LMFDB - Embedded newform 6014.2.a.i.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.56730 q^{3} +1.00000 q^{4} +4.16992 q^{5} +1.56730 q^{6} +1.53618 q^{7} +1.00000 q^{8} -0.543558 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.56730 q^{3} +1.00000 q^{4} +4.16992 q^{5} +1.56730 q^{6} +1.53618 q^{7} +1.00000 q^{8} -0.543558 q^{9} +4.16992 q^{10} -3.34021 q^{11} +1.56730 q^{12} +6.13924 q^{13} +1.53618 q^{14} +6.53554 q^{15} +1.00000 q^{16} -1.87065 q^{17} -0.543558 q^{18} +0.663856 q^{19} +4.16992 q^{20} +2.40767 q^{21} -3.34021 q^{22} +4.67116 q^{23} +1.56730 q^{24} +12.3883 q^{25} +6.13924 q^{26} -5.55383 q^{27} +1.53618 q^{28} +3.93638 q^{29} +6.53554 q^{30} -1.00000 q^{31} +1.00000 q^{32} -5.23512 q^{33} -1.87065 q^{34} +6.40577 q^{35} -0.543558 q^{36} -10.5165 q^{37} +0.663856 q^{38} +9.62206 q^{39} +4.16992 q^{40} -10.8210 q^{41} +2.40767 q^{42} +4.34914 q^{43} -3.34021 q^{44} -2.26660 q^{45} +4.67116 q^{46} +12.5315 q^{47} +1.56730 q^{48} -4.64014 q^{49} +12.3883 q^{50} -2.93187 q^{51} +6.13924 q^{52} -5.12469 q^{53} -5.55383 q^{54} -13.9284 q^{55} +1.53618 q^{56} +1.04046 q^{57} +3.93638 q^{58} -7.99415 q^{59} +6.53554 q^{60} +7.40917 q^{61} -1.00000 q^{62} -0.835006 q^{63} +1.00000 q^{64} +25.6002 q^{65} -5.23512 q^{66} -4.09700 q^{67} -1.87065 q^{68} +7.32113 q^{69} +6.40577 q^{70} -2.81609 q^{71} -0.543558 q^{72} -15.2483 q^{73} -10.5165 q^{74} +19.4162 q^{75} +0.663856 q^{76} -5.13117 q^{77} +9.62206 q^{78} -3.13973 q^{79} +4.16992 q^{80} -7.07387 q^{81} -10.8210 q^{82} -7.79095 q^{83} +2.40767 q^{84} -7.80046 q^{85} +4.34914 q^{86} +6.16951 q^{87} -3.34021 q^{88} +12.8055 q^{89} -2.26660 q^{90} +9.43101 q^{91} +4.67116 q^{92} -1.56730 q^{93} +12.5315 q^{94} +2.76823 q^{95} +1.56730 q^{96} -1.00000 q^{97} -4.64014 q^{98} +1.81560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * 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
$3$	1.56730	0.904883	0.452442	−	0.891794i	$-0.350553\pi$
$3$	1.56730	0.904883	0.452442	+	0.891794i	$0.350553\pi$
$4$	1.00000	0.500000
$5$	4.16992	1.86485	0.932424	−	0.361367i	$-0.117690\pi$
$5$	4.16992	1.86485	0.932424	+	0.361367i	$0.117690\pi$
$6$	1.56730	0.639849
$7$	1.53618	0.580623	0.290312	−	0.956932i	$-0.406241\pi$
$7$	1.53618	0.580623	0.290312	+	0.956932i	$0.406241\pi$
$8$	1.00000	0.353553
$9$	−0.543558	−0.181186
$10$	4.16992	1.31865
$11$	−3.34021	−1.00711	−0.503555	−	0.863963i	$-0.667975\pi$
$11$	−3.34021	−1.00711	−0.503555	+	0.863963i	$0.667975\pi$
$12$	1.56730	0.452442
$13$	6.13924	1.70272	0.851360	−	0.524582i	$-0.175778\pi$
$13$	6.13924	1.70272	0.851360	+	0.524582i	$0.175778\pi$
$14$	1.53618	0.410563
$15$	6.53554	1.68747
$16$	1.00000	0.250000
$17$	−1.87065	−0.453699	−0.226849	−	0.973930i	$-0.572842\pi$
$17$	−1.87065	−0.453699	−0.226849	+	0.973930i	$0.572842\pi$
$18$	−0.543558	−0.128118
$19$	0.663856	0.152299	0.0761495	−	0.997096i	$-0.475737\pi$
$19$	0.663856	0.152299	0.0761495	+	0.997096i	$0.475737\pi$
$20$	4.16992	0.932424
$21$	2.40767	0.525396
$22$	−3.34021	−0.712134
$23$	4.67116	0.974004	0.487002	−	0.873401i	$-0.338090\pi$
$23$	4.67116	0.974004	0.487002	+	0.873401i	$0.338090\pi$
$24$	1.56730	0.319925
$25$	12.3883	2.47765
$26$	6.13924	1.20400
$27$	−5.55383	−1.06884
$28$	1.53618	0.290312
$29$	3.93638	0.730968	0.365484	−	0.930818i	$-0.380903\pi$
$29$	3.93638	0.730968	0.365484	+	0.930818i	$0.380903\pi$
$30$	6.53554	1.19322
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−5.23512	−0.911317
$34$	−1.87065	−0.320813
$35$	6.40577	1.08277
$36$	−0.543558	−0.0905930
$37$	−10.5165	−1.72890	−0.864452	−	0.502716i	$-0.832334\pi$
$37$	−10.5165	−1.72890	−0.864452	+	0.502716i	$0.832334\pi$
$38$	0.663856	0.107692
$39$	9.62206	1.54076
$40$	4.16992	0.659323
$41$	−10.8210	−1.68995	−0.844976	−	0.534805i	$-0.820385\pi$
$41$	−10.8210	−1.68995	−0.844976	+	0.534805i	$0.820385\pi$
$42$	2.40767	0.371511
$43$	4.34914	0.663237	0.331618	−	0.943414i	$-0.392405\pi$
$43$	4.34914	0.663237	0.331618	+	0.943414i	$0.392405\pi$
$44$	−3.34021	−0.503555
$45$	−2.26660	−0.337884
$46$	4.67116	0.688725
$47$	12.5315	1.82790	0.913951	−	0.405824i	$-0.133015\pi$
$47$	12.5315	1.82790	0.913951	+	0.405824i	$0.133015\pi$
$48$	1.56730	0.226221
$49$	−4.64014	−0.662877
$50$	12.3883	1.75197
$51$	−2.93187	−0.410544
$52$	6.13924	0.851360
$53$	−5.12469	−0.703930	−0.351965	−	0.936013i	$-0.614486\pi$
$53$	−5.12469	−0.703930	−0.351965	+	0.936013i	$0.614486\pi$
$54$	−5.55383	−0.755781
$55$	−13.9284	−1.87811
$56$	1.53618	0.205281
$57$	1.04046	0.137813
$58$	3.93638	0.516872
$59$	−7.99415	−1.04075	−0.520375	−	0.853938i	$-0.674208\pi$
$59$	−7.99415	−1.04075	−0.520375	+	0.853938i	$0.674208\pi$
$60$	6.53554	0.843735
$61$	7.40917	0.948647	0.474324	−	0.880351i	$-0.342693\pi$
$61$	7.40917	0.948647	0.474324	+	0.880351i	$0.342693\pi$
$62$	−1.00000	−0.127000
$63$	−0.835006	−0.105201
$64$	1.00000	0.125000
$65$	25.6002	3.17531
$66$	−5.23512	−0.644399
$67$	−4.09700	−0.500529	−0.250264	−	0.968178i	$-0.580518\pi$
$67$	−4.09700	−0.500529	−0.250264	+	0.968178i	$0.580518\pi$
$68$	−1.87065	−0.226849
$69$	7.32113	0.881360
$70$	6.40577	0.765636
$71$	−2.81609	−0.334208	−0.167104	−	0.985939i	$-0.553442\pi$
$71$	−2.81609	−0.334208	−0.167104	+	0.985939i	$0.553442\pi$
$72$	−0.543558	−0.0640590
$73$	−15.2483	−1.78468	−0.892340	−	0.451365i	$-0.850937\pi$
$73$	−15.2483	−1.78468	−0.892340	+	0.451365i	$0.850937\pi$
$74$	−10.5165	−1.22252
$75$	19.4162	2.24199
$76$	0.663856	0.0761495
$77$	−5.13117	−0.584751
$78$	9.62206	1.08948
$79$	−3.13973	−0.353247	−0.176624	−	0.984278i	$-0.556518\pi$
$79$	−3.13973	−0.353247	−0.176624	+	0.984278i	$0.556518\pi$
$80$	4.16992	0.466212
$81$	−7.07387	−0.785986
$82$	−10.8210	−1.19498
$83$	−7.79095	−0.855168	−0.427584	−	0.903976i	$-0.640635\pi$
$83$	−7.79095	−0.855168	−0.427584	+	0.903976i	$0.640635\pi$
$84$	2.40767	0.262698
$85$	−7.80046	−0.846079
$86$	4.34914	0.468979
$87$	6.16951	0.661441
$88$	−3.34021	−0.356067
$89$	12.8055	1.35738	0.678688	−	0.734427i	$-0.262549\pi$
$89$	12.8055	1.35738	0.678688	+	0.734427i	$0.262549\pi$
$90$	−2.26660	−0.238920
$91$	9.43101	0.988638
$92$	4.67116	0.487002
$93$	−1.56730	−0.162522
$94$	12.5315	1.29252
$95$	2.76823	0.284014
$96$	1.56730	0.159962
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−4.64014	−0.468725
$99$	1.81560	0.182474
$100$	12.3883	1.23883
$101$	16.5261	1.64441	0.822204	−	0.569193i	$-0.192744\pi$
$101$	16.5261	1.64441	0.822204	+	0.569193i	$0.192744\pi$
$102$	−2.93187	−0.290299
$103$	−6.46359	−0.636877	−0.318438	−	0.947944i	$-0.603158\pi$
$103$	−6.46359	−0.636877	−0.318438	+	0.947944i	$0.603158\pi$
$104$	6.13924	0.602002
$105$	10.0398	0.979784
$106$	−5.12469	−0.497754
$107$	−16.3923	−1.58470	−0.792351	−	0.610066i	$-0.791143\pi$
$107$	−16.3923	−1.58470	−0.792351	+	0.610066i	$0.791143\pi$
$108$	−5.55383	−0.534418
$109$	−8.92652	−0.855006	−0.427503	−	0.904014i	$-0.640607\pi$
$109$	−8.92652	−0.855006	−0.427503	+	0.904014i	$0.640607\pi$
$110$	−13.9284	−1.32802
$111$	−16.4826	−1.56446
$112$	1.53618	0.145156
$113$	4.62130	0.434736	0.217368	−	0.976090i	$-0.430253\pi$
$113$	4.62130	0.434736	0.217368	+	0.976090i	$0.430253\pi$
$114$	1.04046	0.0974484
$115$	19.4784	1.81637
$116$	3.93638	0.365484
$117$	−3.33704	−0.308509
$118$	−7.99415	−0.735921
$119$	−2.87366	−0.263428
$120$	6.53554	0.596610
$121$	0.156979	0.0142708
$122$	7.40917	0.670795
$123$	−16.9597	−1.52921
$124$	−1.00000	−0.0898027
$125$	30.8086	2.75560
$126$	−0.835006	−0.0743882
$127$	14.1621	1.25668	0.628342	−	0.777937i	$-0.283734\pi$
$127$	14.1621	1.25668	0.628342	+	0.777937i	$0.283734\pi$
$128$	1.00000	0.0883883
$129$	6.81642	0.600152
$130$	25.6002	2.24528
$131$	4.16328	0.363747	0.181874	−	0.983322i	$-0.441784\pi$
$131$	4.16328	0.363747	0.181874	+	0.983322i	$0.441784\pi$
$132$	−5.23512	−0.455659
$133$	1.01980	0.0884283
$134$	−4.09700	−0.353927
$135$	−23.1591	−1.99322
$136$	−1.87065	−0.160407
$137$	1.17104	0.100049	0.0500244	−	0.998748i	$-0.484070\pi$
$137$	1.17104	0.100049	0.0500244	+	0.998748i	$0.484070\pi$
$138$	7.32113	0.623216
$139$	16.4860	1.39833	0.699163	−	0.714962i	$-0.253556\pi$
$139$	16.4860	1.39833	0.699163	+	0.714962i	$0.253556\pi$
$140$	6.40577	0.541387
$141$	19.6406	1.65404
$142$	−2.81609	−0.236321
$143$	−20.5063	−1.71483
$144$	−0.543558	−0.0452965
$145$	16.4144	1.36314
$146$	−15.2483	−1.26196
$147$	−7.27251	−0.599826
$148$	−10.5165	−0.864452
$149$	−10.7934	−0.884233	−0.442116	−	0.896958i	$-0.645772\pi$
$149$	−10.7934	−0.884233	−0.442116	+	0.896958i	$0.645772\pi$
$150$	19.4162	1.58533
$151$	10.9334	0.889751	0.444875	−	0.895593i	$-0.353248\pi$
$151$	10.9334	0.889751	0.444875	+	0.895593i	$0.353248\pi$
$152$	0.663856	0.0538458
$153$	1.01681	0.0822039
$154$	−5.13117	−0.413482
$155$	−4.16992	−0.334936
$156$	9.62206	0.770381
$157$	0.798002	0.0636875	0.0318438	−	0.999493i	$-0.489862\pi$
$157$	0.798002	0.0636875	0.0318438	+	0.999493i	$0.489862\pi$
$158$	−3.13973	−0.249783
$159$	−8.03194	−0.636974
$160$	4.16992	0.329662
$161$	7.17576	0.565529
$162$	−7.07387	−0.555776
$163$	14.7499	1.15530	0.577649	−	0.816285i	$-0.303970\pi$
$163$	14.7499	1.15530	0.577649	+	0.816285i	$0.303970\pi$
$164$	−10.8210	−0.844976
$165$	−21.8301	−1.69947
$166$	−7.79095	−0.604695
$167$	2.55296	0.197554	0.0987770	−	0.995110i	$-0.468507\pi$
$167$	2.55296	0.197554	0.0987770	+	0.995110i	$0.468507\pi$
$168$	2.40767	0.185756
$169$	24.6903	1.89925
$170$	−7.80046	−0.598268
$171$	−0.360844	−0.0275944
$172$	4.34914	0.331618
$173$	−8.09197	−0.615221	−0.307611	−	0.951512i	$-0.599529\pi$
$173$	−8.09197	−0.615221	−0.307611	+	0.951512i	$0.599529\pi$
$174$	6.16951	0.467709
$175$	19.0307	1.43858
$176$	−3.34021	−0.251778
$177$	−12.5293	−0.941757
$178$	12.8055	0.959810
$179$	10.2528	0.766327	0.383164	−	0.923680i	$-0.374835\pi$
$179$	10.2528	0.766327	0.383164	+	0.923680i	$0.374835\pi$
$180$	−2.26660	−0.168942
$181$	−13.7688	−1.02342	−0.511712	−	0.859157i	$-0.670988\pi$
$181$	−13.7688	−1.02342	−0.511712	+	0.859157i	$0.670988\pi$
$182$	9.43101	0.699073
$183$	11.6124	0.858415
$184$	4.67116	0.344363
$185$	−43.8531	−3.22414
$186$	−1.56730	−0.114920
$187$	6.24835	0.456924
$188$	12.5315	0.913951
$189$	−8.53171	−0.620591
$190$	2.76823	0.200828
$191$	−15.8626	−1.14778	−0.573889	−	0.818933i	$-0.694566\pi$
$191$	−15.8626	−1.14778	−0.573889	+	0.818933i	$0.694566\pi$
$192$	1.56730	0.113110
$193$	−21.8983	−1.57628	−0.788138	−	0.615499i	$-0.788955\pi$
$193$	−21.8983	−1.57628	−0.788138	+	0.615499i	$0.788955\pi$
$194$	−1.00000	−0.0717958
$195$	40.1233	2.87329
$196$	−4.64014	−0.331438
$197$	2.25111	0.160385	0.0801924	−	0.996779i	$-0.474447\pi$
$197$	2.25111	0.160385	0.0801924	+	0.996779i	$0.474447\pi$
$198$	1.81560	0.129029
$199$	15.1943	1.07710	0.538549	−	0.842594i	$-0.318973\pi$
$199$	15.1943	1.07710	0.538549	+	0.842594i	$0.318973\pi$
$200$	12.3883	0.875983
$201$	−6.42125	−0.452920
$202$	16.5261	1.16277
$203$	6.04701	0.424417
$204$	−2.93187	−0.205272
$205$	−45.1226	−3.15150
$206$	−6.46359	−0.450340
$207$	−2.53905	−0.176476
$208$	6.13924	0.425680
$209$	−2.21742	−0.153382
$210$	10.0398	0.692812
$211$	20.7518	1.42861	0.714306	−	0.699834i	$-0.246743\pi$
$211$	20.7518	1.42861	0.714306	+	0.699834i	$0.246743\pi$
$212$	−5.12469	−0.351965
$213$	−4.41367	−0.302420
$214$	−16.3923	−1.12055
$215$	18.1356	1.23684
$216$	−5.55383	−0.377890
$217$	−1.53618	−0.104283
$218$	−8.92652	−0.604580
$219$	−23.8987	−1.61493
$220$	−13.9284	−0.939053
$221$	−11.4844	−0.772522
$222$	−16.4826	−1.10624
$223$	11.3916	0.762838	0.381419	−	0.924402i	$-0.375435\pi$
$223$	11.3916	0.762838	0.381419	+	0.924402i	$0.375435\pi$
$224$	1.53618	0.102641
$225$	−6.73375	−0.448917
$226$	4.62130	0.307405
$227$	14.9691	0.993532	0.496766	−	0.867885i	$-0.334521\pi$
$227$	14.9691	0.993532	0.496766	+	0.867885i	$0.334521\pi$
$228$	1.04046	0.0689064
$229$	1.10825	0.0732355	0.0366177	−	0.999329i	$-0.488342\pi$
$229$	1.10825	0.0732355	0.0366177	+	0.999329i	$0.488342\pi$
$230$	19.4784	1.28437
$231$	−8.04211	−0.529132
$232$	3.93638	0.258436
$233$	−6.61913	−0.433634	−0.216817	−	0.976212i	$-0.569567\pi$
$233$	−6.61913	−0.433634	−0.216817	+	0.976212i	$0.569567\pi$
$234$	−3.33704	−0.218149
$235$	52.2553	3.40876
$236$	−7.99415	−0.520375
$237$	−4.92091	−0.319647
$238$	−2.87366	−0.186272
$239$	−4.36019	−0.282037	−0.141019	−	0.990007i	$-0.545038\pi$
$239$	−4.36019	−0.282037	−0.141019	+	0.990007i	$0.545038\pi$
$240$	6.53554	0.421867
$241$	−22.1586	−1.42736	−0.713679	−	0.700473i	$-0.752972\pi$
$241$	−22.1586	−1.42736	−0.713679	+	0.700473i	$0.752972\pi$
$242$	0.156979	0.0100910
$243$	5.57459	0.357610
$244$	7.40917	0.474324
$245$	−19.3490	−1.23616
$246$	−16.9597	−1.08131
$247$	4.07557	0.259322
$248$	−1.00000	−0.0635001
$249$	−12.2108	−0.773828
$250$	30.8086	1.94850
$251$	−23.5221	−1.48470	−0.742350	−	0.670012i	$-0.766289\pi$
$251$	−23.5221	−1.48470	−0.742350	+	0.670012i	$0.766289\pi$
$252$	−0.835006	−0.0526004
$253$	−15.6026	−0.980930
$254$	14.1621	0.888610
$255$	−12.2257	−0.765602
$256$	1.00000	0.0625000
$257$	−15.0148	−0.936595	−0.468298	−	0.883571i	$-0.655132\pi$
$257$	−15.0148	−0.936595	−0.468298	+	0.883571i	$0.655132\pi$
$258$	6.81642	0.424372
$259$	−16.1553	−1.00384
$260$	25.6002	1.58766
$261$	−2.13965	−0.132441
$262$	4.16328	0.257208
$263$	17.0795	1.05316	0.526582	−	0.850124i	$-0.323473\pi$
$263$	17.0795	1.05316	0.526582	+	0.850124i	$0.323473\pi$
$264$	−5.23512	−0.322199
$265$	−21.3696	−1.31272
$266$	1.01980	0.0625282
$267$	20.0700	1.22827
$268$	−4.09700	−0.250264
$269$	22.1811	1.35241	0.676204	−	0.736714i	$-0.263624\pi$
$269$	22.1811	1.35241	0.676204	+	0.736714i	$0.263624\pi$
$270$	−23.1591	−1.40942
$271$	−9.59398	−0.582793	−0.291396	−	0.956602i	$-0.594120\pi$
$271$	−9.59398	−0.582793	−0.291396	+	0.956602i	$0.594120\pi$
$272$	−1.87065	−0.113425
$273$	14.7813	0.894602
$274$	1.17104	0.0707452
$275$	−41.3794	−2.49527
$276$	7.32113	0.440680
$277$	−5.81608	−0.349455	−0.174727	−	0.984617i	$-0.555904\pi$
$277$	−5.81608	−0.349455	−0.174727	+	0.984617i	$0.555904\pi$
$278$	16.4860	0.988766
$279$	0.543558	0.0325420
$280$	6.40577	0.382818
$281$	−8.30140	−0.495220	−0.247610	−	0.968860i	$-0.579645\pi$
$281$	−8.30140	−0.495220	−0.247610	+	0.968860i	$0.579645\pi$
$282$	19.6406	1.16958
$283$	−10.6209	−0.631345	−0.315672	−	0.948868i	$-0.602230\pi$
$283$	−10.6209	−0.631345	−0.315672	+	0.948868i	$0.602230\pi$
$284$	−2.81609	−0.167104
$285$	4.33866	0.257000
$286$	−20.5063	−1.21257
$287$	−16.6230	−0.981225
$288$	−0.543558	−0.0320295
$289$	−13.5007	−0.794158
$290$	16.4144	0.963888
$291$	−1.56730	−0.0918770
$292$	−15.2483	−0.892340
$293$	−26.9583	−1.57492	−0.787459	−	0.616367i	$-0.788604\pi$
$293$	−26.9583	−1.57492	−0.787459	+	0.616367i	$0.788604\pi$
$294$	−7.27251	−0.424141
$295$	−33.3350	−1.94084
$296$	−10.5165	−0.611260
$297$	18.5509	1.07644
$298$	−10.7934	−0.625247
$299$	28.6774	1.65846
$300$	19.4162	1.12099
$301$	6.68107	0.385091
$302$	10.9334	0.629149
$303$	25.9014	1.48800
$304$	0.663856	0.0380747
$305$	30.8957	1.76908
$306$	1.01681	0.0581269
$307$	24.1407	1.37778	0.688892	−	0.724864i	$-0.258097\pi$
$307$	24.1407	1.37778	0.688892	+	0.724864i	$0.258097\pi$
$308$	−5.13117	−0.292376
$309$	−10.1304	−0.576299
$310$	−4.16992	−0.236836
$311$	−19.4514	−1.10298	−0.551492	−	0.834180i	$-0.685941\pi$
$311$	−19.4514	−1.10298	−0.551492	+	0.834180i	$0.685941\pi$
$312$	9.62206	0.544742
$313$	31.4239	1.77618	0.888091	−	0.459668i	$-0.152032\pi$
$313$	31.4239	1.77618	0.888091	+	0.459668i	$0.152032\pi$
$314$	0.798002	0.0450339
$315$	−3.48191	−0.196183
$316$	−3.13973	−0.176624
$317$	−27.7657	−1.55947	−0.779737	−	0.626107i	$-0.784647\pi$
$317$	−27.7657	−1.55947	−0.779737	+	0.626107i	$0.784647\pi$
$318$	−8.03194	−0.450409
$319$	−13.1483	−0.736165
$320$	4.16992	0.233106
$321$	−25.6917	−1.43397
$322$	7.17576	0.399890
$323$	−1.24184	−0.0690978
$324$	−7.07387	−0.392993
$325$	76.0546	4.21875
$326$	14.7499	0.816919
$327$	−13.9906	−0.773680
$328$	−10.8210	−0.597488
$329$	19.2506	1.06132
$330$	−21.8301	−1.20170
$331$	−18.5291	−1.01845	−0.509225	−	0.860634i	$-0.670068\pi$
$331$	−18.5291	−1.01845	−0.509225	+	0.860634i	$0.670068\pi$
$332$	−7.79095	−0.427584
$333$	5.71634	0.313253
$334$	2.55296	0.139692
$335$	−17.0842	−0.933410
$336$	2.40767	0.131349
$337$	13.3165	0.725398	0.362699	−	0.931906i	$-0.381855\pi$
$337$	13.3165	0.725398	0.362699	+	0.931906i	$0.381855\pi$
$338$	24.6903	1.34298
$339$	7.24299	0.393385
$340$	−7.80046	−0.423039
$341$	3.34021	0.180882
$342$	−0.360844	−0.0195122
$343$	−17.8814	−0.965505
$344$	4.34914	0.234490
$345$	30.5286	1.64360
$346$	−8.09197	−0.435027
$347$	30.1328	1.61761	0.808807	−	0.588074i	$-0.200114\pi$
$347$	30.1328	1.61761	0.808807	+	0.588074i	$0.200114\pi$
$348$	6.16951	0.330720
$349$	32.3266	1.73041	0.865203	−	0.501422i	$-0.167190\pi$
$349$	32.3266	1.73041	0.865203	+	0.501422i	$0.167190\pi$
$350$	19.0307	1.01723
$351$	−34.0963	−1.81993
$352$	−3.34021	−0.178034
$353$	28.7087	1.52801	0.764005	−	0.645210i	$-0.223230\pi$
$353$	28.7087	1.52801	0.764005	+	0.645210i	$0.223230\pi$
$354$	−12.5293	−0.665923
$355$	−11.7429	−0.623248
$356$	12.8055	0.678688
$357$	−4.50390	−0.238372
$358$	10.2528	0.541875
$359$	−10.9398	−0.577379	−0.288690	−	0.957423i	$-0.593220\pi$
$359$	−10.9398	−0.577379	−0.288690	+	0.957423i	$0.593220\pi$
$360$	−2.26660	−0.119460
$361$	−18.5593	−0.976805
$362$	−13.7688	−0.723670
$363$	0.246033	0.0129134
$364$	9.43101	0.494319
$365$	−63.5843	−3.32815
$366$	11.6124	0.606991
$367$	4.60025	0.240131	0.120066	−	0.992766i	$-0.461689\pi$
$367$	4.60025	0.240131	0.120066	+	0.992766i	$0.461689\pi$
$368$	4.67116	0.243501
$369$	5.88183	0.306196
$370$	−43.8531	−2.27981
$371$	−7.87246	−0.408718
$372$	−1.56730	−0.0812609
$373$	−13.1954	−0.683234	−0.341617	−	0.939839i	$-0.610975\pi$
$373$	−13.1954	−0.683234	−0.341617	+	0.939839i	$0.610975\pi$
$374$	6.24835	0.323094
$375$	48.2864	2.49350
$376$	12.5315	0.646261
$377$	24.1664	1.24463
$378$	−8.53171	−0.438824
$379$	0.928140	0.0476754	0.0238377	−	0.999716i	$-0.492412\pi$
$379$	0.928140	0.0476754	0.0238377	+	0.999716i	$0.492412\pi$
$380$	2.76823	0.142007
$381$	22.1963	1.13715
$382$	−15.8626	−0.811601
$383$	−35.5036	−1.81415	−0.907074	−	0.420972i	$-0.861689\pi$
$383$	−35.5036	−1.81415	−0.907074	+	0.420972i	$0.861689\pi$
$384$	1.56730	0.0799811
$385$	−21.3966	−1.09047
$386$	−21.8983	−1.11460
$387$	−2.36401	−0.120169
$388$	−1.00000	−0.0507673
$389$	−20.2917	−1.02883	−0.514414	−	0.857542i	$-0.671990\pi$
$389$	−20.2917	−1.02883	−0.514414	+	0.857542i	$0.671990\pi$
$390$	40.1233	2.03172
$391$	−8.73809	−0.441904
$392$	−4.64014	−0.234362
$393$	6.52513	0.329149
$394$	2.25111	0.113409
$395$	−13.0924	−0.658752
$396$	1.81560	0.0912372
$397$	−16.3796	−0.822069	−0.411035	−	0.911620i	$-0.634832\pi$
$397$	−16.3796	−0.822069	−0.411035	+	0.911620i	$0.634832\pi$
$398$	15.1943	0.761623
$399$	1.59834	0.0800173
$400$	12.3883	0.619414
$401$	−22.1720	−1.10722	−0.553608	−	0.832777i	$-0.686749\pi$
$401$	−22.1720	−1.10722	−0.553608	+	0.832777i	$0.686749\pi$
$402$	−6.42125	−0.320263
$403$	−6.13924	−0.305817
$404$	16.5261	0.822204
$405$	−29.4975	−1.46574
$406$	6.04701	0.300108
$407$	35.1273	1.74120
$408$	−2.93187	−0.145149
$409$	34.4157	1.70175	0.850873	−	0.525372i	$-0.176074\pi$
$409$	34.4157	1.70175	0.850873	+	0.525372i	$0.176074\pi$
$410$	−45.1226	−2.22845
$411$	1.83538	0.0905325
$412$	−6.46359	−0.318438
$413$	−12.2805	−0.604284
$414$	−2.53905	−0.124787
$415$	−32.4877	−1.59476
$416$	6.13924	0.301001
$417$	25.8386	1.26532
$418$	−2.21742	−0.108457
$419$	−17.9699	−0.877886	−0.438943	−	0.898515i	$-0.644647\pi$
$419$	−17.9699	−0.877886	−0.438943	+	0.898515i	$0.644647\pi$
$420$	10.0398	0.489892
$421$	17.4769	0.851774	0.425887	−	0.904776i	$-0.359962\pi$
$421$	17.4769	0.851774	0.425887	+	0.904776i	$0.359962\pi$
$422$	20.7518	1.01018
$423$	−6.81158	−0.331191
$424$	−5.12469	−0.248877
$425$	−23.1741	−1.12411
$426$	−4.41367	−0.213843
$427$	11.3819	0.550807
$428$	−16.3923	−0.792351
$429$	−32.1397	−1.55172
$430$	18.1356	0.874575
$431$	32.1974	1.55089	0.775447	−	0.631412i	$-0.217524\pi$
$431$	32.1974	1.55089	0.775447	+	0.631412i	$0.217524\pi$
$432$	−5.55383	−0.267209
$433$	−23.1347	−1.11178	−0.555892	−	0.831254i	$-0.687623\pi$
$433$	−23.1347	−1.11178	−0.555892	+	0.831254i	$0.687623\pi$
$434$	−1.53618	−0.0737392
$435$	25.7264	1.23349
$436$	−8.92652	−0.427503
$437$	3.10098	0.148340
$438$	−23.8987	−1.14193
$439$	−6.70593	−0.320057	−0.160028	−	0.987112i	$-0.551159\pi$
$439$	−6.70593	−0.320057	−0.160028	+	0.987112i	$0.551159\pi$
$440$	−13.9284	−0.664011
$441$	2.52218	0.120104
$442$	−11.4844	−0.546255
$443$	23.4644	1.11483	0.557414	−	0.830235i	$-0.311794\pi$
$443$	23.4644	1.11483	0.557414	+	0.830235i	$0.311794\pi$
$444$	−16.4826	−0.782228
$445$	53.3978	2.53130
$446$	11.3916	0.539408
$447$	−16.9166	−0.800127
$448$	1.53618	0.0725779
$449$	−20.8551	−0.984215	−0.492107	−	0.870535i	$-0.663773\pi$
$449$	−20.8551	−0.984215	−0.492107	+	0.870535i	$0.663773\pi$
$450$	−6.73375	−0.317432
$451$	36.1443	1.70197
$452$	4.62130	0.217368
$453$	17.1360	0.805120
$454$	14.9691	0.702533
$455$	39.3266	1.84366
$456$	1.04046	0.0487242
$457$	−2.91510	−0.136363	−0.0681813	−	0.997673i	$-0.521720\pi$
$457$	−2.91510	−0.136363	−0.0681813	+	0.997673i	$0.521720\pi$
$458$	1.10825	0.0517853
$459$	10.3893	0.484929
$460$	19.4784	0.908185
$461$	−9.24684	−0.430668	−0.215334	−	0.976540i	$-0.569084\pi$
$461$	−9.24684	−0.430668	−0.215334	+	0.976540i	$0.569084\pi$
$462$	−8.04211	−0.374153
$463$	−5.63737	−0.261991	−0.130995	−	0.991383i	$-0.541817\pi$
$463$	−5.63737	−0.261991	−0.130995	+	0.991383i	$0.541817\pi$
$464$	3.93638	0.182742
$465$	−6.53554	−0.303078
$466$	−6.61913	−0.306625
$467$	−19.3655	−0.896127	−0.448064	−	0.894002i	$-0.647886\pi$
$467$	−19.3655	−0.896127	−0.448064	+	0.894002i	$0.647886\pi$
$468$	−3.33704	−0.154255
$469$	−6.29375	−0.290619
$470$	52.2553	2.41036
$471$	1.25071	0.0576298
$472$	−7.99415	−0.367961
$473$	−14.5270	−0.667953
$474$	−4.92091	−0.226025
$475$	8.22403	0.377344
$476$	−2.87366	−0.131714
$477$	2.78557	0.127542
$478$	−4.36019	−0.199430
$479$	−4.24864	−0.194125	−0.0970627	−	0.995278i	$-0.530945\pi$
$479$	−4.24864	−0.194125	−0.0970627	+	0.995278i	$0.530945\pi$
$480$	6.53554	0.298305
$481$	−64.5634	−2.94384
$482$	−22.1586	−1.00929
$483$	11.2466	0.511738
$484$	0.156979	0.00713540
$485$	−4.16992	−0.189347
$486$	5.57459	0.252869
$487$	29.5826	1.34052	0.670258	−	0.742128i	$-0.266183\pi$
$487$	29.5826	1.34052	0.670258	+	0.742128i	$0.266183\pi$
$488$	7.40917	0.335397
$489$	23.1175	1.04541
$490$	−19.3490	−0.874100
$491$	−11.9015	−0.537109	−0.268554	−	0.963265i	$-0.586546\pi$
$491$	−11.9015	−0.537109	−0.268554	+	0.963265i	$0.586546\pi$
$492$	−16.9597	−0.764605
$493$	−7.36359	−0.331639
$494$	4.07557	0.183369
$495$	7.57090	0.340287
$496$	−1.00000	−0.0449013
$497$	−4.32603	−0.194049
$498$	−12.2108	−0.547179
$499$	−0.240343	−0.0107592	−0.00537962	−	0.999986i	$-0.501712\pi$
$499$	−0.240343	−0.0107592	−0.00537962	+	0.999986i	$0.501712\pi$
$500$	30.8086	1.37780
$501$	4.00126	0.178763
$502$	−23.5221	−1.04984
$503$	30.3743	1.35432	0.677162	−	0.735834i	$-0.263210\pi$
$503$	30.3743	1.35432	0.677162	+	0.735834i	$0.263210\pi$
$504$	−0.835006	−0.0371941
$505$	68.9126	3.06657
$506$	−15.6026	−0.693622
$507$	38.6972	1.71860
$508$	14.1621	0.628342
$509$	1.83884	0.0815051	0.0407526	−	0.999169i	$-0.487024\pi$
$509$	1.83884	0.0815051	0.0407526	+	0.999169i	$0.487024\pi$
$510$	−12.2257	−0.541363
$511$	−23.4242	−1.03623
$512$	1.00000	0.0441942
$513$	−3.68694	−0.162783
$514$	−15.0148	−0.662273
$515$	−26.9527	−1.18768
$516$	6.81642	0.300076
$517$	−41.8577	−1.84090
$518$	−16.1553	−0.709823
$519$	−12.6826	−0.556703
$520$	25.6002	1.12264
$521$	−23.1505	−1.01424	−0.507120	−	0.861876i	$-0.669290\pi$
$521$	−23.1505	−1.01424	−0.507120	+	0.861876i	$0.669290\pi$
$522$	−2.13965	−0.0936501
$523$	0.738244	0.0322812	0.0161406	−	0.999870i	$-0.494862\pi$
$523$	0.738244	0.0322812	0.0161406	+	0.999870i	$0.494862\pi$
$524$	4.16328	0.181874
$525$	29.8269	1.30175
$526$	17.0795	0.744700
$527$	1.87065	0.0814867
$528$	−5.23512	−0.227829
$529$	−1.18026	−0.0513157
$530$	−21.3696	−0.928234
$531$	4.34529	0.188569
$532$	1.01980	0.0442141
$533$	−66.4326	−2.87751
$534$	20.0700	0.868516
$535$	−68.3546	−2.95523
$536$	−4.09700	−0.176964
$537$	16.0692	0.693437
$538$	22.1811	0.956297
$539$	15.4990	0.667590
$540$	−23.1591	−0.996608
$541$	33.9595	1.46003	0.730017	−	0.683429i	$-0.239512\pi$
$541$	33.9595	1.46003	0.730017	+	0.683429i	$0.239512\pi$
$542$	−9.59398	−0.412097
$543$	−21.5798	−0.926079
$544$	−1.87065	−0.0802033
$545$	−37.2229	−1.59445
$546$	14.7813	0.632579
$547$	2.45626	0.105022	0.0525109	−	0.998620i	$-0.483278\pi$
$547$	2.45626	0.105022	0.0525109	+	0.998620i	$0.483278\pi$
$548$	1.17104	0.0500244
$549$	−4.02732	−0.171882
$550$	−41.3794	−1.76442
$551$	2.61319	0.111326
$552$	7.32113	0.311608
$553$	−4.82320	−0.205103
$554$	−5.81608	−0.247102
$555$	−68.7311	−2.91747
$556$	16.4860	0.699163
$557$	2.00775	0.0850712	0.0425356	−	0.999095i	$-0.486456\pi$
$557$	2.00775	0.0850712	0.0425356	+	0.999095i	$0.486456\pi$
$558$	0.543558	0.0230107
$559$	26.7004	1.12931
$560$	6.40577	0.270693
$561$	9.79306	0.413463
$562$	−8.30140	−0.350173
$563$	7.99788	0.337070	0.168535	−	0.985696i	$-0.446096\pi$
$563$	7.99788	0.337070	0.168535	+	0.985696i	$0.446096\pi$
$564$	19.6406	0.827019
$565$	19.2705	0.810716
$566$	−10.6209	−0.446428
$567$	−10.8668	−0.456361
$568$	−2.81609	−0.118161
$569$	40.5033	1.69799	0.848994	−	0.528403i	$-0.177209\pi$
$569$	40.5033	1.69799	0.848994	+	0.528403i	$0.177209\pi$
$570$	4.33866	0.181726
$571$	−18.1280	−0.758634	−0.379317	−	0.925267i	$-0.623841\pi$
$571$	−18.1280	−0.758634	−0.379317	+	0.925267i	$0.623841\pi$
$572$	−20.5063	−0.857413
$573$	−24.8615	−1.03860
$574$	−16.6230	−0.693831
$575$	57.8676	2.41325
$576$	−0.543558	−0.0226483
$577$	34.5259	1.43733	0.718665	−	0.695356i	$-0.244753\pi$
$577$	34.5259	1.43733	0.718665	+	0.695356i	$0.244753\pi$
$578$	−13.5007	−0.561554
$579$	−34.3213	−1.42635
$580$	16.4144	0.681572
$581$	−11.9683	−0.496530
$582$	−1.56730	−0.0649668
$583$	17.1175	0.708935
$584$	−15.2483	−0.630979
$585$	−13.9152	−0.575322
$586$	−26.9583	−1.11364
$587$	42.8543	1.76879	0.884393	−	0.466743i	$-0.154573\pi$
$587$	42.8543	1.76879	0.884393	+	0.466743i	$0.154573\pi$
$588$	−7.27251	−0.299913
$589$	−0.663856	−0.0273537
$590$	−33.3350	−1.37238
$591$	3.52817	0.145130
$592$	−10.5165	−0.432226
$593$	−25.6924	−1.05506	−0.527530	−	0.849537i	$-0.676882\pi$
$593$	−25.6924	−1.05506	−0.527530	+	0.849537i	$0.676882\pi$
$594$	18.5509	0.761155
$595$	−11.9829	−0.491253
$596$	−10.7934	−0.442116
$597$	23.8141	0.974648
$598$	28.6774	1.17271
$599$	−32.7645	−1.33872	−0.669361	−	0.742938i	$-0.733432\pi$
$599$	−32.7645	−1.33872	−0.669361	+	0.742938i	$0.733432\pi$
$600$	19.4162	0.792663
$601$	−31.6774	−1.29215	−0.646075	−	0.763274i	$-0.723591\pi$
$601$	−31.6774	−1.29215	−0.646075	+	0.763274i	$0.723591\pi$
$602$	6.68107	0.272300
$603$	2.22696	0.0906888
$604$	10.9334	0.444875
$605$	0.654590	0.0266129
$606$	25.9014	1.05217
$607$	−38.8202	−1.57566	−0.787831	−	0.615891i	$-0.788796\pi$
$607$	−38.8202	−1.57566	−0.787831	+	0.615891i	$0.788796\pi$
$608$	0.663856	0.0269229
$609$	9.47750	0.384048
$610$	30.8957	1.25093
$611$	76.9337	3.11241
$612$	1.01681	0.0411019
$613$	−18.6899	−0.754877	−0.377439	−	0.926035i	$-0.623195\pi$
$613$	−18.6899	−0.754877	−0.377439	+	0.926035i	$0.623195\pi$
$614$	24.1407	0.974241
$615$	−70.7209	−2.85174
$616$	−5.13117	−0.206741
$617$	38.8575	1.56434	0.782171	−	0.623064i	$-0.214112\pi$
$617$	38.8575	1.56434	0.782171	+	0.623064i	$0.214112\pi$
$618$	−10.1304	−0.407505
$619$	18.1800	0.730718	0.365359	−	0.930867i	$-0.380946\pi$
$619$	18.1800	0.730718	0.365359	+	0.930867i	$0.380946\pi$
$620$	−4.16992	−0.167468
$621$	−25.9428	−1.04105
$622$	−19.4514	−0.779928
$623$	19.6715	0.788124
$624$	9.62206	0.385191
$625$	66.5280	2.66112
$626$	31.4239	1.25595
$627$	−3.47536	−0.138793
$628$	0.798002	0.0318438
$629$	19.6727	0.784401
$630$	−3.48191	−0.138723
$631$	18.9099	0.752792	0.376396	−	0.926459i	$-0.377163\pi$
$631$	18.9099	0.752792	0.376396	+	0.926459i	$0.377163\pi$
$632$	−3.13973	−0.124892
$633$	32.5243	1.29273
$634$	−27.7657	−1.10272
$635$	59.0550	2.34352
$636$	−8.03194	−0.318487
$637$	−28.4869	−1.12869
$638$	−13.1483	−0.520548
$639$	1.53071	0.0605539
$640$	4.16992	0.164831
$641$	19.6494	0.776106	0.388053	−	0.921637i	$-0.373148\pi$
$641$	19.6494	0.776106	0.388053	+	0.921637i	$0.373148\pi$
$642$	−25.6917	−1.01397
$643$	37.7471	1.48860	0.744301	−	0.667845i	$-0.232783\pi$
$643$	37.7471	1.48860	0.744301	+	0.667845i	$0.232783\pi$
$644$	7.17576	0.282765
$645$	28.4239	1.11919
$646$	−1.24184	−0.0488595
$647$	16.5432	0.650382	0.325191	−	0.945648i	$-0.394571\pi$
$647$	16.5432	0.650382	0.325191	+	0.945648i	$0.394571\pi$
$648$	−7.07387	−0.277888
$649$	26.7021	1.04815
$650$	76.0546	2.98311
$651$	−2.40767	−0.0943639
$652$	14.7499	0.577649
$653$	22.5859	0.883855	0.441928	−	0.897051i	$-0.354295\pi$
$653$	22.5859	0.883855	0.441928	+	0.897051i	$0.354295\pi$
$654$	−13.9906	−0.547075
$655$	17.3606	0.678333
$656$	−10.8210	−0.422488
$657$	8.28834	0.323359
$658$	19.2506	0.750468
$659$	17.7904	0.693017	0.346508	−	0.938047i	$-0.387367\pi$
$659$	17.7904	0.693017	0.346508	+	0.938047i	$0.387367\pi$
$660$	−21.8301	−0.849734
$661$	17.3129	0.673395	0.336698	−	0.941613i	$-0.390690\pi$
$661$	17.3129	0.673395	0.336698	+	0.941613i	$0.390690\pi$
$662$	−18.5291	−0.720153
$663$	−17.9995	−0.699042
$664$	−7.79095	−0.302348
$665$	4.25251	0.164905
$666$	5.71634	0.221503
$667$	18.3875	0.711966
$668$	2.55296	0.0987770
$669$	17.8541	0.690280
$670$	−17.0842	−0.660020
$671$	−24.7482	−0.955392
$672$	2.40767	0.0928778
$673$	43.6913	1.68418	0.842088	−	0.539339i	$-0.181326\pi$
$673$	43.6913	1.68418	0.842088	+	0.539339i	$0.181326\pi$
$674$	13.3165	0.512934
$675$	−68.8024	−2.64821
$676$	24.6903	0.949627
$677$	13.7109	0.526954	0.263477	−	0.964666i	$-0.415131\pi$
$677$	13.7109	0.526954	0.263477	+	0.964666i	$0.415131\pi$
$678$	7.24299	0.278165
$679$	−1.53618	−0.0589533
$680$	−7.80046	−0.299134
$681$	23.4611	0.899030
$682$	3.34021	0.127903
$683$	−36.1307	−1.38250	−0.691251	−	0.722614i	$-0.742940\pi$
$683$	−36.1307	−1.38250	−0.691251	+	0.722614i	$0.742940\pi$
$684$	−0.360844	−0.0137972
$685$	4.88315	0.186576
$686$	−17.8814	−0.682715
$687$	1.73697	0.0662695
$688$	4.34914	0.165809
$689$	−31.4617	−1.19860
$690$	30.5286	1.16220
$691$	41.8860	1.59342	0.796710	−	0.604362i	$-0.206572\pi$
$691$	41.8860	1.59342	0.796710	+	0.604362i	$0.206572\pi$
$692$	−8.09197	−0.307611
$693$	2.78909	0.105949
$694$	30.1328	1.14383
$695$	68.7455	2.60766
$696$	6.16951	0.233855
$697$	20.2422	0.766729
$698$	32.3266	1.22358
$699$	−10.3742	−0.392388
$700$	19.0307	0.719292
$701$	27.1981	1.02726	0.513630	−	0.858012i	$-0.328301\pi$
$701$	27.1981	1.02726	0.513630	+	0.858012i	$0.328301\pi$
$702$	−34.0963	−1.28688
$703$	−6.98145	−0.263310
$704$	−3.34021	−0.125889
$705$	81.8999	3.08453
$706$	28.7087	1.08047
$707$	25.3871	0.954781
$708$	−12.5293	−0.470879
$709$	−32.2358	−1.21064	−0.605320	−	0.795982i	$-0.706955\pi$
$709$	−32.2358	−1.21064	−0.605320	+	0.795982i	$0.706955\pi$
$710$	−11.7429	−0.440703
$711$	1.70663	0.0640035
$712$	12.8055	0.479905
$713$	−4.67116	−0.174936
$714$	−4.50390	−0.168554
$715$	−85.5099	−3.19789
$716$	10.2528	0.383164
$717$	−6.83374	−0.255211
$718$	−10.9398	−0.408269
$719$	−6.12464	−0.228411	−0.114205	−	0.993457i	$-0.536432\pi$
$719$	−6.12464	−0.228411	−0.114205	+	0.993457i	$0.536432\pi$
$720$	−2.26660	−0.0844711
$721$	−9.92927	−0.369785
$722$	−18.5593	−0.690705
$723$	−34.7292	−1.29159
$724$	−13.7688	−0.511712
$725$	48.7650	1.81109
$726$	0.246033	0.00913116
$727$	18.2115	0.675429	0.337714	−	0.941249i	$-0.390346\pi$
$727$	18.2115	0.675429	0.337714	+	0.941249i	$0.390346\pi$
$728$	9.43101	0.349536
$729$	29.9587	1.10958
$730$	−63.5843	−2.35336
$731$	−8.13570	−0.300910
$732$	11.6124	0.429208
$733$	−52.9993	−1.95757	−0.978787	−	0.204879i	$-0.934320\pi$
$733$	−52.9993	−1.95757	−0.978787	+	0.204879i	$0.934320\pi$
$734$	4.60025	0.169798
$735$	−30.3258	−1.11858
$736$	4.67116	0.172181
$737$	13.6848	0.504088
$738$	5.88183	0.216513
$739$	20.2362	0.744401	0.372201	−	0.928152i	$-0.378603\pi$
$739$	20.2362	0.744401	0.372201	+	0.928152i	$0.378603\pi$
$740$	−43.8531	−1.61207
$741$	6.38766	0.234657
$742$	−7.87246	−0.289007
$743$	3.62615	0.133030	0.0665152	−	0.997785i	$-0.478812\pi$
$743$	3.62615	0.133030	0.0665152	+	0.997785i	$0.478812\pi$
$744$	−1.56730	−0.0574602
$745$	−45.0078	−1.64896
$746$	−13.1954	−0.483120
$747$	4.23484	0.154945
$748$	6.24835	0.228462
$749$	−25.1816	−0.920114
$750$	48.2864	1.76317
$751$	1.38623	0.0505841	0.0252921	−	0.999680i	$-0.491948\pi$
$751$	1.38623	0.0505841	0.0252921	+	0.999680i	$0.491948\pi$
$752$	12.5315	0.456976
$753$	−36.8663	−1.34348
$754$	24.1664	0.880089
$755$	45.5916	1.65925
$756$	−8.53171	−0.310295
$757$	−22.8926	−0.832045	−0.416023	−	0.909354i	$-0.636576\pi$
$757$	−22.8926	−0.832045	−0.416023	+	0.909354i	$0.636576\pi$
$758$	0.928140	0.0337116
$759$	−24.4541	−0.887627
$760$	2.76823	0.100414
$761$	−36.6058	−1.32696	−0.663479	−	0.748195i	$-0.730921\pi$
$761$	−36.6058	−1.32696	−0.663479	+	0.748195i	$0.730921\pi$
$762$	22.1963	0.804089
$763$	−13.7128	−0.496436
$764$	−15.8626	−0.573889
$765$	4.24000	0.153298
$766$	−35.5036	−1.28280
$767$	−49.0780	−1.77211
$768$	1.56730	0.0565552
$769$	20.9790	0.756523	0.378261	−	0.925699i	$-0.376522\pi$
$769$	20.9790	0.756523	0.378261	+	0.925699i	$0.376522\pi$
$770$	−21.3966	−0.771080
$771$	−23.5327	−0.847509
$772$	−21.8983	−0.788138
$773$	25.7894	0.927580	0.463790	−	0.885945i	$-0.346489\pi$
$773$	25.7894	0.927580	0.463790	+	0.885945i	$0.346489\pi$
$774$	−2.36401	−0.0849725
$775$	−12.3883	−0.445000
$776$	−1.00000	−0.0358979
$777$	−25.3203	−0.908359
$778$	−20.2917	−0.727491
$779$	−7.18356	−0.257378
$780$	40.1233	1.43664
$781$	9.40632	0.336585
$782$	−8.73809	−0.312474
$783$	−21.8620	−0.781285
$784$	−4.64014	−0.165719
$785$	3.32761	0.118767
$786$	6.52513	0.232744
$787$	−32.7475	−1.16732	−0.583661	−	0.811997i	$-0.698380\pi$
$787$	−32.7475	−1.16732	−0.583661	+	0.811997i	$0.698380\pi$
$788$	2.25111	0.0801924
$789$	26.7687	0.952991
$790$	−13.0924	−0.465808
$791$	7.09917	0.252418
$792$	1.81560	0.0645144
$793$	45.4867	1.61528
$794$	−16.3796	−0.581291
$795$	−33.4926	−1.18786
$796$	15.1943	0.538549
$797$	−22.4365	−0.794742	−0.397371	−	0.917658i	$-0.630077\pi$
$797$	−22.4365	−0.794742	−0.397371	+	0.917658i	$0.630077\pi$
$798$	1.59834	0.0565808
$799$	−23.4420	−0.829317
$800$	12.3883	0.437992
$801$	−6.96051	−0.245938
$802$	−22.1720	−0.782920
$803$	50.9325	1.79737
$804$	−6.42125	−0.226460
$805$	29.9224	1.05463
$806$	−6.13924	−0.216246
$807$	34.7646	1.22377
$808$	16.5261	0.581386
$809$	−47.5336	−1.67119	−0.835596	−	0.549345i	$-0.814877\pi$
$809$	−47.5336	−1.67119	−0.835596	+	0.549345i	$0.814877\pi$
$810$	−29.4975	−1.03644
$811$	−15.8183	−0.555455	−0.277727	−	0.960660i	$-0.589581\pi$
$811$	−15.8183	−0.555455	−0.277727	+	0.960660i	$0.589581\pi$
$812$	6.04701	0.212208
$813$	−15.0367	−0.527360
$814$	35.1273	1.23121
$815$	61.5058	2.15445
$816$	−2.93187	−0.102636
$817$	2.88720	0.101010
$818$	34.4157	1.20332
$819$	−5.12630	−0.179128
$820$	−45.1226	−1.57575
$821$	−11.8149	−0.412342	−0.206171	−	0.978516i	$-0.566100\pi$
$821$	−11.8149	−0.412342	−0.206171	+	0.978516i	$0.566100\pi$
$822$	1.83538	0.0640161
$823$	−37.0037	−1.28987	−0.644935	−	0.764238i	$-0.723115\pi$
$823$	−37.0037	−1.28987	−0.644935	+	0.764238i	$0.723115\pi$
$824$	−6.46359	−0.225170
$825$	−64.8541	−2.25793
$826$	−12.2805	−0.427293
$827$	−47.9900	−1.66878	−0.834388	−	0.551178i	$-0.814179\pi$
$827$	−47.9900	−1.66878	−0.834388	+	0.551178i	$0.814179\pi$
$828$	−2.53905	−0.0882380
$829$	−14.5963	−0.506949	−0.253475	−	0.967342i	$-0.581573\pi$
$829$	−14.5963	−0.506949	−0.253475	+	0.967342i	$0.581573\pi$
$830$	−32.4877	−1.12766
$831$	−9.11557	−0.316216
$832$	6.13924	0.212840
$833$	8.68006	0.300746
$834$	25.8386	0.894718
$835$	10.6456	0.368408
$836$	−2.21742	−0.0766909
$837$	5.55383	0.191969
$838$	−17.9699	−0.620759
$839$	25.2533	0.871839	0.435920	−	0.899986i	$-0.356423\pi$
$839$	25.2533	0.871839	0.435920	+	0.899986i	$0.356423\pi$
$840$	10.0398	0.346406
$841$	−13.5049	−0.465686
$842$	17.4769	0.602295
$843$	−13.0108	−0.448116
$844$	20.7518	0.714306
$845$	102.957	3.54182
$846$	−6.81158	−0.234187
$847$	0.241148	0.00828595
$848$	−5.12469	−0.175982
$849$	−16.6461	−0.571293
$850$	−23.1741	−0.794865
$851$	−49.1243	−1.68396
$852$	−4.41367	−0.151210
$853$	55.0521	1.88495	0.942474	−	0.334279i	$-0.108493\pi$
$853$	55.0521	1.88495	0.942474	+	0.334279i	$0.108493\pi$
$854$	11.3819	0.389479
$855$	−1.50469	−0.0514594
$856$	−16.3923	−0.560277
$857$	11.0584	0.377747	0.188873	−	0.982001i	$-0.439516\pi$
$857$	11.0584	0.377747	0.188873	+	0.982001i	$0.439516\pi$
$858$	−32.1397	−1.09723
$859$	−30.9611	−1.05638	−0.528190	−	0.849126i	$-0.677129\pi$
$859$	−30.9611	−1.05638	−0.528190	+	0.849126i	$0.677129\pi$
$860$	18.1356	0.618418
$861$	−26.0533	−0.887894
$862$	32.1974	1.09665
$863$	−21.3082	−0.725339	−0.362669	−	0.931918i	$-0.618135\pi$
$863$	−21.3082	−0.725339	−0.362669	+	0.931918i	$0.618135\pi$
$864$	−5.55383	−0.188945
$865$	−33.7429	−1.14729
$866$	−23.1347	−0.786150
$867$	−21.1597	−0.718620
$868$	−1.53618	−0.0521415
$869$	10.4873	0.355759
$870$	25.7264	0.872206
$871$	−25.1525	−0.852260
$872$	−8.92652	−0.302290
$873$	0.543558	0.0183967
$874$	3.10098	0.104892
$875$	47.3276	1.59997
$876$	−23.8987	−0.807463
$877$	−8.94499	−0.302051	−0.151025	−	0.988530i	$-0.548258\pi$
$877$	−8.94499	−0.302051	−0.151025	+	0.988530i	$0.548258\pi$
$878$	−6.70593	−0.226314
$879$	−42.2518	−1.42512
$880$	−13.9284	−0.469527
$881$	7.73494	0.260597	0.130298	−	0.991475i	$-0.458406\pi$
$881$	7.73494	0.260597	0.130298	+	0.991475i	$0.458406\pi$
$882$	2.52218	0.0849264
$883$	22.8121	0.767688	0.383844	−	0.923398i	$-0.374600\pi$
$883$	22.8121	0.767688	0.383844	+	0.923398i	$0.374600\pi$
$884$	−11.4844	−0.386261
$885$	−52.2461	−1.75623
$886$	23.4644	0.788302
$887$	−32.2014	−1.08122	−0.540609	−	0.841274i	$-0.681806\pi$
$887$	−32.2014	−1.08122	−0.540609	+	0.841274i	$0.681806\pi$
$888$	−16.4826	−0.553119
$889$	21.7556	0.729660
$890$	53.3978	1.78990
$891$	23.6282	0.791574
$892$	11.3916	0.381419
$893$	8.31909	0.278388
$894$	−16.9166	−0.565775
$895$	42.7532	1.42908
$896$	1.53618	0.0513203
$897$	44.9462	1.50071
$898$	−20.8551	−0.695945
$899$	−3.93638	−0.131286
$900$	−6.73375	−0.224458
$901$	9.58648	0.319372
$902$	36.1443	1.20347
$903$	10.4713	0.348462
$904$	4.62130	0.153702
$905$	−57.4147	−1.90853
$906$	17.1360	0.569306
$907$	−19.0083	−0.631160	−0.315580	−	0.948899i	$-0.602199\pi$
$907$	−19.0083	−0.631160	−0.315580	+	0.948899i	$0.602199\pi$
$908$	14.9691	0.496766
$909$	−8.98289	−0.297944
$910$	39.3266	1.30366
$911$	33.7460	1.11805	0.559027	−	0.829150i	$-0.311175\pi$
$911$	33.7460	1.11805	0.559027	+	0.829150i	$0.311175\pi$
$912$	1.04046	0.0344532
$913$	26.0234	0.861249
$914$	−2.91510	−0.0964229
$915$	48.4229	1.60081
$916$	1.10825	0.0366177
$917$	6.39557	0.211200
$918$	10.3893	0.342897
$919$	−35.3309	−1.16546	−0.582729	−	0.812666i	$-0.698015\pi$
$919$	−35.3309	−1.16546	−0.582729	+	0.812666i	$0.698015\pi$
$920$	19.4784	0.642183
$921$	37.8359	1.24673
$922$	−9.24684	−0.304528
$923$	−17.2887	−0.569063
$924$	−8.04211	−0.264566
$925$	−130.281	−4.28363
$926$	−5.63737	−0.185256
$927$	3.51334	0.115393
$928$	3.93638	0.129218
$929$	1.34041	0.0439774	0.0219887	−	0.999758i	$-0.493000\pi$
$929$	1.34041	0.0439774	0.0219887	+	0.999758i	$0.493000\pi$
$930$	−6.53554	−0.214309
$931$	−3.08038	−0.100955
$932$	−6.61913	−0.216817
$933$	−30.4862	−0.998073
$934$	−19.3655	−0.633658
$935$	26.0551	0.852094
$936$	−3.33704	−0.109074
$937$	−18.9306	−0.618434	−0.309217	−	0.950991i	$-0.600067\pi$
$937$	−18.9306	−0.618434	−0.309217	+	0.950991i	$0.600067\pi$
$938$	−6.29375	−0.205498
$939$	49.2507	1.60724
$940$	52.2553	1.70438
$941$	−11.2982	−0.368310	−0.184155	−	0.982897i	$-0.558955\pi$
$941$	−11.2982	−0.368310	−0.184155	+	0.982897i	$0.558955\pi$
$942$	1.25071	0.0407504
$943$	−50.5465	−1.64602
$944$	−7.99415	−0.260188
$945$	−35.5766	−1.15731
$946$	−14.5270	−0.472314
$947$	−17.0366	−0.553616	−0.276808	−	0.960925i	$-0.589277\pi$
$947$	−17.0366	−0.553616	−0.276808	+	0.960925i	$0.589277\pi$
$948$	−4.92091	−0.159824
$949$	−93.6131	−3.03881
$950$	8.22403	0.266823
$951$	−43.5172	−1.41114
$952$	−2.87366	−0.0931358
$953$	−22.6859	−0.734870	−0.367435	−	0.930049i	$-0.619764\pi$
$953$	−22.6859	−0.734870	−0.367435	+	0.930049i	$0.619764\pi$
$954$	2.78557	0.0901860
$955$	−66.1459	−2.14043
$956$	−4.36019	−0.141019
$957$	−20.6074	−0.666144
$958$	−4.24864	−0.137267
$959$	1.79893	0.0580906
$960$	6.53554	0.210934
$961$	1.00000	0.0322581
$962$	−64.5634	−2.08161
$963$	8.91016	0.287126
$964$	−22.1586	−0.713679
$965$	−91.3144	−2.93951
$966$	11.2466	0.361854
$967$	34.2435	1.10120	0.550599	−	0.834770i	$-0.314399\pi$
$967$	34.2435	1.10120	0.550599	+	0.834770i	$0.314399\pi$
$968$	0.156979	0.00504549
$969$	−1.94634	−0.0625255
$970$	−4.16992	−0.133888
$971$	−57.7669	−1.85383	−0.926914	−	0.375274i	$-0.877549\pi$
$971$	−57.7669	−1.85383	−0.926914	+	0.375274i	$0.877549\pi$
$972$	5.57459	0.178805
$973$	25.3256	0.811900
$974$	29.5826	0.947888
$975$	119.201	3.81748
$976$	7.40917	0.237162
$977$	31.8747	1.01976	0.509882	−	0.860245i	$-0.329689\pi$
$977$	31.8747	1.01976	0.509882	+	0.860245i	$0.329689\pi$
$978$	23.1175	0.739217
$979$	−42.7729	−1.36703
$980$	−19.3490	−0.618082
$981$	4.85208	0.154915
$982$	−11.9015	−0.379793
$983$	7.36918	0.235040	0.117520	−	0.993071i	$-0.462506\pi$
$983$	7.36918	0.235040	0.117520	+	0.993071i	$0.462506\pi$
$984$	−16.9597	−0.540657
$985$	9.38696	0.299093
$986$	−7.36359	−0.234504
$987$	30.1716	0.960373
$988$	4.07557	0.129661
$989$	20.3155	0.645996
$990$	7.57090	0.240619
$991$	24.0339	0.763462	0.381731	−	0.924274i	$-0.375328\pi$
$991$	24.0339	0.763462	0.381731	+	0.924274i	$0.375328\pi$
$992$	−1.00000	−0.0317500
$993$	−29.0407	−0.921578
$994$	−4.32603	−0.137213
$995$	63.3592	2.00862
$996$	−12.2108	−0.386914
$997$	14.9667	0.473999	0.237000	−	0.971510i	$-0.423836\pi$
$997$	14.9667	0.473999	0.237000	+	0.971510i	$0.423836\pi$
$998$	−0.240343	−0.00760793
$999$	58.4069	1.84791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.17	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.17	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.56730 q^{3} +1.00000 q^{4} +4.16992 q^{5} +1.56730 q^{6} +1.53618 q^{7} +1.00000 q^{8} -0.543558 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.56730 q^{3} +1.00000 q^{4} +4.16992 q^{5} +1.56730 q^{6} +1.53618 q^{7} +1.00000 q^{8} -0.543558 q^{9} +4.16992 q^{10} -3.34021 q^{11} +1.56730 q^{12} +6.13924 q^{13} +1.53618 q^{14} +6.53554 q^{15} +1.00000 q^{16} -1.87065 q^{17} -0.543558 q^{18} +0.663856 q^{19} +4.16992 q^{20} +2.40767 q^{21} -3.34021 q^{22} +4.67116 q^{23} +1.56730 q^{24} +12.3883 q^{25} +6.13924 q^{26} -5.55383 q^{27} +1.53618 q^{28} +3.93638 q^{29} +6.53554 q^{30} -1.00000 q^{31} +1.00000 q^{32} -5.23512 q^{33} -1.87065 q^{34} +6.40577 q^{35} -0.543558 q^{36} -10.5165 q^{37} +0.663856 q^{38} +9.62206 q^{39} +4.16992 q^{40} -10.8210 q^{41} +2.40767 q^{42} +4.34914 q^{43} -3.34021 q^{44} -2.26660 q^{45} +4.67116 q^{46} +12.5315 q^{47} +1.56730 q^{48} -4.64014 q^{49} +12.3883 q^{50} -2.93187 q^{51} +6.13924 q^{52} -5.12469 q^{53} -5.55383 q^{54} -13.9284 q^{55} +1.53618 q^{56} +1.04046 q^{57} +3.93638 q^{58} -7.99415 q^{59} +6.53554 q^{60} +7.40917 q^{61} -1.00000 q^{62} -0.835006 q^{63} +1.00000 q^{64} +25.6002 q^{65} -5.23512 q^{66} -4.09700 q^{67} -1.87065 q^{68} +7.32113 q^{69} +6.40577 q^{70} -2.81609 q^{71} -0.543558 q^{72} -15.2483 q^{73} -10.5165 q^{74} +19.4162 q^{75} +0.663856 q^{76} -5.13117 q^{77} +9.62206 q^{78} -3.13973 q^{79} +4.16992 q^{80} -7.07387 q^{81} -10.8210 q^{82} -7.79095 q^{83} +2.40767 q^{84} -7.80046 q^{85} +4.34914 q^{86} +6.16951 q^{87} -3.34021 q^{88} +12.8055 q^{89} -2.26660 q^{90} +9.43101 q^{91} +4.67116 q^{92} -1.56730 q^{93} +12.5315 q^{94} +2.76823 q^{95} +1.56730 q^{96} -1.00000 q^{97} -4.64014 q^{98} +1.81560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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