LMFDB - Embedded newform 8041.2.a.g.1.16

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:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.85886 q^{2} +3.31260 q^{3} +1.45535 q^{4} +0.943187 q^{5} -6.15766 q^{6} -1.28029 q^{7} +1.01243 q^{8} +7.97335 q^{9} +O(q^{10})$	\(q-1.85886 q^{2} +3.31260 q^{3} +1.45535 q^{4} +0.943187 q^{5} -6.15766 q^{6} -1.28029 q^{7} +1.01243 q^{8} +7.97335 q^{9} -1.75325 q^{10} -1.00000 q^{11} +4.82099 q^{12} -3.54307 q^{13} +2.37987 q^{14} +3.12440 q^{15} -4.79266 q^{16} +1.00000 q^{17} -14.8213 q^{18} -3.35662 q^{19} +1.37266 q^{20} -4.24108 q^{21} +1.85886 q^{22} +3.29817 q^{23} +3.35378 q^{24} -4.11040 q^{25} +6.58607 q^{26} +16.4747 q^{27} -1.86326 q^{28} -6.51572 q^{29} -5.80782 q^{30} +0.322173 q^{31} +6.88400 q^{32} -3.31260 q^{33} -1.85886 q^{34} -1.20755 q^{35} +11.6040 q^{36} -10.0135 q^{37} +6.23947 q^{38} -11.7368 q^{39} +0.954911 q^{40} -8.39914 q^{41} +7.88356 q^{42} +1.00000 q^{43} -1.45535 q^{44} +7.52036 q^{45} -6.13083 q^{46} +6.51522 q^{47} -15.8762 q^{48} -5.36087 q^{49} +7.64064 q^{50} +3.31260 q^{51} -5.15640 q^{52} +3.17636 q^{53} -30.6242 q^{54} -0.943187 q^{55} -1.29620 q^{56} -11.1191 q^{57} +12.1118 q^{58} +1.42476 q^{59} +4.54710 q^{60} -10.7885 q^{61} -0.598873 q^{62} -10.2082 q^{63} -3.21106 q^{64} -3.34178 q^{65} +6.15766 q^{66} +12.2670 q^{67} +1.45535 q^{68} +10.9255 q^{69} +2.24466 q^{70} -4.14908 q^{71} +8.07246 q^{72} -6.21252 q^{73} +18.6137 q^{74} -13.6161 q^{75} -4.88505 q^{76} +1.28029 q^{77} +21.8170 q^{78} -16.6114 q^{79} -4.52037 q^{80} +30.6542 q^{81} +15.6128 q^{82} -0.588060 q^{83} -6.17224 q^{84} +0.943187 q^{85} -1.85886 q^{86} -21.5840 q^{87} -1.01243 q^{88} +11.0170 q^{89} -13.9793 q^{90} +4.53614 q^{91} +4.79998 q^{92} +1.06723 q^{93} -12.1109 q^{94} -3.16592 q^{95} +22.8040 q^{96} -17.6870 q^{97} +9.96509 q^{98} -7.97335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−1.85886	−1.31441	−0.657205	−	0.753712i	$-0.728261\pi$
$2$	−1.85886	−1.31441	−0.657205	+	0.753712i	$0.728261\pi$
$3$	3.31260	1.91253	0.956267	−	0.292497i	$-0.0944861\pi$
$3$	3.31260	1.91253	0.956267	+	0.292497i	$0.0944861\pi$
$4$	1.45535	0.727674
$5$	0.943187	0.421806	0.210903	−	0.977507i	$-0.432360\pi$
$5$	0.943187	0.421806	0.210903	+	0.977507i	$0.432360\pi$
$6$	−6.15766	−2.51385
$7$	−1.28029	−0.483902	−0.241951	−	0.970288i	$-0.577787\pi$
$7$	−1.28029	−0.483902	−0.241951	+	0.970288i	$0.577787\pi$
$8$	1.01243	0.357948
$9$	7.97335	2.65778
$10$	−1.75325	−0.554426
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.82099	1.39170
$13$	−3.54307	−0.982672	−0.491336	−	0.870970i	$-0.663491\pi$
$13$	−3.54307	−0.982672	−0.491336	+	0.870970i	$0.663491\pi$
$14$	2.37987	0.636046
$15$	3.12440	0.806718
$16$	−4.79266	−1.19816
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−14.8213	−3.49342
$19$	−3.35662	−0.770061	−0.385031	−	0.922904i	$-0.625809\pi$
$19$	−3.35662	−0.770061	−0.385031	+	0.922904i	$0.625809\pi$
$20$	1.37266	0.306937
$21$	−4.24108	−0.925479
$22$	1.85886	0.396310
$23$	3.29817	0.687716	0.343858	−	0.939022i	$-0.388266\pi$
$23$	3.29817	0.687716	0.343858	+	0.939022i	$0.388266\pi$
$24$	3.35378	0.684588
$25$	−4.11040	−0.822080
$26$	6.58607	1.29163
$27$	16.4747	3.17056
$28$	−1.86326	−0.352123
$29$	−6.51572	−1.20994	−0.604970	−	0.796249i	$-0.706815\pi$
$29$	−6.51572	−1.20994	−0.604970	+	0.796249i	$0.706815\pi$
$30$	−5.80782	−1.06036
$31$	0.322173	0.0578639	0.0289320	−	0.999581i	$-0.490789\pi$
$31$	0.322173	0.0578639	0.0289320	+	0.999581i	$0.490789\pi$
$32$	6.88400	1.21693
$33$	−3.31260	−0.576650
$34$	−1.85886	−0.318791
$35$	−1.20755	−0.204113
$36$	11.6040	1.93400
$37$	−10.0135	−1.64621	−0.823106	−	0.567888i	$-0.807761\pi$
$37$	−10.0135	−1.64621	−0.823106	+	0.567888i	$0.807761\pi$
$38$	6.23947	1.01218
$39$	−11.7368	−1.87939
$40$	0.954911	0.150985
$41$	−8.39914	−1.31172	−0.655862	−	0.754880i	$-0.727695\pi$
$41$	−8.39914	−1.31172	−0.655862	+	0.754880i	$0.727695\pi$
$42$	7.88356	1.21646
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.45535	−0.219402
$45$	7.52036	1.12107
$46$	−6.13083	−0.903941
$47$	6.51522	0.950343	0.475171	−	0.879893i	$-0.342386\pi$
$47$	6.51522	0.950343	0.475171	+	0.879893i	$0.342386\pi$
$48$	−15.8762	−2.29153
$49$	−5.36087	−0.765839
$50$	7.64064	1.08055
$51$	3.31260	0.463857
$52$	−5.15640	−0.715065
$53$	3.17636	0.436307	0.218154	−	0.975914i	$-0.429997\pi$
$53$	3.17636	0.436307	0.218154	+	0.975914i	$0.429997\pi$
$54$	−30.6242	−4.16742
$55$	−0.943187	−0.127179
$56$	−1.29620	−0.173212
$57$	−11.1191	−1.47277
$58$	12.1118	1.59036
$59$	1.42476	0.185487	0.0927437	−	0.995690i	$-0.470436\pi$
$59$	1.42476	0.185487	0.0927437	+	0.995690i	$0.470436\pi$
$60$	4.54710	0.587027
$61$	−10.7885	−1.38132	−0.690660	−	0.723180i	$-0.742680\pi$
$61$	−10.7885	−1.38132	−0.690660	+	0.723180i	$0.742680\pi$
$62$	−0.598873	−0.0760569
$63$	−10.2082	−1.28611
$64$	−3.21106	−0.401382
$65$	−3.34178	−0.414497
$66$	6.15766	0.757955
$67$	12.2670	1.49866	0.749328	−	0.662199i	$-0.230377\pi$
$67$	12.2670	1.49866	0.749328	+	0.662199i	$0.230377\pi$
$68$	1.45535	0.176487
$69$	10.9255	1.31528
$70$	2.24466	0.268288
$71$	−4.14908	−0.492405	−0.246203	−	0.969218i	$-0.579183\pi$
$71$	−4.14908	−0.492405	−0.246203	+	0.969218i	$0.579183\pi$
$72$	8.07246	0.951348
$73$	−6.21252	−0.727120	−0.363560	−	0.931571i	$-0.618439\pi$
$73$	−6.21252	−0.727120	−0.363560	+	0.931571i	$0.618439\pi$
$74$	18.6137	2.16380
$75$	−13.6161	−1.57225
$76$	−4.88505	−0.560353
$77$	1.28029	0.145902
$78$	21.8170	2.47029
$79$	−16.6114	−1.86893	−0.934464	−	0.356059i	$-0.884120\pi$
$79$	−16.6114	−1.86893	−0.934464	+	0.356059i	$0.884120\pi$
$80$	−4.52037	−0.505393
$81$	30.6542	3.40603
$82$	15.6128	1.72414
$83$	−0.588060	−0.0645480	−0.0322740	−	0.999479i	$-0.510275\pi$
$83$	−0.588060	−0.0645480	−0.0322740	+	0.999479i	$0.510275\pi$
$84$	−6.17224	−0.673447
$85$	0.943187	0.102303
$86$	−1.85886	−0.200446
$87$	−21.5840	−2.31405
$88$	−1.01243	−0.107925
$89$	11.0170	1.16780	0.583902	−	0.811824i	$-0.301525\pi$
$89$	11.0170	1.16780	0.583902	+	0.811824i	$0.301525\pi$
$90$	−13.9793	−1.47354
$91$	4.53614	0.475517
$92$	4.79998	0.500433
$93$	1.06723	0.110667
$94$	−12.1109	−1.24914
$95$	−3.16592	−0.324816
$96$	22.8040	2.32742
$97$	−17.6870	−1.79584	−0.897919	−	0.440161i	$-0.854922\pi$
$97$	−17.6870	−1.79584	−0.897919	+	0.440161i	$0.854922\pi$
$98$	9.96509	1.00663
$99$	−7.97335	−0.801352
$100$	−5.98206	−0.598206
$101$	7.30402	0.726777	0.363389	−	0.931638i	$-0.381620\pi$
$101$	7.30402	0.726777	0.363389	+	0.931638i	$0.381620\pi$
$102$	−6.15766	−0.609699
$103$	−11.4162	−1.12487	−0.562436	−	0.826841i	$-0.690136\pi$
$103$	−11.4162	−1.12487	−0.562436	+	0.826841i	$0.690136\pi$
$104$	−3.58711	−0.351746
$105$	−4.00013	−0.390373
$106$	−5.90440	−0.573486
$107$	4.24267	0.410154	0.205077	−	0.978746i	$-0.434255\pi$
$107$	4.24267	0.410154	0.205077	+	0.978746i	$0.434255\pi$
$108$	23.9765	2.30714
$109$	4.18320	0.400678	0.200339	−	0.979727i	$-0.435796\pi$
$109$	4.18320	0.400678	0.200339	+	0.979727i	$0.435796\pi$
$110$	1.75325	0.167166
$111$	−33.1708	−3.14844
$112$	6.13597	0.579795
$113$	−8.54508	−0.803854	−0.401927	−	0.915672i	$-0.631659\pi$
$113$	−8.54508	−0.803854	−0.401927	+	0.915672i	$0.631659\pi$
$114$	20.6689	1.93582
$115$	3.11079	0.290083
$116$	−9.48264	−0.880441
$117$	−28.2502	−2.61173
$118$	−2.64842	−0.243807
$119$	−1.28029	−0.117364
$120$	3.16324	0.288763
$121$	1.00000	0.0909091
$122$	20.0542	1.81562
$123$	−27.8230	−2.50872
$124$	0.468873	0.0421061
$125$	−8.59281	−0.768564
$126$	18.9755	1.69047
$127$	3.12850	0.277610	0.138805	−	0.990320i	$-0.455674\pi$
$127$	3.12850	0.277610	0.138805	+	0.990320i	$0.455674\pi$
$128$	−7.79911	−0.689350
$129$	3.31260	0.291659
$130$	6.21189	0.544819
$131$	5.20463	0.454730	0.227365	−	0.973810i	$-0.426989\pi$
$131$	5.20463	0.454730	0.227365	+	0.973810i	$0.426989\pi$
$132$	−4.82099	−0.419613
$133$	4.29743	0.372634
$134$	−22.8026	−1.96985
$135$	15.5388	1.33736
$136$	1.01243	0.0868152
$137$	−16.4360	−1.40422	−0.702111	−	0.712067i	$-0.747759\pi$
$137$	−16.4360	−1.40422	−0.702111	+	0.712067i	$0.747759\pi$
$138$	−20.3090	−1.72882
$139$	5.99258	0.508284	0.254142	−	0.967167i	$-0.418207\pi$
$139$	5.99258	0.508284	0.254142	+	0.967167i	$0.418207\pi$
$140$	−1.75740	−0.148528
$141$	21.5824	1.81756
$142$	7.71255	0.647223
$143$	3.54307	0.296287
$144$	−38.2135	−3.18446
$145$	−6.14554	−0.510359
$146$	11.5482	0.955734
$147$	−17.7584	−1.46469
$148$	−14.5732	−1.19791
$149$	−4.15148	−0.340102	−0.170051	−	0.985435i	$-0.554393\pi$
$149$	−4.15148	−0.340102	−0.170051	+	0.985435i	$0.554393\pi$
$150$	25.3104	2.06659
$151$	18.2745	1.48716	0.743578	−	0.668649i	$-0.233127\pi$
$151$	18.2745	1.48716	0.743578	+	0.668649i	$0.233127\pi$
$152$	−3.39834	−0.275642
$153$	7.97335	0.644607
$154$	−2.37987	−0.191775
$155$	0.303869	0.0244074
$156$	−17.0811	−1.36758
$157$	−8.99189	−0.717631	−0.358816	−	0.933408i	$-0.616819\pi$
$157$	−8.99189	−0.717631	−0.358816	+	0.933408i	$0.616819\pi$
$158$	30.8782	2.45654
$159$	10.5220	0.834452
$160$	6.49290	0.513309
$161$	−4.22260	−0.332787
$162$	−56.9818	−4.47691
$163$	−4.18972	−0.328164	−0.164082	−	0.986447i	$-0.552466\pi$
$163$	−4.18972	−0.328164	−0.164082	+	0.986447i	$0.552466\pi$
$164$	−12.2237	−0.954508
$165$	−3.12440	−0.243235
$166$	1.09312	0.0848425
$167$	9.88467	0.764899	0.382449	−	0.923976i	$-0.375081\pi$
$167$	9.88467	0.764899	0.382449	+	0.923976i	$0.375081\pi$
$168$	−4.29380	−0.331274
$169$	−0.446632	−0.0343563
$170$	−1.75325	−0.134468
$171$	−26.7635	−2.04665
$172$	1.45535	0.110969
$173$	−16.0141	−1.21753	−0.608763	−	0.793352i	$-0.708334\pi$
$173$	−16.0141	−1.21753	−0.608763	+	0.793352i	$0.708334\pi$
$174$	40.1216	3.04161
$175$	5.26248	0.397806
$176$	4.79266	0.361260
$177$	4.71965	0.354751
$178$	−20.4791	−1.53497
$179$	4.67448	0.349387	0.174694	−	0.984623i	$-0.444107\pi$
$179$	4.67448	0.349387	0.174694	+	0.984623i	$0.444107\pi$
$180$	10.9447	0.815772
$181$	−5.40048	−0.401415	−0.200707	−	0.979651i	$-0.564324\pi$
$181$	−5.40048	−0.401415	−0.200707	+	0.979651i	$0.564324\pi$
$182$	−8.43204	−0.625025
$183$	−35.7379	−2.64182
$184$	3.33917	0.246167
$185$	−9.44462	−0.694382
$186$	−1.98383	−0.145461
$187$	−1.00000	−0.0731272
$188$	9.48192	0.691540
$189$	−21.0924	−1.53424
$190$	5.88499	0.426942
$191$	21.9393	1.58747	0.793737	−	0.608261i	$-0.208133\pi$
$191$	21.9393	1.58747	0.793737	+	0.608261i	$0.208133\pi$
$192$	−10.6370	−0.767657
$193$	−14.1725	−1.02016	−0.510078	−	0.860128i	$-0.670383\pi$
$193$	−14.1725	−1.02016	−0.510078	+	0.860128i	$0.670383\pi$
$194$	32.8775	2.36047
$195$	−11.0700	−0.792739
$196$	−7.80193	−0.557281
$197$	−0.784799	−0.0559146	−0.0279573	−	0.999609i	$-0.508900\pi$
$197$	−0.784799	−0.0559146	−0.0279573	+	0.999609i	$0.508900\pi$
$198$	14.8213	1.05330
$199$	−8.61482	−0.610688	−0.305344	−	0.952242i	$-0.598771\pi$
$199$	−8.61482	−0.610688	−0.305344	+	0.952242i	$0.598771\pi$
$200$	−4.16149	−0.294262
$201$	40.6358	2.86623
$202$	−13.5771	−0.955283
$203$	8.34198	0.585492
$204$	4.82099	0.337537
$205$	−7.92196	−0.553293
$206$	21.2211	1.47854
$207$	26.2975	1.82780
$208$	16.9807	1.17740
$209$	3.35662	0.232182
$210$	7.43567	0.513110
$211$	28.4532	1.95880	0.979400	−	0.201928i	$-0.0647207\pi$
$211$	28.4532	1.95880	0.979400	+	0.201928i	$0.0647207\pi$
$212$	4.62271	0.317489
$213$	−13.7443	−0.941742
$214$	−7.88651	−0.539111
$215$	0.943187	0.0643248
$216$	16.6795	1.13490
$217$	−0.412473	−0.0280005
$218$	−7.77597	−0.526655
$219$	−20.5796	−1.39064
$220$	−1.37266	−0.0925450
$221$	−3.54307	−0.238333
$222$	61.6598	4.13834
$223$	−9.78566	−0.655296	−0.327648	−	0.944800i	$-0.606256\pi$
$223$	−9.78566	−0.655296	−0.327648	+	0.944800i	$0.606256\pi$
$224$	−8.81349	−0.588876
$225$	−32.7736	−2.18491
$226$	15.8841	1.05659
$227$	22.7185	1.50788	0.753939	−	0.656944i	$-0.228151\pi$
$227$	22.7185	1.50788	0.753939	+	0.656944i	$0.228151\pi$
$228$	−16.1822	−1.07169
$229$	−3.97620	−0.262754	−0.131377	−	0.991332i	$-0.541940\pi$
$229$	−3.97620	−0.262754	−0.131377	+	0.991332i	$0.541940\pi$
$230$	−5.78251	−0.381288
$231$	4.24108	0.279042
$232$	−6.59671	−0.433095
$233$	20.0057	1.31062	0.655308	−	0.755362i	$-0.272539\pi$
$233$	20.0057	1.31062	0.655308	+	0.755362i	$0.272539\pi$
$234$	52.5130	3.43288
$235$	6.14507	0.400860
$236$	2.07352	0.134974
$237$	−55.0270	−3.57438
$238$	2.37987	0.154264
$239$	3.22453	0.208577	0.104289	−	0.994547i	$-0.466743\pi$
$239$	3.22453	0.208577	0.104289	+	0.994547i	$0.466743\pi$
$240$	−14.9742	−0.966581
$241$	−2.86703	−0.184682	−0.0923408	−	0.995727i	$-0.529435\pi$
$241$	−2.86703	−0.184682	−0.0923408	+	0.995727i	$0.529435\pi$
$242$	−1.85886	−0.119492
$243$	52.1211	3.34357
$244$	−15.7010	−1.00515
$245$	−5.05630	−0.323035
$246$	51.7190	3.29748
$247$	11.8927	0.756717
$248$	0.326177	0.0207123
$249$	−1.94801	−0.123450
$250$	15.9728	1.01021
$251$	19.6281	1.23892	0.619458	−	0.785030i	$-0.287352\pi$
$251$	19.6281	1.23892	0.619458	+	0.785030i	$0.287352\pi$
$252$	−14.8564	−0.935867
$253$	−3.29817	−0.207354
$254$	−5.81543	−0.364893
$255$	3.12440	0.195658
$256$	20.9195	1.30747
$257$	−28.8242	−1.79801	−0.899004	−	0.437941i	$-0.855708\pi$
$257$	−28.8242	−1.79801	−0.899004	+	0.437941i	$0.855708\pi$
$258$	−6.15766	−0.383359
$259$	12.8202	0.796606
$260$	−4.86345	−0.301618
$261$	−51.9521	−3.21575
$262$	−9.67466	−0.597702
$263$	−17.5011	−1.07916	−0.539581	−	0.841933i	$-0.681418\pi$
$263$	−17.5011	−1.07916	−0.539581	+	0.841933i	$0.681418\pi$
$264$	−3.35378	−0.206411
$265$	2.99590	0.184037
$266$	−7.98830	−0.489794
$267$	36.4951	2.23346
$268$	17.8528	1.09053
$269$	7.07228	0.431204	0.215602	−	0.976481i	$-0.430829\pi$
$269$	7.07228	0.431204	0.215602	+	0.976481i	$0.430829\pi$
$270$	−28.8843	−1.75784
$271$	−19.4556	−1.18184	−0.590920	−	0.806730i	$-0.701235\pi$
$271$	−19.4556	−1.18184	−0.590920	+	0.806730i	$0.701235\pi$
$272$	−4.79266	−0.290598
$273$	15.0265	0.909442
$274$	30.5522	1.84572
$275$	4.11040	0.247866
$276$	15.9005	0.957095
$277$	6.25814	0.376015	0.188007	−	0.982168i	$-0.439797\pi$
$277$	6.25814	0.376015	0.188007	+	0.982168i	$0.439797\pi$
$278$	−11.1393	−0.668093
$279$	2.56880	0.153790
$280$	−1.22256	−0.0730618
$281$	−9.10585	−0.543210	−0.271605	−	0.962409i	$-0.587554\pi$
$281$	−9.10585	−0.543210	−0.271605	+	0.962409i	$0.587554\pi$
$282$	−40.1185	−2.38902
$283$	3.50582	0.208399	0.104200	−	0.994556i	$-0.466772\pi$
$283$	3.50582	0.208399	0.104200	+	0.994556i	$0.466772\pi$
$284$	−6.03836	−0.358311
$285$	−10.4874	−0.621222
$286$	−6.58607	−0.389442
$287$	10.7533	0.634747
$288$	54.8886	3.23434
$289$	1.00000	0.0588235
$290$	11.4237	0.670822
$291$	−58.5899	−3.43460
$292$	−9.04137	−0.529106
$293$	5.99704	0.350351	0.175175	−	0.984537i	$-0.443951\pi$
$293$	5.99704	0.350351	0.175175	+	0.984537i	$0.443951\pi$
$294$	33.0104	1.92521
$295$	1.34381	0.0782397
$296$	−10.1380	−0.589259
$297$	−16.4747	−0.955961
$298$	7.71700	0.447034
$299$	−11.6857	−0.675799
$300$	−19.8162	−1.14409
$301$	−1.28029	−0.0737944
$302$	−33.9696	−1.95473
$303$	24.1953	1.38999
$304$	16.0871	0.922660
$305$	−10.1755	−0.582649
$306$	−14.8213	−0.847278
$307$	−34.4336	−1.96523	−0.982614	−	0.185659i	$-0.940558\pi$
$307$	−34.4336	−1.96523	−0.982614	+	0.185659i	$0.940558\pi$
$308$	1.86326	0.106169
$309$	−37.8174	−2.15135
$310$	−0.564849	−0.0320813
$311$	20.4432	1.15923	0.579615	−	0.814890i	$-0.303203\pi$
$311$	20.4432	1.15923	0.579615	+	0.814890i	$0.303203\pi$
$312$	−11.8827	−0.672725
$313$	11.8151	0.667827	0.333914	−	0.942604i	$-0.391631\pi$
$313$	11.8151	0.667827	0.333914	+	0.942604i	$0.391631\pi$
$314$	16.7146	0.943262
$315$	−9.62820	−0.542488
$316$	−24.1753	−1.35997
$317$	−30.5989	−1.71861	−0.859303	−	0.511467i	$-0.829102\pi$
$317$	−30.5989	−1.71861	−0.859303	+	0.511467i	$0.829102\pi$
$318$	−19.5590	−1.09681
$319$	6.51572	0.364810
$320$	−3.02863	−0.169305
$321$	14.0543	0.784434
$322$	7.84921	0.437419
$323$	−3.35662	−0.186767
$324$	44.6126	2.47848
$325$	14.5634	0.807835
$326$	7.78808	0.431342
$327$	13.8573	0.766310
$328$	−8.50354	−0.469530
$329$	−8.34134	−0.459873
$330$	5.80782	0.319710
$331$	13.9574	0.767166	0.383583	−	0.923506i	$-0.374690\pi$
$331$	13.9574	0.767166	0.383583	+	0.923506i	$0.374690\pi$
$332$	−0.855832	−0.0469699
$333$	−79.8413	−4.37527
$334$	−18.3742	−1.00539
$335$	11.5701	0.632142
$336$	20.3260	1.10888
$337$	−8.71417	−0.474691	−0.237346	−	0.971425i	$-0.576277\pi$
$337$	−8.71417	−0.474691	−0.237346	+	0.971425i	$0.576277\pi$
$338$	0.830225	0.0451583
$339$	−28.3065	−1.53740
$340$	1.37266	0.0744432
$341$	−0.322173	−0.0174466
$342$	49.7495	2.69014
$343$	15.8254	0.854493
$344$	1.01243	0.0545866
$345$	10.3048	0.554793
$346$	29.7678	1.60033
$347$	−16.4211	−0.881529	−0.440765	−	0.897623i	$-0.645293\pi$
$347$	−16.4211	−0.881529	−0.440765	+	0.897623i	$0.645293\pi$
$348$	−31.4122	−1.68387
$349$	−20.5731	−1.10125	−0.550626	−	0.834752i	$-0.685611\pi$
$349$	−20.5731	−1.10125	−0.550626	+	0.834752i	$0.685611\pi$
$350$	−9.78220	−0.522881
$351$	−58.3712	−3.11562
$352$	−6.88400	−0.366919
$353$	16.8883	0.898872	0.449436	−	0.893313i	$-0.351625\pi$
$353$	16.8883	0.898872	0.449436	+	0.893313i	$0.351625\pi$
$354$	−8.77316	−0.466288
$355$	−3.91336	−0.207700
$356$	16.0336	0.849780
$357$	−4.24108	−0.224462
$358$	−8.68919	−0.459238
$359$	−21.3144	−1.12493	−0.562466	−	0.826820i	$-0.690147\pi$
$359$	−21.3144	−1.12493	−0.562466	+	0.826820i	$0.690147\pi$
$360$	7.61384	0.401284
$361$	−7.73311	−0.407006
$362$	10.0387	0.527623
$363$	3.31260	0.173867
$364$	6.60167	0.346021
$365$	−5.85956	−0.306704
$366$	66.4316	3.47244
$367$	29.0656	1.51721	0.758605	−	0.651551i	$-0.225881\pi$
$367$	29.0656	1.51721	0.758605	+	0.651551i	$0.225881\pi$
$368$	−15.8070	−0.823997
$369$	−66.9692	−3.48628
$370$	17.5562	0.912703
$371$	−4.06665	−0.211130
$372$	1.55319	0.0805293
$373$	0.918147	0.0475399	0.0237699	−	0.999717i	$-0.492433\pi$
$373$	0.918147	0.0475399	0.0237699	+	0.999717i	$0.492433\pi$
$374$	1.85886	0.0961192
$375$	−28.4646	−1.46990
$376$	6.59621	0.340174
$377$	23.0857	1.18897
$378$	39.2077	2.01662
$379$	15.8601	0.814678	0.407339	−	0.913277i	$-0.366457\pi$
$379$	15.8601	0.814678	0.407339	+	0.913277i	$0.366457\pi$
$380$	−4.60751	−0.236360
$381$	10.3635	0.530937
$382$	−40.7821	−2.08659
$383$	−34.9460	−1.78566	−0.892828	−	0.450398i	$-0.851282\pi$
$383$	−34.9460	−1.78566	−0.892828	+	0.450398i	$0.851282\pi$
$384$	−25.8354	−1.31841
$385$	1.20755	0.0615423
$386$	26.3446	1.34090
$387$	7.97335	0.405308
$388$	−25.7407	−1.30678
$389$	−24.2776	−1.23092	−0.615460	−	0.788168i	$-0.711030\pi$
$389$	−24.2776	−1.23092	−0.615460	+	0.788168i	$0.711030\pi$
$390$	20.5775	1.04198
$391$	3.29817	0.166796
$392$	−5.42751	−0.274131
$393$	17.2409	0.869687
$394$	1.45883	0.0734947
$395$	−15.6676	−0.788325
$396$	−11.6040	−0.583123
$397$	−22.2645	−1.11742	−0.558711	−	0.829362i	$-0.688704\pi$
$397$	−22.2645	−1.11742	−0.558711	+	0.829362i	$0.688704\pi$
$398$	16.0137	0.802695
$399$	14.2357	0.712675
$400$	19.6997	0.984987
$401$	8.25181	0.412076	0.206038	−	0.978544i	$-0.433943\pi$
$401$	8.25181	0.412076	0.206038	+	0.978544i	$0.433943\pi$
$402$	−75.5361	−3.76740
$403$	−1.14148	−0.0568613
$404$	10.6299	0.528857
$405$	28.9127	1.43668
$406$	−15.5065	−0.769577
$407$	10.0135	0.496352
$408$	3.35378	0.166037
$409$	14.9500	0.739229	0.369614	−	0.929185i	$-0.379490\pi$
$409$	14.9500	0.739229	0.369614	+	0.929185i	$0.379490\pi$
$410$	14.7258	0.727254
$411$	−54.4460	−2.68562
$412$	−16.6145	−0.818540
$413$	−1.82409	−0.0897578
$414$	−48.8832	−2.40248
$415$	−0.554650	−0.0272267
$416$	−24.3905	−1.19584
$417$	19.8510	0.972109
$418$	−6.23947	−0.305183
$419$	9.64781	0.471326	0.235663	−	0.971835i	$-0.424274\pi$
$419$	9.64781	0.471326	0.235663	+	0.971835i	$0.424274\pi$
$420$	−5.82158	−0.284064
$421$	18.6504	0.908964	0.454482	−	0.890756i	$-0.349824\pi$
$421$	18.6504	0.908964	0.454482	+	0.890756i	$0.349824\pi$
$422$	−52.8905	−2.57467
$423$	51.9481	2.52581
$424$	3.21585	0.156175
$425$	−4.11040	−0.199384
$426$	25.5486	1.23783
$427$	13.8123	0.668424
$428$	6.17456	0.298459
$429$	11.7368	0.566658
$430$	−1.75325	−0.0845492
$431$	−1.02082	−0.0491710	−0.0245855	−	0.999698i	$-0.507827\pi$
$431$	−1.02082	−0.0491710	−0.0245855	+	0.999698i	$0.507827\pi$
$432$	−78.9578	−3.79886
$433$	37.7907	1.81611	0.908053	−	0.418854i	$-0.137568\pi$
$433$	37.7907	1.81611	0.908053	+	0.418854i	$0.137568\pi$
$434$	0.766728	0.0368041
$435$	−20.3577	−0.976079
$436$	6.08801	0.291563
$437$	−11.0707	−0.529583
$438$	38.2545	1.82787
$439$	14.0791	0.671957	0.335978	−	0.941870i	$-0.390933\pi$
$439$	14.0791	0.671957	0.335978	+	0.941870i	$0.390933\pi$
$440$	−0.954911	−0.0455236
$441$	−42.7441	−2.03543
$442$	6.58607	0.313267
$443$	−16.8399	−0.800087	−0.400044	−	0.916496i	$-0.631005\pi$
$443$	−16.8399	−0.800087	−0.400044	+	0.916496i	$0.631005\pi$
$444$	−48.2751	−2.29103
$445$	10.3911	0.492586
$446$	18.1901	0.861328
$447$	−13.7522	−0.650457
$448$	4.11107	0.194230
$449$	24.5218	1.15725	0.578627	−	0.815592i	$-0.303589\pi$
$449$	24.5218	1.15725	0.578627	+	0.815592i	$0.303589\pi$
$450$	60.9215	2.87187
$451$	8.39914	0.395500
$452$	−12.4361	−0.584944
$453$	60.5361	2.84424
$454$	−42.2304	−1.98197
$455$	4.27843	0.200576
$456$	−11.2574	−0.527174
$457$	5.13092	0.240014	0.120007	−	0.992773i	$-0.461708\pi$
$457$	5.13092	0.240014	0.120007	+	0.992773i	$0.461708\pi$
$458$	7.39118	0.345367
$459$	16.4747	0.768975
$460$	4.52728	0.211086
$461$	−4.93593	−0.229889	−0.114945	−	0.993372i	$-0.536669\pi$
$461$	−4.93593	−0.229889	−0.114945	+	0.993372i	$0.536669\pi$
$462$	−7.88356	−0.366776
$463$	−2.36012	−0.109684	−0.0548419	−	0.998495i	$-0.517465\pi$
$463$	−2.36012	−0.109684	−0.0548419	+	0.998495i	$0.517465\pi$
$464$	31.2276	1.44971
$465$	1.00660	0.0466799
$466$	−37.1877	−1.72269
$467$	20.6048	0.953475	0.476738	−	0.879046i	$-0.341819\pi$
$467$	20.6048	0.953475	0.476738	+	0.879046i	$0.341819\pi$
$468$	−41.1138	−1.90049
$469$	−15.7053	−0.725203
$470$	−11.4228	−0.526895
$471$	−29.7866	−1.37249
$472$	1.44247	0.0663949
$473$	−1.00000	−0.0459800
$474$	102.287	4.69821
$475$	13.7970	0.633052
$476$	−1.86326	−0.0854024
$477$	25.3263	1.15961
$478$	−5.99394	−0.274156
$479$	9.43578	0.431132	0.215566	−	0.976489i	$-0.430840\pi$
$479$	9.43578	0.431132	0.215566	+	0.976489i	$0.430840\pi$
$480$	21.5084	0.981720
$481$	35.4786	1.61769
$482$	5.32940	0.242747
$483$	−13.9878	−0.636467
$484$	1.45535	0.0661522
$485$	−16.6821	−0.757495
$486$	−96.8857	−4.39483
$487$	−28.5570	−1.29404	−0.647020	−	0.762473i	$-0.723985\pi$
$487$	−28.5570	−1.29404	−0.647020	+	0.762473i	$0.723985\pi$
$488$	−10.9226	−0.494441
$489$	−13.8789	−0.627624
$490$	9.39894	0.424601
$491$	−18.8039	−0.848607	−0.424304	−	0.905520i	$-0.639481\pi$
$491$	−18.8039	−0.848607	−0.424304	+	0.905520i	$0.639481\pi$
$492$	−40.4922	−1.82553
$493$	−6.51572	−0.293453
$494$	−22.1069	−0.994637
$495$	−7.52036	−0.338015
$496$	−1.54406	−0.0693305
$497$	5.31201	0.238276
$498$	3.62107	0.162264
$499$	−12.3897	−0.554640	−0.277320	−	0.960778i	$-0.589446\pi$
$499$	−12.3897	−0.554640	−0.277320	+	0.960778i	$0.589446\pi$
$500$	−12.5055	−0.559264
$501$	32.7440	1.46289
$502$	−36.4859	−1.62844
$503$	35.4862	1.58225	0.791126	−	0.611653i	$-0.209495\pi$
$503$	35.4862	1.58225	0.791126	+	0.611653i	$0.209495\pi$
$504$	−10.3350	−0.460360
$505$	6.88905	0.306559
$506$	6.13083	0.272548
$507$	−1.47951	−0.0657076
$508$	4.55306	0.202009
$509$	19.5505	0.866560	0.433280	−	0.901259i	$-0.357356\pi$
$509$	19.5505	0.866560	0.433280	+	0.901259i	$0.357356\pi$
$510$	−5.80782	−0.257175
$511$	7.95379	0.351855
$512$	−23.2882	−1.02920
$513$	−55.2994	−2.44153
$514$	53.5801	2.36332
$515$	−10.7676	−0.474478
$516$	4.82099	0.212232
$517$	−6.51522	−0.286539
$518$	−23.8308	−1.04707
$519$	−53.0482	−2.32856
$520$	−3.38332	−0.148368
$521$	9.59821	0.420505	0.210253	−	0.977647i	$-0.432571\pi$
$521$	9.59821	0.420505	0.210253	+	0.977647i	$0.432571\pi$
$522$	96.5715	4.22682
$523$	−21.9654	−0.960478	−0.480239	−	0.877138i	$-0.659450\pi$
$523$	−21.9654	−0.960478	−0.480239	+	0.877138i	$0.659450\pi$
$524$	7.57454	0.330895
$525$	17.4325	0.760818
$526$	32.5320	1.41846
$527$	0.322173	0.0140341
$528$	15.8762	0.690922
$529$	−12.1221	−0.527047
$530$	−5.56896	−0.241900
$531$	11.3601	0.492985
$532$	6.25425	0.271156
$533$	29.7588	1.28899
$534$	−67.8391	−2.93569
$535$	4.00163	0.173006
$536$	12.4195	0.536441
$537$	15.4847	0.668215
$538$	−13.1464	−0.566779
$539$	5.36087	0.230909
$540$	22.6143	0.973164
$541$	27.0384	1.16247	0.581235	−	0.813736i	$-0.302570\pi$
$541$	27.0384	1.16247	0.581235	+	0.813736i	$0.302570\pi$
$542$	36.1651	1.55342
$543$	−17.8897	−0.767719
$544$	6.88400	0.295149
$545$	3.94554	0.169008
$546$	−27.9320	−1.19538
$547$	−28.5198	−1.21942	−0.609708	−	0.792626i	$-0.708713\pi$
$547$	−28.5198	−1.21942	−0.609708	+	0.792626i	$0.708713\pi$
$548$	−23.9201	−1.02182
$549$	−86.0201	−3.67125
$550$	−7.64064	−0.325798
$551$	21.8708	0.931727
$552$	11.0613	0.470802
$553$	21.2673	0.904378
$554$	−11.6330	−0.494238
$555$	−31.2863	−1.32803
$556$	8.72128	0.369865
$557$	13.1962	0.559142	0.279571	−	0.960125i	$-0.409808\pi$
$557$	13.1962	0.559142	0.279571	+	0.960125i	$0.409808\pi$
$558$	−4.77502	−0.202143
$559$	−3.54307	−0.149856
$560$	5.78737	0.244561
$561$	−3.31260	−0.139858
$562$	16.9265	0.714000
$563$	33.0690	1.39369	0.696845	−	0.717222i	$-0.254586\pi$
$563$	33.0690	1.39369	0.696845	+	0.717222i	$0.254586\pi$
$564$	31.4098	1.32259
$565$	−8.05961	−0.339070
$566$	−6.51681	−0.273922
$567$	−39.2462	−1.64818
$568$	−4.20066	−0.176256
$569$	18.1691	0.761688	0.380844	−	0.924639i	$-0.375634\pi$
$569$	18.1691	0.761688	0.380844	+	0.924639i	$0.375634\pi$
$570$	19.4946	0.816540
$571$	3.24713	0.135888	0.0679442	−	0.997689i	$-0.478356\pi$
$571$	3.24713	0.135888	0.0679442	+	0.997689i	$0.478356\pi$
$572$	5.15640	0.215600
$573$	72.6763	3.03610
$574$	−19.9888	−0.834317
$575$	−13.5568	−0.565357
$576$	−25.6029	−1.06679
$577$	−29.3846	−1.22330	−0.611648	−	0.791130i	$-0.709493\pi$
$577$	−29.3846	−1.22330	−0.611648	+	0.791130i	$0.709493\pi$
$578$	−1.85886	−0.0773182
$579$	−46.9478	−1.95108
$580$	−8.94390	−0.371375
$581$	0.752884	0.0312349
$582$	108.910	4.51447
$583$	−3.17636	−0.131552
$584$	−6.28974	−0.260271
$585$	−26.6452	−1.10164
$586$	−11.1476	−0.460504
$587$	−38.9668	−1.60833	−0.804165	−	0.594406i	$-0.797387\pi$
$587$	−38.9668	−1.60833	−0.804165	+	0.594406i	$0.797387\pi$
$588$	−25.8447	−1.06582
$589$	−1.08141	−0.0445588
$590$	−2.49795	−0.102839
$591$	−2.59973	−0.106938
$592$	47.9914	1.97243
$593$	−14.1572	−0.581365	−0.290682	−	0.956820i	$-0.593882\pi$
$593$	−14.1572	−0.581365	−0.290682	+	0.956820i	$0.593882\pi$
$594$	30.6242	1.25652
$595$	−1.20755	−0.0495046
$596$	−6.04184	−0.247484
$597$	−28.5375	−1.16796
$598$	21.7220	0.888277
$599$	−6.92580	−0.282981	−0.141490	−	0.989940i	$-0.545189\pi$
$599$	−6.92580	−0.282981	−0.141490	+	0.989940i	$0.545189\pi$
$600$	−13.7854	−0.562786
$601$	−20.9555	−0.854794	−0.427397	−	0.904064i	$-0.640569\pi$
$601$	−20.9555	−0.854794	−0.427397	+	0.904064i	$0.640569\pi$
$602$	2.37987	0.0969961
$603$	97.8093	3.98310
$604$	26.5957	1.08216
$605$	0.943187	0.0383460
$606$	−44.9756	−1.82701
$607$	31.8935	1.29452	0.647259	−	0.762270i	$-0.275915\pi$
$607$	31.8935	1.29452	0.647259	+	0.762270i	$0.275915\pi$
$608$	−23.1070	−0.937112
$609$	27.6337	1.11977
$610$	18.9148	0.765840
$611$	−23.0839	−0.933875
$612$	11.6040	0.469064
$613$	−38.2938	−1.54667	−0.773337	−	0.633996i	$-0.781414\pi$
$613$	−38.2938	−1.54667	−0.773337	+	0.633996i	$0.781414\pi$
$614$	64.0071	2.58312
$615$	−26.2423	−1.05819
$616$	1.29620	0.0522254
$617$	45.6248	1.83679	0.918393	−	0.395669i	$-0.129487\pi$
$617$	45.6248	1.83679	0.918393	+	0.395669i	$0.129487\pi$
$618$	70.2970	2.82776
$619$	−3.29046	−0.132255	−0.0661273	−	0.997811i	$-0.521064\pi$
$619$	−3.29046	−0.132255	−0.0661273	+	0.997811i	$0.521064\pi$
$620$	0.442235	0.0177606
$621$	54.3365	2.18045
$622$	−38.0011	−1.52370
$623$	−14.1049	−0.565103
$624$	56.2505	2.25182
$625$	12.4474	0.497895
$626$	−21.9625	−0.877799
$627$	11.1191	0.444056
$628$	−13.0863	−0.522201
$629$	−10.0135	−0.399265
$630$	17.8974	0.713051
$631$	30.0293	1.19545	0.597723	−	0.801703i	$-0.296072\pi$
$631$	30.0293	1.19545	0.597723	+	0.801703i	$0.296072\pi$
$632$	−16.8179	−0.668979
$633$	94.2543	3.74627
$634$	56.8790	2.25895
$635$	2.95076	0.117097
$636$	15.3132	0.607209
$637$	18.9940	0.752568
$638$	−12.1118	−0.479510
$639$	−33.0821	−1.30871
$640$	−7.35602	−0.290772
$641$	5.08003	0.200649	0.100325	−	0.994955i	$-0.468012\pi$
$641$	5.08003	0.200649	0.100325	+	0.994955i	$0.468012\pi$
$642$	−26.1249	−1.03107
$643$	34.5575	1.36282	0.681408	−	0.731904i	$-0.261368\pi$
$643$	34.5575	1.36282	0.681408	+	0.731904i	$0.261368\pi$
$644$	−6.14535	−0.242161
$645$	3.12440	0.123023
$646$	6.23947	0.245489
$647$	45.1815	1.77627	0.888135	−	0.459583i	$-0.152001\pi$
$647$	45.1815	1.77627	0.888135	+	0.459583i	$0.152001\pi$
$648$	31.0353	1.21918
$649$	−1.42476	−0.0559266
$650$	−27.0714	−1.06183
$651$	−1.36636	−0.0535519
$652$	−6.09749	−0.238796
$653$	6.68020	0.261417	0.130708	−	0.991421i	$-0.458275\pi$
$653$	6.68020	0.261417	0.130708	+	0.991421i	$0.458275\pi$
$654$	−25.7587	−1.00725
$655$	4.90894	0.191808
$656$	40.2542	1.57166
$657$	−49.5346	−1.93253
$658$	15.5054	0.604462
$659$	−37.0358	−1.44271	−0.721354	−	0.692566i	$-0.756480\pi$
$659$	−37.0358	−1.44271	−0.721354	+	0.692566i	$0.756480\pi$
$660$	−4.54710	−0.176995
$661$	34.3829	1.33734	0.668670	−	0.743559i	$-0.266864\pi$
$661$	34.3829	1.33734	0.668670	+	0.743559i	$0.266864\pi$
$662$	−25.9447	−1.00837
$663$	−11.7368	−0.455820
$664$	−0.595370	−0.0231048
$665$	4.05328	0.157179
$666$	148.413	5.75090
$667$	−21.4900	−0.832095
$668$	14.3856	0.556597
$669$	−32.4160	−1.25328
$670$	−21.5071	−0.830894
$671$	10.7885	0.416484
$672$	−29.1956	−1.12624
$673$	37.4467	1.44346	0.721732	−	0.692173i	$-0.243346\pi$
$673$	37.4467	1.44346	0.721732	+	0.692173i	$0.243346\pi$
$674$	16.1984	0.623939
$675$	−67.7177	−2.60646
$676$	−0.650005	−0.0250002
$677$	−31.3125	−1.20344	−0.601720	−	0.798707i	$-0.705517\pi$
$677$	−31.3125	−1.20344	−0.601720	+	0.798707i	$0.705517\pi$
$678$	52.6177	2.02077
$679$	22.6443	0.869010
$680$	0.954911	0.0366192
$681$	75.2573	2.88387
$682$	0.598873	0.0229320
$683$	30.8163	1.17915	0.589576	−	0.807713i	$-0.299295\pi$
$683$	30.8163	1.17915	0.589576	+	0.807713i	$0.299295\pi$
$684$	−38.9502	−1.48930
$685$	−15.5022	−0.592309
$686$	−29.4172	−1.12315
$687$	−13.1716	−0.502527
$688$	−4.79266	−0.182718
$689$	−11.2541	−0.428747
$690$	−19.1552	−0.729225
$691$	−3.22077	−0.122524	−0.0612619	−	0.998122i	$-0.519512\pi$
$691$	−3.22077	−0.122524	−0.0612619	+	0.998122i	$0.519512\pi$
$692$	−23.3060	−0.885962
$693$	10.2082	0.387776
$694$	30.5244	1.15869
$695$	5.65212	0.214397
$696$	−21.8523	−0.828309
$697$	−8.39914	−0.318140
$698$	38.2424	1.44750
$699$	66.2709	2.50660
$700$	7.65874	0.289473
$701$	−31.0900	−1.17425	−0.587127	−	0.809495i	$-0.699741\pi$
$701$	−31.0900	−1.17425	−0.587127	+	0.809495i	$0.699741\pi$
$702$	108.504	4.09521
$703$	33.6116	1.26768
$704$	3.21106	0.121021
$705$	20.3562	0.766659
$706$	−31.3929	−1.18149
$707$	−9.35123	−0.351689
$708$	6.86874	0.258143
$709$	−12.1758	−0.457273	−0.228636	−	0.973512i	$-0.573427\pi$
$709$	−12.1758	−0.457273	−0.228636	+	0.973512i	$0.573427\pi$
$710$	7.27437	0.273002
$711$	−132.448	−4.96720
$712$	11.1540	0.418013
$713$	1.06258	0.0397940
$714$	7.88356	0.295035
$715$	3.34178	0.124975
$716$	6.80300	0.254240
$717$	10.6816	0.398911
$718$	39.6205	1.47862
$719$	7.71558	0.287742	0.143871	−	0.989596i	$-0.454045\pi$
$719$	7.71558	0.287742	0.143871	+	0.989596i	$0.454045\pi$
$720$	−36.0425	−1.34322
$721$	14.6160	0.544328
$722$	14.3747	0.534973
$723$	−9.49734	−0.353210
$724$	−7.85958	−0.292099
$725$	26.7822	0.994666
$726$	−6.15766	−0.228532
$727$	18.5549	0.688163	0.344082	−	0.938940i	$-0.388190\pi$
$727$	18.5549	0.688163	0.344082	+	0.938940i	$0.388190\pi$
$728$	4.59253	0.170210
$729$	80.6940	2.98867
$730$	10.8921	0.403134
$731$	1.00000	0.0369863
$732$	−52.0110	−1.92238
$733$	19.8352	0.732629	0.366315	−	0.930491i	$-0.380619\pi$
$733$	19.8352	0.732629	0.366315	+	0.930491i	$0.380619\pi$
$734$	−54.0287	−1.99424
$735$	−16.7495	−0.617816
$736$	22.7046	0.836903
$737$	−12.2670	−0.451862
$738$	124.486	4.58240
$739$	−1.56707	−0.0576456	−0.0288228	−	0.999585i	$-0.509176\pi$
$739$	−1.56707	−0.0576456	−0.0288228	+	0.999585i	$0.509176\pi$
$740$	−13.7452	−0.505284
$741$	39.3960	1.44725
$742$	7.55932	0.277511
$743$	−0.973473	−0.0357133	−0.0178566	−	0.999841i	$-0.505684\pi$
$743$	−0.973473	−0.0357133	−0.0178566	+	0.999841i	$0.505684\pi$
$744$	1.08050	0.0396129
$745$	−3.91562	−0.143457
$746$	−1.70670	−0.0624869
$747$	−4.68881	−0.171554
$748$	−1.45535	−0.0532128
$749$	−5.43183	−0.198475
$750$	52.9116	1.93206
$751$	27.3002	0.996199	0.498099	−	0.867120i	$-0.334031\pi$
$751$	27.3002	0.996199	0.498099	+	0.867120i	$0.334031\pi$
$752$	−31.2252	−1.13867
$753$	65.0202	2.36947
$754$	−42.9130	−1.56280
$755$	17.2363	0.627291
$756$	−30.6967	−1.11643
$757$	−13.6539	−0.496260	−0.248130	−	0.968727i	$-0.579816\pi$
$757$	−13.6539	−0.496260	−0.248130	+	0.968727i	$0.579816\pi$
$758$	−29.4816	−1.07082
$759$	−10.9255	−0.396572
$760$	−3.20527	−0.116267
$761$	−45.0451	−1.63288	−0.816442	−	0.577427i	$-0.804057\pi$
$761$	−45.0451	−1.63288	−0.816442	+	0.577427i	$0.804057\pi$
$762$	−19.2642	−0.697869
$763$	−5.35569	−0.193889
$764$	31.9294	1.15516
$765$	7.52036	0.271899
$766$	64.9595	2.34708
$767$	−5.04802	−0.182273
$768$	69.2982	2.50058
$769$	−36.2208	−1.30615	−0.653077	−	0.757291i	$-0.726522\pi$
$769$	−36.2208	−1.30615	−0.653077	+	0.757291i	$0.726522\pi$
$770$	−2.24466	−0.0808919
$771$	−95.4833	−3.43875
$772$	−20.6259	−0.742341
$773$	−7.92742	−0.285130	−0.142565	−	0.989785i	$-0.545535\pi$
$773$	−7.92742	−0.285130	−0.142565	+	0.989785i	$0.545535\pi$
$774$	−14.8213	−0.532741
$775$	−1.32426	−0.0475688
$776$	−17.9068	−0.642817
$777$	42.4681	1.52354
$778$	45.1285	1.61793
$779$	28.1927	1.01011
$780$	−16.1107	−0.576855
$781$	4.14908	0.148466
$782$	−6.13083	−0.219238
$783$	−107.345	−3.83619
$784$	25.6928	0.917601
$785$	−8.48103	−0.302701
$786$	−32.0483	−1.14313
$787$	46.3341	1.65163	0.825817	−	0.563938i	$-0.190714\pi$
$787$	46.3341	1.65163	0.825817	+	0.563938i	$0.190714\pi$
$788$	−1.14215	−0.0406876
$789$	−57.9742	−2.06393
$790$	29.1239	1.03618
$791$	10.9401	0.388987
$792$	−8.07246	−0.286842
$793$	38.2243	1.35738
$794$	41.3865	1.46875
$795$	9.92424	0.351977
$796$	−12.5376	−0.444382
$797$	−43.0850	−1.52615	−0.763075	−	0.646310i	$-0.776311\pi$
$797$	−43.0850	−1.52615	−0.763075	+	0.646310i	$0.776311\pi$
$798$	−26.4621	−0.936748
$799$	6.51522	0.230492
$800$	−28.2960	−1.00041
$801$	87.8426	3.10377
$802$	−15.3389	−0.541637
$803$	6.21252	0.219235
$804$	59.1392	2.08568
$805$	−3.98270	−0.140372
$806$	2.12185	0.0747390
$807$	23.4277	0.824693
$808$	7.39481	0.260149
$809$	−26.3872	−0.927723	−0.463861	−	0.885908i	$-0.653536\pi$
$809$	−26.3872	−0.927723	−0.463861	+	0.885908i	$0.653536\pi$
$810$	−53.7445	−1.88839
$811$	−46.8754	−1.64602	−0.823009	−	0.568028i	$-0.807706\pi$
$811$	−46.8754	−1.64602	−0.823009	+	0.568028i	$0.807706\pi$
$812$	12.1405	0.426047
$813$	−64.4485	−2.26031
$814$	−18.6137	−0.652410
$815$	−3.95168	−0.138421
$816$	−15.8762	−0.555778
$817$	−3.35662	−0.117433
$818$	−27.7899	−0.971650
$819$	36.1683	1.26382
$820$	−11.5292	−0.402617
$821$	−50.4348	−1.76019	−0.880093	−	0.474801i	$-0.842520\pi$
$821$	−50.4348	−1.76019	−0.880093	+	0.474801i	$0.842520\pi$
$822$	101.207	3.53001
$823$	28.2008	0.983017	0.491508	−	0.870873i	$-0.336446\pi$
$823$	28.2008	0.983017	0.491508	+	0.870873i	$0.336446\pi$
$824$	−11.5581	−0.402646
$825$	13.6161	0.474053
$826$	3.39073	0.117979
$827$	−17.5382	−0.609864	−0.304932	−	0.952374i	$-0.598634\pi$
$827$	−17.5382	−0.609864	−0.304932	+	0.952374i	$0.598634\pi$
$828$	38.2719	1.33004
$829$	49.5341	1.72039	0.860196	−	0.509964i	$-0.170341\pi$
$829$	49.5341	1.72039	0.860196	+	0.509964i	$0.170341\pi$
$830$	1.03102	0.0357871
$831$	20.7307	0.719141
$832$	11.3770	0.394427
$833$	−5.36087	−0.185743
$834$	−36.9002	−1.27775
$835$	9.32309	0.322639
$836$	4.88505	0.168953
$837$	5.30771	0.183461
$838$	−17.9339	−0.619516
$839$	−48.7441	−1.68283	−0.841416	−	0.540387i	$-0.818278\pi$
$839$	−48.7441	−1.68283	−0.841416	+	0.540387i	$0.818278\pi$
$840$	−4.04985	−0.139733
$841$	13.4546	0.463952
$842$	−34.6684	−1.19475
$843$	−30.1641	−1.03891
$844$	41.4093	1.42537
$845$	−0.421257	−0.0144917
$846$	−96.5641	−3.31994
$847$	−1.28029	−0.0439911
$848$	−15.2232	−0.522768
$849$	11.6134	0.398570
$850$	7.64064	0.262072
$851$	−33.0263	−1.13213
$852$	−20.0027	−0.685281
$853$	21.3435	0.730787	0.365393	−	0.930853i	$-0.380934\pi$
$853$	21.3435	0.730787	0.365393	+	0.930853i	$0.380934\pi$
$854$	−25.6751	−0.878583
$855$	−25.2430	−0.863291
$856$	4.29541	0.146814
$857$	29.3366	1.00212	0.501060	−	0.865413i	$-0.332944\pi$
$857$	29.3366	1.00212	0.501060	+	0.865413i	$0.332944\pi$
$858$	−21.8170	−0.744821
$859$	−32.3320	−1.10315	−0.551577	−	0.834124i	$-0.685974\pi$
$859$	−32.3320	−1.10315	−0.551577	+	0.834124i	$0.685974\pi$
$860$	1.37266	0.0468075
$861$	35.6214	1.21397
$862$	1.89755	0.0646309
$863$	−10.6727	−0.363302	−0.181651	−	0.983363i	$-0.558144\pi$
$863$	−10.6727	−0.363302	−0.181651	+	0.983363i	$0.558144\pi$
$864$	113.412	3.85836
$865$	−15.1042	−0.513560
$866$	−70.2476	−2.38711
$867$	3.31260	0.112502
$868$	−0.600292	−0.0203752
$869$	16.6114	0.563503
$870$	37.8421	1.28297
$871$	−43.4630	−1.47269
$872$	4.23520	0.143422
$873$	−141.024	−4.77295
$874$	20.5788	0.696090
$875$	11.0012	0.371910
$876$	−29.9505	−1.01193
$877$	−7.10112	−0.239788	−0.119894	−	0.992787i	$-0.538255\pi$
$877$	−7.10112	−0.239788	−0.119894	+	0.992787i	$0.538255\pi$
$878$	−26.1709	−0.883226
$879$	19.8658	0.670057
$880$	4.52037	0.152382
$881$	37.4879	1.26300	0.631499	−	0.775376i	$-0.282440\pi$
$881$	37.4879	1.26300	0.631499	+	0.775376i	$0.282440\pi$
$882$	79.4551	2.67539
$883$	41.8715	1.40909	0.704544	−	0.709660i	$-0.251151\pi$
$883$	41.8715	1.40909	0.704544	+	0.709660i	$0.251151\pi$
$884$	−5.15640	−0.173429
$885$	4.45152	0.149636
$886$	31.3029	1.05164
$887$	−20.6477	−0.693282	−0.346641	−	0.937998i	$-0.612678\pi$
$887$	−20.6477	−0.693282	−0.346641	+	0.937998i	$0.612678\pi$
$888$	−33.5831	−1.12698
$889$	−4.00537	−0.134336
$890$	−19.3156	−0.647460
$891$	−30.6542	−1.02696
$892$	−14.2415	−0.476842
$893$	−21.8691	−0.731822
$894$	25.5634	0.854967
$895$	4.40891	0.147374
$896$	9.98508	0.333578
$897$	−38.7100	−1.29249
$898$	−45.5825	−1.52111
$899$	−2.09919	−0.0700118
$900$	−47.6970	−1.58990
$901$	3.17636	0.105820
$902$	−15.6128	−0.519849
$903$	−4.24108	−0.141134
$904$	−8.65130	−0.287738
$905$	−5.09366	−0.169319
$906$	−112.528	−3.73849
$907$	−47.5322	−1.57828	−0.789140	−	0.614214i	$-0.789473\pi$
$907$	−47.5322	−1.57828	−0.789140	+	0.614214i	$0.789473\pi$
$908$	33.0633	1.09724
$909$	58.2375	1.93162
$910$	−7.95299	−0.263639
$911$	9.03738	0.299422	0.149711	−	0.988730i	$-0.452166\pi$
$911$	9.03738	0.299422	0.149711	+	0.988730i	$0.452166\pi$
$912$	53.2903	1.76462
$913$	0.588060	0.0194619
$914$	−9.53765	−0.315477
$915$	−33.7075	−1.11434
$916$	−5.78675	−0.191200
$917$	−6.66341	−0.220045
$918$	−30.6242	−1.01075
$919$	−9.72750	−0.320881	−0.160440	−	0.987046i	$-0.551291\pi$
$919$	−9.72750	−0.320881	−0.160440	+	0.987046i	$0.551291\pi$
$920$	3.14946	0.103835
$921$	−114.065	−3.75856
$922$	9.17518	0.302169
$923$	14.7005	0.483873
$924$	6.17224	0.203052
$925$	41.1596	1.35332
$926$	4.38712	0.144170
$927$	−91.0253	−2.98966
$928$	−44.8542	−1.47241
$929$	22.3297	0.732613	0.366306	−	0.930494i	$-0.380622\pi$
$929$	22.3297	0.732613	0.366306	+	0.930494i	$0.380622\pi$
$930$	−1.87112	−0.0613565
$931$	17.9944	0.589742
$932$	29.1152	0.953701
$933$	67.7204	2.21707
$934$	−38.3013	−1.25326
$935$	−0.943187	−0.0308455
$936$	−28.6013	−0.934863
$937$	1.41138	0.0461077	0.0230538	−	0.999734i	$-0.492661\pi$
$937$	1.41138	0.0461077	0.0230538	+	0.999734i	$0.492661\pi$
$938$	29.1939	0.953214
$939$	39.1387	1.27724
$940$	8.94322	0.291696
$941$	−9.34919	−0.304775	−0.152387	−	0.988321i	$-0.548696\pi$
$941$	−9.34919	−0.304775	−0.152387	+	0.988321i	$0.548696\pi$
$942$	55.3690	1.80402
$943$	−27.7018	−0.902094
$944$	−6.82837	−0.222245
$945$	−19.8940	−0.647153
$946$	1.85886	0.0604366
$947$	22.9351	0.745291	0.372646	−	0.927974i	$-0.378451\pi$
$947$	22.9351	0.745291	0.372646	+	0.927974i	$0.378451\pi$
$948$	−80.0834	−2.60099
$949$	22.0114	0.714520
$950$	−25.6467	−0.832089
$951$	−101.362	−3.28689
$952$	−1.29620	−0.0420101
$953$	9.55768	0.309604	0.154802	−	0.987946i	$-0.450526\pi$
$953$	9.55768	0.309604	0.154802	+	0.987946i	$0.450526\pi$
$954$	−47.0779	−1.52420
$955$	20.6929	0.669606
$956$	4.69281	0.151776
$957$	21.5840	0.697712
$958$	−17.5398	−0.566684
$959$	21.0428	0.679506
$960$	−10.0326	−0.323802
$961$	−30.8962	−0.996652
$962$	−65.9497	−2.12630
$963$	33.8283	1.09010
$964$	−4.17253	−0.134388
$965$	−13.3673	−0.430308
$966$	26.0013	0.836579
$967$	−20.7944	−0.668703	−0.334352	−	0.942448i	$-0.608517\pi$
$967$	−20.7944	−0.668703	−0.334352	+	0.942448i	$0.608517\pi$
$968$	1.01243	0.0325407
$969$	−11.1191	−0.357199
$970$	31.0096	0.995659
$971$	−55.6084	−1.78456	−0.892280	−	0.451482i	$-0.850895\pi$
$971$	−55.6084	−1.78456	−0.892280	+	0.451482i	$0.850895\pi$
$972$	75.8544	2.43303
$973$	−7.67221	−0.245960
$974$	53.0834	1.70090
$975$	48.2429	1.54501
$976$	51.7054	1.65505
$977$	−41.0713	−1.31399	−0.656994	−	0.753896i	$-0.728172\pi$
$977$	−41.0713	−1.31399	−0.656994	+	0.753896i	$0.728172\pi$
$978$	25.7988	0.824956
$979$	−11.0170	−0.352106
$980$	−7.35868	−0.235064
$981$	33.3541	1.06491
$982$	34.9537	1.11542
$983$	−57.0873	−1.82080	−0.910400	−	0.413729i	$-0.864226\pi$
$983$	−57.0873	−1.82080	−0.910400	+	0.413729i	$0.864226\pi$
$984$	−28.1689	−0.897991
$985$	−0.740212	−0.0235851
$986$	12.1118	0.385718
$987$	−27.6316	−0.879523
$988$	17.3081	0.550643
$989$	3.29817	0.104876
$990$	13.9793	0.444290
$991$	−8.28906	−0.263311	−0.131655	−	0.991296i	$-0.542029\pi$
$991$	−8.28906	−0.263311	−0.131655	+	0.991296i	$0.542029\pi$
$992$	2.21784	0.0704164
$993$	46.2352	1.46723
$994$	−9.87426	−0.313193
$995$	−8.12538	−0.257592
$996$	−2.83503	−0.0898314
$997$	10.5266	0.333382	0.166691	−	0.986009i	$-0.446692\pi$
$997$	10.5266	0.333382	0.166691	+	0.986009i	$0.446692\pi$
$998$	23.0307	0.729025
$999$	−164.970	−5.21942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.16	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.16	✓	69	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)

\(f(q)\)	\(=\)	\(q-1.85886 q^{2} +3.31260 q^{3} +1.45535 q^{4} +0.943187 q^{5} -6.15766 q^{6} -1.28029 q^{7} +1.01243 q^{8} +7.97335 q^{9} +O(q^{10})\)	\(q-1.85886 q^{2} +3.31260 q^{3} +1.45535 q^{4} +0.943187 q^{5} -6.15766 q^{6} -1.28029 q^{7} +1.01243 q^{8} +7.97335 q^{9} -1.75325 q^{10} -1.00000 q^{11} +4.82099 q^{12} -3.54307 q^{13} +2.37987 q^{14} +3.12440 q^{15} -4.79266 q^{16} +1.00000 q^{17} -14.8213 q^{18} -3.35662 q^{19} +1.37266 q^{20} -4.24108 q^{21} +1.85886 q^{22} +3.29817 q^{23} +3.35378 q^{24} -4.11040 q^{25} +6.58607 q^{26} +16.4747 q^{27} -1.86326 q^{28} -6.51572 q^{29} -5.80782 q^{30} +0.322173 q^{31} +6.88400 q^{32} -3.31260 q^{33} -1.85886 q^{34} -1.20755 q^{35} +11.6040 q^{36} -10.0135 q^{37} +6.23947 q^{38} -11.7368 q^{39} +0.954911 q^{40} -8.39914 q^{41} +7.88356 q^{42} +1.00000 q^{43} -1.45535 q^{44} +7.52036 q^{45} -6.13083 q^{46} +6.51522 q^{47} -15.8762 q^{48} -5.36087 q^{49} +7.64064 q^{50} +3.31260 q^{51} -5.15640 q^{52} +3.17636 q^{53} -30.6242 q^{54} -0.943187 q^{55} -1.29620 q^{56} -11.1191 q^{57} +12.1118 q^{58} +1.42476 q^{59} +4.54710 q^{60} -10.7885 q^{61} -0.598873 q^{62} -10.2082 q^{63} -3.21106 q^{64} -3.34178 q^{65} +6.15766 q^{66} +12.2670 q^{67} +1.45535 q^{68} +10.9255 q^{69} +2.24466 q^{70} -4.14908 q^{71} +8.07246 q^{72} -6.21252 q^{73} +18.6137 q^{74} -13.6161 q^{75} -4.88505 q^{76} +1.28029 q^{77} +21.8170 q^{78} -16.6114 q^{79} -4.52037 q^{80} +30.6542 q^{81} +15.6128 q^{82} -0.588060 q^{83} -6.17224 q^{84} +0.943187 q^{85} -1.85886 q^{86} -21.5840 q^{87} -1.01243 q^{88} +11.0170 q^{89} -13.9793 q^{90} +4.53614 q^{91} +4.79998 q^{92} +1.06723 q^{93} -12.1109 q^{94} -3.16592 q^{95} +22.8040 q^{96} -17.6870 q^{97} +9.96509 q^{98} -7.97335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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