$
$522$	109.621	4.79796
$523$	13.5887	0.594193	0.297096	−	0.954847i	$-0.403982\pi$
$523$	13.5887	0.594193	0.297096	+	0.954847i	$0.403982\pi$
$524$	−61.5538	−2.68899
$525$	−2.79340	−0.121914
$526$	−0.781483	−0.0340743
$527$	−41.2979	−1.79896
$528$	−4.35477	−0.189517
$529$	64.4379	2.80165
$530$	25.9776	1.12840
$531$	−9.72898	−0.422202
$532$	−22.9245	−0.993901
$533$	41.7599	1.80882
$534$	59.5509	2.57702
$535$	−12.2320	−0.528836
$536$	3.29451	0.142301
$537$	−69.5119	−2.99966
$538$	46.1775	1.99085
$539$	13.0730	0.563096
$540$	15.2523	0.656353
$541$	−20.4162	−0.877759	−0.438880	−	0.898546i	$-0.644625\pi$
$541$	−20.4162	−0.877759	−0.438880	+	0.898546i	$0.644625\pi$
$542$	−32.4672	−1.39459
$543$	−53.1867	−2.28246
$544$	−28.1430	−1.20662
$545$	5.45015	0.233459
$546$	−24.9824	−1.06915
$547$	29.5148	1.26196	0.630982	−	0.775798i	$-0.282652\pi$
$547$	29.5148	1.26196	0.630982	+	0.775798i	$0.282652\pi$
$548$	−4.94836	−0.211383
$549$	7.57469	0.323280
$550$	4.90820	0.209286
$551$	75.9365	3.23500
$552$	62.8268	2.67409
$553$	−4.84257	−0.205927
$554$	−5.59310	−0.237628
$555$	4.49569	0.190831
$556$	26.1025	1.10699
$557$	22.3808	0.948303	0.474152	−	0.880443i	$-0.342755\pi$
$557$	22.3808	0.948303	0.474152	+	0.880443i	$0.342755\pi$
$558$	−101.574	−4.29998
$559$	−2.48006	−0.104895
$560$	0.717171	0.0303060
$561$	−26.6149	−1.12368
$562$	−57.7652	−2.43668
$563$	9.98124	0.420659	0.210329	−	0.977631i	$-0.432546\pi$
$563$	9.98124	0.420659	0.210329	+	0.977631i	$0.432546\pi$
$564$	−32.9565	−1.38772
$565$	−13.5765	−0.571169
$566$	54.0675	2.27263
$567$	−0.484489	−0.0203466
$568$	−31.5530	−1.32393
$569$	21.9897	0.921858	0.460929	−	0.887437i	$-0.347516\pi$
$569$	21.9897	0.921858	0.460929	+	0.887437i	$0.347516\pi$
$570$	46.8385	1.96185
$571$	−17.2567	−0.722171	−0.361085	−	0.932533i	$-0.617594\pi$
$571$	−17.2567	−0.722171	−0.361085	+	0.932533i	$0.617594\pi$
$572$	26.5790	1.11132
$573$	60.3542	2.52133
$574$	23.7058	0.989460
$575$	9.35083	0.389956
$576$	−62.3710	−2.59879
$577$	−9.94220	−0.413899	−0.206950	−	0.978352i	$-0.566354\pi$
$577$	−9.94220	−0.413899	−0.206950	+	0.978352i	$0.566354\pi$
$578$	−4.85844	−0.202085
$579$	−29.4626	−1.22442
$580$	31.2583	1.29793
$581$	2.38481	0.0989385
$582$	−60.3068	−2.49980
$583$	−25.1498	−1.04160
$584$	−17.2855	−0.715279
$585$	18.9908	0.785174
$586$	−61.6491	−2.54670
$587$	−12.6155	−0.520697	−0.260349	−	0.965515i	$-0.583838\pi$
$587$	−12.6155	−0.520697	−0.260349	+	0.965515i	$0.583838\pi$
$588$	51.3538	2.11780
$589$	−70.3627	−2.89924
$590$	−4.58168	−0.188625
$591$	−45.5519	−1.87375
$592$	−1.15421	−0.0474379
$593$	43.2515	1.77613	0.888064	−	0.459720i	$-0.152050\pi$
$593$	43.2515	1.77613	0.888064	+	0.459720i	$0.152050\pi$
$594$	−24.3868	−1.00060
$595$	4.38311	0.179690
$596$	49.4135	2.02406
$597$	−55.3197	−2.26408
$598$	83.6278	3.41980
$599$	5.60334	0.228946	0.114473	−	0.993426i	$-0.463482\pi$
$599$	5.60334	0.228946	0.114473	+	0.993426i	$0.463482\pi$
$600$	6.71885	0.274296
$601$	21.3673	0.871591	0.435796	−	0.900046i	$-0.356467\pi$
$601$	21.3673	0.871591	0.435796	+	0.900046i	$0.356467\pi$
$602$	−1.40785	−0.0573798
$603$	−6.53965	−0.266315
$604$	57.9627	2.35847
$605$	6.24820	0.254026
$606$	−29.0929	−1.18182
$607$	24.0464	0.976015	0.488008	−	0.872839i	$-0.337724\pi$
$607$	24.0464	0.976015	0.488008	+	0.872839i	$0.337724\pi$
$608$	−47.9496	−1.94461
$609$	28.4443	1.15262
$610$	3.56716	0.144430
$611$	−15.2870	−0.618448
$612$	−64.2407	−2.59678
$613$	−27.4796	−1.10989	−0.554945	−	0.831887i	$-0.687261\pi$
$613$	−27.4796	−1.10989	−0.554945	+	0.831887i	$0.687261\pi$
$614$	35.0425	1.41420
$615$	−29.3275	−1.18260
$616$	5.25788	0.211846
$617$	−9.79724	−0.394422	−0.197211	−	0.980361i	$-0.563188\pi$
$617$	−9.79724	−0.394422	−0.197211	+	0.980361i	$0.563188\pi$
$618$	−88.0920	−3.54358
$619$	−9.25420	−0.371958	−0.185979	−	0.982554i	$-0.559546\pi$
$619$	−9.25420	−0.371958	−0.185979	+	0.982554i	$0.559546\pi$
$620$	−28.9639	−1.16322
$621$	−46.4604	−1.86439
$622$	35.3817	1.41868
$623$	9.49472	0.380398
$624$	−7.93494	−0.317652
$625$	1.00000	0.0400000
$626$	−55.2216	−2.20710
$627$	−45.3460	−1.81095
$628$	−45.2127	−1.80418
$629$	−7.05417	−0.281268
$630$	10.7805	0.429505
$631$	−43.7267	−1.74073	−0.870366	−	0.492405i	$-0.836118\pi$
$631$	−43.7267	−1.74073	−0.870366	+	0.492405i	$0.836118\pi$
$632$	11.6477	0.463319
$633$	6.80450	0.270455
$634$	−26.8223	−1.06525
$635$	18.7921	0.745743
$636$	−98.7942	−3.91744
$637$	23.8208	0.943813
$638$	−49.9787	−1.97868
$639$	62.6331	2.47773
$640$	−16.5128	−0.652726
$641$	22.1642	0.875431	0.437716	−	0.899113i	$-0.355788\pi$
$641$	22.1642	0.875431	0.437716	+	0.899113i	$0.355788\pi$
$642$	76.8271	3.03212
$643$	−4.00500	−0.157942	−0.0789710	−	0.996877i	$-0.525163\pi$
$643$	−4.00500	−0.157942	−0.0789710	+	0.996877i	$0.525163\pi$
$644$	28.7450	1.13271
$645$	1.74172	0.0685800
$646$	−73.4941	−2.89159
$647$	−16.6772	−0.655649	−0.327824	−	0.944739i	$-0.606315\pi$
$647$	−16.6772	−0.655649	−0.327824	+	0.944739i	$0.606315\pi$
$648$	1.16532	0.0457782
$649$	4.43568	0.174116
$650$	8.94336	0.350788
$651$	−26.3565	−1.03299
$652$	20.9141	0.819060
$653$	9.76788	0.382247	0.191123	−	0.981566i	$-0.438787\pi$
$653$	9.76788	0.382247	0.191123	+	0.981566i	$0.438787\pi$
$654$	−34.2314	−1.33855
$655$	20.0518	0.783488
$656$	7.52947	0.293977
$657$	34.3119	1.33864
$658$	−8.67798	−0.338303
$659$	19.6583	0.765778	0.382889	−	0.923794i	$-0.374929\pi$
$659$	19.6583	0.765778	0.382889	+	0.923794i	$0.374929\pi$
$660$	−18.6661	−0.726577
$661$	−26.4119	−1.02731	−0.513653	−	0.857998i	$-0.671708\pi$
$661$	−26.4119	−1.02731	−0.513653	+	0.857998i	$0.671708\pi$
$662$	27.5985	1.07265
$663$	−48.4957	−1.88342
$664$	−5.73609	−0.222603
$665$	7.46787	0.289592
$666$	−17.3501	−0.672303
$667$	−95.2167	−3.68681
$668$	11.9536	0.462497
$669$	15.5857	0.602580
$670$	−3.07972	−0.118980
$671$	−3.45349	−0.133320
$672$	−17.9610	−0.692861
$673$	20.0744	0.773813	0.386906	−	0.922119i	$-0.373544\pi$
$673$	20.0744	0.773813	0.386906	+	0.922119i	$0.373544\pi$
$674$	−15.9784	−0.615464
$675$	−4.96858	−0.191241
$676$	8.52371	0.327835
$677$	−8.63993	−0.332059	−0.166030	−	0.986121i	$-0.553095\pi$
$677$	−8.63993	−0.332059	−0.166030	+	0.986121i	$0.553095\pi$
$678$	85.2716	3.27484
$679$	−9.61523	−0.368999
$680$	−10.5425	−0.404287
$681$	−34.3501	−1.31630
$682$	46.3103	1.77331
$683$	11.3482	0.434228	0.217114	−	0.976146i	$-0.430336\pi$
$683$	11.3482	0.434228	0.217114	+	0.976146i	$0.430336\pi$
$684$	−109.452	−4.18501
$685$	1.61198	0.0615905
$686$	29.3057	1.11890
$687$	−76.6832	−2.92565
$688$	−0.447165	−0.0170480
$689$	−45.8262	−1.74584
$690$	−58.7308	−2.23584
$691$	−12.9912	−0.494208	−0.247104	−	0.968989i	$-0.579479\pi$
$691$	−12.9912	−0.494208	−0.247104	+	0.968989i	$0.579479\pi$
$692$	−2.63791	−0.100278
$693$	−10.4370	−0.396468
$694$	32.9182	1.24956
$695$	−8.50316	−0.322543
$696$	−68.4161	−2.59331
$697$	46.0176	1.74304
$698$	−60.8322	−2.30253
$699$	37.5149	1.41894
$700$	3.07406	0.116188
$701$	−21.4748	−0.811094	−0.405547	−	0.914074i	$-0.632919\pi$
$701$	−21.4748	−0.811094	−0.405547	+	0.914074i	$0.632919\pi$
$702$	−44.4358	−1.67712
$703$	−12.0188	−0.453297
$704$	28.4365	1.07174
$705$	10.7359	0.404338
$706$	−61.4824	−2.31392
$707$	−4.63853	−0.174450
$708$	17.4244	0.654847
$709$	−25.9341	−0.973975	−0.486988	−	0.873409i	$-0.661904\pi$
$709$	−25.9341	−0.973975	−0.486988	+	0.873409i	$0.661904\pi$
$710$	29.4959	1.10696
$711$	−23.1207	−0.867096
$712$	−22.8373	−0.855864
$713$	88.2278	3.30416
$714$	−27.5295	−1.03027
$715$	−8.65838	−0.323805
$716$	76.4959	2.85879
$717$	−18.4100	−0.687535
$718$	−67.3950	−2.51516
$719$	9.27887	0.346044	0.173022	−	0.984918i	$-0.444647\pi$
$719$	9.27887	0.346044	0.173022	+	0.984918i	$0.444647\pi$
$720$	3.42412	0.127609
$721$	−14.0453	−0.523073
$722$	−82.4376	−3.06801
$723$	−19.5481	−0.727003
$724$	58.5305	2.17527
$725$	−10.1827	−0.378176
$726$	−39.2438	−1.45647
$727$	8.24072	0.305631	0.152816	−	0.988255i	$-0.451166\pi$
$727$	8.24072	0.305631	0.152816	+	0.988255i	$0.451166\pi$
$728$	9.58054	0.355078
$729$	−43.8924	−1.62565
$730$	16.1585	0.598055
$731$	−2.73292	−0.101081
$732$	−13.5661	−0.501416
$733$	−51.0585	−1.88589	−0.942945	−	0.332950i	$-0.891956\pi$
$733$	−51.0585	−1.88589	−0.942945	+	0.332950i	$0.891956\pi$
$734$	35.7090	1.31805
$735$	−16.7290	−0.617059
$736$	60.1240	2.21620
$737$	2.98159	0.109828
$738$	113.183	4.16632
$739$	−32.3767	−1.19099	−0.595497	−	0.803357i	$-0.703045\pi$
$739$	−32.3767	−1.19099	−0.595497	+	0.803357i	$0.703045\pi$
$740$	−4.94738	−0.181869
$741$	−82.6263	−3.03535
$742$	−26.0141	−0.955008
$743$	−0.0396019	−0.00145285	−0.000726426	−	1.00000i	$-0.500231\pi$
$743$	−0.0396019	−0.00145285	−0.000726426		1.00000i	$0.500231\pi$
$744$	63.3943	2.32415
$745$	−16.0970	−0.589747
$746$	44.3324	1.62312
$747$	11.3862	0.416600
$748$	29.2889	1.07091
$749$	12.2492	0.447576
$750$	−6.28081	−0.229343
$751$	7.73424	0.282227	0.141113	−	0.989993i	$-0.454932\pi$
$751$	7.73424	0.282227	0.141113	+	0.989993i	$0.454932\pi$
$752$	−2.75631	−0.100512
$753$	7.34601	0.267703
$754$	−91.0676	−3.31649
$755$	−18.8820	−0.687185
$756$	−15.2737	−0.555499
$757$	−15.6813	−0.569947	−0.284974	−	0.958535i	$-0.591985\pi$
$757$	−15.6813	−0.569947	−0.284974	+	0.958535i	$0.591985\pi$
$758$	59.0706	2.14554
$759$	56.8593	2.06386
$760$	−17.9622	−0.651558
$761$	−33.4011	−1.21079	−0.605394	−	0.795926i	$-0.706984\pi$
$761$	−33.4011	−1.21079	−0.605394	+	0.795926i	$0.706984\pi$
$762$	−118.030	−4.27577
$763$	−5.45781	−0.197586
$764$	−66.4181	−2.40292
$765$	20.9271	0.756619
$766$	−61.2650	−2.21359
$767$	8.08239	0.291838
$768$	30.9359	1.11630
$769$	−12.9411	−0.466667	−0.233333	−	0.972397i	$-0.574963\pi$
$769$	−12.9411	−0.466667	−0.233333	+	0.972397i	$0.574963\pi$
$770$	−4.91509	−0.177128
$771$	76.5912	2.75836
$772$	32.4227	1.16692
$773$	7.91898	0.284826	0.142413	−	0.989807i	$-0.454514\pi$
$773$	7.91898	0.284826	0.142413	+	0.989807i	$0.454514\pi$
$774$	−6.72176	−0.241609
$775$	9.43529	0.338926
$776$	23.1272	0.830217
$777$	−4.50200	−0.161509
$778$	−28.9604	−1.03828
$779$	78.4041	2.80912
$780$	−34.0121	−1.21783
$781$	−28.5560	−1.02181
$782$	92.1542	3.29543
$783$	50.5936	1.80807
$784$	4.29497	0.153392
$785$	14.7285	0.525682
$786$	−125.942	−4.49218
$787$	−34.5089	−1.23011	−0.615054	−	0.788485i	$-0.710866\pi$
$787$	−34.5089	−1.23011	−0.615054	+	0.788485i	$0.710866\pi$
$788$	50.1286	1.78576
$789$	−0.968166	−0.0344676
$790$	−10.8883	−0.387387
$791$	13.5956	0.483404
$792$	25.1037	0.892020
$793$	−6.29270	−0.223460
$794$	53.4912	1.89833
$795$	32.1832	1.14142
$796$	60.8777	2.15775
$797$	2.74919	0.0973812	0.0486906	−	0.998814i	$-0.484495\pi$
$797$	2.74919	0.0973812	0.0486906	+	0.998814i	$0.484495\pi$
$798$	−46.9043	−1.66040
$799$	−16.8457	−0.595957
$800$	6.42981	0.227328
$801$	45.3323	1.60174
$802$	33.1875	1.17189
$803$	−15.6437	−0.552053
$804$	11.7123	0.413062
$805$	−9.36396	−0.330036
$806$	84.3832	2.97227
$807$	57.2084	2.01383
$808$	11.1569	0.392498
$809$	−34.4902	−1.21261	−0.606306	−	0.795232i	$-0.707349\pi$
$809$	−34.4902	−1.21261	−0.606306	+	0.795232i	$0.707349\pi$
$810$	−1.08935	−0.0382758
$811$	−45.4491	−1.59593	−0.797967	−	0.602702i	$-0.794091\pi$
$811$	−45.4491	−1.59593	−0.797967	+	0.602702i	$0.794091\pi$
$812$	−31.3022	−1.09849
$813$	−40.2230	−1.41068
$814$	7.91034	0.277257
$815$	−6.81299	−0.238649
$816$	−8.74396	−0.306100
$817$	−4.65631	−0.162904
$818$	44.1323	1.54305
$819$	−19.0175	−0.664525
$820$	32.2741	1.12706
$821$	−26.3478	−0.919545	−0.459773	−	0.888037i	$-0.652069\pi$
$821$	−26.3478	−0.919545	−0.459773	+	0.888037i	$0.652069\pi$
$822$	−10.1245	−0.353134
$823$	−16.4244	−0.572517	−0.286259	−	0.958152i	$-0.592412\pi$
$823$	−16.4244	−0.572517	−0.286259	+	0.958152i	$0.592412\pi$
$824$	33.7826	1.17687
$825$	6.08068	0.211702
$826$	4.58812	0.159641
$827$	41.9156	1.45755	0.728774	−	0.684754i	$-0.240090\pi$
$827$	41.9156	1.45755	0.728774	+	0.684754i	$0.240090\pi$
$828$	137.242	4.76950
$829$	−5.37160	−0.186563	−0.0932816	−	0.995640i	$-0.529736\pi$
$829$	−5.37160	−0.186563	−0.0932816	+	0.995640i	$0.529736\pi$
$830$	5.36212	0.186122
$831$	−6.92919	−0.240371
$832$	51.8149	1.79636
$833$	26.2494	0.909489
$834$	53.4067	1.84932
$835$	−3.89400	−0.134757
$836$	49.9020	1.72590
$837$	−46.8800	−1.62041
$838$	64.2186	2.21840
$839$	−29.3709	−1.01400	−0.506998	−	0.861947i	$-0.669245\pi$
$839$	−29.3709	−1.01400	−0.506998	+	0.861947i	$0.669245\pi$
$840$	−6.72829	−0.232148
$841$	74.6875	2.57543
$842$	36.3069	1.25122
$843$	−71.5643	−2.46480
$844$	−7.48816	−0.257753
$845$	−2.77669	−0.0955209
$846$	−41.4328	−1.42449
$847$	−6.25698	−0.214992
$848$	−8.26265	−0.283741
$849$	66.9833	2.29886
$850$	9.85520	0.338031
$851$	15.0703	0.516605
$852$	−112.174	−3.84303
$853$	−4.08315	−0.139804	−0.0699021	−	0.997554i	$-0.522269\pi$
$853$	−4.08315	−0.139804	−0.0699021	+	0.997554i	$0.522269\pi$
$854$	−3.57217	−0.122237
$855$	35.6552	1.21938
$856$	−29.4626	−1.00701
$857$	−7.42936	−0.253782	−0.126891	−	0.991917i	$-0.540500\pi$
$857$	−7.42936	−0.253782	−0.126891	+	0.991917i	$0.540500\pi$
$858$	54.3817	1.85656
$859$	−1.89467	−0.0646453	−0.0323227	−	0.999477i	$-0.510290\pi$
$859$	−1.89467	−0.0646453	−0.0323227	+	0.999477i	$0.510290\pi$
$860$	−1.91671	−0.0653593
$861$	29.3687	1.00088
$862$	70.1252	2.38848
$863$	33.3391	1.13488	0.567439	−	0.823416i	$-0.307934\pi$
$863$	33.3391	1.13488	0.567439	+	0.823416i	$0.307934\pi$
$864$	−31.9470	−1.08686
$865$	0.859327	0.0292180
$866$	0.460747	0.0156568
$867$	−6.01904	−0.204417
$868$	29.0046	0.984480
$869$	10.5413	0.357590
$870$	63.9557	2.16830
$871$	5.43283	0.184085
$872$	13.1275	0.444552
$873$	−45.9077	−1.55374
$874$	157.011	5.31098
$875$	−1.00140	−0.0338537
$876$	−61.4517	−2.07626
$877$	34.1271	1.15239	0.576196	−	0.817312i	$-0.304537\pi$
$877$	34.1271	1.15239	0.576196	+	0.817312i	$0.304537\pi$
$878$	−40.2575	−1.35863
$879$	−76.3760	−2.57610
$880$	−1.56114	−0.0526260
$881$	3.19830	0.107754	0.0538768	−	0.998548i	$-0.482842\pi$
$881$	3.19830	0.107754	0.0538768	+	0.998548i	$0.482842\pi$
$882$	64.5619	2.17391
$883$	−21.8919	−0.736721	−0.368360	−	0.929683i	$-0.620081\pi$
$883$	−21.8919	−0.736721	−0.368360	+	0.929683i	$0.620081\pi$
$884$	53.3682	1.79497
$885$	−5.67616	−0.190802
$886$	26.6571	0.895564
$887$	−2.78344	−0.0934589	−0.0467294	−	0.998908i	$-0.514880\pi$
$887$	−2.78344	−0.0934589	−0.0467294	+	0.998908i	$0.514880\pi$
$888$	10.8285	0.363381
$889$	−18.8185	−0.631153
$890$	21.3484	0.715600
$891$	1.05464	0.0353317
$892$	−17.1517	−0.574281
$893$	−28.7014	−0.960456
$894$	101.102	3.38136
$895$	−24.9193	−0.832961
$896$	16.5360	0.552429
$897$	103.605	3.45927
$898$	−27.7137	−0.924818
$899$	−96.0768	−3.20434
$900$	14.6770	0.489234
$901$	−50.4985	−1.68235
$902$	−51.6028	−1.71819
$903$	−1.74416	−0.0580421
$904$	−32.7010	−1.08762
$905$	−19.0669	−0.633805
$906$	118.594	3.94002
$907$	−45.8718	−1.52315	−0.761573	−	0.648079i	$-0.775573\pi$
$907$	−45.8718	−1.52315	−0.761573	+	0.648079i	$0.775573\pi$
$908$	37.8014	1.25448
$909$	−22.1466	−0.734556
$910$	−8.95593	−0.296886
$911$	23.1365	0.766547	0.383273	−	0.923635i	$-0.374797\pi$
$911$	23.1365	0.766547	0.383273	+	0.923635i	$0.374797\pi$
$912$	−14.8978	−0.493317
$913$	−5.19126	−0.171806
$914$	−61.3277	−2.02854
$915$	4.41929	0.146097
$916$	84.3878	2.78825
$917$	−20.0800	−0.663099
$918$	−48.9664	−1.61613
$919$	−37.4319	−1.23476	−0.617382	−	0.786663i	$-0.711807\pi$
$919$	−37.4319	−1.23476	−0.617382	+	0.786663i	$0.711807\pi$
$920$	22.5228	0.742555
$921$	43.4136	1.43053
$922$	−36.1220	−1.18962
$923$	−52.0327	−1.71268
$924$	18.6923	0.614933
$925$	1.61166	0.0529910
$926$	−44.3582	−1.45770
$927$	−67.0588	−2.20250
$928$	−65.4728	−2.14925
$929$	1.21215	0.0397694	0.0198847	−	0.999802i	$-0.493670\pi$
$929$	1.21215	0.0397694	0.0198847	+	0.999802i	$0.493670\pi$
$930$	−59.2613	−1.94325
$931$	44.7234	1.46575
$932$	−41.2841	−1.35231
$933$	43.8338	1.43505
$934$	−29.6808	−0.971186
$935$	−9.54116	−0.312029
$936$	45.7421	1.49513
$937$	−33.7365	−1.10212	−0.551062	−	0.834465i	$-0.685777\pi$
$937$	−33.7365	−1.10212	−0.551062	+	0.834465i	$0.685777\pi$
$938$	3.08405	0.100698
$939$	−68.4131	−2.23258
$940$	−11.8146	−0.385349
$941$	−60.0217	−1.95665	−0.978327	−	0.207068i	$-0.933608\pi$
$941$	−60.0217	−1.95665	−0.978327	+	0.207068i	$0.933608\pi$
$942$	−92.5069	−3.01404
$943$	−98.3109	−3.20144
$944$	1.45729	0.0474306
$945$	4.97556	0.161855
$946$	3.06462	0.0996393
$947$	5.66332	0.184033	0.0920165	−	0.995757i	$-0.470669\pi$
$947$	5.66332	0.184033	0.0920165	+	0.995757i	$0.470669\pi$
$948$	41.4086	1.34489
$949$	−28.5047	−0.925303
$950$	16.7911	0.544777
$951$	−33.2297	−1.07755
$952$	10.5573	0.342165
$953$	34.9468	1.13204	0.566018	−	0.824393i	$-0.308483\pi$
$953$	34.9468	1.13204	0.566018	+	0.824393i	$0.308483\pi$
$954$	−124.204	−4.02125
$955$	21.6364	0.700136
$956$	20.2597	0.655246
$957$	−61.9177	−2.00152
$958$	65.3846	2.11248
$959$	−1.61424	−0.0521266
$960$	−36.3890	−1.17445
$961$	58.0247	1.87176
$962$	14.4137	0.464715
$963$	58.4836	1.88461
$964$	21.5122	0.692861
$965$	−10.5620	−0.340004
$966$	58.8133	1.89229
$967$	41.1884	1.32453	0.662265	−	0.749270i	$-0.269596\pi$
$967$	41.1884	1.32453	0.662265	+	0.749270i	$0.269596\pi$
$968$	15.0497	0.483715
$969$	−91.0506	−2.92497
$970$	−21.6194	−0.694156
$971$	−6.73170	−0.216031	−0.108015	−	0.994149i	$-0.534450\pi$
$971$	−6.73170	−0.216031	−0.108015	+	0.994149i	$0.534450\pi$
$972$	49.8997	1.60053
$973$	8.51510	0.272982
$974$	−20.8921	−0.669427
$975$	11.0798	0.354837
$976$	−1.13460	−0.0363176
$977$	−36.0495	−1.15333	−0.576663	−	0.816982i	$-0.695645\pi$
$977$	−36.0495	−1.15333	−0.576663	+	0.816982i	$0.695645\pi$
$978$	42.7911	1.36831
$979$	−20.6681	−0.660557
$980$	18.4098	0.588080
$981$	−26.0582	−0.831975
$982$	−53.9933	−1.72299
$983$	12.8706	0.410508	0.205254	−	0.978709i	$-0.434198\pi$
$983$	12.8706	0.410508	0.205254	+	0.978709i	$0.434198\pi$
$984$	−70.6394	−2.25190
$985$	−16.3299	−0.520314
$986$	−100.353	−3.19588
$987$	−10.7510	−0.342208
$988$	90.9279	2.89280
$989$	5.83854	0.185655
$990$	−23.4670	−0.745830
$991$	4.59283	0.145896	0.0729481	−	0.997336i	$-0.476759\pi$
$991$	4.59283	0.145896	0.0729481	+	0.997336i	$0.476759\pi$
$992$	60.6671	1.92618
$993$	34.1913	1.08503
$994$	−29.5373	−0.936867
$995$	−19.8315	−0.628702
$996$	−20.3924	−0.646158
$997$	41.6796	1.32001	0.660004	−	0.751262i	$-0.270555\pi$
$997$	41.6796	1.32001	0.660004	+	0.751262i	$0.270555\pi$
$998$	25.8712	0.818939
$999$	−8.00766	−0.253351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8045.2.a.b.1.14	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8045.2.a.b.1.14	✓	126	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:	\( N \)	\(=\)	\( 8045 = 5 \cdot 1609 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25161 q^{2} -2.78948 q^{3} +3.06974 q^{4} -1.00000 q^{5} +6.28081 q^{6} +1.00140 q^{7} -2.40864 q^{8} +4.78119 q^{9} +O(q^{10})\)	\(q-2.25161 q^{2} -2.78948 q^{3} +3.06974 q^{4} -1.00000 q^{5} +6.28081 q^{6} +1.00140 q^{7} -2.40864 q^{8} +4.78119 q^{9} +2.25161 q^{10} -2.17986 q^{11} -8.56298 q^{12} -3.97199 q^{13} -2.25477 q^{14} +2.78948 q^{15} -0.716165 q^{16} -4.37696 q^{17} -10.7654 q^{18} -7.45740 q^{19} -3.06974 q^{20} -2.79340 q^{21} +4.90820 q^{22} +9.35083 q^{23} +6.71885 q^{24} +1.00000 q^{25} +8.94336 q^{26} -4.96858 q^{27} +3.07406 q^{28} -10.1827 q^{29} -6.28081 q^{30} +9.43529 q^{31} +6.42981 q^{32} +6.08068 q^{33} +9.85520 q^{34} -1.00140 q^{35} +14.6770 q^{36} +1.61166 q^{37} +16.7911 q^{38} +11.0798 q^{39} +2.40864 q^{40} -10.5136 q^{41} +6.28964 q^{42} +0.624388 q^{43} -6.69161 q^{44} -4.78119 q^{45} -21.0544 q^{46} +3.84871 q^{47} +1.99773 q^{48} -5.99719 q^{49} -2.25161 q^{50} +12.2094 q^{51} -12.1930 q^{52} +11.5374 q^{53} +11.1873 q^{54} +2.17986 q^{55} -2.41203 q^{56} +20.8022 q^{57} +22.9275 q^{58} -2.03485 q^{59} +8.56298 q^{60} +1.58427 q^{61} -21.2446 q^{62} +4.78790 q^{63} -13.0451 q^{64} +3.97199 q^{65} -13.6913 q^{66} -1.36779 q^{67} -13.4361 q^{68} -26.0839 q^{69} +2.25477 q^{70} +13.0999 q^{71} -11.5162 q^{72} +7.17644 q^{73} -3.62883 q^{74} -2.78948 q^{75} -22.8923 q^{76} -2.18292 q^{77} -24.9473 q^{78} -4.83578 q^{79} +0.716165 q^{80} -0.483809 q^{81} +23.6725 q^{82} +2.38146 q^{83} -8.57501 q^{84} +4.37696 q^{85} -1.40588 q^{86} +28.4044 q^{87} +5.25051 q^{88} +9.48140 q^{89} +10.7654 q^{90} -3.97757 q^{91} +28.7046 q^{92} -26.3195 q^{93} -8.66580 q^{94} +7.45740 q^{95} -17.9358 q^{96} -9.60174 q^{97} +13.5033 q^{98} -10.4223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9}+O(q^{10}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9	\( 126 q + 5 q^{2} - 9 q^{3} + 109 q^{4} - 126 q^{5} - 21 q^{6} - 23 q^{7} + 12 q^{8} + 109 q^{9} - 5 q^{10} - 44 q^{11} - 11 q^{12} - 35 q^{13} - 14 q^{14} + 9 q^{15} + 75 q^{16} + 11 q^{17} - 15 q^{18} - 130 q^{19} - 109 q^{20} - 44 q^{21} - 14 q^{22} + 75 q^{23} - 63 q^{24} + 126 q^{25} - 43 q^{26} - 42 q^{27} - 77 q^{28} - 24 q^{29} + 21 q^{30} - 78 q^{31} + 24 q^{32} - 29 q^{33} - 57 q^{34} + 23 q^{35} + 50 q^{36} - 31 q^{37} - 3 q^{38} - 57 q^{39} - 12 q^{40} - 38 q^{41} - 10 q^{42} - 100 q^{43} - 90 q^{44} - 109 q^{45} - 96 q^{46} + 12 q^{47} - 22 q^{48} + 65 q^{49} + 5 q^{50} - 74 q^{51} - 112 q^{52} + 20 q^{53} - 90 q^{54} + 44 q^{55} - 57 q^{56} + 6 q^{57} - 35 q^{58} - 97 q^{59} + 11 q^{60} - 102 q^{61} - 16 q^{62} - 15 q^{63} + 4 q^{64} + 35 q^{65} - 83 q^{66} - 121 q^{67} + 41 q^{68} - 71 q^{69} + 14 q^{70} - 32 q^{71} - 32 q^{72} - 85 q^{73} - 42 q^{74} - 9 q^{75} - 275 q^{76} + 13 q^{77} + 10 q^{78} - 97 q^{79} - 75 q^{80} + 86 q^{81} - 55 q^{82} - 73 q^{83} - 111 q^{84} - 11 q^{85} - 56 q^{86} - q^{87} - 37 q^{88} - 67 q^{89} + 15 q^{90} - 180 q^{91} + 98 q^{92} - 44 q^{93} - 86 q^{94} + 130 q^{95} - 179 q^{96} - 50 q^{97} + 18 q^{98} - 217 q^{99}+O(q^{100}) \) 126 * q + 5 * q^2 - 9 * q^3 + 109 * q^4 - 126 * q^5 - 21 * q^6 - 23 * q^7 + 12 * q^8 + 109 * q^9 - 5 * q^10 - 44 * q^11 - 11 * q^12 - 35 * q^13 - 14 * q^14 + 9 * q^15 + 75 * q^16 + 11 * q^17 - 15 * q^18 - 130 * q^19 - 109 * q^20 - 44 * q^21 - 14 * q^22 + 75 * q^23 - 63 * q^24 + 126 * q^25 - 43 * q^26 - 42 * q^27 - 77 * q^28 - 24 * q^29 + 21 * q^30 - 78 * q^31 + 24 * q^32 - 29 * q^33 - 57 * q^34 + 23 * q^35 + 50 * q^36 - 31 * q^37 - 3 * q^38 - 57 * q^39 - 12 * q^40 - 38 * q^41 - 10 * q^42 - 100 * q^43 - 90 * q^44 - 109 * q^45 - 96 * q^46 + 12 * q^47 - 22 * q^48 + 65 * q^49 + 5 * q^50 - 74 * q^51 - 112 * q^52 + 20 * q^53 - 90 * q^54 + 44 * q^55 - 57 * q^56 + 6 * q^57 - 35 * q^58 - 97 * q^59 + 11 * q^60 - 102 * q^61 - 16 * q^62 - 15 * q^63 + 4 * q^64 + 35 * q^65 - 83 * q^66 - 121 * q^67 + 41 * q^68 - 71 * q^69 + 14 * q^70 - 32 * q^71 - 32 * q^72 - 85 * q^73 - 42 * q^74 - 9 * q^75 - 275 * q^76 + 13 * q^77 + 10 * q^78 - 97 * q^79 - 75 * q^80 + 86 * q^81 - 55 * q^82 - 73 * q^83 - 111 * q^84 - 11 * q^85 - 56 * q^86 - q^87 - 37 * q^88 - 67 * q^89 + 15 * q^90 - 180 * q^91 + 98 * q^92 - 44 * q^93 - 86 * q^94 + 130 * q^95 - 179 * q^96 - 50 * q^97 + 18 * q^98 - 217 * q^99

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