LMFDB - Embedded newform 8043.2.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45063 q^{2} +1.00000 q^{3} +4.00561 q^{4} +2.55159 q^{5} -2.45063 q^{6} -1.00000 q^{7} -4.91502 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.45063 q^{2} +1.00000 q^{3} +4.00561 q^{4} +2.55159 q^{5} -2.45063 q^{6} -1.00000 q^{7} -4.91502 q^{8} +1.00000 q^{9} -6.25302 q^{10} -4.54790 q^{11} +4.00561 q^{12} -1.98375 q^{13} +2.45063 q^{14} +2.55159 q^{15} +4.03370 q^{16} -0.0223972 q^{17} -2.45063 q^{18} +7.33723 q^{19} +10.2207 q^{20} -1.00000 q^{21} +11.1452 q^{22} -6.17767 q^{23} -4.91502 q^{24} +1.51062 q^{25} +4.86144 q^{26} +1.00000 q^{27} -4.00561 q^{28} -3.26329 q^{29} -6.25302 q^{30} +2.76821 q^{31} -0.0550758 q^{32} -4.54790 q^{33} +0.0548873 q^{34} -2.55159 q^{35} +4.00561 q^{36} -0.724945 q^{37} -17.9809 q^{38} -1.98375 q^{39} -12.5411 q^{40} +5.40354 q^{41} +2.45063 q^{42} -6.24559 q^{43} -18.2171 q^{44} +2.55159 q^{45} +15.1392 q^{46} -1.89913 q^{47} +4.03370 q^{48} +1.00000 q^{49} -3.70197 q^{50} -0.0223972 q^{51} -7.94612 q^{52} +9.71731 q^{53} -2.45063 q^{54} -11.6044 q^{55} +4.91502 q^{56} +7.33723 q^{57} +7.99714 q^{58} -6.81216 q^{59} +10.2207 q^{60} -3.07206 q^{61} -6.78388 q^{62} -1.00000 q^{63} -7.93242 q^{64} -5.06171 q^{65} +11.1452 q^{66} +11.2197 q^{67} -0.0897143 q^{68} -6.17767 q^{69} +6.25302 q^{70} -1.31709 q^{71} -4.91502 q^{72} -9.81968 q^{73} +1.77658 q^{74} +1.51062 q^{75} +29.3901 q^{76} +4.54790 q^{77} +4.86144 q^{78} +9.83963 q^{79} +10.2923 q^{80} +1.00000 q^{81} -13.2421 q^{82} -3.52096 q^{83} -4.00561 q^{84} -0.0571484 q^{85} +15.3057 q^{86} -3.26329 q^{87} +22.3530 q^{88} -3.23187 q^{89} -6.25302 q^{90} +1.98375 q^{91} -24.7453 q^{92} +2.76821 q^{93} +4.65407 q^{94} +18.7216 q^{95} -0.0550758 q^{96} -10.5640 q^{97} -2.45063 q^{98} -4.54790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * 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 $

$2$	−2.45063	−1.73286	−0.866430	−	0.499298i	$-0.833591\pi$
$2$	−2.45063	−1.73286	−0.866430	+	0.499298i	$0.833591\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.00561	2.00281
$5$	2.55159	1.14111	0.570553	−	0.821261i	$-0.306729\pi$
$5$	2.55159	1.14111	0.570553	+	0.821261i	$0.306729\pi$
$6$	−2.45063	−1.00047
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.91502	−1.73772
$9$	1.00000	0.333333
$10$	−6.25302	−1.97738
$11$	−4.54790	−1.37124	−0.685621	−	0.727958i	$-0.740469\pi$
$11$	−4.54790	−1.37124	−0.685621	+	0.727958i	$0.740469\pi$
$12$	4.00561	1.15632
$13$	−1.98375	−0.550192	−0.275096	−	0.961417i	$-0.588710\pi$
$13$	−1.98375	−0.550192	−0.275096	+	0.961417i	$0.588710\pi$
$14$	2.45063	0.654960
$15$	2.55159	0.658818
$16$	4.03370	1.00842
$17$	−0.0223972	−0.00543211	−0.00271605	−	0.999996i	$-0.500865\pi$
$17$	−0.0223972	−0.00543211	−0.00271605	+	0.999996i	$0.500865\pi$
$18$	−2.45063	−0.577620
$19$	7.33723	1.68328	0.841638	−	0.540041i	$-0.181591\pi$
$19$	7.33723	1.68328	0.841638	+	0.540041i	$0.181591\pi$
$20$	10.2207	2.28541
$21$	−1.00000	−0.218218
$22$	11.1452	2.37617
$23$	−6.17767	−1.28813	−0.644066	−	0.764970i	$-0.722754\pi$
$23$	−6.17767	−1.28813	−0.644066	+	0.764970i	$0.722754\pi$
$24$	−4.91502	−1.00327
$25$	1.51062	0.302123
$26$	4.86144	0.953407
$27$	1.00000	0.192450
$28$	−4.00561	−0.756989
$29$	−3.26329	−0.605978	−0.302989	−	0.952994i	$-0.597985\pi$
$29$	−3.26329	−0.605978	−0.302989	+	0.952994i	$0.597985\pi$
$30$	−6.25302	−1.14164
$31$	2.76821	0.497186	0.248593	−	0.968608i	$-0.420032\pi$
$31$	2.76821	0.497186	0.248593	+	0.968608i	$0.420032\pi$
$32$	−0.0550758	−0.00973612
$33$	−4.54790	−0.791687
$34$	0.0548873	0.00941309
$35$	−2.55159	−0.431298
$36$	4.00561	0.667602
$37$	−0.724945	−0.119180	−0.0595901	−	0.998223i	$-0.518979\pi$
$37$	−0.724945	−0.119180	−0.0595901	+	0.998223i	$0.518979\pi$
$38$	−17.9809	−2.91688
$39$	−1.98375	−0.317654
$40$	−12.5411	−1.98293
$41$	5.40354	0.843891	0.421946	−	0.906621i	$-0.361347\pi$
$41$	5.40354	0.843891	0.421946	+	0.906621i	$0.361347\pi$
$42$	2.45063	0.378141
$43$	−6.24559	−0.952444	−0.476222	−	0.879325i	$-0.657994\pi$
$43$	−6.24559	−0.952444	−0.476222	+	0.879325i	$0.657994\pi$
$44$	−18.2171	−2.74633
$45$	2.55159	0.380369
$46$	15.1392	2.23215
$47$	−1.89913	−0.277016	−0.138508	−	0.990361i	$-0.544231\pi$
$47$	−1.89913	−0.277016	−0.138508	+	0.990361i	$0.544231\pi$
$48$	4.03370	0.582214
$49$	1.00000	0.142857
$50$	−3.70197	−0.523538
$51$	−0.0223972	−0.00313623
$52$	−7.94612	−1.10193
$53$	9.71731	1.33478	0.667388	−	0.744710i	$-0.267412\pi$
$53$	9.71731	1.33478	0.667388	+	0.744710i	$0.267412\pi$
$54$	−2.45063	−0.333489
$55$	−11.6044	−1.56473
$56$	4.91502	0.656797
$57$	7.33723	0.971840
$58$	7.99714	1.05008
$59$	−6.81216	−0.886868	−0.443434	−	0.896307i	$-0.646240\pi$
$59$	−6.81216	−0.886868	−0.443434	+	0.896307i	$0.646240\pi$
$60$	10.2207	1.31948
$61$	−3.07206	−0.393337	−0.196668	−	0.980470i	$-0.563012\pi$
$61$	−3.07206	−0.393337	−0.196668	+	0.980470i	$0.563012\pi$
$62$	−6.78388	−0.861553
$63$	−1.00000	−0.125988
$64$	−7.93242	−0.991553
$65$	−5.06171	−0.627828
$66$	11.1452	1.37188
$67$	11.2197	1.37070	0.685351	−	0.728212i	$-0.259649\pi$
$67$	11.2197	1.37070	0.685351	+	0.728212i	$0.259649\pi$
$68$	−0.0897143	−0.0108795
$69$	−6.17767	−0.743704
$70$	6.25302	0.747379
$71$	−1.31709	−0.156310	−0.0781550	−	0.996941i	$-0.524903\pi$
$71$	−1.31709	−0.156310	−0.0781550	+	0.996941i	$0.524903\pi$
$72$	−4.91502	−0.579241
$73$	−9.81968	−1.14931	−0.574653	−	0.818397i	$-0.694863\pi$
$73$	−9.81968	−1.14931	−0.574653	+	0.818397i	$0.694863\pi$
$74$	1.77658	0.206523
$75$	1.51062	0.174431
$76$	29.3901	3.37128
$77$	4.54790	0.518281
$78$	4.86144	0.550450
$79$	9.83963	1.10704	0.553522	−	0.832834i	$-0.313283\pi$
$79$	9.83963	1.10704	0.553522	+	0.832834i	$0.313283\pi$
$80$	10.2923	1.15072
$81$	1.00000	0.111111
$82$	−13.2421	−1.46235
$83$	−3.52096	−0.386475	−0.193238	−	0.981152i	$-0.561899\pi$
$83$	−3.52096	−0.386475	−0.193238	+	0.981152i	$0.561899\pi$
$84$	−4.00561	−0.437048
$85$	−0.0571484	−0.00619861
$86$	15.3057	1.65045
$87$	−3.26329	−0.349862
$88$	22.3530	2.38284
$89$	−3.23187	−0.342577	−0.171289	−	0.985221i	$-0.554793\pi$
$89$	−3.23187	−0.342577	−0.171289	+	0.985221i	$0.554793\pi$
$90$	−6.25302	−0.659126
$91$	1.98375	0.207953
$92$	−24.7453	−2.57988
$93$	2.76821	0.287050
$94$	4.65407	0.480031
$95$	18.7216	1.92080
$96$	−0.0550758	−0.00562115
$97$	−10.5640	−1.07261	−0.536307	−	0.844023i	$-0.680181\pi$
$97$	−10.5640	−1.07261	−0.536307	+	0.844023i	$0.680181\pi$
$98$	−2.45063	−0.247551
$99$	−4.54790	−0.457081
$100$	6.05095	0.605095
$101$	15.8634	1.57847	0.789235	−	0.614092i	$-0.210477\pi$
$101$	15.8634	1.57847	0.789235	+	0.614092i	$0.210477\pi$
$102$	0.0548873	0.00543465
$103$	4.58412	0.451687	0.225843	−	0.974164i	$-0.427486\pi$
$103$	4.58412	0.451687	0.225843	+	0.974164i	$0.427486\pi$
$104$	9.75015	0.956081
$105$	−2.55159	−0.249010
$106$	−23.8136	−2.31298
$107$	0.682614	0.0659908	0.0329954	−	0.999456i	$-0.489495\pi$
$107$	0.682614	0.0659908	0.0329954	+	0.999456i	$0.489495\pi$
$108$	4.00561	0.385440
$109$	14.7520	1.41298	0.706491	−	0.707722i	$-0.250277\pi$
$109$	14.7520	1.41298	0.706491	+	0.707722i	$0.250277\pi$
$110$	28.4381	2.71146
$111$	−0.724945	−0.0688088
$112$	−4.03370	−0.381148
$113$	−5.20056	−0.489227	−0.244614	−	0.969621i	$-0.578661\pi$
$113$	−5.20056	−0.489227	−0.244614	+	0.969621i	$0.578661\pi$
$114$	−17.9809	−1.68406
$115$	−15.7629	−1.46990
$116$	−13.0715	−1.21366
$117$	−1.98375	−0.183397
$118$	16.6941	1.53682
$119$	0.0223972	0.00205314
$120$	−12.5411	−1.14484
$121$	9.68336	0.880306
$122$	7.52849	0.681598
$123$	5.40354	0.487221
$124$	11.0884	0.995766
$125$	−8.90348	−0.796351
$126$	2.45063	0.218320
$127$	17.9084	1.58912	0.794558	−	0.607189i	$-0.207703\pi$
$127$	17.9084	1.58912	0.794558	+	0.607189i	$0.207703\pi$
$128$	19.5496	1.72796
$129$	−6.24559	−0.549894
$130$	12.4044	1.08794
$131$	0.340618	0.0297599	0.0148800	−	0.999889i	$-0.495263\pi$
$131$	0.340618	0.0297599	0.0148800	+	0.999889i	$0.495263\pi$
$132$	−18.2171	−1.58560
$133$	−7.33723	−0.636219
$134$	−27.4954	−2.37524
$135$	2.55159	0.219606
$136$	0.110082	0.00943949
$137$	−20.8621	−1.78237	−0.891185	−	0.453641i	$-0.850125\pi$
$137$	−20.8621	−1.78237	−0.891185	+	0.453641i	$0.850125\pi$
$138$	15.1392	1.28873
$139$	−0.710090	−0.0602291	−0.0301145	−	0.999546i	$-0.509587\pi$
$139$	−0.710090	−0.0602291	−0.0301145	+	0.999546i	$0.509587\pi$
$140$	−10.2207	−0.863805
$141$	−1.89913	−0.159935
$142$	3.22771	0.270863
$143$	9.02188	0.754447
$144$	4.03370	0.336141
$145$	−8.32659	−0.691486
$146$	24.0644	1.99159
$147$	1.00000	0.0824786
$148$	−2.90385	−0.238695
$149$	−16.0390	−1.31396	−0.656981	−	0.753907i	$-0.728167\pi$
$149$	−16.0390	−1.31396	−0.656981	+	0.753907i	$0.728167\pi$
$150$	−3.70197	−0.302265
$151$	−5.57810	−0.453940	−0.226970	−	0.973902i	$-0.572882\pi$
$151$	−5.57810	−0.453940	−0.226970	+	0.973902i	$0.572882\pi$
$152$	−36.0626	−2.92507
$153$	−0.0223972	−0.00181070
$154$	−11.1452	−0.898108
$155$	7.06335	0.567342
$156$	−7.94612	−0.636199
$157$	−9.10313	−0.726509	−0.363254	−	0.931690i	$-0.618334\pi$
$157$	−9.10313	−0.726509	−0.363254	+	0.931690i	$0.618334\pi$
$158$	−24.1133	−1.91835
$159$	9.71731	0.770633
$160$	−0.140531	−0.0111100
$161$	6.17767	0.486868
$162$	−2.45063	−0.192540
$163$	−11.6153	−0.909780	−0.454890	−	0.890548i	$-0.650322\pi$
$163$	−11.6153	−0.909780	−0.454890	+	0.890548i	$0.650322\pi$
$164$	21.6445	1.69015
$165$	−11.6044	−0.903399
$166$	8.62858	0.669707
$167$	−10.8280	−0.837892	−0.418946	−	0.908011i	$-0.637600\pi$
$167$	−10.8280	−0.837892	−0.418946	+	0.908011i	$0.637600\pi$
$168$	4.91502	0.379202
$169$	−9.06475	−0.697288
$170$	0.140050	0.0107413
$171$	7.33723	0.561092
$172$	−25.0174	−1.90756
$173$	−12.6971	−0.965342	−0.482671	−	0.875802i	$-0.660333\pi$
$173$	−12.6971	−0.965342	−0.482671	+	0.875802i	$0.660333\pi$
$174$	7.99714	0.606262
$175$	−1.51062	−0.114192
$176$	−18.3448	−1.38279
$177$	−6.81216	−0.512034
$178$	7.92013	0.593639
$179$	−11.4687	−0.857209	−0.428605	−	0.903492i	$-0.640995\pi$
$179$	−11.4687	−0.857209	−0.428605	+	0.903492i	$0.640995\pi$
$180$	10.2207	0.761805
$181$	1.28594	0.0955833	0.0477916	−	0.998857i	$-0.484782\pi$
$181$	1.28594	0.0955833	0.0477916	+	0.998857i	$0.484782\pi$
$182$	−4.86144	−0.360354
$183$	−3.07206	−0.227093
$184$	30.3634	2.23842
$185$	−1.84976	−0.135997
$186$	−6.78388	−0.497418
$187$	0.101860	0.00744874
$188$	−7.60717	−0.554810
$189$	−1.00000	−0.0727393
$190$	−45.8799	−3.32847
$191$	−11.4461	−0.828211	−0.414106	−	0.910229i	$-0.635906\pi$
$191$	−11.4461	−0.828211	−0.414106	+	0.910229i	$0.635906\pi$
$192$	−7.93242	−0.572473
$193$	−14.6505	−1.05457	−0.527284	−	0.849689i	$-0.676790\pi$
$193$	−14.6505	−1.05457	−0.527284	+	0.849689i	$0.676790\pi$
$194$	25.8886	1.85869
$195$	−5.06171	−0.362477
$196$	4.00561	0.286115
$197$	−14.8136	−1.05543	−0.527714	−	0.849422i	$-0.676951\pi$
$197$	−14.8136	−1.05543	−0.527714	+	0.849422i	$0.676951\pi$
$198$	11.1452	0.792057
$199$	−5.96659	−0.422960	−0.211480	−	0.977382i	$-0.567828\pi$
$199$	−5.96659	−0.422960	−0.211480	+	0.977382i	$0.567828\pi$
$200$	−7.42471	−0.525007
$201$	11.2197	0.791376
$202$	−38.8755	−2.73527
$203$	3.26329	0.229038
$204$	−0.0897143	−0.00628126
$205$	13.7876	0.962969
$206$	−11.2340	−0.782710
$207$	−6.17767	−0.429378
$208$	−8.00183	−0.554827
$209$	−33.3690	−2.30818
$210$	6.25302	0.431499
$211$	−9.47020	−0.651956	−0.325978	−	0.945377i	$-0.605693\pi$
$211$	−9.47020	−0.651956	−0.325978	+	0.945377i	$0.605693\pi$
$212$	38.9238	2.67330
$213$	−1.31709	−0.0902456
$214$	−1.67284	−0.114353
$215$	−15.9362	−1.08684
$216$	−4.91502	−0.334425
$217$	−2.76821	−0.187919
$218$	−36.1517	−2.44850
$219$	−9.81968	−0.663552
$220$	−46.4826	−3.13386
$221$	0.0444303	0.00298870
$222$	1.77658	0.119236
$223$	9.30305	0.622978	0.311489	−	0.950250i	$-0.399172\pi$
$223$	9.30305	0.622978	0.311489	+	0.950250i	$0.399172\pi$
$224$	0.0550758	0.00367991
$225$	1.51062	0.100708
$226$	12.7447	0.847763
$227$	3.84741	0.255361	0.127681	−	0.991815i	$-0.459247\pi$
$227$	3.84741	0.255361	0.127681	+	0.991815i	$0.459247\pi$
$228$	29.3901	1.94641
$229$	9.05266	0.598216	0.299108	−	0.954219i	$-0.403311\pi$
$229$	9.05266	0.598216	0.299108	+	0.954219i	$0.403311\pi$
$230$	38.6291	2.54713
$231$	4.54790	0.299230
$232$	16.0392	1.05302
$233$	−24.0059	−1.57268	−0.786338	−	0.617796i	$-0.788026\pi$
$233$	−24.0059	−1.57268	−0.786338	+	0.617796i	$0.788026\pi$
$234$	4.86144	0.317802
$235$	−4.84580	−0.316105
$236$	−27.2869	−1.77622
$237$	9.83963	0.639152
$238$	−0.0548873	−0.00355781
$239$	−21.2591	−1.37514	−0.687568	−	0.726120i	$-0.741322\pi$
$239$	−21.2591	−1.37514	−0.687568	+	0.726120i	$0.741322\pi$
$240$	10.2923	0.664368
$241$	9.73292	0.626952	0.313476	−	0.949596i	$-0.398506\pi$
$241$	9.73292	0.626952	0.313476	+	0.949596i	$0.398506\pi$
$242$	−23.7304	−1.52545
$243$	1.00000	0.0641500
$244$	−12.3055	−0.787777
$245$	2.55159	0.163015
$246$	−13.2421	−0.844286
$247$	−14.5552	−0.926126
$248$	−13.6058	−0.863970
$249$	−3.52096	−0.223131
$250$	21.8192	1.37997
$251$	23.7097	1.49654	0.748271	−	0.663393i	$-0.230884\pi$
$251$	23.7097	1.49654	0.748271	+	0.663393i	$0.230884\pi$
$252$	−4.00561	−0.252330
$253$	28.0954	1.76634
$254$	−43.8870	−2.75372
$255$	−0.0571484	−0.00357877
$256$	−32.0441	−2.00276
$257$	−4.83764	−0.301764	−0.150882	−	0.988552i	$-0.548211\pi$
$257$	−4.83764	−0.301764	−0.150882	+	0.988552i	$0.548211\pi$
$258$	15.3057	0.952889
$259$	0.724945	0.0450459
$260$	−20.2752	−1.25742
$261$	−3.26329	−0.201993
$262$	−0.834730	−0.0515698
$263$	13.9764	0.861822	0.430911	−	0.902395i	$-0.358192\pi$
$263$	13.9764	0.861822	0.430911	+	0.902395i	$0.358192\pi$
$264$	22.3530	1.37573
$265$	24.7946	1.52312
$266$	17.9809	1.10248
$267$	−3.23187	−0.197787
$268$	44.9417	2.74525
$269$	−24.2703	−1.47979	−0.739894	−	0.672724i	$-0.765124\pi$
$269$	−24.2703	−1.47979	−0.739894	+	0.672724i	$0.765124\pi$
$270$	−6.25302	−0.380547
$271$	−5.17290	−0.314231	−0.157116	−	0.987580i	$-0.550220\pi$
$271$	−5.17290	−0.314231	−0.157116	+	0.987580i	$0.550220\pi$
$272$	−0.0903433	−0.00547787
$273$	1.98375	0.120062
$274$	51.1254	3.08860
$275$	−6.87013	−0.414285
$276$	−24.7453	−1.48949
$277$	−23.1436	−1.39056	−0.695281	−	0.718738i	$-0.744720\pi$
$277$	−23.1436	−1.39056	−0.695281	+	0.718738i	$0.744720\pi$
$278$	1.74017	0.104369
$279$	2.76821	0.165729
$280$	12.5411	0.749475
$281$	−31.0543	−1.85254	−0.926271	−	0.376858i	$-0.877004\pi$
$281$	−31.0543	−1.85254	−0.926271	+	0.376858i	$0.877004\pi$
$282$	4.65407	0.277146
$283$	−12.4795	−0.741830	−0.370915	−	0.928667i	$-0.620956\pi$
$283$	−12.4795	−0.741830	−0.370915	+	0.928667i	$0.620956\pi$
$284$	−5.27575	−0.313058
$285$	18.7216	1.10897
$286$	−22.1093	−1.30735
$287$	−5.40354	−0.318961
$288$	−0.0550758	−0.00324537
$289$	−16.9995	−0.999970
$290$	20.4054	1.19825
$291$	−10.5640	−0.619274
$292$	−39.3338	−2.30184
$293$	13.0227	0.760795	0.380397	−	0.924823i	$-0.375787\pi$
$293$	13.0227	0.760795	0.380397	+	0.924823i	$0.375787\pi$
$294$	−2.45063	−0.142924
$295$	−17.3819	−1.01201
$296$	3.56312	0.207102
$297$	−4.54790	−0.263896
$298$	39.3056	2.27691
$299$	12.2549	0.708721
$300$	6.05095	0.349351
$301$	6.24559	0.359990
$302$	13.6699	0.786614
$303$	15.8634	0.911330
$304$	29.5962	1.69746
$305$	−7.83864	−0.448839
$306$	0.0548873	0.00313770
$307$	21.7677	1.24235	0.621174	−	0.783672i	$-0.286656\pi$
$307$	21.7677	1.24235	0.621174	+	0.783672i	$0.286656\pi$
$308$	18.2171	1.03802
$309$	4.58412	0.260781
$310$	−17.3097	−0.983124
$311$	−1.99744	−0.113264	−0.0566321	−	0.998395i	$-0.518036\pi$
$311$	−1.99744	−0.113264	−0.0566321	+	0.998395i	$0.518036\pi$
$312$	9.75015	0.551994
$313$	22.1641	1.25279	0.626394	−	0.779506i	$-0.284530\pi$
$313$	22.1641	1.25279	0.626394	+	0.779506i	$0.284530\pi$
$314$	22.3084	1.25894
$315$	−2.55159	−0.143766
$316$	39.4137	2.21719
$317$	−27.0836	−1.52117	−0.760584	−	0.649240i	$-0.775087\pi$
$317$	−27.0836	−1.52117	−0.760584	+	0.649240i	$0.775087\pi$
$318$	−23.8136	−1.33540
$319$	14.8411	0.830943
$320$	−20.2403	−1.13147
$321$	0.682614	0.0380998
$322$	−15.1392	−0.843675
$323$	−0.164333	−0.00914374
$324$	4.00561	0.222534
$325$	−2.99668	−0.166226
$326$	28.4649	1.57652
$327$	14.7520	0.815785
$328$	−26.5585	−1.46645
$329$	1.89913	0.104702
$330$	28.4381	1.56546
$331$	−17.9432	−0.986246	−0.493123	−	0.869960i	$-0.664145\pi$
$331$	−17.9432	−0.986246	−0.493123	+	0.869960i	$0.664145\pi$
$332$	−14.1036	−0.774034
$333$	−0.724945	−0.0397268
$334$	26.5354	1.45195
$335$	28.6281	1.56412
$336$	−4.03370	−0.220056
$337$	−5.09146	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$337$	−5.09146	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$338$	22.2144	1.20830
$339$	−5.20056	−0.282456
$340$	−0.228914	−0.0124146
$341$	−12.5895	−0.681762
$342$	−17.9809	−0.972295
$343$	−1.00000	−0.0539949
$344$	30.6972	1.65508
$345$	−15.7629	−0.848645
$346$	31.1159	1.67280
$347$	0.306006	0.0164273	0.00821363	−	0.999966i	$-0.497385\pi$
$347$	0.306006	0.0164273	0.00821363	+	0.999966i	$0.497385\pi$
$348$	−13.0715	−0.700705
$349$	−10.2532	−0.548841	−0.274421	−	0.961610i	$-0.588486\pi$
$349$	−10.2532	−0.548841	−0.274421	+	0.961610i	$0.588486\pi$
$350$	3.70197	0.197879
$351$	−1.98375	−0.105885
$352$	0.250479	0.0133506
$353$	−20.4505	−1.08847	−0.544235	−	0.838933i	$-0.683180\pi$
$353$	−20.4505	−1.08847	−0.544235	+	0.838933i	$0.683180\pi$
$354$	16.6941	0.887283
$355$	−3.36068	−0.178366
$356$	−12.9456	−0.686116
$357$	0.0223972	0.00118538
$358$	28.1055	1.48542
$359$	31.5121	1.66315	0.831573	−	0.555416i	$-0.187441\pi$
$359$	31.5121	1.66315	0.831573	+	0.555416i	$0.187441\pi$
$360$	−12.5411	−0.660975
$361$	34.8350	1.83342
$362$	−3.15137	−0.165632
$363$	9.68336	0.508245
$364$	7.94612	0.416490
$365$	−25.0558	−1.31148
$366$	7.52849	0.393521
$367$	−27.4642	−1.43362	−0.716809	−	0.697269i	$-0.754398\pi$
$367$	−27.4642	−1.43362	−0.716809	+	0.697269i	$0.754398\pi$
$368$	−24.9188	−1.29898
$369$	5.40354	0.281297
$370$	4.53310	0.235664
$371$	−9.71731	−0.504498
$372$	11.0884	0.574906
$373$	6.00478	0.310916	0.155458	−	0.987843i	$-0.450315\pi$
$373$	6.00478	0.310916	0.155458	+	0.987843i	$0.450315\pi$
$374$	−0.249622	−0.0129076
$375$	−8.90348	−0.459774
$376$	9.33425	0.481377
$377$	6.47355	0.333405
$378$	2.45063	0.126047
$379$	16.7642	0.861120	0.430560	−	0.902562i	$-0.358316\pi$
$379$	16.7642	0.861120	0.430560	+	0.902562i	$0.358316\pi$
$380$	74.9915	3.84698
$381$	17.9084	0.917476
$382$	28.0502	1.43517
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	19.5496	0.997637
$385$	11.6044	0.591414
$386$	35.9031	1.82742
$387$	−6.24559	−0.317481
$388$	−42.3154	−2.14824
$389$	−17.4638	−0.885450	−0.442725	−	0.896658i	$-0.645988\pi$
$389$	−17.4638	−0.885450	−0.442725	+	0.896658i	$0.645988\pi$
$390$	12.4044	0.628121
$391$	0.138362	0.00699728
$392$	−4.91502	−0.248246
$393$	0.340618	0.0171819
$394$	36.3028	1.82891
$395$	25.1067	1.26326
$396$	−18.2171	−0.915444
$397$	28.6629	1.43855	0.719275	−	0.694726i	$-0.244474\pi$
$397$	28.6629	1.43855	0.719275	+	0.694726i	$0.244474\pi$
$398$	14.6219	0.732931
$399$	−7.33723	−0.367321
$400$	6.09337	0.304669
$401$	−30.1917	−1.50770	−0.753850	−	0.657046i	$-0.771806\pi$
$401$	−30.1917	−1.50770	−0.753850	+	0.657046i	$0.771806\pi$
$402$	−27.4954	−1.37134
$403$	−5.49143	−0.273548
$404$	63.5427	3.16137
$405$	2.55159	0.126790
$406$	−7.99714	−0.396891
$407$	3.29698	0.163425
$408$	0.110082	0.00544989
$409$	9.28686	0.459206	0.229603	−	0.973284i	$-0.426257\pi$
$409$	9.28686	0.459206	0.229603	+	0.973284i	$0.426257\pi$
$410$	−33.7884	−1.66869
$411$	−20.8621	−1.02905
$412$	18.3622	0.904640
$413$	6.81216	0.335205
$414$	15.1392	0.744051
$415$	−8.98404	−0.441009
$416$	0.109257	0.00535674
$417$	−0.710090	−0.0347733
$418$	81.7752	3.99975
$419$	37.5140	1.83268	0.916339	−	0.400404i	$-0.131130\pi$
$419$	37.5140	1.83268	0.916339	+	0.400404i	$0.131130\pi$
$420$	−10.2207	−0.498718
$421$	28.7335	1.40039	0.700193	−	0.713953i	$-0.253097\pi$
$421$	28.7335	1.40039	0.700193	+	0.713953i	$0.253097\pi$
$422$	23.2080	1.12975
$423$	−1.89913	−0.0923388
$424$	−47.7608	−2.31947
$425$	−0.0338335	−0.00164117
$426$	3.22771	0.156383
$427$	3.07206	0.148667
$428$	2.73428	0.132167
$429$	9.02188	0.435580
$430$	39.0538	1.88334
$431$	−21.0665	−1.01474	−0.507369	−	0.861729i	$-0.669382\pi$
$431$	−21.0665	−1.01474	−0.507369	+	0.861729i	$0.669382\pi$
$432$	4.03370	0.194071
$433$	−9.77141	−0.469584	−0.234792	−	0.972046i	$-0.575441\pi$
$433$	−9.77141	−0.469584	−0.234792	+	0.972046i	$0.575441\pi$
$434$	6.78388	0.325637
$435$	−8.32659	−0.399229
$436$	59.0906	2.82993
$437$	−45.3270	−2.16828
$438$	24.0644	1.14984
$439$	4.02106	0.191915	0.0959573	−	0.995385i	$-0.469409\pi$
$439$	4.02106	0.191915	0.0959573	+	0.995385i	$0.469409\pi$
$440$	57.0357	2.71907
$441$	1.00000	0.0476190
$442$	−0.108882	−0.00517901
$443$	−39.2042	−1.86265	−0.931323	−	0.364193i	$-0.881345\pi$
$443$	−39.2042	−1.86265	−0.931323	+	0.364193i	$0.881345\pi$
$444$	−2.90385	−0.137811
$445$	−8.24641	−0.390917
$446$	−22.7984	−1.07953
$447$	−16.0390	−0.758617
$448$	7.93242	0.374772
$449$	−14.4413	−0.681528	−0.340764	−	0.940149i	$-0.610686\pi$
$449$	−14.4413	−0.681528	−0.340764	+	0.940149i	$0.610686\pi$
$450$	−3.70197	−0.174513
$451$	−24.5747	−1.15718
$452$	−20.8314	−0.979827
$453$	−5.57810	−0.262082
$454$	−9.42859	−0.442506
$455$	5.06171	0.237297
$456$	−36.0626	−1.68879
$457$	−9.58106	−0.448183	−0.224091	−	0.974568i	$-0.571941\pi$
$457$	−9.58106	−0.448183	−0.224091	+	0.974568i	$0.571941\pi$
$458$	−22.1848	−1.03663
$459$	−0.0223972	−0.00104541
$460$	−63.1400	−2.94392
$461$	19.2279	0.895531	0.447766	−	0.894151i	$-0.352220\pi$
$461$	19.2279	0.895531	0.447766	+	0.894151i	$0.352220\pi$
$462$	−11.1452	−0.518523
$463$	18.5484	0.862019	0.431010	−	0.902347i	$-0.358157\pi$
$463$	18.5484	0.862019	0.431010	+	0.902347i	$0.358157\pi$
$464$	−13.1631	−0.611083
$465$	7.06335	0.327555
$466$	58.8296	2.72523
$467$	−16.7993	−0.777378	−0.388689	−	0.921369i	$-0.627072\pi$
$467$	−16.7993	−0.777378	−0.388689	+	0.921369i	$0.627072\pi$
$468$	−7.94612	−0.367309
$469$	−11.2197	−0.518077
$470$	11.8753	0.547766
$471$	−9.10313	−0.419450
$472$	33.4819	1.54113
$473$	28.4043	1.30603
$474$	−24.1133	−1.10756
$475$	11.0838	0.508557
$476$	0.0897143	0.00411205
$477$	9.71731	0.444925
$478$	52.0982	2.38292
$479$	−10.9683	−0.501153	−0.250577	−	0.968097i	$-0.580620\pi$
$479$	−10.9683	−0.501153	−0.250577	+	0.968097i	$0.580620\pi$
$480$	−0.140531	−0.00641433
$481$	1.43811	0.0655721
$482$	−23.8518	−1.08642
$483$	6.17767	0.281094
$484$	38.7878	1.76308
$485$	−26.9551	−1.22397
$486$	−2.45063	−0.111163
$487$	−15.4297	−0.699186	−0.349593	−	0.936902i	$-0.613680\pi$
$487$	−15.4297	−0.699186	−0.349593	+	0.936902i	$0.613680\pi$
$488$	15.0992	0.683510
$489$	−11.6153	−0.525262
$490$	−6.25302	−0.282483
$491$	−17.8281	−0.804570	−0.402285	−	0.915515i	$-0.631784\pi$
$491$	−17.8281	−0.804570	−0.402285	+	0.915515i	$0.631784\pi$
$492$	21.6445	0.975808
$493$	0.0730885	0.00329174
$494$	35.6695	1.60485
$495$	−11.6044	−0.521578
$496$	11.1661	0.501374
$497$	1.31709	0.0590796
$498$	8.62858	0.386656
$499$	31.1549	1.39468	0.697342	−	0.716739i	$-0.254366\pi$
$499$	31.1549	1.39468	0.697342	+	0.716739i	$0.254366\pi$
$500$	−35.6639	−1.59494
$501$	−10.8280	−0.483757
$502$	−58.1038	−2.59330
$503$	−10.4602	−0.466395	−0.233198	−	0.972429i	$-0.574919\pi$
$503$	−10.4602	−0.466395	−0.233198	+	0.972429i	$0.574919\pi$
$504$	4.91502	0.218932
$505$	40.4770	1.80120
$506$	−68.8516	−3.06082
$507$	−9.06475	−0.402580
$508$	71.7342	3.18269
$509$	15.7756	0.699243	0.349622	−	0.936891i	$-0.386310\pi$
$509$	15.7756	0.699243	0.349622	+	0.936891i	$0.386310\pi$
$510$	0.140050	0.00620151
$511$	9.81968	0.434397
$512$	39.4292	1.74254
$513$	7.33723	0.323947
$514$	11.8553	0.522914
$515$	11.6968	0.515422
$516$	−25.0174	−1.10133
$517$	8.63704	0.379857
$518$	−1.77658	−0.0780583
$519$	−12.6971	−0.557341
$520$	24.8784	1.09099
$521$	43.4193	1.90223	0.951117	−	0.308831i	$-0.0999379\pi$
$521$	43.4193	1.90223	0.951117	+	0.308831i	$0.0999379\pi$
$522$	7.99714	0.350025
$523$	−13.4343	−0.587440	−0.293720	−	0.955891i	$-0.594893\pi$
$523$	−13.4343	−0.587440	−0.293720	+	0.955891i	$0.594893\pi$
$524$	1.36438	0.0596033
$525$	−1.51062	−0.0659288
$526$	−34.2510	−1.49342
$527$	−0.0620001	−0.00270077
$528$	−18.3448	−0.798356
$529$	15.1636	0.659286
$530$	−60.7625	−2.63936
$531$	−6.81216	−0.295623
$532$	−29.3901	−1.27422
$533$	−10.7193	−0.464302
$534$	7.92013	0.342738
$535$	1.74175	0.0753025
$536$	−55.1450	−2.38190
$537$	−11.4687	−0.494910
$538$	59.4777	2.56427
$539$	−4.54790	−0.195892
$540$	10.2207	0.439828
$541$	−43.1403	−1.85475	−0.927373	−	0.374137i	$-0.877939\pi$
$541$	−43.1403	−1.85475	−0.927373	+	0.374137i	$0.877939\pi$
$542$	12.6769	0.544519
$543$	1.28594	0.0551850
$544$	0.00123354	5.28877e−5 0
$545$	37.6410	1.61236
$546$	−4.86144	−0.208050
$547$	−3.35640	−0.143509	−0.0717546	−	0.997422i	$-0.522860\pi$
$547$	−3.35640	−0.143509	−0.0717546	+	0.997422i	$0.522860\pi$
$548$	−83.5654	−3.56974
$549$	−3.07206	−0.131112
$550$	16.8362	0.717897
$551$	−23.9435	−1.02003
$552$	30.3634	1.29235
$553$	−9.83963	−0.418423
$554$	56.7164	2.40965
$555$	−1.84976	−0.0785181
$556$	−2.84434	−0.120627
$557$	15.9986	0.677883	0.338942	−	0.940807i	$-0.389931\pi$
$557$	15.9986	0.677883	0.338942	+	0.940807i	$0.389931\pi$
$558$	−6.78388	−0.287184
$559$	12.3897	0.524027
$560$	−10.2923	−0.434931
$561$	0.101860	0.00430053
$562$	76.1027	3.21020
$563$	35.3323	1.48908	0.744540	−	0.667578i	$-0.232669\pi$
$563$	35.3323	1.48908	0.744540	+	0.667578i	$0.232669\pi$
$564$	−7.60717	−0.320320
$565$	−13.2697	−0.558261
$566$	30.5827	1.28549
$567$	−1.00000	−0.0419961
$568$	6.47353	0.271623
$569$	−15.5290	−0.651011	−0.325505	−	0.945540i	$-0.605534\pi$
$569$	−15.5290	−0.651011	−0.325505	+	0.945540i	$0.605534\pi$
$570$	−45.8799	−1.92170
$571$	−13.3656	−0.559333	−0.279667	−	0.960097i	$-0.590224\pi$
$571$	−13.3656	−0.559333	−0.279667	+	0.960097i	$0.590224\pi$
$572$	36.1381	1.51101
$573$	−11.4461	−0.478168
$574$	13.2421	0.552715
$575$	−9.33209	−0.389175
$576$	−7.93242	−0.330518
$577$	3.83927	0.159831	0.0799154	−	0.996802i	$-0.474535\pi$
$577$	3.83927	0.159831	0.0799154	+	0.996802i	$0.474535\pi$
$578$	41.6596	1.73281
$579$	−14.6505	−0.608855
$580$	−33.3531	−1.38491
$581$	3.52096	0.146074
$582$	25.8886	1.07312
$583$	−44.1933	−1.83030
$584$	48.2639	1.99717
$585$	−5.06171	−0.209276
$586$	−31.9139	−1.31835
$587$	−27.1377	−1.12009	−0.560046	−	0.828461i	$-0.689217\pi$
$587$	−27.1377	−1.12009	−0.560046	+	0.828461i	$0.689217\pi$
$588$	4.00561	0.165189
$589$	20.3110	0.836901
$590$	42.5966	1.75367
$591$	−14.8136	−0.609351
$592$	−2.92421	−0.120184
$593$	41.6180	1.70904	0.854522	−	0.519415i	$-0.173850\pi$
$593$	41.6180	1.70904	0.854522	+	0.519415i	$0.173850\pi$
$594$	11.1452	0.457294
$595$	0.0571484	0.00234286
$596$	−64.2458	−2.63161
$597$	−5.96659	−0.244196
$598$	−30.0324	−1.22811
$599$	−18.7081	−0.764390	−0.382195	−	0.924082i	$-0.624832\pi$
$599$	−18.7081	−0.764390	−0.382195	+	0.924082i	$0.624832\pi$
$600$	−7.42471	−0.303113
$601$	38.5531	1.57261	0.786307	−	0.617836i	$-0.211991\pi$
$601$	38.5531	1.57261	0.786307	+	0.617836i	$0.211991\pi$
$602$	−15.3057	−0.623812
$603$	11.2197	0.456901
$604$	−22.3437	−0.909153
$605$	24.7080	1.00452
$606$	−38.8755	−1.57921
$607$	32.9032	1.33550	0.667749	−	0.744386i	$-0.267258\pi$
$607$	32.9032	1.33550	0.667749	+	0.744386i	$0.267258\pi$
$608$	−0.404104	−0.0163886
$609$	3.26329	0.132235
$610$	19.2096	0.777775
$611$	3.76739	0.152412
$612$	−0.0897143	−0.00362649
$613$	18.0686	0.729786	0.364893	−	0.931049i	$-0.381106\pi$
$613$	18.0686	0.729786	0.364893	+	0.931049i	$0.381106\pi$
$614$	−53.3447	−2.15282
$615$	13.7876	0.555971
$616$	−22.3530	−0.900628
$617$	−0.490978	−0.0197660	−0.00988301	−	0.999951i	$-0.503146\pi$
$617$	−0.490978	−0.0197660	−0.00988301	+	0.999951i	$0.503146\pi$
$618$	−11.2340	−0.451898
$619$	5.37974	0.216230	0.108115	−	0.994138i	$-0.465519\pi$
$619$	5.37974	0.216230	0.108115	+	0.994138i	$0.465519\pi$
$620$	28.2930	1.13627
$621$	−6.17767	−0.247901
$622$	4.89499	0.196271
$623$	3.23187	0.129482
$624$	−8.00183	−0.320330
$625$	−30.2711	−1.21084
$626$	−54.3161	−2.17091
$627$	−33.3690	−1.33263
$628$	−36.4636	−1.45506
$629$	0.0162367	0.000647400 0
$630$	6.25302	0.249126
$631$	−5.85915	−0.233249	−0.116625	−	0.993176i	$-0.537207\pi$
$631$	−5.85915	−0.233249	−0.116625	+	0.993176i	$0.537207\pi$
$632$	−48.3620	−1.92374
$633$	−9.47020	−0.376407
$634$	66.3720	2.63597
$635$	45.6950	1.81335
$636$	38.9238	1.54343
$637$	−1.98375	−0.0785989
$638$	−36.3702	−1.43991
$639$	−1.31709	−0.0521033
$640$	49.8826	1.97178
$641$	21.6041	0.853310	0.426655	−	0.904414i	$-0.359692\pi$
$641$	21.6041	0.853310	0.426655	+	0.904414i	$0.359692\pi$
$642$	−1.67284	−0.0660216
$643$	3.15131	0.124276	0.0621378	−	0.998068i	$-0.480208\pi$
$643$	3.15131	0.124276	0.0621378	+	0.998068i	$0.480208\pi$
$644$	24.7453	0.975103
$645$	−15.9362	−0.627487
$646$	0.402721	0.0158448
$647$	−18.6955	−0.734998	−0.367499	−	0.930024i	$-0.619786\pi$
$647$	−18.6955	−0.734998	−0.367499	+	0.930024i	$0.619786\pi$
$648$	−4.91502	−0.193080
$649$	30.9810	1.21611
$650$	7.34377	0.288047
$651$	−2.76821	−0.108495
$652$	−46.5264	−1.82211
$653$	−12.4426	−0.486916	−0.243458	−	0.969911i	$-0.578282\pi$
$653$	−12.4426	−0.486916	−0.243458	+	0.969911i	$0.578282\pi$
$654$	−36.1517	−1.41364
$655$	0.869117	0.0339592
$656$	21.7962	0.851000
$657$	−9.81968	−0.383102
$658$	−4.65407	−0.181435
$659$	−8.08066	−0.314778	−0.157389	−	0.987537i	$-0.550308\pi$
$659$	−8.08066	−0.314778	−0.157389	+	0.987537i	$0.550308\pi$
$660$	−46.4826	−1.80933
$661$	−10.4659	−0.407075	−0.203538	−	0.979067i	$-0.565244\pi$
$661$	−10.4659	−0.407075	−0.203538	+	0.979067i	$0.565244\pi$
$662$	43.9722	1.70903
$663$	0.0444303	0.00172553
$664$	17.3056	0.671586
$665$	−18.7216	−0.725993
$666$	1.77658	0.0688409
$667$	20.1595	0.780581
$668$	−43.3726	−1.67813
$669$	9.30305	0.359677
$670$	−70.1569	−2.71040
$671$	13.9714	0.539360
$672$	0.0550758	0.00212460
$673$	−1.89728	−0.0731349	−0.0365674	−	0.999331i	$-0.511642\pi$
$673$	−1.89728	−0.0731349	−0.0365674	+	0.999331i	$0.511642\pi$
$674$	12.4773	0.480608
$675$	1.51062	0.0581437
$676$	−36.3099	−1.39653
$677$	0.579894	0.0222871	0.0111436	−	0.999938i	$-0.496453\pi$
$677$	0.579894	0.0222871	0.0111436	+	0.999938i	$0.496453\pi$
$678$	12.7447	0.489456
$679$	10.5640	0.405410
$680$	0.280885	0.0107715
$681$	3.84741	0.147433
$682$	30.8524	1.18140
$683$	−16.7687	−0.641637	−0.320819	−	0.947141i	$-0.603958\pi$
$683$	−16.7687	−0.641637	−0.320819	+	0.947141i	$0.603958\pi$
$684$	29.3901	1.12376
$685$	−53.2315	−2.03387
$686$	2.45063	0.0935657
$687$	9.05266	0.345380
$688$	−25.1928	−0.960467
$689$	−19.2767	−0.734383
$690$	38.6291	1.47058
$691$	−10.9459	−0.416401	−0.208200	−	0.978086i	$-0.566761\pi$
$691$	−10.9459	−0.416401	−0.208200	+	0.978086i	$0.566761\pi$
$692$	−50.8596	−1.93339
$693$	4.54790	0.172760
$694$	−0.749909	−0.0284661
$695$	−1.81186	−0.0687278
$696$	16.0392	0.607962
$697$	−0.121024	−0.00458411
$698$	25.1268	0.951065
$699$	−24.0059	−0.907985
$700$	−6.05095	−0.228704
$701$	18.1408	0.685168	0.342584	−	0.939487i	$-0.388698\pi$
$701$	18.1408	0.685168	0.342584	+	0.939487i	$0.388698\pi$
$702$	4.86144	0.183483
$703$	−5.31909	−0.200613
$704$	36.0758	1.35966
$705$	−4.84580	−0.182503
$706$	50.1167	1.88617
$707$	−15.8634	−0.596605
$708$	−27.2869	−1.02550
$709$	−5.49141	−0.206234	−0.103117	−	0.994669i	$-0.532882\pi$
$709$	−5.49141	−0.206234	−0.103117	+	0.994669i	$0.532882\pi$
$710$	8.23579	0.309084
$711$	9.83963	0.369015
$712$	15.8847	0.595304
$713$	−17.1011	−0.640441
$714$	−0.0548873	−0.00205410
$715$	23.0201	0.860904
$716$	−45.9391	−1.71682
$717$	−21.2591	−0.793935
$718$	−77.2247	−2.88200
$719$	−18.6831	−0.696761	−0.348380	−	0.937353i	$-0.613268\pi$
$719$	−18.6831	−0.696761	−0.348380	+	0.937353i	$0.613268\pi$
$720$	10.2923	0.383573
$721$	−4.58412	−0.170722
$722$	−85.3679	−3.17706
$723$	9.73292	0.361971
$724$	5.15098	0.191435
$725$	−4.92959	−0.183080
$726$	−23.7304	−0.880717
$727$	10.8807	0.403544	0.201772	−	0.979433i	$-0.435330\pi$
$727$	10.8807	0.403544	0.201772	+	0.979433i	$0.435330\pi$
$728$	−9.75015	−0.361365
$729$	1.00000	0.0370370
$730$	61.4026	2.27261
$731$	0.139884	0.00517378
$732$	−12.3055	−0.454823
$733$	−45.5265	−1.68156	−0.840780	−	0.541377i	$-0.817903\pi$
$733$	−45.5265	−1.68156	−0.840780	+	0.541377i	$0.817903\pi$
$734$	67.3047	2.48426
$735$	2.55159	0.0941169
$736$	0.340240	0.0125414
$737$	−51.0260	−1.87957
$738$	−13.2421	−0.487449
$739$	51.3140	1.88762	0.943809	−	0.330492i	$-0.107215\pi$
$739$	51.3140	1.88762	0.943809	+	0.330492i	$0.107215\pi$
$740$	−7.40943	−0.272376
$741$	−14.5552	−0.534699
$742$	23.8136	0.874224
$743$	23.5537	0.864102	0.432051	−	0.901849i	$-0.357790\pi$
$743$	23.5537	0.864102	0.432051	+	0.901849i	$0.357790\pi$
$744$	−13.6058	−0.498814
$745$	−40.9249	−1.49937
$746$	−14.7155	−0.538774
$747$	−3.52096	−0.128825
$748$	0.408011	0.0149184
$749$	−0.682614	−0.0249422
$750$	21.8192	0.796723
$751$	19.4021	0.707994	0.353997	−	0.935247i	$-0.384822\pi$
$751$	19.4021	0.707994	0.353997	+	0.935247i	$0.384822\pi$
$752$	−7.66051	−0.279350
$753$	23.7097	0.864029
$754$	−15.8643	−0.577744
$755$	−14.2330	−0.517993
$756$	−4.00561	−0.145683
$757$	−16.9892	−0.617484	−0.308742	−	0.951146i	$-0.599908\pi$
$757$	−16.9892	−0.617484	−0.308742	+	0.951146i	$0.599908\pi$
$758$	−41.0830	−1.49220
$759$	28.0954	1.01980
$760$	−92.0171	−3.33781
$761$	35.4307	1.28436	0.642182	−	0.766553i	$-0.278030\pi$
$761$	35.4307	1.28436	0.642182	+	0.766553i	$0.278030\pi$
$762$	−43.8870	−1.58986
$763$	−14.7520	−0.534057
$764$	−45.8486	−1.65875
$765$	−0.0571484	−0.00206620
$766$	−2.45063	−0.0885450
$767$	13.5136	0.487948
$768$	−32.0441	−1.15629
$769$	0.235620	0.00849667	0.00424834	−	0.999991i	$-0.498648\pi$
$769$	0.235620	0.00849667	0.00424834	+	0.999991i	$0.498648\pi$
$770$	−28.4381	−1.02484
$771$	−4.83764	−0.174223
$772$	−58.6843	−2.11210
$773$	−18.3801	−0.661087	−0.330543	−	0.943791i	$-0.607232\pi$
$773$	−18.3801	−0.661087	−0.330543	+	0.943791i	$0.607232\pi$
$774$	15.3057	0.550151
$775$	4.18171	0.150211
$776$	51.9224	1.86391
$777$	0.724945	0.0260073
$778$	42.7974	1.53436
$779$	39.6470	1.42050
$780$	−20.2752	−0.725970
$781$	5.98999	0.214339
$782$	−0.339075	−0.0121253
$783$	−3.26329	−0.116621
$784$	4.03370	0.144061
$785$	−23.2275	−0.829024
$786$	−0.834730	−0.0297738
$787$	−18.6680	−0.665441	−0.332720	−	0.943026i	$-0.607967\pi$
$787$	−18.6680	−0.665441	−0.332720	+	0.943026i	$0.607967\pi$
$788$	−59.3376	−2.11382
$789$	13.9764	0.497573
$790$	−61.5274	−2.18905
$791$	5.20056	0.184911
$792$	22.3530	0.794279
$793$	6.09419	0.216411
$794$	−70.2423	−2.49280
$795$	24.7946	0.879374
$796$	−23.8998	−0.847107
$797$	12.9960	0.460342	0.230171	−	0.973150i	$-0.426071\pi$
$797$	12.9960	0.460342	0.230171	+	0.973150i	$0.426071\pi$
$798$	17.9809	0.636516
$799$	0.0425351	0.00150478
$800$	−0.0831985	−0.00294151
$801$	−3.23187	−0.114192
$802$	73.9888	2.61264
$803$	44.6589	1.57598
$804$	44.9417	1.58497
$805$	15.7629	0.555569
$806$	13.4575	0.474020
$807$	−24.2703	−0.854356
$808$	−77.9690	−2.74294
$809$	−11.7521	−0.413180	−0.206590	−	0.978428i	$-0.566237\pi$
$809$	−11.7521	−0.413180	−0.206590	+	0.978428i	$0.566237\pi$
$810$	−6.25302	−0.219709
$811$	24.4228	0.857601	0.428801	−	0.903399i	$-0.358936\pi$
$811$	24.4228	0.857601	0.428801	+	0.903399i	$0.358936\pi$
$812$	13.0715	0.458719
$813$	−5.17290	−0.181421
$814$	−8.07968	−0.283193
$815$	−29.6375	−1.03816
$816$	−0.0903433	−0.00316265
$817$	−45.8254	−1.60323
$818$	−22.7587	−0.795739
$819$	1.98375	0.0693177
$820$	55.2279	1.92864
$821$	−6.73370	−0.235008	−0.117504	−	0.993072i	$-0.537489\pi$
$821$	−6.73370	−0.235008	−0.117504	+	0.993072i	$0.537489\pi$
$822$	51.1254	1.78320
$823$	−39.6497	−1.38210	−0.691051	−	0.722806i	$-0.742852\pi$
$823$	−39.6497	−1.38210	−0.691051	+	0.722806i	$0.742852\pi$
$824$	−22.5310	−0.784906
$825$	−6.87013	−0.239187
$826$	−16.6941	−0.580863
$827$	47.1248	1.63869	0.819345	−	0.573300i	$-0.194337\pi$
$827$	47.1248	1.63869	0.819345	+	0.573300i	$0.194337\pi$
$828$	−24.7453	−0.859960
$829$	10.4909	0.364362	0.182181	−	0.983265i	$-0.441684\pi$
$829$	10.4909	0.364362	0.182181	+	0.983265i	$0.441684\pi$
$830$	22.0166	0.764207
$831$	−23.1436	−0.802842
$832$	15.7359	0.545545
$833$	−0.0223972	−0.000776016 0
$834$	1.74017	0.0602572
$835$	−27.6285	−0.956124
$836$	−133.663	−4.62284
$837$	2.76821	0.0956834
$838$	−91.9330	−3.17577
$839$	18.0079	0.621702	0.310851	−	0.950459i	$-0.399386\pi$
$839$	18.0079	0.621702	0.310851	+	0.950459i	$0.399386\pi$
$840$	12.5411	0.432710
$841$	−18.3509	−0.632790
$842$	−70.4154	−2.42667
$843$	−31.0543	−1.06957
$844$	−37.9339	−1.30574
$845$	−23.1295	−0.795680
$846$	4.65407	0.160010
$847$	−9.68336	−0.332724
$848$	39.1967	1.34602
$849$	−12.4795	−0.428296
$850$	0.0829136	0.00284391
$851$	4.47847	0.153520
$852$	−5.27575	−0.180744
$853$	51.8425	1.77505	0.887526	−	0.460757i	$-0.152422\pi$
$853$	51.8425	1.77505	0.887526	+	0.460757i	$0.152422\pi$
$854$	−7.52849	−0.257620
$855$	18.7216	0.640266
$856$	−3.35506	−0.114674
$857$	43.7290	1.49376	0.746878	−	0.664961i	$-0.231552\pi$
$857$	43.7290	1.49376	0.746878	+	0.664961i	$0.231552\pi$
$858$	−22.1093	−0.754800
$859$	−32.1999	−1.09865	−0.549323	−	0.835610i	$-0.685115\pi$
$859$	−32.1999	−1.09865	−0.549323	+	0.835610i	$0.685115\pi$
$860$	−63.8342	−2.17673
$861$	−5.40354	−0.184152
$862$	51.6263	1.75840
$863$	−31.4807	−1.07161	−0.535807	−	0.844340i	$-0.679993\pi$
$863$	−31.4807	−1.07161	−0.535807	+	0.844340i	$0.679993\pi$
$864$	−0.0550758	−0.00187372
$865$	−32.3978	−1.10156
$866$	23.9462	0.813724
$867$	−16.9995	−0.577333
$868$	−11.0884	−0.376364
$869$	−44.7496	−1.51803
$870$	20.4054	0.691809
$871$	−22.2570	−0.754150
$872$	−72.5062	−2.45537
$873$	−10.5640	−0.357538
$874$	111.080	3.75733
$875$	8.90348	0.300992
$876$	−39.3338	−1.32897
$877$	26.6858	0.901115	0.450558	−	0.892747i	$-0.351225\pi$
$877$	26.6858	0.901115	0.450558	+	0.892747i	$0.351225\pi$
$878$	−9.85414	−0.332561
$879$	13.0227	0.439245
$880$	−46.8085	−1.57791
$881$	−0.291002	−0.00980410	−0.00490205	−	0.999988i	$-0.501560\pi$
$881$	−0.291002	−0.00980410	−0.00490205	+	0.999988i	$0.501560\pi$
$882$	−2.45063	−0.0825172
$883$	16.9298	0.569734	0.284867	−	0.958567i	$-0.408050\pi$
$883$	16.9298	0.569734	0.284867	+	0.958567i	$0.408050\pi$
$884$	0.177970	0.00598579
$885$	−17.3819	−0.584285
$886$	96.0751	3.22771
$887$	24.4810	0.821993	0.410996	−	0.911637i	$-0.365181\pi$
$887$	24.4810	0.821993	0.410996	+	0.911637i	$0.365181\pi$
$888$	3.56312	0.119570
$889$	−17.9084	−0.600629
$890$	20.2089	0.677405
$891$	−4.54790	−0.152360
$892$	37.2644	1.24770
$893$	−13.9344	−0.466295
$894$	39.3056	1.31458
$895$	−29.2634	−0.978167
$896$	−19.5496	−0.653107
$897$	12.2549	0.409180
$898$	35.3904	1.18099
$899$	−9.03349	−0.301284
$900$	6.05095	0.201698
$901$	−0.217640	−0.00725065
$902$	60.2237	2.00523
$903$	6.24559	0.207840
$904$	25.5608	0.850141
$905$	3.28120	0.109071
$906$	13.6699	0.454152
$907$	12.9582	0.430271	0.215135	−	0.976584i	$-0.430981\pi$
$907$	12.9582	0.430271	0.215135	+	0.976584i	$0.430981\pi$
$908$	15.4112	0.511439
$909$	15.8634	0.526157
$910$	−12.4044	−0.411202
$911$	17.4103	0.576828	0.288414	−	0.957506i	$-0.406872\pi$
$911$	17.4103	0.576828	0.288414	+	0.957506i	$0.406872\pi$
$912$	29.5962	0.980027
$913$	16.0129	0.529951
$914$	23.4797	0.776639
$915$	−7.83864	−0.259137
$916$	36.2614	1.19811
$917$	−0.340618	−0.0112482
$918$	0.0548873	0.00181155
$919$	−55.3501	−1.82583	−0.912916	−	0.408147i	$-0.866175\pi$
$919$	−55.3501	−1.82583	−0.912916	+	0.408147i	$0.866175\pi$
$920$	77.4749	2.55427
$921$	21.7677	0.717270
$922$	−47.1205	−1.55183
$923$	2.61278	0.0860005
$924$	18.2171	0.599299
$925$	−1.09511	−0.0360072
$926$	−45.4555	−1.49376
$927$	4.58412	0.150562
$928$	0.179729	0.00589988
$929$	−50.8082	−1.66696	−0.833481	−	0.552548i	$-0.813655\pi$
$929$	−50.8082	−1.66696	−0.833481	+	0.552548i	$0.813655\pi$
$930$	−17.3097	−0.567607
$931$	7.33723	0.240468
$932$	−96.1581	−3.14976
$933$	−1.99744	−0.0653932
$934$	41.1689	1.34709
$935$	0.259905	0.00849980
$936$	9.75015	0.318694
$937$	−19.0876	−0.623565	−0.311783	−	0.950153i	$-0.600926\pi$
$937$	−19.0876	−0.623565	−0.311783	+	0.950153i	$0.600926\pi$
$938$	27.4954	0.897755
$939$	22.1641	0.723298
$940$	−19.4104	−0.633097
$941$	14.3673	0.468361	0.234181	−	0.972193i	$-0.424759\pi$
$941$	14.3673	0.468361	0.234181	+	0.972193i	$0.424759\pi$
$942$	22.3084	0.726848
$943$	−33.3813	−1.08704
$944$	−27.4782	−0.894339
$945$	−2.55159	−0.0830033
$946$	−69.6086	−2.26317
$947$	−2.47446	−0.0804092	−0.0402046	−	0.999191i	$-0.512801\pi$
$947$	−2.47446	−0.0804092	−0.0402046	+	0.999191i	$0.512801\pi$
$948$	39.4137	1.28010
$949$	19.4798	0.632339
$950$	−27.1622	−0.881259
$951$	−27.0836	−0.878246
$952$	−0.110082	−0.00356779
$953$	−11.6565	−0.377591	−0.188795	−	0.982016i	$-0.560458\pi$
$953$	−11.6565	−0.377591	−0.188795	+	0.982016i	$0.560458\pi$
$954$	−23.8136	−0.770993
$955$	−29.2058	−0.945077
$956$	−85.1556	−2.75413
$957$	14.8411	0.479745
$958$	26.8792	0.868429
$959$	20.8621	0.673672
$960$	−20.2403	−0.653253
$961$	−23.3370	−0.752806
$962$	−3.52428	−0.113627
$963$	0.682614	0.0219969
$964$	38.9863	1.25566
$965$	−37.3822	−1.20337
$966$	−15.1392	−0.487096
$967$	−13.5255	−0.434952	−0.217476	−	0.976066i	$-0.569782\pi$
$967$	−13.5255	−0.434952	−0.217476	+	0.976066i	$0.569782\pi$
$968$	−47.5939	−1.52973
$969$	−0.164333	−0.00527914
$970$	66.0570	2.12096
$971$	46.6183	1.49605	0.748026	−	0.663670i	$-0.231002\pi$
$971$	46.6183	1.49605	0.748026	+	0.663670i	$0.231002\pi$
$972$	4.00561	0.128480
$973$	0.710090	0.0227644
$974$	37.8125	1.21159
$975$	−2.99668	−0.0959707
$976$	−12.3917	−0.396650
$977$	−54.7815	−1.75262	−0.876308	−	0.481752i	$-0.840001\pi$
$977$	−54.7815	−1.75262	−0.876308	+	0.481752i	$0.840001\pi$
$978$	28.4649	0.910206
$979$	14.6982	0.469757
$980$	10.2207	0.326488
$981$	14.7520	0.470994
$982$	43.6901	1.39421
$983$	6.85047	0.218496	0.109248	−	0.994015i	$-0.465156\pi$
$983$	6.85047	0.218496	0.109248	+	0.994015i	$0.465156\pi$
$984$	−26.5585	−0.846654
$985$	−37.7983	−1.20436
$986$	−0.179113	−0.00570413
$987$	1.89913	0.0604499
$988$	−58.3025	−1.85485
$989$	38.5832	1.22687
$990$	28.4381	0.903821
$991$	−42.2689	−1.34271	−0.671357	−	0.741134i	$-0.734288\pi$
$991$	−42.2689	−1.34271	−0.671357	+	0.741134i	$0.734288\pi$
$992$	−0.152462	−0.00484066
$993$	−17.9432	−0.569409
$994$	−3.22771	−0.102377
$995$	−15.2243	−0.482643
$996$	−14.1036	−0.446889
$997$	−19.4986	−0.617525	−0.308763	−	0.951139i	$-0.599915\pi$
$997$	−19.4986	−0.617525	−0.308763	+	0.951139i	$0.599915\pi$
$998$	−76.3492	−2.41679
$999$	−0.724945	−0.0229363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.5	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45063 q^{2} +1.00000 q^{3} +4.00561 q^{4} +2.55159 q^{5} -2.45063 q^{6} -1.00000 q^{7} -4.91502 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.45063 q^{2} +1.00000 q^{3} +4.00561 q^{4} +2.55159 q^{5} -2.45063 q^{6} -1.00000 q^{7} -4.91502 q^{8} +1.00000 q^{9} -6.25302 q^{10} -4.54790 q^{11} +4.00561 q^{12} -1.98375 q^{13} +2.45063 q^{14} +2.55159 q^{15} +4.03370 q^{16} -0.0223972 q^{17} -2.45063 q^{18} +7.33723 q^{19} +10.2207 q^{20} -1.00000 q^{21} +11.1452 q^{22} -6.17767 q^{23} -4.91502 q^{24} +1.51062 q^{25} +4.86144 q^{26} +1.00000 q^{27} -4.00561 q^{28} -3.26329 q^{29} -6.25302 q^{30} +2.76821 q^{31} -0.0550758 q^{32} -4.54790 q^{33} +0.0548873 q^{34} -2.55159 q^{35} +4.00561 q^{36} -0.724945 q^{37} -17.9809 q^{38} -1.98375 q^{39} -12.5411 q^{40} +5.40354 q^{41} +2.45063 q^{42} -6.24559 q^{43} -18.2171 q^{44} +2.55159 q^{45} +15.1392 q^{46} -1.89913 q^{47} +4.03370 q^{48} +1.00000 q^{49} -3.70197 q^{50} -0.0223972 q^{51} -7.94612 q^{52} +9.71731 q^{53} -2.45063 q^{54} -11.6044 q^{55} +4.91502 q^{56} +7.33723 q^{57} +7.99714 q^{58} -6.81216 q^{59} +10.2207 q^{60} -3.07206 q^{61} -6.78388 q^{62} -1.00000 q^{63} -7.93242 q^{64} -5.06171 q^{65} +11.1452 q^{66} +11.2197 q^{67} -0.0897143 q^{68} -6.17767 q^{69} +6.25302 q^{70} -1.31709 q^{71} -4.91502 q^{72} -9.81968 q^{73} +1.77658 q^{74} +1.51062 q^{75} +29.3901 q^{76} +4.54790 q^{77} +4.86144 q^{78} +9.83963 q^{79} +10.2923 q^{80} +1.00000 q^{81} -13.2421 q^{82} -3.52096 q^{83} -4.00561 q^{84} -0.0571484 q^{85} +15.3057 q^{86} -3.26329 q^{87} +22.3530 q^{88} -3.23187 q^{89} -6.25302 q^{90} +1.98375 q^{91} -24.7453 q^{92} +2.76821 q^{93} +4.65407 q^{94} +18.7216 q^{95} -0.0550758 q^{96} -10.5640 q^{97} -2.45063 q^{98} -4.54790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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