LMFDB - Embedded newform 8007.2.a.d.1.17

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			1.17
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)

$f(q)$	$=$	$q-0.656002 q^{2} +1.00000 q^{3} -1.56966 q^{4} +0.401662 q^{5} -0.656002 q^{6} -2.40151 q^{7} +2.34170 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.656002 q^{2} +1.00000 q^{3} -1.56966 q^{4} +0.401662 q^{5} -0.656002 q^{6} -2.40151 q^{7} +2.34170 q^{8} +1.00000 q^{9} -0.263491 q^{10} -2.15082 q^{11} -1.56966 q^{12} -2.63035 q^{13} +1.57539 q^{14} +0.401662 q^{15} +1.60316 q^{16} +1.00000 q^{17} -0.656002 q^{18} +8.20108 q^{19} -0.630474 q^{20} -2.40151 q^{21} +1.41094 q^{22} -1.35869 q^{23} +2.34170 q^{24} -4.83867 q^{25} +1.72552 q^{26} +1.00000 q^{27} +3.76956 q^{28} -5.90013 q^{29} -0.263491 q^{30} -1.43735 q^{31} -5.73509 q^{32} -2.15082 q^{33} -0.656002 q^{34} -0.964596 q^{35} -1.56966 q^{36} +10.4942 q^{37} -5.37992 q^{38} -2.63035 q^{39} +0.940575 q^{40} +8.14415 q^{41} +1.57539 q^{42} -4.51775 q^{43} +3.37606 q^{44} +0.401662 q^{45} +0.891306 q^{46} +6.57606 q^{47} +1.60316 q^{48} -1.23276 q^{49} +3.17417 q^{50} +1.00000 q^{51} +4.12876 q^{52} -2.06189 q^{53} -0.656002 q^{54} -0.863904 q^{55} -5.62362 q^{56} +8.20108 q^{57} +3.87049 q^{58} +10.6757 q^{59} -0.630474 q^{60} +6.32162 q^{61} +0.942903 q^{62} -2.40151 q^{63} +0.555904 q^{64} -1.05651 q^{65} +1.41094 q^{66} -8.60559 q^{67} -1.56966 q^{68} -1.35869 q^{69} +0.632776 q^{70} -7.94810 q^{71} +2.34170 q^{72} -12.5294 q^{73} -6.88419 q^{74} -4.83867 q^{75} -12.8729 q^{76} +5.16522 q^{77} +1.72552 q^{78} +5.61323 q^{79} +0.643930 q^{80} +1.00000 q^{81} -5.34258 q^{82} -9.02913 q^{83} +3.76956 q^{84} +0.401662 q^{85} +2.96365 q^{86} -5.90013 q^{87} -5.03659 q^{88} +1.19446 q^{89} -0.263491 q^{90} +6.31681 q^{91} +2.13269 q^{92} -1.43735 q^{93} -4.31391 q^{94} +3.29406 q^{95} -5.73509 q^{96} +2.65756 q^{97} +0.808691 q^{98} -2.15082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.656002	−0.463863	−0.231932	−	0.972732i	$-0.574505\pi$
$2$	−0.656002	−0.463863	−0.231932	+	0.972732i	$0.574505\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.56966	−0.784831
$5$	0.401662	0.179629	0.0898144	−	0.995959i	$-0.471373\pi$
$5$	0.401662	0.179629	0.0898144	+	0.995959i	$0.471373\pi$
$6$	−0.656002	−0.267812
$7$	−2.40151	−0.907685	−0.453842	−	0.891082i	$-0.649947\pi$
$7$	−2.40151	−0.907685	−0.453842	+	0.891082i	$0.649947\pi$
$8$	2.34170	0.827918
$9$	1.00000	0.333333
$10$	−0.263491	−0.0833232
$11$	−2.15082	−0.648497	−0.324249	−	0.945972i	$-0.605111\pi$
$11$	−2.15082	−0.648497	−0.324249	+	0.945972i	$0.605111\pi$
$12$	−1.56966	−0.453122
$13$	−2.63035	−0.729528	−0.364764	−	0.931100i	$-0.618850\pi$
$13$	−2.63035	−0.729528	−0.364764	+	0.931100i	$0.618850\pi$
$14$	1.57539	0.421042
$15$	0.401662	0.103709
$16$	1.60316	0.400790
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.656002	−0.154621
$19$	8.20108	1.88146	0.940728	−	0.339162i	$-0.110143\pi$
$19$	8.20108	1.88146	0.940728	+	0.339162i	$0.110143\pi$
$20$	−0.630474	−0.140978
$21$	−2.40151	−0.524052
$22$	1.41094	0.300814
$23$	−1.35869	−0.283307	−0.141654	−	0.989916i	$-0.545242\pi$
$23$	−1.35869	−0.283307	−0.141654	+	0.989916i	$0.545242\pi$
$24$	2.34170	0.477998
$25$	−4.83867	−0.967733
$26$	1.72552	0.338401
$27$	1.00000	0.192450
$28$	3.76956	0.712379
$29$	−5.90013	−1.09563	−0.547813	−	0.836601i	$-0.684540\pi$
$29$	−5.90013	−1.09563	−0.547813	+	0.836601i	$0.684540\pi$
$30$	−0.263491	−0.0481067
$31$	−1.43735	−0.258155	−0.129078	−	0.991634i	$-0.541202\pi$
$31$	−1.43735	−0.258155	−0.129078	+	0.991634i	$0.541202\pi$
$32$	−5.73509	−1.01383
$33$	−2.15082	−0.374410
$34$	−0.656002	−0.112503
$35$	−0.964596	−0.163046
$36$	−1.56966	−0.261610
$37$	10.4942	1.72523	0.862615	−	0.505860i	$-0.168825\pi$
$37$	10.4942	1.72523	0.862615	+	0.505860i	$0.168825\pi$
$38$	−5.37992	−0.872738
$39$	−2.63035	−0.421193
$40$	0.940575	0.148718
$41$	8.14415	1.27190	0.635951	−	0.771729i	$-0.280608\pi$
$41$	8.14415	1.27190	0.635951	+	0.771729i	$0.280608\pi$
$42$	1.57539	0.243089
$43$	−4.51775	−0.688951	−0.344475	−	0.938795i	$-0.611943\pi$
$43$	−4.51775	−0.688951	−0.344475	+	0.938795i	$0.611943\pi$
$44$	3.37606	0.508961
$45$	0.401662	0.0598763
$46$	0.891306	0.131416
$47$	6.57606	0.959217	0.479609	−	0.877483i	$-0.340779\pi$
$47$	6.57606	0.959217	0.479609	+	0.877483i	$0.340779\pi$
$48$	1.60316	0.231396
$49$	−1.23276	−0.176108
$50$	3.17417	0.448896
$51$	1.00000	0.140028
$52$	4.12876	0.572556
$53$	−2.06189	−0.283223	−0.141611	−	0.989922i	$-0.545228\pi$
$53$	−2.06189	−0.283223	−0.141611	+	0.989922i	$0.545228\pi$
$54$	−0.656002	−0.0892705
$55$	−0.863904	−0.116489
$56$	−5.62362	−0.751488
$57$	8.20108	1.08626
$58$	3.87049	0.508221
$59$	10.6757	1.38986	0.694932	−	0.719076i	$-0.255435\pi$
$59$	10.6757	1.38986	0.694932	+	0.719076i	$0.255435\pi$
$60$	−0.630474	−0.0813938
$61$	6.32162	0.809401	0.404700	−	0.914449i	$-0.367376\pi$
$61$	6.32162	0.809401	0.404700	+	0.914449i	$0.367376\pi$
$62$	0.942903	0.119749
$63$	−2.40151	−0.302562
$64$	0.555904	0.0694880
$65$	−1.05651	−0.131044
$66$	1.41094	0.173675
$67$	−8.60559	−1.05134	−0.525670	−	0.850689i	$-0.676185\pi$
$67$	−8.60559	−1.05134	−0.525670	+	0.850689i	$0.676185\pi$
$68$	−1.56966	−0.190349
$69$	−1.35869	−0.163568
$70$	0.632776	0.0756312
$71$	−7.94810	−0.943266	−0.471633	−	0.881795i	$-0.656335\pi$
$71$	−7.94810	−0.943266	−0.471633	+	0.881795i	$0.656335\pi$
$72$	2.34170	0.275973
$73$	−12.5294	−1.46646	−0.733228	−	0.679983i	$-0.761987\pi$
$73$	−12.5294	−1.46646	−0.733228	+	0.679983i	$0.761987\pi$
$74$	−6.88419	−0.800271
$75$	−4.83867	−0.558721
$76$	−12.8729	−1.47662
$77$	5.16522	0.588631
$78$	1.72552	0.195376
$79$	5.61323	0.631538	0.315769	−	0.948836i	$-0.397738\pi$
$79$	5.61323	0.631538	0.315769	+	0.948836i	$0.397738\pi$
$80$	0.643930	0.0719935
$81$	1.00000	0.111111
$82$	−5.34258	−0.589989
$83$	−9.02913	−0.991076	−0.495538	−	0.868586i	$-0.665029\pi$
$83$	−9.02913	−0.991076	−0.495538	+	0.868586i	$0.665029\pi$
$84$	3.76956	0.411292
$85$	0.401662	0.0435664
$86$	2.96365	0.319579
$87$	−5.90013	−0.632560
$88$	−5.03659	−0.536902
$89$	1.19446	0.126613	0.0633065	−	0.997994i	$-0.479835\pi$
$89$	1.19446	0.126613	0.0633065	+	0.997994i	$0.479835\pi$
$90$	−0.263491	−0.0277744
$91$	6.31681	0.662182
$92$	2.13269	0.222348
$93$	−1.43735	−0.149046
$94$	−4.31391	−0.444946
$95$	3.29406	0.337964
$96$	−5.73509	−0.585335
$97$	2.65756	0.269834	0.134917	−	0.990857i	$-0.456923\pi$
$97$	2.65756	0.269834	0.134917	+	0.990857i	$0.456923\pi$
$98$	0.808691	0.0816901
$99$	−2.15082	−0.216166
$100$	7.59507	0.759507
$101$	1.59818	0.159025	0.0795125	−	0.996834i	$-0.474664\pi$
$101$	1.59818	0.159025	0.0795125	+	0.996834i	$0.474664\pi$
$102$	−0.656002	−0.0649539
$103$	7.27925	0.717246	0.358623	−	0.933482i	$-0.383246\pi$
$103$	7.27925	0.717246	0.358623	+	0.933482i	$0.383246\pi$
$104$	−6.15951	−0.603989
$105$	−0.964596	−0.0941349
$106$	1.35261	0.131377
$107$	−5.92750	−0.573033	−0.286517	−	0.958075i	$-0.592497\pi$
$107$	−5.92750	−0.573033	−0.286517	+	0.958075i	$0.592497\pi$
$108$	−1.56966	−0.151041
$109$	10.7482	1.02949	0.514747	−	0.857342i	$-0.327886\pi$
$109$	10.7482	1.02949	0.514747	+	0.857342i	$0.327886\pi$
$110$	0.566723	0.0540349
$111$	10.4942	0.996062
$112$	−3.85001	−0.363791
$113$	−2.02607	−0.190597	−0.0952984	−	0.995449i	$-0.530381\pi$
$113$	−2.02607	−0.190597	−0.0952984	+	0.995449i	$0.530381\pi$
$114$	−5.37992	−0.503876
$115$	−0.545737	−0.0508902
$116$	9.26121	0.859881
$117$	−2.63035	−0.243176
$118$	−7.00331	−0.644707
$119$	−2.40151	−0.220146
$120$	0.940575	0.0858623
$121$	−6.37396	−0.579451
$122$	−4.14700	−0.375451
$123$	8.14415	0.734333
$124$	2.25615	0.202608
$125$	−3.95182	−0.353462
$126$	1.57539	0.140347
$127$	−6.26024	−0.555506	−0.277753	−	0.960652i	$-0.589590\pi$
$127$	−6.26024	−0.555506	−0.277753	+	0.960652i	$0.589590\pi$
$128$	11.1055	0.981597
$129$	−4.51775	−0.397766
$130$	0.693075	0.0607867
$131$	10.1368	0.885658	0.442829	−	0.896606i	$-0.353975\pi$
$131$	10.1368	0.885658	0.442829	+	0.896606i	$0.353975\pi$
$132$	3.37606	0.293849
$133$	−19.6950	−1.70777
$134$	5.64528	0.487678
$135$	0.401662	0.0345696
$136$	2.34170	0.200799
$137$	3.14543	0.268732	0.134366	−	0.990932i	$-0.457100\pi$
$137$	3.14543	0.268732	0.134366	+	0.990932i	$0.457100\pi$
$138$	0.891306	0.0758730
$139$	1.86479	0.158169	0.0790846	−	0.996868i	$-0.474800\pi$
$139$	1.86479	0.158169	0.0790846	+	0.996868i	$0.474800\pi$
$140$	1.51409	0.127964
$141$	6.57606	0.553804
$142$	5.21397	0.437546
$143$	5.65742	0.473097
$144$	1.60316	0.133597
$145$	−2.36986	−0.196806
$146$	8.21931	0.680235
$147$	−1.23276	−0.101676
$148$	−16.4723	−1.35401
$149$	−10.3688	−0.849449	−0.424724	−	0.905323i	$-0.639629\pi$
$149$	−10.3688	−0.849449	−0.424724	+	0.905323i	$0.639629\pi$
$150$	3.17417	0.259170
$151$	4.60327	0.374608	0.187304	−	0.982302i	$-0.440025\pi$
$151$	4.60327	0.374608	0.187304	+	0.982302i	$0.440025\pi$
$152$	19.2045	1.55769
$153$	1.00000	0.0808452
$154$	−3.38839	−0.273044
$155$	−0.577329	−0.0463721
$156$	4.12876	0.330566
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−3.68229	−0.292947
$159$	−2.06189	−0.163519
$160$	−2.30357	−0.182113
$161$	3.26292	0.257154
$162$	−0.656002	−0.0515404
$163$	−9.58162	−0.750490	−0.375245	−	0.926926i	$-0.622441\pi$
$163$	−9.58162	−0.750490	−0.375245	+	0.926926i	$0.622441\pi$
$164$	−12.7836	−0.998228
$165$	−0.863904	−0.0672549
$166$	5.92312	0.459724
$167$	−6.76138	−0.523211	−0.261606	−	0.965175i	$-0.584252\pi$
$167$	−6.76138	−0.523211	−0.261606	+	0.965175i	$0.584252\pi$
$168$	−5.62362	−0.433872
$169$	−6.08125	−0.467788
$170$	−0.263491	−0.0202089
$171$	8.20108	0.627152
$172$	7.09134	0.540710
$173$	11.8331	0.899651	0.449826	−	0.893116i	$-0.351486\pi$
$173$	11.8331	0.899651	0.449826	+	0.893116i	$0.351486\pi$
$174$	3.87049	0.293421
$175$	11.6201	0.878397
$176$	−3.44812	−0.259911
$177$	10.6757	0.802438
$178$	−0.783571	−0.0587311
$179$	7.14678	0.534176	0.267088	−	0.963672i	$-0.413939\pi$
$179$	7.14678	0.534176	0.267088	+	0.963672i	$0.413939\pi$
$180$	−0.630474	−0.0469928
$181$	5.06232	0.376280	0.188140	−	0.982142i	$-0.439754\pi$
$181$	5.06232	0.376280	0.188140	+	0.982142i	$0.439754\pi$
$182$	−4.14384	−0.307162
$183$	6.32162	0.467308
$184$	−3.18166	−0.234555
$185$	4.21511	0.309901
$186$	0.942903	0.0691370
$187$	−2.15082	−0.157284
$188$	−10.3222	−0.752823
$189$	−2.40151	−0.174684
$190$	−2.16091	−0.156769
$191$	−8.96009	−0.648329	−0.324165	−	0.946001i	$-0.605083\pi$
$191$	−8.96009	−0.648329	−0.324165	+	0.946001i	$0.605083\pi$
$192$	0.555904	0.0401189
$193$	−17.8725	−1.28649	−0.643247	−	0.765659i	$-0.722413\pi$
$193$	−17.8725	−1.28649	−0.643247	+	0.765659i	$0.722413\pi$
$194$	−1.74336	−0.125166
$195$	−1.05651	−0.0756585
$196$	1.93501	0.138215
$197$	−2.58653	−0.184282	−0.0921411	−	0.995746i	$-0.529371\pi$
$197$	−2.58653	−0.184282	−0.0921411	+	0.995746i	$0.529371\pi$
$198$	1.41094	0.100271
$199$	−8.34940	−0.591873	−0.295937	−	0.955208i	$-0.595632\pi$
$199$	−8.34940	−0.591873	−0.295937	+	0.955208i	$0.595632\pi$
$200$	−11.3307	−0.801203
$201$	−8.60559	−0.606992
$202$	−1.04841	−0.0737658
$203$	14.1692	0.994483
$204$	−1.56966	−0.109898
$205$	3.27120	0.228470
$206$	−4.77520	−0.332704
$207$	−1.35869	−0.0944358
$208$	−4.21688	−0.292388
$209$	−17.6391	−1.22012
$210$	0.632776	0.0436657
$211$	−13.6550	−0.940052	−0.470026	−	0.882653i	$-0.655756\pi$
$211$	−13.6550	−0.940052	−0.470026	+	0.882653i	$0.655756\pi$
$212$	3.23647	0.222282
$213$	−7.94810	−0.544595
$214$	3.88845	0.265809
$215$	−1.81461	−0.123755
$216$	2.34170	0.159333
$217$	3.45180	0.234324
$218$	−7.05085	−0.477544
$219$	−12.5294	−0.846659
$220$	1.35604	0.0914240
$221$	−2.63035	−0.176937
$222$	−6.88419	−0.462037
$223$	−14.6765	−0.982809	−0.491404	−	0.870932i	$-0.663516\pi$
$223$	−14.6765	−0.982809	−0.491404	+	0.870932i	$0.663516\pi$
$224$	13.7729	0.920238
$225$	−4.83867	−0.322578
$226$	1.32911	0.0884108
$227$	−27.9387	−1.85436	−0.927180	−	0.374616i	$-0.877774\pi$
$227$	−27.9387	−1.85436	−0.927180	+	0.374616i	$0.877774\pi$
$228$	−12.8729	−0.852530
$229$	−20.6498	−1.36458	−0.682289	−	0.731082i	$-0.739015\pi$
$229$	−20.6498	−1.36458	−0.682289	+	0.731082i	$0.739015\pi$
$230$	0.358004	0.0236061
$231$	5.16522	0.339846
$232$	−13.8164	−0.907088
$233$	6.21812	0.407362	0.203681	−	0.979037i	$-0.434709\pi$
$233$	6.21812	0.407362	0.203681	+	0.979037i	$0.434709\pi$
$234$	1.72552	0.112800
$235$	2.64136	0.172303
$236$	−16.7573	−1.09081
$237$	5.61323	0.364619
$238$	1.57539	0.102118
$239$	−0.115622	−0.00747893	−0.00373947	−	0.999993i	$-0.501190\pi$
$239$	−0.115622	−0.00747893	−0.00373947	+	0.999993i	$0.501190\pi$
$240$	0.643930	0.0415655
$241$	−0.557880	−0.0359362	−0.0179681	−	0.999839i	$-0.505720\pi$
$241$	−0.557880	−0.0359362	−0.0179681	+	0.999839i	$0.505720\pi$
$242$	4.18133	0.268786
$243$	1.00000	0.0641500
$244$	−9.92281	−0.635243
$245$	−0.495152	−0.0316341
$246$	−5.34258	−0.340630
$247$	−21.5717	−1.37258
$248$	−3.36584	−0.213731
$249$	−9.02913	−0.572198
$250$	2.59240	0.163958
$251$	9.82024	0.619848	0.309924	−	0.950761i	$-0.399696\pi$
$251$	9.82024	0.619848	0.309924	+	0.950761i	$0.399696\pi$
$252$	3.76956	0.237460
$253$	2.92231	0.183724
$254$	4.10673	0.257679
$255$	0.401662	0.0251531
$256$	−8.39703	−0.524815
$257$	10.7772	0.672261	0.336130	−	0.941815i	$-0.390882\pi$
$257$	10.7772	0.672261	0.336130	+	0.941815i	$0.390882\pi$
$258$	2.96365	0.184509
$259$	−25.2018	−1.56597
$260$	1.65837	0.102848
$261$	−5.90013	−0.365209
$262$	−6.64977	−0.410824
$263$	22.6990	1.39968	0.699839	−	0.714301i	$-0.253255\pi$
$263$	22.6990	1.39968	0.699839	+	0.714301i	$0.253255\pi$
$264$	−5.03659	−0.309981
$265$	−0.828185	−0.0508750
$266$	12.9199	0.792171
$267$	1.19446	0.0731000
$268$	13.5079	0.825124
$269$	−22.2819	−1.35855	−0.679277	−	0.733882i	$-0.737707\pi$
$269$	−22.2819	−1.35855	−0.679277	+	0.733882i	$0.737707\pi$
$270$	−0.263491	−0.0160356
$271$	1.65398	0.100472	0.0502360	−	0.998737i	$-0.484003\pi$
$271$	1.65398	0.100472	0.0502360	+	0.998737i	$0.484003\pi$
$272$	1.60316	0.0972059
$273$	6.31681	0.382311
$274$	−2.06341	−0.124655
$275$	10.4071	0.627573
$276$	2.13269	0.128373
$277$	−16.0579	−0.964826	−0.482413	−	0.875944i	$-0.660240\pi$
$277$	−16.0579	−0.964826	−0.482413	+	0.875944i	$0.660240\pi$
$278$	−1.22330	−0.0733689
$279$	−1.43735	−0.0860518
$280$	−2.25880	−0.134989
$281$	−13.3236	−0.794820	−0.397410	−	0.917641i	$-0.630091\pi$
$281$	−13.3236	−0.794820	−0.397410	+	0.917641i	$0.630091\pi$
$282$	−4.31391	−0.256889
$283$	−24.8026	−1.47436	−0.737179	−	0.675697i	$-0.763843\pi$
$283$	−24.8026	−1.47436	−0.737179	+	0.675697i	$0.763843\pi$
$284$	12.4758	0.740304
$285$	3.29406	0.195123
$286$	−3.71128	−0.219452
$287$	−19.5582	−1.15449
$288$	−5.73509	−0.337943
$289$	1.00000	0.0588235
$290$	1.55463	0.0912911
$291$	2.65756	0.155789
$292$	19.6669	1.15092
$293$	6.60096	0.385632	0.192816	−	0.981235i	$-0.438238\pi$
$293$	6.60096	0.385632	0.192816	+	0.981235i	$0.438238\pi$
$294$	0.808691	0.0471638
$295$	4.28804	0.249660
$296$	24.5742	1.42835
$297$	−2.15082	−0.124803
$298$	6.80198	0.394028
$299$	3.57385	0.206681
$300$	7.59507	0.438502
$301$	10.8494	0.625350
$302$	−3.01975	−0.173767
$303$	1.59818	0.0918131
$304$	13.1476	0.754069
$305$	2.53916	0.145392
$306$	−0.656002	−0.0375011
$307$	−19.0379	−1.08655	−0.543274	−	0.839555i	$-0.682816\pi$
$307$	−19.0379	−1.08655	−0.543274	+	0.839555i	$0.682816\pi$
$308$	−8.10765	−0.461976
$309$	7.27925	0.414102
$310$	0.378729	0.0215103
$311$	−24.6416	−1.39730	−0.698649	−	0.715465i	$-0.746215\pi$
$311$	−24.6416	−1.39730	−0.698649	+	0.715465i	$0.746215\pi$
$312$	−6.15951	−0.348713
$313$	27.3929	1.54834	0.774169	−	0.632979i	$-0.218168\pi$
$313$	27.3929	1.54834	0.774169	+	0.632979i	$0.218168\pi$
$314$	0.656002	0.0370203
$315$	−0.964596	−0.0543488
$316$	−8.81088	−0.495651
$317$	−21.7353	−1.22078	−0.610388	−	0.792102i	$-0.708987\pi$
$317$	−21.7353	−1.22078	−0.610388	+	0.792102i	$0.708987\pi$
$318$	1.35261	0.0758503
$319$	12.6901	0.710511
$320$	0.223286	0.0124820
$321$	−5.92750	−0.330841
$322$	−2.14048	−0.119284
$323$	8.20108	0.456320
$324$	−1.56966	−0.0872034
$325$	12.7274	0.705989
$326$	6.28556	0.348125
$327$	10.7482	0.594378
$328$	19.0712	1.05303
$329$	−15.7925	−0.870667
$330$	0.566723	0.0311971
$331$	3.83082	0.210561	0.105281	−	0.994443i	$-0.466426\pi$
$331$	3.83082	0.210561	0.105281	+	0.994443i	$0.466426\pi$
$332$	14.1727	0.777827
$333$	10.4942	0.575077
$334$	4.43547	0.242698
$335$	−3.45654	−0.188851
$336$	−3.85001	−0.210035
$337$	1.33196	0.0725564	0.0362782	−	0.999342i	$-0.488450\pi$
$337$	1.33196	0.0725564	0.0362782	+	0.999342i	$0.488450\pi$
$338$	3.98931	0.216990
$339$	−2.02607	−0.110041
$340$	−0.630474	−0.0341923
$341$	3.09148	0.167413
$342$	−5.37992	−0.290913
$343$	19.7710	1.06754
$344$	−10.5792	−0.570394
$345$	−0.545737	−0.0293815
$346$	−7.76251	−0.417315
$347$	−6.40391	−0.343780	−0.171890	−	0.985116i	$-0.554987\pi$
$347$	−6.40391	−0.343780	−0.171890	+	0.985116i	$0.554987\pi$
$348$	9.26121	0.496453
$349$	−6.18987	−0.331336	−0.165668	−	0.986182i	$-0.552978\pi$
$349$	−6.18987	−0.331336	−0.165668	+	0.986182i	$0.552978\pi$
$350$	−7.62281	−0.407456
$351$	−2.63035	−0.140398
$352$	12.3352	0.657466
$353$	−25.4659	−1.35541	−0.677707	−	0.735332i	$-0.737026\pi$
$353$	−25.4659	−1.35541	−0.677707	+	0.735332i	$0.737026\pi$
$354$	−7.00331	−0.372222
$355$	−3.19245	−0.169438
$356$	−1.87490	−0.0993698
$357$	−2.40151	−0.127101
$358$	−4.68830	−0.247785
$359$	12.4601	0.657618	0.328809	−	0.944396i	$-0.393353\pi$
$359$	12.4601	0.657618	0.328809	+	0.944396i	$0.393353\pi$
$360$	0.940575	0.0495726
$361$	48.2577	2.53988
$362$	−3.32089	−0.174542
$363$	−6.37396	−0.334546
$364$	−9.91526	−0.519701
$365$	−5.03259	−0.263418
$366$	−4.14700	−0.216767
$367$	−12.2876	−0.641409	−0.320704	−	0.947179i	$-0.603920\pi$
$367$	−12.2876	−0.641409	−0.320704	+	0.947179i	$0.603920\pi$
$368$	−2.17821	−0.113547
$369$	8.14415	0.423968
$370$	−2.76512	−0.143752
$371$	4.95165	0.257077
$372$	2.25615	0.116976
$373$	−2.00985	−0.104066	−0.0520330	−	0.998645i	$-0.516570\pi$
$373$	−2.00985	−0.104066	−0.0520330	+	0.998645i	$0.516570\pi$
$374$	1.41094	0.0729581
$375$	−3.95182	−0.204071
$376$	15.3992	0.794153
$377$	15.5194	0.799291
$378$	1.57539	0.0810295
$379$	33.9288	1.74280	0.871402	−	0.490569i	$-0.163211\pi$
$379$	33.9288	1.74280	0.871402	+	0.490569i	$0.163211\pi$
$380$	−5.17057	−0.265244
$381$	−6.26024	−0.320722
$382$	5.87783	0.300736
$383$	−17.8840	−0.913832	−0.456916	−	0.889510i	$-0.651046\pi$
$383$	−17.8840	−0.913832	−0.456916	+	0.889510i	$0.651046\pi$
$384$	11.1055	0.566725
$385$	2.07467	0.105735
$386$	11.7244	0.596757
$387$	−4.51775	−0.229650
$388$	−4.17146	−0.211774
$389$	−12.2191	−0.619534	−0.309767	−	0.950813i	$-0.600251\pi$
$389$	−12.2191	−0.619534	−0.309767	+	0.950813i	$0.600251\pi$
$390$	0.693075	0.0350952
$391$	−1.35869	−0.0687121
$392$	−2.88675	−0.145803
$393$	10.1368	0.511335
$394$	1.69677	0.0854818
$395$	2.25462	0.113442
$396$	3.37606	0.169654
$397$	23.9062	1.19982	0.599910	−	0.800067i	$-0.295203\pi$
$397$	23.9062	1.19982	0.599910	+	0.800067i	$0.295203\pi$
$398$	5.47722	0.274548
$399$	−19.6950	−0.985981
$400$	−7.75716	−0.387858
$401$	−23.1981	−1.15846	−0.579229	−	0.815165i	$-0.696646\pi$
$401$	−23.1981	−1.15846	−0.579229	+	0.815165i	$0.696646\pi$
$402$	5.64528	0.281561
$403$	3.78073	0.188332
$404$	−2.50860	−0.124808
$405$	0.401662	0.0199588
$406$	−9.29503	−0.461304
$407$	−22.5711	−1.11881
$408$	2.34170	0.115932
$409$	9.43836	0.466697	0.233348	−	0.972393i	$-0.425032\pi$
$409$	9.43836	0.466697	0.233348	+	0.972393i	$0.425032\pi$
$410$	−2.14591	−0.105979
$411$	3.14543	0.155152
$412$	−11.4260	−0.562917
$413$	−25.6379	−1.26156
$414$	0.891306	0.0438053
$415$	−3.62666	−0.178026
$416$	15.0853	0.739617
$417$	1.86479	0.0913190
$418$	11.5713	0.565969
$419$	−29.0410	−1.41875	−0.709374	−	0.704832i	$-0.751022\pi$
$419$	−29.0410	−1.41875	−0.709374	+	0.704832i	$0.751022\pi$
$420$	1.51409	0.0738800
$421$	−14.5431	−0.708785	−0.354393	−	0.935097i	$-0.615312\pi$
$421$	−14.5431	−0.708785	−0.354393	+	0.935097i	$0.615312\pi$
$422$	8.95774	0.436056
$423$	6.57606	0.319739
$424$	−4.82834	−0.234485
$425$	−4.83867	−0.234710
$426$	5.21397	0.252618
$427$	−15.1814	−0.734681
$428$	9.30417	0.449734
$429$	5.65742	0.273143
$430$	1.19039	0.0574056
$431$	5.63894	0.271618	0.135809	−	0.990735i	$-0.456637\pi$
$431$	5.63894	0.271618	0.135809	+	0.990735i	$0.456637\pi$
$432$	1.60316	0.0771321
$433$	−2.09606	−0.100730	−0.0503650	−	0.998731i	$-0.516038\pi$
$433$	−2.09606	−0.100730	−0.0503650	+	0.998731i	$0.516038\pi$
$434$	−2.26439	−0.108694
$435$	−2.36986	−0.113626
$436$	−16.8711	−0.807978
$437$	−11.1428	−0.533030
$438$	8.21931	0.392734
$439$	18.5790	0.886725	0.443363	−	0.896342i	$-0.353785\pi$
$439$	18.5790	0.886725	0.443363	+	0.896342i	$0.353785\pi$
$440$	−2.02301	−0.0964432
$441$	−1.23276	−0.0587027
$442$	1.72552	0.0820744
$443$	−20.9805	−0.996812	−0.498406	−	0.866944i	$-0.666081\pi$
$443$	−20.9805	−0.996812	−0.498406	+	0.866944i	$0.666081\pi$
$444$	−16.4723	−0.781740
$445$	0.479771	0.0227433
$446$	9.62778	0.455889
$447$	−10.3688	−0.490429
$448$	−1.33501	−0.0630732
$449$	8.04268	0.379557	0.189779	−	0.981827i	$-0.439223\pi$
$449$	8.04268	0.379557	0.189779	+	0.981827i	$0.439223\pi$
$450$	3.17417	0.149632
$451$	−17.5166	−0.824825
$452$	3.18025	0.149586
$453$	4.60327	0.216280
$454$	18.3279	0.860169
$455$	2.53723	0.118947
$456$	19.2045	0.899333
$457$	10.5766	0.494750	0.247375	−	0.968920i	$-0.420432\pi$
$457$	10.5766	0.494750	0.247375	+	0.968920i	$0.420432\pi$
$458$	13.5463	0.632978
$459$	1.00000	0.0466760
$460$	0.856622	0.0399402
$461$	−36.8900	−1.71814	−0.859069	−	0.511861i	$-0.828956\pi$
$461$	−36.8900	−1.71814	−0.859069	+	0.511861i	$0.828956\pi$
$462$	−3.38839	−0.157642
$463$	−29.3770	−1.36526	−0.682632	−	0.730762i	$-0.739165\pi$
$463$	−29.3770	−1.36526	−0.682632	+	0.730762i	$0.739165\pi$
$464$	−9.45886	−0.439116
$465$	−0.577329	−0.0267730
$466$	−4.07909	−0.188960
$467$	−10.0251	−0.463906	−0.231953	−	0.972727i	$-0.574512\pi$
$467$	−10.0251	−0.463906	−0.231953	+	0.972727i	$0.574512\pi$
$468$	4.12876	0.190852
$469$	20.6664	0.954286
$470$	−1.73273	−0.0799251
$471$	−1.00000	−0.0460776
$472$	24.9994	1.15069
$473$	9.71688	0.446783
$474$	−3.68229	−0.169133
$475$	−39.6823	−1.82075
$476$	3.76956	0.172777
$477$	−2.06189	−0.0944076
$478$	0.0758479	0.00346920
$479$	−7.55017	−0.344976	−0.172488	−	0.985012i	$-0.555181\pi$
$479$	−7.55017	−0.344976	−0.172488	+	0.985012i	$0.555181\pi$
$480$	−2.30357	−0.105143
$481$	−27.6034	−1.25860
$482$	0.365970	0.0166695
$483$	3.26292	0.148468
$484$	10.0050	0.454771
$485$	1.06744	0.0484700
$486$	−0.656002	−0.0297568
$487$	−4.62626	−0.209636	−0.104818	−	0.994491i	$-0.533426\pi$
$487$	−4.62626	−0.209636	−0.104818	+	0.994491i	$0.533426\pi$
$488$	14.8034	0.670117
$489$	−9.58162	−0.433296
$490$	0.324821	0.0146739
$491$	−8.76756	−0.395674	−0.197837	−	0.980235i	$-0.563392\pi$
$491$	−8.76756	−0.395674	−0.197837	+	0.980235i	$0.563392\pi$
$492$	−12.7836	−0.576327
$493$	−5.90013	−0.265728
$494$	14.1511	0.636687
$495$	−0.863904	−0.0388296
$496$	−2.30430	−0.103466
$497$	19.0874	0.856188
$498$	5.92312	0.265422
$499$	10.2772	0.460072	0.230036	−	0.973182i	$-0.426116\pi$
$499$	10.2772	0.460072	0.230036	+	0.973182i	$0.426116\pi$
$500$	6.20302	0.277408
$501$	−6.76138	−0.302076
$502$	−6.44210	−0.287525
$503$	−10.0793	−0.449415	−0.224707	−	0.974426i	$-0.572143\pi$
$503$	−10.0793	−0.449415	−0.224707	+	0.974426i	$0.572143\pi$
$504$	−5.62362	−0.250496
$505$	0.641929	0.0285655
$506$	−1.91704	−0.0852229
$507$	−6.08125	−0.270078
$508$	9.82646	0.435979
$509$	24.5221	1.08692	0.543461	−	0.839435i	$-0.317114\pi$
$509$	24.5221	1.08692	0.543461	+	0.839435i	$0.317114\pi$
$510$	−0.263491	−0.0116676
$511$	30.0895	1.33108
$512$	−16.7025	−0.738154
$513$	8.20108	0.362086
$514$	−7.06983	−0.311837
$515$	2.92380	0.128838
$516$	7.09134	0.312179
$517$	−14.1439	−0.622050
$518$	16.5324	0.726394
$519$	11.8331	0.519414
$520$	−2.47404	−0.108494
$521$	−23.1628	−1.01478	−0.507391	−	0.861716i	$-0.669390\pi$
$521$	−23.1628	−1.01478	−0.507391	+	0.861716i	$0.669390\pi$
$522$	3.87049	0.169407
$523$	45.1493	1.97424	0.987120	−	0.159980i	$-0.0511429\pi$
$523$	45.1493	1.97424	0.987120	+	0.159980i	$0.0511429\pi$
$524$	−15.9114	−0.695092
$525$	11.6201	0.507143
$526$	−14.8906	−0.649259
$527$	−1.43735	−0.0626119
$528$	−3.44812	−0.150060
$529$	−21.1539	−0.919737
$530$	0.543291	0.0235990
$531$	10.6757	0.463288
$532$	30.9144	1.34031
$533$	−21.4220	−0.927889
$534$	−0.783571	−0.0339084
$535$	−2.38085	−0.102933
$536$	−20.1517	−0.870423
$537$	7.14678	0.308407
$538$	14.6170	0.630183
$539$	2.65144	0.114206
$540$	−0.630474	−0.0271313
$541$	15.2516	0.655720	0.327860	−	0.944726i	$-0.393673\pi$
$541$	15.2516	0.655720	0.327860	+	0.944726i	$0.393673\pi$
$542$	−1.08501	−0.0466053
$543$	5.06232	0.217245
$544$	−5.73509	−0.245890
$545$	4.31716	0.184927
$546$	−4.14384	−0.177340
$547$	−5.43846	−0.232532	−0.116266	−	0.993218i	$-0.537092\pi$
$547$	−5.43846	−0.232532	−0.116266	+	0.993218i	$0.537092\pi$
$548$	−4.93726	−0.210909
$549$	6.32162	0.269800
$550$	−6.82709	−0.291108
$551$	−48.3874	−2.06137
$552$	−3.18166	−0.135421
$553$	−13.4802	−0.573238
$554$	10.5340	0.447547
$555$	4.21511	0.178922
$556$	−2.92709	−0.124136
$557$	27.0315	1.14536	0.572681	−	0.819779i	$-0.305904\pi$
$557$	27.0315	1.14536	0.572681	+	0.819779i	$0.305904\pi$
$558$	0.942903	0.0399163
$559$	11.8833	0.502609
$560$	−1.54640	−0.0653474
$561$	−2.15082	−0.0908078
$562$	8.74031	0.368688
$563$	−27.3107	−1.15101	−0.575505	−	0.817798i	$-0.695195\pi$
$563$	−27.3107	−1.15101	−0.575505	+	0.817798i	$0.695195\pi$
$564$	−10.3222	−0.434643
$565$	−0.813796	−0.0342367
$566$	16.2705	0.683901
$567$	−2.40151	−0.100854
$568$	−18.6121	−0.780946
$569$	−4.91578	−0.206080	−0.103040	−	0.994677i	$-0.532857\pi$
$569$	−4.91578	−0.206080	−0.103040	+	0.994677i	$0.532857\pi$
$570$	−2.16091	−0.0905106
$571$	−0.154810	−0.00647858	−0.00323929	−	0.999995i	$-0.501031\pi$
$571$	−0.154810	−0.00647858	−0.00323929	+	0.999995i	$0.501031\pi$
$572$	−8.88024	−0.371301
$573$	−8.96009	−0.374313
$574$	12.8302	0.535524
$575$	6.57427	0.274166
$576$	0.555904	0.0231627
$577$	−23.1089	−0.962037	−0.481019	−	0.876710i	$-0.659733\pi$
$577$	−23.1089	−0.962037	−0.481019	+	0.876710i	$0.659733\pi$
$578$	−0.656002	−0.0272861
$579$	−17.8725	−0.742757
$580$	3.71988	0.154460
$581$	21.6835	0.899584
$582$	−1.74336	−0.0722647
$583$	4.43477	0.183669
$584$	−29.3402	−1.21410
$585$	−1.05651	−0.0436815
$586$	−4.33024	−0.178881
$587$	−37.5082	−1.54813	−0.774064	−	0.633107i	$-0.781779\pi$
$587$	−37.5082	−1.54813	−0.774064	+	0.633107i	$0.781779\pi$
$588$	1.93501	0.0797985
$589$	−11.7878	−0.485708
$590$	−2.81296	−0.115808
$591$	−2.58653	−0.106395
$592$	16.8238	0.691456
$593$	0.562298	0.0230908	0.0115454	−	0.999933i	$-0.496325\pi$
$593$	0.562298	0.0230908	0.0115454	+	0.999933i	$0.496325\pi$
$594$	1.41094	0.0578917
$595$	−0.964596	−0.0395446
$596$	16.2756	0.666673
$597$	−8.34940	−0.341718
$598$	−2.34445	−0.0958717
$599$	−6.29532	−0.257220	−0.128610	−	0.991695i	$-0.541051\pi$
$599$	−6.29532	−0.257220	−0.128610	+	0.991695i	$0.541051\pi$
$600$	−11.3307	−0.462575
$601$	4.21725	0.172025	0.0860126	−	0.996294i	$-0.472587\pi$
$601$	4.21725	0.172025	0.0860126	+	0.996294i	$0.472587\pi$
$602$	−7.11724	−0.290077
$603$	−8.60559	−0.350447
$604$	−7.22557	−0.294004
$605$	−2.56018	−0.104086
$606$	−1.04841	−0.0425887
$607$	17.1933	0.697856	0.348928	−	0.937150i	$-0.386546\pi$
$607$	17.1933	0.697856	0.348928	+	0.937150i	$0.386546\pi$
$608$	−47.0339	−1.90748
$609$	14.1692	0.574165
$610$	−1.66569	−0.0674419
$611$	−17.2974	−0.699776
$612$	−1.56966	−0.0634498
$613$	−31.5664	−1.27495	−0.637477	−	0.770470i	$-0.720022\pi$
$613$	−31.5664	−1.27495	−0.637477	+	0.770470i	$0.720022\pi$
$614$	12.4889	0.504010
$615$	3.27120	0.131907
$616$	12.0954	0.487338
$617$	−27.3894	−1.10265	−0.551327	−	0.834289i	$-0.685878\pi$
$617$	−27.3894	−1.10265	−0.551327	+	0.834289i	$0.685878\pi$
$618$	−4.77520	−0.192087
$619$	3.96516	0.159373	0.0796866	−	0.996820i	$-0.474608\pi$
$619$	3.96516	0.159373	0.0796866	+	0.996820i	$0.474608\pi$
$620$	0.906211	0.0363943
$621$	−1.35869	−0.0545225
$622$	16.1649	0.648155
$623$	−2.86852	−0.114925
$624$	−4.21688	−0.168810
$625$	22.6060	0.904242
$626$	−17.9698	−0.718217
$627$	−17.6391	−0.704436
$628$	1.56966	0.0626363
$629$	10.4942	0.418430
$630$	0.632776	0.0252104
$631$	15.3597	0.611461	0.305730	−	0.952118i	$-0.401099\pi$
$631$	15.3597	0.611461	0.305730	+	0.952118i	$0.401099\pi$
$632$	13.1445	0.522861
$633$	−13.6550	−0.542739
$634$	14.2584	0.566274
$635$	−2.51450	−0.0997850
$636$	3.23647	0.128335
$637$	3.24259	0.128476
$638$	−8.32475	−0.329580
$639$	−7.94810	−0.314422
$640$	4.46066	0.176323
$641$	8.38921	0.331354	0.165677	−	0.986180i	$-0.447019\pi$
$641$	8.38921	0.331354	0.165677	+	0.986180i	$0.447019\pi$
$642$	3.88845	0.153465
$643$	11.7540	0.463532	0.231766	−	0.972772i	$-0.425550\pi$
$643$	11.7540	0.463532	0.231766	+	0.972772i	$0.425550\pi$
$644$	−5.12168	−0.201822
$645$	−1.81461	−0.0714503
$646$	−5.37992	−0.211670
$647$	−6.03111	−0.237108	−0.118554	−	0.992948i	$-0.537826\pi$
$647$	−6.03111	−0.237108	−0.118554	+	0.992948i	$0.537826\pi$
$648$	2.34170	0.0919908
$649$	−22.9616	−0.901323
$650$	−8.34920	−0.327482
$651$	3.45180	0.135287
$652$	15.0399	0.589008
$653$	16.0719	0.628941	0.314470	−	0.949267i	$-0.398173\pi$
$653$	16.0719	0.628941	0.314470	+	0.949267i	$0.398173\pi$
$654$	−7.05085	−0.275710
$655$	4.07158	0.159090
$656$	13.0564	0.509766
$657$	−12.5294	−0.488819
$658$	10.3599	0.403870
$659$	−15.3524	−0.598043	−0.299022	−	0.954246i	$-0.596660\pi$
$659$	−15.3524	−0.598043	−0.299022	+	0.954246i	$0.596660\pi$
$660$	1.35604	0.0527837
$661$	9.61998	0.374174	0.187087	−	0.982343i	$-0.440095\pi$
$661$	9.61998	0.374174	0.187087	+	0.982343i	$0.440095\pi$
$662$	−2.51303	−0.0976715
$663$	−2.63035	−0.102154
$664$	−21.1435	−0.820529
$665$	−7.91072	−0.306765
$666$	−6.88419	−0.266757
$667$	8.01647	0.310399
$668$	10.6131	0.410632
$669$	−14.6765	−0.567425
$670$	2.26750	0.0876011
$671$	−13.5967	−0.524894
$672$	13.7729	0.531299
$673$	−30.0368	−1.15783	−0.578917	−	0.815387i	$-0.696524\pi$
$673$	−30.0368	−1.15783	−0.578917	+	0.815387i	$0.696524\pi$
$674$	−0.873767	−0.0336562
$675$	−4.83867	−0.186240
$676$	9.54550	0.367135
$677$	−16.9073	−0.649799	−0.324900	−	0.945748i	$-0.605331\pi$
$677$	−16.9073	−0.649799	−0.324900	+	0.945748i	$0.605331\pi$
$678$	1.32911	0.0510440
$679$	−6.38214	−0.244924
$680$	0.940575	0.0360694
$681$	−27.9387	−1.07062
$682$	−2.02802	−0.0776568
$683$	2.45347	0.0938794	0.0469397	−	0.998898i	$-0.485053\pi$
$683$	2.45347	0.0938794	0.0469397	+	0.998898i	$0.485053\pi$
$684$	−12.8729	−0.492208
$685$	1.26340	0.0482720
$686$	−12.9698	−0.495191
$687$	−20.6498	−0.787840
$688$	−7.24269	−0.276125
$689$	5.42350	0.206619
$690$	0.358004	0.0136290
$691$	11.5021	0.437560	0.218780	−	0.975774i	$-0.429792\pi$
$691$	11.5021	0.437560	0.218780	+	0.975774i	$0.429792\pi$
$692$	−18.5739	−0.706074
$693$	5.16522	0.196210
$694$	4.20098	0.159467
$695$	0.749015	0.0284118
$696$	−13.8164	−0.523708
$697$	8.14415	0.308482
$698$	4.06057	0.153695
$699$	6.21812	0.235191
$700$	−18.2396	−0.689393
$701$	32.1391	1.21388	0.606938	−	0.794749i	$-0.292398\pi$
$701$	32.1391	1.21388	0.606938	+	0.794749i	$0.292398\pi$
$702$	1.72552	0.0651254
$703$	86.0635	3.24595
$704$	−1.19565	−0.0450628
$705$	2.64136	0.0994792
$706$	16.7057	0.628727
$707$	−3.83804	−0.144345
$708$	−16.7573	−0.629778
$709$	13.6182	0.511441	0.255721	−	0.966751i	$-0.417687\pi$
$709$	13.6182	0.511441	0.255721	+	0.966751i	$0.417687\pi$
$710$	2.09425	0.0785960
$711$	5.61323	0.210513
$712$	2.79708	0.104825
$713$	1.95292	0.0731373
$714$	1.57539	0.0589576
$715$	2.27237	0.0849819
$716$	−11.2180	−0.419238
$717$	−0.115622	−0.00431797
$718$	−8.17384	−0.305045
$719$	13.1608	0.490816	0.245408	−	0.969420i	$-0.421078\pi$
$719$	13.1608	0.490816	0.245408	+	0.969420i	$0.421078\pi$
$720$	0.643930	0.0239978
$721$	−17.4812	−0.651034
$722$	−31.6571	−1.17816
$723$	−0.557880	−0.0207478
$724$	−7.94614	−0.295316
$725$	28.5488	1.06027
$726$	4.18133	0.155184
$727$	−50.0607	−1.85665	−0.928324	−	0.371771i	$-0.878751\pi$
$727$	−50.0607	−1.85665	−0.928324	+	0.371771i	$0.878751\pi$
$728$	14.7921	0.548232
$729$	1.00000	0.0370370
$730$	3.30139	0.122190
$731$	−4.51775	−0.167095
$732$	−9.92281	−0.366758
$733$	38.2228	1.41179	0.705897	−	0.708315i	$-0.250544\pi$
$733$	38.2228	1.41179	0.705897	+	0.708315i	$0.250544\pi$
$734$	8.06070	0.297526
$735$	−0.495152	−0.0182640
$736$	7.79223	0.287225
$737$	18.5091	0.681791
$738$	−5.34258	−0.196663
$739$	13.5563	0.498676	0.249338	−	0.968416i	$-0.419787\pi$
$739$	13.5563	0.498676	0.249338	+	0.968416i	$0.419787\pi$
$740$	−6.61630	−0.243220
$741$	−21.5717	−0.792457
$742$	−3.24829	−0.119249
$743$	12.2051	0.447763	0.223881	−	0.974616i	$-0.428127\pi$
$743$	12.2051	0.447763	0.223881	+	0.974616i	$0.428127\pi$
$744$	−3.36584	−0.123398
$745$	−4.16477	−0.152586
$746$	1.31846	0.0482724
$747$	−9.02913	−0.330359
$748$	3.37606	0.123441
$749$	14.2349	0.520134
$750$	2.59240	0.0946612
$751$	43.2319	1.57755	0.788777	−	0.614679i	$-0.210715\pi$
$751$	43.2319	1.57755	0.788777	+	0.614679i	$0.210715\pi$
$752$	10.5425	0.384445
$753$	9.82024	0.357870
$754$	−10.1808	−0.370762
$755$	1.84896	0.0672905
$756$	3.76956	0.137097
$757$	33.6728	1.22386	0.611929	−	0.790913i	$-0.290394\pi$
$757$	33.6728	1.22386	0.611929	+	0.790913i	$0.290394\pi$
$758$	−22.2573	−0.808423
$759$	2.92231	0.106073
$760$	7.71372	0.279806
$761$	−40.2822	−1.46023	−0.730114	−	0.683325i	$-0.760533\pi$
$761$	−40.2822	−1.46023	−0.730114	+	0.683325i	$0.760533\pi$
$762$	4.10673	0.148771
$763$	−25.8120	−0.934455
$764$	14.0643	0.508829
$765$	0.401662	0.0145221
$766$	11.7320	0.423893
$767$	−28.0810	−1.01394
$768$	−8.39703	−0.303002
$769$	5.06951	0.182811	0.0914056	−	0.995814i	$-0.470864\pi$
$769$	5.06951	0.182811	0.0914056	+	0.995814i	$0.470864\pi$
$770$	−1.36099	−0.0490467
$771$	10.7772	0.388130
$772$	28.0538	1.00968
$773$	−47.5603	−1.71062	−0.855312	−	0.518113i	$-0.826635\pi$
$773$	−47.5603	−1.71062	−0.855312	+	0.518113i	$0.826635\pi$
$774$	2.96365	0.106526
$775$	6.95485	0.249826
$776$	6.22321	0.223400
$777$	−25.2018	−0.904111
$778$	8.01576	0.287379
$779$	66.7908	2.39303
$780$	1.65837	0.0593791
$781$	17.0950	0.611706
$782$	0.891306	0.0318730
$783$	−5.90013	−0.210853
$784$	−1.97631	−0.0705824
$785$	−0.401662	−0.0143359
$786$	−6.64977	−0.237189
$787$	−17.3240	−0.617535	−0.308767	−	0.951138i	$-0.599916\pi$
$787$	−17.3240	−0.617535	−0.308767	+	0.951138i	$0.599916\pi$
$788$	4.05997	0.144630
$789$	22.6990	0.808105
$790$	−1.47904	−0.0526218
$791$	4.86563	0.173002
$792$	−5.03659	−0.178967
$793$	−16.6281	−0.590481
$794$	−15.6825	−0.556553
$795$	−0.828185	−0.0293727
$796$	13.1057	0.464521
$797$	−16.1869	−0.573368	−0.286684	−	0.958025i	$-0.592553\pi$
$797$	−16.1869	−0.573368	−0.286684	+	0.958025i	$0.592553\pi$
$798$	12.9199	0.457360
$799$	6.57606	0.232644
$800$	27.7502	0.981117
$801$	1.19446	0.0422043
$802$	15.2180	0.537366
$803$	26.9485	0.950993
$804$	13.5079	0.476386
$805$	1.31059	0.0461923
$806$	−2.48017	−0.0873601
$807$	−22.2819	−0.784362
$808$	3.74247	0.131660
$809$	13.7540	0.483564	0.241782	−	0.970331i	$-0.422268\pi$
$809$	13.7540	0.483564	0.241782	+	0.970331i	$0.422268\pi$
$810$	−0.263491	−0.00925814
$811$	−21.6584	−0.760531	−0.380265	−	0.924877i	$-0.624167\pi$
$811$	−21.6584	−0.760531	−0.380265	+	0.924877i	$0.624167\pi$
$812$	−22.2409	−0.780501
$813$	1.65398	0.0580076
$814$	14.8067	0.518974
$815$	−3.84857	−0.134810
$816$	1.60316	0.0561219
$817$	−37.0504	−1.29623
$818$	−6.19158	−0.216484
$819$	6.31681	0.220727
$820$	−5.13468	−0.179311
$821$	−46.7141	−1.63033	−0.815166	−	0.579227i	$-0.803354\pi$
$821$	−46.7141	−1.63033	−0.815166	+	0.579227i	$0.803354\pi$
$822$	−2.06341	−0.0719695
$823$	18.9092	0.659133	0.329567	−	0.944132i	$-0.393097\pi$
$823$	18.9092	0.659133	0.329567	+	0.944132i	$0.393097\pi$
$824$	17.0459	0.593821
$825$	10.4071	0.362329
$826$	16.8185	0.585190
$827$	−14.8585	−0.516680	−0.258340	−	0.966054i	$-0.583175\pi$
$827$	−14.8585	−0.516680	−0.258340	+	0.966054i	$0.583175\pi$
$828$	2.13269	0.0741161
$829$	−22.4443	−0.779522	−0.389761	−	0.920916i	$-0.627442\pi$
$829$	−22.4443	−0.779522	−0.389761	+	0.920916i	$0.627442\pi$
$830$	2.37910	0.0825796
$831$	−16.0579	−0.557043
$832$	−1.46222	−0.0506934
$833$	−1.23276	−0.0427125
$834$	−1.22330	−0.0423595
$835$	−2.71579	−0.0939838
$836$	27.6874	0.957587
$837$	−1.43735	−0.0496820
$838$	19.0510	0.658105
$839$	30.7250	1.06075	0.530373	−	0.847764i	$-0.322052\pi$
$839$	30.7250	1.06075	0.530373	+	0.847764i	$0.322052\pi$
$840$	−2.25880	−0.0779359
$841$	5.81151	0.200397
$842$	9.54027	0.328779
$843$	−13.3236	−0.458890
$844$	21.4338	0.737782
$845$	−2.44261	−0.0840283
$846$	−4.31391	−0.148315
$847$	15.3071	0.525959
$848$	−3.30555	−0.113513
$849$	−24.8026	−0.851221
$850$	3.17417	0.108873
$851$	−14.2584	−0.488771
$852$	12.4758	0.427415
$853$	−6.53356	−0.223705	−0.111852	−	0.993725i	$-0.535678\pi$
$853$	−6.53356	−0.223705	−0.111852	+	0.993725i	$0.535678\pi$
$854$	9.95905	0.340792
$855$	3.29406	0.112655
$856$	−13.8805	−0.474424
$857$	−12.5104	−0.427348	−0.213674	−	0.976905i	$-0.568543\pi$
$857$	−12.5104	−0.427348	−0.213674	+	0.976905i	$0.568543\pi$
$858$	−3.71128	−0.126701
$859$	33.2800	1.13550	0.567750	−	0.823201i	$-0.307814\pi$
$859$	33.2800	1.13550	0.567750	+	0.823201i	$0.307814\pi$
$860$	2.84833	0.0971271
$861$	−19.5582	−0.666543
$862$	−3.69916	−0.125994
$863$	36.2506	1.23399	0.616993	−	0.786969i	$-0.288351\pi$
$863$	36.2506	1.23399	0.616993	+	0.786969i	$0.288351\pi$
$864$	−5.73509	−0.195112
$865$	4.75290	0.161603
$866$	1.37502	0.0467250
$867$	1.00000	0.0339618
$868$	−5.41816	−0.183904
$869$	−12.0731	−0.409551
$870$	1.55463	0.0527070
$871$	22.6357	0.766983
$872$	25.1692	0.852335
$873$	2.65756	0.0899447
$874$	7.30967	0.247253
$875$	9.49034	0.320832
$876$	19.6669	0.664484
$877$	−2.53933	−0.0857469	−0.0428735	−	0.999081i	$-0.513651\pi$
$877$	−2.53933	−0.0857469	−0.0428735	+	0.999081i	$0.513651\pi$
$878$	−12.1878	−0.411319
$879$	6.60096	0.222645
$880$	−1.38498	−0.0466876
$881$	−10.9936	−0.370383	−0.185192	−	0.982702i	$-0.559291\pi$
$881$	−10.9936	−0.370383	−0.185192	+	0.982702i	$0.559291\pi$
$882$	0.808691	0.0272300
$883$	−35.4656	−1.19351	−0.596756	−	0.802423i	$-0.703544\pi$
$883$	−35.4656	−1.19351	−0.596756	+	0.802423i	$0.703544\pi$
$884$	4.12876	0.138865
$885$	4.28804	0.144141
$886$	13.7632	0.462385
$887$	−9.91095	−0.332777	−0.166389	−	0.986060i	$-0.553211\pi$
$887$	−9.91095	−0.332777	−0.166389	+	0.986060i	$0.553211\pi$
$888$	24.5742	0.824658
$889$	15.0340	0.504225
$890$	−0.314731	−0.0105498
$891$	−2.15082	−0.0720553
$892$	23.0371	0.771338
$893$	53.9308	1.80472
$894$	6.80198	0.227492
$895$	2.87059	0.0959534
$896$	−26.6699	−0.890980
$897$	3.57385	0.119327
$898$	−5.27601	−0.176063
$899$	8.48054	0.282842
$900$	7.59507	0.253169
$901$	−2.06189	−0.0686916
$902$	11.4909	0.382606
$903$	10.8494	0.361046
$904$	−4.74446	−0.157798
$905$	2.03335	0.0675907
$906$	−3.01975	−0.100324
$907$	−50.3979	−1.67343	−0.836717	−	0.547635i	$-0.815528\pi$
$907$	−50.3979	−1.67343	−0.836717	+	0.547635i	$0.815528\pi$
$908$	43.8544	1.45536
$909$	1.59818	0.0530083
$910$	−1.66442	−0.0551751
$911$	25.3433	0.839662	0.419831	−	0.907602i	$-0.362089\pi$
$911$	25.3433	0.839662	0.419831	+	0.907602i	$0.362089\pi$
$912$	13.1476	0.435362
$913$	19.4201	0.642710
$914$	−6.93824	−0.229497
$915$	2.53916	0.0839420
$916$	32.4132	1.07096
$917$	−24.3437	−0.803898
$918$	−0.656002	−0.0216513
$919$	−7.02061	−0.231589	−0.115794	−	0.993273i	$-0.536941\pi$
$919$	−7.02061	−0.231589	−0.115794	+	0.993273i	$0.536941\pi$
$920$	−1.27795	−0.0421329
$921$	−19.0379	−0.627319
$922$	24.1999	0.796981
$923$	20.9063	0.688139
$924$	−8.10765	−0.266722
$925$	−50.7778	−1.66956
$926$	19.2713	0.633296
$927$	7.27925	0.239082
$928$	33.8377	1.11078
$929$	−23.0222	−0.755334	−0.377667	−	0.925942i	$-0.623274\pi$
$929$	−23.0222	−0.755334	−0.377667	+	0.925942i	$0.623274\pi$
$930$	0.378729	0.0124190
$931$	−10.1099	−0.331340
$932$	−9.76034	−0.319711
$933$	−24.6416	−0.806730
$934$	6.57648	0.215189
$935$	−0.863904	−0.0282527
$936$	−6.15951	−0.201330
$937$	−11.0709	−0.361671	−0.180836	−	0.983513i	$-0.557880\pi$
$937$	−11.0709	−0.361671	−0.180836	+	0.983513i	$0.557880\pi$
$938$	−13.5572	−0.442658
$939$	27.3929	0.893934
$940$	−4.14604	−0.135229
$941$	−20.1002	−0.655248	−0.327624	−	0.944808i	$-0.606248\pi$
$941$	−20.1002	−0.655248	−0.327624	+	0.944808i	$0.606248\pi$
$942$	0.656002	0.0213737
$943$	−11.0654	−0.360339
$944$	17.1149	0.557044
$945$	−0.964596	−0.0313783
$946$	−6.37429	−0.207246
$947$	17.4806	0.568042	0.284021	−	0.958818i	$-0.408331\pi$
$947$	17.4806	0.568042	0.284021	+	0.958818i	$0.408331\pi$
$948$	−8.81088	−0.286164
$949$	32.9567	1.06982
$950$	26.0316	0.844578
$951$	−21.7353	−0.704816
$952$	−5.62362	−0.182263
$953$	−46.8359	−1.51716	−0.758582	−	0.651577i	$-0.774108\pi$
$953$	−46.8359	−1.51716	−0.758582	+	0.651577i	$0.774108\pi$
$954$	1.35261	0.0437922
$955$	−3.59893	−0.116459
$956$	0.181487	0.00586970
$957$	12.6901	0.410214
$958$	4.95293	0.160022
$959$	−7.55377	−0.243924
$960$	0.223286	0.00720651
$961$	−28.9340	−0.933356
$962$	18.1079	0.583821
$963$	−5.92750	−0.191011
$964$	0.875683	0.0282039
$965$	−7.17872	−0.231091
$966$	−2.14048	−0.0688688
$967$	−38.3543	−1.23339	−0.616695	−	0.787202i	$-0.711529\pi$
$967$	−38.3543	−1.23339	−0.616695	+	0.787202i	$0.711529\pi$
$968$	−14.9259	−0.479738
$969$	8.20108	0.263457
$970$	−0.700243	−0.0224834
$971$	−24.5641	−0.788301	−0.394150	−	0.919046i	$-0.628961\pi$
$971$	−24.5641	−0.788301	−0.394150	+	0.919046i	$0.628961\pi$
$972$	−1.56966	−0.0503469
$973$	−4.47830	−0.143568
$974$	3.03483	0.0972424
$975$	12.7274	0.407603
$976$	10.1346	0.324400
$977$	−9.96778	−0.318898	−0.159449	−	0.987206i	$-0.550972\pi$
$977$	−9.96778	−0.318898	−0.159449	+	0.987206i	$0.550972\pi$
$978$	6.28556	0.200990
$979$	−2.56908	−0.0821082
$980$	0.777221	0.0248274
$981$	10.7482	0.343164
$982$	5.75154	0.183539
$983$	5.87005	0.187226	0.0936128	−	0.995609i	$-0.470158\pi$
$983$	5.87005	0.187226	0.0936128	+	0.995609i	$0.470158\pi$
$984$	19.0712	0.607967
$985$	−1.03891	−0.0331024
$986$	3.87049	0.123262
$987$	−15.7925	−0.502680
$988$	33.8603	1.07724
$989$	6.13825	0.195185
$990$	0.566723	0.0180116
$991$	−10.9230	−0.346981	−0.173491	−	0.984836i	$-0.555505\pi$
$991$	−10.9230	−0.346981	−0.173491	+	0.984836i	$0.555505\pi$
$992$	8.24331	0.261725
$993$	3.83082	0.121567
$994$	−12.5214	−0.397154
$995$	−3.35364	−0.106318
$996$	14.1727	0.449078
$997$	−25.5616	−0.809543	−0.404772	−	0.914418i	$-0.632649\pi$
$997$	−25.5616	−0.809543	−0.404772	+	0.914418i	$0.632649\pi$
$998$	−6.74188	−0.213411
$999$	10.4942	0.332021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-0.656002 q^{2} +1.00000 q^{3} -1.56966 q^{4} +0.401662 q^{5} -0.656002 q^{6} -2.40151 q^{7} +2.34170 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.656002 q^{2} +1.00000 q^{3} -1.56966 q^{4} +0.401662 q^{5} -0.656002 q^{6} -2.40151 q^{7} +2.34170 q^{8} +1.00000 q^{9} -0.263491 q^{10} -2.15082 q^{11} -1.56966 q^{12} -2.63035 q^{13} +1.57539 q^{14} +0.401662 q^{15} +1.60316 q^{16} +1.00000 q^{17} -0.656002 q^{18} +8.20108 q^{19} -0.630474 q^{20} -2.40151 q^{21} +1.41094 q^{22} -1.35869 q^{23} +2.34170 q^{24} -4.83867 q^{25} +1.72552 q^{26} +1.00000 q^{27} +3.76956 q^{28} -5.90013 q^{29} -0.263491 q^{30} -1.43735 q^{31} -5.73509 q^{32} -2.15082 q^{33} -0.656002 q^{34} -0.964596 q^{35} -1.56966 q^{36} +10.4942 q^{37} -5.37992 q^{38} -2.63035 q^{39} +0.940575 q^{40} +8.14415 q^{41} +1.57539 q^{42} -4.51775 q^{43} +3.37606 q^{44} +0.401662 q^{45} +0.891306 q^{46} +6.57606 q^{47} +1.60316 q^{48} -1.23276 q^{49} +3.17417 q^{50} +1.00000 q^{51} +4.12876 q^{52} -2.06189 q^{53} -0.656002 q^{54} -0.863904 q^{55} -5.62362 q^{56} +8.20108 q^{57} +3.87049 q^{58} +10.6757 q^{59} -0.630474 q^{60} +6.32162 q^{61} +0.942903 q^{62} -2.40151 q^{63} +0.555904 q^{64} -1.05651 q^{65} +1.41094 q^{66} -8.60559 q^{67} -1.56966 q^{68} -1.35869 q^{69} +0.632776 q^{70} -7.94810 q^{71} +2.34170 q^{72} -12.5294 q^{73} -6.88419 q^{74} -4.83867 q^{75} -12.8729 q^{76} +5.16522 q^{77} +1.72552 q^{78} +5.61323 q^{79} +0.643930 q^{80} +1.00000 q^{81} -5.34258 q^{82} -9.02913 q^{83} +3.76956 q^{84} +0.401662 q^{85} +2.96365 q^{86} -5.90013 q^{87} -5.03659 q^{88} +1.19446 q^{89} -0.263491 q^{90} +6.31681 q^{91} +2.13269 q^{92} -1.43735 q^{93} -4.31391 q^{94} +3.29406 q^{95} -5.73509 q^{96} +2.65756 q^{97} +0.808691 q^{98} -2.15082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 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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