LMFDB - Embedded newform 6013.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88015 q^{2} -2.98311 q^{3} +1.53497 q^{4} +2.43013 q^{5} +5.60869 q^{6} +1.00000 q^{7} +0.874328 q^{8} +5.89893 q^{9} +O(q^{10})$	\(q-1.88015 q^{2} -2.98311 q^{3} +1.53497 q^{4} +2.43013 q^{5} +5.60869 q^{6} +1.00000 q^{7} +0.874328 q^{8} +5.89893 q^{9} -4.56900 q^{10} +4.23272 q^{11} -4.57898 q^{12} +2.14838 q^{13} -1.88015 q^{14} -7.24933 q^{15} -4.71381 q^{16} +3.69258 q^{17} -11.0909 q^{18} +1.95008 q^{19} +3.73017 q^{20} -2.98311 q^{21} -7.95815 q^{22} -1.47812 q^{23} -2.60822 q^{24} +0.905511 q^{25} -4.03929 q^{26} -8.64783 q^{27} +1.53497 q^{28} +2.82206 q^{29} +13.6298 q^{30} +7.67949 q^{31} +7.11402 q^{32} -12.6267 q^{33} -6.94260 q^{34} +2.43013 q^{35} +9.05468 q^{36} -0.784587 q^{37} -3.66645 q^{38} -6.40886 q^{39} +2.12473 q^{40} -7.66749 q^{41} +5.60869 q^{42} +7.36081 q^{43} +6.49709 q^{44} +14.3351 q^{45} +2.77909 q^{46} +6.79326 q^{47} +14.0618 q^{48} +1.00000 q^{49} -1.70250 q^{50} -11.0154 q^{51} +3.29770 q^{52} +7.85333 q^{53} +16.2592 q^{54} +10.2860 q^{55} +0.874328 q^{56} -5.81731 q^{57} -5.30589 q^{58} +0.0575512 q^{59} -11.1275 q^{60} +12.7978 q^{61} -14.4386 q^{62} +5.89893 q^{63} -3.94781 q^{64} +5.22084 q^{65} +23.7400 q^{66} +11.3642 q^{67} +5.66799 q^{68} +4.40940 q^{69} -4.56900 q^{70} +0.760785 q^{71} +5.15760 q^{72} -4.23400 q^{73} +1.47514 q^{74} -2.70124 q^{75} +2.99332 q^{76} +4.23272 q^{77} +12.0496 q^{78} -4.10291 q^{79} -11.4551 q^{80} +8.10061 q^{81} +14.4160 q^{82} +5.25120 q^{83} -4.57898 q^{84} +8.97342 q^{85} -13.8394 q^{86} -8.41850 q^{87} +3.70079 q^{88} +2.50755 q^{89} -26.9523 q^{90} +2.14838 q^{91} -2.26887 q^{92} -22.9087 q^{93} -12.7724 q^{94} +4.73895 q^{95} -21.2219 q^{96} +2.23817 q^{97} -1.88015 q^{98} +24.9685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) $ 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.88015	−1.32947	−0.664734	−	0.747080i	$-0.731455\pi$
$2$	−1.88015	−1.32947	−0.664734	+	0.747080i	$0.731455\pi$
$3$	−2.98311	−1.72230	−0.861149	−	0.508352i	$-0.830255\pi$
$3$	−2.98311	−1.72230	−0.861149	+	0.508352i	$0.830255\pi$
$4$	1.53497	0.767485
$5$	2.43013	1.08679	0.543393	−	0.839479i	$-0.317140\pi$
$5$	2.43013	1.08679	0.543393	+	0.839479i	$0.317140\pi$
$6$	5.60869	2.28974
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.874328	0.309122
$9$	5.89893	1.96631
$10$	−4.56900	−1.44485
$11$	4.23272	1.27621	0.638106	−	0.769948i	$-0.279718\pi$
$11$	4.23272	1.27621	0.638106	+	0.769948i	$0.279718\pi$
$12$	−4.57898	−1.32184
$13$	2.14838	0.595854	0.297927	−	0.954589i	$-0.403705\pi$
$13$	2.14838	0.595854	0.297927	+	0.954589i	$0.403705\pi$
$14$	−1.88015	−0.502492
$15$	−7.24933	−1.87177
$16$	−4.71381	−1.17845
$17$	3.69258	0.895581	0.447790	−	0.894139i	$-0.352211\pi$
$17$	3.69258	0.895581	0.447790	+	0.894139i	$0.352211\pi$
$18$	−11.0909	−2.61415
$19$	1.95008	0.447380	0.223690	−	0.974660i	$-0.428190\pi$
$19$	1.95008	0.447380	0.223690	+	0.974660i	$0.428190\pi$
$20$	3.73017	0.834091
$21$	−2.98311	−0.650968
$22$	−7.95815	−1.69668
$23$	−1.47812	−0.308210	−0.154105	−	0.988055i	$-0.549249\pi$
$23$	−1.47812	−0.308210	−0.154105	+	0.988055i	$0.549249\pi$
$24$	−2.60822	−0.532400
$25$	0.905511	0.181102
$26$	−4.03929	−0.792169
$27$	−8.64783	−1.66428
$28$	1.53497	0.290082
$29$	2.82206	0.524043	0.262021	−	0.965062i	$-0.415611\pi$
$29$	2.82206	0.524043	0.262021	+	0.965062i	$0.415611\pi$
$30$	13.6298	2.48846
$31$	7.67949	1.37928	0.689638	−	0.724154i	$-0.257769\pi$
$31$	7.67949	1.37928	0.689638	+	0.724154i	$0.257769\pi$
$32$	7.11402	1.25759
$33$	−12.6267	−2.19802
$34$	−6.94260	−1.19065
$35$	2.43013	0.410766
$36$	9.05468	1.50911
$37$	−0.784587	−0.128985	−0.0644927	−	0.997918i	$-0.520543\pi$
$37$	−0.784587	−0.128985	−0.0644927	+	0.997918i	$0.520543\pi$
$38$	−3.66645	−0.594777
$39$	−6.40886	−1.02624
$40$	2.12473	0.335949
$41$	−7.66749	−1.19746	−0.598731	−	0.800951i	$-0.704328\pi$
$41$	−7.66749	−1.19746	−0.598731	+	0.800951i	$0.704328\pi$
$42$	5.60869	0.865440
$43$	7.36081	1.12251	0.561256	−	0.827642i	$-0.310318\pi$
$43$	7.36081	1.12251	0.561256	+	0.827642i	$0.310318\pi$
$44$	6.49709	0.979474
$45$	14.3351	2.13696
$46$	2.77909	0.409755
$47$	6.79326	0.990899	0.495449	−	0.868637i	$-0.335003\pi$
$47$	6.79326	0.990899	0.495449	+	0.868637i	$0.335003\pi$
$48$	14.0618	2.02965
$49$	1.00000	0.142857
$50$	−1.70250	−0.240770
$51$	−11.0154	−1.54246
$52$	3.29770	0.457309
$53$	7.85333	1.07874	0.539369	−	0.842070i	$-0.318663\pi$
$53$	7.85333	1.07874	0.539369	+	0.842070i	$0.318663\pi$
$54$	16.2592	2.21260
$55$	10.2860	1.38697
$56$	0.874328	0.116837
$57$	−5.81731	−0.770522
$58$	−5.30589	−0.696698
$59$	0.0575512	0.00749253	0.00374626	−	0.999993i	$-0.498808\pi$
$59$	0.0575512	0.00749253	0.00374626	+	0.999993i	$0.498808\pi$
$60$	−11.1275	−1.43655
$61$	12.7978	1.63860	0.819298	−	0.573368i	$-0.194363\pi$
$61$	12.7978	1.63860	0.819298	+	0.573368i	$0.194363\pi$
$62$	−14.4386	−1.83370
$63$	5.89893	0.743196
$64$	−3.94781	−0.493476
$65$	5.22084	0.647566
$66$	23.7400	2.92220
$67$	11.3642	1.38836	0.694180	−	0.719802i	$-0.255767\pi$
$67$	11.3642	1.38836	0.694180	+	0.719802i	$0.255767\pi$
$68$	5.66799	0.687345
$69$	4.40940	0.530829
$70$	−4.56900	−0.546100
$71$	0.760785	0.0902885	0.0451443	−	0.998980i	$-0.485625\pi$
$71$	0.760785	0.0902885	0.0451443	+	0.998980i	$0.485625\pi$
$72$	5.15760	0.607829
$73$	−4.23400	−0.495553	−0.247776	−	0.968817i	$-0.579700\pi$
$73$	−4.23400	−0.495553	−0.247776	+	0.968817i	$0.579700\pi$
$74$	1.47514	0.171482
$75$	−2.70124	−0.311912
$76$	2.99332	0.343357
$77$	4.23272	0.482363
$78$	12.0496	1.36435
$79$	−4.10291	−0.461614	−0.230807	−	0.973000i	$-0.574137\pi$
$79$	−4.10291	−0.461614	−0.230807	+	0.973000i	$0.574137\pi$
$80$	−11.4551	−1.28072
$81$	8.10061	0.900068
$82$	14.4160	1.59199
$83$	5.25120	0.576394	0.288197	−	0.957571i	$-0.406944\pi$
$83$	5.25120	0.576394	0.288197	+	0.957571i	$0.406944\pi$
$84$	−4.57898	−0.499608
$85$	8.97342	0.973304
$86$	−13.8394	−1.49234
$87$	−8.41850	−0.902558
$88$	3.70079	0.394505
$89$	2.50755	0.265800	0.132900	−	0.991129i	$-0.457571\pi$
$89$	2.50755	0.265800	0.132900	+	0.991129i	$0.457571\pi$
$90$	−26.9523	−2.84102
$91$	2.14838	0.225212
$92$	−2.26887	−0.236546
$93$	−22.9087	−2.37553
$94$	−12.7724	−1.31737
$95$	4.73895	0.486206
$96$	−21.2219	−2.16595
$97$	2.23817	0.227251	0.113626	−	0.993524i	$-0.463754\pi$
$97$	2.23817	0.227251	0.113626	+	0.993524i	$0.463754\pi$
$98$	−1.88015	−0.189924
$99$	24.9685	2.50943
$100$	1.38993	0.138993
$101$	−10.7269	−1.06737	−0.533685	−	0.845683i	$-0.679193\pi$
$101$	−10.7269	−1.06737	−0.533685	+	0.845683i	$0.679193\pi$
$102$	20.7105	2.05065
$103$	15.8544	1.56218	0.781090	−	0.624418i	$-0.214664\pi$
$103$	15.8544	1.56218	0.781090	+	0.624418i	$0.214664\pi$
$104$	1.87839	0.184192
$105$	−7.24933	−0.707462
$106$	−14.7655	−1.43415
$107$	1.60570	0.155229	0.0776146	−	0.996983i	$-0.475270\pi$
$107$	1.60570	0.155229	0.0776146	+	0.996983i	$0.475270\pi$
$108$	−13.2742	−1.27731
$109$	−11.9969	−1.14909	−0.574547	−	0.818472i	$-0.694822\pi$
$109$	−11.9969	−1.14909	−0.574547	+	0.818472i	$0.694822\pi$
$110$	−19.3393	−1.84393
$111$	2.34051	0.222151
$112$	−4.71381	−0.445413
$113$	21.0140	1.97683	0.988417	−	0.151765i	$-0.0484956\pi$
$113$	21.0140	1.97683	0.988417	+	0.151765i	$0.0484956\pi$
$114$	10.9374	1.02438
$115$	−3.59202	−0.334958
$116$	4.33177	0.402195
$117$	12.6732	1.17164
$118$	−0.108205	−0.00996108
$119$	3.69258	0.338498
$120$	−6.33829	−0.578604
$121$	6.91591	0.628719
$122$	−24.0619	−2.17846
$123$	22.8730	2.06239
$124$	11.7878	1.05857
$125$	−9.95012	−0.889966
$126$	−11.0909	−0.988055
$127$	12.1581	1.07886	0.539430	−	0.842031i	$-0.318640\pi$
$127$	12.1581	1.07886	0.539430	+	0.842031i	$0.318640\pi$
$128$	−6.80555	−0.601531
$129$	−21.9581	−1.93330
$130$	−9.81597	−0.860918
$131$	−18.7159	−1.63522	−0.817610	−	0.575773i	$-0.804701\pi$
$131$	−18.7159	−1.63522	−0.817610	+	0.575773i	$0.804701\pi$
$132$	−19.3815	−1.68695
$133$	1.95008	0.169094
$134$	−21.3664	−1.84578
$135$	−21.0153	−1.80871
$136$	3.22852	0.276844
$137$	0.152629	0.0130400	0.00652000	−	0.999979i	$-0.497925\pi$
$137$	0.152629	0.0130400	0.00652000	+	0.999979i	$0.497925\pi$
$138$	−8.29033	−0.705720
$139$	8.07727	0.685105	0.342552	−	0.939499i	$-0.388709\pi$
$139$	8.07727	0.685105	0.342552	+	0.939499i	$0.388709\pi$
$140$	3.73017	0.315257
$141$	−20.2650	−1.70662
$142$	−1.43039	−0.120036
$143$	9.09350	0.760437
$144$	−27.8064	−2.31720
$145$	6.85795	0.569522
$146$	7.96057	0.658821
$147$	−2.98311	−0.246043
$148$	−1.20432	−0.0989943
$149$	−5.66945	−0.464460	−0.232230	−	0.972661i	$-0.574602\pi$
$149$	−5.66945	−0.464460	−0.232230	+	0.972661i	$0.574602\pi$
$150$	5.07873	0.414677
$151$	20.4524	1.66439	0.832196	−	0.554482i	$-0.187083\pi$
$151$	20.4524	1.66439	0.832196	+	0.554482i	$0.187083\pi$
$152$	1.70501	0.138295
$153$	21.7823	1.76099
$154$	−7.95815	−0.641286
$155$	18.6621	1.49898
$156$	−9.83740	−0.787623
$157$	−16.0509	−1.28100	−0.640501	−	0.767957i	$-0.721273\pi$
$157$	−16.0509	−1.28100	−0.640501	+	0.767957i	$0.721273\pi$
$158$	7.71410	0.613700
$159$	−23.4273	−1.85791
$160$	17.2880	1.36673
$161$	−1.47812	−0.116492
$162$	−15.2304	−1.19661
$163$	−6.98218	−0.546887	−0.273443	−	0.961888i	$-0.588163\pi$
$163$	−6.98218	−0.546887	−0.273443	+	0.961888i	$0.588163\pi$
$164$	−11.7694	−0.919033
$165$	−30.6844	−2.38877
$166$	−9.87305	−0.766297
$167$	17.5545	1.35841	0.679205	−	0.733949i	$-0.262325\pi$
$167$	17.5545	1.35841	0.679205	+	0.733949i	$0.262325\pi$
$168$	−2.60822	−0.201228
$169$	−8.38445	−0.644958
$170$	−16.8714	−1.29398
$171$	11.5034	0.879688
$172$	11.2986	0.861511
$173$	−9.85217	−0.749047	−0.374523	−	0.927217i	$-0.622194\pi$
$173$	−9.85217	−0.749047	−0.374523	+	0.927217i	$0.622194\pi$
$174$	15.8281	1.19992
$175$	0.905511	0.0684502
$176$	−19.9522	−1.50396
$177$	−0.171681	−0.0129044
$178$	−4.71457	−0.353372
$179$	−4.06461	−0.303803	−0.151902	−	0.988396i	$-0.548540\pi$
$179$	−4.06461	−0.303803	−0.151902	+	0.988396i	$0.548540\pi$
$180$	22.0040	1.64008
$181$	2.19599	0.163226	0.0816132	−	0.996664i	$-0.473993\pi$
$181$	2.19599	0.163226	0.0816132	+	0.996664i	$0.473993\pi$
$182$	−4.03929	−0.299412
$183$	−38.1774	−2.82215
$184$	−1.29236	−0.0952743
$185$	−1.90665	−0.140179
$186$	43.0719	3.15819
$187$	15.6296	1.14295
$188$	10.4274	0.760499
$189$	−8.64783	−0.629037
$190$	−8.90994	−0.646395
$191$	−23.0059	−1.66464	−0.832322	−	0.554292i	$-0.812989\pi$
$191$	−23.0059	−1.66464	−0.832322	+	0.554292i	$0.812989\pi$
$192$	11.7767	0.849914
$193$	−24.1237	−1.73646	−0.868231	−	0.496160i	$-0.834743\pi$
$193$	−24.1237	−1.73646	−0.868231	+	0.496160i	$0.834743\pi$
$194$	−4.20809	−0.302124
$195$	−15.5743	−1.11530
$196$	1.53497	0.109641
$197$	7.86021	0.560017	0.280008	−	0.959998i	$-0.409663\pi$
$197$	7.86021	0.560017	0.280008	+	0.959998i	$0.409663\pi$
$198$	−46.9446	−3.33621
$199$	19.6170	1.39061	0.695307	−	0.718713i	$-0.255268\pi$
$199$	19.6170	1.39061	0.695307	+	0.718713i	$0.255268\pi$
$200$	0.791714	0.0559826
$201$	−33.9007	−2.39117
$202$	20.1683	1.41903
$203$	2.82206	0.198070
$204$	−16.9082	−1.18381
$205$	−18.6330	−1.30138
$206$	−29.8087	−2.07687
$207$	−8.71934	−0.606036
$208$	−10.1271	−0.702186
$209$	8.25416	0.570952
$210$	13.6298	0.940548
$211$	−18.8520	−1.29782	−0.648912	−	0.760863i	$-0.724776\pi$
$211$	−18.8520	−1.29782	−0.648912	+	0.760863i	$0.724776\pi$
$212$	12.0546	0.827915
$213$	−2.26950	−0.155504
$214$	−3.01897	−0.206372
$215$	17.8877	1.21993
$216$	−7.56104	−0.514464
$217$	7.67949	0.521318
$218$	22.5560	1.52768
$219$	12.6305	0.853489
$220$	15.7888	1.06448
$221$	7.93307	0.533636
$222$	−4.40051	−0.295343
$223$	−4.50235	−0.301499	−0.150750	−	0.988572i	$-0.548169\pi$
$223$	−4.50235	−0.301499	−0.150750	+	0.988572i	$0.548169\pi$
$224$	7.11402	0.475325
$225$	5.34155	0.356103
$226$	−39.5096	−2.62814
$227$	−18.8493	−1.25107	−0.625535	−	0.780196i	$-0.715119\pi$
$227$	−18.8493	−1.25107	−0.625535	+	0.780196i	$0.715119\pi$
$228$	−8.92940	−0.591364
$229$	−29.9967	−1.98223	−0.991117	−	0.132990i	$-0.957542\pi$
$229$	−29.9967	−1.98223	−0.991117	+	0.132990i	$0.957542\pi$
$230$	6.75354	0.445315
$231$	−12.6267	−0.830773
$232$	2.46740	0.161993
$233$	0.676619	0.0443268	0.0221634	−	0.999754i	$-0.492945\pi$
$233$	0.676619	0.0443268	0.0221634	+	0.999754i	$0.492945\pi$
$234$	−23.8275	−1.55765
$235$	16.5085	1.07689
$236$	0.0883393	0.00575040
$237$	12.2394	0.795036
$238$	−6.94260	−0.450022
$239$	25.9148	1.67629	0.838143	−	0.545450i	$-0.183641\pi$
$239$	25.9148	1.67629	0.838143	+	0.545450i	$0.183641\pi$
$240$	34.1719	2.20579
$241$	−1.06026	−0.0682974	−0.0341487	−	0.999417i	$-0.510872\pi$
$241$	−1.06026	−0.0682974	−0.0341487	+	0.999417i	$0.510872\pi$
$242$	−13.0029	−0.835861
$243$	1.77849	0.114090
$244$	19.6443	1.25760
$245$	2.43013	0.155255
$246$	−43.0046	−2.74187
$247$	4.18953	0.266573
$248$	6.71439	0.426364
$249$	−15.6649	−0.992723
$250$	18.7077	1.18318
$251$	−1.84779	−0.116631	−0.0583156	−	0.998298i	$-0.518573\pi$
$251$	−1.84779	−0.116631	−0.0583156	+	0.998298i	$0.518573\pi$
$252$	9.05468	0.570391
$253$	−6.25647	−0.393341
$254$	−22.8591	−1.43431
$255$	−26.7687	−1.67632
$256$	20.6911	1.29319
$257$	0.561345	0.0350157	0.0175079	−	0.999847i	$-0.494427\pi$
$257$	0.561345	0.0350157	0.0175079	+	0.999847i	$0.494427\pi$
$258$	41.2845	2.57026
$259$	−0.784587	−0.0487519
$260$	8.01383	0.496997
$261$	16.6471	1.03043
$262$	35.1888	2.17397
$263$	0.519382	0.0320265	0.0160132	−	0.999872i	$-0.494903\pi$
$263$	0.519382	0.0320265	0.0160132	+	0.999872i	$0.494903\pi$
$264$	−11.0398	−0.679455
$265$	19.0846	1.17236
$266$	−3.66645	−0.224805
$267$	−7.48029	−0.457786
$268$	17.4437	1.06554
$269$	8.89410	0.542283	0.271142	−	0.962539i	$-0.412599\pi$
$269$	8.89410	0.542283	0.271142	+	0.962539i	$0.412599\pi$
$270$	39.5120	2.40462
$271$	−22.9266	−1.39269	−0.696345	−	0.717707i	$-0.745192\pi$
$271$	−22.9266	−1.39269	−0.696345	+	0.717707i	$0.745192\pi$
$272$	−17.4061	−1.05540
$273$	−6.40886	−0.387882
$274$	−0.286966	−0.0173363
$275$	3.83277	0.231125
$276$	6.76829	0.407403
$277$	−22.8258	−1.37147	−0.685734	−	0.727852i	$-0.740519\pi$
$277$	−22.8258	−1.37147	−0.685734	+	0.727852i	$0.740519\pi$
$278$	−15.1865	−0.910825
$279$	45.3008	2.71209
$280$	2.12473	0.126977
$281$	−0.582712	−0.0347617	−0.0173808	−	0.999849i	$-0.505533\pi$
$281$	−0.582712	−0.0347617	−0.0173808	+	0.999849i	$0.505533\pi$
$282$	38.1013	2.26890
$283$	−9.54163	−0.567191	−0.283596	−	0.958944i	$-0.591527\pi$
$283$	−9.54163	−0.567191	−0.283596	+	0.958944i	$0.591527\pi$
$284$	1.16778	0.0692951
$285$	−14.1368	−0.837392
$286$	−17.0972	−1.01098
$287$	−7.66749	−0.452598
$288$	41.9651	2.47282
$289$	−3.36489	−0.197935
$290$	−12.8940	−0.757161
$291$	−6.67670	−0.391395
$292$	−6.49906	−0.380329
$293$	17.4206	1.01772	0.508860	−	0.860849i	$-0.330067\pi$
$293$	17.4206	1.01772	0.508860	+	0.860849i	$0.330067\pi$
$294$	5.60869	0.327106
$295$	0.139857	0.00814277
$296$	−0.685987	−0.0398722
$297$	−36.6038	−2.12397
$298$	10.6594	0.617484
$299$	−3.17557	−0.183648
$300$	−4.14632	−0.239388
$301$	7.36081	0.424270
$302$	−38.4536	−2.21276
$303$	31.9996	1.83833
$304$	−9.19232	−0.527216
$305$	31.1004	1.78080
$306$	−40.9539	−2.34118
$307$	0.601170	0.0343106	0.0171553	−	0.999853i	$-0.494539\pi$
$307$	0.601170	0.0343106	0.0171553	+	0.999853i	$0.494539\pi$
$308$	6.49709	0.370206
$309$	−47.2954	−2.69054
$310$	−35.0876	−1.99284
$311$	−3.03774	−0.172254	−0.0861271	−	0.996284i	$-0.527449\pi$
$311$	−3.03774	−0.172254	−0.0861271	+	0.996284i	$0.527449\pi$
$312$	−5.60345	−0.317233
$313$	−18.4034	−1.04022	−0.520110	−	0.854099i	$-0.674109\pi$
$313$	−18.4034	−1.04022	−0.520110	+	0.854099i	$0.674109\pi$
$314$	30.1782	1.70305
$315$	14.3351	0.807694
$316$	−6.29784	−0.354281
$317$	−4.91107	−0.275833	−0.137917	−	0.990444i	$-0.544041\pi$
$317$	−4.91107	−0.275833	−0.137917	+	0.990444i	$0.544041\pi$
$318$	44.0469	2.47003
$319$	11.9450	0.668790
$320$	−9.59368	−0.536303
$321$	−4.78999	−0.267351
$322$	2.77909	0.154873
$323$	7.20083	0.400665
$324$	12.4342	0.690789
$325$	1.94538	0.107911
$326$	13.1276	0.727068
$327$	35.7880	1.97908
$328$	−6.70390	−0.370161
$329$	6.79326	0.374524
$330$	57.6912	3.17580
$331$	1.64051	0.0901703	0.0450852	−	0.998983i	$-0.485644\pi$
$331$	1.64051	0.0901703	0.0450852	+	0.998983i	$0.485644\pi$
$332$	8.06043	0.442374
$333$	−4.62823	−0.253625
$334$	−33.0052	−1.80596
$335$	27.6165	1.50885
$336$	14.0618	0.767134
$337$	18.4121	1.00297	0.501484	−	0.865167i	$-0.332787\pi$
$337$	18.4121	1.00297	0.501484	+	0.865167i	$0.332787\pi$
$338$	15.7640	0.857450
$339$	−62.6871	−3.40470
$340$	13.7739	0.746996
$341$	32.5051	1.76025
$342$	−21.6282	−1.16952
$343$	1.00000	0.0539949
$344$	6.43576	0.346993
$345$	10.7154	0.576897
$346$	18.5236	0.995834
$347$	−23.4993	−1.26151	−0.630755	−	0.775982i	$-0.717255\pi$
$347$	−23.4993	−1.26151	−0.630755	+	0.775982i	$0.717255\pi$
$348$	−12.9221	−0.692699
$349$	15.5154	0.830522	0.415261	−	0.909702i	$-0.363690\pi$
$349$	15.5154	0.830522	0.415261	+	0.909702i	$0.363690\pi$
$350$	−1.70250	−0.0910023
$351$	−18.5789	−0.991666
$352$	30.1116	1.60496
$353$	−25.1106	−1.33650	−0.668252	−	0.743935i	$-0.732957\pi$
$353$	−25.1106	−1.33650	−0.668252	+	0.743935i	$0.732957\pi$
$354$	0.322787	0.0171559
$355$	1.84880	0.0981242
$356$	3.84901	0.203997
$357$	−11.0154	−0.582994
$358$	7.64209	0.403897
$359$	−31.3686	−1.65557	−0.827786	−	0.561043i	$-0.810400\pi$
$359$	−31.3686	−1.65557	−0.827786	+	0.561043i	$0.810400\pi$
$360$	12.5336	0.660580
$361$	−15.1972	−0.799851
$362$	−4.12879	−0.217004
$363$	−20.6309	−1.08284
$364$	3.29770	0.172847
$365$	−10.2892	−0.538559
$366$	71.7792	3.75196
$367$	17.9629	0.937655	0.468828	−	0.883290i	$-0.344677\pi$
$367$	17.9629	0.937655	0.468828	+	0.883290i	$0.344677\pi$
$368$	6.96758	0.363210
$369$	−45.2300	−2.35458
$370$	3.58478	0.186364
$371$	7.85333	0.407725
$372$	−35.1642	−1.82318
$373$	4.96081	0.256861	0.128431	−	0.991718i	$-0.459006\pi$
$373$	4.96081	0.256861	0.128431	+	0.991718i	$0.459006\pi$
$374$	−29.3861	−1.51952
$375$	29.6823	1.53279
$376$	5.93954	0.306308
$377$	6.06286	0.312253
$378$	16.2592	0.836285
$379$	1.00499	0.0516226	0.0258113	−	0.999667i	$-0.491783\pi$
$379$	1.00499	0.0516226	0.0258113	+	0.999667i	$0.491783\pi$
$380$	7.27414	0.373156
$381$	−36.2690	−1.85812
$382$	43.2545	2.21309
$383$	35.2561	1.80150	0.900752	−	0.434335i	$-0.143016\pi$
$383$	35.2561	1.80150	0.900752	+	0.434335i	$0.143016\pi$
$384$	20.3017	1.03602
$385$	10.2860	0.524225
$386$	45.3562	2.30857
$387$	43.4209	2.20721
$388$	3.43552	0.174412
$389$	11.5459	0.585399	0.292700	−	0.956204i	$-0.405446\pi$
$389$	11.5459	0.585399	0.292700	+	0.956204i	$0.405446\pi$
$390$	29.2821	1.48276
$391$	−5.45807	−0.276027
$392$	0.874328	0.0441602
$393$	55.8317	2.81634
$394$	−14.7784	−0.744525
$395$	−9.97059	−0.501675
$396$	38.3259	1.92595
$397$	15.4627	0.776049	0.388025	−	0.921649i	$-0.373158\pi$
$397$	15.4627	0.776049	0.388025	+	0.921649i	$0.373158\pi$
$398$	−36.8830	−1.84878
$399$	−5.81731	−0.291230
$400$	−4.26840	−0.213420
$401$	0.531699	0.0265518	0.0132759	−	0.999912i	$-0.495774\pi$
$401$	0.531699	0.0265518	0.0132759	+	0.999912i	$0.495774\pi$
$402$	63.7384	3.17898
$403$	16.4985	0.821848
$404$	−16.4655	−0.819190
$405$	19.6855	0.978181
$406$	−5.30589	−0.263327
$407$	−3.32094	−0.164613
$408$	−9.63103	−0.476807
$409$	−6.36430	−0.314695	−0.157347	−	0.987543i	$-0.550294\pi$
$409$	−6.36430	−0.314695	−0.157347	+	0.987543i	$0.550294\pi$
$410$	35.0328	1.73015
$411$	−0.455310	−0.0224588
$412$	24.3360	1.19895
$413$	0.0575512	0.00283191
$414$	16.3937	0.805705
$415$	12.7611	0.626417
$416$	15.2836	0.749342
$417$	−24.0954	−1.17996
$418$	−15.5191	−0.759062
$419$	10.7068	0.523060	0.261530	−	0.965195i	$-0.415773\pi$
$419$	10.7068	0.523060	0.261530	+	0.965195i	$0.415773\pi$
$420$	−11.1275	−0.542966
$421$	40.6602	1.98166	0.990828	−	0.135126i	$-0.0431440\pi$
$421$	40.6602	1.98166	0.990828	+	0.135126i	$0.0431440\pi$
$422$	35.4446	1.72542
$423$	40.0730	1.94841
$424$	6.86639	0.333461
$425$	3.34367	0.162192
$426$	4.26701	0.206737
$427$	12.7978	0.619331
$428$	2.46471	0.119136
$429$	−27.1269	−1.30970
$430$	−33.6315	−1.62186
$431$	−14.1760	−0.682835	−0.341418	−	0.939912i	$-0.610907\pi$
$431$	−14.1760	−0.682835	−0.341418	+	0.939912i	$0.610907\pi$
$432$	40.7642	1.96127
$433$	−7.21247	−0.346609	−0.173305	−	0.984868i	$-0.555445\pi$
$433$	−7.21247	−0.346609	−0.173305	+	0.984868i	$0.555445\pi$
$434$	−14.4386	−0.693075
$435$	−20.4580	−0.980887
$436$	−18.4149	−0.881912
$437$	−2.88246	−0.137887
$438$	−23.7472	−1.13469
$439$	−12.6409	−0.603318	−0.301659	−	0.953416i	$-0.597540\pi$
$439$	−12.6409	−0.603318	−0.301659	+	0.953416i	$0.597540\pi$
$440$	8.99337	0.428742
$441$	5.89893	0.280902
$442$	−14.9154	−0.709452
$443$	−37.1124	−1.76326	−0.881632	−	0.471938i	$-0.843555\pi$
$443$	−37.1124	−1.76326	−0.881632	+	0.471938i	$0.843555\pi$
$444$	3.59261	0.170498
$445$	6.09366	0.288867
$446$	8.46509	0.400834
$447$	16.9126	0.799938
$448$	−3.94781	−0.186517
$449$	20.7910	0.981187	0.490593	−	0.871389i	$-0.336780\pi$
$449$	20.7910	0.981187	0.490593	+	0.871389i	$0.336780\pi$
$450$	−10.0429	−0.473428
$451$	−32.4543	−1.52822
$452$	32.2559	1.51719
$453$	−61.0117	−2.86658
$454$	35.4395	1.66326
$455$	5.22084	0.244757
$456$	−5.08624	−0.238185
$457$	−34.8733	−1.63130	−0.815652	−	0.578543i	$-0.803622\pi$
$457$	−34.8733	−1.63130	−0.815652	+	0.578543i	$0.803622\pi$
$458$	56.3983	2.63532
$459$	−31.9328	−1.49049
$460$	−5.51364	−0.257075
$461$	21.6083	1.00640	0.503200	−	0.864170i	$-0.332156\pi$
$461$	21.6083	1.00640	0.503200	+	0.864170i	$0.332156\pi$
$462$	23.7400	1.10449
$463$	−40.4373	−1.87928	−0.939640	−	0.342164i	$-0.888840\pi$
$463$	−40.4373	−1.87928	−0.939640	+	0.342164i	$0.888840\pi$
$464$	−13.3026	−0.617559
$465$	−55.6711	−2.58169
$466$	−1.27215	−0.0589310
$467$	−8.53926	−0.395150	−0.197575	−	0.980288i	$-0.563307\pi$
$467$	−8.53926	−0.395150	−0.197575	+	0.980288i	$0.563307\pi$
$468$	19.4529	0.899212
$469$	11.3642	0.524751
$470$	−31.0384	−1.43170
$471$	47.8816	2.20627
$472$	0.0503186	0.00231610
$473$	31.1562	1.43256
$474$	−23.0120	−1.05698
$475$	1.76582	0.0810215
$476$	5.66799	0.259792
$477$	46.3263	2.12113
$478$	−48.7237	−2.22857
$479$	4.78033	0.218419	0.109209	−	0.994019i	$-0.465168\pi$
$479$	4.78033	0.218419	0.109209	+	0.994019i	$0.465168\pi$
$480$	−51.5718	−2.35392
$481$	−1.68559	−0.0768565
$482$	1.99345	0.0907992
$483$	4.40940	0.200634
$484$	10.6157	0.482532
$485$	5.43903	0.246974
$486$	−3.34382	−0.151679
$487$	−10.1337	−0.459202	−0.229601	−	0.973285i	$-0.573742\pi$
$487$	−10.1337	−0.459202	−0.229601	+	0.973285i	$0.573742\pi$
$488$	11.1895	0.506526
$489$	20.8286	0.941902
$490$	−4.56900	−0.206407
$491$	−10.9689	−0.495019	−0.247510	−	0.968885i	$-0.579612\pi$
$491$	−10.9689	−0.495019	−0.247510	+	0.968885i	$0.579612\pi$
$492$	35.1093	1.58285
$493$	10.4207	0.469323
$494$	−7.87695	−0.354401
$495$	60.6767	2.72721
$496$	−36.1996	−1.62541
$497$	0.760785	0.0341259
$498$	29.4524	1.31979
$499$	−14.5869	−0.652998	−0.326499	−	0.945198i	$-0.605869\pi$
$499$	−14.5869	−0.652998	−0.326499	+	0.945198i	$0.605869\pi$
$500$	−15.2731	−0.683035
$501$	−52.3670	−2.33959
$502$	3.47412	0.155058
$503$	17.3342	0.772896	0.386448	−	0.922311i	$-0.373702\pi$
$503$	17.3342	0.772896	0.386448	+	0.922311i	$0.373702\pi$
$504$	5.15760	0.229738
$505$	−26.0678	−1.16000
$506$	11.7631	0.522934
$507$	25.0117	1.11081
$508$	18.6624	0.828008
$509$	−0.936121	−0.0414928	−0.0207464	−	0.999785i	$-0.506604\pi$
$509$	−0.936121	−0.0414928	−0.0207464	+	0.999785i	$0.506604\pi$
$510$	50.3292	2.22861
$511$	−4.23400	−0.187301
$512$	−25.2913	−1.11773
$513$	−16.8640	−0.744564
$514$	−1.05541	−0.0465523
$515$	38.5282	1.69775
$516$	−33.7050	−1.48378
$517$	28.7539	1.26460
$518$	1.47514	0.0648140
$519$	29.3901	1.29008
$520$	4.56473	0.200177
$521$	11.4178	0.500221	0.250110	−	0.968217i	$-0.419533\pi$
$521$	11.4178	0.500221	0.250110	+	0.968217i	$0.419533\pi$
$522$	−31.2991	−1.36992
$523$	−10.1144	−0.442270	−0.221135	−	0.975243i	$-0.570976\pi$
$523$	−10.1144	−0.442270	−0.221135	+	0.975243i	$0.570976\pi$
$524$	−28.7284	−1.25501
$525$	−2.70124	−0.117892
$526$	−0.976518	−0.0425782
$527$	28.3571	1.23525
$528$	59.5196	2.59026
$529$	−20.8152	−0.905007
$530$	−35.8819	−1.55861
$531$	0.339491	0.0147326
$532$	2.99332	0.129777
$533$	−16.4727	−0.713512
$534$	14.0641	0.608612
$535$	3.90206	0.168701
$536$	9.93605	0.429172
$537$	12.1252	0.523240
$538$	−16.7223	−0.720948
$539$	4.23272	0.182316
$540$	−32.2579	−1.38816
$541$	−25.4254	−1.09312	−0.546561	−	0.837419i	$-0.684064\pi$
$541$	−25.4254	−1.09312	−0.546561	+	0.837419i	$0.684064\pi$
$542$	43.1054	1.85154
$543$	−6.55086	−0.281124
$544$	26.2690	1.12628
$545$	−29.1539	−1.24882
$546$	12.0496	0.515676
$547$	−13.4628	−0.575630	−0.287815	−	0.957686i	$-0.592929\pi$
$547$	−13.4628	−0.575630	−0.287815	+	0.957686i	$0.592929\pi$
$548$	0.234281	0.0100080
$549$	75.4937	3.22199
$550$	−7.20619	−0.307273
$551$	5.50325	0.234446
$552$	3.85526	0.164091
$553$	−4.10291	−0.174474
$554$	42.9159	1.82332
$555$	5.68773	0.241431
$556$	12.3984	0.525808
$557$	−2.42993	−0.102959	−0.0514797	−	0.998674i	$-0.516394\pi$
$557$	−2.42993	−0.102959	−0.0514797	+	0.998674i	$0.516394\pi$
$558$	−85.1724	−3.60563
$559$	15.8138	0.668854
$560$	−11.4551	−0.484068
$561$	−46.6249	−1.96850
$562$	1.09559	0.0462145
$563$	−27.4660	−1.15755	−0.578776	−	0.815486i	$-0.696470\pi$
$563$	−27.4660	−1.15755	−0.578776	+	0.815486i	$0.696470\pi$
$564$	−31.1062	−1.30981
$565$	51.0667	2.14839
$566$	17.9397	0.754062
$567$	8.10061	0.340194
$568$	0.665175	0.0279101
$569$	4.63762	0.194419	0.0972096	−	0.995264i	$-0.469008\pi$
$569$	4.63762	0.194419	0.0972096	+	0.995264i	$0.469008\pi$
$570$	26.5793	1.11329
$571$	28.7389	1.20269	0.601343	−	0.798991i	$-0.294633\pi$
$571$	28.7389	1.20269	0.601343	+	0.798991i	$0.294633\pi$
$572$	13.9582	0.583624
$573$	68.6289	2.86702
$574$	14.4160	0.601714
$575$	−1.33846	−0.0558174
$576$	−23.2879	−0.970328
$577$	43.0307	1.79139	0.895695	−	0.444669i	$-0.146679\pi$
$577$	43.0307	1.79139	0.895695	+	0.444669i	$0.146679\pi$
$578$	6.32650	0.263148
$579$	71.9636	2.99071
$580$	10.5267	0.437099
$581$	5.25120	0.217857
$582$	12.5532	0.520347
$583$	33.2409	1.37670
$584$	−3.70191	−0.153186
$585$	30.7974	1.27332
$586$	−32.7533	−1.35303
$587$	48.0993	1.98527	0.992634	−	0.121148i	$-0.0386576\pi$
$587$	48.0993	1.98527	0.992634	+	0.121148i	$0.0386576\pi$
$588$	−4.57898	−0.188834
$589$	14.9757	0.617061
$590$	−0.262952	−0.0108255
$591$	−23.4479	−0.964516
$592$	3.69839	0.152003
$593$	1.23744	0.0508154	0.0254077	−	0.999677i	$-0.491912\pi$
$593$	1.23744	0.0508154	0.0254077	+	0.999677i	$0.491912\pi$
$594$	68.8208	2.82375
$595$	8.97342	0.367874
$596$	−8.70243	−0.356466
$597$	−58.5197	−2.39505
$598$	5.97056	0.244154
$599$	−47.3178	−1.93335	−0.966676	−	0.256001i	$-0.917595\pi$
$599$	−47.3178	−1.93335	−0.966676	+	0.256001i	$0.917595\pi$
$600$	−2.36177	−0.0964188
$601$	1.79915	0.0733887	0.0366943	−	0.999327i	$-0.488317\pi$
$601$	1.79915	0.0733887	0.0366943	+	0.999327i	$0.488317\pi$
$602$	−13.8394	−0.564053
$603$	67.0367	2.72995
$604$	31.3938	1.27740
$605$	16.8065	0.683282
$606$	−60.1641	−2.44400
$607$	17.3578	0.704531	0.352265	−	0.935900i	$-0.385411\pi$
$607$	17.3578	0.704531	0.352265	+	0.935900i	$0.385411\pi$
$608$	13.8729	0.562622
$609$	−8.41850	−0.341135
$610$	−58.4734	−2.36752
$611$	14.5945	0.590431
$612$	33.4351	1.35153
$613$	−42.6739	−1.72358	−0.861792	−	0.507262i	$-0.830658\pi$
$613$	−42.6739	−1.72358	−0.861792	+	0.507262i	$0.830658\pi$
$614$	−1.13029	−0.0456148
$615$	55.5842	2.24137
$616$	3.70079	0.149109
$617$	−31.8052	−1.28043	−0.640215	−	0.768196i	$-0.721155\pi$
$617$	−31.8052	−1.28043	−0.640215	+	0.768196i	$0.721155\pi$
$618$	88.9225	3.57699
$619$	13.8175	0.555372	0.277686	−	0.960672i	$-0.410433\pi$
$619$	13.8175	0.555372	0.277686	+	0.960672i	$0.410433\pi$
$620$	28.6458	1.15044
$621$	12.7825	0.512946
$622$	5.71140	0.229006
$623$	2.50755	0.100463
$624$	30.2101	1.20937
$625$	−28.7076	−1.14830
$626$	34.6011	1.38294
$627$	−24.6230	−0.983350
$628$	−24.6377	−0.983150
$629$	−2.89715	−0.115517
$630$	−26.9523	−1.07380
$631$	14.6615	0.583666	0.291833	−	0.956469i	$-0.405735\pi$
$631$	14.6615	0.583666	0.291833	+	0.956469i	$0.405735\pi$
$632$	−3.58729	−0.142695
$633$	56.2375	2.23524
$634$	9.23355	0.366711
$635$	29.5458	1.17249
$636$	−35.9602	−1.42592
$637$	2.14838	0.0851221
$638$	−22.4584	−0.889135
$639$	4.48782	0.177535
$640$	−16.5383	−0.653735
$641$	−22.2032	−0.876973	−0.438487	−	0.898738i	$-0.644485\pi$
$641$	−22.2032	−0.876973	−0.438487	+	0.898738i	$0.644485\pi$
$642$	9.00591	0.355435
$643$	−13.0624	−0.515131	−0.257565	−	0.966261i	$-0.582920\pi$
$643$	−13.0624	−0.515131	−0.257565	+	0.966261i	$0.582920\pi$
$644$	−2.26887	−0.0894060
$645$	−53.3609	−2.10108
$646$	−13.5387	−0.532671
$647$	30.8403	1.21246	0.606229	−	0.795290i	$-0.292681\pi$
$647$	30.8403	1.21246	0.606229	+	0.795290i	$0.292681\pi$
$648$	7.08260	0.278231
$649$	0.243598	0.00956206
$650$	−3.65762	−0.143464
$651$	−22.9087	−0.897865
$652$	−10.7174	−0.419727
$653$	11.8203	0.462565	0.231282	−	0.972887i	$-0.425708\pi$
$653$	11.8203	0.462565	0.231282	+	0.972887i	$0.425708\pi$
$654$	−67.2869	−2.63113
$655$	−45.4821	−1.77713
$656$	36.1431	1.41115
$657$	−24.9761	−0.974410
$658$	−12.7724	−0.497918
$659$	−4.67184	−0.181989	−0.0909945	−	0.995851i	$-0.529005\pi$
$659$	−4.67184	−0.181989	−0.0909945	+	0.995851i	$0.529005\pi$
$660$	−47.0996	−1.83335
$661$	−30.9954	−1.20558	−0.602790	−	0.797900i	$-0.705944\pi$
$661$	−30.9954	−1.20558	−0.602790	+	0.797900i	$0.705944\pi$
$662$	−3.08440	−0.119879
$663$	−23.6652	−0.919080
$664$	4.59127	0.178176
$665$	4.73895	0.183769
$666$	8.70177	0.337187
$667$	−4.17134	−0.161515
$668$	26.9457	1.04256
$669$	13.4310	0.519272
$670$	−51.9231	−2.00597
$671$	54.1697	2.09120
$672$	−21.2219	−0.818652
$673$	−24.7072	−0.952393	−0.476196	−	0.879339i	$-0.657985\pi$
$673$	−24.7072	−0.952393	−0.476196	+	0.879339i	$0.657985\pi$
$674$	−34.6175	−1.33341
$675$	−7.83071	−0.301404
$676$	−12.8699	−0.494995
$677$	47.7495	1.83516	0.917580	−	0.397550i	$-0.130140\pi$
$677$	47.7495	1.83516	0.917580	+	0.397550i	$0.130140\pi$
$678$	117.861	4.52643
$679$	2.23817	0.0858930
$680$	7.84572	0.300869
$681$	56.2294	2.15472
$682$	−61.1145	−2.34020
$683$	13.1543	0.503337	0.251668	−	0.967814i	$-0.419021\pi$
$683$	13.1543	0.503337	0.251668	+	0.967814i	$0.419021\pi$
$684$	17.6574	0.675147
$685$	0.370908	0.0141717
$686$	−1.88015	−0.0717845
$687$	89.4833	3.41400
$688$	−34.6974	−1.32283
$689$	16.8720	0.642771
$690$	−20.1465	−0.766966
$691$	−23.6172	−0.898442	−0.449221	−	0.893421i	$-0.648299\pi$
$691$	−23.6172	−0.898442	−0.449221	+	0.893421i	$0.648299\pi$
$692$	−15.1228	−0.574882
$693$	24.9685	0.948476
$694$	44.1823	1.67714
$695$	19.6288	0.744562
$696$	−7.36053	−0.279000
$697$	−28.3128	−1.07242
$698$	−29.1714	−1.10415
$699$	−2.01843	−0.0763439
$700$	1.38993	0.0525345
$701$	−12.5807	−0.475167	−0.237583	−	0.971367i	$-0.576355\pi$
$701$	−12.5807	−0.475167	−0.237583	+	0.971367i	$0.576355\pi$
$702$	34.9311	1.31839
$703$	−1.53001	−0.0577055
$704$	−16.7100	−0.629781
$705$	−49.2466	−1.85473
$706$	47.2118	1.77684
$707$	−10.7269	−0.403428
$708$	−0.263526	−0.00990390
$709$	12.0330	0.451910	0.225955	−	0.974138i	$-0.427450\pi$
$709$	12.0330	0.451910	0.225955	+	0.974138i	$0.427450\pi$
$710$	−3.47603	−0.130453
$711$	−24.2028	−0.907676
$712$	2.19242	0.0821645
$713$	−11.3512	−0.425106
$714$	20.7105	0.775072
$715$	22.0984	0.826432
$716$	−6.23906	−0.233164
$717$	−77.3065	−2.88707
$718$	58.9778	2.20103
$719$	−2.47787	−0.0924090	−0.0462045	−	0.998932i	$-0.514713\pi$
$719$	−2.47787	−0.0924090	−0.0462045	+	0.998932i	$0.514713\pi$
$720$	−67.5731	−2.51830
$721$	15.8544	0.590449
$722$	28.5730	1.06338
$723$	3.16287	0.117628
$724$	3.37077	0.125274
$725$	2.55540	0.0949053
$726$	38.7892	1.43960
$727$	−29.3758	−1.08949	−0.544744	−	0.838602i	$-0.683373\pi$
$727$	−29.3758	−1.08949	−0.544744	+	0.838602i	$0.683373\pi$
$728$	1.87839	0.0696178
$729$	−29.6073	−1.09657
$730$	19.3452	0.715997
$731$	27.1803	1.00530
$732$	−58.6011	−2.16596
$733$	−4.26488	−0.157527	−0.0787635	−	0.996893i	$-0.525097\pi$
$733$	−4.26488	−0.157527	−0.0787635	+	0.996893i	$0.525097\pi$
$734$	−33.7729	−1.24658
$735$	−7.24933	−0.267395
$736$	−10.5154	−0.387602
$737$	48.1015	1.77184
$738$	85.0393	3.13034
$739$	20.3320	0.747924	0.373962	−	0.927444i	$-0.377999\pi$
$739$	20.3320	0.747924	0.373962	+	0.927444i	$0.377999\pi$
$740$	−2.92664	−0.107585
$741$	−12.4978	−0.459119
$742$	−14.7655	−0.542057
$743$	31.1891	1.14422	0.572108	−	0.820178i	$-0.306126\pi$
$743$	31.1891	1.14422	0.572108	+	0.820178i	$0.306126\pi$
$744$	−20.0298	−0.734327
$745$	−13.7775	−0.504768
$746$	−9.32708	−0.341489
$747$	30.9765	1.13337
$748$	23.9910	0.877198
$749$	1.60570	0.0586712
$750$	−55.8072	−2.03779
$751$	−13.3310	−0.486454	−0.243227	−	0.969969i	$-0.578206\pi$
$751$	−13.3310	−0.486454	−0.243227	+	0.969969i	$0.578206\pi$
$752$	−32.0221	−1.16773
$753$	5.51215	0.200874
$754$	−11.3991	−0.415131
$755$	49.7019	1.80884
$756$	−13.2742	−0.482776
$757$	−49.4978	−1.79903	−0.899515	−	0.436890i	$-0.856080\pi$
$757$	−49.4978	−1.79903	−0.899515	+	0.436890i	$0.856080\pi$
$758$	−1.88952	−0.0686306
$759$	18.6637	0.677451
$760$	4.14340	0.150297
$761$	−14.9291	−0.541178	−0.270589	−	0.962695i	$-0.587218\pi$
$761$	−14.9291	−0.541178	−0.270589	+	0.962695i	$0.587218\pi$
$762$	68.1912	2.47031
$763$	−11.9969	−0.434317
$764$	−35.3133	−1.27759
$765$	52.9336	1.91382
$766$	−66.2868	−2.39504
$767$	0.123642	0.00446446
$768$	−61.7237	−2.22726
$769$	−21.6466	−0.780597	−0.390298	−	0.920688i	$-0.627628\pi$
$769$	−21.6466	−0.780597	−0.390298	+	0.920688i	$0.627628\pi$
$770$	−19.3393	−0.696940
$771$	−1.67455	−0.0603075
$772$	−37.0292	−1.33271
$773$	37.3725	1.34419	0.672097	−	0.740463i	$-0.265394\pi$
$773$	37.3725	1.34419	0.672097	+	0.740463i	$0.265394\pi$
$774$	−81.6379	−2.93441
$775$	6.95386	0.249790
$776$	1.95689	0.0702484
$777$	2.34051	0.0839653
$778$	−21.7080	−0.778269
$779$	−14.9523	−0.535720
$780$	−23.9061	−0.855977
$781$	3.22019	0.115227
$782$	10.2620	0.366969
$783$	−24.4047	−0.872152
$784$	−4.71381	−0.168350
$785$	−39.0057	−1.39217
$786$	−104.972	−3.74423
$787$	10.9711	0.391078	0.195539	−	0.980696i	$-0.437354\pi$
$787$	10.9711	0.391078	0.195539	+	0.980696i	$0.437354\pi$
$788$	12.0652	0.429804
$789$	−1.54937	−0.0551592
$790$	18.7462	0.666961
$791$	21.0140	0.747173
$792$	21.8307	0.775720
$793$	27.4947	0.976365
$794$	−29.0722	−1.03173
$795$	−56.9314	−2.01915
$796$	30.1115	1.06728
$797$	−25.3396	−0.897575	−0.448788	−	0.893639i	$-0.648144\pi$
$797$	−25.3396	−0.897575	−0.448788	+	0.893639i	$0.648144\pi$
$798$	10.9374	0.387181
$799$	25.0846	0.887430
$800$	6.44182	0.227753
$801$	14.7919	0.522645
$802$	−0.999675	−0.0352997
$803$	−17.9213	−0.632430
$804$	−52.0365	−1.83519
$805$	−3.59202	−0.126602
$806$	−31.0197	−1.09262
$807$	−26.5321	−0.933973
$808$	−9.37886	−0.329947
$809$	−3.46266	−0.121741	−0.0608703	−	0.998146i	$-0.519388\pi$
$809$	−3.46266	−0.121741	−0.0608703	+	0.998146i	$0.519388\pi$
$810$	−37.0117	−1.30046
$811$	−23.3024	−0.818259	−0.409129	−	0.912476i	$-0.634168\pi$
$811$	−23.3024	−0.818259	−0.409129	+	0.912476i	$0.634168\pi$
$812$	4.33177	0.152015
$813$	68.3924	2.39863
$814$	6.24386	0.218847
$815$	−16.9676	−0.594348
$816$	51.9242	1.81771
$817$	14.3542	0.502190
$818$	11.9659	0.418376
$819$	12.6732	0.442836
$820$	−28.6010	−0.998792
$821$	−6.34524	−0.221450	−0.110725	−	0.993851i	$-0.535317\pi$
$821$	−6.34524	−0.221450	−0.110725	+	0.993851i	$0.535317\pi$
$822$	0.856051	0.0298582
$823$	−11.8112	−0.411712	−0.205856	−	0.978582i	$-0.565998\pi$
$823$	−11.8112	−0.411712	−0.205856	+	0.978582i	$0.565998\pi$
$824$	13.8619	0.482904
$825$	−11.4336	−0.398066
$826$	−0.108205	−0.00376493
$827$	−11.6699	−0.405801	−0.202901	−	0.979199i	$-0.565037\pi$
$827$	−11.6699	−0.405801	−0.202901	+	0.979199i	$0.565037\pi$
$828$	−13.3839	−0.465123
$829$	−5.73727	−0.199263	−0.0996317	−	0.995024i	$-0.531766\pi$
$829$	−5.73727	−0.199263	−0.0996317	+	0.995024i	$0.531766\pi$
$830$	−23.9928	−0.832801
$831$	68.0918	2.36208
$832$	−8.48141	−0.294040
$833$	3.69258	0.127940
$834$	45.3029	1.56871
$835$	42.6597	1.47630
$836$	12.6699	0.438197
$837$	−66.4109	−2.29550
$838$	−20.1304	−0.695392
$839$	−18.9897	−0.655598	−0.327799	−	0.944747i	$-0.606307\pi$
$839$	−18.9897	−0.655598	−0.327799	+	0.944747i	$0.606307\pi$
$840$	−6.33829	−0.218692
$841$	−21.0360	−0.725379
$842$	−76.4473	−2.63455
$843$	1.73829	0.0598700
$844$	−28.9372	−0.996060
$845$	−20.3753	−0.700930
$846$	−75.3433	−2.59035
$847$	6.91591	0.237633
$848$	−37.0191	−1.27124
$849$	28.4637	0.976872
$850$	−6.28660	−0.215629
$851$	1.15972	0.0397545
$852$	−3.48362	−0.119347
$853$	37.3041	1.27727	0.638633	−	0.769511i	$-0.279500\pi$
$853$	37.3041	1.27727	0.638633	+	0.769511i	$0.279500\pi$
$854$	−24.0619	−0.823381
$855$	27.9548	0.956032
$856$	1.40391	0.0479847
$857$	42.9116	1.46583	0.732916	−	0.680319i	$-0.238159\pi$
$857$	42.9116	1.46583	0.732916	+	0.680319i	$0.238159\pi$
$858$	51.0027	1.74120
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	27.4570	0.936277
$861$	22.8730	0.779508
$862$	26.6531	0.907808
$863$	12.0886	0.411499	0.205750	−	0.978605i	$-0.434037\pi$
$863$	12.0886	0.411499	0.205750	+	0.978605i	$0.434037\pi$
$864$	−61.5208	−2.09298
$865$	−23.9420	−0.814053
$866$	13.5605	0.460806
$867$	10.0378	0.340903
$868$	11.7878	0.400103
$869$	−17.3665	−0.589117
$870$	38.4642	1.30406
$871$	24.4147	0.827260
$872$	−10.4892	−0.355210
$873$	13.2028	0.446847
$874$	5.41946	0.183316
$875$	−9.95012	−0.336376
$876$	19.3874	0.655040
$877$	−5.98177	−0.201990	−0.100995	−	0.994887i	$-0.532203\pi$
$877$	−5.98177	−0.201990	−0.100995	+	0.994887i	$0.532203\pi$
$878$	23.7668	0.802092
$879$	−51.9674	−1.75282
$880$	−48.4864	−1.63448
$881$	−23.4919	−0.791463	−0.395731	−	0.918366i	$-0.629509\pi$
$881$	−23.4919	−0.791463	−0.395731	+	0.918366i	$0.629509\pi$
$882$	−11.0909	−0.373450
$883$	−10.9339	−0.367955	−0.183977	−	0.982930i	$-0.558897\pi$
$883$	−10.9339	−0.367955	−0.183977	+	0.982930i	$0.558897\pi$
$884$	12.1770	0.409557
$885$	−0.417208	−0.0140243
$886$	69.7769	2.34420
$887$	−4.72661	−0.158704	−0.0793520	−	0.996847i	$-0.525285\pi$
$887$	−4.72661	−0.158704	−0.0793520	+	0.996847i	$0.525285\pi$
$888$	2.04637	0.0686718
$889$	12.1581	0.407771
$890$	−11.4570	−0.384040
$891$	34.2876	1.14868
$892$	−6.91096	−0.231396
$893$	13.2474	0.443308
$894$	−31.7982	−1.06349
$895$	−9.87752	−0.330169
$896$	−6.80555	−0.227357
$897$	9.47307	0.316297
$898$	−39.0902	−1.30446
$899$	21.6720	0.722800
$900$	8.19911	0.273304
$901$	28.9990	0.966097
$902$	61.0191	2.03171
$903$	−21.9581	−0.730719
$904$	18.3732	0.611082
$905$	5.33652	0.177392
$906$	114.711	3.81102
$907$	50.5053	1.67700	0.838500	−	0.544901i	$-0.183433\pi$
$907$	50.5053	1.67700	0.838500	+	0.544901i	$0.183433\pi$
$908$	−28.9331	−0.960178
$909$	−63.2775	−2.09878
$910$	−9.81597	−0.325396
$911$	−34.4612	−1.14175	−0.570875	−	0.821037i	$-0.693396\pi$
$911$	−34.4612	−1.14175	−0.570875	+	0.821037i	$0.693396\pi$
$912$	27.4217	0.908023
$913$	22.2269	0.735601
$914$	65.5671	2.16877
$915$	−92.7758	−3.06707
$916$	−46.0439	−1.52133
$917$	−18.7159	−0.618055
$918$	60.0384	1.98156
$919$	−19.1409	−0.631400	−0.315700	−	0.948859i	$-0.602239\pi$
$919$	−19.1409	−0.631400	−0.315700	+	0.948859i	$0.602239\pi$
$920$	−3.14061	−0.103543
$921$	−1.79335	−0.0590930
$922$	−40.6270	−1.33798
$923$	1.63446	0.0537988
$924$	−19.3815	−0.637606
$925$	−0.710452	−0.0233595
$926$	76.0282	2.49844
$927$	93.5240	3.07173
$928$	20.0762	0.659032
$929$	9.31605	0.305650	0.152825	−	0.988253i	$-0.451163\pi$
$929$	9.31605	0.305650	0.152825	+	0.988253i	$0.451163\pi$
$930$	104.670	3.43227
$931$	1.95008	0.0639114
$932$	1.03859	0.0340201
$933$	9.06190	0.296673
$934$	16.0551	0.525339
$935$	37.9820	1.24214
$936$	11.0805	0.362178
$937$	−18.0358	−0.589202	−0.294601	−	0.955620i	$-0.595187\pi$
$937$	−18.0358	−0.589202	−0.294601	+	0.955620i	$0.595187\pi$
$938$	−21.3664	−0.697639
$939$	54.8993	1.79157
$940$	25.3400	0.826500
$941$	−34.1725	−1.11399	−0.556996	−	0.830515i	$-0.688046\pi$
$941$	−34.1725	−1.11399	−0.556996	+	0.830515i	$0.688046\pi$
$942$	−90.0247	−2.93316
$943$	11.3335	0.369069
$944$	−0.271285	−0.00882959
$945$	−21.0153	−0.683628
$946$	−58.5784	−1.90455
$947$	42.3790	1.37713	0.688566	−	0.725174i	$-0.258241\pi$
$947$	42.3790	1.37713	0.688566	+	0.725174i	$0.258241\pi$
$948$	18.7871	0.610178
$949$	−9.09626	−0.295277
$950$	−3.32001	−0.107715
$951$	14.6502	0.475067
$952$	3.22852	0.104637
$953$	10.7973	0.349757	0.174879	−	0.984590i	$-0.444047\pi$
$953$	10.7973	0.349757	0.174879	+	0.984590i	$0.444047\pi$
$954$	−87.1004	−2.81998
$955$	−55.9071	−1.80911
$956$	39.7784	1.28652
$957$	−35.6331	−1.15186
$958$	−8.98774	−0.290381
$959$	0.152629	0.00492866
$960$	28.6190	0.923674
$961$	27.9746	0.902405
$962$	3.16917	0.102178
$963$	9.47194	0.305229
$964$	−1.62747	−0.0524172
$965$	−58.6236	−1.88716
$966$	−8.29033	−0.266737
$967$	−10.9672	−0.352680	−0.176340	−	0.984329i	$-0.556426\pi$
$967$	−10.9672	−0.352680	−0.176340	+	0.984329i	$0.556426\pi$
$968$	6.04677	0.194351
$969$	−21.4809	−0.690065
$970$	−10.2262	−0.328343
$971$	−29.4700	−0.945739	−0.472869	−	0.881133i	$-0.656782\pi$
$971$	−29.4700	−0.945739	−0.472869	+	0.881133i	$0.656782\pi$
$972$	2.72992	0.0875623
$973$	8.07727	0.258945
$974$	19.0529	0.610495
$975$	−5.80329	−0.185854
$976$	−60.3266	−1.93101
$977$	−11.8726	−0.379837	−0.189918	−	0.981800i	$-0.560822\pi$
$977$	−11.8726	−0.379837	−0.189918	+	0.981800i	$0.560822\pi$
$978$	−39.1609	−1.25223
$979$	10.6138	0.339217
$980$	3.73017	0.119156
$981$	−70.7688	−2.25948
$982$	20.6232	0.658112
$983$	−3.50769	−0.111878	−0.0559390	−	0.998434i	$-0.517815\pi$
$983$	−3.50769	−0.111878	−0.0559390	+	0.998434i	$0.517815\pi$
$984$	19.9985	0.637528
$985$	19.1013	0.608618
$986$	−19.5924	−0.623949
$987$	−20.2650	−0.645043
$988$	6.43080	0.204591
$989$	−10.8802	−0.345969
$990$	−114.081	−3.62574
$991$	36.4756	1.15868	0.579342	−	0.815085i	$-0.303310\pi$
$991$	36.4756	1.15868	0.579342	+	0.815085i	$0.303310\pi$
$992$	54.6320	1.73457
$993$	−4.89380	−0.155300
$994$	−1.43039	−0.0453692
$995$	47.6718	1.51130
$996$	−24.0451	−0.761899
$997$	−22.8953	−0.725102	−0.362551	−	0.931964i	$-0.618094\pi$
$997$	−22.8953	−0.725102	−0.362551	+	0.931964i	$0.618094\pi$
$998$	27.4255	0.868140
$999$	6.78498	0.214667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.18	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.18	✓	109	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88015 q^{2} -2.98311 q^{3} +1.53497 q^{4} +2.43013 q^{5} +5.60869 q^{6} +1.00000 q^{7} +0.874328 q^{8} +5.89893 q^{9} +O(q^{10})\)	\(q-1.88015 q^{2} -2.98311 q^{3} +1.53497 q^{4} +2.43013 q^{5} +5.60869 q^{6} +1.00000 q^{7} +0.874328 q^{8} +5.89893 q^{9} -4.56900 q^{10} +4.23272 q^{11} -4.57898 q^{12} +2.14838 q^{13} -1.88015 q^{14} -7.24933 q^{15} -4.71381 q^{16} +3.69258 q^{17} -11.0909 q^{18} +1.95008 q^{19} +3.73017 q^{20} -2.98311 q^{21} -7.95815 q^{22} -1.47812 q^{23} -2.60822 q^{24} +0.905511 q^{25} -4.03929 q^{26} -8.64783 q^{27} +1.53497 q^{28} +2.82206 q^{29} +13.6298 q^{30} +7.67949 q^{31} +7.11402 q^{32} -12.6267 q^{33} -6.94260 q^{34} +2.43013 q^{35} +9.05468 q^{36} -0.784587 q^{37} -3.66645 q^{38} -6.40886 q^{39} +2.12473 q^{40} -7.66749 q^{41} +5.60869 q^{42} +7.36081 q^{43} +6.49709 q^{44} +14.3351 q^{45} +2.77909 q^{46} +6.79326 q^{47} +14.0618 q^{48} +1.00000 q^{49} -1.70250 q^{50} -11.0154 q^{51} +3.29770 q^{52} +7.85333 q^{53} +16.2592 q^{54} +10.2860 q^{55} +0.874328 q^{56} -5.81731 q^{57} -5.30589 q^{58} +0.0575512 q^{59} -11.1275 q^{60} +12.7978 q^{61} -14.4386 q^{62} +5.89893 q^{63} -3.94781 q^{64} +5.22084 q^{65} +23.7400 q^{66} +11.3642 q^{67} +5.66799 q^{68} +4.40940 q^{69} -4.56900 q^{70} +0.760785 q^{71} +5.15760 q^{72} -4.23400 q^{73} +1.47514 q^{74} -2.70124 q^{75} +2.99332 q^{76} +4.23272 q^{77} +12.0496 q^{78} -4.10291 q^{79} -11.4551 q^{80} +8.10061 q^{81} +14.4160 q^{82} +5.25120 q^{83} -4.57898 q^{84} +8.97342 q^{85} -13.8394 q^{86} -8.41850 q^{87} +3.70079 q^{88} +2.50755 q^{89} -26.9523 q^{90} +2.14838 q^{91} -2.26887 q^{92} -22.9087 q^{93} -12.7724 q^{94} +4.73895 q^{95} -21.2219 q^{96} +2.23817 q^{97} -1.88015 q^{98} +24.9685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

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