LMFDB - Embedded newform 8041.2.a.j.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.62978 q^{2} +1.21378 q^{3} +4.91575 q^{4} +1.03630 q^{5} -3.19199 q^{6} +4.97586 q^{7} -7.66780 q^{8} -1.52673 q^{9} +O(q^{10})$	\(q-2.62978 q^{2} +1.21378 q^{3} +4.91575 q^{4} +1.03630 q^{5} -3.19199 q^{6} +4.97586 q^{7} -7.66780 q^{8} -1.52673 q^{9} -2.72523 q^{10} +1.00000 q^{11} +5.96666 q^{12} -4.96941 q^{13} -13.0854 q^{14} +1.25784 q^{15} +10.3331 q^{16} +1.00000 q^{17} +4.01497 q^{18} +0.115825 q^{19} +5.09417 q^{20} +6.03962 q^{21} -2.62978 q^{22} +3.52297 q^{23} -9.30705 q^{24} -3.92609 q^{25} +13.0685 q^{26} -5.49447 q^{27} +24.4601 q^{28} +8.50373 q^{29} -3.30784 q^{30} +8.64528 q^{31} -11.8383 q^{32} +1.21378 q^{33} -2.62978 q^{34} +5.15646 q^{35} -7.50502 q^{36} -0.835464 q^{37} -0.304596 q^{38} -6.03179 q^{39} -7.94610 q^{40} +9.76371 q^{41} -15.8829 q^{42} +1.00000 q^{43} +4.91575 q^{44} -1.58214 q^{45} -9.26464 q^{46} +5.23354 q^{47} +12.5422 q^{48} +17.7592 q^{49} +10.3248 q^{50} +1.21378 q^{51} -24.4284 q^{52} -8.52130 q^{53} +14.4493 q^{54} +1.03630 q^{55} -38.1539 q^{56} +0.140587 q^{57} -22.3630 q^{58} +7.29048 q^{59} +6.18322 q^{60} -7.89897 q^{61} -22.7352 q^{62} -7.59679 q^{63} +10.4658 q^{64} -5.14978 q^{65} -3.19199 q^{66} +3.71740 q^{67} +4.91575 q^{68} +4.27612 q^{69} -13.5604 q^{70} +11.1775 q^{71} +11.7066 q^{72} -5.58860 q^{73} +2.19709 q^{74} -4.76543 q^{75} +0.569369 q^{76} +4.97586 q^{77} +15.8623 q^{78} +2.14655 q^{79} +10.7082 q^{80} -2.08891 q^{81} -25.6764 q^{82} -13.4253 q^{83} +29.6893 q^{84} +1.03630 q^{85} -2.62978 q^{86} +10.3217 q^{87} -7.66780 q^{88} -5.98888 q^{89} +4.16069 q^{90} -24.7271 q^{91} +17.3180 q^{92} +10.4935 q^{93} -13.7631 q^{94} +0.120029 q^{95} -14.3691 q^{96} -9.81623 q^{97} -46.7028 q^{98} -1.52673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62978	−1.85954	−0.929768	−	0.368145i	$-0.879993\pi$
$2$	−2.62978	−1.85954	−0.929768	+	0.368145i	$0.879993\pi$
$3$	1.21378	0.700778	0.350389	−	0.936604i	$-0.386049\pi$
$3$	1.21378	0.700778	0.350389	+	0.936604i	$0.386049\pi$
$4$	4.91575	2.45788
$5$	1.03630	0.463445	0.231723	−	0.972782i	$-0.425564\pi$
$5$	1.03630	0.463445	0.231723	+	0.972782i	$0.425564\pi$
$6$	−3.19199	−1.30312
$7$	4.97586	1.88070	0.940349	−	0.340211i	$-0.110498\pi$
$7$	4.97586	1.88070	0.940349	+	0.340211i	$0.110498\pi$
$8$	−7.66780	−2.71098
$9$	−1.52673	−0.508910
$10$	−2.72523	−0.861794
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.96666	1.72243
$13$	−4.96941	−1.37827	−0.689133	−	0.724635i	$-0.742009\pi$
$13$	−4.96941	−1.37827	−0.689133	+	0.724635i	$0.742009\pi$
$14$	−13.0854	−3.49723
$15$	1.25784	0.324772
$16$	10.3331	2.58328
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.01497	0.946336
$19$	0.115825	0.0265722	0.0132861	−	0.999912i	$-0.495771\pi$
$19$	0.115825	0.0265722	0.0132861	+	0.999912i	$0.495771\pi$
$20$	5.09417	1.13909
$21$	6.03962	1.31795
$22$	−2.62978	−0.560671
$23$	3.52297	0.734590	0.367295	−	0.930105i	$-0.380284\pi$
$23$	3.52297	0.734590	0.367295	+	0.930105i	$0.380284\pi$
$24$	−9.30705	−1.89979
$25$	−3.92609	−0.785218
$26$	13.0685	2.56294
$27$	−5.49447	−1.05741
$28$	24.4601	4.62253
$29$	8.50373	1.57910	0.789551	−	0.613685i	$-0.210313\pi$
$29$	8.50373	1.57910	0.789551	+	0.613685i	$0.210313\pi$
$30$	−3.30784	−0.603926
$31$	8.64528	1.55274	0.776369	−	0.630278i	$-0.217059\pi$
$31$	8.64528	1.55274	0.776369	+	0.630278i	$0.217059\pi$
$32$	−11.8383	−2.09273
$33$	1.21378	0.211293
$34$	−2.62978	−0.451004
$35$	5.15646	0.871601
$36$	−7.50502	−1.25084
$37$	−0.835464	−0.137350	−0.0686748	−	0.997639i	$-0.521877\pi$
$37$	−0.835464	−0.137350	−0.0686748	+	0.997639i	$0.521877\pi$
$38$	−0.304596	−0.0494119
$39$	−6.03179	−0.965859
$40$	−7.94610	−1.25639
$41$	9.76371	1.52484	0.762418	−	0.647085i	$-0.224012\pi$
$41$	9.76371	1.52484	0.762418	+	0.647085i	$0.224012\pi$
$42$	−15.8829	−2.45078
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	4.91575	0.741078
$45$	−1.58214	−0.235852
$46$	−9.26464	−1.36600
$47$	5.23354	0.763390	0.381695	−	0.924288i	$-0.375340\pi$
$47$	5.23354	0.763390	0.381695	+	0.924288i	$0.375340\pi$
$48$	12.5422	1.81031
$49$	17.7592	2.53703
$50$	10.3248	1.46014
$51$	1.21378	0.169964
$52$	−24.4284	−3.38761
$53$	−8.52130	−1.17049	−0.585245	−	0.810856i	$-0.699002\pi$
$53$	−8.52130	−1.17049	−0.585245	+	0.810856i	$0.699002\pi$
$54$	14.4493	1.96630
$55$	1.03630	0.139734
$56$	−38.1539	−5.09853
$57$	0.140587	0.0186212
$58$	−22.3630	−2.93640
$59$	7.29048	0.949140	0.474570	−	0.880218i	$-0.342604\pi$
$59$	7.29048	0.949140	0.474570	+	0.880218i	$0.342604\pi$
$60$	6.18322	0.798251
$61$	−7.89897	−1.01136	−0.505680	−	0.862721i	$-0.668758\pi$
$61$	−7.89897	−1.01136	−0.505680	+	0.862721i	$0.668758\pi$
$62$	−22.7352	−2.88737
$63$	−7.59679	−0.957106
$64$	10.4658	1.30823
$65$	−5.14978	−0.638751
$66$	−3.19199	−0.392906
$67$	3.71740	0.454153	0.227076	−	0.973877i	$-0.427083\pi$
$67$	3.71740	0.454153	0.227076	+	0.973877i	$0.427083\pi$
$68$	4.91575	0.596123
$69$	4.27612	0.514785
$70$	−13.5604	−1.62077
$71$	11.1775	1.32652	0.663260	−	0.748389i	$-0.269172\pi$
$71$	11.1775	1.32652	0.663260	+	0.748389i	$0.269172\pi$
$72$	11.7066	1.37964
$73$	−5.58860	−0.654096	−0.327048	−	0.945008i	$-0.606054\pi$
$73$	−5.58860	−0.654096	−0.327048	+	0.945008i	$0.606054\pi$
$74$	2.19709	0.255406
$75$	−4.76543	−0.550264
$76$	0.569369	0.0653111
$77$	4.97586	0.567052
$78$	15.8623	1.79605
$79$	2.14655	0.241506	0.120753	−	0.992683i	$-0.461469\pi$
$79$	2.14655	0.241506	0.120753	+	0.992683i	$0.461469\pi$
$80$	10.7082	1.19721
$81$	−2.08891	−0.232101
$82$	−25.6764	−2.83549
$83$	−13.4253	−1.47362	−0.736811	−	0.676098i	$-0.763669\pi$
$83$	−13.4253	−1.47362	−0.736811	+	0.676098i	$0.763669\pi$
$84$	29.6893	3.23937
$85$	1.03630	0.112402
$86$	−2.62978	−0.283577
$87$	10.3217	1.10660
$88$	−7.66780	−0.817390
$89$	−5.98888	−0.634820	−0.317410	−	0.948288i	$-0.602813\pi$
$89$	−5.98888	−0.634820	−0.317410	+	0.948288i	$0.602813\pi$
$90$	4.16069	0.438575
$91$	−24.7271	−2.59210
$92$	17.3180	1.80553
$93$	10.4935	1.08813
$94$	−13.7631	−1.41955
$95$	0.120029	0.0123148
$96$	−14.3691	−1.46654
$97$	−9.81623	−0.996687	−0.498343	−	0.866980i	$-0.666058\pi$
$97$	−9.81623	−0.996687	−0.498343	+	0.866980i	$0.666058\pi$
$98$	−46.7028	−4.71770
$99$	−1.52673	−0.153442
$100$	−19.2997	−1.92997
$101$	9.49363	0.944651	0.472326	−	0.881424i	$-0.343415\pi$
$101$	9.49363	0.944651	0.472326	+	0.881424i	$0.343415\pi$
$102$	−3.19199	−0.316054
$103$	16.2610	1.60224	0.801121	−	0.598503i	$-0.204238\pi$
$103$	16.2610	1.60224	0.801121	+	0.598503i	$0.204238\pi$
$104$	38.1044	3.73645
$105$	6.25883	0.610799
$106$	22.4092	2.17657
$107$	−5.80470	−0.561162	−0.280581	−	0.959830i	$-0.590527\pi$
$107$	−5.80470	−0.561162	−0.280581	+	0.959830i	$0.590527\pi$
$108$	−27.0095	−2.59899
$109$	−8.45851	−0.810178	−0.405089	−	0.914277i	$-0.632760\pi$
$109$	−8.45851	−0.810178	−0.405089	+	0.914277i	$0.632760\pi$
$110$	−2.72523	−0.259841
$111$	−1.01407	−0.0962516
$112$	51.4162	4.85837
$113$	−5.89233	−0.554304	−0.277152	−	0.960826i	$-0.589390\pi$
$113$	−5.89233	−0.554304	−0.277152	+	0.960826i	$0.589390\pi$
$114$	−0.369713	−0.0346268
$115$	3.65084	0.340442
$116$	41.8022	3.88124
$117$	7.58694	0.701413
$118$	−19.1724	−1.76496
$119$	4.97586	0.456136
$120$	−9.64485	−0.880450
$121$	1.00000	0.0909091
$122$	20.7726	1.88066
$123$	11.8510	1.06857
$124$	42.4981	3.81644
$125$	−9.25007	−0.827351
$126$	19.9779	1.77977
$127$	−14.6467	−1.29968	−0.649841	−	0.760070i	$-0.725164\pi$
$127$	−14.6467	−1.29968	−0.649841	+	0.760070i	$0.725164\pi$
$128$	−3.84631	−0.339969
$129$	1.21378	0.106868
$130$	13.5428	1.18778
$131$	4.12908	0.360759	0.180380	−	0.983597i	$-0.442267\pi$
$131$	4.12908	0.360759	0.180380	+	0.983597i	$0.442267\pi$
$132$	5.96666	0.519331
$133$	0.576331	0.0499742
$134$	−9.77596	−0.844514
$135$	−5.69389	−0.490052
$136$	−7.66780	−0.657508
$137$	10.1308	0.865536	0.432768	−	0.901505i	$-0.357537\pi$
$137$	10.1308	0.865536	0.432768	+	0.901505i	$0.357537\pi$
$138$	−11.2453	−0.957261
$139$	−10.4483	−0.886215	−0.443107	−	0.896469i	$-0.646124\pi$
$139$	−10.4483	−0.886215	−0.443107	+	0.896469i	$0.646124\pi$
$140$	25.3479	2.14229
$141$	6.35238	0.534967
$142$	−29.3943	−2.46671
$143$	−4.96941	−0.415563
$144$	−15.7759	−1.31466
$145$	8.81237	0.731828
$146$	14.6968	1.21632
$147$	21.5558	1.77789
$148$	−4.10694	−0.337588
$149$	−2.82672	−0.231574	−0.115787	−	0.993274i	$-0.536939\pi$
$149$	−2.82672	−0.231574	−0.115787	+	0.993274i	$0.536939\pi$
$150$	12.5320	1.02324
$151$	−3.42685	−0.278873	−0.139437	−	0.990231i	$-0.544529\pi$
$151$	−3.42685	−0.278873	−0.139437	+	0.990231i	$0.544529\pi$
$152$	−0.888126	−0.0720365
$153$	−1.52673	−0.123429
$154$	−13.0854	−1.05445
$155$	8.95907	0.719610
$156$	−29.6508	−2.37396
$157$	10.5845	0.844736	0.422368	−	0.906424i	$-0.361199\pi$
$157$	10.5845	0.844736	0.422368	+	0.906424i	$0.361199\pi$
$158$	−5.64497	−0.449090
$159$	−10.3430	−0.820255
$160$	−12.2680	−0.969867
$161$	17.5298	1.38154
$162$	5.49338	0.431601
$163$	−6.11078	−0.478634	−0.239317	−	0.970942i	$-0.576923\pi$
$163$	−6.11078	−0.478634	−0.239317	+	0.970942i	$0.576923\pi$
$164$	47.9960	3.74786
$165$	1.25784	0.0979226
$166$	35.3057	2.74026
$167$	−4.86491	−0.376458	−0.188229	−	0.982125i	$-0.560275\pi$
$167$	−4.86491	−0.376458	−0.188229	+	0.982125i	$0.560275\pi$
$168$	−46.3106	−3.57294
$169$	11.6950	0.899618
$170$	−2.72523	−0.209016
$171$	−0.176834	−0.0135228
$172$	4.91575	0.374823
$173$	5.41350	0.411581	0.205790	−	0.978596i	$-0.434023\pi$
$173$	5.41350	0.411581	0.205790	+	0.978596i	$0.434023\pi$
$174$	−27.1438	−2.05776
$175$	−19.5357	−1.47676
$176$	10.3331	0.778889
$177$	8.84907	0.665136
$178$	15.7495	1.18047
$179$	20.5700	1.53747	0.768735	−	0.639567i	$-0.220886\pi$
$179$	20.5700	1.53747	0.768735	+	0.639567i	$0.220886\pi$
$180$	−7.77742	−0.579695
$181$	20.1776	1.49979	0.749894	−	0.661558i	$-0.230104\pi$
$181$	20.1776	1.49979	0.749894	+	0.661558i	$0.230104\pi$
$182$	65.0269	4.82011
$183$	−9.58764	−0.708739
$184$	−27.0134	−1.99145
$185$	−0.865788	−0.0636540
$186$	−27.5956	−2.02341
$187$	1.00000	0.0731272
$188$	25.7268	1.87632
$189$	−27.3397	−1.98867
$190$	−0.315651	−0.0228997
$191$	23.7258	1.71674	0.858369	−	0.513033i	$-0.171478\pi$
$191$	23.7258	1.71674	0.858369	+	0.513033i	$0.171478\pi$
$192$	12.7033	0.916779
$193$	11.6452	0.838236	0.419118	−	0.907932i	$-0.362339\pi$
$193$	11.6452	0.838236	0.419118	+	0.907932i	$0.362339\pi$
$194$	25.8145	1.85338
$195$	−6.25072	−0.447623
$196$	87.2998	6.23570
$197$	−25.3113	−1.80335	−0.901677	−	0.432411i	$-0.857663\pi$
$197$	−25.3113	−1.80335	−0.901677	+	0.432411i	$0.857663\pi$
$198$	4.01497	0.285331
$199$	−12.3856	−0.877992	−0.438996	−	0.898489i	$-0.644666\pi$
$199$	−12.3856	−0.877992	−0.438996	+	0.898489i	$0.644666\pi$
$200$	30.1045	2.12871
$201$	4.51212	0.318260
$202$	−24.9662	−1.75661
$203$	42.3134	2.96982
$204$	5.96666	0.417750
$205$	10.1181	0.706678
$206$	−42.7628	−2.97943
$207$	−5.37862	−0.373840
$208$	−51.3495	−3.56045
$209$	0.115825	0.00801181
$210$	−16.4594	−1.13580
$211$	−16.7739	−1.15476	−0.577380	−	0.816475i	$-0.695925\pi$
$211$	−16.7739	−1.15476	−0.577380	+	0.816475i	$0.695925\pi$
$212$	−41.8886	−2.87692
$213$	13.5670	0.929597
$214$	15.2651	1.04350
$215$	1.03630	0.0706748
$216$	42.1305	2.86662
$217$	43.0177	2.92023
$218$	22.2440	1.50656
$219$	−6.78335	−0.458376
$220$	5.09417	0.343449
$221$	−4.96941	−0.334279
$222$	2.66679	0.178983
$223$	6.72264	0.450181	0.225091	−	0.974338i	$-0.427732\pi$
$223$	6.72264	0.450181	0.225091	+	0.974338i	$0.427732\pi$
$224$	−58.9056	−3.93580
$225$	5.99408	0.399605
$226$	15.4955	1.03075
$227$	7.86616	0.522095	0.261048	−	0.965326i	$-0.415932\pi$
$227$	7.86616	0.522095	0.261048	+	0.965326i	$0.415932\pi$
$228$	0.691091	0.0457686
$229$	−3.30575	−0.218450	−0.109225	−	0.994017i	$-0.534837\pi$
$229$	−3.30575	−0.218450	−0.109225	+	0.994017i	$0.534837\pi$
$230$	−9.60090	−0.633065
$231$	6.03962	0.397378
$232$	−65.2049	−4.28091
$233$	28.8082	1.88729	0.943645	−	0.330960i	$-0.107372\pi$
$233$	28.8082	1.88729	0.943645	+	0.330960i	$0.107372\pi$
$234$	−19.9520	−1.30430
$235$	5.42349	0.353790
$236$	35.8382	2.33287
$237$	2.60545	0.169242
$238$	−13.0854	−0.848202
$239$	−23.2866	−1.50628	−0.753142	−	0.657858i	$-0.771463\pi$
$239$	−23.2866	−1.50628	−0.753142	+	0.657858i	$0.771463\pi$
$240$	12.9974	0.838979
$241$	−9.10383	−0.586429	−0.293215	−	0.956047i	$-0.594725\pi$
$241$	−9.10383	−0.586429	−0.293215	+	0.956047i	$0.594725\pi$
$242$	−2.62978	−0.169049
$243$	13.9479	0.894760
$244$	−38.8294	−2.48580
$245$	18.4038	1.17577
$246$	−31.1656	−1.98705
$247$	−0.575584	−0.0366235
$248$	−66.2903	−4.20944
$249$	−16.2955	−1.03268
$250$	24.3257	1.53849
$251$	19.9273	1.25780	0.628900	−	0.777486i	$-0.283505\pi$
$251$	19.9273	1.25780	0.628900	+	0.777486i	$0.283505\pi$
$252$	−37.3440	−2.35245
$253$	3.52297	0.221487
$254$	38.5175	2.41681
$255$	1.25784	0.0787689
$256$	−10.8167	−0.676045
$257$	14.5013	0.904568	0.452284	−	0.891874i	$-0.350609\pi$
$257$	14.5013	0.904568	0.452284	+	0.891874i	$0.350609\pi$
$258$	−3.19199	−0.198724
$259$	−4.15715	−0.258313
$260$	−25.3150	−1.56997
$261$	−12.9829	−0.803621
$262$	−10.8586	−0.670846
$263$	−10.9827	−0.677223	−0.338612	−	0.940926i	$-0.609957\pi$
$263$	−10.9827	−0.677223	−0.338612	+	0.940926i	$0.609957\pi$
$264$	−9.30705	−0.572809
$265$	−8.83059	−0.542459
$266$	−1.51563	−0.0929289
$267$	−7.26921	−0.444868
$268$	18.2738	1.11625
$269$	−15.0893	−0.920011	−0.460005	−	0.887916i	$-0.652152\pi$
$269$	−15.0893	−0.920011	−0.460005	+	0.887916i	$0.652152\pi$
$270$	14.9737	0.911270
$271$	6.20822	0.377122	0.188561	−	0.982061i	$-0.439618\pi$
$271$	6.20822	0.377122	0.188561	+	0.982061i	$0.439618\pi$
$272$	10.3331	0.626538
$273$	−30.0133	−1.81649
$274$	−26.6419	−1.60950
$275$	−3.92609	−0.236752
$276$	21.0204	1.26528
$277$	−1.48786	−0.0893970	−0.0446985	−	0.999001i	$-0.514233\pi$
$277$	−1.48786	−0.0893970	−0.0446985	+	0.999001i	$0.514233\pi$
$278$	27.4768	1.64795
$279$	−13.1990	−0.790204
$280$	−39.5387	−2.36289
$281$	−5.10045	−0.304267	−0.152134	−	0.988360i	$-0.548614\pi$
$281$	−5.10045	−0.304267	−0.152134	+	0.988360i	$0.548614\pi$
$282$	−16.7054	−0.994791
$283$	22.7387	1.35168	0.675839	−	0.737050i	$-0.263782\pi$
$283$	22.7387	1.35168	0.675839	+	0.737050i	$0.263782\pi$
$284$	54.9456	3.26042
$285$	0.145690	0.00862991
$286$	13.0685	0.772755
$287$	48.5829	2.86776
$288$	18.0738	1.06501
$289$	1.00000	0.0588235
$290$	−23.1746	−1.36086
$291$	−11.9148	−0.698456
$292$	−27.4722	−1.60769
$293$	23.7633	1.38827	0.694133	−	0.719847i	$-0.255788\pi$
$293$	23.7633	1.38827	0.694133	+	0.719847i	$0.255788\pi$
$294$	−56.6871	−3.30606
$295$	7.55509	0.439874
$296$	6.40617	0.372351
$297$	−5.49447	−0.318821
$298$	7.43366	0.430620
$299$	−17.5071	−1.01246
$300$	−23.4257	−1.35248
$301$	4.97586	0.286804
$302$	9.01187	0.518575
$303$	11.5232	0.661991
$304$	1.19684	0.0686434
$305$	−8.18567	−0.468710
$306$	4.01497	0.229520
$307$	−10.5867	−0.604216	−0.302108	−	0.953274i	$-0.597690\pi$
$307$	−10.5867	−0.604216	−0.302108	+	0.953274i	$0.597690\pi$
$308$	24.4601	1.39374
$309$	19.7373	1.12282
$310$	−23.5604	−1.33814
$311$	11.8549	0.672232	0.336116	−	0.941821i	$-0.390887\pi$
$311$	11.8549	0.672232	0.336116	+	0.941821i	$0.390887\pi$
$312$	46.2505	2.61842
$313$	19.6362	1.10990	0.554952	−	0.831883i	$-0.312737\pi$
$313$	19.6362	1.10990	0.554952	+	0.831883i	$0.312737\pi$
$314$	−27.8350	−1.57082
$315$	−7.87252	−0.443566
$316$	10.5519	0.593592
$317$	−1.81142	−0.101740	−0.0508698	−	0.998705i	$-0.516199\pi$
$317$	−1.81142	−0.101740	−0.0508698	+	0.998705i	$0.516199\pi$
$318$	27.1999	1.52529
$319$	8.50373	0.476117
$320$	10.8457	0.606293
$321$	−7.04565	−0.393250
$322$	−46.0996	−2.56903
$323$	0.115825	0.00644470
$324$	−10.2686	−0.570476
$325$	19.5104	1.08224
$326$	16.0700	0.890037
$327$	−10.2668	−0.567755
$328$	−74.8661	−4.13379
$329$	26.0414	1.43571
$330$	−3.30784	−0.182091
$331$	−30.4015	−1.67102	−0.835509	−	0.549477i	$-0.814827\pi$
$331$	−30.4015	−1.67102	−0.835509	+	0.549477i	$0.814827\pi$
$332$	−65.9957	−3.62198
$333$	1.27553	0.0698985
$334$	12.7937	0.700038
$335$	3.85233	0.210475
$336$	62.4081	3.40464
$337$	30.2858	1.64977	0.824886	−	0.565299i	$-0.191239\pi$
$337$	30.2858	1.64977	0.824886	+	0.565299i	$0.191239\pi$
$338$	−30.7554	−1.67287
$339$	−7.15201	−0.388444
$340$	5.09417	0.276270
$341$	8.64528	0.468168
$342$	0.465035	0.0251462
$343$	53.5362	2.89068
$344$	−7.66780	−0.413420
$345$	4.43133	0.238575
$346$	−14.2363	−0.765350
$347$	9.99056	0.536322	0.268161	−	0.963374i	$-0.413584\pi$
$347$	9.99056	0.536322	0.268161	+	0.963374i	$0.413584\pi$
$348$	50.7389	2.71989
$349$	14.5474	0.778706	0.389353	−	0.921089i	$-0.372699\pi$
$349$	14.5474	0.778706	0.389353	+	0.921089i	$0.372699\pi$
$350$	51.3746	2.74609
$351$	27.3043	1.45739
$352$	−11.8383	−0.630982
$353$	23.1884	1.23420	0.617098	−	0.786886i	$-0.288308\pi$
$353$	23.1884	1.23420	0.617098	+	0.786886i	$0.288308\pi$
$354$	−23.2711	−1.23685
$355$	11.5832	0.614770
$356$	−29.4399	−1.56031
$357$	6.03962	0.319651
$358$	−54.0945	−2.85898
$359$	−9.04820	−0.477546	−0.238773	−	0.971075i	$-0.576745\pi$
$359$	−9.04820	−0.477546	−0.238773	+	0.971075i	$0.576745\pi$
$360$	12.1315	0.639389
$361$	−18.9866	−0.999294
$362$	−53.0627	−2.78891
$363$	1.21378	0.0637071
$364$	−121.552	−6.37107
$365$	−5.79144	−0.303138
$366$	25.2134	1.31793
$367$	−10.6878	−0.557896	−0.278948	−	0.960306i	$-0.589986\pi$
$367$	−10.6878	−0.557896	−0.278948	+	0.960306i	$0.589986\pi$
$368$	36.4033	1.89765
$369$	−14.9065	−0.776003
$370$	2.27683	0.118367
$371$	−42.4008	−2.20134
$372$	51.5835	2.67448
$373$	13.7908	0.714061	0.357031	−	0.934093i	$-0.383789\pi$
$373$	13.7908	0.714061	0.357031	+	0.934093i	$0.383789\pi$
$374$	−2.62978	−0.135983
$375$	−11.2276	−0.579790
$376$	−40.1297	−2.06953
$377$	−42.2585	−2.17642
$378$	71.8975	3.69801
$379$	−16.4202	−0.843449	−0.421725	−	0.906724i	$-0.638575\pi$
$379$	−16.4202	−0.843449	−0.421725	+	0.906724i	$0.638575\pi$
$380$	0.590035	0.0302681
$381$	−17.7779	−0.910789
$382$	−62.3937	−3.19234
$383$	20.4116	1.04298	0.521491	−	0.853257i	$-0.325376\pi$
$383$	20.4116	1.04298	0.521491	+	0.853257i	$0.325376\pi$
$384$	−4.66859	−0.238243
$385$	5.15646	0.262798
$386$	−30.6242	−1.55873
$387$	−1.52673	−0.0776080
$388$	−48.2541	−2.44973
$389$	−32.2518	−1.63523	−0.817616	−	0.575764i	$-0.804705\pi$
$389$	−32.2518	−1.63523	−0.817616	+	0.575764i	$0.804705\pi$
$390$	16.4380	0.832371
$391$	3.52297	0.178164
$392$	−136.174	−6.87782
$393$	5.01181	0.252812
$394$	66.5631	3.35340
$395$	2.22446	0.111925
$396$	−7.50502	−0.377142
$397$	−30.2330	−1.51735	−0.758676	−	0.651468i	$-0.774153\pi$
$397$	−30.2330	−1.51735	−0.758676	+	0.651468i	$0.774153\pi$
$398$	32.5714	1.63266
$399$	0.699541	0.0350209
$400$	−40.5688	−2.02844
$401$	21.8202	1.08965	0.544825	−	0.838549i	$-0.316596\pi$
$401$	21.8202	1.08965	0.544825	+	0.838549i	$0.316596\pi$
$402$	−11.8659	−0.591817
$403$	−42.9620	−2.14009
$404$	46.6683	2.32184
$405$	−2.16473	−0.107566
$406$	−111.275	−5.52248
$407$	−0.835464	−0.0414124
$408$	−9.30705	−0.460767
$409$	−24.5741	−1.21511	−0.607555	−	0.794278i	$-0.707850\pi$
$409$	−24.5741	−1.21511	−0.607555	+	0.794278i	$0.707850\pi$
$410$	−26.6084	−1.31409
$411$	12.2966	0.606549
$412$	79.9349	3.93811
$413$	36.2764	1.78505
$414$	14.1446	0.695169
$415$	−13.9126	−0.682944
$416$	58.8293	2.88434
$417$	−12.6820	−0.621040
$418$	−0.304596	−0.0148983
$419$	31.3993	1.53396	0.766978	−	0.641673i	$-0.221759\pi$
$419$	31.3993	1.53396	0.766978	+	0.641673i	$0.221759\pi$
$420$	30.7669	1.50127
$421$	22.7285	1.10772	0.553859	−	0.832611i	$-0.313155\pi$
$421$	22.7285	1.10772	0.553859	+	0.832611i	$0.313155\pi$
$422$	44.1116	2.14732
$423$	−7.99020	−0.388497
$424$	65.3396	3.17317
$425$	−3.92609	−0.190443
$426$	−35.6783	−1.72862
$427$	−39.3042	−1.90206
$428$	−28.5345	−1.37927
$429$	−6.03179	−0.291218
$430$	−2.72523	−0.131422
$431$	15.3846	0.741049	0.370524	−	0.928823i	$-0.379178\pi$
$431$	15.3846	0.741049	0.370524	+	0.928823i	$0.379178\pi$
$432$	−56.7750	−2.73159
$433$	−9.67705	−0.465049	−0.232525	−	0.972591i	$-0.574699\pi$
$433$	−9.67705	−0.465049	−0.232525	+	0.972591i	$0.574699\pi$
$434$	−113.127	−5.43028
$435$	10.6963	0.512849
$436$	−41.5800	−1.99132
$437$	0.408049	0.0195196
$438$	17.8387	0.852368
$439$	22.7811	1.08728	0.543640	−	0.839318i	$-0.317046\pi$
$439$	22.7811	1.08728	0.543640	+	0.839318i	$0.317046\pi$
$440$	−7.94610	−0.378816
$441$	−27.1135	−1.29112
$442$	13.0685	0.621604
$443$	14.2396	0.676542	0.338271	−	0.941049i	$-0.390158\pi$
$443$	14.2396	0.676542	0.338271	+	0.941049i	$0.390158\pi$
$444$	−4.98493	−0.236574
$445$	−6.20625	−0.294205
$446$	−17.6791	−0.837128
$447$	−3.43103	−0.162282
$448$	52.0765	2.46038
$449$	29.2643	1.38107	0.690535	−	0.723299i	$-0.257375\pi$
$449$	29.2643	1.38107	0.690535	+	0.723299i	$0.257375\pi$
$450$	−15.7631	−0.743081
$451$	9.76371	0.459755
$452$	−28.9652	−1.36241
$453$	−4.15946	−0.195428
$454$	−20.6863	−0.970855
$455$	−25.6246	−1.20130
$456$	−1.07799	−0.0504816
$457$	−7.69030	−0.359737	−0.179869	−	0.983691i	$-0.557567\pi$
$457$	−7.69030	−0.359737	−0.179869	+	0.983691i	$0.557567\pi$
$458$	8.69340	0.406216
$459$	−5.49447	−0.256460
$460$	17.9466	0.836765
$461$	−6.72941	−0.313420	−0.156710	−	0.987645i	$-0.550089\pi$
$461$	−6.72941	−0.313420	−0.156710	+	0.987645i	$0.550089\pi$
$462$	−15.8829	−0.738938
$463$	15.5697	0.723585	0.361792	−	0.932259i	$-0.382165\pi$
$463$	15.5697	0.723585	0.361792	+	0.932259i	$0.382165\pi$
$464$	87.8701	4.07927
$465$	10.8744	0.504287
$466$	−75.7594	−3.50948
$467$	−19.1722	−0.887182	−0.443591	−	0.896229i	$-0.646296\pi$
$467$	−19.1722	−0.887182	−0.443591	+	0.896229i	$0.646296\pi$
$468$	37.2955	1.72399
$469$	18.4973	0.854125
$470$	−14.2626	−0.657885
$471$	12.8473	0.591973
$472$	−55.9019	−2.57309
$473$	1.00000	0.0459800
$474$	−6.85177	−0.314712
$475$	−0.454741	−0.0208650
$476$	24.4601	1.12113
$477$	13.0097	0.595674
$478$	61.2387	2.80099
$479$	−12.8179	−0.585663	−0.292831	−	0.956164i	$-0.594597\pi$
$479$	−12.8179	−0.585663	−0.292831	+	0.956164i	$0.594597\pi$
$480$	−14.8906	−0.679662
$481$	4.15177	0.189304
$482$	23.9411	1.09049
$483$	21.2774	0.968155
$484$	4.91575	0.223443
$485$	−10.1725	−0.461910
$486$	−36.6800	−1.66384
$487$	−13.2869	−0.602085	−0.301042	−	0.953611i	$-0.597335\pi$
$487$	−13.2869	−0.602085	−0.301042	+	0.953611i	$0.597335\pi$
$488$	60.5677	2.74177
$489$	−7.41717	−0.335416
$490$	−48.3979	−2.18639
$491$	31.7364	1.43224	0.716122	−	0.697975i	$-0.245915\pi$
$491$	31.7364	1.43224	0.716122	+	0.697975i	$0.245915\pi$
$492$	58.2567	2.62642
$493$	8.50373	0.382989
$494$	1.51366	0.0681028
$495$	−1.58214	−0.0711120
$496$	89.3328	4.01116
$497$	55.6175	2.49479
$498$	42.8535	1.92031
$499$	37.8117	1.69269	0.846343	−	0.532638i	$-0.178799\pi$
$499$	37.8117	1.69269	0.846343	+	0.532638i	$0.178799\pi$
$500$	−45.4711	−2.03353
$501$	−5.90495	−0.263814
$502$	−52.4045	−2.33893
$503$	−11.5504	−0.515009	−0.257504	−	0.966277i	$-0.582900\pi$
$503$	−11.5504	−0.515009	−0.257504	+	0.966277i	$0.582900\pi$
$504$	58.2507	2.59469
$505$	9.83821	0.437794
$506$	−9.26464	−0.411863
$507$	14.1952	0.630433
$508$	−71.9994	−3.19446
$509$	−0.790255	−0.0350274	−0.0175137	−	0.999847i	$-0.505575\pi$
$509$	−0.790255	−0.0350274	−0.0175137	+	0.999847i	$0.505575\pi$
$510$	−3.30784	−0.146474
$511$	−27.8081	−1.23016
$512$	36.1382	1.59710
$513$	−0.636399	−0.0280977
$514$	−38.1353	−1.68208
$515$	16.8512	0.742551
$516$	5.96666	0.262668
$517$	5.23354	0.230171
$518$	10.9324	0.480343
$519$	6.57082	0.288427
$520$	39.4874	1.73164
$521$	37.3316	1.63553	0.817763	−	0.575554i	$-0.195214\pi$
$521$	37.3316	1.63553	0.817763	+	0.575554i	$0.195214\pi$
$522$	34.1422	1.49436
$523$	−23.1091	−1.01049	−0.505246	−	0.862976i	$-0.668598\pi$
$523$	−23.1091	−1.01049	−0.505246	+	0.862976i	$0.668598\pi$
$524$	20.2975	0.886702
$525$	−23.7121	−1.03488
$526$	28.8821	1.25932
$527$	8.64528	0.376594
$528$	12.5422	0.545828
$529$	−10.5887	−0.460378
$530$	23.2225	1.00872
$531$	−11.1306	−0.483026
$532$	2.83310	0.122831
$533$	−48.5199	−2.10163
$534$	19.1164	0.827249
$535$	−6.01539	−0.260068
$536$	−28.5043	−1.23120
$537$	24.9675	1.07743
$538$	39.6816	1.71079
$539$	17.7592	0.764942
$540$	−27.9898	−1.20449
$541$	36.6252	1.57464	0.787320	−	0.616545i	$-0.211468\pi$
$541$	36.6252	1.57464	0.787320	+	0.616545i	$0.211468\pi$
$542$	−16.3263	−0.701273
$543$	24.4912	1.05102
$544$	−11.8383	−0.507562
$545$	−8.76552	−0.375473
$546$	78.9285	3.37783
$547$	−25.0970	−1.07307	−0.536534	−	0.843879i	$-0.680267\pi$
$547$	−25.0970	−1.07307	−0.536534	+	0.843879i	$0.680267\pi$
$548$	49.8007	2.12738
$549$	12.0596	0.514691
$550$	10.3248	0.440249
$551$	0.984948	0.0419602
$552$	−32.7884	−1.39557
$553$	10.6810	0.454200
$554$	3.91276	0.166237
$555$	−1.05088	−0.0446073
$556$	−51.3614	−2.17821
$557$	1.55372	0.0658333	0.0329166	−	0.999458i	$-0.489520\pi$
$557$	1.55372	0.0658333	0.0329166	+	0.999458i	$0.489520\pi$
$558$	34.7105	1.46941
$559$	−4.96941	−0.210184
$560$	53.2824	2.25159
$561$	1.21378	0.0512460
$562$	13.4131	0.565796
$563$	−31.7562	−1.33836	−0.669182	−	0.743098i	$-0.733355\pi$
$563$	−31.7562	−1.33836	−0.669182	+	0.743098i	$0.733355\pi$
$564$	31.2268	1.31488
$565$	−6.10619	−0.256889
$566$	−59.7979	−2.51349
$567$	−10.3941	−0.436512
$568$	−85.7065	−3.59616
$569$	19.0309	0.797815	0.398907	−	0.916991i	$-0.369389\pi$
$569$	19.0309	0.797815	0.398907	+	0.916991i	$0.369389\pi$
$570$	−0.383132	−0.0160476
$571$	−26.2124	−1.09696	−0.548478	−	0.836165i	$-0.684793\pi$
$571$	−26.2124	−1.09696	−0.548478	+	0.836165i	$0.684793\pi$
$572$	−24.4284	−1.02140
$573$	28.7980	1.20305
$574$	−127.762	−5.33270
$575$	−13.8315	−0.576813
$576$	−15.9785	−0.665771
$577$	−28.9969	−1.20716	−0.603578	−	0.797304i	$-0.706259\pi$
$577$	−28.9969	−1.20716	−0.603578	+	0.797304i	$0.706259\pi$
$578$	−2.62978	−0.109385
$579$	14.1347	0.587418
$580$	43.3195	1.79874
$581$	−66.8026	−2.77144
$582$	31.3333	1.29881
$583$	−8.52130	−0.352916
$584$	42.8523	1.77324
$585$	7.86232	0.325067
$586$	−62.4923	−2.58153
$587$	−47.8729	−1.97593	−0.987963	−	0.154691i	$-0.950562\pi$
$587$	−47.8729	−1.97593	−0.987963	+	0.154691i	$0.950562\pi$
$588$	105.963	4.36984
$589$	1.00134	0.0412596
$590$	−19.8682	−0.817963
$591$	−30.7224	−1.26375
$592$	−8.63296	−0.354812
$593$	0.231760	0.00951726	0.00475863	−	0.999989i	$-0.498485\pi$
$593$	0.231760	0.00951726	0.00475863	+	0.999989i	$0.498485\pi$
$594$	14.4493	0.592860
$595$	5.15646	0.211394
$596$	−13.8955	−0.569180
$597$	−15.0334	−0.615278
$598$	46.0398	1.88271
$599$	−15.3181	−0.625881	−0.312940	−	0.949773i	$-0.601314\pi$
$599$	−15.3181	−0.625881	−0.312940	+	0.949773i	$0.601314\pi$
$600$	36.5403	1.49175
$601$	−22.3648	−0.912277	−0.456139	−	0.889909i	$-0.650768\pi$
$601$	−22.3648	−0.912277	−0.456139	+	0.889909i	$0.650768\pi$
$602$	−13.0854	−0.533322
$603$	−5.67547	−0.231123
$604$	−16.8456	−0.685436
$605$	1.03630	0.0421314
$606$	−30.3035	−1.23100
$607$	−13.6268	−0.553096	−0.276548	−	0.961000i	$-0.589190\pi$
$607$	−13.6268	−0.553096	−0.276548	+	0.961000i	$0.589190\pi$
$608$	−1.37117	−0.0556084
$609$	51.3593	2.08118
$610$	21.5265	0.871583
$611$	−26.0076	−1.05216
$612$	−7.50502	−0.303373
$613$	26.8510	1.08450	0.542251	−	0.840217i	$-0.317572\pi$
$613$	26.8510	1.08450	0.542251	+	0.840217i	$0.317572\pi$
$614$	27.8408	1.12356
$615$	12.2812	0.495224
$616$	−38.1539	−1.53726
$617$	16.9338	0.681730	0.340865	−	0.940112i	$-0.389280\pi$
$617$	16.9338	0.681730	0.340865	+	0.940112i	$0.389280\pi$
$618$	−51.9048	−2.08792
$619$	31.8729	1.28108	0.640539	−	0.767925i	$-0.278711\pi$
$619$	31.8729	1.28108	0.640539	+	0.767925i	$0.278711\pi$
$620$	44.0406	1.76871
$621$	−19.3568	−0.776763
$622$	−31.1759	−1.25004
$623$	−29.7999	−1.19391
$624$	−62.3272	−2.49509
$625$	10.0447	0.401786
$626$	−51.6389	−2.06391
$627$	0.140587	0.00561450
$628$	52.0309	2.07626
$629$	−0.835464	−0.0333121
$630$	20.7030	0.824828
$631$	30.7997	1.22612	0.613059	−	0.790037i	$-0.289939\pi$
$631$	30.7997	1.22612	0.613059	+	0.790037i	$0.289939\pi$
$632$	−16.4593	−0.654717
$633$	−20.3599	−0.809231
$634$	4.76364	0.189188
$635$	−15.1783	−0.602332
$636$	−50.8437	−2.01608
$637$	−88.2527	−3.49670
$638$	−22.3630	−0.885358
$639$	−17.0650	−0.675079
$640$	−3.98591	−0.157557
$641$	16.7851	0.662973	0.331486	−	0.943460i	$-0.392450\pi$
$641$	16.7851	0.662973	0.331486	+	0.943460i	$0.392450\pi$
$642$	18.5285	0.731263
$643$	−18.0719	−0.712685	−0.356343	−	0.934355i	$-0.615976\pi$
$643$	−18.0719	−0.712685	−0.356343	+	0.934355i	$0.615976\pi$
$644$	86.1722	3.39566
$645$	1.25784	0.0495273
$646$	−0.304596	−0.0119842
$647$	−43.3220	−1.70316	−0.851582	−	0.524221i	$-0.824356\pi$
$647$	−43.3220	−1.70316	−0.851582	+	0.524221i	$0.824356\pi$
$648$	16.0173	0.629220
$649$	7.29048	0.286176
$650$	−51.3080	−2.01247
$651$	52.2142	2.04644
$652$	−30.0391	−1.17642
$653$	−26.7302	−1.04603	−0.523017	−	0.852322i	$-0.675194\pi$
$653$	−26.7302	−1.04603	−0.523017	+	0.852322i	$0.675194\pi$
$654$	26.9995	1.05576
$655$	4.27895	0.167192
$656$	100.890	3.93908
$657$	8.53228	0.332876
$658$	−68.4831	−2.66975
$659$	3.17322	0.123611	0.0618056	−	0.998088i	$-0.480314\pi$
$659$	3.17322	0.123611	0.0618056	+	0.998088i	$0.480314\pi$
$660$	6.18322	0.240682
$661$	28.2017	1.09692	0.548460	−	0.836177i	$-0.315214\pi$
$661$	28.2017	1.09692	0.548460	+	0.836177i	$0.315214\pi$
$662$	79.9493	3.10732
$663$	−6.03179	−0.234255
$664$	102.943	3.99496
$665$	0.597249	0.0231603
$666$	−3.35436	−0.129979
$667$	29.9584	1.15999
$668$	−23.9147	−0.925288
$669$	8.15983	0.315477
$670$	−10.1308	−0.391386
$671$	−7.89897	−0.304936
$672$	−71.4987	−2.75812
$673$	−10.2936	−0.396790	−0.198395	−	0.980122i	$-0.563573\pi$
$673$	−10.2936	−0.396790	−0.198395	+	0.980122i	$0.563573\pi$
$674$	−79.6451	−3.06781
$675$	21.5718	0.830299
$676$	57.4899	2.21115
$677$	9.30249	0.357524	0.178762	−	0.983892i	$-0.442791\pi$
$677$	9.30249	0.357524	0.178762	+	0.983892i	$0.442791\pi$
$678$	18.8082	0.722326
$679$	−48.8442	−1.87447
$680$	−7.94610	−0.304719
$681$	9.54781	0.365873
$682$	−22.7352	−0.870576
$683$	−26.7065	−1.02190	−0.510948	−	0.859611i	$-0.670706\pi$
$683$	−26.7065	−1.02190	−0.510948	+	0.859611i	$0.670706\pi$
$684$	−0.869273	−0.0332375
$685$	10.4985	0.401129
$686$	−140.789	−5.37533
$687$	−4.01246	−0.153085
$688$	10.3331	0.393947
$689$	42.3458	1.61325
$690$	−11.6534	−0.443638
$691$	33.4352	1.27194	0.635968	−	0.771715i	$-0.280601\pi$
$691$	33.4352	1.27194	0.635968	+	0.771715i	$0.280601\pi$
$692$	26.6114	1.01161
$693$	−7.59679	−0.288578
$694$	−26.2730	−0.997310
$695$	−10.8275	−0.410712
$696$	−79.1446	−2.99997
$697$	9.76371	0.369827
$698$	−38.2565	−1.44803
$699$	34.9670	1.32257
$700$	−96.0326	−3.62969
$701$	−7.39066	−0.279142	−0.139571	−	0.990212i	$-0.544572\pi$
$701$	−7.39066	−0.279142	−0.139571	+	0.990212i	$0.544572\pi$
$702$	−71.8043	−2.71008
$703$	−0.0967680	−0.00364967
$704$	10.4658	0.394446
$705$	6.58295	0.247928
$706$	−60.9805	−2.29503
$707$	47.2390	1.77660
$708$	43.4998	1.63482
$709$	−45.3080	−1.70158	−0.850788	−	0.525509i	$-0.823875\pi$
$709$	−45.3080	−1.70158	−0.850788	+	0.525509i	$0.823875\pi$
$710$	−30.4612	−1.14319
$711$	−3.27721	−0.122905
$712$	45.9215	1.72098
$713$	30.4571	1.14063
$714$	−15.8829	−0.594402
$715$	−5.14978	−0.192591
$716$	101.117	3.77891
$717$	−28.2649	−1.05557
$718$	23.7948	0.888013
$719$	−9.05235	−0.337596	−0.168798	−	0.985651i	$-0.553988\pi$
$719$	−9.05235	−0.337596	−0.168798	+	0.985651i	$0.553988\pi$
$720$	−16.3485	−0.609272
$721$	80.9123	3.01333
$722$	49.9306	1.85822
$723$	−11.0501	−0.410957
$724$	99.1880	3.68629
$725$	−33.3864	−1.23994
$726$	−3.19199	−0.118466
$727$	34.0948	1.26451	0.632253	−	0.774762i	$-0.282130\pi$
$727$	34.0948	1.26451	0.632253	+	0.774762i	$0.282130\pi$
$728$	189.602	7.02713
$729$	23.1965	0.859129
$730$	15.2302	0.563696
$731$	1.00000	0.0369863
$732$	−47.1305	−1.74199
$733$	10.3204	0.381192	0.190596	−	0.981669i	$-0.438958\pi$
$733$	10.3204	0.381192	0.190596	+	0.981669i	$0.438958\pi$
$734$	28.1065	1.03743
$735$	22.3382	0.823957
$736$	−41.7059	−1.53730
$737$	3.71740	0.136932
$738$	39.2009	1.44301
$739$	17.1350	0.630320	0.315160	−	0.949039i	$-0.397942\pi$
$739$	17.1350	0.630320	0.315160	+	0.949039i	$0.397942\pi$
$740$	−4.25600	−0.156454
$741$	−0.698634	−0.0256650
$742$	111.505	4.09347
$743$	7.78464	0.285591	0.142795	−	0.989752i	$-0.454391\pi$
$743$	7.78464	0.285591	0.142795	+	0.989752i	$0.454391\pi$
$744$	−80.4620	−2.94988
$745$	−2.92932	−0.107322
$746$	−36.2668	−1.32782
$747$	20.4969	0.749941
$748$	4.91575	0.179738
$749$	−28.8834	−1.05538
$750$	29.5261	1.07814
$751$	25.2267	0.920535	0.460267	−	0.887780i	$-0.347754\pi$
$751$	25.2267	0.920535	0.460267	+	0.887780i	$0.347754\pi$
$752$	54.0788	1.97205
$753$	24.1874	0.881439
$754$	111.131	4.04714
$755$	−3.55123	−0.129243
$756$	−134.395	−4.88791
$757$	−49.7924	−1.80974	−0.904868	−	0.425691i	$-0.860031\pi$
$757$	−49.7924	−1.80974	−0.904868	+	0.425691i	$0.860031\pi$
$758$	43.1815	1.56842
$759$	4.27612	0.155213
$760$	−0.920360	−0.0333850
$761$	40.7943	1.47879	0.739397	−	0.673270i	$-0.235111\pi$
$761$	40.7943	1.47879	0.739397	+	0.673270i	$0.235111\pi$
$762$	46.7520	1.69365
$763$	−42.0884	−1.52370
$764$	116.630	4.21953
$765$	−1.58214	−0.0572025
$766$	−53.6780	−1.93946
$767$	−36.2294	−1.30817
$768$	−13.1291	−0.473757
$769$	−12.0482	−0.434470	−0.217235	−	0.976119i	$-0.569704\pi$
$769$	−12.0482	−0.434470	−0.217235	+	0.976119i	$0.569704\pi$
$770$	−13.5604	−0.488682
$771$	17.6015	0.633902
$772$	57.2447	2.06028
$773$	53.7991	1.93502	0.967509	−	0.252835i	$-0.0813629\pi$
$773$	53.7991	1.93502	0.967509	+	0.252835i	$0.0813629\pi$
$774$	4.01497	0.144315
$775$	−33.9422	−1.21924
$776$	75.2688	2.70199
$777$	−5.04589	−0.181020
$778$	84.8153	3.04077
$779$	1.13089	0.0405182
$780$	−30.7270	−1.10020
$781$	11.1775	0.399961
$782$	−9.26464	−0.331303
$783$	−46.7235	−1.66976
$784$	183.508	6.55386
$785$	10.9687	0.391489
$786$	−13.1800	−0.470114
$787$	−1.03362	−0.0368446	−0.0184223	−	0.999830i	$-0.505864\pi$
$787$	−1.03362	−0.0368446	−0.0184223	+	0.999830i	$0.505864\pi$
$788$	−124.424	−4.43242
$789$	−13.3306	−0.474583
$790$	−5.84986	−0.208129
$791$	−29.3194	−1.04248
$792$	11.7066	0.415978
$793$	39.2532	1.39392
$794$	79.5063	2.82157
$795$	−10.7184	−0.380143
$796$	−60.8846	−2.15800
$797$	21.6744	0.767748	0.383874	−	0.923385i	$-0.374590\pi$
$797$	21.6744	0.767748	0.383874	+	0.923385i	$0.374590\pi$
$798$	−1.83964	−0.0651226
$799$	5.23354	0.185149
$800$	46.4782	1.64325
$801$	9.14340	0.323066
$802$	−57.3825	−2.02625
$803$	−5.58860	−0.197217
$804$	22.1805	0.782245
$805$	18.1661	0.640269
$806$	112.981	3.97957
$807$	−18.3151	−0.644723
$808$	−72.7952	−2.56093
$809$	−52.6705	−1.85180	−0.925898	−	0.377775i	$-0.876689\pi$
$809$	−52.6705	−1.85180	−0.925898	+	0.377775i	$0.876689\pi$
$810$	5.69276	0.200023
$811$	−37.1172	−1.30336	−0.651681	−	0.758493i	$-0.725936\pi$
$811$	−37.1172	−1.30336	−0.651681	+	0.758493i	$0.725936\pi$
$812$	208.002	7.29944
$813$	7.53543	0.264279
$814$	2.19709	0.0770079
$815$	−6.33258	−0.221821
$816$	12.5422	0.439064
$817$	0.115825	0.00405222
$818$	64.6245	2.25954
$819$	37.7516	1.31915
$820$	49.7380	1.73693
$821$	−7.74209	−0.270201	−0.135100	−	0.990832i	$-0.543136\pi$
$821$	−7.74209	−0.270201	−0.135100	+	0.990832i	$0.543136\pi$
$822$	−32.3375	−1.12790
$823$	12.0480	0.419967	0.209983	−	0.977705i	$-0.432659\pi$
$823$	12.0480	0.419967	0.209983	+	0.977705i	$0.432659\pi$
$824$	−124.686	−4.34364
$825$	−4.76543	−0.165911
$826$	−95.3991	−3.31936
$827$	41.7322	1.45117	0.725586	−	0.688132i	$-0.241569\pi$
$827$	41.7322	1.45117	0.725586	+	0.688132i	$0.241569\pi$
$828$	−26.4400	−0.918852
$829$	29.4084	1.02140	0.510699	−	0.859760i	$-0.329387\pi$
$829$	29.4084	1.02140	0.510699	+	0.859760i	$0.329387\pi$
$830$	36.5872	1.26996
$831$	−1.80594	−0.0626475
$832$	−52.0090	−1.80309
$833$	17.7592	0.615319
$834$	33.3509	1.15485
$835$	−5.04149	−0.174468
$836$	0.569369	0.0196920
$837$	−47.5012	−1.64188
$838$	−82.5733	−2.85245
$839$	1.86735	0.0644681	0.0322340	−	0.999480i	$-0.489738\pi$
$839$	1.86735	0.0644681	0.0322340	+	0.999480i	$0.489738\pi$
$840$	−47.9914	−1.65586
$841$	43.3134	1.49357
$842$	−59.7709	−2.05984
$843$	−6.19084	−0.213224
$844$	−82.4562	−2.83826
$845$	12.1195	0.416924
$846$	21.0125	0.722424
$847$	4.97586	0.170973
$848$	−88.0517	−3.02371
$849$	27.5999	0.947226
$850$	10.3248	0.354137
$851$	−2.94331	−0.100896
$852$	66.6921	2.28483
$853$	18.1574	0.621697	0.310848	−	0.950459i	$-0.399387\pi$
$853$	18.1574	0.621697	0.310848	+	0.950459i	$0.399387\pi$
$854$	103.361	3.53695
$855$	−0.183252	−0.00626710
$856$	44.5093	1.52130
$857$	27.3385	0.933866	0.466933	−	0.884293i	$-0.345359\pi$
$857$	27.3385	0.933866	0.466933	+	0.884293i	$0.345359\pi$
$858$	15.8623	0.541530
$859$	−20.6920	−0.706002	−0.353001	−	0.935623i	$-0.614839\pi$
$859$	−20.6920	−0.706002	−0.353001	+	0.935623i	$0.614839\pi$
$860$	5.09417	0.173710
$861$	58.9691	2.00966
$862$	−40.4581	−1.37801
$863$	−26.8048	−0.912447	−0.456223	−	0.889865i	$-0.650798\pi$
$863$	−26.8048	−0.912447	−0.456223	+	0.889865i	$0.650798\pi$
$864$	65.0450	2.21288
$865$	5.60998	0.190745
$866$	25.4485	0.864776
$867$	1.21378	0.0412223
$868$	211.465	7.17757
$869$	2.14655	0.0728169
$870$	−28.1290	−0.953662
$871$	−18.4733	−0.625944
$872$	64.8581	2.19637
$873$	14.9867	0.507224
$874$	−1.07308	−0.0362975
$875$	−46.0271	−1.55600
$876$	−33.3453	−1.12663
$877$	−20.9266	−0.706642	−0.353321	−	0.935502i	$-0.614948\pi$
$877$	−20.9266	−0.706642	−0.353321	+	0.935502i	$0.614948\pi$
$878$	−59.9092	−2.02184
$879$	28.8435	0.972867
$880$	10.7082	0.360972
$881$	1.70793	0.0575417	0.0287708	−	0.999586i	$-0.490841\pi$
$881$	1.70793	0.0575417	0.0287708	+	0.999586i	$0.490841\pi$
$882$	71.3025	2.40088
$883$	23.4126	0.787896	0.393948	−	0.919133i	$-0.371109\pi$
$883$	23.4126	0.787896	0.393948	+	0.919133i	$0.371109\pi$
$884$	−24.4284	−0.821616
$885$	9.17025	0.308254
$886$	−37.4470	−1.25806
$887$	−12.6990	−0.426390	−0.213195	−	0.977010i	$-0.568387\pi$
$887$	−12.6990	−0.426390	−0.213195	+	0.977010i	$0.568387\pi$
$888$	7.77571	0.260936
$889$	−72.8798	−2.44431
$890$	16.3211	0.547084
$891$	−2.08891	−0.0699811
$892$	33.0468	1.10649
$893$	0.606177	0.0202849
$894$	9.02285	0.301769
$895$	21.3165	0.712534
$896$	−19.1387	−0.639379
$897$	−21.2498	−0.709510
$898$	−76.9589	−2.56815
$899$	73.5171	2.45193
$900$	29.4654	0.982181
$901$	−8.52130	−0.283886
$902$	−25.6764	−0.854931
$903$	6.03962	0.200986
$904$	45.1812	1.50270
$905$	20.9099	0.695070
$906$	10.9385	0.363406
$907$	−30.9849	−1.02884	−0.514418	−	0.857540i	$-0.671992\pi$
$907$	−30.9849	−1.02884	−0.514418	+	0.857540i	$0.671992\pi$
$908$	38.6681	1.28325
$909$	−14.4942	−0.480742
$910$	67.3870	2.23386
$911$	12.2549	0.406022	0.203011	−	0.979176i	$-0.434927\pi$
$911$	12.2549	0.406022	0.203011	+	0.979176i	$0.434927\pi$
$912$	1.45270	0.0481038
$913$	−13.4253	−0.444314
$914$	20.2238	0.668945
$915$	−9.93563	−0.328462
$916$	−16.2502	−0.536923
$917$	20.5457	0.678480
$918$	14.4493	0.476897
$919$	−27.6284	−0.911378	−0.455689	−	0.890139i	$-0.650607\pi$
$919$	−27.6284	−0.911378	−0.455689	+	0.890139i	$0.650607\pi$
$920$	−27.9939	−0.922930
$921$	−12.8500	−0.423422
$922$	17.6969	0.582816
$923$	−55.5454	−1.82830
$924$	29.6893	0.976705
$925$	3.28011	0.107849
$926$	−40.9449	−1.34553
$927$	−24.8261	−0.815396
$928$	−100.669	−3.30464
$929$	46.0754	1.51168	0.755842	−	0.654754i	$-0.227228\pi$
$929$	46.0754	1.51168	0.755842	+	0.654754i	$0.227228\pi$
$930$	−28.5972	−0.937740
$931$	2.05697	0.0674143
$932$	141.614	4.63873
$933$	14.3893	0.471086
$934$	50.4186	1.64975
$935$	1.03630	0.0338905
$936$	−58.1751	−1.90151
$937$	5.10047	0.166625	0.0833125	−	0.996523i	$-0.473450\pi$
$937$	5.10047	0.166625	0.0833125	+	0.996523i	$0.473450\pi$
$938$	−48.6438	−1.58828
$939$	23.8341	0.777796
$940$	26.6606	0.869571
$941$	−31.9030	−1.04001	−0.520004	−	0.854164i	$-0.674069\pi$
$941$	−31.9030	−1.04001	−0.520004	+	0.854164i	$0.674069\pi$
$942$	−33.7856	−1.10080
$943$	34.3972	1.12013
$944$	75.3334	2.45189
$945$	−28.3320	−0.921641
$946$	−2.62978	−0.0855016
$947$	−59.6795	−1.93932	−0.969662	−	0.244450i	$-0.921393\pi$
$947$	−59.6795	−1.93932	−0.969662	+	0.244450i	$0.921393\pi$
$948$	12.8078	0.415977
$949$	27.7721	0.901519
$950$	1.19587	0.0387991
$951$	−2.19867	−0.0712969
$952$	−38.1539	−1.23657
$953$	52.9918	1.71657	0.858286	−	0.513172i	$-0.171530\pi$
$953$	52.9918	1.71657	0.858286	+	0.513172i	$0.171530\pi$
$954$	−34.2127	−1.10768
$955$	24.5869	0.795614
$956$	−114.471	−3.70226
$957$	10.3217	0.333653
$958$	33.7082	1.08906
$959$	50.4097	1.62781
$960$	13.1643	0.424877
$961$	43.7409	1.41100
$962$	−10.9182	−0.352018
$963$	8.86221	0.285581
$964$	−44.7522	−1.44137
$965$	12.0678	0.388477
$966$	−55.9549	−1.80032
$967$	55.6147	1.78845	0.894224	−	0.447619i	$-0.147728\pi$
$967$	55.6147	1.78845	0.894224	+	0.447619i	$0.147728\pi$
$968$	−7.66780	−0.246452
$969$	0.140587	0.00451630
$970$	26.7515	0.858938
$971$	−40.8904	−1.31224	−0.656118	−	0.754658i	$-0.727803\pi$
$971$	−40.8904	−1.31224	−0.656118	+	0.754658i	$0.727803\pi$
$972$	68.5646	2.19921
$973$	−51.9894	−1.66670
$974$	34.9415	1.11960
$975$	23.6814	0.758410
$976$	−81.6211	−2.61263
$977$	26.0233	0.832560	0.416280	−	0.909236i	$-0.363334\pi$
$977$	26.0233	0.832560	0.416280	+	0.909236i	$0.363334\pi$
$978$	19.5055	0.623718
$979$	−5.98888	−0.191406
$980$	90.4684	2.88991
$981$	12.9139	0.412308
$982$	−83.4599	−2.66331
$983$	12.8524	0.409929	0.204965	−	0.978769i	$-0.434292\pi$
$983$	12.8524	0.409929	0.204965	+	0.978769i	$0.434292\pi$
$984$	−90.8713	−2.89687
$985$	−26.2300	−0.835756
$986$	−22.3630	−0.712181
$987$	31.6086	1.00611
$988$	−2.82943	−0.0900161
$989$	3.52297	0.112024
$990$	4.16069	0.132235
$991$	51.8628	1.64748	0.823738	−	0.566970i	$-0.191884\pi$
$991$	51.8628	1.64748	0.823738	+	0.566970i	$0.191884\pi$
$992$	−102.345	−3.24946
$993$	−36.9008	−1.17101
$994$	−146.262	−4.63915
$995$	−12.8351	−0.406902
$996$	−80.1045	−2.53821
$997$	16.3044	0.516367	0.258183	−	0.966096i	$-0.416876\pi$
$997$	16.3044	0.516367	0.258183	+	0.966096i	$0.416876\pi$
$998$	−99.4366	−3.14761
$999$	4.59043	0.145235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.4	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.62978 q^{2} +1.21378 q^{3} +4.91575 q^{4} +1.03630 q^{5} -3.19199 q^{6} +4.97586 q^{7} -7.66780 q^{8} -1.52673 q^{9} +O(q^{10})\)	\(q-2.62978 q^{2} +1.21378 q^{3} +4.91575 q^{4} +1.03630 q^{5} -3.19199 q^{6} +4.97586 q^{7} -7.66780 q^{8} -1.52673 q^{9} -2.72523 q^{10} +1.00000 q^{11} +5.96666 q^{12} -4.96941 q^{13} -13.0854 q^{14} +1.25784 q^{15} +10.3331 q^{16} +1.00000 q^{17} +4.01497 q^{18} +0.115825 q^{19} +5.09417 q^{20} +6.03962 q^{21} -2.62978 q^{22} +3.52297 q^{23} -9.30705 q^{24} -3.92609 q^{25} +13.0685 q^{26} -5.49447 q^{27} +24.4601 q^{28} +8.50373 q^{29} -3.30784 q^{30} +8.64528 q^{31} -11.8383 q^{32} +1.21378 q^{33} -2.62978 q^{34} +5.15646 q^{35} -7.50502 q^{36} -0.835464 q^{37} -0.304596 q^{38} -6.03179 q^{39} -7.94610 q^{40} +9.76371 q^{41} -15.8829 q^{42} +1.00000 q^{43} +4.91575 q^{44} -1.58214 q^{45} -9.26464 q^{46} +5.23354 q^{47} +12.5422 q^{48} +17.7592 q^{49} +10.3248 q^{50} +1.21378 q^{51} -24.4284 q^{52} -8.52130 q^{53} +14.4493 q^{54} +1.03630 q^{55} -38.1539 q^{56} +0.140587 q^{57} -22.3630 q^{58} +7.29048 q^{59} +6.18322 q^{60} -7.89897 q^{61} -22.7352 q^{62} -7.59679 q^{63} +10.4658 q^{64} -5.14978 q^{65} -3.19199 q^{66} +3.71740 q^{67} +4.91575 q^{68} +4.27612 q^{69} -13.5604 q^{70} +11.1775 q^{71} +11.7066 q^{72} -5.58860 q^{73} +2.19709 q^{74} -4.76543 q^{75} +0.569369 q^{76} +4.97586 q^{77} +15.8623 q^{78} +2.14655 q^{79} +10.7082 q^{80} -2.08891 q^{81} -25.6764 q^{82} -13.4253 q^{83} +29.6893 q^{84} +1.03630 q^{85} -2.62978 q^{86} +10.3217 q^{87} -7.66780 q^{88} -5.98888 q^{89} +4.16069 q^{90} -24.7271 q^{91} +17.3180 q^{92} +10.4935 q^{93} -13.7631 q^{94} +0.120029 q^{95} -14.3691 q^{96} -9.81623 q^{97} -46.7028 q^{98} -1.52673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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