LMFDB - Embedded newform 6038.2.a.b.1.18

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:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.61049 q^{3} +1.00000 q^{4} +1.72129 q^{5} -1.61049 q^{6} +1.31284 q^{7} +1.00000 q^{8} -0.406311 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.61049 q^{3} +1.00000 q^{4} +1.72129 q^{5} -1.61049 q^{6} +1.31284 q^{7} +1.00000 q^{8} -0.406311 q^{9} +1.72129 q^{10} -2.23670 q^{11} -1.61049 q^{12} -6.29151 q^{13} +1.31284 q^{14} -2.77213 q^{15} +1.00000 q^{16} +3.76808 q^{17} -0.406311 q^{18} +1.88014 q^{19} +1.72129 q^{20} -2.11433 q^{21} -2.23670 q^{22} +1.25397 q^{23} -1.61049 q^{24} -2.03715 q^{25} -6.29151 q^{26} +5.48584 q^{27} +1.31284 q^{28} -6.80576 q^{29} -2.77213 q^{30} +2.08197 q^{31} +1.00000 q^{32} +3.60218 q^{33} +3.76808 q^{34} +2.25979 q^{35} -0.406311 q^{36} +9.67122 q^{37} +1.88014 q^{38} +10.1324 q^{39} +1.72129 q^{40} +0.741141 q^{41} -2.11433 q^{42} -6.36486 q^{43} -2.23670 q^{44} -0.699380 q^{45} +1.25397 q^{46} -4.11464 q^{47} -1.61049 q^{48} -5.27644 q^{49} -2.03715 q^{50} -6.06846 q^{51} -6.29151 q^{52} -8.21736 q^{53} +5.48584 q^{54} -3.85001 q^{55} +1.31284 q^{56} -3.02795 q^{57} -6.80576 q^{58} +4.53438 q^{59} -2.77213 q^{60} -1.41430 q^{61} +2.08197 q^{62} -0.533422 q^{63} +1.00000 q^{64} -10.8295 q^{65} +3.60218 q^{66} +8.25818 q^{67} +3.76808 q^{68} -2.01951 q^{69} +2.25979 q^{70} -11.5169 q^{71} -0.406311 q^{72} -9.64717 q^{73} +9.67122 q^{74} +3.28082 q^{75} +1.88014 q^{76} -2.93643 q^{77} +10.1324 q^{78} +1.60267 q^{79} +1.72129 q^{80} -7.61598 q^{81} +0.741141 q^{82} -3.02718 q^{83} -2.11433 q^{84} +6.48596 q^{85} -6.36486 q^{86} +10.9606 q^{87} -2.23670 q^{88} +10.0196 q^{89} -0.699380 q^{90} -8.25977 q^{91} +1.25397 q^{92} -3.35300 q^{93} -4.11464 q^{94} +3.23626 q^{95} -1.61049 q^{96} -17.8938 q^{97} -5.27644 q^{98} +0.908793 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * 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
$3$	−1.61049	−0.929819	−0.464909	−	0.885358i	$-0.653913\pi$
$3$	−1.61049	−0.929819	−0.464909	+	0.885358i	$0.653913\pi$
$4$	1.00000	0.500000
$5$	1.72129	0.769785	0.384893	−	0.922961i	$-0.374238\pi$
$5$	1.72129	0.769785	0.384893	+	0.922961i	$0.374238\pi$
$6$	−1.61049	−0.657481
$7$	1.31284	0.496208	0.248104	−	0.968733i	$-0.420193\pi$
$7$	1.31284	0.496208	0.248104	+	0.968733i	$0.420193\pi$
$8$	1.00000	0.353553
$9$	−0.406311	−0.135437
$10$	1.72129	0.544321
$11$	−2.23670	−0.674389	−0.337195	−	0.941435i	$-0.609478\pi$
$11$	−2.23670	−0.674389	−0.337195	+	0.941435i	$0.609478\pi$
$12$	−1.61049	−0.464909
$13$	−6.29151	−1.74495	−0.872476	−	0.488658i	$-0.837487\pi$
$13$	−6.29151	−1.74495	−0.872476	+	0.488658i	$0.837487\pi$
$14$	1.31284	0.350872
$15$	−2.77213	−0.715761
$16$	1.00000	0.250000
$17$	3.76808	0.913893	0.456946	−	0.889494i	$-0.348943\pi$
$17$	3.76808	0.913893	0.456946	+	0.889494i	$0.348943\pi$
$18$	−0.406311	−0.0957684
$19$	1.88014	0.431333	0.215666	−	0.976467i	$-0.430808\pi$
$19$	1.88014	0.431333	0.215666	+	0.976467i	$0.430808\pi$
$20$	1.72129	0.384893
$21$	−2.11433	−0.461384
$22$	−2.23670	−0.476865
$23$	1.25397	0.261471	0.130736	−	0.991417i	$-0.458266\pi$
$23$	1.25397	0.261471	0.130736	+	0.991417i	$0.458266\pi$
$24$	−1.61049	−0.328741
$25$	−2.03715	−0.407430
$26$	−6.29151	−1.23387
$27$	5.48584	1.05575
$28$	1.31284	0.248104
$29$	−6.80576	−1.26380	−0.631899	−	0.775050i	$-0.717724\pi$
$29$	−6.80576	−1.26380	−0.631899	+	0.775050i	$0.717724\pi$
$30$	−2.77213	−0.506119
$31$	2.08197	0.373932	0.186966	−	0.982366i	$-0.440134\pi$
$31$	2.08197	0.373932	0.186966	+	0.982366i	$0.440134\pi$
$32$	1.00000	0.176777
$33$	3.60218	0.627060
$34$	3.76808	0.646220
$35$	2.25979	0.381974
$36$	−0.406311	−0.0677185
$37$	9.67122	1.58994	0.794969	−	0.606650i	$-0.207487\pi$
$37$	9.67122	1.58994	0.794969	+	0.606650i	$0.207487\pi$
$38$	1.88014	0.304998
$39$	10.1324	1.62249
$40$	1.72129	0.272160
$41$	0.741141	0.115747	0.0578734	−	0.998324i	$-0.481568\pi$
$41$	0.741141	0.115747	0.0578734	+	0.998324i	$0.481568\pi$
$42$	−2.11433	−0.326248
$43$	−6.36486	−0.970632	−0.485316	−	0.874339i	$-0.661295\pi$
$43$	−6.36486	−0.970632	−0.485316	+	0.874339i	$0.661295\pi$
$44$	−2.23670	−0.337195
$45$	−0.699380	−0.104257
$46$	1.25397	0.184888
$47$	−4.11464	−0.600182	−0.300091	−	0.953911i	$-0.597017\pi$
$47$	−4.11464	−0.600182	−0.300091	+	0.953911i	$0.597017\pi$
$48$	−1.61049	−0.232455
$49$	−5.27644	−0.753777
$50$	−2.03715	−0.288097
$51$	−6.06846	−0.849755
$52$	−6.29151	−0.872476
$53$	−8.21736	−1.12874	−0.564371	−	0.825521i	$-0.690881\pi$
$53$	−8.21736	−1.12874	−0.564371	+	0.825521i	$0.690881\pi$
$54$	5.48584	0.746528
$55$	−3.85001	−0.519135
$56$	1.31284	0.175436
$57$	−3.02795	−0.401061
$58$	−6.80576	−0.893641
$59$	4.53438	0.590326	0.295163	−	0.955447i	$-0.404626\pi$
$59$	4.53438	0.590326	0.295163	+	0.955447i	$0.404626\pi$
$60$	−2.77213	−0.357881
$61$	−1.41430	−0.181083	−0.0905416	−	0.995893i	$-0.528860\pi$
$61$	−1.41430	−0.181083	−0.0905416	+	0.995893i	$0.528860\pi$
$62$	2.08197	0.264410
$63$	−0.533422	−0.0672049
$64$	1.00000	0.125000
$65$	−10.8295	−1.34324
$66$	3.60218	0.443398
$67$	8.25818	1.00890	0.504449	−	0.863442i	$-0.331696\pi$
$67$	8.25818	1.00890	0.504449	+	0.863442i	$0.331696\pi$
$68$	3.76808	0.456946
$69$	−2.01951	−0.243121
$70$	2.25979	0.270096
$71$	−11.5169	−1.36681	−0.683404	−	0.730041i	$-0.739501\pi$
$71$	−11.5169	−1.36681	−0.683404	+	0.730041i	$0.739501\pi$
$72$	−0.406311	−0.0478842
$73$	−9.64717	−1.12912	−0.564558	−	0.825393i	$-0.690953\pi$
$73$	−9.64717	−1.12912	−0.564558	+	0.825393i	$0.690953\pi$
$74$	9.67122	1.12426
$75$	3.28082	0.378836
$76$	1.88014	0.215666
$77$	−2.93643	−0.334637
$78$	10.1324	1.14727
$79$	1.60267	0.180315	0.0901575	−	0.995928i	$-0.471263\pi$
$79$	1.60267	0.180315	0.0901575	+	0.995928i	$0.471263\pi$
$80$	1.72129	0.192446
$81$	−7.61598	−0.846220
$82$	0.741141	0.0818453
$83$	−3.02718	−0.332276	−0.166138	−	0.986102i	$-0.553130\pi$
$83$	−3.02718	−0.332276	−0.166138	+	0.986102i	$0.553130\pi$
$84$	−2.11433	−0.230692
$85$	6.48596	0.703501
$86$	−6.36486	−0.686341
$87$	10.9606	1.17510
$88$	−2.23670	−0.238433
$89$	10.0196	1.06208	0.531038	−	0.847348i	$-0.321802\pi$
$89$	10.0196	1.06208	0.531038	+	0.847348i	$0.321802\pi$
$90$	−0.699380	−0.0737211
$91$	−8.25977	−0.865859
$92$	1.25397	0.130736
$93$	−3.35300	−0.347689
$94$	−4.11464	−0.424393
$95$	3.23626	0.332034
$96$	−1.61049	−0.164370
$97$	−17.8938	−1.81684	−0.908422	−	0.418055i	$-0.862712\pi$
$97$	−17.8938	−1.81684	−0.908422	+	0.418055i	$0.862712\pi$
$98$	−5.27644	−0.533001
$99$	0.908793	0.0913372
$100$	−2.03715	−0.203715
$101$	−5.57658	−0.554890	−0.277445	−	0.960741i	$-0.589488\pi$
$101$	−5.57658	−0.554890	−0.277445	+	0.960741i	$0.589488\pi$
$102$	−6.06846	−0.600867
$103$	−12.7221	−1.25355	−0.626773	−	0.779202i	$-0.715624\pi$
$103$	−12.7221	−1.25355	−0.626773	+	0.779202i	$0.715624\pi$
$104$	−6.29151	−0.616933
$105$	−3.63937	−0.355166
$106$	−8.21736	−0.798141
$107$	−12.9379	−1.25076	−0.625378	−	0.780322i	$-0.715055\pi$
$107$	−12.9379	−1.25076	−0.625378	+	0.780322i	$0.715055\pi$
$108$	5.48584	0.527875
$109$	3.55845	0.340837	0.170419	−	0.985372i	$-0.445488\pi$
$109$	3.55845	0.340837	0.170419	+	0.985372i	$0.445488\pi$
$110$	−3.85001	−0.367084
$111$	−15.5754	−1.47835
$112$	1.31284	0.124052
$113$	9.49956	0.893644	0.446822	−	0.894623i	$-0.352556\pi$
$113$	9.49956	0.893644	0.446822	+	0.894623i	$0.352556\pi$
$114$	−3.02795	−0.283593
$115$	2.15845	0.201277
$116$	−6.80576	−0.631899
$117$	2.55631	0.236331
$118$	4.53438	0.417423
$119$	4.94689	0.453481
$120$	−2.77213	−0.253060
$121$	−5.99719	−0.545199
$122$	−1.41430	−0.128045
$123$	−1.19360	−0.107624
$124$	2.08197	0.186966
$125$	−12.1130	−1.08342
$126$	−0.533422	−0.0475210
$127$	−22.1829	−1.96841	−0.984205	−	0.177030i	$-0.943351\pi$
$127$	−22.1829	−1.96841	−0.984205	+	0.177030i	$0.943351\pi$
$128$	1.00000	0.0883883
$129$	10.2506	0.902512
$130$	−10.8295	−0.949813
$131$	3.50956	0.306632	0.153316	−	0.988177i	$-0.451005\pi$
$131$	3.50956	0.306632	0.153316	+	0.988177i	$0.451005\pi$
$132$	3.60218	0.313530
$133$	2.46832	0.214031
$134$	8.25818	0.713398
$135$	9.44274	0.812701
$136$	3.76808	0.323110
$137$	18.5705	1.58658	0.793291	−	0.608842i	$-0.208366\pi$
$137$	18.5705	1.58658	0.793291	+	0.608842i	$0.208366\pi$
$138$	−2.01951	−0.171913
$139$	−14.0697	−1.19338	−0.596690	−	0.802472i	$-0.703518\pi$
$139$	−14.0697	−1.19338	−0.596690	+	0.802472i	$0.703518\pi$
$140$	2.25979	0.190987
$141$	6.62660	0.558061
$142$	−11.5169	−0.966479
$143$	14.0722	1.17678
$144$	−0.406311	−0.0338592
$145$	−11.7147	−0.972854
$146$	−9.64717	−0.798405
$147$	8.49768	0.700877
$148$	9.67122	0.794969
$149$	−17.5392	−1.43686	−0.718432	−	0.695597i	$-0.755140\pi$
$149$	−17.5392	−1.43686	−0.718432	+	0.695597i	$0.755140\pi$
$150$	3.28082	0.267878
$151$	2.03570	0.165663	0.0828316	−	0.996564i	$-0.473604\pi$
$151$	2.03570	0.165663	0.0828316	+	0.996564i	$0.473604\pi$
$152$	1.88014	0.152499
$153$	−1.53101	−0.123775
$154$	−2.93643	−0.236624
$155$	3.58368	0.287848
$156$	10.1324	0.811244
$157$	17.9036	1.42886	0.714432	−	0.699705i	$-0.246685\pi$
$157$	17.9036	1.42886	0.714432	+	0.699705i	$0.246685\pi$
$158$	1.60267	0.127502
$159$	13.2340	1.04953
$160$	1.72129	0.136080
$161$	1.64627	0.129744
$162$	−7.61598	−0.598368
$163$	1.73690	0.136045	0.0680223	−	0.997684i	$-0.478331\pi$
$163$	1.73690	0.136045	0.0680223	+	0.997684i	$0.478331\pi$
$164$	0.741141	0.0578734
$165$	6.20041	0.482701
$166$	−3.02718	−0.234955
$167$	−8.42376	−0.651850	−0.325925	−	0.945396i	$-0.605676\pi$
$167$	−8.42376	−0.651850	−0.325925	+	0.945396i	$0.605676\pi$
$168$	−2.11433	−0.163124
$169$	26.5831	2.04486
$170$	6.48596	0.497450
$171$	−0.763919	−0.0584183
$172$	−6.36486	−0.485316
$173$	26.0588	1.98122	0.990608	−	0.136732i	$-0.0436598\pi$
$173$	26.0588	1.98122	0.990608	+	0.136732i	$0.0436598\pi$
$174$	10.9606	0.830924
$175$	−2.67446	−0.202170
$176$	−2.23670	−0.168597
$177$	−7.30259	−0.548896
$178$	10.0196	0.751002
$179$	−16.0455	−1.19930	−0.599650	−	0.800263i	$-0.704693\pi$
$179$	−16.0455	−1.19930	−0.599650	+	0.800263i	$0.704693\pi$
$180$	−0.699380	−0.0521287
$181$	13.8714	1.03105	0.515527	−	0.856873i	$-0.327596\pi$
$181$	13.8714	1.03105	0.515527	+	0.856873i	$0.327596\pi$
$182$	−8.25977	−0.612255
$183$	2.27773	0.168375
$184$	1.25397	0.0924441
$185$	16.6470	1.22391
$186$	−3.35300	−0.245854
$187$	−8.42804	−0.616319
$188$	−4.11464	−0.300091
$189$	7.20205	0.523872
$190$	3.23626	0.234783
$191$	−27.0933	−1.96040	−0.980200	−	0.198010i	$-0.936552\pi$
$191$	−27.0933	−1.96040	−0.980200	+	0.198010i	$0.936552\pi$
$192$	−1.61049	−0.116227
$193$	−3.63777	−0.261853	−0.130926	−	0.991392i	$-0.541795\pi$
$193$	−3.63777	−0.261853	−0.130926	+	0.991392i	$0.541795\pi$
$194$	−17.8938	−1.28470
$195$	17.4409	1.24897
$196$	−5.27644	−0.376889
$197$	−1.04244	−0.0742711	−0.0371356	−	0.999310i	$-0.511823\pi$
$197$	−1.04244	−0.0742711	−0.0371356	+	0.999310i	$0.511823\pi$
$198$	0.908793	0.0645851
$199$	19.0412	1.34979	0.674896	−	0.737913i	$-0.264189\pi$
$199$	19.0412	1.34979	0.674896	+	0.737913i	$0.264189\pi$
$200$	−2.03715	−0.144048
$201$	−13.2998	−0.938092
$202$	−5.57658	−0.392367
$203$	−8.93490	−0.627107
$204$	−6.06846	−0.424877
$205$	1.27572	0.0891002
$206$	−12.7221	−0.886390
$207$	−0.509502	−0.0354129
$208$	−6.29151	−0.436238
$209$	−4.20529	−0.290886
$210$	−3.63937	−0.251141
$211$	12.5524	0.864145	0.432073	−	0.901839i	$-0.357782\pi$
$211$	12.5524	0.864145	0.432073	+	0.901839i	$0.357782\pi$
$212$	−8.21736	−0.564371
$213$	18.5479	1.27088
$214$	−12.9379	−0.884418
$215$	−10.9558	−0.747178
$216$	5.48584	0.373264
$217$	2.73330	0.185548
$218$	3.55845	0.241008
$219$	15.5367	1.04987
$220$	−3.85001	−0.259567
$221$	−23.7069	−1.59470
$222$	−15.5754	−1.04535
$223$	−3.88154	−0.259927	−0.129964	−	0.991519i	$-0.541486\pi$
$223$	−3.88154	−0.259927	−0.129964	+	0.991519i	$0.541486\pi$
$224$	1.31284	0.0877180
$225$	0.827717	0.0551811
$226$	9.49956	0.631901
$227$	−7.94668	−0.527439	−0.263720	−	0.964599i	$-0.584949\pi$
$227$	−7.94668	−0.527439	−0.263720	+	0.964599i	$0.584949\pi$
$228$	−3.02795	−0.200531
$229$	−20.3486	−1.34468	−0.672338	−	0.740244i	$-0.734710\pi$
$229$	−20.3486	−1.34468	−0.672338	+	0.740244i	$0.734710\pi$
$230$	2.15845	0.142324
$231$	4.72910	0.311152
$232$	−6.80576	−0.446820
$233$	25.0901	1.64371	0.821853	−	0.569699i	$-0.192940\pi$
$233$	25.0901	1.64371	0.821853	+	0.569699i	$0.192940\pi$
$234$	2.55631	0.167111
$235$	−7.08250	−0.462011
$236$	4.53438	0.295163
$237$	−2.58110	−0.167660
$238$	4.94689	0.320659
$239$	3.90574	0.252642	0.126321	−	0.991989i	$-0.459683\pi$
$239$	3.90574	0.252642	0.126321	+	0.991989i	$0.459683\pi$
$240$	−2.77213	−0.178940
$241$	−9.47296	−0.610207	−0.305103	−	0.952319i	$-0.598691\pi$
$241$	−9.47296	−0.610207	−0.305103	+	0.952319i	$0.598691\pi$
$242$	−5.99719	−0.385514
$243$	−4.19204	−0.268919
$244$	−1.41430	−0.0905416
$245$	−9.08230	−0.580247
$246$	−1.19360	−0.0761013
$247$	−11.8289	−0.752654
$248$	2.08197	0.132205
$249$	4.87526	0.308957
$250$	−12.1130	−0.766093
$251$	−6.20710	−0.391789	−0.195894	−	0.980625i	$-0.562761\pi$
$251$	−6.20710	−0.391789	−0.195894	+	0.980625i	$0.562761\pi$
$252$	−0.533422	−0.0336024
$253$	−2.80475	−0.176333
$254$	−22.1829	−1.39188
$255$	−10.4456	−0.654129
$256$	1.00000	0.0625000
$257$	−12.6460	−0.788833	−0.394417	−	0.918932i	$-0.629053\pi$
$257$	−12.6460	−0.788833	−0.394417	+	0.918932i	$0.629053\pi$
$258$	10.2506	0.638172
$259$	12.6968	0.788940
$260$	−10.8295	−0.671619
$261$	2.76525	0.171165
$262$	3.50956	0.216821
$263$	−20.0362	−1.23549	−0.617744	−	0.786380i	$-0.711953\pi$
$263$	−20.0362	−1.23549	−0.617744	+	0.786380i	$0.711953\pi$
$264$	3.60218	0.221699
$265$	−14.1445	−0.868889
$266$	2.46832	0.151343
$267$	−16.1365	−0.987539
$268$	8.25818	0.504449
$269$	6.75044	0.411582	0.205791	−	0.978596i	$-0.434023\pi$
$269$	6.75044	0.411582	0.205791	+	0.978596i	$0.434023\pi$
$270$	9.44274	0.574667
$271$	9.67344	0.587619	0.293810	−	0.955864i	$-0.405077\pi$
$271$	9.67344	0.587619	0.293810	+	0.955864i	$0.405077\pi$
$272$	3.76808	0.228473
$273$	13.3023	0.805092
$274$	18.5705	1.12188
$275$	4.55649	0.274767
$276$	−2.01951	−0.121560
$277$	27.7165	1.66532	0.832662	−	0.553781i	$-0.186815\pi$
$277$	27.7165	1.66532	0.832662	+	0.553781i	$0.186815\pi$
$278$	−14.0697	−0.843847
$279$	−0.845926	−0.0506443
$280$	2.25979	0.135048
$281$	−26.8952	−1.60444	−0.802218	−	0.597031i	$-0.796347\pi$
$281$	−26.8952	−1.60444	−0.802218	+	0.597031i	$0.796347\pi$
$282$	6.62660	0.394608
$283$	−19.8146	−1.17786	−0.588929	−	0.808185i	$-0.700450\pi$
$283$	−19.8146	−1.17786	−0.588929	+	0.808185i	$0.700450\pi$
$284$	−11.5169	−0.683404
$285$	−5.21198	−0.308731
$286$	14.0722	0.832106
$287$	0.973002	0.0574345
$288$	−0.406311	−0.0239421
$289$	−2.80161	−0.164800
$290$	−11.7147	−0.687912
$291$	28.8179	1.68934
$292$	−9.64717	−0.564558
$293$	−1.42662	−0.0833439	−0.0416720	−	0.999131i	$-0.513268\pi$
$293$	−1.42662	−0.0833439	−0.0416720	+	0.999131i	$0.513268\pi$
$294$	8.49768	0.495595
$295$	7.80499	0.454424
$296$	9.67122	0.562128
$297$	−12.2702	−0.711987
$298$	−17.5392	−1.01602
$299$	−7.88938	−0.456255
$300$	3.28082	0.189418
$301$	−8.35606	−0.481636
$302$	2.03570	0.117142
$303$	8.98104	0.515947
$304$	1.88014	0.107833
$305$	−2.43443	−0.139395
$306$	−1.53101	−0.0875220
$307$	−4.57436	−0.261073	−0.130536	−	0.991444i	$-0.541670\pi$
$307$	−4.57436	−0.261073	−0.130536	+	0.991444i	$0.541670\pi$
$308$	−2.93643	−0.167319
$309$	20.4888	1.16557
$310$	3.58368	0.203539
$311$	29.1413	1.65245	0.826225	−	0.563340i	$-0.190484\pi$
$311$	29.1413	1.65245	0.826225	+	0.563340i	$0.190484\pi$
$312$	10.1324	0.573636
$313$	11.5738	0.654189	0.327094	−	0.944992i	$-0.393930\pi$
$313$	11.5738	0.654189	0.327094	+	0.944992i	$0.393930\pi$
$314$	17.9036	1.01036
$315$	−0.918176	−0.0517333
$316$	1.60267	0.0901575
$317$	0.312114	0.0175301	0.00876503	−	0.999962i	$-0.497210\pi$
$317$	0.312114	0.0175301	0.00876503	+	0.999962i	$0.497210\pi$
$318$	13.2340	0.742127
$319$	15.2224	0.852292
$320$	1.72129	0.0962232
$321$	20.8364	1.16298
$322$	1.64627	0.0917430
$323$	7.08449	0.394192
$324$	−7.61598	−0.423110
$325$	12.8168	0.710946
$326$	1.73690	0.0961981
$327$	−5.73086	−0.316917
$328$	0.741141	0.0409227
$329$	−5.40188	−0.297815
$330$	6.20041	0.341321
$331$	−16.7185	−0.918932	−0.459466	−	0.888195i	$-0.651959\pi$
$331$	−16.7185	−0.918932	−0.459466	+	0.888195i	$0.651959\pi$
$332$	−3.02718	−0.166138
$333$	−3.92952	−0.215336
$334$	−8.42376	−0.460928
$335$	14.2148	0.776635
$336$	−2.11433	−0.115346
$337$	−9.98203	−0.543756	−0.271878	−	0.962332i	$-0.587645\pi$
$337$	−9.98203	−0.543756	−0.271878	+	0.962332i	$0.587645\pi$
$338$	26.5831	1.44593
$339$	−15.2990	−0.830927
$340$	6.48596	0.351751
$341$	−4.65673	−0.252176
$342$	−0.763919	−0.0413080
$343$	−16.1170	−0.870239
$344$	−6.36486	−0.343170
$345$	−3.47618	−0.187151
$346$	26.0588	1.40093
$347$	31.8055	1.70741	0.853704	−	0.520758i	$-0.174351\pi$
$347$	31.8055	1.70741	0.853704	+	0.520758i	$0.174351\pi$
$348$	10.9606	0.587552
$349$	23.2221	1.24305	0.621524	−	0.783395i	$-0.286514\pi$
$349$	23.2221	1.24305	0.621524	+	0.783395i	$0.286514\pi$
$350$	−2.67446	−0.142956
$351$	−34.5142	−1.84223
$352$	−2.23670	−0.119216
$353$	−37.2041	−1.98018	−0.990088	−	0.140451i	$-0.955145\pi$
$353$	−37.2041	−1.98018	−0.990088	+	0.140451i	$0.955145\pi$
$354$	−7.30259	−0.388128
$355$	−19.8240	−1.05215
$356$	10.0196	0.531038
$357$	−7.96694	−0.421655
$358$	−16.0455	−0.848033
$359$	−29.1472	−1.53833	−0.769164	−	0.639051i	$-0.779327\pi$
$359$	−29.1472	−1.53833	−0.769164	+	0.639051i	$0.779327\pi$
$360$	−0.699380	−0.0368605
$361$	−15.4651	−0.813952
$362$	13.8714	0.729066
$363$	9.65844	0.506937
$364$	−8.25977	−0.432930
$365$	−16.6056	−0.869177
$366$	2.27773	0.119059
$367$	−21.8352	−1.13979	−0.569893	−	0.821719i	$-0.693015\pi$
$367$	−21.8352	−1.13979	−0.569893	+	0.821719i	$0.693015\pi$
$368$	1.25397	0.0653678
$369$	−0.301134	−0.0156764
$370$	16.6470	0.865436
$371$	−10.7881	−0.560091
$372$	−3.35300	−0.173845
$373$	8.26328	0.427857	0.213928	−	0.976849i	$-0.431374\pi$
$373$	8.26328	0.427857	0.213928	+	0.976849i	$0.431374\pi$
$374$	−8.42804	−0.435803
$375$	19.5079	1.00738
$376$	−4.11464	−0.212196
$377$	42.8185	2.20527
$378$	7.20205	0.370433
$379$	9.20605	0.472883	0.236442	−	0.971646i	$-0.424019\pi$
$379$	9.20605	0.472883	0.236442	+	0.971646i	$0.424019\pi$
$380$	3.23626	0.166017
$381$	35.7254	1.83027
$382$	−27.0933	−1.38621
$383$	6.38408	0.326211	0.163106	−	0.986609i	$-0.447849\pi$
$383$	6.38408	0.326211	0.163106	+	0.986609i	$0.447849\pi$
$384$	−1.61049	−0.0821852
$385$	−5.05446	−0.257599
$386$	−3.63777	−0.185158
$387$	2.58611	0.131459
$388$	−17.8938	−0.908422
$389$	12.3086	0.624070	0.312035	−	0.950071i	$-0.398989\pi$
$389$	12.3086	0.624070	0.312035	+	0.950071i	$0.398989\pi$
$390$	17.4409	0.883154
$391$	4.72506	0.238957
$392$	−5.27644	−0.266501
$393$	−5.65212	−0.285112
$394$	−1.04244	−0.0525176
$395$	2.75867	0.138804
$396$	0.908793	0.0456686
$397$	21.9763	1.10296	0.551479	−	0.834189i	$-0.314064\pi$
$397$	21.9763	1.10296	0.551479	+	0.834189i	$0.314064\pi$
$398$	19.0412	0.954447
$399$	−3.97522	−0.199010
$400$	−2.03715	−0.101858
$401$	5.21524	0.260437	0.130218	−	0.991485i	$-0.458432\pi$
$401$	5.21524	0.260437	0.130218	+	0.991485i	$0.458432\pi$
$402$	−13.2998	−0.663331
$403$	−13.0987	−0.652494
$404$	−5.57658	−0.277445
$405$	−13.1093	−0.651408
$406$	−8.93490	−0.443432
$407$	−21.6316	−1.07224
$408$	−6.06846	−0.300434
$409$	30.4266	1.50450	0.752248	−	0.658880i	$-0.228969\pi$
$409$	30.4266	1.50450	0.752248	+	0.658880i	$0.228969\pi$
$410$	1.27572	0.0630033
$411$	−29.9076	−1.47523
$412$	−12.7221	−0.626773
$413$	5.95293	0.292924
$414$	−0.509502	−0.0250407
$415$	−5.21066	−0.255781
$416$	−6.29151	−0.308467
$417$	22.6592	1.10963
$418$	−4.20529	−0.205687
$419$	−14.1223	−0.689921	−0.344961	−	0.938617i	$-0.612108\pi$
$419$	−14.1223	−0.689921	−0.344961	+	0.938617i	$0.612108\pi$
$420$	−3.63937	−0.177583
$421$	−29.8086	−1.45278	−0.726391	−	0.687282i	$-0.758804\pi$
$421$	−29.8086	−1.45278	−0.726391	+	0.687282i	$0.758804\pi$
$422$	12.5524	0.611043
$423$	1.67182	0.0812868
$424$	−8.21736	−0.399070
$425$	−7.67614	−0.372348
$426$	18.5479	0.898650
$427$	−1.85676	−0.0898549
$428$	−12.9379	−0.625378
$429$	−22.6632	−1.09419
$430$	−10.9558	−0.528335
$431$	−39.2362	−1.88994	−0.944971	−	0.327154i	$-0.893911\pi$
$431$	−39.2362	−1.88994	−0.944971	+	0.327154i	$0.893911\pi$
$432$	5.48584	0.263938
$433$	−7.47957	−0.359445	−0.179723	−	0.983717i	$-0.557520\pi$
$433$	−7.47957	−0.359445	−0.179723	+	0.983717i	$0.557520\pi$
$434$	2.73330	0.131202
$435$	18.8665	0.904578
$436$	3.55845	0.170419
$437$	2.35764	0.112781
$438$	15.5367	0.742372
$439$	1.20989	0.0577448	0.0288724	−	0.999583i	$-0.490808\pi$
$439$	1.20989	0.0577448	0.0288724	+	0.999583i	$0.490808\pi$
$440$	−3.85001	−0.183542
$441$	2.14388	0.102089
$442$	−23.7069	−1.12762
$443$	2.23364	0.106124	0.0530618	−	0.998591i	$-0.483102\pi$
$443$	2.23364	0.106124	0.0530618	+	0.998591i	$0.483102\pi$
$444$	−15.5754	−0.739177
$445$	17.2467	0.817571
$446$	−3.88154	−0.183796
$447$	28.2467	1.33602
$448$	1.31284	0.0620260
$449$	−37.4990	−1.76969	−0.884843	−	0.465889i	$-0.845735\pi$
$449$	−37.4990	−1.76969	−0.884843	+	0.465889i	$0.845735\pi$
$450$	0.827717	0.0390189
$451$	−1.65771	−0.0780584
$452$	9.49956	0.446822
$453$	−3.27849	−0.154037
$454$	−7.94668	−0.372956
$455$	−14.2175	−0.666526
$456$	−3.02795	−0.141797
$457$	15.6280	0.731045	0.365522	−	0.930803i	$-0.380890\pi$
$457$	15.6280	0.731045	0.365522	+	0.930803i	$0.380890\pi$
$458$	−20.3486	−0.950829
$459$	20.6711	0.964843
$460$	2.15845	0.100638
$461$	−5.33359	−0.248410	−0.124205	−	0.992257i	$-0.539638\pi$
$461$	−5.33359	−0.248410	−0.124205	+	0.992257i	$0.539638\pi$
$462$	4.72910	0.220018
$463$	8.03022	0.373196	0.186598	−	0.982436i	$-0.440254\pi$
$463$	8.03022	0.373196	0.186598	+	0.982436i	$0.440254\pi$
$464$	−6.80576	−0.315950
$465$	−5.77149	−0.267646
$466$	25.0901	1.16228
$467$	−21.0637	−0.974712	−0.487356	−	0.873203i	$-0.662039\pi$
$467$	−21.0637	−0.974712	−0.487356	+	0.873203i	$0.662039\pi$
$468$	2.55631	0.118165
$469$	10.8417	0.500623
$470$	−7.08250	−0.326691
$471$	−28.8336	−1.32858
$472$	4.53438	0.208712
$473$	14.2363	0.654584
$474$	−2.58110	−0.118554
$475$	−3.83012	−0.175738
$476$	4.94689	0.226740
$477$	3.33880	0.152873
$478$	3.90574	0.178645
$479$	−1.11120	−0.0507718	−0.0253859	−	0.999678i	$-0.508081\pi$
$479$	−1.11120	−0.0507718	−0.0253859	+	0.999678i	$0.508081\pi$
$480$	−2.77213	−0.126530
$481$	−60.8466	−2.77437
$482$	−9.47296	−0.431481
$483$	−2.65131	−0.120639
$484$	−5.99719	−0.272600
$485$	−30.8005	−1.39858
$486$	−4.19204	−0.190155
$487$	−27.7527	−1.25760	−0.628798	−	0.777569i	$-0.716453\pi$
$487$	−27.7527	−1.25760	−0.628798	+	0.777569i	$0.716453\pi$
$488$	−1.41430	−0.0640226
$489$	−2.79727	−0.126497
$490$	−9.08230	−0.410297
$491$	35.2482	1.59073	0.795365	−	0.606130i	$-0.207279\pi$
$491$	35.2482	1.59073	0.795365	+	0.606130i	$0.207279\pi$
$492$	−1.19360	−0.0538118
$493$	−25.6446	−1.15498
$494$	−11.8289	−0.532207
$495$	1.56430	0.0703100
$496$	2.08197	0.0934831
$497$	−15.1199	−0.678221
$498$	4.87526	0.218465
$499$	−10.8011	−0.483525	−0.241763	−	0.970335i	$-0.577726\pi$
$499$	−10.8011	−0.483525	−0.241763	+	0.970335i	$0.577726\pi$
$500$	−12.1130	−0.541710
$501$	13.5664	0.606102
$502$	−6.20710	−0.277037
$503$	−8.44852	−0.376701	−0.188350	−	0.982102i	$-0.560314\pi$
$503$	−8.44852	−0.376701	−0.188350	+	0.982102i	$0.560314\pi$
$504$	−0.533422	−0.0237605
$505$	−9.59892	−0.427146
$506$	−2.80475	−0.124687
$507$	−42.8119	−1.90135
$508$	−22.1829	−0.984205
$509$	−11.4770	−0.508709	−0.254355	−	0.967111i	$-0.581863\pi$
$509$	−11.4770	−0.508709	−0.254355	+	0.967111i	$0.581863\pi$
$510$	−10.4456	−0.462539
$511$	−12.6652	−0.560276
$512$	1.00000	0.0441942
$513$	10.3141	0.455380
$514$	−12.6460	−0.557789
$515$	−21.8984	−0.964961
$516$	10.2506	0.451256
$517$	9.20320	0.404756
$518$	12.6968	0.557865
$519$	−41.9676	−1.84217
$520$	−10.8295	−0.474906
$521$	−4.98798	−0.218527	−0.109264	−	0.994013i	$-0.534849\pi$
$521$	−4.98798	−0.218527	−0.109264	+	0.994013i	$0.534849\pi$
$522$	2.76525	0.121032
$523$	30.6743	1.34129	0.670647	−	0.741777i	$-0.266017\pi$
$523$	30.6743	1.34129	0.670647	+	0.741777i	$0.266017\pi$
$524$	3.50956	0.153316
$525$	4.30720	0.187982
$526$	−20.0362	−0.873621
$527$	7.84501	0.341734
$528$	3.60218	0.156765
$529$	−21.4276	−0.931633
$530$	−14.1445	−0.614397
$531$	−1.84237	−0.0799519
$532$	2.46832	0.107015
$533$	−4.66290	−0.201972
$534$	−16.1365	−0.698296
$535$	−22.2699	−0.962814
$536$	8.25818	0.356699
$537$	25.8412	1.11513
$538$	6.75044	0.291032
$539$	11.8018	0.508339
$540$	9.44274	0.406351
$541$	33.6762	1.44785	0.723927	−	0.689877i	$-0.242335\pi$
$541$	33.6762	1.44785	0.723927	+	0.689877i	$0.242335\pi$
$542$	9.67344	0.415510
$543$	−22.3398	−0.958694
$544$	3.76808	0.161555
$545$	6.12513	0.262372
$546$	13.3023	0.569286
$547$	14.3909	0.615312	0.307656	−	0.951498i	$-0.400455\pi$
$547$	14.3909	0.615312	0.307656	+	0.951498i	$0.400455\pi$
$548$	18.5705	0.793291
$549$	0.574647	0.0245253
$550$	4.55649	0.194289
$551$	−12.7958	−0.545118
$552$	−2.01951	−0.0859563
$553$	2.10406	0.0894737
$554$	27.7165	1.17756
$555$	−26.8099	−1.13802
$556$	−14.0697	−0.596690
$557$	41.5199	1.75925	0.879627	−	0.475665i	$-0.157792\pi$
$557$	41.5199	1.75925	0.879627	+	0.475665i	$0.157792\pi$
$558$	−0.845926	−0.0358109
$559$	40.0446	1.69371
$560$	2.25979	0.0954935
$561$	13.5733	0.573065
$562$	−26.8952	−1.13451
$563$	−9.26976	−0.390674	−0.195337	−	0.980736i	$-0.562580\pi$
$563$	−9.26976	−0.390674	−0.195337	+	0.980736i	$0.562580\pi$
$564$	6.62660	0.279030
$565$	16.3515	0.687914
$566$	−19.8146	−0.832871
$567$	−9.99859	−0.419901
$568$	−11.5169	−0.483239
$569$	16.8087	0.704657	0.352329	−	0.935876i	$-0.385390\pi$
$569$	16.8087	0.704657	0.352329	+	0.935876i	$0.385390\pi$
$570$	−5.21198	−0.218306
$571$	−3.61663	−0.151351	−0.0756757	−	0.997132i	$-0.524111\pi$
$571$	−3.61663	−0.151351	−0.0756757	+	0.997132i	$0.524111\pi$
$572$	14.0722	0.588388
$573$	43.6335	1.82282
$574$	0.973002	0.0406123
$575$	−2.55453	−0.106531
$576$	−0.406311	−0.0169296
$577$	7.41609	0.308736	0.154368	−	0.988013i	$-0.450666\pi$
$577$	7.41609	0.308736	0.154368	+	0.988013i	$0.450666\pi$
$578$	−2.80161	−0.116531
$579$	5.85861	0.243475
$580$	−11.7147	−0.486427
$581$	−3.97421	−0.164878
$582$	28.8179	1.19454
$583$	18.3797	0.761211
$584$	−9.64717	−0.399203
$585$	4.40016	0.181924
$586$	−1.42662	−0.0589330
$587$	−19.5166	−0.805535	−0.402768	−	0.915302i	$-0.631952\pi$
$587$	−19.5166	−0.805535	−0.402768	+	0.915302i	$0.631952\pi$
$588$	8.49768	0.350438
$589$	3.91438	0.161289
$590$	7.80499	0.321326
$591$	1.67885	0.0690587
$592$	9.67122	0.397485
$593$	12.1446	0.498721	0.249360	−	0.968411i	$-0.419780\pi$
$593$	12.1446	0.498721	0.249360	+	0.968411i	$0.419780\pi$
$594$	−12.2702	−0.503451
$595$	8.51505	0.349083
$596$	−17.5392	−0.718432
$597$	−30.6657	−1.25506
$598$	−7.88938	−0.322621
$599$	10.1734	0.415672	0.207836	−	0.978164i	$-0.433358\pi$
$599$	10.1734	0.415672	0.207836	+	0.978164i	$0.433358\pi$
$600$	3.28082	0.133939
$601$	−40.6674	−1.65886	−0.829428	−	0.558613i	$-0.811334\pi$
$601$	−40.6674	−1.65886	−0.829428	+	0.558613i	$0.811334\pi$
$602$	−8.35606	−0.340568
$603$	−3.35539	−0.136642
$604$	2.03570	0.0828316
$605$	−10.3229	−0.419687
$606$	8.98104	0.364830
$607$	22.4411	0.910855	0.455427	−	0.890273i	$-0.349487\pi$
$607$	22.4411	0.910855	0.455427	+	0.890273i	$0.349487\pi$
$608$	1.88014	0.0762495
$609$	14.3896	0.583096
$610$	−2.43443	−0.0985673
$611$	25.8873	1.04729
$612$	−1.53101	−0.0618874
$613$	9.90648	0.400119	0.200059	−	0.979784i	$-0.435886\pi$
$613$	9.90648	0.400119	0.200059	+	0.979784i	$0.435886\pi$
$614$	−4.57436	−0.184606
$615$	−2.05454	−0.0828470
$616$	−2.93643	−0.118312
$617$	−40.7790	−1.64170	−0.820850	−	0.571145i	$-0.806500\pi$
$617$	−40.7790	−1.64170	−0.820850	+	0.571145i	$0.806500\pi$
$618$	20.4888	0.824182
$619$	15.2058	0.611171	0.305585	−	0.952165i	$-0.401148\pi$
$619$	15.2058	0.611171	0.305585	+	0.952165i	$0.401148\pi$
$620$	3.58368	0.143924
$621$	6.87909	0.276049
$622$	29.1413	1.16846
$623$	13.1542	0.527011
$624$	10.1324	0.405622
$625$	−10.6643	−0.426570
$626$	11.5738	0.462581
$627$	6.77259	0.270471
$628$	17.9036	0.714432
$629$	36.4419	1.45303
$630$	−0.918176	−0.0365810
$631$	−3.02684	−0.120497	−0.0602483	−	0.998183i	$-0.519189\pi$
$631$	−3.02684	−0.120497	−0.0602483	+	0.998183i	$0.519189\pi$
$632$	1.60267	0.0637510
$633$	−20.2156	−0.803499
$634$	0.312114	0.0123956
$635$	−38.1832	−1.51525
$636$	13.2340	0.524763
$637$	33.1968	1.31531
$638$	15.2224	0.602661
$639$	4.67945	0.185116
$640$	1.72129	0.0680401
$641$	43.0171	1.69907	0.849536	−	0.527530i	$-0.176882\pi$
$641$	43.0171	1.69907	0.849536	+	0.527530i	$0.176882\pi$
$642$	20.8364	0.822348
$643$	−32.0220	−1.26283	−0.631413	−	0.775447i	$-0.717525\pi$
$643$	−32.0220	−1.26283	−0.631413	+	0.775447i	$0.717525\pi$
$644$	1.64627	0.0648721
$645$	17.6442	0.694741
$646$	7.08449	0.278736
$647$	−16.2573	−0.639142	−0.319571	−	0.947562i	$-0.603539\pi$
$647$	−16.2573	−0.639142	−0.319571	+	0.947562i	$0.603539\pi$
$648$	−7.61598	−0.299184
$649$	−10.1420	−0.398109
$650$	12.8168	0.502715
$651$	−4.40196	−0.172526
$652$	1.73690	0.0680223
$653$	23.7365	0.928879	0.464440	−	0.885605i	$-0.346256\pi$
$653$	23.7365	0.928879	0.464440	+	0.885605i	$0.346256\pi$
$654$	−5.73086	−0.224094
$655$	6.04098	0.236041
$656$	0.741141	0.0289367
$657$	3.91975	0.152924
$658$	−5.40188	−0.210587
$659$	43.9169	1.71076	0.855379	−	0.518002i	$-0.173324\pi$
$659$	43.9169	1.71076	0.855379	+	0.518002i	$0.173324\pi$
$660$	6.20041	0.241351
$661$	50.0703	1.94751	0.973754	−	0.227605i	$-0.0730894\pi$
$661$	50.0703	1.94751	0.973754	+	0.227605i	$0.0730894\pi$
$662$	−16.7185	−0.649783
$663$	38.1798	1.48278
$664$	−3.02718	−0.117477
$665$	4.24871	0.164758
$666$	−3.92952	−0.152266
$667$	−8.53424	−0.330447
$668$	−8.42376	−0.325925
$669$	6.25120	0.241685
$670$	14.2148	0.549164
$671$	3.16337	0.122120
$672$	−2.11433	−0.0815619
$673$	−0.341300	−0.0131561	−0.00657807	−	0.999978i	$-0.502094\pi$
$673$	−0.341300	−0.0131561	−0.00657807	+	0.999978i	$0.502094\pi$
$674$	−9.98203	−0.384493
$675$	−11.1755	−0.430145
$676$	26.5831	1.02243
$677$	8.27673	0.318101	0.159050	−	0.987270i	$-0.449157\pi$
$677$	8.27673	0.318101	0.159050	+	0.987270i	$0.449157\pi$
$678$	−15.2990	−0.587554
$679$	−23.4918	−0.901533
$680$	6.48596	0.248725
$681$	12.7981	0.490423
$682$	−4.65673	−0.178315
$683$	2.36048	0.0903214	0.0451607	−	0.998980i	$-0.485620\pi$
$683$	2.36048	0.0903214	0.0451607	+	0.998980i	$0.485620\pi$
$684$	−0.763919	−0.0292092
$685$	31.9652	1.22133
$686$	−16.1170	−0.615352
$687$	32.7714	1.25031
$688$	−6.36486	−0.242658
$689$	51.6996	1.96960
$690$	−3.47618	−0.132336
$691$	−26.0491	−0.990954	−0.495477	−	0.868621i	$-0.665007\pi$
$691$	−26.0491	−0.990954	−0.495477	+	0.868621i	$0.665007\pi$
$692$	26.0588	0.990608
$693$	1.19310	0.0453222
$694$	31.8055	1.20732
$695$	−24.2181	−0.918646
$696$	10.9606	0.415462
$697$	2.79268	0.105780
$698$	23.2221	0.878968
$699$	−40.4074	−1.52835
$700$	−2.67446	−0.101085
$701$	−10.7036	−0.404270	−0.202135	−	0.979358i	$-0.564788\pi$
$701$	−10.7036	−0.404270	−0.202135	+	0.979358i	$0.564788\pi$
$702$	−34.5142	−1.30266
$703$	18.1832	0.685792
$704$	−2.23670	−0.0842986
$705$	11.4063	0.429587
$706$	−37.2041	−1.40020
$707$	−7.32117	−0.275341
$708$	−7.30259	−0.274448
$709$	30.7148	1.15352	0.576759	−	0.816914i	$-0.304317\pi$
$709$	30.7148	1.15352	0.576759	+	0.816914i	$0.304317\pi$
$710$	−19.8240	−0.743981
$711$	−0.651184	−0.0244213
$712$	10.0196	0.375501
$713$	2.61073	0.0977726
$714$	−7.96694	−0.298155
$715$	24.2224	0.905865
$716$	−16.0455	−0.599650
$717$	−6.29017	−0.234911
$718$	−29.1472	−1.08776
$719$	23.9489	0.893141	0.446571	−	0.894748i	$-0.352645\pi$
$719$	23.9489	0.893141	0.446571	+	0.894748i	$0.352645\pi$
$720$	−0.699380	−0.0260643
$721$	−16.7021	−0.622019
$722$	−15.4651	−0.575551
$723$	15.2561	0.567382
$724$	13.8714	0.515527
$725$	13.8644	0.514910
$726$	9.65844	0.358458
$727$	−31.2029	−1.15725	−0.578625	−	0.815594i	$-0.696411\pi$
$727$	−31.2029	−1.15725	−0.578625	+	0.815594i	$0.696411\pi$
$728$	−8.25977	−0.306127
$729$	29.5992	1.09627
$730$	−16.6056	−0.614601
$731$	−23.9833	−0.887053
$732$	2.27773	0.0841873
$733$	−36.2042	−1.33723	−0.668617	−	0.743607i	$-0.733113\pi$
$733$	−36.2042	−1.33723	−0.668617	+	0.743607i	$0.733113\pi$
$734$	−21.8352	−0.805950
$735$	14.6270	0.539525
$736$	1.25397	0.0462220
$737$	−18.4710	−0.680390
$738$	−0.301134	−0.0110849
$739$	−1.28263	−0.0471822	−0.0235911	−	0.999722i	$-0.507510\pi$
$739$	−1.28263	−0.0471822	−0.0235911	+	0.999722i	$0.507510\pi$
$740$	16.6470	0.611956
$741$	19.0504	0.699832
$742$	−10.7881	−0.396044
$743$	42.5442	1.56079	0.780397	−	0.625284i	$-0.215017\pi$
$743$	42.5442	1.56079	0.780397	+	0.625284i	$0.215017\pi$
$744$	−3.35300	−0.122927
$745$	−30.1900	−1.10608
$746$	8.26328	0.302540
$747$	1.22998	0.0450025
$748$	−8.42804	−0.308160
$749$	−16.9855	−0.620635
$750$	19.5079	0.712328
$751$	−24.7422	−0.902856	−0.451428	−	0.892308i	$-0.649085\pi$
$751$	−24.7422	−0.902856	−0.451428	+	0.892308i	$0.649085\pi$
$752$	−4.11464	−0.150045
$753$	9.99650	0.364293
$754$	42.8185	1.55936
$755$	3.50404	0.127525
$756$	7.20205	0.261936
$757$	1.78535	0.0648895	0.0324447	−	0.999474i	$-0.489671\pi$
$757$	1.78535	0.0648895	0.0324447	+	0.999474i	$0.489671\pi$
$758$	9.20605	0.334379
$759$	4.51704	0.163958
$760$	3.23626	0.117392
$761$	−1.46031	−0.0529361	−0.0264681	−	0.999650i	$-0.508426\pi$
$761$	−1.46031	−0.0529361	−0.0264681	+	0.999650i	$0.508426\pi$
$762$	35.7254	1.29419
$763$	4.67168	0.169126
$764$	−27.0933	−0.980200
$765$	−2.63532	−0.0952800
$766$	6.38408	0.230666
$767$	−28.5281	−1.03009
$768$	−1.61049	−0.0581137
$769$	−23.7739	−0.857309	−0.428655	−	0.903468i	$-0.641012\pi$
$769$	−23.7739	−0.857309	−0.428655	+	0.903468i	$0.641012\pi$
$770$	−5.05446	−0.182150
$771$	20.3662	0.733472
$772$	−3.63777	−0.130926
$773$	−11.7760	−0.423553	−0.211776	−	0.977318i	$-0.567925\pi$
$773$	−11.7760	−0.423553	−0.211776	+	0.977318i	$0.567925\pi$
$774$	2.58611	0.0929558
$775$	−4.24128	−0.152351
$776$	−17.8938	−0.642351
$777$	−20.4481	−0.733572
$778$	12.3086	0.441284
$779$	1.39345	0.0499254
$780$	17.4409	0.624484
$781$	25.7599	0.921760
$782$	4.72506	0.168968
$783$	−37.3353	−1.33426
$784$	−5.27644	−0.188444
$785$	30.8173	1.09992
$786$	−5.65212	−0.201605
$787$	50.5182	1.80078	0.900389	−	0.435085i	$-0.143282\pi$
$787$	50.5182	1.80078	0.900389	+	0.435085i	$0.143282\pi$
$788$	−1.04244	−0.0371356
$789$	32.2682	1.14878
$790$	2.75867	0.0981491
$791$	12.4714	0.443433
$792$	0.908793	0.0322926
$793$	8.89811	0.315981
$794$	21.9763	0.779909
$795$	22.7796	0.807909
$796$	19.0412	0.674896
$797$	4.50051	0.159416	0.0797081	−	0.996818i	$-0.474601\pi$
$797$	4.50051	0.159416	0.0797081	+	0.996818i	$0.474601\pi$
$798$	−3.97522	−0.140721
$799$	−15.5043	−0.548502
$800$	−2.03715	−0.0720242
$801$	−4.07108	−0.143844
$802$	5.21524	0.184157
$803$	21.5778	0.761463
$804$	−13.2998	−0.469046
$805$	2.83371	0.0998752
$806$	−13.0987	−0.461383
$807$	−10.8715	−0.382696
$808$	−5.57658	−0.196183
$809$	−10.3118	−0.362544	−0.181272	−	0.983433i	$-0.558021\pi$
$809$	−10.3118	−0.362544	−0.181272	+	0.983433i	$0.558021\pi$
$810$	−13.1093	−0.460615
$811$	8.06658	0.283256	0.141628	−	0.989920i	$-0.454766\pi$
$811$	8.06658	0.283256	0.141628	+	0.989920i	$0.454766\pi$
$812$	−8.93490	−0.313554
$813$	−15.5790	−0.546380
$814$	−21.6316	−0.758186
$815$	2.98972	0.104725
$816$	−6.06846	−0.212439
$817$	−11.9668	−0.418665
$818$	30.4266	1.06384
$819$	3.35603	0.117269
$820$	1.27572	0.0445501
$821$	6.14672	0.214522	0.107261	−	0.994231i	$-0.465792\pi$
$821$	6.14672	0.214522	0.107261	+	0.994231i	$0.465792\pi$
$822$	−29.9076	−1.04315
$823$	−28.0941	−0.979299	−0.489650	−	0.871919i	$-0.662875\pi$
$823$	−28.0941	−0.979299	−0.489650	+	0.871919i	$0.662875\pi$
$824$	−12.7221	−0.443195
$825$	−7.33819	−0.255483
$826$	5.95293	0.207129
$827$	12.9873	0.451612	0.225806	−	0.974172i	$-0.427499\pi$
$827$	12.9873	0.451612	0.225806	+	0.974172i	$0.427499\pi$
$828$	−0.509502	−0.0177064
$829$	−3.91256	−0.135889	−0.0679444	−	0.997689i	$-0.521644\pi$
$829$	−3.91256	−0.135889	−0.0679444	+	0.997689i	$0.521644\pi$
$830$	−5.21066	−0.180865
$831$	−44.6373	−1.54845
$832$	−6.29151	−0.218119
$833$	−19.8820	−0.688872
$834$	22.6592	0.784625
$835$	−14.4998	−0.501785
$836$	−4.20529	−0.145443
$837$	11.4213	0.394779
$838$	−14.1223	−0.487848
$839$	51.9460	1.79338	0.896688	−	0.442664i	$-0.145966\pi$
$839$	51.9460	1.79338	0.896688	+	0.442664i	$0.145966\pi$
$840$	−3.63937	−0.125570
$841$	17.3184	0.597187
$842$	−29.8086	−1.02727
$843$	43.3146	1.49183
$844$	12.5524	0.432073
$845$	45.7573	1.57410
$846$	1.67182	0.0574784
$847$	−7.87338	−0.270532
$848$	−8.21736	−0.282185
$849$	31.9113	1.09519
$850$	−7.67614	−0.263289
$851$	12.1274	0.415723
$852$	18.5479	0.635442
$853$	−14.7727	−0.505806	−0.252903	−	0.967492i	$-0.581385\pi$
$853$	−14.7727	−0.505806	−0.252903	+	0.967492i	$0.581385\pi$
$854$	−1.85676	−0.0635370
$855$	−1.31493	−0.0449696
$856$	−12.9379	−0.442209
$857$	−0.820091	−0.0280138	−0.0140069	−	0.999902i	$-0.504459\pi$
$857$	−0.820091	−0.0280138	−0.0140069	+	0.999902i	$0.504459\pi$
$858$	−22.6632	−0.773708
$859$	3.15746	0.107731	0.0538656	−	0.998548i	$-0.482846\pi$
$859$	3.15746	0.107731	0.0538656	+	0.998548i	$0.482846\pi$
$860$	−10.9558	−0.373589
$861$	−1.56701	−0.0534037
$862$	−39.2362	−1.33639
$863$	48.8491	1.66284	0.831421	−	0.555643i	$-0.187528\pi$
$863$	48.8491	1.66284	0.831421	+	0.555643i	$0.187528\pi$
$864$	5.48584	0.186632
$865$	44.8549	1.52511
$866$	−7.47957	−0.254166
$867$	4.51197	0.153234
$868$	2.73330	0.0927742
$869$	−3.58469	−0.121602
$870$	18.8665	0.639633
$871$	−51.9565	−1.76048
$872$	3.55845	0.120504
$873$	7.27046	0.246068
$874$	2.35764	0.0797483
$875$	−15.9025	−0.537602
$876$	15.5367	0.524937
$877$	20.6871	0.698555	0.349278	−	0.937019i	$-0.386427\pi$
$877$	20.6871	0.698555	0.349278	+	0.937019i	$0.386427\pi$
$878$	1.20989	0.0408317
$879$	2.29756	0.0774947
$880$	−3.85001	−0.129784
$881$	51.5242	1.73589	0.867947	−	0.496657i	$-0.165439\pi$
$881$	51.5242	1.73589	0.867947	+	0.496657i	$0.165439\pi$
$882$	2.14388	0.0721880
$883$	27.9187	0.939538	0.469769	−	0.882789i	$-0.344337\pi$
$883$	27.9187	0.939538	0.469769	+	0.882789i	$0.344337\pi$
$884$	−23.7069	−0.797349
$885$	−12.5699	−0.422532
$886$	2.23364	0.0750407
$887$	2.76759	0.0929267	0.0464633	−	0.998920i	$-0.485205\pi$
$887$	2.76759	0.0929267	0.0464633	+	0.998920i	$0.485205\pi$
$888$	−15.5754	−0.522677
$889$	−29.1226	−0.976741
$890$	17.2467	0.578110
$891$	17.0346	0.570681
$892$	−3.88154	−0.129964
$893$	−7.73608	−0.258878
$894$	28.2467	0.944711
$895$	−27.6190	−0.923203
$896$	1.31284	0.0438590
$897$	12.7058	0.424234
$898$	−37.4990	−1.25136
$899$	−14.1694	−0.472575
$900$	0.827717	0.0275906
$901$	−30.9636	−1.03155
$902$	−1.65771	−0.0551956
$903$	13.4574	0.447834
$904$	9.49956	0.315951
$905$	23.8768	0.793691
$906$	−3.27849	−0.108920
$907$	2.18716	0.0726233	0.0363117	−	0.999341i	$-0.488439\pi$
$907$	2.18716	0.0726233	0.0363117	+	0.999341i	$0.488439\pi$
$908$	−7.94668	−0.263720
$909$	2.26582	0.0751526
$910$	−14.2175	−0.471305
$911$	−2.33581	−0.0773888	−0.0386944	−	0.999251i	$-0.512320\pi$
$911$	−2.33581	−0.0773888	−0.0386944	+	0.999251i	$0.512320\pi$
$912$	−3.02795	−0.100265
$913$	6.77088	0.224084
$914$	15.6280	0.516927
$915$	3.92064	0.129612
$916$	−20.3486	−0.672338
$917$	4.60750	0.152153
$918$	20.6711	0.682247
$919$	−19.4195	−0.640589	−0.320294	−	0.947318i	$-0.603782\pi$
$919$	−19.4195	−0.640589	−0.320294	+	0.947318i	$0.603782\pi$
$920$	2.15845	0.0711621
$921$	7.36698	0.242750
$922$	−5.33359	−0.175652
$923$	72.4589	2.38501
$924$	4.72910	0.155576
$925$	−19.7017	−0.647789
$926$	8.03022	0.263889
$927$	5.16912	0.169776
$928$	−6.80576	−0.223410
$929$	11.3872	0.373603	0.186802	−	0.982398i	$-0.440188\pi$
$929$	11.3872	0.373603	0.186802	+	0.982398i	$0.440188\pi$
$930$	−5.77149	−0.189255
$931$	−9.92042	−0.325129
$932$	25.0901	0.821853
$933$	−46.9318	−1.53648
$934$	−21.0637	−0.689226
$935$	−14.5071	−0.474434
$936$	2.55631	0.0835556
$937$	39.8464	1.30173	0.650863	−	0.759195i	$-0.274407\pi$
$937$	39.8464	1.30173	0.650863	+	0.759195i	$0.274407\pi$
$938$	10.8417	0.353994
$939$	−18.6395	−0.608277
$940$	−7.08250	−0.231006
$941$	59.4190	1.93700	0.968502	−	0.249005i	$-0.0801037\pi$
$941$	59.4190	1.93700	0.968502	+	0.249005i	$0.0801037\pi$
$942$	−28.8336	−0.939451
$943$	0.929370	0.0302645
$944$	4.53438	0.147581
$945$	12.3968	0.403269
$946$	14.2363	0.462861
$947$	25.4466	0.826902	0.413451	−	0.910526i	$-0.364323\pi$
$947$	25.4466	0.826902	0.413451	+	0.910526i	$0.364323\pi$
$948$	−2.58110	−0.0838301
$949$	60.6953	1.97025
$950$	−3.83012	−0.124266
$951$	−0.502658	−0.0162998
$952$	4.94689	0.160330
$953$	−25.2347	−0.817432	−0.408716	−	0.912662i	$-0.634023\pi$
$953$	−25.2347	−0.817432	−0.408716	+	0.912662i	$0.634023\pi$
$954$	3.33880	0.108098
$955$	−46.6354	−1.50909
$956$	3.90574	0.126321
$957$	−24.5156	−0.792477
$958$	−1.11120	−0.0359011
$959$	24.3801	0.787275
$960$	−2.77213	−0.0894701
$961$	−26.6654	−0.860174
$962$	−60.8466	−1.96177
$963$	5.25681	0.169398
$964$	−9.47296	−0.305103
$965$	−6.26167	−0.201570
$966$	−2.65131	−0.0853044
$967$	13.5302	0.435101	0.217550	−	0.976049i	$-0.430193\pi$
$967$	13.5302	0.435101	0.217550	+	0.976049i	$0.430193\pi$
$968$	−5.99719	−0.192757
$969$	−11.4095	−0.366527
$970$	−30.8005	−0.988945
$971$	−33.4522	−1.07353	−0.536766	−	0.843731i	$-0.680354\pi$
$971$	−33.4522	−1.07353	−0.536766	+	0.843731i	$0.680354\pi$
$972$	−4.19204	−0.134460
$973$	−18.4714	−0.592165
$974$	−27.7527	−0.889255
$975$	−20.6413	−0.661051
$976$	−1.41430	−0.0452708
$977$	47.4627	1.51847	0.759233	−	0.650819i	$-0.225575\pi$
$977$	47.4627	1.51847	0.759233	+	0.650819i	$0.225575\pi$
$978$	−2.79727	−0.0894468
$979$	−22.4108	−0.716253
$980$	−9.08230	−0.290123
$981$	−1.44583	−0.0461620
$982$	35.2482	1.12482
$983$	33.9408	1.08254	0.541272	−	0.840848i	$-0.317943\pi$
$983$	33.9408	1.08254	0.541272	+	0.840848i	$0.317943\pi$
$984$	−1.19360	−0.0380507
$985$	−1.79435	−0.0571728
$986$	−25.6446	−0.816692
$987$	8.69969	0.276914
$988$	−11.8289	−0.376327
$989$	−7.98136	−0.253792
$990$	1.56430	0.0497167
$991$	25.4683	0.809026	0.404513	−	0.914532i	$-0.367441\pi$
$991$	25.4683	0.809026	0.404513	+	0.914532i	$0.367441\pi$
$992$	2.08197	0.0661026
$993$	26.9250	0.854440
$994$	−15.1199	−0.479575
$995$	32.7754	1.03905
$996$	4.87526	0.154478
$997$	−34.6545	−1.09752	−0.548760	−	0.835980i	$-0.684900\pi$
$997$	−34.6545	−1.09752	−0.548760	+	0.835980i	$0.684900\pi$
$998$	−10.8011	−0.341904
$999$	53.0548	1.67858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.b.1.18	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.b.1.18	✓	54	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.61049 q^{3} +1.00000 q^{4} +1.72129 q^{5} -1.61049 q^{6} +1.31284 q^{7} +1.00000 q^{8} -0.406311 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.61049 q^{3} +1.00000 q^{4} +1.72129 q^{5} -1.61049 q^{6} +1.31284 q^{7} +1.00000 q^{8} -0.406311 q^{9} +1.72129 q^{10} -2.23670 q^{11} -1.61049 q^{12} -6.29151 q^{13} +1.31284 q^{14} -2.77213 q^{15} +1.00000 q^{16} +3.76808 q^{17} -0.406311 q^{18} +1.88014 q^{19} +1.72129 q^{20} -2.11433 q^{21} -2.23670 q^{22} +1.25397 q^{23} -1.61049 q^{24} -2.03715 q^{25} -6.29151 q^{26} +5.48584 q^{27} +1.31284 q^{28} -6.80576 q^{29} -2.77213 q^{30} +2.08197 q^{31} +1.00000 q^{32} +3.60218 q^{33} +3.76808 q^{34} +2.25979 q^{35} -0.406311 q^{36} +9.67122 q^{37} +1.88014 q^{38} +10.1324 q^{39} +1.72129 q^{40} +0.741141 q^{41} -2.11433 q^{42} -6.36486 q^{43} -2.23670 q^{44} -0.699380 q^{45} +1.25397 q^{46} -4.11464 q^{47} -1.61049 q^{48} -5.27644 q^{49} -2.03715 q^{50} -6.06846 q^{51} -6.29151 q^{52} -8.21736 q^{53} +5.48584 q^{54} -3.85001 q^{55} +1.31284 q^{56} -3.02795 q^{57} -6.80576 q^{58} +4.53438 q^{59} -2.77213 q^{60} -1.41430 q^{61} +2.08197 q^{62} -0.533422 q^{63} +1.00000 q^{64} -10.8295 q^{65} +3.60218 q^{66} +8.25818 q^{67} +3.76808 q^{68} -2.01951 q^{69} +2.25979 q^{70} -11.5169 q^{71} -0.406311 q^{72} -9.64717 q^{73} +9.67122 q^{74} +3.28082 q^{75} +1.88014 q^{76} -2.93643 q^{77} +10.1324 q^{78} +1.60267 q^{79} +1.72129 q^{80} -7.61598 q^{81} +0.741141 q^{82} -3.02718 q^{83} -2.11433 q^{84} +6.48596 q^{85} -6.36486 q^{86} +10.9606 q^{87} -2.23670 q^{88} +10.0196 q^{89} -0.699380 q^{90} -8.25977 q^{91} +1.25397 q^{92} -3.35300 q^{93} -4.11464 q^{94} +3.23626 q^{95} -1.61049 q^{96} -17.8938 q^{97} -5.27644 q^{98} +0.908793 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * q^99

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