LMFDB - Embedded newform 8027.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47345 q^{2} -2.21693 q^{3} +4.11797 q^{4} -0.996079 q^{5} +5.48348 q^{6} +1.88032 q^{7} -5.23870 q^{8} +1.91479 q^{9} +O(q^{10})$	\(q-2.47345 q^{2} -2.21693 q^{3} +4.11797 q^{4} -0.996079 q^{5} +5.48348 q^{6} +1.88032 q^{7} -5.23870 q^{8} +1.91479 q^{9} +2.46376 q^{10} -1.24882 q^{11} -9.12926 q^{12} -0.803083 q^{13} -4.65088 q^{14} +2.20824 q^{15} +4.72174 q^{16} -0.930436 q^{17} -4.73613 q^{18} +6.20106 q^{19} -4.10182 q^{20} -4.16854 q^{21} +3.08890 q^{22} +1.00000 q^{23} +11.6138 q^{24} -4.00783 q^{25} +1.98639 q^{26} +2.40585 q^{27} +7.74309 q^{28} -1.98858 q^{29} -5.46198 q^{30} +9.15227 q^{31} -1.20160 q^{32} +2.76855 q^{33} +2.30139 q^{34} -1.87295 q^{35} +7.88503 q^{36} +0.596239 q^{37} -15.3380 q^{38} +1.78038 q^{39} +5.21816 q^{40} -8.17800 q^{41} +10.3107 q^{42} +6.27933 q^{43} -5.14261 q^{44} -1.90728 q^{45} -2.47345 q^{46} +5.78681 q^{47} -10.4678 q^{48} -3.46440 q^{49} +9.91317 q^{50} +2.06271 q^{51} -3.30707 q^{52} -4.20753 q^{53} -5.95075 q^{54} +1.24393 q^{55} -9.85042 q^{56} -13.7473 q^{57} +4.91866 q^{58} -5.45655 q^{59} +9.09346 q^{60} -4.99497 q^{61} -22.6377 q^{62} +3.60040 q^{63} -6.47138 q^{64} +0.799934 q^{65} -6.84788 q^{66} -1.85913 q^{67} -3.83151 q^{68} -2.21693 q^{69} +4.63264 q^{70} +1.82003 q^{71} -10.0310 q^{72} +10.1626 q^{73} -1.47477 q^{74} +8.88508 q^{75} +25.5358 q^{76} -2.34818 q^{77} -4.40369 q^{78} +11.3664 q^{79} -4.70322 q^{80} -11.0780 q^{81} +20.2279 q^{82} +10.6081 q^{83} -17.1659 q^{84} +0.926788 q^{85} -15.5316 q^{86} +4.40854 q^{87} +6.54220 q^{88} -0.00820211 q^{89} +4.71756 q^{90} -1.51005 q^{91} +4.11797 q^{92} -20.2899 q^{93} -14.3134 q^{94} -6.17674 q^{95} +2.66386 q^{96} +3.33566 q^{97} +8.56904 q^{98} -2.39123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.47345	−1.74900	−0.874498	−	0.485030i	$-0.838809\pi$
$2$	−2.47345	−1.74900	−0.874498	+	0.485030i	$0.838809\pi$
$3$	−2.21693	−1.27995	−0.639973	−	0.768397i	$-0.721054\pi$
$3$	−2.21693	−1.27995	−0.639973	+	0.768397i	$0.721054\pi$
$4$	4.11797	2.05899
$5$	−0.996079	−0.445460	−0.222730	−	0.974880i	$-0.571497\pi$
$5$	−0.996079	−0.445460	−0.222730	+	0.974880i	$0.571497\pi$
$6$	5.48348	2.23862
$7$	1.88032	0.710693	0.355347	−	0.934735i	$-0.384363\pi$
$7$	1.88032	0.710693	0.355347	+	0.934735i	$0.384363\pi$
$8$	−5.23870	−1.85216
$9$	1.91479	0.638262
$10$	2.46376	0.779108
$11$	−1.24882	−0.376534	−0.188267	−	0.982118i	$-0.560287\pi$
$11$	−1.24882	−0.376534	−0.188267	+	0.982118i	$0.560287\pi$
$12$	−9.12926	−2.63539
$13$	−0.803083	−0.222735	−0.111368	−	0.993779i	$-0.535523\pi$
$13$	−0.803083	−0.222735	−0.111368	+	0.993779i	$0.535523\pi$
$14$	−4.65088	−1.24300
$15$	2.20824	0.570165
$16$	4.72174	1.18043
$17$	−0.930436	−0.225664	−0.112832	−	0.993614i	$-0.535992\pi$
$17$	−0.930436	−0.225664	−0.112832	+	0.993614i	$0.535992\pi$
$18$	−4.73613	−1.11632
$19$	6.20106	1.42262	0.711310	−	0.702879i	$-0.248102\pi$
$19$	6.20106	1.42262	0.711310	+	0.702879i	$0.248102\pi$
$20$	−4.10182	−0.917196
$21$	−4.16854	−0.909649
$22$	3.08890	0.658556
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	11.6138	2.37066
$25$	−4.00783	−0.801565
$26$	1.98639	0.389563
$27$	2.40585	0.463005
$28$	7.74309	1.46331
$29$	−1.98858	−0.369270	−0.184635	−	0.982807i	$-0.559110\pi$
$29$	−1.98858	−0.369270	−0.184635	+	0.982807i	$0.559110\pi$
$30$	−5.46198	−0.997216
$31$	9.15227	1.64380	0.821898	−	0.569635i	$-0.192915\pi$
$31$	9.15227	1.64380	0.821898	+	0.569635i	$0.192915\pi$
$32$	−1.20160	−0.212414
$33$	2.76855	0.481943
$34$	2.30139	0.394685
$35$	−1.87295	−0.316586
$36$	7.88503	1.31417
$37$	0.596239	0.0980211	0.0490106	−	0.998798i	$-0.484393\pi$
$37$	0.596239	0.0980211	0.0490106	+	0.998798i	$0.484393\pi$
$38$	−15.3380	−2.48816
$39$	1.78038	0.285089
$40$	5.21816	0.825063
$41$	−8.17800	−1.27719	−0.638594	−	0.769544i	$-0.720484\pi$
$41$	−8.17800	−1.27719	−0.638594	+	0.769544i	$0.720484\pi$
$42$	10.3107	1.59097
$43$	6.27933	0.957589	0.478795	−	0.877927i	$-0.341074\pi$
$43$	6.27933	0.957589	0.478795	+	0.877927i	$0.341074\pi$
$44$	−5.14261	−0.775278
$45$	−1.90728	−0.284320
$46$	−2.47345	−0.364691
$47$	5.78681	0.844093	0.422046	−	0.906574i	$-0.361312\pi$
$47$	5.78681	0.844093	0.422046	+	0.906574i	$0.361312\pi$
$48$	−10.4678	−1.51089
$49$	−3.46440	−0.494915
$50$	9.91317	1.40193
$51$	2.06271	0.288838
$52$	−3.30707	−0.458608
$53$	−4.20753	−0.577948	−0.288974	−	0.957337i	$-0.593314\pi$
$53$	−4.20753	−0.577948	−0.288974	+	0.957337i	$0.593314\pi$
$54$	−5.95075	−0.809794
$55$	1.24393	0.167731
$56$	−9.85042	−1.31632
$57$	−13.7473	−1.82088
$58$	4.91866	0.645851
$59$	−5.45655	−0.710382	−0.355191	−	0.934794i	$-0.615584\pi$
$59$	−5.45655	−0.710382	−0.355191	+	0.934794i	$0.615584\pi$
$60$	9.09346	1.17396
$61$	−4.99497	−0.639541	−0.319770	−	0.947495i	$-0.603606\pi$
$61$	−4.99497	−0.639541	−0.319770	+	0.947495i	$0.603606\pi$
$62$	−22.6377	−2.87499
$63$	3.60040	0.453608
$64$	−6.47138	−0.808923
$65$	0.799934	0.0992196
$66$	−6.84788	−0.842916
$67$	−1.85913	−0.227129	−0.113565	−	0.993531i	$-0.536227\pi$
$67$	−1.85913	−0.227129	−0.113565	+	0.993531i	$0.536227\pi$
$68$	−3.83151	−0.464639
$69$	−2.21693	−0.266887
$70$	4.63264	0.553707
$71$	1.82003	0.215998	0.107999	−	0.994151i	$-0.465556\pi$
$71$	1.82003	0.215998	0.107999	+	0.994151i	$0.465556\pi$
$72$	−10.0310	−1.18216
$73$	10.1626	1.18945	0.594724	−	0.803930i	$-0.297261\pi$
$73$	10.1626	1.18945	0.594724	+	0.803930i	$0.297261\pi$
$74$	−1.47477	−0.171438
$75$	8.88508	1.02596
$76$	25.5358	2.92915
$77$	−2.34818	−0.267600
$78$	−4.40369	−0.498619
$79$	11.3664	1.27882	0.639411	−	0.768865i	$-0.279178\pi$
$79$	11.3664	1.27882	0.639411	+	0.768865i	$0.279178\pi$
$80$	−4.70322	−0.525837
$81$	−11.0780	−1.23088
$82$	20.2279	2.23380
$83$	10.6081	1.16439	0.582195	−	0.813049i	$-0.302194\pi$
$83$	10.6081	1.16439	0.582195	+	0.813049i	$0.302194\pi$
$84$	−17.1659	−1.87295
$85$	0.926788	0.100524
$86$	−15.5316	−1.67482
$87$	4.40854	0.472646
$88$	6.54220	0.697401
$89$	−0.00820211	−0.000869422 0	−0.000434711	−	1.00000i	$-0.500138\pi$
$89$	−0.00820211	−0.000869422 0	−0.000434711		1.00000i	$0.500138\pi$
$90$	4.71756	0.497275
$91$	−1.51005	−0.158296
$92$	4.11797	0.429328
$93$	−20.2899	−2.10397
$94$	−14.3134	−1.47631
$95$	−6.17674	−0.633720
$96$	2.66386	0.271879
$97$	3.33566	0.338685	0.169342	−	0.985557i	$-0.445836\pi$
$97$	3.33566	0.338685	0.169342	+	0.985557i	$0.445836\pi$
$98$	8.56904	0.865604
$99$	−2.39123	−0.240327
$100$	−16.5041	−1.65041
$101$	14.0354	1.39658	0.698288	−	0.715817i	$-0.253945\pi$
$101$	14.0354	1.39658	0.698288	+	0.715817i	$0.253945\pi$
$102$	−5.10202	−0.505176
$103$	−7.69035	−0.757753	−0.378876	−	0.925447i	$-0.623689\pi$
$103$	−7.69035	−0.757753	−0.378876	+	0.925447i	$0.623689\pi$
$104$	4.20711	0.412541
$105$	4.15219	0.405212
$106$	10.4071	1.01083
$107$	11.2230	1.08497	0.542483	−	0.840067i	$-0.317484\pi$
$107$	11.2230	1.08497	0.542483	+	0.840067i	$0.317484\pi$
$108$	9.90721	0.953321
$109$	−3.52532	−0.337665	−0.168832	−	0.985645i	$-0.554000\pi$
$109$	−3.52532	−0.337665	−0.168832	+	0.985645i	$0.554000\pi$
$110$	−3.07679	−0.293360
$111$	−1.32182	−0.125462
$112$	8.87837	0.838927
$113$	−10.0578	−0.946159	−0.473080	−	0.881020i	$-0.656858\pi$
$113$	−10.0578	−0.946159	−0.473080	+	0.881020i	$0.656858\pi$
$114$	34.0033	3.18470
$115$	−0.996079	−0.0928849
$116$	−8.18891	−0.760321
$117$	−1.53773	−0.142163
$118$	13.4965	1.24245
$119$	−1.74952	−0.160378
$120$	−11.5683	−1.05604
$121$	−9.44044	−0.858222
$122$	12.3548	1.11855
$123$	18.1301	1.63473
$124$	37.6888	3.38455
$125$	8.97251	0.802526
$126$	−8.90543	−0.793359
$127$	13.7835	1.22309	0.611543	−	0.791211i	$-0.290549\pi$
$127$	13.7835	1.22309	0.611543	+	0.791211i	$0.290549\pi$
$128$	18.4099	1.62722
$129$	−13.9208	−1.22566
$130$	−1.97860	−0.173535
$131$	4.21251	0.368049	0.184024	−	0.982922i	$-0.441087\pi$
$131$	4.21251	0.368049	0.184024	+	0.982922i	$0.441087\pi$
$132$	11.4008	0.992314
$133$	11.6600	1.01105
$134$	4.59848	0.397248
$135$	−2.39641	−0.206250
$136$	4.87427	0.417966
$137$	−4.96817	−0.424459	−0.212230	−	0.977220i	$-0.568072\pi$
$137$	−4.96817	−0.424459	−0.212230	+	0.977220i	$0.568072\pi$
$138$	5.48348	0.466784
$139$	12.1301	1.02886	0.514431	−	0.857532i	$-0.328003\pi$
$139$	12.1301	1.02886	0.514431	+	0.857532i	$0.328003\pi$
$140$	−7.71273	−0.651845
$141$	−12.8290	−1.08039
$142$	−4.50177	−0.377780
$143$	1.00291	0.0838673
$144$	9.04111	0.753426
$145$	1.98078	0.164495
$146$	−25.1368	−2.08034
$147$	7.68035	0.633464
$148$	2.45530	0.201824
$149$	−11.4974	−0.941906	−0.470953	−	0.882158i	$-0.656090\pi$
$149$	−11.4974	−0.941906	−0.470953	+	0.882158i	$0.656090\pi$
$150$	−21.9768	−1.79440
$151$	15.9740	1.29994	0.649972	−	0.759958i	$-0.274781\pi$
$151$	15.9740	1.29994	0.649972	+	0.759958i	$0.274781\pi$
$152$	−32.4855	−2.63492
$153$	−1.78158	−0.144033
$154$	5.80812	0.468031
$155$	−9.11638	−0.732245
$156$	7.33155	0.586994
$157$	9.65439	0.770504	0.385252	−	0.922811i	$-0.374115\pi$
$157$	9.65439	0.770504	0.385252	+	0.922811i	$0.374115\pi$
$158$	−28.1143	−2.23665
$159$	9.32780	0.739743
$160$	1.19689	0.0946222
$161$	1.88032	0.148190
$162$	27.4008	2.15281
$163$	4.16764	0.326434	0.163217	−	0.986590i	$-0.447813\pi$
$163$	4.16764	0.326434	0.163217	+	0.986590i	$0.447813\pi$
$164$	−33.6768	−2.62971
$165$	−2.75770	−0.214686
$166$	−26.2386	−2.03651
$167$	−18.4989	−1.43148	−0.715742	−	0.698365i	$-0.753911\pi$
$167$	−18.4989	−1.43148	−0.715742	+	0.698365i	$0.753911\pi$
$168$	21.8377	1.68482
$169$	−12.3551	−0.950389
$170$	−2.29237	−0.175816
$171$	11.8737	0.908004
$172$	25.8581	1.97166
$173$	−2.67985	−0.203745	−0.101872	−	0.994797i	$-0.532483\pi$
$173$	−2.67985	−0.203745	−0.101872	+	0.994797i	$0.532483\pi$
$174$	−10.9043	−0.826655
$175$	−7.53599	−0.569667
$176$	−5.89661	−0.444474
$177$	12.0968	0.909250
$178$	0.0202875	0.00152061
$179$	−1.19995	−0.0896888	−0.0448444	−	0.998994i	$-0.514279\pi$
$179$	−1.19995	−0.0896888	−0.0448444	+	0.998994i	$0.514279\pi$
$180$	−7.85411	−0.585411
$181$	−2.32566	−0.172865	−0.0864324	−	0.996258i	$-0.527547\pi$
$181$	−2.32566	−0.172865	−0.0864324	+	0.996258i	$0.527547\pi$
$182$	3.73504	0.276860
$183$	11.0735	0.818578
$184$	−5.23870	−0.386202
$185$	−0.593901	−0.0436645
$186$	50.1862	3.67983
$187$	1.16195	0.0849701
$188$	23.8299	1.73797
$189$	4.52376	0.329055
$190$	15.2779	1.10837
$191$	10.0552	0.727569	0.363785	−	0.931483i	$-0.381484\pi$
$191$	10.0552	0.727569	0.363785	+	0.931483i	$0.381484\pi$
$192$	14.3466	1.03538
$193$	11.0793	0.797506	0.398753	−	0.917058i	$-0.369443\pi$
$193$	11.0793	0.797506	0.398753	+	0.917058i	$0.369443\pi$
$194$	−8.25059	−0.592358
$195$	−1.77340	−0.126996
$196$	−14.2663	−1.01902
$197$	−17.0512	−1.21485	−0.607423	−	0.794378i	$-0.707797\pi$
$197$	−17.0512	−1.21485	−0.607423	+	0.794378i	$0.707797\pi$
$198$	5.91458	0.420331
$199$	−12.2991	−0.871858	−0.435929	−	0.899981i	$-0.643580\pi$
$199$	−12.2991	−0.871858	−0.435929	+	0.899981i	$0.643580\pi$
$200$	20.9958	1.48463
$201$	4.12157	0.290713
$202$	−34.7160	−2.44261
$203$	−3.73916	−0.262438
$204$	8.49419	0.594712
$205$	8.14593	0.568937
$206$	19.0217	1.32531
$207$	1.91479	0.133087
$208$	−3.79195	−0.262924
$209$	−7.74401	−0.535665
$210$	−10.2703	−0.708715
$211$	−18.0793	−1.24463	−0.622315	−	0.782767i	$-0.713808\pi$
$211$	−18.0793	−1.24463	−0.622315	+	0.782767i	$0.713808\pi$
$212$	−17.3265	−1.18999
$213$	−4.03489	−0.276466
$214$	−27.7595	−1.89760
$215$	−6.25471	−0.426568
$216$	−12.6035	−0.857560
$217$	17.2092	1.16823
$218$	8.71972	0.590574
$219$	−22.5299	−1.52243
$220$	5.12245	0.345355
$221$	0.747217	0.0502633
$222$	3.26946	0.219432
$223$	1.42297	0.0952889	0.0476445	−	0.998864i	$-0.484829\pi$
$223$	1.42297	0.0952889	0.0476445	+	0.998864i	$0.484829\pi$
$224$	−2.25939	−0.150962
$225$	−7.67413	−0.511608
$226$	24.8775	1.65483
$227$	−2.02413	−0.134346	−0.0671732	−	0.997741i	$-0.521398\pi$
$227$	−2.02413	−0.134346	−0.0671732	+	0.997741i	$0.521398\pi$
$228$	−56.6110	−3.74916
$229$	7.52010	0.496942	0.248471	−	0.968639i	$-0.420072\pi$
$229$	7.52010	0.496942	0.248471	+	0.968639i	$0.420072\pi$
$230$	2.46376	0.162455
$231$	5.20576	0.342514
$232$	10.4176	0.683947
$233$	2.01986	0.132326	0.0661628	−	0.997809i	$-0.478924\pi$
$233$	2.01986	0.132326	0.0661628	+	0.997809i	$0.478924\pi$
$234$	3.80351	0.248643
$235$	−5.76412	−0.376010
$236$	−22.4699	−1.46267
$237$	−25.1986	−1.63682
$238$	4.32734	0.280500
$239$	2.95181	0.190937	0.0954684	−	0.995432i	$-0.469565\pi$
$239$	2.95181	0.190937	0.0954684	+	0.995432i	$0.469565\pi$
$240$	10.4267	0.673042
$241$	−6.58757	−0.424343	−0.212171	−	0.977232i	$-0.568053\pi$
$241$	−6.58757	−0.424343	−0.212171	+	0.977232i	$0.568053\pi$
$242$	23.3505	1.50103
$243$	17.3415	1.11246
$244$	−20.5691	−1.31680
$245$	3.45082	0.220465
$246$	−44.8439	−2.85914
$247$	−4.97996	−0.316867
$248$	−47.9460	−3.04457
$249$	−23.5174	−1.49036
$250$	−22.1931	−1.40361
$251$	−24.3433	−1.53653	−0.768267	−	0.640129i	$-0.778881\pi$
$251$	−24.3433	−1.53653	−0.768267	+	0.640129i	$0.778881\pi$
$252$	14.8264	0.933973
$253$	−1.24882	−0.0785127
$254$	−34.0928	−2.13917
$255$	−2.05463	−0.128666
$256$	−32.5931	−2.03707
$257$	27.9423	1.74299	0.871496	−	0.490402i	$-0.163150\pi$
$257$	27.9423	1.74299	0.871496	+	0.490402i	$0.163150\pi$
$258$	34.4326	2.14368
$259$	1.12112	0.0696630
$260$	3.29410	0.204292
$261$	−3.80770	−0.235691
$262$	−10.4194	−0.643716
$263$	8.05654	0.496788	0.248394	−	0.968659i	$-0.420097\pi$
$263$	8.05654	0.496788	0.248394	+	0.968659i	$0.420097\pi$
$264$	−14.5036	−0.892636
$265$	4.19103	0.257453
$266$	−28.8404	−1.76832
$267$	0.0181835	0.00111281
$268$	−7.65586	−0.467656
$269$	−4.58006	−0.279251	−0.139626	−	0.990204i	$-0.544590\pi$
$269$	−4.58006	−0.279251	−0.139626	+	0.990204i	$0.544590\pi$
$270$	5.92742	0.360731
$271$	−26.1138	−1.58630	−0.793150	−	0.609026i	$-0.791560\pi$
$271$	−26.1138	−1.58630	−0.793150	+	0.609026i	$0.791560\pi$
$272$	−4.39327	−0.266381
$273$	3.34768	0.202611
$274$	12.2885	0.742377
$275$	5.00506	0.301816
$276$	−9.12926	−0.549517
$277$	1.98074	0.119011	0.0595055	−	0.998228i	$-0.481048\pi$
$277$	1.98074	0.119011	0.0595055	+	0.998228i	$0.481048\pi$
$278$	−30.0032	−1.79947
$279$	17.5246	1.04917
$280$	9.81180	0.586367
$281$	12.3291	0.735494	0.367747	−	0.929926i	$-0.380129\pi$
$281$	12.3291	0.735494	0.367747	+	0.929926i	$0.380129\pi$
$282$	31.7318	1.88960
$283$	−8.94343	−0.531632	−0.265816	−	0.964024i	$-0.585641\pi$
$283$	−8.94343	−0.531632	−0.265816	+	0.964024i	$0.585641\pi$
$284$	7.49484	0.444737
$285$	13.6934	0.811128
$286$	−2.48064	−0.146684
$287$	−15.3772	−0.907690
$288$	−2.30080	−0.135576
$289$	−16.1343	−0.949076
$290$	−4.89937	−0.287701
$291$	−7.39492	−0.433498
$292$	41.8495	2.44905
$293$	−5.02944	−0.293823	−0.146911	−	0.989150i	$-0.546933\pi$
$293$	−5.02944	−0.293823	−0.146911	+	0.989150i	$0.546933\pi$
$294$	−18.9970	−1.10793
$295$	5.43515	0.316447
$296$	−3.12352	−0.181551
$297$	−3.00447	−0.174337
$298$	28.4383	1.64739
$299$	−0.803083	−0.0464435
$300$	36.5885	2.11244
$301$	11.8071	0.680552
$302$	−39.5109	−2.27360
$303$	−31.1156	−1.78754
$304$	29.2798	1.67931
$305$	4.97539	0.284890
$306$	4.40667	0.251912
$307$	3.91098	0.223212	0.111606	−	0.993753i	$-0.464401\pi$
$307$	3.91098	0.223212	0.111606	+	0.993753i	$0.464401\pi$
$308$	−9.66974	−0.550985
$309$	17.0490	0.969883
$310$	22.5489	1.28069
$311$	−9.26473	−0.525355	−0.262677	−	0.964884i	$-0.584605\pi$
$311$	−9.26473	−0.525355	−0.262677	+	0.964884i	$0.584605\pi$
$312$	−9.32687	−0.528030
$313$	5.70321	0.322365	0.161182	−	0.986925i	$-0.448469\pi$
$313$	5.70321	0.322365	0.161182	+	0.986925i	$0.448469\pi$
$314$	−23.8797	−1.34761
$315$	−3.58629	−0.202064
$316$	46.8066	2.63307
$317$	−17.3218	−0.972890	−0.486445	−	0.873711i	$-0.661707\pi$
$317$	−17.3218	−0.972890	−0.486445	+	0.873711i	$0.661707\pi$
$318$	−23.0719	−1.29381
$319$	2.48338	0.139043
$320$	6.44601	0.360343
$321$	−24.8806	−1.38870
$322$	−4.65088	−0.259183
$323$	−5.76968	−0.321034
$324$	−45.6187	−2.53437
$325$	3.21862	0.178537
$326$	−10.3085	−0.570932
$327$	7.81540	0.432193
$328$	42.8421	2.36556
$329$	10.8810	0.599891
$330$	6.82103	0.375486
$331$	0.926427	0.0509210	0.0254605	−	0.999676i	$-0.491895\pi$
$331$	0.926427	0.0509210	0.0254605	+	0.999676i	$0.491895\pi$
$332$	43.6838	2.39746
$333$	1.14167	0.0625631
$334$	45.7560	2.50366
$335$	1.85184	0.101177
$336$	−19.6827	−1.07378
$337$	11.6513	0.634687	0.317344	−	0.948311i	$-0.397209\pi$
$337$	11.6513	0.634687	0.317344	+	0.948311i	$0.397209\pi$
$338$	30.5597	1.66223
$339$	22.2975	1.21103
$340$	3.81648	0.206978
$341$	−11.4295	−0.618945
$342$	−29.3690	−1.58809
$343$	−19.6764	−1.06243
$344$	−32.8955	−1.77361
$345$	2.20824	0.118888
$346$	6.62847	0.356349
$347$	9.18483	0.493067	0.246534	−	0.969134i	$-0.420708\pi$
$347$	9.18483	0.493067	0.246534	+	0.969134i	$0.420708\pi$
$348$	18.1543	0.973170
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	18.6399	0.996345
$351$	−1.93209	−0.103128
$352$	1.50058	0.0799812
$353$	1.27850	0.0680475	0.0340237	−	0.999421i	$-0.489168\pi$
$353$	1.27850	0.0680475	0.0340237	+	0.999421i	$0.489168\pi$
$354$	−29.9208	−1.59027
$355$	−1.81290	−0.0962186
$356$	−0.0337760	−0.00179013
$357$	3.87856	0.205275
$358$	2.96803	0.156865
$359$	−12.2638	−0.647258	−0.323629	−	0.946184i	$-0.604903\pi$
$359$	−12.2638	−0.647258	−0.323629	+	0.946184i	$0.604903\pi$
$360$	9.99165	0.526606
$361$	19.4531	1.02385
$362$	5.75240	0.302340
$363$	20.9288	1.09848
$364$	−6.21834	−0.325930
$365$	−10.1228	−0.529852
$366$	−27.3898	−1.43169
$367$	5.59851	0.292240	0.146120	−	0.989267i	$-0.453321\pi$
$367$	5.59851	0.292240	0.146120	+	0.989267i	$0.453321\pi$
$368$	4.72174	0.246138
$369$	−15.6591	−0.815181
$370$	1.46899	0.0763690
$371$	−7.91149	−0.410744
$372$	−83.5534	−4.33204
$373$	31.0890	1.60973	0.804863	−	0.593461i	$-0.202239\pi$
$373$	31.0890	1.60973	0.804863	+	0.593461i	$0.202239\pi$
$374$	−2.87403	−0.148612
$375$	−19.8914	−1.02719
$376$	−30.3154	−1.56340
$377$	1.59699	0.0822494
$378$	−11.1893	−0.575515
$379$	−31.6292	−1.62468	−0.812342	−	0.583181i	$-0.801808\pi$
$379$	−31.6292	−1.62468	−0.812342	+	0.583181i	$0.801808\pi$
$380$	−25.4356	−1.30482
$381$	−30.5571	−1.56549
$382$	−24.8711	−1.27252
$383$	−24.3120	−1.24228	−0.621142	−	0.783698i	$-0.713331\pi$
$383$	−24.3120	−1.24228	−0.621142	+	0.783698i	$0.713331\pi$
$384$	−40.8134	−2.08275
$385$	2.33897	0.119205
$386$	−27.4041	−1.39483
$387$	12.0236	0.611193
$388$	13.7361	0.697347
$389$	−8.45824	−0.428850	−0.214425	−	0.976740i	$-0.568788\pi$
$389$	−8.45824	−0.428850	−0.214425	+	0.976740i	$0.568788\pi$
$390$	4.38642	0.222115
$391$	−0.930436	−0.0470542
$392$	18.1490	0.916662
$393$	−9.33885	−0.471083
$394$	42.1753	2.12476
$395$	−11.3219	−0.569664
$396$	−9.84699	−0.494830
$397$	−19.2627	−0.966765	−0.483383	−	0.875409i	$-0.660592\pi$
$397$	−19.2627	−0.966765	−0.483383	+	0.875409i	$0.660592\pi$
$398$	30.4212	1.52488
$399$	−25.8493	−1.29408
$400$	−18.9239	−0.946195
$401$	−25.2703	−1.26194	−0.630968	−	0.775809i	$-0.717342\pi$
$401$	−25.2703	−1.26194	−0.630968	+	0.775809i	$0.717342\pi$
$402$	−10.1945	−0.508456
$403$	−7.35003	−0.366131
$404$	57.7975	2.87553
$405$	11.0345	0.548310
$406$	9.24864	0.459002
$407$	−0.744596	−0.0369083
$408$	−10.8059	−0.534973
$409$	−11.4224	−0.564801	−0.282401	−	0.959297i	$-0.591131\pi$
$409$	−11.4224	−0.564801	−0.282401	+	0.959297i	$0.591131\pi$
$410$	−20.1486	−0.995068
$411$	11.0141	0.543285
$412$	−31.6686	−1.56020
$413$	−10.2600	−0.504864
$414$	−4.73613	−0.232768
$415$	−10.5665	−0.518689
$416$	0.964982	0.0473122
$417$	−26.8916	−1.31689
$418$	19.1545	0.936875
$419$	21.0921	1.03041	0.515207	−	0.857066i	$-0.327715\pi$
$419$	21.0921	1.03041	0.515207	+	0.857066i	$0.327715\pi$
$420$	17.0986	0.834326
$421$	−10.2148	−0.497838	−0.248919	−	0.968524i	$-0.580075\pi$
$421$	−10.2148	−0.497838	−0.248919	+	0.968524i	$0.580075\pi$
$422$	44.7183	2.17685
$423$	11.0805	0.538752
$424$	22.0420	1.07045
$425$	3.72903	0.180884
$426$	9.98011	0.483538
$427$	−9.39214	−0.454517
$428$	46.2159	2.23393
$429$	−2.22338	−0.107346
$430$	15.4707	0.746065
$431$	17.3087	0.833729	0.416865	−	0.908969i	$-0.363129\pi$
$431$	17.3087	0.833729	0.416865	+	0.908969i	$0.363129\pi$
$432$	11.3598	0.546548
$433$	3.03391	0.145801	0.0729003	−	0.997339i	$-0.476775\pi$
$433$	3.03391	0.145801	0.0729003	+	0.997339i	$0.476775\pi$
$434$	−42.5661	−2.04324
$435$	−4.39126	−0.210545
$436$	−14.5172	−0.695247
$437$	6.20106	0.296637
$438$	55.7266	2.66272
$439$	18.3388	0.875261	0.437631	−	0.899155i	$-0.355818\pi$
$439$	18.3388	0.875261	0.437631	+	0.899155i	$0.355818\pi$
$440$	−6.51655	−0.310664
$441$	−6.63359	−0.315885
$442$	−1.84821	−0.0879102
$443$	2.87170	0.136438	0.0682192	−	0.997670i	$-0.478268\pi$
$443$	2.87170	0.136438	0.0682192	+	0.997670i	$0.478268\pi$
$444$	−5.44322	−0.258324
$445$	0.00816995	0.000387293 0
$446$	−3.51964	−0.166660
$447$	25.4890	1.20559
$448$	−12.1683	−0.574896
$449$	4.84889	0.228833	0.114417	−	0.993433i	$-0.463500\pi$
$449$	4.84889	0.228833	0.114417	+	0.993433i	$0.463500\pi$
$450$	18.9816	0.894801
$451$	10.2129	0.480905
$452$	−41.4178	−1.94813
$453$	−35.4132	−1.66386
$454$	5.00660	0.234971
$455$	1.50413	0.0705147
$456$	72.0181	3.37255
$457$	−30.4075	−1.42240	−0.711201	−	0.702989i	$-0.751848\pi$
$457$	−30.4075	−1.42240	−0.711201	+	0.702989i	$0.751848\pi$
$458$	−18.6006	−0.869149
$459$	−2.23849	−0.104484
$460$	−4.10182	−0.191249
$461$	24.2902	1.13131	0.565653	−	0.824643i	$-0.308624\pi$
$461$	24.2902	1.13131	0.565653	+	0.824643i	$0.308624\pi$
$462$	−12.8762	−0.599055
$463$	13.3552	0.620666	0.310333	−	0.950628i	$-0.399559\pi$
$463$	13.3552	0.620666	0.310333	+	0.950628i	$0.399559\pi$
$464$	−9.38955	−0.435899
$465$	20.2104	0.937235
$466$	−4.99603	−0.231437
$467$	−17.1338	−0.792859	−0.396430	−	0.918065i	$-0.629751\pi$
$467$	−17.1338	−0.792859	−0.396430	+	0.918065i	$0.629751\pi$
$468$	−6.33233	−0.292712
$469$	−3.49576	−0.161419
$470$	14.2573	0.657639
$471$	−21.4031	−0.986204
$472$	28.5852	1.31574
$473$	−7.84177	−0.360565
$474$	62.3275	2.86280
$475$	−24.8528	−1.14032
$476$	−7.20445	−0.330216
$477$	−8.05651	−0.368882
$478$	−7.30116	−0.333948
$479$	4.78030	0.218417	0.109209	−	0.994019i	$-0.465168\pi$
$479$	4.78030	0.218417	0.109209	+	0.994019i	$0.465168\pi$
$480$	−2.65341	−0.121111
$481$	−0.478829	−0.0218327
$482$	16.2940	0.742173
$483$	−4.16854	−0.189675
$484$	−38.8755	−1.76707
$485$	−3.32258	−0.150871
$486$	−42.8934	−1.94569
$487$	−20.1740	−0.914170	−0.457085	−	0.889423i	$-0.651107\pi$
$487$	−20.1740	−0.914170	−0.457085	+	0.889423i	$0.651107\pi$
$488$	26.1672	1.18453
$489$	−9.23936	−0.417818
$490$	−8.53545	−0.385592
$491$	−8.25587	−0.372582	−0.186291	−	0.982495i	$-0.559647\pi$
$491$	−8.25587	−0.372582	−0.186291	+	0.982495i	$0.559647\pi$
$492$	74.6591	3.36589
$493$	1.85025	0.0833309
$494$	12.3177	0.554199
$495$	2.38185	0.107056
$496$	43.2146	1.94039
$497$	3.42224	0.153508
$498$	58.1692	2.60663
$499$	12.2623	0.548934	0.274467	−	0.961597i	$-0.411499\pi$
$499$	12.2623	0.548934	0.274467	+	0.961597i	$0.411499\pi$
$500$	36.9485	1.65239
$501$	41.0107	1.83222
$502$	60.2120	2.68739
$503$	31.4085	1.40043	0.700217	−	0.713930i	$-0.253086\pi$
$503$	31.4085	1.40043	0.700217	+	0.713930i	$0.253086\pi$
$504$	−18.8614	−0.840155
$505$	−13.9804	−0.622119
$506$	3.08890	0.137318
$507$	27.3903	1.21645
$508$	56.7600	2.51832
$509$	30.4049	1.34767	0.673837	−	0.738880i	$-0.264645\pi$
$509$	30.4049	1.34767	0.673837	+	0.738880i	$0.264645\pi$
$510$	5.08202	0.225036
$511$	19.1090	0.845333
$512$	43.7979	1.93561
$513$	14.9188	0.658681
$514$	−69.1140	−3.04849
$515$	7.66020	0.337549
$516$	−57.3256	−2.52362
$517$	−7.22669	−0.317830
$518$	−2.77304	−0.121840
$519$	5.94103	0.260782
$520$	−4.19061	−0.183771
$521$	−34.6938	−1.51996	−0.759982	−	0.649944i	$-0.774792\pi$
$521$	−34.6938	−1.51996	−0.759982	+	0.649944i	$0.774792\pi$
$522$	9.41817	0.412222
$523$	35.2593	1.54178	0.770890	−	0.636968i	$-0.219812\pi$
$523$	35.2593	1.54178	0.770890	+	0.636968i	$0.219812\pi$
$524$	17.3470	0.757807
$525$	16.7068	0.729143
$526$	−19.9275	−0.868880
$527$	−8.51560	−0.370945
$528$	13.0724	0.568902
$529$	1.00000	0.0434783
$530$	−10.3663	−0.450284
$531$	−10.4481	−0.453410
$532$	48.0153	2.08173
$533$	6.56761	0.284475
$534$	−0.0449761	−0.00194630
$535$	−11.1790	−0.483309
$536$	9.73945	0.420680
$537$	2.66022	0.114797
$538$	11.3286	0.488409
$539$	4.32642	0.186352
$540$	−9.86836	−0.424667
$541$	−19.0635	−0.819604	−0.409802	−	0.912175i	$-0.634402\pi$
$541$	−19.0635	−0.819604	−0.409802	+	0.912175i	$0.634402\pi$
$542$	64.5912	2.77443
$543$	5.15582	0.221257
$544$	1.11801	0.0479343
$545$	3.51150	0.150416
$546$	−8.28033	−0.354365
$547$	−26.7725	−1.14471	−0.572354	−	0.820006i	$-0.693970\pi$
$547$	−26.7725	−1.14471	−0.572354	+	0.820006i	$0.693970\pi$
$548$	−20.4588	−0.873955
$549$	−9.56430	−0.408194
$550$	−12.3798	−0.527876
$551$	−12.3313	−0.525331
$552$	11.6138	0.494318
$553$	21.3725	0.908850
$554$	−4.89926	−0.208150
$555$	1.31664	0.0558882
$556$	49.9514	2.11841
$557$	−26.9576	−1.14223	−0.571115	−	0.820870i	$-0.693489\pi$
$557$	−26.9576	−1.14223	−0.571115	+	0.820870i	$0.693489\pi$
$558$	−43.3463	−1.83500
$559$	−5.04282	−0.213289
$560$	−8.84356	−0.373708
$561$	−2.57596	−0.108757
$562$	−30.4955	−1.28638
$563$	23.1606	0.976103	0.488052	−	0.872815i	$-0.337708\pi$
$563$	23.1606	0.976103	0.488052	+	0.872815i	$0.337708\pi$
$564$	−52.8293	−2.22451
$565$	10.0184	0.421476
$566$	22.1211	0.929821
$567$	−20.8301	−0.874781
$568$	−9.53461	−0.400063
$569$	−2.35378	−0.0986755	−0.0493378	−	0.998782i	$-0.515711\pi$
$569$	−2.35378	−0.0986755	−0.0493378	+	0.998782i	$0.515711\pi$
$570$	−33.8700	−1.41866
$571$	8.63857	0.361513	0.180757	−	0.983528i	$-0.442145\pi$
$571$	8.63857	0.361513	0.180757	+	0.983528i	$0.442145\pi$
$572$	4.12994	0.172682
$573$	−22.2917	−0.931249
$574$	38.0349	1.58754
$575$	−4.00783	−0.167138
$576$	−12.3913	−0.516304
$577$	18.7681	0.781326	0.390663	−	0.920534i	$-0.372246\pi$
$577$	18.7681	0.781326	0.390663	+	0.920534i	$0.372246\pi$
$578$	39.9074	1.65993
$579$	−24.5621	−1.02076
$580$	8.15680	0.338693
$581$	19.9466	0.827524
$582$	18.2910	0.758186
$583$	5.25445	0.217617
$584$	−53.2390	−2.20305
$585$	1.53170	0.0633281
$586$	12.4401	0.513895
$587$	−16.1141	−0.665099	−0.332549	−	0.943086i	$-0.607909\pi$
$587$	−16.1141	−0.665099	−0.332549	+	0.943086i	$0.607909\pi$
$588$	31.6274	1.30429
$589$	56.7537	2.33850
$590$	−13.4436	−0.553464
$591$	37.8013	1.55494
$592$	2.81529	0.115708
$593$	21.6882	0.890629	0.445315	−	0.895374i	$-0.353092\pi$
$593$	21.6882	0.890629	0.445315	+	0.895374i	$0.353092\pi$
$594$	7.43142	0.304915
$595$	1.74266	0.0714419
$596$	−47.3461	−1.93937
$597$	27.2662	1.11593
$598$	1.98639	0.0812294
$599$	−38.1893	−1.56037	−0.780186	−	0.625548i	$-0.784875\pi$
$599$	−38.1893	−1.56037	−0.780186	+	0.625548i	$0.784875\pi$
$600$	−46.5462	−1.90024
$601$	33.5784	1.36969	0.684845	−	0.728689i	$-0.259870\pi$
$601$	33.5784	1.36969	0.684845	+	0.728689i	$0.259870\pi$
$602$	−29.2044	−1.19028
$603$	−3.55984	−0.144968
$604$	65.7804	2.67656
$605$	9.40343	0.382304
$606$	76.9629	3.12640
$607$	21.4948	0.872448	0.436224	−	0.899838i	$-0.356316\pi$
$607$	21.4948	0.872448	0.436224	+	0.899838i	$0.356316\pi$
$608$	−7.45117	−0.302185
$609$	8.28947	0.335906
$610$	−12.3064	−0.498271
$611$	−4.64729	−0.188009
$612$	−7.33651	−0.296561
$613$	−4.55578	−0.184006	−0.0920031	−	0.995759i	$-0.529327\pi$
$613$	−4.55578	−0.184006	−0.0920031	+	0.995759i	$0.529327\pi$
$614$	−9.67364	−0.390396
$615$	−18.0590	−0.728208
$616$	12.3014	0.495638
$617$	32.5855	1.31184	0.655921	−	0.754829i	$-0.272280\pi$
$617$	32.5855	1.31184	0.655921	+	0.754829i	$0.272280\pi$
$618$	−42.1699	−1.69632
$619$	19.2418	0.773391	0.386696	−	0.922207i	$-0.373616\pi$
$619$	19.2418	0.773391	0.386696	+	0.922207i	$0.373616\pi$
$620$	−37.5410	−1.50768
$621$	2.40585	0.0965433
$622$	22.9159	0.918843
$623$	−0.0154226	−0.000617892 0
$624$	8.40649	0.336529
$625$	11.1018	0.444072
$626$	−14.1066	−0.563814
$627$	17.1679	0.685622
$628$	39.7565	1.58646
$629$	−0.554762	−0.0221198
$630$	8.87052	0.353410
$631$	−22.4410	−0.893361	−0.446680	−	0.894694i	$-0.647394\pi$
$631$	−22.4410	−0.893361	−0.446680	+	0.894694i	$0.647394\pi$
$632$	−59.5452	−2.36858
$633$	40.0806	1.59306
$634$	42.8447	1.70158
$635$	−13.7294	−0.544836
$636$	38.4116	1.52312
$637$	2.78220	0.110235
$638$	−6.14253	−0.243185
$639$	3.48497	0.137863
$640$	−18.3377	−0.724860
$641$	28.4505	1.12373	0.561864	−	0.827229i	$-0.310084\pi$
$641$	28.4505	1.12373	0.561864	+	0.827229i	$0.310084\pi$
$642$	61.5410	2.42883
$643$	45.8015	1.80624	0.903118	−	0.429392i	$-0.141272\pi$
$643$	45.8015	1.80624	0.903118	+	0.429392i	$0.141272\pi$
$644$	7.74309	0.305121
$645$	13.8663	0.545984
$646$	14.2710	0.561487
$647$	−13.0083	−0.511410	−0.255705	−	0.966755i	$-0.582308\pi$
$647$	−13.0083	−0.511410	−0.255705	+	0.966755i	$0.582308\pi$
$648$	58.0341	2.27979
$649$	6.81425	0.267483
$650$	−7.96110	−0.312260
$651$	−38.1516	−1.49528
$652$	17.1622	0.672124
$653$	20.2771	0.793506	0.396753	−	0.917925i	$-0.370137\pi$
$653$	20.2771	0.793506	0.396753	+	0.917925i	$0.370137\pi$
$654$	−19.3310	−0.755903
$655$	−4.19599	−0.163951
$656$	−38.6144	−1.50764
$657$	19.4593	0.759179
$658$	−26.9137	−1.04921
$659$	−8.00052	−0.311656	−0.155828	−	0.987784i	$-0.549805\pi$
$659$	−8.00052	−0.311656	−0.155828	+	0.987784i	$0.549805\pi$
$660$	−11.3561	−0.442036
$661$	21.4404	0.833936	0.416968	−	0.908921i	$-0.363093\pi$
$661$	21.4404	0.833936	0.416968	+	0.908921i	$0.363093\pi$
$662$	−2.29147	−0.0890606
$663$	−1.65653	−0.0643343
$664$	−55.5726	−2.15664
$665$	−11.6142	−0.450381
$666$	−2.82387	−0.109423
$667$	−1.98858	−0.0769981
$668$	−76.1777	−2.94740
$669$	−3.15462	−0.121965
$670$	−4.58045	−0.176958
$671$	6.23783	0.240809
$672$	5.00890	0.193223
$673$	−20.8839	−0.805016	−0.402508	−	0.915416i	$-0.631861\pi$
$673$	−20.8839	−0.805016	−0.402508	+	0.915416i	$0.631861\pi$
$674$	−28.8190	−1.11006
$675$	−9.64222	−0.371129
$676$	−50.8778	−1.95684
$677$	−0.643454	−0.0247299	−0.0123650	−	0.999924i	$-0.503936\pi$
$677$	−0.643454	−0.0247299	−0.0123650	+	0.999924i	$0.503936\pi$
$678$	−55.1518	−2.11809
$679$	6.27210	0.240701
$680$	−4.85516	−0.186187
$681$	4.48736	0.171956
$682$	28.2705	1.08253
$683$	−12.6589	−0.484380	−0.242190	−	0.970229i	$-0.577866\pi$
$683$	−12.6589	−0.484380	−0.242190	+	0.970229i	$0.577866\pi$
$684$	48.8955	1.86957
$685$	4.94869	0.189080
$686$	48.6687	1.85818
$687$	−16.6715	−0.636059
$688$	29.6494	1.13037
$689$	3.37899	0.128729
$690$	−5.46198	−0.207934
$691$	40.4132	1.53739	0.768695	−	0.639616i	$-0.220907\pi$
$691$	40.4132	1.53739	0.768695	+	0.639616i	$0.220907\pi$
$692$	−11.0355	−0.419508
$693$	−4.49626	−0.170799
$694$	−22.7182	−0.862372
$695$	−12.0825	−0.458317
$696$	−23.0950	−0.875415
$697$	7.60910	0.288215
$698$	2.47345	0.0936216
$699$	−4.47790	−0.169370
$700$	−31.0330	−1.17294
$701$	12.3709	0.467244	0.233622	−	0.972328i	$-0.424942\pi$
$701$	12.3709	0.467244	0.233622	+	0.972328i	$0.424942\pi$
$702$	4.77894	0.180370
$703$	3.69731	0.139447
$704$	8.08160	0.304587
$705$	12.7787	0.481272
$706$	−3.16230	−0.119015
$707$	26.3911	0.992538
$708$	49.8142	1.87213
$709$	−4.78560	−0.179727	−0.0898635	−	0.995954i	$-0.528643\pi$
$709$	−4.78560	−0.179727	−0.0898635	+	0.995954i	$0.528643\pi$
$710$	4.48412	0.168286
$711$	21.7642	0.816223
$712$	0.0429684	0.00161031
$713$	9.15227	0.342755
$714$	−9.59343	−0.359025
$715$	−0.998975	−0.0373595
$716$	−4.94137	−0.184668
$717$	−6.54396	−0.244389
$718$	30.3339	1.13205
$719$	−1.10112	−0.0410648	−0.0205324	−	0.999789i	$-0.506536\pi$
$719$	−1.10112	−0.0410648	−0.0205324	+	0.999789i	$0.506536\pi$
$720$	−9.00567	−0.335621
$721$	−14.4603	−0.538530
$722$	−48.1163	−1.79070
$723$	14.6042	0.543136
$724$	−9.57698	−0.355926
$725$	7.96988	0.295994
$726$	−51.7665	−1.92123
$727$	43.1755	1.60129	0.800645	−	0.599140i	$-0.204491\pi$
$727$	43.1755	1.60129	0.800645	+	0.599140i	$0.204491\pi$
$728$	7.91070	0.293190
$729$	−5.21111	−0.193004
$730$	25.0383	0.926708
$731$	−5.84252	−0.216093
$732$	45.6004	1.68544
$733$	−34.1276	−1.26053	−0.630266	−	0.776379i	$-0.717054\pi$
$733$	−34.1276	−1.26053	−0.630266	+	0.776379i	$0.717054\pi$
$734$	−13.8477	−0.511126
$735$	−7.65023	−0.282183
$736$	−1.20160	−0.0442915
$737$	2.32173	0.0855219
$738$	38.7321	1.42575
$739$	37.6423	1.38470	0.692348	−	0.721564i	$-0.256576\pi$
$739$	37.6423	1.38470	0.692348	+	0.721564i	$0.256576\pi$
$740$	−2.44567	−0.0899046
$741$	11.0402	0.405573
$742$	19.5687	0.718390
$743$	−12.0911	−0.443580	−0.221790	−	0.975094i	$-0.571190\pi$
$743$	−12.0911	−0.443580	−0.221790	+	0.975094i	$0.571190\pi$
$744$	106.293	3.89689
$745$	11.4523	0.419582
$746$	−76.8971	−2.81540
$747$	20.3122	0.743185
$748$	4.78487	0.174952
$749$	21.1028	0.771079
$750$	49.2005	1.79655
$751$	−6.55647	−0.239249	−0.119624	−	0.992819i	$-0.538169\pi$
$751$	−6.55647	−0.239249	−0.119624	+	0.992819i	$0.538169\pi$
$752$	27.3238	0.996396
$753$	53.9674	1.96668
$754$	−3.95009	−0.143854
$755$	−15.9113	−0.579073
$756$	18.6287	0.677519
$757$	−9.99695	−0.363345	−0.181673	−	0.983359i	$-0.558151\pi$
$757$	−9.99695	−0.363345	−0.181673	+	0.983359i	$0.558151\pi$
$758$	78.2334	2.84157
$759$	2.76855	0.100492
$760$	32.3581	1.17375
$761$	−33.1512	−1.20173	−0.600864	−	0.799351i	$-0.705177\pi$
$761$	−33.1512	−1.20173	−0.600864	+	0.799351i	$0.705177\pi$
$762$	75.5814	2.73803
$763$	−6.62873	−0.239976
$764$	41.4070	1.49805
$765$	1.77460	0.0641608
$766$	60.1346	2.17275
$767$	4.38206	0.158227
$768$	72.2568	2.60734
$769$	−14.8882	−0.536883	−0.268442	−	0.963296i	$-0.586509\pi$
$769$	−14.8882	−0.536883	−0.268442	+	0.963296i	$0.586509\pi$
$770$	−5.78534	−0.208489
$771$	−61.9462	−2.23094
$772$	45.6242	1.64205
$773$	−26.2647	−0.944675	−0.472337	−	0.881418i	$-0.656590\pi$
$773$	−26.2647	−0.944675	−0.472337	+	0.881418i	$0.656590\pi$
$774$	−29.7397	−1.06897
$775$	−36.6807	−1.31761
$776$	−17.4745	−0.627298
$777$	−2.48544	−0.0891648
$778$	20.9211	0.750056
$779$	−50.7122	−1.81695
$780$	−7.30280	−0.261482
$781$	−2.27290	−0.0813306
$782$	2.30139	0.0822975
$783$	−4.78422	−0.170974
$784$	−16.3580	−0.584215
$785$	−9.61654	−0.343229
$786$	23.0992	0.823921
$787$	43.2697	1.54240	0.771199	−	0.636595i	$-0.219658\pi$
$787$	43.2697	1.54240	0.771199	+	0.636595i	$0.219658\pi$
$788$	−70.2163	−2.50135
$789$	−17.8608	−0.635862
$790$	28.0041	0.996340
$791$	−18.9119	−0.672429
$792$	12.5269	0.445124
$793$	4.01138	0.142448
$794$	47.6453	1.69087
$795$	−9.29123	−0.329526
$796$	−50.6472	−1.79514
$797$	37.8635	1.34119	0.670596	−	0.741822i	$-0.266038\pi$
$797$	37.8635	1.34119	0.670596	+	0.741822i	$0.266038\pi$
$798$	63.9371	2.26335
$799$	−5.38426	−0.190481
$800$	4.81579	0.170264
$801$	−0.0157053	−0.000554919 0
$802$	62.5048	2.20712
$803$	−12.6913	−0.447867
$804$	16.9725	0.598574
$805$	−1.87295	−0.0660126
$806$	18.1800	0.640361
$807$	10.1537	0.357426
$808$	−73.5274	−2.58668
$809$	−19.5049	−0.685756	−0.342878	−	0.939380i	$-0.611402\pi$
$809$	−19.5049	−0.685756	−0.342878	+	0.939380i	$0.611402\pi$
$810$	−27.2934	−0.958991
$811$	26.6080	0.934332	0.467166	−	0.884170i	$-0.345275\pi$
$811$	26.6080	0.934332	0.467166	+	0.884170i	$0.345275\pi$
$812$	−15.3978	−0.540355
$813$	57.8925	2.03038
$814$	1.84172	0.0645524
$815$	−4.15129	−0.145414
$816$	9.73959	0.340954
$817$	38.9385	1.36229
$818$	28.2528	0.987835
$819$	−2.89142	−0.101035
$820$	33.5447	1.17143
$821$	−16.0876	−0.561461	−0.280730	−	0.959787i	$-0.590577\pi$
$821$	−16.0876	−0.561461	−0.280730	+	0.959787i	$0.590577\pi$
$822$	−27.2428	−0.950203
$823$	19.2338	0.670450	0.335225	−	0.942138i	$-0.391188\pi$
$823$	19.2338	0.670450	0.335225	+	0.942138i	$0.391188\pi$
$824$	40.2874	1.40348
$825$	−11.0959	−0.386309
$826$	25.3777	0.883004
$827$	55.7430	1.93837	0.969186	−	0.246329i	$-0.0792244\pi$
$827$	55.7430	1.93837	0.969186	+	0.246329i	$0.0792244\pi$
$828$	7.88503	0.274024
$829$	11.7010	0.406392	0.203196	−	0.979138i	$-0.434867\pi$
$829$	11.7010	0.406392	0.203196	+	0.979138i	$0.434867\pi$
$830$	26.1357	0.907185
$831$	−4.39116	−0.152328
$832$	5.19705	0.180175
$833$	3.22341	0.111684
$834$	66.5151	2.30323
$835$	18.4263	0.637669
$836$	−31.8896	−1.10293
$837$	22.0190	0.761086
$838$	−52.1702	−1.80219
$839$	−43.1397	−1.48935	−0.744674	−	0.667429i	$-0.767395\pi$
$839$	−43.1397	−1.48935	−0.744674	+	0.667429i	$0.767395\pi$
$840$	−21.7521	−0.750518
$841$	−25.0456	−0.863640
$842$	25.2658	0.870716
$843$	−27.3328	−0.941392
$844$	−74.4500	−2.56268
$845$	12.3066	0.423360
$846$	−27.4071	−0.942275
$847$	−17.7510	−0.609933
$848$	−19.8668	−0.682230
$849$	19.8270	0.680460
$850$	−9.22357	−0.316366
$851$	0.596239	0.0204388
$852$	−16.6156	−0.569239
$853$	−30.3211	−1.03817	−0.519087	−	0.854722i	$-0.673728\pi$
$853$	−30.3211	−1.03817	−0.519087	+	0.854722i	$0.673728\pi$
$854$	23.2310	0.794949
$855$	−11.8271	−0.404479
$856$	−58.7938	−2.00953
$857$	11.1027	0.379262	0.189631	−	0.981855i	$-0.439271\pi$
$857$	11.1027	0.379262	0.189631	+	0.981855i	$0.439271\pi$
$858$	5.49942	0.187747
$859$	57.8849	1.97501	0.987504	−	0.157596i	$-0.0503742\pi$
$859$	57.8849	1.97501	0.987504	+	0.157596i	$0.0503742\pi$
$860$	−25.7567	−0.878297
$861$	34.0903	1.16179
$862$	−42.8122	−1.45819
$863$	9.66847	0.329118	0.164559	−	0.986367i	$-0.447380\pi$
$863$	9.66847	0.329118	0.164559	+	0.986367i	$0.447380\pi$
$864$	−2.89086	−0.0983490
$865$	2.66934	0.0907602
$866$	−7.50424	−0.255005
$867$	35.7686	1.21477
$868$	70.8669	2.40538
$869$	−14.1946	−0.481520
$870$	10.8616	0.368242
$871$	1.49304	0.0505897
$872$	18.4681	0.625409
$873$	6.38707	0.216169
$874$	−15.3380	−0.518816
$875$	16.8712	0.570350
$876$	−92.7774	−3.13466
$877$	2.94980	0.0996075	0.0498038	−	0.998759i	$-0.484140\pi$
$877$	2.94980	0.0996075	0.0498038	+	0.998759i	$0.484140\pi$
$878$	−45.3601	−1.53083
$879$	11.1499	0.376077
$880$	5.87349	0.197995
$881$	1.11750	0.0376495	0.0188248	−	0.999823i	$-0.494008\pi$
$881$	1.11750	0.0376495	0.0188248	+	0.999823i	$0.494008\pi$
$882$	16.4079	0.552482
$883$	27.5305	0.926475	0.463238	−	0.886234i	$-0.346688\pi$
$883$	27.5305	0.926475	0.463238	+	0.886234i	$0.346688\pi$
$884$	3.07702	0.103491
$885$	−12.0494	−0.405035
$886$	−7.10300	−0.238630
$887$	−22.6434	−0.760291	−0.380146	−	0.924927i	$-0.624126\pi$
$887$	−22.6434	−0.760291	−0.380146	+	0.924927i	$0.624126\pi$
$888$	6.92463	0.232375
$889$	25.9173	0.869240
$890$	−0.0202080	−0.000677373 0
$891$	13.8344	0.463469
$892$	5.85974	0.196199
$893$	35.8843	1.20082
$894$	−63.0459	−2.10857
$895$	1.19525	0.0399528
$896$	34.6164	1.15645
$897$	1.78038	0.0594451
$898$	−11.9935	−0.400228
$899$	−18.2000	−0.607004
$900$	−31.6018	−1.05339
$901$	3.91484	0.130422
$902$	−25.2610	−0.841100
$903$	−26.1756	−0.871070
$904$	52.6899	1.75244
$905$	2.31654	0.0770043
$906$	87.5929	2.91008
$907$	−5.54157	−0.184005	−0.0920024	−	0.995759i	$-0.529327\pi$
$907$	−5.54157	−0.184005	−0.0920024	+	0.995759i	$0.529327\pi$
$908$	−8.33532	−0.276617
$909$	26.8748	0.891382
$910$	−3.72040	−0.123330
$911$	31.3445	1.03849	0.519245	−	0.854626i	$-0.326213\pi$
$911$	31.3445	1.03849	0.519245	+	0.854626i	$0.326213\pi$
$912$	−64.9112	−2.14943
$913$	−13.2476	−0.438432
$914$	75.2115	2.48777
$915$	−11.0301	−0.364644
$916$	30.9675	1.02320
$917$	7.92086	0.261570
$918$	5.53679	0.182741
$919$	−24.5040	−0.808312	−0.404156	−	0.914690i	$-0.632435\pi$
$919$	−24.5040	−0.808312	−0.404156	+	0.914690i	$0.632435\pi$
$920$	5.21816	0.172038
$921$	−8.67039	−0.285699
$922$	−60.0806	−1.97865
$923$	−1.46164	−0.0481104
$924$	21.4372	0.705231
$925$	−2.38962	−0.0785703
$926$	−33.0333	−1.08554
$927$	−14.7254	−0.483645
$928$	2.38947	0.0784383
$929$	−45.8559	−1.50448	−0.752242	−	0.658887i	$-0.771027\pi$
$929$	−45.8559	−1.50448	−0.752242	+	0.658887i	$0.771027\pi$
$930$	−49.9895	−1.63922
$931$	−21.4830	−0.704076
$932$	8.31773	0.272456
$933$	20.5393	0.672426
$934$	42.3797	1.38671
$935$	−1.15739	−0.0378508
$936$	8.05571	0.263309
$937$	−45.3678	−1.48210	−0.741051	−	0.671449i	$-0.765672\pi$
$937$	−45.3678	−1.48210	−0.741051	+	0.671449i	$0.765672\pi$
$938$	8.64661	0.282322
$939$	−12.6436	−0.412609
$940$	−23.7365	−0.774198
$941$	45.2869	1.47631	0.738155	−	0.674631i	$-0.235697\pi$
$941$	45.2869	1.47631	0.738155	+	0.674631i	$0.235697\pi$
$942$	52.9396	1.72487
$943$	−8.17800	−0.266312
$944$	−25.7644	−0.838559
$945$	−4.50602	−0.146581
$946$	19.3962	0.630626
$947$	−18.0556	−0.586727	−0.293364	−	0.956001i	$-0.594775\pi$
$947$	−18.0556	−0.586727	−0.293364	+	0.956001i	$0.594775\pi$
$948$	−103.767	−3.37019
$949$	−8.16145	−0.264932
$950$	61.4721	1.99442
$951$	38.4013	1.24525
$952$	9.16519	0.297045
$953$	20.1576	0.652969	0.326484	−	0.945203i	$-0.394136\pi$
$953$	20.1576	0.652969	0.326484	+	0.945203i	$0.394136\pi$
$954$	19.9274	0.645174
$955$	−10.0158	−0.324103
$956$	12.1555	0.393136
$957$	−5.50549	−0.177967
$958$	−11.8238	−0.382011
$959$	−9.34174	−0.301660
$960$	−14.2904	−0.461219
$961$	52.7640	1.70206
$962$	1.18436	0.0381854
$963$	21.4896	0.692493
$964$	−27.1274	−0.873715
$965$	−11.0359	−0.355257
$966$	10.3107	0.331741
$967$	0.828369	0.0266385	0.0133193	−	0.999911i	$-0.495760\pi$
$967$	0.828369	0.0266385	0.0133193	+	0.999911i	$0.495760\pi$
$968$	49.4557	1.58956
$969$	12.7910	0.410906
$970$	8.21824	0.263872
$971$	−16.0775	−0.515952	−0.257976	−	0.966151i	$-0.583056\pi$
$971$	−16.0775	−0.515952	−0.257976	+	0.966151i	$0.583056\pi$
$972$	71.4119	2.29054
$973$	22.8084	0.731205
$974$	49.8994	1.59888
$975$	−7.13545	−0.228517
$976$	−23.5850	−0.754936
$977$	14.2178	0.454869	0.227434	−	0.973793i	$-0.426966\pi$
$977$	14.2178	0.454869	0.227434	+	0.973793i	$0.426966\pi$
$978$	22.8531	0.730762
$979$	0.0102430	0.000327367 0
$980$	14.2104	0.453934
$981$	−6.75024	−0.215519
$982$	20.4205	0.651644
$983$	52.5542	1.67622	0.838109	−	0.545502i	$-0.183661\pi$
$983$	52.5542	1.67622	0.838109	+	0.545502i	$0.183661\pi$
$984$	−94.9779	−3.02779
$985$	16.9843	0.541166
$986$	−4.57650	−0.145745
$987$	−24.1225	−0.767828
$988$	−20.5073	−0.652425
$989$	6.27933	0.199671
$990$	−5.89139	−0.187241
$991$	−6.47337	−0.205633	−0.102817	−	0.994700i	$-0.532786\pi$
$991$	−6.47337	−0.205633	−0.102817	+	0.994700i	$0.532786\pi$
$992$	−10.9973	−0.349166
$993$	−2.05382	−0.0651761
$994$	−8.46475	−0.268486
$995$	12.2508	0.388378
$996$	−96.8440	−3.06862
$997$	29.4835	0.933752	0.466876	−	0.884323i	$-0.345379\pi$
$997$	29.4835	0.933752	0.466876	+	0.884323i	$0.345379\pi$
$998$	−30.3301	−0.960083
$999$	1.43446	0.0453843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.13	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.13	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47345 q^{2} -2.21693 q^{3} +4.11797 q^{4} -0.996079 q^{5} +5.48348 q^{6} +1.88032 q^{7} -5.23870 q^{8} +1.91479 q^{9} +O(q^{10})\)	\(q-2.47345 q^{2} -2.21693 q^{3} +4.11797 q^{4} -0.996079 q^{5} +5.48348 q^{6} +1.88032 q^{7} -5.23870 q^{8} +1.91479 q^{9} +2.46376 q^{10} -1.24882 q^{11} -9.12926 q^{12} -0.803083 q^{13} -4.65088 q^{14} +2.20824 q^{15} +4.72174 q^{16} -0.930436 q^{17} -4.73613 q^{18} +6.20106 q^{19} -4.10182 q^{20} -4.16854 q^{21} +3.08890 q^{22} +1.00000 q^{23} +11.6138 q^{24} -4.00783 q^{25} +1.98639 q^{26} +2.40585 q^{27} +7.74309 q^{28} -1.98858 q^{29} -5.46198 q^{30} +9.15227 q^{31} -1.20160 q^{32} +2.76855 q^{33} +2.30139 q^{34} -1.87295 q^{35} +7.88503 q^{36} +0.596239 q^{37} -15.3380 q^{38} +1.78038 q^{39} +5.21816 q^{40} -8.17800 q^{41} +10.3107 q^{42} +6.27933 q^{43} -5.14261 q^{44} -1.90728 q^{45} -2.47345 q^{46} +5.78681 q^{47} -10.4678 q^{48} -3.46440 q^{49} +9.91317 q^{50} +2.06271 q^{51} -3.30707 q^{52} -4.20753 q^{53} -5.95075 q^{54} +1.24393 q^{55} -9.85042 q^{56} -13.7473 q^{57} +4.91866 q^{58} -5.45655 q^{59} +9.09346 q^{60} -4.99497 q^{61} -22.6377 q^{62} +3.60040 q^{63} -6.47138 q^{64} +0.799934 q^{65} -6.84788 q^{66} -1.85913 q^{67} -3.83151 q^{68} -2.21693 q^{69} +4.63264 q^{70} +1.82003 q^{71} -10.0310 q^{72} +10.1626 q^{73} -1.47477 q^{74} +8.88508 q^{75} +25.5358 q^{76} -2.34818 q^{77} -4.40369 q^{78} +11.3664 q^{79} -4.70322 q^{80} -11.0780 q^{81} +20.2279 q^{82} +10.6081 q^{83} -17.1659 q^{84} +0.926788 q^{85} -15.5316 q^{86} +4.40854 q^{87} +6.54220 q^{88} -0.00820211 q^{89} +4.71756 q^{90} -1.51005 q^{91} +4.11797 q^{92} -20.2899 q^{93} -14.3134 q^{94} -6.17674 q^{95} +2.66386 q^{96} +3.33566 q^{97} +8.56904 q^{98} -2.39123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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