LMFDB - Embedded newform 8047.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69703 q^{2} +2.83475 q^{3} +5.27397 q^{4} -3.14903 q^{5} -7.64541 q^{6} +1.25916 q^{7} -8.82999 q^{8} +5.03583 q^{9} +O(q^{10})$	\(q-2.69703 q^{2} +2.83475 q^{3} +5.27397 q^{4} -3.14903 q^{5} -7.64541 q^{6} +1.25916 q^{7} -8.82999 q^{8} +5.03583 q^{9} +8.49303 q^{10} -0.202090 q^{11} +14.9504 q^{12} -1.00000 q^{13} -3.39599 q^{14} -8.92673 q^{15} +13.2668 q^{16} +3.46438 q^{17} -13.5818 q^{18} +0.526795 q^{19} -16.6079 q^{20} +3.56940 q^{21} +0.545041 q^{22} -1.58172 q^{23} -25.0308 q^{24} +4.91641 q^{25} +2.69703 q^{26} +5.77107 q^{27} +6.64076 q^{28} -3.89365 q^{29} +24.0757 q^{30} +0.402260 q^{31} -18.1210 q^{32} -0.572874 q^{33} -9.34353 q^{34} -3.96513 q^{35} +26.5588 q^{36} +3.74896 q^{37} -1.42078 q^{38} -2.83475 q^{39} +27.8059 q^{40} -10.5742 q^{41} -9.62678 q^{42} -4.17618 q^{43} -1.06581 q^{44} -15.8580 q^{45} +4.26595 q^{46} +1.91545 q^{47} +37.6081 q^{48} -5.41452 q^{49} -13.2597 q^{50} +9.82066 q^{51} -5.27397 q^{52} +10.1654 q^{53} -15.5647 q^{54} +0.636387 q^{55} -11.1183 q^{56} +1.49333 q^{57} +10.5013 q^{58} -8.34443 q^{59} -47.0793 q^{60} +3.49040 q^{61} -1.08491 q^{62} +6.34090 q^{63} +22.3392 q^{64} +3.14903 q^{65} +1.54506 q^{66} +1.54515 q^{67} +18.2710 q^{68} -4.48379 q^{69} +10.6941 q^{70} -13.6046 q^{71} -44.4663 q^{72} +12.3127 q^{73} -10.1110 q^{74} +13.9368 q^{75} +2.77830 q^{76} -0.254463 q^{77} +7.64541 q^{78} +2.12875 q^{79} -41.7776 q^{80} +1.25207 q^{81} +28.5189 q^{82} -6.98505 q^{83} +18.8249 q^{84} -10.9094 q^{85} +11.2633 q^{86} -11.0375 q^{87} +1.78445 q^{88} -3.78793 q^{89} +42.7695 q^{90} -1.25916 q^{91} -8.34194 q^{92} +1.14031 q^{93} -5.16602 q^{94} -1.65890 q^{95} -51.3685 q^{96} -17.3152 q^{97} +14.6031 q^{98} -1.01769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) $ 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.69703	−1.90709	−0.953544	−	0.301254i	$-0.902595\pi$
$2$	−2.69703	−1.90709	−0.953544	+	0.301254i	$0.902595\pi$
$3$	2.83475	1.63665	0.818323	−	0.574759i	$-0.194904\pi$
$3$	2.83475	1.63665	0.818323	+	0.574759i	$0.194904\pi$
$4$	5.27397	2.63698
$5$	−3.14903	−1.40829	−0.704145	−	0.710056i	$-0.748670\pi$
$5$	−3.14903	−1.40829	−0.704145	+	0.710056i	$0.748670\pi$
$6$	−7.64541	−3.12123
$7$	1.25916	0.475917	0.237958	−	0.971275i	$-0.423522\pi$
$7$	1.25916	0.475917	0.237958	+	0.971275i	$0.423522\pi$
$8$	−8.82999	−3.12187
$9$	5.03583	1.67861
$10$	8.49303	2.68573
$11$	−0.202090	−0.0609323	−0.0304661	−	0.999536i	$-0.509699\pi$
$11$	−0.202090	−0.0609323	−0.0304661	+	0.999536i	$0.509699\pi$
$12$	14.9504	4.31581
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.39599	−0.907615
$15$	−8.92673	−2.30487
$16$	13.2668	3.31670
$17$	3.46438	0.840235	0.420118	−	0.907470i	$-0.361989\pi$
$17$	3.46438	0.840235	0.420118	+	0.907470i	$0.361989\pi$
$18$	−13.5818	−3.20125
$19$	0.526795	0.120855	0.0604275	−	0.998173i	$-0.480754\pi$
$19$	0.526795	0.120855	0.0604275	+	0.998173i	$0.480754\pi$
$20$	−16.6079	−3.71364
$21$	3.56940	0.778907
$22$	0.545041	0.116203
$23$	−1.58172	−0.329812	−0.164906	−	0.986309i	$-0.552732\pi$
$23$	−1.58172	−0.329812	−0.164906	+	0.986309i	$0.552732\pi$
$24$	−25.0308	−5.10940
$25$	4.91641	0.983282
$26$	2.69703	0.528931
$27$	5.77107	1.11064
$28$	6.64076	1.25499
$29$	−3.89365	−0.723032	−0.361516	−	0.932366i	$-0.617741\pi$
$29$	−3.89365	−0.723032	−0.361516	+	0.932366i	$0.617741\pi$
$30$	24.0757	4.39559
$31$	0.402260	0.0722481	0.0361241	−	0.999347i	$-0.488499\pi$
$31$	0.402260	0.0722481	0.0361241	+	0.999347i	$0.488499\pi$
$32$	−18.1210	−3.20337
$33$	−0.572874	−0.0997246
$34$	−9.34353	−1.60240
$35$	−3.96513	−0.670229
$36$	26.5588	4.42646
$37$	3.74896	0.616325	0.308162	−	0.951334i	$-0.400286\pi$
$37$	3.74896	0.616325	0.308162	+	0.951334i	$0.400286\pi$
$38$	−1.42078	−0.230481
$39$	−2.83475	−0.453924
$40$	27.8059	4.39650
$41$	−10.5742	−1.65141	−0.825705	−	0.564102i	$-0.809223\pi$
$41$	−10.5742	−1.65141	−0.825705	+	0.564102i	$0.809223\pi$
$42$	−9.62678	−1.48544
$43$	−4.17618	−0.636861	−0.318431	−	0.947946i	$-0.603156\pi$
$43$	−4.17618	−0.636861	−0.318431	+	0.947946i	$0.603156\pi$
$44$	−1.06581	−0.160677
$45$	−15.8580	−2.36397
$46$	4.26595	0.628979
$47$	1.91545	0.279397	0.139698	−	0.990194i	$-0.455387\pi$
$47$	1.91545	0.279397	0.139698	+	0.990194i	$0.455387\pi$
$48$	37.6081	5.42826
$49$	−5.41452	−0.773503
$50$	−13.2597	−1.87520
$51$	9.82066	1.37517
$52$	−5.27397	−0.731368
$53$	10.1654	1.39633	0.698164	−	0.715938i	$-0.254001\pi$
$53$	10.1654	1.39633	0.698164	+	0.715938i	$0.254001\pi$
$54$	−15.5647	−2.11809
$55$	0.636387	0.0858103
$56$	−11.1183	−1.48575
$57$	1.49333	0.197797
$58$	10.5013	1.37889
$59$	−8.34443	−1.08635	−0.543176	−	0.839619i	$-0.682778\pi$
$59$	−8.34443	−1.08635	−0.543176	+	0.839619i	$0.682778\pi$
$60$	−47.0793	−6.07791
$61$	3.49040	0.446899	0.223450	−	0.974715i	$-0.428268\pi$
$61$	3.49040	0.446899	0.223450	+	0.974715i	$0.428268\pi$
$62$	−1.08491	−0.137783
$63$	6.34090	0.798878
$64$	22.3392	2.79240
$65$	3.14903	0.390589
$66$	1.54506	0.190183
$67$	1.54515	0.188771	0.0943853	−	0.995536i	$-0.469911\pi$
$67$	1.54515	0.188771	0.0943853	+	0.995536i	$0.469911\pi$
$68$	18.2710	2.21569
$69$	−4.48379	−0.539785
$70$	10.6941	1.27819
$71$	−13.6046	−1.61457	−0.807286	−	0.590160i	$-0.799065\pi$
$71$	−13.6046	−1.61457	−0.807286	+	0.590160i	$0.799065\pi$
$72$	−44.4663	−5.24040
$73$	12.3127	1.44110	0.720549	−	0.693404i	$-0.243890\pi$
$73$	12.3127	1.44110	0.720549	+	0.693404i	$0.243890\pi$
$74$	−10.1110	−1.17539
$75$	13.9368	1.60928
$76$	2.77830	0.318693
$77$	−0.254463	−0.0289987
$78$	7.64541	0.865673
$79$	2.12875	0.239504	0.119752	−	0.992804i	$-0.461790\pi$
$79$	2.12875	0.239504	0.119752	+	0.992804i	$0.461790\pi$
$80$	−41.7776	−4.67088
$81$	1.25207	0.139119
$82$	28.5189	3.14939
$83$	−6.98505	−0.766709	−0.383355	−	0.923601i	$-0.625231\pi$
$83$	−6.98505	−0.766709	−0.383355	+	0.923601i	$0.625231\pi$
$84$	18.8249	2.05397
$85$	−10.9094	−1.18329
$86$	11.2633	1.21455
$87$	−11.0375	−1.18335
$88$	1.78445	0.190223
$89$	−3.78793	−0.401520	−0.200760	−	0.979640i	$-0.564341\pi$
$89$	−3.78793	−0.401520	−0.200760	+	0.979640i	$0.564341\pi$
$90$	42.7695	4.50830
$91$	−1.25916	−0.131996
$92$	−8.34194	−0.869708
$93$	1.14031	0.118245
$94$	−5.16602	−0.532835
$95$	−1.65890	−0.170199
$96$	−51.3685	−5.24278
$97$	−17.3152	−1.75809	−0.879044	−	0.476740i	$-0.841818\pi$
$97$	−17.3152	−1.75809	−0.879044	+	0.476740i	$0.841818\pi$
$98$	14.6031	1.47514
$99$	−1.01769	−0.102281
$100$	25.9290	2.59290
$101$	−6.56165	−0.652909	−0.326454	−	0.945213i	$-0.605854\pi$
$101$	−6.56165	−0.652909	−0.326454	+	0.945213i	$0.605854\pi$
$102$	−26.4866	−2.62256
$103$	−12.0590	−1.18821	−0.594106	−	0.804386i	$-0.702494\pi$
$103$	−12.0590	−1.18821	−0.594106	+	0.804386i	$0.702494\pi$
$104$	8.82999	0.865852
$105$	−11.2402	−1.09693
$106$	−27.4164	−2.66292
$107$	−8.87952	−0.858416	−0.429208	−	0.903206i	$-0.641207\pi$
$107$	−8.87952	−0.858416	−0.429208	+	0.903206i	$0.641207\pi$
$108$	30.4364	2.92875
$109$	−3.65924	−0.350492	−0.175246	−	0.984525i	$-0.556072\pi$
$109$	−3.65924	−0.350492	−0.175246	+	0.984525i	$0.556072\pi$
$110$	−1.71635	−0.163648
$111$	10.6274	1.00871
$112$	16.7050	1.57847
$113$	5.94261	0.559034	0.279517	−	0.960141i	$-0.409826\pi$
$113$	5.94261	0.559034	0.279517	+	0.960141i	$0.409826\pi$
$114$	−4.02757	−0.377216
$115$	4.98089	0.464470
$116$	−20.5350	−1.90662
$117$	−5.03583	−0.465562
$118$	22.5052	2.07177
$119$	4.36220	0.399882
$120$	78.8229	7.19552
$121$	−10.9592	−0.996287
$122$	−9.41370	−0.852276
$123$	−29.9752	−2.70277
$124$	2.12151	0.190517
$125$	0.263230	0.0235440
$126$	−17.1016	−1.52353
$127$	13.3896	1.18814	0.594068	−	0.804415i	$-0.297521\pi$
$127$	13.3896	1.18814	0.594068	+	0.804415i	$0.297521\pi$
$128$	−24.0076	−2.12199
$129$	−11.8384	−1.04232
$130$	−8.49303	−0.744888
$131$	4.59644	0.401592	0.200796	−	0.979633i	$-0.435647\pi$
$131$	4.59644	0.401592	0.200796	+	0.979633i	$0.435647\pi$
$132$	−3.02132	−0.262972
$133$	0.663318	0.0575170
$134$	−4.16732	−0.360002
$135$	−18.1733	−1.56411
$136$	−30.5904	−2.62311
$137$	4.62723	0.395331	0.197665	−	0.980270i	$-0.436664\pi$
$137$	4.62723	0.395331	0.197665	+	0.980270i	$0.436664\pi$
$138$	12.0929	1.02942
$139$	8.91076	0.755801	0.377900	−	0.925846i	$-0.376646\pi$
$139$	8.91076	0.755801	0.377900	+	0.925846i	$0.376646\pi$
$140$	−20.9120	−1.76738
$141$	5.42983	0.457274
$142$	36.6921	3.07913
$143$	0.202090	0.0168996
$144$	66.8093	5.56744
$145$	12.2612	1.01824
$146$	−33.2078	−2.74830
$147$	−15.3488	−1.26595
$148$	19.7719	1.62524
$149$	18.9053	1.54878	0.774391	−	0.632707i	$-0.218056\pi$
$149$	18.9053	1.54878	0.774391	+	0.632707i	$0.218056\pi$
$150$	−37.5880	−3.06905
$151$	17.7921	1.44790	0.723952	−	0.689851i	$-0.242324\pi$
$151$	17.7921	1.44790	0.723952	+	0.689851i	$0.242324\pi$
$152$	−4.65159	−0.377294
$153$	17.4460	1.41043
$154$	0.686293	0.0553031
$155$	−1.26673	−0.101746
$156$	−14.9504	−1.19699
$157$	−2.33441	−0.186307	−0.0931533	−	0.995652i	$-0.529695\pi$
$157$	−2.33441	−0.186307	−0.0931533	+	0.995652i	$0.529695\pi$
$158$	−5.74131	−0.456754
$159$	28.8165	2.28529
$160$	57.0636	4.51127
$161$	−1.99164	−0.156963
$162$	−3.37687	−0.265312
$163$	15.7312	1.23217	0.616083	−	0.787681i	$-0.288719\pi$
$163$	15.7312	1.23217	0.616083	+	0.787681i	$0.288719\pi$
$164$	−55.7679	−4.35474
$165$	1.80400	0.140441
$166$	18.8389	1.46218
$167$	−5.02863	−0.389127	−0.194564	−	0.980890i	$-0.562329\pi$
$167$	−5.02863	−0.389127	−0.194564	+	0.980890i	$0.562329\pi$
$168$	−31.5178	−2.43165
$169$	1.00000	0.0769231
$170$	29.4231	2.25665
$171$	2.65285	0.202868
$172$	−22.0250	−1.67939
$173$	−8.71104	−0.662288	−0.331144	−	0.943580i	$-0.607435\pi$
$173$	−8.71104	−0.662288	−0.331144	+	0.943580i	$0.607435\pi$
$174$	29.7685	2.25675
$175$	6.19054	0.467960
$176$	−2.68108	−0.202094
$177$	−23.6544	−1.77797
$178$	10.2162	0.765733
$179$	3.03748	0.227032	0.113516	−	0.993536i	$-0.463789\pi$
$179$	3.03748	0.227032	0.113516	+	0.993536i	$0.463789\pi$
$180$	−83.6345	−6.23375
$181$	−7.81062	−0.580559	−0.290280	−	0.956942i	$-0.593748\pi$
$181$	−7.81062	−0.580559	−0.290280	+	0.956942i	$0.593748\pi$
$182$	3.39599	0.251727
$183$	9.89441	0.731416
$184$	13.9666	1.02963
$185$	−11.8056	−0.867964
$186$	−3.07545	−0.225503
$187$	−0.700114	−0.0511974
$188$	10.1020	0.736765
$189$	7.26668	0.528574
$190$	4.47409	0.324585
$191$	−4.71284	−0.341009	−0.170505	−	0.985357i	$-0.554540\pi$
$191$	−4.71284	−0.341009	−0.170505	+	0.985357i	$0.554540\pi$
$192$	63.3262	4.57017
$193$	−3.71428	−0.267360	−0.133680	−	0.991025i	$-0.542679\pi$
$193$	−3.71428	−0.267360	−0.133680	+	0.991025i	$0.542679\pi$
$194$	46.6995	3.35283
$195$	8.92673	0.639257
$196$	−28.5560	−2.03972
$197$	7.26084	0.517314	0.258657	−	0.965969i	$-0.416720\pi$
$197$	7.26084	0.517314	0.258657	+	0.965969i	$0.416720\pi$
$198$	2.74473	0.195060
$199$	−9.41359	−0.667312	−0.333656	−	0.942695i	$-0.608282\pi$
$199$	−9.41359	−0.667312	−0.333656	+	0.942695i	$0.608282\pi$
$200$	−43.4118	−3.06968
$201$	4.38013	0.308950
$202$	17.6970	1.24515
$203$	−4.90272	−0.344103
$204$	51.7938	3.62629
$205$	33.2985	2.32567
$206$	32.5236	2.26603
$207$	−7.96527	−0.553625
$208$	−13.2668	−0.919887
$209$	−0.106460	−0.00736398
$210$	30.3151	2.09194
$211$	−4.62603	−0.318469	−0.159235	−	0.987241i	$-0.550903\pi$
$211$	−4.62603	−0.318469	−0.159235	+	0.987241i	$0.550903\pi$
$212$	53.6121	3.68210
$213$	−38.5658	−2.64248
$214$	23.9483	1.63707
$215$	13.1509	0.896886
$216$	−50.9585	−3.46728
$217$	0.506509	0.0343841
$218$	9.86908	0.668419
$219$	34.9036	2.35857
$220$	3.35628	0.226281
$221$	−3.46438	−0.233039
$222$	−28.6623	−1.92369
$223$	−12.1550	−0.813961	−0.406980	−	0.913437i	$-0.633418\pi$
$223$	−12.1550	−0.813961	−0.406980	+	0.913437i	$0.633418\pi$
$224$	−22.8172	−1.52454
$225$	24.7582	1.65055
$226$	−16.0274	−1.06613
$227$	−25.7978	−1.71226	−0.856128	−	0.516763i	$-0.827137\pi$
$227$	−25.7978	−1.71226	−0.856128	+	0.516763i	$0.827137\pi$
$228$	7.87580	0.521587
$229$	−5.99048	−0.395862	−0.197931	−	0.980216i	$-0.563422\pi$
$229$	−5.99048	−0.395862	−0.197931	+	0.980216i	$0.563422\pi$
$230$	−13.4336	−0.885786
$231$	−0.721339	−0.0474606
$232$	34.3809	2.25721
$233$	5.61104	0.367592	0.183796	−	0.982964i	$-0.441161\pi$
$233$	5.61104	0.367592	0.183796	+	0.982964i	$0.441161\pi$
$234$	13.5818	0.887868
$235$	−6.03181	−0.393472
$236$	−44.0082	−2.86469
$237$	6.03449	0.391982
$238$	−11.7650	−0.762610
$239$	−5.99573	−0.387832	−0.193916	−	0.981018i	$-0.562119\pi$
$239$	−5.99573	−0.387832	−0.193916	+	0.981018i	$0.562119\pi$
$240$	−118.429	−7.64457
$241$	−12.8485	−0.827643	−0.413822	−	0.910358i	$-0.635806\pi$
$241$	−12.8485	−0.827643	−0.413822	+	0.910358i	$0.635806\pi$
$242$	29.5572	1.90001
$243$	−13.7639	−0.882954
$244$	18.4082	1.17847
$245$	17.0505	1.08932
$246$	80.8440	5.15443
$247$	−0.526795	−0.0335192
$248$	−3.55195	−0.225549
$249$	−19.8009	−1.25483
$250$	−0.709940	−0.0449005
$251$	−20.0844	−1.26771	−0.633857	−	0.773450i	$-0.718529\pi$
$251$	−20.0844	−1.26771	−0.633857	+	0.773450i	$0.718529\pi$
$252$	33.4417	2.10663
$253$	0.319649	0.0200962
$254$	−36.1122	−2.26588
$255$	−30.9256	−1.93663
$256$	20.0707	1.25442
$257$	21.0170	1.31100	0.655502	−	0.755193i	$-0.272457\pi$
$257$	21.0170	1.31100	0.655502	+	0.755193i	$0.272457\pi$
$258$	31.9286	1.98779
$259$	4.72053	0.293319
$260$	16.6079	1.02998
$261$	−19.6077	−1.21369
$262$	−12.3967	−0.765872
$263$	13.8832	0.856075	0.428037	−	0.903761i	$-0.359205\pi$
$263$	13.8832	0.856075	0.428037	+	0.903761i	$0.359205\pi$
$264$	5.05847	0.311327
$265$	−32.0113	−1.96644
$266$	−1.78899	−0.109690
$267$	−10.7378	−0.657145
$268$	8.14909	0.497785
$269$	21.2243	1.29407	0.647033	−	0.762462i	$-0.276010\pi$
$269$	21.2243	1.29407	0.647033	+	0.762462i	$0.276010\pi$
$270$	49.0139	2.98289
$271$	6.59106	0.400378	0.200189	−	0.979757i	$-0.435844\pi$
$271$	6.59106	0.400378	0.200189	+	0.979757i	$0.435844\pi$
$272$	45.9612	2.78681
$273$	−3.56940	−0.216030
$274$	−12.4798	−0.753930
$275$	−0.993555	−0.0599136
$276$	−23.6474	−1.42340
$277$	−3.66473	−0.220192	−0.110096	−	0.993921i	$-0.535116\pi$
$277$	−3.66473	−0.220192	−0.110096	+	0.993921i	$0.535116\pi$
$278$	−24.0326	−1.44138
$279$	2.02571	0.121276
$280$	35.0120	2.09237
$281$	−7.88935	−0.470639	−0.235320	−	0.971918i	$-0.575614\pi$
$281$	−7.88935	−0.470639	−0.235320	+	0.971918i	$0.575614\pi$
$282$	−14.6444	−0.872061
$283$	5.10602	0.303522	0.151761	−	0.988417i	$-0.451506\pi$
$283$	5.10602	0.303522	0.151761	+	0.988417i	$0.451506\pi$
$284$	−71.7504	−4.25760
$285$	−4.70256	−0.278556
$286$	−0.545041	−0.0322290
$287$	−13.3146	−0.785934
$288$	−91.2541	−5.37720
$289$	−4.99809	−0.294005
$290$	−33.0689	−1.94187
$291$	−49.0842	−2.87737
$292$	64.9370	3.80015
$293$	−24.3398	−1.42194	−0.710972	−	0.703220i	$-0.751745\pi$
$293$	−24.3398	−1.42194	−0.710972	+	0.703220i	$0.751745\pi$
$294$	41.3963	2.41428
$295$	26.2769	1.52990
$296$	−33.1033	−1.92409
$297$	−1.16627	−0.0676740
$298$	−50.9882	−2.95367
$299$	1.58172	0.0914733
$300$	73.5023	4.24366
$301$	−5.25847	−0.303093
$302$	−47.9859	−2.76128
$303$	−18.6007	−1.06858
$304$	6.98889	0.400840
$305$	−10.9914	−0.629364
$306$	−47.0524	−2.68981
$307$	−0.423220	−0.0241544	−0.0120772	−	0.999927i	$-0.503844\pi$
$307$	−0.423220	−0.0241544	−0.0120772	+	0.999927i	$0.503844\pi$
$308$	−1.34203	−0.0764691
$309$	−34.1844	−1.94468
$310$	3.41641	0.194039
$311$	2.06346	0.117008	0.0585041	−	0.998287i	$-0.481367\pi$
$311$	2.06346	0.117008	0.0585041	+	0.998287i	$0.481367\pi$
$312$	25.0308	1.41709
$313$	−17.4832	−0.988210	−0.494105	−	0.869402i	$-0.664504\pi$
$313$	−17.4832	−0.988210	−0.494105	+	0.869402i	$0.664504\pi$
$314$	6.29598	0.355303
$315$	−19.9677	−1.12505
$316$	11.2270	0.631567
$317$	−16.4727	−0.925197	−0.462599	−	0.886568i	$-0.653083\pi$
$317$	−16.4727	−0.925197	−0.462599	+	0.886568i	$0.653083\pi$
$318$	−77.7189	−4.35826
$319$	0.786865	0.0440560
$320$	−70.3469	−3.93251
$321$	−25.1713	−1.40492
$322$	5.37150	0.299342
$323$	1.82502	0.101547
$324$	6.60338	0.366855
$325$	−4.91641	−0.272713
$326$	−42.4276	−2.34985
$327$	−10.3730	−0.573631
$328$	93.3699	5.15549
$329$	2.41185	0.132970
$330$	−4.86544	−0.267834
$331$	5.67037	0.311672	0.155836	−	0.987783i	$-0.450193\pi$
$331$	5.67037	0.311672	0.155836	+	0.987783i	$0.450193\pi$
$332$	−36.8390	−2.02180
$333$	18.8791	1.03457
$334$	13.5624	0.742100
$335$	−4.86574	−0.265844
$336$	47.3545	2.58340
$337$	−14.2510	−0.776303	−0.388152	−	0.921595i	$-0.626886\pi$
$337$	−14.2510	−0.776303	−0.388152	+	0.921595i	$0.626886\pi$
$338$	−2.69703	−0.146699
$339$	16.8458	0.914941
$340$	−57.5360	−3.12033
$341$	−0.0812926	−0.00440224
$342$	−7.15481	−0.386888
$343$	−15.6318	−0.844040
$344$	36.8756	1.98820
$345$	14.1196	0.760173
$346$	23.4939	1.26304
$347$	−23.5455	−1.26399	−0.631995	−	0.774972i	$-0.717764\pi$
$347$	−23.5455	−1.26399	−0.631995	+	0.774972i	$0.717764\pi$
$348$	−58.2116	−3.12047
$349$	−10.6059	−0.567720	−0.283860	−	0.958866i	$-0.591615\pi$
$349$	−10.6059	−0.567720	−0.283860	+	0.958866i	$0.591615\pi$
$350$	−16.6961	−0.892442
$351$	−5.77107	−0.308037
$352$	3.66206	0.195188
$353$	−36.2183	−1.92770	−0.963852	−	0.266437i	$-0.914153\pi$
$353$	−36.2183	−1.92770	−0.963852	+	0.266437i	$0.914153\pi$
$354$	63.7966	3.39075
$355$	42.8414	2.27379
$356$	−19.9774	−1.05880
$357$	12.3658	0.654465
$358$	−8.19216	−0.432969
$359$	29.5623	1.56024	0.780118	−	0.625632i	$-0.215159\pi$
$359$	29.5623	1.56024	0.780118	+	0.625632i	$0.215159\pi$
$360$	140.026	7.38001
$361$	−18.7225	−0.985394
$362$	21.0655	1.10718
$363$	−31.0665	−1.63057
$364$	−6.64076	−0.348070
$365$	−38.7733	−2.02948
$366$	−26.6855	−1.39487
$367$	−31.1869	−1.62794	−0.813970	−	0.580907i	$-0.802698\pi$
$367$	−31.1869	−1.62794	−0.813970	+	0.580907i	$0.802698\pi$
$368$	−20.9844	−1.09389
$369$	−53.2498	−2.77207
$370$	31.8400	1.65528
$371$	12.7999	0.664536
$372$	6.01395	0.311809
$373$	7.48467	0.387542	0.193771	−	0.981047i	$-0.437928\pi$
$373$	7.48467	0.387542	0.193771	+	0.981047i	$0.437928\pi$
$374$	1.88823	0.0976380
$375$	0.746193	0.0385332
$376$	−16.9134	−0.872242
$377$	3.89365	0.200533
$378$	−19.5985	−1.00804
$379$	28.2806	1.45268	0.726339	−	0.687336i	$-0.241220\pi$
$379$	28.2806	1.45268	0.726339	+	0.687336i	$0.241220\pi$
$380$	−8.74896	−0.448812
$381$	37.9563	1.94456
$382$	12.7107	0.650335
$383$	17.7212	0.905510	0.452755	−	0.891635i	$-0.350441\pi$
$383$	17.7212	0.905510	0.452755	+	0.891635i	$0.350441\pi$
$384$	−68.0555	−3.47294
$385$	0.801311	0.0408386
$386$	10.0175	0.509879
$387$	−21.0305	−1.06904
$388$	−91.3196	−4.63605
$389$	−31.5560	−1.59995	−0.799976	−	0.600031i	$-0.795155\pi$
$389$	−31.5560	−1.59995	−0.799976	+	0.600031i	$0.795155\pi$
$390$	−24.0757	−1.21912
$391$	−5.47968	−0.277119
$392$	47.8102	2.41478
$393$	13.0298	0.657264
$394$	−19.5827	−0.986562
$395$	−6.70352	−0.337291
$396$	−5.36725	−0.269715
$397$	−11.1910	−0.561660	−0.280830	−	0.959758i	$-0.590610\pi$
$397$	−11.1910	−0.561660	−0.280830	+	0.959758i	$0.590610\pi$
$398$	25.3887	1.27262
$399$	1.88034	0.0941349
$400$	65.2250	3.26125
$401$	−6.14799	−0.307016	−0.153508	−	0.988147i	$-0.549057\pi$
$401$	−6.14799	−0.307016	−0.153508	+	0.988147i	$0.549057\pi$
$402$	−11.8133	−0.589196
$403$	−0.402260	−0.0200380
$404$	−34.6060	−1.72171
$405$	−3.94281	−0.195920
$406$	13.2228	0.656235
$407$	−0.757625	−0.0375541
$408$	−86.7163	−4.29310
$409$	28.3075	1.39971	0.699857	−	0.714283i	$-0.253247\pi$
$409$	28.3075	1.39971	0.699857	+	0.714283i	$0.253247\pi$
$410$	−89.8069	−4.43525
$411$	13.1170	0.647016
$412$	−63.5990	−3.13330
$413$	−10.5070	−0.517013
$414$	21.4826	1.05581
$415$	21.9962	1.07975
$416$	18.1210	0.888454
$417$	25.2598	1.23698
$418$	0.287125	0.0140438
$419$	−1.47218	−0.0719209	−0.0359605	−	0.999353i	$-0.511449\pi$
$419$	−1.47218	−0.0719209	−0.0359605	+	0.999353i	$0.511449\pi$
$420$	−59.2803	−2.89258
$421$	24.1143	1.17526	0.587629	−	0.809131i	$-0.300061\pi$
$421$	24.1143	1.17526	0.587629	+	0.809131i	$0.300061\pi$
$422$	12.4766	0.607349
$423$	9.64587	0.468998
$424$	−89.7606	−4.35916
$425$	17.0323	0.826188
$426$	104.013	5.03945
$427$	4.39496	0.212687
$428$	−46.8303	−2.26363
$429$	0.572874	0.0276586
$430$	−35.4684	−1.71044
$431$	27.7998	1.33907	0.669534	−	0.742782i	$-0.266494\pi$
$431$	27.7998	1.33907	0.669534	+	0.742782i	$0.266494\pi$
$432$	76.5636	3.68367
$433$	−9.74262	−0.468201	−0.234100	−	0.972212i	$-0.575214\pi$
$433$	−9.74262	−0.468201	−0.234100	+	0.972212i	$0.575214\pi$
$434$	−1.36607	−0.0655735
$435$	34.7575	1.66650
$436$	−19.2987	−0.924241
$437$	−0.833243	−0.0398594
$438$	−94.1361	−4.49799
$439$	−17.0460	−0.813562	−0.406781	−	0.913526i	$-0.633349\pi$
$439$	−17.0460	−0.813562	−0.406781	+	0.913526i	$0.633349\pi$
$440$	−5.61929	−0.267889
$441$	−27.2666	−1.29841
$442$	9.34353	0.444426
$443$	−32.5540	−1.54669	−0.773344	−	0.633986i	$-0.781418\pi$
$443$	−32.5540	−1.54669	−0.773344	+	0.633986i	$0.781418\pi$
$444$	56.0484	2.65994
$445$	11.9283	0.565456
$446$	32.7825	1.55229
$447$	53.5919	2.53481
$448$	28.1286	1.32895
$449$	33.8987	1.59978	0.799890	−	0.600146i	$-0.204891\pi$
$449$	33.8987	1.59978	0.799890	+	0.600146i	$0.204891\pi$
$450$	−66.7736	−3.14774
$451$	2.13693	0.100624
$452$	31.3412	1.47416
$453$	50.4363	2.36970
$454$	69.5773	3.26542
$455$	3.96513	0.185888
$456$	−13.1861	−0.617497
$457$	−13.2032	−0.617619	−0.308810	−	0.951124i	$-0.599931\pi$
$457$	−13.2032	−0.617619	−0.308810	+	0.951124i	$0.599931\pi$
$458$	16.1565	0.754943
$459$	19.9932	0.933201
$460$	26.2691	1.22480
$461$	−24.9810	−1.16348	−0.581740	−	0.813375i	$-0.697628\pi$
$461$	−24.9810	−1.16348	−0.581740	+	0.813375i	$0.697628\pi$
$462$	1.94547	0.0905115
$463$	−30.2348	−1.40513	−0.702566	−	0.711619i	$-0.747962\pi$
$463$	−30.2348	−1.40513	−0.702566	+	0.711619i	$0.747962\pi$
$464$	−51.6563	−2.39808
$465$	−3.59087	−0.166523
$466$	−15.1331	−0.701030
$467$	−6.91087	−0.319797	−0.159898	−	0.987133i	$-0.551117\pi$
$467$	−6.91087	−0.319797	−0.159898	+	0.987133i	$0.551117\pi$
$468$	−26.5588	−1.22768
$469$	1.94559	0.0898391
$470$	16.2680	0.750386
$471$	−6.61749	−0.304918
$472$	73.6812	3.39145
$473$	0.843962	0.0388054
$474$	−16.2752	−0.747545
$475$	2.58994	0.118835
$476$	23.0061	1.05448
$477$	51.1913	2.34389
$478$	16.1707	0.739629
$479$	16.6523	0.760864	0.380432	−	0.924809i	$-0.375775\pi$
$479$	16.6523	0.760864	0.380432	+	0.924809i	$0.375775\pi$
$480$	161.761	7.38335
$481$	−3.74896	−0.170938
$482$	34.6527	1.57839
$483$	−5.64580	−0.256893
$484$	−57.7983	−2.62719
$485$	54.5260	2.47590
$486$	37.1216	1.68387
$487$	15.1975	0.688666	0.344333	−	0.938848i	$-0.388105\pi$
$487$	15.1975	0.688666	0.344333	+	0.938848i	$0.388105\pi$
$488$	−30.8202	−1.39516
$489$	44.5942	2.01662
$490$	−45.9857	−2.07742
$491$	0.800298	0.0361169	0.0180585	−	0.999837i	$-0.494251\pi$
$491$	0.800298	0.0361169	0.0180585	+	0.999837i	$0.494251\pi$
$492$	−158.088	−7.12717
$493$	−13.4891	−0.607517
$494$	1.42078	0.0639240
$495$	3.20473	0.144042
$496$	5.33671	0.239625
$497$	−17.1304	−0.768402
$498$	53.4036	2.39307
$499$	−15.4556	−0.691887	−0.345943	−	0.938255i	$-0.612441\pi$
$499$	−15.4556	−0.691887	−0.345943	+	0.938255i	$0.612441\pi$
$500$	1.38827	0.0620852
$501$	−14.2549	−0.636863
$502$	54.1681	2.41764
$503$	−19.3699	−0.863663	−0.431832	−	0.901954i	$-0.642132\pi$
$503$	−19.3699	−0.863663	−0.431832	+	0.901954i	$0.642132\pi$
$504$	−55.9901	−2.49400
$505$	20.6629	0.919485
$506$	−0.862103	−0.0383252
$507$	2.83475	0.125896
$508$	70.6164	3.13310
$509$	−2.33382	−0.103445	−0.0517223	−	0.998662i	$-0.516471\pi$
$509$	−2.33382	−0.103445	−0.0517223	+	0.998662i	$0.516471\pi$
$510$	83.4072	3.69333
$511$	15.5037	0.685843
$512$	−6.11604	−0.270293
$513$	3.04017	0.134227
$514$	−56.6835	−2.50020
$515$	37.9743	1.67335
$516$	−62.4355	−2.74857
$517$	−0.387092	−0.0170243
$518$	−12.7314	−0.559386
$519$	−24.6936	−1.08393
$520$	−27.8059	−1.21937
$521$	−4.46833	−0.195761	−0.0978805	−	0.995198i	$-0.531206\pi$
$521$	−4.46833	−0.195761	−0.0978805	+	0.995198i	$0.531206\pi$
$522$	52.8826	2.31461
$523$	−21.0384	−0.919946	−0.459973	−	0.887933i	$-0.652141\pi$
$523$	−21.0384	−0.919946	−0.459973	+	0.887933i	$0.652141\pi$
$524$	24.2415	1.05899
$525$	17.5486	0.765885
$526$	−37.4434	−1.63261
$527$	1.39358	0.0607054
$528$	−7.60021	−0.330756
$529$	−20.4982	−0.891224
$530$	86.3353	3.75017
$531$	−42.0211	−1.82356
$532$	3.49832	0.151671
$533$	10.5742	0.458019
$534$	28.9603	1.25323
$535$	27.9619	1.20890
$536$	−13.6437	−0.589317
$537$	8.61050	0.371570
$538$	−57.2425	−2.46790
$539$	1.09422	0.0471313
$540$	−95.8453	−4.12452
$541$	20.2271	0.869630	0.434815	−	0.900520i	$-0.356814\pi$
$541$	20.2271	0.869630	0.434815	+	0.900520i	$0.356814\pi$
$542$	−17.7763	−0.763557
$543$	−22.1412	−0.950170
$544$	−62.7779	−2.69158
$545$	11.5231	0.493594
$546$	9.62678	0.411988
$547$	−5.03031	−0.215081	−0.107540	−	0.994201i	$-0.534297\pi$
$547$	−5.03031	−0.215081	−0.107540	+	0.994201i	$0.534297\pi$
$548$	24.4038	1.04248
$549$	17.5770	0.750169
$550$	2.67965	0.114261
$551$	−2.05115	−0.0873821
$552$	39.5918	1.68514
$553$	2.68044	0.113984
$554$	9.88389	0.419926
$555$	−33.4659	−1.42055
$556$	46.9951	1.99303
$557$	−25.6724	−1.08778	−0.543888	−	0.839158i	$-0.683048\pi$
$557$	−25.6724	−1.08778	−0.543888	+	0.839158i	$0.683048\pi$
$558$	−5.46341	−0.231285
$559$	4.17618	0.176634
$560$	−52.6046	−2.22295
$561$	−1.98465	−0.0837921
$562$	21.2778	0.897551
$563$	6.81718	0.287310	0.143655	−	0.989628i	$-0.454114\pi$
$563$	6.81718	0.287310	0.143655	+	0.989628i	$0.454114\pi$
$564$	28.6367	1.20582
$565$	−18.7135	−0.787282
$566$	−13.7711	−0.578842
$567$	1.57656	0.0662091
$568$	120.129	5.04049
$569$	6.71934	0.281689	0.140845	−	0.990032i	$-0.455018\pi$
$569$	6.71934	0.281689	0.140845	+	0.990032i	$0.455018\pi$
$570$	12.6829	0.531230
$571$	15.2660	0.638862	0.319431	−	0.947609i	$-0.396508\pi$
$571$	15.2660	0.638862	0.319431	+	0.947609i	$0.396508\pi$
$572$	1.06581	0.0445639
$573$	−13.3597	−0.558112
$574$	35.9098	1.49885
$575$	−7.77638	−0.324298
$576$	112.496	4.68735
$577$	−39.0567	−1.62595	−0.812976	−	0.582297i	$-0.802154\pi$
$577$	−39.0567	−1.62595	−0.812976	+	0.582297i	$0.802154\pi$
$578$	13.4800	0.560693
$579$	−10.5291	−0.437573
$580$	64.6653	2.68508
$581$	−8.79529	−0.364890
$582$	132.382	5.48739
$583$	−2.05433	−0.0850815
$584$	−108.721	−4.49892
$585$	15.8580	0.655647
$586$	65.6451	2.71177
$587$	−7.83192	−0.323258	−0.161629	−	0.986852i	$-0.551675\pi$
$587$	−7.83192	−0.323258	−0.161629	+	0.986852i	$0.551675\pi$
$588$	−80.9493	−3.33829
$589$	0.211909	0.00873155
$590$	−70.8695	−2.91765
$591$	20.5827	0.846659
$592$	49.7367	2.04416
$593$	−4.05737	−0.166616	−0.0833081	−	0.996524i	$-0.526549\pi$
$593$	−4.05737	−0.166616	−0.0833081	+	0.996524i	$0.526549\pi$
$594$	3.14547	0.129060
$595$	−13.7367	−0.563150
$596$	99.7060	4.08412
$597$	−26.6852	−1.09215
$598$	−4.26595	−0.174448
$599$	27.1457	1.10914	0.554572	−	0.832135i	$-0.312882\pi$
$599$	27.1457	1.10914	0.554572	+	0.832135i	$0.312882\pi$
$600$	−123.062	−5.02398
$601$	11.8194	0.482121	0.241061	−	0.970510i	$-0.422505\pi$
$601$	11.8194	0.482121	0.241061	+	0.970510i	$0.422505\pi$
$602$	14.1822	0.578025
$603$	7.78113	0.316872
$604$	93.8351	3.81810
$605$	34.5108	1.40306
$606$	50.1666	2.03788
$607$	25.9450	1.05307	0.526537	−	0.850152i	$-0.323490\pi$
$607$	25.9450	1.05307	0.526537	+	0.850152i	$0.323490\pi$
$608$	−9.54604	−0.387143
$609$	−13.8980	−0.563175
$610$	29.6441	1.20025
$611$	−1.91545	−0.0774908
$612$	92.0097	3.71927
$613$	4.62051	0.186621	0.0933104	−	0.995637i	$-0.470255\pi$
$613$	4.62051	0.186621	0.0933104	+	0.995637i	$0.470255\pi$
$614$	1.14144	0.0460646
$615$	94.3929	3.80629
$616$	2.24690	0.0905303
$617$	14.2150	0.572275	0.286137	−	0.958189i	$-0.407629\pi$
$617$	14.2150	0.572275	0.286137	+	0.958189i	$0.407629\pi$
$618$	92.1964	3.70868
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	−6.68070	−0.268303
$621$	−9.12821	−0.366303
$622$	−5.56521	−0.223145
$623$	−4.76960	−0.191090
$624$	−37.6081	−1.50553
$625$	−25.4110	−1.01644
$626$	47.1528	1.88460
$627$	−0.301787	−0.0120522
$628$	−12.3116	−0.491287
$629$	12.9878	0.517858
$630$	53.8535	2.14557
$631$	−30.7193	−1.22292	−0.611458	−	0.791277i	$-0.709417\pi$
$631$	−30.7193	−1.22292	−0.611458	+	0.791277i	$0.709417\pi$
$632$	−18.7969	−0.747699
$633$	−13.1137	−0.521221
$634$	44.4273	1.76443
$635$	−42.1643	−1.67324
$636$	151.977	6.02629
$637$	5.41452	0.214531
$638$	−2.12220	−0.0840187
$639$	−68.5106	−2.71024
$640$	75.6006	2.98838
$641$	4.45770	0.176069	0.0880344	−	0.996117i	$-0.471941\pi$
$641$	4.45770	0.176069	0.0880344	+	0.996117i	$0.471941\pi$
$642$	67.8876	2.67931
$643$	12.7126	0.501336	0.250668	−	0.968073i	$-0.419350\pi$
$643$	12.7126	0.501336	0.250668	+	0.968073i	$0.419350\pi$
$644$	−10.5038	−0.413909
$645$	37.2796	1.46788
$646$	−4.92213	−0.193658
$647$	3.05917	0.120268	0.0601342	−	0.998190i	$-0.480847\pi$
$647$	3.05917	0.120268	0.0601342	+	0.998190i	$0.480847\pi$
$648$	−11.0558	−0.434312
$649$	1.68632	0.0661939
$650$	13.2597	0.520088
$651$	1.43583	0.0562746
$652$	82.9661	3.24920
$653$	10.7045	0.418901	0.209451	−	0.977819i	$-0.432832\pi$
$653$	10.7045	0.418901	0.209451	+	0.977819i	$0.432832\pi$
$654$	27.9764	1.09396
$655$	−14.4743	−0.565559
$656$	−140.286	−5.47723
$657$	62.0049	2.41904
$658$	−6.50484	−0.253585
$659$	−28.0726	−1.09355	−0.546777	−	0.837278i	$-0.684145\pi$
$659$	−28.0726	−1.09355	−0.546777	+	0.837278i	$0.684145\pi$
$660$	9.51423	0.370341
$661$	26.5348	1.03208	0.516042	−	0.856564i	$-0.327405\pi$
$661$	26.5348	1.03208	0.516042	+	0.856564i	$0.327405\pi$
$662$	−15.2932	−0.594385
$663$	−9.82066	−0.381403
$664$	61.6779	2.39357
$665$	−2.08881	−0.0810006
$666$	−50.9175	−1.97301
$667$	6.15866	0.238464
$668$	−26.5208	−1.02612
$669$	−34.4565	−1.33217
$670$	13.1230	0.506987
$671$	−0.705372	−0.0272306
$672$	−64.6811	−2.49513
$673$	26.2037	1.01008	0.505039	−	0.863096i	$-0.331478\pi$
$673$	26.2037	1.01008	0.505039	+	0.863096i	$0.331478\pi$
$674$	38.4355	1.48048
$675$	28.3729	1.09207
$676$	5.27397	0.202845
$677$	−18.3372	−0.704756	−0.352378	−	0.935858i	$-0.614627\pi$
$677$	−18.3372	−0.704756	−0.352378	+	0.935858i	$0.614627\pi$
$678$	−45.4337	−1.74487
$679$	−21.8025	−0.836704
$680$	96.3302	3.69410
$681$	−73.1303	−2.80236
$682$	0.219249	0.00839546
$683$	−23.8138	−0.911210	−0.455605	−	0.890182i	$-0.650577\pi$
$683$	−23.8138	−0.911210	−0.455605	+	0.890182i	$0.650577\pi$
$684$	13.9910	0.534961
$685$	−14.5713	−0.556740
$686$	42.1595	1.60966
$687$	−16.9815	−0.647886
$688$	−55.4045	−2.11228
$689$	−10.1654	−0.387272
$690$	−38.0810	−1.44972
$691$	34.6109	1.31666	0.658331	−	0.752729i	$-0.271263\pi$
$691$	34.6109	1.31666	0.658331	+	0.752729i	$0.271263\pi$
$692$	−45.9417	−1.74644
$693$	−1.28143	−0.0486775
$694$	63.5030	2.41054
$695$	−28.0603	−1.06439
$696$	97.4613	3.69426
$697$	−36.6330	−1.38757
$698$	28.6044	1.08269
$699$	15.9059	0.601617
$700$	32.6487	1.23400
$701$	−15.5553	−0.587514	−0.293757	−	0.955880i	$-0.594906\pi$
$701$	−15.5553	−0.587514	−0.293757	+	0.955880i	$0.594906\pi$
$702$	15.5647	0.587453
$703$	1.97493	0.0744860
$704$	−4.51452	−0.170147
$705$	−17.0987	−0.643974
$706$	97.6818	3.67630
$707$	−8.26216	−0.310730
$708$	−124.753	−4.68849
$709$	−6.56124	−0.246413	−0.123206	−	0.992381i	$-0.539318\pi$
$709$	−6.56124	−0.246413	−0.123206	+	0.992381i	$0.539318\pi$
$710$	−115.545	−4.33631
$711$	10.7200	0.402033
$712$	33.4474	1.25349
$713$	−0.636263	−0.0238283
$714$	−33.3508	−1.24812
$715$	−0.636387	−0.0237995
$716$	16.0196	0.598679
$717$	−16.9964	−0.634743
$718$	−79.7303	−2.97551
$719$	41.6829	1.55451	0.777255	−	0.629186i	$-0.216612\pi$
$719$	41.6829	1.55451	0.777255	+	0.629186i	$0.216612\pi$
$720$	−210.385	−7.84058
$721$	−15.1842	−0.565491
$722$	50.4951	1.87923
$723$	−36.4223	−1.35456
$724$	−41.1930	−1.53093
$725$	−19.1428	−0.710944
$726$	83.7873	3.10964
$727$	11.4307	0.423939	0.211970	−	0.977276i	$-0.432012\pi$
$727$	11.4307	0.423939	0.211970	+	0.977276i	$0.432012\pi$
$728$	11.1183	0.412073
$729$	−42.7734	−1.58420
$730$	104.573	3.87041
$731$	−14.4679	−0.535113
$732$	52.1828	1.92873
$733$	−38.3685	−1.41717	−0.708586	−	0.705624i	$-0.750667\pi$
$733$	−38.3685	−1.41717	−0.708586	+	0.705624i	$0.750667\pi$
$734$	84.1119	3.10463
$735$	48.3340	1.78283
$736$	28.6623	1.05651
$737$	−0.312259	−0.0115022
$738$	143.616	5.28659
$739$	−7.62184	−0.280374	−0.140187	−	0.990125i	$-0.544770\pi$
$739$	−7.62184	−0.280374	−0.140187	+	0.990125i	$0.544770\pi$
$740$	−62.2623	−2.28881
$741$	−1.49333	−0.0548590
$742$	−34.5216	−1.26733
$743$	39.0210	1.43154	0.715770	−	0.698336i	$-0.246076\pi$
$743$	39.0210	1.43154	0.715770	+	0.698336i	$0.246076\pi$
$744$	−10.0689	−0.369144
$745$	−59.5334	−2.18114
$746$	−20.1864	−0.739076
$747$	−35.1755	−1.28701
$748$	−3.69238	−0.135007
$749$	−11.1807	−0.408535
$750$	−2.01250	−0.0734863
$751$	8.32305	0.303713	0.151856	−	0.988403i	$-0.451475\pi$
$751$	8.32305	0.303713	0.151856	+	0.988403i	$0.451475\pi$
$752$	25.4119	0.926676
$753$	−56.9342	−2.07480
$754$	−10.5013	−0.382434
$755$	−56.0280	−2.03907
$756$	38.3243	1.39384
$757$	29.0547	1.05601	0.528005	−	0.849241i	$-0.322940\pi$
$757$	29.0547	1.05601	0.528005	+	0.849241i	$0.322940\pi$
$758$	−76.2737	−2.77039
$759$	0.906126	0.0328903
$760$	14.6480	0.531340
$761$	−35.4063	−1.28348	−0.641739	−	0.766923i	$-0.721787\pi$
$761$	−35.4063	−1.28348	−0.641739	+	0.766923i	$0.721787\pi$
$762$	−102.369	−3.70844
$763$	−4.60756	−0.166805
$764$	−24.8554	−0.899236
$765$	−54.9381	−1.98629
$766$	−47.7945	−1.72689
$767$	8.34443	0.301300
$768$	56.8954	2.05303
$769$	−2.49797	−0.0900790	−0.0450395	−	0.998985i	$-0.514341\pi$
$769$	−2.49797	−0.0900790	−0.0450395	+	0.998985i	$0.514341\pi$
$770$	−2.16116	−0.0778828
$771$	59.5780	2.14565
$772$	−19.5890	−0.705023
$773$	−5.51350	−0.198307	−0.0991534	−	0.995072i	$-0.531613\pi$
$773$	−5.51350	−0.198307	−0.0991534	+	0.995072i	$0.531613\pi$
$774$	56.7199	2.03876
$775$	1.97768	0.0710402
$776$	152.893	5.48853
$777$	13.3815	0.480060
$778$	85.1075	3.05125
$779$	−5.57043	−0.199581
$780$	47.0793	1.68571
$781$	2.74935	0.0983796
$782$	14.7789	0.528491
$783$	−22.4705	−0.803030
$784$	−71.8334	−2.56548
$785$	7.35115	0.262374
$786$	−35.1416	−1.25346
$787$	13.5822	0.484155	0.242077	−	0.970257i	$-0.422171\pi$
$787$	13.5822	0.484155	0.242077	+	0.970257i	$0.422171\pi$
$788$	38.2934	1.36415
$789$	39.3555	1.40109
$790$	18.0796	0.643243
$791$	7.48269	0.266054
$792$	8.98617	0.319310
$793$	−3.49040	−0.123948
$794$	30.1824	1.07113
$795$	−90.7440	−3.21836
$796$	−49.6470	−1.75969
$797$	−20.0489	−0.710170	−0.355085	−	0.934834i	$-0.615548\pi$
$797$	−20.0489	−0.710170	−0.355085	+	0.934834i	$0.615548\pi$
$798$	−5.07134	−0.179524
$799$	6.63584	0.234759
$800$	−89.0901	−3.14981
$801$	−19.0754	−0.673995
$802$	16.5813	0.585506
$803$	−2.48828	−0.0878094
$804$	23.1007	0.814697
$805$	6.27173	0.221049
$806$	1.08491	0.0382143
$807$	60.1656	2.11793
$808$	57.9393	2.03830
$809$	4.61562	0.162277	0.0811383	−	0.996703i	$-0.474144\pi$
$809$	4.61562	0.162277	0.0811383	+	0.996703i	$0.474144\pi$
$810$	10.6339	0.373637
$811$	5.07797	0.178312	0.0891559	−	0.996018i	$-0.471583\pi$
$811$	5.07797	0.178312	0.0891559	+	0.996018i	$0.471583\pi$
$812$	−25.8568	−0.907395
$813$	18.6840	0.655277
$814$	2.04334	0.0716189
$815$	−49.5382	−1.73525
$816$	130.289	4.56102
$817$	−2.19999	−0.0769679
$818$	−76.3460	−2.66938
$819$	−6.34090	−0.221569
$820$	175.615	6.13274
$821$	−12.9872	−0.453256	−0.226628	−	0.973981i	$-0.572770\pi$
$821$	−12.9872	−0.453256	−0.226628	+	0.973981i	$0.572770\pi$
$822$	−35.3771	−1.23392
$823$	−9.24846	−0.322381	−0.161191	−	0.986923i	$-0.551533\pi$
$823$	−9.24846	−0.322381	−0.161191	+	0.986923i	$0.551533\pi$
$824$	106.481	3.70945
$825$	−2.81648	−0.0980573
$826$	28.3376	0.985990
$827$	−28.3731	−0.986630	−0.493315	−	0.869851i	$-0.664215\pi$
$827$	−28.3731	−0.986630	−0.493315	+	0.869851i	$0.664215\pi$
$828$	−42.0086	−1.45990
$829$	8.84914	0.307343	0.153672	−	0.988122i	$-0.450890\pi$
$829$	8.84914	0.307343	0.153672	+	0.988122i	$0.450890\pi$
$830$	−59.3243	−2.05918
$831$	−10.3886	−0.360377
$832$	−22.3392	−0.774473
$833$	−18.7579	−0.649924
$834$	−68.1264	−2.35903
$835$	15.8353	0.548004
$836$	−0.561465	−0.0194187
$837$	2.32147	0.0802418
$838$	3.97053	0.137160
$839$	−40.4715	−1.39723	−0.698616	−	0.715496i	$-0.746201\pi$
$839$	−40.4715	−1.39723	−0.698616	+	0.715496i	$0.746201\pi$
$840$	99.2505	3.42447
$841$	−13.8395	−0.477224
$842$	−65.0369	−2.24132
$843$	−22.3644	−0.770270
$844$	−24.3976	−0.839799
$845$	−3.14903	−0.108330
$846$	−26.0152	−0.894421
$847$	−13.7993	−0.474150
$848$	134.863	4.63120
$849$	14.4743	0.496757
$850$	−45.9366	−1.57561
$851$	−5.92980	−0.203271
$852$	−203.395	−6.96818
$853$	−35.1525	−1.20360	−0.601800	−	0.798647i	$-0.705550\pi$
$853$	−35.1525	−1.20360	−0.601800	+	0.798647i	$0.705550\pi$
$854$	−11.8533	−0.405613
$855$	−8.35391	−0.285698
$856$	78.4061	2.67986
$857$	−11.7185	−0.400298	−0.200149	−	0.979765i	$-0.564143\pi$
$857$	−11.7185	−0.400298	−0.200149	+	0.979765i	$0.564143\pi$
$858$	−1.54506	−0.0527474
$859$	−26.9078	−0.918082	−0.459041	−	0.888415i	$-0.651807\pi$
$859$	−26.9078	−0.918082	−0.459041	+	0.888415i	$0.651807\pi$
$860$	69.3576	2.36507
$861$	−37.7435	−1.28630
$862$	−74.9768	−2.55372
$863$	5.06732	0.172494	0.0862468	−	0.996274i	$-0.472513\pi$
$863$	5.06732	0.172494	0.0862468	+	0.996274i	$0.472513\pi$
$864$	−104.577	−3.55779
$865$	27.4314	0.932694
$866$	26.2761	0.892900
$867$	−14.1683	−0.481182
$868$	2.67131	0.0906703
$869$	−0.430199	−0.0145935
$870$	−93.7421	−3.17816
$871$	−1.54515	−0.0523555
$872$	32.3111	1.09419
$873$	−87.1962	−2.95114
$874$	2.24728	0.0760154
$875$	0.331449	0.0112050
$876$	184.080	6.21950
$877$	0.539949	0.0182328	0.00911640	−	0.999958i	$-0.497098\pi$
$877$	0.539949	0.0182328	0.00911640	+	0.999958i	$0.497098\pi$
$878$	45.9736	1.55153
$879$	−68.9973	−2.32722
$880$	8.44281	0.284607
$881$	−6.96435	−0.234635	−0.117318	−	0.993094i	$-0.537430\pi$
$881$	−6.96435	−0.234635	−0.117318	+	0.993094i	$0.537430\pi$
$882$	73.5388	2.47618
$883$	17.3262	0.583074	0.291537	−	0.956560i	$-0.405833\pi$
$883$	17.3262	0.583074	0.291537	+	0.956560i	$0.405833\pi$
$884$	−18.2710	−0.614521
$885$	74.4885	2.50390
$886$	87.7992	2.94967
$887$	53.5104	1.79670	0.898352	−	0.439277i	$-0.144765\pi$
$887$	53.5104	1.79670	0.898352	+	0.439277i	$0.144765\pi$
$888$	−93.8396	−3.14905
$889$	16.8596	0.565454
$890$	−32.1710	−1.07837
$891$	−0.253030	−0.00847684
$892$	−64.1052	−2.14640
$893$	1.00905	0.0337666
$894$	−144.539	−4.83410
$895$	−9.56511	−0.319726
$896$	−30.2293	−1.00989
$897$	4.48379	0.149709
$898$	−91.4259	−3.05092
$899$	−1.56626	−0.0522377
$900$	130.574	4.35246
$901$	35.2169	1.17324
$902$	−5.76337	−0.191899
$903$	−14.9065	−0.496056
$904$	−52.4732	−1.74523
$905$	24.5959	0.817596
$906$	−136.028	−4.51923
$907$	−35.5463	−1.18030	−0.590148	−	0.807295i	$-0.700931\pi$
$907$	−35.5463	−1.18030	−0.590148	+	0.807295i	$0.700931\pi$
$908$	−136.057	−4.51519
$909$	−33.0434	−1.09598
$910$	−10.6941	−0.354505
$911$	40.1291	1.32954	0.664768	−	0.747050i	$-0.268531\pi$
$911$	40.1291	1.32954	0.664768	+	0.747050i	$0.268531\pi$
$912$	19.8118	0.656033
$913$	1.41161	0.0467173
$914$	35.6094	1.17785
$915$	−31.1578	−1.03005
$916$	−31.5936	−1.04388
$917$	5.78764	0.191125
$918$	−53.9221	−1.77970
$919$	−55.5720	−1.83315	−0.916576	−	0.399861i	$-0.869058\pi$
$919$	−55.5720	−1.83315	−0.916576	+	0.399861i	$0.869058\pi$
$920$	−43.9812	−1.45002
$921$	−1.19972	−0.0395322
$922$	67.3744	2.21886
$923$	13.6046	0.447802
$924$	−3.80432	−0.125153
$925$	18.4314	0.606021
$926$	81.5442	2.67971
$927$	−60.7273	−1.99454
$928$	70.5567	2.31614
$929$	11.1347	0.365317	0.182658	−	0.983176i	$-0.441530\pi$
$929$	11.1347	0.365317	0.182658	+	0.983176i	$0.441530\pi$
$930$	9.68468	0.317573
$931$	−2.85234	−0.0934818
$932$	29.5925	0.969333
$933$	5.84940	0.191501
$934$	18.6388	0.609880
$935$	2.20468	0.0721009
$936$	44.4663	1.45343
$937$	3.71526	0.121372	0.0606861	−	0.998157i	$-0.480671\pi$
$937$	3.71526	0.121372	0.0606861	+	0.998157i	$0.480671\pi$
$938$	−5.24732	−0.171331
$939$	−49.5606	−1.61735
$940$	−31.8116	−1.03758
$941$	13.8341	0.450978	0.225489	−	0.974246i	$-0.427602\pi$
$941$	13.8341	0.450978	0.225489	+	0.974246i	$0.427602\pi$
$942$	17.8476	0.581505
$943$	16.7254	0.544654
$944$	−110.704	−3.60310
$945$	−22.8830	−0.744385
$946$	−2.27619	−0.0740053
$947$	−8.27456	−0.268887	−0.134444	−	0.990921i	$-0.542925\pi$
$947$	−8.27456	−0.268887	−0.134444	+	0.990921i	$0.542925\pi$
$948$	31.8257	1.03365
$949$	−12.3127	−0.399689
$950$	−6.98515	−0.226628
$951$	−46.6960	−1.51422
$952$	−38.5182	−1.24838
$953$	1.59614	0.0517040	0.0258520	−	0.999666i	$-0.491770\pi$
$953$	1.59614	0.0517040	0.0258520	+	0.999666i	$0.491770\pi$
$954$	−138.064	−4.47000
$955$	14.8409	0.480240
$956$	−31.6213	−1.02271
$957$	2.23057	0.0721041
$958$	−44.9118	−1.45103
$959$	5.82641	0.188145
$960$	−199.416	−6.43613
$961$	−30.8382	−0.994780
$962$	10.1110	0.325993
$963$	−44.7157	−1.44094
$964$	−67.7625	−2.18248
$965$	11.6964	0.376520
$966$	15.2269	0.489917
$967$	−17.9607	−0.577578	−0.288789	−	0.957393i	$-0.593253\pi$
$967$	−17.9607	−0.577578	−0.288789	+	0.957393i	$0.593253\pi$
$968$	96.7692	3.11028
$969$	5.17347	0.166196
$970$	−147.058	−4.72176
$971$	54.7413	1.75673	0.878366	−	0.477988i	$-0.158634\pi$
$971$	54.7413	1.75673	0.878366	+	0.477988i	$0.158634\pi$
$972$	−72.5903	−2.32834
$973$	11.2201	0.359698
$974$	−40.9882	−1.31335
$975$	−13.9368	−0.446335
$976$	46.3064	1.48223
$977$	3.04305	0.0973559	0.0486779	−	0.998815i	$-0.484499\pi$
$977$	3.04305	0.0973559	0.0486779	+	0.998815i	$0.484499\pi$
$978$	−120.272	−3.84587
$979$	0.765501	0.0244655
$980$	89.9238	2.87251
$981$	−18.4273	−0.588339
$982$	−2.15843	−0.0688782
$983$	−9.16190	−0.292219	−0.146110	−	0.989268i	$-0.546675\pi$
$983$	−9.16190	−0.292219	−0.146110	+	0.989268i	$0.546675\pi$
$984$	264.681	8.43771
$985$	−22.8646	−0.728528
$986$	36.3804	1.15859
$987$	6.83701	0.217624
$988$	−2.77830	−0.0883895
$989$	6.60555	0.210044
$990$	−8.64326	−0.274701
$991$	28.9538	0.919747	0.459873	−	0.887984i	$-0.347895\pi$
$991$	28.9538	0.919747	0.459873	+	0.887984i	$0.347895\pi$
$992$	−7.28935	−0.231437
$993$	16.0741	0.510096
$994$	46.2011	1.46541
$995$	29.6437	0.939769
$996$	−104.429	−3.30897
$997$	−15.6103	−0.494383	−0.247192	−	0.968967i	$-0.579508\pi$
$997$	−15.6103	−0.494383	−0.247192	+	0.968967i	$0.579508\pi$
$998$	41.6842	1.31949
$999$	21.6355	0.684516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.c.1.6	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.c.1.6	✓	151	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69703 q^{2} +2.83475 q^{3} +5.27397 q^{4} -3.14903 q^{5} -7.64541 q^{6} +1.25916 q^{7} -8.82999 q^{8} +5.03583 q^{9} +O(q^{10})\)	\(q-2.69703 q^{2} +2.83475 q^{3} +5.27397 q^{4} -3.14903 q^{5} -7.64541 q^{6} +1.25916 q^{7} -8.82999 q^{8} +5.03583 q^{9} +8.49303 q^{10} -0.202090 q^{11} +14.9504 q^{12} -1.00000 q^{13} -3.39599 q^{14} -8.92673 q^{15} +13.2668 q^{16} +3.46438 q^{17} -13.5818 q^{18} +0.526795 q^{19} -16.6079 q^{20} +3.56940 q^{21} +0.545041 q^{22} -1.58172 q^{23} -25.0308 q^{24} +4.91641 q^{25} +2.69703 q^{26} +5.77107 q^{27} +6.64076 q^{28} -3.89365 q^{29} +24.0757 q^{30} +0.402260 q^{31} -18.1210 q^{32} -0.572874 q^{33} -9.34353 q^{34} -3.96513 q^{35} +26.5588 q^{36} +3.74896 q^{37} -1.42078 q^{38} -2.83475 q^{39} +27.8059 q^{40} -10.5742 q^{41} -9.62678 q^{42} -4.17618 q^{43} -1.06581 q^{44} -15.8580 q^{45} +4.26595 q^{46} +1.91545 q^{47} +37.6081 q^{48} -5.41452 q^{49} -13.2597 q^{50} +9.82066 q^{51} -5.27397 q^{52} +10.1654 q^{53} -15.5647 q^{54} +0.636387 q^{55} -11.1183 q^{56} +1.49333 q^{57} +10.5013 q^{58} -8.34443 q^{59} -47.0793 q^{60} +3.49040 q^{61} -1.08491 q^{62} +6.34090 q^{63} +22.3392 q^{64} +3.14903 q^{65} +1.54506 q^{66} +1.54515 q^{67} +18.2710 q^{68} -4.48379 q^{69} +10.6941 q^{70} -13.6046 q^{71} -44.4663 q^{72} +12.3127 q^{73} -10.1110 q^{74} +13.9368 q^{75} +2.77830 q^{76} -0.254463 q^{77} +7.64541 q^{78} +2.12875 q^{79} -41.7776 q^{80} +1.25207 q^{81} +28.5189 q^{82} -6.98505 q^{83} +18.8249 q^{84} -10.9094 q^{85} +11.2633 q^{86} -11.0375 q^{87} +1.78445 q^{88} -3.78793 q^{89} +42.7695 q^{90} -1.25916 q^{91} -8.34194 q^{92} +1.14031 q^{93} -5.16602 q^{94} -1.65890 q^{95} -51.3685 q^{96} -17.3152 q^{97} +14.6031 q^{98} -1.01769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

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