LMFDB - Embedded newform 8007.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61866 q^{2} +1.00000 q^{3} +4.85739 q^{4} +0.391872 q^{5} -2.61866 q^{6} +2.70632 q^{7} -7.48254 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61866 q^{2} +1.00000 q^{3} +4.85739 q^{4} +0.391872 q^{5} -2.61866 q^{6} +2.70632 q^{7} -7.48254 q^{8} +1.00000 q^{9} -1.02618 q^{10} -3.87613 q^{11} +4.85739 q^{12} -0.879543 q^{13} -7.08695 q^{14} +0.391872 q^{15} +9.87946 q^{16} +1.00000 q^{17} -2.61866 q^{18} +0.781148 q^{19} +1.90348 q^{20} +2.70632 q^{21} +10.1503 q^{22} -7.15872 q^{23} -7.48254 q^{24} -4.84644 q^{25} +2.30323 q^{26} +1.00000 q^{27} +13.1457 q^{28} -3.67061 q^{29} -1.02618 q^{30} +9.68606 q^{31} -10.9059 q^{32} -3.87613 q^{33} -2.61866 q^{34} +1.06053 q^{35} +4.85739 q^{36} -2.30940 q^{37} -2.04556 q^{38} -0.879543 q^{39} -2.93220 q^{40} -4.05914 q^{41} -7.08695 q^{42} +4.55208 q^{43} -18.8279 q^{44} +0.391872 q^{45} +18.7463 q^{46} -3.63900 q^{47} +9.87946 q^{48} +0.324188 q^{49} +12.6912 q^{50} +1.00000 q^{51} -4.27228 q^{52} +4.75786 q^{53} -2.61866 q^{54} -1.51895 q^{55} -20.2502 q^{56} +0.781148 q^{57} +9.61208 q^{58} +5.18257 q^{59} +1.90348 q^{60} +9.15247 q^{61} -25.3645 q^{62} +2.70632 q^{63} +8.79991 q^{64} -0.344668 q^{65} +10.1503 q^{66} -12.5875 q^{67} +4.85739 q^{68} -7.15872 q^{69} -2.77718 q^{70} +6.72352 q^{71} -7.48254 q^{72} -3.80747 q^{73} +6.04755 q^{74} -4.84644 q^{75} +3.79434 q^{76} -10.4901 q^{77} +2.30323 q^{78} -0.140935 q^{79} +3.87149 q^{80} +1.00000 q^{81} +10.6295 q^{82} +8.27486 q^{83} +13.1457 q^{84} +0.391872 q^{85} -11.9203 q^{86} -3.67061 q^{87} +29.0033 q^{88} +1.59746 q^{89} -1.02618 q^{90} -2.38033 q^{91} -34.7727 q^{92} +9.68606 q^{93} +9.52931 q^{94} +0.306110 q^{95} -10.9059 q^{96} +9.61258 q^{97} -0.848938 q^{98} -3.87613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * 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 $

$2$	−2.61866	−1.85167	−0.925837	−	0.377924i	$-0.876638\pi$
$2$	−2.61866	−1.85167	−0.925837	+	0.377924i	$0.876638\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.85739	2.42870
$5$	0.391872	0.175251	0.0876253	−	0.996154i	$-0.472072\pi$
$5$	0.391872	0.175251	0.0876253	+	0.996154i	$0.472072\pi$
$6$	−2.61866	−1.06906
$7$	2.70632	1.02289	0.511447	−	0.859315i	$-0.329110\pi$
$7$	2.70632	1.02289	0.511447	+	0.859315i	$0.329110\pi$
$8$	−7.48254	−2.64548
$9$	1.00000	0.333333
$10$	−1.02618	−0.324507
$11$	−3.87613	−1.16870	−0.584349	−	0.811503i	$-0.698650\pi$
$11$	−3.87613	−1.16870	−0.584349	+	0.811503i	$0.698650\pi$
$12$	4.85739	1.40221
$13$	−0.879543	−0.243941	−0.121971	−	0.992534i	$-0.538921\pi$
$13$	−0.879543	−0.243941	−0.121971	+	0.992534i	$0.538921\pi$
$14$	−7.08695	−1.89407
$15$	0.391872	0.101181
$16$	9.87946	2.46987
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.61866	−0.617225
$19$	0.781148	0.179208	0.0896038	−	0.995977i	$-0.471440\pi$
$19$	0.781148	0.179208	0.0896038	+	0.995977i	$0.471440\pi$
$20$	1.90348	0.425630
$21$	2.70632	0.590568
$22$	10.1503	2.16405
$23$	−7.15872	−1.49270	−0.746348	−	0.665556i	$-0.768194\pi$
$23$	−7.15872	−1.49270	−0.746348	+	0.665556i	$0.768194\pi$
$24$	−7.48254	−1.52737
$25$	−4.84644	−0.969287
$26$	2.30323	0.451700
$27$	1.00000	0.192450
$28$	13.1457	2.48430
$29$	−3.67061	−0.681614	−0.340807	−	0.940133i	$-0.610700\pi$
$29$	−3.67061	−0.681614	−0.340807	+	0.940133i	$0.610700\pi$
$30$	−1.02618	−0.187354
$31$	9.68606	1.73967	0.869834	−	0.493345i	$-0.164226\pi$
$31$	9.68606	1.73967	0.869834	+	0.493345i	$0.164226\pi$
$32$	−10.9059	−1.92791
$33$	−3.87613	−0.674748
$34$	−2.61866	−0.449097
$35$	1.06053	0.179263
$36$	4.85739	0.809565
$37$	−2.30940	−0.379664	−0.189832	−	0.981817i	$-0.560794\pi$
$37$	−2.30940	−0.379664	−0.189832	+	0.981817i	$0.560794\pi$
$38$	−2.04556	−0.331834
$39$	−0.879543	−0.140840
$40$	−2.93220	−0.463621
$41$	−4.05914	−0.633931	−0.316966	−	0.948437i	$-0.602664\pi$
$41$	−4.05914	−0.633931	−0.316966	+	0.948437i	$0.602664\pi$
$42$	−7.08695	−1.09354
$43$	4.55208	0.694185	0.347093	−	0.937831i	$-0.387169\pi$
$43$	4.55208	0.694185	0.347093	+	0.937831i	$0.387169\pi$
$44$	−18.8279	−2.83841
$45$	0.391872	0.0584169
$46$	18.7463	2.76399
$47$	−3.63900	−0.530803	−0.265401	−	0.964138i	$-0.585504\pi$
$47$	−3.63900	−0.530803	−0.265401	+	0.964138i	$0.585504\pi$
$48$	9.87946	1.42598
$49$	0.324188	0.0463125
$50$	12.6912	1.79480
$51$	1.00000	0.140028
$52$	−4.27228	−0.592459
$53$	4.75786	0.653542	0.326771	−	0.945104i	$-0.394039\pi$
$53$	4.75786	0.653542	0.326771	+	0.945104i	$0.394039\pi$
$54$	−2.61866	−0.356355
$55$	−1.51895	−0.204815
$56$	−20.2502	−2.70604
$57$	0.781148	0.103466
$58$	9.61208	1.26213
$59$	5.18257	0.674713	0.337356	−	0.941377i	$-0.390467\pi$
$59$	5.18257	0.674713	0.337356	+	0.941377i	$0.390467\pi$
$60$	1.90348	0.245738
$61$	9.15247	1.17185	0.585927	−	0.810364i	$-0.300731\pi$
$61$	9.15247	1.17185	0.585927	+	0.810364i	$0.300731\pi$
$62$	−25.3645	−3.22130
$63$	2.70632	0.340965
$64$	8.79991	1.09999
$65$	−0.344668	−0.0427509
$66$	10.1503	1.24941
$67$	−12.5875	−1.53781	−0.768905	−	0.639363i	$-0.779198\pi$
$67$	−12.5875	−1.53781	−0.768905	+	0.639363i	$0.779198\pi$
$68$	4.85739	0.589045
$69$	−7.15872	−0.861808
$70$	−2.77718	−0.331936
$71$	6.72352	0.797934	0.398967	−	0.916965i	$-0.369369\pi$
$71$	6.72352	0.797934	0.398967	+	0.916965i	$0.369369\pi$
$72$	−7.48254	−0.881826
$73$	−3.80747	−0.445631	−0.222815	−	0.974861i	$-0.571525\pi$
$73$	−3.80747	−0.445631	−0.222815	+	0.974861i	$0.571525\pi$
$74$	6.04755	0.703013
$75$	−4.84644	−0.559618
$76$	3.79434	0.435241
$77$	−10.4901	−1.19545
$78$	2.30323	0.260789
$79$	−0.140935	−0.0158564	−0.00792819	−	0.999969i	$-0.502524\pi$
$79$	−0.140935	−0.0158564	−0.00792819	+	0.999969i	$0.502524\pi$
$80$	3.87149	0.432845
$81$	1.00000	0.111111
$82$	10.6295	1.17383
$83$	8.27486	0.908284	0.454142	−	0.890929i	$-0.349946\pi$
$83$	8.27486	0.908284	0.454142	+	0.890929i	$0.349946\pi$
$84$	13.1457	1.43431
$85$	0.391872	0.0425045
$86$	−11.9203	−1.28540
$87$	−3.67061	−0.393530
$88$	29.0033	3.09176
$89$	1.59746	0.169330	0.0846650	−	0.996409i	$-0.473018\pi$
$89$	1.59746	0.169330	0.0846650	+	0.996409i	$0.473018\pi$
$90$	−1.02618	−0.108169
$91$	−2.38033	−0.249526
$92$	−34.7727	−3.62530
$93$	9.68606	1.00440
$94$	9.52931	0.982874
$95$	0.306110	0.0314062
$96$	−10.9059	−1.11308
$97$	9.61258	0.976010	0.488005	−	0.872841i	$-0.337725\pi$
$97$	9.61258	0.976010	0.488005	+	0.872841i	$0.337725\pi$
$98$	−0.848938	−0.0857557
$99$	−3.87613	−0.389566
$100$	−23.5410	−2.35410
$101$	7.07312	0.703802	0.351901	−	0.936037i	$-0.385535\pi$
$101$	7.07312	0.703802	0.351901	+	0.936037i	$0.385535\pi$
$102$	−2.61866	−0.259286
$103$	−10.8773	−1.07177	−0.535885	−	0.844291i	$-0.680022\pi$
$103$	−10.8773	−1.07177	−0.535885	+	0.844291i	$0.680022\pi$
$104$	6.58121	0.645341
$105$	1.06053	0.103497
$106$	−12.4592	−1.21015
$107$	−8.81213	−0.851901	−0.425951	−	0.904746i	$-0.640060\pi$
$107$	−8.81213	−0.851901	−0.425951	+	0.904746i	$0.640060\pi$
$108$	4.85739	0.467403
$109$	−14.9197	−1.42904	−0.714522	−	0.699613i	$-0.753356\pi$
$109$	−14.9197	−1.42904	−0.714522	+	0.699613i	$0.753356\pi$
$110$	3.97761	0.379250
$111$	−2.30940	−0.219199
$112$	26.7370	2.52641
$113$	19.0110	1.78840	0.894202	−	0.447663i	$-0.147744\pi$
$113$	19.0110	1.78840	0.894202	+	0.447663i	$0.147744\pi$
$114$	−2.04556	−0.191584
$115$	−2.80530	−0.261596
$116$	−17.8296	−1.65543
$117$	−0.879543	−0.0813138
$118$	−13.5714	−1.24935
$119$	2.70632	0.248088
$120$	−2.93220	−0.267672
$121$	4.02439	0.365853
$122$	−23.9672	−2.16989
$123$	−4.05914	−0.366000
$124$	47.0490	4.22512
$125$	−3.85854	−0.345119
$126$	−7.08695	−0.631355
$127$	14.6166	1.29702	0.648508	−	0.761208i	$-0.275393\pi$
$127$	14.6166	1.29702	0.648508	+	0.761208i	$0.275393\pi$
$128$	−1.23222	−0.108914
$129$	4.55208	0.400788
$130$	0.902570	0.0791606
$131$	−3.89751	−0.340527	−0.170264	−	0.985399i	$-0.554462\pi$
$131$	−3.89751	−0.340527	−0.170264	+	0.985399i	$0.554462\pi$
$132$	−18.8279	−1.63876
$133$	2.11404	0.183310
$134$	32.9624	2.84752
$135$	0.391872	0.0337270
$136$	−7.48254	−0.641622
$137$	−8.73913	−0.746634	−0.373317	−	0.927704i	$-0.621780\pi$
$137$	−8.73913	−0.746634	−0.373317	+	0.927704i	$0.621780\pi$
$138$	18.7463	1.59579
$139$	−4.99249	−0.423457	−0.211729	−	0.977329i	$-0.567909\pi$
$139$	−4.99249	−0.423457	−0.211729	+	0.977329i	$0.567909\pi$
$140$	5.15142	0.435375
$141$	−3.63900	−0.306459
$142$	−17.6066	−1.47751
$143$	3.40922	0.285094
$144$	9.87946	0.823288
$145$	−1.43841	−0.119453
$146$	9.97048	0.825163
$147$	0.324188	0.0267385
$148$	−11.2177	−0.922087
$149$	1.59168	0.130396	0.0651978	−	0.997872i	$-0.479232\pi$
$149$	1.59168	0.130396	0.0651978	+	0.997872i	$0.479232\pi$
$150$	12.6912	1.03623
$151$	−13.3108	−1.08322	−0.541610	−	0.840630i	$-0.682185\pi$
$151$	−13.3108	−1.08322	−0.541610	+	0.840630i	$0.682185\pi$
$152$	−5.84497	−0.474089
$153$	1.00000	0.0808452
$154$	27.4699	2.21359
$155$	3.79570	0.304878
$156$	−4.27228	−0.342056
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	0.369060	0.0293608
$159$	4.75786	0.377323
$160$	−4.27371	−0.337867
$161$	−19.3738	−1.52687
$162$	−2.61866	−0.205742
$163$	−1.01200	−0.0792656	−0.0396328	−	0.999214i	$-0.512619\pi$
$163$	−1.01200	−0.0792656	−0.0396328	+	0.999214i	$0.512619\pi$
$164$	−19.7168	−1.53963
$165$	−1.51895	−0.118250
$166$	−21.6691	−1.68185
$167$	−20.9452	−1.62079	−0.810393	−	0.585887i	$-0.800746\pi$
$167$	−20.9452	−1.62079	−0.810393	+	0.585887i	$0.800746\pi$
$168$	−20.2502	−1.56233
$169$	−12.2264	−0.940493
$170$	−1.02618	−0.0787045
$171$	0.781148	0.0597358
$172$	22.1112	1.68596
$173$	−13.6840	−1.04038	−0.520190	−	0.854051i	$-0.674139\pi$
$173$	−13.6840	−1.04038	−0.520190	+	0.854051i	$0.674139\pi$
$174$	9.61208	0.728690
$175$	−13.1160	−0.991478
$176$	−38.2941	−2.88652
$177$	5.18257	0.389546
$178$	−4.18320	−0.313544
$179$	−14.9452	−1.11706	−0.558528	−	0.829486i	$-0.688634\pi$
$179$	−14.9452	−1.11706	−0.558528	+	0.829486i	$0.688634\pi$
$180$	1.90348	0.141877
$181$	−0.490896	−0.0364880	−0.0182440	−	0.999834i	$-0.505808\pi$
$181$	−0.490896	−0.0364880	−0.0182440	+	0.999834i	$0.505808\pi$
$182$	6.23327	0.462041
$183$	9.15247	0.676570
$184$	53.5654	3.94889
$185$	−0.904991	−0.0665363
$186$	−25.3645	−1.85982
$187$	−3.87613	−0.283451
$188$	−17.6760	−1.28916
$189$	2.70632	0.196856
$190$	−0.801599	−0.0581541
$191$	−25.6590	−1.85662	−0.928309	−	0.371810i	$-0.878737\pi$
$191$	−25.6590	−1.85662	−0.928309	+	0.371810i	$0.878737\pi$
$192$	8.79991	0.635079
$193$	−22.2380	−1.60073	−0.800363	−	0.599516i	$-0.795360\pi$
$193$	−22.2380	−1.60073	−0.800363	+	0.599516i	$0.795360\pi$
$194$	−25.1721	−1.80725
$195$	−0.344668	−0.0246822
$196$	1.57471	0.112479
$197$	−12.8093	−0.912624	−0.456312	−	0.889820i	$-0.650830\pi$
$197$	−12.8093	−0.912624	−0.456312	+	0.889820i	$0.650830\pi$
$198$	10.1503	0.721349
$199$	11.2524	0.797662	0.398831	−	0.917024i	$-0.369416\pi$
$199$	11.2524	0.797662	0.398831	+	0.917024i	$0.369416\pi$
$200$	36.2636	2.56423
$201$	−12.5875	−0.887855
$202$	−18.5221	−1.30321
$203$	−9.93385	−0.697220
$204$	4.85739	0.340085
$205$	−1.59066	−0.111097
$206$	28.4839	1.98457
$207$	−7.15872	−0.497565
$208$	−8.68941	−0.602502
$209$	−3.02783	−0.209439
$210$	−2.77718	−0.191643
$211$	1.49139	0.102672	0.0513358	−	0.998681i	$-0.483652\pi$
$211$	1.49139	0.102672	0.0513358	+	0.998681i	$0.483652\pi$
$212$	23.1108	1.58725
$213$	6.72352	0.460688
$214$	23.0760	1.57744
$215$	1.78383	0.121656
$216$	−7.48254	−0.509122
$217$	26.2136	1.77950
$218$	39.0696	2.64612
$219$	−3.80747	−0.257285
$220$	−7.37812	−0.497433
$221$	−0.879543	−0.0591645
$222$	6.04755	0.405885
$223$	0.324302	0.0217169	0.0108584	−	0.999941i	$-0.496544\pi$
$223$	0.324302	0.0217169	0.0108584	+	0.999941i	$0.496544\pi$
$224$	−29.5149	−1.97204
$225$	−4.84644	−0.323096
$226$	−49.7834	−3.31154
$227$	−11.1736	−0.741620	−0.370810	−	0.928709i	$-0.620920\pi$
$227$	−11.1736	−0.741620	−0.370810	+	0.928709i	$0.620920\pi$
$228$	3.79434	0.251286
$229$	5.24503	0.346601	0.173301	−	0.984869i	$-0.444557\pi$
$229$	5.24503	0.346601	0.173301	+	0.984869i	$0.444557\pi$
$230$	7.34614	0.484390
$231$	−10.4901	−0.690195
$232$	27.4655	1.80320
$233$	−7.60970	−0.498528	−0.249264	−	0.968436i	$-0.580189\pi$
$233$	−7.60970	−0.498528	−0.249264	+	0.968436i	$0.580189\pi$
$234$	2.30323	0.150567
$235$	−1.42602	−0.0930235
$236$	25.1738	1.63867
$237$	−0.140935	−0.00915468
$238$	−7.08695	−0.459379
$239$	−3.44532	−0.222859	−0.111430	−	0.993772i	$-0.535543\pi$
$239$	−3.44532	−0.222859	−0.111430	+	0.993772i	$0.535543\pi$
$240$	3.87149	0.249903
$241$	−2.98641	−0.192372	−0.0961858	−	0.995363i	$-0.530664\pi$
$241$	−2.98641	−0.192372	−0.0961858	+	0.995363i	$0.530664\pi$
$242$	−10.5385	−0.677441
$243$	1.00000	0.0641500
$244$	44.4571	2.84607
$245$	0.127040	0.00811630
$246$	10.6295	0.677713
$247$	−0.687053	−0.0437161
$248$	−72.4763	−4.60225
$249$	8.27486	0.524398
$250$	10.1042	0.639047
$251$	12.8036	0.808153	0.404077	−	0.914725i	$-0.367593\pi$
$251$	12.8036	0.808153	0.404077	+	0.914725i	$0.367593\pi$
$252$	13.1457	0.828099
$253$	27.7481	1.74451
$254$	−38.2760	−2.40165
$255$	0.391872	0.0245400
$256$	−14.3731	−0.898316
$257$	−1.48289	−0.0925001	−0.0462500	−	0.998930i	$-0.514727\pi$
$257$	−1.48289	−0.0925001	−0.0462500	+	0.998930i	$0.514727\pi$
$258$	−11.9203	−0.742128
$259$	−6.24999	−0.388356
$260$	−1.67419	−0.103829
$261$	−3.67061	−0.227205
$262$	10.2063	0.630546
$263$	−8.72599	−0.538067	−0.269034	−	0.963131i	$-0.586704\pi$
$263$	−8.72599	−0.538067	−0.269034	+	0.963131i	$0.586704\pi$
$264$	29.0033	1.78503
$265$	1.86447	0.114534
$266$	−5.53595	−0.339431
$267$	1.59746	0.0977627
$268$	−61.1425	−3.73487
$269$	−12.1715	−0.742110	−0.371055	−	0.928611i	$-0.621004\pi$
$269$	−12.1715	−0.742110	−0.371055	+	0.928611i	$0.621004\pi$
$270$	−1.02618	−0.0624514
$271$	−16.7651	−1.01841	−0.509203	−	0.860647i	$-0.670060\pi$
$271$	−16.7651	−1.01841	−0.509203	+	0.860647i	$0.670060\pi$
$272$	9.87946	0.599030
$273$	−2.38033	−0.144064
$274$	22.8848	1.38252
$275$	18.7854	1.13280
$276$	−34.7727	−2.09307
$277$	4.07354	0.244756	0.122378	−	0.992484i	$-0.460948\pi$
$277$	4.07354	0.244756	0.122378	+	0.992484i	$0.460948\pi$
$278$	13.0736	0.784104
$279$	9.68606	0.579889
$280$	−7.93548	−0.474236
$281$	−0.849166	−0.0506570	−0.0253285	−	0.999679i	$-0.508063\pi$
$281$	−0.849166	−0.0506570	−0.0253285	+	0.999679i	$0.508063\pi$
$282$	9.52931	0.567462
$283$	−6.02602	−0.358210	−0.179105	−	0.983830i	$-0.557320\pi$
$283$	−6.02602	−0.358210	−0.179105	+	0.983830i	$0.557320\pi$
$284$	32.6587	1.93794
$285$	0.306110	0.0181324
$286$	−8.92760	−0.527900
$287$	−10.9853	−0.648445
$288$	−10.9059	−0.642636
$289$	1.00000	0.0588235
$290$	3.76671	0.221189
$291$	9.61258	0.563500
$292$	−18.4944	−1.08230
$293$	−11.8952	−0.694926	−0.347463	−	0.937694i	$-0.612957\pi$
$293$	−11.8952	−0.694926	−0.347463	+	0.937694i	$0.612957\pi$
$294$	−0.848938	−0.0495111
$295$	2.03090	0.118244
$296$	17.2802	1.00439
$297$	−3.87613	−0.224916
$298$	−4.16807	−0.241450
$299$	6.29640	0.364130
$300$	−23.5410	−1.35914
$301$	12.3194	0.710078
$302$	34.8566	2.00577
$303$	7.07312	0.406340
$304$	7.71732	0.442618
$305$	3.58660	0.205368
$306$	−2.61866	−0.149699
$307$	−19.0694	−1.08835	−0.544173	−	0.838973i	$-0.683157\pi$
$307$	−19.0694	−1.08835	−0.544173	+	0.838973i	$0.683157\pi$
$308$	−50.9543	−2.90339
$309$	−10.8773	−0.618786
$310$	−9.93965	−0.564534
$311$	−21.9044	−1.24209	−0.621043	−	0.783776i	$-0.713291\pi$
$311$	−21.9044	−1.24209	−0.621043	+	0.783776i	$0.713291\pi$
$312$	6.58121	0.372588
$313$	−5.48313	−0.309925	−0.154962	−	0.987920i	$-0.549526\pi$
$313$	−5.48313	−0.309925	−0.154962	+	0.987920i	$0.549526\pi$
$314$	2.61866	0.147780
$315$	1.06053	0.0597543
$316$	−0.684574	−0.0385103
$317$	12.1960	0.684995	0.342497	−	0.939519i	$-0.388727\pi$
$317$	12.1960	0.684995	0.342497	+	0.939519i	$0.388727\pi$
$318$	−12.4592	−0.698678
$319$	14.2277	0.796601
$320$	3.44844	0.192774
$321$	−8.81213	−0.491845
$322$	50.7334	2.82726
$323$	0.781148	0.0434642
$324$	4.85739	0.269855
$325$	4.26265	0.236449
$326$	2.65008	0.146774
$327$	−14.9197	−0.825059
$328$	30.3727	1.67705
$329$	−9.84831	−0.542955
$330$	3.97761	0.218960
$331$	17.3938	0.956050	0.478025	−	0.878346i	$-0.341353\pi$
$331$	17.3938	0.956050	0.478025	+	0.878346i	$0.341353\pi$
$332$	40.1942	2.20595
$333$	−2.30940	−0.126555
$334$	54.8483	3.00116
$335$	−4.93270	−0.269502
$336$	26.7370	1.45862
$337$	9.64782	0.525550	0.262775	−	0.964857i	$-0.415362\pi$
$337$	9.64782	0.525550	0.262775	+	0.964857i	$0.415362\pi$
$338$	32.0168	1.74149
$339$	19.0110	1.03254
$340$	1.90348	0.103231
$341$	−37.5444	−2.03314
$342$	−2.04556	−0.110611
$343$	−18.0669	−0.975521
$344$	−34.0611	−1.83645
$345$	−2.80530	−0.151032
$346$	35.8339	1.92644
$347$	−7.31764	−0.392831	−0.196416	−	0.980521i	$-0.562930\pi$
$347$	−7.31764	−0.392831	−0.196416	+	0.980521i	$0.562930\pi$
$348$	−17.8296	−0.955765
$349$	−5.95954	−0.319007	−0.159503	−	0.987197i	$-0.550989\pi$
$349$	−5.95954	−0.319007	−0.159503	+	0.987197i	$0.550989\pi$
$350$	34.3464	1.83589
$351$	−0.879543	−0.0469465
$352$	42.2726	2.25314
$353$	29.7332	1.58254	0.791269	−	0.611468i	$-0.209421\pi$
$353$	29.7332	1.58254	0.791269	+	0.611468i	$0.209421\pi$
$354$	−13.5714	−0.721311
$355$	2.63476	0.139838
$356$	7.75947	0.411251
$357$	2.70632	0.143234
$358$	39.1364	2.06842
$359$	7.85640	0.414645	0.207322	−	0.978273i	$-0.433525\pi$
$359$	7.85640	0.414645	0.207322	+	0.978273i	$0.433525\pi$
$360$	−2.93220	−0.154540
$361$	−18.3898	−0.967885
$362$	1.28549	0.0675638
$363$	4.02439	0.211226
$364$	−11.5622	−0.606023
$365$	−1.49204	−0.0780970
$366$	−23.9672	−1.25279
$367$	−27.3721	−1.42881	−0.714405	−	0.699732i	$-0.753303\pi$
$367$	−27.3721	−1.42881	−0.714405	+	0.699732i	$0.753303\pi$
$368$	−70.7243	−3.68676
$369$	−4.05914	−0.211310
$370$	2.36987	0.123203
$371$	12.8763	0.668504
$372$	47.0490	2.43938
$373$	2.49846	0.129365	0.0646826	−	0.997906i	$-0.479397\pi$
$373$	2.49846	0.129365	0.0646826	+	0.997906i	$0.479397\pi$
$374$	10.1503	0.524858
$375$	−3.85854	−0.199254
$376$	27.2290	1.40423
$377$	3.22846	0.166274
$378$	−7.08695	−0.364513
$379$	−34.4068	−1.76736	−0.883680	−	0.468091i	$-0.844942\pi$
$379$	−34.4068	−1.76736	−0.883680	+	0.468091i	$0.844942\pi$
$380$	1.48690	0.0762762
$381$	14.6166	0.748832
$382$	67.1922	3.43785
$383$	−22.3851	−1.14383	−0.571913	−	0.820314i	$-0.693799\pi$
$383$	−22.3851	−1.14383	−0.571913	+	0.820314i	$0.693799\pi$
$384$	−1.23222	−0.0628816
$385$	−4.11076	−0.209504
$386$	58.2338	2.96402
$387$	4.55208	0.231395
$388$	46.6921	2.37043
$389$	−17.3773	−0.881063	−0.440532	−	0.897737i	$-0.645210\pi$
$389$	−17.3773	−0.881063	−0.440532	+	0.897737i	$0.645210\pi$
$390$	0.902570	0.0457034
$391$	−7.15872	−0.362032
$392$	−2.42575	−0.122519
$393$	−3.89751	−0.196604
$394$	33.5432	1.68988
$395$	−0.0552283	−0.00277884
$396$	−18.8279	−0.946136
$397$	34.3145	1.72219	0.861096	−	0.508442i	$-0.169778\pi$
$397$	34.3145	1.72219	0.861096	+	0.508442i	$0.169778\pi$
$398$	−29.4663	−1.47701
$399$	2.11404	0.105834
$400$	−47.8802	−2.39401
$401$	−6.87177	−0.343160	−0.171580	−	0.985170i	$-0.554887\pi$
$401$	−6.87177	−0.343160	−0.171580	+	0.985170i	$0.554887\pi$
$402$	32.9624	1.64402
$403$	−8.51930	−0.424377
$404$	34.3569	1.70932
$405$	0.391872	0.0194723
$406$	26.0134	1.29102
$407$	8.95155	0.443712
$408$	−7.48254	−0.370441
$409$	5.39190	0.266612	0.133306	−	0.991075i	$-0.457441\pi$
$409$	5.39190	0.266612	0.133306	+	0.991075i	$0.457441\pi$
$410$	4.16541	0.205715
$411$	−8.73913	−0.431069
$412$	−52.8351	−2.60300
$413$	14.0257	0.690160
$414$	18.7463	0.921328
$415$	3.24269	0.159177
$416$	9.59220	0.470296
$417$	−4.99249	−0.244483
$418$	7.92886	0.387813
$419$	6.20516	0.303142	0.151571	−	0.988446i	$-0.451567\pi$
$419$	6.20516	0.303142	0.151571	+	0.988446i	$0.451567\pi$
$420$	5.15142	0.251364
$421$	−27.6830	−1.34919	−0.674594	−	0.738189i	$-0.735681\pi$
$421$	−27.6830	−1.34919	−0.674594	+	0.738189i	$0.735681\pi$
$422$	−3.90545	−0.190114
$423$	−3.63900	−0.176934
$424$	−35.6009	−1.72893
$425$	−4.84644	−0.235087
$426$	−17.6066	−0.853043
$427$	24.7695	1.19868
$428$	−42.8040	−2.06901
$429$	3.40922	0.164599
$430$	−4.67125	−0.225268
$431$	25.2433	1.21593	0.607963	−	0.793966i	$-0.291987\pi$
$431$	25.2433	1.21593	0.607963	+	0.793966i	$0.291987\pi$
$432$	9.87946	0.475326
$433$	−33.2993	−1.60026	−0.800130	−	0.599827i	$-0.795236\pi$
$433$	−33.2993	−1.60026	−0.800130	+	0.599827i	$0.795236\pi$
$434$	−68.6446	−3.29504
$435$	−1.43841	−0.0689664
$436$	−72.4706	−3.47071
$437$	−5.59201	−0.267502
$438$	9.97048	0.476408
$439$	17.8394	0.851426	0.425713	−	0.904858i	$-0.360023\pi$
$439$	17.8394	0.851426	0.425713	+	0.904858i	$0.360023\pi$
$440$	11.3656	0.541833
$441$	0.324188	0.0154375
$442$	2.30323	0.109553
$443$	16.8449	0.800325	0.400162	−	0.916444i	$-0.368954\pi$
$443$	16.8449	0.800325	0.400162	+	0.916444i	$0.368954\pi$
$444$	−11.2177	−0.532367
$445$	0.625999	0.0296752
$446$	−0.849237	−0.0402126
$447$	1.59168	0.0752839
$448$	23.8154	1.12517
$449$	1.62318	0.0766026	0.0383013	−	0.999266i	$-0.487805\pi$
$449$	1.62318	0.0766026	0.0383013	+	0.999266i	$0.487805\pi$
$450$	12.6912	0.598268
$451$	15.7338	0.740874
$452$	92.3439	4.34349
$453$	−13.3108	−0.625397
$454$	29.2600	1.37324
$455$	−0.932784	−0.0437296
$456$	−5.84497	−0.273716
$457$	35.7604	1.67280	0.836400	−	0.548120i	$-0.184656\pi$
$457$	35.7604	1.67280	0.836400	+	0.548120i	$0.184656\pi$
$458$	−13.7350	−0.641792
$459$	1.00000	0.0466760
$460$	−13.6264	−0.635336
$461$	30.2999	1.41121	0.705603	−	0.708608i	$-0.250676\pi$
$461$	30.2999	1.41121	0.705603	+	0.708608i	$0.250676\pi$
$462$	27.4699	1.27802
$463$	22.2230	1.03279	0.516395	−	0.856350i	$-0.327274\pi$
$463$	22.2230	1.03279	0.516395	+	0.856350i	$0.327274\pi$
$464$	−36.2636	−1.68350
$465$	3.79570	0.176021
$466$	19.9272	0.923111
$467$	−24.1414	−1.11713	−0.558566	−	0.829460i	$-0.688648\pi$
$467$	−24.1414	−1.11713	−0.558566	+	0.829460i	$0.688648\pi$
$468$	−4.27228	−0.197486
$469$	−34.0659	−1.57302
$470$	3.73427	0.172249
$471$	−1.00000	−0.0460776
$472$	−38.7788	−1.78494
$473$	−17.6444	−0.811292
$474$	0.369060	0.0169515
$475$	−3.78578	−0.173704
$476$	13.1457	0.602531
$477$	4.75786	0.217847
$478$	9.02213	0.412663
$479$	22.1696	1.01296	0.506478	−	0.862253i	$-0.330947\pi$
$479$	22.1696	1.01296	0.506478	+	0.862253i	$0.330947\pi$
$480$	−4.27371	−0.195067
$481$	2.03122	0.0926156
$482$	7.82040	0.356209
$483$	−19.3738	−0.881539
$484$	19.5480	0.888546
$485$	3.76691	0.171046
$486$	−2.61866	−0.118785
$487$	−34.9745	−1.58485	−0.792423	−	0.609972i	$-0.791181\pi$
$487$	−34.9745	−1.58485	−0.792423	+	0.609972i	$0.791181\pi$
$488$	−68.4837	−3.10011
$489$	−1.01200	−0.0457640
$490$	−0.332675	−0.0150287
$491$	3.44709	0.155565	0.0777826	−	0.996970i	$-0.475216\pi$
$491$	3.44709	0.155565	0.0777826	+	0.996970i	$0.475216\pi$
$492$	−19.7168	−0.888904
$493$	−3.67061	−0.165316
$494$	1.79916	0.0809480
$495$	−1.51895	−0.0682716
$496$	95.6930	4.29674
$497$	18.1960	0.816202
$498$	−21.6691	−0.971014
$499$	34.6388	1.55065	0.775323	−	0.631565i	$-0.217587\pi$
$499$	34.6388	1.55065	0.775323	+	0.631565i	$0.217587\pi$
$500$	−18.7425	−0.838188
$501$	−20.9452	−0.935761
$502$	−33.5282	−1.49644
$503$	2.15558	0.0961126	0.0480563	−	0.998845i	$-0.484697\pi$
$503$	2.15558	0.0961126	0.0480563	+	0.998845i	$0.484697\pi$
$504$	−20.2502	−0.902014
$505$	2.77176	0.123342
$506$	−72.6630	−3.23026
$507$	−12.2264	−0.542994
$508$	70.9986	3.15005
$509$	−21.8008	−0.966303	−0.483151	−	0.875537i	$-0.660508\pi$
$509$	−21.8008	−0.966303	−0.483151	+	0.875537i	$0.660508\pi$
$510$	−1.02618	−0.0454401
$511$	−10.3042	−0.455833
$512$	40.1026	1.77230
$513$	0.781148	0.0344885
$514$	3.88319	0.171280
$515$	−4.26250	−0.187828
$516$	22.1112	0.973392
$517$	14.1052	0.620348
$518$	16.3666	0.719108
$519$	−13.6840	−0.600663
$520$	2.57900	0.113096
$521$	0.227868	0.00998307	0.00499154	−	0.999988i	$-0.498411\pi$
$521$	0.227868	0.00998307	0.00499154	+	0.999988i	$0.498411\pi$
$522$	9.61208	0.420709
$523$	5.00478	0.218844	0.109422	−	0.993995i	$-0.465100\pi$
$523$	5.00478	0.218844	0.109422	+	0.993995i	$0.465100\pi$
$524$	−18.9318	−0.827037
$525$	−13.1160	−0.572430
$526$	22.8504	0.996325
$527$	9.68606	0.421931
$528$	−38.2941	−1.66654
$529$	28.2472	1.22814
$530$	−4.88242	−0.212079
$531$	5.18257	0.224904
$532$	10.2687	0.445205
$533$	3.57019	0.154642
$534$	−4.18320	−0.181025
$535$	−3.45323	−0.149296
$536$	94.1866	4.06824
$537$	−14.9452	−0.644932
$538$	31.8731	1.37415
$539$	−1.25659	−0.0541253
$540$	1.90348	0.0819126
$541$	−4.01452	−0.172598	−0.0862990	−	0.996269i	$-0.527504\pi$
$541$	−4.01452	−0.172598	−0.0862990	+	0.996269i	$0.527504\pi$
$542$	43.9020	1.88575
$543$	−0.490896	−0.0210663
$544$	−10.9059	−0.467586
$545$	−5.84660	−0.250441
$546$	6.23327	0.266759
$547$	−32.4958	−1.38942	−0.694710	−	0.719290i	$-0.744467\pi$
$547$	−32.4958	−1.38942	−0.694710	+	0.719290i	$0.744467\pi$
$548$	−42.4494	−1.81335
$549$	9.15247	0.390618
$550$	−49.1927	−2.09758
$551$	−2.86729	−0.122150
$552$	53.5654	2.27989
$553$	−0.381414	−0.0162194
$554$	−10.6672	−0.453207
$555$	−0.904991	−0.0384147
$556$	−24.2505	−1.02845
$557$	−8.92857	−0.378316	−0.189158	−	0.981947i	$-0.560576\pi$
$557$	−8.92857	−0.378316	−0.189158	+	0.981947i	$0.560576\pi$
$558$	−25.3645	−1.07377
$559$	−4.00375	−0.169340
$560$	10.4775	0.442755
$561$	−3.87613	−0.163650
$562$	2.22368	0.0938002
$563$	11.0524	0.465802	0.232901	−	0.972500i	$-0.425178\pi$
$563$	11.0524	0.465802	0.232901	+	0.972500i	$0.425178\pi$
$564$	−17.6760	−0.744296
$565$	7.44988	0.313419
$566$	15.7801	0.663288
$567$	2.70632	0.113655
$568$	−50.3090	−2.11092
$569$	16.0183	0.671521	0.335760	−	0.941947i	$-0.391007\pi$
$569$	16.0183	0.671521	0.335760	+	0.941947i	$0.391007\pi$
$570$	−0.801599	−0.0335753
$571$	14.8700	0.622290	0.311145	−	0.950363i	$-0.399288\pi$
$571$	14.8700	0.622290	0.311145	+	0.950363i	$0.399288\pi$
$572$	16.5599	0.692405
$573$	−25.6590	−1.07192
$574$	28.7669	1.20071
$575$	34.6943	1.44685
$576$	8.79991	0.366663
$577$	−39.3660	−1.63883	−0.819415	−	0.573201i	$-0.805701\pi$
$577$	−39.3660	−1.63883	−0.819415	+	0.573201i	$0.805701\pi$
$578$	−2.61866	−0.108922
$579$	−22.2380	−0.924179
$580$	−6.98691	−0.290116
$581$	22.3945	0.929078
$582$	−25.1721	−1.04342
$583$	−18.4421	−0.763793
$584$	28.4895	1.17891
$585$	−0.344668	−0.0142503
$586$	31.1496	1.28678
$587$	23.1584	0.955851	0.477925	−	0.878400i	$-0.341389\pi$
$587$	23.1584	0.955851	0.477925	+	0.878400i	$0.341389\pi$
$588$	1.57471	0.0649398
$589$	7.56624	0.311762
$590$	−5.31825	−0.218949
$591$	−12.8093	−0.526904
$592$	−22.8157	−0.937718
$593$	33.4582	1.37397	0.686983	−	0.726674i	$-0.258935\pi$
$593$	33.4582	1.37397	0.686983	+	0.726674i	$0.258935\pi$
$594$	10.1503	0.416471
$595$	1.06053	0.0434776
$596$	7.73141	0.316691
$597$	11.2524	0.460531
$598$	−16.4881	−0.674250
$599$	29.3151	1.19778	0.598892	−	0.800830i	$-0.295608\pi$
$599$	29.3151	1.19778	0.598892	+	0.800830i	$0.295608\pi$
$600$	36.2636	1.48046
$601$	23.2241	0.947329	0.473665	−	0.880705i	$-0.342931\pi$
$601$	23.2241	0.947329	0.473665	+	0.880705i	$0.342931\pi$
$602$	−32.2603	−1.31483
$603$	−12.5875	−0.512603
$604$	−64.6559	−2.63081
$605$	1.57705	0.0641160
$606$	−18.5221	−0.752409
$607$	30.2991	1.22980	0.614901	−	0.788604i	$-0.289196\pi$
$607$	30.2991	1.22980	0.614901	+	0.788604i	$0.289196\pi$
$608$	−8.51911	−0.345495
$609$	−9.93385	−0.402540
$610$	−9.39209	−0.380274
$611$	3.20066	0.129485
$612$	4.85739	0.196348
$613$	29.3090	1.18378	0.591890	−	0.806019i	$-0.298382\pi$
$613$	29.3090	1.18378	0.591890	+	0.806019i	$0.298382\pi$
$614$	49.9362	2.01526
$615$	−1.59066	−0.0641418
$616$	78.4923	3.16255
$617$	−30.9162	−1.24464	−0.622319	−	0.782764i	$-0.713809\pi$
$617$	−30.9162	−1.24464	−0.622319	+	0.782764i	$0.713809\pi$
$618$	28.4839	1.14579
$619$	−45.1207	−1.81356	−0.906778	−	0.421609i	$-0.861465\pi$
$619$	−45.1207	−1.81356	−0.906778	+	0.421609i	$0.861465\pi$
$620$	18.4372	0.740455
$621$	−7.15872	−0.287269
$622$	57.3603	2.29994
$623$	4.32323	0.173207
$624$	−8.68941	−0.347855
$625$	22.7201	0.908805
$626$	14.3585	0.573880
$627$	−3.02783	−0.120920
$628$	−4.85739	−0.193831
$629$	−2.30940	−0.0920819
$630$	−2.77718	−0.110645
$631$	9.13970	0.363846	0.181923	−	0.983313i	$-0.441768\pi$
$631$	9.13970	0.363846	0.181923	+	0.983313i	$0.441768\pi$
$632$	1.05455	0.0419477
$633$	1.49139	0.0592775
$634$	−31.9372	−1.26839
$635$	5.72785	0.227303
$636$	23.1108	0.916402
$637$	−0.285137	−0.0112975
$638$	−37.2577	−1.47505
$639$	6.72352	0.265978
$640$	−0.482874	−0.0190873
$641$	−0.537652	−0.0212360	−0.0106180	−	0.999944i	$-0.503380\pi$
$641$	−0.537652	−0.0212360	−0.0106180	+	0.999944i	$0.503380\pi$
$642$	23.0760	0.910737
$643$	26.7386	1.05447	0.527233	−	0.849721i	$-0.323229\pi$
$643$	26.7386	1.05447	0.527233	+	0.849721i	$0.323229\pi$
$644$	−94.1061	−3.70830
$645$	1.78383	0.0702383
$646$	−2.04556	−0.0804815
$647$	3.58904	0.141100	0.0705499	−	0.997508i	$-0.477525\pi$
$647$	3.58904	0.141100	0.0705499	+	0.997508i	$0.477525\pi$
$648$	−7.48254	−0.293942
$649$	−20.0883	−0.788535
$650$	−11.1624	−0.437827
$651$	26.2136	1.02739
$652$	−4.91566	−0.192512
$653$	−24.9026	−0.974512	−0.487256	−	0.873259i	$-0.662002\pi$
$653$	−24.9026	−0.974512	−0.487256	+	0.873259i	$0.662002\pi$
$654$	39.0696	1.52774
$655$	−1.52733	−0.0596776
$656$	−40.1021	−1.56572
$657$	−3.80747	−0.148544
$658$	25.7894	1.00538
$659$	18.1702	0.707809	0.353904	−	0.935282i	$-0.384854\pi$
$659$	18.1702	0.707809	0.353904	+	0.935282i	$0.384854\pi$
$660$	−7.37812	−0.287193
$661$	−10.7806	−0.419316	−0.209658	−	0.977775i	$-0.567235\pi$
$661$	−10.7806	−0.419316	−0.209658	+	0.977775i	$0.567235\pi$
$662$	−45.5485	−1.77029
$663$	−0.879543	−0.0341586
$664$	−61.9170	−2.40284
$665$	0.828433	0.0321252
$666$	6.04755	0.234338
$667$	26.2768	1.01744
$668$	−101.739	−3.93639
$669$	0.324302	0.0125382
$670$	12.9171	0.499030
$671$	−35.4762	−1.36954
$672$	−29.5149	−1.13856
$673$	−15.7832	−0.608396	−0.304198	−	0.952609i	$-0.598389\pi$
$673$	−15.7832	−0.608396	−0.304198	+	0.952609i	$0.598389\pi$
$674$	−25.2644	−0.973147
$675$	−4.84644	−0.186539
$676$	−59.3884	−2.28417
$677$	11.6629	0.448241	0.224121	−	0.974561i	$-0.428049\pi$
$677$	11.6629	0.448241	0.224121	+	0.974561i	$0.428049\pi$
$678$	−49.7834	−1.91192
$679$	26.0148	0.998355
$680$	−2.93220	−0.112445
$681$	−11.1736	−0.428174
$682$	98.3161	3.76472
$683$	19.7026	0.753900	0.376950	−	0.926234i	$-0.376973\pi$
$683$	19.7026	0.753900	0.376950	+	0.926234i	$0.376973\pi$
$684$	3.79434	0.145080
$685$	−3.42462	−0.130848
$686$	47.3111	1.80635
$687$	5.24503	0.200110
$688$	44.9721	1.71454
$689$	−4.18474	−0.159426
$690$	7.34614	0.279663
$691$	42.4946	1.61657	0.808286	−	0.588790i	$-0.200396\pi$
$691$	42.4946	1.61657	0.808286	+	0.588790i	$0.200396\pi$
$692$	−66.4688	−2.52676
$693$	−10.4901	−0.398485
$694$	19.1624	0.727395
$695$	−1.95642	−0.0742111
$696$	27.4655	1.04108
$697$	−4.05914	−0.153751
$698$	15.6060	0.590697
$699$	−7.60970	−0.287825
$700$	−63.7097	−2.40800
$701$	−39.0106	−1.47341	−0.736705	−	0.676215i	$-0.763619\pi$
$701$	−39.0106	−1.47341	−0.736705	+	0.676215i	$0.763619\pi$
$702$	2.30323	0.0869296
$703$	−1.80398	−0.0680386
$704$	−34.1096	−1.28555
$705$	−1.42602	−0.0537071
$706$	−77.8612	−2.93035
$707$	19.1422	0.719915
$708$	25.1738	0.946088
$709$	8.06959	0.303060	0.151530	−	0.988453i	$-0.451580\pi$
$709$	8.06959	0.303060	0.151530	+	0.988453i	$0.451580\pi$
$710$	−6.89954	−0.258935
$711$	−0.140935	−0.00528546
$712$	−11.9530	−0.447959
$713$	−69.3397	−2.59679
$714$	−7.08695	−0.265222
$715$	1.33598	0.0499628
$716$	−72.5946	−2.71299
$717$	−3.44532	−0.128668
$718$	−20.5733	−0.767787
$719$	4.95029	0.184615	0.0923074	−	0.995731i	$-0.470576\pi$
$719$	4.95029	0.184615	0.0923074	+	0.995731i	$0.470576\pi$
$720$	3.87149	0.144282
$721$	−29.4374	−1.09631
$722$	48.1567	1.79221
$723$	−2.98641	−0.111066
$724$	−2.38447	−0.0886182
$725$	17.7894	0.660680
$726$	−10.5385	−0.391121
$727$	26.1208	0.968767	0.484384	−	0.874856i	$-0.339044\pi$
$727$	26.1208	0.968767	0.484384	+	0.874856i	$0.339044\pi$
$728$	17.8109	0.660116
$729$	1.00000	0.0370370
$730$	3.90715	0.144610
$731$	4.55208	0.168365
$732$	44.4571	1.64318
$733$	24.9227	0.920540	0.460270	−	0.887779i	$-0.347753\pi$
$733$	24.9227	0.920540	0.460270	+	0.887779i	$0.347753\pi$
$734$	71.6782	2.64569
$735$	0.127040	0.00468595
$736$	78.0722	2.87778
$737$	48.7908	1.79723
$738$	10.6295	0.391278
$739$	−46.4394	−1.70830	−0.854150	−	0.520027i	$-0.825922\pi$
$739$	−46.4394	−1.70830	−0.854150	+	0.520027i	$0.825922\pi$
$740$	−4.39589	−0.161596
$741$	−0.687053	−0.0252395
$742$	−33.7187	−1.23785
$743$	10.1029	0.370640	0.185320	−	0.982678i	$-0.440668\pi$
$743$	10.1029	0.370640	0.185320	+	0.982678i	$0.440668\pi$
$744$	−72.4763	−2.65711
$745$	0.623735	0.0228519
$746$	−6.54261	−0.239542
$747$	8.27486	0.302761
$748$	−18.8279	−0.688415
$749$	−23.8485	−0.871405
$750$	10.1042	0.368954
$751$	−31.7088	−1.15707	−0.578535	−	0.815658i	$-0.696375\pi$
$751$	−31.7088	−1.15707	−0.578535	+	0.815658i	$0.696375\pi$
$752$	−35.9514	−1.31101
$753$	12.8036	0.466587
$754$	−8.45423	−0.307885
$755$	−5.21615	−0.189835
$756$	13.1457	0.478103
$757$	−19.4954	−0.708571	−0.354286	−	0.935137i	$-0.615276\pi$
$757$	−19.4954	−0.708571	−0.354286	+	0.935137i	$0.615276\pi$
$758$	90.0999	3.27258
$759$	27.7481	1.00719
$760$	−2.29048	−0.0830845
$761$	−25.4616	−0.922984	−0.461492	−	0.887144i	$-0.652686\pi$
$761$	−25.4616	−0.922984	−0.461492	+	0.887144i	$0.652686\pi$
$762$	−38.2760	−1.38659
$763$	−40.3774	−1.46176
$764$	−124.636	−4.50916
$765$	0.391872	0.0141682
$766$	58.6191	2.11799
$767$	−4.55829	−0.164590
$768$	−14.3731	−0.518643
$769$	−40.6906	−1.46734	−0.733671	−	0.679505i	$-0.762195\pi$
$769$	−40.6906	−1.46734	−0.733671	+	0.679505i	$0.762195\pi$
$770$	10.7647	0.387933
$771$	−1.48289	−0.0534049
$772$	−108.019	−3.88767
$773$	−34.2735	−1.23273	−0.616366	−	0.787460i	$-0.711396\pi$
$773$	−34.2735	−1.23273	−0.616366	+	0.787460i	$0.711396\pi$
$774$	−11.9203	−0.428468
$775$	−46.9429	−1.68624
$776$	−71.9265	−2.58201
$777$	−6.24999	−0.224217
$778$	45.5052	1.63144
$779$	−3.17079	−0.113605
$780$	−1.67419	−0.0599456
$781$	−26.0612	−0.932544
$782$	18.7463	0.670365
$783$	−3.67061	−0.131177
$784$	3.20280	0.114386
$785$	−0.391872	−0.0139865
$786$	10.2063	0.364046
$787$	−8.73703	−0.311442	−0.155721	−	0.987801i	$-0.549770\pi$
$787$	−8.73703	−0.311442	−0.155721	+	0.987801i	$0.549770\pi$
$788$	−62.2197	−2.21649
$789$	−8.72599	−0.310653
$790$	0.144624	0.00514550
$791$	51.4499	1.82935
$792$	29.0033	1.03059
$793$	−8.04999	−0.285863
$794$	−89.8579	−3.18894
$795$	1.86447	0.0661260
$796$	54.6574	1.93728
$797$	−32.7692	−1.16075	−0.580373	−	0.814351i	$-0.697093\pi$
$797$	−32.7692	−1.16075	−0.580373	+	0.814351i	$0.697093\pi$
$798$	−5.53595	−0.195971
$799$	−3.63900	−0.128739
$800$	52.8547	1.86870
$801$	1.59746	0.0564433
$802$	17.9948	0.635420
$803$	14.7583	0.520807
$804$	−61.1425	−2.15633
$805$	−7.59206	−0.267585
$806$	22.3092	0.785807
$807$	−12.1715	−0.428458
$808$	−52.9249	−1.86189
$809$	35.5094	1.24844	0.624222	−	0.781247i	$-0.285416\pi$
$809$	35.5094	1.24844	0.624222	+	0.781247i	$0.285416\pi$
$810$	−1.02618	−0.0360563
$811$	34.1015	1.19747	0.598734	−	0.800948i	$-0.295671\pi$
$811$	34.1015	1.19747	0.598734	+	0.800948i	$0.295671\pi$
$812$	−48.2526	−1.69333
$813$	−16.7651	−0.587977
$814$	−23.4411	−0.821609
$815$	−0.396573	−0.0138913
$816$	9.87946	0.345850
$817$	3.55584	0.124403
$818$	−14.1196	−0.493679
$819$	−2.38033	−0.0831754
$820$	−7.72648	−0.269820
$821$	28.8063	1.00535	0.502673	−	0.864477i	$-0.332350\pi$
$821$	28.8063	1.00535	0.502673	+	0.864477i	$0.332350\pi$
$822$	22.8848	0.798200
$823$	−15.6620	−0.545945	−0.272972	−	0.962022i	$-0.588007\pi$
$823$	−15.6620	−0.545945	−0.272972	+	0.962022i	$0.588007\pi$
$824$	81.3896	2.83534
$825$	18.7854	0.654024
$826$	−36.7286	−1.27795
$827$	−47.5715	−1.65422	−0.827112	−	0.562037i	$-0.810018\pi$
$827$	−47.5715	−1.65422	−0.827112	+	0.562037i	$0.810018\pi$
$828$	−34.7727	−1.20843
$829$	29.1738	1.01325	0.506625	−	0.862167i	$-0.330893\pi$
$829$	29.1738	1.01325	0.506625	+	0.862167i	$0.330893\pi$
$830$	−8.49150	−0.294744
$831$	4.07354	0.141310
$832$	−7.73990	−0.268333
$833$	0.324188	0.0112324
$834$	13.0736	0.452703
$835$	−8.20783	−0.284044
$836$	−14.7074	−0.508664
$837$	9.68606	0.334799
$838$	−16.2492	−0.561320
$839$	−2.80487	−0.0968347	−0.0484174	−	0.998827i	$-0.515418\pi$
$839$	−2.80487	−0.0968347	−0.0484174	+	0.998827i	$0.515418\pi$
$840$	−7.93548	−0.273800
$841$	−15.5266	−0.535402
$842$	72.4925	2.49826
$843$	−0.849166	−0.0292468
$844$	7.24427	0.249358
$845$	−4.79119	−0.164822
$846$	9.52931	0.327625
$847$	10.8913	0.374229
$848$	47.0051	1.61416
$849$	−6.02602	−0.206813
$850$	12.6912	0.435304
$851$	16.5324	0.566722
$852$	32.6587	1.11887
$853$	−19.3944	−0.664052	−0.332026	−	0.943270i	$-0.607732\pi$
$853$	−19.3944	−0.664052	−0.332026	+	0.943270i	$0.607732\pi$
$854$	−64.8630	−2.21957
$855$	0.306110	0.0104687
$856$	65.9371	2.25368
$857$	−10.0050	−0.341765	−0.170883	−	0.985291i	$-0.554662\pi$
$857$	−10.0050	−0.341765	−0.170883	+	0.985291i	$0.554662\pi$
$858$	−8.92760	−0.304783
$859$	−22.0484	−0.752282	−0.376141	−	0.926562i	$-0.622749\pi$
$859$	−22.0484	−0.752282	−0.376141	+	0.926562i	$0.622749\pi$
$860$	8.66477	0.295466
$861$	−10.9853	−0.374380
$862$	−66.1036	−2.25150
$863$	−32.7101	−1.11347	−0.556733	−	0.830692i	$-0.687945\pi$
$863$	−32.7101	−1.11347	−0.556733	+	0.830692i	$0.687945\pi$
$864$	−10.9059	−0.371026
$865$	−5.36240	−0.182327
$866$	87.1995	2.96316
$867$	1.00000	0.0339618
$868$	127.330	4.32185
$869$	0.546281	0.0185313
$870$	3.76671	0.127703
$871$	11.0713	0.375135
$872$	111.637	3.78051
$873$	9.61258	0.325337
$874$	14.6436	0.495327
$875$	−10.4425	−0.353020
$876$	−18.4944	−0.624867
$877$	−22.8372	−0.771157	−0.385578	−	0.922675i	$-0.625998\pi$
$877$	−22.8372	−0.771157	−0.385578	+	0.922675i	$0.625998\pi$
$878$	−46.7152	−1.57656
$879$	−11.8952	−0.401216
$880$	−15.0064	−0.505865
$881$	−15.4113	−0.519220	−0.259610	−	0.965714i	$-0.583594\pi$
$881$	−15.4113	−0.519220	−0.259610	+	0.965714i	$0.583594\pi$
$882$	−0.848938	−0.0285852
$883$	−35.4220	−1.19204	−0.596022	−	0.802968i	$-0.703253\pi$
$883$	−35.4220	−1.19204	−0.596022	+	0.802968i	$0.703253\pi$
$884$	−4.27228	−0.143692
$885$	2.03090	0.0682681
$886$	−44.1111	−1.48194
$887$	4.20899	0.141324	0.0706620	−	0.997500i	$-0.477489\pi$
$887$	4.20899	0.141324	0.0706620	+	0.997500i	$0.477489\pi$
$888$	17.2802	0.579886
$889$	39.5573	1.32671
$890$	−1.63928	−0.0549487
$891$	−3.87613	−0.129855
$892$	1.57526	0.0527437
$893$	−2.84260	−0.0951239
$894$	−4.16807	−0.139401
$895$	−5.85660	−0.195765
$896$	−3.33479	−0.111408
$897$	6.29640	0.210231
$898$	−4.25056	−0.141843
$899$	−35.5537	−1.18578
$900$	−23.5410	−0.784701
$901$	4.75786	0.158507
$902$	−41.2014	−1.37186
$903$	12.3194	0.409964
$904$	−142.251	−4.73118
$905$	−0.192368	−0.00639454
$906$	34.8566	1.15803
$907$	−47.2297	−1.56824	−0.784119	−	0.620611i	$-0.786885\pi$
$907$	−47.2297	−1.56824	−0.784119	+	0.620611i	$0.786885\pi$
$908$	−54.2747	−1.80117
$909$	7.07312	0.234601
$910$	2.44265	0.0809730
$911$	41.5468	1.37651	0.688253	−	0.725470i	$-0.258378\pi$
$911$	41.5468	1.37651	0.688253	+	0.725470i	$0.258378\pi$
$912$	7.71732	0.255546
$913$	−32.0744	−1.06151
$914$	−93.6443	−3.09748
$915$	3.58660	0.118569
$916$	25.4771	0.841788
$917$	−10.5479	−0.348324
$918$	−2.61866	−0.0864287
$919$	−6.55323	−0.216171	−0.108086	−	0.994142i	$-0.534472\pi$
$919$	−6.55323	−0.216171	−0.108086	+	0.994142i	$0.534472\pi$
$920$	20.9908	0.692046
$921$	−19.0694	−0.628357
$922$	−79.3451	−2.61309
$923$	−5.91362	−0.194649
$924$	−50.9543	−1.67627
$925$	11.1924	0.368003
$926$	−58.1945	−1.91239
$927$	−10.8773	−0.357256
$928$	40.0312	1.31409
$929$	30.2174	0.991400	0.495700	−	0.868494i	$-0.334911\pi$
$929$	30.2174	0.991400	0.495700	+	0.868494i	$0.334911\pi$
$930$	−9.93965	−0.325934
$931$	0.253238	0.00829955
$932$	−36.9633	−1.21077
$933$	−21.9044	−0.717119
$934$	63.2182	2.06856
$935$	−1.51895	−0.0496749
$936$	6.58121	0.215114
$937$	−13.8857	−0.453627	−0.226814	−	0.973938i	$-0.572831\pi$
$937$	−13.8857	−0.453627	−0.226814	+	0.973938i	$0.572831\pi$
$938$	89.2070	2.91271
$939$	−5.48313	−0.178935
$940$	−6.92675	−0.225926
$941$	−38.2262	−1.24614	−0.623070	−	0.782166i	$-0.714115\pi$
$941$	−38.2262	−1.24614	−0.623070	+	0.782166i	$0.714115\pi$
$942$	2.61866	0.0853206
$943$	29.0582	0.946267
$944$	51.2010	1.66645
$945$	1.06053	0.0344991
$946$	46.2048	1.50225
$947$	24.9608	0.811119	0.405559	−	0.914069i	$-0.367077\pi$
$947$	24.9608	0.811119	0.405559	+	0.914069i	$0.367077\pi$
$948$	−0.684574	−0.0222339
$949$	3.34883	0.108708
$950$	9.91368	0.321642
$951$	12.1960	0.395482
$952$	−20.2502	−0.656312
$953$	−43.7615	−1.41757	−0.708787	−	0.705423i	$-0.750757\pi$
$953$	−43.7615	−1.41757	−0.708787	+	0.705423i	$0.750757\pi$
$954$	−12.4592	−0.403382
$955$	−10.0550	−0.325373
$956$	−16.7353	−0.541257
$957$	14.2277	0.459918
$958$	−58.0548	−1.87566
$959$	−23.6509	−0.763728
$960$	3.44844	0.111298
$961$	62.8197	2.02644
$962$	−5.31908	−0.171494
$963$	−8.81213	−0.283967
$964$	−14.5062	−0.467212
$965$	−8.71445	−0.280528
$966$	50.7334	1.63232
$967$	−16.2154	−0.521453	−0.260726	−	0.965413i	$-0.583962\pi$
$967$	−16.2154	−0.521453	−0.260726	+	0.965413i	$0.583962\pi$
$968$	−30.1126	−0.967857
$969$	0.781148	0.0250941
$970$	−9.86425	−0.316722
$971$	−19.5867	−0.628567	−0.314283	−	0.949329i	$-0.601764\pi$
$971$	−19.5867	−0.628567	−0.314283	+	0.949329i	$0.601764\pi$
$972$	4.85739	0.155801
$973$	−13.5113	−0.433152
$974$	91.5864	2.93462
$975$	4.26265	0.136514
$976$	90.4214	2.89432
$977$	−23.6735	−0.757382	−0.378691	−	0.925523i	$-0.623626\pi$
$977$	−23.6735	−0.757382	−0.378691	+	0.925523i	$0.623626\pi$
$978$	2.65008	0.0847401
$979$	−6.19195	−0.197895
$980$	0.617083	0.0197120
$981$	−14.9197	−0.476348
$982$	−9.02677	−0.288056
$983$	9.13160	0.291253	0.145626	−	0.989340i	$-0.453480\pi$
$983$	9.13160	0.291253	0.145626	+	0.989340i	$0.453480\pi$
$984$	30.3727	0.968246
$985$	−5.01961	−0.159938
$986$	9.61208	0.306111
$987$	−9.84831	−0.313475
$988$	−3.33728	−0.106173
$989$	−32.5870	−1.03621
$990$	3.97761	0.126417
$991$	−22.5440	−0.716132	−0.358066	−	0.933696i	$-0.616564\pi$
$991$	−22.5440	−0.716132	−0.358066	+	0.933696i	$0.616564\pi$
$992$	−105.635	−3.35392
$993$	17.3938	0.551976
$994$	−47.6492	−1.51134
$995$	4.40951	0.139791
$996$	40.1942	1.27360
$997$	9.32791	0.295418	0.147709	−	0.989031i	$-0.452810\pi$
$997$	9.32791	0.295418	0.147709	+	0.989031i	$0.452810\pi$
$998$	−90.7073	−2.87129
$999$	−2.30940	−0.0730663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.2	✓	40	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61866 q^{2} +1.00000 q^{3} +4.85739 q^{4} +0.391872 q^{5} -2.61866 q^{6} +2.70632 q^{7} -7.48254 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61866 q^{2} +1.00000 q^{3} +4.85739 q^{4} +0.391872 q^{5} -2.61866 q^{6} +2.70632 q^{7} -7.48254 q^{8} +1.00000 q^{9} -1.02618 q^{10} -3.87613 q^{11} +4.85739 q^{12} -0.879543 q^{13} -7.08695 q^{14} +0.391872 q^{15} +9.87946 q^{16} +1.00000 q^{17} -2.61866 q^{18} +0.781148 q^{19} +1.90348 q^{20} +2.70632 q^{21} +10.1503 q^{22} -7.15872 q^{23} -7.48254 q^{24} -4.84644 q^{25} +2.30323 q^{26} +1.00000 q^{27} +13.1457 q^{28} -3.67061 q^{29} -1.02618 q^{30} +9.68606 q^{31} -10.9059 q^{32} -3.87613 q^{33} -2.61866 q^{34} +1.06053 q^{35} +4.85739 q^{36} -2.30940 q^{37} -2.04556 q^{38} -0.879543 q^{39} -2.93220 q^{40} -4.05914 q^{41} -7.08695 q^{42} +4.55208 q^{43} -18.8279 q^{44} +0.391872 q^{45} +18.7463 q^{46} -3.63900 q^{47} +9.87946 q^{48} +0.324188 q^{49} +12.6912 q^{50} +1.00000 q^{51} -4.27228 q^{52} +4.75786 q^{53} -2.61866 q^{54} -1.51895 q^{55} -20.2502 q^{56} +0.781148 q^{57} +9.61208 q^{58} +5.18257 q^{59} +1.90348 q^{60} +9.15247 q^{61} -25.3645 q^{62} +2.70632 q^{63} +8.79991 q^{64} -0.344668 q^{65} +10.1503 q^{66} -12.5875 q^{67} +4.85739 q^{68} -7.15872 q^{69} -2.77718 q^{70} +6.72352 q^{71} -7.48254 q^{72} -3.80747 q^{73} +6.04755 q^{74} -4.84644 q^{75} +3.79434 q^{76} -10.4901 q^{77} +2.30323 q^{78} -0.140935 q^{79} +3.87149 q^{80} +1.00000 q^{81} +10.6295 q^{82} +8.27486 q^{83} +13.1457 q^{84} +0.391872 q^{85} -11.9203 q^{86} -3.67061 q^{87} +29.0033 q^{88} +1.59746 q^{89} -1.02618 q^{90} -2.38033 q^{91} -34.7727 q^{92} +9.68606 q^{93} +9.52931 q^{94} +0.306110 q^{95} -10.9059 q^{96} +9.61258 q^{97} -0.848938 q^{98} -3.87613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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