LMFDB - Embedded newform 6026.2.a.k.1.14

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:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.824185 q^{3} +1.00000 q^{4} +2.25531 q^{5} -0.824185 q^{6} +4.15544 q^{7} +1.00000 q^{8} -2.32072 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.824185 q^{3} +1.00000 q^{4} +2.25531 q^{5} -0.824185 q^{6} +4.15544 q^{7} +1.00000 q^{8} -2.32072 q^{9} +2.25531 q^{10} +3.06561 q^{11} -0.824185 q^{12} +0.209871 q^{13} +4.15544 q^{14} -1.85879 q^{15} +1.00000 q^{16} -5.46830 q^{17} -2.32072 q^{18} -2.86573 q^{19} +2.25531 q^{20} -3.42485 q^{21} +3.06561 q^{22} -1.00000 q^{23} -0.824185 q^{24} +0.0864007 q^{25} +0.209871 q^{26} +4.38526 q^{27} +4.15544 q^{28} +0.222235 q^{29} -1.85879 q^{30} +0.767975 q^{31} +1.00000 q^{32} -2.52663 q^{33} -5.46830 q^{34} +9.37177 q^{35} -2.32072 q^{36} +11.4924 q^{37} -2.86573 q^{38} -0.172972 q^{39} +2.25531 q^{40} -7.80134 q^{41} -3.42485 q^{42} +5.05218 q^{43} +3.06561 q^{44} -5.23393 q^{45} -1.00000 q^{46} +9.96814 q^{47} -0.824185 q^{48} +10.2676 q^{49} +0.0864007 q^{50} +4.50689 q^{51} +0.209871 q^{52} +7.04307 q^{53} +4.38526 q^{54} +6.91389 q^{55} +4.15544 q^{56} +2.36189 q^{57} +0.222235 q^{58} +9.54145 q^{59} -1.85879 q^{60} +12.2977 q^{61} +0.767975 q^{62} -9.64360 q^{63} +1.00000 q^{64} +0.473323 q^{65} -2.52663 q^{66} +4.36767 q^{67} -5.46830 q^{68} +0.824185 q^{69} +9.37177 q^{70} -0.0474587 q^{71} -2.32072 q^{72} +0.529392 q^{73} +11.4924 q^{74} -0.0712101 q^{75} -2.86573 q^{76} +12.7390 q^{77} -0.172972 q^{78} +12.1981 q^{79} +2.25531 q^{80} +3.34790 q^{81} -7.80134 q^{82} -14.7807 q^{83} -3.42485 q^{84} -12.3327 q^{85} +5.05218 q^{86} -0.183163 q^{87} +3.06561 q^{88} -6.37607 q^{89} -5.23393 q^{90} +0.872105 q^{91} -1.00000 q^{92} -0.632953 q^{93} +9.96814 q^{94} -6.46308 q^{95} -0.824185 q^{96} -13.9574 q^{97} +10.2676 q^{98} -7.11443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	−0.824185	−0.475843	−0.237922	−	0.971284i	$-0.576466\pi$
$3$	−0.824185	−0.475843	−0.237922	+	0.971284i	$0.576466\pi$
$4$	1.00000	0.500000
$5$	2.25531	1.00860	0.504302	−	0.863528i	$-0.331750\pi$
$5$	2.25531	1.00860	0.504302	+	0.863528i	$0.331750\pi$
$6$	−0.824185	−0.336472
$7$	4.15544	1.57061	0.785304	−	0.619111i	$-0.212507\pi$
$7$	4.15544	1.57061	0.785304	+	0.619111i	$0.212507\pi$
$8$	1.00000	0.353553
$9$	−2.32072	−0.773573
$10$	2.25531	0.713190
$11$	3.06561	0.924317	0.462158	−	0.886797i	$-0.347075\pi$
$11$	3.06561	0.924317	0.462158	+	0.886797i	$0.347075\pi$
$12$	−0.824185	−0.237922
$13$	0.209871	0.0582077	0.0291038	−	0.999576i	$-0.490735\pi$
$13$	0.209871	0.0582077	0.0291038	+	0.999576i	$0.490735\pi$
$14$	4.15544	1.11059
$15$	−1.85879	−0.479937
$16$	1.00000	0.250000
$17$	−5.46830	−1.32626	−0.663128	−	0.748506i	$-0.730772\pi$
$17$	−5.46830	−1.32626	−0.663128	+	0.748506i	$0.730772\pi$
$18$	−2.32072	−0.546999
$19$	−2.86573	−0.657442	−0.328721	−	0.944427i	$-0.606618\pi$
$19$	−2.86573	−0.657442	−0.328721	+	0.944427i	$0.606618\pi$
$20$	2.25531	0.504302
$21$	−3.42485	−0.747363
$22$	3.06561	0.653591
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.824185	−0.168236
$25$	0.0864007	0.0172801
$26$	0.209871	0.0411591
$27$	4.38526	0.843943
$28$	4.15544	0.785304
$29$	0.222235	0.0412680	0.0206340	−	0.999787i	$-0.493432\pi$
$29$	0.222235	0.0412680	0.0206340	+	0.999787i	$0.493432\pi$
$30$	−1.85879	−0.339367
$31$	0.767975	0.137932	0.0689662	−	0.997619i	$-0.478030\pi$
$31$	0.767975	0.137932	0.0689662	+	0.997619i	$0.478030\pi$
$32$	1.00000	0.176777
$33$	−2.52663	−0.439830
$34$	−5.46830	−0.937805
$35$	9.37177	1.58412
$36$	−2.32072	−0.386787
$37$	11.4924	1.88935	0.944673	−	0.328014i	$-0.106379\pi$
$37$	11.4924	1.88935	0.944673	+	0.328014i	$0.106379\pi$
$38$	−2.86573	−0.464882
$39$	−0.172972	−0.0276977
$40$	2.25531	0.356595
$41$	−7.80134	−1.21837	−0.609183	−	0.793030i	$-0.708502\pi$
$41$	−7.80134	−1.21837	−0.609183	+	0.793030i	$0.708502\pi$
$42$	−3.42485	−0.528465
$43$	5.05218	0.770450	0.385225	−	0.922823i	$-0.374124\pi$
$43$	5.05218	0.770450	0.385225	+	0.922823i	$0.374124\pi$
$44$	3.06561	0.462158
$45$	−5.23393	−0.780228
$46$	−1.00000	−0.147442
$47$	9.96814	1.45400	0.727001	−	0.686636i	$-0.240913\pi$
$47$	9.96814	1.45400	0.727001	+	0.686636i	$0.240913\pi$
$48$	−0.824185	−0.118961
$49$	10.2676	1.46681
$50$	0.0864007	0.0122189
$51$	4.50689	0.631090
$52$	0.209871	0.0291038
$53$	7.04307	0.967440	0.483720	−	0.875223i	$-0.339285\pi$
$53$	7.04307	0.967440	0.483720	+	0.875223i	$0.339285\pi$
$54$	4.38526	0.596758
$55$	6.91389	0.932269
$56$	4.15544	0.555293
$57$	2.36189	0.312840
$58$	0.222235	0.0291809
$59$	9.54145	1.24219	0.621096	−	0.783735i	$-0.286688\pi$
$59$	9.54145	1.24219	0.621096	+	0.783735i	$0.286688\pi$
$60$	−1.85879	−0.239968
$61$	12.2977	1.57456	0.787281	−	0.616594i	$-0.211488\pi$
$61$	12.2977	1.57456	0.787281	+	0.616594i	$0.211488\pi$
$62$	0.767975	0.0975329
$63$	−9.64360	−1.21498
$64$	1.00000	0.125000
$65$	0.473323	0.0587085
$66$	−2.52663	−0.311007
$67$	4.36767	0.533596	0.266798	−	0.963753i	$-0.414034\pi$
$67$	4.36767	0.533596	0.266798	+	0.963753i	$0.414034\pi$
$68$	−5.46830	−0.663128
$69$	0.824185	0.0992202
$70$	9.37177	1.12014
$71$	−0.0474587	−0.00563231	−0.00281616	−	0.999996i	$-0.500896\pi$
$71$	−0.0474587	−0.00563231	−0.00281616	+	0.999996i	$0.500896\pi$
$72$	−2.32072	−0.273499
$73$	0.529392	0.0619606	0.0309803	−	0.999520i	$-0.490137\pi$
$73$	0.529392	0.0619606	0.0309803	+	0.999520i	$0.490137\pi$
$74$	11.4924	1.33597
$75$	−0.0712101	−0.00822264
$76$	−2.86573	−0.328721
$77$	12.7390	1.45174
$78$	−0.172972	−0.0195853
$79$	12.1981	1.37240	0.686199	−	0.727414i	$-0.259278\pi$
$79$	12.1981	1.37240	0.686199	+	0.727414i	$0.259278\pi$
$80$	2.25531	0.252151
$81$	3.34790	0.371989
$82$	−7.80134	−0.861514
$83$	−14.7807	−1.62240	−0.811198	−	0.584772i	$-0.801184\pi$
$83$	−14.7807	−1.62240	−0.811198	+	0.584772i	$0.801184\pi$
$84$	−3.42485	−0.373681
$85$	−12.3327	−1.33767
$86$	5.05218	0.544791
$87$	−0.183163	−0.0196371
$88$	3.06561	0.326795
$89$	−6.37607	−0.675862	−0.337931	−	0.941171i	$-0.609727\pi$
$89$	−6.37607	−0.675862	−0.337931	+	0.941171i	$0.609727\pi$
$90$	−5.23393	−0.551705
$91$	0.872105	0.0914214
$92$	−1.00000	−0.104257
$93$	−0.632953	−0.0656342
$94$	9.96814	1.02814
$95$	−6.46308	−0.663099
$96$	−0.824185	−0.0841180
$97$	−13.9574	−1.41716	−0.708580	−	0.705631i	$-0.750664\pi$
$97$	−13.9574	−1.41716	−0.708580	+	0.705631i	$0.750664\pi$
$98$	10.2676	1.03719
$99$	−7.11443	−0.715027
$100$	0.0864007	0.00864007
$101$	−15.2659	−1.51901	−0.759506	−	0.650500i	$-0.774559\pi$
$101$	−15.2659	−1.51901	−0.759506	+	0.650500i	$0.774559\pi$
$102$	4.50689	0.446248
$103$	−0.200499	−0.0197558	−0.00987788	−	0.999951i	$-0.503144\pi$
$103$	−0.200499	−0.0197558	−0.00987788	+	0.999951i	$0.503144\pi$
$104$	0.209871	0.0205795
$105$	−7.72407	−0.753792
$106$	7.04307	0.684084
$107$	16.4801	1.59319	0.796594	−	0.604514i	$-0.206633\pi$
$107$	16.4801	1.59319	0.796594	+	0.604514i	$0.206633\pi$
$108$	4.38526	0.421971
$109$	−0.481098	−0.0460808	−0.0230404	−	0.999735i	$-0.507335\pi$
$109$	−0.481098	−0.0460808	−0.0230404	+	0.999735i	$0.507335\pi$
$110$	6.91389	0.659213
$111$	−9.47189	−0.899032
$112$	4.15544	0.392652
$113$	10.1773	0.957399	0.478700	−	0.877979i	$-0.341108\pi$
$113$	10.1773	0.957399	0.478700	+	0.877979i	$0.341108\pi$
$114$	2.36189	0.221211
$115$	−2.25531	−0.210308
$116$	0.222235	0.0206340
$117$	−0.487051	−0.0450279
$118$	9.54145	0.878362
$119$	−22.7232	−2.08303
$120$	−1.85879	−0.169683
$121$	−1.60203	−0.145639
$122$	12.2977	1.11338
$123$	6.42975	0.579751
$124$	0.767975	0.0689662
$125$	−11.0817	−0.991174
$126$	−9.64360	−0.859120
$127$	10.5602	0.937069	0.468535	−	0.883445i	$-0.344782\pi$
$127$	10.5602	0.937069	0.468535	+	0.883445i	$0.344782\pi$
$128$	1.00000	0.0883883
$129$	−4.16393	−0.366613
$130$	0.473323	0.0415132
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−2.52663	−0.219915
$133$	−11.9083	−1.03258
$134$	4.36767	0.377309
$135$	9.89009	0.851203
$136$	−5.46830	−0.468903
$137$	−0.650925	−0.0556123	−0.0278062	−	0.999613i	$-0.508852\pi$
$137$	−0.650925	−0.0556123	−0.0278062	+	0.999613i	$0.508852\pi$
$138$	0.824185	0.0701593
$139$	−6.34132	−0.537863	−0.268932	−	0.963159i	$-0.586671\pi$
$139$	−6.34132	−0.537863	−0.268932	+	0.963159i	$0.586671\pi$
$140$	9.37177	0.792060
$141$	−8.21559	−0.691877
$142$	−0.0474587	−0.00398265
$143$	0.643382	0.0538023
$144$	−2.32072	−0.193393
$145$	0.501208	0.0416230
$146$	0.529392	0.0438128
$147$	−8.46244	−0.697970
$148$	11.4924	0.944673
$149$	−13.9668	−1.14421	−0.572104	−	0.820181i	$-0.693872\pi$
$149$	−13.9668	−1.14421	−0.572104	+	0.820181i	$0.693872\pi$
$150$	−0.0712101	−0.00581428
$151$	1.20249	0.0978569	0.0489284	−	0.998802i	$-0.484419\pi$
$151$	1.20249	0.0978569	0.0489284	+	0.998802i	$0.484419\pi$
$152$	−2.86573	−0.232441
$153$	12.6904	1.02596
$154$	12.7390	1.02653
$155$	1.73202	0.139119
$156$	−0.172972	−0.0138489
$157$	19.5629	1.56129	0.780643	−	0.624977i	$-0.214892\pi$
$157$	19.5629	1.56129	0.780643	+	0.624977i	$0.214892\pi$
$158$	12.1981	0.970432
$159$	−5.80479	−0.460350
$160$	2.25531	0.178298
$161$	−4.15544	−0.327494
$162$	3.34790	0.263036
$163$	8.18416	0.641033	0.320516	−	0.947243i	$-0.396144\pi$
$163$	8.18416	0.641033	0.320516	+	0.947243i	$0.396144\pi$
$164$	−7.80134	−0.609183
$165$	−5.69832	−0.443614
$166$	−14.7807	−1.14721
$167$	9.84127	0.761540	0.380770	−	0.924670i	$-0.375659\pi$
$167$	9.84127	0.761540	0.380770	+	0.924670i	$0.375659\pi$
$168$	−3.42485	−0.264233
$169$	−12.9560	−0.996612
$170$	−12.3327	−0.945873
$171$	6.65055	0.508580
$172$	5.05218	0.385225
$173$	−3.30211	−0.251055	−0.125527	−	0.992090i	$-0.540062\pi$
$173$	−3.30211	−0.251055	−0.125527	+	0.992090i	$0.540062\pi$
$174$	−0.183163	−0.0138855
$175$	0.359033	0.0271403
$176$	3.06561	0.231079
$177$	−7.86392	−0.591088
$178$	−6.37607	−0.477907
$179$	23.6495	1.76764	0.883822	−	0.467823i	$-0.154962\pi$
$179$	23.6495	1.76764	0.883822	+	0.467823i	$0.154962\pi$
$180$	−5.23393	−0.390114
$181$	9.84227	0.731570	0.365785	−	0.930699i	$-0.380800\pi$
$181$	9.84227	0.731570	0.365785	+	0.930699i	$0.380800\pi$
$182$	0.872105	0.0646447
$183$	−10.1356	−0.749245
$184$	−1.00000	−0.0737210
$185$	25.9190	1.90560
$186$	−0.632953	−0.0464104
$187$	−16.7637	−1.22588
$188$	9.96814	0.727001
$189$	18.2226	1.32550
$190$	−6.46308	−0.468881
$191$	−23.5378	−1.70313	−0.851566	−	0.524247i	$-0.824347\pi$
$191$	−23.5378	−1.70313	−0.851566	+	0.524247i	$0.824347\pi$
$192$	−0.824185	−0.0594804
$193$	−14.0370	−1.01041	−0.505203	−	0.863001i	$-0.668582\pi$
$193$	−14.0370	−1.01041	−0.505203	+	0.863001i	$0.668582\pi$
$194$	−13.9574	−1.00208
$195$	−0.390105	−0.0279360
$196$	10.2676	0.733403
$197$	6.16466	0.439214	0.219607	−	0.975588i	$-0.429522\pi$
$197$	6.16466	0.439214	0.219607	+	0.975588i	$0.429522\pi$
$198$	−7.11443	−0.505600
$199$	2.11199	0.149715	0.0748573	−	0.997194i	$-0.476150\pi$
$199$	2.11199	0.149715	0.0748573	+	0.997194i	$0.476150\pi$
$200$	0.0864007	0.00610945
$201$	−3.59977	−0.253908
$202$	−15.2659	−1.07410
$203$	0.923483	0.0648158
$204$	4.50689	0.315545
$205$	−17.5944	−1.22885
$206$	−0.200499	−0.0139694
$207$	2.32072	0.161301
$208$	0.209871	0.0145519
$209$	−8.78520	−0.607685
$210$	−7.72407	−0.533012
$211$	−10.3157	−0.710164	−0.355082	−	0.934835i	$-0.615547\pi$
$211$	−10.3157	−0.710164	−0.355082	+	0.934835i	$0.615547\pi$
$212$	7.04307	0.483720
$213$	0.0391147	0.00268010
$214$	16.4801	1.12655
$215$	11.3942	0.777078
$216$	4.38526	0.298379
$217$	3.19127	0.216638
$218$	−0.481098	−0.0325840
$219$	−0.436317	−0.0294836
$220$	6.91389	0.466134
$221$	−1.14764	−0.0771984
$222$	−9.47189	−0.635712
$223$	−12.5057	−0.837445	−0.418723	−	0.908114i	$-0.637522\pi$
$223$	−12.5057	−0.837445	−0.418723	+	0.908114i	$0.637522\pi$
$224$	4.15544	0.277647
$225$	−0.200512	−0.0133675
$226$	10.1773	0.676983
$227$	−6.14970	−0.408170	−0.204085	−	0.978953i	$-0.565422\pi$
$227$	−6.14970	−0.408170	−0.204085	+	0.978953i	$0.565422\pi$
$228$	2.36189	0.156420
$229$	−14.4401	−0.954228	−0.477114	−	0.878841i	$-0.658317\pi$
$229$	−14.4401	−0.954228	−0.477114	+	0.878841i	$0.658317\pi$
$230$	−2.25531	−0.148710
$231$	−10.4992	−0.690800
$232$	0.222235	0.0145904
$233$	−22.8307	−1.49569	−0.747844	−	0.663875i	$-0.768911\pi$
$233$	−22.8307	−1.49569	−0.747844	+	0.663875i	$0.768911\pi$
$234$	−0.487051	−0.0318395
$235$	22.4812	1.46651
$236$	9.54145	0.621096
$237$	−10.0535	−0.653046
$238$	−22.7232	−1.47292
$239$	3.49004	0.225752	0.112876	−	0.993609i	$-0.463994\pi$
$239$	3.49004	0.225752	0.112876	+	0.993609i	$0.463994\pi$
$240$	−1.85879	−0.119984
$241$	9.01997	0.581027	0.290514	−	0.956871i	$-0.406174\pi$
$241$	9.01997	0.581027	0.290514	+	0.956871i	$0.406174\pi$
$242$	−1.60203	−0.102982
$243$	−15.9151	−1.02095
$244$	12.2977	0.787281
$245$	23.1567	1.47943
$246$	6.42975	0.409946
$247$	−0.601432	−0.0382682
$248$	0.767975	0.0487665
$249$	12.1820	0.772006
$250$	−11.0817	−0.700866
$251$	14.0730	0.888280	0.444140	−	0.895957i	$-0.353509\pi$
$251$	14.0730	0.888280	0.444140	+	0.895957i	$0.353509\pi$
$252$	−9.64360	−0.607490
$253$	−3.06561	−0.192733
$254$	10.5602	0.662608
$255$	10.1644	0.636520
$256$	1.00000	0.0625000
$257$	−1.35237	−0.0843587	−0.0421793	−	0.999110i	$-0.513430\pi$
$257$	−1.35237	−0.0843587	−0.0421793	+	0.999110i	$0.513430\pi$
$258$	−4.16393	−0.259235
$259$	47.7561	2.96742
$260$	0.473323	0.0293542
$261$	−0.515745	−0.0319238
$262$	−1.00000	−0.0617802
$263$	−6.48664	−0.399983	−0.199992	−	0.979798i	$-0.564091\pi$
$263$	−6.48664	−0.399983	−0.199992	+	0.979798i	$0.564091\pi$
$264$	−2.52663	−0.155503
$265$	15.8843	0.975763
$266$	−11.9083	−0.730147
$267$	5.25506	0.321604
$268$	4.36767	0.266798
$269$	0.633390	0.0386185	0.0193092	−	0.999814i	$-0.493853\pi$
$269$	0.633390	0.0386185	0.0193092	+	0.999814i	$0.493853\pi$
$270$	9.89009	0.601892
$271$	−7.52314	−0.456998	−0.228499	−	0.973544i	$-0.573382\pi$
$271$	−7.52314	−0.456998	−0.228499	+	0.973544i	$0.573382\pi$
$272$	−5.46830	−0.331564
$273$	−0.718775	−0.0435023
$274$	−0.650925	−0.0393238
$275$	0.264871	0.0159723
$276$	0.824185	0.0496101
$277$	22.8762	1.37449	0.687247	−	0.726423i	$-0.258819\pi$
$277$	22.8762	1.37449	0.687247	+	0.726423i	$0.258819\pi$
$278$	−6.34132	−0.380327
$279$	−1.78225	−0.106701
$280$	9.37177	0.560071
$281$	−4.44823	−0.265359	−0.132680	−	0.991159i	$-0.542358\pi$
$281$	−4.44823	−0.265359	−0.132680	+	0.991159i	$0.542358\pi$
$282$	−8.21559	−0.489231
$283$	−3.86270	−0.229614	−0.114807	−	0.993388i	$-0.536625\pi$
$283$	−3.86270	−0.229614	−0.114807	+	0.993388i	$0.536625\pi$
$284$	−0.0474587	−0.00281616
$285$	5.32677	0.315531
$286$	0.643382	0.0380440
$287$	−32.4180	−1.91357
$288$	−2.32072	−0.136750
$289$	12.9023	0.758957
$290$	0.501208	0.0294319
$291$	11.5035	0.674346
$292$	0.529392	0.0309803
$293$	4.56717	0.266817	0.133408	−	0.991061i	$-0.457408\pi$
$293$	4.56717	0.266817	0.133408	+	0.991061i	$0.457408\pi$
$294$	−8.46244	−0.493539
$295$	21.5189	1.25288
$296$	11.4924	0.667985
$297$	13.4435	0.780070
$298$	−13.9668	−0.809077
$299$	−0.209871	−0.0121371
$300$	−0.0712101	−0.00411132
$301$	20.9940	1.21007
$302$	1.20249	0.0691953
$303$	12.5819	0.722812
$304$	−2.86573	−0.164361
$305$	27.7351	1.58811
$306$	12.6904	0.725461
$307$	11.6904	0.667204	0.333602	−	0.942714i	$-0.391736\pi$
$307$	11.6904	0.667204	0.333602	+	0.942714i	$0.391736\pi$
$308$	12.7390	0.725869
$309$	0.165248	0.00940065
$310$	1.73202	0.0983720
$311$	−32.4617	−1.84074	−0.920368	−	0.391053i	$-0.872111\pi$
$311$	−32.4617	−1.84074	−0.920368	+	0.391053i	$0.872111\pi$
$312$	−0.172972	−0.00979263
$313$	−30.9224	−1.74784	−0.873918	−	0.486073i	$-0.838429\pi$
$313$	−30.9224	−1.74784	−0.873918	+	0.486073i	$0.838429\pi$
$314$	19.5629	1.10400
$315$	−21.7493	−1.22543
$316$	12.1981	0.686199
$317$	8.61235	0.483718	0.241859	−	0.970311i	$-0.422243\pi$
$317$	8.61235	0.483718	0.241859	+	0.970311i	$0.422243\pi$
$318$	−5.80479	−0.325517
$319$	0.681286	0.0381447
$320$	2.25531	0.126075
$321$	−13.5826	−0.758108
$322$	−4.15544	−0.231573
$323$	15.6706	0.871938
$324$	3.34790	0.185994
$325$	0.0181330	0.00100584
$326$	8.18416	0.453279
$327$	0.396513	0.0219272
$328$	−7.80134	−0.430757
$329$	41.4220	2.28367
$330$	−5.69832	−0.313682
$331$	7.57614	0.416422	0.208211	−	0.978084i	$-0.433236\pi$
$331$	7.57614	0.416422	0.208211	+	0.978084i	$0.433236\pi$
$332$	−14.7807	−0.811198
$333$	−26.6707	−1.46155
$334$	9.84127	0.538490
$335$	9.85043	0.538186
$336$	−3.42485	−0.186841
$337$	−28.0850	−1.52989	−0.764943	−	0.644098i	$-0.777233\pi$
$337$	−28.0850	−1.52989	−0.764943	+	0.644098i	$0.777233\pi$
$338$	−12.9560	−0.704711
$339$	−8.38797	−0.455572
$340$	−12.3327	−0.668833
$341$	2.35431	0.127493
$342$	6.65055	0.359620
$343$	13.5785	0.733170
$344$	5.05218	0.272395
$345$	1.85879	0.100074
$346$	−3.30211	−0.177523
$347$	3.02101	0.162177	0.0810883	−	0.996707i	$-0.474160\pi$
$347$	3.02101	0.162177	0.0810883	+	0.996707i	$0.474160\pi$
$348$	−0.183163	−0.00981855
$349$	22.1929	1.18796	0.593979	−	0.804481i	$-0.297556\pi$
$349$	22.1929	1.18796	0.593979	+	0.804481i	$0.297556\pi$
$350$	0.359033	0.0191911
$351$	0.920337	0.0491240
$352$	3.06561	0.163398
$353$	26.7561	1.42408	0.712041	−	0.702138i	$-0.247771\pi$
$353$	26.7561	1.42408	0.712041	+	0.702138i	$0.247771\pi$
$354$	−7.86392	−0.417962
$355$	−0.107034	−0.00568077
$356$	−6.37607	−0.337931
$357$	18.7281	0.991195
$358$	23.6495	1.24991
$359$	−18.1217	−0.956429	−0.478214	−	0.878243i	$-0.658716\pi$
$359$	−18.1217	−0.956429	−0.478214	+	0.878243i	$0.658716\pi$
$360$	−5.23393	−0.275852
$361$	−10.7876	−0.567769
$362$	9.84227	0.517298
$363$	1.32036	0.0693012
$364$	0.872105	0.0457107
$365$	1.19394	0.0624937
$366$	−10.1356	−0.529796
$367$	−13.0074	−0.678982	−0.339491	−	0.940609i	$-0.610255\pi$
$367$	−13.0074	−0.678982	−0.339491	+	0.940609i	$0.610255\pi$
$368$	−1.00000	−0.0521286
$369$	18.1047	0.942495
$370$	25.9190	1.34746
$371$	29.2670	1.51947
$372$	−0.632953	−0.0328171
$373$	16.7663	0.868124	0.434062	−	0.900883i	$-0.357080\pi$
$373$	16.7663	0.868124	0.434062	+	0.900883i	$0.357080\pi$
$374$	−16.7637	−0.866829
$375$	9.13334	0.471644
$376$	9.96814	0.514068
$377$	0.0466407	0.00240212
$378$	18.2226	0.937272
$379$	−24.0413	−1.23492	−0.617458	−	0.786604i	$-0.711838\pi$
$379$	−24.0413	−1.23492	−0.617458	+	0.786604i	$0.711838\pi$
$380$	−6.46308	−0.331549
$381$	−8.70358	−0.445898
$382$	−23.5378	−1.20430
$383$	−5.87123	−0.300006	−0.150003	−	0.988686i	$-0.547928\pi$
$383$	−5.87123	−0.300006	−0.150003	+	0.988686i	$0.547928\pi$
$384$	−0.824185	−0.0420590
$385$	28.7302	1.46423
$386$	−14.0370	−0.714464
$387$	−11.7247	−0.596000
$388$	−13.9574	−0.708580
$389$	3.63300	0.184200	0.0921002	−	0.995750i	$-0.470642\pi$
$389$	3.63300	0.184200	0.0921002	+	0.995750i	$0.470642\pi$
$390$	−0.390105	−0.0197538
$391$	5.46830	0.276544
$392$	10.2676	0.518594
$393$	0.824185	0.0415746
$394$	6.16466	0.310571
$395$	27.5105	1.38421
$396$	−7.11443	−0.357513
$397$	2.94710	0.147911	0.0739553	−	0.997262i	$-0.476438\pi$
$397$	2.94710	0.147911	0.0739553	+	0.997262i	$0.476438\pi$
$398$	2.11199	0.105864
$399$	9.81467	0.491348
$400$	0.0864007	0.00432004
$401$	−8.09035	−0.404013	−0.202006	−	0.979384i	$-0.564746\pi$
$401$	−8.09035	−0.404013	−0.202006	+	0.979384i	$0.564746\pi$
$402$	−3.59977	−0.179540
$403$	0.161176	0.00802873
$404$	−15.2659	−0.759506
$405$	7.55053	0.375189
$406$	0.923483	0.0458317
$407$	35.2314	1.74635
$408$	4.50689	0.223124
$409$	−18.0396	−0.891999	−0.445999	−	0.895033i	$-0.647152\pi$
$409$	−18.0396	−0.891999	−0.445999	+	0.895033i	$0.647152\pi$
$410$	−17.5944	−0.868926
$411$	0.536483	0.0264627
$412$	−0.200499	−0.00987788
$413$	39.6489	1.95099
$414$	2.32072	0.114057
$415$	−33.3350	−1.63635
$416$	0.209871	0.0102898
$417$	5.22641	0.255939
$418$	−8.78520	−0.429698
$419$	−34.2142	−1.67147	−0.835736	−	0.549132i	$-0.814959\pi$
$419$	−34.2142	−1.67147	−0.835736	+	0.549132i	$0.814959\pi$
$420$	−7.72407	−0.376896
$421$	−6.36020	−0.309977	−0.154989	−	0.987916i	$-0.549534\pi$
$421$	−6.36020	−0.309977	−0.154989	+	0.987916i	$0.549534\pi$
$422$	−10.3157	−0.502161
$423$	−23.1333	−1.12478
$424$	7.04307	0.342042
$425$	−0.472465	−0.0229179
$426$	0.0391147	0.00189511
$427$	51.1024	2.47302
$428$	16.4801	0.796594
$429$	−0.530266	−0.0256015
$430$	11.3942	0.549477
$431$	4.86366	0.234274	0.117137	−	0.993116i	$-0.462628\pi$
$431$	4.86366	0.234274	0.117137	+	0.993116i	$0.462628\pi$
$432$	4.38526	0.210986
$433$	6.76371	0.325043	0.162522	−	0.986705i	$-0.448037\pi$
$433$	6.76371	0.325043	0.162522	+	0.986705i	$0.448037\pi$
$434$	3.19127	0.153186
$435$	−0.413088	−0.0198060
$436$	−0.481098	−0.0230404
$437$	2.86573	0.137086
$438$	−0.436317	−0.0208480
$439$	−23.3531	−1.11458	−0.557290	−	0.830318i	$-0.688159\pi$
$439$	−23.3531	−1.11458	−0.557290	+	0.830318i	$0.688159\pi$
$440$	6.91389	0.329607
$441$	−23.8283	−1.13468
$442$	−1.14764	−0.0545875
$443$	5.86714	0.278756	0.139378	−	0.990239i	$-0.455490\pi$
$443$	5.86714	0.278756	0.139378	+	0.990239i	$0.455490\pi$
$444$	−9.47189	−0.449516
$445$	−14.3800	−0.681676
$446$	−12.5057	−0.592163
$447$	11.5112	0.544463
$448$	4.15544	0.196326
$449$	14.8912	0.702759	0.351379	−	0.936233i	$-0.385713\pi$
$449$	14.8912	0.702759	0.351379	+	0.936233i	$0.385713\pi$
$450$	−0.200512	−0.00945222
$451$	−23.9159	−1.12616
$452$	10.1773	0.478700
$453$	−0.991070	−0.0465645
$454$	−6.14970	−0.288620
$455$	1.96686	0.0922079
$456$	2.36189	0.110605
$457$	−31.2478	−1.46171	−0.730856	−	0.682532i	$-0.760879\pi$
$457$	−31.2478	−1.46171	−0.730856	+	0.682532i	$0.760879\pi$
$458$	−14.4401	−0.674741
$459$	−23.9799	−1.11928
$460$	−2.25531	−0.105154
$461$	27.6299	1.28685	0.643427	−	0.765507i	$-0.277512\pi$
$461$	27.6299	1.28685	0.643427	+	0.765507i	$0.277512\pi$
$462$	−10.4992	−0.488469
$463$	25.4804	1.18418	0.592088	−	0.805873i	$-0.298304\pi$
$463$	25.4804	1.18418	0.592088	+	0.805873i	$0.298304\pi$
$464$	0.222235	0.0103170
$465$	−1.42750	−0.0661988
$466$	−22.8307	−1.05761
$467$	−25.4904	−1.17956	−0.589778	−	0.807565i	$-0.700785\pi$
$467$	−25.4904	−1.17956	−0.589778	+	0.807565i	$0.700785\pi$
$468$	−0.487051	−0.0225140
$469$	18.1496	0.838069
$470$	22.4812	1.03698
$471$	−16.1234	−0.742928
$472$	9.54145	0.439181
$473$	15.4880	0.712140
$474$	−10.0535	−0.461774
$475$	−0.247601	−0.0113607
$476$	−22.7232	−1.04151
$477$	−16.3450	−0.748386
$478$	3.49004	0.159631
$479$	−38.9438	−1.77939	−0.889693	−	0.456560i	$-0.849082\pi$
$479$	−38.9438	−1.77939	−0.889693	+	0.456560i	$0.849082\pi$
$480$	−1.85879	−0.0848417
$481$	2.41193	0.109974
$482$	9.01997	0.410848
$483$	3.42485	0.155836
$484$	−1.60203	−0.0728193
$485$	−31.4782	−1.42935
$486$	−15.9151	−0.721921
$487$	−20.0653	−0.909243	−0.454622	−	0.890685i	$-0.650226\pi$
$487$	−20.0653	−0.909243	−0.454622	+	0.890685i	$0.650226\pi$
$488$	12.2977	0.556692
$489$	−6.74526	−0.305031
$490$	23.1567	1.04611
$491$	−15.9992	−0.722035	−0.361017	−	0.932559i	$-0.617570\pi$
$491$	−15.9992	−0.722035	−0.361017	+	0.932559i	$0.617570\pi$
$492$	6.42975	0.289875
$493$	−1.21525	−0.0547320
$494$	−0.601432	−0.0270597
$495$	−16.0452	−0.721178
$496$	0.767975	0.0344831
$497$	−0.197212	−0.00884615
$498$	12.1820	0.545890
$499$	2.35542	0.105443	0.0527214	−	0.998609i	$-0.483210\pi$
$499$	2.35542	0.105443	0.0527214	+	0.998609i	$0.483210\pi$
$500$	−11.0817	−0.495587
$501$	−8.11102	−0.362374
$502$	14.0730	0.628109
$503$	−22.0305	−0.982293	−0.491147	−	0.871077i	$-0.663422\pi$
$503$	−22.0305	−0.982293	−0.491147	+	0.871077i	$0.663422\pi$
$504$	−9.64360	−0.429560
$505$	−34.4292	−1.53208
$506$	−3.06561	−0.136283
$507$	10.6781	0.474231
$508$	10.5602	0.468535
$509$	−26.0515	−1.15471	−0.577356	−	0.816493i	$-0.695915\pi$
$509$	−26.0515	−1.15471	−0.577356	+	0.816493i	$0.695915\pi$
$510$	10.1644	0.450087
$511$	2.19985	0.0973158
$512$	1.00000	0.0441942
$513$	−12.5669	−0.554844
$514$	−1.35237	−0.0596506
$515$	−0.452187	−0.0199257
$516$	−4.16393	−0.183307
$517$	30.5584	1.34396
$518$	47.7561	2.09828
$519$	2.72155	0.119463
$520$	0.473323	0.0207566
$521$	42.4551	1.85999	0.929997	−	0.367567i	$-0.119809\pi$
$521$	42.4551	1.85999	0.929997	+	0.367567i	$0.119809\pi$
$522$	−0.515745	−0.0225736
$523$	18.1363	0.793045	0.396523	−	0.918025i	$-0.370217\pi$
$523$	18.1363	0.793045	0.396523	+	0.918025i	$0.370217\pi$
$524$	−1.00000	−0.0436852
$525$	−0.295909	−0.0129145
$526$	−6.48664	−0.282831
$527$	−4.19952	−0.182934
$528$	−2.52663	−0.109957
$529$	1.00000	0.0434783
$530$	15.8843	0.689969
$531$	−22.1430	−0.960926
$532$	−11.9083	−0.516292
$533$	−1.63727	−0.0709182
$534$	5.25506	0.227409
$535$	37.1676	1.60689
$536$	4.36767	0.188655
$537$	−19.4915	−0.841121
$538$	0.633390	0.0273074
$539$	31.4766	1.35579
$540$	9.89009	0.425602
$541$	23.4028	1.00617	0.503083	−	0.864238i	$-0.332199\pi$
$541$	23.4028	1.00617	0.503083	+	0.864238i	$0.332199\pi$
$542$	−7.52314	−0.323147
$543$	−8.11185	−0.348113
$544$	−5.46830	−0.234451
$545$	−1.08502	−0.0464772
$546$	−0.718775	−0.0307607
$547$	13.3154	0.569324	0.284662	−	0.958628i	$-0.408119\pi$
$547$	13.3154	0.569324	0.284662	+	0.958628i	$0.408119\pi$
$548$	−0.650925	−0.0278062
$549$	−28.5396	−1.21804
$550$	0.264871	0.0112941
$551$	−0.636865	−0.0271313
$552$	0.824185	0.0350796
$553$	50.6886	2.15550
$554$	22.8762	0.971915
$555$	−21.3620	−0.906767
$556$	−6.34132	−0.268932
$557$	−22.2361	−0.942174	−0.471087	−	0.882087i	$-0.656138\pi$
$557$	−22.2361	−0.942174	−0.471087	+	0.882087i	$0.656138\pi$
$558$	−1.78225	−0.0754489
$559$	1.06031	0.0448461
$560$	9.37177	0.396030
$561$	13.8164	0.583327
$562$	−4.44823	−0.187637
$563$	−7.40147	−0.311935	−0.155967	−	0.987762i	$-0.549849\pi$
$563$	−7.40147	−0.311935	−0.155967	+	0.987762i	$0.549849\pi$
$564$	−8.21559	−0.345939
$565$	22.9529	0.965636
$566$	−3.86270	−0.162362
$567$	13.9120	0.584248
$568$	−0.0474587	−0.00199132
$569$	0.430261	0.0180375	0.00901875	−	0.999959i	$-0.497129\pi$
$569$	0.430261	0.0180375	0.00901875	+	0.999959i	$0.497129\pi$
$570$	5.32677	0.223114
$571$	34.0690	1.42574	0.712871	−	0.701295i	$-0.247394\pi$
$571$	34.0690	1.42574	0.712871	+	0.701295i	$0.247394\pi$
$572$	0.643382	0.0269012
$573$	19.3995	0.810424
$574$	−32.4180	−1.35310
$575$	−0.0864007	−0.00360316
$576$	−2.32072	−0.0966967
$577$	2.34253	0.0975210	0.0487605	−	0.998811i	$-0.484473\pi$
$577$	2.34253	0.0975210	0.0487605	+	0.998811i	$0.484473\pi$
$578$	12.9023	0.536664
$579$	11.5691	0.480794
$580$	0.501208	0.0208115
$581$	−61.4203	−2.54815
$582$	11.5035	0.476834
$583$	21.5913	0.894221
$584$	0.529392	0.0219064
$585$	−1.09845	−0.0454153
$586$	4.56717	0.188668
$587$	−43.1137	−1.77949	−0.889745	−	0.456457i	$-0.849118\pi$
$587$	−43.1137	−1.77949	−0.889745	+	0.456457i	$0.849118\pi$
$588$	−8.46244	−0.348985
$589$	−2.20081	−0.0906826
$590$	21.5189	0.885918
$591$	−5.08082	−0.208997
$592$	11.4924	0.472336
$593$	32.3037	1.32655	0.663276	−	0.748375i	$-0.269165\pi$
$593$	32.3037	1.32655	0.663276	+	0.748375i	$0.269165\pi$
$594$	13.4435	0.551593
$595$	−51.2476	−2.10095
$596$	−13.9668	−0.572104
$597$	−1.74067	−0.0712407
$598$	−0.209871	−0.00858226
$599$	35.3631	1.44490	0.722448	−	0.691426i	$-0.243017\pi$
$599$	35.3631	1.44490	0.722448	+	0.691426i	$0.243017\pi$
$600$	−0.0712101	−0.00290714
$601$	−11.9186	−0.486168	−0.243084	−	0.970005i	$-0.578159\pi$
$601$	−11.9186	−0.486168	−0.243084	+	0.970005i	$0.578159\pi$
$602$	20.9940	0.855652
$603$	−10.1361	−0.412775
$604$	1.20249	0.0489284
$605$	−3.61306	−0.146892
$606$	12.5819	0.511105
$607$	12.2134	0.495727	0.247863	−	0.968795i	$-0.420272\pi$
$607$	12.2134	0.495727	0.247863	+	0.968795i	$0.420272\pi$
$608$	−2.86573	−0.116221
$609$	−0.761121	−0.0308422
$610$	27.7351	1.12296
$611$	2.09202	0.0846342
$612$	12.6904	0.512978
$613$	9.98861	0.403436	0.201718	−	0.979444i	$-0.435348\pi$
$613$	9.98861	0.403436	0.201718	+	0.979444i	$0.435348\pi$
$614$	11.6904	0.471785
$615$	14.5010	0.584738
$616$	12.7390	0.513267
$617$	5.21515	0.209954	0.104977	−	0.994475i	$-0.466523\pi$
$617$	5.21515	0.209954	0.104977	+	0.994475i	$0.466523\pi$
$618$	0.165248	0.00664726
$619$	23.8109	0.957040	0.478520	−	0.878077i	$-0.341173\pi$
$619$	23.8109	0.957040	0.478520	+	0.878077i	$0.341173\pi$
$620$	1.73202	0.0695595
$621$	−4.38526	−0.175974
$622$	−32.4617	−1.30160
$623$	−26.4953	−1.06151
$624$	−0.172972	−0.00692443
$625$	−25.4245	−1.01698
$626$	−30.9224	−1.23591
$627$	7.24063	0.289163
$628$	19.5629	0.780643
$629$	−62.8441	−2.50576
$630$	−21.7493	−0.866511
$631$	−18.7233	−0.745364	−0.372682	−	0.927959i	$-0.621562\pi$
$631$	−18.7233	−0.745364	−0.372682	+	0.927959i	$0.621562\pi$
$632$	12.1981	0.485216
$633$	8.50206	0.337926
$634$	8.61235	0.342040
$635$	23.8166	0.945131
$636$	−5.80479	−0.230175
$637$	2.15488	0.0853794
$638$	0.681286	0.0269724
$639$	0.110138	0.00435701
$640$	2.25531	0.0891488
$641$	−7.69338	−0.303870	−0.151935	−	0.988390i	$-0.548551\pi$
$641$	−7.69338	−0.303870	−0.151935	+	0.988390i	$0.548551\pi$
$642$	−13.5826	−0.536063
$643$	21.9923	0.867291	0.433646	−	0.901083i	$-0.357227\pi$
$643$	21.9923	0.867291	0.433646	+	0.901083i	$0.357227\pi$
$644$	−4.15544	−0.163747
$645$	−9.39093	−0.369767
$646$	15.6706	0.616553
$647$	20.2043	0.794312	0.397156	−	0.917751i	$-0.369997\pi$
$647$	20.2043	0.794312	0.397156	+	0.917751i	$0.369997\pi$
$648$	3.34790	0.131518
$649$	29.2504	1.14818
$650$	0.0181330	0.000711234 0
$651$	−2.63020	−0.103086
$652$	8.18416	0.320516
$653$	28.7937	1.12678	0.563392	−	0.826189i	$-0.309496\pi$
$653$	28.7937	1.12678	0.563392	+	0.826189i	$0.309496\pi$
$654$	0.396513	0.0155049
$655$	−2.25531	−0.0881221
$656$	−7.80134	−0.304591
$657$	−1.22857	−0.0479311
$658$	41.4220	1.61480
$659$	−38.0654	−1.48282	−0.741409	−	0.671054i	$-0.765842\pi$
$659$	−38.0654	−1.48282	−0.741409	+	0.671054i	$0.765842\pi$
$660$	−5.69832	−0.221807
$661$	−20.7101	−0.805530	−0.402765	−	0.915303i	$-0.631951\pi$
$661$	−20.7101	−0.805530	−0.402765	+	0.915303i	$0.631951\pi$
$662$	7.57614	0.294455
$663$	0.945864	0.0367343
$664$	−14.7807	−0.573603
$665$	−26.8569	−1.04147
$666$	−26.6707	−1.03347
$667$	−0.222235	−0.00860498
$668$	9.84127	0.380770
$669$	10.3070	0.398493
$670$	9.85043	0.380555
$671$	37.7001	1.45539
$672$	−3.42485	−0.132116
$673$	−34.5288	−1.33099	−0.665493	−	0.746404i	$-0.731779\pi$
$673$	−34.5288	−1.33099	−0.665493	+	0.746404i	$0.731779\pi$
$674$	−28.0850	−1.08179
$675$	0.378889	0.0145835
$676$	−12.9560	−0.498306
$677$	23.4472	0.901148	0.450574	−	0.892739i	$-0.351219\pi$
$677$	23.4472	0.901148	0.450574	+	0.892739i	$0.351219\pi$
$678$	−8.38797	−0.322138
$679$	−57.9991	−2.22580
$680$	−12.3327	−0.472937
$681$	5.06849	0.194225
$682$	2.35431	0.0901513
$683$	0.684522	0.0261925	0.0130963	−	0.999914i	$-0.495831\pi$
$683$	0.684522	0.0261925	0.0130963	+	0.999914i	$0.495831\pi$
$684$	6.65055	0.254290
$685$	−1.46804	−0.0560907
$686$	13.5785	0.518429
$687$	11.9013	0.454063
$688$	5.05218	0.192613
$689$	1.47814	0.0563125
$690$	1.85879	0.0707628
$691$	−5.94518	−0.226165	−0.113083	−	0.993586i	$-0.536072\pi$
$691$	−5.94518	−0.226165	−0.113083	+	0.993586i	$0.536072\pi$
$692$	−3.30211	−0.125527
$693$	−29.5635	−1.12303
$694$	3.02101	0.114676
$695$	−14.3016	−0.542491
$696$	−0.183163	−0.00694276
$697$	42.6601	1.61587
$698$	22.1929	0.840013
$699$	18.8167	0.711713
$700$	0.359033	0.0135702
$701$	−7.79942	−0.294580	−0.147290	−	0.989093i	$-0.547055\pi$
$701$	−7.79942	−0.294580	−0.147290	+	0.989093i	$0.547055\pi$
$702$	0.920337	0.0347359
$703$	−32.9342	−1.24214
$704$	3.06561	0.115540
$705$	−18.5287	−0.697830
$706$	26.7561	1.00698
$707$	−63.4364	−2.38577
$708$	−7.86392	−0.295544
$709$	9.54500	0.358470	0.179235	−	0.983806i	$-0.442638\pi$
$709$	9.54500	0.358470	0.179235	+	0.983806i	$0.442638\pi$
$710$	−0.107034	−0.00401691
$711$	−28.3085	−1.06165
$712$	−6.37607	−0.238953
$713$	−0.767975	−0.0287609
$714$	18.7281	0.700881
$715$	1.45102	0.0542652
$716$	23.6495	0.883822
$717$	−2.87643	−0.107422
$718$	−18.1217	−0.676297
$719$	−44.7510	−1.66893	−0.834466	−	0.551060i	$-0.814224\pi$
$719$	−44.7510	−1.66893	−0.834466	+	0.551060i	$0.814224\pi$
$720$	−5.23393	−0.195057
$721$	−0.833161	−0.0310286
$722$	−10.7876	−0.401474
$723$	−7.43412	−0.276478
$724$	9.84227	0.365785
$725$	0.0192013	0.000713117 0
$726$	1.32036	0.0490033
$727$	−9.93359	−0.368416	−0.184208	−	0.982887i	$-0.558972\pi$
$727$	−9.93359	−0.368416	−0.184208	+	0.982887i	$0.558972\pi$
$728$	0.872105	0.0323224
$729$	3.07324	0.113824
$730$	1.19394	0.0441897
$731$	−27.6268	−1.02181
$732$	−10.1356	−0.374623
$733$	16.5898	0.612757	0.306379	−	0.951910i	$-0.400883\pi$
$733$	16.5898	0.612757	0.306379	+	0.951910i	$0.400883\pi$
$734$	−13.0074	−0.480113
$735$	−19.0854	−0.703975
$736$	−1.00000	−0.0368605
$737$	13.3896	0.493211
$738$	18.1047	0.666444
$739$	21.1089	0.776503	0.388251	−	0.921553i	$-0.373079\pi$
$739$	21.1089	0.776503	0.388251	+	0.921553i	$0.373079\pi$
$740$	25.9190	0.952800
$741$	0.495691	0.0182097
$742$	29.2670	1.07443
$743$	12.4247	0.455819	0.227910	−	0.973682i	$-0.426811\pi$
$743$	12.4247	0.455819	0.227910	+	0.973682i	$0.426811\pi$
$744$	−0.632953	−0.0232052
$745$	−31.4995	−1.15405
$746$	16.7663	0.613856
$747$	34.3019	1.25504
$748$	−16.7637	−0.612941
$749$	68.4819	2.50227
$750$	9.13334	0.333502
$751$	−0.161009	−0.00587530	−0.00293765	−	0.999996i	$-0.500935\pi$
$751$	−0.161009	−0.00587530	−0.00293765	+	0.999996i	$0.500935\pi$
$752$	9.96814	0.363501
$753$	−11.5988	−0.422682
$754$	0.0466407	0.00169855
$755$	2.71197	0.0986987
$756$	18.2226	0.662751
$757$	−36.9871	−1.34432	−0.672159	−	0.740407i	$-0.734633\pi$
$757$	−36.9871	−1.34432	−0.672159	+	0.740407i	$0.734633\pi$
$758$	−24.0413	−0.873218
$759$	2.52663	0.0917109
$760$	−6.46308	−0.234441
$761$	40.0041	1.45015	0.725075	−	0.688670i	$-0.241805\pi$
$761$	40.0041	1.45015	0.725075	+	0.688670i	$0.241805\pi$
$762$	−8.70358	−0.315298
$763$	−1.99917	−0.0723748
$764$	−23.5378	−0.851566
$765$	28.6207	1.03478
$766$	−5.87123	−0.212136
$767$	2.00247	0.0723051
$768$	−0.824185	−0.0297402
$769$	26.3853	0.951479	0.475740	−	0.879586i	$-0.342180\pi$
$769$	26.3853	0.951479	0.475740	+	0.879586i	$0.342180\pi$
$770$	28.7302	1.03537
$771$	1.11460	0.0401415
$772$	−14.0370	−0.505203
$773$	−29.0544	−1.04501	−0.522507	−	0.852635i	$-0.675003\pi$
$773$	−29.0544	−1.04501	−0.522507	+	0.852635i	$0.675003\pi$
$774$	−11.7247	−0.421435
$775$	0.0663536	0.00238349
$776$	−13.9574	−0.501041
$777$	−39.3598	−1.41203
$778$	3.63300	0.130249
$779$	22.3565	0.801005
$780$	−0.390105	−0.0139680
$781$	−0.145490	−0.00520604
$782$	5.46830	0.195546
$783$	0.974557	0.0348278
$784$	10.2676	0.366702
$785$	44.1202	1.57472
$786$	0.824185	0.0293977
$787$	9.38150	0.334414	0.167207	−	0.985922i	$-0.446525\pi$
$787$	9.38150	0.334414	0.167207	+	0.985922i	$0.446525\pi$
$788$	6.16466	0.219607
$789$	5.34619	0.190329
$790$	27.5105	0.978781
$791$	42.2911	1.50370
$792$	−7.11443	−0.252800
$793$	2.58093	0.0916517
$794$	2.94710	0.104589
$795$	−13.0916	−0.464310
$796$	2.11199	0.0748573
$797$	−40.5105	−1.43495	−0.717477	−	0.696582i	$-0.754703\pi$
$797$	−40.5105	−1.43495	−0.717477	+	0.696582i	$0.754703\pi$
$798$	9.81467	0.347435
$799$	−54.5088	−1.92838
$800$	0.0864007	0.00305473
$801$	14.7971	0.522829
$802$	−8.09035	−0.285680
$803$	1.62291	0.0572713
$804$	−3.59977	−0.126954
$805$	−9.37177	−0.330312
$806$	0.161176	0.00567717
$807$	−0.522030	−0.0183763
$808$	−15.2659	−0.537052
$809$	3.48796	0.122630	0.0613151	−	0.998118i	$-0.480471\pi$
$809$	3.48796	0.122630	0.0613151	+	0.998118i	$0.480471\pi$
$810$	7.55053	0.265299
$811$	−18.9962	−0.667048	−0.333524	−	0.942742i	$-0.608238\pi$
$811$	−18.9962	−0.667048	−0.333524	+	0.942742i	$0.608238\pi$
$812$	0.923483	0.0324079
$813$	6.20046	0.217460
$814$	35.2314	1.23486
$815$	18.4578	0.646547
$816$	4.50689	0.157773
$817$	−14.4782	−0.506527
$818$	−18.0396	−0.630738
$819$	−2.02391	−0.0707212
$820$	−17.5944	−0.614423
$821$	42.8189	1.49439	0.747196	−	0.664604i	$-0.231400\pi$
$821$	42.8189	1.49439	0.747196	+	0.664604i	$0.231400\pi$
$822$	0.536483	0.0187120
$823$	−12.8812	−0.449011	−0.224506	−	0.974473i	$-0.572077\pi$
$823$	−12.8812	−0.449011	−0.224506	+	0.974473i	$0.572077\pi$
$824$	−0.200499	−0.00698472
$825$	−0.218303	−0.00760032
$826$	39.6489	1.37956
$827$	−33.9641	−1.18105	−0.590524	−	0.807020i	$-0.701079\pi$
$827$	−33.9641	−1.18105	−0.590524	+	0.807020i	$0.701079\pi$
$828$	2.32072	0.0806506
$829$	−16.4653	−0.571862	−0.285931	−	0.958250i	$-0.592303\pi$
$829$	−16.4653	−0.571862	−0.285931	+	0.958250i	$0.592303\pi$
$830$	−33.3350	−1.15708
$831$	−18.8542	−0.654044
$832$	0.209871	0.00727596
$833$	−56.1465	−1.94536
$834$	5.22641	0.180976
$835$	22.1951	0.768092
$836$	−8.78520	−0.303843
$837$	3.36777	0.116407
$838$	−34.2142	−1.18191
$839$	10.6075	0.366213	0.183106	−	0.983093i	$-0.441385\pi$
$839$	10.6075	0.366213	0.183106	+	0.983093i	$0.441385\pi$
$840$	−7.72407	−0.266506
$841$	−28.9506	−0.998297
$842$	−6.36020	−0.219187
$843$	3.66616	0.126269
$844$	−10.3157	−0.355082
$845$	−29.2196	−1.00519
$846$	−23.1333	−0.795338
$847$	−6.65711	−0.228741
$848$	7.04307	0.241860
$849$	3.18358	0.109260
$850$	−0.472465	−0.0162054
$851$	−11.4924	−0.393956
$852$	0.0391147	0.00134005
$853$	31.6274	1.08290	0.541451	−	0.840732i	$-0.317875\pi$
$853$	31.6274	1.08290	0.541451	+	0.840732i	$0.317875\pi$
$854$	51.1024	1.74869
$855$	14.9990	0.512955
$856$	16.4801	0.563277
$857$	30.9586	1.05753	0.528763	−	0.848769i	$-0.322656\pi$
$857$	30.9586	1.05753	0.528763	+	0.848769i	$0.322656\pi$
$858$	−0.530266	−0.0181030
$859$	−25.9871	−0.886669	−0.443334	−	0.896356i	$-0.646205\pi$
$859$	−25.9871	−0.886669	−0.443334	+	0.896356i	$0.646205\pi$
$860$	11.3942	0.388539
$861$	26.7184	0.910561
$862$	4.86366	0.165657
$863$	−38.6855	−1.31687	−0.658436	−	0.752637i	$-0.728782\pi$
$863$	−38.6855	−1.31687	−0.658436	+	0.752637i	$0.728782\pi$
$864$	4.38526	0.149189
$865$	−7.44727	−0.253215
$866$	6.76371	0.229840
$867$	−10.6339	−0.361145
$868$	3.19127	0.108319
$869$	37.3948	1.26853
$870$	−0.413088	−0.0140050
$871$	0.916646	0.0310594
$872$	−0.481098	−0.0162920
$873$	32.3912	1.09628
$874$	2.86573	0.0969346
$875$	−46.0491	−1.55675
$876$	−0.436317	−0.0147418
$877$	−29.3532	−0.991187	−0.495594	−	0.868555i	$-0.665049\pi$
$877$	−29.3532	−0.991187	−0.495594	+	0.868555i	$0.665049\pi$
$878$	−23.3531	−0.788128
$879$	−3.76419	−0.126963
$880$	6.91389	0.233067
$881$	49.5968	1.67096	0.835479	−	0.549522i	$-0.185190\pi$
$881$	49.5968	1.67096	0.835479	+	0.549522i	$0.185190\pi$
$882$	−23.8283	−0.802342
$883$	3.66923	0.123479	0.0617397	−	0.998092i	$-0.480335\pi$
$883$	3.66923	0.123479	0.0617397	+	0.998092i	$0.480335\pi$
$884$	−1.14764	−0.0385992
$885$	−17.7355	−0.596173
$886$	5.86714	0.197110
$887$	38.6420	1.29747	0.648736	−	0.761013i	$-0.275298\pi$
$887$	38.6420	1.29747	0.648736	+	0.761013i	$0.275298\pi$
$888$	−9.47189	−0.317856
$889$	43.8824	1.47177
$890$	−14.3800	−0.482018
$891$	10.2634	0.343835
$892$	−12.5057	−0.418723
$893$	−28.5660	−0.955923
$894$	11.5112	0.384994
$895$	53.3368	1.78285
$896$	4.15544	0.138823
$897$	0.172972	0.00577538
$898$	14.8912	0.496926
$899$	0.170671	0.00569220
$900$	−0.200512	−0.00668373
$901$	−38.5136	−1.28307
$902$	−23.9159	−0.796312
$903$	−17.3029	−0.575806
$904$	10.1773	0.338492
$905$	22.1973	0.737864
$906$	−0.991070	−0.0329261
$907$	−16.3212	−0.541938	−0.270969	−	0.962588i	$-0.587344\pi$
$907$	−16.3212	−0.541938	−0.270969	+	0.962588i	$0.587344\pi$
$908$	−6.14970	−0.204085
$909$	35.4278	1.17507
$910$	1.96686	0.0652008
$911$	−39.1466	−1.29698	−0.648492	−	0.761221i	$-0.724600\pi$
$911$	−39.1466	−1.29698	−0.648492	+	0.761221i	$0.724600\pi$
$912$	2.36189	0.0782099
$913$	−45.3120	−1.49961
$914$	−31.2478	−1.03359
$915$	−22.8589	−0.755691
$916$	−14.4401	−0.477114
$917$	−4.15544	−0.137225
$918$	−23.9799	−0.791454
$919$	8.40680	0.277315	0.138657	−	0.990340i	$-0.455721\pi$
$919$	8.40680	0.277315	0.138657	+	0.990340i	$0.455721\pi$
$920$	−2.25531	−0.0743552
$921$	−9.63502	−0.317485
$922$	27.6299	0.909944
$923$	−0.00996020	−0.000327844 0
$924$	−10.4992	−0.345400
$925$	0.992955	0.0326482
$926$	25.4804	0.837339
$927$	0.465302	0.0152825
$928$	0.222235	0.00729522
$929$	−26.2451	−0.861074	−0.430537	−	0.902573i	$-0.641676\pi$
$929$	−26.2451	−0.861074	−0.430537	+	0.902573i	$0.641676\pi$
$930$	−1.42750	−0.0468096
$931$	−29.4243	−0.964341
$932$	−22.8307	−0.747844
$933$	26.7545	0.875902
$934$	−25.4904	−0.834073
$935$	−37.8072	−1.23643
$936$	−0.487051	−0.0159198
$937$	20.3973	0.666350	0.333175	−	0.942865i	$-0.391880\pi$
$937$	20.3973	0.666350	0.333175	+	0.942865i	$0.391880\pi$
$938$	18.1496	0.592604
$939$	25.4858	0.831696
$940$	22.4812	0.733256
$941$	−38.2328	−1.24635	−0.623176	−	0.782081i	$-0.714158\pi$
$941$	−38.2328	−1.24635	−0.623176	+	0.782081i	$0.714158\pi$
$942$	−16.1234	−0.525329
$943$	7.80134	0.254047
$944$	9.54145	0.310548
$945$	41.0976	1.33691
$946$	15.4880	0.503559
$947$	−12.0137	−0.390393	−0.195197	−	0.980764i	$-0.562535\pi$
$947$	−12.0137	−0.390393	−0.195197	+	0.980764i	$0.562535\pi$
$948$	−10.0535	−0.326523
$949$	0.111104	0.00360659
$950$	−0.247601	−0.00803323
$951$	−7.09817	−0.230174
$952$	−22.7232	−0.736462
$953$	38.8678	1.25905	0.629525	−	0.776980i	$-0.283249\pi$
$953$	38.8678	1.25905	0.629525	+	0.776980i	$0.283249\pi$
$954$	−16.3450	−0.529189
$955$	−53.0848	−1.71778
$956$	3.49004	0.112876
$957$	−0.561506	−0.0181509
$958$	−38.9438	−1.25822
$959$	−2.70488	−0.0873451
$960$	−1.85879	−0.0599921
$961$	−30.4102	−0.980975
$962$	2.41193	0.0777637
$963$	−38.2456	−1.23245
$964$	9.01997	0.290514
$965$	−31.6577	−1.01910
$966$	3.42485	0.110193
$967$	49.3289	1.58631	0.793155	−	0.609020i	$-0.208437\pi$
$967$	49.3289	1.58631	0.793155	+	0.609020i	$0.208437\pi$
$968$	−1.60203	−0.0514910
$969$	−12.9155	−0.414906
$970$	−31.4782	−1.01070
$971$	−18.9602	−0.608461	−0.304230	−	0.952598i	$-0.598399\pi$
$971$	−18.9602	−0.608461	−0.304230	+	0.952598i	$0.598399\pi$
$972$	−15.9151	−0.510476
$973$	−26.3509	−0.844772
$974$	−20.0653	−0.642932
$975$	−0.0149449	−0.000478621 0
$976$	12.2977	0.393641
$977$	−41.1309	−1.31589	−0.657947	−	0.753064i	$-0.728575\pi$
$977$	−41.1309	−1.31589	−0.657947	+	0.753064i	$0.728575\pi$
$978$	−6.74526	−0.215690
$979$	−19.5466	−0.624710
$980$	23.1567	0.739713
$981$	1.11649	0.0356469
$982$	−15.9992	−0.510556
$983$	−60.7210	−1.93670	−0.968349	−	0.249601i	$-0.919701\pi$
$983$	−60.7210	−1.93670	−0.968349	+	0.249601i	$0.919701\pi$
$984$	6.42975	0.204973
$985$	13.9032	0.442993
$986$	−1.21525	−0.0387014
$987$	−34.1393	−1.08667
$988$	−0.601432	−0.0191341
$989$	−5.05218	−0.160650
$990$	−16.0452	−0.509950
$991$	−57.3966	−1.82326	−0.911631	−	0.411010i	$-0.865176\pi$
$991$	−57.3966	−1.82326	−0.911631	+	0.411010i	$0.865176\pi$
$992$	0.767975	0.0243832
$993$	−6.24413	−0.198152
$994$	−0.197212	−0.00625517
$995$	4.76317	0.151003
$996$	12.1820	0.386003
$997$	−6.72680	−0.213040	−0.106520	−	0.994311i	$-0.533971\pi$
$997$	−6.72680	−0.213040	−0.106520	+	0.994311i	$0.533971\pi$
$998$	2.35542	0.0745594
$999$	50.3973	1.59450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.14	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.14	✓	35	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.824185 q^{3} +1.00000 q^{4} +2.25531 q^{5} -0.824185 q^{6} +4.15544 q^{7} +1.00000 q^{8} -2.32072 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.824185 q^{3} +1.00000 q^{4} +2.25531 q^{5} -0.824185 q^{6} +4.15544 q^{7} +1.00000 q^{8} -2.32072 q^{9} +2.25531 q^{10} +3.06561 q^{11} -0.824185 q^{12} +0.209871 q^{13} +4.15544 q^{14} -1.85879 q^{15} +1.00000 q^{16} -5.46830 q^{17} -2.32072 q^{18} -2.86573 q^{19} +2.25531 q^{20} -3.42485 q^{21} +3.06561 q^{22} -1.00000 q^{23} -0.824185 q^{24} +0.0864007 q^{25} +0.209871 q^{26} +4.38526 q^{27} +4.15544 q^{28} +0.222235 q^{29} -1.85879 q^{30} +0.767975 q^{31} +1.00000 q^{32} -2.52663 q^{33} -5.46830 q^{34} +9.37177 q^{35} -2.32072 q^{36} +11.4924 q^{37} -2.86573 q^{38} -0.172972 q^{39} +2.25531 q^{40} -7.80134 q^{41} -3.42485 q^{42} +5.05218 q^{43} +3.06561 q^{44} -5.23393 q^{45} -1.00000 q^{46} +9.96814 q^{47} -0.824185 q^{48} +10.2676 q^{49} +0.0864007 q^{50} +4.50689 q^{51} +0.209871 q^{52} +7.04307 q^{53} +4.38526 q^{54} +6.91389 q^{55} +4.15544 q^{56} +2.36189 q^{57} +0.222235 q^{58} +9.54145 q^{59} -1.85879 q^{60} +12.2977 q^{61} +0.767975 q^{62} -9.64360 q^{63} +1.00000 q^{64} +0.473323 q^{65} -2.52663 q^{66} +4.36767 q^{67} -5.46830 q^{68} +0.824185 q^{69} +9.37177 q^{70} -0.0474587 q^{71} -2.32072 q^{72} +0.529392 q^{73} +11.4924 q^{74} -0.0712101 q^{75} -2.86573 q^{76} +12.7390 q^{77} -0.172972 q^{78} +12.1981 q^{79} +2.25531 q^{80} +3.34790 q^{81} -7.80134 q^{82} -14.7807 q^{83} -3.42485 q^{84} -12.3327 q^{85} +5.05218 q^{86} -0.183163 q^{87} +3.06561 q^{88} -6.37607 q^{89} -5.23393 q^{90} +0.872105 q^{91} -1.00000 q^{92} -0.632953 q^{93} +9.96814 q^{94} -6.46308 q^{95} -0.824185 q^{96} -13.9574 q^{97} +10.2676 q^{98} -7.11443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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