LMFDB - Embedded newform 6034.2.a.m.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.00804327 q^{3} +1.00000 q^{4} +3.67628 q^{5} -0.00804327 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.99994 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.00804327 q^{3} +1.00000 q^{4} +3.67628 q^{5} -0.00804327 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.99994 q^{9} +3.67628 q^{10} -3.60308 q^{11} -0.00804327 q^{12} -5.05961 q^{13} +1.00000 q^{14} -0.0295693 q^{15} +1.00000 q^{16} -4.25537 q^{17} -2.99994 q^{18} -7.20088 q^{19} +3.67628 q^{20} -0.00804327 q^{21} -3.60308 q^{22} -5.45457 q^{23} -0.00804327 q^{24} +8.51503 q^{25} -5.05961 q^{26} +0.0482591 q^{27} +1.00000 q^{28} +5.38015 q^{29} -0.0295693 q^{30} +8.43957 q^{31} +1.00000 q^{32} +0.0289805 q^{33} -4.25537 q^{34} +3.67628 q^{35} -2.99994 q^{36} -6.72749 q^{37} -7.20088 q^{38} +0.0406958 q^{39} +3.67628 q^{40} -2.42117 q^{41} -0.00804327 q^{42} +1.62203 q^{43} -3.60308 q^{44} -11.0286 q^{45} -5.45457 q^{46} +11.8922 q^{47} -0.00804327 q^{48} +1.00000 q^{49} +8.51503 q^{50} +0.0342271 q^{51} -5.05961 q^{52} -6.86493 q^{53} +0.0482591 q^{54} -13.2459 q^{55} +1.00000 q^{56} +0.0579186 q^{57} +5.38015 q^{58} -3.53286 q^{59} -0.0295693 q^{60} -1.04894 q^{61} +8.43957 q^{62} -2.99994 q^{63} +1.00000 q^{64} -18.6006 q^{65} +0.0289805 q^{66} -12.1661 q^{67} -4.25537 q^{68} +0.0438726 q^{69} +3.67628 q^{70} -9.30064 q^{71} -2.99994 q^{72} -2.31874 q^{73} -6.72749 q^{74} -0.0684887 q^{75} -7.20088 q^{76} -3.60308 q^{77} +0.0406958 q^{78} +2.18286 q^{79} +3.67628 q^{80} +8.99942 q^{81} -2.42117 q^{82} -11.3539 q^{83} -0.00804327 q^{84} -15.6439 q^{85} +1.62203 q^{86} -0.0432740 q^{87} -3.60308 q^{88} +3.87667 q^{89} -11.0286 q^{90} -5.05961 q^{91} -5.45457 q^{92} -0.0678817 q^{93} +11.8922 q^{94} -26.4724 q^{95} -0.00804327 q^{96} -5.64654 q^{97} +1.00000 q^{98} +10.8090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.00804327	−0.00464379	−0.00232189	−	0.999997i	$-0.500739\pi$
$3$	−0.00804327	−0.00464379	−0.00232189	+	0.999997i	$0.500739\pi$
$4$	1.00000	0.500000
$5$	3.67628	1.64408	0.822041	−	0.569428i	$-0.192835\pi$
$5$	3.67628	1.64408	0.822041	+	0.569428i	$0.192835\pi$
$6$	−0.00804327	−0.00328365
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.99994	−0.999978
$10$	3.67628	1.16254
$11$	−3.60308	−1.08637	−0.543184	−	0.839613i	$-0.682782\pi$
$11$	−3.60308	−1.08637	−0.543184	+	0.839613i	$0.682782\pi$
$12$	−0.00804327	−0.00232189
$13$	−5.05961	−1.40328	−0.701642	−	0.712530i	$-0.747549\pi$
$13$	−5.05961	−1.40328	−0.701642	+	0.712530i	$0.747549\pi$
$14$	1.00000	0.267261
$15$	−0.0295693	−0.00763476
$16$	1.00000	0.250000
$17$	−4.25537	−1.03208	−0.516039	−	0.856565i	$-0.672594\pi$
$17$	−4.25537	−1.03208	−0.516039	+	0.856565i	$0.672594\pi$
$18$	−2.99994	−0.707092
$19$	−7.20088	−1.65200	−0.825998	−	0.563674i	$-0.809388\pi$
$19$	−7.20088	−1.65200	−0.825998	+	0.563674i	$0.809388\pi$
$20$	3.67628	0.822041
$21$	−0.00804327	−0.00175519
$22$	−3.60308	−0.768179
$23$	−5.45457	−1.13736	−0.568678	−	0.822560i	$-0.692545\pi$
$23$	−5.45457	−1.13736	−0.568678	+	0.822560i	$0.692545\pi$
$24$	−0.00804327	−0.00164183
$25$	8.51503	1.70301
$26$	−5.05961	−0.992272
$27$	0.0482591	0.00928747
$28$	1.00000	0.188982
$29$	5.38015	0.999068	0.499534	−	0.866294i	$-0.333505\pi$
$29$	5.38015	0.999068	0.499534	+	0.866294i	$0.333505\pi$
$30$	−0.0295693	−0.00539859
$31$	8.43957	1.51579	0.757896	−	0.652376i	$-0.226228\pi$
$31$	8.43957	1.51579	0.757896	+	0.652376i	$0.226228\pi$
$32$	1.00000	0.176777
$33$	0.0289805	0.00504486
$34$	−4.25537	−0.729790
$35$	3.67628	0.621405
$36$	−2.99994	−0.499989
$37$	−6.72749	−1.10599	−0.552997	−	0.833183i	$-0.686516\pi$
$37$	−6.72749	−1.10599	−0.552997	+	0.833183i	$0.686516\pi$
$38$	−7.20088	−1.16814
$39$	0.0406958	0.00651655
$40$	3.67628	0.581271
$41$	−2.42117	−0.378123	−0.189061	−	0.981965i	$-0.560545\pi$
$41$	−2.42117	−0.378123	−0.189061	+	0.981965i	$0.560545\pi$
$42$	−0.00804327	−0.00124110
$43$	1.62203	0.247358	0.123679	−	0.992322i	$-0.460531\pi$
$43$	1.62203	0.247358	0.123679	+	0.992322i	$0.460531\pi$
$44$	−3.60308	−0.543184
$45$	−11.0286	−1.64405
$46$	−5.45457	−0.804233
$47$	11.8922	1.73465	0.867326	−	0.497741i	$-0.165837\pi$
$47$	11.8922	1.73465	0.867326	+	0.497741i	$0.165837\pi$
$48$	−0.00804327	−0.00116095
$49$	1.00000	0.142857
$50$	8.51503	1.20421
$51$	0.0342271	0.00479275
$52$	−5.05961	−0.701642
$53$	−6.86493	−0.942971	−0.471485	−	0.881874i	$-0.656282\pi$
$53$	−6.86493	−0.942971	−0.471485	+	0.881874i	$0.656282\pi$
$54$	0.0482591	0.00656723
$55$	−13.2459	−1.78608
$56$	1.00000	0.133631
$57$	0.0579186	0.00767151
$58$	5.38015	0.706448
$59$	−3.53286	−0.459940	−0.229970	−	0.973198i	$-0.573863\pi$
$59$	−3.53286	−0.459940	−0.229970	+	0.973198i	$0.573863\pi$
$60$	−0.0295693	−0.00381738
$61$	−1.04894	−0.134303	−0.0671516	−	0.997743i	$-0.521391\pi$
$61$	−1.04894	−0.134303	−0.0671516	+	0.997743i	$0.521391\pi$
$62$	8.43957	1.07183
$63$	−2.99994	−0.377956
$64$	1.00000	0.125000
$65$	−18.6006	−2.30711
$66$	0.0289805	0.00356726
$67$	−12.1661	−1.48633	−0.743165	−	0.669108i	$-0.766676\pi$
$67$	−12.1661	−1.48633	−0.743165	+	0.669108i	$0.766676\pi$
$68$	−4.25537	−0.516039
$69$	0.0438726	0.00528164
$70$	3.67628	0.439399
$71$	−9.30064	−1.10378	−0.551892	−	0.833916i	$-0.686094\pi$
$71$	−9.30064	−1.10378	−0.551892	+	0.833916i	$0.686094\pi$
$72$	−2.99994	−0.353546
$73$	−2.31874	−0.271388	−0.135694	−	0.990751i	$-0.543326\pi$
$73$	−2.31874	−0.271388	−0.135694	+	0.990751i	$0.543326\pi$
$74$	−6.72749	−0.782055
$75$	−0.0684887	−0.00790840
$76$	−7.20088	−0.825998
$77$	−3.60308	−0.410609
$78$	0.0406958	0.00460790
$79$	2.18286	0.245591	0.122796	−	0.992432i	$-0.460814\pi$
$79$	2.18286	0.245591	0.122796	+	0.992432i	$0.460814\pi$
$80$	3.67628	0.411021
$81$	8.99942	0.999935
$82$	−2.42117	−0.267373
$83$	−11.3539	−1.24625	−0.623125	−	0.782122i	$-0.714137\pi$
$83$	−11.3539	−1.24625	−0.623125	+	0.782122i	$0.714137\pi$
$84$	−0.00804327	−0.000877593 0
$85$	−15.6439	−1.69682
$86$	1.62203	0.174908
$87$	−0.0432740	−0.00463946
$88$	−3.60308	−0.384089
$89$	3.87667	0.410926	0.205463	−	0.978665i	$-0.434130\pi$
$89$	3.87667	0.410926	0.205463	+	0.978665i	$0.434130\pi$
$90$	−11.0286	−1.16252
$91$	−5.05961	−0.530392
$92$	−5.45457	−0.568678
$93$	−0.0678817	−0.00703901
$94$	11.8922	1.22658
$95$	−26.4724	−2.71602
$96$	−0.00804327	−0.000820913 0
$97$	−5.64654	−0.573319	−0.286660	−	0.958033i	$-0.592545\pi$
$97$	−5.64654	−0.573319	−0.286660	+	0.958033i	$0.592545\pi$
$98$	1.00000	0.101015
$99$	10.8090	1.08635
$100$	8.51503	0.851503
$101$	−6.63060	−0.659769	−0.329885	−	0.944021i	$-0.607010\pi$
$101$	−6.63060	−0.659769	−0.329885	+	0.944021i	$0.607010\pi$
$102$	0.0342271	0.00338899
$103$	−3.07660	−0.303146	−0.151573	−	0.988446i	$-0.548434\pi$
$103$	−3.07660	−0.303146	−0.151573	+	0.988446i	$0.548434\pi$
$104$	−5.05961	−0.496136
$105$	−0.0295693	−0.00288567
$106$	−6.86493	−0.666781
$107$	18.6160	1.79968	0.899838	−	0.436224i	$-0.143684\pi$
$107$	18.6160	1.79968	0.899838	+	0.436224i	$0.143684\pi$
$108$	0.0482591	0.00464374
$109$	9.63832	0.923183	0.461592	−	0.887093i	$-0.347279\pi$
$109$	9.63832	0.923183	0.461592	+	0.887093i	$0.347279\pi$
$110$	−13.2459	−1.26295
$111$	0.0541111	0.00513600
$112$	1.00000	0.0944911
$113$	−13.1349	−1.23563	−0.617813	−	0.786325i	$-0.711981\pi$
$113$	−13.1349	−1.23563	−0.617813	+	0.786325i	$0.711981\pi$
$114$	0.0579186	0.00542458
$115$	−20.0525	−1.86991
$116$	5.38015	0.499534
$117$	15.1785	1.40325
$118$	−3.53286	−0.325226
$119$	−4.25537	−0.390089
$120$	−0.0295693	−0.00269930
$121$	1.98216	0.180197
$122$	−1.04894	−0.0949667
$123$	0.0194741	0.00175592
$124$	8.43957	0.757896
$125$	12.9222	1.15580
$126$	−2.99994	−0.267255
$127$	10.2959	0.913612	0.456806	−	0.889566i	$-0.348993\pi$
$127$	10.2959	0.913612	0.456806	+	0.889566i	$0.348993\pi$
$128$	1.00000	0.0883883
$129$	−0.0130465	−0.00114868
$130$	−18.6006	−1.63138
$131$	−13.1782	−1.15139	−0.575694	−	0.817665i	$-0.695268\pi$
$131$	−13.1782	−1.15139	−0.575694	+	0.817665i	$0.695268\pi$
$132$	0.0289805	0.00252243
$133$	−7.20088	−0.624396
$134$	−12.1661	−1.05099
$135$	0.177414	0.0152694
$136$	−4.25537	−0.364895
$137$	6.71144	0.573397	0.286699	−	0.958021i	$-0.407442\pi$
$137$	6.71144	0.573397	0.286699	+	0.958021i	$0.407442\pi$
$138$	0.0438726	0.00373468
$139$	−20.1114	−1.70583	−0.852914	−	0.522052i	$-0.825167\pi$
$139$	−20.1114	−1.70583	−0.852914	+	0.522052i	$0.825167\pi$
$140$	3.67628	0.310702
$141$	−0.0956520	−0.00805535
$142$	−9.30064	−0.780493
$143$	18.2302	1.52448
$144$	−2.99994	−0.249995
$145$	19.7789	1.64255
$146$	−2.31874	−0.191900
$147$	−0.00804327	−0.000663398 0
$148$	−6.72749	−0.552997
$149$	−5.97613	−0.489584	−0.244792	−	0.969576i	$-0.578720\pi$
$149$	−5.97613	−0.489584	−0.244792	+	0.969576i	$0.578720\pi$
$150$	−0.0684887	−0.00559208
$151$	11.6553	0.948497	0.474248	−	0.880391i	$-0.342720\pi$
$151$	11.6553	0.948497	0.474248	+	0.880391i	$0.342720\pi$
$152$	−7.20088	−0.584069
$153$	12.7658	1.03206
$154$	−3.60308	−0.290344
$155$	31.0262	2.49208
$156$	0.0406958	0.00325828
$157$	−23.2638	−1.85665	−0.928326	−	0.371768i	$-0.878752\pi$
$157$	−23.2638	−1.85665	−0.928326	+	0.371768i	$0.878752\pi$
$158$	2.18286	0.173659
$159$	0.0552165	0.00437895
$160$	3.67628	0.290635
$161$	−5.45457	−0.429880
$162$	8.99942	0.707061
$163$	13.7297	1.07539	0.537697	−	0.843138i	$-0.319295\pi$
$163$	13.7297	1.07539	0.537697	+	0.843138i	$0.319295\pi$
$164$	−2.42117	−0.189061
$165$	0.106541	0.00829417
$166$	−11.3539	−0.881233
$167$	17.2313	1.33340	0.666698	−	0.745328i	$-0.267707\pi$
$167$	17.2313	1.33340	0.666698	+	0.745328i	$0.267707\pi$
$168$	−0.00804327	−0.000620552 0
$169$	12.5997	0.969207
$170$	−15.6439	−1.19983
$171$	21.6022	1.65196
$172$	1.62203	0.123679
$173$	19.1073	1.45270	0.726349	−	0.687326i	$-0.241216\pi$
$173$	19.1073	1.45270	0.726349	+	0.687326i	$0.241216\pi$
$174$	−0.0432740	−0.00328059
$175$	8.51503	0.643676
$176$	−3.60308	−0.271592
$177$	0.0284158	0.00213586
$178$	3.87667	0.290569
$179$	−17.4364	−1.30325	−0.651627	−	0.758539i	$-0.725913\pi$
$179$	−17.4364	−1.30325	−0.651627	+	0.758539i	$0.725913\pi$
$180$	−11.0286	−0.822023
$181$	−14.6608	−1.08973	−0.544863	−	0.838525i	$-0.683418\pi$
$181$	−14.6608	−1.08973	−0.544863	+	0.838525i	$0.683418\pi$
$182$	−5.05961	−0.375043
$183$	0.00843692	0.000623675 0
$184$	−5.45457	−0.402116
$185$	−24.7322	−1.81834
$186$	−0.0678817	−0.00497733
$187$	15.3324	1.12122
$188$	11.8922	0.867326
$189$	0.0482591	0.00351033
$190$	−26.4724	−1.92051
$191$	−17.4442	−1.26221	−0.631107	−	0.775696i	$-0.717399\pi$
$191$	−17.4442	−1.26221	−0.631107	+	0.775696i	$0.717399\pi$
$192$	−0.00804327	−0.000580473 0
$193$	17.1234	1.23257	0.616286	−	0.787522i	$-0.288637\pi$
$193$	17.1234	1.23257	0.616286	+	0.787522i	$0.288637\pi$
$194$	−5.64654	−0.405398
$195$	0.149609	0.0107137
$196$	1.00000	0.0714286
$197$	1.01990	0.0726646	0.0363323	−	0.999340i	$-0.488433\pi$
$197$	1.01990	0.0726646	0.0363323	+	0.999340i	$0.488433\pi$
$198$	10.8090	0.768162
$199$	17.4049	1.23380	0.616901	−	0.787041i	$-0.288388\pi$
$199$	17.4049	1.23380	0.616901	+	0.787041i	$0.288388\pi$
$200$	8.51503	0.602104
$201$	0.0978556	0.00690220
$202$	−6.63060	−0.466527
$203$	5.38015	0.377612
$204$	0.0342271	0.00239637
$205$	−8.90089	−0.621665
$206$	−3.07660	−0.214357
$207$	16.3634	1.13733
$208$	−5.05961	−0.350821
$209$	25.9453	1.79468
$210$	−0.0295693	−0.00204048
$211$	−21.0824	−1.45137	−0.725687	−	0.688025i	$-0.758478\pi$
$211$	−21.0824	−1.45137	−0.725687	+	0.688025i	$0.758478\pi$
$212$	−6.86493	−0.471485
$213$	0.0748076	0.00512573
$214$	18.6160	1.27256
$215$	5.96305	0.406677
$216$	0.0482591	0.00328362
$217$	8.43957	0.572915
$218$	9.63832	0.652789
$219$	0.0186503	0.00126027
$220$	−13.2459	−0.893040
$221$	21.5305	1.44830
$222$	0.0541111	0.00363170
$223$	28.2233	1.88997	0.944985	−	0.327113i	$-0.106076\pi$
$223$	28.2233	1.88997	0.944985	+	0.327113i	$0.106076\pi$
$224$	1.00000	0.0668153
$225$	−25.5445	−1.70297
$226$	−13.1349	−0.873719
$227$	21.3480	1.41692	0.708458	−	0.705753i	$-0.249391\pi$
$227$	21.3480	1.41692	0.708458	+	0.705753i	$0.249391\pi$
$228$	0.0579186	0.00383576
$229$	−7.49251	−0.495119	−0.247560	−	0.968873i	$-0.579629\pi$
$229$	−7.49251	−0.495119	−0.247560	+	0.968873i	$0.579629\pi$
$230$	−20.0525	−1.32222
$231$	0.0289805	0.00190678
$232$	5.38015	0.353224
$233$	−11.3480	−0.743434	−0.371717	−	0.928346i	$-0.621231\pi$
$233$	−11.3480	−0.743434	−0.371717	+	0.928346i	$0.621231\pi$
$234$	15.1785	0.992250
$235$	43.7189	2.85191
$236$	−3.53286	−0.229970
$237$	−0.0175574	−0.00114047
$238$	−4.25537	−0.275835
$239$	18.9903	1.22838	0.614190	−	0.789159i	$-0.289483\pi$
$239$	18.9903	1.22838	0.614190	+	0.789159i	$0.289483\pi$
$240$	−0.0295693	−0.00190869
$241$	−3.35203	−0.215923	−0.107962	−	0.994155i	$-0.534432\pi$
$241$	−3.35203	−0.215923	−0.107962	+	0.994155i	$0.534432\pi$
$242$	1.98216	0.127418
$243$	−0.217162	−0.0139310
$244$	−1.04894	−0.0671516
$245$	3.67628	0.234869
$246$	0.0194741	0.00124162
$247$	36.4337	2.31822
$248$	8.43957	0.535913
$249$	0.0913224	0.00578732
$250$	12.9222	0.817274
$251$	−8.32729	−0.525614	−0.262807	−	0.964848i	$-0.584648\pi$
$251$	−8.32729	−0.525614	−0.262807	+	0.964848i	$0.584648\pi$
$252$	−2.99994	−0.188978
$253$	19.6532	1.23559
$254$	10.2959	0.646021
$255$	0.125828	0.00787967
$256$	1.00000	0.0625000
$257$	−24.0267	−1.49875	−0.749373	−	0.662148i	$-0.769645\pi$
$257$	−24.0267	−1.49875	−0.749373	+	0.662148i	$0.769645\pi$
$258$	−0.0130465	−0.000812237 0
$259$	−6.72749	−0.418026
$260$	−18.6006	−1.15356
$261$	−16.1401	−0.999046
$262$	−13.1782	−0.814155
$263$	−7.01033	−0.432275	−0.216138	−	0.976363i	$-0.569346\pi$
$263$	−7.01033	−0.432275	−0.216138	+	0.976363i	$0.569346\pi$
$264$	0.0289805	0.00178363
$265$	−25.2374	−1.55032
$266$	−7.20088	−0.441514
$267$	−0.0311811	−0.00190825
$268$	−12.1661	−0.743165
$269$	10.4599	0.637754	0.318877	−	0.947796i	$-0.396694\pi$
$269$	10.4599	0.637754	0.318877	+	0.947796i	$0.396694\pi$
$270$	0.177414	0.0107971
$271$	3.54452	0.215314	0.107657	−	0.994188i	$-0.465665\pi$
$271$	3.54452	0.215314	0.107657	+	0.994188i	$0.465665\pi$
$272$	−4.25537	−0.258020
$273$	0.0406958	0.00246302
$274$	6.71144	0.405453
$275$	−30.6803	−1.85009
$276$	0.0438726	0.00264082
$277$	−20.4046	−1.22599	−0.612996	−	0.790086i	$-0.710036\pi$
$277$	−20.4046	−1.22599	−0.612996	+	0.790086i	$0.710036\pi$
$278$	−20.1114	−1.20620
$279$	−25.3182	−1.51576
$280$	3.67628	0.219700
$281$	22.7551	1.35745	0.678726	−	0.734391i	$-0.262532\pi$
$281$	22.7551	1.35745	0.678726	+	0.734391i	$0.262532\pi$
$282$	−0.0956520	−0.00569599
$283$	−23.5185	−1.39803	−0.699015	−	0.715107i	$-0.746378\pi$
$283$	−23.5185	−1.39803	−0.699015	+	0.715107i	$0.746378\pi$
$284$	−9.30064	−0.551892
$285$	0.212925	0.0126126
$286$	18.2302	1.07797
$287$	−2.42117	−0.142917
$288$	−2.99994	−0.176773
$289$	1.10815	0.0651854
$290$	19.7789	1.16146
$291$	0.0454166	0.00266237
$292$	−2.31874	−0.135694
$293$	11.1622	0.652104	0.326052	−	0.945352i	$-0.394282\pi$
$293$	11.1622	0.652104	0.326052	+	0.945352i	$0.394282\pi$
$294$	−0.00804327	−0.000469093 0
$295$	−12.9878	−0.756179
$296$	−6.72749	−0.391028
$297$	−0.173881	−0.0100896
$298$	−5.97613	−0.346188
$299$	27.5980	1.59603
$300$	−0.0684887	−0.00395420
$301$	1.62203	0.0934925
$302$	11.6553	0.670688
$303$	0.0533317	0.00306383
$304$	−7.20088	−0.412999
$305$	−3.85620	−0.220806
$306$	12.7658	0.729774
$307$	14.9617	0.853907	0.426953	−	0.904274i	$-0.359587\pi$
$307$	14.9617	0.853907	0.426953	+	0.904274i	$0.359587\pi$
$308$	−3.60308	−0.205304
$309$	0.0247459	0.00140774
$310$	31.0262	1.76217
$311$	−7.03415	−0.398870	−0.199435	−	0.979911i	$-0.563911\pi$
$311$	−7.03415	−0.398870	−0.199435	+	0.979911i	$0.563911\pi$
$312$	0.0406958	0.00230395
$313$	−7.86480	−0.444545	−0.222272	−	0.974985i	$-0.571347\pi$
$313$	−7.86480	−0.444545	−0.222272	+	0.974985i	$0.571347\pi$
$314$	−23.2638	−1.31285
$315$	−11.0286	−0.621391
$316$	2.18286	0.122796
$317$	−17.7786	−0.998545	−0.499273	−	0.866445i	$-0.666399\pi$
$317$	−17.7786	−0.998545	−0.499273	+	0.866445i	$0.666399\pi$
$318$	0.0552165	0.00309639
$319$	−19.3851	−1.08536
$320$	3.67628	0.205510
$321$	−0.149734	−0.00835731
$322$	−5.45457	−0.303971
$323$	30.6424	1.70499
$324$	8.99942	0.499968
$325$	−43.0828	−2.38980
$326$	13.7297	0.760418
$327$	−0.0775236	−0.00428706
$328$	−2.42117	−0.133687
$329$	11.8922	0.655637
$330$	0.106541	0.00586486
$331$	6.22370	0.342085	0.171043	−	0.985264i	$-0.445286\pi$
$331$	6.22370	0.342085	0.171043	+	0.985264i	$0.445286\pi$
$332$	−11.3539	−0.623125
$333$	20.1820	1.10597
$334$	17.2313	0.942853
$335$	−44.7261	−2.44365
$336$	−0.00804327	−0.000438796 0
$337$	3.00215	0.163538	0.0817688	−	0.996651i	$-0.473943\pi$
$337$	3.00215	0.163538	0.0817688	+	0.996651i	$0.473943\pi$
$338$	12.5997	0.685333
$339$	0.105647	0.00573798
$340$	−15.6439	−0.848411
$341$	−30.4084	−1.64671
$342$	21.6022	1.16811
$343$	1.00000	0.0539949
$344$	1.62203	0.0874542
$345$	0.161288	0.00868345
$346$	19.1073	1.02721
$347$	14.3532	0.770522	0.385261	−	0.922808i	$-0.374111\pi$
$347$	14.3532	0.770522	0.385261	+	0.922808i	$0.374111\pi$
$348$	−0.0432740	−0.00231973
$349$	−11.5459	−0.618038	−0.309019	−	0.951056i	$-0.600001\pi$
$349$	−11.5459	−0.618038	−0.309019	+	0.951056i	$0.600001\pi$
$350$	8.51503	0.455148
$351$	−0.244172	−0.0130330
$352$	−3.60308	−0.192045
$353$	2.33498	0.124278	0.0621391	−	0.998067i	$-0.480208\pi$
$353$	2.33498	0.124278	0.0621391	+	0.998067i	$0.480208\pi$
$354$	0.0284158	0.00151028
$355$	−34.1918	−1.81471
$356$	3.87667	0.205463
$357$	0.0342271	0.00181149
$358$	−17.4364	−0.921540
$359$	−33.1350	−1.74880	−0.874399	−	0.485208i	$-0.838744\pi$
$359$	−33.1350	−1.74880	−0.874399	+	0.485208i	$0.838744\pi$
$360$	−11.0286	−0.581258
$361$	32.8527	1.72909
$362$	−14.6608	−0.770553
$363$	−0.0159431	−0.000836795 0
$364$	−5.05961	−0.265196
$365$	−8.52434	−0.446185
$366$	0.00843692	0.000441005 0
$367$	26.5067	1.38364	0.691820	−	0.722070i	$-0.256809\pi$
$367$	26.5067	1.38364	0.691820	+	0.722070i	$0.256809\pi$
$368$	−5.45457	−0.284339
$369$	7.26334	0.378115
$370$	−24.7322	−1.28576
$371$	−6.86493	−0.356409
$372$	−0.0678817	−0.00351950
$373$	0.807279	0.0417993	0.0208997	−	0.999782i	$-0.493347\pi$
$373$	0.807279	0.0417993	0.0208997	+	0.999782i	$0.493347\pi$
$374$	15.3324	0.792820
$375$	−0.103937	−0.00536729
$376$	11.8922	0.613292
$377$	−27.2215	−1.40198
$378$	0.0482591	0.00248218
$379$	35.8614	1.84208	0.921039	−	0.389469i	$-0.127342\pi$
$379$	35.8614	1.84208	0.921039	+	0.389469i	$0.127342\pi$
$380$	−26.4724	−1.35801
$381$	−0.0828126	−0.00424262
$382$	−17.4442	−0.892520
$383$	−5.11537	−0.261383	−0.130692	−	0.991423i	$-0.541720\pi$
$383$	−5.11537	−0.261383	−0.130692	+	0.991423i	$0.541720\pi$
$384$	−0.00804327	−0.000410457 0
$385$	−13.2459	−0.675074
$386$	17.1234	0.871560
$387$	−4.86600	−0.247352
$388$	−5.64654	−0.286660
$389$	−20.0433	−1.01624	−0.508118	−	0.861287i	$-0.669659\pi$
$389$	−20.0433	−1.01624	−0.508118	+	0.861287i	$0.669659\pi$
$390$	0.149609	0.00757576
$391$	23.2112	1.17384
$392$	1.00000	0.0505076
$393$	0.105996	0.00534680
$394$	1.01990	0.0513817
$395$	8.02481	0.403772
$396$	10.8090	0.543173
$397$	−3.94502	−0.197995	−0.0989975	−	0.995088i	$-0.531564\pi$
$397$	−3.94502	−0.197995	−0.0989975	+	0.995088i	$0.531564\pi$
$398$	17.4049	0.872430
$399$	0.0579186	0.00289956
$400$	8.51503	0.425752
$401$	1.21403	0.0606256	0.0303128	−	0.999540i	$-0.490350\pi$
$401$	1.21403	0.0606256	0.0303128	+	0.999540i	$0.490350\pi$
$402$	0.0978556	0.00488059
$403$	−42.7009	−2.12709
$404$	−6.63060	−0.329885
$405$	33.0844	1.64398
$406$	5.38015	0.267012
$407$	24.2397	1.20152
$408$	0.0342271	0.00169449
$409$	3.37254	0.166761	0.0833806	−	0.996518i	$-0.473428\pi$
$409$	3.37254	0.166761	0.0833806	+	0.996518i	$0.473428\pi$
$410$	−8.90089	−0.439583
$411$	−0.0539819	−0.00266273
$412$	−3.07660	−0.151573
$413$	−3.53286	−0.173841
$414$	16.3634	0.804215
$415$	−41.7401	−2.04894
$416$	−5.05961	−0.248068
$417$	0.161762	0.00792150
$418$	25.9453	1.26903
$419$	14.1407	0.690817	0.345409	−	0.938452i	$-0.387740\pi$
$419$	14.1407	0.690817	0.345409	+	0.938452i	$0.387740\pi$
$420$	−0.0295693	−0.00144283
$421$	24.9368	1.21535	0.607674	−	0.794187i	$-0.292103\pi$
$421$	24.9368	1.21535	0.607674	+	0.794187i	$0.292103\pi$
$422$	−21.0824	−1.02628
$423$	−35.6757	−1.73461
$424$	−6.86493	−0.333391
$425$	−36.2346	−1.75764
$426$	0.0748076	0.00362444
$427$	−1.04894	−0.0507618
$428$	18.6160	0.899838
$429$	−0.146630	−0.00707938
$430$	5.96305	0.287564
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	0.0482591	0.00232187
$433$	23.8411	1.14573	0.572866	−	0.819649i	$-0.305832\pi$
$433$	23.8411	1.14573	0.572866	+	0.819649i	$0.305832\pi$
$434$	8.43957	0.405112
$435$	−0.159087	−0.00762765
$436$	9.63832	0.461592
$437$	39.2777	1.87891
$438$	0.0186503	0.000891144 0
$439$	1.62172	0.0774007	0.0387004	−	0.999251i	$-0.487678\pi$
$439$	1.62172	0.0774007	0.0387004	+	0.999251i	$0.487678\pi$
$440$	−13.2459	−0.631474
$441$	−2.99994	−0.142854
$442$	21.5305	1.02410
$443$	−7.44042	−0.353505	−0.176752	−	0.984255i	$-0.556559\pi$
$443$	−7.44042	−0.353505	−0.176752	+	0.984255i	$0.556559\pi$
$444$	0.0541111	0.00256800
$445$	14.2517	0.675596
$446$	28.2233	1.33641
$447$	0.0480677	0.00227352
$448$	1.00000	0.0472456
$449$	41.3656	1.95216	0.976081	−	0.217406i	$-0.0697595\pi$
$449$	41.3656	1.95216	0.976081	+	0.217406i	$0.0697595\pi$
$450$	−25.5445	−1.20418
$451$	8.72365	0.410781
$452$	−13.1349	−0.617813
$453$	−0.0937469	−0.00440461
$454$	21.3480	1.00191
$455$	−18.6006	−0.872007
$456$	0.0579186	0.00271229
$457$	−10.7143	−0.501192	−0.250596	−	0.968092i	$-0.580627\pi$
$457$	−10.7143	−0.501192	−0.250596	+	0.968092i	$0.580627\pi$
$458$	−7.49251	−0.350102
$459$	−0.205360	−0.00958540
$460$	−20.0525	−0.934954
$461$	−19.1525	−0.892019	−0.446009	−	0.895028i	$-0.647155\pi$
$461$	−19.1525	−0.892019	−0.446009	+	0.895028i	$0.647155\pi$
$462$	0.0289805	0.00134830
$463$	1.76427	0.0819924	0.0409962	−	0.999159i	$-0.486947\pi$
$463$	1.76427	0.0819924	0.0409962	+	0.999159i	$0.486947\pi$
$464$	5.38015	0.249767
$465$	−0.249552	−0.0115727
$466$	−11.3480	−0.525687
$467$	40.3408	1.86675	0.933375	−	0.358904i	$-0.116849\pi$
$467$	40.3408	1.86675	0.933375	+	0.358904i	$0.116849\pi$
$468$	15.1785	0.701627
$469$	−12.1661	−0.561780
$470$	43.7189	2.01660
$471$	0.187117	0.00862189
$472$	−3.53286	−0.162613
$473$	−5.84431	−0.268722
$474$	−0.0175574	−0.000806436 0
$475$	−61.3157	−2.81336
$476$	−4.25537	−0.195044
$477$	20.5944	0.942951
$478$	18.9903	0.868595
$479$	11.5365	0.527114	0.263557	−	0.964644i	$-0.415104\pi$
$479$	11.5365	0.527114	0.263557	+	0.964644i	$0.415104\pi$
$480$	−0.0295693	−0.00134965
$481$	34.0385	1.55202
$482$	−3.35203	−0.152681
$483$	0.0438726	0.00199627
$484$	1.98216	0.0900984
$485$	−20.7583	−0.942584
$486$	−0.217162	−0.00985067
$487$	−14.8135	−0.671262	−0.335631	−	0.941994i	$-0.608950\pi$
$487$	−14.8135	−0.671262	−0.335631	+	0.941994i	$0.608950\pi$
$488$	−1.04894	−0.0474834
$489$	−0.110432	−0.00499390
$490$	3.67628	0.166077
$491$	1.74825	0.0788976	0.0394488	−	0.999222i	$-0.487440\pi$
$491$	1.74825	0.0788976	0.0394488	+	0.999222i	$0.487440\pi$
$492$	0.0194741	0.000877960 0
$493$	−22.8945	−1.03112
$494$	36.4337	1.63923
$495$	39.7369	1.78604
$496$	8.43957	0.378948
$497$	−9.30064	−0.417191
$498$	0.0913224	0.00409225
$499$	7.34260	0.328700	0.164350	−	0.986402i	$-0.447447\pi$
$499$	7.34260	0.328700	0.164350	+	0.986402i	$0.447447\pi$
$500$	12.9222	0.577900
$501$	−0.138596	−0.00619200
$502$	−8.32729	−0.371665
$503$	41.2397	1.83879	0.919393	−	0.393341i	$-0.128681\pi$
$503$	41.2397	1.83879	0.919393	+	0.393341i	$0.128681\pi$
$504$	−2.99994	−0.133628
$505$	−24.3759	−1.08471
$506$	19.6532	0.873693
$507$	−0.101343	−0.00450079
$508$	10.2959	0.456806
$509$	−7.15620	−0.317193	−0.158597	−	0.987343i	$-0.550697\pi$
$509$	−7.15620	−0.317193	−0.158597	+	0.987343i	$0.550697\pi$
$510$	0.125828	0.00557177
$511$	−2.31874	−0.102575
$512$	1.00000	0.0441942
$513$	−0.347508	−0.0153429
$514$	−24.0267	−1.05977
$515$	−11.3104	−0.498397
$516$	−0.0130465	−0.000574338 0
$517$	−42.8484	−1.88447
$518$	−6.72749	−0.295589
$519$	−0.153685	−0.00674602
$520$	−18.6006	−0.815688
$521$	18.0507	0.790816	0.395408	−	0.918506i	$-0.370603\pi$
$521$	18.0507	0.790816	0.395408	+	0.918506i	$0.370603\pi$
$522$	−16.1401	−0.706432
$523$	−27.4308	−1.19947	−0.599733	−	0.800200i	$-0.704727\pi$
$523$	−27.4308	−1.19947	−0.599733	+	0.800200i	$0.704727\pi$
$524$	−13.1782	−0.575694
$525$	−0.0684887	−0.00298909
$526$	−7.01033	−0.305665
$527$	−35.9135	−1.56441
$528$	0.0289805	0.00126122
$529$	6.75236	0.293581
$530$	−25.2374	−1.09624
$531$	10.5984	0.459930
$532$	−7.20088	−0.312198
$533$	12.2502	0.530614
$534$	−0.0311811	−0.00134934
$535$	68.4376	2.95882
$536$	−12.1661	−0.525497
$537$	0.140245	0.00605203
$538$	10.4599	0.450960
$539$	−3.60308	−0.155196
$540$	0.177414	0.00763468
$541$	−30.5733	−1.31445	−0.657224	−	0.753696i	$-0.728269\pi$
$541$	−30.5733	−1.31445	−0.657224	+	0.753696i	$0.728269\pi$
$542$	3.54452	0.152250
$543$	0.117921	0.00506046
$544$	−4.25537	−0.182447
$545$	35.4331	1.51779
$546$	0.0406958	0.00174162
$547$	−42.0481	−1.79785	−0.898924	−	0.438104i	$-0.855650\pi$
$547$	−42.0481	−1.79785	−0.898924	+	0.438104i	$0.855650\pi$
$548$	6.71144	0.286699
$549$	3.14676	0.134300
$550$	−30.6803	−1.30821
$551$	−38.7418	−1.65046
$552$	0.0438726	0.00186734
$553$	2.18286	0.0928248
$554$	−20.4046	−0.866907
$555$	0.198927	0.00844400
$556$	−20.1114	−0.852914
$557$	−29.8321	−1.26403	−0.632013	−	0.774958i	$-0.717771\pi$
$557$	−29.8321	−1.26403	−0.632013	+	0.774958i	$0.717771\pi$
$558$	−25.3182	−1.07180
$559$	−8.20686	−0.347113
$560$	3.67628	0.155351
$561$	−0.123323	−0.00520669
$562$	22.7551	0.959864
$563$	16.6815	0.703042	0.351521	−	0.936180i	$-0.385665\pi$
$563$	16.6815	0.703042	0.351521	+	0.936180i	$0.385665\pi$
$564$	−0.0956520	−0.00402767
$565$	−48.2875	−2.03147
$566$	−23.5185	−0.988556
$567$	8.99942	0.377940
$568$	−9.30064	−0.390246
$569$	38.3267	1.60674	0.803370	−	0.595480i	$-0.203038\pi$
$569$	38.3267	1.60674	0.803370	+	0.595480i	$0.203038\pi$
$570$	0.212925	0.00891845
$571$	4.55935	0.190803	0.0954014	−	0.995439i	$-0.469587\pi$
$571$	4.55935	0.190803	0.0954014	+	0.995439i	$0.469587\pi$
$572$	18.2302	0.762242
$573$	0.140308	0.00586145
$574$	−2.42117	−0.101058
$575$	−46.4458	−1.93693
$576$	−2.99994	−0.124997
$577$	32.7745	1.36442	0.682210	−	0.731156i	$-0.261019\pi$
$577$	32.7745	1.36442	0.682210	+	0.731156i	$0.261019\pi$
$578$	1.10815	0.0460931
$579$	−0.137728	−0.00572380
$580$	19.7789	0.821275
$581$	−11.3539	−0.471039
$582$	0.0454166	0.00188258
$583$	24.7349	1.02441
$584$	−2.31874	−0.0959502
$585$	55.8005	2.30706
$586$	11.1622	0.461107
$587$	3.66236	0.151162	0.0755808	−	0.997140i	$-0.475919\pi$
$587$	3.66236	0.151162	0.0755808	+	0.997140i	$0.475919\pi$
$588$	−0.00804327	−0.000331699 0
$589$	−60.7723	−2.50408
$590$	−12.9878	−0.534699
$591$	−0.00820331	−0.000337439 0
$592$	−6.72749	−0.276498
$593$	19.4037	0.796816	0.398408	−	0.917208i	$-0.369563\pi$
$593$	19.4037	0.796816	0.398408	+	0.917208i	$0.369563\pi$
$594$	−0.173881	−0.00713444
$595$	−15.6439	−0.641338
$596$	−5.97613	−0.244792
$597$	−0.139992	−0.00572951
$598$	27.5980	1.12857
$599$	15.7059	0.641726	0.320863	−	0.947126i	$-0.396027\pi$
$599$	15.7059	0.641726	0.320863	+	0.947126i	$0.396027\pi$
$600$	−0.0684887	−0.00279604
$601$	−42.6411	−1.73937	−0.869683	−	0.493612i	$-0.835676\pi$
$601$	−42.6411	−1.73937	−0.869683	+	0.493612i	$0.835676\pi$
$602$	1.62203	0.0661092
$603$	36.4976	1.48630
$604$	11.6553	0.474248
$605$	7.28699	0.296258
$606$	0.0533317	0.00216645
$607$	−8.63014	−0.350287	−0.175143	−	0.984543i	$-0.556039\pi$
$607$	−8.63014	−0.350287	−0.175143	+	0.984543i	$0.556039\pi$
$608$	−7.20088	−0.292034
$609$	−0.0432740	−0.00175355
$610$	−3.85620	−0.156133
$611$	−60.1698	−2.43421
$612$	12.7658	0.516028
$613$	−26.3179	−1.06297	−0.531484	−	0.847068i	$-0.678365\pi$
$613$	−26.3179	−1.06297	−0.531484	+	0.847068i	$0.678365\pi$
$614$	14.9617	0.603803
$615$	0.0715922	0.00288688
$616$	−3.60308	−0.145172
$617$	17.2089	0.692804	0.346402	−	0.938086i	$-0.387403\pi$
$617$	17.2089	0.692804	0.346402	+	0.938086i	$0.387403\pi$
$618$	0.0247459	0.000995426 0
$619$	−6.01725	−0.241854	−0.120927	−	0.992661i	$-0.538587\pi$
$619$	−6.01725	−0.241854	−0.120927	+	0.992661i	$0.538587\pi$
$620$	31.0262	1.24604
$621$	−0.263233	−0.0105632
$622$	−7.03415	−0.282044
$623$	3.87667	0.155315
$624$	0.0406958	0.00162914
$625$	4.93060	0.197224
$626$	−7.86480	−0.314340
$627$	−0.208685	−0.00833409
$628$	−23.2638	−0.928326
$629$	28.6280	1.14147
$630$	−11.0286	−0.439390
$631$	−14.9168	−0.593828	−0.296914	−	0.954904i	$-0.595957\pi$
$631$	−14.9168	−0.593828	−0.296914	+	0.954904i	$0.595957\pi$
$632$	2.18286	0.0868296
$633$	0.169572	0.00673987
$634$	−17.7786	−0.706078
$635$	37.8506	1.50205
$636$	0.0552165	0.00218948
$637$	−5.05961	−0.200469
$638$	−19.3851	−0.767463
$639$	27.9013	1.10376
$640$	3.67628	0.145318
$641$	−35.8076	−1.41432	−0.707158	−	0.707055i	$-0.750023\pi$
$641$	−35.8076	−1.41432	−0.707158	+	0.707055i	$0.750023\pi$
$642$	−0.149734	−0.00590951
$643$	7.84327	0.309308	0.154654	−	0.987969i	$-0.450574\pi$
$643$	7.84327	0.309308	0.154654	+	0.987969i	$0.450574\pi$
$644$	−5.45457	−0.214940
$645$	−0.0479624	−0.00188852
$646$	30.6424	1.20561
$647$	−13.4672	−0.529449	−0.264725	−	0.964324i	$-0.585281\pi$
$647$	−13.4672	−0.529449	−0.264725	+	0.964324i	$0.585281\pi$
$648$	8.99942	0.353531
$649$	12.7292	0.499664
$650$	−43.0828	−1.68984
$651$	−0.0678817	−0.00266050
$652$	13.7297	0.537697
$653$	−25.7253	−1.00671	−0.503355	−	0.864080i	$-0.667901\pi$
$653$	−25.7253	−1.00671	−0.503355	+	0.864080i	$0.667901\pi$
$654$	−0.0775236	−0.00303141
$655$	−48.4469	−1.89298
$656$	−2.42117	−0.0945307
$657$	6.95608	0.271382
$658$	11.8922	0.463605
$659$	−10.6933	−0.416551	−0.208276	−	0.978070i	$-0.566785\pi$
$659$	−10.6933	−0.416551	−0.208276	+	0.978070i	$0.566785\pi$
$660$	0.106541	0.00414708
$661$	20.5741	0.800240	0.400120	−	0.916463i	$-0.368968\pi$
$661$	20.5741	0.800240	0.400120	+	0.916463i	$0.368968\pi$
$662$	6.22370	0.241891
$663$	−0.173176	−0.00672559
$664$	−11.3539	−0.440616
$665$	−26.4724	−1.02656
$666$	20.1820	0.782039
$667$	−29.3464	−1.13630
$668$	17.2313	0.666698
$669$	−0.227008	−0.00877662
$670$	−44.7261	−1.72792
$671$	3.77942	0.145903
$672$	−0.00804327	−0.000310276 0
$673$	−38.8725	−1.49843	−0.749213	−	0.662329i	$-0.769568\pi$
$673$	−38.8725	−1.49843	−0.749213	+	0.662329i	$0.769568\pi$
$674$	3.00215	0.115638
$675$	0.410928	0.0158166
$676$	12.5997	0.484603
$677$	−32.1969	−1.23743	−0.618714	−	0.785616i	$-0.712346\pi$
$677$	−32.1969	−1.23743	−0.618714	+	0.785616i	$0.712346\pi$
$678$	0.105647	0.00405736
$679$	−5.64654	−0.216694
$680$	−15.6439	−0.599917
$681$	−0.171708	−0.00657986
$682$	−30.4084	−1.16440
$683$	8.55728	0.327435	0.163718	−	0.986507i	$-0.447651\pi$
$683$	8.55728	0.327435	0.163718	+	0.986507i	$0.447651\pi$
$684$	21.6022	0.825980
$685$	24.6731	0.942712
$686$	1.00000	0.0381802
$687$	0.0602643	0.00229923
$688$	1.62203	0.0618395
$689$	34.7339	1.32326
$690$	0.161288	0.00614013
$691$	17.1130	0.651009	0.325504	−	0.945541i	$-0.394466\pi$
$691$	17.1130	0.651009	0.325504	+	0.945541i	$0.394466\pi$
$692$	19.1073	0.726349
$693$	10.8090	0.410600
$694$	14.3532	0.544841
$695$	−73.9352	−2.80452
$696$	−0.0432740	−0.00164030
$697$	10.3030	0.390252
$698$	−11.5459	−0.437019
$699$	0.0912752	0.00345235
$700$	8.51503	0.321838
$701$	35.5121	1.34127	0.670637	−	0.741786i	$-0.266021\pi$
$701$	35.5121	1.34127	0.670637	+	0.741786i	$0.266021\pi$
$702$	−0.244172	−0.00921570
$703$	48.4439	1.82710
$704$	−3.60308	−0.135796
$705$	−0.351643	−0.0132437
$706$	2.33498	0.0878780
$707$	−6.63060	−0.249369
$708$	0.0284158	0.00106793
$709$	24.6240	0.924773	0.462387	−	0.886678i	$-0.346993\pi$
$709$	24.6240	0.924773	0.462387	+	0.886678i	$0.346993\pi$
$710$	−34.1918	−1.28319
$711$	−6.54845	−0.245586
$712$	3.87667	0.145284
$713$	−46.0342	−1.72400
$714$	0.0342271	0.00128092
$715$	67.0192	2.50638
$716$	−17.4364	−0.651627
$717$	−0.152744	−0.00570433
$718$	−33.1350	−1.23659
$719$	9.82335	0.366349	0.183175	−	0.983080i	$-0.441363\pi$
$719$	9.82335	0.366349	0.183175	+	0.983080i	$0.441363\pi$
$720$	−11.0286	−0.411012
$721$	−3.07660	−0.114578
$722$	32.8527	1.22265
$723$	0.0269613	0.00100270
$724$	−14.6608	−0.544863
$725$	45.8121	1.70142
$726$	−0.0159431	−0.000591703 0
$727$	35.1134	1.30228	0.651142	−	0.758956i	$-0.274290\pi$
$727$	35.1134	1.30228	0.651142	+	0.758956i	$0.274290\pi$
$728$	−5.05961	−0.187522
$729$	−26.9965	−0.999871
$730$	−8.52434	−0.315500
$731$	−6.90235	−0.255293
$732$	0.00843692	0.000311838 0
$733$	31.0350	1.14630	0.573152	−	0.819449i	$-0.305721\pi$
$733$	31.0350	1.14630	0.573152	+	0.819449i	$0.305721\pi$
$734$	26.5067	0.978382
$735$	−0.0295693	−0.00109068
$736$	−5.45457	−0.201058
$737$	43.8355	1.61470
$738$	7.26334	0.267367
$739$	41.7988	1.53760	0.768798	−	0.639492i	$-0.220855\pi$
$739$	41.7988	1.53760	0.768798	+	0.639492i	$0.220855\pi$
$740$	−24.7322	−0.909172
$741$	−0.293046	−0.0107653
$742$	−6.86493	−0.252020
$743$	18.3509	0.673231	0.336615	−	0.941642i	$-0.390718\pi$
$743$	18.3509	0.673231	0.336615	+	0.941642i	$0.390718\pi$
$744$	−0.0678817	−0.00248867
$745$	−21.9699	−0.804916
$746$	0.807279	0.0295566
$747$	34.0609	1.24622
$748$	15.3324	0.560609
$749$	18.6160	0.680214
$750$	−0.103937	−0.00379524
$751$	−43.1154	−1.57330	−0.786651	−	0.617398i	$-0.788187\pi$
$751$	−43.1154	−1.57330	−0.786651	+	0.617398i	$0.788187\pi$
$752$	11.8922	0.433663
$753$	0.0669787	0.00244084
$754$	−27.2215	−0.991347
$755$	42.8482	1.55941
$756$	0.0482591	0.00175517
$757$	11.7488	0.427018	0.213509	−	0.976941i	$-0.431511\pi$
$757$	11.7488	0.427018	0.213509	+	0.976941i	$0.431511\pi$
$758$	35.8614	1.30255
$759$	−0.158076	−0.00573781
$760$	−26.4724	−0.960257
$761$	−5.68188	−0.205968	−0.102984	−	0.994683i	$-0.532839\pi$
$761$	−5.68188	−0.205968	−0.102984	+	0.994683i	$0.532839\pi$
$762$	−0.0828126	−0.00299999
$763$	9.63832	0.348930
$764$	−17.4442	−0.631107
$765$	46.9307	1.69678
$766$	−5.11537	−0.184826
$767$	17.8749	0.645426
$768$	−0.00804327	−0.000290237 0
$769$	−10.9305	−0.394165	−0.197082	−	0.980387i	$-0.563147\pi$
$769$	−10.9305	−0.394165	−0.197082	+	0.980387i	$0.563147\pi$
$770$	−13.2459	−0.477350
$771$	0.193254	0.00695986
$772$	17.1234	0.616286
$773$	−42.3246	−1.52231	−0.761156	−	0.648569i	$-0.775368\pi$
$773$	−42.3246	−1.52231	−0.761156	+	0.648569i	$0.775368\pi$
$774$	−4.86600	−0.174905
$775$	71.8632	2.58140
$776$	−5.64654	−0.202699
$777$	0.0541111	0.00194122
$778$	−20.0433	−0.718588
$779$	17.4345	0.624657
$780$	0.149609	0.00535687
$781$	33.5109	1.19912
$782$	23.2112	0.830031
$783$	0.259641	0.00927881
$784$	1.00000	0.0357143
$785$	−85.5241	−3.05249
$786$	0.105996	0.00378076
$787$	−44.5269	−1.58721	−0.793607	−	0.608431i	$-0.791799\pi$
$787$	−44.5269	−1.58721	−0.793607	+	0.608431i	$0.791799\pi$
$788$	1.01990	0.0363323
$789$	0.0563860	0.00200739
$790$	8.02481	0.285510
$791$	−13.1349	−0.467023
$792$	10.8090	0.384081
$793$	5.30724	0.188466
$794$	−3.94502	−0.140004
$795$	0.202991	0.00719936
$796$	17.4049	0.616901
$797$	−37.2080	−1.31797	−0.658987	−	0.752154i	$-0.729015\pi$
$797$	−37.2080	−1.31797	−0.658987	+	0.752154i	$0.729015\pi$
$798$	0.0579186	0.00205030
$799$	−50.6056	−1.79030
$800$	8.51503	0.301052
$801$	−11.6298	−0.410917
$802$	1.21403	0.0428688
$803$	8.35461	0.294828
$804$	0.0978556	0.00345110
$805$	−20.0525	−0.706759
$806$	−42.7009	−1.50408
$807$	−0.0841321	−0.00296159
$808$	−6.63060	−0.233264
$809$	10.8896	0.382859	0.191430	−	0.981506i	$-0.438688\pi$
$809$	10.8896	0.382859	0.191430	+	0.981506i	$0.438688\pi$
$810$	33.0844	1.16247
$811$	24.7326	0.868479	0.434240	−	0.900797i	$-0.357017\pi$
$811$	24.7326	0.868479	0.434240	+	0.900797i	$0.357017\pi$
$812$	5.38015	0.188806
$813$	−0.0285096	−0.000999874 0
$814$	24.2397	0.849600
$815$	50.4742	1.76804
$816$	0.0342271	0.00119819
$817$	−11.6801	−0.408634
$818$	3.37254	0.117918
$819$	15.1785	0.530380
$820$	−8.90089	−0.310832
$821$	−13.9820	−0.487976	−0.243988	−	0.969778i	$-0.578456\pi$
$821$	−13.9820	−0.487976	−0.243988	+	0.969778i	$0.578456\pi$
$822$	−0.0539819	−0.00188284
$823$	−46.6363	−1.62564	−0.812820	−	0.582515i	$-0.802069\pi$
$823$	−46.6363	−1.62564	−0.812820	+	0.582515i	$0.802069\pi$
$824$	−3.07660	−0.107178
$825$	0.246770	0.00859143
$826$	−3.53286	−0.122924
$827$	1.01238	0.0352040	0.0176020	−	0.999845i	$-0.494397\pi$
$827$	1.01238	0.0352040	0.0176020	+	0.999845i	$0.494397\pi$
$828$	16.3634	0.568666
$829$	−48.6340	−1.68913	−0.844565	−	0.535453i	$-0.820141\pi$
$829$	−48.6340	−1.68913	−0.844565	+	0.535453i	$0.820141\pi$
$830$	−41.7401	−1.44882
$831$	0.164120	0.00569325
$832$	−5.05961	−0.175411
$833$	−4.25537	−0.147440
$834$	0.161762	0.00560135
$835$	63.3470	2.19221
$836$	25.9453	0.897338
$837$	0.407286	0.0140779
$838$	14.1407	0.488482
$839$	−21.3569	−0.737321	−0.368661	−	0.929564i	$-0.620184\pi$
$839$	−21.3569	−0.737321	−0.368661	+	0.929564i	$0.620184\pi$
$840$	−0.0295693	−0.00102024
$841$	−0.0540379	−0.00186338
$842$	24.9368	0.859380
$843$	−0.183025	−0.00630372
$844$	−21.0824	−0.725687
$845$	46.3200	1.59346
$846$	−35.6757	−1.22656
$847$	1.98216	0.0681080
$848$	−6.86493	−0.235743
$849$	0.189166	0.00649215
$850$	−36.2346	−1.24284
$851$	36.6956	1.25791
$852$	0.0748076	0.00256287
$853$	26.1396	0.895005	0.447502	−	0.894283i	$-0.352314\pi$
$853$	26.1396	0.895005	0.447502	+	0.894283i	$0.352314\pi$
$854$	−1.04894	−0.0358940
$855$	79.4156	2.71596
$856$	18.6160	0.636282
$857$	2.73904	0.0935638	0.0467819	−	0.998905i	$-0.485103\pi$
$857$	2.73904	0.0935638	0.0467819	+	0.998905i	$0.485103\pi$
$858$	−0.146630	−0.00500587
$859$	8.65838	0.295420	0.147710	−	0.989031i	$-0.452810\pi$
$859$	8.65838	0.295420	0.147710	+	0.989031i	$0.452810\pi$
$860$	5.96305	0.203338
$861$	0.0194741	0.000663676 0
$862$	−1.00000	−0.0340601
$863$	−41.0294	−1.39666	−0.698328	−	0.715778i	$-0.746072\pi$
$863$	−41.0294	−1.39666	−0.698328	+	0.715778i	$0.746072\pi$
$864$	0.0482591	0.00164181
$865$	70.2436	2.38835
$866$	23.8411	0.810155
$867$	−0.00891317	−0.000302707 0
$868$	8.43957	0.286458
$869$	−7.86502	−0.266803
$870$	−0.159087	−0.00539356
$871$	61.5560	2.08574
$872$	9.63832	0.326395
$873$	16.9393	0.573307
$874$	39.2777	1.32859
$875$	12.9222	0.436851
$876$	0.0186503	0.000630134 0
$877$	8.64418	0.291893	0.145947	−	0.989292i	$-0.453377\pi$
$877$	8.64418	0.291893	0.145947	+	0.989292i	$0.453377\pi$
$878$	1.62172	0.0547306
$879$	−0.0897808	−0.00302823
$880$	−13.2459	−0.446520
$881$	9.47119	0.319092	0.159546	−	0.987190i	$-0.448997\pi$
$881$	9.47119	0.319092	0.159546	+	0.987190i	$0.448997\pi$
$882$	−2.99994	−0.101013
$883$	−25.4208	−0.855478	−0.427739	−	0.903902i	$-0.640690\pi$
$883$	−25.4208	−0.855478	−0.427739	+	0.903902i	$0.640690\pi$
$884$	21.5305	0.724150
$885$	0.104464	0.00351153
$886$	−7.44042	−0.249966
$887$	26.0472	0.874580	0.437290	−	0.899321i	$-0.355938\pi$
$887$	26.0472	0.874580	0.437290	+	0.899321i	$0.355938\pi$
$888$	0.0541111	0.00181585
$889$	10.2959	0.345313
$890$	14.2517	0.477719
$891$	−32.4256	−1.08630
$892$	28.2233	0.944985
$893$	−85.6341	−2.86564
$894$	0.0480677	0.00160762
$895$	−64.1009	−2.14266
$896$	1.00000	0.0334077
$897$	−0.221978	−0.00741164
$898$	41.3656	1.38039
$899$	45.4061	1.51438
$900$	−25.5445	−0.851485
$901$	29.2128	0.973220
$902$	8.72365	0.290466
$903$	−0.0130465	−0.000434159 0
$904$	−13.1349	−0.436860
$905$	−53.8971	−1.79160
$906$	−0.0937469	−0.00311453
$907$	21.7891	0.723495	0.361747	−	0.932276i	$-0.382180\pi$
$907$	21.7891	0.723495	0.361747	+	0.932276i	$0.382180\pi$
$908$	21.3480	0.708458
$909$	19.8914	0.659755
$910$	−18.6006	−0.616602
$911$	−22.0127	−0.729314	−0.364657	−	0.931142i	$-0.618814\pi$
$911$	−22.0127	−0.729314	−0.364657	+	0.931142i	$0.618814\pi$
$912$	0.0579186	0.00191788
$913$	40.9089	1.35389
$914$	−10.7143	−0.354397
$915$	0.0310165	0.00102537
$916$	−7.49251	−0.247560
$917$	−13.1782	−0.435184
$918$	−0.205360	−0.00677790
$919$	−8.31675	−0.274344	−0.137172	−	0.990547i	$-0.543801\pi$
$919$	−8.31675	−0.274344	−0.137172	+	0.990547i	$0.543801\pi$
$920$	−20.0525	−0.661112
$921$	−0.120341	−0.00396536
$922$	−19.1525	−0.630752
$923$	47.0577	1.54892
$924$	0.0289805	0.000953389 0
$925$	−57.2848	−1.88351
$926$	1.76427	0.0579774
$927$	9.22959	0.303139
$928$	5.38015	0.176612
$929$	−44.2451	−1.45163	−0.725817	−	0.687888i	$-0.758538\pi$
$929$	−44.2451	−1.45163	−0.725817	+	0.687888i	$0.758538\pi$
$930$	−0.249552	−0.00818314
$931$	−7.20088	−0.235999
$932$	−11.3480	−0.371717
$933$	0.0565776	0.00185227
$934$	40.3408	1.31999
$935$	56.3662	1.84337
$936$	15.1785	0.496125
$937$	21.1189	0.689924	0.344962	−	0.938617i	$-0.387892\pi$
$937$	21.1189	0.689924	0.344962	+	0.938617i	$0.387892\pi$
$938$	−12.1661	−0.397239
$939$	0.0632587	0.00206437
$940$	43.7189	1.42595
$941$	−35.1986	−1.14744	−0.573721	−	0.819051i	$-0.694501\pi$
$941$	−35.1986	−1.14744	−0.573721	+	0.819051i	$0.694501\pi$
$942$	0.187117	0.00609660
$943$	13.2064	0.430060
$944$	−3.53286	−0.114985
$945$	0.177414	0.00577128
$946$	−5.84431	−0.190015
$947$	25.7086	0.835419	0.417709	−	0.908581i	$-0.362833\pi$
$947$	25.7086	0.835419	0.417709	+	0.908581i	$0.362833\pi$
$948$	−0.0175574	−0.000570236 0
$949$	11.7319	0.380835
$950$	−61.3157	−1.98934
$951$	0.142998	0.00463703
$952$	−4.25537	−0.137917
$953$	−24.9156	−0.807097	−0.403548	−	0.914958i	$-0.632223\pi$
$953$	−24.9156	−0.807097	−0.403548	+	0.914958i	$0.632223\pi$
$954$	20.5944	0.666767
$955$	−64.1296	−2.07518
$956$	18.9903	0.614190
$957$	0.155919	0.00504016
$958$	11.5365	0.372726
$959$	6.71144	0.216724
$960$	−0.0295693	−0.000954346 0
$961$	40.2263	1.29762
$962$	34.0385	1.09745
$963$	−55.8468	−1.79964
$964$	−3.35203	−0.107962
$965$	62.9505	2.02645
$966$	0.0438726	0.00141158
$967$	−16.6784	−0.536341	−0.268170	−	0.963371i	$-0.586419\pi$
$967$	−16.6784	−0.536341	−0.268170	+	0.963371i	$0.586419\pi$
$968$	1.98216	0.0637092
$969$	−0.246465	−0.00791760
$970$	−20.7583	−0.666507
$971$	−45.0491	−1.44570	−0.722848	−	0.691007i	$-0.757167\pi$
$971$	−45.0491	−1.44570	−0.722848	+	0.691007i	$0.757167\pi$
$972$	−0.217162	−0.00696548
$973$	−20.1114	−0.644742
$974$	−14.8135	−0.474654
$975$	0.346526	0.0110977
$976$	−1.04894	−0.0335758
$977$	−35.5982	−1.13889	−0.569444	−	0.822030i	$-0.692841\pi$
$977$	−35.5982	−1.13889	−0.569444	+	0.822030i	$0.692841\pi$
$978$	−0.110432	−0.00353122
$979$	−13.9679	−0.446417
$980$	3.67628	0.117434
$981$	−28.9143	−0.923163
$982$	1.74825	0.0557890
$983$	46.1059	1.47055	0.735274	−	0.677770i	$-0.237053\pi$
$983$	46.1059	1.47055	0.735274	+	0.677770i	$0.237053\pi$
$984$	0.0194741	0.000620812 0
$985$	3.74943	0.119467
$986$	−22.8945	−0.729109
$987$	−0.0956520	−0.00304464
$988$	36.4337	1.15911
$989$	−8.84750	−0.281334
$990$	39.7369	1.26292
$991$	−37.6985	−1.19753	−0.598767	−	0.800923i	$-0.704342\pi$
$991$	−37.6985	−1.19753	−0.598767	+	0.800923i	$0.704342\pi$
$992$	8.43957	0.267957
$993$	−0.0500589	−0.00158857
$994$	−9.30064	−0.294998
$995$	63.9853	2.02847
$996$	0.0913224	0.00289366
$997$	24.0356	0.761216	0.380608	−	0.924737i	$-0.375715\pi$
$997$	24.0356	0.761216	0.380608	+	0.924737i	$0.375715\pi$
$998$	7.34260	0.232426
$999$	−0.324663	−0.0102719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.12	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.12	✓	21	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.00804327 q^{3} +1.00000 q^{4} +3.67628 q^{5} -0.00804327 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.99994 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.00804327 q^{3} +1.00000 q^{4} +3.67628 q^{5} -0.00804327 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.99994 q^{9} +3.67628 q^{10} -3.60308 q^{11} -0.00804327 q^{12} -5.05961 q^{13} +1.00000 q^{14} -0.0295693 q^{15} +1.00000 q^{16} -4.25537 q^{17} -2.99994 q^{18} -7.20088 q^{19} +3.67628 q^{20} -0.00804327 q^{21} -3.60308 q^{22} -5.45457 q^{23} -0.00804327 q^{24} +8.51503 q^{25} -5.05961 q^{26} +0.0482591 q^{27} +1.00000 q^{28} +5.38015 q^{29} -0.0295693 q^{30} +8.43957 q^{31} +1.00000 q^{32} +0.0289805 q^{33} -4.25537 q^{34} +3.67628 q^{35} -2.99994 q^{36} -6.72749 q^{37} -7.20088 q^{38} +0.0406958 q^{39} +3.67628 q^{40} -2.42117 q^{41} -0.00804327 q^{42} +1.62203 q^{43} -3.60308 q^{44} -11.0286 q^{45} -5.45457 q^{46} +11.8922 q^{47} -0.00804327 q^{48} +1.00000 q^{49} +8.51503 q^{50} +0.0342271 q^{51} -5.05961 q^{52} -6.86493 q^{53} +0.0482591 q^{54} -13.2459 q^{55} +1.00000 q^{56} +0.0579186 q^{57} +5.38015 q^{58} -3.53286 q^{59} -0.0295693 q^{60} -1.04894 q^{61} +8.43957 q^{62} -2.99994 q^{63} +1.00000 q^{64} -18.6006 q^{65} +0.0289805 q^{66} -12.1661 q^{67} -4.25537 q^{68} +0.0438726 q^{69} +3.67628 q^{70} -9.30064 q^{71} -2.99994 q^{72} -2.31874 q^{73} -6.72749 q^{74} -0.0684887 q^{75} -7.20088 q^{76} -3.60308 q^{77} +0.0406958 q^{78} +2.18286 q^{79} +3.67628 q^{80} +8.99942 q^{81} -2.42117 q^{82} -11.3539 q^{83} -0.00804327 q^{84} -15.6439 q^{85} +1.62203 q^{86} -0.0432740 q^{87} -3.60308 q^{88} +3.87667 q^{89} -11.0286 q^{90} -5.05961 q^{91} -5.45457 q^{92} -0.0678817 q^{93} +11.8922 q^{94} -26.4724 q^{95} -0.00804327 q^{96} -5.64654 q^{97} +1.00000 q^{98} +10.8090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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