LMFDB - Embedded newform 8018.2.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.949118 q^{3} +1.00000 q^{4} -3.26613 q^{5} +0.949118 q^{6} +3.22650 q^{7} -1.00000 q^{8} -2.09917 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.949118 q^{3} +1.00000 q^{4} -3.26613 q^{5} +0.949118 q^{6} +3.22650 q^{7} -1.00000 q^{8} -2.09917 q^{9} +3.26613 q^{10} -5.15132 q^{11} -0.949118 q^{12} +3.20396 q^{13} -3.22650 q^{14} +3.09994 q^{15} +1.00000 q^{16} +4.62298 q^{17} +2.09917 q^{18} -1.00000 q^{19} -3.26613 q^{20} -3.06233 q^{21} +5.15132 q^{22} -3.01926 q^{23} +0.949118 q^{24} +5.66758 q^{25} -3.20396 q^{26} +4.83972 q^{27} +3.22650 q^{28} +8.93346 q^{29} -3.09994 q^{30} +4.37513 q^{31} -1.00000 q^{32} +4.88921 q^{33} -4.62298 q^{34} -10.5382 q^{35} -2.09917 q^{36} -3.61334 q^{37} +1.00000 q^{38} -3.04094 q^{39} +3.26613 q^{40} -8.25611 q^{41} +3.06233 q^{42} +5.82278 q^{43} -5.15132 q^{44} +6.85617 q^{45} +3.01926 q^{46} -1.00542 q^{47} -0.949118 q^{48} +3.41032 q^{49} -5.66758 q^{50} -4.38775 q^{51} +3.20396 q^{52} -5.20001 q^{53} -4.83972 q^{54} +16.8248 q^{55} -3.22650 q^{56} +0.949118 q^{57} -8.93346 q^{58} -10.1953 q^{59} +3.09994 q^{60} +0.600499 q^{61} -4.37513 q^{62} -6.77299 q^{63} +1.00000 q^{64} -10.4645 q^{65} -4.88921 q^{66} -5.63112 q^{67} +4.62298 q^{68} +2.86563 q^{69} +10.5382 q^{70} +1.87920 q^{71} +2.09917 q^{72} -7.71742 q^{73} +3.61334 q^{74} -5.37921 q^{75} -1.00000 q^{76} -16.6207 q^{77} +3.04094 q^{78} -3.33597 q^{79} -3.26613 q^{80} +1.70406 q^{81} +8.25611 q^{82} -4.70664 q^{83} -3.06233 q^{84} -15.0992 q^{85} -5.82278 q^{86} -8.47891 q^{87} +5.15132 q^{88} +10.0445 q^{89} -6.85617 q^{90} +10.3376 q^{91} -3.01926 q^{92} -4.15252 q^{93} +1.00542 q^{94} +3.26613 q^{95} +0.949118 q^{96} +4.01813 q^{97} -3.41032 q^{98} +10.8135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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
$3$	−0.949118	−0.547974	−0.273987	−	0.961733i	$-0.588342\pi$
$3$	−0.949118	−0.547974	−0.273987	+	0.961733i	$0.588342\pi$
$4$	1.00000	0.500000
$5$	−3.26613	−1.46066	−0.730328	−	0.683097i	$-0.760633\pi$
$5$	−3.26613	−1.46066	−0.730328	+	0.683097i	$0.760633\pi$
$6$	0.949118	0.387476
$7$	3.22650	1.21950	0.609752	−	0.792592i	$-0.291269\pi$
$7$	3.22650	1.21950	0.609752	+	0.792592i	$0.291269\pi$
$8$	−1.00000	−0.353553
$9$	−2.09917	−0.699725
$10$	3.26613	1.03284
$11$	−5.15132	−1.55318	−0.776590	−	0.630006i	$-0.783052\pi$
$11$	−5.15132	−1.55318	−0.776590	+	0.630006i	$0.783052\pi$
$12$	−0.949118	−0.273987
$13$	3.20396	0.888618	0.444309	−	0.895874i	$-0.353449\pi$
$13$	3.20396	0.888618	0.444309	+	0.895874i	$0.353449\pi$
$14$	−3.22650	−0.862319
$15$	3.09994	0.800401
$16$	1.00000	0.250000
$17$	4.62298	1.12124	0.560618	−	0.828074i	$-0.310564\pi$
$17$	4.62298	1.12124	0.560618	+	0.828074i	$0.310564\pi$
$18$	2.09917	0.494780
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.26613	−0.730328
$21$	−3.06233	−0.668256
$22$	5.15132	1.09826
$23$	−3.01926	−0.629559	−0.314779	−	0.949165i	$-0.601931\pi$
$23$	−3.01926	−0.629559	−0.314779	+	0.949165i	$0.601931\pi$
$24$	0.949118	0.193738
$25$	5.66758	1.13352
$26$	−3.20396	−0.628348
$27$	4.83972	0.931405
$28$	3.22650	0.609752
$29$	8.93346	1.65890	0.829451	−	0.558580i	$-0.188654\pi$
$29$	8.93346	1.65890	0.829451	+	0.558580i	$0.188654\pi$
$30$	−3.09994	−0.565969
$31$	4.37513	0.785797	0.392899	−	0.919582i	$-0.371472\pi$
$31$	4.37513	0.785797	0.392899	+	0.919582i	$0.371472\pi$
$32$	−1.00000	−0.176777
$33$	4.88921	0.851102
$34$	−4.62298	−0.792834
$35$	−10.5382	−1.78128
$36$	−2.09917	−0.349862
$37$	−3.61334	−0.594029	−0.297015	−	0.954873i	$-0.595991\pi$
$37$	−3.61334	−0.594029	−0.297015	+	0.954873i	$0.595991\pi$
$38$	1.00000	0.162221
$39$	−3.04094	−0.486939
$40$	3.26613	0.516420
$41$	−8.25611	−1.28939	−0.644694	−	0.764441i	$-0.723015\pi$
$41$	−8.25611	−1.28939	−0.644694	+	0.764441i	$0.723015\pi$
$42$	3.06233	0.472528
$43$	5.82278	0.887965	0.443983	−	0.896035i	$-0.353565\pi$
$43$	5.82278	0.887965	0.443983	+	0.896035i	$0.353565\pi$
$44$	−5.15132	−0.776590
$45$	6.85617	1.02206
$46$	3.01926	0.445165
$47$	−1.00542	−0.146655	−0.0733276	−	0.997308i	$-0.523362\pi$
$47$	−1.00542	−0.146655	−0.0733276	+	0.997308i	$0.523362\pi$
$48$	−0.949118	−0.136993
$49$	3.41032	0.487189
$50$	−5.66758	−0.801517
$51$	−4.38775	−0.614408
$52$	3.20396	0.444309
$53$	−5.20001	−0.714276	−0.357138	−	0.934052i	$-0.616247\pi$
$53$	−5.20001	−0.714276	−0.357138	+	0.934052i	$0.616247\pi$
$54$	−4.83972	−0.658602
$55$	16.8248	2.26866
$56$	−3.22650	−0.431160
$57$	0.949118	0.125714
$58$	−8.93346	−1.17302
$59$	−10.1953	−1.32731	−0.663655	−	0.748039i	$-0.730996\pi$
$59$	−10.1953	−1.32731	−0.663655	+	0.748039i	$0.730996\pi$
$60$	3.09994	0.400201
$61$	0.600499	0.0768861	0.0384430	−	0.999261i	$-0.487760\pi$
$61$	0.600499	0.0768861	0.0384430	+	0.999261i	$0.487760\pi$
$62$	−4.37513	−0.555642
$63$	−6.77299	−0.853317
$64$	1.00000	0.125000
$65$	−10.4645	−1.29797
$66$	−4.88921	−0.601820
$67$	−5.63112	−0.687950	−0.343975	−	0.938979i	$-0.611774\pi$
$67$	−5.63112	−0.687950	−0.343975	+	0.938979i	$0.611774\pi$
$68$	4.62298	0.560618
$69$	2.86563	0.344982
$70$	10.5382	1.25955
$71$	1.87920	0.223020	0.111510	−	0.993763i	$-0.464431\pi$
$71$	1.87920	0.223020	0.111510	+	0.993763i	$0.464431\pi$
$72$	2.09917	0.247390
$73$	−7.71742	−0.903255	−0.451628	−	0.892207i	$-0.649156\pi$
$73$	−7.71742	−0.903255	−0.451628	+	0.892207i	$0.649156\pi$
$74$	3.61334	0.420042
$75$	−5.37921	−0.621137
$76$	−1.00000	−0.114708
$77$	−16.6207	−1.89411
$78$	3.04094	0.344318
$79$	−3.33597	−0.375326	−0.187663	−	0.982233i	$-0.560091\pi$
$79$	−3.33597	−0.375326	−0.187663	+	0.982233i	$0.560091\pi$
$80$	−3.26613	−0.365164
$81$	1.70406	0.189340
$82$	8.25611	0.911734
$83$	−4.70664	−0.516621	−0.258310	−	0.966062i	$-0.583166\pi$
$83$	−4.70664	−0.516621	−0.258310	+	0.966062i	$0.583166\pi$
$84$	−3.06233	−0.334128
$85$	−15.0992	−1.63774
$86$	−5.82278	−0.627886
$87$	−8.47891	−0.909034
$88$	5.15132	0.549132
$89$	10.0445	1.06472	0.532359	−	0.846518i	$-0.321306\pi$
$89$	10.0445	1.06472	0.532359	+	0.846518i	$0.321306\pi$
$90$	−6.85617	−0.722704
$91$	10.3376	1.08367
$92$	−3.01926	−0.314779
$93$	−4.15252	−0.430596
$94$	1.00542	0.103701
$95$	3.26613	0.335098
$96$	0.949118	0.0968690
$97$	4.01813	0.407979	0.203989	−	0.978973i	$-0.434609\pi$
$97$	4.01813	0.407979	0.203989	+	0.978973i	$0.434609\pi$
$98$	−3.41032	−0.344494
$99$	10.8135	1.08680
$100$	5.66758	0.566758
$101$	−9.76507	−0.971661	−0.485831	−	0.874053i	$-0.661483\pi$
$101$	−9.76507	−0.971661	−0.485831	+	0.874053i	$0.661483\pi$
$102$	4.38775	0.434452
$103$	9.42018	0.928197	0.464099	−	0.885783i	$-0.346378\pi$
$103$	9.42018	0.928197	0.464099	+	0.885783i	$0.346378\pi$
$104$	−3.20396	−0.314174
$105$	10.0020	0.976092
$106$	5.20001	0.505069
$107$	6.99849	0.676569	0.338285	−	0.941044i	$-0.390153\pi$
$107$	6.99849	0.676569	0.338285	+	0.941044i	$0.390153\pi$
$108$	4.83972	0.465702
$109$	−18.2767	−1.75059	−0.875296	−	0.483587i	$-0.839334\pi$
$109$	−18.2767	−1.75059	−0.875296	+	0.483587i	$0.839334\pi$
$110$	−16.8248	−1.60419
$111$	3.42949	0.325513
$112$	3.22650	0.304876
$113$	−11.0200	−1.03667	−0.518337	−	0.855177i	$-0.673449\pi$
$113$	−11.0200	−1.03667	−0.518337	+	0.855177i	$0.673449\pi$
$114$	−0.949118	−0.0888931
$115$	9.86128	0.919569
$116$	8.93346	0.829451
$117$	−6.72567	−0.621788
$118$	10.1953	0.938550
$119$	14.9160	1.36735
$120$	−3.09994	−0.282985
$121$	15.5361	1.41237
$122$	−0.600499	−0.0543667
$123$	7.83602	0.706550
$124$	4.37513	0.392899
$125$	−2.18041	−0.195022
$126$	6.77299	0.603386
$127$	0.553740	0.0491365	0.0245682	−	0.999698i	$-0.492179\pi$
$127$	0.553740	0.0491365	0.0245682	+	0.999698i	$0.492179\pi$
$128$	−1.00000	−0.0883883
$129$	−5.52651	−0.486582
$130$	10.4645	0.917800
$131$	7.67551	0.670613	0.335306	−	0.942109i	$-0.391160\pi$
$131$	7.67551	0.670613	0.335306	+	0.942109i	$0.391160\pi$
$132$	4.88921	0.425551
$133$	−3.22650	−0.279773
$134$	5.63112	0.486454
$135$	−15.8071	−1.36046
$136$	−4.62298	−0.396417
$137$	2.69579	0.230317	0.115159	−	0.993347i	$-0.463262\pi$
$137$	2.69579	0.230317	0.115159	+	0.993347i	$0.463262\pi$
$138$	−2.86563	−0.243939
$139$	9.87353	0.837462	0.418731	−	0.908110i	$-0.362475\pi$
$139$	9.87353	0.837462	0.418731	+	0.908110i	$0.362475\pi$
$140$	−10.5382	−0.890638
$141$	0.954260	0.0803632
$142$	−1.87920	−0.157699
$143$	−16.5046	−1.38018
$144$	−2.09917	−0.174931
$145$	−29.1778	−2.42308
$146$	7.71742	0.638698
$147$	−3.23680	−0.266967
$148$	−3.61334	−0.297015
$149$	−3.88422	−0.318207	−0.159104	−	0.987262i	$-0.550860\pi$
$149$	−3.88422	−0.318207	−0.159104	+	0.987262i	$0.550860\pi$
$150$	5.37921	0.439210
$151$	−2.36242	−0.192251	−0.0961257	−	0.995369i	$-0.530645\pi$
$151$	−2.36242	−0.192251	−0.0961257	+	0.995369i	$0.530645\pi$
$152$	1.00000	0.0811107
$153$	−9.70443	−0.784557
$154$	16.6207	1.33934
$155$	−14.2897	−1.14778
$156$	−3.04094	−0.243470
$157$	7.44364	0.594067	0.297034	−	0.954867i	$-0.404003\pi$
$157$	7.44364	0.594067	0.297034	+	0.954867i	$0.404003\pi$
$158$	3.33597	0.265396
$159$	4.93542	0.391404
$160$	3.26613	0.258210
$161$	−9.74164	−0.767749
$162$	−1.70406	−0.133883
$163$	1.00321	0.0785776	0.0392888	−	0.999228i	$-0.487491\pi$
$163$	1.00321	0.0785776	0.0392888	+	0.999228i	$0.487491\pi$
$164$	−8.25611	−0.644694
$165$	−15.9688	−1.24317
$166$	4.70664	0.365306
$167$	−18.2124	−1.40932	−0.704660	−	0.709546i	$-0.748900\pi$
$167$	−18.2124	−1.40932	−0.704660	+	0.709546i	$0.748900\pi$
$168$	3.06233	0.236264
$169$	−2.73465	−0.210358
$170$	15.0992	1.15806
$171$	2.09917	0.160528
$172$	5.82278	0.443983
$173$	−8.48666	−0.645229	−0.322615	−	0.946530i	$-0.604562\pi$
$173$	−8.48666	−0.645229	−0.322615	+	0.946530i	$0.604562\pi$
$174$	8.47891	0.642784
$175$	18.2865	1.38233
$176$	−5.15132	−0.388295
$177$	9.67651	0.727331
$178$	−10.0445	−0.752870
$179$	−10.1372	−0.757692	−0.378846	−	0.925460i	$-0.623679\pi$
$179$	−10.1372	−0.757692	−0.378846	+	0.925460i	$0.623679\pi$
$180$	6.85617	0.511029
$181$	15.6231	1.16126	0.580629	−	0.814168i	$-0.302807\pi$
$181$	15.6231	1.16126	0.580629	+	0.814168i	$0.302807\pi$
$182$	−10.3376	−0.766273
$183$	−0.569945	−0.0421315
$184$	3.01926	0.222583
$185$	11.8016	0.867673
$186$	4.15252	0.304477
$187$	−23.8144	−1.74148
$188$	−1.00542	−0.0733276
$189$	15.6154	1.13585
$190$	−3.26613	−0.236950
$191$	27.3939	1.98215	0.991077	−	0.133289i	$-0.0425539\pi$
$191$	27.3939	1.98215	0.991077	+	0.133289i	$0.0425539\pi$
$192$	−0.949118	−0.0684967
$193$	−17.0405	−1.22660	−0.613302	−	0.789848i	$-0.710159\pi$
$193$	−17.0405	−1.22660	−0.613302	+	0.789848i	$0.710159\pi$
$194$	−4.01813	−0.288485
$195$	9.93208	0.711251
$196$	3.41032	0.243594
$197$	12.2372	0.871868	0.435934	−	0.899979i	$-0.356418\pi$
$197$	12.2372	0.871868	0.435934	+	0.899979i	$0.356418\pi$
$198$	−10.8135	−0.768483
$199$	18.7093	1.32627	0.663135	−	0.748500i	$-0.269225\pi$
$199$	18.7093	1.32627	0.663135	+	0.748500i	$0.269225\pi$
$200$	−5.66758	−0.400759
$201$	5.34460	0.376979
$202$	9.76507	0.687068
$203$	28.8238	2.02304
$204$	−4.38775	−0.307204
$205$	26.9655	1.88335
$206$	−9.42018	−0.656335
$207$	6.33795	0.440518
$208$	3.20396	0.222155
$209$	5.15132	0.356324
$210$	−10.0020	−0.690201
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−5.20001	−0.357138
$213$	−1.78358	−0.122209
$214$	−6.99849	−0.478407
$215$	−19.0179	−1.29701
$216$	−4.83972	−0.329301
$217$	14.1164	0.958282
$218$	18.2767	1.23786
$219$	7.32474	0.494960
$220$	16.8248	1.13433
$221$	14.8118	0.996351
$222$	−3.42949	−0.230172
$223$	3.91031	0.261854	0.130927	−	0.991392i	$-0.458205\pi$
$223$	3.91031	0.261854	0.130927	+	0.991392i	$0.458205\pi$
$224$	−3.22650	−0.215580
$225$	−11.8972	−0.793150
$226$	11.0200	0.733039
$227$	−18.2140	−1.20891	−0.604453	−	0.796641i	$-0.706608\pi$
$227$	−18.2140	−1.20891	−0.604453	+	0.796641i	$0.706608\pi$
$228$	0.949118	0.0628569
$229$	−21.5747	−1.42569	−0.712847	−	0.701320i	$-0.752594\pi$
$229$	−21.5747	−1.42569	−0.712847	+	0.701320i	$0.752594\pi$
$230$	−9.86128	−0.650233
$231$	15.7750	1.03792
$232$	−8.93346	−0.586510
$233$	19.1787	1.25644	0.628218	−	0.778037i	$-0.283784\pi$
$233$	19.1787	1.25644	0.628218	+	0.778037i	$0.283784\pi$
$234$	6.72567	0.439671
$235$	3.28382	0.214213
$236$	−10.1953	−0.663655
$237$	3.16623	0.205669
$238$	−14.9160	−0.966864
$239$	0.156735	0.0101383	0.00506916	−	0.999987i	$-0.498386\pi$
$239$	0.156735	0.0101383	0.00506916	+	0.999987i	$0.498386\pi$
$240$	3.09994	0.200100
$241$	8.82705	0.568601	0.284300	−	0.958735i	$-0.408239\pi$
$241$	8.82705	0.568601	0.284300	+	0.958735i	$0.408239\pi$
$242$	−15.5361	−0.998695
$243$	−16.1365	−1.03516
$244$	0.600499	0.0384430
$245$	−11.1385	−0.711615
$246$	−7.83602	−0.499606
$247$	−3.20396	−0.203863
$248$	−4.37513	−0.277821
$249$	4.46716	0.283095
$250$	2.18041	0.137901
$251$	0.119645	0.00755195	0.00377597	−	0.999993i	$-0.498798\pi$
$251$	0.119645	0.00755195	0.00377597	+	0.999993i	$0.498798\pi$
$252$	−6.77299	−0.426658
$253$	15.5532	0.977818
$254$	−0.553740	−0.0347447
$255$	14.3310	0.897439
$256$	1.00000	0.0625000
$257$	19.4630	1.21407	0.607033	−	0.794676i	$-0.292359\pi$
$257$	19.4630	1.21407	0.607033	+	0.794676i	$0.292359\pi$
$258$	5.52651	0.344065
$259$	−11.6585	−0.724421
$260$	−10.4645	−0.648983
$261$	−18.7529	−1.16077
$262$	−7.67551	−0.474195
$263$	−13.1213	−0.809094	−0.404547	−	0.914517i	$-0.632571\pi$
$263$	−13.1213	−0.809094	−0.404547	+	0.914517i	$0.632571\pi$
$264$	−4.88921	−0.300910
$265$	16.9839	1.04331
$266$	3.22650	0.197830
$267$	−9.53345	−0.583438
$268$	−5.63112	−0.343975
$269$	25.8999	1.57915	0.789573	−	0.613656i	$-0.210302\pi$
$269$	25.8999	1.57915	0.789573	+	0.613656i	$0.210302\pi$
$270$	15.8071	0.961992
$271$	23.1282	1.40494	0.702470	−	0.711713i	$-0.252080\pi$
$271$	23.1282	1.40494	0.702470	+	0.711713i	$0.252080\pi$
$272$	4.62298	0.280309
$273$	−9.81159	−0.593824
$274$	−2.69579	−0.162859
$275$	−29.1955	−1.76056
$276$	2.86563	0.172491
$277$	−30.7639	−1.84842	−0.924212	−	0.381879i	$-0.875277\pi$
$277$	−30.7639	−1.84842	−0.924212	+	0.381879i	$0.875277\pi$
$278$	−9.87353	−0.592175
$279$	−9.18417	−0.549842
$280$	10.5382	0.629776
$281$	21.2342	1.26673	0.633364	−	0.773854i	$-0.281674\pi$
$281$	21.2342	1.26673	0.633364	+	0.773854i	$0.281674\pi$
$282$	−0.954260	−0.0568253
$283$	−13.4715	−0.800799	−0.400399	−	0.916341i	$-0.631129\pi$
$283$	−13.4715	−0.800799	−0.400399	+	0.916341i	$0.631129\pi$
$284$	1.87920	0.111510
$285$	−3.09994	−0.183625
$286$	16.5046	0.975938
$287$	−26.6383	−1.57241
$288$	2.09917	0.123695
$289$	4.37191	0.257171
$290$	29.1778	1.71338
$291$	−3.81368	−0.223562
$292$	−7.71742	−0.451628
$293$	−24.0424	−1.40457	−0.702287	−	0.711894i	$-0.747838\pi$
$293$	−24.0424	−1.40457	−0.702287	+	0.711894i	$0.747838\pi$
$294$	3.23680	0.188774
$295$	33.2990	1.93874
$296$	3.61334	0.210021
$297$	−24.9309	−1.44664
$298$	3.88422	0.225007
$299$	−9.67358	−0.559438
$300$	−5.37921	−0.310569
$301$	18.7872	1.08288
$302$	2.36242	0.135942
$303$	9.26821	0.532445
$304$	−1.00000	−0.0573539
$305$	−1.96131	−0.112304
$306$	9.70443	0.554766
$307$	10.5564	0.602485	0.301242	−	0.953548i	$-0.402599\pi$
$307$	10.5564	0.602485	0.301242	+	0.953548i	$0.402599\pi$
$308$	−16.6207	−0.947054
$309$	−8.94086	−0.508628
$310$	14.2897	0.811602
$311$	−1.66500	−0.0944135	−0.0472067	−	0.998885i	$-0.515032\pi$
$311$	−1.66500	−0.0944135	−0.0472067	+	0.998885i	$0.515032\pi$
$312$	3.04094	0.172159
$313$	−2.19081	−0.123832	−0.0619159	−	0.998081i	$-0.519721\pi$
$313$	−2.19081	−0.123832	−0.0619159	+	0.998081i	$0.519721\pi$
$314$	−7.44364	−0.420069
$315$	22.1214	1.24640
$316$	−3.33597	−0.187663
$317$	15.5722	0.874624	0.437312	−	0.899310i	$-0.355931\pi$
$317$	15.5722	0.874624	0.437312	+	0.899310i	$0.355931\pi$
$318$	−4.93542	−0.276765
$319$	−46.0191	−2.57657
$320$	−3.26613	−0.182582
$321$	−6.64239	−0.370742
$322$	9.74164	0.542881
$323$	−4.62298	−0.257229
$324$	1.70406	0.0946698
$325$	18.1587	1.00726
$326$	−1.00321	−0.0555627
$327$	17.3468	0.959279
$328$	8.25611	0.455867
$329$	−3.24398	−0.178846
$330$	15.9688	0.879052
$331$	−29.7515	−1.63529	−0.817644	−	0.575723i	$-0.804720\pi$
$331$	−29.7515	−1.63529	−0.817644	+	0.575723i	$0.804720\pi$
$332$	−4.70664	−0.258310
$333$	7.58503	0.415657
$334$	18.2124	0.996539
$335$	18.3919	1.00486
$336$	−3.06233	−0.167064
$337$	16.7770	0.913904	0.456952	−	0.889491i	$-0.348941\pi$
$337$	16.7770	0.913904	0.456952	+	0.889491i	$0.348941\pi$
$338$	2.73465	0.148745
$339$	10.4593	0.568070
$340$	−15.0992	−0.818870
$341$	−22.5377	−1.22048
$342$	−2.09917	−0.113510
$343$	−11.5821	−0.625375
$344$	−5.82278	−0.313943
$345$	−9.35952	−0.503900
$346$	8.48666	0.456246
$347$	12.6733	0.680340	0.340170	−	0.940364i	$-0.389515\pi$
$347$	12.6733	0.680340	0.340170	+	0.940364i	$0.389515\pi$
$348$	−8.47891	−0.454517
$349$	12.4997	0.669095	0.334548	−	0.942379i	$-0.391416\pi$
$349$	12.4997	0.669095	0.334548	+	0.942379i	$0.391416\pi$
$350$	−18.2865	−0.977453
$351$	15.5063	0.827663
$352$	5.15132	0.274566
$353$	7.83442	0.416984	0.208492	−	0.978024i	$-0.433144\pi$
$353$	7.83442	0.416984	0.208492	+	0.978024i	$0.433144\pi$
$354$	−9.67651	−0.514301
$355$	−6.13769	−0.325755
$356$	10.0445	0.532359
$357$	−14.1571	−0.749273
$358$	10.1372	0.535769
$359$	−22.2087	−1.17213	−0.586064	−	0.810265i	$-0.699323\pi$
$359$	−22.2087	−1.17213	−0.586064	+	0.810265i	$0.699323\pi$
$360$	−6.85617	−0.361352
$361$	1.00000	0.0526316
$362$	−15.6231	−0.821133
$363$	−14.7456	−0.773941
$364$	10.3376	0.541837
$365$	25.2061	1.31935
$366$	0.569945	0.0297915
$367$	−1.03518	−0.0540360	−0.0270180	−	0.999635i	$-0.508601\pi$
$367$	−1.03518	−0.0540360	−0.0270180	+	0.999635i	$0.508601\pi$
$368$	−3.01926	−0.157390
$369$	17.3310	0.902216
$370$	−11.8016	−0.613537
$371$	−16.7778	−0.871062
$372$	−4.15252	−0.215298
$373$	−25.3354	−1.31182	−0.655909	−	0.754840i	$-0.727715\pi$
$373$	−25.3354	−1.31182	−0.655909	+	0.754840i	$0.727715\pi$
$374$	23.8144	1.23141
$375$	2.06947	0.106867
$376$	1.00542	0.0518504
$377$	28.6224	1.47413
$378$	−15.6154	−0.803168
$379$	12.5467	0.644481	0.322241	−	0.946658i	$-0.395564\pi$
$379$	12.5467	0.644481	0.322241	+	0.946658i	$0.395564\pi$
$380$	3.26613	0.167549
$381$	−0.525565	−0.0269255
$382$	−27.3939	−1.40159
$383$	−2.08373	−0.106474	−0.0532368	−	0.998582i	$-0.516954\pi$
$383$	−2.08373	−0.106474	−0.0532368	+	0.998582i	$0.516954\pi$
$384$	0.949118	0.0484345
$385$	54.2854	2.76664
$386$	17.0405	0.867340
$387$	−12.2230	−0.621331
$388$	4.01813	0.203989
$389$	15.0615	0.763648	0.381824	−	0.924235i	$-0.375296\pi$
$389$	15.0615	0.763648	0.381824	+	0.924235i	$0.375296\pi$
$390$	−9.93208	−0.502931
$391$	−13.9580	−0.705884
$392$	−3.41032	−0.172247
$393$	−7.28497	−0.367478
$394$	−12.2372	−0.616504
$395$	10.8957	0.548222
$396$	10.8135	0.543399
$397$	4.41444	0.221554	0.110777	−	0.993845i	$-0.464666\pi$
$397$	4.41444	0.221554	0.110777	+	0.993845i	$0.464666\pi$
$398$	−18.7093	−0.937815
$399$	3.06233	0.153308
$400$	5.66758	0.283379
$401$	7.79373	0.389200	0.194600	−	0.980883i	$-0.437659\pi$
$401$	7.79373	0.389200	0.194600	+	0.980883i	$0.437659\pi$
$402$	−5.34460	−0.266564
$403$	14.0177	0.698274
$404$	−9.76507	−0.485831
$405$	−5.56566	−0.276560
$406$	−28.8238	−1.43050
$407$	18.6135	0.922635
$408$	4.38775	0.217226
$409$	19.9662	0.987267	0.493634	−	0.869670i	$-0.335668\pi$
$409$	19.9662	0.987267	0.493634	+	0.869670i	$0.335668\pi$
$410$	−26.9655	−1.33173
$411$	−2.55863	−0.126208
$412$	9.42018	0.464099
$413$	−32.8951	−1.61866
$414$	−6.33795	−0.311493
$415$	15.3725	0.754605
$416$	−3.20396	−0.157087
$417$	−9.37115	−0.458907
$418$	−5.15132	−0.251959
$419$	−12.8572	−0.628117	−0.314059	−	0.949404i	$-0.601689\pi$
$419$	−12.8572	−0.628117	−0.314059	+	0.949404i	$0.601689\pi$
$420$	10.0020	0.488046
$421$	21.6223	1.05381	0.526904	−	0.849925i	$-0.323353\pi$
$421$	21.6223	1.05381	0.526904	+	0.849925i	$0.323353\pi$
$422$	−1.00000	−0.0486792
$423$	2.11055	0.102618
$424$	5.20001	0.252535
$425$	26.2011	1.27094
$426$	1.78358	0.0864147
$427$	1.93751	0.0937628
$428$	6.99849	0.338285
$429$	15.6648	0.756305
$430$	19.0179	0.917126
$431$	−1.58756	−0.0764700	−0.0382350	−	0.999269i	$-0.512174\pi$
$431$	−1.58756	−0.0764700	−0.0382350	+	0.999269i	$0.512174\pi$
$432$	4.83972	0.232851
$433$	36.6233	1.76000	0.880001	−	0.474973i	$-0.157542\pi$
$433$	36.6233	1.76000	0.880001	+	0.474973i	$0.157542\pi$
$434$	−14.1164	−0.677608
$435$	27.6932	1.32779
$436$	−18.2767	−0.875296
$437$	3.01926	0.144431
$438$	−7.32474	−0.349990
$439$	32.5796	1.55494	0.777469	−	0.628922i	$-0.216503\pi$
$439$	32.5796	1.55494	0.777469	+	0.628922i	$0.216503\pi$
$440$	−16.8248	−0.802093
$441$	−7.15886	−0.340898
$442$	−14.8118	−0.704527
$443$	−0.154447	−0.00733801	−0.00366901	−	0.999993i	$-0.501168\pi$
$443$	−0.154447	−0.00733801	−0.00366901	+	0.999993i	$0.501168\pi$
$444$	3.42949	0.162756
$445$	−32.8067	−1.55519
$446$	−3.91031	−0.185159
$447$	3.68658	0.174369
$448$	3.22650	0.152438
$449$	19.2904	0.910370	0.455185	−	0.890397i	$-0.349573\pi$
$449$	19.2904	0.910370	0.455185	+	0.890397i	$0.349573\pi$
$450$	11.8972	0.560841
$451$	42.5298	2.00265
$452$	−11.0200	−0.518337
$453$	2.24222	0.105349
$454$	18.2140	0.854826
$455$	−33.7639	−1.58287
$456$	−0.949118	−0.0444465
$457$	−4.03898	−0.188936	−0.0944678	−	0.995528i	$-0.530115\pi$
$457$	−4.03898	−0.188936	−0.0944678	+	0.995528i	$0.530115\pi$
$458$	21.5747	1.00812
$459$	22.3739	1.04432
$460$	9.86128	0.459785
$461$	−8.84943	−0.412159	−0.206079	−	0.978535i	$-0.566071\pi$
$461$	−8.84943	−0.412159	−0.206079	+	0.978535i	$0.566071\pi$
$462$	−15.7750	−0.733921
$463$	−0.962905	−0.0447500	−0.0223750	−	0.999750i	$-0.507123\pi$
$463$	−0.962905	−0.0447500	−0.0223750	+	0.999750i	$0.507123\pi$
$464$	8.93346	0.414725
$465$	13.5627	0.628953
$466$	−19.1787	−0.888435
$467$	21.5110	0.995412	0.497706	−	0.867346i	$-0.334176\pi$
$467$	21.5110	0.995412	0.497706	+	0.867346i	$0.334176\pi$
$468$	−6.72567	−0.310894
$469$	−18.1688	−0.838958
$470$	−3.28382	−0.151471
$471$	−7.06490	−0.325533
$472$	10.1953	0.469275
$473$	−29.9950	−1.37917
$474$	−3.16623	−0.145430
$475$	−5.66758	−0.260047
$476$	14.9160	0.683676
$477$	10.9157	0.499796
$478$	−0.156735	−0.00716887
$479$	5.71947	0.261329	0.130665	−	0.991427i	$-0.458289\pi$
$479$	5.71947	0.261329	0.130665	+	0.991427i	$0.458289\pi$
$480$	−3.09994	−0.141492
$481$	−11.5770	−0.527865
$482$	−8.82705	−0.402061
$483$	9.24597	0.420706
$484$	15.5361	0.706184
$485$	−13.1237	−0.595917
$486$	16.1365	0.731967
$487$	−6.95539	−0.315179	−0.157589	−	0.987505i	$-0.550372\pi$
$487$	−6.95539	−0.315179	−0.157589	+	0.987505i	$0.550372\pi$
$488$	−0.600499	−0.0271833
$489$	−0.952166	−0.0430584
$490$	11.1385	0.503188
$491$	24.5069	1.10598	0.552990	−	0.833188i	$-0.313487\pi$
$491$	24.5069	1.10598	0.552990	+	0.833188i	$0.313487\pi$
$492$	7.83602	0.353275
$493$	41.2992	1.86002
$494$	3.20396	0.144153
$495$	−35.3183	−1.58744
$496$	4.37513	0.196449
$497$	6.06323	0.271973
$498$	−4.46716	−0.200178
$499$	26.8422	1.20162	0.600810	−	0.799391i	$-0.294845\pi$
$499$	26.8422	1.20162	0.600810	+	0.799391i	$0.294845\pi$
$500$	−2.18041	−0.0975108
$501$	17.2857	0.772270
$502$	−0.119645	−0.00534003
$503$	16.5175	0.736481	0.368240	−	0.929731i	$-0.379960\pi$
$503$	16.5175	0.736481	0.368240	+	0.929731i	$0.379960\pi$
$504$	6.77299	0.301693
$505$	31.8940	1.41926
$506$	−15.5532	−0.691422
$507$	2.59550	0.115270
$508$	0.553740	0.0245682
$509$	10.9273	0.484344	0.242172	−	0.970233i	$-0.422140\pi$
$509$	10.9273	0.484344	0.242172	+	0.970233i	$0.422140\pi$
$510$	−14.3310	−0.634585
$511$	−24.9003	−1.10152
$512$	−1.00000	−0.0441942
$513$	−4.83972	−0.213679
$514$	−19.4630	−0.858475
$515$	−30.7675	−1.35578
$516$	−5.52651	−0.243291
$517$	5.17922	0.227782
$518$	11.6585	0.512243
$519$	8.05485	0.353569
$520$	10.4645	0.458900
$521$	34.9736	1.53222	0.766110	−	0.642710i	$-0.222190\pi$
$521$	34.9736	1.53222	0.766110	+	0.642710i	$0.222190\pi$
$522$	18.7529	0.820792
$523$	22.8236	0.998008	0.499004	−	0.866600i	$-0.333699\pi$
$523$	22.8236	0.998008	0.499004	+	0.866600i	$0.333699\pi$
$524$	7.67551	0.335306
$525$	−17.3560	−0.757479
$526$	13.1213	0.572116
$527$	20.2261	0.881064
$528$	4.88921	0.212775
$529$	−13.8841	−0.603656
$530$	−16.9839	−0.737733
$531$	21.4016	0.928752
$532$	−3.22650	−0.139887
$533$	−26.4522	−1.14577
$534$	9.53345	0.412553
$535$	−22.8579	−0.988235
$536$	5.63112	0.243227
$537$	9.62144	0.415196
$538$	−25.8999	−1.11663
$539$	−17.5676	−0.756692
$540$	−15.8071	−0.680231
$541$	−40.6570	−1.74798	−0.873991	−	0.485942i	$-0.838477\pi$
$541$	−40.6570	−1.74798	−0.873991	+	0.485942i	$0.838477\pi$
$542$	−23.1282	−0.993443
$543$	−14.8282	−0.636339
$544$	−4.62298	−0.198208
$545$	59.6941	2.55701
$546$	9.81159	0.419897
$547$	3.26130	0.139443	0.0697216	−	0.997566i	$-0.477789\pi$
$547$	3.26130	0.139443	0.0697216	+	0.997566i	$0.477789\pi$
$548$	2.69579	0.115159
$549$	−1.26055	−0.0537991
$550$	29.1955	1.24490
$551$	−8.93346	−0.380578
$552$	−2.86563	−0.121969
$553$	−10.7635	−0.457712
$554$	30.7639	1.30703
$555$	−11.2011	−0.475462
$556$	9.87353	0.418731
$557$	−0.344876	−0.0146129	−0.00730644	−	0.999973i	$-0.502326\pi$
$557$	−0.344876	−0.0146129	−0.00730644	+	0.999973i	$0.502326\pi$
$558$	9.18417	0.388797
$559$	18.6559	0.789062
$560$	−10.5382	−0.445319
$561$	22.6027	0.954286
$562$	−21.2342	−0.895712
$563$	−20.1981	−0.851249	−0.425624	−	0.904900i	$-0.639946\pi$
$563$	−20.1981	−0.851249	−0.425624	+	0.904900i	$0.639946\pi$
$564$	0.954260	0.0401816
$565$	35.9927	1.51422
$566$	13.4715	0.566250
$567$	5.49814	0.230900
$568$	−1.87920	−0.0788493
$569$	−3.00751	−0.126081	−0.0630407	−	0.998011i	$-0.520080\pi$
$569$	−3.00751	−0.126081	−0.0630407	+	0.998011i	$0.520080\pi$
$570$	3.09994	0.129842
$571$	24.5322	1.02664	0.513319	−	0.858198i	$-0.328416\pi$
$571$	24.5322	1.02664	0.513319	+	0.858198i	$0.328416\pi$
$572$	−16.5046	−0.690092
$573$	−26.0001	−1.08617
$574$	26.6383	1.11186
$575$	−17.1119	−0.713615
$576$	−2.09917	−0.0874656
$577$	−5.05190	−0.210313	−0.105157	−	0.994456i	$-0.533534\pi$
$577$	−5.05190	−0.210313	−0.105157	+	0.994456i	$0.533534\pi$
$578$	−4.37191	−0.181847
$579$	16.1735	0.672147
$580$	−29.1778	−1.21154
$581$	−15.1860	−0.630021
$582$	3.81368	0.158082
$583$	26.7869	1.10940
$584$	7.71742	0.319349
$585$	21.9669	0.908219
$586$	24.0424	0.993184
$587$	27.5110	1.13550	0.567750	−	0.823201i	$-0.307814\pi$
$587$	27.5110	1.13550	0.567750	+	0.823201i	$0.307814\pi$
$588$	−3.23680	−0.133483
$589$	−4.37513	−0.180274
$590$	−33.2990	−1.37090
$591$	−11.6146	−0.477761
$592$	−3.61334	−0.148507
$593$	−0.754287	−0.0309749	−0.0154874	−	0.999880i	$-0.504930\pi$
$593$	−0.754287	−0.0309749	−0.0154874	+	0.999880i	$0.504930\pi$
$594$	24.9309	1.02293
$595$	−48.7177	−1.99723
$596$	−3.88422	−0.159104
$597$	−17.7574	−0.726761
$598$	9.67358	0.395582
$599$	−20.6282	−0.842845	−0.421422	−	0.906864i	$-0.638469\pi$
$599$	−20.6282	−0.842845	−0.421422	+	0.906864i	$0.638469\pi$
$600$	5.37921	0.219605
$601$	0.794300	0.0324002	0.0162001	−	0.999869i	$-0.494843\pi$
$601$	0.794300	0.0324002	0.0162001	+	0.999869i	$0.494843\pi$
$602$	−18.7872	−0.765709
$603$	11.8207	0.481376
$604$	−2.36242	−0.0961257
$605$	−50.7427	−2.06299
$606$	−9.26821	−0.376495
$607$	43.4300	1.76277	0.881385	−	0.472398i	$-0.156611\pi$
$607$	43.4300	1.76277	0.881385	+	0.472398i	$0.156611\pi$
$608$	1.00000	0.0405554
$609$	−27.3572	−1.10857
$610$	1.96131	0.0794110
$611$	−3.22131	−0.130320
$612$	−9.70443	−0.392278
$613$	17.4333	0.704123	0.352062	−	0.935977i	$-0.385481\pi$
$613$	17.4333	0.704123	0.352062	+	0.935977i	$0.385481\pi$
$614$	−10.5564	−0.426021
$615$	−25.5934	−1.03203
$616$	16.6207	0.669669
$617$	42.3049	1.70313	0.851566	−	0.524247i	$-0.175653\pi$
$617$	42.3049	1.70313	0.851566	+	0.524247i	$0.175653\pi$
$618$	8.94086	0.359654
$619$	−40.5966	−1.63171	−0.815857	−	0.578254i	$-0.803734\pi$
$619$	−40.5966	−1.63171	−0.815857	+	0.578254i	$0.803734\pi$
$620$	−14.2897	−0.573890
$621$	−14.6124	−0.586374
$622$	1.66500	0.0667604
$623$	32.4087	1.29843
$624$	−3.04094	−0.121735
$625$	−21.2164	−0.848657
$626$	2.19081	0.0875622
$627$	−4.88921	−0.195256
$628$	7.44364	0.297034
$629$	−16.7044	−0.666047
$630$	−22.1214	−0.881340
$631$	32.0013	1.27395	0.636976	−	0.770883i	$-0.280185\pi$
$631$	32.0013	1.27395	0.636976	+	0.770883i	$0.280185\pi$
$632$	3.33597	0.132698
$633$	−0.949118	−0.0377241
$634$	−15.5722	−0.618452
$635$	−1.80858	−0.0717715
$636$	4.93542	0.195702
$637$	10.9265	0.432925
$638$	46.0191	1.82191
$639$	−3.94476	−0.156052
$640$	3.26613	0.129105
$641$	2.16377	0.0854638	0.0427319	−	0.999087i	$-0.486394\pi$
$641$	2.16377	0.0854638	0.0427319	+	0.999087i	$0.486394\pi$
$642$	6.64239	0.262154
$643$	8.29390	0.327080	0.163540	−	0.986537i	$-0.447709\pi$
$643$	8.29390	0.327080	0.163540	+	0.986537i	$0.447709\pi$
$644$	−9.74164	−0.383875
$645$	18.0503	0.710728
$646$	4.62298	0.181889
$647$	30.1103	1.18376	0.591879	−	0.806027i	$-0.298386\pi$
$647$	30.1103	1.18376	0.591879	+	0.806027i	$0.298386\pi$
$648$	−1.70406	−0.0669417
$649$	52.5190	2.06155
$650$	−18.1587	−0.712243
$651$	−13.3981	−0.525113
$652$	1.00321	0.0392888
$653$	10.0642	0.393842	0.196921	−	0.980419i	$-0.436906\pi$
$653$	10.0642	0.393842	0.196921	+	0.980419i	$0.436906\pi$
$654$	−17.3468	−0.678312
$655$	−25.0692	−0.979535
$656$	−8.25611	−0.322347
$657$	16.2002	0.632030
$658$	3.24398	0.126464
$659$	−24.1164	−0.939441	−0.469721	−	0.882815i	$-0.655645\pi$
$659$	−24.1164	−0.939441	−0.469721	+	0.882815i	$0.655645\pi$
$660$	−15.9688	−0.621584
$661$	43.2338	1.68160	0.840801	−	0.541345i	$-0.182085\pi$
$661$	43.2338	1.68160	0.840801	+	0.541345i	$0.182085\pi$
$662$	29.7515	1.15632
$663$	−14.0582	−0.545974
$664$	4.70664	0.182653
$665$	10.5382	0.408653
$666$	−7.58503	−0.293914
$667$	−26.9724	−1.04438
$668$	−18.2124	−0.704660
$669$	−3.71135	−0.143489
$670$	−18.3919	−0.710543
$671$	−3.09336	−0.119418
$672$	3.06233	0.118132
$673$	21.5579	0.830996	0.415498	−	0.909594i	$-0.363607\pi$
$673$	21.5579	0.830996	0.415498	+	0.909594i	$0.363607\pi$
$674$	−16.7770	−0.646227
$675$	27.4295	1.05576
$676$	−2.73465	−0.105179
$677$	−50.3044	−1.93336	−0.966678	−	0.255994i	$-0.917597\pi$
$677$	−50.3044	−1.93336	−0.966678	+	0.255994i	$0.917597\pi$
$678$	−10.4593	−0.401686
$679$	12.9645	0.497532
$680$	15.0992	0.579029
$681$	17.2873	0.662449
$682$	22.5377	0.863013
$683$	−1.03866	−0.0397434	−0.0198717	−	0.999803i	$-0.506326\pi$
$683$	−1.03866	−0.0397434	−0.0198717	+	0.999803i	$0.506326\pi$
$684$	2.09917	0.0802639
$685$	−8.80481	−0.336414
$686$	11.5821	0.442207
$687$	20.4769	0.781242
$688$	5.82278	0.221991
$689$	−16.6606	−0.634719
$690$	9.35952	0.356311
$691$	17.7308	0.674512	0.337256	−	0.941413i	$-0.390501\pi$
$691$	17.7308	0.674512	0.337256	+	0.941413i	$0.390501\pi$
$692$	−8.48666	−0.322615
$693$	34.8898	1.32535
$694$	−12.6733	−0.481073
$695$	−32.2482	−1.22324
$696$	8.47891	0.321392
$697$	−38.1678	−1.44571
$698$	−12.4997	−0.473122
$699$	−18.2028	−0.688494
$700$	18.2865	0.691164
$701$	−5.04450	−0.190528	−0.0952641	−	0.995452i	$-0.530370\pi$
$701$	−5.04450	−0.190528	−0.0952641	+	0.995452i	$0.530370\pi$
$702$	−15.5063	−0.585246
$703$	3.61334	0.136280
$704$	−5.15132	−0.194148
$705$	−3.11673	−0.117383
$706$	−7.83442	−0.294852
$707$	−31.5070	−1.18494
$708$	9.67651	0.363666
$709$	−37.2577	−1.39924	−0.699622	−	0.714513i	$-0.746648\pi$
$709$	−37.2577	−1.39924	−0.699622	+	0.714513i	$0.746648\pi$
$710$	6.13769	0.230343
$711$	7.00279	0.262625
$712$	−10.0445	−0.376435
$713$	−13.2097	−0.494705
$714$	14.1571	0.529816
$715$	53.9061	2.01597
$716$	−10.1372	−0.378846
$717$	−0.148760	−0.00555553
$718$	22.2087	0.828820
$719$	−4.75037	−0.177159	−0.0885795	−	0.996069i	$-0.528233\pi$
$719$	−4.75037	−0.177159	−0.0885795	+	0.996069i	$0.528233\pi$
$720$	6.85617	0.255514
$721$	30.3942	1.13194
$722$	−1.00000	−0.0372161
$723$	−8.37792	−0.311578
$724$	15.6231	0.580629
$725$	50.6311	1.88039
$726$	14.7456	0.547259
$727$	25.4435	0.943646	0.471823	−	0.881693i	$-0.343596\pi$
$727$	25.4435	0.943646	0.471823	+	0.881693i	$0.343596\pi$
$728$	−10.3376	−0.383136
$729$	10.2033	0.377900
$730$	−25.2061	−0.932918
$731$	26.9186	0.995619
$732$	−0.569945	−0.0210658
$733$	−38.5330	−1.42325	−0.711624	−	0.702561i	$-0.752040\pi$
$733$	−38.5330	−1.42325	−0.711624	+	0.702561i	$0.752040\pi$
$734$	1.03518	0.0382092
$735$	10.5718	0.389946
$736$	3.01926	0.111291
$737$	29.0077	1.06851
$738$	−17.3310	−0.637963
$739$	−1.39090	−0.0511650	−0.0255825	−	0.999673i	$-0.508144\pi$
$739$	−1.39090	−0.0511650	−0.0255825	+	0.999673i	$0.508144\pi$
$740$	11.8016	0.433836
$741$	3.04094	0.111712
$742$	16.7778	0.615934
$743$	−31.5057	−1.15583	−0.577916	−	0.816096i	$-0.696134\pi$
$743$	−31.5057	−1.15583	−0.577916	+	0.816096i	$0.696134\pi$
$744$	4.15252	0.152239
$745$	12.6863	0.464792
$746$	25.3354	0.927596
$747$	9.88006	0.361492
$748$	−23.8144	−0.870741
$749$	22.5806	0.825079
$750$	−2.06947	−0.0755662
$751$	−12.2013	−0.445233	−0.222616	−	0.974906i	$-0.571460\pi$
$751$	−12.2013	−0.445233	−0.222616	+	0.974906i	$0.571460\pi$
$752$	−1.00542	−0.0366638
$753$	−0.113558	−0.00413827
$754$	−28.6224	−1.04237
$755$	7.71598	0.280813
$756$	15.6154	0.567926
$757$	13.5758	0.493422	0.246711	−	0.969089i	$-0.420650\pi$
$757$	13.5758	0.493422	0.246711	+	0.969089i	$0.420650\pi$
$758$	−12.5467	−0.455717
$759$	−14.7618	−0.535819
$760$	−3.26613	−0.118475
$761$	−49.0183	−1.77691	−0.888456	−	0.458963i	$-0.848221\pi$
$761$	−49.0183	−1.77691	−0.888456	+	0.458963i	$0.848221\pi$
$762$	0.525565	0.0190392
$763$	−58.9699	−2.13485
$764$	27.3939	0.991077
$765$	31.6959	1.14597
$766$	2.08373	0.0752882
$767$	−32.6652	−1.17947
$768$	−0.949118	−0.0342484
$769$	−1.03334	−0.0372633	−0.0186316	−	0.999826i	$-0.505931\pi$
$769$	−1.03334	−0.0372633	−0.0186316	+	0.999826i	$0.505931\pi$
$770$	−54.2854	−1.95631
$771$	−18.4727	−0.665277
$772$	−17.0405	−0.613302
$773$	−5.82265	−0.209426	−0.104713	−	0.994502i	$-0.533392\pi$
$773$	−5.82265	−0.209426	−0.104713	+	0.994502i	$0.533392\pi$
$774$	12.2230	0.439348
$775$	24.7964	0.890714
$776$	−4.01813	−0.144242
$777$	11.0653	0.396964
$778$	−15.0615	−0.539981
$779$	8.25611	0.295806
$780$	9.93208	0.355626
$781$	−9.68033	−0.346389
$782$	13.9580	0.499136
$783$	43.2354	1.54511
$784$	3.41032	0.121797
$785$	−24.3119	−0.867728
$786$	7.28497	0.259846
$787$	32.4180	1.15558	0.577788	−	0.816187i	$-0.303916\pi$
$787$	32.4180	1.15558	0.577788	+	0.816187i	$0.303916\pi$
$788$	12.2372	0.435934
$789$	12.4537	0.443362
$790$	−10.8957	−0.387652
$791$	−35.5560	−1.26423
$792$	−10.8135	−0.384241
$793$	1.92398	0.0683224
$794$	−4.41444	−0.156663
$795$	−16.1197	−0.571707
$796$	18.7093	0.663135
$797$	44.1738	1.56472	0.782359	−	0.622828i	$-0.214016\pi$
$797$	44.1738	1.56472	0.782359	+	0.622828i	$0.214016\pi$
$798$	−3.06233	−0.108405
$799$	−4.64802	−0.164435
$800$	−5.66758	−0.200379
$801$	−21.0852	−0.745010
$802$	−7.79373	−0.275206
$803$	39.7548	1.40292
$804$	5.34460	0.188489
$805$	31.8174	1.12142
$806$	−14.0177	−0.493754
$807$	−24.5821	−0.865331
$808$	9.76507	0.343534
$809$	−10.7025	−0.376281	−0.188141	−	0.982142i	$-0.560246\pi$
$809$	−10.7025	−0.376281	−0.188141	+	0.982142i	$0.560246\pi$
$810$	5.56566	0.195557
$811$	52.6366	1.84832	0.924161	−	0.382002i	$-0.124765\pi$
$811$	52.6366	1.84832	0.924161	+	0.382002i	$0.124765\pi$
$812$	28.8238	1.01152
$813$	−21.9514	−0.769871
$814$	−18.6135	−0.652401
$815$	−3.27662	−0.114775
$816$	−4.38775	−0.153602
$817$	−5.82278	−0.203713
$818$	−19.9662	−0.698103
$819$	−21.7004	−0.758273
$820$	26.9655	0.941676
$821$	50.3434	1.75700	0.878498	−	0.477746i	$-0.158546\pi$
$821$	50.3434	1.75700	0.878498	+	0.477746i	$0.158546\pi$
$822$	2.55863	0.0892424
$823$	−8.01521	−0.279393	−0.139696	−	0.990194i	$-0.544613\pi$
$823$	−8.01521	−0.279393	−0.139696	+	0.990194i	$0.544613\pi$
$824$	−9.42018	−0.328167
$825$	27.7100	0.964738
$826$	32.8951	1.14457
$827$	45.8385	1.59396	0.796980	−	0.604006i	$-0.206430\pi$
$827$	45.8385	1.59396	0.796980	+	0.604006i	$0.206430\pi$
$828$	6.33795	0.220259
$829$	5.10796	0.177407	0.0887034	−	0.996058i	$-0.471728\pi$
$829$	5.10796	0.177407	0.0887034	+	0.996058i	$0.471728\pi$
$830$	−15.3725	−0.533587
$831$	29.1986	1.01289
$832$	3.20396	0.111077
$833$	15.7658	0.546254
$834$	9.37115	0.324496
$835$	59.4841	2.05853
$836$	5.15132	0.178162
$837$	21.1744	0.731895
$838$	12.8572	0.444146
$839$	15.5259	0.536015	0.268007	−	0.963417i	$-0.413635\pi$
$839$	15.5259	0.536015	0.268007	+	0.963417i	$0.413635\pi$
$840$	−10.0020	−0.345101
$841$	50.8067	1.75195
$842$	−21.6223	−0.745155
$843$	−20.1538	−0.694134
$844$	1.00000	0.0344214
$845$	8.93171	0.307260
$846$	−2.11055	−0.0725621
$847$	50.1271	1.72239
$848$	−5.20001	−0.178569
$849$	12.7861	0.438817
$850$	−26.2011	−0.898690
$851$	10.9096	0.373977
$852$	−1.78358	−0.0611044
$853$	43.8829	1.50252	0.751260	−	0.660006i	$-0.229446\pi$
$853$	43.8829	1.50252	0.751260	+	0.660006i	$0.229446\pi$
$854$	−1.93751	−0.0663003
$855$	−6.85617	−0.234476
$856$	−6.99849	−0.239203
$857$	−6.62229	−0.226213	−0.113107	−	0.993583i	$-0.536080\pi$
$857$	−6.62229	−0.226213	−0.113107	+	0.993583i	$0.536080\pi$
$858$	−15.6648	−0.534788
$859$	36.7706	1.25460	0.627299	−	0.778779i	$-0.284161\pi$
$859$	36.7706	1.25460	0.627299	+	0.778779i	$0.284161\pi$
$860$	−19.0179	−0.648506
$861$	25.2829	0.861640
$862$	1.58756	0.0540724
$863$	9.18036	0.312503	0.156252	−	0.987717i	$-0.450059\pi$
$863$	9.18036	0.312503	0.156252	+	0.987717i	$0.450059\pi$
$864$	−4.83972	−0.164651
$865$	27.7185	0.942458
$866$	−36.6233	−1.24451
$867$	−4.14946	−0.140923
$868$	14.1164	0.479141
$869$	17.1846	0.582949
$870$	−27.6932	−0.938887
$871$	−18.0419	−0.611325
$872$	18.2767	0.618928
$873$	−8.43475	−0.285473
$874$	−3.01926	−0.102128
$875$	−7.03510	−0.237830
$876$	7.32474	0.247480
$877$	−10.4930	−0.354324	−0.177162	−	0.984182i	$-0.556692\pi$
$877$	−10.4930	−0.354324	−0.177162	+	0.984182i	$0.556692\pi$
$878$	−32.5796	−1.09951
$879$	22.8191	0.769670
$880$	16.8248	0.567166
$881$	−33.8170	−1.13933	−0.569663	−	0.821879i	$-0.692926\pi$
$881$	−33.8170	−1.13933	−0.569663	+	0.821879i	$0.692926\pi$
$882$	7.15886	0.241051
$883$	33.2308	1.11831	0.559153	−	0.829065i	$-0.311126\pi$
$883$	33.2308	1.11831	0.559153	+	0.829065i	$0.311126\pi$
$884$	14.8118	0.498176
$885$	−31.6047	−1.06238
$886$	0.154447	0.00518876
$887$	4.99405	0.167684	0.0838419	−	0.996479i	$-0.473281\pi$
$887$	4.99405	0.167684	0.0838419	+	0.996479i	$0.473281\pi$
$888$	−3.42949	−0.115086
$889$	1.78664	0.0599221
$890$	32.8067	1.09968
$891$	−8.77813	−0.294079
$892$	3.91031	0.130927
$893$	1.00542	0.0336450
$894$	−3.68658	−0.123298
$895$	33.1095	1.10673
$896$	−3.22650	−0.107790
$897$	9.18137	0.306557
$898$	−19.2904	−0.643729
$899$	39.0851	1.30356
$900$	−11.8972	−0.396575
$901$	−24.0395	−0.800872
$902$	−42.5298	−1.41609
$903$	−17.8313	−0.593388
$904$	11.0200	0.366519
$905$	−51.0271	−1.69620
$906$	−2.24222	−0.0744928
$907$	10.2420	0.340082	0.170041	−	0.985437i	$-0.445610\pi$
$907$	10.2420	0.340082	0.170041	+	0.985437i	$0.445610\pi$
$908$	−18.2140	−0.604453
$909$	20.4986	0.679895
$910$	33.7639	1.11926
$911$	−40.4369	−1.33973	−0.669867	−	0.742481i	$-0.733649\pi$
$911$	−40.4369	−1.33973	−0.669867	+	0.742481i	$0.733649\pi$
$912$	0.949118	0.0314284
$913$	24.2454	0.802405
$914$	4.03898	0.133598
$915$	1.86151	0.0615397
$916$	−21.5747	−0.712847
$917$	24.7651	0.817814
$918$	−22.3739	−0.738449
$919$	19.3663	0.638835	0.319418	−	0.947614i	$-0.396513\pi$
$919$	19.3663	0.638835	0.319418	+	0.947614i	$0.396513\pi$
$920$	−9.86128	−0.325117
$921$	−10.0193	−0.330146
$922$	8.84943	0.291440
$923$	6.02087	0.198179
$924$	15.7750	0.518961
$925$	−20.4789	−0.673342
$926$	0.962905	0.0316430
$927$	−19.7746	−0.649483
$928$	−8.93346	−0.293255
$929$	57.6263	1.89066	0.945329	−	0.326118i	$-0.105741\pi$
$929$	57.6263	1.89066	0.945329	+	0.326118i	$0.105741\pi$
$930$	−13.5627	−0.444737
$931$	−3.41032	−0.111769
$932$	19.1787	0.628218
$933$	1.58028	0.0517361
$934$	−21.5110	−0.703863
$935$	77.7809	2.54371
$936$	6.72567	0.219835
$937$	2.24945	0.0734864	0.0367432	−	0.999325i	$-0.488302\pi$
$937$	2.24945	0.0734864	0.0367432	+	0.999325i	$0.488302\pi$
$938$	18.1688	0.593233
$939$	2.07933	0.0678565
$940$	3.28382	0.107106
$941$	−47.3516	−1.54362	−0.771808	−	0.635855i	$-0.780647\pi$
$941$	−47.3516	−1.54362	−0.771808	+	0.635855i	$0.780647\pi$
$942$	7.06490	0.230187
$943$	24.9273	0.811745
$944$	−10.1953	−0.331828
$945$	−51.0018	−1.65909
$946$	29.9950	0.975220
$947$	−14.3142	−0.465150	−0.232575	−	0.972578i	$-0.574715\pi$
$947$	−14.3142	−0.465150	−0.232575	+	0.972578i	$0.574715\pi$
$948$	3.16623	0.102834
$949$	−24.7263	−0.802649
$950$	5.66758	0.183881
$951$	−14.7799	−0.479271
$952$	−14.9160	−0.483432
$953$	−29.6797	−0.961419	−0.480710	−	0.876880i	$-0.659621\pi$
$953$	−29.6797	−0.961419	−0.480710	+	0.876880i	$0.659621\pi$
$954$	−10.9157	−0.353409
$955$	−89.4720	−2.89525
$956$	0.156735	0.00506916
$957$	43.6775	1.41189
$958$	−5.71947	−0.184788
$959$	8.69799	0.280873
$960$	3.09994	0.100050
$961$	−11.8582	−0.382523
$962$	11.5770	0.373257
$963$	−14.6910	−0.473412
$964$	8.82705	0.284300
$965$	55.6565	1.79165
$966$	−9.24597	−0.297484
$967$	−25.0414	−0.805276	−0.402638	−	0.915359i	$-0.631907\pi$
$967$	−25.0414	−0.805276	−0.402638	+	0.915359i	$0.631907\pi$
$968$	−15.5361	−0.499348
$969$	4.38775	0.140955
$970$	13.1237	0.421377
$971$	−14.7229	−0.472481	−0.236241	−	0.971695i	$-0.575915\pi$
$971$	−14.7229	−0.472481	−0.236241	+	0.971695i	$0.575915\pi$
$972$	−16.1365	−0.517579
$973$	31.8570	1.02129
$974$	6.95539	0.222865
$975$	−17.2348	−0.551954
$976$	0.600499	0.0192215
$977$	31.3557	1.00316	0.501580	−	0.865111i	$-0.332752\pi$
$977$	31.3557	1.00316	0.501580	+	0.865111i	$0.332752\pi$
$978$	0.952166	0.0304469
$979$	−51.7426	−1.65370
$980$	−11.1385	−0.355808
$981$	38.3660	1.22493
$982$	−24.5069	−0.782046
$983$	58.4213	1.86335	0.931675	−	0.363294i	$-0.118348\pi$
$983$	58.4213	1.86335	0.931675	+	0.363294i	$0.118348\pi$
$984$	−7.83602	−0.249803
$985$	−39.9684	−1.27350
$986$	−41.2992	−1.31523
$987$	3.07892	0.0980032
$988$	−3.20396	−0.101932
$989$	−17.5805	−0.559026
$990$	35.3183	1.12249
$991$	−29.1746	−0.926761	−0.463380	−	0.886159i	$-0.653364\pi$
$991$	−29.1746	−0.926761	−0.463380	+	0.886159i	$0.653364\pi$
$992$	−4.37513	−0.138911
$993$	28.2377	0.896095
$994$	−6.06323	−0.192314
$995$	−61.1071	−1.93723
$996$	4.46716	0.141547
$997$	−35.9166	−1.13749	−0.568745	−	0.822514i	$-0.692571\pi$
$997$	−35.9166	−1.13749	−0.568745	+	0.822514i	$0.692571\pi$
$998$	−26.8422	−0.849674
$999$	−17.4876	−0.553282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.15	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.15	✓	41	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.949118 q^{3} +1.00000 q^{4} -3.26613 q^{5} +0.949118 q^{6} +3.22650 q^{7} -1.00000 q^{8} -2.09917 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.949118 q^{3} +1.00000 q^{4} -3.26613 q^{5} +0.949118 q^{6} +3.22650 q^{7} -1.00000 q^{8} -2.09917 q^{9} +3.26613 q^{10} -5.15132 q^{11} -0.949118 q^{12} +3.20396 q^{13} -3.22650 q^{14} +3.09994 q^{15} +1.00000 q^{16} +4.62298 q^{17} +2.09917 q^{18} -1.00000 q^{19} -3.26613 q^{20} -3.06233 q^{21} +5.15132 q^{22} -3.01926 q^{23} +0.949118 q^{24} +5.66758 q^{25} -3.20396 q^{26} +4.83972 q^{27} +3.22650 q^{28} +8.93346 q^{29} -3.09994 q^{30} +4.37513 q^{31} -1.00000 q^{32} +4.88921 q^{33} -4.62298 q^{34} -10.5382 q^{35} -2.09917 q^{36} -3.61334 q^{37} +1.00000 q^{38} -3.04094 q^{39} +3.26613 q^{40} -8.25611 q^{41} +3.06233 q^{42} +5.82278 q^{43} -5.15132 q^{44} +6.85617 q^{45} +3.01926 q^{46} -1.00542 q^{47} -0.949118 q^{48} +3.41032 q^{49} -5.66758 q^{50} -4.38775 q^{51} +3.20396 q^{52} -5.20001 q^{53} -4.83972 q^{54} +16.8248 q^{55} -3.22650 q^{56} +0.949118 q^{57} -8.93346 q^{58} -10.1953 q^{59} +3.09994 q^{60} +0.600499 q^{61} -4.37513 q^{62} -6.77299 q^{63} +1.00000 q^{64} -10.4645 q^{65} -4.88921 q^{66} -5.63112 q^{67} +4.62298 q^{68} +2.86563 q^{69} +10.5382 q^{70} +1.87920 q^{71} +2.09917 q^{72} -7.71742 q^{73} +3.61334 q^{74} -5.37921 q^{75} -1.00000 q^{76} -16.6207 q^{77} +3.04094 q^{78} -3.33597 q^{79} -3.26613 q^{80} +1.70406 q^{81} +8.25611 q^{82} -4.70664 q^{83} -3.06233 q^{84} -15.0992 q^{85} -5.82278 q^{86} -8.47891 q^{87} +5.15132 q^{88} +10.0445 q^{89} -6.85617 q^{90} +10.3376 q^{91} -3.01926 q^{92} -4.15252 q^{93} +1.00542 q^{94} +3.26613 q^{95} +0.949118 q^{96} +4.01813 q^{97} -3.41032 q^{98} +10.8135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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