LMFDB - Embedded newform 6019.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40942 q^{2} +1.96845 q^{3} +3.80532 q^{4} +3.79888 q^{5} -4.74282 q^{6} +2.98166 q^{7} -4.34977 q^{8} +0.874791 q^{9} +O(q^{10})$	\(q-2.40942 q^{2} +1.96845 q^{3} +3.80532 q^{4} +3.79888 q^{5} -4.74282 q^{6} +2.98166 q^{7} -4.34977 q^{8} +0.874791 q^{9} -9.15310 q^{10} -1.35974 q^{11} +7.49057 q^{12} +1.00000 q^{13} -7.18407 q^{14} +7.47790 q^{15} +2.86980 q^{16} -5.35064 q^{17} -2.10774 q^{18} -0.464250 q^{19} +14.4559 q^{20} +5.86924 q^{21} +3.27619 q^{22} +0.348953 q^{23} -8.56230 q^{24} +9.43148 q^{25} -2.40942 q^{26} -4.18337 q^{27} +11.3461 q^{28} +6.54744 q^{29} -18.0174 q^{30} +5.96916 q^{31} +1.78498 q^{32} -2.67658 q^{33} +12.8919 q^{34} +11.3270 q^{35} +3.32886 q^{36} -5.40752 q^{37} +1.11857 q^{38} +1.96845 q^{39} -16.5242 q^{40} +9.42203 q^{41} -14.1415 q^{42} -4.35586 q^{43} -5.17425 q^{44} +3.32323 q^{45} -0.840776 q^{46} -12.0977 q^{47} +5.64905 q^{48} +1.89028 q^{49} -22.7244 q^{50} -10.5325 q^{51} +3.80532 q^{52} +8.04339 q^{53} +10.0795 q^{54} -5.16550 q^{55} -12.9695 q^{56} -0.913853 q^{57} -15.7755 q^{58} +10.2915 q^{59} +28.4558 q^{60} -4.39575 q^{61} -14.3822 q^{62} +2.60833 q^{63} -10.0404 q^{64} +3.79888 q^{65} +6.44902 q^{66} +10.5521 q^{67} -20.3609 q^{68} +0.686897 q^{69} -27.2914 q^{70} +13.5565 q^{71} -3.80514 q^{72} -6.73002 q^{73} +13.0290 q^{74} +18.5654 q^{75} -1.76662 q^{76} -4.05429 q^{77} -4.74282 q^{78} -0.0421621 q^{79} +10.9020 q^{80} -10.8591 q^{81} -22.7017 q^{82} +6.91709 q^{83} +22.3343 q^{84} -20.3264 q^{85} +10.4951 q^{86} +12.8883 q^{87} +5.91456 q^{88} +7.31082 q^{89} -8.00705 q^{90} +2.98166 q^{91} +1.32788 q^{92} +11.7500 q^{93} +29.1484 q^{94} -1.76363 q^{95} +3.51365 q^{96} -19.0292 q^{97} -4.55448 q^{98} -1.18949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.40942	−1.70372	−0.851859	−	0.523770i	$-0.824525\pi$
$2$	−2.40942	−1.70372	−0.851859	+	0.523770i	$0.824525\pi$
$3$	1.96845	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$3$	1.96845	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$4$	3.80532	1.90266
$5$	3.79888	1.69891	0.849455	−	0.527661i	$-0.176931\pi$
$5$	3.79888	1.69891	0.849455	+	0.527661i	$0.176931\pi$
$6$	−4.74282	−1.93625
$7$	2.98166	1.12696	0.563480	−	0.826130i	$-0.309462\pi$
$7$	2.98166	1.12696	0.563480	+	0.826130i	$0.309462\pi$
$8$	−4.34977	−1.53788
$9$	0.874791	0.291597
$10$	−9.15310	−2.89447
$11$	−1.35974	−0.409978	−0.204989	−	0.978764i	$-0.565716\pi$
$11$	−1.35974	−0.409978	−0.204989	+	0.978764i	$0.565716\pi$
$12$	7.49057	2.16234
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−7.18407	−1.92002
$15$	7.47790	1.93079
$16$	2.86980	0.717449
$17$	−5.35064	−1.29772	−0.648860	−	0.760908i	$-0.724754\pi$
$17$	−5.35064	−1.29772	−0.648860	+	0.760908i	$0.724754\pi$
$18$	−2.10774	−0.496799
$19$	−0.464250	−0.106506	−0.0532531	−	0.998581i	$-0.516959\pi$
$19$	−0.464250	−0.106506	−0.0532531	+	0.998581i	$0.516959\pi$
$20$	14.4559	3.23245
$21$	5.86924	1.28077
$22$	3.27619	0.698487
$23$	0.348953	0.0727618	0.0363809	−	0.999338i	$-0.488417\pi$
$23$	0.348953	0.0727618	0.0363809	+	0.999338i	$0.488417\pi$
$24$	−8.56230	−1.74777
$25$	9.43148	1.88630
$26$	−2.40942	−0.472527
$27$	−4.18337	−0.805089
$28$	11.3461	2.14422
$29$	6.54744	1.21583	0.607914	−	0.794003i	$-0.292006\pi$
$29$	6.54744	1.21583	0.607914	+	0.794003i	$0.292006\pi$
$30$	−18.0174	−3.28952
$31$	5.96916	1.07209	0.536046	−	0.844188i	$-0.319917\pi$
$31$	5.96916	1.07209	0.536046	+	0.844188i	$0.319917\pi$
$32$	1.78498	0.315543
$33$	−2.67658	−0.465933
$34$	12.8919	2.21095
$35$	11.3270	1.91460
$36$	3.32886	0.554809
$37$	−5.40752	−0.888991	−0.444496	−	0.895781i	$-0.646617\pi$
$37$	−5.40752	−0.888991	−0.444496	+	0.895781i	$0.646617\pi$
$38$	1.11857	0.181457
$39$	1.96845	0.315204
$40$	−16.5242	−2.61271
$41$	9.42203	1.47147	0.735737	−	0.677267i	$-0.236836\pi$
$41$	9.42203	1.47147	0.735737	+	0.677267i	$0.236836\pi$
$42$	−14.1415	−2.18208
$43$	−4.35586	−0.664262	−0.332131	−	0.943233i	$-0.607768\pi$
$43$	−4.35586	−0.664262	−0.332131	+	0.943233i	$0.607768\pi$
$44$	−5.17425	−0.780047
$45$	3.32323	0.495397
$46$	−0.840776	−0.123966
$47$	−12.0977	−1.76463	−0.882314	−	0.470660i	$-0.844016\pi$
$47$	−12.0977	−1.76463	−0.882314	+	0.470660i	$0.844016\pi$
$48$	5.64905	0.815370
$49$	1.89028	0.270040
$50$	−22.7244	−3.21372
$51$	−10.5325	−1.47484
$52$	3.80532	0.527702
$53$	8.04339	1.10484	0.552422	−	0.833564i	$-0.313704\pi$
$53$	8.04339	1.10484	0.552422	+	0.833564i	$0.313704\pi$
$54$	10.0795	1.37165
$55$	−5.16550	−0.696515
$56$	−12.9695	−1.73312
$57$	−0.913853	−0.121043
$58$	−15.7755	−2.07143
$59$	10.2915	1.33984	0.669919	−	0.742434i	$-0.266329\pi$
$59$	10.2915	1.33984	0.669919	+	0.742434i	$0.266329\pi$
$60$	28.4558	3.67362
$61$	−4.39575	−0.562819	−0.281409	−	0.959588i	$-0.590802\pi$
$61$	−4.39575	−0.562819	−0.281409	+	0.959588i	$0.590802\pi$
$62$	−14.3822	−1.82654
$63$	2.60833	0.328618
$64$	−10.0404	−1.25505
$65$	3.79888	0.471193
$66$	6.44902	0.793820
$67$	10.5521	1.28914	0.644572	−	0.764544i	$-0.277036\pi$
$67$	10.5521	1.28914	0.644572	+	0.764544i	$0.277036\pi$
$68$	−20.3609	−2.46912
$69$	0.686897	0.0826926
$70$	−27.2914	−3.26195
$71$	13.5565	1.60886	0.804430	−	0.594048i	$-0.202471\pi$
$71$	13.5565	1.60886	0.804430	+	0.594048i	$0.202471\pi$
$72$	−3.80514	−0.448440
$73$	−6.73002	−0.787689	−0.393844	−	0.919177i	$-0.628855\pi$
$73$	−6.73002	−0.787689	−0.393844	+	0.919177i	$0.628855\pi$
$74$	13.0290	1.51459
$75$	18.5654	2.14375
$76$	−1.76662	−0.202645
$77$	−4.05429	−0.462029
$78$	−4.74282	−0.537019
$79$	−0.0421621	−0.00474360	−0.00237180	−	0.999997i	$-0.500755\pi$
$79$	−0.0421621	−0.00474360	−0.00237180	+	0.999997i	$0.500755\pi$
$80$	10.9020	1.21888
$81$	−10.8591	−1.20657
$82$	−22.7017	−2.50698
$83$	6.91709	0.759249	0.379625	−	0.925141i	$-0.376053\pi$
$83$	6.91709	0.759249	0.379625	+	0.925141i	$0.376053\pi$
$84$	22.3343	2.43687
$85$	−20.3264	−2.20471
$86$	10.4951	1.13172
$87$	12.8883	1.38177
$88$	5.91456	0.630495
$89$	7.31082	0.774945	0.387473	−	0.921881i	$-0.373348\pi$
$89$	7.31082	0.774945	0.387473	+	0.921881i	$0.373348\pi$
$90$	−8.00705	−0.844018
$91$	2.98166	0.312563
$92$	1.32788	0.138441
$93$	11.7500	1.21842
$94$	29.1484	3.00643
$95$	−1.76363	−0.180945
$96$	3.51365	0.358610
$97$	−19.0292	−1.93213	−0.966063	−	0.258308i	$-0.916835\pi$
$97$	−19.0292	−1.93213	−0.966063	+	0.258308i	$0.916835\pi$
$98$	−4.55448	−0.460072
$99$	−1.18949	−0.119548
$100$	35.8898	3.58898
$101$	17.9181	1.78292	0.891459	−	0.453101i	$-0.149682\pi$
$101$	17.9181	1.78292	0.891459	+	0.453101i	$0.149682\pi$
$102$	25.3771	2.51271
$103$	16.3380	1.60983	0.804914	−	0.593391i	$-0.202211\pi$
$103$	16.3380	1.60983	0.804914	+	0.593391i	$0.202211\pi$
$104$	−4.34977	−0.426530
$105$	22.2965	2.17592
$106$	−19.3799	−1.88234
$107$	−17.8426	−1.72491	−0.862456	−	0.506132i	$-0.831075\pi$
$107$	−17.8426	−1.72491	−0.862456	+	0.506132i	$0.831075\pi$
$108$	−15.9190	−1.53181
$109$	13.6468	1.30713	0.653565	−	0.756870i	$-0.273272\pi$
$109$	13.6468	1.30713	0.653565	+	0.756870i	$0.273272\pi$
$110$	12.4459	1.18667
$111$	−10.6444	−1.01032
$112$	8.55675	0.808537
$113$	12.9067	1.21416	0.607078	−	0.794642i	$-0.292341\pi$
$113$	12.9067	1.21416	0.607078	+	0.794642i	$0.292341\pi$
$114$	2.20186	0.206223
$115$	1.32563	0.123616
$116$	24.9151	2.31331
$117$	0.874791	0.0808745
$118$	−24.7966	−2.28271
$119$	−15.9538	−1.46248
$120$	−32.5271	−2.96931
$121$	−9.15110	−0.831918
$122$	10.5912	0.958885
$123$	18.5468	1.67231
$124$	22.7145	2.03983
$125$	16.8347	1.50574
$126$	−6.28456	−0.559873
$127$	15.4858	1.37414	0.687072	−	0.726589i	$-0.258896\pi$
$127$	15.4858	1.37414	0.687072	+	0.726589i	$0.258896\pi$
$128$	20.6215	1.82270
$129$	−8.57428	−0.754924
$130$	−9.15310	−0.802780
$131$	6.46771	0.565086	0.282543	−	0.959255i	$-0.408822\pi$
$131$	6.46771	0.565086	0.282543	+	0.959255i	$0.408822\pi$
$132$	−10.1852	−0.886512
$133$	−1.38423	−0.120028
$134$	−25.4245	−2.19634
$135$	−15.8921	−1.36777
$136$	23.2740	1.99573
$137$	5.71992	0.488685	0.244343	−	0.969689i	$-0.421428\pi$
$137$	5.71992	0.488685	0.244343	+	0.969689i	$0.421428\pi$
$138$	−1.65502	−0.140885
$139$	−9.24212	−0.783906	−0.391953	−	0.919985i	$-0.628200\pi$
$139$	−9.24212	−0.783906	−0.391953	+	0.919985i	$0.628200\pi$
$140$	43.1026	3.64284
$141$	−23.8137	−2.00547
$142$	−32.6633	−2.74104
$143$	−1.35974	−0.113707
$144$	2.51047	0.209206
$145$	24.8729	2.06558
$146$	16.2155	1.34200
$147$	3.72092	0.306896
$148$	−20.5773	−1.69145
$149$	−14.7710	−1.21009	−0.605043	−	0.796193i	$-0.706844\pi$
$149$	−14.7710	−1.21009	−0.605043	+	0.796193i	$0.706844\pi$
$150$	−44.7319	−3.65234
$151$	7.02158	0.571408	0.285704	−	0.958318i	$-0.407773\pi$
$151$	7.02158	0.571408	0.285704	+	0.958318i	$0.407773\pi$
$152$	2.01938	0.163793
$153$	−4.68069	−0.378411
$154$	9.76849	0.787167
$155$	22.6761	1.82139
$156$	7.49057	0.599726
$157$	8.38122	0.668894	0.334447	−	0.942415i	$-0.391451\pi$
$157$	8.38122	0.668894	0.334447	+	0.942415i	$0.391451\pi$
$158$	0.101586	0.00808177
$159$	15.8330	1.25564
$160$	6.78094	0.536080
$161$	1.04046	0.0819997
$162$	26.1642	2.05565
$163$	−1.15700	−0.0906234	−0.0453117	−	0.998973i	$-0.514428\pi$
$163$	−1.15700	−0.0906234	−0.0453117	+	0.998973i	$0.514428\pi$
$164$	35.8538	2.79971
$165$	−10.1680	−0.791579
$166$	−16.6662	−1.29355
$167$	−3.69814	−0.286171	−0.143086	−	0.989710i	$-0.545702\pi$
$167$	−3.69814	−0.286171	−0.143086	+	0.989710i	$0.545702\pi$
$168$	−25.5298	−1.96967
$169$	1.00000	0.0769231
$170$	48.9750	3.75621
$171$	−0.406122	−0.0310569
$172$	−16.5754	−1.26386
$173$	10.8437	0.824429	0.412215	−	0.911087i	$-0.364755\pi$
$173$	10.8437	0.824429	0.412215	+	0.911087i	$0.364755\pi$
$174$	−31.0534	−2.35415
$175$	28.1214	2.12578
$176$	−3.90219	−0.294138
$177$	20.2583	1.52271
$178$	−17.6149	−1.32029
$179$	14.3534	1.07282	0.536412	−	0.843957i	$-0.319780\pi$
$179$	14.3534	1.07282	0.536412	+	0.843957i	$0.319780\pi$
$180$	12.6459	0.942571
$181$	−2.86648	−0.213064	−0.106532	−	0.994309i	$-0.533975\pi$
$181$	−2.86648	−0.213064	−0.106532	+	0.994309i	$0.533975\pi$
$182$	−7.18407	−0.532519
$183$	−8.65282	−0.639635
$184$	−1.51787	−0.111899
$185$	−20.5425	−1.51032
$186$	−28.3107	−2.07584
$187$	7.27549	0.532037
$188$	−46.0355	−3.35749
$189$	−12.4734	−0.907303
$190$	4.24933	0.308279
$191$	9.98592	0.722556	0.361278	−	0.932458i	$-0.382341\pi$
$191$	9.98592	0.722556	0.361278	+	0.932458i	$0.382341\pi$
$192$	−19.7640	−1.42634
$193$	21.0903	1.51812	0.759058	−	0.651023i	$-0.225660\pi$
$193$	21.0903	1.51812	0.759058	+	0.651023i	$0.225660\pi$
$194$	45.8494	3.29180
$195$	7.47790	0.535503
$196$	7.19311	0.513793
$197$	21.9933	1.56696	0.783481	−	0.621416i	$-0.213442\pi$
$197$	21.9933	1.56696	0.783481	+	0.621416i	$0.213442\pi$
$198$	2.86599	0.203677
$199$	6.89206	0.488565	0.244283	−	0.969704i	$-0.421448\pi$
$199$	6.89206	0.488565	0.244283	+	0.969704i	$0.421448\pi$
$200$	−41.0248	−2.90089
$201$	20.7713	1.46509
$202$	−43.1723	−3.03759
$203$	19.5222	1.37019
$204$	−40.0793	−2.80611
$205$	35.7932	2.49990
$206$	−39.3651	−2.74270
$207$	0.305261	0.0212171
$208$	2.86980	0.198985
$209$	0.631261	0.0436652
$210$	−53.7218	−3.70715
$211$	−2.65984	−0.183111	−0.0915555	−	0.995800i	$-0.529184\pi$
$211$	−2.65984	−0.183111	−0.0915555	+	0.995800i	$0.529184\pi$
$212$	30.6076	2.10214
$213$	26.6853	1.82844
$214$	42.9904	2.93876
$215$	−16.5474	−1.12852
$216$	18.1967	1.23813
$217$	17.7980	1.20821
$218$	−32.8810	−2.22698
$219$	−13.2477	−0.895196
$220$	−19.6563	−1.32523
$221$	−5.35064	−0.359923
$222$	25.6469	1.72131
$223$	−16.0654	−1.07582	−0.537909	−	0.843003i	$-0.680786\pi$
$223$	−16.0654	−1.07582	−0.537909	+	0.843003i	$0.680786\pi$
$224$	5.32221	0.355605
$225$	8.25058	0.550038
$226$	−31.0976	−2.06858
$227$	−20.8531	−1.38407	−0.692034	−	0.721865i	$-0.743285\pi$
$227$	−20.8531	−1.38407	−0.692034	+	0.721865i	$0.743285\pi$
$228$	−3.47750	−0.230303
$229$	10.7531	0.710582	0.355291	−	0.934756i	$-0.384382\pi$
$229$	10.7531	0.710582	0.355291	+	0.934756i	$0.384382\pi$
$230$	−3.19401	−0.210606
$231$	−7.98065	−0.525088
$232$	−28.4798	−1.86979
$233$	0.626680	0.0410551	0.0205276	−	0.999789i	$-0.493465\pi$
$233$	0.626680	0.0410551	0.0205276	+	0.999789i	$0.493465\pi$
$234$	−2.10774	−0.137787
$235$	−45.9576	−2.99795
$236$	39.1624	2.54925
$237$	−0.0829939	−0.00539103
$238$	38.4394	2.49165
$239$	−28.2026	−1.82427	−0.912136	−	0.409888i	$-0.865568\pi$
$239$	−28.2026	−1.82427	−0.912136	+	0.409888i	$0.865568\pi$
$240$	21.4601	1.38524
$241$	23.5647	1.51794	0.758969	−	0.651127i	$-0.225703\pi$
$241$	23.5647	1.51794	0.758969	+	0.651127i	$0.225703\pi$
$242$	22.0489	1.41735
$243$	−8.82552	−0.566157
$244$	−16.7272	−1.07085
$245$	7.18094	0.458773
$246$	−44.6870	−2.84914
$247$	−0.464250	−0.0295395
$248$	−25.9645	−1.64875
$249$	13.6159	0.862875
$250$	−40.5618	−2.56535
$251$	21.3320	1.34647	0.673233	−	0.739430i	$-0.264905\pi$
$251$	21.3320	1.34647	0.673233	+	0.739430i	$0.264905\pi$
$252$	9.92551	0.625248
$253$	−0.474487	−0.0298307
$254$	−37.3119	−2.34116
$255$	−40.0115	−2.50562
$256$	−29.6052	−1.85033
$257$	−14.8026	−0.923363	−0.461682	−	0.887046i	$-0.652754\pi$
$257$	−14.8026	−0.923363	−0.461682	+	0.887046i	$0.652754\pi$
$258$	20.6591	1.28618
$259$	−16.1234	−1.00186
$260$	14.4559	0.896519
$261$	5.72764	0.354532
$262$	−15.5834	−0.962748
$263$	−20.5880	−1.26951	−0.634756	−	0.772713i	$-0.718899\pi$
$263$	−20.5880	−1.26951	−0.634756	+	0.772713i	$0.718899\pi$
$264$	11.6425	0.716547
$265$	30.5559	1.87703
$266$	3.33521	0.204495
$267$	14.3910	0.880713
$268$	40.1541	2.45280
$269$	−16.5054	−1.00635	−0.503177	−	0.864183i	$-0.667836\pi$
$269$	−16.5054	−1.00635	−0.503177	+	0.864183i	$0.667836\pi$
$270$	38.2908	2.33030
$271$	3.47966	0.211374	0.105687	−	0.994399i	$-0.466296\pi$
$271$	3.47966	0.211374	0.105687	+	0.994399i	$0.466296\pi$
$272$	−15.3552	−0.931049
$273$	5.86924	0.355223
$274$	−13.7817	−0.832583
$275$	−12.8244	−0.773340
$276$	2.61386	0.157336
$277$	−7.34184	−0.441129	−0.220564	−	0.975372i	$-0.570790\pi$
$277$	−7.34184	−0.441129	−0.220564	+	0.975372i	$0.570790\pi$
$278$	22.2682	1.33556
$279$	5.22177	0.312619
$280$	−49.2696	−2.94442
$281$	−10.2069	−0.608894	−0.304447	−	0.952529i	$-0.598472\pi$
$281$	−10.2069	−0.608894	−0.304447	+	0.952529i	$0.598472\pi$
$282$	57.3772	3.41676
$283$	−11.5910	−0.689012	−0.344506	−	0.938784i	$-0.611954\pi$
$283$	−11.5910	−0.689012	−0.344506	+	0.938784i	$0.611954\pi$
$284$	51.5867	3.06111
$285$	−3.47162	−0.205641
$286$	3.27619	0.193725
$287$	28.0933	1.65829
$288$	1.56149	0.0920115
$289$	11.6293	0.684079
$290$	−59.9294	−3.51917
$291$	−37.4581	−2.19583
$292$	−25.6098	−1.49870
$293$	−20.2337	−1.18207	−0.591033	−	0.806647i	$-0.701280\pi$
$293$	−20.2337	−1.18207	−0.591033	+	0.806647i	$0.701280\pi$
$294$	−8.96526	−0.522864
$295$	39.0961	2.27626
$296$	23.5215	1.36716
$297$	5.68830	0.330069
$298$	35.5895	2.06164
$299$	0.348953	0.0201805
$300$	70.6472	4.07882
$301$	−12.9877	−0.748597
$302$	−16.9180	−0.973519
$303$	35.2709	2.02626
$304$	−1.33230	−0.0764129
$305$	−16.6989	−0.956178
$306$	11.2778	0.644707
$307$	−32.1512	−1.83496	−0.917482	−	0.397777i	$-0.869782\pi$
$307$	−32.1512	−1.83496	−0.917482	+	0.397777i	$0.869782\pi$
$308$	−15.4278	−0.879083
$309$	32.1605	1.82955
$310$	−54.6363	−3.10314
$311$	19.0223	1.07865	0.539327	−	0.842097i	$-0.318679\pi$
$311$	19.0223	1.07865	0.539327	+	0.842097i	$0.318679\pi$
$312$	−8.56230	−0.484745
$313$	16.6498	0.941103	0.470552	−	0.882373i	$-0.344055\pi$
$313$	16.6498	0.941103	0.470552	+	0.882373i	$0.344055\pi$
$314$	−20.1939	−1.13961
$315$	9.90872	0.558293
$316$	−0.160440	−0.00902546
$317$	17.2713	0.970054	0.485027	−	0.874499i	$-0.338810\pi$
$317$	17.2713	0.970054	0.485027	+	0.874499i	$0.338810\pi$
$318$	−38.1484	−2.13926
$319$	−8.90283	−0.498463
$320$	−38.1422	−2.13221
$321$	−35.1223	−1.96034
$322$	−2.50690	−0.139704
$323$	2.48403	0.138215
$324$	−41.3224	−2.29569
$325$	9.43148	0.523164
$326$	2.78771	0.154397
$327$	26.8631	1.48553
$328$	−40.9837	−2.26294
$329$	−36.0711	−1.98867
$330$	24.4990	1.34863
$331$	−25.3882	−1.39546	−0.697730	−	0.716361i	$-0.745806\pi$
$331$	−25.3882	−1.39546	−0.697730	+	0.716361i	$0.745806\pi$
$332$	26.3217	1.44459
$333$	−4.73045	−0.259227
$334$	8.91039	0.487555
$335$	40.0861	2.19014
$336$	16.8435	0.918890
$337$	1.07138	0.0583620	0.0291810	−	0.999574i	$-0.490710\pi$
$337$	1.07138	0.0583620	0.0291810	+	0.999574i	$0.490710\pi$
$338$	−2.40942	−0.131055
$339$	25.4061	1.37987
$340$	−77.3485	−4.19481
$341$	−8.11652	−0.439534
$342$	0.978519	0.0529123
$343$	−15.2354	−0.822636
$344$	18.9470	1.02155
$345$	2.60944	0.140487
$346$	−26.1270	−1.40460
$347$	−24.9425	−1.33898	−0.669491	−	0.742820i	$-0.733488\pi$
$347$	−24.9425	−1.33898	−0.669491	+	0.742820i	$0.733488\pi$
$348$	49.0440	2.62904
$349$	−22.1295	−1.18456	−0.592282	−	0.805730i	$-0.701773\pi$
$349$	−22.1295	−1.18456	−0.592282	+	0.805730i	$0.701773\pi$
$350$	−67.7564	−3.62173
$351$	−4.18337	−0.223292
$352$	−2.42712	−0.129366
$353$	11.1777	0.594929	0.297464	−	0.954733i	$-0.403859\pi$
$353$	11.1777	0.594929	0.297464	+	0.954733i	$0.403859\pi$
$354$	−48.8107	−2.59426
$355$	51.4995	2.73331
$356$	27.8200	1.47446
$357$	−31.4042	−1.66209
$358$	−34.5834	−1.82779
$359$	−24.9829	−1.31855	−0.659273	−	0.751904i	$-0.729136\pi$
$359$	−24.9829	−1.31855	−0.659273	+	0.751904i	$0.729136\pi$
$360$	−14.4553	−0.761859
$361$	−18.7845	−0.988656
$362$	6.90657	0.363001
$363$	−18.0135	−0.945462
$364$	11.3461	0.594700
$365$	−25.5665	−1.33821
$366$	20.8483	1.08976
$367$	15.8460	0.827154	0.413577	−	0.910469i	$-0.364279\pi$
$367$	15.8460	0.827154	0.413577	+	0.910469i	$0.364279\pi$
$368$	1.00143	0.0522029
$369$	8.24231	0.429077
$370$	49.4956	2.57315
$371$	23.9826	1.24512
$372$	44.7124	2.31823
$373$	−22.7260	−1.17671	−0.588355	−	0.808603i	$-0.700224\pi$
$373$	−22.7260	−1.17671	−0.588355	+	0.808603i	$0.700224\pi$
$374$	−17.5297	−0.906441
$375$	33.1382	1.71125
$376$	52.6221	2.71378
$377$	6.54744	0.337210
$378$	30.0536	1.54579
$379$	−26.9277	−1.38319	−0.691593	−	0.722288i	$-0.743091\pi$
$379$	−26.9277	−1.38319	−0.691593	+	0.722288i	$0.743091\pi$
$380$	−6.71117	−0.344276
$381$	30.4830	1.56169
$382$	−24.0603	−1.23103
$383$	18.3810	0.939223	0.469611	−	0.882873i	$-0.344394\pi$
$383$	18.3810	0.939223	0.469611	+	0.882873i	$0.344394\pi$
$384$	40.5924	2.07147
$385$	−15.4017	−0.784945
$386$	−50.8155	−2.58644
$387$	−3.81047	−0.193697
$388$	−72.4122	−3.67617
$389$	−7.01558	−0.355704	−0.177852	−	0.984057i	$-0.556915\pi$
$389$	−7.01558	−0.355704	−0.177852	+	0.984057i	$0.556915\pi$
$390$	−18.0174	−0.912347
$391$	−1.86712	−0.0944245
$392$	−8.22227	−0.415287
$393$	12.7314	0.642212
$394$	−52.9913	−2.66966
$395$	−0.160169	−0.00805896
$396$	−4.52639	−0.227460
$397$	−19.9878	−1.00316	−0.501579	−	0.865112i	$-0.667247\pi$
$397$	−19.9878	−1.00316	−0.501579	+	0.865112i	$0.667247\pi$
$398$	−16.6059	−0.832378
$399$	−2.72479	−0.136410
$400$	27.0664	1.35332
$401$	−8.97325	−0.448103	−0.224051	−	0.974577i	$-0.571928\pi$
$401$	−8.97325	−0.448103	−0.224051	+	0.974577i	$0.571928\pi$
$402$	−50.0468	−2.49611
$403$	5.96916	0.297345
$404$	68.1841	3.39228
$405$	−41.2525	−2.04985
$406$	−47.0373	−2.33442
$407$	7.35284	0.364467
$408$	45.8138	2.26812
$409$	−28.1013	−1.38952	−0.694761	−	0.719241i	$-0.744490\pi$
$409$	−28.1013	−1.38952	−0.694761	+	0.719241i	$0.744490\pi$
$410$	−86.2408	−4.25913
$411$	11.2594	0.555383
$412$	62.1712	3.06295
$413$	30.6857	1.50994
$414$	−0.735503	−0.0361480
$415$	26.2772	1.28990
$416$	1.78498	0.0875160
$417$	−18.1926	−0.890898
$418$	−1.52097	−0.0743932
$419$	4.88591	0.238692	0.119346	−	0.992853i	$-0.461920\pi$
$419$	4.88591	0.238692	0.119346	+	0.992853i	$0.461920\pi$
$420$	84.8453	4.14003
$421$	−14.6092	−0.712008	−0.356004	−	0.934484i	$-0.615861\pi$
$421$	−14.6092	−0.712008	−0.356004	+	0.934484i	$0.615861\pi$
$422$	6.40868	0.311970
$423$	−10.5829	−0.514561
$424$	−34.9869	−1.69911
$425$	−50.4644	−2.44789
$426$	−64.2960	−3.11515
$427$	−13.1066	−0.634274
$428$	−67.8968	−3.28192
$429$	−2.67658	−0.129227
$430$	39.8696	1.92268
$431$	23.9704	1.15461	0.577306	−	0.816528i	$-0.304104\pi$
$431$	23.9704	1.15461	0.577306	+	0.816528i	$0.304104\pi$
$432$	−12.0054	−0.577611
$433$	−1.84235	−0.0885378	−0.0442689	−	0.999020i	$-0.514096\pi$
$433$	−1.84235	−0.0885378	−0.0442689	+	0.999020i	$0.514096\pi$
$434$	−42.8829	−2.05844
$435$	48.9611	2.34750
$436$	51.9306	2.48702
$437$	−0.162002	−0.00774959
$438$	31.9193	1.52516
$439$	−22.6241	−1.07979	−0.539894	−	0.841733i	$-0.681536\pi$
$439$	−22.6241	−1.07979	−0.539894	+	0.841733i	$0.681536\pi$
$440$	22.4687	1.07115
$441$	1.65360	0.0787428
$442$	12.8919	0.613207
$443$	33.7257	1.60236	0.801179	−	0.598425i	$-0.204207\pi$
$443$	33.7257	1.60236	0.801179	+	0.598425i	$0.204207\pi$
$444$	−40.5054	−1.92230
$445$	27.7729	1.31656
$446$	38.7083	1.83289
$447$	−29.0759	−1.37524
$448$	−29.9369	−1.41439
$449$	−29.2451	−1.38016	−0.690080	−	0.723733i	$-0.742425\pi$
$449$	−29.2451	−1.38016	−0.690080	+	0.723733i	$0.742425\pi$
$450$	−19.8791	−0.937111
$451$	−12.8115	−0.603272
$452$	49.1139	2.31013
$453$	13.8216	0.649397
$454$	50.2439	2.35806
$455$	11.3270	0.531016
$456$	3.97505	0.186149
$457$	−20.4471	−0.956476	−0.478238	−	0.878230i	$-0.658724\pi$
$457$	−20.4471	−0.956476	−0.478238	+	0.878230i	$0.658724\pi$
$458$	−25.9086	−1.21063
$459$	22.3837	1.04478
$460$	5.04445	0.235198
$461$	−9.29392	−0.432861	−0.216430	−	0.976298i	$-0.569441\pi$
$461$	−9.29392	−0.432861	−0.216430	+	0.976298i	$0.569441\pi$
$462$	19.2288	0.894603
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	18.7898	0.872296
$465$	44.6368	2.06998
$466$	−1.50994	−0.0699464
$467$	−1.99786	−0.0924499	−0.0462250	−	0.998931i	$-0.514719\pi$
$467$	−1.99786	−0.0924499	−0.0462250	+	0.998931i	$0.514719\pi$
$468$	3.32886	0.153876
$469$	31.4627	1.45281
$470$	110.731	5.10766
$471$	16.4980	0.760187
$472$	−44.7656	−2.06050
$473$	5.92284	0.272333
$474$	0.199967	0.00918480
$475$	−4.37857	−0.200902
$476$	−60.7091	−2.78260
$477$	7.03629	0.322169
$478$	67.9519	3.10805
$479$	−28.7019	−1.31142	−0.655711	−	0.755012i	$-0.727631\pi$
$479$	−28.7019	−1.31142	−0.655711	+	0.755012i	$0.727631\pi$
$480$	13.3479	0.609247
$481$	−5.40752	−0.246562
$482$	−56.7774	−2.58614
$483$	2.04809	0.0931913
$484$	−34.8228	−1.58286
$485$	−72.2897	−3.28251
$486$	21.2644	0.964573
$487$	−15.8019	−0.716053	−0.358027	−	0.933711i	$-0.616550\pi$
$487$	−15.8019	−0.716053	−0.358027	+	0.933711i	$0.616550\pi$
$488$	19.1205	0.865545
$489$	−2.27750	−0.102992
$490$	−17.3019	−0.781621
$491$	8.88482	0.400966	0.200483	−	0.979697i	$-0.435749\pi$
$491$	8.88482	0.400966	0.200483	+	0.979697i	$0.435749\pi$
$492$	70.5764	3.18183
$493$	−35.0330	−1.57781
$494$	1.11857	0.0503270
$495$	−4.51873	−0.203102
$496$	17.1303	0.769172
$497$	40.4208	1.81312
$498$	−32.8065	−1.47010
$499$	−12.1289	−0.542966	−0.271483	−	0.962443i	$-0.587514\pi$
$499$	−12.1289	−0.542966	−0.271483	+	0.962443i	$0.587514\pi$
$500$	64.0612	2.86490
$501$	−7.27961	−0.325229
$502$	−51.3979	−2.29400
$503$	−35.1481	−1.56718	−0.783588	−	0.621280i	$-0.786613\pi$
$503$	−35.1481	−1.56718	−0.783588	+	0.621280i	$0.786613\pi$
$504$	−11.3456	−0.505374
$505$	68.0687	3.02902
$506$	1.14324	0.0508232
$507$	1.96845	0.0874219
$508$	58.9284	2.61453
$509$	−6.51863	−0.288933	−0.144466	−	0.989510i	$-0.546147\pi$
$509$	−6.51863	−0.288933	−0.144466	+	0.989510i	$0.546147\pi$
$510$	96.4047	4.26887
$511$	−20.0666	−0.887694
$512$	30.0884	1.32973
$513$	1.94213	0.0857470
$514$	35.6658	1.57315
$515$	62.0660	2.73495
$516$	−32.6279	−1.43636
$517$	16.4497	0.723459
$518$	38.8480	1.70688
$519$	21.3452	0.936951
$520$	−16.5242	−0.724636
$521$	32.8255	1.43811	0.719055	−	0.694953i	$-0.244575\pi$
$521$	32.8255	1.43811	0.719055	+	0.694953i	$0.244575\pi$
$522$	−13.8003	−0.604023
$523$	31.0532	1.35786	0.678930	−	0.734203i	$-0.262444\pi$
$523$	31.0532	1.35786	0.678930	+	0.734203i	$0.262444\pi$
$524$	24.6117	1.07517
$525$	55.3556	2.41592
$526$	49.6052	2.16289
$527$	−31.9388	−1.39128
$528$	−7.68125	−0.334284
$529$	−22.8782	−0.994706
$530$	−73.6220	−3.19794
$531$	9.00291	0.390693
$532$	−5.26745	−0.228373
$533$	9.42203	0.408113
$534$	−34.6739	−1.50049
$535$	−67.7820	−2.93047
$536$	−45.8992	−1.98254
$537$	28.2539	1.21925
$538$	39.7686	1.71455
$539$	−2.57029	−0.110710
$540$	−60.4744	−2.60241
$541$	16.9229	0.727572	0.363786	−	0.931483i	$-0.381484\pi$
$541$	16.9229	0.727572	0.363786	+	0.931483i	$0.381484\pi$
$542$	−8.38397	−0.360122
$543$	−5.64252	−0.242144
$544$	−9.55080	−0.409487
$545$	51.8427	2.22070
$546$	−14.1415	−0.605199
$547$	21.6589	0.926067	0.463034	−	0.886341i	$-0.346761\pi$
$547$	21.6589	0.926067	0.463034	+	0.886341i	$0.346761\pi$
$548$	21.7661	0.929801
$549$	−3.84537	−0.164116
$550$	30.8994	1.31755
$551$	−3.03965	−0.129493
$552$	−2.98784	−0.127171
$553$	−0.125713	−0.00534585
$554$	17.6896	0.751559
$555$	−40.4369	−1.71645
$556$	−35.1692	−1.49151
$557$	6.22229	0.263647	0.131824	−	0.991273i	$-0.457917\pi$
$557$	6.22229	0.263647	0.131824	+	0.991273i	$0.457917\pi$
$558$	−12.5814	−0.532615
$559$	−4.35586	−0.184233
$560$	32.5061	1.37363
$561$	14.3214	0.604651
$562$	24.5928	1.03738
$563$	−34.7521	−1.46463	−0.732314	−	0.680967i	$-0.761560\pi$
$563$	−34.7521	−1.46463	−0.732314	+	0.680967i	$0.761560\pi$
$564$	−90.6186	−3.81573
$565$	49.0309	2.06274
$566$	27.9276	1.17388
$567$	−32.3782	−1.35975
$568$	−58.9676	−2.47422
$569$	14.8984	0.624572	0.312286	−	0.949988i	$-0.398905\pi$
$569$	14.8984	0.624572	0.312286	+	0.949988i	$0.398905\pi$
$570$	8.36459	0.350354
$571$	35.5341	1.48705	0.743527	−	0.668706i	$-0.233151\pi$
$571$	35.5341	1.48705	0.743527	+	0.668706i	$0.233151\pi$
$572$	−5.17425	−0.216346
$573$	19.6568	0.821173
$574$	−67.6885	−2.82527
$575$	3.29115	0.137250
$576$	−8.78323	−0.365968
$577$	−8.07042	−0.335976	−0.167988	−	0.985789i	$-0.553727\pi$
$577$	−8.07042	−0.335976	−0.167988	+	0.985789i	$0.553727\pi$
$578$	−28.0200	−1.16548
$579$	41.5153	1.72532
$580$	94.6493	3.93010
$581$	20.6244	0.855644
$582$	90.2523	3.74108
$583$	−10.9369	−0.452962
$584$	29.2740	1.21137
$585$	3.32323	0.137398
$586$	48.7516	2.01391
$587$	41.4942	1.71265	0.856324	−	0.516439i	$-0.172743\pi$
$587$	41.4942	1.71265	0.856324	+	0.516439i	$0.172743\pi$
$588$	14.1593	0.583918
$589$	−2.77118	−0.114185
$590$	−94.1991	−3.87812
$591$	43.2928	1.78083
$592$	−15.5185	−0.637806
$593$	−18.9446	−0.777962	−0.388981	−	0.921246i	$-0.627173\pi$
$593$	−18.9446	−0.777962	−0.388981	+	0.921246i	$0.627173\pi$
$594$	−13.7055	−0.562344
$595$	−60.6064	−2.48462
$596$	−56.2082	−2.30238
$597$	13.5667	0.555247
$598$	−0.840776	−0.0343819
$599$	−22.0190	−0.899671	−0.449835	−	0.893111i	$-0.648517\pi$
$599$	−22.0190	−0.899671	−0.449835	+	0.893111i	$0.648517\pi$
$600$	−80.7551	−3.29681
$601$	30.4177	1.24076	0.620382	−	0.784300i	$-0.286978\pi$
$601$	30.4177	1.24076	0.620382	+	0.784300i	$0.286978\pi$
$602$	31.2928	1.27540
$603$	9.23088	0.375911
$604$	26.7193	1.08719
$605$	−34.7639	−1.41335
$606$	−84.9825	−3.45218
$607$	−43.4327	−1.76288	−0.881439	−	0.472298i	$-0.843424\pi$
$607$	−43.4327	−1.76288	−0.881439	+	0.472298i	$0.843424\pi$
$608$	−0.828679	−0.0336074
$609$	38.4285	1.55720
$610$	40.2348	1.62906
$611$	−12.0977	−0.489420
$612$	−17.8115	−0.719988
$613$	−16.4712	−0.665264	−0.332632	−	0.943057i	$-0.607937\pi$
$613$	−16.4712	−0.665264	−0.332632	+	0.943057i	$0.607937\pi$
$614$	77.4657	3.12626
$615$	70.4570	2.84110
$616$	17.6352	0.710543
$617$	−7.76497	−0.312606	−0.156303	−	0.987709i	$-0.549958\pi$
$617$	−7.76497	−0.312606	−0.156303	+	0.987709i	$0.549958\pi$
$618$	−77.4882	−3.11703
$619$	11.4567	0.460483	0.230241	−	0.973134i	$-0.426048\pi$
$619$	11.4567	0.460483	0.230241	+	0.973134i	$0.426048\pi$
$620$	86.2898	3.46548
$621$	−1.45980	−0.0585797
$622$	−45.8326	−1.83772
$623$	21.7984	0.873333
$624$	5.64905	0.226143
$625$	16.7954	0.671817
$626$	−40.1164	−1.60337
$627$	1.24260	0.0496248
$628$	31.8932	1.27268
$629$	28.9337	1.15366
$630$	−23.8743	−0.951174
$631$	−47.3705	−1.88579	−0.942896	−	0.333088i	$-0.891910\pi$
$631$	−47.3705	−1.88579	−0.942896	+	0.333088i	$0.891910\pi$
$632$	0.183395	0.00729507
$633$	−5.23576	−0.208103
$634$	−41.6139	−1.65270
$635$	58.8287	2.33455
$636$	60.2496	2.38905
$637$	1.89028	0.0748955
$638$	21.4507	0.849241
$639$	11.8591	0.469139
$640$	78.3387	3.09661
$641$	42.0887	1.66240	0.831201	−	0.555971i	$-0.187654\pi$
$641$	42.0887	1.66240	0.831201	+	0.555971i	$0.187654\pi$
$642$	84.6244	3.33986
$643$	−23.6015	−0.930752	−0.465376	−	0.885113i	$-0.654081\pi$
$643$	−23.6015	−0.930752	−0.465376	+	0.885113i	$0.654081\pi$
$644$	3.95927	0.156017
$645$	−32.5727	−1.28255
$646$	−5.98509	−0.235480
$647$	22.1765	0.871847	0.435924	−	0.899984i	$-0.356422\pi$
$647$	22.1765	0.871847	0.435924	+	0.899984i	$0.356422\pi$
$648$	47.2346	1.85555
$649$	−13.9938	−0.549304
$650$	−22.7244	−0.891325
$651$	35.0344	1.37311
$652$	−4.40276	−0.172425
$653$	−32.1685	−1.25885	−0.629425	−	0.777061i	$-0.716710\pi$
$653$	−32.1685	−1.25885	−0.629425	+	0.777061i	$0.716710\pi$
$654$	−64.7246	−2.53093
$655$	24.5700	0.960031
$656$	27.0393	1.05571
$657$	−5.88736	−0.229688
$658$	86.9106	3.38813
$659$	−9.86041	−0.384107	−0.192053	−	0.981384i	$-0.561515\pi$
$659$	−9.86041	−0.384107	−0.192053	+	0.981384i	$0.561515\pi$
$660$	−38.6925	−1.50610
$661$	−39.1877	−1.52422	−0.762112	−	0.647445i	$-0.775838\pi$
$661$	−39.1877	−1.52422	−0.762112	+	0.647445i	$0.775838\pi$
$662$	61.1708	2.37747
$663$	−10.5325	−0.409047
$664$	−30.0877	−1.16763
$665$	−5.25854	−0.203917
$666$	11.3977	0.441650
$667$	2.28475	0.0884659
$668$	−14.0726	−0.544486
$669$	−31.6239	−1.22265
$670$	−96.5844	−3.73138
$671$	5.97709	0.230743
$672$	10.4765	0.404140
$673$	−8.81593	−0.339829	−0.169914	−	0.985459i	$-0.554349\pi$
$673$	−8.81593	−0.339829	−0.169914	+	0.985459i	$0.554349\pi$
$674$	−2.58142	−0.0994325
$675$	−39.4553	−1.51864
$676$	3.80532	0.146358
$677$	−41.2658	−1.58597	−0.792987	−	0.609238i	$-0.791475\pi$
$677$	−41.2658	−1.58597	−0.792987	+	0.609238i	$0.791475\pi$
$678$	−61.2140	−2.35091
$679$	−56.7386	−2.17743
$680$	88.4153	3.39057
$681$	−41.0482	−1.57297
$682$	19.5561	0.748843
$683$	37.8839	1.44959	0.724794	−	0.688966i	$-0.241935\pi$
$683$	37.8839	1.44959	0.724794	+	0.688966i	$0.241935\pi$
$684$	−1.54542	−0.0590907
$685$	21.7293	0.830233
$686$	36.7086	1.40154
$687$	21.1668	0.807565
$688$	−12.5004	−0.476574
$689$	8.04339	0.306429
$690$	−6.28724	−0.239351
$691$	9.72707	0.370035	0.185018	−	0.982735i	$-0.440766\pi$
$691$	9.72707	0.370035	0.185018	+	0.982735i	$0.440766\pi$
$692$	41.2636	1.56861
$693$	−3.54665	−0.134726
$694$	60.0970	2.28125
$695$	−35.1097	−1.33179
$696$	−56.0611	−2.12499
$697$	−50.4139	−1.90956
$698$	53.3193	2.01817
$699$	1.23359	0.0466585
$700$	107.011	4.04463
$701$	6.44327	0.243359	0.121680	−	0.992569i	$-0.461172\pi$
$701$	6.44327	0.243359	0.121680	+	0.992569i	$0.461172\pi$
$702$	10.0795	0.380426
$703$	2.51044	0.0946832
$704$	13.6523	0.514541
$705$	−90.4653	−3.40712
$706$	−26.9318	−1.01359
$707$	53.4257	2.00928
$708$	77.0891	2.89719
$709$	24.2266	0.909850	0.454925	−	0.890530i	$-0.349666\pi$
$709$	24.2266	0.909850	0.454925	+	0.890530i	$0.349666\pi$
$710$	−124.084	−4.65679
$711$	−0.0368830	−0.00138322
$712$	−31.8004	−1.19177
$713$	2.08296	0.0780074
$714$	75.6659	2.83173
$715$	−5.16550	−0.193179
$716$	54.6192	2.04122
$717$	−55.5153	−2.07326
$718$	60.1943	2.24643
$719$	−1.73010	−0.0645218	−0.0322609	−	0.999479i	$-0.510271\pi$
$719$	−1.73010	−0.0645218	−0.0322609	+	0.999479i	$0.510271\pi$
$720$	9.53698	0.355422
$721$	48.7142	1.81421
$722$	45.2597	1.68439
$723$	46.3860	1.72511
$724$	−10.9079	−0.405388
$725$	61.7520	2.29341
$726$	43.4021	1.61080
$727$	−5.42521	−0.201210	−0.100605	−	0.994926i	$-0.532078\pi$
$727$	−5.42521	−0.201210	−0.100605	+	0.994926i	$0.532078\pi$
$728$	−12.9695	−0.480682
$729$	15.2048	0.563139
$730$	61.6005	2.27994
$731$	23.3066	0.862027
$732$	−32.9267	−1.21701
$733$	−40.4962	−1.49576	−0.747880	−	0.663834i	$-0.768928\pi$
$733$	−40.4962	−1.49576	−0.747880	+	0.663834i	$0.768928\pi$
$734$	−38.1797	−1.40924
$735$	14.1353	0.521389
$736$	0.622876	0.0229595
$737$	−14.3481	−0.528520
$738$	−19.8592	−0.731027
$739$	−33.6260	−1.23695	−0.618476	−	0.785804i	$-0.712250\pi$
$739$	−33.6260	−1.23695	−0.618476	+	0.785804i	$0.712250\pi$
$740$	−78.1708	−2.87362
$741$	−0.913853	−0.0335712
$742$	−57.7843	−2.12133
$743$	−33.3696	−1.22421	−0.612106	−	0.790776i	$-0.709677\pi$
$743$	−33.3696	−1.22421	−0.612106	+	0.790776i	$0.709677\pi$
$744$	−51.1097	−1.87377
$745$	−56.1131	−2.05583
$746$	54.7566	2.00478
$747$	6.05101	0.221395
$748$	27.6855	1.01228
$749$	−53.2006	−1.94391
$750$	−79.8438	−2.91548
$751$	−15.3016	−0.558362	−0.279181	−	0.960239i	$-0.590063\pi$
$751$	−15.3016	−0.558362	−0.279181	+	0.960239i	$0.590063\pi$
$752$	−34.7179	−1.26603
$753$	41.9910	1.53024
$754$	−15.7755	−0.574511
$755$	26.6741	0.970771
$756$	−47.4651	−1.72629
$757$	1.51186	0.0549495	0.0274747	−	0.999622i	$-0.491253\pi$
$757$	1.51186	0.0549495	0.0274747	+	0.999622i	$0.491253\pi$
$758$	64.8803	2.35656
$759$	−0.934003	−0.0339021
$760$	7.67138	0.278270
$761$	−16.7833	−0.608394	−0.304197	−	0.952609i	$-0.598388\pi$
$761$	−16.7833	−0.608394	−0.304197	+	0.952609i	$0.598388\pi$
$762$	−73.4465	−2.66069
$763$	40.6902	1.47308
$764$	37.9996	1.37478
$765$	−17.7814	−0.642887
$766$	−44.2875	−1.60017
$767$	10.2915	0.371604
$768$	−58.2764	−2.10287
$769$	10.7003	0.385863	0.192931	−	0.981212i	$-0.438201\pi$
$769$	10.7003	0.385863	0.192931	+	0.981212i	$0.438201\pi$
$770$	37.1093	1.33733
$771$	−29.1382	−1.04939
$772$	80.2554	2.88846
$773$	1.82049	0.0654785	0.0327393	−	0.999464i	$-0.489577\pi$
$773$	1.82049	0.0654785	0.0327393	+	0.999464i	$0.489577\pi$
$774$	9.18102	0.330005
$775$	56.2980	2.02228
$776$	82.7727	2.97137
$777$	−31.7380	−1.13860
$778$	16.9035	0.606020
$779$	−4.37418	−0.156721
$780$	28.4558	1.01888
$781$	−18.4333	−0.659597
$782$	4.49869	0.160873
$783$	−27.3903	−0.978850
$784$	5.42471	0.193740
$785$	31.8392	1.13639
$786$	−30.6752	−1.09415
$787$	6.76296	0.241073	0.120537	−	0.992709i	$-0.461538\pi$
$787$	6.76296	0.241073	0.120537	+	0.992709i	$0.461538\pi$
$788$	83.6916	2.98139
$789$	−40.5265	−1.44278
$790$	0.385914	0.0137302
$791$	38.4832	1.36831
$792$	5.17401	0.183850
$793$	−4.39575	−0.156098
$794$	48.1590	1.70910
$795$	60.1477	2.13322
$796$	26.2265	0.929572
$797$	29.6515	1.05031	0.525156	−	0.851006i	$-0.324007\pi$
$797$	29.6515	1.05031	0.525156	+	0.851006i	$0.324007\pi$
$798$	6.56518	0.232405
$799$	64.7303	2.29000
$800$	16.8350	0.595208
$801$	6.39544	0.225972
$802$	21.6204	0.763441
$803$	9.15109	0.322935
$804$	79.0412	2.78757
$805$	3.95258	0.139310
$806$	−14.3822	−0.506592
$807$	−32.4901	−1.14371
$808$	−77.9396	−2.74191
$809$	6.75725	0.237572	0.118786	−	0.992920i	$-0.462100\pi$
$809$	6.75725	0.237572	0.118786	+	0.992920i	$0.462100\pi$
$810$	99.3946	3.49237
$811$	−22.0639	−0.774767	−0.387383	−	0.921919i	$-0.626621\pi$
$811$	−22.0639	−0.774767	−0.387383	+	0.921919i	$0.626621\pi$
$812$	74.2882	2.60700
$813$	6.84953	0.240224
$814$	−17.7161	−0.620949
$815$	−4.39531	−0.153961
$816$	−30.2260	−1.05812
$817$	2.02221	0.0707481
$818$	67.7080	2.36735
$819$	2.60833	0.0911423
$820$	136.204	4.75646
$821$	28.9030	1.00872	0.504361	−	0.863493i	$-0.331728\pi$
$821$	28.9030	1.00872	0.504361	+	0.863493i	$0.331728\pi$
$822$	−27.1286	−0.946217
$823$	−25.8587	−0.901376	−0.450688	−	0.892682i	$-0.648821\pi$
$823$	−25.8587	−0.901376	−0.450688	+	0.892682i	$0.648821\pi$
$824$	−71.0664	−2.47572
$825$	−25.2441	−0.878888
$826$	−73.9348	−2.57252
$827$	1.67988	0.0584153	0.0292076	−	0.999573i	$-0.490702\pi$
$827$	1.67988	0.0584153	0.0292076	+	0.999573i	$0.490702\pi$
$828$	1.16162	0.0403689
$829$	12.5308	0.435212	0.217606	−	0.976037i	$-0.430175\pi$
$829$	12.5308	0.435212	0.217606	+	0.976037i	$0.430175\pi$
$830$	−63.3128	−2.19762
$831$	−14.4520	−0.501336
$832$	−10.0404	−0.348087
$833$	−10.1142	−0.350436
$834$	43.8338	1.51784
$835$	−14.0488	−0.486179
$836$	2.40215	0.0830800
$837$	−24.9712	−0.863130
$838$	−11.7722	−0.406664
$839$	23.3722	0.806899	0.403450	−	0.915002i	$-0.367811\pi$
$839$	23.3722	0.806899	0.403450	+	0.915002i	$0.367811\pi$
$840$	−96.9847	−3.34629
$841$	13.8690	0.478240
$842$	35.1997	1.21306
$843$	−20.0918	−0.691999
$844$	−10.1215	−0.348398
$845$	3.79888	0.130685
$846$	25.4988	0.876667
$847$	−27.2854	−0.937539
$848$	23.0829	0.792670
$849$	−22.8162	−0.783052
$850$	121.590	4.17051
$851$	−1.88697	−0.0646846
$852$	101.546	3.47890
$853$	35.4852	1.21499	0.607495	−	0.794324i	$-0.292175\pi$
$853$	35.4852	1.21499	0.607495	+	0.794324i	$0.292175\pi$
$854$	31.5794	1.08063
$855$	−1.54281	−0.0527629
$856$	77.6113	2.65270
$857$	8.63612	0.295004	0.147502	−	0.989062i	$-0.452877\pi$
$857$	8.63612	0.295004	0.147502	+	0.989062i	$0.452877\pi$
$858$	6.44902	0.220166
$859$	−29.4235	−1.00392	−0.501959	−	0.864892i	$-0.667387\pi$
$859$	−29.4235	−1.00392	−0.501959	+	0.864892i	$0.667387\pi$
$860$	−62.9680	−2.14719
$861$	55.3002	1.88462
$862$	−57.7547	−1.96713
$863$	49.9460	1.70018	0.850090	−	0.526637i	$-0.176547\pi$
$863$	49.9460	1.70018	0.850090	+	0.526637i	$0.176547\pi$
$864$	−7.46724	−0.254041
$865$	41.1938	1.40063
$866$	4.43900	0.150844
$867$	22.8918	0.777445
$868$	67.7270	2.29880
$869$	0.0573296	0.00194477
$870$	−117.968	−3.99949
$871$	10.5521	0.357544
$872$	−59.3606	−2.01020
$873$	−16.6466	−0.563402
$874$	0.390330	0.0132031
$875$	50.1952	1.69691
$876$	−50.4117	−1.70325
$877$	2.32070	0.0783644	0.0391822	−	0.999232i	$-0.487525\pi$
$877$	2.32070	0.0783644	0.0391822	+	0.999232i	$0.487525\pi$
$878$	54.5110	1.83966
$879$	−39.8290	−1.34340
$880$	−14.8239	−0.499715
$881$	34.4169	1.15954	0.579768	−	0.814782i	$-0.303143\pi$
$881$	34.4169	1.15954	0.579768	+	0.814782i	$0.303143\pi$
$882$	−3.98422	−0.134156
$883$	−16.1718	−0.544225	−0.272113	−	0.962265i	$-0.587722\pi$
$883$	−16.1718	−0.544225	−0.272113	+	0.962265i	$0.587722\pi$
$884$	−20.3609	−0.684810
$885$	76.9587	2.58694
$886$	−81.2595	−2.72997
$887$	−14.9127	−0.500718	−0.250359	−	0.968153i	$-0.580549\pi$
$887$	−14.9127	−0.500718	−0.250359	+	0.968153i	$0.580549\pi$
$888$	46.3008	1.55375
$889$	46.1734	1.54861
$890$	−66.9167	−2.24305
$891$	14.7656	0.494666
$892$	−61.1339	−2.04692
$893$	5.61635	0.187944
$894$	70.0561	2.34303
$895$	54.5268	1.82263
$896$	61.4863	2.05411
$897$	0.686897	0.0229348
$898$	70.4637	2.35140
$899$	39.0827	1.30348
$900$	31.3960	1.04653
$901$	−43.0373	−1.43378
$902$	30.8684	1.02781
$903$	−25.5656	−0.850769
$904$	−56.1410	−1.86722
$905$	−10.8894	−0.361977
$906$	−33.3021	−1.10639
$907$	19.6522	0.652540	0.326270	−	0.945277i	$-0.394208\pi$
$907$	19.6522	0.652540	0.326270	+	0.945277i	$0.394208\pi$
$908$	−79.3526	−2.63341
$909$	15.6746	0.519894
$910$	−27.2914	−0.904702
$911$	−41.8501	−1.38656	−0.693278	−	0.720670i	$-0.743834\pi$
$911$	−41.8501	−1.38656	−0.693278	+	0.720670i	$0.743834\pi$
$912$	−2.62257	−0.0868420
$913$	−9.40546	−0.311275
$914$	49.2657	1.62957
$915$	−32.8710	−1.08668
$916$	40.9188	1.35199
$917$	19.2845	0.636830
$918$	−53.9317	−1.78001
$919$	−48.7532	−1.60822	−0.804109	−	0.594481i	$-0.797357\pi$
$919$	−48.7532	−1.60822	−0.804109	+	0.594481i	$0.797357\pi$
$920$	−5.76619	−0.190106
$921$	−63.2879	−2.08541
$922$	22.3930	0.737473
$923$	13.5565	0.446217
$924$	−30.3689	−0.999064
$925$	−51.0009	−1.67690
$926$	2.40942	0.0791785
$927$	14.2923	0.469421
$928$	11.6871	0.383647
$929$	−35.0004	−1.14833	−0.574163	−	0.818741i	$-0.694672\pi$
$929$	−35.0004	−1.14833	−0.574163	+	0.818741i	$0.694672\pi$
$930$	−107.549	−3.52667
$931$	−0.877562	−0.0287609
$932$	2.38471	0.0781139
$933$	37.4443	1.22587
$934$	4.81369	0.157509
$935$	27.6387	0.903882
$936$	−3.80514	−0.124375
$937$	−0.390074	−0.0127431	−0.00637157	−	0.999980i	$-0.502028\pi$
$937$	−0.390074	−0.0127431	−0.00637157	+	0.999980i	$0.502028\pi$
$938$	−75.8070	−2.47519
$939$	32.7743	1.06955
$940$	−174.883	−5.70407
$941$	−46.3152	−1.50983	−0.754915	−	0.655822i	$-0.772322\pi$
$941$	−46.3152	−1.50983	−0.754915	+	0.655822i	$0.772322\pi$
$942$	−39.7506	−1.29515
$943$	3.28785	0.107067
$944$	29.5345	0.961266
$945$	−47.3848	−1.54143
$946$	−14.2706	−0.463978
$947$	−5.85330	−0.190207	−0.0951033	−	0.995467i	$-0.530318\pi$
$947$	−5.85330	−0.190207	−0.0951033	+	0.995467i	$0.530318\pi$
$948$	−0.315818	−0.0102573
$949$	−6.73002	−0.218466
$950$	10.5498	0.342281
$951$	33.9977	1.10245
$952$	69.3952	2.24911
$953$	−45.8648	−1.48571	−0.742854	−	0.669454i	$-0.766528\pi$
$953$	−45.8648	−1.48571	−0.742854	+	0.669454i	$0.766528\pi$
$954$	−16.9534	−0.548886
$955$	37.9353	1.22756
$956$	−107.320	−3.47097
$957$	−17.5248	−0.566495
$958$	69.1549	2.23429
$959$	17.0548	0.550729
$960$	−75.0809	−2.42323
$961$	4.63088	0.149383
$962$	13.0290	0.420072
$963$	−15.6086	−0.502979
$964$	89.6712	2.88812
$965$	80.1196	2.57914
$966$	−4.93471	−0.158772
$967$	−44.0292	−1.41588	−0.707941	−	0.706272i	$-0.750376\pi$
$967$	−44.0292	−1.41588	−0.707941	+	0.706272i	$0.750376\pi$
$968$	39.8052	1.27939
$969$	4.88970	0.157080
$970$	174.176	5.59247
$971$	−41.9576	−1.34648	−0.673241	−	0.739423i	$-0.735098\pi$
$971$	−41.9576	−1.34648	−0.673241	+	0.739423i	$0.735098\pi$
$972$	−33.5839	−1.07720
$973$	−27.5568	−0.883432
$974$	38.0735	1.21995
$975$	18.5654	0.594568
$976$	−12.6149	−0.403794
$977$	−17.1842	−0.549772	−0.274886	−	0.961477i	$-0.588640\pi$
$977$	−17.1842	−0.549772	−0.274886	+	0.961477i	$0.588640\pi$
$978$	5.48746	0.175470
$979$	−9.94083	−0.317710
$980$	27.3257	0.872889
$981$	11.9381	0.381156
$982$	−21.4073	−0.683134
$983$	17.0681	0.544387	0.272194	−	0.962243i	$-0.412251\pi$
$983$	17.0681	0.544387	0.272194	+	0.962243i	$0.412251\pi$
$984$	−80.6742	−2.57180
$985$	83.5501	2.66213
$986$	84.4092	2.68814
$987$	−71.0042	−2.26009
$988$	−1.76662	−0.0562036
$989$	−1.51999	−0.0483329
$990$	10.8875	0.346028
$991$	43.0949	1.36895	0.684477	−	0.729035i	$-0.260031\pi$
$991$	43.0949	1.36895	0.684477	+	0.729035i	$0.260031\pi$
$992$	10.6549	0.338292
$993$	−49.9753	−1.58592
$994$	−97.3908	−3.08905
$995$	26.1821	0.830028
$996$	51.8129	1.64176
$997$	−42.6534	−1.35085	−0.675423	−	0.737431i	$-0.736039\pi$
$997$	−42.6534	−1.35085	−0.675423	+	0.737431i	$0.736039\pi$
$998$	29.2237	0.925061
$999$	22.6216	0.715717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.14	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.14	✓	130	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40942 q^{2} +1.96845 q^{3} +3.80532 q^{4} +3.79888 q^{5} -4.74282 q^{6} +2.98166 q^{7} -4.34977 q^{8} +0.874791 q^{9} +O(q^{10})\)	\(q-2.40942 q^{2} +1.96845 q^{3} +3.80532 q^{4} +3.79888 q^{5} -4.74282 q^{6} +2.98166 q^{7} -4.34977 q^{8} +0.874791 q^{9} -9.15310 q^{10} -1.35974 q^{11} +7.49057 q^{12} +1.00000 q^{13} -7.18407 q^{14} +7.47790 q^{15} +2.86980 q^{16} -5.35064 q^{17} -2.10774 q^{18} -0.464250 q^{19} +14.4559 q^{20} +5.86924 q^{21} +3.27619 q^{22} +0.348953 q^{23} -8.56230 q^{24} +9.43148 q^{25} -2.40942 q^{26} -4.18337 q^{27} +11.3461 q^{28} +6.54744 q^{29} -18.0174 q^{30} +5.96916 q^{31} +1.78498 q^{32} -2.67658 q^{33} +12.8919 q^{34} +11.3270 q^{35} +3.32886 q^{36} -5.40752 q^{37} +1.11857 q^{38} +1.96845 q^{39} -16.5242 q^{40} +9.42203 q^{41} -14.1415 q^{42} -4.35586 q^{43} -5.17425 q^{44} +3.32323 q^{45} -0.840776 q^{46} -12.0977 q^{47} +5.64905 q^{48} +1.89028 q^{49} -22.7244 q^{50} -10.5325 q^{51} +3.80532 q^{52} +8.04339 q^{53} +10.0795 q^{54} -5.16550 q^{55} -12.9695 q^{56} -0.913853 q^{57} -15.7755 q^{58} +10.2915 q^{59} +28.4558 q^{60} -4.39575 q^{61} -14.3822 q^{62} +2.60833 q^{63} -10.0404 q^{64} +3.79888 q^{65} +6.44902 q^{66} +10.5521 q^{67} -20.3609 q^{68} +0.686897 q^{69} -27.2914 q^{70} +13.5565 q^{71} -3.80514 q^{72} -6.73002 q^{73} +13.0290 q^{74} +18.5654 q^{75} -1.76662 q^{76} -4.05429 q^{77} -4.74282 q^{78} -0.0421621 q^{79} +10.9020 q^{80} -10.8591 q^{81} -22.7017 q^{82} +6.91709 q^{83} +22.3343 q^{84} -20.3264 q^{85} +10.4951 q^{86} +12.8883 q^{87} +5.91456 q^{88} +7.31082 q^{89} -8.00705 q^{90} +2.98166 q^{91} +1.32788 q^{92} +11.7500 q^{93} +29.1484 q^{94} -1.76363 q^{95} +3.51365 q^{96} -19.0292 q^{97} -4.55448 q^{98} -1.18949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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