LMFDB - Embedded newform 5054.2.a.bf.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.19520000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 $ x^8 - 2x^7 - 12x^6 + 16x^5 + 50x^4 - 24x^3 - 72x^2 - 32*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.761439$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.13415 q^{3} +1.00000 q^{4} -1.04552 q^{5} -2.13415 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.55458 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.13415 q^{3} +1.00000 q^{4} -1.04552 q^{5} -2.13415 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.55458 q^{9} +1.04552 q^{10} -2.42021 q^{11} +2.13415 q^{12} +1.15517 q^{13} +1.00000 q^{14} -2.23129 q^{15} +1.00000 q^{16} +3.05251 q^{17} -1.55458 q^{18} -1.04552 q^{20} -2.13415 q^{21} +2.42021 q^{22} -0.514528 q^{23} -2.13415 q^{24} -3.90689 q^{25} -1.15517 q^{26} -3.08473 q^{27} -1.00000 q^{28} +5.57522 q^{29} +2.23129 q^{30} +2.17892 q^{31} -1.00000 q^{32} -5.16509 q^{33} -3.05251 q^{34} +1.04552 q^{35} +1.55458 q^{36} -1.13825 q^{37} +2.46531 q^{39} +1.04552 q^{40} +1.73850 q^{41} +2.13415 q^{42} -6.37863 q^{43} -2.42021 q^{44} -1.62534 q^{45} +0.514528 q^{46} -0.273517 q^{47} +2.13415 q^{48} +1.00000 q^{49} +3.90689 q^{50} +6.51450 q^{51} +1.15517 q^{52} -6.18481 q^{53} +3.08473 q^{54} +2.53037 q^{55} +1.00000 q^{56} -5.57522 q^{58} -10.2131 q^{59} -2.23129 q^{60} -9.38737 q^{61} -2.17892 q^{62} -1.55458 q^{63} +1.00000 q^{64} -1.20775 q^{65} +5.16509 q^{66} +4.12745 q^{67} +3.05251 q^{68} -1.09808 q^{69} -1.04552 q^{70} -11.0844 q^{71} -1.55458 q^{72} -1.05367 q^{73} +1.13825 q^{74} -8.33788 q^{75} +2.42021 q^{77} -2.46531 q^{78} +13.4572 q^{79} -1.04552 q^{80} -11.2470 q^{81} -1.73850 q^{82} +15.1827 q^{83} -2.13415 q^{84} -3.19145 q^{85} +6.37863 q^{86} +11.8983 q^{87} +2.42021 q^{88} +9.44592 q^{89} +1.62534 q^{90} -1.15517 q^{91} -0.514528 q^{92} +4.65013 q^{93} +0.273517 q^{94} -2.13415 q^{96} -12.6176 q^{97} -1.00000 q^{98} -3.76242 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} - 6 q^{13} + 8 q^{14} - 8 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} + 6 q^{20} + 4 q^{21} - 4 q^{22} + 20 q^{23} + 4 q^{24} - 8 q^{25} + 6 q^{26} - 22 q^{27} - 8 q^{28} - 16 q^{29} + 8 q^{30} - 22 q^{31} - 8 q^{32} + 8 q^{33} - 2 q^{34} - 6 q^{35} + 8 q^{36} + 12 q^{37} + 8 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{42} + 4 q^{44} - 4 q^{45} - 20 q^{46} + 6 q^{47} - 4 q^{48} + 8 q^{49} + 8 q^{50} + 4 q^{51} - 6 q^{52} - 16 q^{53} + 22 q^{54} + 18 q^{55} + 8 q^{56} + 16 q^{58} - 14 q^{59} - 8 q^{60} + 10 q^{61} + 22 q^{62} - 8 q^{63} + 8 q^{64} - 32 q^{65} - 8 q^{66} + 20 q^{67} + 2 q^{68} - 40 q^{69} + 6 q^{70} - 8 q^{72} - 18 q^{73} - 12 q^{74} - 16 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{79} + 6 q^{80} + 12 q^{81} + 36 q^{82} + 36 q^{83} + 4 q^{84} - 16 q^{85} + 28 q^{87} - 4 q^{88} - 18 q^{89} + 4 q^{90} + 6 q^{91} + 20 q^{92} + 16 q^{93} - 6 q^{94} + 4 q^{96} - 26 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9 - 6 * q^10 + 4 * q^11 - 4 * q^12 - 6 * q^13 + 8 * q^14 - 8 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 + 6 * q^20 + 4 * q^21 - 4 * q^22 + 20 * q^23 + 4 * q^24 - 8 * q^25 + 6 * q^26 - 22 * q^27 - 8 * q^28 - 16 * q^29 + 8 * q^30 - 22 * q^31 - 8 * q^32 + 8 * q^33 - 2 * q^34 - 6 * q^35 + 8 * q^36 + 12 * q^37 + 8 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^42 + 4 * q^44 - 4 * q^45 - 20 * q^46 + 6 * q^47 - 4 * q^48 + 8 * q^49 + 8 * q^50 + 4 * q^51 - 6 * q^52 - 16 * q^53 + 22 * q^54 + 18 * q^55 + 8 * q^56 + 16 * q^58 - 14 * q^59 - 8 * q^60 + 10 * q^61 + 22 * q^62 - 8 * q^63 + 8 * q^64 - 32 * q^65 - 8 * q^66 + 20 * q^67 + 2 * q^68 - 40 * q^69 + 6 * q^70 - 8 * q^72 - 18 * q^73 - 12 * q^74 - 16 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^79 + 6 * q^80 + 12 * q^81 + 36 * q^82 + 36 * q^83 + 4 * q^84 - 16 * q^85 + 28 * q^87 - 4 * q^88 - 18 * q^89 + 4 * q^90 + 6 * q^91 + 20 * q^92 + 16 * q^93 - 6 * q^94 + 4 * q^96 - 26 * q^97 - 8 * q^98 + 4 * 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
$3$	2.13415	1.23215	0.616075	−	0.787687i	$-0.288722\pi$
$3$	2.13415	1.23215	0.616075	+	0.787687i	$0.288722\pi$
$4$	1.00000	0.500000
$5$	−1.04552	−0.467570	−0.233785	−	0.972288i	$-0.575111\pi$
$5$	−1.04552	−0.467570	−0.233785	+	0.972288i	$0.575111\pi$
$6$	−2.13415	−0.871262
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.55458	0.518194
$10$	1.04552	0.330622
$11$	−2.42021	−0.729721	−0.364861	−	0.931062i	$-0.618883\pi$
$11$	−2.42021	−0.729721	−0.364861	+	0.931062i	$0.618883\pi$
$12$	2.13415	0.616075
$13$	1.15517	0.320387	0.160194	−	0.987086i	$-0.448788\pi$
$13$	1.15517	0.320387	0.160194	+	0.987086i	$0.448788\pi$
$14$	1.00000	0.267261
$15$	−2.23129	−0.576116
$16$	1.00000	0.250000
$17$	3.05251	0.740341	0.370171	−	0.928964i	$-0.379299\pi$
$17$	3.05251	0.740341	0.370171	+	0.928964i	$0.379299\pi$
$18$	−1.55458	−0.366419
$19$	0	0
$19$	0	0
$20$	−1.04552	−0.233785
$21$	−2.13415	−0.465709
$22$	2.42021	0.515991
$23$	−0.514528	−0.107287	−0.0536433	−	0.998560i	$-0.517083\pi$
$23$	−0.514528	−0.107287	−0.0536433	+	0.998560i	$0.517083\pi$
$24$	−2.13415	−0.435631
$25$	−3.90689	−0.781379
$26$	−1.15517	−0.226548
$27$	−3.08473	−0.593657
$28$	−1.00000	−0.188982
$29$	5.57522	1.03529	0.517646	−	0.855595i	$-0.326808\pi$
$29$	5.57522	1.03529	0.517646	+	0.855595i	$0.326808\pi$
$30$	2.23129	0.407376
$31$	2.17892	0.391345	0.195673	−	0.980669i	$-0.437311\pi$
$31$	2.17892	0.391345	0.195673	+	0.980669i	$0.437311\pi$
$32$	−1.00000	−0.176777
$33$	−5.16509	−0.899126
$34$	−3.05251	−0.523500
$35$	1.04552	0.176725
$36$	1.55458	0.259097
$37$	−1.13825	−0.187127	−0.0935633	−	0.995613i	$-0.529826\pi$
$37$	−1.13825	−0.187127	−0.0935633	+	0.995613i	$0.529826\pi$
$38$	0	0
$39$	2.46531	0.394765
$40$	1.04552	0.165311
$41$	1.73850	0.271508	0.135754	−	0.990743i	$-0.456654\pi$
$41$	1.73850	0.271508	0.135754	+	0.990743i	$0.456654\pi$
$42$	2.13415	0.329306
$43$	−6.37863	−0.972732	−0.486366	−	0.873755i	$-0.661678\pi$
$43$	−6.37863	−0.972732	−0.486366	+	0.873755i	$0.661678\pi$
$44$	−2.42021	−0.364861
$45$	−1.62534	−0.242292
$46$	0.514528	0.0758631
$47$	−0.273517	−0.0398966	−0.0199483	−	0.999801i	$-0.506350\pi$
$47$	−0.273517	−0.0398966	−0.0199483	+	0.999801i	$0.506350\pi$
$48$	2.13415	0.308038
$49$	1.00000	0.142857
$50$	3.90689	0.552518
$51$	6.51450	0.912212
$52$	1.15517	0.160194
$53$	−6.18481	−0.849549	−0.424774	−	0.905299i	$-0.639647\pi$
$53$	−6.18481	−0.849549	−0.424774	+	0.905299i	$0.639647\pi$
$54$	3.08473	0.419779
$55$	2.53037	0.341196
$56$	1.00000	0.133631
$57$	0	0
$58$	−5.57522	−0.732062
$59$	−10.2131	−1.32964	−0.664818	−	0.747005i	$-0.731491\pi$
$59$	−10.2131	−1.32964	−0.664818	+	0.747005i	$0.731491\pi$
$60$	−2.23129	−0.288058
$61$	−9.38737	−1.20193	−0.600965	−	0.799275i	$-0.705217\pi$
$61$	−9.38737	−1.20193	−0.600965	+	0.799275i	$0.705217\pi$
$62$	−2.17892	−0.276723
$63$	−1.55458	−0.195859
$64$	1.00000	0.125000
$65$	−1.20775	−0.149803
$66$	5.16509	0.635778
$67$	4.12745	0.504249	0.252124	−	0.967695i	$-0.418871\pi$
$67$	4.12745	0.504249	0.252124	+	0.967695i	$0.418871\pi$
$68$	3.05251	0.370171
$69$	−1.09808	−0.132193
$70$	−1.04552	−0.124963
$71$	−11.0844	−1.31547	−0.657737	−	0.753248i	$-0.728486\pi$
$71$	−11.0844	−1.31547	−0.657737	+	0.753248i	$0.728486\pi$
$72$	−1.55458	−0.183209
$73$	−1.05367	−0.123323	−0.0616615	−	0.998097i	$-0.519640\pi$
$73$	−1.05367	−0.123323	−0.0616615	+	0.998097i	$0.519640\pi$
$74$	1.13825	0.132318
$75$	−8.33788	−0.962776
$76$	0	0
$77$	2.42021	0.275809
$78$	−2.46531	−0.279141
$79$	13.4572	1.51406	0.757029	−	0.653381i	$-0.226650\pi$
$79$	13.4572	1.51406	0.757029	+	0.653381i	$0.226650\pi$
$80$	−1.04552	−0.116892
$81$	−11.2470	−1.24967
$82$	−1.73850	−0.191985
$83$	15.1827	1.66652	0.833261	−	0.552880i	$-0.186471\pi$
$83$	15.1827	1.66652	0.833261	+	0.552880i	$0.186471\pi$
$84$	−2.13415	−0.232855
$85$	−3.19145	−0.346161
$86$	6.37863	0.687825
$87$	11.8983	1.27563
$88$	2.42021	0.257995
$89$	9.44592	1.00127	0.500633	−	0.865660i	$-0.333101\pi$
$89$	9.44592	1.00127	0.500633	+	0.865660i	$0.333101\pi$
$90$	1.62534	0.171326
$91$	−1.15517	−0.121095
$92$	−0.514528	−0.0536433
$93$	4.65013	0.482196
$94$	0.273517	0.0282112
$95$	0	0
$96$	−2.13415	−0.217815
$97$	−12.6176	−1.28112	−0.640559	−	0.767909i	$-0.721297\pi$
$97$	−12.6176	−1.28112	−0.640559	+	0.767909i	$0.721297\pi$
$98$	−1.00000	−0.101015
$99$	−3.76242	−0.378137
$100$	−3.90689	−0.390689
$101$	−1.49415	−0.148673	−0.0743366	−	0.997233i	$-0.523684\pi$
$101$	−1.49415	−0.148673	−0.0743366	+	0.997233i	$0.523684\pi$
$102$	−6.51450	−0.645031
$103$	−19.3707	−1.90865	−0.954325	−	0.298772i	$-0.903423\pi$
$103$	−19.3707	−1.90865	−0.954325	+	0.298772i	$0.903423\pi$
$104$	−1.15517	−0.113274
$105$	2.23129	0.217751
$106$	6.18481	0.600722
$107$	−8.80175	−0.850897	−0.425449	−	0.904983i	$-0.639884\pi$
$107$	−8.80175	−0.850897	−0.425449	+	0.904983i	$0.639884\pi$
$108$	−3.08473	−0.296829
$109$	−16.6094	−1.59089	−0.795447	−	0.606023i	$-0.792764\pi$
$109$	−16.6094	−1.59089	−0.795447	+	0.606023i	$0.792764\pi$
$110$	−2.53037	−0.241262
$111$	−2.42919	−0.230568
$112$	−1.00000	−0.0944911
$113$	6.81605	0.641200	0.320600	−	0.947215i	$-0.396115\pi$
$113$	6.81605	0.641200	0.320600	+	0.947215i	$0.396115\pi$
$114$	0	0
$115$	0.537949	0.0501640
$116$	5.57522	0.517646
$117$	1.79581	0.166023
$118$	10.2131	0.940195
$119$	−3.05251	−0.279823
$120$	2.23129	0.203688
$121$	−5.14258	−0.467507
$122$	9.38737	0.849893
$123$	3.71022	0.334539
$124$	2.17892	0.195673
$125$	9.31231	0.832919
$126$	1.55458	0.138493
$127$	2.87127	0.254784	0.127392	−	0.991852i	$-0.459339\pi$
$127$	2.87127	0.254784	0.127392	+	0.991852i	$0.459339\pi$
$128$	−1.00000	−0.0883883
$129$	−13.6129	−1.19855
$130$	1.20775	0.105927
$131$	3.59135	0.313778	0.156889	−	0.987616i	$-0.449854\pi$
$131$	3.59135	0.313778	0.156889	+	0.987616i	$0.449854\pi$
$132$	−5.16509	−0.449563
$133$	0	0
$134$	−4.12745	−0.356558
$135$	3.22514	0.277576
$136$	−3.05251	−0.261750
$137$	−3.24610	−0.277333	−0.138666	−	0.990339i	$-0.544282\pi$
$137$	−3.24610	−0.277333	−0.138666	+	0.990339i	$0.544282\pi$
$138$	1.09808	0.0934747
$139$	6.21267	0.526951	0.263476	−	0.964666i	$-0.415131\pi$
$139$	6.21267	0.526951	0.263476	+	0.964666i	$0.415131\pi$
$140$	1.04552	0.0883624
$141$	−0.583726	−0.0491586
$142$	11.0844	0.930181
$143$	−2.79576	−0.233793
$144$	1.55458	0.129549
$145$	−5.82899	−0.484071
$146$	1.05367	0.0872026
$147$	2.13415	0.176021
$148$	−1.13825	−0.0935633
$149$	−15.3029	−1.25366	−0.626831	−	0.779155i	$-0.715648\pi$
$149$	−15.3029	−1.25366	−0.626831	+	0.779155i	$0.715648\pi$
$150$	8.33788	0.680785
$151$	−8.44026	−0.686859	−0.343429	−	0.939179i	$-0.611589\pi$
$151$	−8.44026	−0.686859	−0.343429	+	0.939179i	$0.611589\pi$
$152$	0	0
$153$	4.74537	0.383641
$154$	−2.42021	−0.195026
$155$	−2.27810	−0.182981
$156$	2.46531	0.197383
$157$	−1.70931	−0.136418	−0.0682089	−	0.997671i	$-0.521728\pi$
$157$	−1.70931	−0.136418	−0.0682089	+	0.997671i	$0.521728\pi$
$158$	−13.4572	−1.07060
$159$	−13.1993	−1.04677
$160$	1.04552	0.0826554
$161$	0.514528	0.0405505
$162$	11.2470	0.883649
$163$	19.0388	1.49123	0.745616	−	0.666376i	$-0.232155\pi$
$163$	19.0388	1.49123	0.745616	+	0.666376i	$0.232155\pi$
$164$	1.73850	0.135754
$165$	5.40019	0.420404
$166$	−15.1827	−1.17841
$167$	−7.85185	−0.607594	−0.303797	−	0.952737i	$-0.598255\pi$
$167$	−7.85185	−0.607594	−0.303797	+	0.952737i	$0.598255\pi$
$168$	2.13415	0.164653
$169$	−11.6656	−0.897352
$170$	3.19145	0.244773
$171$	0	0
$172$	−6.37863	−0.486366
$173$	−8.12917	−0.618049	−0.309025	−	0.951054i	$-0.600003\pi$
$173$	−8.12917	−0.618049	−0.309025	+	0.951054i	$0.600003\pi$
$174$	−11.8983	−0.902010
$175$	3.90689	0.295333
$176$	−2.42021	−0.182430
$177$	−21.7963	−1.63831
$178$	−9.44592	−0.708002
$179$	−14.2499	−1.06509	−0.532544	−	0.846402i	$-0.678764\pi$
$179$	−14.2499	−1.06509	−0.532544	+	0.846402i	$0.678764\pi$
$180$	−1.62534	−0.121146
$181$	−16.9244	−1.25798	−0.628992	−	0.777412i	$-0.716532\pi$
$181$	−16.9244	−1.25798	−0.628992	+	0.777412i	$0.716532\pi$
$182$	1.15517	0.0856271
$183$	−20.0340	−1.48096
$184$	0.514528	0.0379315
$185$	1.19006	0.0874947
$186$	−4.65013	−0.340964
$187$	−7.38771	−0.540243
$188$	−0.273517	−0.0199483
$189$	3.08473	0.224381
$190$	0	0
$191$	−13.4517	−0.973328	−0.486664	−	0.873589i	$-0.661786\pi$
$191$	−13.4517	−0.973328	−0.486664	+	0.873589i	$0.661786\pi$
$192$	2.13415	0.154019
$193$	−23.6578	−1.70293	−0.851463	−	0.524415i	$-0.824284\pi$
$193$	−23.6578	−1.70293	−0.851463	+	0.524415i	$0.824284\pi$
$194$	12.6176	0.905888
$195$	−2.57752	−0.184580
$196$	1.00000	0.0714286
$197$	16.5603	1.17988	0.589938	−	0.807449i	$-0.299152\pi$
$197$	16.5603	1.17988	0.589938	+	0.807449i	$0.299152\pi$
$198$	3.76242	0.267383
$199$	7.68305	0.544637	0.272318	−	0.962207i	$-0.412210\pi$
$199$	7.68305	0.544637	0.272318	+	0.962207i	$0.412210\pi$
$200$	3.90689	0.276259
$201$	8.80859	0.621310
$202$	1.49415	0.105128
$203$	−5.57522	−0.391303
$204$	6.51450	0.456106
$205$	−1.81763	−0.126949
$206$	19.3707	1.34962
$207$	−0.799877	−0.0555953
$208$	1.15517	0.0800968
$209$	0	0
$210$	−2.23129	−0.153974
$211$	−19.3109	−1.32942	−0.664708	−	0.747104i	$-0.731444\pi$
$211$	−19.3109	−1.32942	−0.664708	+	0.747104i	$0.731444\pi$
$212$	−6.18481	−0.424774
$213$	−23.6557	−1.62086
$214$	8.80175	0.601675
$215$	6.66897	0.454820
$216$	3.08473	0.209889
$217$	−2.17892	−0.147915
$218$	16.6094	1.12493
$219$	−2.24869	−0.151953
$220$	2.53037	0.170598
$221$	3.52617	0.237196
$222$	2.42919	0.163036
$223$	9.51413	0.637113	0.318557	−	0.947904i	$-0.396802\pi$
$223$	9.51413	0.637113	0.318557	+	0.947904i	$0.396802\pi$
$224$	1.00000	0.0668153
$225$	−6.07359	−0.404906
$226$	−6.81605	−0.453397
$227$	25.2920	1.67869	0.839343	−	0.543602i	$-0.182940\pi$
$227$	25.2920	1.67869	0.839343	+	0.543602i	$0.182940\pi$
$228$	0	0
$229$	21.2960	1.40728	0.703639	−	0.710558i	$-0.251557\pi$
$229$	21.2960	1.40728	0.703639	+	0.710558i	$0.251557\pi$
$230$	−0.537949	−0.0354713
$231$	5.16509	0.339838
$232$	−5.57522	−0.366031
$233$	−12.7292	−0.833915	−0.416958	−	0.908926i	$-0.636904\pi$
$233$	−12.7292	−0.833915	−0.416958	+	0.908926i	$0.636904\pi$
$234$	−1.79581	−0.117396
$235$	0.285967	0.0186544
$236$	−10.2131	−0.664818
$237$	28.7197	1.86555
$238$	3.05251	0.197865
$239$	7.53887	0.487649	0.243824	−	0.969819i	$-0.421598\pi$
$239$	7.53887	0.487649	0.243824	+	0.969819i	$0.421598\pi$
$240$	−2.23129	−0.144029
$241$	−24.0728	−1.55067	−0.775333	−	0.631552i	$-0.782418\pi$
$241$	−24.0728	−1.55067	−0.775333	+	0.631552i	$0.782418\pi$
$242$	5.14258	0.330577
$243$	−14.7486	−0.946123
$244$	−9.38737	−0.600965
$245$	−1.04552	−0.0667957
$246$	−3.71022	−0.236555
$247$	0	0
$248$	−2.17892	−0.138362
$249$	32.4022	2.05341
$250$	−9.31231	−0.588962
$251$	0.365805	0.0230894	0.0115447	−	0.999933i	$-0.496325\pi$
$251$	0.365805	0.0230894	0.0115447	+	0.999933i	$0.496325\pi$
$252$	−1.55458	−0.0979295
$253$	1.24527	0.0782893
$254$	−2.87127	−0.180160
$255$	−6.81102	−0.426523
$256$	1.00000	0.0625000
$257$	−8.33390	−0.519855	−0.259927	−	0.965628i	$-0.583699\pi$
$257$	−8.33390	−0.519855	−0.259927	+	0.965628i	$0.583699\pi$
$258$	13.6129	0.847504
$259$	1.13825	0.0707272
$260$	−1.20775	−0.0749017
$261$	8.66713	0.536482
$262$	−3.59135	−0.221874
$263$	−22.5679	−1.39160	−0.695799	−	0.718237i	$-0.744950\pi$
$263$	−22.5679	−1.39160	−0.695799	+	0.718237i	$0.744950\pi$
$264$	5.16509	0.317889
$265$	6.46633	0.397223
$266$	0	0
$267$	20.1590	1.23371
$268$	4.12745	0.252124
$269$	−20.4358	−1.24599	−0.622996	−	0.782225i	$-0.714085\pi$
$269$	−20.4358	−1.24599	−0.622996	+	0.782225i	$0.714085\pi$
$270$	−3.22514	−0.196276
$271$	17.2844	1.04995	0.524976	−	0.851117i	$-0.324074\pi$
$271$	17.2844	1.04995	0.524976	+	0.851117i	$0.324074\pi$
$272$	3.05251	0.185085
$273$	−2.46531	−0.149207
$274$	3.24610	0.196104
$275$	9.45550	0.570188
$276$	−1.09808	−0.0660966
$277$	−21.1338	−1.26981	−0.634904	−	0.772591i	$-0.718960\pi$
$277$	−21.1338	−1.26981	−0.634904	+	0.772591i	$0.718960\pi$
$278$	−6.21267	−0.372611
$279$	3.38731	0.202793
$280$	−1.04552	−0.0624816
$281$	19.0891	1.13876	0.569380	−	0.822074i	$-0.307183\pi$
$281$	19.0891	1.13876	0.569380	+	0.822074i	$0.307183\pi$
$282$	0.583726	0.0347604
$283$	−21.5165	−1.27902	−0.639512	−	0.768781i	$-0.720864\pi$
$283$	−21.5165	−1.27902	−0.639512	+	0.768781i	$0.720864\pi$
$284$	−11.0844	−0.657737
$285$	0	0
$286$	2.79576	0.165317
$287$	−1.73850	−0.102620
$288$	−1.55458	−0.0916047
$289$	−7.68221	−0.451895
$290$	5.82899	0.342290
$291$	−26.9277	−1.57853
$292$	−1.05367	−0.0616615
$293$	11.3698	0.664231	0.332116	−	0.943239i	$-0.392238\pi$
$293$	11.3698	0.664231	0.332116	+	0.943239i	$0.392238\pi$
$294$	−2.13415	−0.124466
$295$	10.6780	0.621698
$296$	1.13825	0.0661592
$297$	7.46570	0.433204
$298$	15.3029	0.886473
$299$	−0.594369	−0.0343732
$300$	−8.33788	−0.481388
$301$	6.37863	0.367658
$302$	8.44026	0.485682
$303$	−3.18873	−0.183188
$304$	0	0
$305$	9.81466	0.561986
$306$	−4.74537	−0.271275
$307$	9.12185	0.520612	0.260306	−	0.965526i	$-0.416177\pi$
$307$	9.12185	0.520612	0.260306	+	0.965526i	$0.416177\pi$
$308$	2.42021	0.137904
$309$	−41.3399	−2.35174
$310$	2.27810	0.129387
$311$	17.3492	0.983782	0.491891	−	0.870657i	$-0.336306\pi$
$311$	17.3492	0.983782	0.491891	+	0.870657i	$0.336306\pi$
$312$	−2.46531	−0.139571
$313$	−2.42580	−0.137114	−0.0685571	−	0.997647i	$-0.521840\pi$
$313$	−2.42580	−0.137114	−0.0685571	+	0.997647i	$0.521840\pi$
$314$	1.70931	0.0964619
$315$	1.62534	0.0915777
$316$	13.4572	0.757029
$317$	8.88675	0.499130	0.249565	−	0.968358i	$-0.419712\pi$
$317$	8.88675	0.499130	0.249565	+	0.968358i	$0.419712\pi$
$318$	13.1993	0.740179
$319$	−13.4932	−0.755474
$320$	−1.04552	−0.0584462
$321$	−18.7842	−1.04843
$322$	−0.514528	−0.0286735
$323$	0	0
$324$	−11.2470	−0.624834
$325$	−4.51313	−0.250344
$326$	−19.0388	−1.05446
$327$	−35.4469	−1.96022
$328$	−1.73850	−0.0959927
$329$	0.273517	0.0150795
$330$	−5.40019	−0.297271
$331$	−19.5033	−1.07200	−0.536000	−	0.844218i	$-0.680065\pi$
$331$	−19.5033	−1.07200	−0.536000	+	0.844218i	$0.680065\pi$
$332$	15.1827	0.833261
$333$	−1.76950	−0.0969679
$334$	7.85185	0.429634
$335$	−4.31533	−0.235771
$336$	−2.13415	−0.116427
$337$	5.72554	0.311890	0.155945	−	0.987766i	$-0.450158\pi$
$337$	5.72554	0.311890	0.155945	+	0.987766i	$0.450158\pi$
$338$	11.6656	0.634524
$339$	14.5465	0.790055
$340$	−3.19145	−0.173081
$341$	−5.27344	−0.285573
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	6.37863	0.343913
$345$	1.14806	0.0618095
$346$	8.12917	0.437027
$347$	34.0907	1.83009	0.915044	−	0.403355i	$-0.132156\pi$
$347$	34.0907	1.83009	0.915044	+	0.403355i	$0.132156\pi$
$348$	11.8983	0.637817
$349$	31.1329	1.66651	0.833253	−	0.552892i	$-0.186476\pi$
$349$	31.1329	1.66651	0.833253	+	0.552892i	$0.186476\pi$
$350$	−3.90689	−0.208832
$351$	−3.56340	−0.190200
$352$	2.42021	0.128998
$353$	7.00294	0.372729	0.186364	−	0.982481i	$-0.440330\pi$
$353$	7.00294	0.372729	0.186364	+	0.982481i	$0.440330\pi$
$354$	21.7963	1.15846
$355$	11.5889	0.615076
$356$	9.44592	0.500633
$357$	−6.51450	−0.344784
$358$	14.2499	0.753131
$359$	1.04073	0.0549274	0.0274637	−	0.999623i	$-0.491257\pi$
$359$	1.04073	0.0549274	0.0274637	+	0.999623i	$0.491257\pi$
$360$	1.62534	0.0856631
$361$	0	0
$362$	16.9244	0.889529
$363$	−10.9750	−0.576039
$364$	−1.15517	−0.0605475
$365$	1.10163	0.0576621
$366$	20.0340	1.04720
$367$	−2.88851	−0.150779	−0.0753896	−	0.997154i	$-0.524020\pi$
$367$	−2.88851	−0.150779	−0.0753896	+	0.997154i	$0.524020\pi$
$368$	−0.514528	−0.0268216
$369$	2.70264	0.140694
$370$	−1.19006	−0.0618681
$371$	6.18481	0.321099
$372$	4.65013	0.241098
$373$	7.01824	0.363391	0.181695	−	0.983355i	$-0.441842\pi$
$373$	7.01824	0.363391	0.181695	+	0.983355i	$0.441842\pi$
$374$	7.38771	0.382009
$375$	19.8738	1.02628
$376$	0.273517	0.0141056
$377$	6.44034	0.331694
$378$	−3.08473	−0.158662
$379$	−14.5650	−0.748151	−0.374076	−	0.927398i	$-0.622040\pi$
$379$	−14.5650	−0.748151	−0.374076	+	0.927398i	$0.622040\pi$
$380$	0	0
$381$	6.12772	0.313933
$382$	13.4517	0.688247
$383$	−12.1342	−0.620027	−0.310014	−	0.950732i	$-0.600334\pi$
$383$	−12.1342	−0.620027	−0.310014	+	0.950732i	$0.600334\pi$
$384$	−2.13415	−0.108908
$385$	−2.53037	−0.128960
$386$	23.6578	1.20415
$387$	−9.91610	−0.504064
$388$	−12.6176	−0.640559
$389$	24.2664	1.23036	0.615179	−	0.788388i	$-0.289084\pi$
$389$	24.2664	1.23036	0.615179	+	0.788388i	$0.289084\pi$
$390$	2.57752	0.130518
$391$	−1.57060	−0.0794287
$392$	−1.00000	−0.0505076
$393$	7.66447	0.386622
$394$	−16.5603	−0.834298
$395$	−14.0698	−0.707928
$396$	−3.76242	−0.189069
$397$	−14.1299	−0.709161	−0.354581	−	0.935025i	$-0.615376\pi$
$397$	−14.1299	−0.709161	−0.354581	+	0.935025i	$0.615376\pi$
$398$	−7.68305	−0.385116
$399$	0	0
$400$	−3.90689	−0.195345
$401$	13.7977	0.689025	0.344512	−	0.938782i	$-0.388044\pi$
$401$	13.7977	0.689025	0.344512	+	0.938782i	$0.388044\pi$
$402$	−8.80859	−0.439333
$403$	2.51703	0.125382
$404$	−1.49415	−0.0743366
$405$	11.7590	0.584307
$406$	5.57522	0.276693
$407$	2.75480	0.136550
$408$	−6.51450	−0.322516
$409$	−12.7520	−0.630544	−0.315272	−	0.949001i	$-0.602096\pi$
$409$	−12.7520	−0.630544	−0.315272	+	0.949001i	$0.602096\pi$
$410$	1.81763	0.0897665
$411$	−6.92765	−0.341716
$412$	−19.3707	−0.954325
$413$	10.2131	0.502555
$414$	0.799877	0.0393118
$415$	−15.8738	−0.779215
$416$	−1.15517	−0.0566370
$417$	13.2587	0.649283
$418$	0	0
$419$	25.8240	1.26159	0.630793	−	0.775951i	$-0.282730\pi$
$419$	25.8240	1.26159	0.630793	+	0.775951i	$0.282730\pi$
$420$	2.23129	0.108876
$421$	−5.42077	−0.264192	−0.132096	−	0.991237i	$-0.542171\pi$
$421$	−5.42077	−0.264192	−0.132096	+	0.991237i	$0.542171\pi$
$422$	19.3109	0.940039
$423$	−0.425205	−0.0206742
$424$	6.18481	0.300361
$425$	−11.9258	−0.578487
$426$	23.6557	1.14612
$427$	9.38737	0.454287
$428$	−8.80175	−0.425449
$429$	−5.96656	−0.288068
$430$	−6.66897	−0.321606
$431$	34.0208	1.63872	0.819362	−	0.573276i	$-0.194328\pi$
$431$	34.0208	1.63872	0.819362	+	0.573276i	$0.194328\pi$
$432$	−3.08473	−0.148414
$433$	13.3211	0.640172	0.320086	−	0.947389i	$-0.396288\pi$
$433$	13.3211	0.640172	0.320086	+	0.947389i	$0.396288\pi$
$434$	2.17892	0.104591
$435$	−12.4399	−0.596448
$436$	−16.6094	−0.795447
$437$	0	0
$438$	2.24869	0.107447
$439$	−22.4500	−1.07148	−0.535739	−	0.844384i	$-0.679967\pi$
$439$	−22.4500	−1.07148	−0.535739	+	0.844384i	$0.679967\pi$
$440$	−2.53037	−0.120631
$441$	1.55458	0.0740277
$442$	−3.52617	−0.167723
$443$	−7.75275	−0.368344	−0.184172	−	0.982894i	$-0.558960\pi$
$443$	−7.75275	−0.368344	−0.184172	+	0.982894i	$0.558960\pi$
$444$	−2.42919	−0.115284
$445$	−9.87588	−0.468162
$446$	−9.51413	−0.450507
$447$	−32.6586	−1.54470
$448$	−1.00000	−0.0472456
$449$	−22.0007	−1.03828	−0.519139	−	0.854690i	$-0.673747\pi$
$449$	−22.0007	−1.03828	−0.519139	+	0.854690i	$0.673747\pi$
$450$	6.07359	0.286312
$451$	−4.20754	−0.198125
$452$	6.81605	0.320600
$453$	−18.0128	−0.846313
$454$	−25.2920	−1.18701
$455$	1.20775	0.0566203
$456$	0	0
$457$	−23.2272	−1.08652	−0.543262	−	0.839563i	$-0.682811\pi$
$457$	−23.2272	−1.08652	−0.543262	+	0.839563i	$0.682811\pi$
$458$	−21.2960	−0.995096
$459$	−9.41617	−0.439509
$460$	0.537949	0.0250820
$461$	7.71392	0.359273	0.179637	−	0.983733i	$-0.442508\pi$
$461$	7.71392	0.359273	0.179637	+	0.983733i	$0.442508\pi$
$462$	−5.16509	−0.240302
$463$	24.4450	1.13605	0.568027	−	0.823010i	$-0.307707\pi$
$463$	24.4450	1.13605	0.568027	+	0.823010i	$0.307707\pi$
$464$	5.57522	0.258823
$465$	−4.86180	−0.225460
$466$	12.7292	0.589667
$467$	−33.8146	−1.56475	−0.782377	−	0.622806i	$-0.785993\pi$
$467$	−33.8146	−1.56475	−0.782377	+	0.622806i	$0.785993\pi$
$468$	1.79581	0.0830114
$469$	−4.12745	−0.190588
$470$	−0.285967	−0.0131907
$471$	−3.64792	−0.168087
$472$	10.2131	0.470097
$473$	15.4376	0.709823
$474$	−28.7197	−1.31914
$475$	0	0
$476$	−3.05251	−0.139911
$477$	−9.61479	−0.440231
$478$	−7.53887	−0.344820
$479$	19.3169	0.882610	0.441305	−	0.897357i	$-0.354516\pi$
$479$	19.3169	0.882610	0.441305	+	0.897357i	$0.354516\pi$
$480$	2.23129	0.101844
$481$	−1.31487	−0.0599530
$482$	24.0728	1.09649
$483$	1.09808	0.0499643
$484$	−5.14258	−0.233754
$485$	13.1919	0.599012
$486$	14.7486	0.669010
$487$	−1.36447	−0.0618301	−0.0309150	−	0.999522i	$-0.509842\pi$
$487$	−1.36447	−0.0618301	−0.0309150	+	0.999522i	$0.509842\pi$
$488$	9.38737	0.424946
$489$	40.6315	1.83742
$490$	1.04552	0.0472317
$491$	19.9180	0.898889	0.449444	−	0.893308i	$-0.351622\pi$
$491$	19.9180	0.898889	0.449444	+	0.893308i	$0.351622\pi$
$492$	3.71022	0.167269
$493$	17.0184	0.766469
$494$	0	0
$495$	3.93367	0.176806
$496$	2.17892	0.0978364
$497$	11.0844	0.497202
$498$	−32.4022	−1.45198
$499$	19.6662	0.880381	0.440190	−	0.897905i	$-0.354911\pi$
$499$	19.6662	0.880381	0.440190	+	0.897905i	$0.354911\pi$
$500$	9.31231	0.416459
$501$	−16.7570	−0.748648
$502$	−0.365805	−0.0163267
$503$	32.8861	1.46632	0.733158	−	0.680058i	$-0.238045\pi$
$503$	32.8861	1.46632	0.733158	+	0.680058i	$0.238045\pi$
$504$	1.55458	0.0692466
$505$	1.56216	0.0695151
$506$	−1.24527	−0.0553589
$507$	−24.8961	−1.10567
$508$	2.87127	0.127392
$509$	26.7240	1.18452	0.592259	−	0.805748i	$-0.298236\pi$
$509$	26.7240	1.18452	0.592259	+	0.805748i	$0.298236\pi$
$510$	6.81102	0.301597
$511$	1.05367	0.0466117
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	8.33390	0.367593
$515$	20.2524	0.892427
$516$	−13.6129	−0.599276
$517$	0.661970	0.0291134
$518$	−1.13825	−0.0500117
$519$	−17.3488	−0.761530
$520$	1.20775	0.0529635
$521$	23.0195	1.00850	0.504250	−	0.863558i	$-0.331769\pi$
$521$	23.0195	1.00850	0.504250	+	0.863558i	$0.331769\pi$
$522$	−8.66713	−0.379350
$523$	−10.1838	−0.445306	−0.222653	−	0.974898i	$-0.571472\pi$
$523$	−10.1838	−0.445306	−0.222653	+	0.974898i	$0.571472\pi$
$524$	3.59135	0.156889
$525$	8.33788	0.363895
$526$	22.5679	0.984008
$527$	6.65116	0.289729
$528$	−5.16509	−0.224782
$529$	−22.7353	−0.988490
$530$	−6.46633	−0.280879
$531$	−15.8772	−0.689010
$532$	0	0
$533$	2.00827	0.0869878
$534$	−20.1590	−0.872365
$535$	9.20239	0.397854
$536$	−4.12745	−0.178279
$537$	−30.4114	−1.31235
$538$	20.4358	0.881050
$539$	−2.42021	−0.104246
$540$	3.22514	0.138788
$541$	10.7486	0.462117	0.231059	−	0.972940i	$-0.425781\pi$
$541$	10.7486	0.462117	0.231059	+	0.972940i	$0.425781\pi$
$542$	−17.2844	−0.742429
$543$	−36.1193	−1.55003
$544$	−3.05251	−0.130875
$545$	17.3654	0.743854
$546$	2.46531	0.105505
$547$	−0.512859	−0.0219283	−0.0109641	−	0.999940i	$-0.503490\pi$
$547$	−0.512859	−0.0219283	−0.0109641	+	0.999940i	$0.503490\pi$
$548$	−3.24610	−0.138666
$549$	−14.5934	−0.622833
$550$	−9.45550	−0.403184
$551$	0	0
$552$	1.09808	0.0467373
$553$	−13.4572	−0.572260
$554$	21.1338	0.897890
$555$	2.53976	0.107807
$556$	6.21267	0.263476
$557$	−44.1525	−1.87080	−0.935401	−	0.353590i	$-0.884961\pi$
$557$	−44.1525	−1.87080	−0.935401	+	0.353590i	$0.884961\pi$
$558$	−3.38731	−0.143396
$559$	−7.36841	−0.311651
$560$	1.04552	0.0441812
$561$	−15.7665	−0.665660
$562$	−19.0891	−0.805225
$563$	−10.1263	−0.426772	−0.213386	−	0.976968i	$-0.568449\pi$
$563$	−10.1263	−0.426772	−0.213386	+	0.976968i	$0.568449\pi$
$564$	−0.583726	−0.0245793
$565$	−7.12630	−0.299806
$566$	21.5165	0.904406
$567$	11.2470	0.472330
$568$	11.0844	0.465090
$569$	23.0647	0.966922	0.483461	−	0.875366i	$-0.339379\pi$
$569$	23.0647	0.966922	0.483461	+	0.875366i	$0.339379\pi$
$570$	0	0
$571$	−9.68457	−0.405287	−0.202643	−	0.979253i	$-0.564953\pi$
$571$	−9.68457	−0.405287	−0.202643	+	0.979253i	$0.564953\pi$
$572$	−2.79576	−0.116897
$573$	−28.7078	−1.19929
$574$	1.73850	0.0725636
$575$	2.01021	0.0838314
$576$	1.55458	0.0647743
$577$	31.4649	1.30990	0.654950	−	0.755672i	$-0.272690\pi$
$577$	31.4649	1.30990	0.654950	+	0.755672i	$0.272690\pi$
$578$	7.68221	0.319538
$579$	−50.4892	−2.09826
$580$	−5.82899	−0.242036
$581$	−15.1827	−0.629886
$582$	26.9277	1.11619
$583$	14.9685	0.619934
$584$	1.05367	0.0436013
$585$	−1.87755	−0.0776272
$586$	−11.3698	−0.469683
$587$	−32.2780	−1.33226	−0.666128	−	0.745838i	$-0.732049\pi$
$587$	−32.2780	−1.33226	−0.666128	+	0.745838i	$0.732049\pi$
$588$	2.13415	0.0880107
$589$	0	0
$590$	−10.6780	−0.439607
$591$	35.3422	1.45378
$592$	−1.13825	−0.0467817
$593$	−38.8819	−1.59669	−0.798345	−	0.602200i	$-0.794291\pi$
$593$	−38.8819	−1.59669	−0.798345	+	0.602200i	$0.794291\pi$
$594$	−7.46570	−0.306322
$595$	3.19145	0.130837
$596$	−15.3029	−0.626831
$597$	16.3968	0.671074
$598$	0.594369	0.0243056
$599$	37.9488	1.55055	0.775273	−	0.631626i	$-0.217612\pi$
$599$	37.9488	1.55055	0.775273	+	0.631626i	$0.217612\pi$
$600$	8.33788	0.340393
$601$	25.7005	1.04835	0.524173	−	0.851612i	$-0.324375\pi$
$601$	25.7005	1.04835	0.524173	+	0.851612i	$0.324375\pi$
$602$	−6.37863	−0.259973
$603$	6.41647	0.261299
$604$	−8.44026	−0.343429
$605$	5.37666	0.218592
$606$	3.18873	0.129533
$607$	−26.8607	−1.09024	−0.545121	−	0.838357i	$-0.683516\pi$
$607$	−26.8607	−1.09024	−0.545121	+	0.838357i	$0.683516\pi$
$608$	0	0
$609$	−11.8983	−0.482145
$610$	−9.81466	−0.397384
$611$	−0.315960	−0.0127824
$612$	4.74537	0.191820
$613$	31.4009	1.26827	0.634135	−	0.773223i	$-0.281357\pi$
$613$	31.4009	1.26827	0.634135	+	0.773223i	$0.281357\pi$
$614$	−9.12185	−0.368128
$615$	−3.87910	−0.156420
$616$	−2.42021	−0.0975131
$617$	−11.9350	−0.480484	−0.240242	−	0.970713i	$-0.577227\pi$
$617$	−11.9350	−0.480484	−0.240242	+	0.970713i	$0.577227\pi$
$618$	41.3399	1.66293
$619$	−2.76014	−0.110940	−0.0554698	−	0.998460i	$-0.517666\pi$
$619$	−2.76014	−0.110940	−0.0554698	+	0.998460i	$0.517666\pi$
$620$	−2.27810	−0.0914907
$621$	1.58718	0.0636914
$622$	−17.3492	−0.695639
$623$	−9.44592	−0.378443
$624$	2.46531	0.0986913
$625$	9.79827	0.391931
$626$	2.42580	0.0969543
$627$	0	0
$628$	−1.70931	−0.0682089
$629$	−3.47450	−0.138538
$630$	−1.62534	−0.0647552
$631$	26.0991	1.03899	0.519495	−	0.854473i	$-0.326120\pi$
$631$	26.0991	1.03899	0.519495	+	0.854473i	$0.326120\pi$
$632$	−13.4572	−0.535300
$633$	−41.2122	−1.63804
$634$	−8.88675	−0.352938
$635$	−3.00197	−0.119129
$636$	−13.1993	−0.523386
$637$	1.15517	0.0457696
$638$	13.4932	0.534201
$639$	−17.2316	−0.681671
$640$	1.04552	0.0413277
$641$	−30.2320	−1.19409	−0.597046	−	0.802207i	$-0.703659\pi$
$641$	−30.2320	−1.19409	−0.597046	+	0.802207i	$0.703659\pi$
$642$	18.7842	0.741354
$643$	−5.69885	−0.224741	−0.112370	−	0.993666i	$-0.535844\pi$
$643$	−5.69885	−0.224741	−0.112370	+	0.993666i	$0.535844\pi$
$644$	0.514528	0.0202753
$645$	14.2326	0.560406
$646$	0	0
$647$	−38.9990	−1.53321	−0.766605	−	0.642119i	$-0.778055\pi$
$647$	−38.9990	−1.53321	−0.766605	+	0.642119i	$0.778055\pi$
$648$	11.2470	0.441825
$649$	24.7179	0.970263
$650$	4.51313	0.177020
$651$	−4.65013	−0.182253
$652$	19.0388	0.745616
$653$	9.49438	0.371544	0.185772	−	0.982593i	$-0.440521\pi$
$653$	9.49438	0.371544	0.185772	+	0.982593i	$0.440521\pi$
$654$	35.4469	1.38608
$655$	−3.75482	−0.146713
$656$	1.73850	0.0678771
$657$	−1.63802	−0.0639053
$658$	−0.273517	−0.0106628
$659$	−34.7488	−1.35362	−0.676811	−	0.736157i	$-0.736638\pi$
$659$	−34.7488	−1.35362	−0.676811	+	0.736157i	$0.736638\pi$
$660$	5.40019	0.210202
$661$	42.2506	1.64336	0.821679	−	0.569950i	$-0.193038\pi$
$661$	42.2506	1.64336	0.821679	+	0.569950i	$0.193038\pi$
$662$	19.5033	0.758019
$663$	7.52537	0.292261
$664$	−15.1827	−0.589204
$665$	0	0
$666$	1.76950	0.0685667
$667$	−2.86861	−0.111073
$668$	−7.85185	−0.303797
$669$	20.3045	0.785019
$670$	4.31533	0.166716
$671$	22.7194	0.877074
$672$	2.13415	0.0823265
$673$	−27.7918	−1.07130	−0.535648	−	0.844441i	$-0.679933\pi$
$673$	−27.7918	−1.07130	−0.535648	+	0.844441i	$0.679933\pi$
$674$	−5.72554	−0.220540
$675$	12.0517	0.463871
$676$	−11.6656	−0.448676
$677$	−6.95181	−0.267180	−0.133590	−	0.991037i	$-0.542650\pi$
$677$	−6.95181	−0.267180	−0.133590	+	0.991037i	$0.542650\pi$
$678$	−14.5465	−0.558653
$679$	12.6176	0.484217
$680$	3.19145	0.122386
$681$	53.9768	2.06839
$682$	5.27344	0.201931
$683$	27.6511	1.05804	0.529020	−	0.848609i	$-0.322560\pi$
$683$	27.6511	1.05804	0.529020	+	0.848609i	$0.322560\pi$
$684$	0	0
$685$	3.39385	0.129672
$686$	1.00000	0.0381802
$687$	45.4487	1.73398
$688$	−6.37863	−0.243183
$689$	−7.14452	−0.272184
$690$	−1.14806	−0.0437059
$691$	−28.9707	−1.10210	−0.551050	−	0.834472i	$-0.685773\pi$
$691$	−28.9707	−1.10210	−0.551050	+	0.834472i	$0.685773\pi$
$692$	−8.12917	−0.309025
$693$	3.76242	0.142922
$694$	−34.0907	−1.29407
$695$	−6.49545	−0.246387
$696$	−11.8983	−0.451005
$697$	5.30678	0.201009
$698$	−31.1329	−1.17840
$699$	−27.1659	−1.02751
$700$	3.90689	0.147667
$701$	36.1561	1.36560	0.682798	−	0.730607i	$-0.260763\pi$
$701$	36.1561	1.36560	0.682798	+	0.730607i	$0.260763\pi$
$702$	3.56340	0.134492
$703$	0	0
$704$	−2.42021	−0.0912151
$705$	0.610296	0.0229851
$706$	−7.00294	−0.263559
$707$	1.49415	0.0561932
$708$	−21.7963	−0.819156
$709$	−38.9545	−1.46297	−0.731483	−	0.681860i	$-0.761171\pi$
$709$	−38.9545	−1.46297	−0.731483	+	0.681860i	$0.761171\pi$
$710$	−11.5889	−0.434924
$711$	20.9204	0.784576
$712$	−9.44592	−0.354001
$713$	−1.12112	−0.0419861
$714$	6.51450	0.243799
$715$	2.92302	0.109315
$716$	−14.2499	−0.532544
$717$	16.0890	0.600856
$718$	−1.04073	−0.0388395
$719$	−32.1104	−1.19751	−0.598757	−	0.800931i	$-0.704338\pi$
$719$	−32.1104	−1.19751	−0.598757	+	0.800931i	$0.704338\pi$
$720$	−1.62534	−0.0605730
$721$	19.3707	0.721402
$722$	0	0
$723$	−51.3749	−1.91065
$724$	−16.9244	−0.628992
$725$	−21.7818	−0.808955
$726$	10.9750	0.407321
$727$	30.2622	1.12236	0.561181	−	0.827693i	$-0.310347\pi$
$727$	30.2622	1.12236	0.561181	+	0.827693i	$0.310347\pi$
$728$	1.15517	0.0428135
$729$	2.26540	0.0839035
$730$	−1.10163	−0.0407733
$731$	−19.4708	−0.720154
$732$	−20.0340	−0.740479
$733$	−2.13269	−0.0787727	−0.0393864	−	0.999224i	$-0.512540\pi$
$733$	−2.13269	−0.0787727	−0.0393864	+	0.999224i	$0.512540\pi$
$734$	2.88851	0.106617
$735$	−2.23129	−0.0823023
$736$	0.514528	0.0189658
$737$	−9.98931	−0.367961
$738$	−2.70264	−0.0994857
$739$	10.6328	0.391133	0.195567	−	0.980690i	$-0.437345\pi$
$739$	10.6328	0.391133	0.195567	+	0.980690i	$0.437345\pi$
$740$	1.19006	0.0437474
$741$	0	0
$742$	−6.18481	−0.227051
$743$	−30.3286	−1.11265	−0.556324	−	0.830966i	$-0.687789\pi$
$743$	−30.3286	−1.11265	−0.556324	+	0.830966i	$0.687789\pi$
$744$	−4.65013	−0.170482
$745$	15.9995	0.586175
$746$	−7.01824	−0.256956
$747$	23.6028	0.863582
$748$	−7.38771	−0.270121
$749$	8.80175	0.321609
$750$	−19.8738	−0.725690
$751$	11.9117	0.434664	0.217332	−	0.976098i	$-0.430265\pi$
$751$	11.9117	0.434664	0.217332	+	0.976098i	$0.430265\pi$
$752$	−0.273517	−0.00997415
$753$	0.780681	0.0284496
$754$	−6.44034	−0.234543
$755$	8.82444	0.321154
$756$	3.08473	0.112191
$757$	2.55529	0.0928738	0.0464369	−	0.998921i	$-0.485213\pi$
$757$	2.55529	0.0928738	0.0464369	+	0.998921i	$0.485213\pi$
$758$	14.5650	0.529023
$759$	2.65758	0.0964642
$760$	0	0
$761$	−17.1391	−0.621293	−0.310647	−	0.950525i	$-0.600546\pi$
$761$	−17.1391	−0.621293	−0.310647	+	0.950525i	$0.600546\pi$
$762$	−6.12772	−0.221984
$763$	16.6094	0.601301
$764$	−13.4517	−0.486664
$765$	−4.96137	−0.179379
$766$	12.1342	0.438425
$767$	−11.7979	−0.425998
$768$	2.13415	0.0770094
$769$	−30.9530	−1.11620	−0.558098	−	0.829775i	$-0.688469\pi$
$769$	−30.9530	−1.11620	−0.558098	+	0.829775i	$0.688469\pi$
$770$	2.53037	0.0911883
$771$	−17.7858	−0.640539
$772$	−23.6578	−0.851463
$773$	−49.9764	−1.79753	−0.898763	−	0.438435i	$-0.855533\pi$
$773$	−49.9764	−1.79753	−0.898763	+	0.438435i	$0.855533\pi$
$774$	9.91610	0.356427
$775$	−8.51280	−0.305789
$776$	12.6176	0.452944
$777$	2.42919	0.0871465
$778$	−24.2664	−0.869994
$779$	0	0
$780$	−2.57752	−0.0922901
$781$	26.8265	0.959929
$782$	1.57060	0.0561646
$783$	−17.1981	−0.614608
$784$	1.00000	0.0357143
$785$	1.78711	0.0637848
$786$	−7.66447	−0.273383
$787$	−33.0457	−1.17795	−0.588976	−	0.808150i	$-0.700469\pi$
$787$	−33.0457	−1.17795	−0.588976	+	0.808150i	$0.700469\pi$
$788$	16.5603	0.589938
$789$	−48.1633	−1.71466
$790$	14.0698	0.500581
$791$	−6.81605	−0.242351
$792$	3.76242	0.133692
$793$	−10.8440	−0.385083
$794$	14.1299	0.501453
$795$	13.8001	0.489439
$796$	7.68305	0.272318
$797$	53.7061	1.90237	0.951184	−	0.308624i	$-0.0998685\pi$
$797$	53.7061	1.90237	0.951184	+	0.308624i	$0.0998685\pi$
$798$	0	0
$799$	−0.834913	−0.0295371
$800$	3.90689	0.138130
$801$	14.6845	0.518850
$802$	−13.7977	−0.487214
$803$	2.55011	0.0899915
$804$	8.80859	0.310655
$805$	−0.537949	−0.0189602
$806$	−2.51703	−0.0886585
$807$	−43.6130	−1.53525
$808$	1.49415	0.0525639
$809$	−38.4512	−1.35187	−0.675936	−	0.736960i	$-0.736260\pi$
$809$	−38.4512	−1.35187	−0.675936	+	0.736960i	$0.736260\pi$
$810$	−11.7590	−0.413168
$811$	−34.6028	−1.21507	−0.607535	−	0.794293i	$-0.707842\pi$
$811$	−34.6028	−1.21507	−0.607535	+	0.794293i	$0.707842\pi$
$812$	−5.57522	−0.195652
$813$	36.8875	1.29370
$814$	−2.75480	−0.0965556
$815$	−19.9054	−0.697255
$816$	6.51450	0.228053
$817$	0	0
$818$	12.7520	0.445862
$819$	−1.79581	−0.0627507
$820$	−1.81763	−0.0634745
$821$	5.21981	0.182173	0.0910864	−	0.995843i	$-0.470966\pi$
$821$	5.21981	0.182173	0.0910864	+	0.995843i	$0.470966\pi$
$822$	6.92765	0.241630
$823$	−5.08619	−0.177294	−0.0886468	−	0.996063i	$-0.528254\pi$
$823$	−5.08619	−0.177294	−0.0886468	+	0.996063i	$0.528254\pi$
$824$	19.3707	0.674809
$825$	20.1794	0.702558
$826$	−10.2131	−0.355360
$827$	18.5906	0.646459	0.323229	−	0.946321i	$-0.395231\pi$
$827$	18.5906	0.646459	0.323229	+	0.946321i	$0.395231\pi$
$828$	−0.799877	−0.0277976
$829$	−0.766359	−0.0266168	−0.0133084	−	0.999911i	$-0.504236\pi$
$829$	−0.766359	−0.0266168	−0.0133084	+	0.999911i	$0.504236\pi$
$830$	15.8738	0.550988
$831$	−45.1027	−1.56459
$832$	1.15517	0.0400484
$833$	3.05251	0.105763
$834$	−13.2587	−0.459113
$835$	8.20925	0.284093
$836$	0	0
$837$	−6.72138	−0.232325
$838$	−25.8240	−0.892076
$839$	41.0401	1.41686	0.708431	−	0.705780i	$-0.249403\pi$
$839$	41.0401	1.41686	0.708431	+	0.705780i	$0.249403\pi$
$840$	−2.23129	−0.0769868
$841$	2.08304	0.0718290
$842$	5.42077	0.186812
$843$	40.7390	1.40312
$844$	−19.3109	−0.664708
$845$	12.1966	0.419575
$846$	0.425205	0.0146189
$847$	5.14258	0.176701
$848$	−6.18481	−0.212387
$849$	−45.9194	−1.57595
$850$	11.9258	0.409052
$851$	0.585660	0.0200762
$852$	−23.6557	−0.810431
$853$	18.3849	0.629488	0.314744	−	0.949177i	$-0.398081\pi$
$853$	18.3849	0.629488	0.314744	+	0.949177i	$0.398081\pi$
$854$	−9.38737	−0.321229
$855$	0	0
$856$	8.80175	0.300838
$857$	9.11999	0.311533	0.155766	−	0.987794i	$-0.450215\pi$
$857$	9.11999	0.311533	0.155766	+	0.987794i	$0.450215\pi$
$858$	5.96656	0.203695
$859$	−34.9079	−1.19104	−0.595521	−	0.803340i	$-0.703054\pi$
$859$	−34.9079	−1.19104	−0.595521	+	0.803340i	$0.703054\pi$
$860$	6.66897	0.227410
$861$	−3.71022	−0.126444
$862$	−34.0208	−1.15875
$863$	−9.40882	−0.320280	−0.160140	−	0.987094i	$-0.551195\pi$
$863$	−9.40882	−0.320280	−0.160140	+	0.987094i	$0.551195\pi$
$864$	3.08473	0.104945
$865$	8.49919	0.288981
$866$	−13.3211	−0.452670
$867$	−16.3950	−0.556802
$868$	−2.17892	−0.0739573
$869$	−32.5694	−1.10484
$870$	12.4399	0.421753
$871$	4.76792	0.161555
$872$	16.6094	0.562466
$873$	−19.6150	−0.663868
$874$	0	0
$875$	−9.31231	−0.314814
$876$	−2.24869	−0.0759763
$877$	53.5586	1.80854	0.904272	−	0.426957i	$-0.140414\pi$
$877$	53.5586	1.80854	0.904272	+	0.426957i	$0.140414\pi$
$878$	22.4500	0.757649
$879$	24.2648	0.818433
$880$	2.53037	0.0852989
$881$	−27.8500	−0.938289	−0.469144	−	0.883121i	$-0.655438\pi$
$881$	−27.8500	−0.938289	−0.469144	+	0.883121i	$0.655438\pi$
$882$	−1.55458	−0.0523455
$883$	−53.9182	−1.81449	−0.907246	−	0.420601i	$-0.861819\pi$
$883$	−53.9182	−1.81449	−0.907246	+	0.420601i	$0.861819\pi$
$884$	3.52617	0.118598
$885$	22.7884	0.766025
$886$	7.75275	0.260459
$887$	39.8816	1.33909	0.669547	−	0.742770i	$-0.266488\pi$
$887$	39.8816	1.33909	0.669547	+	0.742770i	$0.266488\pi$
$888$	2.42919	0.0815181
$889$	−2.87127	−0.0962995
$890$	9.87588	0.331040
$891$	27.2202	0.911910
$892$	9.51413	0.318557
$893$	0	0
$894$	32.6586	1.09227
$895$	14.8985	0.498003
$896$	1.00000	0.0334077
$897$	−1.26847	−0.0423530
$898$	22.0007	0.734174
$899$	12.1479	0.405157
$900$	−6.07359	−0.202453
$901$	−18.8792	−0.628956
$902$	4.20754	0.140096
$903$	13.6129	0.453010
$904$	−6.81605	−0.226698
$905$	17.6948	0.588195
$906$	18.0128	0.598434
$907$	38.8333	1.28944	0.644719	−	0.764420i	$-0.276974\pi$
$907$	38.8333	1.28944	0.644719	+	0.764420i	$0.276974\pi$
$908$	25.2920	0.839343
$909$	−2.32277	−0.0770416
$910$	−1.20775	−0.0400366
$911$	−24.5969	−0.814931	−0.407466	−	0.913221i	$-0.633587\pi$
$911$	−24.5969	−0.814931	−0.407466	+	0.913221i	$0.633587\pi$
$912$	0	0
$913$	−36.7454	−1.21610
$914$	23.2272	0.768288
$915$	20.9459	0.692451
$916$	21.2960	0.703639
$917$	−3.59135	−0.118597
$918$	9.41617	0.310780
$919$	−22.9886	−0.758323	−0.379161	−	0.925331i	$-0.623787\pi$
$919$	−22.9886	−0.758323	−0.379161	+	0.925331i	$0.623787\pi$
$920$	−0.537949	−0.0177356
$921$	19.4674	0.641472
$922$	−7.71392	−0.254044
$923$	−12.8044	−0.421461
$924$	5.16509	0.169919
$925$	4.44701	0.146217
$926$	−24.4450	−0.803311
$927$	−30.1133	−0.989051
$928$	−5.57522	−0.183015
$929$	34.9140	1.14549	0.572746	−	0.819733i	$-0.305878\pi$
$929$	34.9140	1.14549	0.572746	+	0.819733i	$0.305878\pi$
$930$	4.86180	0.159425
$931$	0	0
$932$	−12.7292	−0.416958
$933$	37.0257	1.21217
$934$	33.8146	1.10645
$935$	7.72398	0.252601
$936$	−1.79581	−0.0586979
$937$	33.9944	1.11055	0.555274	−	0.831667i	$-0.312613\pi$
$937$	33.9944	1.11055	0.555274	+	0.831667i	$0.312613\pi$
$938$	4.12745	0.134766
$939$	−5.17701	−0.168945
$940$	0.285967	0.00932722
$941$	25.6708	0.836843	0.418421	−	0.908253i	$-0.362584\pi$
$941$	25.6708	0.836843	0.418421	+	0.908253i	$0.362584\pi$
$942$	3.64792	0.118856
$943$	−0.894508	−0.0291292
$944$	−10.2131	−0.332409
$945$	−3.22514	−0.104914
$946$	−15.4376	−0.501920
$947$	42.6574	1.38618	0.693089	−	0.720852i	$-0.256249\pi$
$947$	42.6574	1.38618	0.693089	+	0.720852i	$0.256249\pi$
$948$	28.7197	0.932774
$949$	−1.21717	−0.0395111
$950$	0	0
$951$	18.9656	0.615003
$952$	3.05251	0.0989323
$953$	−21.5394	−0.697731	−0.348865	−	0.937173i	$-0.613433\pi$
$953$	−21.5394	−0.697731	−0.348865	+	0.937173i	$0.613433\pi$
$954$	9.61479	0.311290
$955$	14.0639	0.455099
$956$	7.53887	0.243824
$957$	−28.7965	−0.930858
$958$	−19.3169	−0.624100
$959$	3.24610	0.104822
$960$	−2.23129	−0.0720145
$961$	−26.2523	−0.846849
$962$	1.31487	0.0423931
$963$	−13.6831	−0.440930
$964$	−24.0728	−0.775333
$965$	24.7346	0.796237
$966$	−1.09808	−0.0353301
$967$	8.45314	0.271835	0.135917	−	0.990720i	$-0.456602\pi$
$967$	8.45314	0.271835	0.135917	+	0.990720i	$0.456602\pi$
$968$	5.14258	0.165289
$969$	0	0
$970$	−13.1919	−0.423566
$971$	−33.4395	−1.07313	−0.536563	−	0.843860i	$-0.680278\pi$
$971$	−33.4395	−1.07313	−0.536563	+	0.843860i	$0.680278\pi$
$972$	−14.7486	−0.473061
$973$	−6.21267	−0.199169
$974$	1.36447	0.0437205
$975$	−9.63169	−0.308461
$976$	−9.38737	−0.300482
$977$	38.5495	1.23331	0.616654	−	0.787234i	$-0.288488\pi$
$977$	38.5495	1.23331	0.616654	+	0.787234i	$0.288488\pi$
$978$	−40.6315	−1.29925
$979$	−22.8611	−0.730645
$980$	−1.04552	−0.0333978
$981$	−25.8207	−0.824392
$982$	−19.9180	−0.635610
$983$	4.75637	0.151705	0.0758524	−	0.997119i	$-0.475832\pi$
$983$	4.75637	0.151705	0.0758524	+	0.997119i	$0.475832\pi$
$984$	−3.71022	−0.118277
$985$	−17.3141	−0.551674
$986$	−17.0184	−0.541976
$987$	0.583726	0.0185802
$988$	0	0
$989$	3.28198	0.104361
$990$	−3.93367	−0.125020
$991$	11.1093	0.352897	0.176449	−	0.984310i	$-0.443539\pi$
$991$	11.1093	0.352897	0.176449	+	0.984310i	$0.443539\pi$
$992$	−2.17892	−0.0691808
$993$	−41.6230	−1.32087
$994$	−11.0844	−0.351575
$995$	−8.03276	−0.254656
$996$	32.4022	1.02670
$997$	2.17801	0.0689784	0.0344892	−	0.999405i	$-0.489020\pi$
$997$	2.17801	0.0689784	0.0344892	+	0.999405i	$0.489020\pi$
$998$	−19.6662	−0.622523
$999$	3.51119	0.111089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bf.1.8	✓	8
19.18	odd	2		5054.2.a.bi.1.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.bf.1.8	✓	8	1.1	even	1	trivial
5054.2.a.bi.1.1	yes	8	19.18	odd	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.13415 q^{3} +1.00000 q^{4} -1.04552 q^{5} -2.13415 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.55458 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.13415 q^{3} +1.00000 q^{4} -1.04552 q^{5} -2.13415 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.55458 q^{9} +1.04552 q^{10} -2.42021 q^{11} +2.13415 q^{12} +1.15517 q^{13} +1.00000 q^{14} -2.23129 q^{15} +1.00000 q^{16} +3.05251 q^{17} -1.55458 q^{18} -1.04552 q^{20} -2.13415 q^{21} +2.42021 q^{22} -0.514528 q^{23} -2.13415 q^{24} -3.90689 q^{25} -1.15517 q^{26} -3.08473 q^{27} -1.00000 q^{28} +5.57522 q^{29} +2.23129 q^{30} +2.17892 q^{31} -1.00000 q^{32} -5.16509 q^{33} -3.05251 q^{34} +1.04552 q^{35} +1.55458 q^{36} -1.13825 q^{37} +2.46531 q^{39} +1.04552 q^{40} +1.73850 q^{41} +2.13415 q^{42} -6.37863 q^{43} -2.42021 q^{44} -1.62534 q^{45} +0.514528 q^{46} -0.273517 q^{47} +2.13415 q^{48} +1.00000 q^{49} +3.90689 q^{50} +6.51450 q^{51} +1.15517 q^{52} -6.18481 q^{53} +3.08473 q^{54} +2.53037 q^{55} +1.00000 q^{56} -5.57522 q^{58} -10.2131 q^{59} -2.23129 q^{60} -9.38737 q^{61} -2.17892 q^{62} -1.55458 q^{63} +1.00000 q^{64} -1.20775 q^{65} +5.16509 q^{66} +4.12745 q^{67} +3.05251 q^{68} -1.09808 q^{69} -1.04552 q^{70} -11.0844 q^{71} -1.55458 q^{72} -1.05367 q^{73} +1.13825 q^{74} -8.33788 q^{75} +2.42021 q^{77} -2.46531 q^{78} +13.4572 q^{79} -1.04552 q^{80} -11.2470 q^{81} -1.73850 q^{82} +15.1827 q^{83} -2.13415 q^{84} -3.19145 q^{85} +6.37863 q^{86} +11.8983 q^{87} +2.42021 q^{88} +9.44592 q^{89} +1.62534 q^{90} -1.15517 q^{91} -0.514528 q^{92} +4.65013 q^{93} +0.273517 q^{94} -2.13415 q^{96} -12.6176 q^{97} -1.00000 q^{98} -3.76242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 4 q^{3} + 8 q^{4} + 6 q^{5} + 4 q^{6} - 8 q^{7} - 8 q^{8} + 8 q^{9} - 6 q^{10} + 4 q^{11} - 4 q^{12} - 6 q^{13} + 8 q^{14} - 8 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} + 6 q^{20} + 4 q^{21} - 4 q^{22} + 20 q^{23} + 4 q^{24} - 8 q^{25} + 6 q^{26} - 22 q^{27} - 8 q^{28} - 16 q^{29} + 8 q^{30} - 22 q^{31} - 8 q^{32} + 8 q^{33} - 2 q^{34} - 6 q^{35} + 8 q^{36} + 12 q^{37} + 8 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{42} + 4 q^{44} - 4 q^{45} - 20 q^{46} + 6 q^{47} - 4 q^{48} + 8 q^{49} + 8 q^{50} + 4 q^{51} - 6 q^{52} - 16 q^{53} + 22 q^{54} + 18 q^{55} + 8 q^{56} + 16 q^{58} - 14 q^{59} - 8 q^{60} + 10 q^{61} + 22 q^{62} - 8 q^{63} + 8 q^{64} - 32 q^{65} - 8 q^{66} + 20 q^{67} + 2 q^{68} - 40 q^{69} + 6 q^{70} - 8 q^{72} - 18 q^{73} - 12 q^{74} - 16 q^{75} - 4 q^{77} - 8 q^{78} - 4 q^{79} + 6 q^{80} + 12 q^{81} + 36 q^{82} + 36 q^{83} + 4 q^{84} - 16 q^{85} + 28 q^{87} - 4 q^{88} - 18 q^{89} + 4 q^{90} + 6 q^{91} + 20 q^{92} + 16 q^{93} - 6 q^{94} + 4 q^{96} - 26 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 4 * q^3 + 8 * q^4 + 6 * q^5 + 4 * q^6 - 8 * q^7 - 8 * q^8 + 8 * q^9 - 6 * q^10 + 4 * q^11 - 4 * q^12 - 6 * q^13 + 8 * q^14 - 8 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 + 6 * q^20 + 4 * q^21 - 4 * q^22 + 20 * q^23 + 4 * q^24 - 8 * q^25 + 6 * q^26 - 22 * q^27 - 8 * q^28 - 16 * q^29 + 8 * q^30 - 22 * q^31 - 8 * q^32 + 8 * q^33 - 2 * q^34 - 6 * q^35 + 8 * q^36 + 12 * q^37 + 8 * q^39 - 6 * q^40 - 36 * q^41 - 4 * q^42 + 4 * q^44 - 4 * q^45 - 20 * q^46 + 6 * q^47 - 4 * q^48 + 8 * q^49 + 8 * q^50 + 4 * q^51 - 6 * q^52 - 16 * q^53 + 22 * q^54 + 18 * q^55 + 8 * q^56 + 16 * q^58 - 14 * q^59 - 8 * q^60 + 10 * q^61 + 22 * q^62 - 8 * q^63 + 8 * q^64 - 32 * q^65 - 8 * q^66 + 20 * q^67 + 2 * q^68 - 40 * q^69 + 6 * q^70 - 8 * q^72 - 18 * q^73 - 12 * q^74 - 16 * q^75 - 4 * q^77 - 8 * q^78 - 4 * q^79 + 6 * q^80 + 12 * q^81 + 36 * q^82 + 36 * q^83 + 4 * q^84 - 16 * q^85 + 28 * q^87 - 4 * q^88 - 18 * q^89 + 4 * q^90 + 6 * q^91 + 20 * q^92 + 16 * q^93 - 6 * q^94 + 4 * q^96 - 26 * q^97 - 8 * q^98 + 4 * q^99

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