LMFDB - Embedded newform 6041.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34195 q^{2} +3.16467 q^{3} +3.48474 q^{4} -1.79579 q^{5} -7.41150 q^{6} -1.00000 q^{7} -3.47719 q^{8} +7.01511 q^{9} +O(q^{10})$	\(q-2.34195 q^{2} +3.16467 q^{3} +3.48474 q^{4} -1.79579 q^{5} -7.41150 q^{6} -1.00000 q^{7} -3.47719 q^{8} +7.01511 q^{9} +4.20566 q^{10} -0.00153293 q^{11} +11.0280 q^{12} -1.08361 q^{13} +2.34195 q^{14} -5.68308 q^{15} +1.17393 q^{16} -0.00109281 q^{17} -16.4291 q^{18} +1.26286 q^{19} -6.25787 q^{20} -3.16467 q^{21} +0.00359004 q^{22} -8.17763 q^{23} -11.0041 q^{24} -1.77513 q^{25} +2.53776 q^{26} +12.7065 q^{27} -3.48474 q^{28} +1.89370 q^{29} +13.3095 q^{30} -0.166564 q^{31} +4.20509 q^{32} -0.00485120 q^{33} +0.00255931 q^{34} +1.79579 q^{35} +24.4458 q^{36} -8.17094 q^{37} -2.95756 q^{38} -3.42926 q^{39} +6.24431 q^{40} +8.76786 q^{41} +7.41150 q^{42} +2.67444 q^{43} -0.00534185 q^{44} -12.5977 q^{45} +19.1516 q^{46} +3.03158 q^{47} +3.71509 q^{48} +1.00000 q^{49} +4.15727 q^{50} -0.00345839 q^{51} -3.77610 q^{52} +1.20270 q^{53} -29.7580 q^{54} +0.00275282 q^{55} +3.47719 q^{56} +3.99653 q^{57} -4.43495 q^{58} +14.9895 q^{59} -19.8041 q^{60} -13.7034 q^{61} +0.390084 q^{62} -7.01511 q^{63} -12.1960 q^{64} +1.94594 q^{65} +0.0113613 q^{66} +12.9275 q^{67} -0.00380817 q^{68} -25.8795 q^{69} -4.20566 q^{70} -16.5976 q^{71} -24.3929 q^{72} -16.7917 q^{73} +19.1360 q^{74} -5.61769 q^{75} +4.40074 q^{76} +0.00153293 q^{77} +8.03117 q^{78} -12.6265 q^{79} -2.10813 q^{80} +19.1665 q^{81} -20.5339 q^{82} -9.97860 q^{83} -11.0280 q^{84} +0.00196246 q^{85} -6.26342 q^{86} +5.99293 q^{87} +0.00533028 q^{88} +2.65021 q^{89} +29.5032 q^{90} +1.08361 q^{91} -28.4969 q^{92} -0.527119 q^{93} -7.09982 q^{94} -2.26784 q^{95} +13.3077 q^{96} -2.05929 q^{97} -2.34195 q^{98} -0.0107537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.34195	−1.65601	−0.828005	−	0.560721i	$-0.810524\pi$
$2$	−2.34195	−1.65601	−0.828005	+	0.560721i	$0.810524\pi$
$3$	3.16467	1.82712	0.913560	−	0.406703i	$-0.133322\pi$
$3$	3.16467	1.82712	0.913560	+	0.406703i	$0.133322\pi$
$4$	3.48474	1.74237
$5$	−1.79579	−0.803103	−0.401551	−	0.915837i	$-0.631529\pi$
$5$	−1.79579	−0.803103	−0.401551	+	0.915837i	$0.631529\pi$
$6$	−7.41150	−3.02573
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.47719	−1.22937
$9$	7.01511	2.33837
$10$	4.20566	1.32995
$11$	−0.00153293	−0.000462195 0	−0.000231098	−	1.00000i	$-0.500074\pi$
$11$	−0.00153293	−0.000462195 0	−0.000231098		1.00000i	$0.500074\pi$
$12$	11.0280	3.18352
$13$	−1.08361	−0.300539	−0.150270	−	0.988645i	$-0.548014\pi$
$13$	−1.08361	−0.300539	−0.150270	+	0.988645i	$0.548014\pi$
$14$	2.34195	0.625913
$15$	−5.68308	−1.46737
$16$	1.17393	0.293482
$17$	−0.00109281	−0.000265046 0	−0.000132523	−	1.00000i	$-0.500042\pi$
$17$	−0.00109281	−0.000265046 0	−0.000132523		1.00000i	$0.500042\pi$
$18$	−16.4291	−3.87236
$19$	1.26286	0.289720	0.144860	−	0.989452i	$-0.453727\pi$
$19$	1.26286	0.289720	0.144860	+	0.989452i	$0.453727\pi$
$20$	−6.25787	−1.39930
$21$	−3.16467	−0.690587
$22$	0.00359004	0.000765400 0
$23$	−8.17763	−1.70515	−0.852576	−	0.522603i	$-0.824961\pi$
$23$	−8.17763	−1.70515	−0.852576	+	0.522603i	$0.824961\pi$
$24$	−11.0041	−2.24621
$25$	−1.77513	−0.355026
$26$	2.53776	0.497696
$27$	12.7065	2.44536
$28$	−3.48474	−0.658554
$29$	1.89370	0.351651	0.175826	−	0.984421i	$-0.443741\pi$
$29$	1.89370	0.351651	0.175826	+	0.984421i	$0.443741\pi$
$30$	13.3095	2.42997
$31$	−0.166564	−0.0299157	−0.0149579	−	0.999888i	$-0.504761\pi$
$31$	−0.166564	−0.0299157	−0.0149579	+	0.999888i	$0.504761\pi$
$32$	4.20509	0.743363
$33$	−0.00485120	−0.000844486 0
$34$	0.00255931	0.000438919 0
$35$	1.79579	0.303544
$36$	24.4458	4.07431
$37$	−8.17094	−1.34330	−0.671648	−	0.740871i	$-0.734413\pi$
$37$	−8.17094	−1.34330	−0.671648	+	0.740871i	$0.734413\pi$
$38$	−2.95756	−0.479780
$39$	−3.42926	−0.549121
$40$	6.24431	0.987311
$41$	8.76786	1.36931	0.684655	−	0.728868i	$-0.259953\pi$
$41$	8.76786	1.36931	0.684655	+	0.728868i	$0.259953\pi$
$42$	7.41150	1.14362
$43$	2.67444	0.407849	0.203924	−	0.978987i	$-0.434630\pi$
$43$	2.67444	0.407849	0.203924	+	0.978987i	$0.434630\pi$
$44$	−0.00534185	−0.000805315 0
$45$	−12.5977	−1.87795
$46$	19.1516	2.82375
$47$	3.03158	0.442202	0.221101	−	0.975251i	$-0.429035\pi$
$47$	3.03158	0.442202	0.221101	+	0.975251i	$0.429035\pi$
$48$	3.71509	0.536227
$49$	1.00000	0.142857
$50$	4.15727	0.587927
$51$	−0.00345839	−0.000484271 0
$52$	−3.77610	−0.523650
$53$	1.20270	0.165204	0.0826020	−	0.996583i	$-0.473677\pi$
$53$	1.20270	0.165204	0.0826020	+	0.996583i	$0.473677\pi$
$54$	−29.7580	−4.04955
$55$	0.00275282	0.000371190 0
$56$	3.47719	0.464659
$57$	3.99653	0.529354
$58$	−4.43495	−0.582338
$59$	14.9895	1.95147	0.975736	−	0.218952i	$-0.0702637\pi$
$59$	14.9895	1.95147	0.975736	+	0.218952i	$0.0702637\pi$
$60$	−19.8041	−2.55669
$61$	−13.7034	−1.75454	−0.877270	−	0.479997i	$-0.840638\pi$
$61$	−13.7034	−1.75454	−0.877270	+	0.479997i	$0.840638\pi$
$62$	0.390084	0.0495408
$63$	−7.01511	−0.883821
$64$	−12.1960	−1.52450
$65$	1.94594	0.241364
$66$	0.0113613	0.00139848
$67$	12.9275	1.57934	0.789672	−	0.613529i	$-0.210251\pi$
$67$	12.9275	1.57934	0.789672	+	0.613529i	$0.210251\pi$
$68$	−0.00380817	−0.000461808 0
$69$	−25.8795	−3.11552
$70$	−4.20566	−0.502672
$71$	−16.5976	−1.96977	−0.984884	−	0.173213i	$-0.944585\pi$
$71$	−16.5976	−1.96977	−0.984884	+	0.173213i	$0.944585\pi$
$72$	−24.3929	−2.87473
$73$	−16.7917	−1.96532	−0.982660	−	0.185417i	$-0.940636\pi$
$73$	−16.7917	−1.96532	−0.982660	+	0.185417i	$0.940636\pi$
$74$	19.1360	2.22451
$75$	−5.61769	−0.648675
$76$	4.40074	0.504800
$77$	0.00153293	0.000174693 0
$78$	8.03117	0.909350
$79$	−12.6265	−1.42059	−0.710297	−	0.703902i	$-0.751440\pi$
$79$	−12.6265	−1.42059	−0.710297	+	0.703902i	$0.751440\pi$
$80$	−2.10813	−0.235696
$81$	19.1665	2.12961
$82$	−20.5339	−2.26759
$83$	−9.97860	−1.09529	−0.547647	−	0.836710i	$-0.684476\pi$
$83$	−9.97860	−1.09529	−0.547647	+	0.836710i	$0.684476\pi$
$84$	−11.0280	−1.20326
$85$	0.00196246	0.000212859 0
$86$	−6.26342	−0.675402
$87$	5.99293	0.642509
$88$	0.00533028	0.000568209 0
$89$	2.65021	0.280921	0.140461	−	0.990086i	$-0.455142\pi$
$89$	2.65021	0.280921	0.140461	+	0.990086i	$0.455142\pi$
$90$	29.5032	3.10991
$91$	1.08361	0.113593
$92$	−28.4969	−2.97101
$93$	−0.527119	−0.0546597
$94$	−7.09982	−0.732291
$95$	−2.26784	−0.232675
$96$	13.3077	1.35821
$97$	−2.05929	−0.209089	−0.104545	−	0.994520i	$-0.533339\pi$
$97$	−2.05929	−0.209089	−0.104545	+	0.994520i	$0.533339\pi$
$98$	−2.34195	−0.236573
$99$	−0.0107537	−0.00108078
$100$	−6.18586	−0.618586
$101$	−13.3654	−1.32990	−0.664952	−	0.746886i	$-0.731548\pi$
$101$	−13.3654	−1.32990	−0.664952	+	0.746886i	$0.731548\pi$
$102$	0.00809938	0.000801958 0
$103$	15.9216	1.56880	0.784402	−	0.620253i	$-0.212970\pi$
$103$	15.9216	1.56880	0.784402	+	0.620253i	$0.212970\pi$
$104$	3.76791	0.369474
$105$	5.68308	0.554612
$106$	−2.81667	−0.273579
$107$	6.66888	0.644705	0.322352	−	0.946620i	$-0.395526\pi$
$107$	6.66888	0.644705	0.322352	+	0.946620i	$0.395526\pi$
$108$	44.2788	4.26073
$109$	2.11203	0.202296	0.101148	−	0.994871i	$-0.467748\pi$
$109$	2.11203	0.202296	0.101148	+	0.994871i	$0.467748\pi$
$110$	−0.00644697	−0.000614695 0
$111$	−25.8583	−2.45436
$112$	−1.17393	−0.110926
$113$	−19.7987	−1.86251	−0.931254	−	0.364370i	$-0.881284\pi$
$113$	−19.7987	−1.86251	−0.931254	+	0.364370i	$0.881284\pi$
$114$	−9.35969	−0.876615
$115$	14.6853	1.36941
$116$	6.59905	0.612706
$117$	−7.60164	−0.702772
$118$	−35.1048	−3.23166
$119$	0.00109281	0.000100178 0
$120$	19.7611	1.80394
$121$	−11.0000	−1.00000
$122$	32.0927	2.90554
$123$	27.7473	2.50189
$124$	−0.580431	−0.0521243
$125$	12.1667	1.08823
$126$	16.4291	1.46362
$127$	8.29613	0.736162	0.368081	−	0.929794i	$-0.380015\pi$
$127$	8.29613	0.736162	0.368081	+	0.929794i	$0.380015\pi$
$128$	20.1522	1.78122
$129$	8.46372	0.745189
$130$	−4.55729	−0.399701
$131$	−3.65194	−0.319072	−0.159536	−	0.987192i	$-0.551000\pi$
$131$	−3.65194	−0.319072	−0.159536	+	0.987192i	$0.551000\pi$
$132$	−0.0169052	−0.00147141
$133$	−1.26286	−0.109504
$134$	−30.2756	−2.61541
$135$	−22.8182	−1.96388
$136$	0.00379991	0.000325840 0
$137$	12.7992	1.09351	0.546755	−	0.837292i	$-0.315863\pi$
$137$	12.7992	1.09351	0.546755	+	0.837292i	$0.315863\pi$
$138$	60.6084	5.15933
$139$	0.730920	0.0619958	0.0309979	−	0.999519i	$-0.490131\pi$
$139$	0.730920	0.0619958	0.0309979	+	0.999519i	$0.490131\pi$
$140$	6.25787	0.528886
$141$	9.59395	0.807956
$142$	38.8707	3.26196
$143$	0.00166109	0.000138908 0
$144$	8.23523	0.686269
$145$	−3.40069	−0.282412
$146$	39.3254	3.25459
$147$	3.16467	0.261017
$148$	−28.4736	−2.34052
$149$	−19.2854	−1.57992	−0.789962	−	0.613156i	$-0.789900\pi$
$149$	−19.2854	−1.57992	−0.789962	+	0.613156i	$0.789900\pi$
$150$	13.1564	1.07421
$151$	−12.1434	−0.988219	−0.494110	−	0.869400i	$-0.664506\pi$
$151$	−12.1434	−0.988219	−0.494110	+	0.869400i	$0.664506\pi$
$152$	−4.39120	−0.356174
$153$	−0.00766620	−0.000619776 0
$154$	−0.00359004	−0.000289294 0
$155$	0.299114	0.0240254
$156$	−11.9501	−0.956772
$157$	−17.2023	−1.37289	−0.686445	−	0.727181i	$-0.740830\pi$
$157$	−17.2023	−1.37289	−0.686445	+	0.727181i	$0.740830\pi$
$158$	29.5707	2.35252
$159$	3.80615	0.301847
$160$	−7.55147	−0.596996
$161$	8.17763	0.644487
$162$	−44.8869	−3.52665
$163$	−9.67812	−0.758049	−0.379024	−	0.925387i	$-0.623740\pi$
$163$	−9.67812	−0.758049	−0.379024	+	0.925387i	$0.623740\pi$
$164$	30.5537	2.38584
$165$	0.00871175	0.000678209 0
$166$	23.3694	1.81382
$167$	16.8989	1.30768	0.653838	−	0.756634i	$-0.273158\pi$
$167$	16.8989	1.30768	0.653838	+	0.756634i	$0.273158\pi$
$168$	11.0041	0.848987
$169$	−11.8258	−0.909676
$170$	−0.00459600	−0.000352497 0
$171$	8.85911	0.677473
$172$	9.31974	0.710623
$173$	13.5892	1.03317	0.516586	−	0.856236i	$-0.327203\pi$
$173$	13.5892	1.03317	0.516586	+	0.856236i	$0.327203\pi$
$174$	−14.0351	−1.06400
$175$	1.77513	0.134187
$176$	−0.00179954	−0.000135646 0
$177$	47.4369	3.56557
$178$	−6.20665	−0.465208
$179$	−6.02312	−0.450189	−0.225095	−	0.974337i	$-0.572269\pi$
$179$	−6.02312	−0.450189	−0.225095	+	0.974337i	$0.572269\pi$
$180$	−43.8996	−3.27209
$181$	−15.9506	−1.18560	−0.592798	−	0.805351i	$-0.701977\pi$
$181$	−15.9506	−1.18560	−0.592798	+	0.805351i	$0.701977\pi$
$182$	−2.53776	−0.188111
$183$	−43.3667	−3.20576
$184$	28.4351	2.09627
$185$	14.6733	1.07880
$186$	1.23449	0.0905169
$187$	1.67520e−6 0	1.22503e−7 0
$188$	10.5643	0.770479
$189$	−12.7065	−0.924261
$190$	5.31116	0.385312
$191$	16.5285	1.19596	0.597981	−	0.801510i	$-0.295970\pi$
$191$	16.5285	1.19596	0.597981	+	0.801510i	$0.295970\pi$
$192$	−38.5962	−2.78544
$193$	−2.03008	−0.146129	−0.0730643	−	0.997327i	$-0.523278\pi$
$193$	−2.03008	−0.146129	−0.0730643	+	0.997327i	$0.523278\pi$
$194$	4.82276	0.346254
$195$	6.15824	0.441001
$196$	3.48474	0.248910
$197$	−0.355265	−0.0253116	−0.0126558	−	0.999920i	$-0.504029\pi$
$197$	−0.355265	−0.0253116	−0.0126558	+	0.999920i	$0.504029\pi$
$198$	0.0251845	0.00178979
$199$	−18.0394	−1.27878	−0.639391	−	0.768882i	$-0.720813\pi$
$199$	−18.0394	−1.27878	−0.639391	+	0.768882i	$0.720813\pi$
$200$	6.17246	0.436459
$201$	40.9112	2.88565
$202$	31.3011	2.20233
$203$	−1.89370	−0.132912
$204$	−0.0120516	−0.000843779 0
$205$	−15.7452	−1.09970
$206$	−37.2877	−2.59795
$207$	−57.3670	−3.98728
$208$	−1.27208	−0.0882027
$209$	−0.00193588	−0.000133907 0
$210$	−13.3095	−0.918443
$211$	−6.85265	−0.471756	−0.235878	−	0.971783i	$-0.575797\pi$
$211$	−6.85265	−0.471756	−0.235878	+	0.971783i	$0.575797\pi$
$212$	4.19110	0.287846
$213$	−52.5258	−3.59901
$214$	−15.6182	−1.06764
$215$	−4.80275	−0.327544
$216$	−44.1828	−3.00626
$217$	0.166564	0.0113071
$218$	−4.94627	−0.335004
$219$	−53.1401	−3.59088
$220$	0.00959286	0.000646750 0
$221$	0.00118418	7.96567e−5 0
$222$	60.5589	4.06445
$223$	−3.39342	−0.227240	−0.113620	−	0.993524i	$-0.536245\pi$
$223$	−3.39342	−0.227240	−0.113620	+	0.993524i	$0.536245\pi$
$224$	−4.20509	−0.280965
$225$	−12.4527	−0.830182
$226$	46.3677	3.08433
$227$	12.3210	0.817772	0.408886	−	0.912586i	$-0.365917\pi$
$227$	12.3210	0.817772	0.408886	+	0.912586i	$0.365917\pi$
$228$	13.9269	0.922330
$229$	9.02818	0.596599	0.298300	−	0.954472i	$-0.403581\pi$
$229$	9.02818	0.596599	0.298300	+	0.954472i	$0.403581\pi$
$230$	−34.3923	−2.26776
$231$	0.00485120	0.000319186 0
$232$	−6.58475	−0.432310
$233$	6.80583	0.445865	0.222932	−	0.974834i	$-0.428437\pi$
$233$	6.80583	0.445865	0.222932	+	0.974834i	$0.428437\pi$
$234$	17.8027	1.16380
$235$	−5.44409	−0.355134
$236$	52.2346	3.40018
$237$	−39.9587	−2.59560
$238$	−0.00255931	−0.000165896 0
$239$	−30.2561	−1.95710	−0.978551	−	0.206004i	$-0.933954\pi$
$239$	−30.2561	−1.95710	−0.978551	+	0.206004i	$0.933954\pi$
$240$	−6.67152	−0.430645
$241$	5.84055	0.376223	0.188111	−	0.982148i	$-0.439763\pi$
$241$	5.84055	0.376223	0.188111	+	0.982148i	$0.439763\pi$
$242$	25.7615	1.65601
$243$	22.5360	1.44568
$244$	−47.7528	−3.05706
$245$	−1.79579	−0.114729
$246$	−64.9829	−4.14316
$247$	−1.36845	−0.0870723
$248$	0.579173	0.0367775
$249$	−31.5789	−2.00123
$250$	−28.4939	−1.80211
$251$	−14.6602	−0.925346	−0.462673	−	0.886529i	$-0.653110\pi$
$251$	−14.6602	−0.925346	−0.462673	+	0.886529i	$0.653110\pi$
$252$	−24.4458	−1.53994
$253$	0.0125357	0.000788113 0
$254$	−19.4291	−1.21909
$255$	0.00621055	0.000388919 0
$256$	−22.8036	−1.42522
$257$	−6.39649	−0.399002	−0.199501	−	0.979898i	$-0.563932\pi$
$257$	−6.39649	−0.399002	−0.199501	+	0.979898i	$0.563932\pi$
$258$	−19.8216	−1.23404
$259$	8.17094	0.507718
$260$	6.78108	0.420545
$261$	13.2845	0.822291
$262$	8.55267	0.528386
$263$	28.0960	1.73248	0.866238	−	0.499631i	$-0.166531\pi$
$263$	28.0960	1.73248	0.866238	+	0.499631i	$0.166531\pi$
$264$	0.0168685	0.00103819
$265$	−2.15980	−0.132676
$266$	2.95756	0.181340
$267$	8.38701	0.513277
$268$	45.0489	2.75180
$269$	−10.8215	−0.659801	−0.329901	−	0.944016i	$-0.607015\pi$
$269$	−10.8215	−0.659801	−0.329901	+	0.944016i	$0.607015\pi$
$270$	53.4392	3.25220
$271$	22.7581	1.38246	0.691229	−	0.722636i	$-0.257070\pi$
$271$	22.7581	1.38246	0.691229	+	0.722636i	$0.257070\pi$
$272$	−0.00128288	−7.77862e−5 0
$273$	3.42926	0.207548
$274$	−29.9752	−1.81087
$275$	0.00272115	0.000164091 0
$276$	−90.1831	−5.42839
$277$	−16.3014	−0.979457	−0.489728	−	0.871875i	$-0.662904\pi$
$277$	−16.3014	−0.979457	−0.489728	+	0.871875i	$0.662904\pi$
$278$	−1.71178	−0.102666
$279$	−1.16846	−0.0699541
$280$	−6.24431	−0.373169
$281$	0.830780	0.0495602	0.0247801	−	0.999693i	$-0.492111\pi$
$281$	0.830780	0.0495602	0.0247801	+	0.999693i	$0.492111\pi$
$282$	−22.4686	−1.33798
$283$	26.8195	1.59426	0.797128	−	0.603811i	$-0.206352\pi$
$283$	26.8195	1.59426	0.797128	+	0.603811i	$0.206352\pi$
$284$	−57.8382	−3.43206
$285$	−7.17695	−0.425126
$286$	−0.00389020	−0.000230033 0
$287$	−8.76786	−0.517550
$288$	29.4992	1.73826
$289$	−17.0000	−1.00000
$290$	7.96426	0.467677
$291$	−6.51697	−0.382031
$292$	−58.5147	−3.42431
$293$	13.2691	0.775190	0.387595	−	0.921830i	$-0.373306\pi$
$293$	13.2691	0.775190	0.387595	+	0.921830i	$0.373306\pi$
$294$	−7.41150	−0.432247
$295$	−26.9181	−1.56723
$296$	28.4119	1.65141
$297$	−0.0194781	−0.00113024
$298$	45.1656	2.61637
$299$	8.86135	0.512465
$300$	−19.5762	−1.13023
$301$	−2.67444	−0.154152
$302$	28.4393	1.63650
$303$	−42.2969	−2.42990
$304$	1.48251	0.0850276
$305$	24.6085	1.40908
$306$	0.0179539	0.00102635
$307$	−14.1695	−0.808699	−0.404349	−	0.914605i	$-0.632502\pi$
$307$	−14.1695	−0.808699	−0.404349	+	0.914605i	$0.632502\pi$
$308$	0.00534185	0.000304380 0
$309$	50.3866	2.86639
$310$	−0.700510	−0.0397863
$311$	−8.83446	−0.500956	−0.250478	−	0.968122i	$-0.580588\pi$
$311$	−8.83446	−0.500956	−0.250478	+	0.968122i	$0.580588\pi$
$312$	11.9242	0.675074
$313$	−22.8506	−1.29159	−0.645797	−	0.763509i	$-0.723475\pi$
$313$	−22.8506	−1.29159	−0.645797	+	0.763509i	$0.723475\pi$
$314$	40.2869	2.27352
$315$	12.5977	0.709799
$316$	−44.0001	−2.47520
$317$	−23.2475	−1.30571	−0.652853	−	0.757484i	$-0.726428\pi$
$317$	−23.2475	−1.30571	−0.652853	+	0.757484i	$0.726428\pi$
$318$	−8.91383	−0.499863
$319$	−0.00290290	−0.000162531 0
$320$	21.9014	1.22433
$321$	21.1048	1.17795
$322$	−19.1516	−1.06728
$323$	−0.00138007	−7.67892e−5 0
$324$	66.7901	3.71056
$325$	1.92355	0.106699
$326$	22.6657	1.25534
$327$	6.68387	0.369619
$328$	−30.4875	−1.68339
$329$	−3.03158	−0.167137
$330$	−0.0204025	−0.00112312
$331$	−9.79226	−0.538231	−0.269116	−	0.963108i	$-0.586731\pi$
$331$	−9.79226	−0.538231	−0.269116	+	0.963108i	$0.586731\pi$
$332$	−34.7728	−1.90841
$333$	−57.3201	−3.14112
$334$	−39.5764	−2.16552
$335$	−23.2151	−1.26838
$336$	−3.71509	−0.202675
$337$	−24.3017	−1.32380	−0.661898	−	0.749594i	$-0.730249\pi$
$337$	−24.3017	−1.32380	−0.661898	+	0.749594i	$0.730249\pi$
$338$	27.6954	1.50643
$339$	−62.6564	−3.40303
$340$	0.00683868	0.000370879 0
$341$	0.000255330 0	1.38269e−5 0
$342$	−20.7476	−1.12190
$343$	−1.00000	−0.0539949
$344$	−9.29954	−0.501398
$345$	46.4741	2.50208
$346$	−31.8254	−1.71094
$347$	2.11122	0.113336	0.0566681	−	0.998393i	$-0.481952\pi$
$347$	2.11122	0.113336	0.0566681	+	0.998393i	$0.481952\pi$
$348$	20.8838	1.11949
$349$	21.0541	1.12700	0.563501	−	0.826116i	$-0.309454\pi$
$349$	21.0541	1.12700	0.563501	+	0.826116i	$0.309454\pi$
$350$	−4.15727	−0.222215
$351$	−13.7689	−0.734928
$352$	−0.00644610	−0.000343578 0
$353$	31.0288	1.65150	0.825748	−	0.564040i	$-0.190753\pi$
$353$	31.0288	1.65150	0.825748	+	0.564040i	$0.190753\pi$
$354$	−111.095	−5.90463
$355$	29.8058	1.58193
$356$	9.23527	0.489468
$357$	0.00345839	0.000183037 0
$358$	14.1059	0.745518
$359$	−13.4186	−0.708206	−0.354103	−	0.935207i	$-0.615214\pi$
$359$	−13.4186	−0.708206	−0.354103	+	0.935207i	$0.615214\pi$
$360$	43.8045	2.30870
$361$	−17.4052	−0.916062
$362$	37.3555	1.96336
$363$	−34.8113	−1.82712
$364$	3.77610	0.197921
$365$	30.1544	1.57835
$366$	101.563	5.30877
$367$	24.1172	1.25891	0.629453	−	0.777039i	$-0.283279\pi$
$367$	24.1172	1.25891	0.629453	+	0.777039i	$0.283279\pi$
$368$	−9.59993	−0.500431
$369$	61.5075	3.20195
$370$	−34.3642	−1.78651
$371$	−1.20270	−0.0624412
$372$	−1.83687	−0.0952373
$373$	15.7816	0.817138	0.408569	−	0.912727i	$-0.366028\pi$
$373$	15.7816	0.817138	0.408569	+	0.912727i	$0.366028\pi$
$374$	−3.92324e−6 0	−2.02866e−7 0
$375$	38.5036	1.98832
$376$	−10.5414	−0.543630
$377$	−2.05203	−0.105685
$378$	29.7580	1.53059
$379$	−34.3162	−1.76271	−0.881354	−	0.472457i	$-0.843367\pi$
$379$	−34.3162	−1.76271	−0.881354	+	0.472457i	$0.843367\pi$
$380$	−7.90282	−0.405406
$381$	26.2545	1.34506
$382$	−38.7090	−1.98052
$383$	−37.4579	−1.91401	−0.957004	−	0.290075i	$-0.906320\pi$
$383$	−37.4579	−1.91401	−0.957004	+	0.290075i	$0.906320\pi$
$384$	63.7750	3.25451
$385$	−0.00275282	−0.000140297 0
$386$	4.75436	0.241990
$387$	18.7615	0.953702
$388$	−7.17609	−0.364311
$389$	2.84529	0.144262	0.0721309	−	0.997395i	$-0.477020\pi$
$389$	2.84529	0.144262	0.0721309	+	0.997395i	$0.477020\pi$
$390$	−14.4223	−0.730302
$391$	0.00893661	0.000451944 0
$392$	−3.47719	−0.175624
$393$	−11.5572	−0.582982
$394$	0.832014	0.0419163
$395$	22.6746	1.14088
$396$	−0.0374737	−0.00188312
$397$	−23.3448	−1.17164	−0.585821	−	0.810441i	$-0.699228\pi$
$397$	−23.3448	−1.17164	−0.585821	+	0.810441i	$0.699228\pi$
$398$	42.2475	2.11767
$399$	−3.99653	−0.200077
$400$	−2.08387	−0.104194
$401$	32.8802	1.64196	0.820980	−	0.570957i	$-0.193428\pi$
$401$	32.8802	1.64196	0.820980	+	0.570957i	$0.193428\pi$
$402$	−95.8121	−4.77867
$403$	0.180490	0.00899085
$404$	−46.5748	−2.31718
$405$	−34.4190	−1.71029
$406$	4.43495	0.220103
$407$	0.0125255	0.000620864 0
$408$	0.0120255	0.000595349 0
$409$	6.23500	0.308301	0.154150	−	0.988047i	$-0.450736\pi$
$409$	6.23500	0.308301	0.154150	+	0.988047i	$0.450736\pi$
$410$	36.8746	1.82111
$411$	40.5053	1.99798
$412$	55.4827	2.73343
$413$	−14.9895	−0.737587
$414$	134.351	6.60297
$415$	17.9195	0.879633
$416$	−4.55668	−0.223410
$417$	2.31312	0.113274
$418$	0.00453373	0.000221752 0
$419$	−24.7313	−1.20821	−0.604103	−	0.796907i	$-0.706468\pi$
$419$	−24.7313	−1.20821	−0.604103	+	0.796907i	$0.706468\pi$
$420$	19.8041	0.966339
$421$	33.1909	1.61762	0.808812	−	0.588067i	$-0.200111\pi$
$421$	33.1909	1.61762	0.808812	+	0.588067i	$0.200111\pi$
$422$	16.0486	0.781232
$423$	21.2669	1.03403
$424$	−4.18202	−0.203097
$425$	0.00193988	9.40982e−5 0
$426$	123.013	5.95999
$427$	13.7034	0.663154
$428$	23.2393	1.12331
$429$	0.00525681	0.000253801 0
$430$	11.2478	0.542417
$431$	14.9364	0.719462	0.359731	−	0.933056i	$-0.382869\pi$
$431$	14.9364	0.719462	0.359731	+	0.933056i	$0.382869\pi$
$432$	14.9165	0.717670
$433$	−7.20200	−0.346106	−0.173053	−	0.984912i	$-0.555363\pi$
$433$	−7.20200	−0.346106	−0.173053	+	0.984912i	$0.555363\pi$
$434$	−0.390084	−0.0187246
$435$	−10.7621	−0.516001
$436$	7.35987	0.352474
$437$	−10.3272	−0.494017
$438$	124.452	5.94653
$439$	26.7022	1.27443	0.637213	−	0.770688i	$-0.280087\pi$
$439$	26.7022	1.27443	0.637213	+	0.770688i	$0.280087\pi$
$440$	−0.00957207	−0.000456330 0
$441$	7.01511	0.334053
$442$	−0.00277330	−0.000131912 0
$443$	−10.0082	−0.475506	−0.237753	−	0.971326i	$-0.576411\pi$
$443$	−10.0082	−0.475506	−0.237753	+	0.971326i	$0.576411\pi$
$444$	−90.1095	−4.27641
$445$	−4.75922	−0.225609
$446$	7.94722	0.376312
$447$	−61.0320	−2.88671
$448$	12.1960	0.576206
$449$	−1.17084	−0.0552555	−0.0276278	−	0.999618i	$-0.508795\pi$
$449$	−1.17084	−0.0552555	−0.0276278	+	0.999618i	$0.508795\pi$
$450$	29.1637	1.37479
$451$	−0.0134405	−0.000632888 0
$452$	−68.9934	−3.24518
$453$	−38.4299	−1.80560
$454$	−28.8551	−1.35424
$455$	−1.94594	−0.0912269
$456$	−13.8967	−0.650772
$457$	−6.00788	−0.281037	−0.140518	−	0.990078i	$-0.544877\pi$
$457$	−6.00788	−0.281037	−0.140518	+	0.990078i	$0.544877\pi$
$458$	−21.1436	−0.987974
$459$	−0.0138858	−0.000648134 0
$460$	51.1745	2.38602
$461$	−7.74693	−0.360810	−0.180405	−	0.983592i	$-0.557741\pi$
$461$	−7.74693	−0.360810	−0.180405	+	0.983592i	$0.557741\pi$
$462$	−0.0113613	−0.000528575 0
$463$	22.0721	1.02578	0.512889	−	0.858455i	$-0.328575\pi$
$463$	22.0721	1.02578	0.512889	+	0.858455i	$0.328575\pi$
$464$	2.22306	0.103203
$465$	0.946596	0.0438973
$466$	−15.9389	−0.738356
$467$	38.1573	1.76571	0.882855	−	0.469647i	$-0.155619\pi$
$467$	38.1573	1.76571	0.882855	+	0.469647i	$0.155619\pi$
$468$	−26.4897	−1.22449
$469$	−12.9275	−0.596936
$470$	12.7498	0.588105
$471$	−54.4394	−2.50844
$472$	−52.1214	−2.39908
$473$	−0.00409973	−0.000188506 0
$474$	93.5814	4.29834
$475$	−2.24174	−0.102858
$476$	0.00380817	0.000174547 0
$477$	8.43709	0.386308
$478$	70.8583	3.24098
$479$	24.8036	1.13331	0.566653	−	0.823957i	$-0.308238\pi$
$479$	24.8036	1.13331	0.566653	+	0.823957i	$0.308238\pi$
$480$	−23.8979	−1.09078
$481$	8.85411	0.403713
$482$	−13.6783	−0.623029
$483$	25.8795	1.17756
$484$	−38.3321	−1.74237
$485$	3.69806	0.167920
$486$	−52.7781	−2.39406
$487$	20.0007	0.906317	0.453158	−	0.891430i	$-0.350297\pi$
$487$	20.0007	0.906317	0.453158	+	0.891430i	$0.350297\pi$
$488$	47.6493	2.15698
$489$	−30.6280	−1.38505
$490$	4.20566	0.189992
$491$	−1.86374	−0.0841094	−0.0420547	−	0.999115i	$-0.513390\pi$
$491$	−1.86374	−0.0841094	−0.0420547	+	0.999115i	$0.513390\pi$
$492$	96.6922	4.35922
$493$	−0.00206946	−9.32038e−5 0
$494$	3.20484	0.144193
$495$	0.0193113	0.000867980 0
$496$	−0.195534	−0.00877972
$497$	16.5976	0.744503
$498$	73.9564	3.31406
$499$	−8.54117	−0.382355	−0.191178	−	0.981555i	$-0.561231\pi$
$499$	−8.54117	−0.382355	−0.191178	+	0.981555i	$0.561231\pi$
$500$	42.3979	1.89609
$501$	53.4794	2.38928
$502$	34.3336	1.53238
$503$	17.9650	0.801018	0.400509	−	0.916293i	$-0.368833\pi$
$503$	17.9650	0.801018	0.400509	+	0.916293i	$0.368833\pi$
$504$	24.3929	1.08654
$505$	24.0014	1.06805
$506$	−0.0293580	−0.00130512
$507$	−37.4247	−1.66209
$508$	28.9098	1.28267
$509$	0.268951	0.0119210	0.00596052	−	0.999982i	$-0.498103\pi$
$509$	0.268951	0.0119210	0.00596052	+	0.999982i	$0.498103\pi$
$510$	−0.0145448	−0.000644055 0
$511$	16.7917	0.742821
$512$	13.1004	0.578961
$513$	16.0465	0.708472
$514$	14.9803	0.660752
$515$	−28.5919	−1.25991
$516$	29.4939	1.29839
$517$	−0.00464720	−0.000204384 0
$518$	−19.1360	−0.840786
$519$	43.0054	1.88773
$520$	−6.76639	−0.296726
$521$	−1.17137	−0.0513187	−0.0256593	−	0.999671i	$-0.508169\pi$
$521$	−1.17137	−0.0513187	−0.0256593	+	0.999671i	$0.508169\pi$
$522$	−31.1117	−1.36172
$523$	−9.04265	−0.395407	−0.197704	−	0.980262i	$-0.563348\pi$
$523$	−9.04265	−0.395407	−0.197704	+	0.980262i	$0.563348\pi$
$524$	−12.7261	−0.555940
$525$	5.61769	0.245176
$526$	−65.7996	−2.86900
$527$	0.000182023 0	7.92905e−6 0
$528$	−0.00569496	−0.000247841 0
$529$	43.8736	1.90755
$530$	5.05816	0.219712
$531$	105.153	4.56326
$532$	−4.40074	−0.190796
$533$	−9.50093	−0.411531
$534$	−19.6420	−0.849992
$535$	−11.9759	−0.517764
$536$	−44.9513	−1.94160
$537$	−19.0612	−0.822550
$538$	25.3435	1.09264
$539$	−0.00153293	−6.60279e−5 0
$540$	−79.5155	−3.42180
$541$	−30.1682	−1.29703	−0.648516	−	0.761201i	$-0.724610\pi$
$541$	−30.1682	−1.29703	−0.648516	+	0.761201i	$0.724610\pi$
$542$	−53.2984	−2.28936
$543$	−50.4782	−2.16623
$544$	−0.00459538	−0.000197025 0
$545$	−3.79277	−0.162464
$546$	−8.03117	−0.343702
$547$	7.42850	0.317620	0.158810	−	0.987309i	$-0.449234\pi$
$547$	7.42850	0.317620	0.158810	+	0.987309i	$0.449234\pi$
$548$	44.6019	1.90530
$549$	−96.1309	−4.10277
$550$	−0.00637279	−0.000271737 0
$551$	2.39148	0.101880
$552$	89.9877	3.83013
$553$	12.6265	0.536934
$554$	38.1771	1.62199
$555$	46.4362	1.97111
$556$	2.54707	0.108020
$557$	30.5763	1.29556	0.647779	−	0.761828i	$-0.275698\pi$
$557$	30.5763	1.29556	0.647779	+	0.761828i	$0.275698\pi$
$558$	2.73648	0.115845
$559$	−2.89805	−0.122575
$560$	2.10813	0.0890847
$561$	5.30146e−6 0	2.23828e−7 0
$562$	−1.94565	−0.0820721
$563$	−41.6783	−1.75653	−0.878266	−	0.478172i	$-0.841299\pi$
$563$	−41.6783	−1.75653	−0.878266	+	0.478172i	$0.841299\pi$
$564$	33.4324	1.40776
$565$	35.5544	1.49579
$566$	−62.8100	−2.64010
$567$	−19.1665	−0.804915
$568$	57.7128	2.42158
$569$	−34.2673	−1.43656	−0.718280	−	0.695754i	$-0.755070\pi$
$569$	−34.2673	−1.43656	−0.718280	+	0.695754i	$0.755070\pi$
$570$	16.8081	0.704012
$571$	−37.4453	−1.56704	−0.783519	−	0.621368i	$-0.786577\pi$
$571$	−37.4453	−1.56704	−0.783519	+	0.621368i	$0.786577\pi$
$572$	0.00578848	0.000242029 0
$573$	52.3072	2.18517
$574$	20.5339	0.857068
$575$	14.5163	0.605374
$576$	−85.5562	−3.56484
$577$	16.8755	0.702535	0.351268	−	0.936275i	$-0.385751\pi$
$577$	16.8755	0.702535	0.351268	+	0.936275i	$0.385751\pi$
$578$	39.8132	1.65601
$579$	−6.42454	−0.266995
$580$	−11.8505	−0.492066
$581$	9.97860	0.413982
$582$	15.2624	0.632648
$583$	−0.00184366	−7.63564e−5 0
$584$	58.3879	2.41611
$585$	13.6510	0.564398
$586$	−31.0756	−1.28372
$587$	−32.5781	−1.34464	−0.672321	−	0.740260i	$-0.734702\pi$
$587$	−32.5781	−1.34464	−0.672321	+	0.740260i	$0.734702\pi$
$588$	11.0280	0.454788
$589$	−0.210347	−0.00866719
$590$	63.0409	2.59535
$591$	−1.12430	−0.0462473
$592$	−9.59209	−0.394233
$593$	−17.2647	−0.708977	−0.354488	−	0.935060i	$-0.615345\pi$
$593$	−17.2647	−0.708977	−0.354488	+	0.935060i	$0.615345\pi$
$594$	0.0456168	0.00187168
$595$	−0.00196246	−8.04532e−5 0
$596$	−67.2047	−2.75281
$597$	−57.0888	−2.33649
$598$	−20.7529	−0.848647
$599$	−35.0057	−1.43029	−0.715146	−	0.698975i	$-0.753640\pi$
$599$	−35.0057	−1.43029	−0.715146	+	0.698975i	$0.753640\pi$
$600$	19.5338	0.797463
$601$	−28.6547	−1.16885	−0.584425	−	0.811447i	$-0.698680\pi$
$601$	−28.6547	−1.16885	−0.584425	+	0.811447i	$0.698680\pi$
$602$	6.26342	0.255278
$603$	90.6878	3.69309
$604$	−42.3167	−1.72184
$605$	19.7537	0.803103
$606$	99.0574	4.02393
$607$	1.82531	0.0740872	0.0370436	−	0.999314i	$-0.488206\pi$
$607$	1.82531	0.0740872	0.0370436	+	0.999314i	$0.488206\pi$
$608$	5.31045	0.215367
$609$	−5.99293	−0.242846
$610$	−57.6318	−2.33344
$611$	−3.28505	−0.132899
$612$	−0.0267147	−0.00107988
$613$	47.5023	1.91860	0.959300	−	0.282388i	$-0.0911264\pi$
$613$	47.5023	1.91860	0.959300	+	0.282388i	$0.0911264\pi$
$614$	33.1844	1.33921
$615$	−49.8285	−2.00928
$616$	−0.00533028	−0.000214763 0
$617$	5.50811	0.221748	0.110874	−	0.993834i	$-0.464635\pi$
$617$	5.50811	0.221748	0.110874	+	0.993834i	$0.464635\pi$
$618$	−118.003	−4.74678
$619$	20.0123	0.804361	0.402181	−	0.915560i	$-0.368252\pi$
$619$	20.0123	0.804361	0.402181	+	0.915560i	$0.368252\pi$
$620$	1.04233	0.0418611
$621$	−103.909	−4.16972
$622$	20.6899	0.829589
$623$	−2.65021	−0.106178
$624$	−4.02570	−0.161157
$625$	−12.9733	−0.518931
$626$	53.5151	2.13889
$627$	−0.00612640	−0.000244665 0
$628$	−59.9454	−2.39208
$629$	0.00892931	0.000356035 0
$630$	−29.5032	−1.17543
$631$	−3.87192	−0.154139	−0.0770694	−	0.997026i	$-0.524556\pi$
$631$	−3.87192	−0.154139	−0.0770694	+	0.997026i	$0.524556\pi$
$632$	43.9048	1.74644
$633$	−21.6863	−0.861955
$634$	54.4444	2.16226
$635$	−14.8981	−0.591214
$636$	13.2634	0.525930
$637$	−1.08361	−0.0429342
$638$	0.00679846	0.000269154 0
$639$	−116.434	−4.60605
$640$	−36.1892	−1.43050
$641$	−34.3501	−1.35675	−0.678373	−	0.734717i	$-0.737315\pi$
$641$	−34.3501	−1.35675	−0.678373	+	0.734717i	$0.737315\pi$
$642$	−49.4264	−1.95070
$643$	−31.9987	−1.26191	−0.630953	−	0.775821i	$-0.717336\pi$
$643$	−31.9987	−1.26191	−0.630953	+	0.775821i	$0.717336\pi$
$644$	28.4969	1.12293
$645$	−15.1991	−0.598463
$646$	0.00323206	0.000127164 0
$647$	−33.9119	−1.33321	−0.666607	−	0.745410i	$-0.732254\pi$
$647$	−33.9119	−1.33321	−0.666607	+	0.745410i	$0.732254\pi$
$648$	−66.6453	−2.61808
$649$	−0.0229779	−0.000901960 0
$650$	−4.50485	−0.176695
$651$	0.527119	0.0206594
$652$	−33.7257	−1.32080
$653$	6.80546	0.266318	0.133159	−	0.991095i	$-0.457488\pi$
$653$	6.80546	0.266318	0.133159	+	0.991095i	$0.457488\pi$
$654$	−15.6533	−0.612093
$655$	6.55813	0.256247
$656$	10.2928	0.401867
$657$	−117.796	−4.59565
$658$	7.09982	0.276780
$659$	20.0854	0.782415	0.391207	−	0.920303i	$-0.372057\pi$
$659$	20.0854	0.782415	0.391207	+	0.920303i	$0.372057\pi$
$660$	0.0303582	0.00118169
$661$	−36.2535	−1.41010	−0.705048	−	0.709159i	$-0.749075\pi$
$661$	−36.2535	−1.41010	−0.705048	+	0.709159i	$0.749075\pi$
$662$	22.9330	0.891316
$663$	0.00374754	0.000145542 0
$664$	34.6975	1.34652
$665$	2.26784	0.0879429
$666$	134.241	5.20173
$667$	−15.4860	−0.599619
$668$	58.8883	2.27845
$669$	−10.7390	−0.415195
$670$	54.3686	2.10044
$671$	0.0210063	0.000810940 0
$672$	−13.3077	−0.513356
$673$	15.6818	0.604488	0.302244	−	0.953231i	$-0.402264\pi$
$673$	15.6818	0.604488	0.302244	+	0.953231i	$0.402264\pi$
$674$	56.9134	2.19222
$675$	−22.5557	−0.868168
$676$	−41.2098	−1.58499
$677$	−5.38266	−0.206872	−0.103436	−	0.994636i	$-0.532984\pi$
$677$	−5.38266	−0.206872	−0.103436	+	0.994636i	$0.532984\pi$
$678$	146.738	5.63545
$679$	2.05929	0.0790283
$680$	−0.00682386	−0.000261683 0
$681$	38.9918	1.49417
$682$	−0.000597971 0	−2.28975e−5 0
$683$	−27.6768	−1.05903	−0.529513	−	0.848302i	$-0.677625\pi$
$683$	−27.6768	−1.05903	−0.529513	+	0.848302i	$0.677625\pi$
$684$	30.8717	1.18041
$685$	−22.9847	−0.878202
$686$	2.34195	0.0894161
$687$	28.5712	1.09006
$688$	3.13960	0.119696
$689$	−1.30326	−0.0496502
$690$	−108.840	−4.14347
$691$	−26.9768	−1.02624	−0.513122	−	0.858316i	$-0.671511\pi$
$691$	−26.9768	−1.02624	−0.513122	+	0.858316i	$0.671511\pi$
$692$	47.3550	1.80017
$693$	0.0107537	0.000408498 0
$694$	−4.94437	−0.187686
$695$	−1.31258	−0.0497890
$696$	−20.8385	−0.789882
$697$	−0.00958162	−0.000362930 0
$698$	−49.3078	−1.86633
$699$	21.5382	0.814649
$700$	6.18586	0.233804
$701$	8.29363	0.313246	0.156623	−	0.987658i	$-0.449939\pi$
$701$	8.29363	0.313246	0.156623	+	0.987658i	$0.449939\pi$
$702$	32.2460	1.21705
$703$	−10.3188	−0.389180
$704$	0.0186956	0.000704615 0
$705$	−17.2287	−0.648872
$706$	−72.6679	−2.73489
$707$	13.3654	0.502656
$708$	165.305	6.21255
$709$	12.3068	0.462190	0.231095	−	0.972931i	$-0.425769\pi$
$709$	12.3068	0.462190	0.231095	+	0.972931i	$0.425769\pi$
$710$	−69.8037	−2.61969
$711$	−88.5765	−3.32188
$712$	−9.21526	−0.345356
$713$	1.36210	0.0510109
$714$	−0.00809938	−0.000303112 0
$715$	−0.00298298	−0.000111557 0
$716$	−20.9890	−0.784396
$717$	−95.7504	−3.57586
$718$	31.4257	1.17280
$719$	22.5709	0.841754	0.420877	−	0.907118i	$-0.361722\pi$
$719$	22.5709	0.841754	0.420877	+	0.907118i	$0.361722\pi$
$720$	−14.7888	−0.551144
$721$	−15.9216	−0.592952
$722$	40.7621	1.51701
$723$	18.4834	0.687405
$724$	−55.5836	−2.06575
$725$	−3.36156	−0.124845
$726$	81.5264	3.02573
$727$	−11.6584	−0.432388	−0.216194	−	0.976350i	$-0.569364\pi$
$727$	−11.6584	−0.432388	−0.216194	+	0.976350i	$0.569364\pi$
$728$	−3.76791	−0.139648
$729$	13.8194	0.511831
$730$	−70.6202	−2.61377
$731$	−0.00292267	−0.000108099 0
$732$	−151.122	−5.58561
$733$	2.14387	0.0791855	0.0395928	−	0.999216i	$-0.487394\pi$
$733$	2.14387	0.0791855	0.0395928	+	0.999216i	$0.487394\pi$
$734$	−56.4812	−2.08476
$735$	−5.68308	−0.209624
$736$	−34.3877	−1.26755
$737$	−0.0198169	−0.000729965 0
$738$	−144.048	−5.30246
$739$	5.06531	0.186330	0.0931652	−	0.995651i	$-0.470302\pi$
$739$	5.06531	0.186330	0.0931652	+	0.995651i	$0.470302\pi$
$740$	51.1327	1.87967
$741$	−4.33068	−0.159092
$742$	2.81667	0.103403
$743$	2.46865	0.0905660	0.0452830	−	0.998974i	$-0.485581\pi$
$743$	2.46865	0.0905660	0.0452830	+	0.998974i	$0.485581\pi$
$744$	1.83289	0.0671970
$745$	34.6326	1.26884
$746$	−36.9597	−1.35319
$747$	−70.0010	−2.56120
$748$	5.83764e−6 0	2.13445e−7 0
$749$	−6.66888	−0.243676
$750$	−90.1736	−3.29268
$751$	−16.0959	−0.587349	−0.293674	−	0.955905i	$-0.594878\pi$
$751$	−16.0959	−0.587349	−0.293674	+	0.955905i	$0.594878\pi$
$752$	3.55886	0.129778
$753$	−46.3947	−1.69072
$754$	4.80576	0.175015
$755$	21.8071	0.793641
$756$	−44.2788	−1.61040
$757$	29.8009	1.08313	0.541566	−	0.840658i	$-0.317832\pi$
$757$	29.8009	1.08313	0.541566	+	0.840658i	$0.317832\pi$
$758$	80.3670	2.91906
$759$	0.0396713	0.00143998
$760$	7.88569	0.286044
$761$	−19.9168	−0.721983	−0.360992	−	0.932569i	$-0.617562\pi$
$761$	−19.9168	−0.721983	−0.360992	+	0.932569i	$0.617562\pi$
$762$	−61.4867	−2.22743
$763$	−2.11203	−0.0764606
$764$	57.5976	2.08381
$765$	0.0137669	0.000497744 0
$766$	87.7245	3.16962
$767$	−16.2428	−0.586494
$768$	−72.1656	−2.60405
$769$	30.8351	1.11194	0.555971	−	0.831202i	$-0.312347\pi$
$769$	30.8351	1.11194	0.555971	+	0.831202i	$0.312347\pi$
$770$	0.00644697	0.000232333 0
$771$	−20.2428	−0.729025
$772$	−7.07431	−0.254610
$773$	−22.9567	−0.825693	−0.412847	−	0.910801i	$-0.635465\pi$
$773$	−22.9567	−0.825693	−0.412847	+	0.910801i	$0.635465\pi$
$774$	−43.9386	−1.57934
$775$	0.295672	0.0106209
$776$	7.16054	0.257048
$777$	25.8583	0.927662
$778$	−6.66353	−0.238899
$779$	11.0726	0.396717
$780$	21.4599	0.768386
$781$	0.0254429	0.000910417 0
$782$	−0.0209291	−0.000748424 0
$783$	24.0623	0.859915
$784$	1.17393	0.0419260
$785$	30.8917	1.10257
$786$	27.0663	0.965424
$787$	−23.0140	−0.820359	−0.410179	−	0.912005i	$-0.634534\pi$
$787$	−23.0140	−0.820359	−0.410179	+	0.912005i	$0.634534\pi$
$788$	−1.23801	−0.0441021
$789$	88.9146	3.16544
$790$	−53.1028	−1.88931
$791$	19.7987	0.703962
$792$	0.0373925	0.00132868
$793$	14.8491	0.527308
$794$	54.6724	1.94025
$795$	−6.83506	−0.242415
$796$	−62.8627	−2.22811
$797$	5.45599	0.193261	0.0966305	−	0.995320i	$-0.469193\pi$
$797$	5.45599	0.193261	0.0966305	+	0.995320i	$0.469193\pi$
$798$	9.35969	0.331329
$799$	−0.00331295	−0.000117204 0
$800$	−7.46459	−0.263913
$801$	18.5915	0.656898
$802$	−77.0039	−2.71910
$803$	0.0257405	0.000908361 0
$804$	142.565	5.02787
$805$	−14.6853	−0.517589
$806$	−0.422699	−0.0148889
$807$	−34.2466	−1.20554
$808$	46.4739	1.63495
$809$	42.3818	1.49006	0.745032	−	0.667029i	$-0.232434\pi$
$809$	42.3818	1.49006	0.745032	+	0.667029i	$0.232434\pi$
$810$	80.6076	2.83226
$811$	−5.53458	−0.194345	−0.0971727	−	0.995268i	$-0.530980\pi$
$811$	−5.53458	−0.194345	−0.0971727	+	0.995268i	$0.530980\pi$
$812$	−6.59905	−0.231581
$813$	72.0219	2.52592
$814$	−0.0293340	−0.00102816
$815$	17.3799	0.608791
$816$	−0.00405989	−0.000142125 0
$817$	3.37745	0.118162
$818$	−14.6021	−0.510549
$819$	7.60164	0.265623
$820$	−54.8681	−1.91608
$821$	27.9154	0.974256	0.487128	−	0.873331i	$-0.338045\pi$
$821$	27.9154	0.974256	0.487128	+	0.873331i	$0.338045\pi$
$822$	−94.8613	−3.30867
$823$	33.1440	1.15533	0.577664	−	0.816275i	$-0.303965\pi$
$823$	33.1440	1.15533	0.577664	+	0.816275i	$0.303965\pi$
$824$	−55.3624	−1.92864
$825$	0.00861152	0.000299815 0
$826$	35.1048	1.22145
$827$	12.4416	0.432636	0.216318	−	0.976323i	$-0.430595\pi$
$827$	12.4416	0.432636	0.216318	+	0.976323i	$0.430595\pi$
$828$	−199.909	−6.94731
$829$	−29.3471	−1.01927	−0.509633	−	0.860392i	$-0.670219\pi$
$829$	−29.3471	−1.01927	−0.509633	+	0.860392i	$0.670219\pi$
$830$	−41.9666	−1.45668
$831$	−51.5885	−1.78959
$832$	13.2157	0.458171
$833$	−0.00109281	−3.78637e−5 0
$834$	−5.41721	−0.187583
$835$	−30.3469	−1.05020
$836$	−0.00674602	−0.000233316 0
$837$	−2.11644	−0.0731549
$838$	57.9196	2.00080
$839$	−33.9485	−1.17203	−0.586015	−	0.810300i	$-0.699304\pi$
$839$	−33.9485	−1.17203	−0.586015	+	0.810300i	$0.699304\pi$
$840$	−19.7611	−0.681824
$841$	−25.4139	−0.876341
$842$	−77.7314	−2.67880
$843$	2.62914	0.0905524
$844$	−23.8797	−0.821973
$845$	21.2367	0.730563
$846$	−49.8060	−1.71237
$847$	11.0000	0.377964
$848$	1.41188	0.0484843
$849$	84.8748	2.91290
$850$	−0.00454312	−0.000155828 0
$851$	66.8189	2.29052
$852$	−183.039	−6.27080
$853$	−3.68147	−0.126051	−0.0630255	−	0.998012i	$-0.520075\pi$
$853$	−3.68147	−0.126051	−0.0630255	+	0.998012i	$0.520075\pi$
$854$	−32.0927	−1.09819
$855$	−15.9091	−0.544081
$856$	−23.1889	−0.792582
$857$	46.2145	1.57866	0.789328	−	0.613971i	$-0.210429\pi$
$857$	46.2145	1.57866	0.789328	+	0.613971i	$0.210429\pi$
$858$	−0.0123112	−0.000420297 0
$859$	35.8421	1.22292	0.611459	−	0.791276i	$-0.290583\pi$
$859$	35.8421	1.22292	0.611459	+	0.791276i	$0.290583\pi$
$860$	−16.7363	−0.570703
$861$	−27.7473	−0.945627
$862$	−34.9804	−1.19144
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	53.4320	1.81779
$865$	−24.4035	−0.829743
$866$	16.8667	0.573155
$867$	−53.7993	−1.82712
$868$	0.580431	0.0197011
$869$	0.0193555	0.000656592 0
$870$	25.2042	0.854503
$871$	−14.0084	−0.474655
$872$	−7.34392	−0.248697
$873$	−14.4462	−0.488928
$874$	24.1858	0.818098
$875$	−12.1667	−0.411310
$876$	−185.179	−6.25663
$877$	−41.4179	−1.39858	−0.699292	−	0.714836i	$-0.746501\pi$
$877$	−41.4179	−1.39858	−0.699292	+	0.714836i	$0.746501\pi$
$878$	−62.5353	−2.11046
$879$	41.9923	1.41637
$880$	0.00323161	0.000108938 0
$881$	10.9134	0.367682	0.183841	−	0.982956i	$-0.441147\pi$
$881$	10.9134	0.367682	0.183841	+	0.982956i	$0.441147\pi$
$882$	−16.4291	−0.553195
$883$	−29.6686	−0.998427	−0.499214	−	0.866479i	$-0.666378\pi$
$883$	−29.6686	−0.998427	−0.499214	+	0.866479i	$0.666378\pi$
$884$	0.00412656	0.000138791 0
$885$	−85.1868	−2.86352
$886$	23.4388	0.787442
$887$	22.3819	0.751512	0.375756	−	0.926719i	$-0.377383\pi$
$887$	22.3819	0.751512	0.375756	+	0.926719i	$0.377383\pi$
$888$	89.9142	3.01732
$889$	−8.29613	−0.278243
$890$	11.1459	0.373610
$891$	−0.0293808	−0.000984293 0
$892$	−11.8252	−0.395936
$893$	3.82847	0.128115
$894$	142.934	4.78043
$895$	10.8163	0.361548
$896$	−20.1522	−0.673238
$897$	28.0432	0.936336
$898$	2.74206	0.0915037
$899$	−0.315422	−0.0105199
$900$	−43.3945	−1.44648
$901$	−0.00131433	−4.37866e−5 0
$902$	0.0314770	0.00104807
$903$	−8.46372	−0.281655
$904$	68.8439	2.28971
$905$	28.6439	0.952156
$906$	90.0010	2.99008
$907$	−32.9138	−1.09288	−0.546442	−	0.837497i	$-0.684018\pi$
$907$	−32.9138	−1.09288	−0.546442	+	0.837497i	$0.684018\pi$
$908$	42.9354	1.42486
$909$	−93.7596	−3.10981
$910$	4.55729	0.151073
$911$	−44.5150	−1.47485	−0.737424	−	0.675430i	$-0.763958\pi$
$911$	−44.5150	−1.47485	−0.737424	+	0.675430i	$0.763958\pi$
$912$	4.69164	0.155356
$913$	0.0152965	0.000506239 0
$914$	14.0702	0.465399
$915$	77.8776	2.57455
$916$	31.4609	1.03950
$917$	3.65194	0.120598
$918$	0.0325199	0.00107332
$919$	34.7148	1.14514	0.572568	−	0.819857i	$-0.305947\pi$
$919$	34.7148	1.14514	0.572568	+	0.819857i	$0.305947\pi$
$920$	−51.0636	−1.68352
$921$	−44.8419	−1.47759
$922$	18.1429	0.597506
$923$	17.9853	0.591993
$924$	0.0169052	0.000556140 0
$925$	14.5045	0.476905
$926$	−51.6918	−1.69870
$927$	111.692	3.66844
$928$	7.96318	0.261404
$929$	32.1629	1.05523	0.527616	−	0.849483i	$-0.323086\pi$
$929$	32.1629	1.05523	0.527616	+	0.849483i	$0.323086\pi$
$930$	−2.21688	−0.0726944
$931$	1.26286	0.0413886
$932$	23.7165	0.776861
$933$	−27.9581	−0.915308
$934$	−89.3626	−2.92403
$935$	−3.00832e−6 0	−9.83825e−8 0
$936$	26.4323	0.863967
$937$	16.6310	0.543313	0.271656	−	0.962394i	$-0.412429\pi$
$937$	16.6310	0.543313	0.271656	+	0.962394i	$0.412429\pi$
$938$	30.2756	0.988532
$939$	−72.3147	−2.35990
$940$	−18.9712	−0.618774
$941$	20.8948	0.681150	0.340575	−	0.940217i	$-0.389378\pi$
$941$	20.8948	0.681150	0.340575	+	0.940217i	$0.389378\pi$
$942$	127.495	4.15400
$943$	−71.7002	−2.33488
$944$	17.5966	0.572721
$945$	22.8182	0.742276
$946$	0.00960137	0.000312167 0
$947$	29.0074	0.942614	0.471307	−	0.881969i	$-0.343782\pi$
$947$	29.0074	0.942614	0.471307	+	0.881969i	$0.343782\pi$
$948$	−139.246	−4.52249
$949$	18.1956	0.590656
$950$	5.25005	0.170334
$951$	−73.5704	−2.38568
$952$	−0.00379991	−0.000123156 0
$953$	8.09170	0.262116	0.131058	−	0.991375i	$-0.458163\pi$
$953$	8.09170	0.262116	0.131058	+	0.991375i	$0.458163\pi$
$954$	−19.7593	−0.639730
$955$	−29.6818	−0.960480
$956$	−105.434	−3.41000
$957$	−0.00918672	−0.000296965 0
$958$	−58.0888	−1.87677
$959$	−12.7992	−0.413308
$960$	69.3108	2.23700
$961$	−30.9723	−0.999105
$962$	−20.7359	−0.668552
$963$	46.7829	1.50756
$964$	20.3528	0.655519
$965$	3.64561	0.117356
$966$	−60.6084	−1.95004
$967$	57.0515	1.83465	0.917326	−	0.398136i	$-0.130343\pi$
$967$	57.0515	1.83465	0.917326	+	0.398136i	$0.130343\pi$
$968$	38.2490	1.22937
$969$	−0.00436746	−0.000140303 0
$970$	−8.66068	−0.278078
$971$	25.3540	0.813647	0.406824	−	0.913507i	$-0.366636\pi$
$971$	25.3540	0.813647	0.406824	+	0.913507i	$0.366636\pi$
$972$	78.5319	2.51891
$973$	−0.730920	−0.0234322
$974$	−46.8406	−1.50087
$975$	6.08738	0.194952
$976$	−16.0868	−0.514926
$977$	12.2278	0.391202	0.195601	−	0.980684i	$-0.437334\pi$
$977$	12.2278	0.391202	0.195601	+	0.980684i	$0.437334\pi$
$978$	71.7293	2.29365
$979$	−0.00406257	−0.000129840 0
$980$	−6.25787	−0.199900
$981$	14.8161	0.473043
$982$	4.36479	0.139286
$983$	52.5067	1.67470	0.837352	−	0.546664i	$-0.184103\pi$
$983$	52.5067	1.67470	0.837352	+	0.546664i	$0.184103\pi$
$984$	−96.4827	−3.07576
$985$	0.637982	0.0203278
$986$	0.00484657	0.000154346 0
$987$	−9.59395	−0.305379
$988$	−4.76868	−0.151712
$989$	−21.8706	−0.695445
$990$	−0.0452262	−0.00143738
$991$	9.74660	0.309611	0.154806	−	0.987945i	$-0.450525\pi$
$991$	9.74660	0.309611	0.154806	+	0.987945i	$0.450525\pi$
$992$	−0.700416	−0.0222382
$993$	−30.9892	−0.983413
$994$	−38.8707	−1.23290
$995$	32.3951	1.02699
$996$	−110.044	−3.48689
$997$	−41.9189	−1.32759	−0.663793	−	0.747916i	$-0.731055\pi$
$997$	−41.9189	−1.32759	−0.663793	+	0.747916i	$0.731055\pi$
$998$	20.0030	0.633184
$999$	−103.824	−3.28485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.12	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.12	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34195 q^{2} +3.16467 q^{3} +3.48474 q^{4} -1.79579 q^{5} -7.41150 q^{6} -1.00000 q^{7} -3.47719 q^{8} +7.01511 q^{9} +O(q^{10})\)	\(q-2.34195 q^{2} +3.16467 q^{3} +3.48474 q^{4} -1.79579 q^{5} -7.41150 q^{6} -1.00000 q^{7} -3.47719 q^{8} +7.01511 q^{9} +4.20566 q^{10} -0.00153293 q^{11} +11.0280 q^{12} -1.08361 q^{13} +2.34195 q^{14} -5.68308 q^{15} +1.17393 q^{16} -0.00109281 q^{17} -16.4291 q^{18} +1.26286 q^{19} -6.25787 q^{20} -3.16467 q^{21} +0.00359004 q^{22} -8.17763 q^{23} -11.0041 q^{24} -1.77513 q^{25} +2.53776 q^{26} +12.7065 q^{27} -3.48474 q^{28} +1.89370 q^{29} +13.3095 q^{30} -0.166564 q^{31} +4.20509 q^{32} -0.00485120 q^{33} +0.00255931 q^{34} +1.79579 q^{35} +24.4458 q^{36} -8.17094 q^{37} -2.95756 q^{38} -3.42926 q^{39} +6.24431 q^{40} +8.76786 q^{41} +7.41150 q^{42} +2.67444 q^{43} -0.00534185 q^{44} -12.5977 q^{45} +19.1516 q^{46} +3.03158 q^{47} +3.71509 q^{48} +1.00000 q^{49} +4.15727 q^{50} -0.00345839 q^{51} -3.77610 q^{52} +1.20270 q^{53} -29.7580 q^{54} +0.00275282 q^{55} +3.47719 q^{56} +3.99653 q^{57} -4.43495 q^{58} +14.9895 q^{59} -19.8041 q^{60} -13.7034 q^{61} +0.390084 q^{62} -7.01511 q^{63} -12.1960 q^{64} +1.94594 q^{65} +0.0113613 q^{66} +12.9275 q^{67} -0.00380817 q^{68} -25.8795 q^{69} -4.20566 q^{70} -16.5976 q^{71} -24.3929 q^{72} -16.7917 q^{73} +19.1360 q^{74} -5.61769 q^{75} +4.40074 q^{76} +0.00153293 q^{77} +8.03117 q^{78} -12.6265 q^{79} -2.10813 q^{80} +19.1665 q^{81} -20.5339 q^{82} -9.97860 q^{83} -11.0280 q^{84} +0.00196246 q^{85} -6.26342 q^{86} +5.99293 q^{87} +0.00533028 q^{88} +2.65021 q^{89} +29.5032 q^{90} +1.08361 q^{91} -28.4969 q^{92} -0.527119 q^{93} -7.09982 q^{94} -2.26784 q^{95} +13.3077 q^{96} -2.05929 q^{97} -2.34195 q^{98} -0.0107537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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