LMFDB - Embedded newform 6017.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64280 q^{2} -2.08644 q^{3} +4.98439 q^{4} +2.06491 q^{5} +5.51405 q^{6} +1.23299 q^{7} -7.88714 q^{8} +1.35325 q^{9} +O(q^{10})$	\(q-2.64280 q^{2} -2.08644 q^{3} +4.98439 q^{4} +2.06491 q^{5} +5.51405 q^{6} +1.23299 q^{7} -7.88714 q^{8} +1.35325 q^{9} -5.45715 q^{10} +1.00000 q^{11} -10.3996 q^{12} -2.09401 q^{13} -3.25854 q^{14} -4.30832 q^{15} +10.8753 q^{16} -0.272413 q^{17} -3.57636 q^{18} +0.942642 q^{19} +10.2923 q^{20} -2.57256 q^{21} -2.64280 q^{22} +0.723963 q^{23} +16.4561 q^{24} -0.736140 q^{25} +5.53404 q^{26} +3.43586 q^{27} +6.14570 q^{28} -1.30071 q^{29} +11.3860 q^{30} -9.46217 q^{31} -12.9671 q^{32} -2.08644 q^{33} +0.719934 q^{34} +2.54601 q^{35} +6.74511 q^{36} +4.59610 q^{37} -2.49121 q^{38} +4.36903 q^{39} -16.2862 q^{40} -8.53745 q^{41} +6.79877 q^{42} -4.60214 q^{43} +4.98439 q^{44} +2.79433 q^{45} -1.91329 q^{46} -0.972619 q^{47} -22.6908 q^{48} -5.47974 q^{49} +1.94547 q^{50} +0.568375 q^{51} -10.4373 q^{52} -0.725041 q^{53} -9.08028 q^{54} +2.06491 q^{55} -9.72475 q^{56} -1.96677 q^{57} +3.43750 q^{58} -9.66991 q^{59} -21.4743 q^{60} +9.73833 q^{61} +25.0066 q^{62} +1.66854 q^{63} +12.5187 q^{64} -4.32394 q^{65} +5.51405 q^{66} +4.14318 q^{67} -1.35781 q^{68} -1.51051 q^{69} -6.72860 q^{70} -3.37696 q^{71} -10.6732 q^{72} +13.5527 q^{73} -12.1466 q^{74} +1.53592 q^{75} +4.69849 q^{76} +1.23299 q^{77} -11.5465 q^{78} -5.32475 q^{79} +22.4566 q^{80} -11.2285 q^{81} +22.5628 q^{82} +14.7990 q^{83} -12.8226 q^{84} -0.562510 q^{85} +12.1625 q^{86} +2.71385 q^{87} -7.88714 q^{88} -18.6259 q^{89} -7.38487 q^{90} -2.58189 q^{91} +3.60851 q^{92} +19.7423 q^{93} +2.57044 q^{94} +1.94647 q^{95} +27.0551 q^{96} +4.59240 q^{97} +14.4818 q^{98} +1.35325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.64280	−1.86874	−0.934371	−	0.356303i	$-0.884037\pi$
$2$	−2.64280	−1.86874	−0.934371	+	0.356303i	$0.884037\pi$
$3$	−2.08644	−1.20461	−0.602304	−	0.798267i	$-0.705751\pi$
$3$	−2.08644	−1.20461	−0.602304	+	0.798267i	$0.705751\pi$
$4$	4.98439	2.49219
$5$	2.06491	0.923456	0.461728	−	0.887021i	$-0.347230\pi$
$5$	2.06491	0.923456	0.461728	+	0.887021i	$0.347230\pi$
$6$	5.51405	2.25110
$7$	1.23299	0.466026	0.233013	−	0.972474i	$-0.425142\pi$
$7$	1.23299	0.466026	0.233013	+	0.972474i	$0.425142\pi$
$8$	−7.88714	−2.78852
$9$	1.35325	0.451082
$10$	−5.45715	−1.72570
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−10.3996	−3.00212
$13$	−2.09401	−0.580773	−0.290387	−	0.956909i	$-0.593784\pi$
$13$	−2.09401	−0.580773	−0.290387	+	0.956909i	$0.593784\pi$
$14$	−3.25854	−0.870882
$15$	−4.30832	−1.11240
$16$	10.8753	2.71884
$17$	−0.272413	−0.0660700	−0.0330350	−	0.999454i	$-0.510517\pi$
$17$	−0.272413	−0.0660700	−0.0330350	+	0.999454i	$0.510517\pi$
$18$	−3.57636	−0.842956
$19$	0.942642	0.216257	0.108128	−	0.994137i	$-0.465514\pi$
$19$	0.942642	0.216257	0.108128	+	0.994137i	$0.465514\pi$
$20$	10.2923	2.30143
$21$	−2.57256	−0.561379
$22$	−2.64280	−0.563447
$23$	0.723963	0.150957	0.0754783	−	0.997147i	$-0.475952\pi$
$23$	0.723963	0.150957	0.0754783	+	0.997147i	$0.475952\pi$
$24$	16.4561	3.35908
$25$	−0.736140	−0.147228
$26$	5.53404	1.08531
$27$	3.43586	0.661231
$28$	6.14570	1.16143
$29$	−1.30071	−0.241535	−0.120767	−	0.992681i	$-0.538536\pi$
$29$	−1.30071	−0.241535	−0.120767	+	0.992681i	$0.538536\pi$
$30$	11.3860	2.07879
$31$	−9.46217	−1.69946	−0.849728	−	0.527221i	$-0.823234\pi$
$31$	−9.46217	−1.69946	−0.849728	+	0.527221i	$0.823234\pi$
$32$	−12.9671	−2.29228
$33$	−2.08644	−0.363203
$34$	0.719934	0.123468
$35$	2.54601	0.430355
$36$	6.74511	1.12418
$37$	4.59610	0.755594	0.377797	−	0.925888i	$-0.376682\pi$
$37$	4.59610	0.755594	0.377797	+	0.925888i	$0.376682\pi$
$38$	−2.49121	−0.404128
$39$	4.36903	0.699605
$40$	−16.2862	−2.57508
$41$	−8.53745	−1.33333	−0.666663	−	0.745359i	$-0.732278\pi$
$41$	−8.53745	−1.33333	−0.666663	+	0.745359i	$0.732278\pi$
$42$	6.79877	1.04907
$43$	−4.60214	−0.701820	−0.350910	−	0.936409i	$-0.614128\pi$
$43$	−4.60214	−0.701820	−0.350910	+	0.936409i	$0.614128\pi$
$44$	4.98439	0.751425
$45$	2.79433	0.416555
$46$	−1.91329	−0.282099
$47$	−0.972619	−0.141871	−0.0709355	−	0.997481i	$-0.522598\pi$
$47$	−0.972619	−0.141871	−0.0709355	+	0.997481i	$0.522598\pi$
$48$	−22.6908	−3.27513
$49$	−5.47974	−0.782820
$50$	1.94547	0.275131
$51$	0.568375	0.0795884
$52$	−10.4373	−1.44740
$53$	−0.725041	−0.0995921	−0.0497960	−	0.998759i	$-0.515857\pi$
$53$	−0.725041	−0.0995921	−0.0497960	+	0.998759i	$0.515857\pi$
$54$	−9.08028	−1.23567
$55$	2.06491	0.278433
$56$	−9.72475	−1.29953
$57$	−1.96677	−0.260505
$58$	3.43750	0.451366
$59$	−9.66991	−1.25891	−0.629457	−	0.777035i	$-0.716723\pi$
$59$	−9.66991	−1.25891	−0.629457	+	0.777035i	$0.716723\pi$
$60$	−21.4743	−2.77233
$61$	9.73833	1.24687	0.623433	−	0.781877i	$-0.285737\pi$
$61$	9.73833	1.24687	0.623433	+	0.781877i	$0.285737\pi$
$62$	25.0066	3.17584
$63$	1.66854	0.210216
$64$	12.5187	1.56484
$65$	−4.32394	−0.536319
$66$	5.51405	0.678733
$67$	4.14318	0.506170	0.253085	−	0.967444i	$-0.418555\pi$
$67$	4.14318	0.506170	0.253085	+	0.967444i	$0.418555\pi$
$68$	−1.35781	−0.164659
$69$	−1.51051	−0.181844
$70$	−6.72860	−0.804222
$71$	−3.37696	−0.400771	−0.200386	−	0.979717i	$-0.564219\pi$
$71$	−3.37696	−0.400771	−0.200386	+	0.979717i	$0.564219\pi$
$72$	−10.6732	−1.25785
$73$	13.5527	1.58622	0.793111	−	0.609077i	$-0.208460\pi$
$73$	13.5527	1.58622	0.793111	+	0.609077i	$0.208460\pi$
$74$	−12.1466	−1.41201
$75$	1.53592	0.177352
$76$	4.69849	0.538954
$77$	1.23299	0.140512
$78$	−11.5465	−1.30738
$79$	−5.32475	−0.599081	−0.299541	−	0.954084i	$-0.596833\pi$
$79$	−5.32475	−0.599081	−0.299541	+	0.954084i	$0.596833\pi$
$80$	22.4566	2.51073
$81$	−11.2285	−1.24761
$82$	22.5628	2.49164
$83$	14.7990	1.62440	0.812199	−	0.583380i	$-0.198270\pi$
$83$	14.7990	1.62440	0.812199	+	0.583380i	$0.198270\pi$
$84$	−12.8226	−1.39907
$85$	−0.562510	−0.0610127
$86$	12.1625	1.31152
$87$	2.71385	0.290955
$88$	−7.88714	−0.840772
$89$	−18.6259	−1.97435	−0.987173	−	0.159657i	$-0.948961\pi$
$89$	−18.6259	−1.97435	−0.987173	+	0.159657i	$0.948961\pi$
$90$	−7.38487	−0.778433
$91$	−2.58189	−0.270656
$92$	3.60851	0.376213
$93$	19.7423	2.04718
$94$	2.57044	0.265120
$95$	1.94647	0.199704
$96$	27.0551	2.76130
$97$	4.59240	0.466288	0.233144	−	0.972442i	$-0.425099\pi$
$97$	4.59240	0.466288	0.233144	+	0.972442i	$0.425099\pi$
$98$	14.4818	1.46289
$99$	1.35325	0.136006
$100$	−3.66921	−0.366921
$101$	15.1440	1.50689	0.753443	−	0.657513i	$-0.228392\pi$
$101$	15.1440	1.50689	0.753443	+	0.657513i	$0.228392\pi$
$102$	−1.50210	−0.148730
$103$	−0.315514	−0.0310885	−0.0155443	−	0.999879i	$-0.504948\pi$
$103$	−0.315514	−0.0310885	−0.0155443	+	0.999879i	$0.504948\pi$
$104$	16.5157	1.61950
$105$	−5.31211	−0.518409
$106$	1.91614	0.186112
$107$	5.72010	0.552983	0.276492	−	0.961016i	$-0.410828\pi$
$107$	5.72010	0.552983	0.276492	+	0.961016i	$0.410828\pi$
$108$	17.1256	1.64792
$109$	16.2217	1.55376	0.776878	−	0.629651i	$-0.216802\pi$
$109$	16.2217	1.55376	0.776878	+	0.629651i	$0.216802\pi$
$110$	−5.45715	−0.520318
$111$	−9.58950	−0.910195
$112$	13.4092	1.26705
$113$	7.17485	0.674954	0.337477	−	0.941334i	$-0.390427\pi$
$113$	7.17485	0.674954	0.337477	+	0.941334i	$0.390427\pi$
$114$	5.19778	0.486816
$115$	1.49492	0.139402
$116$	−6.48322	−0.601952
$117$	−2.83371	−0.261977
$118$	25.5556	2.35259
$119$	−0.335883	−0.0307903
$120$	33.9803	3.10196
$121$	1.00000	0.0909091
$122$	−25.7365	−2.33007
$123$	17.8129	1.60614
$124$	−47.1631	−4.23538
$125$	−11.8446	−1.05942
$126$	−4.40961	−0.392840
$127$	18.4211	1.63461	0.817304	−	0.576207i	$-0.195468\pi$
$127$	18.4211	1.63461	0.817304	+	0.576207i	$0.195468\pi$
$128$	−7.15022	−0.631996
$129$	9.60211	0.845419
$130$	11.4273	1.00224
$131$	−0.803899	−0.0702370	−0.0351185	−	0.999383i	$-0.511181\pi$
$131$	−0.803899	−0.0702370	−0.0351185	+	0.999383i	$0.511181\pi$
$132$	−10.3996	−0.905173
$133$	1.16227	0.100781
$134$	−10.9496	−0.945900
$135$	7.09474	0.610618
$136$	2.14856	0.184238
$137$	12.1157	1.03511	0.517557	−	0.855649i	$-0.326842\pi$
$137$	12.1157	1.03511	0.517557	+	0.855649i	$0.326842\pi$
$138$	3.99197	0.339819
$139$	5.16704	0.438263	0.219131	−	0.975695i	$-0.429678\pi$
$139$	5.16704	0.438263	0.219131	+	0.975695i	$0.429678\pi$
$140$	12.6903	1.07253
$141$	2.02931	0.170899
$142$	8.92462	0.748938
$143$	−2.09401	−0.175110
$144$	14.7170	1.22642
$145$	−2.68584	−0.223047
$146$	−35.8170	−2.96424
$147$	11.4332	0.942991
$148$	22.9087	1.88309
$149$	−12.2411	−1.00283	−0.501415	−	0.865207i	$-0.667187\pi$
$149$	−12.2411	−1.00283	−0.501415	+	0.865207i	$0.667187\pi$
$150$	−4.05912	−0.331425
$151$	15.6847	1.27641	0.638203	−	0.769868i	$-0.279678\pi$
$151$	15.6847	1.27641	0.638203	+	0.769868i	$0.279678\pi$
$152$	−7.43475	−0.603038
$153$	−0.368643	−0.0298030
$154$	−3.25854	−0.262581
$155$	−19.5386	−1.56937
$156$	21.7769	1.74355
$157$	−13.9598	−1.11411	−0.557057	−	0.830474i	$-0.688069\pi$
$157$	−13.9598	−1.11411	−0.557057	+	0.830474i	$0.688069\pi$
$158$	14.0723	1.11953
$159$	1.51276	0.119969
$160$	−26.7759	−2.11682
$161$	0.892638	0.0703497
$162$	29.6746	2.33145
$163$	20.8621	1.63405	0.817024	−	0.576604i	$-0.195623\pi$
$163$	20.8621	1.63405	0.817024	+	0.576604i	$0.195623\pi$
$164$	−42.5540	−3.32291
$165$	−4.30832	−0.335402
$166$	−39.1107	−3.03558
$167$	−8.36884	−0.647600	−0.323800	−	0.946126i	$-0.604961\pi$
$167$	−8.36884	−0.647600	−0.323800	+	0.946126i	$0.604961\pi$
$168$	20.2902	1.56542
$169$	−8.61513	−0.662702
$170$	1.48660	0.114017
$171$	1.27563	0.0975497
$172$	−22.9389	−1.74907
$173$	−3.84438	−0.292283	−0.146141	−	0.989264i	$-0.546685\pi$
$173$	−3.84438	−0.292283	−0.146141	+	0.989264i	$0.546685\pi$
$174$	−7.17216	−0.543720
$175$	−0.907653	−0.0686121
$176$	10.8753	0.819760
$177$	20.1757	1.51650
$178$	49.2246	3.68954
$179$	17.8600	1.33492	0.667460	−	0.744646i	$-0.267382\pi$
$179$	17.8600	1.33492	0.667460	+	0.744646i	$0.267382\pi$
$180$	13.9280	1.03814
$181$	5.89850	0.438432	0.219216	−	0.975676i	$-0.429650\pi$
$181$	5.89850	0.438432	0.219216	+	0.975676i	$0.429650\pi$
$182$	6.82341	0.505785
$183$	−20.3185	−1.50199
$184$	−5.70999	−0.420946
$185$	9.49054	0.697758
$186$	−52.1749	−3.82565
$187$	−0.272413	−0.0199208
$188$	−4.84791	−0.353570
$189$	4.23638	0.308151
$190$	−5.14414	−0.373195
$191$	−6.94314	−0.502388	−0.251194	−	0.967937i	$-0.580823\pi$
$191$	−6.94314	−0.502388	−0.251194	+	0.967937i	$0.580823\pi$
$192$	−26.1195	−1.88501
$193$	1.18641	0.0853994	0.0426997	−	0.999088i	$-0.486404\pi$
$193$	1.18641	0.0853994	0.0426997	+	0.999088i	$0.486404\pi$
$194$	−12.1368	−0.871371
$195$	9.02166	0.646054
$196$	−27.3131	−1.95094
$197$	1.28285	0.0913994	0.0456997	−	0.998955i	$-0.485448\pi$
$197$	1.28285	0.0913994	0.0456997	+	0.998955i	$0.485448\pi$
$198$	−3.57636	−0.254161
$199$	20.1064	1.42530	0.712651	−	0.701518i	$-0.247494\pi$
$199$	20.1064	1.42530	0.712651	+	0.701518i	$0.247494\pi$
$200$	5.80604	0.410549
$201$	−8.64451	−0.609737
$202$	−40.0226	−2.81598
$203$	−1.60376	−0.112562
$204$	2.83300	0.198350
$205$	−17.6291	−1.23127
$206$	0.833841	0.0580964
$207$	0.979700	0.0680939
$208$	−22.7731	−1.57903
$209$	0.942642	0.0652039
$210$	14.0389	0.968773
$211$	−19.7967	−1.36286	−0.681432	−	0.731882i	$-0.738642\pi$
$211$	−19.7967	−1.36286	−0.681432	+	0.731882i	$0.738642\pi$
$212$	−3.61389	−0.248203
$213$	7.04583	0.482772
$214$	−15.1171	−1.03338
$215$	−9.50302	−0.648100
$216$	−27.0991	−1.84386
$217$	−11.6668	−0.791991
$218$	−42.8707	−2.90357
$219$	−28.2769	−1.91078
$220$	10.2923	0.693908
$221$	0.570436	0.0383717
$222$	25.3431	1.70092
$223$	−2.97328	−0.199106	−0.0995528	−	0.995032i	$-0.531741\pi$
$223$	−2.97328	−0.199106	−0.0995528	+	0.995032i	$0.531741\pi$
$224$	−15.9883	−1.06826
$225$	−0.996180	−0.0664120
$226$	−18.9617	−1.26131
$227$	−0.967365	−0.0642063	−0.0321031	−	0.999485i	$-0.510220\pi$
$227$	−0.967365	−0.0642063	−0.0321031	+	0.999485i	$0.510220\pi$
$228$	−9.80314	−0.649229
$229$	7.01698	0.463695	0.231848	−	0.972752i	$-0.425523\pi$
$229$	7.01698	0.463695	0.231848	+	0.972752i	$0.425523\pi$
$230$	−3.95077	−0.260506
$231$	−2.57256	−0.169262
$232$	10.2588	0.673526
$233$	−15.8945	−1.04128	−0.520641	−	0.853776i	$-0.674307\pi$
$233$	−15.8945	−1.04128	−0.520641	+	0.853776i	$0.674307\pi$
$234$	7.48892	0.489566
$235$	−2.00837	−0.131012
$236$	−48.1986	−3.13746
$237$	11.1098	0.721659
$238$	0.887671	0.0575392
$239$	−9.56312	−0.618587	−0.309294	−	0.950967i	$-0.600093\pi$
$239$	−9.56312	−0.618587	−0.309294	+	0.950967i	$0.600093\pi$
$240$	−46.8545	−3.02444
$241$	17.6206	1.13504	0.567521	−	0.823359i	$-0.307902\pi$
$241$	17.6206	1.13504	0.567521	+	0.823359i	$0.307902\pi$
$242$	−2.64280	−0.169886
$243$	13.1200	0.841647
$244$	48.5396	3.10743
$245$	−11.3152	−0.722900
$246$	−47.0760	−3.00145
$247$	−1.97390	−0.125596
$248$	74.6295	4.73898
$249$	−30.8772	−1.95676
$250$	31.3030	1.97977
$251$	22.7691	1.43717	0.718587	−	0.695437i	$-0.244789\pi$
$251$	22.7691	1.43717	0.718587	+	0.695437i	$0.244789\pi$
$252$	8.31664	0.523899
$253$	0.723963	0.0455151
$254$	−48.6833	−3.05466
$255$	1.17364	0.0734965
$256$	−6.14077	−0.383798
$257$	−9.45925	−0.590052	−0.295026	−	0.955489i	$-0.595328\pi$
$257$	−9.45925	−0.590052	−0.295026	+	0.955489i	$0.595328\pi$
$258$	−25.3765	−1.57987
$259$	5.66694	0.352127
$260$	−21.5522	−1.33661
$261$	−1.76018	−0.108952
$262$	2.12454	0.131255
$263$	−22.5917	−1.39306	−0.696531	−	0.717526i	$-0.745274\pi$
$263$	−22.5917	−1.39306	−0.696531	+	0.717526i	$0.745274\pi$
$264$	16.4561	1.01280
$265$	−1.49715	−0.0919689
$266$	−3.07164	−0.188334
$267$	38.8620	2.37831
$268$	20.6512	1.26147
$269$	9.06884	0.552937	0.276468	−	0.961023i	$-0.410836\pi$
$269$	9.06884	0.552937	0.276468	+	0.961023i	$0.410836\pi$
$270$	−18.7500	−1.14109
$271$	18.1209	1.10077	0.550383	−	0.834912i	$-0.314482\pi$
$271$	18.1209	1.10077	0.550383	+	0.834912i	$0.314482\pi$
$272$	−2.96259	−0.179633
$273$	5.38697	0.326034
$274$	−32.0193	−1.93436
$275$	−0.736140	−0.0443909
$276$	−7.52895	−0.453190
$277$	8.53121	0.512591	0.256295	−	0.966599i	$-0.417498\pi$
$277$	8.53121	0.512591	0.256295	+	0.966599i	$0.417498\pi$
$278$	−13.6555	−0.819000
$279$	−12.8047	−0.766595
$280$	−20.0808	−1.20005
$281$	−28.9590	−1.72755	−0.863775	−	0.503878i	$-0.831906\pi$
$281$	−28.9590	−1.72755	−0.863775	+	0.503878i	$0.831906\pi$
$282$	−5.36307	−0.319366
$283$	31.5073	1.87291	0.936457	−	0.350783i	$-0.114085\pi$
$283$	31.5073	1.87291	0.936457	+	0.350783i	$0.114085\pi$
$284$	−16.8321	−0.998799
$285$	−4.06120	−0.240565
$286$	5.53404	0.327235
$287$	−10.5266	−0.621365
$288$	−17.5477	−1.03401
$289$	−16.9258	−0.995635
$290$	7.09814	0.416817
$291$	−9.58179	−0.561694
$292$	67.5518	3.95317
$293$	5.83511	0.340891	0.170445	−	0.985367i	$-0.445479\pi$
$293$	5.83511	0.340891	0.170445	+	0.985367i	$0.445479\pi$
$294$	−30.2156	−1.76221
$295$	−19.9675	−1.16255
$296$	−36.2501	−2.10699
$297$	3.43586	0.199369
$298$	32.3508	1.87403
$299$	−1.51598	−0.0876716
$300$	7.65560	0.441996
$301$	−5.67439	−0.327067
$302$	−41.4516	−2.38527
$303$	−31.5971	−1.81521
$304$	10.2516	0.587967
$305$	20.1088	1.15143
$306$	0.974248	0.0556941
$307$	−32.0967	−1.83185	−0.915927	−	0.401344i	$-0.868543\pi$
$307$	−32.0967	−1.83185	−0.915927	+	0.401344i	$0.868543\pi$
$308$	6.14570	0.350184
$309$	0.658303	0.0374495
$310$	51.6365	2.93275
$311$	11.7201	0.664585	0.332293	−	0.943176i	$-0.392178\pi$
$311$	11.7201	0.664585	0.332293	+	0.943176i	$0.392178\pi$
$312$	−34.4591	−1.95086
$313$	−1.61416	−0.0912378	−0.0456189	−	0.998959i	$-0.514526\pi$
$313$	−1.61416	−0.0912378	−0.0456189	+	0.998959i	$0.514526\pi$
$314$	36.8930	2.08199
$315$	3.44539	0.194125
$316$	−26.5406	−1.49303
$317$	9.08808	0.510437	0.255219	−	0.966883i	$-0.417853\pi$
$317$	9.08808	0.510437	0.255219	+	0.966883i	$0.417853\pi$
$318$	−3.99791	−0.224192
$319$	−1.30071	−0.0728255
$320$	25.8500	1.44506
$321$	−11.9347	−0.666128
$322$	−2.35906	−0.131465
$323$	−0.256788	−0.0142881
$324$	−55.9670	−3.10928
$325$	1.54148	0.0855061
$326$	−55.1344	−3.05361
$327$	−33.8456	−1.87167
$328$	67.3361	3.71801
$329$	−1.19923	−0.0661156
$330$	11.3860	0.626780
$331$	25.5545	1.40460	0.702300	−	0.711881i	$-0.252156\pi$
$331$	25.5545	1.40460	0.702300	+	0.711881i	$0.252156\pi$
$332$	73.7638	4.04831
$333$	6.21966	0.340835
$334$	22.1172	1.21020
$335$	8.55530	0.467426
$336$	−27.9775	−1.52630
$337$	26.8254	1.46127	0.730637	−	0.682766i	$-0.239223\pi$
$337$	26.8254	1.46127	0.730637	+	0.682766i	$0.239223\pi$
$338$	22.7681	1.23842
$339$	−14.9699	−0.813055
$340$	−2.80377	−0.152056
$341$	−9.46217	−0.512406
$342$	−3.37123	−0.182295
$343$	−15.3874	−0.830841
$344$	36.2977	1.95704
$345$	−3.11906	−0.167925
$346$	10.1599	0.546201
$347$	−28.5229	−1.53119	−0.765594	−	0.643324i	$-0.777555\pi$
$347$	−28.5229	−1.53119	−0.765594	+	0.643324i	$0.777555\pi$
$348$	13.5269	0.725116
$349$	18.9340	1.01351	0.506757	−	0.862089i	$-0.330844\pi$
$349$	18.9340	1.01351	0.506757	+	0.862089i	$0.330844\pi$
$350$	2.39875	0.128218
$351$	−7.19471	−0.384025
$352$	−12.9671	−0.691147
$353$	19.4414	1.03476	0.517381	−	0.855755i	$-0.326907\pi$
$353$	19.4414	1.03476	0.517381	+	0.855755i	$0.326907\pi$
$354$	−53.3204	−2.83394
$355$	−6.97312	−0.370095
$356$	−92.8389	−4.92045
$357$	0.700801	0.0370903
$358$	−47.2004	−2.49462
$359$	10.3653	0.547058	0.273529	−	0.961864i	$-0.411809\pi$
$359$	10.3653	0.547058	0.273529	+	0.961864i	$0.411809\pi$
$360$	−22.0393	−1.16157
$361$	−18.1114	−0.953233
$362$	−15.5885	−0.819316
$363$	−2.08644	−0.109510
$364$	−12.8691	−0.674526
$365$	27.9851	1.46481
$366$	53.6977	2.80682
$367$	−4.59022	−0.239608	−0.119804	−	0.992798i	$-0.538227\pi$
$367$	−4.59022	−0.239608	−0.119804	+	0.992798i	$0.538227\pi$
$368$	7.87334	0.410426
$369$	−11.5533	−0.601440
$370$	−25.0816	−1.30393
$371$	−0.893968	−0.0464125
$372$	98.4032	5.10197
$373$	−15.5113	−0.803146	−0.401573	−	0.915827i	$-0.631536\pi$
$373$	−15.5113	−0.803146	−0.401573	+	0.915827i	$0.631536\pi$
$374$	0.719934	0.0372269
$375$	24.7131	1.27618
$376$	7.67118	0.395611
$377$	2.72369	0.140277
$378$	−11.1959	−0.575854
$379$	20.2279	1.03904	0.519518	−	0.854460i	$-0.326112\pi$
$379$	20.2279	1.03904	0.519518	+	0.854460i	$0.326112\pi$
$380$	9.70197	0.497701
$381$	−38.4346	−1.96906
$382$	18.3493	0.938833
$383$	−16.6825	−0.852435	−0.426218	−	0.904621i	$-0.640154\pi$
$383$	−16.6825	−0.852435	−0.426218	+	0.904621i	$0.640154\pi$
$384$	14.9185	0.761308
$385$	2.54601	0.129757
$386$	−3.13543	−0.159589
$387$	−6.22784	−0.316579
$388$	22.8903	1.16208
$389$	−36.7410	−1.86284	−0.931421	−	0.363944i	$-0.881430\pi$
$389$	−36.7410	−1.86284	−0.931421	+	0.363944i	$0.881430\pi$
$390$	−23.8424	−1.20731
$391$	−0.197217	−0.00997370
$392$	43.2194	2.18291
$393$	1.67729	0.0846081
$394$	−3.39032	−0.170802
$395$	−10.9951	−0.553226
$396$	6.74511	0.338954
$397$	0.678580	0.0340570	0.0170285	−	0.999855i	$-0.494579\pi$
$397$	0.678580	0.0340570	0.0170285	+	0.999855i	$0.494579\pi$
$398$	−53.1371	−2.66352
$399$	−2.42501	−0.121402
$400$	−8.00578	−0.400289
$401$	17.9102	0.894392	0.447196	−	0.894436i	$-0.352423\pi$
$401$	17.9102	0.894392	0.447196	+	0.894436i	$0.352423\pi$
$402$	22.8457	1.13944
$403$	19.8139	0.986999
$404$	75.4837	3.75545
$405$	−23.1858	−1.15211
$406$	4.23840	0.210348
$407$	4.59610	0.227820
$408$	−4.48285	−0.221934
$409$	12.3594	0.611132	0.305566	−	0.952171i	$-0.401154\pi$
$409$	12.3594	0.611132	0.305566	+	0.952171i	$0.401154\pi$
$410$	46.5901	2.30092
$411$	−25.2787	−1.24691
$412$	−1.57265	−0.0774787
$413$	−11.9229	−0.586687
$414$	−2.58915	−0.127250
$415$	30.5586	1.50006
$416$	27.1532	1.33129
$417$	−10.7807	−0.527935
$418$	−2.49121	−0.121849
$419$	−16.4588	−0.804067	−0.402033	−	0.915625i	$-0.631696\pi$
$419$	−16.4588	−0.804067	−0.402033	+	0.915625i	$0.631696\pi$
$420$	−26.4776	−1.29198
$421$	−28.9890	−1.41284	−0.706418	−	0.707795i	$-0.749690\pi$
$421$	−28.9890	−1.41284	−0.706418	+	0.707795i	$0.749690\pi$
$422$	52.3188	2.54684
$423$	−1.31619	−0.0639955
$424$	5.71850	0.277715
$425$	0.200535	0.00972735
$426$	−18.6207	−0.902177
$427$	12.0073	0.581072
$428$	28.5112	1.37814
$429$	4.36903	0.210939
$430$	25.1146	1.21113
$431$	28.3924	1.36761	0.683806	−	0.729664i	$-0.260324\pi$
$431$	28.3924	1.36761	0.683806	+	0.729664i	$0.260324\pi$
$432$	37.3661	1.79778
$433$	25.2507	1.21347	0.606736	−	0.794903i	$-0.292478\pi$
$433$	25.2507	1.21347	0.606736	+	0.794903i	$0.292478\pi$
$434$	30.8329	1.48003
$435$	5.60386	0.268684
$436$	80.8552	3.87226
$437$	0.682438	0.0326454
$438$	74.7302	3.57075
$439$	13.4495	0.641911	0.320955	−	0.947094i	$-0.395996\pi$
$439$	13.4495	0.641911	0.320955	+	0.947094i	$0.395996\pi$
$440$	−16.2862	−0.776416
$441$	−7.41544	−0.353116
$442$	−1.50755	−0.0717067
$443$	21.9231	1.04160	0.520798	−	0.853680i	$-0.325635\pi$
$443$	21.9231	1.04160	0.520798	+	0.853680i	$0.325635\pi$
$444$	−47.7978	−2.26838
$445$	−38.4609	−1.82322
$446$	7.85778	0.372077
$447$	25.5404	1.20802
$448$	15.4354	0.729254
$449$	−24.7164	−1.16644	−0.583220	−	0.812315i	$-0.698207\pi$
$449$	−24.7164	−1.16644	−0.583220	+	0.812315i	$0.698207\pi$
$450$	2.63270	0.124107
$451$	−8.53745	−0.402013
$452$	35.7623	1.68211
$453$	−32.7253	−1.53757
$454$	2.55655	0.119985
$455$	−5.33137	−0.249939
$456$	15.5122	0.726424
$457$	11.5443	0.540017	0.270009	−	0.962858i	$-0.412973\pi$
$457$	11.5443	0.540017	0.270009	+	0.962858i	$0.412973\pi$
$458$	−18.5445	−0.866526
$459$	−0.935974	−0.0436875
$460$	7.45125	0.347416
$461$	32.2930	1.50404	0.752019	−	0.659142i	$-0.229080\pi$
$461$	32.2930	1.50404	0.752019	+	0.659142i	$0.229080\pi$
$462$	6.79877	0.316307
$463$	2.20453	0.102453	0.0512266	−	0.998687i	$-0.483687\pi$
$463$	2.20453	0.102453	0.0512266	+	0.998687i	$0.483687\pi$
$464$	−14.1456	−0.656694
$465$	40.7661	1.89048
$466$	42.0059	1.94589
$467$	11.0252	0.510186	0.255093	−	0.966916i	$-0.417894\pi$
$467$	11.0252	0.510186	0.255093	+	0.966916i	$0.417894\pi$
$468$	−14.1243	−0.652896
$469$	5.10850	0.235888
$470$	5.30772	0.244827
$471$	29.1263	1.34207
$472$	76.2679	3.51051
$473$	−4.60214	−0.211607
$474$	−29.3610	−1.34859
$475$	−0.693917	−0.0318391
$476$	−1.67417	−0.0767355
$477$	−0.981160	−0.0449242
$478$	25.2734	1.15598
$479$	2.54956	0.116492	0.0582461	−	0.998302i	$-0.481449\pi$
$479$	2.54956	0.116492	0.0582461	+	0.998302i	$0.481449\pi$
$480$	55.8663	2.54994
$481$	−9.62426	−0.438829
$482$	−46.5677	−2.12110
$483$	−1.86244	−0.0847439
$484$	4.98439	0.226563
$485$	9.48291	0.430597
$486$	−34.6735	−1.57282
$487$	−23.3030	−1.05596	−0.527980	−	0.849257i	$-0.677051\pi$
$487$	−23.3030	−1.05596	−0.527980	+	0.849257i	$0.677051\pi$
$488$	−76.8076	−3.47691
$489$	−43.5276	−1.96839
$490$	29.9037	1.35091
$491$	44.2794	1.99830	0.999151	−	0.0411993i	$-0.0131179\pi$
$491$	44.2794	1.99830	0.999151	+	0.0411993i	$0.0131179\pi$
$492$	88.7865	4.00280
$493$	0.354330	0.0159582
$494$	5.21662	0.234707
$495$	2.79433	0.125596
$496$	−102.904	−4.62054
$497$	−4.16375	−0.186770
$498$	81.6023	3.65669
$499$	−21.5418	−0.964341	−0.482171	−	0.876077i	$-0.660151\pi$
$499$	−21.5418	−0.964341	−0.482171	+	0.876077i	$0.660151\pi$
$500$	−59.0382	−2.64027
$501$	17.4611	0.780105
$502$	−60.1742	−2.68571
$503$	11.5829	0.516454	0.258227	−	0.966084i	$-0.416862\pi$
$503$	11.5829	0.516454	0.258227	+	0.966084i	$0.416862\pi$
$504$	−13.1600	−0.586193
$505$	31.2711	1.39154
$506$	−1.91329	−0.0850560
$507$	17.9750	0.798297
$508$	91.8179	4.07376
$509$	0.184402	0.00817345	0.00408673	−	0.999992i	$-0.498699\pi$
$509$	0.184402	0.00817345	0.00408673	+	0.999992i	$0.498699\pi$
$510$	−3.10171	−0.137346
$511$	16.7103	0.739221
$512$	30.5293	1.34922
$513$	3.23878	0.142996
$514$	24.9989	1.10265
$515$	−0.651509	−0.0287089
$516$	47.8606	2.10695
$517$	−0.972619	−0.0427757
$518$	−14.9766	−0.658033
$519$	8.02108	0.352086
$520$	34.1035	1.49554
$521$	−19.1034	−0.836935	−0.418468	−	0.908232i	$-0.637433\pi$
$521$	−19.1034	−0.836935	−0.418468	+	0.908232i	$0.637433\pi$
$522$	4.65179	0.203603
$523$	12.9191	0.564913	0.282456	−	0.959280i	$-0.408851\pi$
$523$	12.9191	0.564913	0.282456	+	0.959280i	$0.408851\pi$
$524$	−4.00694	−0.175044
$525$	1.89377	0.0826508
$526$	59.7053	2.60327
$527$	2.57762	0.112283
$528$	−22.6908	−0.987490
$529$	−22.4759	−0.977212
$530$	3.95666	0.171866
$531$	−13.0858	−0.567874
$532$	5.79319	0.251167
$533$	17.8775	0.774360
$534$	−102.704	−4.44445
$535$	11.8115	0.510656
$536$	−32.6778	−1.41147
$537$	−37.2639	−1.60806
$538$	−23.9671	−1.03330
$539$	−5.47974	−0.236029
$540$	35.3629	1.52178
$541$	−11.6659	−0.501554	−0.250777	−	0.968045i	$-0.580686\pi$
$541$	−11.6659	−0.501554	−0.250777	+	0.968045i	$0.580686\pi$
$542$	−47.8899	−2.05705
$543$	−12.3069	−0.528139
$544$	3.53240	0.151451
$545$	33.4963	1.43483
$546$	−14.2367	−0.609273
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	60.3893	2.57970
$549$	13.1784	0.562439
$550$	1.94547	0.0829552
$551$	−1.22610	−0.0522336
$552$	11.9136	0.507075
$553$	−6.56536	−0.279188
$554$	−22.5463	−0.957899
$555$	−19.8015	−0.840525
$556$	25.7545	1.09224
$557$	−24.9094	−1.05544	−0.527722	−	0.849417i	$-0.676954\pi$
$557$	−24.9094	−1.05544	−0.527722	+	0.849417i	$0.676954\pi$
$558$	33.8401	1.43257
$559$	9.63692	0.407598
$560$	27.6888	1.17006
$561$	0.568375	0.0239968
$562$	76.5328	3.22834
$563$	−7.45396	−0.314147	−0.157073	−	0.987587i	$-0.550206\pi$
$563$	−7.45396	−0.314147	−0.157073	+	0.987587i	$0.550206\pi$
$564$	10.1149	0.425914
$565$	14.8154	0.623290
$566$	−83.2674	−3.49999
$567$	−13.8446	−0.581418
$568$	26.6345	1.11756
$569$	24.9328	1.04524	0.522619	−	0.852566i	$-0.324955\pi$
$569$	24.9328	1.04524	0.522619	+	0.852566i	$0.324955\pi$
$570$	10.7329	0.449554
$571$	34.4780	1.44286	0.721429	−	0.692489i	$-0.243486\pi$
$571$	34.4780	1.44286	0.721429	+	0.692489i	$0.243486\pi$
$572$	−10.4373	−0.436407
$573$	14.4865	0.605181
$574$	27.8197	1.16117
$575$	−0.532938	−0.0222251
$576$	16.9409	0.705870
$577$	−3.61072	−0.150316	−0.0751582	−	0.997172i	$-0.523946\pi$
$577$	−3.61072	−0.150316	−0.0751582	+	0.997172i	$0.523946\pi$
$578$	44.7315	1.86058
$579$	−2.47537	−0.102873
$580$	−13.3873	−0.555876
$581$	18.2470	0.757012
$582$	25.3227	1.04966
$583$	−0.725041	−0.0300281
$584$	−106.892	−4.42322
$585$	−5.85136	−0.241924
$586$	−15.4210	−0.637037
$587$	7.85779	0.324326	0.162163	−	0.986764i	$-0.448153\pi$
$587$	7.85779	0.324326	0.162163	+	0.986764i	$0.448153\pi$
$588$	56.9873	2.35012
$589$	−8.91944	−0.367519
$590$	52.7701	2.17251
$591$	−2.67660	−0.110100
$592$	49.9841	2.05434
$593$	−25.4012	−1.04310	−0.521552	−	0.853220i	$-0.674647\pi$
$593$	−25.4012	−1.04310	−0.521552	+	0.853220i	$0.674647\pi$
$594$	−9.08028	−0.372568
$595$	−0.693568	−0.0284335
$596$	−61.0144	−2.49925
$597$	−41.9508	−1.71693
$598$	4.00644	0.163835
$599$	−4.73594	−0.193505	−0.0967527	−	0.995308i	$-0.530846\pi$
$599$	−4.73594	−0.193505	−0.0967527	+	0.995308i	$0.530846\pi$
$600$	−12.1140	−0.494551
$601$	28.5718	1.16547	0.582734	−	0.812663i	$-0.301983\pi$
$601$	28.5718	1.16547	0.582734	+	0.812663i	$0.301983\pi$
$602$	14.9963	0.611203
$603$	5.60674	0.228324
$604$	78.1789	3.18105
$605$	2.06491	0.0839506
$606$	83.5049	3.39215
$607$	12.7383	0.517032	0.258516	−	0.966007i	$-0.416767\pi$
$607$	12.7383	0.517032	0.258516	+	0.966007i	$0.416767\pi$
$608$	−12.2233	−0.495721
$609$	3.34615	0.135593
$610$	−53.1435	−2.15172
$611$	2.03667	0.0823949
$612$	−1.83746	−0.0742748
$613$	19.4015	0.783621	0.391810	−	0.920046i	$-0.371849\pi$
$613$	19.4015	0.783621	0.391810	+	0.920046i	$0.371849\pi$
$614$	84.8251	3.42326
$615$	36.7821	1.48320
$616$	−9.72475	−0.391822
$617$	21.3472	0.859405	0.429702	−	0.902971i	$-0.358618\pi$
$617$	21.3472	0.859405	0.429702	+	0.902971i	$0.358618\pi$
$618$	−1.73976	−0.0699835
$619$	10.9027	0.438219	0.219109	−	0.975700i	$-0.429685\pi$
$619$	10.9027	0.438219	0.219109	+	0.975700i	$0.429685\pi$
$620$	−97.3877	−3.91118
$621$	2.48743	0.0998172
$622$	−30.9738	−1.24194
$623$	−22.9656	−0.920096
$624$	47.5147	1.90211
$625$	−20.7774	−0.831096
$626$	4.26590	0.170500
$627$	−1.96677	−0.0785452
$628$	−69.5811	−2.77659
$629$	−1.25204	−0.0499221
$630$	−9.10546	−0.362770
$631$	24.1824	0.962686	0.481343	−	0.876532i	$-0.340149\pi$
$631$	24.1824	0.962686	0.481343	+	0.876532i	$0.340149\pi$
$632$	41.9970	1.67055
$633$	41.3048	1.64172
$634$	−24.0180	−0.953875
$635$	38.0379	1.50949
$636$	7.54017	0.298987
$637$	11.4746	0.454641
$638$	3.43750	0.136092
$639$	−4.56986	−0.180781
$640$	−14.7646	−0.583621
$641$	−21.6256	−0.854160	−0.427080	−	0.904214i	$-0.640458\pi$
$641$	−21.6256	−0.854160	−0.427080	+	0.904214i	$0.640458\pi$
$642$	31.5409	1.24482
$643$	26.0415	1.02698	0.513488	−	0.858097i	$-0.328353\pi$
$643$	26.0415	1.02698	0.513488	+	0.858097i	$0.328353\pi$
$644$	4.44925	0.175325
$645$	19.8275	0.780708
$646$	0.678640	0.0267007
$647$	−34.8017	−1.36820	−0.684099	−	0.729389i	$-0.739804\pi$
$647$	−34.8017	−1.36820	−0.684099	+	0.729389i	$0.739804\pi$
$648$	88.5604	3.47898
$649$	−9.66991	−0.379577
$650$	−4.07383	−0.159789
$651$	24.3420	0.954040
$652$	103.985	4.07236
$653$	16.1643	0.632559	0.316279	−	0.948666i	$-0.397566\pi$
$653$	16.1643	0.632559	0.316279	+	0.948666i	$0.397566\pi$
$654$	89.4472	3.49766
$655$	−1.65998	−0.0648608
$656$	−92.8477	−3.62510
$657$	18.3401	0.715517
$658$	3.16932	0.123553
$659$	−28.2681	−1.10117	−0.550584	−	0.834780i	$-0.685595\pi$
$659$	−28.2681	−1.10117	−0.550584	+	0.834780i	$0.685595\pi$
$660$	−21.4743	−0.835888
$661$	8.95075	0.348144	0.174072	−	0.984733i	$-0.444308\pi$
$661$	8.95075	0.348144	0.174072	+	0.984733i	$0.444308\pi$
$662$	−67.5353	−2.62484
$663$	−1.19018	−0.0462228
$664$	−116.722	−4.52967
$665$	2.39998	0.0930672
$666$	−16.4373	−0.636932
$667$	−0.941662	−0.0364613
$668$	−41.7135	−1.61394
$669$	6.20358	0.239844
$670$	−22.6099	−0.873498
$671$	9.73833	0.375944
$672$	33.3586	1.28684
$673$	2.33513	0.0900126	0.0450063	−	0.998987i	$-0.485669\pi$
$673$	2.33513	0.0900126	0.0450063	+	0.998987i	$0.485669\pi$
$674$	−70.8942	−2.73074
$675$	−2.52927	−0.0973518
$676$	−42.9412	−1.65158
$677$	−13.9106	−0.534629	−0.267314	−	0.963609i	$-0.586136\pi$
$677$	−13.9106	−0.534629	−0.267314	+	0.963609i	$0.586136\pi$
$678$	39.5625	1.51939
$679$	5.66238	0.217302
$680$	4.43659	0.170135
$681$	2.01835	0.0773434
$682$	25.0066	0.957553
$683$	−5.30387	−0.202947	−0.101474	−	0.994838i	$-0.532356\pi$
$683$	−5.30387	−0.202947	−0.101474	+	0.994838i	$0.532356\pi$
$684$	6.35822	0.243113
$685$	25.0178	0.955882
$686$	40.6658	1.55263
$687$	−14.6405	−0.558571
$688$	−50.0499	−1.90813
$689$	1.51824	0.0578404
$690$	8.24306	0.313808
$691$	21.2018	0.806554	0.403277	−	0.915078i	$-0.367871\pi$
$691$	21.2018	0.806554	0.403277	+	0.915078i	$0.367871\pi$
$692$	−19.1619	−0.728425
$693$	1.66854	0.0633826
$694$	75.3803	2.86140
$695$	10.6695	0.404717
$696$	−21.4045	−0.811335
$697$	2.32572	0.0880928
$698$	−50.0387	−1.89399
$699$	33.1629	1.25434
$700$	−4.52410	−0.170995
$701$	30.4046	1.14837	0.574183	−	0.818727i	$-0.305320\pi$
$701$	30.4046	1.14837	0.574183	+	0.818727i	$0.305320\pi$
$702$	19.0142	0.717644
$703$	4.33248	0.163402
$704$	12.5187	0.471816
$705$	4.19035	0.157818
$706$	−51.3798	−1.93370
$707$	18.6724	0.702248
$708$	100.564	3.77941
$709$	−0.578987	−0.0217443	−0.0108722	−	0.999941i	$-0.503461\pi$
$709$	−0.578987	−0.0217443	−0.0108722	+	0.999941i	$0.503461\pi$
$710$	18.4286	0.691611
$711$	−7.20570	−0.270235
$712$	146.905	5.50551
$713$	−6.85026	−0.256544
$714$	−1.85208	−0.0693122
$715$	−4.32394	−0.161706
$716$	89.0212	3.32688
$717$	19.9529	0.745155
$718$	−27.3933	−1.02231
$719$	9.42753	0.351587	0.175794	−	0.984427i	$-0.443751\pi$
$719$	9.42753	0.351587	0.175794	+	0.984427i	$0.443751\pi$
$720$	30.3893	1.13254
$721$	−0.389026	−0.0144881
$722$	47.8649	1.78135
$723$	−36.7644	−1.36728
$724$	29.4004	1.09266
$725$	0.957502	0.0355607
$726$	5.51405	0.204646
$727$	16.8172	0.623715	0.311857	−	0.950129i	$-0.399049\pi$
$727$	16.8172	0.623715	0.311857	+	0.950129i	$0.399049\pi$
$728$	20.3637	0.754729
$729$	6.31129	0.233751
$730$	−73.9590	−2.73735
$731$	1.25369	0.0463692
$732$	−101.275	−3.74324
$733$	−12.8473	−0.474526	−0.237263	−	0.971445i	$-0.576250\pi$
$733$	−12.8473	−0.474526	−0.237263	+	0.971445i	$0.576250\pi$
$734$	12.1310	0.447765
$735$	23.6085	0.870812
$736$	−9.38768	−0.346034
$737$	4.14318	0.152616
$738$	30.5330	1.12394
$739$	13.4311	0.494071	0.247036	−	0.969006i	$-0.420544\pi$
$739$	13.4311	0.494071	0.247036	+	0.969006i	$0.420544\pi$
$740$	47.3045	1.73895
$741$	4.11843	0.151294
$742$	2.36258	0.0867330
$743$	38.6219	1.41690	0.708451	−	0.705760i	$-0.249394\pi$
$743$	38.6219	1.41690	0.708451	+	0.705760i	$0.249394\pi$
$744$	−155.710	−5.70861
$745$	−25.2768	−0.926070
$746$	40.9933	1.50087
$747$	20.0267	0.732737
$748$	−1.35781	−0.0496466
$749$	7.05282	0.257705
$750$	−65.3119	−2.38485
$751$	19.2516	0.702500	0.351250	−	0.936282i	$-0.385757\pi$
$751$	19.2516	0.702500	0.351250	+	0.936282i	$0.385757\pi$
$752$	−10.5776	−0.385724
$753$	−47.5065	−1.73123
$754$	−7.19816	−0.262141
$755$	32.3876	1.17871
$756$	21.1157	0.767972
$757$	−52.2193	−1.89794	−0.948972	−	0.315361i	$-0.897874\pi$
$757$	−52.2193	−1.89794	−0.948972	+	0.315361i	$0.897874\pi$
$758$	−53.4582	−1.94169
$759$	−1.51051	−0.0548279
$760$	−15.3521	−0.556879
$761$	−0.0814737	−0.00295342	−0.00147671	−	0.999999i	$-0.500470\pi$
$761$	−0.0814737	−0.00295342	−0.00147671	+	0.999999i	$0.500470\pi$
$762$	101.575	3.67967
$763$	20.0012	0.724091
$764$	−34.6073	−1.25205
$765$	−0.761214	−0.0275218
$766$	44.0885	1.59298
$767$	20.2489	0.731144
$768$	12.8124	0.462326
$769$	−44.2099	−1.59425	−0.797124	−	0.603816i	$-0.793646\pi$
$769$	−44.2099	−1.59425	−0.797124	+	0.603816i	$0.793646\pi$
$770$	−6.72860	−0.242482
$771$	19.7362	0.710781
$772$	5.91351	0.212832
$773$	26.0586	0.937263	0.468631	−	0.883394i	$-0.344747\pi$
$773$	26.0586	0.937263	0.468631	+	0.883394i	$0.344747\pi$
$774$	16.4589	0.591604
$775$	6.96549	0.250208
$776$	−36.2209	−1.30025
$777$	−11.8238	−0.424175
$778$	97.0990	3.48117
$779$	−8.04776	−0.288341
$780$	44.9674	1.61009
$781$	−3.37696	−0.120837
$782$	0.521205	0.0186383
$783$	−4.46904	−0.159710
$784$	−59.5940	−2.12836
$785$	−28.8258	−1.02884
$786$	−4.43274	−0.158111
$787$	−33.6200	−1.19842	−0.599212	−	0.800590i	$-0.704519\pi$
$787$	−33.6200	−1.19842	−0.599212	+	0.800590i	$0.704519\pi$
$788$	6.39423	0.227785
$789$	47.1363	1.67810
$790$	29.0580	1.03384
$791$	8.84652	0.314546
$792$	−10.6732	−0.379257
$793$	−20.3921	−0.724146
$794$	−1.79335	−0.0636437
$795$	3.12371	0.110787
$796$	100.218	3.55213
$797$	0.536309	0.0189970	0.00949852	−	0.999955i	$-0.496976\pi$
$797$	0.536309	0.0189970	0.00949852	+	0.999955i	$0.496976\pi$
$798$	6.40880	0.226869
$799$	0.264954	0.00937341
$800$	9.54559	0.337487
$801$	−25.2055	−0.890592
$802$	−47.3330	−1.67139
$803$	13.5527	0.478264
$804$	−43.0876	−1.51958
$805$	1.84322	0.0649649
$806$	−52.3641	−1.84445
$807$	−18.9216	−0.666073
$808$	−119.443	−4.20199
$809$	16.8062	0.590873	0.295437	−	0.955362i	$-0.404535\pi$
$809$	16.8062	0.590873	0.295437	+	0.955362i	$0.404535\pi$
$810$	61.2754	2.15300
$811$	1.22451	0.0429985	0.0214993	−	0.999769i	$-0.493156\pi$
$811$	1.22451	0.0429985	0.0214993	+	0.999769i	$0.493156\pi$
$812$	−7.99374	−0.280525
$813$	−37.8082	−1.32599
$814$	−12.1466	−0.425737
$815$	43.0784	1.50897
$816$	6.18127	0.216388
$817$	−4.33817	−0.151773
$818$	−32.6634	−1.14205
$819$	−3.49393	−0.122088
$820$	−87.8702	−3.06856
$821$	54.0660	1.88692	0.943458	−	0.331493i	$-0.107552\pi$
$821$	54.0660	1.88692	0.943458	+	0.331493i	$0.107552\pi$
$822$	66.8065	2.33015
$823$	−4.14838	−0.144604	−0.0723018	−	0.997383i	$-0.523034\pi$
$823$	−4.14838	−0.144604	−0.0723018	+	0.997383i	$0.523034\pi$
$824$	2.48850	0.0866911
$825$	1.53592	0.0534737
$826$	31.5098	1.09637
$827$	−12.6413	−0.439582	−0.219791	−	0.975547i	$-0.570537\pi$
$827$	−12.6413	−0.439582	−0.219791	+	0.975547i	$0.570537\pi$
$828$	4.88320	0.169703
$829$	−8.76013	−0.304252	−0.152126	−	0.988361i	$-0.548612\pi$
$829$	−8.76013	−0.304252	−0.152126	+	0.988361i	$0.548612\pi$
$830$	−80.7602	−2.80323
$831$	−17.7999	−0.617471
$832$	−26.2142	−0.908815
$833$	1.49275	0.0517209
$834$	28.4913	0.986574
$835$	−17.2809	−0.598031
$836$	4.69849	0.162501
$837$	−32.5107	−1.12373
$838$	43.4974	1.50259
$839$	−18.3871	−0.634795	−0.317397	−	0.948293i	$-0.602809\pi$
$839$	−18.3871	−0.634795	−0.317397	+	0.948293i	$0.602809\pi$
$840$	41.8974	1.44560
$841$	−27.3082	−0.941661
$842$	76.6120	2.64022
$843$	60.4213	2.08102
$844$	−98.6746	−3.39652
$845$	−17.7895	−0.611977
$846$	3.47843	0.119591
$847$	1.23299	0.0423660
$848$	−7.88507	−0.270774
$849$	−65.7382	−2.25613
$850$	−0.529972	−0.0181779
$851$	3.32740	0.114062
$852$	35.1192	1.20316
$853$	20.5753	0.704486	0.352243	−	0.935909i	$-0.385419\pi$
$853$	20.5753	0.704486	0.352243	+	0.935909i	$0.385419\pi$
$854$	−31.7328	−1.08587
$855$	2.63406	0.0900829
$856$	−45.1152	−1.54201
$857$	−2.67960	−0.0915335	−0.0457667	−	0.998952i	$-0.514573\pi$
$857$	−2.67960	−0.0915335	−0.0457667	+	0.998952i	$0.514573\pi$
$858$	−11.5465	−0.394190
$859$	44.6601	1.52378	0.761892	−	0.647704i	$-0.224271\pi$
$859$	44.6601	1.52378	0.761892	+	0.647704i	$0.224271\pi$
$860$	−47.3667	−1.61519
$861$	21.9631	0.748502
$862$	−75.0353	−2.55571
$863$	−17.5287	−0.596685	−0.298342	−	0.954459i	$-0.596434\pi$
$863$	−17.5287	−0.596685	−0.298342	+	0.954459i	$0.596434\pi$
$864$	−44.5530	−1.51572
$865$	−7.93830	−0.269910
$866$	−66.7326	−2.26767
$867$	35.3147	1.19935
$868$	−58.1517	−1.97380
$869$	−5.32475	−0.180630
$870$	−14.8099	−0.502102
$871$	−8.67585	−0.293970
$872$	−127.943	−4.33268
$873$	6.21465	0.210334
$874$	−1.80355	−0.0610058
$875$	−14.6043	−0.493715
$876$	−140.943	−4.76203
$877$	−21.7318	−0.733831	−0.366915	−	0.930254i	$-0.619586\pi$
$877$	−21.7318	−0.733831	−0.366915	+	0.930254i	$0.619586\pi$
$878$	−35.5444	−1.19956
$879$	−12.1746	−0.410640
$880$	22.4566	0.757012
$881$	1.17903	0.0397224	0.0198612	−	0.999803i	$-0.493678\pi$
$881$	1.17903	0.0397224	0.0198612	+	0.999803i	$0.493678\pi$
$882$	19.5975	0.659883
$883$	8.87320	0.298607	0.149303	−	0.988791i	$-0.452297\pi$
$883$	8.87320	0.298607	0.149303	+	0.988791i	$0.452297\pi$
$884$	2.84327	0.0956296
$885$	41.6611	1.40042
$886$	−57.9382	−1.94647
$887$	−17.8759	−0.600215	−0.300108	−	0.953905i	$-0.597023\pi$
$887$	−17.8759	−0.600215	−0.300108	+	0.953905i	$0.597023\pi$
$888$	75.6337	2.53810
$889$	22.7130	0.761770
$890$	101.644	3.40713
$891$	−11.2285	−0.376168
$892$	−14.8200	−0.496210
$893$	−0.916831	−0.0306806
$894$	−67.4981	−2.25747
$895$	36.8793	1.23274
$896$	−8.81615	−0.294527
$897$	3.16301	0.105610
$898$	65.3205	2.17977
$899$	12.3075	0.410478
$900$	−4.96535	−0.165512
$901$	0.197511	0.00658004
$902$	22.5628	0.751258
$903$	11.8393	0.393987
$904$	−56.5891	−1.88212
$905$	12.1799	0.404873
$906$	86.4865	2.87332
$907$	49.4549	1.64212	0.821061	−	0.570840i	$-0.193382\pi$
$907$	49.4549	1.64212	0.821061	+	0.570840i	$0.193382\pi$
$908$	−4.82172	−0.160014
$909$	20.4936	0.679730
$910$	14.0897	0.467071
$911$	44.5328	1.47544	0.737719	−	0.675108i	$-0.235903\pi$
$911$	44.5328	1.47544	0.737719	+	0.675108i	$0.235903\pi$
$912$	−21.3893	−0.708270
$913$	14.7990	0.489774
$914$	−30.5091	−1.00915
$915$	−41.9559	−1.38702
$916$	34.9753	1.15562
$917$	−0.991199	−0.0327323
$918$	2.47359	0.0816406
$919$	−5.03420	−0.166063	−0.0830315	−	0.996547i	$-0.526460\pi$
$919$	−5.03420	−0.166063	−0.0830315	+	0.996547i	$0.526460\pi$
$920$	−11.7906	−0.388725
$921$	66.9679	2.20667
$922$	−85.3440	−2.81066
$923$	7.07138	0.232757
$924$	−12.8226	−0.421834
$925$	−3.38337	−0.111245
$926$	−5.82613	−0.191459
$927$	−0.426969	−0.0140235
$928$	16.8663	0.553665
$929$	42.8393	1.40551	0.702756	−	0.711431i	$-0.251952\pi$
$929$	42.8393	1.40551	0.702756	+	0.711431i	$0.251952\pi$
$930$	−107.737	−3.53282
$931$	−5.16543	−0.169290
$932$	−79.2243	−2.59508
$933$	−24.4533	−0.800565
$934$	−29.1374	−0.953406
$935$	−0.562510	−0.0183960
$936$	22.3499	0.730528
$937$	3.44928	0.112683	0.0563415	−	0.998412i	$-0.482056\pi$
$937$	3.44928	0.112683	0.0563415	+	0.998412i	$0.482056\pi$
$938$	−13.5007	−0.440814
$939$	3.36786	0.109906
$940$	−10.0105	−0.326507
$941$	−6.39382	−0.208433	−0.104216	−	0.994555i	$-0.533233\pi$
$941$	−6.39382	−0.208433	−0.104216	+	0.994555i	$0.533233\pi$
$942$	−76.9751	−2.50798
$943$	−6.18080	−0.201274
$944$	−105.164	−3.42278
$945$	8.74774	0.284564
$946$	12.1625	0.395438
$947$	16.1243	0.523968	0.261984	−	0.965072i	$-0.415623\pi$
$947$	16.1243	0.523968	0.261984	+	0.965072i	$0.415623\pi$
$948$	55.3755	1.79851
$949$	−28.3794	−0.921235
$950$	1.83388	0.0594990
$951$	−18.9618	−0.614877
$952$	2.64915	0.0858596
$953$	44.7075	1.44822	0.724109	−	0.689686i	$-0.242251\pi$
$953$	44.7075	1.44822	0.724109	+	0.689686i	$0.242251\pi$
$954$	2.59301	0.0839517
$955$	−14.3370	−0.463933
$956$	−47.6663	−1.54164
$957$	2.71385	0.0877263
$958$	−6.73797	−0.217694
$959$	14.9385	0.482390
$960$	−53.9345	−1.74073
$961$	58.5328	1.88815
$962$	25.4350	0.820057
$963$	7.74071	0.249441
$964$	87.8279	2.82875
$965$	2.44982	0.0788626
$966$	4.92205	0.158364
$967$	41.9841	1.35012	0.675059	−	0.737764i	$-0.264118\pi$
$967$	41.9841	1.35012	0.675059	+	0.737764i	$0.264118\pi$
$968$	−7.88714	−0.253502
$969$	0.535774	0.0172116
$970$	−25.0614	−0.804674
$971$	−25.0982	−0.805441	−0.402720	−	0.915323i	$-0.631935\pi$
$971$	−25.0982	−0.805441	−0.402720	+	0.915323i	$0.631935\pi$
$972$	65.3951	2.09755
$973$	6.37091	0.204242
$974$	61.5852	1.97332
$975$	−3.21622	−0.103001
$976$	105.908	3.39002
$977$	−15.9195	−0.509309	−0.254655	−	0.967032i	$-0.581962\pi$
$977$	−15.9195	−0.509309	−0.254655	+	0.967032i	$0.581962\pi$
$978$	115.035	3.67841
$979$	−18.6259	−0.595287
$980$	−56.3992	−1.80161
$981$	21.9519	0.700872
$982$	−117.022	−3.73431
$983$	46.6027	1.48640	0.743198	−	0.669071i	$-0.233308\pi$
$983$	46.6027	1.48640	0.743198	+	0.669071i	$0.233308\pi$
$984$	−140.493	−4.47875
$985$	2.64897	0.0844033
$986$	−0.936422	−0.0298217
$987$	2.50212	0.0796434
$988$	−9.83868	−0.313010
$989$	−3.33178	−0.105944
$990$	−7.38487	−0.234706
$991$	1.64345	0.0522058	0.0261029	−	0.999659i	$-0.491690\pi$
$991$	1.64345	0.0522058	0.0261029	+	0.999659i	$0.491690\pi$
$992$	122.697	3.89562
$993$	−53.3180	−1.69199
$994$	11.0040	0.349025
$995$	41.5179	1.31621
$996$	−153.904	−4.87664
$997$	−5.28013	−0.167223	−0.0836117	−	0.996498i	$-0.526646\pi$
$997$	−5.28013	−0.167223	−0.0836117	+	0.996498i	$0.526646\pi$
$998$	56.9305	1.80210
$999$	15.7915	0.499622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.6	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.6	✓	119	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64280 q^{2} -2.08644 q^{3} +4.98439 q^{4} +2.06491 q^{5} +5.51405 q^{6} +1.23299 q^{7} -7.88714 q^{8} +1.35325 q^{9} +O(q^{10})\)	\(q-2.64280 q^{2} -2.08644 q^{3} +4.98439 q^{4} +2.06491 q^{5} +5.51405 q^{6} +1.23299 q^{7} -7.88714 q^{8} +1.35325 q^{9} -5.45715 q^{10} +1.00000 q^{11} -10.3996 q^{12} -2.09401 q^{13} -3.25854 q^{14} -4.30832 q^{15} +10.8753 q^{16} -0.272413 q^{17} -3.57636 q^{18} +0.942642 q^{19} +10.2923 q^{20} -2.57256 q^{21} -2.64280 q^{22} +0.723963 q^{23} +16.4561 q^{24} -0.736140 q^{25} +5.53404 q^{26} +3.43586 q^{27} +6.14570 q^{28} -1.30071 q^{29} +11.3860 q^{30} -9.46217 q^{31} -12.9671 q^{32} -2.08644 q^{33} +0.719934 q^{34} +2.54601 q^{35} +6.74511 q^{36} +4.59610 q^{37} -2.49121 q^{38} +4.36903 q^{39} -16.2862 q^{40} -8.53745 q^{41} +6.79877 q^{42} -4.60214 q^{43} +4.98439 q^{44} +2.79433 q^{45} -1.91329 q^{46} -0.972619 q^{47} -22.6908 q^{48} -5.47974 q^{49} +1.94547 q^{50} +0.568375 q^{51} -10.4373 q^{52} -0.725041 q^{53} -9.08028 q^{54} +2.06491 q^{55} -9.72475 q^{56} -1.96677 q^{57} +3.43750 q^{58} -9.66991 q^{59} -21.4743 q^{60} +9.73833 q^{61} +25.0066 q^{62} +1.66854 q^{63} +12.5187 q^{64} -4.32394 q^{65} +5.51405 q^{66} +4.14318 q^{67} -1.35781 q^{68} -1.51051 q^{69} -6.72860 q^{70} -3.37696 q^{71} -10.6732 q^{72} +13.5527 q^{73} -12.1466 q^{74} +1.53592 q^{75} +4.69849 q^{76} +1.23299 q^{77} -11.5465 q^{78} -5.32475 q^{79} +22.4566 q^{80} -11.2285 q^{81} +22.5628 q^{82} +14.7990 q^{83} -12.8226 q^{84} -0.562510 q^{85} +12.1625 q^{86} +2.71385 q^{87} -7.88714 q^{88} -18.6259 q^{89} -7.38487 q^{90} -2.58189 q^{91} +3.60851 q^{92} +19.7423 q^{93} +2.57044 q^{94} +1.94647 q^{95} +27.0551 q^{96} +4.59240 q^{97} +14.4818 q^{98} +1.35325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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