LMFDB - Embedded newform 503.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88946 q^{2} -1.08803 q^{3} +1.57004 q^{4} +3.67682 q^{5} -2.05579 q^{6} +1.62501 q^{7} -0.812389 q^{8} -1.81619 q^{9} +O(q^{10})$	\(q+1.88946 q^{2} -1.08803 q^{3} +1.57004 q^{4} +3.67682 q^{5} -2.05579 q^{6} +1.62501 q^{7} -0.812389 q^{8} -1.81619 q^{9} +6.94719 q^{10} -0.444097 q^{11} -1.70825 q^{12} +6.96112 q^{13} +3.07039 q^{14} -4.00050 q^{15} -4.67505 q^{16} -2.64454 q^{17} -3.43160 q^{18} +4.48749 q^{19} +5.77276 q^{20} -1.76807 q^{21} -0.839101 q^{22} -7.32387 q^{23} +0.883906 q^{24} +8.51902 q^{25} +13.1527 q^{26} +5.24017 q^{27} +2.55134 q^{28} -6.81726 q^{29} -7.55877 q^{30} +5.57222 q^{31} -7.20853 q^{32} +0.483191 q^{33} -4.99674 q^{34} +5.97488 q^{35} -2.85149 q^{36} +1.88078 q^{37} +8.47890 q^{38} -7.57392 q^{39} -2.98701 q^{40} +2.69229 q^{41} -3.34068 q^{42} -3.72008 q^{43} -0.697250 q^{44} -6.67779 q^{45} -13.8381 q^{46} -9.38780 q^{47} +5.08661 q^{48} -4.35933 q^{49} +16.0963 q^{50} +2.87735 q^{51} +10.9292 q^{52} +5.46030 q^{53} +9.90106 q^{54} -1.63286 q^{55} -1.32014 q^{56} -4.88253 q^{57} -12.8809 q^{58} -11.1052 q^{59} -6.28095 q^{60} +11.2532 q^{61} +10.5285 q^{62} -2.95133 q^{63} -4.27008 q^{64} +25.5948 q^{65} +0.912968 q^{66} -6.74986 q^{67} -4.15204 q^{68} +7.96861 q^{69} +11.2893 q^{70} -13.5015 q^{71} +1.47545 q^{72} -0.377804 q^{73} +3.55366 q^{74} -9.26897 q^{75} +7.04553 q^{76} -0.721663 q^{77} -14.3106 q^{78} -13.3256 q^{79} -17.1893 q^{80} -0.252910 q^{81} +5.08696 q^{82} -1.00812 q^{83} -2.77594 q^{84} -9.72351 q^{85} -7.02893 q^{86} +7.41740 q^{87} +0.360779 q^{88} -6.79299 q^{89} -12.6174 q^{90} +11.3119 q^{91} -11.4988 q^{92} -6.06275 q^{93} -17.7378 q^{94} +16.4997 q^{95} +7.84311 q^{96} -14.5945 q^{97} -8.23676 q^{98} +0.806562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * 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 $

$2$	1.88946	1.33605	0.668023	−	0.744140i	$-0.267141\pi$
$2$	1.88946	1.33605	0.668023	+	0.744140i	$0.267141\pi$
$3$	−1.08803	−0.628176	−0.314088	−	0.949394i	$-0.601699\pi$
$3$	−1.08803	−0.628176	−0.314088	+	0.949394i	$0.601699\pi$
$4$	1.57004	0.785020
$5$	3.67682	1.64433	0.822163	−	0.569253i	$-0.192767\pi$
$5$	3.67682	1.64433	0.822163	+	0.569253i	$0.192767\pi$
$6$	−2.05579	−0.839272
$7$	1.62501	0.614197	0.307099	−	0.951678i	$-0.400642\pi$
$7$	1.62501	0.614197	0.307099	+	0.951678i	$0.400642\pi$
$8$	−0.812389	−0.287223
$9$	−1.81619	−0.605395
$10$	6.94719	2.19689
$11$	−0.444097	−0.133900	−0.0669501	−	0.997756i	$-0.521327\pi$
$11$	−0.444097	−0.133900	−0.0669501	+	0.997756i	$0.521327\pi$
$12$	−1.70825	−0.493131
$13$	6.96112	1.93067	0.965333	−	0.261021i	$-0.0840593\pi$
$13$	6.96112	1.93067	0.965333	+	0.261021i	$0.0840593\pi$
$14$	3.07039	0.820596
$15$	−4.00050	−1.03292
$16$	−4.67505	−1.16876
$17$	−2.64454	−0.641396	−0.320698	−	0.947182i	$-0.603917\pi$
$17$	−2.64454	−0.641396	−0.320698	+	0.947182i	$0.603917\pi$
$18$	−3.43160	−0.808836
$19$	4.48749	1.02950	0.514750	−	0.857340i	$-0.327885\pi$
$19$	4.48749	1.02950	0.514750	+	0.857340i	$0.327885\pi$
$20$	5.77276	1.29083
$21$	−1.76807	−0.385824
$22$	−0.839101	−0.178897
$23$	−7.32387	−1.52713	−0.763567	−	0.645729i	$-0.776554\pi$
$23$	−7.32387	−1.52713	−0.763567	+	0.645729i	$0.776554\pi$
$24$	0.883906	0.180426
$25$	8.51902	1.70380
$26$	13.1527	2.57946
$27$	5.24017	1.00847
$28$	2.55134	0.482157
$29$	−6.81726	−1.26593	−0.632967	−	0.774179i	$-0.718163\pi$
$29$	−6.81726	−1.26593	−0.632967	+	0.774179i	$0.718163\pi$
$30$	−7.55877	−1.38004
$31$	5.57222	1.00080	0.500400	−	0.865794i	$-0.333186\pi$
$31$	5.57222	1.00080	0.500400	+	0.865794i	$0.333186\pi$
$32$	−7.20853	−1.27430
$33$	0.483191	0.0841128
$34$	−4.99674	−0.856935
$35$	5.97488	1.00994
$36$	−2.85149	−0.475248
$37$	1.88078	0.309199	0.154599	−	0.987977i	$-0.450591\pi$
$37$	1.88078	0.309199	0.154599	+	0.987977i	$0.450591\pi$
$38$	8.47890	1.37546
$39$	−7.57392	−1.21280
$40$	−2.98701	−0.472288
$41$	2.69229	0.420465	0.210233	−	0.977651i	$-0.432578\pi$
$41$	2.69229	0.420465	0.210233	+	0.977651i	$0.432578\pi$
$42$	−3.34068	−0.515478
$43$	−3.72008	−0.567308	−0.283654	−	0.958927i	$-0.591547\pi$
$43$	−3.72008	−0.567308	−0.283654	+	0.958927i	$0.591547\pi$
$44$	−0.697250	−0.105114
$45$	−6.67779	−0.995467
$46$	−13.8381	−2.04032
$47$	−9.38780	−1.36935	−0.684676	−	0.728848i	$-0.740056\pi$
$47$	−9.38780	−1.36935	−0.684676	+	0.728848i	$0.740056\pi$
$48$	5.08661	0.734189
$49$	−4.35933	−0.622762
$50$	16.0963	2.27636
$51$	2.87735	0.402909
$52$	10.9292	1.51561
$53$	5.46030	0.750029	0.375015	−	0.927019i	$-0.377638\pi$
$53$	5.46030	0.750029	0.375015	+	0.927019i	$0.377638\pi$
$54$	9.90106	1.34736
$55$	−1.63286	−0.220175
$56$	−1.32014	−0.176412
$57$	−4.88253	−0.646707
$58$	−12.8809	−1.69135
$59$	−11.1052	−1.44577	−0.722886	−	0.690967i	$-0.757185\pi$
$59$	−11.1052	−1.44577	−0.722886	+	0.690967i	$0.757185\pi$
$60$	−6.28095	−0.810867
$61$	11.2532	1.44083	0.720415	−	0.693544i	$-0.243952\pi$
$61$	11.2532	1.44083	0.720415	+	0.693544i	$0.243952\pi$
$62$	10.5285	1.33712
$63$	−2.95133	−0.371832
$64$	−4.27008	−0.533760
$65$	25.5948	3.17464
$66$	0.912968	0.112379
$67$	−6.74986	−0.824627	−0.412313	−	0.911042i	$-0.635279\pi$
$67$	−6.74986	−0.824627	−0.412313	+	0.911042i	$0.635279\pi$
$68$	−4.15204	−0.503509
$69$	7.96861	0.959308
$70$	11.2893	1.34933
$71$	−13.5015	−1.60233	−0.801167	−	0.598441i	$-0.795787\pi$
$71$	−13.5015	−1.60233	−0.801167	+	0.598441i	$0.795787\pi$
$72$	1.47545	0.173883
$73$	−0.377804	−0.0442186	−0.0221093	−	0.999756i	$-0.507038\pi$
$73$	−0.377804	−0.0442186	−0.0221093	+	0.999756i	$0.507038\pi$
$74$	3.55366	0.413104
$75$	−9.26897	−1.07029
$76$	7.04553	0.808178
$77$	−0.721663	−0.0822411
$78$	−14.3106	−1.62035
$79$	−13.3256	−1.49924	−0.749622	−	0.661866i	$-0.769765\pi$
$79$	−13.3256	−1.49924	−0.749622	+	0.661866i	$0.769765\pi$
$80$	−17.1893	−1.92183
$81$	−0.252910	−0.0281011
$82$	5.08696	0.561761
$83$	−1.00812	−0.110656	−0.0553279	−	0.998468i	$-0.517620\pi$
$83$	−1.00812	−0.110656	−0.0553279	+	0.998468i	$0.517620\pi$
$84$	−2.77594	−0.302879
$85$	−9.72351	−1.05466
$86$	−7.02893	−0.757949
$87$	7.41740	0.795228
$88$	0.360779	0.0384592
$89$	−6.79299	−0.720055	−0.360028	−	0.932942i	$-0.617233\pi$
$89$	−6.79299	−0.720055	−0.360028	+	0.932942i	$0.617233\pi$
$90$	−12.6174	−1.32999
$91$	11.3119	1.18581
$92$	−11.4988	−1.19883
$93$	−6.06275	−0.628678
$94$	−17.7378	−1.82952
$95$	16.4997	1.69283
$96$	7.84311	0.800484
$97$	−14.5945	−1.48185	−0.740924	−	0.671589i	$-0.765612\pi$
$97$	−14.5945	−1.48185	−0.740924	+	0.671589i	$0.765612\pi$
$98$	−8.23676	−0.832039
$99$	0.806562	0.0810625
$100$	13.3752	1.33752
$101$	14.9813	1.49070	0.745350	−	0.666674i	$-0.232283\pi$
$101$	14.9813	1.49070	0.745350	+	0.666674i	$0.232283\pi$
$102$	5.43662	0.538305
$103$	−0.348097	−0.0342990	−0.0171495	−	0.999853i	$-0.505459\pi$
$103$	−0.348097	−0.0342990	−0.0171495	+	0.999853i	$0.505459\pi$
$104$	−5.65514	−0.554532
$105$	−6.50087	−0.634420
$106$	10.3170	1.00207
$107$	9.93506	0.960458	0.480229	−	0.877143i	$-0.340553\pi$
$107$	9.93506	0.960458	0.480229	+	0.877143i	$0.340553\pi$
$108$	8.22727	0.791670
$109$	9.50257	0.910181	0.455091	−	0.890445i	$-0.349607\pi$
$109$	9.50257	0.910181	0.455091	+	0.890445i	$0.349607\pi$
$110$	−3.08522	−0.294165
$111$	−2.04635	−0.194231
$112$	−7.59702	−0.717851
$113$	−9.80733	−0.922596	−0.461298	−	0.887245i	$-0.652616\pi$
$113$	−9.80733	−0.922596	−0.461298	+	0.887245i	$0.652616\pi$
$114$	−9.22532	−0.864030
$115$	−26.9286	−2.51110
$116$	−10.7034	−0.993783
$117$	−12.6427	−1.16882
$118$	−20.9828	−1.93162
$119$	−4.29742	−0.393943
$120$	3.24996	0.296680
$121$	−10.8028	−0.982071
$122$	21.2625	1.92501
$123$	−2.92930	−0.264126
$124$	8.74861	0.785648
$125$	12.9388	1.15728
$126$	−5.57640	−0.496785
$127$	−6.46825	−0.573964	−0.286982	−	0.957936i	$-0.592652\pi$
$127$	−6.46825	−0.573964	−0.286982	+	0.957936i	$0.592652\pi$
$128$	6.34893	0.561172
$129$	4.04757	0.356369
$130$	48.3602	4.24147
$131$	10.3312	0.902645	0.451322	−	0.892361i	$-0.350952\pi$
$131$	10.3312	0.902645	0.451322	+	0.892361i	$0.350952\pi$
$132$	0.758630	0.0660303
$133$	7.29222	0.632316
$134$	−12.7536	−1.10174
$135$	19.2672	1.65825
$136$	2.14840	0.184224
$137$	6.01949	0.514280	0.257140	−	0.966374i	$-0.417220\pi$
$137$	6.01949	0.514280	0.257140	+	0.966374i	$0.417220\pi$
$138$	15.0563	1.28168
$139$	12.0786	1.02450	0.512248	−	0.858837i	$-0.328813\pi$
$139$	12.0786	1.02450	0.512248	+	0.858837i	$0.328813\pi$
$140$	9.38081	0.792823
$141$	10.2142	0.860194
$142$	−25.5105	−2.14079
$143$	−3.09141	−0.258516
$144$	8.49077	0.707564
$145$	−25.0659	−2.08161
$146$	−0.713844	−0.0590781
$147$	4.74309	0.391204
$148$	2.95291	0.242727
$149$	3.60830	0.295604	0.147802	−	0.989017i	$-0.452780\pi$
$149$	3.60830	0.295604	0.147802	+	0.989017i	$0.452780\pi$
$150$	−17.5133	−1.42996
$151$	14.3421	1.16715	0.583573	−	0.812061i	$-0.301654\pi$
$151$	14.3421	1.16715	0.583573	+	0.812061i	$0.301654\pi$
$152$	−3.64559	−0.295696
$153$	4.80298	0.388298
$154$	−1.36355	−0.109878
$155$	20.4881	1.64564
$156$	−11.8914	−0.952070
$157$	19.7274	1.57442	0.787211	−	0.616684i	$-0.211524\pi$
$157$	19.7274	1.57442	0.787211	+	0.616684i	$0.211524\pi$
$158$	−25.1781	−2.00306
$159$	−5.94098	−0.471150
$160$	−26.5045	−2.09536
$161$	−11.9014	−0.937961
$162$	−0.477861	−0.0375443
$163$	−6.34095	−0.496661	−0.248331	−	0.968675i	$-0.579882\pi$
$163$	−6.34095	−0.496661	−0.248331	+	0.968675i	$0.579882\pi$
$164$	4.22701	0.330074
$165$	1.77661	0.138309
$166$	−1.90480	−0.147841
$167$	−0.899922	−0.0696381	−0.0348190	−	0.999394i	$-0.511085\pi$
$167$	−0.899922	−0.0696381	−0.0348190	+	0.999394i	$0.511085\pi$
$168$	1.43636	0.110817
$169$	35.4571	2.72747
$170$	−18.3721	−1.40908
$171$	−8.15011	−0.623254
$172$	−5.84068	−0.445348
$173$	20.7113	1.57465	0.787327	−	0.616536i	$-0.211464\pi$
$173$	20.7113	1.57465	0.787327	+	0.616536i	$0.211464\pi$
$174$	14.0148	1.06246
$175$	13.8435	1.04647
$176$	2.07618	0.156498
$177$	12.0828	0.908199
$178$	−12.8350	−0.962027
$179$	0.727433	0.0543709	0.0271855	−	0.999630i	$-0.491346\pi$
$179$	0.727433	0.0543709	0.0271855	+	0.999630i	$0.491346\pi$
$180$	−10.4844	−0.781462
$181$	17.7066	1.31612	0.658059	−	0.752966i	$-0.271378\pi$
$181$	17.7066	1.31612	0.658059	+	0.752966i	$0.271378\pi$
$182$	21.3733	1.58430
$183$	−12.2439	−0.905094
$184$	5.94984	0.438628
$185$	6.91531	0.508424
$186$	−11.4553	−0.839943
$187$	1.17443	0.0858830
$188$	−14.7392	−1.07497
$189$	8.51534	0.619400
$190$	31.1754	2.26170
$191$	14.3592	1.03899	0.519497	−	0.854473i	$-0.326119\pi$
$191$	14.3592	1.03899	0.519497	+	0.854473i	$0.326119\pi$
$192$	4.64598	0.335295
$193$	5.92814	0.426717	0.213359	−	0.976974i	$-0.431560\pi$
$193$	5.92814	0.426717	0.213359	+	0.976974i	$0.431560\pi$
$194$	−27.5757	−1.97982
$195$	−27.8479	−1.99423
$196$	−6.84433	−0.488881
$197$	9.89369	0.704896	0.352448	−	0.935831i	$-0.385349\pi$
$197$	9.89369	0.704896	0.352448	+	0.935831i	$0.385349\pi$
$198$	1.52396	0.108303
$199$	4.63808	0.328785	0.164393	−	0.986395i	$-0.447434\pi$
$199$	4.63808	0.328785	0.164393	+	0.986395i	$0.447434\pi$
$200$	−6.92076	−0.489372
$201$	7.34406	0.518010
$202$	28.3066	1.99164
$203$	−11.0781	−0.777533
$204$	4.51755	0.316292
$205$	9.89908	0.691381
$206$	−0.657713	−0.0458251
$207$	13.3015	0.924520
$208$	−32.5436	−2.25649
$209$	−1.99288	−0.137850
$210$	−12.2831	−0.847614
$211$	−21.2753	−1.46465	−0.732326	−	0.680955i	$-0.761565\pi$
$211$	−21.2753	−1.46465	−0.732326	+	0.680955i	$0.761565\pi$
$212$	8.57289	0.588788
$213$	14.6901	1.00655
$214$	18.7718	1.28322
$215$	−13.6781	−0.932838
$216$	−4.25705	−0.289656
$217$	9.05493	0.614689
$218$	17.9547	1.21604
$219$	0.411063	0.0277771
$220$	−2.56366	−0.172842
$221$	−18.4090	−1.23832
$222$	−3.86649	−0.259502
$223$	6.33262	0.424064	0.212032	−	0.977263i	$-0.431992\pi$
$223$	6.33262	0.424064	0.212032	+	0.977263i	$0.431992\pi$
$224$	−11.7139	−0.782671
$225$	−15.4721	−1.03148
$226$	−18.5305	−1.23263
$227$	6.86948	0.455943	0.227972	−	0.973668i	$-0.426791\pi$
$227$	6.86948	0.455943	0.227972	+	0.973668i	$0.426791\pi$
$228$	−7.66577	−0.507678
$229$	−2.10060	−0.138811	−0.0694057	−	0.997589i	$-0.522110\pi$
$229$	−2.10060	−0.138811	−0.0694057	+	0.997589i	$0.522110\pi$
$230$	−50.8804	−3.35495
$231$	0.785192	0.0516619
$232$	5.53827	0.363605
$233$	−11.5359	−0.755741	−0.377871	−	0.925858i	$-0.623344\pi$
$233$	−11.5359	−0.755741	−0.377871	+	0.925858i	$0.623344\pi$
$234$	−23.8878	−1.56159
$235$	−34.5173	−2.25166
$236$	−17.4356	−1.13496
$237$	14.4987	0.941789
$238$	−8.11977	−0.526327
$239$	0.509199	0.0329373	0.0164687	−	0.999864i	$-0.494758\pi$
$239$	0.509199	0.0329373	0.0164687	+	0.999864i	$0.494758\pi$
$240$	18.7026	1.20724
$241$	−21.4263	−1.38019	−0.690095	−	0.723718i	$-0.742431\pi$
$241$	−21.4263	−1.38019	−0.690095	+	0.723718i	$0.742431\pi$
$242$	−20.4114	−1.31209
$243$	−15.4453	−0.990818
$244$	17.6680	1.13108
$245$	−16.0285	−1.02402
$246$	−5.53478	−0.352885
$247$	31.2379	1.98762
$248$	−4.52681	−0.287453
$249$	1.09687	0.0695112
$250$	24.4473	1.54619
$251$	−0.188092	−0.0118723	−0.00593613	−	0.999982i	$-0.501890\pi$
$251$	−0.188092	−0.0118723	−0.00593613	+	0.999982i	$0.501890\pi$
$252$	−4.63370	−0.291896
$253$	3.25251	0.204483
$254$	−12.2215	−0.766843
$255$	10.5795	0.662514
$256$	20.5362	1.28351
$257$	−17.1373	−1.06900	−0.534498	−	0.845170i	$-0.679499\pi$
$257$	−17.1373	−1.06900	−0.534498	+	0.845170i	$0.679499\pi$
$258$	7.64770	0.476125
$259$	3.05630	0.189909
$260$	40.1848	2.49216
$261$	12.3814	0.766390
$262$	19.5204	1.20598
$263$	9.83295	0.606326	0.303163	−	0.952939i	$-0.401957\pi$
$263$	9.83295	0.606326	0.303163	+	0.952939i	$0.401957\pi$
$264$	−0.392540	−0.0241591
$265$	20.0765	1.23329
$266$	13.7783	0.844803
$267$	7.39099	0.452321
$268$	−10.5976	−0.647349
$269$	−5.98584	−0.364963	−0.182481	−	0.983209i	$-0.558413\pi$
$269$	−5.98584	−0.364963	−0.182481	+	0.983209i	$0.558413\pi$
$270$	36.4044	2.21550
$271$	3.21445	0.195264	0.0976320	−	0.995223i	$-0.468873\pi$
$271$	3.21445	0.195264	0.0976320	+	0.995223i	$0.468873\pi$
$272$	12.3634	0.749640
$273$	−12.3077	−0.744897
$274$	11.3736	0.687102
$275$	−3.78327	−0.228140
$276$	12.5110	0.753076
$277$	−8.08036	−0.485502	−0.242751	−	0.970089i	$-0.578050\pi$
$277$	−8.08036	−0.485502	−0.242751	+	0.970089i	$0.578050\pi$
$278$	22.8220	1.36878
$279$	−10.1202	−0.605880
$280$	−4.85393	−0.290078
$281$	−0.364131	−0.0217222	−0.0108611	−	0.999941i	$-0.503457\pi$
$281$	−0.364131	−0.0217222	−0.0108611	+	0.999941i	$0.503457\pi$
$282$	19.2993	1.14926
$283$	18.4654	1.09765	0.548826	−	0.835936i	$-0.315075\pi$
$283$	18.4654	1.09765	0.548826	+	0.835936i	$0.315075\pi$
$284$	−21.1979	−1.25786
$285$	−17.9522	−1.06340
$286$	−5.84108	−0.345390
$287$	4.37501	0.258249
$288$	13.0920	0.771455
$289$	−10.0064	−0.588611
$290$	−47.3608	−2.78112
$291$	15.8793	0.930861
$292$	−0.593168	−0.0347125
$293$	−24.6728	−1.44140	−0.720699	−	0.693248i	$-0.756179\pi$
$293$	−24.6728	−1.44140	−0.720699	+	0.693248i	$0.756179\pi$
$294$	8.96186	0.522667
$295$	−40.8318	−2.37732
$296$	−1.52793	−0.0888091
$297$	−2.32714	−0.135034
$298$	6.81773	0.394940
$299$	−50.9823	−2.94838
$300$	−14.5527	−0.840198
$301$	−6.04518	−0.348439
$302$	27.0988	1.55936
$303$	−16.3002	−0.936421
$304$	−20.9792	−1.20324
$305$	41.3761	2.36919
$306$	9.07502	0.518784
$307$	30.4706	1.73905	0.869526	−	0.493888i	$-0.164425\pi$
$307$	30.4706	1.73905	0.869526	+	0.493888i	$0.164425\pi$
$308$	−1.13304	−0.0645609
$309$	0.378741	0.0215458
$310$	38.7113	2.19865
$311$	12.1823	0.690794	0.345397	−	0.938457i	$-0.387744\pi$
$311$	12.1823	0.690794	0.345397	+	0.938457i	$0.387744\pi$
$312$	6.15297	0.348343
$313$	−31.0316	−1.75401	−0.877004	−	0.480482i	$-0.840462\pi$
$313$	−31.0316	−1.75401	−0.877004	+	0.480482i	$0.840462\pi$
$314$	37.2741	2.10350
$315$	−10.8515	−0.611413
$316$	−20.9217	−1.17694
$317$	24.4624	1.37394	0.686972	−	0.726683i	$-0.258939\pi$
$317$	24.4624	1.37394	0.686972	+	0.726683i	$0.258939\pi$
$318$	−11.2252	−0.629478
$319$	3.02752	0.169509
$320$	−15.7003	−0.877674
$321$	−10.8097	−0.603337
$322$	−22.4871	−1.25316
$323$	−11.8673	−0.660317
$324$	−0.397078	−0.0220599
$325$	59.3019	3.28948
$326$	−11.9809	−0.663563
$327$	−10.3391	−0.571754
$328$	−2.18719	−0.120767
$329$	−15.2553	−0.841052
$330$	3.35682	0.184787
$331$	−16.5187	−0.907949	−0.453975	−	0.891015i	$-0.649994\pi$
$331$	−16.5187	−0.907949	−0.453975	+	0.891015i	$0.649994\pi$
$332$	−1.58279	−0.0868670
$333$	−3.41585	−0.187188
$334$	−1.70036	−0.0930397
$335$	−24.8180	−1.35595
$336$	8.26580	0.450937
$337$	31.4723	1.71441	0.857203	−	0.514979i	$-0.172200\pi$
$337$	31.4723	1.71441	0.857203	+	0.514979i	$0.172200\pi$
$338$	66.9946	3.64403
$339$	10.6707	0.579552
$340$	−15.2663	−0.827932
$341$	−2.47460	−0.134007
$342$	−15.3993	−0.832697
$343$	−18.4591	−0.996696
$344$	3.02216	0.162944
$345$	29.2992	1.57741
$346$	39.1332	2.10381
$347$	4.69804	0.252204	0.126102	−	0.992017i	$-0.459753\pi$
$347$	4.69804	0.252204	0.126102	+	0.992017i	$0.459753\pi$
$348$	11.6456	0.624270
$349$	0.337268	0.0180536	0.00902678	−	0.999959i	$-0.497127\pi$
$349$	0.337268	0.0180536	0.00902678	+	0.999959i	$0.497127\pi$
$350$	26.1567	1.39814
$351$	36.4774	1.94702
$352$	3.20128	0.170629
$353$	28.8116	1.53349	0.766743	−	0.641954i	$-0.221876\pi$
$353$	28.8116	1.53349	0.766743	+	0.641954i	$0.221876\pi$
$354$	22.8299	1.21340
$355$	−49.6426	−2.63476
$356$	−10.6653	−0.565258
$357$	4.67573	0.247466
$358$	1.37445	0.0726421
$359$	−23.5557	−1.24322	−0.621612	−	0.783326i	$-0.713522\pi$
$359$	−23.5557	−1.24322	−0.621612	+	0.783326i	$0.713522\pi$
$360$	5.42497	0.285921
$361$	1.13753	0.0598701
$362$	33.4557	1.75840
$363$	11.7538	0.616913
$364$	17.7601	0.930884
$365$	−1.38912	−0.0727098
$366$	−23.1343	−1.20925
$367$	32.4009	1.69132	0.845658	−	0.533726i	$-0.179209\pi$
$367$	32.4009	1.69132	0.845658	+	0.533726i	$0.179209\pi$
$368$	34.2395	1.78486
$369$	−4.88970	−0.254548
$370$	13.0662	0.679278
$371$	8.87305	0.460666
$372$	−9.51877	−0.493525
$373$	−19.0971	−0.988810	−0.494405	−	0.869232i	$-0.664614\pi$
$373$	−19.0971	−0.988810	−0.494405	+	0.869232i	$0.664614\pi$
$374$	2.21904	0.114744
$375$	−14.0779	−0.726978
$376$	7.62655	0.393309
$377$	−47.4557	−2.44409
$378$	16.0893	0.827547
$379$	−20.0690	−1.03087	−0.515437	−	0.856928i	$-0.672370\pi$
$379$	−20.0690	−1.03087	−0.515437	+	0.856928i	$0.672370\pi$
$380$	25.9052	1.32891
$381$	7.03766	0.360550
$382$	27.1310	1.38814
$383$	23.9798	1.22531	0.612656	−	0.790350i	$-0.290101\pi$
$383$	23.9798	1.22531	0.612656	+	0.790350i	$0.290101\pi$
$384$	−6.90784	−0.352514
$385$	−2.65343	−0.135231
$386$	11.2010	0.570114
$387$	6.75637	0.343445
$388$	−22.9140	−1.16328
$389$	5.94704	0.301527	0.150764	−	0.988570i	$-0.451827\pi$
$389$	5.94704	0.301527	0.150764	+	0.988570i	$0.451827\pi$
$390$	−52.6174	−2.66439
$391$	19.3683	0.979497
$392$	3.54148	0.178872
$393$	−11.2407	−0.567019
$394$	18.6937	0.941774
$395$	−48.9958	−2.46524
$396$	1.26633	0.0636357
$397$	−34.7059	−1.74184	−0.870920	−	0.491425i	$-0.836476\pi$
$397$	−34.7059	−1.74184	−0.870920	+	0.491425i	$0.836476\pi$
$398$	8.76345	0.439272
$399$	−7.93417	−0.397205
$400$	−39.8269	−1.99134
$401$	−2.22066	−0.110895	−0.0554474	−	0.998462i	$-0.517658\pi$
$401$	−2.22066	−0.110895	−0.0554474	+	0.998462i	$0.517658\pi$
$402$	13.8763	0.692086
$403$	38.7889	1.93221
$404$	23.5213	1.17023
$405$	−0.929904	−0.0462073
$406$	−20.9316	−1.03882
$407$	−0.835250	−0.0414018
$408$	−2.33753	−0.115725
$409$	−22.2378	−1.09959	−0.549795	−	0.835300i	$-0.685294\pi$
$409$	−22.2378	−1.09959	−0.549795	+	0.835300i	$0.685294\pi$
$410$	18.7039	0.923718
$411$	−6.54940	−0.323058
$412$	−0.546526	−0.0269254
$413$	−18.0461	−0.887989
$414$	25.1326	1.23520
$415$	−3.70668	−0.181954
$416$	−50.1794	−2.46025
$417$	−13.1419	−0.643564
$418$	−3.76545	−0.184174
$419$	−13.8531	−0.676767	−0.338384	−	0.941008i	$-0.609880\pi$
$419$	−13.8531	−0.676767	−0.338384	+	0.941008i	$0.609880\pi$
$420$	−10.2066	−0.498032
$421$	9.06617	0.441858	0.220929	−	0.975290i	$-0.429091\pi$
$421$	9.06617	0.441858	0.220929	+	0.975290i	$0.429091\pi$
$422$	−40.1987	−1.95684
$423$	17.0500	0.828999
$424$	−4.43589	−0.215426
$425$	−22.5289	−1.09281
$426$	27.7562	1.34479
$427$	18.2867	0.884953
$428$	15.5984	0.753979
$429$	3.36355	0.162394
$430$	−25.8441	−1.24631
$431$	−6.69719	−0.322592	−0.161296	−	0.986906i	$-0.551567\pi$
$431$	−6.69719	−0.322592	−0.161296	+	0.986906i	$0.551567\pi$
$432$	−24.4981	−1.17866
$433$	16.8557	0.810034	0.405017	−	0.914309i	$-0.367266\pi$
$433$	16.8557	0.810034	0.405017	+	0.914309i	$0.367266\pi$
$434$	17.1089	0.821252
$435$	27.2725	1.30761
$436$	14.9194	0.714511
$437$	−32.8658	−1.57218
$438$	0.776685	0.0371115
$439$	13.3161	0.635545	0.317772	−	0.948167i	$-0.397065\pi$
$439$	13.3161	0.635545	0.317772	+	0.948167i	$0.397065\pi$
$440$	1.32652	0.0632394
$441$	7.91736	0.377017
$442$	−34.7829	−1.65445
$443$	−37.0767	−1.76157	−0.880784	−	0.473519i	$-0.842984\pi$
$443$	−37.0767	−1.76157	−0.880784	+	0.473519i	$0.842984\pi$
$444$	−3.21286	−0.152475
$445$	−24.9766	−1.18400
$446$	11.9652	0.566569
$447$	−3.92595	−0.185691
$448$	−6.93893	−0.327834
$449$	7.08211	0.334225	0.167113	−	0.985938i	$-0.446556\pi$
$449$	7.08211	0.334225	0.167113	+	0.985938i	$0.446556\pi$
$450$	−29.2339	−1.37810
$451$	−1.19564	−0.0563004
$452$	−15.3979	−0.724256
$453$	−15.6047	−0.733172
$454$	12.9796	0.609162
$455$	41.5919	1.94986
$456$	3.96651	0.185749
$457$	4.25876	0.199216	0.0996082	−	0.995027i	$-0.468241\pi$
$457$	4.25876	0.199216	0.0996082	+	0.995027i	$0.468241\pi$
$458$	−3.96898	−0.185458
$459$	−13.8578	−0.646829
$460$	−42.2790	−1.97127
$461$	18.7753	0.874452	0.437226	−	0.899352i	$-0.355961\pi$
$461$	18.7753	0.874452	0.437226	+	0.899352i	$0.355961\pi$
$462$	1.48359	0.0690226
$463$	−9.28290	−0.431413	−0.215706	−	0.976458i	$-0.569205\pi$
$463$	−9.28290	−0.431413	−0.215706	+	0.976458i	$0.569205\pi$
$464$	31.8711	1.47958
$465$	−22.2917	−1.03375
$466$	−21.7965	−1.00971
$467$	8.54771	0.395541	0.197770	−	0.980248i	$-0.436630\pi$
$467$	8.54771	0.395541	0.197770	+	0.980248i	$0.436630\pi$
$468$	−19.8495	−0.917544
$469$	−10.9686	−0.506483
$470$	−65.2189	−3.00832
$471$	−21.4641	−0.989013
$472$	9.02174	0.415259
$473$	1.65208	0.0759626
$474$	27.3946	1.25827
$475$	38.2290	1.75407
$476$	−6.74712	−0.309254
$477$	−9.91691	−0.454064
$478$	0.962108	0.0440058
$479$	0.720515	0.0329212	0.0164606	−	0.999865i	$-0.494760\pi$
$479$	0.720515	0.0329212	0.0164606	+	0.999865i	$0.494760\pi$
$480$	28.8377	1.31626
$481$	13.0924	0.596960
$482$	−40.4841	−1.84400
$483$	12.9491	0.589204
$484$	−16.9608	−0.770945
$485$	−53.6614	−2.43664
$486$	−29.1832	−1.32378
$487$	40.4584	1.83334	0.916672	−	0.399641i	$-0.130865\pi$
$487$	40.4584	1.83334	0.916672	+	0.399641i	$0.130865\pi$
$488$	−9.14201	−0.413839
$489$	6.89915	0.311991
$490$	−30.2851	−1.36814
$491$	−15.7811	−0.712190	−0.356095	−	0.934450i	$-0.615892\pi$
$491$	−15.7811	−0.712190	−0.356095	+	0.934450i	$0.615892\pi$
$492$	−4.59912	−0.207344
$493$	18.0285	0.811964
$494$	59.0226	2.65555
$495$	2.96559	0.133293
$496$	−26.0504	−1.16970
$497$	−21.9401	−0.984149
$498$	2.07248	0.0928702
$499$	−40.8096	−1.82689	−0.913444	−	0.406965i	$-0.866587\pi$
$499$	−40.8096	−1.82689	−0.913444	+	0.406965i	$0.866587\pi$
$500$	20.3145	0.908491
$501$	0.979144	0.0437449
$502$	−0.355391	−0.0158619
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	2.39763	0.106799
$505$	55.0837	2.45119
$506$	6.14547	0.273199
$507$	−38.5785	−1.71333
$508$	−10.1554	−0.450574
$509$	15.5394	0.688773	0.344387	−	0.938828i	$-0.388087\pi$
$509$	15.5394	0.688773	0.344387	+	0.938828i	$0.388087\pi$
$510$	19.9895	0.885149
$511$	−0.613937	−0.0271590
$512$	26.1043	1.15366
$513$	23.5152	1.03822
$514$	−32.3802	−1.42823
$515$	−1.27989	−0.0563987
$516$	6.35485	0.279757
$517$	4.16909	0.183356
$518$	5.77474	0.253727
$519$	−22.5346	−0.989159
$520$	−20.7929	−0.911830
$521$	0.0128309	0.000562132 0	0.000281066	−	1.00000i	$-0.499911\pi$
$521$	0.0128309	0.000562132 0	0.000281066		1.00000i	$0.499911\pi$
$522$	23.3941	1.02393
$523$	21.2701	0.930078	0.465039	−	0.885290i	$-0.346040\pi$
$523$	21.2701	0.930078	0.465039	+	0.885290i	$0.346040\pi$
$524$	16.2205	0.708594
$525$	−15.0622	−0.657368
$526$	18.5789	0.810079
$527$	−14.7360	−0.641909
$528$	−2.25895	−0.0983080
$529$	30.6391	1.33214
$530$	37.9337	1.64774
$531$	20.1691	0.875264
$532$	11.4491	0.496381
$533$	18.7413	0.811778
$534$	13.9649	0.604322
$535$	36.5295	1.57931
$536$	5.48351	0.236852
$537$	−0.791471	−0.0341545
$538$	−11.3100	−0.487607
$539$	1.93596	0.0833879
$540$	30.2502	1.30176
$541$	−29.2729	−1.25854	−0.629270	−	0.777187i	$-0.716646\pi$
$541$	−29.2729	−1.25854	−0.629270	+	0.777187i	$0.716646\pi$
$542$	6.07356	0.260882
$543$	−19.2653	−0.826753
$544$	19.0633	0.817330
$545$	34.9393	1.49663
$546$	−23.2549	−0.995217
$547$	−22.3283	−0.954690	−0.477345	−	0.878716i	$-0.658401\pi$
$547$	−22.3283	−0.954690	−0.477345	+	0.878716i	$0.658401\pi$
$548$	9.45085	0.403720
$549$	−20.4380	−0.872271
$550$	−7.14832	−0.304805
$551$	−30.5924	−1.30328
$552$	−6.47361	−0.275535
$553$	−21.6542	−0.920832
$554$	−15.2675	−0.648653
$555$	−7.52408	−0.319379
$556$	18.9640	0.804251
$557$	−36.2502	−1.53597	−0.767985	−	0.640468i	$-0.778740\pi$
$557$	−36.2502	−1.53597	−0.767985	+	0.640468i	$0.778740\pi$
$558$	−19.1216	−0.809483
$559$	−25.8959	−1.09528
$560$	−27.9329	−1.18038
$561$	−1.27782	−0.0539496
$562$	−0.688009	−0.0290219
$563$	18.9489	0.798602	0.399301	−	0.916820i	$-0.369253\pi$
$563$	18.9489	0.798602	0.399301	+	0.916820i	$0.369253\pi$
$564$	16.0368	0.675269
$565$	−36.0598	−1.51705
$566$	34.8895	1.46651
$567$	−0.410981	−0.0172596
$568$	10.9685	0.460227
$569$	24.2317	1.01584	0.507922	−	0.861403i	$-0.330414\pi$
$569$	24.2317	1.01584	0.507922	+	0.861403i	$0.330414\pi$
$570$	−33.9199	−1.42075
$571$	43.1512	1.80582	0.902911	−	0.429827i	$-0.141426\pi$
$571$	43.1512	1.80582	0.902911	+	0.429827i	$0.141426\pi$
$572$	−4.85363	−0.202941
$573$	−15.6232	−0.652670
$574$	8.26638	0.345032
$575$	−62.3923	−2.60194
$576$	7.75525	0.323136
$577$	21.8954	0.911518	0.455759	−	0.890103i	$-0.349368\pi$
$577$	21.8954	0.911518	0.455759	+	0.890103i	$0.349368\pi$
$578$	−18.9066	−0.786412
$579$	−6.45001	−0.268053
$580$	−39.3544	−1.63410
$581$	−1.63821	−0.0679644
$582$	30.0032	1.24367
$583$	−2.42490	−0.100429
$584$	0.306924	0.0127006
$585$	−46.4849	−1.92191
$586$	−46.6181	−1.92577
$587$	24.1518	0.996850	0.498425	−	0.866933i	$-0.333912\pi$
$587$	24.1518	0.996850	0.498425	+	0.866933i	$0.333912\pi$
$588$	7.44685	0.307103
$589$	25.0053	1.03032
$590$	−77.1499	−3.17621
$591$	−10.7647	−0.442799
$592$	−8.79277	−0.361380
$593$	24.4219	1.00289	0.501444	−	0.865190i	$-0.332802\pi$
$593$	24.4219	1.00289	0.501444	+	0.865190i	$0.332802\pi$
$594$	−4.39703	−0.180412
$595$	−15.8008	−0.647771
$596$	5.66518	0.232055
$597$	−5.04638	−0.206535
$598$	−96.3288	−3.93918
$599$	−24.1038	−0.984854	−0.492427	−	0.870354i	$-0.663890\pi$
$599$	−24.1038	−0.984854	−0.492427	+	0.870354i	$0.663890\pi$
$600$	7.53001	0.307412
$601$	−16.4944	−0.672821	−0.336410	−	0.941715i	$-0.609213\pi$
$601$	−16.4944	−0.672821	−0.336410	+	0.941715i	$0.609213\pi$
$602$	−11.4221	−0.465530
$603$	12.2590	0.499225
$604$	22.5177	0.916233
$605$	−39.7199	−1.61484
$606$	−30.7985	−1.25110
$607$	38.2300	1.55171	0.775854	−	0.630912i	$-0.217319\pi$
$607$	38.2300	1.55171	0.775854	+	0.630912i	$0.217319\pi$
$608$	−32.3482	−1.31189
$609$	12.0534	0.488427
$610$	78.1784	3.16535
$611$	−65.3496	−2.64376
$612$	7.54088	0.304822
$613$	21.5346	0.869773	0.434886	−	0.900485i	$-0.356789\pi$
$613$	21.5346	0.869773	0.434886	+	0.900485i	$0.356789\pi$
$614$	57.5729	2.32345
$615$	−10.7705	−0.434309
$616$	0.586271	0.0236215
$617$	8.20984	0.330516	0.165258	−	0.986250i	$-0.447154\pi$
$617$	8.20984	0.330516	0.165258	+	0.986250i	$0.447154\pi$
$618$	0.715613	0.0287862
$619$	21.7969	0.876091	0.438046	−	0.898953i	$-0.355671\pi$
$619$	21.7969	0.876091	0.438046	+	0.898953i	$0.355671\pi$
$620$	32.1671	1.29186
$621$	−38.3783	−1.54007
$622$	23.0179	0.922933
$623$	−11.0387	−0.442256
$624$	35.4085	1.41747
$625$	4.97865	0.199146
$626$	−58.6328	−2.34344
$627$	2.16831	0.0865941
$628$	30.9729	1.23595
$629$	−4.97381	−0.198319
$630$	−20.5034	−0.816876
$631$	0.416993	0.0166002	0.00830012	−	0.999966i	$-0.497358\pi$
$631$	0.416993	0.0166002	0.00830012	+	0.999966i	$0.497358\pi$
$632$	10.8256	0.430617
$633$	23.1482	0.920058
$634$	46.2206	1.83565
$635$	−23.7826	−0.943784
$636$	−9.32757	−0.369862
$637$	−30.3458	−1.20235
$638$	5.72037	0.226471
$639$	24.5212	0.970045
$640$	23.3439	0.922749
$641$	3.93254	0.155326	0.0776629	−	0.996980i	$-0.475254\pi$
$641$	3.93254	0.155326	0.0776629	+	0.996980i	$0.475254\pi$
$642$	−20.4244	−0.806086
$643$	−26.3585	−1.03948	−0.519739	−	0.854325i	$-0.673971\pi$
$643$	−26.3585	−1.03948	−0.519739	+	0.854325i	$0.673971\pi$
$644$	−18.6857	−0.736318
$645$	14.8822	0.585986
$646$	−22.4228	−0.882214
$647$	0.284750	0.0111947	0.00559734	−	0.999984i	$-0.498218\pi$
$647$	0.284750	0.0111947	0.00559734	+	0.999984i	$0.498218\pi$
$648$	0.205461	0.00807127
$649$	4.93178	0.193589
$650$	112.048	4.39490
$651$	−9.85205	−0.386132
$652$	−9.95554	−0.389889
$653$	−21.6597	−0.847609	−0.423805	−	0.905754i	$-0.639306\pi$
$653$	−21.6597	−0.847609	−0.423805	+	0.905754i	$0.639306\pi$
$654$	−19.5353	−0.763890
$655$	37.9861	1.48424
$656$	−12.5866	−0.491424
$657$	0.686163	0.0267698
$658$	−28.8242	−1.12368
$659$	20.3180	0.791476	0.395738	−	0.918363i	$-0.370489\pi$
$659$	20.3180	0.791476	0.395738	+	0.918363i	$0.370489\pi$
$660$	2.78935	0.108575
$661$	−40.4018	−1.57145	−0.785724	−	0.618578i	$-0.787709\pi$
$661$	−40.4018	−1.57145	−0.785724	+	0.618578i	$0.787709\pi$
$662$	−31.2113	−1.21306
$663$	20.0295	0.777883
$664$	0.818987	0.0317829
$665$	26.8122	1.03973
$666$	−6.45410	−0.250091
$667$	49.9287	1.93325
$668$	−1.41291	−0.0546673
$669$	−6.89010	−0.266387
$670$	−46.8926	−1.81162
$671$	−4.99752	−0.192927
$672$	12.7452	0.491655
$673$	3.82061	0.147274	0.0736369	−	0.997285i	$-0.476539\pi$
$673$	3.82061	0.147274	0.0736369	+	0.997285i	$0.476539\pi$
$674$	59.4655	2.29053
$675$	44.6411	1.71824
$676$	55.6691	2.14112
$677$	38.4091	1.47618	0.738090	−	0.674702i	$-0.235728\pi$
$677$	38.4091	1.47618	0.738090	+	0.674702i	$0.235728\pi$
$678$	20.1618	0.774309
$679$	−23.7163	−0.910147
$680$	7.89928	0.302924
$681$	−7.47422	−0.286413
$682$	−4.67565	−0.179040
$683$	2.05708	0.0787118	0.0393559	−	0.999225i	$-0.487469\pi$
$683$	2.05708	0.0787118	0.0393559	+	0.999225i	$0.487469\pi$
$684$	−12.7960	−0.489267
$685$	22.1326	0.845644
$686$	−34.8776	−1.33163
$687$	2.28552	0.0871979
$688$	17.3916	0.663048
$689$	38.0097	1.44806
$690$	55.3595	2.10750
$691$	−46.0370	−1.75133	−0.875665	−	0.482919i	$-0.839577\pi$
$691$	−46.0370	−1.75133	−0.875665	+	0.482919i	$0.839577\pi$
$692$	32.5176	1.23614
$693$	1.31067	0.0497884
$694$	8.87673	0.336956
$695$	44.4110	1.68461
$696$	−6.02581	−0.228408
$697$	−7.11988	−0.269685
$698$	0.637253	0.0241204
$699$	12.5514	0.474738
$700$	21.7349	0.821502
$701$	8.97682	0.339050	0.169525	−	0.985526i	$-0.445777\pi$
$701$	8.97682	0.339050	0.169525	+	0.985526i	$0.445777\pi$
$702$	68.9224	2.60131
$703$	8.43999	0.318320
$704$	1.89633	0.0714705
$705$	37.5559	1.41444
$706$	54.4382	2.04881
$707$	24.3449	0.915583
$708$	18.9705	0.712955
$709$	12.9810	0.487513	0.243756	−	0.969837i	$-0.421620\pi$
$709$	12.9810	0.487513	0.243756	+	0.969837i	$0.421620\pi$
$710$	−93.7975	−3.52016
$711$	24.2017	0.907635
$712$	5.51855	0.206816
$713$	−40.8102	−1.52836
$714$	8.83458	0.330626
$715$	−11.3666	−0.425085
$716$	1.14210	0.0426823
$717$	−0.554025	−0.0206904
$718$	−44.5075	−1.66100
$719$	−33.0346	−1.23198	−0.615991	−	0.787754i	$-0.711244\pi$
$719$	−33.0346	−1.23198	−0.615991	+	0.787754i	$0.711244\pi$
$720$	31.2190	1.16347
$721$	−0.565662	−0.0210664
$722$	2.14931	0.0799892
$723$	23.3125	0.867002
$724$	27.8000	1.03318
$725$	−58.0764	−2.15690
$726$	22.2082	0.824224
$727$	17.1741	0.636952	0.318476	−	0.947931i	$-0.396829\pi$
$727$	17.1741	0.636952	0.318476	+	0.947931i	$0.396829\pi$
$728$	−9.18967	−0.340592
$729$	17.5637	0.650509
$730$	−2.62468	−0.0971437
$731$	9.83792	0.363869
$732$	−19.2234	−0.710517
$733$	10.1322	0.374242	0.187121	−	0.982337i	$-0.440084\pi$
$733$	10.1322	0.374242	0.187121	+	0.982337i	$0.440084\pi$
$734$	61.2201	2.25968
$735$	17.4395	0.643266
$736$	52.7943	1.94603
$737$	2.99759	0.110418
$738$	−9.23887	−0.340088
$739$	−29.3839	−1.08091	−0.540453	−	0.841374i	$-0.681747\pi$
$739$	−29.3839	−1.08091	−0.540453	+	0.841374i	$0.681747\pi$
$740$	10.8573	0.399123
$741$	−33.9878	−1.24857
$742$	16.7652	0.615471
$743$	8.73127	0.320319	0.160160	−	0.987091i	$-0.448799\pi$
$743$	8.73127	0.320319	0.160160	+	0.987091i	$0.448799\pi$
$744$	4.92532	0.180571
$745$	13.2671	0.486069
$746$	−36.0831	−1.32110
$747$	1.83094	0.0669905
$748$	1.84391	0.0674199
$749$	16.1446	0.589911
$750$	−26.5995	−0.971276
$751$	18.2247	0.665030	0.332515	−	0.943098i	$-0.392103\pi$
$751$	18.2247	0.665030	0.332515	+	0.943098i	$0.392103\pi$
$752$	43.8885	1.60045
$753$	0.204650	0.00745786
$754$	−89.6655	−3.26542
$755$	52.7335	1.91917
$756$	13.3694	0.486241
$757$	−21.5058	−0.781640	−0.390820	−	0.920467i	$-0.627809\pi$
$757$	−21.5058	−0.781640	−0.390820	+	0.920467i	$0.627809\pi$
$758$	−37.9194	−1.37729
$759$	−3.53883	−0.128451
$760$	−13.4042	−0.486220
$761$	−34.3434	−1.24495	−0.622474	−	0.782641i	$-0.713872\pi$
$761$	−34.3434	−1.24495	−0.622474	+	0.782641i	$0.713872\pi$
$762$	13.2974	0.481712
$763$	15.4418	0.559031
$764$	22.5445	0.815631
$765$	17.6597	0.638488
$766$	45.3088	1.63707
$767$	−77.3045	−2.79130
$768$	−22.3440	−0.806270
$769$	−20.2341	−0.729660	−0.364830	−	0.931074i	$-0.618873\pi$
$769$	−20.2341	−0.729660	−0.364830	+	0.931074i	$0.618873\pi$
$770$	−5.01353	−0.180675
$771$	18.6459	0.671517
$772$	9.30742	0.334981
$773$	21.5030	0.773409	0.386704	−	0.922204i	$-0.373613\pi$
$773$	21.5030	0.773409	0.386704	+	0.922204i	$0.373613\pi$
$774$	12.7658	0.458859
$775$	47.4699	1.70517
$776$	11.8564	0.425621
$777$	−3.32535	−0.119296
$778$	11.2367	0.402854
$779$	12.0816	0.432869
$780$	−43.7224	−1.56551
$781$	5.99597	0.214553
$782$	36.5955	1.30865
$783$	−35.7236	−1.27666
$784$	20.3801	0.727861
$785$	72.5343	2.58886
$786$	−21.2388	−0.757564
$787$	9.43366	0.336273	0.168137	−	0.985764i	$-0.446225\pi$
$787$	9.43366	0.336273	0.168137	+	0.985764i	$0.446225\pi$
$788$	15.5335	0.553358
$789$	−10.6986	−0.380879
$790$	−92.5753	−3.29368
$791$	−15.9370	−0.566656
$792$	−0.655242	−0.0232830
$793$	78.3351	2.78176
$794$	−65.5753	−2.32718
$795$	−21.8439	−0.774724
$796$	7.28198	0.258103
$797$	−15.0608	−0.533482	−0.266741	−	0.963768i	$-0.585947\pi$
$797$	−15.0608	−0.533482	−0.266741	+	0.963768i	$0.585947\pi$
$798$	−14.9913	−0.530685
$799$	24.8265	0.878297
$800$	−61.4096	−2.17116
$801$	12.3373	0.435918
$802$	−4.19585	−0.148160
$803$	0.167782	0.00592088
$804$	11.5305	0.406649
$805$	−43.7593	−1.54231
$806$	73.2898	2.58152
$807$	6.51278	0.229261
$808$	−12.1707	−0.428163
$809$	−11.1181	−0.390890	−0.195445	−	0.980715i	$-0.562615\pi$
$809$	−11.1181	−0.390890	−0.195445	+	0.980715i	$0.562615\pi$
$810$	−1.75701	−0.0617351
$811$	13.3948	0.470356	0.235178	−	0.971952i	$-0.424433\pi$
$811$	13.3948	0.470356	0.235178	+	0.971952i	$0.424433\pi$
$812$	−17.3931	−0.610379
$813$	−3.49743	−0.122660
$814$	−1.57817	−0.0553147
$815$	−23.3145	−0.816673
$816$	−13.4518	−0.470906
$817$	−16.6938	−0.584043
$818$	−42.0174	−1.46910
$819$	−20.5445	−0.717884
$820$	15.5419	0.542748
$821$	17.8389	0.622583	0.311292	−	0.950314i	$-0.399238\pi$
$821$	17.8389	0.622583	0.311292	+	0.950314i	$0.399238\pi$
$822$	−12.3748	−0.431621
$823$	13.8929	0.484278	0.242139	−	0.970242i	$-0.422151\pi$
$823$	13.8929	0.484278	0.242139	+	0.970242i	$0.422151\pi$
$824$	0.282790	0.00985146
$825$	4.11632	0.143312
$826$	−34.0973	−1.18640
$827$	34.8154	1.21065	0.605325	−	0.795978i	$-0.293043\pi$
$827$	34.8154	1.21065	0.605325	+	0.795978i	$0.293043\pi$
$828$	20.8839	0.725767
$829$	28.7227	0.997581	0.498791	−	0.866723i	$-0.333778\pi$
$829$	28.7227	0.997581	0.498791	+	0.866723i	$0.333778\pi$
$830$	−7.00361	−0.243099
$831$	8.79170	0.304981
$832$	−29.7245	−1.03051
$833$	11.5284	0.399437
$834$	−24.8311	−0.859831
$835$	−3.30885	−0.114508
$836$	−3.12890	−0.108215
$837$	29.1993	1.00928
$838$	−26.1748	−0.904192
$839$	31.7200	1.09510	0.547549	−	0.836774i	$-0.315561\pi$
$839$	31.7200	1.09510	0.547549	+	0.836774i	$0.315561\pi$
$840$	5.28123	0.182220
$841$	17.4750	0.602587
$842$	17.1301	0.590343
$843$	0.396186	0.0136454
$844$	−33.4031	−1.14978
$845$	130.370	4.48485
$846$	32.2152	1.10758
$847$	−17.5547	−0.603185
$848$	−25.5272	−0.876607
$849$	−20.0909	−0.689518
$850$	−42.5674	−1.46005
$851$	−13.7746	−0.472188
$852$	23.0640	0.790160
$853$	−29.2937	−1.00300	−0.501498	−	0.865159i	$-0.667217\pi$
$853$	−29.2937	−1.00300	−0.501498	+	0.865159i	$0.667217\pi$
$854$	34.5518	1.18234
$855$	−29.9665	−1.02483
$856$	−8.07114	−0.275866
$857$	−23.3315	−0.796988	−0.398494	−	0.917171i	$-0.630467\pi$
$857$	−23.3315	−0.796988	−0.398494	+	0.917171i	$0.630467\pi$
$858$	6.35528	0.216966
$859$	−26.4734	−0.903261	−0.451630	−	0.892205i	$-0.649157\pi$
$859$	−26.4734	−0.903261	−0.451630	+	0.892205i	$0.649157\pi$
$860$	−21.4752	−0.732297
$861$	−4.76015	−0.162225
$862$	−12.6540	−0.430998
$863$	13.0103	0.442875	0.221438	−	0.975175i	$-0.428925\pi$
$863$	13.0103	0.442875	0.221438	+	0.975175i	$0.428925\pi$
$864$	−37.7739	−1.28509
$865$	76.1519	2.58924
$866$	31.8481	1.08224
$867$	10.8873	0.369751
$868$	14.2166	0.482543
$869$	5.91784	0.200749
$870$	51.5301	1.74703
$871$	−46.9865	−1.59208
$872$	−7.71979	−0.261425
$873$	26.5064	0.897104
$874$	−62.0984	−2.10051
$875$	21.0258	0.710800
$876$	0.645386	0.0218056
$877$	−33.7884	−1.14095	−0.570476	−	0.821314i	$-0.693241\pi$
$877$	−33.7884	−1.14095	−0.570476	+	0.821314i	$0.693241\pi$
$878$	25.1603	0.849118
$879$	26.8447	0.905451
$880$	7.63373	0.257333
$881$	−30.3070	−1.02107	−0.510535	−	0.859857i	$-0.670553\pi$
$881$	−30.3070	−1.02107	−0.510535	+	0.859857i	$0.670553\pi$
$882$	14.9595	0.503712
$883$	−16.8677	−0.567645	−0.283822	−	0.958877i	$-0.591603\pi$
$883$	−16.8677	−0.567645	−0.283822	+	0.958877i	$0.591603\pi$
$884$	−28.9028	−0.972107
$885$	44.4263	1.49337
$886$	−70.0548	−2.35354
$887$	−7.70638	−0.258755	−0.129377	−	0.991595i	$-0.541298\pi$
$887$	−7.70638	−0.258755	−0.129377	+	0.991595i	$0.541298\pi$
$888$	1.66244	0.0557877
$889$	−10.5110	−0.352527
$890$	−47.1922	−1.58189
$891$	0.112316	0.00376274
$892$	9.94248	0.332899
$893$	−42.1276	−1.40975
$894$	−7.41791	−0.248092
$895$	2.67464	0.0894035
$896$	10.3171	0.344670
$897$	55.4704	1.85210
$898$	13.3813	0.446541
$899$	−37.9873	−1.26695
$900$	−24.2919	−0.809729
$901$	−14.4400	−0.481066
$902$	−2.25910	−0.0752199
$903$	6.57736	0.218881
$904$	7.96737	0.264991
$905$	65.1039	2.16413
$906$	−29.4844	−0.979553
$907$	−12.9574	−0.430244	−0.215122	−	0.976587i	$-0.569015\pi$
$907$	−12.9574	−0.430244	−0.215122	+	0.976587i	$0.569015\pi$
$908$	10.7854	0.357925
$909$	−27.2089	−0.902462
$910$	78.5859	2.60510
$911$	−16.1166	−0.533965	−0.266983	−	0.963701i	$-0.586027\pi$
$911$	−16.1166	−0.533965	−0.266983	+	0.963701i	$0.586027\pi$
$912$	22.8261	0.755847
$913$	0.447703	0.0148168
$914$	8.04674	0.266162
$915$	−45.0186	−1.48827
$916$	−3.29802	−0.108970
$917$	16.7884	0.554402
$918$	−26.1838	−0.864193
$919$	−42.9283	−1.41607	−0.708037	−	0.706176i	$-0.750419\pi$
$919$	−42.9283	−1.41607	−0.708037	+	0.706176i	$0.750419\pi$
$920$	21.8765	0.721247
$921$	−33.1530	−1.09243
$922$	35.4751	1.16831
$923$	−93.9855	−3.09357
$924$	1.23278	0.0405556
$925$	16.0224	0.526815
$926$	−17.5396	−0.576387
$927$	0.632209	0.0207645
$928$	49.1424	1.61318
$929$	−46.6902	−1.53186	−0.765928	−	0.642926i	$-0.777720\pi$
$929$	−46.6902	−1.53186	−0.765928	+	0.642926i	$0.777720\pi$
$930$	−42.1191	−1.38114
$931$	−19.5624	−0.641133
$932$	−18.1118	−0.593272
$933$	−13.2547	−0.433940
$934$	16.1505	0.528461
$935$	4.31818	0.141220
$936$	10.2708	0.335711
$937$	−32.5383	−1.06298	−0.531490	−	0.847064i	$-0.678368\pi$
$937$	−32.5383	−1.06298	−0.531490	+	0.847064i	$0.678368\pi$
$938$	−20.7247	−0.676685
$939$	33.7634	1.10183
$940$	−54.1935	−1.76760
$941$	16.3652	0.533492	0.266746	−	0.963767i	$-0.414052\pi$
$941$	16.3652	0.533492	0.266746	+	0.963767i	$0.414052\pi$
$942$	−40.5554	−1.32137
$943$	−19.7180	−0.642107
$944$	51.9174	1.68977
$945$	31.3094	1.01849
$946$	3.12152	0.101490
$947$	−36.4764	−1.18532	−0.592661	−	0.805452i	$-0.701923\pi$
$947$	−36.4764	−1.18532	−0.592661	+	0.805452i	$0.701923\pi$
$948$	22.7635	0.739323
$949$	−2.62994	−0.0853714
$950$	72.2320	2.34351
$951$	−26.6159	−0.863079
$952$	3.49118	0.113150
$953$	−12.5154	−0.405412	−0.202706	−	0.979240i	$-0.564974\pi$
$953$	−12.5154	−0.405412	−0.202706	+	0.979240i	$0.564974\pi$
$954$	−18.7376	−0.606651
$955$	52.7961	1.70844
$956$	0.799462	0.0258565
$957$	−3.29404	−0.106481
$958$	1.36138	0.0439842
$959$	9.78175	0.315869
$960$	17.0824	0.551334
$961$	0.0496228	0.00160074
$962$	24.7374	0.797566
$963$	−18.0439	−0.581457
$964$	−33.6402	−1.08348
$965$	21.7967	0.701661
$966$	24.4667	0.787204
$967$	−21.7860	−0.700589	−0.350295	−	0.936640i	$-0.613919\pi$
$967$	−21.7860	−0.700589	−0.350295	+	0.936640i	$0.613919\pi$
$968$	8.77606	0.282073
$969$	12.9121	0.414795
$970$	−101.391	−3.25546
$971$	23.2256	0.745345	0.372673	−	0.927963i	$-0.378441\pi$
$971$	23.2256	0.745345	0.372673	+	0.927963i	$0.378441\pi$
$972$	−24.2498	−0.777812
$973$	19.6279	0.629243
$974$	76.4443	2.44943
$975$	−64.5224	−2.06637
$976$	−52.6095	−1.68399
$977$	−54.9006	−1.75643	−0.878213	−	0.478270i	$-0.841264\pi$
$977$	−54.9006	−1.75643	−0.878213	+	0.478270i	$0.841264\pi$
$978$	13.0356	0.416834
$979$	3.01674	0.0964155
$980$	−25.1654	−0.803879
$981$	−17.2584	−0.551020
$982$	−29.8177	−0.951519
$983$	29.8038	0.950594	0.475297	−	0.879825i	$-0.342341\pi$
$983$	29.8038	0.950594	0.475297	+	0.879825i	$0.342341\pi$
$984$	2.37973	0.0758631
$985$	36.3774	1.15908
$986$	34.0641	1.08482
$987$	16.5983	0.528328
$988$	49.0448	1.56032
$989$	27.2454	0.866354
$990$	5.60334	0.178086
$991$	−45.0849	−1.43217	−0.716084	−	0.698014i	$-0.754067\pi$
$991$	−45.0849	−1.43217	−0.716084	+	0.698014i	$0.754067\pi$
$992$	−40.1675	−1.27532
$993$	17.9729	0.570351
$994$	−41.4549	−1.31487
$995$	17.0534	0.540630
$996$	1.72213	0.0545677
$997$	36.4935	1.15576	0.577881	−	0.816121i	$-0.303880\pi$
$997$	36.4935	1.15576	0.577881	+	0.816121i	$0.303880\pi$
$998$	−77.1079	−2.44081
$999$	9.85562	0.311818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.20	✓	26
3.2	odd	2		4527.2.a.o.1.7		26
4.3	odd	2		8048.2.a.u.1.18		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.20	✓	26	1.1	even	1	trivial
4527.2.a.o.1.7		26	3.2	odd	2
8048.2.a.u.1.18		26	4.3	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88946 q^{2} -1.08803 q^{3} +1.57004 q^{4} +3.67682 q^{5} -2.05579 q^{6} +1.62501 q^{7} -0.812389 q^{8} -1.81619 q^{9} +O(q^{10})\)	\(q+1.88946 q^{2} -1.08803 q^{3} +1.57004 q^{4} +3.67682 q^{5} -2.05579 q^{6} +1.62501 q^{7} -0.812389 q^{8} -1.81619 q^{9} +6.94719 q^{10} -0.444097 q^{11} -1.70825 q^{12} +6.96112 q^{13} +3.07039 q^{14} -4.00050 q^{15} -4.67505 q^{16} -2.64454 q^{17} -3.43160 q^{18} +4.48749 q^{19} +5.77276 q^{20} -1.76807 q^{21} -0.839101 q^{22} -7.32387 q^{23} +0.883906 q^{24} +8.51902 q^{25} +13.1527 q^{26} +5.24017 q^{27} +2.55134 q^{28} -6.81726 q^{29} -7.55877 q^{30} +5.57222 q^{31} -7.20853 q^{32} +0.483191 q^{33} -4.99674 q^{34} +5.97488 q^{35} -2.85149 q^{36} +1.88078 q^{37} +8.47890 q^{38} -7.57392 q^{39} -2.98701 q^{40} +2.69229 q^{41} -3.34068 q^{42} -3.72008 q^{43} -0.697250 q^{44} -6.67779 q^{45} -13.8381 q^{46} -9.38780 q^{47} +5.08661 q^{48} -4.35933 q^{49} +16.0963 q^{50} +2.87735 q^{51} +10.9292 q^{52} +5.46030 q^{53} +9.90106 q^{54} -1.63286 q^{55} -1.32014 q^{56} -4.88253 q^{57} -12.8809 q^{58} -11.1052 q^{59} -6.28095 q^{60} +11.2532 q^{61} +10.5285 q^{62} -2.95133 q^{63} -4.27008 q^{64} +25.5948 q^{65} +0.912968 q^{66} -6.74986 q^{67} -4.15204 q^{68} +7.96861 q^{69} +11.2893 q^{70} -13.5015 q^{71} +1.47545 q^{72} -0.377804 q^{73} +3.55366 q^{74} -9.26897 q^{75} +7.04553 q^{76} -0.721663 q^{77} -14.3106 q^{78} -13.3256 q^{79} -17.1893 q^{80} -0.252910 q^{81} +5.08696 q^{82} -1.00812 q^{83} -2.77594 q^{84} -9.72351 q^{85} -7.02893 q^{86} +7.41740 q^{87} +0.360779 q^{88} -6.79299 q^{89} -12.6174 q^{90} +11.3119 q^{91} -11.4988 q^{92} -6.06275 q^{93} -17.7378 q^{94} +16.4997 q^{95} +7.84311 q^{96} -14.5945 q^{97} -8.23676 q^{98} +0.806562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

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