LMFDB - Embedded newform 8041.2.a.j.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.26888 q^{2} +0.654424 q^{3} +3.14780 q^{4} -0.968068 q^{5} -1.48481 q^{6} +1.81018 q^{7} -2.60421 q^{8} -2.57173 q^{9} +O(q^{10})$	\(q-2.26888 q^{2} +0.654424 q^{3} +3.14780 q^{4} -0.968068 q^{5} -1.48481 q^{6} +1.81018 q^{7} -2.60421 q^{8} -2.57173 q^{9} +2.19643 q^{10} +1.00000 q^{11} +2.05999 q^{12} +3.55823 q^{13} -4.10708 q^{14} -0.633527 q^{15} -0.386967 q^{16} +1.00000 q^{17} +5.83493 q^{18} -4.84794 q^{19} -3.04728 q^{20} +1.18463 q^{21} -2.26888 q^{22} -7.36907 q^{23} -1.70426 q^{24} -4.06284 q^{25} -8.07319 q^{26} -3.64627 q^{27} +5.69809 q^{28} +7.99930 q^{29} +1.43739 q^{30} -2.59561 q^{31} +6.08640 q^{32} +0.654424 q^{33} -2.26888 q^{34} -1.75238 q^{35} -8.09528 q^{36} -7.56763 q^{37} +10.9994 q^{38} +2.32859 q^{39} +2.52105 q^{40} +1.85905 q^{41} -2.68777 q^{42} +1.00000 q^{43} +3.14780 q^{44} +2.48961 q^{45} +16.7195 q^{46} -3.71881 q^{47} -0.253240 q^{48} -3.72324 q^{49} +9.21809 q^{50} +0.654424 q^{51} +11.2006 q^{52} -8.29080 q^{53} +8.27294 q^{54} -0.968068 q^{55} -4.71409 q^{56} -3.17261 q^{57} -18.1494 q^{58} -4.79436 q^{59} -1.99421 q^{60} +14.1516 q^{61} +5.88912 q^{62} -4.65530 q^{63} -13.0353 q^{64} -3.44461 q^{65} -1.48481 q^{66} -4.30268 q^{67} +3.14780 q^{68} -4.82250 q^{69} +3.97593 q^{70} +14.1314 q^{71} +6.69732 q^{72} +2.83925 q^{73} +17.1700 q^{74} -2.65882 q^{75} -15.2603 q^{76} +1.81018 q^{77} -5.28329 q^{78} +0.315578 q^{79} +0.374610 q^{80} +5.32898 q^{81} -4.21795 q^{82} +9.58463 q^{83} +3.72896 q^{84} -0.968068 q^{85} -2.26888 q^{86} +5.23493 q^{87} -2.60421 q^{88} +13.9904 q^{89} -5.64862 q^{90} +6.44105 q^{91} -23.1963 q^{92} -1.69863 q^{93} +8.43751 q^{94} +4.69314 q^{95} +3.98308 q^{96} +17.3930 q^{97} +8.44757 q^{98} -2.57173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.26888	−1.60434	−0.802169	−	0.597097i	$-0.796321\pi$
$2$	−2.26888	−1.60434	−0.802169	+	0.597097i	$0.796321\pi$
$3$	0.654424	0.377832	0.188916	−	0.981993i	$-0.439503\pi$
$3$	0.654424	0.377832	0.188916	+	0.981993i	$0.439503\pi$
$4$	3.14780	1.57390
$5$	−0.968068	−0.432933	−0.216467	−	0.976290i	$-0.569453\pi$
$5$	−0.968068	−0.432933	−0.216467	+	0.976290i	$0.569453\pi$
$6$	−1.48481	−0.606170
$7$	1.81018	0.684185	0.342092	−	0.939666i	$-0.388864\pi$
$7$	1.81018	0.684185	0.342092	+	0.939666i	$0.388864\pi$
$8$	−2.60421	−0.920727
$9$	−2.57173	−0.857243
$10$	2.19643	0.694571
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.05999	0.594669
$13$	3.55823	0.986876	0.493438	−	0.869781i	$-0.335740\pi$
$13$	3.55823	0.986876	0.493438	+	0.869781i	$0.335740\pi$
$14$	−4.10708	−1.09766
$15$	−0.633527	−0.163576
$16$	−0.386967	−0.0967417
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.83493	1.37531
$19$	−4.84794	−1.11219	−0.556097	−	0.831117i	$-0.687702\pi$
$19$	−4.84794	−1.11219	−0.556097	+	0.831117i	$0.687702\pi$
$20$	−3.04728	−0.681393
$21$	1.18463	0.258507
$22$	−2.26888	−0.483726
$23$	−7.36907	−1.53656	−0.768279	−	0.640115i	$-0.778887\pi$
$23$	−7.36907	−1.53656	−0.768279	+	0.640115i	$0.778887\pi$
$24$	−1.70426	−0.347880
$25$	−4.06284	−0.812569
$26$	−8.07319	−1.58328
$27$	−3.64627	−0.701726
$28$	5.69809	1.07684
$29$	7.99930	1.48543	0.742716	−	0.669606i	$-0.233537\pi$
$29$	7.99930	1.48543	0.742716	+	0.669606i	$0.233537\pi$
$30$	1.43739	0.262431
$31$	−2.59561	−0.466186	−0.233093	−	0.972454i	$-0.574885\pi$
$31$	−2.59561	−0.466186	−0.233093	+	0.972454i	$0.574885\pi$
$32$	6.08640	1.07593
$33$	0.654424	0.113921
$34$	−2.26888	−0.389109
$35$	−1.75238	−0.296206
$36$	−8.09528	−1.34921
$37$	−7.56763	−1.24411	−0.622055	−	0.782973i	$-0.713702\pi$
$37$	−7.56763	−1.24411	−0.622055	+	0.782973i	$0.713702\pi$
$38$	10.9994	1.78434
$39$	2.32859	0.372873
$40$	2.52105	0.398613
$41$	1.85905	0.290335	0.145167	−	0.989407i	$-0.453628\pi$
$41$	1.85905	0.290335	0.145167	+	0.989407i	$0.453628\pi$
$42$	−2.68777	−0.414732
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.14780	0.474548
$45$	2.48961	0.371129
$46$	16.7195	2.46516
$47$	−3.71881	−0.542444	−0.271222	−	0.962517i	$-0.587428\pi$
$47$	−3.71881	−0.542444	−0.271222	+	0.962517i	$0.587428\pi$
$48$	−0.253240	−0.0365521
$49$	−3.72324	−0.531891
$50$	9.21809	1.30363
$51$	0.654424	0.0916377
$52$	11.2006	1.55324
$53$	−8.29080	−1.13883	−0.569415	−	0.822050i	$-0.692830\pi$
$53$	−8.29080	−1.13883	−0.569415	+	0.822050i	$0.692830\pi$
$54$	8.27294	1.12580
$55$	−0.968068	−0.130534
$56$	−4.71409	−0.629947
$57$	−3.17261	−0.420223
$58$	−18.1494	−2.38314
$59$	−4.79436	−0.624173	−0.312086	−	0.950054i	$-0.601028\pi$
$59$	−4.79436	−0.624173	−0.312086	+	0.950054i	$0.601028\pi$
$60$	−1.99421	−0.257452
$61$	14.1516	1.81193	0.905966	−	0.423352i	$-0.139146\pi$
$61$	14.1516	1.81193	0.905966	+	0.423352i	$0.139146\pi$
$62$	5.88912	0.747919
$63$	−4.65530	−0.586513
$64$	−13.0353	−1.62942
$65$	−3.44461	−0.427252
$66$	−1.48481	−0.182767
$67$	−4.30268	−0.525656	−0.262828	−	0.964843i	$-0.584655\pi$
$67$	−4.30268	−0.525656	−0.262828	+	0.964843i	$0.584655\pi$
$68$	3.14780	0.381726
$69$	−4.82250	−0.580560
$70$	3.97593	0.475215
$71$	14.1314	1.67708	0.838542	−	0.544837i	$-0.183409\pi$
$71$	14.1314	1.67708	0.838542	+	0.544837i	$0.183409\pi$
$72$	6.69732	0.789287
$73$	2.83925	0.332309	0.166155	−	0.986100i	$-0.446865\pi$
$73$	2.83925	0.332309	0.166155	+	0.986100i	$0.446865\pi$
$74$	17.1700	1.99597
$75$	−2.65882	−0.307014
$76$	−15.2603	−1.75048
$77$	1.81018	0.206289
$78$	−5.28329	−0.598214
$79$	0.315578	0.0355053	0.0177526	−	0.999842i	$-0.494349\pi$
$79$	0.315578	0.0355053	0.0177526	+	0.999842i	$0.494349\pi$
$80$	0.374610	0.0418827
$81$	5.32898	0.592109
$82$	−4.21795	−0.465795
$83$	9.58463	1.05205	0.526025	−	0.850469i	$-0.323682\pi$
$83$	9.58463	1.05205	0.526025	+	0.850469i	$0.323682\pi$
$84$	3.72896	0.406863
$85$	−0.968068	−0.105002
$86$	−2.26888	−0.244659
$87$	5.23493	0.561244
$88$	−2.60421	−0.277610
$89$	13.9904	1.48298	0.741488	−	0.670966i	$-0.234120\pi$
$89$	13.9904	1.48298	0.741488	+	0.670966i	$0.234120\pi$
$90$	−5.64862	−0.595416
$91$	6.44105	0.675206
$92$	−23.1963	−2.41839
$93$	−1.69863	−0.176140
$94$	8.43751	0.870263
$95$	4.69314	0.481506
$96$	3.98308	0.406522
$97$	17.3930	1.76600	0.882998	−	0.469377i	$-0.155522\pi$
$97$	17.3930	1.76600	0.882998	+	0.469377i	$0.155522\pi$
$98$	8.44757	0.853333
$99$	−2.57173	−0.258469
$100$	−12.7890	−1.27890
$101$	−17.5068	−1.74199	−0.870994	−	0.491294i	$-0.836524\pi$
$101$	−17.5068	−1.74199	−0.870994	+	0.491294i	$0.836524\pi$
$102$	−1.48481	−0.147018
$103$	8.82769	0.869818	0.434909	−	0.900474i	$-0.356781\pi$
$103$	8.82769	0.869818	0.434909	+	0.900474i	$0.356781\pi$
$104$	−9.26638	−0.908644
$105$	−1.14680	−0.111916
$106$	18.8108	1.82707
$107$	10.9388	1.05749	0.528745	−	0.848781i	$-0.322663\pi$
$107$	10.9388	1.05749	0.528745	+	0.848781i	$0.322663\pi$
$108$	−11.4777	−1.10444
$109$	−14.5544	−1.39406	−0.697031	−	0.717041i	$-0.745496\pi$
$109$	−14.5544	−1.39406	−0.697031	+	0.717041i	$0.745496\pi$
$110$	2.19643	0.209421
$111$	−4.95244	−0.470064
$112$	−0.700480	−0.0661892
$113$	9.18926	0.864453	0.432227	−	0.901765i	$-0.357728\pi$
$113$	9.18926	0.864453	0.432227	+	0.901765i	$0.357728\pi$
$114$	7.19826	0.674179
$115$	7.13377	0.665227
$116$	25.1802	2.33792
$117$	−9.15081	−0.845993
$118$	10.8778	1.00138
$119$	1.81018	0.165939
$120$	1.64984	0.150609
$121$	1.00000	0.0909091
$122$	−32.1083	−2.90695
$123$	1.21661	0.109698
$124$	−8.17046	−0.733729
$125$	8.77345	0.784721
$126$	10.5623	0.940964
$127$	6.42299	0.569948	0.284974	−	0.958535i	$-0.408015\pi$
$127$	6.42299	0.569948	0.284974	+	0.958535i	$0.408015\pi$
$128$	17.4028	1.53820
$129$	0.654424	0.0576188
$130$	7.81540	0.685456
$131$	10.0152	0.875036	0.437518	−	0.899210i	$-0.355858\pi$
$131$	10.0152	0.875036	0.437518	+	0.899210i	$0.355858\pi$
$132$	2.05999	0.179299
$133$	−8.77566	−0.760946
$134$	9.76224	0.843329
$135$	3.52984	0.303800
$136$	−2.60421	−0.223309
$137$	−20.1159	−1.71861	−0.859307	−	0.511461i	$-0.829104\pi$
$137$	−20.1159	−1.71861	−0.859307	+	0.511461i	$0.829104\pi$
$138$	10.9416	0.931415
$139$	−22.4797	−1.90670	−0.953350	−	0.301867i	$-0.902390\pi$
$139$	−22.4797	−1.90670	−0.953350	+	0.301867i	$0.902390\pi$
$140$	−5.51614	−0.466199
$141$	−2.43368	−0.204953
$142$	−32.0623	−2.69061
$143$	3.55823	0.297554
$144$	0.995174	0.0829311
$145$	−7.74387	−0.643093
$146$	−6.44190	−0.533136
$147$	−2.43658	−0.200965
$148$	−23.8214	−1.95810
$149$	6.68632	0.547764	0.273882	−	0.961763i	$-0.411692\pi$
$149$	6.68632	0.547764	0.273882	+	0.961763i	$0.411692\pi$
$150$	6.03254	0.492555
$151$	−21.1487	−1.72106	−0.860528	−	0.509404i	$-0.829866\pi$
$151$	−21.1487	−1.72106	−0.860528	+	0.509404i	$0.829866\pi$
$152$	12.6251	1.02403
$153$	−2.57173	−0.207912
$154$	−4.10708	−0.330958
$155$	2.51273	0.201827
$156$	7.32994	0.586865
$157$	16.1279	1.28715	0.643575	−	0.765383i	$-0.277450\pi$
$157$	16.1279	1.28715	0.643575	+	0.765383i	$0.277450\pi$
$158$	−0.716007	−0.0569624
$159$	−5.42570	−0.430286
$160$	−5.89205	−0.465807
$161$	−13.3394	−1.05129
$162$	−12.0908	−0.949942
$163$	12.9992	1.01818	0.509089	−	0.860714i	$-0.329983\pi$
$163$	12.9992	1.01818	0.509089	+	0.860714i	$0.329983\pi$
$164$	5.85191	0.456957
$165$	−0.633527	−0.0493200
$166$	−21.7463	−1.68784
$167$	24.9283	1.92901	0.964505	−	0.264065i	$-0.0850633\pi$
$167$	24.9283	1.92901	0.964505	+	0.264065i	$0.0850633\pi$
$168$	−3.08502	−0.238014
$169$	−0.338981	−0.0260754
$170$	2.19643	0.168458
$171$	12.4676	0.953421
$172$	3.14780	0.240017
$173$	9.67419	0.735515	0.367758	−	0.929922i	$-0.380126\pi$
$173$	9.67419	0.735515	0.367758	+	0.929922i	$0.380126\pi$
$174$	−11.8774	−0.900424
$175$	−7.35449	−0.555947
$176$	−0.386967	−0.0291687
$177$	−3.13755	−0.235832
$178$	−31.7424	−2.37919
$179$	−14.1103	−1.05465	−0.527326	−	0.849663i	$-0.676805\pi$
$179$	−14.1103	−1.05465	−0.527326	+	0.849663i	$0.676805\pi$
$180$	7.83679	0.584120
$181$	−4.06005	−0.301781	−0.150890	−	0.988550i	$-0.548214\pi$
$181$	−4.06005	−0.301781	−0.150890	+	0.988550i	$0.548214\pi$
$182$	−14.6139	−1.08326
$183$	9.26117	0.684605
$184$	19.1906	1.41475
$185$	7.32598	0.538617
$186$	3.85398	0.282588
$187$	1.00000	0.0731272
$188$	−11.7061	−0.853752
$189$	−6.60042	−0.480110
$190$	−10.6482	−0.772498
$191$	6.78214	0.490738	0.245369	−	0.969430i	$-0.421091\pi$
$191$	6.78214	0.490738	0.245369	+	0.969430i	$0.421091\pi$
$192$	−8.53064	−0.615646
$193$	−19.9960	−1.43934	−0.719671	−	0.694315i	$-0.755707\pi$
$193$	−19.9960	−1.43934	−0.719671	+	0.694315i	$0.755707\pi$
$194$	−39.4626	−2.83325
$195$	−2.25424	−0.161429
$196$	−11.7200	−0.837143
$197$	7.21511	0.514055	0.257028	−	0.966404i	$-0.417257\pi$
$197$	7.21511	0.514055	0.257028	+	0.966404i	$0.417257\pi$
$198$	5.83493	0.414671
$199$	22.2752	1.57905	0.789523	−	0.613721i	$-0.210328\pi$
$199$	22.2752	1.57905	0.789523	+	0.613721i	$0.210328\pi$
$200$	10.5805	0.748154
$201$	−2.81578	−0.198609
$202$	39.7206	2.79474
$203$	14.4802	1.01631
$204$	2.05999	0.144228
$205$	−1.79969	−0.125696
$206$	−20.0289	−1.39548
$207$	18.9513	1.31720
$208$	−1.37692	−0.0954721
$209$	−4.84794	−0.335339
$210$	2.60195	0.179551
$211$	18.0658	1.24370	0.621852	−	0.783135i	$-0.286381\pi$
$211$	18.0658	1.24370	0.621852	+	0.783135i	$0.286381\pi$
$212$	−26.0978	−1.79240
$213$	9.24790	0.633655
$214$	−24.8187	−1.69657
$215$	−0.968068	−0.0660217
$216$	9.49566	0.646098
$217$	−4.69853	−0.318957
$218$	33.0222	2.23655
$219$	1.85807	0.125557
$220$	−3.04728	−0.205448
$221$	3.55823	0.239353
$222$	11.2365	0.754142
$223$	−13.6552	−0.914420	−0.457210	−	0.889359i	$-0.651151\pi$
$223$	−13.6552	−0.914420	−0.457210	+	0.889359i	$0.651151\pi$
$224$	11.0175	0.736137
$225$	10.4485	0.696569
$226$	−20.8493	−1.38687
$227$	24.1755	1.60459	0.802293	−	0.596931i	$-0.203613\pi$
$227$	24.1755	1.60459	0.802293	+	0.596931i	$0.203613\pi$
$228$	−9.98673	−0.661388
$229$	3.55989	0.235244	0.117622	−	0.993058i	$-0.462473\pi$
$229$	3.55989	0.235244	0.117622	+	0.993058i	$0.462473\pi$
$230$	−16.1856	−1.06725
$231$	1.18463	0.0779427
$232$	−20.8319	−1.36768
$233$	−4.44301	−0.291071	−0.145536	−	0.989353i	$-0.546491\pi$
$233$	−4.44301	−0.291071	−0.145536	+	0.989353i	$0.546491\pi$
$234$	20.7621	1.35726
$235$	3.60006	0.234842
$236$	−15.0917	−0.982385
$237$	0.206522	0.0134150
$238$	−4.10708	−0.266222
$239$	12.0797	0.781371	0.390686	−	0.920524i	$-0.372238\pi$
$239$	12.0797	0.781371	0.390686	+	0.920524i	$0.372238\pi$
$240$	0.245154	0.0158246
$241$	−13.6638	−0.880165	−0.440082	−	0.897957i	$-0.645051\pi$
$241$	−13.6638	−0.880165	−0.440082	+	0.897957i	$0.645051\pi$
$242$	−2.26888	−0.145849
$243$	14.4262	0.925443
$244$	44.5465	2.85180
$245$	3.60435	0.230274
$246$	−2.76033	−0.175992
$247$	−17.2501	−1.09760
$248$	6.75952	0.429230
$249$	6.27241	0.397498
$250$	−19.9059	−1.25896
$251$	15.9799	1.00864	0.504322	−	0.863516i	$-0.331742\pi$
$251$	15.9799	1.00864	0.504322	+	0.863516i	$0.331742\pi$
$252$	−14.6539	−0.923111
$253$	−7.36907	−0.463290
$254$	−14.5730	−0.914389
$255$	−0.633527	−0.0396730
$256$	−13.4141	−0.838379
$257$	−13.6291	−0.850160	−0.425080	−	0.905156i	$-0.639754\pi$
$257$	−13.6291	−0.850160	−0.425080	+	0.905156i	$0.639754\pi$
$258$	−1.48481	−0.0924400
$259$	−13.6988	−0.851201
$260$	−10.8429	−0.672451
$261$	−20.5720	−1.27338
$262$	−22.7233	−1.40385
$263$	−28.3881	−1.75049	−0.875244	−	0.483682i	$-0.839299\pi$
$263$	−28.3881	−1.75049	−0.875244	+	0.483682i	$0.839299\pi$
$264$	−1.70426	−0.104890
$265$	8.02606	0.493037
$266$	19.9109	1.22081
$267$	9.15563	0.560316
$268$	−13.5440	−0.827329
$269$	21.8036	1.32939	0.664694	−	0.747116i	$-0.268562\pi$
$269$	21.8036	1.32939	0.664694	+	0.747116i	$0.268562\pi$
$270$	−8.00877	−0.487398
$271$	15.1598	0.920894	0.460447	−	0.887687i	$-0.347689\pi$
$271$	15.1598	0.920894	0.460447	+	0.887687i	$0.347689\pi$
$272$	−0.386967	−0.0234633
$273$	4.21518	0.255114
$274$	45.6404	2.75724
$275$	−4.06284	−0.244999
$276$	−15.1802	−0.913743
$277$	25.0059	1.50246	0.751230	−	0.660041i	$-0.229461\pi$
$277$	25.0059	1.50246	0.751230	+	0.660041i	$0.229461\pi$
$278$	51.0036	3.05899
$279$	6.67521	0.399634
$280$	4.56357	0.272725
$281$	19.1877	1.14464	0.572322	−	0.820029i	$-0.306043\pi$
$281$	19.1877	1.14464	0.572322	+	0.820029i	$0.306043\pi$
$282$	5.52171	0.328813
$283$	12.2974	0.731003	0.365501	−	0.930811i	$-0.380898\pi$
$283$	12.2974	0.731003	0.365501	+	0.930811i	$0.380898\pi$
$284$	44.4826	2.63956
$285$	3.07130	0.181928
$286$	−8.07319	−0.477378
$287$	3.36522	0.198642
$288$	−15.6526	−0.922337
$289$	1.00000	0.0588235
$290$	17.5699	1.03174
$291$	11.3824	0.667249
$292$	8.93738	0.523021
$293$	15.6074	0.911796	0.455898	−	0.890032i	$-0.349318\pi$
$293$	15.6074	0.911796	0.455898	+	0.890032i	$0.349318\pi$
$294$	5.52829	0.322416
$295$	4.64127	0.270225
$296$	19.7077	1.14549
$297$	−3.64627	−0.211578
$298$	−15.1704	−0.878799
$299$	−26.2209	−1.51639
$300$	−8.36943	−0.483209
$301$	1.81018	0.104337
$302$	47.9837	2.76115
$303$	−11.4568	−0.658178
$304$	1.87599	0.107596
$305$	−13.6997	−0.784445
$306$	5.83493	0.333561
$307$	−9.02362	−0.515005	−0.257503	−	0.966278i	$-0.582900\pi$
$307$	−9.02362	−0.515005	−0.257503	+	0.966278i	$0.582900\pi$
$308$	5.69809	0.324679
$309$	5.77705	0.328645
$310$	−5.70107	−0.323799
$311$	8.48774	0.481296	0.240648	−	0.970613i	$-0.422640\pi$
$311$	8.48774	0.481296	0.240648	+	0.970613i	$0.422640\pi$
$312$	−6.06414	−0.343314
$313$	10.3944	0.587523	0.293762	−	0.955879i	$-0.405093\pi$
$313$	10.3944	0.587523	0.293762	+	0.955879i	$0.405093\pi$
$314$	−36.5923	−2.06502
$315$	4.50665	0.253921
$316$	0.993375	0.0558817
$317$	−31.8125	−1.78677	−0.893384	−	0.449293i	$-0.851676\pi$
$317$	−31.8125	−1.78677	−0.893384	+	0.449293i	$0.851676\pi$
$318$	12.3102	0.690324
$319$	7.99930	0.447875
$320$	12.6191	0.705430
$321$	7.15858	0.399553
$322$	30.2654	1.68662
$323$	−4.84794	−0.269747
$324$	16.7745	0.931919
$325$	−14.4565	−0.801905
$326$	−29.4936	−1.63350
$327$	−9.52477	−0.526721
$328$	−4.84135	−0.267319
$329$	−6.73172	−0.371132
$330$	1.43739	0.0791260
$331$	4.20246	0.230988	0.115494	−	0.993308i	$-0.463155\pi$
$331$	4.20246	0.230988	0.115494	+	0.993308i	$0.463155\pi$
$332$	30.1705	1.65582
$333$	19.4619	1.06650
$334$	−56.5592	−3.09478
$335$	4.16529	0.227574
$336$	−0.458411	−0.0250084
$337$	18.7531	1.02154	0.510772	−	0.859716i	$-0.329360\pi$
$337$	18.7531	1.02154	0.510772	+	0.859716i	$0.329360\pi$
$338$	0.769105	0.0418338
$339$	6.01367	0.326618
$340$	−3.04728	−0.165262
$341$	−2.59561	−0.140560
$342$	−28.2874	−1.52961
$343$	−19.4110	−1.04810
$344$	−2.60421	−0.140410
$345$	4.66851	0.251344
$346$	−21.9495	−1.18001
$347$	19.5899	1.05164	0.525819	−	0.850596i	$-0.323759\pi$
$347$	19.5899	1.05164	0.525819	+	0.850596i	$0.323759\pi$
$348$	16.4785	0.883341
$349$	−21.4986	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$349$	−21.4986	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$350$	16.6864	0.891927
$351$	−12.9743	−0.692516
$352$	6.08640	0.324406
$353$	−7.00756	−0.372975	−0.186487	−	0.982457i	$-0.559710\pi$
$353$	−7.00756	−0.372975	−0.186487	+	0.982457i	$0.559710\pi$
$354$	7.11870	0.378355
$355$	−13.6801	−0.726065
$356$	44.0388	2.33405
$357$	1.18463	0.0626971
$358$	32.0145	1.69202
$359$	−2.25680	−0.119109	−0.0595547	−	0.998225i	$-0.518968\pi$
$359$	−2.25680	−0.119109	−0.0595547	+	0.998225i	$0.518968\pi$
$360$	−6.48347	−0.341709
$361$	4.50256	0.236977
$362$	9.21174	0.484158
$363$	0.654424	0.0343483
$364$	20.2751	1.06271
$365$	−2.74859	−0.143868
$366$	−21.0124	−1.09834
$367$	−19.8758	−1.03751	−0.518753	−	0.854924i	$-0.673604\pi$
$367$	−19.8758	−1.03751	−0.518753	+	0.854924i	$0.673604\pi$
$368$	2.85159	0.148649
$369$	−4.78097	−0.248887
$370$	−16.6217	−0.864123
$371$	−15.0079	−0.779170
$372$	−5.34694	−0.277226
$373$	−15.3983	−0.797294	−0.398647	−	0.917104i	$-0.630520\pi$
$373$	−15.3983	−0.797294	−0.398647	+	0.917104i	$0.630520\pi$
$374$	−2.26888	−0.117321
$375$	5.74156	0.296493
$376$	9.68455	0.499443
$377$	28.4634	1.46594
$378$	14.9755	0.770258
$379$	−34.2454	−1.75907	−0.879533	−	0.475838i	$-0.842145\pi$
$379$	−34.2454	−1.75907	−0.879533	+	0.475838i	$0.842145\pi$
$380$	14.7731	0.757842
$381$	4.20336	0.215345
$382$	−15.3878	−0.787310
$383$	29.4784	1.50628	0.753138	−	0.657862i	$-0.228539\pi$
$383$	29.4784	1.50628	0.753138	+	0.657862i	$0.228539\pi$
$384$	11.3888	0.581182
$385$	−1.75238	−0.0893096
$386$	45.3684	2.30919
$387$	−2.57173	−0.130728
$388$	54.7498	2.77950
$389$	−11.9208	−0.604407	−0.302203	−	0.953243i	$-0.597722\pi$
$389$	−11.9208	−0.604407	−0.302203	+	0.953243i	$0.597722\pi$
$390$	5.11458	0.258987
$391$	−7.36907	−0.372670
$392$	9.69610	0.489727
$393$	6.55421	0.330616
$394$	−16.3702	−0.824718
$395$	−0.305501	−0.0153714
$396$	−8.09528	−0.406803
$397$	−6.38995	−0.320703	−0.160351	−	0.987060i	$-0.551263\pi$
$397$	−6.38995	−0.320703	−0.160351	+	0.987060i	$0.551263\pi$
$398$	−50.5396	−2.53332
$399$	−5.74300	−0.287510
$400$	1.57219	0.0786093
$401$	2.67473	0.133570	0.0667848	−	0.997767i	$-0.478726\pi$
$401$	2.67473	0.133570	0.0667848	+	0.997767i	$0.478726\pi$
$402$	6.38865	0.318637
$403$	−9.23579	−0.460067
$404$	−55.1077	−2.74171
$405$	−5.15882	−0.256344
$406$	−32.8538	−1.63050
$407$	−7.56763	−0.375113
$408$	−1.70426	−0.0843733
$409$	3.75111	0.185481	0.0927403	−	0.995690i	$-0.470437\pi$
$409$	3.75111	0.185481	0.0927403	+	0.995690i	$0.470437\pi$
$410$	4.08326	0.201658
$411$	−13.1643	−0.649347
$412$	27.7878	1.36900
$413$	−8.67867	−0.427049
$414$	−42.9981	−2.11324
$415$	−9.27858	−0.455468
$416$	21.6568	1.06181
$417$	−14.7112	−0.720412
$418$	10.9994	0.537997
$419$	−26.5650	−1.29778	−0.648892	−	0.760881i	$-0.724767\pi$
$419$	−26.5650	−1.29778	−0.648892	+	0.760881i	$0.724767\pi$
$420$	−3.60989	−0.176145
$421$	−19.5653	−0.953553	−0.476777	−	0.879024i	$-0.658195\pi$
$421$	−19.5653	−0.953553	−0.476777	+	0.879024i	$0.658195\pi$
$422$	−40.9891	−1.99532
$423$	9.56377	0.465006
$424$	21.5910	1.04855
$425$	−4.06284	−0.197077
$426$	−20.9823	−1.01660
$427$	25.6170	1.23970
$428$	34.4330	1.66438
$429$	2.32859	0.112426
$430$	2.19643	0.105921
$431$	34.0784	1.64150	0.820750	−	0.571287i	$-0.193556\pi$
$431$	34.0784	1.64150	0.820750	+	0.571287i	$0.193556\pi$
$432$	1.41099	0.0678861
$433$	−7.36781	−0.354074	−0.177037	−	0.984204i	$-0.556651\pi$
$433$	−7.36781	−0.354074	−0.177037	+	0.984204i	$0.556651\pi$
$434$	10.6604	0.511715
$435$	−5.06777	−0.242981
$436$	−45.8144	−2.19411
$437$	35.7248	1.70895
$438$	−4.21574	−0.201436
$439$	−6.48225	−0.309381	−0.154691	−	0.987963i	$-0.549438\pi$
$439$	−6.48225	−0.309381	−0.154691	+	0.987963i	$0.549438\pi$
$440$	2.52105	0.120186
$441$	9.57516	0.455960
$442$	−8.07319	−0.384002
$443$	−10.8793	−0.516893	−0.258447	−	0.966026i	$-0.583211\pi$
$443$	−10.8793	−0.516893	−0.258447	+	0.966026i	$0.583211\pi$
$444$	−15.5893	−0.739834
$445$	−13.5436	−0.642030
$446$	30.9820	1.46704
$447$	4.37569	0.206963
$448$	−23.5964	−1.11482
$449$	−20.0663	−0.946987	−0.473494	−	0.880797i	$-0.657007\pi$
$449$	−20.0663	−0.946987	−0.473494	+	0.880797i	$0.657007\pi$
$450$	−23.7064	−1.11753
$451$	1.85905	0.0875392
$452$	28.9259	1.36056
$453$	−13.8402	−0.650269
$454$	−54.8513	−2.57430
$455$	−6.23538	−0.292319
$456$	8.26214	0.386910
$457$	2.75446	0.128848	0.0644241	−	0.997923i	$-0.479479\pi$
$457$	2.75446	0.128848	0.0644241	+	0.997923i	$0.479479\pi$
$458$	−8.07695	−0.377411
$459$	−3.64627	−0.170193
$460$	22.4556	1.04700
$461$	17.8701	0.832296	0.416148	−	0.909297i	$-0.363380\pi$
$461$	17.8701	0.832296	0.416148	+	0.909297i	$0.363380\pi$
$462$	−2.68777	−0.125046
$463$	−15.5482	−0.722587	−0.361294	−	0.932452i	$-0.617665\pi$
$463$	−15.5482	−0.722587	−0.361294	+	0.932452i	$0.617665\pi$
$464$	−3.09546	−0.143703
$465$	1.64439	0.0762568
$466$	10.0806	0.466977
$467$	−8.86413	−0.410183	−0.205091	−	0.978743i	$-0.565749\pi$
$467$	−8.86413	−0.410183	−0.205091	+	0.978743i	$0.565749\pi$
$468$	−28.8049	−1.33151
$469$	−7.78863	−0.359646
$470$	−8.16809	−0.376766
$471$	10.5545	0.486326
$472$	12.4855	0.574693
$473$	1.00000	0.0459800
$474$	−0.468572	−0.0215222
$475$	19.6964	0.903735
$476$	5.69809	0.261171
$477$	21.3217	0.976254
$478$	−27.4073	−1.25358
$479$	39.4044	1.80044	0.900218	−	0.435440i	$-0.143407\pi$
$479$	39.4044	1.80044	0.900218	+	0.435440i	$0.143407\pi$
$480$	−3.85590	−0.175997
$481$	−26.9274	−1.22778
$482$	31.0015	1.41208
$483$	−8.72960	−0.397211
$484$	3.14780	0.143082
$485$	−16.8377	−0.764558
$486$	−32.7313	−1.48472
$487$	26.3199	1.19267	0.596335	−	0.802736i	$-0.296623\pi$
$487$	26.3199	1.19267	0.596335	+	0.802736i	$0.296623\pi$
$488$	−36.8538	−1.66829
$489$	8.50700	0.384700
$490$	−8.17782	−0.369436
$491$	10.5119	0.474394	0.237197	−	0.971462i	$-0.423771\pi$
$491$	10.5119	0.474394	0.237197	+	0.971462i	$0.423771\pi$
$492$	3.82963	0.172653
$493$	7.99930	0.360270
$494$	39.1384	1.76092
$495$	2.48961	0.111900
$496$	1.00442	0.0450996
$497$	25.5803	1.14743
$498$	−14.2313	−0.637721
$499$	27.3220	1.22310	0.611550	−	0.791206i	$-0.290546\pi$
$499$	27.3220	1.22310	0.611550	+	0.791206i	$0.290546\pi$
$500$	27.6170	1.23507
$501$	16.3137	0.728841
$502$	−36.2565	−1.61821
$503$	4.46103	0.198907	0.0994537	−	0.995042i	$-0.468290\pi$
$503$	4.46103	0.198907	0.0994537	+	0.995042i	$0.468290\pi$
$504$	12.1234	0.540018
$505$	16.9477	0.754164
$506$	16.7195	0.743273
$507$	−0.221837	−0.00985213
$508$	20.2183	0.897041
$509$	10.2339	0.453612	0.226806	−	0.973940i	$-0.427172\pi$
$509$	10.2339	0.453612	0.226806	+	0.973940i	$0.427172\pi$
$510$	1.43739	0.0636489
$511$	5.13956	0.227361
$512$	−4.37072	−0.193160
$513$	17.6769	0.780455
$514$	30.9227	1.36394
$515$	−8.54580	−0.376573
$516$	2.05999	0.0906862
$517$	−3.71881	−0.163553
$518$	31.0808	1.36561
$519$	6.33102	0.277901
$520$	8.97049	0.393382
$521$	23.7011	1.03837	0.519183	−	0.854663i	$-0.326236\pi$
$521$	23.7011	1.03837	0.519183	+	0.854663i	$0.326236\pi$
$522$	46.6754	2.04293
$523$	−38.7691	−1.69526	−0.847628	−	0.530591i	$-0.821970\pi$
$523$	−38.7691	−1.69526	−0.847628	+	0.530591i	$0.821970\pi$
$524$	31.5260	1.37722
$525$	−4.81295	−0.210054
$526$	64.4092	2.80837
$527$	−2.59561	−0.113067
$528$	−0.253240	−0.0110209
$529$	31.3032	1.36101
$530$	−18.2101	−0.790998
$531$	12.3298	0.535068
$532$	−27.6240	−1.19765
$533$	6.61493	0.286524
$534$	−20.7730	−0.898935
$535$	−10.5895	−0.457822
$536$	11.2051	0.483986
$537$	−9.23411	−0.398481
$538$	−49.4696	−2.13279
$539$	−3.72324	−0.160371
$540$	11.1112	0.478151
$541$	−11.3462	−0.487812	−0.243906	−	0.969799i	$-0.578429\pi$
$541$	−11.3462	−0.487812	−0.243906	+	0.969799i	$0.578429\pi$
$542$	−34.3958	−1.47742
$543$	−2.65699	−0.114022
$544$	6.08640	0.260952
$545$	14.0897	0.603536
$546$	−9.56371	−0.409289
$547$	18.4261	0.787842	0.393921	−	0.919144i	$-0.371118\pi$
$547$	18.4261	0.787842	0.393921	+	0.919144i	$0.371118\pi$
$548$	−63.3206	−2.70492
$549$	−36.3942	−1.55327
$550$	9.21809	0.393061
$551$	−38.7802	−1.65209
$552$	12.5588	0.534538
$553$	0.571253	0.0242922
$554$	−56.7353	−2.41045
$555$	4.79430	0.203507
$556$	−70.7614	−3.00095
$557$	−0.497729	−0.0210895	−0.0105447	−	0.999944i	$-0.503357\pi$
$557$	−0.497729	−0.0210895	−0.0105447	+	0.999944i	$0.503357\pi$
$558$	−15.1452	−0.641148
$559$	3.55823	0.150497
$560$	0.678113	0.0286555
$561$	0.654424	0.0276298
$562$	−43.5346	−1.83640
$563$	23.0984	0.973480	0.486740	−	0.873547i	$-0.338186\pi$
$563$	23.0984	0.973480	0.486740	+	0.873547i	$0.338186\pi$
$564$	−7.66072	−0.322575
$565$	−8.89584	−0.374251
$566$	−27.9012	−1.17277
$567$	9.64643	0.405112
$568$	−36.8010	−1.54414
$569$	−5.81738	−0.243877	−0.121939	−	0.992538i	$-0.538911\pi$
$569$	−5.81738	−0.243877	−0.121939	+	0.992538i	$0.538911\pi$
$570$	−6.96841	−0.291874
$571$	−22.2688	−0.931920	−0.465960	−	0.884806i	$-0.654291\pi$
$571$	−22.2688	−0.931920	−0.465960	+	0.884806i	$0.654291\pi$
$572$	11.2006	0.468320
$573$	4.43839	0.185417
$574$	−7.63526	−0.318690
$575$	29.9394	1.24856
$576$	33.5234	1.39681
$577$	−14.5687	−0.606504	−0.303252	−	0.952910i	$-0.598072\pi$
$577$	−14.5687	−0.606504	−0.303252	+	0.952910i	$0.598072\pi$
$578$	−2.26888	−0.0943728
$579$	−13.0858	−0.543829
$580$	−24.3761	−1.01216
$581$	17.3499	0.719797
$582$	−25.8253	−1.07049
$583$	−8.29080	−0.343370
$584$	−7.39400	−0.305966
$585$	8.85861	0.366258
$586$	−35.4113	−1.46283
$587$	28.5016	1.17639	0.588193	−	0.808720i	$-0.299839\pi$
$587$	28.5016	1.17639	0.588193	+	0.808720i	$0.299839\pi$
$588$	−7.66985	−0.316299
$589$	12.5834	0.518489
$590$	−10.5305	−0.433532
$591$	4.72174	0.194226
$592$	2.92842	0.120357
$593$	40.9865	1.68312	0.841558	−	0.540167i	$-0.181639\pi$
$593$	40.9865	1.68312	0.841558	+	0.540167i	$0.181639\pi$
$594$	8.27294	0.339443
$595$	−1.75238	−0.0718406
$596$	21.0472	0.862126
$597$	14.5774	0.596614
$598$	59.4919	2.43280
$599$	8.64990	0.353425	0.176713	−	0.984262i	$-0.443454\pi$
$599$	8.64990	0.353425	0.176713	+	0.984262i	$0.443454\pi$
$600$	6.92413	0.282676
$601$	1.52981	0.0624024	0.0312012	−	0.999513i	$-0.490067\pi$
$601$	1.52981	0.0624024	0.0312012	+	0.999513i	$0.490067\pi$
$602$	−4.10708	−0.167392
$603$	11.0653	0.450615
$604$	−66.5718	−2.70877
$605$	−0.968068	−0.0393576
$606$	25.9941	1.05594
$607$	−19.8845	−0.807088	−0.403544	−	0.914960i	$-0.632222\pi$
$607$	−19.8845	−0.807088	−0.403544	+	0.914960i	$0.632222\pi$
$608$	−29.5065	−1.19665
$609$	9.47618	0.383994
$610$	31.0830	1.25852
$611$	−13.2324	−0.535325
$612$	−8.09528	−0.327232
$613$	−22.9660	−0.927586	−0.463793	−	0.885943i	$-0.653512\pi$
$613$	−22.9660	−0.927586	−0.463793	+	0.885943i	$0.653512\pi$
$614$	20.4735	0.826242
$615$	−1.17776	−0.0474918
$616$	−4.71409	−0.189936
$617$	−42.0033	−1.69099	−0.845494	−	0.533985i	$-0.820694\pi$
$617$	−42.0033	−1.69099	−0.845494	+	0.533985i	$0.820694\pi$
$618$	−13.1074	−0.527257
$619$	17.8147	0.716033	0.358017	−	0.933715i	$-0.383453\pi$
$619$	17.8147	0.716033	0.358017	+	0.933715i	$0.383453\pi$
$620$	7.90956	0.317656
$621$	26.8696	1.07824
$622$	−19.2576	−0.772160
$623$	25.3251	1.01463
$624$	−0.901088	−0.0360724
$625$	11.8209	0.472837
$626$	−23.5835	−0.942586
$627$	−3.17261	−0.126702
$628$	50.7675	2.02584
$629$	−7.56763	−0.301741
$630$	−10.2250	−0.407375
$631$	−40.0166	−1.59304	−0.796519	−	0.604614i	$-0.793327\pi$
$631$	−40.0166	−1.59304	−0.796519	+	0.604614i	$0.793327\pi$
$632$	−0.821831	−0.0326907
$633$	11.8227	0.469911
$634$	72.1786	2.86658
$635$	−6.21789	−0.246750
$636$	−17.0790	−0.677227
$637$	−13.2482	−0.524911
$638$	−18.1494	−0.718542
$639$	−36.3420	−1.43767
$640$	−16.8471	−0.665940
$641$	−24.7790	−0.978710	−0.489355	−	0.872085i	$-0.662768\pi$
$641$	−24.7790	−0.978710	−0.489355	+	0.872085i	$0.662768\pi$
$642$	−16.2419	−0.641018
$643$	33.7086	1.32934	0.664668	−	0.747139i	$-0.268573\pi$
$643$	33.7086	1.32934	0.664668	+	0.747139i	$0.268573\pi$
$644$	−41.9896	−1.65462
$645$	−0.633527	−0.0249451
$646$	10.9994	0.432765
$647$	13.0771	0.514112	0.257056	−	0.966396i	$-0.417247\pi$
$647$	13.0771	0.514112	0.257056	+	0.966396i	$0.417247\pi$
$648$	−13.8778	−0.545171
$649$	−4.79436	−0.188195
$650$	32.8001	1.28653
$651$	−3.07483	−0.120512
$652$	40.9189	1.60251
$653$	−1.62862	−0.0637329	−0.0318665	−	0.999492i	$-0.510145\pi$
$653$	−1.62862	−0.0637329	−0.0318665	+	0.999492i	$0.510145\pi$
$654$	21.6105	0.845038
$655$	−9.69544	−0.378832
$656$	−0.719390	−0.0280875
$657$	−7.30178	−0.284870
$658$	15.2734	0.595421
$659$	18.9684	0.738902	0.369451	−	0.929250i	$-0.379546\pi$
$659$	18.9684	0.738902	0.369451	+	0.929250i	$0.379546\pi$
$660$	−1.99421	−0.0776247
$661$	−15.6090	−0.607121	−0.303561	−	0.952812i	$-0.598176\pi$
$661$	−15.6090	−0.607121	−0.303561	+	0.952812i	$0.598176\pi$
$662$	−9.53485	−0.370583
$663$	2.32859	0.0904350
$664$	−24.9604	−0.968651
$665$	8.49544	0.329439
$666$	−44.1566	−1.71103
$667$	−58.9474	−2.28245
$668$	78.4692	3.03607
$669$	−8.93629	−0.345497
$670$	−9.45052	−0.365105
$671$	14.1516	0.546318
$672$	7.21011	0.278136
$673$	36.4052	1.40332	0.701659	−	0.712513i	$-0.252443\pi$
$673$	36.4052	1.40332	0.701659	+	0.712513i	$0.252443\pi$
$674$	−42.5483	−1.63890
$675$	14.8142	0.570200
$676$	−1.06704	−0.0410401
$677$	−0.0296180	−0.00113831	−0.000569156	−	1.00000i	$-0.500181\pi$
$677$	−0.0296180	−0.00113831	−0.000569156		1.00000i	$0.500181\pi$
$678$	−13.6443	−0.524005
$679$	31.4846	1.20827
$680$	2.52105	0.0966780
$681$	15.8210	0.606264
$682$	5.88912	0.225506
$683$	−36.6564	−1.40262	−0.701309	−	0.712858i	$-0.747401\pi$
$683$	−36.6564	−1.40262	−0.701309	+	0.712858i	$0.747401\pi$
$684$	39.2455	1.50059
$685$	19.4735	0.744045
$686$	44.0412	1.68150
$687$	2.32968	0.0888828
$688$	−0.386967	−0.0147530
$689$	−29.5006	−1.12388
$690$	−10.5923	−0.403241
$691$	13.4801	0.512805	0.256403	−	0.966570i	$-0.417463\pi$
$691$	13.4801	0.512805	0.256403	+	0.966570i	$0.417463\pi$
$692$	30.4524	1.15763
$693$	−4.65530	−0.176840
$694$	−44.4470	−1.68718
$695$	21.7618	0.825474
$696$	−13.6329	−0.516752
$697$	1.85905	0.0704165
$698$	48.7775	1.84626
$699$	−2.90761	−0.109976
$700$	−23.1504	−0.875004
$701$	−15.7723	−0.595713	−0.297856	−	0.954611i	$-0.596272\pi$
$701$	−15.7723	−0.595713	−0.297856	+	0.954611i	$0.596272\pi$
$702$	29.4370	1.11103
$703$	36.6874	1.38369
$704$	−13.0353	−0.491288
$705$	2.35597	0.0887308
$706$	15.8993	0.598378
$707$	−31.6904	−1.19184
$708$	−9.87636	−0.371176
$709$	27.8722	1.04676	0.523381	−	0.852099i	$-0.324670\pi$
$709$	27.8722	1.04676	0.523381	+	0.852099i	$0.324670\pi$
$710$	31.0385	1.16485
$711$	−0.811581	−0.0304366
$712$	−36.4338	−1.36542
$713$	19.1272	0.716321
$714$	−2.68777	−0.100587
$715$	−3.44461	−0.128821
$716$	−44.4163	−1.65992
$717$	7.90525	0.295227
$718$	5.12040	0.191092
$719$	5.58871	0.208424	0.104212	−	0.994555i	$-0.466768\pi$
$719$	5.58871	0.208424	0.104212	+	0.994555i	$0.466768\pi$
$720$	−0.963396	−0.0359037
$721$	15.9797	0.595116
$722$	−10.2158	−0.380191
$723$	−8.94194	−0.332554
$724$	−12.7802	−0.474972
$725$	−32.4999	−1.20702
$726$	−1.48481	−0.0551063
$727$	30.6023	1.13498	0.567488	−	0.823382i	$-0.307915\pi$
$727$	30.6023	1.13498	0.567488	+	0.823382i	$0.307915\pi$
$728$	−16.7738	−0.621680
$729$	−6.54607	−0.242447
$730$	6.23620	0.230812
$731$	1.00000	0.0369863
$732$	29.1523	1.07750
$733$	34.0003	1.25583	0.627914	−	0.778283i	$-0.283909\pi$
$733$	34.0003	1.25583	0.627914	+	0.778283i	$0.283909\pi$
$734$	45.0956	1.66451
$735$	2.35877	0.0870047
$736$	−44.8511	−1.65323
$737$	−4.30268	−0.158491
$738$	10.8474	0.399299
$739$	40.7938	1.50062	0.750312	−	0.661084i	$-0.229903\pi$
$739$	40.7938	1.50062	0.750312	+	0.661084i	$0.229903\pi$
$740$	23.0607	0.847728
$741$	−11.2889	−0.414708
$742$	34.0510	1.25005
$743$	−21.7604	−0.798313	−0.399157	−	0.916883i	$-0.630697\pi$
$743$	−21.7604	−0.798313	−0.399157	+	0.916883i	$0.630697\pi$
$744$	4.42359	0.162177
$745$	−6.47281	−0.237145
$746$	34.9368	1.27913
$747$	−24.6491	−0.901863
$748$	3.14780	0.115095
$749$	19.8011	0.723518
$750$	−13.0269	−0.475674
$751$	16.4297	0.599528	0.299764	−	0.954013i	$-0.403092\pi$
$751$	16.4297	0.599528	0.299764	+	0.954013i	$0.403092\pi$
$752$	1.43905	0.0524769
$753$	10.4576	0.381098
$754$	−64.5798	−2.35186
$755$	20.4734	0.745102
$756$	−20.7768	−0.755644
$757$	36.0582	1.31056	0.655279	−	0.755387i	$-0.272551\pi$
$757$	36.0582	1.31056	0.655279	+	0.755387i	$0.272551\pi$
$758$	77.6984	2.82213
$759$	−4.82250	−0.175046
$760$	−12.2219	−0.443336
$761$	19.7761	0.716885	0.358442	−	0.933552i	$-0.383308\pi$
$761$	19.7761	0.716885	0.358442	+	0.933552i	$0.383308\pi$
$762$	−9.53690	−0.345485
$763$	−26.3462	−0.953796
$764$	21.3488	0.772372
$765$	2.48961	0.0900120
$766$	−66.8829	−2.41658
$767$	−17.0595	−0.615981
$768$	−8.77849	−0.316766
$769$	−16.3780	−0.590605	−0.295302	−	0.955404i	$-0.595420\pi$
$769$	−16.3780	−0.590605	−0.295302	+	0.955404i	$0.595420\pi$
$770$	3.97593	0.143283
$771$	−8.91921	−0.321218
$772$	−62.9433	−2.26538
$773$	2.86226	0.102948	0.0514742	−	0.998674i	$-0.483608\pi$
$773$	2.86226	0.102948	0.0514742	+	0.998674i	$0.483608\pi$
$774$	5.83493	0.209732
$775$	10.5456	0.378808
$776$	−45.2951	−1.62600
$777$	−8.96481	−0.321611
$778$	27.0467	0.969672
$779$	−9.01256	−0.322909
$780$	−7.09588	−0.254073
$781$	14.1314	0.505660
$782$	16.7195	0.597888
$783$	−29.1676	−1.04237
$784$	1.44077	0.0514561
$785$	−15.6130	−0.557250
$786$	−14.8707	−0.530420
$787$	47.8343	1.70511	0.852554	−	0.522639i	$-0.175052\pi$
$787$	47.8343	1.70511	0.852554	+	0.522639i	$0.175052\pi$
$788$	22.7117	0.809071
$789$	−18.5779	−0.661390
$790$	0.693143	0.0246609
$791$	16.6342	0.591446
$792$	6.69732	0.237979
$793$	50.3548	1.78815
$794$	14.4980	0.514515
$795$	5.25245	0.186285
$796$	70.1178	2.48526
$797$	31.3080	1.10899	0.554494	−	0.832188i	$-0.312912\pi$
$797$	31.3080	1.10899	0.554494	+	0.832188i	$0.312912\pi$
$798$	13.0302	0.461263
$799$	−3.71881	−0.131562
$800$	−24.7281	−0.874270
$801$	−35.9794	−1.27127
$802$	−6.06863	−0.214291
$803$	2.83925	0.100195
$804$	−8.86349	−0.312591
$805$	12.9134	0.455138
$806$	20.9549	0.738103
$807$	14.2688	0.502285
$808$	45.5913	1.60389
$809$	−7.12766	−0.250595	−0.125298	−	0.992119i	$-0.539989\pi$
$809$	−7.12766	−0.250595	−0.125298	+	0.992119i	$0.539989\pi$
$810$	11.7047	0.411262
$811$	43.1598	1.51555	0.757773	−	0.652518i	$-0.226287\pi$
$811$	43.1598	1.51555	0.757773	+	0.652518i	$0.226287\pi$
$812$	45.5807	1.59957
$813$	9.92095	0.347943
$814$	17.1700	0.601808
$815$	−12.5841	−0.440803
$816$	−0.253240	−0.00886518
$817$	−4.84794	−0.169608
$818$	−8.51081	−0.297574
$819$	−16.5646	−0.578815
$820$	−5.66505	−0.197832
$821$	17.8483	0.622911	0.311456	−	0.950261i	$-0.399184\pi$
$821$	17.8483	0.622911	0.311456	+	0.950261i	$0.399184\pi$
$822$	29.8681	1.04177
$823$	−28.9802	−1.01019	−0.505094	−	0.863065i	$-0.668542\pi$
$823$	−28.9802	−1.01019	−0.505094	+	0.863065i	$0.668542\pi$
$824$	−22.9891	−0.800865
$825$	−2.65882	−0.0925683
$826$	19.6908	0.685131
$827$	30.6810	1.06688	0.533441	−	0.845838i	$-0.320899\pi$
$827$	30.6810	1.06688	0.533441	+	0.845838i	$0.320899\pi$
$828$	59.6547	2.07314
$829$	31.1394	1.08151	0.540757	−	0.841179i	$-0.318138\pi$
$829$	31.1394	1.08151	0.540757	+	0.841179i	$0.318138\pi$
$830$	21.0519	0.730724
$831$	16.3645	0.567677
$832$	−46.3828	−1.60803
$833$	−3.72324	−0.129003
$834$	33.3779	1.15578
$835$	−24.1323	−0.835133
$836$	−15.2603	−0.527790
$837$	9.46431	0.327134
$838$	60.2726	2.08208
$839$	−51.9366	−1.79305	−0.896525	−	0.442993i	$-0.853917\pi$
$839$	−51.9366	−1.79305	−0.896525	+	0.442993i	$0.853917\pi$
$840$	2.98651	0.103044
$841$	34.9888	1.20651
$842$	44.3912	1.52982
$843$	12.5569	0.432483
$844$	56.8676	1.95746
$845$	0.328156	0.0112889
$846$	−21.6990	−0.746027
$847$	1.81018	0.0621986
$848$	3.20827	0.110172
$849$	8.04769	0.276196
$850$	9.21809	0.316178
$851$	55.7664	1.91165
$852$	29.1105	0.997309
$853$	−7.03745	−0.240958	−0.120479	−	0.992716i	$-0.538443\pi$
$853$	−7.03745	−0.240958	−0.120479	+	0.992716i	$0.538443\pi$
$854$	−58.1219	−1.98889
$855$	−12.0695	−0.412768
$856$	−28.4868	−0.973659
$857$	32.9687	1.12619	0.563094	−	0.826393i	$-0.309611\pi$
$857$	32.9687	1.12619	0.563094	+	0.826393i	$0.309611\pi$
$858$	−5.28329	−0.180368
$859$	−22.6709	−0.773520	−0.386760	−	0.922180i	$-0.626406\pi$
$859$	−22.6709	−0.773520	−0.386760	+	0.922180i	$0.626406\pi$
$860$	−3.04728	−0.103911
$861$	2.20228	0.0750535
$862$	−77.3198	−2.63352
$863$	−41.5480	−1.41431	−0.707155	−	0.707058i	$-0.750022\pi$
$863$	−41.5480	−1.41431	−0.707155	+	0.707058i	$0.750022\pi$
$864$	−22.1927	−0.755010
$865$	−9.36528	−0.318429
$866$	16.7166	0.568054
$867$	0.654424	0.0222254
$868$	−14.7900	−0.502006
$869$	0.315578	0.0107052
$870$	11.4981	0.389824
$871$	−15.3099	−0.518757
$872$	37.9028	1.28355
$873$	−44.7302	−1.51389
$874$	−81.0552	−2.74173
$875$	15.8815	0.536894
$876$	5.84884	0.197614
$877$	42.8331	1.44637	0.723185	−	0.690655i	$-0.242678\pi$
$877$	42.8331	1.44637	0.723185	+	0.690655i	$0.242678\pi$
$878$	14.7074	0.496352
$879$	10.2139	0.344506
$880$	0.374610	0.0126281
$881$	28.0970	0.946612	0.473306	−	0.880898i	$-0.343061\pi$
$881$	28.0970	0.946612	0.473306	+	0.880898i	$0.343061\pi$
$882$	−21.7249	−0.731514
$883$	29.1559	0.981172	0.490586	−	0.871393i	$-0.336783\pi$
$883$	29.1559	0.981172	0.490586	+	0.871393i	$0.336783\pi$
$884$	11.2006	0.376717
$885$	3.03736	0.102100
$886$	24.6839	0.829271
$887$	−43.5924	−1.46369	−0.731845	−	0.681471i	$-0.761341\pi$
$887$	−43.5924	−1.46369	−0.731845	+	0.681471i	$0.761341\pi$
$888$	12.8972	0.432801
$889$	11.6268	0.389950
$890$	30.7288	1.03003
$891$	5.32898	0.178528
$892$	−42.9838	−1.43920
$893$	18.0286	0.603303
$894$	−9.92789	−0.332038
$895$	13.6597	0.456594
$896$	31.5022	1.05242
$897$	−17.1596	−0.572941
$898$	45.5280	1.51929
$899$	−20.7631	−0.692487
$900$	32.8899	1.09633
$901$	−8.29080	−0.276207
$902$	−4.21795	−0.140442
$903$	1.18463	0.0394219
$904$	−23.9308	−0.795926
$905$	3.93040	0.130651
$906$	31.4017	1.04325
$907$	−16.2688	−0.540195	−0.270098	−	0.962833i	$-0.587056\pi$
$907$	−16.2688	−0.540195	−0.270098	+	0.962833i	$0.587056\pi$
$908$	76.0996	2.52546
$909$	45.0226	1.49331
$910$	14.1473	0.468978
$911$	−11.0011	−0.364484	−0.182242	−	0.983254i	$-0.558335\pi$
$911$	−11.0011	−0.364484	−0.182242	+	0.983254i	$0.558335\pi$
$912$	1.22769	0.0406530
$913$	9.58463	0.317205
$914$	−6.24952	−0.206716
$915$	−8.96544	−0.296388
$916$	11.2058	0.370251
$917$	18.1294	0.598686
$918$	8.27294	0.273048
$919$	11.3109	0.373111	0.186556	−	0.982444i	$-0.440268\pi$
$919$	11.3109	0.373111	0.186556	+	0.982444i	$0.440268\pi$
$920$	−18.5778	−0.612493
$921$	−5.90527	−0.194585
$922$	−40.5451	−1.33528
$923$	50.2826	1.65507
$924$	3.72896	0.122674
$925$	30.7461	1.01093
$926$	35.2770	1.15927
$927$	−22.7024	−0.745645
$928$	48.6869	1.59823
$929$	51.7569	1.69809	0.849044	−	0.528322i	$-0.177179\pi$
$929$	51.7569	1.69809	0.849044	+	0.528322i	$0.177179\pi$
$930$	−3.73092	−0.122342
$931$	18.0501	0.591567
$932$	−13.9857	−0.458117
$933$	5.55458	0.181849
$934$	20.1116	0.658072
$935$	−0.968068	−0.0316592
$936$	23.8306	0.778928
$937$	13.0178	0.425272	0.212636	−	0.977132i	$-0.431795\pi$
$937$	13.0178	0.425272	0.212636	+	0.977132i	$0.431795\pi$
$938$	17.6714	0.576993
$939$	6.80231	0.221985
$940$	11.3323	0.369618
$941$	−27.7311	−0.904009	−0.452004	−	0.892016i	$-0.649291\pi$
$941$	−27.7311	−0.904009	−0.452004	+	0.892016i	$0.649291\pi$
$942$	−23.9469	−0.780231
$943$	−13.6995	−0.446116
$944$	1.85526	0.0603835
$945$	6.38966	0.207856
$946$	−2.26888	−0.0737675
$947$	12.6634	0.411504	0.205752	−	0.978604i	$-0.434036\pi$
$947$	12.6634	0.411504	0.205752	+	0.978604i	$0.434036\pi$
$948$	0.650088	0.0211139
$949$	10.1027	0.327948
$950$	−44.6888	−1.44990
$951$	−20.8189	−0.675098
$952$	−4.71409	−0.152785
$953$	53.2090	1.72361	0.861805	−	0.507240i	$-0.169334\pi$
$953$	53.2090	1.72361	0.861805	+	0.507240i	$0.169334\pi$
$954$	−48.3763	−1.56624
$955$	−6.56557	−0.212457
$956$	38.0245	1.22980
$957$	5.23493	0.169221
$958$	−89.4038	−2.88851
$959$	−36.4134	−1.17585
$960$	8.25825	0.266534
$961$	−24.2628	−0.782671
$962$	61.0949	1.96978
$963$	−28.1315	−0.906525
$964$	−43.0110	−1.38529
$965$	19.3575	0.623139
$966$	19.8064	0.637260
$967$	−28.9666	−0.931502	−0.465751	−	0.884916i	$-0.654216\pi$
$967$	−28.9666	−0.931502	−0.465751	+	0.884916i	$0.654216\pi$
$968$	−2.60421	−0.0837025
$969$	−3.17261	−0.101919
$970$	38.2025	1.22661
$971$	3.85560	0.123732	0.0618661	−	0.998084i	$-0.480295\pi$
$971$	3.85560	0.123732	0.0618661	+	0.998084i	$0.480295\pi$
$972$	45.4108	1.45655
$973$	−40.6923	−1.30453
$974$	−59.7166	−1.91344
$975$	−9.46071	−0.302985
$976$	−5.47621	−0.175289
$977$	−54.2208	−1.73468	−0.867339	−	0.497719i	$-0.834171\pi$
$977$	−54.2208	−1.73468	−0.867339	+	0.497719i	$0.834171\pi$
$978$	−19.3013	−0.617188
$979$	13.9904	0.447134
$980$	11.3458	0.362427
$981$	37.4301	1.19505
$982$	−23.8501	−0.761087
$983$	−22.7208	−0.724680	−0.362340	−	0.932046i	$-0.618022\pi$
$983$	−22.7208	−0.724680	−0.362340	+	0.932046i	$0.618022\pi$
$984$	−3.16830	−0.101002
$985$	−6.98472	−0.222552
$986$	−18.1494	−0.577995
$987$	−4.40540	−0.140225
$988$	−54.2999	−1.72751
$989$	−7.36907	−0.234323
$990$	−5.64862	−0.179525
$991$	−12.2064	−0.387750	−0.193875	−	0.981026i	$-0.562106\pi$
$991$	−12.2064	−0.387750	−0.193875	+	0.981026i	$0.562106\pi$
$992$	−15.7979	−0.501585
$993$	2.75019	0.0872746
$994$	−58.0386	−1.84087
$995$	−21.5639	−0.683622
$996$	19.7443	0.625622
$997$	15.7306	0.498192	0.249096	−	0.968479i	$-0.419866\pi$
$997$	15.7306	0.498192	0.249096	+	0.968479i	$0.419866\pi$
$998$	−61.9902	−1.96226
$999$	27.5936	0.873024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.11	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.26888 q^{2} +0.654424 q^{3} +3.14780 q^{4} -0.968068 q^{5} -1.48481 q^{6} +1.81018 q^{7} -2.60421 q^{8} -2.57173 q^{9} +O(q^{10})\)	\(q-2.26888 q^{2} +0.654424 q^{3} +3.14780 q^{4} -0.968068 q^{5} -1.48481 q^{6} +1.81018 q^{7} -2.60421 q^{8} -2.57173 q^{9} +2.19643 q^{10} +1.00000 q^{11} +2.05999 q^{12} +3.55823 q^{13} -4.10708 q^{14} -0.633527 q^{15} -0.386967 q^{16} +1.00000 q^{17} +5.83493 q^{18} -4.84794 q^{19} -3.04728 q^{20} +1.18463 q^{21} -2.26888 q^{22} -7.36907 q^{23} -1.70426 q^{24} -4.06284 q^{25} -8.07319 q^{26} -3.64627 q^{27} +5.69809 q^{28} +7.99930 q^{29} +1.43739 q^{30} -2.59561 q^{31} +6.08640 q^{32} +0.654424 q^{33} -2.26888 q^{34} -1.75238 q^{35} -8.09528 q^{36} -7.56763 q^{37} +10.9994 q^{38} +2.32859 q^{39} +2.52105 q^{40} +1.85905 q^{41} -2.68777 q^{42} +1.00000 q^{43} +3.14780 q^{44} +2.48961 q^{45} +16.7195 q^{46} -3.71881 q^{47} -0.253240 q^{48} -3.72324 q^{49} +9.21809 q^{50} +0.654424 q^{51} +11.2006 q^{52} -8.29080 q^{53} +8.27294 q^{54} -0.968068 q^{55} -4.71409 q^{56} -3.17261 q^{57} -18.1494 q^{58} -4.79436 q^{59} -1.99421 q^{60} +14.1516 q^{61} +5.88912 q^{62} -4.65530 q^{63} -13.0353 q^{64} -3.44461 q^{65} -1.48481 q^{66} -4.30268 q^{67} +3.14780 q^{68} -4.82250 q^{69} +3.97593 q^{70} +14.1314 q^{71} +6.69732 q^{72} +2.83925 q^{73} +17.1700 q^{74} -2.65882 q^{75} -15.2603 q^{76} +1.81018 q^{77} -5.28329 q^{78} +0.315578 q^{79} +0.374610 q^{80} +5.32898 q^{81} -4.21795 q^{82} +9.58463 q^{83} +3.72896 q^{84} -0.968068 q^{85} -2.26888 q^{86} +5.23493 q^{87} -2.60421 q^{88} +13.9904 q^{89} -5.64862 q^{90} +6.44105 q^{91} -23.1963 q^{92} -1.69863 q^{93} +8.43751 q^{94} +4.69314 q^{95} +3.98308 q^{96} +17.3930 q^{97} +8.44757 q^{98} -2.57173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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