LMFDB - Embedded newform 8041.2.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73828 q^{2} +2.71256 q^{3} +1.02162 q^{4} -1.00305 q^{5} -4.71518 q^{6} +1.91856 q^{7} +1.70071 q^{8} +4.35796 q^{9} +O(q^{10})$	\(q-1.73828 q^{2} +2.71256 q^{3} +1.02162 q^{4} -1.00305 q^{5} -4.71518 q^{6} +1.91856 q^{7} +1.70071 q^{8} +4.35796 q^{9} +1.74357 q^{10} +1.00000 q^{11} +2.77119 q^{12} +6.51880 q^{13} -3.33500 q^{14} -2.72082 q^{15} -4.99953 q^{16} +1.00000 q^{17} -7.57536 q^{18} -0.645703 q^{19} -1.02473 q^{20} +5.20421 q^{21} -1.73828 q^{22} +4.75758 q^{23} +4.61326 q^{24} -3.99390 q^{25} -11.3315 q^{26} +3.68355 q^{27} +1.96003 q^{28} +6.97508 q^{29} +4.72954 q^{30} +5.23359 q^{31} +5.28917 q^{32} +2.71256 q^{33} -1.73828 q^{34} -1.92441 q^{35} +4.45216 q^{36} -0.654072 q^{37} +1.12241 q^{38} +17.6826 q^{39} -1.70589 q^{40} +9.47139 q^{41} -9.04637 q^{42} +1.00000 q^{43} +1.02162 q^{44} -4.37124 q^{45} -8.27000 q^{46} +1.37344 q^{47} -13.5615 q^{48} -3.31912 q^{49} +6.94251 q^{50} +2.71256 q^{51} +6.65971 q^{52} -3.32487 q^{53} -6.40304 q^{54} -1.00305 q^{55} +3.26291 q^{56} -1.75151 q^{57} -12.1246 q^{58} -6.00887 q^{59} -2.77963 q^{60} -0.664019 q^{61} -9.09744 q^{62} +8.36103 q^{63} +0.805005 q^{64} -6.53865 q^{65} -4.71518 q^{66} +12.9481 q^{67} +1.02162 q^{68} +12.9052 q^{69} +3.34515 q^{70} -12.9188 q^{71} +7.41161 q^{72} +1.15650 q^{73} +1.13696 q^{74} -10.8337 q^{75} -0.659660 q^{76} +1.91856 q^{77} -30.7373 q^{78} +10.1389 q^{79} +5.01476 q^{80} -3.08204 q^{81} -16.4639 q^{82} -15.9249 q^{83} +5.31670 q^{84} -1.00305 q^{85} -1.73828 q^{86} +18.9203 q^{87} +1.70071 q^{88} +12.1599 q^{89} +7.59843 q^{90} +12.5067 q^{91} +4.86042 q^{92} +14.1964 q^{93} -2.38742 q^{94} +0.647670 q^{95} +14.3472 q^{96} -2.72699 q^{97} +5.76955 q^{98} +4.35796 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.73828	−1.22915	−0.614575	−	0.788859i	$-0.710672\pi$
$2$	−1.73828	−1.22915	−0.614575	+	0.788859i	$0.710672\pi$
$3$	2.71256	1.56610	0.783048	−	0.621962i	$-0.213664\pi$
$3$	2.71256	1.56610	0.783048	+	0.621962i	$0.213664\pi$
$4$	1.02162	0.510808
$5$	−1.00305	−0.448576	−0.224288	−	0.974523i	$-0.572006\pi$
$5$	−1.00305	−0.448576	−0.224288	+	0.974523i	$0.572006\pi$
$6$	−4.71518	−1.92496
$7$	1.91856	0.725149	0.362574	−	0.931955i	$-0.381898\pi$
$7$	1.91856	0.725149	0.362574	+	0.931955i	$0.381898\pi$
$8$	1.70071	0.601290
$9$	4.35796	1.45265
$10$	1.74357	0.551366
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.77119	0.799974
$13$	6.51880	1.80799	0.903995	−	0.427543i	$-0.140621\pi$
$13$	6.51880	1.80799	0.903995	+	0.427543i	$0.140621\pi$
$14$	−3.33500	−0.891316
$15$	−2.72082	−0.702512
$16$	−4.99953	−1.24988
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−7.57536	−1.78553
$19$	−0.645703	−0.148135	−0.0740673	−	0.997253i	$-0.523598\pi$
$19$	−0.645703	−0.148135	−0.0740673	+	0.997253i	$0.523598\pi$
$20$	−1.02473	−0.229136
$21$	5.20421	1.13565
$22$	−1.73828	−0.370602
$23$	4.75758	0.992024	0.496012	−	0.868316i	$-0.334797\pi$
$23$	4.75758	0.992024	0.496012	+	0.868316i	$0.334797\pi$
$24$	4.61326	0.941678
$25$	−3.99390	−0.798780
$26$	−11.3315	−2.22229
$27$	3.68355	0.708900
$28$	1.96003	0.370411
$29$	6.97508	1.29524	0.647620	−	0.761964i	$-0.275765\pi$
$29$	6.97508	1.29524	0.647620	+	0.761964i	$0.275765\pi$
$30$	4.72954	0.863492
$31$	5.23359	0.939980	0.469990	−	0.882672i	$-0.344257\pi$
$31$	5.23359	0.939980	0.469990	+	0.882672i	$0.344257\pi$
$32$	5.28917	0.935003
$33$	2.71256	0.472195
$34$	−1.73828	−0.298112
$35$	−1.92441	−0.325284
$36$	4.45216	0.742027
$37$	−0.654072	−0.107529	−0.0537644	−	0.998554i	$-0.517122\pi$
$37$	−0.654072	−0.107529	−0.0537644	+	0.998554i	$0.517122\pi$
$38$	1.12241	0.182079
$39$	17.6826	2.83149
$40$	−1.70589	−0.269724
$41$	9.47139	1.47918	0.739591	−	0.673056i	$-0.235019\pi$
$41$	9.47139	1.47918	0.739591	+	0.673056i	$0.235019\pi$
$42$	−9.04637	−1.39589
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.02162	0.154014
$45$	−4.37124	−0.651625
$46$	−8.27000	−1.21935
$47$	1.37344	0.200336	0.100168	−	0.994971i	$-0.468062\pi$
$47$	1.37344	0.200336	0.100168	+	0.994971i	$0.468062\pi$
$48$	−13.5615	−1.95744
$49$	−3.31912	−0.474160
$50$	6.94251	0.981820
$51$	2.71256	0.379834
$52$	6.65971	0.923535
$53$	−3.32487	−0.456706	−0.228353	−	0.973578i	$-0.573334\pi$
$53$	−3.32487	−0.456706	−0.228353	+	0.973578i	$0.573334\pi$
$54$	−6.40304	−0.871344
$55$	−1.00305	−0.135251
$56$	3.26291	0.436025
$57$	−1.75151	−0.231993
$58$	−12.1246	−1.59204
$59$	−6.00887	−0.782288	−0.391144	−	0.920330i	$-0.627921\pi$
$59$	−6.00887	−0.782288	−0.391144	+	0.920330i	$0.627921\pi$
$60$	−2.77963	−0.358849
$61$	−0.664019	−0.0850189	−0.0425095	−	0.999096i	$-0.513535\pi$
$61$	−0.664019	−0.0850189	−0.0425095	+	0.999096i	$0.513535\pi$
$62$	−9.09744	−1.15538
$63$	8.36103	1.05339
$64$	0.805005	0.100626
$65$	−6.53865	−0.811020
$66$	−4.71518	−0.580399
$67$	12.9481	1.58186	0.790931	−	0.611906i	$-0.209597\pi$
$67$	12.9481	1.58186	0.790931	+	0.611906i	$0.209597\pi$
$68$	1.02162	0.123889
$69$	12.9052	1.55360
$70$	3.34515	0.399822
$71$	−12.9188	−1.53318	−0.766588	−	0.642140i	$-0.778047\pi$
$71$	−12.9188	−1.53318	−0.766588	+	0.642140i	$0.778047\pi$
$72$	7.41161	0.873467
$73$	1.15650	0.135358	0.0676788	−	0.997707i	$-0.478441\pi$
$73$	1.15650	0.135358	0.0676788	+	0.997707i	$0.478441\pi$
$74$	1.13696	0.132169
$75$	−10.8337	−1.25097
$76$	−0.659660	−0.0756682
$77$	1.91856	0.218641
$78$	−30.7373	−3.48032
$79$	10.1389	1.14071	0.570356	−	0.821398i	$-0.306805\pi$
$79$	10.1389	1.14071	0.570356	+	0.821398i	$0.306805\pi$
$80$	5.01476	0.560667
$81$	−3.08204	−0.342449
$82$	−16.4639	−1.81814
$83$	−15.9249	−1.74799	−0.873994	−	0.485938i	$-0.838478\pi$
$83$	−15.9249	−1.74799	−0.873994	+	0.485938i	$0.838478\pi$
$84$	5.31670	0.580100
$85$	−1.00305	−0.108796
$86$	−1.73828	−0.187443
$87$	18.9203	2.02847
$88$	1.70071	0.181296
$89$	12.1599	1.28895	0.644475	−	0.764625i	$-0.277076\pi$
$89$	12.1599	1.28895	0.644475	+	0.764625i	$0.277076\pi$
$90$	7.59843	0.800945
$91$	12.5067	1.31106
$92$	4.86042	0.506734
$93$	14.1964	1.47210
$94$	−2.38742	−0.246243
$95$	0.647670	0.0664495
$96$	14.3472	1.46430
$97$	−2.72699	−0.276884	−0.138442	−	0.990371i	$-0.544209\pi$
$97$	−2.72699	−0.276884	−0.138442	+	0.990371i	$0.544209\pi$
$98$	5.76955	0.582813
$99$	4.35796	0.437992
$100$	−4.08023	−0.408023
$101$	−8.59300	−0.855035	−0.427518	−	0.904007i	$-0.640612\pi$
$101$	−8.59300	−0.855035	−0.427518	+	0.904007i	$0.640612\pi$
$102$	−4.71518	−0.466873
$103$	−13.5679	−1.33688	−0.668440	−	0.743766i	$-0.733038\pi$
$103$	−13.5679	−1.33688	−0.668440	+	0.743766i	$0.733038\pi$
$104$	11.0866	1.08713
$105$	−5.22006	−0.509426
$106$	5.77955	0.561360
$107$	7.34589	0.710154	0.355077	−	0.934837i	$-0.384455\pi$
$107$	7.34589	0.710154	0.355077	+	0.934837i	$0.384455\pi$
$108$	3.76317	0.362112
$109$	−13.4662	−1.28983	−0.644916	−	0.764254i	$-0.723108\pi$
$109$	−13.4662	−1.28983	−0.644916	+	0.764254i	$0.723108\pi$
$110$	1.74357	0.166243
$111$	−1.77421	−0.168400
$112$	−9.59192	−0.906351
$113$	19.2657	1.81237	0.906185	−	0.422882i	$-0.138982\pi$
$113$	19.2657	1.81237	0.906185	+	0.422882i	$0.138982\pi$
$114$	3.04461	0.285154
$115$	−4.77207	−0.444998
$116$	7.12585	0.661618
$117$	28.4087	2.62639
$118$	10.4451	0.961548
$119$	1.91856	0.175874
$120$	−4.62731	−0.422414
$121$	1.00000	0.0909091
$122$	1.15425	0.104501
$123$	25.6917	2.31654
$124$	5.34672	0.480149
$125$	9.02129	0.806889
$126$	−14.5338	−1.29477
$127$	3.91481	0.347383	0.173692	−	0.984800i	$-0.444430\pi$
$127$	3.91481	0.347383	0.173692	+	0.984800i	$0.444430\pi$
$128$	−11.9777	−1.05869
$129$	2.71256	0.238827
$130$	11.3660	0.996865
$131$	−8.42384	−0.735994	−0.367997	−	0.929827i	$-0.619956\pi$
$131$	−8.42384	−0.735994	−0.367997	+	0.929827i	$0.619956\pi$
$132$	2.77119	0.241201
$133$	−1.23882	−0.107420
$134$	−22.5074	−1.94434
$135$	−3.69477	−0.317995
$136$	1.70071	0.145834
$137$	16.7671	1.43251	0.716253	−	0.697841i	$-0.245856\pi$
$137$	16.7671	1.43251	0.716253	+	0.697841i	$0.245856\pi$
$138$	−22.4329	−1.90961
$139$	18.7394	1.58945	0.794726	−	0.606968i	$-0.207615\pi$
$139$	18.7394	1.58945	0.794726	+	0.606968i	$0.207615\pi$
$140$	−1.96600	−0.166158
$141$	3.72552	0.313746
$142$	22.4564	1.88450
$143$	6.51880	0.545130
$144$	−21.7878	−1.81565
$145$	−6.99632	−0.581013
$146$	−2.01031	−0.166375
$147$	−9.00329	−0.742579
$148$	−0.668210	−0.0549265
$149$	−13.6632	−1.11933	−0.559665	−	0.828719i	$-0.689070\pi$
$149$	−13.6632	−1.11933	−0.559665	+	0.828719i	$0.689070\pi$
$150$	18.8320	1.53762
$151$	5.01324	0.407972	0.203986	−	0.978974i	$-0.434610\pi$
$151$	5.01324	0.407972	0.203986	+	0.978974i	$0.434610\pi$
$152$	−1.09815	−0.0890718
$153$	4.35796	0.352320
$154$	−3.33500	−0.268742
$155$	−5.24953	−0.421652
$156$	18.0648	1.44634
$157$	−22.6278	−1.80589	−0.902946	−	0.429753i	$-0.858601\pi$
$157$	−22.6278	−1.80589	−0.902946	+	0.429753i	$0.858601\pi$
$158$	−17.6242	−1.40211
$159$	−9.01890	−0.715245
$160$	−5.30528	−0.419419
$161$	9.12772	0.719365
$162$	5.35746	0.420921
$163$	−17.2810	−1.35355	−0.676777	−	0.736188i	$-0.736624\pi$
$163$	−17.2810	−1.35355	−0.676777	+	0.736188i	$0.736624\pi$
$164$	9.67612	0.755578
$165$	−2.72082	−0.211815
$166$	27.6820	2.14854
$167$	−13.1928	−1.02089	−0.510444	−	0.859911i	$-0.670519\pi$
$167$	−13.1928	−1.02089	−0.510444	+	0.859911i	$0.670519\pi$
$168$	8.85083	0.682856
$169$	29.4948	2.26883
$170$	1.74357	0.133726
$171$	−2.81395	−0.215188
$172$	1.02162	0.0778974
$173$	−2.00093	−0.152128	−0.0760638	−	0.997103i	$-0.524235\pi$
$173$	−2.00093	−0.152128	−0.0760638	+	0.997103i	$0.524235\pi$
$174$	−32.8888	−2.49329
$175$	−7.66255	−0.579234
$176$	−4.99953	−0.376854
$177$	−16.2994	−1.22514
$178$	−21.1374	−1.58431
$179$	3.38728	0.253177	0.126589	−	0.991955i	$-0.459597\pi$
$179$	3.38728	0.253177	0.126589	+	0.991955i	$0.459597\pi$
$180$	−4.46572	−0.332855
$181$	−2.97143	−0.220865	−0.110432	−	0.993884i	$-0.535224\pi$
$181$	−2.97143	−0.220865	−0.110432	+	0.993884i	$0.535224\pi$
$182$	−21.7402	−1.61149
$183$	−1.80119	−0.133148
$184$	8.09125	0.596495
$185$	0.656064	0.0482348
$186$	−24.6773	−1.80943
$187$	1.00000	0.0731272
$188$	1.40312	0.102333
$189$	7.06713	0.514058
$190$	−1.12583	−0.0816764
$191$	26.6453	1.92799	0.963993	−	0.265928i	$-0.0856782\pi$
$191$	26.6453	1.92799	0.963993	+	0.265928i	$0.0856782\pi$
$192$	2.18362	0.157589
$193$	−4.80106	−0.345588	−0.172794	−	0.984958i	$-0.555279\pi$
$193$	−4.80106	−0.345588	−0.172794	+	0.984958i	$0.555279\pi$
$194$	4.74028	0.340332
$195$	−17.7365	−1.27014
$196$	−3.39086	−0.242204
$197$	−6.94457	−0.494780	−0.247390	−	0.968916i	$-0.579573\pi$
$197$	−6.94457	−0.494780	−0.247390	+	0.968916i	$0.579573\pi$
$198$	−7.57536	−0.538357
$199$	−15.0763	−1.06873	−0.534366	−	0.845253i	$-0.679449\pi$
$199$	−15.0763	−1.06873	−0.534366	+	0.845253i	$0.679449\pi$
$200$	−6.79245	−0.480299
$201$	35.1224	2.47735
$202$	14.9370	1.05097
$203$	13.3821	0.939241
$204$	2.77119	0.194022
$205$	−9.50023	−0.663525
$206$	23.5847	1.64323
$207$	20.7334	1.44107
$208$	−32.5910	−2.25978
$209$	−0.645703	−0.0446642
$210$	9.07392	0.626160
$211$	−20.5176	−1.41249	−0.706245	−	0.707967i	$-0.749613\pi$
$211$	−20.5176	−1.41249	−0.706245	+	0.707967i	$0.749613\pi$
$212$	−3.39674	−0.233289
$213$	−35.0429	−2.40110
$214$	−12.7692	−0.872885
$215$	−1.00305	−0.0684071
$216$	6.26464	0.426255
$217$	10.0410	0.681625
$218$	23.4081	1.58540
$219$	3.13706	0.211983
$220$	−1.02473	−0.0690871
$221$	6.51880	0.438502
$222$	3.08407	0.206989
$223$	16.6898	1.11763	0.558815	−	0.829292i	$-0.311256\pi$
$223$	16.6898	1.11763	0.558815	+	0.829292i	$0.311256\pi$
$224$	10.1476	0.678016
$225$	−17.4053	−1.16035
$226$	−33.4893	−2.22767
$227$	−5.94499	−0.394583	−0.197291	−	0.980345i	$-0.563214\pi$
$227$	−5.94499	−0.394583	−0.197291	+	0.980345i	$0.563214\pi$
$228$	−1.78937	−0.118504
$229$	−25.5371	−1.68754	−0.843768	−	0.536708i	$-0.819668\pi$
$229$	−25.5371	−1.68754	−0.843768	+	0.536708i	$0.819668\pi$
$230$	8.29519	0.546969
$231$	5.20421	0.342412
$232$	11.8626	0.778815
$233$	18.3218	1.20030	0.600150	−	0.799888i	$-0.295108\pi$
$233$	18.3218	1.20030	0.600150	+	0.799888i	$0.295108\pi$
$234$	−49.3823	−3.22822
$235$	−1.37762	−0.0898659
$236$	−6.13875	−0.399599
$237$	27.5023	1.78646
$238$	−3.33500	−0.216176
$239$	−1.51527	−0.0980149	−0.0490074	−	0.998798i	$-0.515606\pi$
$239$	−1.51527	−0.0980149	−0.0490074	+	0.998798i	$0.515606\pi$
$240$	13.6028	0.878058
$241$	−6.25007	−0.402602	−0.201301	−	0.979529i	$-0.564517\pi$
$241$	−6.25007	−0.402602	−0.201301	+	0.979529i	$0.564517\pi$
$242$	−1.73828	−0.111741
$243$	−19.4109	−1.24521
$244$	−0.678372	−0.0434283
$245$	3.32923	0.212696
$246$	−44.6593	−2.84737
$247$	−4.20921	−0.267826
$248$	8.90080	0.565201
$249$	−43.1972	−2.73751
$250$	−15.6815	−0.991787
$251$	−14.2921	−0.902107	−0.451053	−	0.892497i	$-0.648952\pi$
$251$	−14.2921	−0.902107	−0.451053	+	0.892497i	$0.648952\pi$
$252$	8.54175	0.538080
$253$	4.75758	0.299107
$254$	−6.80503	−0.426986
$255$	−2.72082	−0.170384
$256$	19.2105	1.20066
$257$	−19.6832	−1.22781	−0.613903	−	0.789382i	$-0.710401\pi$
$257$	−19.6832	−1.22781	−0.613903	+	0.789382i	$0.710401\pi$
$258$	−4.71518	−0.293554
$259$	−1.25488	−0.0779743
$260$	−6.67999	−0.414275
$261$	30.3971	1.88154
$262$	14.6430	0.904647
$263$	−18.1031	−1.11629	−0.558143	−	0.829745i	$-0.688486\pi$
$263$	−18.1031	−1.11629	−0.558143	+	0.829745i	$0.688486\pi$
$264$	4.61326	0.283927
$265$	3.33500	0.204867
$266$	2.15342	0.132035
$267$	32.9845	2.01862
$268$	13.2280	0.808027
$269$	1.47461	0.0899086	0.0449543	−	0.998989i	$-0.485686\pi$
$269$	1.47461	0.0899086	0.0449543	+	0.998989i	$0.485686\pi$
$270$	6.42254	0.390864
$271$	−8.97382	−0.545121	−0.272560	−	0.962139i	$-0.587870\pi$
$271$	−8.97382	−0.545121	−0.272560	+	0.962139i	$0.587870\pi$
$272$	−4.99953	−0.303141
$273$	33.9252	2.05325
$274$	−29.1458	−1.76076
$275$	−3.99390	−0.240841
$276$	13.1842	0.793593
$277$	14.9936	0.900879	0.450439	−	0.892807i	$-0.351267\pi$
$277$	14.9936	0.900879	0.450439	+	0.892807i	$0.351267\pi$
$278$	−32.5742	−1.95367
$279$	22.8078	1.36547
$280$	−3.27285	−0.195590
$281$	20.9991	1.25270	0.626349	−	0.779542i	$-0.284548\pi$
$281$	20.9991	1.25270	0.626349	+	0.779542i	$0.284548\pi$
$282$	−6.47600	−0.385640
$283$	12.6634	0.752762	0.376381	−	0.926465i	$-0.377168\pi$
$283$	12.6634	0.752762	0.376381	+	0.926465i	$0.377168\pi$
$284$	−13.1980	−0.783158
$285$	1.75684	0.104066
$286$	−11.3315	−0.670046
$287$	18.1715	1.07263
$288$	23.0500	1.35824
$289$	1.00000	0.0588235
$290$	12.1616	0.714151
$291$	−7.39712	−0.433627
$292$	1.18149	0.0691417
$293$	−16.8401	−0.983809	−0.491904	−	0.870649i	$-0.663699\pi$
$293$	−16.8401	−0.983809	−0.491904	+	0.870649i	$0.663699\pi$
$294$	15.6502	0.912740
$295$	6.02717	0.350915
$296$	−1.11238	−0.0646560
$297$	3.68355	0.213741
$298$	23.7504	1.37582
$299$	31.0137	1.79357
$300$	−11.0679	−0.639003
$301$	1.91856	0.110584
$302$	−8.71441	−0.501458
$303$	−23.3090	−1.33907
$304$	3.22821	0.185151
$305$	0.666041	0.0381374
$306$	−7.57536	−0.433054
$307$	−11.2413	−0.641578	−0.320789	−	0.947151i	$-0.603948\pi$
$307$	−11.2413	−0.641578	−0.320789	+	0.947151i	$0.603948\pi$
$308$	1.96003	0.111683
$309$	−36.8036	−2.09368
$310$	9.12515	0.518274
$311$	5.57659	0.316219	0.158110	−	0.987422i	$-0.449460\pi$
$311$	5.57659	0.316219	0.158110	+	0.987422i	$0.449460\pi$
$312$	30.0729	1.70254
$313$	−27.9294	−1.57866	−0.789331	−	0.613967i	$-0.789573\pi$
$313$	−27.9294	−1.57866	−0.789331	+	0.613967i	$0.789573\pi$
$314$	39.3334	2.21971
$315$	−8.38649	−0.472525
$316$	10.3580	0.582684
$317$	34.2628	1.92439	0.962194	−	0.272364i	$-0.0878055\pi$
$317$	34.2628	1.92439	0.962194	+	0.272364i	$0.0878055\pi$
$318$	15.6774	0.879143
$319$	6.97508	0.390529
$320$	−0.807456	−0.0451382
$321$	19.9261	1.11217
$322$	−15.8665	−0.884207
$323$	−0.645703	−0.0359279
$324$	−3.14866	−0.174926
$325$	−26.0354	−1.44419
$326$	30.0392	1.66372
$327$	−36.5279	−2.02000
$328$	16.1080	0.889418
$329$	2.63502	0.145274
$330$	4.72954	0.260353
$331$	3.43714	0.188922	0.0944610	−	0.995529i	$-0.469887\pi$
$331$	3.43714	0.188922	0.0944610	+	0.995529i	$0.469887\pi$
$332$	−16.2691	−0.892885
$333$	−2.85042	−0.156202
$334$	22.9327	1.25482
$335$	−12.9875	−0.709584
$336$	−26.0186	−1.41943
$337$	−0.346351	−0.0188669	−0.00943346	−	0.999956i	$-0.503003\pi$
$337$	−0.346351	−0.0188669	−0.00943346	+	0.999956i	$0.503003\pi$
$338$	−51.2702	−2.78873
$339$	52.2594	2.83834
$340$	−1.02473	−0.0555736
$341$	5.23359	0.283415
$342$	4.89143	0.264498
$343$	−19.7979	−1.06898
$344$	1.70071	0.0916959
$345$	−12.9445	−0.696909
$346$	3.47817	0.186988
$347$	35.3760	1.89908	0.949542	−	0.313640i	$-0.101549\pi$
$347$	35.3760	1.89908	0.949542	+	0.313640i	$0.101549\pi$
$348$	19.3293	1.03616
$349$	−8.72306	−0.466934	−0.233467	−	0.972365i	$-0.575007\pi$
$349$	−8.72306	−0.466934	−0.233467	+	0.972365i	$0.575007\pi$
$350$	13.3196	0.711965
$351$	24.0123	1.28168
$352$	5.28917	0.281914
$353$	7.34047	0.390694	0.195347	−	0.980734i	$-0.437417\pi$
$353$	7.34047	0.390694	0.195347	+	0.980734i	$0.437417\pi$
$354$	28.3329	1.50588
$355$	12.9581	0.687745
$356$	12.4228	0.658406
$357$	5.20421	0.275436
$358$	−5.88804	−0.311193
$359$	−3.09087	−0.163130	−0.0815650	−	0.996668i	$-0.525992\pi$
$359$	−3.09087	−0.163130	−0.0815650	+	0.996668i	$0.525992\pi$
$360$	−7.43419	−0.391816
$361$	−18.5831	−0.978056
$362$	5.16518	0.271476
$363$	2.71256	0.142372
$364$	12.7771	0.669700
$365$	−1.16002	−0.0607182
$366$	3.13097	0.163658
$367$	26.5980	1.38840	0.694201	−	0.719781i	$-0.255758\pi$
$367$	26.5980	1.38840	0.694201	+	0.719781i	$0.255758\pi$
$368$	−23.7857	−1.23991
$369$	41.2760	2.14874
$370$	−1.14042	−0.0592877
$371$	−6.37897	−0.331180
$372$	14.5033	0.751959
$373$	−37.6039	−1.94706	−0.973529	−	0.228565i	$-0.926597\pi$
$373$	−37.6039	−1.94706	−0.973529	+	0.228565i	$0.926597\pi$
$374$	−1.73828	−0.0898843
$375$	24.4708	1.26366
$376$	2.33581	0.120460
$377$	45.4692	2.34178
$378$	−12.2846	−0.631854
$379$	7.62421	0.391629	0.195815	−	0.980641i	$-0.437265\pi$
$379$	7.62421	0.391629	0.195815	+	0.980641i	$0.437265\pi$
$380$	0.661669	0.0339429
$381$	10.6191	0.544035
$382$	−46.3170	−2.36978
$383$	33.7237	1.72320	0.861601	−	0.507586i	$-0.169462\pi$
$383$	33.7237	1.72320	0.861601	+	0.507586i	$0.169462\pi$
$384$	−32.4901	−1.65800
$385$	−1.92441	−0.0980768
$386$	8.34559	0.424779
$387$	4.35796	0.221528
$388$	−2.78594	−0.141435
$389$	24.4515	1.23974	0.619871	−	0.784704i	$-0.287185\pi$
$389$	24.4515	1.23974	0.619871	+	0.784704i	$0.287185\pi$
$390$	30.8309	1.56119
$391$	4.75758	0.240601
$392$	−5.64484	−0.285108
$393$	−22.8501	−1.15264
$394$	12.0716	0.608159
$395$	−10.1697	−0.511696
$396$	4.45216	0.223730
$397$	0.404617	0.0203072	0.0101536	−	0.999948i	$-0.496768\pi$
$397$	0.404617	0.0203072	0.0101536	+	0.999948i	$0.496768\pi$
$398$	26.2068	1.31363
$399$	−3.36038	−0.168229
$400$	19.9676	0.998382
$401$	23.5867	1.17786	0.588931	−	0.808184i	$-0.299549\pi$
$401$	23.5867	1.17786	0.588931	+	0.808184i	$0.299549\pi$
$402$	−61.0526	−3.04503
$403$	34.1167	1.69948
$404$	−8.77874	−0.436759
$405$	3.09143	0.153614
$406$	−23.2619	−1.15447
$407$	−0.654072	−0.0324211
$408$	4.61326	0.228390
$409$	18.7932	0.929265	0.464633	−	0.885504i	$-0.346186\pi$
$409$	18.7932	0.929265	0.464633	+	0.885504i	$0.346186\pi$
$410$	16.5141	0.815571
$411$	45.4816	2.24344
$412$	−13.8611	−0.682889
$413$	−11.5284	−0.567275
$414$	−36.0404	−1.77129
$415$	15.9734	0.784104
$416$	34.4791	1.69048
$417$	50.8316	2.48923
$418$	1.12241	0.0548990
$419$	−4.88463	−0.238630	−0.119315	−	0.992856i	$-0.538070\pi$
$419$	−4.88463	−0.238630	−0.119315	+	0.992856i	$0.538070\pi$
$420$	−5.33289	−0.260219
$421$	−16.4314	−0.800815	−0.400408	−	0.916337i	$-0.631131\pi$
$421$	−16.4314	−0.800815	−0.400408	+	0.916337i	$0.631131\pi$
$422$	35.6654	1.73616
$423$	5.98538	0.291019
$424$	−5.65463	−0.274613
$425$	−3.99390	−0.193733
$426$	60.9143	2.95131
$427$	−1.27396	−0.0616513
$428$	7.50468	0.362752
$429$	17.6826	0.853725
$430$	1.74357	0.0840826
$431$	37.8404	1.82271	0.911354	−	0.411623i	$-0.135038\pi$
$431$	37.8404	1.82271	0.911354	+	0.411623i	$0.135038\pi$
$432$	−18.4160	−0.886042
$433$	−16.3296	−0.784751	−0.392375	−	0.919805i	$-0.628347\pi$
$433$	−16.3296	−0.784751	−0.392375	+	0.919805i	$0.628347\pi$
$434$	−17.4540	−0.837819
$435$	−18.9779	−0.909921
$436$	−13.7573	−0.658856
$437$	−3.07199	−0.146953
$438$	−5.45309	−0.260559
$439$	−13.7765	−0.657514	−0.328757	−	0.944414i	$-0.606630\pi$
$439$	−13.7765	−0.657514	−0.328757	+	0.944414i	$0.606630\pi$
$440$	−1.70589	−0.0813249
$441$	−14.4646	−0.688790
$442$	−11.3315	−0.538984
$443$	7.54597	0.358520	0.179260	−	0.983802i	$-0.442630\pi$
$443$	7.54597	0.358520	0.179260	+	0.983802i	$0.442630\pi$
$444$	−1.81256	−0.0860201
$445$	−12.1970	−0.578191
$446$	−29.0115	−1.37373
$447$	−37.0621	−1.75298
$448$	1.54445	0.0729685
$449$	10.0748	0.475461	0.237730	−	0.971331i	$-0.423597\pi$
$449$	10.0748	0.475461	0.237730	+	0.971331i	$0.423597\pi$
$450$	30.2552	1.42624
$451$	9.47139	0.445990
$452$	19.6822	0.925772
$453$	13.5987	0.638922
$454$	10.3340	0.485001
$455$	−12.5448	−0.588110
$456$	−2.97880	−0.139495
$457$	14.8430	0.694327	0.347163	−	0.937805i	$-0.387145\pi$
$457$	14.8430	0.694327	0.347163	+	0.937805i	$0.387145\pi$
$458$	44.3905	2.07423
$459$	3.68355	0.171934
$460$	−4.87522	−0.227308
$461$	3.00223	0.139828	0.0699139	−	0.997553i	$-0.477728\pi$
$461$	3.00223	0.139828	0.0699139	+	0.997553i	$0.477728\pi$
$462$	−9.04637	−0.420875
$463$	−7.04016	−0.327184	−0.163592	−	0.986528i	$-0.552308\pi$
$463$	−7.04016	−0.327184	−0.163592	+	0.986528i	$0.552308\pi$
$464$	−34.8721	−1.61890
$465$	−14.2396	−0.660348
$466$	−31.8484	−1.47535
$467$	−32.8334	−1.51935	−0.759675	−	0.650303i	$-0.774642\pi$
$467$	−32.8334	−1.51935	−0.759675	+	0.650303i	$0.774642\pi$
$468$	29.0228	1.34158
$469$	24.8417	1.14708
$470$	2.39469	0.110459
$471$	−61.3791	−2.82820
$472$	−10.2193	−0.470382
$473$	1.00000	0.0459800
$474$	−47.8066	−2.19583
$475$	2.57887	0.118327
$476$	1.96003	0.0898380
$477$	−14.4897	−0.663436
$478$	2.63397	0.120475
$479$	−34.1397	−1.55988	−0.779942	−	0.625851i	$-0.784752\pi$
$479$	−34.1397	−1.55988	−0.779942	+	0.625851i	$0.784752\pi$
$480$	−14.3909	−0.656851
$481$	−4.26376	−0.194411
$482$	10.8644	0.494858
$483$	24.7594	1.12659
$484$	1.02162	0.0464371
$485$	2.73530	0.124203
$486$	33.7415	1.53055
$487$	28.1357	1.27495	0.637476	−	0.770471i	$-0.279979\pi$
$487$	28.1357	1.27495	0.637476	+	0.770471i	$0.279979\pi$
$488$	−1.12930	−0.0511211
$489$	−46.8758	−2.11980
$490$	−5.78712	−0.261436
$491$	−30.6172	−1.38174	−0.690868	−	0.722981i	$-0.742772\pi$
$491$	−30.6172	−1.38174	−0.690868	+	0.722981i	$0.742772\pi$
$492$	26.2470	1.18331
$493$	6.97508	0.314142
$494$	7.31679	0.329198
$495$	−4.37124	−0.196472
$496$	−26.1655	−1.17487
$497$	−24.7855	−1.11178
$498$	75.0889	3.36481
$499$	−10.2086	−0.457001	−0.228501	−	0.973544i	$-0.573382\pi$
$499$	−10.2086	−0.457001	−0.228501	+	0.973544i	$0.573382\pi$
$500$	9.21629	0.412165
$501$	−35.7862	−1.59881
$502$	24.8436	1.10882
$503$	35.4049	1.57863	0.789313	−	0.613991i	$-0.210437\pi$
$503$	35.4049	1.57863	0.789313	+	0.613991i	$0.210437\pi$
$504$	14.2196	0.633393
$505$	8.61917	0.383548
$506$	−8.27000	−0.367647
$507$	80.0062	3.55320
$508$	3.99943	0.177446
$509$	0.0822089	0.00364384	0.00182192	−	0.999998i	$-0.499420\pi$
$509$	0.0822089	0.00364384	0.00182192	+	0.999998i	$0.499420\pi$
$510$	4.72954	0.209428
$511$	2.21881	0.0981544
$512$	−9.43793	−0.417101
$513$	−2.37848	−0.105013
$514$	34.2149	1.50916
$515$	13.6092	0.599692
$516$	2.77119	0.121995
$517$	1.37344	0.0604036
$518$	2.18133	0.0958421
$519$	−5.42763	−0.238246
$520$	−11.1203	−0.487659
$521$	−25.0397	−1.09701	−0.548504	−	0.836148i	$-0.684803\pi$
$521$	−25.0397	−1.09701	−0.548504	+	0.836148i	$0.684803\pi$
$522$	−52.8387	−2.31269
$523$	7.13145	0.311837	0.155918	−	0.987770i	$-0.450166\pi$
$523$	7.13145	0.311837	0.155918	+	0.987770i	$0.450166\pi$
$524$	−8.60592	−0.375951
$525$	−20.7851	−0.907136
$526$	31.4683	1.37208
$527$	5.23359	0.227979
$528$	−13.5615	−0.590189
$529$	−0.365427	−0.0158881
$530$	−5.79715	−0.251812
$531$	−26.1864	−1.13639
$532$	−1.26560	−0.0548707
$533$	61.7421	2.67435
$534$	−57.3363	−2.48118
$535$	−7.36826	−0.318558
$536$	22.0209	0.951158
$537$	9.18820	0.396500
$538$	−2.56329	−0.110511
$539$	−3.31912	−0.142964
$540$	−3.77463	−0.162434
$541$	−2.08035	−0.0894413	−0.0447207	−	0.999000i	$-0.514240\pi$
$541$	−2.08035	−0.0894413	−0.0447207	+	0.999000i	$0.514240\pi$
$542$	15.5990	0.670035
$543$	−8.06017	−0.345895
$544$	5.28917	0.226771
$545$	13.5072	0.578587
$546$	−58.9715	−2.52375
$547$	12.6144	0.539351	0.269675	−	0.962951i	$-0.413084\pi$
$547$	12.6144	0.539351	0.269675	+	0.962951i	$0.413084\pi$
$548$	17.1295	0.731735
$549$	−2.89377	−0.123503
$550$	6.94251	0.296030
$551$	−4.50383	−0.191870
$552$	21.9480	0.934167
$553$	19.4521	0.827186
$554$	−26.0631	−1.10731
$555$	1.77961	0.0755402
$556$	19.1444	0.811904
$557$	−29.4322	−1.24708	−0.623542	−	0.781790i	$-0.714307\pi$
$557$	−29.4322	−1.24708	−0.623542	+	0.781790i	$0.714307\pi$
$558$	−39.6463	−1.67836
$559$	6.51880	0.275716
$560$	9.62113	0.406567
$561$	2.71256	0.114524
$562$	−36.5022	−1.53975
$563$	7.86597	0.331511	0.165756	−	0.986167i	$-0.446994\pi$
$563$	7.86597	0.331511	0.165756	+	0.986167i	$0.446994\pi$
$564$	3.80605	0.160264
$565$	−19.3244	−0.812985
$566$	−22.0126	−0.925257
$567$	−5.91310	−0.248327
$568$	−21.9710	−0.921884
$569$	−30.0944	−1.26162	−0.630811	−	0.775936i	$-0.717278\pi$
$569$	−30.0944	−1.26162	−0.630811	+	0.775936i	$0.717278\pi$
$570$	−3.05388	−0.127913
$571$	−3.99271	−0.167090	−0.0835449	−	0.996504i	$-0.526624\pi$
$571$	−3.99271	−0.167090	−0.0835449	+	0.996504i	$0.526624\pi$
$572$	6.65971	0.278456
$573$	72.2769	3.01941
$574$	−31.5871	−1.31842
$575$	−19.0013	−0.792409
$576$	3.50818	0.146174
$577$	−20.9039	−0.870241	−0.435120	−	0.900372i	$-0.643294\pi$
$577$	−20.9039	−0.870241	−0.435120	+	0.900372i	$0.643294\pi$
$578$	−1.73828	−0.0723029
$579$	−13.0232	−0.541224
$580$	−7.14755	−0.296786
$581$	−30.5530	−1.26755
$582$	12.8583	0.532992
$583$	−3.32487	−0.137702
$584$	1.96686	0.0813893
$585$	−28.4952	−1.17813
$586$	29.2728	1.20925
$587$	38.0186	1.56920	0.784598	−	0.620004i	$-0.212869\pi$
$587$	38.0186	1.56920	0.784598	+	0.620004i	$0.212869\pi$
$588$	−9.19790	−0.379315
$589$	−3.37935	−0.139244
$590$	−10.4769	−0.431327
$591$	−18.8375	−0.774873
$592$	3.27005	0.134398
$593$	−36.3283	−1.49182	−0.745911	−	0.666045i	$-0.767986\pi$
$593$	−36.3283	−1.49182	−0.745911	+	0.666045i	$0.767986\pi$
$594$	−6.40304	−0.262720
$595$	−1.92441	−0.0788929
$596$	−13.9585	−0.571763
$597$	−40.8953	−1.67374
$598$	−53.9105	−2.20457
$599$	25.9606	1.06072	0.530362	−	0.847772i	$-0.322056\pi$
$599$	25.9606	1.06072	0.530362	+	0.847772i	$0.322056\pi$
$600$	−18.4249	−0.752193
$601$	−1.84844	−0.0753993	−0.0376996	−	0.999289i	$-0.512003\pi$
$601$	−1.84844	−0.0753993	−0.0376996	+	0.999289i	$0.512003\pi$
$602$	−3.33500	−0.135924
$603$	56.4273	2.29790
$604$	5.12160	0.208395
$605$	−1.00305	−0.0407796
$606$	40.5175	1.64591
$607$	35.5192	1.44168	0.720840	−	0.693102i	$-0.243756\pi$
$607$	35.5192	1.44168	0.720840	+	0.693102i	$0.243756\pi$
$608$	−3.41524	−0.138506
$609$	36.2998	1.47094
$610$	−1.15777	−0.0468766
$611$	8.95315	0.362206
$612$	4.45216	0.179968
$613$	20.0787	0.810973	0.405486	−	0.914101i	$-0.367102\pi$
$613$	20.0787	0.810973	0.405486	+	0.914101i	$0.367102\pi$
$614$	19.5406	0.788595
$615$	−25.7699	−1.03914
$616$	3.26291	0.131466
$617$	46.1262	1.85697	0.928484	−	0.371371i	$-0.121112\pi$
$617$	46.1262	1.85697	0.928484	+	0.371371i	$0.121112\pi$
$618$	63.9749	2.57345
$619$	−37.7568	−1.51757	−0.758787	−	0.651339i	$-0.774208\pi$
$619$	−37.7568	−1.51757	−0.758787	+	0.651339i	$0.774208\pi$
$620$	−5.36300	−0.215383
$621$	17.5248	0.703246
$622$	−9.69367	−0.388681
$623$	23.3296	0.934680
$624$	−88.4048	−3.53903
$625$	10.9207	0.436829
$626$	48.5491	1.94041
$627$	−1.75151	−0.0699484
$628$	−23.1169	−0.922464
$629$	−0.654072	−0.0260796
$630$	14.5781	0.580804
$631$	1.49485	0.0595092	0.0297546	−	0.999557i	$-0.490527\pi$
$631$	1.49485	0.0595092	0.0297546	+	0.999557i	$0.490527\pi$
$632$	17.2432	0.685899
$633$	−55.6552	−2.21210
$634$	−59.5583	−2.36536
$635$	−3.92673	−0.155828
$636$	−9.21385	−0.365353
$637$	−21.6367	−0.857276
$638$	−12.1246	−0.480019
$639$	−56.2995	−2.22717
$640$	12.0141	0.474901
$641$	41.7650	1.64962	0.824809	−	0.565411i	$-0.191283\pi$
$641$	41.7650	1.64962	0.824809	+	0.565411i	$0.191283\pi$
$642$	−34.6372	−1.36702
$643$	−2.01265	−0.0793710	−0.0396855	−	0.999212i	$-0.512636\pi$
$643$	−2.01265	−0.0793710	−0.0396855	+	0.999212i	$0.512636\pi$
$644$	9.32502	0.367457
$645$	−2.72082	−0.107132
$646$	1.12241	0.0441607
$647$	−10.5484	−0.414701	−0.207351	−	0.978267i	$-0.566484\pi$
$647$	−10.5484	−0.414701	−0.207351	+	0.978267i	$0.566484\pi$
$648$	−5.24165	−0.205912
$649$	−6.00887	−0.235869
$650$	45.2569	1.77512
$651$	27.2367	1.06749
$652$	−17.6546	−0.691406
$653$	32.3630	1.26646	0.633230	−	0.773963i	$-0.281729\pi$
$653$	32.3630	1.26646	0.633230	+	0.773963i	$0.281729\pi$
$654$	63.4957	2.48288
$655$	8.44949	0.330149
$656$	−47.3525	−1.84881
$657$	5.03997	0.196628
$658$	−4.58041	−0.178563
$659$	22.0220	0.857855	0.428927	−	0.903339i	$-0.358892\pi$
$659$	22.0220	0.857855	0.428927	+	0.903339i	$0.358892\pi$
$660$	−2.77963	−0.108197
$661$	−23.5021	−0.914127	−0.457063	−	0.889434i	$-0.651099\pi$
$661$	−23.5021	−0.914127	−0.457063	+	0.889434i	$0.651099\pi$
$662$	−5.97470	−0.232213
$663$	17.6826	0.686736
$664$	−27.0836	−1.05105
$665$	1.24260	0.0481858
$666$	4.95483	0.191996
$667$	33.1845	1.28491
$668$	−13.4780	−0.521478
$669$	45.2720	1.75032
$670$	22.5759	0.872185
$671$	−0.664019	−0.0256342
$672$	27.5260	1.06184
$673$	−9.40321	−0.362467	−0.181234	−	0.983440i	$-0.558009\pi$
$673$	−9.40321	−0.362467	−0.181234	+	0.983440i	$0.558009\pi$
$674$	0.602054	0.0231903
$675$	−14.7117	−0.566255
$676$	30.1323	1.15894
$677$	34.4457	1.32386	0.661929	−	0.749567i	$-0.269738\pi$
$677$	34.4457	1.32386	0.661929	+	0.749567i	$0.269738\pi$
$678$	−90.8415	−3.48875
$679$	−5.23191	−0.200782
$680$	−1.70589	−0.0654177
$681$	−16.1261	−0.617954
$682$	−9.09744	−0.348359
$683$	18.5880	0.711249	0.355624	−	0.934629i	$-0.384268\pi$
$683$	18.5880	0.711249	0.355624	+	0.934629i	$0.384268\pi$
$684$	−2.87478	−0.109920
$685$	−16.8181	−0.642587
$686$	34.4142	1.31394
$687$	−69.2707	−2.64284
$688$	−4.99953	−0.190605
$689$	−21.6742	−0.825720
$690$	22.5012	0.856605
$691$	−14.8211	−0.563822	−0.281911	−	0.959441i	$-0.590968\pi$
$691$	−14.8211	−0.563822	−0.281911	+	0.959441i	$0.590968\pi$
$692$	−2.04418	−0.0777080
$693$	8.36103	0.317609
$694$	−61.4934	−2.33426
$695$	−18.7964	−0.712989
$696$	32.1779	1.21970
$697$	9.47139	0.358754
$698$	15.1631	0.573932
$699$	49.6989	1.87978
$700$	−7.82818	−0.295877
$701$	6.34593	0.239682	0.119841	−	0.992793i	$-0.461761\pi$
$701$	6.34593	0.239682	0.119841	+	0.992793i	$0.461761\pi$
$702$	−41.7402	−1.57538
$703$	0.422336	0.0159287
$704$	0.805005	0.0303397
$705$	−3.73687	−0.140739
$706$	−12.7598	−0.480221
$707$	−16.4862	−0.620028
$708$	−16.6517	−0.625810
$709$	10.1001	0.379318	0.189659	−	0.981850i	$-0.439262\pi$
$709$	10.1001	0.379318	0.189659	+	0.981850i	$0.439262\pi$
$710$	−22.5248	−0.845341
$711$	44.1848	1.65706
$712$	20.6805	0.775033
$713$	24.8992	0.932483
$714$	−9.04637	−0.338552
$715$	−6.53865	−0.244532
$716$	3.46050	0.129325
$717$	−4.11026	−0.153501
$718$	5.37280	0.200511
$719$	22.9728	0.856739	0.428370	−	0.903604i	$-0.359088\pi$
$719$	22.9728	0.856739	0.428370	+	0.903604i	$0.359088\pi$
$720$	21.8541	0.814456
$721$	−26.0308	−0.969437
$722$	32.3026	1.20218
$723$	−16.9537	−0.630514
$724$	−3.03566	−0.112819
$725$	−27.8578	−1.03461
$726$	−4.71518	−0.174997
$727$	11.7756	0.436735	0.218367	−	0.975867i	$-0.429927\pi$
$727$	11.7756	0.436735	0.218367	+	0.975867i	$0.429927\pi$
$728$	21.2703	0.788329
$729$	−43.4070	−1.60767
$730$	2.01644	0.0746317
$731$	1.00000	0.0369863
$732$	−1.84012	−0.0680129
$733$	−5.16842	−0.190900	−0.0954500	−	0.995434i	$-0.530429\pi$
$733$	−5.16842	−0.190900	−0.0954500	+	0.995434i	$0.530429\pi$
$734$	−46.2347	−1.70655
$735$	9.03071	0.333103
$736$	25.1637	0.927545
$737$	12.9481	0.476949
$738$	−71.7492	−2.64112
$739$	−41.0301	−1.50932	−0.754659	−	0.656117i	$-0.772198\pi$
$739$	−41.0301	−1.50932	−0.754659	+	0.656117i	$0.772198\pi$
$740$	0.670245	0.0246387
$741$	−11.4177	−0.419441
$742$	11.0884	0.407069
$743$	24.1532	0.886096	0.443048	−	0.896498i	$-0.353897\pi$
$743$	24.1532	0.886096	0.443048	+	0.896498i	$0.353897\pi$
$744$	24.1439	0.885159
$745$	13.7048	0.502104
$746$	65.3661	2.39322
$747$	−69.4002	−2.53922
$748$	1.02162	0.0373540
$749$	14.0936	0.514967
$750$	−42.5370	−1.55323
$751$	−1.22172	−0.0445811	−0.0222906	−	0.999752i	$-0.507096\pi$
$751$	−1.22172	−0.0445811	−0.0222906	+	0.999752i	$0.507096\pi$
$752$	−6.86654	−0.250397
$753$	−38.7680	−1.41279
$754$	−79.0381	−2.87840
$755$	−5.02851	−0.183006
$756$	7.21989	0.262585
$757$	30.2803	1.10056	0.550278	−	0.834982i	$-0.314522\pi$
$757$	30.2803	1.10056	0.550278	+	0.834982i	$0.314522\pi$
$758$	−13.2530	−0.481371
$759$	12.9052	0.468429
$760$	1.10150	0.0399555
$761$	−54.4394	−1.97343	−0.986713	−	0.162471i	$-0.948054\pi$
$761$	−54.4394	−1.97343	−0.986713	+	0.162471i	$0.948054\pi$
$762$	−18.4590	−0.668700
$763$	−25.8358	−0.935319
$764$	27.2212	0.984830
$765$	−4.37124	−0.158042
$766$	−58.6213	−2.11807
$767$	−39.1706	−1.41437
$768$	52.1096	1.88034
$769$	2.75387	0.0993070	0.0496535	−	0.998767i	$-0.484188\pi$
$769$	2.75387	0.0993070	0.0496535	+	0.998767i	$0.484188\pi$
$770$	3.34515	0.120551
$771$	−53.3918	−1.92286
$772$	−4.90484	−0.176529
$773$	−9.54228	−0.343212	−0.171606	−	0.985166i	$-0.554896\pi$
$773$	−9.54228	−0.343212	−0.171606	+	0.985166i	$0.554896\pi$
$774$	−7.57536	−0.272291
$775$	−20.9024	−0.750837
$776$	−4.63781	−0.166488
$777$	−3.40393	−0.122115
$778$	−42.5036	−1.52383
$779$	−6.11571	−0.219118
$780$	−18.1199	−0.648795
$781$	−12.9188	−0.462270
$782$	−8.27000	−0.295735
$783$	25.6931	0.918195
$784$	16.5940	0.592644
$785$	22.6967	0.810079
$786$	39.7199	1.41676
$787$	−45.7605	−1.63119	−0.815593	−	0.578625i	$-0.803589\pi$
$787$	−45.7605	−1.63119	−0.815593	+	0.578625i	$0.803589\pi$
$788$	−7.09468	−0.252738
$789$	−49.1057	−1.74821
$790$	17.6779	0.628950
$791$	36.9626	1.31424
$792$	7.41161	0.263360
$793$	−4.32861	−0.153713
$794$	−0.703338	−0.0249605
$795$	9.04636	0.320842
$796$	−15.4022	−0.545916
$797$	37.3345	1.32246	0.661229	−	0.750184i	$-0.270035\pi$
$797$	37.3345	1.32246	0.661229	+	0.750184i	$0.270035\pi$
$798$	5.84127	0.206779
$799$	1.37344	0.0485887
$800$	−21.1244	−0.746861
$801$	52.9925	1.87240
$802$	−41.0002	−1.44777
$803$	1.15650	0.0408119
$804$	35.8816	1.26545
$805$	−9.15552	−0.322690
$806$	−59.3044	−2.08891
$807$	3.99997	0.140805
$808$	−14.6142	−0.514124
$809$	0.383409	0.0134799	0.00673996	−	0.999977i	$-0.497855\pi$
$809$	0.383409	0.0134799	0.00673996	+	0.999977i	$0.497855\pi$
$810$	−5.37377	−0.188815
$811$	6.83317	0.239945	0.119973	−	0.992777i	$-0.461719\pi$
$811$	6.83317	0.239945	0.119973	+	0.992777i	$0.461719\pi$
$812$	13.6714	0.479772
$813$	−24.3420	−0.853711
$814$	1.13696	0.0398504
$815$	17.3337	0.607171
$816$	−13.5615	−0.474748
$817$	−0.645703	−0.0225903
$818$	−32.6679	−1.14221
$819$	54.5039	1.90452
$820$	−9.70559	−0.338934
$821$	−38.7817	−1.35349	−0.676746	−	0.736217i	$-0.736610\pi$
$821$	−38.7817	−1.35349	−0.676746	+	0.736217i	$0.736610\pi$
$822$	−79.0597	−2.75752
$823$	7.00732	0.244260	0.122130	−	0.992514i	$-0.461028\pi$
$823$	7.00732	0.244260	0.122130	+	0.992514i	$0.461028\pi$
$824$	−23.0749	−0.803853
$825$	−10.8337	−0.377180
$826$	20.0396	0.697265
$827$	13.5718	0.471937	0.235968	−	0.971761i	$-0.424174\pi$
$827$	13.5718	0.471937	0.235968	+	0.971761i	$0.424174\pi$
$828$	21.1815	0.736109
$829$	−38.3815	−1.33304	−0.666521	−	0.745486i	$-0.732218\pi$
$829$	−38.3815	−1.33304	−0.666521	+	0.745486i	$0.732218\pi$
$830$	−27.7663	−0.963781
$831$	40.6710	1.41086
$832$	5.24766	0.181930
$833$	−3.31912	−0.115001
$834$	−88.3595	−3.05964
$835$	13.2330	0.457946
$836$	−0.659660	−0.0228148
$837$	19.2782	0.666352
$838$	8.49084	0.293311
$839$	−8.30321	−0.286659	−0.143329	−	0.989675i	$-0.545781\pi$
$839$	−8.30321	−0.286659	−0.143329	+	0.989675i	$0.545781\pi$
$840$	−8.87779	−0.306313
$841$	19.6517	0.677646
$842$	28.5623	0.984322
$843$	56.9611	1.96185
$844$	−20.9611	−0.721511
$845$	−29.5846	−1.01774
$846$	−10.4043	−0.357706
$847$	1.91856	0.0659226
$848$	16.6228	0.570829
$849$	34.3502	1.17890
$850$	6.94251	0.238126
$851$	−3.11180	−0.106671
$852$	−35.8004	−1.22650
$853$	−19.3929	−0.663999	−0.331999	−	0.943280i	$-0.607723\pi$
$853$	−19.3929	−0.663999	−0.331999	+	0.943280i	$0.607723\pi$
$854$	2.21450	0.0757787
$855$	2.82252	0.0965282
$856$	12.4932	0.427009
$857$	39.6359	1.35394	0.676969	−	0.736012i	$-0.263293\pi$
$857$	39.6359	1.35394	0.676969	+	0.736012i	$0.263293\pi$
$858$	−30.7373	−1.04936
$859$	31.1168	1.06169	0.530846	−	0.847468i	$-0.321874\pi$
$859$	31.1168	1.06169	0.530846	+	0.847468i	$0.321874\pi$
$860$	−1.02473	−0.0349429
$861$	49.2911	1.67984
$862$	−65.7772	−2.24038
$863$	−17.1350	−0.583282	−0.291641	−	0.956528i	$-0.594201\pi$
$863$	−17.1350	−0.583282	−0.291641	+	0.956528i	$0.594201\pi$
$864$	19.4829	0.662823
$865$	2.00702	0.0682407
$866$	28.3854	0.964576
$867$	2.71256	0.0921233
$868$	10.2580	0.348180
$869$	10.1389	0.343938
$870$	32.9889	1.11843
$871$	84.4060	2.85999
$872$	−22.9021	−0.775563
$873$	−11.8841	−0.402217
$874$	5.33997	0.180627
$875$	17.3079	0.585114
$876$	3.20487	0.108283
$877$	39.4066	1.33067	0.665333	−	0.746546i	$-0.268289\pi$
$877$	39.4066	1.33067	0.665333	+	0.746546i	$0.268289\pi$
$878$	23.9473	0.808183
$879$	−45.6797	−1.54074
$880$	5.01476	0.169047
$881$	−29.4027	−0.990602	−0.495301	−	0.868721i	$-0.664942\pi$
$881$	−29.4027	−0.990602	−0.495301	+	0.868721i	$0.664942\pi$
$882$	25.1435	0.846626
$883$	34.3859	1.15718	0.578588	−	0.815620i	$-0.303604\pi$
$883$	34.3859	1.15718	0.578588	+	0.815620i	$0.303604\pi$
$884$	6.65971	0.223990
$885$	16.3490	0.549567
$886$	−13.1170	−0.440675
$887$	−12.2822	−0.412398	−0.206199	−	0.978510i	$-0.566109\pi$
$887$	−12.2822	−0.412398	−0.206199	+	0.978510i	$0.566109\pi$
$888$	−3.01740	−0.101257
$889$	7.51080	0.251904
$890$	21.2017	0.710684
$891$	−3.08204	−0.103252
$892$	17.0505	0.570894
$893$	−0.886832	−0.0296767
$894$	64.4243	2.15467
$895$	−3.39760	−0.113569
$896$	−22.9799	−0.767705
$897$	84.1265	2.80890
$898$	−17.5129	−0.584412
$899$	36.5047	1.21750
$900$	−17.7815	−0.592716
$901$	−3.32487	−0.110767
$902$	−16.4639	−0.548189
$903$	5.20421	0.173185
$904$	32.7654	1.08976
$905$	2.98048	0.0990745
$906$	−23.6383	−0.785331
$907$	−30.4473	−1.01099	−0.505494	−	0.862830i	$-0.668690\pi$
$907$	−30.4473	−1.01099	−0.505494	+	0.862830i	$0.668690\pi$
$908$	−6.07349	−0.201556
$909$	−37.4480	−1.24207
$910$	21.8064	0.722875
$911$	−20.4981	−0.679133	−0.339566	−	0.940582i	$-0.610280\pi$
$911$	−20.4981	−0.679133	−0.339566	+	0.940582i	$0.610280\pi$
$912$	8.75672	0.289964
$913$	−15.9249	−0.527038
$914$	−25.8013	−0.853431
$915$	1.80667	0.0597268
$916$	−26.0890	−0.862006
$917$	−16.1617	−0.533705
$918$	−6.40304	−0.211332
$919$	46.1231	1.52146	0.760730	−	0.649068i	$-0.224841\pi$
$919$	46.1231	1.52146	0.760730	+	0.649068i	$0.224841\pi$
$920$	−8.11589	−0.267573
$921$	−30.4928	−1.00477
$922$	−5.21871	−0.171869
$923$	−84.2149	−2.77197
$924$	5.31670	0.174907
$925$	2.61230	0.0858918
$926$	12.2378	0.402158
$927$	−59.1282	−1.94203
$928$	36.8924	1.21105
$929$	17.3747	0.570046	0.285023	−	0.958521i	$-0.407999\pi$
$929$	17.3747	0.570046	0.285023	+	0.958521i	$0.407999\pi$
$930$	24.7525	0.811666
$931$	2.14316	0.0702394
$932$	18.7178	0.613122
$933$	15.1268	0.495230
$934$	57.0737	1.86751
$935$	−1.00305	−0.0328031
$936$	48.3148	1.57922
$937$	10.2370	0.334427	0.167213	−	0.985921i	$-0.446523\pi$
$937$	10.2370	0.334427	0.167213	+	0.985921i	$0.446523\pi$
$938$	−43.1819	−1.40994
$939$	−75.7601	−2.47234
$940$	−1.40740	−0.0459042
$941$	34.1405	1.11295	0.556475	−	0.830865i	$-0.312154\pi$
$941$	34.1405	1.11295	0.556475	+	0.830865i	$0.312154\pi$
$942$	106.694	3.47628
$943$	45.0609	1.46738
$944$	30.0415	0.977768
$945$	−7.08865	−0.230594
$946$	−1.73828	−0.0565163
$947$	−6.07427	−0.197387	−0.0986936	−	0.995118i	$-0.531466\pi$
$947$	−6.07427	−0.197387	−0.0986936	+	0.995118i	$0.531466\pi$
$948$	28.0967	0.912539
$949$	7.53897	0.244725
$950$	−4.48280	−0.145441
$951$	92.9397	3.01378
$952$	3.26291	0.105752
$953$	−37.4663	−1.21365	−0.606825	−	0.794835i	$-0.707557\pi$
$953$	−37.4663	−1.21365	−0.606825	+	0.794835i	$0.707557\pi$
$954$	25.1871	0.815462
$955$	−26.7264	−0.864847
$956$	−1.54803	−0.0500668
$957$	18.9203	0.611606
$958$	59.3444	1.91733
$959$	32.1686	1.03878
$960$	−2.19027	−0.0706907
$961$	−3.60954	−0.116437
$962$	7.41161	0.238960
$963$	32.0131	1.03161
$964$	−6.38517	−0.205652
$965$	4.81568	0.155022
$966$	−43.0388	−1.38475
$967$	−24.4207	−0.785317	−0.392659	−	0.919684i	$-0.628445\pi$
$967$	−24.4207	−0.785317	−0.392659	+	0.919684i	$0.628445\pi$
$968$	1.70071	0.0546628
$969$	−1.75151	−0.0562665
$970$	−4.75471	−0.152665
$971$	−49.7852	−1.59768	−0.798841	−	0.601542i	$-0.794553\pi$
$971$	−49.7852	−1.59768	−0.798841	+	0.601542i	$0.794553\pi$
$972$	−19.8305	−0.636062
$973$	35.9526	1.15259
$974$	−48.9077	−1.56710
$975$	−70.6226	−2.26173
$976$	3.31978	0.106264
$977$	23.9893	0.767485	0.383743	−	0.923440i	$-0.374635\pi$
$977$	23.9893	0.767485	0.383743	+	0.923440i	$0.374635\pi$
$978$	81.4832	2.60554
$979$	12.1599	0.388633
$980$	3.40119	0.108647
$981$	−58.6854	−1.87368
$982$	53.2213	1.69836
$983$	−48.8932	−1.55945	−0.779726	−	0.626121i	$-0.784642\pi$
$983$	−48.8932	−1.55945	−0.779726	+	0.626121i	$0.784642\pi$
$984$	43.6940	1.39291
$985$	6.96572	0.221946
$986$	−12.1246	−0.386127
$987$	7.14765	0.227512
$988$	−4.30020	−0.136807
$989$	4.75758	0.151282
$990$	7.59843	0.241494
$991$	18.6807	0.593412	0.296706	−	0.954969i	$-0.404112\pi$
$991$	18.6807	0.593412	0.296706	+	0.954969i	$0.404112\pi$
$992$	27.6814	0.878884
$993$	9.32342	0.295870
$994$	43.0841	1.36654
$995$	15.1222	0.479407
$996$	−44.1310	−1.39834
$997$	−18.5437	−0.587286	−0.293643	−	0.955915i	$-0.594868\pi$
$997$	−18.5437	−0.587286	−0.293643	+	0.955915i	$0.594868\pi$
$998$	17.7455	0.561723
$999$	−2.40931	−0.0762271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.17	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.17	✓	82	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73828 q^{2} +2.71256 q^{3} +1.02162 q^{4} -1.00305 q^{5} -4.71518 q^{6} +1.91856 q^{7} +1.70071 q^{8} +4.35796 q^{9} +O(q^{10})\)	\(q-1.73828 q^{2} +2.71256 q^{3} +1.02162 q^{4} -1.00305 q^{5} -4.71518 q^{6} +1.91856 q^{7} +1.70071 q^{8} +4.35796 q^{9} +1.74357 q^{10} +1.00000 q^{11} +2.77119 q^{12} +6.51880 q^{13} -3.33500 q^{14} -2.72082 q^{15} -4.99953 q^{16} +1.00000 q^{17} -7.57536 q^{18} -0.645703 q^{19} -1.02473 q^{20} +5.20421 q^{21} -1.73828 q^{22} +4.75758 q^{23} +4.61326 q^{24} -3.99390 q^{25} -11.3315 q^{26} +3.68355 q^{27} +1.96003 q^{28} +6.97508 q^{29} +4.72954 q^{30} +5.23359 q^{31} +5.28917 q^{32} +2.71256 q^{33} -1.73828 q^{34} -1.92441 q^{35} +4.45216 q^{36} -0.654072 q^{37} +1.12241 q^{38} +17.6826 q^{39} -1.70589 q^{40} +9.47139 q^{41} -9.04637 q^{42} +1.00000 q^{43} +1.02162 q^{44} -4.37124 q^{45} -8.27000 q^{46} +1.37344 q^{47} -13.5615 q^{48} -3.31912 q^{49} +6.94251 q^{50} +2.71256 q^{51} +6.65971 q^{52} -3.32487 q^{53} -6.40304 q^{54} -1.00305 q^{55} +3.26291 q^{56} -1.75151 q^{57} -12.1246 q^{58} -6.00887 q^{59} -2.77963 q^{60} -0.664019 q^{61} -9.09744 q^{62} +8.36103 q^{63} +0.805005 q^{64} -6.53865 q^{65} -4.71518 q^{66} +12.9481 q^{67} +1.02162 q^{68} +12.9052 q^{69} +3.34515 q^{70} -12.9188 q^{71} +7.41161 q^{72} +1.15650 q^{73} +1.13696 q^{74} -10.8337 q^{75} -0.659660 q^{76} +1.91856 q^{77} -30.7373 q^{78} +10.1389 q^{79} +5.01476 q^{80} -3.08204 q^{81} -16.4639 q^{82} -15.9249 q^{83} +5.31670 q^{84} -1.00305 q^{85} -1.73828 q^{86} +18.9203 q^{87} +1.70071 q^{88} +12.1599 q^{89} +7.59843 q^{90} +12.5067 q^{91} +4.86042 q^{92} +14.1964 q^{93} -2.38742 q^{94} +0.647670 q^{95} +14.3472 q^{96} -2.72699 q^{97} +5.76955 q^{98} +4.35796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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