LMFDB - Embedded newform 6038.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.07733 q^{3} +1.00000 q^{4} +0.607795 q^{5} -3.07733 q^{6} +4.61887 q^{7} +1.00000 q^{8} +6.46998 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.07733 q^{3} +1.00000 q^{4} +0.607795 q^{5} -3.07733 q^{6} +4.61887 q^{7} +1.00000 q^{8} +6.46998 q^{9} +0.607795 q^{10} -5.95001 q^{11} -3.07733 q^{12} -0.724531 q^{13} +4.61887 q^{14} -1.87039 q^{15} +1.00000 q^{16} -4.89639 q^{17} +6.46998 q^{18} -1.61953 q^{19} +0.607795 q^{20} -14.2138 q^{21} -5.95001 q^{22} -5.60057 q^{23} -3.07733 q^{24} -4.63058 q^{25} -0.724531 q^{26} -10.6783 q^{27} +4.61887 q^{28} +6.26111 q^{29} -1.87039 q^{30} +9.23385 q^{31} +1.00000 q^{32} +18.3102 q^{33} -4.89639 q^{34} +2.80733 q^{35} +6.46998 q^{36} +8.78276 q^{37} -1.61953 q^{38} +2.22962 q^{39} +0.607795 q^{40} -4.74524 q^{41} -14.2138 q^{42} +4.45923 q^{43} -5.95001 q^{44} +3.93243 q^{45} -5.60057 q^{46} +8.78460 q^{47} -3.07733 q^{48} +14.3340 q^{49} -4.63058 q^{50} +15.0678 q^{51} -0.724531 q^{52} -7.84105 q^{53} -10.6783 q^{54} -3.61639 q^{55} +4.61887 q^{56} +4.98383 q^{57} +6.26111 q^{58} +14.0946 q^{59} -1.87039 q^{60} -11.1513 q^{61} +9.23385 q^{62} +29.8840 q^{63} +1.00000 q^{64} -0.440366 q^{65} +18.3102 q^{66} +4.40364 q^{67} -4.89639 q^{68} +17.2348 q^{69} +2.80733 q^{70} -1.76898 q^{71} +6.46998 q^{72} -2.71781 q^{73} +8.78276 q^{74} +14.2499 q^{75} -1.61953 q^{76} -27.4823 q^{77} +2.22962 q^{78} +0.808488 q^{79} +0.607795 q^{80} +13.4507 q^{81} -4.74524 q^{82} -1.67688 q^{83} -14.2138 q^{84} -2.97600 q^{85} +4.45923 q^{86} -19.2675 q^{87} -5.95001 q^{88} +3.61976 q^{89} +3.93243 q^{90} -3.34651 q^{91} -5.60057 q^{92} -28.4156 q^{93} +8.78460 q^{94} -0.984342 q^{95} -3.07733 q^{96} +15.6087 q^{97} +14.3340 q^{98} -38.4964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * 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
$3$	−3.07733	−1.77670	−0.888350	−	0.459168i	$-0.848148\pi$
$3$	−3.07733	−1.77670	−0.888350	+	0.459168i	$0.848148\pi$
$4$	1.00000	0.500000
$5$	0.607795	0.271814	0.135907	−	0.990722i	$-0.456605\pi$
$5$	0.607795	0.271814	0.135907	+	0.990722i	$0.456605\pi$
$6$	−3.07733	−1.25632
$7$	4.61887	1.74577	0.872885	−	0.487927i	$-0.162247\pi$
$7$	4.61887	1.74577	0.872885	+	0.487927i	$0.162247\pi$
$8$	1.00000	0.353553
$9$	6.46998	2.15666
$10$	0.607795	0.192202
$11$	−5.95001	−1.79399	−0.896997	−	0.442036i	$-0.854256\pi$
$11$	−5.95001	−1.79399	−0.896997	+	0.442036i	$0.854256\pi$
$12$	−3.07733	−0.888350
$13$	−0.724531	−0.200949	−0.100474	−	0.994940i	$-0.532036\pi$
$13$	−0.724531	−0.200949	−0.100474	+	0.994940i	$0.532036\pi$
$14$	4.61887	1.23445
$15$	−1.87039	−0.482932
$16$	1.00000	0.250000
$17$	−4.89639	−1.18755	−0.593774	−	0.804632i	$-0.702363\pi$
$17$	−4.89639	−1.18755	−0.593774	+	0.804632i	$0.702363\pi$
$18$	6.46998	1.52499
$19$	−1.61953	−0.371545	−0.185773	−	0.982593i	$-0.559479\pi$
$19$	−1.61953	−0.371545	−0.185773	+	0.982593i	$0.559479\pi$
$20$	0.607795	0.135907
$21$	−14.2138	−3.10171
$22$	−5.95001	−1.26855
$23$	−5.60057	−1.16780	−0.583900	−	0.811826i	$-0.698474\pi$
$23$	−5.60057	−1.16780	−0.583900	+	0.811826i	$0.698474\pi$
$24$	−3.07733	−0.628158
$25$	−4.63058	−0.926117
$26$	−0.724531	−0.142092
$27$	−10.6783	−2.05504
$28$	4.61887	0.872885
$29$	6.26111	1.16266	0.581330	−	0.813668i	$-0.302533\pi$
$29$	6.26111	1.16266	0.581330	+	0.813668i	$0.302533\pi$
$30$	−1.87039	−0.341485
$31$	9.23385	1.65845	0.829224	−	0.558917i	$-0.188783\pi$
$31$	9.23385	1.65845	0.829224	+	0.558917i	$0.188783\pi$
$32$	1.00000	0.176777
$33$	18.3102	3.18739
$34$	−4.89639	−0.839724
$35$	2.80733	0.474525
$36$	6.46998	1.07833
$37$	8.78276	1.44388	0.721939	−	0.691957i	$-0.243251\pi$
$37$	8.78276	1.44388	0.721939	+	0.691957i	$0.243251\pi$
$38$	−1.61953	−0.262722
$39$	2.22962	0.357025
$40$	0.607795	0.0961009
$41$	−4.74524	−0.741082	−0.370541	−	0.928816i	$-0.620828\pi$
$41$	−4.74524	−0.741082	−0.370541	+	0.928816i	$0.620828\pi$
$42$	−14.2138	−2.19324
$43$	4.45923	0.680026	0.340013	−	0.940421i	$-0.389569\pi$
$43$	4.45923	0.680026	0.340013	+	0.940421i	$0.389569\pi$
$44$	−5.95001	−0.896997
$45$	3.93243	0.586211
$46$	−5.60057	−0.825759
$47$	8.78460	1.28137	0.640683	−	0.767806i	$-0.278651\pi$
$47$	8.78460	1.28137	0.640683	+	0.767806i	$0.278651\pi$
$48$	−3.07733	−0.444175
$49$	14.3340	2.04771
$50$	−4.63058	−0.654864
$51$	15.0678	2.10992
$52$	−0.724531	−0.100474
$53$	−7.84105	−1.07705	−0.538525	−	0.842609i	$-0.681018\pi$
$53$	−7.84105	−1.07705	−0.538525	+	0.842609i	$0.681018\pi$
$54$	−10.6783	−1.45313
$55$	−3.61639	−0.487634
$56$	4.61887	0.617223
$57$	4.98383	0.660124
$58$	6.26111	0.822124
$59$	14.0946	1.83496	0.917478	−	0.397786i	$-0.130221\pi$
$59$	14.0946	1.83496	0.917478	+	0.397786i	$0.130221\pi$
$60$	−1.87039	−0.241466
$61$	−11.1513	−1.42777	−0.713887	−	0.700260i	$-0.753067\pi$
$61$	−11.1513	−1.42777	−0.713887	+	0.700260i	$0.753067\pi$
$62$	9.23385	1.17270
$63$	29.8840	3.76503
$64$	1.00000	0.125000
$65$	−0.440366	−0.0546207
$66$	18.3102	2.25382
$67$	4.40364	0.537990	0.268995	−	0.963142i	$-0.413308\pi$
$67$	4.40364	0.537990	0.268995	+	0.963142i	$0.413308\pi$
$68$	−4.89639	−0.593774
$69$	17.2348	2.07483
$70$	2.80733	0.335540
$71$	−1.76898	−0.209940	−0.104970	−	0.994475i	$-0.533475\pi$
$71$	−1.76898	−0.209940	−0.104970	+	0.994475i	$0.533475\pi$
$72$	6.46998	0.762495
$73$	−2.71781	−0.318095	−0.159048	−	0.987271i	$-0.550842\pi$
$73$	−2.71781	−0.318095	−0.159048	+	0.987271i	$0.550842\pi$
$74$	8.78276	1.02098
$75$	14.2499	1.64543
$76$	−1.61953	−0.185773
$77$	−27.4823	−3.13190
$78$	2.22962	0.252455
$79$	0.808488	0.0909620	0.0454810	−	0.998965i	$-0.485518\pi$
$79$	0.808488	0.0909620	0.0454810	+	0.998965i	$0.485518\pi$
$80$	0.607795	0.0679536
$81$	13.4507	1.49452
$82$	−4.74524	−0.524024
$83$	−1.67688	−0.184062	−0.0920308	−	0.995756i	$-0.529336\pi$
$83$	−1.67688	−0.184062	−0.0920308	+	0.995756i	$0.529336\pi$
$84$	−14.2138	−1.55085
$85$	−2.97600	−0.322793
$86$	4.45923	0.480851
$87$	−19.2675	−2.06570
$88$	−5.95001	−0.634273
$89$	3.61976	0.383694	0.191847	−	0.981425i	$-0.438552\pi$
$89$	3.61976	0.383694	0.191847	+	0.981425i	$0.438552\pi$
$90$	3.93243	0.414514
$91$	−3.34651	−0.350810
$92$	−5.60057	−0.583900
$93$	−28.4156	−2.94656
$94$	8.78460	0.906062
$95$	−0.984342	−0.100991
$96$	−3.07733	−0.314079
$97$	15.6087	1.58482	0.792410	−	0.609988i	$-0.208826\pi$
$97$	15.6087	1.58482	0.792410	+	0.609988i	$0.208826\pi$
$98$	14.3340	1.44795
$99$	−38.4964	−3.86904
$100$	−4.63058	−0.463058
$101$	−18.1126	−1.80227	−0.901137	−	0.433535i	$-0.857266\pi$
$101$	−18.1126	−1.80227	−0.901137	+	0.433535i	$0.857266\pi$
$102$	15.0678	1.49194
$103$	12.8267	1.26385	0.631927	−	0.775028i	$-0.282264\pi$
$103$	12.8267	1.26385	0.631927	+	0.775028i	$0.282264\pi$
$104$	−0.724531	−0.0710461
$105$	−8.63909	−0.843088
$106$	−7.84105	−0.761590
$107$	−0.724267	−0.0700175	−0.0350087	−	0.999387i	$-0.511146\pi$
$107$	−0.724267	−0.0700175	−0.0350087	+	0.999387i	$0.511146\pi$
$108$	−10.6783	−1.02752
$109$	−2.08320	−0.199534	−0.0997671	−	0.995011i	$-0.531810\pi$
$109$	−2.08320	−0.199534	−0.0997671	+	0.995011i	$0.531810\pi$
$110$	−3.61639	−0.344809
$111$	−27.0275	−2.56534
$112$	4.61887	0.436442
$113$	13.7744	1.29578	0.647892	−	0.761732i	$-0.275651\pi$
$113$	13.7744	1.29578	0.647892	+	0.761732i	$0.275651\pi$
$114$	4.98383	0.466778
$115$	−3.40400	−0.317425
$116$	6.26111	0.581330
$117$	−4.68770	−0.433378
$118$	14.0946	1.29751
$119$	−22.6158	−2.07319
$120$	−1.87039	−0.170742
$121$	24.4026	2.21842
$122$	−11.1513	−1.00959
$123$	14.6027	1.31668
$124$	9.23385	0.829224
$125$	−5.85343	−0.523546
$126$	29.8840	2.66228
$127$	−3.74137	−0.331993	−0.165997	−	0.986126i	$-0.553084\pi$
$127$	−3.74137	−0.331993	−0.165997	+	0.986126i	$0.553084\pi$
$128$	1.00000	0.0883883
$129$	−13.7225	−1.20820
$130$	−0.440366	−0.0386227
$131$	22.7407	1.98686	0.993432	−	0.114421i	$-0.0365013\pi$
$131$	22.7407	1.98686	0.993432	+	0.114421i	$0.0365013\pi$
$132$	18.3102	1.59369
$133$	−7.48039	−0.648632
$134$	4.40364	0.380417
$135$	−6.49022	−0.558589
$136$	−4.89639	−0.419862
$137$	14.3624	1.22706	0.613531	−	0.789671i	$-0.289749\pi$
$137$	14.3624	1.22706	0.613531	+	0.789671i	$0.289749\pi$
$138$	17.2348	1.46713
$139$	9.83272	0.834001	0.417000	−	0.908906i	$-0.363081\pi$
$139$	9.83272	0.834001	0.417000	+	0.908906i	$0.363081\pi$
$140$	2.80733	0.237263
$141$	−27.0331	−2.27660
$142$	−1.76898	−0.148450
$143$	4.31096	0.360501
$144$	6.46998	0.539165
$145$	3.80548	0.316028
$146$	−2.71781	−0.224927
$147$	−44.1104	−3.63816
$148$	8.78276	0.721939
$149$	13.8883	1.13777	0.568885	−	0.822417i	$-0.307375\pi$
$149$	13.8883	1.13777	0.568885	+	0.822417i	$0.307375\pi$
$150$	14.2499	1.16350
$151$	5.73315	0.466557	0.233279	−	0.972410i	$-0.425055\pi$
$151$	5.73315	0.466557	0.233279	+	0.972410i	$0.425055\pi$
$152$	−1.61953	−0.131361
$153$	−31.6795	−2.56114
$154$	−27.4823	−2.21459
$155$	5.61229	0.450790
$156$	2.22962	0.178513
$157$	−11.5209	−0.919466	−0.459733	−	0.888057i	$-0.652055\pi$
$157$	−11.5209	−0.919466	−0.459733	+	0.888057i	$0.652055\pi$
$158$	0.808488	0.0643199
$159$	24.1295	1.91360
$160$	0.607795	0.0480504
$161$	−25.8683	−2.03871
$162$	13.4507	1.05679
$163$	−12.8096	−1.00333	−0.501664	−	0.865063i	$-0.667279\pi$
$163$	−12.8096	−1.00333	−0.501664	+	0.865063i	$0.667279\pi$
$164$	−4.74524	−0.370541
$165$	11.1288	0.866378
$166$	−1.67688	−0.130151
$167$	9.86074	0.763047	0.381524	−	0.924359i	$-0.375400\pi$
$167$	9.86074	0.763047	0.381524	+	0.924359i	$0.375400\pi$
$168$	−14.2138	−1.09662
$169$	−12.4751	−0.959620
$170$	−2.97600	−0.228249
$171$	−10.4783	−0.801297
$172$	4.45923	0.340013
$173$	0.304267	0.0231330	0.0115665	−	0.999933i	$-0.496318\pi$
$173$	0.304267	0.0231330	0.0115665	+	0.999933i	$0.496318\pi$
$174$	−19.2675	−1.46067
$175$	−21.3881	−1.61679
$176$	−5.95001	−0.448499
$177$	−43.3737	−3.26017
$178$	3.61976	0.271312
$179$	−20.4850	−1.53112	−0.765559	−	0.643366i	$-0.777537\pi$
$179$	−20.4850	−1.53112	−0.765559	+	0.643366i	$0.777537\pi$
$180$	3.93243	0.293106
$181$	13.5044	1.00378	0.501888	−	0.864933i	$-0.332639\pi$
$181$	13.5044	1.00378	0.501888	+	0.864933i	$0.332639\pi$
$182$	−3.34651	−0.248060
$183$	34.3162	2.53673
$184$	−5.60057	−0.412879
$185$	5.33812	0.392467
$186$	−28.4156	−2.08353
$187$	29.1336	2.13046
$188$	8.78460	0.640683
$189$	−49.3217	−3.58762
$190$	−0.984342	−0.0714117
$191$	4.55794	0.329801	0.164900	−	0.986310i	$-0.447270\pi$
$191$	4.55794	0.329801	0.164900	+	0.986310i	$0.447270\pi$
$192$	−3.07733	−0.222087
$193$	21.4931	1.54711	0.773554	−	0.633731i	$-0.218477\pi$
$193$	21.4931	1.54711	0.773554	+	0.633731i	$0.218477\pi$
$194$	15.6087	1.12064
$195$	1.35515	0.0970446
$196$	14.3340	1.02385
$197$	−26.3250	−1.87558	−0.937789	−	0.347204i	$-0.887131\pi$
$197$	−26.3250	−1.87558	−0.937789	+	0.347204i	$0.887131\pi$
$198$	−38.4964	−2.73582
$199$	−13.0343	−0.923978	−0.461989	−	0.886886i	$-0.652864\pi$
$199$	−13.0343	−0.923978	−0.461989	+	0.886886i	$0.652864\pi$
$200$	−4.63058	−0.327432
$201$	−13.5515	−0.955847
$202$	−18.1126	−1.27440
$203$	28.9193	2.02973
$204$	15.0678	1.05496
$205$	−2.88413	−0.201437
$206$	12.8267	0.893680
$207$	−36.2356	−2.51855
$208$	−0.724531	−0.0502372
$209$	9.63621	0.666550
$210$	−8.63909	−0.596154
$211$	25.9048	1.78336	0.891679	−	0.452668i	$-0.149528\pi$
$211$	25.9048	1.78336	0.891679	+	0.452668i	$0.149528\pi$
$212$	−7.84105	−0.538525
$213$	5.44375	0.372999
$214$	−0.724267	−0.0495098
$215$	2.71030	0.184841
$216$	−10.6783	−0.726566
$217$	42.6499	2.89527
$218$	−2.08320	−0.141092
$219$	8.36360	0.565160
$220$	−3.61639	−0.243817
$221$	3.54758	0.238636
$222$	−27.0275	−1.81397
$223$	22.0545	1.47688	0.738438	−	0.674321i	$-0.235564\pi$
$223$	22.0545	1.47688	0.738438	+	0.674321i	$0.235564\pi$
$224$	4.61887	0.308611
$225$	−29.9598	−1.99732
$226$	13.7744	0.916257
$227$	22.8959	1.51965	0.759826	−	0.650126i	$-0.225284\pi$
$227$	22.8959	1.51965	0.759826	+	0.650126i	$0.225284\pi$
$228$	4.98383	0.330062
$229$	2.85120	0.188412	0.0942062	−	0.995553i	$-0.469969\pi$
$229$	2.85120	0.188412	0.0942062	+	0.995553i	$0.469969\pi$
$230$	−3.40400	−0.224453
$231$	84.5723	5.56445
$232$	6.26111	0.411062
$233$	−3.17403	−0.207938	−0.103969	−	0.994581i	$-0.533154\pi$
$233$	−3.17403	−0.207938	−0.103969	+	0.994581i	$0.533154\pi$
$234$	−4.68770	−0.306445
$235$	5.33924	0.348294
$236$	14.0946	0.917478
$237$	−2.48799	−0.161612
$238$	−22.6158	−1.46596
$239$	−4.92726	−0.318718	−0.159359	−	0.987221i	$-0.550943\pi$
$239$	−4.92726	−0.318718	−0.159359	+	0.987221i	$0.550943\pi$
$240$	−1.87039	−0.120733
$241$	6.42032	0.413569	0.206784	−	0.978387i	$-0.433700\pi$
$241$	6.42032	0.413569	0.206784	+	0.978387i	$0.433700\pi$
$242$	24.4026	1.56866
$243$	−9.35748	−0.600283
$244$	−11.1513	−0.713887
$245$	8.71212	0.556597
$246$	14.6027	0.931033
$247$	1.17340	0.0746615
$248$	9.23385	0.586350
$249$	5.16032	0.327022
$250$	−5.85343	−0.370203
$251$	−15.1862	−0.958545	−0.479273	−	0.877666i	$-0.659099\pi$
$251$	−15.1862	−0.958545	−0.479273	+	0.877666i	$0.659099\pi$
$252$	29.8840	1.88252
$253$	33.3234	2.09503
$254$	−3.74137	−0.234755
$255$	9.15815	0.573506
$256$	1.00000	0.0625000
$257$	−2.33311	−0.145535	−0.0727677	−	0.997349i	$-0.523183\pi$
$257$	−2.33311	−0.145535	−0.0727677	+	0.997349i	$0.523183\pi$
$258$	−13.7225	−0.854328
$259$	40.5664	2.52068
$260$	−0.440366	−0.0273104
$261$	40.5093	2.50746
$262$	22.7407	1.40493
$263$	26.4603	1.63161	0.815805	−	0.578327i	$-0.196294\pi$
$263$	26.4603	1.63161	0.815805	+	0.578327i	$0.196294\pi$
$264$	18.3102	1.12691
$265$	−4.76575	−0.292758
$266$	−7.48039	−0.458652
$267$	−11.1392	−0.681708
$268$	4.40364	0.268995
$269$	−16.6331	−1.01414	−0.507070	−	0.861905i	$-0.669271\pi$
$269$	−16.6331	−1.01414	−0.507070	+	0.861905i	$0.669271\pi$
$270$	−6.49022	−0.394982
$271$	3.20661	0.194788	0.0973939	−	0.995246i	$-0.468949\pi$
$271$	3.20661	0.194788	0.0973939	+	0.995246i	$0.468949\pi$
$272$	−4.89639	−0.296887
$273$	10.2983	0.623284
$274$	14.3624	0.867664
$275$	27.5520	1.66145
$276$	17.2348	1.03741
$277$	−23.8754	−1.43453	−0.717266	−	0.696799i	$-0.754607\pi$
$277$	−23.8754	−1.43453	−0.717266	+	0.696799i	$0.754607\pi$
$278$	9.83272	0.589728
$279$	59.7428	3.57671
$280$	2.80733	0.167770
$281$	17.1916	1.02557	0.512784	−	0.858518i	$-0.328614\pi$
$281$	17.1916	1.02557	0.512784	+	0.858518i	$0.328614\pi$
$282$	−27.0331	−1.60980
$283$	−17.9207	−1.06527	−0.532637	−	0.846344i	$-0.678799\pi$
$283$	−17.9207	−1.06527	−0.532637	+	0.846344i	$0.678799\pi$
$284$	−1.76898	−0.104970
$285$	3.02915	0.179431
$286$	4.31096	0.254913
$287$	−21.9176	−1.29376
$288$	6.46998	0.381247
$289$	6.97462	0.410272
$290$	3.80548	0.223465
$291$	−48.0331	−2.81575
$292$	−2.71781	−0.159048
$293$	−18.3658	−1.07294	−0.536470	−	0.843920i	$-0.680242\pi$
$293$	−18.3658	−1.07294	−0.536470	+	0.843920i	$0.680242\pi$
$294$	−44.1104	−2.57257
$295$	8.56661	0.498768
$296$	8.78276	0.510488
$297$	63.5359	3.68673
$298$	13.8883	0.804525
$299$	4.05778	0.234668
$300$	14.2499	0.822716
$301$	20.5966	1.18717
$302$	5.73315	0.329906
$303$	55.7386	3.20210
$304$	−1.61953	−0.0928863
$305$	−6.77770	−0.388090
$306$	−31.6795	−1.81100
$307$	−0.0763418	−0.00435706	−0.00217853	−	0.999998i	$-0.500693\pi$
$307$	−0.0763418	−0.00435706	−0.00217853	+	0.999998i	$0.500693\pi$
$308$	−27.4823	−1.56595
$309$	−39.4721	−2.24549
$310$	5.61229	0.318757
$311$	8.41472	0.477155	0.238577	−	0.971123i	$-0.423319\pi$
$311$	8.41472	0.477155	0.238577	+	0.971123i	$0.423319\pi$
$312$	2.22962	0.126228
$313$	29.1320	1.64664	0.823319	−	0.567578i	$-0.192120\pi$
$313$	29.1320	1.64664	0.823319	+	0.567578i	$0.192120\pi$
$314$	−11.5209	−0.650161
$315$	18.1634	1.02339
$316$	0.808488	0.0454810
$317$	9.37439	0.526518	0.263259	−	0.964725i	$-0.415203\pi$
$317$	9.37439	0.526518	0.263259	+	0.964725i	$0.415203\pi$
$318$	24.1295	1.35312
$319$	−37.2537	−2.08581
$320$	0.607795	0.0339768
$321$	2.22881	0.124400
$322$	−25.8683	−1.44158
$323$	7.92984	0.441228
$324$	13.4507	0.747262
$325$	3.35500	0.186102
$326$	−12.8096	−0.709460
$327$	6.41069	0.354512
$328$	−4.74524	−0.262012
$329$	40.5749	2.23697
$330$	11.1288	0.612622
$331$	2.35558	0.129474	0.0647372	−	0.997902i	$-0.479379\pi$
$331$	2.35558	0.129474	0.0647372	+	0.997902i	$0.479379\pi$
$332$	−1.67688	−0.0920308
$333$	56.8243	3.11395
$334$	9.86074	0.539556
$335$	2.67651	0.146233
$336$	−14.2138	−0.775427
$337$	−18.2646	−0.994937	−0.497468	−	0.867482i	$-0.665737\pi$
$337$	−18.2646	−0.994937	−0.497468	+	0.867482i	$0.665737\pi$
$338$	−12.4751	−0.678554
$339$	−42.3883	−2.30222
$340$	−2.97600	−0.161396
$341$	−54.9415	−2.97525
$342$	−10.4783	−0.566603
$343$	33.8746	1.82906
$344$	4.45923	0.240425
$345$	10.4752	0.563968
$346$	0.304267	0.0163575
$347$	3.71621	0.199497	0.0997484	−	0.995013i	$-0.468196\pi$
$347$	3.71621	0.199497	0.0997484	+	0.995013i	$0.468196\pi$
$348$	−19.2675	−1.03285
$349$	28.1850	1.50871	0.754355	−	0.656467i	$-0.227950\pi$
$349$	28.1850	1.50871	0.754355	+	0.656467i	$0.227950\pi$
$350$	−21.3881	−1.14324
$351$	7.73675	0.412957
$352$	−5.95001	−0.317137
$353$	−4.93999	−0.262929	−0.131465	−	0.991321i	$-0.541968\pi$
$353$	−4.93999	−0.262929	−0.131465	+	0.991321i	$0.541968\pi$
$354$	−43.3737	−2.30529
$355$	−1.07518	−0.0570646
$356$	3.61976	0.191847
$357$	69.5963	3.68343
$358$	−20.4850	−1.08266
$359$	−3.95380	−0.208674	−0.104337	−	0.994542i	$-0.533272\pi$
$359$	−3.95380	−0.208674	−0.104337	+	0.994542i	$0.533272\pi$
$360$	3.93243	0.207257
$361$	−16.3771	−0.861954
$362$	13.5044	0.709776
$363$	−75.0949	−3.94146
$364$	−3.34651	−0.175405
$365$	−1.65187	−0.0864629
$366$	34.3162	1.79374
$367$	−5.63436	−0.294111	−0.147056	−	0.989128i	$-0.546980\pi$
$367$	−5.63436	−0.294111	−0.147056	+	0.989128i	$0.546980\pi$
$368$	−5.60057	−0.291950
$369$	−30.7016	−1.59826
$370$	5.33812	0.277516
$371$	−36.2168	−1.88028
$372$	−28.4156	−1.47328
$373$	23.4741	1.21544	0.607722	−	0.794150i	$-0.292084\pi$
$373$	23.4741	1.21544	0.607722	+	0.794150i	$0.292084\pi$
$374$	29.1336	1.50646
$375$	18.0129	0.930184
$376$	8.78460	0.453031
$377$	−4.53637	−0.233635
$378$	−49.3217	−2.53683
$379$	3.38038	0.173639	0.0868193	−	0.996224i	$-0.472330\pi$
$379$	3.38038	0.173639	0.0868193	+	0.996224i	$0.472330\pi$
$380$	−0.984342	−0.0504957
$381$	11.5135	0.589852
$382$	4.55794	0.233204
$383$	21.8127	1.11458	0.557289	−	0.830319i	$-0.311842\pi$
$383$	21.8127	1.11458	0.557289	+	0.830319i	$0.311842\pi$
$384$	−3.07733	−0.157040
$385$	−16.7036	−0.851296
$386$	21.4931	1.09397
$387$	28.8511	1.46659
$388$	15.6087	0.792410
$389$	8.87224	0.449840	0.224920	−	0.974377i	$-0.427788\pi$
$389$	8.87224	0.449840	0.224920	+	0.974377i	$0.427788\pi$
$390$	1.35515	0.0686209
$391$	27.4226	1.38682
$392$	14.3340	0.723975
$393$	−69.9807	−3.53006
$394$	−26.3250	−1.32623
$395$	0.491395	0.0247248
$396$	−38.4964	−1.93452
$397$	−10.0497	−0.504382	−0.252191	−	0.967677i	$-0.581151\pi$
$397$	−10.0497	−0.504382	−0.252191	+	0.967677i	$0.581151\pi$
$398$	−13.0343	−0.653351
$399$	23.0197	1.15242
$400$	−4.63058	−0.231529
$401$	12.6421	0.631314	0.315657	−	0.948873i	$-0.397775\pi$
$401$	12.6421	0.631314	0.315657	+	0.948873i	$0.397775\pi$
$402$	−13.5515	−0.675886
$403$	−6.69021	−0.333263
$404$	−18.1126	−0.901137
$405$	8.17529	0.406233
$406$	28.9193	1.43524
$407$	−52.2575	−2.59031
$408$	15.0678	0.745968
$409$	−11.9968	−0.593202	−0.296601	−	0.955002i	$-0.595853\pi$
$409$	−11.9968	−0.593202	−0.296601	+	0.955002i	$0.595853\pi$
$410$	−2.88413	−0.142437
$411$	−44.1979	−2.18012
$412$	12.8267	0.631927
$413$	65.1010	3.20341
$414$	−36.2356	−1.78088
$415$	−1.01920	−0.0500306
$416$	−0.724531	−0.0355230
$417$	−30.2586	−1.48177
$418$	9.63621	0.471322
$419$	−6.45613	−0.315403	−0.157701	−	0.987487i	$-0.550408\pi$
$419$	−6.45613	−0.315403	−0.157701	+	0.987487i	$0.550408\pi$
$420$	−8.63909	−0.421544
$421$	−23.5158	−1.14609	−0.573044	−	0.819524i	$-0.694238\pi$
$421$	−23.5158	−1.14609	−0.573044	+	0.819524i	$0.694238\pi$
$422$	25.9048	1.26102
$423$	56.8362	2.76347
$424$	−7.84105	−0.380795
$425$	22.6731	1.09981
$426$	5.44375	0.263750
$427$	−51.5063	−2.49257
$428$	−0.724267	−0.0350087
$429$	−13.2663	−0.640502
$430$	2.71030	0.130702
$431$	−2.91653	−0.140484	−0.0702422	−	0.997530i	$-0.522377\pi$
$431$	−2.91653	−0.140484	−0.0702422	+	0.997530i	$0.522377\pi$
$432$	−10.6783	−0.513760
$433$	12.0161	0.577459	0.288729	−	0.957411i	$-0.406767\pi$
$433$	12.0161	0.577459	0.288729	+	0.957411i	$0.406767\pi$
$434$	42.6499	2.04726
$435$	−11.7107	−0.561486
$436$	−2.08320	−0.0997671
$437$	9.07028	0.433890
$438$	8.36360	0.399628
$439$	30.1924	1.44101	0.720503	−	0.693452i	$-0.243911\pi$
$439$	30.1924	1.44101	0.720503	+	0.693452i	$0.243911\pi$
$440$	−3.61639	−0.172405
$441$	92.7405	4.41621
$442$	3.54758	0.168741
$443$	−31.2467	−1.48458	−0.742288	−	0.670080i	$-0.766260\pi$
$443$	−31.2467	−1.48458	−0.742288	+	0.670080i	$0.766260\pi$
$444$	−27.0275	−1.28267
$445$	2.20007	0.104293
$446$	22.0545	1.04431
$447$	−42.7388	−2.02148
$448$	4.61887	0.218221
$449$	−26.6338	−1.25693	−0.628464	−	0.777839i	$-0.716316\pi$
$449$	−26.6338	−1.25693	−0.628464	+	0.777839i	$0.716316\pi$
$450$	−29.9598	−1.41232
$451$	28.2342	1.32950
$452$	13.7744	0.647892
$453$	−17.6428	−0.828932
$454$	22.8959	1.07456
$455$	−2.03400	−0.0953552
$456$	4.98383	0.233389
$457$	−0.893147	−0.0417796	−0.0208898	−	0.999782i	$-0.506650\pi$
$457$	−0.893147	−0.0417796	−0.0208898	+	0.999782i	$0.506650\pi$
$458$	2.85120	0.133228
$459$	52.2851	2.44046
$460$	−3.40400	−0.158712
$461$	14.7223	0.685686	0.342843	−	0.939393i	$-0.388610\pi$
$461$	14.7223	0.685686	0.342843	+	0.939393i	$0.388610\pi$
$462$	84.5723	3.93466
$463$	−2.53655	−0.117883	−0.0589417	−	0.998261i	$-0.518773\pi$
$463$	−2.53655	−0.117883	−0.0589417	+	0.998261i	$0.518773\pi$
$464$	6.26111	0.290665
$465$	−17.2709	−0.800918
$466$	−3.17403	−0.147034
$467$	−25.2441	−1.16816	−0.584079	−	0.811697i	$-0.698544\pi$
$467$	−25.2441	−1.16816	−0.584079	+	0.811697i	$0.698544\pi$
$468$	−4.68770	−0.216689
$469$	20.3398	0.939207
$470$	5.33924	0.246281
$471$	35.4536	1.63361
$472$	14.0946	0.648755
$473$	−26.5324	−1.21996
$474$	−2.48799	−0.114277
$475$	7.49936	0.344094
$476$	−22.6158	−1.03659
$477$	−50.7314	−2.32283
$478$	−4.92726	−0.225367
$479$	−14.6026	−0.667210	−0.333605	−	0.942713i	$-0.608265\pi$
$479$	−14.6026	−0.667210	−0.333605	+	0.942713i	$0.608265\pi$
$480$	−1.87039	−0.0853712
$481$	−6.36338	−0.290145
$482$	6.42032	0.292437
$483$	79.6054	3.62217
$484$	24.4026	1.10921
$485$	9.48688	0.430777
$486$	−9.35748	−0.424464
$487$	−35.6064	−1.61348	−0.806740	−	0.590907i	$-0.798770\pi$
$487$	−35.6064	−1.61348	−0.806740	+	0.590907i	$0.798770\pi$
$488$	−11.1513	−0.504795
$489$	39.4195	1.78261
$490$	8.71212	0.393573
$491$	−1.01709	−0.0459005	−0.0229503	−	0.999737i	$-0.507306\pi$
$491$	−1.01709	−0.0459005	−0.0229503	+	0.999737i	$0.507306\pi$
$492$	14.6027	0.658340
$493$	−30.6568	−1.38071
$494$	1.17340	0.0527937
$495$	−23.3980	−1.05166
$496$	9.23385	0.414612
$497$	−8.17070	−0.366506
$498$	5.16032	0.231239
$499$	39.7362	1.77884	0.889418	−	0.457096i	$-0.151110\pi$
$499$	39.7362	1.77884	0.889418	+	0.457096i	$0.151110\pi$
$500$	−5.85343	−0.261773
$501$	−30.3448	−1.35571
$502$	−15.1862	−0.677794
$503$	18.6269	0.830534	0.415267	−	0.909700i	$-0.363688\pi$
$503$	18.6269	0.830534	0.415267	+	0.909700i	$0.363688\pi$
$504$	29.8840	1.33114
$505$	−11.0088	−0.489884
$506$	33.3234	1.48141
$507$	38.3899	1.70496
$508$	−3.74137	−0.165997
$509$	18.4677	0.818568	0.409284	−	0.912407i	$-0.365779\pi$
$509$	18.4677	0.818568	0.409284	+	0.912407i	$0.365779\pi$
$510$	9.15815	0.405530
$511$	−12.5532	−0.555321
$512$	1.00000	0.0441942
$513$	17.2938	0.763540
$514$	−2.33311	−0.102909
$515$	7.79602	0.343534
$516$	−13.7225	−0.604101
$517$	−52.2684	−2.29876
$518$	40.5664	1.78239
$519$	−0.936330	−0.0411003
$520$	−0.440366	−0.0193113
$521$	23.1816	1.01561	0.507803	−	0.861473i	$-0.330458\pi$
$521$	23.1816	1.01561	0.507803	+	0.861473i	$0.330458\pi$
$522$	40.5093	1.77304
$523$	21.1485	0.924758	0.462379	−	0.886682i	$-0.346996\pi$
$523$	21.1485	0.924758	0.462379	+	0.886682i	$0.346996\pi$
$524$	22.7407	0.993432
$525$	65.8182	2.87254
$526$	26.4603	1.15372
$527$	−45.2125	−1.96949
$528$	18.3102	0.796847
$529$	8.36638	0.363756
$530$	−4.76575	−0.207011
$531$	91.1916	3.95738
$532$	−7.48039	−0.324316
$533$	3.43807	0.148919
$534$	−11.1392	−0.482041
$535$	−0.440206	−0.0190318
$536$	4.40364	0.190208
$537$	63.0390	2.72033
$538$	−16.6331	−0.717105
$539$	−85.2872	−3.67358
$540$	−6.49022	−0.279294
$541$	−25.8072	−1.10954	−0.554769	−	0.832005i	$-0.687193\pi$
$541$	−25.8072	−1.10954	−0.554769	+	0.832005i	$0.687193\pi$
$542$	3.20661	0.137736
$543$	−41.5576	−1.78341
$544$	−4.89639	−0.209931
$545$	−1.26616	−0.0542362
$546$	10.2983	0.440728
$547$	−5.80328	−0.248130	−0.124065	−	0.992274i	$-0.539593\pi$
$547$	−5.80328	−0.248130	−0.124065	+	0.992274i	$0.539593\pi$
$548$	14.3624	0.613531
$549$	−72.1486	−3.07923
$550$	27.5520	1.17482
$551$	−10.1401	−0.431981
$552$	17.2348	0.733563
$553$	3.73430	0.158799
$554$	−23.8754	−1.01437
$555$	−16.4272	−0.697295
$556$	9.83272	0.417000
$557$	−1.32944	−0.0563301	−0.0281651	−	0.999603i	$-0.508966\pi$
$557$	−1.32944	−0.0563301	−0.0281651	+	0.999603i	$0.508966\pi$
$558$	59.7428	2.52912
$559$	−3.23085	−0.136650
$560$	2.80733	0.118631
$561$	−89.6537	−3.78518
$562$	17.1916	0.725186
$563$	−39.3488	−1.65836	−0.829178	−	0.558985i	$-0.811191\pi$
$563$	−39.3488	−1.65836	−0.829178	+	0.558985i	$0.811191\pi$
$564$	−27.0331	−1.13830
$565$	8.37200	0.352213
$566$	−17.9207	−0.753262
$567$	62.1271	2.60909
$568$	−1.76898	−0.0742248
$569$	26.0599	1.09249	0.546245	−	0.837626i	$-0.316057\pi$
$569$	26.0599	1.09249	0.546245	+	0.837626i	$0.316057\pi$
$570$	3.02915	0.126877
$571$	−1.32259	−0.0553486	−0.0276743	−	0.999617i	$-0.508810\pi$
$571$	−1.32259	−0.0553486	−0.0276743	+	0.999617i	$0.508810\pi$
$572$	4.31096	0.180250
$573$	−14.0263	−0.585957
$574$	−21.9176	−0.914825
$575$	25.9339	1.08152
$576$	6.46998	0.269583
$577$	−24.0490	−1.00117	−0.500586	−	0.865687i	$-0.666882\pi$
$577$	−24.0490	−1.00117	−0.500586	+	0.865687i	$0.666882\pi$
$578$	6.97462	0.290106
$579$	−66.1414	−2.74874
$580$	3.80548	0.158014
$581$	−7.74529	−0.321329
$582$	−48.0331	−1.99104
$583$	46.6543	1.93222
$584$	−2.71781	−0.112464
$585$	−2.84916	−0.117798
$586$	−18.3658	−0.758683
$587$	31.8822	1.31592	0.657960	−	0.753053i	$-0.271419\pi$
$587$	31.8822	1.31592	0.657960	+	0.753053i	$0.271419\pi$
$588$	−44.1104	−1.81908
$589$	−14.9545	−0.616189
$590$	8.56661	0.352682
$591$	81.0108	3.33234
$592$	8.78276	0.360969
$593$	−18.3617	−0.754023	−0.377011	−	0.926209i	$-0.623048\pi$
$593$	−18.3617	−0.754023	−0.377011	+	0.926209i	$0.623048\pi$
$594$	63.5359	2.60691
$595$	−13.7458	−0.563522
$596$	13.8883	0.568885
$597$	40.1109	1.64163
$598$	4.05778	0.165935
$599$	−17.0123	−0.695103	−0.347552	−	0.937661i	$-0.612987\pi$
$599$	−17.0123	−0.695103	−0.347552	+	0.937661i	$0.612987\pi$
$600$	14.2499	0.581748
$601$	33.3745	1.36138	0.680688	−	0.732573i	$-0.261681\pi$
$601$	33.3745	1.36138	0.680688	+	0.732573i	$0.261681\pi$
$602$	20.5966	0.839455
$603$	28.4915	1.16026
$604$	5.73315	0.233279
$605$	14.8318	0.602998
$606$	55.7386	2.26422
$607$	−29.4228	−1.19423	−0.597117	−	0.802154i	$-0.703687\pi$
$607$	−29.4228	−1.19423	−0.597117	+	0.802154i	$0.703687\pi$
$608$	−1.61953	−0.0656806
$609$	−88.9942	−3.60623
$610$	−6.77770	−0.274421
$611$	−6.36471	−0.257489
$612$	−31.6795	−1.28057
$613$	40.2971	1.62758	0.813792	−	0.581156i	$-0.197399\pi$
$613$	40.2971	1.62758	0.813792	+	0.581156i	$0.197399\pi$
$614$	−0.0763418	−0.00308090
$615$	8.87544	0.357892
$616$	−27.4823	−1.10729
$617$	29.2428	1.17727	0.588636	−	0.808398i	$-0.299665\pi$
$617$	29.2428	1.17727	0.588636	+	0.808398i	$0.299665\pi$
$618$	−39.4721	−1.58780
$619$	44.5106	1.78903	0.894515	−	0.447037i	$-0.147521\pi$
$619$	44.5106	1.78903	0.894515	+	0.447037i	$0.147521\pi$
$620$	5.61229	0.225395
$621$	59.8045	2.39987
$622$	8.41472	0.337399
$623$	16.7192	0.669840
$624$	2.22962	0.0892563
$625$	19.5952	0.783810
$626$	29.1320	1.16435
$627$	−29.6538	−1.18426
$628$	−11.5209	−0.459733
$629$	−43.0038	−1.71467
$630$	18.1634	0.723646
$631$	21.9443	0.873591	0.436795	−	0.899561i	$-0.356113\pi$
$631$	21.9443	0.873591	0.436795	+	0.899561i	$0.356113\pi$
$632$	0.808488	0.0321599
$633$	−79.7176	−3.16849
$634$	9.37439	0.372304
$635$	−2.27399	−0.0902405
$636$	24.1295	0.956798
$637$	−10.3854	−0.411484
$638$	−37.2537	−1.47489
$639$	−11.4453	−0.452768
$640$	0.607795	0.0240252
$641$	−23.8619	−0.942488	−0.471244	−	0.882003i	$-0.656195\pi$
$641$	−23.8619	−0.942488	−0.471244	+	0.882003i	$0.656195\pi$
$642$	2.22881	0.0879641
$643$	41.8210	1.64926	0.824629	−	0.565674i	$-0.191384\pi$
$643$	41.8210	1.64926	0.824629	+	0.565674i	$0.191384\pi$
$644$	−25.8683	−1.01935
$645$	−8.34049	−0.328407
$646$	7.92984	0.311995
$647$	29.2718	1.15079	0.575397	−	0.817875i	$-0.304848\pi$
$647$	29.2718	1.15079	0.575397	+	0.817875i	$0.304848\pi$
$648$	13.4507	0.528394
$649$	−83.8628	−3.29190
$650$	3.35500	0.131594
$651$	−131.248	−5.14402
$652$	−12.8096	−0.501664
$653$	−13.2156	−0.517168	−0.258584	−	0.965989i	$-0.583256\pi$
$653$	−13.2156	−0.517168	−0.258584	+	0.965989i	$0.583256\pi$
$654$	6.41069	0.250678
$655$	13.8217	0.540058
$656$	−4.74524	−0.185270
$657$	−17.5842	−0.686024
$658$	40.5749	1.58178
$659$	−12.5592	−0.489237	−0.244618	−	0.969619i	$-0.578663\pi$
$659$	−12.5592	−0.489237	−0.244618	+	0.969619i	$0.578663\pi$
$660$	11.1288	0.433189
$661$	33.9007	1.31858	0.659292	−	0.751887i	$-0.270856\pi$
$661$	33.9007	1.31858	0.659292	+	0.751887i	$0.270856\pi$
$662$	2.35558	0.0915523
$663$	−10.9171	−0.423985
$664$	−1.67688	−0.0650756
$665$	−4.54655	−0.176308
$666$	56.8243	2.20190
$667$	−35.0658	−1.35775
$668$	9.86074	0.381524
$669$	−67.8690	−2.62397
$670$	2.67651	0.103403
$671$	66.3502	2.56142
$672$	−14.2138	−0.548309
$673$	−14.7010	−0.566682	−0.283341	−	0.959019i	$-0.591443\pi$
$673$	−14.7010	−0.566682	−0.283341	+	0.959019i	$0.591443\pi$
$674$	−18.2646	−0.703526
$675$	49.4467	1.90321
$676$	−12.4751	−0.479810
$677$	10.5940	0.407162	0.203581	−	0.979058i	$-0.434742\pi$
$677$	10.5940	0.407162	0.203581	+	0.979058i	$0.434742\pi$
$678$	−42.3883	−1.62791
$679$	72.0945	2.76673
$680$	−2.97600	−0.114124
$681$	−70.4582	−2.69997
$682$	−54.9415	−2.10382
$683$	32.6606	1.24972	0.624862	−	0.780735i	$-0.285155\pi$
$683$	32.6606	1.24972	0.624862	+	0.780735i	$0.285155\pi$
$684$	−10.4783	−0.400649
$685$	8.72940	0.333533
$686$	33.8746	1.29334
$687$	−8.77408	−0.334752
$688$	4.45923	0.170006
$689$	5.68108	0.216432
$690$	10.4752	0.398786
$691$	40.2830	1.53244	0.766218	−	0.642580i	$-0.222136\pi$
$691$	40.2830	1.53244	0.766218	+	0.642580i	$0.222136\pi$
$692$	0.304267	0.0115665
$693$	−177.810	−6.75445
$694$	3.71621	0.141066
$695$	5.97628	0.226693
$696$	−19.2675	−0.730334
$697$	23.2345	0.880071
$698$	28.1850	1.06682
$699$	9.76756	0.369443
$700$	−21.3881	−0.808393
$701$	−18.2802	−0.690432	−0.345216	−	0.938523i	$-0.612194\pi$
$701$	−18.2802	−0.690432	−0.345216	+	0.938523i	$0.612194\pi$
$702$	7.73675	0.292005
$703$	−14.2239	−0.536466
$704$	−5.95001	−0.224249
$705$	−16.4306	−0.618813
$706$	−4.93999	−0.185919
$707$	−83.6599	−3.14635
$708$	−43.3737	−1.63008
$709$	10.6715	0.400778	0.200389	−	0.979716i	$-0.435779\pi$
$709$	10.6715	0.400778	0.200389	+	0.979716i	$0.435779\pi$
$710$	−1.07518	−0.0403507
$711$	5.23091	0.196174
$712$	3.61976	0.135656
$713$	−51.7148	−1.93673
$714$	69.5963	2.60458
$715$	2.62018	0.0979893
$716$	−20.4850	−0.765559
$717$	15.1628	0.566265
$718$	−3.95380	−0.147555
$719$	23.5364	0.877759	0.438879	−	0.898546i	$-0.355376\pi$
$719$	23.5364	0.877759	0.438879	+	0.898546i	$0.355376\pi$
$720$	3.93243	0.146553
$721$	59.2449	2.20640
$722$	−16.3771	−0.609494
$723$	−19.7575	−0.734788
$724$	13.5044	0.501888
$725$	−28.9926	−1.07676
$726$	−75.0949	−2.78703
$727$	−25.0778	−0.930085	−0.465043	−	0.885288i	$-0.653961\pi$
$727$	−25.0778	−0.930085	−0.465043	+	0.885288i	$0.653961\pi$
$728$	−3.34651	−0.124030
$729$	−11.5561	−0.428003
$730$	−1.65187	−0.0611385
$731$	−21.8341	−0.807564
$732$	34.3162	1.26836
$733$	−0.0706587	−0.00260984	−0.00130492	−	0.999999i	$-0.500415\pi$
$733$	−0.0706587	−0.00260984	−0.00130492	+	0.999999i	$0.500415\pi$
$734$	−5.63436	−0.207968
$735$	−26.8101	−0.988905
$736$	−5.60057	−0.206440
$737$	−26.2017	−0.965152
$738$	−30.7016	−1.13014
$739$	0.270534	0.00995177	0.00497589	−	0.999988i	$-0.498416\pi$
$739$	0.270534	0.00995177	0.00497589	+	0.999988i	$0.498416\pi$
$740$	5.33812	0.196233
$741$	−3.61094	−0.132651
$742$	−36.2168	−1.32956
$743$	−36.8770	−1.35289	−0.676443	−	0.736495i	$-0.736479\pi$
$743$	−36.8770	−1.35289	−0.676443	+	0.736495i	$0.736479\pi$
$744$	−28.4156	−1.04177
$745$	8.44122	0.309262
$746$	23.4741	0.859448
$747$	−10.8494	−0.396958
$748$	29.1336	1.06523
$749$	−3.34529	−0.122234
$750$	18.0129	0.657740
$751$	−51.4450	−1.87726	−0.938628	−	0.344931i	$-0.887902\pi$
$751$	−51.4450	−1.87726	−0.938628	+	0.344931i	$0.887902\pi$
$752$	8.78460	0.320341
$753$	46.7330	1.70305
$754$	−4.53637	−0.165205
$755$	3.48458	0.126817
$756$	−49.3217	−1.79381
$757$	−12.1781	−0.442622	−0.221311	−	0.975203i	$-0.571034\pi$
$757$	−12.1781	−0.442622	−0.221311	+	0.975203i	$0.571034\pi$
$758$	3.38038	0.122781
$759$	−102.547	−3.72223
$760$	−0.984342	−0.0357058
$761$	−53.9090	−1.95420	−0.977100	−	0.212780i	$-0.931748\pi$
$761$	−53.9090	−1.95420	−0.977100	+	0.212780i	$0.931748\pi$
$762$	11.5135	0.417088
$763$	−9.62202	−0.348340
$764$	4.55794	0.164900
$765$	−19.2547	−0.696155
$766$	21.8127	0.788125
$767$	−10.2119	−0.368732
$768$	−3.07733	−0.111044
$769$	50.8427	1.83343	0.916717	−	0.399538i	$-0.130830\pi$
$769$	50.8427	1.83343	0.916717	+	0.399538i	$0.130830\pi$
$770$	−16.7036	−0.601957
$771$	7.17975	0.258572
$772$	21.4931	0.773554
$773$	6.86542	0.246932	0.123466	−	0.992349i	$-0.460599\pi$
$773$	6.86542	0.246932	0.123466	+	0.992349i	$0.460599\pi$
$774$	28.8511	1.03703
$775$	−42.7581	−1.53592
$776$	15.6087	0.560319
$777$	−124.836	−4.47848
$778$	8.87224	0.318085
$779$	7.68505	0.275345
$780$	1.35515	0.0485223
$781$	10.5255	0.376630
$782$	27.4226	0.980629
$783$	−66.8580	−2.38931
$784$	14.3340	0.511927
$785$	−7.00233	−0.249924
$786$	−69.9807	−2.49613
$787$	−34.1032	−1.21565	−0.607824	−	0.794072i	$-0.707957\pi$
$787$	−34.1032	−1.21565	−0.607824	+	0.794072i	$0.707957\pi$
$788$	−26.3250	−0.937789
$789$	−81.4271	−2.89888
$790$	0.491395	0.0174831
$791$	63.6220	2.26214
$792$	−38.4964	−1.36791
$793$	8.07944	0.286909
$794$	−10.0497	−0.356652
$795$	14.6658	0.520143
$796$	−13.0343	−0.461989
$797$	8.45316	0.299426	0.149713	−	0.988729i	$-0.452165\pi$
$797$	8.45316	0.299426	0.149713	+	0.988729i	$0.452165\pi$
$798$	23.0197	0.814887
$799$	−43.0128	−1.52168
$800$	−4.63058	−0.163716
$801$	23.4198	0.827497
$802$	12.6421	0.446407
$803$	16.1710	0.570661
$804$	−13.5515	−0.477923
$805$	−15.7226	−0.554150
$806$	−6.69021	−0.235652
$807$	51.1857	1.80182
$808$	−18.1126	−0.637200
$809$	17.0181	0.598323	0.299162	−	0.954202i	$-0.403293\pi$
$809$	17.0181	0.598323	0.299162	+	0.954202i	$0.403293\pi$
$810$	8.17529	0.287250
$811$	17.9011	0.628592	0.314296	−	0.949325i	$-0.398232\pi$
$811$	17.9011	0.628592	0.314296	+	0.949325i	$0.398232\pi$
$812$	28.9193	1.01487
$813$	−9.86781	−0.346079
$814$	−52.2575	−1.83162
$815$	−7.78563	−0.272719
$816$	15.0678	0.527479
$817$	−7.22185	−0.252660
$818$	−11.9968	−0.419457
$819$	−21.6519	−0.756578
$820$	−2.88413	−0.100718
$821$	−17.0938	−0.596577	−0.298289	−	0.954476i	$-0.596416\pi$
$821$	−17.0938	−0.596577	−0.298289	+	0.954476i	$0.596416\pi$
$822$	−44.1979	−1.54158
$823$	43.1863	1.50538	0.752690	−	0.658376i	$-0.228756\pi$
$823$	43.1863	1.50538	0.752690	+	0.658376i	$0.228756\pi$
$824$	12.8267	0.446840
$825$	−84.7868	−2.95190
$826$	65.1010	2.26515
$827$	−3.51018	−0.122061	−0.0610304	−	0.998136i	$-0.519439\pi$
$827$	−3.51018	−0.122061	−0.0610304	+	0.998136i	$0.519439\pi$
$828$	−36.2356	−1.25927
$829$	−13.0047	−0.451673	−0.225836	−	0.974165i	$-0.572511\pi$
$829$	−13.0047	−0.451673	−0.225836	+	0.974165i	$0.572511\pi$
$830$	−1.01920	−0.0353769
$831$	73.4725	2.54873
$832$	−0.724531	−0.0251186
$833$	−70.1847	−2.43175
$834$	−30.2586	−1.04777
$835$	5.99331	0.207407
$836$	9.63621	0.333275
$837$	−98.6017	−3.40817
$838$	−6.45613	−0.223023
$839$	9.37273	0.323582	0.161791	−	0.986825i	$-0.448273\pi$
$839$	9.37273	0.323582	0.161791	+	0.986825i	$0.448273\pi$
$840$	−8.63909	−0.298077
$841$	10.2015	0.351777
$842$	−23.5158	−0.810407
$843$	−52.9044	−1.82213
$844$	25.9048	0.891679
$845$	−7.58228	−0.260838
$846$	56.8362	1.95407
$847$	112.712	3.87285
$848$	−7.84105	−0.269263
$849$	55.1479	1.89267
$850$	22.6731	0.777682
$851$	−49.1885	−1.68616
$852$	5.44375	0.186500
$853$	−37.4437	−1.28205	−0.641025	−	0.767520i	$-0.721490\pi$
$853$	−37.4437	−1.28205	−0.641025	+	0.767520i	$0.721490\pi$
$854$	−51.5063	−1.76251
$855$	−6.36867	−0.217804
$856$	−0.724267	−0.0247549
$857$	45.0988	1.54055	0.770273	−	0.637714i	$-0.220120\pi$
$857$	45.0988	1.54055	0.770273	+	0.637714i	$0.220120\pi$
$858$	−13.2663	−0.452903
$859$	20.4874	0.699021	0.349510	−	0.936933i	$-0.386348\pi$
$859$	20.4874	0.699021	0.349510	+	0.936933i	$0.386348\pi$
$860$	2.71030	0.0924204
$861$	67.4479	2.29862
$862$	−2.91653	−0.0993374
$863$	28.8128	0.980800	0.490400	−	0.871497i	$-0.336851\pi$
$863$	28.8128	0.980800	0.490400	+	0.871497i	$0.336851\pi$
$864$	−10.6783	−0.363283
$865$	0.184932	0.00628787
$866$	12.0161	0.408325
$867$	−21.4632	−0.728930
$868$	42.6499	1.44763
$869$	−4.81051	−0.163185
$870$	−11.7107	−0.397031
$871$	−3.19057	−0.108108
$872$	−2.08320	−0.0705460
$873$	100.988	3.41792
$874$	9.07028	0.306807
$875$	−27.0362	−0.913991
$876$	8.36360	0.282580
$877$	54.3443	1.83508	0.917539	−	0.397646i	$-0.130173\pi$
$877$	54.3443	1.83508	0.917539	+	0.397646i	$0.130173\pi$
$878$	30.1924	1.01894
$879$	56.5176	1.90629
$880$	−3.61639	−0.121908
$881$	8.25404	0.278086	0.139043	−	0.990286i	$-0.455597\pi$
$881$	8.25404	0.278086	0.139043	+	0.990286i	$0.455597\pi$
$882$	92.7405	3.12274
$883$	−16.4206	−0.552598	−0.276299	−	0.961072i	$-0.589108\pi$
$883$	−16.4206	−0.552598	−0.276299	+	0.961072i	$0.589108\pi$
$884$	3.54758	0.119318
$885$	−26.3623	−0.886160
$886$	−31.2467	−1.04975
$887$	−8.59402	−0.288559	−0.144279	−	0.989537i	$-0.546086\pi$
$887$	−8.59402	−0.288559	−0.144279	+	0.989537i	$0.546086\pi$
$888$	−27.0275	−0.906983
$889$	−17.2809	−0.579584
$890$	2.20007	0.0737466
$891$	−80.0319	−2.68117
$892$	22.0545	0.738438
$893$	−14.2269	−0.476085
$894$	−42.7388	−1.42940
$895$	−12.4507	−0.416180
$896$	4.61887	0.154306
$897$	−12.4872	−0.416934
$898$	−26.6338	−0.888782
$899$	57.8142	1.92821
$900$	−29.9598	−0.998660
$901$	38.3928	1.27905
$902$	28.2342	0.940096
$903$	−63.3826	−2.10924
$904$	13.7744	0.458129
$905$	8.20792	0.272841
$906$	−17.6428	−0.586143
$907$	41.7065	1.38484	0.692421	−	0.721494i	$-0.256544\pi$
$907$	41.7065	1.38484	0.692421	+	0.721494i	$0.256544\pi$
$908$	22.8959	0.759826
$909$	−117.188	−3.88689
$910$	−2.03400	−0.0674263
$911$	−18.4127	−0.610039	−0.305020	−	0.952346i	$-0.598663\pi$
$911$	−18.4127	−0.610039	−0.305020	+	0.952346i	$0.598663\pi$
$912$	4.98383	0.165031
$913$	9.97745	0.330205
$914$	−0.893147	−0.0295427
$915$	20.8572	0.689519
$916$	2.85120	0.0942062
$917$	105.036	3.46861
$918$	52.2851	1.72566
$919$	−17.3675	−0.572902	−0.286451	−	0.958095i	$-0.592476\pi$
$919$	−17.3675	−0.572902	−0.286451	+	0.958095i	$0.592476\pi$
$920$	−3.40400	−0.112227
$921$	0.234929	0.00774118
$922$	14.7223	0.484853
$923$	1.28168	0.0421871
$924$	84.5723	2.78222
$925$	−40.6693	−1.33720
$926$	−2.53655	−0.0833561
$927$	82.9886	2.72570
$928$	6.26111	0.205531
$929$	−11.4704	−0.376330	−0.188165	−	0.982137i	$-0.560254\pi$
$929$	−11.4704	−0.376330	−0.188165	+	0.982137i	$0.560254\pi$
$930$	−17.2709	−0.566335
$931$	−23.2143	−0.760817
$932$	−3.17403	−0.103969
$933$	−25.8949	−0.847761
$934$	−25.2441	−0.826013
$935$	17.7072	0.579089
$936$	−4.68770	−0.153222
$937$	−11.3988	−0.372384	−0.186192	−	0.982513i	$-0.559615\pi$
$937$	−11.3988	−0.372384	−0.186192	+	0.982513i	$0.559615\pi$
$938$	20.3398	0.664119
$939$	−89.6489	−2.92558
$940$	5.33924	0.174147
$941$	−46.9464	−1.53041	−0.765205	−	0.643787i	$-0.777362\pi$
$941$	−46.9464	−1.53041	−0.765205	+	0.643787i	$0.777362\pi$
$942$	35.4536	1.15514
$943$	26.5760	0.865435
$944$	14.0946	0.458739
$945$	−29.9775	−0.975167
$946$	−26.5324	−0.862644
$947$	−2.10596	−0.0684346	−0.0342173	−	0.999414i	$-0.510894\pi$
$947$	−2.10596	−0.0684346	−0.0342173	+	0.999414i	$0.510894\pi$
$948$	−2.48799	−0.0808061
$949$	1.96914	0.0639208
$950$	7.49936	0.243311
$951$	−28.8481	−0.935464
$952$	−22.6158	−0.732982
$953$	18.1770	0.588810	0.294405	−	0.955681i	$-0.404878\pi$
$953$	18.1770	0.588810	0.294405	+	0.955681i	$0.404878\pi$
$954$	−50.7314	−1.64249
$955$	2.77029	0.0896446
$956$	−4.92726	−0.159359
$957$	114.642	3.70585
$958$	−14.6026	−0.471788
$959$	66.3380	2.14217
$960$	−1.87039	−0.0603666
$961$	54.2639	1.75045
$962$	−6.36338	−0.205164
$963$	−4.68599	−0.151004
$964$	6.42032	0.206784
$965$	13.0634	0.420526
$966$	79.6054	2.56126
$967$	−3.09835	−0.0996361	−0.0498180	−	0.998758i	$-0.515864\pi$
$967$	−3.09835	−0.0996361	−0.0498180	+	0.998758i	$0.515864\pi$
$968$	24.4026	0.784329
$969$	−24.4028	−0.783930
$970$	9.48688	0.304605
$971$	−11.1491	−0.357792	−0.178896	−	0.983868i	$-0.557253\pi$
$971$	−11.1491	−0.357792	−0.178896	+	0.983868i	$0.557253\pi$
$972$	−9.35748	−0.300141
$973$	45.4161	1.45597
$974$	−35.6064	−1.14090
$975$	−10.3245	−0.330647
$976$	−11.1513	−0.356944
$977$	18.1405	0.580366	0.290183	−	0.956971i	$-0.406284\pi$
$977$	18.1405	0.580366	0.290183	+	0.956971i	$0.406284\pi$
$978$	39.4195	1.26050
$979$	−21.5376	−0.688344
$980$	8.71212	0.278298
$981$	−13.4782	−0.430327
$982$	−1.01709	−0.0324566
$983$	42.0163	1.34011	0.670055	−	0.742311i	$-0.266270\pi$
$983$	42.0163	1.34011	0.670055	+	0.742311i	$0.266270\pi$
$984$	14.6027	0.465517
$985$	−16.0002	−0.509809
$986$	−30.6568	−0.976313
$987$	−124.863	−3.97442
$988$	1.17340	0.0373308
$989$	−24.9742	−0.794134
$990$	−23.3980	−0.743636
$991$	23.2807	0.739536	0.369768	−	0.929124i	$-0.379437\pi$
$991$	23.2807	0.739536	0.369768	+	0.929124i	$0.379437\pi$
$992$	9.23385	0.293175
$993$	−7.24891	−0.230037
$994$	−8.17070	−0.259159
$995$	−7.92219	−0.251150
$996$	5.16032	0.163511
$997$	−15.6207	−0.494714	−0.247357	−	0.968924i	$-0.579562\pi$
$997$	−15.6207	−0.494714	−0.247357	+	0.968924i	$0.579562\pi$
$998$	39.7362	1.25783
$999$	−93.7849	−2.96722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.1	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.1	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.07733 q^{3} +1.00000 q^{4} +0.607795 q^{5} -3.07733 q^{6} +4.61887 q^{7} +1.00000 q^{8} +6.46998 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.07733 q^{3} +1.00000 q^{4} +0.607795 q^{5} -3.07733 q^{6} +4.61887 q^{7} +1.00000 q^{8} +6.46998 q^{9} +0.607795 q^{10} -5.95001 q^{11} -3.07733 q^{12} -0.724531 q^{13} +4.61887 q^{14} -1.87039 q^{15} +1.00000 q^{16} -4.89639 q^{17} +6.46998 q^{18} -1.61953 q^{19} +0.607795 q^{20} -14.2138 q^{21} -5.95001 q^{22} -5.60057 q^{23} -3.07733 q^{24} -4.63058 q^{25} -0.724531 q^{26} -10.6783 q^{27} +4.61887 q^{28} +6.26111 q^{29} -1.87039 q^{30} +9.23385 q^{31} +1.00000 q^{32} +18.3102 q^{33} -4.89639 q^{34} +2.80733 q^{35} +6.46998 q^{36} +8.78276 q^{37} -1.61953 q^{38} +2.22962 q^{39} +0.607795 q^{40} -4.74524 q^{41} -14.2138 q^{42} +4.45923 q^{43} -5.95001 q^{44} +3.93243 q^{45} -5.60057 q^{46} +8.78460 q^{47} -3.07733 q^{48} +14.3340 q^{49} -4.63058 q^{50} +15.0678 q^{51} -0.724531 q^{52} -7.84105 q^{53} -10.6783 q^{54} -3.61639 q^{55} +4.61887 q^{56} +4.98383 q^{57} +6.26111 q^{58} +14.0946 q^{59} -1.87039 q^{60} -11.1513 q^{61} +9.23385 q^{62} +29.8840 q^{63} +1.00000 q^{64} -0.440366 q^{65} +18.3102 q^{66} +4.40364 q^{67} -4.89639 q^{68} +17.2348 q^{69} +2.80733 q^{70} -1.76898 q^{71} +6.46998 q^{72} -2.71781 q^{73} +8.78276 q^{74} +14.2499 q^{75} -1.61953 q^{76} -27.4823 q^{77} +2.22962 q^{78} +0.808488 q^{79} +0.607795 q^{80} +13.4507 q^{81} -4.74524 q^{82} -1.67688 q^{83} -14.2138 q^{84} -2.97600 q^{85} +4.45923 q^{86} -19.2675 q^{87} -5.95001 q^{88} +3.61976 q^{89} +3.93243 q^{90} -3.34651 q^{91} -5.60057 q^{92} -28.4156 q^{93} +8.78460 q^{94} -0.984342 q^{95} -3.07733 q^{96} +15.6087 q^{97} +14.3340 q^{98} -38.4964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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