LMFDB - Embedded newform 8013.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$116$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18030 q^{2} -1.00000 q^{3} +2.75372 q^{4} +1.60452 q^{5} +2.18030 q^{6} +4.21617 q^{7} -1.64333 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18030 q^{2} -1.00000 q^{3} +2.75372 q^{4} +1.60452 q^{5} +2.18030 q^{6} +4.21617 q^{7} -1.64333 q^{8} +1.00000 q^{9} -3.49835 q^{10} +2.92472 q^{11} -2.75372 q^{12} +0.434613 q^{13} -9.19252 q^{14} -1.60452 q^{15} -1.92448 q^{16} -7.66422 q^{17} -2.18030 q^{18} -0.461164 q^{19} +4.41840 q^{20} -4.21617 q^{21} -6.37677 q^{22} -6.81500 q^{23} +1.64333 q^{24} -2.42550 q^{25} -0.947587 q^{26} -1.00000 q^{27} +11.6101 q^{28} +4.62126 q^{29} +3.49835 q^{30} +5.68311 q^{31} +7.48260 q^{32} -2.92472 q^{33} +16.7103 q^{34} +6.76494 q^{35} +2.75372 q^{36} -1.51311 q^{37} +1.00548 q^{38} -0.434613 q^{39} -2.63676 q^{40} -3.16081 q^{41} +9.19252 q^{42} +3.60474 q^{43} +8.05384 q^{44} +1.60452 q^{45} +14.8588 q^{46} -4.57809 q^{47} +1.92448 q^{48} +10.7761 q^{49} +5.28833 q^{50} +7.66422 q^{51} +1.19680 q^{52} -2.49252 q^{53} +2.18030 q^{54} +4.69278 q^{55} -6.92855 q^{56} +0.461164 q^{57} -10.0758 q^{58} +3.63804 q^{59} -4.41840 q^{60} +0.336312 q^{61} -12.3909 q^{62} +4.21617 q^{63} -12.4654 q^{64} +0.697347 q^{65} +6.37677 q^{66} -6.98241 q^{67} -21.1051 q^{68} +6.81500 q^{69} -14.7496 q^{70} -10.4205 q^{71} -1.64333 q^{72} -9.92098 q^{73} +3.29903 q^{74} +2.42550 q^{75} -1.26991 q^{76} +12.3311 q^{77} +0.947587 q^{78} -7.48776 q^{79} -3.08787 q^{80} +1.00000 q^{81} +6.89151 q^{82} -6.86095 q^{83} -11.6101 q^{84} -12.2974 q^{85} -7.85942 q^{86} -4.62126 q^{87} -4.80627 q^{88} +0.0993936 q^{89} -3.49835 q^{90} +1.83240 q^{91} -18.7666 q^{92} -5.68311 q^{93} +9.98162 q^{94} -0.739948 q^{95} -7.48260 q^{96} -15.3372 q^{97} -23.4951 q^{98} +2.92472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) $ 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * 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 $

$2$	−2.18030	−1.54171	−0.770853	−	0.637013i	$-0.780170\pi$
$2$	−2.18030	−1.54171	−0.770853	+	0.637013i	$0.780170\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.75372	1.37686
$5$	1.60452	0.717565	0.358783	−	0.933421i	$-0.383192\pi$
$5$	1.60452	0.717565	0.358783	+	0.933421i	$0.383192\pi$
$6$	2.18030	0.890105
$7$	4.21617	1.59356	0.796781	−	0.604269i	$-0.206535\pi$
$7$	4.21617	1.59356	0.796781	+	0.604269i	$0.206535\pi$
$8$	−1.64333	−0.581005
$9$	1.00000	0.333333
$10$	−3.49835	−1.10627
$11$	2.92472	0.881835	0.440918	−	0.897548i	$-0.354653\pi$
$11$	2.92472	0.881835	0.440918	+	0.897548i	$0.354653\pi$
$12$	−2.75372	−0.794929
$13$	0.434613	0.120540	0.0602699	−	0.998182i	$-0.480804\pi$
$13$	0.434613	0.120540	0.0602699	+	0.998182i	$0.480804\pi$
$14$	−9.19252	−2.45680
$15$	−1.60452	−0.414286
$16$	−1.92448	−0.481120
$17$	−7.66422	−1.85885	−0.929423	−	0.369017i	$-0.879694\pi$
$17$	−7.66422	−1.85885	−0.929423	+	0.369017i	$0.879694\pi$
$18$	−2.18030	−0.513902
$19$	−0.461164	−0.105798	−0.0528991	−	0.998600i	$-0.516846\pi$
$19$	−0.461164	−0.105798	−0.0528991	+	0.998600i	$0.516846\pi$
$20$	4.41840	0.987985
$21$	−4.21617	−0.920043
$22$	−6.37677	−1.35953
$23$	−6.81500	−1.42103	−0.710513	−	0.703684i	$-0.751537\pi$
$23$	−6.81500	−1.42103	−0.710513	+	0.703684i	$0.751537\pi$
$24$	1.64333	0.335443
$25$	−2.42550	−0.485100
$26$	−0.947587	−0.185837
$27$	−1.00000	−0.192450
$28$	11.6101	2.19411
$29$	4.62126	0.858147	0.429074	−	0.903270i	$-0.358840\pi$
$29$	4.62126	0.858147	0.429074	+	0.903270i	$0.358840\pi$
$30$	3.49835	0.638708
$31$	5.68311	1.02072	0.510359	−	0.859962i	$-0.329513\pi$
$31$	5.68311	1.02072	0.510359	+	0.859962i	$0.329513\pi$
$32$	7.48260	1.32275
$33$	−2.92472	−0.509128
$34$	16.7103	2.86579
$35$	6.76494	1.14348
$36$	2.75372	0.458953
$37$	−1.51311	−0.248753	−0.124377	−	0.992235i	$-0.539693\pi$
$37$	−1.51311	−0.248753	−0.124377	+	0.992235i	$0.539693\pi$
$38$	1.00548	0.163110
$39$	−0.434613	−0.0695937
$40$	−2.63676	−0.416909
$41$	−3.16081	−0.493635	−0.246818	−	0.969062i	$-0.579385\pi$
$41$	−3.16081	−0.493635	−0.246818	+	0.969062i	$0.579385\pi$
$42$	9.19252	1.41844
$43$	3.60474	0.549717	0.274859	−	0.961485i	$-0.411369\pi$
$43$	3.60474	0.549717	0.274859	+	0.961485i	$0.411369\pi$
$44$	8.05384	1.21416
$45$	1.60452	0.239188
$46$	14.8588	2.19080
$47$	−4.57809	−0.667783	−0.333892	−	0.942611i	$-0.608362\pi$
$47$	−4.57809	−0.667783	−0.333892	+	0.942611i	$0.608362\pi$
$48$	1.92448	0.277775
$49$	10.7761	1.53944
$50$	5.28833	0.747882
$51$	7.66422	1.07320
$52$	1.19680	0.165966
$53$	−2.49252	−0.342374	−0.171187	−	0.985239i	$-0.554760\pi$
$53$	−2.49252	−0.342374	−0.171187	+	0.985239i	$0.554760\pi$
$54$	2.18030	0.296702
$55$	4.69278	0.632774
$56$	−6.92855	−0.925866
$57$	0.461164	0.0610826
$58$	−10.0758	−1.32301
$59$	3.63804	0.473632	0.236816	−	0.971555i	$-0.423896\pi$
$59$	3.63804	0.473632	0.236816	+	0.971555i	$0.423896\pi$
$60$	−4.41840	−0.570414
$61$	0.336312	0.0430604	0.0215302	−	0.999768i	$-0.493146\pi$
$61$	0.336312	0.0430604	0.0215302	+	0.999768i	$0.493146\pi$
$62$	−12.3909	−1.57365
$63$	4.21617	0.531187
$64$	−12.4654	−1.55817
$65$	0.697347	0.0864952
$66$	6.37677	0.784926
$67$	−6.98241	−0.853038	−0.426519	−	0.904479i	$-0.640260\pi$
$67$	−6.98241	−0.853038	−0.426519	+	0.904479i	$0.640260\pi$
$68$	−21.1051	−2.55937
$69$	6.81500	0.820430
$70$	−14.7496	−1.76292
$71$	−10.4205	−1.23668	−0.618342	−	0.785910i	$-0.712195\pi$
$71$	−10.4205	−1.23668	−0.618342	+	0.785910i	$0.712195\pi$
$72$	−1.64333	−0.193668
$73$	−9.92098	−1.16116	−0.580581	−	0.814202i	$-0.697175\pi$
$73$	−9.92098	−1.16116	−0.580581	+	0.814202i	$0.697175\pi$
$74$	3.29903	0.383505
$75$	2.42550	0.280073
$76$	−1.26991	−0.145669
$77$	12.3311	1.40526
$78$	0.947587	0.107293
$79$	−7.48776	−0.842439	−0.421219	−	0.906959i	$-0.638398\pi$
$79$	−7.48776	−0.842439	−0.421219	+	0.906959i	$0.638398\pi$
$80$	−3.08787	−0.345235
$81$	1.00000	0.111111
$82$	6.89151	0.761040
$83$	−6.86095	−0.753087	−0.376543	−	0.926399i	$-0.622887\pi$
$83$	−6.86095	−0.753087	−0.376543	+	0.926399i	$0.622887\pi$
$84$	−11.6101	−1.26677
$85$	−12.2974	−1.33384
$86$	−7.85942	−0.847503
$87$	−4.62126	−0.495452
$88$	−4.80627	−0.512350
$89$	0.0993936	0.0105357	0.00526785	−	0.999986i	$-0.498323\pi$
$89$	0.0993936	0.0105357	0.00526785	+	0.999986i	$0.498323\pi$
$90$	−3.49835	−0.368758
$91$	1.83240	0.192088
$92$	−18.7666	−1.95655
$93$	−5.68311	−0.589312
$94$	9.98162	1.02953
$95$	−0.739948	−0.0759171
$96$	−7.48260	−0.763690
$97$	−15.3372	−1.55726	−0.778629	−	0.627484i	$-0.784085\pi$
$97$	−15.3372	−1.55726	−0.778629	+	0.627484i	$0.784085\pi$
$98$	−23.4951	−2.37336
$99$	2.92472	0.293945
$100$	−6.67914	−0.667914
$101$	−4.07559	−0.405536	−0.202768	−	0.979227i	$-0.564994\pi$
$101$	−4.07559	−0.405536	−0.202768	+	0.979227i	$0.564994\pi$
$102$	−16.7103	−1.65457
$103$	2.68377	0.264439	0.132220	−	0.991220i	$-0.457790\pi$
$103$	2.68377	0.264439	0.132220	+	0.991220i	$0.457790\pi$
$104$	−0.714212	−0.0700342
$105$	−6.76494	−0.660191
$106$	5.43445	0.527841
$107$	−14.3041	−1.38283	−0.691416	−	0.722457i	$-0.743013\pi$
$107$	−14.3041	−1.38283	−0.691416	+	0.722457i	$0.743013\pi$
$108$	−2.75372	−0.264976
$109$	6.52129	0.624626	0.312313	−	0.949979i	$-0.398896\pi$
$109$	6.52129	0.624626	0.312313	+	0.949979i	$0.398896\pi$
$110$	−10.2317	−0.975552
$111$	1.51311	0.143618
$112$	−8.11392	−0.766694
$113$	−19.6397	−1.84755	−0.923773	−	0.382940i	$-0.874912\pi$
$113$	−19.6397	−1.84755	−0.923773	+	0.382940i	$0.874912\pi$
$114$	−1.00548	−0.0941715
$115$	−10.9348	−1.01968
$116$	12.7257	1.18155
$117$	0.434613	0.0401800
$118$	−7.93202	−0.730201
$119$	−32.3136	−2.96218
$120$	2.63676	0.240702
$121$	−2.44603	−0.222366
$122$	−0.733263	−0.0663865
$123$	3.16081	0.285000
$124$	15.6497	1.40538
$125$	−11.9144	−1.06566
$126$	−9.19252	−0.818934
$127$	16.9622	1.50515	0.752576	−	0.658505i	$-0.228811\pi$
$127$	16.9622	1.50515	0.752576	+	0.658505i	$0.228811\pi$
$128$	12.2131	1.07949
$129$	−3.60474	−0.317380
$130$	−1.52043	−0.133350
$131$	18.1913	1.58938	0.794692	−	0.607013i	$-0.207632\pi$
$131$	18.1913	1.58938	0.794692	+	0.607013i	$0.207632\pi$
$132$	−8.05384	−0.700997
$133$	−1.94434	−0.168596
$134$	15.2238	1.31513
$135$	−1.60452	−0.138095
$136$	12.5948	1.08000
$137$	−2.68518	−0.229411	−0.114705	−	0.993400i	$-0.536592\pi$
$137$	−2.68518	−0.229411	−0.114705	+	0.993400i	$0.536592\pi$
$138$	−14.8588	−1.26486
$139$	19.5804	1.66079	0.830394	−	0.557176i	$-0.188115\pi$
$139$	19.5804	1.66079	0.830394	+	0.557176i	$0.188115\pi$
$140$	18.6287	1.57442
$141$	4.57809	0.385545
$142$	22.7198	1.90660
$143$	1.27112	0.106296
$144$	−1.92448	−0.160373
$145$	7.41493	0.615776
$146$	21.6307	1.79017
$147$	−10.7761	−0.888795
$148$	−4.16667	−0.342498
$149$	−11.4817	−0.940621	−0.470311	−	0.882501i	$-0.655858\pi$
$149$	−11.4817	−0.940621	−0.470311	+	0.882501i	$0.655858\pi$
$150$	−5.28833	−0.431790
$151$	−10.3960	−0.846014	−0.423007	−	0.906126i	$-0.639025\pi$
$151$	−10.3960	−0.846014	−0.423007	+	0.906126i	$0.639025\pi$
$152$	0.757844	0.0614693
$153$	−7.66422	−0.619615
$154$	−26.8855	−2.16650
$155$	9.11870	0.732431
$156$	−1.19680	−0.0958207
$157$	−4.80170	−0.383218	−0.191609	−	0.981471i	$-0.561370\pi$
$157$	−4.80170	−0.383218	−0.191609	+	0.981471i	$0.561370\pi$
$158$	16.3256	1.29879
$159$	2.49252	0.197670
$160$	12.0060	0.949159
$161$	−28.7332	−2.26449
$162$	−2.18030	−0.171301
$163$	21.6904	1.69892	0.849460	−	0.527653i	$-0.176928\pi$
$163$	21.6904	1.69892	0.849460	+	0.527653i	$0.176928\pi$
$164$	−8.70397	−0.679666
$165$	−4.69278	−0.365332
$166$	14.9589	1.16104
$167$	−16.9717	−1.31331	−0.656653	−	0.754193i	$-0.728028\pi$
$167$	−16.9717	−1.31331	−0.656653	+	0.754193i	$0.728028\pi$
$168$	6.92855	0.534549
$169$	−12.8111	−0.985470
$170$	26.8121	2.05639
$171$	−0.461164	−0.0352661
$172$	9.92643	0.756883
$173$	23.6923	1.80129	0.900645	−	0.434556i	$-0.143095\pi$
$173$	23.6923	1.80129	0.900645	+	0.434556i	$0.143095\pi$
$174$	10.0758	0.763841
$175$	−10.2263	−0.773037
$176$	−5.62856	−0.424268
$177$	−3.63804	−0.273451
$178$	−0.216708	−0.0162429
$179$	−8.68359	−0.649042	−0.324521	−	0.945879i	$-0.605203\pi$
$179$	−8.68359	−0.649042	−0.324521	+	0.945879i	$0.605203\pi$
$180$	4.41840	0.329328
$181$	−7.09032	−0.527019	−0.263510	−	0.964657i	$-0.584880\pi$
$181$	−7.09032	−0.527019	−0.263510	+	0.964657i	$0.584880\pi$
$182$	−3.99518	−0.296143
$183$	−0.336312	−0.0248609
$184$	11.1993	0.825622
$185$	−2.42782	−0.178497
$186$	12.3909	0.908545
$187$	−22.4157	−1.63920
$188$	−12.6068	−0.919443
$189$	−4.21617	−0.306681
$190$	1.61331	0.117042
$191$	−9.87948	−0.714854	−0.357427	−	0.933941i	$-0.616346\pi$
$191$	−9.87948	−0.714854	−0.357427	+	0.933941i	$0.616346\pi$
$192$	12.4654	0.899611
$193$	−9.52942	−0.685942	−0.342971	−	0.939346i	$-0.611433\pi$
$193$	−9.52942	−0.685942	−0.342971	+	0.939346i	$0.611433\pi$
$194$	33.4398	2.40083
$195$	−0.697347	−0.0499380
$196$	29.6742	2.11959
$197$	19.0741	1.35897	0.679487	−	0.733687i	$-0.262202\pi$
$197$	19.0741	1.35897	0.679487	+	0.733687i	$0.262202\pi$
$198$	−6.37677	−0.453177
$199$	6.55398	0.464599	0.232300	−	0.972644i	$-0.425375\pi$
$199$	6.55398	0.464599	0.232300	+	0.972644i	$0.425375\pi$
$200$	3.98590	0.281846
$201$	6.98241	0.492501
$202$	8.88601	0.625217
$203$	19.4840	1.36751
$204$	21.1051	1.47765
$205$	−5.07159	−0.354215
$206$	−5.85142	−0.407688
$207$	−6.81500	−0.473675
$208$	−0.836403	−0.0579941
$209$	−1.34877	−0.0932966
$210$	14.7496	1.01782
$211$	−4.13455	−0.284634	−0.142317	−	0.989821i	$-0.545455\pi$
$211$	−4.13455	−0.284634	−0.142317	+	0.989821i	$0.545455\pi$
$212$	−6.86370	−0.471401
$213$	10.4205	0.713999
$214$	31.1873	2.13192
$215$	5.78389	0.394458
$216$	1.64333	0.111814
$217$	23.9610	1.62658
$218$	−14.2184	−0.962990
$219$	9.92098	0.670398
$220$	12.9226	0.871240
$221$	−3.33097	−0.224065
$222$	−3.29903	−0.221416
$223$	−15.5732	−1.04286	−0.521428	−	0.853295i	$-0.674600\pi$
$223$	−15.5732	−1.04286	−0.521428	+	0.853295i	$0.674600\pi$
$224$	31.5479	2.10788
$225$	−2.42550	−0.161700
$226$	42.8204	2.84837
$227$	2.65168	0.175998	0.0879992	−	0.996121i	$-0.471953\pi$
$227$	2.65168	0.175998	0.0879992	+	0.996121i	$0.471953\pi$
$228$	1.26991	0.0841021
$229$	7.65636	0.505947	0.252973	−	0.967473i	$-0.418592\pi$
$229$	7.65636	0.505947	0.252973	+	0.967473i	$0.418592\pi$
$230$	23.8412	1.57204
$231$	−12.3311	−0.811327
$232$	−7.59426	−0.498587
$233$	13.7849	0.903081	0.451541	−	0.892251i	$-0.350875\pi$
$233$	13.7849	0.903081	0.451541	+	0.892251i	$0.350875\pi$
$234$	−0.947587	−0.0619457
$235$	−7.34566	−0.479178
$236$	10.0181	0.652124
$237$	7.48776	0.486382
$238$	70.4534	4.56682
$239$	11.0276	0.713315	0.356658	−	0.934235i	$-0.383916\pi$
$239$	11.0276	0.713315	0.356658	+	0.934235i	$0.383916\pi$
$240$	3.08787	0.199321
$241$	−9.89513	−0.637401	−0.318701	−	0.947855i	$-0.603246\pi$
$241$	−9.89513	−0.637401	−0.318701	+	0.947855i	$0.603246\pi$
$242$	5.33308	0.342823
$243$	−1.00000	−0.0641500
$244$	0.926109	0.0592881
$245$	17.2905	1.10465
$246$	−6.89151	−0.439387
$247$	−0.200428	−0.0127529
$248$	−9.33923	−0.593042
$249$	6.86095	0.434795
$250$	25.9770	1.64293
$251$	2.81208	0.177497	0.0887484	−	0.996054i	$-0.471713\pi$
$251$	2.81208	0.177497	0.0887484	+	0.996054i	$0.471713\pi$
$252$	11.6101	0.731369
$253$	−19.9319	−1.25311
$254$	−36.9827	−2.32050
$255$	12.2974	0.770094
$256$	−1.69744	−0.106090
$257$	−16.2311	−1.01247	−0.506233	−	0.862397i	$-0.668962\pi$
$257$	−16.2311	−1.01247	−0.506233	+	0.862397i	$0.668962\pi$
$258$	7.85942	0.489306
$259$	−6.37951	−0.396404
$260$	1.92029	0.119092
$261$	4.62126	0.286049
$262$	−39.6626	−2.45036
$263$	−8.92663	−0.550440	−0.275220	−	0.961381i	$-0.588751\pi$
$263$	−8.92663	−0.550440	−0.275220	+	0.961381i	$0.588751\pi$
$264$	4.80627	0.295806
$265$	−3.99931	−0.245676
$266$	4.23926	0.259925
$267$	−0.0993936	−0.00608279
$268$	−19.2276	−1.17451
$269$	−23.4586	−1.43030	−0.715149	−	0.698972i	$-0.753641\pi$
$269$	−23.4586	−1.43030	−0.715149	+	0.698972i	$0.753641\pi$
$270$	3.49835	0.212903
$271$	9.58082	0.581993	0.290997	−	0.956724i	$-0.406013\pi$
$271$	9.58082	0.581993	0.290997	+	0.956724i	$0.406013\pi$
$272$	14.7496	0.894327
$273$	−1.83240	−0.110902
$274$	5.85451	0.353684
$275$	−7.09391	−0.427779
$276$	18.7666	1.12962
$277$	3.94045	0.236759	0.118379	−	0.992968i	$-0.462230\pi$
$277$	3.94045	0.236759	0.118379	+	0.992968i	$0.462230\pi$
$278$	−42.6912	−2.56045
$279$	5.68311	0.340239
$280$	−11.1170	−0.664369
$281$	−18.7839	−1.12055	−0.560276	−	0.828306i	$-0.689305\pi$
$281$	−18.7839	−1.12055	−0.560276	+	0.828306i	$0.689305\pi$
$282$	−9.98162	−0.594397
$283$	8.20152	0.487530	0.243765	−	0.969834i	$-0.421617\pi$
$283$	8.20152	0.487530	0.243765	+	0.969834i	$0.421617\pi$
$284$	−28.6950	−1.70274
$285$	0.739948	0.0438308
$286$	−2.77142	−0.163878
$287$	−13.3265	−0.786638
$288$	7.48260	0.440917
$289$	41.7402	2.45531
$290$	−16.1668	−0.949346
$291$	15.3372	0.899083
$292$	−27.3196	−1.59876
$293$	−6.94276	−0.405600	−0.202800	−	0.979220i	$-0.565004\pi$
$293$	−6.94276	−0.405600	−0.202800	+	0.979220i	$0.565004\pi$
$294$	23.4951	1.37026
$295$	5.83732	0.339862
$296$	2.48653	0.144527
$297$	−2.92472	−0.169709
$298$	25.0337	1.45016
$299$	−2.96189	−0.171290
$300$	6.67914	0.385621
$301$	15.1982	0.876008
$302$	22.6664	1.30430
$303$	4.07559	0.234136
$304$	0.887500	0.0509016
$305$	0.539621	0.0308986
$306$	16.7103	0.955264
$307$	−16.1498	−0.921720	−0.460860	−	0.887473i	$-0.652459\pi$
$307$	−16.1498	−0.921720	−0.460860	+	0.887473i	$0.652459\pi$
$308$	33.9563	1.93484
$309$	−2.68377	−0.152674
$310$	−19.8815	−1.12919
$311$	−24.5232	−1.39058	−0.695290	−	0.718729i	$-0.744724\pi$
$311$	−24.5232	−1.39058	−0.695290	+	0.718729i	$0.744724\pi$
$312$	0.714212	0.0404343
$313$	−22.2229	−1.25611	−0.628056	−	0.778168i	$-0.716149\pi$
$313$	−22.2229	−1.25611	−0.628056	+	0.778168i	$0.716149\pi$
$314$	10.4692	0.590809
$315$	6.76494	0.381161
$316$	−20.6192	−1.15992
$317$	9.01965	0.506594	0.253297	−	0.967389i	$-0.418485\pi$
$317$	9.01965	0.506594	0.253297	+	0.967389i	$0.418485\pi$
$318$	−5.43445	−0.304749
$319$	13.5159	0.756745
$320$	−20.0010	−1.11809
$321$	14.3041	0.798378
$322$	62.6470	3.49118
$323$	3.53446	0.196663
$324$	2.75372	0.152984
$325$	−1.05415	−0.0584739
$326$	−47.2915	−2.61924
$327$	−6.52129	−0.360628
$328$	5.19425	0.286804
$329$	−19.3020	−1.06415
$330$	10.2317	0.563235
$331$	4.03257	0.221650	0.110825	−	0.993840i	$-0.464651\pi$
$331$	4.03257	0.221650	0.110825	+	0.993840i	$0.464651\pi$
$332$	−18.8931	−1.03689
$333$	−1.51311	−0.0829178
$334$	37.0033	2.02473
$335$	−11.2035	−0.612110
$336$	8.11392	0.442651
$337$	25.2946	1.37788	0.688942	−	0.724816i	$-0.258075\pi$
$337$	25.2946	1.37788	0.688942	+	0.724816i	$0.258075\pi$
$338$	27.9321	1.51931
$339$	19.6397	1.06668
$340$	−33.8636	−1.83651
$341$	16.6215	0.900105
$342$	1.00548	0.0543699
$343$	15.9205	0.859626
$344$	−5.92377	−0.319388
$345$	10.9348	0.588712
$346$	−51.6563	−2.77706
$347$	−19.5980	−1.05208	−0.526038	−	0.850461i	$-0.676323\pi$
$347$	−19.5980	−1.05208	−0.526038	+	0.850461i	$0.676323\pi$
$348$	−12.7257	−0.682167
$349$	−15.2951	−0.818729	−0.409364	−	0.912371i	$-0.634249\pi$
$349$	−15.2951	−0.818729	−0.409364	+	0.912371i	$0.634249\pi$
$350$	22.2965	1.19180
$351$	−0.434613	−0.0231979
$352$	21.8845	1.16645
$353$	−34.1124	−1.81562	−0.907810	−	0.419382i	$-0.862247\pi$
$353$	−34.1124	−1.81562	−0.907810	+	0.419382i	$0.862247\pi$
$354$	7.93202	0.421582
$355$	−16.7199	−0.887401
$356$	0.273702	0.0145062
$357$	32.3136	1.71022
$358$	18.9328	1.00063
$359$	−36.6700	−1.93537	−0.967685	−	0.252163i	$-0.918858\pi$
$359$	−36.6700	−1.93537	−0.967685	+	0.252163i	$0.918858\pi$
$360$	−2.63676	−0.138970
$361$	−18.7873	−0.988807
$362$	15.4590	0.812509
$363$	2.44603	0.128383
$364$	5.04591	0.264477
$365$	−15.9185	−0.833210
$366$	0.733263	0.0383282
$367$	18.2897	0.954713	0.477357	−	0.878710i	$-0.341595\pi$
$367$	18.2897	0.954713	0.477357	+	0.878710i	$0.341595\pi$
$368$	13.1153	0.683684
$369$	−3.16081	−0.164545
$370$	5.29338	0.275190
$371$	−10.5089	−0.545594
$372$	−15.6497	−0.811398
$373$	−5.39469	−0.279326	−0.139663	−	0.990199i	$-0.544602\pi$
$373$	−5.39469	−0.279326	−0.139663	+	0.990199i	$0.544602\pi$
$374$	48.8729	2.52716
$375$	11.9144	0.615257
$376$	7.52331	0.387985
$377$	2.00846	0.103441
$378$	9.19252	0.472812
$379$	27.7057	1.42315	0.711574	−	0.702611i	$-0.247983\pi$
$379$	27.7057	1.42315	0.711574	+	0.702611i	$0.247983\pi$
$380$	−2.03761	−0.104527
$381$	−16.9622	−0.869000
$382$	21.5403	1.10210
$383$	−5.38073	−0.274942	−0.137471	−	0.990506i	$-0.543897\pi$
$383$	−5.38073	−0.274942	−0.137471	+	0.990506i	$0.543897\pi$
$384$	−12.2131	−0.623246
$385$	19.7855	1.00836
$386$	20.7770	1.05752
$387$	3.60474	0.183239
$388$	−42.2343	−2.14412
$389$	−23.6629	−1.19976	−0.599879	−	0.800091i	$-0.704784\pi$
$389$	−23.6629	−1.19976	−0.599879	+	0.800091i	$0.704784\pi$
$390$	1.52043	0.0769898
$391$	52.2316	2.64147
$392$	−17.7086	−0.894420
$393$	−18.1913	−0.917631
$394$	−41.5873	−2.09514
$395$	−12.0143	−0.604505
$396$	8.05384	0.404721
$397$	6.68099	0.335309	0.167655	−	0.985846i	$-0.446381\pi$
$397$	6.68099	0.335309	0.167655	+	0.985846i	$0.446381\pi$
$398$	−14.2897	−0.716276
$399$	1.94434	0.0973389
$400$	4.66783	0.233391
$401$	30.0569	1.50097	0.750486	−	0.660886i	$-0.229819\pi$
$401$	30.0569	1.50097	0.750486	+	0.660886i	$0.229819\pi$
$402$	−15.2238	−0.759293
$403$	2.46995	0.123037
$404$	−11.2230	−0.558366
$405$	1.60452	0.0797295
$406$	−42.4810	−2.10830
$407$	−4.42541	−0.219360
$408$	−12.5948	−0.623537
$409$	−11.1469	−0.551180	−0.275590	−	0.961275i	$-0.588873\pi$
$409$	−11.1469	−0.551180	−0.275590	+	0.961275i	$0.588873\pi$
$410$	11.0576	0.546096
$411$	2.68518	0.132450
$412$	7.39033	0.364095
$413$	15.3386	0.754761
$414$	14.8588	0.730268
$415$	−11.0086	−0.540389
$416$	3.25203	0.159444
$417$	−19.5804	−0.958857
$418$	2.94073	0.143836
$419$	18.1963	0.888947	0.444473	−	0.895792i	$-0.353391\pi$
$419$	18.1963	0.888947	0.444473	+	0.895792i	$0.353391\pi$
$420$	−18.6287	−0.908989
$421$	25.3439	1.23519	0.617594	−	0.786497i	$-0.288108\pi$
$421$	25.3439	1.23519	0.617594	+	0.786497i	$0.288108\pi$
$422$	9.01457	0.438822
$423$	−4.57809	−0.222594
$424$	4.09603	0.198921
$425$	18.5896	0.901726
$426$	−22.7198	−1.10078
$427$	1.41795	0.0686194
$428$	−39.3895	−1.90396
$429$	−1.27112	−0.0613702
$430$	−12.6106	−0.608138
$431$	18.6849	0.900020	0.450010	−	0.893024i	$-0.351420\pi$
$431$	18.6849	0.900020	0.450010	+	0.893024i	$0.351420\pi$
$432$	1.92448	0.0925915
$433$	0.719929	0.0345976	0.0172988	−	0.999850i	$-0.494493\pi$
$433$	0.719929	0.0345976	0.0172988	+	0.999850i	$0.494493\pi$
$434$	−52.2421	−2.50770
$435$	−7.41493	−0.355519
$436$	17.9578	0.860021
$437$	3.14283	0.150342
$438$	−21.6307	−1.03356
$439$	8.69677	0.415074	0.207537	−	0.978227i	$-0.433455\pi$
$439$	8.69677	0.415074	0.207537	+	0.978227i	$0.433455\pi$
$440$	−7.71178	−0.367645
$441$	10.7761	0.513146
$442$	7.26251	0.345442
$443$	0.663129	0.0315062	0.0157531	−	0.999876i	$-0.494985\pi$
$443$	0.663129	0.0315062	0.0157531	+	0.999876i	$0.494985\pi$
$444$	4.16667	0.197741
$445$	0.159479	0.00756005
$446$	33.9542	1.60778
$447$	11.4817	0.543068
$448$	−52.5561	−2.48304
$449$	−28.4646	−1.34333	−0.671663	−	0.740857i	$-0.734420\pi$
$449$	−28.4646	−1.34333	−0.671663	+	0.740857i	$0.734420\pi$
$450$	5.28833	0.249294
$451$	−9.24447	−0.435305
$452$	−54.0821	−2.54381
$453$	10.3960	0.488446
$454$	−5.78147	−0.271338
$455$	2.94013	0.137835
$456$	−0.757844	−0.0354893
$457$	−10.3187	−0.482689	−0.241344	−	0.970440i	$-0.577588\pi$
$457$	−10.3187	−0.482689	−0.241344	+	0.970440i	$0.577588\pi$
$458$	−16.6932	−0.780021
$459$	7.66422	0.357735
$460$	−30.1114	−1.40395
$461$	−9.36843	−0.436331	−0.218166	−	0.975912i	$-0.570007\pi$
$461$	−9.36843	−0.436331	−0.218166	+	0.975912i	$0.570007\pi$
$462$	26.8855	1.25083
$463$	17.2683	0.802527	0.401264	−	0.915963i	$-0.368571\pi$
$463$	17.2683	0.802527	0.401264	+	0.915963i	$0.368571\pi$
$464$	−8.89353	−0.412872
$465$	−9.11870	−0.422869
$466$	−30.0553	−1.39229
$467$	20.6397	0.955092	0.477546	−	0.878607i	$-0.341526\pi$
$467$	20.6397	0.955092	0.477546	+	0.878607i	$0.341526\pi$
$468$	1.19680	0.0553221
$469$	−29.4390	−1.35937
$470$	16.0158	0.738752
$471$	4.80170	0.221251
$472$	−5.97849	−0.275182
$473$	10.5428	0.484760
$474$	−16.3256	−0.749859
$475$	1.11855	0.0513228
$476$	−88.9825	−4.07851
$477$	−2.49252	−0.114125
$478$	−24.0435	−1.09972
$479$	2.74384	0.125369	0.0626846	−	0.998033i	$-0.480034\pi$
$479$	2.74384	0.125369	0.0626846	+	0.998033i	$0.480034\pi$
$480$	−12.0060	−0.547997
$481$	−0.657616	−0.0299847
$482$	21.5744	0.982685
$483$	28.7332	1.30740
$484$	−6.73567	−0.306167
$485$	−24.6089	−1.11743
$486$	2.18030	0.0989005
$487$	38.2235	1.73207	0.866037	−	0.499980i	$-0.166659\pi$
$487$	38.2235	1.73207	0.866037	+	0.499980i	$0.166659\pi$
$488$	−0.552672	−0.0250183
$489$	−21.6904	−0.980872
$490$	−37.6984	−1.70304
$491$	7.13071	0.321805	0.160902	−	0.986970i	$-0.448560\pi$
$491$	7.13071	0.321805	0.160902	+	0.986970i	$0.448560\pi$
$492$	8.70397	0.392405
$493$	−35.4184	−1.59516
$494$	0.436993	0.0196612
$495$	4.69278	0.210925
$496$	−10.9370	−0.491087
$497$	−43.9345	−1.97073
$498$	−14.9589	−0.670326
$499$	−12.4189	−0.555944	−0.277972	−	0.960589i	$-0.589662\pi$
$499$	−12.4189	−0.555944	−0.277972	+	0.960589i	$0.589662\pi$
$500$	−32.8089	−1.46726
$501$	16.9717	0.758238
$502$	−6.13118	−0.273648
$503$	21.3023	0.949823	0.474912	−	0.880033i	$-0.342480\pi$
$503$	21.3023	0.949823	0.474912	+	0.880033i	$0.342480\pi$
$504$	−6.92855	−0.308622
$505$	−6.53938	−0.290998
$506$	43.4577	1.93193
$507$	12.8111	0.568961
$508$	46.7091	2.07238
$509$	25.5575	1.13282	0.566409	−	0.824124i	$-0.308332\pi$
$509$	25.5575	1.13282	0.566409	+	0.824124i	$0.308332\pi$
$510$	−26.8121	−1.18726
$511$	−41.8285	−1.85038
$512$	−20.7252	−0.915934
$513$	0.461164	0.0203609
$514$	35.3886	1.56092
$515$	4.30617	0.189752
$516$	−9.92643	−0.436987
$517$	−13.3896	−0.588875
$518$	13.9093	0.611138
$519$	−23.6923	−1.03998
$520$	−1.14597	−0.0502541
$521$	27.3789	1.19949	0.599745	−	0.800191i	$-0.295269\pi$
$521$	27.3789	1.19949	0.599745	+	0.800191i	$0.295269\pi$
$522$	−10.0758	−0.441004
$523$	−3.80108	−0.166210	−0.0831048	−	0.996541i	$-0.526484\pi$
$523$	−3.80108	−0.166210	−0.0831048	+	0.996541i	$0.526484\pi$
$524$	50.0938	2.18836
$525$	10.2263	0.446313
$526$	19.4627	0.848616
$527$	−43.5566	−1.89736
$528$	5.62856	0.244952
$529$	23.4442	1.01931
$530$	8.71971	0.378760
$531$	3.63804	0.157877
$532$	−5.35417	−0.232133
$533$	−1.37373	−0.0595027
$534$	0.216708	0.00937787
$535$	−22.9513	−0.992272
$536$	11.4744	0.495619
$537$	8.68359	0.374724
$538$	51.1469	2.20510
$539$	31.5169	1.35753
$540$	−4.41840	−0.190138
$541$	6.88091	0.295833	0.147917	−	0.989000i	$-0.452743\pi$
$541$	6.88091	0.295833	0.147917	+	0.989000i	$0.452743\pi$
$542$	−20.8891	−0.897263
$543$	7.09032	0.304275
$544$	−57.3483	−2.45879
$545$	10.4636	0.448210
$546$	3.99518	0.170978
$547$	25.4482	1.08809	0.544043	−	0.839057i	$-0.316893\pi$
$547$	25.4482	1.08809	0.544043	+	0.839057i	$0.316893\pi$
$548$	−7.39424	−0.315866
$549$	0.336312	0.0143535
$550$	15.4669	0.659509
$551$	−2.13116	−0.0907905
$552$	−11.1993	−0.476673
$553$	−31.5696	−1.34248
$554$	−8.59137	−0.365012
$555$	2.42782	0.103055
$556$	53.9189	2.28667
$557$	44.0015	1.86440	0.932201	−	0.361940i	$-0.117886\pi$
$557$	44.0015	1.86440	0.932201	+	0.361940i	$0.117886\pi$
$558$	−12.3909	−0.524549
$559$	1.56666	0.0662629
$560$	−13.0190	−0.550153
$561$	22.4157	0.946390
$562$	40.9545	1.72756
$563$	−22.7139	−0.957279	−0.478639	−	0.878012i	$-0.658870\pi$
$563$	−22.7139	−0.957279	−0.478639	+	0.878012i	$0.658870\pi$
$564$	12.6068	0.530841
$565$	−31.5124	−1.32573
$566$	−17.8818	−0.751628
$567$	4.21617	0.177062
$568$	17.1243	0.718519
$569$	−15.0575	−0.631241	−0.315621	−	0.948885i	$-0.602213\pi$
$569$	−15.0575	−0.631241	−0.315621	+	0.948885i	$0.602213\pi$
$570$	−1.61331	−0.0675742
$571$	−0.403046	−0.0168670	−0.00843348	−	0.999964i	$-0.502684\pi$
$571$	−0.403046	−0.0168670	−0.00843348	+	0.999964i	$0.502684\pi$
$572$	3.50030	0.146355
$573$	9.87948	0.412721
$574$	29.0558	1.21276
$575$	16.5298	0.689340
$576$	−12.4654	−0.519391
$577$	−14.3738	−0.598390	−0.299195	−	0.954192i	$-0.596718\pi$
$577$	−14.3738	−0.598390	−0.299195	+	0.954192i	$0.596718\pi$
$578$	−91.0062	−3.78536
$579$	9.52942	0.396029
$580$	20.4186	0.847837
$581$	−28.9269	−1.20009
$582$	−33.4398	−1.38612
$583$	−7.28992	−0.301918
$584$	16.3034	0.674641
$585$	0.697347	0.0288317
$586$	15.1373	0.625317
$587$	−4.17379	−0.172271	−0.0861354	−	0.996283i	$-0.527452\pi$
$587$	−4.17379	−0.172271	−0.0861354	+	0.996283i	$0.527452\pi$
$588$	−29.6742	−1.22374
$589$	−2.62085	−0.107990
$590$	−12.7271	−0.523967
$591$	−19.0741	−0.784604
$592$	2.91194	0.119680
$593$	30.2637	1.24278	0.621391	−	0.783501i	$-0.286568\pi$
$593$	30.2637	1.24278	0.621391	+	0.783501i	$0.286568\pi$
$594$	6.37677	0.261642
$595$	−51.8480	−2.12556
$596$	−31.6175	−1.29510
$597$	−6.55398	−0.268237
$598$	6.45780	0.264079
$599$	3.65320	0.149266	0.0746328	−	0.997211i	$-0.476222\pi$
$599$	3.65320	0.149266	0.0746328	+	0.997211i	$0.476222\pi$
$600$	−3.98590	−0.162724
$601$	41.8984	1.70907	0.854536	−	0.519392i	$-0.173841\pi$
$601$	41.8984	1.70907	0.854536	+	0.519392i	$0.173841\pi$
$602$	−33.1366	−1.35055
$603$	−6.98241	−0.284346
$604$	−28.6276	−1.16484
$605$	−3.92471	−0.159562
$606$	−8.88601	−0.360969
$607$	35.6076	1.44527	0.722634	−	0.691231i	$-0.242931\pi$
$607$	35.6076	1.44527	0.722634	+	0.691231i	$0.242931\pi$
$608$	−3.45071	−0.139945
$609$	−19.4840	−0.789532
$610$	−1.17654	−0.0476366
$611$	−1.98970	−0.0804945
$612$	−21.1051	−0.853122
$613$	2.68515	0.108452	0.0542260	−	0.998529i	$-0.482731\pi$
$613$	2.68515	0.108452	0.0542260	+	0.998529i	$0.482731\pi$
$614$	35.2115	1.42102
$615$	5.07159	0.204506
$616$	−20.2640	−0.816462
$617$	7.23511	0.291275	0.145637	−	0.989338i	$-0.453477\pi$
$617$	7.23511	0.291275	0.145637	+	0.989338i	$0.453477\pi$
$618$	5.85142	0.235379
$619$	−23.0879	−0.927980	−0.463990	−	0.885841i	$-0.653583\pi$
$619$	−23.0879	−0.927980	−0.463990	+	0.885841i	$0.653583\pi$
$620$	25.1103	1.00845
$621$	6.81500	0.273477
$622$	53.4679	2.14387
$623$	0.419060	0.0167893
$624$	0.836403	0.0334829
$625$	−6.98943	−0.279577
$626$	48.4526	1.93656
$627$	1.34877	0.0538648
$628$	−13.2225	−0.527636
$629$	11.5968	0.462394
$630$	−14.7496	−0.587639
$631$	−9.45358	−0.376341	−0.188170	−	0.982136i	$-0.560256\pi$
$631$	−9.45358	−0.376341	−0.188170	+	0.982136i	$0.560256\pi$
$632$	12.3049	0.489461
$633$	4.13455	0.164334
$634$	−19.6656	−0.781019
$635$	27.2163	1.08005
$636$	6.86370	0.272163
$637$	4.68341	0.185564
$638$	−29.4687	−1.16668
$639$	−10.4205	−0.412228
$640$	19.5962	0.774607
$641$	25.9559	1.02520	0.512598	−	0.858629i	$-0.328683\pi$
$641$	25.9559	1.02520	0.512598	+	0.858629i	$0.328683\pi$
$642$	−31.1873	−1.23086
$643$	23.9997	0.946456	0.473228	−	0.880940i	$-0.343089\pi$
$643$	23.9997	0.946456	0.473228	+	0.880940i	$0.343089\pi$
$644$	−79.1230	−3.11788
$645$	−5.78389	−0.227740
$646$	−7.70619	−0.303196
$647$	−43.2931	−1.70203	−0.851014	−	0.525144i	$-0.824012\pi$
$647$	−43.2931	−1.70203	−0.851014	+	0.525144i	$0.824012\pi$
$648$	−1.64333	−0.0645561
$649$	10.6402	0.417665
$650$	2.29837	0.0901496
$651$	−23.9610	−0.939104
$652$	59.7291	2.33917
$653$	10.6548	0.416953	0.208477	−	0.978027i	$-0.433149\pi$
$653$	10.6548	0.416953	0.208477	+	0.978027i	$0.433149\pi$
$654$	14.2184	0.555982
$655$	29.1884	1.14049
$656$	6.08291	0.237498
$657$	−9.92098	−0.387054
$658$	42.0842	1.64061
$659$	43.3135	1.68726	0.843628	−	0.536928i	$-0.180415\pi$
$659$	43.3135	1.68726	0.843628	+	0.536928i	$0.180415\pi$
$660$	−12.9226	−0.503011
$661$	23.0399	0.896149	0.448075	−	0.893996i	$-0.352110\pi$
$661$	23.0399	0.896149	0.448075	+	0.893996i	$0.352110\pi$
$662$	−8.79221	−0.341719
$663$	3.33097	0.129364
$664$	11.2748	0.437547
$665$	−3.11975	−0.120979
$666$	3.29903	0.127835
$667$	−31.4939	−1.21945
$668$	−46.7351	−1.80824
$669$	15.5732	0.602093
$670$	24.4269	0.943694
$671$	0.983619	0.0379722
$672$	−31.5479	−1.21699
$673$	−8.56404	−0.330120	−0.165060	−	0.986284i	$-0.552782\pi$
$673$	−8.56404	−0.330120	−0.165060	+	0.986284i	$0.552782\pi$
$674$	−55.1498	−2.12429
$675$	2.42550	0.0933576
$676$	−35.2782	−1.35685
$677$	5.99011	0.230219	0.115109	−	0.993353i	$-0.463278\pi$
$677$	5.99011	0.230219	0.115109	+	0.993353i	$0.463278\pi$
$678$	−42.8204	−1.64451
$679$	−64.6643	−2.48159
$680$	20.2087	0.774969
$681$	−2.65168	−0.101613
$682$	−36.2399	−1.38770
$683$	−15.3834	−0.588631	−0.294315	−	0.955708i	$-0.595092\pi$
$683$	−15.3834	−0.588631	−0.294315	+	0.955708i	$0.595092\pi$
$684$	−1.26991	−0.0485564
$685$	−4.30844	−0.164617
$686$	−34.7115	−1.32529
$687$	−7.65636	−0.292108
$688$	−6.93724	−0.264480
$689$	−1.08328	−0.0412698
$690$	−23.8412	−0.907620
$691$	3.43703	0.130751	0.0653754	−	0.997861i	$-0.479176\pi$
$691$	3.43703	0.130751	0.0653754	+	0.997861i	$0.479176\pi$
$692$	65.2418	2.48012
$693$	12.3311	0.468420
$694$	42.7295	1.62199
$695$	31.4172	1.19172
$696$	7.59426	0.287860
$697$	24.2251	0.917591
$698$	33.3480	1.26224
$699$	−13.7849	−0.521394
$700$	−28.1604	−1.06436
$701$	−29.5110	−1.11462	−0.557308	−	0.830306i	$-0.688166\pi$
$701$	−29.5110	−1.11462	−0.557308	+	0.830306i	$0.688166\pi$
$702$	0.947587	0.0357644
$703$	0.697790	0.0263177
$704$	−36.4577	−1.37405
$705$	7.34566	0.276654
$706$	74.3753	2.79915
$707$	−17.1834	−0.646246
$708$	−10.0181	−0.376504
$709$	12.1134	0.454927	0.227463	−	0.973787i	$-0.426957\pi$
$709$	12.1134	0.454927	0.227463	+	0.973787i	$0.426957\pi$
$710$	36.4544	1.36811
$711$	−7.48776	−0.280813
$712$	−0.163336	−0.00612129
$713$	−38.7304	−1.45047
$714$	−70.4534	−2.63665
$715$	2.03954	0.0762745
$716$	−23.9121	−0.893639
$717$	−11.0276	−0.411833
$718$	79.9517	2.98377
$719$	−17.1833	−0.640828	−0.320414	−	0.947278i	$-0.603822\pi$
$719$	−17.1833	−0.640828	−0.320414	+	0.947278i	$0.603822\pi$
$720$	−3.08787	−0.115078
$721$	11.3152	0.421400
$722$	40.9620	1.52445
$723$	9.89513	0.368004
$724$	−19.5247	−0.725631
$725$	−11.2089	−0.416288
$726$	−5.33308	−0.197929
$727$	−28.1433	−1.04378	−0.521889	−	0.853013i	$-0.674772\pi$
$727$	−28.1433	−1.04378	−0.521889	+	0.853013i	$0.674772\pi$
$728$	−3.01124	−0.111604
$729$	1.00000	0.0370370
$730$	34.7070	1.28456
$731$	−27.6275	−1.02184
$732$	−0.926109	−0.0342300
$733$	5.29949	0.195741	0.0978706	−	0.995199i	$-0.468797\pi$
$733$	5.29949	0.195741	0.0978706	+	0.995199i	$0.468797\pi$
$734$	−39.8770	−1.47189
$735$	−17.2905	−0.637768
$736$	−50.9939	−1.87966
$737$	−20.4216	−0.752239
$738$	6.89151	0.253680
$739$	−47.8674	−1.76083	−0.880414	−	0.474205i	$-0.842736\pi$
$739$	−47.8674	−1.76083	−0.880414	+	0.474205i	$0.842736\pi$
$740$	−6.68552	−0.245765
$741$	0.200428	0.00736289
$742$	22.9126	0.841146
$743$	38.0997	1.39774	0.698872	−	0.715247i	$-0.253686\pi$
$743$	38.0997	1.39774	0.698872	+	0.715247i	$0.253686\pi$
$744$	9.33923	0.342393
$745$	−18.4227	−0.674957
$746$	11.7621	0.430639
$747$	−6.86095	−0.251029
$748$	−61.7264	−2.25694
$749$	−60.3086	−2.20363
$750$	−25.9770	−0.948545
$751$	−17.3977	−0.634850	−0.317425	−	0.948283i	$-0.602818\pi$
$751$	−17.3977	−0.634850	−0.317425	+	0.948283i	$0.602818\pi$
$752$	8.81044	0.321284
$753$	−2.81208	−0.102478
$754$	−4.37905	−0.159476
$755$	−16.6806	−0.607070
$756$	−11.6101	−0.422256
$757$	−23.4776	−0.853308	−0.426654	−	0.904415i	$-0.640308\pi$
$757$	−23.4776	−0.853308	−0.426654	+	0.904415i	$0.640308\pi$
$758$	−60.4069	−2.19408
$759$	19.9319	0.723484
$760$	1.21598	0.0441082
$761$	16.5803	0.601036	0.300518	−	0.953776i	$-0.402841\pi$
$761$	16.5803	0.601036	0.300518	+	0.953776i	$0.402841\pi$
$762$	36.9827	1.33974
$763$	27.4948	0.995380
$764$	−27.2053	−0.984253
$765$	−12.2974	−0.444614
$766$	11.7316	0.423881
$767$	1.58114	0.0570915
$768$	1.69744	0.0612512
$769$	−15.9791	−0.576221	−0.288111	−	0.957597i	$-0.593027\pi$
$769$	−15.9791	−0.576221	−0.288111	+	0.957597i	$0.593027\pi$
$770$	−43.1385	−1.55460
$771$	16.2311	0.584547
$772$	−26.2413	−0.944445
$773$	−0.853547	−0.0307000	−0.0153500	−	0.999882i	$-0.504886\pi$
$773$	−0.853547	−0.0307000	−0.0153500	+	0.999882i	$0.504886\pi$
$774$	−7.85942	−0.282501
$775$	−13.7844	−0.495150
$776$	25.2041	0.904774
$777$	6.37951	0.228864
$778$	51.5923	1.84967
$779$	1.45765	0.0522257
$780$	−1.92029	−0.0687576
$781$	−30.4769	−1.09055
$782$	−113.881	−4.07237
$783$	−4.62126	−0.165151
$784$	−20.7383	−0.740654
$785$	−7.70445	−0.274984
$786$	39.6626	1.41472
$787$	−54.4606	−1.94131	−0.970655	−	0.240476i	$-0.922696\pi$
$787$	−54.4606	−1.94131	−0.970655	+	0.240476i	$0.922696\pi$
$788$	52.5247	1.87112
$789$	8.92663	0.317796
$790$	26.1948	0.931969
$791$	−82.8042	−2.94418
$792$	−4.80627	−0.170783
$793$	0.146166	0.00519049
$794$	−14.5666	−0.516948
$795$	3.99931	0.141841
$796$	18.0478	0.639687
$797$	6.37227	0.225717	0.112859	−	0.993611i	$-0.463999\pi$
$797$	6.37227	0.225717	0.112859	+	0.993611i	$0.463999\pi$
$798$	−4.23926	−0.150068
$799$	35.0875	1.24131
$800$	−18.1491	−0.641666
$801$	0.0993936	0.00351190
$802$	−65.5332	−2.31406
$803$	−29.0161	−1.02395
$804$	19.2276	0.678105
$805$	−46.1031	−1.62492
$806$	−5.38524	−0.189687
$807$	23.4586	0.825782
$808$	6.69753	0.235618
$809$	−15.6564	−0.550451	−0.275225	−	0.961380i	$-0.588752\pi$
$809$	−15.6564	−0.550451	−0.275225	+	0.961380i	$0.588752\pi$
$810$	−3.49835	−0.122919
$811$	50.7463	1.78194	0.890972	−	0.454058i	$-0.150024\pi$
$811$	50.7463	1.78194	0.890972	+	0.454058i	$0.150024\pi$
$812$	53.6535	1.88287
$813$	−9.58082	−0.336014
$814$	9.64873	0.338188
$815$	34.8027	1.21909
$816$	−14.7496	−0.516340
$817$	−1.66237	−0.0581591
$818$	24.3037	0.849758
$819$	1.83240	0.0640292
$820$	−13.9657	−0.487704
$821$	37.3462	1.30339	0.651696	−	0.758480i	$-0.274058\pi$
$821$	37.3462	1.30339	0.651696	+	0.758480i	$0.274058\pi$
$822$	−5.85451	−0.204200
$823$	−35.2027	−1.22709	−0.613544	−	0.789660i	$-0.710257\pi$
$823$	−35.2027	−1.22709	−0.613544	+	0.789660i	$0.710257\pi$
$824$	−4.41031	−0.153640
$825$	7.09391	0.246978
$826$	−33.4427	−1.16362
$827$	−42.3575	−1.47291	−0.736457	−	0.676485i	$-0.763502\pi$
$827$	−42.3575	−1.47291	−0.736457	+	0.676485i	$0.763502\pi$
$828$	−18.7666	−0.652184
$829$	25.8640	0.898295	0.449148	−	0.893458i	$-0.351728\pi$
$829$	25.8640	0.898295	0.449148	+	0.893458i	$0.351728\pi$
$830$	24.0020	0.833121
$831$	−3.94045	−0.136693
$832$	−5.41761	−0.187822
$833$	−82.5901	−2.86158
$834$	42.6912	1.47828
$835$	−27.2314	−0.942383
$836$	−3.71414	−0.128456
$837$	−5.68311	−0.196437
$838$	−39.6734	−1.37050
$839$	−18.9892	−0.655579	−0.327790	−	0.944751i	$-0.606304\pi$
$839$	−18.9892	−0.655579	−0.327790	+	0.944751i	$0.606304\pi$
$840$	11.1170	0.383574
$841$	−7.64392	−0.263583
$842$	−55.2574	−1.90430
$843$	18.7839	0.646951
$844$	−11.3854	−0.391901
$845$	−20.5557	−0.707139
$846$	9.98162	0.343175
$847$	−10.3129	−0.354354
$848$	4.79681	0.164723
$849$	−8.20152	−0.281475
$850$	−40.5309	−1.39020
$851$	10.3118	0.353485
$852$	28.6950	0.983076
$853$	−44.9313	−1.53842	−0.769208	−	0.638998i	$-0.779349\pi$
$853$	−44.9313	−1.53842	−0.769208	+	0.638998i	$0.779349\pi$
$854$	−3.09156	−0.105791
$855$	−0.739948	−0.0253057
$856$	23.5064	0.803432
$857$	2.51453	0.0858946	0.0429473	−	0.999077i	$-0.486325\pi$
$857$	2.51453	0.0858946	0.0429473	+	0.999077i	$0.486325\pi$
$858$	2.77142	0.0946148
$859$	−16.3169	−0.556726	−0.278363	−	0.960476i	$-0.589792\pi$
$859$	−16.3169	−0.556726	−0.278363	+	0.960476i	$0.589792\pi$
$860$	15.9272	0.543113
$861$	13.3265	0.454166
$862$	−40.7387	−1.38757
$863$	35.3102	1.20197	0.600987	−	0.799259i	$-0.294774\pi$
$863$	35.3102	1.20197	0.600987	+	0.799259i	$0.294774\pi$
$864$	−7.48260	−0.254563
$865$	38.0148	1.29254
$866$	−1.56966	−0.0533393
$867$	−41.7402	−1.41757
$868$	65.9817	2.23956
$869$	−21.8996	−0.742892
$870$	16.1668	0.548105
$871$	−3.03465	−0.102825
$872$	−10.7166	−0.362911
$873$	−15.3372	−0.519086
$874$	−6.85232	−0.231783
$875$	−50.2331	−1.69819
$876$	27.3196	0.923042
$877$	10.1419	0.342467	0.171234	−	0.985230i	$-0.445225\pi$
$877$	10.1419	0.342467	0.171234	+	0.985230i	$0.445225\pi$
$878$	−18.9616	−0.639922
$879$	6.94276	0.234173
$880$	−9.03116	−0.304440
$881$	48.9170	1.64805	0.824027	−	0.566550i	$-0.191722\pi$
$881$	48.9170	1.64805	0.824027	+	0.566550i	$0.191722\pi$
$882$	−23.4951	−0.791120
$883$	−37.3276	−1.25617	−0.628087	−	0.778143i	$-0.716162\pi$
$883$	−37.3276	−1.25617	−0.628087	+	0.778143i	$0.716162\pi$
$884$	−9.17253	−0.308506
$885$	−5.83732	−0.196219
$886$	−1.44582	−0.0485733
$887$	9.74940	0.327353	0.163676	−	0.986514i	$-0.447665\pi$
$887$	9.74940	0.327353	0.163676	+	0.986514i	$0.447665\pi$
$888$	−2.48653	−0.0834426
$889$	71.5155	2.39855
$890$	−0.347713	−0.0116554
$891$	2.92472	0.0979817
$892$	−42.8840	−1.43586
$893$	2.11125	0.0706503
$894$	−25.0337	−0.837251
$895$	−13.9330	−0.465730
$896$	51.4924	1.72024
$897$	2.96189	0.0988945
$898$	62.0613	2.07101
$899$	26.2632	0.875926
$900$	−6.67914	−0.222638
$901$	19.1032	0.636421
$902$	20.1557	0.671112
$903$	−15.1982	−0.505764
$904$	32.2745	1.07343
$905$	−11.3766	−0.378171
$906$	−22.6664	−0.753041
$907$	27.1169	0.900401	0.450200	−	0.892928i	$-0.351353\pi$
$907$	27.1169	0.900401	0.450200	+	0.892928i	$0.351353\pi$
$908$	7.30198	0.242325
$909$	−4.07559	−0.135179
$910$	−6.41037	−0.212502
$911$	11.8122	0.391356	0.195678	−	0.980668i	$-0.437309\pi$
$911$	11.8122	0.391356	0.195678	+	0.980668i	$0.437309\pi$
$912$	−0.887500	−0.0293881
$913$	−20.0663	−0.664099
$914$	22.4979	0.744164
$915$	−0.539621	−0.0178393
$916$	21.0835	0.696617
$917$	76.6977	2.53278
$918$	−16.7103	−0.551522
$919$	−9.65814	−0.318593	−0.159296	−	0.987231i	$-0.550923\pi$
$919$	−9.65814	−0.318593	−0.159296	+	0.987231i	$0.550923\pi$
$920$	17.9695	0.592438
$921$	16.1498	0.532155
$922$	20.4260	0.672695
$923$	−4.52887	−0.149070
$924$	−33.9563	−1.11708
$925$	3.67005	0.120670
$926$	−37.6502	−1.23726
$927$	2.68377	0.0881464
$928$	34.5791	1.13511
$929$	30.0039	0.984396	0.492198	−	0.870483i	$-0.336194\pi$
$929$	30.0039	0.984396	0.492198	+	0.870483i	$0.336194\pi$
$930$	19.8815	0.651940
$931$	−4.96953	−0.162870
$932$	37.9598	1.24341
$933$	24.5232	0.802852
$934$	−45.0008	−1.47247
$935$	−35.9665	−1.17623
$936$	−0.714212	−0.0233447
$937$	30.5255	0.997224	0.498612	−	0.866825i	$-0.333843\pi$
$937$	30.5255	0.997224	0.498612	+	0.866825i	$0.333843\pi$
$938$	64.1859	2.09575
$939$	22.2229	0.725217
$940$	−20.2279	−0.659760
$941$	−47.6452	−1.55319	−0.776594	−	0.630001i	$-0.783054\pi$
$941$	−47.6452	−1.55319	−0.776594	+	0.630001i	$0.783054\pi$
$942$	−10.4692	−0.341104
$943$	21.5409	0.701468
$944$	−7.00132	−0.227874
$945$	−6.76494	−0.220064
$946$	−22.9866	−0.747358
$947$	−18.9013	−0.614209	−0.307105	−	0.951676i	$-0.599360\pi$
$947$	−18.9013	−0.614209	−0.307105	+	0.951676i	$0.599360\pi$
$948$	20.6192	0.669679
$949$	−4.31178	−0.139966
$950$	−2.43878	−0.0791246
$951$	−9.01965	−0.292482
$952$	53.1019	1.72104
$953$	20.8020	0.673844	0.336922	−	0.941533i	$-0.390614\pi$
$953$	20.8020	0.673844	0.336922	+	0.941533i	$0.390614\pi$
$954$	5.43445	0.175947
$955$	−15.8519	−0.512954
$956$	30.3668	0.982134
$957$	−13.5159	−0.436907
$958$	−5.98240	−0.193283
$959$	−11.3212	−0.365580
$960$	20.0010	0.645529
$961$	1.29779	0.0418643
$962$	1.43380	0.0462276
$963$	−14.3041	−0.460944
$964$	−27.2484	−0.877611
$965$	−15.2902	−0.492208
$966$	−62.6470	−2.01563
$967$	25.9665	0.835025	0.417513	−	0.908671i	$-0.362902\pi$
$967$	25.9665	0.835025	0.417513	+	0.908671i	$0.362902\pi$
$968$	4.01963	0.129196
$969$	−3.53446	−0.113543
$970$	53.6549	1.72276
$971$	18.4195	0.591110	0.295555	−	0.955326i	$-0.404495\pi$
$971$	18.4195	0.591110	0.295555	+	0.955326i	$0.404495\pi$
$972$	−2.75372	−0.0883255
$973$	82.5543	2.64657
$974$	−83.3388	−2.67035
$975$	1.05415	0.0337599
$976$	−0.647226	−0.0207172
$977$	−3.32596	−0.106407	−0.0532035	−	0.998584i	$-0.516943\pi$
$977$	−3.32596	−0.106407	−0.0532035	+	0.998584i	$0.516943\pi$
$978$	47.2915	1.51222
$979$	0.290698	0.00929075
$980$	47.6130	1.52094
$981$	6.52129	0.208209
$982$	−15.5471	−0.496128
$983$	−26.8118	−0.855163	−0.427581	−	0.903977i	$-0.640634\pi$
$983$	−26.8118	−0.855163	−0.427581	+	0.903977i	$0.640634\pi$
$984$	−5.19425	−0.165587
$985$	30.6049	0.975153
$986$	77.2227	2.45927
$987$	19.3020	0.614389
$988$	−0.551921	−0.0175589
$989$	−24.5663	−0.781163
$990$	−10.2317	−0.325184
$991$	−26.0734	−0.828247	−0.414124	−	0.910221i	$-0.635912\pi$
$991$	−26.0734	−0.828247	−0.414124	+	0.910221i	$0.635912\pi$
$992$	42.5245	1.35015
$993$	−4.03257	−0.127970
$994$	95.7904	3.03829
$995$	10.5160	0.333380
$996$	18.8931	0.598651
$997$	−7.70655	−0.244069	−0.122034	−	0.992526i	$-0.538942\pi$
$997$	−7.70655	−0.244069	−0.122034	+	0.992526i	$0.538942\pi$
$998$	27.0768	0.857103
$999$	1.51311	0.0478726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.c.1.19	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.c.1.19	✓	116	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18030 q^{2} -1.00000 q^{3} +2.75372 q^{4} +1.60452 q^{5} +2.18030 q^{6} +4.21617 q^{7} -1.64333 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18030 q^{2} -1.00000 q^{3} +2.75372 q^{4} +1.60452 q^{5} +2.18030 q^{6} +4.21617 q^{7} -1.64333 q^{8} +1.00000 q^{9} -3.49835 q^{10} +2.92472 q^{11} -2.75372 q^{12} +0.434613 q^{13} -9.19252 q^{14} -1.60452 q^{15} -1.92448 q^{16} -7.66422 q^{17} -2.18030 q^{18} -0.461164 q^{19} +4.41840 q^{20} -4.21617 q^{21} -6.37677 q^{22} -6.81500 q^{23} +1.64333 q^{24} -2.42550 q^{25} -0.947587 q^{26} -1.00000 q^{27} +11.6101 q^{28} +4.62126 q^{29} +3.49835 q^{30} +5.68311 q^{31} +7.48260 q^{32} -2.92472 q^{33} +16.7103 q^{34} +6.76494 q^{35} +2.75372 q^{36} -1.51311 q^{37} +1.00548 q^{38} -0.434613 q^{39} -2.63676 q^{40} -3.16081 q^{41} +9.19252 q^{42} +3.60474 q^{43} +8.05384 q^{44} +1.60452 q^{45} +14.8588 q^{46} -4.57809 q^{47} +1.92448 q^{48} +10.7761 q^{49} +5.28833 q^{50} +7.66422 q^{51} +1.19680 q^{52} -2.49252 q^{53} +2.18030 q^{54} +4.69278 q^{55} -6.92855 q^{56} +0.461164 q^{57} -10.0758 q^{58} +3.63804 q^{59} -4.41840 q^{60} +0.336312 q^{61} -12.3909 q^{62} +4.21617 q^{63} -12.4654 q^{64} +0.697347 q^{65} +6.37677 q^{66} -6.98241 q^{67} -21.1051 q^{68} +6.81500 q^{69} -14.7496 q^{70} -10.4205 q^{71} -1.64333 q^{72} -9.92098 q^{73} +3.29903 q^{74} +2.42550 q^{75} -1.26991 q^{76} +12.3311 q^{77} +0.947587 q^{78} -7.48776 q^{79} -3.08787 q^{80} +1.00000 q^{81} +6.89151 q^{82} -6.86095 q^{83} -11.6101 q^{84} -12.2974 q^{85} -7.85942 q^{86} -4.62126 q^{87} -4.80627 q^{88} +0.0993936 q^{89} -3.49835 q^{90} +1.83240 q^{91} -18.7666 q^{92} -5.68311 q^{93} +9.98162 q^{94} -0.739948 q^{95} -7.48260 q^{96} -15.3372 q^{97} -23.4951 q^{98} +2.92472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * q^99

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