LMFDB - Embedded newform 1027.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1027,2,Mod(1,1027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1027, 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("1027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1027 = 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1027.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:	$8.20063628759$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58989 q^{2} -0.636530 q^{3} +4.70755 q^{4} +2.12345 q^{5} +1.64855 q^{6} +0.927268 q^{7} -7.01226 q^{8} -2.59483 q^{9} +O(q^{10})$	\(q-2.58989 q^{2} -0.636530 q^{3} +4.70755 q^{4} +2.12345 q^{5} +1.64855 q^{6} +0.927268 q^{7} -7.01226 q^{8} -2.59483 q^{9} -5.49952 q^{10} +2.14644 q^{11} -2.99650 q^{12} +1.00000 q^{13} -2.40153 q^{14} -1.35164 q^{15} +8.74591 q^{16} +3.66492 q^{17} +6.72033 q^{18} -2.80156 q^{19} +9.99625 q^{20} -0.590234 q^{21} -5.55905 q^{22} +4.49312 q^{23} +4.46351 q^{24} -0.490949 q^{25} -2.58989 q^{26} +3.56128 q^{27} +4.36516 q^{28} +6.98981 q^{29} +3.50061 q^{30} -1.84862 q^{31} -8.62645 q^{32} -1.36627 q^{33} -9.49175 q^{34} +1.96901 q^{35} -12.2153 q^{36} +7.60072 q^{37} +7.25573 q^{38} -0.636530 q^{39} -14.8902 q^{40} +2.51957 q^{41} +1.52864 q^{42} -6.69294 q^{43} +10.1045 q^{44} -5.51000 q^{45} -11.6367 q^{46} -3.40153 q^{47} -5.56703 q^{48} -6.14017 q^{49} +1.27150 q^{50} -2.33283 q^{51} +4.70755 q^{52} -4.08151 q^{53} -9.22333 q^{54} +4.55786 q^{55} -6.50224 q^{56} +1.78328 q^{57} -18.1029 q^{58} -6.41662 q^{59} -6.36292 q^{60} -6.68755 q^{61} +4.78772 q^{62} -2.40610 q^{63} +4.84977 q^{64} +2.12345 q^{65} +3.53850 q^{66} +9.41841 q^{67} +17.2528 q^{68} -2.86001 q^{69} -5.09953 q^{70} +10.3509 q^{71} +18.1956 q^{72} +8.30024 q^{73} -19.6851 q^{74} +0.312504 q^{75} -13.1885 q^{76} +1.99032 q^{77} +1.64855 q^{78} -1.00000 q^{79} +18.5715 q^{80} +5.51763 q^{81} -6.52543 q^{82} +10.2717 q^{83} -2.77856 q^{84} +7.78229 q^{85} +17.3340 q^{86} -4.44922 q^{87} -15.0514 q^{88} +4.39908 q^{89} +14.2703 q^{90} +0.927268 q^{91} +21.1516 q^{92} +1.17670 q^{93} +8.80959 q^{94} -5.94897 q^{95} +5.49099 q^{96} +9.61600 q^{97} +15.9024 q^{98} -5.56964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 9 q^{2} + 4 q^{3} + 23 q^{4} + 17 q^{5} + 2 q^{6} + 8 q^{7} + 21 q^{8} + 17 q^{9}+O(q^{10}) $ 21 * q + 9 * q^2 + 4 * q^3 + 23 * q^4 + 17 * q^5 + 2 * q^6 + 8 * q^7 + 21 * q^8 + 17 * q^9	\( 21 q + 9 q^{2} + 4 q^{3} + 23 q^{4} + 17 q^{5} + 2 q^{6} + 8 q^{7} + 21 q^{8} + 17 q^{9} + 2 q^{10} + 10 q^{11} + 11 q^{12} + 21 q^{13} + 4 q^{14} + 6 q^{15} + 19 q^{16} + 13 q^{17} + 22 q^{18} + 3 q^{19} + 17 q^{20} + 12 q^{21} - 2 q^{22} + 5 q^{23} - 6 q^{24} + 22 q^{25} + 9 q^{26} + q^{27} + 11 q^{28} + 36 q^{29} + 24 q^{30} + 5 q^{31} + 26 q^{32} - 8 q^{34} - 6 q^{35} - 11 q^{36} + 32 q^{37} + 5 q^{38} + 4 q^{39} - 6 q^{40} + 53 q^{41} + q^{42} + 11 q^{43} + 21 q^{44} + 4 q^{45} - 16 q^{46} + 27 q^{47} - 23 q^{48} - 3 q^{49} + 7 q^{50} - 2 q^{51} + 23 q^{52} + 43 q^{53} - 2 q^{54} - 20 q^{55} + 23 q^{56} + 21 q^{57} - 16 q^{58} + 17 q^{59} + 36 q^{60} + 4 q^{61} - 36 q^{62} - q^{63} + 37 q^{64} + 17 q^{65} - 32 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} + 19 q^{70} + 24 q^{71} - 35 q^{72} + 31 q^{73} - 18 q^{74} - 34 q^{75} - 22 q^{76} + 53 q^{77} + 2 q^{78} - 21 q^{79} + 12 q^{80} + 9 q^{81} + 18 q^{82} + 21 q^{83} - 29 q^{84} - q^{85} + 63 q^{86} - 4 q^{87} - 14 q^{88} + 24 q^{89} - 4 q^{90} + 8 q^{91} + 8 q^{92} + 7 q^{93} - 6 q^{94} + 19 q^{95} + 10 q^{96} + 14 q^{97} - 30 q^{98} + 28 q^{99}+O(q^{100}) \) 21 * q + 9 * q^2 + 4 * q^3 + 23 * q^4 + 17 * q^5 + 2 * q^6 + 8 * q^7 + 21 * q^8 + 17 * q^9 + 2 * q^10 + 10 * q^11 + 11 * q^12 + 21 * q^13 + 4 * q^14 + 6 * q^15 + 19 * q^16 + 13 * q^17 + 22 * q^18 + 3 * q^19 + 17 * q^20 + 12 * q^21 - 2 * q^22 + 5 * q^23 - 6 * q^24 + 22 * q^25 + 9 * q^26 + q^27 + 11 * q^28 + 36 * q^29 + 24 * q^30 + 5 * q^31 + 26 * q^32 - 8 * q^34 - 6 * q^35 - 11 * q^36 + 32 * q^37 + 5 * q^38 + 4 * q^39 - 6 * q^40 + 53 * q^41 + q^42 + 11 * q^43 + 21 * q^44 + 4 * q^45 - 16 * q^46 + 27 * q^47 - 23 * q^48 - 3 * q^49 + 7 * q^50 - 2 * q^51 + 23 * q^52 + 43 * q^53 - 2 * q^54 - 20 * q^55 + 23 * q^56 + 21 * q^57 - 16 * q^58 + 17 * q^59 + 36 * q^60 + 4 * q^61 - 36 * q^62 - q^63 + 37 * q^64 + 17 * q^65 - 32 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 + 19 * q^70 + 24 * q^71 - 35 * q^72 + 31 * q^73 - 18 * q^74 - 34 * q^75 - 22 * q^76 + 53 * q^77 + 2 * q^78 - 21 * q^79 + 12 * q^80 + 9 * q^81 + 18 * q^82 + 21 * q^83 - 29 * q^84 - q^85 + 63 * q^86 - 4 * q^87 - 14 * q^88 + 24 * q^89 - 4 * q^90 + 8 * q^91 + 8 * q^92 + 7 * q^93 - 6 * q^94 + 19 * q^95 + 10 * q^96 + 14 * q^97 - 30 * q^98 + 28 * 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 $

$2$	−2.58989	−1.83133	−0.915666	−	0.401941i	$-0.868336\pi$
$2$	−2.58989	−1.83133	−0.915666	+	0.401941i	$0.868336\pi$
$3$	−0.636530	−0.367501	−0.183750	−	0.982973i	$-0.558824\pi$
$3$	−0.636530	−0.367501	−0.183750	+	0.982973i	$0.558824\pi$
$4$	4.70755	2.35377
$5$	2.12345	0.949637	0.474818	−	0.880084i	$-0.342514\pi$
$5$	2.12345	0.949637	0.474818	+	0.880084i	$0.342514\pi$
$6$	1.64855	0.673016
$7$	0.927268	0.350474	0.175237	−	0.984526i	$-0.443931\pi$
$7$	0.927268	0.350474	0.175237	+	0.984526i	$0.443931\pi$
$8$	−7.01226	−2.47921
$9$	−2.59483	−0.864943
$10$	−5.49952	−1.73910
$11$	2.14644	0.647175	0.323588	−	0.946198i	$-0.395111\pi$
$11$	2.14644	0.647175	0.323588	+	0.946198i	$0.395111\pi$
$12$	−2.99650	−0.865014
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.40153	−0.641835
$15$	−1.35164	−0.348992
$16$	8.74591	2.18648
$17$	3.66492	0.888874	0.444437	−	0.895810i	$-0.353404\pi$
$17$	3.66492	0.888874	0.444437	+	0.895810i	$0.353404\pi$
$18$	6.72033	1.58400
$19$	−2.80156	−0.642721	−0.321361	−	0.946957i	$-0.604140\pi$
$19$	−2.80156	−0.642721	−0.321361	+	0.946957i	$0.604140\pi$
$20$	9.99625	2.23523
$21$	−0.590234	−0.128800
$22$	−5.55905	−1.18519
$23$	4.49312	0.936880	0.468440	−	0.883495i	$-0.344816\pi$
$23$	4.49312	0.936880	0.468440	+	0.883495i	$0.344816\pi$
$24$	4.46351	0.911111
$25$	−0.490949	−0.0981897
$26$	−2.58989	−0.507920
$27$	3.56128	0.685368
$28$	4.36516	0.824938
$29$	6.98981	1.29797	0.648987	−	0.760799i	$-0.275193\pi$
$29$	6.98981	1.29797	0.648987	+	0.760799i	$0.275193\pi$
$30$	3.50061	0.639121
$31$	−1.84862	−0.332021	−0.166011	−	0.986124i	$-0.553089\pi$
$31$	−1.84862	−0.332021	−0.166011	+	0.986124i	$0.553089\pi$
$32$	−8.62645	−1.52495
$33$	−1.36627	−0.237838
$34$	−9.49175	−1.62782
$35$	1.96901	0.332823
$36$	−12.2153	−2.03588
$37$	7.60072	1.24955	0.624776	−	0.780804i	$-0.285190\pi$
$37$	7.60072	1.24955	0.624776	+	0.780804i	$0.285190\pi$
$38$	7.25573	1.17704
$39$	−0.636530	−0.101926
$40$	−14.8902	−2.35435
$41$	2.51957	0.393491	0.196746	−	0.980455i	$-0.436963\pi$
$41$	2.51957	0.393491	0.196746	+	0.980455i	$0.436963\pi$
$42$	1.52864	0.235875
$43$	−6.69294	−1.02066	−0.510332	−	0.859977i	$-0.670478\pi$
$43$	−6.69294	−1.02066	−0.510332	+	0.859977i	$0.670478\pi$
$44$	10.1045	1.52330
$45$	−5.51000	−0.821382
$46$	−11.6367	−1.71574
$47$	−3.40153	−0.496163	−0.248082	−	0.968739i	$-0.579800\pi$
$47$	−3.40153	−0.496163	−0.248082	+	0.968739i	$0.579800\pi$
$48$	−5.56703	−0.803532
$49$	−6.14017	−0.877168
$50$	1.27150	0.179818
$51$	−2.33283	−0.326662
$52$	4.70755	0.652819
$53$	−4.08151	−0.560639	−0.280320	−	0.959907i	$-0.590440\pi$
$53$	−4.08151	−0.560639	−0.280320	+	0.959907i	$0.590440\pi$
$54$	−9.22333	−1.25514
$55$	4.55786	0.614582
$56$	−6.50224	−0.868899
$57$	1.78328	0.236201
$58$	−18.1029	−2.37702
$59$	−6.41662	−0.835372	−0.417686	−	0.908591i	$-0.637159\pi$
$59$	−6.41662	−0.835372	−0.417686	+	0.908591i	$0.637159\pi$
$60$	−6.36292	−0.821449
$61$	−6.68755	−0.856253	−0.428126	−	0.903719i	$-0.640826\pi$
$61$	−6.68755	−0.856253	−0.428126	+	0.903719i	$0.640826\pi$
$62$	4.78772	0.608041
$63$	−2.40610	−0.303140
$64$	4.84977	0.606221
$65$	2.12345	0.263382
$66$	3.53850	0.435559
$67$	9.41841	1.15064	0.575321	−	0.817928i	$-0.304877\pi$
$67$	9.41841	1.15064	0.575321	+	0.817928i	$0.304877\pi$
$68$	17.2528	2.09221
$69$	−2.86001	−0.344304
$70$	−5.09953	−0.609510
$71$	10.3509	1.22843	0.614213	−	0.789140i	$-0.289473\pi$
$71$	10.3509	1.22843	0.614213	+	0.789140i	$0.289473\pi$
$72$	18.1956	2.14437
$73$	8.30024	0.971469	0.485735	−	0.874106i	$-0.338552\pi$
$73$	8.30024	0.971469	0.485735	+	0.874106i	$0.338552\pi$
$74$	−19.6851	−2.28834
$75$	0.312504	0.0360848
$76$	−13.1885	−1.51282
$77$	1.99032	0.226818
$78$	1.64855	0.186661
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	18.5715	2.07636
$81$	5.51763	0.613070
$82$	−6.52543	−0.720613
$83$	10.2717	1.12746	0.563732	−	0.825958i	$-0.309365\pi$
$83$	10.2717	1.12746	0.563732	+	0.825958i	$0.309365\pi$
$84$	−2.77856	−0.303165
$85$	7.78229	0.844108
$86$	17.3340	1.86917
$87$	−4.44922	−0.477007
$88$	−15.0514	−1.60448
$89$	4.39908	0.466301	0.233151	−	0.972441i	$-0.425097\pi$
$89$	4.39908	0.466301	0.233151	+	0.972441i	$0.425097\pi$
$90$	14.2703	1.50422
$91$	0.927268	0.0972041
$92$	21.1516	2.20520
$93$	1.17670	0.122018
$94$	8.80959	0.908640
$95$	−5.94897	−0.610352
$96$	5.49099	0.560422
$97$	9.61600	0.976357	0.488178	−	0.872744i	$-0.337662\pi$
$97$	9.61600	0.976357	0.488178	+	0.872744i	$0.337662\pi$
$98$	15.9024	1.60638
$99$	−5.56964	−0.559770
$100$	−2.31116	−0.231116
$101$	9.94972	0.990035	0.495017	−	0.868883i	$-0.335162\pi$
$101$	9.94972	0.990035	0.495017	+	0.868883i	$0.335162\pi$
$102$	6.04179	0.598226
$103$	−4.78857	−0.471831	−0.235916	−	0.971774i	$-0.575809\pi$
$103$	−4.78857	−0.471831	−0.235916	+	0.971774i	$0.575809\pi$
$104$	−7.01226	−0.687608
$105$	−1.25333	−0.122313
$106$	10.5707	1.02672
$107$	9.85578	0.952794	0.476397	−	0.879230i	$-0.341942\pi$
$107$	9.85578	0.952794	0.476397	+	0.879230i	$0.341942\pi$
$108$	16.7649	1.61320
$109$	−1.70440	−0.163252	−0.0816258	−	0.996663i	$-0.526011\pi$
$109$	−1.70440	−0.163252	−0.0816258	+	0.996663i	$0.526011\pi$
$110$	−11.8044	−1.12550
$111$	−4.83809	−0.459211
$112$	8.10980	0.766304
$113$	19.8285	1.86530	0.932652	−	0.360776i	$-0.117488\pi$
$113$	19.8285	1.86530	0.932652	+	0.360776i	$0.117488\pi$
$114$	−4.61849	−0.432562
$115$	9.54093	0.889696
$116$	32.9048	3.05514
$117$	−2.59483	−0.239892
$118$	16.6183	1.52984
$119$	3.39837	0.311528
$120$	9.47806	0.865225
$121$	−6.39280	−0.581164
$122$	17.3200	1.56808
$123$	−1.60378	−0.144608
$124$	−8.70245	−0.781503
$125$	−11.6598	−1.04288
$126$	6.23155	0.555151
$127$	−0.686774	−0.0609414	−0.0304707	−	0.999536i	$-0.509701\pi$
$127$	−0.686774	−0.0609414	−0.0304707	+	0.999536i	$0.509701\pi$
$128$	4.69252	0.414764
$129$	4.26026	0.375095
$130$	−5.49952	−0.482339
$131$	−10.9094	−0.953162	−0.476581	−	0.879131i	$-0.658124\pi$
$131$	−10.9094	−0.953162	−0.476581	+	0.879131i	$0.658124\pi$
$132$	−6.43179	−0.559816
$133$	−2.59780	−0.225257
$134$	−24.3927	−2.10721
$135$	7.56221	0.650851
$136$	−25.6994	−2.20370
$137$	−10.3984	−0.888392	−0.444196	−	0.895930i	$-0.646511\pi$
$137$	−10.3984	−0.888392	−0.444196	+	0.895930i	$0.646511\pi$
$138$	7.40711	0.630535
$139$	4.96853	0.421425	0.210712	−	0.977548i	$-0.432422\pi$
$139$	4.96853	0.421425	0.210712	+	0.977548i	$0.432422\pi$
$140$	9.26921	0.783391
$141$	2.16517	0.182341
$142$	−26.8077	−2.24966
$143$	2.14644	0.179494
$144$	−22.6941	−1.89118
$145$	14.8425	1.23260
$146$	−21.4967	−1.77908
$147$	3.90841	0.322360
$148$	35.7808	2.94116
$149$	2.17155	0.177900	0.0889500	−	0.996036i	$-0.471649\pi$
$149$	2.17155	0.177900	0.0889500	+	0.996036i	$0.471649\pi$
$150$	−0.809351	−0.0660832
$151$	6.36132	0.517677	0.258839	−	0.965921i	$-0.416660\pi$
$151$	6.36132	0.517677	0.258839	+	0.965921i	$0.416660\pi$
$152$	19.6452	1.59344
$153$	−9.50984	−0.768825
$154$	−5.15473	−0.415380
$155$	−3.92545	−0.315300
$156$	−2.99650	−0.239912
$157$	3.62543	0.289341	0.144670	−	0.989480i	$-0.453788\pi$
$157$	3.62543	0.289341	0.144670	+	0.989480i	$0.453788\pi$
$158$	2.58989	0.206041
$159$	2.59801	0.206035
$160$	−18.3179	−1.44815
$161$	4.16633	0.328353
$162$	−14.2901	−1.12273
$163$	14.2869	1.11903	0.559516	−	0.828819i	$-0.310987\pi$
$163$	14.2869	1.11903	0.559516	+	0.828819i	$0.310987\pi$
$164$	11.8610	0.926189
$165$	−2.90122	−0.225859
$166$	−26.6026	−2.06476
$167$	12.7998	0.990476	0.495238	−	0.868757i	$-0.335081\pi$
$167$	12.7998	0.990476	0.495238	+	0.868757i	$0.335081\pi$
$168$	4.13888	0.319321
$169$	1.00000	0.0769231
$170$	−20.1553	−1.54584
$171$	7.26956	0.555917
$172$	−31.5074	−2.40241
$173$	−22.8848	−1.73990	−0.869950	−	0.493140i	$-0.835849\pi$
$173$	−22.8848	−1.73990	−0.869950	+	0.493140i	$0.835849\pi$
$174$	11.5230	0.873557
$175$	−0.455241	−0.0344130
$176$	18.7725	1.41503
$177$	4.08437	0.307000
$178$	−11.3931	−0.853952
$179$	−6.36757	−0.475935	−0.237967	−	0.971273i	$-0.576481\pi$
$179$	−6.36757	−0.475935	−0.237967	+	0.971273i	$0.576481\pi$
$180$	−25.9386	−1.93335
$181$	3.57014	0.265366	0.132683	−	0.991159i	$-0.457641\pi$
$181$	3.57014	0.265366	0.132683	+	0.991159i	$0.457641\pi$
$182$	−2.40153	−0.178013
$183$	4.25683	0.314674
$184$	−31.5069	−2.32272
$185$	16.1398	1.18662
$186$	−3.04753	−0.223456
$187$	7.86653	0.575257
$188$	−16.0128	−1.16786
$189$	3.30226	0.240204
$190$	15.4072	1.11776
$191$	−8.29043	−0.599875	−0.299937	−	0.953959i	$-0.596966\pi$
$191$	−8.29043	−0.599875	−0.299937	+	0.953959i	$0.596966\pi$
$192$	−3.08702	−0.222787
$193$	19.5181	1.40494	0.702471	−	0.711712i	$-0.252080\pi$
$193$	19.5181	1.40494	0.702471	+	0.711712i	$0.252080\pi$
$194$	−24.9044	−1.78803
$195$	−1.35164	−0.0967931
$196$	−28.9052	−2.06465
$197$	21.5398	1.53465	0.767323	−	0.641261i	$-0.221588\pi$
$197$	21.5398	1.53465	0.767323	+	0.641261i	$0.221588\pi$
$198$	14.4248	1.02512
$199$	−0.954017	−0.0676285	−0.0338143	−	0.999428i	$-0.510765\pi$
$199$	−0.954017	−0.0676285	−0.0338143	+	0.999428i	$0.510765\pi$
$200$	3.44266	0.243433
$201$	−5.99510	−0.422862
$202$	−25.7687	−1.81308
$203$	6.48143	0.454907
$204$	−10.9819	−0.768888
$205$	5.35020	0.373674
$206$	12.4019	0.864080
$207$	−11.6589	−0.810348
$208$	8.74591	0.606419
$209$	−6.01337	−0.415953
$210$	3.24600	0.223995
$211$	−14.9678	−1.03043	−0.515214	−	0.857062i	$-0.672287\pi$
$211$	−14.9678	−1.03043	−0.515214	+	0.857062i	$0.672287\pi$
$212$	−19.2139	−1.31962
$213$	−6.58866	−0.451448
$214$	−25.5254	−1.74488
$215$	−14.2122	−0.969261
$216$	−24.9726	−1.69917
$217$	−1.71416	−0.116365
$218$	4.41421	0.298968
$219$	−5.28335	−0.357016
$220$	21.4563	1.44659
$221$	3.66492	0.246529
$222$	12.5301	0.840968
$223$	−16.4205	−1.09960	−0.549799	−	0.835297i	$-0.685296\pi$
$223$	−16.4205	−1.09960	−0.549799	+	0.835297i	$0.685296\pi$
$224$	−7.99903	−0.534458
$225$	1.27393	0.0849285
$226$	−51.3536	−3.41599
$227$	−4.32917	−0.287337	−0.143669	−	0.989626i	$-0.545890\pi$
$227$	−4.32917	−0.287337	−0.143669	+	0.989626i	$0.545890\pi$
$228$	8.39486	0.555963
$229$	20.0520	1.32507	0.662536	−	0.749030i	$-0.269480\pi$
$229$	20.0520	1.32507	0.662536	+	0.749030i	$0.269480\pi$
$230$	−24.7100	−1.62933
$231$	−1.26690	−0.0833560
$232$	−49.0143	−3.21795
$233$	18.5029	1.21217	0.606083	−	0.795401i	$-0.292740\pi$
$233$	18.5029	1.21217	0.606083	+	0.795401i	$0.292740\pi$
$234$	6.72033	0.439322
$235$	−7.22298	−0.471175
$236$	−30.2065	−1.96628
$237$	0.636530	0.0413471
$238$	−8.80140	−0.570510
$239$	11.7770	0.761793	0.380897	−	0.924618i	$-0.375615\pi$
$239$	11.7770	0.761793	0.380897	+	0.924618i	$0.375615\pi$
$240$	−11.8213	−0.763064
$241$	3.49781	0.225314	0.112657	−	0.993634i	$-0.464064\pi$
$241$	3.49781	0.225314	0.112657	+	0.993634i	$0.464064\pi$
$242$	16.5567	1.06430
$243$	−14.1960	−0.910672
$244$	−31.4820	−2.01543
$245$	−13.0384	−0.832991
$246$	4.15363	0.264826
$247$	−2.80156	−0.178259
$248$	12.9630	0.823150
$249$	−6.53824	−0.414344
$250$	30.1976	1.90986
$251$	−8.20567	−0.517937	−0.258969	−	0.965886i	$-0.583383\pi$
$251$	−8.20567	−0.517937	−0.258969	+	0.965886i	$0.583383\pi$
$252$	−11.3268	−0.713524
$253$	9.64420	0.606326
$254$	1.77867	0.111604
$255$	−4.95366	−0.310210
$256$	−21.8527	−1.36579
$257$	19.2384	1.20006	0.600030	−	0.799978i	$-0.295155\pi$
$257$	19.2384	1.20006	0.600030	+	0.799978i	$0.295155\pi$
$258$	−11.0336	−0.686923
$259$	7.04791	0.437936
$260$	9.99625	0.619941
$261$	−18.1374	−1.12267
$262$	28.2543	1.74555
$263$	−17.5080	−1.07959	−0.539793	−	0.841798i	$-0.681498\pi$
$263$	−17.5080	−1.07959	−0.539793	+	0.841798i	$0.681498\pi$
$264$	9.58066	0.589649
$265$	−8.66690	−0.532404
$266$	6.72801	0.412521
$267$	−2.80014	−0.171366
$268$	44.3376	2.70835
$269$	12.2476	0.746747	0.373374	−	0.927681i	$-0.378201\pi$
$269$	12.2476	0.746747	0.373374	+	0.927681i	$0.378201\pi$
$270$	−19.5853	−1.19192
$271$	18.4581	1.12125	0.560625	−	0.828070i	$-0.310561\pi$
$271$	18.4581	1.12125	0.560625	+	0.828070i	$0.310561\pi$
$272$	32.0531	1.94350
$273$	−0.590234	−0.0357226
$274$	26.9306	1.62694
$275$	−1.05379	−0.0635460
$276$	−13.4636	−0.810415
$277$	9.00184	0.540868	0.270434	−	0.962739i	$-0.412833\pi$
$277$	9.00184	0.540868	0.270434	+	0.962739i	$0.412833\pi$
$278$	−12.8680	−0.771768
$279$	4.79685	0.287180
$280$	−13.8072	−0.825139
$281$	17.6714	1.05419	0.527093	−	0.849808i	$-0.323282\pi$
$281$	17.6714	1.05419	0.527093	+	0.849808i	$0.323282\pi$
$282$	−5.60757	−0.333926
$283$	−6.07812	−0.361307	−0.180653	−	0.983547i	$-0.557821\pi$
$283$	−6.07812	−0.361307	−0.180653	+	0.983547i	$0.557821\pi$
$284$	48.7274	2.89144
$285$	3.78670	0.224305
$286$	−5.55905	−0.328713
$287$	2.33632	0.137909
$288$	22.3842	1.31900
$289$	−3.56835	−0.209903
$290$	−38.4405	−2.25731
$291$	−6.12087	−0.358812
$292$	39.0738	2.28662
$293$	13.8140	0.807024	0.403512	−	0.914974i	$-0.367789\pi$
$293$	13.8140	0.807024	0.403512	+	0.914974i	$0.367789\pi$
$294$	−10.1224	−0.590348
$295$	−13.6254	−0.793300
$296$	−53.2982	−3.09790
$297$	7.64406	0.443553
$298$	−5.62408	−0.325794
$299$	4.49312	0.259844
$300$	1.47113	0.0849355
$301$	−6.20615	−0.357717
$302$	−16.4751	−0.948038
$303$	−6.33330	−0.363839
$304$	−24.5022	−1.40530
$305$	−14.2007	−0.813129
$306$	24.6295	1.40797
$307$	−6.06756	−0.346294	−0.173147	−	0.984896i	$-0.555394\pi$
$307$	−6.06756	−0.346294	−0.173147	+	0.984896i	$0.555394\pi$
$308$	9.36954	0.533879
$309$	3.04807	0.173398
$310$	10.1665	0.577418
$311$	−10.2476	−0.581091	−0.290545	−	0.956861i	$-0.593837\pi$
$311$	−10.2476	−0.581091	−0.290545	+	0.956861i	$0.593837\pi$
$312$	4.46351	0.252697
$313$	−15.7552	−0.890535	−0.445268	−	0.895398i	$-0.646891\pi$
$313$	−15.7552	−0.890535	−0.445268	+	0.895398i	$0.646891\pi$
$314$	−9.38948	−0.529879
$315$	−5.10925	−0.287873
$316$	−4.70755	−0.264820
$317$	−15.2556	−0.856840	−0.428420	−	0.903580i	$-0.640930\pi$
$317$	−15.2556	−0.856840	−0.428420	+	0.903580i	$0.640930\pi$
$318$	−6.72856	−0.377319
$319$	15.0032	0.840017
$320$	10.2982	0.575690
$321$	−6.27350	−0.350153
$322$	−10.7903	−0.601322
$323$	−10.2675	−0.571298
$324$	25.9745	1.44303
$325$	−0.490949	−0.0272329
$326$	−37.0014	−2.04932
$327$	1.08490	0.0599951
$328$	−17.6679	−0.975547
$329$	−3.15413	−0.173893
$330$	7.51384	0.413623
$331$	−16.8602	−0.926718	−0.463359	−	0.886171i	$-0.653356\pi$
$331$	−16.8602	−0.926718	−0.463359	+	0.886171i	$0.653356\pi$
$332$	48.3544	2.65380
$333$	−19.7226	−1.08079
$334$	−33.1500	−1.81389
$335$	19.9996	1.09269
$336$	−5.16213	−0.281617
$337$	33.8594	1.84444	0.922218	−	0.386670i	$-0.126375\pi$
$337$	33.8594	1.84444	0.922218	+	0.386670i	$0.126375\pi$
$338$	−2.58989	−0.140872
$339$	−12.6214	−0.685501
$340$	36.6355	1.98684
$341$	−3.96794	−0.214876
$342$	−18.8274	−1.01807
$343$	−12.1845	−0.657899
$344$	46.9327	2.53044
$345$	−6.07309	−0.326964
$346$	59.2692	3.18633
$347$	12.1472	0.652093	0.326047	−	0.945354i	$-0.394283\pi$
$347$	12.1472	0.652093	0.326047	+	0.945354i	$0.394283\pi$
$348$	−20.9449	−1.12277
$349$	−7.65794	−0.409920	−0.204960	−	0.978770i	$-0.565706\pi$
$349$	−7.65794	−0.409920	−0.204960	+	0.978770i	$0.565706\pi$
$350$	1.17903	0.0630216
$351$	3.56128	0.190087
$352$	−18.5161	−0.986913
$353$	−25.8504	−1.37588	−0.687939	−	0.725769i	$-0.741484\pi$
$353$	−25.8504	−1.37588	−0.687939	+	0.725769i	$0.741484\pi$
$354$	−10.5781	−0.562219
$355$	21.9797	1.16656
$356$	20.7089	1.09757
$357$	−2.16316	−0.114487
$358$	16.4913	0.871594
$359$	−29.2144	−1.54188	−0.770938	−	0.636910i	$-0.780212\pi$
$359$	−29.2144	−1.54188	−0.770938	+	0.636910i	$0.780212\pi$
$360$	38.6375	2.03638
$361$	−11.1513	−0.586909
$362$	−9.24627	−0.485973
$363$	4.06921	0.213578
$364$	4.36516	0.228797
$365$	17.6252	0.922543
$366$	−11.0247	−0.576272
$367$	−19.6619	−1.02634	−0.513172	−	0.858286i	$-0.671530\pi$
$367$	−19.6619	−1.02634	−0.513172	+	0.858286i	$0.671530\pi$
$368$	39.2964	2.04847
$369$	−6.53786	−0.340348
$370$	−41.8003	−2.17309
$371$	−3.78466	−0.196490
$372$	5.53937	0.287203
$373$	3.80996	0.197272	0.0986362	−	0.995124i	$-0.468552\pi$
$373$	3.80996	0.197272	0.0986362	+	0.995124i	$0.468552\pi$
$374$	−20.3735	−1.05349
$375$	7.42180	0.383260
$376$	23.8524	1.23009
$377$	6.98981	0.359993
$378$	−8.55250	−0.439893
$379$	−26.9407	−1.38385	−0.691926	−	0.721968i	$-0.743238\pi$
$379$	−26.9407	−1.38385	−0.691926	+	0.721968i	$0.743238\pi$
$380$	−28.0051	−1.43663
$381$	0.437153	0.0223960
$382$	21.4713	1.09857
$383$	−14.5935	−0.745694	−0.372847	−	0.927893i	$-0.621618\pi$
$383$	−14.5935	−0.745694	−0.372847	+	0.927893i	$0.621618\pi$
$384$	−2.98693	−0.152426
$385$	4.22636	0.215395
$386$	−50.5498	−2.57291
$387$	17.3670	0.882817
$388$	45.2678	2.29812
$389$	22.3649	1.13395	0.566974	−	0.823736i	$-0.308114\pi$
$389$	22.3649	1.13395	0.566974	+	0.823736i	$0.308114\pi$
$390$	3.50061	0.177260
$391$	16.4669	0.832769
$392$	43.0565	2.17468
$393$	6.94418	0.350288
$394$	−55.7858	−2.81045
$395$	−2.12345	−0.106843
$396$	−26.2193	−1.31757
$397$	11.6119	0.582785	0.291393	−	0.956604i	$-0.405881\pi$
$397$	11.6119	0.582785	0.291393	+	0.956604i	$0.405881\pi$
$398$	2.47080	0.123850
$399$	1.65358	0.0827823
$400$	−4.29379	−0.214690
$401$	8.00284	0.399643	0.199821	−	0.979832i	$-0.435964\pi$
$401$	8.00284	0.399643	0.199821	+	0.979832i	$0.435964\pi$
$402$	15.5267	0.774400
$403$	−1.84862	−0.0920862
$404$	46.8388	2.33032
$405$	11.7164	0.582194
$406$	−16.7862	−0.833085
$407$	16.3145	0.808679
$408$	16.3584	0.809863
$409$	10.2973	0.509170	0.254585	−	0.967050i	$-0.418061\pi$
$409$	10.2973	0.509170	0.254585	+	0.967050i	$0.418061\pi$
$410$	−13.8564	−0.684321
$411$	6.61887	0.326485
$412$	−22.5424	−1.11058
$413$	−5.94992	−0.292777
$414$	30.1953	1.48402
$415$	21.8114	1.07068
$416$	−8.62645	−0.422946
$417$	−3.16262	−0.154874
$418$	15.5740	0.761748
$419$	−15.2934	−0.747132	−0.373566	−	0.927604i	$-0.621865\pi$
$419$	−15.2934	−0.747132	−0.373566	+	0.927604i	$0.621865\pi$
$420$	−5.90013	−0.287897
$421$	−32.4966	−1.58379	−0.791895	−	0.610658i	$-0.790905\pi$
$421$	−32.4966	−1.58379	−0.791895	+	0.610658i	$0.790905\pi$
$422$	38.7651	1.88705
$423$	8.82638	0.429153
$424$	28.6206	1.38994
$425$	−1.79929	−0.0872783
$426$	17.0639	0.826750
$427$	−6.20115	−0.300095
$428$	46.3966	2.24266
$429$	−1.36627	−0.0659643
$430$	36.8080	1.77504
$431$	−14.4337	−0.695247	−0.347624	−	0.937634i	$-0.613011\pi$
$431$	−14.4337	−0.695247	−0.347624	+	0.937634i	$0.613011\pi$
$432$	31.1466	1.49854
$433$	−22.1088	−1.06248	−0.531240	−	0.847222i	$-0.678274\pi$
$433$	−22.1088	−1.06248	−0.531240	+	0.847222i	$0.678274\pi$
$434$	4.43950	0.213103
$435$	−9.44771	−0.452983
$436$	−8.02353	−0.384257
$437$	−12.5877	−0.602153
$438$	13.6833	0.653814
$439$	−24.2241	−1.15615	−0.578076	−	0.815983i	$-0.696196\pi$
$439$	−24.2241	−1.15615	−0.578076	+	0.815983i	$0.696196\pi$
$440$	−31.9609	−1.52368
$441$	15.9327	0.758700
$442$	−9.49175	−0.451477
$443$	−9.90528	−0.470614	−0.235307	−	0.971921i	$-0.575610\pi$
$443$	−9.90528	−0.470614	−0.235307	+	0.971921i	$0.575610\pi$
$444$	−22.7755	−1.08088
$445$	9.34123	0.442817
$446$	42.5274	2.01373
$447$	−1.38226	−0.0653784
$448$	4.49703	0.212465
$449$	−0.856509	−0.0404212	−0.0202106	−	0.999796i	$-0.506434\pi$
$449$	−0.856509	−0.0404212	−0.0202106	+	0.999796i	$0.506434\pi$
$450$	−3.29934	−0.155532
$451$	5.40811	0.254658
$452$	93.3434	4.39051
$453$	−4.04917	−0.190247
$454$	11.2121	0.526210
$455$	1.96901	0.0923086
$456$	−12.5048	−0.585591
$457$	−3.90166	−0.182512	−0.0912560	−	0.995827i	$-0.529088\pi$
$457$	−3.90166	−0.182512	−0.0912560	+	0.995827i	$0.529088\pi$
$458$	−51.9325	−2.42665
$459$	13.0518	0.609206
$460$	44.9144	2.09414
$461$	13.6688	0.636618	0.318309	−	0.947987i	$-0.396885\pi$
$461$	13.6688	0.636618	0.318309	+	0.947987i	$0.396885\pi$
$462$	3.28114	0.152652
$463$	−33.4514	−1.55462	−0.777309	−	0.629119i	$-0.783416\pi$
$463$	−33.4514	−1.55462	−0.777309	+	0.629119i	$0.783416\pi$
$464$	61.1322	2.83799
$465$	2.49867	0.115873
$466$	−47.9206	−2.21988
$467$	−23.9405	−1.10783	−0.553917	−	0.832572i	$-0.686867\pi$
$467$	−23.9405	−1.10783	−0.553917	+	0.832572i	$0.686867\pi$
$468$	−12.2153	−0.564652
$469$	8.73339	0.403271
$470$	18.7067	0.862878
$471$	−2.30770	−0.106333
$472$	44.9950	2.07106
$473$	−14.3660	−0.660549
$474$	−1.64855	−0.0757202
$475$	1.37542	0.0631086
$476$	15.9980	0.733266
$477$	10.5908	0.484921
$478$	−30.5013	−1.39510
$479$	40.8823	1.86796	0.933980	−	0.357326i	$-0.116312\pi$
$479$	40.8823	1.86796	0.933980	+	0.357326i	$0.116312\pi$
$480$	11.6599	0.532198
$481$	7.60072	0.346563
$482$	−9.05895	−0.412624
$483$	−2.65199	−0.120670
$484$	−30.0944	−1.36793
$485$	20.4191	0.927184
$486$	36.7660	1.66774
$487$	3.58078	0.162260	0.0811302	−	0.996704i	$-0.474147\pi$
$487$	3.58078	0.162260	0.0811302	+	0.996704i	$0.474147\pi$
$488$	46.8948	2.12283
$489$	−9.09402	−0.411246
$490$	33.7680	1.52548
$491$	24.7587	1.11734	0.558672	−	0.829389i	$-0.311311\pi$
$491$	24.7587	1.11734	0.558672	+	0.829389i	$0.311311\pi$
$492$	−7.54989	−0.340375
$493$	25.6171	1.15374
$494$	7.25573	0.326451
$495$	−11.8269	−0.531578
$496$	−16.1678	−0.725957
$497$	9.59807	0.430532
$498$	16.9333	0.758801
$499$	−23.4086	−1.04791	−0.523955	−	0.851746i	$-0.675544\pi$
$499$	−23.4086	−1.04791	−0.523955	+	0.851746i	$0.675544\pi$
$500$	−54.8889	−2.45471
$501$	−8.14744	−0.364001
$502$	21.2518	0.948515
$503$	−41.0640	−1.83095	−0.915477	−	0.402370i	$-0.868186\pi$
$503$	−41.0640	−1.83095	−0.915477	+	0.402370i	$0.868186\pi$
$504$	16.8722	0.751548
$505$	21.1278	0.940173
$506$	−24.9775	−1.11038
$507$	−0.636530	−0.0282693
$508$	−3.23302	−0.143442
$509$	7.50562	0.332681	0.166340	−	0.986068i	$-0.446805\pi$
$509$	7.50562	0.332681	0.166340	+	0.986068i	$0.446805\pi$
$510$	12.8295	0.568098
$511$	7.69655	0.340475
$512$	47.2110	2.08645
$513$	−9.97712	−0.440501
$514$	−49.8254	−2.19771
$515$	−10.1683	−0.448069
$516$	20.0554	0.882889
$517$	−7.30116	−0.321105
$518$	−18.2533	−0.802006
$519$	14.5669	0.639415
$520$	−14.8902	−0.652978
$521$	24.8291	1.08778	0.543892	−	0.839156i	$-0.316950\pi$
$521$	24.8291	1.08778	0.543892	+	0.839156i	$0.316950\pi$
$522$	46.9738	2.05599
$523$	14.8123	0.647697	0.323849	−	0.946109i	$-0.395023\pi$
$523$	14.8123	0.647697	0.323849	+	0.946109i	$0.395023\pi$
$524$	−51.3567	−2.24353
$525$	0.289775	0.0126468
$526$	45.3437	1.97708
$527$	−6.77504	−0.295125
$528$	−11.9493	−0.520026
$529$	−2.81187	−0.122255
$530$	22.4464	0.975007
$531$	16.6500	0.722549
$532$	−12.2292	−0.530205
$533$	2.51957	0.109135
$534$	7.25208	0.313828
$535$	20.9283	0.904809
$536$	−66.0443	−2.85268
$537$	4.05315	0.174906
$538$	−31.7199	−1.36754
$539$	−13.1795	−0.567681
$540$	35.5994	1.53196
$541$	−18.9739	−0.815751	−0.407876	−	0.913037i	$-0.633730\pi$
$541$	−18.9739	−0.815751	−0.407876	+	0.913037i	$0.633730\pi$
$542$	−47.8045	−2.05338
$543$	−2.27250	−0.0975223
$544$	−31.6152	−1.35549
$545$	−3.61921	−0.155030
$546$	1.52864	0.0654199
$547$	24.1363	1.03199	0.515997	−	0.856591i	$-0.327422\pi$
$547$	24.1363	1.03199	0.515997	+	0.856591i	$0.327422\pi$
$548$	−48.9508	−2.09107
$549$	17.3530	0.740610
$550$	2.72921	0.116374
$551$	−19.5823	−0.834236
$552$	20.0551	0.853602
$553$	−0.927268	−0.0394315
$554$	−23.3138	−0.990508
$555$	−10.2735	−0.436084
$556$	23.3896	0.991939
$557$	−43.4345	−1.84038	−0.920189	−	0.391474i	$-0.871965\pi$
$557$	−43.4345	−1.84038	−0.920189	+	0.391474i	$0.871965\pi$
$558$	−12.4233	−0.525921
$559$	−6.69294	−0.283081
$560$	17.2208	0.727711
$561$	−5.00728	−0.211408
$562$	−45.7669	−1.93056
$563$	8.24984	0.347690	0.173845	−	0.984773i	$-0.444381\pi$
$563$	8.24984	0.347690	0.173845	+	0.984773i	$0.444381\pi$
$564$	10.1927	0.429188
$565$	42.1048	1.77136
$566$	15.7417	0.661673
$567$	5.11632	0.214865
$568$	−72.5832	−3.04552
$569$	16.4012	0.687573	0.343786	−	0.939048i	$-0.388290\pi$
$569$	16.4012	0.687573	0.343786	+	0.939048i	$0.388290\pi$
$570$	−9.80715	−0.410777
$571$	−19.5875	−0.819711	−0.409856	−	0.912150i	$-0.634421\pi$
$571$	−19.5875	−0.819711	−0.409856	+	0.912150i	$0.634421\pi$
$572$	10.1045	0.422489
$573$	5.27711	0.220455
$574$	−6.05082	−0.252556
$575$	−2.20589	−0.0919920
$576$	−12.5843	−0.524346
$577$	40.9002	1.70270	0.851348	−	0.524601i	$-0.175786\pi$
$577$	40.9002	1.70270	0.851348	+	0.524601i	$0.175786\pi$
$578$	9.24165	0.384402
$579$	−12.4238	−0.516318
$580$	69.8719	2.90127
$581$	9.52461	0.395147
$582$	15.8524	0.657104
$583$	−8.76072	−0.362832
$584$	−58.2034	−2.40847
$585$	−5.51000	−0.227810
$586$	−35.7768	−1.47793
$587$	−47.3263	−1.95337	−0.976684	−	0.214683i	$-0.931128\pi$
$587$	−47.3263	−1.95337	−0.976684	+	0.214683i	$0.931128\pi$
$588$	18.3990	0.758762
$589$	5.17901	0.213397
$590$	35.2883	1.45280
$591$	−13.7107	−0.563984
$592$	66.4752	2.73211
$593$	−28.2652	−1.16071	−0.580357	−	0.814362i	$-0.697087\pi$
$593$	−28.2652	−1.16071	−0.580357	+	0.814362i	$0.697087\pi$
$594$	−19.7973	−0.812293
$595$	7.21627	0.295838
$596$	10.2227	0.418737
$597$	0.607261	0.0248535
$598$	−11.6367	−0.475860
$599$	−35.6219	−1.45547	−0.727737	−	0.685857i	$-0.759428\pi$
$599$	−35.6219	−1.45547	−0.727737	+	0.685857i	$0.759428\pi$
$600$	−2.19136	−0.0894617
$601$	8.79248	0.358653	0.179326	−	0.983790i	$-0.442608\pi$
$601$	8.79248	0.358653	0.179326	+	0.983790i	$0.442608\pi$
$602$	16.0733	0.655098
$603$	−24.4392	−0.995240
$604$	29.9462	1.21849
$605$	−13.5748	−0.551895
$606$	16.4026	0.666309
$607$	−22.9664	−0.932177	−0.466089	−	0.884738i	$-0.654337\pi$
$607$	−22.9664	−0.932177	−0.466089	+	0.884738i	$0.654337\pi$
$608$	24.1675	0.980121
$609$	−4.12562	−0.167179
$610$	36.7783	1.48911
$611$	−3.40153	−0.137611
$612$	−44.7680	−1.80964
$613$	−10.3754	−0.419059	−0.209530	−	0.977802i	$-0.567193\pi$
$613$	−10.3754	−0.419059	−0.209530	+	0.977802i	$0.567193\pi$
$614$	15.7143	0.634179
$615$	−3.40556	−0.137325
$616$	−13.9567	−0.562330
$617$	−24.5774	−0.989447	−0.494723	−	0.869050i	$-0.664731\pi$
$617$	−24.5774	−0.989447	−0.494723	+	0.869050i	$0.664731\pi$
$618$	−7.89417	−0.317550
$619$	8.28415	0.332968	0.166484	−	0.986044i	$-0.446759\pi$
$619$	8.28415	0.332968	0.166484	+	0.986044i	$0.446759\pi$
$620$	−18.4792	−0.742144
$621$	16.0013	0.642108
$622$	26.5403	1.06417
$623$	4.07912	0.163427
$624$	−5.56703	−0.222860
$625$	−22.3042	−0.892169
$626$	40.8042	1.63086
$627$	3.82769	0.152863
$628$	17.0669	0.681043
$629$	27.8561	1.11069
$630$	13.2324	0.527191
$631$	−4.50939	−0.179516	−0.0897580	−	0.995964i	$-0.528609\pi$
$631$	−4.50939	−0.179516	−0.0897580	+	0.995964i	$0.528609\pi$
$632$	7.01226	0.278933
$633$	9.52747	0.378683
$634$	39.5104	1.56916
$635$	−1.45833	−0.0578722
$636$	12.2302	0.484961
$637$	−6.14017	−0.243283
$638$	−38.8566	−1.53835
$639$	−26.8588	−1.06252
$640$	9.96434	0.393875
$641$	−16.9448	−0.669279	−0.334640	−	0.942346i	$-0.608615\pi$
$641$	−16.9448	−0.669279	−0.334640	+	0.942346i	$0.608615\pi$
$642$	16.2477	0.641246
$643$	6.13272	0.241851	0.120925	−	0.992662i	$-0.461414\pi$
$643$	6.13272	0.241851	0.120925	+	0.992662i	$0.461414\pi$
$644$	19.6132	0.772868
$645$	9.04646	0.356204
$646$	26.5917	1.04624
$647$	−4.89052	−0.192266	−0.0961331	−	0.995368i	$-0.530647\pi$
$647$	−4.89052	−0.192266	−0.0961331	+	0.995368i	$0.530647\pi$
$648$	−38.6910	−1.51993
$649$	−13.7729	−0.540632
$650$	1.27150	0.0498725
$651$	1.09112	0.0427643
$652$	67.2560	2.63395
$653$	−23.3515	−0.913816	−0.456908	−	0.889514i	$-0.651043\pi$
$653$	−23.3515	−0.913816	−0.456908	+	0.889514i	$0.651043\pi$
$654$	−2.80978	−0.109871
$655$	−23.1657	−0.905157
$656$	22.0360	0.860359
$657$	−21.5377	−0.840265
$658$	8.16885	0.318455
$659$	35.9790	1.40154	0.700772	−	0.713385i	$-0.252839\pi$
$659$	35.9790	1.40154	0.700772	+	0.713385i	$0.252839\pi$
$660$	−13.6576	−0.531622
$661$	20.5631	0.799812	0.399906	−	0.916556i	$-0.369043\pi$
$661$	20.5631	0.799812	0.399906	+	0.916556i	$0.369043\pi$
$662$	43.6660	1.69713
$663$	−2.33283	−0.0905997
$664$	−72.0277	−2.79522
$665$	−5.51630	−0.213913
$666$	51.0794	1.97929
$667$	31.4060	1.21605
$668$	60.2555	2.33136
$669$	10.4522	0.404104
$670$	−51.7967	−2.00108
$671$	−14.3544	−0.554146
$672$	5.09162	0.196414
$673$	−1.61455	−0.0622362	−0.0311181	−	0.999516i	$-0.509907\pi$
$673$	−1.61455	−0.0622362	−0.0311181	+	0.999516i	$0.509907\pi$
$674$	−87.6921	−3.37777
$675$	−1.74840	−0.0672961
$676$	4.70755	0.181060
$677$	−31.3118	−1.20341	−0.601705	−	0.798718i	$-0.705512\pi$
$677$	−31.3118	−1.20341	−0.601705	+	0.798718i	$0.705512\pi$
$678$	32.6881	1.25538
$679$	8.91661	0.342188
$680$	−54.5714	−2.09272
$681$	2.75565	0.105597
$682$	10.2765	0.393509
$683$	50.6696	1.93882	0.969408	−	0.245453i	$-0.0789368\pi$
$683$	50.6696	1.93882	0.969408	+	0.245453i	$0.0789368\pi$
$684$	34.2218	1.30850
$685$	−22.0804	−0.843650
$686$	31.5565	1.20483
$687$	−12.7637	−0.486965
$688$	−58.5359	−2.23166
$689$	−4.08151	−0.155493
$690$	15.7287	0.598780
$691$	−28.0156	−1.06576	−0.532881	−	0.846190i	$-0.678891\pi$
$691$	−28.0156	−1.06576	−0.532881	+	0.846190i	$0.678891\pi$
$692$	−107.731	−4.09533
$693$	−5.16455	−0.196185
$694$	−31.4598	−1.19420
$695$	10.5504	0.400201
$696$	31.1991	1.18260
$697$	9.23404	0.349764
$698$	19.8333	0.750700
$699$	−11.7777	−0.445472
$700$	−2.14307	−0.0810004
$701$	−29.0163	−1.09593	−0.547965	−	0.836501i	$-0.684597\pi$
$701$	−29.0163	−1.09593	−0.547965	+	0.836501i	$0.684597\pi$
$702$	−9.22333	−0.348112
$703$	−21.2939	−0.803113
$704$	10.4097	0.392331
$705$	4.59764	0.173157
$706$	66.9498	2.51969
$707$	9.22606	0.346982
$708$	19.2274	0.722609
$709$	−31.1166	−1.16861	−0.584305	−	0.811534i	$-0.698633\pi$
$709$	−31.1166	−1.16861	−0.584305	+	0.811534i	$0.698633\pi$
$710$	−56.9250	−2.13636
$711$	2.59483	0.0973137
$712$	−30.8475	−1.15606
$713$	−8.30606	−0.311064
$714$	5.60236	0.209663
$715$	4.55786	0.170454
$716$	−29.9757	−1.12024
$717$	−7.49644	−0.279960
$718$	75.6622	2.82369
$719$	−39.4038	−1.46951	−0.734757	−	0.678330i	$-0.762704\pi$
$719$	−39.4038	−1.46951	−0.734757	+	0.678330i	$0.762704\pi$
$720$	−48.1899	−1.79593
$721$	−4.44029	−0.165365
$722$	28.8806	1.07483
$723$	−2.22646	−0.0828030
$724$	16.8066	0.624612
$725$	−3.43164	−0.127448
$726$	−10.5388	−0.391133
$727$	49.8154	1.84755	0.923775	−	0.382936i	$-0.125087\pi$
$727$	49.8154	1.84755	0.923775	+	0.382936i	$0.125087\pi$
$728$	−6.50224	−0.240989
$729$	−7.51672	−0.278397
$730$	−45.6473	−1.68948
$731$	−24.5291	−0.907242
$732$	20.0392	0.740671
$733$	−13.4733	−0.497648	−0.248824	−	0.968549i	$-0.580044\pi$
$733$	−13.4733	−0.497648	−0.248824	+	0.968549i	$0.580044\pi$
$734$	50.9223	1.87958
$735$	8.29932	0.306125
$736$	−38.7597	−1.42870
$737$	20.2160	0.744667
$738$	16.9324	0.623289
$739$	19.4989	0.717277	0.358639	−	0.933476i	$-0.383241\pi$
$739$	19.4989	0.717277	0.358639	+	0.933476i	$0.383241\pi$
$740$	75.9788	2.79304
$741$	1.78328	0.0655103
$742$	9.80186	0.359838
$743$	−39.9730	−1.46647	−0.733233	−	0.679977i	$-0.761990\pi$
$743$	−39.9730	−1.46647	−0.733233	+	0.679977i	$0.761990\pi$
$744$	−8.25133	−0.302508
$745$	4.61118	0.168940
$746$	−9.86740	−0.361271
$747$	−26.6533	−0.975192
$748$	37.0320	1.35403
$749$	9.13895	0.333930
$750$	−19.2217	−0.701876
$751$	40.5501	1.47969	0.739846	−	0.672776i	$-0.234898\pi$
$751$	40.5501	1.47969	0.739846	+	0.672776i	$0.234898\pi$
$752$	−29.7494	−1.08485
$753$	5.22316	0.190342
$754$	−18.1029	−0.659267
$755$	13.5080	0.491605
$756$	15.5455	0.565386
$757$	15.2954	0.555921	0.277961	−	0.960592i	$-0.410341\pi$
$757$	15.2954	0.555921	0.277961	+	0.960592i	$0.410341\pi$
$758$	69.7736	2.53429
$759$	−6.13883	−0.222825
$760$	41.7157	1.51319
$761$	−7.01389	−0.254253	−0.127127	−	0.991886i	$-0.540575\pi$
$761$	−7.01389	−0.254253	−0.127127	+	0.991886i	$0.540575\pi$
$762$	−1.13218	−0.0410145
$763$	−1.58043	−0.0572155
$764$	−39.0276	−1.41197
$765$	−20.1937	−0.730105
$766$	37.7956	1.36561
$767$	−6.41662	−0.231691
$768$	13.9099	0.501929
$769$	8.93818	0.322319	0.161160	−	0.986928i	$-0.448477\pi$
$769$	8.93818	0.322319	0.161160	+	0.986928i	$0.448477\pi$
$770$	−10.9458	−0.394460
$771$	−12.2458	−0.441023
$772$	91.8823	3.30692
$773$	49.2304	1.77069	0.885346	−	0.464932i	$-0.153921\pi$
$773$	49.2304	1.77069	0.885346	+	0.464932i	$0.153921\pi$
$774$	−44.9788	−1.61673
$775$	0.907576	0.0326011
$776$	−67.4299	−2.42059
$777$	−4.48621	−0.160942
$778$	−57.9228	−2.07663
$779$	−7.05873	−0.252905
$780$	−6.36292	−0.227829
$781$	22.2176	0.795007
$782$	−42.6476	−1.52508
$783$	24.8926	0.889590
$784$	−53.7014	−1.91791
$785$	7.69843	0.274769
$786$	−17.9847	−0.641493
$787$	−1.68609	−0.0601028	−0.0300514	−	0.999548i	$-0.509567\pi$
$787$	−1.68609	−0.0601028	−0.0300514	+	0.999548i	$0.509567\pi$
$788$	101.400	3.61221
$789$	11.1443	0.396749
$790$	5.49952	0.195664
$791$	18.3863	0.653742
$792$	39.0558	1.38779
$793$	−6.68755	−0.237482
$794$	−30.0736	−1.06727
$795$	5.51675	0.195659
$796$	−4.49108	−0.159182
$797$	−38.1162	−1.35014	−0.675072	−	0.737752i	$-0.735887\pi$
$797$	−38.1162	−1.35014	−0.675072	+	0.737752i	$0.735887\pi$
$798$	−4.28258	−0.151602
$799$	−12.4663	−0.441027
$800$	4.23514	0.149735
$801$	−11.4148	−0.403324
$802$	−20.7265	−0.731878
$803$	17.8159	0.628711
$804$	−28.2222	−0.995321
$805$	8.84700	0.311816
$806$	4.78772	0.168640
$807$	−7.79595	−0.274430
$808$	−69.7700	−2.45450
$809$	37.5730	1.32100	0.660498	−	0.750828i	$-0.270345\pi$
$809$	37.5730	1.32100	0.660498	+	0.750828i	$0.270345\pi$
$810$	−30.3443	−1.06619
$811$	−8.92007	−0.313226	−0.156613	−	0.987660i	$-0.550058\pi$
$811$	−8.92007	−0.313226	−0.156613	+	0.987660i	$0.550058\pi$
$812$	30.5116	1.07075
$813$	−11.7491	−0.412060
$814$	−42.2528	−1.48096
$815$	30.3375	1.06267
$816$	−20.4027	−0.714239
$817$	18.7507	0.656003
$818$	−26.6690	−0.932459
$819$	−2.40610	−0.0840760
$820$	25.1863	0.879544
$821$	9.68753	0.338097	0.169049	−	0.985608i	$-0.445931\pi$
$821$	9.68753	0.338097	0.169049	+	0.985608i	$0.445931\pi$
$822$	−17.1422	−0.597902
$823$	−22.2053	−0.774029	−0.387014	−	0.922074i	$-0.626494\pi$
$823$	−22.2053	−0.774029	−0.387014	+	0.922074i	$0.626494\pi$
$824$	33.5787	1.16977
$825$	0.670770	0.0233532
$826$	15.4097	0.536171
$827$	−5.36382	−0.186518	−0.0932592	−	0.995642i	$-0.529729\pi$
$827$	−5.36382	−0.186518	−0.0932592	+	0.995642i	$0.529729\pi$
$828$	−54.8847	−1.90738
$829$	2.12808	0.0739111	0.0369556	−	0.999317i	$-0.488234\pi$
$829$	2.12808	0.0739111	0.0369556	+	0.999317i	$0.488234\pi$
$830$	−56.4893	−1.96077
$831$	−5.72994	−0.198769
$832$	4.84977	0.168135
$833$	−22.5033	−0.779691
$834$	8.19084	0.283626
$835$	27.1797	0.940593
$836$	−28.3082	−0.979060
$837$	−6.58344	−0.227557
$838$	39.6083	1.36825
$839$	27.4129	0.946398	0.473199	−	0.880956i	$-0.343099\pi$
$839$	27.4129	0.946398	0.473199	+	0.880956i	$0.343099\pi$
$840$	8.78871	0.303239
$841$	19.8574	0.684738
$842$	84.1628	2.90044
$843$	−11.2484	−0.387414
$844$	−70.4617	−2.42539
$845$	2.12345	0.0730490
$846$	−22.8594	−0.785922
$847$	−5.92784	−0.203683
$848$	−35.6965	−1.22582
$849$	3.86891	0.132781
$850$	4.65996	0.159835
$851$	34.1510	1.17068
$852$	−31.0164	−1.06261
$853$	−28.9849	−0.992424	−0.496212	−	0.868202i	$-0.665276\pi$
$853$	−28.9849	−0.992424	−0.496212	+	0.868202i	$0.665276\pi$
$854$	16.0603	0.549573
$855$	15.4366	0.527920
$856$	−69.1113	−2.36218
$857$	8.53182	0.291441	0.145721	−	0.989326i	$-0.453450\pi$
$857$	8.53182	0.291441	0.145721	+	0.989326i	$0.453450\pi$
$858$	3.53850	0.120802
$859$	30.9911	1.05740	0.528701	−	0.848808i	$-0.322679\pi$
$859$	30.9911	1.05740	0.528701	+	0.848808i	$0.322679\pi$
$860$	−66.9044	−2.28142
$861$	−1.48714	−0.0506816
$862$	37.3818	1.27323
$863$	−44.3014	−1.50804	−0.754019	−	0.656852i	$-0.771887\pi$
$863$	−44.3014	−1.50804	−0.754019	+	0.656852i	$0.771887\pi$
$864$	−30.7212	−1.04516
$865$	−48.5948	−1.65227
$866$	57.2593	1.94575
$867$	2.27136	0.0771396
$868$	−8.06951	−0.273897
$869$	−2.14644	−0.0728129
$870$	24.4686	0.829562
$871$	9.41841	0.319131
$872$	11.9517	0.404735
$873$	−24.9519	−0.844493
$874$	32.6009	1.10274
$875$	−10.8117	−0.365503
$876$	−24.8716	−0.840334
$877$	−14.7855	−0.499270	−0.249635	−	0.968340i	$-0.580311\pi$
$877$	−14.7855	−0.499270	−0.249635	+	0.968340i	$0.580311\pi$
$878$	62.7378	2.11730
$879$	−8.79304	−0.296582
$880$	39.8626	1.34377
$881$	7.22660	0.243470	0.121735	−	0.992563i	$-0.461154\pi$
$881$	7.22660	0.243470	0.121735	+	0.992563i	$0.461154\pi$
$882$	−41.2640	−1.38943
$883$	−22.5064	−0.757402	−0.378701	−	0.925519i	$-0.623629\pi$
$883$	−22.5064	−0.757402	−0.378701	+	0.925519i	$0.623629\pi$
$884$	17.2528	0.580274
$885$	8.67297	0.291539
$886$	25.6536	0.861850
$887$	17.7005	0.594326	0.297163	−	0.954827i	$-0.403960\pi$
$887$	17.7005	0.594326	0.297163	+	0.954827i	$0.403960\pi$
$888$	33.9259	1.13848
$889$	−0.636824	−0.0213584
$890$	−24.1928	−0.810944
$891$	11.8432	0.396764
$892$	−77.3003	−2.58821
$893$	9.52957	0.318895
$894$	3.57989	0.119730
$895$	−13.5212	−0.451965
$896$	4.35123	0.145364
$897$	−2.86001	−0.0954929
$898$	2.21827	0.0740245
$899$	−12.9215	−0.430955
$900$	5.99707	0.199902
$901$	−14.9584	−0.498338
$902$	−14.0064	−0.466363
$903$	3.95041	0.131461
$904$	−139.042	−4.62448
$905$	7.58101	0.252001
$906$	10.4869	0.348405
$907$	−42.6846	−1.41732	−0.708660	−	0.705550i	$-0.750700\pi$
$907$	−42.6846	−1.41732	−0.708660	+	0.705550i	$0.750700\pi$
$908$	−20.3798	−0.676327
$909$	−25.8178	−0.856324
$910$	−5.09953	−0.169048
$911$	−2.02085	−0.0669537	−0.0334769	−	0.999439i	$-0.510658\pi$
$911$	−2.02085	−0.0669537	−0.0334769	+	0.999439i	$0.510658\pi$
$912$	15.5964	0.516447
$913$	22.0475	0.729667
$914$	10.1049	0.334240
$915$	9.03917	0.298826
$916$	94.3956	3.11892
$917$	−10.1160	−0.334059
$918$	−33.8028	−1.11566
$919$	−4.67768	−0.154302	−0.0771512	−	0.997019i	$-0.524582\pi$
$919$	−4.67768	−0.154302	−0.0771512	+	0.997019i	$0.524582\pi$
$920$	−66.9035	−2.20574
$921$	3.86219	0.127263
$922$	−35.4006	−1.16586
$923$	10.3509	0.340704
$924$	−5.96400	−0.196201
$925$	−3.73156	−0.122693
$926$	86.6355	2.84702
$927$	12.4255	0.408107
$928$	−60.2972	−1.97935
$929$	2.21179	0.0725666	0.0362833	−	0.999342i	$-0.488448\pi$
$929$	2.21179	0.0725666	0.0362833	+	0.999342i	$0.488448\pi$
$930$	−6.47128	−0.212202
$931$	17.2020	0.563774
$932$	87.1034	2.85317
$933$	6.52294	0.213551
$934$	62.0033	2.02881
$935$	16.7042	0.546286
$936$	18.1956	0.594742
$937$	51.8556	1.69405	0.847025	−	0.531553i	$-0.178391\pi$
$937$	51.8556	1.69405	0.847025	+	0.531553i	$0.178391\pi$
$938$	−22.6186	−0.738522
$939$	10.0286	0.327272
$940$	−34.0025	−1.10904
$941$	−31.2612	−1.01909	−0.509543	−	0.860445i	$-0.670185\pi$
$941$	−31.2612	−1.01909	−0.509543	+	0.860445i	$0.670185\pi$
$942$	5.97669	0.194731
$943$	11.3207	0.368654
$944$	−56.1191	−1.82652
$945$	7.01219	0.228107
$946$	37.2064	1.20968
$947$	58.2826	1.89393	0.946965	−	0.321336i	$-0.104132\pi$
$947$	58.2826	1.89393	0.946965	+	0.321336i	$0.104132\pi$
$948$	2.99650	0.0973217
$949$	8.30024	0.269437
$950$	−3.56219	−0.115573
$951$	9.71065	0.314889
$952$	−23.8302	−0.772342
$953$	−47.6094	−1.54222	−0.771109	−	0.636703i	$-0.780298\pi$
$953$	−47.6094	−1.54222	−0.771109	+	0.636703i	$0.780298\pi$
$954$	−27.4291	−0.888051
$955$	−17.6043	−0.569663
$956$	55.4409	1.79309
$957$	−9.54998	−0.308707
$958$	−105.881	−3.42085
$959$	−9.64207	−0.311359
$960$	−6.55515	−0.211566
$961$	−27.5826	−0.889762
$962$	−19.6851	−0.634672
$963$	−25.5741	−0.824113
$964$	16.4661	0.530337
$965$	41.4457	1.33419
$966$	6.86838	0.220987
$967$	21.5201	0.692040	0.346020	−	0.938227i	$-0.387533\pi$
$967$	21.5201	0.692040	0.346020	+	0.938227i	$0.387533\pi$
$968$	44.8280	1.44083
$969$	6.53557	0.209953
$970$	−52.8833	−1.69798
$971$	−23.1981	−0.744461	−0.372231	−	0.928140i	$-0.621407\pi$
$971$	−23.1981	−0.744461	−0.372231	+	0.928140i	$0.621407\pi$
$972$	−66.8282	−2.14352
$973$	4.60716	0.147699
$974$	−9.27383	−0.297153
$975$	0.312504	0.0100081
$976$	−58.4887	−1.87218
$977$	−40.4940	−1.29552	−0.647759	−	0.761845i	$-0.724294\pi$
$977$	−40.4940	−1.29552	−0.647759	+	0.761845i	$0.724294\pi$
$978$	23.5525	0.753127
$979$	9.44234	0.301779
$980$	−61.3787	−1.96067
$981$	4.42262	0.141203
$982$	−64.1224	−2.04623
$983$	6.85809	0.218739	0.109370	−	0.994001i	$-0.465117\pi$
$983$	6.85809	0.218739	0.109370	+	0.994001i	$0.465117\pi$
$984$	11.2462	0.358514
$985$	45.7387	1.45736
$986$	−66.3455	−2.11287
$987$	2.00770	0.0639057
$988$	−13.1885	−0.419581
$989$	−30.0722	−0.956241
$990$	30.6303	0.973496
$991$	17.0729	0.542340	0.271170	−	0.962532i	$-0.412589\pi$
$991$	17.0729	0.542340	0.271170	+	0.962532i	$0.412589\pi$
$992$	15.9470	0.506318
$993$	10.7320	0.340570
$994$	−24.8580	−0.788447
$995$	−2.02581	−0.0642225
$996$	−30.7791	−0.975272
$997$	7.47508	0.236738	0.118369	−	0.992970i	$-0.462233\pi$
$997$	7.47508	0.236738	0.118369	+	0.992970i	$0.462233\pi$
$998$	60.6257	1.91907
$999$	27.0683	0.856403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1027.2.a.d.1.1	✓	21
3.2	odd	2		9243.2.a.o.1.21		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1027.2.a.d.1.1	✓	21	1.1	even	1	trivial
9243.2.a.o.1.21		21	3.2	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:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58989 q^{2} -0.636530 q^{3} +4.70755 q^{4} +2.12345 q^{5} +1.64855 q^{6} +0.927268 q^{7} -7.01226 q^{8} -2.59483 q^{9} +O(q^{10})\)	\(q-2.58989 q^{2} -0.636530 q^{3} +4.70755 q^{4} +2.12345 q^{5} +1.64855 q^{6} +0.927268 q^{7} -7.01226 q^{8} -2.59483 q^{9} -5.49952 q^{10} +2.14644 q^{11} -2.99650 q^{12} +1.00000 q^{13} -2.40153 q^{14} -1.35164 q^{15} +8.74591 q^{16} +3.66492 q^{17} +6.72033 q^{18} -2.80156 q^{19} +9.99625 q^{20} -0.590234 q^{21} -5.55905 q^{22} +4.49312 q^{23} +4.46351 q^{24} -0.490949 q^{25} -2.58989 q^{26} +3.56128 q^{27} +4.36516 q^{28} +6.98981 q^{29} +3.50061 q^{30} -1.84862 q^{31} -8.62645 q^{32} -1.36627 q^{33} -9.49175 q^{34} +1.96901 q^{35} -12.2153 q^{36} +7.60072 q^{37} +7.25573 q^{38} -0.636530 q^{39} -14.8902 q^{40} +2.51957 q^{41} +1.52864 q^{42} -6.69294 q^{43} +10.1045 q^{44} -5.51000 q^{45} -11.6367 q^{46} -3.40153 q^{47} -5.56703 q^{48} -6.14017 q^{49} +1.27150 q^{50} -2.33283 q^{51} +4.70755 q^{52} -4.08151 q^{53} -9.22333 q^{54} +4.55786 q^{55} -6.50224 q^{56} +1.78328 q^{57} -18.1029 q^{58} -6.41662 q^{59} -6.36292 q^{60} -6.68755 q^{61} +4.78772 q^{62} -2.40610 q^{63} +4.84977 q^{64} +2.12345 q^{65} +3.53850 q^{66} +9.41841 q^{67} +17.2528 q^{68} -2.86001 q^{69} -5.09953 q^{70} +10.3509 q^{71} +18.1956 q^{72} +8.30024 q^{73} -19.6851 q^{74} +0.312504 q^{75} -13.1885 q^{76} +1.99032 q^{77} +1.64855 q^{78} -1.00000 q^{79} +18.5715 q^{80} +5.51763 q^{81} -6.52543 q^{82} +10.2717 q^{83} -2.77856 q^{84} +7.78229 q^{85} +17.3340 q^{86} -4.44922 q^{87} -15.0514 q^{88} +4.39908 q^{89} +14.2703 q^{90} +0.927268 q^{91} +21.1516 q^{92} +1.17670 q^{93} +8.80959 q^{94} -5.94897 q^{95} +5.49099 q^{96} +9.61600 q^{97} +15.9024 q^{98} -5.56964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 9 q^{2} + 4 q^{3} + 23 q^{4} + 17 q^{5} + 2 q^{6} + 8 q^{7} + 21 q^{8} + 17 q^{9}+O(q^{10}) \) 21 * q + 9 * q^2 + 4 * q^3 + 23 * q^4 + 17 * q^5 + 2 * q^6 + 8 * q^7 + 21 * q^8 + 17 * q^9	\( 21 q + 9 q^{2} + 4 q^{3} + 23 q^{4} + 17 q^{5} + 2 q^{6} + 8 q^{7} + 21 q^{8} + 17 q^{9} + 2 q^{10} + 10 q^{11} + 11 q^{12} + 21 q^{13} + 4 q^{14} + 6 q^{15} + 19 q^{16} + 13 q^{17} + 22 q^{18} + 3 q^{19} + 17 q^{20} + 12 q^{21} - 2 q^{22} + 5 q^{23} - 6 q^{24} + 22 q^{25} + 9 q^{26} + q^{27} + 11 q^{28} + 36 q^{29} + 24 q^{30} + 5 q^{31} + 26 q^{32} - 8 q^{34} - 6 q^{35} - 11 q^{36} + 32 q^{37} + 5 q^{38} + 4 q^{39} - 6 q^{40} + 53 q^{41} + q^{42} + 11 q^{43} + 21 q^{44} + 4 q^{45} - 16 q^{46} + 27 q^{47} - 23 q^{48} - 3 q^{49} + 7 q^{50} - 2 q^{51} + 23 q^{52} + 43 q^{53} - 2 q^{54} - 20 q^{55} + 23 q^{56} + 21 q^{57} - 16 q^{58} + 17 q^{59} + 36 q^{60} + 4 q^{61} - 36 q^{62} - q^{63} + 37 q^{64} + 17 q^{65} - 32 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} + 19 q^{70} + 24 q^{71} - 35 q^{72} + 31 q^{73} - 18 q^{74} - 34 q^{75} - 22 q^{76} + 53 q^{77} + 2 q^{78} - 21 q^{79} + 12 q^{80} + 9 q^{81} + 18 q^{82} + 21 q^{83} - 29 q^{84} - q^{85} + 63 q^{86} - 4 q^{87} - 14 q^{88} + 24 q^{89} - 4 q^{90} + 8 q^{91} + 8 q^{92} + 7 q^{93} - 6 q^{94} + 19 q^{95} + 10 q^{96} + 14 q^{97} - 30 q^{98} + 28 q^{99}+O(q^{100}) \) 21 * q + 9 * q^2 + 4 * q^3 + 23 * q^4 + 17 * q^5 + 2 * q^6 + 8 * q^7 + 21 * q^8 + 17 * q^9 + 2 * q^10 + 10 * q^11 + 11 * q^12 + 21 * q^13 + 4 * q^14 + 6 * q^15 + 19 * q^16 + 13 * q^17 + 22 * q^18 + 3 * q^19 + 17 * q^20 + 12 * q^21 - 2 * q^22 + 5 * q^23 - 6 * q^24 + 22 * q^25 + 9 * q^26 + q^27 + 11 * q^28 + 36 * q^29 + 24 * q^30 + 5 * q^31 + 26 * q^32 - 8 * q^34 - 6 * q^35 - 11 * q^36 + 32 * q^37 + 5 * q^38 + 4 * q^39 - 6 * q^40 + 53 * q^41 + q^42 + 11 * q^43 + 21 * q^44 + 4 * q^45 - 16 * q^46 + 27 * q^47 - 23 * q^48 - 3 * q^49 + 7 * q^50 - 2 * q^51 + 23 * q^52 + 43 * q^53 - 2 * q^54 - 20 * q^55 + 23 * q^56 + 21 * q^57 - 16 * q^58 + 17 * q^59 + 36 * q^60 + 4 * q^61 - 36 * q^62 - q^63 + 37 * q^64 + 17 * q^65 - 32 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 + 19 * q^70 + 24 * q^71 - 35 * q^72 + 31 * q^73 - 18 * q^74 - 34 * q^75 - 22 * q^76 + 53 * q^77 + 2 * q^78 - 21 * q^79 + 12 * q^80 + 9 * q^81 + 18 * q^82 + 21 * q^83 - 29 * q^84 - q^85 + 63 * q^86 - 4 * q^87 - 14 * q^88 + 24 * q^89 - 4 * q^90 + 8 * q^91 + 8 * q^92 + 7 * q^93 - 6 * q^94 + 19 * q^95 + 10 * q^96 + 14 * q^97 - 30 * q^98 + 28 * q^99

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