LMFDB - Embedded newform 8018.2.a.d.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.26
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.62956 q^{3} +1.00000 q^{4} -1.52015 q^{5} +1.62956 q^{6} -1.42559 q^{7} +1.00000 q^{8} -0.344547 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.62956 q^{3} +1.00000 q^{4} -1.52015 q^{5} +1.62956 q^{6} -1.42559 q^{7} +1.00000 q^{8} -0.344547 q^{9} -1.52015 q^{10} -3.50306 q^{11} +1.62956 q^{12} -0.327222 q^{13} -1.42559 q^{14} -2.47716 q^{15} +1.00000 q^{16} +7.06141 q^{17} -0.344547 q^{18} +1.00000 q^{19} -1.52015 q^{20} -2.32309 q^{21} -3.50306 q^{22} +3.94413 q^{23} +1.62956 q^{24} -2.68916 q^{25} -0.327222 q^{26} -5.45013 q^{27} -1.42559 q^{28} -4.95453 q^{29} -2.47716 q^{30} +4.87086 q^{31} +1.00000 q^{32} -5.70844 q^{33} +7.06141 q^{34} +2.16711 q^{35} -0.344547 q^{36} -6.24209 q^{37} +1.00000 q^{38} -0.533226 q^{39} -1.52015 q^{40} +4.65843 q^{41} -2.32309 q^{42} +5.36669 q^{43} -3.50306 q^{44} +0.523762 q^{45} +3.94413 q^{46} -6.86192 q^{47} +1.62956 q^{48} -4.96768 q^{49} -2.68916 q^{50} +11.5070 q^{51} -0.327222 q^{52} -7.45216 q^{53} -5.45013 q^{54} +5.32516 q^{55} -1.42559 q^{56} +1.62956 q^{57} -4.95453 q^{58} -7.68218 q^{59} -2.47716 q^{60} +11.7673 q^{61} +4.87086 q^{62} +0.491185 q^{63} +1.00000 q^{64} +0.497425 q^{65} -5.70844 q^{66} -10.1259 q^{67} +7.06141 q^{68} +6.42717 q^{69} +2.16711 q^{70} +1.58834 q^{71} -0.344547 q^{72} -6.38251 q^{73} -6.24209 q^{74} -4.38214 q^{75} +1.00000 q^{76} +4.99395 q^{77} -0.533226 q^{78} -10.3154 q^{79} -1.52015 q^{80} -7.84764 q^{81} +4.65843 q^{82} -12.8669 q^{83} -2.32309 q^{84} -10.7344 q^{85} +5.36669 q^{86} -8.07369 q^{87} -3.50306 q^{88} -11.7102 q^{89} +0.523762 q^{90} +0.466486 q^{91} +3.94413 q^{92} +7.93734 q^{93} -6.86192 q^{94} -1.52015 q^{95} +1.62956 q^{96} -6.31541 q^{97} -4.96768 q^{98} +1.20697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.62956	0.940825	0.470412	−	0.882447i	$-0.344105\pi$
$3$	1.62956	0.940825	0.470412	+	0.882447i	$0.344105\pi$
$4$	1.00000	0.500000
$5$	−1.52015	−0.679830	−0.339915	−	0.940456i	$-0.610398\pi$
$5$	−1.52015	−0.679830	−0.339915	+	0.940456i	$0.610398\pi$
$6$	1.62956	0.665263
$7$	−1.42559	−0.538824	−0.269412	−	0.963025i	$-0.586829\pi$
$7$	−1.42559	−0.538824	−0.269412	+	0.963025i	$0.586829\pi$
$8$	1.00000	0.353553
$9$	−0.344547	−0.114849
$10$	−1.52015	−0.480712
$11$	−3.50306	−1.05621	−0.528107	−	0.849178i	$-0.677098\pi$
$11$	−3.50306	−1.05621	−0.528107	+	0.849178i	$0.677098\pi$
$12$	1.62956	0.470412
$13$	−0.327222	−0.0907550	−0.0453775	−	0.998970i	$-0.514449\pi$
$13$	−0.327222	−0.0907550	−0.0453775	+	0.998970i	$0.514449\pi$
$14$	−1.42559	−0.381006
$15$	−2.47716	−0.639600
$16$	1.00000	0.250000
$17$	7.06141	1.71264	0.856322	−	0.516442i	$-0.172744\pi$
$17$	7.06141	1.71264	0.856322	+	0.516442i	$0.172744\pi$
$18$	−0.344547	−0.0812106
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.52015	−0.339915
$21$	−2.32309	−0.506939
$22$	−3.50306	−0.746856
$23$	3.94413	0.822407	0.411204	−	0.911544i	$-0.365109\pi$
$23$	3.94413	0.822407	0.411204	+	0.911544i	$0.365109\pi$
$24$	1.62956	0.332632
$25$	−2.68916	−0.537832
$26$	−0.327222	−0.0641735
$27$	−5.45013	−1.04888
$28$	−1.42559	−0.269412
$29$	−4.95453	−0.920034	−0.460017	−	0.887910i	$-0.652157\pi$
$29$	−4.95453	−0.920034	−0.460017	+	0.887910i	$0.652157\pi$
$30$	−2.47716	−0.452266
$31$	4.87086	0.874832	0.437416	−	0.899259i	$-0.355894\pi$
$31$	4.87086	0.874832	0.437416	+	0.899259i	$0.355894\pi$
$32$	1.00000	0.176777
$33$	−5.70844	−0.993712
$34$	7.06141	1.21102
$35$	2.16711	0.366308
$36$	−0.344547	−0.0574246
$37$	−6.24209	−1.02619	−0.513097	−	0.858331i	$-0.671502\pi$
$37$	−6.24209	−1.02619	−0.513097	+	0.858331i	$0.671502\pi$
$38$	1.00000	0.162221
$39$	−0.533226	−0.0853846
$40$	−1.52015	−0.240356
$41$	4.65843	0.727525	0.363763	−	0.931492i	$-0.381492\pi$
$41$	4.65843	0.727525	0.363763	+	0.931492i	$0.381492\pi$
$42$	−2.32309	−0.358460
$43$	5.36669	0.818413	0.409206	−	0.912442i	$-0.365806\pi$
$43$	5.36669	0.818413	0.409206	+	0.912442i	$0.365806\pi$
$44$	−3.50306	−0.528107
$45$	0.523762	0.0780778
$46$	3.94413	0.581530
$47$	−6.86192	−1.00091	−0.500457	−	0.865762i	$-0.666835\pi$
$47$	−6.86192	−1.00091	−0.500457	+	0.865762i	$0.666835\pi$
$48$	1.62956	0.235206
$49$	−4.96768	−0.709669
$50$	−2.68916	−0.380305
$51$	11.5070	1.61130
$52$	−0.327222	−0.0453775
$53$	−7.45216	−1.02363	−0.511816	−	0.859095i	$-0.671027\pi$
$53$	−7.45216	−1.02363	−0.511816	+	0.859095i	$0.671027\pi$
$54$	−5.45013	−0.741668
$55$	5.32516	0.718045
$56$	−1.42559	−0.190503
$57$	1.62956	0.215840
$58$	−4.95453	−0.650562
$59$	−7.68218	−1.00014	−0.500068	−	0.865986i	$-0.666692\pi$
$59$	−7.68218	−1.00014	−0.500068	+	0.865986i	$0.666692\pi$
$60$	−2.47716	−0.319800
$61$	11.7673	1.50665	0.753325	−	0.657648i	$-0.228449\pi$
$61$	11.7673	1.50665	0.753325	+	0.657648i	$0.228449\pi$
$62$	4.87086	0.618600
$63$	0.491185	0.0618835
$64$	1.00000	0.125000
$65$	0.497425	0.0616979
$66$	−5.70844	−0.702660
$67$	−10.1259	−1.23708	−0.618539	−	0.785754i	$-0.712275\pi$
$67$	−10.1259	−1.23708	−0.618539	+	0.785754i	$0.712275\pi$
$68$	7.06141	0.856322
$69$	6.42717	0.773741
$70$	2.16711	0.259019
$71$	1.58834	0.188502	0.0942508	−	0.995548i	$-0.469954\pi$
$71$	1.58834	0.188502	0.0942508	+	0.995548i	$0.469954\pi$
$72$	−0.344547	−0.0406053
$73$	−6.38251	−0.747017	−0.373508	−	0.927627i	$-0.621845\pi$
$73$	−6.38251	−0.747017	−0.373508	+	0.927627i	$0.621845\pi$
$74$	−6.24209	−0.725629
$75$	−4.38214	−0.506005
$76$	1.00000	0.114708
$77$	4.99395	0.569113
$78$	−0.533226	−0.0603760
$79$	−10.3154	−1.16057	−0.580286	−	0.814413i	$-0.697059\pi$
$79$	−10.3154	−1.16057	−0.580286	+	0.814413i	$0.697059\pi$
$80$	−1.52015	−0.169957
$81$	−7.84764	−0.871961
$82$	4.65843	0.514438
$83$	−12.8669	−1.41233	−0.706164	−	0.708048i	$-0.749576\pi$
$83$	−12.8669	−1.41233	−0.706164	+	0.708048i	$0.749576\pi$
$84$	−2.32309	−0.253469
$85$	−10.7344	−1.16431
$86$	5.36669	0.578705
$87$	−8.07369	−0.865591
$88$	−3.50306	−0.373428
$89$	−11.7102	−1.24128	−0.620639	−	0.784096i	$-0.713127\pi$
$89$	−11.7102	−1.24128	−0.620639	+	0.784096i	$0.713127\pi$
$90$	0.523762	0.0552094
$91$	0.466486	0.0489010
$92$	3.94413	0.411204
$93$	7.93734	0.823064
$94$	−6.86192	−0.707753
$95$	−1.52015	−0.155964
$96$	1.62956	0.166316
$97$	−6.31541	−0.641232	−0.320616	−	0.947209i	$-0.603890\pi$
$97$	−6.31541	−0.641232	−0.320616	+	0.947209i	$0.603890\pi$
$98$	−4.96768	−0.501812
$99$	1.20697	0.121305
$100$	−2.68916	−0.268916
$101$	−11.1263	−1.10711	−0.553556	−	0.832812i	$-0.686729\pi$
$101$	−11.1263	−1.10711	−0.553556	+	0.832812i	$0.686729\pi$
$102$	11.5070	1.13936
$103$	−8.71434	−0.858649	−0.429325	−	0.903150i	$-0.641248\pi$
$103$	−8.71434	−0.858649	−0.429325	+	0.903150i	$0.641248\pi$
$104$	−0.327222	−0.0320867
$105$	3.53143	0.344632
$106$	−7.45216	−0.723818
$107$	−11.8617	−1.14671	−0.573357	−	0.819305i	$-0.694359\pi$
$107$	−11.8617	−1.14671	−0.573357	+	0.819305i	$0.694359\pi$
$108$	−5.45013	−0.524439
$109$	1.62194	0.155354	0.0776770	−	0.996979i	$-0.475250\pi$
$109$	1.62194	0.155354	0.0776770	+	0.996979i	$0.475250\pi$
$110$	5.32516	0.507735
$111$	−10.1718	−0.965468
$112$	−1.42559	−0.134706
$113$	19.3284	1.81827	0.909134	−	0.416505i	$-0.136745\pi$
$113$	19.3284	1.81827	0.909134	+	0.416505i	$0.136745\pi$
$114$	1.62956	0.152622
$115$	−5.99564	−0.559097
$116$	−4.95453	−0.460017
$117$	0.112743	0.0104231
$118$	−7.68218	−0.707202
$119$	−10.0667	−0.922814
$120$	−2.47716	−0.226133
$121$	1.27145	0.115587
$122$	11.7673	1.06536
$123$	7.59118	0.684474
$124$	4.87086	0.437416
$125$	11.6886	1.04546
$126$	0.491185	0.0437582
$127$	2.74186	0.243301	0.121650	−	0.992573i	$-0.461181\pi$
$127$	2.74186	0.243301	0.121650	+	0.992573i	$0.461181\pi$
$128$	1.00000	0.0883883
$129$	8.74533	0.769983
$130$	0.497425	0.0436270
$131$	15.6535	1.36765	0.683824	−	0.729647i	$-0.260315\pi$
$131$	15.6535	1.36765	0.683824	+	0.729647i	$0.260315\pi$
$132$	−5.70844	−0.496856
$133$	−1.42559	−0.123615
$134$	−10.1259	−0.874747
$135$	8.28498	0.713058
$136$	7.06141	0.605511
$137$	2.78339	0.237801	0.118901	−	0.992906i	$-0.462063\pi$
$137$	2.78339	0.237801	0.118901	+	0.992906i	$0.462063\pi$
$138$	6.42717	0.547117
$139$	−14.5906	−1.23756	−0.618781	−	0.785563i	$-0.712373\pi$
$139$	−14.5906	−1.23756	−0.618781	+	0.785563i	$0.712373\pi$
$140$	2.16711	0.183154
$141$	−11.1819	−0.941684
$142$	1.58834	0.133291
$143$	1.14628	0.0958567
$144$	−0.344547	−0.0287123
$145$	7.53161	0.625466
$146$	−6.38251	−0.528220
$147$	−8.09511	−0.667674
$148$	−6.24209	−0.513097
$149$	1.62226	0.132900	0.0664502	−	0.997790i	$-0.478833\pi$
$149$	1.62226	0.132900	0.0664502	+	0.997790i	$0.478833\pi$
$150$	−4.38214	−0.357800
$151$	9.73848	0.792506	0.396253	−	0.918141i	$-0.370310\pi$
$151$	9.73848	0.792506	0.396253	+	0.918141i	$0.370310\pi$
$152$	1.00000	0.0811107
$153$	−2.43299	−0.196696
$154$	4.99395	0.402424
$155$	−7.40441	−0.594737
$156$	−0.533226	−0.0426923
$157$	−16.8416	−1.34410	−0.672052	−	0.740504i	$-0.734587\pi$
$157$	−16.8416	−1.34410	−0.672052	+	0.740504i	$0.734587\pi$
$158$	−10.3154	−0.820648
$159$	−12.1437	−0.963059
$160$	−1.52015	−0.120178
$161$	−5.62272	−0.443133
$162$	−7.84764	−0.616569
$163$	20.1974	1.58198	0.790989	−	0.611830i	$-0.209566\pi$
$163$	20.1974	1.58198	0.790989	+	0.611830i	$0.209566\pi$
$164$	4.65843	0.363763
$165$	8.67765	0.675554
$166$	−12.8669	−0.998667
$167$	7.72092	0.597463	0.298732	−	0.954337i	$-0.403436\pi$
$167$	7.72092	0.597463	0.298732	+	0.954337i	$0.403436\pi$
$168$	−2.32309	−0.179230
$169$	−12.8929	−0.991764
$170$	−10.7344	−0.823289
$171$	−0.344547	−0.0263482
$172$	5.36669	0.409206
$173$	−13.7865	−1.04817	−0.524083	−	0.851667i	$-0.675592\pi$
$173$	−13.7865	−1.04817	−0.524083	+	0.851667i	$0.675592\pi$
$174$	−8.07369	−0.612065
$175$	3.83365	0.289797
$176$	−3.50306	−0.264053
$177$	−12.5186	−0.940952
$178$	−11.7102	−0.877716
$179$	−7.13282	−0.533132	−0.266566	−	0.963817i	$-0.585889\pi$
$179$	−7.13282	−0.533132	−0.266566	+	0.963817i	$0.585889\pi$
$180$	0.523762	0.0390389
$181$	17.5682	1.30583	0.652915	−	0.757431i	$-0.273546\pi$
$181$	17.5682	1.30583	0.652915	+	0.757431i	$0.273546\pi$
$182$	0.466486	0.0345782
$183$	19.1755	1.41749
$184$	3.94413	0.290765
$185$	9.48889	0.697637
$186$	7.93734	0.581994
$187$	−24.7366	−1.80892
$188$	−6.86192	−0.500457
$189$	7.76967	0.565160
$190$	−1.52015	−0.110283
$191$	−12.7850	−0.925088	−0.462544	−	0.886596i	$-0.653063\pi$
$191$	−12.7850	−0.925088	−0.462544	+	0.886596i	$0.653063\pi$
$192$	1.62956	0.117603
$193$	−16.4619	−1.18496	−0.592478	−	0.805587i	$-0.701850\pi$
$193$	−16.4619	−1.18496	−0.592478	+	0.805587i	$0.701850\pi$
$194$	−6.31541	−0.453420
$195$	0.810581	0.0580469
$196$	−4.96768	−0.354834
$197$	7.78989	0.555007	0.277503	−	0.960725i	$-0.410493\pi$
$197$	7.78989	0.555007	0.277503	+	0.960725i	$0.410493\pi$
$198$	1.20697	0.0857757
$199$	−8.53546	−0.605063	−0.302531	−	0.953139i	$-0.597832\pi$
$199$	−8.53546	−0.605063	−0.302531	+	0.953139i	$0.597832\pi$
$200$	−2.68916	−0.190152
$201$	−16.5008	−1.16387
$202$	−11.1263	−0.782846
$203$	7.06316	0.495736
$204$	11.5070	0.805649
$205$	−7.08150	−0.494593
$206$	−8.71434	−0.607157
$207$	−1.35894	−0.0944528
$208$	−0.327222	−0.0226888
$209$	−3.50306	−0.242312
$210$	3.53143	0.243692
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−7.45216	−0.511816
$213$	2.58829	0.177347
$214$	−11.8617	−0.810850
$215$	−8.15815	−0.556381
$216$	−5.45013	−0.370834
$217$	−6.94387	−0.471381
$218$	1.62194	0.109852
$219$	−10.4007	−0.702812
$220$	5.32516	0.359023
$221$	−2.31065	−0.155431
$222$	−10.1718	−0.682689
$223$	9.56096	0.640250	0.320125	−	0.947375i	$-0.396275\pi$
$223$	9.56096	0.640250	0.320125	+	0.947375i	$0.396275\pi$
$224$	−1.42559	−0.0952515
$225$	0.926543	0.0617695
$226$	19.3284	1.28571
$227$	1.98217	0.131561	0.0657806	−	0.997834i	$-0.479046\pi$
$227$	1.98217	0.131561	0.0657806	+	0.997834i	$0.479046\pi$
$228$	1.62956	0.107920
$229$	8.45219	0.558537	0.279268	−	0.960213i	$-0.409908\pi$
$229$	8.45219	0.558537	0.279268	+	0.960213i	$0.409908\pi$
$230$	−5.99564	−0.395341
$231$	8.13792	0.535436
$232$	−4.95453	−0.325281
$233$	−1.46640	−0.0960672	−0.0480336	−	0.998846i	$-0.515295\pi$
$233$	−1.46640	−0.0960672	−0.0480336	+	0.998846i	$0.515295\pi$
$234$	0.112743	0.00737027
$235$	10.4311	0.680451
$236$	−7.68218	−0.500068
$237$	−16.8095	−1.09189
$238$	−10.0667	−0.652528
$239$	4.35381	0.281625	0.140812	−	0.990036i	$-0.455029\pi$
$239$	4.35381	0.281625	0.140812	+	0.990036i	$0.455029\pi$
$240$	−2.47716	−0.159900
$241$	−4.00178	−0.257777	−0.128889	−	0.991659i	$-0.541141\pi$
$241$	−4.00178	−0.257777	−0.128889	+	0.991659i	$0.541141\pi$
$242$	1.27145	0.0817322
$243$	3.56221	0.228516
$244$	11.7673	0.753325
$245$	7.55159	0.482454
$246$	7.59118	0.483996
$247$	−0.327222	−0.0208206
$248$	4.87086	0.309300
$249$	−20.9674	−1.32875
$250$	11.6886	0.739254
$251$	−8.66934	−0.547204	−0.273602	−	0.961843i	$-0.588215\pi$
$251$	−8.66934	−0.547204	−0.273602	+	0.961843i	$0.588215\pi$
$252$	0.491185	0.0309417
$253$	−13.8165	−0.868638
$254$	2.74186	0.172039
$255$	−17.4923	−1.09541
$256$	1.00000	0.0625000
$257$	22.4206	1.39856	0.699281	−	0.714847i	$-0.253504\pi$
$257$	22.4206	1.39856	0.699281	+	0.714847i	$0.253504\pi$
$258$	8.74533	0.544460
$259$	8.89869	0.552938
$260$	0.497425	0.0308490
$261$	1.70707	0.105665
$262$	15.6535	0.967074
$263$	−29.7553	−1.83479	−0.917394	−	0.397980i	$-0.869711\pi$
$263$	−29.7553	−1.83479	−0.917394	+	0.397980i	$0.869711\pi$
$264$	−5.70844	−0.351330
$265$	11.3284	0.695896
$266$	−1.42559	−0.0874088
$267$	−19.0824	−1.16782
$268$	−10.1259	−0.618539
$269$	−24.6623	−1.50369	−0.751843	−	0.659342i	$-0.770835\pi$
$269$	−24.6623	−1.50369	−0.751843	+	0.659342i	$0.770835\pi$
$270$	8.28498	0.504208
$271$	13.7975	0.838141	0.419070	−	0.907954i	$-0.362356\pi$
$271$	13.7975	0.838141	0.419070	+	0.907954i	$0.362356\pi$
$272$	7.06141	0.428161
$273$	0.760165	0.0460073
$274$	2.78339	0.168151
$275$	9.42030	0.568065
$276$	6.42717	0.386870
$277$	−20.9965	−1.26156	−0.630778	−	0.775963i	$-0.717264\pi$
$277$	−20.9965	−1.26156	−0.630778	+	0.775963i	$0.717264\pi$
$278$	−14.5906	−0.875089
$279$	−1.67824	−0.100474
$280$	2.16711	0.129510
$281$	25.0488	1.49429	0.747143	−	0.664663i	$-0.231425\pi$
$281$	25.0488	1.49429	0.747143	+	0.664663i	$0.231425\pi$
$282$	−11.1819	−0.665871
$283$	13.7855	0.819460	0.409730	−	0.912207i	$-0.365623\pi$
$283$	13.7855	0.819460	0.409730	+	0.912207i	$0.365623\pi$
$284$	1.58834	0.0942508
$285$	−2.47716	−0.146734
$286$	1.14628	0.0677809
$287$	−6.64104	−0.392008
$288$	−0.344547	−0.0203027
$289$	32.8635	1.93315
$290$	7.53161	0.442271
$291$	−10.2913	−0.603287
$292$	−6.38251	−0.373508
$293$	−20.5099	−1.19820	−0.599099	−	0.800675i	$-0.704475\pi$
$293$	−20.5099	−1.19820	−0.599099	+	0.800675i	$0.704475\pi$
$294$	−8.09511	−0.472117
$295$	11.6780	0.679921
$296$	−6.24209	−0.362814
$297$	19.0921	1.10784
$298$	1.62226	0.0939747
$299$	−1.29060	−0.0746376
$300$	−4.38214	−0.253003
$301$	−7.65073	−0.440981
$302$	9.73848	0.560387
$303$	−18.1310	−1.04160
$304$	1.00000	0.0573539
$305$	−17.8880	−1.02427
$306$	−2.43299	−0.139085
$307$	−26.1353	−1.49162	−0.745812	−	0.666157i	$-0.767938\pi$
$307$	−26.1353	−1.49162	−0.745812	+	0.666157i	$0.767938\pi$
$308$	4.99395	0.284557
$309$	−14.2005	−0.807838
$310$	−7.40441	−0.420542
$311$	10.0044	0.567296	0.283648	−	0.958929i	$-0.408455\pi$
$311$	10.0044	0.567296	0.283648	+	0.958929i	$0.408455\pi$
$312$	−0.533226	−0.0301880
$313$	−24.2682	−1.37172	−0.685860	−	0.727734i	$-0.740574\pi$
$313$	−24.2682	−1.37172	−0.685860	+	0.727734i	$0.740574\pi$
$314$	−16.8416	−0.950425
$315$	−0.746672	−0.0420702
$316$	−10.3154	−0.580286
$317$	11.2965	0.634476	0.317238	−	0.948346i	$-0.397245\pi$
$317$	11.2965	0.634476	0.317238	+	0.948346i	$0.397245\pi$
$318$	−12.1437	−0.680985
$319$	17.3560	0.971752
$320$	−1.52015	−0.0849787
$321$	−19.3293	−1.07886
$322$	−5.62272	−0.313342
$323$	7.06141	0.392907
$324$	−7.84764	−0.435980
$325$	0.879952	0.0488109
$326$	20.1974	1.11863
$327$	2.64305	0.146161
$328$	4.65843	0.257219
$329$	9.78231	0.539316
$330$	8.67765	0.477689
$331$	20.6671	1.13597	0.567983	−	0.823041i	$-0.307724\pi$
$331$	20.6671	1.13597	0.567983	+	0.823041i	$0.307724\pi$
$332$	−12.8669	−0.706164
$333$	2.15070	0.117857
$334$	7.72092	0.422470
$335$	15.3929	0.841003
$336$	−2.32309	−0.126735
$337$	−5.66886	−0.308803	−0.154401	−	0.988008i	$-0.549345\pi$
$337$	−5.66886	−0.308803	−0.154401	+	0.988008i	$0.549345\pi$
$338$	−12.8929	−0.701283
$339$	31.4968	1.71067
$340$	−10.7344	−0.582153
$341$	−17.0629	−0.924010
$342$	−0.344547	−0.0186310
$343$	17.0611	0.921211
$344$	5.36669	0.289353
$345$	−9.77024	−0.526012
$346$	−13.7865	−0.741165
$347$	4.62204	0.248124	0.124062	−	0.992274i	$-0.460408\pi$
$347$	4.62204	0.248124	0.124062	+	0.992274i	$0.460408\pi$
$348$	−8.07369	−0.432795
$349$	−16.3215	−0.873668	−0.436834	−	0.899542i	$-0.643900\pi$
$349$	−16.3215	−0.873668	−0.436834	+	0.899542i	$0.643900\pi$
$350$	3.83365	0.204917
$351$	1.78340	0.0951909
$352$	−3.50306	−0.186714
$353$	−5.51396	−0.293478	−0.146739	−	0.989175i	$-0.546878\pi$
$353$	−5.51396	−0.293478	−0.146739	+	0.989175i	$0.546878\pi$
$354$	−12.5186	−0.665353
$355$	−2.41451	−0.128149
$356$	−11.7102	−0.620639
$357$	−16.4043	−0.868206
$358$	−7.13282	−0.376981
$359$	−26.6426	−1.40614	−0.703072	−	0.711119i	$-0.748189\pi$
$359$	−26.6426	−1.40614	−0.703072	+	0.711119i	$0.748189\pi$
$360$	0.523762	0.0276047
$361$	1.00000	0.0526316
$362$	17.5682	0.923362
$363$	2.07191	0.108747
$364$	0.466486	0.0244505
$365$	9.70234	0.507844
$366$	19.1755	1.00232
$367$	23.5630	1.22998	0.614989	−	0.788535i	$-0.289160\pi$
$367$	23.5630	1.22998	0.614989	+	0.788535i	$0.289160\pi$
$368$	3.94413	0.205602
$369$	−1.60505	−0.0835557
$370$	9.48889	0.493304
$371$	10.6238	0.551558
$372$	7.93734	0.411532
$373$	11.3236	0.586314	0.293157	−	0.956064i	$-0.405294\pi$
$373$	11.3236	0.586314	0.293157	+	0.956064i	$0.405294\pi$
$374$	−24.7366	−1.27910
$375$	19.0473	0.983598
$376$	−6.86192	−0.353876
$377$	1.62123	0.0834977
$378$	7.76967	0.399629
$379$	21.6431	1.11173	0.555865	−	0.831273i	$-0.312387\pi$
$379$	21.6431	1.11173	0.555865	+	0.831273i	$0.312387\pi$
$380$	−1.52015	−0.0779818
$381$	4.46801	0.228903
$382$	−12.7850	−0.654136
$383$	22.6512	1.15742	0.578712	−	0.815532i	$-0.303556\pi$
$383$	22.6512	1.15742	0.578712	+	0.815532i	$0.303556\pi$
$384$	1.62956	0.0831579
$385$	−7.59152	−0.386900
$386$	−16.4619	−0.837890
$387$	−1.84908	−0.0939940
$388$	−6.31541	−0.320616
$389$	−1.55684	−0.0789347	−0.0394674	−	0.999221i	$-0.512566\pi$
$389$	−1.55684	−0.0789347	−0.0394674	+	0.999221i	$0.512566\pi$
$390$	0.810581	0.0410454
$391$	27.8511	1.40849
$392$	−4.96768	−0.250906
$393$	25.5082	1.28672
$394$	7.78989	0.392449
$395$	15.6809	0.788991
$396$	1.20697	0.0606526
$397$	4.03370	0.202446	0.101223	−	0.994864i	$-0.467724\pi$
$397$	4.03370	0.202446	0.101223	+	0.994864i	$0.467724\pi$
$398$	−8.53546	−0.427844
$399$	−2.32309	−0.116300
$400$	−2.68916	−0.134458
$401$	−23.0812	−1.15262	−0.576309	−	0.817232i	$-0.695508\pi$
$401$	−23.0812	−1.15262	−0.576309	+	0.817232i	$0.695508\pi$
$402$	−16.5008	−0.822983
$403$	−1.59385	−0.0793954
$404$	−11.1263	−0.553556
$405$	11.9296	0.592785
$406$	7.06316	0.350539
$407$	21.8664	1.08388
$408$	11.5070	0.569680
$409$	−8.14260	−0.402626	−0.201313	−	0.979527i	$-0.564521\pi$
$409$	−8.14260	−0.402626	−0.201313	+	0.979527i	$0.564521\pi$
$410$	−7.08150	−0.349730
$411$	4.53569	0.223729
$412$	−8.71434	−0.429325
$413$	10.9517	0.538897
$414$	−1.35894	−0.0667882
$415$	19.5596	0.960142
$416$	−0.327222	−0.0160434
$417$	−23.7763	−1.16433
$418$	−3.50306	−0.171340
$419$	11.6787	0.570541	0.285271	−	0.958447i	$-0.407917\pi$
$419$	11.6787	0.570541	0.285271	+	0.958447i	$0.407917\pi$
$420$	3.53143	0.172316
$421$	27.7661	1.35324	0.676619	−	0.736333i	$-0.263444\pi$
$421$	27.7661	1.35324	0.676619	+	0.736333i	$0.263444\pi$
$422$	−1.00000	−0.0486792
$423$	2.36426	0.114954
$424$	−7.45216	−0.361909
$425$	−18.9893	−0.921114
$426$	2.58829	0.125403
$427$	−16.7754	−0.811820
$428$	−11.8617	−0.573357
$429$	1.86793	0.0901843
$430$	−8.15815	−0.393421
$431$	30.7191	1.47968	0.739842	−	0.672780i	$-0.234900\pi$
$431$	30.7191	1.47968	0.739842	+	0.672780i	$0.234900\pi$
$432$	−5.45013	−0.262219
$433$	−4.72388	−0.227015	−0.113508	−	0.993537i	$-0.536209\pi$
$433$	−4.72388	−0.227015	−0.113508	+	0.993537i	$0.536209\pi$
$434$	−6.94387	−0.333316
$435$	12.2732	0.588454
$436$	1.62194	0.0776770
$437$	3.94413	0.188673
$438$	−10.4007	−0.496963
$439$	30.9909	1.47912	0.739558	−	0.673093i	$-0.235035\pi$
$439$	30.9909	1.47912	0.739558	+	0.673093i	$0.235035\pi$
$440$	5.32516	0.253867
$441$	1.71160	0.0815048
$442$	−2.31065	−0.109906
$443$	−4.30227	−0.204407	−0.102203	−	0.994764i	$-0.532589\pi$
$443$	−4.30227	−0.204407	−0.102203	+	0.994764i	$0.532589\pi$
$444$	−10.1718	−0.482734
$445$	17.8012	0.843857
$446$	9.56096	0.452725
$447$	2.64356	0.125036
$448$	−1.42559	−0.0673530
$449$	16.3203	0.770202	0.385101	−	0.922874i	$-0.374167\pi$
$449$	16.3203	0.770202	0.385101	+	0.922874i	$0.374167\pi$
$450$	0.926543	0.0436777
$451$	−16.3188	−0.768422
$452$	19.3284	0.909134
$453$	15.8694	0.745609
$454$	1.98217	0.0930278
$455$	−0.709126	−0.0332443
$456$	1.62956	0.0763109
$457$	37.2612	1.74301	0.871504	−	0.490389i	$-0.163145\pi$
$457$	37.2612	1.74301	0.871504	+	0.490389i	$0.163145\pi$
$458$	8.45219	0.394945
$459$	−38.4856	−1.79635
$460$	−5.99564	−0.279548
$461$	−7.36442	−0.342995	−0.171498	−	0.985185i	$-0.554861\pi$
$461$	−7.36442	−0.342995	−0.171498	+	0.985185i	$0.554861\pi$
$462$	8.13792	0.378610
$463$	−7.88459	−0.366428	−0.183214	−	0.983073i	$-0.558650\pi$
$463$	−7.88459	−0.366428	−0.183214	+	0.983073i	$0.558650\pi$
$464$	−4.95453	−0.230008
$465$	−12.0659	−0.559543
$466$	−1.46640	−0.0679298
$467$	23.7987	1.10127	0.550637	−	0.834745i	$-0.314385\pi$
$467$	23.7987	1.10127	0.550637	+	0.834745i	$0.314385\pi$
$468$	0.112743	0.00521157
$469$	14.4355	0.666568
$470$	10.4311	0.481151
$471$	−27.4443	−1.26457
$472$	−7.68218	−0.353601
$473$	−18.7999	−0.864419
$474$	−16.8095	−0.772086
$475$	−2.68916	−0.123387
$476$	−10.0667	−0.461407
$477$	2.56762	0.117563
$478$	4.35381	0.199139
$479$	4.30397	0.196654	0.0983268	−	0.995154i	$-0.468651\pi$
$479$	4.30397	0.196654	0.0983268	+	0.995154i	$0.468651\pi$
$480$	−2.47716	−0.113066
$481$	2.04255	0.0931322
$482$	−4.00178	−0.182276
$483$	−9.16254	−0.416910
$484$	1.27145	0.0577934
$485$	9.60033	0.435929
$486$	3.56221	0.161585
$487$	5.13273	0.232586	0.116293	−	0.993215i	$-0.462899\pi$
$487$	5.13273	0.232586	0.116293	+	0.993215i	$0.462899\pi$
$488$	11.7673	0.532681
$489$	32.9127	1.48836
$490$	7.55159	0.341146
$491$	−2.42727	−0.109541	−0.0547707	−	0.998499i	$-0.517443\pi$
$491$	−2.42727	−0.109541	−0.0547707	+	0.998499i	$0.517443\pi$
$492$	7.59118	0.342237
$493$	−34.9860	−1.57569
$494$	−0.327222	−0.0147224
$495$	−1.83477	−0.0824669
$496$	4.87086	0.218708
$497$	−2.26433	−0.101569
$498$	−20.9674	−0.939570
$499$	24.6543	1.10368	0.551840	−	0.833950i	$-0.313926\pi$
$499$	24.6543	1.10368	0.551840	+	0.833950i	$0.313926\pi$
$500$	11.6886	0.522732
$501$	12.5817	0.562108
$502$	−8.66934	−0.386932
$503$	−11.6497	−0.519436	−0.259718	−	0.965685i	$-0.583630\pi$
$503$	−11.6497	−0.519436	−0.259718	+	0.965685i	$0.583630\pi$
$504$	0.491185	0.0218791
$505$	16.9136	0.752647
$506$	−13.8165	−0.614219
$507$	−21.0097	−0.933075
$508$	2.74186	0.121650
$509$	27.1375	1.20285	0.601424	−	0.798930i	$-0.294600\pi$
$509$	27.1375	1.20285	0.601424	+	0.798930i	$0.294600\pi$
$510$	−17.4923	−0.774570
$511$	9.09887	0.402510
$512$	1.00000	0.0441942
$513$	−5.45013	−0.240629
$514$	22.4206	0.988932
$515$	13.2471	0.583735
$516$	8.74533	0.384991
$517$	24.0377	1.05718
$518$	8.89869	0.390986
$519$	−22.4658	−0.986140
$520$	0.497425	0.0218135
$521$	21.6033	0.946459	0.473230	−	0.880939i	$-0.343088\pi$
$521$	21.6033	0.946459	0.473230	+	0.880939i	$0.343088\pi$
$522$	1.70707	0.0747165
$523$	−40.6023	−1.77541	−0.887707	−	0.460408i	$-0.847703\pi$
$523$	−40.6023	−1.77541	−0.887707	+	0.460408i	$0.847703\pi$
$524$	15.6535	0.683824
$525$	6.24715	0.272648
$526$	−29.7553	−1.29739
$527$	34.3952	1.49828
$528$	−5.70844	−0.248428
$529$	−7.44387	−0.323646
$530$	11.3284	0.492073
$531$	2.64688	0.114865
$532$	−1.42559	−0.0618074
$533$	−1.52434	−0.0660266
$534$	−19.0824	−0.825777
$535$	18.0315	0.779570
$536$	−10.1259	−0.437373
$537$	−11.6233	−0.501584
$538$	−24.6623	−1.06327
$539$	17.4021	0.749562
$540$	8.28498	0.356529
$541$	33.8106	1.45363	0.726815	−	0.686834i	$-0.241000\pi$
$541$	33.8106	1.45363	0.726815	+	0.686834i	$0.241000\pi$
$542$	13.7975	0.592655
$543$	28.6283	1.22856
$544$	7.06141	0.302756
$545$	−2.46559	−0.105614
$546$	0.760165	0.0325320
$547$	−20.4431	−0.874084	−0.437042	−	0.899441i	$-0.643974\pi$
$547$	−20.4431	−0.874084	−0.437042	+	0.899441i	$0.643974\pi$
$548$	2.78339	0.118901
$549$	−4.05440	−0.173038
$550$	9.42030	0.401683
$551$	−4.95453	−0.211070
$552$	6.42717	0.273559
$553$	14.7056	0.625344
$554$	−20.9965	−0.892055
$555$	15.4627	0.656354
$556$	−14.5906	−0.618781
$557$	38.0819	1.61358	0.806790	−	0.590838i	$-0.201203\pi$
$557$	38.0819	1.61358	0.806790	+	0.590838i	$0.201203\pi$
$558$	−1.67824	−0.0710457
$559$	−1.75610	−0.0742751
$560$	2.16711	0.0915771
$561$	−40.3096	−1.70187
$562$	25.0488	1.05662
$563$	−32.3814	−1.36471	−0.682357	−	0.731019i	$-0.739045\pi$
$563$	−32.3814	−1.36471	−0.682357	+	0.731019i	$0.739045\pi$
$564$	−11.1819	−0.470842
$565$	−29.3820	−1.23611
$566$	13.7855	0.579446
$567$	11.1876	0.469833
$568$	1.58834	0.0666454
$569$	39.7819	1.66774	0.833872	−	0.551958i	$-0.186119\pi$
$569$	39.7819	1.66774	0.833872	+	0.551958i	$0.186119\pi$
$570$	−2.47716	−0.103757
$571$	−41.7870	−1.74873	−0.874365	−	0.485268i	$-0.838722\pi$
$571$	−41.7870	−1.74873	−0.874365	+	0.485268i	$0.838722\pi$
$572$	1.14628	0.0479283
$573$	−20.8338	−0.870346
$574$	−6.64104	−0.277192
$575$	−10.6064	−0.442317
$576$	−0.344547	−0.0143561
$577$	−21.9651	−0.914419	−0.457209	−	0.889359i	$-0.651151\pi$
$577$	−21.9651	−0.914419	−0.457209	+	0.889359i	$0.651151\pi$
$578$	32.8635	1.36694
$579$	−26.8256	−1.11484
$580$	7.53161	0.312733
$581$	18.3430	0.760996
$582$	−10.2913	−0.426588
$583$	26.1054	1.08117
$584$	−6.38251	−0.264110
$585$	−0.171386	−0.00708596
$586$	−20.5099	−0.847254
$587$	−43.1832	−1.78236	−0.891180	−	0.453649i	$-0.850122\pi$
$587$	−43.1832	−1.78236	−0.891180	+	0.453649i	$0.850122\pi$
$588$	−8.09511	−0.333837
$589$	4.87086	0.200700
$590$	11.6780	0.480777
$591$	12.6941	0.522164
$592$	−6.24209	−0.256548
$593$	10.0308	0.411917	0.205958	−	0.978561i	$-0.433969\pi$
$593$	10.0308	0.411917	0.205958	+	0.978561i	$0.433969\pi$
$594$	19.0921	0.783360
$595$	15.3029	0.627356
$596$	1.62226	0.0664502
$597$	−13.9090	−0.569258
$598$	−1.29060	−0.0527767
$599$	15.6254	0.638438	0.319219	−	0.947681i	$-0.396579\pi$
$599$	15.6254	0.638438	0.319219	+	0.947681i	$0.396579\pi$
$600$	−4.38214	−0.178900
$601$	−36.2302	−1.47786	−0.738930	−	0.673782i	$-0.764669\pi$
$601$	−36.2302	−1.47786	−0.738930	+	0.673782i	$0.764669\pi$
$602$	−7.65073	−0.311820
$603$	3.48886	0.142077
$604$	9.73848	0.396253
$605$	−1.93279	−0.0785793
$606$	−18.1310	−0.736521
$607$	10.5977	0.430148	0.215074	−	0.976598i	$-0.431001\pi$
$607$	10.5977	0.430148	0.215074	+	0.976598i	$0.431001\pi$
$608$	1.00000	0.0405554
$609$	11.5098	0.466401
$610$	−17.8880	−0.724265
$611$	2.24537	0.0908379
$612$	−2.43299	−0.0983479
$613$	13.3244	0.538169	0.269084	−	0.963117i	$-0.413279\pi$
$613$	13.3244	0.538169	0.269084	+	0.963117i	$0.413279\pi$
$614$	−26.1353	−1.05474
$615$	−11.5397	−0.465325
$616$	4.99395	0.201212
$617$	39.2924	1.58185	0.790926	−	0.611912i	$-0.209599\pi$
$617$	39.2924	1.58185	0.790926	+	0.611912i	$0.209599\pi$
$618$	−14.2005	−0.571228
$619$	−18.3982	−0.739484	−0.369742	−	0.929134i	$-0.620554\pi$
$619$	−18.3982	−0.739484	−0.369742	+	0.929134i	$0.620554\pi$
$620$	−7.40441	−0.297368
$621$	−21.4960	−0.862604
$622$	10.0044	0.401139
$623$	16.6940	0.668830
$624$	−0.533226	−0.0213461
$625$	−4.32263	−0.172905
$626$	−24.2682	−0.969952
$627$	−5.70844	−0.227973
$628$	−16.8416	−0.672052
$629$	−44.0780	−1.75750
$630$	−0.746672	−0.0297481
$631$	−43.0155	−1.71242	−0.856210	−	0.516628i	$-0.827187\pi$
$631$	−43.0155	−1.71242	−0.856210	+	0.516628i	$0.827187\pi$
$632$	−10.3154	−0.410324
$633$	−1.62956	−0.0647690
$634$	11.2965	0.448643
$635$	−4.16802	−0.165403
$636$	−12.1437	−0.481529
$637$	1.62553	0.0644060
$638$	17.3560	0.687133
$639$	−0.547260	−0.0216493
$640$	−1.52015	−0.0600890
$641$	−24.1307	−0.953104	−0.476552	−	0.879146i	$-0.658114\pi$
$641$	−24.1307	−0.953104	−0.476552	+	0.879146i	$0.658114\pi$
$642$	−19.3293	−0.762867
$643$	27.6429	1.09013	0.545064	−	0.838394i	$-0.316505\pi$
$643$	27.6429	1.09013	0.545064	+	0.838394i	$0.316505\pi$
$644$	−5.62272	−0.221566
$645$	−13.2942	−0.523457
$646$	7.06141	0.277828
$647$	37.9100	1.49040	0.745198	−	0.666843i	$-0.232355\pi$
$647$	37.9100	1.49040	0.745198	+	0.666843i	$0.232355\pi$
$648$	−7.84764	−0.308285
$649$	26.9112	1.05636
$650$	0.879952	0.0345145
$651$	−11.3154	−0.443487
$652$	20.1974	0.790989
$653$	−33.1030	−1.29542	−0.647710	−	0.761887i	$-0.724273\pi$
$653$	−33.1030	−1.29542	−0.647710	+	0.761887i	$0.724273\pi$
$654$	2.64305	0.103351
$655$	−23.7955	−0.929768
$656$	4.65843	0.181881
$657$	2.19908	0.0857942
$658$	9.78231	0.381354
$659$	−2.62207	−0.102141	−0.0510706	−	0.998695i	$-0.516263\pi$
$659$	−2.62207	−0.102141	−0.0510706	+	0.998695i	$0.516263\pi$
$660$	8.67765	0.337777
$661$	33.0845	1.28684	0.643419	−	0.765515i	$-0.277515\pi$
$661$	33.0845	1.28684	0.643419	+	0.765515i	$0.277515\pi$
$662$	20.6671	0.803249
$663$	−3.76533	−0.146233
$664$	−12.8669	−0.499333
$665$	2.16711	0.0840369
$666$	2.15070	0.0833378
$667$	−19.5413	−0.756643
$668$	7.72092	0.298732
$669$	15.5801	0.602362
$670$	15.3929	0.594679
$671$	−41.2217	−1.59134
$672$	−2.32309	−0.0896150
$673$	−20.8359	−0.803164	−0.401582	−	0.915823i	$-0.631540\pi$
$673$	−20.8359	−0.803164	−0.401582	+	0.915823i	$0.631540\pi$
$674$	−5.66886	−0.218357
$675$	14.6563	0.564120
$676$	−12.8929	−0.495882
$677$	−39.6430	−1.52360	−0.761801	−	0.647811i	$-0.775685\pi$
$677$	−39.6430	−1.52360	−0.761801	+	0.647811i	$0.775685\pi$
$678$	31.4968	1.20963
$679$	9.00321	0.345511
$680$	−10.7344	−0.411644
$681$	3.23006	0.123776
$682$	−17.0629	−0.653373
$683$	15.4185	0.589971	0.294986	−	0.955502i	$-0.404685\pi$
$683$	15.4185	0.589971	0.294986	+	0.955502i	$0.404685\pi$
$684$	−0.344547	−0.0131741
$685$	−4.23116	−0.161664
$686$	17.0611	0.651394
$687$	13.7733	0.525485
$688$	5.36669	0.204603
$689$	2.43851	0.0928998
$690$	−9.77024	−0.371947
$691$	−1.95233	−0.0742702	−0.0371351	−	0.999310i	$-0.511823\pi$
$691$	−1.95233	−0.0742702	−0.0371351	+	0.999310i	$0.511823\pi$
$692$	−13.7865	−0.524083
$693$	−1.72065	−0.0653622
$694$	4.62204	0.175450
$695$	22.1799	0.841331
$696$	−8.07369	−0.306032
$697$	32.8951	1.24599
$698$	−16.3215	−0.617776
$699$	−2.38959	−0.0903824
$700$	3.83365	0.144898
$701$	−4.45534	−0.168276	−0.0841379	−	0.996454i	$-0.526814\pi$
$701$	−4.45534	−0.168276	−0.0841379	+	0.996454i	$0.526814\pi$
$702$	1.78340	0.0673101
$703$	−6.24209	−0.235425
$704$	−3.50306	−0.132027
$705$	16.9981	0.640185
$706$	−5.51396	−0.207521
$707$	15.8616	0.596538
$708$	−12.5186	−0.470476
$709$	−8.51635	−0.319838	−0.159919	−	0.987130i	$-0.551123\pi$
$709$	−8.51635	−0.319838	−0.159919	+	0.987130i	$0.551123\pi$
$710$	−2.41451	−0.0906150
$711$	3.55414	0.133291
$712$	−11.7102	−0.438858
$713$	19.2113	0.719468
$714$	−16.4043	−0.613914
$715$	−1.74251	−0.0651662
$716$	−7.13282	−0.266566
$717$	7.09478	0.264960
$718$	−26.6426	−0.994294
$719$	−29.9892	−1.11841	−0.559204	−	0.829030i	$-0.688893\pi$
$719$	−29.9892	−1.11841	−0.559204	+	0.829030i	$0.688893\pi$
$720$	0.523762	0.0195195
$721$	12.4231	0.462661
$722$	1.00000	0.0372161
$723$	−6.52112	−0.242523
$724$	17.5682	0.652915
$725$	13.3235	0.494824
$726$	2.07191	0.0768956
$727$	23.0706	0.855642	0.427821	−	0.903864i	$-0.359281\pi$
$727$	23.0706	0.855642	0.427821	+	0.903864i	$0.359281\pi$
$728$	0.466486	0.0172891
$729$	29.3477	1.08695
$730$	9.70234	0.359100
$731$	37.8964	1.40165
$732$	19.1755	0.708747
$733$	6.92788	0.255887	0.127944	−	0.991781i	$-0.459162\pi$
$733$	6.92788	0.255887	0.127944	+	0.991781i	$0.459162\pi$
$734$	23.5630	0.869726
$735$	12.3057	0.453904
$736$	3.94413	0.145382
$737$	35.4718	1.30662
$738$	−1.60505	−0.0590828
$739$	−24.9384	−0.917375	−0.458687	−	0.888598i	$-0.651680\pi$
$739$	−24.9384	−0.917375	−0.458687	+	0.888598i	$0.651680\pi$
$740$	9.48889	0.348818
$741$	−0.533226	−0.0195886
$742$	10.6238	0.390010
$743$	−1.72305	−0.0632124	−0.0316062	−	0.999500i	$-0.510062\pi$
$743$	−1.72305	−0.0632124	−0.0316062	+	0.999500i	$0.510062\pi$
$744$	7.93734	0.290997
$745$	−2.46606	−0.0903496
$746$	11.3236	0.414587
$747$	4.43326	0.162205
$748$	−24.7366	−0.904459
$749$	16.9100	0.617877
$750$	19.0473	0.695509
$751$	10.0321	0.366078	0.183039	−	0.983106i	$-0.441407\pi$
$751$	10.0321	0.366078	0.183039	+	0.983106i	$0.441407\pi$
$752$	−6.86192	−0.250228
$753$	−14.1272	−0.514823
$754$	1.62123	0.0590418
$755$	−14.8039	−0.538769
$756$	7.76967	0.282580
$757$	−32.8486	−1.19390	−0.596952	−	0.802277i	$-0.703622\pi$
$757$	−32.8486	−1.19390	−0.596952	+	0.802277i	$0.703622\pi$
$758$	21.6431	0.786112
$759$	−22.5148	−0.817236
$760$	−1.52015	−0.0551415
$761$	−11.7106	−0.424510	−0.212255	−	0.977214i	$-0.568081\pi$
$761$	−11.7106	−0.424510	−0.212255	+	0.977214i	$0.568081\pi$
$762$	4.46801	0.161859
$763$	−2.31223	−0.0837084
$764$	−12.7850	−0.462544
$765$	3.69850	0.133720
$766$	22.6512	0.818422
$767$	2.51378	0.0907673
$768$	1.62956	0.0588015
$769$	−49.6102	−1.78899	−0.894495	−	0.447078i	$-0.852465\pi$
$769$	−49.6102	−1.78899	−0.894495	+	0.447078i	$0.852465\pi$
$770$	−7.59152	−0.273580
$771$	36.5357	1.31580
$772$	−16.4619	−0.592478
$773$	1.44430	0.0519479	0.0259740	−	0.999663i	$-0.491731\pi$
$773$	1.44430	0.0519479	0.0259740	+	0.999663i	$0.491731\pi$
$774$	−1.84908	−0.0664638
$775$	−13.0985	−0.470513
$776$	−6.31541	−0.226710
$777$	14.5009	0.520218
$778$	−1.55684	−0.0558153
$779$	4.65843	0.166906
$780$	0.810581	0.0290235
$781$	−5.56407	−0.199098
$782$	27.8511	0.995953
$783$	27.0028	0.965003
$784$	−4.96768	−0.177417
$785$	25.6016	0.913761
$786$	25.5082	0.909847
$787$	−25.4553	−0.907385	−0.453693	−	0.891158i	$-0.649894\pi$
$787$	−25.4553	−0.907385	−0.453693	+	0.891158i	$0.649894\pi$
$788$	7.78989	0.277503
$789$	−48.4879	−1.72621
$790$	15.6809	0.557901
$791$	−27.5545	−0.979726
$792$	1.20697	0.0428879
$793$	−3.85052	−0.136736
$794$	4.03370	0.143151
$795$	18.4602	0.654716
$796$	−8.53546	−0.302531
$797$	31.6030	1.11944	0.559718	−	0.828683i	$-0.310909\pi$
$797$	31.6030	1.11944	0.559718	+	0.828683i	$0.310909\pi$
$798$	−2.32309	−0.0822363
$799$	−48.4548	−1.71421
$800$	−2.68916	−0.0950761
$801$	4.03472	0.142560
$802$	−23.0812	−0.815024
$803$	22.3583	0.789009
$804$	−16.5008	−0.581937
$805$	8.54736	0.301255
$806$	−1.59385	−0.0561410
$807$	−40.1886	−1.41470
$808$	−11.1263	−0.391423
$809$	14.3356	0.504011	0.252006	−	0.967726i	$-0.418910\pi$
$809$	14.3356	0.504011	0.252006	+	0.967726i	$0.418910\pi$
$810$	11.9296	0.419162
$811$	−23.0487	−0.809349	−0.404675	−	0.914461i	$-0.632615\pi$
$811$	−23.0487	−0.809349	−0.404675	+	0.914461i	$0.632615\pi$
$812$	7.06316	0.247868
$813$	22.4839	0.788543
$814$	21.8664	0.766419
$815$	−30.7029	−1.07548
$816$	11.5070	0.402824
$817$	5.36669	0.187757
$818$	−8.14260	−0.284699
$819$	−0.160726	−0.00561624
$820$	−7.08150	−0.247297
$821$	55.3217	1.93074	0.965370	−	0.260884i	$-0.0840139\pi$
$821$	55.3217	1.93074	0.965370	+	0.260884i	$0.0840139\pi$
$822$	4.53569	0.158200
$823$	−6.36151	−0.221748	−0.110874	−	0.993834i	$-0.535365\pi$
$823$	−6.36151	−0.221748	−0.110874	+	0.993834i	$0.535365\pi$
$824$	−8.71434	−0.303578
$825$	15.3509	0.534450
$826$	10.9517	0.381058
$827$	−52.9033	−1.83963	−0.919815	−	0.392353i	$-0.871661\pi$
$827$	−52.9033	−1.83963	−0.919815	+	0.392353i	$0.871661\pi$
$828$	−1.35894	−0.0472264
$829$	14.3982	0.500070	0.250035	−	0.968237i	$-0.419558\pi$
$829$	14.3982	0.500070	0.250035	+	0.968237i	$0.419558\pi$
$830$	19.5596	0.678923
$831$	−34.2149	−1.18690
$832$	−0.327222	−0.0113444
$833$	−35.0788	−1.21541
$834$	−23.7763	−0.823305
$835$	−11.7369	−0.406173
$836$	−3.50306	−0.121156
$837$	−26.5468	−0.917592
$838$	11.6787	0.403434
$839$	55.2730	1.90824	0.954118	−	0.299430i	$-0.0967966\pi$
$839$	55.2730	1.90824	0.954118	+	0.299430i	$0.0967966\pi$
$840$	3.53143	0.121846
$841$	−4.45259	−0.153538
$842$	27.7661	0.956884
$843$	40.8184	1.40586
$844$	−1.00000	−0.0344214
$845$	19.5991	0.674230
$846$	2.36426	0.0812848
$847$	−1.81258	−0.0622809
$848$	−7.45216	−0.255908
$849$	22.4642	0.770968
$850$	−18.9893	−0.651326
$851$	−24.6196	−0.843949
$852$	2.58829	0.0886735
$853$	−55.1321	−1.88769	−0.943844	−	0.330393i	$-0.892819\pi$
$853$	−55.1321	−1.88769	−0.943844	+	0.330393i	$0.892819\pi$
$854$	−16.7754	−0.574043
$855$	0.523762	0.0179123
$856$	−11.8617	−0.405425
$857$	55.0328	1.87989	0.939943	−	0.341331i	$-0.110878\pi$
$857$	55.0328	1.87989	0.939943	+	0.341331i	$0.110878\pi$
$858$	1.86793	0.0637699
$859$	−44.3228	−1.51227	−0.756137	−	0.654413i	$-0.772916\pi$
$859$	−44.3228	−1.51227	−0.756137	+	0.654413i	$0.772916\pi$
$860$	−8.15815	−0.278191
$861$	−10.8219	−0.368811
$862$	30.7191	1.04630
$863$	54.8023	1.86549	0.932746	−	0.360535i	$-0.117406\pi$
$863$	54.8023	1.86549	0.932746	+	0.360535i	$0.117406\pi$
$864$	−5.45013	−0.185417
$865$	20.9574	0.712574
$866$	−4.72388	−0.160524
$867$	53.5530	1.81875
$868$	−6.94387	−0.235690
$869$	36.1355	1.22581
$870$	12.2732	0.416100
$871$	3.31342	0.112271
$872$	1.62194	0.0549259
$873$	2.17596	0.0736450
$874$	3.94413	0.133412
$875$	−16.6633	−0.563321
$876$	−10.4007	−0.351406
$877$	27.9072	0.942360	0.471180	−	0.882037i	$-0.343828\pi$
$877$	27.9072	0.942360	0.471180	+	0.882037i	$0.343828\pi$
$878$	30.9909	1.04589
$879$	−33.4220	−1.12729
$880$	5.32516	0.179511
$881$	−22.4449	−0.756189	−0.378094	−	0.925767i	$-0.623421\pi$
$881$	−22.4449	−0.756189	−0.378094	+	0.925767i	$0.623421\pi$
$882$	1.71160	0.0576326
$883$	35.9979	1.21143	0.605713	−	0.795683i	$-0.292888\pi$
$883$	35.9979	1.21143	0.605713	+	0.795683i	$0.292888\pi$
$884$	−2.31065	−0.0777155
$885$	19.0300	0.639687
$886$	−4.30227	−0.144537
$887$	−22.5197	−0.756139	−0.378069	−	0.925777i	$-0.623412\pi$
$887$	−22.5197	−0.756139	−0.378069	+	0.925777i	$0.623412\pi$
$888$	−10.1718	−0.341345
$889$	−3.90878	−0.131096
$890$	17.8012	0.596697
$891$	27.4908	0.920976
$892$	9.56096	0.320125
$893$	−6.86192	−0.229625
$894$	2.64356	0.0884137
$895$	10.8429	0.362439
$896$	−1.42559	−0.0476258
$897$	−2.10311	−0.0702209
$898$	16.3203	0.544615
$899$	−24.1328	−0.804875
$900$	0.926543	0.0308848
$901$	−52.6228	−1.75312
$902$	−16.3188	−0.543356
$903$	−12.4673	−0.414885
$904$	19.3284	0.642855
$905$	−26.7061	−0.887742
$906$	15.8694	0.527225
$907$	12.8461	0.426549	0.213274	−	0.976992i	$-0.431587\pi$
$907$	12.8461	0.426549	0.213274	+	0.976992i	$0.431587\pi$
$908$	1.98217	0.0657806
$909$	3.83355	0.127151
$910$	−0.709126	−0.0235073
$911$	−48.2479	−1.59852	−0.799262	−	0.600983i	$-0.794776\pi$
$911$	−48.2479	−1.59852	−0.799262	+	0.600983i	$0.794776\pi$
$912$	1.62956	0.0539600
$913$	45.0736	1.49172
$914$	37.2612	1.23249
$915$	−29.1495	−0.963654
$916$	8.45219	0.279268
$917$	−22.3155	−0.736922
$918$	−38.4856	−1.27021
$919$	−0.145706	−0.00480641	−0.00240320	−	0.999997i	$-0.500765\pi$
$919$	−0.145706	−0.00480641	−0.00240320	+	0.999997i	$0.500765\pi$
$920$	−5.99564	−0.197671
$921$	−42.5890	−1.40336
$922$	−7.36442	−0.242534
$923$	−0.519741	−0.0171075
$924$	8.13792	0.267718
$925$	16.7860	0.551920
$926$	−7.88459	−0.259104
$927$	3.00250	0.0986151
$928$	−4.95453	−0.162641
$929$	18.5437	0.608399	0.304199	−	0.952608i	$-0.401611\pi$
$929$	18.5437	0.608399	0.304199	+	0.952608i	$0.401611\pi$
$930$	−12.0659	−0.395657
$931$	−4.96768	−0.162809
$932$	−1.46640	−0.0480336
$933$	16.3027	0.533726
$934$	23.7987	0.778718
$935$	37.6032	1.22976
$936$	0.112743	0.00368514
$937$	−35.8021	−1.16961	−0.584803	−	0.811176i	$-0.698828\pi$
$937$	−35.8021	−1.16961	−0.584803	+	0.811176i	$0.698828\pi$
$938$	14.4355	0.471335
$939$	−39.5464	−1.29055
$940$	10.4311	0.340225
$941$	22.9263	0.747375	0.373688	−	0.927555i	$-0.378093\pi$
$941$	22.9263	0.747375	0.373688	+	0.927555i	$0.378093\pi$
$942$	−27.4443	−0.894183
$943$	18.3735	0.598322
$944$	−7.68218	−0.250034
$945$	−11.8110	−0.384213
$946$	−18.7999	−0.611236
$947$	−24.7545	−0.804413	−0.402206	−	0.915549i	$-0.631757\pi$
$947$	−24.7545	−0.804413	−0.402206	+	0.915549i	$0.631757\pi$
$948$	−16.8095	−0.545947
$949$	2.08850	0.0677955
$950$	−2.68916	−0.0872478
$951$	18.4083	0.596931
$952$	−10.0667	−0.326264
$953$	−39.8651	−1.29136	−0.645678	−	0.763609i	$-0.723425\pi$
$953$	−39.8651	−1.29136	−0.645678	+	0.763609i	$0.723425\pi$
$954$	2.56762	0.0831298
$955$	19.4350	0.628902
$956$	4.35381	0.140812
$957$	28.2827	0.914248
$958$	4.30397	0.139055
$959$	−3.96799	−0.128133
$960$	−2.47716	−0.0799500
$961$	−7.27472	−0.234668
$962$	2.04255	0.0658544
$963$	4.08692	0.131699
$964$	−4.00178	−0.128889
$965$	25.0245	0.805568
$966$	−9.16254	−0.294800
$967$	10.8275	0.348188	0.174094	−	0.984729i	$-0.444300\pi$
$967$	10.8275	0.348188	0.174094	+	0.984729i	$0.444300\pi$
$968$	1.27145	0.0408661
$969$	11.5070	0.369657
$970$	9.60033	0.308248
$971$	−44.5554	−1.42985	−0.714925	−	0.699201i	$-0.753539\pi$
$971$	−44.5554	−1.42985	−0.714925	+	0.699201i	$0.753539\pi$
$972$	3.56221	0.114258
$973$	20.8003	0.666828
$974$	5.13273	0.164463
$975$	1.43393	0.0459225
$976$	11.7673	0.376663
$977$	37.7422	1.20748	0.603741	−	0.797181i	$-0.293676\pi$
$977$	37.7422	1.20748	0.603741	+	0.797181i	$0.293676\pi$
$978$	32.9127	1.05243
$979$	41.0215	1.31105
$980$	7.55159	0.241227
$981$	−0.558836	−0.0178423
$982$	−2.42727	−0.0774575
$983$	8.10040	0.258363	0.129181	−	0.991621i	$-0.458765\pi$
$983$	8.10040	0.258363	0.129181	+	0.991621i	$0.458765\pi$
$984$	7.59118	0.241998
$985$	−11.8418	−0.377310
$986$	−34.9860	−1.11418
$987$	15.9408	0.507402
$988$	−0.327222	−0.0104103
$989$	21.1669	0.673069
$990$	−1.83477	−0.0583129
$991$	−2.48829	−0.0790431	−0.0395215	−	0.999219i	$-0.512583\pi$
$991$	−2.48829	−0.0790431	−0.0395215	+	0.999219i	$0.512583\pi$
$992$	4.87086	0.154650
$993$	33.6782	1.06874
$994$	−2.26433	−0.0718203
$995$	12.9751	0.411340
$996$	−20.9674	−0.664377
$997$	50.1594	1.58856	0.794282	−	0.607549i	$-0.207847\pi$
$997$	50.1594	1.58856	0.794282	+	0.607549i	$0.207847\pi$
$998$	24.6543	0.780419
$999$	34.0202	1.07635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.26	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.26	✓	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.62956 q^{3} +1.00000 q^{4} -1.52015 q^{5} +1.62956 q^{6} -1.42559 q^{7} +1.00000 q^{8} -0.344547 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.62956 q^{3} +1.00000 q^{4} -1.52015 q^{5} +1.62956 q^{6} -1.42559 q^{7} +1.00000 q^{8} -0.344547 q^{9} -1.52015 q^{10} -3.50306 q^{11} +1.62956 q^{12} -0.327222 q^{13} -1.42559 q^{14} -2.47716 q^{15} +1.00000 q^{16} +7.06141 q^{17} -0.344547 q^{18} +1.00000 q^{19} -1.52015 q^{20} -2.32309 q^{21} -3.50306 q^{22} +3.94413 q^{23} +1.62956 q^{24} -2.68916 q^{25} -0.327222 q^{26} -5.45013 q^{27} -1.42559 q^{28} -4.95453 q^{29} -2.47716 q^{30} +4.87086 q^{31} +1.00000 q^{32} -5.70844 q^{33} +7.06141 q^{34} +2.16711 q^{35} -0.344547 q^{36} -6.24209 q^{37} +1.00000 q^{38} -0.533226 q^{39} -1.52015 q^{40} +4.65843 q^{41} -2.32309 q^{42} +5.36669 q^{43} -3.50306 q^{44} +0.523762 q^{45} +3.94413 q^{46} -6.86192 q^{47} +1.62956 q^{48} -4.96768 q^{49} -2.68916 q^{50} +11.5070 q^{51} -0.327222 q^{52} -7.45216 q^{53} -5.45013 q^{54} +5.32516 q^{55} -1.42559 q^{56} +1.62956 q^{57} -4.95453 q^{58} -7.68218 q^{59} -2.47716 q^{60} +11.7673 q^{61} +4.87086 q^{62} +0.491185 q^{63} +1.00000 q^{64} +0.497425 q^{65} -5.70844 q^{66} -10.1259 q^{67} +7.06141 q^{68} +6.42717 q^{69} +2.16711 q^{70} +1.58834 q^{71} -0.344547 q^{72} -6.38251 q^{73} -6.24209 q^{74} -4.38214 q^{75} +1.00000 q^{76} +4.99395 q^{77} -0.533226 q^{78} -10.3154 q^{79} -1.52015 q^{80} -7.84764 q^{81} +4.65843 q^{82} -12.8669 q^{83} -2.32309 q^{84} -10.7344 q^{85} +5.36669 q^{86} -8.07369 q^{87} -3.50306 q^{88} -11.7102 q^{89} +0.523762 q^{90} +0.466486 q^{91} +3.94413 q^{92} +7.93734 q^{93} -6.86192 q^{94} -1.52015 q^{95} +1.62956 q^{96} -6.31541 q^{97} -4.96768 q^{98} +1.20697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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