LMFDB - Embedded newform 8026.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.44392 q^{3} +1.00000 q^{4} +2.01179 q^{5} -2.44392 q^{6} +1.54759 q^{7} +1.00000 q^{8} +2.97273 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.44392 q^{3} +1.00000 q^{4} +2.01179 q^{5} -2.44392 q^{6} +1.54759 q^{7} +1.00000 q^{8} +2.97273 q^{9} +2.01179 q^{10} +2.58792 q^{11} -2.44392 q^{12} +3.71756 q^{13} +1.54759 q^{14} -4.91666 q^{15} +1.00000 q^{16} +0.451141 q^{17} +2.97273 q^{18} +1.98340 q^{19} +2.01179 q^{20} -3.78218 q^{21} +2.58792 q^{22} -3.96760 q^{23} -2.44392 q^{24} -0.952685 q^{25} +3.71756 q^{26} +0.0666402 q^{27} +1.54759 q^{28} -6.63828 q^{29} -4.91666 q^{30} +4.92083 q^{31} +1.00000 q^{32} -6.32466 q^{33} +0.451141 q^{34} +3.11343 q^{35} +2.97273 q^{36} +11.0886 q^{37} +1.98340 q^{38} -9.08542 q^{39} +2.01179 q^{40} +12.2027 q^{41} -3.78218 q^{42} +2.33962 q^{43} +2.58792 q^{44} +5.98052 q^{45} -3.96760 q^{46} -8.14310 q^{47} -2.44392 q^{48} -4.60496 q^{49} -0.952685 q^{50} -1.10255 q^{51} +3.71756 q^{52} +9.46772 q^{53} +0.0666402 q^{54} +5.20636 q^{55} +1.54759 q^{56} -4.84727 q^{57} -6.63828 q^{58} +7.16769 q^{59} -4.91666 q^{60} +0.529394 q^{61} +4.92083 q^{62} +4.60057 q^{63} +1.00000 q^{64} +7.47897 q^{65} -6.32466 q^{66} -8.87243 q^{67} +0.451141 q^{68} +9.69649 q^{69} +3.11343 q^{70} +11.9264 q^{71} +2.97273 q^{72} -0.623423 q^{73} +11.0886 q^{74} +2.32828 q^{75} +1.98340 q^{76} +4.00504 q^{77} -9.08542 q^{78} +12.1265 q^{79} +2.01179 q^{80} -9.08106 q^{81} +12.2027 q^{82} -13.4577 q^{83} -3.78218 q^{84} +0.907602 q^{85} +2.33962 q^{86} +16.2234 q^{87} +2.58792 q^{88} -2.15640 q^{89} +5.98052 q^{90} +5.75327 q^{91} -3.96760 q^{92} -12.0261 q^{93} -8.14310 q^{94} +3.99020 q^{95} -2.44392 q^{96} -6.48983 q^{97} -4.60496 q^{98} +7.69319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−2.44392	−1.41100	−0.705498	−	0.708712i	$-0.749277\pi$
$3$	−2.44392	−1.41100	−0.705498	+	0.708712i	$0.749277\pi$
$4$	1.00000	0.500000
$5$	2.01179	0.899702	0.449851	−	0.893104i	$-0.351477\pi$
$5$	2.01179	0.899702	0.449851	+	0.893104i	$0.351477\pi$
$6$	−2.44392	−0.997725
$7$	1.54759	0.584934	0.292467	−	0.956276i	$-0.405524\pi$
$7$	1.54759	0.584934	0.292467	+	0.956276i	$0.405524\pi$
$8$	1.00000	0.353553
$9$	2.97273	0.990911
$10$	2.01179	0.636185
$11$	2.58792	0.780287	0.390143	−	0.920754i	$-0.372425\pi$
$11$	2.58792	0.780287	0.390143	+	0.920754i	$0.372425\pi$
$12$	−2.44392	−0.705498
$13$	3.71756	1.03107	0.515533	−	0.856869i	$-0.327594\pi$
$13$	3.71756	1.03107	0.515533	+	0.856869i	$0.327594\pi$
$14$	1.54759	0.413611
$15$	−4.91666	−1.26948
$16$	1.00000	0.250000
$17$	0.451141	0.109418	0.0547089	−	0.998502i	$-0.482577\pi$
$17$	0.451141	0.109418	0.0547089	+	0.998502i	$0.482577\pi$
$18$	2.97273	0.700680
$19$	1.98340	0.455024	0.227512	−	0.973775i	$-0.426941\pi$
$19$	1.98340	0.455024	0.227512	+	0.973775i	$0.426941\pi$
$20$	2.01179	0.449851
$21$	−3.78218	−0.825340
$22$	2.58792	0.551746
$23$	−3.96760	−0.827302	−0.413651	−	0.910435i	$-0.635747\pi$
$23$	−3.96760	−0.827302	−0.413651	+	0.910435i	$0.635747\pi$
$24$	−2.44392	−0.498863
$25$	−0.952685	−0.190537
$26$	3.71756	0.729074
$27$	0.0666402	0.0128249
$28$	1.54759	0.292467
$29$	−6.63828	−1.23270	−0.616349	−	0.787473i	$-0.711389\pi$
$29$	−6.63828	−1.23270	−0.616349	+	0.787473i	$0.711389\pi$
$30$	−4.91666	−0.897655
$31$	4.92083	0.883808	0.441904	−	0.897062i	$-0.354303\pi$
$31$	4.92083	0.883808	0.441904	+	0.897062i	$0.354303\pi$
$32$	1.00000	0.176777
$33$	−6.32466	−1.10098
$34$	0.451141	0.0773700
$35$	3.11343	0.526266
$36$	2.97273	0.495455
$37$	11.0886	1.82295	0.911476	−	0.411354i	$-0.134944\pi$
$37$	11.0886	1.82295	0.911476	+	0.411354i	$0.134944\pi$
$38$	1.98340	0.321751
$39$	−9.08542	−1.45483
$40$	2.01179	0.318093
$41$	12.2027	1.90574	0.952868	−	0.303384i	$-0.0981164\pi$
$41$	12.2027	1.90574	0.952868	+	0.303384i	$0.0981164\pi$
$42$	−3.78218	−0.583604
$43$	2.33962	0.356789	0.178395	−	0.983959i	$-0.442910\pi$
$43$	2.33962	0.356789	0.178395	+	0.983959i	$0.442910\pi$
$44$	2.58792	0.390143
$45$	5.98052	0.891524
$46$	−3.96760	−0.584991
$47$	−8.14310	−1.18779	−0.593897	−	0.804541i	$-0.702411\pi$
$47$	−8.14310	−1.18779	−0.593897	+	0.804541i	$0.702411\pi$
$48$	−2.44392	−0.352749
$49$	−4.60496	−0.657852
$50$	−0.952685	−0.134730
$51$	−1.10255	−0.154388
$52$	3.71756	0.515533
$53$	9.46772	1.30049	0.650246	−	0.759724i	$-0.274666\pi$
$53$	9.46772	1.30049	0.650246	+	0.759724i	$0.274666\pi$
$54$	0.0666402	0.00906859
$55$	5.20636	0.702025
$56$	1.54759	0.206806
$57$	−4.84727	−0.642037
$58$	−6.63828	−0.871649
$59$	7.16769	0.933153	0.466577	−	0.884481i	$-0.345487\pi$
$59$	7.16769	0.933153	0.466577	+	0.884481i	$0.345487\pi$
$60$	−4.91666	−0.634738
$61$	0.529394	0.0677820	0.0338910	−	0.999426i	$-0.489210\pi$
$61$	0.529394	0.0677820	0.0338910	+	0.999426i	$0.489210\pi$
$62$	4.92083	0.624946
$63$	4.60057	0.579618
$64$	1.00000	0.125000
$65$	7.47897	0.927652
$66$	−6.32466	−0.778512
$67$	−8.87243	−1.08394	−0.541970	−	0.840398i	$-0.682321\pi$
$67$	−8.87243	−1.08394	−0.541970	+	0.840398i	$0.682321\pi$
$68$	0.451141	0.0547089
$69$	9.69649	1.16732
$70$	3.11343	0.372127
$71$	11.9264	1.41541	0.707704	−	0.706509i	$-0.249731\pi$
$71$	11.9264	1.41541	0.707704	+	0.706509i	$0.249731\pi$
$72$	2.97273	0.350340
$73$	−0.623423	−0.0729661	−0.0364831	−	0.999334i	$-0.511615\pi$
$73$	−0.623423	−0.0729661	−0.0364831	+	0.999334i	$0.511615\pi$
$74$	11.0886	1.28902
$75$	2.32828	0.268847
$76$	1.98340	0.227512
$77$	4.00504	0.456417
$78$	−9.08542	−1.02872
$79$	12.1265	1.36433	0.682167	−	0.731197i	$-0.261038\pi$
$79$	12.1265	1.36433	0.682167	+	0.731197i	$0.261038\pi$
$80$	2.01179	0.224925
$81$	−9.08106	−1.00901
$82$	12.2027	1.34756
$83$	−13.4577	−1.47717	−0.738587	−	0.674159i	$-0.764506\pi$
$83$	−13.4577	−1.47717	−0.738587	+	0.674159i	$0.764506\pi$
$84$	−3.78218	−0.412670
$85$	0.907602	0.0984433
$86$	2.33962	0.252288
$87$	16.2234	1.73933
$88$	2.58792	0.275873
$89$	−2.15640	−0.228578	−0.114289	−	0.993448i	$-0.536459\pi$
$89$	−2.15640	−0.228578	−0.114289	+	0.993448i	$0.536459\pi$
$90$	5.98052	0.630403
$91$	5.75327	0.603107
$92$	−3.96760	−0.413651
$93$	−12.0261	−1.24705
$94$	−8.14310	−0.839897
$95$	3.99020	0.409386
$96$	−2.44392	−0.249431
$97$	−6.48983	−0.658943	−0.329471	−	0.944166i	$-0.606871\pi$
$97$	−6.48983	−0.658943	−0.329471	+	0.944166i	$0.606871\pi$
$98$	−4.60496	−0.465171
$99$	7.69319	0.773194
$100$	−0.952685	−0.0952685
$101$	−16.1388	−1.60587	−0.802936	−	0.596065i	$-0.796730\pi$
$101$	−16.1388	−1.60587	−0.802936	+	0.596065i	$0.796730\pi$
$102$	−1.10255	−0.109169
$103$	−16.4341	−1.61930	−0.809651	−	0.586912i	$-0.800343\pi$
$103$	−16.4341	−1.61930	−0.809651	+	0.586912i	$0.800343\pi$
$104$	3.71756	0.364537
$105$	−7.60898	−0.742560
$106$	9.46772	0.919586
$107$	−0.137239	−0.0132674	−0.00663371	−	0.999978i	$-0.502112\pi$
$107$	−0.137239	−0.0132674	−0.00663371	+	0.999978i	$0.502112\pi$
$108$	0.0666402	0.00641246
$109$	15.7095	1.50469	0.752346	−	0.658768i	$-0.228922\pi$
$109$	15.7095	1.50469	0.752346	+	0.658768i	$0.228922\pi$
$110$	5.20636	0.496407
$111$	−27.0996	−2.57218
$112$	1.54759	0.146234
$113$	3.83706	0.360960	0.180480	−	0.983579i	$-0.442235\pi$
$113$	3.83706	0.360960	0.180480	+	0.983579i	$0.442235\pi$
$114$	−4.84727	−0.453989
$115$	−7.98200	−0.744325
$116$	−6.63828	−0.616349
$117$	11.0513	1.02170
$118$	7.16769	0.659839
$119$	0.698181	0.0640022
$120$	−4.91666	−0.448827
$121$	−4.30268	−0.391153
$122$	0.529394	0.0479291
$123$	−29.8223	−2.68899
$124$	4.92083	0.441904
$125$	−11.9756	−1.07113
$126$	4.60057	0.409852
$127$	−19.6110	−1.74019	−0.870096	−	0.492882i	$-0.835943\pi$
$127$	−19.6110	−1.74019	−0.870096	+	0.492882i	$0.835943\pi$
$128$	1.00000	0.0883883
$129$	−5.71785	−0.503428
$130$	7.47897	0.655949
$131$	0.967270	0.0845108	0.0422554	−	0.999107i	$-0.486546\pi$
$131$	0.967270	0.0845108	0.0422554	+	0.999107i	$0.486546\pi$
$132$	−6.32466	−0.550491
$133$	3.06950	0.266159
$134$	−8.87243	−0.766461
$135$	0.134066	0.0115386
$136$	0.451141	0.0386850
$137$	18.5197	1.58225	0.791124	−	0.611656i	$-0.209496\pi$
$137$	18.5197	1.58225	0.791124	+	0.611656i	$0.209496\pi$
$138$	9.69649	0.825420
$139$	9.52864	0.808209	0.404104	−	0.914713i	$-0.367583\pi$
$139$	9.52864	0.808209	0.404104	+	0.914713i	$0.367583\pi$
$140$	3.11343	0.263133
$141$	19.9011	1.67597
$142$	11.9264	1.00084
$143$	9.62075	0.804528
$144$	2.97273	0.247728
$145$	−13.3548	−1.10906
$146$	−0.623423	−0.0515949
$147$	11.2541	0.928226
$148$	11.0886	0.911476
$149$	4.68104	0.383485	0.191743	−	0.981445i	$-0.438586\pi$
$149$	4.68104	0.383485	0.191743	+	0.981445i	$0.438586\pi$
$150$	2.32828	0.190104
$151$	−15.9850	−1.30084	−0.650420	−	0.759575i	$-0.725407\pi$
$151$	−15.9850	−1.30084	−0.650420	+	0.759575i	$0.725407\pi$
$152$	1.98340	0.160875
$153$	1.34112	0.108423
$154$	4.00504	0.322735
$155$	9.89970	0.795163
$156$	−9.08542	−0.727416
$157$	7.61146	0.607460	0.303730	−	0.952758i	$-0.401768\pi$
$157$	7.61146	0.607460	0.303730	+	0.952758i	$0.401768\pi$
$158$	12.1265	0.964729
$159$	−23.1383	−1.83499
$160$	2.01179	0.159046
$161$	−6.14023	−0.483918
$162$	−9.08106	−0.713475
$163$	−1.35600	−0.106210	−0.0531051	−	0.998589i	$-0.516912\pi$
$163$	−1.35600	−0.106210	−0.0531051	+	0.998589i	$0.516912\pi$
$164$	12.2027	0.952868
$165$	−12.7239	−0.990555
$166$	−13.4577	−1.04452
$167$	4.61782	0.357337	0.178669	−	0.983909i	$-0.442821\pi$
$167$	4.61782	0.357337	0.178669	+	0.983909i	$0.442821\pi$
$168$	−3.78218	−0.291802
$169$	0.820286	0.0630989
$170$	0.907602	0.0696099
$171$	5.89613	0.450888
$172$	2.33962	0.178395
$173$	8.10420	0.616151	0.308075	−	0.951362i	$-0.400315\pi$
$173$	8.10420	0.616151	0.308075	+	0.951362i	$0.400315\pi$
$174$	16.2234	1.22989
$175$	−1.47437	−0.111452
$176$	2.58792	0.195072
$177$	−17.5172	−1.31668
$178$	−2.15640	−0.161629
$179$	0.0428166	0.00320026	0.00160013	−	0.999999i	$-0.499491\pi$
$179$	0.0428166	0.00320026	0.00160013	+	0.999999i	$0.499491\pi$
$180$	5.98052	0.445762
$181$	−12.1522	−0.903268	−0.451634	−	0.892203i	$-0.649159\pi$
$181$	−12.1522	−0.903268	−0.451634	+	0.892203i	$0.649159\pi$
$182$	5.75327	0.426461
$183$	−1.29380	−0.0956402
$184$	−3.96760	−0.292496
$185$	22.3079	1.64011
$186$	−12.0261	−0.881797
$187$	1.16752	0.0853772
$188$	−8.14310	−0.593897
$189$	0.103132	0.00750174
$190$	3.99020	0.289479
$191$	−5.88172	−0.425586	−0.212793	−	0.977097i	$-0.568256\pi$
$191$	−5.88172	−0.425586	−0.212793	+	0.977097i	$0.568256\pi$
$192$	−2.44392	−0.176375
$193$	12.0640	0.868384	0.434192	−	0.900820i	$-0.357034\pi$
$193$	12.0640	0.868384	0.434192	+	0.900820i	$0.357034\pi$
$194$	−6.48983	−0.465943
$195$	−18.2780	−1.30891
$196$	−4.60496	−0.328926
$197$	−11.5021	−0.819492	−0.409746	−	0.912200i	$-0.634383\pi$
$197$	−11.5021	−0.819492	−0.409746	+	0.912200i	$0.634383\pi$
$198$	7.69319	0.546731
$199$	−9.89653	−0.701546	−0.350773	−	0.936460i	$-0.614081\pi$
$199$	−9.89653	−0.701546	−0.350773	+	0.936460i	$0.614081\pi$
$200$	−0.952685	−0.0673650
$201$	21.6835	1.52943
$202$	−16.1388	−1.13552
$203$	−10.2733	−0.721047
$204$	−1.10255	−0.0771940
$205$	24.5493	1.71459
$206$	−16.4341	−1.14502
$207$	−11.7946	−0.819783
$208$	3.71756	0.257767
$209$	5.13289	0.355049
$210$	−7.60898	−0.525069
$211$	10.7118	0.737434	0.368717	−	0.929542i	$-0.379797\pi$
$211$	10.7118	0.737434	0.368717	+	0.929542i	$0.379797\pi$
$212$	9.46772	0.650246
$213$	−29.1472	−1.99714
$214$	−0.137239	−0.00938149
$215$	4.70684	0.321004
$216$	0.0666402	0.00453429
$217$	7.61544	0.516970
$218$	15.7095	1.06398
$219$	1.52359	0.102955
$220$	5.20636	0.351013
$221$	1.67715	0.112817
$222$	−27.0996	−1.81880
$223$	8.27298	0.553999	0.277000	−	0.960870i	$-0.410660\pi$
$223$	8.27298	0.553999	0.277000	+	0.960870i	$0.410660\pi$
$224$	1.54759	0.103403
$225$	−2.83208	−0.188805
$226$	3.83706	0.255237
$227$	−4.53288	−0.300858	−0.150429	−	0.988621i	$-0.548066\pi$
$227$	−4.53288	−0.300858	−0.150429	+	0.988621i	$0.548066\pi$
$228$	−4.84727	−0.321019
$229$	−0.740080	−0.0489058	−0.0244529	−	0.999701i	$-0.507784\pi$
$229$	−0.740080	−0.0489058	−0.0244529	+	0.999701i	$0.507784\pi$
$230$	−7.98200	−0.526317
$231$	−9.78798	−0.644002
$232$	−6.63828	−0.435824
$233$	18.5535	1.21548	0.607740	−	0.794136i	$-0.292076\pi$
$233$	18.5535	1.21548	0.607740	+	0.794136i	$0.292076\pi$
$234$	11.0513	0.722448
$235$	−16.3822	−1.06866
$236$	7.16769	0.466577
$237$	−29.6361	−1.92507
$238$	0.698181	0.0452564
$239$	−21.2596	−1.37517	−0.687586	−	0.726103i	$-0.741330\pi$
$239$	−21.2596	−1.37517	−0.687586	+	0.726103i	$0.741330\pi$
$240$	−4.91666	−0.317369
$241$	18.5786	1.19675	0.598376	−	0.801215i	$-0.295813\pi$
$241$	18.5786	1.19675	0.598376	+	0.801215i	$0.295813\pi$
$242$	−4.30268	−0.276587
$243$	21.9934	1.41088
$244$	0.529394	0.0338910
$245$	−9.26423	−0.591870
$246$	−29.8223	−1.90140
$247$	7.37343	0.469160
$248$	4.92083	0.312473
$249$	32.8895	2.08429
$250$	−11.9756	−0.757402
$251$	29.2123	1.84386	0.921931	−	0.387353i	$-0.126611\pi$
$251$	29.2123	1.84386	0.921931	+	0.387353i	$0.126611\pi$
$252$	4.60057	0.289809
$253$	−10.2678	−0.645533
$254$	−19.6110	−1.23050
$255$	−2.21811	−0.138903
$256$	1.00000	0.0625000
$257$	1.16094	0.0724175	0.0362087	−	0.999344i	$-0.488472\pi$
$257$	1.16094	0.0724175	0.0362087	+	0.999344i	$0.488472\pi$
$258$	−5.71785	−0.355978
$259$	17.1606	1.06631
$260$	7.47897	0.463826
$261$	−19.7338	−1.22149
$262$	0.967270	0.0597582
$263$	−0.0147234	−0.000907885 0	−0.000453943	−	1.00000i	$-0.500144\pi$
$263$	−0.0147234	−0.000907885 0	−0.000453943		1.00000i	$0.500144\pi$
$264$	−6.32466	−0.389256
$265$	19.0471	1.17005
$266$	3.06950	0.188203
$267$	5.27006	0.322522
$268$	−8.87243	−0.541970
$269$	32.4393	1.97786	0.988929	−	0.148390i	$-0.0474090\pi$
$269$	32.4393	1.97786	0.988929	+	0.148390i	$0.0474090\pi$
$270$	0.134066	0.00815902
$271$	−25.0693	−1.52285	−0.761426	−	0.648252i	$-0.775500\pi$
$271$	−25.0693	−1.52285	−0.761426	+	0.648252i	$0.775500\pi$
$272$	0.451141	0.0273544
$273$	−14.0605	−0.850981
$274$	18.5197	1.11882
$275$	−2.46547	−0.148674
$276$	9.69649	0.583660
$277$	−0.684030	−0.0410994	−0.0205497	−	0.999789i	$-0.506542\pi$
$277$	−0.684030	−0.0410994	−0.0205497	+	0.999789i	$0.506542\pi$
$278$	9.52864	0.571490
$279$	14.6283	0.875774
$280$	3.11343	0.186063
$281$	19.5746	1.16772	0.583861	−	0.811854i	$-0.301541\pi$
$281$	19.5746	1.16772	0.583861	+	0.811854i	$0.301541\pi$
$282$	19.9011	1.18509
$283$	−7.93016	−0.471399	−0.235699	−	0.971826i	$-0.575738\pi$
$283$	−7.93016	−0.471399	−0.235699	+	0.971826i	$0.575738\pi$
$284$	11.9264	0.707704
$285$	−9.75172	−0.577642
$286$	9.62075	0.568887
$287$	18.8847	1.11473
$288$	2.97273	0.175170
$289$	−16.7965	−0.988028
$290$	−13.3548	−0.784224
$291$	15.8606	0.929766
$292$	−0.623423	−0.0364831
$293$	16.5114	0.964604	0.482302	−	0.876005i	$-0.339801\pi$
$293$	16.5114	0.964604	0.482302	+	0.876005i	$0.339801\pi$
$294$	11.2541	0.656355
$295$	14.4199	0.839560
$296$	11.0886	0.644511
$297$	0.172459	0.0100071
$298$	4.68104	0.271165
$299$	−14.7498	−0.853004
$300$	2.32828	0.134424
$301$	3.62078	0.208698
$302$	−15.9850	−0.919833
$303$	39.4419	2.26588
$304$	1.98340	0.113756
$305$	1.06503	0.0609836
$306$	1.34112	0.0766668
$307$	9.23924	0.527311	0.263656	−	0.964617i	$-0.415072\pi$
$307$	9.23924	0.527311	0.263656	+	0.964617i	$0.415072\pi$
$308$	4.00504	0.228208
$309$	40.1636	2.28483
$310$	9.89970	0.562265
$311$	−2.43771	−0.138230	−0.0691150	−	0.997609i	$-0.522018\pi$
$311$	−2.43771	−0.138230	−0.0691150	+	0.997609i	$0.522018\pi$
$312$	−9.08542	−0.514361
$313$	−3.37064	−0.190520	−0.0952600	−	0.995452i	$-0.530368\pi$
$313$	−3.37064	−0.190520	−0.0952600	+	0.995452i	$0.530368\pi$
$314$	7.61146	0.429539
$315$	9.25541	0.521483
$316$	12.1265	0.682167
$317$	32.8819	1.84683	0.923416	−	0.383801i	$-0.125385\pi$
$317$	32.8819	1.84683	0.923416	+	0.383801i	$0.125385\pi$
$318$	−23.1383	−1.29753
$319$	−17.1793	−0.961857
$320$	2.01179	0.112463
$321$	0.335402	0.0187203
$322$	−6.14023	−0.342181
$323$	0.894794	0.0497877
$324$	−9.08106	−0.504503
$325$	−3.54167	−0.196456
$326$	−1.35600	−0.0751020
$327$	−38.3926	−2.12312
$328$	12.2027	0.673780
$329$	−12.6022	−0.694781
$330$	−12.7239	−0.700428
$331$	−8.51863	−0.468226	−0.234113	−	0.972209i	$-0.575219\pi$
$331$	−8.51863	−0.468226	−0.234113	+	0.972209i	$0.575219\pi$
$332$	−13.4577	−0.738587
$333$	32.9634	1.80638
$334$	4.61782	0.252676
$335$	−17.8495	−0.975222
$336$	−3.78218	−0.206335
$337$	−13.2866	−0.723770	−0.361885	−	0.932223i	$-0.617867\pi$
$337$	−13.2866	−0.723770	−0.361885	+	0.932223i	$0.617867\pi$
$338$	0.820286	0.0446177
$339$	−9.37745	−0.509313
$340$	0.907602	0.0492216
$341$	12.7347	0.689623
$342$	5.89613	0.318826
$343$	−17.9597	−0.969735
$344$	2.33962	0.126144
$345$	19.5073	1.05024
$346$	8.10420	0.435684
$347$	−6.62123	−0.355447	−0.177723	−	0.984081i	$-0.556873\pi$
$347$	−6.62123	−0.355447	−0.177723	+	0.984081i	$0.556873\pi$
$348$	16.2234	0.869666
$349$	−19.2594	−1.03093	−0.515465	−	0.856910i	$-0.672381\pi$
$349$	−19.2594	−1.03093	−0.515465	+	0.856910i	$0.672381\pi$
$350$	−1.47437	−0.0788083
$351$	0.247739	0.0132234
$352$	2.58792	0.137937
$353$	−27.1789	−1.44659	−0.723293	−	0.690541i	$-0.757372\pi$
$353$	−27.1789	−1.44659	−0.723293	+	0.690541i	$0.757372\pi$
$354$	−17.5172	−0.931031
$355$	23.9935	1.27344
$356$	−2.15640	−0.114289
$357$	−1.70630	−0.0903069
$358$	0.0428166	0.00226293
$359$	24.2455	1.27963	0.639813	−	0.768531i	$-0.279012\pi$
$359$	24.2455	1.27963	0.639813	+	0.768531i	$0.279012\pi$
$360$	5.98052	0.315201
$361$	−15.0661	−0.792953
$362$	−12.1522	−0.638707
$363$	10.5154	0.551915
$364$	5.75327	0.301553
$365$	−1.25420	−0.0656478
$366$	−1.29380	−0.0676278
$367$	1.35924	0.0709516	0.0354758	−	0.999371i	$-0.488705\pi$
$367$	1.35924	0.0709516	0.0354758	+	0.999371i	$0.488705\pi$
$368$	−3.96760	−0.206826
$369$	36.2753	1.88842
$370$	22.3079	1.15973
$371$	14.6522	0.760702
$372$	−12.0261	−0.623525
$373$	12.2204	0.632750	0.316375	−	0.948634i	$-0.397534\pi$
$373$	12.2204	0.632750	0.316375	+	0.948634i	$0.397534\pi$
$374$	1.16752	0.0603708
$375$	29.2673	1.51136
$376$	−8.14310	−0.419948
$377$	−24.6782	−1.27099
$378$	0.103132	0.00530453
$379$	−4.69365	−0.241097	−0.120548	−	0.992707i	$-0.538465\pi$
$379$	−4.69365	−0.241097	−0.120548	+	0.992707i	$0.538465\pi$
$380$	3.99020	0.204693
$381$	47.9276	2.45540
$382$	−5.88172	−0.300935
$383$	26.5501	1.35665	0.678324	−	0.734763i	$-0.262706\pi$
$383$	26.5501	1.35665	0.678324	+	0.734763i	$0.262706\pi$
$384$	−2.44392	−0.124716
$385$	8.05731	0.410639
$386$	12.0640	0.614040
$387$	6.95507	0.353546
$388$	−6.48983	−0.329471
$389$	−1.43944	−0.0729824	−0.0364912	−	0.999334i	$-0.511618\pi$
$389$	−1.43944	−0.0729824	−0.0364912	+	0.999334i	$0.511618\pi$
$390$	−18.2780	−0.925542
$391$	−1.78995	−0.0905215
$392$	−4.60496	−0.232586
$393$	−2.36393	−0.119244
$394$	−11.5021	−0.579468
$395$	24.3959	1.22749
$396$	7.69319	0.386597
$397$	19.8437	0.995926	0.497963	−	0.867198i	$-0.334081\pi$
$397$	19.8437	0.995926	0.497963	+	0.867198i	$0.334081\pi$
$398$	−9.89653	−0.496068
$399$	−7.50160	−0.375550
$400$	−0.952685	−0.0476343
$401$	−4.59931	−0.229678	−0.114839	−	0.993384i	$-0.536635\pi$
$401$	−4.59931	−0.229678	−0.114839	+	0.993384i	$0.536635\pi$
$402$	21.6835	1.08147
$403$	18.2935	0.911265
$404$	−16.1388	−0.802936
$405$	−18.2692	−0.907805
$406$	−10.2733	−0.509857
$407$	28.6963	1.42242
$408$	−1.10255	−0.0545844
$409$	−12.2003	−0.603266	−0.301633	−	0.953424i	$-0.597532\pi$
$409$	−12.2003	−0.603266	−0.301633	+	0.953424i	$0.597532\pi$
$410$	24.5493	1.21240
$411$	−45.2607	−2.23255
$412$	−16.4341	−0.809651
$413$	11.0926	0.545834
$414$	−11.7946	−0.579674
$415$	−27.0741	−1.32901
$416$	3.71756	0.182269
$417$	−23.2872	−1.14038
$418$	5.13289	0.251058
$419$	18.6860	0.912869	0.456435	−	0.889757i	$-0.349126\pi$
$419$	18.6860	0.912869	0.456435	+	0.889757i	$0.349126\pi$
$420$	−7.60898	−0.371280
$421$	29.7556	1.45020	0.725100	−	0.688643i	$-0.241793\pi$
$421$	29.7556	1.45020	0.725100	+	0.688643i	$0.241793\pi$
$422$	10.7118	0.521444
$423$	−24.2073	−1.17700
$424$	9.46772	0.459793
$425$	−0.429795	−0.0208481
$426$	−29.1472	−1.41219
$427$	0.819286	0.0396480
$428$	−0.137239	−0.00663371
$429$	−23.5123	−1.13519
$430$	4.70684	0.226984
$431$	2.60145	0.125308	0.0626538	−	0.998035i	$-0.480044\pi$
$431$	2.60145	0.125308	0.0626538	+	0.998035i	$0.480044\pi$
$432$	0.0666402	0.00320623
$433$	−13.9671	−0.671215	−0.335608	−	0.942002i	$-0.608942\pi$
$433$	−13.9671	−0.671215	−0.335608	+	0.942002i	$0.608942\pi$
$434$	7.61544	0.365553
$435$	32.6381	1.56488
$436$	15.7095	0.752346
$437$	−7.86936	−0.376442
$438$	1.52359	0.0728002
$439$	16.0997	0.768399	0.384199	−	0.923250i	$-0.374478\pi$
$439$	16.0997	0.768399	0.384199	+	0.923250i	$0.374478\pi$
$440$	5.20636	0.248203
$441$	−13.6893	−0.651872
$442$	1.67715	0.0797737
$443$	−34.7710	−1.65202	−0.826011	−	0.563655i	$-0.809395\pi$
$443$	−34.7710	−1.65202	−0.826011	+	0.563655i	$0.809395\pi$
$444$	−27.0996	−1.28609
$445$	−4.33823	−0.205652
$446$	8.27298	0.391737
$447$	−11.4401	−0.541097
$448$	1.54759	0.0731168
$449$	19.7654	0.932788	0.466394	−	0.884577i	$-0.345553\pi$
$449$	19.7654	0.932788	0.466394	+	0.884577i	$0.345553\pi$
$450$	−2.83208	−0.133505
$451$	31.5795	1.48702
$452$	3.83706	0.180480
$453$	39.0660	1.83548
$454$	−4.53288	−0.212739
$455$	11.5744	0.542616
$456$	−4.84727	−0.226994
$457$	27.7941	1.30015	0.650077	−	0.759868i	$-0.274736\pi$
$457$	27.7941	1.30015	0.650077	+	0.759868i	$0.274736\pi$
$458$	−0.740080	−0.0345817
$459$	0.0300641	0.00140327
$460$	−7.98200	−0.372163
$461$	−8.67607	−0.404085	−0.202043	−	0.979377i	$-0.564758\pi$
$461$	−8.67607	−0.404085	−0.202043	+	0.979377i	$0.564758\pi$
$462$	−9.78798	−0.455378
$463$	10.3205	0.479634	0.239817	−	0.970818i	$-0.422912\pi$
$463$	10.3205	0.479634	0.239817	+	0.970818i	$0.422912\pi$
$464$	−6.63828	−0.308174
$465$	−24.1941	−1.12197
$466$	18.5535	0.859474
$467$	−38.7001	−1.79083	−0.895414	−	0.445235i	$-0.853120\pi$
$467$	−38.7001	−1.79083	−0.895414	+	0.445235i	$0.853120\pi$
$468$	11.0513	0.510848
$469$	−13.7309	−0.634033
$470$	−16.3822	−0.755657
$471$	−18.6018	−0.857124
$472$	7.16769	0.329920
$473$	6.05475	0.278398
$474$	−29.6361	−1.36123
$475$	−1.88956	−0.0866989
$476$	0.698181	0.0320011
$477$	28.1450	1.28867
$478$	−21.2596	−0.972393
$479$	20.3467	0.929666	0.464833	−	0.885398i	$-0.346114\pi$
$479$	20.3467	0.929666	0.464833	+	0.885398i	$0.346114\pi$
$480$	−4.91666	−0.224414
$481$	41.2225	1.87959
$482$	18.5786	0.846232
$483$	15.0062	0.682806
$484$	−4.30268	−0.195576
$485$	−13.0562	−0.592852
$486$	21.9934	0.997643
$487$	2.12235	0.0961727	0.0480863	−	0.998843i	$-0.484688\pi$
$487$	2.12235	0.0961727	0.0480863	+	0.998843i	$0.484688\pi$
$488$	0.529394	0.0239646
$489$	3.31396	0.149862
$490$	−9.26423	−0.418515
$491$	−4.39404	−0.198300	−0.0991501	−	0.995072i	$-0.531612\pi$
$491$	−4.39404	−0.198300	−0.0991501	+	0.995072i	$0.531612\pi$
$492$	−29.8223	−1.34449
$493$	−2.99480	−0.134879
$494$	7.37343	0.331746
$495$	15.4771	0.695644
$496$	4.92083	0.220952
$497$	18.4573	0.827921
$498$	32.8895	1.47381
$499$	27.0828	1.21239	0.606197	−	0.795315i	$-0.292694\pi$
$499$	27.0828	1.21239	0.606197	+	0.795315i	$0.292694\pi$
$500$	−11.9756	−0.535564
$501$	−11.2856	−0.504202
$502$	29.2123	1.30381
$503$	−6.92966	−0.308978	−0.154489	−	0.987994i	$-0.549373\pi$
$503$	−6.92966	−0.308978	−0.154489	+	0.987994i	$0.549373\pi$
$504$	4.60057	0.204926
$505$	−32.4680	−1.44481
$506$	−10.2678	−0.456461
$507$	−2.00471	−0.0890324
$508$	−19.6110	−0.870096
$509$	3.69771	0.163898	0.0819490	−	0.996637i	$-0.473886\pi$
$509$	3.69771	0.163898	0.0819490	+	0.996637i	$0.473886\pi$
$510$	−2.21811	−0.0982193
$511$	−0.964804	−0.0426804
$512$	1.00000	0.0441942
$513$	0.132174	0.00583565
$514$	1.16094	0.0512069
$515$	−33.0620	−1.45689
$516$	−5.71785	−0.251714
$517$	−21.0737	−0.926820
$518$	17.1606	0.753993
$519$	−19.8060	−0.869386
$520$	7.47897	0.327975
$521$	30.1976	1.32298	0.661490	−	0.749954i	$-0.269924\pi$
$521$	30.1976	1.32298	0.661490	+	0.749954i	$0.269924\pi$
$522$	−19.7338	−0.863726
$523$	−45.5296	−1.99087	−0.995435	−	0.0954398i	$-0.969574\pi$
$523$	−45.5296	−1.99087	−0.995435	+	0.0954398i	$0.969574\pi$
$524$	0.967270	0.0422554
$525$	3.60323	0.157258
$526$	−0.0147234	−0.000641972 0
$527$	2.21999	0.0967042
$528$	−6.32466	−0.275245
$529$	−7.25813	−0.315571
$530$	19.0471	0.827353
$531$	21.3076	0.924672
$532$	3.06950	0.133080
$533$	45.3642	1.96494
$534$	5.27006	0.228058
$535$	−0.276097	−0.0119367
$536$	−8.87243	−0.383230
$537$	−0.104640	−0.00451555
$538$	32.4393	1.39856
$539$	−11.9173	−0.513313
$540$	0.134066	0.00576930
$541$	−5.77901	−0.248459	−0.124230	−	0.992254i	$-0.539646\pi$
$541$	−5.77901	−0.248459	−0.124230	+	0.992254i	$0.539646\pi$
$542$	−25.0693	−1.07682
$543$	29.6990	1.27451
$544$	0.451141	0.0193425
$545$	31.6042	1.35377
$546$	−14.0605	−0.601735
$547$	11.0157	0.470996	0.235498	−	0.971875i	$-0.424328\pi$
$547$	11.0157	0.470996	0.235498	+	0.971875i	$0.424328\pi$
$548$	18.5197	0.791124
$549$	1.57375	0.0671659
$550$	−2.46547	−0.105128
$551$	−13.1664	−0.560907
$552$	9.69649	0.412710
$553$	18.7668	0.798045
$554$	−0.684030	−0.0290616
$555$	−54.5188	−2.31419
$556$	9.52864	0.404104
$557$	−18.3840	−0.778954	−0.389477	−	0.921036i	$-0.627344\pi$
$557$	−18.3840	−0.778954	−0.389477	+	0.921036i	$0.627344\pi$
$558$	14.6283	0.619266
$559$	8.69770	0.367874
$560$	3.11343	0.131567
$561$	−2.85331	−0.120467
$562$	19.5746	0.825704
$563$	14.8484	0.625787	0.312894	−	0.949788i	$-0.398702\pi$
$563$	14.8484	0.625787	0.312894	+	0.949788i	$0.398702\pi$
$564$	19.9011	0.837986
$565$	7.71937	0.324756
$566$	−7.93016	−0.333329
$567$	−14.0538	−0.590203
$568$	11.9264	0.500422
$569$	−30.6539	−1.28508	−0.642539	−	0.766253i	$-0.722119\pi$
$569$	−30.6539	−1.28508	−0.642539	+	0.766253i	$0.722119\pi$
$570$	−9.75172	−0.408454
$571$	−13.2464	−0.554347	−0.277173	−	0.960820i	$-0.589398\pi$
$571$	−13.2464	−0.554347	−0.277173	+	0.960820i	$0.589398\pi$
$572$	9.62075	0.402264
$573$	14.3744	0.600501
$574$	18.8847	0.788234
$575$	3.77988	0.157632
$576$	2.97273	0.123864
$577$	38.0401	1.58363	0.791814	−	0.610762i	$-0.209137\pi$
$577$	38.0401	1.58363	0.791814	+	0.610762i	$0.209137\pi$
$578$	−16.7965	−0.698641
$579$	−29.4833	−1.22529
$580$	−13.3548	−0.554530
$581$	−20.8270	−0.864049
$582$	15.8606	0.657444
$583$	24.5017	1.01476
$584$	−0.623423	−0.0257974
$585$	22.2330	0.919221
$586$	16.5114	0.682078
$587$	23.5176	0.970676	0.485338	−	0.874327i	$-0.338697\pi$
$587$	23.5176	0.970676	0.485338	+	0.874327i	$0.338697\pi$
$588$	11.2541	0.464113
$589$	9.76000	0.402154
$590$	14.4199	0.593658
$591$	28.1102	1.15630
$592$	11.0886	0.455738
$593$	−1.75033	−0.0718776	−0.0359388	−	0.999354i	$-0.511442\pi$
$593$	−1.75033	−0.0718776	−0.0359388	+	0.999354i	$0.511442\pi$
$594$	0.172459	0.00707610
$595$	1.40460	0.0575829
$596$	4.68104	0.191743
$597$	24.1863	0.989879
$598$	−14.7498	−0.603165
$599$	−13.3808	−0.546726	−0.273363	−	0.961911i	$-0.588136\pi$
$599$	−13.3808	−0.546726	−0.273363	+	0.961911i	$0.588136\pi$
$600$	2.32828	0.0950518
$601$	3.67115	0.149749	0.0748747	−	0.997193i	$-0.476144\pi$
$601$	3.67115	0.149749	0.0748747	+	0.997193i	$0.476144\pi$
$602$	3.62078	0.147572
$603$	−26.3753	−1.07409
$604$	−15.9850	−0.650420
$605$	−8.65610	−0.351921
$606$	39.4419	1.60222
$607$	40.2187	1.63243	0.816213	−	0.577752i	$-0.196070\pi$
$607$	40.2187	1.63243	0.816213	+	0.577752i	$0.196070\pi$
$608$	1.98340	0.0804376
$609$	25.1072	1.01739
$610$	1.06503	0.0431219
$611$	−30.2725	−1.22469
$612$	1.34112	0.0542116
$613$	25.6405	1.03561	0.517805	−	0.855499i	$-0.326749\pi$
$613$	25.6405	1.03561	0.517805	+	0.855499i	$0.326749\pi$
$614$	9.23924	0.372865
$615$	−59.9964	−2.41929
$616$	4.00504	0.161368
$617$	12.7198	0.512081	0.256041	−	0.966666i	$-0.417582\pi$
$617$	12.7198	0.512081	0.256041	+	0.966666i	$0.417582\pi$
$618$	40.1636	1.61562
$619$	30.2369	1.21532	0.607662	−	0.794196i	$-0.292107\pi$
$619$	30.2369	1.21532	0.607662	+	0.794196i	$0.292107\pi$
$620$	9.89970	0.397582
$621$	−0.264402	−0.0106101
$622$	−2.43771	−0.0977433
$623$	−3.33722	−0.133703
$624$	−9.08542	−0.363708
$625$	−19.3290	−0.773159
$626$	−3.37064	−0.134718
$627$	−12.5443	−0.500973
$628$	7.61146	0.303730
$629$	5.00251	0.199463
$630$	9.25541	0.368744
$631$	−2.35741	−0.0938471	−0.0469235	−	0.998898i	$-0.514942\pi$
$631$	−2.35741	−0.0938471	−0.0469235	+	0.998898i	$0.514942\pi$
$632$	12.1265	0.482365
$633$	−26.1789	−1.04052
$634$	32.8819	1.30591
$635$	−39.4532	−1.56565
$636$	−23.1383	−0.917494
$637$	−17.1192	−0.678289
$638$	−17.1793	−0.680136
$639$	35.4541	1.40254
$640$	2.01179	0.0795231
$641$	−34.3894	−1.35830	−0.679149	−	0.734000i	$-0.737651\pi$
$641$	−34.3894	−1.35830	−0.679149	+	0.734000i	$0.737651\pi$
$642$	0.335402	0.0132372
$643$	−14.2710	−0.562795	−0.281398	−	0.959591i	$-0.590798\pi$
$643$	−14.2710	−0.562795	−0.281398	+	0.959591i	$0.590798\pi$
$644$	−6.14023	−0.241959
$645$	−11.5031	−0.452935
$646$	0.894794	0.0352052
$647$	−17.1600	−0.674630	−0.337315	−	0.941392i	$-0.609519\pi$
$647$	−17.1600	−0.674630	−0.337315	+	0.941392i	$0.609519\pi$
$648$	−9.08106	−0.356738
$649$	18.5494	0.728127
$650$	−3.54167	−0.138916
$651$	−18.6115	−0.729442
$652$	−1.35600	−0.0531051
$653$	39.7212	1.55441	0.777206	−	0.629246i	$-0.216636\pi$
$653$	39.7212	1.55441	0.777206	+	0.629246i	$0.216636\pi$
$654$	−38.3926	−1.50127
$655$	1.94595	0.0760345
$656$	12.2027	0.476434
$657$	−1.85327	−0.0723029
$658$	−12.6022	−0.491285
$659$	−21.2924	−0.829432	−0.414716	−	0.909951i	$-0.636119\pi$
$659$	−21.2924	−0.829432	−0.414716	+	0.909951i	$0.636119\pi$
$660$	−12.7239	−0.495277
$661$	25.9585	1.00967	0.504834	−	0.863217i	$-0.331554\pi$
$661$	25.9585	1.00967	0.504834	+	0.863217i	$0.331554\pi$
$662$	−8.51863	−0.331086
$663$	−4.09880	−0.159184
$664$	−13.4577	−0.522260
$665$	6.17520	0.239464
$666$	32.9634	1.27731
$667$	26.3381	1.01981
$668$	4.61782	0.178669
$669$	−20.2185	−0.781691
$670$	−17.8495	−0.689586
$671$	1.37003	0.0528894
$672$	−3.78218	−0.145901
$673$	−37.6908	−1.45287	−0.726437	−	0.687233i	$-0.758825\pi$
$673$	−37.6908	−1.45287	−0.726437	+	0.687233i	$0.758825\pi$
$674$	−13.2866	−0.511783
$675$	−0.0634872	−0.00244362
$676$	0.820286	0.0315495
$677$	20.0328	0.769922	0.384961	−	0.922933i	$-0.374215\pi$
$677$	20.0328	0.769922	0.384961	+	0.922933i	$0.374215\pi$
$678$	−9.37745	−0.360139
$679$	−10.0436	−0.385438
$680$	0.907602	0.0348050
$681$	11.0780	0.424510
$682$	12.7347	0.487637
$683$	−27.3025	−1.04470	−0.522350	−	0.852731i	$-0.674945\pi$
$683$	−27.3025	−1.04470	−0.522350	+	0.852731i	$0.674945\pi$
$684$	5.89613	0.225444
$685$	37.2579	1.42355
$686$	−17.9597	−0.685706
$687$	1.80869	0.0690060
$688$	2.33962	0.0891973
$689$	35.1969	1.34089
$690$	19.5073	0.742632
$691$	−45.5304	−1.73206	−0.866029	−	0.499993i	$-0.833336\pi$
$691$	−45.5304	−1.73206	−0.866029	+	0.499993i	$0.833336\pi$
$692$	8.10420	0.308075
$693$	11.9059	0.452268
$694$	−6.62123	−0.251339
$695$	19.1697	0.727147
$696$	16.2234	0.614947
$697$	5.50512	0.208521
$698$	−19.2594	−0.728978
$699$	−45.3432	−1.71504
$700$	−1.47437	−0.0557259
$701$	0.362974	0.0137094	0.00685468	−	0.999977i	$-0.497818\pi$
$701$	0.362974	0.0137094	0.00685468	+	0.999977i	$0.497818\pi$
$702$	0.247739	0.00935032
$703$	21.9931	0.829487
$704$	2.58792	0.0975358
$705$	40.0369	1.50788
$706$	−27.1789	−1.02289
$707$	−24.9763	−0.939330
$708$	−17.5172	−0.658338
$709$	16.0127	0.601371	0.300686	−	0.953723i	$-0.402784\pi$
$709$	16.0127	0.601371	0.300686	+	0.953723i	$0.402784\pi$
$710$	23.9935	0.900462
$711$	36.0487	1.35193
$712$	−2.15640	−0.0808144
$713$	−19.5239	−0.731176
$714$	−1.70630	−0.0638566
$715$	19.3550	0.723835
$716$	0.0428166	0.00160013
$717$	51.9568	1.94036
$718$	24.2455	0.904832
$719$	−48.7231	−1.81707	−0.908533	−	0.417814i	$-0.862797\pi$
$719$	−48.7231	−1.81707	−0.908533	+	0.417814i	$0.862797\pi$
$720$	5.98052	0.222881
$721$	−25.4333	−0.947185
$722$	−15.0661	−0.560703
$723$	−45.4046	−1.68861
$724$	−12.1522	−0.451634
$725$	6.32419	0.234875
$726$	10.5154	0.390263
$727$	−8.64597	−0.320661	−0.160331	−	0.987063i	$-0.551256\pi$
$727$	−8.64597	−0.320661	−0.160331	+	0.987063i	$0.551256\pi$
$728$	5.75327	0.213230
$729$	−26.5070	−0.981740
$730$	−1.25420	−0.0464200
$731$	1.05550	0.0390391
$732$	−1.29380	−0.0478201
$733$	28.5504	1.05453	0.527267	−	0.849700i	$-0.323217\pi$
$733$	28.5504	1.05453	0.527267	+	0.849700i	$0.323217\pi$
$734$	1.35924	0.0501703
$735$	22.6410	0.835127
$736$	−3.96760	−0.146248
$737$	−22.9611	−0.845783
$738$	36.2753	1.33531
$739$	−35.4551	−1.30424	−0.652119	−	0.758117i	$-0.726120\pi$
$739$	−35.4551	−1.30424	−0.652119	+	0.758117i	$0.726120\pi$
$740$	22.3079	0.820056
$741$	−18.0201	−0.661983
$742$	14.6522	0.537898
$743$	−4.01288	−0.147218	−0.0736091	−	0.997287i	$-0.523452\pi$
$743$	−4.01288	−0.147218	−0.0736091	+	0.997287i	$0.523452\pi$
$744$	−12.0261	−0.440899
$745$	9.41728	0.345022
$746$	12.2204	0.447422
$747$	−40.0061	−1.46375
$748$	1.16752	0.0426886
$749$	−0.212390	−0.00776058
$750$	29.2673	1.06869
$751$	−12.7084	−0.463735	−0.231868	−	0.972747i	$-0.574484\pi$
$751$	−12.7084	−0.463735	−0.231868	+	0.972747i	$0.574484\pi$
$752$	−8.14310	−0.296948
$753$	−71.3924	−2.60168
$754$	−24.6782	−0.898728
$755$	−32.1585	−1.17037
$756$	0.103132	0.00375087
$757$	−22.3155	−0.811072	−0.405536	−	0.914079i	$-0.632915\pi$
$757$	−22.3155	−0.811072	−0.405536	+	0.914079i	$0.632915\pi$
$758$	−4.69365	−0.170481
$759$	25.0937	0.910845
$760$	3.99020	0.144740
$761$	−8.28776	−0.300431	−0.150216	−	0.988653i	$-0.547997\pi$
$761$	−8.28776	−0.300431	−0.150216	+	0.988653i	$0.547997\pi$
$762$	47.9276	1.73623
$763$	24.3118	0.880147
$764$	−5.88172	−0.212793
$765$	2.69806	0.0975485
$766$	26.5501	0.959295
$767$	26.6463	0.962144
$768$	−2.44392	−0.0881873
$769$	42.9424	1.54854	0.774272	−	0.632853i	$-0.218116\pi$
$769$	42.9424	1.54854	0.774272	+	0.632853i	$0.218116\pi$
$770$	8.05731	0.290365
$771$	−2.83724	−0.102181
$772$	12.0640	0.434192
$773$	−35.8357	−1.28892	−0.644460	−	0.764638i	$-0.722918\pi$
$773$	−35.8357	−1.28892	−0.644460	+	0.764638i	$0.722918\pi$
$774$	6.95507	0.249995
$775$	−4.68801	−0.168398
$776$	−6.48983	−0.232971
$777$	−41.9391	−1.50456
$778$	−1.43944	−0.0516063
$779$	24.2028	0.867156
$780$	−18.2780	−0.654457
$781$	30.8647	1.10442
$782$	−1.78995	−0.0640084
$783$	−0.442377	−0.0158092
$784$	−4.60496	−0.164463
$785$	15.3127	0.546533
$786$	−2.36393	−0.0843185
$787$	34.6607	1.23552	0.617760	−	0.786367i	$-0.288040\pi$
$787$	34.6607	1.23552	0.617760	+	0.786367i	$0.288040\pi$
$788$	−11.5021	−0.409746
$789$	0.0359828	0.00128102
$790$	24.3959	0.867968
$791$	5.93819	0.211138
$792$	7.69319	0.273366
$793$	1.96806	0.0698878
$794$	19.8437	0.704226
$795$	−46.5495	−1.65094
$796$	−9.89653	−0.350773
$797$	10.9259	0.387014	0.193507	−	0.981099i	$-0.438014\pi$
$797$	10.9259	0.387014	0.193507	+	0.981099i	$0.438014\pi$
$798$	−7.50160	−0.265554
$799$	−3.67369	−0.129966
$800$	−0.952685	−0.0336825
$801$	−6.41039	−0.226500
$802$	−4.59931	−0.162407
$803$	−1.61337	−0.0569345
$804$	21.6835	0.764717
$805$	−12.3529	−0.435381
$806$	18.2935	0.644362
$807$	−79.2789	−2.79075
$808$	−16.1388	−0.567762
$809$	−28.7430	−1.01055	−0.505276	−	0.862958i	$-0.668609\pi$
$809$	−28.7430	−1.01055	−0.505276	+	0.862958i	$0.668609\pi$
$810$	−18.2692	−0.641915
$811$	−43.2247	−1.51783	−0.758913	−	0.651192i	$-0.774269\pi$
$811$	−43.2247	−1.51783	−0.758913	+	0.651192i	$0.774269\pi$
$812$	−10.2733	−0.360524
$813$	61.2673	2.14874
$814$	28.6963	1.00581
$815$	−2.72800	−0.0955575
$816$	−1.10255	−0.0385970
$817$	4.64042	0.162348
$818$	−12.2003	−0.426574
$819$	17.1029	0.597625
$820$	24.5493	0.857297
$821$	15.6765	0.547113	0.273556	−	0.961856i	$-0.411800\pi$
$821$	15.6765	0.547113	0.273556	+	0.961856i	$0.411800\pi$
$822$	−45.2607	−1.57865
$823$	7.39184	0.257663	0.128832	−	0.991666i	$-0.458877\pi$
$823$	7.39184	0.257663	0.128832	+	0.991666i	$0.458877\pi$
$824$	−16.4341	−0.572509
$825$	6.02541	0.209778
$826$	11.0926	0.385963
$827$	18.9154	0.657755	0.328877	−	0.944373i	$-0.393330\pi$
$827$	18.9154	0.657755	0.328877	+	0.944373i	$0.393330\pi$
$828$	−11.7946	−0.409891
$829$	47.1322	1.63697	0.818484	−	0.574529i	$-0.194815\pi$
$829$	47.1322	1.63697	0.818484	+	0.574529i	$0.194815\pi$
$830$	−27.0741	−0.939755
$831$	1.67171	0.0579910
$832$	3.71756	0.128883
$833$	−2.07749	−0.0719806
$834$	−23.2872	−0.806370
$835$	9.29009	0.321497
$836$	5.13289	0.177525
$837$	0.327925	0.0113348
$838$	18.6860	0.645496
$839$	−36.4575	−1.25865	−0.629326	−	0.777141i	$-0.716669\pi$
$839$	−36.4575	−1.25865	−0.629326	+	0.777141i	$0.716669\pi$
$840$	−7.60898	−0.262535
$841$	15.0668	0.519543
$842$	29.7556	1.02545
$843$	−47.8387	−1.64765
$844$	10.7118	0.368717
$845$	1.65025	0.0567702
$846$	−24.2073	−0.832263
$847$	−6.65879	−0.228799
$848$	9.46772	0.325123
$849$	19.3807	0.665142
$850$	−0.429795	−0.0147419
$851$	−43.9951	−1.50813
$852$	−29.1472	−0.998568
$853$	−43.5624	−1.49155	−0.745775	−	0.666198i	$-0.767921\pi$
$853$	−43.5624	−1.49155	−0.745775	+	0.666198i	$0.767921\pi$
$854$	0.819286	0.0280354
$855$	11.8618	0.405665
$856$	−0.137239	−0.00469074
$857$	−30.4444	−1.03996	−0.519981	−	0.854178i	$-0.674061\pi$
$857$	−30.4444	−1.03996	−0.519981	+	0.854178i	$0.674061\pi$
$858$	−23.5123	−0.802698
$859$	52.8711	1.80394	0.901969	−	0.431801i	$-0.142122\pi$
$859$	52.8711	1.80394	0.901969	+	0.431801i	$0.142122\pi$
$860$	4.70684	0.160502
$861$	−46.1528	−1.57288
$862$	2.60145	0.0886059
$863$	−23.2773	−0.792368	−0.396184	−	0.918171i	$-0.629666\pi$
$863$	−23.2773	−0.792368	−0.396184	+	0.918171i	$0.629666\pi$
$864$	0.0666402	0.00226715
$865$	16.3040	0.554352
$866$	−13.9671	−0.474621
$867$	41.0492	1.39410
$868$	7.61544	0.258485
$869$	31.3823	1.06457
$870$	32.6381	1.10654
$871$	−32.9838	−1.11761
$872$	15.7095	0.531989
$873$	−19.2925	−0.652954
$874$	−7.86936	−0.266185
$875$	−18.5333	−0.626540
$876$	1.52359	0.0514775
$877$	−29.5097	−0.996472	−0.498236	−	0.867042i	$-0.666019\pi$
$877$	−29.5097	−0.996472	−0.498236	+	0.867042i	$0.666019\pi$
$878$	16.0997	0.543340
$879$	−40.3524	−1.36105
$880$	5.20636	0.175506
$881$	33.5781	1.13128	0.565638	−	0.824654i	$-0.308630\pi$
$881$	33.5781	1.13128	0.565638	+	0.824654i	$0.308630\pi$
$882$	−13.6893	−0.460943
$883$	−43.3455	−1.45869	−0.729346	−	0.684145i	$-0.760176\pi$
$883$	−43.3455	−1.45869	−0.729346	+	0.684145i	$0.760176\pi$
$884$	1.67715	0.0564085
$885$	−35.2411	−1.18462
$886$	−34.7710	−1.16816
$887$	50.8131	1.70614	0.853069	−	0.521799i	$-0.174739\pi$
$887$	50.8131	1.70614	0.853069	+	0.521799i	$0.174739\pi$
$888$	−27.0996	−0.909402
$889$	−30.3498	−1.01790
$890$	−4.33823	−0.145418
$891$	−23.5010	−0.787314
$892$	8.27298	0.277000
$893$	−16.1511	−0.540475
$894$	−11.4401	−0.382613
$895$	0.0861381	0.00287928
$896$	1.54759	0.0517014
$897$	36.0473	1.20359
$898$	19.7654	0.659581
$899$	−32.6659	−1.08947
$900$	−2.83208	−0.0944026
$901$	4.27128	0.142297
$902$	31.5795	1.05148
$903$	−8.84889	−0.294473
$904$	3.83706	0.127619
$905$	−24.4478	−0.812671
$906$	39.0660	1.29788
$907$	−23.2700	−0.772667	−0.386333	−	0.922359i	$-0.626259\pi$
$907$	−23.2700	−0.772667	−0.386333	+	0.922359i	$0.626259\pi$
$908$	−4.53288	−0.150429
$909$	−47.9764	−1.59128
$910$	11.5744	0.383687
$911$	5.20144	0.172331	0.0861657	−	0.996281i	$-0.472539\pi$
$911$	5.20144	0.172331	0.0861657	+	0.996281i	$0.472539\pi$
$912$	−4.84727	−0.160509
$913$	−34.8274	−1.15262
$914$	27.7941	0.919348
$915$	−2.60285	−0.0860476
$916$	−0.740080	−0.0244529
$917$	1.49694	0.0494333
$918$	0.0300641	0.000992264 0
$919$	−36.4389	−1.20201	−0.601004	−	0.799246i	$-0.705232\pi$
$919$	−36.4389	−1.20201	−0.601004	+	0.799246i	$0.705232\pi$
$920$	−7.98200	−0.263159
$921$	−22.5799	−0.744034
$922$	−8.67607	−0.285731
$923$	44.3373	1.45938
$924$	−9.78798	−0.322001
$925$	−10.5639	−0.347340
$926$	10.3205	0.339153
$927$	−48.8542	−1.60458
$928$	−6.63828	−0.217912
$929$	45.9406	1.50726	0.753631	−	0.657298i	$-0.228301\pi$
$929$	45.9406	1.50726	0.753631	+	0.657298i	$0.228301\pi$
$930$	−24.1941	−0.793354
$931$	−9.13350	−0.299338
$932$	18.5535	0.607740
$933$	5.95757	0.195042
$934$	−38.7001	−1.26631
$935$	2.34880	0.0768140
$936$	11.0513	0.361224
$937$	−24.8310	−0.811194	−0.405597	−	0.914052i	$-0.632936\pi$
$937$	−24.8310	−0.811194	−0.405597	+	0.914052i	$0.632936\pi$
$938$	−13.7309	−0.448329
$939$	8.23757	0.268823
$940$	−16.3822	−0.534330
$941$	13.5115	0.440463	0.220231	−	0.975448i	$-0.429319\pi$
$941$	13.5115	0.440463	0.220231	+	0.975448i	$0.429319\pi$
$942$	−18.6018	−0.606078
$943$	−48.4153	−1.57662
$944$	7.16769	0.233288
$945$	0.207480	0.00674932
$946$	6.05475	0.196857
$947$	35.0306	1.13834	0.569170	−	0.822220i	$-0.307265\pi$
$947$	35.0306	1.13834	0.569170	+	0.822220i	$0.307265\pi$
$948$	−29.6361	−0.962535
$949$	−2.31762	−0.0752330
$950$	−1.88956	−0.0613054
$951$	−80.3607	−2.60587
$952$	0.698181	0.0226282
$953$	23.7787	0.770266	0.385133	−	0.922861i	$-0.374156\pi$
$953$	23.7787	0.770266	0.385133	+	0.922861i	$0.374156\pi$
$954$	28.1450	0.911228
$955$	−11.8328	−0.382901
$956$	−21.2596	−0.687586
$957$	41.9848	1.35718
$958$	20.3467	0.657373
$959$	28.6610	0.925511
$960$	−4.91666	−0.158684
$961$	−6.78541	−0.218884
$962$	41.2225	1.32907
$963$	−0.407976	−0.0131468
$964$	18.5786	0.598376
$965$	24.2702	0.781286
$966$	15.0062	0.482817
$967$	36.2248	1.16491	0.582455	−	0.812863i	$-0.302092\pi$
$967$	36.2248	1.16491	0.582455	+	0.812863i	$0.302092\pi$
$968$	−4.30268	−0.138293
$969$	−2.18680	−0.0702502
$970$	−13.0562	−0.419210
$971$	−29.7886	−0.955961	−0.477981	−	0.878370i	$-0.658631\pi$
$971$	−29.7886	−0.955961	−0.477981	+	0.878370i	$0.658631\pi$
$972$	21.9934	0.705440
$973$	14.7464	0.472749
$974$	2.12235	0.0680044
$975$	8.65555	0.277199
$976$	0.529394	0.0169455
$977$	21.1251	0.675853	0.337926	−	0.941173i	$-0.390274\pi$
$977$	21.1251	0.675853	0.337926	+	0.941173i	$0.390274\pi$
$978$	3.31396	0.105969
$979$	−5.58058	−0.178356
$980$	−9.26423	−0.295935
$981$	46.7000	1.49102
$982$	−4.39404	−0.140219
$983$	10.6594	0.339982	0.169991	−	0.985446i	$-0.445626\pi$
$983$	10.6594	0.339982	0.169991	+	0.985446i	$0.445626\pi$
$984$	−29.8223	−0.950701
$985$	−23.1399	−0.737298
$986$	−2.99480	−0.0953738
$987$	30.7987	0.980334
$988$	7.37343	0.234580
$989$	−9.28270	−0.295173
$990$	15.4771	0.491895
$991$	−14.9092	−0.473607	−0.236803	−	0.971558i	$-0.576100\pi$
$991$	−14.9092	−0.473607	−0.236803	+	0.971558i	$0.576100\pi$
$992$	4.92083	0.156237
$993$	20.8188	0.660666
$994$	18.4573	0.585429
$995$	−19.9098	−0.631182
$996$	32.8895	1.04214
$997$	19.4383	0.615617	0.307809	−	0.951448i	$-0.400404\pi$
$997$	19.4383	0.615617	0.307809	+	0.951448i	$0.400404\pi$
$998$	27.0828	0.857292
$999$	0.738946	0.0233792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.14	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.14	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.44392 q^{3} +1.00000 q^{4} +2.01179 q^{5} -2.44392 q^{6} +1.54759 q^{7} +1.00000 q^{8} +2.97273 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.44392 q^{3} +1.00000 q^{4} +2.01179 q^{5} -2.44392 q^{6} +1.54759 q^{7} +1.00000 q^{8} +2.97273 q^{9} +2.01179 q^{10} +2.58792 q^{11} -2.44392 q^{12} +3.71756 q^{13} +1.54759 q^{14} -4.91666 q^{15} +1.00000 q^{16} +0.451141 q^{17} +2.97273 q^{18} +1.98340 q^{19} +2.01179 q^{20} -3.78218 q^{21} +2.58792 q^{22} -3.96760 q^{23} -2.44392 q^{24} -0.952685 q^{25} +3.71756 q^{26} +0.0666402 q^{27} +1.54759 q^{28} -6.63828 q^{29} -4.91666 q^{30} +4.92083 q^{31} +1.00000 q^{32} -6.32466 q^{33} +0.451141 q^{34} +3.11343 q^{35} +2.97273 q^{36} +11.0886 q^{37} +1.98340 q^{38} -9.08542 q^{39} +2.01179 q^{40} +12.2027 q^{41} -3.78218 q^{42} +2.33962 q^{43} +2.58792 q^{44} +5.98052 q^{45} -3.96760 q^{46} -8.14310 q^{47} -2.44392 q^{48} -4.60496 q^{49} -0.952685 q^{50} -1.10255 q^{51} +3.71756 q^{52} +9.46772 q^{53} +0.0666402 q^{54} +5.20636 q^{55} +1.54759 q^{56} -4.84727 q^{57} -6.63828 q^{58} +7.16769 q^{59} -4.91666 q^{60} +0.529394 q^{61} +4.92083 q^{62} +4.60057 q^{63} +1.00000 q^{64} +7.47897 q^{65} -6.32466 q^{66} -8.87243 q^{67} +0.451141 q^{68} +9.69649 q^{69} +3.11343 q^{70} +11.9264 q^{71} +2.97273 q^{72} -0.623423 q^{73} +11.0886 q^{74} +2.32828 q^{75} +1.98340 q^{76} +4.00504 q^{77} -9.08542 q^{78} +12.1265 q^{79} +2.01179 q^{80} -9.08106 q^{81} +12.2027 q^{82} -13.4577 q^{83} -3.78218 q^{84} +0.907602 q^{85} +2.33962 q^{86} +16.2234 q^{87} +2.58792 q^{88} -2.15640 q^{89} +5.98052 q^{90} +5.75327 q^{91} -3.96760 q^{92} -12.0261 q^{93} -8.14310 q^{94} +3.99020 q^{95} -2.44392 q^{96} -6.48983 q^{97} -4.60496 q^{98} +7.69319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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