LMFDB - Embedded newform 6005.2.a.g.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47572 q^{2} +3.00665 q^{3} +4.12920 q^{4} -1.00000 q^{5} -7.44362 q^{6} +1.05496 q^{7} -5.27130 q^{8} +6.03992 q^{9} +O(q^{10})$	\(q-2.47572 q^{2} +3.00665 q^{3} +4.12920 q^{4} -1.00000 q^{5} -7.44362 q^{6} +1.05496 q^{7} -5.27130 q^{8} +6.03992 q^{9} +2.47572 q^{10} -4.26355 q^{11} +12.4150 q^{12} +6.24323 q^{13} -2.61178 q^{14} -3.00665 q^{15} +4.79188 q^{16} -1.74936 q^{17} -14.9532 q^{18} -0.170851 q^{19} -4.12920 q^{20} +3.17189 q^{21} +10.5554 q^{22} +8.30924 q^{23} -15.8489 q^{24} +1.00000 q^{25} -15.4565 q^{26} +9.13996 q^{27} +4.35613 q^{28} +4.52194 q^{29} +7.44362 q^{30} +1.07132 q^{31} -1.32076 q^{32} -12.8190 q^{33} +4.33093 q^{34} -1.05496 q^{35} +24.9400 q^{36} -1.66215 q^{37} +0.422978 q^{38} +18.7712 q^{39} +5.27130 q^{40} -9.93490 q^{41} -7.85271 q^{42} +5.58640 q^{43} -17.6050 q^{44} -6.03992 q^{45} -20.5714 q^{46} +0.676349 q^{47} +14.4075 q^{48} -5.88706 q^{49} -2.47572 q^{50} -5.25971 q^{51} +25.7795 q^{52} +12.7354 q^{53} -22.6280 q^{54} +4.26355 q^{55} -5.56101 q^{56} -0.513687 q^{57} -11.1951 q^{58} +10.6473 q^{59} -12.4150 q^{60} +0.475098 q^{61} -2.65228 q^{62} +6.37187 q^{63} -6.31393 q^{64} -6.24323 q^{65} +31.7362 q^{66} -3.21663 q^{67} -7.22346 q^{68} +24.9829 q^{69} +2.61178 q^{70} -9.08189 q^{71} -31.8382 q^{72} -0.196811 q^{73} +4.11503 q^{74} +3.00665 q^{75} -0.705476 q^{76} -4.49787 q^{77} -46.4722 q^{78} +14.4504 q^{79} -4.79188 q^{80} +9.36086 q^{81} +24.5960 q^{82} -12.0569 q^{83} +13.0974 q^{84} +1.74936 q^{85} -13.8304 q^{86} +13.5959 q^{87} +22.4745 q^{88} -7.42923 q^{89} +14.9532 q^{90} +6.58635 q^{91} +34.3105 q^{92} +3.22107 q^{93} -1.67445 q^{94} +0.170851 q^{95} -3.97106 q^{96} +12.3104 q^{97} +14.5747 q^{98} -25.7515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.47572	−1.75060	−0.875300	−	0.483581i	$-0.839336\pi$
$2$	−2.47572	−1.75060	−0.875300	+	0.483581i	$0.839336\pi$
$3$	3.00665	1.73589	0.867944	−	0.496662i	$-0.165441\pi$
$3$	3.00665	1.73589	0.867944	+	0.496662i	$0.165441\pi$
$4$	4.12920	2.06460
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−7.44362	−3.03884
$7$	1.05496	0.398737	0.199368	−	0.979925i	$-0.436111\pi$
$7$	1.05496	0.398737	0.199368	+	0.979925i	$0.436111\pi$
$8$	−5.27130	−1.86369
$9$	6.03992	2.01331
$10$	2.47572	0.782892
$11$	−4.26355	−1.28551	−0.642754	−	0.766072i	$-0.722208\pi$
$11$	−4.26355	−1.28551	−0.642754	+	0.766072i	$0.722208\pi$
$12$	12.4150	3.58391
$13$	6.24323	1.73156	0.865780	−	0.500425i	$-0.166823\pi$
$13$	6.24323	1.73156	0.865780	+	0.500425i	$0.166823\pi$
$14$	−2.61178	−0.698029
$15$	−3.00665	−0.776313
$16$	4.79188	1.19797
$17$	−1.74936	−0.424282	−0.212141	−	0.977239i	$-0.568044\pi$
$17$	−1.74936	−0.424282	−0.212141	+	0.977239i	$0.568044\pi$
$18$	−14.9532	−3.52449
$19$	−0.170851	−0.0391958	−0.0195979	−	0.999808i	$-0.506239\pi$
$19$	−0.170851	−0.0391958	−0.0195979	+	0.999808i	$0.506239\pi$
$20$	−4.12920	−0.923317
$21$	3.17189	0.692163
$22$	10.5554	2.25041
$23$	8.30924	1.73260	0.866298	−	0.499527i	$-0.166493\pi$
$23$	8.30924	1.73260	0.866298	+	0.499527i	$0.166493\pi$
$24$	−15.8489	−3.23515
$25$	1.00000	0.200000
$26$	−15.4565	−3.03127
$27$	9.13996	1.75899
$28$	4.35613	0.823232
$29$	4.52194	0.839702	0.419851	−	0.907593i	$-0.362082\pi$
$29$	4.52194	0.839702	0.419851	+	0.907593i	$0.362082\pi$
$30$	7.44362	1.35901
$31$	1.07132	0.192414	0.0962070	−	0.995361i	$-0.469329\pi$
$31$	1.07132	0.192414	0.0962070	+	0.995361i	$0.469329\pi$
$32$	−1.32076	−0.233480
$33$	−12.8190	−2.23150
$34$	4.33093	0.742748
$35$	−1.05496	−0.178321
$36$	24.9400	4.15667
$37$	−1.66215	−0.273256	−0.136628	−	0.990622i	$-0.543627\pi$
$37$	−1.66215	−0.273256	−0.136628	+	0.990622i	$0.543627\pi$
$38$	0.422978	0.0686162
$39$	18.7712	3.00579
$40$	5.27130	0.833466
$41$	−9.93490	−1.55157	−0.775785	−	0.630997i	$-0.782646\pi$
$41$	−9.93490	−1.55157	−0.775785	+	0.630997i	$0.782646\pi$
$42$	−7.85271	−1.21170
$43$	5.58640	0.851918	0.425959	−	0.904742i	$-0.359937\pi$
$43$	5.58640	0.851918	0.425959	+	0.904742i	$0.359937\pi$
$44$	−17.6050	−2.65406
$45$	−6.03992	−0.900378
$46$	−20.5714	−3.03308
$47$	0.676349	0.0986556	0.0493278	−	0.998783i	$-0.484292\pi$
$47$	0.676349	0.0986556	0.0493278	+	0.998783i	$0.484292\pi$
$48$	14.4075	2.07954
$49$	−5.88706	−0.841009
$50$	−2.47572	−0.350120
$51$	−5.25971	−0.736506
$52$	25.7795	3.57498
$53$	12.7354	1.74935	0.874674	−	0.484712i	$-0.161076\pi$
$53$	12.7354	1.74935	0.874674	+	0.484712i	$0.161076\pi$
$54$	−22.6280	−3.07928
$55$	4.26355	0.574897
$56$	−5.56101	−0.743121
$57$	−0.513687	−0.0680395
$58$	−11.1951	−1.46998
$59$	10.6473	1.38616	0.693078	−	0.720863i	$-0.256254\pi$
$59$	10.6473	1.38616	0.693078	+	0.720863i	$0.256254\pi$
$60$	−12.4150	−1.60277
$61$	0.475098	0.0608301	0.0304151	−	0.999537i	$-0.490317\pi$
$61$	0.475098	0.0608301	0.0304151	+	0.999537i	$0.490317\pi$
$62$	−2.65228	−0.336840
$63$	6.37187	0.802780
$64$	−6.31393	−0.789241
$65$	−6.24323	−0.774377
$66$	31.7362	3.90646
$67$	−3.21663	−0.392974	−0.196487	−	0.980506i	$-0.562953\pi$
$67$	−3.21663	−0.392974	−0.196487	+	0.980506i	$0.562953\pi$
$68$	−7.22346	−0.875973
$69$	24.9829	3.00759
$70$	2.61178	0.312168
$71$	−9.08189	−1.07782	−0.538911	−	0.842363i	$-0.681164\pi$
$71$	−9.08189	−1.07782	−0.538911	+	0.842363i	$0.681164\pi$
$72$	−31.8382	−3.75217
$73$	−0.196811	−0.0230350	−0.0115175	−	0.999934i	$-0.503666\pi$
$73$	−0.196811	−0.0230350	−0.0115175	+	0.999934i	$0.503666\pi$
$74$	4.11503	0.478363
$75$	3.00665	0.347178
$76$	−0.705476	−0.0809236
$77$	−4.49787	−0.512580
$78$	−46.4722	−5.26194
$79$	14.4504	1.62580	0.812901	−	0.582402i	$-0.197887\pi$
$79$	14.4504	1.62580	0.812901	+	0.582402i	$0.197887\pi$
$80$	−4.79188	−0.535749
$81$	9.36086	1.04010
$82$	24.5960	2.71618
$83$	−12.0569	−1.32341	−0.661707	−	0.749762i	$-0.730168\pi$
$83$	−12.0569	−1.32341	−0.661707	+	0.749762i	$0.730168\pi$
$84$	13.0974	1.42904
$85$	1.74936	0.189745
$86$	−13.8304	−1.49137
$87$	13.5959	1.45763
$88$	22.4745	2.39579
$89$	−7.42923	−0.787497	−0.393748	−	0.919218i	$-0.628822\pi$
$89$	−7.42923	−0.787497	−0.393748	+	0.919218i	$0.628822\pi$
$90$	14.9532	1.57620
$91$	6.58635	0.690437
$92$	34.3105	3.57712
$93$	3.22107	0.334009
$94$	−1.67445	−0.172706
$95$	0.170851	0.0175289
$96$	−3.97106	−0.405294
$97$	12.3104	1.24994	0.624968	−	0.780650i	$-0.285112\pi$
$97$	12.3104	1.24994	0.624968	+	0.780650i	$0.285112\pi$
$98$	14.5747	1.47227
$99$	−25.7515	−2.58812
$100$	4.12920	0.412920
$101$	−1.90143	−0.189200	−0.0945999	−	0.995515i	$-0.530157\pi$
$101$	−1.90143	−0.189200	−0.0945999	+	0.995515i	$0.530157\pi$
$102$	13.0216	1.28933
$103$	−0.391888	−0.0386139	−0.0193069	−	0.999814i	$-0.506146\pi$
$103$	−0.391888	−0.0386139	−0.0193069	+	0.999814i	$0.506146\pi$
$104$	−32.9099	−3.22709
$105$	−3.17189	−0.309545
$106$	−31.5294	−3.06241
$107$	−12.4370	−1.20233	−0.601163	−	0.799126i	$-0.705296\pi$
$107$	−12.4370	−1.20233	−0.601163	+	0.799126i	$0.705296\pi$
$108$	37.7407	3.63160
$109$	9.85066	0.943522	0.471761	−	0.881726i	$-0.343618\pi$
$109$	9.85066	0.943522	0.471761	+	0.881726i	$0.343618\pi$
$110$	−10.5554	−1.00641
$111$	−4.99751	−0.474342
$112$	5.05524	0.477675
$113$	1.98876	0.187087	0.0935435	−	0.995615i	$-0.470181\pi$
$113$	1.98876	0.187087	0.0935435	+	0.995615i	$0.470181\pi$
$114$	1.27175	0.119110
$115$	−8.30924	−0.774841
$116$	18.6720	1.73365
$117$	37.7086	3.48616
$118$	−26.3597	−2.42660
$119$	−1.84550	−0.169177
$120$	15.8489	1.44680
$121$	7.17786	0.652533
$122$	−1.17621	−0.106489
$123$	−29.8707	−2.69335
$124$	4.42367	0.397258
$125$	−1.00000	−0.0894427
$126$	−15.7750	−1.40535
$127$	6.47468	0.574535	0.287267	−	0.957850i	$-0.407253\pi$
$127$	6.47468	0.574535	0.287267	+	0.957850i	$0.407253\pi$
$128$	18.2730	1.61512
$129$	16.7963	1.47883
$130$	15.4565	1.35562
$131$	−6.62979	−0.579247	−0.289624	−	0.957141i	$-0.593530\pi$
$131$	−6.62979	−0.579247	−0.289624	+	0.957141i	$0.593530\pi$
$132$	−52.9321	−4.60715
$133$	−0.180240	−0.0156288
$134$	7.96348	0.687940
$135$	−9.13996	−0.786642
$136$	9.22141	0.790729
$137$	−13.7309	−1.17311	−0.586555	−	0.809909i	$-0.699516\pi$
$137$	−13.7309	−1.17311	−0.586555	+	0.809909i	$0.699516\pi$
$138$	−61.8508	−5.26509
$139$	−5.83394	−0.494828	−0.247414	−	0.968910i	$-0.579581\pi$
$139$	−5.83394	−0.494828	−0.247414	+	0.968910i	$0.579581\pi$
$140$	−4.35613	−0.368161
$141$	2.03354	0.171255
$142$	22.4842	1.88684
$143$	−26.6183	−2.22594
$144$	28.9426	2.41188
$145$	−4.52194	−0.375526
$146$	0.487249	0.0403250
$147$	−17.7003	−1.45990
$148$	−6.86336	−0.564165
$149$	−1.86164	−0.152511	−0.0762556	−	0.997088i	$-0.524296\pi$
$149$	−1.86164	−0.152511	−0.0762556	+	0.997088i	$0.524296\pi$
$150$	−7.44362	−0.607769
$151$	−19.5560	−1.59145	−0.795723	−	0.605661i	$-0.792909\pi$
$151$	−19.5560	−1.59145	−0.795723	+	0.605661i	$0.792909\pi$
$152$	0.900605	0.0730487
$153$	−10.5660	−0.854210
$154$	11.1355	0.897322
$155$	−1.07132	−0.0860501
$156$	77.5099	6.20576
$157$	10.0120	0.799041	0.399520	−	0.916724i	$-0.369177\pi$
$157$	10.0120	0.799041	0.399520	+	0.916724i	$0.369177\pi$
$158$	−35.7753	−2.84613
$159$	38.2910	3.03667
$160$	1.32076	0.104415
$161$	8.76591	0.690850
$162$	−23.1749	−1.82079
$163$	19.2322	1.50638	0.753189	−	0.657804i	$-0.228514\pi$
$163$	19.2322	1.50638	0.753189	+	0.657804i	$0.228514\pi$
$164$	−41.0232	−3.20337
$165$	12.8190	0.997957
$166$	29.8495	2.31677
$167$	−7.29758	−0.564704	−0.282352	−	0.959311i	$-0.591115\pi$
$167$	−7.29758	−0.564704	−0.282352	+	0.959311i	$0.591115\pi$
$168$	−16.7200	−1.28997
$169$	25.9779	1.99830
$170$	−4.33093	−0.332167
$171$	−1.03192	−0.0789132
$172$	23.0674	1.75887
$173$	8.92020	0.678190	0.339095	−	0.940752i	$-0.389879\pi$
$173$	8.92020	0.678190	0.339095	+	0.940752i	$0.389879\pi$
$174$	−33.6596	−2.55173
$175$	1.05496	0.0797474
$176$	−20.4304	−1.54000
$177$	32.0126	2.40621
$178$	18.3927	1.37859
$179$	−0.998132	−0.0746039	−0.0373020	−	0.999304i	$-0.511876\pi$
$179$	−0.998132	−0.0746039	−0.0373020	+	0.999304i	$0.511876\pi$
$180$	−24.9400	−1.85892
$181$	−0.416091	−0.0309278	−0.0154639	−	0.999880i	$-0.504923\pi$
$181$	−0.416091	−0.0309278	−0.0154639	+	0.999880i	$0.504923\pi$
$182$	−16.3060	−1.20868
$183$	1.42845	0.105594
$184$	−43.8005	−3.22902
$185$	1.66215	0.122204
$186$	−7.97446	−0.584716
$187$	7.45849	0.545419
$188$	2.79278	0.203684
$189$	9.64228	0.701373
$190$	−0.422978	−0.0306861
$191$	1.94250	0.140554	0.0702772	−	0.997528i	$-0.477612\pi$
$191$	1.94250	0.140554	0.0702772	+	0.997528i	$0.477612\pi$
$192$	−18.9837	−1.37003
$193$	−1.52650	−0.109880	−0.0549401	−	0.998490i	$-0.517497\pi$
$193$	−1.52650	−0.109880	−0.0549401	+	0.998490i	$0.517497\pi$
$194$	−30.4772	−2.18814
$195$	−18.7712	−1.34423
$196$	−24.3088	−1.73635
$197$	22.7844	1.62332	0.811662	−	0.584127i	$-0.198563\pi$
$197$	22.7844	1.62332	0.811662	+	0.584127i	$0.198563\pi$
$198$	63.7535	4.53077
$199$	26.7803	1.89841	0.949204	−	0.314663i	$-0.101891\pi$
$199$	26.7803	1.89841	0.949204	+	0.314663i	$0.101891\pi$
$200$	−5.27130	−0.372737
$201$	−9.67127	−0.682158
$202$	4.70742	0.331213
$203$	4.77046	0.334820
$204$	−21.7184	−1.52059
$205$	9.93490	0.693883
$206$	0.970206	0.0675975
$207$	50.1871	3.48825
$208$	29.9168	2.07436
$209$	0.728430	0.0503866
$210$	7.85271	0.541889
$211$	15.7712	1.08574	0.542868	−	0.839818i	$-0.317338\pi$
$211$	15.7712	1.08574	0.542868	+	0.839818i	$0.317338\pi$
$212$	52.5872	3.61170
$213$	−27.3060	−1.87098
$214$	30.7905	2.10479
$215$	−5.58640	−0.380989
$216$	−48.1795	−3.27820
$217$	1.13019	0.0767225
$218$	−24.3875	−1.65173
$219$	−0.591741	−0.0399861
$220$	17.6050	1.18693
$221$	−10.9217	−0.734670
$222$	12.3724	0.830384
$223$	20.7101	1.38685	0.693425	−	0.720529i	$-0.256101\pi$
$223$	20.7101	1.38685	0.693425	+	0.720529i	$0.256101\pi$
$224$	−1.39335	−0.0930970
$225$	6.03992	0.402661
$226$	−4.92362	−0.327514
$227$	−1.89135	−0.125533	−0.0627667	−	0.998028i	$-0.519992\pi$
$227$	−1.89135	−0.125533	−0.0627667	+	0.998028i	$0.519992\pi$
$228$	−2.12112	−0.140474
$229$	24.4678	1.61687	0.808437	−	0.588582i	$-0.200314\pi$
$229$	24.4678	1.61687	0.808437	+	0.588582i	$0.200314\pi$
$230$	20.5714	1.35644
$231$	−13.5235	−0.889781
$232$	−23.8365	−1.56494
$233$	−1.90583	−0.124855	−0.0624274	−	0.998050i	$-0.519884\pi$
$233$	−1.90583	−0.124855	−0.0624274	+	0.998050i	$0.519884\pi$
$234$	−93.3560	−6.10287
$235$	−0.676349	−0.0441201
$236$	43.9647	2.86186
$237$	43.4473	2.82221
$238$	4.56895	0.296161
$239$	−5.37788	−0.347866	−0.173933	−	0.984757i	$-0.555648\pi$
$239$	−5.37788	−0.347866	−0.173933	+	0.984757i	$0.555648\pi$
$240$	−14.4075	−0.929999
$241$	21.1682	1.36357	0.681783	−	0.731555i	$-0.261205\pi$
$241$	21.1682	1.36357	0.681783	+	0.731555i	$0.261205\pi$
$242$	−17.7704	−1.14232
$243$	0.724912	0.0465031
$244$	1.96178	0.125590
$245$	5.88706	0.376111
$246$	73.9516	4.71498
$247$	−1.06666	−0.0678699
$248$	−5.64723	−0.358599
$249$	−36.2508	−2.29730
$250$	2.47572	0.156578
$251$	16.8662	1.06459	0.532294	−	0.846560i	$-0.321330\pi$
$251$	16.8662	1.06459	0.532294	+	0.846560i	$0.321330\pi$
$252$	26.3107	1.65742
$253$	−35.4269	−2.22727
$254$	−16.0295	−1.00578
$255$	5.25971	0.329376
$256$	−32.6111	−2.03820
$257$	−31.2387	−1.94862	−0.974309	−	0.225215i	$-0.927691\pi$
$257$	−31.2387	−1.94862	−0.974309	+	0.225215i	$0.927691\pi$
$258$	−41.5830	−2.58885
$259$	−1.75350	−0.108957
$260$	−25.7795	−1.59878
$261$	27.3121	1.69058
$262$	16.4135	1.01403
$263$	15.7242	0.969599	0.484799	−	0.874625i	$-0.338893\pi$
$263$	15.7242	0.969599	0.484799	+	0.874625i	$0.338893\pi$
$264$	67.5727	4.15881
$265$	−12.7354	−0.782332
$266$	0.446225	0.0273598
$267$	−22.3371	−1.36701
$268$	−13.2821	−0.811333
$269$	−4.00811	−0.244379	−0.122189	−	0.992507i	$-0.538992\pi$
$269$	−4.00811	−0.244379	−0.122189	+	0.992507i	$0.538992\pi$
$270$	22.6280	1.37710
$271$	3.14287	0.190916	0.0954580	−	0.995433i	$-0.469568\pi$
$271$	3.14287	0.190916	0.0954580	+	0.995433i	$0.469568\pi$
$272$	−8.38273	−0.508278
$273$	19.8028	1.19852
$274$	33.9939	2.05365
$275$	−4.26355	−0.257102
$276$	103.160	6.20947
$277$	−15.3469	−0.922108	−0.461054	−	0.887372i	$-0.652529\pi$
$277$	−15.3469	−0.922108	−0.461054	+	0.887372i	$0.652529\pi$
$278$	14.4432	0.866246
$279$	6.47066	0.387388
$280$	5.56101	0.332334
$281$	21.4769	1.28120	0.640602	−	0.767873i	$-0.278685\pi$
$281$	21.4769	1.28120	0.640602	+	0.767873i	$0.278685\pi$
$282$	−5.03448	−0.299799
$283$	−29.5061	−1.75396	−0.876979	−	0.480528i	$-0.840445\pi$
$283$	−29.5061	−1.75396	−0.876979	+	0.480528i	$0.840445\pi$
$284$	−37.5009	−2.22527
$285$	0.513687	0.0304282
$286$	65.8996	3.89672
$287$	−10.4809	−0.618668
$288$	−7.97729	−0.470066
$289$	−13.9397	−0.819985
$290$	11.1951	0.657396
$291$	37.0131	2.16975
$292$	−0.812671	−0.0475580
$293$	14.7214	0.860032	0.430016	−	0.902821i	$-0.358508\pi$
$293$	14.7214	0.860032	0.430016	+	0.902821i	$0.358508\pi$
$294$	43.8210	2.55570
$295$	−10.6473	−0.619908
$296$	8.76172	0.509264
$297$	−38.9687	−2.26119
$298$	4.60889	0.266986
$299$	51.8765	3.00009
$300$	12.4150	0.716782
$301$	5.89342	0.339691
$302$	48.4152	2.78598
$303$	−5.71694	−0.328430
$304$	−0.818696	−0.0469554
$305$	−0.475098	−0.0272041
$306$	26.1585	1.49538
$307$	2.94099	0.167851	0.0839256	−	0.996472i	$-0.473254\pi$
$307$	2.94099	0.167851	0.0839256	+	0.996472i	$0.473254\pi$
$308$	−18.5726	−1.05827
$309$	−1.17827	−0.0670294
$310$	2.65228	0.150639
$311$	33.5405	1.90191	0.950953	−	0.309335i	$-0.100106\pi$
$311$	33.5405	1.90191	0.950953	+	0.309335i	$0.100106\pi$
$312$	−98.9486	−5.60186
$313$	18.1038	1.02329	0.511644	−	0.859198i	$-0.329037\pi$
$313$	18.1038	1.02329	0.511644	+	0.859198i	$0.329037\pi$
$314$	−24.7868	−1.39880
$315$	−6.37187	−0.359014
$316$	59.6687	3.35663
$317$	4.94391	0.277678	0.138839	−	0.990315i	$-0.455663\pi$
$317$	4.94391	0.277678	0.138839	+	0.990315i	$0.455663\pi$
$318$	−94.7978	−5.31600
$319$	−19.2795	−1.07944
$320$	6.31393	0.352959
$321$	−37.3935	−2.08710
$322$	−21.7019	−1.20940
$323$	0.298879	0.0166301
$324$	38.6528	2.14738
$325$	6.24323	0.346312
$326$	−47.6135	−2.63707
$327$	29.6175	1.63785
$328$	52.3699	2.89164
$329$	0.713520	0.0393376
$330$	−31.7362	−1.74702
$331$	3.26059	0.179218	0.0896092	−	0.995977i	$-0.471438\pi$
$331$	3.26059	0.179218	0.0896092	+	0.995977i	$0.471438\pi$
$332$	−49.7852	−2.73232
$333$	−10.0393	−0.550149
$334$	18.0668	0.988570
$335$	3.21663	0.175743
$336$	15.1993	0.829190
$337$	−4.34582	−0.236732	−0.118366	−	0.992970i	$-0.537766\pi$
$337$	−4.34582	−0.236732	−0.118366	+	0.992970i	$0.537766\pi$
$338$	−64.3141	−3.49822
$339$	5.97950	0.324762
$340$	7.22346	0.391747
$341$	−4.56761	−0.247350
$342$	2.55476	0.138145
$343$	−13.5953	−0.734078
$344$	−29.4476	−1.58771
$345$	−24.9829	−1.34504
$346$	−22.0839	−1.18724
$347$	−11.4797	−0.616263	−0.308131	−	0.951344i	$-0.599704\pi$
$347$	−11.4797	−0.616263	−0.308131	+	0.951344i	$0.599704\pi$
$348$	56.1400	3.00942
$349$	−28.7451	−1.53869	−0.769344	−	0.638835i	$-0.779417\pi$
$349$	−28.7451	−1.53869	−0.769344	+	0.638835i	$0.779417\pi$
$350$	−2.61178	−0.139606
$351$	57.0628	3.04579
$352$	5.63113	0.300140
$353$	20.4949	1.09083	0.545417	−	0.838165i	$-0.316371\pi$
$353$	20.4949	1.09083	0.545417	+	0.838165i	$0.316371\pi$
$354$	−79.2542	−4.21231
$355$	9.08189	0.482017
$356$	−30.6768	−1.62586
$357$	−5.54877	−0.293672
$358$	2.47110	0.130602
$359$	32.5474	1.71779	0.858893	−	0.512155i	$-0.171153\pi$
$359$	32.5474	1.71779	0.858893	+	0.512155i	$0.171153\pi$
$360$	31.8382	1.67802
$361$	−18.9708	−0.998464
$362$	1.03012	0.0541422
$363$	21.5813	1.13272
$364$	27.1963	1.42548
$365$	0.196811	0.0103016
$366$	−3.53645	−0.184853
$367$	−14.1938	−0.740909	−0.370455	−	0.928851i	$-0.620798\pi$
$367$	−14.1938	−0.740909	−0.370455	+	0.928851i	$0.620798\pi$
$368$	39.8169	2.07560
$369$	−60.0060	−3.12379
$370$	−4.11503	−0.213930
$371$	13.4354	0.697530
$372$	13.3004	0.689595
$373$	−5.99125	−0.310215	−0.155108	−	0.987898i	$-0.549572\pi$
$373$	−5.99125	−0.310215	−0.155108	+	0.987898i	$0.549572\pi$
$374$	−18.4651	−0.954810
$375$	−3.00665	−0.155263
$376$	−3.56524	−0.183863
$377$	28.2315	1.45400
$378$	−23.8716	−1.22782
$379$	−20.9397	−1.07560	−0.537799	−	0.843073i	$-0.680744\pi$
$379$	−20.9397	−1.07560	−0.537799	+	0.843073i	$0.680744\pi$
$380$	0.705476	0.0361901
$381$	19.4671	0.997327
$382$	−4.80909	−0.246054
$383$	−18.3330	−0.936775	−0.468387	−	0.883523i	$-0.655165\pi$
$383$	−18.3330	−0.936775	−0.468387	+	0.883523i	$0.655165\pi$
$384$	54.9406	2.80367
$385$	4.49787	0.229233
$386$	3.77920	0.192356
$387$	33.7414	1.71517
$388$	50.8323	2.58062
$389$	−33.4810	−1.69755	−0.848777	−	0.528752i	$-0.822660\pi$
$389$	−33.4810	−1.69755	−0.848777	+	0.528752i	$0.822660\pi$
$390$	46.4722	2.35321
$391$	−14.5359	−0.735110
$392$	31.0325	1.56738
$393$	−19.9334	−1.00551
$394$	−56.4079	−2.84179
$395$	−14.4504	−0.727080
$396$	−106.333	−5.34344
$397$	−8.64040	−0.433649	−0.216825	−	0.976211i	$-0.569570\pi$
$397$	−8.64040	−0.433649	−0.216825	+	0.976211i	$0.569570\pi$
$398$	−66.3006	−3.32335
$399$	−0.541919	−0.0271299
$400$	4.79188	0.239594
$401$	2.43017	0.121357	0.0606786	−	0.998157i	$-0.480674\pi$
$401$	2.43017	0.121357	0.0606786	+	0.998157i	$0.480674\pi$
$402$	23.9434	1.19419
$403$	6.68847	0.333176
$404$	−7.85140	−0.390622
$405$	−9.36086	−0.465145
$406$	−11.8103	−0.586136
$407$	7.08668	0.351273
$408$	27.7255	1.37262
$409$	17.4679	0.863733	0.431867	−	0.901937i	$-0.357855\pi$
$409$	17.4679	0.863733	0.431867	+	0.901937i	$0.357855\pi$
$410$	−24.5960	−1.21471
$411$	−41.2840	−2.03639
$412$	−1.61818	−0.0797222
$413$	11.2324	0.552712
$414$	−124.249	−6.10652
$415$	12.0569	0.591849
$416$	−8.24581	−0.404284
$417$	−17.5406	−0.858966
$418$	−1.80339	−0.0882067
$419$	−28.4699	−1.39084	−0.695422	−	0.718601i	$-0.744783\pi$
$419$	−28.4699	−1.39084	−0.695422	+	0.718601i	$0.744783\pi$
$420$	−13.0974	−0.639085
$421$	−24.2399	−1.18138	−0.590689	−	0.806899i	$-0.701144\pi$
$421$	−24.2399	−1.18138	−0.590689	+	0.806899i	$0.701144\pi$
$422$	−39.0451	−1.90069
$423$	4.08509	0.198624
$424$	−67.1324	−3.26024
$425$	−1.74936	−0.0848565
$426$	67.6021	3.27533
$427$	0.501209	0.0242552
$428$	−51.3547	−2.48232
$429$	−80.0319	−3.86397
$430$	13.8304	0.666960
$431$	35.3296	1.70177	0.850883	−	0.525355i	$-0.176067\pi$
$431$	35.3296	1.70177	0.850883	+	0.525355i	$0.176067\pi$
$432$	43.7976	2.10721
$433$	35.1517	1.68928	0.844641	−	0.535333i	$-0.179814\pi$
$433$	35.1517	1.68928	0.844641	+	0.535333i	$0.179814\pi$
$434$	−2.79804	−0.134310
$435$	−13.5959	−0.651872
$436$	40.6753	1.94800
$437$	−1.41964	−0.0679105
$438$	1.46499	0.0699997
$439$	6.92691	0.330603	0.165302	−	0.986243i	$-0.447140\pi$
$439$	6.92691	0.330603	0.165302	+	0.986243i	$0.447140\pi$
$440$	−22.4745	−1.07143
$441$	−35.5574	−1.69321
$442$	27.0390	1.28611
$443$	29.3421	1.39409	0.697043	−	0.717029i	$-0.254499\pi$
$443$	29.3421	1.39409	0.697043	+	0.717029i	$0.254499\pi$
$444$	−20.6357	−0.979327
$445$	7.42923	0.352179
$446$	−51.2724	−2.42782
$447$	−5.59728	−0.264742
$448$	−6.66093	−0.314700
$449$	5.63285	0.265831	0.132915	−	0.991127i	$-0.457566\pi$
$449$	5.63285	0.265831	0.132915	+	0.991127i	$0.457566\pi$
$450$	−14.9532	−0.704899
$451$	42.3579	1.99456
$452$	8.21199	0.386260
$453$	−58.7980	−2.76257
$454$	4.68246	0.219759
$455$	−6.58635	−0.308773
$456$	2.70780	0.126804
$457$	−14.3967	−0.673449	−0.336725	−	0.941603i	$-0.609319\pi$
$457$	−14.3967	−0.673449	−0.336725	+	0.941603i	$0.609319\pi$
$458$	−60.5754	−2.83050
$459$	−15.9891	−0.746306
$460$	−34.3105	−1.59974
$461$	−21.1564	−0.985352	−0.492676	−	0.870213i	$-0.663981\pi$
$461$	−21.1564	−0.985352	−0.492676	+	0.870213i	$0.663981\pi$
$462$	33.4804	1.55765
$463$	−16.8923	−0.785051	−0.392525	−	0.919741i	$-0.628398\pi$
$463$	−16.8923	−0.785051	−0.392525	+	0.919741i	$0.628398\pi$
$464$	21.6686	1.00594
$465$	−3.22107	−0.149373
$466$	4.71830	0.218571
$467$	−15.4287	−0.713955	−0.356977	−	0.934113i	$-0.616193\pi$
$467$	−15.4287	−0.713955	−0.356977	+	0.934113i	$0.616193\pi$
$468$	155.706	7.19752
$469$	−3.39341	−0.156693
$470$	1.67445	0.0772367
$471$	30.1024	1.38705
$472$	−56.1249	−2.58336
$473$	−23.8179	−1.09515
$474$	−107.564	−4.94056
$475$	−0.170851	−0.00783916
$476$	−7.62045	−0.349283
$477$	76.9210	3.52197
$478$	13.3141	0.608974
$479$	14.5066	0.662825	0.331413	−	0.943486i	$-0.392475\pi$
$479$	14.5066	0.662825	0.331413	+	0.943486i	$0.392475\pi$
$480$	3.97106	0.181253
$481$	−10.3772	−0.473160
$482$	−52.4067	−2.38706
$483$	26.3560	1.19924
$484$	29.6388	1.34722
$485$	−12.3104	−0.558988
$486$	−1.79468	−0.0814084
$487$	−2.55761	−0.115896	−0.0579482	−	0.998320i	$-0.518456\pi$
$487$	−2.55761	−0.115896	−0.0579482	+	0.998320i	$0.518456\pi$
$488$	−2.50439	−0.113368
$489$	57.8243	2.61490
$490$	−14.5747	−0.658419
$491$	−17.1346	−0.773276	−0.386638	−	0.922232i	$-0.626364\pi$
$491$	−17.1346	−0.773276	−0.386638	+	0.922232i	$0.626364\pi$
$492$	−123.342	−5.56069
$493$	−7.91050	−0.356271
$494$	2.64075	0.118813
$495$	25.7515	1.15744
$496$	5.13362	0.230506
$497$	−9.58102	−0.429768
$498$	89.7468	4.02165
$499$	−5.85213	−0.261977	−0.130989	−	0.991384i	$-0.541815\pi$
$499$	−5.85213	−0.261977	−0.130989	+	0.991384i	$0.541815\pi$
$500$	−4.12920	−0.184663
$501$	−21.9412	−0.980262
$502$	−41.7561	−1.86367
$503$	32.3539	1.44259	0.721295	−	0.692628i	$-0.243547\pi$
$503$	32.3539	1.44259	0.721295	+	0.692628i	$0.243547\pi$
$504$	−33.5880	−1.49613
$505$	1.90143	0.0846127
$506$	87.7070	3.89905
$507$	78.1064	3.46883
$508$	26.7352	1.18618
$509$	−10.9819	−0.486762	−0.243381	−	0.969931i	$-0.578257\pi$
$509$	−10.9819	−0.486762	−0.243381	+	0.969931i	$0.578257\pi$
$510$	−13.0216	−0.576605
$511$	−0.207627	−0.00918490
$512$	44.1900	1.95294
$513$	−1.56157	−0.0689449
$514$	77.3384	3.41125
$515$	0.391888	0.0172687
$516$	69.3554	3.05320
$517$	−2.88365	−0.126823
$518$	4.34119	0.190741
$519$	26.8199	1.17726
$520$	32.9099	1.44320
$521$	3.47470	0.152229	0.0761147	−	0.997099i	$-0.475748\pi$
$521$	3.47470	0.152229	0.0761147	+	0.997099i	$0.475748\pi$
$522$	−67.6172	−2.95953
$523$	−39.0149	−1.70600	−0.853001	−	0.521909i	$-0.825220\pi$
$523$	−39.0149	−1.70600	−0.853001	+	0.521909i	$0.825220\pi$
$524$	−27.3757	−1.19591
$525$	3.17189	0.138433
$526$	−38.9289	−1.69738
$527$	−1.87412	−0.0816378
$528$	−61.4271	−2.67327
$529$	46.0435	2.00189
$530$	31.5294	1.36955
$531$	64.3086	2.79076
$532$	−0.744248	−0.0322672
$533$	−62.0258	−2.68664
$534$	55.3003	2.39308
$535$	12.4370	0.537697
$536$	16.9558	0.732380
$537$	−3.00103	−0.129504
$538$	9.92296	0.427809
$539$	25.0998	1.08112
$540$	−37.7407	−1.62410
$541$	29.5554	1.27069	0.635343	−	0.772230i	$-0.280859\pi$
$541$	29.5554	1.27069	0.635343	+	0.772230i	$0.280859\pi$
$542$	−7.78088	−0.334217
$543$	−1.25104	−0.0536872
$544$	2.31049	0.0990613
$545$	−9.85066	−0.421956
$546$	−49.0263	−2.09813
$547$	27.6308	1.18141	0.590704	−	0.806889i	$-0.298850\pi$
$547$	27.6308	1.18141	0.590704	+	0.806889i	$0.298850\pi$
$548$	−56.6976	−2.42200
$549$	2.86956	0.122470
$550$	10.5554	0.450082
$551$	−0.772575	−0.0329128
$552$	−131.693	−5.60521
$553$	15.2446	0.648267
$554$	37.9947	1.61424
$555$	4.99751	0.212132
$556$	−24.0895	−1.02162
$557$	20.4628	0.867039	0.433519	−	0.901144i	$-0.357272\pi$
$557$	20.4628	0.867039	0.433519	+	0.901144i	$0.357272\pi$
$558$	−16.0195	−0.678162
$559$	34.8772	1.47515
$560$	−5.05524	−0.213623
$561$	22.4250	0.946785
$562$	−53.1708	−2.24287
$563$	−20.8219	−0.877539	−0.438770	−	0.898600i	$-0.644586\pi$
$563$	−20.8219	−0.877539	−0.438770	+	0.898600i	$0.644586\pi$
$564$	8.39689	0.353573
$565$	−1.98876	−0.0836678
$566$	73.0490	3.07048
$567$	9.87532	0.414724
$568$	47.8734	2.00872
$569$	−31.0594	−1.30208	−0.651040	−	0.759044i	$-0.725667\pi$
$569$	−31.0594	−1.30208	−0.651040	+	0.759044i	$0.725667\pi$
$570$	−1.27175	−0.0532676
$571$	−34.8010	−1.45638	−0.728189	−	0.685377i	$-0.759638\pi$
$571$	−34.8010	−1.45638	−0.728189	+	0.685377i	$0.759638\pi$
$572$	−109.912	−4.59566
$573$	5.84041	0.243987
$574$	25.9478	1.08304
$575$	8.30924	0.346519
$576$	−38.1356	−1.58898
$577$	4.89788	0.203902	0.101951	−	0.994789i	$-0.467492\pi$
$577$	4.89788	0.203902	0.101951	+	0.994789i	$0.467492\pi$
$578$	34.5109	1.43546
$579$	−4.58966	−0.190740
$580$	−18.6720	−0.775311
$581$	−12.7195	−0.527694
$582$	−91.6342	−3.79836
$583$	−54.2982	−2.24880
$584$	1.03745	0.0429300
$585$	−37.7086	−1.55906
$586$	−36.4460	−1.50557
$587$	−16.0316	−0.661693	−0.330847	−	0.943685i	$-0.607334\pi$
$587$	−16.0316	−0.661693	−0.330847	+	0.943685i	$0.607334\pi$
$588$	−73.0881	−3.01410
$589$	−0.183035	−0.00754182
$590$	26.3597	1.08521
$591$	68.5047	2.81791
$592$	−7.96484	−0.327353
$593$	−10.1454	−0.416620	−0.208310	−	0.978063i	$-0.566796\pi$
$593$	−10.1454	−0.416620	−0.208310	+	0.978063i	$0.566796\pi$
$594$	96.4756	3.95844
$595$	1.84550	0.0756583
$596$	−7.68706	−0.314874
$597$	80.5190	3.29542
$598$	−128.432	−5.25196
$599$	8.81967	0.360362	0.180181	−	0.983633i	$-0.442332\pi$
$599$	8.81967	0.360362	0.180181	+	0.983633i	$0.442332\pi$
$600$	−15.8489	−0.647030
$601$	−29.6476	−1.20935	−0.604675	−	0.796472i	$-0.706697\pi$
$601$	−29.6476	−1.20935	−0.604675	+	0.796472i	$0.706697\pi$
$602$	−14.5905	−0.594663
$603$	−19.4282	−0.791177
$604$	−80.7506	−3.28570
$605$	−7.17786	−0.291821
$606$	14.1536	0.574949
$607$	−21.4442	−0.870392	−0.435196	−	0.900336i	$-0.643321\pi$
$607$	−21.4442	−0.870392	−0.435196	+	0.900336i	$0.643321\pi$
$608$	0.225653	0.00915142
$609$	14.3431	0.581211
$610$	1.17621	0.0476234
$611$	4.22260	0.170828
$612$	−43.6291	−1.76360
$613$	−26.1194	−1.05495	−0.527477	−	0.849569i	$-0.676862\pi$
$613$	−26.1194	−1.05495	−0.527477	+	0.849569i	$0.676862\pi$
$614$	−7.28107	−0.293840
$615$	29.8707	1.20450
$616$	23.7096	0.955288
$617$	2.98676	0.120242	0.0601211	−	0.998191i	$-0.480851\pi$
$617$	2.98676	0.120242	0.0601211	+	0.998191i	$0.480851\pi$
$618$	2.91707	0.117342
$619$	9.61392	0.386416	0.193208	−	0.981158i	$-0.438111\pi$
$619$	9.61392	0.386416	0.193208	+	0.981158i	$0.438111\pi$
$620$	−4.42367	−0.177659
$621$	75.9461	3.04761
$622$	−83.0369	−3.32948
$623$	−7.83753	−0.314004
$624$	89.9493	3.60085
$625$	1.00000	0.0400000
$626$	−44.8200	−1.79137
$627$	2.19013	0.0874654
$628$	41.3413	1.64970
$629$	2.90771	0.115938
$630$	15.7750	0.628490
$631$	−30.7746	−1.22512	−0.612558	−	0.790426i	$-0.709859\pi$
$631$	−30.7746	−1.22512	−0.612558	+	0.790426i	$0.709859\pi$
$632$	−76.1726	−3.02998
$633$	47.4185	1.88471
$634$	−12.2397	−0.486103
$635$	−6.47468	−0.256940
$636$	158.111	6.26951
$637$	−36.7543	−1.45626
$638$	47.7307	1.88968
$639$	−54.8539	−2.16999
$640$	−18.2730	−0.722306
$641$	27.1564	1.07261	0.536307	−	0.844023i	$-0.319819\pi$
$641$	27.1564	1.07261	0.536307	+	0.844023i	$0.319819\pi$
$642$	92.5760	3.65368
$643$	47.9739	1.89191	0.945954	−	0.324301i	$-0.105129\pi$
$643$	47.9739	1.89191	0.945954	+	0.324301i	$0.105129\pi$
$644$	36.1962	1.42633
$645$	−16.7963	−0.661355
$646$	−0.739942	−0.0291126
$647$	−37.4123	−1.47083	−0.735414	−	0.677618i	$-0.763012\pi$
$647$	−37.4123	−1.47083	−0.735414	+	0.677618i	$0.763012\pi$
$648$	−49.3439	−1.93841
$649$	−45.3951	−1.78192
$650$	−15.4565	−0.606254
$651$	3.39809	0.133182
$652$	79.4134	3.11007
$653$	27.9253	1.09280	0.546401	−	0.837524i	$-0.315997\pi$
$653$	27.9253	1.09280	0.546401	+	0.837524i	$0.315997\pi$
$654$	−73.3246	−2.86722
$655$	6.62979	0.259047
$656$	−47.6069	−1.85874
$657$	−1.18872	−0.0463765
$658$	−1.76648	−0.0688644
$659$	4.73281	0.184364	0.0921820	−	0.995742i	$-0.470616\pi$
$659$	4.73281	0.184364	0.0921820	+	0.995742i	$0.470616\pi$
$660$	52.9321	2.06038
$661$	1.20016	0.0466807	0.0233403	−	0.999728i	$-0.492570\pi$
$661$	1.20016	0.0466807	0.0233403	+	0.999728i	$0.492570\pi$
$662$	−8.07232	−0.313740
$663$	−32.8376	−1.27531
$664$	63.5554	2.46643
$665$	0.180240	0.00698942
$666$	24.8544	0.963090
$667$	37.5739	1.45487
$668$	−30.1332	−1.16589
$669$	62.2679	2.40742
$670$	−7.96348	−0.307656
$671$	−2.02561	−0.0781976
$672$	−4.18930	−0.161606
$673$	−17.6044	−0.678598	−0.339299	−	0.940679i	$-0.610190\pi$
$673$	−17.6044	−0.678598	−0.339299	+	0.940679i	$0.610190\pi$
$674$	10.7590	0.414423
$675$	9.13996	0.351797
$676$	107.268	4.12569
$677$	−26.6270	−1.02336	−0.511679	−	0.859177i	$-0.670976\pi$
$677$	−26.6270	−1.02336	−0.511679	+	0.859177i	$0.670976\pi$
$678$	−14.8036	−0.568528
$679$	12.9870	0.498396
$680$	−9.22141	−0.353625
$681$	−5.68662	−0.217912
$682$	11.3081	0.433010
$683$	23.4791	0.898402	0.449201	−	0.893431i	$-0.351709\pi$
$683$	23.4791	0.898402	0.449201	+	0.893431i	$0.351709\pi$
$684$	−4.26102	−0.162924
$685$	13.7309	0.524631
$686$	33.6582	1.28508
$687$	73.5659	2.80671
$688$	26.7694	1.02057
$689$	79.5103	3.02910
$690$	61.8508	2.35462
$691$	−7.24215	−0.275504	−0.137752	−	0.990467i	$-0.543988\pi$
$691$	−7.24215	−0.275504	−0.137752	+	0.990467i	$0.543988\pi$
$692$	36.8333	1.40019
$693$	−27.1668	−1.03198
$694$	28.4206	1.07883
$695$	5.83394	0.221294
$696$	−71.6679	−2.71656
$697$	17.3797	0.658304
$698$	71.1648	2.69363
$699$	−5.73015	−0.216734
$700$	4.35613	0.164646
$701$	43.2162	1.63225	0.816126	−	0.577874i	$-0.196118\pi$
$701$	43.2162	1.63225	0.816126	+	0.577874i	$0.196118\pi$
$702$	−141.272	−5.33196
$703$	0.283980	0.0107105
$704$	26.9197	1.01458
$705$	−2.03354	−0.0765876
$706$	−50.7397	−1.90962
$707$	−2.00593	−0.0754409
$708$	132.186	4.96786
$709$	−5.57479	−0.209366	−0.104683	−	0.994506i	$-0.533383\pi$
$709$	−5.57479	−0.209366	−0.104683	+	0.994506i	$0.533383\pi$
$710$	−22.4842	−0.843818
$711$	87.2795	3.27324
$712$	39.1617	1.46765
$713$	8.90182	0.333376
$714$	13.7372	0.514103
$715$	26.6183	0.995469
$716$	−4.12149	−0.154027
$717$	−16.1694	−0.603856
$718$	−80.5783	−3.00716
$719$	22.9850	0.857195	0.428597	−	0.903496i	$-0.359008\pi$
$719$	22.9850	0.857195	0.428597	+	0.903496i	$0.359008\pi$
$720$	−28.9426	−1.07863
$721$	−0.413426	−0.0153968
$722$	46.9664	1.74791
$723$	63.6454	2.36700
$724$	−1.71812	−0.0638535
$725$	4.52194	0.167940
$726$	−53.4292	−1.98294
$727$	−6.47941	−0.240308	−0.120154	−	0.992755i	$-0.538339\pi$
$727$	−6.47941	−0.240308	−0.120154	+	0.992755i	$0.538339\pi$
$728$	−34.7186	−1.28676
$729$	−25.9030	−0.959371
$730$	−0.487249	−0.0180339
$731$	−9.77263	−0.361454
$732$	5.89836	0.218010
$733$	−40.6349	−1.50088	−0.750442	−	0.660936i	$-0.770160\pi$
$733$	−40.6349	−1.50088	−0.750442	+	0.660936i	$0.770160\pi$
$734$	35.1398	1.29704
$735$	17.7003	0.652886
$736$	−10.9745	−0.404526
$737$	13.7143	0.505171
$738$	148.558	5.46850
$739$	2.15976	0.0794481	0.0397240	−	0.999211i	$-0.487352\pi$
$739$	2.15976	0.0794481	0.0397240	+	0.999211i	$0.487352\pi$
$740$	6.86336	0.252302
$741$	−3.20707	−0.117815
$742$	−33.2622	−1.22109
$743$	7.06017	0.259012	0.129506	−	0.991579i	$-0.458661\pi$
$743$	7.06017	0.259012	0.129506	+	0.991579i	$0.458661\pi$
$744$	−16.9792	−0.622488
$745$	1.86164	0.0682051
$746$	14.8327	0.543062
$747$	−72.8226	−2.66444
$748$	30.7976	1.12607
$749$	−13.1205	−0.479412
$750$	7.44362	0.271803
$751$	39.1978	1.43035	0.715174	−	0.698946i	$-0.246347\pi$
$751$	39.1978	1.43035	0.715174	+	0.698946i	$0.246347\pi$
$752$	3.24098	0.118186
$753$	50.7108	1.84801
$754$	−69.8933	−2.54536
$755$	19.5560	0.711716
$756$	39.8149	1.44805
$757$	22.0309	0.800726	0.400363	−	0.916357i	$-0.368884\pi$
$757$	22.0309	0.800726	0.400363	+	0.916357i	$0.368884\pi$
$758$	51.8408	1.88294
$759$	−106.516	−3.86629
$760$	−0.900605	−0.0326684
$761$	16.5133	0.598606	0.299303	−	0.954158i	$-0.403246\pi$
$761$	16.5133	0.598606	0.299303	+	0.954158i	$0.403246\pi$
$762$	−48.1950	−1.74592
$763$	10.3920	0.376217
$764$	8.02097	0.290188
$765$	10.5660	0.382014
$766$	45.3875	1.63992
$767$	66.4733	2.40021
$768$	−98.0501	−3.53808
$769$	44.2172	1.59451	0.797256	−	0.603641i	$-0.206284\pi$
$769$	44.2172	1.59451	0.797256	+	0.603641i	$0.206284\pi$
$770$	−11.1355	−0.401295
$771$	−93.9238	−3.38258
$772$	−6.30324	−0.226858
$773$	10.8504	0.390263	0.195131	−	0.980777i	$-0.437487\pi$
$773$	10.8504	0.390263	0.195131	+	0.980777i	$0.437487\pi$
$774$	−83.5343	−3.00258
$775$	1.07132	0.0384828
$776$	−64.8921	−2.32949
$777$	−5.27216	−0.189138
$778$	82.8896	2.97174
$779$	1.69738	0.0608151
$780$	−77.5099	−2.77530
$781$	38.7211	1.38555
$782$	35.9867	1.28688
$783$	41.3303	1.47702
$784$	−28.2101	−1.00750
$785$	−10.0120	−0.357342
$786$	49.3496	1.76024
$787$	−29.7637	−1.06096	−0.530480	−	0.847698i	$-0.677988\pi$
$787$	−29.7637	−1.06096	−0.530480	+	0.847698i	$0.677988\pi$
$788$	94.0815	3.35151
$789$	47.2772	1.68311
$790$	35.7753	1.27283
$791$	2.09806	0.0745985
$792$	135.744	4.82345
$793$	2.96615	0.105331
$794$	21.3912	0.759146
$795$	−38.2910	−1.35804
$796$	110.581	3.91945
$797$	−7.99680	−0.283261	−0.141631	−	0.989920i	$-0.545234\pi$
$797$	−7.99680	−0.283261	−0.141631	+	0.989920i	$0.545234\pi$
$798$	1.34164	0.0474935
$799$	−1.18318	−0.0418578
$800$	−1.32076	−0.0466959
$801$	−44.8719	−1.58547
$802$	−6.01644	−0.212448
$803$	0.839113	0.0296117
$804$	−39.9346	−1.40838
$805$	−8.76591	−0.308958
$806$	−16.5588	−0.583258
$807$	−12.0510	−0.424214
$808$	10.0230	0.352609
$809$	−1.66773	−0.0586342	−0.0293171	−	0.999570i	$-0.509333\pi$
$809$	−1.66773	−0.0586342	−0.0293171	+	0.999570i	$0.509333\pi$
$810$	23.1749	0.814282
$811$	−25.5166	−0.896011	−0.448005	−	0.894031i	$-0.647865\pi$
$811$	−25.5166	−0.896011	−0.448005	+	0.894031i	$0.647865\pi$
$812$	19.6982	0.691270
$813$	9.44951	0.331409
$814$	−17.5446	−0.614939
$815$	−19.2322	−0.673673
$816$	−25.2039	−0.882313
$817$	−0.954440	−0.0333916
$818$	−43.2457	−1.51205
$819$	39.7810	1.39006
$820$	41.0232	1.43259
$821$	−8.89737	−0.310520	−0.155260	−	0.987874i	$-0.549622\pi$
$821$	−8.89737	−0.310520	−0.155260	+	0.987874i	$0.549622\pi$
$822$	102.208	3.56490
$823$	39.3278	1.37088	0.685440	−	0.728129i	$-0.259610\pi$
$823$	39.3278	1.37088	0.685440	+	0.728129i	$0.259610\pi$
$824$	2.06576	0.0719642
$825$	−12.8190	−0.446300
$826$	−27.8084	−0.967577
$827$	−38.3630	−1.33401	−0.667006	−	0.745052i	$-0.732425\pi$
$827$	−38.3630	−1.33401	−0.667006	+	0.745052i	$0.732425\pi$
$828$	207.233	7.20183
$829$	38.1718	1.32576	0.662880	−	0.748726i	$-0.269334\pi$
$829$	38.1718	1.32576	0.662880	+	0.748726i	$0.269334\pi$
$830$	−29.8495	−1.03609
$831$	−46.1428	−1.60068
$832$	−39.4193	−1.36662
$833$	10.2986	0.356825
$834$	43.4256	1.50371
$835$	7.29758	0.252543
$836$	3.00783	0.104028
$837$	9.79178	0.338453
$838$	70.4835	2.43481
$839$	−19.7398	−0.681495	−0.340747	−	0.940155i	$-0.610680\pi$
$839$	−19.7398	−0.681495	−0.340747	+	0.940155i	$0.610680\pi$
$840$	16.7200	0.576894
$841$	−8.55209	−0.294900
$842$	60.0111	2.06812
$843$	64.5734	2.22403
$844$	65.1225	2.24161
$845$	−25.9779	−0.893667
$846$	−10.1135	−0.347711
$847$	7.57234	0.260189
$848$	61.0267	2.09567
$849$	−88.7145	−3.04468
$850$	4.33093	0.148550
$851$	−13.8112	−0.473443
$852$	−112.752	−3.86282
$853$	12.4615	0.426675	0.213337	−	0.976979i	$-0.431567\pi$
$853$	12.4615	0.426675	0.213337	+	0.976979i	$0.431567\pi$
$854$	−1.24085	−0.0424612
$855$	1.03192	0.0352910
$856$	65.5590	2.24076
$857$	−3.81966	−0.130477	−0.0652385	−	0.997870i	$-0.520781\pi$
$857$	−3.81966	−0.130477	−0.0652385	+	0.997870i	$0.520781\pi$
$858$	198.137	6.76427
$859$	−12.9451	−0.441680	−0.220840	−	0.975310i	$-0.570880\pi$
$859$	−12.9451	−0.441680	−0.220840	+	0.975310i	$0.570880\pi$
$860$	−23.0674	−0.786590
$861$	−31.5124	−1.07394
$862$	−87.4662	−2.97911
$863$	−1.99855	−0.0680314	−0.0340157	−	0.999421i	$-0.510830\pi$
$863$	−1.99855	−0.0680314	−0.0340157	+	0.999421i	$0.510830\pi$
$864$	−12.0717	−0.410687
$865$	−8.92020	−0.303296
$866$	−87.0258	−2.95726
$867$	−41.9119	−1.42340
$868$	4.66679	0.158401
$869$	−61.6102	−2.08998
$870$	33.6596	1.14117
$871$	−20.0822	−0.680458
$872$	−51.9258	−1.75843
$873$	74.3541	2.51650
$874$	3.51463	0.118884
$875$	−1.05496	−0.0356641
$876$	−2.44341	−0.0825553
$877$	−16.0864	−0.543200	−0.271600	−	0.962410i	$-0.587553\pi$
$877$	−16.0864	−0.543200	−0.271600	+	0.962410i	$0.587553\pi$
$878$	−17.1491	−0.578754
$879$	44.2620	1.49292
$880$	20.4304	0.688710
$881$	29.9839	1.01018	0.505091	−	0.863066i	$-0.331459\pi$
$881$	29.9839	1.01018	0.505091	+	0.863066i	$0.331459\pi$
$882$	88.0302	2.96413
$883$	58.1856	1.95810	0.979051	−	0.203616i	$-0.0652693\pi$
$883$	58.1856	1.95810	0.979051	+	0.203616i	$0.0652693\pi$
$884$	−45.0977	−1.51680
$885$	−32.0126	−1.07609
$886$	−72.6429	−2.44049
$887$	−40.6072	−1.36346	−0.681728	−	0.731605i	$-0.738771\pi$
$887$	−40.6072	−1.36346	−0.681728	+	0.731605i	$0.738771\pi$
$888$	26.3434	0.884026
$889$	6.83052	0.229088
$890$	−18.3927	−0.616525
$891$	−39.9105	−1.33705
$892$	85.5161	2.86329
$893$	−0.115555	−0.00386689
$894$	13.8573	0.463458
$895$	0.998132	0.0333639
$896$	19.2773	0.644010
$897$	155.974	5.20783
$898$	−13.9454	−0.465363
$899$	4.84442	0.161570
$900$	24.9400	0.831334
$901$	−22.2789	−0.742217
$902$	−104.866	−3.49167
$903$	17.7194	0.589666
$904$	−10.4834	−0.348671
$905$	0.416091	0.0138313
$906$	145.567	4.83615
$907$	−6.49382	−0.215624	−0.107812	−	0.994171i	$-0.534384\pi$
$907$	−6.49382	−0.215624	−0.107812	+	0.994171i	$0.534384\pi$
$908$	−7.80976	−0.259176
$909$	−11.4845	−0.380917
$910$	16.3060	0.540538
$911$	14.8134	0.490791	0.245395	−	0.969423i	$-0.421082\pi$
$911$	14.8134	0.490791	0.245395	+	0.969423i	$0.421082\pi$
$912$	−2.46153	−0.0815093
$913$	51.4051	1.70126
$914$	35.6422	1.17894
$915$	−1.42845	−0.0472232
$916$	101.032	3.33820
$917$	−6.99415	−0.230967
$918$	39.5845	1.30648
$919$	18.7065	0.617071	0.308536	−	0.951213i	$-0.400161\pi$
$919$	18.7065	0.617071	0.308536	+	0.951213i	$0.400161\pi$
$920$	43.8005	1.44406
$921$	8.84252	0.291371
$922$	52.3774	1.72496
$923$	−56.7003	−1.86631
$924$	−55.8412	−1.83704
$925$	−1.66215	−0.0546513
$926$	41.8206	1.37431
$927$	−2.36697	−0.0777416
$928$	−5.97239	−0.196053
$929$	36.5848	1.20031	0.600155	−	0.799884i	$-0.295106\pi$
$929$	36.5848	1.20031	0.600155	+	0.799884i	$0.295106\pi$
$930$	7.97446	0.261493
$931$	1.00581	0.0329640
$932$	−7.86954	−0.257775
$933$	100.844	3.30150
$934$	38.1971	1.24985
$935$	−7.45849	−0.243919
$936$	−198.773	−6.49711
$937$	−24.2488	−0.792173	−0.396086	−	0.918213i	$-0.629632\pi$
$937$	−24.2488	−0.792173	−0.396086	+	0.918213i	$0.629632\pi$
$938$	8.40114	0.274307
$939$	54.4317	1.77631
$940$	−2.79278	−0.0910904
$941$	−53.3562	−1.73936	−0.869681	−	0.493613i	$-0.835676\pi$
$941$	−53.3562	−1.73936	−0.869681	+	0.493613i	$0.835676\pi$
$942$	−74.5252	−2.42816
$943$	−82.5515	−2.68825
$944$	51.0204	1.66057
$945$	−9.64228	−0.313663
$946$	58.9665	1.91717
$947$	−40.3056	−1.30976	−0.654878	−	0.755735i	$-0.727280\pi$
$947$	−40.3056	−1.30976	−0.654878	+	0.755735i	$0.727280\pi$
$948$	179.403	5.82673
$949$	−1.22874	−0.0398864
$950$	0.422978	0.0137232
$951$	14.8646	0.482017
$952$	9.72821	0.315293
$953$	15.9873	0.517879	0.258940	−	0.965893i	$-0.416627\pi$
$953$	15.9873	0.517879	0.258940	+	0.965893i	$0.416627\pi$
$954$	−190.435	−6.16556
$955$	−1.94250	−0.0628578
$956$	−22.2063	−0.718204
$957$	−57.9666	−1.87379
$958$	−35.9144	−1.16034
$959$	−14.4855	−0.467762
$960$	18.9837	0.612698
$961$	−29.8523	−0.962977
$962$	25.6911	0.828314
$963$	−75.1182	−2.42065
$964$	87.4078	2.81522
$965$	1.52650	0.0491399
$966$	−65.2501	−2.09939
$967$	−9.29247	−0.298826	−0.149413	−	0.988775i	$-0.547738\pi$
$967$	−9.29247	−0.298826	−0.149413	+	0.988775i	$0.547738\pi$
$968$	−37.8367	−1.21612
$969$	0.898624	0.0288680
$970$	30.4772	0.978565
$971$	45.2599	1.45246	0.726230	−	0.687452i	$-0.241271\pi$
$971$	45.2599	1.45246	0.726230	+	0.687452i	$0.241271\pi$
$972$	2.99331	0.0960104
$973$	−6.15456	−0.197306
$974$	6.33194	0.202888
$975$	18.7712	0.601159
$976$	2.27662	0.0728727
$977$	43.1106	1.37923	0.689615	−	0.724176i	$-0.257780\pi$
$977$	43.1106	1.37923	0.689615	+	0.724176i	$0.257780\pi$
$978$	−143.157	−4.57765
$979$	31.6749	1.01233
$980$	24.3088	0.776518
$981$	59.4972	1.89960
$982$	42.4206	1.35370
$983$	43.8662	1.39912	0.699558	−	0.714576i	$-0.253380\pi$
$983$	43.8662	1.39912	0.699558	+	0.714576i	$0.253380\pi$
$984$	157.458	5.01956
$985$	−22.7844	−0.725973
$986$	19.5842	0.623688
$987$	2.14530	0.0682857
$988$	−4.40445	−0.140124
$989$	46.4188	1.47603
$990$	−63.7535	−2.02622
$991$	37.1766	1.18095	0.590477	−	0.807055i	$-0.298940\pi$
$991$	37.1766	1.18095	0.590477	+	0.807055i	$0.298940\pi$
$992$	−1.41495	−0.0449247
$993$	9.80345	0.311103
$994$	23.7199	0.752351
$995$	−26.7803	−0.848993
$996$	−149.687	−4.74300
$997$	−33.4998	−1.06095	−0.530475	−	0.847701i	$-0.677986\pi$
$997$	−33.4998	−1.06095	−0.530475	+	0.847701i	$0.677986\pi$
$998$	14.4883	0.458618
$999$	−15.1920	−0.480654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.14	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.14	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47572 q^{2} +3.00665 q^{3} +4.12920 q^{4} -1.00000 q^{5} -7.44362 q^{6} +1.05496 q^{7} -5.27130 q^{8} +6.03992 q^{9} +O(q^{10})\)	\(q-2.47572 q^{2} +3.00665 q^{3} +4.12920 q^{4} -1.00000 q^{5} -7.44362 q^{6} +1.05496 q^{7} -5.27130 q^{8} +6.03992 q^{9} +2.47572 q^{10} -4.26355 q^{11} +12.4150 q^{12} +6.24323 q^{13} -2.61178 q^{14} -3.00665 q^{15} +4.79188 q^{16} -1.74936 q^{17} -14.9532 q^{18} -0.170851 q^{19} -4.12920 q^{20} +3.17189 q^{21} +10.5554 q^{22} +8.30924 q^{23} -15.8489 q^{24} +1.00000 q^{25} -15.4565 q^{26} +9.13996 q^{27} +4.35613 q^{28} +4.52194 q^{29} +7.44362 q^{30} +1.07132 q^{31} -1.32076 q^{32} -12.8190 q^{33} +4.33093 q^{34} -1.05496 q^{35} +24.9400 q^{36} -1.66215 q^{37} +0.422978 q^{38} +18.7712 q^{39} +5.27130 q^{40} -9.93490 q^{41} -7.85271 q^{42} +5.58640 q^{43} -17.6050 q^{44} -6.03992 q^{45} -20.5714 q^{46} +0.676349 q^{47} +14.4075 q^{48} -5.88706 q^{49} -2.47572 q^{50} -5.25971 q^{51} +25.7795 q^{52} +12.7354 q^{53} -22.6280 q^{54} +4.26355 q^{55} -5.56101 q^{56} -0.513687 q^{57} -11.1951 q^{58} +10.6473 q^{59} -12.4150 q^{60} +0.475098 q^{61} -2.65228 q^{62} +6.37187 q^{63} -6.31393 q^{64} -6.24323 q^{65} +31.7362 q^{66} -3.21663 q^{67} -7.22346 q^{68} +24.9829 q^{69} +2.61178 q^{70} -9.08189 q^{71} -31.8382 q^{72} -0.196811 q^{73} +4.11503 q^{74} +3.00665 q^{75} -0.705476 q^{76} -4.49787 q^{77} -46.4722 q^{78} +14.4504 q^{79} -4.79188 q^{80} +9.36086 q^{81} +24.5960 q^{82} -12.0569 q^{83} +13.0974 q^{84} +1.74936 q^{85} -13.8304 q^{86} +13.5959 q^{87} +22.4745 q^{88} -7.42923 q^{89} +14.9532 q^{90} +6.58635 q^{91} +34.3105 q^{92} +3.22107 q^{93} -1.67445 q^{94} +0.170851 q^{95} -3.97106 q^{96} +12.3104 q^{97} +14.5747 q^{98} -25.7515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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