LMFDB - Embedded newform 8023.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32032 q^{2} +0.985491 q^{3} +3.38390 q^{4} +2.02170 q^{5} -2.28666 q^{6} +0.848897 q^{7} -3.21110 q^{8} -2.02881 q^{9} +O(q^{10})$	\(q-2.32032 q^{2} +0.985491 q^{3} +3.38390 q^{4} +2.02170 q^{5} -2.28666 q^{6} +0.848897 q^{7} -3.21110 q^{8} -2.02881 q^{9} -4.69101 q^{10} +0.725783 q^{11} +3.33480 q^{12} -1.62059 q^{13} -1.96972 q^{14} +1.99237 q^{15} +0.682991 q^{16} +5.65920 q^{17} +4.70749 q^{18} +3.31389 q^{19} +6.84125 q^{20} +0.836580 q^{21} -1.68405 q^{22} -6.39857 q^{23} -3.16451 q^{24} -0.912711 q^{25} +3.76029 q^{26} -4.95584 q^{27} +2.87258 q^{28} +3.15859 q^{29} -4.62294 q^{30} -0.751970 q^{31} +4.83744 q^{32} +0.715252 q^{33} -13.1312 q^{34} +1.71622 q^{35} -6.86529 q^{36} -1.37857 q^{37} -7.68931 q^{38} -1.59707 q^{39} -6.49190 q^{40} +0.367890 q^{41} -1.94114 q^{42} -12.2380 q^{43} +2.45598 q^{44} -4.10165 q^{45} +14.8468 q^{46} -0.793413 q^{47} +0.673081 q^{48} -6.27937 q^{49} +2.11779 q^{50} +5.57709 q^{51} -5.48391 q^{52} -1.58270 q^{53} +11.4992 q^{54} +1.46732 q^{55} -2.72589 q^{56} +3.26581 q^{57} -7.32895 q^{58} -2.81685 q^{59} +6.74199 q^{60} +1.58367 q^{61} +1.74481 q^{62} -1.72225 q^{63} -12.5904 q^{64} -3.27635 q^{65} -1.65962 q^{66} -0.371789 q^{67} +19.1502 q^{68} -6.30573 q^{69} -3.98218 q^{70} +1.00000 q^{71} +6.51471 q^{72} -9.19737 q^{73} +3.19872 q^{74} -0.899468 q^{75} +11.2139 q^{76} +0.616115 q^{77} +3.70573 q^{78} -12.0102 q^{79} +1.38081 q^{80} +1.20249 q^{81} -0.853623 q^{82} -4.68687 q^{83} +2.83090 q^{84} +11.4412 q^{85} +28.3962 q^{86} +3.11276 q^{87} -2.33056 q^{88} -7.86150 q^{89} +9.51716 q^{90} -1.37571 q^{91} -21.6521 q^{92} -0.741059 q^{93} +1.84098 q^{94} +6.69971 q^{95} +4.76725 q^{96} +10.3054 q^{97} +14.5702 q^{98} -1.47247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.32032	−1.64072	−0.820358	−	0.571850i	$-0.806226\pi$
$2$	−2.32032	−1.64072	−0.820358	+	0.571850i	$0.806226\pi$
$3$	0.985491	0.568973	0.284487	−	0.958680i	$-0.408177\pi$
$3$	0.985491	0.568973	0.284487	+	0.958680i	$0.408177\pi$
$4$	3.38390	1.69195
$5$	2.02170	0.904134	0.452067	−	0.891984i	$-0.350687\pi$
$5$	2.02170	0.904134	0.452067	+	0.891984i	$0.350687\pi$
$6$	−2.28666	−0.933524
$7$	0.848897	0.320853	0.160426	−	0.987048i	$-0.448713\pi$
$7$	0.848897	0.320853	0.160426	+	0.987048i	$0.448713\pi$
$8$	−3.21110	−1.13530
$9$	−2.02881	−0.676269
$10$	−4.69101	−1.48343
$11$	0.725783	0.218832	0.109416	−	0.993996i	$-0.465102\pi$
$11$	0.725783	0.218832	0.109416	+	0.993996i	$0.465102\pi$
$12$	3.33480	0.962675
$13$	−1.62059	−0.449470	−0.224735	−	0.974420i	$-0.572152\pi$
$13$	−1.62059	−0.449470	−0.224735	+	0.974420i	$0.572152\pi$
$14$	−1.96972	−0.526429
$15$	1.99237	0.514428
$16$	0.682991	0.170748
$17$	5.65920	1.37256	0.686279	−	0.727338i	$-0.259243\pi$
$17$	5.65920	1.37256	0.686279	+	0.727338i	$0.259243\pi$
$18$	4.70749	1.10957
$19$	3.31389	0.760259	0.380130	−	0.924933i	$-0.375879\pi$
$19$	3.31389	0.760259	0.380130	+	0.924933i	$0.375879\pi$
$20$	6.84125	1.52975
$21$	0.836580	0.182557
$22$	−1.68405	−0.359041
$23$	−6.39857	−1.33419	−0.667097	−	0.744971i	$-0.732463\pi$
$23$	−6.39857	−1.33419	−0.667097	+	0.744971i	$0.732463\pi$
$24$	−3.16451	−0.645953
$25$	−0.912711	−0.182542
$26$	3.76029	0.737453
$27$	−4.95584	−0.953752
$28$	2.87258	0.542867
$29$	3.15859	0.586535	0.293268	−	0.956030i	$-0.405257\pi$
$29$	3.15859	0.586535	0.293268	+	0.956030i	$0.405257\pi$
$30$	−4.62294	−0.844030
$31$	−0.751970	−0.135058	−0.0675289	−	0.997717i	$-0.521511\pi$
$31$	−0.751970	−0.135058	−0.0675289	+	0.997717i	$0.521511\pi$
$32$	4.83744	0.855147
$33$	0.715252	0.124509
$34$	−13.1312	−2.25198
$35$	1.71622	0.290094
$36$	−6.86529	−1.14421
$37$	−1.37857	−0.226635	−0.113318	−	0.993559i	$-0.536148\pi$
$37$	−1.37857	−0.226635	−0.113318	+	0.993559i	$0.536148\pi$
$38$	−7.68931	−1.24737
$39$	−1.59707	−0.255736
$40$	−6.49190	−1.02646
$41$	0.367890	0.0574547	0.0287274	−	0.999587i	$-0.490855\pi$
$41$	0.367890	0.0574547	0.0287274	+	0.999587i	$0.490855\pi$
$42$	−1.94114	−0.299524
$43$	−12.2380	−1.86628	−0.933142	−	0.359508i	$-0.882944\pi$
$43$	−12.2380	−1.86628	−0.933142	+	0.359508i	$0.882944\pi$
$44$	2.45598	0.370253
$45$	−4.10165	−0.611438
$46$	14.8468	2.18903
$47$	−0.793413	−0.115731	−0.0578656	−	0.998324i	$-0.518429\pi$
$47$	−0.793413	−0.115731	−0.0578656	+	0.998324i	$0.518429\pi$
$48$	0.673081	0.0971509
$49$	−6.27937	−0.897053
$50$	2.11779	0.299500
$51$	5.57709	0.780949
$52$	−5.48391	−0.760482
$53$	−1.58270	−0.217401	−0.108701	−	0.994075i	$-0.534669\pi$
$53$	−1.58270	−0.217401	−0.108701	+	0.994075i	$0.534669\pi$
$54$	11.4992	1.56484
$55$	1.46732	0.197853
$56$	−2.72589	−0.364263
$57$	3.26581	0.432567
$58$	−7.32895	−0.962338
$59$	−2.81685	−0.366722	−0.183361	−	0.983046i	$-0.558698\pi$
$59$	−2.81685	−0.366722	−0.183361	+	0.983046i	$0.558698\pi$
$60$	6.74199	0.870387
$61$	1.58367	0.202768	0.101384	−	0.994847i	$-0.467673\pi$
$61$	1.58367	0.202768	0.101384	+	0.994847i	$0.467673\pi$
$62$	1.74481	0.221591
$63$	−1.72225	−0.216983
$64$	−12.5904	−1.57380
$65$	−3.27635	−0.406381
$66$	−1.65962	−0.204285
$67$	−0.371789	−0.0454213	−0.0227106	−	0.999742i	$-0.507230\pi$
$67$	−0.371789	−0.0454213	−0.0227106	+	0.999742i	$0.507230\pi$
$68$	19.1502	2.32230
$69$	−6.30573	−0.759121
$70$	−3.98218	−0.475962
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	6.51471	0.767766
$73$	−9.19737	−1.07647	−0.538235	−	0.842795i	$-0.680909\pi$
$73$	−9.19737	−1.07647	−0.538235	+	0.842795i	$0.680909\pi$
$74$	3.19872	0.371844
$75$	−0.899468	−0.103862
$76$	11.2139	1.28632
$77$	0.616115	0.0702128
$78$	3.70573	0.419591
$79$	−12.0102	−1.35126	−0.675628	−	0.737243i	$-0.736127\pi$
$79$	−12.0102	−1.35126	−0.675628	+	0.737243i	$0.736127\pi$
$80$	1.38081	0.154379
$81$	1.20249	0.133610
$82$	−0.853623	−0.0942669
$83$	−4.68687	−0.514451	−0.257226	−	0.966351i	$-0.582808\pi$
$83$	−4.68687	−0.514451	−0.257226	+	0.966351i	$0.582808\pi$
$84$	2.83090	0.308877
$85$	11.4412	1.24098
$86$	28.3962	3.06204
$87$	3.11276	0.333723
$88$	−2.33056	−0.248439
$89$	−7.86150	−0.833318	−0.416659	−	0.909063i	$-0.636799\pi$
$89$	−7.86150	−0.833318	−0.416659	+	0.909063i	$0.636799\pi$
$90$	9.51716	1.00320
$91$	−1.37571	−0.144214
$92$	−21.6521	−2.25739
$93$	−0.741059	−0.0768442
$94$	1.84098	0.189882
$95$	6.69971	0.687376
$96$	4.76725	0.486556
$97$	10.3054	1.04636	0.523179	−	0.852223i	$-0.324746\pi$
$97$	10.3054	1.04636	0.523179	+	0.852223i	$0.324746\pi$
$98$	14.5702	1.47181
$99$	−1.47247	−0.147989
$100$	−3.08853	−0.308853
$101$	−10.0675	−1.00175	−0.500876	−	0.865519i	$-0.666989\pi$
$101$	−10.0675	−1.00175	−0.500876	+	0.865519i	$0.666989\pi$
$102$	−12.9407	−1.28132
$103$	3.40517	0.335522	0.167761	−	0.985828i	$-0.446346\pi$
$103$	3.40517	0.335522	0.167761	+	0.985828i	$0.446346\pi$
$104$	5.20387	0.510282
$105$	1.69132	0.165056
$106$	3.67239	0.356694
$107$	4.16500	0.402645	0.201323	−	0.979525i	$-0.435476\pi$
$107$	4.16500	0.402645	0.201323	+	0.979525i	$0.435476\pi$
$108$	−16.7701	−1.61370
$109$	17.4160	1.66815	0.834075	−	0.551652i	$-0.186002\pi$
$109$	17.4160	1.66815	0.834075	+	0.551652i	$0.186002\pi$
$110$	−3.40465	−0.324621
$111$	−1.35857	−0.128949
$112$	0.579789	0.0547849
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−7.57774	−0.709720
$115$	−12.9360	−1.20629
$116$	10.6884	0.992389
$117$	3.28786	0.303963
$118$	6.53600	0.601687
$119$	4.80408	0.440389
$120$	−6.39770	−0.584028
$121$	−10.4732	−0.952113
$122$	−3.67462	−0.332685
$123$	0.362552	0.0326902
$124$	−2.54459	−0.228511
$125$	−11.9538	−1.06918
$126$	3.99617	0.356008
$127$	13.8070	1.22517	0.612586	−	0.790404i	$-0.290129\pi$
$127$	13.8070	1.22517	0.612586	+	0.790404i	$0.290129\pi$
$128$	19.5390	1.72702
$129$	−12.0605	−1.06187
$130$	7.60219	0.666756
$131$	17.8580	1.56026	0.780129	−	0.625618i	$-0.215153\pi$
$131$	17.8580	1.56026	0.780129	+	0.625618i	$0.215153\pi$
$132$	2.42034	0.210664
$133$	2.81315	0.243931
$134$	0.862671	0.0745234
$135$	−10.0192	−0.862320
$136$	−18.1723	−1.55826
$137$	−17.2277	−1.47186	−0.735929	−	0.677059i	$-0.763254\pi$
$137$	−17.2277	−1.47186	−0.735929	+	0.677059i	$0.763254\pi$
$138$	14.6313	1.24550
$139$	1.16926	0.0991757	0.0495878	−	0.998770i	$-0.484209\pi$
$139$	1.16926	0.0991757	0.0495878	+	0.998770i	$0.484209\pi$
$140$	5.80751	0.490825
$141$	−0.781901	−0.0658480
$142$	−2.32032	−0.194717
$143$	−1.17620	−0.0983584
$144$	−1.38566	−0.115472
$145$	6.38573	0.530306
$146$	21.3409	1.76618
$147$	−6.18826	−0.510399
$148$	−4.66494	−0.383456
$149$	−12.2138	−1.00059	−0.500295	−	0.865855i	$-0.666775\pi$
$149$	−12.2138	−1.00059	−0.500295	+	0.865855i	$0.666775\pi$
$150$	2.08706	0.170408
$151$	14.7354	1.19915	0.599575	−	0.800319i	$-0.295336\pi$
$151$	14.7354	1.19915	0.599575	+	0.800319i	$0.295336\pi$
$152$	−10.6412	−0.863119
$153$	−11.4814	−0.928219
$154$	−1.42959	−0.115199
$155$	−1.52026	−0.122110
$156$	−5.40434	−0.432694
$157$	−16.2417	−1.29623	−0.648114	−	0.761543i	$-0.724442\pi$
$157$	−16.2417	−1.29623	−0.648114	+	0.761543i	$0.724442\pi$
$158$	27.8676	2.21703
$159$	−1.55974	−0.123695
$160$	9.77988	0.773167
$161$	−5.43172	−0.428080
$162$	−2.79016	−0.219216
$163$	11.8862	0.931002	0.465501	−	0.885047i	$-0.345874\pi$
$163$	11.8862	0.931002	0.465501	+	0.885047i	$0.345874\pi$
$164$	1.24490	0.0972106
$165$	1.44603	0.112573
$166$	10.8751	0.844069
$167$	−21.8259	−1.68894	−0.844468	−	0.535606i	$-0.820083\pi$
$167$	−21.8259	−1.68894	−0.844468	+	0.535606i	$0.820083\pi$
$168$	−2.68634	−0.207256
$169$	−10.3737	−0.797977
$170$	−26.5474	−2.03609
$171$	−6.72325	−0.514140
$172$	−41.4123	−3.15766
$173$	−5.17031	−0.393091	−0.196546	−	0.980495i	$-0.562972\pi$
$173$	−5.17031	−0.393091	−0.196546	+	0.980495i	$0.562972\pi$
$174$	−7.22261	−0.547545
$175$	−0.774798	−0.0585692
$176$	0.495704	0.0373651
$177$	−2.77598	−0.208655
$178$	18.2412	1.36724
$179$	−12.6855	−0.948158	−0.474079	−	0.880482i	$-0.657219\pi$
$179$	−12.6855	−0.948158	−0.474079	+	0.880482i	$0.657219\pi$
$180$	−13.8796	−1.03452
$181$	−25.9438	−1.92838	−0.964192	−	0.265205i	$-0.914560\pi$
$181$	−25.9438	−1.92838	−0.964192	+	0.265205i	$0.914560\pi$
$182$	3.19210	0.236614
$183$	1.56069	0.115369
$184$	20.5465	1.51470
$185$	−2.78706	−0.204908
$186$	1.71950	0.126080
$187$	4.10735	0.300359
$188$	−2.68483	−0.195812
$189$	−4.20700	−0.306014
$190$	−15.5455	−1.12779
$191$	0.337405	0.0244138	0.0122069	−	0.999925i	$-0.496114\pi$
$191$	0.337405	0.0244138	0.0122069	+	0.999925i	$0.496114\pi$
$192$	−12.4077	−0.895451
$193$	16.8534	1.21313	0.606567	−	0.795032i	$-0.292546\pi$
$193$	16.8534	1.21313	0.606567	+	0.795032i	$0.292546\pi$
$194$	−23.9119	−1.71678
$195$	−3.22881	−0.231220
$196$	−21.2488	−1.51777
$197$	−7.16347	−0.510376	−0.255188	−	0.966891i	$-0.582137\pi$
$197$	−7.16347	−0.510376	−0.255188	+	0.966891i	$0.582137\pi$
$198$	3.41662	0.242809
$199$	2.37743	0.168531	0.0842657	−	0.996443i	$-0.473146\pi$
$199$	2.37743	0.168531	0.0842657	+	0.996443i	$0.473146\pi$
$200$	2.93081	0.207240
$201$	−0.366395	−0.0258435
$202$	23.3598	1.64359
$203$	2.68132	0.188191
$204$	18.8723	1.32133
$205$	0.743764	0.0519467
$206$	−7.90110	−0.550496
$207$	12.9815	0.902275
$208$	−1.10685	−0.0767460
$209$	2.40517	0.166369
$210$	−3.92440	−0.270809
$211$	19.3430	1.33163	0.665813	−	0.746118i	$-0.268085\pi$
$211$	19.3430	1.33163	0.665813	+	0.746118i	$0.268085\pi$
$212$	−5.35572	−0.367832
$213$	0.985491	0.0675247
$214$	−9.66414	−0.660627
$215$	−24.7417	−1.68737
$216$	15.9137	1.08279
$217$	−0.638344	−0.0433336
$218$	−40.4107	−2.73696
$219$	−9.06392	−0.612483
$220$	4.96526	0.334758
$221$	−9.17123	−0.616924
$222$	3.15231	0.211569
$223$	−16.5149	−1.10592	−0.552960	−	0.833208i	$-0.686502\pi$
$223$	−16.5149	−1.10592	−0.552960	+	0.833208i	$0.686502\pi$
$224$	4.10649	0.274376
$225$	1.85172	0.123448
$226$	−2.32032	−0.154346
$227$	−23.0059	−1.52696	−0.763478	−	0.645834i	$-0.776510\pi$
$227$	−23.0059	−1.52696	−0.763478	+	0.645834i	$0.776510\pi$
$228$	11.0512	0.731883
$229$	15.2330	1.00663	0.503313	−	0.864104i	$-0.332114\pi$
$229$	15.2330	1.00663	0.503313	+	0.864104i	$0.332114\pi$
$230$	30.0157	1.97918
$231$	0.607175	0.0399492
$232$	−10.1426	−0.665891
$233$	−13.0148	−0.852630	−0.426315	−	0.904575i	$-0.640188\pi$
$233$	−13.0148	−0.852630	−0.426315	+	0.904575i	$0.640188\pi$
$234$	−7.62890	−0.498717
$235$	−1.60405	−0.104637
$236$	−9.53193	−0.620476
$237$	−11.8360	−0.768829
$238$	−11.1470	−0.722554
$239$	5.25585	0.339973	0.169986	−	0.985446i	$-0.445628\pi$
$239$	5.25585	0.339973	0.169986	+	0.985446i	$0.445628\pi$
$240$	1.36077	0.0878374
$241$	14.1304	0.910221	0.455110	−	0.890435i	$-0.349600\pi$
$241$	14.1304	0.910221	0.455110	+	0.890435i	$0.349600\pi$
$242$	24.3013	1.56215
$243$	16.0526	1.02977
$244$	5.35898	0.343073
$245$	−12.6950	−0.811056
$246$	−0.841237	−0.0536353
$247$	−5.37045	−0.341714
$248$	2.41465	0.153330
$249$	−4.61887	−0.292709
$250$	27.7366	1.75422
$251$	−6.88801	−0.434767	−0.217384	−	0.976086i	$-0.569752\pi$
$251$	−6.88801	−0.434767	−0.217384	+	0.976086i	$0.569752\pi$
$252$	−5.82792	−0.367125
$253$	−4.64397	−0.291964
$254$	−32.0367	−2.01016
$255$	11.2752	0.706082
$256$	−20.1559	−1.25974
$257$	−3.18659	−0.198774	−0.0993872	−	0.995049i	$-0.531688\pi$
$257$	−3.18659	−0.198774	−0.0993872	+	0.995049i	$0.531688\pi$
$258$	27.9842	1.74222
$259$	−1.17026	−0.0727165
$260$	−11.0868	−0.687577
$261$	−6.40817	−0.396656
$262$	−41.4363	−2.55994
$263$	−26.9049	−1.65903	−0.829515	−	0.558485i	$-0.811383\pi$
$263$	−26.9049	−1.65903	−0.829515	+	0.558485i	$0.811383\pi$
$264$	−2.29675	−0.141355
$265$	−3.19976	−0.196560
$266$	−6.52743	−0.400222
$267$	−7.74744	−0.474135
$268$	−1.25810	−0.0768505
$269$	−20.7997	−1.26818	−0.634090	−	0.773259i	$-0.718625\pi$
$269$	−20.7997	−1.26818	−0.634090	+	0.773259i	$0.718625\pi$
$270$	23.2479	1.41482
$271$	0.238442	0.0144843	0.00724217	−	0.999974i	$-0.497695\pi$
$271$	0.238442	0.0144843	0.00724217	+	0.999974i	$0.497695\pi$
$272$	3.86518	0.234361
$273$	−1.35575	−0.0820538
$274$	39.9737	2.41490
$275$	−0.662430	−0.0399461
$276$	−21.3380	−1.28439
$277$	−12.6480	−0.759944	−0.379972	−	0.924998i	$-0.624066\pi$
$277$	−12.6480	−0.759944	−0.379972	+	0.924998i	$0.624066\pi$
$278$	−2.71307	−0.162719
$279$	1.52560	0.0913354
$280$	−5.51095	−0.329342
$281$	25.0185	1.49248	0.746239	−	0.665678i	$-0.231857\pi$
$281$	25.0185	1.49248	0.746239	+	0.665678i	$0.231857\pi$
$282$	1.81426	0.108038
$283$	−0.0386359	−0.00229666	−0.00114833	−	0.999999i	$-0.500366\pi$
$283$	−0.0386359	−0.00229666	−0.00114833	+	0.999999i	$0.500366\pi$
$284$	3.38390	0.200798
$285$	6.60250	0.391099
$286$	2.72915	0.161378
$287$	0.312300	0.0184345
$288$	−9.81425	−0.578310
$289$	15.0266	0.883915
$290$	−14.8170	−0.870082
$291$	10.1559	0.595349
$292$	−31.1230	−1.82134
$293$	33.0967	1.93353	0.966765	−	0.255667i	$-0.0822951\pi$
$293$	33.0967	1.93353	0.966765	+	0.255667i	$0.0822951\pi$
$294$	14.3588	0.837421
$295$	−5.69483	−0.331566
$296$	4.42672	0.257298
$297$	−3.59687	−0.208711
$298$	28.3399	1.64169
$299$	10.3694	0.599680
$300$	−3.04371	−0.175729
$301$	−10.3888	−0.598802
$302$	−34.1909	−1.96746
$303$	−9.92140	−0.569970
$304$	2.26336	0.129813
$305$	3.20171	0.183329
$306$	26.6406	1.52294
$307$	7.85860	0.448514	0.224257	−	0.974530i	$-0.428004\pi$
$307$	7.85860	0.448514	0.224257	+	0.974530i	$0.428004\pi$
$308$	2.08487	0.118797
$309$	3.35577	0.190903
$310$	3.52750	0.200348
$311$	0.950453	0.0538953	0.0269476	−	0.999637i	$-0.491421\pi$
$311$	0.950453	0.0538953	0.0269476	+	0.999637i	$0.491421\pi$
$312$	5.12837	0.290337
$313$	−15.5177	−0.877110	−0.438555	−	0.898704i	$-0.644510\pi$
$313$	−15.5177	−0.877110	−0.438555	+	0.898704i	$0.644510\pi$
$314$	37.6860	2.12674
$315$	−3.48188	−0.196182
$316$	−40.6414	−2.28626
$317$	18.4014	1.03353	0.516764	−	0.856128i	$-0.327137\pi$
$317$	18.4014	1.03353	0.516764	+	0.856128i	$0.327137\pi$
$318$	3.61910	0.202949
$319$	2.29245	0.128353
$320$	−25.4541	−1.42293
$321$	4.10456	0.229094
$322$	12.6034	0.702358
$323$	18.7540	1.04350
$324$	4.06911	0.226061
$325$	1.47913	0.0820473
$326$	−27.5799	−1.52751
$327$	17.1633	0.949132
$328$	−1.18133	−0.0652281
$329$	−0.673526	−0.0371327
$330$	−3.35526	−0.184701
$331$	−22.4257	−1.23263	−0.616314	−	0.787500i	$-0.711375\pi$
$331$	−22.4257	−1.23263	−0.616314	+	0.787500i	$0.711375\pi$
$332$	−15.8599	−0.870426
$333$	2.79685	0.153266
$334$	50.6431	2.77106
$335$	−0.751647	−0.0410669
$336$	0.571377	0.0311711
$337$	9.94986	0.542003	0.271002	−	0.962579i	$-0.412645\pi$
$337$	9.94986	0.542003	0.271002	+	0.962579i	$0.412645\pi$
$338$	24.0703	1.30925
$339$	0.985491	0.0535245
$340$	38.7160	2.09967
$341$	−0.545767	−0.0295549
$342$	15.6001	0.843558
$343$	−11.2728	−0.608675
$344$	39.2976	2.11878
$345$	−12.7483	−0.686346
$346$	11.9968	0.644952
$347$	31.7678	1.70538	0.852692	−	0.522414i	$-0.174969\pi$
$347$	31.7678	1.70538	0.852692	+	0.522414i	$0.174969\pi$
$348$	10.5333	0.564643
$349$	−24.7221	−1.32335	−0.661673	−	0.749793i	$-0.730153\pi$
$349$	−24.7221	−1.32335	−0.661673	+	0.749793i	$0.730153\pi$
$350$	1.79778	0.0960955
$351$	8.03138	0.428683
$352$	3.51093	0.187133
$353$	−2.84331	−0.151334	−0.0756671	−	0.997133i	$-0.524109\pi$
$353$	−2.84331	−0.151334	−0.0756671	+	0.997133i	$0.524109\pi$
$354$	6.44116	0.342344
$355$	2.02170	0.107301
$356$	−26.6026	−1.40993
$357$	4.73437	0.250570
$358$	29.4345	1.55566
$359$	29.5036	1.55714	0.778571	−	0.627557i	$-0.215945\pi$
$359$	29.5036	1.55714	0.778571	+	0.627557i	$0.215945\pi$
$360$	13.1708	0.694163
$361$	−8.01811	−0.422006
$362$	60.1979	3.16393
$363$	−10.3213	−0.541727
$364$	−4.65527	−0.244003
$365$	−18.5944	−0.973273
$366$	−3.62130	−0.189289
$367$	16.9506	0.884814	0.442407	−	0.896814i	$-0.354125\pi$
$367$	16.9506	0.884814	0.442407	+	0.896814i	$0.354125\pi$
$368$	−4.37017	−0.227811
$369$	−0.746378	−0.0388549
$370$	6.46687	0.336197
$371$	−1.34355	−0.0697538
$372$	−2.50767	−0.130017
$373$	1.76162	0.0912133	0.0456066	−	0.998959i	$-0.485478\pi$
$373$	1.76162	0.0912133	0.0456066	+	0.998959i	$0.485478\pi$
$374$	−9.53039	−0.492805
$375$	−11.7803	−0.608333
$376$	2.54773	0.131389
$377$	−5.11877	−0.263630
$378$	9.76160	0.502082
$379$	0.875762	0.0449849	0.0224924	−	0.999747i	$-0.492840\pi$
$379$	0.875762	0.0449849	0.0224924	+	0.999747i	$0.492840\pi$
$380$	22.6712	1.16301
$381$	13.6066	0.697090
$382$	−0.782890	−0.0400561
$383$	18.2423	0.932138	0.466069	−	0.884748i	$-0.345670\pi$
$383$	18.2423	0.932138	0.466069	+	0.884748i	$0.345670\pi$
$384$	19.2555	0.982626
$385$	1.24560	0.0634818
$386$	−39.1054	−1.99041
$387$	24.8286	1.26211
$388$	34.8725	1.77039
$389$	−23.7438	−1.20386	−0.601929	−	0.798549i	$-0.705601\pi$
$389$	−23.7438	−1.20386	−0.601929	+	0.798549i	$0.705601\pi$
$390$	7.49189	0.379366
$391$	−36.2108	−1.83126
$392$	20.1637	1.01842
$393$	17.5989	0.887745
$394$	16.6216	0.837382
$395$	−24.2811	−1.22172
$396$	−4.98271	−0.250391
$397$	10.0401	0.503899	0.251949	−	0.967740i	$-0.418928\pi$
$397$	10.0401	0.503899	0.251949	+	0.967740i	$0.418928\pi$
$398$	−5.51640	−0.276512
$399$	2.77234	0.138790
$400$	−0.623374	−0.0311687
$401$	12.5433	0.626383	0.313191	−	0.949690i	$-0.398602\pi$
$401$	12.5433	0.626383	0.313191	+	0.949690i	$0.398602\pi$
$402$	0.850154	0.0424018
$403$	1.21863	0.0607044
$404$	−34.0674	−1.69491
$405$	2.43108	0.120801
$406$	−6.22152	−0.308769
$407$	−1.00054	−0.0495950
$408$	−17.9086	−0.886608
$409$	−24.2793	−1.20053	−0.600267	−	0.799800i	$-0.704939\pi$
$409$	−24.2793	−1.20053	−0.600267	+	0.799800i	$0.704939\pi$
$410$	−1.72577	−0.0852299
$411$	−16.9777	−0.837448
$412$	11.5228	0.567686
$413$	−2.39121	−0.117664
$414$	−30.1212	−1.48038
$415$	−9.47547	−0.465133
$416$	−7.83950	−0.384363
$417$	1.15230	0.0564283
$418$	−5.58077	−0.272964
$419$	−4.56248	−0.222892	−0.111446	−	0.993771i	$-0.535548\pi$
$419$	−4.56248	−0.222892	−0.111446	+	0.993771i	$0.535548\pi$
$420$	5.72325	0.279266
$421$	30.3825	1.48075	0.740376	−	0.672193i	$-0.234647\pi$
$421$	30.3825	1.48075	0.740376	+	0.672193i	$0.234647\pi$
$422$	−44.8820	−2.18482
$423$	1.60968	0.0782655
$424$	5.08223	0.246815
$425$	−5.16522	−0.250550
$426$	−2.28666	−0.110789
$427$	1.34437	0.0650586
$428$	14.0939	0.681256
$429$	−1.15913	−0.0559633
$430$	57.4088	2.76850
$431$	23.5547	1.13459	0.567295	−	0.823514i	$-0.307990\pi$
$431$	23.5547	1.13459	0.567295	+	0.823514i	$0.307990\pi$
$432$	−3.38480	−0.162851
$433$	−20.5252	−0.986377	−0.493188	−	0.869922i	$-0.664169\pi$
$433$	−20.5252	−0.986377	−0.493188	+	0.869922i	$0.664169\pi$
$434$	1.48117	0.0710982
$435$	6.29308	0.301730
$436$	58.9340	2.82243
$437$	−21.2042	−1.01433
$438$	21.0312	1.00491
$439$	−0.275006	−0.0131253	−0.00656267	−	0.999978i	$-0.502089\pi$
$439$	−0.275006	−0.0131253	−0.00656267	+	0.999978i	$0.502089\pi$
$440$	−4.71171	−0.224622
$441$	12.7396	0.606650
$442$	21.2802	1.01220
$443$	0.776319	0.0368840	0.0184420	−	0.999830i	$-0.494129\pi$
$443$	0.776319	0.0368840	0.0184420	+	0.999830i	$0.494129\pi$
$444$	−4.59725	−0.218176
$445$	−15.8936	−0.753431
$446$	38.3200	1.81450
$447$	−12.0365	−0.569309
$448$	−10.6880	−0.504959
$449$	9.21618	0.434939	0.217469	−	0.976067i	$-0.430220\pi$
$449$	9.21618	0.434939	0.217469	+	0.976067i	$0.430220\pi$
$450$	−4.29658	−0.202543
$451$	0.267008	0.0125729
$452$	3.38390	0.159165
$453$	14.5216	0.682284
$454$	53.3811	2.50530
$455$	−2.78128	−0.130389
$456$	−10.4869	−0.491092
$457$	19.6929	0.921194	0.460597	−	0.887609i	$-0.347635\pi$
$457$	19.6929	0.921194	0.460597	+	0.887609i	$0.347635\pi$
$458$	−35.3456	−1.65159
$459$	−28.0461	−1.30908
$460$	−43.7742	−2.04098
$461$	37.2932	1.73692	0.868460	−	0.495760i	$-0.165110\pi$
$461$	37.2932	1.73692	0.868460	+	0.495760i	$0.165110\pi$
$462$	−1.40884	−0.0655453
$463$	15.8335	0.735845	0.367923	−	0.929856i	$-0.380069\pi$
$463$	15.8335	0.735845	0.367923	+	0.929856i	$0.380069\pi$
$464$	2.15729	0.100150
$465$	−1.49820	−0.0694775
$466$	30.1986	1.39892
$467$	−18.3489	−0.849088	−0.424544	−	0.905407i	$-0.639566\pi$
$467$	−18.3489	−0.849088	−0.424544	+	0.905407i	$0.639566\pi$
$468$	11.1258	0.514290
$469$	−0.315610	−0.0145735
$470$	3.72191	0.171679
$471$	−16.0060	−0.737520
$472$	9.04518	0.416338
$473$	−8.88216	−0.408402
$474$	27.4633	1.26143
$475$	−3.02463	−0.138779
$476$	16.2565	0.745117
$477$	3.21100	0.147022
$478$	−12.1953	−0.557799
$479$	−23.2742	−1.06343	−0.531713	−	0.846925i	$-0.678451\pi$
$479$	−23.2742	−1.06343	−0.531713	+	0.846925i	$0.678451\pi$
$480$	9.63798	0.439912
$481$	2.23409	0.101866
$482$	−32.7872	−1.49341
$483$	−5.35291	−0.243566
$484$	−35.4404	−1.61093
$485$	20.8345	0.946047
$486$	−37.2472	−1.68957
$487$	−23.3671	−1.05887	−0.529433	−	0.848352i	$-0.677595\pi$
$487$	−23.3671	−1.05887	−0.529433	+	0.848352i	$0.677595\pi$
$488$	−5.08532	−0.230202
$489$	11.7138	0.529715
$490$	29.4566	1.33071
$491$	−9.97910	−0.450351	−0.225175	−	0.974318i	$-0.572295\pi$
$491$	−9.97910	−0.450351	−0.225175	+	0.974318i	$0.572295\pi$
$492$	1.22684	0.0553102
$493$	17.8751	0.805054
$494$	12.4612	0.560656
$495$	−2.97691	−0.133802
$496$	−0.513589	−0.0230608
$497$	0.848897	0.0380782
$498$	10.7173	0.480253
$499$	−1.60656	−0.0719193	−0.0359597	−	0.999353i	$-0.511449\pi$
$499$	−1.60656	−0.0719193	−0.0359597	+	0.999353i	$0.511449\pi$
$500$	−40.4503	−1.80899
$501$	−21.5092	−0.960959
$502$	15.9824	0.713330
$503$	2.61636	0.116658	0.0583289	−	0.998297i	$-0.481423\pi$
$503$	2.61636	0.116658	0.0583289	+	0.998297i	$0.481423\pi$
$504$	5.53032	0.246340
$505$	−20.3535	−0.905717
$506$	10.7755	0.479030
$507$	−10.2232	−0.454027
$508$	46.7215	2.07293
$509$	−3.11003	−0.137850	−0.0689248	−	0.997622i	$-0.521957\pi$
$509$	−3.11003	−0.137850	−0.0689248	+	0.997622i	$0.521957\pi$
$510$	−26.1622	−1.15848
$511$	−7.80761	−0.345388
$512$	7.69024	0.339864
$513$	−16.4231	−0.725099
$514$	7.39393	0.326132
$515$	6.88425	0.303356
$516$	−40.8115	−1.79662
$517$	−0.575846	−0.0253257
$518$	2.71539	0.119307
$519$	−5.09529	−0.223659
$520$	10.5207	0.461363
$521$	−26.9272	−1.17970	−0.589852	−	0.807512i	$-0.700814\pi$
$521$	−26.9272	−1.17970	−0.589852	+	0.807512i	$0.700814\pi$
$522$	14.8690	0.650800
$523$	−25.1762	−1.10088	−0.550438	−	0.834876i	$-0.685539\pi$
$523$	−25.1762	−1.10088	−0.550438	+	0.834876i	$0.685539\pi$
$524$	60.4296	2.63988
$525$	−0.763556	−0.0333243
$526$	62.4282	2.72200
$527$	−4.25555	−0.185375
$528$	0.488511	0.0212597
$529$	17.9417	0.780073
$530$	7.42448	0.322499
$531$	5.71484	0.248003
$532$	9.51944	0.412720
$533$	−0.596197	−0.0258242
$534$	17.9766	0.777922
$535$	8.42039	0.364045
$536$	1.19385	0.0515666
$537$	−12.5014	−0.539477
$538$	48.2621	2.08073
$539$	−4.55746	−0.196304
$540$	−33.9042	−1.45900
$541$	34.7829	1.49543	0.747717	−	0.664017i	$-0.231150\pi$
$541$	34.7829	1.49543	0.747717	+	0.664017i	$0.231150\pi$
$542$	−0.553263	−0.0237647
$543$	−25.5673	−1.09720
$544$	27.3761	1.17374
$545$	35.2100	1.50823
$546$	3.14578	0.134627
$547$	7.64297	0.326790	0.163395	−	0.986561i	$-0.447756\pi$
$547$	7.64297	0.326790	0.163395	+	0.986561i	$0.447756\pi$
$548$	−58.2967	−2.49031
$549$	−3.21296	−0.137126
$550$	1.53705	0.0655402
$551$	10.4672	0.445919
$552$	20.2483	0.861827
$553$	−10.1954	−0.433554
$554$	29.3474	1.24685
$555$	−2.74662	−0.116587
$556$	3.95667	0.167800
$557$	−35.3879	−1.49943	−0.749717	−	0.661758i	$-0.769811\pi$
$557$	−35.3879	−1.49943	−0.749717	+	0.661758i	$0.769811\pi$
$558$	−3.53989	−0.149856
$559$	19.8328	0.838839
$560$	1.17216	0.0495329
$561$	4.04776	0.170896
$562$	−58.0510	−2.44873
$563$	15.9866	0.673755	0.336877	−	0.941548i	$-0.390629\pi$
$563$	15.9866	0.673755	0.336877	+	0.941548i	$0.390629\pi$
$564$	−2.64588	−0.111412
$565$	2.02170	0.0850537
$566$	0.0896477	0.00376817
$567$	1.02079	0.0428691
$568$	−3.21110	−0.134735
$569$	5.57518	0.233724	0.116862	−	0.993148i	$-0.462717\pi$
$569$	5.57518	0.233724	0.116862	+	0.993148i	$0.462717\pi$
$570$	−15.3199	−0.641682
$571$	−17.4471	−0.730140	−0.365070	−	0.930980i	$-0.618955\pi$
$571$	−17.4471	−0.730140	−0.365070	+	0.930980i	$0.618955\pi$
$572$	−3.98013	−0.166418
$573$	0.332510	0.0138908
$574$	−0.724638	−0.0302458
$575$	5.84005	0.243547
$576$	25.5435	1.06431
$577$	19.4055	0.807861	0.403930	−	0.914790i	$-0.367644\pi$
$577$	19.4055	0.807861	0.403930	+	0.914790i	$0.367644\pi$
$578$	−34.8665	−1.45025
$579$	16.6089	0.690241
$580$	21.6087	0.897252
$581$	−3.97867	−0.165063
$582$	−23.5650	−0.976799
$583$	−1.14870	−0.0475743
$584$	29.5337	1.22211
$585$	6.64708	0.274823
$586$	−76.7951	−3.17237
$587$	−6.85899	−0.283101	−0.141550	−	0.989931i	$-0.545209\pi$
$587$	−6.85899	−0.283101	−0.141550	+	0.989931i	$0.545209\pi$
$588$	−20.9405	−0.863571
$589$	−2.49195	−0.102679
$590$	13.2139	0.544006
$591$	−7.05953	−0.290390
$592$	−0.941550	−0.0386975
$593$	−6.87811	−0.282450	−0.141225	−	0.989978i	$-0.545104\pi$
$593$	−6.87811	−0.282450	−0.141225	+	0.989978i	$0.545104\pi$
$594$	8.34590	0.342436
$595$	9.71242	0.398171
$596$	−41.3302	−1.69295
$597$	2.34293	0.0958899
$598$	−24.0605	−0.983905
$599$	−40.6212	−1.65974	−0.829868	−	0.557960i	$-0.811584\pi$
$599$	−40.6212	−1.65974	−0.829868	+	0.557960i	$0.811584\pi$
$600$	2.88828	0.117914
$601$	6.48847	0.264670	0.132335	−	0.991205i	$-0.457752\pi$
$601$	6.48847	0.264670	0.132335	+	0.991205i	$0.457752\pi$
$602$	24.1055	0.982465
$603$	0.754289	0.0307170
$604$	49.8631	2.02890
$605$	−21.1738	−0.860837
$606$	23.0209	0.935159
$607$	−20.7869	−0.843712	−0.421856	−	0.906663i	$-0.638621\pi$
$607$	−20.7869	−0.843712	−0.421856	+	0.906663i	$0.638621\pi$
$608$	16.0308	0.650134
$609$	2.64241	0.107076
$610$	−7.42900	−0.300791
$611$	1.28580	0.0520177
$612$	−38.8521	−1.57050
$613$	−6.19859	−0.250359	−0.125179	−	0.992134i	$-0.539951\pi$
$613$	−6.19859	−0.250359	−0.125179	+	0.992134i	$0.539951\pi$
$614$	−18.2345	−0.735885
$615$	0.732972	0.0295563
$616$	−1.97841	−0.0797123
$617$	39.9776	1.60944	0.804719	−	0.593656i	$-0.202316\pi$
$617$	39.9776	1.60944	0.804719	+	0.593656i	$0.202316\pi$
$618$	−7.78646	−0.313217
$619$	37.6600	1.51368	0.756841	−	0.653599i	$-0.226742\pi$
$619$	37.6600	1.51368	0.756841	+	0.653599i	$0.226742\pi$
$620$	−5.14441	−0.206605
$621$	31.7103	1.27249
$622$	−2.20536	−0.0884269
$623$	−6.67360	−0.267372
$624$	−1.09079	−0.0436664
$625$	−19.6034	−0.784136
$626$	36.0060	1.43909
$627$	2.37027	0.0946595
$628$	−54.9603	−2.19316
$629$	−7.80159	−0.311070
$630$	8.07908	0.321878
$631$	41.0962	1.63601	0.818007	−	0.575209i	$-0.195079\pi$
$631$	41.0962	1.63601	0.818007	+	0.575209i	$0.195079\pi$
$632$	38.5661	1.53408
$633$	19.0623	0.757660
$634$	−42.6973	−1.69573
$635$	27.9136	1.10772
$636$	−5.27801	−0.209287
$637$	10.1763	0.403199
$638$	−5.31923	−0.210590
$639$	−2.02881	−0.0802584
$640$	39.5020	1.56145
$641$	17.8520	0.705111	0.352556	−	0.935791i	$-0.385313\pi$
$641$	17.8520	0.705111	0.352556	+	0.935791i	$0.385313\pi$
$642$	−9.52392	−0.375879
$643$	16.3082	0.643134	0.321567	−	0.946887i	$-0.395790\pi$
$643$	16.3082	0.643134	0.321567	+	0.946887i	$0.395790\pi$
$644$	−18.3804	−0.724290
$645$	−24.3827	−0.960068
$646$	−43.5153	−1.71209
$647$	−29.9672	−1.17813	−0.589067	−	0.808084i	$-0.700504\pi$
$647$	−29.9672	−1.17813	−0.589067	+	0.808084i	$0.700504\pi$
$648$	−3.86131	−0.151687
$649$	−2.04442	−0.0802505
$650$	−3.43206	−0.134616
$651$	−0.629082	−0.0246557
$652$	40.2219	1.57521
$653$	−16.0072	−0.626408	−0.313204	−	0.949686i	$-0.601402\pi$
$653$	−16.0072	−0.626408	−0.313204	+	0.949686i	$0.601402\pi$
$654$	−39.8244	−1.55726
$655$	36.1035	1.41068
$656$	0.251265	0.00981027
$657$	18.6597	0.727984
$658$	1.56280	0.0609242
$659$	−50.4027	−1.96341	−0.981706	−	0.190402i	$-0.939021\pi$
$659$	−50.4027	−1.96341	−0.981706	+	0.190402i	$0.939021\pi$
$660$	4.89322	0.190468
$661$	49.5083	1.92565	0.962826	−	0.270123i	$-0.0870645\pi$
$661$	49.5083	1.92565	0.962826	+	0.270123i	$0.0870645\pi$
$662$	52.0349	2.02239
$663$	−9.03816	−0.351013
$664$	15.0500	0.584054
$665$	5.68736	0.220547
$666$	−6.48960	−0.251467
$667$	−20.2104	−0.782552
$668$	−73.8566	−2.85760
$669$	−16.2753	−0.629239
$670$	1.74407	0.0673791
$671$	1.14940	0.0443721
$672$	4.04691	0.156113
$673$	−0.966366	−0.0372507	−0.0186253	−	0.999827i	$-0.505929\pi$
$673$	−0.966366	−0.0372507	−0.0186253	+	0.999827i	$0.505929\pi$
$674$	−23.0869	−0.889274
$675$	4.52325	0.174100
$676$	−35.1036	−1.35014
$677$	−11.5814	−0.445109	−0.222554	−	0.974920i	$-0.571439\pi$
$677$	−11.5814	−0.445109	−0.222554	+	0.974920i	$0.571439\pi$
$678$	−2.28666	−0.0878185
$679$	8.74824	0.335727
$680$	−36.7390	−1.40887
$681$	−22.6721	−0.868797
$682$	1.26636	0.0484913
$683$	47.8086	1.82934	0.914672	−	0.404197i	$-0.132449\pi$
$683$	47.8086	1.82934	0.914672	+	0.404197i	$0.132449\pi$
$684$	−22.7508	−0.869900
$685$	−34.8292	−1.33076
$686$	26.1566	0.998663
$687$	15.0120	0.572744
$688$	−8.35847	−0.318664
$689$	2.56491	0.0977153
$690$	29.5802	1.12610
$691$	−9.72697	−0.370031	−0.185016	−	0.982736i	$-0.559234\pi$
$691$	−9.72697	−0.370031	−0.185016	+	0.982736i	$0.559234\pi$
$692$	−17.4958	−0.665092
$693$	−1.24998	−0.0474828
$694$	−73.7115	−2.79805
$695$	2.36391	0.0896681
$696$	−9.99539	−0.378874
$697$	2.08196	0.0788599
$698$	57.3634	2.17124
$699$	−12.8260	−0.485123
$700$	−2.62184	−0.0990962
$701$	−48.0987	−1.81666	−0.908331	−	0.418252i	$-0.862643\pi$
$701$	−48.0987	−1.81666	−0.908331	+	0.418252i	$0.862643\pi$
$702$	−18.6354	−0.703348
$703$	−4.56843	−0.172301
$704$	−9.13791	−0.344398
$705$	−1.58077	−0.0595354
$706$	6.59741	0.248297
$707$	−8.54625	−0.321415
$708$	−9.39363	−0.353034
$709$	−8.49197	−0.318923	−0.159461	−	0.987204i	$-0.550976\pi$
$709$	−8.49197	−0.318923	−0.159461	+	0.987204i	$0.550976\pi$
$710$	−4.69101	−0.176050
$711$	24.3665	0.913813
$712$	25.2441	0.946062
$713$	4.81153	0.180193
$714$	−10.9853	−0.411114
$715$	−2.37792	−0.0889291
$716$	−42.9265	−1.60424
$717$	5.17959	0.193435
$718$	−68.4579	−2.55483
$719$	27.6278	1.03034	0.515172	−	0.857087i	$-0.327728\pi$
$719$	27.6278	1.03034	0.515172	+	0.857087i	$0.327728\pi$
$720$	−2.80139	−0.104402
$721$	2.89064	0.107653
$722$	18.6046	0.692392
$723$	13.9254	0.517891
$724$	−87.7911	−3.26273
$725$	−2.88288	−0.107067
$726$	23.9487	0.888820
$727$	6.54243	0.242645	0.121323	−	0.992613i	$-0.461286\pi$
$727$	6.54243	0.242645	0.121323	+	0.992613i	$0.461286\pi$
$728$	4.41755	0.163725
$729$	12.2122	0.452303
$730$	43.1449	1.59687
$731$	−69.2575	−2.56158
$732$	5.28122	0.195200
$733$	−15.5172	−0.573141	−0.286570	−	0.958059i	$-0.592515\pi$
$733$	−15.5172	−0.573141	−0.286570	+	0.958059i	$0.592515\pi$
$734$	−39.3309	−1.45173
$735$	−12.5108	−0.461469
$736$	−30.9527	−1.14093
$737$	−0.269838	−0.00993962
$738$	1.73184	0.0637498
$739$	−29.1545	−1.07246	−0.536232	−	0.844070i	$-0.680153\pi$
$739$	−29.1545	−1.07246	−0.536232	+	0.844070i	$0.680153\pi$
$740$	−9.43113	−0.346695
$741$	−5.29253	−0.194426
$742$	3.11748	0.114446
$743$	−50.8860	−1.86683	−0.933413	−	0.358803i	$-0.883185\pi$
$743$	−50.8860	−1.86683	−0.933413	+	0.358803i	$0.883185\pi$
$744$	2.37962	0.0872409
$745$	−24.6926	−0.904668
$746$	−4.08753	−0.149655
$747$	9.50877	0.347908
$748$	13.8989	0.508193
$749$	3.53565	0.129190
$750$	27.3341	0.998102
$751$	16.2450	0.592790	0.296395	−	0.955065i	$-0.404216\pi$
$751$	16.2450	0.592790	0.296395	+	0.955065i	$0.404216\pi$
$752$	−0.541894	−0.0197609
$753$	−6.78807	−0.247371
$754$	11.8772	0.432542
$755$	29.7906	1.08419
$756$	−14.2361	−0.517761
$757$	1.64447	0.0597693	0.0298846	−	0.999553i	$-0.490486\pi$
$757$	1.64447	0.0597693	0.0298846	+	0.999553i	$0.490486\pi$
$758$	−2.03205	−0.0738075
$759$	−4.57659	−0.166120
$760$	−21.5135	−0.780375
$761$	−36.9693	−1.34014	−0.670068	−	0.742300i	$-0.733735\pi$
$761$	−36.9693	−1.34014	−0.670068	+	0.742300i	$0.733735\pi$
$762$	−31.5718	−1.14373
$763$	14.7844	0.535230
$764$	1.14175	0.0413069
$765$	−23.2121	−0.839234
$766$	−42.3281	−1.52937
$767$	4.56495	0.164831
$768$	−19.8634	−0.716760
$769$	−17.6737	−0.637331	−0.318665	−	0.947867i	$-0.603235\pi$
$769$	−17.6737	−0.637331	−0.318665	+	0.947867i	$0.603235\pi$
$770$	−2.89020	−0.104156
$771$	−3.14036	−0.113097
$772$	57.0303	2.05257
$773$	−48.6114	−1.74843	−0.874216	−	0.485537i	$-0.838624\pi$
$773$	−48.6114	−1.74843	−0.874216	+	0.485537i	$0.838624\pi$
$774$	−57.6105	−2.07077
$775$	0.686331	0.0246537
$776$	−33.0918	−1.18793
$777$	−1.15328	−0.0413737
$778$	55.0933	1.97519
$779$	1.21915	0.0436805
$780$	−10.9260	−0.391213
$781$	0.725783	0.0259706
$782$	84.0207	3.00458
$783$	−15.6535	−0.559409
$784$	−4.28876	−0.153170
$785$	−32.8359	−1.17196
$786$	−40.8351	−1.45654
$787$	−20.8106	−0.741819	−0.370910	−	0.928669i	$-0.620954\pi$
$787$	−20.8106	−0.741819	−0.370910	+	0.928669i	$0.620954\pi$
$788$	−24.2405	−0.863531
$789$	−26.5146	−0.943943
$790$	56.3401	2.00449
$791$	0.848897	0.0301833
$792$	4.72827	0.168012
$793$	−2.56647	−0.0911381
$794$	−23.2963	−0.826755
$795$	−3.15333	−0.111837
$796$	8.04499	0.285147
$797$	19.3854	0.686667	0.343333	−	0.939214i	$-0.388444\pi$
$797$	19.3854	0.686667	0.343333	+	0.939214i	$0.388444\pi$
$798$	−6.43272	−0.227716
$799$	−4.49009	−0.158848
$800$	−4.41519	−0.156101
$801$	15.9495	0.563547
$802$	−29.1045	−1.02772
$803$	−6.67529	−0.235566
$804$	−1.23984	−0.0437259
$805$	−10.9813	−0.387041
$806$	−2.82762	−0.0995987
$807$	−20.4979	−0.721561
$808$	32.3277	1.13728
$809$	25.2569	0.887984	0.443992	−	0.896031i	$-0.353562\pi$
$809$	25.2569	0.887984	0.443992	+	0.896031i	$0.353562\pi$
$810$	−5.64089	−0.198201
$811$	−23.7294	−0.833251	−0.416625	−	0.909078i	$-0.636787\pi$
$811$	−23.7294	−0.833251	−0.416625	+	0.909078i	$0.636787\pi$
$812$	9.07331	0.318411
$813$	0.234983	0.00824120
$814$	2.32158	0.0813713
$815$	24.0305	0.841751
$816$	3.80910	0.133345
$817$	−40.5556	−1.41886
$818$	56.3358	1.96974
$819$	2.79105	0.0975274
$820$	2.51683	0.0878913
$821$	−19.7996	−0.691011	−0.345505	−	0.938417i	$-0.612292\pi$
$821$	−19.7996	−0.691011	−0.345505	+	0.938417i	$0.612292\pi$
$822$	39.3937	1.37401
$823$	−32.3923	−1.12913	−0.564563	−	0.825390i	$-0.690955\pi$
$823$	−32.3923	−1.12913	−0.564563	+	0.825390i	$0.690955\pi$
$824$	−10.9344	−0.380916
$825$	−0.652819	−0.0227282
$826$	5.54838	0.193053
$827$	−36.4028	−1.26585	−0.632924	−	0.774214i	$-0.718146\pi$
$827$	−36.4028	−1.26585	−0.632924	+	0.774214i	$0.718146\pi$
$828$	43.9280	1.52660
$829$	−15.7880	−0.548340	−0.274170	−	0.961681i	$-0.588403\pi$
$829$	−15.7880	−0.548340	−0.274170	+	0.961681i	$0.588403\pi$
$830$	21.9862	0.763151
$831$	−12.4645	−0.432388
$832$	20.4039	0.707377
$833$	−35.5362	−1.23126
$834$	−2.67371	−0.0925828
$835$	−44.1254	−1.52702
$836$	8.13885	0.281488
$837$	3.72664	0.128812
$838$	10.5864	0.365702
$839$	11.4409	0.394982	0.197491	−	0.980305i	$-0.436721\pi$
$839$	11.4409	0.394982	0.197491	+	0.980305i	$0.436721\pi$
$840$	−5.43099	−0.187387
$841$	−19.0233	−0.655976
$842$	−70.4973	−2.42950
$843$	24.6555	0.849180
$844$	65.4548	2.25305
$845$	−20.9725	−0.721478
$846$	−3.73499	−0.128412
$847$	−8.89070	−0.305488
$848$	−1.08097	−0.0371208
$849$	−0.0380753	−0.00130674
$850$	11.9850	0.411081
$851$	8.82086	0.302375
$852$	3.33480	0.114248
$853$	39.2640	1.34437	0.672187	−	0.740381i	$-0.265355\pi$
$853$	39.2640	1.34437	0.672187	+	0.740381i	$0.265355\pi$
$854$	−3.11937	−0.106743
$855$	−13.5924	−0.464851
$856$	−13.3742	−0.457122
$857$	27.5535	0.941211	0.470605	−	0.882344i	$-0.344036\pi$
$857$	27.5535	0.941211	0.470605	+	0.882344i	$0.344036\pi$
$858$	2.68955	0.0918199
$859$	43.9811	1.50062	0.750308	−	0.661088i	$-0.229905\pi$
$859$	43.9811	1.50062	0.750308	+	0.661088i	$0.229905\pi$
$860$	−83.7235	−2.85495
$861$	0.307769	0.0104887
$862$	−54.6546	−1.86154
$863$	−14.9102	−0.507548	−0.253774	−	0.967264i	$-0.581672\pi$
$863$	−14.9102	−0.507548	−0.253774	+	0.967264i	$0.581672\pi$
$864$	−23.9736	−0.815599
$865$	−10.4528	−0.355407
$866$	47.6251	1.61837
$867$	14.8085	0.502924
$868$	−2.16010	−0.0733184
$869$	−8.71682	−0.295698
$870$	−14.6020	−0.495054
$871$	0.602517	0.0204155
$872$	−55.9245	−1.89384
$873$	−20.9077	−0.707619
$874$	49.2006	1.66423
$875$	−10.1475	−0.343048
$876$	−30.6714	−1.03629
$877$	41.4622	1.40008	0.700040	−	0.714103i	$-0.253165\pi$
$877$	41.4622	1.40008	0.700040	+	0.714103i	$0.253165\pi$
$878$	0.638104	0.0215350
$879$	32.6165	1.10013
$880$	1.00217	0.0337830
$881$	−16.2105	−0.546146	−0.273073	−	0.961993i	$-0.588040\pi$
$881$	−16.2105	−0.546146	−0.273073	+	0.961993i	$0.588040\pi$
$882$	−29.5601	−0.995341
$883$	19.3253	0.650347	0.325174	−	0.945654i	$-0.394577\pi$
$883$	19.3253	0.650347	0.325174	+	0.945654i	$0.394577\pi$
$884$	−31.0346	−1.04380
$885$	−5.61220	−0.188652
$886$	−1.80131	−0.0605162
$887$	−22.7621	−0.764276	−0.382138	−	0.924105i	$-0.624812\pi$
$887$	−22.7621	−0.764276	−0.382138	+	0.924105i	$0.624812\pi$
$888$	4.36249	0.146396
$889$	11.7207	0.393100
$890$	36.8784	1.23617
$891$	0.872746	0.0292381
$892$	−55.8849	−1.87116
$893$	−2.62929	−0.0879858
$894$	27.9287	0.934075
$895$	−25.6463	−0.857262
$896$	16.5866	0.554118
$897$	10.2190	0.341202
$898$	−21.3845	−0.713611
$899$	−2.37516	−0.0792161
$900$	6.26603	0.208868
$901$	−8.95684	−0.298396
$902$	−0.619545	−0.0206286
$903$	−10.2381	−0.340702
$904$	−3.21110	−0.106800
$905$	−52.4506	−1.74352
$906$	−33.6948	−1.11943
$907$	8.54025	0.283574	0.141787	−	0.989897i	$-0.454715\pi$
$907$	8.54025	0.283574	0.141787	+	0.989897i	$0.454715\pi$
$908$	−77.8497	−2.58353
$909$	20.4250	0.677454
$910$	6.45347	0.213931
$911$	−5.04423	−0.167123	−0.0835613	−	0.996503i	$-0.526629\pi$
$911$	−5.04423	−0.167123	−0.0835613	+	0.996503i	$0.526629\pi$
$912$	2.23052	0.0738599
$913$	−3.40165	−0.112578
$914$	−45.6938	−1.51142
$915$	3.15525	0.104309
$916$	51.5471	1.70316
$917$	15.1596	0.500613
$918$	65.0761	2.14783
$919$	18.4644	0.609085	0.304542	−	0.952499i	$-0.401497\pi$
$919$	18.4644	0.609085	0.304542	+	0.952499i	$0.401497\pi$
$920$	41.5389	1.36950
$921$	7.74458	0.255193
$922$	−86.5324	−2.84979
$923$	−1.62059	−0.0533423
$924$	2.05462	0.0675921
$925$	1.25823	0.0413705
$926$	−36.7389	−1.20731
$927$	−6.90844	−0.226903
$928$	15.2795	0.501574
$929$	−39.0254	−1.28038	−0.640191	−	0.768216i	$-0.721145\pi$
$929$	−39.0254	−1.28038	−0.640191	+	0.768216i	$0.721145\pi$
$930$	3.47631	0.113993
$931$	−20.8092	−0.681993
$932$	−44.0409	−1.44261
$933$	0.936663	0.0306650
$934$	42.5755	1.39311
$935$	8.30385	0.271565
$936$	−10.5577	−0.345088
$937$	−15.6281	−0.510547	−0.255274	−	0.966869i	$-0.582166\pi$
$937$	−15.6281	−0.510547	−0.255274	+	0.966869i	$0.582166\pi$
$938$	0.732318	0.0239110
$939$	−15.2925	−0.499052
$940$	−5.42794	−0.177040
$941$	−16.9732	−0.553311	−0.276655	−	0.960969i	$-0.589226\pi$
$941$	−16.9732	−0.553311	−0.276655	+	0.960969i	$0.589226\pi$
$942$	37.1392	1.21006
$943$	−2.35397	−0.0766557
$944$	−1.92388	−0.0626170
$945$	−8.50531	−0.276678
$946$	20.6095	0.670072
$947$	−10.3482	−0.336271	−0.168136	−	0.985764i	$-0.553775\pi$
$947$	−10.3482	−0.336271	−0.168136	+	0.985764i	$0.553775\pi$
$948$	−40.0518	−1.30082
$949$	14.9051	0.483841
$950$	7.01812	0.227698
$951$	18.1344	0.588049
$952$	−15.4264	−0.499972
$953$	10.4935	0.339917	0.169958	−	0.985451i	$-0.445637\pi$
$953$	10.4935	0.339917	0.169958	+	0.985451i	$0.445637\pi$
$954$	−7.45057	−0.241221
$955$	0.682134	0.0220733
$956$	17.7853	0.575217
$957$	2.25919	0.0730292
$958$	54.0037	1.74478
$959$	−14.6245	−0.472250
$960$	−25.0848	−0.809608
$961$	−30.4345	−0.981759
$962$	−5.18381	−0.167133
$963$	−8.44998	−0.272297
$964$	47.8160	1.54005
$965$	34.0726	1.09684
$966$	12.4205	0.399623
$967$	29.1628	0.937812	0.468906	−	0.883248i	$-0.344648\pi$
$967$	29.1628	0.937812	0.468906	+	0.883248i	$0.344648\pi$
$968$	33.6306	1.08093
$969$	18.4819	0.593723
$970$	−48.3428	−1.55219
$971$	−4.47434	−0.143588	−0.0717942	−	0.997419i	$-0.522872\pi$
$971$	−4.47434	−0.143588	−0.0717942	+	0.997419i	$0.522872\pi$
$972$	54.3203	1.74233
$973$	0.992584	0.0318208
$974$	54.2193	1.73730
$975$	1.45767	0.0466827
$976$	1.08163	0.0346222
$977$	22.3391	0.714690	0.357345	−	0.933972i	$-0.383682\pi$
$977$	22.3391	0.714690	0.357345	+	0.933972i	$0.383682\pi$
$978$	−27.1798	−0.869113
$979$	−5.70575	−0.182356
$980$	−42.9588	−1.37227
$981$	−35.3337	−1.12812
$982$	23.1547	0.738898
$983$	25.9139	0.826525	0.413263	−	0.910612i	$-0.364389\pi$
$983$	25.9139	0.826525	0.413263	+	0.910612i	$0.364389\pi$
$984$	−1.16419	−0.0371130
$985$	−14.4824	−0.461448
$986$	−41.4760	−1.32086
$987$	−0.663754	−0.0211275
$988$	−18.1731	−0.578163
$989$	78.3059	2.48998
$990$	6.90739	0.219531
$991$	32.6067	1.03579	0.517893	−	0.855446i	$-0.326717\pi$
$991$	32.6067	1.03579	0.517893	+	0.855446i	$0.326717\pi$
$992$	−3.63761	−0.115494
$993$	−22.1003	−0.701333
$994$	−1.96972	−0.0624756
$995$	4.80646	0.152375
$996$	−15.6298	−0.495249
$997$	53.9864	1.70977	0.854884	−	0.518819i	$-0.173628\pi$
$997$	53.9864	1.70977	0.854884	+	0.518819i	$0.173628\pi$
$998$	3.72773	0.117999
$999$	6.83197	0.216154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.20	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.20	✓	155	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32032 q^{2} +0.985491 q^{3} +3.38390 q^{4} +2.02170 q^{5} -2.28666 q^{6} +0.848897 q^{7} -3.21110 q^{8} -2.02881 q^{9} +O(q^{10})\)	\(q-2.32032 q^{2} +0.985491 q^{3} +3.38390 q^{4} +2.02170 q^{5} -2.28666 q^{6} +0.848897 q^{7} -3.21110 q^{8} -2.02881 q^{9} -4.69101 q^{10} +0.725783 q^{11} +3.33480 q^{12} -1.62059 q^{13} -1.96972 q^{14} +1.99237 q^{15} +0.682991 q^{16} +5.65920 q^{17} +4.70749 q^{18} +3.31389 q^{19} +6.84125 q^{20} +0.836580 q^{21} -1.68405 q^{22} -6.39857 q^{23} -3.16451 q^{24} -0.912711 q^{25} +3.76029 q^{26} -4.95584 q^{27} +2.87258 q^{28} +3.15859 q^{29} -4.62294 q^{30} -0.751970 q^{31} +4.83744 q^{32} +0.715252 q^{33} -13.1312 q^{34} +1.71622 q^{35} -6.86529 q^{36} -1.37857 q^{37} -7.68931 q^{38} -1.59707 q^{39} -6.49190 q^{40} +0.367890 q^{41} -1.94114 q^{42} -12.2380 q^{43} +2.45598 q^{44} -4.10165 q^{45} +14.8468 q^{46} -0.793413 q^{47} +0.673081 q^{48} -6.27937 q^{49} +2.11779 q^{50} +5.57709 q^{51} -5.48391 q^{52} -1.58270 q^{53} +11.4992 q^{54} +1.46732 q^{55} -2.72589 q^{56} +3.26581 q^{57} -7.32895 q^{58} -2.81685 q^{59} +6.74199 q^{60} +1.58367 q^{61} +1.74481 q^{62} -1.72225 q^{63} -12.5904 q^{64} -3.27635 q^{65} -1.65962 q^{66} -0.371789 q^{67} +19.1502 q^{68} -6.30573 q^{69} -3.98218 q^{70} +1.00000 q^{71} +6.51471 q^{72} -9.19737 q^{73} +3.19872 q^{74} -0.899468 q^{75} +11.2139 q^{76} +0.616115 q^{77} +3.70573 q^{78} -12.0102 q^{79} +1.38081 q^{80} +1.20249 q^{81} -0.853623 q^{82} -4.68687 q^{83} +2.83090 q^{84} +11.4412 q^{85} +28.3962 q^{86} +3.11276 q^{87} -2.33056 q^{88} -7.86150 q^{89} +9.51716 q^{90} -1.37571 q^{91} -21.6521 q^{92} -0.741059 q^{93} +1.84098 q^{94} +6.69971 q^{95} +4.76725 q^{96} +10.3054 q^{97} +14.5702 q^{98} -1.47247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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