LMFDB - Embedded newform 8041.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12431 q^{2} +0.433471 q^{3} +2.51268 q^{4} +3.47058 q^{5} -0.920826 q^{6} +2.89316 q^{7} -1.08909 q^{8} -2.81210 q^{9} +O(q^{10})$	\(q-2.12431 q^{2} +0.433471 q^{3} +2.51268 q^{4} +3.47058 q^{5} -0.920826 q^{6} +2.89316 q^{7} -1.08909 q^{8} -2.81210 q^{9} -7.37258 q^{10} +1.00000 q^{11} +1.08917 q^{12} -3.57765 q^{13} -6.14596 q^{14} +1.50440 q^{15} -2.71180 q^{16} +1.00000 q^{17} +5.97377 q^{18} -0.355121 q^{19} +8.72046 q^{20} +1.25410 q^{21} -2.12431 q^{22} -2.26187 q^{23} -0.472089 q^{24} +7.04493 q^{25} +7.60004 q^{26} -2.51938 q^{27} +7.26958 q^{28} -7.81548 q^{29} -3.19580 q^{30} -3.74786 q^{31} +7.93887 q^{32} +0.433471 q^{33} -2.12431 q^{34} +10.0409 q^{35} -7.06591 q^{36} -11.0951 q^{37} +0.754386 q^{38} -1.55081 q^{39} -3.77977 q^{40} -5.17665 q^{41} -2.66409 q^{42} -1.00000 q^{43} +2.51268 q^{44} -9.75963 q^{45} +4.80490 q^{46} +12.0661 q^{47} -1.17549 q^{48} +1.37036 q^{49} -14.9656 q^{50} +0.433471 q^{51} -8.98950 q^{52} -1.62170 q^{53} +5.35193 q^{54} +3.47058 q^{55} -3.15091 q^{56} -0.153935 q^{57} +16.6025 q^{58} -0.413248 q^{59} +3.78007 q^{60} +0.282661 q^{61} +7.96160 q^{62} -8.13586 q^{63} -11.4410 q^{64} -12.4165 q^{65} -0.920826 q^{66} +7.11868 q^{67} +2.51268 q^{68} -0.980455 q^{69} -21.3300 q^{70} +10.9390 q^{71} +3.06263 q^{72} -12.8855 q^{73} +23.5694 q^{74} +3.05377 q^{75} -0.892306 q^{76} +2.89316 q^{77} +3.29440 q^{78} +11.8710 q^{79} -9.41152 q^{80} +7.34423 q^{81} +10.9968 q^{82} +9.63822 q^{83} +3.15115 q^{84} +3.47058 q^{85} +2.12431 q^{86} -3.38778 q^{87} -1.08909 q^{88} -4.91133 q^{89} +20.7324 q^{90} -10.3507 q^{91} -5.68335 q^{92} -1.62459 q^{93} -25.6320 q^{94} -1.23248 q^{95} +3.44127 q^{96} -5.27598 q^{97} -2.91107 q^{98} -2.81210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−2.12431	−1.50211	−0.751056	−	0.660239i	$-0.770455\pi$
$2$	−2.12431	−1.50211	−0.751056	+	0.660239i	$0.770455\pi$
$3$	0.433471	0.250265	0.125132	−	0.992140i	$-0.460064\pi$
$3$	0.433471	0.250265	0.125132	+	0.992140i	$0.460064\pi$
$4$	2.51268	1.25634
$5$	3.47058	1.55209	0.776045	−	0.630677i	$-0.217223\pi$
$5$	3.47058	1.55209	0.776045	+	0.630677i	$0.217223\pi$
$6$	−0.920826	−0.375926
$7$	2.89316	1.09351	0.546755	−	0.837292i	$-0.315863\pi$
$7$	2.89316	1.09351	0.546755	+	0.837292i	$0.315863\pi$
$8$	−1.08909	−0.385051
$9$	−2.81210	−0.937368
$10$	−7.37258	−2.33141
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.08917	0.314418
$13$	−3.57765	−0.992263	−0.496131	−	0.868247i	$-0.665247\pi$
$13$	−3.57765	−0.992263	−0.496131	+	0.868247i	$0.665247\pi$
$14$	−6.14596	−1.64258
$15$	1.50440	0.388434
$16$	−2.71180	−0.677950
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.97377	1.40803
$19$	−0.355121	−0.0814704	−0.0407352	−	0.999170i	$-0.512970\pi$
$19$	−0.355121	−0.0814704	−0.0407352	+	0.999170i	$0.512970\pi$
$20$	8.72046	1.94995
$21$	1.25410	0.273667
$22$	−2.12431	−0.452904
$23$	−2.26187	−0.471632	−0.235816	−	0.971798i	$-0.575776\pi$
$23$	−2.26187	−0.471632	−0.235816	+	0.971798i	$0.575776\pi$
$24$	−0.472089	−0.0963648
$25$	7.04493	1.40899
$26$	7.60004	1.49049
$27$	−2.51938	−0.484855
$28$	7.26958	1.37382
$29$	−7.81548	−1.45130	−0.725649	−	0.688065i	$-0.758460\pi$
$29$	−7.81548	−1.45130	−0.725649	+	0.688065i	$0.758460\pi$
$30$	−3.19580	−0.583471
$31$	−3.74786	−0.673135	−0.336567	−	0.941659i	$-0.609266\pi$
$31$	−3.74786	−0.673135	−0.336567	+	0.941659i	$0.609266\pi$
$32$	7.93887	1.40341
$33$	0.433471	0.0754576
$34$	−2.12431	−0.364316
$35$	10.0409	1.69723
$36$	−7.06591	−1.17765
$37$	−11.0951	−1.82402	−0.912010	−	0.410168i	$-0.865470\pi$
$37$	−11.0951	−1.82402	−0.912010	+	0.410168i	$0.865470\pi$
$38$	0.754386	0.122378
$39$	−1.55081	−0.248328
$40$	−3.77977	−0.597635
$41$	−5.17665	−0.808457	−0.404229	−	0.914658i	$-0.632460\pi$
$41$	−5.17665	−0.808457	−0.404229	+	0.914658i	$0.632460\pi$
$42$	−2.66409	−0.411079
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	2.51268	0.378801
$45$	−9.75963	−1.45488
$46$	4.80490	0.708444
$47$	12.0661	1.76002	0.880008	−	0.474959i	$-0.157537\pi$
$47$	12.0661	1.76002	0.880008	+	0.474959i	$0.157537\pi$
$48$	−1.17549	−0.169667
$49$	1.37036	0.195766
$50$	−14.9656	−2.11645
$51$	0.433471	0.0606981
$52$	−8.98950	−1.24662
$53$	−1.62170	−0.222758	−0.111379	−	0.993778i	$-0.535527\pi$
$53$	−1.62170	−0.222758	−0.111379	+	0.993778i	$0.535527\pi$
$54$	5.35193	0.728306
$55$	3.47058	0.467973
$56$	−3.15091	−0.421058
$57$	−0.153935	−0.0203892
$58$	16.6025	2.18001
$59$	−0.413248	−0.0538003	−0.0269002	−	0.999638i	$-0.508564\pi$
$59$	−0.413248	−0.0538003	−0.0269002	+	0.999638i	$0.508564\pi$
$60$	3.78007	0.488005
$61$	0.282661	0.0361910	0.0180955	−	0.999836i	$-0.494240\pi$
$61$	0.282661	0.0361910	0.0180955	+	0.999836i	$0.494240\pi$
$62$	7.96160	1.01112
$63$	−8.13586	−1.02502
$64$	−11.4410	−1.43013
$65$	−12.4165	−1.54008
$66$	−0.920826	−0.113346
$67$	7.11868	0.869685	0.434843	−	0.900506i	$-0.356804\pi$
$67$	7.11868	0.869685	0.434843	+	0.900506i	$0.356804\pi$
$68$	2.51268	0.304707
$69$	−0.980455	−0.118033
$70$	−21.3300	−2.54943
$71$	10.9390	1.29822	0.649110	−	0.760695i	$-0.275141\pi$
$71$	10.9390	1.29822	0.649110	+	0.760695i	$0.275141\pi$
$72$	3.06263	0.360935
$73$	−12.8855	−1.50814	−0.754069	−	0.656795i	$-0.771912\pi$
$73$	−12.8855	−1.50814	−0.754069	+	0.656795i	$0.771912\pi$
$74$	23.5694	2.73988
$75$	3.05377	0.352619
$76$	−0.892306	−0.102354
$77$	2.89316	0.329706
$78$	3.29440	0.373017
$79$	11.8710	1.33559	0.667793	−	0.744347i	$-0.267239\pi$
$79$	11.8710	1.33559	0.667793	+	0.744347i	$0.267239\pi$
$80$	−9.41152	−1.05224
$81$	7.34423	0.816026
$82$	10.9968	1.21439
$83$	9.63822	1.05793	0.528966	−	0.848643i	$-0.322580\pi$
$83$	9.63822	1.05793	0.528966	+	0.848643i	$0.322580\pi$
$84$	3.15115	0.343819
$85$	3.47058	0.376437
$86$	2.12431	0.229070
$87$	−3.38778	−0.363209
$88$	−1.08909	−0.116097
$89$	−4.91133	−0.520600	−0.260300	−	0.965528i	$-0.583821\pi$
$89$	−4.91133	−0.520600	−0.260300	+	0.965528i	$0.583821\pi$
$90$	20.7324	2.18539
$91$	−10.3507	−1.08505
$92$	−5.68335	−0.592530
$93$	−1.62459	−0.168462
$94$	−25.6320	−2.64374
$95$	−1.23248	−0.126449
$96$	3.44127	0.351223
$97$	−5.27598	−0.535695	−0.267848	−	0.963461i	$-0.586312\pi$
$97$	−5.27598	−0.535695	−0.267848	+	0.963461i	$0.586312\pi$
$98$	−2.91107	−0.294063
$99$	−2.81210	−0.282627
$100$	17.7017	1.77017
$101$	−5.45565	−0.542858	−0.271429	−	0.962458i	$-0.587496\pi$
$101$	−5.45565	−0.542858	−0.271429	+	0.962458i	$0.587496\pi$
$102$	−0.920826	−0.0911753
$103$	−14.3130	−1.41030	−0.705149	−	0.709059i	$-0.749120\pi$
$103$	−14.3130	−1.41030	−0.705149	+	0.709059i	$0.749120\pi$
$104$	3.89639	0.382072
$105$	4.35246	0.424756
$106$	3.44500	0.334608
$107$	5.83995	0.564570	0.282285	−	0.959331i	$-0.408908\pi$
$107$	5.83995	0.564570	0.282285	+	0.959331i	$0.408908\pi$
$108$	−6.33039	−0.609142
$109$	11.3202	1.08428	0.542139	−	0.840289i	$-0.317615\pi$
$109$	11.3202	1.08428	0.542139	+	0.840289i	$0.317615\pi$
$110$	−7.37258	−0.702948
$111$	−4.80940	−0.456488
$112$	−7.84566	−0.741346
$113$	−15.0093	−1.41196	−0.705979	−	0.708233i	$-0.749493\pi$
$113$	−15.0093	−1.41196	−0.705979	+	0.708233i	$0.749493\pi$
$114$	0.327005	0.0306268
$115$	−7.85000	−0.732016
$116$	−19.6378	−1.82332
$117$	10.0607	0.930115
$118$	0.877866	0.0808141
$119$	2.89316	0.265215
$120$	−1.63842	−0.149567
$121$	1.00000	0.0909091
$122$	−0.600458	−0.0543629
$123$	−2.24393	−0.202328
$124$	−9.41716	−0.845686
$125$	7.09709	0.634783
$126$	17.2831	1.53970
$127$	−4.60031	−0.408212	−0.204106	−	0.978949i	$-0.565429\pi$
$127$	−4.60031	−0.408212	−0.204106	+	0.978949i	$0.565429\pi$
$128$	8.42646	0.744801
$129$	−0.433471	−0.0381650
$130$	26.3765	2.31338
$131$	−5.02251	−0.438819	−0.219410	−	0.975633i	$-0.570413\pi$
$131$	−5.02251	−0.438819	−0.219410	+	0.975633i	$0.570413\pi$
$132$	1.08917	0.0948005
$133$	−1.02742	−0.0890887
$134$	−15.1223	−1.30636
$135$	−8.74371	−0.752539
$136$	−1.08909	−0.0933887
$137$	−13.0805	−1.11755	−0.558773	−	0.829320i	$-0.688728\pi$
$137$	−13.0805	−1.11755	−0.558773	+	0.829320i	$0.688728\pi$
$138$	2.08279	0.177299
$139$	−4.08169	−0.346205	−0.173102	−	0.984904i	$-0.555379\pi$
$139$	−4.08169	−0.346205	−0.173102	+	0.984904i	$0.555379\pi$
$140$	25.2297	2.13230
$141$	5.23029	0.440470
$142$	−23.2378	−1.95007
$143$	−3.57765	−0.299179
$144$	7.62586	0.635488
$145$	−27.1242	−2.25255
$146$	27.3728	2.26539
$147$	0.594013	0.0489934
$148$	−27.8784	−2.29159
$149$	−13.0444	−1.06864	−0.534319	−	0.845283i	$-0.679432\pi$
$149$	−13.0444	−1.06864	−0.534319	+	0.845283i	$0.679432\pi$
$150$	−6.48715	−0.529674
$151$	14.8097	1.20520	0.602599	−	0.798044i	$-0.294132\pi$
$151$	14.8097	1.20520	0.602599	+	0.798044i	$0.294132\pi$
$152$	0.386759	0.0313703
$153$	−2.81210	−0.227345
$154$	−6.14596	−0.495255
$155$	−13.0072	−1.04477
$156$	−3.89669	−0.311985
$157$	−2.02590	−0.161684	−0.0808420	−	0.996727i	$-0.525761\pi$
$157$	−2.02590	−0.161684	−0.0808420	+	0.996727i	$0.525761\pi$
$158$	−25.2175	−2.00620
$159$	−0.702962	−0.0557485
$160$	27.5525	2.17822
$161$	−6.54394	−0.515735
$162$	−15.6014	−1.22576
$163$	−22.9967	−1.80124	−0.900620	−	0.434608i	$-0.856887\pi$
$163$	−22.9967	−1.80124	−0.900620	+	0.434608i	$0.856887\pi$
$164$	−13.0073	−1.01570
$165$	1.50440	0.117117
$166$	−20.4745	−1.58913
$167$	−3.54543	−0.274353	−0.137177	−	0.990547i	$-0.543803\pi$
$167$	−3.54543	−0.274353	−0.137177	+	0.990547i	$0.543803\pi$
$168$	−1.36583	−0.105376
$169$	−0.200387	−0.0154144
$170$	−7.37258	−0.565451
$171$	0.998637	0.0763677
$172$	−2.51268	−0.191590
$173$	3.63474	0.276344	0.138172	−	0.990408i	$-0.455877\pi$
$173$	3.63474	0.276344	0.138172	+	0.990408i	$0.455877\pi$
$174$	7.19669	0.545580
$175$	20.3821	1.54074
$176$	−2.71180	−0.204410
$177$	−0.179131	−0.0134643
$178$	10.4332	0.782000
$179$	−2.60357	−0.194600	−0.0972999	−	0.995255i	$-0.531021\pi$
$179$	−2.60357	−0.194600	−0.0972999	+	0.995255i	$0.531021\pi$
$180$	−24.5228	−1.82782
$181$	−25.4447	−1.89129	−0.945645	−	0.325200i	$-0.894569\pi$
$181$	−25.4447	−1.89129	−0.945645	+	0.325200i	$0.894569\pi$
$182$	21.9881	1.62987
$183$	0.122525	0.00905733
$184$	2.46338	0.181603
$185$	−38.5064	−2.83104
$186$	3.45112	0.253049
$187$	1.00000	0.0731272
$188$	30.3181	2.21118
$189$	−7.28896	−0.530194
$190$	2.61816	0.189941
$191$	−17.5203	−1.26772	−0.633861	−	0.773447i	$-0.718531\pi$
$191$	−17.5203	−1.26772	−0.633861	+	0.773447i	$0.718531\pi$
$192$	−4.95935	−0.357910
$193$	−10.9841	−0.790650	−0.395325	−	0.918541i	$-0.629368\pi$
$193$	−10.9841	−0.790650	−0.395325	+	0.918541i	$0.629368\pi$
$194$	11.2078	0.804674
$195$	−5.38221	−0.385428
$196$	3.44328	0.245949
$197$	−18.7957	−1.33914	−0.669569	−	0.742750i	$-0.733521\pi$
$197$	−18.7957	−1.33914	−0.669569	+	0.742750i	$0.733521\pi$
$198$	5.97377	0.424537
$199$	2.28415	0.161919	0.0809595	−	0.996717i	$-0.474202\pi$
$199$	2.28415	0.161919	0.0809595	+	0.996717i	$0.474202\pi$
$200$	−7.67256	−0.542532
$201$	3.08574	0.217652
$202$	11.5895	0.815433
$203$	−22.6114	−1.58701
$204$	1.08917	0.0762575
$205$	−17.9660	−1.25480
$206$	30.4051	2.11843
$207$	6.36061	0.442093
$208$	9.70188	0.672704
$209$	−0.355121	−0.0245642
$210$	−9.24595	−0.638031
$211$	−7.75355	−0.533777	−0.266888	−	0.963727i	$-0.585995\pi$
$211$	−7.75355	−0.533777	−0.266888	+	0.963727i	$0.585995\pi$
$212$	−4.07482	−0.279860
$213$	4.74174	0.324899
$214$	−12.4059	−0.848047
$215$	−3.47058	−0.236692
$216$	2.74383	0.186694
$217$	−10.8431	−0.736080
$218$	−24.0476	−1.62871
$219$	−5.58551	−0.377434
$220$	8.72046	0.587933
$221$	−3.57765	−0.240659
$222$	10.2166	0.685696
$223$	17.5037	1.17213	0.586066	−	0.810264i	$-0.300676\pi$
$223$	17.5037	1.17213	0.586066	+	0.810264i	$0.300676\pi$
$224$	22.9684	1.53464
$225$	−19.8111	−1.32074
$226$	31.8844	2.12092
$227$	−9.11742	−0.605145	−0.302572	−	0.953126i	$-0.597845\pi$
$227$	−9.11742	−0.605145	−0.302572	+	0.953126i	$0.597845\pi$
$228$	−0.386789	−0.0256157
$229$	16.8766	1.11524	0.557619	−	0.830097i	$-0.311715\pi$
$229$	16.8766	1.11524	0.557619	+	0.830097i	$0.311715\pi$
$230$	16.6758	1.09957
$231$	1.25410	0.0825138
$232$	8.51175	0.558824
$233$	15.7304	1.03053	0.515265	−	0.857031i	$-0.327693\pi$
$233$	15.7304	1.03053	0.515265	+	0.857031i	$0.327693\pi$
$234$	−21.3721	−1.39714
$235$	41.8762	2.73170
$236$	−1.03836	−0.0675915
$237$	5.14572	0.334250
$238$	−6.14596	−0.398383
$239$	26.7299	1.72901	0.864506	−	0.502622i	$-0.167631\pi$
$239$	26.7299	1.72901	0.864506	+	0.502622i	$0.167631\pi$
$240$	−4.07962	−0.263338
$241$	14.8608	0.957266	0.478633	−	0.878015i	$-0.341133\pi$
$241$	14.8608	0.957266	0.478633	+	0.878015i	$0.341133\pi$
$242$	−2.12431	−0.136556
$243$	10.7416	0.689077
$244$	0.710236	0.0454682
$245$	4.75595	0.303847
$246$	4.76679	0.303920
$247$	1.27050	0.0808400
$248$	4.08175	0.259192
$249$	4.17789	0.264763
$250$	−15.0764	−0.953515
$251$	−21.5693	−1.36144	−0.680720	−	0.732543i	$-0.738333\pi$
$251$	−21.5693	−1.36144	−0.680720	+	0.732543i	$0.738333\pi$
$252$	−20.4428	−1.28778
$253$	−2.26187	−0.142202
$254$	9.77247	0.613179
$255$	1.50440	0.0942090
$256$	4.98162	0.311351
$257$	−0.262644	−0.0163833	−0.00819165	−	0.999966i	$-0.502608\pi$
$257$	−0.262644	−0.0163833	−0.00819165	+	0.999966i	$0.502608\pi$
$258$	0.920826	0.0573281
$259$	−32.0998	−1.99459
$260$	−31.1988	−1.93487
$261$	21.9779	1.36040
$262$	10.6694	0.659155
$263$	−7.85461	−0.484336	−0.242168	−	0.970234i	$-0.577859\pi$
$263$	−7.85461	−0.484336	−0.242168	+	0.970234i	$0.577859\pi$
$264$	−0.472089	−0.0290551
$265$	−5.62825	−0.345741
$266$	2.18256	0.133821
$267$	−2.12892	−0.130288
$268$	17.8870	1.09262
$269$	10.6218	0.647625	0.323812	−	0.946121i	$-0.395035\pi$
$269$	10.6218	0.647625	0.323812	+	0.946121i	$0.395035\pi$
$270$	18.5743	1.13040
$271$	−16.7258	−1.01602	−0.508010	−	0.861351i	$-0.669619\pi$
$271$	−16.7258	−1.01602	−0.508010	+	0.861351i	$0.669619\pi$
$272$	−2.71180	−0.164427
$273$	−4.48674	−0.271550
$274$	27.7871	1.67868
$275$	7.04493	0.424825
$276$	−2.46357	−0.148289
$277$	8.71557	0.523668	0.261834	−	0.965113i	$-0.415673\pi$
$277$	8.71557	0.523668	0.261834	+	0.965113i	$0.415673\pi$
$278$	8.67077	0.520038
$279$	10.5394	0.630975
$280$	−10.9355	−0.653520
$281$	−2.01519	−0.120216	−0.0601081	−	0.998192i	$-0.519145\pi$
$281$	−2.01519	−0.120216	−0.0601081	+	0.998192i	$0.519145\pi$
$282$	−11.1107	−0.661635
$283$	0.539150	0.0320491	0.0160246	−	0.999872i	$-0.494899\pi$
$283$	0.539150	0.0320491	0.0160246	+	0.999872i	$0.494899\pi$
$284$	27.4862	1.63101
$285$	−0.534243	−0.0316458
$286$	7.60004	0.449400
$287$	−14.9769	−0.884057
$288$	−22.3249	−1.31551
$289$	1.00000	0.0588235
$290$	57.6202	3.38357
$291$	−2.28699	−0.134066
$292$	−32.3772	−1.89473
$293$	−12.8612	−0.751359	−0.375680	−	0.926750i	$-0.622591\pi$
$293$	−12.8612	−0.751359	−0.375680	+	0.926750i	$0.622591\pi$
$294$	−1.26187	−0.0735935
$295$	−1.43421	−0.0835030
$296$	12.0835	0.702341
$297$	−2.51938	−0.146189
$298$	27.7103	1.60521
$299$	8.09218	0.467983
$300$	7.67316	0.443010
$301$	−2.89316	−0.166759
$302$	−31.4604	−1.81034
$303$	−2.36487	−0.135858
$304$	0.963017	0.0552328
$305$	0.980997	0.0561717
$306$	5.97377	0.341498
$307$	19.3814	1.10615	0.553076	−	0.833131i	$-0.313454\pi$
$307$	19.3814	1.10615	0.553076	+	0.833131i	$0.313454\pi$
$308$	7.26958	0.414223
$309$	−6.20426	−0.352948
$310$	27.6314	1.56936
$311$	19.9118	1.12909	0.564547	−	0.825401i	$-0.309051\pi$
$311$	19.9118	1.12909	0.564547	+	0.825401i	$0.309051\pi$
$312$	1.68897	0.0956192
$313$	−12.8186	−0.724552	−0.362276	−	0.932071i	$-0.618000\pi$
$313$	−12.8186	−0.724552	−0.362276	+	0.932071i	$0.618000\pi$
$314$	4.30362	0.242868
$315$	−28.2361	−1.59093
$316$	29.8279	1.67795
$317$	6.25510	0.351321	0.175661	−	0.984451i	$-0.443794\pi$
$317$	6.25510	0.351321	0.175661	+	0.984451i	$0.443794\pi$
$318$	1.49331	0.0837405
$319$	−7.81548	−0.437583
$320$	−39.7069	−2.21968
$321$	2.53145	0.141292
$322$	13.9013	0.774691
$323$	−0.355121	−0.0197595
$324$	18.4537	1.02521
$325$	−25.2043	−1.39808
$326$	48.8520	2.70566
$327$	4.90698	0.271357
$328$	5.63784	0.311298
$329$	34.9090	1.92460
$330$	−3.19580	−0.175923
$331$	−28.4191	−1.56205	−0.781026	−	0.624498i	$-0.785304\pi$
$331$	−28.4191	−1.56205	−0.781026	+	0.624498i	$0.785304\pi$
$332$	24.2178	1.32912
$333$	31.2005	1.70978
$334$	7.53158	0.412110
$335$	24.7060	1.34983
$336$	−3.40087	−0.185533
$337$	14.6737	0.799329	0.399664	−	0.916662i	$-0.369127\pi$
$337$	14.6737	0.799329	0.399664	+	0.916662i	$0.369127\pi$
$338$	0.425684	0.0231542
$339$	−6.50611	−0.353363
$340$	8.72046	0.472933
$341$	−3.74786	−0.202958
$342$	−2.12141	−0.114713
$343$	−16.2874	−0.879439
$344$	1.08909	0.0587198
$345$	−3.40275	−0.183198
$346$	−7.72130	−0.415100
$347$	16.3607	0.878288	0.439144	−	0.898417i	$-0.355282\pi$
$347$	16.3607	0.878288	0.439144	+	0.898417i	$0.355282\pi$
$348$	−8.51242	−0.456313
$349$	13.5639	0.726060	0.363030	−	0.931777i	$-0.381742\pi$
$349$	13.5639	0.726060	0.363030	+	0.931777i	$0.381742\pi$
$350$	−43.2978	−2.31437
$351$	9.01347	0.481103
$352$	7.93887	0.423143
$353$	−3.57483	−0.190269	−0.0951344	−	0.995464i	$-0.530328\pi$
$353$	−3.57483	−0.190269	−0.0951344	+	0.995464i	$0.530328\pi$
$354$	0.380530	0.0202249
$355$	37.9647	2.01496
$356$	−12.3406	−0.654051
$357$	1.25410	0.0663740
$358$	5.53078	0.292311
$359$	−36.7770	−1.94102	−0.970509	−	0.241064i	$-0.922503\pi$
$359$	−36.7770	−1.94102	−0.970509	+	0.241064i	$0.922503\pi$
$360$	10.6291	0.560203
$361$	−18.8739	−0.993363
$362$	54.0524	2.84093
$363$	0.433471	0.0227513
$364$	−26.0080	−1.36319
$365$	−44.7203	−2.34077
$366$	−0.260281	−0.0136051
$367$	11.1517	0.582114	0.291057	−	0.956706i	$-0.405993\pi$
$367$	11.1517	0.582114	0.291057	+	0.956706i	$0.405993\pi$
$368$	6.13373	0.319743
$369$	14.5573	0.757822
$370$	81.7993	4.25255
$371$	−4.69184	−0.243588
$372$	−4.08207	−0.211645
$373$	−21.1676	−1.09602	−0.548008	−	0.836473i	$-0.684614\pi$
$373$	−21.1676	−1.09602	−0.548008	+	0.836473i	$0.684614\pi$
$374$	−2.12431	−0.109845
$375$	3.07638	0.158864
$376$	−13.1410	−0.677696
$377$	27.9611	1.44007
$378$	15.4840	0.796411
$379$	6.48333	0.333026	0.166513	−	0.986039i	$-0.446749\pi$
$379$	6.48333	0.333026	0.166513	+	0.986039i	$0.446749\pi$
$380$	−3.09682	−0.158863
$381$	−1.99410	−0.102161
$382$	37.2184	1.90426
$383$	2.23010	0.113953	0.0569764	−	0.998376i	$-0.481854\pi$
$383$	2.23010	0.113953	0.0569764	+	0.998376i	$0.481854\pi$
$384$	3.65263	0.186397
$385$	10.0409	0.511734
$386$	23.3335	1.18764
$387$	2.81210	0.142947
$388$	−13.2569	−0.673015
$389$	18.3135	0.928531	0.464266	−	0.885696i	$-0.346318\pi$
$389$	18.3135	0.928531	0.464266	+	0.885696i	$0.346318\pi$
$390$	11.4335	0.578956
$391$	−2.26187	−0.114388
$392$	−1.49245	−0.0753800
$393$	−2.17711	−0.109821
$394$	39.9278	2.01153
$395$	41.1991	2.07295
$396$	−7.06591	−0.355076
$397$	−33.8424	−1.69850	−0.849251	−	0.527989i	$-0.822946\pi$
$397$	−33.8424	−1.69850	−0.849251	+	0.527989i	$0.822946\pi$
$398$	−4.85223	−0.243221
$399$	−0.445358	−0.0222958
$400$	−19.1044	−0.955222
$401$	−0.0506623	−0.00252996	−0.00126498	−	0.999999i	$-0.500403\pi$
$401$	−0.0506623	−0.00252996	−0.00126498	+	0.999999i	$0.500403\pi$
$402$	−6.55507	−0.326937
$403$	13.4085	0.667927
$404$	−13.7083	−0.682014
$405$	25.4887	1.26655
$406$	48.0336	2.38387
$407$	−11.0951	−0.549963
$408$	−0.472089	−0.0233719
$409$	25.1531	1.24374	0.621871	−	0.783120i	$-0.286373\pi$
$409$	25.1531	1.24374	0.621871	+	0.783120i	$0.286373\pi$
$410$	38.1653	1.88485
$411$	−5.67004	−0.279682
$412$	−35.9639	−1.77181
$413$	−1.19559	−0.0588313
$414$	−13.5119	−0.664073
$415$	33.4502	1.64201
$416$	−28.4025	−1.39255
$417$	−1.76930	−0.0866428
$418$	0.754386	0.0368982
$419$	−7.56516	−0.369582	−0.184791	−	0.982778i	$-0.559161\pi$
$419$	−7.56516	−0.369582	−0.184791	+	0.982778i	$0.559161\pi$
$420$	10.9363	0.533638
$421$	−14.0457	−0.684546	−0.342273	−	0.939601i	$-0.611197\pi$
$421$	−14.0457	−0.684546	−0.342273	+	0.939601i	$0.611197\pi$
$422$	16.4709	0.801792
$423$	−33.9310	−1.64978
$424$	1.76618	0.0857733
$425$	7.04493	0.341729
$426$	−10.0729	−0.488034
$427$	0.817782	0.0395753
$428$	14.6739	0.709291
$429$	−1.55081	−0.0748738
$430$	7.37258	0.355537
$431$	−10.7384	−0.517249	−0.258624	−	0.965978i	$-0.583269\pi$
$431$	−10.7384	−0.517249	−0.258624	+	0.965978i	$0.583269\pi$
$432$	6.83205	0.328707
$433$	−25.3338	−1.21746	−0.608732	−	0.793376i	$-0.708322\pi$
$433$	−25.3338	−1.21746	−0.608732	+	0.793376i	$0.708322\pi$
$434$	23.0342	1.10568
$435$	−11.7576	−0.563733
$436$	28.4440	1.36222
$437$	0.803237	0.0384240
$438$	11.8653	0.566948
$439$	−15.8453	−0.756257	−0.378129	−	0.925753i	$-0.623432\pi$
$439$	−15.8453	−0.756257	−0.378129	+	0.925753i	$0.623432\pi$
$440$	−3.77977	−0.180194
$441$	−3.85360	−0.183505
$442$	7.60004	0.361497
$443$	30.1983	1.43477	0.717383	−	0.696679i	$-0.245340\pi$
$443$	30.1983	1.43477	0.717383	+	0.696679i	$0.245340\pi$
$444$	−12.0845	−0.573504
$445$	−17.0452	−0.808019
$446$	−37.1831	−1.76067
$447$	−5.65437	−0.267442
$448$	−33.1006	−1.56386
$449$	−16.7829	−0.792035	−0.396017	−	0.918243i	$-0.629608\pi$
$449$	−16.7829	−0.792035	−0.396017	+	0.918243i	$0.629608\pi$
$450$	42.0848	1.98390
$451$	−5.17665	−0.243759
$452$	−37.7136	−1.77390
$453$	6.41959	0.301619
$454$	19.3682	0.908995
$455$	−35.9230	−1.68410
$456$	0.167649	0.00785087
$457$	35.6204	1.66625	0.833126	−	0.553084i	$-0.186549\pi$
$457$	35.6204	1.66625	0.833126	+	0.553084i	$0.186549\pi$
$458$	−35.8511	−1.67521
$459$	−2.51938	−0.117595
$460$	−19.7245	−0.919661
$461$	15.9811	0.744316	0.372158	−	0.928169i	$-0.378618\pi$
$461$	15.9811	0.744316	0.372158	+	0.928169i	$0.378618\pi$
$462$	−2.66409	−0.123945
$463$	−33.0820	−1.53745	−0.768727	−	0.639578i	$-0.779109\pi$
$463$	−33.0820	−1.53745	−0.768727	+	0.639578i	$0.779109\pi$
$464$	21.1940	0.983907
$465$	−5.63826	−0.261468
$466$	−33.4161	−1.54797
$467$	15.7066	0.726816	0.363408	−	0.931630i	$-0.381613\pi$
$467$	15.7066	0.726816	0.363408	+	0.931630i	$0.381613\pi$
$468$	25.2794	1.16854
$469$	20.5955	0.951010
$470$	−88.9580	−4.10332
$471$	−0.878167	−0.0404638
$472$	0.450064	0.0207159
$473$	−1.00000	−0.0459800
$474$	−10.9311	−0.502081
$475$	−2.50180	−0.114791
$476$	7.26958	0.333201
$477$	4.56040	0.208806
$478$	−56.7825	−2.59717
$479$	−1.78862	−0.0817243	−0.0408622	−	0.999165i	$-0.513010\pi$
$479$	−1.78862	−0.0817243	−0.0408622	+	0.999165i	$0.513010\pi$
$480$	11.9432	0.545131
$481$	39.6944	1.80991
$482$	−31.5688	−1.43792
$483$	−2.83661	−0.129070
$484$	2.51268	0.114213
$485$	−18.3107	−0.831447
$486$	−22.8186	−1.03507
$487$	26.5110	1.20133	0.600664	−	0.799502i	$-0.294903\pi$
$487$	26.5110	1.20133	0.600664	+	0.799502i	$0.294903\pi$
$488$	−0.307843	−0.0139354
$489$	−9.96840	−0.450787
$490$	−10.1031	−0.456412
$491$	−22.6554	−1.02242	−0.511211	−	0.859455i	$-0.670803\pi$
$491$	−22.6554	−1.02242	−0.511211	+	0.859455i	$0.670803\pi$
$492$	−5.63828	−0.254193
$493$	−7.81548	−0.351991
$494$	−2.69893	−0.121431
$495$	−9.75963	−0.438663
$496$	10.1634	0.456352
$497$	31.6482	1.41962
$498$	−8.87512	−0.397704
$499$	16.8318	0.753493	0.376747	−	0.926316i	$-0.377043\pi$
$499$	16.8318	0.753493	0.376747	+	0.926316i	$0.377043\pi$
$500$	17.8327	0.797503
$501$	−1.53684	−0.0686610
$502$	45.8198	2.04504
$503$	1.39809	0.0623376	0.0311688	−	0.999514i	$-0.490077\pi$
$503$	1.39809	0.0623376	0.0311688	+	0.999514i	$0.490077\pi$
$504$	8.86068	0.394686
$505$	−18.9343	−0.842565
$506$	4.80490	0.213604
$507$	−0.0868621	−0.00385768
$508$	−11.5591	−0.512852
$509$	−23.5601	−1.04428	−0.522142	−	0.852858i	$-0.674867\pi$
$509$	−23.5601	−1.04428	−0.522142	+	0.852858i	$0.674867\pi$
$510$	−3.19580	−0.141512
$511$	−37.2799	−1.64917
$512$	−27.4354	−1.21249
$513$	0.894685	0.0395013
$514$	0.557937	0.0246096
$515$	−49.6743	−2.18891
$516$	−1.08917	−0.0479482
$517$	12.0661	0.530665
$518$	68.1899	2.99609
$519$	1.57555	0.0691592
$520$	13.5227	0.593011
$521$	4.46467	0.195601	0.0978003	−	0.995206i	$-0.468819\pi$
$521$	4.46467	0.195601	0.0978003	+	0.995206i	$0.468819\pi$
$522$	−46.6878	−2.04347
$523$	21.0574	0.920774	0.460387	−	0.887718i	$-0.347711\pi$
$523$	21.0574	0.920774	0.460387	+	0.887718i	$0.347711\pi$
$524$	−12.6200	−0.551306
$525$	8.83505	0.385593
$526$	16.6856	0.727527
$527$	−3.74786	−0.163259
$528$	−1.17549	−0.0511565
$529$	−17.8840	−0.777563
$530$	11.9561	0.519341
$531$	1.16210	0.0504307
$532$	−2.58158	−0.111926
$533$	18.5203	0.802202
$534$	4.52248	0.195707
$535$	20.2680	0.876263
$536$	−7.75288	−0.334874
$537$	−1.12857	−0.0487015
$538$	−22.5640	−0.972805
$539$	1.37036	0.0590257
$540$	−21.9701	−0.945444
$541$	8.15963	0.350810	0.175405	−	0.984496i	$-0.443877\pi$
$541$	8.15963	0.350810	0.175405	+	0.984496i	$0.443877\pi$
$542$	35.5307	1.52617
$543$	−11.0296	−0.473323
$544$	7.93887	0.340376
$545$	39.2877	1.68290
$546$	9.53121	0.407898
$547$	30.0473	1.28473	0.642365	−	0.766399i	$-0.277953\pi$
$547$	30.0473	1.28473	0.642365	+	0.766399i	$0.277953\pi$
$548$	−32.8672	−1.40402
$549$	−0.794871	−0.0339243
$550$	−14.9656	−0.638135
$551$	2.77544	0.118238
$552$	1.06780	0.0454487
$553$	34.3445	1.46048
$554$	−18.5146	−0.786608
$555$	−16.6914	−0.708511
$556$	−10.2560	−0.434951
$557$	−18.0730	−0.765777	−0.382889	−	0.923794i	$-0.625071\pi$
$557$	−18.0730	−0.765777	−0.382889	+	0.923794i	$0.625071\pi$
$558$	−22.3888	−0.947795
$559$	3.57765	0.151319
$560$	−27.2290	−1.15064
$561$	0.433471	0.0183012
$562$	4.28088	0.180578
$563$	3.95144	0.166533	0.0832666	−	0.996527i	$-0.473465\pi$
$563$	3.95144	0.166533	0.0832666	+	0.996527i	$0.473465\pi$
$564$	13.1420	0.553380
$565$	−52.0911	−2.19149
$566$	−1.14532	−0.0481414
$567$	21.2480	0.892333
$568$	−11.9135	−0.499881
$569$	11.1562	0.467694	0.233847	−	0.972273i	$-0.424868\pi$
$569$	11.1562	0.467694	0.233847	+	0.972273i	$0.424868\pi$
$570$	1.13490	0.0475356
$571$	27.3235	1.14345	0.571727	−	0.820444i	$-0.306274\pi$
$571$	27.3235	1.14345	0.571727	+	0.820444i	$0.306274\pi$
$572$	−8.98950	−0.375870
$573$	−7.59453	−0.317266
$574$	31.8155	1.32795
$575$	−15.9347	−0.664523
$576$	32.1733	1.34055
$577$	−10.0749	−0.419425	−0.209712	−	0.977763i	$-0.567253\pi$
$577$	−10.0749	−0.419425	−0.209712	+	0.977763i	$0.567253\pi$
$578$	−2.12431	−0.0883595
$579$	−4.76127	−0.197872
$580$	−68.1545	−2.82996
$581$	27.8849	1.15686
$582$	4.85826	0.201381
$583$	−1.62170	−0.0671641
$584$	14.0335	0.580711
$585$	34.9166	1.44362
$586$	27.3211	1.12863
$587$	−0.150547	−0.00621373	−0.00310686	−	0.999995i	$-0.500989\pi$
$587$	−0.150547	−0.00621373	−0.00310686	+	0.999995i	$0.500989\pi$
$588$	1.49256	0.0615523
$589$	1.33094	0.0548406
$590$	3.04671	0.125431
$591$	−8.14739	−0.335139
$592$	30.0876	1.23659
$593$	29.6858	1.21905	0.609526	−	0.792766i	$-0.291360\pi$
$593$	29.6858	1.21905	0.609526	+	0.792766i	$0.291360\pi$
$594$	5.35193	0.219593
$595$	10.0409	0.411638
$596$	−32.7764	−1.34257
$597$	0.990113	0.0405226
$598$	−17.1903	−0.702963
$599$	−40.3991	−1.65066	−0.825332	−	0.564648i	$-0.809012\pi$
$599$	−40.3991	−1.65066	−0.825332	+	0.564648i	$0.809012\pi$
$600$	−3.32583	−0.135777
$601$	−9.71269	−0.396189	−0.198094	−	0.980183i	$-0.563475\pi$
$601$	−9.71269	−0.396189	−0.198094	+	0.980183i	$0.563475\pi$
$602$	6.14596	0.250490
$603$	−20.0185	−0.815215
$604$	37.2121	1.51414
$605$	3.47058	0.141099
$606$	5.02371	0.204074
$607$	−45.7697	−1.85774	−0.928868	−	0.370411i	$-0.879217\pi$
$607$	−45.7697	−1.85774	−0.928868	+	0.370411i	$0.879217\pi$
$608$	−2.81926	−0.114336
$609$	−9.80139	−0.397172
$610$	−2.08394	−0.0843762
$611$	−43.1682	−1.74640
$612$	−7.06591	−0.285623
$613$	−5.63133	−0.227447	−0.113724	−	0.993512i	$-0.536278\pi$
$613$	−5.63133	−0.227447	−0.113724	+	0.993512i	$0.536278\pi$
$614$	−41.1720	−1.66157
$615$	−7.78774	−0.314032
$616$	−3.15091	−0.126954
$617$	−25.6655	−1.03325	−0.516627	−	0.856210i	$-0.672813\pi$
$617$	−25.6655	−1.03325	−0.516627	+	0.856210i	$0.672813\pi$
$618$	13.1797	0.530167
$619$	37.6861	1.51473	0.757366	−	0.652991i	$-0.226486\pi$
$619$	37.6861	1.51473	0.757366	+	0.652991i	$0.226486\pi$
$620$	−32.6830	−1.31258
$621$	5.69850	0.228673
$622$	−42.2987	−1.69602
$623$	−14.2093	−0.569282
$624$	4.20549	0.168354
$625$	−10.5936	−0.423745
$626$	27.2307	1.08836
$627$	−0.153935	−0.00614756
$628$	−5.09043	−0.203130
$629$	−11.0951	−0.442390
$630$	59.9822	2.38975
$631$	4.12054	0.164036	0.0820180	−	0.996631i	$-0.473863\pi$
$631$	4.12054	0.164036	0.0820180	+	0.996631i	$0.473863\pi$
$632$	−12.9285	−0.514269
$633$	−3.36094	−0.133585
$634$	−13.2878	−0.527724
$635$	−15.9657	−0.633581
$636$	−1.76632	−0.0700391
$637$	−4.90269	−0.194251
$638$	16.6025	0.657298
$639$	−30.7616	−1.21691
$640$	29.2447	1.15600
$641$	−20.4311	−0.806981	−0.403491	−	0.914984i	$-0.632203\pi$
$641$	−20.4311	−0.806981	−0.403491	+	0.914984i	$0.632203\pi$
$642$	−5.37758	−0.212236
$643$	10.1341	0.399652	0.199826	−	0.979831i	$-0.435962\pi$
$643$	10.1341	0.399652	0.199826	+	0.979831i	$0.435962\pi$
$644$	−16.4428	−0.647938
$645$	−1.50440	−0.0592356
$646$	0.754386	0.0296809
$647$	−31.5722	−1.24123	−0.620616	−	0.784114i	$-0.713118\pi$
$647$	−31.5722	−1.24123	−0.620616	+	0.784114i	$0.713118\pi$
$648$	−7.99853	−0.314212
$649$	−0.413248	−0.0162214
$650$	53.5417	2.10008
$651$	−4.70019	−0.184215
$652$	−57.7833	−2.26297
$653$	6.08707	0.238206	0.119103	−	0.992882i	$-0.461998\pi$
$653$	6.08707	0.238206	0.119103	+	0.992882i	$0.461998\pi$
$654$	−10.4239	−0.407608
$655$	−17.4310	−0.681087
$656$	14.0380	0.548093
$657$	36.2355	1.41368
$658$	−74.1575	−2.89096
$659$	−2.78924	−0.108653	−0.0543267	−	0.998523i	$-0.517301\pi$
$659$	−2.78924	−0.108653	−0.0543267	+	0.998523i	$0.517301\pi$
$660$	3.78007	0.147139
$661$	33.9048	1.31875	0.659373	−	0.751816i	$-0.270822\pi$
$661$	33.9048	1.31875	0.659373	+	0.751816i	$0.270822\pi$
$662$	60.3708	2.34638
$663$	−1.55081	−0.0602285
$664$	−10.4969	−0.407358
$665$	−3.56575	−0.138274
$666$	−66.2795	−2.56828
$667$	17.6776	0.684478
$668$	−8.90853	−0.344681
$669$	7.58733	0.293343
$670$	−52.4830	−2.02760
$671$	0.282661	0.0109120
$672$	9.95615	0.384067
$673$	14.0014	0.539715	0.269857	−	0.962900i	$-0.413023\pi$
$673$	14.0014	0.539715	0.269857	+	0.962900i	$0.413023\pi$
$674$	−31.1715	−1.20068
$675$	−17.7488	−0.683153
$676$	−0.503509	−0.0193657
$677$	14.1285	0.543002	0.271501	−	0.962438i	$-0.412480\pi$
$677$	14.1285	0.543002	0.271501	+	0.962438i	$0.412480\pi$
$678$	13.8210	0.530791
$679$	−15.2643	−0.585788
$680$	−3.77977	−0.144948
$681$	−3.95214	−0.151446
$682$	7.96160	0.304865
$683$	−41.4905	−1.58759	−0.793795	−	0.608185i	$-0.791898\pi$
$683$	−41.4905	−1.58759	−0.793795	+	0.608185i	$0.791898\pi$
$684$	2.50926	0.0959438
$685$	−45.3971	−1.73453
$686$	34.5995	1.32102
$687$	7.31553	0.279105
$688$	2.71180	0.103386
$689$	5.80190	0.221035
$690$	7.22848	0.275183
$691$	45.7942	1.74209	0.871047	−	0.491200i	$-0.163441\pi$
$691$	45.7942	1.74209	0.871047	+	0.491200i	$0.163441\pi$
$692$	9.13294	0.347182
$693$	−8.13586	−0.309056
$694$	−34.7551	−1.31929
$695$	−14.1658	−0.537341
$696$	3.68960	0.139854
$697$	−5.17665	−0.196080
$698$	−28.8139	−1.09062
$699$	6.81866	0.257906
$700$	51.2137	1.93569
$701$	−12.8179	−0.484126	−0.242063	−	0.970261i	$-0.577824\pi$
$701$	−12.8179	−0.484126	−0.242063	+	0.970261i	$0.577824\pi$
$702$	−19.1474	−0.722671
$703$	3.94010	0.148604
$704$	−11.4410	−0.431199
$705$	18.1521	0.683649
$706$	7.59403	0.285805
$707$	−15.7841	−0.593621
$708$	−0.450099	−0.0169158
$709$	1.93738	0.0727599	0.0363800	−	0.999338i	$-0.488417\pi$
$709$	1.93738	0.0727599	0.0363800	+	0.999338i	$0.488417\pi$
$710$	−80.6486	−3.02669
$711$	−33.3823	−1.25194
$712$	5.34888	0.200458
$713$	8.47716	0.317472
$714$	−2.66409	−0.0997012
$715$	−12.4165	−0.464352
$716$	−6.54193	−0.244484
$717$	11.5866	0.432711
$718$	78.1257	2.91563
$719$	30.0338	1.12007	0.560037	−	0.828468i	$-0.310787\pi$
$719$	30.0338	1.12007	0.560037	+	0.828468i	$0.310787\pi$
$720$	26.4662	0.986335
$721$	−41.4097	−1.54218
$722$	40.0939	1.49214
$723$	6.44171	0.239570
$724$	−63.9344	−2.37610
$725$	−55.0595	−2.04486
$726$	−0.920826	−0.0341751
$727$	−21.8421	−0.810078	−0.405039	−	0.914299i	$-0.632742\pi$
$727$	−21.8421	−0.810078	−0.405039	+	0.914299i	$0.632742\pi$
$728$	11.2729	0.417800
$729$	−17.3765	−0.643574
$730$	94.9997	3.51610
$731$	−1.00000	−0.0369863
$732$	0.307867	0.0113791
$733$	34.4924	1.27401	0.637003	−	0.770862i	$-0.280174\pi$
$733$	34.4924	1.27401	0.637003	+	0.770862i	$0.280174\pi$
$734$	−23.6896	−0.874400
$735$	2.06157	0.0760421
$736$	−17.9567	−0.661892
$737$	7.11868	0.262220
$738$	−30.9241	−1.13833
$739$	−18.6202	−0.684954	−0.342477	−	0.939526i	$-0.611266\pi$
$739$	−18.6202	−0.684954	−0.342477	+	0.939526i	$0.611266\pi$
$740$	−96.7542	−3.55675
$741$	0.550725	0.0202314
$742$	9.96692	0.365897
$743$	−18.8995	−0.693354	−0.346677	−	0.937985i	$-0.612690\pi$
$743$	−18.8995	−0.693354	−0.346677	+	0.937985i	$0.612690\pi$
$744$	1.76932	0.0648665
$745$	−45.2716	−1.65862
$746$	44.9665	1.64634
$747$	−27.1037	−0.991671
$748$	2.51268	0.0918727
$749$	16.8959	0.617363
$750$	−6.53518	−0.238631
$751$	−15.8584	−0.578681	−0.289341	−	0.957226i	$-0.593436\pi$
$751$	−15.8584	−0.578681	−0.289341	+	0.957226i	$0.593436\pi$
$752$	−32.7207	−1.19320
$753$	−9.34966	−0.340721
$754$	−59.3979	−2.16314
$755$	51.3983	1.87058
$756$	−18.3148	−0.666104
$757$	42.3498	1.53923	0.769614	−	0.638509i	$-0.220448\pi$
$757$	42.3498	1.53923	0.769614	+	0.638509i	$0.220448\pi$
$758$	−13.7726	−0.500242
$759$	−0.980455	−0.0355882
$760$	1.34228	0.0486895
$761$	41.5297	1.50545	0.752725	−	0.658335i	$-0.228739\pi$
$761$	41.5297	1.50545	0.752725	+	0.658335i	$0.228739\pi$
$762$	4.23608	0.153457
$763$	32.7511	1.18567
$764$	−44.0228	−1.59269
$765$	−9.75963	−0.352860
$766$	−4.73742	−0.171170
$767$	1.47846	0.0533841
$768$	2.15939	0.0779203
$769$	38.8036	1.39929	0.699647	−	0.714489i	$-0.253341\pi$
$769$	38.8036	1.39929	0.699647	+	0.714489i	$0.253341\pi$
$770$	−21.3300	−0.768681
$771$	−0.113849	−0.00410016
$772$	−27.5994	−0.993325
$773$	−15.4977	−0.557415	−0.278707	−	0.960376i	$-0.589906\pi$
$773$	−15.4977	−0.557415	−0.278707	+	0.960376i	$0.589906\pi$
$774$	−5.97377	−0.214723
$775$	−26.4034	−0.948437
$776$	5.74602	0.206270
$777$	−13.9143	−0.499174
$778$	−38.9035	−1.39476
$779$	1.83834	0.0658653
$780$	−13.5238	−0.484229
$781$	10.9390	0.391428
$782$	4.80490	0.171823
$783$	19.6901	0.703668
$784$	−3.71615	−0.132720
$785$	−7.03103	−0.250948
$786$	4.62486	0.164963
$787$	−2.68214	−0.0956079	−0.0478039	−	0.998857i	$-0.515222\pi$
$787$	−2.68214	−0.0956079	−0.0478039	+	0.998857i	$0.515222\pi$
$788$	−47.2276	−1.68241
$789$	−3.40475	−0.121212
$790$	−87.5195	−3.11380
$791$	−43.4243	−1.54399
$792$	3.06263	0.108826
$793$	−1.01126	−0.0359110
$794$	71.8917	2.55134
$795$	−2.43969	−0.0865267
$796$	5.73934	0.203425
$797$	−54.3344	−1.92462	−0.962312	−	0.271947i	$-0.912333\pi$
$797$	−54.3344	−1.92462	−0.962312	+	0.271947i	$0.912333\pi$
$798$	0.946076	0.0334907
$799$	12.0661	0.426866
$800$	55.9288	1.97738
$801$	13.8112	0.487994
$802$	0.107622	0.00380028
$803$	−12.8855	−0.454721
$804$	7.75349	0.273444
$805$	−22.7113	−0.800467
$806$	−28.4838	−1.00330
$807$	4.60426	0.162078
$808$	5.94170	0.209028
$809$	49.2762	1.73246	0.866229	−	0.499647i	$-0.166537\pi$
$809$	49.2762	1.73246	0.866229	+	0.499647i	$0.166537\pi$
$810$	−54.1459	−1.90249
$811$	−14.2537	−0.500515	−0.250258	−	0.968179i	$-0.580515\pi$
$811$	−14.2537	−0.500515	−0.250258	+	0.968179i	$0.580515\pi$
$812$	−56.8152	−1.99382
$813$	−7.25015	−0.254274
$814$	23.5694	0.826105
$815$	−79.8119	−2.79569
$816$	−1.17549	−0.0411503
$817$	0.355121	0.0124241
$818$	−53.4329	−1.86824
$819$	29.1073	1.01709
$820$	−45.1428	−1.57645
$821$	25.3444	0.884527	0.442263	−	0.896885i	$-0.354176\pi$
$821$	25.3444	0.884527	0.442263	+	0.896885i	$0.354176\pi$
$822$	12.0449	0.420114
$823$	42.8346	1.49312	0.746560	−	0.665319i	$-0.231704\pi$
$823$	42.8346	1.49312	0.746560	+	0.665319i	$0.231704\pi$
$824$	15.5881	0.543037
$825$	3.05377	0.106319
$826$	2.53981	0.0883711
$827$	8.85297	0.307848	0.153924	−	0.988083i	$-0.450809\pi$
$827$	8.85297	0.307848	0.153924	+	0.988083i	$0.450809\pi$
$828$	15.9822	0.555419
$829$	−31.2304	−1.08468	−0.542338	−	0.840160i	$-0.682461\pi$
$829$	−31.2304	−1.08468	−0.542338	+	0.840160i	$0.682461\pi$
$830$	−71.0585	−2.46648
$831$	3.77795	0.131056
$832$	40.9320	1.41906
$833$	1.37036	0.0474803
$834$	3.75853	0.130147
$835$	−12.3047	−0.425821
$836$	−0.892306	−0.0308610
$837$	9.44227	0.326373
$838$	16.0707	0.555154
$839$	−49.8740	−1.72184	−0.860920	−	0.508740i	$-0.830111\pi$
$839$	−49.8740	−1.72184	−0.860920	+	0.508740i	$0.830111\pi$
$840$	−4.74022	−0.163553
$841$	32.0817	1.10626
$842$	29.8374	1.02826
$843$	−0.873527	−0.0300859
$844$	−19.4822	−0.670605
$845$	−0.695460	−0.0239245
$846$	72.0799	2.47816
$847$	2.89316	0.0994101
$848$	4.39773	0.151019
$849$	0.233706	0.00802077
$850$	−14.9656	−0.513316
$851$	25.0956	0.860266
$852$	11.9145	0.408183
$853$	15.7702	0.539962	0.269981	−	0.962866i	$-0.412983\pi$
$853$	15.7702	0.539962	0.269981	+	0.962866i	$0.412983\pi$
$854$	−1.73722	−0.0594465
$855$	3.46585	0.118530
$856$	−6.36023	−0.217388
$857$	−35.2765	−1.20502	−0.602512	−	0.798110i	$-0.705833\pi$
$857$	−35.2765	−1.20502	−0.602512	+	0.798110i	$0.705833\pi$
$858$	3.29440	0.112469
$859$	27.1072	0.924884	0.462442	−	0.886649i	$-0.346973\pi$
$859$	27.1072	0.924884	0.462442	+	0.886649i	$0.346973\pi$
$860$	−8.72046	−0.297365
$861$	−6.49204	−0.221248
$862$	22.8116	0.776966
$863$	29.5775	1.00683	0.503414	−	0.864045i	$-0.332077\pi$
$863$	29.5775	1.00683	0.503414	+	0.864045i	$0.332077\pi$
$864$	−20.0010	−0.680449
$865$	12.6147	0.428911
$866$	53.8167	1.82877
$867$	0.433471	0.0147215
$868$	−27.2453	−0.924767
$869$	11.8710	0.402694
$870$	24.9767	0.846789
$871$	−25.4682	−0.862957
$872$	−12.3287	−0.417503
$873$	14.8366	0.502143
$874$	−1.70632	−0.0577172
$875$	20.5330	0.694142
$876$	−14.0346	−0.474185
$877$	54.3278	1.83452	0.917260	−	0.398288i	$-0.130396\pi$
$877$	54.3278	1.83452	0.917260	+	0.398288i	$0.130396\pi$
$878$	33.6604	1.13598
$879$	−5.57496	−0.188039
$880$	−9.41152	−0.317262
$881$	−31.0423	−1.04584	−0.522921	−	0.852381i	$-0.675158\pi$
$881$	−31.0423	−1.04584	−0.522921	+	0.852381i	$0.675158\pi$
$882$	8.18623	0.275645
$883$	46.7865	1.57449	0.787245	−	0.616640i	$-0.211507\pi$
$883$	46.7865	1.57449	0.787245	+	0.616640i	$0.211507\pi$
$884$	−8.98950	−0.302350
$885$	−0.621689	−0.0208979
$886$	−64.1505	−2.15518
$887$	10.5058	0.352751	0.176376	−	0.984323i	$-0.443563\pi$
$887$	10.5058	0.352751	0.176376	+	0.984323i	$0.443563\pi$
$888$	5.23787	0.175771
$889$	−13.3094	−0.446384
$890$	36.2092	1.21373
$891$	7.34423	0.246041
$892$	43.9811	1.47260
$893$	−4.28491	−0.143389
$894$	12.0116	0.401729
$895$	−9.03589	−0.302037
$896$	24.3791	0.814448
$897$	3.50773	0.117120
$898$	35.6521	1.18972
$899$	29.2913	0.976919
$900$	−49.7789	−1.65930
$901$	−1.62170	−0.0540268
$902$	10.9968	0.366153
$903$	−1.25410	−0.0417339
$904$	16.3465	0.543676
$905$	−88.3079	−2.93546
$906$	−13.6372	−0.453065
$907$	−42.4211	−1.40857	−0.704285	−	0.709918i	$-0.748732\pi$
$907$	−42.4211	−1.40857	−0.704285	+	0.709918i	$0.748732\pi$
$908$	−22.9092	−0.760268
$909$	15.3419	0.508857
$910$	76.3115	2.52970
$911$	−9.95928	−0.329966	−0.164983	−	0.986296i	$-0.552757\pi$
$911$	−9.95928	−0.329966	−0.164983	+	0.986296i	$0.552757\pi$
$912$	0.417440	0.0138228
$913$	9.63822	0.318978
$914$	−75.6686	−2.50290
$915$	0.425234	0.0140578
$916$	42.4055	1.40112
$917$	−14.5309	−0.479853
$918$	5.35193	0.176640
$919$	44.0568	1.45330	0.726649	−	0.687009i	$-0.241077\pi$
$919$	44.0568	1.45330	0.726649	+	0.687009i	$0.241077\pi$
$920$	8.54935	0.281864
$921$	8.40126	0.276831
$922$	−33.9488	−1.11805
$923$	−39.1359	−1.28818
$924$	3.15115	0.103665
$925$	−78.1640	−2.57002
$926$	70.2764	2.30943
$927$	40.2495	1.32197
$928$	−62.0461	−2.03676
$929$	−56.7306	−1.86127	−0.930635	−	0.365949i	$-0.880745\pi$
$929$	−56.7306	−1.86127	−0.930635	+	0.365949i	$0.880745\pi$
$930$	11.9774	0.392754
$931$	−0.486645	−0.0159491
$932$	39.5254	1.29470
$933$	8.63118	0.282572
$934$	−33.3657	−1.09176
$935$	3.47058	0.113500
$936$	−10.9570	−0.358142
$937$	−29.0927	−0.950417	−0.475209	−	0.879873i	$-0.657627\pi$
$937$	−29.0927	−0.950417	−0.475209	+	0.879873i	$0.657627\pi$
$938$	−43.7511	−1.42852
$939$	−5.55651	−0.181330
$940$	105.222	3.43195
$941$	17.9127	0.583937	0.291968	−	0.956428i	$-0.405690\pi$
$941$	17.9127	0.583937	0.291968	+	0.956428i	$0.405690\pi$
$942$	1.86550	0.0607812
$943$	11.7089	0.381294
$944$	1.12065	0.0364739
$945$	−25.2969	−0.822909
$946$	2.12431	0.0690672
$947$	−3.13892	−0.102001	−0.0510006	−	0.998699i	$-0.516241\pi$
$947$	−3.13892	−0.102001	−0.0510006	+	0.998699i	$0.516241\pi$
$948$	12.9295	0.419932
$949$	46.1000	1.49647
$950$	5.31460	0.172428
$951$	2.71141	0.0879233
$952$	−3.15091	−0.102122
$953$	−27.1344	−0.878968	−0.439484	−	0.898250i	$-0.644839\pi$
$953$	−27.1344	−0.878968	−0.439484	+	0.898250i	$0.644839\pi$
$954$	−9.68768	−0.313650
$955$	−60.8055	−1.96762
$956$	67.1637	2.17223
$957$	−3.38778	−0.109511
$958$	3.79959	0.122759
$959$	−37.8441	−1.22205
$960$	−17.2118	−0.555509
$961$	−16.9536	−0.546889
$962$	−84.3230	−2.71868
$963$	−16.4226	−0.529209
$964$	37.3403	1.20265
$965$	−38.1211	−1.22716
$966$	6.02583	0.193878
$967$	45.4822	1.46261	0.731305	−	0.682051i	$-0.238912\pi$
$967$	45.4822	1.46261	0.731305	+	0.682051i	$0.238912\pi$
$968$	−1.08909	−0.0350047
$969$	−0.153935	−0.00494510
$970$	38.8976	1.24893
$971$	−6.63324	−0.212871	−0.106435	−	0.994320i	$-0.533944\pi$
$971$	−6.63324	−0.212871	−0.106435	+	0.994320i	$0.533944\pi$
$972$	26.9903	0.865715
$973$	−11.8090	−0.378578
$974$	−56.3175	−1.80453
$975$	−10.9253	−0.349891
$976$	−0.766519	−0.0245357
$977$	−57.2498	−1.83158	−0.915792	−	0.401653i	$-0.868436\pi$
$977$	−57.2498	−1.83158	−0.915792	+	0.401653i	$0.868436\pi$
$978$	21.1759	0.677132
$979$	−4.91133	−0.156967
$980$	11.9502	0.381735
$981$	−31.8336	−1.01637
$982$	48.1269	1.53579
$983$	51.5031	1.64269	0.821347	−	0.570428i	$-0.193223\pi$
$983$	51.5031	1.64269	0.821347	+	0.570428i	$0.193223\pi$
$984$	2.44384	0.0779068
$985$	−65.2320	−2.07846
$986$	16.6025	0.528730
$987$	15.1321	0.481658
$988$	3.19236	0.101563
$989$	2.26187	0.0719232
$990$	20.7324	0.658920
$991$	12.7729	0.405744	0.202872	−	0.979205i	$-0.434972\pi$
$991$	12.7729	0.405744	0.202872	+	0.979205i	$0.434972\pi$
$992$	−29.7538	−0.944683
$993$	−12.3188	−0.390927
$994$	−67.2306	−2.13242
$995$	7.92733	0.251313
$996$	10.4977	0.332632
$997$	6.93886	0.219756	0.109878	−	0.993945i	$-0.464954\pi$
$997$	6.93886	0.219756	0.109878	+	0.993945i	$0.464954\pi$
$998$	−35.7558	−1.13183
$999$	27.9527	0.884385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.10	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.10	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12431 q^{2} +0.433471 q^{3} +2.51268 q^{4} +3.47058 q^{5} -0.920826 q^{6} +2.89316 q^{7} -1.08909 q^{8} -2.81210 q^{9} +O(q^{10})\)	\(q-2.12431 q^{2} +0.433471 q^{3} +2.51268 q^{4} +3.47058 q^{5} -0.920826 q^{6} +2.89316 q^{7} -1.08909 q^{8} -2.81210 q^{9} -7.37258 q^{10} +1.00000 q^{11} +1.08917 q^{12} -3.57765 q^{13} -6.14596 q^{14} +1.50440 q^{15} -2.71180 q^{16} +1.00000 q^{17} +5.97377 q^{18} -0.355121 q^{19} +8.72046 q^{20} +1.25410 q^{21} -2.12431 q^{22} -2.26187 q^{23} -0.472089 q^{24} +7.04493 q^{25} +7.60004 q^{26} -2.51938 q^{27} +7.26958 q^{28} -7.81548 q^{29} -3.19580 q^{30} -3.74786 q^{31} +7.93887 q^{32} +0.433471 q^{33} -2.12431 q^{34} +10.0409 q^{35} -7.06591 q^{36} -11.0951 q^{37} +0.754386 q^{38} -1.55081 q^{39} -3.77977 q^{40} -5.17665 q^{41} -2.66409 q^{42} -1.00000 q^{43} +2.51268 q^{44} -9.75963 q^{45} +4.80490 q^{46} +12.0661 q^{47} -1.17549 q^{48} +1.37036 q^{49} -14.9656 q^{50} +0.433471 q^{51} -8.98950 q^{52} -1.62170 q^{53} +5.35193 q^{54} +3.47058 q^{55} -3.15091 q^{56} -0.153935 q^{57} +16.6025 q^{58} -0.413248 q^{59} +3.78007 q^{60} +0.282661 q^{61} +7.96160 q^{62} -8.13586 q^{63} -11.4410 q^{64} -12.4165 q^{65} -0.920826 q^{66} +7.11868 q^{67} +2.51268 q^{68} -0.980455 q^{69} -21.3300 q^{70} +10.9390 q^{71} +3.06263 q^{72} -12.8855 q^{73} +23.5694 q^{74} +3.05377 q^{75} -0.892306 q^{76} +2.89316 q^{77} +3.29440 q^{78} +11.8710 q^{79} -9.41152 q^{80} +7.34423 q^{81} +10.9968 q^{82} +9.63822 q^{83} +3.15115 q^{84} +3.47058 q^{85} +2.12431 q^{86} -3.38778 q^{87} -1.08909 q^{88} -4.91133 q^{89} +20.7324 q^{90} -10.3507 q^{91} -5.68335 q^{92} -1.62459 q^{93} -25.6320 q^{94} -1.23248 q^{95} +3.44127 q^{96} -5.27598 q^{97} -2.91107 q^{98} -2.81210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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