LMFDB - Embedded newform 8007.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23101 q^{2} -1.00000 q^{3} +2.97739 q^{4} +0.320461 q^{5} +2.23101 q^{6} +0.645663 q^{7} -2.18055 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23101 q^{2} -1.00000 q^{3} +2.97739 q^{4} +0.320461 q^{5} +2.23101 q^{6} +0.645663 q^{7} -2.18055 q^{8} +1.00000 q^{9} -0.714950 q^{10} +3.13620 q^{11} -2.97739 q^{12} +1.44258 q^{13} -1.44048 q^{14} -0.320461 q^{15} -1.08994 q^{16} +1.00000 q^{17} -2.23101 q^{18} +5.27816 q^{19} +0.954136 q^{20} -0.645663 q^{21} -6.99687 q^{22} -1.47811 q^{23} +2.18055 q^{24} -4.89730 q^{25} -3.21840 q^{26} -1.00000 q^{27} +1.92239 q^{28} -0.913802 q^{29} +0.714950 q^{30} +3.95801 q^{31} +6.79278 q^{32} -3.13620 q^{33} -2.23101 q^{34} +0.206910 q^{35} +2.97739 q^{36} -1.82548 q^{37} -11.7756 q^{38} -1.44258 q^{39} -0.698782 q^{40} +5.92891 q^{41} +1.44048 q^{42} -4.59019 q^{43} +9.33767 q^{44} +0.320461 q^{45} +3.29767 q^{46} -3.20741 q^{47} +1.08994 q^{48} -6.58312 q^{49} +10.9259 q^{50} -1.00000 q^{51} +4.29511 q^{52} +1.53727 q^{53} +2.23101 q^{54} +1.00503 q^{55} -1.40790 q^{56} -5.27816 q^{57} +2.03870 q^{58} -7.87522 q^{59} -0.954136 q^{60} -2.43098 q^{61} -8.83035 q^{62} +0.645663 q^{63} -12.9748 q^{64} +0.462289 q^{65} +6.99687 q^{66} -5.18233 q^{67} +2.97739 q^{68} +1.47811 q^{69} -0.461617 q^{70} -3.67765 q^{71} -2.18055 q^{72} -6.02742 q^{73} +4.07266 q^{74} +4.89730 q^{75} +15.7151 q^{76} +2.02493 q^{77} +3.21840 q^{78} -10.8898 q^{79} -0.349284 q^{80} +1.00000 q^{81} -13.2274 q^{82} -2.81526 q^{83} -1.92239 q^{84} +0.320461 q^{85} +10.2407 q^{86} +0.913802 q^{87} -6.83865 q^{88} +8.86995 q^{89} -0.714950 q^{90} +0.931419 q^{91} -4.40090 q^{92} -3.95801 q^{93} +7.15574 q^{94} +1.69144 q^{95} -6.79278 q^{96} -17.5017 q^{97} +14.6870 q^{98} +3.13620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−2.23101	−1.57756	−0.788780	−	0.614676i	$-0.789287\pi$
$2$	−2.23101	−1.57756	−0.788780	+	0.614676i	$0.789287\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.97739	1.48869
$5$	0.320461	0.143314	0.0716572	−	0.997429i	$-0.477171\pi$
$5$	0.320461	0.143314	0.0716572	+	0.997429i	$0.477171\pi$
$6$	2.23101	0.910804
$7$	0.645663	0.244038	0.122019	−	0.992528i	$-0.461063\pi$
$7$	0.645663	0.244038	0.122019	+	0.992528i	$0.461063\pi$
$8$	−2.18055	−0.770943
$9$	1.00000	0.333333
$10$	−0.714950	−0.226087
$11$	3.13620	0.945599	0.472799	−	0.881170i	$-0.343244\pi$
$11$	3.13620	0.945599	0.472799	+	0.881170i	$0.343244\pi$
$12$	−2.97739	−0.859497
$13$	1.44258	0.400099	0.200049	−	0.979786i	$-0.435890\pi$
$13$	1.44258	0.400099	0.200049	+	0.979786i	$0.435890\pi$
$14$	−1.44048	−0.384984
$15$	−0.320461	−0.0827426
$16$	−1.08994	−0.272486
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.23101	−0.525853
$19$	5.27816	1.21089	0.605447	−	0.795886i	$-0.292994\pi$
$19$	5.27816	1.21089	0.605447	+	0.795886i	$0.292994\pi$
$20$	0.954136	0.213351
$21$	−0.645663	−0.140895
$22$	−6.99687	−1.49174
$23$	−1.47811	−0.308207	−0.154103	−	0.988055i	$-0.549249\pi$
$23$	−1.47811	−0.308207	−0.154103	+	0.988055i	$0.549249\pi$
$24$	2.18055	0.445104
$25$	−4.89730	−0.979461
$26$	−3.21840	−0.631180
$27$	−1.00000	−0.192450
$28$	1.92239	0.363297
$29$	−0.913802	−0.169689	−0.0848444	−	0.996394i	$-0.527039\pi$
$29$	−0.913802	−0.169689	−0.0848444	+	0.996394i	$0.527039\pi$
$30$	0.714950	0.130531
$31$	3.95801	0.710880	0.355440	−	0.934699i	$-0.384331\pi$
$31$	3.95801	0.710880	0.355440	+	0.934699i	$0.384331\pi$
$32$	6.79278	1.20080
$33$	−3.13620	−0.545942
$34$	−2.23101	−0.382614
$35$	0.206910	0.0349741
$36$	2.97739	0.496231
$37$	−1.82548	−0.300108	−0.150054	−	0.988678i	$-0.547945\pi$
$37$	−1.82548	−0.300108	−0.150054	+	0.988678i	$0.547945\pi$
$38$	−11.7756	−1.91026
$39$	−1.44258	−0.230997
$40$	−0.698782	−0.110487
$41$	5.92891	0.925941	0.462970	−	0.886374i	$-0.346784\pi$
$41$	5.92891	0.925941	0.462970	+	0.886374i	$0.346784\pi$
$42$	1.44048	0.222271
$43$	−4.59019	−0.699997	−0.349999	−	0.936750i	$-0.613818\pi$
$43$	−4.59019	−0.699997	−0.349999	+	0.936750i	$0.613818\pi$
$44$	9.33767	1.40771
$45$	0.320461	0.0477715
$46$	3.29767	0.486214
$47$	−3.20741	−0.467848	−0.233924	−	0.972255i	$-0.575157\pi$
$47$	−3.20741	−0.467848	−0.233924	+	0.972255i	$0.575157\pi$
$48$	1.08994	0.157320
$49$	−6.58312	−0.940446
$50$	10.9259	1.54516
$51$	−1.00000	−0.140028
$52$	4.29511	0.595624
$53$	1.53727	0.211160	0.105580	−	0.994411i	$-0.466330\pi$
$53$	1.53727	0.211160	0.105580	+	0.994411i	$0.466330\pi$
$54$	2.23101	0.303601
$55$	1.00503	0.135518
$56$	−1.40790	−0.188139
$57$	−5.27816	−0.699110
$58$	2.03870	0.267694
$59$	−7.87522	−1.02527	−0.512633	−	0.858608i	$-0.671330\pi$
$59$	−7.87522	−1.02527	−0.512633	+	0.858608i	$0.671330\pi$
$60$	−0.954136	−0.123178
$61$	−2.43098	−0.311255	−0.155627	−	0.987816i	$-0.549740\pi$
$61$	−2.43098	−0.311255	−0.155627	+	0.987816i	$0.549740\pi$
$62$	−8.83035	−1.12146
$63$	0.645663	0.0813460
$64$	−12.9748	−1.62186
$65$	0.462289	0.0573399
$66$	6.99687	0.861256
$67$	−5.18233	−0.633123	−0.316561	−	0.948572i	$-0.602528\pi$
$67$	−5.18233	−0.633123	−0.316561	+	0.948572i	$0.602528\pi$
$68$	2.97739	0.361061
$69$	1.47811	0.177943
$70$	−0.461617	−0.0551738
$71$	−3.67765	−0.436457	−0.218228	−	0.975898i	$-0.570028\pi$
$71$	−3.67765	−0.436457	−0.218228	+	0.975898i	$0.570028\pi$
$72$	−2.18055	−0.256981
$73$	−6.02742	−0.705456	−0.352728	−	0.935726i	$-0.614746\pi$
$73$	−6.02742	−0.705456	−0.352728	+	0.935726i	$0.614746\pi$
$74$	4.07266	0.473437
$75$	4.89730	0.565492
$76$	15.7151	1.80265
$77$	2.02493	0.230762
$78$	3.21840	0.364412
$79$	−10.8898	−1.22519	−0.612596	−	0.790396i	$-0.709875\pi$
$79$	−10.8898	−1.22519	−0.612596	+	0.790396i	$0.709875\pi$
$80$	−0.349284	−0.0390511
$81$	1.00000	0.111111
$82$	−13.2274	−1.46073
$83$	−2.81526	−0.309015	−0.154507	−	0.987992i	$-0.549379\pi$
$83$	−2.81526	−0.309015	−0.154507	+	0.987992i	$0.549379\pi$
$84$	−1.92239	−0.209750
$85$	0.320461	0.0347589
$86$	10.2407	1.10429
$87$	0.913802	0.0979699
$88$	−6.83865	−0.729002
$89$	8.86995	0.940213	0.470107	−	0.882610i	$-0.344215\pi$
$89$	8.86995	0.940213	0.470107	+	0.882610i	$0.344215\pi$
$90$	−0.714950	−0.0753623
$91$	0.931419	0.0976393
$92$	−4.40090	−0.458825
$93$	−3.95801	−0.410427
$94$	7.15574	0.738058
$95$	1.69144	0.173538
$96$	−6.79278	−0.693285
$97$	−17.5017	−1.77703	−0.888515	−	0.458847i	$-0.848263\pi$
$97$	−17.5017	−1.77703	−0.888515	+	0.458847i	$0.848263\pi$
$98$	14.6870	1.48361
$99$	3.13620	0.315200
$100$	−14.5812	−1.45812
$101$	−9.07001	−0.902500	−0.451250	−	0.892398i	$-0.649022\pi$
$101$	−9.07001	−0.902500	−0.451250	+	0.892398i	$0.649022\pi$
$102$	2.23101	0.220902
$103$	0.117199	0.0115479	0.00577396	−	0.999983i	$-0.498162\pi$
$103$	0.117199	0.0115479	0.00577396	+	0.999983i	$0.498162\pi$
$104$	−3.14562	−0.308453
$105$	−0.206910	−0.0201923
$106$	−3.42965	−0.333117
$107$	−13.9145	−1.34516	−0.672581	−	0.740024i	$-0.734814\pi$
$107$	−13.9145	−1.34516	−0.672581	+	0.740024i	$0.734814\pi$
$108$	−2.97739	−0.286499
$109$	−7.42244	−0.710941	−0.355471	−	0.934687i	$-0.615679\pi$
$109$	−7.42244	−0.710941	−0.355471	+	0.934687i	$0.615679\pi$
$110$	−2.24222	−0.213788
$111$	1.82548	0.173267
$112$	−0.703736	−0.0664968
$113$	9.37213	0.881656	0.440828	−	0.897592i	$-0.354685\pi$
$113$	9.37213	0.881656	0.440828	+	0.897592i	$0.354685\pi$
$114$	11.7756	1.10289
$115$	−0.473676	−0.0441705
$116$	−2.72074	−0.252615
$117$	1.44258	0.133366
$118$	17.5697	1.61742
$119$	0.645663	0.0591879
$120$	0.698782	0.0637898
$121$	−1.16427	−0.105843
$122$	5.42352	0.491022
$123$	−5.92891	−0.534592
$124$	11.7845	1.05828
$125$	−3.17170	−0.283685
$126$	−1.44048	−0.128328
$127$	−14.0697	−1.24849	−0.624243	−	0.781230i	$-0.714593\pi$
$127$	−14.0697	−1.24849	−0.624243	+	0.781230i	$0.714593\pi$
$128$	15.3614	1.35777
$129$	4.59019	0.404144
$130$	−1.03137	−0.0904572
$131$	−11.7806	−1.02928	−0.514640	−	0.857407i	$-0.672074\pi$
$131$	−11.7806	−1.02928	−0.514640	+	0.857407i	$0.672074\pi$
$132$	−9.33767	−0.812740
$133$	3.40792	0.295504
$134$	11.5618	0.998788
$135$	−0.320461	−0.0275809
$136$	−2.18055	−0.186981
$137$	−3.05503	−0.261009	−0.130504	−	0.991448i	$-0.541660\pi$
$137$	−3.05503	−0.261009	−0.130504	+	0.991448i	$0.541660\pi$
$138$	−3.29767	−0.280716
$139$	19.3173	1.63848	0.819238	−	0.573454i	$-0.194397\pi$
$139$	19.3173	1.63848	0.819238	+	0.573454i	$0.194397\pi$
$140$	0.616051	0.0520658
$141$	3.20741	0.270112
$142$	8.20486	0.688536
$143$	4.52421	0.378333
$144$	−1.08994	−0.0908286
$145$	−0.292838	−0.0243189
$146$	13.4472	1.11290
$147$	6.58312	0.542966
$148$	−5.43517	−0.446768
$149$	16.5627	1.35687	0.678434	−	0.734662i	$-0.262659\pi$
$149$	16.5627	1.35687	0.678434	+	0.734662i	$0.262659\pi$
$150$	−10.9259	−0.892097
$151$	−3.61129	−0.293883	−0.146941	−	0.989145i	$-0.546943\pi$
$151$	−3.61129	−0.293883	−0.146941	+	0.989145i	$0.546943\pi$
$152$	−11.5093	−0.933529
$153$	1.00000	0.0808452
$154$	−4.51763	−0.364041
$155$	1.26839	0.101879
$156$	−4.29511	−0.343884
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	24.2951	1.93281
$159$	−1.53727	−0.121913
$160$	2.17682	0.172093
$161$	−0.954360	−0.0752141
$162$	−2.23101	−0.175284
$163$	−0.130735	−0.0102399	−0.00511997	−	0.999987i	$-0.501630\pi$
$163$	−0.130735	−0.0102399	−0.00511997	+	0.999987i	$0.501630\pi$
$164$	17.6527	1.37844
$165$	−1.00503	−0.0782413
$166$	6.28086	0.487489
$167$	−9.34730	−0.723316	−0.361658	−	0.932311i	$-0.617789\pi$
$167$	−9.34730	−0.723316	−0.361658	+	0.932311i	$0.617789\pi$
$168$	1.40790	0.108622
$169$	−10.9190	−0.839921
$170$	−0.714950	−0.0548342
$171$	5.27816	0.403631
$172$	−13.6668	−1.04208
$173$	−24.0903	−1.83155	−0.915774	−	0.401694i	$-0.868422\pi$
$173$	−24.0903	−1.83155	−0.915774	+	0.401694i	$0.868422\pi$
$174$	−2.03870	−0.154553
$175$	−3.16201	−0.239026
$176$	−3.41828	−0.257662
$177$	7.87522	0.591937
$178$	−19.7889	−1.48324
$179$	−12.4950	−0.933919	−0.466960	−	0.884279i	$-0.654651\pi$
$179$	−12.4950	−0.933919	−0.466960	+	0.884279i	$0.654651\pi$
$180$	0.954136	0.0711171
$181$	−1.98964	−0.147889	−0.0739445	−	0.997262i	$-0.523559\pi$
$181$	−1.98964	−0.147889	−0.0739445	+	0.997262i	$0.523559\pi$
$182$	−2.07800	−0.154032
$183$	2.43098	0.179703
$184$	3.22309	0.237610
$185$	−0.584996	−0.0430097
$186$	8.83035	0.647473
$187$	3.13620	0.229341
$188$	−9.54969	−0.696483
$189$	−0.645663	−0.0469651
$190$	−3.77362	−0.273767
$191$	2.03905	0.147541	0.0737703	−	0.997275i	$-0.476497\pi$
$191$	2.03905	0.147541	0.0737703	+	0.997275i	$0.476497\pi$
$192$	12.9748	0.936379
$193$	−5.29653	−0.381252	−0.190626	−	0.981663i	$-0.561052\pi$
$193$	−5.29653	−0.381252	−0.190626	+	0.981663i	$0.561052\pi$
$194$	39.0464	2.80337
$195$	−0.462289	−0.0331052
$196$	−19.6005	−1.40003
$197$	8.97810	0.639663	0.319831	−	0.947474i	$-0.396374\pi$
$197$	8.97810	0.639663	0.319831	+	0.947474i	$0.396374\pi$
$198$	−6.99687	−0.497246
$199$	11.2170	0.795154	0.397577	−	0.917569i	$-0.369851\pi$
$199$	11.2170	0.795154	0.397577	+	0.917569i	$0.369851\pi$
$200$	10.6788	0.755108
$201$	5.18233	0.365534
$202$	20.2352	1.42375
$203$	−0.590009	−0.0414105
$204$	−2.97739	−0.208459
$205$	1.89998	0.132701
$206$	−0.261471	−0.0182175
$207$	−1.47811	−0.102736
$208$	−1.57233	−0.109021
$209$	16.5534	1.14502
$210$	0.461617	0.0318546
$211$	−0.883917	−0.0608514	−0.0304257	−	0.999537i	$-0.509686\pi$
$211$	−0.883917	−0.0608514	−0.0304257	+	0.999537i	$0.509686\pi$
$212$	4.57703	0.314352
$213$	3.67765	0.251988
$214$	31.0432	2.12207
$215$	−1.47098	−0.100320
$216$	2.18055	0.148368
$217$	2.55554	0.173482
$218$	16.5595	1.12155
$219$	6.02742	0.407295
$220$	2.99236	0.201745
$221$	1.44258	0.0970382
$222$	−4.07266	−0.273339
$223$	−7.51404	−0.503177	−0.251589	−	0.967834i	$-0.580953\pi$
$223$	−7.51404	−0.503177	−0.251589	+	0.967834i	$0.580953\pi$
$224$	4.38585	0.293042
$225$	−4.89730	−0.326487
$226$	−20.9093	−1.39086
$227$	−5.15890	−0.342408	−0.171204	−	0.985236i	$-0.554766\pi$
$227$	−5.15890	−0.342408	−0.171204	+	0.985236i	$0.554766\pi$
$228$	−15.7151	−1.04076
$229$	−16.7774	−1.10868	−0.554341	−	0.832290i	$-0.687029\pi$
$229$	−16.7774	−1.10868	−0.554341	+	0.832290i	$0.687029\pi$
$230$	1.05677	0.0696815
$231$	−2.02493	−0.133230
$232$	1.99260	0.130820
$233$	13.4122	0.878661	0.439331	−	0.898325i	$-0.355216\pi$
$233$	13.4122	0.878661	0.439331	+	0.898325i	$0.355216\pi$
$234$	−3.21840	−0.210393
$235$	−1.02785	−0.0670494
$236$	−23.4476	−1.52631
$237$	10.8898	0.707365
$238$	−1.44048	−0.0933724
$239$	−5.82378	−0.376709	−0.188355	−	0.982101i	$-0.560315\pi$
$239$	−5.82378	−0.376709	−0.188355	+	0.982101i	$0.560315\pi$
$240$	0.349284	0.0225462
$241$	−13.5584	−0.873370	−0.436685	−	0.899614i	$-0.643848\pi$
$241$	−13.5584	−0.873370	−0.436685	+	0.899614i	$0.643848\pi$
$242$	2.59749	0.166973
$243$	−1.00000	−0.0641500
$244$	−7.23795	−0.463363
$245$	−2.10963	−0.134779
$246$	13.2274	0.843351
$247$	7.61415	0.484477
$248$	−8.63066	−0.548048
$249$	2.81526	0.178410
$250$	7.07608	0.447530
$251$	6.27210	0.395891	0.197946	−	0.980213i	$-0.436573\pi$
$251$	6.27210	0.395891	0.197946	+	0.980213i	$0.436573\pi$
$252$	1.92239	0.121099
$253$	−4.63564	−0.291440
$254$	31.3896	1.96956
$255$	−0.320461	−0.0200680
$256$	−8.32166	−0.520104
$257$	16.2473	1.01348	0.506741	−	0.862098i	$-0.330850\pi$
$257$	16.2473	1.01348	0.506741	+	0.862098i	$0.330850\pi$
$258$	−10.2407	−0.637561
$259$	−1.17865	−0.0732376
$260$	1.37641	0.0853616
$261$	−0.913802	−0.0565629
$262$	26.2827	1.62375
$263$	28.1292	1.73452	0.867261	−	0.497854i	$-0.165878\pi$
$263$	28.1292	1.73452	0.867261	+	0.497854i	$0.165878\pi$
$264$	6.83865	0.420890
$265$	0.492633	0.0302622
$266$	−7.60308	−0.466175
$267$	−8.86995	−0.542832
$268$	−15.4298	−0.942525
$269$	25.3426	1.54517	0.772584	−	0.634912i	$-0.218964\pi$
$269$	25.3426	1.54517	0.772584	+	0.634912i	$0.218964\pi$
$270$	0.714950	0.0435105
$271$	−6.86970	−0.417304	−0.208652	−	0.977990i	$-0.566908\pi$
$271$	−6.86970	−0.417304	−0.208652	+	0.977990i	$0.566908\pi$
$272$	−1.08994	−0.0660875
$273$	−0.931419	−0.0563721
$274$	6.81579	0.411757
$275$	−15.3589	−0.926177
$276$	4.40090	0.264903
$277$	−0.778402	−0.0467697	−0.0233848	−	0.999727i	$-0.507444\pi$
$277$	−0.778402	−0.0467697	−0.0233848	+	0.999727i	$0.507444\pi$
$278$	−43.0971	−2.58479
$279$	3.95801	0.236960
$280$	−0.451178	−0.0269631
$281$	28.0478	1.67319	0.836595	−	0.547823i	$-0.184543\pi$
$281$	28.0478	1.67319	0.836595	+	0.547823i	$0.184543\pi$
$282$	−7.15574	−0.426118
$283$	−18.0239	−1.07141	−0.535706	−	0.844404i	$-0.679955\pi$
$283$	−18.0239	−1.07141	−0.535706	+	0.844404i	$0.679955\pi$
$284$	−10.9498	−0.649750
$285$	−1.69144	−0.100192
$286$	−10.0935	−0.596843
$287$	3.82808	0.225965
$288$	6.79278	0.400268
$289$	1.00000	0.0588235
$290$	0.653323	0.0383644
$291$	17.5017	1.02597
$292$	−17.9460	−1.05021
$293$	−27.6495	−1.61530	−0.807651	−	0.589661i	$-0.799261\pi$
$293$	−27.6495	−1.61530	−0.807651	+	0.589661i	$0.799261\pi$
$294$	−14.6870	−0.856562
$295$	−2.52370	−0.146935
$296$	3.98057	0.231366
$297$	−3.13620	−0.181981
$298$	−36.9514	−2.14054
$299$	−2.13228	−0.123313
$300$	14.5812	0.841844
$301$	−2.96372	−0.170826
$302$	8.05681	0.463618
$303$	9.07001	0.521058
$304$	−5.75289	−0.329951
$305$	−0.779032	−0.0446073
$306$	−2.23101	−0.127538
$307$	−3.58602	−0.204665	−0.102333	−	0.994750i	$-0.532631\pi$
$307$	−3.58602	−0.204665	−0.102333	+	0.994750i	$0.532631\pi$
$308$	6.02899	0.343534
$309$	−0.117199	−0.00666720
$310$	−2.82978	−0.160721
$311$	−10.3322	−0.585885	−0.292943	−	0.956130i	$-0.594634\pi$
$311$	−10.3322	−0.585885	−0.292943	+	0.956130i	$0.594634\pi$
$312$	3.14562	0.178086
$313$	−15.3311	−0.866567	−0.433284	−	0.901258i	$-0.642645\pi$
$313$	−15.3311	−0.866567	−0.433284	+	0.901258i	$0.642645\pi$
$314$	−2.23101	−0.125903
$315$	0.206910	0.0116580
$316$	−32.4230	−1.82394
$317$	11.2627	0.632575	0.316287	−	0.948663i	$-0.397564\pi$
$317$	11.2627	0.632575	0.316287	+	0.948663i	$0.397564\pi$
$318$	3.42965	0.192325
$319$	−2.86586	−0.160458
$320$	−4.15793	−0.232435
$321$	13.9145	0.776629
$322$	2.12918	0.118655
$323$	5.27816	0.293685
$324$	2.97739	0.165410
$325$	−7.06474	−0.391881
$326$	0.291670	0.0161541
$327$	7.42244	0.410462
$328$	−12.9283	−0.713847
$329$	−2.07091	−0.114173
$330$	2.24222	0.123430
$331$	13.3695	0.734854	0.367427	−	0.930052i	$-0.380239\pi$
$331$	13.3695	0.734854	0.367427	+	0.930052i	$0.380239\pi$
$332$	−8.38211	−0.460028
$333$	−1.82548	−0.100036
$334$	20.8539	1.14107
$335$	−1.66073	−0.0907356
$336$	0.703736	0.0383920
$337$	−9.62132	−0.524107	−0.262053	−	0.965053i	$-0.584400\pi$
$337$	−9.62132	−0.524107	−0.262053	+	0.965053i	$0.584400\pi$
$338$	24.3603	1.32503
$339$	−9.37213	−0.509024
$340$	0.954136	0.0517453
$341$	12.4131	0.672207
$342$	−11.7756	−0.636752
$343$	−8.77012	−0.473542
$344$	10.0092	0.539658
$345$	0.473676	0.0255018
$346$	53.7455	2.88938
$347$	17.1156	0.918816	0.459408	−	0.888225i	$-0.348062\pi$
$347$	17.1156	0.918816	0.459408	+	0.888225i	$0.348062\pi$
$348$	2.72074	0.145847
$349$	3.06538	0.164086	0.0820429	−	0.996629i	$-0.473856\pi$
$349$	3.06538	0.164086	0.0820429	+	0.996629i	$0.473856\pi$
$350$	7.05446	0.377077
$351$	−1.44258	−0.0769991
$352$	21.3035	1.13548
$353$	−17.9693	−0.956411	−0.478206	−	0.878248i	$-0.658713\pi$
$353$	−17.9693	−0.956411	−0.478206	+	0.878248i	$0.658713\pi$
$354$	−17.5697	−0.933816
$355$	−1.17854	−0.0625505
$356$	26.4093	1.39969
$357$	−0.645663	−0.0341721
$358$	27.8764	1.47331
$359$	11.0702	0.584265	0.292133	−	0.956378i	$-0.405635\pi$
$359$	11.0702	0.584265	0.292133	+	0.956378i	$0.405635\pi$
$360$	−0.698782	−0.0368291
$361$	8.85899	0.466263
$362$	4.43890	0.233304
$363$	1.16427	0.0611083
$364$	2.77320	0.145355
$365$	−1.93155	−0.101102
$366$	−5.42352	−0.283492
$367$	9.56610	0.499346	0.249673	−	0.968330i	$-0.419677\pi$
$367$	9.56610	0.499346	0.249673	+	0.968330i	$0.419677\pi$
$368$	1.61105	0.0839819
$369$	5.92891	0.308647
$370$	1.30513	0.0678504
$371$	0.992556	0.0515309
$372$	−11.7845	−0.611000
$373$	−9.75750	−0.505224	−0.252612	−	0.967568i	$-0.581290\pi$
$373$	−9.75750	−0.505224	−0.252612	+	0.967568i	$0.581290\pi$
$374$	−6.99687	−0.361800
$375$	3.17170	0.163786
$376$	6.99392	0.360684
$377$	−1.31823	−0.0678923
$378$	1.44048	0.0740902
$379$	−5.86082	−0.301050	−0.150525	−	0.988606i	$-0.548096\pi$
$379$	−5.86082	−0.301050	−0.150525	+	0.988606i	$0.548096\pi$
$380$	5.03608	0.258346
$381$	14.0697	0.720814
$382$	−4.54914	−0.232754
$383$	33.8249	1.72837	0.864187	−	0.503171i	$-0.167833\pi$
$383$	33.8249	1.72837	0.864187	+	0.503171i	$0.167833\pi$
$384$	−15.3614	−0.783908
$385$	0.648910	0.0330715
$386$	11.8166	0.601448
$387$	−4.59019	−0.233332
$388$	−52.1094	−2.64545
$389$	30.2676	1.53463	0.767315	−	0.641270i	$-0.221592\pi$
$389$	30.2676	1.53463	0.767315	+	0.641270i	$0.221592\pi$
$390$	1.03137	0.0522255
$391$	−1.47811	−0.0747511
$392$	14.3549	0.725029
$393$	11.7806	0.594255
$394$	−20.0302	−1.00911
$395$	−3.48974	−0.175588
$396$	9.33767	0.469236
$397$	6.42289	0.322356	0.161178	−	0.986925i	$-0.448471\pi$
$397$	6.42289	0.322356	0.161178	+	0.986925i	$0.448471\pi$
$398$	−25.0253	−1.25440
$399$	−3.40792	−0.170609
$400$	5.33778	0.266889
$401$	−11.7960	−0.589065	−0.294533	−	0.955641i	$-0.595164\pi$
$401$	−11.7960	−0.589065	−0.294533	+	0.955641i	$0.595164\pi$
$402$	−11.5618	−0.576651
$403$	5.70974	0.284422
$404$	−27.0049	−1.34355
$405$	0.320461	0.0159238
$406$	1.31631	0.0653275
$407$	−5.72507	−0.283781
$408$	2.18055	0.107954
$409$	14.6814	0.725951	0.362975	−	0.931799i	$-0.381761\pi$
$409$	14.6814	0.725951	0.362975	+	0.931799i	$0.381761\pi$
$410$	−4.23888	−0.209343
$411$	3.05503	0.150693
$412$	0.348946	0.0171913
$413$	−5.08474	−0.250204
$414$	3.29767	0.162071
$415$	−0.902180	−0.0442863
$416$	9.79911	0.480441
$417$	−19.3173	−0.945974
$418$	−36.9306	−1.80634
$419$	−1.82310	−0.0890641	−0.0445320	−	0.999008i	$-0.514180\pi$
$419$	−1.82310	−0.0890641	−0.0445320	+	0.999008i	$0.514180\pi$
$420$	−0.616051	−0.0300602
$421$	35.5079	1.73055	0.865276	−	0.501296i	$-0.167143\pi$
$421$	35.5079	1.73055	0.865276	+	0.501296i	$0.167143\pi$
$422$	1.97202	0.0959966
$423$	−3.20741	−0.155949
$424$	−3.35209	−0.162792
$425$	−4.89730	−0.237554
$426$	−8.20486	−0.397527
$427$	−1.56959	−0.0759579
$428$	−41.4287	−2.00253
$429$	−4.52421	−0.218431
$430$	3.28176	0.158260
$431$	2.73681	0.131827	0.0659137	−	0.997825i	$-0.479004\pi$
$431$	2.73681	0.131827	0.0659137	+	0.997825i	$0.479004\pi$
$432$	1.08994	0.0524399
$433$	26.4010	1.26875	0.634377	−	0.773024i	$-0.281257\pi$
$433$	26.4010	1.26875	0.634377	+	0.773024i	$0.281257\pi$
$434$	−5.70143	−0.273678
$435$	0.292838	0.0140405
$436$	−22.0995	−1.05837
$437$	−7.80169	−0.373205
$438$	−13.4472	−0.642533
$439$	−24.9043	−1.18862	−0.594308	−	0.804238i	$-0.702574\pi$
$439$	−24.9043	−1.18862	−0.594308	+	0.804238i	$0.702574\pi$
$440$	−2.19152	−0.104477
$441$	−6.58312	−0.313482
$442$	−3.21840	−0.153084
$443$	21.2434	1.00931	0.504653	−	0.863322i	$-0.331620\pi$
$443$	21.2434	1.00931	0.504653	+	0.863322i	$0.331620\pi$
$444$	5.43517	0.257942
$445$	2.84247	0.134746
$446$	16.7639	0.793792
$447$	−16.5627	−0.783388
$448$	−8.37738	−0.395794
$449$	−1.80405	−0.0851382	−0.0425691	−	0.999094i	$-0.513554\pi$
$449$	−1.80405	−0.0851382	−0.0425691	+	0.999094i	$0.513554\pi$
$450$	10.9259	0.515053
$451$	18.5942	0.875569
$452$	27.9045	1.31252
$453$	3.61129	0.169673
$454$	11.5095	0.540169
$455$	0.298483	0.0139931
$456$	11.5093	0.538973
$457$	−5.03839	−0.235686	−0.117843	−	0.993032i	$-0.537598\pi$
$457$	−5.03839	−0.235686	−0.117843	+	0.993032i	$0.537598\pi$
$458$	37.4305	1.74901
$459$	−1.00000	−0.0466760
$460$	−1.41032	−0.0657563
$461$	33.8517	1.57663	0.788315	−	0.615272i	$-0.210954\pi$
$461$	33.8517	1.57663	0.788315	+	0.615272i	$0.210954\pi$
$462$	4.51763	0.210179
$463$	−12.7515	−0.592614	−0.296307	−	0.955093i	$-0.595755\pi$
$463$	−12.7515	−0.592614	−0.296307	+	0.955093i	$0.595755\pi$
$464$	0.995992	0.0462378
$465$	−1.26839	−0.0588201
$466$	−29.9226	−1.38614
$467$	−16.9029	−0.782175	−0.391088	−	0.920353i	$-0.627901\pi$
$467$	−16.9029	−0.782175	−0.391088	+	0.920353i	$0.627901\pi$
$468$	4.29511	0.198541
$469$	−3.34604	−0.154506
$470$	2.29313	0.105774
$471$	−1.00000	−0.0460776
$472$	17.1723	0.790421
$473$	−14.3957	−0.661917
$474$	−24.2951	−1.11591
$475$	−25.8488	−1.18602
$476$	1.92239	0.0881126
$477$	1.53727	0.0703865
$478$	12.9929	0.594281
$479$	−29.7512	−1.35937	−0.679684	−	0.733505i	$-0.737883\pi$
$479$	−29.7512	−1.35937	−0.679684	+	0.733505i	$0.737883\pi$
$480$	−2.17682	−0.0993578
$481$	−2.63340	−0.120073
$482$	30.2488	1.37779
$483$	0.954360	0.0434249
$484$	−3.46648	−0.157567
$485$	−5.60862	−0.254674
$486$	2.23101	0.101200
$487$	30.2009	1.36853	0.684266	−	0.729233i	$-0.260123\pi$
$487$	30.2009	1.36853	0.684266	+	0.729233i	$0.260123\pi$
$488$	5.30088	0.239959
$489$	0.130735	0.00591204
$490$	4.70660	0.212623
$491$	15.9082	0.717925	0.358963	−	0.933352i	$-0.383131\pi$
$491$	15.9082	0.717925	0.358963	+	0.933352i	$0.383131\pi$
$492$	−17.6527	−0.795844
$493$	−0.913802	−0.0411556
$494$	−16.9872	−0.764291
$495$	1.00503	0.0451727
$496$	−4.31401	−0.193705
$497$	−2.37452	−0.106512
$498$	−6.28086	−0.281452
$499$	28.7924	1.28892	0.644462	−	0.764637i	$-0.277082\pi$
$499$	28.7924	1.28892	0.644462	+	0.764637i	$0.277082\pi$
$500$	−9.44337	−0.422320
$501$	9.34730	0.417607
$502$	−13.9931	−0.624542
$503$	23.9105	1.06612	0.533059	−	0.846078i	$-0.321042\pi$
$503$	23.9105	1.06612	0.533059	+	0.846078i	$0.321042\pi$
$504$	−1.40790	−0.0627131
$505$	−2.90658	−0.129341
$506$	10.3421	0.459764
$507$	10.9190	0.484929
$508$	−41.8910	−1.85861
$509$	−31.1497	−1.38069	−0.690343	−	0.723483i	$-0.742540\pi$
$509$	−31.1497	−1.38069	−0.690343	+	0.723483i	$0.742540\pi$
$510$	0.714950	0.0316585
$511$	−3.89169	−0.172158
$512$	−12.1571	−0.537273
$513$	−5.27816	−0.233037
$514$	−36.2479	−1.59883
$515$	0.0375576	0.00165498
$516$	13.6668	0.601646
$517$	−10.0591	−0.442397
$518$	2.62957	0.115537
$519$	24.0903	1.05744
$520$	−1.00805	−0.0442058
$521$	6.47012	0.283461	0.141731	−	0.989905i	$-0.454733\pi$
$521$	6.47012	0.283461	0.141731	+	0.989905i	$0.454733\pi$
$522$	2.03870	0.0892314
$523$	12.3803	0.541353	0.270677	−	0.962670i	$-0.412753\pi$
$523$	12.3803	0.541353	0.270677	+	0.962670i	$0.412753\pi$
$524$	−35.0755	−1.53228
$525$	3.16201	0.138001
$526$	−62.7565	−2.73631
$527$	3.95801	0.172414
$528$	3.41828	0.148761
$529$	−20.8152	−0.905009
$530$	−1.09907	−0.0477404
$531$	−7.87522	−0.341755
$532$	10.1467	0.439915
$533$	8.55291	0.370468
$534$	19.7889	0.856350
$535$	−4.45904	−0.192781
$536$	11.3004	0.488101
$537$	12.4950	0.539199
$538$	−56.5396	−2.43759
$539$	−20.6460	−0.889284
$540$	−0.954136	−0.0410595
$541$	−28.9803	−1.24596	−0.622979	−	0.782238i	$-0.714078\pi$
$541$	−28.9803	−1.24596	−0.622979	+	0.782238i	$0.714078\pi$
$542$	15.3263	0.658322
$543$	1.98964	0.0853837
$544$	6.79278	0.291238
$545$	−2.37860	−0.101888
$546$	2.07800	0.0889303
$547$	−39.1120	−1.67231	−0.836154	−	0.548495i	$-0.815201\pi$
$547$	−39.1120	−1.67231	−0.836154	+	0.548495i	$0.815201\pi$
$548$	−9.09600	−0.388562
$549$	−2.43098	−0.103752
$550$	34.2658	1.46110
$551$	−4.82320	−0.205475
$552$	−3.22309	−0.137184
$553$	−7.03112	−0.298993
$554$	1.73662	0.0737819
$555$	0.584996	0.0248317
$556$	57.5152	2.43919
$557$	−39.7432	−1.68397	−0.841986	−	0.539500i	$-0.818613\pi$
$557$	−39.7432	−1.68397	−0.841986	+	0.539500i	$0.818613\pi$
$558$	−8.83035	−0.373819
$559$	−6.62170	−0.280068
$560$	−0.225520	−0.00952996
$561$	−3.13620	−0.132410
$562$	−62.5747	−2.63955
$563$	−27.4858	−1.15839	−0.579193	−	0.815190i	$-0.696632\pi$
$563$	−27.4858	−1.15839	−0.579193	+	0.815190i	$0.696632\pi$
$564$	9.54969	0.402114
$565$	3.00340	0.126354
$566$	40.2115	1.69022
$567$	0.645663	0.0271153
$568$	8.01931	0.336483
$569$	39.1449	1.64104	0.820520	−	0.571617i	$-0.193684\pi$
$569$	39.1449	1.64104	0.820520	+	0.571617i	$0.193684\pi$
$570$	3.77362	0.158060
$571$	−26.5537	−1.11124	−0.555618	−	0.831438i	$-0.687518\pi$
$571$	−26.5537	−1.11124	−0.555618	+	0.831438i	$0.687518\pi$
$572$	13.4703	0.563222
$573$	−2.03905	−0.0851826
$574$	−8.54047	−0.356473
$575$	7.23874	0.301876
$576$	−12.9748	−0.540618
$577$	−33.1962	−1.38198	−0.690989	−	0.722865i	$-0.742825\pi$
$577$	−33.1962	−1.38198	−0.690989	+	0.722865i	$0.742825\pi$
$578$	−2.23101	−0.0927976
$579$	5.29653	0.220116
$580$	−0.871891	−0.0362033
$581$	−1.81771	−0.0754113
$582$	−39.0464	−1.61853
$583$	4.82117	0.199672
$584$	13.1431	0.543866
$585$	0.462289	0.0191133
$586$	61.6862	2.54823
$587$	−21.3084	−0.879491	−0.439745	−	0.898122i	$-0.644931\pi$
$587$	−21.3084	−0.879491	−0.439745	+	0.898122i	$0.644931\pi$
$588$	19.6005	0.808311
$589$	20.8910	0.860800
$590$	5.63038	0.231799
$591$	−8.97810	−0.369309
$592$	1.98967	0.0817750
$593$	−26.1029	−1.07192	−0.535958	−	0.844245i	$-0.680050\pi$
$593$	−26.1029	−1.07192	−0.535958	+	0.844245i	$0.680050\pi$
$594$	6.99687	0.287085
$595$	0.206910	0.00848248
$596$	49.3135	2.01996
$597$	−11.2170	−0.459082
$598$	4.75714	0.194534
$599$	−7.26445	−0.296817	−0.148409	−	0.988926i	$-0.547415\pi$
$599$	−7.26445	−0.296817	−0.148409	+	0.988926i	$0.547415\pi$
$600$	−10.6788	−0.435962
$601$	33.0190	1.34687	0.673436	−	0.739246i	$-0.264818\pi$
$601$	33.0190	1.34687	0.673436	+	0.739246i	$0.264818\pi$
$602$	6.61207	0.269488
$603$	−5.18233	−0.211041
$604$	−10.7522	−0.437501
$605$	−0.373103	−0.0151688
$606$	−20.2352	−0.822000
$607$	21.2581	0.862841	0.431420	−	0.902151i	$-0.358013\pi$
$607$	21.2581	0.862841	0.431420	+	0.902151i	$0.358013\pi$
$608$	35.8534	1.45405
$609$	0.590009	0.0239084
$610$	1.73803	0.0703706
$611$	−4.62693	−0.187186
$612$	2.97739	0.120354
$613$	−20.2818	−0.819172	−0.409586	−	0.912271i	$-0.634327\pi$
$613$	−20.2818	−0.819172	−0.409586	+	0.912271i	$0.634327\pi$
$614$	8.00044	0.322871
$615$	−1.89998	−0.0766148
$616$	−4.41547	−0.177904
$617$	42.8190	1.72383	0.861913	−	0.507056i	$-0.169266\pi$
$617$	42.8190	1.72383	0.861913	+	0.507056i	$0.169266\pi$
$618$	0.261471	0.0105179
$619$	16.5200	0.663993	0.331997	−	0.943281i	$-0.392278\pi$
$619$	16.5200	0.663993	0.331997	+	0.943281i	$0.392278\pi$
$620$	3.77648	0.151667
$621$	1.47811	0.0593144
$622$	23.0512	0.924268
$623$	5.72701	0.229448
$624$	1.57233	0.0629434
$625$	23.4701	0.938805
$626$	34.2039	1.36706
$627$	−16.5534	−0.661077
$628$	2.97739	0.118811
$629$	−1.82548	−0.0727868
$630$	−0.461617	−0.0183913
$631$	−44.8596	−1.78583	−0.892916	−	0.450223i	$-0.851344\pi$
$631$	−44.8596	−1.78583	−0.892916	+	0.450223i	$0.851344\pi$
$632$	23.7457	0.944553
$633$	0.883917	0.0351326
$634$	−25.1271	−0.997924
$635$	−4.50880	−0.178926
$636$	−4.57703	−0.181491
$637$	−9.49666	−0.376271
$638$	6.39376	0.253131
$639$	−3.67765	−0.145486
$640$	4.92272	0.194588
$641$	7.98965	0.315572	0.157786	−	0.987473i	$-0.449564\pi$
$641$	7.98965	0.315572	0.157786	+	0.987473i	$0.449564\pi$
$642$	−31.0432	−1.22518
$643$	40.8234	1.60992	0.804959	−	0.593330i	$-0.202187\pi$
$643$	40.8234	1.60992	0.804959	+	0.593330i	$0.202187\pi$
$644$	−2.84150	−0.111971
$645$	1.47098	0.0579196
$646$	−11.7756	−0.463305
$647$	20.4525	0.804070	0.402035	−	0.915624i	$-0.368303\pi$
$647$	20.4525	0.804070	0.402035	+	0.915624i	$0.368303\pi$
$648$	−2.18055	−0.0856603
$649$	−24.6982	−0.969490
$650$	15.7615	0.618216
$651$	−2.55554	−0.100160
$652$	−0.389248	−0.0152441
$653$	−30.8355	−1.20669	−0.603344	−	0.797481i	$-0.706165\pi$
$653$	−30.8355	−1.20669	−0.603344	+	0.797481i	$0.706165\pi$
$654$	−16.5595	−0.647528
$655$	−3.77523	−0.147511
$656$	−6.46218	−0.252306
$657$	−6.02742	−0.235152
$658$	4.62020	0.180114
$659$	39.9625	1.55672	0.778360	−	0.627819i	$-0.216052\pi$
$659$	39.9625	1.55672	0.778360	+	0.627819i	$0.216052\pi$
$660$	−2.99236	−0.116477
$661$	−24.7694	−0.963418	−0.481709	−	0.876331i	$-0.659984\pi$
$661$	−24.7694	−0.963418	−0.481709	+	0.876331i	$0.659984\pi$
$662$	−29.8274	−1.15928
$663$	−1.44258	−0.0560250
$664$	6.13882	0.238233
$665$	1.09210	0.0423500
$666$	4.07266	0.157812
$667$	1.35070	0.0522992
$668$	−27.8305	−1.07680
$669$	7.51404	0.290510
$670$	3.70511	0.143141
$671$	−7.62402	−0.294322
$672$	−4.38585	−0.169188
$673$	7.88706	0.304024	0.152012	−	0.988379i	$-0.451425\pi$
$673$	7.88706	0.304024	0.152012	+	0.988379i	$0.451425\pi$
$674$	21.4652	0.826810
$675$	4.89730	0.188497
$676$	−32.5100	−1.25038
$677$	−25.7570	−0.989921	−0.494960	−	0.868916i	$-0.664817\pi$
$677$	−25.7570	−0.989921	−0.494960	+	0.868916i	$0.664817\pi$
$678$	20.9093	0.803016
$679$	−11.3002	−0.433663
$680$	−0.698782	−0.0267971
$681$	5.15890	0.197689
$682$	−27.6937	−1.06045
$683$	−39.2982	−1.50370	−0.751851	−	0.659333i	$-0.770839\pi$
$683$	−39.2982	−1.50370	−0.751851	+	0.659333i	$0.770839\pi$
$684$	15.7151	0.600883
$685$	−0.979017	−0.0374063
$686$	19.5662	0.747041
$687$	16.7774	0.640097
$688$	5.00304	0.190739
$689$	2.21762	0.0844847
$690$	−1.05677	−0.0402307
$691$	−19.4737	−0.740814	−0.370407	−	0.928870i	$-0.620782\pi$
$691$	−19.4737	−0.740814	−0.370407	+	0.928870i	$0.620782\pi$
$692$	−71.7260	−2.72661
$693$	2.02493	0.0769206
$694$	−38.1851	−1.44949
$695$	6.19045	0.234817
$696$	−1.99260	−0.0755292
$697$	5.92891	0.224574
$698$	−6.83887	−0.258855
$699$	−13.4122	−0.507295
$700$	−9.41453	−0.355836
$701$	−32.8773	−1.24176	−0.620879	−	0.783906i	$-0.713224\pi$
$701$	−32.8773	−1.24176	−0.620879	+	0.783906i	$0.713224\pi$
$702$	3.21840	0.121471
$703$	−9.63519	−0.363398
$704$	−40.6917	−1.53362
$705$	1.02785	0.0387110
$706$	40.0897	1.50880
$707$	−5.85617	−0.220244
$708$	23.4476	0.881213
$709$	−51.1842	−1.92226	−0.961132	−	0.276089i	$-0.910962\pi$
$709$	−51.1842	−1.92226	−0.961132	+	0.276089i	$0.910962\pi$
$710$	2.62933	0.0986772
$711$	−10.8898	−0.408398
$712$	−19.3414	−0.724850
$713$	−5.85037	−0.219098
$714$	1.44048	0.0539086
$715$	1.44983	0.0542206
$716$	−37.2024	−1.39032
$717$	5.82378	0.217493
$718$	−24.6978	−0.921713
$719$	−31.4880	−1.17431	−0.587153	−	0.809476i	$-0.699751\pi$
$719$	−31.4880	−1.17431	−0.587153	+	0.809476i	$0.699751\pi$
$720$	−0.349284	−0.0130170
$721$	0.0756709	0.00281813
$722$	−19.7645	−0.735557
$723$	13.5584	0.504241
$724$	−5.92393	−0.220161
$725$	4.47517	0.166204
$726$	−2.59749	−0.0964020
$727$	−25.0623	−0.929508	−0.464754	−	0.885440i	$-0.653857\pi$
$727$	−25.0623	−0.929508	−0.464754	+	0.885440i	$0.653857\pi$
$728$	−2.03101	−0.0752743
$729$	1.00000	0.0370370
$730$	4.30931	0.159495
$731$	−4.59019	−0.169774
$732$	7.23795	0.267522
$733$	−11.8817	−0.438861	−0.219431	−	0.975628i	$-0.570420\pi$
$733$	−11.8817	−0.438861	−0.219431	+	0.975628i	$0.570420\pi$
$734$	−21.3420	−0.787749
$735$	2.10963	0.0778149
$736$	−10.0405	−0.370096
$737$	−16.2528	−0.598680
$738$	−13.2274	−0.486909
$739$	46.3647	1.70555	0.852776	−	0.522277i	$-0.174917\pi$
$739$	46.3647	1.70555	0.852776	+	0.522277i	$0.174917\pi$
$740$	−1.74176	−0.0640283
$741$	−7.61415	−0.279713
$742$	−2.21440	−0.0812931
$743$	17.0732	0.626355	0.313177	−	0.949695i	$-0.398607\pi$
$743$	17.0732	0.626355	0.313177	+	0.949695i	$0.398607\pi$
$744$	8.63066	0.316416
$745$	5.30769	0.194459
$746$	21.7690	0.797021
$747$	−2.81526	−0.103005
$748$	9.33767	0.341419
$749$	−8.98406	−0.328270
$750$	−7.07608	−0.258382
$751$	5.75311	0.209934	0.104967	−	0.994476i	$-0.466526\pi$
$751$	5.75311	0.209934	0.104967	+	0.994476i	$0.466526\pi$
$752$	3.49589	0.127482
$753$	−6.27210	−0.228568
$754$	2.94098	0.107104
$755$	−1.15728	−0.0421176
$756$	−1.92239	−0.0699166
$757$	24.9533	0.906944	0.453472	−	0.891270i	$-0.350185\pi$
$757$	24.9533	0.906944	0.453472	+	0.891270i	$0.350185\pi$
$758$	13.0755	0.474924
$759$	4.63564	0.168263
$760$	−3.68829	−0.133788
$761$	−22.3539	−0.810328	−0.405164	−	0.914244i	$-0.632786\pi$
$761$	−22.3539	−0.810328	−0.405164	+	0.914244i	$0.632786\pi$
$762$	−31.3896	−1.13713
$763$	−4.79240	−0.173497
$764$	6.07104	0.219643
$765$	0.320461	0.0115863
$766$	−75.4636	−2.72661
$767$	−11.3606	−0.410208
$768$	8.32166	0.300282
$769$	9.95076	0.358834	0.179417	−	0.983773i	$-0.442579\pi$
$769$	9.95076	0.358834	0.179417	+	0.983773i	$0.442579\pi$
$770$	−1.44772	−0.0521723
$771$	−16.2473	−0.585134
$772$	−15.7698	−0.567568
$773$	21.0917	0.758614	0.379307	−	0.925271i	$-0.376162\pi$
$773$	21.0917	0.758614	0.379307	+	0.925271i	$0.376162\pi$
$774$	10.2407	0.368096
$775$	−19.3836	−0.696279
$776$	38.1635	1.36999
$777$	1.17865	0.0422837
$778$	−67.5273	−2.42097
$779$	31.2938	1.12122
$780$	−1.37641	−0.0492835
$781$	−11.5338	−0.412713
$782$	3.29767	0.117924
$783$	0.913802	0.0326566
$784$	7.17522	0.256258
$785$	0.320461	0.0114377
$786$	−26.2827	−0.937472
$787$	12.3355	0.439714	0.219857	−	0.975532i	$-0.429441\pi$
$787$	12.3355	0.439714	0.219857	+	0.975532i	$0.429441\pi$
$788$	26.7313	0.952262
$789$	−28.1292	−1.00143
$790$	7.78563	0.277000
$791$	6.05124	0.215157
$792$	−6.83865	−0.243001
$793$	−3.50687	−0.124533
$794$	−14.3295	−0.508535
$795$	−0.492633	−0.0174719
$796$	33.3974	1.18374
$797$	−31.0007	−1.09810	−0.549050	−	0.835789i	$-0.685010\pi$
$797$	−31.0007	−1.09810	−0.549050	+	0.835789i	$0.685010\pi$
$798$	7.60308	0.269146
$799$	−3.20741	−0.113470
$800$	−33.2663	−1.17614
$801$	8.86995	0.313404
$802$	26.3170	0.929285
$803$	−18.9032	−0.667079
$804$	15.4298	0.544167
$805$	−0.305835	−0.0107793
$806$	−12.7385	−0.448693
$807$	−25.3426	−0.892103
$808$	19.7777	0.695775
$809$	12.8962	0.453405	0.226702	−	0.973964i	$-0.427206\pi$
$809$	12.8962	0.453405	0.226702	+	0.973964i	$0.427206\pi$
$810$	−0.714950	−0.0251208
$811$	39.4315	1.38463	0.692314	−	0.721597i	$-0.256591\pi$
$811$	39.4315	1.38463	0.692314	+	0.721597i	$0.256591\pi$
$812$	−1.75668	−0.0616475
$813$	6.86970	0.240931
$814$	12.7727	0.447682
$815$	−0.0418954	−0.00146753
$816$	1.08994	0.0381556
$817$	−24.2278	−0.847622
$818$	−32.7544	−1.14523
$819$	0.931419	0.0325464
$820$	5.65699	0.197551
$821$	−20.3719	−0.710984	−0.355492	−	0.934679i	$-0.615687\pi$
$821$	−20.3719	−0.710984	−0.355492	+	0.934679i	$0.615687\pi$
$822$	−6.81579	−0.237728
$823$	−26.0372	−0.907600	−0.453800	−	0.891104i	$-0.649932\pi$
$823$	−26.0372	−0.907600	−0.453800	+	0.891104i	$0.649932\pi$
$824$	−0.255558	−0.00890278
$825$	15.3589	0.534729
$826$	11.3441	0.394711
$827$	−38.2808	−1.33115	−0.665577	−	0.746329i	$-0.731815\pi$
$827$	−38.2808	−1.33115	−0.665577	+	0.746329i	$0.731815\pi$
$828$	−4.40090	−0.152942
$829$	−19.7383	−0.685538	−0.342769	−	0.939420i	$-0.611365\pi$
$829$	−19.7383	−0.685538	−0.342769	+	0.939420i	$0.611365\pi$
$830$	2.01277	0.0698642
$831$	0.778402	0.0270025
$832$	−18.7172	−0.648902
$833$	−6.58312	−0.228092
$834$	43.0971	1.49233
$835$	−2.99544	−0.103662
$836$	49.2857	1.70458
$837$	−3.95801	−0.136809
$838$	4.06734	0.140504
$839$	−21.4851	−0.741748	−0.370874	−	0.928683i	$-0.620942\pi$
$839$	−21.4851	−0.741748	−0.370874	+	0.928683i	$0.620942\pi$
$840$	0.451178	0.0155671
$841$	−28.1650	−0.971206
$842$	−79.2184	−2.73005
$843$	−28.0478	−0.966016
$844$	−2.63176	−0.0905890
$845$	−3.49910	−0.120373
$846$	7.15574	0.246019
$847$	−0.751727	−0.0258296
$848$	−1.67553	−0.0575380
$849$	18.0239	0.618580
$850$	10.9259	0.374756
$851$	2.69826	0.0924952
$852$	10.9498	0.375133
$853$	6.12318	0.209654	0.104827	−	0.994490i	$-0.466571\pi$
$853$	6.12318	0.209654	0.104827	+	0.994490i	$0.466571\pi$
$854$	3.50177	0.119828
$855$	1.69144	0.0578462
$856$	30.3412	1.03704
$857$	−50.5260	−1.72594	−0.862968	−	0.505258i	$-0.831397\pi$
$857$	−50.5260	−1.72594	−0.862968	+	0.505258i	$0.831397\pi$
$858$	10.0935	0.344587
$859$	5.93971	0.202660	0.101330	−	0.994853i	$-0.467690\pi$
$859$	5.93971	0.202660	0.101330	+	0.994853i	$0.467690\pi$
$860$	−4.37966	−0.149345
$861$	−3.82808	−0.130461
$862$	−6.10584	−0.207966
$863$	−0.143953	−0.00490022	−0.00245011	−	0.999997i	$-0.500780\pi$
$863$	−0.143953	−0.00490022	−0.00245011	+	0.999997i	$0.500780\pi$
$864$	−6.79278	−0.231095
$865$	−7.71998	−0.262487
$866$	−58.9009	−2.00153
$867$	−1.00000	−0.0339618
$868$	7.60884	0.258261
$869$	−34.1524	−1.15854
$870$	−0.653323	−0.0221497
$871$	−7.47591	−0.253312
$872$	16.1850	0.548095
$873$	−17.5017	−0.592343
$874$	17.4056	0.588754
$875$	−2.04785	−0.0692300
$876$	17.9460	0.606338
$877$	−18.8174	−0.635419	−0.317710	−	0.948188i	$-0.602914\pi$
$877$	−18.8174	−0.635419	−0.317710	+	0.948188i	$0.602914\pi$
$878$	55.5615	1.87511
$879$	27.6495	0.932595
$880$	−1.09542	−0.0369267
$881$	30.7788	1.03696	0.518482	−	0.855089i	$-0.326497\pi$
$881$	30.7788	1.03696	0.518482	+	0.855089i	$0.326497\pi$
$882$	14.6870	0.494536
$883$	−31.9810	−1.07625	−0.538123	−	0.842866i	$-0.680866\pi$
$883$	−31.9810	−1.07625	−0.538123	+	0.842866i	$0.680866\pi$
$884$	4.29511	0.144460
$885$	2.52370	0.0848332
$886$	−47.3942	−1.59224
$887$	−22.4785	−0.754754	−0.377377	−	0.926060i	$-0.623174\pi$
$887$	−22.4785	−0.754754	−0.377377	+	0.926060i	$0.623174\pi$
$888$	−3.98057	−0.133579
$889$	−9.08431	−0.304678
$890$	−6.34157	−0.212570
$891$	3.13620	0.105067
$892$	−22.3722	−0.749077
$893$	−16.9292	−0.566514
$894$	36.9514	1.23584
$895$	−4.00415	−0.133844
$896$	9.91829	0.331347
$897$	2.13228	0.0711949
$898$	4.02484	0.134311
$899$	−3.61684	−0.120628
$900$	−14.5812	−0.486039
$901$	1.53727	0.0512137
$902$	−41.4839	−1.38126
$903$	2.96372	0.0986264
$904$	−20.4364	−0.679706
$905$	−0.637602	−0.0211946
$906$	−8.05681	−0.267670
$907$	38.9675	1.29390	0.646948	−	0.762534i	$-0.276045\pi$
$907$	38.9675	1.29390	0.646948	+	0.762534i	$0.276045\pi$
$908$	−15.3600	−0.509741
$909$	−9.07001	−0.300833
$910$	−0.665918	−0.0220750
$911$	31.0084	1.02735	0.513677	−	0.857983i	$-0.328283\pi$
$911$	31.0084	1.02735	0.513677	+	0.857983i	$0.328283\pi$
$912$	5.75289	0.190497
$913$	−8.82920	−0.292204
$914$	11.2407	0.371809
$915$	0.779032	0.0257540
$916$	−49.9528	−1.65049
$917$	−7.60633	−0.251183
$918$	2.23101	0.0736342
$919$	36.9258	1.21807	0.609034	−	0.793144i	$-0.291557\pi$
$919$	36.9258	1.21807	0.609034	+	0.793144i	$0.291557\pi$
$920$	1.03288	0.0340529
$921$	3.58602	0.118163
$922$	−75.5233	−2.48723
$923$	−5.30529	−0.174626
$924$	−6.02899	−0.198339
$925$	8.93995	0.293944
$926$	28.4487	0.934884
$927$	0.117199	0.00384931
$928$	−6.20726	−0.203763
$929$	1.17874	0.0386732	0.0193366	−	0.999813i	$-0.493845\pi$
$929$	1.17874	0.0386732	0.0193366	+	0.999813i	$0.493845\pi$
$930$	2.82978	0.0927922
$931$	−34.7468	−1.13878
$932$	39.9332	1.30806
$933$	10.3322	0.338261
$934$	37.7106	1.23393
$935$	1.00503	0.0328679
$936$	−3.14562	−0.102818
$937$	−44.9257	−1.46766	−0.733829	−	0.679334i	$-0.762269\pi$
$937$	−44.9257	−1.46766	−0.733829	+	0.679334i	$0.762269\pi$
$938$	7.46504	0.243742
$939$	15.3311	0.500313
$940$	−3.06030	−0.0998160
$941$	59.3789	1.93570	0.967849	−	0.251531i	$-0.0809341\pi$
$941$	59.3789	1.93570	0.967849	+	0.251531i	$0.0809341\pi$
$942$	2.23101	0.0726901
$943$	−8.76357	−0.285381
$944$	8.58353	0.279370
$945$	−0.206910	−0.00673078
$946$	32.1170	1.04421
$947$	10.4963	0.341084	0.170542	−	0.985350i	$-0.445448\pi$
$947$	10.4963	0.341084	0.170542	+	0.985350i	$0.445448\pi$
$948$	32.4230	1.05305
$949$	−8.69502	−0.282252
$950$	57.6687	1.87102
$951$	−11.2627	−0.365217
$952$	−1.40790	−0.0456304
$953$	−31.9566	−1.03518	−0.517589	−	0.855630i	$-0.673170\pi$
$953$	−31.9566	−1.03518	−0.517589	+	0.855630i	$0.673170\pi$
$954$	−3.42965	−0.111039
$955$	0.653436	0.0211447
$956$	−17.3397	−0.560805
$957$	2.86586	0.0926402
$958$	66.3752	2.14448
$959$	−1.97252	−0.0636960
$960$	4.15793	0.134197
$961$	−15.3341	−0.494649
$962$	5.87513	0.189422
$963$	−13.9145	−0.448387
$964$	−40.3685	−1.30018
$965$	−1.69733	−0.0546390
$966$	−2.12918	−0.0685053
$967$	16.0502	0.516138	0.258069	−	0.966126i	$-0.416914\pi$
$967$	16.0502	0.516138	0.258069	+	0.966126i	$0.416914\pi$
$968$	2.53875	0.0815987
$969$	−5.27816	−0.169559
$970$	12.5129	0.401764
$971$	10.8288	0.347514	0.173757	−	0.984789i	$-0.444409\pi$
$971$	10.8288	0.347514	0.173757	+	0.984789i	$0.444409\pi$
$972$	−2.97739	−0.0954997
$973$	12.4725	0.399850
$974$	−67.3783	−2.15894
$975$	7.06474	0.226253
$976$	2.64962	0.0848124
$977$	21.7320	0.695268	0.347634	−	0.937630i	$-0.386985\pi$
$977$	21.7320	0.695268	0.347634	+	0.937630i	$0.386985\pi$
$978$	−0.291670	−0.00932659
$979$	27.8179	0.889065
$980$	−6.28119	−0.200645
$981$	−7.42244	−0.236980
$982$	−35.4912	−1.13257
$983$	40.7535	1.29984	0.649918	−	0.760004i	$-0.274803\pi$
$983$	40.7535	1.29984	0.649918	+	0.760004i	$0.274803\pi$
$984$	12.9283	0.412140
$985$	2.87713	0.0916729
$986$	2.03870	0.0649254
$987$	2.07091	0.0659176
$988$	22.6703	0.721238
$989$	6.78479	0.215744
$990$	−2.24222	−0.0712625
$991$	43.8451	1.39279	0.696393	−	0.717661i	$-0.254787\pi$
$991$	43.8451	1.39279	0.696393	+	0.717661i	$0.254787\pi$
$992$	26.8859	0.853628
$993$	−13.3695	−0.424268
$994$	5.29758	0.168029
$995$	3.59462	0.113957
$996$	8.38211	0.265597
$997$	5.21075	0.165026	0.0825130	−	0.996590i	$-0.473705\pi$
$997$	5.21075	0.165026	0.0825130	+	0.996590i	$0.473705\pi$
$998$	−64.2359	−2.03335
$999$	1.82548	0.0577557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.4	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.4	✓	39	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23101 q^{2} -1.00000 q^{3} +2.97739 q^{4} +0.320461 q^{5} +2.23101 q^{6} +0.645663 q^{7} -2.18055 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23101 q^{2} -1.00000 q^{3} +2.97739 q^{4} +0.320461 q^{5} +2.23101 q^{6} +0.645663 q^{7} -2.18055 q^{8} +1.00000 q^{9} -0.714950 q^{10} +3.13620 q^{11} -2.97739 q^{12} +1.44258 q^{13} -1.44048 q^{14} -0.320461 q^{15} -1.08994 q^{16} +1.00000 q^{17} -2.23101 q^{18} +5.27816 q^{19} +0.954136 q^{20} -0.645663 q^{21} -6.99687 q^{22} -1.47811 q^{23} +2.18055 q^{24} -4.89730 q^{25} -3.21840 q^{26} -1.00000 q^{27} +1.92239 q^{28} -0.913802 q^{29} +0.714950 q^{30} +3.95801 q^{31} +6.79278 q^{32} -3.13620 q^{33} -2.23101 q^{34} +0.206910 q^{35} +2.97739 q^{36} -1.82548 q^{37} -11.7756 q^{38} -1.44258 q^{39} -0.698782 q^{40} +5.92891 q^{41} +1.44048 q^{42} -4.59019 q^{43} +9.33767 q^{44} +0.320461 q^{45} +3.29767 q^{46} -3.20741 q^{47} +1.08994 q^{48} -6.58312 q^{49} +10.9259 q^{50} -1.00000 q^{51} +4.29511 q^{52} +1.53727 q^{53} +2.23101 q^{54} +1.00503 q^{55} -1.40790 q^{56} -5.27816 q^{57} +2.03870 q^{58} -7.87522 q^{59} -0.954136 q^{60} -2.43098 q^{61} -8.83035 q^{62} +0.645663 q^{63} -12.9748 q^{64} +0.462289 q^{65} +6.99687 q^{66} -5.18233 q^{67} +2.97739 q^{68} +1.47811 q^{69} -0.461617 q^{70} -3.67765 q^{71} -2.18055 q^{72} -6.02742 q^{73} +4.07266 q^{74} +4.89730 q^{75} +15.7151 q^{76} +2.02493 q^{77} +3.21840 q^{78} -10.8898 q^{79} -0.349284 q^{80} +1.00000 q^{81} -13.2274 q^{82} -2.81526 q^{83} -1.92239 q^{84} +0.320461 q^{85} +10.2407 q^{86} +0.913802 q^{87} -6.83865 q^{88} +8.86995 q^{89} -0.714950 q^{90} +0.931419 q^{91} -4.40090 q^{92} -3.95801 q^{93} +7.15574 q^{94} +1.69144 q^{95} -6.79278 q^{96} -17.5017 q^{97} +14.6870 q^{98} +3.13620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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