LMFDB - Embedded newform 8041.2.a.j.1.3

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			1.3
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65190 q^{2} +1.08303 q^{3} +5.03256 q^{4} +0.484312 q^{5} -2.87208 q^{6} +1.56821 q^{7} -8.04203 q^{8} -1.82705 q^{9} +O(q^{10})$	\(q-2.65190 q^{2} +1.08303 q^{3} +5.03256 q^{4} +0.484312 q^{5} -2.87208 q^{6} +1.56821 q^{7} -8.04203 q^{8} -1.82705 q^{9} -1.28435 q^{10} +1.00000 q^{11} +5.45040 q^{12} +1.02036 q^{13} -4.15873 q^{14} +0.524523 q^{15} +11.2615 q^{16} +1.00000 q^{17} +4.84515 q^{18} -7.33635 q^{19} +2.43733 q^{20} +1.69842 q^{21} -2.65190 q^{22} +4.79280 q^{23} -8.70974 q^{24} -4.76544 q^{25} -2.70590 q^{26} -5.22783 q^{27} +7.89211 q^{28} -6.14051 q^{29} -1.39098 q^{30} -8.14245 q^{31} -13.7803 q^{32} +1.08303 q^{33} -2.65190 q^{34} +0.759504 q^{35} -9.19474 q^{36} +7.46703 q^{37} +19.4552 q^{38} +1.10508 q^{39} -3.89485 q^{40} -10.1278 q^{41} -4.50402 q^{42} +1.00000 q^{43} +5.03256 q^{44} -0.884863 q^{45} -12.7100 q^{46} +1.41818 q^{47} +12.1965 q^{48} -4.54071 q^{49} +12.6375 q^{50} +1.08303 q^{51} +5.13504 q^{52} +10.8066 q^{53} +13.8637 q^{54} +0.484312 q^{55} -12.6116 q^{56} -7.94547 q^{57} +16.2840 q^{58} -1.27321 q^{59} +2.63969 q^{60} +5.68853 q^{61} +21.5929 q^{62} -2.86520 q^{63} +14.0210 q^{64} +0.494174 q^{65} -2.87208 q^{66} +11.3268 q^{67} +5.03256 q^{68} +5.19073 q^{69} -2.01413 q^{70} +4.89737 q^{71} +14.6932 q^{72} +1.41558 q^{73} -19.8018 q^{74} -5.16110 q^{75} -36.9206 q^{76} +1.56821 q^{77} -2.93056 q^{78} -8.10888 q^{79} +5.45409 q^{80} -0.180729 q^{81} +26.8580 q^{82} +6.65886 q^{83} +8.54738 q^{84} +0.484312 q^{85} -2.65190 q^{86} -6.65034 q^{87} -8.04203 q^{88} +11.4605 q^{89} +2.34657 q^{90} +1.60015 q^{91} +24.1200 q^{92} -8.81850 q^{93} -3.76087 q^{94} -3.55308 q^{95} -14.9245 q^{96} +1.82310 q^{97} +12.0415 q^{98} -1.82705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.65190	−1.87517	−0.937587	−	0.347750i	$-0.886946\pi$
$2$	−2.65190	−1.87517	−0.937587	+	0.347750i	$0.886946\pi$
$3$	1.08303	0.625286	0.312643	−	0.949871i	$-0.398786\pi$
$3$	1.08303	0.625286	0.312643	+	0.949871i	$0.398786\pi$
$4$	5.03256	2.51628
$5$	0.484312	0.216591	0.108295	−	0.994119i	$-0.465461\pi$
$5$	0.484312	0.216591	0.108295	+	0.994119i	$0.465461\pi$
$6$	−2.87208	−1.17252
$7$	1.56821	0.592728	0.296364	−	0.955075i	$-0.404226\pi$
$7$	1.56821	0.592728	0.296364	+	0.955075i	$0.404226\pi$
$8$	−8.04203	−2.84329
$9$	−1.82705	−0.609017
$10$	−1.28435	−0.406146
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.45040	1.57339
$13$	1.02036	0.282998	0.141499	−	0.989938i	$-0.454808\pi$
$13$	1.02036	0.282998	0.141499	+	0.989938i	$0.454808\pi$
$14$	−4.15873	−1.11147
$15$	0.524523	0.135431
$16$	11.2615	2.81538
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.84515	1.14201
$19$	−7.33635	−1.68307	−0.841537	−	0.540200i	$-0.818349\pi$
$19$	−7.33635	−1.68307	−0.841537	+	0.540200i	$0.818349\pi$
$20$	2.43733	0.545003
$21$	1.69842	0.370625
$22$	−2.65190	−0.565386
$23$	4.79280	0.999367	0.499684	−	0.866208i	$-0.333450\pi$
$23$	4.79280	0.999367	0.499684	+	0.866208i	$0.333450\pi$
$24$	−8.70974	−1.77787
$25$	−4.76544	−0.953088
$26$	−2.70590	−0.530670
$27$	−5.22783	−1.00610
$28$	7.89211	1.49147
$29$	−6.14051	−1.14026	−0.570132	−	0.821553i	$-0.693108\pi$
$29$	−6.14051	−1.14026	−0.570132	+	0.821553i	$0.693108\pi$
$30$	−1.39098	−0.253957
$31$	−8.14245	−1.46243	−0.731214	−	0.682148i	$-0.761046\pi$
$31$	−8.14245	−1.46243	−0.731214	+	0.682148i	$0.761046\pi$
$32$	−13.7803	−2.43604
$33$	1.08303	0.188531
$34$	−2.65190	−0.454797
$35$	0.759504	0.128380
$36$	−9.19474	−1.53246
$37$	7.46703	1.22757	0.613786	−	0.789472i	$-0.289646\pi$
$37$	7.46703	1.22757	0.613786	+	0.789472i	$0.289646\pi$
$38$	19.4552	3.15606
$39$	1.10508	0.176955
$40$	−3.89485	−0.615830
$41$	−10.1278	−1.58170	−0.790852	−	0.612008i	$-0.790362\pi$
$41$	−10.1278	−1.58170	−0.790852	+	0.612008i	$0.790362\pi$
$42$	−4.50402	−0.694986
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.03256	0.758687
$45$	−0.884863	−0.131908
$46$	−12.7100	−1.87399
$47$	1.41818	0.206863	0.103432	−	0.994637i	$-0.467018\pi$
$47$	1.41818	0.206863	0.103432	+	0.994637i	$0.467018\pi$
$48$	12.1965	1.76042
$49$	−4.54071	−0.648673
$50$	12.6375	1.78721
$51$	1.08303	0.151654
$52$	5.13504	0.712102
$53$	10.8066	1.48441	0.742203	−	0.670175i	$-0.233781\pi$
$53$	10.8066	1.48441	0.742203	+	0.670175i	$0.233781\pi$
$54$	13.8637	1.88661
$55$	0.484312	0.0653046
$56$	−12.6116	−1.68530
$57$	−7.94547	−1.05240
$58$	16.2840	2.13819
$59$	−1.27321	−0.165758	−0.0828792	−	0.996560i	$-0.526412\pi$
$59$	−1.27321	−0.165758	−0.0828792	+	0.996560i	$0.526412\pi$
$60$	2.63969	0.340783
$61$	5.68853	0.728342	0.364171	−	0.931332i	$-0.381352\pi$
$61$	5.68853	0.728342	0.364171	+	0.931332i	$0.381352\pi$
$62$	21.5929	2.74231
$63$	−2.86520	−0.360982
$64$	14.0210	1.75263
$65$	0.494174	0.0612948
$66$	−2.87208	−0.353528
$67$	11.3268	1.38379	0.691893	−	0.722000i	$-0.256777\pi$
$67$	11.3268	1.38379	0.691893	+	0.722000i	$0.256777\pi$
$68$	5.03256	0.610287
$69$	5.19073	0.624891
$70$	−2.01413	−0.240734
$71$	4.89737	0.581211	0.290605	−	0.956843i	$-0.406143\pi$
$71$	4.89737	0.581211	0.290605	+	0.956843i	$0.406143\pi$
$72$	14.6932	1.73161
$73$	1.41558	0.165682	0.0828408	−	0.996563i	$-0.473601\pi$
$73$	1.41558	0.165682	0.0828408	+	0.996563i	$0.473601\pi$
$74$	−19.8018	−2.30191
$75$	−5.16110	−0.595953
$76$	−36.9206	−4.23508
$77$	1.56821	0.178714
$78$	−2.93056	−0.331821
$79$	−8.10888	−0.912320	−0.456160	−	0.889898i	$-0.650775\pi$
$79$	−8.10888	−0.912320	−0.456160	+	0.889898i	$0.650775\pi$
$80$	5.45409	0.609786
$81$	−0.180729	−0.0200810
$82$	26.8580	2.96597
$83$	6.65886	0.730905	0.365452	−	0.930830i	$-0.380914\pi$
$83$	6.65886	0.730905	0.365452	+	0.930830i	$0.380914\pi$
$84$	8.54738	0.932595
$85$	0.484312	0.0525310
$86$	−2.65190	−0.285961
$87$	−6.65034	−0.712991
$88$	−8.04203	−0.857284
$89$	11.4605	1.21481	0.607405	−	0.794392i	$-0.292210\pi$
$89$	11.4605	1.21481	0.607405	+	0.794392i	$0.292210\pi$
$90$	2.34657	0.247350
$91$	1.60015	0.167741
$92$	24.1200	2.51469
$93$	−8.81850	−0.914436
$94$	−3.76087	−0.387905
$95$	−3.55308	−0.364538
$96$	−14.9245	−1.52322
$97$	1.82310	0.185107	0.0925537	−	0.995708i	$-0.470497\pi$
$97$	1.82310	0.185107	0.0925537	+	0.995708i	$0.470497\pi$
$98$	12.0415	1.21638
$99$	−1.82705	−0.183626
$100$	−23.9824	−2.39824
$101$	14.2470	1.41763	0.708813	−	0.705396i	$-0.249231\pi$
$101$	14.2470	1.41763	0.708813	+	0.705396i	$0.249231\pi$
$102$	−2.87208	−0.284378
$103$	−3.92423	−0.386666	−0.193333	−	0.981133i	$-0.561930\pi$
$103$	−3.92423	−0.386666	−0.193333	+	0.981133i	$0.561930\pi$
$104$	−8.20580	−0.804645
$105$	0.822563	0.0802740
$106$	−28.6581	−2.78352
$107$	6.86098	0.663276	0.331638	−	0.943407i	$-0.392399\pi$
$107$	6.86098	0.663276	0.331638	+	0.943407i	$0.392399\pi$
$108$	−26.3094	−2.53162
$109$	−2.06549	−0.197838	−0.0989188	−	0.995096i	$-0.531538\pi$
$109$	−2.06549	−0.197838	−0.0989188	+	0.995096i	$0.531538\pi$
$110$	−1.28435	−0.122458
$111$	8.08700	0.767584
$112$	17.6605	1.66876
$113$	−12.9132	−1.21477	−0.607386	−	0.794407i	$-0.707782\pi$
$113$	−12.9132	−1.21477	−0.607386	+	0.794407i	$0.707782\pi$
$114$	21.0706	1.97344
$115$	2.32121	0.216454
$116$	−30.9025	−2.86922
$117$	−1.86426	−0.172351
$118$	3.37643	0.310826
$119$	1.56821	0.143758
$120$	−4.21823	−0.385070
$121$	1.00000	0.0909091
$122$	−15.0854	−1.36577
$123$	−10.9687	−0.989017
$124$	−40.9774	−3.67988
$125$	−4.72952	−0.423021
$126$	7.59822	0.676903
$127$	12.5242	1.11134	0.555672	−	0.831402i	$-0.312461\pi$
$127$	12.5242	1.11134	0.555672	+	0.831402i	$0.312461\pi$
$128$	−9.62157	−0.850435
$129$	1.08303	0.0953553
$130$	−1.31050	−0.114938
$131$	9.19874	0.803698	0.401849	−	0.915706i	$-0.368368\pi$
$131$	9.19874	0.803698	0.401849	+	0.915706i	$0.368368\pi$
$132$	5.45040	0.474396
$133$	−11.5049	−0.997605
$134$	−30.0375	−2.59484
$135$	−2.53190	−0.217911
$136$	−8.04203	−0.689599
$137$	20.3360	1.73742	0.868710	−	0.495322i	$-0.164950\pi$
$137$	20.3360	1.73742	0.868710	+	0.495322i	$0.164950\pi$
$138$	−13.7653	−1.17178
$139$	17.2386	1.46216	0.731081	−	0.682290i	$-0.239016\pi$
$139$	17.2386	1.46216	0.731081	+	0.682290i	$0.239016\pi$
$140$	3.82225	0.323039
$141$	1.53593	0.129349
$142$	−12.9873	−1.08987
$143$	1.02036	0.0853271
$144$	−20.5754	−1.71462
$145$	−2.97392	−0.246971
$146$	−3.75399	−0.310682
$147$	−4.91772	−0.405607
$148$	37.5783	3.08891
$149$	−7.08661	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$149$	−7.08661	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$150$	13.6867	1.11752
$151$	4.13116	0.336189	0.168095	−	0.985771i	$-0.446239\pi$
$151$	4.13116	0.336189	0.168095	+	0.985771i	$0.446239\pi$
$152$	58.9991	4.78546
$153$	−1.82705	−0.147708
$154$	−4.15873	−0.335120
$155$	−3.94349	−0.316749
$156$	5.56139	0.445267
$157$	11.0556	0.882333	0.441167	−	0.897425i	$-0.354565\pi$
$157$	11.0556	0.882333	0.441167	+	0.897425i	$0.354565\pi$
$158$	21.5039	1.71076
$159$	11.7039	0.928179
$160$	−6.67399	−0.527625
$161$	7.51612	0.592353
$162$	0.479274	0.0376553
$163$	18.9901	1.48742	0.743708	−	0.668504i	$-0.233065\pi$
$163$	18.9901	1.48742	0.743708	+	0.668504i	$0.233065\pi$
$164$	−50.9690	−3.98001
$165$	0.524523	0.0408341
$166$	−17.6586	−1.37057
$167$	−15.6790	−1.21328	−0.606640	−	0.794976i	$-0.707483\pi$
$167$	−15.6790	−1.21328	−0.606640	+	0.794976i	$0.707483\pi$
$168$	−13.6587	−1.05379
$169$	−11.9589	−0.919912
$170$	−1.28435	−0.0985048
$171$	13.4039	1.02502
$172$	5.03256	0.383729
$173$	13.5295	1.02863	0.514316	−	0.857601i	$-0.328046\pi$
$173$	13.5295	1.02863	0.514316	+	0.857601i	$0.328046\pi$
$174$	17.6360	1.33698
$175$	−7.47322	−0.564922
$176$	11.2615	0.848870
$177$	−1.37893	−0.103646
$178$	−30.3921	−2.27798
$179$	25.8414	1.93148	0.965739	−	0.259514i	$-0.0835625\pi$
$179$	25.8414	1.93148	0.965739	+	0.259514i	$0.0835625\pi$
$180$	−4.45313	−0.331916
$181$	17.7521	1.31950	0.659750	−	0.751485i	$-0.270662\pi$
$181$	17.7521	1.31950	0.659750	+	0.751485i	$0.270662\pi$
$182$	−4.24342	−0.314543
$183$	6.16084	0.455422
$184$	−38.5438	−2.84149
$185$	3.61637	0.265881
$186$	23.3858	1.71473
$187$	1.00000	0.0731272
$188$	7.13709	0.520526
$189$	−8.19834	−0.596342
$190$	9.42241	0.683573
$191$	12.6545	0.915647	0.457824	−	0.889043i	$-0.348629\pi$
$191$	12.6545	0.915647	0.457824	+	0.889043i	$0.348629\pi$
$192$	15.1851	1.09589
$193$	−6.34203	−0.456509	−0.228255	−	0.973601i	$-0.573302\pi$
$193$	−6.34203	−0.456509	−0.228255	+	0.973601i	$0.573302\pi$
$194$	−4.83466	−0.347109
$195$	0.535204	0.0383268
$196$	−22.8514	−1.63224
$197$	21.3012	1.51765	0.758823	−	0.651297i	$-0.225775\pi$
$197$	21.3012	1.51765	0.758823	+	0.651297i	$0.225775\pi$
$198$	4.84515	0.344330
$199$	−15.1294	−1.07249	−0.536247	−	0.844061i	$-0.680158\pi$
$199$	−15.1294	−1.07249	−0.536247	+	0.844061i	$0.680158\pi$
$200$	38.3238	2.70990
$201$	12.2672	0.865262
$202$	−37.7815	−2.65830
$203$	−9.62961	−0.675866
$204$	5.45040	0.381604
$205$	−4.90504	−0.342583
$206$	10.4066	0.725065
$207$	−8.75669	−0.608632
$208$	11.4909	0.796747
$209$	−7.33635	−0.507466
$210$	−2.18135	−0.150528
$211$	−17.8984	−1.23218	−0.616090	−	0.787676i	$-0.711284\pi$
$211$	−17.8984	−1.23218	−0.616090	+	0.787676i	$0.711284\pi$
$212$	54.3851	3.73518
$213$	5.30399	0.363423
$214$	−18.1946	−1.24376
$215$	0.484312	0.0330298
$216$	42.0424	2.86062
$217$	−12.7691	−0.866822
$218$	5.47745	0.370980
$219$	1.53312	0.103598
$220$	2.43733	0.164325
$221$	1.02036	0.0686371
$222$	−21.4459	−1.43935
$223$	15.5531	1.04151	0.520757	−	0.853705i	$-0.325650\pi$
$223$	15.5531	1.04151	0.520757	+	0.853705i	$0.325650\pi$
$224$	−21.6105	−1.44391
$225$	8.70671	0.580447
$226$	34.2445	2.27791
$227$	11.9457	0.792863	0.396431	−	0.918064i	$-0.370249\pi$
$227$	11.9457	0.792863	0.396431	+	0.918064i	$0.370249\pi$
$228$	−39.9860	−2.64814
$229$	9.02160	0.596164	0.298082	−	0.954540i	$-0.403653\pi$
$229$	9.02160	0.596164	0.298082	+	0.954540i	$0.403653\pi$
$230$	−6.15561	−0.405889
$231$	1.69842	0.111748
$232$	49.3821	3.24210
$233$	−10.0158	−0.656155	−0.328078	−	0.944651i	$-0.606401\pi$
$233$	−10.0158	−0.656155	−0.328078	+	0.944651i	$0.606401\pi$
$234$	4.94382	0.323187
$235$	0.686843	0.0448047
$236$	−6.40753	−0.417094
$237$	−8.78213	−0.570461
$238$	−4.15873	−0.269571
$239$	10.3697	0.670762	0.335381	−	0.942083i	$-0.391135\pi$
$239$	10.3697	0.670762	0.335381	+	0.942083i	$0.391135\pi$
$240$	5.90693	0.381291
$241$	7.73951	0.498546	0.249273	−	0.968433i	$-0.419808\pi$
$241$	7.73951	0.498546	0.249273	+	0.968433i	$0.419808\pi$
$242$	−2.65190	−0.170470
$243$	15.4878	0.993540
$244$	28.6279	1.83271
$245$	−2.19912	−0.140497
$246$	29.0879	1.85458
$247$	−7.48574	−0.476306
$248$	65.4819	4.15810
$249$	7.21173	0.457025
$250$	12.5422	0.793239
$251$	0.232469	0.0146733	0.00733665	−	0.999973i	$-0.497665\pi$
$251$	0.232469	0.0146733	0.00733665	+	0.999973i	$0.497665\pi$
$252$	−14.4193	−0.908330
$253$	4.79280	0.301321
$254$	−33.2129	−2.08396
$255$	0.524523	0.0328469
$256$	−2.52660	−0.157912
$257$	16.7108	1.04239	0.521196	−	0.853437i	$-0.325486\pi$
$257$	16.7108	1.04239	0.521196	+	0.853437i	$0.325486\pi$
$258$	−2.87208	−0.178808
$259$	11.7099	0.727616
$260$	2.48696	0.154235
$261$	11.2190	0.694440
$262$	−24.3941	−1.50707
$263$	−21.4264	−1.32121	−0.660604	−	0.750734i	$-0.729700\pi$
$263$	−21.4264	−1.32121	−0.660604	+	0.750734i	$0.729700\pi$
$264$	−8.70974	−0.536048
$265$	5.23379	0.321509
$266$	30.5099	1.87068
$267$	12.4120	0.759604
$268$	57.0027	3.48199
$269$	8.20255	0.500118	0.250059	−	0.968231i	$-0.419550\pi$
$269$	8.20255	0.500118	0.250059	+	0.968231i	$0.419550\pi$
$270$	6.71434	0.408622
$271$	−6.08472	−0.369621	−0.184810	−	0.982774i	$-0.559167\pi$
$271$	−6.08472	−0.369621	−0.184810	+	0.982774i	$0.559167\pi$
$272$	11.2615	0.682830
$273$	1.73300	0.104886
$274$	−53.9289	−3.25796
$275$	−4.76544	−0.287367
$276$	26.1227	1.57240
$277$	−24.3509	−1.46310	−0.731552	−	0.681786i	$-0.761204\pi$
$277$	−24.3509	−1.46310	−0.731552	+	0.681786i	$0.761204\pi$
$278$	−45.7151	−2.74181
$279$	14.8767	0.890643
$280$	−6.10795	−0.365020
$281$	30.4146	1.81438	0.907191	−	0.420719i	$-0.138222\pi$
$281$	30.4146	1.81438	0.907191	+	0.420719i	$0.138222\pi$
$282$	−4.07313	−0.242551
$283$	−6.60928	−0.392881	−0.196440	−	0.980516i	$-0.562938\pi$
$283$	−6.60928	−0.392881	−0.196440	+	0.980516i	$0.562938\pi$
$284$	24.6463	1.46249
$285$	−3.84808	−0.227941
$286$	−2.70590	−0.160003
$287$	−15.8826	−0.937520
$288$	25.1774	1.48359
$289$	1.00000	0.0588235
$290$	7.88653	0.463113
$291$	1.97446	0.115745
$292$	7.12401	0.416901
$293$	26.9491	1.57439	0.787193	−	0.616707i	$-0.211534\pi$
$293$	26.9491	1.57439	0.787193	+	0.616707i	$0.211534\pi$
$294$	13.0413	0.760583
$295$	−0.616633	−0.0359018
$296$	−60.0501	−3.49034
$297$	−5.22783	−0.303349
$298$	18.7930	1.08865
$299$	4.89040	0.282819
$300$	−25.9736	−1.49958
$301$	1.56821	0.0903902
$302$	−10.9554	−0.630413
$303$	15.4299	0.886423
$304$	−82.6185	−4.73849
$305$	2.75502	0.157752
$306$	4.84515	0.276979
$307$	32.9525	1.88070	0.940349	−	0.340212i	$-0.110499\pi$
$307$	32.9525	1.88070	0.940349	+	0.340212i	$0.110499\pi$
$308$	7.89211	0.449695
$309$	−4.25005	−0.241777
$310$	10.4577	0.593959
$311$	5.88050	0.333453	0.166726	−	0.986003i	$-0.446680\pi$
$311$	5.88050	0.333453	0.166726	+	0.986003i	$0.446680\pi$
$312$	−8.88710	−0.503133
$313$	−29.2161	−1.65139	−0.825695	−	0.564117i	$-0.809217\pi$
$313$	−29.2161	−1.65139	−0.825695	+	0.564117i	$0.809217\pi$
$314$	−29.3183	−1.65453
$315$	−1.38765	−0.0781853
$316$	−40.8084	−2.29565
$317$	25.6428	1.44024	0.720121	−	0.693848i	$-0.244086\pi$
$317$	25.6428	1.44024	0.720121	+	0.693848i	$0.244086\pi$
$318$	−31.0375	−1.74050
$319$	−6.14051	−0.343802
$320$	6.79054	0.379603
$321$	7.43063	0.414737
$322$	−19.9320	−1.11077
$323$	−7.33635	−0.408205
$324$	−0.909527	−0.0505293
$325$	−4.86248	−0.269722
$326$	−50.3597	−2.78917
$327$	−2.23698	−0.123705
$328$	81.4484	4.49724
$329$	2.22401	0.122614
$330$	−1.39098	−0.0765710
$331$	31.2118	1.71556	0.857779	−	0.514019i	$-0.171844\pi$
$331$	31.2118	1.71556	0.857779	+	0.514019i	$0.171844\pi$
$332$	33.5111	1.83916
$333$	−13.6426	−0.747612
$334$	41.5792	2.27511
$335$	5.48570	0.299716
$336$	19.1268	1.04345
$337$	−31.9453	−1.74017	−0.870087	−	0.492899i	$-0.835937\pi$
$337$	−31.9453	−1.74017	−0.870087	+	0.492899i	$0.835937\pi$
$338$	31.7137	1.72500
$339$	−13.9853	−0.759580
$340$	2.43733	0.132183
$341$	−8.14245	−0.440938
$342$	−35.5457	−1.92209
$343$	−18.0983	−0.977215
$344$	−8.04203	−0.433597
$345$	2.51393	0.135346
$346$	−35.8790	−1.92887
$347$	−0.821024	−0.0440749	−0.0220374	−	0.999757i	$-0.507015\pi$
$347$	−0.821024	−0.0440749	−0.0220374	+	0.999757i	$0.507015\pi$
$348$	−33.4682	−1.79408
$349$	−25.0895	−1.34301	−0.671505	−	0.741000i	$-0.734352\pi$
$349$	−25.0895	−1.34301	−0.671505	+	0.741000i	$0.734352\pi$
$350$	19.8182	1.05933
$351$	−5.33429	−0.284723
$352$	−13.7803	−0.734495
$353$	−8.68853	−0.462444	−0.231222	−	0.972901i	$-0.574272\pi$
$353$	−8.68853	−0.462444	−0.231222	+	0.972901i	$0.574272\pi$
$354$	3.65677	0.194355
$355$	2.37185	0.125885
$356$	57.6756	3.05680
$357$	1.69842	0.0898897
$358$	−68.5288	−3.62186
$359$	12.1388	0.640660	0.320330	−	0.947306i	$-0.396206\pi$
$359$	12.1388	0.640660	0.320330	+	0.947306i	$0.396206\pi$
$360$	7.11610	0.375051
$361$	34.8220	1.83274
$362$	−47.0766	−2.47429
$363$	1.08303	0.0568442
$364$	8.05283	0.422083
$365$	0.685585	0.0358851
$366$	−16.3379	−0.853996
$367$	−11.1331	−0.581141	−0.290571	−	0.956854i	$-0.593845\pi$
$367$	−11.1331	−0.581141	−0.290571	+	0.956854i	$0.593845\pi$
$368$	53.9742	2.81360
$369$	18.5041	0.963284
$370$	−9.59025	−0.498573
$371$	16.9471	0.879850
$372$	−44.3796	−2.30098
$373$	−14.6057	−0.756255	−0.378127	−	0.925754i	$-0.623432\pi$
$373$	−14.6057	−0.756255	−0.378127	+	0.925754i	$0.623432\pi$
$374$	−2.65190	−0.137126
$375$	−5.12220	−0.264509
$376$	−11.4051	−0.588172
$377$	−6.26555	−0.322692
$378$	21.7412	1.11824
$379$	3.50121	0.179845	0.0899226	−	0.995949i	$-0.471338\pi$
$379$	3.50121	0.179845	0.0899226	+	0.995949i	$0.471338\pi$
$380$	−17.8811	−0.917281
$381$	13.5641	0.694908
$382$	−33.5584	−1.71700
$383$	−22.2719	−1.13804	−0.569019	−	0.822324i	$-0.692677\pi$
$383$	−22.2719	−1.13804	−0.569019	+	0.822324i	$0.692677\pi$
$384$	−10.4204	−0.531765
$385$	0.759504	0.0387079
$386$	16.8184	0.856034
$387$	−1.82705	−0.0928742
$388$	9.17484	0.465782
$389$	−4.82631	−0.244704	−0.122352	−	0.992487i	$-0.539044\pi$
$389$	−4.82631	−0.244704	−0.122352	+	0.992487i	$0.539044\pi$
$390$	−1.41931	−0.0718694
$391$	4.79280	0.242382
$392$	36.5166	1.84437
$393$	9.96249	0.502541
$394$	−56.4885	−2.84585
$395$	−3.92723	−0.197600
$396$	−9.19474	−0.462053
$397$	−5.16985	−0.259468	−0.129734	−	0.991549i	$-0.541412\pi$
$397$	−5.16985	−0.259468	−0.129734	+	0.991549i	$0.541412\pi$
$398$	40.1216	2.01111
$399$	−12.4602	−0.623789
$400$	−53.6661	−2.68331
$401$	11.5195	0.575256	0.287628	−	0.957742i	$-0.407133\pi$
$401$	11.5195	0.575256	0.287628	+	0.957742i	$0.407133\pi$
$402$	−32.5314	−1.62252
$403$	−8.30826	−0.413864
$404$	71.6987	3.56715
$405$	−0.0875291	−0.00434935
$406$	25.5367	1.26737
$407$	7.46703	0.370127
$408$	−8.70974	−0.431197
$409$	−13.5590	−0.670449	−0.335224	−	0.942138i	$-0.608812\pi$
$409$	−13.5590	−0.670449	−0.335224	+	0.942138i	$0.608812\pi$
$410$	13.0077	0.642402
$411$	22.0244	1.08638
$412$	−19.7489	−0.972958
$413$	−1.99667	−0.0982497
$414$	23.2218	1.14129
$415$	3.22497	0.158307
$416$	−14.0610	−0.689395
$417$	18.6699	0.914270
$418$	19.4552	0.951587
$419$	1.91395	0.0935028	0.0467514	−	0.998907i	$-0.485113\pi$
$419$	1.91395	0.0935028	0.0467514	+	0.998907i	$0.485113\pi$
$420$	4.13960	0.201992
$421$	10.6250	0.517832	0.258916	−	0.965900i	$-0.416635\pi$
$421$	10.6250	0.517832	0.258916	+	0.965900i	$0.416635\pi$
$422$	47.4648	2.31055
$423$	−2.59109	−0.125983
$424$	−86.9074	−4.22060
$425$	−4.76544	−0.231158
$426$	−14.0656	−0.681482
$427$	8.92082	0.431709
$428$	34.5283	1.66899
$429$	1.10508	0.0533538
$430$	−1.28435	−0.0619367
$431$	−36.9115	−1.77797	−0.888983	−	0.457940i	$-0.848588\pi$
$431$	−36.9115	−1.77797	−0.888983	+	0.457940i	$0.848588\pi$
$432$	−58.8733	−2.83254
$433$	7.31761	0.351662	0.175831	−	0.984420i	$-0.443739\pi$
$433$	7.31761	0.351662	0.175831	+	0.984420i	$0.443739\pi$
$434$	33.8623	1.62544
$435$	−3.22084	−0.154427
$436$	−10.3947	−0.497815
$437$	−35.1616	−1.68201
$438$	−4.06567	−0.194265
$439$	−10.9146	−0.520924	−0.260462	−	0.965484i	$-0.583875\pi$
$439$	−10.9146	−0.520924	−0.260462	+	0.965484i	$0.583875\pi$
$440$	−3.89485	−0.185680
$441$	8.29612	0.395053
$442$	−2.70590	−0.128706
$443$	22.9347	1.08966	0.544831	−	0.838546i	$-0.316594\pi$
$443$	22.9347	1.08966	0.544831	+	0.838546i	$0.316594\pi$
$444$	40.6983	1.93146
$445$	5.55046	0.263117
$446$	−41.2453	−1.95302
$447$	−7.67499	−0.363015
$448$	21.9879	1.03883
$449$	14.4872	0.683693	0.341846	−	0.939756i	$-0.388948\pi$
$449$	14.4872	0.683693	0.341846	+	0.939756i	$0.388948\pi$
$450$	−23.0893	−1.08844
$451$	−10.1278	−0.476902
$452$	−64.9864	−3.05670
$453$	4.47416	0.210214
$454$	−31.6787	−1.48676
$455$	0.774970	0.0363311
$456$	63.8977	2.99228
$457$	−9.74970	−0.456072	−0.228036	−	0.973653i	$-0.573230\pi$
$457$	−9.74970	−0.456072	−0.228036	+	0.973653i	$0.573230\pi$
$458$	−23.9244	−1.11791
$459$	−5.22783	−0.244014
$460$	11.6816	0.544659
$461$	−6.42711	−0.299340	−0.149670	−	0.988736i	$-0.547821\pi$
$461$	−6.42711	−0.299340	−0.149670	+	0.988736i	$0.547821\pi$
$462$	−4.50402	−0.209546
$463$	−25.6703	−1.19300	−0.596501	−	0.802612i	$-0.703443\pi$
$463$	−25.6703	−1.19300	−0.596501	+	0.802612i	$0.703443\pi$
$464$	−69.1515	−3.21028
$465$	−4.27091	−0.198059
$466$	26.5608	1.23041
$467$	−13.8491	−0.640858	−0.320429	−	0.947272i	$-0.603827\pi$
$467$	−13.8491	−0.640858	−0.320429	+	0.947272i	$0.603827\pi$
$468$	−9.38198	−0.433682
$469$	17.7628	0.820209
$470$	−1.82144	−0.0840166
$471$	11.9735	0.551711
$472$	10.2392	0.471299
$473$	1.00000	0.0459800
$474$	23.2893	1.06971
$475$	34.9609	1.60412
$476$	7.89211	0.361734
$477$	−19.7443	−0.904029
$478$	−27.4995	−1.25780
$479$	−23.6330	−1.07982	−0.539910	−	0.841723i	$-0.681542\pi$
$479$	−23.6330	−1.07982	−0.539910	+	0.841723i	$0.681542\pi$
$480$	−7.22811	−0.329917
$481$	7.61908	0.347400
$482$	−20.5244	−0.934860
$483$	8.14016	0.370390
$484$	5.03256	0.228753
$485$	0.882948	0.0400926
$486$	−41.0719	−1.86306
$487$	−18.1556	−0.822710	−0.411355	−	0.911475i	$-0.634944\pi$
$487$	−18.1556	−0.822710	−0.411355	+	0.911475i	$0.634944\pi$
$488$	−45.7474	−2.07089
$489$	20.5668	0.930061
$490$	5.83185	0.263456
$491$	−23.5022	−1.06064	−0.530321	−	0.847797i	$-0.677928\pi$
$491$	−23.5022	−1.06064	−0.530321	+	0.847797i	$0.677928\pi$
$492$	−55.2008	−2.48864
$493$	−6.14051	−0.276554
$494$	19.8514	0.893157
$495$	−0.884863	−0.0397716
$496$	−91.6964	−4.11729
$497$	7.68011	0.344500
$498$	−19.1248	−0.857001
$499$	−30.8475	−1.38093	−0.690463	−	0.723368i	$-0.742593\pi$
$499$	−30.8475	−1.38093	−0.690463	+	0.723368i	$0.742593\pi$
$500$	−23.8016	−1.06444
$501$	−16.9808	−0.758648
$502$	−0.616483	−0.0275150
$503$	8.04226	0.358587	0.179293	−	0.983796i	$-0.442619\pi$
$503$	8.04226	0.358587	0.179293	+	0.983796i	$0.442619\pi$
$504$	23.0421	1.02637
$505$	6.89998	0.307045
$506$	−12.7100	−0.565029
$507$	−12.9518	−0.575208
$508$	63.0288	2.79645
$509$	9.35402	0.414610	0.207305	−	0.978276i	$-0.433531\pi$
$509$	9.35402	0.414610	0.207305	+	0.978276i	$0.433531\pi$
$510$	−1.39098	−0.0615937
$511$	2.21994	0.0982042
$512$	25.9434	1.14655
$513$	38.3532	1.69333
$514$	−44.3154	−1.95467
$515$	−1.90055	−0.0837483
$516$	5.45040	0.239940
$517$	1.41818	0.0623716
$518$	−31.0534	−1.36441
$519$	14.6529	0.643190
$520$	−3.97417	−0.174279
$521$	−5.30658	−0.232486	−0.116243	−	0.993221i	$-0.537085\pi$
$521$	−5.30658	−0.232486	−0.116243	+	0.993221i	$0.537085\pi$
$522$	−29.7517	−1.30220
$523$	1.93256	0.0845048	0.0422524	−	0.999107i	$-0.486547\pi$
$523$	1.93256	0.0845048	0.0422524	+	0.999107i	$0.486547\pi$
$524$	46.2932	2.02233
$525$	−8.09370	−0.353238
$526$	56.8206	2.47750
$527$	−8.14245	−0.354691
$528$	12.1965	0.530786
$529$	−0.0290886	−0.00126472
$530$	−13.8795	−0.602886
$531$	2.32623	0.100950
$532$	−57.8993	−2.51025
$533$	−10.3341	−0.447619
$534$	−32.9154	−1.42439
$535$	3.32286	0.143660
$536$	−91.0903	−3.93450
$537$	27.9870	1.20773
$538$	−21.7523	−0.937809
$539$	−4.54071	−0.195582
$540$	−12.7419	−0.548326
$541$	−36.2145	−1.55698	−0.778491	−	0.627656i	$-0.784015\pi$
$541$	−36.2145	−1.55698	−0.778491	+	0.627656i	$0.784015\pi$
$542$	16.1361	0.693103
$543$	19.2260	0.825065
$544$	−13.7803	−0.590827
$545$	−1.00034	−0.0428498
$546$	−4.59574	−0.196680
$547$	17.5984	0.752454	0.376227	−	0.926528i	$-0.377221\pi$
$547$	17.5984	0.752454	0.376227	+	0.926528i	$0.377221\pi$
$548$	102.342	4.37183
$549$	−10.3932	−0.443573
$550$	12.6375	0.538863
$551$	45.0489	1.91915
$552$	−41.7440	−1.77674
$553$	−12.7164	−0.540758
$554$	64.5761	2.74357
$555$	3.91663	0.166252
$556$	86.7545	3.67921
$557$	−27.6812	−1.17289	−0.586444	−	0.809990i	$-0.699473\pi$
$557$	−27.6812	−1.17289	−0.586444	+	0.809990i	$0.699473\pi$
$558$	−39.4514	−1.67011
$559$	1.02036	0.0431568
$560$	8.55317	0.361437
$561$	1.08303	0.0457255
$562$	−80.6563	−3.40228
$563$	27.8477	1.17364	0.586820	−	0.809718i	$-0.300380\pi$
$563$	27.8477	1.17364	0.586820	+	0.809718i	$0.300380\pi$
$564$	7.72966	0.325477
$565$	−6.25402	−0.263108
$566$	17.5271	0.736720
$567$	−0.283421	−0.0119025
$568$	−39.3848	−1.65255
$569$	−13.4866	−0.565386	−0.282693	−	0.959210i	$-0.591228\pi$
$569$	−13.4866	−0.565386	−0.282693	+	0.959210i	$0.591228\pi$
$570$	10.2047	0.427429
$571$	−29.9641	−1.25396	−0.626979	−	0.779036i	$-0.715709\pi$
$571$	−29.9641	−1.25396	−0.626979	+	0.779036i	$0.715709\pi$
$572$	5.13504	0.214707
$573$	13.7052	0.572542
$574$	42.1190	1.75801
$575$	−22.8398	−0.952485
$576$	−25.6171	−1.06738
$577$	37.3022	1.55291	0.776456	−	0.630171i	$-0.217015\pi$
$577$	37.3022	1.55291	0.776456	+	0.630171i	$0.217015\pi$
$578$	−2.65190	−0.110304
$579$	−6.86859	−0.285449
$580$	−14.9664	−0.621447
$581$	10.4425	0.433228
$582$	−5.23607	−0.217042
$583$	10.8066	0.447565
$584$	−11.3842	−0.471081
$585$	−0.902882	−0.0373296
$586$	−71.4664	−2.95225
$587$	−28.8806	−1.19203	−0.596016	−	0.802973i	$-0.703250\pi$
$587$	−28.8806	−1.19203	−0.596016	+	0.802973i	$0.703250\pi$
$588$	−24.7487	−1.02062
$589$	59.7359	2.46137
$590$	1.63525	0.0673221
$591$	23.0698	0.948963
$592$	84.0901	3.45608
$593$	−21.6510	−0.889100	−0.444550	−	0.895754i	$-0.646636\pi$
$593$	−21.6510	−0.889100	−0.444550	+	0.895754i	$0.646636\pi$
$594$	13.8637	0.568833
$595$	0.759504	0.0311366
$596$	−35.6638	−1.46085
$597$	−16.3855	−0.670615
$598$	−12.9688	−0.530335
$599$	23.0256	0.940802	0.470401	−	0.882453i	$-0.344109\pi$
$599$	23.0256	0.940802	0.470401	+	0.882453i	$0.344109\pi$
$600$	41.5058	1.69447
$601$	0.612719	0.0249933	0.0124967	−	0.999922i	$-0.496022\pi$
$601$	0.612719	0.0249933	0.0124967	+	0.999922i	$0.496022\pi$
$602$	−4.15873	−0.169497
$603$	−20.6946	−0.842750
$604$	20.7903	0.845946
$605$	0.484312	0.0196901
$606$	−40.9184	−1.66220
$607$	5.55922	0.225642	0.112821	−	0.993615i	$-0.464011\pi$
$607$	5.55922	0.225642	0.112821	+	0.993615i	$0.464011\pi$
$608$	101.097	4.10004
$609$	−10.4291	−0.422610
$610$	−7.30604	−0.295813
$611$	1.44706	0.0585419
$612$	−9.19474	−0.371675
$613$	18.0912	0.730695	0.365347	−	0.930871i	$-0.380950\pi$
$613$	18.0912	0.730695	0.365347	+	0.930871i	$0.380950\pi$
$614$	−87.3866	−3.52664
$615$	−5.31229	−0.214212
$616$	−12.6116	−0.508136
$617$	−36.5000	−1.46943	−0.734717	−	0.678374i	$-0.762685\pi$
$617$	−36.5000	−1.46943	−0.734717	+	0.678374i	$0.762685\pi$
$618$	11.2707	0.453373
$619$	39.7950	1.59950	0.799748	−	0.600336i	$-0.204967\pi$
$619$	39.7950	1.59950	0.799748	+	0.600336i	$0.204967\pi$
$620$	−19.8458	−0.797028
$621$	−25.0559	−1.00546
$622$	−15.5945	−0.625282
$623$	17.9725	0.720052
$624$	12.4449	0.498195
$625$	21.5366	0.861466
$626$	77.4780	3.09664
$627$	−7.94547	−0.317311
$628$	55.6380	2.22020
$629$	7.46703	0.297730
$630$	3.67991	0.146611
$631$	−13.1475	−0.523394	−0.261697	−	0.965150i	$-0.584282\pi$
$631$	−13.1475	−0.523394	−0.261697	+	0.965150i	$0.584282\pi$
$632$	65.2118	2.59399
$633$	−19.3845	−0.770465
$634$	−68.0020	−2.70071
$635$	6.06563	0.240707
$636$	58.9005	2.33556
$637$	−4.63318	−0.183573
$638$	16.2840	0.644689
$639$	−8.94775	−0.353967
$640$	−4.65984	−0.184196
$641$	19.1939	0.758113	0.379056	−	0.925374i	$-0.376249\pi$
$641$	19.1939	0.758113	0.379056	+	0.925374i	$0.376249\pi$
$642$	−19.7053	−0.777705
$643$	−40.2102	−1.58573	−0.792867	−	0.609395i	$-0.791413\pi$
$643$	−40.2102	−1.58573	−0.792867	+	0.609395i	$0.791413\pi$
$644$	37.8253	1.49053
$645$	0.524523	0.0206531
$646$	19.4552	0.765456
$647$	4.58287	0.180171	0.0900855	−	0.995934i	$-0.471286\pi$
$647$	4.58287	0.180171	0.0900855	+	0.995934i	$0.471286\pi$
$648$	1.45343	0.0570959
$649$	−1.27321	−0.0499780
$650$	12.8948	0.505776
$651$	−13.8293	−0.542012
$652$	95.5686	3.74276
$653$	12.2990	0.481298	0.240649	−	0.970612i	$-0.422640\pi$
$653$	12.2990	0.481298	0.240649	+	0.970612i	$0.422640\pi$
$654$	5.93223	0.231969
$655$	4.45506	0.174074
$656$	−114.055	−4.45310
$657$	−2.58635	−0.100903
$658$	−5.89785	−0.229922
$659$	13.4355	0.523371	0.261686	−	0.965153i	$-0.415722\pi$
$659$	13.4355	0.523371	0.261686	+	0.965153i	$0.415722\pi$
$660$	2.63969	0.102750
$661$	17.7966	0.692206	0.346103	−	0.938196i	$-0.387505\pi$
$661$	17.7966	0.692206	0.346103	+	0.938196i	$0.387505\pi$
$662$	−82.7706	−3.21697
$663$	1.10508	0.0429178
$664$	−53.5508	−2.07817
$665$	−5.57198	−0.216072
$666$	36.1789	1.40190
$667$	−29.4302	−1.13954
$668$	−78.9057	−3.05295
$669$	16.8445	0.651245
$670$	−14.5475	−0.562019
$671$	5.68853	0.219603
$672$	−23.4048	−0.902858
$673$	26.6423	1.02699	0.513493	−	0.858094i	$-0.328351\pi$
$673$	26.6423	1.02699	0.513493	+	0.858094i	$0.328351\pi$
$674$	84.7157	3.26313
$675$	24.9129	0.958899
$676$	−60.1837	−2.31476
$677$	23.2799	0.894720	0.447360	−	0.894354i	$-0.352364\pi$
$677$	23.2799	0.894720	0.447360	+	0.894354i	$0.352364\pi$
$678$	37.0877	1.42434
$679$	2.85900	0.109718
$680$	−3.89485	−0.149361
$681$	12.9375	0.495766
$682$	21.5929	0.826837
$683$	12.8161	0.490396	0.245198	−	0.969473i	$-0.421147\pi$
$683$	12.8161	0.490396	0.245198	+	0.969473i	$0.421147\pi$
$684$	67.4558	2.57924
$685$	9.84895	0.376309
$686$	47.9948	1.83245
$687$	9.77065	0.372773
$688$	11.2615	0.429342
$689$	11.0267	0.420084
$690$	−6.66669	−0.253797
$691$	31.9623	1.21590	0.607951	−	0.793974i	$-0.291992\pi$
$691$	31.9623	1.21590	0.607951	+	0.793974i	$0.291992\pi$
$692$	68.0882	2.58833
$693$	−2.86520	−0.108840
$694$	2.17727	0.0826481
$695$	8.34888	0.316691
$696$	53.4822	2.02724
$697$	−10.1278	−0.383619
$698$	66.5348	2.51838
$699$	−10.8474	−0.410285
$700$	−37.6094	−1.42150
$701$	−36.7874	−1.38944	−0.694720	−	0.719280i	$-0.744472\pi$
$701$	−36.7874	−1.38944	−0.694720	+	0.719280i	$0.744472\pi$
$702$	14.1460	0.533906
$703$	−54.7807	−2.06609
$704$	14.0210	0.528436
$705$	0.743870	0.0280158
$706$	23.0411	0.867163
$707$	22.3423	0.840267
$708$	−6.93953	−0.260803
$709$	17.7689	0.667324	0.333662	−	0.942693i	$-0.391716\pi$
$709$	17.7689	0.667324	0.333662	+	0.942693i	$0.391716\pi$
$710$	−6.28992	−0.236056
$711$	14.8153	0.555618
$712$	−92.1657	−3.45406
$713$	−39.0251	−1.46150
$714$	−4.50402	−0.168559
$715$	0.494174	0.0184811
$716$	130.048	4.86014
$717$	11.2307	0.419418
$718$	−32.1908	−1.20135
$719$	−18.0141	−0.671811	−0.335906	−	0.941896i	$-0.609042\pi$
$719$	−18.0141	−0.671811	−0.335906	+	0.941896i	$0.609042\pi$
$720$	−9.96491	−0.371370
$721$	−6.15402	−0.229188
$722$	−92.3443	−3.43670
$723$	8.38210	0.311734
$724$	89.3383	3.32023
$725$	29.2622	1.08677
$726$	−2.87208	−0.106593
$727$	3.40152	0.126155	0.0630776	−	0.998009i	$-0.479908\pi$
$727$	3.40152	0.126155	0.0630776	+	0.998009i	$0.479908\pi$
$728$	−12.8684	−0.476935
$729$	17.3158	0.641328
$730$	−1.81810	−0.0672909
$731$	1.00000	0.0369863
$732$	31.0048	1.14597
$733$	23.0184	0.850205	0.425102	−	0.905145i	$-0.360238\pi$
$733$	23.0184	0.850205	0.425102	+	0.905145i	$0.360238\pi$
$734$	29.5237	1.08974
$735$	−2.38171	−0.0878507
$736$	−66.0464	−2.43450
$737$	11.3268	0.417227
$738$	−49.0709	−1.80633
$739$	−40.3901	−1.48578	−0.742888	−	0.669416i	$-0.766544\pi$
$739$	−40.3901	−1.48578	−0.742888	+	0.669416i	$0.766544\pi$
$740$	18.1996	0.669031
$741$	−8.10726	−0.297828
$742$	−44.9420	−1.64987
$743$	−15.2934	−0.561059	−0.280530	−	0.959845i	$-0.590510\pi$
$743$	−15.2934	−0.561059	−0.280530	+	0.959845i	$0.590510\pi$
$744$	70.9187	2.60000
$745$	−3.43213	−0.125744
$746$	38.7328	1.41811
$747$	−12.1661	−0.445134
$748$	5.03256	0.184009
$749$	10.7595	0.393142
$750$	13.5836	0.496001
$751$	12.6008	0.459808	0.229904	−	0.973213i	$-0.426159\pi$
$751$	12.6008	0.459808	0.229904	+	0.973213i	$0.426159\pi$
$752$	15.9709	0.582399
$753$	0.251770	0.00917501
$754$	16.6156	0.605104
$755$	2.00077	0.0728155
$756$	−41.2586	−1.50056
$757$	1.42839	0.0519157	0.0259579	−	0.999663i	$-0.491736\pi$
$757$	1.42839	0.0519157	0.0259579	+	0.999663i	$0.491736\pi$
$758$	−9.28486	−0.337241
$759$	5.19073	0.188412
$760$	28.5740	1.03649
$761$	−29.8787	−1.08310	−0.541550	−	0.840668i	$-0.682162\pi$
$761$	−29.8787	−1.08310	−0.541550	+	0.840668i	$0.682162\pi$
$762$	−35.9705	−1.30307
$763$	−3.23912	−0.117264
$764$	63.6845	2.30402
$765$	−0.884863	−0.0319923
$766$	59.0627	2.13402
$767$	−1.29914	−0.0469093
$768$	−2.73637	−0.0987404
$769$	27.3343	0.985700	0.492850	−	0.870114i	$-0.335955\pi$
$769$	27.3343	0.985700	0.492850	+	0.870114i	$0.335955\pi$
$770$	−2.01413	−0.0725840
$771$	18.0983	0.651793
$772$	−31.9166	−1.14870
$773$	16.4424	0.591393	0.295696	−	0.955282i	$-0.404448\pi$
$773$	16.4424	0.591393	0.295696	+	0.955282i	$0.404448\pi$
$774$	4.84515	0.174155
$775$	38.8024	1.39382
$776$	−14.6614	−0.526314
$777$	12.6821	0.454969
$778$	12.7989	0.458862
$779$	74.3014	2.66212
$780$	2.69345	0.0964409
$781$	4.89737	0.175242
$782$	−12.7100	−0.454509
$783$	32.1015	1.14721
$784$	−51.1354	−1.82626
$785$	5.35436	0.191105
$786$	−26.4195	−0.942352
$787$	−33.9183	−1.20906	−0.604528	−	0.796584i	$-0.706638\pi$
$787$	−33.9183	−1.20906	−0.604528	+	0.796584i	$0.706638\pi$
$788$	107.199	3.81882
$789$	−23.2054	−0.826134
$790$	10.4146	0.370535
$791$	−20.2506	−0.720029
$792$	14.6932	0.522100
$793$	5.80437	0.206119
$794$	13.7099	0.486547
$795$	5.66834	0.201035
$796$	−76.1395	−2.69869
$797$	34.9331	1.23739	0.618697	−	0.785629i	$-0.287661\pi$
$797$	34.9331	1.23739	0.618697	+	0.785629i	$0.287661\pi$
$798$	33.0431	1.16971
$799$	1.41818	0.0501717
$800$	65.6694	2.32176
$801$	−20.9389	−0.739840
$802$	−30.5485	−1.07871
$803$	1.41558	0.0499549
$804$	61.7355	2.17724
$805$	3.64015	0.128298
$806$	22.0327	0.776067
$807$	8.88359	0.312717
$808$	−114.575	−4.03072
$809$	−52.0232	−1.82904	−0.914518	−	0.404544i	$-0.867430\pi$
$809$	−52.0232	−1.82904	−0.914518	+	0.404544i	$0.867430\pi$
$810$	0.232118	0.00815580
$811$	−46.4867	−1.63237	−0.816184	−	0.577792i	$-0.803915\pi$
$811$	−46.4867	−1.63237	−0.816184	+	0.577792i	$0.803915\pi$
$812$	−48.4616	−1.70067
$813$	−6.58992	−0.231119
$814$	−19.8018	−0.694052
$815$	9.19712	0.322161
$816$	12.1965	0.426964
$817$	−7.33635	−0.256666
$818$	35.9570	1.25721
$819$	−2.92355	−0.102157
$820$	−24.6849	−0.862034
$821$	13.2659	0.462982	0.231491	−	0.972837i	$-0.425640\pi$
$821$	13.2659	0.462982	0.231491	+	0.972837i	$0.425640\pi$
$822$	−58.4065	−2.03716
$823$	−47.4929	−1.65550	−0.827748	−	0.561099i	$-0.810379\pi$
$823$	−47.4929	−1.65550	−0.827748	+	0.561099i	$0.810379\pi$
$824$	31.5588	1.09940
$825$	−5.16110	−0.179687
$826$	5.29496	0.184235
$827$	38.7721	1.34824	0.674119	−	0.738623i	$-0.264524\pi$
$827$	38.7721	1.34824	0.674119	+	0.738623i	$0.264524\pi$
$828$	−44.0685	−1.53149
$829$	−43.9338	−1.52588	−0.762942	−	0.646467i	$-0.776246\pi$
$829$	−43.9338	−1.52588	−0.762942	+	0.646467i	$0.776246\pi$
$830$	−8.55228	−0.296854
$831$	−26.3727	−0.914859
$832$	14.3065	0.495989
$833$	−4.54071	−0.157326
$834$	−49.5107	−1.71442
$835$	−7.59355	−0.262786
$836$	−36.9206	−1.27693
$837$	42.5673	1.47134
$838$	−5.07561	−0.175334
$839$	12.1994	0.421170	0.210585	−	0.977576i	$-0.432463\pi$
$839$	12.1994	0.421170	0.210585	+	0.977576i	$0.432463\pi$
$840$	−6.61508	−0.228242
$841$	8.70581	0.300200
$842$	−28.1765	−0.971026
$843$	32.9398	1.13451
$844$	−90.0749	−3.10051
$845$	−5.79182	−0.199245
$846$	6.87131	0.236241
$847$	1.56821	0.0538844
$848$	121.699	4.17917
$849$	−7.15803	−0.245663
$850$	12.6375	0.433461
$851$	35.7880	1.22680
$852$	26.6926	0.914474
$853$	−31.2174	−1.06886	−0.534432	−	0.845211i	$-0.679475\pi$
$853$	−31.2174	−1.06886	−0.534432	+	0.845211i	$0.679475\pi$
$854$	−23.6571	−0.809529
$855$	6.49166	0.222010
$856$	−55.1762	−1.88588
$857$	−30.7427	−1.05015	−0.525075	−	0.851056i	$-0.675963\pi$
$857$	−30.7427	−1.05015	−0.525075	+	0.851056i	$0.675963\pi$
$858$	−2.93056	−0.100048
$859$	42.7205	1.45760	0.728802	−	0.684725i	$-0.240078\pi$
$859$	42.7205	1.45760	0.728802	+	0.684725i	$0.240078\pi$
$860$	2.43733	0.0831122
$861$	−17.2013	−0.586218
$862$	97.8856	3.33400
$863$	11.2589	0.383259	0.191629	−	0.981467i	$-0.438623\pi$
$863$	11.2589	0.383259	0.191629	+	0.981467i	$0.438623\pi$
$864$	72.0413	2.45089
$865$	6.55252	0.222792
$866$	−19.4055	−0.659427
$867$	1.08303	0.0367815
$868$	−64.2612	−2.18117
$869$	−8.10888	−0.275075
$870$	8.54133	0.289578
$871$	11.5574	0.391609
$872$	16.6107	0.562509
$873$	−3.33089	−0.112734
$874$	93.2450	3.15406
$875$	−7.41689	−0.250737
$876$	7.71550	0.260683
$877$	3.08997	0.104341	0.0521704	−	0.998638i	$-0.483386\pi$
$877$	3.08997	0.104341	0.0521704	+	0.998638i	$0.483386\pi$
$878$	28.9443	0.976824
$879$	29.1867	0.984442
$880$	5.45409	0.183857
$881$	−36.8348	−1.24100	−0.620498	−	0.784208i	$-0.713070\pi$
$881$	−36.8348	−1.24100	−0.620498	+	0.784208i	$0.713070\pi$
$882$	−22.0004	−0.740794
$883$	1.84452	0.0620730	0.0310365	−	0.999518i	$-0.490119\pi$
$883$	1.84452	0.0620730	0.0310365	+	0.999518i	$0.490119\pi$
$884$	5.13504	0.172710
$885$	−0.667831	−0.0224489
$886$	−60.8206	−2.04331
$887$	−10.8252	−0.363476	−0.181738	−	0.983347i	$-0.558172\pi$
$887$	−10.8252	−0.363476	−0.181738	+	0.983347i	$0.558172\pi$
$888$	−65.0359	−2.18246
$889$	19.6406	0.658725
$890$	−14.7192	−0.493390
$891$	−0.180729	−0.00605464
$892$	78.2720	2.62074
$893$	−10.4043	−0.348166
$894$	20.3533	0.680716
$895$	12.5153	0.418341
$896$	−15.0887	−0.504076
$897$	5.29643	0.176843
$898$	−38.4185	−1.28204
$899$	49.9988	1.66755
$900$	43.8170	1.46057
$901$	10.8066	0.360022
$902$	26.8580	0.894274
$903$	1.69842	0.0565197
$904$	103.848	3.45394
$905$	8.59753	0.285792
$906$	−11.8650	−0.394189
$907$	25.7796	0.855998	0.427999	−	0.903779i	$-0.359219\pi$
$907$	25.7796	0.855998	0.427999	+	0.903779i	$0.359219\pi$
$908$	60.1173	1.99506
$909$	−26.0300	−0.863359
$910$	−2.05514	−0.0681272
$911$	27.2784	0.903774	0.451887	−	0.892075i	$-0.350751\pi$
$911$	27.2784	0.903774	0.451887	+	0.892075i	$0.350751\pi$
$912$	−89.4781	−2.96291
$913$	6.65886	0.220376
$914$	25.8552	0.855214
$915$	2.98377	0.0986403
$916$	45.4017	1.50012
$917$	14.4256	0.476374
$918$	13.8637	0.457569
$919$	33.1425	1.09327	0.546635	−	0.837371i	$-0.315909\pi$
$919$	33.1425	1.09327	0.546635	+	0.837371i	$0.315909\pi$
$920$	−18.6672	−0.615441
$921$	35.6884	1.17597
$922$	17.0440	0.561315
$923$	4.99710	0.164481
$924$	8.54738	0.281188
$925$	−35.5837	−1.16998
$926$	68.0751	2.23709
$927$	7.16976	0.235486
$928$	84.6183	2.77773
$929$	−0.0748777	−0.00245666	−0.00122833	−	0.999999i	$-0.500391\pi$
$929$	−0.0748777	−0.00245666	−0.00122833	+	0.999999i	$0.500391\pi$
$930$	11.3260	0.371394
$931$	33.3123	1.09176
$932$	−50.4050	−1.65107
$933$	6.36875	0.208503
$934$	36.7263	1.20172
$935$	0.484312	0.0158387
$936$	14.9924	0.490042
$937$	60.6074	1.97996	0.989979	−	0.141214i	$-0.0451007\pi$
$937$	60.6074	1.97996	0.989979	+	0.141214i	$0.0451007\pi$
$938$	−47.1051	−1.53804
$939$	−31.6418	−1.03259
$940$	3.45658	0.112741
$941$	31.7439	1.03482	0.517410	−	0.855737i	$-0.326896\pi$
$941$	31.7439	1.03482	0.517410	+	0.855737i	$0.326896\pi$
$942$	−31.7525	−1.03455
$943$	−48.5407	−1.58070
$944$	−14.3383	−0.466673
$945$	−3.97056	−0.129162
$946$	−2.65190	−0.0862206
$947$	43.7339	1.42116	0.710581	−	0.703616i	$-0.248432\pi$
$947$	43.7339	1.42116	0.710581	+	0.703616i	$0.248432\pi$
$948$	−44.1966	−1.43544
$949$	1.44441	0.0468876
$950$	−92.7128	−3.00800
$951$	27.7718	0.900564
$952$	−12.6116	−0.408744
$953$	−38.8015	−1.25690	−0.628452	−	0.777848i	$-0.716311\pi$
$953$	−38.8015	−1.25690	−0.628452	+	0.777848i	$0.716311\pi$
$954$	52.3598	1.69521
$955$	6.12873	0.198321
$956$	52.1863	1.68783
$957$	−6.65034	−0.214975
$958$	62.6723	2.02485
$959$	31.8911	1.02982
$960$	7.35434	0.237360
$961$	35.2995	1.13869
$962$	−20.2050	−0.651436
$963$	−12.5354	−0.403947
$964$	38.9495	1.25448
$965$	−3.07152	−0.0988758
$966$	−21.5869	−0.694546
$967$	55.5641	1.78682	0.893411	−	0.449240i	$-0.148305\pi$
$967$	55.5641	1.78682	0.893411	+	0.449240i	$0.148305\pi$
$968$	−8.04203	−0.258481
$969$	−7.94547	−0.255245
$970$	−2.34149	−0.0751806
$971$	−34.5549	−1.10892	−0.554459	−	0.832211i	$-0.687075\pi$
$971$	−34.5549	−1.10892	−0.554459	+	0.832211i	$0.687075\pi$
$972$	77.9430	2.50002
$973$	27.0338	0.866665
$974$	48.1469	1.54273
$975$	−5.26620	−0.168653
$976$	64.0615	2.05056
$977$	34.5407	1.10506	0.552528	−	0.833495i	$-0.313663\pi$
$977$	34.5407	1.10506	0.552528	+	0.833495i	$0.313663\pi$
$978$	−54.5409	−1.74403
$979$	11.4605	0.366279
$980$	−11.0672	−0.353529
$981$	3.77375	0.120487
$982$	62.3255	1.98889
$983$	−30.1136	−0.960476	−0.480238	−	0.877138i	$-0.659450\pi$
$983$	−30.1136	−0.960476	−0.480238	+	0.877138i	$0.659450\pi$
$984$	88.2109	2.81206
$985$	10.3164	0.328708
$986$	16.2840	0.518588
$987$	2.40866	0.0766686
$988$	−37.6724	−1.19852
$989$	4.79280	0.152402
$990$	2.34657	0.0745788
$991$	−53.3869	−1.69589	−0.847946	−	0.530083i	$-0.822161\pi$
$991$	−53.3869	−1.69589	−0.847946	+	0.530083i	$0.822161\pi$
$992$	112.206	3.56254
$993$	33.8033	1.07271
$994$	−20.3669	−0.645998
$995$	−7.32734	−0.232292
$996$	36.2934	1.15000
$997$	7.11891	0.225458	0.112729	−	0.993626i	$-0.464041\pi$
$997$	7.11891	0.225458	0.112729	+	0.993626i	$0.464041\pi$
$998$	81.8045	2.58948
$999$	−39.0364	−1.23506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.3	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.3	✓	82	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.65190 q^{2} +1.08303 q^{3} +5.03256 q^{4} +0.484312 q^{5} -2.87208 q^{6} +1.56821 q^{7} -8.04203 q^{8} -1.82705 q^{9} +O(q^{10})\)	\(q-2.65190 q^{2} +1.08303 q^{3} +5.03256 q^{4} +0.484312 q^{5} -2.87208 q^{6} +1.56821 q^{7} -8.04203 q^{8} -1.82705 q^{9} -1.28435 q^{10} +1.00000 q^{11} +5.45040 q^{12} +1.02036 q^{13} -4.15873 q^{14} +0.524523 q^{15} +11.2615 q^{16} +1.00000 q^{17} +4.84515 q^{18} -7.33635 q^{19} +2.43733 q^{20} +1.69842 q^{21} -2.65190 q^{22} +4.79280 q^{23} -8.70974 q^{24} -4.76544 q^{25} -2.70590 q^{26} -5.22783 q^{27} +7.89211 q^{28} -6.14051 q^{29} -1.39098 q^{30} -8.14245 q^{31} -13.7803 q^{32} +1.08303 q^{33} -2.65190 q^{34} +0.759504 q^{35} -9.19474 q^{36} +7.46703 q^{37} +19.4552 q^{38} +1.10508 q^{39} -3.89485 q^{40} -10.1278 q^{41} -4.50402 q^{42} +1.00000 q^{43} +5.03256 q^{44} -0.884863 q^{45} -12.7100 q^{46} +1.41818 q^{47} +12.1965 q^{48} -4.54071 q^{49} +12.6375 q^{50} +1.08303 q^{51} +5.13504 q^{52} +10.8066 q^{53} +13.8637 q^{54} +0.484312 q^{55} -12.6116 q^{56} -7.94547 q^{57} +16.2840 q^{58} -1.27321 q^{59} +2.63969 q^{60} +5.68853 q^{61} +21.5929 q^{62} -2.86520 q^{63} +14.0210 q^{64} +0.494174 q^{65} -2.87208 q^{66} +11.3268 q^{67} +5.03256 q^{68} +5.19073 q^{69} -2.01413 q^{70} +4.89737 q^{71} +14.6932 q^{72} +1.41558 q^{73} -19.8018 q^{74} -5.16110 q^{75} -36.9206 q^{76} +1.56821 q^{77} -2.93056 q^{78} -8.10888 q^{79} +5.45409 q^{80} -0.180729 q^{81} +26.8580 q^{82} +6.65886 q^{83} +8.54738 q^{84} +0.484312 q^{85} -2.65190 q^{86} -6.65034 q^{87} -8.04203 q^{88} +11.4605 q^{89} +2.34657 q^{90} +1.60015 q^{91} +24.1200 q^{92} -8.81850 q^{93} -3.76087 q^{94} -3.55308 q^{95} -14.9245 q^{96} +1.82310 q^{97} +12.0415 q^{98} -1.82705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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