LMFDB - Embedded newform 8018.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.14046 q^{3} +1.00000 q^{4} +1.90163 q^{5} -1.14046 q^{6} +2.39414 q^{7} +1.00000 q^{8} -1.69934 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.14046 q^{3} +1.00000 q^{4} +1.90163 q^{5} -1.14046 q^{6} +2.39414 q^{7} +1.00000 q^{8} -1.69934 q^{9} +1.90163 q^{10} -4.82094 q^{11} -1.14046 q^{12} -2.93868 q^{13} +2.39414 q^{14} -2.16874 q^{15} +1.00000 q^{16} -2.32516 q^{17} -1.69934 q^{18} +1.00000 q^{19} +1.90163 q^{20} -2.73043 q^{21} -4.82094 q^{22} +3.20197 q^{23} -1.14046 q^{24} -1.38379 q^{25} -2.93868 q^{26} +5.35943 q^{27} +2.39414 q^{28} -0.604936 q^{29} -2.16874 q^{30} -2.02761 q^{31} +1.00000 q^{32} +5.49810 q^{33} -2.32516 q^{34} +4.55278 q^{35} -1.69934 q^{36} +3.52215 q^{37} +1.00000 q^{38} +3.35146 q^{39} +1.90163 q^{40} +7.60182 q^{41} -2.73043 q^{42} -3.42519 q^{43} -4.82094 q^{44} -3.23153 q^{45} +3.20197 q^{46} +5.77575 q^{47} -1.14046 q^{48} -1.26809 q^{49} -1.38379 q^{50} +2.65176 q^{51} -2.93868 q^{52} +6.56721 q^{53} +5.35943 q^{54} -9.16766 q^{55} +2.39414 q^{56} -1.14046 q^{57} -0.604936 q^{58} -8.44960 q^{59} -2.16874 q^{60} -4.08156 q^{61} -2.02761 q^{62} -4.06847 q^{63} +1.00000 q^{64} -5.58830 q^{65} +5.49810 q^{66} -4.70179 q^{67} -2.32516 q^{68} -3.65173 q^{69} +4.55278 q^{70} -2.73075 q^{71} -1.69934 q^{72} +9.55631 q^{73} +3.52215 q^{74} +1.57816 q^{75} +1.00000 q^{76} -11.5420 q^{77} +3.35146 q^{78} -15.4282 q^{79} +1.90163 q^{80} -1.01421 q^{81} +7.60182 q^{82} -3.58775 q^{83} -2.73043 q^{84} -4.42161 q^{85} -3.42519 q^{86} +0.689908 q^{87} -4.82094 q^{88} -15.9989 q^{89} -3.23153 q^{90} -7.03562 q^{91} +3.20197 q^{92} +2.31242 q^{93} +5.77575 q^{94} +1.90163 q^{95} -1.14046 q^{96} -4.53892 q^{97} -1.26809 q^{98} +8.19242 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	−1.14046	−0.658447	−0.329224	−	0.944252i	$-0.606787\pi$
$3$	−1.14046	−0.658447	−0.329224	+	0.944252i	$0.606787\pi$
$4$	1.00000	0.500000
$5$	1.90163	0.850437	0.425218	−	0.905091i	$-0.360197\pi$
$5$	1.90163	0.850437	0.425218	+	0.905091i	$0.360197\pi$
$6$	−1.14046	−0.465592
$7$	2.39414	0.904900	0.452450	−	0.891790i	$-0.350550\pi$
$7$	2.39414	0.904900	0.452450	+	0.891790i	$0.350550\pi$
$8$	1.00000	0.353553
$9$	−1.69934	−0.566447
$10$	1.90163	0.601350
$11$	−4.82094	−1.45357	−0.726783	−	0.686867i	$-0.758986\pi$
$11$	−4.82094	−1.45357	−0.726783	+	0.686867i	$0.758986\pi$
$12$	−1.14046	−0.329224
$13$	−2.93868	−0.815044	−0.407522	−	0.913195i	$-0.633607\pi$
$13$	−2.93868	−0.815044	−0.407522	+	0.913195i	$0.633607\pi$
$14$	2.39414	0.639861
$15$	−2.16874	−0.559968
$16$	1.00000	0.250000
$17$	−2.32516	−0.563934	−0.281967	−	0.959424i	$-0.590987\pi$
$17$	−2.32516	−0.563934	−0.281967	+	0.959424i	$0.590987\pi$
$18$	−1.69934	−0.400539
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.90163	0.425218
$21$	−2.73043	−0.595829
$22$	−4.82094	−1.02783
$23$	3.20197	0.667657	0.333829	−	0.942634i	$-0.391659\pi$
$23$	3.20197	0.667657	0.333829	+	0.942634i	$0.391659\pi$
$24$	−1.14046	−0.232796
$25$	−1.38379	−0.276758
$26$	−2.93868	−0.576323
$27$	5.35943	1.03142
$28$	2.39414	0.452450
$29$	−0.604936	−0.112334	−0.0561669	−	0.998421i	$-0.517888\pi$
$29$	−0.604936	−0.112334	−0.0561669	+	0.998421i	$0.517888\pi$
$30$	−2.16874	−0.395957
$31$	−2.02761	−0.364170	−0.182085	−	0.983283i	$-0.558285\pi$
$31$	−2.02761	−0.364170	−0.182085	+	0.983283i	$0.558285\pi$
$32$	1.00000	0.176777
$33$	5.49810	0.957097
$34$	−2.32516	−0.398762
$35$	4.55278	0.769560
$36$	−1.69934	−0.283224
$37$	3.52215	0.579037	0.289519	−	0.957172i	$-0.406505\pi$
$37$	3.52215	0.579037	0.289519	+	0.957172i	$0.406505\pi$
$38$	1.00000	0.162221
$39$	3.35146	0.536663
$40$	1.90163	0.300675
$41$	7.60182	1.18721	0.593603	−	0.804758i	$-0.297705\pi$
$41$	7.60182	1.18721	0.593603	+	0.804758i	$0.297705\pi$
$42$	−2.73043	−0.421315
$43$	−3.42519	−0.522337	−0.261168	−	0.965293i	$-0.584108\pi$
$43$	−3.42519	−0.522337	−0.261168	+	0.965293i	$0.584108\pi$
$44$	−4.82094	−0.726783
$45$	−3.23153	−0.481728
$46$	3.20197	0.472105
$47$	5.77575	0.842480	0.421240	−	0.906949i	$-0.361595\pi$
$47$	5.77575	0.842480	0.421240	+	0.906949i	$0.361595\pi$
$48$	−1.14046	−0.164612
$49$	−1.26809	−0.181155
$50$	−1.38379	−0.195697
$51$	2.65176	0.371321
$52$	−2.93868	−0.407522
$53$	6.56721	0.902075	0.451038	−	0.892505i	$-0.351054\pi$
$53$	6.56721	0.902075	0.451038	+	0.892505i	$0.351054\pi$
$54$	5.35943	0.729326
$55$	−9.16766	−1.23617
$56$	2.39414	0.319931
$57$	−1.14046	−0.151058
$58$	−0.604936	−0.0794320
$59$	−8.44960	−1.10004	−0.550022	−	0.835150i	$-0.685381\pi$
$59$	−8.44960	−1.10004	−0.550022	+	0.835150i	$0.685381\pi$
$60$	−2.16874	−0.279984
$61$	−4.08156	−0.522590	−0.261295	−	0.965259i	$-0.584150\pi$
$61$	−4.08156	−0.522590	−0.261295	+	0.965259i	$0.584150\pi$
$62$	−2.02761	−0.257507
$63$	−4.06847	−0.512579
$64$	1.00000	0.125000
$65$	−5.58830	−0.693143
$66$	5.49810	0.676770
$67$	−4.70179	−0.574415	−0.287207	−	0.957868i	$-0.592727\pi$
$67$	−4.70179	−0.574415	−0.287207	+	0.957868i	$0.592727\pi$
$68$	−2.32516	−0.281967
$69$	−3.65173	−0.439617
$70$	4.55278	0.544161
$71$	−2.73075	−0.324080	−0.162040	−	0.986784i	$-0.551807\pi$
$71$	−2.73075	−0.324080	−0.162040	+	0.986784i	$0.551807\pi$
$72$	−1.69934	−0.200269
$73$	9.55631	1.11848	0.559241	−	0.829005i	$-0.311093\pi$
$73$	9.55631	1.11848	0.559241	+	0.829005i	$0.311093\pi$
$74$	3.52215	0.409441
$75$	1.57816	0.182230
$76$	1.00000	0.114708
$77$	−11.5420	−1.31533
$78$	3.35146	0.379478
$79$	−15.4282	−1.73581	−0.867905	−	0.496729i	$-0.834534\pi$
$79$	−15.4282	−1.73581	−0.867905	+	0.496729i	$0.834534\pi$
$80$	1.90163	0.212609
$81$	−1.01421	−0.112690
$82$	7.60182	0.839481
$83$	−3.58775	−0.393807	−0.196904	−	0.980423i	$-0.563089\pi$
$83$	−3.58775	−0.393807	−0.196904	+	0.980423i	$0.563089\pi$
$84$	−2.73043	−0.297915
$85$	−4.42161	−0.479590
$86$	−3.42519	−0.369348
$87$	0.689908	0.0739659
$88$	−4.82094	−0.513913
$89$	−15.9989	−1.69588	−0.847942	−	0.530088i	$-0.822159\pi$
$89$	−15.9989	−1.69588	−0.847942	+	0.530088i	$0.822159\pi$
$90$	−3.23153	−0.340633
$91$	−7.03562	−0.737534
$92$	3.20197	0.333829
$93$	2.31242	0.239787
$94$	5.77575	0.595723
$95$	1.90163	0.195104
$96$	−1.14046	−0.116398
$97$	−4.53892	−0.460857	−0.230429	−	0.973089i	$-0.574013\pi$
$97$	−4.53892	−0.460857	−0.230429	+	0.973089i	$0.574013\pi$
$98$	−1.26809	−0.128096
$99$	8.19242	0.823369
$100$	−1.38379	−0.138379
$101$	−6.86289	−0.682883	−0.341442	−	0.939903i	$-0.610915\pi$
$101$	−6.86289	−0.682883	−0.341442	+	0.939903i	$0.610915\pi$
$102$	2.65176	0.262564
$103$	−2.54820	−0.251082	−0.125541	−	0.992088i	$-0.540067\pi$
$103$	−2.54820	−0.251082	−0.125541	+	0.992088i	$0.540067\pi$
$104$	−2.93868	−0.288162
$105$	−5.19228	−0.506715
$106$	6.56721	0.637863
$107$	−12.0545	−1.16535	−0.582675	−	0.812705i	$-0.697994\pi$
$107$	−12.0545	−1.16535	−0.582675	+	0.812705i	$0.697994\pi$
$108$	5.35943	0.515711
$109$	−9.42618	−0.902865	−0.451432	−	0.892305i	$-0.649087\pi$
$109$	−9.42618	−0.902865	−0.451432	+	0.892305i	$0.649087\pi$
$110$	−9.16766	−0.874102
$111$	−4.01688	−0.381265
$112$	2.39414	0.226225
$113$	−7.92859	−0.745859	−0.372930	−	0.927860i	$-0.621647\pi$
$113$	−7.92859	−0.745859	−0.372930	+	0.927860i	$0.621647\pi$
$114$	−1.14046	−0.106814
$115$	6.08898	0.567800
$116$	−0.604936	−0.0561669
$117$	4.99383	0.461680
$118$	−8.44960	−0.777849
$119$	−5.56676	−0.510304
$120$	−2.16874	−0.197978
$121$	12.2414	1.11286
$122$	−4.08156	−0.369527
$123$	−8.66960	−0.781712
$124$	−2.02761	−0.182085
$125$	−12.1396	−1.08580
$126$	−4.06847	−0.362448
$127$	13.0827	1.16090	0.580451	−	0.814295i	$-0.302876\pi$
$127$	13.0827	1.16090	0.580451	+	0.814295i	$0.302876\pi$
$128$	1.00000	0.0883883
$129$	3.90630	0.343931
$130$	−5.58830	−0.490126
$131$	−19.5141	−1.70495	−0.852475	−	0.522767i	$-0.824900\pi$
$131$	−19.5141	−1.70495	−0.852475	+	0.522767i	$0.824900\pi$
$132$	5.49810	0.478548
$133$	2.39414	0.207598
$134$	−4.70179	−0.406173
$135$	10.1917	0.877160
$136$	−2.32516	−0.199381
$137$	−23.3673	−1.99641	−0.998203	−	0.0599229i	$-0.980915\pi$
$137$	−23.3673	−1.99641	−0.998203	+	0.0599229i	$0.980915\pi$
$138$	−3.65173	−0.310856
$139$	−11.4619	−0.972187	−0.486093	−	0.873907i	$-0.661579\pi$
$139$	−11.4619	−0.972187	−0.486093	+	0.873907i	$0.661579\pi$
$140$	4.55278	0.384780
$141$	−6.58703	−0.554728
$142$	−2.73075	−0.229159
$143$	14.1672	1.18472
$144$	−1.69934	−0.141612
$145$	−1.15037	−0.0955328
$146$	9.55631	0.790886
$147$	1.44621	0.119281
$148$	3.52215	0.289519
$149$	9.50817	0.778939	0.389470	−	0.921039i	$-0.372658\pi$
$149$	9.50817	0.778939	0.389470	+	0.921039i	$0.372658\pi$
$150$	1.57816	0.128856
$151$	−7.87999	−0.641264	−0.320632	−	0.947204i	$-0.603895\pi$
$151$	−7.87999	−0.641264	−0.320632	+	0.947204i	$0.603895\pi$
$152$	1.00000	0.0811107
$153$	3.95124	0.319439
$154$	−11.5420	−0.930081
$155$	−3.85578	−0.309704
$156$	3.35146	0.268332
$157$	−0.647215	−0.0516533	−0.0258267	−	0.999666i	$-0.508222\pi$
$157$	−0.647215	−0.0516533	−0.0258267	+	0.999666i	$0.508222\pi$
$158$	−15.4282	−1.22740
$159$	−7.48966	−0.593969
$160$	1.90163	0.150337
$161$	7.66598	0.604164
$162$	−1.01421	−0.0796838
$163$	10.3531	0.810919	0.405459	−	0.914113i	$-0.367112\pi$
$163$	10.3531	0.810919	0.405459	+	0.914113i	$0.367112\pi$
$164$	7.60182	0.593603
$165$	10.4554	0.813950
$166$	−3.58775	−0.278464
$167$	12.9384	1.00120	0.500602	−	0.865677i	$-0.333112\pi$
$167$	12.9384	1.00120	0.500602	+	0.865677i	$0.333112\pi$
$168$	−2.73043	−0.210657
$169$	−4.36414	−0.335703
$170$	−4.42161	−0.339122
$171$	−1.69934	−0.129952
$172$	−3.42519	−0.261168
$173$	−20.1901	−1.53503	−0.767514	−	0.641032i	$-0.778507\pi$
$173$	−20.1901	−1.53503	−0.767514	+	0.641032i	$0.778507\pi$
$174$	0.689908	0.0523018
$175$	−3.31298	−0.250438
$176$	−4.82094	−0.363392
$177$	9.63647	0.724321
$178$	−15.9989	−1.19917
$179$	4.10847	0.307082	0.153541	−	0.988142i	$-0.450932\pi$
$179$	4.10847	0.307082	0.153541	+	0.988142i	$0.450932\pi$
$180$	−3.23153	−0.240864
$181$	−7.52973	−0.559681	−0.279840	−	0.960047i	$-0.590282\pi$
$181$	−7.52973	−0.559681	−0.279840	+	0.960047i	$0.590282\pi$
$182$	−7.03562	−0.521515
$183$	4.65487	0.344098
$184$	3.20197	0.236053
$185$	6.69783	0.492434
$186$	2.31242	0.169555
$187$	11.2095	0.819716
$188$	5.77575	0.421240
$189$	12.8312	0.933335
$190$	1.90163	0.137959
$191$	−12.1894	−0.881997	−0.440998	−	0.897508i	$-0.645376\pi$
$191$	−12.1894	−0.881997	−0.440998	+	0.897508i	$0.645376\pi$
$192$	−1.14046	−0.0823059
$193$	19.5976	1.41067	0.705334	−	0.708875i	$-0.250797\pi$
$193$	19.5976	1.41067	0.705334	+	0.708875i	$0.250797\pi$
$194$	−4.53892	−0.325875
$195$	6.37325	0.456398
$196$	−1.26809	−0.0905776
$197$	8.20442	0.584541	0.292270	−	0.956336i	$-0.405589\pi$
$197$	8.20442	0.584541	0.292270	+	0.956336i	$0.405589\pi$
$198$	8.19242	0.582210
$199$	6.16300	0.436883	0.218442	−	0.975850i	$-0.429903\pi$
$199$	6.16300	0.436883	0.218442	+	0.975850i	$0.429903\pi$
$200$	−1.38379	−0.0978486
$201$	5.36222	0.378222
$202$	−6.86289	−0.482871
$203$	−1.44830	−0.101651
$204$	2.65176	0.185660
$205$	14.4559	1.00964
$206$	−2.54820	−0.177542
$207$	−5.44125	−0.378193
$208$	−2.93868	−0.203761
$209$	−4.82094	−0.333471
$210$	−5.19228	−0.358302
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.56721	0.451038
$213$	3.11432	0.213390
$214$	−12.0545	−0.824027
$215$	−6.51346	−0.444214
$216$	5.35943	0.364663
$217$	−4.85439	−0.329538
$218$	−9.42618	−0.638422
$219$	−10.8986	−0.736461
$220$	−9.16766	−0.618083
$221$	6.83291	0.459631
$222$	−4.01688	−0.269595
$223$	−1.96378	−0.131505	−0.0657523	−	0.997836i	$-0.520945\pi$
$223$	−1.96378	−0.131505	−0.0657523	+	0.997836i	$0.520945\pi$
$224$	2.39414	0.159965
$225$	2.35153	0.156769
$226$	−7.92859	−0.527402
$227$	4.30234	0.285556	0.142778	−	0.989755i	$-0.454396\pi$
$227$	4.30234	0.285556	0.142778	+	0.989755i	$0.454396\pi$
$228$	−1.14046	−0.0755291
$229$	0.785254	0.0518910	0.0259455	−	0.999663i	$-0.491740\pi$
$229$	0.785254	0.0518910	0.0259455	+	0.999663i	$0.491740\pi$
$230$	6.08898	0.401495
$231$	13.1632	0.866077
$232$	−0.604936	−0.0397160
$233$	−1.33349	−0.0873598	−0.0436799	−	0.999046i	$-0.513908\pi$
$233$	−1.33349	−0.0873598	−0.0436799	+	0.999046i	$0.513908\pi$
$234$	4.99383	0.326457
$235$	10.9834	0.716476
$236$	−8.44960	−0.550022
$237$	17.5953	1.14294
$238$	−5.56676	−0.360840
$239$	0.532759	0.0344613	0.0172307	−	0.999852i	$-0.494515\pi$
$239$	0.532759	0.0344613	0.0172307	+	0.999852i	$0.494515\pi$
$240$	−2.16874	−0.139992
$241$	7.29043	0.469618	0.234809	−	0.972042i	$-0.424554\pi$
$241$	7.29043	0.469618	0.234809	+	0.972042i	$0.424554\pi$
$242$	12.2414	0.786908
$243$	−14.9216	−0.957222
$244$	−4.08156	−0.261295
$245$	−2.41144	−0.154061
$246$	−8.66960	−0.552754
$247$	−2.93868	−0.186984
$248$	−2.02761	−0.128754
$249$	4.09170	0.259301
$250$	−12.1396	−0.767778
$251$	6.16285	0.388996	0.194498	−	0.980903i	$-0.437692\pi$
$251$	6.16285	0.388996	0.194498	+	0.980903i	$0.437692\pi$
$252$	−4.06847	−0.256289
$253$	−15.4365	−0.970485
$254$	13.0827	0.820882
$255$	5.04268	0.315785
$256$	1.00000	0.0625000
$257$	−1.07167	−0.0668489	−0.0334245	−	0.999441i	$-0.510641\pi$
$257$	−1.07167	−0.0668489	−0.0334245	+	0.999441i	$0.510641\pi$
$258$	3.90630	0.243196
$259$	8.43251	0.523971
$260$	−5.58830	−0.346572
$261$	1.02799	0.0636312
$262$	−19.5141	−1.20558
$263$	21.6730	1.33641	0.668207	−	0.743976i	$-0.267062\pi$
$263$	21.6730	1.33641	0.668207	+	0.743976i	$0.267062\pi$
$264$	5.49810	0.338385
$265$	12.4884	0.767158
$266$	2.39414	0.146794
$267$	18.2462	1.11665
$268$	−4.70179	−0.287207
$269$	−1.69256	−0.103197	−0.0515985	−	0.998668i	$-0.516432\pi$
$269$	−1.69256	−0.103197	−0.0515985	+	0.998668i	$0.516432\pi$
$270$	10.1917	0.620246
$271$	−9.57448	−0.581608	−0.290804	−	0.956783i	$-0.593923\pi$
$271$	−9.57448	−0.581608	−0.290804	+	0.956783i	$0.593923\pi$
$272$	−2.32516	−0.140984
$273$	8.02387	0.485627
$274$	−23.3673	−1.41167
$275$	6.67115	0.402286
$276$	−3.65173	−0.219809
$277$	3.19515	0.191978	0.0959889	−	0.995382i	$-0.469399\pi$
$277$	3.19515	0.191978	0.0959889	+	0.995382i	$0.469399\pi$
$278$	−11.4619	−0.687440
$279$	3.44561	0.206283
$280$	4.55278	0.272081
$281$	−15.6841	−0.935637	−0.467819	−	0.883825i	$-0.654960\pi$
$281$	−15.6841	−0.935637	−0.467819	+	0.883825i	$0.654960\pi$
$282$	−6.58703	−0.392252
$283$	−14.9308	−0.887542	−0.443771	−	0.896140i	$-0.646360\pi$
$283$	−14.9308	−0.887542	−0.443771	+	0.896140i	$0.646360\pi$
$284$	−2.73075	−0.162040
$285$	−2.16874	−0.128465
$286$	14.1672	0.837724
$287$	18.1998	1.07430
$288$	−1.69934	−0.100135
$289$	−11.5936	−0.681978
$290$	−1.15037	−0.0675519
$291$	5.17647	0.303450
$292$	9.55631	0.559241
$293$	2.03761	0.119038	0.0595191	−	0.998227i	$-0.481043\pi$
$293$	2.03761	0.119038	0.0595191	+	0.998227i	$0.481043\pi$
$294$	1.44621	0.0843445
$295$	−16.0681	−0.935518
$296$	3.52215	0.204721
$297$	−25.8375	−1.49924
$298$	9.50817	0.550793
$299$	−9.40958	−0.544170
$300$	1.57816	0.0911151
$301$	−8.20039	−0.472663
$302$	−7.87999	−0.453442
$303$	7.82688	0.449642
$304$	1.00000	0.0573539
$305$	−7.76163	−0.444430
$306$	3.95124	0.225878
$307$	−1.06385	−0.0607171	−0.0303585	−	0.999539i	$-0.509665\pi$
$307$	−1.06385	−0.0607171	−0.0303585	+	0.999539i	$0.509665\pi$
$308$	−11.5420	−0.657667
$309$	2.90613	0.165324
$310$	−3.85578	−0.218994
$311$	18.1752	1.03062	0.515309	−	0.857004i	$-0.327677\pi$
$311$	18.1752	1.03062	0.515309	+	0.857004i	$0.327677\pi$
$312$	3.35146	0.189739
$313$	−7.37917	−0.417095	−0.208548	−	0.978012i	$-0.566874\pi$
$313$	−7.37917	−0.417095	−0.208548	+	0.978012i	$0.566874\pi$
$314$	−0.647215	−0.0365244
$315$	−7.73673	−0.435916
$316$	−15.4282	−0.867905
$317$	8.65810	0.486287	0.243144	−	0.969990i	$-0.421821\pi$
$317$	8.65810	0.486287	0.243144	+	0.969990i	$0.421821\pi$
$318$	−7.48966	−0.419999
$319$	2.91636	0.163285
$320$	1.90163	0.106305
$321$	13.7477	0.767322
$322$	7.66598	0.427208
$323$	−2.32516	−0.129375
$324$	−1.01421	−0.0563450
$325$	4.06651	0.225570
$326$	10.3531	0.573406
$327$	10.7502	0.594489
$328$	7.60182	0.419740
$329$	13.8280	0.762360
$330$	10.4554	0.575550
$331$	−10.5891	−0.582029	−0.291014	−	0.956719i	$-0.593993\pi$
$331$	−10.5891	−0.582029	−0.291014	+	0.956719i	$0.593993\pi$
$332$	−3.58775	−0.196904
$333$	−5.98533	−0.327994
$334$	12.9384	0.707959
$335$	−8.94108	−0.488504
$336$	−2.73043	−0.148957
$337$	24.4995	1.33457	0.667285	−	0.744802i	$-0.267456\pi$
$337$	24.4995	1.33457	0.667285	+	0.744802i	$0.267456\pi$
$338$	−4.36414	−0.237378
$339$	9.04227	0.491109
$340$	−4.42161	−0.239795
$341$	9.77500	0.529346
$342$	−1.69934	−0.0918899
$343$	−19.7950	−1.06883
$344$	−3.42519	−0.184674
$345$	−6.94426	−0.373867
$346$	−20.1901	−1.08543
$347$	−16.7123	−0.897163	−0.448581	−	0.893742i	$-0.648071\pi$
$347$	−16.7123	−0.897163	−0.448581	+	0.893742i	$0.648071\pi$
$348$	0.689908	0.0369830
$349$	−22.3433	−1.19601	−0.598004	−	0.801493i	$-0.704039\pi$
$349$	−22.3433	−1.19601	−0.598004	+	0.801493i	$0.704039\pi$
$350$	−3.31298	−0.177086
$351$	−15.7497	−0.840655
$352$	−4.82094	−0.256957
$353$	18.0206	0.959140	0.479570	−	0.877503i	$-0.340793\pi$
$353$	18.0206	0.959140	0.479570	+	0.877503i	$0.340793\pi$
$354$	9.63647	0.512172
$355$	−5.19288	−0.275610
$356$	−15.9989	−0.847942
$357$	6.34869	0.336009
$358$	4.10847	0.217139
$359$	−4.74870	−0.250627	−0.125313	−	0.992117i	$-0.539994\pi$
$359$	−4.74870	−0.250627	−0.125313	+	0.992117i	$0.539994\pi$
$360$	−3.23153	−0.170316
$361$	1.00000	0.0526316
$362$	−7.52973	−0.395754
$363$	−13.9609	−0.732757
$364$	−7.03562	−0.368767
$365$	18.1726	0.951198
$366$	4.65487	0.243314
$367$	−31.3401	−1.63594	−0.817969	−	0.575262i	$-0.804900\pi$
$367$	−31.3401	−1.63594	−0.817969	+	0.575262i	$0.804900\pi$
$368$	3.20197	0.166914
$369$	−12.9181	−0.672489
$370$	6.69783	0.348204
$371$	15.7228	0.816288
$372$	2.31242	0.119893
$373$	15.4360	0.799244	0.399622	−	0.916680i	$-0.369141\pi$
$373$	15.4360	0.799244	0.399622	+	0.916680i	$0.369141\pi$
$374$	11.2095	0.579627
$375$	13.8448	0.714943
$376$	5.77575	0.297862
$377$	1.77772	0.0915571
$378$	12.8312	0.659967
$379$	20.4755	1.05175	0.525877	−	0.850560i	$-0.323737\pi$
$379$	20.4755	1.05175	0.525877	+	0.850560i	$0.323737\pi$
$380$	1.90163	0.0975518
$381$	−14.9204	−0.764393
$382$	−12.1894	−0.623666
$383$	22.8696	1.16858	0.584290	−	0.811545i	$-0.301373\pi$
$383$	22.8696	1.16858	0.584290	+	0.811545i	$0.301373\pi$
$384$	−1.14046	−0.0581991
$385$	−21.9487	−1.11861
$386$	19.5976	0.997493
$387$	5.82057	0.295876
$388$	−4.53892	−0.230429
$389$	14.4768	0.734005	0.367003	−	0.930220i	$-0.380384\pi$
$389$	14.4768	0.734005	0.367003	+	0.930220i	$0.380384\pi$
$390$	6.37325	0.322722
$391$	−7.44510	−0.376515
$392$	−1.26809	−0.0640480
$393$	22.2551	1.12262
$394$	8.20442	0.413333
$395$	−29.3388	−1.47620
$396$	8.19242	0.411685
$397$	−5.73317	−0.287739	−0.143870	−	0.989597i	$-0.545955\pi$
$397$	−5.73317	−0.287739	−0.143870	+	0.989597i	$0.545955\pi$
$398$	6.16300	0.308923
$399$	−2.73043	−0.136693
$400$	−1.38379	−0.0691894
$401$	−37.7760	−1.88644	−0.943220	−	0.332167i	$-0.892220\pi$
$401$	−37.7760	−1.88644	−0.943220	+	0.332167i	$0.892220\pi$
$402$	5.36222	0.267443
$403$	5.95852	0.296815
$404$	−6.86289	−0.341442
$405$	−1.92865	−0.0958356
$406$	−1.44830	−0.0718781
$407$	−16.9800	−0.841669
$408$	2.65176	0.131282
$409$	−13.0004	−0.642828	−0.321414	−	0.946939i	$-0.604158\pi$
$409$	−13.0004	−0.642828	−0.321414	+	0.946939i	$0.604158\pi$
$410$	14.4559	0.713925
$411$	26.6496	1.31453
$412$	−2.54820	−0.125541
$413$	−20.2295	−0.995431
$414$	−5.44125	−0.267423
$415$	−6.82259	−0.334908
$416$	−2.93868	−0.144081
$417$	13.0719	0.640134
$418$	−4.82094	−0.235800
$419$	38.6433	1.88785	0.943925	−	0.330159i	$-0.107102\pi$
$419$	38.6433	1.88785	0.943925	+	0.330159i	$0.107102\pi$
$420$	−5.19228	−0.253357
$421$	−4.82061	−0.234942	−0.117471	−	0.993076i	$-0.537479\pi$
$421$	−4.82061	−0.234942	−0.117471	+	0.993076i	$0.537479\pi$
$422$	−1.00000	−0.0486792
$423$	−9.81498	−0.477220
$424$	6.56721	0.318932
$425$	3.21753	0.156073
$426$	3.11432	0.150889
$427$	−9.77183	−0.472892
$428$	−12.0545	−0.582675
$429$	−16.1572	−0.780076
$430$	−6.51346	−0.314107
$431$	16.7088	0.804833	0.402416	−	0.915457i	$-0.368170\pi$
$431$	16.7088	0.804833	0.402416	+	0.915457i	$0.368170\pi$
$432$	5.35943	0.257856
$433$	14.2112	0.682947	0.341474	−	0.939891i	$-0.389074\pi$
$433$	14.2112	0.682947	0.341474	+	0.939891i	$0.389074\pi$
$434$	−4.85439	−0.233018
$435$	1.31195	0.0629033
$436$	−9.42618	−0.451432
$437$	3.20197	0.153171
$438$	−10.8986	−0.520756
$439$	23.6895	1.13064	0.565318	−	0.824873i	$-0.308753\pi$
$439$	23.6895	1.13064	0.565318	+	0.824873i	$0.308753\pi$
$440$	−9.16766	−0.437051
$441$	2.15491	0.102615
$442$	6.83291	0.325008
$443$	3.91211	0.185870	0.0929350	−	0.995672i	$-0.470375\pi$
$443$	3.91211	0.185870	0.0929350	+	0.995672i	$0.470375\pi$
$444$	−4.01688	−0.190633
$445$	−30.4241	−1.44224
$446$	−1.96378	−0.0929879
$447$	−10.8437	−0.512890
$448$	2.39414	0.113113
$449$	8.41883	0.397309	0.198655	−	0.980070i	$-0.436343\pi$
$449$	8.41883	0.397309	0.198655	+	0.980070i	$0.436343\pi$
$450$	2.35153	0.110852
$451$	−36.6479	−1.72568
$452$	−7.92859	−0.372930
$453$	8.98684	0.422239
$454$	4.30234	0.201919
$455$	−13.3792	−0.627226
$456$	−1.14046	−0.0534071
$457$	−24.5193	−1.14696	−0.573482	−	0.819218i	$-0.694408\pi$
$457$	−24.5193	−1.14696	−0.573482	+	0.819218i	$0.694408\pi$
$458$	0.785254	0.0366925
$459$	−12.4615	−0.581655
$460$	6.08898	0.283900
$461$	22.0623	1.02754	0.513771	−	0.857927i	$-0.328248\pi$
$461$	22.0623	1.02754	0.513771	+	0.857927i	$0.328248\pi$
$462$	13.1632	0.612409
$463$	17.4055	0.808903	0.404452	−	0.914559i	$-0.367462\pi$
$463$	17.4055	0.808903	0.404452	+	0.914559i	$0.367462\pi$
$464$	−0.604936	−0.0280835
$465$	4.39738	0.203924
$466$	−1.33349	−0.0617727
$467$	16.1044	0.745222	0.372611	−	0.927988i	$-0.378463\pi$
$467$	16.1044	0.745222	0.372611	+	0.927988i	$0.378463\pi$
$468$	4.99383	0.230840
$469$	−11.2567	−0.519788
$470$	10.9834	0.506625
$471$	0.738125	0.0340110
$472$	−8.44960	−0.388925
$473$	16.5126	0.759251
$474$	17.5953	0.808180
$475$	−1.38379	−0.0634925
$476$	−5.56676	−0.255152
$477$	−11.1599	−0.510978
$478$	0.532759	0.0243678
$479$	0.611032	0.0279188	0.0139594	−	0.999903i	$-0.495556\pi$
$479$	0.611032	0.0279188	0.0139594	+	0.999903i	$0.495556\pi$
$480$	−2.16874	−0.0989892
$481$	−10.3505	−0.471941
$482$	7.29043	0.332070
$483$	−8.74277	−0.397810
$484$	12.2414	0.556428
$485$	−8.63136	−0.391930
$486$	−14.9216	−0.676858
$487$	30.5937	1.38633	0.693166	−	0.720778i	$-0.256215\pi$
$487$	30.5937	1.38633	0.693166	+	0.720778i	$0.256215\pi$
$488$	−4.08156	−0.184764
$489$	−11.8074	−0.533947
$490$	−2.41144	−0.108938
$491$	10.4501	0.471608	0.235804	−	0.971801i	$-0.424228\pi$
$491$	10.4501	0.471608	0.235804	+	0.971801i	$0.424228\pi$
$492$	−8.66960	−0.390856
$493$	1.40657	0.0633489
$494$	−2.93868	−0.132218
$495$	15.5790	0.700223
$496$	−2.02761	−0.0910426
$497$	−6.53780	−0.293260
$498$	4.09170	0.183354
$499$	38.1008	1.70563	0.852813	−	0.522217i	$-0.174895\pi$
$499$	38.1008	1.70563	0.852813	+	0.522217i	$0.174895\pi$
$500$	−12.1396	−0.542901
$501$	−14.7558	−0.659240
$502$	6.16285	0.275061
$503$	22.8274	1.01782	0.508912	−	0.860819i	$-0.330048\pi$
$503$	22.8274	1.01782	0.508912	+	0.860819i	$0.330048\pi$
$504$	−4.06847	−0.181224
$505$	−13.0507	−0.580749
$506$	−15.4365	−0.686236
$507$	4.97714	0.221043
$508$	13.0827	0.580451
$509$	−5.93351	−0.262998	−0.131499	−	0.991316i	$-0.541979\pi$
$509$	−5.93351	−0.262998	−0.131499	+	0.991316i	$0.541979\pi$
$510$	5.04268	0.223294
$511$	22.8792	1.01211
$512$	1.00000	0.0441942
$513$	5.35943	0.236625
$514$	−1.07167	−0.0472693
$515$	−4.84574	−0.213529
$516$	3.90630	0.171965
$517$	−27.8445	−1.22460
$518$	8.43251	0.370503
$519$	23.0261	1.01074
$520$	−5.58830	−0.245063
$521$	−39.8184	−1.74448	−0.872238	−	0.489082i	$-0.837332\pi$
$521$	−39.8184	−1.74448	−0.872238	+	0.489082i	$0.837332\pi$
$522$	1.02799	0.0449941
$523$	−32.2310	−1.40936	−0.704681	−	0.709524i	$-0.748910\pi$
$523$	−32.2310	−1.40936	−0.704681	+	0.709524i	$0.748910\pi$
$524$	−19.5141	−0.852475
$525$	3.77834	0.164900
$526$	21.6730	0.944987
$527$	4.71453	0.205368
$528$	5.49810	0.239274
$529$	−12.7474	−0.554233
$530$	12.4884	0.542462
$531$	14.3588	0.623117
$532$	2.39414	0.103799
$533$	−22.3393	−0.967625
$534$	18.2462	0.789591
$535$	−22.9232	−0.991057
$536$	−4.70179	−0.203086
$537$	−4.68556	−0.202197
$538$	−1.69256	−0.0729714
$539$	6.11336	0.263321
$540$	10.1917	0.438580
$541$	−41.3741	−1.77881	−0.889407	−	0.457117i	$-0.848882\pi$
$541$	−41.3741	−1.77881	−0.889407	+	0.457117i	$0.848882\pi$
$542$	−9.57448	−0.411259
$543$	8.58739	0.368520
$544$	−2.32516	−0.0996905
$545$	−17.9252	−0.767829
$546$	8.02387	0.343390
$547$	25.1939	1.07721	0.538606	−	0.842558i	$-0.318951\pi$
$547$	25.1939	1.07721	0.538606	+	0.842558i	$0.318951\pi$
$548$	−23.3673	−0.998203
$549$	6.93597	0.296020
$550$	6.67115	0.284459
$551$	−0.604936	−0.0257712
$552$	−3.65173	−0.155428
$553$	−36.9374	−1.57074
$554$	3.19515	0.135749
$555$	−7.63863	−0.324242
$556$	−11.4619	−0.486093
$557$	−14.3011	−0.605957	−0.302978	−	0.952997i	$-0.597981\pi$
$557$	−14.3011	−0.605957	−0.302978	+	0.952997i	$0.597981\pi$
$558$	3.44561	0.145864
$559$	10.0655	0.425727
$560$	4.55278	0.192390
$561$	−12.7840	−0.539740
$562$	−15.6841	−0.661595
$563$	1.56987	0.0661620	0.0330810	−	0.999453i	$-0.489468\pi$
$563$	1.56987	0.0661620	0.0330810	+	0.999453i	$0.489468\pi$
$564$	−6.58703	−0.277364
$565$	−15.0773	−0.634306
$566$	−14.9308	−0.627587
$567$	−2.42816	−0.101973
$568$	−2.73075	−0.114580
$569$	−32.7189	−1.37165	−0.685825	−	0.727767i	$-0.740558\pi$
$569$	−32.7189	−1.37165	−0.685825	+	0.727767i	$0.740558\pi$
$570$	−2.16874	−0.0908387
$571$	−23.9621	−1.00278	−0.501390	−	0.865221i	$-0.667178\pi$
$571$	−23.9621	−1.00278	−0.501390	+	0.865221i	$0.667178\pi$
$572$	14.1672	0.592361
$573$	13.9016	0.580748
$574$	18.1998	0.759647
$575$	−4.43085	−0.184779
$576$	−1.69934	−0.0708059
$577$	34.8472	1.45071	0.725354	−	0.688376i	$-0.241676\pi$
$577$	34.8472	1.45071	0.725354	+	0.688376i	$0.241676\pi$
$578$	−11.5936	−0.482231
$579$	−22.3504	−0.928851
$580$	−1.15037	−0.0477664
$581$	−8.58959	−0.356356
$582$	5.17647	0.214572
$583$	−31.6601	−1.31123
$584$	9.55631	0.395443
$585$	9.49644	0.392629
$586$	2.03761	0.0841727
$587$	0.683958	0.0282300	0.0141150	−	0.999900i	$-0.495507\pi$
$587$	0.683958	0.0282300	0.0141150	+	0.999900i	$0.495507\pi$
$588$	1.44621	0.0596406
$589$	−2.02761	−0.0835464
$590$	−16.0681	−0.661511
$591$	−9.35684	−0.384889
$592$	3.52215	0.144759
$593$	19.2060	0.788696	0.394348	−	0.918961i	$-0.370970\pi$
$593$	19.2060	0.788696	0.394348	+	0.918961i	$0.370970\pi$
$594$	−25.8375	−1.06012
$595$	−10.5859	−0.433982
$596$	9.50817	0.389470
$597$	−7.02868	−0.287665
$598$	−9.40958	−0.384787
$599$	29.9674	1.22443	0.612217	−	0.790690i	$-0.290278\pi$
$599$	29.9674	1.22443	0.612217	+	0.790690i	$0.290278\pi$
$600$	1.57816	0.0644281
$601$	−23.4925	−0.958281	−0.479140	−	0.877738i	$-0.659051\pi$
$601$	−23.4925	−0.958281	−0.479140	+	0.877738i	$0.659051\pi$
$602$	−8.20039	−0.334223
$603$	7.98995	0.325376
$604$	−7.87999	−0.320632
$605$	23.2787	0.946414
$606$	7.82688	0.317945
$607$	26.8321	1.08908	0.544541	−	0.838734i	$-0.316704\pi$
$607$	26.8321	1.08908	0.544541	+	0.838734i	$0.316704\pi$
$608$	1.00000	0.0405554
$609$	1.65174	0.0669318
$610$	−7.76163	−0.314259
$611$	−16.9731	−0.686658
$612$	3.95124	0.159720
$613$	25.2794	1.02102	0.510512	−	0.859871i	$-0.329456\pi$
$613$	25.2794	1.02102	0.510512	+	0.859871i	$0.329456\pi$
$614$	−1.06385	−0.0429334
$615$	−16.4864	−0.664796
$616$	−11.5420	−0.465041
$617$	35.2161	1.41775	0.708873	−	0.705336i	$-0.249204\pi$
$617$	35.2161	1.41775	0.708873	+	0.705336i	$0.249204\pi$
$618$	2.90613	0.116902
$619$	45.6522	1.83492	0.917459	−	0.397830i	$-0.130237\pi$
$619$	45.6522	1.83492	0.917459	+	0.397830i	$0.130237\pi$
$620$	−3.85578	−0.154852
$621$	17.1607	0.688637
$622$	18.1752	0.728757
$623$	−38.3037	−1.53461
$624$	3.35146	0.134166
$625$	−16.1662	−0.646648
$626$	−7.37917	−0.294931
$627$	5.49810	0.219573
$628$	−0.647215	−0.0258267
$629$	−8.18955	−0.326539
$630$	−7.73673	−0.308239
$631$	−26.8790	−1.07004	−0.535019	−	0.844840i	$-0.679695\pi$
$631$	−26.8790	−1.07004	−0.535019	+	0.844840i	$0.679695\pi$
$632$	−15.4282	−0.613702
$633$	1.14046	0.0453294
$634$	8.65810	0.343857
$635$	24.8785	0.987274
$636$	−7.48966	−0.296984
$637$	3.72650	0.147649
$638$	2.91636	0.115460
$639$	4.64048	0.183574
$640$	1.90163	0.0751687
$641$	−21.3245	−0.842268	−0.421134	−	0.906998i	$-0.638368\pi$
$641$	−21.3245	−0.842268	−0.421134	+	0.906998i	$0.638368\pi$
$642$	13.7477	0.542578
$643$	−9.78045	−0.385703	−0.192852	−	0.981228i	$-0.561774\pi$
$643$	−9.78045	−0.385703	−0.192852	+	0.981228i	$0.561774\pi$
$644$	7.66598	0.302082
$645$	7.42836	0.292491
$646$	−2.32516	−0.0914822
$647$	−43.7024	−1.71812	−0.859060	−	0.511875i	$-0.828951\pi$
$647$	−43.7024	−1.71812	−0.859060	+	0.511875i	$0.828951\pi$
$648$	−1.01421	−0.0398419
$649$	40.7350	1.59899
$650$	4.06651	0.159502
$651$	5.53626	0.216983
$652$	10.3531	0.405459
$653$	−2.38643	−0.0933881	−0.0466941	−	0.998909i	$-0.514869\pi$
$653$	−2.38643	−0.0933881	−0.0466941	+	0.998909i	$0.514869\pi$
$654$	10.7502	0.420367
$655$	−37.1086	−1.44995
$656$	7.60182	0.296801
$657$	−16.2394	−0.633561
$658$	13.8280	0.539070
$659$	38.4464	1.49766	0.748831	−	0.662762i	$-0.230616\pi$
$659$	38.4464	1.49766	0.748831	+	0.662762i	$0.230616\pi$
$660$	10.4554	0.406975
$661$	−26.1296	−1.01632	−0.508161	−	0.861262i	$-0.669675\pi$
$661$	−26.1296	−1.01632	−0.508161	+	0.861262i	$0.669675\pi$
$662$	−10.5891	−0.411557
$663$	−7.79269	−0.302643
$664$	−3.58775	−0.139232
$665$	4.55278	0.176549
$666$	−5.98533	−0.231927
$667$	−1.93699	−0.0750005
$668$	12.9384	0.500602
$669$	2.23962	0.0865889
$670$	−8.94108	−0.345424
$671$	19.6769	0.759620
$672$	−2.73043	−0.105329
$673$	44.6219	1.72005	0.860025	−	0.510252i	$-0.170448\pi$
$673$	44.6219	1.72005	0.860025	+	0.510252i	$0.170448\pi$
$674$	24.4995	0.943684
$675$	−7.41631	−0.285454
$676$	−4.36414	−0.167852
$677$	−17.0043	−0.653528	−0.326764	−	0.945106i	$-0.605958\pi$
$677$	−17.0043	−0.653528	−0.326764	+	0.945106i	$0.605958\pi$
$678$	9.04227	0.347266
$679$	−10.8668	−0.417030
$680$	−4.42161	−0.169561
$681$	−4.90666	−0.188024
$682$	9.77500	0.374304
$683$	13.4028	0.512843	0.256422	−	0.966565i	$-0.417456\pi$
$683$	13.4028	0.512843	0.256422	+	0.966565i	$0.417456\pi$
$684$	−1.69934	−0.0649760
$685$	−44.4361	−1.69782
$686$	−19.7950	−0.755775
$687$	−0.895553	−0.0341675
$688$	−3.42519	−0.130584
$689$	−19.2989	−0.735231
$690$	−6.94426	−0.264364
$691$	11.2690	0.428695	0.214347	−	0.976757i	$-0.431238\pi$
$691$	11.2690	0.428695	0.214347	+	0.976757i	$0.431238\pi$
$692$	−20.1901	−0.767514
$693$	19.6138	0.745067
$694$	−16.7123	−0.634390
$695$	−21.7964	−0.826783
$696$	0.689908	0.0261509
$697$	−17.6755	−0.669506
$698$	−22.3433	−0.845706
$699$	1.52080	0.0575218
$700$	−3.31298	−0.125219
$701$	20.6079	0.778349	0.389175	−	0.921164i	$-0.372760\pi$
$701$	20.6079	0.778349	0.389175	+	0.921164i	$0.372760\pi$
$702$	−15.7497	−0.594433
$703$	3.52215	0.132840
$704$	−4.82094	−0.181696
$705$	−12.5261	−0.471761
$706$	18.0206	0.678215
$707$	−16.4307	−0.617941
$708$	9.63647	0.362161
$709$	−7.23701	−0.271792	−0.135896	−	0.990723i	$-0.543391\pi$
$709$	−7.23701	−0.271792	−0.135896	+	0.990723i	$0.543391\pi$
$710$	−5.19288	−0.194885
$711$	26.2178	0.983246
$712$	−15.9989	−0.599586
$713$	−6.49236	−0.243141
$714$	6.34869	0.237594
$715$	26.9408	1.00753
$716$	4.10847	0.153541
$717$	−0.607593	−0.0226910
$718$	−4.74870	−0.177220
$719$	−10.4831	−0.390953	−0.195476	−	0.980708i	$-0.562625\pi$
$719$	−10.4831	−0.390953	−0.195476	+	0.980708i	$0.562625\pi$
$720$	−3.23153	−0.120432
$721$	−6.10075	−0.227204
$722$	1.00000	0.0372161
$723$	−8.31448	−0.309219
$724$	−7.52973	−0.279840
$725$	0.837103	0.0310892
$726$	−13.9609	−0.518138
$727$	21.1004	0.782569	0.391285	−	0.920270i	$-0.372031\pi$
$727$	21.1004	0.782569	0.391285	+	0.920270i	$0.372031\pi$
$728$	−7.03562	−0.260758
$729$	20.0602	0.742970
$730$	18.1726	0.672598
$731$	7.96412	0.294564
$732$	4.65487	0.172049
$733$	−39.4051	−1.45546	−0.727729	−	0.685864i	$-0.759424\pi$
$733$	−39.4051	−1.45546	−0.727729	+	0.685864i	$0.759424\pi$
$734$	−31.3401	−1.15678
$735$	2.75016	0.101441
$736$	3.20197	0.118026
$737$	22.6670	0.834951
$738$	−12.9181	−0.475522
$739$	−36.8284	−1.35476	−0.677378	−	0.735635i	$-0.736884\pi$
$739$	−36.8284	−1.35476	−0.677378	+	0.735635i	$0.736884\pi$
$740$	6.69783	0.246217
$741$	3.35146	0.123119
$742$	15.7228	0.577203
$743$	40.8084	1.49711	0.748557	−	0.663070i	$-0.230747\pi$
$743$	40.8084	1.49711	0.748557	+	0.663070i	$0.230747\pi$
$744$	2.31242	0.0847774
$745$	18.0811	0.662439
$746$	15.4360	0.565151
$747$	6.09682	0.223071
$748$	11.2095	0.409858
$749$	−28.8601	−1.05453
$750$	13.8448	0.505541
$751$	−7.84625	−0.286314	−0.143157	−	0.989700i	$-0.545725\pi$
$751$	−7.84625	−0.286314	−0.143157	+	0.989700i	$0.545725\pi$
$752$	5.77575	0.210620
$753$	−7.02851	−0.256133
$754$	1.77772	0.0647406
$755$	−14.9849	−0.545355
$756$	12.8312	0.466667
$757$	−50.0526	−1.81919	−0.909597	−	0.415491i	$-0.863610\pi$
$757$	−50.0526	−1.81919	−0.909597	+	0.415491i	$0.863610\pi$
$758$	20.4755	0.743703
$759$	17.6048	0.639013
$760$	1.90163	0.0689795
$761$	−51.7645	−1.87646	−0.938231	−	0.346010i	$-0.887536\pi$
$761$	−51.7645	−1.87646	−0.938231	+	0.346010i	$0.887536\pi$
$762$	−14.9204	−0.540507
$763$	−22.5676	−0.817003
$764$	−12.1894	−0.440998
$765$	7.51382	0.271663
$766$	22.8696	0.826311
$767$	24.8307	0.896585
$768$	−1.14046	−0.0411529
$769$	−10.7044	−0.386012	−0.193006	−	0.981198i	$-0.561824\pi$
$769$	−10.7044	−0.386012	−0.193006	+	0.981198i	$0.561824\pi$
$770$	−21.9487	−0.790975
$771$	1.22220	0.0440165
$772$	19.5976	0.705334
$773$	−38.8711	−1.39810	−0.699049	−	0.715074i	$-0.746393\pi$
$773$	−38.8711	−1.39810	−0.699049	+	0.715074i	$0.746393\pi$
$774$	5.82057	0.209216
$775$	2.80579	0.100787
$776$	−4.53892	−0.162938
$777$	−9.61698	−0.345007
$778$	14.4768	0.519020
$779$	7.60182	0.272364
$780$	6.37325	0.228199
$781$	13.1648	0.471072
$782$	−7.44510	−0.266236
$783$	−3.24211	−0.115864
$784$	−1.26809	−0.0452888
$785$	−1.23077	−0.0439279
$786$	22.2551	0.793812
$787$	38.3829	1.36820	0.684102	−	0.729387i	$-0.260194\pi$
$787$	38.3829	1.36820	0.684102	+	0.729387i	$0.260194\pi$
$788$	8.20442	0.292270
$789$	−24.7173	−0.879958
$790$	−29.3388	−1.04383
$791$	−18.9822	−0.674928
$792$	8.19242	0.291105
$793$	11.9944	0.425934
$794$	−5.73317	−0.203462
$795$	−14.2426	−0.505133
$796$	6.16300	0.218442
$797$	53.6289	1.89963	0.949816	−	0.312808i	$-0.101270\pi$
$797$	53.6289	1.89963	0.949816	+	0.312808i	$0.101270\pi$
$798$	−2.73043	−0.0966562
$799$	−13.4295	−0.475103
$800$	−1.38379	−0.0489243
$801$	27.1877	0.960630
$802$	−37.7760	−1.33392
$803$	−46.0704	−1.62579
$804$	5.36222	0.189111
$805$	14.5779	0.513803
$806$	5.95852	0.209880
$807$	1.93030	0.0679498
$808$	−6.86289	−0.241436
$809$	−20.9760	−0.737476	−0.368738	−	0.929533i	$-0.620210\pi$
$809$	−20.9760	−0.737476	−0.368738	+	0.929533i	$0.620210\pi$
$810$	−1.92865	−0.0677660
$811$	−2.41901	−0.0849429	−0.0424714	−	0.999098i	$-0.513523\pi$
$811$	−2.41901	−0.0849429	−0.0424714	+	0.999098i	$0.513523\pi$
$812$	−1.44830	−0.0508255
$813$	10.9194	0.382958
$814$	−16.9800	−0.595150
$815$	19.6878	0.689635
$816$	2.65176	0.0928302
$817$	−3.42519	−0.119832
$818$	−13.0004	−0.454548
$819$	11.9559	0.417774
$820$	14.4559	0.504821
$821$	−36.0004	−1.25642	−0.628211	−	0.778043i	$-0.716213\pi$
$821$	−36.0004	−1.25642	−0.628211	+	0.778043i	$0.716213\pi$
$822$	26.6496	0.929511
$823$	−16.5293	−0.576176	−0.288088	−	0.957604i	$-0.593020\pi$
$823$	−16.5293	−0.576176	−0.288088	+	0.957604i	$0.593020\pi$
$824$	−2.54820	−0.0887708
$825$	−7.60821	−0.264884
$826$	−20.2295	−0.703876
$827$	−36.9663	−1.28544	−0.642722	−	0.766099i	$-0.722195\pi$
$827$	−36.9663	−1.28544	−0.642722	+	0.766099i	$0.722195\pi$
$828$	−5.44125	−0.189096
$829$	29.6178	1.02867	0.514335	−	0.857589i	$-0.328039\pi$
$829$	29.6178	1.02867	0.514335	+	0.857589i	$0.328039\pi$
$830$	−6.82259	−0.236816
$831$	−3.64395	−0.126407
$832$	−2.93868	−0.101881
$833$	2.94850	0.102160
$834$	13.0719	0.452643
$835$	24.6041	0.851461
$836$	−4.82094	−0.166736
$837$	−10.8669	−0.375613
$838$	38.6433	1.33491
$839$	12.7919	0.441625	0.220813	−	0.975316i	$-0.429129\pi$
$839$	12.7919	0.441625	0.220813	+	0.975316i	$0.429129\pi$
$840$	−5.19228	−0.179151
$841$	−28.6341	−0.987381
$842$	−4.82061	−0.166129
$843$	17.8872	0.616068
$844$	−1.00000	−0.0344214
$845$	−8.29900	−0.285494
$846$	−9.81498	−0.337446
$847$	29.3077	1.00702
$848$	6.56721	0.225519
$849$	17.0280	0.584399
$850$	3.21753	0.110360
$851$	11.2778	0.386598
$852$	3.11432	0.106695
$853$	−28.1712	−0.964564	−0.482282	−	0.876016i	$-0.660192\pi$
$853$	−28.1712	−0.964564	−0.482282	+	0.876016i	$0.660192\pi$
$854$	−9.77183	−0.334385
$855$	−3.23153	−0.110516
$856$	−12.0545	−0.412014
$857$	23.6406	0.807549	0.403775	−	0.914858i	$-0.367698\pi$
$857$	23.6406	0.807549	0.403775	+	0.914858i	$0.367698\pi$
$858$	−16.1572	−0.551597
$859$	28.4571	0.970943	0.485472	−	0.874252i	$-0.338648\pi$
$859$	28.4571	0.970943	0.485472	+	0.874252i	$0.338648\pi$
$860$	−6.51346	−0.222107
$861$	−20.7563	−0.707371
$862$	16.7088	0.569103
$863$	44.4196	1.51206	0.756030	−	0.654537i	$-0.227136\pi$
$863$	44.4196	1.51206	0.756030	+	0.654537i	$0.227136\pi$
$864$	5.35943	0.182332
$865$	−38.3943	−1.30544
$866$	14.2112	0.482917
$867$	13.2221	0.449046
$868$	−4.85439	−0.164769
$869$	74.3785	2.52312
$870$	1.31195	0.0444794
$871$	13.8171	0.468174
$872$	−9.42618	−0.319211
$873$	7.71317	0.261051
$874$	3.20197	0.108308
$875$	−29.0640	−0.982542
$876$	−10.8986	−0.368230
$877$	−36.0516	−1.21737	−0.608687	−	0.793410i	$-0.708304\pi$
$877$	−36.0516	−1.21737	−0.608687	+	0.793410i	$0.708304\pi$
$878$	23.6895	0.799481
$879$	−2.32382	−0.0783804
$880$	−9.16766	−0.309042
$881$	53.9762	1.81851	0.909253	−	0.416244i	$-0.136654\pi$
$881$	53.9762	1.81851	0.909253	+	0.416244i	$0.136654\pi$
$882$	2.15491	0.0725597
$883$	−43.1784	−1.45307	−0.726534	−	0.687131i	$-0.758870\pi$
$883$	−43.1784	−1.45307	−0.726534	+	0.687131i	$0.758870\pi$
$884$	6.83291	0.229816
$885$	18.3250	0.615989
$886$	3.91211	0.131430
$887$	30.4025	1.02082	0.510408	−	0.859932i	$-0.329494\pi$
$887$	30.4025	1.02082	0.510408	+	0.859932i	$0.329494\pi$
$888$	−4.01688	−0.134798
$889$	31.3218	1.05050
$890$	−30.4241	−1.01982
$891$	4.88944	0.163802
$892$	−1.96378	−0.0657523
$893$	5.77575	0.193278
$894$	−10.8437	−0.362668
$895$	7.81281	0.261153
$896$	2.39414	0.0799827
$897$	10.7313	0.358307
$898$	8.41883	0.280940
$899$	1.22658	0.0409086
$900$	2.35153	0.0783843
$901$	−15.2698	−0.508711
$902$	−36.6479	−1.22024
$903$	9.35225	0.311223
$904$	−7.92859	−0.263701
$905$	−14.3188	−0.475973
$906$	8.98684	0.298568
$907$	5.61217	0.186349	0.0931745	−	0.995650i	$-0.470299\pi$
$907$	5.61217	0.186349	0.0931745	+	0.995650i	$0.470299\pi$
$908$	4.30234	0.142778
$909$	11.6624	0.386817
$910$	−13.3792	−0.443516
$911$	−30.4107	−1.00755	−0.503776	−	0.863834i	$-0.668056\pi$
$911$	−30.4107	−1.00755	−0.503776	+	0.863834i	$0.668056\pi$
$912$	−1.14046	−0.0377645
$913$	17.2963	0.572425
$914$	−24.5193	−0.811026
$915$	8.85186	0.292634
$916$	0.785254	0.0259455
$917$	−46.7194	−1.54281
$918$	−12.4615	−0.411292
$919$	37.0728	1.22292	0.611460	−	0.791275i	$-0.290583\pi$
$919$	37.0728	1.22292	0.611460	+	0.791275i	$0.290583\pi$
$920$	6.08898	0.200748
$921$	1.21328	0.0399790
$922$	22.0623	0.726582
$923$	8.02480	0.264140
$924$	13.1632	0.433039
$925$	−4.87390	−0.160253
$926$	17.4055	0.571981
$927$	4.33026	0.142225
$928$	−0.604936	−0.0198580
$929$	−37.9929	−1.24651	−0.623253	−	0.782021i	$-0.714189\pi$
$929$	−37.9929	−1.24651	−0.623253	+	0.782021i	$0.714189\pi$
$930$	4.39738	0.144196
$931$	−1.26809	−0.0415599
$932$	−1.33349	−0.0436799
$933$	−20.7281	−0.678608
$934$	16.1044	0.526952
$935$	21.3163	0.697117
$936$	4.99383	0.163228
$937$	44.1192	1.44131	0.720656	−	0.693293i	$-0.243841\pi$
$937$	44.1192	1.44131	0.720656	+	0.693293i	$0.243841\pi$
$938$	−11.2567	−0.367546
$939$	8.41567	0.274635
$940$	10.9834	0.358238
$941$	−54.7029	−1.78326	−0.891632	−	0.452760i	$-0.850439\pi$
$941$	−54.7029	−1.78326	−0.891632	+	0.452760i	$0.850439\pi$
$942$	0.738125	0.0240494
$943$	24.3408	0.792646
$944$	−8.44960	−0.275011
$945$	24.4003	0.793742
$946$	16.5126	0.536872
$947$	17.1841	0.558410	0.279205	−	0.960232i	$-0.409929\pi$
$947$	17.1841	0.558410	0.279205	+	0.960232i	$0.409929\pi$
$948$	17.5953	0.571470
$949$	−28.0830	−0.911612
$950$	−1.38379	−0.0448960
$951$	−9.87424	−0.320194
$952$	−5.56676	−0.180420
$953$	48.6572	1.57616	0.788081	−	0.615571i	$-0.211075\pi$
$953$	48.6572	1.57616	0.788081	+	0.615571i	$0.211075\pi$
$954$	−11.1599	−0.361316
$955$	−23.1798	−0.750082
$956$	0.532759	0.0172307
$957$	−3.32600	−0.107514
$958$	0.611032	0.0197415
$959$	−55.9447	−1.80655
$960$	−2.16874	−0.0699959
$961$	−26.8888	−0.867380
$962$	−10.3505	−0.333713
$963$	20.4847	0.660110
$964$	7.29043	0.234809
$965$	37.2675	1.19968
$966$	−8.74277	−0.281294
$967$	−39.8318	−1.28090	−0.640451	−	0.767999i	$-0.721253\pi$
$967$	−39.8318	−1.28090	−0.640451	+	0.767999i	$0.721253\pi$
$968$	12.2414	0.393454
$969$	2.65176	0.0851869
$970$	−8.63136	−0.277136
$971$	6.54264	0.209963	0.104982	−	0.994474i	$-0.466522\pi$
$971$	6.54264	0.209963	0.104982	+	0.994474i	$0.466522\pi$
$972$	−14.9216	−0.478611
$973$	−27.4414	−0.879732
$974$	30.5937	0.980284
$975$	−4.63771	−0.148526
$976$	−4.08156	−0.130648
$977$	29.8224	0.954103	0.477052	−	0.878875i	$-0.341706\pi$
$977$	29.8224	0.954103	0.477052	+	0.878875i	$0.341706\pi$
$978$	−11.8074	−0.377558
$979$	77.1299	2.46508
$980$	−2.41144	−0.0770305
$981$	16.0183	0.511425
$982$	10.4501	0.333477
$983$	14.0035	0.446643	0.223322	−	0.974745i	$-0.428310\pi$
$983$	14.0035	0.446643	0.223322	+	0.974745i	$0.428310\pi$
$984$	−8.66960	−0.276377
$985$	15.6018	0.497115
$986$	1.40657	0.0447945
$987$	−15.7703	−0.501974
$988$	−2.93868	−0.0934920
$989$	−10.9674	−0.348742
$990$	15.5790	0.495133
$991$	−16.8095	−0.533971	−0.266986	−	0.963700i	$-0.586028\pi$
$991$	−16.8095	−0.533971	−0.266986	+	0.963700i	$0.586028\pi$
$992$	−2.02761	−0.0643768
$993$	12.0765	0.383235
$994$	−6.53780	−0.207366
$995$	11.7198	0.371542
$996$	4.09170	0.129651
$997$	−31.9755	−1.01267	−0.506336	−	0.862336i	$-0.669001\pi$
$997$	−31.9755	−1.01267	−0.506336	+	0.862336i	$0.669001\pi$
$998$	38.1008	1.20606
$999$	18.8767	0.597232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.12	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.12	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.14046 q^{3} +1.00000 q^{4} +1.90163 q^{5} -1.14046 q^{6} +2.39414 q^{7} +1.00000 q^{8} -1.69934 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.14046 q^{3} +1.00000 q^{4} +1.90163 q^{5} -1.14046 q^{6} +2.39414 q^{7} +1.00000 q^{8} -1.69934 q^{9} +1.90163 q^{10} -4.82094 q^{11} -1.14046 q^{12} -2.93868 q^{13} +2.39414 q^{14} -2.16874 q^{15} +1.00000 q^{16} -2.32516 q^{17} -1.69934 q^{18} +1.00000 q^{19} +1.90163 q^{20} -2.73043 q^{21} -4.82094 q^{22} +3.20197 q^{23} -1.14046 q^{24} -1.38379 q^{25} -2.93868 q^{26} +5.35943 q^{27} +2.39414 q^{28} -0.604936 q^{29} -2.16874 q^{30} -2.02761 q^{31} +1.00000 q^{32} +5.49810 q^{33} -2.32516 q^{34} +4.55278 q^{35} -1.69934 q^{36} +3.52215 q^{37} +1.00000 q^{38} +3.35146 q^{39} +1.90163 q^{40} +7.60182 q^{41} -2.73043 q^{42} -3.42519 q^{43} -4.82094 q^{44} -3.23153 q^{45} +3.20197 q^{46} +5.77575 q^{47} -1.14046 q^{48} -1.26809 q^{49} -1.38379 q^{50} +2.65176 q^{51} -2.93868 q^{52} +6.56721 q^{53} +5.35943 q^{54} -9.16766 q^{55} +2.39414 q^{56} -1.14046 q^{57} -0.604936 q^{58} -8.44960 q^{59} -2.16874 q^{60} -4.08156 q^{61} -2.02761 q^{62} -4.06847 q^{63} +1.00000 q^{64} -5.58830 q^{65} +5.49810 q^{66} -4.70179 q^{67} -2.32516 q^{68} -3.65173 q^{69} +4.55278 q^{70} -2.73075 q^{71} -1.69934 q^{72} +9.55631 q^{73} +3.52215 q^{74} +1.57816 q^{75} +1.00000 q^{76} -11.5420 q^{77} +3.35146 q^{78} -15.4282 q^{79} +1.90163 q^{80} -1.01421 q^{81} +7.60182 q^{82} -3.58775 q^{83} -2.73043 q^{84} -4.42161 q^{85} -3.42519 q^{86} +0.689908 q^{87} -4.82094 q^{88} -15.9989 q^{89} -3.23153 q^{90} -7.03562 q^{91} +3.20197 q^{92} +2.31242 q^{93} +5.77575 q^{94} +1.90163 q^{95} -1.14046 q^{96} -4.53892 q^{97} -1.26809 q^{98} +8.19242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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