LMFDB - Embedded newform 8042.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.42720 q^{3} +1.00000 q^{4} +2.10259 q^{5} -2.42720 q^{6} +2.07633 q^{7} +1.00000 q^{8} +2.89131 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.42720 q^{3} +1.00000 q^{4} +2.10259 q^{5} -2.42720 q^{6} +2.07633 q^{7} +1.00000 q^{8} +2.89131 q^{9} +2.10259 q^{10} -0.543337 q^{11} -2.42720 q^{12} +5.79506 q^{13} +2.07633 q^{14} -5.10342 q^{15} +1.00000 q^{16} +4.06258 q^{17} +2.89131 q^{18} +6.92726 q^{19} +2.10259 q^{20} -5.03968 q^{21} -0.543337 q^{22} +6.63583 q^{23} -2.42720 q^{24} -0.579106 q^{25} +5.79506 q^{26} +0.263814 q^{27} +2.07633 q^{28} +1.44800 q^{29} -5.10342 q^{30} +2.47805 q^{31} +1.00000 q^{32} +1.31879 q^{33} +4.06258 q^{34} +4.36568 q^{35} +2.89131 q^{36} +9.11182 q^{37} +6.92726 q^{38} -14.0658 q^{39} +2.10259 q^{40} +2.05139 q^{41} -5.03968 q^{42} -3.83470 q^{43} -0.543337 q^{44} +6.07924 q^{45} +6.63583 q^{46} -12.4314 q^{47} -2.42720 q^{48} -2.68884 q^{49} -0.579106 q^{50} -9.86071 q^{51} +5.79506 q^{52} -2.49014 q^{53} +0.263814 q^{54} -1.14242 q^{55} +2.07633 q^{56} -16.8139 q^{57} +1.44800 q^{58} -13.7235 q^{59} -5.10342 q^{60} +11.8179 q^{61} +2.47805 q^{62} +6.00332 q^{63} +1.00000 q^{64} +12.1847 q^{65} +1.31879 q^{66} +4.36552 q^{67} +4.06258 q^{68} -16.1065 q^{69} +4.36568 q^{70} -8.92460 q^{71} +2.89131 q^{72} +11.9164 q^{73} +9.11182 q^{74} +1.40561 q^{75} +6.92726 q^{76} -1.12815 q^{77} -14.0658 q^{78} +13.2647 q^{79} +2.10259 q^{80} -9.31426 q^{81} +2.05139 q^{82} -2.15070 q^{83} -5.03968 q^{84} +8.54195 q^{85} -3.83470 q^{86} -3.51459 q^{87} -0.543337 q^{88} -1.13935 q^{89} +6.07924 q^{90} +12.0325 q^{91} +6.63583 q^{92} -6.01472 q^{93} -12.4314 q^{94} +14.5652 q^{95} -2.42720 q^{96} -9.84162 q^{97} -2.68884 q^{98} -1.57096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) $ 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * 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
$3$	−2.42720	−1.40135	−0.700673	−	0.713483i	$-0.747117\pi$
$3$	−2.42720	−1.40135	−0.700673	+	0.713483i	$0.747117\pi$
$4$	1.00000	0.500000
$5$	2.10259	0.940308	0.470154	−	0.882584i	$-0.344198\pi$
$5$	2.10259	0.940308	0.470154	+	0.882584i	$0.344198\pi$
$6$	−2.42720	−0.990901
$7$	2.07633	0.784780	0.392390	−	0.919799i	$-0.371648\pi$
$7$	2.07633	0.784780	0.392390	+	0.919799i	$0.371648\pi$
$8$	1.00000	0.353553
$9$	2.89131	0.963770
$10$	2.10259	0.664898
$11$	−0.543337	−0.163822	−0.0819112	−	0.996640i	$-0.526102\pi$
$11$	−0.543337	−0.163822	−0.0819112	+	0.996640i	$0.526102\pi$
$12$	−2.42720	−0.700673
$13$	5.79506	1.60726	0.803631	−	0.595128i	$-0.202899\pi$
$13$	5.79506	1.60726	0.803631	+	0.595128i	$0.202899\pi$
$14$	2.07633	0.554923
$15$	−5.10342	−1.31770
$16$	1.00000	0.250000
$17$	4.06258	0.985321	0.492660	−	0.870222i	$-0.336025\pi$
$17$	4.06258	0.985321	0.492660	+	0.870222i	$0.336025\pi$
$18$	2.89131	0.681488
$19$	6.92726	1.58922	0.794612	−	0.607118i	$-0.207674\pi$
$19$	6.92726	1.58922	0.794612	+	0.607118i	$0.207674\pi$
$20$	2.10259	0.470154
$21$	−5.03968	−1.09975
$22$	−0.543337	−0.115840
$23$	6.63583	1.38367	0.691833	−	0.722058i	$-0.256804\pi$
$23$	6.63583	1.38367	0.691833	+	0.722058i	$0.256804\pi$
$24$	−2.42720	−0.495451
$25$	−0.579106	−0.115821
$26$	5.79506	1.13651
$27$	0.263814	0.0507711
$28$	2.07633	0.392390
$29$	1.44800	0.268887	0.134443	−	0.990921i	$-0.457075\pi$
$29$	1.44800	0.268887	0.134443	+	0.990921i	$0.457075\pi$
$30$	−5.10342	−0.931752
$31$	2.47805	0.445070	0.222535	−	0.974925i	$-0.428567\pi$
$31$	2.47805	0.445070	0.222535	+	0.974925i	$0.428567\pi$
$32$	1.00000	0.176777
$33$	1.31879	0.229572
$34$	4.06258	0.696727
$35$	4.36568	0.737935
$36$	2.89131	0.481885
$37$	9.11182	1.49797	0.748987	−	0.662585i	$-0.230541\pi$
$37$	9.11182	1.49797	0.748987	+	0.662585i	$0.230541\pi$
$38$	6.92726	1.12375
$39$	−14.0658	−2.25233
$40$	2.10259	0.332449
$41$	2.05139	0.320374	0.160187	−	0.987087i	$-0.448790\pi$
$41$	2.05139	0.320374	0.160187	+	0.987087i	$0.448790\pi$
$42$	−5.03968	−0.777639
$43$	−3.83470	−0.584786	−0.292393	−	0.956298i	$-0.594451\pi$
$43$	−3.83470	−0.584786	−0.292393	+	0.956298i	$0.594451\pi$
$44$	−0.543337	−0.0819112
$45$	6.07924	0.906240
$46$	6.63583	0.978399
$47$	−12.4314	−1.81331	−0.906656	−	0.421871i	$-0.861373\pi$
$47$	−12.4314	−1.81331	−0.906656	+	0.421871i	$0.861373\pi$
$48$	−2.42720	−0.350336
$49$	−2.68884	−0.384120
$50$	−0.579106	−0.0818980
$51$	−9.86071	−1.38077
$52$	5.79506	0.803631
$53$	−2.49014	−0.342048	−0.171024	−	0.985267i	$-0.554708\pi$
$53$	−2.49014	−0.342048	−0.171024	+	0.985267i	$0.554708\pi$
$54$	0.263814	0.0359006
$55$	−1.14242	−0.154043
$56$	2.07633	0.277462
$57$	−16.8139	−2.22705
$58$	1.44800	0.190132
$59$	−13.7235	−1.78664	−0.893322	−	0.449417i	$-0.851632\pi$
$59$	−13.7235	−1.78664	−0.893322	+	0.449417i	$0.851632\pi$
$60$	−5.10342	−0.658848
$61$	11.8179	1.51313	0.756565	−	0.653918i	$-0.226876\pi$
$61$	11.8179	1.51313	0.756565	+	0.653918i	$0.226876\pi$
$62$	2.47805	0.314712
$63$	6.00332	0.756347
$64$	1.00000	0.125000
$65$	12.1847	1.51132
$66$	1.31879	0.162332
$67$	4.36552	0.533333	0.266666	−	0.963789i	$-0.414078\pi$
$67$	4.36552	0.533333	0.266666	+	0.963789i	$0.414078\pi$
$68$	4.06258	0.492660
$69$	−16.1065	−1.93899
$70$	4.36568	0.521799
$71$	−8.92460	−1.05916	−0.529578	−	0.848261i	$-0.677650\pi$
$71$	−8.92460	−1.05916	−0.529578	+	0.848261i	$0.677650\pi$
$72$	2.89131	0.340744
$73$	11.9164	1.39471	0.697354	−	0.716727i	$-0.254360\pi$
$73$	11.9164	1.39471	0.697354	+	0.716727i	$0.254360\pi$
$74$	9.11182	1.05923
$75$	1.40561	0.162306
$76$	6.92726	0.794612
$77$	−1.12815	−0.128565
$78$	−14.0658	−1.59264
$79$	13.2647	1.49240	0.746199	−	0.665723i	$-0.231877\pi$
$79$	13.2647	1.49240	0.746199	+	0.665723i	$0.231877\pi$
$80$	2.10259	0.235077
$81$	−9.31426	−1.03492
$82$	2.05139	0.226538
$83$	−2.15070	−0.236070	−0.118035	−	0.993009i	$-0.537659\pi$
$83$	−2.15070	−0.236070	−0.118035	+	0.993009i	$0.537659\pi$
$84$	−5.03968	−0.549874
$85$	8.54195	0.926505
$86$	−3.83470	−0.413506
$87$	−3.51459	−0.376803
$88$	−0.543337	−0.0579200
$89$	−1.13935	−0.120770	−0.0603852	−	0.998175i	$-0.519233\pi$
$89$	−1.13935	−0.120770	−0.0603852	+	0.998175i	$0.519233\pi$
$90$	6.07924	0.640809
$91$	12.0325	1.26135
$92$	6.63583	0.691833
$93$	−6.01472	−0.623697
$94$	−12.4314	−1.28220
$95$	14.5652	1.49436
$96$	−2.42720	−0.247725
$97$	−9.84162	−0.999265	−0.499633	−	0.866237i	$-0.666532\pi$
$97$	−9.84162	−0.999265	−0.499633	+	0.866237i	$0.666532\pi$
$98$	−2.68884	−0.271614
$99$	−1.57096	−0.157887
$100$	−0.579106	−0.0579106
$101$	1.16416	0.115838	0.0579190	−	0.998321i	$-0.481553\pi$
$101$	1.16416	0.115838	0.0579190	+	0.998321i	$0.481553\pi$
$102$	−9.86071	−0.976355
$103$	−18.5918	−1.83190	−0.915951	−	0.401290i	$-0.868562\pi$
$103$	−18.5918	−1.83190	−0.915951	+	0.401290i	$0.868562\pi$
$104$	5.79506	0.568253
$105$	−10.5964	−1.03410
$106$	−2.49014	−0.241864
$107$	−2.36467	−0.228601	−0.114301	−	0.993446i	$-0.536463\pi$
$107$	−2.36467	−0.228601	−0.114301	+	0.993446i	$0.536463\pi$
$108$	0.263814	0.0253855
$109$	−10.0776	−0.965263	−0.482631	−	0.875824i	$-0.660319\pi$
$109$	−10.0776	−0.965263	−0.482631	+	0.875824i	$0.660319\pi$
$110$	−1.14242	−0.108925
$111$	−22.1162	−2.09918
$112$	2.07633	0.196195
$113$	−5.61565	−0.528276	−0.264138	−	0.964485i	$-0.585087\pi$
$113$	−5.61565	−0.528276	−0.264138	+	0.964485i	$0.585087\pi$
$114$	−16.8139	−1.57476
$115$	13.9524	1.30107
$116$	1.44800	0.134443
$117$	16.7553	1.54903
$118$	−13.7235	−1.26335
$119$	8.43527	0.773260
$120$	−5.10342	−0.465876
$121$	−10.7048	−0.973162
$122$	11.8179	1.06994
$123$	−4.97914	−0.448954
$124$	2.47805	0.222535
$125$	−11.7306	−1.04922
$126$	6.00332	0.534818
$127$	−13.6085	−1.20756	−0.603779	−	0.797152i	$-0.706339\pi$
$127$	−13.6085	−1.20756	−0.603779	+	0.797152i	$0.706339\pi$
$128$	1.00000	0.0883883
$129$	9.30758	0.819487
$130$	12.1847	1.06867
$131$	13.7209	1.19880	0.599399	−	0.800450i	$-0.295406\pi$
$131$	13.7209	1.19880	0.599399	+	0.800450i	$0.295406\pi$
$132$	1.31879	0.114786
$133$	14.3833	1.24719
$134$	4.36552	0.377123
$135$	0.554694	0.0477404
$136$	4.06258	0.348363
$137$	−17.1081	−1.46164	−0.730820	−	0.682570i	$-0.760862\pi$
$137$	−17.1081	−1.46164	−0.730820	+	0.682570i	$0.760862\pi$
$138$	−16.1065	−1.37108
$139$	8.06283	0.683880	0.341940	−	0.939722i	$-0.388916\pi$
$139$	8.06283	0.683880	0.341940	+	0.939722i	$0.388916\pi$
$140$	4.36568	0.368967
$141$	30.1736	2.54108
$142$	−8.92460	−0.748936
$143$	−3.14867	−0.263305
$144$	2.89131	0.240942
$145$	3.04455	0.252836
$146$	11.9164	0.986208
$147$	6.52636	0.538285
$148$	9.11182	0.748987
$149$	−2.12879	−0.174397	−0.0871985	−	0.996191i	$-0.527791\pi$
$149$	−2.12879	−0.174397	−0.0871985	+	0.996191i	$0.527791\pi$
$150$	1.40561	0.114767
$151$	7.45545	0.606716	0.303358	−	0.952877i	$-0.401892\pi$
$151$	7.45545	0.606716	0.303358	+	0.952877i	$0.401892\pi$
$152$	6.92726	0.561875
$153$	11.7462	0.949622
$154$	−1.12815	−0.0909089
$155$	5.21032	0.418503
$156$	−14.0658	−1.12616
$157$	21.2993	1.69987	0.849935	−	0.526887i	$-0.176641\pi$
$157$	21.2993	1.69987	0.849935	+	0.526887i	$0.176641\pi$
$158$	13.2647	1.05528
$159$	6.04408	0.479327
$160$	2.10259	0.166225
$161$	13.7782	1.08587
$162$	−9.31426	−0.731797
$163$	−22.6083	−1.77082	−0.885408	−	0.464815i	$-0.846121\pi$
$163$	−22.6083	−1.77082	−0.885408	+	0.464815i	$0.846121\pi$
$164$	2.05139	0.160187
$165$	2.77288	0.215868
$166$	−2.15070	−0.166926
$167$	−9.10794	−0.704794	−0.352397	−	0.935851i	$-0.614633\pi$
$167$	−9.10794	−0.704794	−0.352397	+	0.935851i	$0.614633\pi$
$168$	−5.03968	−0.388820
$169$	20.5828	1.58329
$170$	8.54195	0.655138
$171$	20.0289	1.53165
$172$	−3.83470	−0.292393
$173$	7.28138	0.553593	0.276797	−	0.960929i	$-0.410727\pi$
$173$	7.28138	0.553593	0.276797	+	0.960929i	$0.410727\pi$
$174$	−3.51459	−0.266440
$175$	−1.20242	−0.0908942
$176$	−0.543337	−0.0409556
$177$	33.3096	2.50371
$178$	−1.13935	−0.0853976
$179$	−17.6121	−1.31639	−0.658195	−	0.752847i	$-0.728680\pi$
$179$	−17.6121	−1.31639	−0.658195	+	0.752847i	$0.728680\pi$
$180$	6.07924	0.453120
$181$	11.4895	0.854007	0.427004	−	0.904250i	$-0.359569\pi$
$181$	11.4895	0.854007	0.427004	+	0.904250i	$0.359569\pi$
$182$	12.0325	0.891907
$183$	−28.6845	−2.12042
$184$	6.63583	0.489200
$185$	19.1584	1.40856
$186$	−6.01472	−0.441021
$187$	−2.20735	−0.161418
$188$	−12.4314	−0.906656
$189$	0.547766	0.0398441
$190$	14.5652	1.05667
$191$	−25.6172	−1.85360	−0.926799	−	0.375558i	$-0.877451\pi$
$191$	−25.6172	−1.85360	−0.926799	+	0.375558i	$0.877451\pi$
$192$	−2.42720	−0.175168
$193$	−11.2784	−0.811835	−0.405918	−	0.913910i	$-0.633048\pi$
$193$	−11.2784	−0.811835	−0.405918	+	0.913910i	$0.633048\pi$
$194$	−9.84162	−0.706587
$195$	−29.5746	−2.11788
$196$	−2.68884	−0.192060
$197$	−17.0055	−1.21159	−0.605795	−	0.795621i	$-0.707145\pi$
$197$	−17.0055	−1.21159	−0.605795	+	0.795621i	$0.707145\pi$
$198$	−1.57096	−0.111643
$199$	5.66195	0.401365	0.200682	−	0.979656i	$-0.435684\pi$
$199$	5.66195	0.401365	0.200682	+	0.979656i	$0.435684\pi$
$200$	−0.579106	−0.0409490
$201$	−10.5960	−0.747384
$202$	1.16416	0.0819098
$203$	3.00653	0.211017
$204$	−9.86071	−0.690387
$205$	4.31324	0.301250
$206$	−18.5918	−1.29535
$207$	19.1862	1.33354
$208$	5.79506	0.401815
$209$	−3.76384	−0.260350
$210$	−10.5964	−0.731220
$211$	−2.27403	−0.156550	−0.0782752	−	0.996932i	$-0.524941\pi$
$211$	−2.27403	−0.156550	−0.0782752	+	0.996932i	$0.524941\pi$
$212$	−2.49014	−0.171024
$213$	21.6618	1.48424
$214$	−2.36467	−0.161645
$215$	−8.06280	−0.549879
$216$	0.263814	0.0179503
$217$	5.14525	0.349282
$218$	−10.0776	−0.682544
$219$	−28.9235	−1.95447
$220$	−1.14242	−0.0770217
$221$	23.5429	1.58367
$222$	−22.1162	−1.48434
$223$	20.6608	1.38355	0.691776	−	0.722113i	$-0.256829\pi$
$223$	20.6608	1.38355	0.691776	+	0.722113i	$0.256829\pi$
$224$	2.07633	0.138731
$225$	−1.67438	−0.111625
$226$	−5.61565	−0.373548
$227$	−0.987652	−0.0655528	−0.0327764	−	0.999463i	$-0.510435\pi$
$227$	−0.987652	−0.0655528	−0.0327764	+	0.999463i	$0.510435\pi$
$228$	−16.8139	−1.11353
$229$	−27.8134	−1.83796	−0.918981	−	0.394302i	$-0.870986\pi$
$229$	−27.8134	−1.83796	−0.918981	+	0.394302i	$0.870986\pi$
$230$	13.9524	0.919996
$231$	2.73825	0.180163
$232$	1.44800	0.0950658
$233$	25.2844	1.65644	0.828219	−	0.560405i	$-0.189354\pi$
$233$	25.2844	1.65644	0.828219	+	0.560405i	$0.189354\pi$
$234$	16.7553	1.09533
$235$	−26.1382	−1.70507
$236$	−13.7235	−0.893322
$237$	−32.1962	−2.09137
$238$	8.43527	0.546777
$239$	−10.5200	−0.680484	−0.340242	−	0.940338i	$-0.610509\pi$
$239$	−10.5200	−0.680484	−0.340242	+	0.940338i	$0.610509\pi$
$240$	−5.10342	−0.329424
$241$	0.910337	0.0586399	0.0293200	−	0.999570i	$-0.490666\pi$
$241$	0.910337	0.0586399	0.0293200	+	0.999570i	$0.490666\pi$
$242$	−10.7048	−0.688130
$243$	21.8161	1.39951
$244$	11.8179	0.756565
$245$	−5.65354	−0.361191
$246$	−4.97914	−0.317459
$247$	40.1439	2.55430
$248$	2.47805	0.157356
$249$	5.22018	0.330815
$250$	−11.7306	−0.741907
$251$	12.4647	0.786764	0.393382	−	0.919375i	$-0.371305\pi$
$251$	12.4647	0.786764	0.393382	+	0.919375i	$0.371305\pi$
$252$	6.00332	0.378174
$253$	−3.60549	−0.226675
$254$	−13.6085	−0.853873
$255$	−20.7330	−1.29835
$256$	1.00000	0.0625000
$257$	−19.0298	−1.18704	−0.593522	−	0.804817i	$-0.702263\pi$
$257$	−19.0298	−1.18704	−0.593522	+	0.804817i	$0.702263\pi$
$258$	9.30758	0.579465
$259$	18.9192	1.17558
$260$	12.1847	0.755660
$261$	4.18661	0.259145
$262$	13.7209	0.847678
$263$	23.5260	1.45068	0.725338	−	0.688393i	$-0.241684\pi$
$263$	23.5260	1.45068	0.725338	+	0.688393i	$0.241684\pi$
$264$	1.31879	0.0811659
$265$	−5.23576	−0.321630
$266$	14.3833	0.881897
$267$	2.76542	0.169241
$268$	4.36552	0.266666
$269$	28.7982	1.75586	0.877930	−	0.478789i	$-0.158924\pi$
$269$	28.7982	1.75586	0.877930	+	0.478789i	$0.158924\pi$
$270$	0.554694	0.0337576
$271$	−14.3708	−0.872967	−0.436483	−	0.899712i	$-0.643776\pi$
$271$	−14.3708	−0.872967	−0.436483	+	0.899712i	$0.643776\pi$
$272$	4.06258	0.246330
$273$	−29.2053	−1.76758
$274$	−17.1081	−1.03354
$275$	0.314650	0.0189741
$276$	−16.1065	−0.969497
$277$	−7.18486	−0.431697	−0.215848	−	0.976427i	$-0.569252\pi$
$277$	−7.18486	−0.431697	−0.215848	+	0.976427i	$0.569252\pi$
$278$	8.06283	0.483576
$279$	7.16480	0.428945
$280$	4.36568	0.260899
$281$	24.5560	1.46489	0.732443	−	0.680828i	$-0.238380\pi$
$281$	24.5560	1.46489	0.732443	+	0.680828i	$0.238380\pi$
$282$	30.1736	1.79681
$283$	−21.0313	−1.25018	−0.625092	−	0.780551i	$-0.714938\pi$
$283$	−21.0313	−1.25018	−0.625092	+	0.780551i	$0.714938\pi$
$284$	−8.92460	−0.529578
$285$	−35.3527	−2.09411
$286$	−3.14867	−0.186185
$287$	4.25937	0.251423
$288$	2.89131	0.170372
$289$	−0.495432	−0.0291431
$290$	3.04455	0.178782
$291$	23.8876	1.40032
$292$	11.9164	0.697354
$293$	−29.4745	−1.72192	−0.860960	−	0.508673i	$-0.830136\pi$
$293$	−29.4745	−1.72192	−0.860960	+	0.508673i	$0.830136\pi$
$294$	6.52636	0.380625
$295$	−28.8549	−1.68000
$296$	9.11182	0.529614
$297$	−0.143340	−0.00831744
$298$	−2.12879	−0.123317
$299$	38.4550	2.22391
$300$	1.40561	0.0811528
$301$	−7.96211	−0.458928
$302$	7.45545	0.429013
$303$	−2.82565	−0.162329
$304$	6.92726	0.397306
$305$	24.8483	1.42281
$306$	11.7462	0.671484
$307$	0.969261	0.0553187	0.0276593	−	0.999617i	$-0.491195\pi$
$307$	0.969261	0.0553187	0.0276593	+	0.999617i	$0.491195\pi$
$308$	−1.12815	−0.0642823
$309$	45.1260	2.56713
$310$	5.21032	0.295926
$311$	2.14607	0.121692	0.0608461	−	0.998147i	$-0.480620\pi$
$311$	2.14607	0.121692	0.0608461	+	0.998147i	$0.480620\pi$
$312$	−14.0658	−0.796319
$313$	−29.2724	−1.65457	−0.827286	−	0.561780i	$-0.810117\pi$
$313$	−29.2724	−1.65457	−0.827286	+	0.561780i	$0.810117\pi$
$314$	21.2993	1.20199
$315$	12.6225	0.711199
$316$	13.2647	0.746199
$317$	−22.2750	−1.25109	−0.625544	−	0.780189i	$-0.715123\pi$
$317$	−22.2750	−1.25109	−0.625544	+	0.780189i	$0.715123\pi$
$318$	6.04408	0.338935
$319$	−0.786752	−0.0440497
$320$	2.10259	0.117538
$321$	5.73953	0.320349
$322$	13.7782	0.767828
$323$	28.1426	1.56589
$324$	−9.31426	−0.517459
$325$	−3.35596	−0.186155
$326$	−22.6083	−1.25216
$327$	24.4605	1.35267
$328$	2.05139	0.113269
$329$	−25.8118	−1.42305
$330$	2.77288	0.152642
$331$	−29.4784	−1.62028	−0.810138	−	0.586239i	$-0.800608\pi$
$331$	−29.4784	−1.62028	−0.810138	+	0.586239i	$0.800608\pi$
$332$	−2.15070	−0.118035
$333$	26.3451	1.44370
$334$	−9.10794	−0.498364
$335$	9.17890	0.501497
$336$	−5.03968	−0.274937
$337$	11.9002	0.648247	0.324123	−	0.946015i	$-0.394931\pi$
$337$	11.9002	0.648247	0.324123	+	0.946015i	$0.394931\pi$
$338$	20.5828	1.11955
$339$	13.6303	0.740297
$340$	8.54195	0.463252
$341$	−1.34642	−0.0729125
$342$	20.0289	1.08304
$343$	−20.1173	−1.08623
$344$	−3.83470	−0.206753
$345$	−33.8654	−1.82325
$346$	7.28138	0.391449
$347$	2.54146	0.136433	0.0682164	−	0.997671i	$-0.478269\pi$
$347$	2.54146	0.136433	0.0682164	+	0.997671i	$0.478269\pi$
$348$	−3.51459	−0.188402
$349$	7.20653	0.385757	0.192878	−	0.981223i	$-0.438218\pi$
$349$	7.20653	0.385757	0.192878	+	0.981223i	$0.438218\pi$
$350$	−1.20242	−0.0642719
$351$	1.52882	0.0816024
$352$	−0.543337	−0.0289600
$353$	−4.16660	−0.221766	−0.110883	−	0.993833i	$-0.535368\pi$
$353$	−4.16660	−0.221766	−0.110883	+	0.993833i	$0.535368\pi$
$354$	33.3096	1.77039
$355$	−18.7648	−0.995932
$356$	−1.13935	−0.0603852
$357$	−20.4741	−1.08360
$358$	−17.6121	−0.930828
$359$	−19.8460	−1.04743	−0.523717	−	0.851892i	$-0.675455\pi$
$359$	−19.8460	−1.04743	−0.523717	+	0.851892i	$0.675455\pi$
$360$	6.07924	0.320404
$361$	28.9870	1.52563
$362$	11.4895	0.603874
$363$	25.9827	1.36374
$364$	12.0325	0.630673
$365$	25.0553	1.31146
$366$	−28.6845	−1.49936
$367$	21.1963	1.10644	0.553219	−	0.833036i	$-0.313399\pi$
$367$	21.1963	1.10644	0.553219	+	0.833036i	$0.313399\pi$
$368$	6.63583	0.345916
$369$	5.93121	0.308766
$370$	19.1584	0.996000
$371$	−5.17037	−0.268432
$372$	−6.01472	−0.311849
$373$	−7.09918	−0.367581	−0.183791	−	0.982965i	$-0.558837\pi$
$373$	−7.09918	−0.367581	−0.183791	+	0.982965i	$0.558837\pi$
$374$	−2.20735	−0.114139
$375$	28.4725	1.47031
$376$	−12.4314	−0.641102
$377$	8.39125	0.432171
$378$	0.547766	0.0281741
$379$	−19.1134	−0.981790	−0.490895	−	0.871219i	$-0.663330\pi$
$379$	−19.1134	−0.981790	−0.490895	+	0.871219i	$0.663330\pi$
$380$	14.5652	0.747180
$381$	33.0306	1.69221
$382$	−25.6172	−1.31069
$383$	−5.63797	−0.288087	−0.144044	−	0.989571i	$-0.546011\pi$
$383$	−5.63797	−0.288087	−0.144044	+	0.989571i	$0.546011\pi$
$384$	−2.42720	−0.123863
$385$	−2.37204	−0.120890
$386$	−11.2784	−0.574054
$387$	−11.0873	−0.563599
$388$	−9.84162	−0.499633
$389$	1.82982	0.0927753	0.0463877	−	0.998924i	$-0.485229\pi$
$389$	1.82982	0.0927753	0.0463877	+	0.998924i	$0.485229\pi$
$390$	−29.5746	−1.49757
$391$	26.9586	1.36335
$392$	−2.68884	−0.135807
$393$	−33.3033	−1.67993
$394$	−17.0055	−0.856724
$395$	27.8903	1.40331
$396$	−1.57096	−0.0789435
$397$	31.6187	1.58690	0.793448	−	0.608637i	$-0.208284\pi$
$397$	31.6187	1.58690	0.793448	+	0.608637i	$0.208284\pi$
$398$	5.66195	0.283808
$399$	−34.9112	−1.74775
$400$	−0.579106	−0.0289553
$401$	16.5535	0.826643	0.413322	−	0.910585i	$-0.364369\pi$
$401$	16.5535	0.826643	0.413322	+	0.910585i	$0.364369\pi$
$402$	−10.5960	−0.528480
$403$	14.3604	0.715345
$404$	1.16416	0.0579190
$405$	−19.5841	−0.973141
$406$	3.00653	0.149212
$407$	−4.95079	−0.245402
$408$	−9.86071	−0.488178
$409$	22.4070	1.10795	0.553977	−	0.832532i	$-0.313109\pi$
$409$	22.4070	1.10795	0.553977	+	0.832532i	$0.313109\pi$
$410$	4.31324	0.213016
$411$	41.5247	2.04826
$412$	−18.5918	−0.915951
$413$	−28.4945	−1.40212
$414$	19.1862	0.942952
$415$	−4.52204	−0.221978
$416$	5.79506	0.284126
$417$	−19.5701	−0.958352
$418$	−3.76384	−0.184096
$419$	−10.2382	−0.500171	−0.250085	−	0.968224i	$-0.580459\pi$
$419$	−10.2382	−0.500171	−0.250085	+	0.968224i	$0.580459\pi$
$420$	−10.5964	−0.517051
$421$	10.8785	0.530185	0.265092	−	0.964223i	$-0.414598\pi$
$421$	10.8785	0.530185	0.265092	+	0.964223i	$0.414598\pi$
$422$	−2.27403	−0.110698
$423$	−35.9431	−1.74761
$424$	−2.49014	−0.120932
$425$	−2.35267	−0.114121
$426$	21.6618	1.04952
$427$	24.5380	1.18747
$428$	−2.36467	−0.114301
$429$	7.64247	0.368982
$430$	−8.06280	−0.388823
$431$	−1.21664	−0.0586033	−0.0293016	−	0.999571i	$-0.509328\pi$
$431$	−1.21664	−0.0586033	−0.0293016	+	0.999571i	$0.509328\pi$
$432$	0.263814	0.0126928
$433$	2.31179	0.111097	0.0555487	−	0.998456i	$-0.482309\pi$
$433$	2.31179	0.111097	0.0555487	+	0.998456i	$0.482309\pi$
$434$	5.14525	0.246980
$435$	−7.38974	−0.354311
$436$	−10.0776	−0.482631
$437$	45.9681	2.19895
$438$	−28.9235	−1.38202
$439$	34.7811	1.66001	0.830006	−	0.557755i	$-0.188337\pi$
$439$	34.7811	1.66001	0.830006	+	0.557755i	$0.188337\pi$
$440$	−1.14242	−0.0544626
$441$	−7.77427	−0.370203
$442$	23.5429	1.11982
$443$	−9.96923	−0.473652	−0.236826	−	0.971552i	$-0.576107\pi$
$443$	−9.96923	−0.473652	−0.236826	+	0.971552i	$0.576107\pi$
$444$	−22.1162	−1.04959
$445$	−2.39558	−0.113561
$446$	20.6608	0.978318
$447$	5.16699	0.244390
$448$	2.07633	0.0980975
$449$	15.2243	0.718481	0.359240	−	0.933245i	$-0.383036\pi$
$449$	15.2243	0.718481	0.359240	+	0.933245i	$0.383036\pi$
$450$	−1.67438	−0.0789308
$451$	−1.11460	−0.0524844
$452$	−5.61565	−0.264138
$453$	−18.0959	−0.850218
$454$	−0.987652	−0.0463528
$455$	25.2994	1.18605
$456$	−16.8139	−0.787382
$457$	26.8112	1.25417	0.627087	−	0.778949i	$-0.284247\pi$
$457$	26.8112	1.25417	0.627087	+	0.778949i	$0.284247\pi$
$458$	−27.8134	−1.29964
$459$	1.07177	0.0500258
$460$	13.9524	0.650536
$461$	−9.37388	−0.436585	−0.218293	−	0.975883i	$-0.570049\pi$
$461$	−9.37388	−0.436585	−0.218293	+	0.975883i	$0.570049\pi$
$462$	2.73825	0.127395
$463$	13.1327	0.610329	0.305165	−	0.952300i	$-0.401288\pi$
$463$	13.1327	0.610329	0.305165	+	0.952300i	$0.401288\pi$
$464$	1.44800	0.0672217
$465$	−12.6465	−0.586468
$466$	25.2844	1.17128
$467$	−3.75916	−0.173953	−0.0869766	−	0.996210i	$-0.527721\pi$
$467$	−3.75916	−0.173953	−0.0869766	+	0.996210i	$0.527721\pi$
$468$	16.7553	0.774515
$469$	9.06427	0.418549
$470$	−26.1382	−1.20567
$471$	−51.6978	−2.38211
$472$	−13.7235	−0.631674
$473$	2.08353	0.0958010
$474$	−32.1962	−1.47882
$475$	−4.01162	−0.184066
$476$	8.43527	0.386630
$477$	−7.19978	−0.329655
$478$	−10.5200	−0.481175
$479$	27.5127	1.25709	0.628543	−	0.777775i	$-0.283652\pi$
$479$	27.5127	1.25709	0.628543	+	0.777775i	$0.283652\pi$
$480$	−5.10342	−0.232938
$481$	52.8036	2.40764
$482$	0.910337	0.0414647
$483$	−33.4424	−1.52168
$484$	−10.7048	−0.486581
$485$	−20.6929	−0.939617
$486$	21.8161	0.989600
$487$	20.9050	0.947296	0.473648	−	0.880714i	$-0.342937\pi$
$487$	20.9050	0.947296	0.473648	+	0.880714i	$0.342937\pi$
$488$	11.8179	0.534972
$489$	54.8748	2.48152
$490$	−5.65354	−0.255401
$491$	−3.94520	−0.178044	−0.0890221	−	0.996030i	$-0.528374\pi$
$491$	−3.94520	−0.178044	−0.0890221	+	0.996030i	$0.528374\pi$
$492$	−4.97914	−0.224477
$493$	5.88262	0.264940
$494$	40.1439	1.80616
$495$	−3.30308	−0.148462
$496$	2.47805	0.111268
$497$	−18.5304	−0.831204
$498$	5.22018	0.233922
$499$	5.92645	0.265305	0.132652	−	0.991163i	$-0.457651\pi$
$499$	5.92645	0.265305	0.132652	+	0.991163i	$0.457651\pi$
$500$	−11.7306	−0.524608
$501$	22.1068	0.987660
$502$	12.4647	0.556326
$503$	−22.4938	−1.00295	−0.501474	−	0.865173i	$-0.667209\pi$
$503$	−22.4938	−1.00295	−0.501474	+	0.865173i	$0.667209\pi$
$504$	6.00332	0.267409
$505$	2.44775	0.108923
$506$	−3.60549	−0.160284
$507$	−49.9585	−2.21874
$508$	−13.6085	−0.603779
$509$	26.3161	1.16644	0.583220	−	0.812314i	$-0.301793\pi$
$509$	26.3161	1.16644	0.583220	+	0.812314i	$0.301793\pi$
$510$	−20.7330	−0.918075
$511$	24.7424	1.09454
$512$	1.00000	0.0441942
$513$	1.82751	0.0806866
$514$	−19.0298	−0.839368
$515$	−39.0909	−1.72255
$516$	9.30758	0.409744
$517$	6.75446	0.297061
$518$	18.9192	0.831260
$519$	−17.6734	−0.775775
$520$	12.1847	0.534333
$521$	−39.3090	−1.72216	−0.861079	−	0.508471i	$-0.830211\pi$
$521$	−39.3090	−1.72216	−0.861079	+	0.508471i	$0.830211\pi$
$522$	4.18661	0.183243
$523$	−35.2190	−1.54002	−0.770010	−	0.638032i	$-0.779749\pi$
$523$	−35.2190	−1.54002	−0.770010	+	0.638032i	$0.779749\pi$
$524$	13.7209	0.599399
$525$	2.91851	0.127374
$526$	23.5260	1.02578
$527$	10.0673	0.438537
$528$	1.31879	0.0573929
$529$	21.0342	0.914530
$530$	−5.23576	−0.227427
$531$	−39.6788	−1.72191
$532$	14.3833	0.623596
$533$	11.8880	0.514924
$534$	2.76542	0.119672
$535$	−4.97193	−0.214955
$536$	4.36552	0.188562
$537$	42.7481	1.84472
$538$	28.7982	1.24158
$539$	1.46095	0.0629275
$540$	0.554694	0.0238702
$541$	20.5298	0.882643	0.441322	−	0.897349i	$-0.354510\pi$
$541$	20.5298	0.882643	0.441322	+	0.897349i	$0.354510\pi$
$542$	−14.3708	−0.617281
$543$	−27.8873	−1.19676
$544$	4.06258	0.174182
$545$	−21.1892	−0.907644
$546$	−29.2053	−1.24987
$547$	19.0894	0.816204	0.408102	−	0.912936i	$-0.366191\pi$
$547$	19.0894	0.816204	0.408102	+	0.912936i	$0.366191\pi$
$548$	−17.1081	−0.730820
$549$	34.1693	1.45831
$550$	0.314650	0.0134167
$551$	10.0307	0.427321
$552$	−16.1065	−0.685538
$553$	27.5420	1.17120
$554$	−7.18486	−0.305256
$555$	−46.5014	−1.97387
$556$	8.06283	0.341940
$557$	−1.40492	−0.0595284	−0.0297642	−	0.999557i	$-0.509476\pi$
$557$	−1.40492	−0.0595284	−0.0297642	+	0.999557i	$0.509476\pi$
$558$	7.16480	0.303310
$559$	−22.2223	−0.939904
$560$	4.36568	0.184484
$561$	5.35769	0.226202
$562$	24.5560	1.03583
$563$	−8.00814	−0.337503	−0.168751	−	0.985659i	$-0.553973\pi$
$563$	−8.00814	−0.337503	−0.168751	+	0.985659i	$0.553973\pi$
$564$	30.1736	1.27054
$565$	−11.8074	−0.496742
$566$	−21.0313	−0.884013
$567$	−19.3395	−0.812183
$568$	−8.92460	−0.374468
$569$	−3.15567	−0.132292	−0.0661462	−	0.997810i	$-0.521070\pi$
$569$	−3.15567	−0.132292	−0.0661462	+	0.997810i	$0.521070\pi$
$570$	−35.3527	−1.48076
$571$	−21.0914	−0.882646	−0.441323	−	0.897348i	$-0.645491\pi$
$571$	−21.0914	−0.882646	−0.441323	+	0.897348i	$0.645491\pi$
$572$	−3.14867	−0.131653
$573$	62.1782	2.59753
$574$	4.25937	0.177783
$575$	−3.84285	−0.160258
$576$	2.89131	0.120471
$577$	23.8203	0.991651	0.495825	−	0.868422i	$-0.334866\pi$
$577$	23.8203	0.991651	0.495825	+	0.868422i	$0.334866\pi$
$578$	−0.495432	−0.0206073
$579$	27.3749	1.13766
$580$	3.04455	0.126418
$581$	−4.46556	−0.185263
$582$	23.8876	0.990173
$583$	1.35299	0.0560351
$584$	11.9164	0.493104
$585$	35.2296	1.45657
$586$	−29.4745	−1.21758
$587$	−22.0825	−0.911441	−0.455721	−	0.890123i	$-0.650618\pi$
$587$	−22.0825	−0.911441	−0.455721	+	0.890123i	$0.650618\pi$
$588$	6.52636	0.269143
$589$	17.1661	0.707316
$590$	−28.8549	−1.18794
$591$	41.2757	1.69786
$592$	9.11182	0.374493
$593$	15.7705	0.647617	0.323808	−	0.946123i	$-0.395037\pi$
$593$	15.7705	0.647617	0.323808	+	0.946123i	$0.395037\pi$
$594$	−0.143340	−0.00588132
$595$	17.7359	0.727103
$596$	−2.12879	−0.0871985
$597$	−13.7427	−0.562451
$598$	38.4550	1.57254
$599$	23.7711	0.971260	0.485630	−	0.874164i	$-0.338590\pi$
$599$	23.7711	0.971260	0.485630	+	0.874164i	$0.338590\pi$
$600$	1.40561	0.0573837
$601$	−9.54239	−0.389242	−0.194621	−	0.980878i	$-0.562348\pi$
$601$	−9.54239	−0.389242	−0.194621	+	0.980878i	$0.562348\pi$
$602$	−7.96211	−0.324511
$603$	12.6221	0.514010
$604$	7.45545	0.303358
$605$	−22.5078	−0.915072
$606$	−2.82565	−0.114784
$607$	−6.65187	−0.269991	−0.134996	−	0.990846i	$-0.543102\pi$
$607$	−6.65187	−0.269991	−0.134996	+	0.990846i	$0.543102\pi$
$608$	6.92726	0.280938
$609$	−7.29745	−0.295708
$610$	24.8483	1.00608
$611$	−72.0410	−2.91447
$612$	11.7462	0.474811
$613$	19.6960	0.795513	0.397756	−	0.917491i	$-0.369789\pi$
$613$	19.6960	0.795513	0.397756	+	0.917491i	$0.369789\pi$
$614$	0.969261	0.0391162
$615$	−10.4691	−0.422155
$616$	−1.12815	−0.0454544
$617$	36.1981	1.45728	0.728640	−	0.684897i	$-0.240153\pi$
$617$	36.1981	1.45728	0.728640	+	0.684897i	$0.240153\pi$
$618$	45.1260	1.81523
$619$	5.39967	0.217031	0.108515	−	0.994095i	$-0.465390\pi$
$619$	5.39967	0.217031	0.108515	+	0.994095i	$0.465390\pi$
$620$	5.21032	0.209252
$621$	1.75063	0.0702502
$622$	2.14607	0.0860494
$623$	−2.36566	−0.0947782
$624$	−14.0658	−0.563082
$625$	−21.7691	−0.870764
$626$	−29.2724	−1.16996
$627$	9.13560	0.364841
$628$	21.2993	0.849935
$629$	37.0175	1.47598
$630$	12.6225	0.502894
$631$	−41.7347	−1.66143	−0.830717	−	0.556695i	$-0.812069\pi$
$631$	−41.7347	−1.66143	−0.830717	+	0.556695i	$0.812069\pi$
$632$	13.2647	0.527642
$633$	5.51952	0.219381
$634$	−22.2750	−0.884653
$635$	−28.6131	−1.13548
$636$	6.04408	0.239664
$637$	−15.5820	−0.617382
$638$	−0.786752	−0.0311478
$639$	−25.8038	−1.02078
$640$	2.10259	0.0831123
$641$	17.5050	0.691405	0.345703	−	0.938344i	$-0.387641\pi$
$641$	17.5050	0.691405	0.345703	+	0.938344i	$0.387641\pi$
$642$	5.73953	0.226521
$643$	28.5871	1.12737	0.563683	−	0.825991i	$-0.309384\pi$
$643$	28.5871	1.12737	0.563683	+	0.825991i	$0.309384\pi$
$644$	13.7782	0.542937
$645$	19.5701	0.770570
$646$	28.1426	1.10725
$647$	16.3060	0.641056	0.320528	−	0.947239i	$-0.396140\pi$
$647$	16.3060	0.641056	0.320528	+	0.947239i	$0.396140\pi$
$648$	−9.31426	−0.365899
$649$	7.45648	0.292692
$650$	−3.35596	−0.131632
$651$	−12.4886	−0.489465
$652$	−22.6083	−0.885408
$653$	37.4267	1.46462	0.732310	−	0.680971i	$-0.238442\pi$
$653$	37.4267	1.46462	0.732310	+	0.680971i	$0.238442\pi$
$654$	24.4605	0.956480
$655$	28.8494	1.12724
$656$	2.05139	0.0800934
$657$	34.4540	1.34418
$658$	−25.8118	−1.00625
$659$	26.0229	1.01371	0.506854	−	0.862032i	$-0.330808\pi$
$659$	26.0229	1.01371	0.506854	+	0.862032i	$0.330808\pi$
$660$	2.77288	0.107934
$661$	2.73114	0.106229	0.0531145	−	0.998588i	$-0.483085\pi$
$661$	2.73114	0.106229	0.0531145	+	0.998588i	$0.483085\pi$
$662$	−29.4784	−1.14571
$663$	−57.1434	−2.21927
$664$	−2.15070	−0.0834632
$665$	30.2422	1.17274
$666$	26.3451	1.02085
$667$	9.60867	0.372049
$668$	−9.10794	−0.352397
$669$	−50.1480	−1.93883
$670$	9.17890	0.354612
$671$	−6.42112	−0.247885
$672$	−5.03968	−0.194410
$673$	43.6449	1.68239	0.841194	−	0.540734i	$-0.181853\pi$
$673$	43.6449	1.68239	0.841194	+	0.540734i	$0.181853\pi$
$674$	11.9002	0.458380
$675$	−0.152776	−0.00588037
$676$	20.5828	0.791645
$677$	−45.9045	−1.76425	−0.882127	−	0.471012i	$-0.843889\pi$
$677$	−45.9045	−1.76425	−0.882127	+	0.471012i	$0.843889\pi$
$678$	13.6303	0.523469
$679$	−20.4345	−0.784204
$680$	8.54195	0.327569
$681$	2.39723	0.0918621
$682$	−1.34642	−0.0515569
$683$	−10.3475	−0.395937	−0.197968	−	0.980208i	$-0.563434\pi$
$683$	−10.3475	−0.395937	−0.197968	+	0.980208i	$0.563434\pi$
$684$	20.0289	0.765823
$685$	−35.9713	−1.37439
$686$	−20.1173	−0.768081
$687$	67.5088	2.57562
$688$	−3.83470	−0.146196
$689$	−14.4305	−0.549760
$690$	−33.8654	−1.28923
$691$	5.89103	0.224105	0.112053	−	0.993702i	$-0.464257\pi$
$691$	5.89103	0.224105	0.112053	+	0.993702i	$0.464257\pi$
$692$	7.28138	0.276797
$693$	−3.26183	−0.123907
$694$	2.54146	0.0964726
$695$	16.9528	0.643058
$696$	−3.51459	−0.133220
$697$	8.33395	0.315671
$698$	7.20653	0.272771
$699$	−61.3704	−2.32124
$700$	−1.20242	−0.0454471
$701$	−21.7973	−0.823273	−0.411637	−	0.911348i	$-0.635043\pi$
$701$	−21.7973	−0.823273	−0.411637	+	0.911348i	$0.635043\pi$
$702$	1.52882	0.0577016
$703$	63.1200	2.38061
$704$	−0.543337	−0.0204778
$705$	63.4428	2.38939
$706$	−4.16660	−0.156812
$707$	2.41718	0.0909074
$708$	33.3096	1.25185
$709$	−4.51782	−0.169670	−0.0848352	−	0.996395i	$-0.527036\pi$
$709$	−4.51782	−0.169670	−0.0848352	+	0.996395i	$0.527036\pi$
$710$	−18.7648	−0.704230
$711$	38.3524	1.43833
$712$	−1.13935	−0.0426988
$713$	16.4439	0.615829
$714$	−20.4741	−0.766224
$715$	−6.62038	−0.247588
$716$	−17.6121	−0.658195
$717$	25.5342	0.953593
$718$	−19.8460	−0.740648
$719$	−11.1446	−0.415622	−0.207811	−	0.978169i	$-0.566634\pi$
$719$	−11.1446	−0.415622	−0.207811	+	0.978169i	$0.566634\pi$
$720$	6.07924	0.226560
$721$	−38.6027	−1.43764
$722$	28.9870	1.07878
$723$	−2.20957	−0.0821748
$724$	11.4895	0.427004
$725$	−0.838546	−0.0311428
$726$	25.9827	0.964307
$727$	−12.7245	−0.471924	−0.235962	−	0.971762i	$-0.575824\pi$
$727$	−12.7245	−0.471924	−0.235962	+	0.971762i	$0.575824\pi$
$728$	12.0325	0.445953
$729$	−25.0094	−0.926274
$730$	25.0553	0.927339
$731$	−15.5788	−0.576202
$732$	−28.6845	−1.06021
$733$	−4.44201	−0.164069	−0.0820347	−	0.996629i	$-0.526142\pi$
$733$	−4.44201	−0.164069	−0.0820347	+	0.996629i	$0.526142\pi$
$734$	21.1963	0.782370
$735$	13.7223	0.506154
$736$	6.63583	0.244600
$737$	−2.37195	−0.0873719
$738$	5.93121	0.218331
$739$	−8.80712	−0.323975	−0.161988	−	0.986793i	$-0.551790\pi$
$739$	−8.80712	−0.323975	−0.161988	+	0.986793i	$0.551790\pi$
$740$	19.1584	0.704278
$741$	−97.4375	−3.57945
$742$	−5.17037	−0.189810
$743$	−18.1669	−0.666477	−0.333239	−	0.942842i	$-0.608142\pi$
$743$	−18.1669	−0.666477	−0.333239	+	0.942842i	$0.608142\pi$
$744$	−6.01472	−0.220510
$745$	−4.47597	−0.163987
$746$	−7.09918	−0.259919
$747$	−6.21833	−0.227517
$748$	−2.20735	−0.0807088
$749$	−4.90984	−0.179402
$750$	28.4725	1.03967
$751$	−25.8294	−0.942530	−0.471265	−	0.881992i	$-0.656202\pi$
$751$	−25.8294	−0.942530	−0.471265	+	0.881992i	$0.656202\pi$
$752$	−12.4314	−0.453328
$753$	−30.2543	−1.10253
$754$	8.39125	0.305591
$755$	15.6758	0.570499
$756$	0.547766	0.0199221
$757$	−17.8672	−0.649395	−0.324698	−	0.945818i	$-0.605263\pi$
$757$	−17.8672	−0.649395	−0.324698	+	0.945818i	$0.605263\pi$
$758$	−19.1134	−0.694230
$759$	8.75126	0.317651
$760$	14.5652	0.528336
$761$	−35.6671	−1.29293	−0.646465	−	0.762943i	$-0.723753\pi$
$761$	−35.6671	−1.29293	−0.646465	+	0.762943i	$0.723753\pi$
$762$	33.0306	1.19657
$763$	−20.9245	−0.757519
$764$	−25.6172	−0.926799
$765$	24.6974	0.892937
$766$	−5.63797	−0.203708
$767$	−79.5284	−2.87160
$768$	−2.42720	−0.0875841
$769$	−43.4031	−1.56515	−0.782577	−	0.622553i	$-0.786095\pi$
$769$	−43.4031	−1.56515	−0.782577	+	0.622553i	$0.786095\pi$
$770$	−2.37204	−0.0854823
$771$	46.1891	1.66346
$772$	−11.2784	−0.405918
$773$	42.3144	1.52194	0.760972	−	0.648784i	$-0.224722\pi$
$773$	42.3144	1.52194	0.760972	+	0.648784i	$0.224722\pi$
$774$	−11.0873	−0.398525
$775$	−1.43505	−0.0515486
$776$	−9.84162	−0.353294
$777$	−45.9206	−1.64739
$778$	1.82982	0.0656021
$779$	14.2105	0.509145
$780$	−29.5746	−1.05894
$781$	4.84907	0.173513
$782$	26.9586	0.964037
$783$	0.382003	0.0136517
$784$	−2.68884	−0.0960300
$785$	44.7838	1.59840
$786$	−33.3033	−1.18789
$787$	−26.6236	−0.949028	−0.474514	−	0.880248i	$-0.657376\pi$
$787$	−26.6236	−0.949028	−0.474514	+	0.880248i	$0.657376\pi$
$788$	−17.0055	−0.605795
$789$	−57.1024	−2.03290
$790$	27.8903	0.992293
$791$	−11.6600	−0.414581
$792$	−1.57096	−0.0558215
$793$	68.4856	2.43200
$794$	31.6187	1.12211
$795$	12.7082	0.450715
$796$	5.66195	0.200682
$797$	6.06321	0.214770	0.107385	−	0.994218i	$-0.465752\pi$
$797$	6.06321	0.214770	0.107385	+	0.994218i	$0.465752\pi$
$798$	−34.9112	−1.23584
$799$	−50.5037	−1.78669
$800$	−0.579106	−0.0204745
$801$	−3.29420	−0.116395
$802$	16.5535	0.584525
$803$	−6.47462	−0.228484
$804$	−10.5960	−0.373692
$805$	28.9699	1.02106
$806$	14.3604	0.505825
$807$	−69.8992	−2.46057
$808$	1.16416	0.0409549
$809$	34.2066	1.20264	0.601319	−	0.799009i	$-0.294642\pi$
$809$	34.2066	1.20264	0.601319	+	0.799009i	$0.294642\pi$
$810$	−19.5841	−0.688115
$811$	−26.4668	−0.929376	−0.464688	−	0.885475i	$-0.653833\pi$
$811$	−26.4668	−0.929376	−0.464688	+	0.885475i	$0.653833\pi$
$812$	3.00653	0.105509
$813$	34.8809	1.22333
$814$	−4.95079	−0.173525
$815$	−47.5359	−1.66511
$816$	−9.86071	−0.345194
$817$	−26.5640	−0.929355
$818$	22.4070	0.783442
$819$	34.7896	1.21565
$820$	4.31324	0.150625
$821$	−1.94218	−0.0677825	−0.0338912	−	0.999426i	$-0.510790\pi$
$821$	−1.94218	−0.0677825	−0.0338912	+	0.999426i	$0.510790\pi$
$822$	41.5247	1.44834
$823$	27.0772	0.943853	0.471926	−	0.881638i	$-0.343559\pi$
$823$	27.0772	0.943853	0.471926	+	0.881638i	$0.343559\pi$
$824$	−18.5918	−0.647675
$825$	−0.763719	−0.0265893
$826$	−28.4945	−0.991450
$827$	56.2000	1.95426	0.977132	−	0.212632i	$-0.0682036\pi$
$827$	56.2000	1.95426	0.977132	+	0.212632i	$0.0682036\pi$
$828$	19.1862	0.666768
$829$	24.9957	0.868136	0.434068	−	0.900880i	$-0.357078\pi$
$829$	24.9957	0.868136	0.434068	+	0.900880i	$0.357078\pi$
$830$	−4.52204	−0.156962
$831$	17.4391	0.604956
$832$	5.79506	0.200908
$833$	−10.9236	−0.378482
$834$	−19.5701	−0.677657
$835$	−19.1503	−0.662723
$836$	−3.76384	−0.130175
$837$	0.653744	0.0225967
$838$	−10.2382	−0.353674
$839$	13.6240	0.470352	0.235176	−	0.971953i	$-0.424433\pi$
$839$	13.6240	0.470352	0.235176	+	0.971953i	$0.424433\pi$
$840$	−10.5964	−0.365610
$841$	−26.9033	−0.927700
$842$	10.8785	0.374897
$843$	−59.6023	−2.05281
$844$	−2.27403	−0.0782752
$845$	43.2772	1.48878
$846$	−35.9431	−1.23575
$847$	−22.2267	−0.763718
$848$	−2.49014	−0.0855119
$849$	51.0473	1.75194
$850$	−2.35267	−0.0806958
$851$	60.4644	2.07269
$852$	21.6618	0.742122
$853$	−37.3572	−1.27909	−0.639544	−	0.768755i	$-0.720877\pi$
$853$	−37.3572	−1.27909	−0.639544	+	0.768755i	$0.720877\pi$
$854$	24.5380	0.839671
$855$	42.1125	1.44022
$856$	−2.36467	−0.0808227
$857$	18.2503	0.623419	0.311709	−	0.950177i	$-0.399098\pi$
$857$	18.2503	0.623419	0.311709	+	0.950177i	$0.399098\pi$
$858$	7.64247	0.260910
$859$	34.8154	1.18789	0.593943	−	0.804507i	$-0.297570\pi$
$859$	34.8154	1.18789	0.593943	+	0.804507i	$0.297570\pi$
$860$	−8.06280	−0.274939
$861$	−10.3384	−0.352330
$862$	−1.21664	−0.0414388
$863$	−53.5109	−1.82153	−0.910766	−	0.412923i	$-0.864508\pi$
$863$	−53.5109	−1.82153	−0.910766	+	0.412923i	$0.864508\pi$
$864$	0.263814	0.00897514
$865$	15.3098	0.520548
$866$	2.31179	0.0785578
$867$	1.20251	0.0408395
$868$	5.14525	0.174641
$869$	−7.20722	−0.244488
$870$	−7.38974	−0.250536
$871$	25.2985	0.857205
$872$	−10.0776	−0.341272
$873$	−28.4552	−0.963062
$874$	45.9681	1.55490
$875$	−24.3566	−0.823403
$876$	−28.9235	−0.977234
$877$	33.1126	1.11813	0.559067	−	0.829122i	$-0.311159\pi$
$877$	33.1126	1.11813	0.559067	+	0.829122i	$0.311159\pi$
$878$	34.7811	1.17381
$879$	71.5406	2.41300
$880$	−1.14242	−0.0385109
$881$	2.25921	0.0761149	0.0380574	−	0.999276i	$-0.487883\pi$
$881$	2.25921	0.0761149	0.0380574	+	0.999276i	$0.487883\pi$
$882$	−7.77427	−0.261773
$883$	−36.1942	−1.21803	−0.609015	−	0.793159i	$-0.708435\pi$
$883$	−36.1942	−1.21803	−0.609015	+	0.793159i	$0.708435\pi$
$884$	23.5429	0.791834
$885$	70.0366	2.35425
$886$	−9.96923	−0.334923
$887$	−41.1206	−1.38069	−0.690347	−	0.723478i	$-0.742542\pi$
$887$	−41.1206	−1.38069	−0.690347	+	0.723478i	$0.742542\pi$
$888$	−22.1162	−0.742172
$889$	−28.2558	−0.947668
$890$	−2.39558	−0.0803000
$891$	5.06078	0.169543
$892$	20.6608	0.691776
$893$	−86.1159	−2.88176
$894$	5.16699	0.172810
$895$	−37.0311	−1.23781
$896$	2.07633	0.0693654
$897$	−93.3381	−3.11647
$898$	15.2243	0.508042
$899$	3.58821	0.119674
$900$	−1.67438	−0.0558125
$901$	−10.1164	−0.337027
$902$	−1.11460	−0.0371121
$903$	19.3256	0.643117
$904$	−5.61565	−0.186774
$905$	24.1577	0.803030
$906$	−18.0959	−0.601195
$907$	−42.9553	−1.42631	−0.713154	−	0.701008i	$-0.752734\pi$
$907$	−42.9553	−1.42631	−0.713154	+	0.701008i	$0.752734\pi$
$908$	−0.987652	−0.0327764
$909$	3.36594	0.111641
$910$	25.2994	0.838667
$911$	−17.4050	−0.576654	−0.288327	−	0.957532i	$-0.593099\pi$
$911$	−17.4050	−0.576654	−0.288327	+	0.957532i	$0.593099\pi$
$912$	−16.8139	−0.556763
$913$	1.16855	0.0386735
$914$	26.8112	0.886835
$915$	−60.3118	−1.99385
$916$	−27.8134	−0.918981
$917$	28.4891	0.940793
$918$	1.07177	0.0353736
$919$	40.5411	1.33733	0.668664	−	0.743565i	$-0.266867\pi$
$919$	40.5411	1.33733	0.668664	+	0.743565i	$0.266867\pi$
$920$	13.9524	0.459998
$921$	−2.35259	−0.0775206
$922$	−9.37388	−0.308712
$923$	−51.7186	−1.70234
$924$	2.73825	0.0900817
$925$	−5.27671	−0.173497
$926$	13.1327	0.431568
$927$	−53.7546	−1.76553
$928$	1.44800	0.0475329
$929$	−26.6479	−0.874289	−0.437144	−	0.899391i	$-0.644010\pi$
$929$	−26.6479	−0.874289	−0.437144	+	0.899391i	$0.644010\pi$
$930$	−12.6465	−0.414695
$931$	−18.6263	−0.610453
$932$	25.2844	0.828219
$933$	−5.20894	−0.170533
$934$	−3.75916	−0.123003
$935$	−4.64116	−0.151782
$936$	16.7553	0.547665
$937$	9.96085	0.325407	0.162703	−	0.986675i	$-0.447979\pi$
$937$	9.96085	0.325407	0.162703	+	0.986675i	$0.447979\pi$
$938$	9.06427	0.295959
$939$	71.0500	2.31863
$940$	−26.1382	−0.852535
$941$	−41.2620	−1.34510	−0.672551	−	0.740050i	$-0.734802\pi$
$941$	−41.2620	−1.34510	−0.672551	+	0.740050i	$0.734802\pi$
$942$	−51.6978	−1.68440
$943$	13.6127	0.443290
$944$	−13.7235	−0.446661
$945$	1.15173	0.0374657
$946$	2.08353	0.0677415
$947$	−12.4793	−0.405522	−0.202761	−	0.979228i	$-0.564992\pi$
$947$	−12.4793	−0.405522	−0.202761	+	0.979228i	$0.564992\pi$
$948$	−32.1962	−1.04568
$949$	69.0563	2.24166
$950$	−4.01162	−0.130154
$951$	54.0659	1.75321
$952$	8.43527	0.273389
$953$	60.4866	1.95935	0.979677	−	0.200581i	$-0.0642831\pi$
$953$	60.4866	1.95935	0.979677	+	0.200581i	$0.0642831\pi$
$954$	−7.19978	−0.233101
$955$	−53.8626	−1.74295
$956$	−10.5200	−0.340242
$957$	1.90961	0.0617288
$958$	27.5127	0.888894
$959$	−35.5220	−1.14707
$960$	−5.10342	−0.164712
$961$	−24.8593	−0.801912
$962$	52.8036	1.70246
$963$	−6.83699	−0.220319
$964$	0.910337	0.0293200
$965$	−23.7138	−0.763375
$966$	−33.4424	−1.07599
$967$	−39.5175	−1.27080	−0.635399	−	0.772184i	$-0.719164\pi$
$967$	−39.5175	−1.27080	−0.635399	+	0.772184i	$0.719164\pi$
$968$	−10.7048	−0.344065
$969$	−68.3077	−2.19436
$970$	−20.6929	−0.664410
$971$	55.3596	1.77657	0.888286	−	0.459290i	$-0.151896\pi$
$971$	55.3596	1.77657	0.888286	+	0.459290i	$0.151896\pi$
$972$	21.8161	0.699753
$973$	16.7411	0.536695
$974$	20.9050	0.669839
$975$	8.14559	0.260868
$976$	11.8179	0.378283
$977$	−18.4753	−0.591077	−0.295539	−	0.955331i	$-0.595499\pi$
$977$	−18.4753	−0.591077	−0.295539	+	0.955331i	$0.595499\pi$
$978$	54.8748	1.75470
$979$	0.619049	0.0197849
$980$	−5.65354	−0.180596
$981$	−29.1376	−0.930291
$982$	−3.94520	−0.125896
$983$	8.02889	0.256082	0.128041	−	0.991769i	$-0.459131\pi$
$983$	8.02889	0.256082	0.128041	+	0.991769i	$0.459131\pi$
$984$	−4.97914	−0.158729
$985$	−35.7556	−1.13927
$986$	5.88262	0.187341
$987$	62.6505	1.99419
$988$	40.1439	1.27715
$989$	−25.4464	−0.809148
$990$	−3.30308	−0.104979
$991$	−21.2697	−0.675654	−0.337827	−	0.941208i	$-0.609692\pi$
$991$	−21.2697	−0.675654	−0.337827	+	0.941208i	$0.609692\pi$
$992$	2.47805	0.0786781
$993$	71.5499	2.27057
$994$	−18.5304	−0.587750
$995$	11.9048	0.377407
$996$	5.22018	0.165408
$997$	18.6705	0.591300	0.295650	−	0.955296i	$-0.404464\pi$
$997$	18.6705	0.591300	0.295650	+	0.955296i	$0.404464\pi$
$998$	5.92645	0.187599
$999$	2.40383	0.0760537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.d.1.17	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.d.1.17	✓	101	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.42720 q^{3} +1.00000 q^{4} +2.10259 q^{5} -2.42720 q^{6} +2.07633 q^{7} +1.00000 q^{8} +2.89131 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.42720 q^{3} +1.00000 q^{4} +2.10259 q^{5} -2.42720 q^{6} +2.07633 q^{7} +1.00000 q^{8} +2.89131 q^{9} +2.10259 q^{10} -0.543337 q^{11} -2.42720 q^{12} +5.79506 q^{13} +2.07633 q^{14} -5.10342 q^{15} +1.00000 q^{16} +4.06258 q^{17} +2.89131 q^{18} +6.92726 q^{19} +2.10259 q^{20} -5.03968 q^{21} -0.543337 q^{22} +6.63583 q^{23} -2.42720 q^{24} -0.579106 q^{25} +5.79506 q^{26} +0.263814 q^{27} +2.07633 q^{28} +1.44800 q^{29} -5.10342 q^{30} +2.47805 q^{31} +1.00000 q^{32} +1.31879 q^{33} +4.06258 q^{34} +4.36568 q^{35} +2.89131 q^{36} +9.11182 q^{37} +6.92726 q^{38} -14.0658 q^{39} +2.10259 q^{40} +2.05139 q^{41} -5.03968 q^{42} -3.83470 q^{43} -0.543337 q^{44} +6.07924 q^{45} +6.63583 q^{46} -12.4314 q^{47} -2.42720 q^{48} -2.68884 q^{49} -0.579106 q^{50} -9.86071 q^{51} +5.79506 q^{52} -2.49014 q^{53} +0.263814 q^{54} -1.14242 q^{55} +2.07633 q^{56} -16.8139 q^{57} +1.44800 q^{58} -13.7235 q^{59} -5.10342 q^{60} +11.8179 q^{61} +2.47805 q^{62} +6.00332 q^{63} +1.00000 q^{64} +12.1847 q^{65} +1.31879 q^{66} +4.36552 q^{67} +4.06258 q^{68} -16.1065 q^{69} +4.36568 q^{70} -8.92460 q^{71} +2.89131 q^{72} +11.9164 q^{73} +9.11182 q^{74} +1.40561 q^{75} +6.92726 q^{76} -1.12815 q^{77} -14.0658 q^{78} +13.2647 q^{79} +2.10259 q^{80} -9.31426 q^{81} +2.05139 q^{82} -2.15070 q^{83} -5.03968 q^{84} +8.54195 q^{85} -3.83470 q^{86} -3.51459 q^{87} -0.543337 q^{88} -1.13935 q^{89} +6.07924 q^{90} +12.0325 q^{91} +6.63583 q^{92} -6.01472 q^{93} -12.4314 q^{94} +14.5652 q^{95} -2.42720 q^{96} -9.84162 q^{97} -2.68884 q^{98} -1.57096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * q^99

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