LMFDB - Embedded newform 8018.2.a.i.1.15

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:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.12203 q^{3} +1.00000 q^{4} -3.99522 q^{5} +1.12203 q^{6} +0.851275 q^{7} -1.00000 q^{8} -1.74104 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.12203 q^{3} +1.00000 q^{4} -3.99522 q^{5} +1.12203 q^{6} +0.851275 q^{7} -1.00000 q^{8} -1.74104 q^{9} +3.99522 q^{10} +1.40809 q^{11} -1.12203 q^{12} -5.92441 q^{13} -0.851275 q^{14} +4.48278 q^{15} +1.00000 q^{16} +1.90629 q^{17} +1.74104 q^{18} +1.00000 q^{19} -3.99522 q^{20} -0.955159 q^{21} -1.40809 q^{22} -1.62963 q^{23} +1.12203 q^{24} +10.9618 q^{25} +5.92441 q^{26} +5.31961 q^{27} +0.851275 q^{28} -9.90714 q^{29} -4.48278 q^{30} +7.86337 q^{31} -1.00000 q^{32} -1.57992 q^{33} -1.90629 q^{34} -3.40103 q^{35} -1.74104 q^{36} +11.9686 q^{37} -1.00000 q^{38} +6.64739 q^{39} +3.99522 q^{40} -7.76149 q^{41} +0.955159 q^{42} -8.87591 q^{43} +1.40809 q^{44} +6.95584 q^{45} +1.62963 q^{46} +1.18344 q^{47} -1.12203 q^{48} -6.27533 q^{49} -10.9618 q^{50} -2.13892 q^{51} -5.92441 q^{52} -5.44831 q^{53} -5.31961 q^{54} -5.62563 q^{55} -0.851275 q^{56} -1.12203 q^{57} +9.90714 q^{58} -14.3336 q^{59} +4.48278 q^{60} -14.4938 q^{61} -7.86337 q^{62} -1.48210 q^{63} +1.00000 q^{64} +23.6694 q^{65} +1.57992 q^{66} -13.0207 q^{67} +1.90629 q^{68} +1.82850 q^{69} +3.40103 q^{70} +2.48302 q^{71} +1.74104 q^{72} -0.617116 q^{73} -11.9686 q^{74} -12.2995 q^{75} +1.00000 q^{76} +1.19867 q^{77} -6.64739 q^{78} +1.13558 q^{79} -3.99522 q^{80} -0.745661 q^{81} +7.76149 q^{82} -8.32289 q^{83} -0.955159 q^{84} -7.61605 q^{85} +8.87591 q^{86} +11.1162 q^{87} -1.40809 q^{88} +10.9558 q^{89} -6.95584 q^{90} -5.04331 q^{91} -1.62963 q^{92} -8.82297 q^{93} -1.18344 q^{94} -3.99522 q^{95} +1.12203 q^{96} +4.65073 q^{97} +6.27533 q^{98} -2.45154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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
$3$	−1.12203	−0.647807	−0.323903	−	0.946090i	$-0.604995\pi$
$3$	−1.12203	−0.647807	−0.323903	+	0.946090i	$0.604995\pi$
$4$	1.00000	0.500000
$5$	−3.99522	−1.78672	−0.893359	−	0.449344i	$-0.851658\pi$
$5$	−3.99522	−1.78672	−0.893359	+	0.449344i	$0.851658\pi$
$6$	1.12203	0.458068
$7$	0.851275	0.321752	0.160876	−	0.986975i	$-0.448568\pi$
$7$	0.851275	0.321752	0.160876	+	0.986975i	$0.448568\pi$
$8$	−1.00000	−0.353553
$9$	−1.74104	−0.580347
$10$	3.99522	1.26340
$11$	1.40809	0.424555	0.212277	−	0.977209i	$-0.431912\pi$
$11$	1.40809	0.424555	0.212277	+	0.977209i	$0.431912\pi$
$12$	−1.12203	−0.323903
$13$	−5.92441	−1.64314	−0.821568	−	0.570110i	$-0.806901\pi$
$13$	−5.92441	−1.64314	−0.821568	+	0.570110i	$0.806901\pi$
$14$	−0.851275	−0.227513
$15$	4.48278	1.15745
$16$	1.00000	0.250000
$17$	1.90629	0.462343	0.231171	−	0.972913i	$-0.425744\pi$
$17$	1.90629	0.462343	0.231171	+	0.972913i	$0.425744\pi$
$18$	1.74104	0.410367
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.99522	−0.893359
$21$	−0.955159	−0.208433
$22$	−1.40809	−0.300206
$23$	−1.62963	−0.339801	−0.169901	−	0.985461i	$-0.554345\pi$
$23$	−1.62963	−0.339801	−0.169901	+	0.985461i	$0.554345\pi$
$24$	1.12203	0.229034
$25$	10.9618	2.19236
$26$	5.92441	1.16187
$27$	5.31961	1.02376
$28$	0.851275	0.160876
$29$	−9.90714	−1.83971	−0.919855	−	0.392258i	$-0.871694\pi$
$29$	−9.90714	−1.83971	−0.919855	+	0.392258i	$0.871694\pi$
$30$	−4.48278	−0.818439
$31$	7.86337	1.41230	0.706152	−	0.708061i	$-0.250430\pi$
$31$	7.86337	1.41230	0.706152	+	0.708061i	$0.250430\pi$
$32$	−1.00000	−0.176777
$33$	−1.57992	−0.275029
$34$	−1.90629	−0.326926
$35$	−3.40103	−0.574880
$36$	−1.74104	−0.290173
$37$	11.9686	1.96763	0.983813	−	0.179199i	$-0.0573506\pi$
$37$	11.9686	1.96763	0.983813	+	0.179199i	$0.0573506\pi$
$38$	−1.00000	−0.162221
$39$	6.64739	1.06443
$40$	3.99522	0.631700
$41$	−7.76149	−1.21214	−0.606071	−	0.795411i	$-0.707255\pi$
$41$	−7.76149	−1.21214	−0.606071	+	0.795411i	$0.707255\pi$
$42$	0.955159	0.147384
$43$	−8.87591	−1.35356	−0.676782	−	0.736183i	$-0.736626\pi$
$43$	−8.87591	−1.35356	−0.676782	+	0.736183i	$0.736626\pi$
$44$	1.40809	0.212277
$45$	6.95584	1.03692
$46$	1.62963	0.240276
$47$	1.18344	0.172623	0.0863113	−	0.996268i	$-0.472492\pi$
$47$	1.18344	0.172623	0.0863113	+	0.996268i	$0.472492\pi$
$48$	−1.12203	−0.161952
$49$	−6.27533	−0.896476
$50$	−10.9618	−1.55023
$51$	−2.13892	−0.299509
$52$	−5.92441	−0.821568
$53$	−5.44831	−0.748382	−0.374191	−	0.927352i	$-0.622080\pi$
$53$	−5.44831	−0.748382	−0.374191	+	0.927352i	$0.622080\pi$
$54$	−5.31961	−0.723907
$55$	−5.62563	−0.758560
$56$	−0.851275	−0.113756
$57$	−1.12203	−0.148617
$58$	9.90714	1.30087
$59$	−14.3336	−1.86608	−0.933040	−	0.359772i	$-0.882854\pi$
$59$	−14.3336	−1.86608	−0.933040	+	0.359772i	$0.882854\pi$
$60$	4.48278	0.578724
$61$	−14.4938	−1.85574	−0.927869	−	0.372907i	$-0.878361\pi$
$61$	−14.4938	−1.85574	−0.927869	+	0.372907i	$0.878361\pi$
$62$	−7.86337	−0.998649
$63$	−1.48210	−0.186728
$64$	1.00000	0.125000
$65$	23.6694	2.93582
$66$	1.57992	0.194475
$67$	−13.0207	−1.59074	−0.795368	−	0.606127i	$-0.792722\pi$
$67$	−13.0207	−1.59074	−0.795368	+	0.606127i	$0.792722\pi$
$68$	1.90629	0.231171
$69$	1.82850	0.220125
$70$	3.40103	0.406501
$71$	2.48302	0.294680	0.147340	−	0.989086i	$-0.452929\pi$
$71$	2.48302	0.294680	0.147340	+	0.989086i	$0.452929\pi$
$72$	1.74104	0.205183
$73$	−0.617116	−0.0722280	−0.0361140	−	0.999348i	$-0.511498\pi$
$73$	−0.617116	−0.0722280	−0.0361140	+	0.999348i	$0.511498\pi$
$74$	−11.9686	−1.39132
$75$	−12.2995	−1.42023
$76$	1.00000	0.114708
$77$	1.19867	0.136601
$78$	−6.64739	−0.752669
$79$	1.13558	0.127763	0.0638813	−	0.997958i	$-0.479652\pi$
$79$	1.13558	0.127763	0.0638813	+	0.997958i	$0.479652\pi$
$80$	−3.99522	−0.446679
$81$	−0.745661	−0.0828513
$82$	7.76149	0.857114
$83$	−8.32289	−0.913556	−0.456778	−	0.889581i	$-0.650997\pi$
$83$	−8.32289	−0.913556	−0.456778	+	0.889581i	$0.650997\pi$
$84$	−0.955159	−0.104216
$85$	−7.61605	−0.826076
$86$	8.87591	0.957114
$87$	11.1162	1.19178
$88$	−1.40809	−0.150103
$89$	10.9558	1.16131	0.580657	−	0.814148i	$-0.302796\pi$
$89$	10.9558	1.16131	0.580657	+	0.814148i	$0.302796\pi$
$90$	−6.95584	−0.733210
$91$	−5.04331	−0.528682
$92$	−1.62963	−0.169901
$93$	−8.82297	−0.914899
$94$	−1.18344	−0.122063
$95$	−3.99522	−0.409901
$96$	1.12203	0.114517
$97$	4.65073	0.472210	0.236105	−	0.971728i	$-0.424129\pi$
$97$	4.65073	0.472210	0.236105	+	0.971728i	$0.424129\pi$
$98$	6.27533	0.633904
$99$	−2.45154	−0.246389
$100$	10.9618	1.09618
$101$	−5.07461	−0.504942	−0.252471	−	0.967604i	$-0.581243\pi$
$101$	−5.07461	−0.504942	−0.252471	+	0.967604i	$0.581243\pi$
$102$	2.13892	0.211785
$103$	−16.6988	−1.64538	−0.822689	−	0.568492i	$-0.807527\pi$
$103$	−16.6988	−1.64538	−0.822689	+	0.568492i	$0.807527\pi$
$104$	5.92441	0.580937
$105$	3.81607	0.372411
$106$	5.44831	0.529186
$107$	−4.70351	−0.454705	−0.227353	−	0.973813i	$-0.573007\pi$
$107$	−4.70351	−0.454705	−0.227353	+	0.973813i	$0.573007\pi$
$108$	5.31961	0.511879
$109$	−0.277453	−0.0265752	−0.0132876	−	0.999912i	$-0.504230\pi$
$109$	−0.277453	−0.0265752	−0.0132876	+	0.999912i	$0.504230\pi$
$110$	5.62563	0.536383
$111$	−13.4292	−1.27464
$112$	0.851275	0.0804379
$113$	−12.7954	−1.20369	−0.601843	−	0.798614i	$-0.705567\pi$
$113$	−12.7954	−1.20369	−0.601843	+	0.798614i	$0.705567\pi$
$114$	1.12203	0.105088
$115$	6.51073	0.607129
$116$	−9.90714	−0.919855
$117$	10.3146	0.953589
$118$	14.3336	1.31952
$119$	1.62278	0.148760
$120$	−4.48278	−0.409220
$121$	−9.01728	−0.819753
$122$	14.4938	1.31220
$123$	8.70866	0.785233
$124$	7.86337	0.706152
$125$	−23.8187	−2.13041
$126$	1.48210	0.132036
$127$	12.2000	1.08257	0.541287	−	0.840838i	$-0.317937\pi$
$127$	12.2000	1.08257	0.541287	+	0.840838i	$0.317937\pi$
$128$	−1.00000	−0.0883883
$129$	9.95908	0.876848
$130$	−23.6694	−2.07594
$131$	11.5822	1.01194	0.505972	−	0.862550i	$-0.331134\pi$
$131$	11.5822	1.01194	0.505972	+	0.862550i	$0.331134\pi$
$132$	−1.57992	−0.137515
$133$	0.851275	0.0738149
$134$	13.0207	1.12482
$135$	−21.2530	−1.82917
$136$	−1.90629	−0.163463
$137$	2.51600	0.214956	0.107478	−	0.994207i	$-0.465722\pi$
$137$	2.51600	0.214956	0.107478	+	0.994207i	$0.465722\pi$
$138$	−1.82850	−0.155652
$139$	−5.66122	−0.480178	−0.240089	−	0.970751i	$-0.577177\pi$
$139$	−5.66122	−0.480178	−0.240089	+	0.970751i	$0.577177\pi$
$140$	−3.40103	−0.287440
$141$	−1.32786	−0.111826
$142$	−2.48302	−0.208370
$143$	−8.34210	−0.697602
$144$	−1.74104	−0.145087
$145$	39.5812	3.28704
$146$	0.617116	0.0510729
$147$	7.04113	0.580743
$148$	11.9686	0.983813
$149$	22.1985	1.81857	0.909285	−	0.416175i	$-0.136629\pi$
$149$	22.1985	1.81857	0.909285	+	0.416175i	$0.136629\pi$
$150$	12.2995	1.00425
$151$	8.01826	0.652516	0.326258	−	0.945281i	$-0.394212\pi$
$151$	8.01826	0.652516	0.326258	+	0.945281i	$0.394212\pi$
$152$	−1.00000	−0.0811107
$153$	−3.31892	−0.268319
$154$	−1.19867	−0.0965917
$155$	−31.4159	−2.52339
$156$	6.64739	0.532217
$157$	3.15890	0.252108	0.126054	−	0.992023i	$-0.459769\pi$
$157$	3.15890	0.252108	0.126054	+	0.992023i	$0.459769\pi$
$158$	−1.13558	−0.0903418
$159$	6.11318	0.484807
$160$	3.99522	0.315850
$161$	−1.38726	−0.109332
$162$	0.745661	0.0585847
$163$	4.59914	0.360233	0.180116	−	0.983645i	$-0.442353\pi$
$163$	4.59914	0.360233	0.180116	+	0.983645i	$0.442353\pi$
$164$	−7.76149	−0.606071
$165$	6.31215	0.491400
$166$	8.32289	0.645982
$167$	−22.6742	−1.75458	−0.877291	−	0.479958i	$-0.840652\pi$
$167$	−22.6742	−1.75458	−0.877291	+	0.479958i	$0.840652\pi$
$168$	0.955159	0.0736922
$169$	22.0987	1.69990
$170$	7.61605	0.584124
$171$	−1.74104	−0.133141
$172$	−8.87591	−0.676782
$173$	−15.7196	−1.19514	−0.597570	−	0.801817i	$-0.703867\pi$
$173$	−15.7196	−1.19514	−0.597570	+	0.801817i	$0.703867\pi$
$174$	−11.1162	−0.842713
$175$	9.33151	0.705396
$176$	1.40809	0.106139
$177$	16.0828	1.20886
$178$	−10.9558	−0.821173
$179$	−4.26993	−0.319150	−0.159575	−	0.987186i	$-0.551012\pi$
$179$	−4.26993	−0.319150	−0.159575	+	0.987186i	$0.551012\pi$
$180$	6.95584	0.518458
$181$	−2.92699	−0.217562	−0.108781	−	0.994066i	$-0.534695\pi$
$181$	−2.92699	−0.217562	−0.108781	+	0.994066i	$0.534695\pi$
$182$	5.04331	0.373835
$183$	16.2625	1.20216
$184$	1.62963	0.120138
$185$	−47.8172	−3.51559
$186$	8.82297	0.646932
$187$	2.68422	0.196290
$188$	1.18344	0.0863113
$189$	4.52845	0.329396
$190$	3.99522	0.289844
$191$	−0.645231	−0.0466873	−0.0233436	−	0.999728i	$-0.507431\pi$
$191$	−0.645231	−0.0466873	−0.0233436	+	0.999728i	$0.507431\pi$
$192$	−1.12203	−0.0809758
$193$	1.06658	0.0767740	0.0383870	−	0.999263i	$-0.487778\pi$
$193$	1.06658	0.0767740	0.0383870	+	0.999263i	$0.487778\pi$
$194$	−4.65073	−0.333903
$195$	−26.5578	−1.90185
$196$	−6.27533	−0.448238
$197$	−0.783286	−0.0558068	−0.0279034	−	0.999611i	$-0.508883\pi$
$197$	−0.783286	−0.0558068	−0.0279034	+	0.999611i	$0.508883\pi$
$198$	2.45154	0.174223
$199$	−16.6925	−1.18330	−0.591651	−	0.806194i	$-0.701523\pi$
$199$	−16.6925	−1.18330	−0.591651	+	0.806194i	$0.701523\pi$
$200$	−10.9618	−0.775117
$201$	14.6097	1.03049
$202$	5.07461	0.357048
$203$	−8.43370	−0.591930
$204$	−2.13892	−0.149754
$205$	31.0089	2.16576
$206$	16.6988	1.16346
$207$	2.83725	0.197202
$208$	−5.92441	−0.410784
$209$	1.40809	0.0973996
$210$	−3.81607	−0.263334
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−5.44831	−0.374191
$213$	−2.78603	−0.190896
$214$	4.70351	0.321525
$215$	35.4613	2.41844
$216$	−5.31961	−0.361953
$217$	6.69389	0.454411
$218$	0.277453	0.0187915
$219$	0.692426	0.0467898
$220$	−5.62563	−0.379280
$221$	−11.2936	−0.759693
$222$	13.4292	0.901307
$223$	5.99365	0.401364	0.200682	−	0.979656i	$-0.435684\pi$
$223$	5.99365	0.401364	0.200682	+	0.979656i	$0.435684\pi$
$224$	−0.851275	−0.0568782
$225$	−19.0849	−1.27233
$226$	12.7954	0.851135
$227$	−14.9466	−0.992042	−0.496021	−	0.868311i	$-0.665206\pi$
$227$	−14.9466	−0.992042	−0.496021	+	0.868311i	$0.665206\pi$
$228$	−1.12203	−0.0743085
$229$	16.3872	1.08290	0.541449	−	0.840733i	$-0.317876\pi$
$229$	16.3872	1.08290	0.541449	+	0.840733i	$0.317876\pi$
$230$	−6.51073	−0.429305
$231$	−1.34495	−0.0884912
$232$	9.90714	0.650436
$233$	−26.8336	−1.75793	−0.878963	−	0.476891i	$-0.841764\pi$
$233$	−26.8336	−1.75793	−0.878963	+	0.476891i	$0.841764\pi$
$234$	−10.3146	−0.674289
$235$	−4.72811	−0.308428
$236$	−14.3336	−0.933040
$237$	−1.27416	−0.0827654
$238$	−1.62278	−0.105189
$239$	−21.5693	−1.39520	−0.697600	−	0.716487i	$-0.745749\pi$
$239$	−21.5693	−1.39520	−0.697600	+	0.716487i	$0.745749\pi$
$240$	4.48278	0.289362
$241$	−10.5162	−0.677409	−0.338704	−	0.940893i	$-0.609989\pi$
$241$	−10.5162	−0.677409	−0.338704	+	0.940893i	$0.609989\pi$
$242$	9.01728	0.579653
$243$	−15.1222	−0.970087
$244$	−14.4938	−0.927869
$245$	25.0713	1.60175
$246$	−8.70866	−0.555244
$247$	−5.92441	−0.376961
$248$	−7.86337	−0.499325
$249$	9.33857	0.591808
$250$	23.8187	1.50643
$251$	−11.2011	−0.707008	−0.353504	−	0.935433i	$-0.615010\pi$
$251$	−11.2011	−0.707008	−0.353504	+	0.935433i	$0.615010\pi$
$252$	−1.48210	−0.0933638
$253$	−2.29466	−0.144264
$254$	−12.2000	−0.765496
$255$	8.54546	0.535138
$256$	1.00000	0.0625000
$257$	23.3131	1.45423	0.727117	−	0.686513i	$-0.240860\pi$
$257$	23.3131	1.45423	0.727117	+	0.686513i	$0.240860\pi$
$258$	−9.95908	−0.620025
$259$	10.1886	0.633087
$260$	23.6694	1.46791
$261$	17.2487	1.06767
$262$	−11.5822	−0.715552
$263$	20.1192	1.24061	0.620303	−	0.784362i	$-0.287010\pi$
$263$	20.1192	1.24061	0.620303	+	0.784362i	$0.287010\pi$
$264$	1.57992	0.0972376
$265$	21.7672	1.33715
$266$	−0.851275	−0.0521950
$267$	−12.2928	−0.752307
$268$	−13.0207	−0.795368
$269$	−15.3411	−0.935361	−0.467680	−	0.883898i	$-0.654910\pi$
$269$	−15.3411	−0.935361	−0.467680	+	0.883898i	$0.654910\pi$
$270$	21.2530	1.29342
$271$	−25.5854	−1.55420	−0.777101	−	0.629376i	$-0.783311\pi$
$271$	−25.5854	−1.55420	−0.777101	+	0.629376i	$0.783311\pi$
$272$	1.90629	0.115586
$273$	5.65876	0.342484
$274$	−2.51600	−0.151997
$275$	15.4352	0.930777
$276$	1.82850	0.110063
$277$	13.8159	0.830115	0.415057	−	0.909795i	$-0.363761\pi$
$277$	13.8159	0.830115	0.415057	+	0.909795i	$0.363761\pi$
$278$	5.66122	0.339537
$279$	−13.6904	−0.819625
$280$	3.40103	0.203251
$281$	−3.80323	−0.226882	−0.113441	−	0.993545i	$-0.536187\pi$
$281$	−3.80323	−0.226882	−0.113441	+	0.993545i	$0.536187\pi$
$282$	1.32786	0.0790730
$283$	10.2864	0.611462	0.305731	−	0.952118i	$-0.401099\pi$
$283$	10.2864	0.611462	0.305731	+	0.952118i	$0.401099\pi$
$284$	2.48302	0.147340
$285$	4.48278	0.265537
$286$	8.34210	0.493279
$287$	−6.60717	−0.390009
$288$	1.74104	0.102592
$289$	−13.3661	−0.786239
$290$	−39.5812	−2.32429
$291$	−5.21828	−0.305901
$292$	−0.617116	−0.0361140
$293$	13.5047	0.788953	0.394477	−	0.918906i	$-0.370926\pi$
$293$	13.5047	0.788953	0.394477	+	0.918906i	$0.370926\pi$
$294$	−7.04113	−0.410647
$295$	57.2661	3.33416
$296$	−11.9686	−0.695661
$297$	7.49048	0.434642
$298$	−22.1985	−1.28592
$299$	9.65459	0.558340
$300$	−12.2995	−0.710113
$301$	−7.55584	−0.435512
$302$	−8.01826	−0.461399
$303$	5.69388	0.327105
$304$	1.00000	0.0573539
$305$	57.9059	3.31568
$306$	3.31892	0.189730
$307$	−4.20637	−0.240070	−0.120035	−	0.992770i	$-0.538301\pi$
$307$	−4.20637	−0.240070	−0.120035	+	0.992770i	$0.538301\pi$
$308$	1.19867	0.0683006
$309$	18.7366	1.06589
$310$	31.4159	1.78430
$311$	−0.175125	−0.00993043	−0.00496522	−	0.999988i	$-0.501580\pi$
$311$	−0.175125	−0.00993043	−0.00496522	+	0.999988i	$0.501580\pi$
$312$	−6.64739	−0.376335
$313$	29.8416	1.68675	0.843373	−	0.537329i	$-0.180567\pi$
$313$	29.8416	1.68675	0.843373	+	0.537329i	$0.180567\pi$
$314$	−3.15890	−0.178267
$315$	5.92133	0.333629
$316$	1.13558	0.0638813
$317$	−10.2111	−0.573514	−0.286757	−	0.958003i	$-0.592577\pi$
$317$	−10.2111	−0.573514	−0.286757	+	0.958003i	$0.592577\pi$
$318$	−6.11318	−0.342810
$319$	−13.9501	−0.781058
$320$	−3.99522	−0.223340
$321$	5.27749	0.294561
$322$	1.38726	0.0773091
$323$	1.90629	0.106069
$324$	−0.745661	−0.0414256
$325$	−64.9423	−3.60235
$326$	−4.59914	−0.254723
$327$	0.311312	0.0172156
$328$	7.76149	0.428557
$329$	1.00743	0.0555416
$330$	−6.31215	−0.347472
$331$	−25.4107	−1.39670	−0.698349	−	0.715758i	$-0.746081\pi$
$331$	−25.4107	−1.39670	−0.698349	+	0.715758i	$0.746081\pi$
$332$	−8.32289	−0.456778
$333$	−20.8378	−1.14190
$334$	22.6742	1.24068
$335$	52.0207	2.84220
$336$	−0.955159	−0.0521082
$337$	25.1304	1.36894	0.684470	−	0.729041i	$-0.260034\pi$
$337$	25.1304	1.36894	0.684470	+	0.729041i	$0.260034\pi$
$338$	−22.0987	−1.20201
$339$	14.3568	0.779756
$340$	−7.61605	−0.413038
$341$	11.0723	0.599600
$342$	1.74104	0.0941446
$343$	−11.3010	−0.610194
$344$	8.87591	0.478557
$345$	−7.30526	−0.393302
$346$	15.7196	0.845091
$347$	−12.1104	−0.650120	−0.325060	−	0.945693i	$-0.605385\pi$
$347$	−12.1104	−0.650120	−0.325060	+	0.945693i	$0.605385\pi$
$348$	11.1162	0.595888
$349$	0.0646768	0.00346207	0.00173103	−	0.999999i	$-0.499449\pi$
$349$	0.0646768	0.00346207	0.00173103	+	0.999999i	$0.499449\pi$
$350$	−9.33151	−0.498790
$351$	−31.5156	−1.68218
$352$	−1.40809	−0.0750514
$353$	−0.583112	−0.0310359	−0.0155180	−	0.999880i	$-0.504940\pi$
$353$	−0.583112	−0.0310359	−0.0155180	+	0.999880i	$0.504940\pi$
$354$	−16.0828	−0.854793
$355$	−9.92022	−0.526510
$356$	10.9558	0.580657
$357$	−1.82081	−0.0963675
$358$	4.26993	0.225673
$359$	23.2319	1.22613	0.613066	−	0.790031i	$-0.289936\pi$
$359$	23.2319	1.22613	0.613066	+	0.790031i	$0.289936\pi$
$360$	−6.95584	−0.366605
$361$	1.00000	0.0526316
$362$	2.92699	0.153839
$363$	10.1177	0.531042
$364$	−5.04331	−0.264341
$365$	2.46552	0.129051
$366$	−16.2625	−0.850055
$367$	5.38043	0.280856	0.140428	−	0.990091i	$-0.455152\pi$
$367$	5.38043	0.280856	0.140428	+	0.990091i	$0.455152\pi$
$368$	−1.62963	−0.0849503
$369$	13.5131	0.703462
$370$	47.8172	2.48590
$371$	−4.63801	−0.240793
$372$	−8.82297	−0.457450
$373$	−20.8239	−1.07822	−0.539111	−	0.842235i	$-0.681240\pi$
$373$	−20.8239	−1.07822	−0.539111	+	0.842235i	$0.681240\pi$
$374$	−2.68422	−0.138798
$375$	26.7254	1.38010
$376$	−1.18344	−0.0610313
$377$	58.6940	3.02290
$378$	−4.52845	−0.232918
$379$	27.1636	1.39530	0.697651	−	0.716438i	$-0.254229\pi$
$379$	27.1636	1.39530	0.697651	+	0.716438i	$0.254229\pi$
$380$	−3.99522	−0.204951
$381$	−13.6888	−0.701299
$382$	0.645231	0.0330129
$383$	8.60180	0.439532	0.219766	−	0.975553i	$-0.429471\pi$
$383$	8.60180	0.439532	0.219766	+	0.975553i	$0.429471\pi$
$384$	1.12203	0.0572586
$385$	−4.78896	−0.244068
$386$	−1.06658	−0.0542874
$387$	15.4533	0.785536
$388$	4.65073	0.236105
$389$	32.3224	1.63881	0.819407	−	0.573213i	$-0.194303\pi$
$389$	32.3224	1.63881	0.819407	+	0.573213i	$0.194303\pi$
$390$	26.5578	1.34481
$391$	−3.10654	−0.157105
$392$	6.27533	0.316952
$393$	−12.9956	−0.655544
$394$	0.783286	0.0394614
$395$	−4.53689	−0.228276
$396$	−2.45154	−0.123194
$397$	4.29325	0.215472	0.107736	−	0.994180i	$-0.465640\pi$
$397$	4.29325	0.215472	0.107736	+	0.994180i	$0.465640\pi$
$398$	16.6925	0.836720
$399$	−0.955159	−0.0478178
$400$	10.9618	0.548090
$401$	−19.5990	−0.978729	−0.489365	−	0.872079i	$-0.662771\pi$
$401$	−19.5990	−0.978729	−0.489365	+	0.872079i	$0.662771\pi$
$402$	−14.6097	−0.728666
$403$	−46.5859	−2.32061
$404$	−5.07461	−0.252471
$405$	2.97908	0.148032
$406$	8.43370	0.418558
$407$	16.8529	0.835365
$408$	2.13892	0.105892
$409$	37.6722	1.86277	0.931385	−	0.364035i	$-0.118601\pi$
$409$	37.6722	1.86277	0.931385	+	0.364035i	$0.118601\pi$
$410$	−31.0089	−1.53142
$411$	−2.82304	−0.139250
$412$	−16.6988	−0.822689
$413$	−12.2019	−0.600415
$414$	−2.83725	−0.139443
$415$	33.2518	1.63227
$416$	5.92441	0.290468
$417$	6.35208	0.311063
$418$	−1.40809	−0.0688719
$419$	−18.7269	−0.914870	−0.457435	−	0.889243i	$-0.651232\pi$
$419$	−18.7269	−0.914870	−0.457435	+	0.889243i	$0.651232\pi$
$420$	3.81607	0.186205
$421$	1.09429	0.0533324	0.0266662	−	0.999644i	$-0.491511\pi$
$421$	1.09429	0.0533324	0.0266662	+	0.999644i	$0.491511\pi$
$422$	1.00000	0.0486792
$423$	−2.06042	−0.100181
$424$	5.44831	0.264593
$425$	20.8964	1.01362
$426$	2.78603	0.134984
$427$	−12.3382	−0.597087
$428$	−4.70351	−0.227353
$429$	9.36012	0.451911
$430$	−35.4613	−1.71009
$431$	16.4807	0.793849	0.396925	−	0.917851i	$-0.370077\pi$
$431$	16.4807	0.793849	0.396925	+	0.917851i	$0.370077\pi$
$432$	5.31961	0.255940
$433$	−1.85814	−0.0892965	−0.0446482	−	0.999003i	$-0.514217\pi$
$433$	−1.85814	−0.0892965	−0.0446482	+	0.999003i	$0.514217\pi$
$434$	−6.69389	−0.321317
$435$	−44.4115	−2.12937
$436$	−0.277453	−0.0132876
$437$	−1.62963	−0.0779557
$438$	−0.692426	−0.0330854
$439$	−2.11611	−0.100997	−0.0504983	−	0.998724i	$-0.516081\pi$
$439$	−2.11611	−0.100997	−0.0504983	+	0.998724i	$0.516081\pi$
$440$	5.62563	0.268191
$441$	10.9256	0.520267
$442$	11.2936	0.537184
$443$	25.6807	1.22013	0.610065	−	0.792352i	$-0.291143\pi$
$443$	25.6807	1.22013	0.610065	+	0.792352i	$0.291143\pi$
$444$	−13.4292	−0.637320
$445$	−43.7709	−2.07494
$446$	−5.99365	−0.283808
$447$	−24.9074	−1.17808
$448$	0.851275	0.0402190
$449$	5.05637	0.238625	0.119313	−	0.992857i	$-0.461931\pi$
$449$	5.05637	0.238625	0.119313	+	0.992857i	$0.461931\pi$
$450$	19.0849	0.899673
$451$	−10.9289	−0.514621
$452$	−12.7954	−0.601843
$453$	−8.99676	−0.422704
$454$	14.9466	0.701480
$455$	20.1491	0.944606
$456$	1.12203	0.0525441
$457$	4.20795	0.196839	0.0984197	−	0.995145i	$-0.468621\pi$
$457$	4.20795	0.196839	0.0984197	+	0.995145i	$0.468621\pi$
$458$	−16.3872	−0.765725
$459$	10.1407	0.473328
$460$	6.51073	0.303564
$461$	−10.4897	−0.488553	−0.244276	−	0.969706i	$-0.578550\pi$
$461$	−10.4897	−0.488553	−0.244276	+	0.969706i	$0.578550\pi$
$462$	1.34495	0.0625727
$463$	−4.87952	−0.226771	−0.113385	−	0.993551i	$-0.536169\pi$
$463$	−4.87952	−0.226771	−0.113385	+	0.993551i	$0.536169\pi$
$464$	−9.90714	−0.459928
$465$	35.2497	1.63467
$466$	26.8336	1.24304
$467$	26.3874	1.22106	0.610531	−	0.791992i	$-0.290956\pi$
$467$	26.3874	1.22106	0.610531	+	0.791992i	$0.290956\pi$
$468$	10.3146	0.476794
$469$	−11.0842	−0.511822
$470$	4.72811	0.218092
$471$	−3.54440	−0.163317
$472$	14.3336	0.659759
$473$	−12.4981	−0.574662
$474$	1.27416	0.0585240
$475$	10.9618	0.502962
$476$	1.62278	0.0743798
$477$	9.48572	0.434321
$478$	21.5693	0.986556
$479$	−36.2065	−1.65432	−0.827158	−	0.561970i	$-0.810044\pi$
$479$	−36.2065	−1.65432	−0.827158	+	0.561970i	$0.810044\pi$
$480$	−4.48278	−0.204610
$481$	−70.9069	−3.23308
$482$	10.5162	0.479000
$483$	1.55656	0.0708257
$484$	−9.01728	−0.409877
$485$	−18.5807	−0.843706
$486$	15.1222	0.685955
$487$	31.2850	1.41766	0.708828	−	0.705381i	$-0.249224\pi$
$487$	31.2850	1.41766	0.708828	+	0.705381i	$0.249224\pi$
$488$	14.4938	0.656102
$489$	−5.16039	−0.233361
$490$	−25.0713	−1.13261
$491$	−23.9434	−1.08055	−0.540275	−	0.841488i	$-0.681680\pi$
$491$	−23.9434	−1.08055	−0.540275	+	0.841488i	$0.681680\pi$
$492$	8.70866	0.392617
$493$	−18.8859	−0.850577
$494$	5.92441	0.266552
$495$	9.79445	0.440228
$496$	7.86337	0.353076
$497$	2.11373	0.0948139
$498$	−9.33857	−0.418471
$499$	9.83897	0.440453	0.220226	−	0.975449i	$-0.429320\pi$
$499$	9.83897	0.440453	0.220226	+	0.975449i	$0.429320\pi$
$500$	−23.8187	−1.06521
$501$	25.4412	1.13663
$502$	11.2011	0.499930
$503$	33.0217	1.47236	0.736181	−	0.676784i	$-0.236627\pi$
$503$	33.0217	1.47236	0.736181	+	0.676784i	$0.236627\pi$
$504$	1.48210	0.0660181
$505$	20.2742	0.902190
$506$	2.29466	0.102010
$507$	−24.7955	−1.10121
$508$	12.2000	0.541287
$509$	−1.78456	−0.0790991	−0.0395496	−	0.999218i	$-0.512592\pi$
$509$	−1.78456	−0.0790991	−0.0395496	+	0.999218i	$0.512592\pi$
$510$	−8.54546	−0.378400
$511$	−0.525336	−0.0232395
$512$	−1.00000	−0.0441942
$513$	5.31961	0.234866
$514$	−23.3131	−1.02830
$515$	66.7152	2.93982
$516$	9.95908	0.438424
$517$	1.66639	0.0732878
$518$	−10.1886	−0.447660
$519$	17.6379	0.774219
$520$	−23.6694	−1.03797
$521$	−9.09848	−0.398612	−0.199306	−	0.979937i	$-0.563869\pi$
$521$	−9.09848	−0.398612	−0.199306	+	0.979937i	$0.563869\pi$
$522$	−17.2487	−0.754956
$523$	−27.4678	−1.20108	−0.600542	−	0.799593i	$-0.705048\pi$
$523$	−27.4678	−1.20108	−0.600542	+	0.799593i	$0.705048\pi$
$524$	11.5822	0.505972
$525$	−10.4703	−0.456960
$526$	−20.1192	−0.877241
$527$	14.9899	0.652968
$528$	−1.57992	−0.0687574
$529$	−20.3443	−0.884535
$530$	−21.7672	−0.945506
$531$	24.9554	1.08297
$532$	0.851275	0.0369075
$533$	45.9823	1.99171
$534$	12.2928	0.531961
$535$	18.7916	0.812430
$536$	13.0207	0.562410
$537$	4.79101	0.206747
$538$	15.3411	0.661400
$539$	−8.83623	−0.380603
$540$	−21.2530	−0.914584
$541$	40.2160	1.72902	0.864511	−	0.502614i	$-0.167628\pi$
$541$	40.2160	1.72902	0.864511	+	0.502614i	$0.167628\pi$
$542$	25.5854	1.09899
$543$	3.28419	0.140938
$544$	−1.90629	−0.0817314
$545$	1.10849	0.0474823
$546$	−5.65876	−0.242173
$547$	−15.1031	−0.645763	−0.322881	−	0.946439i	$-0.604651\pi$
$547$	−15.1031	−0.645763	−0.322881	+	0.946439i	$0.604651\pi$
$548$	2.51600	0.107478
$549$	25.2342	1.07697
$550$	−15.4352	−0.658159
$551$	−9.90714	−0.422058
$552$	−1.82850	−0.0778261
$553$	0.966690	0.0411078
$554$	−13.8159	−0.586980
$555$	53.6525	2.27742
$556$	−5.66122	−0.240089
$557$	−0.526144	−0.0222934	−0.0111467	−	0.999938i	$-0.503548\pi$
$557$	−0.526144	−0.0222934	−0.0111467	+	0.999938i	$0.503548\pi$
$558$	13.6904	0.579563
$559$	52.5846	2.22409
$560$	−3.40103	−0.143720
$561$	−3.01179	−0.127158
$562$	3.80323	0.160430
$563$	17.6027	0.741867	0.370934	−	0.928659i	$-0.379038\pi$
$563$	17.6027	0.741867	0.370934	+	0.928659i	$0.379038\pi$
$564$	−1.32786	−0.0559131
$565$	51.1203	2.15065
$566$	−10.2864	−0.432369
$567$	−0.634763	−0.0266575
$568$	−2.48302	−0.104185
$569$	−14.2887	−0.599013	−0.299507	−	0.954094i	$-0.596822\pi$
$569$	−14.2887	−0.599013	−0.299507	+	0.954094i	$0.596822\pi$
$570$	−4.48278	−0.187763
$571$	33.5882	1.40562	0.702810	−	0.711377i	$-0.251928\pi$
$571$	33.5882	1.40562	0.702810	+	0.711377i	$0.251928\pi$
$572$	−8.34210	−0.348801
$573$	0.723971	0.0302443
$574$	6.60717	0.275778
$575$	−17.8637	−0.744967
$576$	−1.74104	−0.0725433
$577$	19.0345	0.792416	0.396208	−	0.918161i	$-0.370326\pi$
$577$	19.0345	0.792416	0.396208	+	0.918161i	$0.370326\pi$
$578$	13.3661	0.555955
$579$	−1.19674	−0.0497347
$580$	39.5812	1.64352
$581$	−7.08507	−0.293938
$582$	5.21828	0.216305
$583$	−7.67170	−0.317729
$584$	0.617116	0.0255365
$585$	−41.2093	−1.70379
$586$	−13.5047	−0.557874
$587$	24.1987	0.998789	0.499394	−	0.866375i	$-0.333556\pi$
$587$	24.1987	0.998789	0.499394	+	0.866375i	$0.333556\pi$
$588$	7.04113	0.290371
$589$	7.86337	0.324005
$590$	−57.2661	−2.35761
$591$	0.878873	0.0361520
$592$	11.9686	0.491906
$593$	−33.3156	−1.36811	−0.684054	−	0.729432i	$-0.739785\pi$
$593$	−33.3156	−1.36811	−0.684054	+	0.729432i	$0.739785\pi$
$594$	−7.49048	−0.307338
$595$	−6.48335	−0.265791
$596$	22.1985	0.909285
$597$	18.7296	0.766550
$598$	−9.65459	−0.394806
$599$	−24.7551	−1.01147	−0.505734	−	0.862690i	$-0.668778\pi$
$599$	−24.7551	−1.01147	−0.505734	+	0.862690i	$0.668778\pi$
$600$	12.2995	0.502126
$601$	−37.1851	−1.51681	−0.758405	−	0.651784i	$-0.774021\pi$
$601$	−37.1851	−1.51681	−0.758405	+	0.651784i	$0.774021\pi$
$602$	7.55584	0.307953
$603$	22.6696	0.923178
$604$	8.01826	0.326258
$605$	36.0261	1.46467
$606$	−5.69388	−0.231298
$607$	34.9028	1.41666	0.708331	−	0.705881i	$-0.249448\pi$
$607$	34.9028	1.41666	0.708331	+	0.705881i	$0.249448\pi$
$608$	−1.00000	−0.0405554
$609$	9.46290	0.383456
$610$	−57.9059	−2.34454
$611$	−7.01120	−0.283643
$612$	−3.31892	−0.134160
$613$	−1.91448	−0.0773250	−0.0386625	−	0.999252i	$-0.512310\pi$
$613$	−1.91448	−0.0773250	−0.0386625	+	0.999252i	$0.512310\pi$
$614$	4.20637	0.169755
$615$	−34.7930	−1.40299
$616$	−1.19867	−0.0482958
$617$	31.9315	1.28551	0.642757	−	0.766070i	$-0.277790\pi$
$617$	31.9315	1.28551	0.642757	+	0.766070i	$0.277790\pi$
$618$	−18.7366	−0.753695
$619$	34.5022	1.38676	0.693380	−	0.720573i	$-0.256121\pi$
$619$	34.5022	1.38676	0.693380	+	0.720573i	$0.256121\pi$
$620$	−31.4159	−1.26169
$621$	−8.66898	−0.347874
$622$	0.175125	0.00702188
$623$	9.32641	0.373655
$624$	6.64739	0.266109
$625$	40.3521	1.61409
$626$	−29.8416	−1.19271
$627$	−1.57992	−0.0630961
$628$	3.15890	0.126054
$629$	22.8156	0.909718
$630$	−5.92133	−0.235912
$631$	−2.28352	−0.0909057	−0.0454528	−	0.998966i	$-0.514473\pi$
$631$	−2.28352	−0.0909057	−0.0454528	+	0.998966i	$0.514473\pi$
$632$	−1.13558	−0.0451709
$633$	1.12203	0.0445968
$634$	10.2111	0.405535
$635$	−48.7417	−1.93426
$636$	6.11318	0.242403
$637$	37.1777	1.47303
$638$	13.9501	0.552291
$639$	−4.32304	−0.171017
$640$	3.99522	0.157925
$641$	−2.40895	−0.0951480	−0.0475740	−	0.998868i	$-0.515149\pi$
$641$	−2.40895	−0.0951480	−0.0475740	+	0.998868i	$0.515149\pi$
$642$	−5.27749	−0.208286
$643$	24.8767	0.981041	0.490521	−	0.871430i	$-0.336807\pi$
$643$	24.8767	0.981041	0.490521	+	0.871430i	$0.336807\pi$
$644$	−1.38726	−0.0546658
$645$	−39.7887	−1.56668
$646$	−1.90629	−0.0750019
$647$	−31.0114	−1.21918	−0.609591	−	0.792716i	$-0.708666\pi$
$647$	−31.0114	−1.21918	−0.609591	+	0.792716i	$0.708666\pi$
$648$	0.745661	0.0292924
$649$	−20.1830	−0.792253
$650$	64.9423	2.54725
$651$	−7.51077	−0.294370
$652$	4.59914	0.180116
$653$	−24.7288	−0.967712	−0.483856	−	0.875148i	$-0.660764\pi$
$653$	−24.7288	−0.967712	−0.483856	+	0.875148i	$0.660764\pi$
$654$	−0.311312	−0.0121733
$655$	−46.2736	−1.80806
$656$	−7.76149	−0.303035
$657$	1.07442	0.0419173
$658$	−1.00743	−0.0392739
$659$	−28.1512	−1.09662	−0.548308	−	0.836276i	$-0.684728\pi$
$659$	−28.1512	−1.09662	−0.548308	+	0.836276i	$0.684728\pi$
$660$	6.31215	0.245700
$661$	8.16827	0.317709	0.158854	−	0.987302i	$-0.449220\pi$
$661$	8.16827	0.317709	0.158854	+	0.987302i	$0.449220\pi$
$662$	25.4107	0.987614
$663$	12.6719	0.492134
$664$	8.32289	0.322991
$665$	−3.40103	−0.131886
$666$	20.8378	0.807449
$667$	16.1450	0.625135
$668$	−22.6742	−0.877291
$669$	−6.72508	−0.260007
$670$	−52.0207	−2.00974
$671$	−20.4085	−0.787862
$672$	0.955159	0.0368461
$673$	46.7155	1.80075	0.900376	−	0.435113i	$-0.143292\pi$
$673$	46.7155	1.80075	0.900376	+	0.435113i	$0.143292\pi$
$674$	−25.1304	−0.967987
$675$	58.3125	2.24445
$676$	22.0987	0.849949
$677$	1.70028	0.0653472	0.0326736	−	0.999466i	$-0.489598\pi$
$677$	1.70028	0.0653472	0.0326736	+	0.999466i	$0.489598\pi$
$678$	−14.3568	−0.551371
$679$	3.95905	0.151934
$680$	7.61605	0.292062
$681$	16.7706	0.642651
$682$	−11.0723	−0.423981
$683$	20.1470	0.770905	0.385452	−	0.922728i	$-0.374045\pi$
$683$	20.1470	0.770905	0.385452	+	0.922728i	$0.374045\pi$
$684$	−1.74104	−0.0665703
$685$	−10.0520	−0.384066
$686$	11.3010	0.431473
$687$	−18.3870	−0.701509
$688$	−8.87591	−0.338391
$689$	32.2780	1.22969
$690$	7.30526	0.278106
$691$	32.3650	1.23122	0.615610	−	0.788051i	$-0.288909\pi$
$691$	32.3650	1.23122	0.615610	+	0.788051i	$0.288909\pi$
$692$	−15.7196	−0.597570
$693$	−2.08693	−0.0792761
$694$	12.1104	0.459704
$695$	22.6178	0.857943
$696$	−11.1162	−0.421357
$697$	−14.7956	−0.560425
$698$	−0.0646768	−0.00244805
$699$	30.1082	1.13880
$700$	9.33151	0.352698
$701$	−14.8174	−0.559647	−0.279823	−	0.960052i	$-0.590276\pi$
$701$	−14.8174	−0.559647	−0.279823	+	0.960052i	$0.590276\pi$
$702$	31.5156	1.18948
$703$	11.9686	0.451404
$704$	1.40809	0.0530694
$705$	5.30510	0.199802
$706$	0.583112	0.0219457
$707$	−4.31989	−0.162466
$708$	16.0828	0.604430
$709$	−30.7586	−1.15516	−0.577582	−	0.816333i	$-0.696004\pi$
$709$	−30.7586	−1.15516	−0.577582	+	0.816333i	$0.696004\pi$
$710$	9.92022	0.372299
$711$	−1.97709	−0.0741466
$712$	−10.9558	−0.410586
$713$	−12.8144	−0.479902
$714$	1.82081	0.0681421
$715$	33.3286	1.24642
$716$	−4.26993	−0.159575
$717$	24.2015	0.903820
$718$	−23.2319	−0.867007
$719$	−4.45764	−0.166242	−0.0831210	−	0.996539i	$-0.526489\pi$
$719$	−4.45764	−0.166242	−0.0831210	+	0.996539i	$0.526489\pi$
$720$	6.95584	0.259229
$721$	−14.2152	−0.529403
$722$	−1.00000	−0.0372161
$723$	11.7995	0.438830
$724$	−2.92699	−0.108781
$725$	−108.600	−4.03331
$726$	−10.1177	−0.375503
$727$	−29.9381	−1.11034	−0.555172	−	0.831736i	$-0.687347\pi$
$727$	−29.9381	−1.11034	−0.555172	+	0.831736i	$0.687347\pi$
$728$	5.04331	0.186917
$729$	19.2046	0.711280
$730$	−2.46552	−0.0912529
$731$	−16.9201	−0.625811
$732$	16.2625	0.601080
$733$	−7.64868	−0.282510	−0.141255	−	0.989973i	$-0.545114\pi$
$733$	−7.64868	−0.282510	−0.141255	+	0.989973i	$0.545114\pi$
$734$	−5.38043	−0.198595
$735$	−28.1309	−1.03762
$736$	1.62963	0.0600689
$737$	−18.3344	−0.675355
$738$	−13.5131	−0.497423
$739$	−14.2072	−0.522621	−0.261310	−	0.965255i	$-0.584155\pi$
$739$	−14.2072	−0.522621	−0.261310	+	0.965255i	$0.584155\pi$
$740$	−47.8172	−1.75780
$741$	6.64739	0.244198
$742$	4.63801	0.170267
$743$	44.4512	1.63076	0.815379	−	0.578928i	$-0.196529\pi$
$743$	44.4512	1.63076	0.815379	+	0.578928i	$0.196529\pi$
$744$	8.82297	0.323466
$745$	−88.6878	−3.24927
$746$	20.8239	0.762418
$747$	14.4905	0.530179
$748$	2.68422	0.0981450
$749$	−4.00398	−0.146302
$750$	−26.7254	−0.975875
$751$	−33.2270	−1.21247	−0.606234	−	0.795286i	$-0.707321\pi$
$751$	−33.2270	−1.21247	−0.606234	+	0.795286i	$0.707321\pi$
$752$	1.18344	0.0431557
$753$	12.5680	0.458004
$754$	−58.6940	−2.13751
$755$	−32.0347	−1.16586
$756$	4.52845	0.164698
$757$	30.5640	1.11087	0.555434	−	0.831561i	$-0.312552\pi$
$757$	30.5640	1.11087	0.555434	+	0.831561i	$0.312552\pi$
$758$	−27.1636	−0.986628
$759$	2.57469	0.0934553
$760$	3.99522	0.144922
$761$	3.58736	0.130042	0.0650209	−	0.997884i	$-0.479289\pi$
$761$	3.58736	0.130042	0.0650209	+	0.997884i	$0.479289\pi$
$762$	13.6888	0.495893
$763$	−0.236189	−0.00855061
$764$	−0.645231	−0.0233436
$765$	13.2598	0.479411
$766$	−8.60180	−0.310796
$767$	84.9184	3.06623
$768$	−1.12203	−0.0404879
$769$	−33.0887	−1.19321	−0.596605	−	0.802535i	$-0.703484\pi$
$769$	−33.0887	−1.19321	−0.596605	+	0.802535i	$0.703484\pi$
$770$	4.78896	0.172582
$771$	−26.1581	−0.942063
$772$	1.06658	0.0383870
$773$	36.5109	1.31321	0.656604	−	0.754236i	$-0.271992\pi$
$773$	36.5109	1.31321	0.656604	+	0.754236i	$0.271992\pi$
$774$	−15.4533	−0.555458
$775$	86.1967	3.09628
$776$	−4.65073	−0.166952
$777$	−11.4319	−0.410118
$778$	−32.3224	−1.15882
$779$	−7.76149	−0.278084
$780$	−26.5578	−0.950923
$781$	3.49631	0.125108
$782$	3.10654	0.111090
$783$	−52.7021	−1.88342
$784$	−6.27533	−0.224119
$785$	−12.6205	−0.450446
$786$	12.9956	0.463539
$787$	−28.3395	−1.01019	−0.505097	−	0.863063i	$-0.668543\pi$
$787$	−28.3395	−1.01019	−0.505097	+	0.863063i	$0.668543\pi$
$788$	−0.783286	−0.0279034
$789$	−22.5745	−0.803673
$790$	4.53689	0.161415
$791$	−10.8924	−0.387288
$792$	2.45154	0.0871117
$793$	85.8671	3.04923
$794$	−4.29325	−0.152362
$795$	−24.4235	−0.866213
$796$	−16.6925	−0.591651
$797$	−21.1391	−0.748785	−0.374392	−	0.927270i	$-0.622149\pi$
$797$	−21.1391	−0.748785	−0.374392	+	0.927270i	$0.622149\pi$
$798$	0.955159	0.0338123
$799$	2.25598	0.0798109
$800$	−10.9618	−0.387558
$801$	−19.0745	−0.673964
$802$	19.5990	0.692066
$803$	−0.868955	−0.0306648
$804$	14.6097	0.515245
$805$	5.54242	0.195345
$806$	46.5859	1.64092
$807$	17.2132	0.605933
$808$	5.07461	0.178524
$809$	−30.1529	−1.06012	−0.530060	−	0.847960i	$-0.677831\pi$
$809$	−30.1529	−1.06012	−0.530060	+	0.847960i	$0.677831\pi$
$810$	−2.97908	−0.104674
$811$	5.21489	0.183120	0.0915598	−	0.995800i	$-0.470815\pi$
$811$	5.21489	0.183120	0.0915598	+	0.995800i	$0.470815\pi$
$812$	−8.43370	−0.295965
$813$	28.7077	1.00682
$814$	−16.8529	−0.590692
$815$	−18.3746	−0.643634
$816$	−2.13892	−0.0748772
$817$	−8.87591	−0.310529
$818$	−37.6722	−1.31718
$819$	8.78060	0.306819
$820$	31.0089	1.08288
$821$	30.6286	1.06895	0.534473	−	0.845186i	$-0.320510\pi$
$821$	30.6286	1.06895	0.534473	+	0.845186i	$0.320510\pi$
$822$	2.82304	0.0984647
$823$	−46.4632	−1.61961	−0.809803	−	0.586702i	$-0.800426\pi$
$823$	−46.4632	−1.61961	−0.809803	+	0.586702i	$0.800426\pi$
$824$	16.6988	0.581729
$825$	−17.3188	−0.602964
$826$	12.2019	0.424557
$827$	−16.3138	−0.567286	−0.283643	−	0.958930i	$-0.591543\pi$
$827$	−16.3138	−0.567286	−0.283643	+	0.958930i	$0.591543\pi$
$828$	2.83725	0.0986012
$829$	−20.0189	−0.695284	−0.347642	−	0.937627i	$-0.613018\pi$
$829$	−20.0189	−0.695284	−0.347642	+	0.937627i	$0.613018\pi$
$830$	−33.2518	−1.15419
$831$	−15.5019	−0.537754
$832$	−5.92441	−0.205392
$833$	−11.9626	−0.414479
$834$	−6.35208	−0.219955
$835$	90.5885	3.13494
$836$	1.40809	0.0486998
$837$	41.8301	1.44586
$838$	18.7269	0.646911
$839$	−33.2476	−1.14783	−0.573916	−	0.818914i	$-0.694577\pi$
$839$	−33.2476	−1.14783	−0.573916	+	0.818914i	$0.694577\pi$
$840$	−3.81607	−0.131667
$841$	69.1515	2.38453
$842$	−1.09429	−0.0377117
$843$	4.26735	0.146976
$844$	−1.00000	−0.0344214
$845$	−88.2892	−3.03724
$846$	2.06042	0.0708386
$847$	−7.67619	−0.263757
$848$	−5.44831	−0.187096
$849$	−11.5417	−0.396109
$850$	−20.8964	−0.716739
$851$	−19.5044	−0.668601
$852$	−2.78603	−0.0954479
$853$	35.8046	1.22593	0.612963	−	0.790112i	$-0.289978\pi$
$853$	35.8046	1.22593	0.612963	+	0.790112i	$0.289978\pi$
$854$	12.3382	0.422204
$855$	6.95584	0.237885
$856$	4.70351	0.160763
$857$	6.45253	0.220414	0.110207	−	0.993909i	$-0.464849\pi$
$857$	6.45253	0.220414	0.110207	+	0.993909i	$0.464849\pi$
$858$	−9.36012	−0.319549
$859$	4.96574	0.169429	0.0847144	−	0.996405i	$-0.473002\pi$
$859$	4.96574	0.169429	0.0847144	+	0.996405i	$0.473002\pi$
$860$	35.4613	1.20922
$861$	7.41346	0.252650
$862$	−16.4807	−0.561336
$863$	53.5017	1.82122	0.910609	−	0.413268i	$-0.135613\pi$
$863$	53.5017	1.82122	0.910609	+	0.413268i	$0.135613\pi$
$864$	−5.31961	−0.180977
$865$	62.8033	2.13538
$866$	1.85814	0.0631421
$867$	14.9972	0.509331
$868$	6.69389	0.227205
$869$	1.59900	0.0542422
$870$	44.4115	1.50569
$871$	77.1402	2.61380
$872$	0.277453	0.00939574
$873$	−8.09711	−0.274046
$874$	1.62963	0.0551230
$875$	−20.2763	−0.685464
$876$	0.692426	0.0233949
$877$	40.4058	1.36441	0.682203	−	0.731163i	$-0.261022\pi$
$877$	40.4058	1.36441	0.682203	+	0.731163i	$0.261022\pi$
$878$	2.11611	0.0714153
$879$	−15.1527	−0.511089
$880$	−5.62563	−0.189640
$881$	9.41477	0.317192	0.158596	−	0.987344i	$-0.449303\pi$
$881$	9.41477	0.317192	0.158596	+	0.987344i	$0.449303\pi$
$882$	−10.9256	−0.367884
$883$	−23.8172	−0.801514	−0.400757	−	0.916184i	$-0.631253\pi$
$883$	−23.8172	−0.801514	−0.400757	+	0.916184i	$0.631253\pi$
$884$	−11.2936	−0.379846
$885$	−64.2545	−2.15989
$886$	−25.6807	−0.862762
$887$	13.6694	0.458974	0.229487	−	0.973312i	$-0.426295\pi$
$887$	13.6694	0.458974	0.229487	+	0.973312i	$0.426295\pi$
$888$	13.4292	0.450654
$889$	10.3856	0.348320
$890$	43.7709	1.46720
$891$	−1.04996	−0.0351749
$892$	5.99365	0.200682
$893$	1.18344	0.0396024
$894$	24.9074	0.833029
$895$	17.0593	0.570231
$896$	−0.851275	−0.0284391
$897$	−10.8328	−0.361696
$898$	−5.05637	−0.168733
$899$	−77.9035	−2.59823
$900$	−19.0849	−0.636165
$901$	−10.3860	−0.346009
$902$	10.9289	0.363892
$903$	8.47791	0.282127
$904$	12.7954	0.425567
$905$	11.6940	0.388721
$906$	8.99676	0.298897
$907$	−15.4034	−0.511461	−0.255731	−	0.966748i	$-0.582316\pi$
$907$	−15.4034	−0.511461	−0.255731	+	0.966748i	$0.582316\pi$
$908$	−14.9466	−0.496021
$909$	8.83509	0.293042
$910$	−20.1491	−0.667937
$911$	−32.0091	−1.06051	−0.530254	−	0.847839i	$-0.677904\pi$
$911$	−32.0091	−1.06051	−0.530254	+	0.847839i	$0.677904\pi$
$912$	−1.12203	−0.0371543
$913$	−11.7194	−0.387855
$914$	−4.20795	−0.139187
$915$	−64.9723	−2.14792
$916$	16.3872	0.541449
$917$	9.85966	0.325595
$918$	−10.1407	−0.334693
$919$	−2.15382	−0.0710480	−0.0355240	−	0.999369i	$-0.511310\pi$
$919$	−2.15382	−0.0710480	−0.0355240	+	0.999369i	$0.511310\pi$
$920$	−6.51073	−0.214652
$921$	4.71969	0.155519
$922$	10.4897	0.345459
$923$	−14.7104	−0.484200
$924$	−1.34495	−0.0442456
$925$	131.197	4.31375
$926$	4.87952	0.160351
$927$	29.0732	0.954889
$928$	9.90714	0.325218
$929$	51.3511	1.68477	0.842387	−	0.538873i	$-0.181150\pi$
$929$	51.3511	1.68477	0.842387	+	0.538873i	$0.181150\pi$
$930$	−35.2497	−1.15588
$931$	−6.27533	−0.205666
$932$	−26.8336	−0.878963
$933$	0.196496	0.00643300
$934$	−26.3874	−0.863421
$935$	−10.7241	−0.350715
$936$	−10.3146	−0.337145
$937$	−45.2572	−1.47849	−0.739244	−	0.673438i	$-0.764817\pi$
$937$	−45.2572	−1.47849	−0.739244	+	0.673438i	$0.764817\pi$
$938$	11.0842	0.361913
$939$	−33.4833	−1.09269
$940$	−4.72811	−0.154214
$941$	12.3275	0.401864	0.200932	−	0.979605i	$-0.435603\pi$
$941$	12.3275	0.401864	0.200932	+	0.979605i	$0.435603\pi$
$942$	3.54440	0.115483
$943$	12.6484	0.411887
$944$	−14.3336	−0.466520
$945$	−18.0922	−0.588538
$946$	12.4981	0.406348
$947$	−48.8895	−1.58870	−0.794348	−	0.607463i	$-0.792187\pi$
$947$	−48.8895	−1.58870	−0.794348	+	0.607463i	$0.792187\pi$
$948$	−1.27416	−0.0413827
$949$	3.65605	0.118681
$950$	−10.9618	−0.355648
$951$	11.4572	0.371526
$952$	−1.62278	−0.0525945
$953$	52.8226	1.71109	0.855546	−	0.517727i	$-0.173222\pi$
$953$	52.8226	1.71109	0.855546	+	0.517727i	$0.173222\pi$
$954$	−9.48572	−0.307111
$955$	2.57784	0.0834170
$956$	−21.5693	−0.697600
$957$	15.6525	0.505974
$958$	36.2065	1.16978
$959$	2.14181	0.0691625
$960$	4.48278	0.144681
$961$	30.8326	0.994600
$962$	70.9069	2.28613
$963$	8.18899	0.263887
$964$	−10.5162	−0.338704
$965$	−4.26122	−0.137173
$966$	−1.55656	−0.0500813
$967$	−5.68114	−0.182693	−0.0913466	−	0.995819i	$-0.529117\pi$
$967$	−5.68114	−0.182693	−0.0913466	+	0.995819i	$0.529117\pi$
$968$	9.01728	0.289827
$969$	−2.13892	−0.0687120
$970$	18.5807	0.596591
$971$	14.0694	0.451510	0.225755	−	0.974184i	$-0.427515\pi$
$971$	14.0694	0.451510	0.225755	+	0.974184i	$0.427515\pi$
$972$	−15.1222	−0.485044
$973$	−4.81926	−0.154498
$974$	−31.2850	−1.00243
$975$	72.8674	2.33363
$976$	−14.4938	−0.463934
$977$	−32.7772	−1.04864	−0.524318	−	0.851522i	$-0.675680\pi$
$977$	−32.7772	−1.04864	−0.524318	+	0.851522i	$0.675680\pi$
$978$	5.16039	0.165011
$979$	15.4268	0.493041
$980$	25.0713	0.800875
$981$	0.483057	0.0154228
$982$	23.9434	0.764064
$983$	25.6854	0.819236	0.409618	−	0.912257i	$-0.365662\pi$
$983$	25.6854	0.819236	0.409618	+	0.912257i	$0.365662\pi$
$984$	−8.70866	−0.277622
$985$	3.12940	0.0997110
$986$	18.8859	0.601449
$987$	−1.13038	−0.0359802
$988$	−5.92441	−0.188481
$989$	14.4644	0.459943
$990$	−9.79445	−0.311288
$991$	6.03201	0.191613	0.0958066	−	0.995400i	$-0.469457\pi$
$991$	6.03201	0.191613	0.0958066	+	0.995400i	$0.469457\pi$
$992$	−7.86337	−0.249662
$993$	28.5116	0.904790
$994$	−2.11373	−0.0670435
$995$	66.6903	2.11423
$996$	9.33857	0.295904
$997$	7.63680	0.241860	0.120930	−	0.992661i	$-0.461412\pi$
$997$	7.63680	0.241860	0.120930	+	0.992661i	$0.461412\pi$
$998$	−9.83897	−0.311447
$999$	63.6683	2.01437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.15	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.15	✓	43	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.12203 q^{3} +1.00000 q^{4} -3.99522 q^{5} +1.12203 q^{6} +0.851275 q^{7} -1.00000 q^{8} -1.74104 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.12203 q^{3} +1.00000 q^{4} -3.99522 q^{5} +1.12203 q^{6} +0.851275 q^{7} -1.00000 q^{8} -1.74104 q^{9} +3.99522 q^{10} +1.40809 q^{11} -1.12203 q^{12} -5.92441 q^{13} -0.851275 q^{14} +4.48278 q^{15} +1.00000 q^{16} +1.90629 q^{17} +1.74104 q^{18} +1.00000 q^{19} -3.99522 q^{20} -0.955159 q^{21} -1.40809 q^{22} -1.62963 q^{23} +1.12203 q^{24} +10.9618 q^{25} +5.92441 q^{26} +5.31961 q^{27} +0.851275 q^{28} -9.90714 q^{29} -4.48278 q^{30} +7.86337 q^{31} -1.00000 q^{32} -1.57992 q^{33} -1.90629 q^{34} -3.40103 q^{35} -1.74104 q^{36} +11.9686 q^{37} -1.00000 q^{38} +6.64739 q^{39} +3.99522 q^{40} -7.76149 q^{41} +0.955159 q^{42} -8.87591 q^{43} +1.40809 q^{44} +6.95584 q^{45} +1.62963 q^{46} +1.18344 q^{47} -1.12203 q^{48} -6.27533 q^{49} -10.9618 q^{50} -2.13892 q^{51} -5.92441 q^{52} -5.44831 q^{53} -5.31961 q^{54} -5.62563 q^{55} -0.851275 q^{56} -1.12203 q^{57} +9.90714 q^{58} -14.3336 q^{59} +4.48278 q^{60} -14.4938 q^{61} -7.86337 q^{62} -1.48210 q^{63} +1.00000 q^{64} +23.6694 q^{65} +1.57992 q^{66} -13.0207 q^{67} +1.90629 q^{68} +1.82850 q^{69} +3.40103 q^{70} +2.48302 q^{71} +1.74104 q^{72} -0.617116 q^{73} -11.9686 q^{74} -12.2995 q^{75} +1.00000 q^{76} +1.19867 q^{77} -6.64739 q^{78} +1.13558 q^{79} -3.99522 q^{80} -0.745661 q^{81} +7.76149 q^{82} -8.32289 q^{83} -0.955159 q^{84} -7.61605 q^{85} +8.87591 q^{86} +11.1162 q^{87} -1.40809 q^{88} +10.9558 q^{89} -6.95584 q^{90} -5.04331 q^{91} -1.62963 q^{92} -8.82297 q^{93} -1.18344 q^{94} -3.99522 q^{95} +1.12203 q^{96} +4.65073 q^{97} +6.27533 q^{98} -2.45154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

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