LMFDB - Embedded newform 8006.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.29820 q^{3} +1.00000 q^{4} -2.18058 q^{5} +2.29820 q^{6} -2.19565 q^{7} -1.00000 q^{8} +2.28173 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.29820 q^{3} +1.00000 q^{4} -2.18058 q^{5} +2.29820 q^{6} -2.19565 q^{7} -1.00000 q^{8} +2.28173 q^{9} +2.18058 q^{10} +2.01349 q^{11} -2.29820 q^{12} +5.59844 q^{13} +2.19565 q^{14} +5.01140 q^{15} +1.00000 q^{16} -7.63974 q^{17} -2.28173 q^{18} -4.44158 q^{19} -2.18058 q^{20} +5.04604 q^{21} -2.01349 q^{22} -3.40420 q^{23} +2.29820 q^{24} -0.245092 q^{25} -5.59844 q^{26} +1.65073 q^{27} -2.19565 q^{28} +4.10269 q^{29} -5.01140 q^{30} -5.58445 q^{31} -1.00000 q^{32} -4.62740 q^{33} +7.63974 q^{34} +4.78778 q^{35} +2.28173 q^{36} +4.54658 q^{37} +4.44158 q^{38} -12.8663 q^{39} +2.18058 q^{40} +6.57036 q^{41} -5.04604 q^{42} +10.4771 q^{43} +2.01349 q^{44} -4.97548 q^{45} +3.40420 q^{46} +2.02834 q^{47} -2.29820 q^{48} -2.17912 q^{49} +0.245092 q^{50} +17.5577 q^{51} +5.59844 q^{52} -8.39315 q^{53} -1.65073 q^{54} -4.39057 q^{55} +2.19565 q^{56} +10.2077 q^{57} -4.10269 q^{58} +13.0317 q^{59} +5.01140 q^{60} -13.3102 q^{61} +5.58445 q^{62} -5.00987 q^{63} +1.00000 q^{64} -12.2078 q^{65} +4.62740 q^{66} -10.7555 q^{67} -7.63974 q^{68} +7.82353 q^{69} -4.78778 q^{70} -14.9537 q^{71} -2.28173 q^{72} +4.63376 q^{73} -4.54658 q^{74} +0.563270 q^{75} -4.44158 q^{76} -4.42092 q^{77} +12.8663 q^{78} -0.0737574 q^{79} -2.18058 q^{80} -10.6389 q^{81} -6.57036 q^{82} +16.1164 q^{83} +5.04604 q^{84} +16.6590 q^{85} -10.4771 q^{86} -9.42880 q^{87} -2.01349 q^{88} +1.78338 q^{89} +4.97548 q^{90} -12.2922 q^{91} -3.40420 q^{92} +12.8342 q^{93} -2.02834 q^{94} +9.68521 q^{95} +2.29820 q^{96} -9.35237 q^{97} +2.17912 q^{98} +4.59424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) $ 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.29820	−1.32687	−0.663433	−	0.748235i	$-0.730901\pi$
$3$	−2.29820	−1.32687	−0.663433	+	0.748235i	$0.730901\pi$
$4$	1.00000	0.500000
$5$	−2.18058	−0.975183	−0.487591	−	0.873072i	$-0.662124\pi$
$5$	−2.18058	−0.975183	−0.487591	+	0.873072i	$0.662124\pi$
$6$	2.29820	0.938237
$7$	−2.19565	−0.829878	−0.414939	−	0.909849i	$-0.636197\pi$
$7$	−2.19565	−0.829878	−0.414939	+	0.909849i	$0.636197\pi$
$8$	−1.00000	−0.353553
$9$	2.28173	0.760576
$10$	2.18058	0.689558
$11$	2.01349	0.607090	0.303545	−	0.952817i	$-0.401830\pi$
$11$	2.01349	0.607090	0.303545	+	0.952817i	$0.401830\pi$
$12$	−2.29820	−0.663433
$13$	5.59844	1.55273	0.776364	−	0.630285i	$-0.217062\pi$
$13$	5.59844	1.55273	0.776364	+	0.630285i	$0.217062\pi$
$14$	2.19565	0.586812
$15$	5.01140	1.29394
$16$	1.00000	0.250000
$17$	−7.63974	−1.85291	−0.926455	−	0.376406i	$-0.877160\pi$
$17$	−7.63974	−1.85291	−0.926455	+	0.376406i	$0.877160\pi$
$18$	−2.28173	−0.537808
$19$	−4.44158	−1.01897	−0.509485	−	0.860480i	$-0.670164\pi$
$19$	−4.44158	−1.01897	−0.509485	+	0.860480i	$0.670164\pi$
$20$	−2.18058	−0.487591
$21$	5.04604	1.10114
$22$	−2.01349	−0.429277
$23$	−3.40420	−0.709825	−0.354912	−	0.934900i	$-0.615489\pi$
$23$	−3.40420	−0.709825	−0.354912	+	0.934900i	$0.615489\pi$
$24$	2.29820	0.469118
$25$	−0.245092	−0.0490183
$26$	−5.59844	−1.09794
$27$	1.65073	0.317684
$28$	−2.19565	−0.414939
$29$	4.10269	0.761850	0.380925	−	0.924606i	$-0.375606\pi$
$29$	4.10269	0.761850	0.380925	+	0.924606i	$0.375606\pi$
$30$	−5.01140	−0.914952
$31$	−5.58445	−1.00300	−0.501498	−	0.865159i	$-0.667218\pi$
$31$	−5.58445	−1.00300	−0.501498	+	0.865159i	$0.667218\pi$
$32$	−1.00000	−0.176777
$33$	−4.62740	−0.805528
$34$	7.63974	1.31021
$35$	4.78778	0.809282
$36$	2.28173	0.380288
$37$	4.54658	0.747452	0.373726	−	0.927539i	$-0.378080\pi$
$37$	4.54658	0.747452	0.373726	+	0.927539i	$0.378080\pi$
$38$	4.44158	0.720520
$39$	−12.8663	−2.06026
$40$	2.18058	0.344779
$41$	6.57036	1.02612	0.513059	−	0.858354i	$-0.328512\pi$
$41$	6.57036	1.02612	0.513059	+	0.858354i	$0.328512\pi$
$42$	−5.04604	−0.778621
$43$	10.4771	1.59774	0.798871	−	0.601502i	$-0.205431\pi$
$43$	10.4771	1.59774	0.798871	+	0.601502i	$0.205431\pi$
$44$	2.01349	0.303545
$45$	−4.97548	−0.741701
$46$	3.40420	0.501922
$47$	2.02834	0.295863	0.147932	−	0.988998i	$-0.452738\pi$
$47$	2.02834	0.295863	0.147932	+	0.988998i	$0.452738\pi$
$48$	−2.29820	−0.331717
$49$	−2.17912	−0.311303
$50$	0.245092	0.0346612
$51$	17.5577	2.45856
$52$	5.59844	0.776364
$53$	−8.39315	−1.15289	−0.576444	−	0.817137i	$-0.695560\pi$
$53$	−8.39315	−1.15289	−0.576444	+	0.817137i	$0.695560\pi$
$54$	−1.65073	−0.224636
$55$	−4.39057	−0.592024
$56$	2.19565	0.293406
$57$	10.2077	1.35204
$58$	−4.10269	−0.538709
$59$	13.0317	1.69658	0.848292	−	0.529529i	$-0.177631\pi$
$59$	13.0317	1.69658	0.848292	+	0.529529i	$0.177631\pi$
$60$	5.01140	0.646969
$61$	−13.3102	−1.70420	−0.852100	−	0.523379i	$-0.824671\pi$
$61$	−13.3102	−1.70420	−0.852100	+	0.523379i	$0.824671\pi$
$62$	5.58445	0.709226
$63$	−5.00987	−0.631185
$64$	1.00000	0.125000
$65$	−12.2078	−1.51419
$66$	4.62740	0.569594
$67$	−10.7555	−1.31399	−0.656996	−	0.753894i	$-0.728173\pi$
$67$	−10.7555	−1.31399	−0.656996	+	0.753894i	$0.728173\pi$
$68$	−7.63974	−0.926455
$69$	7.82353	0.941843
$70$	−4.78778	−0.572249
$71$	−14.9537	−1.77468	−0.887339	−	0.461117i	$-0.847449\pi$
$71$	−14.9537	−1.77468	−0.887339	+	0.461117i	$0.847449\pi$
$72$	−2.28173	−0.268904
$73$	4.63376	0.542340	0.271170	−	0.962531i	$-0.412589\pi$
$73$	4.63376	0.542340	0.271170	+	0.962531i	$0.412589\pi$
$74$	−4.54658	−0.528529
$75$	0.563270	0.0650408
$76$	−4.44158	−0.509485
$77$	−4.42092	−0.503810
$78$	12.8663	1.45683
$79$	−0.0737574	−0.00829836	−0.00414918	−	0.999991i	$-0.501321\pi$
$79$	−0.0737574	−0.00829836	−0.00414918	+	0.999991i	$0.501321\pi$
$80$	−2.18058	−0.243796
$81$	−10.6389	−1.18210
$82$	−6.57036	−0.725574
$83$	16.1164	1.76900	0.884500	−	0.466539i	$-0.154499\pi$
$83$	16.1164	1.76900	0.884500	+	0.466539i	$0.154499\pi$
$84$	5.04604	0.550569
$85$	16.6590	1.80693
$86$	−10.4771	−1.12977
$87$	−9.42880	−1.01087
$88$	−2.01349	−0.214639
$89$	1.78338	0.189038	0.0945191	−	0.995523i	$-0.469869\pi$
$89$	1.78338	0.189038	0.0945191	+	0.995523i	$0.469869\pi$
$90$	4.97548	0.524462
$91$	−12.2922	−1.28857
$92$	−3.40420	−0.354912
$93$	12.8342	1.33084
$94$	−2.02834	−0.209207
$95$	9.68521	0.993681
$96$	2.29820	0.234559
$97$	−9.35237	−0.949590	−0.474795	−	0.880097i	$-0.657478\pi$
$97$	−9.35237	−0.949590	−0.474795	+	0.880097i	$0.657478\pi$
$98$	2.17912	0.220125
$99$	4.59424	0.461738
$100$	−0.245092	−0.0245092
$101$	9.45194	0.940503	0.470251	−	0.882532i	$-0.344163\pi$
$101$	9.45194	0.940503	0.470251	+	0.882532i	$0.344163\pi$
$102$	−17.5577	−1.73847
$103$	0.291050	0.0286780	0.0143390	−	0.999897i	$-0.495436\pi$
$103$	0.291050	0.0286780	0.0143390	+	0.999897i	$0.495436\pi$
$104$	−5.59844	−0.548972
$105$	−11.0033	−1.07381
$106$	8.39315	0.815215
$107$	19.8580	1.91975	0.959873	−	0.280434i	$-0.0904783\pi$
$107$	19.8580	1.91975	0.959873	+	0.280434i	$0.0904783\pi$
$108$	1.65073	0.158842
$109$	−14.6496	−1.40318	−0.701588	−	0.712583i	$-0.747525\pi$
$109$	−14.6496	−1.40318	−0.701588	+	0.712583i	$0.747525\pi$
$110$	4.39057	0.418624
$111$	−10.4489	−0.991770
$112$	−2.19565	−0.207469
$113$	2.58478	0.243155	0.121578	−	0.992582i	$-0.461205\pi$
$113$	2.58478	0.243155	0.121578	+	0.992582i	$0.461205\pi$
$114$	−10.2077	−0.956034
$115$	7.42311	0.692209
$116$	4.10269	0.380925
$117$	12.7741	1.18097
$118$	−13.0317	−1.19967
$119$	16.7742	1.53769
$120$	−5.01140	−0.457476
$121$	−6.94586	−0.631442
$122$	13.3102	1.20505
$123$	−15.1000	−1.36152
$124$	−5.58445	−0.501498
$125$	11.4373	1.02298
$126$	5.00987	0.446315
$127$	19.5266	1.73270	0.866351	−	0.499435i	$-0.166459\pi$
$127$	19.5266	1.73270	0.866351	+	0.499435i	$0.166459\pi$
$128$	−1.00000	−0.0883883
$129$	−24.0785	−2.11999
$130$	12.2078	1.07070
$131$	21.3411	1.86458	0.932291	−	0.361710i	$-0.117807\pi$
$131$	21.3411	1.86458	0.932291	+	0.361710i	$0.117807\pi$
$132$	−4.62740	−0.402764
$133$	9.75216	0.845619
$134$	10.7555	0.929133
$135$	−3.59955	−0.309800
$136$	7.63974	0.655103
$137$	5.64873	0.482604	0.241302	−	0.970450i	$-0.422426\pi$
$137$	5.64873	0.482604	0.241302	+	0.970450i	$0.422426\pi$
$138$	−7.82353	−0.665983
$139$	−15.8319	−1.34285	−0.671423	−	0.741074i	$-0.734317\pi$
$139$	−15.8319	−1.34285	−0.671423	+	0.741074i	$0.734317\pi$
$140$	4.78778	0.404641
$141$	−4.66152	−0.392571
$142$	14.9537	1.25489
$143$	11.2724	0.942645
$144$	2.28173	0.190144
$145$	−8.94621	−0.742943
$146$	−4.63376	−0.383492
$147$	5.00806	0.413058
$148$	4.54658	0.373726
$149$	9.99395	0.818736	0.409368	−	0.912369i	$-0.365749\pi$
$149$	9.99395	0.818736	0.409368	+	0.912369i	$0.365749\pi$
$150$	−0.563270	−0.0459908
$151$	−14.2196	−1.15717	−0.578586	−	0.815621i	$-0.696395\pi$
$151$	−14.2196	−1.15717	−0.578586	+	0.815621i	$0.696395\pi$
$152$	4.44158	0.360260
$153$	−17.4318	−1.40928
$154$	4.42092	0.356248
$155$	12.1773	0.978106
$156$	−12.8663	−1.03013
$157$	21.3784	1.70618	0.853089	−	0.521765i	$-0.174726\pi$
$157$	21.3784	1.70618	0.853089	+	0.521765i	$0.174726\pi$
$158$	0.0737574	0.00586783
$159$	19.2891	1.52973
$160$	2.18058	0.172390
$161$	7.47443	0.589067
$162$	10.6389	0.835871
$163$	18.9662	1.48555	0.742775	−	0.669541i	$-0.233509\pi$
$163$	18.9662	1.48555	0.742775	+	0.669541i	$0.233509\pi$
$164$	6.57036	0.513059
$165$	10.0904	0.785537
$166$	−16.1164	−1.25087
$167$	18.9064	1.46302	0.731510	−	0.681831i	$-0.238816\pi$
$167$	18.9064	1.46302	0.731510	+	0.681831i	$0.238816\pi$
$168$	−5.04604	−0.389311
$169$	18.3425	1.41096
$170$	−16.6590	−1.27769
$171$	−10.1345	−0.775003
$172$	10.4771	0.798871
$173$	−4.61985	−0.351241	−0.175621	−	0.984458i	$-0.556193\pi$
$173$	−4.61985	−0.351241	−0.175621	+	0.984458i	$0.556193\pi$
$174$	9.42880	0.714795
$175$	0.538135	0.0406792
$176$	2.01349	0.151773
$177$	−29.9495	−2.25114
$178$	−1.78338	−0.133670
$179$	6.41821	0.479719	0.239860	−	0.970808i	$-0.422899\pi$
$179$	6.41821	0.479719	0.239860	+	0.970808i	$0.422899\pi$
$180$	−4.97548	−0.370850
$181$	7.75724	0.576591	0.288295	−	0.957542i	$-0.406911\pi$
$181$	7.75724	0.576591	0.288295	+	0.957542i	$0.406911\pi$
$182$	12.2922	0.911159
$183$	30.5896	2.26125
$184$	3.40420	0.250961
$185$	−9.91415	−0.728903
$186$	−12.8342	−0.941049
$187$	−15.3825	−1.12488
$188$	2.02834	0.147932
$189$	−3.62443	−0.263639
$190$	−9.68521	−0.702639
$191$	−7.55847	−0.546912	−0.273456	−	0.961885i	$-0.588167\pi$
$191$	−7.55847	−0.546912	−0.273456	+	0.961885i	$0.588167\pi$
$192$	−2.29820	−0.165858
$193$	−2.88714	−0.207821	−0.103910	−	0.994587i	$-0.533136\pi$
$193$	−2.88714	−0.207821	−0.103910	+	0.994587i	$0.533136\pi$
$194$	9.35237	0.671461
$195$	28.0560	2.00913
$196$	−2.17912	−0.155652
$197$	11.7090	0.834228	0.417114	−	0.908854i	$-0.363041\pi$
$197$	11.7090	0.834228	0.417114	+	0.908854i	$0.363041\pi$
$198$	−4.59424	−0.326498
$199$	−5.97389	−0.423478	−0.211739	−	0.977326i	$-0.567913\pi$
$199$	−5.97389	−0.423478	−0.211739	+	0.977326i	$0.567913\pi$
$200$	0.245092	0.0173306
$201$	24.7183	1.74349
$202$	−9.45194	−0.665036
$203$	−9.00806	−0.632242
$204$	17.5577	1.22928
$205$	−14.3272	−1.00065
$206$	−0.291050	−0.0202784
$207$	−7.76745	−0.539875
$208$	5.59844	0.388182
$209$	−8.94308	−0.618606
$210$	11.0033	0.759298
$211$	14.0880	0.969856	0.484928	−	0.874554i	$-0.338846\pi$
$211$	14.0880	0.969856	0.484928	+	0.874554i	$0.338846\pi$
$212$	−8.39315	−0.576444
$213$	34.3666	2.35476
$214$	−19.8580	−1.35747
$215$	−22.8461	−1.55809
$216$	−1.65073	−0.112318
$217$	12.2615	0.832365
$218$	14.6496	0.992195
$219$	−10.6493	−0.719613
$220$	−4.39057	−0.296012
$221$	−42.7706	−2.87706
$222$	10.4489	0.701287
$223$	15.0007	1.00452	0.502262	−	0.864716i	$-0.332501\pi$
$223$	15.0007	1.00452	0.502262	+	0.864716i	$0.332501\pi$
$224$	2.19565	0.146703
$225$	−0.559232	−0.0372822
$226$	−2.58478	−0.171937
$227$	21.1405	1.40315	0.701573	−	0.712598i	$-0.252482\pi$
$227$	21.1405	1.40315	0.701573	+	0.712598i	$0.252482\pi$
$228$	10.2077	0.676018
$229$	−10.9570	−0.724061	−0.362030	−	0.932166i	$-0.617916\pi$
$229$	−10.9570	−0.724061	−0.362030	+	0.932166i	$0.617916\pi$
$230$	−7.42311	−0.489466
$231$	10.1602	0.668489
$232$	−4.10269	−0.269354
$233$	0.0335061	0.00219506	0.00109753	−	0.999999i	$-0.499651\pi$
$233$	0.0335061	0.00219506	0.00109753	+	0.999999i	$0.499651\pi$
$234$	−12.7741	−0.835070
$235$	−4.42294	−0.288521
$236$	13.0317	0.848292
$237$	0.169509	0.0110108
$238$	−16.7742	−1.08731
$239$	−2.18499	−0.141335	−0.0706675	−	0.997500i	$-0.522513\pi$
$239$	−2.18499	−0.141335	−0.0706675	+	0.997500i	$0.522513\pi$
$240$	5.01140	0.323484
$241$	6.16740	0.397277	0.198638	−	0.980073i	$-0.436348\pi$
$241$	6.16740	0.397277	0.198638	+	0.980073i	$0.436348\pi$
$242$	6.94586	0.446497
$243$	19.4981	1.25081
$244$	−13.3102	−0.852100
$245$	4.75174	0.303578
$246$	15.1000	0.962741
$247$	−24.8659	−1.58218
$248$	5.58445	0.354613
$249$	−37.0386	−2.34723
$250$	−11.4373	−0.723359
$251$	−12.7541	−0.805030	−0.402515	−	0.915413i	$-0.631864\pi$
$251$	−12.7541	−0.805030	−0.402515	+	0.915413i	$0.631864\pi$
$252$	−5.00987	−0.315592
$253$	−6.85432	−0.430927
$254$	−19.5266	−1.22521
$255$	−38.2858	−2.39755
$256$	1.00000	0.0625000
$257$	−7.67858	−0.478977	−0.239488	−	0.970899i	$-0.576980\pi$
$257$	−7.67858	−0.478977	−0.239488	+	0.970899i	$0.576980\pi$
$258$	24.0785	1.49906
$259$	−9.98269	−0.620294
$260$	−12.2078	−0.757096
$261$	9.36121	0.579444
$262$	−21.3411	−1.31846
$263$	−18.4854	−1.13986	−0.569929	−	0.821694i	$-0.693029\pi$
$263$	−18.4854	−1.13986	−0.569929	+	0.821694i	$0.693029\pi$
$264$	4.62740	0.284797
$265$	18.3019	1.12428
$266$	−9.75216	−0.597943
$267$	−4.09857	−0.250829
$268$	−10.7555	−0.656996
$269$	24.1976	1.47535	0.737677	−	0.675153i	$-0.235923\pi$
$269$	24.1976	1.47535	0.737677	+	0.675153i	$0.235923\pi$
$270$	3.59955	0.219062
$271$	−28.5509	−1.73434	−0.867172	−	0.498009i	$-0.834065\pi$
$271$	−28.5509	−1.73434	−0.867172	+	0.498009i	$0.834065\pi$
$272$	−7.63974	−0.463227
$273$	28.2500	1.70977
$274$	−5.64873	−0.341252
$275$	−0.493489	−0.0297585
$276$	7.82353	0.470921
$277$	13.9646	0.839053	0.419527	−	0.907743i	$-0.362196\pi$
$277$	13.9646	0.839053	0.419527	+	0.907743i	$0.362196\pi$
$278$	15.8319	0.949536
$279$	−12.7422	−0.762855
$280$	−4.78778	−0.286125
$281$	−10.6037	−0.632564	−0.316282	−	0.948665i	$-0.602435\pi$
$281$	−10.6037	−0.632564	−0.316282	+	0.948665i	$0.602435\pi$
$282$	4.66152	0.277590
$283$	−13.8262	−0.821881	−0.410941	−	0.911662i	$-0.634800\pi$
$283$	−13.8262	−0.821881	−0.410941	+	0.911662i	$0.634800\pi$
$284$	−14.9537	−0.887339
$285$	−22.2585	−1.31848
$286$	−11.2724	−0.666551
$287$	−14.4262	−0.851552
$288$	−2.28173	−0.134452
$289$	41.3657	2.43327
$290$	8.94621	0.525340
$291$	21.4936	1.25998
$292$	4.63376	0.271170
$293$	−17.5255	−1.02385	−0.511924	−	0.859031i	$-0.671067\pi$
$293$	−17.5255	−1.02385	−0.511924	+	0.859031i	$0.671067\pi$
$294$	−5.00806	−0.292076
$295$	−28.4166	−1.65448
$296$	−4.54658	−0.264264
$297$	3.32374	0.192863
$298$	−9.99395	−0.578934
$299$	−19.0582	−1.10216
$300$	0.563270	0.0325204
$301$	−23.0040	−1.32593
$302$	14.2196	0.818244
$303$	−21.7225	−1.24792
$304$	−4.44158	−0.254742
$305$	29.0240	1.66191
$306$	17.4318	0.996510
$307$	23.3646	1.33349	0.666743	−	0.745287i	$-0.267688\pi$
$307$	23.3646	1.33349	0.666743	+	0.745287i	$0.267688\pi$
$308$	−4.42092	−0.251905
$309$	−0.668891	−0.0380519
$310$	−12.1773	−0.691625
$311$	12.0788	0.684923	0.342462	−	0.939532i	$-0.388739\pi$
$311$	12.0788	0.684923	0.342462	+	0.939532i	$0.388739\pi$
$312$	12.8663	0.728413
$313$	3.01385	0.170353	0.0851764	−	0.996366i	$-0.472855\pi$
$313$	3.01385	0.170353	0.0851764	+	0.996366i	$0.472855\pi$
$314$	−21.3784	−1.20645
$315$	10.9244	0.615521
$316$	−0.0737574	−0.00414918
$317$	−20.3049	−1.14044	−0.570219	−	0.821493i	$-0.693141\pi$
$317$	−20.3049	−1.14044	−0.570219	+	0.821493i	$0.693141\pi$
$318$	−19.2891	−1.08168
$319$	8.26071	0.462511
$320$	−2.18058	−0.121898
$321$	−45.6377	−2.54725
$322$	−7.47443	−0.416534
$323$	33.9326	1.88806
$324$	−10.6389	−0.591050
$325$	−1.37213	−0.0761121
$326$	−18.9662	−1.05044
$327$	33.6677	1.86183
$328$	−6.57036	−0.362787
$329$	−4.45352	−0.245530
$330$	−10.0904	−0.555458
$331$	−23.3354	−1.28263	−0.641316	−	0.767277i	$-0.721611\pi$
$331$	−23.3354	−1.28263	−0.641316	+	0.767277i	$0.721611\pi$
$332$	16.1164	0.884500
$333$	10.3740	0.568494
$334$	−18.9064	−1.03451
$335$	23.4532	1.28138
$336$	5.04604	0.275284
$337$	−5.87888	−0.320243	−0.160122	−	0.987097i	$-0.551189\pi$
$337$	−5.87888	−0.320243	−0.160122	+	0.987097i	$0.551189\pi$
$338$	−18.3425	−0.997701
$339$	−5.94034	−0.322635
$340$	16.6590	0.903463
$341$	−11.2442	−0.608909
$342$	10.1345	0.548010
$343$	20.1541	1.08822
$344$	−10.4771	−0.564887
$345$	−17.0598	−0.918469
$346$	4.61985	0.248365
$347$	12.1058	0.649875	0.324937	−	0.945736i	$-0.394657\pi$
$347$	12.1058	0.649875	0.324937	+	0.945736i	$0.394657\pi$
$348$	−9.42880	−0.505436
$349$	−6.46652	−0.346145	−0.173072	−	0.984909i	$-0.555369\pi$
$349$	−6.46652	−0.346145	−0.173072	+	0.984909i	$0.555369\pi$
$350$	−0.538135	−0.0287645
$351$	9.24153	0.493277
$352$	−2.01349	−0.107319
$353$	−29.9215	−1.59256	−0.796282	−	0.604926i	$-0.793203\pi$
$353$	−29.9215	−1.59256	−0.796282	+	0.604926i	$0.793203\pi$
$354$	29.9495	1.59180
$355$	32.6077	1.73064
$356$	1.78338	0.0945191
$357$	−38.5505	−2.04031
$358$	−6.41821	−0.339213
$359$	17.6224	0.930076	0.465038	−	0.885291i	$-0.346041\pi$
$359$	17.6224	0.930076	0.465038	+	0.885291i	$0.346041\pi$
$360$	4.97548	0.262231
$361$	0.727659	0.0382979
$362$	−7.75724	−0.407711
$363$	15.9630	0.837839
$364$	−12.2922	−0.644287
$365$	−10.1043	−0.528881
$366$	−30.5896	−1.59894
$367$	8.64327	0.451175	0.225587	−	0.974223i	$-0.427570\pi$
$367$	8.64327	0.451175	0.225587	+	0.974223i	$0.427570\pi$
$368$	−3.40420	−0.177456
$369$	14.9918	0.780440
$370$	9.91415	0.515412
$371$	18.4284	0.956756
$372$	12.8342	0.665422
$373$	−17.9368	−0.928732	−0.464366	−	0.885643i	$-0.653718\pi$
$373$	−17.9368	−0.928732	−0.464366	+	0.885643i	$0.653718\pi$
$374$	15.3825	0.795412
$375$	−26.2853	−1.35736
$376$	−2.02834	−0.104603
$377$	22.9686	1.18294
$378$	3.62443	0.186421
$379$	12.3158	0.632621	0.316310	−	0.948656i	$-0.397556\pi$
$379$	12.3158	0.632621	0.316310	+	0.948656i	$0.397556\pi$
$380$	9.68521	0.496841
$381$	−44.8760	−2.29907
$382$	7.55847	0.386725
$383$	−33.1458	−1.69367	−0.846835	−	0.531856i	$-0.821495\pi$
$383$	−33.1458	−1.69367	−0.846835	+	0.531856i	$0.821495\pi$
$384$	2.29820	0.117280
$385$	9.64014	0.491307
$386$	2.88714	0.146952
$387$	23.9059	1.21520
$388$	−9.35237	−0.474795
$389$	−34.4723	−1.74781	−0.873907	−	0.486094i	$-0.838421\pi$
$389$	−34.4723	−1.74781	−0.873907	+	0.486094i	$0.838421\pi$
$390$	−28.0560	−1.42067
$391$	26.0072	1.31524
$392$	2.17912	0.110062
$393$	−49.0461	−2.47405
$394$	−11.7090	−0.589889
$395$	0.160834	0.00809242
$396$	4.59424	0.230869
$397$	1.10127	0.0552711	0.0276355	−	0.999618i	$-0.491202\pi$
$397$	1.10127	0.0552711	0.0276355	+	0.999618i	$0.491202\pi$
$398$	5.97389	0.299444
$399$	−22.4124	−1.12202
$400$	−0.245092	−0.0122546
$401$	−16.6359	−0.830756	−0.415378	−	0.909649i	$-0.636351\pi$
$401$	−16.6359	−0.830756	−0.415378	+	0.909649i	$0.636351\pi$
$402$	−24.7183	−1.23284
$403$	−31.2642	−1.55738
$404$	9.45194	0.470251
$405$	23.1989	1.15276
$406$	9.00806	0.447062
$407$	9.15448	0.453771
$408$	−17.5577	−0.869234
$409$	−2.83116	−0.139992	−0.0699960	−	0.997547i	$-0.522299\pi$
$409$	−2.83116	−0.139992	−0.0699960	+	0.997547i	$0.522299\pi$
$410$	14.3272	0.707568
$411$	−12.9819	−0.640351
$412$	0.291050	0.0143390
$413$	−28.6131	−1.40796
$414$	7.76745	0.381750
$415$	−35.1429	−1.72510
$416$	−5.59844	−0.274486
$417$	36.3849	1.78178
$418$	8.94308	0.437420
$419$	−19.5984	−0.957445	−0.478722	−	0.877966i	$-0.658900\pi$
$419$	−19.5984	−0.957445	−0.478722	+	0.877966i	$0.658900\pi$
$420$	−11.0033	−0.536905
$421$	−14.0310	−0.683828	−0.341914	−	0.939731i	$-0.611075\pi$
$421$	−14.0310	−0.683828	−0.341914	+	0.939731i	$0.611075\pi$
$422$	−14.0880	−0.685791
$423$	4.62811	0.225026
$424$	8.39315	0.407607
$425$	1.87244	0.0908265
$426$	−34.3666	−1.66507
$427$	29.2246	1.41428
$428$	19.8580	0.959873
$429$	−25.9062	−1.25076
$430$	22.8461	1.10174
$431$	29.7640	1.43368	0.716842	−	0.697236i	$-0.245587\pi$
$431$	29.7640	1.43368	0.716842	+	0.697236i	$0.245587\pi$
$432$	1.65073	0.0794210
$433$	2.06879	0.0994195	0.0497097	−	0.998764i	$-0.484170\pi$
$433$	2.06879	0.0994195	0.0497097	+	0.998764i	$0.484170\pi$
$434$	−12.2615	−0.588571
$435$	20.5602	0.985786
$436$	−14.6496	−0.701588
$437$	15.1200	0.723289
$438$	10.6493	0.508843
$439$	5.10555	0.243675	0.121837	−	0.992550i	$-0.461121\pi$
$439$	5.10555	0.243675	0.121837	+	0.992550i	$0.461121\pi$
$440$	4.39057	0.209312
$441$	−4.97217	−0.236770
$442$	42.7706	2.03439
$443$	−16.1599	−0.767779	−0.383889	−	0.923379i	$-0.625416\pi$
$443$	−16.1599	−0.767779	−0.383889	+	0.923379i	$0.625416\pi$
$444$	−10.4489	−0.495885
$445$	−3.88880	−0.184347
$446$	−15.0007	−0.710305
$447$	−22.9681	−1.08635
$448$	−2.19565	−0.103735
$449$	−4.06368	−0.191777	−0.0958884	−	0.995392i	$-0.530569\pi$
$449$	−4.06368	−0.191777	−0.0958884	+	0.995392i	$0.530569\pi$
$450$	0.559232	0.0263625
$451$	13.2293	0.622945
$452$	2.58478	0.121578
$453$	32.6794	1.53541
$454$	−21.1405	−0.992174
$455$	26.8041	1.25659
$456$	−10.2077	−0.478017
$457$	−5.34026	−0.249807	−0.124903	−	0.992169i	$-0.539862\pi$
$457$	−5.34026	−0.249807	−0.124903	+	0.992169i	$0.539862\pi$
$458$	10.9570	0.511988
$459$	−12.6112	−0.588640
$460$	7.42311	0.346104
$461$	7.71570	0.359356	0.179678	−	0.983725i	$-0.442494\pi$
$461$	7.71570	0.359356	0.179678	+	0.983725i	$0.442494\pi$
$462$	−10.1602	−0.472693
$463$	−32.1685	−1.49500	−0.747498	−	0.664264i	$-0.768745\pi$
$463$	−32.1685	−1.49500	−0.747498	+	0.664264i	$0.768745\pi$
$464$	4.10269	0.190462
$465$	−27.9859	−1.29782
$466$	−0.0335061	−0.00155214
$467$	−19.2142	−0.889126	−0.444563	−	0.895748i	$-0.646641\pi$
$467$	−19.2142	−0.889126	−0.444563	+	0.895748i	$0.646641\pi$
$468$	12.7741	0.590483
$469$	23.6153	1.09045
$470$	4.42294	0.204015
$471$	−49.1317	−2.26387
$472$	−13.0317	−0.599833
$473$	21.0955	0.969974
$474$	−0.169509	−0.00778583
$475$	1.08859	0.0499482
$476$	16.7742	0.768844
$477$	−19.1509	−0.876859
$478$	2.18499	0.0999389
$479$	−17.8270	−0.814537	−0.407269	−	0.913308i	$-0.633519\pi$
$479$	−17.8270	−0.814537	−0.407269	+	0.913308i	$0.633519\pi$
$480$	−5.01140	−0.228738
$481$	25.4537	1.16059
$482$	−6.16740	−0.280917
$483$	−17.1777	−0.781614
$484$	−6.94586	−0.315721
$485$	20.3936	0.926024
$486$	−19.4981	−0.884453
$487$	−34.8874	−1.58090	−0.790449	−	0.612527i	$-0.790153\pi$
$487$	−34.8874	−1.58090	−0.790449	+	0.612527i	$0.790153\pi$
$488$	13.3102	0.602526
$489$	−43.5882	−1.97113
$490$	−4.75174	−0.214662
$491$	−19.2391	−0.868249	−0.434125	−	0.900853i	$-0.642942\pi$
$491$	−19.2391	−0.868249	−0.434125	+	0.900853i	$0.642942\pi$
$492$	−15.1000	−0.680760
$493$	−31.3435	−1.41164
$494$	24.8659	1.11877
$495$	−10.0181	−0.450279
$496$	−5.58445	−0.250749
$497$	32.8331	1.47277
$498$	37.0386	1.65974
$499$	−25.2316	−1.12952	−0.564761	−	0.825255i	$-0.691031\pi$
$499$	−25.2316	−1.12952	−0.564761	+	0.825255i	$0.691031\pi$
$500$	11.4373	0.511492
$501$	−43.4507	−1.94123
$502$	12.7541	0.569243
$503$	−15.8179	−0.705286	−0.352643	−	0.935758i	$-0.614717\pi$
$503$	−15.8179	−0.705286	−0.352643	+	0.935758i	$0.614717\pi$
$504$	5.00987	0.223158
$505$	−20.6107	−0.917162
$506$	6.85432	0.304712
$507$	−42.1548	−1.87216
$508$	19.5266	0.866351
$509$	14.3548	0.636266	0.318133	−	0.948046i	$-0.396944\pi$
$509$	14.3548	0.636266	0.318133	+	0.948046i	$0.396944\pi$
$510$	38.2858	1.69532
$511$	−10.1741	−0.450076
$512$	−1.00000	−0.0441942
$513$	−7.33187	−0.323710
$514$	7.67858	0.338688
$515$	−0.634656	−0.0279663
$516$	−24.0785	−1.06000
$517$	4.08403	0.179616
$518$	9.98269	0.438614
$519$	10.6174	0.466050
$520$	12.2078	0.535348
$521$	−14.6533	−0.641974	−0.320987	−	0.947084i	$-0.604015\pi$
$521$	−14.6533	−0.641974	−0.320987	+	0.947084i	$0.604015\pi$
$522$	−9.36121	−0.409729
$523$	15.0033	0.656048	0.328024	−	0.944669i	$-0.393617\pi$
$523$	15.0033	0.656048	0.328024	+	0.944669i	$0.393617\pi$
$524$	21.3411	0.932291
$525$	−1.23674	−0.0539759
$526$	18.4854	0.806001
$527$	42.6638	1.85846
$528$	−4.62740	−0.201382
$529$	−11.4114	−0.496149
$530$	−18.3019	−0.794984
$531$	29.7348	1.29038
$532$	9.75216	0.422810
$533$	36.7837	1.59328
$534$	4.09857	0.177363
$535$	−43.3019	−1.87210
$536$	10.7555	0.464566
$537$	−14.7503	−0.636524
$538$	−24.1976	−1.04323
$539$	−4.38764	−0.188989
$540$	−3.59955	−0.154900
$541$	37.0282	1.59197	0.795984	−	0.605318i	$-0.206954\pi$
$541$	37.0282	1.59197	0.795984	+	0.605318i	$0.206954\pi$
$542$	28.5509	1.22637
$543$	−17.8277	−0.765059
$544$	7.63974	0.327551
$545$	31.9445	1.36835
$546$	−28.2500	−1.20899
$547$	−14.0568	−0.601026	−0.300513	−	0.953778i	$-0.597158\pi$
$547$	−14.0568	−0.601026	−0.300513	+	0.953778i	$0.597158\pi$
$548$	5.64873	0.241302
$549$	−30.3703	−1.29617
$550$	0.493489	0.0210425
$551$	−18.2224	−0.776301
$552$	−7.82353	−0.332992
$553$	0.161945	0.00688662
$554$	−13.9646	−0.593300
$555$	22.7847	0.967157
$556$	−15.8319	−0.671423
$557$	−8.55696	−0.362570	−0.181285	−	0.983431i	$-0.558026\pi$
$557$	−8.55696	−0.362570	−0.181285	+	0.983431i	$0.558026\pi$
$558$	12.7422	0.539420
$559$	58.6554	2.48086
$560$	4.78778	0.202321
$561$	35.3522	1.49257
$562$	10.6037	0.447290
$563$	19.8470	0.836453	0.418226	−	0.908343i	$-0.362652\pi$
$563$	19.8470	0.836453	0.418226	+	0.908343i	$0.362652\pi$
$564$	−4.66152	−0.196286
$565$	−5.63630	−0.237121
$566$	13.8262	0.581158
$567$	23.3593	0.980998
$568$	14.9537	0.627444
$569$	42.7286	1.79128	0.895638	−	0.444784i	$-0.146720\pi$
$569$	42.7286	1.79128	0.895638	+	0.444784i	$0.146720\pi$
$570$	22.2585	0.932308
$571$	−23.2706	−0.973845	−0.486923	−	0.873445i	$-0.661881\pi$
$571$	−23.2706	−0.973845	−0.486923	+	0.873445i	$0.661881\pi$
$572$	11.2724	0.471323
$573$	17.3709	0.725679
$574$	14.4262	0.602138
$575$	0.834341	0.0347944
$576$	2.28173	0.0950720
$577$	−17.4934	−0.728259	−0.364129	−	0.931348i	$-0.618633\pi$
$577$	−17.4934	−0.728259	−0.364129	+	0.931348i	$0.618633\pi$
$578$	−41.3657	−1.72059
$579$	6.63523	0.275751
$580$	−8.94621	−0.371471
$581$	−35.3859	−1.46805
$582$	−21.4936	−0.890940
$583$	−16.8995	−0.699907
$584$	−4.63376	−0.191746
$585$	−27.8549	−1.15166
$586$	17.5255	0.723970
$587$	5.07693	0.209547	0.104774	−	0.994496i	$-0.466588\pi$
$587$	5.07693	0.209547	0.104774	+	0.994496i	$0.466588\pi$
$588$	5.00806	0.206529
$589$	24.8038	1.02202
$590$	28.4166	1.16989
$591$	−26.9095	−1.10691
$592$	4.54658	0.186863
$593$	18.7248	0.768937	0.384468	−	0.923138i	$-0.374385\pi$
$593$	18.7248	0.768937	0.384468	+	0.923138i	$0.374385\pi$
$594$	−3.32374	−0.136375
$595$	−36.5774	−1.49953
$596$	9.99395	0.409368
$597$	13.7292	0.561899
$598$	19.0582	0.779348
$599$	27.3478	1.11740	0.558700	−	0.829370i	$-0.311300\pi$
$599$	27.3478	1.11740	0.558700	+	0.829370i	$0.311300\pi$
$600$	−0.563270	−0.0229954
$601$	6.75247	0.275439	0.137719	−	0.990471i	$-0.456023\pi$
$601$	6.75247	0.275439	0.137719	+	0.990471i	$0.456023\pi$
$602$	23.0040	0.937575
$603$	−24.5411	−0.999391
$604$	−14.2196	−0.578586
$605$	15.1460	0.615771
$606$	21.7225	0.882414
$607$	−17.0956	−0.693888	−0.346944	−	0.937886i	$-0.612781\pi$
$607$	−17.0956	−0.693888	−0.346944	+	0.937886i	$0.612781\pi$
$608$	4.44158	0.180130
$609$	20.7023	0.838901
$610$	−29.0240	−1.17515
$611$	11.3555	0.459395
$612$	−17.4318	−0.704639
$613$	−25.7527	−1.04014	−0.520071	−	0.854123i	$-0.674094\pi$
$613$	−25.7527	−1.04014	−0.520071	+	0.854123i	$0.674094\pi$
$614$	−23.3646	−0.942918
$615$	32.9267	1.32773
$616$	4.42092	0.178124
$617$	2.04514	0.0823342	0.0411671	−	0.999152i	$-0.486892\pi$
$617$	2.04514	0.0823342	0.0411671	+	0.999152i	$0.486892\pi$
$618$	0.668891	0.0269067
$619$	2.01680	0.0810621	0.0405310	−	0.999178i	$-0.487095\pi$
$619$	2.01680	0.0810621	0.0405310	+	0.999178i	$0.487095\pi$
$620$	12.1773	0.489053
$621$	−5.61943	−0.225500
$622$	−12.0788	−0.484314
$623$	−3.91568	−0.156879
$624$	−12.8663	−0.515066
$625$	−23.7145	−0.948579
$626$	−3.01385	−0.120458
$627$	20.5530	0.820808
$628$	21.3784	0.853089
$629$	−34.7347	−1.38496
$630$	−10.9244	−0.435239
$631$	−32.2125	−1.28236	−0.641179	−	0.767391i	$-0.721555\pi$
$631$	−32.2125	−1.28236	−0.641179	+	0.767391i	$0.721555\pi$
$632$	0.0737574	0.00293391
$633$	−32.3770	−1.28687
$634$	20.3049	0.806411
$635$	−42.5791	−1.68970
$636$	19.2891	0.764864
$637$	−12.1997	−0.483369
$638$	−8.26071	−0.327045
$639$	−34.1203	−1.34978
$640$	2.18058	0.0861948
$641$	−19.4054	−0.766468	−0.383234	−	0.923651i	$-0.625190\pi$
$641$	−19.4054	−0.766468	−0.383234	+	0.923651i	$0.625190\pi$
$642$	45.6377	1.80118
$643$	23.5922	0.930387	0.465193	−	0.885209i	$-0.345985\pi$
$643$	23.5922	0.930387	0.465193	+	0.885209i	$0.345985\pi$
$644$	7.47443	0.294534
$645$	52.5049	2.06738
$646$	−33.9326	−1.33506
$647$	41.8873	1.64676	0.823381	−	0.567490i	$-0.192085\pi$
$647$	41.8873	1.64676	0.823381	+	0.567490i	$0.192085\pi$
$648$	10.6389	0.417936
$649$	26.2392	1.02998
$650$	1.37213	0.0538194
$651$	−28.1794	−1.10444
$652$	18.9662	0.742775
$653$	−17.7598	−0.694994	−0.347497	−	0.937681i	$-0.612968\pi$
$653$	−17.7598	−0.694994	−0.347497	+	0.937681i	$0.612968\pi$
$654$	−33.6677	−1.31651
$655$	−46.5359	−1.81831
$656$	6.57036	0.256529
$657$	10.5730	0.412491
$658$	4.45352	0.173616
$659$	−17.7606	−0.691855	−0.345928	−	0.938261i	$-0.612436\pi$
$659$	−17.7606	−0.691855	−0.345928	+	0.938261i	$0.612436\pi$
$660$	10.0904	0.392768
$661$	11.3689	0.442197	0.221099	−	0.975251i	$-0.429036\pi$
$661$	11.3689	0.442197	0.221099	+	0.975251i	$0.429036\pi$
$662$	23.3354	0.906958
$663$	98.2955	3.81748
$664$	−16.1164	−0.625436
$665$	−21.2653	−0.824634
$666$	−10.3740	−0.401986
$667$	−13.9664	−0.540779
$668$	18.9064	0.731510
$669$	−34.4747	−1.33287
$670$	−23.4532	−0.906075
$671$	−26.8000	−1.03460
$672$	−5.04604	−0.194655
$673$	9.50854	0.366527	0.183264	−	0.983064i	$-0.441334\pi$
$673$	9.50854	0.366527	0.183264	+	0.983064i	$0.441334\pi$
$674$	5.87888	0.226446
$675$	−0.404581	−0.0155723
$676$	18.3425	0.705481
$677$	20.0116	0.769109	0.384554	−	0.923102i	$-0.374355\pi$
$677$	20.0116	0.769109	0.384554	+	0.923102i	$0.374355\pi$
$678$	5.94034	0.228137
$679$	20.5345	0.788043
$680$	−16.6590	−0.638845
$681$	−48.5852	−1.86179
$682$	11.2442	0.430564
$683$	−33.2865	−1.27367	−0.636836	−	0.770999i	$-0.719757\pi$
$683$	−33.2865	−1.27367	−0.636836	+	0.770999i	$0.719757\pi$
$684$	−10.1345	−0.387502
$685$	−12.3175	−0.470627
$686$	−20.1541	−0.769489
$687$	25.1815	0.960733
$688$	10.4771	0.399436
$689$	−46.9885	−1.79012
$690$	17.0598	0.649456
$691$	33.1192	1.25992	0.629958	−	0.776630i	$-0.283072\pi$
$691$	33.1192	1.25992	0.629958	+	0.776630i	$0.283072\pi$
$692$	−4.61985	−0.175621
$693$	−10.0873	−0.383186
$694$	−12.1058	−0.459531
$695$	34.5227	1.30952
$696$	9.42880	0.357398
$697$	−50.1958	−1.90130
$698$	6.46652	0.244761
$699$	−0.0770038	−0.00291255
$700$	0.538135	0.0203396
$701$	5.60254	0.211605	0.105802	−	0.994387i	$-0.466259\pi$
$701$	5.60254	0.211605	0.105802	+	0.994387i	$0.466259\pi$
$702$	−9.24153	−0.348799
$703$	−20.1940	−0.761631
$704$	2.01349	0.0758863
$705$	10.1648	0.382829
$706$	29.9215	1.12611
$707$	−20.7531	−0.780502
$708$	−29.9495	−1.12557
$709$	−11.5768	−0.434778	−0.217389	−	0.976085i	$-0.569754\pi$
$709$	−11.5768	−0.434778	−0.217389	+	0.976085i	$0.569754\pi$
$710$	−32.6077	−1.22374
$711$	−0.168294	−0.00631153
$712$	−1.78338	−0.0668351
$713$	19.0106	0.711952
$714$	38.5505	1.44272
$715$	−24.5803	−0.919251
$716$	6.41821	0.239860
$717$	5.02154	0.187533
$718$	−17.6224	−0.657663
$719$	2.22530	0.0829897	0.0414948	−	0.999139i	$-0.486788\pi$
$719$	2.22530	0.0829897	0.0414948	+	0.999139i	$0.486788\pi$
$720$	−4.97548	−0.185425
$721$	−0.639044	−0.0237992
$722$	−0.727659	−0.0270807
$723$	−14.1739	−0.527134
$724$	7.75724	0.288295
$725$	−1.00553	−0.0373446
$726$	−15.9630	−0.592442
$727$	−1.61322	−0.0598312	−0.0299156	−	0.999552i	$-0.509524\pi$
$727$	−1.61322	−0.0598312	−0.0299156	+	0.999552i	$0.509524\pi$
$728$	12.2922	0.455579
$729$	−12.8939	−0.477553
$730$	10.1043	0.373975
$731$	−80.0423	−2.96047
$732$	30.5896	1.13062
$733$	−5.61249	−0.207302	−0.103651	−	0.994614i	$-0.533053\pi$
$733$	−5.61249	−0.207302	−0.103651	+	0.994614i	$0.533053\pi$
$734$	−8.64327	−0.319029
$735$	−10.9205	−0.402807
$736$	3.40420	0.125480
$737$	−21.6561	−0.797712
$738$	−14.9918	−0.551854
$739$	−1.33294	−0.0490332	−0.0245166	−	0.999699i	$-0.507805\pi$
$739$	−1.33294	−0.0490332	−0.0245166	+	0.999699i	$0.507805\pi$
$740$	−9.91415	−0.364451
$741$	57.1469	2.09934
$742$	−18.4284	−0.676529
$743$	33.1972	1.21789	0.608943	−	0.793214i	$-0.291594\pi$
$743$	33.1972	1.21789	0.608943	+	0.793214i	$0.291594\pi$
$744$	−12.8342	−0.470524
$745$	−21.7926	−0.798418
$746$	17.9368	0.656713
$747$	36.7732	1.34546
$748$	−15.3825	−0.562442
$749$	−43.6012	−1.59315
$750$	26.2853	0.959802
$751$	51.7652	1.88894	0.944469	−	0.328601i	$-0.106577\pi$
$751$	51.7652	1.88894	0.944469	+	0.328601i	$0.106577\pi$
$752$	2.02834	0.0739658
$753$	29.3114	1.06817
$754$	−22.9686	−0.836468
$755$	31.0068	1.12845
$756$	−3.62443	−0.131819
$757$	−51.3484	−1.86629	−0.933145	−	0.359501i	$-0.882947\pi$
$757$	−51.3484	−1.86629	−0.933145	+	0.359501i	$0.882947\pi$
$758$	−12.3158	−0.447330
$759$	15.7526	0.571783
$760$	−9.68521	−0.351319
$761$	−5.76888	−0.209122	−0.104561	−	0.994518i	$-0.533344\pi$
$761$	−5.76888	−0.209122	−0.104561	+	0.994518i	$0.533344\pi$
$762$	44.8760	1.62568
$763$	32.1654	1.16446
$764$	−7.55847	−0.273456
$765$	38.0114	1.37430
$766$	33.1458	1.19760
$767$	72.9572	2.63433
$768$	−2.29820	−0.0829292
$769$	2.84113	0.102454	0.0512268	−	0.998687i	$-0.483687\pi$
$769$	2.84113	0.102454	0.0512268	+	0.998687i	$0.483687\pi$
$770$	−9.64014	−0.347407
$771$	17.6469	0.635538
$772$	−2.88714	−0.103910
$773$	−53.0766	−1.90903	−0.954517	−	0.298157i	$-0.903628\pi$
$773$	−53.0766	−1.90903	−0.954517	+	0.298157i	$0.903628\pi$
$774$	−23.9059	−0.859279
$775$	1.36870	0.0491652
$776$	9.35237	0.335731
$777$	22.9422	0.823047
$778$	34.4723	1.23589
$779$	−29.1828	−1.04558
$780$	28.0560	1.00457
$781$	−30.1091	−1.07739
$782$	−26.0072	−0.930016
$783$	6.77244	0.242027
$784$	−2.17912	−0.0778258
$785$	−46.6171	−1.66384
$786$	49.0461	1.74942
$787$	−34.4979	−1.22972	−0.614858	−	0.788638i	$-0.710787\pi$
$787$	−34.4979	−1.22972	−0.614858	+	0.788638i	$0.710787\pi$
$788$	11.7090	0.417114
$789$	42.4831	1.51244
$790$	−0.160834	−0.00572220
$791$	−5.67527	−0.201789
$792$	−4.59424	−0.163249
$793$	−74.5165	−2.64616
$794$	−1.10127	−0.0390826
$795$	−42.0614	−1.49177
$796$	−5.97389	−0.211739
$797$	−34.9977	−1.23968	−0.619841	−	0.784727i	$-0.712803\pi$
$797$	−34.9977	−1.23968	−0.619841	+	0.784727i	$0.712803\pi$
$798$	22.4124	0.793391
$799$	−15.4960	−0.548208
$800$	0.245092	0.00866530
$801$	4.06919	0.143778
$802$	16.6359	0.587433
$803$	9.33002	0.329249
$804$	24.7183	0.871747
$805$	−16.2986	−0.574449
$806$	31.2642	1.10123
$807$	−55.6110	−1.95760
$808$	−9.45194	−0.332518
$809$	16.1957	0.569410	0.284705	−	0.958615i	$-0.408104\pi$
$809$	16.1957	0.569410	0.284705	+	0.958615i	$0.408104\pi$
$810$	−23.1989	−0.815127
$811$	48.0070	1.68575	0.842876	−	0.538108i	$-0.180861\pi$
$811$	48.0070	1.68575	0.842876	+	0.538108i	$0.180861\pi$
$812$	−9.00806	−0.316121
$813$	65.6157	2.30124
$814$	−9.15448	−0.320864
$815$	−41.3573	−1.44868
$816$	17.5577	0.614641
$817$	−46.5349	−1.62805
$818$	2.83116	0.0989893
$819$	−28.0475	−0.980058
$820$	−14.3272	−0.500326
$821$	19.4097	0.677402	0.338701	−	0.940894i	$-0.390012\pi$
$821$	19.4097	0.677402	0.338701	+	0.940894i	$0.390012\pi$
$822$	12.9819	0.452797
$823$	−43.5040	−1.51646	−0.758228	−	0.651990i	$-0.773934\pi$
$823$	−43.5040	−1.51646	−0.758228	+	0.651990i	$0.773934\pi$
$824$	−0.291050	−0.0101392
$825$	1.13414	0.0394856
$826$	28.6131	0.995576
$827$	38.7787	1.34847	0.674235	−	0.738517i	$-0.264474\pi$
$827$	38.7787	1.34847	0.674235	+	0.738517i	$0.264474\pi$
$828$	−7.76745	−0.269938
$829$	46.3581	1.61008	0.805042	−	0.593218i	$-0.202143\pi$
$829$	46.3581	1.61008	0.805042	+	0.593218i	$0.202143\pi$
$830$	35.1429	1.21983
$831$	−32.0935	−1.11331
$832$	5.59844	0.194091
$833$	16.6479	0.576817
$834$	−36.3849	−1.25991
$835$	−41.2268	−1.42671
$836$	−8.94308	−0.309303
$837$	−9.21844	−0.318636
$838$	19.5984	0.677016
$839$	5.53428	0.191065	0.0955323	−	0.995426i	$-0.469545\pi$
$839$	5.53428	0.191065	0.0955323	+	0.995426i	$0.469545\pi$
$840$	11.0033	0.379649
$841$	−12.1680	−0.419585
$842$	14.0310	0.483539
$843$	24.3694	0.839328
$844$	14.0880	0.484928
$845$	−39.9972	−1.37595
$846$	−4.62811	−0.159118
$847$	15.2507	0.524019
$848$	−8.39315	−0.288222
$849$	31.7753	1.09053
$850$	−1.87244	−0.0642241
$851$	−15.4774	−0.530560
$852$	34.3666	1.17738
$853$	19.8821	0.680751	0.340376	−	0.940290i	$-0.389446\pi$
$853$	19.8821	0.680751	0.340376	+	0.940290i	$0.389446\pi$
$854$	−29.2246	−1.00005
$855$	22.0990	0.755770
$856$	−19.8580	−0.678733
$857$	9.01652	0.307999	0.153999	−	0.988071i	$-0.450785\pi$
$857$	9.01652	0.307999	0.153999	+	0.988071i	$0.450785\pi$
$858$	25.9062	0.884424
$859$	−25.4588	−0.868643	−0.434322	−	0.900758i	$-0.643012\pi$
$859$	−25.4588	−0.868643	−0.434322	+	0.900758i	$0.643012\pi$
$860$	−22.8461	−0.779046
$861$	33.1543	1.12990
$862$	−29.7640	−1.01377
$863$	36.2119	1.23267	0.616334	−	0.787485i	$-0.288617\pi$
$863$	36.2119	1.23267	0.616334	+	0.787485i	$0.288617\pi$
$864$	−1.65073	−0.0561591
$865$	10.0739	0.342524
$866$	−2.06879	−0.0703002
$867$	−95.0666	−3.22863
$868$	12.2615	0.416182
$869$	−0.148510	−0.00503785
$870$	−20.5602	−0.697056
$871$	−60.2139	−2.04027
$872$	14.6496	0.496098
$873$	−21.3396	−0.722235
$874$	−15.1200	−0.511443
$875$	−25.1123	−0.848952
$876$	−10.6493	−0.359807
$877$	42.5254	1.43598	0.717990	−	0.696053i	$-0.245062\pi$
$877$	42.5254	1.43598	0.717990	+	0.696053i	$0.245062\pi$
$878$	−5.10555	−0.172304
$879$	40.2770	1.35851
$880$	−4.39057	−0.148006
$881$	−23.3847	−0.787849	−0.393925	−	0.919143i	$-0.628883\pi$
$881$	−23.3847	−0.787849	−0.393925	+	0.919143i	$0.628883\pi$
$882$	4.97217	0.167422
$883$	1.22040	0.0410696	0.0205348	−	0.999789i	$-0.493463\pi$
$883$	1.22040	0.0410696	0.0205348	+	0.999789i	$0.493463\pi$
$884$	−42.7706	−1.43853
$885$	65.3071	2.19527
$886$	16.1599	0.542902
$887$	27.7542	0.931896	0.465948	−	0.884812i	$-0.345713\pi$
$887$	27.7542	0.931896	0.465948	+	0.884812i	$0.345713\pi$
$888$	10.4489	0.350644
$889$	−42.8735	−1.43793
$890$	3.88880	0.130353
$891$	−21.4213	−0.717641
$892$	15.0007	0.502262
$893$	−9.00902	−0.301475
$894$	22.9681	0.768168
$895$	−13.9954	−0.467814
$896$	2.19565	0.0733515
$897$	43.7996	1.46242
$898$	4.06368	0.135607
$899$	−22.9112	−0.764133
$900$	−0.559232	−0.0186411
$901$	64.1215	2.13620
$902$	−13.2293	−0.440489
$903$	52.8679	1.75933
$904$	−2.58478	−0.0859684
$905$	−16.9152	−0.562281
$906$	−32.6794	−1.08570
$907$	47.5644	1.57935	0.789675	−	0.613526i	$-0.210249\pi$
$907$	47.5644	1.57935	0.789675	+	0.613526i	$0.210249\pi$
$908$	21.1405	0.701573
$909$	21.5667	0.715324
$910$	−26.8041	−0.888547
$911$	−28.9184	−0.958108	−0.479054	−	0.877785i	$-0.659020\pi$
$911$	−28.9184	−0.958108	−0.479054	+	0.877785i	$0.659020\pi$
$912$	10.2077	0.338009
$913$	32.4501	1.07394
$914$	5.34026	0.176640
$915$	−66.7029	−2.20513
$916$	−10.9570	−0.362030
$917$	−46.8576	−1.54737
$918$	12.6112	0.416231
$919$	−43.9827	−1.45086	−0.725428	−	0.688298i	$-0.758358\pi$
$919$	−43.9827	−1.45086	−0.725428	+	0.688298i	$0.758358\pi$
$920$	−7.42311	−0.244733
$921$	−53.6965	−1.76936
$922$	−7.71570	−0.254103
$923$	−83.7174	−2.75559
$924$	10.1602	0.334245
$925$	−1.11433	−0.0366389
$926$	32.1685	1.05712
$927$	0.664097	0.0218118
$928$	−4.10269	−0.134677
$929$	−36.4671	−1.19645	−0.598223	−	0.801330i	$-0.704126\pi$
$929$	−36.4671	−1.19645	−0.598223	+	0.801330i	$0.704126\pi$
$930$	27.9859	0.917694
$931$	9.67876	0.317208
$932$	0.0335061	0.00109753
$933$	−27.7594	−0.908802
$934$	19.2142	0.628707
$935$	33.5428	1.09697
$936$	−12.7741	−0.417535
$937$	−56.9359	−1.86001	−0.930007	−	0.367541i	$-0.880200\pi$
$937$	−56.9359	−1.86001	−0.930007	+	0.367541i	$0.880200\pi$
$938$	−23.6153	−0.771067
$939$	−6.92643	−0.226035
$940$	−4.42294	−0.144260
$941$	14.3286	0.467098	0.233549	−	0.972345i	$-0.424966\pi$
$941$	14.3286	0.467098	0.233549	+	0.972345i	$0.424966\pi$
$942$	49.1317	1.60080
$943$	−22.3668	−0.728363
$944$	13.0317	0.424146
$945$	7.90335	0.257096
$946$	−21.0955	−0.685875
$947$	−40.4568	−1.31467	−0.657334	−	0.753599i	$-0.728316\pi$
$947$	−40.4568	−1.31467	−0.657334	+	0.753599i	$0.728316\pi$
$948$	0.169509	0.00550541
$949$	25.9418	0.842106
$950$	−1.08859	−0.0353187
$951$	46.6648	1.51321
$952$	−16.7742	−0.543655
$953$	−16.1405	−0.522840	−0.261420	−	0.965225i	$-0.584191\pi$
$953$	−16.1405	−0.522840	−0.261420	+	0.965225i	$0.584191\pi$
$954$	19.1509	0.620033
$955$	16.4818	0.533339
$956$	−2.18499	−0.0706675
$957$	−18.9848	−0.613691
$958$	17.8270	0.575965
$959$	−12.4026	−0.400502
$960$	5.01140	0.161742
$961$	0.186092	0.00600298
$962$	−25.4537	−0.820661
$963$	45.3106	1.46011
$964$	6.16740	0.198638
$965$	6.29562	0.202663
$966$	17.1777	0.552685
$967$	8.27587	0.266134	0.133067	−	0.991107i	$-0.457517\pi$
$967$	8.27587	0.266134	0.133067	+	0.991107i	$0.457517\pi$
$968$	6.94586	0.223248
$969$	−77.9838	−2.50520
$970$	−20.3936	−0.654798
$971$	−4.47529	−0.143619	−0.0718095	−	0.997418i	$-0.522877\pi$
$971$	−4.47529	−0.143619	−0.0718095	+	0.997418i	$0.522877\pi$
$972$	19.4981	0.625403
$973$	34.7614	1.11440
$974$	34.8874	1.11786
$975$	3.15343	0.100991
$976$	−13.3102	−0.426050
$977$	−41.5445	−1.32913	−0.664564	−	0.747232i	$-0.731383\pi$
$977$	−41.5445	−1.32913	−0.664564	+	0.747232i	$0.731383\pi$
$978$	43.5882	1.39380
$979$	3.59082	0.114763
$980$	4.75174	0.151789
$981$	−33.4264	−1.06722
$982$	19.2391	0.613945
$983$	11.2537	0.358937	0.179468	−	0.983764i	$-0.442562\pi$
$983$	11.2537	0.358937	0.179468	+	0.983764i	$0.442562\pi$
$984$	15.1000	0.481370
$985$	−25.5323	−0.813525
$986$	31.3435	0.998179
$987$	10.2351	0.325786
$988$	−24.8659	−0.791090
$989$	−35.6661	−1.13412
$990$	10.0181	0.318395
$991$	−31.7804	−1.00954	−0.504769	−	0.863254i	$-0.668422\pi$
$991$	−31.7804	−1.00954	−0.504769	+	0.863254i	$0.668422\pi$
$992$	5.58445	0.177306
$993$	53.6296	1.70188
$994$	−32.8331	−1.04140
$995$	13.0265	0.412968
$996$	−37.0386	−1.17361
$997$	−16.9621	−0.537197	−0.268598	−	0.963252i	$-0.586560\pi$
$997$	−16.9621	−0.537197	−0.268598	+	0.963252i	$0.586560\pi$
$998$	25.2316	0.798692
$999$	7.50519	0.237454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.13	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.13	✓	75	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.29820 q^{3} +1.00000 q^{4} -2.18058 q^{5} +2.29820 q^{6} -2.19565 q^{7} -1.00000 q^{8} +2.28173 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.29820 q^{3} +1.00000 q^{4} -2.18058 q^{5} +2.29820 q^{6} -2.19565 q^{7} -1.00000 q^{8} +2.28173 q^{9} +2.18058 q^{10} +2.01349 q^{11} -2.29820 q^{12} +5.59844 q^{13} +2.19565 q^{14} +5.01140 q^{15} +1.00000 q^{16} -7.63974 q^{17} -2.28173 q^{18} -4.44158 q^{19} -2.18058 q^{20} +5.04604 q^{21} -2.01349 q^{22} -3.40420 q^{23} +2.29820 q^{24} -0.245092 q^{25} -5.59844 q^{26} +1.65073 q^{27} -2.19565 q^{28} +4.10269 q^{29} -5.01140 q^{30} -5.58445 q^{31} -1.00000 q^{32} -4.62740 q^{33} +7.63974 q^{34} +4.78778 q^{35} +2.28173 q^{36} +4.54658 q^{37} +4.44158 q^{38} -12.8663 q^{39} +2.18058 q^{40} +6.57036 q^{41} -5.04604 q^{42} +10.4771 q^{43} +2.01349 q^{44} -4.97548 q^{45} +3.40420 q^{46} +2.02834 q^{47} -2.29820 q^{48} -2.17912 q^{49} +0.245092 q^{50} +17.5577 q^{51} +5.59844 q^{52} -8.39315 q^{53} -1.65073 q^{54} -4.39057 q^{55} +2.19565 q^{56} +10.2077 q^{57} -4.10269 q^{58} +13.0317 q^{59} +5.01140 q^{60} -13.3102 q^{61} +5.58445 q^{62} -5.00987 q^{63} +1.00000 q^{64} -12.2078 q^{65} +4.62740 q^{66} -10.7555 q^{67} -7.63974 q^{68} +7.82353 q^{69} -4.78778 q^{70} -14.9537 q^{71} -2.28173 q^{72} +4.63376 q^{73} -4.54658 q^{74} +0.563270 q^{75} -4.44158 q^{76} -4.42092 q^{77} +12.8663 q^{78} -0.0737574 q^{79} -2.18058 q^{80} -10.6389 q^{81} -6.57036 q^{82} +16.1164 q^{83} +5.04604 q^{84} +16.6590 q^{85} -10.4771 q^{86} -9.42880 q^{87} -2.01349 q^{88} +1.78338 q^{89} +4.97548 q^{90} -12.2922 q^{91} -3.40420 q^{92} +12.8342 q^{93} -2.02834 q^{94} +9.68521 q^{95} +2.29820 q^{96} -9.35237 q^{97} +2.17912 q^{98} +4.59424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

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