LMFDB - Embedded newform 8041.2.a.j.1.57

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			1.57
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)

$f(q)$	$=$	$q+1.48399 q^{2} +1.08986 q^{3} +0.202219 q^{4} -3.88618 q^{5} +1.61734 q^{6} +2.44069 q^{7} -2.66788 q^{8} -1.81220 q^{9} +O(q^{10})$	\(q+1.48399 q^{2} +1.08986 q^{3} +0.202219 q^{4} -3.88618 q^{5} +1.61734 q^{6} +2.44069 q^{7} -2.66788 q^{8} -1.81220 q^{9} -5.76704 q^{10} +1.00000 q^{11} +0.220392 q^{12} -1.10712 q^{13} +3.62195 q^{14} -4.23540 q^{15} -4.36355 q^{16} +1.00000 q^{17} -2.68928 q^{18} -2.46421 q^{19} -0.785860 q^{20} +2.66002 q^{21} +1.48399 q^{22} -5.21978 q^{23} -2.90763 q^{24} +10.1024 q^{25} -1.64295 q^{26} -5.24464 q^{27} +0.493555 q^{28} +4.22387 q^{29} -6.28528 q^{30} -6.14695 q^{31} -1.13968 q^{32} +1.08986 q^{33} +1.48399 q^{34} -9.48495 q^{35} -0.366462 q^{36} +5.89253 q^{37} -3.65686 q^{38} -1.20661 q^{39} +10.3679 q^{40} +3.75745 q^{41} +3.94744 q^{42} +1.00000 q^{43} +0.202219 q^{44} +7.04252 q^{45} -7.74608 q^{46} +6.32083 q^{47} -4.75567 q^{48} -1.04303 q^{49} +14.9918 q^{50} +1.08986 q^{51} -0.223881 q^{52} +10.9946 q^{53} -7.78298 q^{54} -3.88618 q^{55} -6.51148 q^{56} -2.68565 q^{57} +6.26818 q^{58} -5.69363 q^{59} -0.856480 q^{60} -11.0485 q^{61} -9.12200 q^{62} -4.42301 q^{63} +7.03582 q^{64} +4.30246 q^{65} +1.61734 q^{66} +13.2614 q^{67} +0.202219 q^{68} -5.68884 q^{69} -14.0756 q^{70} +11.2531 q^{71} +4.83473 q^{72} -13.3355 q^{73} +8.74445 q^{74} +11.0102 q^{75} -0.498311 q^{76} +2.44069 q^{77} -1.79059 q^{78} +11.9375 q^{79} +16.9575 q^{80} -0.279344 q^{81} +5.57601 q^{82} -10.7694 q^{83} +0.537908 q^{84} -3.88618 q^{85} +1.48399 q^{86} +4.60344 q^{87} -2.66788 q^{88} +4.81627 q^{89} +10.4510 q^{90} -2.70213 q^{91} -1.05554 q^{92} -6.69934 q^{93} +9.38003 q^{94} +9.57635 q^{95} -1.24210 q^{96} +18.8346 q^{97} -1.54784 q^{98} -1.81220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.48399	1.04934	0.524669	−	0.851306i	$-0.324189\pi$
$2$	1.48399	1.04934	0.524669	+	0.851306i	$0.324189\pi$
$3$	1.08986	0.629233	0.314616	−	0.949219i	$-0.398124\pi$
$3$	1.08986	0.629233	0.314616	+	0.949219i	$0.398124\pi$
$4$	0.202219	0.101110
$5$	−3.88618	−1.73795	−0.868976	−	0.494855i	$-0.835221\pi$
$5$	−3.88618	−1.73795	−0.868976	+	0.494855i	$0.835221\pi$
$6$	1.61734	0.660278
$7$	2.44069	0.922494	0.461247	−	0.887272i	$-0.347402\pi$
$7$	2.44069	0.922494	0.461247	+	0.887272i	$0.347402\pi$
$8$	−2.66788	−0.943240
$9$	−1.81220	−0.604066
$10$	−5.76704	−1.82370
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.220392	0.0636216
$13$	−1.10712	−0.307059	−0.153530	−	0.988144i	$-0.549064\pi$
$13$	−1.10712	−0.307059	−0.153530	+	0.988144i	$0.549064\pi$
$14$	3.62195	0.968008
$15$	−4.23540	−1.09358
$16$	−4.36355	−1.09089
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.68928	−0.633869
$19$	−2.46421	−0.565328	−0.282664	−	0.959219i	$-0.591218\pi$
$19$	−2.46421	−0.565328	−0.282664	+	0.959219i	$0.591218\pi$
$20$	−0.785860	−0.175724
$21$	2.66002	0.580464
$22$	1.48399	0.316387
$23$	−5.21978	−1.08840	−0.544199	−	0.838956i	$-0.683166\pi$
$23$	−5.21978	−1.08840	−0.544199	+	0.838956i	$0.683166\pi$
$24$	−2.90763	−0.593517
$25$	10.1024	2.02047
$26$	−1.64295	−0.322209
$27$	−5.24464	−1.00933
$28$	0.493555	0.0932731
$29$	4.22387	0.784353	0.392177	−	0.919890i	$-0.371722\pi$
$29$	4.22387	0.784353	0.392177	+	0.919890i	$0.371722\pi$
$30$	−6.28528	−1.14753
$31$	−6.14695	−1.10402	−0.552012	−	0.833836i	$-0.686140\pi$
$31$	−6.14695	−1.10402	−0.552012	+	0.833836i	$0.686140\pi$
$32$	−1.13968	−0.201469
$33$	1.08986	0.189721
$34$	1.48399	0.254502
$35$	−9.48495	−1.60325
$36$	−0.366462	−0.0610770
$37$	5.89253	0.968727	0.484363	−	0.874867i	$-0.339051\pi$
$37$	5.89253	0.968727	0.484363	+	0.874867i	$0.339051\pi$
$38$	−3.65686	−0.593220
$39$	−1.20661	−0.193212
$40$	10.3679	1.63930
$41$	3.75745	0.586816	0.293408	−	0.955987i	$-0.405211\pi$
$41$	3.75745	0.586816	0.293408	+	0.955987i	$0.405211\pi$
$42$	3.94744	0.609102
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.202219	0.0304857
$45$	7.04252	1.04984
$46$	−7.74608	−1.14210
$47$	6.32083	0.921988	0.460994	−	0.887403i	$-0.347493\pi$
$47$	6.32083	0.921988	0.460994	+	0.887403i	$0.347493\pi$
$48$	−4.75567	−0.686422
$49$	−1.04303	−0.149004
$50$	14.9918	2.12016
$51$	1.08986	0.152611
$52$	−0.223881	−0.0310467
$53$	10.9946	1.51022	0.755109	−	0.655599i	$-0.227584\pi$
$53$	10.9946	1.51022	0.755109	+	0.655599i	$0.227584\pi$
$54$	−7.78298	−1.05913
$55$	−3.88618	−0.524012
$56$	−6.51148	−0.870133
$57$	−2.68565	−0.355723
$58$	6.26818	0.823052
$59$	−5.69363	−0.741248	−0.370624	−	0.928783i	$-0.620856\pi$
$59$	−5.69363	−0.741248	−0.370624	+	0.928783i	$0.620856\pi$
$60$	−0.856480	−0.110571
$61$	−11.0485	−1.41462	−0.707308	−	0.706906i	$-0.750090\pi$
$61$	−11.0485	−1.41462	−0.707308	+	0.706906i	$0.750090\pi$
$62$	−9.12200	−1.15850
$63$	−4.42301	−0.557247
$64$	7.03582	0.879478
$65$	4.30246	0.533654
$66$	1.61734	0.199081
$67$	13.2614	1.62014	0.810071	−	0.586332i	$-0.199428\pi$
$67$	13.2614	1.62014	0.810071	+	0.586332i	$0.199428\pi$
$68$	0.202219	0.0245227
$69$	−5.68884	−0.684856
$70$	−14.0756	−1.68235
$71$	11.2531	1.33549	0.667746	−	0.744389i	$-0.267259\pi$
$71$	11.2531	1.33549	0.667746	+	0.744389i	$0.267259\pi$
$72$	4.83473	0.569779
$73$	−13.3355	−1.56080	−0.780399	−	0.625282i	$-0.784984\pi$
$73$	−13.3355	−1.56080	−0.780399	+	0.625282i	$0.784984\pi$
$74$	8.74445	1.01652
$75$	11.0102	1.27135
$76$	−0.498311	−0.0571602
$77$	2.44069	0.278142
$78$	−1.79059	−0.202744
$79$	11.9375	1.34308	0.671538	−	0.740970i	$-0.265634\pi$
$79$	11.9375	1.34308	0.671538	+	0.740970i	$0.265634\pi$
$80$	16.9575	1.89591
$81$	−0.279344	−0.0310382
$82$	5.57601	0.615768
$83$	−10.7694	−1.18209	−0.591046	−	0.806638i	$-0.701285\pi$
$83$	−10.7694	−1.18209	−0.591046	+	0.806638i	$0.701285\pi$
$84$	0.537908	0.0586905
$85$	−3.88618	−0.421515
$86$	1.48399	0.160023
$87$	4.60344	0.493541
$88$	−2.66788	−0.284397
$89$	4.81627	0.510524	0.255262	−	0.966872i	$-0.417838\pi$
$89$	4.81627	0.510524	0.255262	+	0.966872i	$0.417838\pi$
$90$	10.4510	1.10163
$91$	−2.70213	−0.283260
$92$	−1.05554	−0.110048
$93$	−6.69934	−0.694689
$94$	9.38003	0.967477
$95$	9.57635	0.982513
$96$	−1.24210	−0.126771
$97$	18.8346	1.91236	0.956182	−	0.292771i	$-0.0945775\pi$
$97$	18.8346	1.91236	0.956182	+	0.292771i	$0.0945775\pi$
$98$	−1.54784	−0.156356
$99$	−1.81220	−0.182133
$100$	2.04290	0.204290
$101$	−7.64462	−0.760668	−0.380334	−	0.924849i	$-0.624191\pi$
$101$	−7.64462	−0.760668	−0.380334	+	0.924849i	$0.624191\pi$
$102$	1.61734	0.160141
$103$	−11.9313	−1.17562	−0.587811	−	0.808998i	$-0.700010\pi$
$103$	−11.9313	−1.17562	−0.587811	+	0.808998i	$0.700010\pi$
$104$	2.95366	0.289630
$105$	−10.3373	−1.00882
$106$	16.3158	1.58473
$107$	6.36395	0.615226	0.307613	−	0.951512i	$-0.400470\pi$
$107$	6.36395	0.615226	0.307613	+	0.951512i	$0.400470\pi$
$108$	−1.06057	−0.102053
$109$	17.7754	1.70257	0.851287	−	0.524701i	$-0.175823\pi$
$109$	17.7754	1.70257	0.851287	+	0.524701i	$0.175823\pi$
$110$	−5.76704	−0.549866
$111$	6.42206	0.609555
$112$	−10.6501	−1.00634
$113$	−9.04079	−0.850486	−0.425243	−	0.905079i	$-0.639811\pi$
$113$	−9.04079	−0.850486	−0.425243	+	0.905079i	$0.639811\pi$
$114$	−3.98547	−0.373274
$115$	20.2850	1.89158
$116$	0.854149	0.0793058
$117$	2.00632	0.185484
$118$	−8.44928	−0.777819
$119$	2.44069	0.223738
$120$	11.2996	1.03150
$121$	1.00000	0.0909091
$122$	−16.3958	−1.48441
$123$	4.09511	0.369244
$124$	−1.24303	−0.111628
$125$	−19.8287	−1.77353
$126$	−6.56370	−0.584741
$127$	6.54083	0.580405	0.290202	−	0.956965i	$-0.406277\pi$
$127$	6.54083	0.580405	0.290202	+	0.956965i	$0.406277\pi$
$128$	12.7204	1.12434
$129$	1.08986	0.0959571
$130$	6.38479	0.559983
$131$	13.0230	1.13782	0.568910	−	0.822400i	$-0.307365\pi$
$131$	13.0230	1.13782	0.568910	+	0.822400i	$0.307365\pi$
$132$	0.220392	0.0191826
$133$	−6.01437	−0.521512
$134$	19.6798	1.70008
$135$	20.3816	1.75417
$136$	−2.66788	−0.228769
$137$	16.5668	1.41539	0.707697	−	0.706516i	$-0.249734\pi$
$137$	16.5668	1.41539	0.707697	+	0.706516i	$0.249734\pi$
$138$	−8.44217	−0.718645
$139$	−0.743249	−0.0630416	−0.0315208	−	0.999503i	$-0.510035\pi$
$139$	−0.743249	−0.0630416	−0.0315208	+	0.999503i	$0.510035\pi$
$140$	−1.91804	−0.162104
$141$	6.88884	0.580145
$142$	16.6994	1.40138
$143$	−1.10712	−0.0925819
$144$	7.90761	0.658968
$145$	−16.4147	−1.36317
$146$	−19.7897	−1.63780
$147$	−1.13676	−0.0937584
$148$	1.19158	0.0979477
$149$	−1.24037	−0.101615	−0.0508076	−	0.998708i	$-0.516180\pi$
$149$	−1.24037	−0.101615	−0.0508076	+	0.998708i	$0.516180\pi$
$150$	16.3390	1.33407
$151$	−3.64601	−0.296708	−0.148354	−	0.988934i	$-0.547398\pi$
$151$	−3.64601	−0.296708	−0.148354	+	0.988934i	$0.547398\pi$
$152$	6.57422	0.533240
$153$	−1.81220	−0.146508
$154$	3.62195	0.291865
$155$	23.8881	1.91874
$156$	−0.243999	−0.0195356
$157$	−1.28483	−0.102540	−0.0512702	−	0.998685i	$-0.516327\pi$
$157$	−1.28483	−0.102540	−0.0512702	+	0.998685i	$0.516327\pi$
$158$	17.7151	1.40934
$159$	11.9826	0.950279
$160$	4.42900	0.350143
$161$	−12.7399	−1.00404
$162$	−0.414542	−0.0325695
$163$	−9.58004	−0.750367	−0.375183	−	0.926951i	$-0.622420\pi$
$163$	−9.58004	−0.750367	−0.375183	+	0.926951i	$0.622420\pi$
$164$	0.759830	0.0593328
$165$	−4.23540	−0.329726
$166$	−15.9816	−1.24041
$167$	8.62277	0.667250	0.333625	−	0.942706i	$-0.391728\pi$
$167$	8.62277	0.667250	0.333625	+	0.942706i	$0.391728\pi$
$168$	−7.09662	−0.547516
$169$	−11.7743	−0.905715
$170$	−5.76704	−0.442312
$171$	4.46563	0.341496
$172$	0.202219	0.0154191
$173$	−18.3505	−1.39516	−0.697582	−	0.716505i	$-0.745741\pi$
$173$	−18.3505	−1.39516	−0.697582	+	0.716505i	$0.745741\pi$
$174$	6.83145	0.517891
$175$	24.6568	1.86388
$176$	−4.36355	−0.328915
$177$	−6.20528	−0.466417
$178$	7.14729	0.535712
$179$	20.7907	1.55397	0.776986	−	0.629518i	$-0.216748\pi$
$179$	20.7907	1.55397	0.776986	+	0.629518i	$0.216748\pi$
$180$	1.42413	0.106149
$181$	6.50592	0.483581	0.241790	−	0.970328i	$-0.422265\pi$
$181$	6.50592	0.483581	0.241790	+	0.970328i	$0.422265\pi$
$182$	−4.00993	−0.297236
$183$	−12.0414	−0.890122
$184$	13.9258	1.02662
$185$	−22.8994	−1.68360
$186$	−9.94173	−0.728963
$187$	1.00000	0.0731272
$188$	1.27819	0.0932219
$189$	−12.8005	−0.931102
$190$	14.2112	1.03099
$191$	1.02153	0.0739153	0.0369576	−	0.999317i	$-0.488233\pi$
$191$	1.02153	0.0739153	0.0369576	+	0.999317i	$0.488233\pi$
$192$	7.66808	0.553396
$193$	3.86361	0.278109	0.139054	−	0.990285i	$-0.455594\pi$
$193$	3.86361	0.278109	0.139054	+	0.990285i	$0.455594\pi$
$194$	27.9503	2.00672
$195$	4.68909	0.335793
$196$	−0.210921	−0.0150658
$197$	10.4978	0.747940	0.373970	−	0.927441i	$-0.377996\pi$
$197$	10.4978	0.747940	0.373970	+	0.927441i	$0.377996\pi$
$198$	−2.68928	−0.191119
$199$	−4.28220	−0.303557	−0.151779	−	0.988415i	$-0.548500\pi$
$199$	−4.28220	−0.303557	−0.151779	+	0.988415i	$0.548500\pi$
$200$	−26.9519	−1.90579
$201$	14.4531	1.01945
$202$	−11.3445	−0.798198
$203$	10.3092	0.723562
$204$	0.220392	0.0154305
$205$	−14.6021	−1.01986
$206$	−17.7059	−1.23363
$207$	9.45927	0.657465
$208$	4.83096	0.334967
$209$	−2.46421	−0.170453
$210$	−15.3404	−1.05859
$211$	5.78068	0.397959	0.198979	−	0.980004i	$-0.436237\pi$
$211$	5.78068	0.397959	0.198979	+	0.980004i	$0.436237\pi$
$212$	2.22331	0.152698
$213$	12.2643	0.840336
$214$	9.44402	0.645580
$215$	−3.88618	−0.265035
$216$	13.9921	0.952041
$217$	−15.0028	−1.01846
$218$	26.3785	1.78657
$219$	−14.5338	−0.982106
$220$	−0.785860	−0.0529827
$221$	−1.10712	−0.0744728
$222$	9.53025	0.639629
$223$	15.1247	1.01282	0.506412	−	0.862292i	$-0.330972\pi$
$223$	15.1247	1.01282	0.506412	+	0.862292i	$0.330972\pi$
$224$	−2.78161	−0.185854
$225$	−18.3075	−1.22050
$226$	−13.4164	−0.892447
$227$	1.35024	0.0896184	0.0448092	−	0.998996i	$-0.485732\pi$
$227$	1.35024	0.0896184	0.0448092	+	0.998996i	$0.485732\pi$
$228$	−0.543091	−0.0359671
$229$	5.80407	0.383544	0.191772	−	0.981440i	$-0.438577\pi$
$229$	5.80407	0.383544	0.191772	+	0.981440i	$0.438577\pi$
$230$	30.1026	1.98491
$231$	2.66002	0.175016
$232$	−11.2688	−0.739833
$233$	16.6417	1.09024	0.545118	−	0.838360i	$-0.316485\pi$
$233$	16.6417	1.09024	0.545118	+	0.838360i	$0.316485\pi$
$234$	2.97735	0.194635
$235$	−24.5639	−1.60237
$236$	−1.15136	−0.0749473
$237$	13.0103	0.845108
$238$	3.62195	0.234776
$239$	−21.8295	−1.41203	−0.706016	−	0.708196i	$-0.749509\pi$
$239$	−21.8295	−1.41203	−0.706016	+	0.708196i	$0.749509\pi$
$240$	18.4814	1.19297
$241$	2.64087	0.170114	0.0850568	−	0.996376i	$-0.472893\pi$
$241$	2.64087	0.170114	0.0850568	+	0.996376i	$0.472893\pi$
$242$	1.48399	0.0953943
$243$	15.4295	0.989801
$244$	−2.23422	−0.143031
$245$	4.05340	0.258962
$246$	6.07709	0.387461
$247$	2.72817	0.173589
$248$	16.3994	1.04136
$249$	−11.7371	−0.743811
$250$	−29.4256	−1.86104
$251$	22.4002	1.41389	0.706943	−	0.707270i	$-0.250074\pi$
$251$	22.4002	1.41389	0.706943	+	0.707270i	$0.250074\pi$
$252$	−0.894420	−0.0563431
$253$	−5.21978	−0.328164
$254$	9.70651	0.609040
$255$	−4.23540	−0.265231
$256$	4.80532	0.300333
$257$	−23.3394	−1.45587	−0.727936	−	0.685645i	$-0.759520\pi$
$257$	−23.3394	−1.45587	−0.727936	+	0.685645i	$0.759520\pi$
$258$	1.61734	0.100691
$259$	14.3819	0.893645
$260$	0.870040	0.0539576
$261$	−7.65449	−0.473801
$262$	19.3259	1.19396
$263$	25.3846	1.56528	0.782642	−	0.622473i	$-0.213872\pi$
$263$	25.3846	1.56528	0.782642	+	0.622473i	$0.213872\pi$
$264$	−2.90763	−0.178952
$265$	−42.7268	−2.62469
$266$	−8.92525	−0.547242
$267$	5.24908	0.321238
$268$	2.68172	0.163812
$269$	−0.148802	−0.00907264	−0.00453632	−	0.999990i	$-0.501444\pi$
$269$	−0.148802	−0.00907264	−0.00453632	+	0.999990i	$0.501444\pi$
$270$	30.2460	1.84071
$271$	−11.7489	−0.713693	−0.356846	−	0.934163i	$-0.616148\pi$
$271$	−11.7489	−0.713693	−0.356846	+	0.934163i	$0.616148\pi$
$272$	−4.36355	−0.264579
$273$	−2.94495	−0.178237
$274$	24.5849	1.48523
$275$	10.1024	0.609196
$276$	−1.15039	−0.0692456
$277$	7.96277	0.478436	0.239218	−	0.970966i	$-0.423109\pi$
$277$	7.96277	0.478436	0.239218	+	0.970966i	$0.423109\pi$
$278$	−1.10297	−0.0661519
$279$	11.1395	0.666904
$280$	25.3048	1.51225
$281$	28.6453	1.70884	0.854418	−	0.519586i	$-0.173914\pi$
$281$	28.6453	1.70884	0.854418	+	0.519586i	$0.173914\pi$
$282$	10.2230	0.608768
$283$	24.7199	1.46944	0.734722	−	0.678369i	$-0.237313\pi$
$283$	24.7199	1.46944	0.734722	+	0.678369i	$0.237313\pi$
$284$	2.27559	0.135031
$285$	10.4369	0.618229
$286$	−1.64295	−0.0971496
$287$	9.17078	0.541334
$288$	2.06533	0.121701
$289$	1.00000	0.0588235
$290$	−24.3592	−1.43042
$291$	20.5271	1.20332
$292$	−2.69669	−0.157812
$293$	−10.0618	−0.587815	−0.293908	−	0.955834i	$-0.594956\pi$
$293$	−10.0618	−0.587815	−0.293908	+	0.955834i	$0.594956\pi$
$294$	−1.68694	−0.0983842
$295$	22.1265	1.28825
$296$	−15.7206	−0.913741
$297$	−5.24464	−0.304325
$298$	−1.84070	−0.106629
$299$	5.77891	0.334203
$300$	2.22648	0.128546
$301$	2.44069	0.140679
$302$	−5.41064	−0.311347
$303$	−8.33159	−0.478638
$304$	10.7527	0.616709
$305$	42.9364	2.45853
$306$	−2.68928	−0.153736
$307$	−18.2238	−1.04009	−0.520043	−	0.854140i	$-0.674084\pi$
$307$	−18.2238	−1.04009	−0.520043	+	0.854140i	$0.674084\pi$
$308$	0.493555	0.0281229
$309$	−13.0034	−0.739740
$310$	35.4497	2.01341
$311$	−18.9632	−1.07530	−0.537651	−	0.843167i	$-0.680688\pi$
$311$	−18.9632	−1.07530	−0.537651	+	0.843167i	$0.680688\pi$
$312$	3.21909	0.182245
$313$	12.4896	0.705952	0.352976	−	0.935632i	$-0.385170\pi$
$313$	12.4896	0.705952	0.352976	+	0.935632i	$0.385170\pi$
$314$	−1.90667	−0.107600
$315$	17.1886	0.968469
$316$	2.41400	0.135798
$317$	0.235540	0.0132292	0.00661462	−	0.999978i	$-0.497894\pi$
$317$	0.235540	0.0132292	0.00661462	+	0.999978i	$0.497894\pi$
$318$	17.7820	0.997164
$319$	4.22387	0.236491
$320$	−27.3424	−1.52849
$321$	6.93584	0.387121
$322$	−18.9058	−1.05358
$323$	−2.46421	−0.137112
$324$	−0.0564887	−0.00313826
$325$	−11.1845	−0.620405
$326$	−14.2167	−0.787388
$327$	19.3727	1.07131
$328$	−10.0244	−0.553508
$329$	15.4272	0.850528
$330$	−6.28528	−0.345993
$331$	−9.00396	−0.494903	−0.247451	−	0.968900i	$-0.579593\pi$
$331$	−9.00396	−0.494903	−0.247451	+	0.968900i	$0.579593\pi$
$332$	−2.17777	−0.119521
$333$	−10.6784	−0.585175
$334$	12.7961	0.700171
$335$	−51.5363	−2.81573
$336$	−11.6071	−0.633220
$337$	6.25008	0.340464	0.170232	−	0.985404i	$-0.445548\pi$
$337$	6.25008	0.340464	0.170232	+	0.985404i	$0.445548\pi$
$338$	−17.4729	−0.950401
$339$	−9.85322	−0.535154
$340$	−0.785860	−0.0426193
$341$	−6.14695	−0.332876
$342$	6.62695	0.358344
$343$	−19.6305	−1.05995
$344$	−2.66788	−0.143843
$345$	22.1078	1.19025
$346$	−27.2320	−1.46400
$347$	−20.6901	−1.11070	−0.555350	−	0.831617i	$-0.687416\pi$
$347$	−20.6901	−1.11070	−0.555350	+	0.831617i	$0.687416\pi$
$348$	0.930906	0.0499018
$349$	−22.9887	−1.23056	−0.615278	−	0.788310i	$-0.710956\pi$
$349$	−22.9887	−1.23056	−0.615278	+	0.788310i	$0.710956\pi$
$350$	36.5903	1.95583
$351$	5.80643	0.309924
$352$	−1.13968	−0.0607452
$353$	26.4340	1.40694	0.703471	−	0.710724i	$-0.251633\pi$
$353$	26.4340	1.40694	0.703471	+	0.710724i	$0.251633\pi$
$354$	−9.20856	−0.489429
$355$	−43.7314	−2.32102
$356$	0.973944	0.0516189
$357$	2.66002	0.140783
$358$	30.8532	1.63064
$359$	−2.34766	−0.123905	−0.0619524	−	0.998079i	$-0.519733\pi$
$359$	−2.34766	−0.123905	−0.0619524	+	0.998079i	$0.519733\pi$
$360$	−18.7886	−0.990248
$361$	−12.9277	−0.680404
$362$	9.65470	0.507440
$363$	1.08986	0.0572030
$364$	−0.546424	−0.0286404
$365$	51.8240	2.71259
$366$	−17.8692	−0.934039
$367$	22.2002	1.15884	0.579421	−	0.815028i	$-0.303279\pi$
$367$	22.2002	1.15884	0.579421	+	0.815028i	$0.303279\pi$
$368$	22.7767	1.18732
$369$	−6.80925	−0.354475
$370$	−33.9825	−1.76666
$371$	26.8343	1.39317
$372$	−1.35474	−0.0702398
$373$	−0.521317	−0.0269928	−0.0134964	−	0.999909i	$-0.504296\pi$
$373$	−0.521317	−0.0269928	−0.0134964	+	0.999909i	$0.504296\pi$
$374$	1.48399	0.0767352
$375$	−21.6106	−1.11597
$376$	−16.8632	−0.869655
$377$	−4.67633	−0.240843
$378$	−18.9958	−0.977041
$379$	−6.58159	−0.338074	−0.169037	−	0.985610i	$-0.554066\pi$
$379$	−6.58159	−0.338074	−0.169037	+	0.985610i	$0.554066\pi$
$380$	1.93652	0.0993416
$381$	7.12861	0.365210
$382$	1.51594	0.0775621
$383$	−4.88874	−0.249803	−0.124902	−	0.992169i	$-0.539861\pi$
$383$	−4.88874	−0.249803	−0.124902	+	0.992169i	$0.539861\pi$
$384$	13.8635	0.707470
$385$	−9.48495	−0.483398
$386$	5.73355	0.291830
$387$	−1.81220	−0.0921192
$388$	3.80872	0.193359
$389$	−13.5847	−0.688770	−0.344385	−	0.938828i	$-0.611913\pi$
$389$	−13.5847	−0.688770	−0.344385	+	0.938828i	$0.611913\pi$
$390$	6.95855	0.352360
$391$	−5.21978	−0.263975
$392$	2.78268	0.140547
$393$	14.1932	0.715954
$394$	15.5787	0.784842
$395$	−46.3913	−2.33420
$396$	−0.366462	−0.0184154
$397$	4.90179	0.246014	0.123007	−	0.992406i	$-0.460746\pi$
$397$	4.90179	0.246014	0.123007	+	0.992406i	$0.460746\pi$
$398$	−6.35473	−0.318534
$399$	−6.55484	−0.328152
$400$	−44.0822	−2.20411
$401$	2.98183	0.148906	0.0744528	−	0.997225i	$-0.476279\pi$
$401$	2.98183	0.148906	0.0744528	+	0.997225i	$0.476279\pi$
$402$	21.4483	1.06974
$403$	6.80540	0.339001
$404$	−1.54589	−0.0769110
$405$	1.08558	0.0539428
$406$	15.2987	0.759261
$407$	5.89253	0.292082
$408$	−2.90763	−0.143949
$409$	−19.1137	−0.945114	−0.472557	−	0.881300i	$-0.656669\pi$
$409$	−19.1137	−0.945114	−0.472557	+	0.881300i	$0.656669\pi$
$410$	−21.6694	−1.07017
$411$	18.0555	0.890612
$412$	−2.41273	−0.118867
$413$	−13.8964	−0.683797
$414$	14.0374	0.689902
$415$	41.8516	2.05442
$416$	1.26176	0.0618629
$417$	−0.810040	−0.0396678
$418$	−3.65686	−0.178863
$419$	−29.3492	−1.43380	−0.716901	−	0.697175i	$-0.754440\pi$
$419$	−29.3492	−1.43380	−0.716901	+	0.697175i	$0.754440\pi$
$420$	−2.09040	−0.102001
$421$	3.33249	0.162416	0.0812079	−	0.996697i	$-0.474122\pi$
$421$	3.33249	0.162416	0.0812079	+	0.996697i	$0.474122\pi$
$422$	8.57846	0.417593
$423$	−11.4546	−0.556941
$424$	−29.3322	−1.42450
$425$	10.1024	0.490037
$426$	18.2001	0.881796
$427$	−26.9660	−1.30497
$428$	1.28691	0.0622054
$429$	−1.20661	−0.0582555
$430$	−5.76704	−0.278111
$431$	1.36614	0.0658047	0.0329023	−	0.999459i	$-0.489525\pi$
$431$	1.36614	0.0658047	0.0329023	+	0.999459i	$0.489525\pi$
$432$	22.8852	1.10107
$433$	35.2115	1.69216	0.846079	−	0.533057i	$-0.178957\pi$
$433$	35.2115	1.69216	0.846079	+	0.533057i	$0.178957\pi$
$434$	−22.2640	−1.06871
$435$	−17.8898	−0.857750
$436$	3.59453	0.172147
$437$	12.8626	0.615302
$438$	−21.5680	−1.03056
$439$	20.1067	0.959639	0.479820	−	0.877367i	$-0.340702\pi$
$439$	20.1067	0.959639	0.479820	+	0.877367i	$0.340702\pi$
$440$	10.3679	0.494269
$441$	1.89018	0.0900084
$442$	−1.64295	−0.0781471
$443$	1.90938	0.0907173	0.0453586	−	0.998971i	$-0.485557\pi$
$443$	1.90938	0.0907173	0.0453586	+	0.998971i	$0.485557\pi$
$444$	1.29866	0.0616319
$445$	−18.7169	−0.887265
$446$	22.4448	1.06279
$447$	−1.35184	−0.0639397
$448$	17.1723	0.811313
$449$	−25.0474	−1.18206	−0.591030	−	0.806650i	$-0.701278\pi$
$449$	−25.0474	−1.18206	−0.591030	+	0.806650i	$0.701278\pi$
$450$	−27.1681	−1.28072
$451$	3.75745	0.176932
$452$	−1.82822	−0.0859924
$453$	−3.97366	−0.186699
$454$	2.00374	0.0940399
$455$	10.5010	0.492293
$456$	7.16500	0.335532
$457$	−29.7451	−1.39142	−0.695709	−	0.718324i	$-0.744910\pi$
$457$	−29.7451	−1.39142	−0.695709	+	0.718324i	$0.744910\pi$
$458$	8.61317	0.402467
$459$	−5.24464	−0.244799
$460$	4.10202	0.191257
$461$	9.97229	0.464456	0.232228	−	0.972661i	$-0.425398\pi$
$461$	9.97229	0.464456	0.232228	+	0.972661i	$0.425398\pi$
$462$	3.94744	0.183651
$463$	11.7218	0.544757	0.272378	−	0.962190i	$-0.412190\pi$
$463$	11.7218	0.544757	0.272378	+	0.962190i	$0.412190\pi$
$464$	−18.4311	−0.855641
$465$	26.0348	1.20734
$466$	24.6961	1.14402
$467$	15.0392	0.695932	0.347966	−	0.937507i	$-0.386872\pi$
$467$	15.0392	0.695932	0.347966	+	0.937507i	$0.386872\pi$
$468$	0.405716	0.0187542
$469$	32.3671	1.49457
$470$	−36.4525	−1.68143
$471$	−1.40029	−0.0645218
$472$	15.1899	0.699174
$473$	1.00000	0.0459800
$474$	19.3071	0.886803
$475$	−24.8943	−1.14223
$476$	0.493555	0.0226221
$477$	−19.9243	−0.912272
$478$	−32.3947	−1.48170
$479$	−9.18585	−0.419712	−0.209856	−	0.977732i	$-0.567300\pi$
$479$	−9.18585	−0.419712	−0.209856	+	0.977732i	$0.567300\pi$
$480$	4.82700	0.220322
$481$	−6.52373	−0.297456
$482$	3.91902	0.178507
$483$	−13.8847	−0.631776
$484$	0.202219	0.00919179
$485$	−73.1946	−3.32360
$486$	22.8971	1.03864
$487$	38.4046	1.74028	0.870139	−	0.492806i	$-0.164029\pi$
$487$	38.4046	1.74028	0.870139	+	0.492806i	$0.164029\pi$
$488$	29.4761	1.33432
$489$	−10.4409	−0.472155
$490$	6.01519	0.271739
$491$	37.8902	1.70996	0.854980	−	0.518662i	$-0.173570\pi$
$491$	37.8902	1.70996	0.854980	+	0.518662i	$0.173570\pi$
$492$	0.828111	0.0373341
$493$	4.22387	0.190234
$494$	4.04857	0.182154
$495$	7.04252	0.316538
$496$	26.8225	1.20437
$497$	27.4652	1.23198
$498$	−17.4178	−0.780509
$499$	−11.3058	−0.506117	−0.253059	−	0.967451i	$-0.581437\pi$
$499$	−11.3058	−0.506117	−0.253059	+	0.967451i	$0.581437\pi$
$500$	−4.00975	−0.179321
$501$	9.39764	0.419856
$502$	33.2416	1.48364
$503$	25.1745	1.12248	0.561238	−	0.827654i	$-0.310325\pi$
$503$	25.1745	1.12248	0.561238	+	0.827654i	$0.310325\pi$
$504$	11.8001	0.525618
$505$	29.7084	1.32200
$506$	−7.74608	−0.344355
$507$	−12.8324	−0.569905
$508$	1.32268	0.0586845
$509$	41.7038	1.84849	0.924245	−	0.381800i	$-0.124696\pi$
$509$	41.7038	1.84849	0.924245	+	0.381800i	$0.124696\pi$
$510$	−6.28528	−0.278317
$511$	−32.5477	−1.43983
$512$	−18.3098	−0.809188
$513$	12.9239	0.570603
$514$	−34.6354	−1.52770
$515$	46.3670	2.04317
$516$	0.220392	0.00970220
$517$	6.32083	0.277990
$518$	21.3425	0.937735
$519$	−19.9996	−0.877883
$520$	−11.4785	−0.503364
$521$	−37.4727	−1.64171	−0.820854	−	0.571138i	$-0.806502\pi$
$521$	−37.4727	−1.64171	−0.820854	+	0.571138i	$0.806502\pi$
$522$	−11.3592	−0.497178
$523$	20.2295	0.884576	0.442288	−	0.896873i	$-0.354167\pi$
$523$	20.2295	0.884576	0.442288	+	0.896873i	$0.354167\pi$
$524$	2.63349	0.115045
$525$	26.8725	1.17281
$526$	37.6705	1.64251
$527$	−6.14695	−0.267765
$528$	−4.75567	−0.206964
$529$	4.24606	0.184611
$530$	−63.4060	−2.75418
$531$	10.3180	0.447763
$532$	−1.21622	−0.0527299
$533$	−4.15994	−0.180187
$534$	7.78956	0.337087
$535$	−24.7314	−1.06923
$536$	−35.3800	−1.52818
$537$	22.6590	0.977810
$538$	−0.220821	−0.00952027
$539$	−1.04303	−0.0449265
$540$	4.12155	0.177363
$541$	7.04800	0.303017	0.151509	−	0.988456i	$-0.451587\pi$
$541$	7.04800	0.303017	0.151509	+	0.988456i	$0.451587\pi$
$542$	−17.4352	−0.748905
$543$	7.09056	0.304285
$544$	−1.13968	−0.0488634
$545$	−69.0783	−2.95899
$546$	−4.37028	−0.187031
$547$	−14.0440	−0.600479	−0.300240	−	0.953864i	$-0.597067\pi$
$547$	−14.0440	−0.600479	−0.300240	+	0.953864i	$0.597067\pi$
$548$	3.35012	0.143110
$549$	20.0221	0.854521
$550$	14.9918	0.639252
$551$	−10.4085	−0.443417
$552$	15.1772	0.645983
$553$	29.1358	1.23898
$554$	11.8167	0.502041
$555$	−24.9572	−1.05938
$556$	−0.150299	−0.00637411
$557$	−23.1200	−0.979626	−0.489813	−	0.871828i	$-0.662935\pi$
$557$	−23.1200	−0.979626	−0.489813	+	0.871828i	$0.662935\pi$
$558$	16.5309	0.699808
$559$	−1.10712	−0.0468261
$560$	41.3880	1.74896
$561$	1.08986	0.0460141
$562$	42.5093	1.79315
$563$	−6.18709	−0.260755	−0.130377	−	0.991464i	$-0.541619\pi$
$563$	−6.18709	−0.260755	−0.130377	+	0.991464i	$0.541619\pi$
$564$	1.39306	0.0586583
$565$	35.1341	1.47810
$566$	36.6840	1.54194
$567$	−0.681791	−0.0286325
$568$	−30.0219	−1.25969
$569$	17.9945	0.754368	0.377184	−	0.926138i	$-0.376892\pi$
$569$	17.9945	0.754368	0.377184	+	0.926138i	$0.376892\pi$
$570$	15.4882	0.648731
$571$	2.76772	0.115826	0.0579128	−	0.998322i	$-0.481555\pi$
$571$	2.76772	0.115826	0.0579128	+	0.998322i	$0.481555\pi$
$572$	−0.223881	−0.00936093
$573$	1.11333	0.0465099
$574$	13.6093	0.568042
$575$	−52.7321	−2.19908
$576$	−12.7503	−0.531263
$577$	−26.3881	−1.09855	−0.549276	−	0.835641i	$-0.685096\pi$
$577$	−26.3881	−1.09855	−0.549276	+	0.835641i	$0.685096\pi$
$578$	1.48399	0.0617258
$579$	4.21081	0.174995
$580$	−3.31937	−0.137830
$581$	−26.2847	−1.09047
$582$	30.4620	1.26269
$583$	10.9946	0.455348
$584$	35.5775	1.47221
$585$	−7.79690	−0.322362
$586$	−14.9316	−0.616817
$587$	−21.5947	−0.891308	−0.445654	−	0.895205i	$-0.647029\pi$
$587$	−21.5947	−0.891308	−0.445654	+	0.895205i	$0.647029\pi$
$588$	−0.229875	−0.00947988
$589$	15.1474	0.624136
$590$	32.8354	1.35181
$591$	11.4412	0.470628
$592$	−25.7123	−1.05677
$593$	15.8616	0.651358	0.325679	−	0.945480i	$-0.394407\pi$
$593$	15.8616	0.651358	0.325679	+	0.945480i	$0.394407\pi$
$594$	−7.78298	−0.319339
$595$	−9.48495	−0.388845
$596$	−0.250827	−0.0102743
$597$	−4.66701	−0.191008
$598$	8.57583	0.350692
$599$	−4.33546	−0.177142	−0.0885711	−	0.996070i	$-0.528230\pi$
$599$	−4.33546	−0.177142	−0.0885711	+	0.996070i	$0.528230\pi$
$600$	−29.3739	−1.19919
$601$	11.6366	0.474669	0.237334	−	0.971428i	$-0.423726\pi$
$601$	11.6366	0.474669	0.237334	+	0.971428i	$0.423726\pi$
$602$	3.62195	0.147620
$603$	−24.0323	−0.978673
$604$	−0.737295	−0.0300001
$605$	−3.88618	−0.157996
$606$	−12.3640	−0.502252
$607$	−10.0240	−0.406860	−0.203430	−	0.979089i	$-0.565209\pi$
$607$	−10.0240	−0.406860	−0.203430	+	0.979089i	$0.565209\pi$
$608$	2.80841	0.113896
$609$	11.2356	0.455289
$610$	63.7171	2.57983
$611$	−6.99790	−0.283105
$612$	−0.366462	−0.0148133
$613$	−15.9830	−0.645547	−0.322774	−	0.946476i	$-0.604615\pi$
$613$	−15.9830	−0.645547	−0.322774	+	0.946476i	$0.604615\pi$
$614$	−27.0439	−1.09140
$615$	−15.9143	−0.641727
$616$	−6.51148	−0.262355
$617$	−1.13330	−0.0456250	−0.0228125	−	0.999740i	$-0.507262\pi$
$617$	−1.13330	−0.0456250	−0.0228125	+	0.999740i	$0.507262\pi$
$618$	−19.2970	−0.776237
$619$	20.4293	0.821122	0.410561	−	0.911833i	$-0.365333\pi$
$619$	20.4293	0.821122	0.410561	+	0.911833i	$0.365333\pi$
$620$	4.83065	0.194003
$621$	27.3758	1.09855
$622$	−28.1411	−1.12836
$623$	11.7550	0.470955
$624$	5.26509	0.210772
$625$	26.5460	1.06184
$626$	18.5344	0.740782
$627$	−2.68565	−0.107255
$628$	−0.259817	−0.0103678
$629$	5.89253	0.234951
$630$	25.5077	1.01625
$631$	−5.88192	−0.234156	−0.117078	−	0.993123i	$-0.537353\pi$
$631$	−5.88192	−0.234156	−0.117078	+	0.993123i	$0.537353\pi$
$632$	−31.8479	−1.26684
$633$	6.30015	0.250409
$634$	0.349538	0.0138819
$635$	−25.4188	−1.00871
$636$	2.42311	0.0960825
$637$	1.15476	0.0457531
$638$	6.26818	0.248159
$639$	−20.3928	−0.806726
$640$	−49.4338	−1.95404
$641$	31.4681	1.24292	0.621458	−	0.783447i	$-0.286541\pi$
$641$	31.4681	1.24292	0.621458	+	0.783447i	$0.286541\pi$
$642$	10.2927	0.406220
$643$	−28.5497	−1.12589	−0.562945	−	0.826494i	$-0.690332\pi$
$643$	−28.5497	−1.12589	−0.562945	+	0.826494i	$0.690332\pi$
$644$	−2.57625	−0.101518
$645$	−4.23540	−0.166769
$646$	−3.65686	−0.143877
$647$	24.6889	0.970620	0.485310	−	0.874342i	$-0.338707\pi$
$647$	24.6889	0.970620	0.485310	+	0.874342i	$0.338707\pi$
$648$	0.745256	0.0292764
$649$	−5.69363	−0.223495
$650$	−16.5977	−0.651015
$651$	−16.3510	−0.640846
$652$	−1.93727	−0.0758694
$653$	−33.5920	−1.31456	−0.657278	−	0.753649i	$-0.728292\pi$
$653$	−33.5920	−1.31456	−0.657278	+	0.753649i	$0.728292\pi$
$654$	28.7489	1.12417
$655$	−50.6095	−1.97748
$656$	−16.3958	−0.640149
$657$	24.1665	0.942825
$658$	22.8938	0.892492
$659$	6.70674	0.261257	0.130629	−	0.991431i	$-0.458300\pi$
$659$	6.70674	0.261257	0.130629	+	0.991431i	$0.458300\pi$
$660$	−0.856480	−0.0333385
$661$	24.9899	0.971993	0.485996	−	0.873961i	$-0.338457\pi$
$661$	24.9899	0.971993	0.485996	+	0.873961i	$0.338457\pi$
$662$	−13.3618	−0.519320
$663$	−1.20661	−0.0468607
$664$	28.7314	1.11500
$665$	23.3729	0.906362
$666$	−15.8467	−0.614046
$667$	−22.0477	−0.853689
$668$	1.74369	0.0674655
$669$	16.4838	0.637302
$670$	−76.4792	−2.95465
$671$	−11.0485	−0.426523
$672$	−3.03157	−0.116945
$673$	−29.3634	−1.13187	−0.565937	−	0.824448i	$-0.691485\pi$
$673$	−29.3634	−1.13187	−0.565937	+	0.824448i	$0.691485\pi$
$674$	9.27505	0.357262
$675$	−52.9833	−2.03933
$676$	−2.38099	−0.0915766
$677$	−0.742955	−0.0285541	−0.0142770	−	0.999898i	$-0.504545\pi$
$677$	−0.742955	−0.0285541	−0.0142770	+	0.999898i	$0.504545\pi$
$678$	−14.6221	−0.561557
$679$	45.9695	1.76415
$680$	10.3679	0.397590
$681$	1.47157	0.0563908
$682$	−9.12200	−0.349299
$683$	15.3911	0.588925	0.294462	−	0.955663i	$-0.404859\pi$
$683$	15.3911	0.588925	0.294462	+	0.955663i	$0.404859\pi$
$684$	0.903038	0.0345285
$685$	−64.3814	−2.45989
$686$	−29.1315	−1.11225
$687$	6.32565	0.241338
$688$	−4.36355	−0.166359
$689$	−12.1723	−0.463727
$690$	32.8078	1.24897
$691$	−37.3456	−1.42069	−0.710347	−	0.703851i	$-0.751462\pi$
$691$	−37.3456	−1.42069	−0.710347	+	0.703851i	$0.751462\pi$
$692$	−3.71083	−0.141065
$693$	−4.42301	−0.168016
$694$	−30.7038	−1.16550
$695$	2.88840	0.109563
$696$	−12.2815	−0.465527
$697$	3.75745	0.142324
$698$	−34.1149	−1.29127
$699$	18.1372	0.686012
$700$	4.98608	0.188456
$701$	−37.1646	−1.40369	−0.701844	−	0.712331i	$-0.747639\pi$
$701$	−37.1646	−1.40369	−0.701844	+	0.712331i	$0.747639\pi$
$702$	8.61667	0.325215
$703$	−14.5204	−0.547648
$704$	7.03582	0.265172
$705$	−26.7712	−1.00826
$706$	39.2278	1.47636
$707$	−18.6582	−0.701712
$708$	−1.25483	−0.0471593
$709$	4.56872	0.171582	0.0857909	−	0.996313i	$-0.472658\pi$
$709$	4.56872	0.171582	0.0857909	+	0.996313i	$0.472658\pi$
$710$	−64.8968	−2.43553
$711$	−21.6332	−0.811307
$712$	−12.8493	−0.481546
$713$	32.0857	1.20162
$714$	3.94744	0.147729
$715$	4.30246	0.160903
$716$	4.20429	0.157122
$717$	−23.7912	−0.888497
$718$	−3.48390	−0.130018
$719$	−1.73121	−0.0645634	−0.0322817	−	0.999479i	$-0.510277\pi$
$719$	−1.73121	−0.0645634	−0.0322817	+	0.999479i	$0.510277\pi$
$720$	−30.7304	−1.14525
$721$	−29.1205	−1.08451
$722$	−19.1845	−0.713974
$723$	2.87819	0.107041
$724$	1.31562	0.0488947
$725$	42.6711	1.58477
$726$	1.61734	0.0600253
$727$	24.3091	0.901575	0.450787	−	0.892631i	$-0.351143\pi$
$727$	24.3091	0.901575	0.450787	+	0.892631i	$0.351143\pi$
$728$	7.20898	0.267182
$729$	17.6540	0.653853
$730$	76.9061	2.84642
$731$	1.00000	0.0369863
$732$	−2.43500	−0.0900000
$733$	−11.1161	−0.410582	−0.205291	−	0.978701i	$-0.565814\pi$
$733$	−11.1161	−0.410582	−0.205291	+	0.978701i	$0.565814\pi$
$734$	32.9449	1.21602
$735$	4.41765	0.162947
$736$	5.94888	0.219278
$737$	13.2614	0.488491
$738$	−10.1048	−0.371964
$739$	−11.6470	−0.428442	−0.214221	−	0.976785i	$-0.568721\pi$
$739$	−11.6470	−0.428442	−0.214221	+	0.976785i	$0.568721\pi$
$740$	−4.63071	−0.170228
$741$	2.97333	0.109228
$742$	39.8218	1.46190
$743$	48.8766	1.79311	0.896554	−	0.442934i	$-0.146062\pi$
$743$	48.8766	1.79311	0.896554	+	0.442934i	$0.146062\pi$
$744$	17.8731	0.655258
$745$	4.82031	0.176602
$746$	−0.773627	−0.0283245
$747$	19.5162	0.714061
$748$	0.202219	0.00739388
$749$	15.5324	0.567543
$750$	−32.0698	−1.17102
$751$	−41.6697	−1.52055	−0.760274	−	0.649603i	$-0.774935\pi$
$751$	−41.6697	−1.52055	−0.760274	+	0.649603i	$0.774935\pi$
$752$	−27.5812	−1.00578
$753$	24.4131	0.889664
$754$	−6.93961	−0.252726
$755$	14.1690	0.515665
$756$	−2.58852	−0.0941435
$757$	1.66187	0.0604015	0.0302008	−	0.999544i	$-0.490385\pi$
$757$	1.66187	0.0604015	0.0302008	+	0.999544i	$0.490385\pi$
$758$	−9.76701	−0.354754
$759$	−5.68884	−0.206492
$760$	−25.5486	−0.926745
$761$	17.2379	0.624874	0.312437	−	0.949938i	$-0.398855\pi$
$761$	17.2379	0.624874	0.312437	+	0.949938i	$0.398855\pi$
$762$	10.5788	0.383228
$763$	43.3842	1.57061
$764$	0.206573	0.00747355
$765$	7.04252	0.254623
$766$	−7.25483	−0.262128
$767$	6.30352	0.227607
$768$	5.23715	0.188979
$769$	−26.1158	−0.941758	−0.470879	−	0.882198i	$-0.656063\pi$
$769$	−26.1158	−0.941758	−0.470879	+	0.882198i	$0.656063\pi$
$770$	−14.0756	−0.507248
$771$	−25.4368	−0.916083
$772$	0.781297	0.0281195
$773$	19.5044	0.701524	0.350762	−	0.936465i	$-0.385923\pi$
$773$	19.5044	0.701524	0.350762	+	0.936465i	$0.385923\pi$
$774$	−2.68928	−0.0966642
$775$	−62.0988	−2.23065
$776$	−50.2486	−1.80382
$777$	15.6742	0.562311
$778$	−20.1595	−0.722752
$779$	−9.25915	−0.331743
$780$	0.948225	0.0339519
$781$	11.2531	0.402666
$782$	−7.74608	−0.276999
$783$	−22.1527	−0.791672
$784$	4.55131	0.162547
$785$	4.99307	0.178210
$786$	21.0626	0.751278
$787$	−22.5956	−0.805445	−0.402722	−	0.915322i	$-0.631936\pi$
$787$	−22.5956	−0.805445	−0.402722	+	0.915322i	$0.631936\pi$
$788$	2.12287	0.0756240
$789$	27.6658	0.984927
$790$	−68.8441	−2.44936
$791$	−22.0658	−0.784568
$792$	4.83473	0.171795
$793$	12.2320	0.434371
$794$	7.27420	0.258152
$795$	−46.5664	−1.65154
$796$	−0.865944	−0.0306926
$797$	1.20941	0.0428395	0.0214198	−	0.999771i	$-0.493181\pi$
$797$	1.20941	0.0428395	0.0214198	+	0.999771i	$0.493181\pi$
$798$	−9.72730	−0.344343
$799$	6.32083	0.223615
$800$	−11.5135	−0.407063
$801$	−8.72804	−0.308390
$802$	4.42500	0.156252
$803$	−13.3355	−0.470598
$804$	2.92271	0.103076
$805$	49.5093	1.74497
$806$	10.0991	0.355727
$807$	−0.162174	−0.00570880
$808$	20.3950	0.717493
$809$	−9.54826	−0.335699	−0.167849	−	0.985813i	$-0.553682\pi$
$809$	−9.54826	−0.335699	−0.167849	+	0.985813i	$0.553682\pi$
$810$	1.61099	0.0566043
$811$	18.5732	0.652195	0.326097	−	0.945336i	$-0.394266\pi$
$811$	18.5732	0.652195	0.326097	+	0.945336i	$0.394266\pi$
$812$	2.08471	0.0731591
$813$	−12.8047	−0.449079
$814$	8.74445	0.306493
$815$	37.2297	1.30410
$816$	−4.75567	−0.166482
$817$	−2.46421	−0.0862117
$818$	−28.3646	−0.991744
$819$	4.89680	0.171108
$820$	−2.95283	−0.103117
$821$	37.5998	1.31224	0.656121	−	0.754656i	$-0.272196\pi$
$821$	37.5998	1.31224	0.656121	+	0.754656i	$0.272196\pi$
$822$	26.7941	0.934553
$823$	22.3257	0.778226	0.389113	−	0.921190i	$-0.372782\pi$
$823$	22.3257	0.778226	0.389113	+	0.921190i	$0.372782\pi$
$824$	31.8312	1.10889
$825$	11.0102	0.383326
$826$	−20.6221	−0.717534
$827$	29.2673	1.01772	0.508862	−	0.860848i	$-0.330066\pi$
$827$	29.2673	1.01772	0.508862	+	0.860848i	$0.330066\pi$
$828$	1.91285	0.0664761
$829$	48.7596	1.69349	0.846745	−	0.531999i	$-0.178559\pi$
$829$	48.7596	1.69349	0.846745	+	0.531999i	$0.178559\pi$
$830$	62.1073	2.15578
$831$	8.67833	0.301048
$832$	−7.78948	−0.270052
$833$	−1.04303	−0.0361388
$834$	−1.20209	−0.0416249
$835$	−33.5096	−1.15965
$836$	−0.498311	−0.0172344
$837$	32.2385	1.11433
$838$	−43.5538	−1.50454
$839$	−46.0783	−1.59080	−0.795399	−	0.606086i	$-0.792739\pi$
$839$	−46.0783	−1.59080	−0.795399	+	0.606086i	$0.792739\pi$
$840$	27.5787	0.951556
$841$	−11.1589	−0.384790
$842$	4.94538	0.170429
$843$	31.2195	1.07526
$844$	1.16897	0.0402375
$845$	45.7570	1.57409
$846$	−16.9985	−0.584420
$847$	2.44069	0.0838631
$848$	−47.9753	−1.64748
$849$	26.9413	0.924622
$850$	14.9918	0.514214
$851$	−30.7577	−1.05436
$852$	2.48008	0.0849661
$853$	−36.6154	−1.25369	−0.626844	−	0.779144i	$-0.715654\pi$
$853$	−36.6154	−1.25369	−0.626844	+	0.779144i	$0.715654\pi$
$854$	−40.0172	−1.36936
$855$	−17.3542	−0.593503
$856$	−16.9783	−0.580306
$857$	44.0273	1.50394	0.751972	−	0.659195i	$-0.229103\pi$
$857$	44.0273	1.50394	0.751972	+	0.659195i	$0.229103\pi$
$858$	−1.79059	−0.0611297
$859$	−29.9571	−1.02212	−0.511062	−	0.859544i	$-0.670748\pi$
$859$	−29.9571	−1.02212	−0.511062	+	0.859544i	$0.670748\pi$
$860$	−0.785860	−0.0267976
$861$	9.99490	0.340625
$862$	2.02734	0.0690513
$863$	−25.2119	−0.858221	−0.429111	−	0.903252i	$-0.641173\pi$
$863$	−25.2119	−0.858221	−0.429111	+	0.903252i	$0.641173\pi$
$864$	5.97721	0.203349
$865$	71.3134	2.42473
$866$	52.2535	1.77565
$867$	1.08986	0.0370137
$868$	−3.03386	−0.102976
$869$	11.9375	0.404953
$870$	−26.5482	−0.900069
$871$	−14.6820	−0.497480
$872$	−47.4227	−1.60593
$873$	−34.1320	−1.15519
$874$	19.0880	0.645660
$875$	−48.3957	−1.63607
$876$	−2.93902	−0.0993004
$877$	−4.82045	−0.162775	−0.0813876	−	0.996683i	$-0.525935\pi$
$877$	−4.82045	−0.162775	−0.0813876	+	0.996683i	$0.525935\pi$
$878$	29.8381	1.00699
$879$	−10.9660	−0.369873
$880$	16.9575	0.571638
$881$	24.5518	0.827171	0.413585	−	0.910465i	$-0.364276\pi$
$881$	24.5518	0.827171	0.413585	+	0.910465i	$0.364276\pi$
$882$	2.80500	0.0944492
$883$	−48.3566	−1.62733	−0.813665	−	0.581334i	$-0.802531\pi$
$883$	−48.3566	−1.62733	−0.813665	+	0.581334i	$0.802531\pi$
$884$	−0.223881	−0.00752993
$885$	24.1148	0.810610
$886$	2.83349	0.0951931
$887$	17.7939	0.597459	0.298730	−	0.954338i	$-0.403437\pi$
$887$	17.7939	0.597459	0.298730	+	0.954338i	$0.403437\pi$
$888$	−17.1333	−0.574956
$889$	15.9641	0.535420
$890$	−27.7756	−0.931041
$891$	−0.279344	−0.00935836
$892$	3.05850	0.102406
$893$	−15.5758	−0.521226
$894$	−2.00611	−0.0670943
$895$	−80.7964	−2.70073
$896$	31.0466	1.03720
$897$	6.29822	0.210291
$898$	−37.1700	−1.24038
$899$	−25.9639	−0.865946
$900$	−3.70213	−0.123404
$901$	10.9946	0.366282
$902$	5.57601	0.185661
$903$	2.66002	0.0885199
$904$	24.1198	0.802212
$905$	−25.2831	−0.840440
$906$	−5.89686	−0.195910
$907$	−57.3052	−1.90279	−0.951394	−	0.307975i	$-0.900349\pi$
$907$	−57.3052	−1.90279	−0.951394	+	0.307975i	$0.900349\pi$
$908$	0.273044	0.00906129
$909$	13.8536	0.459494
$910$	15.5833	0.516581
$911$	21.2749	0.704868	0.352434	−	0.935837i	$-0.385354\pi$
$911$	21.2749	0.704868	0.352434	+	0.935837i	$0.385354\pi$
$912$	11.7190	0.388054
$913$	−10.7694	−0.356414
$914$	−44.1414	−1.46007
$915$	46.7948	1.54699
$916$	1.17370	0.0387800
$917$	31.7850	1.04963
$918$	−7.78298	−0.256877
$919$	43.4187	1.43225	0.716126	−	0.697971i	$-0.245914\pi$
$919$	43.4187	1.43225	0.716126	+	0.697971i	$0.245914\pi$
$920$	−54.1180	−1.78422
$921$	−19.8614	−0.654457
$922$	14.7988	0.487371
$923$	−12.4585	−0.410075
$924$	0.537908	0.0176959
$925$	59.5285	1.95729
$926$	17.3950	0.571634
$927$	21.6218	0.710154
$928$	−4.81387	−0.158023
$929$	−9.38963	−0.308064	−0.154032	−	0.988066i	$-0.549226\pi$
$929$	−9.38963	−0.308064	−0.154032	+	0.988066i	$0.549226\pi$
$930$	38.6353	1.26690
$931$	2.57024	0.0842363
$932$	3.36528	0.110233
$933$	−20.6672	−0.676615
$934$	22.3180	0.730268
$935$	−3.88618	−0.127092
$936$	−5.35262	−0.174956
$937$	−30.4138	−0.993576	−0.496788	−	0.867872i	$-0.665487\pi$
$937$	−30.4138	−0.993576	−0.496788	+	0.867872i	$0.665487\pi$
$938$	48.0323	1.56831
$939$	13.6119	0.444208
$940$	−4.96729	−0.162015
$941$	12.8025	0.417349	0.208675	−	0.977985i	$-0.433085\pi$
$941$	12.8025	0.417349	0.208675	+	0.977985i	$0.433085\pi$
$942$	−2.07801	−0.0677052
$943$	−19.6131	−0.638689
$944$	24.8444	0.808617
$945$	49.7452	1.61821
$946$	1.48399	0.0482486
$947$	−32.4945	−1.05593	−0.527964	−	0.849267i	$-0.677044\pi$
$947$	−32.4945	−1.05593	−0.527964	+	0.849267i	$0.677044\pi$
$948$	2.63093	0.0854486
$949$	14.7639	0.479258
$950$	−36.9429	−1.19859
$951$	0.256706	0.00832427
$952$	−6.51148	−0.211038
$953$	54.5999	1.76866	0.884332	−	0.466859i	$-0.154614\pi$
$953$	54.5999	1.76866	0.884332	+	0.466859i	$0.154614\pi$
$954$	−29.5674	−0.957281
$955$	−3.96984	−0.128461
$956$	−4.41435	−0.142770
$957$	4.60344	0.148808
$958$	−13.6317	−0.440420
$959$	40.4343	1.30569
$960$	−29.7995	−0.961775
$961$	6.78500	0.218871
$962$	−9.68113	−0.312132
$963$	−11.5327	−0.371637
$964$	0.534036	0.0172001
$965$	−15.0147	−0.483339
$966$	−20.6047	−0.662946
$967$	−49.7064	−1.59845	−0.799225	−	0.601033i	$-0.794756\pi$
$967$	−49.7064	−1.59845	−0.799225	+	0.601033i	$0.794756\pi$
$968$	−2.66788	−0.0857490
$969$	−2.68565	−0.0862755
$970$	−108.620	−3.48758
$971$	15.8491	0.508622	0.254311	−	0.967122i	$-0.418151\pi$
$971$	15.8491	0.508622	0.254311	+	0.967122i	$0.418151\pi$
$972$	3.12014	0.100078
$973$	−1.81404	−0.0581555
$974$	56.9920	1.82614
$975$	−12.1896	−0.390379
$976$	48.2106	1.54318
$977$	−10.2360	−0.327479	−0.163740	−	0.986504i	$-0.552356\pi$
$977$	−10.2360	−0.327479	−0.163740	+	0.986504i	$0.552356\pi$
$978$	−15.4942	−0.495450
$979$	4.81627	0.153929
$980$	0.819676	0.0261836
$981$	−32.2125	−1.02847
$982$	56.2285	1.79432
$983$	−15.0662	−0.480538	−0.240269	−	0.970706i	$-0.577236\pi$
$983$	−15.0662	−0.480538	−0.240269	+	0.970706i	$0.577236\pi$
$984$	−10.9253	−0.348285
$985$	−40.7965	−1.29988
$986$	6.26818	0.199619
$987$	16.8135	0.535180
$988$	0.551689	0.0175516
$989$	−5.21978	−0.165979
$990$	10.4510	0.332155
$991$	31.8654	1.01224	0.506118	−	0.862464i	$-0.331080\pi$
$991$	31.8654	1.01224	0.506118	+	0.862464i	$0.331080\pi$
$992$	7.00556	0.222427
$993$	−9.81309	−0.311409
$994$	40.7581	1.29277
$995$	16.6414	0.527567
$996$	−2.37348	−0.0752065
$997$	−35.3413	−1.11927	−0.559635	−	0.828739i	$-0.689058\pi$
$997$	−35.3413	−1.11927	−0.559635	+	0.828739i	$0.689058\pi$
$998$	−16.7777	−0.531088
$999$	−30.9042	−0.977766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.57	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.57	✓	82	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.48399 q^{2} +1.08986 q^{3} +0.202219 q^{4} -3.88618 q^{5} +1.61734 q^{6} +2.44069 q^{7} -2.66788 q^{8} -1.81220 q^{9} +O(q^{10})\)	\(q+1.48399 q^{2} +1.08986 q^{3} +0.202219 q^{4} -3.88618 q^{5} +1.61734 q^{6} +2.44069 q^{7} -2.66788 q^{8} -1.81220 q^{9} -5.76704 q^{10} +1.00000 q^{11} +0.220392 q^{12} -1.10712 q^{13} +3.62195 q^{14} -4.23540 q^{15} -4.36355 q^{16} +1.00000 q^{17} -2.68928 q^{18} -2.46421 q^{19} -0.785860 q^{20} +2.66002 q^{21} +1.48399 q^{22} -5.21978 q^{23} -2.90763 q^{24} +10.1024 q^{25} -1.64295 q^{26} -5.24464 q^{27} +0.493555 q^{28} +4.22387 q^{29} -6.28528 q^{30} -6.14695 q^{31} -1.13968 q^{32} +1.08986 q^{33} +1.48399 q^{34} -9.48495 q^{35} -0.366462 q^{36} +5.89253 q^{37} -3.65686 q^{38} -1.20661 q^{39} +10.3679 q^{40} +3.75745 q^{41} +3.94744 q^{42} +1.00000 q^{43} +0.202219 q^{44} +7.04252 q^{45} -7.74608 q^{46} +6.32083 q^{47} -4.75567 q^{48} -1.04303 q^{49} +14.9918 q^{50} +1.08986 q^{51} -0.223881 q^{52} +10.9946 q^{53} -7.78298 q^{54} -3.88618 q^{55} -6.51148 q^{56} -2.68565 q^{57} +6.26818 q^{58} -5.69363 q^{59} -0.856480 q^{60} -11.0485 q^{61} -9.12200 q^{62} -4.42301 q^{63} +7.03582 q^{64} +4.30246 q^{65} +1.61734 q^{66} +13.2614 q^{67} +0.202219 q^{68} -5.68884 q^{69} -14.0756 q^{70} +11.2531 q^{71} +4.83473 q^{72} -13.3355 q^{73} +8.74445 q^{74} +11.0102 q^{75} -0.498311 q^{76} +2.44069 q^{77} -1.79059 q^{78} +11.9375 q^{79} +16.9575 q^{80} -0.279344 q^{81} +5.57601 q^{82} -10.7694 q^{83} +0.537908 q^{84} -3.88618 q^{85} +1.48399 q^{86} +4.60344 q^{87} -2.66788 q^{88} +4.81627 q^{89} +10.4510 q^{90} -2.70213 q^{91} -1.05554 q^{92} -6.69934 q^{93} +9.38003 q^{94} +9.57635 q^{95} -1.24210 q^{96} +18.8346 q^{97} -1.54784 q^{98} -1.81220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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