LMFDB - Embedded newform 5054.2.a.bg.1.3

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:	$0$
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			1.3
Root			$-2.15124$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.30521 q^{3} +1.00000 q^{4} -0.772004 q^{5} +1.30521 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.29642 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.30521 q^{3} +1.00000 q^{4} -0.772004 q^{5} +1.30521 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.29642 q^{9} +0.772004 q^{10} -4.01587 q^{11} -1.30521 q^{12} -2.67057 q^{13} -1.00000 q^{14} +1.00763 q^{15} +1.00000 q^{16} -4.72112 q^{17} +1.29642 q^{18} -0.772004 q^{20} -1.30521 q^{21} +4.01587 q^{22} -4.56856 q^{23} +1.30521 q^{24} -4.40401 q^{25} +2.67057 q^{26} +5.60774 q^{27} +1.00000 q^{28} -5.27409 q^{29} -1.00763 q^{30} +10.0904 q^{31} -1.00000 q^{32} +5.24156 q^{33} +4.72112 q^{34} -0.772004 q^{35} -1.29642 q^{36} -7.99584 q^{37} +3.48566 q^{39} +0.772004 q^{40} -3.42621 q^{41} +1.30521 q^{42} -10.8886 q^{43} -4.01587 q^{44} +1.00084 q^{45} +4.56856 q^{46} -9.84171 q^{47} -1.30521 q^{48} +1.00000 q^{49} +4.40401 q^{50} +6.16206 q^{51} -2.67057 q^{52} -5.96271 q^{53} -5.60774 q^{54} +3.10027 q^{55} -1.00000 q^{56} +5.27409 q^{58} -1.59401 q^{59} +1.00763 q^{60} +5.77528 q^{61} -10.0904 q^{62} -1.29642 q^{63} +1.00000 q^{64} +2.06169 q^{65} -5.24156 q^{66} +15.2120 q^{67} -4.72112 q^{68} +5.96294 q^{69} +0.772004 q^{70} +0.966715 q^{71} +1.29642 q^{72} -2.90368 q^{73} +7.99584 q^{74} +5.74817 q^{75} -4.01587 q^{77} -3.48566 q^{78} +7.17303 q^{79} -0.772004 q^{80} -3.43002 q^{81} +3.42621 q^{82} +7.87177 q^{83} -1.30521 q^{84} +3.64472 q^{85} +10.8886 q^{86} +6.88380 q^{87} +4.01587 q^{88} +1.69809 q^{89} -1.00084 q^{90} -2.67057 q^{91} -4.56856 q^{92} -13.1700 q^{93} +9.84171 q^{94} +1.30521 q^{96} -4.70054 q^{97} -1.00000 q^{98} +5.20626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 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 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 2 q^{10} - 12 q^{11} + 4 q^{12} + 10 q^{13} - 8 q^{14} + 24 q^{15} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 2 q^{20} + 4 q^{21} + 12 q^{22} - 20 q^{23} - 4 q^{24} + 8 q^{25} - 10 q^{26} + 22 q^{27} + 8 q^{28} + 8 q^{29} - 24 q^{30} + 18 q^{31} - 8 q^{32} - 16 q^{33} + 6 q^{34} - 2 q^{35} + 8 q^{36} + 36 q^{37} + 2 q^{40} + 4 q^{41} - 4 q^{42} - 16 q^{43} - 12 q^{44} + 8 q^{45} + 20 q^{46} - 10 q^{47} + 4 q^{48} + 8 q^{49} - 8 q^{50} + 12 q^{51} + 10 q^{52} + 32 q^{53} - 22 q^{54} - 22 q^{55} - 8 q^{56} - 8 q^{58} - 2 q^{59} + 24 q^{60} + 2 q^{61} - 18 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{66} + 44 q^{67} - 6 q^{68} + 2 q^{70} + 8 q^{71} - 8 q^{72} + 30 q^{73} - 36 q^{74} - 16 q^{75} - 12 q^{77} + 60 q^{79} - 2 q^{80} + 12 q^{81} - 4 q^{82} - 28 q^{83} + 4 q^{84} - 16 q^{85} + 16 q^{86} + 24 q^{87} + 12 q^{88} - 22 q^{89} - 8 q^{90} + 10 q^{91} - 20 q^{92} - 16 q^{93} + 10 q^{94} - 4 q^{96} - 6 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 2 * q^10 - 12 * q^11 + 4 * q^12 + 10 * q^13 - 8 * q^14 + 24 * q^15 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 2 * q^20 + 4 * q^21 + 12 * q^22 - 20 * q^23 - 4 * q^24 + 8 * q^25 - 10 * q^26 + 22 * q^27 + 8 * q^28 + 8 * q^29 - 24 * q^30 + 18 * q^31 - 8 * q^32 - 16 * q^33 + 6 * q^34 - 2 * q^35 + 8 * q^36 + 36 * q^37 + 2 * q^40 + 4 * q^41 - 4 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 + 20 * q^46 - 10 * q^47 + 4 * q^48 + 8 * q^49 - 8 * q^50 + 12 * q^51 + 10 * q^52 + 32 * q^53 - 22 * q^54 - 22 * q^55 - 8 * q^56 - 8 * q^58 - 2 * q^59 + 24 * q^60 + 2 * q^61 - 18 * q^62 + 8 * q^63 + 8 * q^64 + 16 * q^66 + 44 * q^67 - 6 * q^68 + 2 * q^70 + 8 * q^71 - 8 * q^72 + 30 * q^73 - 36 * q^74 - 16 * q^75 - 12 * q^77 + 60 * q^79 - 2 * q^80 + 12 * q^81 - 4 * q^82 - 28 * q^83 + 4 * q^84 - 16 * q^85 + 16 * q^86 + 24 * q^87 + 12 * q^88 - 22 * q^89 - 8 * q^90 + 10 * q^91 - 20 * q^92 - 16 * q^93 + 10 * q^94 - 4 * q^96 - 6 * q^97 - 8 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.30521	−0.753564	−0.376782	−	0.926302i	$-0.622969\pi$
$3$	−1.30521	−0.753564	−0.376782	+	0.926302i	$0.622969\pi$
$4$	1.00000	0.500000
$5$	−0.772004	−0.345251	−0.172625	−	0.984988i	$-0.555225\pi$
$5$	−0.772004	−0.345251	−0.172625	+	0.984988i	$0.555225\pi$
$6$	1.30521	0.532850
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−1.29642	−0.432141
$10$	0.772004	0.244129
$11$	−4.01587	−1.21083	−0.605415	−	0.795910i	$-0.706993\pi$
$11$	−4.01587	−1.21083	−0.605415	+	0.795910i	$0.706993\pi$
$12$	−1.30521	−0.376782
$13$	−2.67057	−0.740684	−0.370342	−	0.928895i	$-0.620760\pi$
$13$	−2.67057	−0.740684	−0.370342	+	0.928895i	$0.620760\pi$
$14$	−1.00000	−0.267261
$15$	1.00763	0.260169
$16$	1.00000	0.250000
$17$	−4.72112	−1.14504	−0.572520	−	0.819891i	$-0.694034\pi$
$17$	−4.72112	−1.14504	−0.572520	+	0.819891i	$0.694034\pi$
$18$	1.29642	0.305570
$19$	0	0
$19$	0	0
$20$	−0.772004	−0.172625
$21$	−1.30521	−0.284821
$22$	4.01587	0.856186
$23$	−4.56856	−0.952611	−0.476305	−	0.879280i	$-0.658024\pi$
$23$	−4.56856	−0.952611	−0.476305	+	0.879280i	$0.658024\pi$
$24$	1.30521	0.266425
$25$	−4.40401	−0.880802
$26$	2.67057	0.523743
$27$	5.60774	1.07921
$28$	1.00000	0.188982
$29$	−5.27409	−0.979373	−0.489687	−	0.871899i	$-0.662889\pi$
$29$	−5.27409	−0.979373	−0.489687	+	0.871899i	$0.662889\pi$
$30$	−1.00763	−0.183967
$31$	10.0904	1.81228	0.906141	−	0.422976i	$-0.139015\pi$
$31$	10.0904	1.81228	0.906141	+	0.422976i	$0.139015\pi$
$32$	−1.00000	−0.176777
$33$	5.24156	0.912438
$34$	4.72112	0.809666
$35$	−0.772004	−0.130492
$36$	−1.29642	−0.216070
$37$	−7.99584	−1.31451	−0.657254	−	0.753669i	$-0.728282\pi$
$37$	−7.99584	−1.31451	−0.657254	+	0.753669i	$0.728282\pi$
$38$	0	0
$39$	3.48566	0.558153
$40$	0.772004	0.122065
$41$	−3.42621	−0.535084	−0.267542	−	0.963546i	$-0.586211\pi$
$41$	−3.42621	−0.535084	−0.267542	+	0.963546i	$0.586211\pi$
$42$	1.30521	0.201399
$43$	−10.8886	−1.66050	−0.830251	−	0.557390i	$-0.811803\pi$
$43$	−10.8886	−1.66050	−0.830251	+	0.557390i	$0.811803\pi$
$44$	−4.01587	−0.605415
$45$	1.00084	0.149197
$46$	4.56856	0.673598
$47$	−9.84171	−1.43556	−0.717781	−	0.696269i	$-0.754842\pi$
$47$	−9.84171	−1.43556	−0.717781	+	0.696269i	$0.754842\pi$
$48$	−1.30521	−0.188391
$49$	1.00000	0.142857
$50$	4.40401	0.622821
$51$	6.16206	0.862861
$52$	−2.67057	−0.370342
$53$	−5.96271	−0.819041	−0.409520	−	0.912301i	$-0.634304\pi$
$53$	−5.96271	−0.819041	−0.409520	+	0.912301i	$0.634304\pi$
$54$	−5.60774	−0.763117
$55$	3.10027	0.418040
$56$	−1.00000	−0.133631
$57$	0	0
$58$	5.27409	0.692521
$59$	−1.59401	−0.207522	−0.103761	−	0.994602i	$-0.533088\pi$
$59$	−1.59401	−0.207522	−0.103761	+	0.994602i	$0.533088\pi$
$60$	1.00763	0.130084
$61$	5.77528	0.739449	0.369724	−	0.929141i	$-0.379452\pi$
$61$	5.77528	0.739449	0.369724	+	0.929141i	$0.379452\pi$
$62$	−10.0904	−1.28148
$63$	−1.29642	−0.163334
$64$	1.00000	0.125000
$65$	2.06169	0.255722
$66$	−5.24156	−0.645191
$67$	15.2120	1.85844	0.929222	−	0.369522i	$-0.120478\pi$
$67$	15.2120	1.85844	0.929222	+	0.369522i	$0.120478\pi$
$68$	−4.72112	−0.572520
$69$	5.96294	0.717854
$70$	0.772004	0.0922721
$71$	0.966715	0.114728	0.0573640	−	0.998353i	$-0.481730\pi$
$71$	0.966715	0.114728	0.0573640	+	0.998353i	$0.481730\pi$
$72$	1.29642	0.152785
$73$	−2.90368	−0.339850	−0.169925	−	0.985457i	$-0.554353\pi$
$73$	−2.90368	−0.339850	−0.169925	+	0.985457i	$0.554353\pi$
$74$	7.99584	0.929497
$75$	5.74817	0.663741
$76$	0	0
$77$	−4.01587	−0.457651
$78$	−3.48566	−0.394674
$79$	7.17303	0.807029	0.403515	−	0.914973i	$-0.367788\pi$
$79$	7.17303	0.807029	0.403515	+	0.914973i	$0.367788\pi$
$80$	−0.772004	−0.0863127
$81$	−3.43002	−0.381114
$82$	3.42621	0.378361
$83$	7.87177	0.864039	0.432020	−	0.901864i	$-0.357801\pi$
$83$	7.87177	0.864039	0.432020	+	0.901864i	$0.357801\pi$
$84$	−1.30521	−0.142410
$85$	3.64472	0.395326
$86$	10.8886	1.17415
$87$	6.88380	0.738021
$88$	4.01587	0.428093
$89$	1.69809	0.179997	0.0899987	−	0.995942i	$-0.471314\pi$
$89$	1.69809	0.179997	0.0899987	+	0.995942i	$0.471314\pi$
$90$	−1.00084	−0.105498
$91$	−2.67057	−0.279952
$92$	−4.56856	−0.476305
$93$	−13.1700	−1.36567
$94$	9.84171	1.01510
$95$	0	0
$96$	1.30521	0.133213
$97$	−4.70054	−0.477267	−0.238634	−	0.971110i	$-0.576699\pi$
$97$	−4.70054	−0.477267	−0.238634	+	0.971110i	$0.576699\pi$
$98$	−1.00000	−0.101015
$99$	5.20626	0.523249
$100$	−4.40401	−0.440401
$101$	10.2751	1.02241	0.511207	−	0.859458i	$-0.329199\pi$
$101$	10.2751	1.02241	0.511207	+	0.859458i	$0.329199\pi$
$102$	−6.16206	−0.610135
$103$	−0.355370	−0.0350156	−0.0175078	−	0.999847i	$-0.505573\pi$
$103$	−0.355370	−0.0350156	−0.0175078	+	0.999847i	$0.505573\pi$
$104$	2.67057	0.261871
$105$	1.00763	0.0983345
$106$	5.96271	0.579149
$107$	−2.49005	−0.240722	−0.120361	−	0.992730i	$-0.538405\pi$
$107$	−2.49005	−0.240722	−0.120361	+	0.992730i	$0.538405\pi$
$108$	5.60774	0.539605
$109$	7.77977	0.745166	0.372583	−	0.927999i	$-0.378472\pi$
$109$	7.77977	0.745166	0.372583	+	0.927999i	$0.378472\pi$
$110$	−3.10027	−0.295599
$111$	10.4363	0.990566
$112$	1.00000	0.0944911
$113$	−7.54578	−0.709847	−0.354923	−	0.934895i	$-0.615493\pi$
$113$	−7.54578	−0.709847	−0.354923	+	0.934895i	$0.615493\pi$
$114$	0	0
$115$	3.52695	0.328890
$116$	−5.27409	−0.489687
$117$	3.46219	0.320080
$118$	1.59401	0.146740
$119$	−4.72112	−0.432785
$120$	−1.00763	−0.0919835
$121$	5.12720	0.466109
$122$	−5.77528	−0.522869
$123$	4.47192	0.403220
$124$	10.0904	0.906141
$125$	7.25993	0.649348
$126$	1.29642	0.115494
$127$	−10.9147	−0.968523	−0.484262	−	0.874923i	$-0.660912\pi$
$127$	−10.9147	−0.968523	−0.484262	+	0.874923i	$0.660912\pi$
$128$	−1.00000	−0.0883883
$129$	14.2120	1.25129
$130$	−2.06169	−0.180823
$131$	−16.8368	−1.47103	−0.735517	−	0.677506i	$-0.763061\pi$
$131$	−16.8368	−1.47103	−0.735517	+	0.677506i	$0.763061\pi$
$132$	5.24156	0.456219
$133$	0	0
$134$	−15.2120	−1.31412
$135$	−4.32920	−0.372598
$136$	4.72112	0.404833
$137$	5.08460	0.434407	0.217203	−	0.976126i	$-0.430307\pi$
$137$	5.08460	0.434407	0.217203	+	0.976126i	$0.430307\pi$
$138$	−5.96294	−0.507599
$139$	−22.1630	−1.87984	−0.939919	−	0.341397i	$-0.889100\pi$
$139$	−22.1630	−1.87984	−0.939919	+	0.341397i	$0.889100\pi$
$140$	−0.772004	−0.0652462
$141$	12.8455	1.08179
$142$	−0.966715	−0.0811249
$143$	10.7247	0.896842
$144$	−1.29642	−0.108035
$145$	4.07162	0.338129
$146$	2.90368	0.240310
$147$	−1.30521	−0.107652
$148$	−7.99584	−0.657254
$149$	−3.50855	−0.287431	−0.143716	−	0.989619i	$-0.545905\pi$
$149$	−3.50855	−0.287431	−0.143716	+	0.989619i	$0.545905\pi$
$150$	−5.74817	−0.469336
$151$	−13.0681	−1.06346	−0.531732	−	0.846913i	$-0.678459\pi$
$151$	−13.0681	−1.06346	−0.531732	+	0.846913i	$0.678459\pi$
$152$	0	0
$153$	6.12057	0.494819
$154$	4.01587	0.323608
$155$	−7.78979	−0.625691
$156$	3.48566	0.279077
$157$	−9.26221	−0.739205	−0.369602	−	0.929190i	$-0.620506\pi$
$157$	−9.26221	−0.739205	−0.369602	+	0.929190i	$0.620506\pi$
$158$	−7.17303	−0.570656
$159$	7.78259	0.617200
$160$	0.772004	0.0610323
$161$	−4.56856	−0.360053
$162$	3.43002	0.269488
$163$	2.50601	0.196286	0.0981430	−	0.995172i	$-0.468710\pi$
$163$	2.50601	0.196286	0.0981430	+	0.995172i	$0.468710\pi$
$164$	−3.42621	−0.267542
$165$	−4.04650	−0.315020
$166$	−7.87177	−0.610968
$167$	−0.962633	−0.0744907	−0.0372454	−	0.999306i	$-0.511858\pi$
$167$	−0.962633	−0.0744907	−0.0372454	+	0.999306i	$0.511858\pi$
$168$	1.30521	0.100699
$169$	−5.86803	−0.451387
$170$	−3.64472	−0.279538
$171$	0	0
$172$	−10.8886	−0.830251
$173$	−18.4922	−1.40594	−0.702969	−	0.711221i	$-0.748143\pi$
$173$	−18.4922	−1.40594	−0.702969	+	0.711221i	$0.748143\pi$
$174$	−6.88380	−0.521859
$175$	−4.40401	−0.332912
$176$	−4.01587	−0.302707
$177$	2.08051	0.156381
$178$	−1.69809	−0.127277
$179$	3.85456	0.288103	0.144052	−	0.989570i	$-0.453987\pi$
$179$	3.85456	0.288103	0.144052	+	0.989570i	$0.453987\pi$
$180$	1.00084	0.0745985
$181$	−8.74364	−0.649910	−0.324955	−	0.945730i	$-0.605349\pi$
$181$	−8.74364	−0.649910	−0.324955	+	0.945730i	$0.605349\pi$
$182$	2.67057	0.197956
$183$	−7.53796	−0.557222
$184$	4.56856	0.336799
$185$	6.17282	0.453835
$186$	13.1700	0.965675
$187$	18.9594	1.38645
$188$	−9.84171	−0.717781
$189$	5.60774	0.407903
$190$	0	0
$191$	12.9786	0.939095	0.469548	−	0.882907i	$-0.344417\pi$
$191$	12.9786	0.939095	0.469548	+	0.882907i	$0.344417\pi$
$192$	−1.30521	−0.0941955
$193$	27.2242	1.95964	0.979821	−	0.199876i	$-0.0640539\pi$
$193$	27.2242	1.95964	0.979821	+	0.199876i	$0.0640539\pi$
$194$	4.70054	0.337479
$195$	−2.69095	−0.192703
$196$	1.00000	0.0714286
$197$	21.7044	1.54638	0.773188	−	0.634176i	$-0.218661\pi$
$197$	21.7044	1.54638	0.773188	+	0.634176i	$0.218661\pi$
$198$	−5.20626	−0.369993
$199$	−18.2165	−1.29133	−0.645667	−	0.763619i	$-0.723421\pi$
$199$	−18.2165	−1.29133	−0.645667	+	0.763619i	$0.723421\pi$
$200$	4.40401	0.311411
$201$	−19.8549	−1.40046
$202$	−10.2751	−0.722956
$203$	−5.27409	−0.370168
$204$	6.16206	0.431431
$205$	2.64505	0.184738
$206$	0.355370	0.0247598
$207$	5.92279	0.411662
$208$	−2.67057	−0.185171
$209$	0	0
$210$	−1.00763	−0.0695330
$211$	−3.42072	−0.235492	−0.117746	−	0.993044i	$-0.537567\pi$
$211$	−3.42072	−0.235492	−0.117746	+	0.993044i	$0.537567\pi$
$212$	−5.96271	−0.409520
$213$	−1.26177	−0.0864549
$214$	2.49005	0.170216
$215$	8.40607	0.573289
$216$	−5.60774	−0.381558
$217$	10.0904	0.684978
$218$	−7.77977	−0.526912
$219$	3.78991	0.256099
$220$	3.10027	0.209020
$221$	12.6081	0.848113
$222$	−10.4363	−0.700436
$223$	28.4613	1.90591	0.952954	−	0.303116i	$-0.0980270\pi$
$223$	28.4613	1.90591	0.952954	+	0.303116i	$0.0980270\pi$
$224$	−1.00000	−0.0668153
$225$	5.70946	0.380630
$226$	7.54578	0.501938
$227$	−6.96526	−0.462300	−0.231150	−	0.972918i	$-0.574249\pi$
$227$	−6.96526	−0.462300	−0.231150	+	0.972918i	$0.574249\pi$
$228$	0	0
$229$	−10.5878	−0.699661	−0.349830	−	0.936813i	$-0.613761\pi$
$229$	−10.5878	−0.699661	−0.349830	+	0.936813i	$0.613761\pi$
$230$	−3.52695	−0.232560
$231$	5.24156	0.344869
$232$	5.27409	0.346261
$233$	−23.0345	−1.50904	−0.754521	−	0.656276i	$-0.772131\pi$
$233$	−23.0345	−1.50904	−0.754521	+	0.656276i	$0.772131\pi$
$234$	−3.46219	−0.226331
$235$	7.59784	0.495629
$236$	−1.59401	−0.103761
$237$	−9.36233	−0.608149
$238$	4.72112	0.306025
$239$	−6.94984	−0.449548	−0.224774	−	0.974411i	$-0.572164\pi$
$239$	−6.94984	−0.449548	−0.224774	+	0.974411i	$0.572164\pi$
$240$	1.00763	0.0650421
$241$	21.4750	1.38332	0.691662	−	0.722221i	$-0.256879\pi$
$241$	21.4750	1.38332	0.691662	+	0.722221i	$0.256879\pi$
$242$	−5.12720	−0.329589
$243$	−12.3463	−0.792017
$244$	5.77528	0.369724
$245$	−0.772004	−0.0493215
$246$	−4.47192	−0.285120
$247$	0	0
$248$	−10.0904	−0.640738
$249$	−10.2743	−0.651109
$250$	−7.25993	−0.459158
$251$	14.5668	0.919451	0.459725	−	0.888061i	$-0.347948\pi$
$251$	14.5668	0.919451	0.459725	+	0.888061i	$0.347948\pi$
$252$	−1.29642	−0.0816669
$253$	18.3467	1.15345
$254$	10.9147	0.684849
$255$	−4.75714	−0.297903
$256$	1.00000	0.0625000
$257$	8.40699	0.524414	0.262207	−	0.965012i	$-0.415550\pi$
$257$	8.40699	0.524414	0.262207	+	0.965012i	$0.415550\pi$
$258$	−14.2120	−0.884799
$259$	−7.99584	−0.496837
$260$	2.06169	0.127861
$261$	6.83744	0.423227
$262$	16.8368	1.04018
$263$	29.0073	1.78867	0.894333	−	0.447402i	$-0.147651\pi$
$263$	29.0073	1.78867	0.894333	+	0.447402i	$0.147651\pi$
$264$	−5.24156	−0.322596
$265$	4.60323	0.282774
$266$	0	0
$267$	−2.21637	−0.135640
$268$	15.2120	0.929222
$269$	−18.2468	−1.11253	−0.556263	−	0.831006i	$-0.687765\pi$
$269$	−18.2468	−1.11253	−0.556263	+	0.831006i	$0.687765\pi$
$270$	4.32920	0.263467
$271$	15.7835	0.958779	0.479389	−	0.877602i	$-0.340858\pi$
$271$	15.7835	0.958779	0.479389	+	0.877602i	$0.340858\pi$
$272$	−4.72112	−0.286260
$273$	3.48566	0.210962
$274$	−5.08460	−0.307172
$275$	17.6859	1.06650
$276$	5.96294	0.358927
$277$	26.3565	1.58361	0.791803	−	0.610776i	$-0.209143\pi$
$277$	26.3565	1.58361	0.791803	+	0.610776i	$0.209143\pi$
$278$	22.1630	1.32925
$279$	−13.0814	−0.783161
$280$	0.772004	0.0461361
$281$	12.5092	0.746239	0.373119	−	0.927783i	$-0.378288\pi$
$281$	12.5092	0.746239	0.373119	+	0.927783i	$0.378288\pi$
$282$	−12.8455	−0.764939
$283$	−22.2158	−1.32059	−0.660296	−	0.751005i	$-0.729569\pi$
$283$	−22.2158	−1.32059	−0.660296	+	0.751005i	$0.729569\pi$
$284$	0.966715	0.0573640
$285$	0	0
$286$	−10.7247	−0.634163
$287$	−3.42621	−0.202243
$288$	1.29642	0.0763924
$289$	5.28899	0.311117
$290$	−4.07162	−0.239093
$291$	6.13519	0.359651
$292$	−2.90368	−0.169925
$293$	−25.8146	−1.50810	−0.754052	−	0.656814i	$-0.771903\pi$
$293$	−25.8146	−1.50810	−0.754052	+	0.656814i	$0.771903\pi$
$294$	1.30521	0.0761215
$295$	1.23058	0.0716471
$296$	7.99584	0.464749
$297$	−22.5199	−1.30674
$298$	3.50855	0.203245
$299$	12.2007	0.705584
$300$	5.74817	0.331870
$301$	−10.8886	−0.627610
$302$	13.0681	0.751983
$303$	−13.4112	−0.770455
$304$	0	0
$305$	−4.45854	−0.255295
$306$	−6.12057	−0.349890
$307$	−14.1872	−0.809706	−0.404853	−	0.914382i	$-0.632677\pi$
$307$	−14.1872	−0.809706	−0.404853	+	0.914382i	$0.632677\pi$
$308$	−4.01587	−0.228825
$309$	0.463833	0.0263865
$310$	7.78979	0.442431
$311$	−10.6714	−0.605122	−0.302561	−	0.953130i	$-0.597842\pi$
$311$	−10.6714	−0.605122	−0.302561	+	0.953130i	$0.597842\pi$
$312$	−3.48566	−0.197337
$313$	2.88981	0.163342	0.0816708	−	0.996659i	$-0.473974\pi$
$313$	2.88981	0.163342	0.0816708	+	0.996659i	$0.473974\pi$
$314$	9.26221	0.522697
$315$	1.00084	0.0563911
$316$	7.17303	0.403515
$317$	15.2490	0.856471	0.428236	−	0.903667i	$-0.359135\pi$
$317$	15.2490	0.856471	0.428236	+	0.903667i	$0.359135\pi$
$318$	−7.78259	−0.436426
$319$	21.1800	1.18585
$320$	−0.772004	−0.0431563
$321$	3.25004	0.181399
$322$	4.56856	0.254596
$323$	0	0
$324$	−3.43002	−0.190557
$325$	11.7612	0.652396
$326$	−2.50601	−0.138795
$327$	−10.1542	−0.561531
$328$	3.42621	0.189181
$329$	−9.84171	−0.542591
$330$	4.04650	0.222753
$331$	1.78424	0.0980708	0.0490354	−	0.998797i	$-0.484385\pi$
$331$	1.78424	0.0980708	0.0490354	+	0.998797i	$0.484385\pi$
$332$	7.87177	0.432020
$333$	10.3660	0.568052
$334$	0.962633	0.0526729
$335$	−11.7437	−0.641629
$336$	−1.30521	−0.0712051
$337$	33.1973	1.80837	0.904185	−	0.427141i	$-0.140479\pi$
$337$	33.1973	1.80837	0.904185	+	0.427141i	$0.140479\pi$
$338$	5.86803	0.319179
$339$	9.84884	0.534915
$340$	3.64472	0.197663
$341$	−40.5215	−2.19436
$342$	0	0
$343$	1.00000	0.0539949
$344$	10.8886	0.587076
$345$	−4.60341	−0.247839
$346$	18.4922	0.994148
$347$	9.99011	0.536297	0.268149	−	0.963378i	$-0.413588\pi$
$347$	9.99011	0.536297	0.268149	+	0.963378i	$0.413588\pi$
$348$	6.88380	0.369010
$349$	12.6661	0.678000	0.339000	−	0.940786i	$-0.389911\pi$
$349$	12.6661	0.678000	0.339000	+	0.940786i	$0.389911\pi$
$350$	4.40401	0.235404
$351$	−14.9759	−0.799354
$352$	4.01587	0.214046
$353$	19.7911	1.05337	0.526686	−	0.850060i	$-0.323434\pi$
$353$	19.7911	1.05337	0.526686	+	0.850060i	$0.323434\pi$
$354$	−2.08051	−0.110578
$355$	−0.746308	−0.0396099
$356$	1.69809	0.0899987
$357$	6.16206	0.326131
$358$	−3.85456	−0.203720
$359$	5.84794	0.308643	0.154321	−	0.988021i	$-0.450681\pi$
$359$	5.84794	0.308643	0.154321	+	0.988021i	$0.450681\pi$
$360$	−1.00084	−0.0527491
$361$	0	0
$362$	8.74364	0.459555
$363$	−6.69207	−0.351243
$364$	−2.67057	−0.139976
$365$	2.24165	0.117333
$366$	7.53796	0.394016
$367$	−28.5372	−1.48963	−0.744815	−	0.667271i	$-0.767462\pi$
$367$	−28.5372	−1.48963	−0.744815	+	0.667271i	$0.767462\pi$
$368$	−4.56856	−0.238153
$369$	4.44181	0.231231
$370$	−6.17282	−0.320910
$371$	−5.96271	−0.309568
$372$	−13.1700	−0.682835
$373$	−1.93655	−0.100271	−0.0501355	−	0.998742i	$-0.515965\pi$
$373$	−1.93655	−0.100271	−0.0501355	+	0.998742i	$0.515965\pi$
$374$	−18.9594	−0.980367
$375$	−9.47575	−0.489326
$376$	9.84171	0.507548
$377$	14.0848	0.725406
$378$	−5.60774	−0.288431
$379$	3.53725	0.181696	0.0908480	−	0.995865i	$-0.471042\pi$
$379$	3.53725	0.181696	0.0908480	+	0.995865i	$0.471042\pi$
$380$	0	0
$381$	14.2460	0.729845
$382$	−12.9786	−0.664040
$383$	−10.8421	−0.554007	−0.277004	−	0.960869i	$-0.589341\pi$
$383$	−10.8421	−0.554007	−0.277004	+	0.960869i	$0.589341\pi$
$384$	1.30521	0.0666063
$385$	3.10027	0.158004
$386$	−27.2242	−1.38568
$387$	14.1163	0.717570
$388$	−4.70054	−0.238634
$389$	15.9180	0.807072	0.403536	−	0.914964i	$-0.367781\pi$
$389$	15.9180	0.807072	0.403536	+	0.914964i	$0.367781\pi$
$390$	2.69095	0.136261
$391$	21.5687	1.09078
$392$	−1.00000	−0.0505076
$393$	21.9755	1.10852
$394$	−21.7044	−1.09345
$395$	−5.53761	−0.278627
$396$	5.20626	0.261624
$397$	25.6743	1.28856	0.644278	−	0.764791i	$-0.277158\pi$
$397$	25.6743	1.28856	0.644278	+	0.764791i	$0.277158\pi$
$398$	18.2165	0.913111
$399$	0	0
$400$	−4.40401	−0.220200
$401$	−30.4717	−1.52169	−0.760843	−	0.648936i	$-0.775214\pi$
$401$	−30.4717	−1.52169	−0.760843	+	0.648936i	$0.775214\pi$
$402$	19.8549	0.990273
$403$	−26.9470	−1.34233
$404$	10.2751	0.511207
$405$	2.64799	0.131580
$406$	5.27409	0.261749
$407$	32.1102	1.59164
$408$	−6.16206	−0.305068
$409$	4.71880	0.233330	0.116665	−	0.993171i	$-0.462780\pi$
$409$	4.71880	0.233330	0.116665	+	0.993171i	$0.462780\pi$
$410$	−2.64505	−0.130629
$411$	−6.63648	−0.327353
$412$	−0.355370	−0.0175078
$413$	−1.59401	−0.0784359
$414$	−5.92279	−0.291089
$415$	−6.07704	−0.298310
$416$	2.67057	0.130936
$417$	28.9274	1.41658
$418$	0	0
$419$	−2.87962	−0.140679	−0.0703393	−	0.997523i	$-0.522408\pi$
$419$	−2.87962	−0.140679	−0.0703393	+	0.997523i	$0.522408\pi$
$420$	1.00763	0.0491672
$421$	7.22939	0.352339	0.176169	−	0.984360i	$-0.443629\pi$
$421$	7.22939	0.352339	0.176169	+	0.984360i	$0.443629\pi$
$422$	3.42072	0.166518
$423$	12.7590	0.620365
$424$	5.96271	0.289575
$425$	20.7919	1.00855
$426$	1.26177	0.0611328
$427$	5.77528	0.279485
$428$	−2.49005	−0.120361
$429$	−13.9980	−0.675828
$430$	−8.40607	−0.405377
$431$	32.5545	1.56810	0.784048	−	0.620701i	$-0.213152\pi$
$431$	32.5545	1.56810	0.784048	+	0.620701i	$0.213152\pi$
$432$	5.60774	0.269803
$433$	27.6669	1.32959	0.664793	−	0.747028i	$-0.268520\pi$
$433$	27.6669	1.32959	0.664793	+	0.747028i	$0.268520\pi$
$434$	−10.0904	−0.484353
$435$	−5.31432	−0.254802
$436$	7.77977	0.372583
$437$	0	0
$438$	−3.78991	−0.181089
$439$	6.89246	0.328959	0.164480	−	0.986380i	$-0.447406\pi$
$439$	6.89246	0.328959	0.164480	+	0.986380i	$0.447406\pi$
$440$	−3.10027	−0.147799
$441$	−1.29642	−0.0617344
$442$	−12.6081	−0.599706
$443$	−29.0923	−1.38222	−0.691108	−	0.722751i	$-0.742877\pi$
$443$	−29.0923	−1.38222	−0.691108	+	0.722751i	$0.742877\pi$
$444$	10.4363	0.495283
$445$	−1.31093	−0.0621442
$446$	−28.4613	−1.34768
$447$	4.57940	0.216598
$448$	1.00000	0.0472456
$449$	29.6289	1.39827	0.699136	−	0.714988i	$-0.253568\pi$
$449$	29.6289	1.39827	0.699136	+	0.714988i	$0.253568\pi$
$450$	−5.70946	−0.269146
$451$	13.7592	0.647895
$452$	−7.54578	−0.354923
$453$	17.0566	0.801389
$454$	6.96526	0.326896
$455$	2.06169	0.0966537
$456$	0	0
$457$	−11.3668	−0.531715	−0.265857	−	0.964012i	$-0.585655\pi$
$457$	−11.3668	−0.531715	−0.265857	+	0.964012i	$0.585655\pi$
$458$	10.5878	0.494735
$459$	−26.4748	−1.23574
$460$	3.52695	0.164445
$461$	30.4988	1.42047	0.710236	−	0.703964i	$-0.248588\pi$
$461$	30.4988	1.42047	0.710236	+	0.703964i	$0.248588\pi$
$462$	−5.24156	−0.243859
$463$	−1.39181	−0.0646829	−0.0323415	−	0.999477i	$-0.510296\pi$
$463$	−1.39181	−0.0646829	−0.0323415	+	0.999477i	$0.510296\pi$
$464$	−5.27409	−0.244843
$465$	10.1673	0.471499
$466$	23.0345	1.06705
$467$	−9.45422	−0.437489	−0.218745	−	0.975782i	$-0.570196\pi$
$467$	−9.45422	−0.437489	−0.218745	+	0.975782i	$0.570196\pi$
$468$	3.46219	0.160040
$469$	15.2120	0.702426
$470$	−7.59784	−0.350462
$471$	12.0891	0.557038
$472$	1.59401	0.0733701
$473$	43.7273	2.01058
$474$	9.36233	0.430026
$475$	0	0
$476$	−4.72112	−0.216392
$477$	7.73019	0.353941
$478$	6.94984	0.317878
$479$	17.8467	0.815437	0.407718	−	0.913108i	$-0.366325\pi$
$479$	17.8467	0.815437	0.407718	+	0.913108i	$0.366325\pi$
$480$	−1.00763	−0.0459917
$481$	21.3535	0.973635
$482$	−21.4750	−0.978158
$483$	5.96294	0.271323
$484$	5.12720	0.233054
$485$	3.62883	0.164777
$486$	12.3463	0.560040
$487$	3.02508	0.137079	0.0685397	−	0.997648i	$-0.478166\pi$
$487$	3.02508	0.137079	0.0685397	+	0.997648i	$0.478166\pi$
$488$	−5.77528	−0.261435
$489$	−3.27088	−0.147914
$490$	0.772004	0.0348756
$491$	−18.2325	−0.822823	−0.411412	−	0.911450i	$-0.634964\pi$
$491$	−18.2325	−0.822823	−0.411412	+	0.911450i	$0.634964\pi$
$492$	4.47192	0.201610
$493$	24.8996	1.12142
$494$	0	0
$495$	−4.01925	−0.180652
$496$	10.0904	0.453070
$497$	0.966715	0.0433631
$498$	10.2743	0.460404
$499$	−8.51642	−0.381247	−0.190624	−	0.981663i	$-0.561051\pi$
$499$	−8.51642	−0.381247	−0.190624	+	0.981663i	$0.561051\pi$
$500$	7.25993	0.324674
$501$	1.25644	0.0561336
$502$	−14.5668	−0.650150
$503$	35.5826	1.58655	0.793275	−	0.608863i	$-0.208374\pi$
$503$	35.5826	1.58655	0.793275	+	0.608863i	$0.208374\pi$
$504$	1.29642	0.0577472
$505$	−7.93244	−0.352989
$506$	−18.3467	−0.815612
$507$	7.65903	0.340149
$508$	−10.9147	−0.484262
$509$	−37.2609	−1.65156	−0.825781	−	0.563991i	$-0.809265\pi$
$509$	−37.2609	−1.65156	−0.825781	+	0.563991i	$0.809265\pi$
$510$	4.75714	0.210650
$511$	−2.90368	−0.128451
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−8.40699	−0.370817
$515$	0.274347	0.0120892
$516$	14.2120	0.625647
$517$	39.5230	1.73822
$518$	7.99584	0.351317
$519$	24.1363	1.05946
$520$	−2.06169	−0.0904113
$521$	33.9259	1.48632	0.743160	−	0.669113i	$-0.233326\pi$
$521$	33.9259	1.48632	0.743160	+	0.669113i	$0.233326\pi$
$522$	−6.83744	−0.299267
$523$	−36.5187	−1.59685	−0.798425	−	0.602094i	$-0.794333\pi$
$523$	−36.5187	−1.59685	−0.798425	+	0.602094i	$0.794333\pi$
$524$	−16.8368	−0.735517
$525$	5.74817	0.250870
$526$	−29.0073	−1.26478
$527$	−47.6378	−2.07513
$528$	5.24156	0.228110
$529$	−2.12824	−0.0925323
$530$	−4.60323	−0.199952
$531$	2.06650	0.0896787
$532$	0	0
$533$	9.14994	0.396328
$534$	2.21637	0.0959117
$535$	1.92233	0.0831094
$536$	−15.2120	−0.657059
$537$	−5.03102	−0.217104
$538$	18.2468	0.786675
$539$	−4.01587	−0.172976
$540$	−4.32920	−0.186299
$541$	0.903869	0.0388604	0.0194302	−	0.999811i	$-0.493815\pi$
$541$	0.903869	0.0388604	0.0194302	+	0.999811i	$0.493815\pi$
$542$	−15.7835	−0.677959
$543$	11.4123	0.489749
$544$	4.72112	0.202416
$545$	−6.00601	−0.257269
$546$	−3.48566	−0.149173
$547$	13.9627	0.597003	0.298501	−	0.954409i	$-0.403513\pi$
$547$	13.9627	0.597003	0.298501	+	0.954409i	$0.403513\pi$
$548$	5.08460	0.217203
$549$	−7.48720	−0.319546
$550$	−17.6859	−0.754130
$551$	0	0
$552$	−5.96294	−0.253800
$553$	7.17303	0.305028
$554$	−26.3565	−1.11978
$555$	−8.05683	−0.341994
$556$	−22.1630	−0.939919
$557$	−16.8185	−0.712621	−0.356311	−	0.934368i	$-0.615965\pi$
$557$	−16.8185	−0.712621	−0.356311	+	0.934368i	$0.615965\pi$
$558$	13.0814	0.553778
$559$	29.0789	1.22991
$560$	−0.772004	−0.0326231
$561$	−24.7460	−1.04478
$562$	−12.5092	−0.527670
$563$	−14.4669	−0.609707	−0.304853	−	0.952399i	$-0.598607\pi$
$563$	−14.4669	−0.609707	−0.304853	+	0.952399i	$0.598607\pi$
$564$	12.8455	0.540894
$565$	5.82537	0.245075
$566$	22.2158	0.933800
$567$	−3.43002	−0.144047
$568$	−0.966715	−0.0405624
$569$	−10.7938	−0.452501	−0.226250	−	0.974069i	$-0.572647\pi$
$569$	−10.7938	−0.452501	−0.226250	+	0.974069i	$0.572647\pi$
$570$	0	0
$571$	33.5407	1.40363	0.701817	−	0.712358i	$-0.252373\pi$
$571$	33.5407	1.40363	0.701817	+	0.712358i	$0.252373\pi$
$572$	10.7247	0.448421
$573$	−16.9398	−0.707668
$574$	3.42621	0.143007
$575$	20.1200	0.839062
$576$	−1.29642	−0.0540176
$577$	−34.8625	−1.45134	−0.725671	−	0.688041i	$-0.758471\pi$
$577$	−34.8625	−1.45134	−0.725671	+	0.688041i	$0.758471\pi$
$578$	−5.28899	−0.219993
$579$	−35.5334	−1.47672
$580$	4.07162	0.169065
$581$	7.87177	0.326576
$582$	−6.13519	−0.254312
$583$	23.9454	0.991719
$584$	2.90368	0.120155
$585$	−2.67283	−0.110508
$586$	25.8146	1.06639
$587$	−37.4746	−1.54674	−0.773370	−	0.633954i	$-0.781431\pi$
$587$	−37.4746	−1.54674	−0.773370	+	0.633954i	$0.781431\pi$
$588$	−1.30521	−0.0538260
$589$	0	0
$590$	−1.23058	−0.0506621
$591$	−28.3289	−1.16529
$592$	−7.99584	−0.328627
$593$	19.9616	0.819725	0.409863	−	0.912147i	$-0.365577\pi$
$593$	19.9616	0.819725	0.409863	+	0.912147i	$0.365577\pi$
$594$	22.5199	0.924005
$595$	3.64472	0.149419
$596$	−3.50855	−0.143716
$597$	23.7764	0.973104
$598$	−12.2007	−0.498923
$599$	24.3199	0.993683	0.496842	−	0.867841i	$-0.334493\pi$
$599$	24.3199	0.993683	0.496842	+	0.867841i	$0.334493\pi$
$600$	−5.74817	−0.234668
$601$	−24.4343	−0.996695	−0.498347	−	0.866977i	$-0.666060\pi$
$601$	−24.4343	−0.996695	−0.498347	+	0.866977i	$0.666060\pi$
$602$	10.8886	0.443788
$603$	−19.7212	−0.803110
$604$	−13.0681	−0.531732
$605$	−3.95821	−0.160924
$606$	13.4112	0.544794
$607$	−22.2881	−0.904646	−0.452323	−	0.891854i	$-0.649405\pi$
$607$	−22.2881	−0.904646	−0.452323	+	0.891854i	$0.649405\pi$
$608$	0	0
$609$	6.88380	0.278946
$610$	4.45854	0.180521
$611$	26.2830	1.06330
$612$	6.12057	0.247409
$613$	−3.75838	−0.151799	−0.0758997	−	0.997115i	$-0.524183\pi$
$613$	−3.75838	−0.151799	−0.0758997	+	0.997115i	$0.524183\pi$
$614$	14.1872	0.572548
$615$	−3.45234	−0.139212
$616$	4.01587	0.161804
$617$	−40.3821	−1.62572	−0.812861	−	0.582457i	$-0.802091\pi$
$617$	−40.3821	−1.62572	−0.812861	+	0.582457i	$0.802091\pi$
$618$	−0.463833	−0.0186581
$619$	35.4143	1.42342	0.711710	−	0.702474i	$-0.247921\pi$
$619$	35.4143	1.42342	0.711710	+	0.702474i	$0.247921\pi$
$620$	−7.78979	−0.312846
$621$	−25.6193	−1.02807
$622$	10.6714	0.427886
$623$	1.69809	0.0680326
$624$	3.48566	0.139538
$625$	16.4154	0.656614
$626$	−2.88981	−0.115500
$627$	0	0
$628$	−9.26221	−0.369602
$629$	37.7493	1.50516
$630$	−1.00084	−0.0398746
$631$	−29.0668	−1.15713	−0.578566	−	0.815636i	$-0.696387\pi$
$631$	−29.0668	−1.15713	−0.578566	+	0.815636i	$0.696387\pi$
$632$	−7.17303	−0.285328
$633$	4.46476	0.177458
$634$	−15.2490	−0.605617
$635$	8.42619	0.334383
$636$	7.78259	0.308600
$637$	−2.67057	−0.105812
$638$	−21.1800	−0.838526
$639$	−1.25327	−0.0495786
$640$	0.772004	0.0305161
$641$	35.7759	1.41306	0.706532	−	0.707681i	$-0.250259\pi$
$641$	35.7759	1.41306	0.706532	+	0.707681i	$0.250259\pi$
$642$	−3.25004	−0.128269
$643$	12.0152	0.473835	0.236917	−	0.971530i	$-0.423863\pi$
$643$	12.0152	0.473835	0.236917	+	0.971530i	$0.423863\pi$
$644$	−4.56856	−0.180027
$645$	−10.9717	−0.432010
$646$	0	0
$647$	−20.5831	−0.809203	−0.404602	−	0.914493i	$-0.632590\pi$
$647$	−20.5831	−0.809203	−0.404602	+	0.914493i	$0.632590\pi$
$648$	3.43002	0.134744
$649$	6.40132	0.251274
$650$	−11.7612	−0.461314
$651$	−13.1700	−0.516175
$652$	2.50601	0.0981430
$653$	−48.6479	−1.90374	−0.951871	−	0.306500i	$-0.900842\pi$
$653$	−48.6479	−1.90374	−0.951871	+	0.306500i	$0.900842\pi$
$654$	10.1542	0.397062
$655$	12.9980	0.507875
$656$	−3.42621	−0.133771
$657$	3.76439	0.146863
$658$	9.84171	0.383670
$659$	−23.7875	−0.926628	−0.463314	−	0.886194i	$-0.653340\pi$
$659$	−23.7875	−0.926628	−0.463314	+	0.886194i	$0.653340\pi$
$660$	−4.04650	−0.157510
$661$	−35.7250	−1.38954	−0.694771	−	0.719231i	$-0.744494\pi$
$661$	−35.7250	−1.38954	−0.694771	+	0.719231i	$0.744494\pi$
$662$	−1.78424	−0.0693465
$663$	−16.4562	−0.639108
$664$	−7.87177	−0.305484
$665$	0	0
$666$	−10.3660	−0.401674
$667$	24.0950	0.932962
$668$	−0.962633	−0.0372454
$669$	−37.1480	−1.43622
$670$	11.7437	0.453700
$671$	−23.1928	−0.895346
$672$	1.30521	0.0503496
$673$	−36.1811	−1.39468	−0.697339	−	0.716741i	$-0.745633\pi$
$673$	−36.1811	−1.39468	−0.697339	+	0.716741i	$0.745633\pi$
$674$	−33.1973	−1.27871
$675$	−24.6965	−0.950570
$676$	−5.86803	−0.225694
$677$	11.0953	0.426427	0.213213	−	0.977006i	$-0.431607\pi$
$677$	11.0953	0.426427	0.213213	+	0.977006i	$0.431607\pi$
$678$	−9.84884	−0.378242
$679$	−4.70054	−0.180390
$680$	−3.64472	−0.139769
$681$	9.09114	0.348373
$682$	40.5215	1.55165
$683$	−0.0794389	−0.00303965	−0.00151982	−	0.999999i	$-0.500484\pi$
$683$	−0.0794389	−0.00303965	−0.00151982	+	0.999999i	$0.500484\pi$
$684$	0	0
$685$	−3.92533	−0.149979
$686$	−1.00000	−0.0381802
$687$	13.8193	0.527239
$688$	−10.8886	−0.415125
$689$	15.9238	0.606650
$690$	4.60341	0.175249
$691$	24.5965	0.935694	0.467847	−	0.883809i	$-0.345030\pi$
$691$	24.5965	0.935694	0.467847	+	0.883809i	$0.345030\pi$
$692$	−18.4922	−0.702969
$693$	5.20626	0.197770
$694$	−9.99011	−0.379219
$695$	17.1099	0.649015
$696$	−6.88380	−0.260930
$697$	16.1755	0.612692
$698$	−12.6661	−0.479418
$699$	30.0649	1.13716
$700$	−4.40401	−0.166456
$701$	−25.6308	−0.968061	−0.484030	−	0.875051i	$-0.660828\pi$
$701$	−25.6308	−0.968061	−0.484030	+	0.875051i	$0.660828\pi$
$702$	14.9759	0.565228
$703$	0	0
$704$	−4.01587	−0.151354
$705$	−9.91679	−0.373488
$706$	−19.7911	−0.744846
$707$	10.2751	0.386436
$708$	2.08051	0.0781905
$709$	17.7423	0.666327	0.333164	−	0.942869i	$-0.391884\pi$
$709$	17.7423	0.666327	0.333164	+	0.942869i	$0.391884\pi$
$710$	0.746308	0.0280084
$711$	−9.29928	−0.348750
$712$	−1.69809	−0.0636387
$713$	−46.0984	−1.72640
$714$	−6.16206	−0.230609
$715$	−8.27949	−0.309635
$716$	3.85456	0.144052
$717$	9.07101	0.338763
$718$	−5.84794	−0.218243
$719$	29.3156	1.09329	0.546643	−	0.837366i	$-0.315906\pi$
$719$	29.3156	1.09329	0.546643	+	0.837366i	$0.315906\pi$
$720$	1.00084	0.0372992
$721$	−0.355370	−0.0132347
$722$	0	0
$723$	−28.0294	−1.04242
$724$	−8.74364	−0.324955
$725$	23.2271	0.862634
$726$	6.69207	0.248366
$727$	−2.94744	−0.109314	−0.0546572	−	0.998505i	$-0.517407\pi$
$727$	−2.94744	−0.109314	−0.0546572	+	0.998505i	$0.517407\pi$
$728$	2.67057	0.0989781
$729$	26.4046	0.977949
$730$	−2.24165	−0.0829672
$731$	51.4066	1.90134
$732$	−7.53796	−0.278611
$733$	−24.5630	−0.907256	−0.453628	−	0.891191i	$-0.649871\pi$
$733$	−24.5630	−0.907256	−0.453628	+	0.891191i	$0.649871\pi$
$734$	28.5372	1.05333
$735$	1.00763	0.0371669
$736$	4.56856	0.168399
$737$	−61.0895	−2.25026
$738$	−4.44181	−0.163505
$739$	38.0193	1.39856	0.699281	−	0.714847i	$-0.253504\pi$
$739$	38.0193	1.39856	0.699281	+	0.714847i	$0.253504\pi$
$740$	6.17282	0.226917
$741$	0	0
$742$	5.96271	0.218898
$743$	37.3484	1.37018	0.685090	−	0.728459i	$-0.259763\pi$
$743$	37.3484	1.37018	0.685090	+	0.728459i	$0.259763\pi$
$744$	13.1700	0.482837
$745$	2.70861	0.0992359
$746$	1.93655	0.0709023
$747$	−10.2051	−0.373387
$748$	18.9594	0.693224
$749$	−2.49005	−0.0909843
$750$	9.47575	0.346005
$751$	12.2095	0.445532	0.222766	−	0.974872i	$-0.428491\pi$
$751$	12.2095	0.445532	0.222766	+	0.974872i	$0.428491\pi$
$752$	−9.84171	−0.358890
$753$	−19.0128	−0.692865
$754$	−14.0848	−0.512940
$755$	10.0886	0.367162
$756$	5.60774	0.203952
$757$	−30.0124	−1.09082	−0.545410	−	0.838169i	$-0.683626\pi$
$757$	−30.0124	−1.09082	−0.545410	+	0.838169i	$0.683626\pi$
$758$	−3.53725	−0.128479
$759$	−23.9464	−0.869199
$760$	0	0
$761$	37.1784	1.34771	0.673857	−	0.738862i	$-0.264636\pi$
$761$	37.1784	1.34771	0.673857	+	0.738862i	$0.264636\pi$
$762$	−14.2460	−0.516078
$763$	7.77977	0.281646
$764$	12.9786	0.469548
$765$	−4.72510	−0.170836
$766$	10.8421	0.391742
$767$	4.25691	0.153708
$768$	−1.30521	−0.0470978
$769$	−10.6050	−0.382426	−0.191213	−	0.981549i	$-0.561242\pi$
$769$	−10.6050	−0.382426	−0.191213	+	0.981549i	$0.561242\pi$
$770$	−3.10027	−0.111726
$771$	−10.9729	−0.395180
$772$	27.2242	0.979821
$773$	41.7734	1.50248	0.751242	−	0.660027i	$-0.229455\pi$
$773$	41.7734	1.50248	0.751242	+	0.660027i	$0.229455\pi$
$774$	−14.1163	−0.507399
$775$	−44.4380	−1.59626
$776$	4.70054	0.168739
$777$	10.4363	0.374399
$778$	−15.9180	−0.570686
$779$	0	0
$780$	−2.69095	−0.0963514
$781$	−3.88220	−0.138916
$782$	−21.5687	−0.771296
$783$	−29.5757	−1.05695
$784$	1.00000	0.0357143
$785$	7.15046	0.255211
$786$	−21.9755	−0.783841
$787$	−38.4164	−1.36940	−0.684699	−	0.728826i	$-0.740066\pi$
$787$	−38.4164	−1.36940	−0.684699	+	0.728826i	$0.740066\pi$
$788$	21.7044	0.773188
$789$	−37.8606	−1.34787
$790$	5.53761	0.197019
$791$	−7.54578	−0.268297
$792$	−5.20626	−0.184996
$793$	−15.4233	−0.547698
$794$	−25.6743	−0.911147
$795$	−6.00819	−0.213089
$796$	−18.2165	−0.645667
$797$	12.9029	0.457046	0.228523	−	0.973539i	$-0.426610\pi$
$797$	12.9029	0.457046	0.228523	+	0.973539i	$0.426610\pi$
$798$	0	0
$799$	46.4639	1.64378
$800$	4.40401	0.155705
$801$	−2.20144	−0.0777842
$802$	30.4717	1.07599
$803$	11.6608	0.411500
$804$	−19.8549	−0.700229
$805$	3.52695	0.124309
$806$	26.9470	0.949169
$807$	23.8159	0.838360
$808$	−10.2751	−0.361478
$809$	−21.8130	−0.766903	−0.383452	−	0.923561i	$-0.625265\pi$
$809$	−21.8130	−0.766903	−0.383452	+	0.923561i	$0.625265\pi$
$810$	−2.64799	−0.0930409
$811$	−35.8095	−1.25744	−0.628721	−	0.777631i	$-0.716421\pi$
$811$	−35.8095	−1.25744	−0.628721	+	0.777631i	$0.716421\pi$
$812$	−5.27409	−0.185084
$813$	−20.6008	−0.722501
$814$	−32.1102	−1.12546
$815$	−1.93465	−0.0677679
$816$	6.16206	0.215715
$817$	0	0
$818$	−4.71880	−0.164989
$819$	3.46219	0.120979
$820$	2.64505	0.0923690
$821$	31.4750	1.09849	0.549243	−	0.835663i	$-0.314916\pi$
$821$	31.4750	1.09849	0.549243	+	0.835663i	$0.314916\pi$
$822$	6.63648	0.231474
$823$	23.6595	0.824718	0.412359	−	0.911021i	$-0.364705\pi$
$823$	23.6595	0.824718	0.412359	+	0.911021i	$0.364705\pi$
$824$	0.355370	0.0123799
$825$	−23.0839	−0.803677
$826$	1.59401	0.0554626
$827$	−14.7222	−0.511940	−0.255970	−	0.966685i	$-0.582395\pi$
$827$	−14.7222	−0.511940	−0.255970	+	0.966685i	$0.582395\pi$
$828$	5.92279	0.205831
$829$	2.81249	0.0976817	0.0488409	−	0.998807i	$-0.484447\pi$
$829$	2.81249	0.0976817	0.0488409	+	0.998807i	$0.484447\pi$
$830$	6.07704	0.210937
$831$	−34.4008	−1.19335
$832$	−2.67057	−0.0925855
$833$	−4.72112	−0.163577
$834$	−28.9274	−1.00167
$835$	0.743156	0.0257180
$836$	0	0
$837$	56.5841	1.95583
$838$	2.87962	0.0994748
$839$	−10.5393	−0.363858	−0.181929	−	0.983312i	$-0.558234\pi$
$839$	−10.5393	−0.363858	−0.181929	+	0.983312i	$0.558234\pi$
$840$	−1.00763	−0.0347665
$841$	−1.18402	−0.0408281
$842$	−7.22939	−0.249141
$843$	−16.3272	−0.562339
$844$	−3.42072	−0.117746
$845$	4.53015	0.155842
$846$	−12.7590	−0.438664
$847$	5.12720	0.176173
$848$	−5.96271	−0.204760
$849$	28.9963	0.995152
$850$	−20.7919	−0.713155
$851$	36.5295	1.25221
$852$	−1.26177	−0.0432274
$853$	44.5601	1.52571	0.762855	−	0.646570i	$-0.223797\pi$
$853$	44.5601	1.52571	0.762855	+	0.646570i	$0.223797\pi$
$854$	−5.77528	−0.197626
$855$	0	0
$856$	2.49005	0.0851081
$857$	0.749296	0.0255955	0.0127977	−	0.999918i	$-0.495926\pi$
$857$	0.749296	0.0255955	0.0127977	+	0.999918i	$0.495926\pi$
$858$	13.9980	0.477883
$859$	4.60416	0.157092	0.0785460	−	0.996910i	$-0.474972\pi$
$859$	4.60416	0.157092	0.0785460	+	0.996910i	$0.474972\pi$
$860$	8.40607	0.286645
$861$	4.47192	0.152403
$862$	−32.5545	−1.10881
$863$	23.3877	0.796128	0.398064	−	0.917358i	$-0.369682\pi$
$863$	23.3877	0.796128	0.398064	+	0.917358i	$0.369682\pi$
$864$	−5.60774	−0.190779
$865$	14.2761	0.485401
$866$	−27.6669	−0.940159
$867$	−6.90325	−0.234447
$868$	10.0904	0.342489
$869$	−28.8060	−0.977175
$870$	5.31432	0.180172
$871$	−40.6248	−1.37652
$872$	−7.77977	−0.263456
$873$	6.09388	0.206247
$874$	0	0
$875$	7.25993	0.245431
$876$	3.78991	0.128049
$877$	37.1524	1.25455	0.627274	−	0.778799i	$-0.284171\pi$
$877$	37.1524	1.25455	0.627274	+	0.778799i	$0.284171\pi$
$878$	−6.89246	−0.232609
$879$	33.6935	1.13645
$880$	3.10027	0.104510
$881$	5.56707	0.187559	0.0937797	−	0.995593i	$-0.470105\pi$
$881$	5.56707	0.187559	0.0937797	+	0.995593i	$0.470105\pi$
$882$	1.29642	0.0436528
$883$	−29.2018	−0.982719	−0.491360	−	0.870957i	$-0.663500\pi$
$883$	−29.2018	−0.982719	−0.491360	+	0.870957i	$0.663500\pi$
$884$	12.6081	0.424056
$885$	−1.60617	−0.0539907
$886$	29.0923	0.977375
$887$	−41.7848	−1.40300	−0.701499	−	0.712670i	$-0.747485\pi$
$887$	−41.7848	−1.40300	−0.701499	+	0.712670i	$0.747485\pi$
$888$	−10.4363	−0.350218
$889$	−10.9147	−0.366067
$890$	1.31093	0.0439426
$891$	13.7745	0.461464
$892$	28.4613	0.952954
$893$	0	0
$894$	−4.57940	−0.153158
$895$	−2.97574	−0.0994679
$896$	−1.00000	−0.0334077
$897$	−15.9245	−0.531703
$898$	−29.6289	−0.988728
$899$	−53.2174	−1.77490
$900$	5.70946	0.190315
$901$	28.1507	0.937835
$902$	−13.7592	−0.458131
$903$	14.2120	0.472945
$904$	7.54578	0.250969
$905$	6.75012	0.224382
$906$	−17.0566	−0.566667
$907$	−41.9429	−1.39269	−0.696346	−	0.717706i	$-0.745192\pi$
$907$	−41.9429	−1.39269	−0.696346	+	0.717706i	$0.745192\pi$
$908$	−6.96526	−0.231150
$909$	−13.3209	−0.441827
$910$	−2.06169	−0.0683445
$911$	14.3040	0.473913	0.236956	−	0.971520i	$-0.423850\pi$
$911$	14.3040	0.473913	0.236956	+	0.971520i	$0.423850\pi$
$912$	0	0
$913$	−31.6120	−1.04620
$914$	11.3668	0.375979
$915$	5.81934	0.192381
$916$	−10.5878	−0.349830
$917$	−16.8368	−0.555999
$918$	26.4748	0.873799
$919$	2.11121	0.0696425	0.0348212	−	0.999394i	$-0.488914\pi$
$919$	2.11121	0.0696425	0.0348212	+	0.999394i	$0.488914\pi$
$920$	−3.52695	−0.116280
$921$	18.5173	0.610165
$922$	−30.4988	−1.00443
$923$	−2.58168	−0.0849771
$924$	5.24156	0.172435
$925$	35.2137	1.15782
$926$	1.39181	0.0457377
$927$	0.460709	0.0151317
$928$	5.27409	0.173130
$929$	−48.5325	−1.59230	−0.796149	−	0.605100i	$-0.793133\pi$
$929$	−48.5325	−1.59230	−0.796149	+	0.605100i	$0.793133\pi$
$930$	−10.1673	−0.333400
$931$	0	0
$932$	−23.0345	−0.754521
$933$	13.9285	0.455999
$934$	9.45422	0.309352
$935$	−14.6367	−0.478672
$936$	−3.46219	−0.113165
$937$	29.5935	0.966776	0.483388	−	0.875406i	$-0.339406\pi$
$937$	29.5935	0.966776	0.483388	+	0.875406i	$0.339406\pi$
$938$	−15.2120	−0.496690
$939$	−3.77181	−0.123088
$940$	7.59784	0.247814
$941$	14.2599	0.464859	0.232430	−	0.972613i	$-0.425332\pi$
$941$	14.2599	0.464859	0.232430	+	0.972613i	$0.425332\pi$
$942$	−12.0891	−0.393886
$943$	15.6528	0.509726
$944$	−1.59401	−0.0518805
$945$	−4.32920	−0.140829
$946$	−43.7273	−1.42170
$947$	−54.3122	−1.76491	−0.882454	−	0.470398i	$-0.844110\pi$
$947$	−54.3122	−1.76491	−0.882454	+	0.470398i	$0.844110\pi$
$948$	−9.36233	−0.304074
$949$	7.75449	0.251721
$950$	0	0
$951$	−19.9032	−0.645406
$952$	4.72112	0.153012
$953$	−44.7757	−1.45043	−0.725213	−	0.688524i	$-0.758259\pi$
$953$	−44.7757	−1.45043	−0.725213	+	0.688524i	$0.758259\pi$
$954$	−7.73019	−0.250274
$955$	−10.0195	−0.324223
$956$	−6.94984	−0.224774
$957$	−27.6444	−0.893617
$958$	−17.8467	−0.576601
$959$	5.08460	0.164190
$960$	1.00763	0.0325211
$961$	70.8153	2.28436
$962$	−21.3535	−0.688464
$963$	3.22815	0.104026
$964$	21.4750	0.691662
$965$	−21.0172	−0.676568
$966$	−5.96294	−0.191854
$967$	−22.9056	−0.736594	−0.368297	−	0.929708i	$-0.620059\pi$
$967$	−22.9056	−0.736594	−0.368297	+	0.929708i	$0.620059\pi$
$968$	−5.12720	−0.164794
$969$	0	0
$970$	−3.62883	−0.116515
$971$	20.3656	0.653564	0.326782	−	0.945100i	$-0.394036\pi$
$971$	20.3656	0.653564	0.326782	+	0.945100i	$0.394036\pi$
$972$	−12.3463	−0.396008
$973$	−22.1630	−0.710512
$974$	−3.02508	−0.0969298
$975$	−15.3509	−0.491622
$976$	5.77528	0.184862
$977$	−31.4719	−1.00687	−0.503437	−	0.864032i	$-0.667931\pi$
$977$	−31.4719	−1.00687	−0.503437	+	0.864032i	$0.667931\pi$
$978$	3.27088	0.104591
$979$	−6.81931	−0.217946
$980$	−0.772004	−0.0246608
$981$	−10.0859	−0.322017
$982$	18.2325	0.581824
$983$	−6.28968	−0.200610	−0.100305	−	0.994957i	$-0.531982\pi$
$983$	−6.28968	−0.200610	−0.100305	+	0.994957i	$0.531982\pi$
$984$	−4.47192	−0.142560
$985$	−16.7559	−0.533888
$986$	−24.8996	−0.792965
$987$	12.8455	0.408877
$988$	0	0
$989$	49.7454	1.58181
$990$	4.01925	0.127740
$991$	50.4255	1.60182	0.800909	−	0.598786i	$-0.204350\pi$
$991$	50.4255	1.60182	0.800909	+	0.598786i	$0.204350\pi$
$992$	−10.0904	−0.320369
$993$	−2.32881	−0.0739027
$994$	−0.966715	−0.0306623
$995$	14.0632	0.445834
$996$	−10.2743	−0.325555
$997$	12.2839	0.389034	0.194517	−	0.980899i	$-0.437686\pi$
$997$	12.2839	0.389034	0.194517	+	0.980899i	$0.437686\pi$
$998$	8.51642	0.269583
$999$	−44.8386	−1.41863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bg.1.3	✓	8
19.18	odd	2		5054.2.a.bh.1.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.bg.1.3	✓	8	1.1	even	1	trivial
5054.2.a.bh.1.6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.30521 q^{3} +1.00000 q^{4} -0.772004 q^{5} +1.30521 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.29642 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.30521 q^{3} +1.00000 q^{4} -0.772004 q^{5} +1.30521 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.29642 q^{9} +0.772004 q^{10} -4.01587 q^{11} -1.30521 q^{12} -2.67057 q^{13} -1.00000 q^{14} +1.00763 q^{15} +1.00000 q^{16} -4.72112 q^{17} +1.29642 q^{18} -0.772004 q^{20} -1.30521 q^{21} +4.01587 q^{22} -4.56856 q^{23} +1.30521 q^{24} -4.40401 q^{25} +2.67057 q^{26} +5.60774 q^{27} +1.00000 q^{28} -5.27409 q^{29} -1.00763 q^{30} +10.0904 q^{31} -1.00000 q^{32} +5.24156 q^{33} +4.72112 q^{34} -0.772004 q^{35} -1.29642 q^{36} -7.99584 q^{37} +3.48566 q^{39} +0.772004 q^{40} -3.42621 q^{41} +1.30521 q^{42} -10.8886 q^{43} -4.01587 q^{44} +1.00084 q^{45} +4.56856 q^{46} -9.84171 q^{47} -1.30521 q^{48} +1.00000 q^{49} +4.40401 q^{50} +6.16206 q^{51} -2.67057 q^{52} -5.96271 q^{53} -5.60774 q^{54} +3.10027 q^{55} -1.00000 q^{56} +5.27409 q^{58} -1.59401 q^{59} +1.00763 q^{60} +5.77528 q^{61} -10.0904 q^{62} -1.29642 q^{63} +1.00000 q^{64} +2.06169 q^{65} -5.24156 q^{66} +15.2120 q^{67} -4.72112 q^{68} +5.96294 q^{69} +0.772004 q^{70} +0.966715 q^{71} +1.29642 q^{72} -2.90368 q^{73} +7.99584 q^{74} +5.74817 q^{75} -4.01587 q^{77} -3.48566 q^{78} +7.17303 q^{79} -0.772004 q^{80} -3.43002 q^{81} +3.42621 q^{82} +7.87177 q^{83} -1.30521 q^{84} +3.64472 q^{85} +10.8886 q^{86} +6.88380 q^{87} +4.01587 q^{88} +1.69809 q^{89} -1.00084 q^{90} -2.67057 q^{91} -4.56856 q^{92} -13.1700 q^{93} +9.84171 q^{94} +1.30521 q^{96} -4.70054 q^{97} -1.00000 q^{98} +5.20626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 4 q^{3} + 8 q^{4} - 2 q^{5} - 4 q^{6} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 2 q^{10} - 12 q^{11} + 4 q^{12} + 10 q^{13} - 8 q^{14} + 24 q^{15} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 2 q^{20} + 4 q^{21} + 12 q^{22} - 20 q^{23} - 4 q^{24} + 8 q^{25} - 10 q^{26} + 22 q^{27} + 8 q^{28} + 8 q^{29} - 24 q^{30} + 18 q^{31} - 8 q^{32} - 16 q^{33} + 6 q^{34} - 2 q^{35} + 8 q^{36} + 36 q^{37} + 2 q^{40} + 4 q^{41} - 4 q^{42} - 16 q^{43} - 12 q^{44} + 8 q^{45} + 20 q^{46} - 10 q^{47} + 4 q^{48} + 8 q^{49} - 8 q^{50} + 12 q^{51} + 10 q^{52} + 32 q^{53} - 22 q^{54} - 22 q^{55} - 8 q^{56} - 8 q^{58} - 2 q^{59} + 24 q^{60} + 2 q^{61} - 18 q^{62} + 8 q^{63} + 8 q^{64} + 16 q^{66} + 44 q^{67} - 6 q^{68} + 2 q^{70} + 8 q^{71} - 8 q^{72} + 30 q^{73} - 36 q^{74} - 16 q^{75} - 12 q^{77} + 60 q^{79} - 2 q^{80} + 12 q^{81} - 4 q^{82} - 28 q^{83} + 4 q^{84} - 16 q^{85} + 16 q^{86} + 24 q^{87} + 12 q^{88} - 22 q^{89} - 8 q^{90} + 10 q^{91} - 20 q^{92} - 16 q^{93} + 10 q^{94} - 4 q^{96} - 6 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 4 * q^3 + 8 * q^4 - 2 * q^5 - 4 * q^6 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 2 * q^10 - 12 * q^11 + 4 * q^12 + 10 * q^13 - 8 * q^14 + 24 * q^15 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 2 * q^20 + 4 * q^21 + 12 * q^22 - 20 * q^23 - 4 * q^24 + 8 * q^25 - 10 * q^26 + 22 * q^27 + 8 * q^28 + 8 * q^29 - 24 * q^30 + 18 * q^31 - 8 * q^32 - 16 * q^33 + 6 * q^34 - 2 * q^35 + 8 * q^36 + 36 * q^37 + 2 * q^40 + 4 * q^41 - 4 * q^42 - 16 * q^43 - 12 * q^44 + 8 * q^45 + 20 * q^46 - 10 * q^47 + 4 * q^48 + 8 * q^49 - 8 * q^50 + 12 * q^51 + 10 * q^52 + 32 * q^53 - 22 * q^54 - 22 * q^55 - 8 * q^56 - 8 * q^58 - 2 * q^59 + 24 * q^60 + 2 * q^61 - 18 * q^62 + 8 * q^63 + 8 * q^64 + 16 * q^66 + 44 * q^67 - 6 * q^68 + 2 * q^70 + 8 * q^71 - 8 * q^72 + 30 * q^73 - 36 * q^74 - 16 * q^75 - 12 * q^77 + 60 * q^79 - 2 * q^80 + 12 * q^81 - 4 * q^82 - 28 * q^83 + 4 * q^84 - 16 * q^85 + 16 * q^86 + 24 * q^87 + 12 * q^88 - 22 * q^89 - 8 * q^90 + 10 * q^91 - 20 * q^92 - 16 * q^93 + 10 * q^94 - 4 * q^96 - 6 * q^97 - 8 * q^98 - 52 * q^99

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