LMFDB - Embedded newform 8039.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53338 q^{2} +3.09967 q^{3} +4.41800 q^{4} +3.04096 q^{5} -7.85264 q^{6} -3.65810 q^{7} -6.12571 q^{8} +6.60796 q^{9} +O(q^{10})$	\(q-2.53338 q^{2} +3.09967 q^{3} +4.41800 q^{4} +3.04096 q^{5} -7.85264 q^{6} -3.65810 q^{7} -6.12571 q^{8} +6.60796 q^{9} -7.70391 q^{10} +0.170043 q^{11} +13.6943 q^{12} -3.89273 q^{13} +9.26734 q^{14} +9.42599 q^{15} +6.68272 q^{16} -1.95914 q^{17} -16.7405 q^{18} -2.84614 q^{19} +13.4350 q^{20} -11.3389 q^{21} -0.430783 q^{22} +0.947043 q^{23} -18.9877 q^{24} +4.24746 q^{25} +9.86176 q^{26} +11.1835 q^{27} -16.1615 q^{28} -3.37424 q^{29} -23.8796 q^{30} +1.08273 q^{31} -4.67845 q^{32} +0.527077 q^{33} +4.96323 q^{34} -11.1241 q^{35} +29.1940 q^{36} +1.38308 q^{37} +7.21036 q^{38} -12.0662 q^{39} -18.6280 q^{40} -11.6696 q^{41} +28.7257 q^{42} +5.87938 q^{43} +0.751250 q^{44} +20.0946 q^{45} -2.39922 q^{46} -6.77590 q^{47} +20.7142 q^{48} +6.38169 q^{49} -10.7604 q^{50} -6.07268 q^{51} -17.1981 q^{52} +2.14369 q^{53} -28.3320 q^{54} +0.517094 q^{55} +22.4084 q^{56} -8.82211 q^{57} +8.54821 q^{58} -8.80132 q^{59} +41.6440 q^{60} -2.18716 q^{61} -2.74295 q^{62} -24.1726 q^{63} -1.51318 q^{64} -11.8377 q^{65} -1.33529 q^{66} -4.62984 q^{67} -8.65546 q^{68} +2.93552 q^{69} +28.1817 q^{70} -8.24828 q^{71} -40.4784 q^{72} +2.01005 q^{73} -3.50387 q^{74} +13.1657 q^{75} -12.5743 q^{76} -0.622034 q^{77} +30.5682 q^{78} -9.46457 q^{79} +20.3219 q^{80} +14.8413 q^{81} +29.5636 q^{82} +5.69016 q^{83} -50.0953 q^{84} -5.95766 q^{85} -14.8947 q^{86} -10.4590 q^{87} -1.04163 q^{88} -8.34603 q^{89} -50.9071 q^{90} +14.2400 q^{91} +4.18403 q^{92} +3.35610 q^{93} +17.1659 q^{94} -8.65502 q^{95} -14.5016 q^{96} -11.9231 q^{97} -16.1672 q^{98} +1.12364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * 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 $

$2$	−2.53338	−1.79137	−0.895684	−	0.444691i	$-0.853314\pi$
$2$	−2.53338	−1.79137	−0.895684	+	0.444691i	$0.853314\pi$
$3$	3.09967	1.78960	0.894798	−	0.446471i	$-0.147319\pi$
$3$	3.09967	1.78960	0.894798	+	0.446471i	$0.147319\pi$
$4$	4.41800	2.20900
$5$	3.04096	1.35996	0.679980	−	0.733231i	$-0.261988\pi$
$5$	3.04096	1.35996	0.679980	+	0.733231i	$0.261988\pi$
$6$	−7.85264	−3.20583
$7$	−3.65810	−1.38263	−0.691316	−	0.722553i	$-0.742969\pi$
$7$	−3.65810	−1.38263	−0.691316	+	0.722553i	$0.742969\pi$
$8$	−6.12571	−2.16576
$9$	6.60796	2.20265
$10$	−7.70391	−2.43619
$11$	0.170043	0.0512699	0.0256349	−	0.999671i	$-0.491839\pi$
$11$	0.170043	0.0512699	0.0256349	+	0.999671i	$0.491839\pi$
$12$	13.6943	3.95322
$13$	−3.89273	−1.07965	−0.539825	−	0.841777i	$-0.681509\pi$
$13$	−3.89273	−1.07965	−0.539825	+	0.841777i	$0.681509\pi$
$14$	9.26734	2.47680
$15$	9.42599	2.43378
$16$	6.68272	1.67068
$17$	−1.95914	−0.475160	−0.237580	−	0.971368i	$-0.576354\pi$
$17$	−1.95914	−0.475160	−0.237580	+	0.971368i	$0.576354\pi$
$18$	−16.7405	−3.94576
$19$	−2.84614	−0.652950	−0.326475	−	0.945206i	$-0.605861\pi$
$19$	−2.84614	−0.652950	−0.326475	+	0.945206i	$0.605861\pi$
$20$	13.4350	3.00415
$21$	−11.3389	−2.47435
$22$	−0.430783	−0.0918432
$23$	0.947043	0.197472	0.0987360	−	0.995114i	$-0.468520\pi$
$23$	0.947043	0.197472	0.0987360	+	0.995114i	$0.468520\pi$
$24$	−18.9877	−3.87584
$25$	4.24746	0.849492
$26$	9.86176	1.93405
$27$	11.1835	2.15226
$28$	−16.1615	−3.05423
$29$	−3.37424	−0.626580	−0.313290	−	0.949658i	$-0.601431\pi$
$29$	−3.37424	−0.626580	−0.313290	+	0.949658i	$0.601431\pi$
$30$	−23.8796	−4.35980
$31$	1.08273	0.194463	0.0972317	−	0.995262i	$-0.469001\pi$
$31$	1.08273	0.194463	0.0972317	+	0.995262i	$0.469001\pi$
$32$	−4.67845	−0.827040
$33$	0.527077	0.0917524
$34$	4.96323	0.851187
$35$	−11.1241	−1.88032
$36$	29.1940	4.86566
$37$	1.38308	0.227377	0.113689	−	0.993516i	$-0.463733\pi$
$37$	1.38308	0.227377	0.113689	+	0.993516i	$0.463733\pi$
$38$	7.21036	1.16967
$39$	−12.0662	−1.93214
$40$	−18.6280	−2.94535
$41$	−11.6696	−1.82249	−0.911246	−	0.411863i	$-0.864878\pi$
$41$	−11.6696	−1.82249	−0.911246	+	0.411863i	$0.864878\pi$
$42$	28.7257	4.43248
$43$	5.87938	0.896597	0.448299	−	0.893884i	$-0.352030\pi$
$43$	5.87938	0.896597	0.448299	+	0.893884i	$0.352030\pi$
$44$	0.751250	0.113255
$45$	20.0946	2.99552
$46$	−2.39922	−0.353745
$47$	−6.77590	−0.988367	−0.494184	−	0.869358i	$-0.664533\pi$
$47$	−6.77590	−0.988367	−0.494184	+	0.869358i	$0.664533\pi$
$48$	20.7142	2.98984
$49$	6.38169	0.911670
$50$	−10.7604	−1.52175
$51$	−6.07268	−0.850345
$52$	−17.1981	−2.38495
$53$	2.14369	0.294458	0.147229	−	0.989102i	$-0.452965\pi$
$53$	2.14369	0.294458	0.147229	+	0.989102i	$0.452965\pi$
$54$	−28.3320	−3.85550
$55$	0.517094	0.0697250
$56$	22.4084	2.99445
$57$	−8.82211	−1.16852
$58$	8.54821	1.12244
$59$	−8.80132	−1.14583	−0.572917	−	0.819613i	$-0.694188\pi$
$59$	−8.80132	−1.14583	−0.572917	+	0.819613i	$0.694188\pi$
$60$	41.6440	5.37622
$61$	−2.18716	−0.280037	−0.140018	−	0.990149i	$-0.544716\pi$
$61$	−2.18716	−0.280037	−0.140018	+	0.990149i	$0.544716\pi$
$62$	−2.74295	−0.348355
$63$	−24.1726	−3.04546
$64$	−1.51318	−0.189147
$65$	−11.8377	−1.46828
$66$	−1.33529	−0.164362
$67$	−4.62984	−0.565625	−0.282812	−	0.959175i	$-0.591267\pi$
$67$	−4.62984	−0.565625	−0.282812	+	0.959175i	$0.591267\pi$
$68$	−8.65546	−1.04963
$69$	2.93552	0.353395
$70$	28.1817	3.36835
$71$	−8.24828	−0.978890	−0.489445	−	0.872034i	$-0.662801\pi$
$71$	−8.24828	−0.978890	−0.489445	+	0.872034i	$0.662801\pi$
$72$	−40.4784	−4.77043
$73$	2.01005	0.235259	0.117630	−	0.993058i	$-0.462470\pi$
$73$	2.01005	0.235259	0.117630	+	0.993058i	$0.462470\pi$
$74$	−3.50387	−0.407316
$75$	13.1657	1.52025
$76$	−12.5743	−1.44237
$77$	−0.622034	−0.0708873
$78$	30.5682	3.46117
$79$	−9.46457	−1.06485	−0.532423	−	0.846478i	$-0.678719\pi$
$79$	−9.46457	−1.06485	−0.532423	+	0.846478i	$0.678719\pi$
$80$	20.3219	2.27206
$81$	14.8413	1.64903
$82$	29.5636	3.26475
$83$	5.69016	0.624576	0.312288	−	0.949988i	$-0.398905\pi$
$83$	5.69016	0.624576	0.312288	+	0.949988i	$0.398905\pi$
$84$	−50.0953	−5.46584
$85$	−5.95766	−0.646199
$86$	−14.8947	−1.60614
$87$	−10.4590	−1.12133
$88$	−1.04163	−0.111038
$89$	−8.34603	−0.884678	−0.442339	−	0.896848i	$-0.645851\pi$
$89$	−8.34603	−0.884678	−0.442339	+	0.896848i	$0.645851\pi$
$90$	−50.9071	−5.36608
$91$	14.2400	1.49276
$92$	4.18403	0.436216
$93$	3.35610	0.348011
$94$	17.1659	1.77053
$95$	−8.65502	−0.887987
$96$	−14.5016	−1.48007
$97$	−11.9231	−1.21061	−0.605303	−	0.795995i	$-0.706948\pi$
$97$	−11.9231	−1.21061	−0.605303	+	0.795995i	$0.706948\pi$
$98$	−16.1672	−1.63314
$99$	1.12364	0.112930
$100$	18.7653	1.87653
$101$	3.96883	0.394914	0.197457	−	0.980312i	$-0.436732\pi$
$101$	3.96883	0.394914	0.197457	+	0.980312i	$0.436732\pi$
$102$	15.3844	1.52328
$103$	−9.57747	−0.943696	−0.471848	−	0.881680i	$-0.656413\pi$
$103$	−9.57747	−0.943696	−0.471848	+	0.881680i	$0.656413\pi$
$104$	23.8457	2.33827
$105$	−34.4812	−3.36502
$106$	−5.43077	−0.527483
$107$	0.146333	0.0141465	0.00707327	−	0.999975i	$-0.497748\pi$
$107$	0.146333	0.0141465	0.00707327	+	0.999975i	$0.497748\pi$
$108$	49.4087	4.75435
$109$	10.8240	1.03676	0.518378	−	0.855152i	$-0.326536\pi$
$109$	10.8240	1.03676	0.518378	+	0.855152i	$0.326536\pi$
$110$	−1.31000	−0.124903
$111$	4.28710	0.406913
$112$	−24.4461	−2.30994
$113$	8.35803	0.786257	0.393129	−	0.919483i	$-0.371393\pi$
$113$	8.35803	0.786257	0.393129	+	0.919483i	$0.371393\pi$
$114$	22.3497	2.09324
$115$	2.87992	0.268554
$116$	−14.9074	−1.38412
$117$	−25.7230	−2.37809
$118$	22.2971	2.05261
$119$	7.16671	0.656972
$120$	−57.7408	−5.27099
$121$	−10.9711	−0.997371
$122$	5.54090	0.501649
$123$	−36.1721	−3.26152
$124$	4.78348	0.429570
$125$	−2.28845	−0.204685
$126$	61.2383	5.45554
$127$	2.12646	0.188693	0.0943463	−	0.995539i	$-0.469924\pi$
$127$	2.12646	0.188693	0.0943463	+	0.995539i	$0.469924\pi$
$128$	13.1903	1.16587
$129$	18.2241	1.60455
$130$	29.9892	2.63023
$131$	10.7523	0.939434	0.469717	−	0.882817i	$-0.344356\pi$
$131$	10.7523	0.939434	0.469717	+	0.882817i	$0.344356\pi$
$132$	2.32863	0.202681
$133$	10.4115	0.902790
$134$	11.7291	1.01324
$135$	34.0086	2.92699
$136$	12.0011	1.02909
$137$	−14.5073	−1.23944	−0.619722	−	0.784821i	$-0.712755\pi$
$137$	−14.5073	−1.23944	−0.619722	+	0.784821i	$0.712755\pi$
$138$	−7.43678	−0.633061
$139$	10.2195	0.866806	0.433403	−	0.901200i	$-0.357313\pi$
$139$	10.2195	0.866806	0.433403	+	0.901200i	$0.357313\pi$
$140$	−49.1465	−4.15364
$141$	−21.0031	−1.76878
$142$	20.8960	1.75355
$143$	−0.661931	−0.0553535
$144$	44.1592	3.67993
$145$	−10.2609	−0.852124
$146$	−5.09222	−0.421436
$147$	19.7811	1.63152
$148$	6.11045	0.502276
$149$	0.557647	0.0456842	0.0228421	−	0.999739i	$-0.492729\pi$
$149$	0.557647	0.0456842	0.0228421	+	0.999739i	$0.492729\pi$
$150$	−33.3538	−2.72332
$151$	15.3739	1.25111	0.625554	−	0.780181i	$-0.284873\pi$
$151$	15.3739	1.25111	0.625554	+	0.780181i	$0.284873\pi$
$152$	17.4346	1.41414
$153$	−12.9459	−1.04661
$154$	1.57585	0.126985
$155$	3.29253	0.264462
$156$	−53.3084	−4.26809
$157$	12.1224	0.967473	0.483737	−	0.875214i	$-0.339279\pi$
$157$	12.1224	0.967473	0.483737	+	0.875214i	$0.339279\pi$
$158$	23.9773	1.90753
$159$	6.64473	0.526961
$160$	−14.2270	−1.12474
$161$	−3.46438	−0.273031
$162$	−37.5985	−2.95402
$163$	−2.31212	−0.181099	−0.0905495	−	0.995892i	$-0.528862\pi$
$163$	−2.31212	−0.181099	−0.0905495	+	0.995892i	$0.528862\pi$
$164$	−51.5565	−4.02588
$165$	1.60282	0.124780
$166$	−14.4153	−1.11885
$167$	7.54312	0.583704	0.291852	−	0.956463i	$-0.405729\pi$
$167$	7.54312	0.583704	0.291852	+	0.956463i	$0.405729\pi$
$168$	69.4588	5.35886
$169$	2.15335	0.165643
$170$	15.0930	1.15758
$171$	−18.8072	−1.43822
$172$	25.9751	1.98058
$173$	2.39605	0.182168	0.0910840	−	0.995843i	$-0.470967\pi$
$173$	2.39605	0.182168	0.0910840	+	0.995843i	$0.470967\pi$
$174$	26.4967	2.00871
$175$	−15.5376	−1.17453
$176$	1.13635	0.0856556
$177$	−27.2812	−2.05058
$178$	21.1436	1.58478
$179$	17.7982	1.33030	0.665151	−	0.746709i	$-0.268367\pi$
$179$	17.7982	1.33030	0.665151	+	0.746709i	$0.268367\pi$
$180$	88.7778	6.61711
$181$	11.6522	0.866103	0.433052	−	0.901369i	$-0.357437\pi$
$181$	11.6522	0.866103	0.433052	+	0.901369i	$0.357437\pi$
$182$	−36.0753	−2.67408
$183$	−6.77947	−0.501153
$184$	−5.80130	−0.427678
$185$	4.20590	0.309224
$186$	−8.50226	−0.623416
$187$	−0.333137	−0.0243614
$188$	−29.9359	−2.18330
$189$	−40.9103	−2.97579
$190$	21.9264	1.59071
$191$	0.172674	0.0124943	0.00624713	−	0.999980i	$-0.498011\pi$
$191$	0.172674	0.0124943	0.00624713	+	0.999980i	$0.498011\pi$
$192$	−4.69036	−0.338497
$193$	5.62426	0.404843	0.202421	−	0.979299i	$-0.435119\pi$
$193$	5.62426	0.404843	0.202421	+	0.979299i	$0.435119\pi$
$194$	30.2057	2.16864
$195$	−36.6928	−2.62763
$196$	28.1943	2.01388
$197$	−25.2239	−1.79713	−0.898564	−	0.438842i	$-0.855389\pi$
$197$	−25.2239	−1.79713	−0.898564	+	0.438842i	$0.855389\pi$
$198$	−2.84660	−0.202299
$199$	−22.4091	−1.58854	−0.794268	−	0.607567i	$-0.792145\pi$
$199$	−22.4091	−1.58854	−0.794268	+	0.607567i	$0.792145\pi$
$200$	−26.0187	−1.83980
$201$	−14.3510	−1.01224
$202$	−10.0546	−0.707436
$203$	12.3433	0.866329
$204$	−26.8291	−1.87841
$205$	−35.4870	−2.47852
$206$	24.2633	1.69051
$207$	6.25802	0.434963
$208$	−26.0140	−1.80375
$209$	−0.483967	−0.0334767
$210$	87.3539	6.02799
$211$	−17.2055	−1.18447	−0.592236	−	0.805764i	$-0.701755\pi$
$211$	−17.2055	−1.18447	−0.592236	+	0.805764i	$0.701755\pi$
$212$	9.47081	0.650458
$213$	−25.5669	−1.75182
$214$	−0.370717	−0.0253417
$215$	17.8790	1.21934
$216$	−68.5068	−4.66130
$217$	−3.96072	−0.268871
$218$	−27.4214	−1.85721
$219$	6.23051	0.421019
$220$	2.28452	0.154022
$221$	7.62639	0.513007
$222$	−10.8608	−0.728931
$223$	14.6146	0.978667	0.489334	−	0.872097i	$-0.337240\pi$
$223$	14.6146	0.978667	0.489334	+	0.872097i	$0.337240\pi$
$224$	17.1142	1.14349
$225$	28.0670	1.87114
$226$	−21.1740	−1.40848
$227$	−26.9801	−1.79073	−0.895367	−	0.445329i	$-0.853087\pi$
$227$	−26.9801	−1.79073	−0.895367	+	0.445329i	$0.853087\pi$
$228$	−38.9761	−2.58125
$229$	6.93623	0.458359	0.229180	−	0.973384i	$-0.426396\pi$
$229$	6.93623	0.458359	0.229180	+	0.973384i	$0.426396\pi$
$230$	−7.29593	−0.481079
$231$	−1.92810	−0.126860
$232$	20.6696	1.35702
$233$	15.2545	0.999357	0.499679	−	0.866211i	$-0.333451\pi$
$233$	15.2545	0.999357	0.499679	+	0.866211i	$0.333451\pi$
$234$	65.1661	4.26004
$235$	−20.6053	−1.34414
$236$	−38.8842	−2.53115
$237$	−29.3370	−1.90565
$238$	−18.1560	−1.17688
$239$	9.02484	0.583768	0.291884	−	0.956454i	$-0.405718\pi$
$239$	9.02484	0.583768	0.291884	+	0.956454i	$0.405718\pi$
$240$	62.9913	4.06607
$241$	−3.41349	−0.219882	−0.109941	−	0.993938i	$-0.535066\pi$
$241$	−3.41349	−0.219882	−0.109941	+	0.993938i	$0.535066\pi$
$242$	27.7939	1.78666
$243$	12.4526	0.798834
$244$	−9.66287	−0.618602
$245$	19.4065	1.23983
$246$	91.6374	5.84259
$247$	11.0793	0.704957
$248$	−6.63246	−0.421162
$249$	17.6376	1.11774
$250$	5.79750	0.366666
$251$	−24.0014	−1.51496	−0.757478	−	0.652860i	$-0.773569\pi$
$251$	−24.0014	−1.51496	−0.757478	+	0.652860i	$0.773569\pi$
$252$	−106.794	−6.72742
$253$	0.161038	0.0101244
$254$	−5.38712	−0.338018
$255$	−18.4668	−1.15644
$256$	−30.3898	−1.89936
$257$	11.2064	0.699035	0.349518	−	0.936930i	$-0.386346\pi$
$257$	11.2064	0.699035	0.349518	+	0.936930i	$0.386346\pi$
$258$	−46.1686	−2.87433
$259$	−5.05945	−0.314379
$260$	−52.2987	−3.24343
$261$	−22.2968	−1.38014
$262$	−27.2397	−1.68287
$263$	−23.4398	−1.44536	−0.722680	−	0.691183i	$-0.757090\pi$
$263$	−23.4398	−1.44536	−0.722680	+	0.691183i	$0.757090\pi$
$264$	−3.22872	−0.198714
$265$	6.51888	0.400451
$266$	−26.3762	−1.61723
$267$	−25.8700	−1.58322
$268$	−20.4546	−1.24946
$269$	4.30635	0.262563	0.131281	−	0.991345i	$-0.458091\pi$
$269$	4.30635	0.262563	0.131281	+	0.991345i	$0.458091\pi$
$270$	−86.1566	−5.24332
$271$	6.66409	0.404815	0.202407	−	0.979301i	$-0.435124\pi$
$271$	6.66409	0.404815	0.202407	+	0.979301i	$0.435124\pi$
$272$	−13.0924	−0.793841
$273$	44.1393	2.67143
$274$	36.7525	2.22030
$275$	0.722250	0.0435533
$276$	12.9691	0.780650
$277$	1.27841	0.0768124	0.0384062	−	0.999262i	$-0.487772\pi$
$277$	1.27841	0.0768124	0.0384062	+	0.999262i	$0.487772\pi$
$278$	−25.8898	−1.55277
$279$	7.15461	0.428336
$280$	68.1432	4.07234
$281$	−14.2405	−0.849516	−0.424758	−	0.905307i	$-0.639641\pi$
$281$	−14.2405	−0.849516	−0.424758	+	0.905307i	$0.639641\pi$
$282$	53.2087	3.16853
$283$	−6.30907	−0.375035	−0.187518	−	0.982261i	$-0.560044\pi$
$283$	−6.30907	−0.375035	−0.187518	+	0.982261i	$0.560044\pi$
$284$	−36.4409	−2.16237
$285$	−26.8277	−1.58914
$286$	1.67692	0.0991585
$287$	42.6887	2.51983
$288$	−30.9150	−1.82168
$289$	−13.1618	−0.774223
$290$	25.9948	1.52647
$291$	−36.9577	−2.16650
$292$	8.88042	0.519687
$293$	0.674130	0.0393831	0.0196915	−	0.999806i	$-0.493732\pi$
$293$	0.674130	0.0393831	0.0196915	+	0.999806i	$0.493732\pi$
$294$	−50.1131	−2.92265
$295$	−26.7645	−1.55829
$296$	−8.47235	−0.492445
$297$	1.90167	0.110346
$298$	−1.41273	−0.0818372
$299$	−3.68658	−0.213201
$300$	58.1662	3.35823
$301$	−21.5074	−1.23966
$302$	−38.9478	−2.24119
$303$	12.3021	0.706736
$304$	−19.0200	−1.09087
$305$	−6.65107	−0.380839
$306$	32.7968	1.87487
$307$	−13.5539	−0.773564	−0.386782	−	0.922171i	$-0.626413\pi$
$307$	−13.5539	−0.773564	−0.386782	+	0.922171i	$0.626413\pi$
$308$	−2.74815	−0.156590
$309$	−29.6870	−1.68883
$310$	−8.34122	−0.473750
$311$	−9.13194	−0.517825	−0.258912	−	0.965901i	$-0.583364\pi$
$311$	−9.13194	−0.517825	−0.258912	+	0.965901i	$0.583364\pi$
$312$	73.9139	4.18455
$313$	−1.55639	−0.0879722	−0.0439861	−	0.999032i	$-0.514006\pi$
$313$	−1.55639	−0.0879722	−0.0439861	+	0.999032i	$0.514006\pi$
$314$	−30.7106	−1.73310
$315$	−73.5079	−4.14170
$316$	−41.8145	−2.35225
$317$	10.1853	0.572065	0.286033	−	0.958220i	$-0.407663\pi$
$317$	10.1853	0.572065	0.286033	+	0.958220i	$0.407663\pi$
$318$	−16.8336	−0.943981
$319$	−0.573765	−0.0321247
$320$	−4.60152	−0.257233
$321$	0.453584	0.0253166
$322$	8.77657	0.489099
$323$	5.57599	0.310256
$324$	65.5688	3.64271
$325$	−16.5342	−0.917153
$326$	5.85747	0.324415
$327$	33.5510	1.85537
$328$	71.4848	3.94709
$329$	24.7869	1.36655
$330$	−4.06055	−0.223526
$331$	−18.5752	−1.02098	−0.510492	−	0.859883i	$-0.670537\pi$
$331$	−18.5752	−1.02098	−0.510492	+	0.859883i	$0.670537\pi$
$332$	25.1391	1.37969
$333$	9.13935	0.500833
$334$	−19.1096	−1.04563
$335$	−14.0792	−0.769227
$336$	−75.7748	−4.13385
$337$	−34.5453	−1.88180	−0.940902	−	0.338679i	$-0.890020\pi$
$337$	−34.5453	−1.88180	−0.940902	+	0.338679i	$0.890020\pi$
$338$	−5.45526	−0.296727
$339$	25.9071	1.40708
$340$	−26.3209	−1.42745
$341$	0.184110	0.00997011
$342$	47.6458	2.57639
$343$	2.26184	0.122128
$344$	−36.0154	−1.94182
$345$	8.92681	0.480603
$346$	−6.07009	−0.326330
$347$	15.7789	0.847057	0.423528	−	0.905883i	$-0.360791\pi$
$347$	15.7789	0.847057	0.423528	+	0.905883i	$0.360791\pi$
$348$	−46.2080	−2.47701
$349$	−31.7842	−1.70137	−0.850685	−	0.525676i	$-0.823812\pi$
$349$	−31.7842	−1.70137	−0.850685	+	0.525676i	$0.823812\pi$
$350$	39.3627	2.10402
$351$	−43.5343	−2.32369
$352$	−0.795537	−0.0424022
$353$	−23.5158	−1.25162	−0.625811	−	0.779975i	$-0.715232\pi$
$353$	−23.5158	−1.25162	−0.625811	+	0.779975i	$0.715232\pi$
$354$	69.1135	3.67334
$355$	−25.0827	−1.33125
$356$	−36.8728	−1.95425
$357$	22.2145	1.17571
$358$	−45.0896	−2.38306
$359$	32.2749	1.70341	0.851703	−	0.524025i	$-0.175570\pi$
$359$	32.2749	1.70341	0.851703	+	0.524025i	$0.175570\pi$
$360$	−123.093	−6.48759
$361$	−10.8995	−0.573656
$362$	−29.5195	−1.55151
$363$	−34.0068	−1.78489
$364$	62.9123	3.29750
$365$	6.11250	0.319943
$366$	17.1750	0.897750
$367$	−6.82389	−0.356204	−0.178102	−	0.984012i	$-0.556996\pi$
$367$	−6.82389	−0.356204	−0.178102	+	0.984012i	$0.556996\pi$
$368$	6.32882	0.329913
$369$	−77.1125	−4.01432
$370$	−10.6551	−0.553934
$371$	−7.84182	−0.407127
$372$	14.8272	0.768756
$373$	8.29617	0.429560	0.214780	−	0.976662i	$-0.431097\pi$
$373$	8.29617	0.429560	0.214780	+	0.976662i	$0.431097\pi$
$374$	0.843962	0.0436403
$375$	−7.09344	−0.366304
$376$	41.5072	2.14057
$377$	13.1350	0.676487
$378$	103.641	5.33073
$379$	16.9233	0.869292	0.434646	−	0.900601i	$-0.356873\pi$
$379$	16.9233	0.869292	0.434646	+	0.900601i	$0.356873\pi$
$380$	−38.2379	−1.96156
$381$	6.59132	0.337684
$382$	−0.437449	−0.0223818
$383$	22.5259	1.15102	0.575510	−	0.817795i	$-0.304804\pi$
$383$	22.5259	1.15102	0.575510	+	0.817795i	$0.304804\pi$
$384$	40.8857	2.08644
$385$	−1.89158	−0.0964040
$386$	−14.2484	−0.725222
$387$	38.8507	1.97489
$388$	−52.6762	−2.67423
$389$	30.6306	1.55303	0.776516	−	0.630098i	$-0.216985\pi$
$389$	30.6306	1.55303	0.776516	+	0.630098i	$0.216985\pi$
$390$	92.9568	4.70705
$391$	−1.85539	−0.0938309
$392$	−39.0924	−1.97446
$393$	33.3286	1.68121
$394$	63.9016	3.21932
$395$	−28.7814	−1.44815
$396$	4.96423	0.249462
$397$	23.3269	1.17074	0.585372	−	0.810765i	$-0.300948\pi$
$397$	23.3269	1.17074	0.585372	+	0.810765i	$0.300948\pi$
$398$	56.7706	2.84565
$399$	32.2722	1.61563
$400$	28.3846	1.41923
$401$	18.6762	0.932645	0.466322	−	0.884615i	$-0.345579\pi$
$401$	18.6762	0.932645	0.466322	+	0.884615i	$0.345579\pi$
$402$	36.3564	1.81329
$403$	−4.21476	−0.209952
$404$	17.5343	0.872365
$405$	45.1318	2.24262
$406$	−31.2702	−1.55191
$407$	0.235183	0.0116576
$408$	37.1994	1.84165
$409$	6.90958	0.341657	0.170828	−	0.985301i	$-0.445356\pi$
$409$	6.90958	0.341657	0.170828	+	0.985301i	$0.445356\pi$
$410$	89.9018	4.43994
$411$	−44.9679	−2.21810
$412$	−42.3132	−2.08462
$413$	32.1961	1.58427
$414$	−15.8539	−0.779178
$415$	17.3036	0.849398
$416$	18.2119	0.892913
$417$	31.6771	1.55123
$418$	1.22607	0.0599691
$419$	−2.57087	−0.125595	−0.0627977	−	0.998026i	$-0.520002\pi$
$419$	−2.57087	−0.125595	−0.0627977	+	0.998026i	$0.520002\pi$
$420$	−152.338	−7.43333
$421$	2.07354	0.101058	0.0505290	−	0.998723i	$-0.483909\pi$
$421$	2.07354	0.101058	0.0505290	+	0.998723i	$0.483909\pi$
$422$	43.5879	2.12183
$423$	−44.7749	−2.17703
$424$	−13.1316	−0.637727
$425$	−8.32135	−0.403645
$426$	64.7707	3.13815
$427$	8.00084	0.387188
$428$	0.646499	0.0312497
$429$	−2.05177	−0.0990604
$430$	−45.2942	−2.18428
$431$	−19.2415	−0.926832	−0.463416	−	0.886141i	$-0.653376\pi$
$431$	−19.2415	−0.926832	−0.463416	+	0.886141i	$0.653376\pi$
$432$	74.7362	3.59575
$433$	5.51643	0.265103	0.132551	−	0.991176i	$-0.457683\pi$
$433$	5.51643	0.265103	0.132551	+	0.991176i	$0.457683\pi$
$434$	10.0340	0.481647
$435$	−31.8055	−1.52496
$436$	47.8206	2.29019
$437$	−2.69542	−0.128939
$438$	−15.7842	−0.754199
$439$	14.8003	0.706380	0.353190	−	0.935552i	$-0.385097\pi$
$439$	14.8003	0.706380	0.353190	+	0.935552i	$0.385097\pi$
$440$	−3.16757	−0.151008
$441$	42.1700	2.00809
$442$	−19.3205	−0.918984
$443$	−38.5532	−1.83172	−0.915860	−	0.401498i	$-0.868490\pi$
$443$	−38.5532	−1.83172	−0.915860	+	0.401498i	$0.868490\pi$
$444$	18.9404	0.898871
$445$	−25.3800	−1.20313
$446$	−37.0243	−1.75315
$447$	1.72852	0.0817563
$448$	5.53536	0.261521
$449$	18.5051	0.873308	0.436654	−	0.899630i	$-0.356163\pi$
$449$	18.5051	0.873308	0.436654	+	0.899630i	$0.356163\pi$
$450$	−71.1044	−3.35189
$451$	−1.98434	−0.0934389
$452$	36.9258	1.73684
$453$	47.6539	2.23898
$454$	68.3508	3.20786
$455$	43.3033	2.03009
$456$	54.0417	2.53073
$457$	−14.4840	−0.677532	−0.338766	−	0.940871i	$-0.610010\pi$
$457$	−14.4840	−0.677532	−0.338766	+	0.940871i	$0.610010\pi$
$458$	−17.5721	−0.821090
$459$	−21.9100	−1.02267
$460$	12.7235	0.593236
$461$	3.94914	0.183930	0.0919648	−	0.995762i	$-0.470685\pi$
$461$	3.94914	0.183930	0.0919648	+	0.995762i	$0.470685\pi$
$462$	4.88461	0.227252
$463$	29.8643	1.38791	0.693956	−	0.720018i	$-0.255866\pi$
$463$	29.8643	1.38791	0.693956	+	0.720018i	$0.255866\pi$
$464$	−22.5491	−1.04682
$465$	10.2058	0.473281
$466$	−38.6455	−1.79022
$467$	33.5668	1.55329	0.776643	−	0.629941i	$-0.216921\pi$
$467$	33.5668	1.55329	0.776643	+	0.629941i	$0.216921\pi$
$468$	−113.644	−5.25321
$469$	16.9364	0.782050
$470$	52.2009	2.40785
$471$	37.5755	1.73139
$472$	53.9143	2.48161
$473$	0.999747	0.0459684
$474$	74.3218	3.41371
$475$	−12.0889	−0.554676
$476$	31.6625	1.45125
$477$	14.1654	0.648589
$478$	−22.8633	−1.04574
$479$	−10.0596	−0.459634	−0.229817	−	0.973234i	$-0.573813\pi$
$479$	−10.0596	−0.459634	−0.229817	+	0.973234i	$0.573813\pi$
$480$	−44.0990	−2.01283
$481$	−5.38396	−0.245488
$482$	8.64765	0.393890
$483$	−10.7384	−0.488615
$484$	−48.4703	−2.20319
$485$	−36.2577	−1.64638
$486$	−31.5471	−1.43101
$487$	19.1872	0.869454	0.434727	−	0.900562i	$-0.356845\pi$
$487$	19.1872	0.869454	0.434727	+	0.900562i	$0.356845\pi$
$488$	13.3979	0.606494
$489$	−7.16681	−0.324094
$490$	−49.1639	−2.22100
$491$	−13.7879	−0.622238	−0.311119	−	0.950371i	$-0.600704\pi$
$491$	−13.7879	−0.622238	−0.311119	+	0.950371i	$0.600704\pi$
$492$	−159.808	−7.20471
$493$	6.61059	0.297726
$494$	−28.0680	−1.26284
$495$	3.41694	0.153580
$496$	7.23556	0.324886
$497$	30.1730	1.35344
$498$	−44.6827	−2.00228
$499$	−13.9005	−0.622270	−0.311135	−	0.950366i	$-0.600709\pi$
$499$	−13.9005	−0.622270	−0.311135	+	0.950366i	$0.600709\pi$
$500$	−10.1104	−0.452149
$501$	23.3812	1.04459
$502$	60.8047	2.71384
$503$	1.24041	0.0553073	0.0276537	−	0.999618i	$-0.491196\pi$
$503$	1.24041	0.0553073	0.0276537	+	0.999618i	$0.491196\pi$
$504$	148.074	6.59574
$505$	12.0691	0.537067
$506$	−0.407970	−0.0181365
$507$	6.67469	0.296433
$508$	9.39469	0.416822
$509$	−10.8810	−0.482292	−0.241146	−	0.970489i	$-0.577523\pi$
$509$	−10.8810	−0.482292	−0.241146	+	0.970489i	$0.577523\pi$
$510$	46.7834	2.07160
$511$	−7.35298	−0.325277
$512$	50.6080	2.23658
$513$	−31.8298	−1.40532
$514$	−28.3900	−1.25223
$515$	−29.1247	−1.28339
$516$	80.5143	3.54444
$517$	−1.15219	−0.0506735
$518$	12.8175	0.563168
$519$	7.42695	0.326007
$520$	72.5140	3.17995
$521$	37.4474	1.64060	0.820300	−	0.571934i	$-0.193807\pi$
$521$	37.4474	1.64060	0.820300	+	0.571934i	$0.193807\pi$
$522$	56.4863	2.47234
$523$	12.9011	0.564124	0.282062	−	0.959396i	$-0.408982\pi$
$523$	12.9011	0.564124	0.282062	+	0.959396i	$0.408982\pi$
$524$	47.5037	2.07521
$525$	−48.1615	−2.10194
$526$	59.3818	2.58917
$527$	−2.12121	−0.0924013
$528$	3.52231	0.153289
$529$	−22.1031	−0.961005
$530$	−16.5148	−0.717356
$531$	−58.1588	−2.52388
$532$	45.9979	1.99426
$533$	45.4268	1.96765
$534$	65.5384	2.83612
$535$	0.444993	0.0192387
$536$	28.3610	1.22501
$537$	55.1686	2.38070
$538$	−10.9096	−0.470346
$539$	1.08516	0.0467412
$540$	150.250	6.46573
$541$	−38.1375	−1.63966	−0.819829	−	0.572608i	$-0.805932\pi$
$541$	−38.1375	−1.63966	−0.819829	+	0.572608i	$0.805932\pi$
$542$	−16.8826	−0.725172
$543$	36.1181	1.54998
$544$	9.16571	0.392977
$545$	32.9155	1.40995
$546$	−111.822	−4.78552
$547$	−34.0770	−1.45703	−0.728513	−	0.685032i	$-0.759788\pi$
$547$	−34.0770	−1.45703	−0.728513	+	0.685032i	$0.759788\pi$
$548$	−64.0934	−2.73793
$549$	−14.4527	−0.616825
$550$	−1.82973	−0.0780201
$551$	9.60357	0.409126
$552$	−17.9821	−0.765370
$553$	34.6223	1.47229
$554$	−3.23870	−0.137599
$555$	13.0369	0.553386
$556$	45.1497	1.91478
$557$	24.0452	1.01883	0.509415	−	0.860521i	$-0.329862\pi$
$557$	24.0452	1.01883	0.509415	+	0.860521i	$0.329862\pi$
$558$	−18.1253	−0.767307
$559$	−22.8868	−0.968011
$560$	−74.3396	−3.14142
$561$	−1.03262	−0.0435971
$562$	36.0765	1.52180
$563$	36.5974	1.54240	0.771199	−	0.636594i	$-0.219657\pi$
$563$	36.5974	1.54240	0.771199	+	0.636594i	$0.219657\pi$
$564$	−92.7916	−3.90723
$565$	25.4165	1.06928
$566$	15.9832	0.671826
$567$	−54.2909	−2.28000
$568$	50.5265	2.12005
$569$	−23.2193	−0.973405	−0.486703	−	0.873568i	$-0.661800\pi$
$569$	−23.2193	−0.973405	−0.486703	+	0.873568i	$0.661800\pi$
$570$	67.9647	2.84673
$571$	18.7444	0.784428	0.392214	−	0.919874i	$-0.371709\pi$
$571$	18.7444	0.784428	0.392214	+	0.919874i	$0.371709\pi$
$572$	−2.92441	−0.122276
$573$	0.535233	0.0223597
$574$	−108.147	−4.51395
$575$	4.02252	0.167751
$576$	−9.99903	−0.416626
$577$	5.50732	0.229273	0.114636	−	0.993408i	$-0.463430\pi$
$577$	5.50732	0.229273	0.114636	+	0.993408i	$0.463430\pi$
$578$	33.3438	1.38692
$579$	17.4333	0.724505
$580$	−45.3328	−1.88234
$581$	−20.8152	−0.863558
$582$	93.6277	3.88099
$583$	0.364519	0.0150968
$584$	−12.3130	−0.509515
$585$	−78.2228	−3.23411
$586$	−1.70783	−0.0705496
$587$	−2.65778	−0.109698	−0.0548491	−	0.998495i	$-0.517468\pi$
$587$	−2.65778	−0.109698	−0.0548491	+	0.998495i	$0.517468\pi$
$588$	87.3931	3.60403
$589$	−3.08160	−0.126975
$590$	67.8045	2.79147
$591$	−78.1858	−3.21613
$592$	9.24274	0.379874
$593$	11.6861	0.479891	0.239946	−	0.970786i	$-0.422870\pi$
$593$	11.6861	0.479891	0.239946	+	0.970786i	$0.422870\pi$
$594$	−4.81766	−0.197671
$595$	21.7937	0.893455
$596$	2.46368	0.100916
$597$	−69.4607	−2.84284
$598$	9.33950	0.381921
$599$	−23.6253	−0.965303	−0.482651	−	0.875813i	$-0.660326\pi$
$599$	−23.6253	−0.965303	−0.482651	+	0.875813i	$0.660326\pi$
$600$	−80.6494	−3.29250
$601$	−9.86130	−0.402251	−0.201125	−	0.979565i	$-0.564460\pi$
$601$	−9.86130	−0.402251	−0.201125	+	0.979565i	$0.564460\pi$
$602$	54.4862	2.22069
$603$	−30.5938	−1.24588
$604$	67.9217	2.76370
$605$	−33.3627	−1.35639
$606$	−31.1658	−1.26602
$607$	37.3298	1.51517	0.757584	−	0.652738i	$-0.226380\pi$
$607$	37.3298	1.51517	0.757584	+	0.652738i	$0.226380\pi$
$608$	13.3155	0.540016
$609$	38.2601	1.55038
$610$	16.8497	0.682223
$611$	26.3768	1.06709
$612$	−57.1950	−2.31197
$613$	−22.3001	−0.900693	−0.450347	−	0.892854i	$-0.648700\pi$
$613$	−22.3001	−0.900693	−0.450347	+	0.892854i	$0.648700\pi$
$614$	34.3372	1.38574
$615$	−109.998	−4.43554
$616$	3.81040	0.153525
$617$	31.5230	1.26907	0.634533	−	0.772896i	$-0.281192\pi$
$617$	31.5230	1.26907	0.634533	+	0.772896i	$0.281192\pi$
$618$	75.2084	3.02532
$619$	−22.7408	−0.914028	−0.457014	−	0.889459i	$-0.651081\pi$
$619$	−22.7408	−0.914028	−0.457014	+	0.889459i	$0.651081\pi$
$620$	14.5464	0.584198
$621$	10.5912	0.425012
$622$	23.1346	0.927615
$623$	30.5306	1.22318
$624$	−80.6350	−3.22798
$625$	−28.1964	−1.12786
$626$	3.94291	0.157591
$627$	−1.50014	−0.0599097
$628$	53.5568	2.13715
$629$	−2.70964	−0.108041
$630$	186.223	7.41931
$631$	−48.4427	−1.92847	−0.964237	−	0.265041i	$-0.914614\pi$
$631$	−48.4427	−1.92847	−0.964237	+	0.265041i	$0.914614\pi$
$632$	57.9771	2.30621
$633$	−53.3313	−2.11973
$634$	−25.8033	−1.02478
$635$	6.46648	0.256614
$636$	29.3564	1.16406
$637$	−24.8422	−0.984284
$638$	1.45356	0.0575471
$639$	−54.5043	−2.15616
$640$	40.1113	1.58554
$641$	25.8435	1.02076	0.510378	−	0.859950i	$-0.329506\pi$
$641$	25.8435	1.02076	0.510378	+	0.859950i	$0.329506\pi$
$642$	−1.14910	−0.0453514
$643$	−11.0082	−0.434123	−0.217061	−	0.976158i	$-0.569647\pi$
$643$	−11.0082	−0.434123	−0.217061	+	0.976158i	$0.569647\pi$
$644$	−15.3056	−0.603126
$645$	55.4190	2.18212
$646$	−14.1261	−0.555783
$647$	−4.93515	−0.194021	−0.0970105	−	0.995283i	$-0.530928\pi$
$647$	−4.93515	−0.194021	−0.0970105	+	0.995283i	$0.530928\pi$
$648$	−90.9133	−3.57141
$649$	−1.49660	−0.0587468
$650$	41.8874	1.64296
$651$	−12.2769	−0.481171
$652$	−10.2149	−0.400048
$653$	6.38627	0.249914	0.124957	−	0.992162i	$-0.460121\pi$
$653$	6.38627	0.249914	0.124957	+	0.992162i	$0.460121\pi$
$654$	−84.9973	−3.32366
$655$	32.6974	1.27759
$656$	−77.9850	−3.04480
$657$	13.2824	0.518194
$658$	−62.7946	−2.44799
$659$	46.8059	1.82330	0.911650	−	0.410968i	$-0.134809\pi$
$659$	46.8059	1.82330	0.911650	+	0.410968i	$0.134809\pi$
$660$	7.08127	0.275638
$661$	−37.7279	−1.46744	−0.733722	−	0.679450i	$-0.762219\pi$
$661$	−37.7279	−1.46744	−0.733722	+	0.679450i	$0.762219\pi$
$662$	47.0579	1.82896
$663$	23.6393	0.918074
$664$	−34.8562	−1.35268
$665$	31.6609	1.22776
$666$	−23.1534	−0.897176
$667$	−3.19555	−0.123732
$668$	33.3255	1.28940
$669$	45.3005	1.75142
$670$	35.6678	1.37797
$671$	−0.371911	−0.0143575
$672$	53.0484	2.04639
$673$	18.8843	0.727938	0.363969	−	0.931411i	$-0.381421\pi$
$673$	18.8843	0.727938	0.363969	+	0.931411i	$0.381421\pi$
$674$	87.5163	3.37100
$675$	47.5014	1.82833
$676$	9.51352	0.365905
$677$	−0.619228	−0.0237989	−0.0118994	−	0.999929i	$-0.503788\pi$
$677$	−0.619228	−0.0237989	−0.0118994	+	0.999929i	$0.503788\pi$
$678$	−65.6326	−2.52060
$679$	43.6158	1.67382
$680$	36.4949	1.39951
$681$	−83.6295	−3.20469
$682$	−0.466420	−0.0178601
$683$	−28.4303	−1.08785	−0.543927	−	0.839132i	$-0.683063\pi$
$683$	−28.4303	−1.08785	−0.543927	+	0.839132i	$0.683063\pi$
$684$	−83.0903	−3.17704
$685$	−44.1162	−1.68560
$686$	−5.73009	−0.218776
$687$	21.5000	0.820278
$688$	39.2903	1.49793
$689$	−8.34480	−0.317912
$690$	−22.6150	−0.860938
$691$	−33.4185	−1.27130	−0.635649	−	0.771978i	$-0.719268\pi$
$691$	−33.4185	−1.27130	−0.635649	+	0.771978i	$0.719268\pi$
$692$	10.5857	0.402409
$693$	−4.11038	−0.156140
$694$	−39.9739	−1.51739
$695$	31.0771	1.17882
$696$	64.0689	2.42853
$697$	22.8624	0.865976
$698$	80.5214	3.04778
$699$	47.2840	1.78845
$700$	−68.6452	−2.59455
$701$	37.4300	1.41371	0.706855	−	0.707358i	$-0.250113\pi$
$701$	37.4300	1.41371	0.706855	+	0.707358i	$0.250113\pi$
$702$	110.289	4.16259
$703$	−3.93645	−0.148466
$704$	−0.257305	−0.00969756
$705$	−63.8696	−2.40547
$706$	59.5745	2.24211
$707$	−14.5184	−0.546020
$708$	−120.528	−4.52973
$709$	1.00107	0.0375959	0.0187979	−	0.999823i	$-0.494016\pi$
$709$	1.00107	0.0375959	0.0187979	+	0.999823i	$0.494016\pi$
$710$	63.5440	2.38476
$711$	−62.5415	−2.34549
$712$	51.1253	1.91600
$713$	1.02539	0.0384011
$714$	−56.2776	−2.10614
$715$	−2.01291	−0.0752785
$716$	78.6325	2.93864
$717$	27.9740	1.04471
$718$	−81.7646	−3.05143
$719$	−4.55402	−0.169836	−0.0849182	−	0.996388i	$-0.527063\pi$
$719$	−4.55402	−0.169836	−0.0849182	+	0.996388i	$0.527063\pi$
$720$	134.286	5.00456
$721$	35.0353	1.30478
$722$	27.6124	1.02763
$723$	−10.5807	−0.393500
$724$	51.4796	1.91322
$725$	−14.3319	−0.532275
$726$	86.1519	3.19740
$727$	−1.90812	−0.0707684	−0.0353842	−	0.999374i	$-0.511265\pi$
$727$	−1.90812	−0.0707684	−0.0353842	+	0.999374i	$0.511265\pi$
$728$	−87.2300	−3.23296
$729$	−5.92490	−0.219441
$730$	−15.4853	−0.573136
$731$	−11.5185	−0.426027
$732$	−29.9517	−1.10705
$733$	2.36084	0.0871995	0.0435997	−	0.999049i	$-0.486117\pi$
$733$	2.36084	0.0871995	0.0435997	+	0.999049i	$0.486117\pi$
$734$	17.2875	0.638093
$735$	60.1537	2.21880
$736$	−4.43069	−0.163317
$737$	−0.787271	−0.0289995
$738$	195.355	7.19112
$739$	9.10589	0.334965	0.167483	−	0.985875i	$-0.446436\pi$
$739$	9.10589	0.334965	0.167483	+	0.985875i	$0.446436\pi$
$740$	18.5817	0.683075
$741$	34.3421	1.26159
$742$	19.8663	0.729315
$743$	6.34710	0.232853	0.116426	−	0.993199i	$-0.462856\pi$
$743$	6.34710	0.232853	0.116426	+	0.993199i	$0.462856\pi$
$744$	−20.5585	−0.753709
$745$	1.69578	0.0621287
$746$	−21.0173	−0.769499
$747$	37.6003	1.37572
$748$	−1.47180	−0.0538143
$749$	−0.535301	−0.0195595
$750$	17.9704	0.656185
$751$	−30.0904	−1.09801	−0.549007	−	0.835818i	$-0.684994\pi$
$751$	−30.0904	−1.09801	−0.549007	+	0.835818i	$0.684994\pi$
$752$	−45.2815	−1.65125
$753$	−74.3965	−2.71116
$754$	−33.2759	−1.21184
$755$	46.7514	1.70146
$756$	−180.742	−6.57352
$757$	23.2500	0.845036	0.422518	−	0.906355i	$-0.361146\pi$
$757$	23.2500	0.845036	0.422518	+	0.906355i	$0.361146\pi$
$758$	−42.8731	−1.55722
$759$	0.499165	0.0181185
$760$	53.0181	1.92317
$761$	28.1083	1.01892	0.509462	−	0.860493i	$-0.329845\pi$
$761$	28.1083	1.01892	0.509462	+	0.860493i	$0.329845\pi$
$762$	−16.6983	−0.604916
$763$	−39.5954	−1.43345
$764$	0.762874	0.0275998
$765$	−39.3680	−1.42335
$766$	−57.0666	−2.06190
$767$	34.2612	1.23710
$768$	−94.1982	−3.39909
$769$	−0.684961	−0.0247003	−0.0123502	−	0.999924i	$-0.503931\pi$
$769$	−0.684961	−0.0247003	−0.0123502	+	0.999924i	$0.503931\pi$
$770$	4.79209	0.172695
$771$	34.7361	1.25099
$772$	24.8480	0.894298
$773$	−17.5505	−0.631246	−0.315623	−	0.948885i	$-0.602214\pi$
$773$	−17.5505	−0.631246	−0.315623	+	0.948885i	$0.602214\pi$
$774$	−98.4235	−3.53776
$775$	4.59884	0.165195
$776$	73.0373	2.62189
$777$	−15.6826	−0.562611
$778$	−77.5988	−2.78205
$779$	33.2135	1.19000
$780$	−162.109	−5.80443
$781$	−1.40256	−0.0501876
$782$	4.70039	0.168086
$783$	−37.7358	−1.34857
$784$	42.6471	1.52311
$785$	36.8638	1.31572
$786$	−84.4340	−3.01166
$787$	11.0065	0.392340	0.196170	−	0.980570i	$-0.437149\pi$
$787$	11.0065	0.392340	0.196170	+	0.980570i	$0.437149\pi$
$788$	−111.439	−3.96986
$789$	−72.6557	−2.58661
$790$	72.9141	2.59417
$791$	−30.5745	−1.08710
$792$	−6.88307	−0.244579
$793$	8.51402	0.302342
$794$	−59.0959	−2.09723
$795$	20.2064	0.716646
$796$	−99.0032	−3.50908
$797$	18.5015	0.655356	0.327678	−	0.944789i	$-0.393734\pi$
$797$	18.5015	0.655356	0.327678	+	0.944789i	$0.393734\pi$
$798$	−81.7576	−2.89419
$799$	13.2749	0.469633
$800$	−19.8715	−0.702564
$801$	−55.1503	−1.94864
$802$	−47.3138	−1.67071
$803$	0.341795	0.0120617
$804$	−63.4026	−2.23604
$805$	−10.5350	−0.371311
$806$	10.6776	0.376102
$807$	13.3483	0.469881
$808$	−24.3119	−0.855290
$809$	−31.7178	−1.11514	−0.557570	−	0.830130i	$-0.688266\pi$
$809$	−31.7178	−1.11514	−0.557570	+	0.830130i	$0.688266\pi$
$810$	−114.336	−4.01735
$811$	9.13190	0.320664	0.160332	−	0.987063i	$-0.448743\pi$
$811$	9.13190	0.320664	0.160332	+	0.987063i	$0.448743\pi$
$812$	54.5327	1.91372
$813$	20.6565	0.724454
$814$	−0.595808	−0.0208830
$815$	−7.03107	−0.246287
$816$	−40.5820	−1.42065
$817$	−16.7336	−0.585433
$818$	−17.5046	−0.612033
$819$	94.0974	3.28803
$820$	−156.781	−5.47504
$821$	−39.0171	−1.36171	−0.680853	−	0.732420i	$-0.738391\pi$
$821$	−39.0171	−1.36171	−0.680853	+	0.732420i	$0.738391\pi$
$822$	113.921	3.97344
$823$	−14.1474	−0.493148	−0.246574	−	0.969124i	$-0.579305\pi$
$823$	−14.1474	−0.493148	−0.246574	+	0.969124i	$0.579305\pi$
$824$	58.6687	2.04382
$825$	2.23874	0.0779429
$826$	−81.5648	−2.83800
$827$	20.6637	0.718548	0.359274	−	0.933232i	$-0.383024\pi$
$827$	20.6637	0.718548	0.359274	+	0.933232i	$0.383024\pi$
$828$	27.6479	0.960832
$829$	35.4736	1.23205	0.616025	−	0.787727i	$-0.288742\pi$
$829$	35.4736	1.23205	0.616025	+	0.787727i	$0.288742\pi$
$830$	−43.8364	−1.52158
$831$	3.96266	0.137463
$832$	5.89040	0.204213
$833$	−12.5026	−0.433189
$834$	−80.2500	−2.77883
$835$	22.9384	0.793814
$836$	−2.13817	−0.0739500
$837$	12.1087	0.418537
$838$	6.51300	0.224988
$839$	21.3240	0.736186	0.368093	−	0.929789i	$-0.380011\pi$
$839$	21.3240	0.736186	0.368093	+	0.929789i	$0.380011\pi$
$840$	211.222	7.28784
$841$	−17.6145	−0.607398
$842$	−5.25306	−0.181032
$843$	−44.1408	−1.52029
$844$	−76.0137	−2.61650
$845$	6.54827	0.225267
$846$	113.432	3.89986
$847$	40.1333	1.37900
$848$	14.3257	0.491946
$849$	−19.5560	−0.671161
$850$	21.0811	0.723076
$851$	1.30984	0.0449006
$852$	−112.955	−3.86977
$853$	−32.4898	−1.11243	−0.556215	−	0.831038i	$-0.687747\pi$
$853$	−32.4898	−1.11243	−0.556215	+	0.831038i	$0.687747\pi$
$854$	−20.2692	−0.693596
$855$	−57.1921	−1.95593
$856$	−0.896393	−0.0306381
$857$	32.5228	1.11096	0.555479	−	0.831531i	$-0.312535\pi$
$857$	32.5228	1.11096	0.555479	+	0.831531i	$0.312535\pi$
$858$	5.19791	0.177454
$859$	4.21884	0.143945	0.0719726	−	0.997407i	$-0.477071\pi$
$859$	4.21884	0.143945	0.0719726	+	0.997407i	$0.477071\pi$
$860$	78.9893	2.69351
$861$	132.321	4.50949
$862$	48.7460	1.66030
$863$	6.49132	0.220967	0.110484	−	0.993878i	$-0.464760\pi$
$863$	6.49132	0.220967	0.110484	+	0.993878i	$0.464760\pi$
$864$	−52.3214	−1.78001
$865$	7.28629	0.247741
$866$	−13.9752	−0.474896
$867$	−40.7972	−1.38555
$868$	−17.4985	−0.593936
$869$	−1.60938	−0.0545946
$870$	80.5754	2.73176
$871$	18.0227	0.610676
$872$	−66.3049	−2.24537
$873$	−78.7873	−2.66655
$874$	6.82852	0.230978
$875$	8.37137	0.283004
$876$	27.5264	0.930030
$877$	47.7111	1.61109	0.805544	−	0.592535i	$-0.201873\pi$
$877$	47.7111	1.61109	0.805544	+	0.592535i	$0.201873\pi$
$878$	−37.4948	−1.26539
$879$	2.08958	0.0704798
$880$	3.45560	0.116488
$881$	−39.4951	−1.33062	−0.665312	−	0.746565i	$-0.731701\pi$
$881$	−39.4951	−1.33062	−0.665312	+	0.746565i	$0.731701\pi$
$882$	−106.832	−3.59723
$883$	32.0966	1.08014	0.540069	−	0.841621i	$-0.318398\pi$
$883$	32.0966	1.08014	0.540069	+	0.841621i	$0.318398\pi$
$884$	33.6934	1.13323
$885$	−82.9611	−2.78871
$886$	97.6699	3.28128
$887$	51.9984	1.74593	0.872967	−	0.487779i	$-0.162193\pi$
$887$	51.9984	1.74593	0.872967	+	0.487779i	$0.162193\pi$
$888$	−26.2615	−0.881278
$889$	−7.77879	−0.260892
$890$	64.2971	2.15524
$891$	2.52365	0.0845456
$892$	64.5674	2.16188
$893$	19.2852	0.645355
$894$	−4.37900	−0.146456
$895$	54.1237	1.80916
$896$	−48.2516	−1.61197
$897$	−11.4272	−0.381543
$898$	−46.8803	−1.56442
$899$	−3.65337	−0.121847
$900$	124.000	4.13334
$901$	−4.19978	−0.139915
$902$	5.02708	0.167384
$903$	−66.6657	−2.21850
$904$	−51.1988	−1.70285
$905$	35.4340	1.17787
$906$	−120.725	−4.01083
$907$	−21.2112	−0.704307	−0.352153	−	0.935942i	$-0.614550\pi$
$907$	−21.2112	−0.704307	−0.352153	+	0.935942i	$0.614550\pi$
$908$	−119.198	−3.95573
$909$	26.2259	0.869858
$910$	−109.704	−3.63664
$911$	20.5189	0.679820	0.339910	−	0.940458i	$-0.389603\pi$
$911$	20.5189	0.679820	0.339910	+	0.940458i	$0.389603\pi$
$912$	−58.9557	−1.95222
$913$	0.967571	0.0320219
$914$	36.6934	1.21371
$915$	−20.6161	−0.681548
$916$	30.6443	1.01252
$917$	−39.3330	−1.29889
$918$	55.5063	1.83198
$919$	−49.5649	−1.63500	−0.817498	−	0.575931i	$-0.804640\pi$
$919$	−49.5649	−1.63500	−0.817498	+	0.575931i	$0.804640\pi$
$920$	−17.6416	−0.581625
$921$	−42.0127	−1.38437
$922$	−10.0047	−0.329486
$923$	32.1083	1.05686
$924$	−8.51835	−0.280233
$925$	5.87458	0.193155
$926$	−75.6575	−2.48626
$927$	−63.2875	−2.07864
$928$	15.7862	0.518207
$929$	−16.5960	−0.544497	−0.272248	−	0.962227i	$-0.587767\pi$
$929$	−16.5960	−0.544497	−0.272248	+	0.962227i	$0.587767\pi$
$930$	−25.8550	−0.847820
$931$	−18.1632	−0.595275
$932$	67.3945	2.20758
$933$	−28.3060	−0.926697
$934$	−85.0374	−2.78251
$935$	−1.01306	−0.0331305
$936$	157.572	5.15039
$937$	−9.65970	−0.315569	−0.157784	−	0.987474i	$-0.550435\pi$
$937$	−9.65970	−0.315569	−0.157784	+	0.987474i	$0.550435\pi$
$938$	−42.9063	−1.40094
$939$	−4.82429	−0.157435
$940$	−91.0341	−2.96920
$941$	−49.7991	−1.62341	−0.811703	−	0.584071i	$-0.801459\pi$
$941$	−49.7991	−1.62341	−0.811703	+	0.584071i	$0.801459\pi$
$942$	−95.1928	−3.10155
$943$	−11.0516	−0.359891
$944$	−58.8168	−1.91432
$945$	−124.407	−4.04696
$946$	−2.53274	−0.0823464
$947$	42.5438	1.38249	0.691244	−	0.722621i	$-0.257063\pi$
$947$	42.5438	1.38249	0.691244	+	0.722621i	$0.257063\pi$
$948$	−129.611	−4.20957
$949$	−7.82460	−0.253997
$950$	30.6257	0.993629
$951$	31.5712	1.02377
$952$	−43.9012	−1.42285
$953$	41.4050	1.34124	0.670620	−	0.741801i	$-0.266028\pi$
$953$	41.4050	1.34124	0.670620	+	0.741801i	$0.266028\pi$
$954$	−35.8863	−1.16186
$955$	0.525096	0.0169917
$956$	39.8717	1.28954
$957$	−1.77848	−0.0574902
$958$	25.4847	0.823374
$959$	53.0692	1.71370
$960$	−14.2632	−0.460343
$961$	−29.8277	−0.962184
$962$	13.6396	0.439759
$963$	0.966963	0.0311600
$964$	−15.0808	−0.485719
$965$	17.1032	0.550570
$966$	27.2045	0.875290
$967$	11.2768	0.362637	0.181318	−	0.983424i	$-0.441964\pi$
$967$	11.2768	0.362637	0.181318	+	0.983424i	$0.441964\pi$
$968$	67.2056	2.16007
$969$	17.2837	0.555233
$970$	91.8544	2.94927
$971$	−19.6697	−0.631229	−0.315615	−	0.948887i	$-0.602211\pi$
$971$	−19.6697	−0.631229	−0.315615	+	0.948887i	$0.602211\pi$
$972$	55.0155	1.76462
$973$	−37.3839	−1.19847
$974$	−48.6084	−1.55751
$975$	−51.2506	−1.64133
$976$	−14.6162	−0.467852
$977$	−50.5421	−1.61698	−0.808492	−	0.588507i	$-0.799716\pi$
$977$	−50.5421	−1.61698	−0.808492	+	0.588507i	$0.799716\pi$
$978$	18.1562	0.580572
$979$	−1.41918	−0.0453573
$980$	85.7378	2.73880
$981$	71.5249	2.28361
$982$	34.9299	1.11466
$983$	−16.5151	−0.526750	−0.263375	−	0.964693i	$-0.584836\pi$
$983$	−16.5151	−0.526750	−0.263375	+	0.964693i	$0.584836\pi$
$984$	221.579	7.06369
$985$	−76.7050	−2.44402
$986$	−16.7471	−0.533337
$987$	76.8313	2.44557
$988$	48.9482	1.55725
$989$	5.56802	0.177053
$990$	−8.65640	−0.275118
$991$	44.9994	1.42945	0.714727	−	0.699404i	$-0.246551\pi$
$991$	44.9994	1.42945	0.714727	+	0.699404i	$0.246551\pi$
$992$	−5.06548	−0.160829
$993$	−57.5769	−1.82715
$994$	−76.4396	−2.42452
$995$	−68.1451	−2.16035
$996$	77.9230	2.46908
$997$	−59.0334	−1.86961	−0.934803	−	0.355166i	$-0.884424\pi$
$997$	−59.0334	−1.86961	−0.934803	+	0.355166i	$0.884424\pi$
$998$	35.2151	1.11471
$999$	15.4677	0.489376

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.18	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.18	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53338 q^{2} +3.09967 q^{3} +4.41800 q^{4} +3.04096 q^{5} -7.85264 q^{6} -3.65810 q^{7} -6.12571 q^{8} +6.60796 q^{9} +O(q^{10})\)	\(q-2.53338 q^{2} +3.09967 q^{3} +4.41800 q^{4} +3.04096 q^{5} -7.85264 q^{6} -3.65810 q^{7} -6.12571 q^{8} +6.60796 q^{9} -7.70391 q^{10} +0.170043 q^{11} +13.6943 q^{12} -3.89273 q^{13} +9.26734 q^{14} +9.42599 q^{15} +6.68272 q^{16} -1.95914 q^{17} -16.7405 q^{18} -2.84614 q^{19} +13.4350 q^{20} -11.3389 q^{21} -0.430783 q^{22} +0.947043 q^{23} -18.9877 q^{24} +4.24746 q^{25} +9.86176 q^{26} +11.1835 q^{27} -16.1615 q^{28} -3.37424 q^{29} -23.8796 q^{30} +1.08273 q^{31} -4.67845 q^{32} +0.527077 q^{33} +4.96323 q^{34} -11.1241 q^{35} +29.1940 q^{36} +1.38308 q^{37} +7.21036 q^{38} -12.0662 q^{39} -18.6280 q^{40} -11.6696 q^{41} +28.7257 q^{42} +5.87938 q^{43} +0.751250 q^{44} +20.0946 q^{45} -2.39922 q^{46} -6.77590 q^{47} +20.7142 q^{48} +6.38169 q^{49} -10.7604 q^{50} -6.07268 q^{51} -17.1981 q^{52} +2.14369 q^{53} -28.3320 q^{54} +0.517094 q^{55} +22.4084 q^{56} -8.82211 q^{57} +8.54821 q^{58} -8.80132 q^{59} +41.6440 q^{60} -2.18716 q^{61} -2.74295 q^{62} -24.1726 q^{63} -1.51318 q^{64} -11.8377 q^{65} -1.33529 q^{66} -4.62984 q^{67} -8.65546 q^{68} +2.93552 q^{69} +28.1817 q^{70} -8.24828 q^{71} -40.4784 q^{72} +2.01005 q^{73} -3.50387 q^{74} +13.1657 q^{75} -12.5743 q^{76} -0.622034 q^{77} +30.5682 q^{78} -9.46457 q^{79} +20.3219 q^{80} +14.8413 q^{81} +29.5636 q^{82} +5.69016 q^{83} -50.0953 q^{84} -5.95766 q^{85} -14.8947 q^{86} -10.4590 q^{87} -1.04163 q^{88} -8.34603 q^{89} -50.9071 q^{90} +14.2400 q^{91} +4.18403 q^{92} +3.35610 q^{93} +17.1659 q^{94} -8.65502 q^{95} -14.5016 q^{96} -11.9231 q^{97} -16.1672 q^{98} +1.12364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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