LMFDB - Embedded newform 8049.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42396 q^{2} +1.00000 q^{3} +3.87556 q^{4} -3.49875 q^{5} -2.42396 q^{6} +3.65352 q^{7} -4.54627 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.42396 q^{2} +1.00000 q^{3} +3.87556 q^{4} -3.49875 q^{5} -2.42396 q^{6} +3.65352 q^{7} -4.54627 q^{8} +1.00000 q^{9} +8.48081 q^{10} +2.17370 q^{11} +3.87556 q^{12} +6.81364 q^{13} -8.85596 q^{14} -3.49875 q^{15} +3.26884 q^{16} -0.421441 q^{17} -2.42396 q^{18} -2.20721 q^{19} -13.5596 q^{20} +3.65352 q^{21} -5.26895 q^{22} +0.385037 q^{23} -4.54627 q^{24} +7.24123 q^{25} -16.5159 q^{26} +1.00000 q^{27} +14.1594 q^{28} +8.72492 q^{29} +8.48081 q^{30} -4.63064 q^{31} +1.16902 q^{32} +2.17370 q^{33} +1.02155 q^{34} -12.7827 q^{35} +3.87556 q^{36} +9.80107 q^{37} +5.35017 q^{38} +6.81364 q^{39} +15.9063 q^{40} -5.34627 q^{41} -8.85596 q^{42} +4.14906 q^{43} +8.42429 q^{44} -3.49875 q^{45} -0.933312 q^{46} -11.8649 q^{47} +3.26884 q^{48} +6.34819 q^{49} -17.5524 q^{50} -0.421441 q^{51} +26.4066 q^{52} +14.2918 q^{53} -2.42396 q^{54} -7.60522 q^{55} -16.6099 q^{56} -2.20721 q^{57} -21.1488 q^{58} +2.13849 q^{59} -13.5596 q^{60} -2.41510 q^{61} +11.2245 q^{62} +3.65352 q^{63} -9.37133 q^{64} -23.8392 q^{65} -5.26895 q^{66} +7.50974 q^{67} -1.63332 q^{68} +0.385037 q^{69} +30.9848 q^{70} +9.32563 q^{71} -4.54627 q^{72} +9.42477 q^{73} -23.7573 q^{74} +7.24123 q^{75} -8.55416 q^{76} +7.94164 q^{77} -16.5159 q^{78} -10.4022 q^{79} -11.4369 q^{80} +1.00000 q^{81} +12.9591 q^{82} +9.63330 q^{83} +14.1594 q^{84} +1.47451 q^{85} -10.0571 q^{86} +8.72492 q^{87} -9.88222 q^{88} -11.2943 q^{89} +8.48081 q^{90} +24.8937 q^{91} +1.49223 q^{92} -4.63064 q^{93} +28.7600 q^{94} +7.72246 q^{95} +1.16902 q^{96} +9.82385 q^{97} -15.3877 q^{98} +2.17370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * 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 $

$2$	−2.42396	−1.71400	−0.856998	−	0.515320i	$-0.827673\pi$
$2$	−2.42396	−1.71400	−0.856998	+	0.515320i	$0.827673\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.87556	1.93778
$5$	−3.49875	−1.56469	−0.782344	−	0.622847i	$-0.785976\pi$
$5$	−3.49875	−1.56469	−0.782344	+	0.622847i	$0.785976\pi$
$6$	−2.42396	−0.989576
$7$	3.65352	1.38090	0.690450	−	0.723380i	$-0.257413\pi$
$7$	3.65352	1.38090	0.690450	+	0.723380i	$0.257413\pi$
$8$	−4.54627	−1.60735
$9$	1.00000	0.333333
$10$	8.48081	2.68187
$11$	2.17370	0.655394	0.327697	−	0.944783i	$-0.393727\pi$
$11$	2.17370	0.655394	0.327697	+	0.944783i	$0.393727\pi$
$12$	3.87556	1.11878
$13$	6.81364	1.88976	0.944881	−	0.327413i	$-0.106177\pi$
$13$	6.81364	1.88976	0.944881	+	0.327413i	$0.106177\pi$
$14$	−8.85596	−2.36686
$15$	−3.49875	−0.903373
$16$	3.26884	0.817211
$17$	−0.421441	−0.102214	−0.0511072	−	0.998693i	$-0.516275\pi$
$17$	−0.421441	−0.102214	−0.0511072	+	0.998693i	$0.516275\pi$
$18$	−2.42396	−0.571332
$19$	−2.20721	−0.506368	−0.253184	−	0.967418i	$-0.581478\pi$
$19$	−2.20721	−0.506368	−0.253184	+	0.967418i	$0.581478\pi$
$20$	−13.5596	−3.03202
$21$	3.65352	0.797263
$22$	−5.26895	−1.12334
$23$	0.385037	0.0802857	0.0401429	−	0.999194i	$-0.487219\pi$
$23$	0.385037	0.0802857	0.0401429	+	0.999194i	$0.487219\pi$
$24$	−4.54627	−0.928004
$25$	7.24123	1.44825
$26$	−16.5159	−3.23904
$27$	1.00000	0.192450
$28$	14.1594	2.67588
$29$	8.72492	1.62018	0.810089	−	0.586307i	$-0.199419\pi$
$29$	8.72492	1.62018	0.810089	+	0.586307i	$0.199419\pi$
$30$	8.48081	1.54838
$31$	−4.63064	−0.831687	−0.415843	−	0.909436i	$-0.636514\pi$
$31$	−4.63064	−0.831687	−0.415843	+	0.909436i	$0.636514\pi$
$32$	1.16902	0.206655
$33$	2.17370	0.378392
$34$	1.02155	0.175195
$35$	−12.7827	−2.16068
$36$	3.87556	0.645927
$37$	9.80107	1.61129	0.805643	−	0.592402i	$-0.201820\pi$
$37$	9.80107	1.61129	0.805643	+	0.592402i	$0.201820\pi$
$38$	5.35017	0.867912
$39$	6.81364	1.09105
$40$	15.9063	2.51500
$41$	−5.34627	−0.834947	−0.417473	−	0.908689i	$-0.637084\pi$
$41$	−5.34627	−0.834947	−0.417473	+	0.908689i	$0.637084\pi$
$42$	−8.85596	−1.36650
$43$	4.14906	0.632726	0.316363	−	0.948638i	$-0.397538\pi$
$43$	4.14906	0.632726	0.316363	+	0.948638i	$0.397538\pi$
$44$	8.42429	1.27001
$45$	−3.49875	−0.521562
$46$	−0.933312	−0.137609
$47$	−11.8649	−1.73067	−0.865337	−	0.501191i	$-0.832895\pi$
$47$	−11.8649	−1.73067	−0.865337	+	0.501191i	$0.832895\pi$
$48$	3.26884	0.471817
$49$	6.34819	0.906884
$50$	−17.5524	−2.48229
$51$	−0.421441	−0.0590135
$52$	26.4066	3.66194
$53$	14.2918	1.96313	0.981565	−	0.191127i	$-0.0612142\pi$
$53$	14.2918	1.96313	0.981565	+	0.191127i	$0.0612142\pi$
$54$	−2.42396	−0.329859
$55$	−7.60522	−1.02549
$56$	−16.6099	−2.21959
$57$	−2.20721	−0.292352
$58$	−21.1488	−2.77698
$59$	2.13849	0.278408	0.139204	−	0.990264i	$-0.455546\pi$
$59$	2.13849	0.278408	0.139204	+	0.990264i	$0.455546\pi$
$60$	−13.5596	−1.75054
$61$	−2.41510	−0.309221	−0.154611	−	0.987975i	$-0.549412\pi$
$61$	−2.41510	−0.309221	−0.154611	+	0.987975i	$0.549412\pi$
$62$	11.2245	1.42551
$63$	3.65352	0.460300
$64$	−9.37133	−1.17142
$65$	−23.8392	−2.95689
$66$	−5.26895	−0.648562
$67$	7.50974	0.917461	0.458730	−	0.888576i	$-0.348304\pi$
$67$	7.50974	0.917461	0.458730	+	0.888576i	$0.348304\pi$
$68$	−1.63332	−0.198069
$69$	0.385037	0.0463530
$70$	30.9848	3.70339
$71$	9.32563	1.10675	0.553374	−	0.832933i	$-0.313340\pi$
$71$	9.32563	1.10675	0.553374	+	0.832933i	$0.313340\pi$
$72$	−4.54627	−0.535783
$73$	9.42477	1.10309	0.551543	−	0.834146i	$-0.314039\pi$
$73$	9.42477	1.10309	0.551543	+	0.834146i	$0.314039\pi$
$74$	−23.7573	−2.76174
$75$	7.24123	0.836145
$76$	−8.55416	−0.981229
$77$	7.94164	0.905034
$78$	−16.5159	−1.87006
$79$	−10.4022	−1.17034	−0.585171	−	0.810910i	$-0.698973\pi$
$79$	−10.4022	−1.17034	−0.585171	+	0.810910i	$0.698973\pi$
$80$	−11.4369	−1.27868
$81$	1.00000	0.111111
$82$	12.9591	1.43110
$83$	9.63330	1.05739	0.528696	−	0.848811i	$-0.322681\pi$
$83$	9.63330	1.05739	0.528696	+	0.848811i	$0.322681\pi$
$84$	14.1594	1.54492
$85$	1.47451	0.159934
$86$	−10.0571	−1.08449
$87$	8.72492	0.935410
$88$	−9.88222	−1.05345
$89$	−11.2943	−1.19719	−0.598596	−	0.801051i	$-0.704274\pi$
$89$	−11.2943	−1.19719	−0.598596	+	0.801051i	$0.704274\pi$
$90$	8.48081	0.893956
$91$	24.8937	2.60957
$92$	1.49223	0.155576
$93$	−4.63064	−0.480175
$94$	28.7600	2.96637
$95$	7.72246	0.792307
$96$	1.16902	0.119312
$97$	9.82385	0.997461	0.498730	−	0.866757i	$-0.333800\pi$
$97$	9.82385	0.997461	0.498730	+	0.866757i	$0.333800\pi$
$98$	−15.3877	−1.55439
$99$	2.17370	0.218465
$100$	28.0638	2.80638
$101$	−2.59914	−0.258624	−0.129312	−	0.991604i	$-0.541277\pi$
$101$	−2.59914	−0.258624	−0.129312	+	0.991604i	$0.541277\pi$
$102$	1.02155	0.101149
$103$	5.14115	0.506573	0.253286	−	0.967391i	$-0.418488\pi$
$103$	5.14115	0.506573	0.253286	+	0.967391i	$0.418488\pi$
$104$	−30.9766	−3.03751
$105$	−12.7827	−1.24747
$106$	−34.6427	−3.36480
$107$	6.24347	0.603579	0.301789	−	0.953375i	$-0.402416\pi$
$107$	6.24347	0.603579	0.301789	+	0.953375i	$0.402416\pi$
$108$	3.87556	0.372926
$109$	7.53671	0.721886	0.360943	−	0.932588i	$-0.382455\pi$
$109$	7.53671	0.721886	0.360943	+	0.932588i	$0.382455\pi$
$110$	18.4347	1.75768
$111$	9.80107	0.930276
$112$	11.9428	1.12849
$113$	4.87856	0.458936	0.229468	−	0.973316i	$-0.426301\pi$
$113$	4.87856	0.458936	0.229468	+	0.973316i	$0.426301\pi$
$114$	5.35017	0.501089
$115$	−1.34715	−0.125622
$116$	33.8140	3.13955
$117$	6.81364	0.629921
$118$	−5.18360	−0.477189
$119$	−1.53974	−0.141148
$120$	15.9063	1.45204
$121$	−6.27504	−0.570458
$122$	5.85409	0.530004
$123$	−5.34627	−0.482057
$124$	−17.9463	−1.61163
$125$	−7.84150	−0.701365
$126$	−8.85596	−0.788952
$127$	−16.0446	−1.42372	−0.711862	−	0.702319i	$-0.752148\pi$
$127$	−16.0446	−1.42372	−0.711862	+	0.702319i	$0.752148\pi$
$128$	20.3777	1.80115
$129$	4.14906	0.365304
$130$	57.7851	5.06809
$131$	21.5998	1.88719	0.943594	−	0.331105i	$-0.107422\pi$
$131$	21.5998	1.88719	0.943594	+	0.331105i	$0.107422\pi$
$132$	8.42429	0.733241
$133$	−8.06407	−0.699243
$134$	−18.2033	−1.57252
$135$	−3.49875	−0.301124
$136$	1.91598	0.164294
$137$	−17.4634	−1.49200	−0.745999	−	0.665947i	$-0.768028\pi$
$137$	−17.4634	−1.49200	−0.745999	+	0.665947i	$0.768028\pi$
$138$	−0.933312	−0.0794488
$139$	−17.8184	−1.51134	−0.755670	−	0.654953i	$-0.772688\pi$
$139$	−17.8184	−1.51134	−0.755670	+	0.654953i	$0.772688\pi$
$140$	−49.5402	−4.18691
$141$	−11.8649	−0.999205
$142$	−22.6049	−1.89696
$143$	14.8108	1.23854
$144$	3.26884	0.272404
$145$	−30.5263	−2.53507
$146$	−22.8452	−1.89068
$147$	6.34819	0.523590
$148$	37.9846	3.12232
$149$	12.2138	1.00059	0.500296	−	0.865854i	$-0.333224\pi$
$149$	12.2138	1.00059	0.500296	+	0.865854i	$0.333224\pi$
$150$	−17.5524	−1.43315
$151$	4.24424	0.345391	0.172696	−	0.984975i	$-0.444752\pi$
$151$	4.24424	0.345391	0.172696	+	0.984975i	$0.444752\pi$
$152$	10.0346	0.813910
$153$	−0.421441	−0.0340715
$154$	−19.2502	−1.55122
$155$	16.2014	1.30133
$156$	26.4066	2.11422
$157$	−1.14697	−0.0915383	−0.0457692	−	0.998952i	$-0.514574\pi$
$157$	−1.14697	−0.0915383	−0.0457692	+	0.998952i	$0.514574\pi$
$158$	25.2145	2.00596
$159$	14.2918	1.13341
$160$	−4.09009	−0.323350
$161$	1.40674	0.110867
$162$	−2.42396	−0.190444
$163$	17.0996	1.33935	0.669673	−	0.742656i	$-0.266434\pi$
$163$	17.0996	1.33935	0.669673	+	0.742656i	$0.266434\pi$
$164$	−20.7198	−1.61794
$165$	−7.60522	−0.592065
$166$	−23.3507	−1.81237
$167$	−17.4332	−1.34902	−0.674509	−	0.738267i	$-0.735645\pi$
$167$	−17.4332	−1.34902	−0.674509	+	0.738267i	$0.735645\pi$
$168$	−16.6099	−1.28148
$169$	33.4256	2.57120
$170$	−3.57416	−0.274125
$171$	−2.20721	−0.168789
$172$	16.0799	1.22608
$173$	−15.6289	−1.18824	−0.594122	−	0.804375i	$-0.702500\pi$
$173$	−15.6289	−1.18824	−0.594122	+	0.804375i	$0.702500\pi$
$174$	−21.1488	−1.60329
$175$	26.4560	1.99988
$176$	7.10548	0.535595
$177$	2.13849	0.160739
$178$	27.3768	2.05198
$179$	−22.0208	−1.64591	−0.822955	−	0.568107i	$-0.807676\pi$
$179$	−22.0208	−1.64591	−0.822955	+	0.568107i	$0.807676\pi$
$180$	−13.5596	−1.01067
$181$	−15.6735	−1.16500	−0.582501	−	0.812830i	$-0.697926\pi$
$181$	−15.6735	−1.16500	−0.582501	+	0.812830i	$0.697926\pi$
$182$	−60.3413	−4.47279
$183$	−2.41510	−0.178529
$184$	−1.75048	−0.129047
$185$	−34.2915	−2.52116
$186$	11.2245	0.823017
$187$	−0.916085	−0.0669908
$188$	−45.9831	−3.35366
$189$	3.65352	0.265754
$190$	−18.7189	−1.35801
$191$	−20.7764	−1.50333	−0.751665	−	0.659545i	$-0.770749\pi$
$191$	−20.7764	−1.50333	−0.751665	+	0.659545i	$0.770749\pi$
$192$	−9.37133	−0.676317
$193$	6.08344	0.437896	0.218948	−	0.975737i	$-0.429738\pi$
$193$	6.08344	0.437896	0.218948	+	0.975737i	$0.429738\pi$
$194$	−23.8126	−1.70964
$195$	−23.8392	−1.70716
$196$	24.6028	1.75734
$197$	−20.7215	−1.47635	−0.738174	−	0.674611i	$-0.764312\pi$
$197$	−20.7215	−1.47635	−0.738174	+	0.674611i	$0.764312\pi$
$198$	−5.26895	−0.374448
$199$	−13.5098	−0.957681	−0.478841	−	0.877902i	$-0.658943\pi$
$199$	−13.5098	−0.957681	−0.478841	+	0.877902i	$0.658943\pi$
$200$	−32.9206	−2.32784
$201$	7.50974	0.529696
$202$	6.30019	0.443280
$203$	31.8767	2.23730
$204$	−1.63332	−0.114355
$205$	18.7052	1.30643
$206$	−12.4619	−0.868263
$207$	0.385037	0.0267619
$208$	22.2727	1.54433
$209$	−4.79780	−0.331871
$210$	30.9848	2.13815
$211$	18.9248	1.30283	0.651417	−	0.758720i	$-0.274175\pi$
$211$	18.9248	1.30283	0.651417	+	0.758720i	$0.274175\pi$
$212$	55.3887	3.80411
$213$	9.32563	0.638981
$214$	−15.1339	−1.03453
$215$	−14.5165	−0.990018
$216$	−4.54627	−0.309335
$217$	−16.9181	−1.14848
$218$	−18.2686	−1.23731
$219$	9.42477	0.636867
$220$	−29.4745	−1.98717
$221$	−2.87154	−0.193161
$222$	−23.7573	−1.59449
$223$	18.8326	1.26113	0.630563	−	0.776138i	$-0.282824\pi$
$223$	18.8326	1.26113	0.630563	+	0.776138i	$0.282824\pi$
$224$	4.27102	0.285370
$225$	7.24123	0.482749
$226$	−11.8254	−0.786614
$227$	8.50006	0.564169	0.282084	−	0.959390i	$-0.408974\pi$
$227$	8.50006	0.564169	0.282084	+	0.959390i	$0.408974\pi$
$228$	−8.55416	−0.566513
$229$	−28.4180	−1.87792	−0.938959	−	0.344030i	$-0.888208\pi$
$229$	−28.4180	−1.87792	−0.938959	+	0.344030i	$0.888208\pi$
$230$	3.26542	0.215316
$231$	7.94164	0.522522
$232$	−39.6659	−2.60419
$233$	−14.5121	−0.950722	−0.475361	−	0.879791i	$-0.657683\pi$
$233$	−14.5121	−0.950722	−0.475361	+	0.879791i	$0.657683\pi$
$234$	−16.5159	−1.07968
$235$	41.5123	2.70796
$236$	8.28784	0.539493
$237$	−10.4022	−0.675697
$238$	3.73226	0.241927
$239$	22.5117	1.45616	0.728081	−	0.685491i	$-0.240412\pi$
$239$	22.5117	1.45616	0.728081	+	0.685491i	$0.240412\pi$
$240$	−11.4369	−0.738246
$241$	−0.816581	−0.0526006	−0.0263003	−	0.999654i	$-0.508373\pi$
$241$	−0.816581	−0.0526006	−0.0263003	+	0.999654i	$0.508373\pi$
$242$	15.2104	0.977762
$243$	1.00000	0.0641500
$244$	−9.35985	−0.599203
$245$	−22.2107	−1.41899
$246$	12.9591	0.826243
$247$	−15.0391	−0.956915
$248$	21.0521	1.33681
$249$	9.63330	0.610486
$250$	19.0074	1.20214
$251$	−9.37415	−0.591691	−0.295845	−	0.955236i	$-0.595601\pi$
$251$	−9.37415	−0.591691	−0.295845	+	0.955236i	$0.595601\pi$
$252$	14.1594	0.891960
$253$	0.836954	0.0526188
$254$	38.8913	2.44026
$255$	1.47451	0.0923377
$256$	−30.6519	−1.91574
$257$	−4.41277	−0.275261	−0.137630	−	0.990484i	$-0.543949\pi$
$257$	−4.41277	−0.275261	−0.137630	+	0.990484i	$0.543949\pi$
$258$	−10.0571	−0.626130
$259$	35.8084	2.22502
$260$	−92.3902	−5.72980
$261$	8.72492	0.540059
$262$	−52.3571	−3.23463
$263$	17.0884	1.05371	0.526857	−	0.849954i	$-0.323370\pi$
$263$	17.0884	1.05371	0.526857	+	0.849954i	$0.323370\pi$
$264$	−9.88222	−0.608209
$265$	−50.0034	−3.07169
$266$	19.5469	1.19850
$267$	−11.2943	−0.691199
$268$	29.1044	1.77784
$269$	−10.1442	−0.618500	−0.309250	−	0.950981i	$-0.600078\pi$
$269$	−10.1442	−0.618500	−0.309250	+	0.950981i	$0.600078\pi$
$270$	8.48081	0.516125
$271$	−11.2380	−0.682661	−0.341330	−	0.939943i	$-0.610877\pi$
$271$	−11.2380	−0.682661	−0.341330	+	0.939943i	$0.610877\pi$
$272$	−1.37762	−0.0835307
$273$	24.8937	1.50664
$274$	42.3305	2.55728
$275$	15.7402	0.949173
$276$	1.49223	0.0898219
$277$	−3.28451	−0.197347	−0.0986734	−	0.995120i	$-0.531460\pi$
$277$	−3.28451	−0.197347	−0.0986734	+	0.995120i	$0.531460\pi$
$278$	43.1911	2.59043
$279$	−4.63064	−0.277229
$280$	58.1138	3.47296
$281$	13.3076	0.793864	0.396932	−	0.917848i	$-0.370075\pi$
$281$	13.3076	0.793864	0.396932	+	0.917848i	$0.370075\pi$
$282$	28.7600	1.71263
$283$	−23.0363	−1.36937	−0.684684	−	0.728840i	$-0.740060\pi$
$283$	−23.0363	−1.36937	−0.684684	+	0.728840i	$0.740060\pi$
$284$	36.1420	2.14463
$285$	7.72246	0.457439
$286$	−35.9007	−2.12285
$287$	−19.5327	−1.15298
$288$	1.16902	0.0688850
$289$	−16.8224	−0.989552
$290$	73.9944	4.34510
$291$	9.82385	0.575884
$292$	36.5263	2.13754
$293$	29.5570	1.72674	0.863370	−	0.504571i	$-0.168349\pi$
$293$	29.5570	1.72674	0.863370	+	0.504571i	$0.168349\pi$
$294$	−15.3877	−0.897430
$295$	−7.48203	−0.435621
$296$	−44.5583	−2.58990
$297$	2.17370	0.126131
$298$	−29.6057	−1.71501
$299$	2.62350	0.151721
$300$	28.0638	1.62027
$301$	15.1587	0.873731
$302$	−10.2878	−0.591999
$303$	−2.59914	−0.149316
$304$	−7.21501	−0.413809
$305$	8.44981	0.483835
$306$	1.02155	0.0583983
$307$	19.5962	1.11841	0.559207	−	0.829028i	$-0.311106\pi$
$307$	19.5962	1.11841	0.559207	+	0.829028i	$0.311106\pi$
$308$	30.7783	1.75376
$309$	5.14115	0.292470
$310$	−39.2715	−2.23047
$311$	33.4316	1.89573	0.947867	−	0.318667i	$-0.103235\pi$
$311$	33.4316	1.89573	0.947867	+	0.318667i	$0.103235\pi$
$312$	−30.9766	−1.75371
$313$	5.75248	0.325149	0.162575	−	0.986696i	$-0.448020\pi$
$313$	5.75248	0.325149	0.162575	+	0.986696i	$0.448020\pi$
$314$	2.78021	0.156896
$315$	−12.7827	−0.720225
$316$	−40.3144	−2.26786
$317$	21.6596	1.21652	0.608261	−	0.793737i	$-0.291867\pi$
$317$	21.6596	1.21652	0.608261	+	0.793737i	$0.291867\pi$
$318$	−34.6427	−1.94267
$319$	18.9653	1.06186
$320$	32.7879	1.83290
$321$	6.24347	0.348476
$322$	−3.40987	−0.190025
$323$	0.930207	0.0517581
$324$	3.87556	0.215309
$325$	49.3391	2.73684
$326$	−41.4487	−2.29563
$327$	7.53671	0.416781
$328$	24.3056	1.34205
$329$	−43.3486	−2.38989
$330$	18.4347	1.01480
$331$	−20.5319	−1.12853	−0.564267	−	0.825593i	$-0.690841\pi$
$331$	−20.5319	−1.12853	−0.564267	+	0.825593i	$0.690841\pi$
$332$	37.3344	2.04899
$333$	9.80107	0.537095
$334$	42.2572	2.31221
$335$	−26.2747	−1.43554
$336$	11.9428	0.651532
$337$	9.44753	0.514640	0.257320	−	0.966326i	$-0.417161\pi$
$337$	9.44753	0.514640	0.257320	+	0.966326i	$0.417161\pi$
$338$	−81.0222	−4.40703
$339$	4.87856	0.264967
$340$	5.71457	0.309916
$341$	−10.0656	−0.545083
$342$	5.35017	0.289304
$343$	−2.38141	−0.128584
$344$	−18.8628	−1.01701
$345$	−1.34715	−0.0725279
$346$	37.8838	2.03664
$347$	−3.31427	−0.177919	−0.0889596	−	0.996035i	$-0.528354\pi$
$347$	−3.31427	−0.177919	−0.0889596	+	0.996035i	$0.528354\pi$
$348$	33.8140	1.81262
$349$	−4.44937	−0.238169	−0.119085	−	0.992884i	$-0.537996\pi$
$349$	−4.44937	−0.238169	−0.119085	+	0.992884i	$0.537996\pi$
$350$	−64.1281	−3.42779
$351$	6.81364	0.363685
$352$	2.54109	0.135440
$353$	−15.1380	−0.805715	−0.402858	−	0.915263i	$-0.631983\pi$
$353$	−15.1380	−0.805715	−0.402858	+	0.915263i	$0.631983\pi$
$354$	−5.18360	−0.275505
$355$	−32.6280	−1.73171
$356$	−43.7717	−2.31989
$357$	−1.53974	−0.0814917
$358$	53.3773	2.82108
$359$	10.2307	0.539955	0.269977	−	0.962867i	$-0.412984\pi$
$359$	10.2307	0.539955	0.269977	+	0.962867i	$0.412984\pi$
$360$	15.9063	0.838333
$361$	−14.1282	−0.743592
$362$	37.9919	1.99681
$363$	−6.27504	−0.329354
$364$	96.4771	5.05678
$365$	−32.9749	−1.72598
$366$	5.85409	0.305998
$367$	−7.68871	−0.401348	−0.200674	−	0.979658i	$-0.564313\pi$
$367$	−7.68871	−0.401348	−0.200674	+	0.979658i	$0.564313\pi$
$368$	1.25863	0.0656104
$369$	−5.34627	−0.278316
$370$	83.1210	4.32125
$371$	52.2154	2.71089
$372$	−17.9463	−0.930473
$373$	6.32318	0.327402	0.163701	−	0.986510i	$-0.447657\pi$
$373$	6.32318	0.327402	0.163701	+	0.986510i	$0.447657\pi$
$374$	2.22055	0.114822
$375$	−7.84150	−0.404933
$376$	53.9411	2.78180
$377$	59.4485	3.06175
$378$	−8.85596	−0.455502
$379$	−3.34687	−0.171917	−0.0859587	−	0.996299i	$-0.527395\pi$
$379$	−3.34687	−0.171917	−0.0859587	+	0.996299i	$0.527395\pi$
$380$	29.9288	1.53532
$381$	−16.0446	−0.821988
$382$	50.3612	2.57670
$383$	−17.6149	−0.900077	−0.450039	−	0.893009i	$-0.648590\pi$
$383$	−17.6149	−0.900077	−0.450039	+	0.893009i	$0.648590\pi$
$384$	20.3777	1.03989
$385$	−27.7858	−1.41610
$386$	−14.7460	−0.750551
$387$	4.14906	0.210909
$388$	38.0729	1.93286
$389$	−15.8142	−0.801810	−0.400905	−	0.916120i	$-0.631304\pi$
$389$	−15.8142	−0.801810	−0.400905	+	0.916120i	$0.631304\pi$
$390$	57.7851	2.92606
$391$	−0.162270	−0.00820636
$392$	−28.8606	−1.45768
$393$	21.5998	1.08957
$394$	50.2281	2.53045
$395$	36.3947	1.83122
$396$	8.42429	0.423337
$397$	−0.0602283	−0.00302277	−0.00151139	−	0.999999i	$-0.500481\pi$
$397$	−0.0602283	−0.00302277	−0.00151139	+	0.999999i	$0.500481\pi$
$398$	32.7471	1.64146
$399$	−8.06407	−0.403708
$400$	23.6704	1.18352
$401$	6.64418	0.331795	0.165897	−	0.986143i	$-0.446948\pi$
$401$	6.64418	0.331795	0.165897	+	0.986143i	$0.446948\pi$
$402$	−18.2033	−0.907897
$403$	−31.5515	−1.57169
$404$	−10.0731	−0.501156
$405$	−3.49875	−0.173854
$406$	−77.2676	−3.83473
$407$	21.3046	1.05603
$408$	1.91598	0.0948554
$409$	−8.54005	−0.422278	−0.211139	−	0.977456i	$-0.567717\pi$
$409$	−8.54005	−0.422278	−0.211139	+	0.977456i	$0.567717\pi$
$410$	−45.3407	−2.23922
$411$	−17.4634	−0.861406
$412$	19.9248	0.981627
$413$	7.81301	0.384453
$414$	−0.933312	−0.0458698
$415$	−33.7045	−1.65449
$416$	7.96525	0.390529
$417$	−17.8184	−0.872572
$418$	11.6297	0.568825
$419$	−17.7515	−0.867219	−0.433609	−	0.901101i	$-0.642760\pi$
$419$	−17.7515	−0.867219	−0.433609	+	0.901101i	$0.642760\pi$
$420$	−49.5402	−2.41732
$421$	−6.58519	−0.320942	−0.160471	−	0.987041i	$-0.551301\pi$
$421$	−6.58519	−0.320942	−0.160471	+	0.987041i	$0.551301\pi$
$422$	−45.8728	−2.23305
$423$	−11.8649	−0.576891
$424$	−64.9744	−3.15544
$425$	−3.05175	−0.148032
$426$	−22.6049	−1.09521
$427$	−8.82360	−0.427004
$428$	24.1969	1.16960
$429$	14.8108	0.715071
$430$	35.1874	1.69689
$431$	24.0987	1.16080	0.580398	−	0.814333i	$-0.302897\pi$
$431$	24.0987	1.16080	0.580398	+	0.814333i	$0.302897\pi$
$432$	3.26884	0.157272
$433$	−34.5456	−1.66016	−0.830079	−	0.557646i	$-0.811705\pi$
$433$	−34.5456	−1.66016	−0.830079	+	0.557646i	$0.811705\pi$
$434$	41.0087	1.96848
$435$	−30.5263	−1.46362
$436$	29.2090	1.39886
$437$	−0.849856	−0.0406541
$438$	−22.8452	−1.09159
$439$	−30.2772	−1.44505	−0.722527	−	0.691343i	$-0.757019\pi$
$439$	−30.2772	−1.44505	−0.722527	+	0.691343i	$0.757019\pi$
$440$	34.5754	1.64832
$441$	6.34819	0.302295
$442$	6.96049	0.331077
$443$	10.9851	0.521919	0.260959	−	0.965350i	$-0.415961\pi$
$443$	10.9851	0.521919	0.260959	+	0.965350i	$0.415961\pi$
$444$	37.9846	1.80267
$445$	39.5158	1.87323
$446$	−45.6494	−2.16156
$447$	12.2138	0.577692
$448$	−34.2383	−1.61761
$449$	9.39431	0.443345	0.221672	−	0.975121i	$-0.428848\pi$
$449$	9.39431	0.443345	0.221672	+	0.975121i	$0.428848\pi$
$450$	−17.5524	−0.827429
$451$	−11.6212	−0.547220
$452$	18.9071	0.889317
$453$	4.24424	0.199412
$454$	−20.6038	−0.966983
$455$	−87.0969	−4.08316
$456$	10.0346	0.469911
$457$	−24.8333	−1.16165	−0.580827	−	0.814027i	$-0.697271\pi$
$457$	−24.8333	−1.16165	−0.580827	+	0.814027i	$0.697271\pi$
$458$	68.8841	3.21874
$459$	−0.421441	−0.0196712
$460$	−5.22095	−0.243428
$461$	−31.2928	−1.45745	−0.728725	−	0.684806i	$-0.759887\pi$
$461$	−31.2928	−1.45745	−0.728725	+	0.684806i	$0.759887\pi$
$462$	−19.2502	−0.895600
$463$	30.2634	1.40646	0.703230	−	0.710963i	$-0.251741\pi$
$463$	30.2634	1.40646	0.703230	+	0.710963i	$0.251741\pi$
$464$	28.5204	1.32403
$465$	16.2014	0.751323
$466$	35.1768	1.62953
$467$	19.9611	0.923689	0.461844	−	0.886961i	$-0.347188\pi$
$467$	19.9611	0.923689	0.461844	+	0.886961i	$0.347188\pi$
$468$	26.4066	1.22065
$469$	27.4370	1.26692
$470$	−100.624	−4.64143
$471$	−1.14697	−0.0528497
$472$	−9.72216	−0.447498
$473$	9.01880	0.414685
$474$	25.2145	1.15814
$475$	−15.9829	−0.733345
$476$	−5.96736	−0.273513
$477$	14.2918	0.654377
$478$	−54.5674	−2.49586
$479$	17.7867	0.812694	0.406347	−	0.913719i	$-0.366802\pi$
$479$	17.7867	0.812694	0.406347	+	0.913719i	$0.366802\pi$
$480$	−4.09009	−0.186686
$481$	66.7809	3.04495
$482$	1.97936	0.0901572
$483$	1.40674	0.0640088
$484$	−24.3193	−1.10542
$485$	−34.3712	−1.56071
$486$	−2.42396	−0.109953
$487$	1.01661	0.0460670	0.0230335	−	0.999735i	$-0.492668\pi$
$487$	1.01661	0.0460670	0.0230335	+	0.999735i	$0.492668\pi$
$488$	10.9797	0.497027
$489$	17.0996	0.773272
$490$	53.8378	2.43214
$491$	33.0289	1.49058	0.745288	−	0.666743i	$-0.232312\pi$
$491$	33.0289	1.49058	0.745288	+	0.666743i	$0.232312\pi$
$492$	−20.7198	−0.934120
$493$	−3.67704	−0.165606
$494$	36.4541	1.64015
$495$	−7.60522	−0.341829
$496$	−15.1368	−0.679663
$497$	34.0713	1.52831
$498$	−23.3507	−1.04637
$499$	39.4414	1.76564	0.882819	−	0.469713i	$-0.155643\pi$
$499$	39.4414	1.76564	0.882819	+	0.469713i	$0.155643\pi$
$500$	−30.3902	−1.35909
$501$	−17.4332	−0.778856
$502$	22.7225	1.01416
$503$	29.0174	1.29382	0.646912	−	0.762565i	$-0.276060\pi$
$503$	29.0174	1.29382	0.646912	+	0.762565i	$0.276060\pi$
$504$	−16.6099	−0.739863
$505$	9.09372	0.404665
$506$	−2.02874	−0.0901884
$507$	33.4256	1.48448
$508$	−62.1816	−2.75886
$509$	−21.5552	−0.955419	−0.477710	−	0.878518i	$-0.658533\pi$
$509$	−21.5552	−0.955419	−0.477710	+	0.878518i	$0.658533\pi$
$510$	−3.57416	−0.158266
$511$	34.4336	1.52325
$512$	33.5434	1.48242
$513$	−2.20721	−0.0974505
$514$	10.6964	0.471796
$515$	−17.9876	−0.792628
$516$	16.0799	0.707879
$517$	−25.7907	−1.13427
$518$	−86.7979	−3.81368
$519$	−15.6289	−0.686033
$520$	108.379	4.75275
$521$	34.9106	1.52946	0.764730	−	0.644351i	$-0.222872\pi$
$521$	34.9106	1.52946	0.764730	+	0.644351i	$0.222872\pi$
$522$	−21.1488	−0.925659
$523$	10.4592	0.457348	0.228674	−	0.973503i	$-0.426561\pi$
$523$	10.4592	0.457348	0.228674	+	0.973503i	$0.426561\pi$
$524$	83.7115	3.65695
$525$	26.4560	1.15463
$526$	−41.4215	−1.80606
$527$	1.95154	0.0850104
$528$	7.10548	0.309226
$529$	−22.8517	−0.993554
$530$	121.206	5.26485
$531$	2.13849	0.0928025
$532$	−31.2528	−1.35498
$533$	−36.4275	−1.57785
$534$	27.3768	1.18471
$535$	−21.8443	−0.944412
$536$	−34.1413	−1.47468
$537$	−22.0208	−0.950266
$538$	24.5890	1.06011
$539$	13.7990	0.594367
$540$	−13.5596	−0.583512
$541$	16.0687	0.690849	0.345425	−	0.938446i	$-0.387735\pi$
$541$	16.0687	0.690849	0.345425	+	0.938446i	$0.387735\pi$
$542$	27.2404	1.17008
$543$	−15.6735	−0.672614
$544$	−0.492671	−0.0211231
$545$	−26.3690	−1.12953
$546$	−60.3413	−2.58237
$547$	42.7156	1.82639	0.913194	−	0.407526i	$-0.133608\pi$
$547$	42.7156	1.82639	0.913194	+	0.407526i	$0.133608\pi$
$548$	−67.6804	−2.89116
$549$	−2.41510	−0.103074
$550$	−38.1537	−1.62688
$551$	−19.2577	−0.820406
$552$	−1.75048	−0.0745055
$553$	−38.0047	−1.61612
$554$	7.96149	0.338251
$555$	−34.2915	−1.45559
$556$	−69.0564	−2.92864
$557$	11.7924	0.499662	0.249831	−	0.968289i	$-0.419625\pi$
$557$	11.7924	0.499662	0.249831	+	0.968289i	$0.419625\pi$
$558$	11.2245	0.475169
$559$	28.2702	1.19570
$560$	−41.7847	−1.76573
$561$	−0.916085	−0.0386771
$562$	−32.2570	−1.36068
$563$	35.0427	1.47687	0.738437	−	0.674323i	$-0.235564\pi$
$563$	35.0427	1.47687	0.738437	+	0.674323i	$0.235564\pi$
$564$	−45.9831	−1.93624
$565$	−17.0688	−0.718091
$566$	55.8390	2.34709
$567$	3.65352	0.153433
$568$	−42.3968	−1.77893
$569$	30.3984	1.27437	0.637183	−	0.770712i	$-0.280100\pi$
$569$	30.3984	1.27437	0.637183	+	0.770712i	$0.280100\pi$
$570$	−18.7189	−0.784048
$571$	−8.17731	−0.342210	−0.171105	−	0.985253i	$-0.554734\pi$
$571$	−8.17731	−0.342210	−0.171105	+	0.985253i	$0.554734\pi$
$572$	57.4001	2.40002
$573$	−20.7764	−0.867948
$574$	47.3464	1.97620
$575$	2.78814	0.116274
$576$	−9.37133	−0.390472
$577$	10.0381	0.417892	0.208946	−	0.977927i	$-0.432997\pi$
$577$	10.0381	0.417892	0.208946	+	0.977927i	$0.432997\pi$
$578$	40.7767	1.69609
$579$	6.08344	0.252819
$580$	−118.307	−4.91241
$581$	35.1954	1.46015
$582$	−23.8126	−0.987063
$583$	31.0661	1.28662
$584$	−42.8476	−1.77305
$585$	−23.8392	−0.985629
$586$	−71.6449	−2.95963
$587$	−19.8493	−0.819267	−0.409634	−	0.912250i	$-0.634343\pi$
$587$	−19.8493	−0.819267	−0.409634	+	0.912250i	$0.634343\pi$
$588$	24.6028	1.01460
$589$	10.2208	0.421139
$590$	18.1361	0.746652
$591$	−20.7215	−0.852370
$592$	32.0381	1.31676
$593$	−45.3431	−1.86202	−0.931010	−	0.364995i	$-0.881071\pi$
$593$	−45.3431	−1.86202	−0.931010	+	0.364995i	$0.881071\pi$
$594$	−5.26895	−0.216187
$595$	5.38717	0.220852
$596$	47.3353	1.93893
$597$	−13.5098	−0.552918
$598$	−6.35925	−0.260049
$599$	4.33271	0.177030	0.0885150	−	0.996075i	$-0.471788\pi$
$599$	4.33271	0.177030	0.0885150	+	0.996075i	$0.471788\pi$
$600$	−32.9206	−1.34398
$601$	30.5235	1.24508	0.622540	−	0.782588i	$-0.286101\pi$
$601$	30.5235	1.24508	0.622540	+	0.782588i	$0.286101\pi$
$602$	−36.7439	−1.49757
$603$	7.50974	0.305820
$604$	16.4488	0.669292
$605$	21.9548	0.892588
$606$	6.30019	0.255928
$607$	−20.9255	−0.849341	−0.424671	−	0.905348i	$-0.639610\pi$
$607$	−20.9255	−0.849341	−0.424671	+	0.905348i	$0.639610\pi$
$608$	−2.58026	−0.104643
$609$	31.8767	1.29171
$610$	−20.4820	−0.829291
$611$	−80.8431	−3.27056
$612$	−1.63332	−0.0660230
$613$	−11.2782	−0.455521	−0.227760	−	0.973717i	$-0.573140\pi$
$613$	−11.2782	−0.455521	−0.227760	+	0.973717i	$0.573140\pi$
$614$	−47.5003	−1.91696
$615$	18.7052	0.754268
$616$	−36.1049	−1.45471
$617$	−41.4491	−1.66868	−0.834339	−	0.551252i	$-0.814150\pi$
$617$	−41.4491	−1.66868	−0.834339	+	0.551252i	$0.814150\pi$
$618$	−12.4619	−0.501292
$619$	−27.6713	−1.11220	−0.556101	−	0.831114i	$-0.687703\pi$
$619$	−27.6713	−1.11220	−0.556101	+	0.831114i	$0.687703\pi$
$620$	62.7896	2.52169
$621$	0.385037	0.0154510
$622$	−81.0368	−3.24928
$623$	−41.2639	−1.65320
$624$	22.2727	0.891622
$625$	−8.77073	−0.350829
$626$	−13.9438	−0.557305
$627$	−4.79780	−0.191606
$628$	−4.44516	−0.177381
$629$	−4.13057	−0.164697
$630$	30.9848	1.23446
$631$	−0.842572	−0.0335423	−0.0167711	−	0.999859i	$-0.505339\pi$
$631$	−0.842572	−0.0335423	−0.0167711	+	0.999859i	$0.505339\pi$
$632$	47.2913	1.88115
$633$	18.9248	0.752191
$634$	−52.5018	−2.08511
$635$	56.1358	2.22768
$636$	55.3887	2.19631
$637$	43.2542	1.71380
$638$	−45.9712	−1.82002
$639$	9.32563	0.368916
$640$	−71.2962	−2.81823
$641$	5.65111	0.223205	0.111603	−	0.993753i	$-0.464402\pi$
$641$	5.65111	0.223205	0.111603	+	0.993753i	$0.464402\pi$
$642$	−15.1339	−0.597287
$643$	13.9735	0.551059	0.275530	−	0.961293i	$-0.411147\pi$
$643$	13.9735	0.551059	0.275530	+	0.961293i	$0.411147\pi$
$644$	5.45190	0.214835
$645$	−14.5165	−0.571587
$646$	−2.25478	−0.0887131
$647$	−10.1483	−0.398972	−0.199486	−	0.979901i	$-0.563927\pi$
$647$	−10.1483	−0.398972	−0.199486	+	0.979901i	$0.563927\pi$
$648$	−4.54627	−0.178594
$649$	4.64843	0.182467
$650$	−119.596	−4.69093
$651$	−16.9181	−0.663073
$652$	66.2706	2.59536
$653$	−49.7394	−1.94645	−0.973226	−	0.229850i	$-0.926177\pi$
$653$	−49.7394	−1.94645	−0.973226	+	0.229850i	$0.926177\pi$
$654$	−18.2686	−0.714361
$655$	−75.5724	−2.95286
$656$	−17.4761	−0.682328
$657$	9.42477	0.367695
$658$	105.075	4.09625
$659$	−12.8873	−0.502019	−0.251010	−	0.967985i	$-0.580763\pi$
$659$	−12.8873	−0.502019	−0.251010	+	0.967985i	$0.580763\pi$
$660$	−29.4745	−1.14729
$661$	28.0002	1.08908	0.544540	−	0.838735i	$-0.316704\pi$
$661$	28.0002	1.08908	0.544540	+	0.838735i	$0.316704\pi$
$662$	49.7683	1.93430
$663$	−2.87154	−0.111522
$664$	−43.7956	−1.69960
$665$	28.2141	1.09410
$666$	−23.7573	−0.920579
$667$	3.35942	0.130077
$668$	−67.5632	−2.61410
$669$	18.8326	0.728111
$670$	63.6886	2.46051
$671$	−5.24969	−0.202662
$672$	4.27102	0.164758
$673$	−20.6932	−0.797666	−0.398833	−	0.917024i	$-0.630585\pi$
$673$	−20.6932	−0.797666	−0.398833	+	0.917024i	$0.630585\pi$
$674$	−22.9004	−0.882090
$675$	7.24123	0.278715
$676$	129.543	4.98242
$677$	36.0909	1.38708	0.693542	−	0.720416i	$-0.256049\pi$
$677$	36.0909	1.38708	0.693542	+	0.720416i	$0.256049\pi$
$678$	−11.8254	−0.454152
$679$	35.8916	1.37739
$680$	−6.70355	−0.257069
$681$	8.50006	0.325723
$682$	24.3986	0.934270
$683$	−20.0139	−0.765809	−0.382905	−	0.923788i	$-0.625076\pi$
$683$	−20.0139	−0.765809	−0.382905	+	0.923788i	$0.625076\pi$
$684$	−8.55416	−0.327076
$685$	61.1000	2.33451
$686$	5.77242	0.220392
$687$	−28.4180	−1.08422
$688$	13.5626	0.517070
$689$	97.3792	3.70985
$690$	3.26542	0.124313
$691$	−18.1316	−0.689757	−0.344879	−	0.938647i	$-0.612080\pi$
$691$	−18.1316	−0.689757	−0.344879	+	0.938647i	$0.612080\pi$
$692$	−60.5707	−2.30255
$693$	7.94164	0.301678
$694$	8.03364	0.304953
$695$	62.3422	2.36477
$696$	−39.6659	−1.50353
$697$	2.25314	0.0853436
$698$	10.7851	0.408221
$699$	−14.5121	−0.548900
$700$	102.532	3.87533
$701$	14.2054	0.536531	0.268266	−	0.963345i	$-0.413550\pi$
$701$	14.2054	0.536531	0.268266	+	0.963345i	$0.413550\pi$
$702$	−16.5159	−0.623354
$703$	−21.6330	−0.815903
$704$	−20.3704	−0.767740
$705$	41.5123	1.56344
$706$	36.6939	1.38099
$707$	−9.49599	−0.357133
$708$	8.28784	0.311476
$709$	−23.5869	−0.885826	−0.442913	−	0.896565i	$-0.646055\pi$
$709$	−23.5869	−0.885826	−0.442913	+	0.896565i	$0.646055\pi$
$710$	79.0888	2.96815
$711$	−10.4022	−0.390114
$712$	51.3469	1.92431
$713$	−1.78297	−0.0667726
$714$	3.73226	0.139676
$715$	−51.8192	−1.93793
$716$	−85.3428	−3.18941
$717$	22.5117	0.840716
$718$	−24.7987	−0.925479
$719$	−21.5020	−0.801891	−0.400945	−	0.916102i	$-0.631318\pi$
$719$	−21.5020	−0.801891	−0.400945	+	0.916102i	$0.631318\pi$
$720$	−11.4369	−0.426226
$721$	18.7833	0.699526
$722$	34.2462	1.27451
$723$	−0.816581	−0.0303690
$724$	−60.7436	−2.25752
$725$	63.1792	2.34642
$726$	15.2104	0.564511
$727$	−19.4977	−0.723130	−0.361565	−	0.932347i	$-0.617757\pi$
$727$	−19.4977	−0.723130	−0.361565	+	0.932347i	$0.617757\pi$
$728$	−113.174	−4.19450
$729$	1.00000	0.0370370
$730$	79.9297	2.95833
$731$	−1.74858	−0.0646737
$732$	−9.35985	−0.345950
$733$	44.7340	1.65229	0.826144	−	0.563459i	$-0.190530\pi$
$733$	44.7340	1.65229	0.826144	+	0.563459i	$0.190530\pi$
$734$	18.6371	0.687908
$735$	−22.2107	−0.819254
$736$	0.450115	0.0165914
$737$	16.3239	0.601299
$738$	12.9591	0.477032
$739$	15.3031	0.562933	0.281466	−	0.959571i	$-0.409179\pi$
$739$	15.3031	0.562933	0.281466	+	0.959571i	$0.409179\pi$
$740$	−132.899	−4.88545
$741$	−15.0391	−0.552475
$742$	−126.568	−4.64645
$743$	−6.10219	−0.223868	−0.111934	−	0.993716i	$-0.535704\pi$
$743$	−6.10219	−0.223868	−0.111934	+	0.993716i	$0.535704\pi$
$744$	21.0521	0.771809
$745$	−42.7329	−1.56561
$746$	−15.3271	−0.561165
$747$	9.63330	0.352464
$748$	−3.55034	−0.129813
$749$	22.8106	0.833481
$750$	19.0074	0.694054
$751$	−37.5024	−1.36848	−0.684241	−	0.729256i	$-0.739866\pi$
$751$	−37.5024	−1.36848	−0.684241	+	0.729256i	$0.739866\pi$
$752$	−38.7845	−1.41432
$753$	−9.37415	−0.341613
$754$	−144.100	−5.24783
$755$	−14.8495	−0.540429
$756$	14.1594	0.514973
$757$	34.7278	1.26220	0.631101	−	0.775701i	$-0.282603\pi$
$757$	34.7278	1.26220	0.631101	+	0.775701i	$0.282603\pi$
$758$	8.11267	0.294666
$759$	0.836954	0.0303795
$760$	−35.1084	−1.27352
$761$	44.7245	1.62126	0.810631	−	0.585558i	$-0.199124\pi$
$761$	44.7245	1.62126	0.810631	+	0.585558i	$0.199124\pi$
$762$	38.8913	1.40888
$763$	27.5355	0.996852
$764$	−80.5203	−2.91312
$765$	1.47451	0.0533112
$766$	42.6976	1.54273
$767$	14.5709	0.526124
$768$	−30.6519	−1.10605
$769$	21.8965	0.789606	0.394803	−	0.918766i	$-0.370813\pi$
$769$	21.8965	0.789606	0.394803	+	0.918766i	$0.370813\pi$
$770$	67.3515	2.42718
$771$	−4.41277	−0.158922
$772$	23.5767	0.848546
$773$	42.1065	1.51446	0.757232	−	0.653145i	$-0.226551\pi$
$773$	42.1065	1.51446	0.757232	+	0.653145i	$0.226551\pi$
$774$	−10.0571	−0.361496
$775$	−33.5315	−1.20449
$776$	−44.6619	−1.60327
$777$	35.8084	1.28462
$778$	38.3328	1.37430
$779$	11.8003	0.422790
$780$	−92.3902	−3.30810
$781$	20.2711	0.725357
$782$	0.393336	0.0140657
$783$	8.72492	0.311803
$784$	20.7512	0.741115
$785$	4.01296	0.143229
$786$	−52.3571	−1.86751
$787$	12.9256	0.460750	0.230375	−	0.973102i	$-0.426005\pi$
$787$	12.9256	0.460750	0.230375	+	0.973102i	$0.426005\pi$
$788$	−80.3075	−2.86084
$789$	17.0884	0.608363
$790$	−88.2192	−3.13870
$791$	17.8239	0.633744
$792$	−9.88222	−0.351149
$793$	−16.4556	−0.584355
$794$	0.145991	0.00518102
$795$	−50.0034	−1.77344
$796$	−52.3579	−1.85578
$797$	−46.8383	−1.65910	−0.829549	−	0.558434i	$-0.811402\pi$
$797$	−46.8383	−1.65910	−0.829549	+	0.558434i	$0.811402\pi$
$798$	19.5469	0.691954
$799$	5.00035	0.176900
$800$	8.46512	0.299287
$801$	−11.2943	−0.399064
$802$	−16.1052	−0.568694
$803$	20.4866	0.722956
$804$	29.1044	1.02643
$805$	−4.92182	−0.173471
$806$	76.4794	2.69387
$807$	−10.1442	−0.357091
$808$	11.8164	0.415699
$809$	23.2537	0.817555	0.408778	−	0.912634i	$-0.365955\pi$
$809$	23.2537	0.817555	0.408778	+	0.912634i	$0.365955\pi$
$810$	8.48081	0.297985
$811$	−1.77651	−0.0623816	−0.0311908	−	0.999513i	$-0.509930\pi$
$811$	−1.77651	−0.0623816	−0.0311908	+	0.999513i	$0.509930\pi$
$812$	123.540	4.33540
$813$	−11.2380	−0.394134
$814$	−51.6413	−1.81003
$815$	−59.8273	−2.09566
$816$	−1.37762	−0.0482265
$817$	−9.15783	−0.320392
$818$	20.7007	0.723783
$819$	24.8937	0.869857
$820$	72.4933	2.53158
$821$	0.395446	0.0138012	0.00690058	−	0.999976i	$-0.497803\pi$
$821$	0.395446	0.0138012	0.00690058	+	0.999976i	$0.497803\pi$
$822$	42.3305	1.47645
$823$	17.4516	0.608326	0.304163	−	0.952620i	$-0.401623\pi$
$823$	17.4516	0.608326	0.304163	+	0.952620i	$0.401623\pi$
$824$	−23.3731	−0.814240
$825$	15.7402	0.548005
$826$	−18.9384	−0.658951
$827$	26.4420	0.919477	0.459738	−	0.888054i	$-0.347943\pi$
$827$	26.4420	0.919477	0.459738	+	0.888054i	$0.347943\pi$
$828$	1.49223	0.0518587
$829$	9.10550	0.316247	0.158124	−	0.987419i	$-0.449456\pi$
$829$	9.10550	0.316247	0.158124	+	0.987419i	$0.449456\pi$
$830$	81.6982	2.83579
$831$	−3.28451	−0.113938
$832$	−63.8528	−2.21370
$833$	−2.67539	−0.0926966
$834$	43.1911	1.49558
$835$	60.9942	2.11079
$836$	−18.5942	−0.643092
$837$	−4.63064	−0.160058
$838$	43.0289	1.48641
$839$	−32.9443	−1.13736	−0.568682	−	0.822557i	$-0.692547\pi$
$839$	−32.9443	−1.13736	−0.568682	+	0.822557i	$0.692547\pi$
$840$	58.1138	2.00512
$841$	47.1243	1.62498
$842$	15.9622	0.550094
$843$	13.3076	0.458338
$844$	73.3440	2.52460
$845$	−116.948	−4.02313
$846$	28.7600	0.988789
$847$	−22.9260	−0.787745
$848$	46.7177	1.60429
$849$	−23.0363	−0.790605
$850$	7.39731	0.253726
$851$	3.77377	0.129363
$852$	36.1420	1.23821
$853$	−2.09035	−0.0715723	−0.0357861	−	0.999359i	$-0.511394\pi$
$853$	−2.09035	−0.0715723	−0.0357861	+	0.999359i	$0.511394\pi$
$854$	21.3880	0.731883
$855$	7.72246	0.264102
$856$	−28.3845	−0.970162
$857$	8.20409	0.280246	0.140123	−	0.990134i	$-0.455250\pi$
$857$	8.20409	0.280246	0.140123	+	0.990134i	$0.455250\pi$
$858$	−35.9007	−1.22563
$859$	−46.7897	−1.59644	−0.798222	−	0.602363i	$-0.794226\pi$
$859$	−46.7897	−1.59644	−0.798222	+	0.602363i	$0.794226\pi$
$860$	−56.2596	−1.91844
$861$	−19.5327	−0.665672
$862$	−58.4143	−1.98960
$863$	−14.1151	−0.480483	−0.240241	−	0.970713i	$-0.577227\pi$
$863$	−14.1151	−0.480483	−0.240241	+	0.970713i	$0.577227\pi$
$864$	1.16902	0.0397708
$865$	54.6816	1.85923
$866$	83.7371	2.84550
$867$	−16.8224	−0.571318
$868$	−65.5671	−2.22549
$869$	−22.6113	−0.767035
$870$	73.9944	2.50864
$871$	51.1686	1.73378
$872$	−34.2639	−1.16032
$873$	9.82385	0.332487
$874$	2.06001	0.0696810
$875$	−28.6491	−0.968515
$876$	36.5263	1.23411
$877$	57.1226	1.92889	0.964447	−	0.264277i	$-0.0851335\pi$
$877$	57.1226	1.92889	0.964447	+	0.264277i	$0.0851335\pi$
$878$	73.3907	2.47682
$879$	29.5570	0.996934
$880$	−24.8603	−0.838039
$881$	52.0262	1.75281	0.876404	−	0.481577i	$-0.159936\pi$
$881$	52.0262	1.75281	0.876404	+	0.481577i	$0.159936\pi$
$882$	−15.3877	−0.518132
$883$	−12.3134	−0.414379	−0.207190	−	0.978301i	$-0.566432\pi$
$883$	−12.3134	−0.414379	−0.207190	+	0.978301i	$0.566432\pi$
$884$	−11.1288	−0.374303
$885$	−7.48203	−0.251506
$886$	−26.6274	−0.894566
$887$	−8.68406	−0.291582	−0.145791	−	0.989315i	$-0.546573\pi$
$887$	−8.68406	−0.291582	−0.145791	+	0.989315i	$0.546573\pi$
$888$	−44.5583	−1.49528
$889$	−58.6191	−1.96602
$890$	−95.7846	−3.21071
$891$	2.17370	0.0728216
$892$	72.9869	2.44378
$893$	26.1883	0.876357
$894$	−29.6057	−0.990162
$895$	77.0451	2.57533
$896$	74.4501	2.48720
$897$	2.62350	0.0875962
$898$	−22.7714	−0.759891
$899$	−40.4020	−1.34748
$900$	28.0638	0.935461
$901$	−6.02315	−0.200660
$902$	28.1692	0.937932
$903$	15.1587	0.504449
$904$	−22.1792	−0.737671
$905$	54.8376	1.82286
$906$	−10.2878	−0.341791
$907$	47.7332	1.58495	0.792477	−	0.609902i	$-0.208791\pi$
$907$	47.7332	1.58495	0.792477	+	0.609902i	$0.208791\pi$
$908$	32.9425	1.09323
$909$	−2.59914	−0.0862079
$910$	211.119	6.99852
$911$	0.959251	0.0317814	0.0158907	−	0.999874i	$-0.494942\pi$
$911$	0.959251	0.0317814	0.0158907	+	0.999874i	$0.494942\pi$
$912$	−7.21501	−0.238913
$913$	20.9399	0.693009
$914$	60.1948	1.99107
$915$	8.44981	0.279342
$916$	−110.136	−3.63899
$917$	78.9154	2.60602
$918$	1.02155	0.0337163
$919$	42.2436	1.39349	0.696744	−	0.717320i	$-0.254631\pi$
$919$	42.2436	1.39349	0.696744	+	0.717320i	$0.254631\pi$
$920$	6.12450	0.201919
$921$	19.5962	0.645717
$922$	75.8523	2.49806
$923$	63.5414	2.09149
$924$	30.7783	1.01253
$925$	70.9718	2.33354
$926$	−73.3571	−2.41066
$927$	5.14115	0.168858
$928$	10.1996	0.334818
$929$	−35.1513	−1.15328	−0.576638	−	0.817000i	$-0.695636\pi$
$929$	−35.1513	−1.15328	−0.576638	+	0.817000i	$0.695636\pi$
$930$	−39.2715	−1.28776
$931$	−14.0118	−0.459217
$932$	−56.2427	−1.84229
$933$	33.4316	1.09450
$934$	−48.3848	−1.58320
$935$	3.20515	0.104820
$936$	−30.9766	−1.01250
$937$	−34.4358	−1.12497	−0.562485	−	0.826808i	$-0.690155\pi$
$937$	−34.4358	−1.12497	−0.562485	+	0.826808i	$0.690155\pi$
$938$	−66.5060	−2.17150
$939$	5.75248	0.187725
$940$	160.883	5.24743
$941$	−2.86703	−0.0934624	−0.0467312	−	0.998907i	$-0.514880\pi$
$941$	−2.86703	−0.0934624	−0.0467312	+	0.998907i	$0.514880\pi$
$942$	2.78021	0.0905841
$943$	−2.05851	−0.0670343
$944$	6.99038	0.227518
$945$	−12.7827	−0.415822
$946$	−21.8612	−0.710768
$947$	−18.6271	−0.605301	−0.302650	−	0.953102i	$-0.597871\pi$
$947$	−18.6271	−0.605301	−0.302650	+	0.953102i	$0.597871\pi$
$948$	−40.3144	−1.30935
$949$	64.2170	2.08457
$950$	38.7418	1.25695
$951$	21.6596	0.702359
$952$	7.00008	0.226874
$953$	8.18133	0.265019	0.132510	−	0.991182i	$-0.457696\pi$
$953$	8.18133	0.265019	0.132510	+	0.991182i	$0.457696\pi$
$954$	−34.6427	−1.12160
$955$	72.6915	2.35224
$956$	87.2455	2.82172
$957$	18.9653	0.613063
$958$	−43.1141	−1.39295
$959$	−63.8028	−2.06030
$960$	32.7879	1.05823
$961$	−9.55720	−0.308297
$962$	−161.874	−5.21902
$963$	6.24347	0.201193
$964$	−3.16471	−0.101928
$965$	−21.2844	−0.685170
$966$	−3.40987	−0.109711
$967$	−0.524617	−0.0168705	−0.00843527	−	0.999964i	$-0.502685\pi$
$967$	−0.524617	−0.0168705	−0.00843527	+	0.999964i	$0.502685\pi$
$968$	28.5280	0.916926
$969$	0.930207	0.0298825
$970$	83.3142	2.67506
$971$	−15.5571	−0.499250	−0.249625	−	0.968343i	$-0.580307\pi$
$971$	−15.5571	−0.499250	−0.249625	+	0.968343i	$0.580307\pi$
$972$	3.87556	0.124309
$973$	−65.0999	−2.08701
$974$	−2.46422	−0.0789586
$975$	49.3391	1.58012
$976$	−7.89457	−0.252699
$977$	4.33697	0.138752	0.0693760	−	0.997591i	$-0.477899\pi$
$977$	4.33697	0.138752	0.0693760	+	0.997591i	$0.477899\pi$
$978$	−41.4487	−1.32538
$979$	−24.5504	−0.784633
$980$	−86.0789	−2.74969
$981$	7.53671	0.240629
$982$	−80.0607	−2.55484
$983$	47.8692	1.52679	0.763396	−	0.645931i	$-0.223531\pi$
$983$	47.8692	1.52679	0.763396	+	0.645931i	$0.223531\pi$
$984$	24.3056	0.774834
$985$	72.4994	2.31002
$986$	8.91298	0.283847
$987$	−43.3486	−1.37980
$988$	−58.2849	−1.85429
$989$	1.59754	0.0507988
$990$	18.4347	0.585894
$991$	24.2533	0.770433	0.385216	−	0.922826i	$-0.374127\pi$
$991$	24.2533	0.770433	0.385216	+	0.922826i	$0.374127\pi$
$992$	−5.41329	−0.171872
$993$	−20.5319	−0.651559
$994$	−82.5874	−2.61951
$995$	47.2672	1.49847
$996$	37.3344	1.18299
$997$	−40.9679	−1.29747	−0.648734	−	0.761016i	$-0.724701\pi$
$997$	−40.9679	−1.29747	−0.648734	+	0.761016i	$0.724701\pi$
$998$	−95.6041	−3.02630
$999$	9.80107	0.310092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.d.1.13	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.d.1.13	✓	129	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42396 q^{2} +1.00000 q^{3} +3.87556 q^{4} -3.49875 q^{5} -2.42396 q^{6} +3.65352 q^{7} -4.54627 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.42396 q^{2} +1.00000 q^{3} +3.87556 q^{4} -3.49875 q^{5} -2.42396 q^{6} +3.65352 q^{7} -4.54627 q^{8} +1.00000 q^{9} +8.48081 q^{10} +2.17370 q^{11} +3.87556 q^{12} +6.81364 q^{13} -8.85596 q^{14} -3.49875 q^{15} +3.26884 q^{16} -0.421441 q^{17} -2.42396 q^{18} -2.20721 q^{19} -13.5596 q^{20} +3.65352 q^{21} -5.26895 q^{22} +0.385037 q^{23} -4.54627 q^{24} +7.24123 q^{25} -16.5159 q^{26} +1.00000 q^{27} +14.1594 q^{28} +8.72492 q^{29} +8.48081 q^{30} -4.63064 q^{31} +1.16902 q^{32} +2.17370 q^{33} +1.02155 q^{34} -12.7827 q^{35} +3.87556 q^{36} +9.80107 q^{37} +5.35017 q^{38} +6.81364 q^{39} +15.9063 q^{40} -5.34627 q^{41} -8.85596 q^{42} +4.14906 q^{43} +8.42429 q^{44} -3.49875 q^{45} -0.933312 q^{46} -11.8649 q^{47} +3.26884 q^{48} +6.34819 q^{49} -17.5524 q^{50} -0.421441 q^{51} +26.4066 q^{52} +14.2918 q^{53} -2.42396 q^{54} -7.60522 q^{55} -16.6099 q^{56} -2.20721 q^{57} -21.1488 q^{58} +2.13849 q^{59} -13.5596 q^{60} -2.41510 q^{61} +11.2245 q^{62} +3.65352 q^{63} -9.37133 q^{64} -23.8392 q^{65} -5.26895 q^{66} +7.50974 q^{67} -1.63332 q^{68} +0.385037 q^{69} +30.9848 q^{70} +9.32563 q^{71} -4.54627 q^{72} +9.42477 q^{73} -23.7573 q^{74} +7.24123 q^{75} -8.55416 q^{76} +7.94164 q^{77} -16.5159 q^{78} -10.4022 q^{79} -11.4369 q^{80} +1.00000 q^{81} +12.9591 q^{82} +9.63330 q^{83} +14.1594 q^{84} +1.47451 q^{85} -10.0571 q^{86} +8.72492 q^{87} -9.88222 q^{88} -11.2943 q^{89} +8.48081 q^{90} +24.8937 q^{91} +1.49223 q^{92} -4.63064 q^{93} +28.7600 q^{94} +7.72246 q^{95} +1.16902 q^{96} +9.82385 q^{97} -15.3877 q^{98} +2.17370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * q^99

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