LMFDB - Embedded newform 8042.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.39327 q^{3} +1.00000 q^{4} +3.11355 q^{5} -2.39327 q^{6} -5.17926 q^{7} +1.00000 q^{8} +2.72774 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.39327 q^{3} +1.00000 q^{4} +3.11355 q^{5} -2.39327 q^{6} -5.17926 q^{7} +1.00000 q^{8} +2.72774 q^{9} +3.11355 q^{10} +3.90037 q^{11} -2.39327 q^{12} +4.51832 q^{13} -5.17926 q^{14} -7.45157 q^{15} +1.00000 q^{16} +1.37971 q^{17} +2.72774 q^{18} -2.21170 q^{19} +3.11355 q^{20} +12.3954 q^{21} +3.90037 q^{22} +4.43124 q^{23} -2.39327 q^{24} +4.69421 q^{25} +4.51832 q^{26} +0.651582 q^{27} -5.17926 q^{28} -3.11959 q^{29} -7.45157 q^{30} +7.47996 q^{31} +1.00000 q^{32} -9.33465 q^{33} +1.37971 q^{34} -16.1259 q^{35} +2.72774 q^{36} -0.741608 q^{37} -2.21170 q^{38} -10.8136 q^{39} +3.11355 q^{40} +1.99986 q^{41} +12.3954 q^{42} +0.199593 q^{43} +3.90037 q^{44} +8.49298 q^{45} +4.43124 q^{46} -2.77838 q^{47} -2.39327 q^{48} +19.8248 q^{49} +4.69421 q^{50} -3.30202 q^{51} +4.51832 q^{52} -4.43980 q^{53} +0.651582 q^{54} +12.1440 q^{55} -5.17926 q^{56} +5.29320 q^{57} -3.11959 q^{58} -10.5257 q^{59} -7.45157 q^{60} -9.77296 q^{61} +7.47996 q^{62} -14.1277 q^{63} +1.00000 q^{64} +14.0680 q^{65} -9.33465 q^{66} -8.95674 q^{67} +1.37971 q^{68} -10.6052 q^{69} -16.1259 q^{70} -6.00592 q^{71} +2.72774 q^{72} +14.2555 q^{73} -0.741608 q^{74} -11.2345 q^{75} -2.21170 q^{76} -20.2011 q^{77} -10.8136 q^{78} -1.63826 q^{79} +3.11355 q^{80} -9.74264 q^{81} +1.99986 q^{82} +3.81331 q^{83} +12.3954 q^{84} +4.29580 q^{85} +0.199593 q^{86} +7.46601 q^{87} +3.90037 q^{88} +7.85506 q^{89} +8.49298 q^{90} -23.4016 q^{91} +4.43124 q^{92} -17.9016 q^{93} -2.77838 q^{94} -6.88624 q^{95} -2.39327 q^{96} +17.7619 q^{97} +19.8248 q^{98} +10.6392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) $ 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.39327	−1.38176	−0.690878	−	0.722972i	$-0.742776\pi$
$3$	−2.39327	−1.38176	−0.690878	+	0.722972i	$0.742776\pi$
$4$	1.00000	0.500000
$5$	3.11355	1.39242	0.696212	−	0.717837i	$-0.254868\pi$
$5$	3.11355	1.39242	0.696212	+	0.717837i	$0.254868\pi$
$6$	−2.39327	−0.977049
$7$	−5.17926	−1.95758	−0.978789	−	0.204872i	$-0.934322\pi$
$7$	−5.17926	−1.95758	−0.978789	+	0.204872i	$0.934322\pi$
$8$	1.00000	0.353553
$9$	2.72774	0.909248
$10$	3.11355	0.984592
$11$	3.90037	1.17601	0.588003	−	0.808859i	$-0.299914\pi$
$11$	3.90037	1.17601	0.588003	+	0.808859i	$0.299914\pi$
$12$	−2.39327	−0.690878
$13$	4.51832	1.25316	0.626579	−	0.779358i	$-0.284455\pi$
$13$	4.51832	1.25316	0.626579	+	0.779358i	$0.284455\pi$
$14$	−5.17926	−1.38422
$15$	−7.45157	−1.92399
$16$	1.00000	0.250000
$17$	1.37971	0.334629	0.167314	−	0.985904i	$-0.446490\pi$
$17$	1.37971	0.334629	0.167314	+	0.985904i	$0.446490\pi$
$18$	2.72774	0.642935
$19$	−2.21170	−0.507399	−0.253699	−	0.967283i	$-0.581647\pi$
$19$	−2.21170	−0.507399	−0.253699	+	0.967283i	$0.581647\pi$
$20$	3.11355	0.696212
$21$	12.3954	2.70489
$22$	3.90037	0.831562
$23$	4.43124	0.923977	0.461988	−	0.886886i	$-0.347136\pi$
$23$	4.43124	0.923977	0.461988	+	0.886886i	$0.347136\pi$
$24$	−2.39327	−0.488524
$25$	4.69421	0.938842
$26$	4.51832	0.886116
$27$	0.651582	0.125397
$28$	−5.17926	−0.978789
$29$	−3.11959	−0.579293	−0.289646	−	0.957134i	$-0.593538\pi$
$29$	−3.11959	−0.579293	−0.289646	+	0.957134i	$0.593538\pi$
$30$	−7.45157	−1.36047
$31$	7.47996	1.34344	0.671720	−	0.740805i	$-0.265556\pi$
$31$	7.47996	1.34344	0.671720	+	0.740805i	$0.265556\pi$
$32$	1.00000	0.176777
$33$	−9.33465	−1.62495
$34$	1.37971	0.236618
$35$	−16.1259	−2.72578
$36$	2.72774	0.454624
$37$	−0.741608	−0.121920	−0.0609598	−	0.998140i	$-0.519416\pi$
$37$	−0.741608	−0.121920	−0.0609598	+	0.998140i	$0.519416\pi$
$38$	−2.21170	−0.358785
$39$	−10.8136	−1.73156
$40$	3.11355	0.492296
$41$	1.99986	0.312325	0.156162	−	0.987731i	$-0.450088\pi$
$41$	1.99986	0.312325	0.156162	+	0.987731i	$0.450088\pi$
$42$	12.3954	1.91265
$43$	0.199593	0.0304377	0.0152188	−	0.999884i	$-0.495156\pi$
$43$	0.199593	0.0304377	0.0152188	+	0.999884i	$0.495156\pi$
$44$	3.90037	0.588003
$45$	8.49298	1.26606
$46$	4.43124	0.653350
$47$	−2.77838	−0.405269	−0.202634	−	0.979254i	$-0.564950\pi$
$47$	−2.77838	−0.405269	−0.202634	+	0.979254i	$0.564950\pi$
$48$	−2.39327	−0.345439
$49$	19.8248	2.83211
$50$	4.69421	0.663862
$51$	−3.30202	−0.462375
$52$	4.51832	0.626579
$53$	−4.43980	−0.609853	−0.304927	−	0.952376i	$-0.598632\pi$
$53$	−4.43980	−0.609853	−0.304927	+	0.952376i	$0.598632\pi$
$54$	0.651582	0.0886691
$55$	12.1440	1.63750
$56$	−5.17926	−0.692108
$57$	5.29320	0.701101
$58$	−3.11959	−0.409622
$59$	−10.5257	−1.37033	−0.685165	−	0.728388i	$-0.740270\pi$
$59$	−10.5257	−1.37033	−0.685165	+	0.728388i	$0.740270\pi$
$60$	−7.45157	−0.961994
$61$	−9.77296	−1.25130	−0.625650	−	0.780104i	$-0.715166\pi$
$61$	−9.77296	−1.25130	−0.625650	+	0.780104i	$0.715166\pi$
$62$	7.47996	0.949955
$63$	−14.1277	−1.77992
$64$	1.00000	0.125000
$65$	14.0680	1.74493
$66$	−9.33465	−1.14902
$67$	−8.95674	−1.09424	−0.547120	−	0.837054i	$-0.684276\pi$
$67$	−8.95674	−1.09424	−0.547120	+	0.837054i	$0.684276\pi$
$68$	1.37971	0.167314
$69$	−10.6052	−1.27671
$70$	−16.1259	−1.92741
$71$	−6.00592	−0.712772	−0.356386	−	0.934339i	$-0.615991\pi$
$71$	−6.00592	−0.712772	−0.356386	+	0.934339i	$0.615991\pi$
$72$	2.72774	0.321468
$73$	14.2555	1.66848	0.834238	−	0.551405i	$-0.185908\pi$
$73$	14.2555	1.66848	0.834238	+	0.551405i	$0.185908\pi$
$74$	−0.741608	−0.0862102
$75$	−11.2345	−1.29725
$76$	−2.21170	−0.253699
$77$	−20.2011	−2.30212
$78$	−10.8136	−1.22440
$79$	−1.63826	−0.184319	−0.0921594	−	0.995744i	$-0.529377\pi$
$79$	−1.63826	−0.184319	−0.0921594	+	0.995744i	$0.529377\pi$
$80$	3.11355	0.348106
$81$	−9.74264	−1.08252
$82$	1.99986	0.220847
$83$	3.81331	0.418565	0.209283	−	0.977855i	$-0.432887\pi$
$83$	3.81331	0.418565	0.209283	+	0.977855i	$0.432887\pi$
$84$	12.3954	1.35245
$85$	4.29580	0.465945
$86$	0.199593	0.0215227
$87$	7.46601	0.800441
$88$	3.90037	0.415781
$89$	7.85506	0.832634	0.416317	−	0.909219i	$-0.363321\pi$
$89$	7.85506	0.832634	0.416317	+	0.909219i	$0.363321\pi$
$90$	8.49298	0.895238
$91$	−23.4016	−2.45315
$92$	4.43124	0.461988
$93$	−17.9016	−1.85631
$94$	−2.77838	−0.286568
$95$	−6.88624	−0.706514
$96$	−2.39327	−0.244262
$97$	17.7619	1.80344	0.901722	−	0.432317i	$-0.142304\pi$
$97$	17.7619	1.80344	0.901722	+	0.432317i	$0.142304\pi$
$98$	19.8248	2.00260
$99$	10.6392	1.06928
$100$	4.69421	0.469421
$101$	16.5614	1.64792	0.823961	−	0.566647i	$-0.191760\pi$
$101$	16.5614	1.64792	0.823961	+	0.566647i	$0.191760\pi$
$102$	−3.30202	−0.326949
$103$	−2.22177	−0.218918	−0.109459	−	0.993991i	$-0.534912\pi$
$103$	−2.22177	−0.218918	−0.109459	+	0.993991i	$0.534912\pi$
$104$	4.51832	0.443058
$105$	38.5937	3.76636
$106$	−4.43980	−0.431231
$107$	−7.27165	−0.702977	−0.351489	−	0.936192i	$-0.614324\pi$
$107$	−7.27165	−0.702977	−0.351489	+	0.936192i	$0.614324\pi$
$108$	0.651582	0.0626985
$109$	2.88653	0.276480	0.138240	−	0.990399i	$-0.455856\pi$
$109$	2.88653	0.276480	0.138240	+	0.990399i	$0.455856\pi$
$110$	12.1440	1.15789
$111$	1.77487	0.168463
$112$	−5.17926	−0.489394
$113$	5.49140	0.516588	0.258294	−	0.966066i	$-0.416840\pi$
$113$	5.49140	0.516588	0.258294	+	0.966066i	$0.416840\pi$
$114$	5.29320	0.495753
$115$	13.7969	1.28657
$116$	−3.11959	−0.289646
$117$	12.3248	1.13943
$118$	−10.5257	−0.968970
$119$	−7.14588	−0.655062
$120$	−7.45157	−0.680233
$121$	4.21291	0.382992
$122$	−9.77296	−0.884802
$123$	−4.78620	−0.431557
$124$	7.47996	0.671720
$125$	−0.952089	−0.0851574
$126$	−14.1277	−1.25860
$127$	12.3025	1.09167	0.545833	−	0.837894i	$-0.316213\pi$
$127$	12.3025	1.09167	0.545833	+	0.837894i	$0.316213\pi$
$128$	1.00000	0.0883883
$129$	−0.477680	−0.0420574
$130$	14.0680	1.23385
$131$	−11.5904	−1.01266	−0.506330	−	0.862340i	$-0.668998\pi$
$131$	−11.5904	−1.01266	−0.506330	+	0.862340i	$0.668998\pi$
$132$	−9.33465	−0.812477
$133$	11.4550	0.993272
$134$	−8.95674	−0.773744
$135$	2.02873	0.174606
$136$	1.37971	0.118309
$137$	−2.90821	−0.248465	−0.124232	−	0.992253i	$-0.539647\pi$
$137$	−2.90821	−0.248465	−0.124232	+	0.992253i	$0.539647\pi$
$138$	−10.6052	−0.902770
$139$	−6.31131	−0.535318	−0.267659	−	0.963514i	$-0.586250\pi$
$139$	−6.31131	−0.535318	−0.267659	+	0.963514i	$0.586250\pi$
$140$	−16.1259	−1.36289
$141$	6.64942	0.559982
$142$	−6.00592	−0.504006
$143$	17.6231	1.47372
$144$	2.72774	0.227312
$145$	−9.71300	−0.806620
$146$	14.2555	1.17979
$147$	−47.4460	−3.91328
$148$	−0.741608	−0.0609598
$149$	7.02359	0.575395	0.287698	−	0.957721i	$-0.407110\pi$
$149$	7.02359	0.575395	0.287698	+	0.957721i	$0.407110\pi$
$150$	−11.2345	−0.917295
$151$	4.59038	0.373559	0.186780	−	0.982402i	$-0.440195\pi$
$151$	4.59038	0.373559	0.186780	+	0.982402i	$0.440195\pi$
$152$	−2.21170	−0.179393
$153$	3.76350	0.304261
$154$	−20.2011	−1.62785
$155$	23.2892	1.87064
$156$	−10.8136	−0.865778
$157$	2.83237	0.226048	0.113024	−	0.993592i	$-0.463946\pi$
$157$	2.83237	0.226048	0.113024	+	0.993592i	$0.463946\pi$
$158$	−1.63826	−0.130333
$159$	10.6256	0.842668
$160$	3.11355	0.246148
$161$	−22.9505	−1.80876
$162$	−9.74264	−0.765454
$163$	6.10891	0.478487	0.239243	−	0.970960i	$-0.423101\pi$
$163$	6.10891	0.478487	0.239243	+	0.970960i	$0.423101\pi$
$164$	1.99986	0.156162
$165$	−29.0639	−2.26262
$166$	3.81331	0.295970
$167$	3.25261	0.251694	0.125847	−	0.992050i	$-0.459835\pi$
$167$	3.25261	0.251694	0.125847	+	0.992050i	$0.459835\pi$
$168$	12.3954	0.956324
$169$	7.41524	0.570403
$170$	4.29580	0.329473
$171$	−6.03295	−0.461351
$172$	0.199593	0.0152188
$173$	−4.43255	−0.337001	−0.168500	−	0.985702i	$-0.553892\pi$
$173$	−4.43255	−0.337001	−0.168500	+	0.985702i	$0.553892\pi$
$174$	7.46601	0.565997
$175$	−24.3126	−1.83786
$176$	3.90037	0.294002
$177$	25.1909	1.89346
$178$	7.85506	0.588761
$179$	−12.4924	−0.933725	−0.466862	−	0.884330i	$-0.654616\pi$
$179$	−12.4924	−0.933725	−0.466862	+	0.884330i	$0.654616\pi$
$180$	8.49298	0.633029
$181$	−13.7758	−1.02395	−0.511974	−	0.859001i	$-0.671086\pi$
$181$	−13.7758	−1.02395	−0.511974	+	0.859001i	$0.671086\pi$
$182$	−23.4016	−1.73464
$183$	23.3893	1.72899
$184$	4.43124	0.326675
$185$	−2.30904	−0.169764
$186$	−17.9016	−1.31261
$187$	5.38138	0.393526
$188$	−2.77838	−0.202634
$189$	−3.37471	−0.245474
$190$	−6.88624	−0.499581
$191$	9.82421	0.710855	0.355427	−	0.934704i	$-0.384335\pi$
$191$	9.82421	0.710855	0.355427	+	0.934704i	$0.384335\pi$
$192$	−2.39327	−0.172719
$193$	−2.96231	−0.213232	−0.106616	−	0.994300i	$-0.534001\pi$
$193$	−2.96231	−0.213232	−0.106616	+	0.994300i	$0.534001\pi$
$194$	17.7619	1.27523
$195$	−33.6686	−2.41106
$196$	19.8248	1.41605
$197$	−7.88306	−0.561645	−0.280823	−	0.959760i	$-0.590607\pi$
$197$	−7.88306	−0.561645	−0.280823	+	0.959760i	$0.590607\pi$
$198$	10.6392	0.756096
$199$	10.8757	0.770955	0.385478	−	0.922717i	$-0.374037\pi$
$199$	10.8757	0.770955	0.385478	+	0.922717i	$0.374037\pi$
$200$	4.69421	0.331931
$201$	21.4359	1.51197
$202$	16.5614	1.16526
$203$	16.1572	1.13401
$204$	−3.30202	−0.231188
$205$	6.22666	0.434889
$206$	−2.22177	−0.154798
$207$	12.0873	0.840124
$208$	4.51832	0.313289
$209$	−8.62645	−0.596704
$210$	38.5937	2.66322
$211$	21.9441	1.51069	0.755347	−	0.655325i	$-0.227469\pi$
$211$	21.9441	1.51069	0.755347	+	0.655325i	$0.227469\pi$
$212$	−4.43980	−0.304927
$213$	14.3738	0.984877
$214$	−7.27165	−0.497080
$215$	0.621444	0.0423821
$216$	0.651582	0.0443345
$217$	−38.7407	−2.62989
$218$	2.88653	0.195501
$219$	−34.1172	−2.30543
$220$	12.1440	0.818749
$221$	6.23398	0.419343
$222$	1.77487	0.119121
$223$	27.3330	1.83036	0.915178	−	0.403050i	$-0.132050\pi$
$223$	27.3330	1.83036	0.915178	+	0.403050i	$0.132050\pi$
$224$	−5.17926	−0.346054
$225$	12.8046	0.853640
$226$	5.49140	0.365283
$227$	13.2010	0.876182	0.438091	−	0.898931i	$-0.355655\pi$
$227$	13.2010	0.876182	0.438091	+	0.898931i	$0.355655\pi$
$228$	5.29320	0.350550
$229$	20.5985	1.36118	0.680592	−	0.732663i	$-0.261723\pi$
$229$	20.5985	1.36118	0.680592	+	0.732663i	$0.261723\pi$
$230$	13.7969	0.909740
$231$	48.3466	3.18097
$232$	−3.11959	−0.204811
$233$	21.3130	1.39626	0.698130	−	0.715971i	$-0.254016\pi$
$233$	21.3130	1.39626	0.698130	+	0.715971i	$0.254016\pi$
$234$	12.3248	0.805699
$235$	−8.65064	−0.564305
$236$	−10.5257	−0.685165
$237$	3.92080	0.254684
$238$	−7.14588	−0.463199
$239$	2.42402	0.156797	0.0783983	−	0.996922i	$-0.475019\pi$
$239$	2.42402	0.156797	0.0783983	+	0.996922i	$0.475019\pi$
$240$	−7.45157	−0.480997
$241$	8.55482	0.551064	0.275532	−	0.961292i	$-0.411146\pi$
$241$	8.55482	0.551064	0.275532	+	0.961292i	$0.411146\pi$
$242$	4.21291	0.270816
$243$	21.3620	1.37038
$244$	−9.77296	−0.625650
$245$	61.7255	3.94350
$246$	−4.78620	−0.305157
$247$	−9.99317	−0.635850
$248$	7.47996	0.474978
$249$	−9.12629	−0.578355
$250$	−0.952089	−0.0602154
$251$	−10.3110	−0.650822	−0.325411	−	0.945573i	$-0.605503\pi$
$251$	−10.3110	−0.650822	−0.325411	+	0.945573i	$0.605503\pi$
$252$	−14.1277	−0.889962
$253$	17.2835	1.08660
$254$	12.3025	0.771925
$255$	−10.2810	−0.643822
$256$	1.00000	0.0625000
$257$	13.8787	0.865727	0.432864	−	0.901459i	$-0.357503\pi$
$257$	13.8787	0.865727	0.432864	+	0.901459i	$0.357503\pi$
$258$	−0.477680	−0.0297391
$259$	3.84098	0.238667
$260$	14.0680	0.872463
$261$	−8.50943	−0.526721
$262$	−11.5904	−0.716059
$263$	2.29221	0.141343	0.0706717	−	0.997500i	$-0.477486\pi$
$263$	2.29221	0.141343	0.0706717	+	0.997500i	$0.477486\pi$
$264$	−9.33465	−0.574508
$265$	−13.8235	−0.849174
$266$	11.4550	0.702350
$267$	−18.7993	−1.15050
$268$	−8.95674	−0.547120
$269$	−1.42038	−0.0866019	−0.0433010	−	0.999062i	$-0.513787\pi$
$269$	−1.42038	−0.0866019	−0.0433010	+	0.999062i	$0.513787\pi$
$270$	2.02873	0.123465
$271$	14.2561	0.865996	0.432998	−	0.901395i	$-0.357456\pi$
$271$	14.2561	0.865996	0.432998	+	0.901395i	$0.357456\pi$
$272$	1.37971	0.0836572
$273$	56.0063	3.38966
$274$	−2.90821	−0.175691
$275$	18.3092	1.10408
$276$	−10.6052	−0.638355
$277$	20.4793	1.23048	0.615241	−	0.788339i	$-0.289059\pi$
$277$	20.4793	1.23048	0.615241	+	0.788339i	$0.289059\pi$
$278$	−6.31131	−0.378527
$279$	20.4034	1.22152
$280$	−16.1259	−0.963707
$281$	−7.30450	−0.435750	−0.217875	−	0.975977i	$-0.569912\pi$
$281$	−7.30450	−0.435750	−0.217875	+	0.975977i	$0.569912\pi$
$282$	6.64942	0.395967
$283$	3.43892	0.204423	0.102211	−	0.994763i	$-0.467408\pi$
$283$	3.43892	0.204423	0.102211	+	0.994763i	$0.467408\pi$
$284$	−6.00592	−0.356386
$285$	16.4806	0.976229
$286$	17.6231	1.04208
$287$	−10.3578	−0.611400
$288$	2.72774	0.160734
$289$	−15.0964	−0.888024
$290$	−9.71300	−0.570367
$291$	−42.5089	−2.49192
$292$	14.2555	0.834238
$293$	10.3268	0.603297	0.301648	−	0.953419i	$-0.402463\pi$
$293$	10.3268	0.603297	0.301648	+	0.953419i	$0.402463\pi$
$294$	−47.4460	−2.76711
$295$	−32.7723	−1.90808
$296$	−0.741608	−0.0431051
$297$	2.54141	0.147468
$298$	7.02359	0.406866
$299$	20.0218	1.15789
$300$	−11.2345	−0.648625
$301$	−1.03375	−0.0595841
$302$	4.59038	0.264146
$303$	−39.6359	−2.27702
$304$	−2.21170	−0.126850
$305$	−30.4286	−1.74234
$306$	3.76350	0.215145
$307$	0.920938	0.0525607	0.0262803	−	0.999655i	$-0.491634\pi$
$307$	0.920938	0.0525607	0.0262803	+	0.999655i	$0.491634\pi$
$308$	−20.2011	−1.15106
$309$	5.31731	0.302491
$310$	23.2892	1.32274
$311$	−34.5002	−1.95633	−0.978165	−	0.207831i	$-0.933360\pi$
$311$	−34.5002	−1.95633	−0.978165	+	0.207831i	$0.933360\pi$
$312$	−10.8136	−0.612198
$313$	7.19989	0.406962	0.203481	−	0.979079i	$-0.434774\pi$
$313$	7.19989	0.406962	0.203481	+	0.979079i	$0.434774\pi$
$314$	2.83237	0.159840
$315$	−43.9874	−2.47841
$316$	−1.63826	−0.0921594
$317$	20.2046	1.13480	0.567401	−	0.823442i	$-0.307949\pi$
$317$	20.2046	1.13480	0.567401	+	0.823442i	$0.307949\pi$
$318$	10.6256	0.595856
$319$	−12.1675	−0.681252
$320$	3.11355	0.174053
$321$	17.4030	0.971343
$322$	−22.9505	−1.27898
$323$	−3.05150	−0.169790
$324$	−9.74264	−0.541258
$325$	21.2100	1.17652
$326$	6.10891	0.338341
$327$	−6.90825	−0.382027
$328$	1.99986	0.110424
$329$	14.3900	0.793345
$330$	−29.0639	−1.59992
$331$	24.6701	1.35599	0.677996	−	0.735066i	$-0.262849\pi$
$331$	24.6701	1.35599	0.677996	+	0.735066i	$0.262849\pi$
$332$	3.81331	0.209283
$333$	−2.02292	−0.110855
$334$	3.25261	0.177975
$335$	−27.8873	−1.52364
$336$	12.3954	0.676223
$337$	9.50778	0.517922	0.258961	−	0.965888i	$-0.416620\pi$
$337$	9.50778	0.517922	0.258961	+	0.965888i	$0.416620\pi$
$338$	7.41524	0.403336
$339$	−13.1424	−0.713798
$340$	4.29580	0.232972
$341$	29.1746	1.57989
$342$	−6.03295	−0.326225
$343$	−66.4229	−3.58650
$344$	0.199593	0.0107613
$345$	−33.0197	−1.77772
$346$	−4.43255	−0.238295
$347$	−1.52711	−0.0819794	−0.0409897	−	0.999160i	$-0.513051\pi$
$347$	−1.52711	−0.0819794	−0.0409897	+	0.999160i	$0.513051\pi$
$348$	7.46601	0.400220
$349$	−36.1579	−1.93549	−0.967744	−	0.251935i	$-0.918933\pi$
$349$	−36.1579	−1.93549	−0.967744	+	0.251935i	$0.918933\pi$
$350$	−24.3126	−1.29956
$351$	2.94406	0.157142
$352$	3.90037	0.207891
$353$	3.83648	0.204195	0.102098	−	0.994774i	$-0.467445\pi$
$353$	3.83648	0.204195	0.102098	+	0.994774i	$0.467445\pi$
$354$	25.1909	1.33888
$355$	−18.6998	−0.992480
$356$	7.85506	0.416317
$357$	17.1020	0.905135
$358$	−12.4924	−0.660243
$359$	−3.64310	−0.192275	−0.0961376	−	0.995368i	$-0.530649\pi$
$359$	−3.64310	−0.192275	−0.0961376	+	0.995368i	$0.530649\pi$
$360$	8.49298	0.447619
$361$	−14.1084	−0.742547
$362$	−13.7758	−0.724041
$363$	−10.0826	−0.529201
$364$	−23.4016	−1.22658
$365$	44.3851	2.32322
$366$	23.3893	1.22258
$367$	−8.96146	−0.467785	−0.233892	−	0.972263i	$-0.575146\pi$
$367$	−8.96146	−0.467785	−0.233892	+	0.972263i	$0.575146\pi$
$368$	4.43124	0.230994
$369$	5.45509	0.283981
$370$	−2.30904	−0.120041
$371$	22.9949	1.19383
$372$	−17.9016	−0.928153
$373$	12.9123	0.668574	0.334287	−	0.942471i	$-0.391504\pi$
$373$	12.9123	0.668574	0.334287	+	0.942471i	$0.391504\pi$
$374$	5.38138	0.278265
$375$	2.27861	0.117667
$376$	−2.77838	−0.143284
$377$	−14.0953	−0.725945
$378$	−3.37471	−0.173577
$379$	−11.2261	−0.576645	−0.288322	−	0.957533i	$-0.593097\pi$
$379$	−11.2261	−0.576645	−0.288322	+	0.957533i	$0.593097\pi$
$380$	−6.88624	−0.353257
$381$	−29.4431	−1.50842
$382$	9.82421	0.502650
$383$	5.21906	0.266681	0.133341	−	0.991070i	$-0.457430\pi$
$383$	5.21906	0.266681	0.133341	+	0.991070i	$0.457430\pi$
$384$	−2.39327	−0.122131
$385$	−62.8971	−3.20553
$386$	−2.96231	−0.150777
$387$	0.544439	0.0276754
$388$	17.7619	0.901722
$389$	22.3216	1.13175	0.565875	−	0.824491i	$-0.308538\pi$
$389$	22.3216	1.13175	0.565875	+	0.824491i	$0.308538\pi$
$390$	−33.6686	−1.70488
$391$	6.11382	0.309189
$392$	19.8248	1.00130
$393$	27.7390	1.39925
$394$	−7.88306	−0.397143
$395$	−5.10081	−0.256650
$396$	10.6392	0.534641
$397$	−24.8453	−1.24695	−0.623474	−	0.781844i	$-0.714279\pi$
$397$	−24.8453	−1.24695	−0.623474	+	0.781844i	$0.714279\pi$
$398$	10.8757	0.545148
$399$	−27.4149	−1.37246
$400$	4.69421	0.234711
$401$	16.6956	0.833739	0.416869	−	0.908966i	$-0.363127\pi$
$401$	16.6956	0.833739	0.416869	+	0.908966i	$0.363127\pi$
$402$	21.4359	1.06913
$403$	33.7969	1.68354
$404$	16.5614	0.823961
$405$	−30.3342	−1.50732
$406$	16.1572	0.801866
$407$	−2.89255	−0.143378
$408$	−3.30202	−0.163474
$409$	−15.9656	−0.789449	−0.394725	−	0.918799i	$-0.629160\pi$
$409$	−15.9656	−0.789449	−0.394725	+	0.918799i	$0.629160\pi$
$410$	6.22666	0.307513
$411$	6.96013	0.343318
$412$	−2.22177	−0.109459
$413$	54.5154	2.68253
$414$	12.0873	0.594058
$415$	11.8730	0.582820
$416$	4.51832	0.221529
$417$	15.1047	0.739679
$418$	−8.62645	−0.421934
$419$	−29.9475	−1.46303	−0.731515	−	0.681826i	$-0.761186\pi$
$419$	−29.9475	−1.46303	−0.731515	+	0.681826i	$0.761186\pi$
$420$	38.5937	1.88318
$421$	−11.2553	−0.548550	−0.274275	−	0.961651i	$-0.588438\pi$
$421$	−11.2553	−0.548550	−0.274275	+	0.961651i	$0.588438\pi$
$422$	21.9441	1.06822
$423$	−7.57871	−0.368490
$424$	−4.43980	−0.215616
$425$	6.47665	0.314164
$426$	14.3738	0.696413
$427$	50.6167	2.44952
$428$	−7.27165	−0.351489
$429$	−42.1769	−2.03632
$430$	0.621444	0.0299687
$431$	24.7705	1.19315	0.596576	−	0.802557i	$-0.296527\pi$
$431$	24.7705	1.19315	0.596576	+	0.802557i	$0.296527\pi$
$432$	0.651582	0.0313493
$433$	−40.7104	−1.95642	−0.978209	−	0.207622i	$-0.933428\pi$
$433$	−40.7104	−1.95642	−0.978209	+	0.207622i	$0.933428\pi$
$434$	−38.7407	−1.85961
$435$	23.2458	1.11455
$436$	2.88653	0.138240
$437$	−9.80057	−0.468825
$438$	−34.1172	−1.63018
$439$	−30.4384	−1.45274	−0.726372	−	0.687302i	$-0.758795\pi$
$439$	−30.4384	−1.45274	−0.726372	+	0.687302i	$0.758795\pi$
$440$	12.1440	0.578943
$441$	54.0769	2.57509
$442$	6.23398	0.296520
$443$	23.3009	1.10706	0.553531	−	0.832829i	$-0.313280\pi$
$443$	23.3009	1.10706	0.553531	+	0.832829i	$0.313280\pi$
$444$	1.77487	0.0842316
$445$	24.4571	1.15938
$446$	27.3330	1.29426
$447$	−16.8094	−0.795055
$448$	−5.17926	−0.244697
$449$	−0.208489	−0.00983921	−0.00491961	−	0.999988i	$-0.501566\pi$
$449$	−0.208489	−0.00983921	−0.00491961	+	0.999988i	$0.501566\pi$
$450$	12.8046	0.603615
$451$	7.80018	0.367296
$452$	5.49140	0.258294
$453$	−10.9860	−0.516168
$454$	13.2010	0.619554
$455$	−72.8621	−3.41583
$456$	5.29320	0.247877
$457$	−11.0880	−0.518676	−0.259338	−	0.965787i	$-0.583504\pi$
$457$	−11.0880	−0.518676	−0.259338	+	0.965787i	$0.583504\pi$
$458$	20.5985	0.962502
$459$	0.898994	0.0419615
$460$	13.7969	0.643283
$461$	3.95700	0.184296	0.0921478	−	0.995745i	$-0.470627\pi$
$461$	3.95700	0.184296	0.0921478	+	0.995745i	$0.470627\pi$
$462$	48.3466	2.24929
$463$	41.0719	1.90877	0.954386	−	0.298575i	$-0.0965112\pi$
$463$	41.0719	1.90877	0.954386	+	0.298575i	$0.0965112\pi$
$464$	−3.11959	−0.144823
$465$	−55.7374	−2.58476
$466$	21.3130	0.987305
$467$	5.75160	0.266152	0.133076	−	0.991106i	$-0.457514\pi$
$467$	5.75160	0.266152	0.133076	+	0.991106i	$0.457514\pi$
$468$	12.3248	0.569715
$469$	46.3893	2.14206
$470$	−8.65064	−0.399024
$471$	−6.77863	−0.312343
$472$	−10.5257	−0.484485
$473$	0.778488	0.0357949
$474$	3.92080	0.180088
$475$	−10.3822	−0.476367
$476$	−7.14588	−0.327531
$477$	−12.1106	−0.554508
$478$	2.42402	0.110872
$479$	−2.43702	−0.111350	−0.0556751	−	0.998449i	$-0.517731\pi$
$479$	−2.43702	−0.111350	−0.0556751	+	0.998449i	$0.517731\pi$
$480$	−7.45157	−0.340116
$481$	−3.35083	−0.152784
$482$	8.55482	0.389661
$483$	54.9269	2.49926
$484$	4.21291	0.191496
$485$	55.3025	2.51116
$486$	21.3620	0.969002
$487$	−35.3935	−1.60383	−0.801916	−	0.597436i	$-0.796186\pi$
$487$	−35.3935	−1.60383	−0.801916	+	0.597436i	$0.796186\pi$
$488$	−9.77296	−0.442401
$489$	−14.6203	−0.661151
$490$	61.7255	2.78847
$491$	41.8664	1.88940	0.944702	−	0.327929i	$-0.106351\pi$
$491$	41.8664	1.88940	0.944702	+	0.327929i	$0.106351\pi$
$492$	−4.78620	−0.215778
$493$	−4.30412	−0.193848
$494$	−9.99317	−0.449614
$495$	33.1258	1.48889
$496$	7.47996	0.335860
$497$	31.1063	1.39531
$498$	−9.12629	−0.408959
$499$	1.98085	0.0886752	0.0443376	−	0.999017i	$-0.485882\pi$
$499$	1.98085	0.0886752	0.0443376	+	0.999017i	$0.485882\pi$
$500$	−0.952089	−0.0425787
$501$	−7.78437	−0.347780
$502$	−10.3110	−0.460201
$503$	22.9187	1.02190	0.510948	−	0.859612i	$-0.329294\pi$
$503$	22.9187	1.02190	0.510948	+	0.859612i	$0.329294\pi$
$504$	−14.1277	−0.629298
$505$	51.5648	2.29460
$506$	17.2835	0.768344
$507$	−17.7467	−0.788158
$508$	12.3025	0.545833
$509$	−21.2944	−0.943857	−0.471929	−	0.881637i	$-0.656442\pi$
$509$	−21.2944	−0.943857	−0.471929	+	0.881637i	$0.656442\pi$
$510$	−10.2810	−0.455251
$511$	−73.8328	−3.26617
$512$	1.00000	0.0441942
$513$	−1.44110	−0.0636263
$514$	13.8787	0.612162
$515$	−6.91761	−0.304826
$516$	−0.477680	−0.0210287
$517$	−10.8367	−0.476599
$518$	3.84098	0.168763
$519$	10.6083	0.465652
$520$	14.0680	0.616924
$521$	37.6853	1.65102	0.825511	−	0.564386i	$-0.190887\pi$
$521$	37.6853	1.65102	0.825511	+	0.564386i	$0.190887\pi$
$522$	−8.50943	−0.372448
$523$	7.86442	0.343887	0.171943	−	0.985107i	$-0.444995\pi$
$523$	7.86442	0.343887	0.171943	+	0.985107i	$0.444995\pi$
$524$	−11.5904	−0.506330
$525$	58.1865	2.53947
$526$	2.29221	0.0999449
$527$	10.3202	0.449554
$528$	−9.33465	−0.406238
$529$	−3.36413	−0.146267
$530$	−13.8235	−0.600456
$531$	−28.7114	−1.24597
$532$	11.4550	0.496636
$533$	9.03599	0.391392
$534$	−18.7993	−0.813524
$535$	−22.6407	−0.978842
$536$	−8.95674	−0.386872
$537$	29.8977	1.29018
$538$	−1.42038	−0.0612368
$539$	77.3240	3.33058
$540$	2.02873	0.0873029
$541$	−2.10829	−0.0906424	−0.0453212	−	0.998972i	$-0.514431\pi$
$541$	−2.10829	−0.0906424	−0.0453212	+	0.998972i	$0.514431\pi$
$542$	14.2561	0.612352
$543$	32.9692	1.41485
$544$	1.37971	0.0591546
$545$	8.98737	0.384977
$546$	56.0063	2.39685
$547$	−1.97197	−0.0843153	−0.0421576	−	0.999111i	$-0.513423\pi$
$547$	−1.97197	−0.0843153	−0.0421576	+	0.999111i	$0.513423\pi$
$548$	−2.90821	−0.124232
$549$	−26.6581	−1.13774
$550$	18.3092	0.780706
$551$	6.89959	0.293932
$552$	−10.6052	−0.451385
$553$	8.48499	0.360818
$554$	20.4793	0.870082
$555$	5.52615	0.234572
$556$	−6.31131	−0.267659
$557$	20.0893	0.851209	0.425605	−	0.904909i	$-0.360061\pi$
$557$	20.0893	0.851209	0.425605	+	0.904909i	$0.360061\pi$
$558$	20.4034	0.863745
$559$	0.901826	0.0381432
$560$	−16.1259	−0.681444
$561$	−12.8791	−0.543756
$562$	−7.30450	−0.308122
$563$	−24.7875	−1.04467	−0.522335	−	0.852740i	$-0.674939\pi$
$563$	−24.7875	−1.04467	−0.522335	+	0.852740i	$0.674939\pi$
$564$	6.64942	0.279991
$565$	17.0978	0.719308
$566$	3.43892	0.144549
$567$	50.4597	2.11911
$568$	−6.00592	−0.252003
$569$	10.7833	0.452061	0.226031	−	0.974120i	$-0.427425\pi$
$569$	10.7833	0.452061	0.226031	+	0.974120i	$0.427425\pi$
$570$	16.4806	0.690298
$571$	−14.6193	−0.611800	−0.305900	−	0.952064i	$-0.598957\pi$
$571$	−14.6193	−0.611800	−0.305900	+	0.952064i	$0.598957\pi$
$572$	17.6231	0.736861
$573$	−23.5120	−0.982227
$574$	−10.3578	−0.432325
$575$	20.8012	0.867469
$576$	2.72774	0.113656
$577$	22.9642	0.956014	0.478007	−	0.878356i	$-0.341359\pi$
$577$	22.9642	0.956014	0.478007	+	0.878356i	$0.341359\pi$
$578$	−15.0964	−0.627927
$579$	7.08960	0.294634
$580$	−9.71300	−0.403310
$581$	−19.7502	−0.819374
$582$	−42.5089	−1.76205
$583$	−17.3169	−0.717191
$584$	14.2555	0.589895
$585$	38.3740	1.58657
$586$	10.3268	0.426595
$587$	6.87604	0.283805	0.141902	−	0.989881i	$-0.454678\pi$
$587$	6.87604	0.283805	0.141902	+	0.989881i	$0.454678\pi$
$588$	−47.4460	−1.95664
$589$	−16.5434	−0.681660
$590$	−32.7723	−1.34922
$591$	18.8663	0.776056
$592$	−0.741608	−0.0304799
$593$	−13.4538	−0.552480	−0.276240	−	0.961089i	$-0.589088\pi$
$593$	−13.4538	−0.552480	−0.276240	+	0.961089i	$0.589088\pi$
$594$	2.54141	0.104275
$595$	−22.2491	−0.912123
$596$	7.02359	0.287698
$597$	−26.0284	−1.06527
$598$	20.0218	0.818751
$599$	−9.03530	−0.369172	−0.184586	−	0.982816i	$-0.559094\pi$
$599$	−9.03530	−0.369172	−0.184586	+	0.982816i	$0.559094\pi$
$600$	−11.2345	−0.458647
$601$	32.1278	1.31052	0.655260	−	0.755403i	$-0.272559\pi$
$601$	32.1278	1.31052	0.655260	+	0.755403i	$0.272559\pi$
$602$	−1.03375	−0.0421323
$603$	−24.4317	−0.994935
$604$	4.59038	0.186780
$605$	13.1171	0.533286
$606$	−39.6359	−1.61010
$607$	23.2816	0.944971	0.472485	−	0.881339i	$-0.343357\pi$
$607$	23.2816	0.944971	0.472485	+	0.881339i	$0.343357\pi$
$608$	−2.21170	−0.0896963
$609$	−38.6685	−1.56692
$610$	−30.4286	−1.23202
$611$	−12.5536	−0.507865
$612$	3.76350	0.152130
$613$	29.7679	1.20231	0.601157	−	0.799131i	$-0.294707\pi$
$613$	29.7679	1.20231	0.601157	+	0.799131i	$0.294707\pi$
$614$	0.920938	0.0371660
$615$	−14.9021	−0.600910
$616$	−20.2011	−0.813924
$617$	−4.23437	−0.170469	−0.0852346	−	0.996361i	$-0.527164\pi$
$617$	−4.23437	−0.170469	−0.0852346	+	0.996361i	$0.527164\pi$
$618$	5.31731	0.213893
$619$	−41.1871	−1.65545	−0.827724	−	0.561135i	$-0.810365\pi$
$619$	−41.1871	−1.65545	−0.827724	+	0.561135i	$0.810365\pi$
$620$	23.2892	0.935318
$621$	2.88731	0.115864
$622$	−34.5002	−1.38333
$623$	−40.6834	−1.62995
$624$	−10.8136	−0.432889
$625$	−26.4354	−1.05742
$626$	7.19989	0.287766
$627$	20.6454	0.824499
$628$	2.83237	0.113024
$629$	−1.02320	−0.0407978
$630$	−43.9874	−1.75250
$631$	−22.7296	−0.904852	−0.452426	−	0.891802i	$-0.649441\pi$
$631$	−22.7296	−0.904852	−0.452426	+	0.891802i	$0.649441\pi$
$632$	−1.63826	−0.0651666
$633$	−52.5181	−2.08741
$634$	20.2046	0.802426
$635$	38.3043	1.52006
$636$	10.6256	0.421334
$637$	89.5747	3.54908
$638$	−12.1675	−0.481718
$639$	−16.3826	−0.648087
$640$	3.11355	0.123074
$641$	43.9285	1.73507	0.867535	−	0.497376i	$-0.165703\pi$
$641$	43.9285	1.73507	0.867535	+	0.497376i	$0.165703\pi$
$642$	17.4030	0.686843
$643$	10.2496	0.404205	0.202102	−	0.979364i	$-0.435223\pi$
$643$	10.2496	0.404205	0.202102	+	0.979364i	$0.435223\pi$
$644$	−22.9505	−0.904378
$645$	−1.48728	−0.0585617
$646$	−3.05150	−0.120060
$647$	22.3080	0.877017	0.438508	−	0.898727i	$-0.355507\pi$
$647$	22.3080	0.877017	0.438508	+	0.898727i	$0.355507\pi$
$648$	−9.74264	−0.382727
$649$	−41.0542	−1.61152
$650$	21.2100	0.831923
$651$	92.7169	3.63386
$652$	6.10891	0.239243
$653$	−0.596821	−0.0233554	−0.0116777	−	0.999932i	$-0.503717\pi$
$653$	−0.596821	−0.0233554	−0.0116777	+	0.999932i	$0.503717\pi$
$654$	−6.90825	−0.270134
$655$	−36.0874	−1.41005
$656$	1.99986	0.0780812
$657$	38.8853	1.51706
$658$	14.3900	0.560979
$659$	−27.0465	−1.05358	−0.526792	−	0.849994i	$-0.676605\pi$
$659$	−27.0465	−1.05358	−0.526792	+	0.849994i	$0.676605\pi$
$660$	−29.0639	−1.13131
$661$	46.4285	1.80586	0.902931	−	0.429786i	$-0.141411\pi$
$661$	46.4285	1.80586	0.902931	+	0.429786i	$0.141411\pi$
$662$	24.6701	0.958830
$663$	−14.9196	−0.579429
$664$	3.81331	0.147985
$665$	35.6657	1.38306
$666$	−2.02292	−0.0783865
$667$	−13.8236	−0.535253
$668$	3.25261	0.125847
$669$	−65.4154	−2.52910
$670$	−27.8873	−1.07738
$671$	−38.1182	−1.47154
$672$	12.3954	0.478162
$673$	21.0274	0.810548	0.405274	−	0.914195i	$-0.367176\pi$
$673$	21.0274	0.810548	0.405274	+	0.914195i	$0.367176\pi$
$674$	9.50778	0.366226
$675$	3.05866	0.117728
$676$	7.41524	0.285202
$677$	17.4313	0.669939	0.334970	−	0.942229i	$-0.391274\pi$
$677$	17.4313	0.669939	0.334970	+	0.942229i	$0.391274\pi$
$678$	−13.1424	−0.504731
$679$	−91.9933	−3.53038
$680$	4.29580	0.164736
$681$	−31.5936	−1.21067
$682$	29.1746	1.11715
$683$	−1.38190	−0.0528769	−0.0264384	−	0.999650i	$-0.508417\pi$
$683$	−1.38190	−0.0528769	−0.0264384	+	0.999650i	$0.508417\pi$
$684$	−6.03295	−0.230676
$685$	−9.05486	−0.345968
$686$	−66.4229	−2.53604
$687$	−49.2977	−1.88082
$688$	0.199593	0.00760942
$689$	−20.0604	−0.764242
$690$	−33.0197	−1.25704
$691$	−6.51483	−0.247836	−0.123918	−	0.992292i	$-0.539546\pi$
$691$	−6.51483	−0.247836	−0.123918	+	0.992292i	$0.539546\pi$
$692$	−4.43255	−0.168500
$693$	−55.1033	−2.09320
$694$	−1.52711	−0.0579682
$695$	−19.6506	−0.745389
$696$	7.46601	0.282999
$697$	2.75922	0.104513
$698$	−36.1579	−1.36860
$699$	−51.0077	−1.92929
$700$	−24.3126	−0.918928
$701$	−11.5165	−0.434972	−0.217486	−	0.976063i	$-0.569786\pi$
$701$	−11.5165	−0.434972	−0.217486	+	0.976063i	$0.569786\pi$
$702$	2.94406	0.111116
$703$	1.64021	0.0618619
$704$	3.90037	0.147001
$705$	20.7033	0.779732
$706$	3.83648	0.144388
$707$	−85.7759	−3.22593
$708$	25.1909	0.946731
$709$	10.0644	0.377975	0.188988	−	0.981979i	$-0.439479\pi$
$709$	10.0644	0.377975	0.188988	+	0.981979i	$0.439479\pi$
$710$	−18.6998	−0.701790
$711$	−4.46876	−0.167592
$712$	7.85506	0.294381
$713$	33.1455	1.24131
$714$	17.1020	0.640027
$715$	54.8706	2.05204
$716$	−12.4924	−0.466862
$717$	−5.80133	−0.216655
$718$	−3.64310	−0.135959
$719$	20.1607	0.751869	0.375935	−	0.926646i	$-0.377322\pi$
$719$	20.1607	0.751869	0.375935	+	0.926646i	$0.377322\pi$
$720$	8.49298	0.316515
$721$	11.5072	0.428549
$722$	−14.1084	−0.525060
$723$	−20.4740	−0.761436
$724$	−13.7758	−0.511974
$725$	−14.6440	−0.543864
$726$	−10.0826	−0.374201
$727$	25.0241	0.928093	0.464046	−	0.885811i	$-0.346397\pi$
$727$	25.0241	0.928093	0.464046	+	0.885811i	$0.346397\pi$
$728$	−23.4016	−0.867320
$729$	−21.8972	−0.811008
$730$	44.3851	1.64277
$731$	0.275381	0.0101853
$732$	23.3893	0.864495
$733$	−39.5642	−1.46134	−0.730669	−	0.682731i	$-0.760792\pi$
$733$	−39.5642	−1.46134	−0.730669	+	0.682731i	$0.760792\pi$
$734$	−8.96146	−0.330774
$735$	−147.726	−5.44895
$736$	4.43124	0.163338
$737$	−34.9346	−1.28683
$738$	5.45509	0.200805
$739$	46.8161	1.72216	0.861079	−	0.508471i	$-0.169789\pi$
$739$	46.8161	1.72216	0.861079	+	0.508471i	$0.169789\pi$
$740$	−2.30904	−0.0848819
$741$	23.9164	0.878590
$742$	22.9949	0.844169
$743$	44.9180	1.64788	0.823940	−	0.566677i	$-0.191771\pi$
$743$	44.9180	1.64788	0.823940	+	0.566677i	$0.191771\pi$
$744$	−17.9016	−0.656303
$745$	21.8683	0.801193
$746$	12.9123	0.472753
$747$	10.4017	0.380580
$748$	5.38138	0.196763
$749$	37.6618	1.37613
$750$	2.27861	0.0832030
$751$	42.9744	1.56816	0.784079	−	0.620661i	$-0.213136\pi$
$751$	42.9744	1.56816	0.784079	+	0.620661i	$0.213136\pi$
$752$	−2.77838	−0.101317
$753$	24.6769	0.899277
$754$	−14.0953	−0.513320
$755$	14.2924	0.520153
$756$	−3.37471	−0.122737
$757$	16.2129	0.589267	0.294633	−	0.955610i	$-0.404802\pi$
$757$	16.2129	0.589267	0.294633	+	0.955610i	$0.404802\pi$
$758$	−11.2261	−0.407749
$759$	−41.3640	−1.50142
$760$	−6.88624	−0.249790
$761$	−18.4579	−0.669097	−0.334548	−	0.942379i	$-0.608584\pi$
$761$	−18.4579	−0.669097	−0.334548	+	0.942379i	$0.608584\pi$
$762$	−29.4431	−1.06661
$763$	−14.9501	−0.541230
$764$	9.82421	0.355427
$765$	11.7178	0.423660
$766$	5.21906	0.188572
$767$	−47.5585	−1.71724
$768$	−2.39327	−0.0863597
$769$	22.7834	0.821591	0.410795	−	0.911728i	$-0.365251\pi$
$769$	22.7834	0.821591	0.410795	+	0.911728i	$0.365251\pi$
$770$	−62.8971	−2.26665
$771$	−33.2154	−1.19622
$772$	−2.96231	−0.106616
$773$	−10.6940	−0.384637	−0.192319	−	0.981333i	$-0.561601\pi$
$773$	−10.6940	−0.384637	−0.192319	+	0.981333i	$0.561601\pi$
$774$	0.544439	0.0195695
$775$	35.1125	1.26128
$776$	17.7619	0.637614
$777$	−9.19251	−0.329780
$778$	22.3216	0.800268
$779$	−4.42308	−0.158473
$780$	−33.6686	−1.20553
$781$	−23.4253	−0.838225
$782$	6.11382	0.218630
$783$	−2.03267	−0.0726416
$784$	19.8248	0.708027
$785$	8.81873	0.314754
$786$	27.7390	0.989418
$787$	−14.5587	−0.518962	−0.259481	−	0.965748i	$-0.583551\pi$
$787$	−14.5587	−0.518962	−0.259481	+	0.965748i	$0.583551\pi$
$788$	−7.88306	−0.280823
$789$	−5.48587	−0.195302
$790$	−5.10081	−0.181479
$791$	−28.4414	−1.01126
$792$	10.6392	0.378048
$793$	−44.1574	−1.56807
$794$	−24.8453	−0.881725
$795$	33.0835	1.17335
$796$	10.8757	0.385478
$797$	−43.3226	−1.53457	−0.767283	−	0.641308i	$-0.778392\pi$
$797$	−43.3226	−1.53457	−0.767283	+	0.641308i	$0.778392\pi$
$798$	−27.4149	−0.970475
$799$	−3.83336	−0.135615
$800$	4.69421	0.165965
$801$	21.4266	0.757071
$802$	16.6956	0.589542
$803$	55.6016	1.96214
$804$	21.4359	0.755986
$805$	−71.4577	−2.51855
$806$	33.7969	1.19044
$807$	3.39935	0.119663
$808$	16.5614	0.582628
$809$	31.7422	1.11600	0.557998	−	0.829842i	$-0.311570\pi$
$809$	31.7422	1.11600	0.557998	+	0.829842i	$0.311570\pi$
$810$	−30.3342	−1.06584
$811$	29.0168	1.01892	0.509458	−	0.860496i	$-0.329846\pi$
$811$	29.0168	1.01892	0.509458	+	0.860496i	$0.329846\pi$
$812$	16.1572	0.567005
$813$	−34.1187	−1.19659
$814$	−2.89255	−0.101384
$815$	19.0204	0.666256
$816$	−3.30202	−0.115594
$817$	−0.441440	−0.0154440
$818$	−15.9656	−0.558225
$819$	−63.8335	−2.23052
$820$	6.22666	0.217444
$821$	−45.1060	−1.57421	−0.787104	−	0.616820i	$-0.788421\pi$
$821$	−45.1060	−1.57421	−0.787104	+	0.616820i	$0.788421\pi$
$822$	6.96013	0.242762
$823$	50.5825	1.76320	0.881598	−	0.472001i	$-0.156468\pi$
$823$	50.5825	1.76320	0.881598	+	0.472001i	$0.156468\pi$
$824$	−2.22177	−0.0773991
$825$	−43.8188	−1.52558
$826$	54.5154	1.89683
$827$	18.3909	0.639513	0.319756	−	0.947500i	$-0.396399\pi$
$827$	18.3909	0.639513	0.319756	+	0.947500i	$0.396399\pi$
$828$	12.0873	0.420062
$829$	−30.2510	−1.05066	−0.525330	−	0.850898i	$-0.676058\pi$
$829$	−30.2510	−1.05066	−0.525330	+	0.850898i	$0.676058\pi$
$830$	11.8730	0.412116
$831$	−49.0125	−1.70023
$832$	4.51832	0.156645
$833$	27.3524	0.947706
$834$	15.1047	0.523032
$835$	10.1272	0.350465
$836$	−8.62645	−0.298352
$837$	4.87380	0.168463
$838$	−29.9475	−1.03452
$839$	20.5766	0.710383	0.355191	−	0.934794i	$-0.384416\pi$
$839$	20.5766	0.710383	0.355191	+	0.934794i	$0.384416\pi$
$840$	38.5937	1.33161
$841$	−19.2682	−0.664420
$842$	−11.2553	−0.387883
$843$	17.4816	0.602100
$844$	21.9441	0.755347
$845$	23.0877	0.794242
$846$	−7.57871	−0.260562
$847$	−21.8198	−0.749736
$848$	−4.43980	−0.152463
$849$	−8.23028	−0.282462
$850$	6.47665	0.222147
$851$	−3.28624	−0.112651
$852$	14.3738	0.492438
$853$	−8.15004	−0.279052	−0.139526	−	0.990218i	$-0.544558\pi$
$853$	−8.15004	−0.279052	−0.139526	+	0.990218i	$0.544558\pi$
$854$	50.6167	1.73207
$855$	−18.7839	−0.642396
$856$	−7.27165	−0.248540
$857$	−25.0880	−0.856989	−0.428495	−	0.903544i	$-0.640956\pi$
$857$	−25.0880	−0.856989	−0.428495	+	0.903544i	$0.640956\pi$
$858$	−42.1769	−1.43990
$859$	−8.01119	−0.273338	−0.136669	−	0.990617i	$-0.543640\pi$
$859$	−8.01119	−0.273338	−0.136669	+	0.990617i	$0.543640\pi$
$860$	0.621444	0.0211911
$861$	24.7890	0.844806
$862$	24.7705	0.843686
$863$	33.8128	1.15100	0.575500	−	0.817802i	$-0.304807\pi$
$863$	33.8128	1.15100	0.575500	+	0.817802i	$0.304807\pi$
$864$	0.651582	0.0221673
$865$	−13.8010	−0.469247
$866$	−40.7104	−1.38340
$867$	36.1298	1.22703
$868$	−38.7407	−1.31494
$869$	−6.38983	−0.216760
$870$	23.2458	0.788107
$871$	−40.4694	−1.37125
$872$	2.88653	0.0977503
$873$	48.4498	1.63978
$874$	−9.80057	−0.331509
$875$	4.93112	0.166702
$876$	−34.1172	−1.15271
$877$	−22.7416	−0.767929	−0.383965	−	0.923348i	$-0.625442\pi$
$877$	−22.7416	−0.767929	−0.383965	+	0.923348i	$0.625442\pi$
$878$	−30.4384	−1.02724
$879$	−24.7148	−0.833608
$880$	12.1440	0.409375
$881$	29.9807	1.01008	0.505038	−	0.863097i	$-0.331478\pi$
$881$	29.9807	1.01008	0.505038	+	0.863097i	$0.331478\pi$
$882$	54.0769	1.82086
$883$	34.6064	1.16460	0.582300	−	0.812974i	$-0.302153\pi$
$883$	34.6064	1.16460	0.582300	+	0.812974i	$0.302153\pi$
$884$	6.23398	0.209671
$885$	78.4331	2.63650
$886$	23.3009	0.782810
$887$	−27.5038	−0.923486	−0.461743	−	0.887014i	$-0.652776\pi$
$887$	−27.5038	−0.923486	−0.461743	+	0.887014i	$0.652776\pi$
$888$	1.77487	0.0595607
$889$	−63.7177	−2.13702
$890$	24.4571	0.819805
$891$	−37.9999	−1.27305
$892$	27.3330	0.915178
$893$	6.14495	0.205633
$894$	−16.8094	−0.562189
$895$	−38.8957	−1.30014
$896$	−5.17926	−0.173027
$897$	−47.9175	−1.59992
$898$	−0.208489	−0.00695737
$899$	−23.3344	−0.778245
$900$	12.8046	0.426820
$901$	−6.12563	−0.204074
$902$	7.80018	0.259718
$903$	2.47403	0.0823307
$904$	5.49140	0.182641
$905$	−42.8917	−1.42577
$906$	−10.9860	−0.364986
$907$	−44.3598	−1.47294	−0.736471	−	0.676469i	$-0.763509\pi$
$907$	−44.3598	−1.47294	−0.736471	+	0.676469i	$0.763509\pi$
$908$	13.2010	0.438091
$909$	45.1753	1.49837
$910$	−72.8621	−2.41535
$911$	−17.8918	−0.592783	−0.296391	−	0.955067i	$-0.595783\pi$
$911$	−17.8918	−0.592783	−0.296391	+	0.955067i	$0.595783\pi$
$912$	5.29320	0.175275
$913$	14.8733	0.492236
$914$	−11.0880	−0.366759
$915$	72.8239	2.40749
$916$	20.5985	0.680592
$917$	60.0299	1.98236
$918$	0.898994	0.0296712
$919$	−52.2140	−1.72238	−0.861190	−	0.508283i	$-0.830281\pi$
$919$	−52.2140	−1.72238	−0.861190	+	0.508283i	$0.830281\pi$
$920$	13.7969	0.454870
$921$	−2.20405	−0.0726260
$922$	3.95700	0.130317
$923$	−27.1367	−0.893215
$924$	48.3466	1.59049
$925$	−3.48127	−0.114463
$926$	41.0719	1.34971
$927$	−6.06043	−0.199051
$928$	−3.11959	−0.102405
$929$	20.2038	0.662865	0.331432	−	0.943479i	$-0.392468\pi$
$929$	20.2038	0.662865	0.331432	+	0.943479i	$0.392468\pi$
$930$	−55.7374	−1.82770
$931$	−43.8464	−1.43701
$932$	21.3130	0.698130
$933$	82.5684	2.70317
$934$	5.75160	0.188198
$935$	16.7552	0.547954
$936$	12.3248	0.402850
$937$	22.7938	0.744640	0.372320	−	0.928104i	$-0.378562\pi$
$937$	22.7938	0.744640	0.372320	+	0.928104i	$0.378562\pi$
$938$	46.3893	1.51466
$939$	−17.2313	−0.562322
$940$	−8.65064	−0.282153
$941$	−30.8942	−1.00712	−0.503561	−	0.863960i	$-0.667977\pi$
$941$	−30.8942	−1.00712	−0.503561	+	0.863960i	$0.667977\pi$
$942$	−6.77863	−0.220860
$943$	8.86184	0.288581
$944$	−10.5257	−0.342583
$945$	−10.5074	−0.341804
$946$	0.778488	0.0253108
$947$	6.32666	0.205589	0.102794	−	0.994703i	$-0.467222\pi$
$947$	6.32666	0.205589	0.102794	+	0.994703i	$0.467222\pi$
$948$	3.92080	0.127342
$949$	64.4108	2.09086
$950$	−10.3822	−0.336843
$951$	−48.3550	−1.56802
$952$	−7.14588	−0.231599
$953$	−50.3572	−1.63123	−0.815614	−	0.578596i	$-0.803601\pi$
$953$	−50.3572	−1.63123	−0.815614	+	0.578596i	$0.803601\pi$
$954$	−12.1106	−0.392096
$955$	30.5882	0.989811
$956$	2.42402	0.0783983
$957$	29.1202	0.941324
$958$	−2.43702	−0.0787365
$959$	15.0624	0.486389
$960$	−7.45157	−0.240499
$961$	24.9497	0.804830
$962$	−3.35083	−0.108035
$963$	−19.8352	−0.639181
$964$	8.55482	0.275532
$965$	−9.22330	−0.296908
$966$	54.9269	1.76724
$967$	−37.3489	−1.20106	−0.600529	−	0.799603i	$-0.705043\pi$
$967$	−37.3489	−1.20106	−0.600529	+	0.799603i	$0.705043\pi$
$968$	4.21291	0.135408
$969$	7.30308	0.234609
$970$	55.3025	1.77566
$971$	−4.20963	−0.135094	−0.0675468	−	0.997716i	$-0.521517\pi$
$971$	−4.20963	−0.135094	−0.0675468	+	0.997716i	$0.521517\pi$
$972$	21.3620	0.685188
$973$	32.6879	1.04793
$974$	−35.3935	−1.13408
$975$	−50.7612	−1.62566
$976$	−9.77296	−0.312825
$977$	−45.7615	−1.46404	−0.732020	−	0.681283i	$-0.761422\pi$
$977$	−45.7615	−1.46404	−0.732020	+	0.681283i	$0.761422\pi$
$978$	−14.6203	−0.467505
$979$	30.6376	0.979183
$980$	61.7255	1.97175
$981$	7.87372	0.251389
$982$	41.8664	1.33601
$983$	51.6650	1.64786	0.823930	−	0.566692i	$-0.191777\pi$
$983$	51.6650	1.64786	0.823930	+	0.566692i	$0.191777\pi$
$984$	−4.78620	−0.152578
$985$	−24.5443	−0.782048
$986$	−4.30412	−0.137071
$987$	−34.4391	−1.09621
$988$	−9.99317	−0.317925
$989$	0.884445	0.0281237
$990$	33.1258	1.05281
$991$	−0.0960654	−0.00305162	−0.00152581	−	0.999999i	$-0.500486\pi$
$991$	−0.0960654	−0.00305162	−0.00152581	+	0.999999i	$0.500486\pi$
$992$	7.47996	0.237489
$993$	−59.0422	−1.87365
$994$	31.1063	0.986631
$995$	33.8619	1.07350
$996$	−9.12629	−0.289178
$997$	−9.18326	−0.290837	−0.145418	−	0.989370i	$-0.546453\pi$
$997$	−9.18326	−0.290837	−0.145418	+	0.989370i	$0.546453\pi$
$998$	1.98085	0.0627028
$999$	−0.483219	−0.0152884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.d.1.18	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.d.1.18	✓	101	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.39327 q^{3} +1.00000 q^{4} +3.11355 q^{5} -2.39327 q^{6} -5.17926 q^{7} +1.00000 q^{8} +2.72774 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.39327 q^{3} +1.00000 q^{4} +3.11355 q^{5} -2.39327 q^{6} -5.17926 q^{7} +1.00000 q^{8} +2.72774 q^{9} +3.11355 q^{10} +3.90037 q^{11} -2.39327 q^{12} +4.51832 q^{13} -5.17926 q^{14} -7.45157 q^{15} +1.00000 q^{16} +1.37971 q^{17} +2.72774 q^{18} -2.21170 q^{19} +3.11355 q^{20} +12.3954 q^{21} +3.90037 q^{22} +4.43124 q^{23} -2.39327 q^{24} +4.69421 q^{25} +4.51832 q^{26} +0.651582 q^{27} -5.17926 q^{28} -3.11959 q^{29} -7.45157 q^{30} +7.47996 q^{31} +1.00000 q^{32} -9.33465 q^{33} +1.37971 q^{34} -16.1259 q^{35} +2.72774 q^{36} -0.741608 q^{37} -2.21170 q^{38} -10.8136 q^{39} +3.11355 q^{40} +1.99986 q^{41} +12.3954 q^{42} +0.199593 q^{43} +3.90037 q^{44} +8.49298 q^{45} +4.43124 q^{46} -2.77838 q^{47} -2.39327 q^{48} +19.8248 q^{49} +4.69421 q^{50} -3.30202 q^{51} +4.51832 q^{52} -4.43980 q^{53} +0.651582 q^{54} +12.1440 q^{55} -5.17926 q^{56} +5.29320 q^{57} -3.11959 q^{58} -10.5257 q^{59} -7.45157 q^{60} -9.77296 q^{61} +7.47996 q^{62} -14.1277 q^{63} +1.00000 q^{64} +14.0680 q^{65} -9.33465 q^{66} -8.95674 q^{67} +1.37971 q^{68} -10.6052 q^{69} -16.1259 q^{70} -6.00592 q^{71} +2.72774 q^{72} +14.2555 q^{73} -0.741608 q^{74} -11.2345 q^{75} -2.21170 q^{76} -20.2011 q^{77} -10.8136 q^{78} -1.63826 q^{79} +3.11355 q^{80} -9.74264 q^{81} +1.99986 q^{82} +3.81331 q^{83} +12.3954 q^{84} +4.29580 q^{85} +0.199593 q^{86} +7.46601 q^{87} +3.90037 q^{88} +7.85506 q^{89} +8.49298 q^{90} -23.4016 q^{91} +4.43124 q^{92} -17.9016 q^{93} -2.77838 q^{94} -6.88624 q^{95} -2.39327 q^{96} +17.7619 q^{97} +19.8248 q^{98} +10.6392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * q^99

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