LMFDB - Embedded newform 8005.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, 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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42700 q^{2} +2.14529 q^{3} +3.89034 q^{4} +1.00000 q^{5} -5.20661 q^{6} +0.410687 q^{7} -4.58786 q^{8} +1.60225 q^{9} +O(q^{10})$	\(q-2.42700 q^{2} +2.14529 q^{3} +3.89034 q^{4} +1.00000 q^{5} -5.20661 q^{6} +0.410687 q^{7} -4.58786 q^{8} +1.60225 q^{9} -2.42700 q^{10} -5.25451 q^{11} +8.34589 q^{12} +5.42292 q^{13} -0.996738 q^{14} +2.14529 q^{15} +3.35406 q^{16} -5.75953 q^{17} -3.88867 q^{18} +1.42704 q^{19} +3.89034 q^{20} +0.881041 q^{21} +12.7527 q^{22} +4.28702 q^{23} -9.84227 q^{24} +1.00000 q^{25} -13.1614 q^{26} -2.99857 q^{27} +1.59771 q^{28} -3.57867 q^{29} -5.20661 q^{30} -6.95004 q^{31} +1.03540 q^{32} -11.2724 q^{33} +13.9784 q^{34} +0.410687 q^{35} +6.23331 q^{36} +8.31035 q^{37} -3.46343 q^{38} +11.6337 q^{39} -4.58786 q^{40} -0.0818473 q^{41} -2.13829 q^{42} +1.22064 q^{43} -20.4418 q^{44} +1.60225 q^{45} -10.4046 q^{46} -3.79667 q^{47} +7.19543 q^{48} -6.83134 q^{49} -2.42700 q^{50} -12.3558 q^{51} +21.0970 q^{52} +8.92036 q^{53} +7.27753 q^{54} -5.25451 q^{55} -1.88417 q^{56} +3.06141 q^{57} +8.68545 q^{58} -13.6576 q^{59} +8.34589 q^{60} +4.47737 q^{61} +16.8678 q^{62} +0.658024 q^{63} -9.22104 q^{64} +5.42292 q^{65} +27.3582 q^{66} -1.29195 q^{67} -22.4065 q^{68} +9.19688 q^{69} -0.996738 q^{70} -10.1575 q^{71} -7.35091 q^{72} -5.50703 q^{73} -20.1692 q^{74} +2.14529 q^{75} +5.55167 q^{76} -2.15796 q^{77} -28.2351 q^{78} -2.90118 q^{79} +3.35406 q^{80} -11.2395 q^{81} +0.198644 q^{82} -11.3706 q^{83} +3.42755 q^{84} -5.75953 q^{85} -2.96249 q^{86} -7.67728 q^{87} +24.1069 q^{88} +17.8097 q^{89} -3.88867 q^{90} +2.22712 q^{91} +16.6780 q^{92} -14.9098 q^{93} +9.21452 q^{94} +1.42704 q^{95} +2.22122 q^{96} +7.92083 q^{97} +16.5797 q^{98} -8.41905 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) $ 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * 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 $

$2$	−2.42700	−1.71615	−0.858075	−	0.513525i	$-0.828340\pi$
$2$	−2.42700	−1.71615	−0.858075	+	0.513525i	$0.828340\pi$
$3$	2.14529	1.23858	0.619291	−	0.785162i	$-0.287420\pi$
$3$	2.14529	1.23858	0.619291	+	0.785162i	$0.287420\pi$
$4$	3.89034	1.94517
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.20661	−2.12559
$7$	0.410687	0.155225	0.0776125	−	0.996984i	$-0.475270\pi$
$7$	0.410687	0.155225	0.0776125	+	0.996984i	$0.475270\pi$
$8$	−4.58786	−1.62205
$9$	1.60225	0.534084
$10$	−2.42700	−0.767485
$11$	−5.25451	−1.58429	−0.792146	−	0.610331i	$-0.791036\pi$
$11$	−5.25451	−1.58429	−0.792146	+	0.610331i	$0.791036\pi$
$12$	8.34589	2.40925
$13$	5.42292	1.50405	0.752024	−	0.659136i	$-0.229078\pi$
$13$	5.42292	1.50405	0.752024	+	0.659136i	$0.229078\pi$
$14$	−0.996738	−0.266389
$15$	2.14529	0.553911
$16$	3.35406	0.838516
$17$	−5.75953	−1.39689	−0.698446	−	0.715663i	$-0.746125\pi$
$17$	−5.75953	−1.39689	−0.698446	+	0.715663i	$0.746125\pi$
$18$	−3.88867	−0.916569
$19$	1.42704	0.327385	0.163693	−	0.986511i	$-0.447659\pi$
$19$	1.42704	0.327385	0.163693	+	0.986511i	$0.447659\pi$
$20$	3.89034	0.869906
$21$	0.881041	0.192259
$22$	12.7527	2.71888
$23$	4.28702	0.893905	0.446953	−	0.894558i	$-0.352509\pi$
$23$	4.28702	0.893905	0.446953	+	0.894558i	$0.352509\pi$
$24$	−9.84227	−2.00905
$25$	1.00000	0.200000
$26$	−13.1614	−2.58117
$27$	−2.99857	−0.577074
$28$	1.59771	0.301939
$29$	−3.57867	−0.664543	−0.332271	−	0.943184i	$-0.607815\pi$
$29$	−3.57867	−0.664543	−0.332271	+	0.943184i	$0.607815\pi$
$30$	−5.20661	−0.950593
$31$	−6.95004	−1.24826	−0.624132	−	0.781319i	$-0.714547\pi$
$31$	−6.95004	−1.24826	−0.624132	+	0.781319i	$0.714547\pi$
$32$	1.03540	0.183034
$33$	−11.2724	−1.96228
$34$	13.9784	2.39727
$35$	0.410687	0.0694188
$36$	6.23331	1.03889
$37$	8.31035	1.36621	0.683107	−	0.730319i	$-0.260628\pi$
$37$	8.31035	1.36621	0.683107	+	0.730319i	$0.260628\pi$
$38$	−3.46343	−0.561842
$39$	11.6337	1.86289
$40$	−4.58786	−0.725404
$41$	−0.0818473	−0.0127824	−0.00639120	−	0.999980i	$-0.502034\pi$
$41$	−0.0818473	−0.0127824	−0.00639120	+	0.999980i	$0.502034\pi$
$42$	−2.13829	−0.329945
$43$	1.22064	0.186146	0.0930728	−	0.995659i	$-0.470331\pi$
$43$	1.22064	0.186146	0.0930728	+	0.995659i	$0.470331\pi$
$44$	−20.4418	−3.08172
$45$	1.60225	0.238850
$46$	−10.4046	−1.53408
$47$	−3.79667	−0.553801	−0.276900	−	0.960899i	$-0.589307\pi$
$47$	−3.79667	−0.553801	−0.276900	+	0.960899i	$0.589307\pi$
$48$	7.19543	1.03857
$49$	−6.83134	−0.975905
$50$	−2.42700	−0.343230
$51$	−12.3558	−1.73016
$52$	21.0970	2.92563
$53$	8.92036	1.22531	0.612653	−	0.790352i	$-0.290102\pi$
$53$	8.92036	1.22531	0.612653	+	0.790352i	$0.290102\pi$
$54$	7.27753	0.990346
$55$	−5.25451	−0.708517
$56$	−1.88417	−0.251783
$57$	3.06141	0.405493
$58$	8.68545	1.14045
$59$	−13.6576	−1.77806	−0.889032	−	0.457846i	$-0.848621\pi$
$59$	−13.6576	−1.77806	−0.889032	+	0.457846i	$0.848621\pi$
$60$	8.34589	1.07745
$61$	4.47737	0.573269	0.286634	−	0.958040i	$-0.407463\pi$
$61$	4.47737	0.573269	0.286634	+	0.958040i	$0.407463\pi$
$62$	16.8678	2.14221
$63$	0.658024	0.0829033
$64$	−9.22104	−1.15263
$65$	5.42292	0.672631
$66$	27.3582	3.36756
$67$	−1.29195	−0.157837	−0.0789183	−	0.996881i	$-0.525147\pi$
$67$	−1.29195	−0.157837	−0.0789183	+	0.996881i	$0.525147\pi$
$68$	−22.4065	−2.71719
$69$	9.19688	1.10717
$70$	−0.996738	−0.119133
$71$	−10.1575	−1.20547	−0.602737	−	0.797940i	$-0.705923\pi$
$71$	−10.1575	−1.20547	−0.602737	+	0.797940i	$0.705923\pi$
$72$	−7.35091	−0.866313
$73$	−5.50703	−0.644550	−0.322275	−	0.946646i	$-0.604448\pi$
$73$	−5.50703	−0.644550	−0.322275	+	0.946646i	$0.604448\pi$
$74$	−20.1692	−2.34463
$75$	2.14529	0.247716
$76$	5.55167	0.636820
$77$	−2.15796	−0.245922
$78$	−28.2351	−3.19699
$79$	−2.90118	−0.326408	−0.163204	−	0.986592i	$-0.552183\pi$
$79$	−2.90118	−0.326408	−0.163204	+	0.986592i	$0.552183\pi$
$80$	3.35406	0.374996
$81$	−11.2395	−1.24884
$82$	0.198644	0.0219365
$83$	−11.3706	−1.24808	−0.624041	−	0.781392i	$-0.714510\pi$
$83$	−11.3706	−1.24808	−0.624041	+	0.781392i	$0.714510\pi$
$84$	3.42755	0.373976
$85$	−5.75953	−0.624709
$86$	−2.96249	−0.319454
$87$	−7.67728	−0.823090
$88$	24.1069	2.56981
$89$	17.8097	1.88782	0.943910	−	0.330203i	$-0.107117\pi$
$89$	17.8097	1.88782	0.943910	+	0.330203i	$0.107117\pi$
$90$	−3.88867	−0.409902
$91$	2.22712	0.233466
$92$	16.6780	1.73880
$93$	−14.9098	−1.54608
$94$	9.21452	0.950405
$95$	1.42704	0.146411
$96$	2.22122	0.226702
$97$	7.92083	0.804239	0.402119	−	0.915587i	$-0.368274\pi$
$97$	7.92083	0.804239	0.402119	+	0.915587i	$0.368274\pi$
$98$	16.5797	1.67480
$99$	−8.41905	−0.846146
$100$	3.89034	0.389034
$101$	4.13945	0.411891	0.205945	−	0.978564i	$-0.433973\pi$
$101$	4.13945	0.411891	0.205945	+	0.978564i	$0.433973\pi$
$102$	29.9877	2.96922
$103$	−6.36737	−0.627395	−0.313698	−	0.949523i	$-0.601568\pi$
$103$	−6.36737	−0.627395	−0.313698	+	0.949523i	$0.601568\pi$
$104$	−24.8796	−2.43965
$105$	0.881041	0.0859808
$106$	−21.6497	−2.10281
$107$	−2.10874	−0.203859	−0.101930	−	0.994792i	$-0.532502\pi$
$107$	−2.10874	−0.203859	−0.101930	+	0.994792i	$0.532502\pi$
$108$	−11.6654	−1.12251
$109$	17.6711	1.69259	0.846294	−	0.532716i	$-0.178829\pi$
$109$	17.6711	1.69259	0.846294	+	0.532716i	$0.178829\pi$
$110$	12.7527	1.21592
$111$	17.8281	1.69217
$112$	1.37747	0.130159
$113$	−9.20188	−0.865640	−0.432820	−	0.901480i	$-0.642481\pi$
$113$	−9.20188	−0.865640	−0.432820	+	0.901480i	$0.642481\pi$
$114$	−7.43004	−0.695887
$115$	4.28702	0.399767
$116$	−13.9223	−1.29265
$117$	8.68890	0.803289
$118$	33.1469	3.05142
$119$	−2.36536	−0.216832
$120$	−9.84227	−0.898472
$121$	16.6098	1.50998
$122$	−10.8666	−0.983815
$123$	−0.175586	−0.0158320
$124$	−27.0380	−2.42809
$125$	1.00000	0.0894427
$126$	−1.59703	−0.142274
$127$	−9.66428	−0.857567	−0.428783	−	0.903407i	$-0.641058\pi$
$127$	−9.66428	−0.857567	−0.428783	+	0.903407i	$0.641058\pi$
$128$	20.3087	1.79505
$129$	2.61862	0.230557
$130$	−13.1614	−1.15434
$131$	−11.1120	−0.970863	−0.485431	−	0.874275i	$-0.661337\pi$
$131$	−11.1120	−0.970863	−0.485431	+	0.874275i	$0.661337\pi$
$132$	−43.8535	−3.81696
$133$	0.586066	0.0508184
$134$	3.13556	0.270871
$135$	−2.99857	−0.258076
$136$	26.4239	2.26583
$137$	17.0483	1.45653	0.728265	−	0.685295i	$-0.240327\pi$
$137$	17.0483	1.45653	0.728265	+	0.685295i	$0.240327\pi$
$138$	−22.3209	−1.90008
$139$	4.87886	0.413819	0.206910	−	0.978360i	$-0.433659\pi$
$139$	4.87886	0.413819	0.206910	+	0.978360i	$0.433659\pi$
$140$	1.59771	0.135031
$141$	−8.14494	−0.685928
$142$	24.6523	2.06877
$143$	−28.4948	−2.38285
$144$	5.37406	0.447838
$145$	−3.57867	−0.297193
$146$	13.3656	1.10614
$147$	−14.6552	−1.20874
$148$	32.3301	2.65752
$149$	−17.4985	−1.43353	−0.716766	−	0.697314i	$-0.754378\pi$
$149$	−17.4985	−1.43353	−0.716766	+	0.697314i	$0.754378\pi$
$150$	−5.20661	−0.425118
$151$	5.82712	0.474204	0.237102	−	0.971485i	$-0.423802\pi$
$151$	5.82712	0.474204	0.237102	+	0.971485i	$0.423802\pi$
$152$	−6.54706	−0.531036
$153$	−9.22823	−0.746058
$154$	5.23737	0.422039
$155$	−6.95004	−0.558241
$156$	45.2591	3.62363
$157$	−8.44169	−0.673720	−0.336860	−	0.941555i	$-0.609365\pi$
$157$	−8.44169	−0.673720	−0.336860	+	0.941555i	$0.609365\pi$
$158$	7.04117	0.560165
$159$	19.1367	1.51764
$160$	1.03540	0.0818552
$161$	1.76062	0.138756
$162$	27.2784	2.14319
$163$	−13.5129	−1.05841	−0.529206	−	0.848494i	$-0.677510\pi$
$163$	−13.5129	−1.05841	−0.529206	+	0.848494i	$0.677510\pi$
$164$	−0.318414	−0.0248639
$165$	−11.2724	−0.877557
$166$	27.5964	2.14190
$167$	−20.0523	−1.55169	−0.775845	−	0.630923i	$-0.782676\pi$
$167$	−20.0523	−1.55169	−0.775845	+	0.630923i	$0.782676\pi$
$168$	−4.04209	−0.311854
$169$	16.4081	1.26216
$170$	13.9784	1.07209
$171$	2.28648	0.174851
$172$	4.74870	0.362085
$173$	−17.0207	−1.29406	−0.647030	−	0.762464i	$-0.723989\pi$
$173$	−17.0207	−1.29406	−0.647030	+	0.762464i	$0.723989\pi$
$174$	18.6328	1.41255
$175$	0.410687	0.0310450
$176$	−17.6240	−1.32846
$177$	−29.2994	−2.20228
$178$	−43.2241	−3.23978
$179$	−7.46057	−0.557629	−0.278815	−	0.960345i	$-0.589941\pi$
$179$	−7.46057	−0.557629	−0.278815	+	0.960345i	$0.589941\pi$
$180$	6.23331	0.464604
$181$	−18.0558	−1.34208	−0.671038	−	0.741423i	$-0.734151\pi$
$181$	−18.0558	−1.34208	−0.671038	+	0.741423i	$0.734151\pi$
$182$	−5.40523	−0.400663
$183$	9.60525	0.710040
$184$	−19.6682	−1.44996
$185$	8.31035	0.610989
$186$	36.1862	2.65330
$187$	30.2635	2.21308
$188$	−14.7703	−1.07724
$189$	−1.23147	−0.0895764
$190$	−3.46343	−0.251263
$191$	−5.46200	−0.395216	−0.197608	−	0.980281i	$-0.563317\pi$
$191$	−5.46200	−0.395216	−0.197608	+	0.980281i	$0.563317\pi$
$192$	−19.7818	−1.42763
$193$	19.0584	1.37185	0.685927	−	0.727670i	$-0.259397\pi$
$193$	19.0584	1.37185	0.685927	+	0.727670i	$0.259397\pi$
$194$	−19.2239	−1.38019
$195$	11.6337	0.833108
$196$	−26.5762	−1.89830
$197$	6.87455	0.489791	0.244896	−	0.969549i	$-0.421246\pi$
$197$	6.87455	0.489791	0.244896	+	0.969549i	$0.421246\pi$
$198$	20.4330	1.45211
$199$	26.5894	1.88487	0.942436	−	0.334387i	$-0.108529\pi$
$199$	26.5894	1.88487	0.942436	+	0.334387i	$0.108529\pi$
$200$	−4.58786	−0.324411
$201$	−2.77160	−0.195493
$202$	−10.0465	−0.706866
$203$	−1.46971	−0.103154
$204$	−48.0684	−3.36546
$205$	−0.0818473	−0.00571646
$206$	15.4536	1.07670
$207$	6.86889	0.477421
$208$	18.1888	1.26117
$209$	−7.49839	−0.518674
$210$	−2.13829	−0.147556
$211$	−10.5713	−0.727761	−0.363880	−	0.931446i	$-0.618548\pi$
$211$	−10.5713	−0.727761	−0.363880	+	0.931446i	$0.618548\pi$
$212$	34.7032	2.38343
$213$	−21.7907	−1.49308
$214$	5.11791	0.349853
$215$	1.22064	0.0832469
$216$	13.7570	0.936045
$217$	−2.85429	−0.193762
$218$	−42.8879	−2.90473
$219$	−11.8142	−0.798327
$220$	−20.4418	−1.37819
$221$	−31.2335	−2.10099
$222$	−43.2688	−2.90401
$223$	−26.5415	−1.77735	−0.888675	−	0.458538i	$-0.848373\pi$
$223$	−26.5415	−1.77735	−0.888675	+	0.458538i	$0.848373\pi$
$224$	0.425223	0.0284114
$225$	1.60225	0.106817
$226$	22.3330	1.48557
$227$	21.5924	1.43314	0.716569	−	0.697516i	$-0.245711\pi$
$227$	21.5924	1.43314	0.716569	+	0.697516i	$0.245711\pi$
$228$	11.9099	0.788754
$229$	−9.98145	−0.659592	−0.329796	−	0.944052i	$-0.606980\pi$
$229$	−9.98145	−0.659592	−0.329796	+	0.944052i	$0.606980\pi$
$230$	−10.4046	−0.686059
$231$	−4.62943	−0.304594
$232$	16.4184	1.07792
$233$	3.08423	0.202055	0.101027	−	0.994884i	$-0.467787\pi$
$233$	3.08423	0.202055	0.101027	+	0.994884i	$0.467787\pi$
$234$	−21.0880	−1.37856
$235$	−3.79667	−0.247667
$236$	−53.1326	−3.45863
$237$	−6.22386	−0.404283
$238$	5.74074	0.372117
$239$	−18.8363	−1.21842	−0.609208	−	0.793010i	$-0.708513\pi$
$239$	−18.8363	−1.21842	−0.609208	+	0.793010i	$0.708513\pi$
$240$	7.19543	0.464463
$241$	−3.85351	−0.248226	−0.124113	−	0.992268i	$-0.539609\pi$
$241$	−3.85351	−0.248226	−0.124113	+	0.992268i	$0.539609\pi$
$242$	−40.3121	−2.59136
$243$	−15.1163	−0.969714
$244$	17.4185	1.11511
$245$	−6.83134	−0.436438
$246$	0.426147	0.0271702
$247$	7.73872	0.492403
$248$	31.8858	2.02475
$249$	−24.3931	−1.54585
$250$	−2.42700	−0.153497
$251$	−15.3128	−0.966533	−0.483266	−	0.875473i	$-0.660550\pi$
$251$	−15.3128	−0.966533	−0.483266	+	0.875473i	$0.660550\pi$
$252$	2.55994	0.161261
$253$	−22.5262	−1.41621
$254$	23.4552	1.47171
$255$	−12.3558	−0.773753
$256$	−30.8472	−1.92795
$257$	15.0887	0.941205	0.470603	−	0.882345i	$-0.344037\pi$
$257$	15.0887	0.941205	0.470603	+	0.882345i	$0.344037\pi$
$258$	−6.35539	−0.395670
$259$	3.41295	0.212071
$260$	21.0970	1.30838
$261$	−5.73394	−0.354922
$262$	26.9689	1.66615
$263$	3.79292	0.233882	0.116941	−	0.993139i	$-0.462691\pi$
$263$	3.79292	0.233882	0.116941	+	0.993139i	$0.462691\pi$
$264$	51.7163	3.18292
$265$	8.92036	0.547973
$266$	−1.42238	−0.0872120
$267$	38.2068	2.33822
$268$	−5.02612	−0.307019
$269$	−19.6827	−1.20007	−0.600037	−	0.799972i	$-0.704848\pi$
$269$	−19.6827	−1.20007	−0.600037	+	0.799972i	$0.704848\pi$
$270$	7.27753	0.442896
$271$	−30.3394	−1.84299	−0.921493	−	0.388396i	$-0.873029\pi$
$271$	−30.3394	−1.84299	−0.921493	+	0.388396i	$0.873029\pi$
$272$	−19.3178	−1.17132
$273$	4.77782	0.289167
$274$	−41.3762	−2.49962
$275$	−5.25451	−0.316859
$276$	35.7790	2.15364
$277$	−8.09349	−0.486291	−0.243145	−	0.969990i	$-0.578179\pi$
$277$	−8.09349	−0.486291	−0.243145	+	0.969990i	$0.578179\pi$
$278$	−11.8410	−0.710176
$279$	−11.1357	−0.666678
$280$	−1.88417	−0.112601
$281$	−5.95921	−0.355497	−0.177748	−	0.984076i	$-0.556881\pi$
$281$	−5.95921	−0.355497	−0.177748	+	0.984076i	$0.556881\pi$
$282$	19.7678	1.17715
$283$	−12.3528	−0.734301	−0.367150	−	0.930162i	$-0.619667\pi$
$283$	−12.3528	−0.734301	−0.367150	+	0.930162i	$0.619667\pi$
$284$	−39.5161	−2.34485
$285$	3.06141	0.181342
$286$	69.1569	4.08933
$287$	−0.0336136	−0.00198415
$288$	1.65897	0.0977555
$289$	16.1722	0.951305
$290$	8.68545	0.510027
$291$	16.9925	0.996115
$292$	−21.4242	−1.25376
$293$	−7.76771	−0.453794	−0.226897	−	0.973919i	$-0.572858\pi$
$293$	−7.76771	−0.453794	−0.226897	+	0.973919i	$0.572858\pi$
$294$	35.5681	2.07438
$295$	−13.6576	−0.795174
$296$	−38.1267	−2.21607
$297$	15.7560	0.914255
$298$	42.4689	2.46015
$299$	23.2482	1.34448
$300$	8.34589	0.481850
$301$	0.501300	0.0288945
$302$	−14.1424	−0.813805
$303$	8.88030	0.510160
$304$	4.78638	0.274518
$305$	4.47737	0.256374
$306$	22.3969	1.28035
$307$	−5.14142	−0.293436	−0.146718	−	0.989178i	$-0.546871\pi$
$307$	−5.14142	−0.293436	−0.146718	+	0.989178i	$0.546871\pi$
$308$	−8.39518	−0.478360
$309$	−13.6598	−0.777080
$310$	16.8678	0.958025
$311$	12.2243	0.693178	0.346589	−	0.938017i	$-0.387340\pi$
$311$	12.2243	0.693178	0.346589	+	0.938017i	$0.387340\pi$
$312$	−53.3739	−3.02170
$313$	−3.98299	−0.225132	−0.112566	−	0.993644i	$-0.535907\pi$
$313$	−3.98299	−0.225132	−0.112566	+	0.993644i	$0.535907\pi$
$314$	20.4880	1.15620
$315$	0.658024	0.0370755
$316$	−11.2866	−0.634919
$317$	1.19663	0.0672096	0.0336048	−	0.999435i	$-0.489301\pi$
$317$	1.19663	0.0672096	0.0336048	+	0.999435i	$0.489301\pi$
$318$	−46.4449	−2.60450
$319$	18.8042	1.05283
$320$	−9.22104	−0.515472
$321$	−4.52384	−0.252496
$322$	−4.27303	−0.238127
$323$	−8.21908	−0.457322
$324$	−43.7256	−2.42920
$325$	5.42292	0.300810
$326$	32.7958	1.81639
$327$	37.9096	2.09641
$328$	0.375504	0.0207337
$329$	−1.55924	−0.0859638
$330$	27.3582	1.50602
$331$	10.9218	0.600315	0.300158	−	0.953890i	$-0.402961\pi$
$331$	10.9218	0.600315	0.300158	+	0.953890i	$0.402961\pi$
$332$	−44.2354	−2.42773
$333$	13.3153	0.729673
$334$	48.6669	2.66293
$335$	−1.29195	−0.0705867
$336$	2.95507	0.161212
$337$	1.09511	0.0596544	0.0298272	−	0.999555i	$-0.490504\pi$
$337$	1.09511	0.0596544	0.0298272	+	0.999555i	$0.490504\pi$
$338$	−39.8225	−2.16606
$339$	−19.7407	−1.07217
$340$	−22.4065	−1.21516
$341$	36.5190	1.97762
$342$	−5.54929	−0.300071
$343$	−5.68035	−0.306710
$344$	−5.60012	−0.301938
$345$	9.19688	0.495143
$346$	41.3093	2.22080
$347$	10.9271	0.586596	0.293298	−	0.956021i	$-0.405247\pi$
$347$	10.9271	0.586596	0.293298	+	0.956021i	$0.405247\pi$
$348$	−29.8672	−1.60105
$349$	−30.9601	−1.65726	−0.828629	−	0.559798i	$-0.810879\pi$
$349$	−30.9601	−1.65726	−0.828629	+	0.559798i	$0.810879\pi$
$350$	−0.996738	−0.0532779
$351$	−16.2610	−0.867948
$352$	−5.44049	−0.289979
$353$	−4.53201	−0.241214	−0.120607	−	0.992700i	$-0.538484\pi$
$353$	−4.53201	−0.241214	−0.120607	+	0.992700i	$0.538484\pi$
$354$	71.1097	3.77944
$355$	−10.1575	−0.539104
$356$	69.2856	3.67213
$357$	−5.07438	−0.268565
$358$	18.1068	0.956975
$359$	31.5898	1.66725	0.833623	−	0.552334i	$-0.186263\pi$
$359$	31.5898	1.66725	0.833623	+	0.552334i	$0.186263\pi$
$360$	−7.35091	−0.387427
$361$	−16.9636	−0.892819
$362$	43.8214	2.30320
$363$	35.6328	1.87024
$364$	8.66427	0.454131
$365$	−5.50703	−0.288251
$366$	−23.3120	−1.21854
$367$	−24.7361	−1.29122	−0.645608	−	0.763669i	$-0.723396\pi$
$367$	−24.7361	−1.29122	−0.645608	+	0.763669i	$0.723396\pi$
$368$	14.3789	0.749554
$369$	−0.131140	−0.00682688
$370$	−20.1692	−1.04855
$371$	3.66347	0.190198
$372$	−58.0043	−3.00738
$373$	29.7662	1.54124	0.770618	−	0.637297i	$-0.219948\pi$
$373$	29.7662	1.54124	0.770618	+	0.637297i	$0.219948\pi$
$374$	−73.4495	−3.79798
$375$	2.14529	0.110782
$376$	17.4186	0.898295
$377$	−19.4069	−0.999504
$378$	2.98879	0.153727
$379$	−4.19195	−0.215326	−0.107663	−	0.994187i	$-0.534337\pi$
$379$	−4.19195	−0.215326	−0.107663	+	0.994187i	$0.534337\pi$
$380$	5.55167	0.284795
$381$	−20.7327	−1.06217
$382$	13.2563	0.678250
$383$	−8.75831	−0.447529	−0.223764	−	0.974643i	$-0.571835\pi$
$383$	−8.75831	−0.447529	−0.223764	+	0.974643i	$0.571835\pi$
$384$	43.5679	2.22332
$385$	−2.15796	−0.109980
$386$	−46.2548	−2.35431
$387$	1.95577	0.0994175
$388$	30.8147	1.56438
$389$	3.59088	0.182065	0.0910323	−	0.995848i	$-0.470983\pi$
$389$	3.59088	0.182065	0.0910323	+	0.995848i	$0.470983\pi$
$390$	−28.2351	−1.42974
$391$	−24.6912	−1.24869
$392$	31.3412	1.58297
$393$	−23.8385	−1.20249
$394$	−16.6845	−0.840555
$395$	−2.90118	−0.145974
$396$	−32.7530	−1.64590
$397$	−19.6900	−0.988215	−0.494107	−	0.869401i	$-0.664505\pi$
$397$	−19.6900	−0.988215	−0.494107	+	0.869401i	$0.664505\pi$
$398$	−64.5325	−3.23472
$399$	1.25728	0.0629427
$400$	3.35406	0.167703
$401$	−35.2433	−1.75997	−0.879983	−	0.475005i	$-0.842446\pi$
$401$	−35.2433	−1.75997	−0.879983	+	0.475005i	$0.842446\pi$
$402$	6.72668	0.335496
$403$	−37.6895	−1.87745
$404$	16.1039	0.801197
$405$	−11.2395	−0.558497
$406$	3.56700	0.177027
$407$	−43.6668	−2.16448
$408$	56.6869	2.80642
$409$	−19.3575	−0.957167	−0.478583	−	0.878042i	$-0.658850\pi$
$409$	−19.3575	−0.957167	−0.478583	+	0.878042i	$0.658850\pi$
$410$	0.198644	0.00981031
$411$	36.5734	1.80403
$412$	−24.7712	−1.22039
$413$	−5.60898	−0.276000
$414$	−16.6708	−0.819326
$415$	−11.3706	−0.558159
$416$	5.61487	0.275292
$417$	10.4665	0.512549
$418$	18.1986	0.890123
$419$	5.10097	0.249199	0.124599	−	0.992207i	$-0.460235\pi$
$419$	5.10097	0.249199	0.124599	+	0.992207i	$0.460235\pi$
$420$	3.42755	0.167247
$421$	40.1435	1.95647	0.978236	−	0.207495i	$-0.0665311\pi$
$421$	40.1435	1.95647	0.978236	+	0.207495i	$0.0665311\pi$
$422$	25.6566	1.24895
$423$	−6.08322	−0.295776
$424$	−40.9254	−1.98751
$425$	−5.75953	−0.279378
$426$	52.8862	2.56234
$427$	1.83880	0.0889857
$428$	−8.20370	−0.396541
$429$	−61.1295	−2.95136
$430$	−2.96249	−0.142864
$431$	33.0859	1.59369	0.796845	−	0.604184i	$-0.206501\pi$
$431$	33.0859	1.59369	0.796845	+	0.604184i	$0.206501\pi$
$432$	−10.0574	−0.483886
$433$	−9.12651	−0.438592	−0.219296	−	0.975658i	$-0.570376\pi$
$433$	−9.12651	−0.438592	−0.219296	+	0.975658i	$0.570376\pi$
$434$	6.92737	0.332524
$435$	−7.67728	−0.368097
$436$	68.7467	3.29237
$437$	6.11774	0.292651
$438$	28.6730	1.37005
$439$	3.04253	0.145212	0.0726060	−	0.997361i	$-0.476868\pi$
$439$	3.04253	0.145212	0.0726060	+	0.997361i	$0.476868\pi$
$440$	24.1069	1.14925
$441$	−10.9455	−0.521216
$442$	75.8037	3.60562
$443$	1.35671	0.0644592	0.0322296	−	0.999480i	$-0.489739\pi$
$443$	1.35671	0.0644592	0.0322296	+	0.999480i	$0.489739\pi$
$444$	69.3573	3.29155
$445$	17.8097	0.844259
$446$	64.4163	3.05020
$447$	−37.5393	−1.77555
$448$	−3.78696	−0.178917
$449$	28.8501	1.36152	0.680761	−	0.732506i	$-0.261649\pi$
$449$	28.8501	1.36152	0.680761	+	0.732506i	$0.261649\pi$
$450$	−3.88867	−0.183314
$451$	0.430067	0.0202511
$452$	−35.7984	−1.68382
$453$	12.5008	0.587341
$454$	−52.4048	−2.45948
$455$	2.22712	0.104409
$456$	−14.0453	−0.657732
$457$	−33.2979	−1.55761	−0.778804	−	0.627267i	$-0.784174\pi$
$457$	−33.2979	−1.55761	−0.778804	+	0.627267i	$0.784174\pi$
$458$	24.2250	1.13196
$459$	17.2703	0.806110
$460$	16.6780	0.777614
$461$	13.5632	0.631702	0.315851	−	0.948809i	$-0.397710\pi$
$461$	13.5632	0.631702	0.315851	+	0.948809i	$0.397710\pi$
$462$	11.2356	0.522730
$463$	−23.4650	−1.09051	−0.545255	−	0.838271i	$-0.683567\pi$
$463$	−23.4650	−1.09051	−0.545255	+	0.838271i	$0.683567\pi$
$464$	−12.0031	−0.557230
$465$	−14.9098	−0.691427
$466$	−7.48544	−0.346756
$467$	−1.11542	−0.0516156	−0.0258078	−	0.999667i	$-0.508216\pi$
$467$	−1.11542	−0.0516156	−0.0258078	+	0.999667i	$0.508216\pi$
$468$	33.8028	1.56253
$469$	−0.530586	−0.0245002
$470$	9.21452	0.425034
$471$	−18.1098	−0.834457
$472$	62.6590	2.88411
$473$	−6.41385	−0.294909
$474$	15.1053	0.693810
$475$	1.42704	0.0654771
$476$	−9.20207	−0.421776
$477$	14.2927	0.654417
$478$	45.7156	2.09098
$479$	6.65995	0.304301	0.152151	−	0.988357i	$-0.451380\pi$
$479$	6.65995	0.304301	0.152151	+	0.988357i	$0.451380\pi$
$480$	2.22122	0.101384
$481$	45.0664	2.05485
$482$	9.35247	0.425993
$483$	3.77704	0.171861
$484$	64.6179	2.93718
$485$	7.92083	0.359666
$486$	36.6874	1.66417
$487$	−3.64210	−0.165039	−0.0825196	−	0.996589i	$-0.526297\pi$
$487$	−3.64210	−0.165039	−0.0825196	+	0.996589i	$0.526297\pi$
$488$	−20.5416	−0.929873
$489$	−28.9890	−1.31093
$490$	16.5797	0.748993
$491$	34.7992	1.57047	0.785234	−	0.619199i	$-0.212543\pi$
$491$	34.7992	1.57047	0.785234	+	0.619199i	$0.212543\pi$
$492$	−0.683089	−0.0307960
$493$	20.6115	0.928294
$494$	−18.7819	−0.845038
$495$	−8.41905	−0.378408
$496$	−23.3109	−1.04669
$497$	−4.17155	−0.187120
$498$	59.2022	2.65291
$499$	23.9873	1.07382	0.536908	−	0.843641i	$-0.319592\pi$
$499$	23.9873	1.07382	0.536908	+	0.843641i	$0.319592\pi$
$500$	3.89034	0.173981
$501$	−43.0178	−1.92190
$502$	37.1641	1.65871
$503$	−4.96274	−0.221277	−0.110639	−	0.993861i	$-0.535290\pi$
$503$	−4.96274	−0.221277	−0.110639	+	0.993861i	$0.535290\pi$
$504$	−3.01892	−0.134474
$505$	4.13945	0.184203
$506$	54.6710	2.43042
$507$	35.2001	1.56329
$508$	−37.5974	−1.66811
$509$	−10.5238	−0.466459	−0.233229	−	0.972422i	$-0.574929\pi$
$509$	−10.5238	−0.466459	−0.233229	+	0.972422i	$0.574929\pi$
$510$	29.9877	1.32788
$511$	−2.26167	−0.100050
$512$	34.2487	1.51359
$513$	−4.27907	−0.188926
$514$	−36.6202	−1.61525
$515$	−6.36737	−0.280580
$516$	10.1873	0.448472
$517$	19.9496	0.877383
$518$	−8.28324	−0.363945
$519$	−36.5143	−1.60280
$520$	−24.8796	−1.09104
$521$	17.3829	0.761559	0.380779	−	0.924666i	$-0.375656\pi$
$521$	17.3829	0.761559	0.380779	+	0.924666i	$0.375656\pi$
$522$	13.9163	0.609099
$523$	24.5988	1.07563	0.537815	−	0.843063i	$-0.319250\pi$
$523$	24.5988	1.07563	0.537815	+	0.843063i	$0.319250\pi$
$524$	−43.2296	−1.88849
$525$	0.881041	0.0384518
$526$	−9.20544	−0.401376
$527$	40.0290	1.74369
$528$	−37.8084	−1.64540
$529$	−4.62147	−0.200934
$530$	−21.6497	−0.940404
$531$	−21.8829	−0.949636
$532$	2.28000	0.0988504
$533$	−0.443852	−0.0192254
$534$	−92.7280	−4.01273
$535$	−2.10874	−0.0911686
$536$	5.92728	0.256019
$537$	−16.0051	−0.690669
$538$	47.7699	2.05951
$539$	35.8953	1.54612
$540$	−11.6654	−0.502001
$541$	6.98956	0.300505	0.150252	−	0.988648i	$-0.451991\pi$
$541$	6.98956	0.300505	0.150252	+	0.988648i	$0.451991\pi$
$542$	73.6337	3.16284
$543$	−38.7348	−1.66227
$544$	−5.96339	−0.255678
$545$	17.6711	0.756948
$546$	−11.5958	−0.496253
$547$	0.0325432	0.00139145	0.000695723	−	1.00000i	$-0.499779\pi$
$547$	0.0325432	0.00139145	0.000695723		1.00000i	$0.499779\pi$
$548$	66.3235	2.83320
$549$	7.17389	0.306174
$550$	12.7527	0.543777
$551$	−5.10691	−0.217562
$552$	−42.1940	−1.79590
$553$	−1.19148	−0.0506667
$554$	19.6429	0.834548
$555$	17.8281	0.756760
$556$	18.9804	0.804949
$557$	32.5783	1.38039	0.690194	−	0.723624i	$-0.257525\pi$
$557$	32.5783	1.38039	0.690194	+	0.723624i	$0.257525\pi$
$558$	27.0264	1.14412
$559$	6.61943	0.279972
$560$	1.37747	0.0582088
$561$	64.9238	2.74109
$562$	14.4630	0.610086
$563$	8.60152	0.362511	0.181255	−	0.983436i	$-0.441984\pi$
$563$	8.60152	0.362511	0.181255	+	0.983436i	$0.441984\pi$
$564$	−31.6866	−1.33425
$565$	−9.20188	−0.387126
$566$	29.9804	1.26017
$567$	−4.61593	−0.193851
$568$	46.6012	1.95534
$569$	14.8260	0.621537	0.310769	−	0.950486i	$-0.399414\pi$
$569$	14.8260	0.621537	0.310769	+	0.950486i	$0.399414\pi$
$570$	−7.43004	−0.311210
$571$	−34.9480	−1.46253	−0.731263	−	0.682095i	$-0.761069\pi$
$571$	−34.9480	−1.46253	−0.731263	+	0.682095i	$0.761069\pi$
$572$	−110.854	−4.63505
$573$	−11.7175	−0.489508
$574$	0.0815803	0.00340510
$575$	4.28702	0.178781
$576$	−14.7744	−0.615602
$577$	42.2497	1.75888	0.879439	−	0.476011i	$-0.157918\pi$
$577$	42.2497	1.75888	0.879439	+	0.476011i	$0.157918\pi$
$578$	−39.2499	−1.63258
$579$	40.8857	1.69915
$580$	−13.9223	−0.578090
$581$	−4.66974	−0.193734
$582$	−41.2407	−1.70948
$583$	−46.8721	−1.94124
$584$	25.2655	1.04549
$585$	8.68890	0.359242
$586$	18.8522	0.778779
$587$	2.05270	0.0847238	0.0423619	−	0.999102i	$-0.486512\pi$
$587$	2.05270	0.0847238	0.0423619	+	0.999102i	$0.486512\pi$
$588$	−57.0136	−2.35120
$589$	−9.91798	−0.408663
$590$	33.1469	1.36464
$591$	14.7479	0.606646
$592$	27.8735	1.14559
$593$	−26.3173	−1.08072	−0.540360	−	0.841434i	$-0.681712\pi$
$593$	−26.3173	−1.08072	−0.540360	+	0.841434i	$0.681712\pi$
$594$	−38.2398	−1.56900
$595$	−2.36536	−0.0969704
$596$	−68.0750	−2.78846
$597$	57.0419	2.33457
$598$	−56.4234	−2.30732
$599$	−28.8970	−1.18070	−0.590350	−	0.807147i	$-0.701010\pi$
$599$	−28.8970	−1.18070	−0.590350	+	0.807147i	$0.701010\pi$
$600$	−9.84227	−0.401809
$601$	31.4287	1.28200	0.641002	−	0.767539i	$-0.278519\pi$
$601$	31.4287	1.28200	0.641002	+	0.767539i	$0.278519\pi$
$602$	−1.21666	−0.0495872
$603$	−2.07003	−0.0842981
$604$	22.6695	0.922408
$605$	16.6098	0.675285
$606$	−21.5525	−0.875511
$607$	−18.9620	−0.769645	−0.384822	−	0.922991i	$-0.625737\pi$
$607$	−18.9620	−0.769645	−0.384822	+	0.922991i	$0.625737\pi$
$608$	1.47755	0.0599226
$609$	−3.15296	−0.127764
$610$	−10.8666	−0.439976
$611$	−20.5890	−0.832943
$612$	−35.9009	−1.45121
$613$	11.0293	0.445471	0.222735	−	0.974879i	$-0.428501\pi$
$613$	11.0293	0.445471	0.222735	+	0.974879i	$0.428501\pi$
$614$	12.4782	0.503580
$615$	−0.175586	−0.00708031
$616$	9.90040	0.398898
$617$	6.90881	0.278138	0.139069	−	0.990283i	$-0.455589\pi$
$617$	6.90881	0.278138	0.139069	+	0.990283i	$0.455589\pi$
$618$	33.1524	1.33359
$619$	29.1586	1.17198	0.585991	−	0.810318i	$-0.300706\pi$
$619$	29.1586	1.17198	0.585991	+	0.810318i	$0.300706\pi$
$620$	−27.0380	−1.08587
$621$	−12.8549	−0.515850
$622$	−29.6685	−1.18960
$623$	7.31419	0.293037
$624$	39.0203	1.56206
$625$	1.00000	0.0400000
$626$	9.66672	0.386360
$627$	−16.0862	−0.642420
$628$	−32.8410	−1.31050
$629$	−47.8637	−1.90845
$630$	−1.59703	−0.0636271
$631$	19.5389	0.777832	0.388916	−	0.921273i	$-0.372850\pi$
$631$	19.5389	0.777832	0.388916	+	0.921273i	$0.372850\pi$
$632$	13.3102	0.529451
$633$	−22.6785	−0.901391
$634$	−2.90423	−0.115342
$635$	−9.66428	−0.383515
$636$	74.4484	2.95207
$637$	−37.0458	−1.46781
$638$	−45.6377	−1.80681
$639$	−16.2749	−0.643824
$640$	20.3087	0.802771
$641$	3.75615	0.148359	0.0741795	−	0.997245i	$-0.476366\pi$
$641$	3.75615	0.148359	0.0741795	+	0.997245i	$0.476366\pi$
$642$	10.9794	0.433322
$643$	14.2254	0.560993	0.280497	−	0.959855i	$-0.409501\pi$
$643$	14.2254	0.560993	0.280497	+	0.959855i	$0.409501\pi$
$644$	6.84942	0.269905
$645$	2.61862	0.103108
$646$	19.9477	0.784832
$647$	−31.2084	−1.22693	−0.613465	−	0.789722i	$-0.710225\pi$
$647$	−31.2084	−1.22693	−0.613465	+	0.789722i	$0.710225\pi$
$648$	51.5654	2.02568
$649$	71.7637	2.81697
$650$	−13.1614	−0.516234
$651$	−6.12327	−0.239990
$652$	−52.5697	−2.05879
$653$	−42.5700	−1.66589	−0.832946	−	0.553354i	$-0.813348\pi$
$653$	−42.5700	−1.66589	−0.832946	+	0.553354i	$0.813348\pi$
$654$	−92.0068	−3.59775
$655$	−11.1120	−0.434183
$656$	−0.274521	−0.0107183
$657$	−8.82367	−0.344244
$658$	3.78428	0.147527
$659$	22.1307	0.862091	0.431045	−	0.902330i	$-0.358145\pi$
$659$	22.1307	0.862091	0.431045	+	0.902330i	$0.358145\pi$
$660$	−43.8535	−1.70700
$661$	42.2844	1.64467	0.822336	−	0.569002i	$-0.192670\pi$
$661$	42.2844	1.64467	0.822336	+	0.569002i	$0.192670\pi$
$662$	−26.5072	−1.03023
$663$	−67.0048	−2.60225
$664$	52.1666	2.02446
$665$	0.586066	0.0227267
$666$	−32.3162	−1.25223
$667$	−15.3418	−0.594038
$668$	−78.0101	−3.01830
$669$	−56.9391	−2.20139
$670$	3.13556	0.121137
$671$	−23.5264	−0.908226
$672$	0.912226	0.0351899
$673$	−31.7561	−1.22411	−0.612054	−	0.790816i	$-0.709657\pi$
$673$	−31.7561	−1.22411	−0.612054	+	0.790816i	$0.709657\pi$
$674$	−2.65783	−0.102376
$675$	−2.99857	−0.115415
$676$	63.8331	2.45512
$677$	26.5120	1.01894	0.509469	−	0.860489i	$-0.329842\pi$
$677$	26.5120	1.01894	0.509469	+	0.860489i	$0.329842\pi$
$678$	47.9106	1.84000
$679$	3.25298	0.124838
$680$	26.4239	1.01331
$681$	46.3219	1.77506
$682$	−88.6318	−3.39389
$683$	9.74433	0.372856	0.186428	−	0.982469i	$-0.440309\pi$
$683$	9.74433	0.372856	0.186428	+	0.982469i	$0.440309\pi$
$684$	8.89518	0.340116
$685$	17.0483	0.651380
$686$	13.7862	0.526360
$687$	−21.4131	−0.816959
$688$	4.09410	0.156086
$689$	48.3744	1.84292
$690$	−22.3209	−0.849740
$691$	−27.4274	−1.04339	−0.521694	−	0.853133i	$-0.674700\pi$
$691$	−27.4274	−1.04339	−0.521694	+	0.853133i	$0.674700\pi$
$692$	−66.2163	−2.51717
$693$	−3.45759	−0.131343
$694$	−26.5200	−1.00669
$695$	4.87886	0.185066
$696$	35.2223	1.33510
$697$	0.471402	0.0178556
$698$	75.1403	2.84410
$699$	6.61657	0.250262
$700$	1.59771	0.0603878
$701$	8.14101	0.307482	0.153741	−	0.988111i	$-0.450868\pi$
$701$	8.14101	0.307482	0.153741	+	0.988111i	$0.450868\pi$
$702$	39.4655	1.48953
$703$	11.8592	0.447278
$704$	48.4520	1.82610
$705$	−8.14494	−0.306756
$706$	10.9992	0.413960
$707$	1.70002	0.0639357
$708$	−113.985	−4.28380
$709$	−35.7135	−1.34125	−0.670624	−	0.741798i	$-0.733973\pi$
$709$	−35.7135	−1.34125	−0.670624	+	0.741798i	$0.733973\pi$
$710$	24.6523	0.925183
$711$	−4.64842	−0.174329
$712$	−81.7082	−3.06214
$713$	−29.7950	−1.11583
$714$	12.3155	0.460897
$715$	−28.4948	−1.06564
$716$	−29.0241	−1.08468
$717$	−40.4092	−1.50911
$718$	−76.6685	−2.86124
$719$	−35.5018	−1.32399	−0.661997	−	0.749507i	$-0.730291\pi$
$719$	−35.5018	−1.32399	−0.661997	+	0.749507i	$0.730291\pi$
$720$	5.37406	0.200279
$721$	−2.61499	−0.0973875
$722$	41.1706	1.53221
$723$	−8.26688	−0.307448
$724$	−70.2431	−2.61057
$725$	−3.57867	−0.132909
$726$	−86.4810	−3.20961
$727$	15.0797	0.559275	0.279638	−	0.960106i	$-0.409786\pi$
$727$	15.0797	0.559275	0.279638	+	0.960106i	$0.409786\pi$
$728$	−10.2177	−0.378694
$729$	1.28976	0.0477687
$730$	13.3656	0.494683
$731$	−7.03030	−0.260025
$732$	37.3677	1.38115
$733$	23.1120	0.853663	0.426831	−	0.904331i	$-0.359630\pi$
$733$	23.1120	0.853663	0.426831	+	0.904331i	$0.359630\pi$
$734$	60.0347	2.21592
$735$	−14.6552	−0.540564
$736$	4.43876	0.163615
$737$	6.78855	0.250059
$738$	0.318277	0.0117160
$739$	31.9702	1.17604	0.588022	−	0.808845i	$-0.299907\pi$
$739$	31.9702	1.17604	0.588022	+	0.808845i	$0.299907\pi$
$740$	32.3301	1.18848
$741$	16.6018	0.609882
$742$	−8.89126	−0.326408
$743$	9.19805	0.337444	0.168722	−	0.985664i	$-0.446036\pi$
$743$	9.19805	0.337444	0.168722	+	0.985664i	$0.446036\pi$
$744$	68.4042	2.50782
$745$	−17.4985	−0.641095
$746$	−72.2427	−2.64499
$747$	−18.2185	−0.666581
$748$	117.735	4.30483
$749$	−0.866031	−0.0316441
$750$	−5.20661	−0.190119
$751$	17.1975	0.627547	0.313773	−	0.949498i	$-0.398407\pi$
$751$	17.1975	0.627547	0.313773	+	0.949498i	$0.398407\pi$
$752$	−12.7343	−0.464371
$753$	−32.8503	−1.19713
$754$	47.1005	1.71530
$755$	5.82712	0.212071
$756$	−4.79084	−0.174241
$757$	−1.30677	−0.0474953	−0.0237476	−	0.999718i	$-0.507560\pi$
$757$	−1.30677	−0.0474953	−0.0237476	+	0.999718i	$0.507560\pi$
$758$	10.1739	0.369532
$759$	−48.3251	−1.75409
$760$	−6.54706	−0.237487
$761$	−23.4840	−0.851294	−0.425647	−	0.904889i	$-0.639953\pi$
$761$	−23.4840	−0.851294	−0.425647	+	0.904889i	$0.639953\pi$
$762$	50.3182	1.82284
$763$	7.25730	0.262732
$764$	−21.2490	−0.768763
$765$	−9.22823	−0.333647
$766$	21.2564	0.768026
$767$	−74.0639	−2.67429
$768$	−66.1760	−2.38792
$769$	8.47472	0.305606	0.152803	−	0.988257i	$-0.451170\pi$
$769$	8.47472	0.305606	0.152803	+	0.988257i	$0.451170\pi$
$770$	5.23737	0.188742
$771$	32.3695	1.16576
$772$	74.1437	2.66849
$773$	−54.2099	−1.94980	−0.974898	−	0.222653i	$-0.928528\pi$
$773$	−54.2099	−1.94980	−0.974898	+	0.222653i	$0.928528\pi$
$774$	−4.74666	−0.170615
$775$	−6.95004	−0.249653
$776$	−36.3397	−1.30452
$777$	7.32176	0.262667
$778$	−8.71507	−0.312450
$779$	−0.116799	−0.00418477
$780$	45.2591	1.62054
$781$	53.3726	1.90982
$782$	59.9256	2.14294
$783$	10.7309	0.383491
$784$	−22.9127	−0.818312
$785$	−8.44169	−0.301297
$786$	57.8561	2.06366
$787$	19.0423	0.678783	0.339392	−	0.940645i	$-0.389779\pi$
$787$	19.0423	0.678783	0.339392	+	0.940645i	$0.389779\pi$
$788$	26.7443	0.952727
$789$	8.13691	0.289682
$790$	7.04117	0.250513
$791$	−3.77909	−0.134369
$792$	38.6254	1.37249
$793$	24.2804	0.862224
$794$	47.7878	1.69592
$795$	19.1367	0.678710
$796$	103.442	3.66640
$797$	13.7590	0.487367	0.243684	−	0.969855i	$-0.421644\pi$
$797$	13.7590	0.487367	0.243684	+	0.969855i	$0.421644\pi$
$798$	−3.05142	−0.108019
$799$	21.8670	0.773600
$800$	1.03540	0.0366068
$801$	28.5356	1.00826
$802$	85.5356	3.02037
$803$	28.9367	1.02116
$804$	−10.7825	−0.380268
$805$	1.76062	0.0620538
$806$	91.4726	3.22198
$807$	−42.2250	−1.48639
$808$	−18.9912	−0.668108
$809$	2.90647	0.102186	0.0510931	−	0.998694i	$-0.483729\pi$
$809$	2.90647	0.102186	0.0510931	+	0.998694i	$0.483729\pi$
$810$	27.2784	0.958465
$811$	31.7480	1.11482	0.557411	−	0.830237i	$-0.311795\pi$
$811$	31.7480	1.11482	0.557411	+	0.830237i	$0.311795\pi$
$812$	−5.71769	−0.200651
$813$	−65.0866	−2.28269
$814$	105.979	3.71458
$815$	−13.5129	−0.473336
$816$	−41.4423	−1.45077
$817$	1.74190	0.0609413
$818$	46.9807	1.64264
$819$	3.56842	0.124691
$820$	−0.318414	−0.0111195
$821$	−5.91376	−0.206392	−0.103196	−	0.994661i	$-0.532907\pi$
$821$	−5.91376	−0.206392	−0.103196	+	0.994661i	$0.532907\pi$
$822$	−88.7637	−3.09599
$823$	−2.84755	−0.0992593	−0.0496297	−	0.998768i	$-0.515804\pi$
$823$	−2.84755	−0.0992593	−0.0496297	+	0.998768i	$0.515804\pi$
$824$	29.2126	1.01767
$825$	−11.2724	−0.392455
$826$	13.6130	0.473657
$827$	−31.8029	−1.10590	−0.552948	−	0.833216i	$-0.686497\pi$
$827$	−31.8029	−1.10590	−0.552948	+	0.833216i	$0.686497\pi$
$828$	26.7223	0.928665
$829$	−20.5874	−0.715029	−0.357514	−	0.933908i	$-0.616376\pi$
$829$	−20.5874	−0.715029	−0.357514	+	0.933908i	$0.616376\pi$
$830$	27.5964	0.957885
$831$	−17.3629	−0.602311
$832$	−50.0050	−1.73361
$833$	39.3453	1.36323
$834$	−25.4023	−0.879611
$835$	−20.0523	−0.693937
$836$	−29.1713	−1.00891
$837$	20.8402	0.720341
$838$	−12.3801	−0.427662
$839$	−19.9188	−0.687675	−0.343837	−	0.939029i	$-0.611727\pi$
$839$	−19.9188	−0.687675	−0.343837	+	0.939029i	$0.611727\pi$
$840$	−4.04209	−0.139465
$841$	−16.1931	−0.558383
$842$	−97.4282	−3.35760
$843$	−12.7842	−0.440312
$844$	−41.1261	−1.41562
$845$	16.4081	0.564456
$846$	14.7640	0.507597
$847$	6.82144	0.234387
$848$	29.9195	1.02744
$849$	−26.5004	−0.909491
$850$	13.9784	0.479455
$851$	35.6266	1.22126
$852$	−84.7734	−2.90429
$853$	47.5939	1.62958	0.814792	−	0.579754i	$-0.196851\pi$
$853$	47.5939	1.62958	0.814792	+	0.579754i	$0.196851\pi$
$854$	−4.46277	−0.152713
$855$	2.28648	0.0781959
$856$	9.67459	0.330671
$857$	−48.7607	−1.66564	−0.832818	−	0.553547i	$-0.813274\pi$
$857$	−48.7607	−1.66564	−0.832818	+	0.553547i	$0.813274\pi$
$858$	148.361	5.06497
$859$	−40.4734	−1.38094	−0.690468	−	0.723363i	$-0.742595\pi$
$859$	−40.4734	−1.38094	−0.690468	+	0.723363i	$0.742595\pi$
$860$	4.74870	0.161929
$861$	−0.0721108	−0.00245753
$862$	−80.2995	−2.73501
$863$	−6.05021	−0.205952	−0.102976	−	0.994684i	$-0.532836\pi$
$863$	−6.05021	−0.205952	−0.102976	+	0.994684i	$0.532836\pi$
$864$	−3.10470	−0.105624
$865$	−17.0207	−0.578721
$866$	22.1501	0.752690
$867$	34.6940	1.17827
$868$	−11.1042	−0.376900
$869$	15.2443	0.517126
$870$	18.6328	0.631710
$871$	−7.00613	−0.237394
$872$	−81.0727	−2.74547
$873$	12.6912	0.429531
$874$	−14.8478	−0.502234
$875$	0.410687	0.0138838
$876$	−45.9611	−1.55288
$877$	3.77034	0.127315	0.0636576	−	0.997972i	$-0.479723\pi$
$877$	3.77034	0.127315	0.0636576	+	0.997972i	$0.479723\pi$
$878$	−7.38423	−0.249206
$879$	−16.6640	−0.562061
$880$	−17.6240	−0.594103
$881$	−20.2506	−0.682261	−0.341131	−	0.940016i	$-0.610810\pi$
$881$	−20.2506	−0.682261	−0.341131	+	0.940016i	$0.610810\pi$
$882$	26.5648	0.894484
$883$	28.6488	0.964108	0.482054	−	0.876141i	$-0.339891\pi$
$883$	28.6488	0.964108	0.482054	+	0.876141i	$0.339891\pi$
$884$	−121.509	−4.08679
$885$	−29.2994	−0.984888
$886$	−3.29274	−0.110622
$887$	16.2910	0.546997	0.273499	−	0.961872i	$-0.411819\pi$
$887$	16.2910	0.546997	0.273499	+	0.961872i	$0.411819\pi$
$888$	−81.7927	−2.74478
$889$	−3.96899	−0.133116
$890$	−43.2241	−1.44887
$891$	59.0582	1.97853
$892$	−103.255	−3.45725
$893$	−5.41800	−0.181306
$894$	91.1078	3.04710
$895$	−7.46057	−0.249379
$896$	8.34051	0.278637
$897$	49.8740	1.66524
$898$	−70.0193	−2.33658
$899$	24.8719	0.829525
$900$	6.23331	0.207777
$901$	−51.3771	−1.71162
$902$	−1.04377	−0.0347539
$903$	1.07543	0.0357882
$904$	42.2169	1.40411
$905$	−18.0558	−0.600195
$906$	−30.3396	−1.00796
$907$	−39.5995	−1.31488	−0.657440	−	0.753507i	$-0.728361\pi$
$907$	−39.5995	−1.31488	−0.657440	+	0.753507i	$0.728361\pi$
$908$	84.0018	2.78770
$909$	6.63245	0.219984
$910$	−5.40523	−0.179182
$911$	−24.3002	−0.805103	−0.402551	−	0.915397i	$-0.631877\pi$
$911$	−24.3002	−0.805103	−0.402551	+	0.915397i	$0.631877\pi$
$912$	10.2682	0.340013
$913$	59.7467	1.97733
$914$	80.8140	2.67309
$915$	9.60525	0.317540
$916$	−38.8312	−1.28302
$917$	−4.56357	−0.150702
$918$	−41.9151	−1.38341
$919$	34.2186	1.12877	0.564383	−	0.825513i	$-0.309114\pi$
$919$	34.2186	1.12877	0.564383	+	0.825513i	$0.309114\pi$
$920$	−19.6682	−0.648443
$921$	−11.0298	−0.363445
$922$	−32.9180	−1.08410
$923$	−55.0833	−1.81309
$924$	−18.0101	−0.592488
$925$	8.31035	0.273243
$926$	56.9495	1.87148
$927$	−10.2021	−0.335082
$928$	−3.70534	−0.121634
$929$	−5.65514	−0.185539	−0.0927696	−	0.995688i	$-0.529572\pi$
$929$	−5.65514	−0.185539	−0.0927696	+	0.995688i	$0.529572\pi$
$930$	36.1862	1.18659
$931$	−9.74859	−0.319497
$932$	11.9987	0.393031
$933$	26.2247	0.858558
$934$	2.70713	0.0885801
$935$	30.2635	0.989722
$936$	−39.8634	−1.30298
$937$	−53.1080	−1.73496	−0.867481	−	0.497471i	$-0.834262\pi$
$937$	−53.1080	−1.73496	−0.867481	+	0.497471i	$0.834262\pi$
$938$	1.28773	0.0420460
$939$	−8.54465	−0.278844
$940$	−14.7703	−0.481755
$941$	29.6261	0.965784	0.482892	−	0.875680i	$-0.339586\pi$
$941$	29.6261	0.965784	0.482892	+	0.875680i	$0.339586\pi$
$942$	43.9526	1.43205
$943$	−0.350881	−0.0114263
$944$	−45.8083	−1.49093
$945$	−1.23147	−0.0400598
$946$	15.5664	0.506108
$947$	−57.5296	−1.86946	−0.934730	−	0.355359i	$-0.884359\pi$
$947$	−57.5296	−1.86946	−0.934730	+	0.355359i	$0.884359\pi$
$948$	−24.2129	−0.786399
$949$	−29.8642	−0.969434
$950$	−3.46343	−0.112368
$951$	2.56712	0.0832446
$952$	10.8520	0.351714
$953$	41.9945	1.36034	0.680168	−	0.733057i	$-0.261907\pi$
$953$	41.9945	1.36034	0.680168	+	0.733057i	$0.261907\pi$
$954$	−34.6884	−1.12308
$955$	−5.46200	−0.176746
$956$	−73.2794	−2.37003
$957$	40.3403	1.30402
$958$	−16.1637	−0.522226
$959$	7.00149	0.226090
$960$	−19.7818	−0.638454
$961$	17.3031	0.558164
$962$	−109.376	−3.52643
$963$	−3.37873	−0.108878
$964$	−14.9915	−0.482842
$965$	19.0584	0.613512
$966$	−9.16688	−0.294940
$967$	17.7261	0.570033	0.285017	−	0.958523i	$-0.408001\pi$
$967$	17.7261	0.570033	0.285017	+	0.958523i	$0.408001\pi$
$968$	−76.2035	−2.44927
$969$	−17.6323	−0.566430
$970$	−19.2239	−0.617241
$971$	−29.3176	−0.940845	−0.470423	−	0.882441i	$-0.655899\pi$
$971$	−29.3176	−0.940845	−0.470423	+	0.882441i	$0.655899\pi$
$972$	−58.8077	−1.88626
$973$	2.00368	0.0642351
$974$	8.83938	0.283232
$975$	11.6337	0.372577
$976$	15.0174	0.480695
$977$	−49.4644	−1.58251	−0.791253	−	0.611489i	$-0.790571\pi$
$977$	−49.4644	−1.58251	−0.791253	+	0.611489i	$0.790571\pi$
$978$	70.3564	2.24975
$979$	−93.5809	−2.99086
$980$	−26.5762	−0.848946
$981$	28.3136	0.903985
$982$	−84.4579	−2.69516
$983$	−29.4993	−0.940883	−0.470441	−	0.882431i	$-0.655905\pi$
$983$	−29.4993	−0.940883	−0.470441	+	0.882431i	$0.655905\pi$
$984$	0.805563	0.0256804
$985$	6.87455	0.219041
$986$	−50.0241	−1.59309
$987$	−3.34502	−0.106473
$988$	30.1063	0.957808
$989$	5.23290	0.166397
$990$	20.4330	0.649405
$991$	−8.01715	−0.254673	−0.127337	−	0.991860i	$-0.540643\pi$
$991$	−8.01715	−0.254673	−0.127337	+	0.991860i	$0.540643\pi$
$992$	−7.19604	−0.228475
$993$	23.4304	0.743540
$994$	10.1244	0.321125
$995$	26.5894	0.842940
$996$	−94.8976	−3.00694
$997$	−31.3106	−0.991615	−0.495808	−	0.868432i	$-0.665128\pi$
$997$	−31.3106	−0.991615	−0.495808	+	0.868432i	$0.665128\pi$
$998$	−58.2171	−1.84283
$999$	−24.9191	−0.788407

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.e.1.14	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.e.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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42700 q^{2} +2.14529 q^{3} +3.89034 q^{4} +1.00000 q^{5} -5.20661 q^{6} +0.410687 q^{7} -4.58786 q^{8} +1.60225 q^{9} +O(q^{10})\)	\(q-2.42700 q^{2} +2.14529 q^{3} +3.89034 q^{4} +1.00000 q^{5} -5.20661 q^{6} +0.410687 q^{7} -4.58786 q^{8} +1.60225 q^{9} -2.42700 q^{10} -5.25451 q^{11} +8.34589 q^{12} +5.42292 q^{13} -0.996738 q^{14} +2.14529 q^{15} +3.35406 q^{16} -5.75953 q^{17} -3.88867 q^{18} +1.42704 q^{19} +3.89034 q^{20} +0.881041 q^{21} +12.7527 q^{22} +4.28702 q^{23} -9.84227 q^{24} +1.00000 q^{25} -13.1614 q^{26} -2.99857 q^{27} +1.59771 q^{28} -3.57867 q^{29} -5.20661 q^{30} -6.95004 q^{31} +1.03540 q^{32} -11.2724 q^{33} +13.9784 q^{34} +0.410687 q^{35} +6.23331 q^{36} +8.31035 q^{37} -3.46343 q^{38} +11.6337 q^{39} -4.58786 q^{40} -0.0818473 q^{41} -2.13829 q^{42} +1.22064 q^{43} -20.4418 q^{44} +1.60225 q^{45} -10.4046 q^{46} -3.79667 q^{47} +7.19543 q^{48} -6.83134 q^{49} -2.42700 q^{50} -12.3558 q^{51} +21.0970 q^{52} +8.92036 q^{53} +7.27753 q^{54} -5.25451 q^{55} -1.88417 q^{56} +3.06141 q^{57} +8.68545 q^{58} -13.6576 q^{59} +8.34589 q^{60} +4.47737 q^{61} +16.8678 q^{62} +0.658024 q^{63} -9.22104 q^{64} +5.42292 q^{65} +27.3582 q^{66} -1.29195 q^{67} -22.4065 q^{68} +9.19688 q^{69} -0.996738 q^{70} -10.1575 q^{71} -7.35091 q^{72} -5.50703 q^{73} -20.1692 q^{74} +2.14529 q^{75} +5.55167 q^{76} -2.15796 q^{77} -28.2351 q^{78} -2.90118 q^{79} +3.35406 q^{80} -11.2395 q^{81} +0.198644 q^{82} -11.3706 q^{83} +3.42755 q^{84} -5.75953 q^{85} -2.96249 q^{86} -7.67728 q^{87} +24.1069 q^{88} +17.8097 q^{89} -3.88867 q^{90} +2.22712 q^{91} +16.6780 q^{92} -14.9098 q^{93} +9.21452 q^{94} +1.42704 q^{95} +2.22122 q^{96} +7.92083 q^{97} +16.5797 q^{98} -8.41905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * q^99

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