LMFDB - Embedded newform 8041.2.a.j.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.70166 q^{2} +2.90991 q^{3} +0.895633 q^{4} -0.762355 q^{5} -4.95167 q^{6} +4.85107 q^{7} +1.87925 q^{8} +5.46758 q^{9} +O(q^{10})$	\(q-1.70166 q^{2} +2.90991 q^{3} +0.895633 q^{4} -0.762355 q^{5} -4.95167 q^{6} +4.85107 q^{7} +1.87925 q^{8} +5.46758 q^{9} +1.29727 q^{10} +1.00000 q^{11} +2.60621 q^{12} -1.16100 q^{13} -8.25485 q^{14} -2.21838 q^{15} -4.98911 q^{16} +1.00000 q^{17} -9.30394 q^{18} +3.00298 q^{19} -0.682790 q^{20} +14.1162 q^{21} -1.70166 q^{22} -6.18094 q^{23} +5.46846 q^{24} -4.41882 q^{25} +1.97562 q^{26} +7.18044 q^{27} +4.34478 q^{28} -0.453833 q^{29} +3.77493 q^{30} -6.53377 q^{31} +4.73124 q^{32} +2.90991 q^{33} -1.70166 q^{34} -3.69823 q^{35} +4.89695 q^{36} +1.16400 q^{37} -5.11004 q^{38} -3.37841 q^{39} -1.43266 q^{40} +4.26888 q^{41} -24.0209 q^{42} +1.00000 q^{43} +0.895633 q^{44} -4.16824 q^{45} +10.5178 q^{46} -1.17938 q^{47} -14.5179 q^{48} +16.5328 q^{49} +7.51930 q^{50} +2.90991 q^{51} -1.03983 q^{52} +11.6707 q^{53} -12.2186 q^{54} -0.762355 q^{55} +9.11638 q^{56} +8.73840 q^{57} +0.772268 q^{58} -4.03069 q^{59} -1.98686 q^{60} -5.54122 q^{61} +11.1182 q^{62} +26.5236 q^{63} +1.92727 q^{64} +0.885095 q^{65} -4.95167 q^{66} +2.59019 q^{67} +0.895633 q^{68} -17.9860 q^{69} +6.29312 q^{70} +14.4353 q^{71} +10.2750 q^{72} +0.103162 q^{73} -1.98073 q^{74} -12.8584 q^{75} +2.68957 q^{76} +4.85107 q^{77} +5.74889 q^{78} -0.329877 q^{79} +3.80347 q^{80} +4.49170 q^{81} -7.26416 q^{82} +11.1939 q^{83} +12.6429 q^{84} -0.762355 q^{85} -1.70166 q^{86} -1.32061 q^{87} +1.87925 q^{88} -7.70401 q^{89} +7.09290 q^{90} -5.63209 q^{91} -5.53586 q^{92} -19.0127 q^{93} +2.00690 q^{94} -2.28933 q^{95} +13.7675 q^{96} +5.71368 q^{97} -28.1332 q^{98} +5.46758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.70166	−1.20325	−0.601626	−	0.798778i	$-0.705480\pi$
$2$	−1.70166	−1.20325	−0.601626	+	0.798778i	$0.705480\pi$
$3$	2.90991	1.68004	0.840019	−	0.542557i	$-0.182544\pi$
$3$	2.90991	1.68004	0.840019	+	0.542557i	$0.182544\pi$
$4$	0.895633	0.447817
$5$	−0.762355	−0.340935	−0.170468	−	0.985363i	$-0.554528\pi$
$5$	−0.762355	−0.340935	−0.170468	+	0.985363i	$0.554528\pi$
$6$	−4.95167	−2.02151
$7$	4.85107	1.83353	0.916765	−	0.399426i	$-0.130791\pi$
$7$	4.85107	1.83353	0.916765	+	0.399426i	$0.130791\pi$
$8$	1.87925	0.664416
$9$	5.46758	1.82253
$10$	1.29727	0.410231
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.60621	0.752349
$13$	−1.16100	−0.322004	−0.161002	−	0.986954i	$-0.551473\pi$
$13$	−1.16100	−0.322004	−0.161002	+	0.986954i	$0.551473\pi$
$14$	−8.25485	−2.20620
$15$	−2.21838	−0.572784
$16$	−4.98911	−1.24728
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−9.30394	−2.19296
$19$	3.00298	0.688931	0.344465	−	0.938799i	$-0.388060\pi$
$19$	3.00298	0.688931	0.344465	+	0.938799i	$0.388060\pi$
$20$	−0.682790	−0.152677
$21$	14.1162	3.08040
$22$	−1.70166	−0.362794
$23$	−6.18094	−1.28882	−0.644408	−	0.764682i	$-0.722896\pi$
$23$	−6.18094	−1.28882	−0.644408	+	0.764682i	$0.722896\pi$
$24$	5.46846	1.11624
$25$	−4.41882	−0.883763
$26$	1.97562	0.387452
$27$	7.18044	1.38188
$28$	4.34478	0.821086
$29$	−0.453833	−0.0842747	−0.0421373	−	0.999112i	$-0.513417\pi$
$29$	−0.453833	−0.0842747	−0.0421373	+	0.999112i	$0.513417\pi$
$30$	3.77493	0.689204
$31$	−6.53377	−1.17350	−0.586749	−	0.809769i	$-0.699593\pi$
$31$	−6.53377	−1.17350	−0.586749	+	0.809769i	$0.699593\pi$
$32$	4.73124	0.836373
$33$	2.90991	0.506550
$34$	−1.70166	−0.291832
$35$	−3.69823	−0.625115
$36$	4.89695	0.816158
$37$	1.16400	0.191361	0.0956804	−	0.995412i	$-0.469497\pi$
$37$	1.16400	0.191361	0.0956804	+	0.995412i	$0.469497\pi$
$38$	−5.11004	−0.828958
$39$	−3.37841	−0.540979
$40$	−1.43266	−0.226523
$41$	4.26888	0.666686	0.333343	−	0.942806i	$-0.391823\pi$
$41$	4.26888	0.666686	0.333343	+	0.942806i	$0.391823\pi$
$42$	−24.0209	−3.70650
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.895633	0.135022
$45$	−4.16824	−0.621364
$46$	10.5178	1.55077
$47$	−1.17938	−0.172031	−0.0860153	−	0.996294i	$-0.527413\pi$
$47$	−1.17938	−0.172031	−0.0860153	+	0.996294i	$0.527413\pi$
$48$	−14.5179	−2.09547
$49$	16.5328	2.36184
$50$	7.51930	1.06339
$51$	2.90991	0.407469
$52$	−1.03983	−0.144199
$53$	11.6707	1.60309	0.801547	−	0.597932i	$-0.204011\pi$
$53$	11.6707	1.60309	0.801547	+	0.597932i	$0.204011\pi$
$54$	−12.2186	−1.66275
$55$	−0.762355	−0.102796
$56$	9.11638	1.21823
$57$	8.73840	1.15743
$58$	0.772268	0.101404
$59$	−4.03069	−0.524752	−0.262376	−	0.964966i	$-0.584506\pi$
$59$	−4.03069	−0.524752	−0.262376	+	0.964966i	$0.584506\pi$
$60$	−1.98686	−0.256502
$61$	−5.54122	−0.709481	−0.354740	−	0.934965i	$-0.615431\pi$
$61$	−5.54122	−0.709481	−0.354740	+	0.934965i	$0.615431\pi$
$62$	11.1182	1.41202
$63$	26.5236	3.34166
$64$	1.92727	0.240909
$65$	0.885095	0.109782
$66$	−4.95167	−0.609508
$67$	2.59019	0.316442	0.158221	−	0.987404i	$-0.449424\pi$
$67$	2.59019	0.316442	0.158221	+	0.987404i	$0.449424\pi$
$68$	0.895633	0.108611
$69$	−17.9860	−2.16526
$70$	6.29312	0.752172
$71$	14.4353	1.71316	0.856579	−	0.516016i	$-0.172586\pi$
$71$	14.4353	1.71316	0.856579	+	0.516016i	$0.172586\pi$
$72$	10.2750	1.21092
$73$	0.103162	0.0120742	0.00603710	−	0.999982i	$-0.498078\pi$
$73$	0.103162	0.0120742	0.00603710	+	0.999982i	$0.498078\pi$
$74$	−1.98073	−0.230255
$75$	−12.8584	−1.48476
$76$	2.68957	0.308515
$77$	4.85107	0.552830
$78$	5.74889	0.650934
$79$	−0.329877	−0.0371141	−0.0185571	−	0.999828i	$-0.505907\pi$
$79$	−0.329877	−0.0371141	−0.0185571	+	0.999828i	$0.505907\pi$
$80$	3.80347	0.425241
$81$	4.49170	0.499077
$82$	−7.26416	−0.802192
$83$	11.1939	1.22869	0.614344	−	0.789039i	$-0.289421\pi$
$83$	11.1939	1.22869	0.614344	+	0.789039i	$0.289421\pi$
$84$	12.6429	1.37945
$85$	−0.762355	−0.0826890
$86$	−1.70166	−0.183494
$87$	−1.32061	−0.141585
$88$	1.87925	0.200329
$89$	−7.70401	−0.816624	−0.408312	−	0.912843i	$-0.633882\pi$
$89$	−7.70401	−0.816624	−0.408312	+	0.912843i	$0.633882\pi$
$90$	7.09290	0.747658
$91$	−5.63209	−0.590404
$92$	−5.53586	−0.577153
$93$	−19.0127	−1.97152
$94$	2.00690	0.206996
$95$	−2.28933	−0.234881
$96$	13.7675	1.40514
$97$	5.71368	0.580136	0.290068	−	0.957006i	$-0.406322\pi$
$97$	5.71368	0.580136	0.290068	+	0.957006i	$0.406322\pi$
$98$	−28.1332	−2.84188
$99$	5.46758	0.549513
$100$	−3.95764	−0.395764
$101$	13.6973	1.36294	0.681468	−	0.731848i	$-0.261342\pi$
$101$	13.6973	1.36294	0.681468	+	0.731848i	$0.261342\pi$
$102$	−4.95167	−0.490288
$103$	10.7993	1.06408	0.532042	−	0.846718i	$-0.321425\pi$
$103$	10.7993	1.06408	0.532042	+	0.846718i	$0.321425\pi$
$104$	−2.18181	−0.213945
$105$	−10.7615	−1.05022
$106$	−19.8595	−1.92893
$107$	12.2453	1.18379	0.591897	−	0.806014i	$-0.298379\pi$
$107$	12.2453	1.18379	0.591897	+	0.806014i	$0.298379\pi$
$108$	6.43104	0.618827
$109$	13.4994	1.29301	0.646504	−	0.762911i	$-0.276230\pi$
$109$	13.4994	1.29301	0.646504	+	0.762911i	$0.276230\pi$
$110$	1.29727	0.123689
$111$	3.38714	0.321494
$112$	−24.2025	−2.28692
$113$	11.6167	1.09281	0.546403	−	0.837522i	$-0.315997\pi$
$113$	11.6167	1.09281	0.546403	+	0.837522i	$0.315997\pi$
$114$	−14.8698	−1.39268
$115$	4.71207	0.439403
$116$	−0.406468	−0.0377396
$117$	−6.34787	−0.586861
$118$	6.85885	0.631409
$119$	4.85107	0.444697
$120$	−4.16890	−0.380567
$121$	1.00000	0.0909091
$122$	9.42925	0.853684
$123$	12.4220	1.12006
$124$	−5.85186	−0.525512
$125$	7.18048	0.642241
$126$	−45.1340	−4.02086
$127$	−13.9686	−1.23952	−0.619758	−	0.784793i	$-0.712769\pi$
$127$	−13.9686	−1.23952	−0.619758	+	0.784793i	$0.712769\pi$
$128$	−12.7420	−1.12625
$129$	2.90991	0.256203
$130$	−1.50613	−0.132096
$131$	−0.502347	−0.0438903	−0.0219451	−	0.999759i	$-0.506986\pi$
$131$	−0.502347	−0.0438903	−0.0219451	+	0.999759i	$0.506986\pi$
$132$	2.60621	0.226842
$133$	14.5677	1.26318
$134$	−4.40762	−0.380760
$135$	−5.47404	−0.471130
$136$	1.87925	0.161145
$137$	−6.56384	−0.560787	−0.280394	−	0.959885i	$-0.590465\pi$
$137$	−6.56384	−0.560787	−0.280394	+	0.959885i	$0.590465\pi$
$138$	30.6060	2.60535
$139$	17.4228	1.47778	0.738892	−	0.673823i	$-0.235349\pi$
$139$	17.4228	1.47778	0.738892	+	0.673823i	$0.235349\pi$
$140$	−3.31226	−0.279937
$141$	−3.43190	−0.289018
$142$	−24.5640	−2.06136
$143$	−1.16100	−0.0970878
$144$	−27.2783	−2.27320
$145$	0.345982	0.0287322
$146$	−0.175546	−0.0145283
$147$	48.1091	3.96797
$148$	1.04252	0.0856946
$149$	24.1066	1.97489	0.987446	−	0.157954i	$-0.0504899\pi$
$149$	24.1066	1.97489	0.987446	+	0.157954i	$0.0504899\pi$
$150$	21.8805	1.78654
$151$	16.6535	1.35524	0.677622	−	0.735411i	$-0.263011\pi$
$151$	16.6535	1.35524	0.677622	+	0.735411i	$0.263011\pi$
$152$	5.64336	0.457737
$153$	5.46758	0.442028
$154$	−8.25485	−0.665195
$155$	4.98105	0.400087
$156$	−3.02582	−0.242259
$157$	9.30870	0.742915	0.371458	−	0.928450i	$-0.378858\pi$
$157$	9.30870	0.742915	0.371458	+	0.928450i	$0.378858\pi$
$158$	0.561338	0.0446576
$159$	33.9607	2.69326
$160$	−3.60688	−0.285149
$161$	−29.9842	−2.36308
$162$	−7.64332	−0.600516
$163$	−7.60346	−0.595549	−0.297775	−	0.954636i	$-0.596244\pi$
$163$	−7.60346	−0.595549	−0.297775	+	0.954636i	$0.596244\pi$
$164$	3.82335	0.298553
$165$	−2.21838	−0.172701
$166$	−19.0481	−1.47842
$167$	13.1221	1.01542	0.507710	−	0.861528i	$-0.330492\pi$
$167$	13.1221	1.01542	0.507710	+	0.861528i	$0.330492\pi$
$168$	26.5278	2.04667
$169$	−11.6521	−0.896314
$170$	1.29727	0.0994957
$171$	16.4190	1.25559
$172$	0.895633	0.0682914
$173$	12.7566	0.969865	0.484933	−	0.874551i	$-0.338844\pi$
$173$	12.7566	0.969865	0.484933	+	0.874551i	$0.338844\pi$
$174$	2.24723	0.170362
$175$	−21.4360	−1.62041
$176$	−4.98911	−0.376068
$177$	−11.7290	−0.881602
$178$	13.1096	0.982605
$179$	17.6730	1.32094	0.660470	−	0.750853i	$-0.270357\pi$
$179$	17.6730	1.32094	0.660470	+	0.750853i	$0.270357\pi$
$180$	−3.73321	−0.278257
$181$	−2.86258	−0.212774	−0.106387	−	0.994325i	$-0.533928\pi$
$181$	−2.86258	−0.212774	−0.106387	+	0.994325i	$0.533928\pi$
$182$	9.58389	0.710405
$183$	−16.1245	−1.19195
$184$	−11.6155	−0.856310
$185$	−0.887383	−0.0652417
$186$	32.3530	2.37224
$187$	1.00000	0.0731272
$188$	−1.05629	−0.0770382
$189$	34.8328	2.53371
$190$	3.89566	0.282621
$191$	−26.5347	−1.91998	−0.959992	−	0.280026i	$-0.909657\pi$
$191$	−26.5347	−1.91998	−0.959992	+	0.280026i	$0.909657\pi$
$192$	5.60819	0.404736
$193$	−24.5924	−1.77020	−0.885101	−	0.465400i	$-0.845911\pi$
$193$	−24.5924	−1.77020	−0.885101	+	0.465400i	$0.845911\pi$
$194$	−9.72272	−0.698050
$195$	2.57555	0.184439
$196$	14.8074	1.05767
$197$	−13.9348	−0.992813	−0.496407	−	0.868090i	$-0.665348\pi$
$197$	−13.9348	−0.992813	−0.496407	+	0.868090i	$0.665348\pi$
$198$	−9.30394	−0.661202
$199$	−15.5954	−1.10553	−0.552765	−	0.833337i	$-0.686427\pi$
$199$	−15.5954	−1.10553	−0.552765	+	0.833337i	$0.686427\pi$
$200$	−8.30407	−0.587186
$201$	7.53723	0.531635
$202$	−23.3082	−1.63996
$203$	−2.20157	−0.154520
$204$	2.60621	0.182471
$205$	−3.25440	−0.227297
$206$	−18.3766	−1.28036
$207$	−33.7948	−2.34890
$208$	5.79236	0.401628
$209$	3.00298	0.207720
$210$	18.3124	1.26368
$211$	18.7580	1.29135	0.645676	−	0.763611i	$-0.276575\pi$
$211$	18.7580	1.29135	0.645676	+	0.763611i	$0.276575\pi$
$212$	10.4527	0.717892
$213$	42.0055	2.87817
$214$	−20.8372	−1.42440
$215$	−0.762355	−0.0519922
$216$	13.4939	0.918141
$217$	−31.6957	−2.15165
$218$	−22.9713	−1.55582
$219$	0.300192	0.0202851
$220$	−0.682790	−0.0460337
$221$	−1.16100	−0.0780974
$222$	−5.76375	−0.386838
$223$	0.892655	0.0597766	0.0298883	−	0.999553i	$-0.490485\pi$
$223$	0.892655	0.0597766	0.0298883	+	0.999553i	$0.490485\pi$
$224$	22.9516	1.53352
$225$	−24.1602	−1.61068
$226$	−19.7676	−1.31492
$227$	−5.77038	−0.382994	−0.191497	−	0.981493i	$-0.561334\pi$
$227$	−5.77038	−0.382994	−0.191497	+	0.981493i	$0.561334\pi$
$228$	7.82640	0.518316
$229$	5.49590	0.363179	0.181590	−	0.983374i	$-0.441876\pi$
$229$	5.49590	0.363179	0.181590	+	0.983374i	$0.441876\pi$
$230$	−8.01832	−0.528712
$231$	14.1162	0.928776
$232$	−0.852867	−0.0559934
$233$	7.60808	0.498422	0.249211	−	0.968449i	$-0.419829\pi$
$233$	7.60808	0.498422	0.249211	+	0.968449i	$0.419829\pi$
$234$	10.8019	0.706142
$235$	0.899107	0.0586513
$236$	−3.61002	−0.234992
$237$	−0.959914	−0.0623531
$238$	−8.25485	−0.535082
$239$	13.7662	0.890461	0.445230	−	0.895416i	$-0.353122\pi$
$239$	13.7662	0.890461	0.445230	+	0.895416i	$0.353122\pi$
$240$	11.0678	0.714421
$241$	−29.4154	−1.89481	−0.947406	−	0.320036i	$-0.896305\pi$
$241$	−29.4154	−1.89481	−0.947406	+	0.320036i	$0.896305\pi$
$242$	−1.70166	−0.109387
$243$	−8.47088	−0.543407
$244$	−4.96290	−0.317717
$245$	−12.6039	−0.805233
$246$	−21.1381	−1.34771
$247$	−3.48646	−0.221838
$248$	−12.2786	−0.779691
$249$	32.5732	2.06424
$250$	−12.2187	−0.772779
$251$	−1.42081	−0.0896810	−0.0448405	−	0.998994i	$-0.514278\pi$
$251$	−1.42081	−0.0896810	−0.0448405	+	0.998994i	$0.514278\pi$
$252$	23.7554	1.49645
$253$	−6.18094	−0.388593
$254$	23.7698	1.49145
$255$	−2.21838	−0.138921
$256$	17.8280	1.11425
$257$	5.39743	0.336682	0.168341	−	0.985729i	$-0.446159\pi$
$257$	5.39743	0.336682	0.168341	+	0.985729i	$0.446159\pi$
$258$	−4.95167	−0.308277
$259$	5.64666	0.350866
$260$	0.792720	0.0491624
$261$	−2.48137	−0.153593
$262$	0.854823	0.0528111
$263$	−16.1186	−0.993913	−0.496956	−	0.867776i	$-0.665549\pi$
$263$	−16.1186	−0.993913	−0.496956	+	0.867776i	$0.665549\pi$
$264$	5.46846	0.336560
$265$	−8.89721	−0.546551
$266$	−24.7891	−1.51992
$267$	−22.4180	−1.37196
$268$	2.31986	0.141708
$269$	27.5344	1.67880	0.839400	−	0.543514i	$-0.182907\pi$
$269$	27.5344	1.67880	0.839400	+	0.543514i	$0.182907\pi$
$270$	9.31494	0.566889
$271$	13.0403	0.792144	0.396072	−	0.918219i	$-0.370373\pi$
$271$	13.0403	0.792144	0.396072	+	0.918219i	$0.370373\pi$
$272$	−4.98911	−0.302509
$273$	−16.3889	−0.991901
$274$	11.1694	0.674768
$275$	−4.41882	−0.266465
$276$	−16.1089	−0.969639
$277$	−6.60009	−0.396561	−0.198281	−	0.980145i	$-0.563536\pi$
$277$	−6.60009	−0.396561	−0.198281	+	0.980145i	$0.563536\pi$
$278$	−29.6477	−1.77815
$279$	−35.7239	−2.13873
$280$	−6.94991	−0.415337
$281$	−27.0009	−1.61074	−0.805369	−	0.592774i	$-0.798033\pi$
$281$	−27.0009	−1.61074	−0.805369	+	0.592774i	$0.798033\pi$
$282$	5.83991	0.347761
$283$	−14.9926	−0.891218	−0.445609	−	0.895228i	$-0.647013\pi$
$283$	−14.9926	−0.891218	−0.445609	+	0.895228i	$0.647013\pi$
$284$	12.9288	0.767180
$285$	−6.66176	−0.394609
$286$	1.97562	0.116821
$287$	20.7086	1.22239
$288$	25.8684	1.52431
$289$	1.00000	0.0588235
$290$	−0.588742	−0.0345721
$291$	16.6263	0.974651
$292$	0.0923954	0.00540703
$293$	−32.5125	−1.89940	−0.949700	−	0.313162i	$-0.898612\pi$
$293$	−32.5125	−1.89940	−0.949700	+	0.313162i	$0.898612\pi$
$294$	−81.8652	−4.77447
$295$	3.07282	0.178906
$296$	2.18745	0.127143
$297$	7.18044	0.416651
$298$	−41.0212	−2.37629
$299$	7.17608	0.415004
$300$	−11.5164	−0.664898
$301$	4.85107	0.279611
$302$	−28.3385	−1.63070
$303$	39.8580	2.28978
$304$	−14.9822	−0.859287
$305$	4.22438	0.241887
$306$	−9.30394	−0.531871
$307$	−1.88110	−0.107360	−0.0536800	−	0.998558i	$-0.517095\pi$
$307$	−1.88110	−0.107360	−0.0536800	+	0.998558i	$0.517095\pi$
$308$	4.34478	0.247567
$309$	31.4249	1.78770
$310$	−8.47603	−0.481406
$311$	22.3152	1.26538	0.632689	−	0.774406i	$-0.281951\pi$
$311$	22.3152	1.26538	0.632689	+	0.774406i	$0.281951\pi$
$312$	−6.34889	−0.359435
$313$	−0.459320	−0.0259623	−0.0129811	−	0.999916i	$-0.504132\pi$
$313$	−0.459320	−0.0259623	−0.0129811	+	0.999916i	$0.504132\pi$
$314$	−15.8402	−0.893914
$315$	−20.2204	−1.13929
$316$	−0.295449	−0.0166203
$317$	−9.73978	−0.547041	−0.273520	−	0.961866i	$-0.588188\pi$
$317$	−9.73978	−0.547041	−0.273520	+	0.961866i	$0.588188\pi$
$318$	−57.7894	−3.24067
$319$	−0.453833	−0.0254098
$320$	−1.46926	−0.0821344
$321$	35.6326	1.98882
$322$	51.0227	2.84339
$323$	3.00298	0.167090
$324$	4.02291	0.223495
$325$	5.13025	0.284575
$326$	12.9385	0.716596
$327$	39.2820	2.17230
$328$	8.02230	0.442957
$329$	−5.72126	−0.315423
$330$	3.77493	0.207803
$331$	4.13443	0.227249	0.113624	−	0.993524i	$-0.463754\pi$
$331$	4.13443	0.227249	0.113624	+	0.993524i	$0.463754\pi$
$332$	10.0256	0.550227
$333$	6.36428	0.348760
$334$	−22.3293	−1.22181
$335$	−1.97465	−0.107886
$336$	−70.4271	−3.84211
$337$	−34.2926	−1.86804	−0.934019	−	0.357223i	$-0.883724\pi$
$337$	−34.2926	−1.86804	−0.934019	+	0.357223i	$0.883724\pi$
$338$	19.8278	1.07849
$339$	33.8035	1.83596
$340$	−0.682790	−0.0370295
$341$	−6.53377	−0.353823
$342$	−27.9395	−1.51080
$343$	46.2445	2.49697
$344$	1.87925	0.101322
$345$	13.7117	0.738213
$346$	−21.7073	−1.16699
$347$	−25.6726	−1.37818	−0.689088	−	0.724678i	$-0.741989\pi$
$347$	−25.6726	−1.37818	−0.689088	+	0.724678i	$0.741989\pi$
$348$	−1.18279	−0.0634040
$349$	−17.0157	−0.910829	−0.455414	−	0.890280i	$-0.650509\pi$
$349$	−17.0157	−0.910829	−0.455414	+	0.890280i	$0.650509\pi$
$350$	36.4766	1.94976
$351$	−8.33650	−0.444969
$352$	4.73124	0.252176
$353$	19.4200	1.03362	0.516811	−	0.856100i	$-0.327119\pi$
$353$	19.4200	1.03362	0.516811	+	0.856100i	$0.327119\pi$
$354$	19.9587	1.06079
$355$	−11.0048	−0.584076
$356$	−6.89997	−0.365698
$357$	14.1162	0.747107
$358$	−30.0733	−1.58942
$359$	16.2396	0.857094	0.428547	−	0.903520i	$-0.359026\pi$
$359$	16.2396	0.857094	0.428547	+	0.903520i	$0.359026\pi$
$360$	−7.83317	−0.412844
$361$	−9.98212	−0.525375
$362$	4.87112	0.256021
$363$	2.90991	0.152731
$364$	−5.04429	−0.264393
$365$	−0.0786461	−0.00411652
$366$	27.4383	1.43422
$367$	−4.61048	−0.240665	−0.120333	−	0.992734i	$-0.538396\pi$
$367$	−4.61048	−0.240665	−0.120333	+	0.992734i	$0.538396\pi$
$368$	30.8374	1.60751
$369$	23.3404	1.21505
$370$	1.51002	0.0785022
$371$	56.6153	2.93932
$372$	−17.0284	−0.882881
$373$	6.26221	0.324245	0.162122	−	0.986771i	$-0.448166\pi$
$373$	6.26221	0.324245	0.162122	+	0.986771i	$0.448166\pi$
$374$	−1.70166	−0.0879905
$375$	20.8945	1.07899
$376$	−2.21636	−0.114300
$377$	0.526901	0.0271368
$378$	−59.2734	−3.04870
$379$	−0.362889	−0.0186404	−0.00932018	−	0.999957i	$-0.502967\pi$
$379$	−0.362889	−0.0186404	−0.00932018	+	0.999957i	$0.502967\pi$
$380$	−2.05040	−0.105184
$381$	−40.6475	−2.08243
$382$	45.1530	2.31023
$383$	27.6383	1.41225	0.706126	−	0.708086i	$-0.250441\pi$
$383$	27.6383	1.41225	0.706126	+	0.708086i	$0.250441\pi$
$384$	−37.0782	−1.89214
$385$	−3.69823	−0.188479
$386$	41.8478	2.13000
$387$	5.46758	0.277933
$388$	5.11736	0.259795
$389$	15.2017	0.770759	0.385380	−	0.922758i	$-0.374071\pi$
$389$	15.2017	0.770759	0.385380	+	0.922758i	$0.374071\pi$
$390$	−4.38269	−0.221926
$391$	−6.18094	−0.312584
$392$	31.0694	1.56924
$393$	−1.46179	−0.0737374
$394$	23.7122	1.19461
$395$	0.251484	0.0126535
$396$	4.89695	0.246081
$397$	24.1442	1.21176	0.605881	−	0.795555i	$-0.292821\pi$
$397$	24.1442	1.21176	0.605881	+	0.795555i	$0.292821\pi$
$398$	26.5380	1.33023
$399$	42.3906	2.12218
$400$	22.0459	1.10230
$401$	−22.3239	−1.11480	−0.557401	−	0.830244i	$-0.688201\pi$
$401$	−22.3239	−1.11480	−0.557401	+	0.830244i	$0.688201\pi$
$402$	−12.8258	−0.639691
$403$	7.58571	0.377871
$404$	12.2678	0.610345
$405$	−3.42427	−0.170153
$406$	3.74632	0.185927
$407$	1.16400	0.0576975
$408$	5.46846	0.270729
$409$	−31.0517	−1.53541	−0.767703	−	0.640806i	$-0.778600\pi$
$409$	−31.0517	−1.53541	−0.767703	+	0.640806i	$0.778600\pi$
$410$	5.53786	0.273496
$411$	−19.1002	−0.942143
$412$	9.67218	0.476514
$413$	−19.5532	−0.962148
$414$	57.5071	2.82632
$415$	−8.53370	−0.418903
$416$	−5.49298	−0.269315
$417$	50.6989	2.48273
$418$	−5.11004	−0.249940
$419$	11.1652	0.545455	0.272727	−	0.962091i	$-0.412074\pi$
$419$	11.1652	0.545455	0.272727	+	0.962091i	$0.412074\pi$
$420$	−9.63838	−0.470305
$421$	12.1029	0.589860	0.294930	−	0.955519i	$-0.404704\pi$
$421$	12.1029	0.589860	0.294930	+	0.955519i	$0.404704\pi$
$422$	−31.9196	−1.55382
$423$	−6.44837	−0.313530
$424$	21.9322	1.06512
$425$	−4.41882	−0.214344
$426$	−71.4789	−3.46316
$427$	−26.8808	−1.30085
$428$	10.9673	0.530123
$429$	−3.37841	−0.163111
$430$	1.29727	0.0625597
$431$	−17.9494	−0.864592	−0.432296	−	0.901732i	$-0.642296\pi$
$431$	−17.9494	−0.864592	−0.432296	+	0.901732i	$0.642296\pi$
$432$	−35.8240	−1.72358
$433$	15.5663	0.748069	0.374035	−	0.927415i	$-0.377974\pi$
$433$	15.5663	0.748069	0.374035	+	0.927415i	$0.377974\pi$
$434$	53.9352	2.58897
$435$	1.00678	0.0482712
$436$	12.0905	0.579030
$437$	−18.5612	−0.887905
$438$	−0.510824	−0.0244081
$439$	−27.8099	−1.32729	−0.663646	−	0.748047i	$-0.730992\pi$
$439$	−27.8099	−1.32729	−0.663646	+	0.748047i	$0.730992\pi$
$440$	−1.43266	−0.0682992
$441$	90.3947	4.30451
$442$	1.97562	0.0939709
$443$	−0.274111	−0.0130234	−0.00651170	−	0.999979i	$-0.502073\pi$
$443$	−0.274111	−0.0130234	−0.00651170	+	0.999979i	$0.502073\pi$
$444$	3.03364	0.143970
$445$	5.87319	0.278416
$446$	−1.51899	−0.0719264
$447$	70.1482	3.31789
$448$	9.34932	0.441714
$449$	25.3890	1.19818	0.599092	−	0.800680i	$-0.295529\pi$
$449$	25.3890	1.19818	0.599092	+	0.800680i	$0.295529\pi$
$450$	41.1124	1.93806
$451$	4.26888	0.201014
$452$	10.4043	0.489377
$453$	48.4602	2.27686
$454$	9.81921	0.460838
$455$	4.29365	0.201290
$456$	16.4217	0.769015
$457$	−36.6655	−1.71514	−0.857571	−	0.514366i	$-0.828027\pi$
$457$	−36.6655	−1.71514	−0.857571	+	0.514366i	$0.828027\pi$
$458$	−9.35213	−0.436996
$459$	7.18044	0.335154
$460$	4.22029	0.196772
$461$	−11.4090	−0.531371	−0.265685	−	0.964060i	$-0.585598\pi$
$461$	−11.4090	−0.531371	−0.265685	+	0.964060i	$0.585598\pi$
$462$	−24.0209	−1.11755
$463$	19.2671	0.895418	0.447709	−	0.894179i	$-0.352240\pi$
$463$	19.2671	0.895418	0.447709	+	0.894179i	$0.352240\pi$
$464$	2.26422	0.105114
$465$	14.4944	0.672162
$466$	−12.9463	−0.599728
$467$	−18.7069	−0.865654	−0.432827	−	0.901477i	$-0.642484\pi$
$467$	−18.7069	−0.865654	−0.432827	+	0.901477i	$0.642484\pi$
$468$	−5.68536	−0.262806
$469$	12.5652	0.580207
$470$	−1.52997	−0.0705723
$471$	27.0875	1.24813
$472$	−7.57469	−0.348653
$473$	1.00000	0.0459800
$474$	1.63344	0.0750265
$475$	−13.2696	−0.608851
$476$	4.34478	0.199143
$477$	63.8105	2.92168
$478$	−23.4253	−1.07145
$479$	−40.4258	−1.84710	−0.923550	−	0.383478i	$-0.874726\pi$
$479$	−40.4258	−1.84710	−0.923550	+	0.383478i	$0.874726\pi$
$480$	−10.4957	−0.479061
$481$	−1.35141	−0.0616189
$482$	50.0549	2.27994
$483$	−87.2512	−3.97007
$484$	0.895633	0.0407106
$485$	−4.35585	−0.197789
$486$	14.4145	0.653856
$487$	18.8515	0.854242	0.427121	−	0.904194i	$-0.359528\pi$
$487$	18.8515	0.854242	0.427121	+	0.904194i	$0.359528\pi$
$488$	−10.4134	−0.471390
$489$	−22.1254	−1.00055
$490$	21.4475	0.968899
$491$	−10.0230	−0.452331	−0.226166	−	0.974089i	$-0.572619\pi$
$491$	−10.0230	−0.452331	−0.226166	+	0.974089i	$0.572619\pi$
$492$	11.1256	0.501581
$493$	−0.453833	−0.0204396
$494$	5.93276	0.266928
$495$	−4.16824	−0.187348
$496$	32.5977	1.46368
$497$	70.0267	3.14113
$498$	−55.4283	−2.48380
$499$	−13.9057	−0.622504	−0.311252	−	0.950327i	$-0.600748\pi$
$499$	−13.9057	−0.622504	−0.311252	+	0.950327i	$0.600748\pi$
$500$	6.43107	0.287606
$501$	38.1842	1.70594
$502$	2.41774	0.107909
$503$	10.9632	0.488824	0.244412	−	0.969671i	$-0.421405\pi$
$503$	10.9632	0.488824	0.244412	+	0.969671i	$0.421405\pi$
$504$	49.8445	2.22025
$505$	−10.4422	−0.464673
$506$	10.5178	0.467575
$507$	−33.9065	−1.50584
$508$	−12.5108	−0.555076
$509$	−34.2212	−1.51683	−0.758414	−	0.651773i	$-0.774025\pi$
$509$	−34.2212	−1.51683	−0.758414	+	0.651773i	$0.774025\pi$
$510$	3.77493	0.167157
$511$	0.500446	0.0221384
$512$	−4.85308	−0.214478
$513$	21.5627	0.952017
$514$	−9.18457	−0.405114
$515$	−8.23287	−0.362784
$516$	2.60621	0.114732
$517$	−1.17938	−0.0518692
$518$	−9.60866	−0.422180
$519$	37.1205	1.62941
$520$	1.66332	0.0729412
$521$	−6.92194	−0.303256	−0.151628	−	0.988438i	$-0.548452\pi$
$521$	−6.92194	−0.303256	−0.151628	+	0.988438i	$0.548452\pi$
$522$	4.22244	0.184811
$523$	−4.78597	−0.209276	−0.104638	−	0.994510i	$-0.533368\pi$
$523$	−4.78597	−0.209276	−0.104638	+	0.994510i	$0.533368\pi$
$524$	−0.449919	−0.0196548
$525$	−62.3768	−2.72234
$526$	27.4282	1.19593
$527$	−6.53377	−0.284615
$528$	−14.5179	−0.631809
$529$	15.2040	0.661045
$530$	15.1400	0.657639
$531$	−22.0381	−0.956374
$532$	13.0473	0.565671
$533$	−4.95617	−0.214676
$534$	38.1477	1.65081
$535$	−9.33523	−0.403597
$536$	4.86763	0.210249
$537$	51.4267	2.21923
$538$	−46.8540	−2.02002
$539$	16.5328	0.712120
$540$	−4.90273	−0.210980
$541$	−2.35057	−0.101059	−0.0505295	−	0.998723i	$-0.516091\pi$
$541$	−2.35057	−0.101059	−0.0505295	+	0.998723i	$0.516091\pi$
$542$	−22.1902	−0.953149
$543$	−8.32985	−0.357468
$544$	4.73124	0.202850
$545$	−10.2913	−0.440832
$546$	27.8883	1.19351
$547$	−28.9499	−1.23781	−0.618904	−	0.785466i	$-0.712423\pi$
$547$	−28.9499	−1.23781	−0.618904	+	0.785466i	$0.712423\pi$
$548$	−5.87880	−0.251130
$549$	−30.2971	−1.29305
$550$	7.51930	0.320624
$551$	−1.36285	−0.0580594
$552$	−33.8002	−1.43863
$553$	−1.60026	−0.0680499
$554$	11.2311	0.477163
$555$	−2.58220	−0.109608
$556$	15.6045	0.661777
$557$	24.8573	1.05324	0.526620	−	0.850101i	$-0.323459\pi$
$557$	24.8573	1.05324	0.526620	+	0.850101i	$0.323459\pi$
$558$	60.7898	2.57344
$559$	−1.16100	−0.0491051
$560$	18.4509	0.779692
$561$	2.90991	0.122857
$562$	45.9462	1.93812
$563$	41.9189	1.76667	0.883336	−	0.468740i	$-0.155292\pi$
$563$	41.9189	1.76667	0.883336	+	0.468740i	$0.155292\pi$
$564$	−3.07372	−0.129427
$565$	−8.85604	−0.372576
$566$	25.5123	1.07236
$567$	21.7895	0.915074
$568$	27.1276	1.13825
$569$	−6.29638	−0.263958	−0.131979	−	0.991253i	$-0.542133\pi$
$569$	−6.29638	−0.263958	−0.131979	+	0.991253i	$0.542133\pi$
$570$	11.3360	0.474814
$571$	16.1733	0.676831	0.338415	−	0.940997i	$-0.390109\pi$
$571$	16.1733	0.676831	0.338415	+	0.940997i	$0.390109\pi$
$572$	−1.03983	−0.0434775
$573$	−77.2137	−3.22565
$574$	−35.2389	−1.47084
$575$	27.3124	1.13901
$576$	10.5375	0.439063
$577$	17.0022	0.707812	0.353906	−	0.935281i	$-0.384853\pi$
$577$	17.0022	0.707812	0.353906	+	0.935281i	$0.384853\pi$
$578$	−1.70166	−0.0707796
$579$	−71.5617	−2.97400
$580$	0.309873	0.0128668
$581$	54.3022	2.25284
$582$	−28.2922	−1.17275
$583$	11.6707	0.483351
$584$	0.193868	0.00802229
$585$	4.83933	0.200082
$586$	55.3251	2.28546
$587$	−29.1572	−1.20344	−0.601722	−	0.798705i	$-0.705519\pi$
$587$	−29.1572	−1.20344	−0.601722	+	0.798705i	$0.705519\pi$
$588$	43.0881	1.77692
$589$	−19.6208	−0.808459
$590$	−5.22888	−0.215270
$591$	−40.5490	−1.66796
$592$	−5.80734	−0.238680
$593$	−17.6820	−0.726112	−0.363056	−	0.931767i	$-0.618267\pi$
$593$	−17.6820	−0.726112	−0.363056	+	0.931767i	$0.618267\pi$
$594$	−12.2186	−0.501337
$595$	−3.69823	−0.151613
$596$	21.5907	0.884390
$597$	−45.3813	−1.85733
$598$	−12.2112	−0.499354
$599$	−34.0242	−1.39019	−0.695096	−	0.718917i	$-0.744638\pi$
$599$	−34.0242	−1.39019	−0.695096	+	0.718917i	$0.744638\pi$
$600$	−24.1641	−0.986495
$601$	29.1288	1.18819	0.594094	−	0.804396i	$-0.297511\pi$
$601$	29.1288	1.18819	0.594094	+	0.804396i	$0.297511\pi$
$602$	−8.25485	−0.336442
$603$	14.1621	0.576725
$604$	14.9154	0.606900
$605$	−0.762355	−0.0309941
$606$	−67.8247	−2.75519
$607$	−29.2933	−1.18898	−0.594489	−	0.804104i	$-0.702646\pi$
$607$	−29.2933	−1.18898	−0.594489	+	0.804104i	$0.702646\pi$
$608$	14.2078	0.576203
$609$	−6.40638	−0.259600
$610$	−7.18843	−0.291051
$611$	1.36926	0.0553945
$612$	4.89695	0.197947
$613$	13.9395	0.563012	0.281506	−	0.959560i	$-0.409166\pi$
$613$	13.9395	0.563012	0.281506	+	0.959560i	$0.409166\pi$
$614$	3.20099	0.129181
$615$	−9.47001	−0.381867
$616$	9.11638	0.367309
$617$	0.573538	0.0230898	0.0115449	−	0.999933i	$-0.496325\pi$
$617$	0.573538	0.0230898	0.0115449	+	0.999933i	$0.496325\pi$
$618$	−53.4744	−2.15105
$619$	−47.6883	−1.91676	−0.958378	−	0.285503i	$-0.907839\pi$
$619$	−47.6883	−1.91676	−0.958378	+	0.285503i	$0.907839\pi$
$620$	4.46119	0.179166
$621$	−44.3819	−1.78098
$622$	−37.9728	−1.52257
$623$	−37.3727	−1.49730
$624$	16.8553	0.674750
$625$	16.6200	0.664800
$626$	0.781604	0.0312392
$627$	8.73840	0.348978
$628$	8.33718	0.332690
$629$	1.16400	0.0464118
$630$	34.4081	1.37085
$631$	−16.1955	−0.644731	−0.322366	−	0.946615i	$-0.604478\pi$
$631$	−16.1955	−0.644731	−0.322366	+	0.946615i	$0.604478\pi$
$632$	−0.619923	−0.0246592
$633$	54.5841	2.16952
$634$	16.5738	0.658228
$635$	10.6491	0.422595
$636$	30.4163	1.20609
$637$	−19.1947	−0.760520
$638$	0.772268	0.0305744
$639$	78.9263	3.12228
$640$	9.71395	0.383978
$641$	−30.1235	−1.18981	−0.594904	−	0.803797i	$-0.702810\pi$
$641$	−30.1235	−1.18981	−0.594904	+	0.803797i	$0.702810\pi$
$642$	−60.6345	−2.39305
$643$	−26.6063	−1.04925	−0.524626	−	0.851333i	$-0.675795\pi$
$643$	−26.6063	−1.04925	−0.524626	+	0.851333i	$0.675795\pi$
$644$	−26.8548	−1.05823
$645$	−2.21838	−0.0873488
$646$	−5.11004	−0.201052
$647$	−7.53738	−0.296325	−0.148163	−	0.988963i	$-0.547336\pi$
$647$	−7.53738	−0.296325	−0.148163	+	0.988963i	$0.547336\pi$
$648$	8.44103	0.331595
$649$	−4.03069	−0.158219
$650$	−8.72992	−0.342416
$651$	−92.2317	−3.61485
$652$	−6.80992	−0.266697
$653$	47.4065	1.85516	0.927579	−	0.373627i	$-0.121886\pi$
$653$	47.4065	1.85516	0.927579	+	0.373627i	$0.121886\pi$
$654$	−66.8445	−2.61383
$655$	0.382967	0.0149638
$656$	−21.2979	−0.831543
$657$	0.564047	0.0220056
$658$	9.73562	0.379534
$659$	−30.9022	−1.20378	−0.601889	−	0.798580i	$-0.705585\pi$
$659$	−30.9022	−1.20378	−0.601889	+	0.798580i	$0.705585\pi$
$660$	−1.98686	−0.0773384
$661$	−4.57688	−0.178020	−0.0890100	−	0.996031i	$-0.528370\pi$
$661$	−4.57688	−0.178020	−0.0890100	+	0.996031i	$0.528370\pi$
$662$	−7.03538	−0.273438
$663$	−3.37841	−0.131207
$664$	21.0361	0.816359
$665$	−11.1057	−0.430661
$666$	−10.8298	−0.419647
$667$	2.80512	0.108615
$668$	11.7526	0.454722
$669$	2.59755	0.100427
$670$	3.36017	0.129815
$671$	−5.54122	−0.213916
$672$	66.7870	2.57636
$673$	−16.9192	−0.652186	−0.326093	−	0.945338i	$-0.605732\pi$
$673$	−16.9192	−0.652186	−0.326093	+	0.945338i	$0.605732\pi$
$674$	58.3543	2.24772
$675$	−31.7290	−1.22125
$676$	−10.4360	−0.401384
$677$	−0.491343	−0.0188838	−0.00944191	−	0.999955i	$-0.503005\pi$
$677$	−0.491343	−0.0188838	−0.00944191	+	0.999955i	$0.503005\pi$
$678$	−57.5220	−2.20912
$679$	27.7174	1.06370
$680$	−1.43266	−0.0549399
$681$	−16.7913	−0.643444
$682$	11.1182	0.425739
$683$	−34.0326	−1.30222	−0.651111	−	0.758982i	$-0.725697\pi$
$683$	−34.0326	−1.30222	−0.651111	+	0.758982i	$0.725697\pi$
$684$	14.7054	0.562276
$685$	5.00398	0.191192
$686$	−78.6922	−3.00448
$687$	15.9926	0.610155
$688$	−4.98911	−0.190208
$689$	−13.5497	−0.516202
$690$	−23.3326	−0.888257
$691$	20.4091	0.776397	0.388199	−	0.921576i	$-0.373097\pi$
$691$	20.4091	0.776397	0.388199	+	0.921576i	$0.373097\pi$
$692$	11.4252	0.434322
$693$	26.5236	1.00755
$694$	43.6859	1.65829
$695$	−13.2824	−0.503829
$696$	−2.48177	−0.0940711
$697$	4.26888	0.161695
$698$	28.9549	1.09596
$699$	22.1388	0.837368
$700$	−19.1988	−0.725645
$701$	39.9271	1.50803	0.754013	−	0.656859i	$-0.228115\pi$
$701$	39.9271	1.50803	0.754013	+	0.656859i	$0.228115\pi$
$702$	14.1859	0.535411
$703$	3.49548	0.131834
$704$	1.92727	0.0726368
$705$	2.61632	0.0985364
$706$	−33.0461	−1.24371
$707$	66.4467	2.49899
$708$	−10.5048	−0.394796
$709$	−36.9640	−1.38821	−0.694106	−	0.719873i	$-0.744200\pi$
$709$	−36.9640	−1.38821	−0.694106	+	0.719873i	$0.744200\pi$
$710$	18.7264	0.702791
$711$	−1.80363	−0.0676415
$712$	−14.4778	−0.542578
$713$	40.3848	1.51242
$714$	−24.0209	−0.898958
$715$	0.885095	0.0331007
$716$	15.8285	0.591539
$717$	40.0584	1.49601
$718$	−27.6342	−1.03130
$719$	−43.0630	−1.60598	−0.802989	−	0.595994i	$-0.796758\pi$
$719$	−43.0630	−1.60598	−0.802989	+	0.595994i	$0.796758\pi$
$720$	20.7958	0.775013
$721$	52.3880	1.95103
$722$	16.9861	0.632158
$723$	−85.5961	−3.18335
$724$	−2.56382	−0.0952836
$725$	2.00540	0.0744788
$726$	−4.95167	−0.183774
$727$	43.0776	1.59766	0.798829	−	0.601558i	$-0.205453\pi$
$727$	43.0776	1.59766	0.798829	+	0.601558i	$0.205453\pi$
$728$	−10.5841	−0.392274
$729$	−38.1246	−1.41202
$730$	0.133829	0.00495322
$731$	1.00000	0.0369863
$732$	−14.4416	−0.533777
$733$	−35.5631	−1.31355	−0.656777	−	0.754085i	$-0.728081\pi$
$733$	−35.5631	−1.31355	−0.656777	+	0.754085i	$0.728081\pi$
$734$	7.84545	0.289581
$735$	−36.6762	−1.35282
$736$	−29.2435	−1.07793
$737$	2.59019	0.0954110
$738$	−39.7174	−1.46202
$739$	3.01489	0.110904	0.0554522	−	0.998461i	$-0.482340\pi$
$739$	3.01489	0.110904	0.0554522	+	0.998461i	$0.482340\pi$
$740$	−0.794770	−0.0292163
$741$	−10.1453	−0.372697
$742$	−96.3398	−3.53675
$743$	38.3071	1.40535	0.702675	−	0.711511i	$-0.251989\pi$
$743$	38.3071	1.40535	0.702675	+	0.711511i	$0.251989\pi$
$744$	−35.7296	−1.30991
$745$	−18.3778	−0.673311
$746$	−10.6561	−0.390148
$747$	61.2034	2.23932
$748$	0.895633	0.0327476
$749$	59.4026	2.17052
$750$	−35.5553	−1.29830
$751$	−22.5715	−0.823644	−0.411822	−	0.911264i	$-0.635107\pi$
$751$	−22.5715	−0.823644	−0.411822	+	0.911264i	$0.635107\pi$
$752$	5.88407	0.214570
$753$	−4.13444	−0.150667
$754$	−0.896604	−0.0326524
$755$	−12.6959	−0.462050
$756$	31.1974	1.13464
$757$	36.0553	1.31045	0.655226	−	0.755433i	$-0.272573\pi$
$757$	36.0553	1.31045	0.655226	+	0.755433i	$0.272573\pi$
$758$	0.617512	0.0224291
$759$	−17.9860	−0.652850
$760$	−4.30224	−0.156059
$761$	4.40959	0.159848	0.0799238	−	0.996801i	$-0.474532\pi$
$761$	4.40959	0.159848	0.0799238	+	0.996801i	$0.474532\pi$
$762$	69.1680	2.50569
$763$	65.4865	2.37077
$764$	−23.7654	−0.859801
$765$	−4.16824	−0.150703
$766$	−47.0309	−1.69930
$767$	4.67964	0.168972
$768$	51.8779	1.87198
$769$	14.6180	0.527140	0.263570	−	0.964640i	$-0.415100\pi$
$769$	14.6180	0.527140	0.263570	+	0.964640i	$0.415100\pi$
$770$	6.29312	0.226788
$771$	15.7060	0.565639
$772$	−22.0258	−0.792726
$773$	−53.4906	−1.92392	−0.961962	−	0.273183i	$-0.911924\pi$
$773$	−53.4906	−1.92392	−0.961962	+	0.273183i	$0.911924\pi$
$774$	−9.30394	−0.334423
$775$	28.8715	1.03710
$776$	10.7374	0.385452
$777$	16.4313	0.589468
$778$	−25.8681	−0.927418
$779$	12.8193	0.459301
$780$	2.30675	0.0825947
$781$	14.4353	0.516536
$782$	10.5178	0.376117
$783$	−3.25872	−0.116457
$784$	−82.4842	−2.94586
$785$	−7.09653	−0.253286
$786$	2.48746	0.0887247
$787$	14.9521	0.532984	0.266492	−	0.963837i	$-0.414135\pi$
$787$	14.9521	0.532984	0.266492	+	0.963837i	$0.414135\pi$
$788$	−12.4805	−0.444598
$789$	−46.9036	−1.66981
$790$	−0.427939	−0.0152254
$791$	56.3533	2.00369
$792$	10.2750	0.365105
$793$	6.43336	0.228455
$794$	−41.0851	−1.45806
$795$	−25.8901	−0.918227
$796$	−13.9678	−0.495075
$797$	31.0101	1.09843	0.549217	−	0.835680i	$-0.314926\pi$
$797$	31.0101	1.09843	0.549217	+	0.835680i	$0.314926\pi$
$798$	−72.1342	−2.55352
$799$	−1.17938	−0.0417235
$800$	−20.9065	−0.739156
$801$	−42.1223	−1.48832
$802$	37.9876	1.34139
$803$	0.103162	0.00364051
$804$	6.75059	0.238075
$805$	22.8586	0.805659
$806$	−12.9083	−0.454674
$807$	80.1225	2.82045
$808$	25.7408	0.905557
$809$	27.8537	0.979282	0.489641	−	0.871924i	$-0.337128\pi$
$809$	27.8537	0.979282	0.489641	+	0.871924i	$0.337128\pi$
$810$	5.82692	0.204737
$811$	−35.2939	−1.23934	−0.619668	−	0.784864i	$-0.712733\pi$
$811$	−35.2939	−1.23934	−0.619668	+	0.784864i	$0.712733\pi$
$812$	−1.97180	−0.0691967
$813$	37.9462	1.33083
$814$	−1.98073	−0.0694246
$815$	5.79654	0.203044
$816$	−14.5179	−0.508227
$817$	3.00298	0.105061
$818$	52.8393	1.84748
$819$	−30.7939	−1.07603
$820$	−2.91475	−0.101787
$821$	8.12327	0.283504	0.141752	−	0.989902i	$-0.454726\pi$
$821$	8.12327	0.283504	0.141752	+	0.989902i	$0.454726\pi$
$822$	32.5020	1.13364
$823$	−18.3269	−0.638837	−0.319418	−	0.947614i	$-0.603488\pi$
$823$	−18.3269	−0.638837	−0.319418	+	0.947614i	$0.603488\pi$
$824$	20.2945	0.706994
$825$	−12.8584	−0.447671
$826$	33.2728	1.15771
$827$	−14.7052	−0.511350	−0.255675	−	0.966763i	$-0.582298\pi$
$827$	−14.7052	−0.511350	−0.255675	+	0.966763i	$0.582298\pi$
$828$	−30.2677	−1.05188
$829$	−40.6716	−1.41258	−0.706292	−	0.707921i	$-0.749633\pi$
$829$	−40.6716	−1.41258	−0.706292	+	0.707921i	$0.749633\pi$
$830$	14.5214	0.504046
$831$	−19.2057	−0.666238
$832$	−2.23756	−0.0775736
$833$	16.5328	0.572829
$834$	−86.2720	−2.98736
$835$	−10.0037	−0.346193
$836$	2.68957	0.0930207
$837$	−46.9153	−1.62163
$838$	−18.9993	−0.656320
$839$	19.3637	0.668509	0.334254	−	0.942483i	$-0.391516\pi$
$839$	19.3637	0.668509	0.334254	+	0.942483i	$0.391516\pi$
$840$	−20.2236	−0.697781
$841$	−28.7940	−0.992898
$842$	−20.5950	−0.709751
$843$	−78.5702	−2.70610
$844$	16.8003	0.578289
$845$	8.88301	0.305585
$846$	10.9729	0.377256
$847$	4.85107	0.166685
$848$	−58.2264	−1.99950
$849$	−43.6271	−1.49728
$850$	7.51930	0.257910
$851$	−7.19463	−0.246629
$852$	37.6215	1.28889
$853$	−31.4458	−1.07668	−0.538342	−	0.842726i	$-0.680949\pi$
$853$	−31.4458	−1.07668	−0.538342	+	0.842726i	$0.680949\pi$
$854$	45.7419	1.56526
$855$	−12.5171	−0.428077
$856$	23.0119	0.786532
$857$	−8.41670	−0.287509	−0.143754	−	0.989613i	$-0.545918\pi$
$857$	−8.41670	−0.287509	−0.143754	+	0.989613i	$0.545918\pi$
$858$	5.74889	0.196264
$859$	7.20630	0.245876	0.122938	−	0.992414i	$-0.460768\pi$
$859$	7.20630	0.245876	0.122938	+	0.992414i	$0.460768\pi$
$860$	−0.682790	−0.0232830
$861$	60.2602	2.05366
$862$	30.5437	1.04032
$863$	−12.1313	−0.412956	−0.206478	−	0.978451i	$-0.566200\pi$
$863$	−12.1313	−0.412956	−0.206478	+	0.978451i	$0.566200\pi$
$864$	33.9724	1.15576
$865$	−9.72504	−0.330661
$866$	−26.4885	−0.900116
$867$	2.90991	0.0988258
$868$	−28.3878	−0.963543
$869$	−0.329877	−0.0111903
$870$	−1.71319	−0.0580824
$871$	−3.00722	−0.101896
$872$	25.3688	0.859095
$873$	31.2400	1.05731
$874$	31.5848	1.06837
$875$	34.8330	1.17757
$876$	0.268862	0.00908401
$877$	−40.7127	−1.37477	−0.687385	−	0.726293i	$-0.741242\pi$
$877$	−40.7127	−1.37477	−0.687385	+	0.726293i	$0.741242\pi$
$878$	47.3228	1.59707
$879$	−94.6084	−3.19106
$880$	3.80347	0.128215
$881$	−13.3840	−0.450918	−0.225459	−	0.974253i	$-0.572388\pi$
$881$	−13.3840	−0.450918	−0.225459	+	0.974253i	$0.572388\pi$
$882$	−153.821	−5.17941
$883$	4.13366	0.139109	0.0695544	−	0.997578i	$-0.477842\pi$
$883$	4.13366	0.139109	0.0695544	+	0.997578i	$0.477842\pi$
$884$	−1.03983	−0.0349733
$885$	8.94162	0.300569
$886$	0.466442	0.0156704
$887$	33.9265	1.13914	0.569571	−	0.821942i	$-0.307109\pi$
$887$	33.9265	1.13914	0.569571	+	0.821942i	$0.307109\pi$
$888$	6.36530	0.213605
$889$	−67.7628	−2.27269
$890$	−9.99415	−0.335005
$891$	4.49170	0.150478
$892$	0.799492	0.0267690
$893$	−3.54166	−0.118517
$894$	−119.368	−3.99227
$895$	−13.4731	−0.450355
$896$	−61.8125	−2.06501
$897$	20.8818	0.697222
$898$	−43.2034	−1.44172
$899$	2.96524	0.0988962
$900$	−21.6387	−0.721290
$901$	11.6707	0.388807
$902$	−7.26416	−0.241870
$903$	14.1162	0.469757
$904$	21.8307	0.726078
$905$	2.18230	0.0725421
$906$	−82.4626	−2.73964
$907$	12.7248	0.422519	0.211260	−	0.977430i	$-0.432243\pi$
$907$	12.7248	0.422519	0.211260	+	0.977430i	$0.432243\pi$
$908$	−5.16815	−0.171511
$909$	74.8913	2.48399
$910$	−7.30632	−0.242202
$911$	2.28872	0.0758287	0.0379144	−	0.999281i	$-0.487929\pi$
$911$	2.28872	0.0758287	0.0379144	+	0.999281i	$0.487929\pi$
$912$	−43.5968	−1.44364
$913$	11.1939	0.370463
$914$	62.3921	2.06375
$915$	12.2926	0.406379
$916$	4.92231	0.162638
$917$	−2.43692	−0.0804742
$918$	−12.2186	−0.403275
$919$	−52.0715	−1.71768	−0.858840	−	0.512244i	$-0.828814\pi$
$919$	−52.0715	−1.71768	−0.858840	+	0.512244i	$0.828814\pi$
$920$	8.85517	0.291946
$921$	−5.47383	−0.180369
$922$	19.4142	0.639373
$923$	−16.7594	−0.551643
$924$	12.6429	0.415921
$925$	−5.14351	−0.169118
$926$	−32.7860	−1.07741
$927$	59.0459	1.93932
$928$	−2.14719	−0.0704851
$929$	8.63984	0.283464	0.141732	−	0.989905i	$-0.454733\pi$
$929$	8.63984	0.283464	0.141732	+	0.989905i	$0.454733\pi$
$930$	−24.6645	−0.808780
$931$	49.6478	1.62714
$932$	6.81405	0.223202
$933$	64.9352	2.12588
$934$	31.8328	1.04160
$935$	−0.762355	−0.0249317
$936$	−11.9292	−0.389920
$937$	29.5769	0.966236	0.483118	−	0.875555i	$-0.339504\pi$
$937$	29.5769	0.966236	0.483118	+	0.875555i	$0.339504\pi$
$938$	−21.3816	−0.698135
$939$	−1.33658	−0.0436176
$940$	0.805271	0.0262650
$941$	−44.8128	−1.46085	−0.730427	−	0.682991i	$-0.760679\pi$
$941$	−44.8128	−1.46085	−0.730427	+	0.682991i	$0.760679\pi$
$942$	−46.0936	−1.50181
$943$	−26.3857	−0.859236
$944$	20.1096	0.654510
$945$	−26.5549	−0.863832
$946$	−1.70166	−0.0553256
$947$	−18.6867	−0.607237	−0.303618	−	0.952794i	$-0.598195\pi$
$947$	−18.6867	−0.607237	−0.303618	+	0.952794i	$0.598195\pi$
$948$	−0.859731	−0.0279228
$949$	−0.119771	−0.00388794
$950$	22.5803	0.732602
$951$	−28.3419	−0.919049
$952$	9.11638	0.295464
$953$	25.1447	0.814518	0.407259	−	0.913313i	$-0.366485\pi$
$953$	25.1447	0.814518	0.407259	+	0.913313i	$0.366485\pi$
$954$	−108.583	−3.51552
$955$	20.2289	0.654591
$956$	12.3295	0.398763
$957$	−1.32061	−0.0426894
$958$	68.7907	2.22253
$959$	−31.8416	−1.02822
$960$	−4.27543	−0.137989
$961$	11.6901	0.377100
$962$	2.29963	0.0741431
$963$	66.9520	2.15750
$964$	−26.3454	−0.848528
$965$	18.7481	0.603524
$966$	148.472	4.77700
$967$	7.68107	0.247007	0.123503	−	0.992344i	$-0.460587\pi$
$967$	7.68107	0.247007	0.123503	+	0.992344i	$0.460587\pi$
$968$	1.87925	0.0604015
$969$	8.73840	0.280718
$970$	7.41216	0.237990
$971$	34.2057	1.09771	0.548857	−	0.835916i	$-0.315063\pi$
$971$	34.2057	1.09771	0.548857	+	0.835916i	$0.315063\pi$
$972$	−7.58680	−0.243347
$973$	84.5193	2.70956
$974$	−32.0787	−1.02787
$975$	14.9286	0.478097
$976$	27.6457	0.884919
$977$	39.3289	1.25824	0.629122	−	0.777306i	$-0.283414\pi$
$977$	39.3289	1.25824	0.629122	+	0.777306i	$0.283414\pi$
$978$	37.6498	1.20391
$979$	−7.70401	−0.246221
$980$	−11.2885	−0.360597
$981$	73.8091	2.35654
$982$	17.0557	0.544269
$983$	−48.2168	−1.53788	−0.768938	−	0.639323i	$-0.779215\pi$
$983$	−48.2168	−1.53788	−0.768938	+	0.639323i	$0.779215\pi$
$984$	23.3442	0.744185
$985$	10.6233	0.338485
$986$	0.772268	0.0245940
$987$	−16.6484	−0.529923
$988$	−3.12259	−0.0993429
$989$	−6.18094	−0.196543
$990$	7.09290	0.225427
$991$	−7.02450	−0.223140	−0.111570	−	0.993757i	$-0.535588\pi$
$991$	−7.02450	−0.223140	−0.111570	+	0.993757i	$0.535588\pi$
$992$	−30.9128	−0.981483
$993$	12.0308	0.381787
$994$	−119.161	−3.77957
$995$	11.8892	0.376914
$996$	29.1736	0.924401
$997$	5.96495	0.188912	0.0944559	−	0.995529i	$-0.469889\pi$
$997$	5.96495	0.188912	0.0944559	+	0.995529i	$0.469889\pi$
$998$	23.6627	0.749030
$999$	8.35805	0.264437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.18	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.70166 q^{2} +2.90991 q^{3} +0.895633 q^{4} -0.762355 q^{5} -4.95167 q^{6} +4.85107 q^{7} +1.87925 q^{8} +5.46758 q^{9} +O(q^{10})\)	\(q-1.70166 q^{2} +2.90991 q^{3} +0.895633 q^{4} -0.762355 q^{5} -4.95167 q^{6} +4.85107 q^{7} +1.87925 q^{8} +5.46758 q^{9} +1.29727 q^{10} +1.00000 q^{11} +2.60621 q^{12} -1.16100 q^{13} -8.25485 q^{14} -2.21838 q^{15} -4.98911 q^{16} +1.00000 q^{17} -9.30394 q^{18} +3.00298 q^{19} -0.682790 q^{20} +14.1162 q^{21} -1.70166 q^{22} -6.18094 q^{23} +5.46846 q^{24} -4.41882 q^{25} +1.97562 q^{26} +7.18044 q^{27} +4.34478 q^{28} -0.453833 q^{29} +3.77493 q^{30} -6.53377 q^{31} +4.73124 q^{32} +2.90991 q^{33} -1.70166 q^{34} -3.69823 q^{35} +4.89695 q^{36} +1.16400 q^{37} -5.11004 q^{38} -3.37841 q^{39} -1.43266 q^{40} +4.26888 q^{41} -24.0209 q^{42} +1.00000 q^{43} +0.895633 q^{44} -4.16824 q^{45} +10.5178 q^{46} -1.17938 q^{47} -14.5179 q^{48} +16.5328 q^{49} +7.51930 q^{50} +2.90991 q^{51} -1.03983 q^{52} +11.6707 q^{53} -12.2186 q^{54} -0.762355 q^{55} +9.11638 q^{56} +8.73840 q^{57} +0.772268 q^{58} -4.03069 q^{59} -1.98686 q^{60} -5.54122 q^{61} +11.1182 q^{62} +26.5236 q^{63} +1.92727 q^{64} +0.885095 q^{65} -4.95167 q^{66} +2.59019 q^{67} +0.895633 q^{68} -17.9860 q^{69} +6.29312 q^{70} +14.4353 q^{71} +10.2750 q^{72} +0.103162 q^{73} -1.98073 q^{74} -12.8584 q^{75} +2.68957 q^{76} +4.85107 q^{77} +5.74889 q^{78} -0.329877 q^{79} +3.80347 q^{80} +4.49170 q^{81} -7.26416 q^{82} +11.1939 q^{83} +12.6429 q^{84} -0.762355 q^{85} -1.70166 q^{86} -1.32061 q^{87} +1.87925 q^{88} -7.70401 q^{89} +7.09290 q^{90} -5.63209 q^{91} -5.53586 q^{92} -19.0127 q^{93} +2.00690 q^{94} -2.28933 q^{95} +13.7675 q^{96} +5.71368 q^{97} -28.1332 q^{98} +5.46758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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