LMFDB - Embedded newform 6043.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71539 q^{2} -2.22479 q^{3} +5.37337 q^{4} +1.62014 q^{5} +6.04118 q^{6} -3.35178 q^{7} -9.16003 q^{8} +1.94968 q^{9} +O(q^{10})$	\(q-2.71539 q^{2} -2.22479 q^{3} +5.37337 q^{4} +1.62014 q^{5} +6.04118 q^{6} -3.35178 q^{7} -9.16003 q^{8} +1.94968 q^{9} -4.39933 q^{10} -1.83602 q^{11} -11.9546 q^{12} -1.43506 q^{13} +9.10140 q^{14} -3.60448 q^{15} +14.1263 q^{16} -4.84305 q^{17} -5.29416 q^{18} -0.416975 q^{19} +8.70563 q^{20} +7.45700 q^{21} +4.98552 q^{22} -9.16767 q^{23} +20.3791 q^{24} -2.37513 q^{25} +3.89676 q^{26} +2.33673 q^{27} -18.0103 q^{28} -3.25882 q^{29} +9.78758 q^{30} +9.88921 q^{31} -20.0386 q^{32} +4.08476 q^{33} +13.1508 q^{34} -5.43036 q^{35} +10.4764 q^{36} +3.92531 q^{37} +1.13225 q^{38} +3.19271 q^{39} -14.8406 q^{40} -2.23244 q^{41} -20.2487 q^{42} -0.479431 q^{43} -9.86561 q^{44} +3.15877 q^{45} +24.8938 q^{46} +11.3049 q^{47} -31.4281 q^{48} +4.23443 q^{49} +6.44943 q^{50} +10.7748 q^{51} -7.71111 q^{52} +3.80809 q^{53} -6.34515 q^{54} -2.97462 q^{55} +30.7024 q^{56} +0.927681 q^{57} +8.84899 q^{58} +10.9895 q^{59} -19.3682 q^{60} +5.94819 q^{61} -26.8531 q^{62} -6.53491 q^{63} +26.1599 q^{64} -2.32500 q^{65} -11.0917 q^{66} +3.66699 q^{67} -26.0235 q^{68} +20.3961 q^{69} +14.7456 q^{70} +16.3585 q^{71} -17.8591 q^{72} +3.60186 q^{73} -10.6588 q^{74} +5.28417 q^{75} -2.24056 q^{76} +6.15393 q^{77} -8.66946 q^{78} -3.83294 q^{79} +22.8867 q^{80} -11.0478 q^{81} +6.06195 q^{82} +3.12051 q^{83} +40.0692 q^{84} -7.84643 q^{85} +1.30184 q^{86} +7.25019 q^{87} +16.8180 q^{88} -6.74456 q^{89} -8.57730 q^{90} +4.81001 q^{91} -49.2613 q^{92} -22.0014 q^{93} -30.6973 q^{94} -0.675560 q^{95} +44.5816 q^{96} +14.7789 q^{97} -11.4981 q^{98} -3.57966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) $ 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * 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 $

$2$	−2.71539	−1.92007	−0.960037	−	0.279873i	$-0.909708\pi$
$2$	−2.71539	−1.92007	−0.960037	+	0.279873i	$0.909708\pi$
$3$	−2.22479	−1.28448	−0.642241	−	0.766503i	$-0.721995\pi$
$3$	−2.22479	−1.28448	−0.642241	+	0.766503i	$0.721995\pi$
$4$	5.37337	2.68668
$5$	1.62014	0.724550	0.362275	−	0.932071i	$-0.382000\pi$
$5$	1.62014	0.724550	0.362275	+	0.932071i	$0.382000\pi$
$6$	6.04118	2.46630
$7$	−3.35178	−1.26685	−0.633427	−	0.773803i	$-0.718352\pi$
$7$	−3.35178	−1.26685	−0.633427	+	0.773803i	$0.718352\pi$
$8$	−9.16003	−3.23856
$9$	1.94968	0.649894
$10$	−4.39933	−1.39119
$11$	−1.83602	−0.553581	−0.276790	−	0.960930i	$-0.589271\pi$
$11$	−1.83602	−0.553581	−0.276790	+	0.960930i	$0.589271\pi$
$12$	−11.9546	−3.45100
$13$	−1.43506	−0.398014	−0.199007	−	0.979998i	$-0.563772\pi$
$13$	−1.43506	−0.398014	−0.199007	+	0.979998i	$0.563772\pi$
$14$	9.10140	2.43245
$15$	−3.60448	−0.930672
$16$	14.1263	3.53159
$17$	−4.84305	−1.17461	−0.587306	−	0.809365i	$-0.699811\pi$
$17$	−4.84305	−1.17461	−0.587306	+	0.809365i	$0.699811\pi$
$18$	−5.29416	−1.24785
$19$	−0.416975	−0.0956607	−0.0478303	−	0.998855i	$-0.515231\pi$
$19$	−0.416975	−0.0956607	−0.0478303	+	0.998855i	$0.515231\pi$
$20$	8.70563	1.94664
$21$	7.45700	1.62725
$22$	4.98552	1.06292
$23$	−9.16767	−1.91159	−0.955796	−	0.294032i	$-0.905003\pi$
$23$	−9.16767	−1.91159	−0.955796	+	0.294032i	$0.905003\pi$
$24$	20.3791	4.15987
$25$	−2.37513	−0.475027
$26$	3.89676	0.764217
$27$	2.33673	0.449704
$28$	−18.0103	−3.40364
$29$	−3.25882	−0.605148	−0.302574	−	0.953126i	$-0.597846\pi$
$29$	−3.25882	−0.605148	−0.302574	+	0.953126i	$0.597846\pi$
$30$	9.78758	1.78696
$31$	9.88921	1.77615	0.888077	−	0.459694i	$-0.152041\pi$
$31$	9.88921	1.77615	0.888077	+	0.459694i	$0.152041\pi$
$32$	−20.0386	−3.54235
$33$	4.08476	0.711065
$34$	13.1508	2.25534
$35$	−5.43036	−0.917899
$36$	10.4764	1.74606
$37$	3.92531	0.645317	0.322659	−	0.946515i	$-0.395423\pi$
$37$	3.92531	0.645317	0.322659	+	0.946515i	$0.395423\pi$
$38$	1.13225	0.183676
$39$	3.19271	0.511242
$40$	−14.8406	−2.34650
$41$	−2.23244	−0.348648	−0.174324	−	0.984688i	$-0.555774\pi$
$41$	−2.23244	−0.348648	−0.174324	+	0.984688i	$0.555774\pi$
$42$	−20.2487	−3.12444
$43$	−0.479431	−0.0731125	−0.0365563	−	0.999332i	$-0.511639\pi$
$43$	−0.479431	−0.0731125	−0.0365563	+	0.999332i	$0.511639\pi$
$44$	−9.86561	−1.48730
$45$	3.15877	0.470881
$46$	24.8938	3.67040
$47$	11.3049	1.64899	0.824496	−	0.565867i	$-0.191459\pi$
$47$	11.3049	1.64899	0.824496	+	0.565867i	$0.191459\pi$
$48$	−31.4281	−4.53626
$49$	4.23443	0.604918
$50$	6.44943	0.912087
$51$	10.7748	1.50877
$52$	−7.71111	−1.06934
$53$	3.80809	0.523082	0.261541	−	0.965192i	$-0.415769\pi$
$53$	3.80809	0.523082	0.261541	+	0.965192i	$0.415769\pi$
$54$	−6.34515	−0.863466
$55$	−2.97462	−0.401097
$56$	30.7024	4.10278
$57$	0.927681	0.122874
$58$	8.84899	1.16193
$59$	10.9895	1.43072	0.715358	−	0.698758i	$-0.246263\pi$
$59$	10.9895	1.43072	0.715358	+	0.698758i	$0.246263\pi$
$60$	−19.3682	−2.50042
$61$	5.94819	0.761588	0.380794	−	0.924660i	$-0.375651\pi$
$61$	5.94819	0.761588	0.380794	+	0.924660i	$0.375651\pi$
$62$	−26.8531	−3.41035
$63$	−6.53491	−0.823321
$64$	26.1599	3.26999
$65$	−2.32500	−0.288381
$66$	−11.0917	−1.36530
$67$	3.66699	0.447994	0.223997	−	0.974590i	$-0.428089\pi$
$67$	3.66699	0.447994	0.223997	+	0.974590i	$0.428089\pi$
$68$	−26.0235	−3.15581
$69$	20.3961	2.45541
$70$	14.7456	1.76243
$71$	16.3585	1.94139	0.970697	−	0.240309i	$-0.0772487\pi$
$71$	16.3585	1.94139	0.970697	+	0.240309i	$0.0772487\pi$
$72$	−17.8591	−2.10472
$73$	3.60186	0.421566	0.210783	−	0.977533i	$-0.432399\pi$
$73$	3.60186	0.421566	0.210783	+	0.977533i	$0.432399\pi$
$74$	−10.6588	−1.23906
$75$	5.28417	0.610164
$76$	−2.24056	−0.257010
$77$	6.15393	0.701306
$78$	−8.66946	−0.981623
$79$	−3.83294	−0.431239	−0.215620	−	0.976477i	$-0.569177\pi$
$79$	−3.83294	−0.431239	−0.215620	+	0.976477i	$0.569177\pi$
$80$	22.8867	2.55881
$81$	−11.0478	−1.22753
$82$	6.06195	0.669431
$83$	3.12051	0.342520	0.171260	−	0.985226i	$-0.445216\pi$
$83$	3.12051	0.342520	0.171260	+	0.985226i	$0.445216\pi$
$84$	40.0692	4.37191
$85$	−7.84643	−0.851065
$86$	1.30184	0.140381
$87$	7.25019	0.777302
$88$	16.8180	1.79280
$89$	−6.74456	−0.714921	−0.357461	−	0.933928i	$-0.616357\pi$
$89$	−6.74456	−0.714921	−0.357461	+	0.933928i	$0.616357\pi$
$90$	−8.57730	−0.904127
$91$	4.81001	0.504226
$92$	−49.2613	−5.13584
$93$	−22.0014	−2.28144
$94$	−30.6973	−3.16619
$95$	−0.675560	−0.0693110
$96$	44.5816	4.55009
$97$	14.7789	1.50057	0.750285	−	0.661115i	$-0.229916\pi$
$97$	14.7789	1.50057	0.750285	+	0.661115i	$0.229916\pi$
$98$	−11.4981	−1.16149
$99$	−3.57966	−0.359769
$100$	−12.7625	−1.27625
$101$	3.64001	0.362195	0.181097	−	0.983465i	$-0.442035\pi$
$101$	3.64001	0.362195	0.181097	+	0.983465i	$0.442035\pi$
$102$	−29.2577	−2.89695
$103$	13.3818	1.31855	0.659276	−	0.751901i	$-0.270863\pi$
$103$	13.3818	1.31855	0.659276	+	0.751901i	$0.270863\pi$
$104$	13.1452	1.28899
$105$	12.0814	1.17902
$106$	−10.3405	−1.00436
$107$	−1.72049	−0.166326	−0.0831630	−	0.996536i	$-0.526502\pi$
$107$	−1.72049	−0.166326	−0.0831630	+	0.996536i	$0.526502\pi$
$108$	12.5561	1.20821
$109$	−1.62024	−0.155191	−0.0775954	−	0.996985i	$-0.524724\pi$
$109$	−1.62024	−0.155191	−0.0775954	+	0.996985i	$0.524724\pi$
$110$	8.07726	0.770136
$111$	−8.73299	−0.828898
$112$	−47.3484	−4.47400
$113$	−19.9766	−1.87924	−0.939621	−	0.342218i	$-0.888822\pi$
$113$	−19.9766	−1.87924	−0.939621	+	0.342218i	$0.888822\pi$
$114$	−2.51902	−0.235928
$115$	−14.8529	−1.38504
$116$	−17.5108	−1.62584
$117$	−2.79791	−0.258667
$118$	−29.8409	−2.74708
$119$	16.2328	1.48806
$120$	33.0171	3.01404
$121$	−7.62903	−0.693548
$122$	−16.1517	−1.46231
$123$	4.96671	0.447833
$124$	53.1384	4.77197
$125$	−11.9488	−1.06873
$126$	17.7449	1.58084
$127$	−13.8786	−1.23152	−0.615761	−	0.787933i	$-0.711151\pi$
$127$	−13.8786	−1.23152	−0.615761	+	0.787933i	$0.711151\pi$
$128$	−30.9573	−2.73627
$129$	1.06663	0.0939117
$130$	6.31330	0.553713
$131$	−6.17396	−0.539421	−0.269711	−	0.962941i	$-0.586928\pi$
$131$	−6.17396	−0.539421	−0.269711	+	0.962941i	$0.586928\pi$
$132$	21.9489	1.91041
$133$	1.39761	0.121188
$134$	−9.95733	−0.860182
$135$	3.78584	0.325833
$136$	44.3625	3.80405
$137$	11.5176	0.984018	0.492009	−	0.870590i	$-0.336263\pi$
$137$	11.5176	0.984018	0.492009	+	0.870590i	$0.336263\pi$
$138$	−55.3835	−4.71456
$139$	−9.05668	−0.768178	−0.384089	−	0.923296i	$-0.625484\pi$
$139$	−9.05668	−0.768178	−0.384089	+	0.923296i	$0.625484\pi$
$140$	−29.1793	−2.46610
$141$	−25.1511	−2.11810
$142$	−44.4197	−3.72762
$143$	2.63480	0.220333
$144$	27.5419	2.29516
$145$	−5.27976	−0.438460
$146$	−9.78048	−0.809438
$147$	−9.42070	−0.777006
$148$	21.0921	1.73376
$149$	3.92155	0.321266	0.160633	−	0.987014i	$-0.448646\pi$
$149$	3.92155	0.321266	0.160633	+	0.987014i	$0.448646\pi$
$150$	−14.3486	−1.17156
$151$	4.06832	0.331075	0.165538	−	0.986203i	$-0.447064\pi$
$151$	4.06832	0.331075	0.165538	+	0.986203i	$0.447064\pi$
$152$	3.81950	0.309803
$153$	−9.44241	−0.763374
$154$	−16.7104	−1.34656
$155$	16.0219	1.28691
$156$	17.1556	1.37355
$157$	−17.4236	−1.39055	−0.695276	−	0.718742i	$-0.744718\pi$
$157$	−17.4236	−1.39055	−0.695276	+	0.718742i	$0.744718\pi$
$158$	10.4079	0.828011
$159$	−8.47220	−0.671889
$160$	−32.4653	−2.56661
$161$	30.7280	2.42171
$162$	29.9991	2.35695
$163$	13.9632	1.09368	0.546842	−	0.837236i	$-0.315830\pi$
$163$	13.9632	1.09368	0.546842	+	0.837236i	$0.315830\pi$
$164$	−11.9957	−0.936708
$165$	6.61789	0.515202
$166$	−8.47340	−0.657664
$167$	9.04466	0.699897	0.349948	−	0.936769i	$-0.386199\pi$
$167$	9.04466	0.699897	0.349948	+	0.936769i	$0.386199\pi$
$168$	−68.3063	−5.26995
$169$	−10.9406	−0.841585
$170$	21.3062	1.63411
$171$	−0.812969	−0.0621693
$172$	−2.57616	−0.196430
$173$	−11.6208	−0.883516	−0.441758	−	0.897134i	$-0.645645\pi$
$173$	−11.6208	−0.883516	−0.441758	+	0.897134i	$0.645645\pi$
$174$	−19.6871	−1.49248
$175$	7.96093	0.601790
$176$	−25.9363	−1.95502
$177$	−24.4494	−1.83773
$178$	18.3141	1.37270
$179$	−15.7329	−1.17593	−0.587967	−	0.808885i	$-0.700072\pi$
$179$	−15.7329	−1.17593	−0.587967	+	0.808885i	$0.700072\pi$
$180$	16.9732	1.26511
$181$	23.7666	1.76655	0.883277	−	0.468851i	$-0.155332\pi$
$181$	23.7666	1.76655	0.883277	+	0.468851i	$0.155332\pi$
$182$	−13.0611	−0.968151
$183$	−13.2335	−0.978247
$184$	83.9761	6.19080
$185$	6.35957	0.467565
$186$	59.7425	4.38053
$187$	8.89193	0.650243
$188$	60.7455	4.43032
$189$	−7.83221	−0.569710
$190$	1.83441	0.133082
$191$	14.6839	1.06249	0.531244	−	0.847219i	$-0.321725\pi$
$191$	14.6839	1.06249	0.531244	+	0.847219i	$0.321725\pi$
$192$	−58.2003	−4.20024
$193$	−11.6520	−0.838730	−0.419365	−	0.907818i	$-0.637747\pi$
$193$	−11.6520	−0.838730	−0.419365	+	0.907818i	$0.637747\pi$
$194$	−40.1305	−2.88120
$195$	5.17264	0.370421
$196$	22.7531	1.62522
$197$	2.55586	0.182098	0.0910489	−	0.995846i	$-0.470978\pi$
$197$	2.55586	0.182098	0.0910489	+	0.995846i	$0.470978\pi$
$198$	9.72018	0.690783
$199$	−10.4903	−0.743640	−0.371820	−	0.928305i	$-0.621266\pi$
$199$	−10.4903	−0.743640	−0.371820	+	0.928305i	$0.621266\pi$
$200$	21.7563	1.53840
$201$	−8.15828	−0.575441
$202$	−9.88407	−0.695441
$203$	10.9229	0.766634
$204$	57.8967	4.05358
$205$	−3.61687	−0.252613
$206$	−36.3370	−2.53172
$207$	−17.8741	−1.24233
$208$	−20.2722	−1.40562
$209$	0.765575	0.0529559
$210$	−32.8058	−2.26382
$211$	5.61649	0.386655	0.193328	−	0.981134i	$-0.438072\pi$
$211$	5.61649	0.386655	0.193328	+	0.981134i	$0.438072\pi$
$212$	20.4623	1.40536
$213$	−36.3941	−2.49368
$214$	4.67181	0.319358
$215$	−0.776747	−0.0529737
$216$	−21.4045	−1.45639
$217$	−33.1465	−2.25013
$218$	4.39959	0.297978
$219$	−8.01338	−0.541494
$220$	−15.9837	−1.07762
$221$	6.95007	0.467512
$222$	23.7135	1.59155
$223$	15.4064	1.03169	0.515843	−	0.856683i	$-0.327479\pi$
$223$	15.4064	1.03169	0.515843	+	0.856683i	$0.327479\pi$
$224$	67.1648	4.48764
$225$	−4.63076	−0.308717
$226$	54.2444	3.60828
$227$	−17.6775	−1.17330	−0.586648	−	0.809842i	$-0.699553\pi$
$227$	−17.6775	−1.17330	−0.586648	+	0.809842i	$0.699553\pi$
$228$	4.98477	0.330125
$229$	0.247917	0.0163828	0.00819142	−	0.999966i	$-0.497393\pi$
$229$	0.247917	0.0163828	0.00819142	+	0.999966i	$0.497393\pi$
$230$	40.3316	2.65939
$231$	−13.6912	−0.900815
$232$	29.8509	1.95981
$233$	8.47762	0.555388	0.277694	−	0.960670i	$-0.410430\pi$
$233$	8.47762	0.555388	0.277694	+	0.960670i	$0.410430\pi$
$234$	7.59744	0.496660
$235$	18.3156	1.19478
$236$	59.0509	3.84388
$237$	8.52748	0.553919
$238$	−44.0785	−2.85719
$239$	−4.33057	−0.280121	−0.140061	−	0.990143i	$-0.544730\pi$
$239$	−4.33057	−0.280121	−0.140061	+	0.990143i	$0.544730\pi$
$240$	−50.9181	−3.28675
$241$	11.5878	0.746437	0.373219	−	0.927743i	$-0.378254\pi$
$241$	11.5878	0.746437	0.373219	+	0.927743i	$0.378254\pi$
$242$	20.7158	1.33166
$243$	17.5688	1.12704
$244$	31.9618	2.04615
$245$	6.86038	0.438294
$246$	−13.4866	−0.859872
$247$	0.598385	0.0380743
$248$	−90.5854	−5.75218
$249$	−6.94246	−0.439961
$250$	32.4456	2.05204
$251$	11.1349	0.702831	0.351416	−	0.936220i	$-0.385700\pi$
$251$	11.1349	0.702831	0.351416	+	0.936220i	$0.385700\pi$
$252$	−35.1145	−2.21200
$253$	16.8320	1.05822
$254$	37.6857	2.36461
$255$	17.4567	1.09318
$256$	31.7416	1.98385
$257$	−25.3905	−1.58382	−0.791909	−	0.610640i	$-0.790912\pi$
$257$	−25.3905	−1.58382	−0.791909	+	0.610640i	$0.790912\pi$
$258$	−2.89633	−0.180317
$259$	−13.1568	−0.817522
$260$	−12.4931	−0.774789
$261$	−6.35367	−0.393282
$262$	16.7647	1.03573
$263$	−19.5055	−1.20276	−0.601381	−	0.798963i	$-0.705382\pi$
$263$	−19.5055	−1.20276	−0.601381	+	0.798963i	$0.705382\pi$
$264$	−37.4165	−2.30282
$265$	6.16966	0.378999
$266$	−3.79506	−0.232690
$267$	15.0052	0.918304
$268$	19.7041	1.20362
$269$	6.42360	0.391654	0.195827	−	0.980638i	$-0.437261\pi$
$269$	6.42360	0.391654	0.195827	+	0.980638i	$0.437261\pi$
$270$	−10.2801	−0.625624
$271$	15.5152	0.942483	0.471242	−	0.882004i	$-0.343806\pi$
$271$	15.5152	0.942483	0.471242	+	0.882004i	$0.343806\pi$
$272$	−68.4146	−4.14824
$273$	−10.7012	−0.647669
$274$	−31.2749	−1.88939
$275$	4.36079	0.262966
$276$	109.596	6.59690
$277$	31.5504	1.89568	0.947839	−	0.318750i	$-0.103263\pi$
$277$	31.5504	1.89568	0.947839	+	0.318750i	$0.103263\pi$
$278$	24.5925	1.47496
$279$	19.2808	1.15431
$280$	49.7423	2.97267
$281$	−23.7872	−1.41903	−0.709513	−	0.704693i	$-0.751085\pi$
$281$	−23.7872	−1.41903	−0.709513	+	0.704693i	$0.751085\pi$
$282$	68.2951	4.06691
$283$	9.66868	0.574743	0.287372	−	0.957819i	$-0.407219\pi$
$283$	9.66868	0.574743	0.287372	+	0.957819i	$0.407219\pi$
$284$	87.9001	5.21591
$285$	1.50298	0.0890287
$286$	−7.15452	−0.423056
$287$	7.48265	0.441687
$288$	−39.0688	−2.30215
$289$	6.45512	0.379713
$290$	14.3366	0.841876
$291$	−32.8799	−1.92745
$292$	19.3541	1.13262
$293$	20.4815	1.19654	0.598270	−	0.801295i	$-0.295855\pi$
$293$	20.4815	1.19654	0.598270	+	0.801295i	$0.295855\pi$
$294$	25.5809	1.49191
$295$	17.8046	1.03663
$296$	−35.9560	−2.08990
$297$	−4.29029	−0.248948
$298$	−10.6486	−0.616854
$299$	13.1562	0.760841
$300$	28.3938	1.63932
$301$	1.60695	0.0926228
$302$	−11.0471	−0.635689
$303$	−8.09826	−0.465233
$304$	−5.89034	−0.337834
$305$	9.63693	0.551809
$306$	25.6399	1.46573
$307$	25.5342	1.45732	0.728658	−	0.684878i	$-0.240144\pi$
$307$	25.5342	1.45732	0.728658	+	0.684878i	$0.240144\pi$
$308$	33.0674	1.88419
$309$	−29.7718	−1.69366
$310$	−43.5059	−2.47097
$311$	−11.8326	−0.670967	−0.335483	−	0.942046i	$-0.608900\pi$
$311$	−11.8326	−0.670967	−0.335483	+	0.942046i	$0.608900\pi$
$312$	−29.2453	−1.65569
$313$	4.72490	0.267067	0.133534	−	0.991044i	$-0.457368\pi$
$313$	4.72490	0.267067	0.133534	+	0.991044i	$0.457368\pi$
$314$	47.3119	2.66996
$315$	−10.5875	−0.596537
$316$	−20.5958	−1.15860
$317$	−18.6454	−1.04723	−0.523615	−	0.851955i	$-0.675417\pi$
$317$	−18.6454	−1.04723	−0.523615	+	0.851955i	$0.675417\pi$
$318$	23.0054	1.29008
$319$	5.98326	0.334998
$320$	42.3828	2.36927
$321$	3.82773	0.213643
$322$	−83.4387	−4.64986
$323$	2.01943	0.112364
$324$	−59.3638	−3.29799
$325$	3.40846	0.189067
$326$	−37.9157	−2.09995
$327$	3.60469	0.199340
$328$	20.4492	1.12912
$329$	−37.8916	−2.08903
$330$	−17.9702	−0.989226
$331$	−14.3928	−0.791098	−0.395549	−	0.918445i	$-0.629446\pi$
$331$	−14.3928	−0.791098	−0.395549	+	0.918445i	$0.629446\pi$
$332$	16.7676	0.920243
$333$	7.65311	0.419388
$334$	−24.5598	−1.34385
$335$	5.94105	0.324594
$336$	105.340	5.74678
$337$	−14.7464	−0.803287	−0.401643	−	0.915796i	$-0.631561\pi$
$337$	−14.7464	−0.803287	−0.401643	+	0.915796i	$0.631561\pi$
$338$	29.7080	1.61590
$339$	44.4437	2.41385
$340$	−42.1618	−2.28654
$341$	−18.1568	−0.983245
$342$	2.20753	0.119370
$343$	9.26959	0.500511
$344$	4.39160	0.236779
$345$	33.0447	1.77906
$346$	31.5552	1.69642
$347$	31.7457	1.70420	0.852098	−	0.523382i	$-0.175330\pi$
$347$	31.7457	1.70420	0.852098	+	0.523382i	$0.175330\pi$
$348$	38.9579	2.08836
$349$	2.28861	0.122507	0.0612533	−	0.998122i	$-0.480490\pi$
$349$	2.28861	0.122507	0.0612533	+	0.998122i	$0.480490\pi$
$350$	−21.6171	−1.15548
$351$	−3.35335	−0.178989
$352$	36.7912	1.96098
$353$	−25.1345	−1.33777	−0.668887	−	0.743364i	$-0.733229\pi$
$353$	−25.1345	−1.33777	−0.668887	+	0.743364i	$0.733229\pi$
$354$	66.3898	3.52858
$355$	26.5031	1.40664
$356$	−36.2410	−1.92077
$357$	−36.1146	−1.91139
$358$	42.7211	2.25788
$359$	−30.2082	−1.59433	−0.797164	−	0.603763i	$-0.793667\pi$
$359$	−30.2082	−1.59433	−0.797164	+	0.603763i	$0.793667\pi$
$360$	−28.9344	−1.52498
$361$	−18.8261	−0.990849
$362$	−64.5356	−3.39192
$363$	16.9730	0.890850
$364$	25.8459	1.35470
$365$	5.83554	0.305446
$366$	35.9341	1.87831
$367$	12.9667	0.676858	0.338429	−	0.940992i	$-0.390105\pi$
$367$	12.9667	0.676858	0.338429	+	0.940992i	$0.390105\pi$
$368$	−129.506	−6.75095
$369$	−4.35255	−0.226585
$370$	−17.2687	−0.897759
$371$	−12.7639	−0.662668
$372$	−118.222	−6.12951
$373$	−6.16098	−0.319003	−0.159502	−	0.987198i	$-0.550989\pi$
$373$	−6.16098	−0.319003	−0.159502	+	0.987198i	$0.550989\pi$
$374$	−24.1451	−1.24851
$375$	26.5835	1.37277
$376$	−103.553	−5.34036
$377$	4.67661	0.240857
$378$	21.2675	1.09388
$379$	−11.6135	−0.596543	−0.298272	−	0.954481i	$-0.596410\pi$
$379$	−11.6135	−0.596543	−0.298272	+	0.954481i	$0.596410\pi$
$380$	−3.63003	−0.186217
$381$	30.8768	1.58187
$382$	−39.8725	−2.04006
$383$	0.575213	0.0293920	0.0146960	−	0.999892i	$-0.495322\pi$
$383$	0.575213	0.0293920	0.0146960	+	0.999892i	$0.495322\pi$
$384$	68.8735	3.51469
$385$	9.97026	0.508131
$386$	31.6398	1.61042
$387$	−0.934738	−0.0475154
$388$	79.4124	4.03156
$389$	−1.83871	−0.0932262	−0.0466131	−	0.998913i	$-0.514843\pi$
$389$	−1.83871	−0.0932262	−0.0466131	+	0.998913i	$0.514843\pi$
$390$	−14.0458	−0.711235
$391$	44.3995	2.24538
$392$	−38.7875	−1.95906
$393$	13.7358	0.692877
$394$	−6.94018	−0.349641
$395$	−6.20991	−0.312455
$396$	−19.2348	−0.966586
$397$	15.7190	0.788915	0.394457	−	0.918914i	$-0.370933\pi$
$397$	15.7190	0.788915	0.394457	+	0.918914i	$0.370933\pi$
$398$	28.4854	1.42784
$399$	−3.10938	−0.155664
$400$	−33.5520	−1.67760
$401$	25.0525	1.25106	0.625530	−	0.780200i	$-0.284883\pi$
$401$	25.0525	1.25106	0.625530	+	0.780200i	$0.284883\pi$
$402$	22.1530	1.10489
$403$	−14.1916	−0.706935
$404$	19.5591	0.973103
$405$	−17.8990	−0.889408
$406$	−29.6599	−1.47199
$407$	−7.20695	−0.357235
$408$	−98.6971	−4.88623
$409$	3.09292	0.152935	0.0764676	−	0.997072i	$-0.475636\pi$
$409$	3.09292	0.152935	0.0764676	+	0.997072i	$0.475636\pi$
$410$	9.82124	0.485036
$411$	−25.6243	−1.26395
$412$	71.9056	3.54253
$413$	−36.8345	−1.81251
$414$	48.5351	2.38537
$415$	5.05567	0.248173
$416$	28.7566	1.40991
$417$	20.1492	0.986711
$418$	−2.07884	−0.101679
$419$	−18.8457	−0.920671	−0.460336	−	0.887745i	$-0.652271\pi$
$419$	−18.8457	−0.920671	−0.460336	+	0.887745i	$0.652271\pi$
$420$	64.9179	3.16767
$421$	29.4620	1.43589	0.717944	−	0.696101i	$-0.245083\pi$
$421$	29.4620	1.43589	0.717944	+	0.696101i	$0.245083\pi$
$422$	−15.2510	−0.742407
$423$	22.0410	1.07167
$424$	−34.8822	−1.69403
$425$	11.5029	0.557972
$426$	98.8244	4.78806
$427$	−19.9370	−0.964821
$428$	−9.24483	−0.446866
$429$	−5.86187	−0.283014
$430$	2.10917	0.101713
$431$	−38.5591	−1.85733	−0.928663	−	0.370924i	$-0.879041\pi$
$431$	−38.5591	−1.85733	−0.928663	+	0.370924i	$0.879041\pi$
$432$	33.0095	1.58817
$433$	−13.4459	−0.646168	−0.323084	−	0.946370i	$-0.604720\pi$
$433$	−13.4459	−0.646168	−0.323084	+	0.946370i	$0.604720\pi$
$434$	90.0057	4.32041
$435$	11.7463	0.563194
$436$	−8.70614	−0.416948
$437$	3.82269	0.182864
$438$	21.7595	1.03971
$439$	29.5229	1.40905	0.704527	−	0.709678i	$-0.251159\pi$
$439$	29.5229	1.40905	0.704527	+	0.709678i	$0.251159\pi$
$440$	27.2476	1.29898
$441$	8.25579	0.393133
$442$	−18.8722	−0.897658
$443$	1.56706	0.0744532	0.0372266	−	0.999307i	$-0.488148\pi$
$443$	1.56706	0.0744532	0.0372266	+	0.999307i	$0.488148\pi$
$444$	−46.9256	−2.22699
$445$	−10.9271	−0.517996
$446$	−41.8343	−1.98091
$447$	−8.72462	−0.412660
$448$	−87.6822	−4.14260
$449$	−0.800559	−0.0377807	−0.0188904	−	0.999822i	$-0.506013\pi$
$449$	−0.800559	−0.0377807	−0.0188904	+	0.999822i	$0.506013\pi$
$450$	12.5743	0.592760
$451$	4.09880	0.193005
$452$	−107.342	−5.04893
$453$	−9.05115	−0.425260
$454$	48.0014	2.25282
$455$	7.79290	0.365337
$456$	−8.49759	−0.397936
$457$	−21.7763	−1.01865	−0.509327	−	0.860573i	$-0.670106\pi$
$457$	−21.7763	−1.01865	−0.509327	+	0.860573i	$0.670106\pi$
$458$	−0.673193	−0.0314563
$459$	−11.3169	−0.528228
$460$	−79.8103	−3.72118
$461$	−15.8510	−0.738253	−0.369126	−	0.929379i	$-0.620343\pi$
$461$	−15.8510	−0.738253	−0.369126	+	0.929379i	$0.620343\pi$
$462$	37.1770	1.72963
$463$	−22.2671	−1.03484	−0.517421	−	0.855731i	$-0.673108\pi$
$463$	−22.2671	−1.03484	−0.517421	+	0.855731i	$0.673108\pi$
$464$	−46.0353	−2.13713
$465$	−35.6454	−1.65302
$466$	−23.0201	−1.06639
$467$	38.1731	1.76644	0.883220	−	0.468959i	$-0.155371\pi$
$467$	38.1731	1.76644	0.883220	+	0.468959i	$0.155371\pi$
$468$	−15.0342	−0.694957
$469$	−12.2909	−0.567543
$470$	−49.7341	−2.29406
$471$	38.7638	1.78614
$472$	−100.665	−4.63346
$473$	0.880244	0.0404737
$474$	−23.1555	−1.06357
$475$	0.990372	0.0454414
$476$	87.2250	3.99795
$477$	7.42458	0.339948
$478$	11.7592	0.537853
$479$	19.1868	0.876665	0.438333	−	0.898813i	$-0.355569\pi$
$479$	19.1868	0.876665	0.438333	+	0.898813i	$0.355569\pi$
$480$	72.2285	3.29677
$481$	−5.63306	−0.256845
$482$	−31.4655	−1.43321
$483$	−68.3633	−3.11064
$484$	−40.9936	−1.86335
$485$	23.9439	1.08724
$486$	−47.7062	−2.16400
$487$	−15.2967	−0.693161	−0.346580	−	0.938020i	$-0.612657\pi$
$487$	−15.2967	−0.693161	−0.346580	+	0.938020i	$0.612657\pi$
$488$	−54.4856	−2.46645
$489$	−31.0652	−1.40482
$490$	−18.6286	−0.841556
$491$	−7.07154	−0.319134	−0.159567	−	0.987187i	$-0.551010\pi$
$491$	−7.07154	−0.319134	−0.159567	+	0.987187i	$0.551010\pi$
$492$	26.6879	1.20319
$493$	15.7826	0.710814
$494$	−1.62485	−0.0731055
$495$	−5.79956	−0.260671
$496$	139.698	6.27265
$497$	−54.8300	−2.45946
$498$	18.8515	0.844757
$499$	−6.00874	−0.268988	−0.134494	−	0.990914i	$-0.542941\pi$
$499$	−6.00874	−0.268988	−0.134494	+	0.990914i	$0.542941\pi$
$500$	−64.2052	−2.87134
$501$	−20.1225	−0.899005
$502$	−30.2358	−1.34949
$503$	−10.9091	−0.486414	−0.243207	−	0.969974i	$-0.578199\pi$
$503$	−10.9091	−0.486414	−0.243207	+	0.969974i	$0.578199\pi$
$504$	59.8599	2.66637
$505$	5.89734	0.262428
$506$	−45.7056	−2.03186
$507$	24.3405	1.08100
$508$	−74.5746	−3.30871
$509$	−14.6974	−0.651452	−0.325726	−	0.945464i	$-0.605609\pi$
$509$	−14.6974	−0.651452	−0.325726	+	0.945464i	$0.605609\pi$
$510$	−47.4017	−2.09898
$511$	−12.0727	−0.534063
$512$	−24.2763	−1.07287
$513$	−0.974360	−0.0430190
$514$	68.9453	3.04105
$515$	21.6805	0.955358
$516$	5.73141	0.252311
$517$	−20.7561	−0.912851
$518$	35.7258	1.56970
$519$	25.8539	1.13486
$520$	21.2971	0.933940
$521$	−5.93100	−0.259842	−0.129921	−	0.991524i	$-0.541472\pi$
$521$	−5.93100	−0.259842	−0.129921	+	0.991524i	$0.541472\pi$
$522$	17.2527	0.755131
$523$	3.52394	0.154091	0.0770455	−	0.997028i	$-0.475451\pi$
$523$	3.52394	0.154091	0.0770455	+	0.997028i	$0.475451\pi$
$524$	−33.1750	−1.44925
$525$	−17.7114	−0.772988
$526$	52.9652	2.30939
$527$	−47.8939	−2.08629
$528$	57.7027	2.51119
$529$	61.0462	2.65418
$530$	−16.7531	−0.727706
$531$	21.4261	0.929815
$532$	7.50987	0.325594
$533$	3.20369	0.138767
$534$	−40.7451	−1.76321
$535$	−2.78744	−0.120512
$536$	−33.5897	−1.45086
$537$	35.0024	1.51047
$538$	−17.4426	−0.752004
$539$	−7.77449	−0.334871
$540$	20.3427	0.875412
$541$	2.79564	0.120194	0.0600969	−	0.998193i	$-0.480859\pi$
$541$	2.79564	0.120194	0.0600969	+	0.998193i	$0.480859\pi$
$542$	−42.1300	−1.80964
$543$	−52.8756	−2.26911
$544$	97.0477	4.16089
$545$	−2.62502	−0.112443
$546$	29.0581	1.24357
$547$	−35.9057	−1.53522	−0.767609	−	0.640919i	$-0.778554\pi$
$547$	−35.9057	−1.53522	−0.767609	+	0.640919i	$0.778554\pi$
$548$	61.8885	2.64374
$549$	11.5971	0.494952
$550$	−11.8413	−0.504914
$551$	1.35885	0.0578889
$552$	−186.829	−7.95197
$553$	12.8472	0.546317
$554$	−85.6717	−3.63984
$555$	−14.1487	−0.600579
$556$	−48.6649	−2.06385
$557$	21.0210	0.890687	0.445344	−	0.895360i	$-0.353082\pi$
$557$	21.0210	0.890687	0.445344	+	0.895360i	$0.353082\pi$
$558$	−52.3551	−2.21637
$559$	0.688012	0.0290998
$560$	−76.7112	−3.24164
$561$	−19.7827	−0.835225
$562$	64.5916	2.72463
$563$	−14.2142	−0.599058	−0.299529	−	0.954087i	$-0.596830\pi$
$563$	−14.2142	−0.599058	−0.299529	+	0.954087i	$0.596830\pi$
$564$	−135.146	−5.69067
$565$	−32.3650	−1.36160
$566$	−26.2543	−1.10355
$567$	37.0297	1.55510
$568$	−149.844	−6.28731
$569$	−20.0583	−0.840887	−0.420443	−	0.907319i	$-0.638125\pi$
$569$	−20.0583	−0.840887	−0.420443	+	0.907319i	$0.638125\pi$
$570$	−4.08118	−0.170942
$571$	−27.5299	−1.15209	−0.576044	−	0.817418i	$-0.695405\pi$
$571$	−27.5299	−1.15209	−0.576044	+	0.817418i	$0.695405\pi$
$572$	14.1577	0.591965
$573$	−32.6685	−1.36475
$574$	−20.3183	−0.848071
$575$	21.7745	0.908057
$576$	51.0035	2.12515
$577$	−37.5794	−1.56445	−0.782226	−	0.622995i	$-0.785916\pi$
$577$	−37.5794	−1.56445	−0.782226	+	0.622995i	$0.785916\pi$
$578$	−17.5282	−0.729077
$579$	25.9233	1.07733
$580$	−28.3701	−1.17800
$581$	−10.4592	−0.433923
$582$	89.2819	3.70086
$583$	−6.99174	−0.289568
$584$	−32.9932	−1.36527
$585$	−4.53302	−0.187417
$586$	−55.6152	−2.29744
$587$	41.5927	1.71671	0.858357	−	0.513053i	$-0.171485\pi$
$587$	41.5927	1.71671	0.858357	+	0.513053i	$0.171485\pi$
$588$	−50.6209	−2.08757
$589$	−4.12356	−0.169908
$590$	−48.3466	−1.99040
$591$	−5.68626	−0.233901
$592$	55.4503	2.27899
$593$	−27.3231	−1.12202	−0.561012	−	0.827808i	$-0.689588\pi$
$593$	−27.3231	−1.12202	−0.561012	+	0.827808i	$0.689588\pi$
$594$	11.6498	0.477998
$595$	26.2995	1.07818
$596$	21.0719	0.863140
$597$	23.3388	0.955193
$598$	−35.7242	−1.46087
$599$	26.9991	1.10315	0.551576	−	0.834124i	$-0.314026\pi$
$599$	26.9991	1.10315	0.551576	+	0.834124i	$0.314026\pi$
$600$	−48.4032	−1.97605
$601$	16.5630	0.675620	0.337810	−	0.941214i	$-0.390314\pi$
$601$	16.5630	0.675620	0.337810	+	0.941214i	$0.390314\pi$
$602$	−4.36349	−0.177843
$603$	7.14947	0.291149
$604$	21.8606	0.889494
$605$	−12.3601	−0.502511
$606$	21.9900	0.893282
$607$	15.6768	0.636301	0.318151	−	0.948040i	$-0.396938\pi$
$607$	15.6768	0.636301	0.318151	+	0.948040i	$0.396938\pi$
$608$	8.35558	0.338864
$609$	−24.3010	−0.984728
$610$	−26.1681	−1.05951
$611$	−16.2233	−0.656323
$612$	−50.7376	−2.05094
$613$	39.8942	1.61131	0.805656	−	0.592383i	$-0.201813\pi$
$613$	39.8942	1.61131	0.805656	+	0.592383i	$0.201813\pi$
$614$	−69.3355	−2.79815
$615$	8.04678	0.324477
$616$	−56.3702	−2.27122
$617$	−26.9867	−1.08644	−0.543221	−	0.839590i	$-0.682795\pi$
$617$	−26.9867	−1.08644	−0.543221	+	0.839590i	$0.682795\pi$
$618$	80.8421	3.25195
$619$	18.0716	0.726358	0.363179	−	0.931719i	$-0.381691\pi$
$619$	18.0716	0.726358	0.363179	+	0.931719i	$0.381691\pi$
$620$	86.0918	3.45753
$621$	−21.4224	−0.859651
$622$	32.1302	1.28831
$623$	22.6063	0.905701
$624$	45.1013	1.80550
$625$	−7.48306	−0.299322
$626$	−12.8300	−0.512788
$627$	−1.70324	−0.0680209
$628$	−93.6233	−3.73598
$629$	−19.0105	−0.757997
$630$	28.7492	1.14540
$631$	−34.6215	−1.37826	−0.689130	−	0.724638i	$-0.742007\pi$
$631$	−34.6215	−1.37826	−0.689130	+	0.724638i	$0.742007\pi$
$632$	35.1098	1.39659
$633$	−12.4955	−0.496652
$634$	50.6296	2.01076
$635$	−22.4852	−0.892300
$636$	−45.5243	−1.80515
$637$	−6.07666	−0.240766
$638$	−16.2469	−0.643221
$639$	31.8938	1.26170
$640$	−50.1553	−1.98256
$641$	−28.8489	−1.13946	−0.569732	−	0.821831i	$-0.692953\pi$
$641$	−28.8489	−1.13946	−0.569732	+	0.821831i	$0.692953\pi$
$642$	−10.3938	−0.410210
$643$	−3.27993	−0.129348	−0.0646739	−	0.997906i	$-0.520601\pi$
$643$	−3.27993	−0.129348	−0.0646739	+	0.997906i	$0.520601\pi$
$644$	165.113	6.50636
$645$	1.72810	0.0680437
$646$	−5.48355	−0.215747
$647$	39.3445	1.54679	0.773397	−	0.633922i	$-0.218556\pi$
$647$	39.3445	1.54679	0.773397	+	0.633922i	$0.218556\pi$
$648$	101.198	3.97543
$649$	−20.1770	−0.792017
$650$	−9.25532	−0.363024
$651$	73.7438	2.89025
$652$	75.0295	2.93838
$653$	−21.0737	−0.824678	−0.412339	−	0.911031i	$-0.635288\pi$
$653$	−21.0737	−0.824678	−0.412339	+	0.911031i	$0.635288\pi$
$654$	−9.78815	−0.382747
$655$	−10.0027	−0.390838
$656$	−31.5362	−1.23128
$657$	7.02249	0.273974
$658$	102.891	4.01110
$659$	0.260684	0.0101548	0.00507741	−	0.999987i	$-0.498384\pi$
$659$	0.260684	0.0101548	0.00507741	+	0.999987i	$0.498384\pi$
$660$	35.5604	1.38419
$661$	22.6028	0.879148	0.439574	−	0.898206i	$-0.355129\pi$
$661$	22.6028	0.879148	0.439574	+	0.898206i	$0.355129\pi$
$662$	39.0821	1.51897
$663$	−15.4624	−0.600511
$664$	−28.5839	−1.10927
$665$	2.26433	0.0878068
$666$	−20.7812	−0.805256
$667$	29.8758	1.15680
$668$	48.6003	1.88040
$669$	−34.2759	−1.32518
$670$	−16.1323	−0.623245
$671$	−10.9210	−0.421601
$672$	−149.428	−5.76429
$673$	−2.68919	−0.103661	−0.0518303	−	0.998656i	$-0.516505\pi$
$673$	−2.68919	−0.103661	−0.0518303	+	0.998656i	$0.516505\pi$
$674$	40.0423	1.54237
$675$	−5.55005	−0.213622
$676$	−58.7879	−2.26107
$677$	−40.8389	−1.56957	−0.784784	−	0.619769i	$-0.787226\pi$
$677$	−40.8389	−1.56957	−0.784784	+	0.619769i	$0.787226\pi$
$678$	−120.682	−4.63477
$679$	−49.5356	−1.90100
$680$	71.8735	2.75622
$681$	39.3287	1.50708
$682$	49.3028	1.88790
$683$	−21.5078	−0.822971	−0.411486	−	0.911416i	$-0.634990\pi$
$683$	−21.5078	−0.822971	−0.411486	+	0.911416i	$0.634990\pi$
$684$	−4.36838	−0.167029
$685$	18.6602	0.712970
$686$	−25.1706	−0.961018
$687$	−0.551563	−0.0210435
$688$	−6.77261	−0.258203
$689$	−5.46485	−0.208194
$690$	−89.7293	−3.41594
$691$	−5.34923	−0.203494	−0.101747	−	0.994810i	$-0.532443\pi$
$691$	−5.34923	−0.203494	−0.101747	+	0.994810i	$0.532443\pi$
$692$	−62.4430	−2.37373
$693$	11.9982	0.455775
$694$	−86.2020	−3.27218
$695$	−14.6731	−0.556583
$696$	−66.4119	−2.51734
$697$	10.8118	0.409527
$698$	−6.21449	−0.235222
$699$	−18.8609	−0.713385
$700$	42.7770	1.61682
$701$	51.0379	1.92768	0.963838	−	0.266489i	$-0.0858637\pi$
$701$	51.0379	1.92768	0.963838	+	0.266489i	$0.0858637\pi$
$702$	9.10568	0.343672
$703$	−1.63676	−0.0617315
$704$	−48.0301	−1.81020
$705$	−40.7483	−1.53467
$706$	68.2500	2.56862
$707$	−12.2005	−0.458848
$708$	−131.376	−4.93740
$709$	24.4681	0.918920	0.459460	−	0.888198i	$-0.348043\pi$
$709$	24.4681	0.918920	0.459460	+	0.888198i	$0.348043\pi$
$710$	−71.9663	−2.70085
$711$	−7.47302	−0.280260
$712$	61.7803	2.31531
$713$	−90.6610	−3.39528
$714$	98.0654	3.67001
$715$	4.26875	0.159642
$716$	−84.5388	−3.15936
$717$	9.63459	0.359811
$718$	82.0272	3.06123
$719$	−43.0952	−1.60718	−0.803590	−	0.595183i	$-0.797079\pi$
$719$	−43.0952	−1.60718	−0.803590	+	0.595183i	$0.797079\pi$
$720$	44.6218	1.66296
$721$	−44.8530	−1.67041
$722$	51.1204	1.90250
$723$	−25.7804	−0.958785
$724$	127.707	4.74618
$725$	7.74014	0.287462
$726$	−46.0883	−1.71050
$727$	−1.46902	−0.0544828	−0.0272414	−	0.999629i	$-0.508672\pi$
$727$	−1.46902	−0.0544828	−0.0272414	+	0.999629i	$0.508672\pi$
$728$	−44.0598	−1.63296
$729$	−5.94347	−0.220129
$730$	−15.8458	−0.586479
$731$	2.32191	0.0858788
$732$	−71.1083	−2.62824
$733$	24.1383	0.891568	0.445784	−	0.895141i	$-0.352925\pi$
$733$	24.1383	0.891568	0.445784	+	0.895141i	$0.352925\pi$
$734$	−35.2098	−1.29962
$735$	−15.2629	−0.562980
$736$	183.707	6.77153
$737$	−6.73267	−0.248001
$738$	11.8189	0.435059
$739$	−23.7632	−0.874144	−0.437072	−	0.899427i	$-0.643984\pi$
$739$	−23.7632	−0.874144	−0.437072	+	0.899427i	$0.643984\pi$
$740$	34.1723	1.25620
$741$	−1.33128	−0.0489058
$742$	34.6590	1.27237
$743$	34.1661	1.25343	0.626717	−	0.779247i	$-0.284398\pi$
$743$	34.1661	1.25343	0.626717	+	0.779247i	$0.284398\pi$
$744$	201.533	7.38857
$745$	6.35347	0.232773
$746$	16.7295	0.612510
$747$	6.08400	0.222602
$748$	47.7796	1.74700
$749$	5.76670	0.210711
$750$	−72.1847	−2.63581
$751$	−27.7477	−1.01253	−0.506264	−	0.862378i	$-0.668974\pi$
$751$	−27.7477	−1.01253	−0.506264	+	0.862378i	$0.668974\pi$
$752$	159.697	5.82356
$753$	−24.7729	−0.902774
$754$	−12.6988	−0.462464
$755$	6.59126	0.239881
$756$	−42.0854	−1.53063
$757$	−28.9340	−1.05162	−0.525811	−	0.850601i	$-0.676238\pi$
$757$	−28.9340	−1.05162	−0.525811	+	0.850601i	$0.676238\pi$
$758$	31.5351	1.14541
$759$	−37.4477	−1.35927
$760$	6.18814	0.224468
$761$	−31.3936	−1.13802	−0.569008	−	0.822332i	$-0.692673\pi$
$761$	−31.3936	−1.13802	−0.569008	+	0.822332i	$0.692673\pi$
$762$	−83.8428	−3.03730
$763$	5.43068	0.196604
$764$	78.9019	2.85457
$765$	−15.2981	−0.553103
$766$	−1.56193	−0.0564349
$767$	−15.7707	−0.569446
$768$	−70.6183	−2.54822
$769$	−1.87620	−0.0676575	−0.0338287	−	0.999428i	$-0.510770\pi$
$769$	−1.87620	−0.0676575	−0.0338287	+	0.999428i	$0.510770\pi$
$770$	−27.0732	−0.975650
$771$	56.4885	2.03438
$772$	−62.6105	−2.25340
$773$	49.6083	1.78429	0.892144	−	0.451752i	$-0.149201\pi$
$773$	49.6083	1.78429	0.892144	+	0.451752i	$0.149201\pi$
$774$	2.53818	0.0912331
$775$	−23.4882	−0.843721
$776$	−135.375	−4.85968
$777$	29.2710	1.05009
$778$	4.99282	0.179001
$779$	0.930872	0.0333519
$780$	27.7945	0.995203
$781$	−30.0345	−1.07472
$782$	−120.562	−4.31129
$783$	−7.61499	−0.272138
$784$	59.8170	2.13632
$785$	−28.2287	−1.00753
$786$	−37.2980	−1.33037
$787$	−3.83721	−0.136782	−0.0683908	−	0.997659i	$-0.521786\pi$
$787$	−3.83721	−0.136782	−0.0683908	+	0.997659i	$0.521786\pi$
$788$	13.7336	0.489239
$789$	43.3956	1.54493
$790$	16.8624	0.599936
$791$	66.9572	2.38072
$792$	32.7898	1.16513
$793$	−8.53602	−0.303123
$794$	−42.6833	−1.51477
$795$	−13.7262	−0.486818
$796$	−56.3684	−1.99793
$797$	30.7864	1.09051	0.545256	−	0.838270i	$-0.316432\pi$
$797$	30.7864	1.09051	0.545256	+	0.838270i	$0.316432\pi$
$798$	8.44320	0.298886
$799$	−54.7503	−1.93693
$800$	47.5943	1.68271
$801$	−13.1497	−0.464623
$802$	−68.0273	−2.40213
$803$	−6.61309	−0.233371
$804$	−43.8374	−1.54603
$805$	49.7838	1.75465
$806$	38.5358	1.35737
$807$	−14.2912	−0.503072
$808$	−33.3426	−1.17299
$809$	9.56727	0.336367	0.168184	−	0.985756i	$-0.446210\pi$
$809$	9.56727	0.336367	0.168184	+	0.985756i	$0.446210\pi$
$810$	48.6028	1.70773
$811$	46.5494	1.63457	0.817285	−	0.576233i	$-0.195478\pi$
$811$	46.5494	1.63457	0.817285	+	0.576233i	$0.195478\pi$
$812$	58.6925	2.05970
$813$	−34.5181	−1.21060
$814$	19.5697	0.685918
$815$	22.6224	0.792429
$816$	152.208	5.32835
$817$	0.199911	0.00699399
$818$	−8.39851	−0.293647
$819$	9.37799	0.327693
$820$	−19.4348	−0.678692
$821$	1.28010	0.0446759	0.0223380	−	0.999750i	$-0.492889\pi$
$821$	1.28010	0.0446759	0.0223380	+	0.999750i	$0.492889\pi$
$822$	69.5801	2.42688
$823$	−31.3814	−1.09389	−0.546943	−	0.837170i	$-0.684209\pi$
$823$	−31.3814	−1.09389	−0.546943	+	0.837170i	$0.684209\pi$
$824$	−122.578	−4.27021
$825$	−9.70184	−0.337775
$826$	100.020	3.48015
$827$	−4.93442	−0.171586	−0.0857932	−	0.996313i	$-0.527342\pi$
$827$	−4.93442	−0.171586	−0.0857932	+	0.996313i	$0.527342\pi$
$828$	−96.0439	−3.33776
$829$	−28.6531	−0.995162	−0.497581	−	0.867418i	$-0.665778\pi$
$829$	−28.6531	−0.995162	−0.497581	+	0.867418i	$0.665778\pi$
$830$	−13.7281	−0.476510
$831$	−70.1929	−2.43496
$832$	−37.5411	−1.30150
$833$	−20.5075	−0.710544
$834$	−54.7130	−1.89456
$835$	14.6536	0.507110
$836$	4.11371	0.142276
$837$	23.1084	0.798745
$838$	51.1734	1.76776
$839$	−35.8204	−1.23666	−0.618329	−	0.785919i	$-0.712190\pi$
$839$	−35.8204	−1.23666	−0.618329	+	0.785919i	$0.712190\pi$
$840$	−110.666	−3.81834
$841$	−18.3801	−0.633796
$842$	−80.0008	−2.75701
$843$	52.9215	1.82271
$844$	30.1795	1.03882
$845$	−17.7253	−0.609770
$846$	−59.8501	−2.05769
$847$	25.5708	0.878624
$848$	53.7945	1.84731
$849$	−21.5108	−0.738248
$850$	−31.2349	−1.07135
$851$	−35.9860	−1.23358
$852$	−195.559	−6.69974
$853$	−30.3109	−1.03782	−0.518912	−	0.854828i	$-0.673663\pi$
$853$	−30.3109	−1.03782	−0.518912	+	0.854828i	$0.673663\pi$
$854$	54.1369	1.85253
$855$	−1.31713	−0.0450448
$856$	15.7597	0.538657
$857$	10.2524	0.350215	0.175108	−	0.984549i	$-0.443973\pi$
$857$	10.2524	0.350215	0.175108	+	0.984549i	$0.443973\pi$
$858$	15.9173	0.543407
$859$	40.2293	1.37261	0.686304	−	0.727315i	$-0.259232\pi$
$859$	40.2293	1.37261	0.686304	+	0.727315i	$0.259232\pi$
$860$	−4.17375	−0.142324
$861$	−16.6473	−0.567339
$862$	104.703	3.56620
$863$	28.8869	0.983321	0.491661	−	0.870787i	$-0.336390\pi$
$863$	28.8869	0.983321	0.491661	+	0.870787i	$0.336390\pi$
$864$	−46.8248	−1.59301
$865$	−18.8274	−0.640152
$866$	36.5109	1.24069
$867$	−14.3613	−0.487735
$868$	−178.108	−6.04538
$869$	7.03735	0.238726
$870$	−31.8960	−1.08137
$871$	−5.26236	−0.178308
$872$	14.8414	0.502594
$873$	28.8142	0.975212
$874$	−10.3801	−0.351113
$875$	40.0497	1.35393
$876$	−43.0589	−1.45482
$877$	−23.1006	−0.780053	−0.390027	−	0.920804i	$-0.627534\pi$
$877$	−23.1006	−0.780053	−0.390027	+	0.920804i	$0.627534\pi$
$878$	−80.1664	−2.70549
$879$	−45.5669	−1.53693
$880$	−42.0205	−1.41651
$881$	13.3891	0.451092	0.225546	−	0.974233i	$-0.427583\pi$
$881$	13.3891	0.451092	0.225546	+	0.974233i	$0.427583\pi$
$882$	−22.4177	−0.754844
$883$	46.1437	1.55286	0.776429	−	0.630204i	$-0.217029\pi$
$883$	46.1437	1.55286	0.776429	+	0.630204i	$0.217029\pi$
$884$	37.3453	1.25606
$885$	−39.6116	−1.33153
$886$	−4.25518	−0.142956
$887$	49.3016	1.65539	0.827694	−	0.561180i	$-0.189653\pi$
$887$	49.3016	1.65539	0.827694	+	0.561180i	$0.189653\pi$
$888$	79.9944	2.68444
$889$	46.5178	1.56016
$890$	29.6715	0.994592
$891$	20.2840	0.679538
$892$	82.7840	2.77181
$893$	−4.71387	−0.157744
$894$	23.6908	0.792338
$895$	−25.4896	−0.852023
$896$	103.762	3.46645
$897$	−29.2697	−0.977286
$898$	2.17383	0.0725417
$899$	−32.2272	−1.07484
$900$	−24.8828	−0.829426
$901$	−18.4428	−0.614418
$902$	−11.1299	−0.370584
$903$	−3.57512	−0.118972
$904$	182.986	6.08603
$905$	38.5052	1.27996
$906$	24.5774	0.816531
$907$	−20.5917	−0.683737	−0.341868	−	0.939748i	$-0.611060\pi$
$907$	−20.5917	−0.683737	−0.341868	+	0.939748i	$0.611060\pi$
$908$	−94.9877	−3.15228
$909$	7.09687	0.235388
$910$	−21.1608	−0.701474
$911$	12.5708	0.416491	0.208245	−	0.978077i	$-0.433225\pi$
$911$	12.5708	0.416491	0.208245	+	0.978077i	$0.433225\pi$
$912$	13.1048	0.433942
$913$	−5.72931	−0.189612
$914$	59.1314	1.95589
$915$	−21.4401	−0.708789
$916$	1.33215	0.0440155
$917$	20.6937	0.683368
$918$	30.7299	1.01424
$919$	3.58329	0.118202	0.0591009	−	0.998252i	$-0.481177\pi$
$919$	3.58329	0.118202	0.0591009	+	0.998252i	$0.481177\pi$
$920$	136.053	4.48555
$921$	−56.8083	−1.87190
$922$	43.0416	1.41750
$923$	−23.4754	−0.772702
$924$	−73.5679	−2.42020
$925$	−9.32314	−0.306543
$926$	60.4641	1.98697
$927$	26.0904	0.856920
$928$	65.3021	2.14365
$929$	−11.1432	−0.365598	−0.182799	−	0.983150i	$-0.558516\pi$
$929$	−11.1432	−0.365598	−0.182799	+	0.983150i	$0.558516\pi$
$930$	96.7914	3.17392
$931$	−1.76565	−0.0578669
$932$	45.5534	1.49215
$933$	26.3251	0.861845
$934$	−103.655	−3.39170
$935$	14.4062	0.471133
$936$	25.6290	0.837709
$937$	57.8717	1.89059	0.945293	−	0.326222i	$-0.105776\pi$
$937$	57.8717	1.89059	0.945293	+	0.326222i	$0.105776\pi$
$938$	33.3748	1.08973
$939$	−10.5119	−0.343043
$940$	98.4165	3.20999
$941$	0.635751	0.0207249	0.0103624	−	0.999946i	$-0.496701\pi$
$941$	0.635751	0.0207249	0.0103624	+	0.999946i	$0.496701\pi$
$942$	−105.259	−3.42952
$943$	20.4663	0.666473
$944$	155.242	5.05270
$945$	−12.6893	−0.412783
$946$	−2.39021	−0.0777125
$947$	−54.8993	−1.78399	−0.891993	−	0.452049i	$-0.850693\pi$
$947$	−54.8993	−1.78399	−0.891993	+	0.452049i	$0.850693\pi$
$948$	45.8213	1.48821
$949$	−5.16889	−0.167789
$950$	−2.68925	−0.0872508
$951$	41.4821	1.34515
$952$	−148.693	−4.81917
$953$	−15.8089	−0.512100	−0.256050	−	0.966664i	$-0.582421\pi$
$953$	−15.8089	−0.512100	−0.256050	+	0.966664i	$0.582421\pi$
$954$	−20.1607	−0.652725
$955$	23.7900	0.769826
$956$	−23.2697	−0.752597
$957$	−13.3115	−0.430299
$958$	−52.0996	−1.68326
$959$	−38.6046	−1.24661
$960$	−94.2928	−3.04329
$961$	66.7965	2.15473
$962$	15.2960	0.493162
$963$	−3.35441	−0.108094
$964$	62.2656	2.00544
$965$	−18.8779	−0.607702
$966$	185.633	5.97266
$967$	30.9167	0.994214	0.497107	−	0.867689i	$-0.334396\pi$
$967$	30.9167	0.994214	0.497107	+	0.867689i	$0.334396\pi$
$968$	69.8821	2.24610
$969$	−4.49281	−0.144330
$970$	−65.0172	−2.08758
$971$	−14.6729	−0.470877	−0.235438	−	0.971889i	$-0.575653\pi$
$971$	−14.6729	−0.470877	−0.235438	+	0.971889i	$0.575653\pi$
$972$	94.4036	3.02800
$973$	30.3560	0.973169
$974$	41.5367	1.33092
$975$	−7.58311	−0.242854
$976$	84.0263	2.68962
$977$	−17.7603	−0.568202	−0.284101	−	0.958794i	$-0.591695\pi$
$977$	−17.7603	−0.568202	−0.284101	+	0.958794i	$0.591695\pi$
$978$	84.3543	2.69735
$979$	12.3831	0.395767
$980$	36.8633	1.17756
$981$	−3.15895	−0.100858
$982$	19.2020	0.612761
$983$	8.86653	0.282798	0.141399	−	0.989953i	$-0.454840\pi$
$983$	8.86653	0.282798	0.141399	+	0.989953i	$0.454840\pi$
$984$	−45.4952	−1.45033
$985$	4.14087	0.131939
$986$	−42.8561	−1.36482
$987$	84.3008	2.68333
$988$	3.21534	0.102294
$989$	4.39526	0.139761
$990$	15.7481	0.500507
$991$	21.6771	0.688595	0.344297	−	0.938861i	$-0.388117\pi$
$991$	21.6771	0.688595	0.344297	+	0.938861i	$0.388117\pi$
$992$	−198.166	−6.29176
$993$	32.0209	1.01615
$994$	148.885	4.72235
$995$	−16.9959	−0.538805
$996$	−37.3044	−1.18204
$997$	37.1427	1.17632	0.588161	−	0.808744i	$-0.299852\pi$
$997$	37.1427	1.17632	0.588161	+	0.808744i	$0.299852\pi$
$998$	16.3161	0.516477
$999$	9.17240	0.290202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.b.1.10	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.b.1.10	✓	243	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71539 q^{2} -2.22479 q^{3} +5.37337 q^{4} +1.62014 q^{5} +6.04118 q^{6} -3.35178 q^{7} -9.16003 q^{8} +1.94968 q^{9} +O(q^{10})\)	\(q-2.71539 q^{2} -2.22479 q^{3} +5.37337 q^{4} +1.62014 q^{5} +6.04118 q^{6} -3.35178 q^{7} -9.16003 q^{8} +1.94968 q^{9} -4.39933 q^{10} -1.83602 q^{11} -11.9546 q^{12} -1.43506 q^{13} +9.10140 q^{14} -3.60448 q^{15} +14.1263 q^{16} -4.84305 q^{17} -5.29416 q^{18} -0.416975 q^{19} +8.70563 q^{20} +7.45700 q^{21} +4.98552 q^{22} -9.16767 q^{23} +20.3791 q^{24} -2.37513 q^{25} +3.89676 q^{26} +2.33673 q^{27} -18.0103 q^{28} -3.25882 q^{29} +9.78758 q^{30} +9.88921 q^{31} -20.0386 q^{32} +4.08476 q^{33} +13.1508 q^{34} -5.43036 q^{35} +10.4764 q^{36} +3.92531 q^{37} +1.13225 q^{38} +3.19271 q^{39} -14.8406 q^{40} -2.23244 q^{41} -20.2487 q^{42} -0.479431 q^{43} -9.86561 q^{44} +3.15877 q^{45} +24.8938 q^{46} +11.3049 q^{47} -31.4281 q^{48} +4.23443 q^{49} +6.44943 q^{50} +10.7748 q^{51} -7.71111 q^{52} +3.80809 q^{53} -6.34515 q^{54} -2.97462 q^{55} +30.7024 q^{56} +0.927681 q^{57} +8.84899 q^{58} +10.9895 q^{59} -19.3682 q^{60} +5.94819 q^{61} -26.8531 q^{62} -6.53491 q^{63} +26.1599 q^{64} -2.32500 q^{65} -11.0917 q^{66} +3.66699 q^{67} -26.0235 q^{68} +20.3961 q^{69} +14.7456 q^{70} +16.3585 q^{71} -17.8591 q^{72} +3.60186 q^{73} -10.6588 q^{74} +5.28417 q^{75} -2.24056 q^{76} +6.15393 q^{77} -8.66946 q^{78} -3.83294 q^{79} +22.8867 q^{80} -11.0478 q^{81} +6.06195 q^{82} +3.12051 q^{83} +40.0692 q^{84} -7.84643 q^{85} +1.30184 q^{86} +7.25019 q^{87} +16.8180 q^{88} -6.74456 q^{89} -8.57730 q^{90} +4.81001 q^{91} -49.2613 q^{92} -22.0014 q^{93} -30.6973 q^{94} -0.675560 q^{95} +44.5816 q^{96} +14.7789 q^{97} -11.4981 q^{98} -3.57966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9}+O(q^{10}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9	\( 243 q - 40 q^{2} - 27 q^{3} + 232 q^{4} - 85 q^{5} - 20 q^{6} - 28 q^{7} - 114 q^{8} + 210 q^{9} - 24 q^{10} - 37 q^{11} - 74 q^{12} - 113 q^{13} - 35 q^{14} - 34 q^{15} + 218 q^{16} - 125 q^{17} - 108 q^{18} - 46 q^{19} - 157 q^{20} - 113 q^{21} - 16 q^{22} - 60 q^{23} - 49 q^{24} + 208 q^{25} - 52 q^{26} - 90 q^{27} - 70 q^{28} - 137 q^{29} - 26 q^{30} - 36 q^{31} - 258 q^{32} - 153 q^{33} - 23 q^{34} - 77 q^{35} + 180 q^{36} - 108 q^{37} - 122 q^{38} - 32 q^{39} - 57 q^{40} - 186 q^{41} - 28 q^{42} - 54 q^{43} - 90 q^{44} - 233 q^{45} - 42 q^{46} - 188 q^{47} - 149 q^{48} + 189 q^{49} - 146 q^{50} - 34 q^{51} - 195 q^{52} - 196 q^{53} - 36 q^{54} - 57 q^{55} - 63 q^{56} - 76 q^{57} - 24 q^{58} - 137 q^{59} - 73 q^{60} - 96 q^{61} - 167 q^{62} - 113 q^{63} + 224 q^{64} - 131 q^{65} - 11 q^{66} - 71 q^{67} - 260 q^{68} - 162 q^{69} - 48 q^{70} - 77 q^{71} - 290 q^{72} - 160 q^{73} - 34 q^{74} - 100 q^{75} - 84 q^{76} - 416 q^{77} - 59 q^{78} - 17 q^{79} - 268 q^{80} + 147 q^{81} - 28 q^{82} - 238 q^{83} - 184 q^{84} - 108 q^{85} - 61 q^{86} - 127 q^{87} - 47 q^{88} - 183 q^{89} - 56 q^{90} - 14 q^{91} - 109 q^{92} - 206 q^{93} + q^{94} - 84 q^{95} - 54 q^{96} - 127 q^{97} - 294 q^{98} - 66 q^{99}+O(q^{100}) \) 243 * q - 40 * q^2 - 27 * q^3 + 232 * q^4 - 85 * q^5 - 20 * q^6 - 28 * q^7 - 114 * q^8 + 210 * q^9 - 24 * q^10 - 37 * q^11 - 74 * q^12 - 113 * q^13 - 35 * q^14 - 34 * q^15 + 218 * q^16 - 125 * q^17 - 108 * q^18 - 46 * q^19 - 157 * q^20 - 113 * q^21 - 16 * q^22 - 60 * q^23 - 49 * q^24 + 208 * q^25 - 52 * q^26 - 90 * q^27 - 70 * q^28 - 137 * q^29 - 26 * q^30 - 36 * q^31 - 258 * q^32 - 153 * q^33 - 23 * q^34 - 77 * q^35 + 180 * q^36 - 108 * q^37 - 122 * q^38 - 32 * q^39 - 57 * q^40 - 186 * q^41 - 28 * q^42 - 54 * q^43 - 90 * q^44 - 233 * q^45 - 42 * q^46 - 188 * q^47 - 149 * q^48 + 189 * q^49 - 146 * q^50 - 34 * q^51 - 195 * q^52 - 196 * q^53 - 36 * q^54 - 57 * q^55 - 63 * q^56 - 76 * q^57 - 24 * q^58 - 137 * q^59 - 73 * q^60 - 96 * q^61 - 167 * q^62 - 113 * q^63 + 224 * q^64 - 131 * q^65 - 11 * q^66 - 71 * q^67 - 260 * q^68 - 162 * q^69 - 48 * q^70 - 77 * q^71 - 290 * q^72 - 160 * q^73 - 34 * q^74 - 100 * q^75 - 84 * q^76 - 416 * q^77 - 59 * q^78 - 17 * q^79 - 268 * q^80 + 147 * q^81 - 28 * q^82 - 238 * q^83 - 184 * q^84 - 108 * q^85 - 61 * q^86 - 127 * q^87 - 47 * q^88 - 183 * q^89 - 56 * q^90 - 14 * q^91 - 109 * q^92 - 206 * q^93 + q^94 - 84 * q^95 - 54 * q^96 - 127 * q^97 - 294 * q^98 - 66 * q^99

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