LMFDB - Embedded newform 6026.2.a.i.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.888297 q^{3} +1.00000 q^{4} +2.86945 q^{5} -0.888297 q^{6} -2.14877 q^{7} -1.00000 q^{8} -2.21093 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.888297 q^{3} +1.00000 q^{4} +2.86945 q^{5} -0.888297 q^{6} -2.14877 q^{7} -1.00000 q^{8} -2.21093 q^{9} -2.86945 q^{10} +1.49534 q^{11} +0.888297 q^{12} +6.87552 q^{13} +2.14877 q^{14} +2.54892 q^{15} +1.00000 q^{16} -7.83113 q^{17} +2.21093 q^{18} -1.29905 q^{19} +2.86945 q^{20} -1.90874 q^{21} -1.49534 q^{22} +1.00000 q^{23} -0.888297 q^{24} +3.23375 q^{25} -6.87552 q^{26} -4.62885 q^{27} -2.14877 q^{28} +1.47143 q^{29} -2.54892 q^{30} -3.46846 q^{31} -1.00000 q^{32} +1.32830 q^{33} +7.83113 q^{34} -6.16579 q^{35} -2.21093 q^{36} -2.73694 q^{37} +1.29905 q^{38} +6.10750 q^{39} -2.86945 q^{40} -4.87402 q^{41} +1.90874 q^{42} -11.0010 q^{43} +1.49534 q^{44} -6.34415 q^{45} -1.00000 q^{46} -8.21227 q^{47} +0.888297 q^{48} -2.38279 q^{49} -3.23375 q^{50} -6.95636 q^{51} +6.87552 q^{52} +4.48371 q^{53} +4.62885 q^{54} +4.29080 q^{55} +2.14877 q^{56} -1.15394 q^{57} -1.47143 q^{58} -13.2162 q^{59} +2.54892 q^{60} -15.1592 q^{61} +3.46846 q^{62} +4.75078 q^{63} +1.00000 q^{64} +19.7290 q^{65} -1.32830 q^{66} +4.82253 q^{67} -7.83113 q^{68} +0.888297 q^{69} +6.16579 q^{70} +6.94757 q^{71} +2.21093 q^{72} +6.40200 q^{73} +2.73694 q^{74} +2.87253 q^{75} -1.29905 q^{76} -3.21314 q^{77} -6.10750 q^{78} +10.0257 q^{79} +2.86945 q^{80} +2.52100 q^{81} +4.87402 q^{82} +3.93987 q^{83} -1.90874 q^{84} -22.4710 q^{85} +11.0010 q^{86} +1.30707 q^{87} -1.49534 q^{88} +5.77611 q^{89} +6.34415 q^{90} -14.7739 q^{91} +1.00000 q^{92} -3.08102 q^{93} +8.21227 q^{94} -3.72755 q^{95} -0.888297 q^{96} +1.86419 q^{97} +2.38279 q^{98} -3.30609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	0.888297	0.512858	0.256429	−	0.966563i	$-0.417454\pi$
$3$	0.888297	0.512858	0.256429	+	0.966563i	$0.417454\pi$
$4$	1.00000	0.500000
$5$	2.86945	1.28326	0.641629	−	0.767015i	$-0.278259\pi$
$5$	2.86945	1.28326	0.641629	+	0.767015i	$0.278259\pi$
$6$	−0.888297	−0.362646
$7$	−2.14877	−0.812158	−0.406079	−	0.913838i	$-0.633104\pi$
$7$	−2.14877	−0.812158	−0.406079	+	0.913838i	$0.633104\pi$
$8$	−1.00000	−0.353553
$9$	−2.21093	−0.736976
$10$	−2.86945	−0.907400
$11$	1.49534	0.450862	0.225431	−	0.974259i	$-0.427621\pi$
$11$	1.49534	0.450862	0.225431	+	0.974259i	$0.427621\pi$
$12$	0.888297	0.256429
$13$	6.87552	1.90693	0.953463	−	0.301509i	$-0.0974902\pi$
$13$	6.87552	1.90693	0.953463	+	0.301509i	$0.0974902\pi$
$14$	2.14877	0.574283
$15$	2.54892	0.658129
$16$	1.00000	0.250000
$17$	−7.83113	−1.89933	−0.949664	−	0.313271i	$-0.898575\pi$
$17$	−7.83113	−1.89933	−0.949664	+	0.313271i	$0.898575\pi$
$18$	2.21093	0.521121
$19$	−1.29905	−0.298021	−0.149011	−	0.988836i	$-0.547609\pi$
$19$	−1.29905	−0.298021	−0.149011	+	0.988836i	$0.547609\pi$
$20$	2.86945	0.641629
$21$	−1.90874	−0.416522
$22$	−1.49534	−0.318807
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.888297	−0.181323
$25$	3.23375	0.646749
$26$	−6.87552	−1.34840
$27$	−4.62885	−0.890823
$28$	−2.14877	−0.406079
$29$	1.47143	0.273239	0.136619	−	0.990624i	$-0.456376\pi$
$29$	1.47143	0.273239	0.136619	+	0.990624i	$0.456376\pi$
$30$	−2.54892	−0.465368
$31$	−3.46846	−0.622953	−0.311477	−	0.950254i	$-0.600824\pi$
$31$	−3.46846	−0.622953	−0.311477	+	0.950254i	$0.600824\pi$
$32$	−1.00000	−0.176777
$33$	1.32830	0.231228
$34$	7.83113	1.34303
$35$	−6.16579	−1.04221
$36$	−2.21093	−0.368488
$37$	−2.73694	−0.449950	−0.224975	−	0.974365i	$-0.572230\pi$
$37$	−2.73694	−0.449950	−0.224975	+	0.974365i	$0.572230\pi$
$38$	1.29905	0.210733
$39$	6.10750	0.977983
$40$	−2.86945	−0.453700
$41$	−4.87402	−0.761193	−0.380597	−	0.924741i	$-0.624281\pi$
$41$	−4.87402	−0.761193	−0.380597	+	0.924741i	$0.624281\pi$
$42$	1.90874	0.294526
$43$	−11.0010	−1.67764	−0.838822	−	0.544406i	$-0.816755\pi$
$43$	−11.0010	−1.67764	−0.838822	+	0.544406i	$0.816755\pi$
$44$	1.49534	0.225431
$45$	−6.34415	−0.945730
$46$	−1.00000	−0.147442
$47$	−8.21227	−1.19788	−0.598941	−	0.800793i	$-0.704412\pi$
$47$	−8.21227	−1.19788	−0.598941	+	0.800793i	$0.704412\pi$
$48$	0.888297	0.128215
$49$	−2.38279	−0.340399
$50$	−3.23375	−0.457321
$51$	−6.95636	−0.974086
$52$	6.87552	0.953463
$53$	4.48371	0.615885	0.307943	−	0.951405i	$-0.400359\pi$
$53$	4.48371	0.615885	0.307943	+	0.951405i	$0.400359\pi$
$54$	4.62885	0.629907
$55$	4.29080	0.578571
$56$	2.14877	0.287141
$57$	−1.15394	−0.152843
$58$	−1.47143	−0.193209
$59$	−13.2162	−1.72060	−0.860301	−	0.509786i	$-0.829725\pi$
$59$	−13.2162	−1.72060	−0.860301	+	0.509786i	$0.829725\pi$
$60$	2.54892	0.329065
$61$	−15.1592	−1.94094	−0.970469	−	0.241227i	$-0.922450\pi$
$61$	−15.1592	−1.94094	−0.970469	+	0.241227i	$0.922450\pi$
$62$	3.46846	0.440494
$63$	4.75078	0.598541
$64$	1.00000	0.125000
$65$	19.7290	2.44708
$66$	−1.32830	−0.163503
$67$	4.82253	0.589165	0.294583	−	0.955626i	$-0.404819\pi$
$67$	4.82253	0.589165	0.294583	+	0.955626i	$0.404819\pi$
$68$	−7.83113	−0.949664
$69$	0.888297	0.106938
$70$	6.16579	0.736952
$71$	6.94757	0.824525	0.412262	−	0.911065i	$-0.364739\pi$
$71$	6.94757	0.824525	0.412262	+	0.911065i	$0.364739\pi$
$72$	2.21093	0.260561
$73$	6.40200	0.749297	0.374649	−	0.927167i	$-0.377763\pi$
$73$	6.40200	0.749297	0.374649	+	0.927167i	$0.377763\pi$
$74$	2.73694	0.318163
$75$	2.87253	0.331691
$76$	−1.29905	−0.149011
$77$	−3.21314	−0.366171
$78$	−6.10750	−0.691539
$79$	10.0257	1.12798	0.563989	−	0.825783i	$-0.309266\pi$
$79$	10.0257	1.12798	0.563989	+	0.825783i	$0.309266\pi$
$80$	2.86945	0.320814
$81$	2.52100	0.280111
$82$	4.87402	0.538245
$83$	3.93987	0.432457	0.216229	−	0.976343i	$-0.430624\pi$
$83$	3.93987	0.432457	0.216229	+	0.976343i	$0.430624\pi$
$84$	−1.90874	−0.208261
$85$	−22.4710	−2.43733
$86$	11.0010	1.18627
$87$	1.30707	0.140133
$88$	−1.49534	−0.159404
$89$	5.77611	0.612266	0.306133	−	0.951989i	$-0.400965\pi$
$89$	5.77611	0.612266	0.306133	+	0.951989i	$0.400965\pi$
$90$	6.34415	0.668732
$91$	−14.7739	−1.54873
$92$	1.00000	0.104257
$93$	−3.08102	−0.319487
$94$	8.21227	0.847031
$95$	−3.72755	−0.382438
$96$	−0.888297	−0.0906614
$97$	1.86419	0.189280	0.0946401	−	0.995512i	$-0.469830\pi$
$97$	1.86419	0.189280	0.0946401	+	0.995512i	$0.469830\pi$
$98$	2.38279	0.240698
$99$	−3.30609	−0.332274
$100$	3.23375	0.323375
$101$	12.4986	1.24366	0.621831	−	0.783152i	$-0.286389\pi$
$101$	12.4986	1.24366	0.621831	+	0.783152i	$0.286389\pi$
$102$	6.95636	0.688783
$103$	−13.5984	−1.33989	−0.669944	−	0.742412i	$-0.733682\pi$
$103$	−13.5984	−1.33989	−0.669944	+	0.742412i	$0.733682\pi$
$104$	−6.87552	−0.674200
$105$	−5.47705	−0.534505
$106$	−4.48371	−0.435497
$107$	−17.1357	−1.65657	−0.828283	−	0.560310i	$-0.810682\pi$
$107$	−17.1357	−1.65657	−0.828283	+	0.560310i	$0.810682\pi$
$108$	−4.62885	−0.445411
$109$	−8.95367	−0.857606	−0.428803	−	0.903398i	$-0.641065\pi$
$109$	−8.95367	−0.857606	−0.428803	+	0.903398i	$0.641065\pi$
$110$	−4.29080	−0.409112
$111$	−2.43121	−0.230761
$112$	−2.14877	−0.203040
$113$	14.9142	1.40301	0.701504	−	0.712666i	$-0.252512\pi$
$113$	14.9142	1.40301	0.701504	+	0.712666i	$0.252512\pi$
$114$	1.15394	0.108076
$115$	2.86945	0.267578
$116$	1.47143	0.136619
$117$	−15.2013	−1.40536
$118$	13.2162	1.21665
$119$	16.8273	1.54255
$120$	−2.54892	−0.232684
$121$	−8.76396	−0.796724
$122$	15.1592	1.37245
$123$	−4.32957	−0.390384
$124$	−3.46846	−0.311477
$125$	−5.06818	−0.453311
$126$	−4.75078	−0.423233
$127$	7.67595	0.681130	0.340565	−	0.940221i	$-0.389382\pi$
$127$	7.67595	0.681130	0.340565	+	0.940221i	$0.389382\pi$
$128$	−1.00000	−0.0883883
$129$	−9.77219	−0.860394
$130$	−19.7290	−1.73035
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.32830	0.115614
$133$	2.79135	0.242041
$134$	−4.82253	−0.416603
$135$	−13.2823	−1.14315
$136$	7.83113	0.671514
$137$	18.5406	1.58403	0.792015	−	0.610501i	$-0.209032\pi$
$137$	18.5406	1.58403	0.792015	+	0.610501i	$0.209032\pi$
$138$	−0.888297	−0.0756168
$139$	−4.23067	−0.358841	−0.179421	−	0.983772i	$-0.557422\pi$
$139$	−4.23067	−0.358841	−0.179421	+	0.983772i	$0.557422\pi$
$140$	−6.16579	−0.521104
$141$	−7.29493	−0.614344
$142$	−6.94757	−0.583027
$143$	10.2812	0.859760
$144$	−2.21093	−0.184244
$145$	4.22221	0.350635
$146$	−6.40200	−0.529833
$147$	−2.11663	−0.174576
$148$	−2.73694	−0.224975
$149$	−8.62805	−0.706838	−0.353419	−	0.935465i	$-0.614981\pi$
$149$	−8.62805	−0.706838	−0.353419	+	0.935465i	$0.614981\pi$
$150$	−2.87253	−0.234541
$151$	−10.7728	−0.876677	−0.438338	−	0.898810i	$-0.644433\pi$
$151$	−10.7728	−0.876677	−0.438338	+	0.898810i	$0.644433\pi$
$152$	1.29905	0.105366
$153$	17.3141	1.39976
$154$	3.21314	0.258922
$155$	−9.95256	−0.799409
$156$	6.10750	0.488992
$157$	−21.0032	−1.67624	−0.838119	−	0.545488i	$-0.816344\pi$
$157$	−21.0032	−1.67624	−0.838119	+	0.545488i	$0.816344\pi$
$158$	−10.0257	−0.797600
$159$	3.98287	0.315862
$160$	−2.86945	−0.226850
$161$	−2.14877	−0.169347
$162$	−2.52100	−0.198068
$163$	8.47783	0.664035	0.332017	−	0.943273i	$-0.392271\pi$
$163$	8.47783	0.664035	0.332017	+	0.943273i	$0.392271\pi$
$164$	−4.87402	−0.380597
$165$	3.81150	0.296725
$166$	−3.93987	−0.305793
$167$	−10.0875	−0.780591	−0.390295	−	0.920690i	$-0.627627\pi$
$167$	−10.0875	−0.780591	−0.390295	+	0.920690i	$0.627627\pi$
$168$	1.90874	0.147263
$169$	34.2728	2.63637
$170$	22.4710	1.72345
$171$	2.87210	0.219635
$172$	−11.0010	−0.838822
$173$	−9.40755	−0.715243	−0.357621	−	0.933867i	$-0.616412\pi$
$173$	−9.40755	−0.715243	−0.357621	+	0.933867i	$0.616412\pi$
$174$	−1.30707	−0.0990888
$175$	−6.94857	−0.525263
$176$	1.49534	0.112715
$177$	−11.7399	−0.882425
$178$	−5.77611	−0.432938
$179$	−5.52206	−0.412738	−0.206369	−	0.978474i	$-0.566165\pi$
$179$	−5.52206	−0.412738	−0.206369	+	0.978474i	$0.566165\pi$
$180$	−6.34415	−0.472865
$181$	22.0647	1.64006	0.820029	−	0.572322i	$-0.193957\pi$
$181$	22.0647	1.64006	0.820029	+	0.572322i	$0.193957\pi$
$182$	14.7739	1.09511
$183$	−13.4659	−0.995426
$184$	−1.00000	−0.0737210
$185$	−7.85351	−0.577402
$186$	3.08102	0.225911
$187$	−11.7102	−0.856334
$188$	−8.21227	−0.598941
$189$	9.94633	0.723489
$190$	3.72755	0.270425
$191$	8.60972	0.622977	0.311489	−	0.950250i	$-0.399172\pi$
$191$	8.60972	0.622977	0.311489	+	0.950250i	$0.399172\pi$
$192$	0.888297	0.0641073
$193$	3.34585	0.240839	0.120420	−	0.992723i	$-0.461576\pi$
$193$	3.34585	0.240839	0.120420	+	0.992723i	$0.461576\pi$
$194$	−1.86419	−0.133841
$195$	17.5252	1.25500
$196$	−2.38279	−0.170199
$197$	−12.2456	−0.872461	−0.436231	−	0.899835i	$-0.643687\pi$
$197$	−12.2456	−0.872461	−0.436231	+	0.899835i	$0.643687\pi$
$198$	3.30609	0.234953
$199$	10.2126	0.723954	0.361977	−	0.932187i	$-0.382102\pi$
$199$	10.2126	0.723954	0.361977	+	0.932187i	$0.382102\pi$
$200$	−3.23375	−0.228660
$201$	4.28383	0.302158
$202$	−12.4986	−0.879402
$203$	−3.16177	−0.221913
$204$	−6.95636	−0.487043
$205$	−13.9857	−0.976807
$206$	13.5984	0.947443
$207$	−2.21093	−0.153670
$208$	6.87552	0.476732
$209$	−1.94251	−0.134366
$210$	5.47705	0.377952
$211$	−0.973024	−0.0669857	−0.0334929	−	0.999439i	$-0.510663\pi$
$211$	−0.973024	−0.0669857	−0.0334929	+	0.999439i	$0.510663\pi$
$212$	4.48371	0.307943
$213$	6.17150	0.422864
$214$	17.1357	1.17137
$215$	−31.5670	−2.15285
$216$	4.62885	0.314953
$217$	7.45291	0.505937
$218$	8.95367	0.606419
$219$	5.68687	0.384283
$220$	4.29080	0.289286
$221$	−53.8431	−3.62188
$222$	2.43121	0.163172
$223$	−18.6577	−1.24941	−0.624707	−	0.780859i	$-0.714782\pi$
$223$	−18.6577	−1.24941	−0.624707	+	0.780859i	$0.714782\pi$
$224$	2.14877	0.143571
$225$	−7.14959	−0.476639
$226$	−14.9142	−0.992076
$227$	22.0065	1.46062	0.730311	−	0.683115i	$-0.239375\pi$
$227$	22.0065	1.46062	0.730311	+	0.683115i	$0.239375\pi$
$228$	−1.15394	−0.0764214
$229$	2.44656	0.161673	0.0808365	−	0.996727i	$-0.474241\pi$
$229$	2.44656	0.161673	0.0808365	+	0.996727i	$0.474241\pi$
$230$	−2.86945	−0.189206
$231$	−2.85422	−0.187794
$232$	−1.47143	−0.0966044
$233$	−19.5105	−1.27818	−0.639089	−	0.769133i	$-0.720689\pi$
$233$	−19.5105	−1.27818	−0.639089	+	0.769133i	$0.720689\pi$
$234$	15.2013	0.993740
$235$	−23.5647	−1.53719
$236$	−13.2162	−0.860301
$237$	8.90578	0.578492
$238$	−16.8273	−1.09075
$239$	−1.62909	−0.105377	−0.0526886	−	0.998611i	$-0.516779\pi$
$239$	−1.62909	−0.105377	−0.0526886	+	0.998611i	$0.516779\pi$
$240$	2.54892	0.164532
$241$	−3.21233	−0.206924	−0.103462	−	0.994633i	$-0.532992\pi$
$241$	−3.21233	−0.206924	−0.103462	+	0.994633i	$0.532992\pi$
$242$	8.76396	0.563369
$243$	16.1259	1.03448
$244$	−15.1592	−0.970469
$245$	−6.83731	−0.436819
$246$	4.32957	0.276043
$247$	−8.93162	−0.568305
$248$	3.46846	0.220247
$249$	3.49977	0.221789
$250$	5.06818	0.320540
$251$	−3.13627	−0.197960	−0.0989798	−	0.995089i	$-0.531558\pi$
$251$	−3.13627	−0.197960	−0.0989798	+	0.995089i	$0.531558\pi$
$252$	4.75078	0.299271
$253$	1.49534	0.0940111
$254$	−7.67595	−0.481632
$255$	−19.9609	−1.25000
$256$	1.00000	0.0625000
$257$	−23.5931	−1.47170	−0.735850	−	0.677145i	$-0.763217\pi$
$257$	−23.5931	−1.47170	−0.735850	+	0.677145i	$0.763217\pi$
$258$	9.77219	0.608390
$259$	5.88105	0.365431
$260$	19.7290	1.22354
$261$	−3.25324	−0.201370
$262$	−1.00000	−0.0617802
$263$	−2.85590	−0.176103	−0.0880513	−	0.996116i	$-0.528064\pi$
$263$	−2.85590	−0.176103	−0.0880513	+	0.996116i	$0.528064\pi$
$264$	−1.32830	−0.0817515
$265$	12.8658	0.790340
$266$	−2.79135	−0.171149
$267$	5.13090	0.314006
$268$	4.82253	0.294583
$269$	9.48661	0.578409	0.289205	−	0.957267i	$-0.406609\pi$
$269$	9.48661	0.578409	0.289205	+	0.957267i	$0.406609\pi$
$270$	13.2823	0.808332
$271$	−15.4057	−0.935831	−0.467916	−	0.883773i	$-0.654995\pi$
$271$	−15.4057	−0.935831	−0.467916	+	0.883773i	$0.654995\pi$
$272$	−7.83113	−0.474832
$273$	−13.1236	−0.794277
$274$	−18.5406	−1.12008
$275$	4.83555	0.291594
$276$	0.888297	0.0534692
$277$	−14.5217	−0.872526	−0.436263	−	0.899819i	$-0.643698\pi$
$277$	−14.5217	−0.872526	−0.436263	+	0.899819i	$0.643698\pi$
$278$	4.23067	0.253739
$279$	7.66851	0.459102
$280$	6.16579	0.368476
$281$	−24.5581	−1.46501	−0.732506	−	0.680760i	$-0.761649\pi$
$281$	−24.5581	−1.46501	−0.732506	+	0.680760i	$0.761649\pi$
$282$	7.29493	0.434407
$283$	3.98728	0.237019	0.118510	−	0.992953i	$-0.462188\pi$
$283$	3.98728	0.237019	0.118510	+	0.992953i	$0.462188\pi$
$284$	6.94757	0.412262
$285$	−3.31117	−0.196137
$286$	−10.2812	−0.607942
$287$	10.4731	0.618209
$288$	2.21093	0.130280
$289$	44.3266	2.60745
$290$	−4.22221	−0.247937
$291$	1.65596	0.0970739
$292$	6.40200	0.374649
$293$	31.0884	1.81620	0.908102	−	0.418750i	$-0.137532\pi$
$293$	31.0884	1.81620	0.908102	+	0.418750i	$0.137532\pi$
$294$	2.11663	0.123444
$295$	−37.9232	−2.20798
$296$	2.73694	0.159081
$297$	−6.92170	−0.401638
$298$	8.62805	0.499810
$299$	6.87552	0.397622
$300$	2.87253	0.165845
$301$	23.6387	1.36251
$302$	10.7728	0.619904
$303$	11.1025	0.637822
$304$	−1.29905	−0.0745054
$305$	−43.4986	−2.49072
$306$	−17.3141	−0.989780
$307$	22.5804	1.28873	0.644367	−	0.764716i	$-0.277121\pi$
$307$	22.5804	1.28873	0.644367	+	0.764716i	$0.277121\pi$
$308$	−3.21314	−0.183085
$309$	−12.0794	−0.687172
$310$	9.95256	0.565268
$311$	−31.1172	−1.76449	−0.882247	−	0.470788i	$-0.843970\pi$
$311$	−31.1172	−1.76449	−0.882247	+	0.470788i	$0.843970\pi$
$312$	−6.10750	−0.345769
$313$	−1.89128	−0.106902	−0.0534508	−	0.998570i	$-0.517022\pi$
$313$	−1.89128	−0.106902	−0.0534508	+	0.998570i	$0.517022\pi$
$314$	21.0032	1.18528
$315$	13.6321	0.768083
$316$	10.0257	0.563989
$317$	−14.8805	−0.835772	−0.417886	−	0.908500i	$-0.637229\pi$
$317$	−14.8805	−0.835772	−0.417886	+	0.908500i	$0.637229\pi$
$318$	−3.98287	−0.223348
$319$	2.20029	0.123193
$320$	2.86945	0.160407
$321$	−15.2215	−0.849584
$322$	2.14877	0.119746
$323$	10.1730	0.566040
$324$	2.52100	0.140055
$325$	22.2337	1.23330
$326$	−8.47783	−0.469543
$327$	−7.95351	−0.439830
$328$	4.87402	0.269122
$329$	17.6463	0.972871
$330$	−3.81150	−0.209816
$331$	20.6824	1.13681	0.568403	−	0.822750i	$-0.307561\pi$
$331$	20.6824	1.13681	0.568403	+	0.822750i	$0.307561\pi$
$332$	3.93987	0.216229
$333$	6.05118	0.331603
$334$	10.0875	0.551961
$335$	13.8380	0.756051
$336$	−1.90874	−0.104131
$337$	20.1008	1.09496	0.547479	−	0.836819i	$-0.315588\pi$
$337$	20.1008	1.09496	0.547479	+	0.836819i	$0.315588\pi$
$338$	−34.2728	−1.86420
$339$	13.2482	0.719544
$340$	−22.4710	−1.21866
$341$	−5.18652	−0.280866
$342$	−2.87210	−0.155305
$343$	20.1615	1.08862
$344$	11.0010	0.593137
$345$	2.54892	0.137229
$346$	9.40755	0.505753
$347$	2.12514	0.114084	0.0570418	−	0.998372i	$-0.481833\pi$
$347$	2.12514	0.114084	0.0570418	+	0.998372i	$0.481833\pi$
$348$	1.30707	0.0700663
$349$	−7.05857	−0.377837	−0.188918	−	0.981993i	$-0.560498\pi$
$349$	−7.05857	−0.377837	−0.188918	+	0.981993i	$0.560498\pi$
$350$	6.94857	0.371417
$351$	−31.8258	−1.69873
$352$	−1.49534	−0.0797018
$353$	33.8595	1.80216	0.901079	−	0.433655i	$-0.142776\pi$
$353$	33.8595	1.80216	0.901079	+	0.433655i	$0.142776\pi$
$354$	11.7399	0.623969
$355$	19.9357	1.05808
$356$	5.77611	0.306133
$357$	14.9476	0.791112
$358$	5.52206	0.291850
$359$	−18.6806	−0.985923	−0.492961	−	0.870051i	$-0.664086\pi$
$359$	−18.6806	−0.985923	−0.492961	+	0.870051i	$0.664086\pi$
$360$	6.34415	0.334366
$361$	−17.3125	−0.911183
$362$	−22.0647	−1.15970
$363$	−7.78500	−0.408606
$364$	−14.7739	−0.774363
$365$	18.3702	0.961541
$366$	13.4659	0.703872
$367$	23.7765	1.24112	0.620562	−	0.784158i	$-0.286905\pi$
$367$	23.7765	1.24112	0.620562	+	0.784158i	$0.286905\pi$
$368$	1.00000	0.0521286
$369$	10.7761	0.560981
$370$	7.85351	0.408285
$371$	−9.63446	−0.500196
$372$	−3.08102	−0.159743
$373$	14.5702	0.754417	0.377209	−	0.926128i	$-0.376884\pi$
$373$	14.5702	0.754417	0.377209	+	0.926128i	$0.376884\pi$
$374$	11.7102	0.605519
$375$	−4.50204	−0.232485
$376$	8.21227	0.423516
$377$	10.1169	0.521046
$378$	−9.94633	−0.511584
$379$	−29.3309	−1.50663	−0.753313	−	0.657662i	$-0.771546\pi$
$379$	−29.3309	−1.50663	−0.753313	+	0.657662i	$0.771546\pi$
$380$	−3.72755	−0.191219
$381$	6.81852	0.349323
$382$	−8.60972	−0.440511
$383$	4.49489	0.229678	0.114839	−	0.993384i	$-0.463365\pi$
$383$	4.49489	0.229678	0.114839	+	0.993384i	$0.463365\pi$
$384$	−0.888297	−0.0453307
$385$	−9.21994	−0.469891
$386$	−3.34585	−0.170299
$387$	24.3225	1.23638
$388$	1.86419	0.0946401
$389$	9.33414	0.473260	0.236630	−	0.971600i	$-0.423957\pi$
$389$	9.33414	0.473260	0.236630	+	0.971600i	$0.423957\pi$
$390$	−17.5252	−0.887422
$391$	−7.83113	−0.396037
$392$	2.38279	0.120349
$393$	0.888297	0.0448086
$394$	12.2456	0.616923
$395$	28.7682	1.44748
$396$	−3.30609	−0.166137
$397$	11.3514	0.569709	0.284855	−	0.958571i	$-0.408055\pi$
$397$	11.3514	0.569709	0.284855	+	0.958571i	$0.408055\pi$
$398$	−10.2126	−0.511913
$399$	2.47954	0.124133
$400$	3.23375	0.161687
$401$	5.72551	0.285918	0.142959	−	0.989729i	$-0.454338\pi$
$401$	5.72551	0.285918	0.142959	+	0.989729i	$0.454338\pi$
$402$	−4.28383	−0.213658
$403$	−23.8475	−1.18793
$404$	12.4986	0.621831
$405$	7.23387	0.359454
$406$	3.16177	0.156916
$407$	−4.09265	−0.202865
$408$	6.95636	0.344391
$409$	−17.5673	−0.868649	−0.434325	−	0.900756i	$-0.643013\pi$
$409$	−17.5673	−0.868649	−0.434325	+	0.900756i	$0.643013\pi$
$410$	13.9857	0.690707
$411$	16.4696	0.812383
$412$	−13.5984	−0.669944
$413$	28.3986	1.39740
$414$	2.21093	0.108661
$415$	11.3053	0.554954
$416$	−6.87552	−0.337100
$417$	−3.75809	−0.184035
$418$	1.94251	0.0950114
$419$	11.5650	0.564986	0.282493	−	0.959269i	$-0.408839\pi$
$419$	11.5650	0.564986	0.282493	+	0.959269i	$0.408839\pi$
$420$	−5.47705	−0.267252
$421$	−13.8651	−0.675742	−0.337871	−	0.941192i	$-0.609707\pi$
$421$	−13.8651	−0.675742	−0.337871	+	0.941192i	$0.609707\pi$
$422$	0.973024	0.0473661
$423$	18.1568	0.882811
$424$	−4.48371	−0.217748
$425$	−25.3239	−1.22839
$426$	−6.17150	−0.299010
$427$	32.5736	1.57635
$428$	−17.1357	−0.828283
$429$	9.13278	0.440935
$430$	31.5670	1.52229
$431$	−5.17016	−0.249038	−0.124519	−	0.992217i	$-0.539739\pi$
$431$	−5.17016	−0.249038	−0.124519	+	0.992217i	$0.539739\pi$
$432$	−4.62885	−0.222706
$433$	−17.3921	−0.835812	−0.417906	−	0.908490i	$-0.637236\pi$
$433$	−17.3921	−0.835812	−0.417906	+	0.908490i	$0.637236\pi$
$434$	−7.45291	−0.357751
$435$	3.75057	0.179826
$436$	−8.95367	−0.428803
$437$	−1.29905	−0.0621418
$438$	−5.68687	−0.271729
$439$	−30.9740	−1.47831	−0.739154	−	0.673536i	$-0.764775\pi$
$439$	−30.9740	−1.47831	−0.739154	+	0.673536i	$0.764775\pi$
$440$	−4.29080	−0.204556
$441$	5.26819	0.250866
$442$	53.8431	2.56106
$443$	−11.3353	−0.538557	−0.269278	−	0.963062i	$-0.586785\pi$
$443$	−11.3353	−0.538557	−0.269278	+	0.963062i	$0.586785\pi$
$444$	−2.43121	−0.115380
$445$	16.5743	0.785695
$446$	18.6577	0.883470
$447$	−7.66427	−0.362507
$448$	−2.14877	−0.101520
$449$	21.6997	1.02407	0.512035	−	0.858964i	$-0.328892\pi$
$449$	21.6997	1.02407	0.512035	+	0.858964i	$0.328892\pi$
$450$	7.14959	0.337035
$451$	−7.28830	−0.343193
$452$	14.9142	0.701504
$453$	−9.56943	−0.449611
$454$	−22.0065	−1.03282
$455$	−42.3930	−1.98741
$456$	1.15394	0.0540381
$457$	25.3923	1.18780	0.593902	−	0.804537i	$-0.297587\pi$
$457$	25.3923	1.18780	0.593902	+	0.804537i	$0.297587\pi$
$458$	−2.44656	−0.114320
$459$	36.2491	1.69196
$460$	2.86945	0.133789
$461$	35.7182	1.66356	0.831782	−	0.555102i	$-0.187321\pi$
$461$	35.7182	1.66356	0.831782	+	0.555102i	$0.187321\pi$
$462$	2.85422	0.132790
$463$	−36.2088	−1.68276	−0.841382	−	0.540441i	$-0.818257\pi$
$463$	−36.2088	−1.68276	−0.841382	+	0.540441i	$0.818257\pi$
$464$	1.47143	0.0683096
$465$	−8.84083	−0.409984
$466$	19.5105	0.903809
$467$	−6.50101	−0.300831	−0.150415	−	0.988623i	$-0.548061\pi$
$467$	−6.50101	−0.300831	−0.150415	+	0.988623i	$0.548061\pi$
$468$	−15.2013	−0.702680
$469$	−10.3625	−0.478496
$470$	23.5647	1.08696
$471$	−18.6571	−0.859672
$472$	13.2162	0.608325
$473$	−16.4503	−0.756385
$474$	−8.90578	−0.409056
$475$	−4.20078	−0.192745
$476$	16.8273	0.771277
$477$	−9.91317	−0.453893
$478$	1.62909	0.0745130
$479$	4.84459	0.221355	0.110678	−	0.993856i	$-0.464698\pi$
$479$	4.84459	0.221355	0.110678	+	0.993856i	$0.464698\pi$
$480$	−2.54892	−0.116342
$481$	−18.8179	−0.858022
$482$	3.21233	0.146318
$483$	−1.90874	−0.0868509
$484$	−8.76396	−0.398362
$485$	5.34921	0.242895
$486$	−16.1259	−0.731488
$487$	−15.0083	−0.680089	−0.340045	−	0.940409i	$-0.610442\pi$
$487$	−15.0083	−0.680089	−0.340045	+	0.940409i	$0.610442\pi$
$488$	15.1592	0.686225
$489$	7.53082	0.340556
$490$	6.83731	0.308878
$491$	−33.5653	−1.51478	−0.757390	−	0.652963i	$-0.773526\pi$
$491$	−33.5653	−1.51478	−0.757390	+	0.652963i	$0.773526\pi$
$492$	−4.32957	−0.195192
$493$	−11.5230	−0.518970
$494$	8.93162	0.401852
$495$	−9.48665	−0.426393
$496$	−3.46846	−0.155738
$497$	−14.9287	−0.669645
$498$	−3.49977	−0.156829
$499$	−28.2709	−1.26558	−0.632790	−	0.774323i	$-0.718090\pi$
$499$	−28.2709	−1.26558	−0.632790	+	0.774323i	$0.718090\pi$
$500$	−5.06818	−0.226656
$501$	−8.96065	−0.400332
$502$	3.13627	0.139979
$503$	22.9481	1.02321	0.511603	−	0.859222i	$-0.329052\pi$
$503$	22.9481	1.02321	0.511603	+	0.859222i	$0.329052\pi$
$504$	−4.75078	−0.211616
$505$	35.8642	1.59594
$506$	−1.49534	−0.0664759
$507$	30.4444	1.35208
$508$	7.67595	0.340565
$509$	8.27061	0.366589	0.183294	−	0.983058i	$-0.441324\pi$
$509$	8.27061	0.366589	0.183294	+	0.983058i	$0.441324\pi$
$510$	19.9609	0.883885
$511$	−13.7564	−0.608548
$512$	−1.00000	−0.0441942
$513$	6.01309	0.265484
$514$	23.5931	1.04065
$515$	−39.0199	−1.71942
$516$	−9.77219	−0.430197
$517$	−12.2801	−0.540079
$518$	−5.88105	−0.258398
$519$	−8.35670	−0.366818
$520$	−19.7290	−0.865173
$521$	−13.4327	−0.588499	−0.294249	−	0.955729i	$-0.595070\pi$
$521$	−13.4327	−0.588499	−0.294249	+	0.955729i	$0.595070\pi$
$522$	3.25324	0.142390
$523$	−23.0682	−1.00870	−0.504351	−	0.863499i	$-0.668268\pi$
$523$	−23.0682	−1.00870	−0.504351	+	0.863499i	$0.668268\pi$
$524$	1.00000	0.0436852
$525$	−6.17239	−0.269385
$526$	2.85590	0.124523
$527$	27.1619	1.18319
$528$	1.32830	0.0578070
$529$	1.00000	0.0434783
$530$	−12.8658	−0.558854
$531$	29.2201	1.26804
$532$	2.79135	0.121020
$533$	−33.5114	−1.45154
$534$	−5.13090	−0.222036
$535$	−49.1699	−2.12580
$536$	−4.82253	−0.208301
$537$	−4.90523	−0.211676
$538$	−9.48661	−0.408997
$539$	−3.56308	−0.153473
$540$	−13.2823	−0.571577
$541$	−8.41824	−0.361928	−0.180964	−	0.983490i	$-0.557922\pi$
$541$	−8.41824	−0.361928	−0.180964	+	0.983490i	$0.557922\pi$
$542$	15.4057	0.661733
$543$	19.6000	0.841117
$544$	7.83113	0.335757
$545$	−25.6921	−1.10053
$546$	13.1236	0.561639
$547$	7.70236	0.329329	0.164665	−	0.986350i	$-0.447346\pi$
$547$	7.70236	0.329329	0.164665	+	0.986350i	$0.447346\pi$
$548$	18.5406	0.792015
$549$	33.5159	1.43043
$550$	−4.83555	−0.206188
$551$	−1.91146	−0.0814310
$552$	−0.888297	−0.0378084
$553$	−21.5429	−0.916096
$554$	14.5217	0.616969
$555$	−6.97625	−0.296125
$556$	−4.23067	−0.179421
$557$	−11.2718	−0.477602	−0.238801	−	0.971068i	$-0.576754\pi$
$557$	−11.2718	−0.477602	−0.238801	+	0.971068i	$0.576754\pi$
$558$	−7.66851	−0.324634
$559$	−75.6380	−3.19914
$560$	−6.16579	−0.260552
$561$	−10.4021	−0.439178
$562$	24.5581	1.03592
$563$	−15.9068	−0.670393	−0.335196	−	0.942148i	$-0.608803\pi$
$563$	−15.9068	−0.670393	−0.335196	+	0.942148i	$0.608803\pi$
$564$	−7.29493	−0.307172
$565$	42.7955	1.80042
$566$	−3.98728	−0.167598
$567$	−5.41704	−0.227494
$568$	−6.94757	−0.291514
$569$	36.2453	1.51948	0.759742	−	0.650225i	$-0.225325\pi$
$569$	36.2453	1.51948	0.759742	+	0.650225i	$0.225325\pi$
$570$	3.31117	0.138690
$571$	23.7119	0.992311	0.496155	−	0.868234i	$-0.334745\pi$
$571$	23.7119	0.992311	0.496155	+	0.868234i	$0.334745\pi$
$572$	10.2812	0.429880
$573$	7.64798	0.319499
$574$	−10.4731	−0.437140
$575$	3.23375	0.134857
$576$	−2.21093	−0.0921221
$577$	9.34963	0.389230	0.194615	−	0.980880i	$-0.437654\pi$
$577$	9.34963	0.389230	0.194615	+	0.980880i	$0.437654\pi$
$578$	−44.3266	−1.84374
$579$	2.97210	0.123516
$580$	4.22221	0.175318
$581$	−8.46587	−0.351224
$582$	−1.65596	−0.0686416
$583$	6.70467	0.277679
$584$	−6.40200	−0.264917
$585$	−43.6194	−1.80344
$586$	−31.0884	−1.28425
$587$	−21.2709	−0.877944	−0.438972	−	0.898501i	$-0.644657\pi$
$587$	−21.2709	−0.877944	−0.438972	+	0.898501i	$0.644657\pi$
$588$	−2.11663	−0.0872882
$589$	4.50568	0.185653
$590$	37.9232	1.56127
$591$	−10.8777	−0.447449
$592$	−2.73694	−0.112488
$593$	16.1332	0.662509	0.331255	−	0.943541i	$-0.392528\pi$
$593$	16.1332	0.662509	0.331255	+	0.943541i	$0.392528\pi$
$594$	6.92170	0.284001
$595$	48.2851	1.97949
$596$	−8.62805	−0.353419
$597$	9.07185	0.371286
$598$	−6.87552	−0.281161
$599$	36.7174	1.50023	0.750116	−	0.661306i	$-0.229998\pi$
$599$	36.7174	1.50023	0.750116	+	0.661306i	$0.229998\pi$
$600$	−2.87253	−0.117270
$601$	−35.4335	−1.44536	−0.722681	−	0.691182i	$-0.757090\pi$
$601$	−35.4335	−1.44536	−0.722681	+	0.691182i	$0.757090\pi$
$602$	−23.6387	−0.963442
$603$	−10.6623	−0.434201
$604$	−10.7728	−0.438338
$605$	−25.1478	−1.02240
$606$	−11.1025	−0.451008
$607$	−1.18066	−0.0479217	−0.0239608	−	0.999713i	$-0.507628\pi$
$607$	−1.18066	−0.0479217	−0.0239608	+	0.999713i	$0.507628\pi$
$608$	1.29905	0.0526832
$609$	−2.80859	−0.113810
$610$	43.4986	1.76121
$611$	−56.4637	−2.28428
$612$	17.3141	0.699880
$613$	−2.46986	−0.0997566	−0.0498783	−	0.998755i	$-0.515883\pi$
$613$	−2.46986	−0.0997566	−0.0498783	+	0.998755i	$0.515883\pi$
$614$	−22.5804	−0.911273
$615$	−12.4235	−0.500963
$616$	3.21314	0.129461
$617$	19.7654	0.795726	0.397863	−	0.917445i	$-0.369752\pi$
$617$	19.7654	0.795726	0.397863	+	0.917445i	$0.369752\pi$
$618$	12.0794	0.485904
$619$	5.19737	0.208900	0.104450	−	0.994530i	$-0.466692\pi$
$619$	5.19737	0.208900	0.104450	+	0.994530i	$0.466692\pi$
$620$	−9.95256	−0.399705
$621$	−4.62885	−0.185749
$622$	31.1172	1.24768
$623$	−12.4115	−0.497257
$624$	6.10750	0.244496
$625$	−30.7116	−1.22846
$626$	1.89128	0.0755909
$627$	−1.72553	−0.0689109
$628$	−21.0032	−0.838119
$629$	21.4333	0.854603
$630$	−13.6321	−0.543117
$631$	−16.4053	−0.653086	−0.326543	−	0.945182i	$-0.605884\pi$
$631$	−16.4053	−0.653086	−0.326543	+	0.945182i	$0.605884\pi$
$632$	−10.0257	−0.398800
$633$	−0.864334	−0.0343542
$634$	14.8805	0.590980
$635$	22.0257	0.874065
$636$	3.98287	0.157931
$637$	−16.3829	−0.649116
$638$	−2.20029	−0.0871104
$639$	−15.3606	−0.607655
$640$	−2.86945	−0.113425
$641$	16.1098	0.636300	0.318150	−	0.948040i	$-0.396938\pi$
$641$	16.1098	0.636300	0.318150	+	0.948040i	$0.396938\pi$
$642$	15.2215	0.600746
$643$	5.83140	0.229968	0.114984	−	0.993367i	$-0.463318\pi$
$643$	5.83140	0.229968	0.114984	+	0.993367i	$0.463318\pi$
$644$	−2.14877	−0.0846734
$645$	−28.0408	−1.10411
$646$	−10.1730	−0.400251
$647$	18.5538	0.729426	0.364713	−	0.931120i	$-0.381167\pi$
$647$	18.5538	0.729426	0.364713	+	0.931120i	$0.381167\pi$
$648$	−2.52100	−0.0990341
$649$	−19.7627	−0.775754
$650$	−22.2337	−0.872077
$651$	6.62040	0.259474
$652$	8.47783	0.332017
$653$	−12.6599	−0.495421	−0.247710	−	0.968834i	$-0.579678\pi$
$653$	−12.6599	−0.495421	−0.247710	+	0.968834i	$0.579678\pi$
$654$	7.95351	0.311007
$655$	2.86945	0.112119
$656$	−4.87402	−0.190298
$657$	−14.1544	−0.552214
$658$	−17.6463	−0.687923
$659$	−13.8286	−0.538687	−0.269344	−	0.963044i	$-0.586807\pi$
$659$	−13.8286	−0.538687	−0.269344	+	0.963044i	$0.586807\pi$
$660$	3.81150	0.148363
$661$	36.9623	1.43767	0.718833	−	0.695183i	$-0.244677\pi$
$661$	36.9623	1.43767	0.718833	+	0.695183i	$0.244677\pi$
$662$	−20.6824	−0.803844
$663$	−47.8286	−1.85751
$664$	−3.93987	−0.152897
$665$	8.00964	0.310600
$666$	−6.05118	−0.234478
$667$	1.47143	0.0569742
$668$	−10.0875	−0.390295
$669$	−16.5736	−0.640773
$670$	−13.8380	−0.534609
$671$	−22.6681	−0.875094
$672$	1.90874	0.0736314
$673$	−39.0563	−1.50551	−0.752755	−	0.658300i	$-0.771276\pi$
$673$	−39.0563	−1.50551	−0.752755	+	0.658300i	$0.771276\pi$
$674$	−20.1008	−0.774252
$675$	−14.9685	−0.576139
$676$	34.2728	1.31819
$677$	−3.90091	−0.149924	−0.0749621	−	0.997186i	$-0.523884\pi$
$677$	−3.90091	−0.149924	−0.0749621	+	0.997186i	$0.523884\pi$
$678$	−13.2482	−0.508794
$679$	−4.00572	−0.153725
$680$	22.4710	0.861725
$681$	19.5483	0.749092
$682$	5.18652	0.198602
$683$	−22.1783	−0.848629	−0.424314	−	0.905515i	$-0.639485\pi$
$683$	−22.1783	−0.848629	−0.424314	+	0.905515i	$0.639485\pi$
$684$	2.87210	0.109817
$685$	53.2013	2.03272
$686$	−20.1615	−0.769768
$687$	2.17327	0.0829153
$688$	−11.0010	−0.419411
$689$	30.8279	1.17445
$690$	−2.54892	−0.0970358
$691$	−11.3886	−0.433241	−0.216621	−	0.976256i	$-0.569503\pi$
$691$	−11.3886	−0.433241	−0.216621	+	0.976256i	$0.569503\pi$
$692$	−9.40755	−0.357621
$693$	7.10402	0.269859
$694$	−2.12514	−0.0806693
$695$	−12.1397	−0.460486
$696$	−1.30707	−0.0495444
$697$	38.1690	1.44576
$698$	7.05857	0.267171
$699$	−17.3312	−0.655524
$700$	−6.94857	−0.262631
$701$	−20.5642	−0.776697	−0.388349	−	0.921512i	$-0.626954\pi$
$701$	−20.5642	−0.776697	−0.388349	+	0.921512i	$0.626954\pi$
$702$	31.8258	1.20119
$703$	3.55541	0.134095
$704$	1.49534	0.0563577
$705$	−20.9324	−0.788362
$706$	−33.8595	−1.27432
$707$	−26.8567	−1.01005
$708$	−11.7399	−0.441213
$709$	−35.5163	−1.33384	−0.666921	−	0.745128i	$-0.732388\pi$
$709$	−35.5163	−1.33384	−0.666921	+	0.745128i	$0.732388\pi$
$710$	−19.9357	−0.748174
$711$	−22.1661	−0.831293
$712$	−5.77611	−0.216469
$713$	−3.46846	−0.129895
$714$	−14.9476	−0.559401
$715$	29.5015	1.10329
$716$	−5.52206	−0.206369
$717$	−1.44712	−0.0540436
$718$	18.6806	0.697153
$719$	6.76104	0.252144	0.126072	−	0.992021i	$-0.459763\pi$
$719$	6.76104	0.252144	0.126072	+	0.992021i	$0.459763\pi$
$720$	−6.34415	−0.236433
$721$	29.2198	1.08820
$722$	17.3125	0.644304
$723$	−2.85350	−0.106123
$724$	22.0647	0.820029
$725$	4.75825	0.176717
$726$	7.78500	0.288928
$727$	−37.4105	−1.38748	−0.693740	−	0.720226i	$-0.744038\pi$
$727$	−37.4105	−1.38748	−0.693740	+	0.720226i	$0.744038\pi$
$728$	14.7739	0.547557
$729$	6.76163	0.250431
$730$	−18.3702	−0.679912
$731$	86.1506	3.18640
$732$	−13.4659	−0.497713
$733$	−2.66065	−0.0982733	−0.0491366	−	0.998792i	$-0.515647\pi$
$733$	−2.66065	−0.0982733	−0.0491366	+	0.998792i	$0.515647\pi$
$734$	−23.7765	−0.877607
$735$	−6.07355	−0.224026
$736$	−1.00000	−0.0368605
$737$	7.21131	0.265632
$738$	−10.7761	−0.396674
$739$	10.1172	0.372167	0.186084	−	0.982534i	$-0.440420\pi$
$739$	10.1172	0.372167	0.186084	+	0.982534i	$0.440420\pi$
$740$	−7.85351	−0.288701
$741$	−7.93392	−0.291460
$742$	9.63446	0.353692
$743$	29.0855	1.06704	0.533521	−	0.845787i	$-0.320868\pi$
$743$	29.0855	1.06704	0.533521	+	0.845787i	$0.320868\pi$
$744$	3.08102	0.112956
$745$	−24.7578	−0.907055
$746$	−14.5702	−0.533453
$747$	−8.71078	−0.318711
$748$	−11.7102	−0.428167
$749$	36.8206	1.34539
$750$	4.50204	0.164391
$751$	−38.4742	−1.40395	−0.701973	−	0.712204i	$-0.747697\pi$
$751$	−38.4742	−1.40395	−0.701973	+	0.712204i	$0.747697\pi$
$752$	−8.21227	−0.299471
$753$	−2.78594	−0.101525
$754$	−10.1169	−0.368435
$755$	−30.9120	−1.12500
$756$	9.94633	0.361745
$757$	−21.1410	−0.768381	−0.384191	−	0.923254i	$-0.625519\pi$
$757$	−21.1410	−0.768381	−0.384191	+	0.923254i	$0.625519\pi$
$758$	29.3309	1.06535
$759$	1.32830	0.0482144
$760$	3.72755	0.135212
$761$	38.5314	1.39676	0.698381	−	0.715726i	$-0.253904\pi$
$761$	38.5314	1.39676	0.698381	+	0.715726i	$0.253904\pi$
$762$	−6.81852	−0.247009
$763$	19.2394	0.696512
$764$	8.60972	0.311489
$765$	49.6819	1.79625
$766$	−4.49489	−0.162407
$767$	−90.8683	−3.28106
$768$	0.888297	0.0320536
$769$	37.6293	1.35695	0.678474	−	0.734625i	$-0.262642\pi$
$769$	37.6293	1.35695	0.678474	+	0.734625i	$0.262642\pi$
$770$	9.21994	0.332263
$771$	−20.9577	−0.754773
$772$	3.34585	0.120420
$773$	38.6786	1.39117	0.695586	−	0.718442i	$-0.255145\pi$
$773$	38.6786	1.39117	0.695586	+	0.718442i	$0.255145\pi$
$774$	−24.3225	−0.874256
$775$	−11.2161	−0.402895
$776$	−1.86419	−0.0669207
$777$	5.22412	0.187414
$778$	−9.33414	−0.334645
$779$	6.33157	0.226852
$780$	17.5252	0.627502
$781$	10.3890	0.371747
$782$	7.83113	0.280041
$783$	−6.81105	−0.243407
$784$	−2.38279	−0.0850997
$785$	−60.2676	−2.15104
$786$	−0.888297	−0.0316845
$787$	0.621240	0.0221448	0.0110724	−	0.999939i	$-0.496475\pi$
$787$	0.621240	0.0221448	0.0110724	+	0.999939i	$0.496475\pi$
$788$	−12.2456	−0.436231
$789$	−2.53689	−0.0903157
$790$	−28.7682	−1.02353
$791$	−32.0471	−1.13946
$792$	3.30609	0.117477
$793$	−104.227	−3.70123
$794$	−11.3514	−0.402845
$795$	11.4286	0.405332
$796$	10.2126	0.361977
$797$	−49.1968	−1.74264	−0.871320	−	0.490716i	$-0.836735\pi$
$797$	−49.1968	−1.74264	−0.871320	+	0.490716i	$0.836735\pi$
$798$	−2.47954	−0.0877749
$799$	64.3114	2.27517
$800$	−3.23375	−0.114330
$801$	−12.7706	−0.451226
$802$	−5.72551	−0.202175
$803$	9.57316	0.337829
$804$	4.28383	0.151079
$805$	−6.16579	−0.217315
$806$	23.8475	0.839991
$807$	8.42693	0.296642
$808$	−12.4986	−0.439701
$809$	−4.30605	−0.151393	−0.0756964	−	0.997131i	$-0.524118\pi$
$809$	−4.30605	−0.151393	−0.0756964	+	0.997131i	$0.524118\pi$
$810$	−7.23387	−0.254172
$811$	10.5130	0.369161	0.184581	−	0.982817i	$-0.440907\pi$
$811$	10.5130	0.369161	0.184581	+	0.982817i	$0.440907\pi$
$812$	−3.16177	−0.110956
$813$	−13.6849	−0.479949
$814$	4.09265	0.143447
$815$	24.3267	0.852127
$816$	−6.95636	−0.243521
$817$	14.2909	0.499974
$818$	17.5673	0.614228
$819$	32.6641	1.14137
$820$	−13.9857	−0.488403
$821$	−14.8357	−0.517769	−0.258885	−	0.965908i	$-0.583355\pi$
$821$	−14.8357	−0.517769	−0.258885	+	0.965908i	$0.583355\pi$
$822$	−16.4696	−0.574442
$823$	−10.0718	−0.351083	−0.175541	−	0.984472i	$-0.556168\pi$
$823$	−10.0718	−0.351083	−0.175541	+	0.984472i	$0.556168\pi$
$824$	13.5984	0.473722
$825$	4.29540	0.149547
$826$	−28.3986	−0.988112
$827$	−40.8248	−1.41962	−0.709809	−	0.704395i	$-0.751219\pi$
$827$	−40.8248	−1.41962	−0.709809	+	0.704395i	$0.751219\pi$
$828$	−2.21093	−0.0768351
$829$	27.6272	0.959533	0.479766	−	0.877396i	$-0.340721\pi$
$829$	27.6272	0.959533	0.479766	+	0.877396i	$0.340721\pi$
$830$	−11.3053	−0.392412
$831$	−12.8996	−0.447482
$832$	6.87552	0.238366
$833$	18.6600	0.646529
$834$	3.75809	0.130132
$835$	−28.9454	−1.00170
$836$	−1.94251	−0.0671832
$837$	16.0550	0.554941
$838$	−11.5650	−0.399505
$839$	−23.3755	−0.807012	−0.403506	−	0.914977i	$-0.632209\pi$
$839$	−23.3755	−0.807012	−0.403506	+	0.914977i	$0.632209\pi$
$840$	5.47705	0.188976
$841$	−26.8349	−0.925341
$842$	13.8651	0.477822
$843$	−21.8149	−0.751344
$844$	−0.973024	−0.0334929
$845$	98.3441	3.38314
$846$	−18.1568	−0.624242
$847$	18.8317	0.647066
$848$	4.48371	0.153971
$849$	3.54189	0.121557
$850$	25.3239	0.868602
$851$	−2.73694	−0.0938211
$852$	6.17150	0.211432
$853$	−49.3008	−1.68803	−0.844014	−	0.536321i	$-0.819814\pi$
$853$	−49.3008	−1.68803	−0.844014	+	0.536321i	$0.819814\pi$
$854$	−32.5736	−1.11465
$855$	8.24134	0.281848
$856$	17.1357	0.585685
$857$	8.78162	0.299975	0.149987	−	0.988688i	$-0.452077\pi$
$857$	8.78162	0.299975	0.149987	+	0.988688i	$0.452077\pi$
$858$	−9.13278	−0.311788
$859$	−57.7972	−1.97202	−0.986008	−	0.166701i	$-0.946689\pi$
$859$	−57.7972	−1.97202	−0.986008	+	0.166701i	$0.946689\pi$
$860$	−31.5670	−1.07642
$861$	9.30325	0.317054
$862$	5.17016	0.176096
$863$	−28.6663	−0.975812	−0.487906	−	0.872896i	$-0.662239\pi$
$863$	−28.6663	−0.975812	−0.487906	+	0.872896i	$0.662239\pi$
$864$	4.62885	0.157477
$865$	−26.9945	−0.917841
$866$	17.3921	0.591009
$867$	39.3751	1.33725
$868$	7.45291	0.252968
$869$	14.9918	0.508561
$870$	−3.75057	−0.127156
$871$	33.1574	1.12350
$872$	8.95367	0.303210
$873$	−4.12160	−0.139495
$874$	1.29905	0.0439409
$875$	10.8903	0.368161
$876$	5.68687	0.192142
$877$	22.9529	0.775063	0.387532	−	0.921856i	$-0.373328\pi$
$877$	22.9529	0.775063	0.387532	+	0.921856i	$0.373328\pi$
$878$	30.9740	1.04532
$879$	27.6157	0.931455
$880$	4.29080	0.144643
$881$	11.3285	0.381665	0.190833	−	0.981623i	$-0.438881\pi$
$881$	11.3285	0.381665	0.190833	+	0.981623i	$0.438881\pi$
$882$	−5.26819	−0.177389
$883$	−10.5768	−0.355939	−0.177970	−	0.984036i	$-0.556953\pi$
$883$	−10.5768	−0.355939	−0.177970	+	0.984036i	$0.556953\pi$
$884$	−53.8431	−1.81094
$885$	−33.6871	−1.13238
$886$	11.3353	0.380817
$887$	15.3868	0.516639	0.258319	−	0.966060i	$-0.416831\pi$
$887$	15.3868	0.516639	0.258319	+	0.966060i	$0.416831\pi$
$888$	2.43121	0.0815862
$889$	−16.4938	−0.553185
$890$	−16.5743	−0.555571
$891$	3.76974	0.126291
$892$	−18.6577	−0.624707
$893$	10.6681	0.356995
$894$	7.66427	0.256332
$895$	−15.8453	−0.529649
$896$	2.14877	0.0717853
$897$	6.10750	0.203924
$898$	−21.6997	−0.724128
$899$	−5.10361	−0.170215
$900$	−7.14959	−0.238320
$901$	−35.1125	−1.16977
$902$	7.28830	0.242674
$903$	20.9982	0.698776
$904$	−14.9142	−0.496038
$905$	63.3136	2.10462
$906$	9.56943	0.317923
$907$	16.0984	0.534540	0.267270	−	0.963622i	$-0.413878\pi$
$907$	16.0984	0.534540	0.267270	+	0.963622i	$0.413878\pi$
$908$	22.0065	0.730311
$909$	−27.6336	−0.916549
$910$	42.3930	1.40531
$911$	−41.5425	−1.37636	−0.688182	−	0.725538i	$-0.741591\pi$
$911$	−41.5425	−1.37636	−0.688182	+	0.725538i	$0.741591\pi$
$912$	−1.15394	−0.0382107
$913$	5.89144	0.194978
$914$	−25.3923	−0.839904
$915$	−38.6397	−1.27739
$916$	2.44656	0.0808365
$917$	−2.14877	−0.0709586
$918$	−36.2491	−1.19640
$919$	−13.2529	−0.437173	−0.218586	−	0.975818i	$-0.570145\pi$
$919$	−13.2529	−0.437173	−0.218586	+	0.975818i	$0.570145\pi$
$920$	−2.86945	−0.0946030
$921$	20.0581	0.660938
$922$	−35.7182	−1.17632
$923$	47.7682	1.57231
$924$	−2.85422	−0.0938969
$925$	−8.85057	−0.291005
$926$	36.2088	1.18989
$927$	30.0650	0.987465
$928$	−1.47143	−0.0483022
$929$	−7.76446	−0.254744	−0.127372	−	0.991855i	$-0.540654\pi$
$929$	−7.76446	−0.254744	−0.127372	+	0.991855i	$0.540654\pi$
$930$	8.84083	0.289902
$931$	3.09536	0.101446
$932$	−19.5105	−0.639089
$933$	−27.6413	−0.904935
$934$	6.50101	0.212719
$935$	−33.6018	−1.09890
$936$	15.2013	0.496870
$937$	−7.15902	−0.233875	−0.116938	−	0.993139i	$-0.537308\pi$
$937$	−7.15902	−0.233875	−0.116938	+	0.993139i	$0.537308\pi$
$938$	10.3625	0.338347
$939$	−1.68002	−0.0548254
$940$	−23.5647	−0.768596
$941$	45.9779	1.49884	0.749418	−	0.662097i	$-0.230334\pi$
$941$	45.9779	1.49884	0.749418	+	0.662097i	$0.230334\pi$
$942$	18.6571	0.607880
$943$	−4.87402	−0.158720
$944$	−13.2162	−0.430151
$945$	28.5405	0.928423
$946$	16.4503	0.534845
$947$	4.68722	0.152314	0.0761571	−	0.997096i	$-0.475735\pi$
$947$	4.68722	0.152314	0.0761571	+	0.997096i	$0.475735\pi$
$948$	8.90578	0.289246
$949$	44.0171	1.42886
$950$	4.20078	0.136291
$951$	−13.2183	−0.428632
$952$	−16.8273	−0.545375
$953$	48.2781	1.56388	0.781940	−	0.623354i	$-0.214230\pi$
$953$	48.2781	1.56388	0.781940	+	0.623354i	$0.214230\pi$
$954$	9.91317	0.320951
$955$	24.7052	0.799440
$956$	−1.62909	−0.0526886
$957$	1.95451	0.0631804
$958$	−4.84459	−0.156522
$959$	−39.8395	−1.28648
$960$	2.54892	0.0822661
$961$	−18.9698	−0.611929
$962$	18.8179	0.606713
$963$	37.8857	1.22085
$964$	−3.21233	−0.103462
$965$	9.60074	0.309059
$966$	1.90874	0.0614128
$967$	32.1640	1.03432	0.517162	−	0.855888i	$-0.326988\pi$
$967$	32.1640	1.03432	0.517162	+	0.855888i	$0.326988\pi$
$968$	8.76396	0.281684
$969$	9.03663	0.290298
$970$	−5.34921	−0.171753
$971$	32.0340	1.02802	0.514009	−	0.857785i	$-0.328160\pi$
$971$	32.0340	1.02802	0.514009	+	0.857785i	$0.328160\pi$
$972$	16.1259	0.517240
$973$	9.09074	0.291436
$974$	15.0083	0.480896
$975$	19.7501	0.632510
$976$	−15.1592	−0.485234
$977$	28.6881	0.917813	0.458906	−	0.888485i	$-0.348241\pi$
$977$	28.6881	0.917813	0.458906	+	0.888485i	$0.348241\pi$
$978$	−7.53082	−0.240809
$979$	8.63724	0.276047
$980$	−6.83731	−0.218410
$981$	19.7959	0.632035
$982$	33.5653	1.07111
$983$	−31.5071	−1.00492	−0.502460	−	0.864601i	$-0.667571\pi$
$983$	−31.5071	−1.00492	−0.502460	+	0.864601i	$0.667571\pi$
$984$	4.32957	0.138022
$985$	−35.1381	−1.11959
$986$	11.5230	0.366967
$987$	15.6751	0.498945
$988$	−8.93162	−0.284153
$989$	−11.0010	−0.349813
$990$	9.48665	0.301506
$991$	54.0970	1.71845	0.859224	−	0.511599i	$-0.170947\pi$
$991$	54.0970	1.71845	0.859224	+	0.511599i	$0.170947\pi$
$992$	3.46846	0.110124
$993$	18.3721	0.583021
$994$	14.9287	0.473510
$995$	29.3046	0.929020
$996$	3.49977	0.110895
$997$	−14.0064	−0.443586	−0.221793	−	0.975094i	$-0.571191\pi$
$997$	−14.0064	−0.443586	−0.221793	+	0.975094i	$0.571191\pi$
$998$	28.2709	0.894900
$999$	12.6689	0.400826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.17	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.17	✓	25	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.888297 q^{3} +1.00000 q^{4} +2.86945 q^{5} -0.888297 q^{6} -2.14877 q^{7} -1.00000 q^{8} -2.21093 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.888297 q^{3} +1.00000 q^{4} +2.86945 q^{5} -0.888297 q^{6} -2.14877 q^{7} -1.00000 q^{8} -2.21093 q^{9} -2.86945 q^{10} +1.49534 q^{11} +0.888297 q^{12} +6.87552 q^{13} +2.14877 q^{14} +2.54892 q^{15} +1.00000 q^{16} -7.83113 q^{17} +2.21093 q^{18} -1.29905 q^{19} +2.86945 q^{20} -1.90874 q^{21} -1.49534 q^{22} +1.00000 q^{23} -0.888297 q^{24} +3.23375 q^{25} -6.87552 q^{26} -4.62885 q^{27} -2.14877 q^{28} +1.47143 q^{29} -2.54892 q^{30} -3.46846 q^{31} -1.00000 q^{32} +1.32830 q^{33} +7.83113 q^{34} -6.16579 q^{35} -2.21093 q^{36} -2.73694 q^{37} +1.29905 q^{38} +6.10750 q^{39} -2.86945 q^{40} -4.87402 q^{41} +1.90874 q^{42} -11.0010 q^{43} +1.49534 q^{44} -6.34415 q^{45} -1.00000 q^{46} -8.21227 q^{47} +0.888297 q^{48} -2.38279 q^{49} -3.23375 q^{50} -6.95636 q^{51} +6.87552 q^{52} +4.48371 q^{53} +4.62885 q^{54} +4.29080 q^{55} +2.14877 q^{56} -1.15394 q^{57} -1.47143 q^{58} -13.2162 q^{59} +2.54892 q^{60} -15.1592 q^{61} +3.46846 q^{62} +4.75078 q^{63} +1.00000 q^{64} +19.7290 q^{65} -1.32830 q^{66} +4.82253 q^{67} -7.83113 q^{68} +0.888297 q^{69} +6.16579 q^{70} +6.94757 q^{71} +2.21093 q^{72} +6.40200 q^{73} +2.73694 q^{74} +2.87253 q^{75} -1.29905 q^{76} -3.21314 q^{77} -6.10750 q^{78} +10.0257 q^{79} +2.86945 q^{80} +2.52100 q^{81} +4.87402 q^{82} +3.93987 q^{83} -1.90874 q^{84} -22.4710 q^{85} +11.0010 q^{86} +1.30707 q^{87} -1.49534 q^{88} +5.77611 q^{89} +6.34415 q^{90} -14.7739 q^{91} +1.00000 q^{92} -3.08102 q^{93} +8.21227 q^{94} -3.72755 q^{95} -0.888297 q^{96} +1.86419 q^{97} +2.38279 q^{98} -3.30609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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