LMFDB - Embedded newform 8043.2.a.t.1.28

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:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
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)

$f(q)$	$=$	$q+0.349637 q^{2} -1.00000 q^{3} -1.87775 q^{4} -0.612183 q^{5} -0.349637 q^{6} +1.00000 q^{7} -1.35581 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.349637 q^{2} -1.00000 q^{3} -1.87775 q^{4} -0.612183 q^{5} -0.349637 q^{6} +1.00000 q^{7} -1.35581 q^{8} +1.00000 q^{9} -0.214042 q^{10} +5.37994 q^{11} +1.87775 q^{12} -4.58953 q^{13} +0.349637 q^{14} +0.612183 q^{15} +3.28147 q^{16} -1.09023 q^{17} +0.349637 q^{18} -6.83395 q^{19} +1.14953 q^{20} -1.00000 q^{21} +1.88103 q^{22} +0.119722 q^{23} +1.35581 q^{24} -4.62523 q^{25} -1.60467 q^{26} -1.00000 q^{27} -1.87775 q^{28} +7.00364 q^{29} +0.214042 q^{30} +7.02377 q^{31} +3.85893 q^{32} -5.37994 q^{33} -0.381184 q^{34} -0.612183 q^{35} -1.87775 q^{36} +2.16189 q^{37} -2.38940 q^{38} +4.58953 q^{39} +0.830000 q^{40} -2.37696 q^{41} -0.349637 q^{42} -1.12553 q^{43} -10.1022 q^{44} -0.612183 q^{45} +0.0418593 q^{46} +1.85051 q^{47} -3.28147 q^{48} +1.00000 q^{49} -1.61715 q^{50} +1.09023 q^{51} +8.61801 q^{52} -1.06113 q^{53} -0.349637 q^{54} -3.29351 q^{55} -1.35581 q^{56} +6.83395 q^{57} +2.44873 q^{58} +5.17528 q^{59} -1.14953 q^{60} -11.7736 q^{61} +2.45577 q^{62} +1.00000 q^{63} -5.21371 q^{64} +2.80963 q^{65} -1.88103 q^{66} +2.08589 q^{67} +2.04718 q^{68} -0.119722 q^{69} -0.214042 q^{70} +7.88252 q^{71} -1.35581 q^{72} -9.87172 q^{73} +0.755877 q^{74} +4.62523 q^{75} +12.8325 q^{76} +5.37994 q^{77} +1.60467 q^{78} -9.68423 q^{79} -2.00886 q^{80} +1.00000 q^{81} -0.831074 q^{82} -2.83040 q^{83} +1.87775 q^{84} +0.667419 q^{85} -0.393526 q^{86} -7.00364 q^{87} -7.29416 q^{88} -2.94135 q^{89} -0.214042 q^{90} -4.58953 q^{91} -0.224809 q^{92} -7.02377 q^{93} +0.647006 q^{94} +4.18363 q^{95} -3.85893 q^{96} +6.89570 q^{97} +0.349637 q^{98} +5.37994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	0.349637	0.247231	0.123615	−	0.992330i	$-0.460551\pi$
$2$	0.349637	0.247231	0.123615	+	0.992330i	$0.460551\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.87775	−0.938877
$5$	−0.612183	−0.273776	−0.136888	−	0.990587i	$-0.543710\pi$
$5$	−0.612183	−0.273776	−0.136888	+	0.990587i	$0.543710\pi$
$6$	−0.349637	−0.142739
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.35581	−0.479350
$9$	1.00000	0.333333
$10$	−0.214042	−0.0676859
$11$	5.37994	1.62211	0.811057	−	0.584967i	$-0.198893\pi$
$11$	5.37994	1.62211	0.811057	+	0.584967i	$0.198893\pi$
$12$	1.87775	0.542061
$13$	−4.58953	−1.27291	−0.636453	−	0.771315i	$-0.719599\pi$
$13$	−4.58953	−1.27291	−0.636453	+	0.771315i	$0.719599\pi$
$14$	0.349637	0.0934444
$15$	0.612183	0.158065
$16$	3.28147	0.820367
$17$	−1.09023	−0.264419	−0.132210	−	0.991222i	$-0.542207\pi$
$17$	−1.09023	−0.264419	−0.132210	+	0.991222i	$0.542207\pi$
$18$	0.349637	0.0824102
$19$	−6.83395	−1.56782	−0.783908	−	0.620877i	$-0.786777\pi$
$19$	−6.83395	−1.56782	−0.783908	+	0.620877i	$0.786777\pi$
$20$	1.14953	0.257042
$21$	−1.00000	−0.218218
$22$	1.88103	0.401036
$23$	0.119722	0.0249638	0.0124819	−	0.999922i	$-0.496027\pi$
$23$	0.119722	0.0249638	0.0124819	+	0.999922i	$0.496027\pi$
$24$	1.35581	0.276753
$25$	−4.62523	−0.925047
$26$	−1.60467	−0.314701
$27$	−1.00000	−0.192450
$28$	−1.87775	−0.354862
$29$	7.00364	1.30054	0.650271	−	0.759702i	$-0.274655\pi$
$29$	7.00364	1.30054	0.650271	+	0.759702i	$0.274655\pi$
$30$	0.214042	0.0390785
$31$	7.02377	1.26151	0.630753	−	0.775984i	$-0.282746\pi$
$31$	7.02377	1.26151	0.630753	+	0.775984i	$0.282746\pi$
$32$	3.85893	0.682169
$33$	−5.37994	−0.936528
$34$	−0.381184	−0.0653726
$35$	−0.612183	−0.103478
$36$	−1.87775	−0.312959
$37$	2.16189	0.355413	0.177706	−	0.984084i	$-0.443132\pi$
$37$	2.16189	0.355413	0.177706	+	0.984084i	$0.443132\pi$
$38$	−2.38940	−0.387612
$39$	4.58953	0.734913
$40$	0.830000	0.131235
$41$	−2.37696	−0.371219	−0.185610	−	0.982624i	$-0.559426\pi$
$41$	−2.37696	−0.371219	−0.185610	+	0.982624i	$0.559426\pi$
$42$	−0.349637	−0.0539501
$43$	−1.12553	−0.171641	−0.0858206	−	0.996311i	$-0.527351\pi$
$43$	−1.12553	−0.171641	−0.0858206	+	0.996311i	$0.527351\pi$
$44$	−10.1022	−1.52297
$45$	−0.612183	−0.0912588
$46$	0.0418593	0.00617181
$47$	1.85051	0.269925	0.134962	−	0.990851i	$-0.456909\pi$
$47$	1.85051	0.269925	0.134962	+	0.990851i	$0.456909\pi$
$48$	−3.28147	−0.473639
$49$	1.00000	0.142857
$50$	−1.61715	−0.228700
$51$	1.09023	0.152663
$52$	8.61801	1.19510
$53$	−1.06113	−0.145757	−0.0728785	−	0.997341i	$-0.523219\pi$
$53$	−1.06113	−0.145757	−0.0728785	+	0.997341i	$0.523219\pi$
$54$	−0.349637	−0.0475795
$55$	−3.29351	−0.444096
$56$	−1.35581	−0.181177
$57$	6.83395	0.905179
$58$	2.44873	0.321534
$59$	5.17528	0.673763	0.336882	−	0.941547i	$-0.390628\pi$
$59$	5.17528	0.673763	0.336882	+	0.941547i	$0.390628\pi$
$60$	−1.14953	−0.148403
$61$	−11.7736	−1.50745	−0.753727	−	0.657187i	$-0.771746\pi$
$61$	−11.7736	−1.50745	−0.753727	+	0.657187i	$0.771746\pi$
$62$	2.45577	0.311883
$63$	1.00000	0.125988
$64$	−5.21371	−0.651714
$65$	2.80963	0.348492
$66$	−1.88103	−0.231538
$67$	2.08589	0.254832	0.127416	−	0.991849i	$-0.459332\pi$
$67$	2.08589	0.254832	0.127416	+	0.991849i	$0.459332\pi$
$68$	2.04718	0.248257
$69$	−0.119722	−0.0144128
$70$	−0.214042	−0.0255829
$71$	7.88252	0.935483	0.467742	−	0.883865i	$-0.345068\pi$
$71$	7.88252	0.935483	0.467742	+	0.883865i	$0.345068\pi$
$72$	−1.35581	−0.159783
$73$	−9.87172	−1.15540	−0.577699	−	0.816250i	$-0.696049\pi$
$73$	−9.87172	−1.15540	−0.577699	+	0.816250i	$0.696049\pi$
$74$	0.755877	0.0878689
$75$	4.62523	0.534076
$76$	12.8325	1.47199
$77$	5.37994	0.613101
$78$	1.60467	0.181693
$79$	−9.68423	−1.08956	−0.544781	−	0.838579i	$-0.683387\pi$
$79$	−9.68423	−1.08956	−0.544781	+	0.838579i	$0.683387\pi$
$80$	−2.00886	−0.224597
$81$	1.00000	0.111111
$82$	−0.831074	−0.0917768
$83$	−2.83040	−0.310677	−0.155338	−	0.987861i	$-0.549647\pi$
$83$	−2.83040	−0.310677	−0.155338	+	0.987861i	$0.549647\pi$
$84$	1.87775	0.204880
$85$	0.667419	0.0723918
$86$	−0.393526	−0.0424350
$87$	−7.00364	−0.750869
$88$	−7.29416	−0.777560
$89$	−2.94135	−0.311783	−0.155891	−	0.987774i	$-0.549825\pi$
$89$	−2.94135	−0.311783	−0.155891	+	0.987774i	$0.549825\pi$
$90$	−0.214042	−0.0225620
$91$	−4.58953	−0.481113
$92$	−0.224809	−0.0234379
$93$	−7.02377	−0.728331
$94$	0.647006	0.0667336
$95$	4.18363	0.429231
$96$	−3.85893	−0.393851
$97$	6.89570	0.700152	0.350076	−	0.936721i	$-0.386156\pi$
$97$	6.89570	0.700152	0.350076	+	0.936721i	$0.386156\pi$
$98$	0.349637	0.0353187
$99$	5.37994	0.540705
$100$	8.68505	0.868505
$101$	−6.17049	−0.613987	−0.306993	−	0.951712i	$-0.599323\pi$
$101$	−6.17049	−0.613987	−0.306993	+	0.951712i	$0.599323\pi$
$102$	0.381184	0.0377429
$103$	−10.3481	−1.01963	−0.509816	−	0.860283i	$-0.670287\pi$
$103$	−10.3481	−1.01963	−0.509816	+	0.860283i	$0.670287\pi$
$104$	6.22251	0.610167
$105$	0.612183	0.0597429
$106$	−0.371009	−0.0360356
$107$	7.75209	0.749423	0.374711	−	0.927142i	$-0.377742\pi$
$107$	7.75209	0.749423	0.374711	+	0.927142i	$0.377742\pi$
$108$	1.87775	0.180687
$109$	−9.60405	−0.919901	−0.459950	−	0.887945i	$-0.652133\pi$
$109$	−9.60405	−0.919901	−0.459950	+	0.887945i	$0.652133\pi$
$110$	−1.15153	−0.109794
$111$	−2.16189	−0.205198
$112$	3.28147	0.310070
$113$	5.98505	0.563026	0.281513	−	0.959557i	$-0.409164\pi$
$113$	5.98505	0.563026	0.281513	+	0.959557i	$0.409164\pi$
$114$	2.38940	0.223788
$115$	−0.0732918	−0.00683449
$116$	−13.1511	−1.22105
$117$	−4.58953	−0.424302
$118$	1.80947	0.166575
$119$	−1.09023	−0.0999412
$120$	−0.830000	−0.0757683
$121$	17.9438	1.63125
$122$	−4.11648	−0.372689
$123$	2.37696	0.214324
$124$	−13.1889	−1.18440
$125$	5.89240	0.527032
$126$	0.349637	0.0311481
$127$	6.69418	0.594012	0.297006	−	0.954876i	$-0.404012\pi$
$127$	6.69418	0.594012	0.297006	+	0.954876i	$0.404012\pi$
$128$	−9.54077	−0.843293
$129$	1.12553	0.0990971
$130$	0.982350	0.0861578
$131$	12.0174	1.04997	0.524983	−	0.851113i	$-0.324072\pi$
$131$	12.0174	1.04997	0.524983	+	0.851113i	$0.324072\pi$
$132$	10.1022	0.879285
$133$	−6.83395	−0.592579
$134$	0.729304	0.0630022
$135$	0.612183	0.0526883
$136$	1.47814	0.126749
$137$	−1.73663	−0.148371	−0.0741853	−	0.997244i	$-0.523636\pi$
$137$	−1.73663	−0.148371	−0.0741853	+	0.997244i	$0.523636\pi$
$138$	−0.0418593	−0.00356330
$139$	−18.7276	−1.58845	−0.794226	−	0.607623i	$-0.792123\pi$
$139$	−18.7276	−1.58845	−0.794226	+	0.607623i	$0.792123\pi$
$140$	1.14953	0.0971529
$141$	−1.85051	−0.155841
$142$	2.75602	0.231280
$143$	−24.6914	−2.06480
$144$	3.28147	0.273456
$145$	−4.28750	−0.356058
$146$	−3.45152	−0.285650
$147$	−1.00000	−0.0824786
$148$	−4.05950	−0.333689
$149$	12.8452	1.05232	0.526158	−	0.850387i	$-0.323632\pi$
$149$	12.8452	1.05232	0.526158	+	0.850387i	$0.323632\pi$
$150$	1.61715	0.132040
$151$	0.218108	0.0177494	0.00887471	−	0.999961i	$-0.497175\pi$
$151$	0.218108	0.0177494	0.00887471	+	0.999961i	$0.497175\pi$
$152$	9.26551	0.751532
$153$	−1.09023	−0.0881398
$154$	1.88103	0.151577
$155$	−4.29983	−0.345371
$156$	−8.61801	−0.689993
$157$	6.68892	0.533834	0.266917	−	0.963719i	$-0.413995\pi$
$157$	6.68892	0.533834	0.266917	+	0.963719i	$0.413995\pi$
$158$	−3.38596	−0.269373
$159$	1.06113	0.0841528
$160$	−2.36237	−0.186762
$161$	0.119722	0.00943542
$162$	0.349637	0.0274701
$163$	14.0772	1.10261	0.551304	−	0.834304i	$-0.314130\pi$
$163$	14.0772	1.10261	0.551304	+	0.834304i	$0.314130\pi$
$164$	4.46335	0.348529
$165$	3.29351	0.256399
$166$	−0.989612	−0.0768088
$167$	−2.01387	−0.155838	−0.0779189	−	0.996960i	$-0.524828\pi$
$167$	−2.01387	−0.155838	−0.0779189	+	0.996960i	$0.524828\pi$
$168$	1.35581	0.104603
$169$	8.06377	0.620290
$170$	0.233354	0.0178975
$171$	−6.83395	−0.522606
$172$	2.11346	0.161150
$173$	8.78814	0.668150	0.334075	−	0.942547i	$-0.391576\pi$
$173$	8.78814	0.668150	0.334075	+	0.942547i	$0.391576\pi$
$174$	−2.44873	−0.185638
$175$	−4.62523	−0.349635
$176$	17.6541	1.33073
$177$	−5.17528	−0.388998
$178$	−1.02841	−0.0770823
$179$	10.3262	0.771816	0.385908	−	0.922537i	$-0.373888\pi$
$179$	10.3262	0.771816	0.385908	+	0.922537i	$0.373888\pi$
$180$	1.14953	0.0856808
$181$	−17.6643	−1.31298	−0.656490	−	0.754335i	$-0.727960\pi$
$181$	−17.6643	−1.31298	−0.656490	+	0.754335i	$0.727960\pi$
$182$	−1.60467	−0.118946
$183$	11.7736	0.870329
$184$	−0.162320	−0.0119664
$185$	−1.32347	−0.0973037
$186$	−2.45577	−0.180066
$187$	−5.86537	−0.428918
$188$	−3.47480	−0.253426
$189$	−1.00000	−0.0727393
$190$	1.46275	0.106119
$191$	8.57766	0.620658	0.310329	−	0.950629i	$-0.399561\pi$
$191$	8.57766	0.620658	0.310329	+	0.950629i	$0.399561\pi$
$192$	5.21371	0.376267
$193$	−8.52417	−0.613583	−0.306792	−	0.951777i	$-0.599255\pi$
$193$	−8.52417	−0.613583	−0.306792	+	0.951777i	$0.599255\pi$
$194$	2.41099	0.173099
$195$	−2.80963	−0.201202
$196$	−1.87775	−0.134125
$197$	−2.56035	−0.182418	−0.0912088	−	0.995832i	$-0.529073\pi$
$197$	−2.56035	−0.182418	−0.0912088	+	0.995832i	$0.529073\pi$
$198$	1.88103	0.133679
$199$	3.82329	0.271026	0.135513	−	0.990776i	$-0.456732\pi$
$199$	3.82329	0.271026	0.135513	+	0.990776i	$0.456732\pi$
$200$	6.27092	0.443421
$201$	−2.08589	−0.147127
$202$	−2.15743	−0.151796
$203$	7.00364	0.491559
$204$	−2.04718	−0.143331
$205$	1.45514	0.101631
$206$	−3.61809	−0.252084
$207$	0.119722	0.00832126
$208$	−15.0604	−1.04425
$209$	−36.7663	−2.54318
$210$	0.214042	0.0147703
$211$	11.7839	0.811240	0.405620	−	0.914042i	$-0.367056\pi$
$211$	11.7839	0.811240	0.405620	+	0.914042i	$0.367056\pi$
$212$	1.99253	0.136848
$213$	−7.88252	−0.540102
$214$	2.71042	0.185280
$215$	0.689028	0.0469913
$216$	1.35581	0.0922509
$217$	7.02377	0.476805
$218$	−3.35793	−0.227428
$219$	9.87172	0.667069
$220$	6.18440	0.416952
$221$	5.00364	0.336581
$222$	−0.755877	−0.0507312
$223$	17.1282	1.14699	0.573495	−	0.819209i	$-0.305587\pi$
$223$	17.1282	1.14699	0.573495	+	0.819209i	$0.305587\pi$
$224$	3.85893	0.257836
$225$	−4.62523	−0.308349
$226$	2.09259	0.139197
$227$	26.3199	1.74691	0.873455	−	0.486904i	$-0.161874\pi$
$227$	26.3199	1.74691	0.873455	+	0.486904i	$0.161874\pi$
$228$	−12.8325	−0.849852
$229$	6.04479	0.399451	0.199725	−	0.979852i	$-0.435995\pi$
$229$	6.04479	0.399451	0.199725	+	0.979852i	$0.435995\pi$
$230$	−0.0256255	−0.00168970
$231$	−5.37994	−0.353974
$232$	−9.49557	−0.623415
$233$	5.75862	0.377260	0.188630	−	0.982048i	$-0.439595\pi$
$233$	5.75862	0.377260	0.188630	+	0.982048i	$0.439595\pi$
$234$	−1.60467	−0.104900
$235$	−1.13285	−0.0738990
$236$	−9.71789	−0.632581
$237$	9.68423	0.629058
$238$	−0.381184	−0.0247085
$239$	−17.6369	−1.14084	−0.570419	−	0.821354i	$-0.693219\pi$
$239$	−17.6369	−1.14084	−0.570419	+	0.821354i	$0.693219\pi$
$240$	2.00886	0.129671
$241$	−25.0809	−1.61560	−0.807800	−	0.589457i	$-0.799342\pi$
$241$	−25.0809	−1.61560	−0.807800	+	0.589457i	$0.799342\pi$
$242$	6.27381	0.403296
$243$	−1.00000	−0.0641500
$244$	22.1079	1.41531
$245$	−0.612183	−0.0391109
$246$	0.831074	0.0529874
$247$	31.3646	1.99568
$248$	−9.52287	−0.604703
$249$	2.83040	0.179369
$250$	2.06020	0.130298
$251$	−14.8442	−0.936960	−0.468480	−	0.883474i	$-0.655198\pi$
$251$	−14.8442	−0.936960	−0.468480	+	0.883474i	$0.655198\pi$
$252$	−1.87775	−0.118287
$253$	0.644098	0.0404941
$254$	2.34053	0.146858
$255$	−0.667419	−0.0417954
$256$	7.09162	0.443226
$257$	7.67270	0.478610	0.239305	−	0.970944i	$-0.423080\pi$
$257$	7.67270	0.478610	0.239305	+	0.970944i	$0.423080\pi$
$258$	0.393526	0.0244998
$259$	2.16189	0.134333
$260$	−5.27579	−0.327191
$261$	7.00364	0.433514
$262$	4.20173	0.259584
$263$	12.0209	0.741243	0.370621	−	0.928784i	$-0.379145\pi$
$263$	12.0209	0.741243	0.370621	+	0.928784i	$0.379145\pi$
$264$	7.29416	0.448924
$265$	0.649603	0.0399048
$266$	−2.38940	−0.146504
$267$	2.94135	0.180008
$268$	−3.91679	−0.239256
$269$	−1.19114	−0.0726248	−0.0363124	−	0.999340i	$-0.511561\pi$
$269$	−1.19114	−0.0726248	−0.0363124	+	0.999340i	$0.511561\pi$
$270$	0.214042	0.0130262
$271$	19.3703	1.17666	0.588330	−	0.808621i	$-0.299786\pi$
$271$	19.3703	1.17666	0.588330	+	0.808621i	$0.299786\pi$
$272$	−3.57755	−0.216921
$273$	4.58953	0.277771
$274$	−0.607191	−0.0366817
$275$	−24.8835	−1.50053
$276$	0.224809	0.0135319
$277$	7.53291	0.452609	0.226304	−	0.974057i	$-0.427336\pi$
$277$	7.53291	0.452609	0.226304	+	0.974057i	$0.427336\pi$
$278$	−6.54785	−0.392714
$279$	7.02377	0.420502
$280$	0.830000	0.0496020
$281$	−20.1324	−1.20100	−0.600499	−	0.799625i	$-0.705032\pi$
$281$	−20.1324	−1.20100	−0.600499	+	0.799625i	$0.705032\pi$
$282$	−0.647006	−0.0385287
$283$	2.11325	0.125620	0.0628099	−	0.998026i	$-0.479994\pi$
$283$	2.11325	0.125620	0.0628099	+	0.998026i	$0.479994\pi$
$284$	−14.8014	−0.878304
$285$	−4.18363	−0.247817
$286$	−8.63302	−0.510481
$287$	−2.37696	−0.140308
$288$	3.85893	0.227390
$289$	−15.8114	−0.930082
$290$	−1.49907	−0.0880284
$291$	−6.89570	−0.404233
$292$	18.5367	1.08478
$293$	−16.3419	−0.954703	−0.477352	−	0.878712i	$-0.658403\pi$
$293$	−16.3419	−0.954703	−0.477352	+	0.878712i	$0.658403\pi$
$294$	−0.349637	−0.0203912
$295$	−3.16821	−0.184461
$296$	−2.93111	−0.170367
$297$	−5.37994	−0.312176
$298$	4.49114	0.260165
$299$	−0.549468	−0.0317766
$300$	−8.68505	−0.501432
$301$	−1.12553	−0.0648743
$302$	0.0762587	0.00438820
$303$	6.17049	0.354485
$304$	−22.4254	−1.28619
$305$	7.20759	0.412705
$306$	−0.381184	−0.0217909
$307$	25.4245	1.45105	0.725526	−	0.688195i	$-0.241597\pi$
$307$	25.4245	1.45105	0.725526	+	0.688195i	$0.241597\pi$
$308$	−10.1022	−0.575627
$309$	10.3481	0.588685
$310$	−1.50338	−0.0853862
$311$	28.3892	1.60980	0.804901	−	0.593409i	$-0.202218\pi$
$311$	28.3892	1.60980	0.804901	+	0.593409i	$0.202218\pi$
$312$	−6.22251	−0.352280
$313$	31.4262	1.77631	0.888156	−	0.459542i	$-0.151986\pi$
$313$	31.4262	1.77631	0.888156	+	0.459542i	$0.151986\pi$
$314$	2.33869	0.131980
$315$	−0.612183	−0.0344926
$316$	18.1846	1.02296
$317$	−11.2524	−0.631999	−0.316000	−	0.948759i	$-0.602340\pi$
$317$	−11.2524	−0.631999	−0.316000	+	0.948759i	$0.602340\pi$
$318$	0.371009	0.0208051
$319$	37.6792	2.10963
$320$	3.19174	0.178424
$321$	−7.75209	−0.432679
$322$	0.0418593	0.00233273
$323$	7.45058	0.414561
$324$	−1.87775	−0.104320
$325$	21.2276	1.17750
$326$	4.92189	0.272598
$327$	9.60405	0.531105
$328$	3.22270	0.177944
$329$	1.85051	0.102022
$330$	1.15153	0.0633897
$331$	7.81218	0.429396	0.214698	−	0.976680i	$-0.431123\pi$
$331$	7.81218	0.429396	0.214698	+	0.976680i	$0.431123\pi$
$332$	5.31479	0.291687
$333$	2.16189	0.118471
$334$	−0.704122	−0.0385279
$335$	−1.27694	−0.0697670
$336$	−3.28147	−0.179019
$337$	−12.5554	−0.683936	−0.341968	−	0.939712i	$-0.611094\pi$
$337$	−12.5554	−0.683936	−0.341968	+	0.939712i	$0.611094\pi$
$338$	2.81939	0.153355
$339$	−5.98505	−0.325063
$340$	−1.25325	−0.0679670
$341$	37.7875	2.04631
$342$	−2.38940	−0.129204
$343$	1.00000	0.0539949
$344$	1.52600	0.0822762
$345$	0.0732918	0.00394590
$346$	3.07266	0.165187
$347$	27.1688	1.45850	0.729248	−	0.684250i	$-0.239870\pi$
$347$	27.1688	1.45850	0.729248	+	0.684250i	$0.239870\pi$
$348$	13.1511	0.704973
$349$	−19.9705	−1.06900	−0.534498	−	0.845170i	$-0.679499\pi$
$349$	−19.9705	−1.06900	−0.534498	+	0.845170i	$0.679499\pi$
$350$	−1.61715	−0.0864404
$351$	4.58953	0.244971
$352$	20.7608	1.10656
$353$	34.6419	1.84380	0.921901	−	0.387425i	$-0.126636\pi$
$353$	34.6419	1.84380	0.921901	+	0.387425i	$0.126636\pi$
$354$	−1.80947	−0.0961721
$355$	−4.82554	−0.256113
$356$	5.52314	0.292726
$357$	1.09023	0.0577011
$358$	3.61042	0.190816
$359$	4.08065	0.215369	0.107684	−	0.994185i	$-0.465656\pi$
$359$	4.08065	0.215369	0.107684	+	0.994185i	$0.465656\pi$
$360$	0.830000	0.0437449
$361$	27.7029	1.45805
$362$	−6.17610	−0.324609
$363$	−17.9438	−0.941805
$364$	8.61801	0.451706
$365$	6.04329	0.316320
$366$	4.11648	0.215172
$367$	23.8500	1.24496	0.622480	−	0.782636i	$-0.286125\pi$
$367$	23.8500	1.24496	0.622480	+	0.782636i	$0.286125\pi$
$368$	0.392864	0.0204795
$369$	−2.37696	−0.123740
$370$	−0.462735	−0.0240564
$371$	−1.06113	−0.0550909
$372$	13.1889	0.683813
$373$	17.0632	0.883497	0.441749	−	0.897139i	$-0.354358\pi$
$373$	17.0632	0.883497	0.441749	+	0.897139i	$0.354358\pi$
$374$	−2.05075	−0.106042
$375$	−5.89240	−0.304282
$376$	−2.50893	−0.129388
$377$	−32.1434	−1.65547
$378$	−0.349637	−0.0179834
$379$	22.2674	1.14380	0.571900	−	0.820323i	$-0.306206\pi$
$379$	22.2674	1.14380	0.571900	+	0.820323i	$0.306206\pi$
$380$	−7.85582	−0.402995
$381$	−6.69418	−0.342953
$382$	2.99907	0.153446
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	9.54077	0.486876
$385$	−3.29351	−0.167853
$386$	−2.98036	−0.151696
$387$	−1.12553	−0.0572138
$388$	−12.9484	−0.657357
$389$	30.5873	1.55084	0.775418	−	0.631449i	$-0.217539\pi$
$389$	30.5873	1.55084	0.775418	+	0.631449i	$0.217539\pi$
$390$	−0.982350	−0.0497432
$391$	−0.130525	−0.00660091
$392$	−1.35581	−0.0684785
$393$	−12.0174	−0.606198
$394$	−0.895194	−0.0450992
$395$	5.92852	0.298296
$396$	−10.1022	−0.507655
$397$	24.2598	1.21756	0.608782	−	0.793337i	$-0.291658\pi$
$397$	24.2598	1.21756	0.608782	+	0.793337i	$0.291658\pi$
$398$	1.33676	0.0670059
$399$	6.83395	0.342126
$400$	−15.1776	−0.758878
$401$	−3.32090	−0.165838	−0.0829188	−	0.996556i	$-0.526424\pi$
$401$	−3.32090	−0.165838	−0.0829188	+	0.996556i	$0.526424\pi$
$402$	−0.729304	−0.0363744
$403$	−32.2358	−1.60578
$404$	11.5867	0.576458
$405$	−0.612183	−0.0304196
$406$	2.44873	0.121528
$407$	11.6309	0.576520
$408$	−1.47814	−0.0731788
$409$	16.3934	0.810601	0.405300	−	0.914184i	$-0.367167\pi$
$409$	16.3934	0.810601	0.405300	+	0.914184i	$0.367167\pi$
$410$	0.508769	0.0251263
$411$	1.73663	0.0856618
$412$	19.4313	0.957309
$413$	5.17528	0.254659
$414$	0.0418593	0.00205727
$415$	1.73272	0.0850559
$416$	−17.7107	−0.868338
$417$	18.7276	0.917093
$418$	−12.8548	−0.628751
$419$	32.1934	1.57275	0.786374	−	0.617750i	$-0.211956\pi$
$419$	32.1934	1.57275	0.786374	+	0.617750i	$0.211956\pi$
$420$	−1.14953	−0.0560912
$421$	2.93008	0.142803	0.0714017	−	0.997448i	$-0.477253\pi$
$421$	2.93008	0.142803	0.0714017	+	0.997448i	$0.477253\pi$
$422$	4.12010	0.200563
$423$	1.85051	0.0899749
$424$	1.43868	0.0698685
$425$	5.04256	0.244600
$426$	−2.75602	−0.133530
$427$	−11.7736	−0.569764
$428$	−14.5565	−0.703616
$429$	24.6914	1.19211
$430$	0.240910	0.0116177
$431$	−10.1532	−0.489062	−0.244531	−	0.969642i	$-0.578634\pi$
$431$	−10.1532	−0.489062	−0.244531	+	0.969642i	$0.578634\pi$
$432$	−3.28147	−0.157880
$433$	32.9605	1.58398	0.791991	−	0.610533i	$-0.209045\pi$
$433$	32.9605	1.58398	0.791991	+	0.610533i	$0.209045\pi$
$434$	2.45577	0.117881
$435$	4.28750	0.205570
$436$	18.0340	0.863674
$437$	−0.818176	−0.0391386
$438$	3.45152	0.164920
$439$	−20.2813	−0.967972	−0.483986	−	0.875076i	$-0.660811\pi$
$439$	−20.2813	−0.967972	−0.483986	+	0.875076i	$0.660811\pi$
$440$	4.46536	0.212877
$441$	1.00000	0.0476190
$442$	1.74946	0.0832131
$443$	3.01201	0.143105	0.0715523	−	0.997437i	$-0.477205\pi$
$443$	3.01201	0.143105	0.0715523	+	0.997437i	$0.477205\pi$
$444$	4.05950	0.192655
$445$	1.80065	0.0853588
$446$	5.98866	0.283571
$447$	−12.8452	−0.607555
$448$	−5.21371	−0.246325
$449$	12.8990	0.608740	0.304370	−	0.952554i	$-0.401554\pi$
$449$	12.8990	0.608740	0.304370	+	0.952554i	$0.401554\pi$
$450$	−1.61715	−0.0762333
$451$	−12.7879	−0.602160
$452$	−11.2385	−0.528613
$453$	−0.218108	−0.0102476
$454$	9.20239	0.431890
$455$	2.80963	0.131717
$456$	−9.26551	−0.433897
$457$	24.1955	1.13182	0.565908	−	0.824468i	$-0.308526\pi$
$457$	24.1955	1.13182	0.565908	+	0.824468i	$0.308526\pi$
$458$	2.11348	0.0987565
$459$	1.09023	0.0508875
$460$	0.137624	0.00641675
$461$	6.13191	0.285592	0.142796	−	0.989752i	$-0.454391\pi$
$461$	6.13191	0.285592	0.142796	+	0.989752i	$0.454391\pi$
$462$	−1.88103	−0.0875133
$463$	−2.95211	−0.137196	−0.0685981	−	0.997644i	$-0.521853\pi$
$463$	−2.95211	−0.137196	−0.0685981	+	0.997644i	$0.521853\pi$
$464$	22.9822	1.06692
$465$	4.29983	0.199400
$466$	2.01343	0.0932702
$467$	−15.3581	−0.710690	−0.355345	−	0.934735i	$-0.615637\pi$
$467$	−15.3581	−0.710690	−0.355345	+	0.934735i	$0.615637\pi$
$468$	8.61801	0.398367
$469$	2.08589	0.0963174
$470$	−0.396086	−0.0182701
$471$	−6.68892	−0.308209
$472$	−7.01667	−0.322968
$473$	−6.05527	−0.278422
$474$	3.38596	0.155522
$475$	31.6086	1.45030
$476$	2.04718	0.0938325
$477$	−1.06113	−0.0485856
$478$	−6.16652	−0.282050
$479$	−16.3979	−0.749241	−0.374621	−	0.927178i	$-0.622227\pi$
$479$	−16.3979	−0.749241	−0.374621	+	0.927178i	$0.622227\pi$
$480$	2.36237	0.107827
$481$	−9.92207	−0.452407
$482$	−8.76919	−0.399426
$483$	−0.119722	−0.00544755
$484$	−33.6940	−1.53155
$485$	−4.22143	−0.191685
$486$	−0.349637	−0.0158598
$487$	12.6187	0.571810	0.285905	−	0.958258i	$-0.407706\pi$
$487$	12.6187	0.571810	0.285905	+	0.958258i	$0.407706\pi$
$488$	15.9627	0.722598
$489$	−14.0772	−0.636591
$490$	−0.214042	−0.00966941
$491$	−1.41255	−0.0637476	−0.0318738	−	0.999492i	$-0.510147\pi$
$491$	−1.41255	−0.0637476	−0.0318738	+	0.999492i	$0.510147\pi$
$492$	−4.46335	−0.201224
$493$	−7.63557	−0.343889
$494$	10.9662	0.493394
$495$	−3.29351	−0.148032
$496$	23.0483	1.03490
$497$	7.88252	0.353580
$498$	0.989612	0.0443456
$499$	14.2357	0.637278	0.318639	−	0.947876i	$-0.396774\pi$
$499$	14.2357	0.637278	0.318639	+	0.947876i	$0.396774\pi$
$500$	−11.0645	−0.494818
$501$	2.01387	0.0899730
$502$	−5.19009	−0.231645
$503$	36.5819	1.63111	0.815554	−	0.578681i	$-0.196432\pi$
$503$	36.5819	1.63111	0.815554	+	0.578681i	$0.196432\pi$
$504$	−1.35581	−0.0603924
$505$	3.77747	0.168095
$506$	0.225200	0.0100114
$507$	−8.06377	−0.358125
$508$	−12.5700	−0.557704
$509$	35.1789	1.55928	0.779638	−	0.626230i	$-0.215403\pi$
$509$	35.1789	1.55928	0.779638	+	0.626230i	$0.215403\pi$
$510$	−0.233354	−0.0103331
$511$	−9.87172	−0.436699
$512$	21.5610	0.952872
$513$	6.83395	0.301726
$514$	2.68266	0.118327
$515$	6.33495	0.279151
$516$	−2.11346	−0.0930400
$517$	9.95564	0.437848
$518$	0.755877	0.0332113
$519$	−8.78814	−0.385756
$520$	−3.80931	−0.167049
$521$	9.18985	0.402615	0.201307	−	0.979528i	$-0.435481\pi$
$521$	9.18985	0.402615	0.201307	+	0.979528i	$0.435481\pi$
$522$	2.44873	0.107178
$523$	−28.2939	−1.23720	−0.618602	−	0.785704i	$-0.712301\pi$
$523$	−28.2939	−1.23720	−0.618602	+	0.785704i	$0.712301\pi$
$524$	−22.5657	−0.985789
$525$	4.62523	0.201862
$526$	4.20296	0.183258
$527$	−7.65752	−0.333567
$528$	−17.6541	−0.768297
$529$	−22.9857	−0.999377
$530$	0.227125	0.00986569
$531$	5.17528	0.224588
$532$	12.8325	0.556359
$533$	10.9091	0.472528
$534$	1.02841	0.0445035
$535$	−4.74569	−0.205174
$536$	−2.82806	−0.122154
$537$	−10.3262	−0.445608
$538$	−0.416465	−0.0179551
$539$	5.37994	0.231731
$540$	−1.14953	−0.0494678
$541$	31.9316	1.37285	0.686424	−	0.727202i	$-0.259179\pi$
$541$	31.9316	1.37285	0.686424	+	0.727202i	$0.259179\pi$
$542$	6.77256	0.290906
$543$	17.6643	0.758049
$544$	−4.20712	−0.180379
$545$	5.87943	0.251847
$546$	1.60467	0.0686735
$547$	−23.5876	−1.00853	−0.504266	−	0.863548i	$-0.668237\pi$
$547$	−23.5876	−1.00853	−0.504266	+	0.863548i	$0.668237\pi$
$548$	3.26097	0.139302
$549$	−11.7736	−0.502485
$550$	−8.70018	−0.370977
$551$	−47.8625	−2.03901
$552$	0.162320	0.00690879
$553$	−9.68423	−0.411815
$554$	2.63378	0.111899
$555$	1.32347	0.0561783
$556$	35.1658	1.49136
$557$	0.668075	0.0283072	0.0141536	−	0.999900i	$-0.495495\pi$
$557$	0.668075	0.0283072	0.0141536	+	0.999900i	$0.495495\pi$
$558$	2.45577	0.103961
$559$	5.16564	0.218483
$560$	−2.00886	−0.0848897
$561$	5.86537	0.247636
$562$	−7.03903	−0.296924
$563$	−11.8828	−0.500801	−0.250400	−	0.968142i	$-0.580562\pi$
$563$	−11.8828	−0.500801	−0.250400	+	0.968142i	$0.580562\pi$
$564$	3.47480	0.146316
$565$	−3.66395	−0.154143
$566$	0.738871	0.0310570
$567$	1.00000	0.0419961
$568$	−10.6872	−0.448424
$569$	−29.3330	−1.22970	−0.614851	−	0.788643i	$-0.710784\pi$
$569$	−29.3330	−1.22970	−0.614851	+	0.788643i	$0.710784\pi$
$570$	−1.46275	−0.0612679
$571$	21.2810	0.890580	0.445290	−	0.895386i	$-0.353101\pi$
$571$	21.2810	0.890580	0.445290	+	0.895386i	$0.353101\pi$
$572$	46.3644	1.93859
$573$	−8.57766	−0.358337
$574$	−0.831074	−0.0346884
$575$	−0.553743	−0.0230927
$576$	−5.21371	−0.217238
$577$	12.7037	0.528863	0.264431	−	0.964405i	$-0.414816\pi$
$577$	12.7037	0.528863	0.264431	+	0.964405i	$0.414816\pi$
$578$	−5.52825	−0.229945
$579$	8.52417	0.354252
$580$	8.05088	0.334294
$581$	−2.83040	−0.117425
$582$	−2.41099	−0.0999388
$583$	−5.70880	−0.236434
$584$	13.3841	0.553839
$585$	2.80963	0.116164
$586$	−5.71373	−0.236032
$587$	7.11772	0.293780	0.146890	−	0.989153i	$-0.453074\pi$
$587$	7.11772	0.293780	0.146890	+	0.989153i	$0.453074\pi$
$588$	1.87775	0.0774373
$589$	−48.0001	−1.97781
$590$	−1.10772	−0.0456043
$591$	2.56035	0.105319
$592$	7.09418	0.291569
$593$	25.0077	1.02694	0.513471	−	0.858107i	$-0.328360\pi$
$593$	25.0077	1.02694	0.513471	+	0.858107i	$0.328360\pi$
$594$	−1.88103	−0.0771794
$595$	0.667419	0.0273615
$596$	−24.1200	−0.987995
$597$	−3.82329	−0.156477
$598$	−0.192114	−0.00785614
$599$	−38.6431	−1.57891	−0.789457	−	0.613806i	$-0.789638\pi$
$599$	−38.6431	−1.57891	−0.789457	+	0.613806i	$0.789638\pi$
$600$	−6.27092	−0.256009
$601$	−31.8050	−1.29735	−0.648676	−	0.761064i	$-0.724677\pi$
$601$	−31.8050	−1.29735	−0.648676	+	0.761064i	$0.724677\pi$
$602$	−0.393526	−0.0160389
$603$	2.08589	0.0849440
$604$	−0.409554	−0.0166645
$605$	−10.9849	−0.446599
$606$	2.15743	0.0876396
$607$	35.5428	1.44264	0.721320	−	0.692602i	$-0.243536\pi$
$607$	35.5428	1.44264	0.721320	+	0.692602i	$0.243536\pi$
$608$	−26.3718	−1.06952
$609$	−7.00364	−0.283802
$610$	2.52004	0.102033
$611$	−8.49297	−0.343589
$612$	2.04718	0.0827524
$613$	−23.3088	−0.941434	−0.470717	−	0.882284i	$-0.656005\pi$
$613$	−23.3088	−0.941434	−0.470717	+	0.882284i	$0.656005\pi$
$614$	8.88933	0.358744
$615$	−1.45514	−0.0586767
$616$	−7.29416	−0.293890
$617$	−6.03585	−0.242994	−0.121497	−	0.992592i	$-0.538770\pi$
$617$	−6.03585	−0.242994	−0.121497	+	0.992592i	$0.538770\pi$
$618$	3.61809	0.145541
$619$	−37.4424	−1.50494	−0.752469	−	0.658628i	$-0.771137\pi$
$619$	−37.4424	−1.50494	−0.752469	+	0.658628i	$0.771137\pi$
$620$	8.07402	0.324261
$621$	−0.119722	−0.00480428
$622$	9.92590	0.397992
$623$	−2.94135	−0.117843
$624$	15.0604	0.602898
$625$	19.5189	0.780758
$626$	10.9877	0.439159
$627$	36.7663	1.46830
$628$	−12.5602	−0.501205
$629$	−2.35696	−0.0939781
$630$	−0.214042	−0.00852762
$631$	−32.6895	−1.30135	−0.650674	−	0.759357i	$-0.725514\pi$
$631$	−32.6895	−1.30135	−0.650674	+	0.759357i	$0.725514\pi$
$632$	13.1299	0.522281
$633$	−11.7839	−0.468370
$634$	−3.93426	−0.156250
$635$	−4.09806	−0.162626
$636$	−1.99253	−0.0790091
$637$	−4.58953	−0.181844
$638$	13.1740	0.521565
$639$	7.88252	0.311828
$640$	5.84069	0.230874
$641$	−5.74145	−0.226774	−0.113387	−	0.993551i	$-0.536170\pi$
$641$	−5.74145	−0.226774	−0.113387	+	0.993551i	$0.536170\pi$
$642$	−2.71042	−0.106972
$643$	33.2637	1.31179	0.655897	−	0.754851i	$-0.272291\pi$
$643$	33.2637	1.31179	0.655897	+	0.754851i	$0.272291\pi$
$644$	−0.224809	−0.00885870
$645$	−0.689028	−0.0271305
$646$	2.60500	0.102492
$647$	16.6883	0.656085	0.328043	−	0.944663i	$-0.393611\pi$
$647$	16.6883	0.656085	0.328043	+	0.944663i	$0.393611\pi$
$648$	−1.35581	−0.0532611
$649$	27.8427	1.09292
$650$	7.42196	0.291113
$651$	−7.02377	−0.275283
$652$	−26.4334	−1.03521
$653$	−14.3982	−0.563446	−0.281723	−	0.959496i	$-0.590906\pi$
$653$	−14.3982	−0.563446	−0.281723	+	0.959496i	$0.590906\pi$
$654$	3.35793	0.131305
$655$	−7.35685	−0.287456
$656$	−7.79993	−0.304536
$657$	−9.87172	−0.385132
$658$	0.647006	0.0252229
$659$	16.7753	0.653474	0.326737	−	0.945115i	$-0.394051\pi$
$659$	16.7753	0.653474	0.326737	+	0.945115i	$0.394051\pi$
$660$	−6.18440	−0.240727
$661$	13.9061	0.540883	0.270442	−	0.962736i	$-0.412830\pi$
$661$	13.9061	0.540883	0.270442	+	0.962736i	$0.412830\pi$
$662$	2.73142	0.106160
$663$	−5.00364	−0.194325
$664$	3.83747	0.148923
$665$	4.18363	0.162234
$666$	0.755877	0.0292896
$667$	0.838490	0.0324665
$668$	3.78155	0.146313
$669$	−17.1282	−0.662215
$670$	−0.446467	−0.0172485
$671$	−63.3413	−2.44526
$672$	−3.85893	−0.148862
$673$	21.3784	0.824076	0.412038	−	0.911167i	$-0.364817\pi$
$673$	21.3784	0.824076	0.412038	+	0.911167i	$0.364817\pi$
$674$	−4.38983	−0.169090
$675$	4.62523	0.178025
$676$	−15.1418	−0.582376
$677$	12.9842	0.499024	0.249512	−	0.968372i	$-0.419730\pi$
$677$	12.9842	0.499024	0.249512	+	0.968372i	$0.419730\pi$
$678$	−2.09259	−0.0803656
$679$	6.89570	0.264633
$680$	−0.904891	−0.0347010
$681$	−26.3199	−1.00858
$682$	13.2119	0.505910
$683$	32.5565	1.24574	0.622870	−	0.782325i	$-0.285967\pi$
$683$	32.5565	1.24574	0.622870	+	0.782325i	$0.285967\pi$
$684$	12.8325	0.490662
$685$	1.06314	0.0406203
$686$	0.349637	0.0133492
$687$	−6.04479	−0.230623
$688$	−3.69338	−0.140809
$689$	4.87007	0.185535
$690$	0.0256255	0.000975546 0
$691$	9.13174	0.347388	0.173694	−	0.984800i	$-0.444430\pi$
$691$	9.13174	0.347388	0.173694	+	0.984800i	$0.444430\pi$
$692$	−16.5020	−0.627310
$693$	5.37994	0.204367
$694$	9.49920	0.360585
$695$	11.4647	0.434880
$696$	9.49557	0.359929
$697$	2.59144	0.0981576
$698$	−6.98242	−0.264289
$699$	−5.75862	−0.217811
$700$	8.68505	0.328264
$701$	12.5318	0.473318	0.236659	−	0.971593i	$-0.423948\pi$
$701$	12.5318	0.473318	0.236659	+	0.971593i	$0.423948\pi$
$702$	1.60467	0.0605643
$703$	−14.7743	−0.557222
$704$	−28.0495	−1.05715
$705$	1.13285	0.0426656
$706$	12.1121	0.455844
$707$	−6.17049	−0.232065
$708$	9.71789	0.365221
$709$	−19.0215	−0.714366	−0.357183	−	0.934034i	$-0.616263\pi$
$709$	−19.0215	−0.714366	−0.357183	+	0.934034i	$0.616263\pi$
$710$	−1.68719	−0.0633190
$711$	−9.68423	−0.363187
$712$	3.98790	0.149453
$713$	0.840901	0.0314920
$714$	0.381184	0.0142655
$715$	15.1156	0.565293
$716$	−19.3900	−0.724640
$717$	17.6369	0.658663
$718$	1.42675	0.0532457
$719$	13.8978	0.518299	0.259149	−	0.965837i	$-0.416558\pi$
$719$	13.8978	0.518299	0.259149	+	0.965837i	$0.416558\pi$
$720$	−2.00886	−0.0748657
$721$	−10.3481	−0.385385
$722$	9.68597	0.360474
$723$	25.0809	0.932767
$724$	33.1693	1.23273
$725$	−32.3934	−1.20306
$726$	−6.27381	−0.232843
$727$	1.89161	0.0701558	0.0350779	−	0.999385i	$-0.488832\pi$
$727$	1.89161	0.0701558	0.0350779	+	0.999385i	$0.488832\pi$
$728$	6.22251	0.230622
$729$	1.00000	0.0370370
$730$	2.11296	0.0782041
$731$	1.22708	0.0453853
$732$	−22.1079	−0.817132
$733$	−6.08665	−0.224816	−0.112408	−	0.993662i	$-0.535856\pi$
$733$	−6.08665	−0.224816	−0.112408	+	0.993662i	$0.535856\pi$
$734$	8.33883	0.307792
$735$	0.612183	0.0225807
$736$	0.462000	0.0170295
$737$	11.2220	0.413366
$738$	−0.831074	−0.0305923
$739$	5.53225	0.203507	0.101753	−	0.994810i	$-0.467555\pi$
$739$	5.53225	0.203507	0.101753	+	0.994810i	$0.467555\pi$
$740$	2.48516	0.0913562
$741$	−31.3646	−1.15221
$742$	−0.371009	−0.0136202
$743$	18.6057	0.682577	0.341289	−	0.939959i	$-0.389137\pi$
$743$	18.6057	0.682577	0.341289	+	0.939959i	$0.389137\pi$
$744$	9.52287	0.349125
$745$	−7.86358	−0.288099
$746$	5.96591	0.218428
$747$	−2.83040	−0.103559
$748$	11.0137	0.402702
$749$	7.75209	0.283255
$750$	−2.06020	−0.0752279
$751$	−24.4084	−0.890674	−0.445337	−	0.895363i	$-0.646916\pi$
$751$	−24.4084	−0.890674	−0.445337	+	0.895363i	$0.646916\pi$
$752$	6.07239	0.221437
$753$	14.8442	0.540954
$754$	−11.2385	−0.409282
$755$	−0.133522	−0.00485937
$756$	1.87775	0.0682933
$757$	−3.38070	−0.122873	−0.0614367	−	0.998111i	$-0.519568\pi$
$757$	−3.38070	−0.122873	−0.0614367	+	0.998111i	$0.519568\pi$
$758$	7.78551	0.282782
$759$	−0.644098	−0.0233793
$760$	−5.67219	−0.205752
$761$	−22.6332	−0.820453	−0.410227	−	0.911984i	$-0.634550\pi$
$761$	−22.6332	−0.820453	−0.410227	+	0.911984i	$0.634550\pi$
$762$	−2.34053	−0.0847885
$763$	−9.60405	−0.347690
$764$	−16.1067	−0.582721
$765$	0.667419	0.0241306
$766$	−0.349637	−0.0126329
$767$	−23.7521	−0.857638
$768$	−7.09162	−0.255897
$769$	−12.2644	−0.442267	−0.221133	−	0.975244i	$-0.570976\pi$
$769$	−12.2644	−0.442267	−0.221133	+	0.975244i	$0.570976\pi$
$770$	−1.15153	−0.0414983
$771$	−7.67270	−0.276326
$772$	16.0063	0.576079
$773$	−25.1177	−0.903420	−0.451710	−	0.892165i	$-0.649186\pi$
$773$	−25.1177	−0.903420	−0.451710	+	0.892165i	$0.649186\pi$
$774$	−0.393526	−0.0141450
$775$	−32.4866	−1.16695
$776$	−9.34923	−0.335618
$777$	−2.16189	−0.0775575
$778$	10.6944	0.383414
$779$	16.2441	0.582004
$780$	5.27579	0.188904
$781$	42.4075	1.51746
$782$	−0.0456362	−0.00163195
$783$	−7.00364	−0.250290
$784$	3.28147	0.117195
$785$	−4.09484	−0.146151
$786$	−4.20173	−0.149871
$787$	36.9892	1.31852	0.659261	−	0.751914i	$-0.270869\pi$
$787$	36.9892	1.31852	0.659261	+	0.751914i	$0.270869\pi$
$788$	4.80772	0.171268
$789$	−12.0209	−0.427957
$790$	2.07283	0.0737479
$791$	5.98505	0.212804
$792$	−7.29416	−0.259187
$793$	54.0353	1.91885
$794$	8.48212	0.301019
$795$	−0.649603	−0.0230390
$796$	−7.17920	−0.254460
$797$	−16.7120	−0.591971	−0.295986	−	0.955192i	$-0.595648\pi$
$797$	−16.7120	−0.591971	−0.295986	+	0.955192i	$0.595648\pi$
$798$	2.38940	0.0845839
$799$	−2.01748	−0.0713733
$800$	−17.8485	−0.631039
$801$	−2.94135	−0.103928
$802$	−1.16111	−0.0410001
$803$	−53.1093	−1.87419
$804$	3.91679	0.138134
$805$	−0.0732918	−0.00258320
$806$	−11.2708	−0.396998
$807$	1.19114	0.0419299
$808$	8.36599	0.294314
$809$	28.2609	0.993602	0.496801	−	0.867865i	$-0.334508\pi$
$809$	28.2609	0.993602	0.496801	+	0.867865i	$0.334508\pi$
$810$	−0.214042	−0.00752065
$811$	9.25407	0.324955	0.162477	−	0.986712i	$-0.448052\pi$
$811$	9.25407	0.324955	0.162477	+	0.986712i	$0.448052\pi$
$812$	−13.1511	−0.461513
$813$	−19.3703	−0.679345
$814$	4.06658	0.142533
$815$	−8.61779	−0.301868
$816$	3.57755	0.125239
$817$	7.69180	0.269102
$818$	5.73173	0.200405
$819$	−4.58953	−0.160371
$820$	−2.73239	−0.0954191
$821$	−16.1414	−0.563340	−0.281670	−	0.959511i	$-0.590888\pi$
$821$	−16.1414	−0.563340	−0.281670	+	0.959511i	$0.590888\pi$
$822$	0.607191	0.0211782
$823$	12.2321	0.426383	0.213192	−	0.977010i	$-0.431614\pi$
$823$	12.2321	0.426383	0.213192	+	0.977010i	$0.431614\pi$
$824$	14.0301	0.488760
$825$	24.8835	0.866332
$826$	1.80947	0.0629594
$827$	17.4239	0.605887	0.302943	−	0.953009i	$-0.402031\pi$
$827$	17.4239	0.605887	0.302943	+	0.953009i	$0.402031\pi$
$828$	−0.224809	−0.00781264
$829$	4.04033	0.140326	0.0701632	−	0.997536i	$-0.477648\pi$
$829$	4.04033	0.140326	0.0701632	+	0.997536i	$0.477648\pi$
$830$	0.605823	0.0210284
$831$	−7.53291	−0.261314
$832$	23.9285	0.829571
$833$	−1.09023	−0.0377742
$834$	6.54785	0.226733
$835$	1.23285	0.0426647
$836$	69.0380	2.38773
$837$	−7.02377	−0.242777
$838$	11.2560	0.388832
$839$	−19.4473	−0.671395	−0.335697	−	0.941970i	$-0.608972\pi$
$839$	−19.4473	−0.671395	−0.335697	+	0.941970i	$0.608972\pi$
$840$	−0.830000	−0.0286377
$841$	20.0509	0.691411
$842$	1.02446	0.0353054
$843$	20.1324	0.693397
$844$	−22.1273	−0.761655
$845$	−4.93650	−0.169821
$846$	0.647006	0.0222445
$847$	17.9438	0.616556
$848$	−3.48205	−0.119574
$849$	−2.11325	−0.0725266
$850$	1.76307	0.0604727
$851$	0.258826	0.00887245
$852$	14.8014	0.507089
$853$	−9.83870	−0.336871	−0.168435	−	0.985713i	$-0.553871\pi$
$853$	−9.83870	−0.336871	−0.168435	+	0.985713i	$0.553871\pi$
$854$	−4.11648	−0.140863
$855$	4.18363	0.143077
$856$	−10.5103	−0.359235
$857$	20.5810	0.703034	0.351517	−	0.936181i	$-0.385666\pi$
$857$	20.5810	0.703034	0.351517	+	0.936181i	$0.385666\pi$
$858$	8.63302	0.294727
$859$	−8.25880	−0.281787	−0.140893	−	0.990025i	$-0.544997\pi$
$859$	−8.25880	−0.281787	−0.140893	+	0.990025i	$0.544997\pi$
$860$	−1.29383	−0.0441191
$861$	2.37696	0.0810067
$862$	−3.54993	−0.120911
$863$	8.11866	0.276363	0.138181	−	0.990407i	$-0.455874\pi$
$863$	8.11866	0.276363	0.138181	+	0.990407i	$0.455874\pi$
$864$	−3.85893	−0.131284
$865$	−5.37994	−0.182924
$866$	11.5242	0.391609
$867$	15.8114	0.536983
$868$	−13.1889	−0.447661
$869$	−52.1006	−1.76739
$870$	1.49907	0.0508232
$871$	−9.57325	−0.324377
$872$	13.0212	0.440954
$873$	6.89570	0.233384
$874$	−0.286064	−0.00967627
$875$	5.89240	0.199199
$876$	−18.5367	−0.626296
$877$	9.85708	0.332850	0.166425	−	0.986054i	$-0.446778\pi$
$877$	9.85708	0.332850	0.166425	+	0.986054i	$0.446778\pi$
$878$	−7.09107	−0.239312
$879$	16.3419	0.551198
$880$	−10.8075	−0.364322
$881$	−35.6840	−1.20222	−0.601112	−	0.799165i	$-0.705276\pi$
$881$	−35.6840	−1.20222	−0.601112	+	0.799165i	$0.705276\pi$
$882$	0.349637	0.0117729
$883$	9.28949	0.312616	0.156308	−	0.987708i	$-0.450041\pi$
$883$	9.28949	0.312616	0.156308	+	0.987708i	$0.450041\pi$
$884$	−9.39560	−0.316008
$885$	3.16821	0.106498
$886$	1.05311	0.0353799
$887$	−47.7051	−1.60178	−0.800891	−	0.598810i	$-0.795640\pi$
$887$	−47.7051	−1.60178	−0.800891	+	0.598810i	$0.795640\pi$
$888$	2.93111	0.0983615
$889$	6.69418	0.224515
$890$	0.629572	0.0211033
$891$	5.37994	0.180235
$892$	−32.1626	−1.07688
$893$	−12.6463	−0.423192
$894$	−4.49114	−0.150206
$895$	−6.32151	−0.211305
$896$	−9.54077	−0.318735
$897$	0.549468	0.0183462
$898$	4.50995	0.150499
$899$	49.1919	1.64064
$900$	8.68505	0.289502
$901$	1.15687	0.0385410
$902$	−4.47113	−0.148872
$903$	1.12553	0.0374552
$904$	−8.11457	−0.269887
$905$	10.8138	0.359463
$906$	−0.0762587	−0.00253353
$907$	−23.5002	−0.780312	−0.390156	−	0.920749i	$-0.627579\pi$
$907$	−23.5002	−0.780312	−0.390156	+	0.920749i	$0.627579\pi$
$908$	−49.4222	−1.64013
$909$	−6.17049	−0.204662
$910$	0.982350	0.0325646
$911$	−53.6222	−1.77658	−0.888291	−	0.459282i	$-0.848107\pi$
$911$	−53.6222	−1.77658	−0.888291	+	0.459282i	$0.848107\pi$
$912$	22.4254	0.742579
$913$	−15.2274	−0.503953
$914$	8.45963	0.279820
$915$	−7.20759	−0.238276
$916$	−11.3506	−0.375035
$917$	12.0174	0.396850
$918$	0.381184	0.0125810
$919$	−52.0430	−1.71674	−0.858371	−	0.513030i	$-0.828523\pi$
$919$	−52.0430	−1.71674	−0.858371	+	0.513030i	$0.828523\pi$
$920$	0.0993694	0.00327611
$921$	−25.4245	−0.837765
$922$	2.14394	0.0706070
$923$	−36.1771	−1.19078
$924$	10.1022	0.332338
$925$	−9.99926	−0.328774
$926$	−1.03217	−0.0339191
$927$	−10.3481	−0.339877
$928$	27.0266	0.887190
$929$	−54.9051	−1.80138	−0.900689	−	0.434465i	$-0.856937\pi$
$929$	−54.9051	−1.80138	−0.900689	+	0.434465i	$0.856937\pi$
$930$	1.50338	0.0492977
$931$	−6.83395	−0.223974
$932$	−10.8133	−0.354201
$933$	−28.3892	−0.929419
$934$	−5.36977	−0.175704
$935$	3.59068	0.117428
$936$	6.22251	0.203389
$937$	−14.2900	−0.466833	−0.233416	−	0.972377i	$-0.574990\pi$
$937$	−14.2900	−0.466833	−0.233416	+	0.972377i	$0.574990\pi$
$938$	0.729304	0.0238126
$939$	−31.4262	−1.02555
$940$	2.12721	0.0693821
$941$	12.6930	0.413781	0.206891	−	0.978364i	$-0.433666\pi$
$941$	12.6930	0.413781	0.206891	+	0.978364i	$0.433666\pi$
$942$	−2.33869	−0.0761988
$943$	−0.284575	−0.00926704
$944$	16.9825	0.552733
$945$	0.612183	0.0199143
$946$	−2.11715	−0.0688344
$947$	11.2373	0.365162	0.182581	−	0.983191i	$-0.441555\pi$
$947$	11.2373	0.365162	0.182581	+	0.983191i	$0.441555\pi$
$948$	−18.1846	−0.590608
$949$	45.3065	1.47071
$950$	11.0515	0.358559
$951$	11.2524	0.364885
$952$	1.47814	0.0479068
$953$	−7.46989	−0.241973	−0.120987	−	0.992654i	$-0.538606\pi$
$953$	−7.46989	−0.241973	−0.120987	+	0.992654i	$0.538606\pi$
$954$	−0.371009	−0.0120119
$955$	−5.25110	−0.169921
$956$	33.1178	1.07111
$957$	−37.6792	−1.21799
$958$	−5.73333	−0.185235
$959$	−1.73663	−0.0560788
$960$	−3.19174	−0.103013
$961$	18.3333	0.591398
$962$	−3.46912	−0.111849
$963$	7.75209	0.249808
$964$	47.0957	1.51685
$965$	5.21835	0.167985
$966$	−0.0418593	−0.00134680
$967$	24.9843	0.803441	0.401720	−	0.915762i	$-0.368412\pi$
$967$	24.9843	0.803441	0.401720	+	0.915762i	$0.368412\pi$
$968$	−24.3283	−0.781941
$969$	−7.45058	−0.239347
$970$	−1.47597	−0.0473904
$971$	19.3024	0.619442	0.309721	−	0.950827i	$-0.399764\pi$
$971$	19.3024	0.619442	0.309721	+	0.950827i	$0.399764\pi$
$972$	1.87775	0.0602290
$973$	−18.7276	−0.600378
$974$	4.41198	0.141369
$975$	−21.2276	−0.679828
$976$	−38.6347	−1.23667
$977$	−42.6463	−1.36438	−0.682188	−	0.731177i	$-0.738971\pi$
$977$	−42.6463	−1.36438	−0.682188	+	0.731177i	$0.738971\pi$
$978$	−4.92189	−0.157385
$979$	−15.8243	−0.505747
$980$	1.14953	0.0367203
$981$	−9.60405	−0.306634
$982$	−0.493880	−0.0157604
$983$	37.3515	1.19133	0.595664	−	0.803233i	$-0.296889\pi$
$983$	37.3515	1.19133	0.595664	+	0.803233i	$0.296889\pi$
$984$	−3.22270	−0.102736
$985$	1.56740	0.0499416
$986$	−2.66968	−0.0850198
$987$	−1.85051	−0.0589024
$988$	−58.8951	−1.87370
$989$	−0.134750	−0.00428482
$990$	−1.15153	−0.0365981
$991$	−19.3586	−0.614947	−0.307473	−	0.951557i	$-0.599484\pi$
$991$	−19.3586	−0.614947	−0.307473	+	0.951557i	$0.599484\pi$
$992$	27.1043	0.860561
$993$	−7.81218	−0.247912
$994$	2.75602	0.0874157
$995$	−2.34055	−0.0742005
$996$	−5.31479	−0.168406
$997$	39.6127	1.25455	0.627274	−	0.778799i	$-0.284171\pi$
$997$	39.6127	1.25455	0.627274	+	0.778799i	$0.284171\pi$
$998$	4.97733	0.157555
$999$	−2.16189	−0.0683993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.28	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.28	✓	52	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)

\(f(q)\)	\(=\)	\(q+0.349637 q^{2} -1.00000 q^{3} -1.87775 q^{4} -0.612183 q^{5} -0.349637 q^{6} +1.00000 q^{7} -1.35581 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.349637 q^{2} -1.00000 q^{3} -1.87775 q^{4} -0.612183 q^{5} -0.349637 q^{6} +1.00000 q^{7} -1.35581 q^{8} +1.00000 q^{9} -0.214042 q^{10} +5.37994 q^{11} +1.87775 q^{12} -4.58953 q^{13} +0.349637 q^{14} +0.612183 q^{15} +3.28147 q^{16} -1.09023 q^{17} +0.349637 q^{18} -6.83395 q^{19} +1.14953 q^{20} -1.00000 q^{21} +1.88103 q^{22} +0.119722 q^{23} +1.35581 q^{24} -4.62523 q^{25} -1.60467 q^{26} -1.00000 q^{27} -1.87775 q^{28} +7.00364 q^{29} +0.214042 q^{30} +7.02377 q^{31} +3.85893 q^{32} -5.37994 q^{33} -0.381184 q^{34} -0.612183 q^{35} -1.87775 q^{36} +2.16189 q^{37} -2.38940 q^{38} +4.58953 q^{39} +0.830000 q^{40} -2.37696 q^{41} -0.349637 q^{42} -1.12553 q^{43} -10.1022 q^{44} -0.612183 q^{45} +0.0418593 q^{46} +1.85051 q^{47} -3.28147 q^{48} +1.00000 q^{49} -1.61715 q^{50} +1.09023 q^{51} +8.61801 q^{52} -1.06113 q^{53} -0.349637 q^{54} -3.29351 q^{55} -1.35581 q^{56} +6.83395 q^{57} +2.44873 q^{58} +5.17528 q^{59} -1.14953 q^{60} -11.7736 q^{61} +2.45577 q^{62} +1.00000 q^{63} -5.21371 q^{64} +2.80963 q^{65} -1.88103 q^{66} +2.08589 q^{67} +2.04718 q^{68} -0.119722 q^{69} -0.214042 q^{70} +7.88252 q^{71} -1.35581 q^{72} -9.87172 q^{73} +0.755877 q^{74} +4.62523 q^{75} +12.8325 q^{76} +5.37994 q^{77} +1.60467 q^{78} -9.68423 q^{79} -2.00886 q^{80} +1.00000 q^{81} -0.831074 q^{82} -2.83040 q^{83} +1.87775 q^{84} +0.667419 q^{85} -0.393526 q^{86} -7.00364 q^{87} -7.29416 q^{88} -2.94135 q^{89} -0.214042 q^{90} -4.58953 q^{91} -0.224809 q^{92} -7.02377 q^{93} +0.647006 q^{94} +4.18363 q^{95} -3.85893 q^{96} +6.89570 q^{97} +0.349637 q^{98} +5.37994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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