LMFDB - Embedded newform 5054.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1528713.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1 $ x^6 - 3x^5 - 3x^4 + 7x^3 + 3x^2 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.37826$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.11161 q^{3} +1.00000 q^{4} +0.363595 q^{5} +1.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.76432 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.11161 q^{3} +1.00000 q^{4} +0.363595 q^{5} +1.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.76432 q^{9} -0.363595 q^{10} -0.710892 q^{11} -1.11161 q^{12} +1.73336 q^{13} +1.00000 q^{14} -0.404177 q^{15} +1.00000 q^{16} -2.20455 q^{17} +1.76432 q^{18} +0.363595 q^{20} +1.11161 q^{21} +0.710892 q^{22} +2.29206 q^{23} +1.11161 q^{24} -4.86780 q^{25} -1.73336 q^{26} +5.29608 q^{27} -1.00000 q^{28} +3.33082 q^{29} +0.404177 q^{30} +6.99917 q^{31} -1.00000 q^{32} +0.790236 q^{33} +2.20455 q^{34} -0.363595 q^{35} -1.76432 q^{36} +0.272634 q^{37} -1.92682 q^{39} -0.363595 q^{40} -3.92110 q^{41} -1.11161 q^{42} -8.13563 q^{43} -0.710892 q^{44} -0.641497 q^{45} -2.29206 q^{46} +4.90140 q^{47} -1.11161 q^{48} +1.00000 q^{49} +4.86780 q^{50} +2.45060 q^{51} +1.73336 q^{52} +8.61658 q^{53} -5.29608 q^{54} -0.258477 q^{55} +1.00000 q^{56} -3.33082 q^{58} +3.64280 q^{59} -0.404177 q^{60} +0.857287 q^{61} -6.99917 q^{62} +1.76432 q^{63} +1.00000 q^{64} +0.630240 q^{65} -0.790236 q^{66} +6.95822 q^{67} -2.20455 q^{68} -2.54788 q^{69} +0.363595 q^{70} -1.86238 q^{71} +1.76432 q^{72} +9.28353 q^{73} -0.272634 q^{74} +5.41111 q^{75} +0.710892 q^{77} +1.92682 q^{78} -15.1904 q^{79} +0.363595 q^{80} -0.594237 q^{81} +3.92110 q^{82} -17.0241 q^{83} +1.11161 q^{84} -0.801563 q^{85} +8.13563 q^{86} -3.70259 q^{87} +0.710892 q^{88} +6.47803 q^{89} +0.641497 q^{90} -1.73336 q^{91} +2.29206 q^{92} -7.78036 q^{93} -4.90140 q^{94} +1.11161 q^{96} +0.677178 q^{97} -1.00000 q^{98} +1.25424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 3 q^{31} - 6 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 3 q^{37} - 9 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} + 3 q^{48} + 6 q^{49} - 3 q^{50} - 27 q^{51} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 24 q^{55} + 6 q^{56} - 6 q^{58} + 15 q^{59} - 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} + 3 q^{65} - 6 q^{66} + 15 q^{67} - 9 q^{68} + 24 q^{69} - 3 q^{70} + 21 q^{71} + 3 q^{72} - 33 q^{73} + 3 q^{74} + 33 q^{75} - 3 q^{77} + 9 q^{78} - 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} - 3 q^{84} - 18 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 12 q^{89} + 12 q^{90} - 6 q^{91} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 18 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 3 * q^31 - 6 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 3 * q^37 - 9 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 + 3 * q^48 + 6 * q^49 - 3 * q^50 - 27 * q^51 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 24 * q^55 + 6 * q^56 - 6 * q^58 + 15 * q^59 - 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^65 - 6 * q^66 + 15 * q^67 - 9 * q^68 + 24 * q^69 - 3 * q^70 + 21 * q^71 + 3 * q^72 - 33 * q^73 + 3 * q^74 + 33 * q^75 - 3 * q^77 + 9 * q^78 - 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 - 3 * q^84 - 18 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 12 * q^89 + 12 * q^90 - 6 * q^91 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 18 * q^97 - 6 * q^98

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
$3$	−1.11161	−0.641790	−0.320895	−	0.947115i	$-0.603984\pi$
$3$	−1.11161	−0.641790	−0.320895	+	0.947115i	$0.603984\pi$
$4$	1.00000	0.500000
$5$	0.363595	0.162605	0.0813024	−	0.996689i	$-0.474092\pi$
$5$	0.363595	0.162605	0.0813024	+	0.996689i	$0.474092\pi$
$6$	1.11161	0.453814
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−1.76432	−0.588106
$10$	−0.363595	−0.114979
$11$	−0.710892	−0.214342	−0.107171	−	0.994241i	$-0.534179\pi$
$11$	−0.710892	−0.214342	−0.107171	+	0.994241i	$0.534179\pi$
$12$	−1.11161	−0.320895
$13$	1.73336	0.480746	0.240373	−	0.970681i	$-0.422730\pi$
$13$	1.73336	0.480746	0.240373	+	0.970681i	$0.422730\pi$
$14$	1.00000	0.267261
$15$	−0.404177	−0.104358
$16$	1.00000	0.250000
$17$	−2.20455	−0.534681	−0.267341	−	0.963602i	$-0.586145\pi$
$17$	−2.20455	−0.534681	−0.267341	+	0.963602i	$0.586145\pi$
$18$	1.76432	0.415853
$19$	0	0
$19$	0	0
$20$	0.363595	0.0813024
$21$	1.11161	0.242574
$22$	0.710892	0.151563
$23$	2.29206	0.477927	0.238964	−	0.971028i	$-0.423192\pi$
$23$	2.29206	0.477927	0.238964	+	0.971028i	$0.423192\pi$
$24$	1.11161	0.226907
$25$	−4.86780	−0.973560
$26$	−1.73336	−0.339939
$27$	5.29608	1.01923
$28$	−1.00000	−0.188982
$29$	3.33082	0.618518	0.309259	−	0.950978i	$-0.399919\pi$
$29$	3.33082	0.618518	0.309259	+	0.950978i	$0.399919\pi$
$30$	0.404177	0.0737923
$31$	6.99917	1.25709	0.628544	−	0.777774i	$-0.283651\pi$
$31$	6.99917	1.25709	0.628544	+	0.777774i	$0.283651\pi$
$32$	−1.00000	−0.176777
$33$	0.790236	0.137562
$34$	2.20455	0.378077
$35$	−0.363595	−0.0614588
$36$	−1.76432	−0.294053
$37$	0.272634	0.0448208	0.0224104	−	0.999749i	$-0.492866\pi$
$37$	0.272634	0.0448208	0.0224104	+	0.999749i	$0.492866\pi$
$38$	0	0
$39$	−1.92682	−0.308538
$40$	−0.363595	−0.0574894
$41$	−3.92110	−0.612373	−0.306186	−	0.951972i	$-0.599053\pi$
$41$	−3.92110	−0.612373	−0.306186	+	0.951972i	$0.599053\pi$
$42$	−1.11161	−0.171526
$43$	−8.13563	−1.24067	−0.620336	−	0.784336i	$-0.713004\pi$
$43$	−8.13563	−1.24067	−0.620336	+	0.784336i	$0.713004\pi$
$44$	−0.710892	−0.107171
$45$	−0.641497	−0.0956287
$46$	−2.29206	−0.337946
$47$	4.90140	0.714942	0.357471	−	0.933924i	$-0.383639\pi$
$47$	4.90140	0.714942	0.357471	+	0.933924i	$0.383639\pi$
$48$	−1.11161	−0.160448
$49$	1.00000	0.142857
$50$	4.86780	0.688411
$51$	2.45060	0.343153
$52$	1.73336	0.240373
$53$	8.61658	1.18358	0.591789	−	0.806093i	$-0.298422\pi$
$53$	8.61658	1.18358	0.591789	+	0.806093i	$0.298422\pi$
$54$	−5.29608	−0.720705
$55$	−0.258477	−0.0348530
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.33082	−0.437358
$59$	3.64280	0.474253	0.237126	−	0.971479i	$-0.423794\pi$
$59$	3.64280	0.474253	0.237126	+	0.971479i	$0.423794\pi$
$60$	−0.404177	−0.0521790
$61$	0.857287	0.109764	0.0548822	−	0.998493i	$-0.482522\pi$
$61$	0.857287	0.109764	0.0548822	+	0.998493i	$0.482522\pi$
$62$	−6.99917	−0.888895
$63$	1.76432	0.222283
$64$	1.00000	0.125000
$65$	0.630240	0.0781716
$66$	−0.790236	−0.0972714
$67$	6.95822	0.850082	0.425041	−	0.905174i	$-0.360260\pi$
$67$	6.95822	0.850082	0.425041	+	0.905174i	$0.360260\pi$
$68$	−2.20455	−0.267341
$69$	−2.54788	−0.306729
$70$	0.363595	0.0434579
$71$	−1.86238	−0.221024	−0.110512	−	0.993875i	$-0.535249\pi$
$71$	−1.86238	−0.221024	−0.110512	+	0.993875i	$0.535249\pi$
$72$	1.76432	0.207927
$73$	9.28353	1.08656	0.543278	−	0.839553i	$-0.317183\pi$
$73$	9.28353	1.08656	0.543278	+	0.839553i	$0.317183\pi$
$74$	−0.272634	−0.0316931
$75$	5.41111	0.624821
$76$	0	0
$77$	0.710892	0.0810136
$78$	1.92682	0.218169
$79$	−15.1904	−1.70905	−0.854525	−	0.519411i	$-0.826152\pi$
$79$	−15.1904	−1.70905	−0.854525	+	0.519411i	$0.826152\pi$
$80$	0.363595	0.0406512
$81$	−0.594237	−0.0660263
$82$	3.92110	0.433013
$83$	−17.0241	−1.86864	−0.934320	−	0.356434i	$-0.883992\pi$
$83$	−17.0241	−1.86864	−0.934320	+	0.356434i	$0.883992\pi$
$84$	1.11161	0.121287
$85$	−0.801563	−0.0869417
$86$	8.13563	0.877287
$87$	−3.70259	−0.396959
$88$	0.710892	0.0757813
$89$	6.47803	0.686670	0.343335	−	0.939213i	$-0.388443\pi$
$89$	6.47803	0.686670	0.343335	+	0.939213i	$0.388443\pi$
$90$	0.641497	0.0676197
$91$	−1.73336	−0.181705
$92$	2.29206	0.238964
$93$	−7.78036	−0.806786
$94$	−4.90140	−0.505540
$95$	0	0
$96$	1.11161	0.113454
$97$	0.677178	0.0687570	0.0343785	−	0.999409i	$-0.489055\pi$
$97$	0.677178	0.0687570	0.0343785	+	0.999409i	$0.489055\pi$
$98$	−1.00000	−0.101015
$99$	1.25424	0.126056
$100$	−4.86780	−0.486780
$101$	−4.78477	−0.476102	−0.238051	−	0.971253i	$-0.576509\pi$
$101$	−4.78477	−0.476102	−0.238051	+	0.971253i	$0.576509\pi$
$102$	−2.45060	−0.242646
$103$	−3.41450	−0.336441	−0.168220	−	0.985749i	$-0.553802\pi$
$103$	−3.41450	−0.336441	−0.168220	+	0.985749i	$0.553802\pi$
$104$	−1.73336	−0.169969
$105$	0.404177	0.0394436
$106$	−8.61658	−0.836916
$107$	−9.83019	−0.950321	−0.475160	−	0.879899i	$-0.657610\pi$
$107$	−9.83019	−0.950321	−0.475160	+	0.879899i	$0.657610\pi$
$108$	5.29608	0.509615
$109$	−4.08878	−0.391634	−0.195817	−	0.980640i	$-0.562736\pi$
$109$	−4.08878	−0.391634	−0.195817	+	0.980640i	$0.562736\pi$
$110$	0.258477	0.0246448
$111$	−0.303064	−0.0287656
$112$	−1.00000	−0.0944911
$113$	10.2614	0.965313	0.482656	−	0.875810i	$-0.339672\pi$
$113$	10.2614	0.965313	0.482656	+	0.875810i	$0.339672\pi$
$114$	0	0
$115$	0.833382	0.0777133
$116$	3.33082	0.309259
$117$	−3.05819	−0.282730
$118$	−3.64280	−0.335347
$119$	2.20455	0.202090
$120$	0.404177	0.0368962
$121$	−10.4946	−0.954058
$122$	−0.857287	−0.0776152
$123$	4.35874	0.393015
$124$	6.99917	0.628544
$125$	−3.58788	−0.320910
$126$	−1.76432	−0.157178
$127$	−14.0348	−1.24539	−0.622695	−	0.782464i	$-0.713962\pi$
$127$	−14.0348	−1.24539	−0.622695	+	0.782464i	$0.713962\pi$
$128$	−1.00000	−0.0883883
$129$	9.04367	0.796250
$130$	−0.630240	−0.0552757
$131$	−13.6254	−1.19046	−0.595228	−	0.803557i	$-0.702938\pi$
$131$	−13.6254	−1.19046	−0.595228	+	0.803557i	$0.702938\pi$
$132$	0.790236	0.0687812
$133$	0	0
$134$	−6.95822	−0.601098
$135$	1.92563	0.165732
$136$	2.20455	0.189038
$137$	11.7319	1.00233	0.501163	−	0.865353i	$-0.332906\pi$
$137$	11.7319	1.00233	0.501163	+	0.865353i	$0.332906\pi$
$138$	2.54788	0.216890
$139$	6.53702	0.554463	0.277232	−	0.960803i	$-0.410583\pi$
$139$	6.53702	0.554463	0.277232	+	0.960803i	$0.410583\pi$
$140$	−0.363595	−0.0307294
$141$	−5.44845	−0.458843
$142$	1.86238	0.156287
$143$	−1.23223	−0.103044
$144$	−1.76432	−0.147026
$145$	1.21107	0.100574
$146$	−9.28353	−0.768310
$147$	−1.11161	−0.0916843
$148$	0.272634	0.0224104
$149$	−4.06167	−0.332745	−0.166372	−	0.986063i	$-0.553205\pi$
$149$	−4.06167	−0.332745	−0.166372	+	0.986063i	$0.553205\pi$
$150$	−5.41111	−0.441815
$151$	3.29768	0.268361	0.134181	−	0.990957i	$-0.457160\pi$
$151$	3.29768	0.268361	0.134181	+	0.990957i	$0.457160\pi$
$152$	0	0
$153$	3.88952	0.314449
$154$	−0.710892	−0.0572853
$155$	2.54486	0.204408
$156$	−1.92682	−0.154269
$157$	−8.55738	−0.682953	−0.341477	−	0.939890i	$-0.610927\pi$
$157$	−8.55738	−0.682953	−0.341477	+	0.939890i	$0.610927\pi$
$158$	15.1904	1.20848
$159$	−9.57830	−0.759609
$160$	−0.363595	−0.0287447
$161$	−2.29206	−0.180640
$162$	0.594237	0.0466877
$163$	10.2239	0.800798	0.400399	−	0.916341i	$-0.368872\pi$
$163$	10.2239	0.800798	0.400399	+	0.916341i	$0.368872\pi$
$164$	−3.92110	−0.306186
$165$	0.287326	0.0223683
$166$	17.0241	1.32133
$167$	9.67364	0.748569	0.374285	−	0.927314i	$-0.377888\pi$
$167$	9.67364	0.748569	0.374285	+	0.927314i	$0.377888\pi$
$168$	−1.11161	−0.0857628
$169$	−9.99548	−0.768883
$170$	0.801563	0.0614770
$171$	0	0
$172$	−8.13563	−0.620336
$173$	0.732774	0.0557118	0.0278559	−	0.999612i	$-0.491132\pi$
$173$	0.732774	0.0557118	0.0278559	+	0.999612i	$0.491132\pi$
$174$	3.70259	0.280692
$175$	4.86780	0.367971
$176$	−0.710892	−0.0535855
$177$	−4.04939	−0.304371
$178$	−6.47803	−0.485549
$179$	24.2514	1.81264	0.906319	−	0.422595i	$-0.138881\pi$
$179$	24.2514	1.81264	0.906319	+	0.422595i	$0.138881\pi$
$180$	−0.641497	−0.0478144
$181$	4.94945	0.367889	0.183945	−	0.982937i	$-0.441113\pi$
$181$	4.94945	0.367889	0.183945	+	0.982937i	$0.441113\pi$
$182$	1.73336	0.128485
$183$	−0.952972	−0.0704457
$184$	−2.29206	−0.168973
$185$	0.0991286	0.00728808
$186$	7.78036	0.570484
$187$	1.56719	0.114605
$188$	4.90140	0.357471
$189$	−5.29608	−0.385233
$190$	0	0
$191$	9.18620	0.664690	0.332345	−	0.943158i	$-0.392160\pi$
$191$	9.18620	0.664690	0.332345	+	0.943158i	$0.392160\pi$
$192$	−1.11161	−0.0802238
$193$	−18.8578	−1.35741	−0.678707	−	0.734409i	$-0.737459\pi$
$193$	−18.8578	−1.35741	−0.678707	+	0.734409i	$0.737459\pi$
$194$	−0.677178	−0.0486185
$195$	−0.700583	−0.0501698
$196$	1.00000	0.0714286
$197$	−19.4699	−1.38717	−0.693587	−	0.720372i	$-0.743971\pi$
$197$	−19.4699	−1.38717	−0.693587	+	0.720372i	$0.743971\pi$
$198$	−1.25424	−0.0891348
$199$	10.0754	0.714223	0.357111	−	0.934062i	$-0.383762\pi$
$199$	10.0754	0.714223	0.357111	+	0.934062i	$0.383762\pi$
$200$	4.86780	0.344205
$201$	−7.73485	−0.545574
$202$	4.78477	0.336655
$203$	−3.33082	−0.233778
$204$	2.45060	0.171577
$205$	−1.42569	−0.0995747
$206$	3.41450	0.237900
$207$	−4.04392	−0.281072
$208$	1.73336	0.120187
$209$	0	0
$210$	−0.404177	−0.0278909
$211$	5.47663	0.377027	0.188513	−	0.982071i	$-0.439633\pi$
$211$	5.47663	0.377027	0.188513	+	0.982071i	$0.439633\pi$
$212$	8.61658	0.591789
$213$	2.07025	0.141851
$214$	9.83019	0.671978
$215$	−2.95807	−0.201739
$216$	−5.29608	−0.360352
$217$	−6.99917	−0.475134
$218$	4.08878	0.276927
$219$	−10.3197	−0.697340
$220$	−0.258477	−0.0174265
$221$	−3.82126	−0.257046
$222$	0.303064	0.0203403
$223$	−5.85396	−0.392010	−0.196005	−	0.980603i	$-0.562797\pi$
$223$	−5.85396	−0.392010	−0.196005	+	0.980603i	$0.562797\pi$
$224$	1.00000	0.0668153
$225$	8.58834	0.572556
$226$	−10.2614	−0.682579
$227$	−8.15785	−0.541455	−0.270728	−	0.962656i	$-0.587264\pi$
$227$	−8.15785	−0.541455	−0.270728	+	0.962656i	$0.587264\pi$
$228$	0	0
$229$	−27.6584	−1.82772	−0.913860	−	0.406030i	$-0.866913\pi$
$229$	−27.6584	−1.82772	−0.913860	+	0.406030i	$0.866913\pi$
$230$	−0.833382	−0.0549516
$231$	−0.790236	−0.0519937
$232$	−3.33082	−0.218679
$233$	−3.89805	−0.255370	−0.127685	−	0.991815i	$-0.540755\pi$
$233$	−3.89805	−0.255370	−0.127685	+	0.991815i	$0.540755\pi$
$234$	3.05819	0.199920
$235$	1.78212	0.116253
$236$	3.64280	0.237126
$237$	16.8858	1.09685
$238$	−2.20455	−0.142900
$239$	10.1074	0.653796	0.326898	−	0.945060i	$-0.393997\pi$
$239$	10.1074	0.653796	0.326898	+	0.945060i	$0.393997\pi$
$240$	−0.404177	−0.0260895
$241$	−18.5551	−1.19524	−0.597618	−	0.801781i	$-0.703886\pi$
$241$	−18.5551	−1.19524	−0.597618	+	0.801781i	$0.703886\pi$
$242$	10.4946	0.674621
$243$	−15.2277	−0.976855
$244$	0.857287	0.0548822
$245$	0.363595	0.0232292
$246$	−4.35874	−0.277903
$247$	0	0
$248$	−6.99917	−0.444447
$249$	18.9242	1.19928
$250$	3.58788	0.226918
$251$	17.2756	1.09043	0.545214	−	0.838297i	$-0.316448\pi$
$251$	17.2756	1.09043	0.545214	+	0.838297i	$0.316448\pi$
$252$	1.76432	0.111141
$253$	−1.62941	−0.102440
$254$	14.0348	0.880624
$255$	0.891027	0.0557983
$256$	1.00000	0.0625000
$257$	3.88956	0.242624	0.121312	−	0.992614i	$-0.461290\pi$
$257$	3.88956	0.242624	0.121312	+	0.992614i	$0.461290\pi$
$258$	−9.04367	−0.563034
$259$	−0.272634	−0.0169407
$260$	0.630240	0.0390858
$261$	−5.87663	−0.363754
$262$	13.6254	0.841779
$263$	19.3814	1.19511	0.597555	−	0.801828i	$-0.296139\pi$
$263$	19.3814	1.19511	0.597555	+	0.801828i	$0.296139\pi$
$264$	−0.790236	−0.0486357
$265$	3.13295	0.192455
$266$	0	0
$267$	−7.20106	−0.440698
$268$	6.95822	0.425041
$269$	−30.3820	−1.85242	−0.926212	−	0.377003i	$-0.876954\pi$
$269$	−30.3820	−1.85242	−0.926212	+	0.377003i	$0.876954\pi$
$270$	−1.92563	−0.117190
$271$	−17.4011	−1.05704	−0.528520	−	0.848921i	$-0.677253\pi$
$271$	−17.4011	−1.05704	−0.528520	+	0.848921i	$0.677253\pi$
$272$	−2.20455	−0.133670
$273$	1.92682	0.116616
$274$	−11.7319	−0.708751
$275$	3.46048	0.208675
$276$	−2.54788	−0.153365
$277$	−14.8726	−0.893609	−0.446804	−	0.894632i	$-0.647438\pi$
$277$	−14.8726	−0.893609	−0.446804	+	0.894632i	$0.647438\pi$
$278$	−6.53702	−0.392065
$279$	−12.3487	−0.739300
$280$	0.363595	0.0217290
$281$	−23.2958	−1.38971	−0.694857	−	0.719148i	$-0.744532\pi$
$281$	−23.2958	−1.38971	−0.694857	+	0.719148i	$0.744532\pi$
$282$	5.44845	0.324451
$283$	−1.44172	−0.0857014	−0.0428507	−	0.999081i	$-0.513644\pi$
$283$	−1.44172	−0.0857014	−0.0428507	+	0.999081i	$0.513644\pi$
$284$	−1.86238	−0.110512
$285$	0	0
$286$	1.23223	0.0728632
$287$	3.92110	0.231455
$288$	1.76432	0.103963
$289$	−12.1400	−0.714116
$290$	−1.21107	−0.0711165
$291$	−0.752759	−0.0441275
$292$	9.28353	0.543278
$293$	−4.97737	−0.290781	−0.145391	−	0.989374i	$-0.546444\pi$
$293$	−4.97737	−0.290781	−0.145391	+	0.989374i	$0.546444\pi$
$294$	1.11161	0.0648306
$295$	1.32451	0.0771157
$296$	−0.272634	−0.0158466
$297$	−3.76494	−0.218464
$298$	4.06167	0.235286
$299$	3.97295	0.229762
$300$	5.41111	0.312410
$301$	8.13563	0.468930
$302$	−3.29768	−0.189760
$303$	5.31881	0.305558
$304$	0	0
$305$	0.311706	0.0178482
$306$	−3.88952	−0.222349
$307$	5.20853	0.297266	0.148633	−	0.988892i	$-0.452513\pi$
$307$	5.20853	0.297266	0.148633	+	0.988892i	$0.452513\pi$
$308$	0.710892	0.0405068
$309$	3.79561	0.215924
$310$	−2.54486	−0.144539
$311$	−6.15011	−0.348741	−0.174370	−	0.984680i	$-0.555789\pi$
$311$	−6.15011	−0.348741	−0.174370	+	0.984680i	$0.555789\pi$
$312$	1.92682	0.109085
$313$	18.3769	1.03872	0.519362	−	0.854554i	$-0.326169\pi$
$313$	18.3769	1.03872	0.519362	+	0.854554i	$0.326169\pi$
$314$	8.55738	0.482921
$315$	0.641497	0.0361443
$316$	−15.1904	−0.854525
$317$	−21.2226	−1.19198	−0.595989	−	0.802992i	$-0.703240\pi$
$317$	−21.2226	−1.19198	−0.595989	+	0.802992i	$0.703240\pi$
$318$	9.57830	0.537125
$319$	−2.36785	−0.132574
$320$	0.363595	0.0203256
$321$	10.9274	0.609906
$322$	2.29206	0.127731
$323$	0	0
$324$	−0.594237	−0.0330132
$325$	−8.43763	−0.468035
$326$	−10.2239	−0.566250
$327$	4.54514	0.251347
$328$	3.92110	0.216506
$329$	−4.90140	−0.270223
$330$	−0.287326	−0.0158168
$331$	19.2027	1.05548	0.527739	−	0.849407i	$-0.323040\pi$
$331$	19.2027	1.05548	0.527739	+	0.849407i	$0.323040\pi$
$332$	−17.0241	−0.934320
$333$	−0.481013	−0.0263594
$334$	−9.67364	−0.529318
$335$	2.52997	0.138227
$336$	1.11161	0.0606435
$337$	33.3913	1.81894	0.909471	−	0.415767i	$-0.136487\pi$
$337$	33.3913	1.81894	0.909471	+	0.415767i	$0.136487\pi$
$338$	9.99548	0.543682
$339$	−11.4067	−0.619528
$340$	−0.801563	−0.0434708
$341$	−4.97565	−0.269446
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	8.13563	0.438644
$345$	−0.926398	−0.0498756
$346$	−0.732774	−0.0393942
$347$	23.4803	1.26049	0.630245	−	0.776396i	$-0.282954\pi$
$347$	23.4803	1.26049	0.630245	+	0.776396i	$0.282954\pi$
$348$	−3.70259	−0.198479
$349$	−25.0885	−1.34296	−0.671479	−	0.741024i	$-0.734341\pi$
$349$	−25.0885	−1.34296	−0.671479	+	0.741024i	$0.734341\pi$
$350$	−4.86780	−0.260195
$351$	9.17998	0.489991
$352$	0.710892	0.0378906
$353$	19.5601	1.04108	0.520539	−	0.853838i	$-0.325731\pi$
$353$	19.5601	1.04108	0.520539	+	0.853838i	$0.325731\pi$
$354$	4.04939	0.215223
$355$	−0.677152	−0.0359395
$356$	6.47803	0.343335
$357$	−2.45060	−0.129700
$358$	−24.2514	−1.28173
$359$	−33.6991	−1.77857	−0.889286	−	0.457352i	$-0.848798\pi$
$359$	−33.6991	−1.77857	−0.889286	+	0.457352i	$0.848798\pi$
$360$	0.641497	0.0338099
$361$	0	0
$362$	−4.94945	−0.260137
$363$	11.6660	0.612305
$364$	−1.73336	−0.0908525
$365$	3.37545	0.176679
$366$	0.952972	0.0498126
$367$	−16.0191	−0.836189	−0.418094	−	0.908404i	$-0.637302\pi$
$367$	−16.0191	−0.836189	−0.418094	+	0.908404i	$0.637302\pi$
$368$	2.29206	0.119482
$369$	6.91806	0.360140
$370$	−0.0991286	−0.00515345
$371$	−8.61658	−0.447351
$372$	−7.78036	−0.403393
$373$	−18.9222	−0.979752	−0.489876	−	0.871792i	$-0.662958\pi$
$373$	−18.9222	−0.979752	−0.489876	+	0.871792i	$0.662958\pi$
$374$	−1.56719	−0.0810377
$375$	3.98834	0.205957
$376$	−4.90140	−0.252770
$377$	5.77350	0.297350
$378$	5.29608	0.272401
$379$	5.29741	0.272110	0.136055	−	0.990701i	$-0.456558\pi$
$379$	5.29741	0.272110	0.136055	+	0.990701i	$0.456558\pi$
$380$	0	0
$381$	15.6013	0.799279
$382$	−9.18620	−0.470007
$383$	26.2127	1.33940	0.669702	−	0.742630i	$-0.266422\pi$
$383$	26.2127	1.33940	0.669702	+	0.742630i	$0.266422\pi$
$384$	1.11161	0.0567268
$385$	0.258477	0.0131732
$386$	18.8578	0.959837
$387$	14.3538	0.729646
$388$	0.677178	0.0343785
$389$	−2.55097	−0.129339	−0.0646697	−	0.997907i	$-0.520599\pi$
$389$	−2.55097	−0.129339	−0.0646697	+	0.997907i	$0.520599\pi$
$390$	0.700583	0.0354754
$391$	−5.05295	−0.255539
$392$	−1.00000	−0.0505076
$393$	15.1462	0.764023
$394$	19.4699	0.980881
$395$	−5.52314	−0.277900
$396$	1.25424	0.0630278
$397$	−16.2735	−0.816744	−0.408372	−	0.912816i	$-0.633903\pi$
$397$	−16.2735	−0.816744	−0.408372	+	0.912816i	$0.633903\pi$
$398$	−10.0754	−0.505032
$399$	0	0
$400$	−4.86780	−0.243390
$401$	−0.811872	−0.0405429	−0.0202715	−	0.999795i	$-0.506453\pi$
$401$	−0.811872	−0.0405429	−0.0202715	+	0.999795i	$0.506453\pi$
$402$	7.73485	0.385779
$403$	12.1320	0.604340
$404$	−4.78477	−0.238051
$405$	−0.216062	−0.0107362
$406$	3.33082	0.165306
$407$	−0.193813	−0.00960698
$408$	−2.45060	−0.121323
$409$	−36.7631	−1.81782	−0.908909	−	0.416994i	$-0.863084\pi$
$409$	−36.7631	−1.81782	−0.908909	+	0.416994i	$0.863084\pi$
$410$	1.42569	0.0704099
$411$	−13.0414	−0.643283
$412$	−3.41450	−0.168220
$413$	−3.64280	−0.179251
$414$	4.04392	0.198748
$415$	−6.18989	−0.303850
$416$	−1.73336	−0.0849847
$417$	−7.26664	−0.355849
$418$	0	0
$419$	21.6452	1.05744	0.528718	−	0.848797i	$-0.322673\pi$
$419$	21.6452	1.05744	0.528718	+	0.848797i	$0.322673\pi$
$420$	0.404177	0.0197218
$421$	−19.2194	−0.936696	−0.468348	−	0.883544i	$-0.655151\pi$
$421$	−19.2194	−0.936696	−0.468348	+	0.883544i	$0.655151\pi$
$422$	−5.47663	−0.266598
$423$	−8.64761	−0.420461
$424$	−8.61658	−0.418458
$425$	10.7313	0.520544
$426$	−2.07025	−0.100304
$427$	−0.857287	−0.0414870
$428$	−9.83019	−0.475160
$429$	1.36976	0.0661327
$430$	2.95807	0.142651
$431$	−5.89796	−0.284095	−0.142047	−	0.989860i	$-0.545369\pi$
$431$	−5.89796	−0.284095	−0.142047	+	0.989860i	$0.545369\pi$
$432$	5.29608	0.254808
$433$	−5.94252	−0.285579	−0.142790	−	0.989753i	$-0.545607\pi$
$433$	−5.94252	−0.285579	−0.142790	+	0.989753i	$0.545607\pi$
$434$	6.99917	0.335971
$435$	−1.34624	−0.0645474
$436$	−4.08878	−0.195817
$437$	0	0
$438$	10.3197	0.493094
$439$	−39.7589	−1.89759	−0.948795	−	0.315892i	$-0.897696\pi$
$439$	−39.7589	−1.89759	−0.948795	+	0.315892i	$0.897696\pi$
$440$	0.258477	0.0123224
$441$	−1.76432	−0.0840151
$442$	3.82126	0.181759
$443$	−27.2191	−1.29322	−0.646610	−	0.762821i	$-0.723814\pi$
$443$	−27.2191	−1.29322	−0.646610	+	0.762821i	$0.723814\pi$
$444$	−0.303064	−0.0143828
$445$	2.35538	0.111656
$446$	5.85396	0.277193
$447$	4.51500	0.213552
$448$	−1.00000	−0.0472456
$449$	−34.6875	−1.63701	−0.818503	−	0.574502i	$-0.805196\pi$
$449$	−34.6875	−1.63701	−0.818503	+	0.574502i	$0.805196\pi$
$450$	−8.58834	−0.404858
$451$	2.78748	0.131257
$452$	10.2614	0.482656
$453$	−3.66574	−0.172231
$454$	8.15785	0.382867
$455$	−0.630240	−0.0295461
$456$	0	0
$457$	−22.7325	−1.06338	−0.531690	−	0.846939i	$-0.678443\pi$
$457$	−22.7325	−1.06338	−0.531690	+	0.846939i	$0.678443\pi$
$458$	27.6584	1.29239
$459$	−11.6754	−0.544963
$460$	0.833382	0.0388566
$461$	−38.3128	−1.78440	−0.892201	−	0.451638i	$-0.850840\pi$
$461$	−38.3128	−1.78440	−0.892201	+	0.451638i	$0.850840\pi$
$462$	0.790236	0.0367651
$463$	−0.0716333	−0.00332908	−0.00166454	−	0.999999i	$-0.500530\pi$
$463$	−0.0716333	−0.00332908	−0.00166454	+	0.999999i	$0.500530\pi$
$464$	3.33082	0.154630
$465$	−2.82890	−0.131187
$466$	3.89805	0.180574
$467$	−29.9297	−1.38498	−0.692492	−	0.721426i	$-0.743487\pi$
$467$	−29.9297	−1.38498	−0.692492	+	0.721426i	$0.743487\pi$
$468$	−3.05819	−0.141365
$469$	−6.95822	−0.321301
$470$	−1.78212	−0.0822032
$471$	9.51249	0.438312
$472$	−3.64280	−0.167674
$473$	5.78355	0.265928
$474$	−16.8858	−0.775591
$475$	0	0
$476$	2.20455	0.101045
$477$	−15.2024	−0.696069
$478$	−10.1074	−0.462304
$479$	0.831655	0.0379993	0.0189996	−	0.999819i	$-0.493952\pi$
$479$	0.831655	0.0379993	0.0189996	+	0.999819i	$0.493952\pi$
$480$	0.404177	0.0184481
$481$	0.472572	0.0215474
$482$	18.5551	0.845160
$483$	2.54788	0.115933
$484$	−10.4946	−0.477029
$485$	0.246219	0.0111802
$486$	15.2277	0.690741
$487$	9.45799	0.428583	0.214291	−	0.976770i	$-0.431256\pi$
$487$	9.45799	0.428583	0.214291	+	0.976770i	$0.431256\pi$
$488$	−0.857287	−0.0388076
$489$	−11.3650	−0.513944
$490$	−0.363595	−0.0164256
$491$	0.0689055	0.00310966	0.00155483	−	0.999999i	$-0.499505\pi$
$491$	0.0689055	0.00310966	0.00155483	+	0.999999i	$0.499505\pi$
$492$	4.35874	0.196507
$493$	−7.34295	−0.330710
$494$	0	0
$495$	0.456035	0.0204972
$496$	6.99917	0.314272
$497$	1.86238	0.0835391
$498$	−18.9242	−0.848015
$499$	23.9771	1.07336	0.536682	−	0.843785i	$-0.319677\pi$
$499$	23.9771	1.07336	0.536682	+	0.843785i	$0.319677\pi$
$500$	−3.58788	−0.160455
$501$	−10.7533	−0.480424
$502$	−17.2756	−0.771049
$503$	−11.8780	−0.529612	−0.264806	−	0.964302i	$-0.585308\pi$
$503$	−11.8780	−0.529612	−0.264806	+	0.964302i	$0.585308\pi$
$504$	−1.76432	−0.0785889
$505$	−1.73972	−0.0774164
$506$	1.62941	0.0724359
$507$	11.1111	0.493461
$508$	−14.0348	−0.622695
$509$	−18.7738	−0.832132	−0.416066	−	0.909334i	$-0.636592\pi$
$509$	−18.7738	−0.832132	−0.416066	+	0.909334i	$0.636592\pi$
$510$	−0.891027	−0.0394554
$511$	−9.28353	−0.410679
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−3.88956	−0.171561
$515$	−1.24150	−0.0547069
$516$	9.04367	0.398125
$517$	−3.48436	−0.153242
$518$	0.272634	0.0119789
$519$	−0.814561	−0.0357553
$520$	−0.630240	−0.0276378
$521$	11.7476	0.514670	0.257335	−	0.966322i	$-0.417156\pi$
$521$	11.7476	0.514670	0.257335	+	0.966322i	$0.417156\pi$
$522$	5.87663	0.257213
$523$	2.38414	0.104251	0.0521256	−	0.998641i	$-0.483400\pi$
$523$	2.38414	0.104251	0.0521256	+	0.998641i	$0.483400\pi$
$524$	−13.6254	−0.595228
$525$	−5.41111	−0.236160
$526$	−19.3814	−0.845071
$527$	−15.4300	−0.672141
$528$	0.790236	0.0343906
$529$	−17.7465	−0.771585
$530$	−3.13295	−0.136087
$531$	−6.42706	−0.278911
$532$	0	0
$533$	−6.79666	−0.294396
$534$	7.20106	0.311621
$535$	−3.57421	−0.154527
$536$	−6.95822	−0.300549
$537$	−26.9582	−1.16333
$538$	30.3820	1.30986
$539$	−0.710892	−0.0306203
$540$	1.92563	0.0828658
$541$	−6.38368	−0.274456	−0.137228	−	0.990540i	$-0.543819\pi$
$541$	−6.38368	−0.274456	−0.137228	+	0.990540i	$0.543819\pi$
$542$	17.4011	0.747440
$543$	−5.50187	−0.236108
$544$	2.20455	0.0945192
$545$	−1.48666	−0.0636816
$546$	−1.92682	−0.0824603
$547$	−44.4095	−1.89881	−0.949407	−	0.314049i	$-0.898314\pi$
$547$	−44.4095	−1.89881	−0.949407	+	0.314049i	$0.898314\pi$
$548$	11.7319	0.501163
$549$	−1.51253	−0.0645531
$550$	−3.46048	−0.147555
$551$	0	0
$552$	2.54788	0.108445
$553$	15.1904	0.645960
$554$	14.8726	0.631877
$555$	−0.110193	−0.00467741
$556$	6.53702	0.277232
$557$	−26.8375	−1.13714	−0.568570	−	0.822635i	$-0.692503\pi$
$557$	−26.8375	−1.13714	−0.568570	+	0.822635i	$0.692503\pi$
$558$	12.3487	0.522764
$559$	−14.1019	−0.596448
$560$	−0.363595	−0.0153647
$561$	−1.74211	−0.0735521
$562$	23.2958	0.982676
$563$	2.43829	0.102762	0.0513808	−	0.998679i	$-0.483638\pi$
$563$	2.43829	0.102762	0.0513808	+	0.998679i	$0.483638\pi$
$564$	−5.44845	−0.229421
$565$	3.73100	0.156964
$566$	1.44172	0.0606000
$567$	0.594237	0.0249556
$568$	1.86238	0.0781437
$569$	−23.9448	−1.00382	−0.501908	−	0.864921i	$-0.667369\pi$
$569$	−23.9448	−1.00382	−0.501908	+	0.864921i	$0.667369\pi$
$570$	0	0
$571$	14.5444	0.608666	0.304333	−	0.952566i	$-0.401566\pi$
$571$	14.5444	0.608666	0.304333	+	0.952566i	$0.401566\pi$
$572$	−1.23223	−0.0515220
$573$	−10.2115	−0.426592
$574$	−3.92110	−0.163664
$575$	−11.1573	−0.465291
$576$	−1.76432	−0.0735132
$577$	−3.60073	−0.149900	−0.0749502	−	0.997187i	$-0.523880\pi$
$577$	−3.60073	−0.149900	−0.0749502	+	0.997187i	$0.523880\pi$
$578$	12.1400	0.504956
$579$	20.9626	0.871175
$580$	1.21107	0.0502870
$581$	17.0241	0.706280
$582$	0.752759	0.0312029
$583$	−6.12546	−0.253690
$584$	−9.28353	−0.384155
$585$	−1.11194	−0.0459732
$586$	4.97737	0.205613
$587$	−5.36206	−0.221316	−0.110658	−	0.993859i	$-0.535296\pi$
$587$	−5.36206	−0.221316	−0.110658	+	0.993859i	$0.535296\pi$
$588$	−1.11161	−0.0458421
$589$	0	0
$590$	−1.32451	−0.0545290
$591$	21.6430	0.890275
$592$	0.272634	0.0112052
$593$	2.53647	0.104160	0.0520802	−	0.998643i	$-0.483415\pi$
$593$	2.53647	0.104160	0.0520802	+	0.998643i	$0.483415\pi$
$594$	3.76494	0.154477
$595$	0.801563	0.0328609
$596$	−4.06167	−0.166372
$597$	−11.1999	−0.458381
$598$	−3.97295	−0.162466
$599$	44.9711	1.83747	0.918734	−	0.394877i	$-0.129213\pi$
$599$	44.9711	1.83747	0.918734	+	0.394877i	$0.129213\pi$
$600$	−5.41111	−0.220908
$601$	38.7420	1.58032	0.790160	−	0.612900i	$-0.209997\pi$
$601$	38.7420	1.58032	0.790160	+	0.612900i	$0.209997\pi$
$602$	−8.13563	−0.331583
$603$	−12.2765	−0.499938
$604$	3.29768	0.134181
$605$	−3.81580	−0.155134
$606$	−5.31881	−0.216062
$607$	35.0863	1.42411	0.712055	−	0.702124i	$-0.247765\pi$
$607$	35.0863	1.42411	0.712055	+	0.702124i	$0.247765\pi$
$608$	0	0
$609$	3.70259	0.150036
$610$	−0.311706	−0.0126206
$611$	8.49586	0.343706
$612$	3.88952	0.157224
$613$	39.5791	1.59859	0.799293	−	0.600941i	$-0.205207\pi$
$613$	39.5791	1.59859	0.799293	+	0.600941i	$0.205207\pi$
$614$	−5.20853	−0.210199
$615$	1.58482	0.0639060
$616$	−0.710892	−0.0286426
$617$	−9.01486	−0.362925	−0.181462	−	0.983398i	$-0.558083\pi$
$617$	−9.01486	−0.362925	−0.181462	+	0.983398i	$0.558083\pi$
$618$	−3.79561	−0.152682
$619$	−13.2635	−0.533105	−0.266552	−	0.963820i	$-0.585885\pi$
$619$	−13.2635	−0.533105	−0.266552	+	0.963820i	$0.585885\pi$
$620$	2.54486	0.102204
$621$	12.1389	0.487118
$622$	6.15011	0.246597
$623$	−6.47803	−0.259537
$624$	−1.92682	−0.0771345
$625$	23.0345	0.921378
$626$	−18.3769	−0.734489
$627$	0	0
$628$	−8.55738	−0.341477
$629$	−0.601035	−0.0239648
$630$	−0.641497	−0.0255579
$631$	−5.54078	−0.220575	−0.110287	−	0.993900i	$-0.535177\pi$
$631$	−5.54078	−0.220575	−0.110287	+	0.993900i	$0.535177\pi$
$632$	15.1904	0.604240
$633$	−6.08790	−0.241972
$634$	21.2226	0.842856
$635$	−5.10300	−0.202506
$636$	−9.57830	−0.379804
$637$	1.73336	0.0686780
$638$	2.36785	0.0937442
$639$	3.28583	0.129985
$640$	−0.363595	−0.0143724
$641$	−26.7868	−1.05802	−0.529008	−	0.848617i	$-0.677436\pi$
$641$	−26.7868	−1.05802	−0.529008	+	0.848617i	$0.677436\pi$
$642$	−10.9274	−0.431269
$643$	−42.2730	−1.66708	−0.833542	−	0.552456i	$-0.813691\pi$
$643$	−42.2730	−1.66708	−0.833542	+	0.552456i	$0.813691\pi$
$644$	−2.29206	−0.0903198
$645$	3.28823	0.129474
$646$	0	0
$647$	36.1760	1.42222	0.711112	−	0.703079i	$-0.248192\pi$
$647$	36.1760	1.42222	0.711112	+	0.703079i	$0.248192\pi$
$648$	0.594237	0.0233438
$649$	−2.58964	−0.101652
$650$	8.43763	0.330951
$651$	7.78036	0.304936
$652$	10.2239	0.400399
$653$	42.6640	1.66957	0.834785	−	0.550576i	$-0.185592\pi$
$653$	42.6640	1.66957	0.834785	+	0.550576i	$0.185592\pi$
$654$	−4.54514	−0.177729
$655$	−4.95413	−0.193574
$656$	−3.92110	−0.153093
$657$	−16.3791	−0.639009
$658$	4.90140	0.191076
$659$	−12.7112	−0.495158	−0.247579	−	0.968868i	$-0.579635\pi$
$659$	−12.7112	−0.495158	−0.247579	+	0.968868i	$0.579635\pi$
$660$	0.287326	0.0111842
$661$	−4.69590	−0.182650	−0.0913248	−	0.995821i	$-0.529110\pi$
$661$	−4.69590	−0.182650	−0.0913248	+	0.995821i	$0.529110\pi$
$662$	−19.2027	−0.746335
$663$	4.24777	0.164970
$664$	17.0241	0.660664
$665$	0	0
$666$	0.481013	0.0186389
$667$	7.63444	0.295607
$668$	9.67364	0.374285
$669$	6.50734	0.251588
$670$	−2.52997	−0.0977414
$671$	−0.609438	−0.0235271
$672$	−1.11161	−0.0428814
$673$	−26.6726	−1.02815	−0.514077	−	0.857744i	$-0.671866\pi$
$673$	−26.6726	−1.02815	−0.514077	+	0.857744i	$0.671866\pi$
$674$	−33.3913	−1.28619
$675$	−25.7802	−0.992282
$676$	−9.99548	−0.384441
$677$	2.75335	0.105820	0.0529099	−	0.998599i	$-0.483150\pi$
$677$	2.75335	0.105820	0.0529099	+	0.998599i	$0.483150\pi$
$678$	11.4067	0.438072
$679$	−0.677178	−0.0259877
$680$	0.801563	0.0307385
$681$	9.06837	0.347501
$682$	4.97565	0.190527
$683$	13.8866	0.531356	0.265678	−	0.964062i	$-0.414404\pi$
$683$	13.8866	0.531356	0.265678	+	0.964062i	$0.414404\pi$
$684$	0	0
$685$	4.26567	0.162983
$686$	1.00000	0.0381802
$687$	30.7454	1.17301
$688$	−8.13563	−0.310168
$689$	14.9356	0.569001
$690$	0.926398	0.0352674
$691$	−29.5114	−1.12267	−0.561333	−	0.827590i	$-0.689711\pi$
$691$	−29.5114	−1.12267	−0.561333	+	0.827590i	$0.689711\pi$
$692$	0.732774	0.0278559
$693$	−1.25424	−0.0476446
$694$	−23.4803	−0.891302
$695$	2.37683	0.0901583
$696$	3.70259	0.140346
$697$	8.64425	0.327424
$698$	25.0885	0.949615
$699$	4.33313	0.163894
$700$	4.86780	0.183985
$701$	26.6787	1.00764	0.503820	−	0.863808i	$-0.331927\pi$
$701$	26.6787	1.00764	0.503820	+	0.863808i	$0.331927\pi$
$702$	−9.17998	−0.346476
$703$	0	0
$704$	−0.710892	−0.0267927
$705$	−1.98103	−0.0746100
$706$	−19.5601	−0.736153
$707$	4.78477	0.179950
$708$	−4.04939	−0.152185
$709$	10.1895	0.382675	0.191338	−	0.981524i	$-0.438717\pi$
$709$	10.1895	0.382675	0.191338	+	0.981524i	$0.438717\pi$
$710$	0.677152	0.0254131
$711$	26.8006	1.00510
$712$	−6.47803	−0.242775
$713$	16.0425	0.600797
$714$	2.45060	0.0917115
$715$	−0.448032	−0.0167554
$716$	24.2514	0.906319
$717$	−11.2356	−0.419600
$718$	33.6991	1.25764
$719$	−43.0134	−1.60413	−0.802065	−	0.597237i	$-0.796265\pi$
$719$	−43.0134	−1.60413	−0.802065	+	0.597237i	$0.796265\pi$
$720$	−0.641497	−0.0239072
$721$	3.41450	0.127163
$722$	0	0
$723$	20.6260	0.767091
$724$	4.94945	0.183945
$725$	−16.2138	−0.602164
$726$	−11.6660	−0.432965
$727$	−19.8222	−0.735165	−0.367583	−	0.929991i	$-0.619814\pi$
$727$	−19.8222	−0.735165	−0.367583	+	0.929991i	$0.619814\pi$
$728$	1.73336	0.0642424
$729$	18.7100	0.692962
$730$	−3.37545	−0.124931
$731$	17.9354	0.663364
$732$	−0.952972	−0.0352229
$733$	−29.9929	−1.10781	−0.553906	−	0.832579i	$-0.686863\pi$
$733$	−29.9929	−1.10781	−0.553906	+	0.832579i	$0.686863\pi$
$734$	16.0191	0.591275
$735$	−0.404177	−0.0149083
$736$	−2.29206	−0.0844864
$737$	−4.94654	−0.182208
$738$	−6.91806	−0.254657
$739$	15.5023	0.570260	0.285130	−	0.958489i	$-0.407963\pi$
$739$	15.5023	0.570260	0.285130	+	0.958489i	$0.407963\pi$
$740$	0.0991286	0.00364404
$741$	0	0
$742$	8.61658	0.316325
$743$	−15.1926	−0.557364	−0.278682	−	0.960383i	$-0.589898\pi$
$743$	−15.1926	−0.557364	−0.278682	+	0.960383i	$0.589898\pi$
$744$	7.78036	0.285242
$745$	−1.47680	−0.0541059
$746$	18.9222	0.692790
$747$	30.0360	1.09896
$748$	1.56719	0.0573023
$749$	9.83019	0.359187
$750$	−3.98834	−0.145634
$751$	−32.3791	−1.18153	−0.590765	−	0.806844i	$-0.701174\pi$
$751$	−32.3791	−1.18153	−0.590765	+	0.806844i	$0.701174\pi$
$752$	4.90140	0.178735
$753$	−19.2038	−0.699826
$754$	−5.77350	−0.210258
$755$	1.19902	0.0436368
$756$	−5.29608	−0.192616
$757$	27.1811	0.987914	0.493957	−	0.869486i	$-0.335550\pi$
$757$	27.1811	0.987914	0.493957	+	0.869486i	$0.335550\pi$
$758$	−5.29741	−0.192411
$759$	1.81127	0.0657449
$760$	0	0
$761$	−45.6075	−1.65327	−0.826635	−	0.562739i	$-0.809748\pi$
$761$	−45.6075	−1.65327	−0.826635	+	0.562739i	$0.809748\pi$
$762$	−15.6013	−0.565176
$763$	4.08878	0.148024
$764$	9.18620	0.332345
$765$	1.41421	0.0511309
$766$	−26.2127	−0.947102
$767$	6.31427	0.227995
$768$	−1.11161	−0.0401119
$769$	−41.8778	−1.51015	−0.755076	−	0.655638i	$-0.772400\pi$
$769$	−41.8778	−1.51015	−0.755076	+	0.655638i	$0.772400\pi$
$770$	−0.258477	−0.00931485
$771$	−4.32368	−0.155714
$772$	−18.8578	−0.678707
$773$	17.1005	0.615062	0.307531	−	0.951538i	$-0.400497\pi$
$773$	17.1005	0.615062	0.307531	+	0.951538i	$0.400497\pi$
$774$	−14.3538	−0.515937
$775$	−34.0705	−1.22385
$776$	−0.677178	−0.0243093
$777$	0.303064	0.0108724
$778$	2.55097	0.0914567
$779$	0	0
$780$	−0.700583	−0.0250849
$781$	1.32395	0.0473747
$782$	5.05295	0.180693
$783$	17.6403	0.630412
$784$	1.00000	0.0357143
$785$	−3.11142	−0.111051
$786$	−15.1462	−0.540246
$787$	−9.52303	−0.339459	−0.169730	−	0.985491i	$-0.554289\pi$
$787$	−9.52303	−0.339459	−0.169730	+	0.985491i	$0.554289\pi$
$788$	−19.4699	−0.693587
$789$	−21.5446	−0.767010
$790$	5.52314	0.196505
$791$	−10.2614	−0.364854
$792$	−1.25424	−0.0445674
$793$	1.48598	0.0527688
$794$	16.2735	0.577525
$795$	−3.48263	−0.123516
$796$	10.0754	0.357111
$797$	−31.1914	−1.10486	−0.552428	−	0.833560i	$-0.686299\pi$
$797$	−31.1914	−1.10486	−0.552428	+	0.833560i	$0.686299\pi$
$798$	0	0
$799$	−10.8054	−0.382266
$800$	4.86780	0.172103
$801$	−11.4293	−0.403834
$802$	0.811872	0.0286682
$803$	−6.59958	−0.232894
$804$	−7.73485	−0.272787
$805$	−0.833382	−0.0293728
$806$	−12.1320	−0.427333
$807$	33.7730	1.18887
$808$	4.78477	0.168328
$809$	42.9529	1.51014	0.755072	−	0.655642i	$-0.227602\pi$
$809$	42.9529	1.51014	0.755072	+	0.655642i	$0.227602\pi$
$810$	0.216062	0.00759164
$811$	31.1564	1.09405	0.547025	−	0.837117i	$-0.315760\pi$
$811$	31.1564	1.09405	0.547025	+	0.837117i	$0.315760\pi$
$812$	−3.33082	−0.116889
$813$	19.3433	0.678398
$814$	0.193813	0.00679316
$815$	3.71736	0.130214
$816$	2.45060	0.0857883
$817$	0	0
$818$	36.7631	1.28539
$819$	3.05819	0.106862
$820$	−1.42569	−0.0497873
$821$	26.9185	0.939461	0.469731	−	0.882810i	$-0.344351\pi$
$821$	26.9185	0.939461	0.469731	+	0.882810i	$0.344351\pi$
$822$	13.0414	0.454869
$823$	−13.6068	−0.474304	−0.237152	−	0.971473i	$-0.576214\pi$
$823$	−13.6068	−0.474304	−0.237152	+	0.971473i	$0.576214\pi$
$824$	3.41450	0.118950
$825$	−3.84671	−0.133925
$826$	3.64280	0.126749
$827$	33.4871	1.16446	0.582230	−	0.813024i	$-0.302180\pi$
$827$	33.4871	1.16446	0.582230	+	0.813024i	$0.302180\pi$
$828$	−4.04392	−0.140536
$829$	53.1184	1.84488	0.922440	−	0.386141i	$-0.126192\pi$
$829$	53.1184	1.84488	0.922440	+	0.386141i	$0.126192\pi$
$830$	6.18989	0.214854
$831$	16.5326	0.573509
$832$	1.73336	0.0600933
$833$	−2.20455	−0.0763830
$834$	7.26664	0.251623
$835$	3.51729	0.121721
$836$	0	0
$837$	37.0681	1.28126
$838$	−21.6452	−0.747720
$839$	35.3178	1.21930	0.609652	−	0.792669i	$-0.291309\pi$
$839$	35.3178	1.21930	0.609652	+	0.792669i	$0.291309\pi$
$840$	−0.404177	−0.0139454
$841$	−17.9056	−0.617435
$842$	19.2194	0.662344
$843$	25.8960	0.891904
$844$	5.47663	0.188513
$845$	−3.63431	−0.125024
$846$	8.64761	0.297311
$847$	10.4946	0.360600
$848$	8.61658	0.295895
$849$	1.60263	0.0550023
$850$	−10.7313	−0.368080
$851$	0.624894	0.0214211
$852$	2.07025	0.0709254
$853$	52.9329	1.81239	0.906193	−	0.422864i	$-0.138975\pi$
$853$	52.9329	1.81239	0.906193	+	0.422864i	$0.138975\pi$
$854$	0.857287	0.0293358
$855$	0	0
$856$	9.83019	0.335989
$857$	−38.2468	−1.30648	−0.653242	−	0.757149i	$-0.726592\pi$
$857$	−38.2468	−1.30648	−0.653242	+	0.757149i	$0.726592\pi$
$858$	−1.36976	−0.0467628
$859$	−26.4830	−0.903589	−0.451794	−	0.892122i	$-0.649216\pi$
$859$	−26.4830	−0.903589	−0.451794	+	0.892122i	$0.649216\pi$
$860$	−2.95807	−0.100869
$861$	−4.35874	−0.148546
$862$	5.89796	0.200885
$863$	15.6254	0.531893	0.265947	−	0.963988i	$-0.414315\pi$
$863$	15.6254	0.531893	0.265947	+	0.963988i	$0.414315\pi$
$864$	−5.29608	−0.180176
$865$	0.266433	0.00905900
$866$	5.94252	0.201935
$867$	13.4950	0.458313
$868$	−6.99917	−0.237567
$869$	10.7987	0.366321
$870$	1.34624	0.0456419
$871$	12.0611	0.408674
$872$	4.08878	0.138464
$873$	−1.19476	−0.0404364
$874$	0	0
$875$	3.58788	0.121293
$876$	−10.3197	−0.348670
$877$	−26.1767	−0.883924	−0.441962	−	0.897034i	$-0.645717\pi$
$877$	−26.1767	−0.883924	−0.441962	+	0.897034i	$0.645717\pi$
$878$	39.7589	1.34180
$879$	5.53291	0.186621
$880$	−0.258477	−0.00871325
$881$	−38.5584	−1.29907	−0.649533	−	0.760333i	$-0.725036\pi$
$881$	−38.5584	−1.29907	−0.649533	+	0.760333i	$0.725036\pi$
$882$	1.76432	0.0594076
$883$	40.4044	1.35972	0.679859	−	0.733343i	$-0.262041\pi$
$883$	40.4044	1.35972	0.679859	+	0.733343i	$0.262041\pi$
$884$	−3.82126	−0.128523
$885$	−1.47234	−0.0494921
$886$	27.2191	0.914444
$887$	56.4666	1.89596	0.947981	−	0.318326i	$-0.103121\pi$
$887$	56.4666	1.89596	0.947981	+	0.318326i	$0.103121\pi$
$888$	0.303064	0.0101702
$889$	14.0348	0.470713
$890$	−2.35538	−0.0789526
$891$	0.422438	0.0141522
$892$	−5.85396	−0.196005
$893$	0	0
$894$	−4.51500	−0.151004
$895$	8.81770	0.294743
$896$	1.00000	0.0334077
$897$	−4.41639	−0.147459
$898$	34.6875	1.15754
$899$	23.3130	0.777531
$900$	8.58834	0.286278
$901$	−18.9957	−0.632837
$902$	−2.78748	−0.0928128
$903$	−9.04367	−0.300954
$904$	−10.2614	−0.341290
$905$	1.79959	0.0598205
$906$	3.66574	0.121786
$907$	−11.9005	−0.395148	−0.197574	−	0.980288i	$-0.563306\pi$
$907$	−11.9005	−0.395148	−0.197574	+	0.980288i	$0.563306\pi$
$908$	−8.15785	−0.270728
$909$	8.44184	0.279998
$910$	0.630240	0.0208922
$911$	−11.3797	−0.377027	−0.188514	−	0.982071i	$-0.560367\pi$
$911$	−11.3797	−0.377027	−0.188514	+	0.982071i	$0.560367\pi$
$912$	0	0
$913$	12.1023	0.400528
$914$	22.7325	0.751923
$915$	−0.346496	−0.0114548
$916$	−27.6584	−0.913860
$917$	13.6254	0.449950
$918$	11.6754	0.385347
$919$	−1.42214	−0.0469122	−0.0234561	−	0.999725i	$-0.507467\pi$
$919$	−1.42214	−0.0469122	−0.0234561	+	0.999725i	$0.507467\pi$
$920$	−0.833382	−0.0274758
$921$	−5.78986	−0.190783
$922$	38.3128	1.26176
$923$	−3.22817	−0.106256
$924$	−0.790236	−0.0259969
$925$	−1.32713	−0.0436357
$926$	0.0716333	0.00235402
$927$	6.02426	0.197863
$928$	−3.33082	−0.109340
$929$	38.6024	1.26650	0.633251	−	0.773946i	$-0.281720\pi$
$929$	38.6024	1.26650	0.633251	+	0.773946i	$0.281720\pi$
$930$	2.82890	0.0927634
$931$	0	0
$932$	−3.89805	−0.127685
$933$	6.83654	0.223818
$934$	29.9297	0.979331
$935$	0.569824	0.0186352
$936$	3.05819	0.0999600
$937$	−9.95969	−0.325369	−0.162684	−	0.986678i	$-0.552015\pi$
$937$	−9.95969	−0.325369	−0.162684	+	0.986678i	$0.552015\pi$
$938$	6.95822	0.227194
$939$	−20.4280	−0.666643
$940$	1.78212	0.0581265
$941$	2.30213	0.0750474	0.0375237	−	0.999296i	$-0.488053\pi$
$941$	2.30213	0.0750474	0.0375237	+	0.999296i	$0.488053\pi$
$942$	−9.51249	−0.309934
$943$	−8.98739	−0.292670
$944$	3.64280	0.118563
$945$	−1.92563	−0.0626407
$946$	−5.78355	−0.188039
$947$	22.0889	0.717793	0.358896	−	0.933377i	$-0.383153\pi$
$947$	22.0889	0.717793	0.358896	+	0.933377i	$0.383153\pi$
$948$	16.8858	0.548426
$949$	16.0917	0.522357
$950$	0	0
$951$	23.5913	0.765000
$952$	−2.20455	−0.0714498
$953$	56.8085	1.84021	0.920104	−	0.391675i	$-0.128104\pi$
$953$	56.8085	1.84021	0.920104	+	0.391675i	$0.128104\pi$
$954$	15.2024	0.492195
$955$	3.34006	0.108082
$956$	10.1074	0.326898
$957$	2.63214	0.0850849
$958$	−0.831655	−0.0268696
$959$	−11.7319	−0.378843
$960$	−0.404177	−0.0130448
$961$	17.9883	0.580269
$962$	−0.472572	−0.0152363
$963$	17.3436	0.558889
$964$	−18.5551	−0.597618
$965$	−6.85661	−0.220722
$966$	−2.54788	−0.0819768
$967$	17.9547	0.577385	0.288692	−	0.957422i	$-0.406780\pi$
$967$	17.9547	0.577385	0.288692	+	0.957422i	$0.406780\pi$
$968$	10.4946	0.337310
$969$	0	0
$970$	−0.246219	−0.00790560
$971$	−43.6454	−1.40065	−0.700323	−	0.713826i	$-0.746961\pi$
$971$	−43.6454	−1.40065	−0.700323	+	0.713826i	$0.746961\pi$
$972$	−15.2277	−0.488428
$973$	−6.53702	−0.209567
$974$	−9.45799	−0.303054
$975$	9.37937	0.300380
$976$	0.857287	0.0274411
$977$	17.1215	0.547767	0.273883	−	0.961763i	$-0.411692\pi$
$977$	17.1215	0.547767	0.273883	+	0.961763i	$0.411692\pi$
$978$	11.3650	0.363413
$979$	−4.60518	−0.147182
$980$	0.363595	0.0116146
$981$	7.21391	0.230322
$982$	−0.0689055	−0.00219886
$983$	−53.0137	−1.69087	−0.845437	−	0.534076i	$-0.820660\pi$
$983$	−53.0137	−1.69087	−0.845437	+	0.534076i	$0.820660\pi$
$984$	−4.35874	−0.138952
$985$	−7.07917	−0.225561
$986$	7.34295	0.233847
$987$	5.44845	0.173426
$988$	0	0
$989$	−18.6473	−0.592951
$990$	−0.456035	−0.0144937
$991$	4.33532	0.137716	0.0688580	−	0.997626i	$-0.478064\pi$
$991$	4.33532	0.137716	0.0688580	+	0.997626i	$0.478064\pi$
$992$	−6.99917	−0.222224
$993$	−21.3460	−0.677395
$994$	−1.86238	−0.0590711
$995$	3.66335	0.116136
$996$	18.9242	0.599638
$997$	−49.2177	−1.55874	−0.779370	−	0.626564i	$-0.784461\pi$
$997$	−49.2177	−1.55874	−0.779370	+	0.626564i	$0.784461\pi$
$998$	−23.9771	−0.758983
$999$	1.44389	0.0456827

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bb.1.2		6
19.9	even	9		266.2.u.b.43.1	✓	12
19.17	even	9		266.2.u.b.99.1	yes	12
19.18	odd	2		5054.2.a.bc.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.b.43.1	✓	12	19.9	even	9
266.2.u.b.99.1	yes	12	19.17	even	9
5054.2.a.bb.1.2		6	1.1	even	1	trivial
5054.2.a.bc.1.5		6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.11161 q^{3} +1.00000 q^{4} +0.363595 q^{5} +1.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.76432 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.11161 q^{3} +1.00000 q^{4} +0.363595 q^{5} +1.11161 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.76432 q^{9} -0.363595 q^{10} -0.710892 q^{11} -1.11161 q^{12} +1.73336 q^{13} +1.00000 q^{14} -0.404177 q^{15} +1.00000 q^{16} -2.20455 q^{17} +1.76432 q^{18} +0.363595 q^{20} +1.11161 q^{21} +0.710892 q^{22} +2.29206 q^{23} +1.11161 q^{24} -4.86780 q^{25} -1.73336 q^{26} +5.29608 q^{27} -1.00000 q^{28} +3.33082 q^{29} +0.404177 q^{30} +6.99917 q^{31} -1.00000 q^{32} +0.790236 q^{33} +2.20455 q^{34} -0.363595 q^{35} -1.76432 q^{36} +0.272634 q^{37} -1.92682 q^{39} -0.363595 q^{40} -3.92110 q^{41} -1.11161 q^{42} -8.13563 q^{43} -0.710892 q^{44} -0.641497 q^{45} -2.29206 q^{46} +4.90140 q^{47} -1.11161 q^{48} +1.00000 q^{49} +4.86780 q^{50} +2.45060 q^{51} +1.73336 q^{52} +8.61658 q^{53} -5.29608 q^{54} -0.258477 q^{55} +1.00000 q^{56} -3.33082 q^{58} +3.64280 q^{59} -0.404177 q^{60} +0.857287 q^{61} -6.99917 q^{62} +1.76432 q^{63} +1.00000 q^{64} +0.630240 q^{65} -0.790236 q^{66} +6.95822 q^{67} -2.20455 q^{68} -2.54788 q^{69} +0.363595 q^{70} -1.86238 q^{71} +1.76432 q^{72} +9.28353 q^{73} -0.272634 q^{74} +5.41111 q^{75} +0.710892 q^{77} +1.92682 q^{78} -15.1904 q^{79} +0.363595 q^{80} -0.594237 q^{81} +3.92110 q^{82} -17.0241 q^{83} +1.11161 q^{84} -0.801563 q^{85} +8.13563 q^{86} -3.70259 q^{87} +0.710892 q^{88} +6.47803 q^{89} +0.641497 q^{90} -1.73336 q^{91} +2.29206 q^{92} -7.78036 q^{93} -4.90140 q^{94} +1.11161 q^{96} +0.677178 q^{97} -1.00000 q^{98} +1.25424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 3 q^{31} - 6 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 3 q^{37} - 9 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} + 3 q^{48} + 6 q^{49} - 3 q^{50} - 27 q^{51} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 24 q^{55} + 6 q^{56} - 6 q^{58} + 15 q^{59} - 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} + 3 q^{65} - 6 q^{66} + 15 q^{67} - 9 q^{68} + 24 q^{69} - 3 q^{70} + 21 q^{71} + 3 q^{72} - 33 q^{73} + 3 q^{74} + 33 q^{75} - 3 q^{77} + 9 q^{78} - 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} - 3 q^{84} - 18 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 12 q^{89} + 12 q^{90} - 6 q^{91} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 18 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 3 * q^31 - 6 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 3 * q^37 - 9 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 + 3 * q^48 + 6 * q^49 - 3 * q^50 - 27 * q^51 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 24 * q^55 + 6 * q^56 - 6 * q^58 + 15 * q^59 - 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^65 - 6 * q^66 + 15 * q^67 - 9 * q^68 + 24 * q^69 - 3 * q^70 + 21 * q^71 + 3 * q^72 - 33 * q^73 + 3 * q^74 + 33 * q^75 - 3 * q^77 + 9 * q^78 - 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 - 3 * q^84 - 18 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 12 * q^89 + 12 * q^90 - 6 * q^91 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 18 * q^97 - 6 * q^98

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