LMFDB - Embedded newform 8041.2.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.20191 q^{2} -3.02493 q^{3} +2.84839 q^{4} -2.51341 q^{5} +6.66061 q^{6} +0.0943373 q^{7} -1.86807 q^{8} +6.15021 q^{9} +O(q^{10})$	\(q-2.20191 q^{2} -3.02493 q^{3} +2.84839 q^{4} -2.51341 q^{5} +6.66061 q^{6} +0.0943373 q^{7} -1.86807 q^{8} +6.15021 q^{9} +5.53430 q^{10} -1.00000 q^{11} -8.61618 q^{12} -0.312302 q^{13} -0.207722 q^{14} +7.60290 q^{15} -1.58346 q^{16} +1.00000 q^{17} -13.5422 q^{18} -1.98225 q^{19} -7.15918 q^{20} -0.285364 q^{21} +2.20191 q^{22} -1.69155 q^{23} +5.65079 q^{24} +1.31725 q^{25} +0.687659 q^{26} -9.52917 q^{27} +0.268709 q^{28} +8.36378 q^{29} -16.7409 q^{30} +0.536821 q^{31} +7.22277 q^{32} +3.02493 q^{33} -2.20191 q^{34} -0.237109 q^{35} +17.5182 q^{36} +4.53940 q^{37} +4.36474 q^{38} +0.944692 q^{39} +4.69524 q^{40} -5.00226 q^{41} +0.628344 q^{42} +1.00000 q^{43} -2.84839 q^{44} -15.4580 q^{45} +3.72464 q^{46} +7.01459 q^{47} +4.78985 q^{48} -6.99110 q^{49} -2.90045 q^{50} -3.02493 q^{51} -0.889558 q^{52} +1.75407 q^{53} +20.9823 q^{54} +2.51341 q^{55} -0.176229 q^{56} +5.99618 q^{57} -18.4163 q^{58} -10.7882 q^{59} +21.6560 q^{60} +11.3461 q^{61} -1.18203 q^{62} +0.580194 q^{63} -12.7369 q^{64} +0.784944 q^{65} -6.66061 q^{66} -4.32328 q^{67} +2.84839 q^{68} +5.11683 q^{69} +0.522091 q^{70} -16.1463 q^{71} -11.4890 q^{72} +1.64407 q^{73} -9.99533 q^{74} -3.98458 q^{75} -5.64623 q^{76} -0.0943373 q^{77} -2.08012 q^{78} -9.53631 q^{79} +3.97988 q^{80} +10.3744 q^{81} +11.0145 q^{82} -13.4228 q^{83} -0.812827 q^{84} -2.51341 q^{85} -2.20191 q^{86} -25.2999 q^{87} +1.86807 q^{88} -2.33778 q^{89} +34.0371 q^{90} -0.0294617 q^{91} -4.81820 q^{92} -1.62385 q^{93} -15.4455 q^{94} +4.98222 q^{95} -21.8484 q^{96} -1.95333 q^{97} +15.3937 q^{98} -6.15021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.20191	−1.55698	−0.778491	−	0.627655i	$-0.784015\pi$
$2$	−2.20191	−1.55698	−0.778491	+	0.627655i	$0.784015\pi$
$3$	−3.02493	−1.74644	−0.873222	−	0.487322i	$-0.837974\pi$
$3$	−3.02493	−1.74644	−0.873222	+	0.487322i	$0.837974\pi$
$4$	2.84839	1.42419
$5$	−2.51341	−1.12403	−0.562016	−	0.827126i	$-0.689974\pi$
$5$	−2.51341	−1.12403	−0.562016	+	0.827126i	$0.689974\pi$
$6$	6.66061	2.71918
$7$	0.0943373	0.0356562	0.0178281	−	0.999841i	$-0.494325\pi$
$7$	0.0943373	0.0356562	0.0178281	+	0.999841i	$0.494325\pi$
$8$	−1.86807	−0.660464
$9$	6.15021	2.05007
$10$	5.53430	1.75010
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−8.61618	−2.48728
$13$	−0.312302	−0.0866170	−0.0433085	−	0.999062i	$-0.513790\pi$
$13$	−0.312302	−0.0866170	−0.0433085	+	0.999062i	$0.513790\pi$
$14$	−0.207722	−0.0555160
$15$	7.60290	1.96306
$16$	−1.58346	−0.395864
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−13.5422	−3.19192
$19$	−1.98225	−0.454760	−0.227380	−	0.973806i	$-0.573016\pi$
$19$	−1.98225	−0.454760	−0.227380	+	0.973806i	$0.573016\pi$
$20$	−7.15918	−1.60084
$21$	−0.285364	−0.0622715
$22$	2.20191	0.469448
$23$	−1.69155	−0.352713	−0.176357	−	0.984326i	$-0.556431\pi$
$23$	−1.69155	−0.352713	−0.176357	+	0.984326i	$0.556431\pi$
$24$	5.65079	1.15346
$25$	1.31725	0.263449
$26$	0.687659	0.134861
$27$	−9.52917	−1.83389
$28$	0.268709	0.0507813
$29$	8.36378	1.55312	0.776558	−	0.630046i	$-0.216964\pi$
$29$	8.36378	1.55312	0.776558	+	0.630046i	$0.216964\pi$
$30$	−16.7409	−3.05645
$31$	0.536821	0.0964160	0.0482080	−	0.998837i	$-0.484649\pi$
$31$	0.536821	0.0964160	0.0482080	+	0.998837i	$0.484649\pi$
$32$	7.22277	1.27682
$33$	3.02493	0.526573
$34$	−2.20191	−0.377624
$35$	−0.237109	−0.0400787
$36$	17.5182	2.91970
$37$	4.53940	0.746272	0.373136	−	0.927777i	$-0.378282\pi$
$37$	4.53940	0.746272	0.373136	+	0.927777i	$0.378282\pi$
$38$	4.36474	0.708054
$39$	0.944692	0.151272
$40$	4.69524	0.742383
$41$	−5.00226	−0.781222	−0.390611	−	0.920556i	$-0.627736\pi$
$41$	−5.00226	−0.781222	−0.390611	+	0.920556i	$0.627736\pi$
$42$	0.628344	0.0969556
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−2.84839	−0.429411
$45$	−15.4580	−2.30434
$46$	3.72464	0.549169
$47$	7.01459	1.02318	0.511592	−	0.859229i	$-0.329056\pi$
$47$	7.01459	1.02318	0.511592	+	0.859229i	$0.329056\pi$
$48$	4.78985	0.691355
$49$	−6.99110	−0.998729
$50$	−2.90045	−0.410186
$51$	−3.02493	−0.423575
$52$	−0.889558	−0.123359
$53$	1.75407	0.240941	0.120470	−	0.992717i	$-0.461560\pi$
$53$	1.75407	0.240941	0.120470	+	0.992717i	$0.461560\pi$
$54$	20.9823	2.85533
$55$	2.51341	0.338909
$56$	−0.176229	−0.0235496
$57$	5.99618	0.794214
$58$	−18.4163	−2.41817
$59$	−10.7882	−1.40451	−0.702253	−	0.711927i	$-0.747823\pi$
$59$	−10.7882	−1.40451	−0.702253	+	0.711927i	$0.747823\pi$
$60$	21.6560	2.79578
$61$	11.3461	1.45272	0.726360	−	0.687314i	$-0.241210\pi$
$61$	11.3461	1.45272	0.726360	+	0.687314i	$0.241210\pi$
$62$	−1.18203	−0.150118
$63$	0.580194	0.0730976
$64$	−12.7369	−1.59212
$65$	0.784944	0.0973603
$66$	−6.66061	−0.819865
$67$	−4.32328	−0.528173	−0.264086	−	0.964499i	$-0.585070\pi$
$67$	−4.32328	−0.528173	−0.264086	+	0.964499i	$0.585070\pi$
$68$	2.84839	0.345418
$69$	5.11683	0.615994
$70$	0.522091	0.0624018
$71$	−16.1463	−1.91621	−0.958107	−	0.286409i	$-0.907538\pi$
$71$	−16.1463	−1.91621	−0.958107	+	0.286409i	$0.907538\pi$
$72$	−11.4890	−1.35400
$73$	1.64407	0.192424	0.0962122	−	0.995361i	$-0.469327\pi$
$73$	1.64407	0.192424	0.0962122	+	0.995361i	$0.469327\pi$
$74$	−9.99533	−1.16193
$75$	−3.98458	−0.460099
$76$	−5.64623	−0.647667
$77$	−0.0943373	−0.0107507
$78$	−2.08012	−0.235528
$79$	−9.53631	−1.07292	−0.536459	−	0.843926i	$-0.680238\pi$
$79$	−9.53631	−1.07292	−0.536459	+	0.843926i	$0.680238\pi$
$80$	3.97988	0.444964
$81$	10.3744	1.15272
$82$	11.0145	1.21635
$83$	−13.4228	−1.47335	−0.736673	−	0.676250i	$-0.763604\pi$
$83$	−13.4228	−1.47335	−0.736673	+	0.676250i	$0.763604\pi$
$84$	−0.812827	−0.0886867
$85$	−2.51341	−0.272618
$86$	−2.20191	−0.237438
$87$	−25.2999	−2.71243
$88$	1.86807	0.199137
$89$	−2.33778	−0.247805	−0.123902	−	0.992294i	$-0.539541\pi$
$89$	−2.33778	−0.247805	−0.123902	+	0.992294i	$0.539541\pi$
$90$	34.0371	3.58782
$91$	−0.0294617	−0.00308843
$92$	−4.81820	−0.502332
$93$	−1.62385	−0.168385
$94$	−15.4455	−1.59308
$95$	4.98222	0.511165
$96$	−21.8484	−2.22989
$97$	−1.95333	−0.198331	−0.0991655	−	0.995071i	$-0.531617\pi$
$97$	−1.95333	−0.198331	−0.0991655	+	0.995071i	$0.531617\pi$
$98$	15.3937	1.55500
$99$	−6.15021	−0.618119
$100$	3.75203	0.375203
$101$	−2.93267	−0.291811	−0.145906	−	0.989299i	$-0.546610\pi$
$101$	−2.93267	−0.291811	−0.145906	+	0.989299i	$0.546610\pi$
$102$	6.66061	0.659499
$103$	6.83928	0.673895	0.336947	−	0.941523i	$-0.390606\pi$
$103$	6.83928	0.673895	0.336947	+	0.941523i	$0.390606\pi$
$104$	0.583403	0.0572074
$105$	0.717237	0.0699952
$106$	−3.86231	−0.375140
$107$	−19.4659	−1.88184	−0.940920	−	0.338630i	$-0.890036\pi$
$107$	−19.4659	−1.88184	−0.940920	+	0.338630i	$0.890036\pi$
$108$	−27.1428	−2.61181
$109$	7.62322	0.730172	0.365086	−	0.930974i	$-0.381040\pi$
$109$	7.62322	0.730172	0.365086	+	0.930974i	$0.381040\pi$
$110$	−5.53430	−0.527675
$111$	−13.7314	−1.30332
$112$	−0.149379	−0.0141150
$113$	−3.17351	−0.298539	−0.149269	−	0.988797i	$-0.547692\pi$
$113$	−3.17351	−0.298539	−0.149269	+	0.988797i	$0.547692\pi$
$114$	−13.2030	−1.23658
$115$	4.25157	0.396461
$116$	23.8233	2.21194
$117$	−1.92072	−0.177571
$118$	23.7546	2.18679
$119$	0.0943373	0.00864789
$120$	−14.2028	−1.29653
$121$	1.00000	0.0909091
$122$	−24.9831	−2.26186
$123$	15.1315	1.36436
$124$	1.52908	0.137315
$125$	9.25628	0.827907
$126$	−1.27753	−0.113812
$127$	17.2940	1.53459	0.767297	−	0.641292i	$-0.221601\pi$
$127$	17.2940	1.53459	0.767297	+	0.641292i	$0.221601\pi$
$128$	13.6000	1.20208
$129$	−3.02493	−0.266330
$130$	−1.72837	−0.151588
$131$	10.7491	0.939157	0.469579	−	0.882891i	$-0.344406\pi$
$131$	10.7491	0.939157	0.469579	+	0.882891i	$0.344406\pi$
$132$	8.61618	0.749942
$133$	−0.187001	−0.0162150
$134$	9.51946	0.822356
$135$	23.9507	2.06135
$136$	−1.86807	−0.160186
$137$	1.28507	0.109791	0.0548957	−	0.998492i	$-0.482517\pi$
$137$	1.28507	0.109791	0.0548957	+	0.998492i	$0.482517\pi$
$138$	−11.2668	−0.959093
$139$	18.4769	1.56719	0.783595	−	0.621272i	$-0.213384\pi$
$139$	18.4769	1.56719	0.783595	+	0.621272i	$0.213384\pi$
$140$	−0.675378	−0.0570798
$141$	−21.2187	−1.78693
$142$	35.5527	2.98351
$143$	0.312302	0.0261160
$144$	−9.73859	−0.811549
$145$	−21.0216	−1.74575
$146$	−3.62010	−0.299601
$147$	21.1476	1.74422
$148$	12.9300	1.06284
$149$	−12.8747	−1.05474	−0.527368	−	0.849637i	$-0.676821\pi$
$149$	−12.8747	−1.05474	−0.527368	+	0.849637i	$0.676821\pi$
$150$	8.77366	0.716367
$151$	−11.4108	−0.928597	−0.464298	−	0.885679i	$-0.653693\pi$
$151$	−11.4108	−0.928597	−0.464298	+	0.885679i	$0.653693\pi$
$152$	3.70300	0.300353
$153$	6.15021	0.497215
$154$	0.207722	0.0167387
$155$	−1.34925	−0.108375
$156$	2.69085	0.215440
$157$	22.9413	1.83092	0.915458	−	0.402414i	$-0.131829\pi$
$157$	22.9413	1.83092	0.915458	+	0.402414i	$0.131829\pi$
$158$	20.9980	1.67051
$159$	−5.30595	−0.420790
$160$	−18.1538	−1.43518
$161$	−0.159577	−0.0125764
$162$	−22.8435	−1.79476
$163$	15.8673	1.24282	0.621412	−	0.783484i	$-0.286559\pi$
$163$	15.8673	1.24282	0.621412	+	0.783484i	$0.286559\pi$
$164$	−14.2484	−1.11261
$165$	−7.60290	−0.591885
$166$	29.5558	2.29397
$167$	14.5658	1.12714	0.563568	−	0.826070i	$-0.309428\pi$
$167$	14.5658	1.12714	0.563568	+	0.826070i	$0.309428\pi$
$168$	0.533081	0.0411281
$169$	−12.9025	−0.992497
$170$	5.53430	0.424461
$171$	−12.1913	−0.932290
$172$	2.84839	0.217188
$173$	7.52462	0.572086	0.286043	−	0.958217i	$-0.407660\pi$
$173$	7.52462	0.572086	0.286043	+	0.958217i	$0.407660\pi$
$174$	55.7079	4.22321
$175$	0.124265	0.00939358
$176$	1.58346	0.119358
$177$	32.6336	2.45289
$178$	5.14758	0.385827
$179$	−6.47488	−0.483955	−0.241978	−	0.970282i	$-0.577796\pi$
$179$	−6.47488	−0.483955	−0.241978	+	0.970282i	$0.577796\pi$
$180$	−44.0304	−3.28184
$181$	−15.4568	−1.14889	−0.574447	−	0.818542i	$-0.694783\pi$
$181$	−15.4568	−1.14889	−0.574447	+	0.818542i	$0.694783\pi$
$182$	0.0648719	0.00480863
$183$	−34.3212	−2.53710
$184$	3.15995	0.232954
$185$	−11.4094	−0.838834
$186$	3.57556	0.262173
$187$	−1.00000	−0.0731272
$188$	19.9803	1.45721
$189$	−0.898956	−0.0653894
$190$	−10.9704	−0.795875
$191$	7.94867	0.575146	0.287573	−	0.957759i	$-0.407152\pi$
$191$	7.94867	0.575146	0.287573	+	0.957759i	$0.407152\pi$
$192$	38.5284	2.78055
$193$	21.8143	1.57023	0.785114	−	0.619351i	$-0.212604\pi$
$193$	21.8143	1.57023	0.785114	+	0.619351i	$0.212604\pi$
$194$	4.30106	0.308798
$195$	−2.37440	−0.170034
$196$	−19.9134	−1.42238
$197$	−4.20026	−0.299256	−0.149628	−	0.988742i	$-0.547808\pi$
$197$	−4.20026	−0.299256	−0.149628	+	0.988742i	$0.547808\pi$
$198$	13.5422	0.962401
$199$	−25.4336	−1.80294	−0.901469	−	0.432844i	$-0.857510\pi$
$199$	−25.4336	−1.80294	−0.901469	+	0.432844i	$0.857510\pi$
$200$	−2.46071	−0.173999
$201$	13.0776	0.922425
$202$	6.45746	0.454345
$203$	0.789017	0.0553781
$204$	−8.61618	−0.603253
$205$	12.5727	0.878119
$206$	−15.0595	−1.04924
$207$	−10.4034	−0.723087
$208$	0.494517	0.0342886
$209$	1.98225	0.137115
$210$	−1.57929	−0.108981
$211$	10.5402	0.725619	0.362809	−	0.931863i	$-0.381818\pi$
$211$	10.5402	0.725619	0.362809	+	0.931863i	$0.381818\pi$
$212$	4.99629	0.343146
$213$	48.8415	3.34656
$214$	42.8621	2.92999
$215$	−2.51341	−0.171413
$216$	17.8012	1.21122
$217$	0.0506423	0.00343782
$218$	−16.7856	−1.13686
$219$	−4.97321	−0.336059
$220$	7.15918	0.482672
$221$	−0.312302	−0.0210077
$222$	30.2352	2.02925
$223$	23.0621	1.54435	0.772176	−	0.635408i	$-0.219168\pi$
$223$	23.0621	1.54435	0.772176	+	0.635408i	$0.219168\pi$
$224$	0.681377	0.0455264
$225$	8.10133	0.540089
$226$	6.98777	0.464819
$227$	28.4535	1.88853	0.944264	−	0.329191i	$-0.106776\pi$
$227$	28.4535	1.88853	0.944264	+	0.329191i	$0.106776\pi$
$228$	17.0795	1.13111
$229$	0.693549	0.0458310	0.0229155	−	0.999737i	$-0.492705\pi$
$229$	0.693549	0.0458310	0.0229155	+	0.999737i	$0.492705\pi$
$230$	−9.36157	−0.617283
$231$	0.285364	0.0187756
$232$	−15.6242	−1.02578
$233$	−13.7645	−0.901740	−0.450870	−	0.892590i	$-0.648886\pi$
$233$	−13.7645	−0.901740	−0.450870	+	0.892590i	$0.648886\pi$
$234$	4.22925	0.276475
$235$	−17.6306	−1.15009
$236$	−30.7290	−2.00029
$237$	28.8467	1.87379
$238$	−0.207722	−0.0134646
$239$	11.1875	0.723658	0.361829	−	0.932244i	$-0.382152\pi$
$239$	11.1875	0.723658	0.361829	+	0.932244i	$0.382152\pi$
$240$	−12.0389	−0.777106
$241$	20.8539	1.34332	0.671659	−	0.740860i	$-0.265582\pi$
$241$	20.8539	1.34332	0.671659	+	0.740860i	$0.265582\pi$
$242$	−2.20191	−0.141544
$243$	−2.79448	−0.179266
$244$	32.3181	2.06896
$245$	17.5715	1.12260
$246$	−33.3181	−2.12429
$247$	0.619062	0.0393900
$248$	−1.00282	−0.0636792
$249$	40.6031	2.57312
$250$	−20.3815	−1.28904
$251$	14.6523	0.924843	0.462422	−	0.886660i	$-0.346981\pi$
$251$	14.6523	0.924843	0.462422	+	0.886660i	$0.346981\pi$
$252$	1.65262	0.104105
$253$	1.69155	0.106347
$254$	−38.0797	−2.38934
$255$	7.60290	0.476112
$256$	−4.47206	−0.279504
$257$	−23.9934	−1.49667	−0.748334	−	0.663322i	$-0.769146\pi$
$257$	−23.9934	−1.49667	−0.748334	+	0.663322i	$0.769146\pi$
$258$	6.66061	0.414672
$259$	0.428235	0.0266092
$260$	2.23583	0.138660
$261$	51.4390	3.18399
$262$	−23.6686	−1.46225
$263$	−9.85433	−0.607644	−0.303822	−	0.952729i	$-0.598263\pi$
$263$	−9.85433	−0.607644	−0.303822	+	0.952729i	$0.598263\pi$
$264$	−5.65079	−0.347782
$265$	−4.40871	−0.270825
$266$	0.411758	0.0252465
$267$	7.07164	0.432777
$268$	−12.3144	−0.752221
$269$	5.85952	0.357261	0.178631	−	0.983916i	$-0.442833\pi$
$269$	5.85952	0.357261	0.178631	+	0.983916i	$0.442833\pi$
$270$	−52.7373	−3.20949
$271$	13.2722	0.806227	0.403113	−	0.915150i	$-0.367928\pi$
$271$	13.2722	0.806227	0.403113	+	0.915150i	$0.367928\pi$
$272$	−1.58346	−0.0960112
$273$	0.0891197	0.00539377
$274$	−2.82961	−0.170943
$275$	−1.31725	−0.0794329
$276$	14.5747	0.877296
$277$	1.82075	0.109399	0.0546993	−	0.998503i	$-0.482580\pi$
$277$	1.82075	0.109399	0.0546993	+	0.998503i	$0.482580\pi$
$278$	−40.6844	−2.44009
$279$	3.30156	0.197659
$280$	0.442936	0.0264705
$281$	−9.95218	−0.593697	−0.296849	−	0.954925i	$-0.595936\pi$
$281$	−9.95218	−0.593697	−0.296849	+	0.954925i	$0.595936\pi$
$282$	46.7215	2.78223
$283$	−25.9663	−1.54353	−0.771767	−	0.635905i	$-0.780627\pi$
$283$	−25.9663	−1.54353	−0.771767	+	0.635905i	$0.780627\pi$
$284$	−45.9910	−2.72906
$285$	−15.0709	−0.892722
$286$	−0.687659	−0.0406622
$287$	−0.471900	−0.0278554
$288$	44.4215	2.61756
$289$	1.00000	0.0588235
$290$	46.2877	2.71811
$291$	5.90870	0.346374
$292$	4.68297	0.274050
$293$	22.7634	1.32985	0.664927	−	0.746909i	$-0.268463\pi$
$293$	22.7634	1.32985	0.664927	+	0.746909i	$0.268463\pi$
$294$	−46.5650	−2.71573
$295$	27.1153	1.57871
$296$	−8.47993	−0.492886
$297$	9.52917	0.552938
$298$	28.3489	1.64221
$299$	0.528276	0.0305510
$300$	−11.3496	−0.655271
$301$	0.0943373	0.00543751
$302$	25.1255	1.44581
$303$	8.87112	0.509633
$304$	3.13881	0.180023
$305$	−28.5175	−1.63291
$306$	−13.5422	−0.774155
$307$	−8.15516	−0.465439	−0.232720	−	0.972544i	$-0.574762\pi$
$307$	−8.15516	−0.465439	−0.232720	+	0.972544i	$0.574762\pi$
$308$	−0.268709	−0.0153111
$309$	−20.6884	−1.17692
$310$	2.97093	0.168737
$311$	−22.7543	−1.29028	−0.645139	−	0.764065i	$-0.723201\pi$
$311$	−22.7543	−1.29028	−0.645139	+	0.764065i	$0.723201\pi$
$312$	−1.76475	−0.0999095
$313$	27.6302	1.56175	0.780874	−	0.624688i	$-0.214774\pi$
$313$	27.6302	1.56175	0.780874	+	0.624688i	$0.214774\pi$
$314$	−50.5146	−2.85070
$315$	−1.45827	−0.0821641
$316$	−27.1631	−1.52804
$317$	−1.76914	−0.0993646	−0.0496823	−	0.998765i	$-0.515821\pi$
$317$	−1.76914	−0.0993646	−0.0496823	+	0.998765i	$0.515821\pi$
$318$	11.6832	0.655162
$319$	−8.36378	−0.468282
$320$	32.0132	1.78959
$321$	58.8830	3.28653
$322$	0.351373	0.0195812
$323$	−1.98225	−0.110296
$324$	29.5505	1.64169
$325$	−0.411378	−0.0228192
$326$	−34.9383	−1.93506
$327$	−23.0597	−1.27520
$328$	9.34459	0.515969
$329$	0.661738	0.0364828
$330$	16.7409	0.921555
$331$	16.9300	0.930559	0.465279	−	0.885164i	$-0.345954\pi$
$331$	16.9300	0.930559	0.465279	+	0.885164i	$0.345954\pi$
$332$	−38.2334	−2.09833
$333$	27.9182	1.52991
$334$	−32.0725	−1.75493
$335$	10.8662	0.593684
$336$	0.451861	0.0246511
$337$	18.6611	1.01653	0.508266	−	0.861200i	$-0.330287\pi$
$337$	18.6611	1.01653	0.508266	+	0.861200i	$0.330287\pi$
$338$	28.4100	1.54530
$339$	9.59964	0.521381
$340$	−7.15918	−0.388261
$341$	−0.536821	−0.0290705
$342$	26.8440	1.45156
$343$	−1.31988	−0.0712670
$344$	−1.86807	−0.100720
$345$	−12.8607	−0.692398
$346$	−16.5685	−0.890729
$347$	−27.9499	−1.50043	−0.750216	−	0.661193i	$-0.770050\pi$
$347$	−27.9499	−1.50043	−0.750216	+	0.661193i	$0.770050\pi$
$348$	−72.0639	−3.86303
$349$	34.2739	1.83464	0.917319	−	0.398153i	$-0.130349\pi$
$349$	34.2739	1.83464	0.917319	+	0.398153i	$0.130349\pi$
$350$	−0.273621	−0.0146256
$351$	2.97598	0.158846
$352$	−7.22277	−0.384975
$353$	−30.3921	−1.61761	−0.808805	−	0.588077i	$-0.799885\pi$
$353$	−30.3921	−1.61761	−0.808805	+	0.588077i	$0.799885\pi$
$354$	−71.8562	−3.81911
$355$	40.5824	2.15389
$356$	−6.65892	−0.352922
$357$	−0.285364	−0.0151031
$358$	14.2571	0.753510
$359$	−34.1734	−1.80361	−0.901803	−	0.432148i	$-0.857756\pi$
$359$	−34.1734	−1.80361	−0.901803	+	0.432148i	$0.857756\pi$
$360$	28.8767	1.52194
$361$	−15.0707	−0.793193
$362$	34.0344	1.78881
$363$	−3.02493	−0.158768
$364$	−0.0839185	−0.00439852
$365$	−4.13224	−0.216291
$366$	75.5721	3.95022
$367$	28.1912	1.47157	0.735785	−	0.677215i	$-0.236813\pi$
$367$	28.1912	1.47157	0.735785	+	0.677215i	$0.236813\pi$
$368$	2.67850	0.139627
$369$	−30.7650	−1.60156
$370$	25.1224	1.30605
$371$	0.165475	0.00859102
$372$	−4.62535	−0.239813
$373$	8.61421	0.446027	0.223014	−	0.974815i	$-0.428411\pi$
$373$	8.61421	0.446027	0.223014	+	0.974815i	$0.428411\pi$
$374$	2.20191	0.113858
$375$	−27.9996	−1.44589
$376$	−13.1038	−0.675776
$377$	−2.61203	−0.134526
$378$	1.97942	0.101810
$379$	−6.21002	−0.318987	−0.159494	−	0.987199i	$-0.550986\pi$
$379$	−6.21002	−0.318987	−0.159494	+	0.987199i	$0.550986\pi$
$380$	14.1913	0.727999
$381$	−52.3131	−2.68008
$382$	−17.5022	−0.895492
$383$	−26.0605	−1.33163	−0.665815	−	0.746117i	$-0.731916\pi$
$383$	−26.0605	−1.33163	−0.665815	+	0.746117i	$0.731916\pi$
$384$	−41.1391	−2.09937
$385$	0.237109	0.0120842
$386$	−48.0330	−2.44482
$387$	6.15021	0.312633
$388$	−5.56386	−0.282462
$389$	−10.7142	−0.543230	−0.271615	−	0.962406i	$-0.587558\pi$
$389$	−10.7142	−0.543230	−0.271615	+	0.962406i	$0.587558\pi$
$390$	5.22821	0.264741
$391$	−1.69155	−0.0855456
$392$	13.0599	0.659624
$393$	−32.5154	−1.64019
$394$	9.24857	0.465936
$395$	23.9687	1.20599
$396$	−17.5182	−0.880322
$397$	11.9543	0.599971	0.299985	−	0.953944i	$-0.403018\pi$
$397$	11.9543	0.599971	0.299985	+	0.953944i	$0.403018\pi$
$398$	56.0023	2.80714
$399$	0.565664	0.0283186
$400$	−2.08580	−0.104290
$401$	32.9233	1.64411	0.822056	−	0.569407i	$-0.192827\pi$
$401$	32.9233	1.64411	0.822056	+	0.569407i	$0.192827\pi$
$402$	−28.7957	−1.43620
$403$	−0.167650	−0.00835126
$404$	−8.35338	−0.415596
$405$	−26.0753	−1.29569
$406$	−1.73734	−0.0862227
$407$	−4.53940	−0.225010
$408$	5.65079	0.279756
$409$	−36.7875	−1.81902	−0.909512	−	0.415678i	$-0.863544\pi$
$409$	−36.7875	−1.81902	−0.909512	+	0.415678i	$0.863544\pi$
$410$	−27.6840	−1.36722
$411$	−3.88726	−0.191745
$412$	19.4809	0.959757
$413$	−1.01773	−0.0500793
$414$	22.9073	1.12583
$415$	33.7371	1.65609
$416$	−2.25569	−0.110594
$417$	−55.8913	−2.73701
$418$	−4.36474	−0.213486
$419$	27.8168	1.35894	0.679469	−	0.733705i	$-0.262210\pi$
$419$	27.8168	1.35894	0.679469	+	0.733705i	$0.262210\pi$
$420$	2.04297	0.0996868
$421$	−13.2382	−0.645192	−0.322596	−	0.946537i	$-0.604555\pi$
$421$	−13.2382	−0.645192	−0.322596	+	0.946537i	$0.604555\pi$
$422$	−23.2086	−1.12978
$423$	43.1412	2.09760
$424$	−3.27674	−0.159133
$425$	1.31725	0.0638958
$426$	−107.544	−5.21054
$427$	1.07036	0.0517984
$428$	−55.4464	−2.68011
$429$	−0.944692	−0.0456102
$430$	5.53430	0.266888
$431$	10.0812	0.485592	0.242796	−	0.970077i	$-0.421935\pi$
$431$	10.0812	0.485592	0.242796	+	0.970077i	$0.421935\pi$
$432$	15.0890	0.725971
$433$	36.4085	1.74968	0.874842	−	0.484409i	$-0.160965\pi$
$433$	36.4085	1.74968	0.874842	+	0.484409i	$0.160965\pi$
$434$	−0.111510	−0.00535263
$435$	63.5890	3.04886
$436$	21.7139	1.03991
$437$	3.35309	0.160400
$438$	10.9505	0.523237
$439$	9.02001	0.430501	0.215251	−	0.976559i	$-0.430943\pi$
$439$	9.02001	0.430501	0.215251	+	0.976559i	$0.430943\pi$
$440$	−4.69524	−0.223837
$441$	−42.9967	−2.04746
$442$	0.687659	0.0327086
$443$	−16.4054	−0.779445	−0.389723	−	0.920932i	$-0.627429\pi$
$443$	−16.4054	−0.779445	−0.389723	+	0.920932i	$0.627429\pi$
$444$	−39.1123	−1.85619
$445$	5.87582	0.278540
$446$	−50.7806	−2.40453
$447$	38.9451	1.84204
$448$	−1.20157	−0.0567688
$449$	−24.8090	−1.17081	−0.585404	−	0.810742i	$-0.699064\pi$
$449$	−24.8090	−1.17081	−0.585404	+	0.810742i	$0.699064\pi$
$450$	−17.8384	−0.840909
$451$	5.00226	0.235547
$452$	−9.03939	−0.425177
$453$	34.5169	1.62174
$454$	−62.6520	−2.94040
$455$	0.0740495	0.00347149
$456$	−11.2013	−0.524549
$457$	10.9090	0.510301	0.255150	−	0.966901i	$-0.417875\pi$
$457$	10.9090	0.510301	0.255150	+	0.966901i	$0.417875\pi$
$458$	−1.52713	−0.0713581
$459$	−9.52917	−0.444783
$460$	12.1101	0.564638
$461$	−2.68025	−0.124832	−0.0624158	−	0.998050i	$-0.519880\pi$
$461$	−2.68025	−0.124832	−0.0624158	+	0.998050i	$0.519880\pi$
$462$	−0.628344	−0.0292332
$463$	10.8452	0.504021	0.252010	−	0.967725i	$-0.418908\pi$
$463$	10.8452	0.504021	0.252010	+	0.967725i	$0.418908\pi$
$464$	−13.2437	−0.614823
$465$	4.08140	0.189270
$466$	30.3081	1.40399
$467$	−7.21260	−0.333759	−0.166880	−	0.985977i	$-0.553369\pi$
$467$	−7.21260	−0.333759	−0.166880	+	0.985977i	$0.553369\pi$
$468$	−5.47096	−0.252895
$469$	−0.407847	−0.0188326
$470$	38.8209	1.79067
$471$	−69.3959	−3.19759
$472$	20.1532	0.927626
$473$	−1.00000	−0.0459800
$474$	−63.5176	−2.91746
$475$	−2.61112	−0.119806
$476$	0.268709	0.0123163
$477$	10.7879	0.493945
$478$	−24.6338	−1.12672
$479$	41.0183	1.87417	0.937087	−	0.349096i	$-0.113511\pi$
$479$	41.0183	1.87417	0.937087	+	0.349096i	$0.113511\pi$
$480$	54.9140	2.50647
$481$	−1.41766	−0.0646399
$482$	−45.9183	−2.09152
$483$	0.482708	0.0219640
$484$	2.84839	0.129472
$485$	4.90954	0.222931
$486$	6.15319	0.279114
$487$	−27.8264	−1.26093	−0.630467	−	0.776216i	$-0.717136\pi$
$487$	−27.8264	−1.26093	−0.630467	+	0.776216i	$0.717136\pi$
$488$	−21.1954	−0.959469
$489$	−47.9975	−2.17052
$490$	−38.6908	−1.74787
$491$	33.7552	1.52335	0.761674	−	0.647960i	$-0.224378\pi$
$491$	33.7552	1.52335	0.761674	+	0.647960i	$0.224378\pi$
$492$	43.1004	1.94312
$493$	8.36378	0.376686
$494$	−1.36312	−0.0613295
$495$	15.4580	0.694786
$496$	−0.850034	−0.0381676
$497$	−1.52320	−0.0683248
$498$	−89.4042	−4.00630
$499$	6.36472	0.284924	0.142462	−	0.989800i	$-0.454498\pi$
$499$	6.36472	0.284924	0.142462	+	0.989800i	$0.454498\pi$
$500$	26.3655	1.17910
$501$	−44.0606	−1.96848
$502$	−32.2629	−1.43996
$503$	5.83733	0.260274	0.130137	−	0.991496i	$-0.458458\pi$
$503$	5.83733	0.260274	0.130137	+	0.991496i	$0.458458\pi$
$504$	−1.08385	−0.0482783
$505$	7.37101	0.328006
$506$	−3.72464	−0.165581
$507$	39.0291	1.73334
$508$	49.2600	2.18556
$509$	4.84894	0.214925	0.107463	−	0.994209i	$-0.465727\pi$
$509$	4.84894	0.214925	0.107463	+	0.994209i	$0.465727\pi$
$510$	−16.7409	−0.741298
$511$	0.155098	0.00686111
$512$	−17.3530	−0.766900
$513$	18.8892	0.833980
$514$	52.8312	2.33029
$515$	−17.1899	−0.757480
$516$	−8.61618	−0.379306
$517$	−7.01459	−0.308502
$518$	−0.942932	−0.0414301
$519$	−22.7615	−0.999117
$520$	−1.46633	−0.0643029
$521$	−0.487128	−0.0213415	−0.0106707	−	0.999943i	$-0.503397\pi$
$521$	−0.487128	−0.0213415	−0.0106707	+	0.999943i	$0.503397\pi$
$522$	−113.264	−4.95742
$523$	29.3593	1.28379	0.641896	−	0.766791i	$-0.278148\pi$
$523$	29.3593	1.28379	0.641896	+	0.766791i	$0.278148\pi$
$524$	30.6177	1.33754
$525$	−0.375894	−0.0164054
$526$	21.6983	0.946091
$527$	0.536821	0.0233843
$528$	−4.78985	−0.208451
$529$	−20.1386	−0.875593
$530$	9.70757	0.421670
$531$	−66.3498	−2.87934
$532$	−0.532650	−0.0230933
$533$	1.56222	0.0676671
$534$	−15.5711	−0.673826
$535$	48.9258	2.11525
$536$	8.07621	0.348839
$537$	19.5861	0.845201
$538$	−12.9021	−0.556250
$539$	6.99110	0.301128
$540$	68.2210	2.93576
$541$	10.5784	0.454802	0.227401	−	0.973801i	$-0.426977\pi$
$541$	10.5784	0.454802	0.227401	+	0.973801i	$0.426977\pi$
$542$	−29.2241	−1.25528
$543$	46.7557	2.00648
$544$	7.22277	0.309674
$545$	−19.1603	−0.820737
$546$	−0.196233	−0.00839800
$547$	−9.87028	−0.422023	−0.211011	−	0.977484i	$-0.567676\pi$
$547$	−9.87028	−0.422023	−0.211011	+	0.977484i	$0.567676\pi$
$548$	3.66039	0.156364
$549$	69.7810	2.97818
$550$	2.90045	0.123676
$551$	−16.5791	−0.706295
$552$	−9.55862	−0.406842
$553$	−0.899629	−0.0382561
$554$	−4.00913	−0.170332
$555$	34.5126	1.46498
$556$	52.6294	2.23198
$557$	3.36286	0.142489	0.0712445	−	0.997459i	$-0.477303\pi$
$557$	3.36286	0.142489	0.0712445	+	0.997459i	$0.477303\pi$
$558$	−7.26973	−0.307752
$559$	−0.312302	−0.0132090
$560$	0.375451	0.0158657
$561$	3.02493	0.127713
$562$	21.9138	0.924376
$563$	7.30643	0.307929	0.153965	−	0.988076i	$-0.450796\pi$
$563$	7.30643	0.307929	0.153965	+	0.988076i	$0.450796\pi$
$564$	−60.4390	−2.54494
$565$	7.97634	0.335567
$566$	57.1753	2.40326
$567$	0.978697	0.0411014
$568$	30.1625	1.26559
$569$	−3.74081	−0.156823	−0.0784115	−	0.996921i	$-0.524985\pi$
$569$	−3.74081	−0.156823	−0.0784115	+	0.996921i	$0.524985\pi$
$570$	33.1847	1.38995
$571$	26.2322	1.09778	0.548891	−	0.835894i	$-0.315050\pi$
$571$	26.2322	1.09778	0.548891	+	0.835894i	$0.315050\pi$
$572$	0.889558	0.0371943
$573$	−24.0442	−1.00446
$574$	1.03908	0.0433703
$575$	−2.22819	−0.0929220
$576$	−78.3349	−3.26395
$577$	−28.1223	−1.17075	−0.585374	−	0.810763i	$-0.699052\pi$
$577$	−28.1223	−1.17075	−0.585374	+	0.810763i	$0.699052\pi$
$578$	−2.20191	−0.0915872
$579$	−65.9868	−2.74232
$580$	−59.8778	−2.48629
$581$	−1.26627	−0.0525338
$582$	−13.0104	−0.539299
$583$	−1.75407	−0.0726463
$584$	−3.07125	−0.127089
$585$	4.82757	0.199595
$586$	−50.1229	−2.07056
$587$	−6.64323	−0.274195	−0.137098	−	0.990558i	$-0.543777\pi$
$587$	−6.64323	−0.274195	−0.137098	+	0.990558i	$0.543777\pi$
$588$	60.2366	2.48412
$589$	−1.06412	−0.0438461
$590$	−59.7052	−2.45803
$591$	12.7055	0.522634
$592$	−7.18794	−0.295423
$593$	−8.21696	−0.337430	−0.168715	−	0.985665i	$-0.553962\pi$
$593$	−8.21696	−0.337430	−0.168715	+	0.985665i	$0.553962\pi$
$594$	−20.9823	−0.860915
$595$	−0.237109	−0.00972051
$596$	−36.6722	−1.50215
$597$	76.9348	3.14873
$598$	−1.16321	−0.0475673
$599$	42.0812	1.71939	0.859695	−	0.510807i	$-0.170653\pi$
$599$	42.0812	1.71939	0.859695	+	0.510807i	$0.170653\pi$
$600$	7.44348	0.303879
$601$	18.9011	0.770994	0.385497	−	0.922709i	$-0.374030\pi$
$601$	18.9011	0.770994	0.385497	+	0.922709i	$0.374030\pi$
$602$	−0.207722	−0.00846611
$603$	−26.5891	−1.08279
$604$	−32.5024	−1.32250
$605$	−2.51341	−0.102185
$606$	−19.5334	−0.793489
$607$	−26.3405	−1.06913	−0.534564	−	0.845128i	$-0.679524\pi$
$607$	−26.3405	−1.06913	−0.534564	+	0.845128i	$0.679524\pi$
$608$	−14.3174	−0.580646
$609$	−2.38672	−0.0967148
$610$	62.7928	2.54241
$611$	−2.19067	−0.0886251
$612$	17.5182	0.708131
$613$	−2.75208	−0.111156	−0.0555778	−	0.998454i	$-0.517700\pi$
$613$	−2.75208	−0.111156	−0.0555778	+	0.998454i	$0.517700\pi$
$614$	17.9569	0.724681
$615$	−38.0317	−1.53359
$616$	0.176229	0.00710047
$617$	−10.1401	−0.408224	−0.204112	−	0.978948i	$-0.565431\pi$
$617$	−10.1401	−0.408224	−0.204112	+	0.978948i	$0.565431\pi$
$618$	45.5538	1.83244
$619$	−36.7785	−1.47825	−0.739126	−	0.673567i	$-0.764761\pi$
$619$	−36.7785	−1.47825	−0.739126	+	0.673567i	$0.764761\pi$
$620$	−3.84320	−0.154347
$621$	16.1191	0.646837
$622$	50.1029	2.00894
$623$	−0.220540	−0.00883576
$624$	−1.49588	−0.0598831
$625$	−29.8511	−1.19404
$626$	−60.8390	−2.43162
$627$	−5.99618	−0.239464
$628$	65.3458	2.60758
$629$	4.53940	0.180998
$630$	3.21097	0.127928
$631$	−26.1961	−1.04285	−0.521424	−	0.853298i	$-0.674599\pi$
$631$	−26.1961	−1.04285	−0.521424	+	0.853298i	$0.674599\pi$
$632$	17.8145	0.708623
$633$	−31.8834	−1.26725
$634$	3.89547	0.154709
$635$	−43.4669	−1.72493
$636$	−15.1134	−0.599286
$637$	2.18333	0.0865069
$638$	18.4163	0.729107
$639$	−99.3032	−3.92837
$640$	−34.1825	−1.35118
$641$	25.3086	0.999630	0.499815	−	0.866132i	$-0.333401\pi$
$641$	25.3086	0.999630	0.499815	+	0.866132i	$0.333401\pi$
$642$	−129.655	−5.11707
$643$	−47.6840	−1.88047	−0.940236	−	0.340524i	$-0.889395\pi$
$643$	−47.6840	−1.88047	−0.940236	+	0.340524i	$0.889395\pi$
$644$	−0.454536	−0.0179112
$645$	7.60290	0.299364
$646$	4.36474	0.171728
$647$	−11.3837	−0.447539	−0.223769	−	0.974642i	$-0.571836\pi$
$647$	−11.3837	−0.447539	−0.223769	+	0.974642i	$0.571836\pi$
$648$	−19.3802	−0.761327
$649$	10.7882	0.423475
$650$	0.905816	0.0355290
$651$	−0.153189	−0.00600397
$652$	45.1963	1.77002
$653$	40.5726	1.58773	0.793864	−	0.608096i	$-0.208066\pi$
$653$	40.5726	1.58773	0.793864	+	0.608096i	$0.208066\pi$
$654$	50.7753	1.98547
$655$	−27.0170	−1.05564
$656$	7.92087	0.309258
$657$	10.1114	0.394483
$658$	−1.45708	−0.0568031
$659$	−2.79325	−0.108810	−0.0544048	−	0.998519i	$-0.517326\pi$
$659$	−2.79325	−0.108810	−0.0544048	+	0.998519i	$0.517326\pi$
$660$	−21.6560	−0.842960
$661$	−20.4915	−0.797025	−0.398513	−	0.917163i	$-0.630473\pi$
$661$	−20.4915	−0.797025	−0.398513	+	0.917163i	$0.630473\pi$
$662$	−37.2783	−1.44886
$663$	0.944692	0.0366888
$664$	25.0748	0.973091
$665$	0.470010	0.0182262
$666$	−61.4733	−2.38204
$667$	−14.1478	−0.547804
$668$	41.4891	1.60526
$669$	−69.7613	−2.69713
$670$	−23.9263	−0.924355
$671$	−11.3461	−0.438012
$672$	−2.06112	−0.0795093
$673$	−19.5939	−0.755289	−0.377644	−	0.925951i	$-0.623266\pi$
$673$	−19.5939	−0.755289	−0.377644	+	0.925951i	$0.623266\pi$
$674$	−41.0899	−1.58272
$675$	−12.5523	−0.483136
$676$	−36.7513	−1.41351
$677$	14.0851	0.541335	0.270667	−	0.962673i	$-0.412756\pi$
$677$	14.0851	0.541335	0.270667	+	0.962673i	$0.412756\pi$
$678$	−21.1375	−0.811781
$679$	−0.184272	−0.00707172
$680$	4.69524	0.180054
$681$	−86.0700	−3.29821
$682$	1.18203	0.0452623
$683$	−23.1779	−0.886876	−0.443438	−	0.896305i	$-0.646241\pi$
$683$	−23.1779	−0.886876	−0.443438	+	0.896305i	$0.646241\pi$
$684$	−34.7255	−1.32776
$685$	−3.22992	−0.123409
$686$	2.90626	0.110961
$687$	−2.09794	−0.0800413
$688$	−1.58346	−0.0603687
$689$	−0.547801	−0.0208695
$690$	28.3181	1.07805
$691$	13.8907	0.528426	0.264213	−	0.964464i	$-0.414888\pi$
$691$	13.8907	0.528426	0.264213	+	0.964464i	$0.414888\pi$
$692$	21.4331	0.814762
$693$	−0.580194	−0.0220398
$694$	61.5431	2.33615
$695$	−46.4401	−1.76157
$696$	47.2620	1.79146
$697$	−5.00226	−0.189474
$698$	−75.4678	−2.85650
$699$	41.6366	1.57484
$700$	0.353956	0.0133783
$701$	39.2703	1.48322	0.741609	−	0.670832i	$-0.234063\pi$
$701$	39.2703	1.48322	0.741609	+	0.670832i	$0.234063\pi$
$702$	−6.55282	−0.247320
$703$	−8.99824	−0.339375
$704$	12.7369	0.480042
$705$	53.3313	2.00857
$706$	66.9206	2.51859
$707$	−0.276660	−0.0104049
$708$	92.9533	3.49340
$709$	13.5655	0.509461	0.254731	−	0.967012i	$-0.418013\pi$
$709$	13.5655	0.509461	0.254731	+	0.967012i	$0.418013\pi$
$710$	−89.3585	−3.35357
$711$	−58.6503	−2.19956
$712$	4.36715	0.163666
$713$	−0.908062	−0.0340072
$714$	0.628344	0.0235152
$715$	−0.784944	−0.0293552
$716$	−18.4430	−0.689246
$717$	−33.8414	−1.26383
$718$	75.2467	2.80818
$719$	48.1928	1.79729	0.898645	−	0.438677i	$-0.144553\pi$
$719$	48.1928	1.79729	0.898645	+	0.438677i	$0.144553\pi$
$720$	24.4771	0.912208
$721$	0.645200	0.0240285
$722$	33.1842	1.23499
$723$	−63.0816	−2.34603
$724$	−44.0269	−1.63625
$725$	11.0172	0.409167
$726$	6.66061	0.247199
$727$	21.8379	0.809923	0.404961	−	0.914334i	$-0.367285\pi$
$727$	21.8379	0.809923	0.404961	+	0.914334i	$0.367285\pi$
$728$	0.0550367	0.00203979
$729$	−22.6702	−0.839638
$730$	9.09880	0.336762
$731$	1.00000	0.0369863
$732$	−97.7602	−3.61332
$733$	42.2060	1.55891	0.779456	−	0.626457i	$-0.215495\pi$
$733$	42.2060	1.55891	0.779456	+	0.626457i	$0.215495\pi$
$734$	−62.0744	−2.29121
$735$	−53.1527	−1.96057
$736$	−12.2177	−0.450351
$737$	4.32328	0.159250
$738$	67.7415	2.49360
$739$	−48.2243	−1.77396	−0.886979	−	0.461809i	$-0.847200\pi$
$739$	−48.2243	−1.77396	−0.886979	+	0.461809i	$0.847200\pi$
$740$	−32.4984	−1.19466
$741$	−1.87262	−0.0687924
$742$	−0.364360	−0.0133761
$743$	24.4713	0.897765	0.448882	−	0.893591i	$-0.351822\pi$
$743$	24.4713	0.897765	0.448882	+	0.893591i	$0.351822\pi$
$744$	3.03347	0.111212
$745$	32.3594	1.18556
$746$	−18.9677	−0.694456
$747$	−82.5531	−3.02046
$748$	−2.84839	−0.104147
$749$	−1.83636	−0.0670991
$750$	61.6525	2.25123
$751$	7.66449	0.279681	0.139841	−	0.990174i	$-0.455341\pi$
$751$	7.66449	0.279681	0.139841	+	0.990174i	$0.455341\pi$
$752$	−11.1073	−0.405042
$753$	−44.3221	−1.61519
$754$	5.75143	0.209455
$755$	28.6800	1.04377
$756$	−2.56058	−0.0931273
$757$	−17.3663	−0.631187	−0.315594	−	0.948894i	$-0.602204\pi$
$757$	−17.3663	−0.631187	−0.315594	+	0.948894i	$0.602204\pi$
$758$	13.6739	0.496658
$759$	−5.11683	−0.185729
$760$	−9.30716	−0.337606
$761$	24.2719	0.879856	0.439928	−	0.898033i	$-0.355004\pi$
$761$	24.2719	0.879856	0.439928	+	0.898033i	$0.355004\pi$
$762$	115.189	4.17284
$763$	0.719154	0.0260351
$764$	22.6409	0.819119
$765$	−15.4580	−0.558886
$766$	57.3828	2.07332
$767$	3.36918	0.121654
$768$	13.5277	0.488138
$769$	−30.8202	−1.11140	−0.555702	−	0.831381i	$-0.687551\pi$
$769$	−30.8202	−1.11140	−0.555702	+	0.831381i	$0.687551\pi$
$770$	−0.522091	−0.0188148
$771$	72.5784	2.61385
$772$	62.1356	2.23631
$773$	−33.4782	−1.20413	−0.602063	−	0.798449i	$-0.705654\pi$
$773$	−33.4782	−1.20413	−0.602063	+	0.798449i	$0.705654\pi$
$774$	−13.5422	−0.486764
$775$	0.707126	0.0254007
$776$	3.64897	0.130990
$777$	−1.29538	−0.0464715
$778$	23.5916	0.845800
$779$	9.91575	0.355269
$780$	−6.76322	−0.242162
$781$	16.1463	0.577760
$782$	3.72464	0.133193
$783$	−79.6999	−2.84824
$784$	11.0701	0.395361
$785$	−57.6610	−2.05801
$786$	71.5959	2.55374
$787$	−49.5348	−1.76572	−0.882862	−	0.469633i	$-0.844386\pi$
$787$	−49.5348	−1.76572	−0.882862	+	0.469633i	$0.844386\pi$
$788$	−11.9640	−0.426199
$789$	29.8087	1.06122
$790$	−52.7768	−1.87771
$791$	−0.299380	−0.0106447
$792$	11.4890	0.408245
$793$	−3.54341	−0.125830
$794$	−26.3223	−0.934144
$795$	13.3361	0.472981
$796$	−72.4447	−2.56773
$797$	45.0190	1.59465	0.797327	−	0.603548i	$-0.206247\pi$
$797$	45.0190	1.59465	0.797327	+	0.603548i	$0.206247\pi$
$798$	−1.24554	−0.0440916
$799$	7.01459	0.248159
$800$	9.51416	0.336376
$801$	−14.3779	−0.508017
$802$	−72.4940	−2.55985
$803$	−1.64407	−0.0580181
$804$	37.2502	1.31371
$805$	0.401082	0.0141363
$806$	0.369150	0.0130028
$807$	−17.7247	−0.623937
$808$	5.47844	0.192731
$809$	32.0969	1.12847	0.564234	−	0.825615i	$-0.309171\pi$
$809$	32.0969	1.12847	0.564234	+	0.825615i	$0.309171\pi$
$810$	57.4153	2.01737
$811$	4.06210	0.142640	0.0713199	−	0.997453i	$-0.477279\pi$
$811$	4.06210	0.142640	0.0713199	+	0.997453i	$0.477279\pi$
$812$	2.24743	0.0788692
$813$	−40.1474	−1.40803
$814$	9.99533	0.350336
$815$	−39.8811	−1.39697
$816$	4.78985	0.167678
$817$	−1.98225	−0.0693503
$818$	81.0026	2.83219
$819$	−0.181196	−0.00633149
$820$	35.8121	1.25061
$821$	−46.9357	−1.63807	−0.819034	−	0.573744i	$-0.805490\pi$
$821$	−46.9357	−1.63807	−0.819034	+	0.573744i	$0.805490\pi$
$822$	8.55939	0.298543
$823$	−8.38614	−0.292323	−0.146161	−	0.989261i	$-0.546692\pi$
$823$	−8.38614	−0.292323	−0.146161	+	0.989261i	$0.546692\pi$
$824$	−12.7763	−0.445083
$825$	3.98458	0.138725
$826$	2.24095	0.0779726
$827$	56.1892	1.95389	0.976944	−	0.213495i	$-0.0684848\pi$
$827$	56.1892	1.95389	0.976944	+	0.213495i	$0.0684848\pi$
$828$	−29.6330	−1.02982
$829$	31.8418	1.10591	0.552956	−	0.833210i	$-0.313500\pi$
$829$	31.8418	1.10591	0.552956	+	0.833210i	$0.313500\pi$
$830$	−74.2859	−2.57850
$831$	−5.50766	−0.191059
$832$	3.97777	0.137904
$833$	−6.99110	−0.242227
$834$	123.067	4.26148
$835$	−36.6099	−1.26694
$836$	5.64623	0.195279
$837$	−5.11546	−0.176816
$838$	−61.2499	−2.11584
$839$	−18.9138	−0.652976	−0.326488	−	0.945201i	$-0.605865\pi$
$839$	−18.9138	−0.652976	−0.326488	+	0.945201i	$0.605865\pi$
$840$	−1.33985	−0.0462293
$841$	40.9528	1.41217
$842$	29.1493	1.00455
$843$	30.1047	1.03686
$844$	30.0226	1.03342
$845$	32.4292	1.11560
$846$	−94.9929	−3.26592
$847$	0.0943373	0.00324147
$848$	−2.77750	−0.0953798
$849$	78.5462	2.69570
$850$	−2.90045	−0.0994846
$851$	−7.67864	−0.263220
$852$	139.120	4.76616
$853$	26.6413	0.912181	0.456090	−	0.889933i	$-0.349249\pi$
$853$	26.6413	0.912181	0.456090	+	0.889933i	$0.349249\pi$
$854$	−2.35684	−0.0806493
$855$	30.6417	1.04792
$856$	36.3637	1.24289
$857$	−4.09921	−0.140026	−0.0700131	−	0.997546i	$-0.522304\pi$
$857$	−4.09921	−0.140026	−0.0700131	+	0.997546i	$0.522304\pi$
$858$	2.08012	0.0710142
$859$	−26.3718	−0.899795	−0.449897	−	0.893080i	$-0.648539\pi$
$859$	−26.3718	−0.899795	−0.449897	+	0.893080i	$0.648539\pi$
$860$	−7.15918	−0.244126
$861$	1.42746	0.0486479
$862$	−22.1978	−0.756059
$863$	−19.7942	−0.673801	−0.336901	−	0.941540i	$-0.609379\pi$
$863$	−19.7942	−0.673801	−0.336901	+	0.941540i	$0.609379\pi$
$864$	−68.8270	−2.34154
$865$	−18.9125	−0.643044
$866$	−80.1682	−2.72423
$867$	−3.02493	−0.102732
$868$	0.144249	0.00489613
$869$	9.53631	0.323497
$870$	−140.017	−4.74702
$871$	1.35017	0.0457487
$872$	−14.2407	−0.482252
$873$	−12.0134	−0.406592
$874$	−7.38319	−0.249740
$875$	0.873213	0.0295200
$876$	−14.1656	−0.478613
$877$	20.7039	0.699120	0.349560	−	0.936914i	$-0.386331\pi$
$877$	20.7039	0.699120	0.349560	+	0.936914i	$0.386331\pi$
$878$	−19.8612	−0.670283
$879$	−68.8578	−2.32252
$880$	−3.97988	−0.134162
$881$	−47.8003	−1.61043	−0.805217	−	0.592980i	$-0.797951\pi$
$881$	−47.8003	−1.61043	−0.805217	+	0.592980i	$0.797951\pi$
$882$	94.6747	3.18786
$883$	12.6549	0.425871	0.212935	−	0.977066i	$-0.431698\pi$
$883$	12.6549	0.425871	0.212935	+	0.977066i	$0.431698\pi$
$884$	−0.889558	−0.0299191
$885$	−82.0218	−2.75713
$886$	36.1232	1.21358
$887$	−13.0837	−0.439309	−0.219654	−	0.975578i	$-0.570493\pi$
$887$	−13.0837	−0.439309	−0.219654	+	0.975578i	$0.570493\pi$
$888$	25.6512	0.860798
$889$	1.63147	0.0547177
$890$	−12.9380	−0.433683
$891$	−10.3744	−0.347557
$892$	65.6899	2.19946
$893$	−13.9047	−0.465303
$894$	−85.7534	−2.86802
$895$	16.2740	0.543981
$896$	1.28299	0.0428616
$897$	−1.59800	−0.0533556
$898$	54.6270	1.82293
$899$	4.48986	0.149745
$900$	23.0758	0.769192
$901$	1.75407	0.0584367
$902$	−11.0145	−0.366743
$903$	−0.285364	−0.00949632
$904$	5.92835	0.197174
$905$	38.8493	1.29139
$906$	−76.0029	−2.52503
$907$	−21.5546	−0.715707	−0.357854	−	0.933778i	$-0.616491\pi$
$907$	−21.5546	−0.715707	−0.357854	+	0.933778i	$0.616491\pi$
$908$	81.0467	2.68963
$909$	−18.0365	−0.598234
$910$	−0.163050	−0.00540505
$911$	−26.1049	−0.864895	−0.432447	−	0.901659i	$-0.642350\pi$
$911$	−26.1049	−0.864895	−0.432447	+	0.901659i	$0.642350\pi$
$912$	−9.49470	−0.314401
$913$	13.4228	0.444230
$914$	−24.0205	−0.794529
$915$	86.2634	2.85178
$916$	1.97550	0.0652723
$917$	1.01405	0.0334867
$918$	20.9823	0.692520
$919$	−20.5993	−0.679509	−0.339754	−	0.940514i	$-0.610344\pi$
$919$	−20.5993	−0.679509	−0.339754	+	0.940514i	$0.610344\pi$
$920$	−7.94225	−0.261848
$921$	24.6688	0.812864
$922$	5.90165	0.194361
$923$	5.04252	0.165977
$924$	0.812827	0.0267401
$925$	5.97950	0.196605
$926$	−23.8802	−0.784752
$927$	42.0630	1.38153
$928$	60.4097	1.98304
$929$	−20.8274	−0.683324	−0.341662	−	0.939823i	$-0.610990\pi$
$929$	−20.8274	−0.683324	−0.341662	+	0.939823i	$0.610990\pi$
$930$	−8.98686	−0.294691
$931$	13.8581	0.454182
$932$	−39.2066	−1.28425
$933$	68.8302	2.25340
$934$	15.8815	0.519657
$935$	2.51341	0.0821974
$936$	3.58805	0.117279
$937$	33.4067	1.09135	0.545675	−	0.837997i	$-0.316273\pi$
$937$	33.4067	1.09135	0.545675	+	0.837997i	$0.316273\pi$
$938$	0.898040	0.0293221
$939$	−83.5793	−2.72751
$940$	−50.2187	−1.63795
$941$	42.7732	1.39437	0.697183	−	0.716893i	$-0.254437\pi$
$941$	42.7732	1.39437	0.697183	+	0.716893i	$0.254437\pi$
$942$	152.803	4.97860
$943$	8.46159	0.275547
$944$	17.0827	0.555994
$945$	2.25945	0.0734998
$946$	2.20191	0.0715901
$947$	−12.6813	−0.412088	−0.206044	−	0.978543i	$-0.566059\pi$
$947$	−12.6813	−0.412088	−0.206044	+	0.978543i	$0.566059\pi$
$948$	82.1665	2.66865
$949$	−0.513448	−0.0166672
$950$	5.74943	0.186536
$951$	5.35152	0.173535
$952$	−0.176229	−0.00571162
$953$	−4.07730	−0.132077	−0.0660383	−	0.997817i	$-0.521036\pi$
$953$	−4.07730	−0.132077	−0.0660383	+	0.997817i	$0.521036\pi$
$954$	−23.7540	−0.769064
$955$	−19.9783	−0.646482
$956$	31.8663	1.03063
$957$	25.2999	0.817828
$958$	−90.3184	−2.91806
$959$	0.121230	0.00391474
$960$	−96.8377	−3.12542
$961$	−30.7118	−0.990704
$962$	3.12156	0.100643
$963$	−119.719	−3.85790
$964$	59.4000	1.91315
$965$	−54.8284	−1.76499
$966$	−1.06288	−0.0341976
$967$	−12.9620	−0.416830	−0.208415	−	0.978040i	$-0.566830\pi$
$967$	−12.9620	−0.416830	−0.208415	+	0.978040i	$0.566830\pi$
$968$	−1.86807	−0.0600422
$969$	5.99618	0.192625
$970$	−10.8103	−0.347099
$971$	−41.9999	−1.34784	−0.673920	−	0.738804i	$-0.735391\pi$
$971$	−41.9999	−1.34784	−0.673920	+	0.738804i	$0.735391\pi$
$972$	−7.95977	−0.255310
$973$	1.74306	0.0558800
$974$	61.2711	1.96325
$975$	1.24439	0.0398524
$976$	−17.9661	−0.575080
$977$	−9.74210	−0.311677	−0.155839	−	0.987783i	$-0.549808\pi$
$977$	−9.74210	−0.311677	−0.155839	+	0.987783i	$0.549808\pi$
$978$	105.686	3.37947
$979$	2.33778	0.0747159
$980$	50.0505	1.59881
$981$	46.8844	1.49690
$982$	−74.3257	−2.37183
$983$	−54.2569	−1.73053	−0.865264	−	0.501317i	$-0.832849\pi$
$983$	−54.2569	−1.73053	−0.865264	+	0.501317i	$0.832849\pi$
$984$	−28.2667	−0.901111
$985$	10.5570	0.336373
$986$	−18.4163	−0.586493
$987$	−2.00171	−0.0637152
$988$	1.76333	0.0560990
$989$	−1.69155	−0.0537883
$990$	−34.0371	−1.08177
$991$	−26.7874	−0.850931	−0.425466	−	0.904975i	$-0.639890\pi$
$991$	−26.7874	−0.850931	−0.425466	+	0.904975i	$0.639890\pi$
$992$	3.87734	0.123106
$993$	−51.2122	−1.62517
$994$	3.35394	0.106381
$995$	63.9251	2.02656
$996$	115.653	3.66462
$997$	−9.94484	−0.314956	−0.157478	−	0.987522i	$-0.550336\pi$
$997$	−9.94484	−0.314956	−0.157478	+	0.987522i	$0.550336\pi$
$998$	−14.0145	−0.443622
$999$	−43.2567	−1.36858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.11	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.11	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.20191 q^{2} -3.02493 q^{3} +2.84839 q^{4} -2.51341 q^{5} +6.66061 q^{6} +0.0943373 q^{7} -1.86807 q^{8} +6.15021 q^{9} +O(q^{10})\)	\(q-2.20191 q^{2} -3.02493 q^{3} +2.84839 q^{4} -2.51341 q^{5} +6.66061 q^{6} +0.0943373 q^{7} -1.86807 q^{8} +6.15021 q^{9} +5.53430 q^{10} -1.00000 q^{11} -8.61618 q^{12} -0.312302 q^{13} -0.207722 q^{14} +7.60290 q^{15} -1.58346 q^{16} +1.00000 q^{17} -13.5422 q^{18} -1.98225 q^{19} -7.15918 q^{20} -0.285364 q^{21} +2.20191 q^{22} -1.69155 q^{23} +5.65079 q^{24} +1.31725 q^{25} +0.687659 q^{26} -9.52917 q^{27} +0.268709 q^{28} +8.36378 q^{29} -16.7409 q^{30} +0.536821 q^{31} +7.22277 q^{32} +3.02493 q^{33} -2.20191 q^{34} -0.237109 q^{35} +17.5182 q^{36} +4.53940 q^{37} +4.36474 q^{38} +0.944692 q^{39} +4.69524 q^{40} -5.00226 q^{41} +0.628344 q^{42} +1.00000 q^{43} -2.84839 q^{44} -15.4580 q^{45} +3.72464 q^{46} +7.01459 q^{47} +4.78985 q^{48} -6.99110 q^{49} -2.90045 q^{50} -3.02493 q^{51} -0.889558 q^{52} +1.75407 q^{53} +20.9823 q^{54} +2.51341 q^{55} -0.176229 q^{56} +5.99618 q^{57} -18.4163 q^{58} -10.7882 q^{59} +21.6560 q^{60} +11.3461 q^{61} -1.18203 q^{62} +0.580194 q^{63} -12.7369 q^{64} +0.784944 q^{65} -6.66061 q^{66} -4.32328 q^{67} +2.84839 q^{68} +5.11683 q^{69} +0.522091 q^{70} -16.1463 q^{71} -11.4890 q^{72} +1.64407 q^{73} -9.99533 q^{74} -3.98458 q^{75} -5.64623 q^{76} -0.0943373 q^{77} -2.08012 q^{78} -9.53631 q^{79} +3.97988 q^{80} +10.3744 q^{81} +11.0145 q^{82} -13.4228 q^{83} -0.812827 q^{84} -2.51341 q^{85} -2.20191 q^{86} -25.2999 q^{87} +1.86807 q^{88} -2.33778 q^{89} +34.0371 q^{90} -0.0294617 q^{91} -4.81820 q^{92} -1.62385 q^{93} -15.4455 q^{94} +4.98222 q^{95} -21.8484 q^{96} -1.95333 q^{97} +15.3937 q^{98} -6.15021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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