LMFDB - Embedded newform 8018.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.71717 q^{3} +1.00000 q^{4} +1.96614 q^{5} +1.71717 q^{6} +0.664883 q^{7} -1.00000 q^{8} -0.0513372 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.71717 q^{3} +1.00000 q^{4} +1.96614 q^{5} +1.71717 q^{6} +0.664883 q^{7} -1.00000 q^{8} -0.0513372 q^{9} -1.96614 q^{10} +5.44663 q^{11} -1.71717 q^{12} -0.0515753 q^{13} -0.664883 q^{14} -3.37618 q^{15} +1.00000 q^{16} -7.45253 q^{17} +0.0513372 q^{18} -1.00000 q^{19} +1.96614 q^{20} -1.14172 q^{21} -5.44663 q^{22} -0.569198 q^{23} +1.71717 q^{24} -1.13431 q^{25} +0.0515753 q^{26} +5.23966 q^{27} +0.664883 q^{28} -2.76138 q^{29} +3.37618 q^{30} +4.18029 q^{31} -1.00000 q^{32} -9.35277 q^{33} +7.45253 q^{34} +1.30725 q^{35} -0.0513372 q^{36} +3.80764 q^{37} +1.00000 q^{38} +0.0885634 q^{39} -1.96614 q^{40} +3.76344 q^{41} +1.14172 q^{42} +5.34950 q^{43} +5.44663 q^{44} -0.100936 q^{45} +0.569198 q^{46} +2.90711 q^{47} -1.71717 q^{48} -6.55793 q^{49} +1.13431 q^{50} +12.7972 q^{51} -0.0515753 q^{52} -4.82207 q^{53} -5.23966 q^{54} +10.7088 q^{55} -0.664883 q^{56} +1.71717 q^{57} +2.76138 q^{58} -0.401214 q^{59} -3.37618 q^{60} -7.28561 q^{61} -4.18029 q^{62} -0.0341332 q^{63} +1.00000 q^{64} -0.101404 q^{65} +9.35277 q^{66} -11.1051 q^{67} -7.45253 q^{68} +0.977408 q^{69} -1.30725 q^{70} -15.3423 q^{71} +0.0513372 q^{72} -0.623277 q^{73} -3.80764 q^{74} +1.94780 q^{75} -1.00000 q^{76} +3.62137 q^{77} -0.0885634 q^{78} -3.96744 q^{79} +1.96614 q^{80} -8.84335 q^{81} -3.76344 q^{82} +7.33098 q^{83} -1.14172 q^{84} -14.6527 q^{85} -5.34950 q^{86} +4.74175 q^{87} -5.44663 q^{88} +11.5704 q^{89} +0.100936 q^{90} -0.0342916 q^{91} -0.569198 q^{92} -7.17826 q^{93} -2.90711 q^{94} -1.96614 q^{95} +1.71717 q^{96} -1.39596 q^{97} +6.55793 q^{98} -0.279614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−1.71717	−0.991407	−0.495703	−	0.868492i	$-0.665090\pi$
$3$	−1.71717	−0.991407	−0.495703	+	0.868492i	$0.665090\pi$
$4$	1.00000	0.500000
$5$	1.96614	0.879282	0.439641	−	0.898174i	$-0.355106\pi$
$5$	1.96614	0.879282	0.439641	+	0.898174i	$0.355106\pi$
$6$	1.71717	0.701031
$7$	0.664883	0.251302	0.125651	−	0.992074i	$-0.459898\pi$
$7$	0.664883	0.251302	0.125651	+	0.992074i	$0.459898\pi$
$8$	−1.00000	−0.353553
$9$	−0.0513372	−0.0171124
$10$	−1.96614	−0.621747
$11$	5.44663	1.64222	0.821110	−	0.570770i	$-0.193355\pi$
$11$	5.44663	1.64222	0.821110	+	0.570770i	$0.193355\pi$
$12$	−1.71717	−0.495703
$13$	−0.0515753	−0.0143044	−0.00715221	−	0.999974i	$-0.502277\pi$
$13$	−0.0515753	−0.0143044	−0.00715221	+	0.999974i	$0.502277\pi$
$14$	−0.664883	−0.177698
$15$	−3.37618	−0.871727
$16$	1.00000	0.250000
$17$	−7.45253	−1.80750	−0.903752	−	0.428057i	$-0.859198\pi$
$17$	−7.45253	−1.80750	−0.903752	+	0.428057i	$0.859198\pi$
$18$	0.0513372	0.0121003
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.96614	0.439641
$21$	−1.14172	−0.249143
$22$	−5.44663	−1.16122
$23$	−0.569198	−0.118686	−0.0593430	−	0.998238i	$-0.518901\pi$
$23$	−0.569198	−0.118686	−0.0593430	+	0.998238i	$0.518901\pi$
$24$	1.71717	0.350515
$25$	−1.13431	−0.226863
$26$	0.0515753	0.0101147
$27$	5.23966	1.00837
$28$	0.664883	0.125651
$29$	−2.76138	−0.512775	−0.256388	−	0.966574i	$-0.582532\pi$
$29$	−2.76138	−0.512775	−0.256388	+	0.966574i	$0.582532\pi$
$30$	3.37618	0.616404
$31$	4.18029	0.750803	0.375401	−	0.926862i	$-0.377505\pi$
$31$	4.18029	0.750803	0.375401	+	0.926862i	$0.377505\pi$
$32$	−1.00000	−0.176777
$33$	−9.35277	−1.62811
$34$	7.45253	1.27810
$35$	1.30725	0.220966
$36$	−0.0513372	−0.00855620
$37$	3.80764	0.625972	0.312986	−	0.949758i	$-0.398671\pi$
$37$	3.80764	0.625972	0.312986	+	0.949758i	$0.398671\pi$
$38$	1.00000	0.162221
$39$	0.0885634	0.0141815
$40$	−1.96614	−0.310873
$41$	3.76344	0.587751	0.293875	−	0.955844i	$-0.405055\pi$
$41$	3.76344	0.587751	0.293875	+	0.955844i	$0.405055\pi$
$42$	1.14172	0.176171
$43$	5.34950	0.815790	0.407895	−	0.913029i	$-0.366263\pi$
$43$	5.34950	0.815790	0.407895	+	0.913029i	$0.366263\pi$
$44$	5.44663	0.821110
$45$	−0.100936	−0.0150466
$46$	0.569198	0.0839236
$47$	2.90711	0.424045	0.212022	−	0.977265i	$-0.431995\pi$
$47$	2.90711	0.424045	0.212022	+	0.977265i	$0.431995\pi$
$48$	−1.71717	−0.247852
$49$	−6.55793	−0.936847
$50$	1.13431	0.160416
$51$	12.7972	1.79197
$52$	−0.0515753	−0.00715221
$53$	−4.82207	−0.662363	−0.331181	−	0.943567i	$-0.607447\pi$
$53$	−4.82207	−0.662363	−0.331181	+	0.943567i	$0.607447\pi$
$54$	−5.23966	−0.713027
$55$	10.7088	1.44397
$56$	−0.664883	−0.0888488
$57$	1.71717	0.227444
$58$	2.76138	0.362587
$59$	−0.401214	−0.0522336	−0.0261168	−	0.999659i	$-0.508314\pi$
$59$	−0.401214	−0.0522336	−0.0261168	+	0.999659i	$0.508314\pi$
$60$	−3.37618	−0.435863
$61$	−7.28561	−0.932827	−0.466413	−	0.884567i	$-0.654454\pi$
$61$	−7.28561	−0.932827	−0.466413	+	0.884567i	$0.654454\pi$
$62$	−4.18029	−0.530898
$63$	−0.0341332	−0.00430038
$64$	1.00000	0.125000
$65$	−0.101404	−0.0125776
$66$	9.35277	1.15125
$67$	−11.1051	−1.35671	−0.678354	−	0.734735i	$-0.737306\pi$
$67$	−11.1051	−1.35671	−0.678354	+	0.734735i	$0.737306\pi$
$68$	−7.45253	−0.903752
$69$	0.977408	0.117666
$70$	−1.30725	−0.156246
$71$	−15.3423	−1.82080	−0.910398	−	0.413735i	$-0.864224\pi$
$71$	−15.3423	−1.82080	−0.910398	+	0.413735i	$0.864224\pi$
$72$	0.0513372	0.00605015
$73$	−0.623277	−0.0729490	−0.0364745	−	0.999335i	$-0.511613\pi$
$73$	−0.623277	−0.0729490	−0.0364745	+	0.999335i	$0.511613\pi$
$74$	−3.80764	−0.442629
$75$	1.94780	0.224913
$76$	−1.00000	−0.114708
$77$	3.62137	0.412694
$78$	−0.0885634	−0.0100278
$79$	−3.96744	−0.446371	−0.223186	−	0.974776i	$-0.571646\pi$
$79$	−3.96744	−0.446371	−0.223186	+	0.974776i	$0.571646\pi$
$80$	1.96614	0.219821
$81$	−8.84335	−0.982595
$82$	−3.76344	−0.415602
$83$	7.33098	0.804679	0.402340	−	0.915490i	$-0.368197\pi$
$83$	7.33098	0.804679	0.402340	+	0.915490i	$0.368197\pi$
$84$	−1.14172	−0.124571
$85$	−14.6527	−1.58931
$86$	−5.34950	−0.576851
$87$	4.74175	0.508369
$88$	−5.44663	−0.580612
$89$	11.5704	1.22646	0.613230	−	0.789904i	$-0.289870\pi$
$89$	11.5704	1.22646	0.613230	+	0.789904i	$0.289870\pi$
$90$	0.100936	0.0106396
$91$	−0.0342916	−0.00359473
$92$	−0.569198	−0.0593430
$93$	−7.17826	−0.744351
$94$	−2.90711	−0.299845
$95$	−1.96614	−0.201721
$96$	1.71717	0.175258
$97$	−1.39596	−0.141738	−0.0708691	−	0.997486i	$-0.522577\pi$
$97$	−1.39596	−0.141738	−0.0708691	+	0.997486i	$0.522577\pi$
$98$	6.55793	0.662451
$99$	−0.279614	−0.0281023
$100$	−1.13431	−0.113431
$101$	0.815336	0.0811290	0.0405645	−	0.999177i	$-0.487084\pi$
$101$	0.815336	0.0811290	0.0405645	+	0.999177i	$0.487084\pi$
$102$	−12.7972	−1.26711
$103$	−17.7362	−1.74760	−0.873800	−	0.486286i	$-0.838351\pi$
$103$	−17.7362	−1.74760	−0.873800	+	0.486286i	$0.838351\pi$
$104$	0.0515753	0.00505737
$105$	−2.24477	−0.219067
$106$	4.82207	0.468361
$107$	−9.25934	−0.895135	−0.447567	−	0.894250i	$-0.647709\pi$
$107$	−9.25934	−0.895135	−0.447567	+	0.894250i	$0.647709\pi$
$108$	5.23966	0.504186
$109$	−14.4033	−1.37958	−0.689791	−	0.724008i	$-0.742298\pi$
$109$	−14.4033	−1.37958	−0.689791	+	0.724008i	$0.742298\pi$
$110$	−10.7088	−1.02104
$111$	−6.53835	−0.620593
$112$	0.664883	0.0628256
$113$	4.30841	0.405301	0.202651	−	0.979251i	$-0.435044\pi$
$113$	4.30841	0.405301	0.202651	+	0.979251i	$0.435044\pi$
$114$	−1.71717	−0.160827
$115$	−1.11912	−0.104358
$116$	−2.76138	−0.256388
$117$	0.00264773	0.000244783 0
$118$	0.401214	0.0369347
$119$	−4.95506	−0.454230
$120$	3.37618	0.308202
$121$	18.6657	1.69689
$122$	7.28561	0.659608
$123$	−6.46246	−0.582700
$124$	4.18029	0.375401
$125$	−12.0609	−1.07876
$126$	0.0341332	0.00304083
$127$	1.79062	0.158892	0.0794460	−	0.996839i	$-0.474685\pi$
$127$	1.79062	0.158892	0.0794460	+	0.996839i	$0.474685\pi$
$128$	−1.00000	−0.0883883
$129$	−9.18598	−0.808780
$130$	0.101404	0.00889372
$131$	6.42765	0.561587	0.280793	−	0.959768i	$-0.409402\pi$
$131$	6.42765	0.561587	0.280793	+	0.959768i	$0.409402\pi$
$132$	−9.35277	−0.814054
$133$	−0.664883	−0.0576527
$134$	11.1051	0.959337
$135$	10.3019	0.886644
$136$	7.45253	0.639049
$137$	4.90431	0.419003	0.209502	−	0.977808i	$-0.432816\pi$
$137$	4.90431	0.419003	0.209502	+	0.977808i	$0.432816\pi$
$138$	−0.977408	−0.0832025
$139$	16.7741	1.42276	0.711379	−	0.702809i	$-0.248071\pi$
$139$	16.7741	1.42276	0.711379	+	0.702809i	$0.248071\pi$
$140$	1.30725	0.110483
$141$	−4.99199	−0.420401
$142$	15.3423	1.28750
$143$	−0.280911	−0.0234910
$144$	−0.0513372	−0.00427810
$145$	−5.42925	−0.450874
$146$	0.623277	0.0515828
$147$	11.2611	0.928797
$148$	3.80764	0.312986
$149$	2.19033	0.179439	0.0897193	−	0.995967i	$-0.471403\pi$
$149$	2.19033	0.179439	0.0897193	+	0.995967i	$0.471403\pi$
$150$	−1.94780	−0.159038
$151$	4.02446	0.327506	0.163753	−	0.986501i	$-0.447640\pi$
$151$	4.02446	0.327506	0.163753	+	0.986501i	$0.447640\pi$
$152$	1.00000	0.0811107
$153$	0.382592	0.0309307
$154$	−3.62137	−0.291818
$155$	8.21902	0.660167
$156$	0.0885634	0.00709075
$157$	0.722109	0.0576306	0.0288153	−	0.999585i	$-0.490827\pi$
$157$	0.722109	0.0576306	0.0288153	+	0.999585i	$0.490827\pi$
$158$	3.96744	0.315632
$159$	8.28031	0.656671
$160$	−1.96614	−0.155437
$161$	−0.378450	−0.0298260
$162$	8.84335	0.694799
$163$	2.08633	0.163414	0.0817069	−	0.996656i	$-0.473963\pi$
$163$	2.08633	0.163414	0.0817069	+	0.996656i	$0.473963\pi$
$164$	3.76344	0.293875
$165$	−18.3888	−1.43157
$166$	−7.33098	−0.568994
$167$	−22.3102	−1.72642	−0.863209	−	0.504847i	$-0.831549\pi$
$167$	−22.3102	−1.72642	−0.863209	+	0.504847i	$0.831549\pi$
$168$	1.14172	0.0880853
$169$	−12.9973	−0.999795
$170$	14.6527	1.12381
$171$	0.0513372	0.00392585
$172$	5.34950	0.407895
$173$	−14.6786	−1.11599	−0.557996	−	0.829843i	$-0.688430\pi$
$173$	−14.6786	−1.11599	−0.557996	+	0.829843i	$0.688430\pi$
$174$	−4.74175	−0.359471
$175$	−0.754186	−0.0570111
$176$	5.44663	0.410555
$177$	0.688952	0.0517848
$178$	−11.5704	−0.867238
$179$	3.49821	0.261469	0.130734	−	0.991417i	$-0.458266\pi$
$179$	3.49821	0.261469	0.130734	+	0.991417i	$0.458266\pi$
$180$	−0.100936	−0.00752331
$181$	−15.2807	−1.13581	−0.567904	−	0.823095i	$-0.692245\pi$
$181$	−15.2807	−1.13581	−0.567904	+	0.823095i	$0.692245\pi$
$182$	0.0342916	0.00254186
$183$	12.5106	0.924811
$184$	0.569198	0.0419618
$185$	7.48633	0.550406
$186$	7.17826	0.526336
$187$	−40.5911	−2.96832
$188$	2.90711	0.212022
$189$	3.48376	0.253406
$190$	1.96614	0.142638
$191$	9.10809	0.659039	0.329519	−	0.944149i	$-0.393113\pi$
$191$	9.10809	0.659039	0.329519	+	0.944149i	$0.393113\pi$
$192$	−1.71717	−0.123926
$193$	24.3418	1.75216	0.876080	−	0.482167i	$-0.160150\pi$
$193$	24.3418	1.75216	0.876080	+	0.482167i	$0.160150\pi$
$194$	1.39596	0.100224
$195$	0.174128	0.0124695
$196$	−6.55793	−0.468424
$197$	3.04025	0.216609	0.108304	−	0.994118i	$-0.465458\pi$
$197$	3.04025	0.216609	0.108304	+	0.994118i	$0.465458\pi$
$198$	0.279614	0.0198713
$199$	−7.69027	−0.545149	−0.272575	−	0.962135i	$-0.587875\pi$
$199$	−7.69027	−0.545149	−0.272575	+	0.962135i	$0.587875\pi$
$200$	1.13431	0.0802080
$201$	19.0694	1.34505
$202$	−0.815336	−0.0573669
$203$	−1.83600	−0.128862
$204$	12.7972	0.895986
$205$	7.39943	0.516799
$206$	17.7362	1.23574
$207$	0.0292210	0.00203100
$208$	−0.0515753	−0.00357610
$209$	−5.44663	−0.376751
$210$	2.24477	0.154904
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−4.82207	−0.331181
$213$	26.3453	1.80515
$214$	9.25934	0.632956
$215$	10.5178	0.717310
$216$	−5.23966	−0.356513
$217$	2.77941	0.188678
$218$	14.4033	0.975512
$219$	1.07027	0.0723222
$220$	10.7088	0.721987
$221$	0.384366	0.0258553
$222$	6.53835	0.438825
$223$	7.97029	0.533730	0.266865	−	0.963734i	$-0.414012\pi$
$223$	7.97029	0.533730	0.266865	+	0.963734i	$0.414012\pi$
$224$	−0.664883	−0.0444244
$225$	0.0582324	0.00388216
$226$	−4.30841	−0.286591
$227$	−12.4698	−0.827651	−0.413825	−	0.910356i	$-0.635808\pi$
$227$	−12.4698	−0.827651	−0.413825	+	0.910356i	$0.635808\pi$
$228$	1.71717	0.113722
$229$	10.0271	0.662608	0.331304	−	0.943524i	$-0.392511\pi$
$229$	10.0271	0.662608	0.331304	+	0.943524i	$0.392511\pi$
$230$	1.11912	0.0737926
$231$	−6.21850	−0.409147
$232$	2.76138	0.181294
$233$	2.93800	0.192475	0.0962373	−	0.995358i	$-0.469319\pi$
$233$	2.93800	0.192475	0.0962373	+	0.995358i	$0.469319\pi$
$234$	−0.00264773	−0.000173088 0
$235$	5.71576	0.372855
$236$	−0.401214	−0.0261168
$237$	6.81275	0.442536
$238$	4.95506	0.321189
$239$	27.1772	1.75795	0.878973	−	0.476871i	$-0.158229\pi$
$239$	27.1772	1.75795	0.878973	+	0.476871i	$0.158229\pi$
$240$	−3.37618	−0.217932
$241$	11.4352	0.736608	0.368304	−	0.929705i	$-0.379939\pi$
$241$	11.4352	0.736608	0.368304	+	0.929705i	$0.379939\pi$
$242$	−18.6657	−1.19988
$243$	−0.533453	−0.0342210
$244$	−7.28561	−0.466413
$245$	−12.8938	−0.823753
$246$	6.46246	0.412031
$247$	0.0515753	0.00328166
$248$	−4.18029	−0.265449
$249$	−12.5885	−0.797765
$250$	12.0609	0.762798
$251$	7.49421	0.473030	0.236515	−	0.971628i	$-0.423995\pi$
$251$	7.49421	0.473030	0.236515	+	0.971628i	$0.423995\pi$
$252$	−0.0341332	−0.00215019
$253$	−3.10021	−0.194908
$254$	−1.79062	−0.112354
$255$	25.1611	1.57565
$256$	1.00000	0.0625000
$257$	−11.2392	−0.701085	−0.350542	−	0.936547i	$-0.614003\pi$
$257$	−11.2392	−0.701085	−0.350542	+	0.936547i	$0.614003\pi$
$258$	9.18598	0.571894
$259$	2.53164	0.157308
$260$	−0.101404	−0.00628881
$261$	0.141762	0.00877482
$262$	−6.42765	−0.397102
$263$	−28.5766	−1.76211	−0.881053	−	0.473018i	$-0.843165\pi$
$263$	−28.5766	−1.76211	−0.881053	+	0.473018i	$0.843165\pi$
$264$	9.35277	0.575623
$265$	−9.48085	−0.582404
$266$	0.664883	0.0407666
$267$	−19.8683	−1.21592
$268$	−11.1051	−0.678354
$269$	−25.3611	−1.54629	−0.773146	−	0.634228i	$-0.781318\pi$
$269$	−25.3611	−1.54629	−0.773146	+	0.634228i	$0.781318\pi$
$270$	−10.3019	−0.626952
$271$	22.9209	1.39235	0.696174	−	0.717873i	$-0.254884\pi$
$271$	22.9209	1.39235	0.696174	+	0.717873i	$0.254884\pi$
$272$	−7.45253	−0.451876
$273$	0.0588843	0.00356384
$274$	−4.90431	−0.296280
$275$	−6.17818	−0.372558
$276$	0.977408	0.0588330
$277$	−12.2951	−0.738742	−0.369371	−	0.929282i	$-0.620427\pi$
$277$	−12.2951	−0.738742	−0.369371	+	0.929282i	$0.620427\pi$
$278$	−16.7741	−1.00604
$279$	−0.214604	−0.0128480
$280$	−1.30725	−0.0781232
$281$	−3.01077	−0.179607	−0.0898036	−	0.995959i	$-0.528624\pi$
$281$	−3.01077	−0.179607	−0.0898036	+	0.995959i	$0.528624\pi$
$282$	4.99199	0.297268
$283$	−31.6362	−1.88057	−0.940287	−	0.340382i	$-0.889444\pi$
$283$	−31.6362	−1.88057	−0.940287	+	0.340382i	$0.889444\pi$
$284$	−15.3423	−0.910398
$285$	3.37618	0.199988
$286$	0.280911	0.0166106
$287$	2.50225	0.147703
$288$	0.0513372	0.00302507
$289$	38.5402	2.26707
$290$	5.42925	0.318816
$291$	2.39709	0.140520
$292$	−0.623277	−0.0364745
$293$	−2.89410	−0.169075	−0.0845377	−	0.996420i	$-0.526941\pi$
$293$	−2.89410	−0.169075	−0.0845377	+	0.996420i	$0.526941\pi$
$294$	−11.2611	−0.656758
$295$	−0.788841	−0.0459281
$296$	−3.80764	−0.221315
$297$	28.5384	1.65597
$298$	−2.19033	−0.126882
$299$	0.0293566	0.00169773
$300$	1.94780	0.112457
$301$	3.55679	0.205010
$302$	−4.02446	−0.231582
$303$	−1.40007	−0.0804318
$304$	−1.00000	−0.0573539
$305$	−14.3245	−0.820218
$306$	−0.382592	−0.0218713
$307$	−19.0575	−1.08767	−0.543833	−	0.839193i	$-0.683028\pi$
$307$	−19.0575	−1.08767	−0.543833	+	0.839193i	$0.683028\pi$
$308$	3.62137	0.206347
$309$	30.4560	1.73258
$310$	−8.21902	−0.466809
$311$	3.64366	0.206613	0.103306	−	0.994650i	$-0.467058\pi$
$311$	3.64366	0.206613	0.103306	+	0.994650i	$0.467058\pi$
$312$	−0.0885634	−0.00501392
$313$	22.3322	1.26229	0.631146	−	0.775664i	$-0.282585\pi$
$313$	22.3322	1.26229	0.631146	+	0.775664i	$0.282585\pi$
$314$	−0.722109	−0.0407510
$315$	−0.0671106	−0.00378125
$316$	−3.96744	−0.223186
$317$	8.40912	0.472303	0.236152	−	0.971716i	$-0.424114\pi$
$317$	8.40912	0.472303	0.236152	+	0.971716i	$0.424114\pi$
$318$	−8.28031	−0.464337
$319$	−15.0402	−0.842090
$320$	1.96614	0.109910
$321$	15.8998	0.887443
$322$	0.378450	0.0210902
$323$	7.45253	0.414670
$324$	−8.84335	−0.491297
$325$	0.0585025	0.00324514
$326$	−2.08633	−0.115551
$327$	24.7328	1.36773
$328$	−3.76344	−0.207801
$329$	1.93289	0.106563
$330$	18.3888	1.01227
$331$	24.3203	1.33676	0.668381	−	0.743819i	$-0.266988\pi$
$331$	24.3203	1.33676	0.668381	+	0.743819i	$0.266988\pi$
$332$	7.33098	0.402340
$333$	−0.195473	−0.0107119
$334$	22.3102	1.22076
$335$	−21.8342	−1.19293
$336$	−1.14172	−0.0622857
$337$	−11.1676	−0.608339	−0.304169	−	0.952618i	$-0.598379\pi$
$337$	−11.1676	−0.608339	−0.304169	+	0.952618i	$0.598379\pi$
$338$	12.9973	0.706962
$339$	−7.39826	−0.401818
$340$	−14.6527	−0.794653
$341$	22.7685	1.23298
$342$	−0.0513372	−0.00277600
$343$	−9.01444	−0.486734
$344$	−5.34950	−0.288425
$345$	1.92172	0.103462
$346$	14.6786	0.789126
$347$	−20.9306	−1.12361	−0.561806	−	0.827269i	$-0.689893\pi$
$347$	−20.9306	−1.12361	−0.561806	+	0.827269i	$0.689893\pi$
$348$	4.74175	0.254185
$349$	1.95004	0.104383	0.0521917	−	0.998637i	$-0.483379\pi$
$349$	1.95004	0.104383	0.0521917	+	0.998637i	$0.483379\pi$
$350$	0.754186	0.0403129
$351$	−0.270237	−0.0144242
$352$	−5.44663	−0.290306
$353$	19.6958	1.04830	0.524150	−	0.851626i	$-0.324383\pi$
$353$	19.6958	1.04830	0.524150	+	0.851626i	$0.324383\pi$
$354$	−0.688952	−0.0366174
$355$	−30.1650	−1.60099
$356$	11.5704	0.613230
$357$	8.50867	0.450326
$358$	−3.49821	−0.184886
$359$	−13.0411	−0.688282	−0.344141	−	0.938918i	$-0.611830\pi$
$359$	−13.0411	−0.688282	−0.344141	+	0.938918i	$0.611830\pi$
$360$	0.100936	0.00531979
$361$	1.00000	0.0526316
$362$	15.2807	0.803137
$363$	−32.0522	−1.68230
$364$	−0.0342916	−0.00179737
$365$	−1.22545	−0.0641428
$366$	−12.5106	−0.653940
$367$	2.35542	0.122952	0.0614759	−	0.998109i	$-0.480419\pi$
$367$	2.35542	0.122952	0.0614759	+	0.998109i	$0.480419\pi$
$368$	−0.569198	−0.0296715
$369$	−0.193204	−0.0100578
$370$	−7.48633	−0.389196
$371$	−3.20612	−0.166453
$372$	−7.17826	−0.372175
$373$	4.22862	0.218950	0.109475	−	0.993990i	$-0.465083\pi$
$373$	4.22862	0.218950	0.109475	+	0.993990i	$0.465083\pi$
$374$	40.5911	2.09892
$375$	20.7106	1.06949
$376$	−2.90711	−0.149922
$377$	0.142419	0.00733495
$378$	−3.48376	−0.179185
$379$	−3.50916	−0.180253	−0.0901267	−	0.995930i	$-0.528727\pi$
$379$	−3.50916	−0.180253	−0.0901267	+	0.995930i	$0.528727\pi$
$380$	−1.96614	−0.100861
$381$	−3.07480	−0.157527
$382$	−9.10809	−0.466011
$383$	−13.3488	−0.682092	−0.341046	−	0.940047i	$-0.610781\pi$
$383$	−13.3488	−0.682092	−0.341046	+	0.940047i	$0.610781\pi$
$384$	1.71717	0.0876288
$385$	7.12011	0.362874
$386$	−24.3418	−1.23896
$387$	−0.274628	−0.0139601
$388$	−1.39596	−0.0708691
$389$	0.558264	0.0283051	0.0141526	−	0.999900i	$-0.495495\pi$
$389$	0.558264	0.0283051	0.0141526	+	0.999900i	$0.495495\pi$
$390$	−0.174128	−0.00881730
$391$	4.24196	0.214525
$392$	6.55793	0.331225
$393$	−11.0374	−0.556761
$394$	−3.04025	−0.153165
$395$	−7.80051	−0.392486
$396$	−0.279614	−0.0140512
$397$	−8.33658	−0.418401	−0.209201	−	0.977873i	$-0.567086\pi$
$397$	−8.33658	−0.418401	−0.209201	+	0.977873i	$0.567086\pi$
$398$	7.69027	0.385479
$399$	1.14172	0.0571573
$400$	−1.13431	−0.0567156
$401$	28.0628	1.40139	0.700696	−	0.713460i	$-0.252873\pi$
$401$	28.0628	1.40139	0.700696	+	0.713460i	$0.252873\pi$
$402$	−19.0694	−0.951094
$403$	−0.215600	−0.0107398
$404$	0.815336	0.0405645
$405$	−17.3872	−0.863978
$406$	1.83600	0.0911189
$407$	20.7388	1.02798
$408$	−12.7972	−0.633557
$409$	19.5015	0.964286	0.482143	−	0.876093i	$-0.339859\pi$
$409$	19.5015	0.964286	0.482143	+	0.876093i	$0.339859\pi$
$410$	−7.39943	−0.365432
$411$	−8.42152	−0.415403
$412$	−17.7362	−0.873800
$413$	−0.266761	−0.0131264
$414$	−0.0292210	−0.00143613
$415$	14.4137	0.707540
$416$	0.0515753	0.00252869
$417$	−28.8039	−1.41053
$418$	5.44663	0.266403
$419$	−17.2565	−0.843037	−0.421518	−	0.906820i	$-0.638503\pi$
$419$	−17.2565	−0.843037	−0.421518	+	0.906820i	$0.638503\pi$
$420$	−2.24477	−0.109533
$421$	−0.147683	−0.00719763	−0.00359881	−	0.999994i	$-0.501146\pi$
$421$	−0.147683	−0.00719763	−0.00359881	+	0.999994i	$0.501146\pi$
$422$	1.00000	0.0486792
$423$	−0.149243	−0.00725642
$424$	4.82207	0.234181
$425$	8.45350	0.410055
$426$	−26.3453	−1.27643
$427$	−4.84408	−0.234421
$428$	−9.25934	−0.447567
$429$	0.482372	0.0232891
$430$	−10.5178	−0.507215
$431$	8.58035	0.413301	0.206651	−	0.978415i	$-0.433744\pi$
$431$	8.58035	0.413301	0.206651	+	0.978415i	$0.433744\pi$
$432$	5.23966	0.252093
$433$	−37.1097	−1.78338	−0.891688	−	0.452650i	$-0.850479\pi$
$433$	−37.1097	−1.78338	−0.891688	+	0.452650i	$0.850479\pi$
$434$	−2.77941	−0.133416
$435$	9.32292	0.447000
$436$	−14.4033	−0.689791
$437$	0.569198	0.0272284
$438$	−1.07027	−0.0511395
$439$	−23.4518	−1.11929	−0.559647	−	0.828731i	$-0.689063\pi$
$439$	−23.4518	−1.11929	−0.559647	+	0.828731i	$0.689063\pi$
$440$	−10.7088	−0.510522
$441$	0.336666	0.0160317
$442$	−0.384366	−0.0182824
$443$	2.40260	0.114151	0.0570755	−	0.998370i	$-0.481822\pi$
$443$	2.40260	0.114151	0.0570755	+	0.998370i	$0.481822\pi$
$444$	−6.53835	−0.310296
$445$	22.7490	1.07840
$446$	−7.97029	−0.377404
$447$	−3.76116	−0.177897
$448$	0.664883	0.0314128
$449$	−39.4123	−1.85998	−0.929990	−	0.367585i	$-0.880185\pi$
$449$	−39.4123	−1.85998	−0.929990	+	0.367585i	$0.880185\pi$
$450$	−0.0582324	−0.00274510
$451$	20.4981	0.965216
$452$	4.30841	0.202651
$453$	−6.91067	−0.324691
$454$	12.4698	0.585237
$455$	−0.0674218	−0.00316078
$456$	−1.71717	−0.0804137
$457$	29.3385	1.37240	0.686198	−	0.727415i	$-0.259278\pi$
$457$	29.3385	1.37240	0.686198	+	0.727415i	$0.259278\pi$
$458$	−10.0271	−0.468535
$459$	−39.0487	−1.82264
$460$	−1.11912	−0.0521792
$461$	7.98018	0.371674	0.185837	−	0.982581i	$-0.440500\pi$
$461$	7.98018	0.371674	0.185837	+	0.982581i	$0.440500\pi$
$462$	6.21850	0.289311
$463$	−37.4941	−1.74250	−0.871248	−	0.490843i	$-0.836689\pi$
$463$	−37.4941	−1.74250	−0.871248	+	0.490843i	$0.836689\pi$
$464$	−2.76138	−0.128194
$465$	−14.1134	−0.654495
$466$	−2.93800	−0.136100
$467$	−21.1682	−0.979549	−0.489775	−	0.871849i	$-0.662921\pi$
$467$	−21.1682	−0.979549	−0.489775	+	0.871849i	$0.662921\pi$
$468$	0.00264773	0.000122391 0
$469$	−7.38362	−0.340944
$470$	−5.71576	−0.263648
$471$	−1.23998	−0.0571353
$472$	0.401214	0.0184674
$473$	29.1367	1.33971
$474$	−6.81275	−0.312920
$475$	1.13431	0.0520458
$476$	−4.95506	−0.227115
$477$	0.247552	0.0113346
$478$	−27.1772	−1.24306
$479$	17.7815	0.812456	0.406228	−	0.913772i	$-0.366844\pi$
$479$	17.7815	0.812456	0.406228	+	0.913772i	$0.366844\pi$
$480$	3.37618	0.154101
$481$	−0.196380	−0.00895416
$482$	−11.4352	−0.520861
$483$	0.649862	0.0295698
$484$	18.6657	0.848443
$485$	−2.74464	−0.124628
$486$	0.533453	0.0241979
$487$	−15.8359	−0.717592	−0.358796	−	0.933416i	$-0.616813\pi$
$487$	−15.8359	−0.717592	−0.358796	+	0.933416i	$0.616813\pi$
$488$	7.28561	0.329804
$489$	−3.58258	−0.162010
$490$	12.8938	0.582481
$491$	34.2367	1.54508	0.772540	−	0.634966i	$-0.218986\pi$
$491$	34.2367	1.54508	0.772540	+	0.634966i	$0.218986\pi$
$492$	−6.46246	−0.291350
$493$	20.5793	0.926843
$494$	−0.0515753	−0.00232048
$495$	−0.549760	−0.0247099
$496$	4.18029	0.187701
$497$	−10.2008	−0.457570
$498$	12.5885	0.564105
$499$	7.51190	0.336279	0.168139	−	0.985763i	$-0.446224\pi$
$499$	7.51190	0.336279	0.168139	+	0.985763i	$0.446224\pi$
$500$	−12.0609	−0.539379
$501$	38.3104	1.71158
$502$	−7.49421	−0.334483
$503$	−39.2132	−1.74843	−0.874215	−	0.485539i	$-0.838623\pi$
$503$	−39.2132	−1.74843	−0.874215	+	0.485539i	$0.838623\pi$
$504$	0.0341332	0.00152042
$505$	1.60306	0.0713353
$506$	3.10021	0.137821
$507$	22.3186	0.991204
$508$	1.79062	0.0794460
$509$	5.10912	0.226458	0.113229	−	0.993569i	$-0.463881\pi$
$509$	5.10912	0.226458	0.113229	+	0.993569i	$0.463881\pi$
$510$	−25.1611	−1.11415
$511$	−0.414406	−0.0183323
$512$	−1.00000	−0.0441942
$513$	−5.23966	−0.231336
$514$	11.2392	0.495742
$515$	−34.8718	−1.53663
$516$	−9.18598	−0.404390
$517$	15.8339	0.696375
$518$	−2.53164	−0.111234
$519$	25.2056	1.10640
$520$	0.101404	0.00444686
$521$	−31.1713	−1.36564	−0.682820	−	0.730586i	$-0.739247\pi$
$521$	−31.1713	−1.36564	−0.682820	+	0.730586i	$0.739247\pi$
$522$	−0.141762	−0.00620473
$523$	−25.1686	−1.10054	−0.550272	−	0.834985i	$-0.685476\pi$
$523$	−25.1686	−1.10054	−0.550272	+	0.834985i	$0.685476\pi$
$524$	6.42765	0.280793
$525$	1.29506	0.0565212
$526$	28.5766	1.24600
$527$	−31.1537	−1.35708
$528$	−9.35277	−0.407027
$529$	−22.6760	−0.985914
$530$	9.48085	0.411822
$531$	0.0205972	0.000893842 0
$532$	−0.664883	−0.0288263
$533$	−0.194101	−0.00840743
$534$	19.8683	0.859786
$535$	−18.2051	−0.787076
$536$	11.1051	0.479669
$537$	−6.00702	−0.259222
$538$	25.3611	1.09339
$539$	−35.7186	−1.53851
$540$	10.3019	0.443322
$541$	−14.6435	−0.629573	−0.314787	−	0.949162i	$-0.601933\pi$
$541$	−14.6435	−0.629573	−0.314787	+	0.949162i	$0.601933\pi$
$542$	−22.9209	−0.984539
$543$	26.2396	1.12605
$544$	7.45253	0.319524
$545$	−28.3188	−1.21304
$546$	−0.0588843	−0.00252002
$547$	−3.08583	−0.131940	−0.0659702	−	0.997822i	$-0.521014\pi$
$547$	−3.08583	−0.131940	−0.0659702	+	0.997822i	$0.521014\pi$
$548$	4.90431	0.209502
$549$	0.374023	0.0159629
$550$	6.17818	0.263438
$551$	2.76138	0.117639
$552$	−0.977408	−0.0416012
$553$	−2.63788	−0.112174
$554$	12.2951	0.522369
$555$	−12.8553	−0.545676
$556$	16.7741	0.711379
$557$	10.9246	0.462891	0.231446	−	0.972848i	$-0.425654\pi$
$557$	10.9246	0.462891	0.231446	+	0.972848i	$0.425654\pi$
$558$	0.214604	0.00908493
$559$	−0.275902	−0.0116694
$560$	1.30725	0.0552414
$561$	69.7018	2.94281
$562$	3.01077	0.127002
$563$	−10.5361	−0.444045	−0.222023	−	0.975042i	$-0.571266\pi$
$563$	−10.5361	−0.444045	−0.222023	+	0.975042i	$0.571266\pi$
$564$	−4.99199	−0.210200
$565$	8.47091	0.356374
$566$	31.6362	1.32977
$567$	−5.87980	−0.246928
$568$	15.3423	0.643748
$569$	−40.3961	−1.69349	−0.846746	−	0.531998i	$-0.821441\pi$
$569$	−40.3961	−1.69349	−0.846746	+	0.531998i	$0.821441\pi$
$570$	−3.37618	−0.141413
$571$	−41.3898	−1.73211	−0.866054	−	0.499950i	$-0.833352\pi$
$571$	−41.3898	−1.73211	−0.866054	+	0.499950i	$0.833352\pi$
$572$	−0.280911	−0.0117455
$573$	−15.6401	−0.653375
$574$	−2.50225	−0.104442
$575$	0.645648	0.0269254
$576$	−0.0513372	−0.00213905
$577$	−7.58644	−0.315827	−0.157914	−	0.987453i	$-0.550477\pi$
$577$	−7.58644	−0.315827	−0.157914	+	0.987453i	$0.550477\pi$
$578$	−38.5402	−1.60306
$579$	−41.7989	−1.73710
$580$	−5.42925	−0.225437
$581$	4.87424	0.202218
$582$	−2.39709	−0.0993628
$583$	−26.2640	−1.08775
$584$	0.623277	0.0257914
$585$	0.00520580	0.000215233 0
$586$	2.89410	0.119554
$587$	3.89266	0.160667	0.0803337	−	0.996768i	$-0.474401\pi$
$587$	3.89266	0.160667	0.0803337	+	0.996768i	$0.474401\pi$
$588$	11.2611	0.464398
$589$	−4.18029	−0.172246
$590$	0.788841	0.0324761
$591$	−5.22061	−0.214747
$592$	3.80764	0.156493
$593$	−21.4182	−0.879540	−0.439770	−	0.898110i	$-0.644940\pi$
$593$	−21.4182	−0.879540	−0.439770	+	0.898110i	$0.644940\pi$
$594$	−28.5384	−1.17095
$595$	−9.74232	−0.399396
$596$	2.19033	0.0897193
$597$	13.2055	0.540465
$598$	−0.0293566	−0.00120048
$599$	31.3344	1.28029	0.640145	−	0.768254i	$-0.278874\pi$
$599$	31.3344	1.28029	0.640145	+	0.768254i	$0.278874\pi$
$600$	−1.94780	−0.0795188
$601$	39.0137	1.59140	0.795702	−	0.605688i	$-0.207102\pi$
$601$	39.0137	1.59140	0.795702	+	0.605688i	$0.207102\pi$
$602$	−3.55679	−0.144964
$603$	0.570106	0.0232165
$604$	4.02446	0.163753
$605$	36.6994	1.49204
$606$	1.40007	0.0568739
$607$	−16.4957	−0.669541	−0.334771	−	0.942300i	$-0.608659\pi$
$607$	−16.4957	−0.669541	−0.334771	+	0.942300i	$0.608659\pi$
$608$	1.00000	0.0405554
$609$	3.15271	0.127754
$610$	14.3245	0.579982
$611$	−0.149935	−0.00606571
$612$	0.382592	0.0154654
$613$	−7.40723	−0.299175	−0.149588	−	0.988748i	$-0.547795\pi$
$613$	−7.40723	−0.299175	−0.149588	+	0.988748i	$0.547795\pi$
$614$	19.0575	0.769096
$615$	−12.7061	−0.512358
$616$	−3.62137	−0.145909
$617$	21.7208	0.874446	0.437223	−	0.899353i	$-0.355962\pi$
$617$	21.7208	0.874446	0.437223	+	0.899353i	$0.355962\pi$
$618$	−30.4560	−1.22512
$619$	31.9548	1.28437	0.642185	−	0.766549i	$-0.278028\pi$
$619$	31.9548	1.28437	0.642185	+	0.766549i	$0.278028\pi$
$620$	8.21902	0.330084
$621$	−2.98240	−0.119680
$622$	−3.64366	−0.146097
$623$	7.69297	0.308212
$624$	0.0885634	0.00354537
$625$	−18.0418	−0.721671
$626$	−22.3322	−0.892576
$627$	9.35277	0.373514
$628$	0.722109	0.0288153
$629$	−28.3765	−1.13145
$630$	0.0671106	0.00267375
$631$	31.2137	1.24260	0.621298	−	0.783574i	$-0.286606\pi$
$631$	31.2137	1.24260	0.621298	+	0.783574i	$0.286606\pi$
$632$	3.96744	0.157816
$633$	1.71717	0.0682513
$634$	−8.40912	−0.333969
$635$	3.52061	0.139711
$636$	8.28031	0.328336
$637$	0.338227	0.0134011
$638$	15.0402	0.595448
$639$	0.787630	0.0311582
$640$	−1.96614	−0.0777183
$641$	−6.61615	−0.261322	−0.130661	−	0.991427i	$-0.541710\pi$
$641$	−6.61615	−0.261322	−0.130661	+	0.991427i	$0.541710\pi$
$642$	−15.8998	−0.627517
$643$	0.277025	0.0109248	0.00546240	−	0.999985i	$-0.498261\pi$
$643$	0.277025	0.0109248	0.00546240	+	0.999985i	$0.498261\pi$
$644$	−0.378450	−0.0149130
$645$	−18.0609	−0.711146
$646$	−7.45253	−0.293216
$647$	21.7579	0.855391	0.427695	−	0.903923i	$-0.359326\pi$
$647$	21.7579	0.855391	0.427695	+	0.903923i	$0.359326\pi$
$648$	8.84335	0.347400
$649$	−2.18526	−0.0857791
$650$	−0.0585025	−0.00229466
$651$	−4.77271	−0.187057
$652$	2.08633	0.0817069
$653$	−9.39540	−0.367670	−0.183835	−	0.982957i	$-0.558851\pi$
$653$	−9.39540	−0.367670	−0.183835	+	0.982957i	$0.558851\pi$
$654$	−24.7328	−0.967129
$655$	12.6376	0.493793
$656$	3.76344	0.146938
$657$	0.0319973	0.00124833
$658$	−1.93289	−0.0753517
$659$	24.2046	0.942878	0.471439	−	0.881899i	$-0.343735\pi$
$659$	24.2046	0.942878	0.471439	+	0.881899i	$0.343735\pi$
$660$	−18.3888	−0.715783
$661$	−22.5768	−0.878136	−0.439068	−	0.898454i	$-0.644691\pi$
$661$	−22.5768	−0.878136	−0.439068	+	0.898454i	$0.644691\pi$
$662$	−24.3203	−0.945234
$663$	−0.660021	−0.0256331
$664$	−7.33098	−0.284497
$665$	−1.30725	−0.0506930
$666$	0.195473	0.00757444
$667$	1.57177	0.0608592
$668$	−22.3102	−0.863209
$669$	−13.6863	−0.529143
$670$	21.8342	0.843528
$671$	−39.6820	−1.53191
$672$	1.14172	0.0440426
$673$	19.6184	0.756234	0.378117	−	0.925758i	$-0.376572\pi$
$673$	19.6184	0.756234	0.378117	+	0.925758i	$0.376572\pi$
$674$	11.1676	0.430160
$675$	−5.94341	−0.228762
$676$	−12.9973	−0.499898
$677$	−2.77541	−0.106668	−0.0533338	−	0.998577i	$-0.516985\pi$
$677$	−2.77541	−0.106668	−0.0533338	+	0.998577i	$0.516985\pi$
$678$	7.39826	0.284128
$679$	−0.928150	−0.0356191
$680$	14.6527	0.561904
$681$	21.4128	0.820539
$682$	−22.7685	−0.871851
$683$	17.7505	0.679205	0.339603	−	0.940569i	$-0.389707\pi$
$683$	17.7505	0.679205	0.339603	+	0.940569i	$0.389707\pi$
$684$	0.0513372	0.00196293
$685$	9.64254	0.368422
$686$	9.01444	0.344173
$687$	−17.2182	−0.656914
$688$	5.34950	0.203948
$689$	0.248700	0.00947472
$690$	−1.92172	−0.0731585
$691$	−3.62867	−0.138041	−0.0690206	−	0.997615i	$-0.521987\pi$
$691$	−3.62867	−0.138041	−0.0690206	+	0.997615i	$0.521987\pi$
$692$	−14.6786	−0.557996
$693$	−0.185911	−0.00706218
$694$	20.9306	0.794513
$695$	32.9801	1.25101
$696$	−4.74175	−0.179736
$697$	−28.0471	−1.06236
$698$	−1.95004	−0.0738102
$699$	−5.04503	−0.190821
$700$	−0.754186	−0.0285055
$701$	9.56454	0.361248	0.180624	−	0.983552i	$-0.442188\pi$
$701$	9.56454	0.361248	0.180624	+	0.983552i	$0.442188\pi$
$702$	0.270237	0.0101994
$703$	−3.80764	−0.143608
$704$	5.44663	0.205277
$705$	−9.81492	−0.369651
$706$	−19.6958	−0.741259
$707$	0.542103	0.0203879
$708$	0.688952	0.0258924
$709$	−30.7759	−1.15581	−0.577907	−	0.816102i	$-0.696131\pi$
$709$	−30.7759	−1.15581	−0.577907	+	0.816102i	$0.696131\pi$
$710$	30.1650	1.13207
$711$	0.203677	0.00763848
$712$	−11.5704	−0.433619
$713$	−2.37941	−0.0891097
$714$	−8.50867	−0.318429
$715$	−0.552310	−0.0206552
$716$	3.49821	0.130734
$717$	−46.6678	−1.74284
$718$	13.0411	0.486689
$719$	−10.4775	−0.390744	−0.195372	−	0.980729i	$-0.562591\pi$
$719$	−10.4775	−0.390744	−0.195372	+	0.980729i	$0.562591\pi$
$720$	−0.100936	−0.00376166
$721$	−11.7925	−0.439176
$722$	−1.00000	−0.0372161
$723$	−19.6362	−0.730278
$724$	−15.2807	−0.567904
$725$	3.13227	0.116330
$726$	32.0522	1.18957
$727$	32.8219	1.21730	0.608649	−	0.793440i	$-0.291712\pi$
$727$	32.8219	1.21730	0.608649	+	0.793440i	$0.291712\pi$
$728$	0.0342916	0.00127093
$729$	27.4461	1.01652
$730$	1.22545	0.0453558
$731$	−39.8673	−1.47454
$732$	12.5106	0.462405
$733$	−15.1043	−0.557889	−0.278945	−	0.960307i	$-0.589985\pi$
$733$	−15.1043	−0.557889	−0.278945	+	0.960307i	$0.589985\pi$
$734$	−2.35542	−0.0869401
$735$	22.1408	0.816675
$736$	0.569198	0.0209809
$737$	−60.4855	−2.22801
$738$	0.193204	0.00711195
$739$	−0.843562	−0.0310309	−0.0155155	−	0.999880i	$-0.504939\pi$
$739$	−0.843562	−0.0310309	−0.0155155	+	0.999880i	$0.504939\pi$
$740$	7.48633	0.275203
$741$	−0.0885634	−0.00325346
$742$	3.20612	0.117700
$743$	28.1547	1.03290	0.516448	−	0.856318i	$-0.327254\pi$
$743$	28.1547	1.03290	0.516448	+	0.856318i	$0.327254\pi$
$744$	7.17826	0.263168
$745$	4.30648	0.157777
$746$	−4.22862	−0.154821
$747$	−0.376352	−0.0137700
$748$	−40.5911	−1.48416
$749$	−6.15638	−0.224949
$750$	−20.7106	−0.756243
$751$	−43.1009	−1.57277	−0.786387	−	0.617734i	$-0.788051\pi$
$751$	−43.1009	−1.57277	−0.786387	+	0.617734i	$0.788051\pi$
$752$	2.90711	0.106011
$753$	−12.8688	−0.468965
$754$	−0.142419	−0.00518660
$755$	7.91263	0.287970
$756$	3.48376	0.126703
$757$	5.04390	0.183324	0.0916619	−	0.995790i	$-0.470782\pi$
$757$	5.04390	0.183324	0.0916619	+	0.995790i	$0.470782\pi$
$758$	3.50916	0.127458
$759$	5.32358	0.193234
$760$	1.96614	0.0713192
$761$	40.9204	1.48336	0.741681	−	0.670752i	$-0.234029\pi$
$761$	40.9204	1.48336	0.741681	+	0.670752i	$0.234029\pi$
$762$	3.07480	0.111388
$763$	−9.57649	−0.346692
$764$	9.10809	0.329519
$765$	0.752227	0.0271968
$766$	13.3488	0.482312
$767$	0.0206927	0.000747171 0
$768$	−1.71717	−0.0619629
$769$	−33.5885	−1.21123	−0.605617	−	0.795757i	$-0.707073\pi$
$769$	−33.5885	−1.21123	−0.605617	+	0.795757i	$0.707073\pi$
$770$	−7.12011	−0.256591
$771$	19.2997	0.695060
$772$	24.3418	0.876080
$773$	17.4791	0.628679	0.314340	−	0.949311i	$-0.398217\pi$
$773$	17.4791	0.628679	0.314340	+	0.949311i	$0.398217\pi$
$774$	0.274628	0.00987130
$775$	−4.74176	−0.170329
$776$	1.39596	0.0501120
$777$	−4.34724	−0.155956
$778$	−0.558264	−0.0200147
$779$	−3.76344	−0.134839
$780$	0.174128	0.00623477
$781$	−83.5637	−2.99015
$782$	−4.24196	−0.151692
$783$	−14.4687	−0.517069
$784$	−6.55793	−0.234212
$785$	1.41976	0.0506735
$786$	11.0374	0.393689
$787$	−24.6448	−0.878493	−0.439246	−	0.898367i	$-0.644754\pi$
$787$	−24.6448	−0.878493	−0.439246	+	0.898367i	$0.644754\pi$
$788$	3.04025	0.108304
$789$	49.0707	1.74696
$790$	7.80051	0.277530
$791$	2.86459	0.101853
$792$	0.279614	0.00993567
$793$	0.375757	0.0133435
$794$	8.33658	0.295854
$795$	16.2802	0.577399
$796$	−7.69027	−0.272575
$797$	30.0135	1.06313	0.531567	−	0.847016i	$-0.321603\pi$
$797$	30.0135	1.06313	0.531567	+	0.847016i	$0.321603\pi$
$798$	−1.14172	−0.0404163
$799$	−21.6653	−0.766462
$800$	1.13431	0.0401040
$801$	−0.593992	−0.0209877
$802$	−28.0628	−0.990933
$803$	−3.39476	−0.119798
$804$	19.0694	0.672525
$805$	−0.744084	−0.0262255
$806$	0.215600	0.00759418
$807$	43.5492	1.53300
$808$	−0.815336	−0.0286834
$809$	31.1310	1.09451	0.547254	−	0.836966i	$-0.315673\pi$
$809$	31.1310	1.09451	0.547254	+	0.836966i	$0.315673\pi$
$810$	17.3872	0.610925
$811$	−30.3583	−1.06603	−0.533013	−	0.846107i	$-0.678940\pi$
$811$	−30.3583	−1.06603	−0.533013	+	0.846107i	$0.678940\pi$
$812$	−1.83600	−0.0644308
$813$	−39.3591	−1.38038
$814$	−20.7388	−0.726894
$815$	4.10200	0.143687
$816$	12.7972	0.447993
$817$	−5.34950	−0.187155
$818$	−19.5015	−0.681853
$819$	0.00176043	6.15145e−5 0
$820$	7.39943	0.258399
$821$	37.4264	1.30619	0.653094	−	0.757277i	$-0.273470\pi$
$821$	37.4264	1.30619	0.653094	+	0.757277i	$0.273470\pi$
$822$	8.42152	0.293734
$823$	−34.6012	−1.20612	−0.603061	−	0.797695i	$-0.706052\pi$
$823$	−34.6012	−1.20612	−0.603061	+	0.797695i	$0.706052\pi$
$824$	17.7362	0.617870
$825$	10.6090	0.369357
$826$	0.266761	0.00928179
$827$	−49.4218	−1.71857	−0.859283	−	0.511500i	$-0.829090\pi$
$827$	−49.4218	−1.71857	−0.859283	+	0.511500i	$0.829090\pi$
$828$	0.0292210	0.00101550
$829$	−26.9608	−0.936387	−0.468194	−	0.883626i	$-0.655095\pi$
$829$	−26.9608	−0.936387	−0.468194	+	0.883626i	$0.655095\pi$
$830$	−14.4137	−0.500307
$831$	21.1128	0.732394
$832$	−0.0515753	−0.00178805
$833$	48.8731	1.69335
$834$	28.8039	0.997397
$835$	−43.8649	−1.51801
$836$	−5.44663	−0.188376
$837$	21.9033	0.757089
$838$	17.2565	0.596117
$839$	17.6134	0.608082	0.304041	−	0.952659i	$-0.401664\pi$
$839$	17.6134	0.608082	0.304041	+	0.952659i	$0.401664\pi$
$840$	2.24477	0.0774518
$841$	−21.3748	−0.737061
$842$	0.147683	0.00508949
$843$	5.16999	0.178064
$844$	−1.00000	−0.0344214
$845$	−25.5545	−0.879102
$846$	0.149243	0.00513107
$847$	12.4105	0.426431
$848$	−4.82207	−0.165591
$849$	54.3246	1.86441
$850$	−8.45350	−0.289953
$851$	−2.16730	−0.0742941
$852$	26.3453	0.902574
$853$	−35.3787	−1.21135	−0.605673	−	0.795714i	$-0.707096\pi$
$853$	−35.3787	−1.21135	−0.605673	+	0.795714i	$0.707096\pi$
$854$	4.84408	0.165761
$855$	0.100936	0.00345193
$856$	9.25934	0.316478
$857$	−9.75284	−0.333151	−0.166575	−	0.986029i	$-0.553271\pi$
$857$	−9.75284	−0.333151	−0.166575	+	0.986029i	$0.553271\pi$
$858$	−0.482372	−0.0164679
$859$	−43.9490	−1.49952	−0.749760	−	0.661710i	$-0.769831\pi$
$859$	−43.9490	−1.49952	−0.749760	+	0.661710i	$0.769831\pi$
$860$	10.5178	0.358655
$861$	−4.29678	−0.146434
$862$	−8.58035	−0.292248
$863$	−36.7963	−1.25256	−0.626280	−	0.779598i	$-0.715423\pi$
$863$	−36.7963	−1.25256	−0.626280	+	0.779598i	$0.715423\pi$
$864$	−5.23966	−0.178257
$865$	−28.8601	−0.981273
$866$	37.1097	1.26104
$867$	−66.1799	−2.24759
$868$	2.77941	0.0943392
$869$	−21.6091	−0.733040
$870$	−9.32292	−0.316077
$871$	0.572751	0.0194069
$872$	14.4033	0.487756
$873$	0.0716646	0.00242548
$874$	−0.569198	−0.0192534
$875$	−8.01908	−0.271094
$876$	1.07027	0.0361611
$877$	−44.6268	−1.50694	−0.753470	−	0.657483i	$-0.771621\pi$
$877$	−44.6268	−1.50694	−0.753470	+	0.657483i	$0.771621\pi$
$878$	23.4518	0.791461
$879$	4.96966	0.167622
$880$	10.7088	0.360994
$881$	11.3536	0.382512	0.191256	−	0.981540i	$-0.438744\pi$
$881$	11.3536	0.382512	0.191256	+	0.981540i	$0.438744\pi$
$882$	−0.336666	−0.0113361
$883$	−41.2415	−1.38789	−0.693944	−	0.720029i	$-0.744129\pi$
$883$	−41.2415	−1.38789	−0.693944	+	0.720029i	$0.744129\pi$
$884$	0.384366	0.0129276
$885$	1.35457	0.0455334
$886$	−2.40260	−0.0807169
$887$	−18.4339	−0.618951	−0.309475	−	0.950907i	$-0.600153\pi$
$887$	−18.4339	−0.618951	−0.309475	+	0.950907i	$0.600153\pi$
$888$	6.53835	0.219413
$889$	1.19056	0.0399299
$890$	−22.7490	−0.762547
$891$	−48.1664	−1.61364
$892$	7.97029	0.266865
$893$	−2.90711	−0.0972826
$894$	3.76116	0.125792
$895$	6.87796	0.229905
$896$	−0.664883	−0.0222122
$897$	−0.0504101	−0.00168314
$898$	39.4123	1.31520
$899$	−11.5434	−0.384993
$900$	0.0582324	0.00194108
$901$	35.9366	1.19722
$902$	−20.4981	−0.682511
$903$	−6.10760	−0.203248
$904$	−4.30841	−0.143296
$905$	−30.0440	−0.998695
$906$	6.91067	0.229592
$907$	11.3421	0.376609	0.188305	−	0.982111i	$-0.439701\pi$
$907$	11.3421	0.376609	0.188305	+	0.982111i	$0.439701\pi$
$908$	−12.4698	−0.413825
$909$	−0.0418571	−0.00138831
$910$	0.0674218	0.00223501
$911$	−38.3605	−1.27094	−0.635470	−	0.772125i	$-0.719194\pi$
$911$	−38.3605	−1.27094	−0.635470	+	0.772125i	$0.719194\pi$
$912$	1.71717	0.0568611
$913$	39.9291	1.32146
$914$	−29.3385	−0.970430
$915$	24.5975	0.813170
$916$	10.0271	0.331304
$917$	4.27364	0.141128
$918$	39.0487	1.28880
$919$	−53.0919	−1.75134	−0.875670	−	0.482910i	$-0.839580\pi$
$919$	−53.0919	−1.75134	−0.875670	+	0.482910i	$0.839580\pi$
$920$	1.11912	0.0368963
$921$	32.7248	1.07832
$922$	−7.98018	−0.262813
$923$	0.791283	0.0260454
$924$	−6.21850	−0.204574
$925$	−4.31905	−0.142010
$926$	37.4941	1.23213
$927$	0.910526	0.0299056
$928$	2.76138	0.0906468
$929$	−11.2355	−0.368625	−0.184313	−	0.982868i	$-0.559006\pi$
$929$	−11.2355	−0.368625	−0.184313	+	0.982868i	$0.559006\pi$
$930$	14.1134	0.462798
$931$	6.55793	0.214927
$932$	2.93800	0.0962373
$933$	−6.25677	−0.204837
$934$	21.1682	0.692646
$935$	−79.8076	−2.60999
$936$	−0.00264773	−8.65438e−5 0
$937$	−9.83497	−0.321295	−0.160647	−	0.987012i	$-0.551358\pi$
$937$	−9.83497	−0.321295	−0.160647	+	0.987012i	$0.551358\pi$
$938$	7.38362	0.241084
$939$	−38.3482	−1.25145
$940$	5.71576	0.186428
$941$	−0.178774	−0.00582786	−0.00291393	−	0.999996i	$-0.500928\pi$
$941$	−0.178774	−0.00582786	−0.00291393	+	0.999996i	$0.500928\pi$
$942$	1.23998	0.0404008
$943$	−2.14214	−0.0697577
$944$	−0.401214	−0.0130584
$945$	6.84954	0.222816
$946$	−29.1367	−0.947316
$947$	−36.3394	−1.18087	−0.590436	−	0.807085i	$-0.701044\pi$
$947$	−36.3394	−1.18087	−0.590436	+	0.807085i	$0.701044\pi$
$948$	6.81275	0.221268
$949$	0.0321457	0.00104349
$950$	−1.13431	−0.0368020
$951$	−14.4399	−0.468245
$952$	4.95506	0.160594
$953$	−1.70822	−0.0553347	−0.0276673	−	0.999617i	$-0.508808\pi$
$953$	−1.70822	−0.0553347	−0.0276673	+	0.999617i	$0.508808\pi$
$954$	−0.247552	−0.00801478
$955$	17.9077	0.579481
$956$	27.1772	0.878973
$957$	25.8266	0.834854
$958$	−17.7815	−0.574493
$959$	3.26079	0.105297
$960$	−3.37618	−0.108966
$961$	−13.5252	−0.436295
$962$	0.196380	0.00633155
$963$	0.475349	0.0153179
$964$	11.4352	0.368304
$965$	47.8592	1.54064
$966$	−0.649862	−0.0209090
$967$	−39.2416	−1.26192	−0.630962	−	0.775814i	$-0.717339\pi$
$967$	−39.2416	−1.26192	−0.630962	+	0.775814i	$0.717339\pi$
$968$	−18.6657	−0.599940
$969$	−12.7972	−0.411106
$970$	2.74464	0.0881252
$971$	52.9983	1.70080	0.850399	−	0.526139i	$-0.176361\pi$
$971$	52.9983	1.70080	0.850399	+	0.526139i	$0.176361\pi$
$972$	−0.533453	−0.0171105
$973$	11.1528	0.357542
$974$	15.8359	0.507414
$975$	−0.100459	−0.00321725
$976$	−7.28561	−0.233207
$977$	−19.6760	−0.629491	−0.314746	−	0.949176i	$-0.601919\pi$
$977$	−19.6760	−0.629491	−0.314746	+	0.949176i	$0.601919\pi$
$978$	3.58258	0.114558
$979$	63.0197	2.01412
$980$	−12.8938	−0.411877
$981$	0.739423	0.0236080
$982$	−34.2367	−1.09254
$983$	−39.5305	−1.26083	−0.630414	−	0.776259i	$-0.717115\pi$
$983$	−39.5305	−1.26083	−0.630414	+	0.776259i	$0.717115\pi$
$984$	6.46246	0.206016
$985$	5.97754	0.190460
$986$	−20.5793	−0.655377
$987$	−3.31909	−0.105648
$988$	0.0515753	0.00164083
$989$	−3.04492	−0.0968229
$990$	0.549760	0.0174725
$991$	−61.8294	−1.96407	−0.982037	−	0.188688i	$-0.939577\pi$
$991$	−61.8294	−1.96407	−0.982037	+	0.188688i	$0.939577\pi$
$992$	−4.18029	−0.132724
$993$	−41.7619	−1.32528
$994$	10.2008	0.323551
$995$	−15.1201	−0.479340
$996$	−12.5885	−0.398882
$997$	−14.3653	−0.454954	−0.227477	−	0.973783i	$-0.573048\pi$
$997$	−14.3653	−0.454954	−0.227477	+	0.973783i	$0.573048\pi$
$998$	−7.51190	−0.237785
$999$	19.9507	0.631213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.12	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.12	✓	34	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.71717 q^{3} +1.00000 q^{4} +1.96614 q^{5} +1.71717 q^{6} +0.664883 q^{7} -1.00000 q^{8} -0.0513372 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.71717 q^{3} +1.00000 q^{4} +1.96614 q^{5} +1.71717 q^{6} +0.664883 q^{7} -1.00000 q^{8} -0.0513372 q^{9} -1.96614 q^{10} +5.44663 q^{11} -1.71717 q^{12} -0.0515753 q^{13} -0.664883 q^{14} -3.37618 q^{15} +1.00000 q^{16} -7.45253 q^{17} +0.0513372 q^{18} -1.00000 q^{19} +1.96614 q^{20} -1.14172 q^{21} -5.44663 q^{22} -0.569198 q^{23} +1.71717 q^{24} -1.13431 q^{25} +0.0515753 q^{26} +5.23966 q^{27} +0.664883 q^{28} -2.76138 q^{29} +3.37618 q^{30} +4.18029 q^{31} -1.00000 q^{32} -9.35277 q^{33} +7.45253 q^{34} +1.30725 q^{35} -0.0513372 q^{36} +3.80764 q^{37} +1.00000 q^{38} +0.0885634 q^{39} -1.96614 q^{40} +3.76344 q^{41} +1.14172 q^{42} +5.34950 q^{43} +5.44663 q^{44} -0.100936 q^{45} +0.569198 q^{46} +2.90711 q^{47} -1.71717 q^{48} -6.55793 q^{49} +1.13431 q^{50} +12.7972 q^{51} -0.0515753 q^{52} -4.82207 q^{53} -5.23966 q^{54} +10.7088 q^{55} -0.664883 q^{56} +1.71717 q^{57} +2.76138 q^{58} -0.401214 q^{59} -3.37618 q^{60} -7.28561 q^{61} -4.18029 q^{62} -0.0341332 q^{63} +1.00000 q^{64} -0.101404 q^{65} +9.35277 q^{66} -11.1051 q^{67} -7.45253 q^{68} +0.977408 q^{69} -1.30725 q^{70} -15.3423 q^{71} +0.0513372 q^{72} -0.623277 q^{73} -3.80764 q^{74} +1.94780 q^{75} -1.00000 q^{76} +3.62137 q^{77} -0.0885634 q^{78} -3.96744 q^{79} +1.96614 q^{80} -8.84335 q^{81} -3.76344 q^{82} +7.33098 q^{83} -1.14172 q^{84} -14.6527 q^{85} -5.34950 q^{86} +4.74175 q^{87} -5.44663 q^{88} +11.5704 q^{89} +0.100936 q^{90} -0.0342916 q^{91} -0.569198 q^{92} -7.17826 q^{93} -2.90711 q^{94} -1.96614 q^{95} +1.71717 q^{96} -1.39596 q^{97} +6.55793 q^{98} -0.279614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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