LMFDB - Embedded newform 8002.2.a.d.1.59

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.59
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.99756 q^{3} +1.00000 q^{4} -3.74736 q^{5} +1.99756 q^{6} -0.855155 q^{7} +1.00000 q^{8} +0.990247 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.99756 q^{3} +1.00000 q^{4} -3.74736 q^{5} +1.99756 q^{6} -0.855155 q^{7} +1.00000 q^{8} +0.990247 q^{9} -3.74736 q^{10} +0.952421 q^{11} +1.99756 q^{12} -1.62901 q^{13} -0.855155 q^{14} -7.48559 q^{15} +1.00000 q^{16} +2.22068 q^{17} +0.990247 q^{18} -2.08381 q^{19} -3.74736 q^{20} -1.70822 q^{21} +0.952421 q^{22} +3.03948 q^{23} +1.99756 q^{24} +9.04274 q^{25} -1.62901 q^{26} -4.01460 q^{27} -0.855155 q^{28} +8.41682 q^{29} -7.48559 q^{30} -8.34628 q^{31} +1.00000 q^{32} +1.90252 q^{33} +2.22068 q^{34} +3.20458 q^{35} +0.990247 q^{36} +2.93853 q^{37} -2.08381 q^{38} -3.25404 q^{39} -3.74736 q^{40} -3.76666 q^{41} -1.70822 q^{42} +7.26949 q^{43} +0.952421 q^{44} -3.71082 q^{45} +3.03948 q^{46} +4.50102 q^{47} +1.99756 q^{48} -6.26871 q^{49} +9.04274 q^{50} +4.43595 q^{51} -1.62901 q^{52} -3.34712 q^{53} -4.01460 q^{54} -3.56907 q^{55} -0.855155 q^{56} -4.16253 q^{57} +8.41682 q^{58} -8.99208 q^{59} -7.48559 q^{60} -5.52968 q^{61} -8.34628 q^{62} -0.846815 q^{63} +1.00000 q^{64} +6.10448 q^{65} +1.90252 q^{66} -4.00847 q^{67} +2.22068 q^{68} +6.07154 q^{69} +3.20458 q^{70} -9.49157 q^{71} +0.990247 q^{72} -1.56370 q^{73} +2.93853 q^{74} +18.0634 q^{75} -2.08381 q^{76} -0.814468 q^{77} -3.25404 q^{78} -6.28501 q^{79} -3.74736 q^{80} -10.9902 q^{81} -3.76666 q^{82} -10.3301 q^{83} -1.70822 q^{84} -8.32171 q^{85} +7.26949 q^{86} +16.8131 q^{87} +0.952421 q^{88} -11.8730 q^{89} -3.71082 q^{90} +1.39305 q^{91} +3.03948 q^{92} -16.6722 q^{93} +4.50102 q^{94} +7.80879 q^{95} +1.99756 q^{96} -18.6881 q^{97} -6.26871 q^{98} +0.943132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.99756	1.15329	0.576646	−	0.816994i	$-0.304361\pi$
$3$	1.99756	1.15329	0.576646	+	0.816994i	$0.304361\pi$
$4$	1.00000	0.500000
$5$	−3.74736	−1.67587	−0.837936	−	0.545768i	$-0.816238\pi$
$5$	−3.74736	−1.67587	−0.837936	+	0.545768i	$0.816238\pi$
$6$	1.99756	0.815501
$7$	−0.855155	−0.323218	−0.161609	−	0.986855i	$-0.551668\pi$
$7$	−0.855155	−0.323218	−0.161609	+	0.986855i	$0.551668\pi$
$8$	1.00000	0.353553
$9$	0.990247	0.330082
$10$	−3.74736	−1.18502
$11$	0.952421	0.287166	0.143583	−	0.989638i	$-0.454138\pi$
$11$	0.952421	0.287166	0.143583	+	0.989638i	$0.454138\pi$
$12$	1.99756	0.576646
$13$	−1.62901	−0.451805	−0.225903	−	0.974150i	$-0.572533\pi$
$13$	−1.62901	−0.451805	−0.225903	+	0.974150i	$0.572533\pi$
$14$	−0.855155	−0.228550
$15$	−7.48559	−1.93277
$16$	1.00000	0.250000
$17$	2.22068	0.538595	0.269297	−	0.963057i	$-0.413209\pi$
$17$	2.22068	0.538595	0.269297	+	0.963057i	$0.413209\pi$
$18$	0.990247	0.233403
$19$	−2.08381	−0.478058	−0.239029	−	0.971012i	$-0.576829\pi$
$19$	−2.08381	−0.478058	−0.239029	+	0.971012i	$0.576829\pi$
$20$	−3.74736	−0.837936
$21$	−1.70822	−0.372765
$22$	0.952421	0.203057
$23$	3.03948	0.633775	0.316888	−	0.948463i	$-0.397362\pi$
$23$	3.03948	0.633775	0.316888	+	0.948463i	$0.397362\pi$
$24$	1.99756	0.407750
$25$	9.04274	1.80855
$26$	−1.62901	−0.319474
$27$	−4.01460	−0.772611
$28$	−0.855155	−0.161609
$29$	8.41682	1.56296	0.781482	−	0.623927i	$-0.214464\pi$
$29$	8.41682	1.56296	0.781482	+	0.623927i	$0.214464\pi$
$30$	−7.48559	−1.36667
$31$	−8.34628	−1.49904	−0.749518	−	0.661984i	$-0.769715\pi$
$31$	−8.34628	−1.49904	−0.749518	+	0.661984i	$0.769715\pi$
$32$	1.00000	0.176777
$33$	1.90252	0.331186
$34$	2.22068	0.380844
$35$	3.20458	0.541673
$36$	0.990247	0.165041
$37$	2.93853	0.483092	0.241546	−	0.970389i	$-0.422346\pi$
$37$	2.93853	0.483092	0.241546	+	0.970389i	$0.422346\pi$
$38$	−2.08381	−0.338038
$39$	−3.25404	−0.521063
$40$	−3.74736	−0.592510
$41$	−3.76666	−0.588253	−0.294126	−	0.955767i	$-0.595029\pi$
$41$	−3.76666	−0.588253	−0.294126	+	0.955767i	$0.595029\pi$
$42$	−1.70822	−0.263585
$43$	7.26949	1.10859	0.554294	−	0.832321i	$-0.312989\pi$
$43$	7.26949	1.10859	0.554294	+	0.832321i	$0.312989\pi$
$44$	0.952421	0.143583
$45$	−3.71082	−0.553176
$46$	3.03948	0.448147
$47$	4.50102	0.656542	0.328271	−	0.944584i	$-0.393534\pi$
$47$	4.50102	0.656542	0.328271	+	0.944584i	$0.393534\pi$
$48$	1.99756	0.288323
$49$	−6.26871	−0.895530
$50$	9.04274	1.27884
$51$	4.43595	0.621157
$52$	−1.62901	−0.225903
$53$	−3.34712	−0.459762	−0.229881	−	0.973219i	$-0.573834\pi$
$53$	−3.34712	−0.459762	−0.229881	+	0.973219i	$0.573834\pi$
$54$	−4.01460	−0.546318
$55$	−3.56907	−0.481253
$56$	−0.855155	−0.114275
$57$	−4.16253	−0.551341
$58$	8.41682	1.10518
$59$	−8.99208	−1.17067	−0.585335	−	0.810792i	$-0.699037\pi$
$59$	−8.99208	−1.17067	−0.585335	+	0.810792i	$0.699037\pi$
$60$	−7.48559	−0.966385
$61$	−5.52968	−0.708003	−0.354002	−	0.935245i	$-0.615179\pi$
$61$	−5.52968	−0.708003	−0.354002	+	0.935245i	$0.615179\pi$
$62$	−8.34628	−1.05998
$63$	−0.846815	−0.106689
$64$	1.00000	0.125000
$65$	6.10448	0.757168
$66$	1.90252	0.234184
$67$	−4.00847	−0.489712	−0.244856	−	0.969559i	$-0.578741\pi$
$67$	−4.00847	−0.489712	−0.244856	+	0.969559i	$0.578741\pi$
$68$	2.22068	0.269297
$69$	6.07154	0.730928
$70$	3.20458	0.383020
$71$	−9.49157	−1.12644	−0.563221	−	0.826306i	$-0.690438\pi$
$71$	−9.49157	−1.12644	−0.563221	+	0.826306i	$0.690438\pi$
$72$	0.990247	0.116702
$73$	−1.56370	−0.183017	−0.0915087	−	0.995804i	$-0.529169\pi$
$73$	−1.56370	−0.183017	−0.0915087	+	0.995804i	$0.529169\pi$
$74$	2.93853	0.341597
$75$	18.0634	2.08578
$76$	−2.08381	−0.239029
$77$	−0.814468	−0.0928172
$78$	−3.25404	−0.368447
$79$	−6.28501	−0.707119	−0.353559	−	0.935412i	$-0.615029\pi$
$79$	−6.28501	−0.707119	−0.353559	+	0.935412i	$0.615029\pi$
$80$	−3.74736	−0.418968
$81$	−10.9902	−1.22113
$82$	−3.76666	−0.415958
$83$	−10.3301	−1.13388	−0.566939	−	0.823760i	$-0.691872\pi$
$83$	−10.3301	−1.13388	−0.566939	+	0.823760i	$0.691872\pi$
$84$	−1.70822	−0.186383
$85$	−8.32171	−0.902616
$86$	7.26949	0.783889
$87$	16.8131	1.80255
$88$	0.952421	0.101528
$89$	−11.8730	−1.25853	−0.629267	−	0.777190i	$-0.716645\pi$
$89$	−11.8730	−1.25853	−0.629267	+	0.777190i	$0.716645\pi$
$90$	−3.71082	−0.391154
$91$	1.39305	0.146032
$92$	3.03948	0.316888
$93$	−16.6722	−1.72883
$94$	4.50102	0.464245
$95$	7.80879	0.801164
$96$	1.99756	0.203875
$97$	−18.6881	−1.89749	−0.948745	−	0.316043i	$-0.897646\pi$
$97$	−18.6881	−1.89749	−0.948745	+	0.316043i	$0.897646\pi$
$98$	−6.26871	−0.633235
$99$	0.943132	0.0947883
$100$	9.04274	0.904274
$101$	−8.42487	−0.838305	−0.419153	−	0.907916i	$-0.637673\pi$
$101$	−8.42487	−0.838305	−0.419153	+	0.907916i	$0.637673\pi$
$102$	4.43595	0.439224
$103$	5.59750	0.551538	0.275769	−	0.961224i	$-0.411067\pi$
$103$	5.59750	0.551538	0.275769	+	0.961224i	$0.411067\pi$
$104$	−1.62901	−0.159737
$105$	6.40134	0.624707
$106$	−3.34712	−0.325101
$107$	0.0658625	0.00636717	0.00318359	−	0.999995i	$-0.498987\pi$
$107$	0.0658625	0.00636717	0.00318359	+	0.999995i	$0.498987\pi$
$108$	−4.01460	−0.386305
$109$	7.97843	0.764195	0.382097	−	0.924122i	$-0.375202\pi$
$109$	7.97843	0.764195	0.382097	+	0.924122i	$0.375202\pi$
$110$	−3.56907	−0.340297
$111$	5.86989	0.557146
$112$	−0.855155	−0.0808046
$113$	−1.70168	−0.160081	−0.0800403	−	0.996792i	$-0.525505\pi$
$113$	−1.70168	−0.160081	−0.0800403	+	0.996792i	$0.525505\pi$
$114$	−4.16253	−0.389857
$115$	−11.3900	−1.06213
$116$	8.41682	0.781482
$117$	−1.61312	−0.149133
$118$	−8.99208	−0.827788
$119$	−1.89903	−0.174084
$120$	−7.48559	−0.683337
$121$	−10.0929	−0.917536
$122$	−5.52968	−0.500634
$123$	−7.52412	−0.678427
$124$	−8.34628	−0.749518
$125$	−15.1496	−1.35502
$126$	−0.846815	−0.0754403
$127$	−9.65709	−0.856928	−0.428464	−	0.903559i	$-0.640945\pi$
$127$	−9.65709	−0.856928	−0.428464	+	0.903559i	$0.640945\pi$
$128$	1.00000	0.0883883
$129$	14.5212	1.27852
$130$	6.10448	0.535398
$131$	−9.59247	−0.838098	−0.419049	−	0.907964i	$-0.637636\pi$
$131$	−9.59247	−0.838098	−0.419049	+	0.907964i	$0.637636\pi$
$132$	1.90252	0.165593
$133$	1.78198	0.154517
$134$	−4.00847	−0.346279
$135$	15.0442	1.29480
$136$	2.22068	0.190422
$137$	−20.8669	−1.78278	−0.891389	−	0.453238i	$-0.850269\pi$
$137$	−20.8669	−1.78278	−0.891389	+	0.453238i	$0.850269\pi$
$138$	6.07154	0.516844
$139$	−14.7477	−1.25089	−0.625443	−	0.780270i	$-0.715082\pi$
$139$	−14.7477	−1.25089	−0.625443	+	0.780270i	$0.715082\pi$
$140$	3.20458	0.270836
$141$	8.99107	0.757185
$142$	−9.49157	−0.796515
$143$	−1.55150	−0.129743
$144$	0.990247	0.0825206
$145$	−31.5409	−2.61933
$146$	−1.56370	−0.129413
$147$	−12.5221	−1.03281
$148$	2.93853	0.241546
$149$	−3.79747	−0.311101	−0.155550	−	0.987828i	$-0.549715\pi$
$149$	−3.79747	−0.311101	−0.155550	+	0.987828i	$0.549715\pi$
$150$	18.0634	1.47487
$151$	16.4772	1.34089	0.670446	−	0.741959i	$-0.266103\pi$
$151$	16.4772	1.34089	0.670446	+	0.741959i	$0.266103\pi$
$152$	−2.08381	−0.169019
$153$	2.19902	0.177781
$154$	−0.814468	−0.0656317
$155$	31.2766	2.51219
$156$	−3.25404	−0.260532
$157$	0.911632	0.0727561	0.0363781	−	0.999338i	$-0.488418\pi$
$157$	0.911632	0.0727561	0.0363781	+	0.999338i	$0.488418\pi$
$158$	−6.28501	−0.500008
$159$	−6.68607	−0.530240
$160$	−3.74736	−0.296255
$161$	−2.59923	−0.204848
$162$	−10.9902	−0.863468
$163$	10.9720	0.859394	0.429697	−	0.902973i	$-0.358620\pi$
$163$	10.9720	0.859394	0.429697	+	0.902973i	$0.358620\pi$
$164$	−3.76666	−0.294126
$165$	−7.12943	−0.555025
$166$	−10.3301	−0.801772
$167$	4.55637	0.352582	0.176291	−	0.984338i	$-0.443590\pi$
$167$	4.55637	0.352582	0.176291	+	0.984338i	$0.443590\pi$
$168$	−1.70822	−0.131792
$169$	−10.3463	−0.795872
$170$	−8.32171	−0.638246
$171$	−2.06348	−0.157799
$172$	7.26949	0.554294
$173$	3.30128	0.250992	0.125496	−	0.992094i	$-0.459948\pi$
$173$	3.30128	0.250992	0.125496	+	0.992094i	$0.459948\pi$
$174$	16.8131	1.27460
$175$	−7.73295	−0.584556
$176$	0.952421	0.0717914
$177$	−17.9622	−1.35012
$178$	−11.8730	−0.889917
$179$	2.65933	0.198768	0.0993838	−	0.995049i	$-0.468313\pi$
$179$	2.65933	0.198768	0.0993838	+	0.995049i	$0.468313\pi$
$180$	−3.71082	−0.276588
$181$	−2.81071	−0.208918	−0.104459	−	0.994529i	$-0.533311\pi$
$181$	−2.81071	−0.208918	−0.104459	+	0.994529i	$0.533311\pi$
$182$	1.39305	0.103260
$183$	−11.0459	−0.816534
$184$	3.03948	0.224073
$185$	−11.0117	−0.809600
$186$	−16.6722	−1.22247
$187$	2.11502	0.154666
$188$	4.50102	0.328271
$189$	3.43311	0.249722
$190$	7.80879	0.566509
$191$	0.699159	0.0505894	0.0252947	−	0.999680i	$-0.491948\pi$
$191$	0.699159	0.0505894	0.0252947	+	0.999680i	$0.491948\pi$
$192$	1.99756	0.144161
$193$	9.43764	0.679336	0.339668	−	0.940545i	$-0.389685\pi$
$193$	9.43764	0.679336	0.339668	+	0.940545i	$0.389685\pi$
$194$	−18.6881	−1.34173
$195$	12.1941	0.873235
$196$	−6.26871	−0.447765
$197$	15.4795	1.10287	0.551435	−	0.834218i	$-0.314081\pi$
$197$	15.4795	1.10287	0.551435	+	0.834218i	$0.314081\pi$
$198$	0.943132	0.0670254
$199$	−3.58362	−0.254036	−0.127018	−	0.991900i	$-0.540541\pi$
$199$	−3.58362	−0.254036	−0.127018	+	0.991900i	$0.540541\pi$
$200$	9.04274	0.639418
$201$	−8.00716	−0.564781
$202$	−8.42487	−0.592771
$203$	−7.19769	−0.505179
$204$	4.43595	0.310579
$205$	14.1150	0.985837
$206$	5.59750	0.389996
$207$	3.00984	0.209198
$208$	−1.62901	−0.112951
$209$	−1.98466	−0.137282
$210$	6.40134	0.441734
$211$	9.82806	0.676591	0.338296	−	0.941040i	$-0.390150\pi$
$211$	9.82806	0.676591	0.338296	+	0.941040i	$0.390150\pi$
$212$	−3.34712	−0.229881
$213$	−18.9600	−1.29912
$214$	0.0658625	0.00450227
$215$	−27.2414	−1.85785
$216$	−4.01460	−0.273159
$217$	7.13737	0.484516
$218$	7.97843	0.540367
$219$	−3.12359	−0.211072
$220$	−3.56907	−0.240626
$221$	−3.61751	−0.243340
$222$	5.86989	0.393961
$223$	21.5589	1.44369	0.721845	−	0.692055i	$-0.243294\pi$
$223$	21.5589	1.44369	0.721845	+	0.692055i	$0.243294\pi$
$224$	−0.855155	−0.0571375
$225$	8.95454	0.596970
$226$	−1.70168	−0.113194
$227$	−0.870905	−0.0578040	−0.0289020	−	0.999582i	$-0.509201\pi$
$227$	−0.870905	−0.0578040	−0.0289020	+	0.999582i	$0.509201\pi$
$228$	−4.16253	−0.275670
$229$	−10.5632	−0.698038	−0.349019	−	0.937116i	$-0.613485\pi$
$229$	−10.5632	−0.698038	−0.349019	+	0.937116i	$0.613485\pi$
$230$	−11.3900	−0.751037
$231$	−1.62695	−0.107045
$232$	8.41682	0.552592
$233$	18.6915	1.22452	0.612260	−	0.790657i	$-0.290261\pi$
$233$	18.6915	1.22452	0.612260	+	0.790657i	$0.290261\pi$
$234$	−1.61312	−0.105453
$235$	−16.8670	−1.10028
$236$	−8.99208	−0.585335
$237$	−12.5547	−0.815514
$238$	−1.89903	−0.123096
$239$	−4.43448	−0.286843	−0.143421	−	0.989662i	$-0.545810\pi$
$239$	−4.43448	−0.286843	−0.143421	+	0.989662i	$0.545810\pi$
$240$	−7.48559	−0.483192
$241$	18.5595	1.19552	0.597760	−	0.801675i	$-0.296058\pi$
$241$	18.5595	1.19552	0.597760	+	0.801675i	$0.296058\pi$
$242$	−10.0929	−0.648796
$243$	−9.90968	−0.635706
$244$	−5.52968	−0.354002
$245$	23.4911	1.50079
$246$	−7.52412	−0.479721
$247$	3.39454	0.215989
$248$	−8.34628	−0.529989
$249$	−20.6350	−1.30769
$250$	−15.1496	−0.958145
$251$	17.8499	1.12668	0.563339	−	0.826226i	$-0.309516\pi$
$251$	17.8499	1.12668	0.563339	+	0.826226i	$0.309516\pi$
$252$	−0.846815	−0.0533443
$253$	2.89486	0.181999
$254$	−9.65709	−0.605940
$255$	−16.6231	−1.04098
$256$	1.00000	0.0625000
$257$	17.1200	1.06792	0.533959	−	0.845511i	$-0.320704\pi$
$257$	17.1200	1.06792	0.533959	+	0.845511i	$0.320704\pi$
$258$	14.5212	0.904053
$259$	−2.51290	−0.156144
$260$	6.10448	0.378584
$261$	8.33473	0.515907
$262$	−9.59247	−0.592625
$263$	13.7057	0.845129	0.422564	−	0.906333i	$-0.361130\pi$
$263$	13.7057	0.845129	0.422564	+	0.906333i	$0.361130\pi$
$264$	1.90252	0.117092
$265$	12.5429	0.770503
$266$	1.78198	0.109260
$267$	−23.7170	−1.45146
$268$	−4.00847	−0.244856
$269$	1.71200	0.104382	0.0521912	−	0.998637i	$-0.483379\pi$
$269$	1.71200	0.104382	0.0521912	+	0.998637i	$0.483379\pi$
$270$	15.0442	0.915560
$271$	−3.12373	−0.189753	−0.0948764	−	0.995489i	$-0.530246\pi$
$271$	−3.12373	−0.189753	−0.0948764	+	0.995489i	$0.530246\pi$
$272$	2.22068	0.134649
$273$	2.78271	0.168417
$274$	−20.8669	−1.26061
$275$	8.61249	0.519353
$276$	6.07154	0.365464
$277$	−2.16573	−0.130126	−0.0650632	−	0.997881i	$-0.520725\pi$
$277$	−2.16573	−0.130126	−0.0650632	+	0.997881i	$0.520725\pi$
$278$	−14.7477	−0.884511
$279$	−8.26488	−0.494805
$280$	3.20458	0.191510
$281$	−0.284008	−0.0169425	−0.00847126	−	0.999964i	$-0.502697\pi$
$281$	−0.284008	−0.0169425	−0.00847126	+	0.999964i	$0.502697\pi$
$282$	8.99107	0.535410
$283$	−8.88577	−0.528204	−0.264102	−	0.964495i	$-0.585076\pi$
$283$	−8.88577	−0.528204	−0.264102	+	0.964495i	$0.585076\pi$
$284$	−9.49157	−0.563221
$285$	15.5985	0.923977
$286$	−1.55150	−0.0917421
$287$	3.22108	0.190134
$288$	0.990247	0.0583509
$289$	−12.0686	−0.709916
$290$	−31.5409	−1.85215
$291$	−37.3306	−2.18836
$292$	−1.56370	−0.0915087
$293$	4.85477	0.283619	0.141809	−	0.989894i	$-0.454708\pi$
$293$	4.85477	0.283619	0.141809	+	0.989894i	$0.454708\pi$
$294$	−12.5221	−0.730305
$295$	33.6966	1.96189
$296$	2.93853	0.170799
$297$	−3.82359	−0.221867
$298$	−3.79747	−0.219981
$299$	−4.95133	−0.286343
$300$	18.0634	1.04289
$301$	−6.21655	−0.358316
$302$	16.4772	0.948153
$303$	−16.8292	−0.966811
$304$	−2.08381	−0.119515
$305$	20.7217	1.18652
$306$	2.19902	0.125710
$307$	−10.6121	−0.605667	−0.302833	−	0.953044i	$-0.597933\pi$
$307$	−10.6121	−0.605667	−0.302833	+	0.953044i	$0.597933\pi$
$308$	−0.814468	−0.0464086
$309$	11.1813	0.636085
$310$	31.2766	1.77639
$311$	−1.86023	−0.105484	−0.0527421	−	0.998608i	$-0.516796\pi$
$311$	−1.86023	−0.105484	−0.0527421	+	0.998608i	$0.516796\pi$
$312$	−3.25404	−0.184224
$313$	10.9649	0.619775	0.309888	−	0.950773i	$-0.399709\pi$
$313$	10.9649	0.619775	0.309888	+	0.950773i	$0.399709\pi$
$314$	0.911632	0.0514464
$315$	3.17332	0.178797
$316$	−6.28501	−0.353559
$317$	29.6443	1.66499	0.832495	−	0.554032i	$-0.186912\pi$
$317$	29.6443	1.66499	0.832495	+	0.554032i	$0.186912\pi$
$318$	−6.68607	−0.374936
$319$	8.01636	0.448830
$320$	−3.74736	−0.209484
$321$	0.131564	0.00734321
$322$	−2.59923	−0.144849
$323$	−4.62748	−0.257480
$324$	−10.9902	−0.610564
$325$	−14.7307	−0.817111
$326$	10.9720	0.607683
$327$	15.9374	0.881340
$328$	−3.76666	−0.207979
$329$	−3.84908	−0.212206
$330$	−7.12943	−0.392462
$331$	−6.00751	−0.330203	−0.165101	−	0.986277i	$-0.552795\pi$
$331$	−6.00751	−0.330203	−0.165101	+	0.986277i	$0.552795\pi$
$332$	−10.3301	−0.566939
$333$	2.90987	0.159460
$334$	4.55637	0.249313
$335$	15.0212	0.820695
$336$	−1.70822	−0.0931913
$337$	27.7754	1.51302	0.756511	−	0.653981i	$-0.226902\pi$
$337$	27.7754	1.51302	0.756511	+	0.653981i	$0.226902\pi$
$338$	−10.3463	−0.562767
$339$	−3.39921	−0.184620
$340$	−8.32171	−0.451308
$341$	−7.94917	−0.430472
$342$	−2.06348	−0.111580
$343$	11.3468	0.612670
$344$	7.26949	0.391945
$345$	−22.7523	−1.22494
$346$	3.30128	0.177478
$347$	−8.98009	−0.482076	−0.241038	−	0.970516i	$-0.577488\pi$
$347$	−8.98009	−0.482076	−0.241038	+	0.970516i	$0.577488\pi$
$348$	16.8131	0.901277
$349$	7.04569	0.377147	0.188574	−	0.982059i	$-0.439614\pi$
$349$	7.04569	0.377147	0.188574	+	0.982059i	$0.439614\pi$
$350$	−7.73295	−0.413343
$351$	6.53981	0.349069
$352$	0.952421	0.0507642
$353$	−0.998717	−0.0531563	−0.0265782	−	0.999647i	$-0.508461\pi$
$353$	−0.998717	−0.0531563	−0.0265782	+	0.999647i	$0.508461\pi$
$354$	−17.9622	−0.954681
$355$	35.5684	1.88777
$356$	−11.8730	−0.629267
$357$	−3.79343	−0.200769
$358$	2.65933	0.140550
$359$	−4.09908	−0.216341	−0.108171	−	0.994132i	$-0.534499\pi$
$359$	−4.09908	−0.216341	−0.108171	+	0.994132i	$0.534499\pi$
$360$	−3.71082	−0.195577
$361$	−14.6577	−0.771460
$362$	−2.81071	−0.147728
$363$	−20.1612	−1.05819
$364$	1.39305	0.0730159
$365$	5.85976	0.306714
$366$	−11.0459	−0.577377
$367$	−20.4339	−1.06664	−0.533320	−	0.845913i	$-0.679056\pi$
$367$	−20.4339	−1.06664	−0.533320	+	0.845913i	$0.679056\pi$
$368$	3.03948	0.158444
$369$	−3.72992	−0.194172
$370$	−11.0117	−0.572473
$371$	2.86231	0.148604
$372$	−16.6722	−0.864413
$373$	29.4742	1.52612	0.763058	−	0.646330i	$-0.223697\pi$
$373$	29.4742	1.52612	0.763058	+	0.646330i	$0.223697\pi$
$374$	2.11502	0.109365
$375$	−30.2623	−1.56274
$376$	4.50102	0.232123
$377$	−13.7111	−0.706155
$378$	3.43311	0.176580
$379$	29.9303	1.53741	0.768707	−	0.639601i	$-0.220900\pi$
$379$	29.9303	1.53741	0.768707	+	0.639601i	$0.220900\pi$
$380$	7.80879	0.400582
$381$	−19.2906	−0.988288
$382$	0.699159	0.0357721
$383$	4.18507	0.213847	0.106923	−	0.994267i	$-0.465900\pi$
$383$	4.18507	0.213847	0.106923	+	0.994267i	$0.465900\pi$
$384$	1.99756	0.101938
$385$	3.05211	0.155550
$386$	9.43764	0.480363
$387$	7.19859	0.365925
$388$	−18.6881	−0.948745
$389$	5.30753	0.269102	0.134551	−	0.990907i	$-0.457041\pi$
$389$	5.30753	0.269102	0.134551	+	0.990907i	$0.457041\pi$
$390$	12.1941	0.617471
$391$	6.74972	0.341348
$392$	−6.26871	−0.316618
$393$	−19.1615	−0.966572
$394$	15.4795	0.779847
$395$	23.5522	1.18504
$396$	0.943132	0.0473941
$397$	−18.4042	−0.923682	−0.461841	−	0.886963i	$-0.652811\pi$
$397$	−18.4042	−0.923682	−0.461841	+	0.886963i	$0.652811\pi$
$398$	−3.58362	−0.179630
$399$	3.55961	0.178203
$400$	9.04274	0.452137
$401$	−25.5462	−1.27572	−0.637859	−	0.770153i	$-0.720180\pi$
$401$	−25.5462	−1.27572	−0.637859	+	0.770153i	$0.720180\pi$
$402$	−8.00716	−0.399361
$403$	13.5961	0.677272
$404$	−8.42487	−0.419153
$405$	41.1841	2.04645
$406$	−7.19769	−0.357215
$407$	2.79872	0.138727
$408$	4.43595	0.219612
$409$	−17.2155	−0.851252	−0.425626	−	0.904899i	$-0.639946\pi$
$409$	−17.2155	−0.851252	−0.425626	+	0.904899i	$0.639946\pi$
$410$	14.1150	0.697092
$411$	−41.6829	−2.05606
$412$	5.59750	0.275769
$413$	7.68963	0.378382
$414$	3.00984	0.147925
$415$	38.7107	1.90023
$416$	−1.62901	−0.0798686
$417$	−29.4595	−1.44264
$418$	−1.98466	−0.0970730
$419$	−5.07760	−0.248057	−0.124028	−	0.992279i	$-0.539581\pi$
$419$	−5.07760	−0.248057	−0.124028	+	0.992279i	$0.539581\pi$
$420$	6.40134	0.312353
$421$	−19.5215	−0.951419	−0.475710	−	0.879602i	$-0.657809\pi$
$421$	−19.5215	−0.951419	−0.475710	+	0.879602i	$0.657809\pi$
$422$	9.82806	0.478422
$423$	4.45713	0.216713
$424$	−3.34712	−0.162550
$425$	20.0811	0.974074
$426$	−18.9600	−0.918614
$427$	4.72874	0.228840
$428$	0.0658625	0.00318359
$429$	−3.09921	−0.149631
$430$	−27.2414	−1.31370
$431$	−2.37031	−0.114174	−0.0570870	−	0.998369i	$-0.518181\pi$
$431$	−2.37031	−0.114174	−0.0570870	+	0.998369i	$0.518181\pi$
$432$	−4.01460	−0.193153
$433$	−7.53292	−0.362009	−0.181004	−	0.983482i	$-0.557935\pi$
$433$	−7.53292	−0.362009	−0.181004	+	0.983482i	$0.557935\pi$
$434$	7.13737	0.342605
$435$	−63.0048	−3.02085
$436$	7.97843	0.382097
$437$	−6.33369	−0.302982
$438$	−3.12359	−0.149251
$439$	17.2204	0.821887	0.410943	−	0.911661i	$-0.365199\pi$
$439$	17.2204	0.821887	0.410943	+	0.911661i	$0.365199\pi$
$440$	−3.56907	−0.170149
$441$	−6.20757	−0.295599
$442$	−3.61751	−0.172067
$443$	2.43818	0.115841	0.0579207	−	0.998321i	$-0.481553\pi$
$443$	2.43818	0.115841	0.0579207	+	0.998321i	$0.481553\pi$
$444$	5.86989	0.278573
$445$	44.4924	2.10914
$446$	21.5589	1.02084
$447$	−7.58567	−0.358790
$448$	−0.855155	−0.0404023
$449$	−17.6910	−0.834891	−0.417446	−	0.908702i	$-0.637075\pi$
$449$	−17.6910	−0.834891	−0.417446	+	0.908702i	$0.637075\pi$
$450$	8.95454	0.422121
$451$	−3.58744	−0.168926
$452$	−1.70168	−0.0800403
$453$	32.9141	1.54644
$454$	−0.870905	−0.0408736
$455$	−5.22028	−0.244730
$456$	−4.16253	−0.194928
$457$	−3.87771	−0.181392	−0.0906959	−	0.995879i	$-0.528909\pi$
$457$	−3.87771	−0.181392	−0.0906959	+	0.995879i	$0.528909\pi$
$458$	−10.5632	−0.493588
$459$	−8.91516	−0.416124
$460$	−11.3900	−0.531063
$461$	21.5989	1.00596	0.502981	−	0.864298i	$-0.332237\pi$
$461$	21.5989	1.00596	0.502981	+	0.864298i	$0.332237\pi$
$462$	−1.62695	−0.0756925
$463$	−30.8470	−1.43358	−0.716792	−	0.697288i	$-0.754390\pi$
$463$	−30.8470	−1.43358	−0.716792	+	0.697288i	$0.754390\pi$
$464$	8.41682	0.390741
$465$	62.4768	2.89729
$466$	18.6915	0.865866
$467$	19.4628	0.900632	0.450316	−	0.892869i	$-0.351311\pi$
$467$	19.4628	0.900632	0.450316	+	0.892869i	$0.351311\pi$
$468$	−1.61312	−0.0745664
$469$	3.42786	0.158284
$470$	−16.8670	−0.778016
$471$	1.82104	0.0839091
$472$	−8.99208	−0.413894
$473$	6.92361	0.318348
$474$	−12.5547	−0.576656
$475$	−18.8433	−0.864591
$476$	−1.89903	−0.0870419
$477$	−3.31447	−0.151759
$478$	−4.43448	−0.202828
$479$	−32.6779	−1.49309	−0.746545	−	0.665335i	$-0.768289\pi$
$479$	−32.6779	−1.49309	−0.746545	+	0.665335i	$0.768289\pi$
$480$	−7.48559	−0.341669
$481$	−4.78689	−0.218263
$482$	18.5595	0.845360
$483$	−5.19211	−0.236249
$484$	−10.0929	−0.458768
$485$	70.0311	3.17995
$486$	−9.90968	−0.449512
$487$	24.8078	1.12415	0.562075	−	0.827086i	$-0.310003\pi$
$487$	24.8078	1.12415	0.562075	+	0.827086i	$0.310003\pi$
$488$	−5.52968	−0.250317
$489$	21.9172	0.991132
$490$	23.4911	1.06122
$491$	−28.4052	−1.28191	−0.640954	−	0.767579i	$-0.721461\pi$
$491$	−28.4052	−1.28191	−0.640954	+	0.767579i	$0.721461\pi$
$492$	−7.52412	−0.339214
$493$	18.6911	0.841805
$494$	3.39454	0.152727
$495$	−3.53426	−0.158853
$496$	−8.34628	−0.374759
$497$	8.11677	0.364087
$498$	−20.6350	−0.924678
$499$	−33.9156	−1.51827	−0.759135	−	0.650933i	$-0.774378\pi$
$499$	−33.9156	−1.51827	−0.759135	+	0.650933i	$0.774378\pi$
$500$	−15.1496	−0.677511
$501$	9.10162	0.406630
$502$	17.8499	0.796682
$503$	−21.9311	−0.977860	−0.488930	−	0.872323i	$-0.662613\pi$
$503$	−21.9311	−0.977860	−0.488930	+	0.872323i	$0.662613\pi$
$504$	−0.846815	−0.0377201
$505$	31.5710	1.40489
$506$	2.89486	0.128692
$507$	−20.6674	−0.917873
$508$	−9.65709	−0.428464
$509$	−17.4128	−0.771811	−0.385905	−	0.922538i	$-0.626111\pi$
$509$	−17.4128	−0.771811	−0.385905	+	0.922538i	$0.626111\pi$
$510$	−16.6231	−0.736084
$511$	1.33721	0.0591546
$512$	1.00000	0.0441942
$513$	8.36566	0.369353
$514$	17.1200	0.755132
$515$	−20.9759	−0.924307
$516$	14.5212	0.639262
$517$	4.28687	0.188536
$518$	−2.51290	−0.110411
$519$	6.59451	0.289467
$520$	6.10448	0.267699
$521$	−21.8146	−0.955715	−0.477857	−	0.878437i	$-0.658586\pi$
$521$	−21.8146	−0.955715	−0.477857	+	0.878437i	$0.658586\pi$
$522$	8.33473	0.364801
$523$	6.73303	0.294415	0.147207	−	0.989106i	$-0.452972\pi$
$523$	6.73303	0.294415	0.147207	+	0.989106i	$0.452972\pi$
$524$	−9.59247	−0.419049
$525$	−15.4470	−0.674163
$526$	13.7057	0.597596
$527$	−18.5345	−0.807373
$528$	1.90252	0.0827965
$529$	−13.7616	−0.598329
$530$	12.5429	0.544828
$531$	−8.90438	−0.386417
$532$	1.78198	0.0772586
$533$	6.13591	0.265776
$534$	−23.7170	−1.02633
$535$	−0.246811	−0.0106706
$536$	−4.00847	−0.173139
$537$	5.31217	0.229237
$538$	1.71200	0.0738095
$539$	−5.97045	−0.257165
$540$	15.0442	0.647398
$541$	−23.8140	−1.02384	−0.511922	−	0.859032i	$-0.671066\pi$
$541$	−23.8140	−1.02384	−0.511922	+	0.859032i	$0.671066\pi$
$542$	−3.12373	−0.134176
$543$	−5.61456	−0.240944
$544$	2.22068	0.0952110
$545$	−29.8981	−1.28069
$546$	2.78271	0.119089
$547$	−23.5984	−1.00899	−0.504497	−	0.863413i	$-0.668322\pi$
$547$	−23.5984	−1.00899	−0.504497	+	0.863413i	$0.668322\pi$
$548$	−20.8669	−0.891389
$549$	−5.47575	−0.233699
$550$	8.61249	0.367238
$551$	−17.5390	−0.747188
$552$	6.07154	0.258422
$553$	5.37466	0.228554
$554$	−2.16573	−0.0920132
$555$	−21.9966	−0.933705
$556$	−14.7477	−0.625443
$557$	1.58018	0.0669543	0.0334772	−	0.999439i	$-0.489342\pi$
$557$	1.58018	0.0669543	0.0334772	+	0.999439i	$0.489342\pi$
$558$	−8.26488	−0.349880
$559$	−11.8420	−0.500865
$560$	3.20458	0.135418
$561$	4.22489	0.178375
$562$	−0.284008	−0.0119802
$563$	−24.0710	−1.01447	−0.507236	−	0.861807i	$-0.669333\pi$
$563$	−24.0710	−1.01447	−0.507236	+	0.861807i	$0.669333\pi$
$564$	8.99107	0.378592
$565$	6.37682	0.268275
$566$	−8.88577	−0.373497
$567$	9.39829	0.394691
$568$	−9.49157	−0.398258
$569$	−10.0851	−0.422788	−0.211394	−	0.977401i	$-0.567800\pi$
$569$	−10.0851	−0.422788	−0.211394	+	0.977401i	$0.567800\pi$
$570$	15.5985	0.653350
$571$	3.04630	0.127484	0.0637418	−	0.997966i	$-0.479697\pi$
$571$	3.04630	0.127484	0.0637418	+	0.997966i	$0.479697\pi$
$572$	−1.55150	−0.0648715
$573$	1.39661	0.0583443
$574$	3.22108	0.134445
$575$	27.4852	1.14621
$576$	0.990247	0.0412603
$577$	−17.2846	−0.719568	−0.359784	−	0.933036i	$-0.617150\pi$
$577$	−17.2846	−0.719568	−0.359784	+	0.933036i	$0.617150\pi$
$578$	−12.0686	−0.501986
$579$	18.8523	0.783473
$580$	−31.5409	−1.30966
$581$	8.83385	0.366490
$582$	−37.3306	−1.54740
$583$	−3.18787	−0.132028
$584$	−1.56370	−0.0647064
$585$	6.04494	0.249928
$586$	4.85477	0.200549
$587$	−36.0268	−1.48698	−0.743492	−	0.668745i	$-0.766832\pi$
$587$	−36.0268	−1.48698	−0.743492	+	0.668745i	$0.766832\pi$
$588$	−12.5221	−0.516404
$589$	17.3920	0.716627
$590$	33.6966	1.38727
$591$	30.9213	1.27193
$592$	2.93853	0.120773
$593$	−12.8323	−0.526959	−0.263480	−	0.964665i	$-0.584870\pi$
$593$	−12.8323	−0.526959	−0.263480	+	0.964665i	$0.584870\pi$
$594$	−3.82359	−0.156884
$595$	7.11635	0.291742
$596$	−3.79747	−0.155550
$597$	−7.15849	−0.292978
$598$	−4.95133	−0.202475
$599$	−1.73844	−0.0710306	−0.0355153	−	0.999369i	$-0.511307\pi$
$599$	−1.73844	−0.0710306	−0.0355153	+	0.999369i	$0.511307\pi$
$600$	18.0634	0.737436
$601$	26.8523	1.09533	0.547664	−	0.836698i	$-0.315517\pi$
$601$	26.8523	1.09533	0.547664	+	0.836698i	$0.315517\pi$
$602$	−6.21655	−0.253367
$603$	−3.96937	−0.161645
$604$	16.4772	0.670446
$605$	37.8218	1.53767
$606$	−16.8292	−0.683639
$607$	12.7671	0.518201	0.259101	−	0.965850i	$-0.416574\pi$
$607$	12.7671	0.518201	0.259101	+	0.965850i	$0.416574\pi$
$608$	−2.08381	−0.0845096
$609$	−14.3778	−0.582619
$610$	20.7217	0.838998
$611$	−7.33220	−0.296629
$612$	2.19902	0.0888903
$613$	27.0701	1.09335	0.546676	−	0.837344i	$-0.315893\pi$
$613$	27.0701	1.09335	0.546676	+	0.837344i	$0.315893\pi$
$614$	−10.6121	−0.428271
$615$	28.1956	1.13696
$616$	−0.814468	−0.0328158
$617$	26.4695	1.06562	0.532811	−	0.846234i	$-0.321136\pi$
$617$	26.4695	1.06562	0.532811	+	0.846234i	$0.321136\pi$
$618$	11.1813	0.449780
$619$	−13.6166	−0.547298	−0.273649	−	0.961830i	$-0.588231\pi$
$619$	−13.6166	−0.547298	−0.273649	+	0.961830i	$0.588231\pi$
$620$	31.2766	1.25610
$621$	−12.2023	−0.489662
$622$	−1.86023	−0.0745885
$623$	10.1532	0.406781
$624$	−3.25404	−0.130266
$625$	11.5574	0.462296
$626$	10.9649	0.438247
$627$	−3.96448	−0.158326
$628$	0.911632	0.0363781
$629$	6.52555	0.260191
$630$	3.17332	0.126428
$631$	15.4328	0.614371	0.307185	−	0.951650i	$-0.400613\pi$
$631$	15.4328	0.614371	0.307185	+	0.951650i	$0.400613\pi$
$632$	−6.28501	−0.250004
$633$	19.6321	0.780307
$634$	29.6443	1.17733
$635$	36.1886	1.43610
$636$	−6.68607	−0.265120
$637$	10.2118	0.404605
$638$	8.01636	0.317371
$639$	−9.39900	−0.371819
$640$	−3.74736	−0.148128
$641$	13.2879	0.524840	0.262420	−	0.964954i	$-0.415479\pi$
$641$	13.2879	0.524840	0.262420	+	0.964954i	$0.415479\pi$
$642$	0.131564	0.00519243
$643$	6.38186	0.251676	0.125838	−	0.992051i	$-0.459838\pi$
$643$	6.38186	0.251676	0.125838	+	0.992051i	$0.459838\pi$
$644$	−2.59923	−0.102424
$645$	−54.4164	−2.14264
$646$	−4.62748	−0.182066
$647$	44.7377	1.75882	0.879410	−	0.476065i	$-0.157937\pi$
$647$	44.7377	1.75882	0.879410	+	0.476065i	$0.157937\pi$
$648$	−10.9902	−0.431734
$649$	−8.56424	−0.336176
$650$	−14.7307	−0.577785
$651$	14.2573	0.558789
$652$	10.9720	0.429697
$653$	−17.1010	−0.669214	−0.334607	−	0.942358i	$-0.608604\pi$
$653$	−17.1010	−0.669214	−0.334607	+	0.942358i	$0.608604\pi$
$654$	15.9374	0.623201
$655$	35.9465	1.40454
$656$	−3.76666	−0.147063
$657$	−1.54845	−0.0604108
$658$	−3.84908	−0.150053
$659$	19.1414	0.745643	0.372822	−	0.927903i	$-0.378390\pi$
$659$	19.1414	0.745643	0.372822	+	0.927903i	$0.378390\pi$
$660$	−7.12943	−0.277513
$661$	−16.9834	−0.660579	−0.330290	−	0.943880i	$-0.607146\pi$
$661$	−16.9834	−0.660579	−0.330290	+	0.943880i	$0.607146\pi$
$662$	−6.00751	−0.233489
$663$	−7.22619	−0.280642
$664$	−10.3301	−0.400886
$665$	−6.67773	−0.258951
$666$	2.90987	0.112755
$667$	25.5828	0.990569
$668$	4.55637	0.176291
$669$	43.0652	1.66500
$670$	15.0212	0.580319
$671$	−5.26658	−0.203314
$672$	−1.70822	−0.0658962
$673$	41.3650	1.59450	0.797252	−	0.603647i	$-0.206286\pi$
$673$	41.3650	1.59450	0.797252	+	0.603647i	$0.206286\pi$
$674$	27.7754	1.06987
$675$	−36.3030	−1.39730
$676$	−10.3463	−0.397936
$677$	−18.4469	−0.708971	−0.354486	−	0.935061i	$-0.615344\pi$
$677$	−18.4469	−0.708971	−0.354486	+	0.935061i	$0.615344\pi$
$678$	−3.39921	−0.130546
$679$	15.9812	0.613303
$680$	−8.32171	−0.319123
$681$	−1.73969	−0.0666649
$682$	−7.94917	−0.304390
$683$	−47.4270	−1.81475	−0.907373	−	0.420327i	$-0.861915\pi$
$683$	−47.4270	−1.81475	−0.907373	+	0.420327i	$0.861915\pi$
$684$	−2.06348	−0.0788993
$685$	78.1958	2.98771
$686$	11.3468	0.433223
$687$	−21.1007	−0.805042
$688$	7.26949	0.277147
$689$	5.45248	0.207723
$690$	−22.7523	−0.866165
$691$	−5.87162	−0.223367	−0.111683	−	0.993744i	$-0.535624\pi$
$691$	−5.87162	−0.223367	−0.111683	+	0.993744i	$0.535624\pi$
$692$	3.30128	0.125496
$693$	−0.806524	−0.0306373
$694$	−8.98009	−0.340879
$695$	55.2651	2.09633
$696$	16.8131	0.637299
$697$	−8.36455	−0.316830
$698$	7.04569	0.266683
$699$	37.3374	1.41223
$700$	−7.73295	−0.292278
$701$	11.8302	0.446819	0.223409	−	0.974725i	$-0.428281\pi$
$701$	11.8302	0.446819	0.223409	+	0.974725i	$0.428281\pi$
$702$	6.53981	0.246829
$703$	−6.12333	−0.230946
$704$	0.952421	0.0358957
$705$	−33.6928	−1.26894
$706$	−0.998717	−0.0375872
$707$	7.20457	0.270956
$708$	−17.9622	−0.675062
$709$	18.3363	0.688634	0.344317	−	0.938853i	$-0.388111\pi$
$709$	18.3363	0.688634	0.344317	+	0.938853i	$0.388111\pi$
$710$	35.5684	1.33486
$711$	−6.22371	−0.233407
$712$	−11.8730	−0.444959
$713$	−25.3684	−0.950053
$714$	−3.79343	−0.141965
$715$	5.81403	0.217433
$716$	2.65933	0.0993838
$717$	−8.85814	−0.330813
$718$	−4.09908	−0.152976
$719$	−13.6079	−0.507489	−0.253745	−	0.967271i	$-0.581662\pi$
$719$	−13.6079	−0.507489	−0.253745	+	0.967271i	$0.581662\pi$
$720$	−3.71082	−0.138294
$721$	−4.78673	−0.178267
$722$	−14.6577	−0.545505
$723$	37.0736	1.37878
$724$	−2.81071	−0.104459
$725$	76.1111	2.82670
$726$	−20.1612	−0.748251
$727$	11.3726	0.421788	0.210894	−	0.977509i	$-0.432363\pi$
$727$	11.3726	0.421788	0.210894	+	0.977509i	$0.432363\pi$
$728$	1.39305	0.0516300
$729$	13.1753	0.487973
$730$	5.85976	0.216879
$731$	16.1432	0.597079
$732$	−11.0459	−0.408267
$733$	19.6155	0.724515	0.362257	−	0.932078i	$-0.382006\pi$
$733$	19.6155	0.724515	0.362257	+	0.932078i	$0.382006\pi$
$734$	−20.4339	−0.754229
$735$	46.9250	1.73085
$736$	3.03948	0.112037
$737$	−3.81775	−0.140629
$738$	−3.72992	−0.137300
$739$	14.5408	0.534893	0.267446	−	0.963573i	$-0.413820\pi$
$739$	14.5408	0.534893	0.267446	+	0.963573i	$0.413820\pi$
$740$	−11.0117	−0.404800
$741$	6.78079	0.249099
$742$	2.86231	0.105079
$743$	23.1466	0.849165	0.424583	−	0.905389i	$-0.360421\pi$
$743$	23.1466	0.849165	0.424583	+	0.905389i	$0.360421\pi$
$744$	−16.6722	−0.611233
$745$	14.2305	0.521365
$746$	29.4742	1.07913
$747$	−10.2294	−0.374273
$748$	2.11502	0.0773330
$749$	−0.0563227	−0.00205799
$750$	−30.2623	−1.10502
$751$	−6.27956	−0.229145	−0.114572	−	0.993415i	$-0.536550\pi$
$751$	−6.27956	−0.229145	−0.114572	+	0.993415i	$0.536550\pi$
$752$	4.50102	0.164135
$753$	35.6563	1.29939
$754$	−13.7111	−0.499327
$755$	−61.7459	−2.24716
$756$	3.43311	0.124861
$757$	−21.3907	−0.777457	−0.388728	−	0.921352i	$-0.627086\pi$
$757$	−21.3907	−0.777457	−0.388728	+	0.921352i	$0.627086\pi$
$758$	29.9303	1.08712
$759$	5.78266	0.209897
$760$	7.80879	0.283254
$761$	31.0266	1.12471	0.562357	−	0.826895i	$-0.309895\pi$
$761$	31.0266	1.12471	0.562357	+	0.826895i	$0.309895\pi$
$762$	−19.2906	−0.698825
$763$	−6.82280	−0.247002
$764$	0.699159	0.0252947
$765$	−8.24055	−0.297938
$766$	4.18507	0.151213
$767$	14.6482	0.528914
$768$	1.99756	0.0720807
$769$	5.64506	0.203566	0.101783	−	0.994807i	$-0.467545\pi$
$769$	5.64506	0.203566	0.101783	+	0.994807i	$0.467545\pi$
$770$	3.05211	0.109990
$771$	34.1983	1.23162
$772$	9.43764	0.339668
$773$	28.4644	1.02379	0.511896	−	0.859047i	$-0.328943\pi$
$773$	28.4644	1.02379	0.511896	+	0.859047i	$0.328943\pi$
$774$	7.19859	0.258748
$775$	−75.4732	−2.71108
$776$	−18.6881	−0.670864
$777$	−5.01967	−0.180080
$778$	5.30753	0.190284
$779$	7.84899	0.281219
$780$	12.1941	0.436618
$781$	−9.03997	−0.323476
$782$	6.74972	0.241370
$783$	−33.7902	−1.20756
$784$	−6.26871	−0.223882
$785$	−3.41622	−0.121930
$786$	−19.1615	−0.683469
$787$	9.74353	0.347319	0.173660	−	0.984806i	$-0.444441\pi$
$787$	9.74353	0.347319	0.173660	+	0.984806i	$0.444441\pi$
$788$	15.4795	0.551435
$789$	27.3779	0.974680
$790$	23.5522	0.837950
$791$	1.45520	0.0517410
$792$	0.943132	0.0335127
$793$	9.00789	0.319879
$794$	−18.4042	−0.653142
$795$	25.0551	0.888614
$796$	−3.58362	−0.127018
$797$	−54.3758	−1.92609	−0.963045	−	0.269341i	$-0.913194\pi$
$797$	−54.3758	−1.92609	−0.963045	+	0.269341i	$0.913194\pi$
$798$	3.55961	0.126009
$799$	9.99535	0.353610
$800$	9.04274	0.319709
$801$	−11.7572	−0.415419
$802$	−25.5462	−0.902069
$803$	−1.48930	−0.0525563
$804$	−8.00716	−0.282391
$805$	9.74025	0.343299
$806$	13.5961	0.478904
$807$	3.41982	0.120383
$808$	−8.42487	−0.296386
$809$	−19.7034	−0.692735	−0.346368	−	0.938099i	$-0.612585\pi$
$809$	−19.7034	−0.692735	−0.346368	+	0.938099i	$0.612585\pi$
$810$	41.1841	1.44706
$811$	−13.5528	−0.475904	−0.237952	−	0.971277i	$-0.576476\pi$
$811$	−13.5528	−0.475904	−0.237952	+	0.971277i	$0.576476\pi$
$812$	−7.19769	−0.252589
$813$	−6.23983	−0.218840
$814$	2.79872	0.0980950
$815$	−41.1161	−1.44023
$816$	4.43595	0.155289
$817$	−15.1482	−0.529969
$818$	−17.2155	−0.601926
$819$	1.37947	0.0482025
$820$	14.1150	0.492918
$821$	34.8155	1.21507	0.607534	−	0.794293i	$-0.292159\pi$
$821$	34.8155	1.21507	0.607534	+	0.794293i	$0.292159\pi$
$822$	−41.6829	−1.45386
$823$	−36.7434	−1.28079	−0.640397	−	0.768044i	$-0.721230\pi$
$823$	−36.7434	−1.28079	−0.640397	+	0.768044i	$0.721230\pi$
$824$	5.59750	0.194998
$825$	17.2040	0.598965
$826$	7.68963	0.267556
$827$	−33.5039	−1.16505	−0.582523	−	0.812814i	$-0.697934\pi$
$827$	−33.5039	−1.16505	−0.582523	+	0.812814i	$0.697934\pi$
$828$	3.00984	0.104599
$829$	−23.7184	−0.823774	−0.411887	−	0.911235i	$-0.635130\pi$
$829$	−23.7184	−0.823774	−0.411887	+	0.911235i	$0.635130\pi$
$830$	38.7107	1.34367
$831$	−4.32618	−0.150074
$832$	−1.62901	−0.0564756
$833$	−13.9208	−0.482328
$834$	−29.4595	−1.02010
$835$	−17.0744	−0.590883
$836$	−1.98466	−0.0686409
$837$	33.5070	1.15817
$838$	−5.07760	−0.175403
$839$	29.7033	1.02547	0.512735	−	0.858547i	$-0.328632\pi$
$839$	29.7033	1.02547	0.512735	+	0.858547i	$0.328632\pi$
$840$	6.40134	0.220867
$841$	41.8429	1.44286
$842$	−19.5215	−0.672755
$843$	−0.567324	−0.0195397
$844$	9.82806	0.338296
$845$	38.7715	1.33378
$846$	4.45713	0.153239
$847$	8.63099	0.296564
$848$	−3.34712	−0.114941
$849$	−17.7499	−0.609174
$850$	20.0811	0.688775
$851$	8.93161	0.306172
$852$	−18.9600	−0.649559
$853$	21.8258	0.747302	0.373651	−	0.927569i	$-0.378106\pi$
$853$	21.8258	0.747302	0.373651	+	0.927569i	$0.378106\pi$
$854$	4.72874	0.161814
$855$	7.73263	0.264450
$856$	0.0658625	0.00225113
$857$	47.0091	1.60580	0.802900	−	0.596113i	$-0.203289\pi$
$857$	47.0091	1.60580	0.802900	+	0.596113i	$0.203289\pi$
$858$	−3.09921	−0.105805
$859$	27.9568	0.953874	0.476937	−	0.878937i	$-0.341747\pi$
$859$	27.9568	0.953874	0.476937	+	0.878937i	$0.341747\pi$
$860$	−27.2414	−0.928925
$861$	6.43429	0.219280
$862$	−2.37031	−0.0807332
$863$	−11.8938	−0.404870	−0.202435	−	0.979296i	$-0.564886\pi$
$863$	−11.8938	−0.404870	−0.202435	+	0.979296i	$0.564886\pi$
$864$	−4.01460	−0.136580
$865$	−12.3711	−0.420630
$866$	−7.53292	−0.255979
$867$	−24.1077	−0.818740
$868$	7.13737	0.242258
$869$	−5.98597	−0.203060
$870$	−63.0048	−2.13606
$871$	6.52982	0.221255
$872$	7.97843	0.270184
$873$	−18.5058	−0.626328
$874$	−6.33369	−0.214240
$875$	12.9553	0.437968
$876$	−3.12359	−0.105536
$877$	−54.1842	−1.82967	−0.914835	−	0.403829i	$-0.867679\pi$
$877$	−54.1842	−1.82967	−0.914835	+	0.403829i	$0.867679\pi$
$878$	17.2204	0.581162
$879$	9.69770	0.327095
$880$	−3.56907	−0.120313
$881$	−30.9849	−1.04391	−0.521954	−	0.852974i	$-0.674797\pi$
$881$	−30.9849	−1.04391	−0.521954	+	0.852974i	$0.674797\pi$
$882$	−6.20757	−0.209020
$883$	−3.81921	−0.128527	−0.0642633	−	0.997933i	$-0.520470\pi$
$883$	−3.81921	−0.128527	−0.0642633	+	0.997933i	$0.520470\pi$
$884$	−3.61751	−0.121670
$885$	67.3110	2.26263
$886$	2.43818	0.0819123
$887$	21.8025	0.732056	0.366028	−	0.930604i	$-0.380717\pi$
$887$	21.8025	0.732056	0.366028	+	0.930604i	$0.380717\pi$
$888$	5.86989	0.196981
$889$	8.25831	0.276975
$890$	44.4924	1.49139
$891$	−10.4672	−0.350666
$892$	21.5589	0.721845
$893$	−9.37927	−0.313865
$894$	−7.58567	−0.253703
$895$	−9.96548	−0.333109
$896$	−0.855155	−0.0285687
$897$	−9.89059	−0.330237
$898$	−17.6910	−0.590357
$899$	−70.2492	−2.34294
$900$	8.95454	0.298485
$901$	−7.43289	−0.247626
$902$	−3.58744	−0.119449
$903$	−12.4179	−0.413243
$904$	−1.70168	−0.0565971
$905$	10.5327	0.350120
$906$	32.9141	1.09350
$907$	42.8898	1.42413	0.712066	−	0.702113i	$-0.247760\pi$
$907$	42.8898	1.42413	0.712066	+	0.702113i	$0.247760\pi$
$908$	−0.870905	−0.0289020
$909$	−8.34270	−0.276710
$910$	−5.22028	−0.173051
$911$	−17.6105	−0.583461	−0.291730	−	0.956501i	$-0.594231\pi$
$911$	−17.6105	−0.583461	−0.291730	+	0.956501i	$0.594231\pi$
$912$	−4.16253	−0.137835
$913$	−9.83861	−0.325611
$914$	−3.87771	−0.128263
$915$	41.3929	1.36841
$916$	−10.5632	−0.349019
$917$	8.20305	0.270889
$918$	−8.91516	−0.294244
$919$	10.5735	0.348787	0.174393	−	0.984676i	$-0.444204\pi$
$919$	10.5735	0.348787	0.174393	+	0.984676i	$0.444204\pi$
$920$	−11.3900	−0.375518
$921$	−21.1984	−0.698511
$922$	21.5989	0.711322
$923$	15.4618	0.508932
$924$	−1.62695	−0.0535227
$925$	26.5724	0.873694
$926$	−30.8470	−1.01370
$927$	5.54291	0.182053
$928$	8.41682	0.276296
$929$	7.63297	0.250430	0.125215	−	0.992130i	$-0.460038\pi$
$929$	7.63297	0.250430	0.125215	+	0.992130i	$0.460038\pi$
$930$	62.4768	2.04870
$931$	13.0628	0.428115
$932$	18.6915	0.612260
$933$	−3.71593	−0.121654
$934$	19.4628	0.636843
$935$	−7.92577	−0.259200
$936$	−1.61312	−0.0527264
$937$	44.6700	1.45931	0.729653	−	0.683818i	$-0.239682\pi$
$937$	44.6700	1.45931	0.729653	+	0.683818i	$0.239682\pi$
$938$	3.42786	0.111924
$939$	21.9031	0.714782
$940$	−16.8670	−0.550140
$941$	−42.9092	−1.39880	−0.699400	−	0.714730i	$-0.746549\pi$
$941$	−42.9092	−1.39880	−0.699400	+	0.714730i	$0.746549\pi$
$942$	1.82104	0.0593327
$943$	−11.4487	−0.372820
$944$	−8.99208	−0.292667
$945$	−12.8651	−0.418502
$946$	6.92361	0.225106
$947$	−34.6156	−1.12485	−0.562427	−	0.826847i	$-0.690132\pi$
$947$	−34.6156	−1.12485	−0.562427	+	0.826847i	$0.690132\pi$
$948$	−12.5547	−0.407757
$949$	2.54728	0.0826882
$950$	−18.8433	−0.611358
$951$	59.2163	1.92022
$952$	−1.89903	−0.0615479
$953$	8.28957	0.268526	0.134263	−	0.990946i	$-0.457133\pi$
$953$	8.28957	0.268526	0.134263	+	0.990946i	$0.457133\pi$
$954$	−3.31447	−0.107310
$955$	−2.62000	−0.0847813
$956$	−4.43448	−0.143421
$957$	16.0132	0.517632
$958$	−32.6779	−1.05577
$959$	17.8444	0.576227
$960$	−7.48559	−0.241596
$961$	38.6604	1.24711
$962$	−4.78689	−0.154335
$963$	0.0652202	0.00210169
$964$	18.5595	0.597760
$965$	−35.3663	−1.13848
$966$	−5.19211	−0.167054
$967$	23.2240	0.746832	0.373416	−	0.927664i	$-0.378186\pi$
$967$	23.2240	0.746832	0.373416	+	0.927664i	$0.378186\pi$
$968$	−10.0929	−0.324398
$969$	−9.24366	−0.296949
$970$	70.0311	2.24856
$971$	3.69073	0.118441	0.0592207	−	0.998245i	$-0.481138\pi$
$971$	3.69073	0.118441	0.0592207	+	0.998245i	$0.481138\pi$
$972$	−9.90968	−0.317853
$973$	12.6116	0.404310
$974$	24.8078	0.794894
$975$	−29.4254	−0.942368
$976$	−5.52968	−0.177001
$977$	43.6774	1.39737	0.698683	−	0.715432i	$-0.253770\pi$
$977$	43.6774	1.39737	0.698683	+	0.715432i	$0.253770\pi$
$978$	21.9172	0.700836
$979$	−11.3081	−0.361407
$980$	23.4911	0.750397
$981$	7.90061	0.252247
$982$	−28.4052	−0.906446
$983$	−11.3963	−0.363486	−0.181743	−	0.983346i	$-0.558174\pi$
$983$	−11.3963	−0.363486	−0.181743	+	0.983346i	$0.558174\pi$
$984$	−7.52412	−0.239860
$985$	−58.0074	−1.84827
$986$	18.6911	0.595246
$987$	−7.68876	−0.244736
$988$	3.39454	0.107995
$989$	22.0955	0.702595
$990$	−3.53426	−0.112326
$991$	−14.2631	−0.453083	−0.226542	−	0.974001i	$-0.572742\pi$
$991$	−14.2631	−0.453083	−0.226542	+	0.974001i	$0.572742\pi$
$992$	−8.34628	−0.264995
$993$	−12.0004	−0.380820
$994$	8.11677	0.257448
$995$	13.4291	0.425732
$996$	−20.6350	−0.653846
$997$	51.2456	1.62296	0.811482	−	0.584377i	$-0.198661\pi$
$997$	51.2456	1.62296	0.811482	+	0.584377i	$0.198661\pi$
$998$	−33.9156	−1.07358
$999$	−11.7970	−0.373242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.59	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.59	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.99756 q^{3} +1.00000 q^{4} -3.74736 q^{5} +1.99756 q^{6} -0.855155 q^{7} +1.00000 q^{8} +0.990247 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.99756 q^{3} +1.00000 q^{4} -3.74736 q^{5} +1.99756 q^{6} -0.855155 q^{7} +1.00000 q^{8} +0.990247 q^{9} -3.74736 q^{10} +0.952421 q^{11} +1.99756 q^{12} -1.62901 q^{13} -0.855155 q^{14} -7.48559 q^{15} +1.00000 q^{16} +2.22068 q^{17} +0.990247 q^{18} -2.08381 q^{19} -3.74736 q^{20} -1.70822 q^{21} +0.952421 q^{22} +3.03948 q^{23} +1.99756 q^{24} +9.04274 q^{25} -1.62901 q^{26} -4.01460 q^{27} -0.855155 q^{28} +8.41682 q^{29} -7.48559 q^{30} -8.34628 q^{31} +1.00000 q^{32} +1.90252 q^{33} +2.22068 q^{34} +3.20458 q^{35} +0.990247 q^{36} +2.93853 q^{37} -2.08381 q^{38} -3.25404 q^{39} -3.74736 q^{40} -3.76666 q^{41} -1.70822 q^{42} +7.26949 q^{43} +0.952421 q^{44} -3.71082 q^{45} +3.03948 q^{46} +4.50102 q^{47} +1.99756 q^{48} -6.26871 q^{49} +9.04274 q^{50} +4.43595 q^{51} -1.62901 q^{52} -3.34712 q^{53} -4.01460 q^{54} -3.56907 q^{55} -0.855155 q^{56} -4.16253 q^{57} +8.41682 q^{58} -8.99208 q^{59} -7.48559 q^{60} -5.52968 q^{61} -8.34628 q^{62} -0.846815 q^{63} +1.00000 q^{64} +6.10448 q^{65} +1.90252 q^{66} -4.00847 q^{67} +2.22068 q^{68} +6.07154 q^{69} +3.20458 q^{70} -9.49157 q^{71} +0.990247 q^{72} -1.56370 q^{73} +2.93853 q^{74} +18.0634 q^{75} -2.08381 q^{76} -0.814468 q^{77} -3.25404 q^{78} -6.28501 q^{79} -3.74736 q^{80} -10.9902 q^{81} -3.76666 q^{82} -10.3301 q^{83} -1.70822 q^{84} -8.32171 q^{85} +7.26949 q^{86} +16.8131 q^{87} +0.952421 q^{88} -11.8730 q^{89} -3.71082 q^{90} +1.39305 q^{91} +3.03948 q^{92} -16.6722 q^{93} +4.50102 q^{94} +7.80879 q^{95} +1.99756 q^{96} -18.6881 q^{97} -6.26871 q^{98} +0.943132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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