LMFDB - Embedded newform 138.4.d.a.137.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(137,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("138.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			137.20
Character	$\chi$	$=$	138.137
Dual form			138.4.d.a.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +(2.34341 - 4.63772i) q^{3} -4.00000 q^{4} +10.8839 q^{5} +(9.27544 + 4.68682i) q^{6} -21.8179i q^{7} -8.00000i q^{8} +(-16.0169 - 21.7361i) q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +(2.34341 - 4.63772i) q^{3} -4.00000 q^{4} +10.8839 q^{5} +(9.27544 + 4.68682i) q^{6} -21.8179i q^{7} -8.00000i q^{8} +(-16.0169 - 21.7361i) q^{9} +21.7678i q^{10} -10.5986 q^{11} +(-9.37363 + 18.5509i) q^{12} -57.2594 q^{13} +43.6358 q^{14} +(25.5055 - 50.4766i) q^{15} +16.0000 q^{16} +114.219 q^{17} +(43.4723 - 32.0338i) q^{18} -113.444i q^{19} -43.5357 q^{20} +(-101.185 - 51.1283i) q^{21} -21.1971i q^{22} +(99.6450 + 47.3062i) q^{23} +(-37.1018 - 18.7473i) q^{24} -6.54035 q^{25} -114.519i q^{26} +(-138.340 + 23.3452i) q^{27} +87.2717i q^{28} -126.097i q^{29} +(100.953 + 51.0109i) q^{30} +289.289 q^{31} +32.0000i q^{32} +(-24.8368 + 49.1532i) q^{33} +228.439i q^{34} -237.464i q^{35} +(64.0675 + 86.9445i) q^{36} +84.7151i q^{37} +226.887 q^{38} +(-134.182 + 265.553i) q^{39} -87.0713i q^{40} +299.551i q^{41} +(102.257 - 202.371i) q^{42} +365.488i q^{43} +42.3943 q^{44} +(-174.326 - 236.574i) q^{45} +(-94.6123 + 199.290i) q^{46} -254.505i q^{47} +(37.4945 - 74.2035i) q^{48} -133.021 q^{49} -13.0807i q^{50} +(267.663 - 529.718i) q^{51} +229.038 q^{52} -467.085 q^{53} +(-46.6904 - 276.680i) q^{54} -115.354 q^{55} -174.543 q^{56} +(-526.120 - 265.845i) q^{57} +252.193 q^{58} +304.305i q^{59} +(-102.022 + 201.906i) q^{60} +697.918i q^{61} +578.578i q^{62} +(-474.237 + 349.455i) q^{63} -64.0000 q^{64} -623.206 q^{65} +(-98.3063 - 49.6735i) q^{66} -671.692i q^{67} -456.878 q^{68} +(452.902 - 351.268i) q^{69} +474.929 q^{70} +354.578i q^{71} +(-173.889 + 128.135i) q^{72} -321.406 q^{73} -169.430 q^{74} +(-15.3267 + 30.3323i) q^{75} +453.774i q^{76} +231.239i q^{77} +(-531.106 - 268.364i) q^{78} +78.6582i q^{79} +174.143 q^{80} +(-215.919 + 696.290i) q^{81} -599.101 q^{82} +506.936 q^{83} +(404.741 + 204.513i) q^{84} +1243.16 q^{85} -730.976 q^{86} +(-584.801 - 295.496i) q^{87} +84.7885i q^{88} +1122.44 q^{89} +(473.149 - 348.653i) q^{90} +1249.28i q^{91} +(-398.580 - 189.225i) q^{92} +(677.922 - 1341.64i) q^{93} +509.010 q^{94} -1234.71i q^{95} +(148.407 + 74.9890i) q^{96} -553.523i q^{97} -266.043i q^{98} +(169.756 + 230.372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) $ 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9	$ 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) $ 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	2.34341	−	4.63772i	0.450989	−	0.892530i
$3$	2.34341	−	4.63772i	0.450989	−	0.892530i
$4$	−4.00000			−0.500000
$5$	10.8839			0.973487			0.486744	−	0.873545i	$-0.338185\pi$
$5$	10.8839			0.973487			0.486744	+	0.873545i	$0.338185\pi$
$6$	9.27544	+	4.68682i	0.631114	+	0.318897i
$7$		−	21.8179i		−	1.17806i	−0.808112	−	0.589028i	$-0.799511\pi$
$7$		−	21.8179i		−	1.17806i	0.808112	−	0.589028i	$-0.200489\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−16.0169	−	21.7361i	−0.593218	−	0.805042i
$10$			21.7678i			0.688359i
$11$	−10.5986			−0.290508			−0.145254	−	0.989394i	$-0.546400\pi$
$11$	−10.5986			−0.290508			−0.145254	+	0.989394i	$0.546400\pi$
$12$	−9.37363	+	18.5509i	−0.225494	+	0.446265i
$13$	−57.2594			−1.22161			−0.610804	−	0.791782i	$-0.709154\pi$
$13$	−57.2594			−1.22161			−0.610804	+	0.791782i	$0.709154\pi$
$14$	43.6358			0.833012
$15$	25.5055	−	50.4766i	0.439032	−	0.868866i
$16$	16.0000			0.250000
$17$	114.219			1.62955			0.814773	−	0.579780i	$-0.196861\pi$
$17$	114.219			1.62955			0.814773	+	0.579780i	$0.196861\pi$
$18$	43.4723	−	32.0338i	0.569251	−	0.419468i
$19$		−	113.444i		−	1.36978i	−0.728648	−	0.684888i	$-0.759851\pi$
$19$		−	113.444i		−	1.36978i	0.728648	−	0.684888i	$-0.240149\pi$
$20$	−43.5357			−0.486744
$21$	−101.185	−	51.1283i	−1.05145	−	0.531291i
$22$		−	21.1971i		−	0.205420i
$23$	99.6450	+	47.3062i	0.903366	+	0.428870i
$23$	99.6450	+	47.3062i	0.903366	+	0.428870i
$24$	−37.1018	−	18.7473i	−0.315557	−	0.159449i
$25$	−6.54035			−0.0523228
$26$		−	114.519i		−	0.863807i
$27$	−138.340	+	23.3452i	−0.986058	+	0.166399i
$28$			87.2717i			0.589028i
$29$		−	126.097i		−	0.807433i	−0.914884	−	0.403717i	$-0.867718\pi$
$29$		−	126.097i		−	0.807433i	0.914884	−	0.403717i	$-0.132282\pi$
$30$	100.953	+	51.0109i	0.614381	+	0.310442i
$31$	289.289			1.67606			0.838030	−	0.545624i	$-0.183707\pi$
$31$	289.289			1.67606			0.838030	+	0.545624i	$0.183707\pi$
$32$			32.0000i			0.176777i
$33$	−24.8368	+	49.1532i	−0.131016	+	0.259287i
$34$			228.439i			1.15226i
$35$		−	237.464i		−	1.14682i
$36$	64.0675	+	86.9445i	0.296609	+	0.402521i
$37$			84.7151i			0.376408i	0.982130	+	0.188204i	$0.0602665\pi$
$37$			84.7151i			0.376408i	−0.982130	+	0.188204i	$0.939733\pi$
$38$	226.887			0.968578
$39$	−134.182	+	265.553i	−0.550932	+	1.09032i
$40$		−	87.0713i		−	0.344180i
$41$			299.551i			1.14102i	0.821290	+	0.570511i	$0.193255\pi$
$41$			299.551i			1.14102i	−0.821290	+	0.570511i	$0.806745\pi$
$42$	102.257	−	202.371i	0.375679	−	0.743488i
$43$			365.488i			1.29619i	0.761558	+	0.648097i	$0.224435\pi$
$43$			365.488i			1.29619i	−0.761558	+	0.648097i	$0.775565\pi$
$44$	42.3943			0.145254
$45$	−174.326	−	236.574i	−0.577490	−	0.783698i
$46$	−94.6123	+	199.290i	−0.303257	+	0.638776i
$47$		−	254.505i		−	0.789859i	−0.918712	−	0.394929i	$-0.870769\pi$
$47$		−	254.505i		−	0.789859i	0.918712	−	0.394929i	$-0.129231\pi$
$48$	37.4945	−	74.2035i	0.112747	−	0.223132i
$49$	−133.021			−0.387817
$50$		−	13.0807i		−	0.0369978i
$51$	267.663	−	529.718i	0.734908	−	1.45442i
$52$	229.038			0.610804
$53$	−467.085			−1.21055			−0.605274	−	0.796017i	$-0.706936\pi$
$53$	−467.085			−1.21055			−0.605274	+	0.796017i	$0.706936\pi$
$54$	−46.6904	−	276.680i	−0.117662	−	0.697249i
$55$	−115.354			−0.282806
$56$	−174.543			−0.416506
$57$	−526.120	−	265.845i	−1.22257	−	0.617754i
$58$	252.193			0.570941
$59$			304.305i			0.671476i	0.941955	+	0.335738i	$0.108986\pi$
$59$			304.305i			0.671476i	−0.941955	+	0.335738i	$0.891014\pi$
$60$	−102.022	+	201.906i	−0.219516	+	0.434433i
$61$			697.918i			1.46491i	0.680818	+	0.732453i	$0.261625\pi$
$61$			697.918i			1.46491i	−0.680818	+	0.732453i	$0.738375\pi$
$62$			578.578i			1.18515i
$63$	−474.237	+	349.455i	−0.948385	+	0.698844i
$64$	−64.0000			−0.125000
$65$	−623.206			−1.18922
$66$	−98.3063	−	49.6735i	−0.183344	−	0.0926422i
$67$		−	671.692i		−	1.22478i	−0.790556	−	0.612389i	$-0.790208\pi$
$67$		−	671.692i		−	1.22478i	0.790556	−	0.612389i	$-0.209792\pi$
$68$	−456.878			−0.814773
$69$	452.902	−	351.268i	0.790188	−	0.612865i
$70$	474.929			0.810926
$71$			354.578i			0.592685i	0.955082	+	0.296343i	$0.0957670\pi$
$71$			354.578i			0.592685i	−0.955082	+	0.296343i	$0.904233\pi$
$72$	−173.889	+	128.135i	−0.284625	+	0.209734i
$73$	−321.406			−0.515311			−0.257656	−	0.966237i	$-0.582950\pi$
$73$	−321.406			−0.515311			−0.257656	+	0.966237i	$0.582950\pi$
$74$	−169.430			−0.266160
$75$	−15.3267	+	30.3323i	−0.0235970	+	0.0466996i
$76$			453.774i			0.684888i
$77$			231.239i			0.342235i
$78$	−531.106	−	268.364i	−0.770973	−	0.389567i
$79$			78.6582i			0.112022i	0.998430	+	0.0560110i	$0.0178382\pi$
$79$			78.6582i			0.112022i	−0.998430	+	0.0560110i	$0.982162\pi$
$80$	174.143			0.243372
$81$	−215.919	+	696.290i	−0.296185	+	0.955131i
$82$	−599.101			−0.806825
$83$	506.936			0.670404			0.335202	−	0.942146i	$-0.391195\pi$
$83$	506.936			0.670404			0.335202	+	0.942146i	$0.391195\pi$
$84$	404.741	+	204.513i	0.525725	+	0.265645i
$85$	1243.16			1.58634
$86$	−730.976			−0.916548
$87$	−584.801	−	295.496i	−0.720658	−	0.364143i
$88$			84.7885i			0.102710i
$89$	1122.44			1.33683			0.668416	−	0.743788i	$-0.266973\pi$
$89$	1122.44			1.33683			0.668416	+	0.743788i	$0.266973\pi$
$90$	473.149	−	348.653i	0.554158	−	0.408347i
$91$			1249.28i			1.43912i
$92$	−398.580	−	189.225i	−0.451683	−	0.214435i
$93$	677.922	−	1341.64i	0.755885	−	1.49593i
$94$	509.010			0.558514
$95$		−	1234.71i		−	1.33346i
$96$	148.407	+	74.9890i	0.157778	+	0.0797243i
$97$		−	553.523i		−	0.579399i	−0.957118	−	0.289700i	$-0.906445\pi$
$97$		−	553.523i		−	0.579399i	0.957118	−	0.289700i	$-0.0935554\pi$
$98$		−	266.043i		−	0.274228i
$99$	169.756	+	230.372i	0.172334	+	0.233871i
$100$	26.1614			0.0261614
$101$			619.354i			0.610179i	0.952324	+	0.305089i	$0.0986863\pi$
$101$			619.354i			0.610179i	−0.952324	+	0.305089i	$0.901314\pi$
$102$	1059.44	+	535.326i	1.02843	+	0.519658i
$103$			1232.74i			1.17928i	0.807667	+	0.589639i	$0.200730\pi$
$103$			1232.74i			1.17928i	−0.807667	+	0.589639i	$0.799270\pi$
$104$			458.075i			0.431903i
$105$	−1101.29	−	556.476i	−1.02357	−	0.517205i
$106$		−	934.169i		−	0.855986i
$107$	998.586			0.902215			0.451107	−	0.892470i	$-0.351029\pi$
$107$	998.586			0.902215			0.451107	+	0.892470i	$0.351029\pi$
$108$	553.361	−	93.3808i	0.493029	−	0.0831997i
$109$		−	1042.56i		−	0.916140i	−0.888916	−	0.458070i	$-0.848541\pi$
$109$		−	1042.56i		−	0.916140i	0.888916	−	0.458070i	$-0.151459\pi$
$110$		−	230.708i		−	0.199974i
$111$	392.885	+	198.522i	0.335955	+	0.169756i
$112$		−	349.087i		−	0.294514i
$113$	1720.22			1.43208			0.716039	−	0.698060i	$-0.245953\pi$
$113$	1720.22			1.43208			0.716039	+	0.698060i	$0.245953\pi$
$114$	531.689	−	1052.24i	0.436818	−	0.864484i
$115$	1084.53	+	514.876i	0.879415	+	0.417500i
$116$			504.387i			0.403717i
$117$	917.117	+	1244.60i	0.724679	+	0.983445i
$118$	−608.609			−0.474805
$119$		−	2492.03i		−	1.91970i
$120$	−403.812	−	204.044i	−0.307191	−	0.155221i
$121$	−1218.67			−0.915605
$122$	−1395.84			−1.03584
$123$	1389.23	+	701.969i	1.01840	+	0.514589i
$124$	−1157.16			−0.838030
$125$	−1431.67			−1.02442
$126$	−698.910	−	948.474i	−0.494157	−	0.670609i
$127$	−417.436			−0.291665			−0.145833	−	0.989309i	$-0.546586\pi$
$127$	−417.436			−0.291665			−0.145833	+	0.989309i	$0.546586\pi$
$128$		−	128.000i		−	0.0883883i
$129$	1695.03	+	856.487i	1.15689	+	0.584570i
$130$		−	1246.41i		−	0.840905i
$131$			994.475i			0.663265i	0.943409	+	0.331633i	$0.107599\pi$
$131$			994.475i			0.663265i	−0.943409	+	0.331633i	$0.892401\pi$
$132$	99.3470	−	196.613i	0.0655079	−	0.129643i
$133$	−2475.10			−1.61367
$134$	1343.38			0.866049
$135$	−1505.68	+	254.087i	−0.959915	+	0.161988i
$136$		−	913.756i		−	0.576132i
$137$	−1322.32			−0.824624			−0.412312	−	0.911043i	$-0.635279\pi$
$137$	−1322.32			−0.824624			−0.412312	+	0.911043i	$0.635279\pi$
$138$	702.536	+	905.803i	0.433361	+	0.558747i
$139$	642.320			0.391949			0.195974	−	0.980609i	$-0.437213\pi$
$139$	642.320			0.391949			0.195974	+	0.980609i	$0.437213\pi$
$140$			949.857i			0.573411i
$141$	−1180.32	−	596.409i	−0.704972	−	0.356217i
$142$	−709.156			−0.419092
$143$	606.867			0.354887
$144$	−256.270	−	347.778i	−0.148304	−	0.201260i
$145$		−	1372.43i		−	0.786026i
$146$		−	642.812i		−	0.364380i
$147$	−311.723	+	616.916i	−0.174901	+	0.346138i
$148$		−	338.860i		−	0.188204i
$149$	69.6174			0.0382770			0.0191385	−	0.999817i	$-0.493908\pi$
$149$	69.6174			0.0382770			0.0191385	+	0.999817i	$0.493908\pi$
$150$	−60.6646	−	30.6534i	−0.0330216	−	0.0166856i
$151$	1839.55			0.991394			0.495697	−	0.868496i	$-0.334913\pi$
$151$	1839.55			0.991394			0.495697	+	0.868496i	$0.334913\pi$
$152$	−907.549			−0.484289
$153$	−1829.44	−	2482.69i	−0.966676	−	1.31185i
$154$	−462.477			−0.241997
$155$	3148.60			1.63162
$156$	536.728	−	1062.21i	0.275466	−	0.545160i
$157$		−	686.113i		−	0.348776i	−0.984677	−	0.174388i	$-0.944205\pi$
$157$		−	686.113i		−	0.348776i	0.984677	−	0.174388i	$-0.0557947\pi$
$158$	−157.316			−0.0792115
$159$	−1094.57	+	2166.21i	−0.545943	+	1.08045i
$160$			348.285i			0.172090i
$161$	1032.12	−	2174.05i	0.505234	−	1.06422i
$162$	−1392.58	−	431.838i	−0.675379	−	0.209435i
$163$	2558.16			1.22927			0.614633	−	0.788813i	$-0.289304\pi$
$163$	2558.16			1.22927			0.614633	+	0.788813i	$0.289304\pi$
$164$		−	1198.20i		−	0.570511i
$165$	−270.321	+	534.979i	−0.127542	+	0.252412i
$166$			1013.87i			0.474047i
$167$			722.148i			0.334620i	0.985904	+	0.167310i	$0.0535080\pi$
$167$			722.148i			0.334620i	−0.985904	+	0.167310i	$0.946492\pi$
$168$	−409.026	+	809.483i	−0.187840	+	0.371744i
$169$	1081.64			0.492325
$170$			2486.31i			1.12171i
$171$	−2465.83	+	1817.01i	−1.10273	+	0.812576i
$172$		−	1461.95i		−	0.648097i
$173$			2672.05i			1.17429i	0.809482	+	0.587145i	$0.199748\pi$
$173$			2672.05i			1.17429i	−0.809482	+	0.587145i	$0.800252\pi$
$174$	590.992	−	1169.60i	0.257488	−	0.509582i
$175$			142.697i			0.0616392i
$176$	−169.577			−0.0726270
$177$	1411.28	+	713.109i	0.599312	+	0.302828i
$178$			2244.87i			0.945283i
$179$		−	1537.45i		−	0.641982i	−0.947082	−	0.320991i	$-0.895984\pi$
$179$		−	1537.45i		−	0.641982i	0.947082	−	0.320991i	$-0.104016\pi$
$180$	697.306	+	946.297i	0.288745	+	0.391849i
$181$		−	2480.61i		−	1.01869i	−0.860563	−	0.509344i	$-0.829888\pi$
$181$		−	2480.61i		−	1.01869i	0.860563	−	0.509344i	$-0.170112\pi$
$182$	−2498.56			−1.01761
$183$	3236.75	+	1635.51i	1.30747	+	0.660656i
$184$	378.449	−	797.160i	0.151629	−	0.319388i
$185$			922.032i			0.366428i
$186$	2683.28	+	1355.84i	1.05778	+	0.534491i
$187$	−1210.56			−0.473396
$188$			1018.02i			0.394929i
$189$	509.343	+	3018.29i	0.196028	+	1.16163i
$190$	2469.42			0.942898
$191$	2283.68			0.865139			0.432570	−	0.901601i	$-0.357607\pi$
$191$	2283.68			0.865139			0.432570	+	0.901601i	$0.357607\pi$
$192$	−149.978	+	296.814i	−0.0563736	+	0.111566i
$193$	−3711.80			−1.38436			−0.692179	−	0.721726i	$-0.743349\pi$
$193$	−3711.80			−1.38436			−0.692179	+	0.721726i	$0.743349\pi$
$194$	1107.05			0.409697
$195$	−1460.43	+	2890.26i	−0.536325	+	1.06141i
$196$	532.085			0.193909
$197$		−	3550.99i		−	1.28425i	−0.766600	−	0.642125i	$-0.778053\pi$
$197$		−	3550.99i		−	1.28425i	0.766600	−	0.642125i	$-0.221947\pi$
$198$	−460.744	+	339.512i	−0.165372	+	0.121859i
$199$			501.412i			0.178614i	0.996004	+	0.0893070i	$0.0284652\pi$
$199$			501.412i			0.178614i	−0.996004	+	0.0893070i	$0.971535\pi$
$200$			52.3228i			0.0184989i
$201$	−3115.12	−	1574.05i	−1.09315	−	0.552362i
$202$	−1238.71			−0.431462
$203$	−2751.17			−0.951202
$204$	−1070.65	+	2118.87i	−0.367454	+	0.727209i
$205$			3260.28i			1.11077i
$206$	−2465.48			−0.833875
$207$	−567.749	−	2923.59i	−0.190634	−	0.981661i
$208$	−916.150			−0.305402
$209$			1202.34i			0.397931i
$210$	1112.95	−	2202.59i	0.365719	−	0.723776i
$211$	−5985.97			−1.95304			−0.976520	−	0.215429i	$-0.930885\pi$
$211$	−5985.97			−1.95304			−0.976520	+	0.215429i	$0.930885\pi$
$212$	1868.34			0.605274
$213$	1644.43	+	830.920i	0.528989	+	0.267294i
$214$			1997.17i			0.637962i
$215$			3977.94i			1.26183i
$216$	186.762	+	1106.72i	0.0588311	+	0.348624i
$217$		−	6311.68i		−	1.97449i
$218$	2085.12			0.647809
$219$	−753.185	+	1490.59i	−0.232400	+	0.459930i
$220$	461.416			0.141403
$221$	−6540.14			−1.99067
$222$	−397.044	+	785.770i	−0.120035	+	0.237556i
$223$	3360.05			1.00899			0.504496	−	0.863414i	$-0.331678\pi$
$223$	3360.05			1.00899			0.504496	+	0.863414i	$0.331678\pi$
$224$	698.173			0.208253
$225$	104.756	+	142.162i	0.0310388	+	0.0421220i
$226$			3440.44i			1.01263i
$227$	−864.868			−0.252878			−0.126439	−	0.991974i	$-0.540355\pi$
$227$	−864.868			−0.252878			−0.126439	+	0.991974i	$0.540355\pi$
$228$	2104.48	+	1063.38i	0.611283	+	0.308877i
$229$		−	644.141i		−	0.185878i	−0.995672	−	0.0929390i	$-0.970374\pi$
$229$		−	644.141i		−	0.185878i	0.995672	−	0.0929390i	$-0.0296262\pi$
$230$	−1029.75	+	2169.06i	−0.295217	+	0.621840i
$231$	1072.42	+	541.886i	0.305455	+	0.154344i
$232$	−1008.77			−0.285471
$233$		−	5314.43i		−	1.49425i	−0.664685	−	0.747124i	$-0.731434\pi$
$233$		−	5314.43i		−	1.49425i	0.664685	−	0.747124i	$-0.268566\pi$
$234$	−2489.20	+	1834.23i	−0.695401	+	0.512426i
$235$		−	2770.01i		−	0.768917i
$236$		−	1217.22i		−	0.335738i
$237$	364.795	+	184.328i	0.0999830	+	0.0505207i
$238$	4984.06			1.35743
$239$			3518.25i			0.952204i	0.879390	+	0.476102i	$0.157951\pi$
$239$			3518.25i			0.952204i	−0.879390	+	0.476102i	$0.842049\pi$
$240$	408.087	−	807.625i	0.109758	−	0.217217i
$241$		−	4742.64i		−	1.26763i	−0.773483	−	0.633817i	$-0.781487\pi$
$241$		−	4742.64i		−	1.26763i	0.773483	−	0.633817i	$-0.218513\pi$
$242$		−	2437.34i		−	0.647431i
$243$	2723.21	+	2633.06i	0.718906	+	0.695107i
$244$		−	2791.67i		−	0.732453i
$245$	−1447.79			−0.377535
$246$	−1403.94	+	2778.46i	−0.363869	+	0.720115i
$247$			6495.71i			1.67333i
$248$		−	2314.31i		−	0.592577i
$249$	1187.96	−	2351.03i	0.302345	−	0.598355i
$250$		−	2863.35i		−	0.724376i
$251$	−930.257			−0.233933			−0.116967	−	0.993136i	$-0.537317\pi$
$251$	−930.257			−0.233933			−0.116967	+	0.993136i	$0.537317\pi$
$252$	1896.95	−	1397.82i	0.474193	−	0.349422i
$253$	−1056.09	−	501.377i	−0.262435	−	0.124590i
$254$		−	834.873i		−	0.206238i
$255$	2913.22	−	5765.41i	0.715423	−	1.41586i
$256$	256.000			0.0625000
$257$		−	1399.11i		−	0.339588i	−0.985480	−	0.169794i	$-0.945690\pi$
$257$		−	1399.11i		−	0.339588i	0.985480	−	0.169794i	$-0.0543102\pi$
$258$	−1712.97	+	3390.06i	−0.413353	+	0.818046i
$259$	1848.31			0.443429
$260$	2492.83			0.594610
$261$	−2740.85	+	2019.68i	−0.650017	+	0.478984i
$262$	−1988.95			−0.468999
$263$	4854.60			1.13820			0.569101	−	0.822267i	$-0.307291\pi$
$263$	4854.60			1.13820			0.569101	+	0.822267i	$0.307291\pi$
$264$	393.225	+	198.694i	0.0916718	+	0.0463211i
$265$	−5083.71			−1.17845
$266$		−	4950.21i		−	1.14104i
$267$	2630.33	−	5205.55i	0.602896	−	1.19316i
$268$			2686.77i			0.612389i
$269$			4990.97i			1.13124i	0.824665	+	0.565622i	$0.191364\pi$
$269$			4990.97i			1.13124i	−0.824665	+	0.565622i	$0.808636\pi$
$270$	−508.174	−	3011.37i	−0.114543	−	0.678763i
$271$	−5973.67			−1.33902			−0.669510	−	0.742803i	$-0.733496\pi$
$271$	−5973.67			−1.33902			−0.669510	+	0.742803i	$0.733496\pi$
$272$	1827.51			0.407387
$273$	5793.81	+	2927.57i	1.28446	+	0.649029i
$274$		−	2644.64i		−	0.583097i
$275$	69.3183			0.0152002
$276$	−1811.61	+	1405.07i	−0.395094	+	0.306433i
$277$	2759.86			0.598642			0.299321	−	0.954152i	$-0.403240\pi$
$277$	2759.86			0.598642			0.299321	+	0.954152i	$0.403240\pi$
$278$			1284.64i			0.277150i
$279$	−4633.51	−	6288.03i	−0.994269	−	1.34930i
$280$	−1899.71			−0.405463
$281$	−902.764			−0.191653			−0.0958263	−	0.995398i	$-0.530549\pi$
$281$	−902.764			−0.191653			−0.0958263	+	0.995398i	$0.530549\pi$
$282$	1192.82	−	2360.64i	0.251884	−	0.498491i
$283$		−	7168.41i		−	1.50572i	−0.658183	−	0.752858i	$-0.728675\pi$
$283$		−	7168.41i		−	1.50572i	0.658183	−	0.752858i	$-0.271325\pi$
$284$		−	1418.31i		−	0.296343i
$285$	−5726.24	−	2893.43i	−1.19015	−	0.601376i
$286$			1213.73i			0.250943i
$287$	6535.57			1.34419
$288$	695.556	−	512.540i	0.142313	−	0.104867i
$289$	8133.09			1.65542
$290$	2744.85			0.555804
$291$	−2567.08	−	1297.13i	−0.517131	−	0.261303i
$292$	1285.62			0.257656
$293$	601.951			0.120022			0.0600109	−	0.998198i	$-0.480886\pi$
$293$	601.951			0.120022			0.0600109	+	0.998198i	$0.480886\pi$
$294$	−1233.83	−	623.447i	−0.244757	−	0.123674i
$295$			3312.03i			0.653673i
$296$	677.721			0.133080
$297$	1466.21	−	247.425i	0.286458	−	0.0483403i
$298$			139.235i			0.0270660i
$299$	−5705.61	−	2708.72i	−1.10356	−	0.523911i
$300$	61.3068	−	121.329i	0.0117985	−	0.0233498i
$301$	7974.18			1.52699
$302$			3679.10i			0.701021i
$303$	2872.39	+	1451.40i	0.544603	+	0.275184i
$304$		−	1815.10i		−	0.342444i
$305$			7596.08i			1.42607i
$306$	4965.38	−	3658.88i	0.927620	−	0.683543i
$307$	−9095.26			−1.69086			−0.845429	−	0.534087i	$-0.820655\pi$
$307$	−9095.26			−1.69086			−0.845429	+	0.534087i	$0.820655\pi$
$308$		−	924.954i		−	0.171117i
$309$	5717.11	+	2888.82i	1.05254	+	0.531841i
$310$			6297.20i			1.15373i
$311$			2085.16i			0.380188i	0.981766	+	0.190094i	$0.0608793\pi$
$311$			2085.16i			0.380188i	−0.981766	+	0.190094i	$0.939121\pi$
$312$	2124.42	+	1073.46i	0.385487	+	0.194784i
$313$			7530.75i			1.35995i	0.733237	+	0.679973i	$0.238008\pi$
$313$			7530.75i			1.35995i	−0.733237	+	0.679973i	$0.761992\pi$
$314$	1372.23			0.246622
$315$	−5161.56	+	3803.44i	−0.923241	+	0.680316i
$316$		−	314.633i		−	0.0560110i
$317$			5822.34i			1.03159i	0.856711	+	0.515797i	$0.172504\pi$
$317$			5822.34i			1.03159i	−0.856711	+	0.515797i	$0.827496\pi$
$318$	−4332.41	−	2189.14i	−0.763993	−	0.386040i
$319$			1336.44i			0.234566i
$320$	−696.571			−0.121686
$321$	2340.09	−	4631.16i	0.406889	−	0.805253i
$322$	4348.09	+	2064.24i	0.752515	+	0.357254i
$323$		−	12957.5i		−	2.23211i
$324$	863.676	−	2785.16i	0.148093	−	0.477565i
$325$	374.496			0.0639179
$326$			5116.31i			0.869222i
$327$	−4835.11	−	2443.15i	−0.817682	−	0.413169i
$328$	2396.40			0.403413
$329$	−5552.77			−0.930498
$330$	−1069.96	−	540.642i	−0.178483	−	0.0901860i
$331$	9020.57			1.49793			0.748965	−	0.662609i	$-0.230551\pi$
$331$	9020.57			1.49793			0.748965	+	0.662609i	$0.230551\pi$
$332$	−2027.75			−0.335202
$333$	1841.38	−	1356.87i	0.303024	−	0.223292i
$334$	−1444.30			−0.236612
$335$		−	7310.64i		−	1.19231i
$336$	−1618.97	−	818.052i	−0.262863	−	0.132823i
$337$			7456.58i			1.20530i	0.798006	+	0.602649i	$0.205888\pi$
$337$			7456.58i			1.20530i	−0.798006	+	0.602649i	$0.794112\pi$
$338$			2163.28i			0.348126i
$339$	4031.18	−	7977.90i	0.645851	−	1.27817i
$340$	−4972.62			−0.793171
$341$	−3066.05			−0.486909
$342$	−3634.03	−	4931.65i	−0.574578	−	0.779746i
$343$		−	4581.30i		−	0.721186i
$344$	2923.90			0.458274
$345$	4929.34	−	3823.17i	0.769237	−	0.596616i
$346$	−5344.10			−0.830348
$347$		−	4527.76i		−	0.700469i	−0.936662	−	0.350235i	$-0.886102\pi$
$347$		−	4527.76i		−	0.700469i	0.936662	−	0.350235i	$-0.113898\pi$
$348$	2339.20	+	1181.98i	0.360329	+	0.182072i
$349$	1114.89			0.170999			0.0854993	−	0.996338i	$-0.472751\pi$
$349$	1114.89			0.170999			0.0854993	+	0.996338i	$0.472751\pi$
$350$	−285.393			−0.0435855
$351$	7921.27	−	1336.73i	1.20458	−	0.203275i
$352$		−	339.154i		−	0.0513550i
$353$			817.597i			0.123276i	0.998099	+	0.0616378i	$0.0196324\pi$
$353$			817.597i			0.123276i	−0.998099	+	0.0616378i	$0.980368\pi$
$354$	−1426.22	+	2822.56i	−0.214132	+	0.423778i
$355$			3859.20i			0.576971i
$356$	−4489.75			−0.668416
$357$	−11557.3	−	5839.84i	−1.71339	−	0.865763i
$358$	3074.91			0.453950
$359$	5448.72			0.801038			0.400519	−	0.916288i	$-0.368830\pi$
$359$	5448.72			0.801038			0.400519	+	0.916288i	$0.368830\pi$
$360$	−1892.59	+	1394.61i	−0.277079	+	0.204174i
$361$	−6010.45			−0.876287
$362$	4961.22			0.720321
$363$	−2855.84	+	5651.85i	−0.412928	+	0.817205i
$364$		−	4997.12i		−	0.719561i
$365$	−3498.15			−0.501649
$366$	−3271.01	+	6473.50i	−0.467155	+	0.924522i
$367$		−	168.276i		−	0.0239345i	−0.999928	−	0.0119672i	$-0.996191\pi$
$367$		−	168.276i		−	0.0239345i	0.999928	−	0.0119672i	$-0.00380938\pi$
$368$	1594.32	+	756.899i	0.225842	+	0.107218i
$369$	6511.07	−	4797.87i	0.918571	−	0.676875i
$370$	−1844.06			−0.259104
$371$			10190.8i			1.42609i
$372$	−2711.69	+	5366.57i	−0.377942	+	0.747966i
$373$			8526.68i			1.18363i	0.806073	+	0.591816i	$0.201589\pi$
$373$			8526.68i			1.18363i	−0.806073	+	0.591816i	$0.798411\pi$
$374$		−	2421.12i		−	0.334742i
$375$	−3355.00	+	6639.70i	−0.462003	+	0.914327i
$376$	−2036.04			−0.279257
$377$			7220.22i			0.986366i
$378$	−6036.59	+	1018.69i	−0.821398	+	0.138613i
$379$		−	1545.20i		−	0.209423i	−0.994503	−	0.104712i	$-0.966608\pi$
$379$		−	1545.20i		−	0.209423i	0.994503	−	0.104712i	$-0.0333920\pi$
$380$			4938.84i			0.666730i
$381$	−978.223	+	1935.95i	−0.131538	+	0.260320i
$382$			4567.37i			0.611746i
$383$	5941.15			0.792633			0.396316	−	0.918114i	$-0.370288\pi$
$383$	5941.15			0.792633			0.396316	+	0.918114i	$0.370288\pi$
$384$	−593.628	−	299.956i	−0.0788892	−	0.0398622i
$385$			2516.78i			0.333161i
$386$		−	7423.60i		−	0.978889i
$387$	7944.29	−	5853.98i	1.04349	−	0.768926i
$388$			2214.09i			0.289700i
$389$	−8342.65			−1.08738			−0.543688	−	0.839288i	$-0.682972\pi$
$389$	−8342.65			−1.08738			−0.543688	+	0.839288i	$0.682972\pi$
$390$	−5780.51	−	2920.85i	−0.750532	−	0.379239i
$391$	11381.4	+	5403.29i	1.47208	+	0.698864i
$392$			1064.17i			0.137114i
$393$	4612.10	+	2330.46i	0.591984	+	0.299125i
$394$	7101.97			0.908102
$395$			856.110i			0.109052i
$396$	−679.024	−	921.487i	−0.0861672	−	0.116936i
$397$	12254.3			1.54918			0.774591	−	0.632462i	$-0.217956\pi$
$397$	12254.3			1.54918			0.774591	+	0.632462i	$0.217956\pi$
$398$	−1002.82			−0.126299
$399$	−5800.17	+	11478.8i	−0.727749	+	1.44025i
$400$	−104.646			−0.0130807
$401$	−5605.08			−0.698016			−0.349008	−	0.937120i	$-0.613481\pi$
$401$	−5605.08			−0.698016			−0.349008	+	0.937120i	$0.613481\pi$
$402$	3148.09	−	6230.23i	0.390579	−	0.772975i
$403$	−16564.5			−2.04749
$404$		−	2477.42i		−	0.305089i
$405$	−2350.04	+	7578.36i	−0.288332	+	0.929807i
$406$		−	5502.33i		−	0.672601i
$407$		−	897.859i		−	0.109349i
$408$	−4237.74	−	2141.30i	−0.514215	−	0.259829i
$409$	−5378.51			−0.650245			−0.325123	−	0.945672i	$-0.605406\pi$
$409$	−5378.51			−0.650245			−0.325123	+	0.945672i	$0.605406\pi$
$410$	−6520.57			−0.785434
$411$	−3098.74	+	6132.55i	−0.371896	+	0.736001i
$412$		−	4930.97i		−	0.589639i
$413$	6639.29			0.791037
$414$	5847.19	−	1135.50i	0.694139	−	0.134799i
$415$	5517.45			0.652629
$416$		−	1832.30i		−	0.215952i
$417$	1505.22	−	2978.90i	0.176765	−	0.349826i
$418$	−2404.68			−0.281380
$419$	−8349.36			−0.973491			−0.486746	−	0.873544i	$-0.661816\pi$
$419$	−8349.36			−0.973491			−0.486746	+	0.873544i	$0.661816\pi$
$420$	4405.17	+	2225.90i	0.511787	+	0.258602i
$421$			9197.86i			1.06479i	0.846496	+	0.532395i	$0.178708\pi$
$421$			9197.86i			1.06479i	−0.846496	+	0.532395i	$0.821292\pi$
$422$		−	11971.9i		−	1.38101i
$423$	−5531.95	+	4076.37i	−0.635869	+	0.468558i
$424$			3736.68i			0.427993i
$425$	−747.035			−0.0852624
$426$	−1661.84	+	3288.87i	−0.189006	+	0.374052i
$427$	15227.1			1.72574
$428$	−3994.34			−0.451107
$429$	1422.14	−	2814.48i	0.160050	−	0.316747i
$430$	−7955.88			−0.892248
$431$	−14207.2			−1.58779			−0.793896	−	0.608053i	$-0.791951\pi$
$431$	−14207.2			−1.58779			−0.793896	+	0.608053i	$0.791951\pi$
$432$	−2213.44	+	373.523i	−0.246515	+	0.0415999i
$433$			3114.44i			0.345659i	0.984952	+	0.172829i	$0.0552910\pi$
$433$			3114.44i			0.345659i	−0.984952	+	0.172829i	$0.944709\pi$
$434$	12623.4			1.39618
$435$	−6364.92	−	3216.15i	−0.701551	−	0.354489i
$436$			4170.25i			0.458070i
$437$	5366.58	−	11304.1i	0.587456	−	1.23741i
$438$	−2981.18	−	1506.37i	−0.325220	−	0.164331i
$439$	−8269.58			−0.899055			−0.449528	−	0.893266i	$-0.648408\pi$
$439$	−8269.58			−0.899055			−0.449528	+	0.893266i	$0.648408\pi$
$440$			922.831i			0.0999869i
$441$	2130.59	+	2891.37i	0.230060	+	0.312209i
$442$		−	13080.3i		−	1.40761i
$443$		−	5073.97i		−	0.544179i	−0.962272	−	0.272090i	$-0.912285\pi$
$443$		−	5073.97i		−	0.544179i	0.962272	−	0.272090i	$-0.0877147\pi$
$444$	−1571.54	−	794.088i	−0.167977	−	0.0848778i
$445$	12216.5			1.30139
$446$			6720.09i			0.713466i
$447$	163.142	−	322.866i	0.0172625	−	0.0341634i
$448$			1396.35i			0.147257i
$449$		−	3625.22i		−	0.381035i	−0.981684	−	0.190518i	$-0.938983\pi$
$449$		−	3625.22i		−	0.381035i	0.981684	−	0.190518i	$-0.0610166\pi$
$450$	−284.324	+	209.512i	−0.0297848	+	0.0219477i
$451$		−	3174.81i		−	0.331476i
$452$	−6880.89			−0.716039
$453$	4310.81	−	8531.32i	0.447108	−	0.884848i
$454$		−	1729.74i		−	0.178812i
$455$			13597.1i			1.40097i
$456$	−2126.76	+	4208.96i	−0.218409	+	0.432242i
$457$			2136.11i			0.218650i	0.994006	+	0.109325i	$0.0348689\pi$
$457$			2136.11i			0.218650i	−0.994006	+	0.109325i	$0.965131\pi$
$458$	1288.28			0.131436
$459$	−15801.1	+	2666.48i	−1.60683	+	0.271156i
$460$	−4338.11	−	2059.51i	−0.439708	−	0.208750i
$461$			16072.6i			1.62381i	0.583789	+	0.811905i	$0.301570\pi$
$461$			16072.6i			1.62381i	−0.583789	+	0.811905i	$0.698430\pi$
$462$	−1083.77	+	2144.84i	−0.109138	+	0.215989i
$463$	5419.34			0.543970			0.271985	−	0.962302i	$-0.412320\pi$
$463$	5419.34			0.543970			0.271985	+	0.962302i	$0.412320\pi$
$464$		−	2017.55i		−	0.201858i
$465$	7378.45	−	14602.3i	0.735844	−	1.45627i
$466$	10628.9			1.05659
$467$	11598.4			1.14927			0.574635	−	0.818410i	$-0.305144\pi$
$467$	11598.4			1.14927			0.574635	+	0.818410i	$0.305144\pi$
$468$	−3668.47	−	4978.39i	−0.362340	−	0.491723i
$469$	−14654.9			−1.44286
$470$	5540.02			0.543707
$471$	−3182.00	−	1607.84i	−0.311293	−	0.157294i
$472$	2434.44			0.237403
$473$		−	3873.65i		−	0.376555i
$474$	−368.657	+	729.590i	−0.0357235	+	0.0706986i
$475$			741.960i			0.0716705i
$476$			9968.12i			0.959849i
$477$	7481.24	+	10152.6i	0.718118	+	0.974541i
$478$	−7036.51			−0.673310
$479$	5374.35			0.512652			0.256326	−	0.966590i	$-0.417488\pi$
$479$	5374.35			0.512652			0.256326	+	0.966590i	$0.417488\pi$
$480$	1615.25	+	816.175i	0.153595	+	0.0776106i
$481$		−	4850.74i		−	0.459822i
$482$	9485.27			0.896353
$483$	−7663.93	−	9881.37i	−0.721990	−	0.930886i
$484$	4874.68			0.457803
$485$		−	6024.50i		−	0.564038i
$486$	−5266.13	+	5446.42i	−0.491515	+	0.508343i
$487$	−6983.42			−0.649792			−0.324896	−	0.945750i	$-0.605329\pi$
$487$	−6983.42			−0.649792			−0.324896	+	0.945750i	$0.605329\pi$
$488$	5583.34			0.517922
$489$	5994.80	−	11864.0i	0.554385	−	1.09716i
$490$		−	2895.59i		−	0.266958i
$491$		−	8559.41i		−	0.786723i	−0.919384	−	0.393361i	$-0.871312\pi$
$491$		−	8559.41i		−	0.786723i	0.919384	−	0.393361i	$-0.128688\pi$
$492$	−5556.93	−	2807.88i	−0.509198	−	0.257294i
$493$		−	14402.7i		−	1.31575i
$494$	−12991.4			−1.18322
$495$	1847.61	+	2507.35i	0.167765	+	0.227670i
$496$	4628.63			0.419015
$497$	7736.15			0.698217
$498$	4702.06	+	2375.92i	0.423101	+	0.213790i
$499$	−18995.8			−1.70415			−0.852073	−	0.523423i	$-0.824655\pi$
$499$	−18995.8			−1.70415			−0.852073	+	0.523423i	$0.824655\pi$
$500$	5726.70			0.512211
$501$	3349.12	+	1692.29i	0.298658	+	0.150910i
$502$		−	1860.51i		−	0.165416i
$503$	−11330.9			−1.00441			−0.502206	−	0.864748i	$-0.667478\pi$
$503$	−11330.9			−1.00441			−0.502206	+	0.864748i	$0.667478\pi$
$504$	2795.64	+	3793.90i	0.247079	+	0.335305i
$505$			6741.00i			0.594001i
$506$	1002.75	−	2112.19i	0.0880986	−	0.185570i
$507$	2534.72	−	5016.33i	0.222033	−	0.439414i
$508$	1669.75			0.145833
$509$			8569.51i			0.746242i	0.927783	+	0.373121i	$0.121712\pi$
$509$			8569.51i			0.746242i	−0.927783	+	0.373121i	$0.878288\pi$
$510$	11530.8	+	5826.44i	1.00116	+	0.505881i
$511$			7012.40i			0.607066i
$512$			512.000i			0.0441942i
$513$	2648.36	+	15693.8i	0.227930	+	1.35068i
$514$	2798.22			0.240125
$515$			13417.1i			1.14801i
$516$	−6780.12	−	3425.95i	−0.578446	−	0.292285i
$517$			2697.39i			0.229460i
$518$			3696.61i			0.313552i
$519$	12392.2	+	6261.70i	1.04809	+	0.529592i
$520$			4985.65i			0.420452i
$521$	4048.12			0.340405			0.170203	−	0.985409i	$-0.445558\pi$
$521$	4048.12			0.340405			0.170203	+	0.985409i	$0.445558\pi$
$522$	−4039.35	−	5481.71i	−0.338693	−	0.459632i
$523$		−	23230.1i		−	1.94222i	−0.238631	−	0.971110i	$-0.576699\pi$
$523$		−	23230.1i		−	1.94222i	0.238631	−	0.971110i	$-0.423301\pi$
$524$		−	3977.90i		−	0.331633i
$525$	661.787	+	334.397i	0.0550148	+	0.0277986i
$526$			9709.19i			0.804831i
$527$	33042.5			2.73122
$528$	−397.388	+	786.451i	−0.0327540	+	0.0648217i
$529$	7691.25	+	9427.65i	0.632140	+	0.774854i
$530$		−	10167.4i		−	0.833292i
$531$	6614.40	−	4874.01i	0.540566	−	0.398331i
$532$	9900.41			0.806837
$533$		−	17152.1i		−	1.39388i
$534$	10411.1	+	5260.65i	0.843693	+	0.426312i
$535$	10868.5			0.878294
$536$	−5373.53			−0.433025
$537$	−7130.28	−	3602.88i	−0.572988	−	0.289527i
$538$	−9981.93			−0.799910
$539$	1409.84			0.112664
$540$	6022.73	−	1016.35i	0.479958	−	0.0809938i
$541$	−24127.3			−1.91740			−0.958699	−	0.284423i	$-0.908198\pi$
$541$	−24127.3			−1.91740			−0.958699	+	0.284423i	$0.908198\pi$
$542$		−	11947.3i		−	0.946831i
$543$	−11504.4	−	5813.08i	−0.909208	−	0.459417i
$544$			3655.02i			0.288066i
$545$		−	11347.2i		−	0.891851i
$546$	−5855.15	+	11587.6i	−0.458932	+	0.908250i
$547$	−13147.0			−1.02765			−0.513825	−	0.857895i	$-0.671772\pi$
$547$	−13147.0			−1.02765			−0.513825	+	0.857895i	$0.671772\pi$
$548$	5289.28			0.412312
$549$	15170.0	−	11178.5i	1.17931	−	0.869008i
$550$			138.637i			0.0107482i
$551$	−14304.9			−1.10600
$552$	−2810.14	−	3623.21i	−0.216681	−	0.279374i
$553$	1716.16			0.131968
$554$			5519.72i			0.423304i
$555$	4276.13	+	2160.70i	0.327048	+	0.165255i
$556$	−2569.28			−0.195974
$557$	17149.8			1.30460			0.652299	−	0.757962i	$-0.273805\pi$
$557$	17149.8			1.30460			0.652299	+	0.757962i	$0.273805\pi$
$558$	12576.1	−	9267.02i	0.954098	−	0.703054i
$559$		−	20927.6i		−	1.58344i
$560$		−	3799.43i		−	0.286706i
$561$	−2836.84	+	5614.25i	−0.213496	+	0.422520i
$562$		−	1805.53i		−	0.135519i
$563$	−11494.3			−0.860439			−0.430220	−	0.902724i	$-0.641564\pi$
$563$	−11494.3			−0.860439			−0.430220	+	0.902724i	$0.641564\pi$
$564$	4721.29	+	2385.63i	0.352486	+	0.178109i
$565$	18722.7			1.39411
$566$	14336.8			1.06470
$567$	15191.6	+	4710.90i	1.12520	+	0.348923i
$568$	2836.62			0.209546
$569$	−17741.2			−1.30712			−0.653559	−	0.756876i	$-0.726725\pi$
$569$	−17741.2			−1.30712			−0.653559	+	0.756876i	$0.726725\pi$
$570$	5786.86	−	11452.5i	0.425237	−	0.841565i
$571$		−	4401.50i		−	0.322587i	−0.986906	−	0.161293i	$-0.948433\pi$
$571$		−	4401.50i		−	0.322587i	0.986906	−	0.161293i	$-0.0515665\pi$
$572$	−2427.47			−0.177443
$573$	5351.60	−	10591.1i	0.390168	−	0.772162i
$574$			13071.1i			0.950486i
$575$	−651.713	−	309.399i	−0.0472666	−	0.0224397i
$576$	1025.08	+	1391.11i	0.0741522	+	0.100630i
$577$	−19288.4			−1.39165			−0.695827	−	0.718209i	$-0.744962\pi$
$577$	−19288.4			−1.39165			−0.695827	+	0.718209i	$0.744962\pi$
$578$			16266.2i			1.17056i
$579$	−8698.25	+	17214.3i	−0.624330	+	1.23558i
$580$			5489.70i			0.393013i
$581$		−	11060.3i		−	0.789773i
$582$	2594.26	−	5134.17i	0.184769	−	0.365667i
$583$	4950.43			0.351674
$584$			2571.25i			0.182190i
$585$	9981.82	+	13546.1i	0.705466	+	0.957371i
$586$			1203.90i			0.0848682i
$587$		−	15199.2i		−	1.06872i	−0.845258	−	0.534359i	$-0.820553\pi$
$587$		−	15199.2i		−	1.06872i	0.845258	−	0.534359i	$-0.179447\pi$
$588$	1246.89	−	2467.66i	0.0874507	−	0.173069i
$589$		−	32818.0i		−	2.29583i
$590$	−6624.05			−0.462217
$591$	−16468.5	−	8321.41i	−1.14623	−	0.579183i
$592$			1355.44i			0.0941019i
$593$			28258.0i			1.95686i	0.206582	+	0.978429i	$0.433766\pi$
$593$			28258.0i			1.95686i	−0.206582	+	0.978429i	$0.566234\pi$
$594$	494.851	+	2932.41i	0.0341818	+	0.202556i
$595$		−	27123.1i		−	1.86880i
$596$	−278.470			−0.0191385
$597$	2325.41	+	1175.01i	0.159418	+	0.0805529i
$598$	5417.45	−	11411.2i	0.370461	−	0.780334i
$599$			12584.5i			0.858413i	0.903206	+	0.429207i	$0.141207\pi$
$599$			12584.5i			0.858413i	−0.903206	+	0.429207i	$0.858793\pi$
$600$	242.658	+	122.614i	0.0165108	+	0.00834280i
$601$	11623.5			0.788907			0.394453	−	0.918916i	$-0.370934\pi$
$601$	11623.5			0.788907			0.394453	+	0.918916i	$0.370934\pi$
$602$			15948.4i			1.07975i
$603$	−14600.0	+	10758.4i	−0.985998	+	0.726561i
$604$	−7358.20			−0.495697
$605$	−13263.9			−0.891330
$606$	−2902.80	+	5744.78i	−0.194584	+	0.385092i
$607$	−356.633			−0.0238473			−0.0119236	−	0.999929i	$-0.503796\pi$
$607$	−356.633			−0.0238473			−0.0119236	+	0.999929i	$0.503796\pi$
$608$	3630.20			0.242145
$609$	−6447.10	+	12759.1i	−0.428982	+	0.848976i
$610$	−15192.2			−1.00838
$611$			14572.8i			0.964897i
$612$	7317.76	+	9930.76i	0.483338	+	0.655927i
$613$		−	27137.1i		−	1.78802i	−0.448047	−	0.894010i	$-0.647880\pi$
$613$		−	27137.1i		−	1.78802i	0.448047	−	0.894010i	$-0.352120\pi$
$614$		−	18190.5i		−	1.19562i
$615$	15120.3	+	7640.17i	0.991396	+	0.500946i
$616$	1849.91			0.120998
$617$	4164.50			0.271728			0.135864	−	0.990727i	$-0.456619\pi$
$617$	4164.50			0.271728			0.135864	+	0.990727i	$0.456619\pi$
$618$	−5777.63	+	11434.2i	−0.376069	+	0.744258i
$619$			15299.4i			0.993434i	0.867913	+	0.496717i	$0.165461\pi$
$619$			15299.4i			0.993434i	−0.867913	+	0.496717i	$0.834539\pi$
$620$	−12594.4			−0.815811
$621$	−14889.3	−	4218.11i	−0.962135	−	0.272572i
$622$	−4170.32			−0.268834
$623$		−	24489.2i		−	1.57486i
$624$	−2146.91	+	4248.85i	−0.137733	+	0.272580i
$625$	−14764.7			−0.944940
$626$	−15061.5			−0.961627
$627$	5576.11	+	2817.57i	0.355165	+	0.179462i
$628$			2744.45i			0.174388i
$629$			9676.12i			0.613374i
$630$	−7606.88	−	10323.1i	−0.481056	−	0.652830i
$631$			19697.8i			1.24272i	0.783524	+	0.621361i	$0.213420\pi$
$631$			19697.8i			1.24272i	−0.783524	+	0.621361i	$0.786580\pi$
$632$	629.266			0.0396058
$633$	−14027.6	+	27761.3i	−0.880799	+	1.74315i
$634$	−11644.7			−0.729447
$635$	−4543.34			−0.283932
$636$	4378.28	−	8664.83i	0.272972	−	0.540225i
$637$	7616.72			0.473761
$638$	−2672.89			−0.165863
$639$	7707.15	−	5679.23i	0.477136	−	0.351591i
$640$		−	1393.14i		−	0.0860449i
$641$	−16305.2			−1.00471			−0.502353	−	0.864663i	$-0.667532\pi$
$641$	−16305.2			−1.00471			−0.502353	+	0.864663i	$0.667532\pi$
$642$	9262.32	+	4680.19i	0.569400	+	0.287714i
$643$		−	27798.7i		−	1.70494i	−0.522777	−	0.852469i	$-0.675104\pi$
$643$		−	27798.7i		−	1.70494i	0.522777	−	0.852469i	$-0.324896\pi$
$644$	−4128.49	+	8696.18i	−0.252617	+	0.532108i
$645$	18448.6	+	9321.93i	1.12622	+	0.569071i
$646$	25914.9			1.57834
$647$		−	27022.7i		−	1.64200i	−0.570929	−	0.820999i	$-0.693417\pi$
$647$		−	27022.7i		−	1.64200i	0.570929	−	0.820999i	$-0.306583\pi$
$648$	5570.32	+	1727.35i	0.337690	+	0.104717i
$649$		−	3225.19i		−	0.195069i
$650$			748.992i			0.0451968i
$651$	−29271.8	−	14790.8i	−1.76229	−	0.890475i
$652$	−10232.6			−0.614633
$653$			10675.4i			0.639757i	0.947459	+	0.319878i	$0.103642\pi$
$653$			10675.4i			0.639757i	−0.947459	+	0.319878i	$0.896358\pi$
$654$	4886.29	−	9670.21i	0.292155	−	0.578188i
$655$			10823.8i			0.645680i
$656$			4792.81i			0.285256i
$657$	5147.92	+	6986.12i	0.305692	+	0.414847i
$658$		−	11105.5i		−	0.657961i
$659$	−11027.6			−0.651856			−0.325928	−	0.945395i	$-0.605677\pi$
$659$	−11027.6			−0.651856			−0.325928	+	0.945395i	$0.605677\pi$
$660$	1081.28	−	2139.92i	0.0637711	−	0.126206i
$661$			32451.1i			1.90953i	0.297361	+	0.954765i	$0.403894\pi$
$661$			32451.1i			1.90953i	−0.297361	+	0.954765i	$0.596106\pi$
$662$			18041.1i			1.05920i
$663$	−15326.2	+	30331.3i	−0.897769	+	1.77673i
$664$		−	4055.49i		−	0.237023i
$665$	−26938.8			−1.57089
$666$	2713.74	+	3682.76i	0.157891	+	0.214270i
$667$	5965.15	−	12564.9i	0.346284	−	0.729408i
$668$		−	2888.59i		−	0.167310i
$669$	7873.96	−	15583.0i	0.455045	−	0.900556i
$670$	14621.3			0.843088
$671$		−	7396.93i		−	0.425567i
$672$	1636.10	−	3237.93i	0.0939198	−	0.185872i
$673$	−11825.2			−0.677306			−0.338653	−	0.940911i	$-0.609971\pi$
$673$	−11825.2			−0.677306			−0.338653	+	0.940911i	$0.609971\pi$
$674$	−14913.2			−0.852275
$675$	904.793	−	152.686i	0.0515933	−	0.00870648i
$676$	−4326.55			−0.246162
$677$	−20118.7			−1.14213			−0.571066	−	0.820904i	$-0.693470\pi$
$677$	−20118.7			−1.14213			−0.571066	+	0.820904i	$0.693470\pi$
$678$	15955.8	+	8062.36i	0.903804	+	0.456686i
$679$	−12076.7			−0.682565
$680$		−	9945.24i		−	0.560857i
$681$	−2026.74	+	4011.01i	−0.114045	+	0.225701i
$682$		−	6132.10i		−	0.344296i
$683$			21040.7i			1.17877i	0.807852	+	0.589386i	$0.200630\pi$
$683$			21040.7i			1.17877i	−0.807852	+	0.589386i	$0.799370\pi$
$684$	9863.30	−	7268.05i	0.551364	−	0.406288i
$685$	−14392.0			−0.802761
$686$	9162.59			0.509955
$687$	−2987.35	−	1509.49i	−0.165902	−	0.0838289i
$688$			5847.81i			0.324049i
$689$	26745.0			1.47881
$690$	7646.34	+	9858.69i	0.421871	+	0.543933i
$691$	18617.3			1.02495			0.512473	−	0.858703i	$-0.328730\pi$
$691$	18617.3			1.02495			0.512473	+	0.858703i	$0.328730\pi$
$692$		−	10688.2i		−	0.587145i
$693$	5026.23	−	3703.72i	0.275513	−	0.203020i
$694$	9055.52			0.495307
$695$	6990.96			0.381557
$696$	−2363.97	+	4678.41i	−0.128744	+	0.254791i
$697$			34214.5i			1.85935i
$698$			2229.77i			0.120914i
$699$	−24646.8	−	12453.9i	−1.33366	−	0.673889i
$700$		−	570.787i		−	0.0308196i
$701$	9866.96			0.531626			0.265813	−	0.964025i	$-0.414360\pi$
$701$	9866.96			0.531626			0.265813	+	0.964025i	$0.414360\pi$
$702$	2673.46	+	15842.5i	0.143737	+	0.851764i
$703$	9610.39			0.515594
$704$	678.308			0.0363135
$705$	−12846.5	−	6491.26i	−0.686281	−	0.346773i
$706$	−1635.19			−0.0871690
$707$	13513.0			0.718825
$708$	−5645.12	−	2852.44i	−0.299656	−	0.151414i
$709$		−	33.7969i		−	0.00179022i	−1.00000		0.000895112i	$-0.999715\pi$
$709$		−	33.7969i		−	0.00179022i	1.00000		0.000895112i	$-0.000284923\pi$
$710$	−7718.39			−0.407980
$711$	1709.73	−	1259.86i	0.0901824	−	0.0664535i
$712$		−	8979.49i		−	0.472641i
$713$	28826.2	+	13685.2i	1.51410	+	0.718812i
$714$	11679.7	−	23114.7i	0.612187	−	1.21155i
$715$	6605.09			0.345478
$716$			6149.82i			0.320991i
$717$	16316.7	+	8244.70i	0.849871	+	0.429434i
$718$			10897.4i			0.566419i
$719$		−	899.131i		−	0.0466369i	−0.999728	−	0.0233184i	$-0.992577\pi$
$719$		−	899.131i		−	0.0466369i	0.999728	−	0.0233184i	$-0.00742316\pi$
$720$	−2789.22	−	3785.19i	−0.144372	−	0.195925i
$721$	26895.8			1.38926
$722$		−	12020.9i		−	0.619628i
$723$	−21995.0	−	11113.9i	−1.13140	−	0.571689i
$724$			9922.44i			0.509344i
$725$			824.716i			0.0422471i
$726$	−11303.7	−	5711.68i	−0.577851	−	0.291984i
$727$			21188.1i			1.08091i	0.841372	+	0.540456i	$0.181748\pi$
$727$			21188.1i			1.08091i	−0.841372	+	0.540456i	$0.818252\pi$
$728$	9994.24			0.508807
$729$	18593.0	−	6459.15i	0.944622	−	0.328159i
$730$		−	6996.31i		−	0.354719i
$731$			41745.8i			2.11221i
$732$	−12947.0	−	6542.03i	−0.653736	−	0.330328i
$733$			22353.8i			1.12641i	0.826318	+	0.563204i	$0.190431\pi$
$733$			22353.8i			1.12641i	−0.826318	+	0.563204i	$0.809569\pi$
$734$	336.553			0.0169242
$735$	−3392.77	+	6714.46i	−0.170264	+	0.336961i
$736$	−1513.80	+	3188.64i	−0.0758143	+	0.159694i
$737$			7118.97i			0.355808i
$738$	9595.73	+	13022.1i	0.478623	+	0.649528i
$739$	923.698			0.0459794			0.0229897	−	0.999736i	$-0.492682\pi$
$739$	923.698			0.0459794			0.0229897	+	0.999736i	$0.492682\pi$
$740$		−	3688.13i		−	0.183214i
$741$	30125.3	+	15222.1i	1.49350	+	0.754653i
$742$	−20381.6			−1.00840
$743$	33416.4			1.64997			0.824986	−	0.565153i	$-0.191183\pi$
$743$	33416.4			1.64997			0.824986	+	0.565153i	$0.191183\pi$
$744$	−10733.1	−	5423.38i	−0.528892	−	0.267246i
$745$	757.710			0.0372622
$746$	−17053.4			−0.836954
$747$	−8119.54	−	11018.8i	−0.397695	−	0.539703i
$748$	4842.25			0.236698
$749$		−	21787.1i		−	1.06286i
$750$	−13279.4	−	6709.99i	−0.646527	−	0.326686i
$751$			29846.4i			1.45022i	0.688635	+	0.725108i	$0.258210\pi$
$751$			29846.4i			1.45022i	−0.688635	+	0.725108i	$0.741790\pi$
$752$		−	4072.08i		−	0.197465i
$753$	−2179.97	+	4314.27i	−0.105501	+	0.208792i
$754$	−14440.4			−0.697466
$755$	20021.5			0.965109
$756$	−2037.37	−	12073.2i	−0.0980140	−	0.580816i
$757$			18544.8i			0.890387i	0.895434	+	0.445194i	$0.146865\pi$
$757$			18544.8i			0.890387i	−0.895434	+	0.445194i	$0.853135\pi$
$758$	3090.39			0.148085
$759$	−4800.11	+	3722.94i	−0.229556	+	0.178042i
$760$	−9877.69			−0.471449
$761$		−	19671.3i		−	0.937035i	−0.883454	−	0.468518i	$-0.844788\pi$
$761$		−	19671.3i		−	0.937035i	0.883454	−	0.468518i	$-0.155212\pi$
$762$	−3871.90	−	1956.45i	−0.184074	−	0.0930113i
$763$	−22746.5			−1.07926
$764$	−9134.74			−0.432570
$765$	−19911.5	−	27021.4i	−0.941047	−	1.27707i
$766$			11882.3i			0.560476i
$767$		−	17424.3i		−	0.820280i
$768$	599.912	−	1187.26i	0.0281868	−	0.0557831i
$769$			5569.11i			0.261154i	0.991438	+	0.130577i	$0.0416829\pi$
$769$			5569.11i			0.261154i	−0.991438	+	0.130577i	$0.958317\pi$
$770$	−5033.56			−0.235581
$771$	−6488.68	−	3278.69i	−0.303092	−	0.153150i
$772$	14847.2			0.692179
$773$	−22579.3			−1.05061			−0.525304	−	0.850914i	$-0.676049\pi$
$773$	−22579.3			−1.05061			−0.525304	+	0.850914i	$0.676049\pi$
$774$	11708.0	+	15888.6i	0.543713	+	0.737860i
$775$	−1892.05			−0.0876961
$776$	−4428.18			−0.204849
$777$	4331.34	−	8571.93i	0.199982	−	0.395774i
$778$		−	16685.3i		−	0.768890i
$779$	33982.1			1.56295
$780$	5841.71	−	11561.0i	0.268162	−	0.530707i
$781$		−	3758.02i		−	0.172180i
$782$	−10806.6	+	22762.8i	−0.494172	+	1.04092i
$783$	2943.75	+	17444.2i	0.134356	+	0.796176i
$784$	−2128.34			−0.0969543
$785$		−	7467.60i		−	0.339529i
$786$	−4660.92	+	9224.20i	−0.211513	+	0.418596i
$787$		−	12325.7i		−	0.558279i	−0.960251	−	0.279139i	$-0.909951\pi$
$787$		−	12325.7i		−	0.558279i	0.960251	−	0.279139i	$-0.0900491\pi$
$788$			14203.9i			0.642125i
$789$	11376.3	−	22514.3i	0.513317	−	1.01588i
$790$	−1712.22			−0.0771114
$791$		−	37531.6i		−	1.68707i
$792$	1842.97	−	1358.05i	0.0826859	−	0.0609294i
$793$		−	39962.4i		−	1.78954i
$794$			24508.6i			1.09544i
$795$	−11913.2	+	23576.8i	−0.531469	+	1.05180i
$796$		−	2005.65i		−	0.0893070i
$797$	−10368.6			−0.460820			−0.230410	−	0.973094i	$-0.574007\pi$
$797$	−10368.6			−0.460820			−0.230410	+	0.973094i	$0.574007\pi$
$798$	−22957.7	−	11600.3i	−1.01841	−	0.514596i
$799$		−	29069.4i		−	1.28711i
$800$		−	209.291i		−	0.00924945i
$801$	−17977.9	−	24397.4i	−0.793033	−	1.07621i
$802$		−	11210.2i		−	0.493572i
$803$	3406.44			0.149702
$804$	12460.5	+	6296.19i	0.546576	+	0.276181i
$805$	11233.5	−	23662.1i	0.491838	−	1.03600i
$806$		−	33129.0i		−	1.44779i
$807$	23146.7	+	11695.9i	1.00967	+	0.510179i
$808$	4954.83			0.215731
$809$		−	29964.1i		−	1.30220i	−0.758991	−	0.651102i	$-0.774307\pi$
$809$		−	29964.1i		−	1.30220i	0.758991	−	0.651102i	$-0.225693\pi$
$810$	−15156.7	−	4700.09i	−0.657473	−	0.203882i
$811$	−13277.9			−0.574906			−0.287453	−	0.957795i	$-0.592809\pi$
$811$	−13277.9			−0.574906			−0.287453	+	0.957795i	$0.592809\pi$
$812$	11004.7			0.475601
$813$	−13998.7	+	27704.2i	−0.603884	+	1.19512i
$814$	1795.72			0.0773217
$815$	27842.8			1.19667
$816$	4282.60	−	8475.49i	0.183727	−	0.363605i
$817$	41462.3			1.77550
$818$		−	10757.0i		−	0.459793i
$819$	27154.5	−	20009.6i	1.15855	−	0.853713i
$820$		−	13041.1i		−	0.555386i
$821$			23294.6i			0.990238i	0.868825	+	0.495119i	$0.164876\pi$
$821$			23294.6i			0.990238i	−0.868825	+	0.495119i	$0.835124\pi$
$822$	−12265.1	−	6197.47i	−0.520431	−	0.262970i
$823$	11000.7			0.465928			0.232964	−	0.972485i	$-0.425158\pi$
$823$	11000.7			0.465928			0.232964	+	0.972485i	$0.425158\pi$
$824$	9861.93			0.416938
$825$	162.441	−	321.479i	0.00685511	−	0.0135666i
$826$			13278.6i			0.559347i
$827$	−259.872			−0.0109270			−0.00546350	−	0.999985i	$-0.501739\pi$
$827$	−259.872			−0.0109270			−0.00546350	+	0.999985i	$0.501739\pi$
$828$	2271.00	+	11694.4i	0.0953171	+	0.490831i
$829$	−10639.1			−0.445732			−0.222866	−	0.974849i	$-0.571541\pi$
$829$	−10639.1			−0.445732			−0.222866	+	0.974849i	$0.571541\pi$
$830$			11034.9i			0.461479i
$831$	6467.47	−	12799.5i	0.269981	−	0.534306i
$832$	3664.60			0.152701
$833$	−15193.6			−0.631966
$834$	5957.80	+	3010.43i	0.247364	+	0.124991i
$835$			7859.80i			0.325748i
$836$		−	4809.36i		−	0.198965i
$837$	−40020.3	+	6753.51i	−1.65269	+	0.278895i
$838$		−	16698.7i		−	0.688362i
$839$	11414.8			0.469706			0.234853	−	0.972031i	$-0.424539\pi$
$839$	11414.8			0.469706			0.234853	+	0.972031i	$0.424539\pi$
$840$	−4451.81	+	8810.34i	−0.182859	+	0.361888i
$841$	8488.64			0.348052
$842$	−18395.7			−0.752920
$843$	−2115.54	+	4186.76i	−0.0864332	+	0.171056i
$844$	23943.9			0.976520
$845$	11772.5			0.479272
$846$	−8152.75	−	11063.9i	−0.331321	−	0.449627i
$847$			26588.8i			1.07863i
$848$	−7473.35			−0.302637
$849$	−33245.1	−	16798.5i	−1.34390	−	0.679062i
$850$		−	1494.07i		−	0.0602896i
$851$	−4007.55	+	8441.44i	−0.161430	+	0.340034i
$852$	−6577.73	−	3323.68i	−0.264495	−	0.133647i
$853$	−15505.0			−0.622369			−0.311185	−	0.950349i	$-0.600726\pi$
$853$	−15505.0			−0.622369			−0.311185	+	0.950349i	$0.600726\pi$
$854$			30454.2i			1.22028i
$855$	−26837.8	+	19776.2i	−1.07349	+	0.791032i
$856$		−	7988.69i		−	0.318981i
$857$		−	12174.6i		−	0.485270i	−0.970118	−	0.242635i	$-0.921988\pi$
$857$		−	12174.6i		−	0.485270i	0.970118	−	0.242635i	$-0.0780118\pi$
$858$	5628.96	+	2844.27i	0.223974	+	0.113172i
$859$	−389.206			−0.0154593			−0.00772966	−	0.999970i	$-0.502460\pi$
$859$	−389.206			−0.0154593			−0.00772966	+	0.999970i	$0.502460\pi$
$860$		−	15911.8i		−	0.630914i
$861$	15315.5	−	30310.1i	0.606215	−	1.19973i
$862$		−	28414.5i		−	1.12274i
$863$		−	23693.5i		−	0.934574i	−0.884106	−	0.467287i	$-0.845231\pi$
$863$		−	23693.5i		−	0.934574i	0.884106	−	0.467287i	$-0.154769\pi$
$864$	−747.046	−	4426.89i	−0.0294155	−	0.174312i
$865$			29082.3i			1.14316i
$866$	−6228.88			−0.244418
$867$	19059.1	−	37719.0i	0.746577	−	1.47751i
$868$			25246.7i			0.987247i
$869$		−	833.664i		−	0.0325433i
$870$	6432.30	−	12729.8i	0.250662	−	0.496072i
$871$			38460.6i			1.49620i
$872$	−8340.49			−0.323904
$873$	−12031.4	+	8865.71i	−0.466441	+	0.343710i
$874$	22608.2	+	10733.2i	0.874980	+	0.415394i
$875$			31236.1i			1.20683i
$876$	3012.74	−	5962.36i	0.116200	−	0.229965i
$877$	−13683.0			−0.526843			−0.263422	−	0.964681i	$-0.584851\pi$
$877$	−13683.0			−0.526843			−0.263422	+	0.964681i	$0.584851\pi$
$878$		−	16539.2i		−	0.635728i
$879$	1410.62	−	2791.68i	0.0541285	−	0.107123i
$880$	−1845.66			−0.0707014
$881$	36403.5			1.39213			0.696065	−	0.717979i	$-0.254933\pi$
$881$	36403.5			1.39213			0.696065	+	0.717979i	$0.254933\pi$
$882$	−5782.74	+	4261.17i	−0.220765	+	0.162677i
$883$	13924.0			0.530669			0.265335	−	0.964156i	$-0.414518\pi$
$883$	13924.0			0.530669			0.265335	+	0.964156i	$0.414518\pi$
$884$	26160.5			0.995333
$885$	15360.2	+	7761.42i	0.583423	+	0.294799i
$886$	10147.9			0.384793
$887$		−	3666.91i		−	0.138808i	−0.997589	−	0.0694041i	$-0.977890\pi$
$887$		−	3666.91i		−	0.138808i	0.997589	−	0.0694041i	$-0.0221098\pi$
$888$	1588.18	−	3143.08i	0.0600177	−	0.118778i
$889$			9107.59i			0.343598i
$890$			24433.0i			0.920221i
$891$	2288.43	−	7379.68i	0.0860441	−	0.277473i
$892$	−13440.2			−0.504496
$893$	−28871.9			−1.08193
$894$	645.732	+	326.284i	0.0241572	+	0.0122064i
$895$		−	16733.5i		−	0.624961i
$896$	−2792.69			−0.104126
$897$	−25932.9	+	20113.4i	−0.965299	+	0.748680i
$898$	7250.44			0.269432
$899$		−	36478.4i		−	1.35331i
$900$	−419.024	−	568.647i	−0.0155194	−	0.0210610i
$901$	−53350.2			−1.97264
$902$	6349.61			0.234389
$903$	18686.8	−	36982.0i	0.688656	−	1.36288i
$904$		−	13761.8i		−	0.506316i
$905$		−	26998.8i		−	0.991679i
$906$	17062.6	+	8621.63i	0.625682	+	0.316153i
$907$			20915.3i			0.765691i	0.923812	+	0.382845i	$0.125056\pi$
$907$			20915.3i			0.765691i	−0.923812	+	0.382845i	$0.874944\pi$
$908$	3459.47			0.126439
$909$	13462.4	−	9920.12i	0.491220	−	0.361969i
$910$	−27194.1			−0.990634
$911$	18080.6			0.657561			0.328781	−	0.944406i	$-0.393362\pi$
$911$	18080.6			0.657561			0.328781	+	0.944406i	$0.393362\pi$
$912$	−8417.91	−	4253.51i	−0.305641	−	0.154438i
$913$	−5372.80			−0.194758
$914$	−4272.22			−0.154609
$915$	35228.5	+	17800.7i	1.27281	+	0.643140i
$916$			2576.57i			0.0929390i
$917$	21697.4			0.781364
$918$	−5332.95	−	31602.3i	−0.191736	−	1.13620i
$919$			21465.5i			0.770491i	0.922814	+	0.385245i	$0.125883\pi$
$919$			21465.5i			0.770491i	−0.922814	+	0.385245i	$0.874117\pi$
$920$	4119.01	−	8676.22i	0.147608	−	0.310920i
$921$	−21313.9	+	42181.2i	−0.762559	+	1.50914i
$922$	−32145.2			−1.14821
$923$		−	20302.9i		−	0.724029i
$924$	−4289.68	−	2167.54i	−0.152727	−	0.0771721i
$925$		−	554.066i		−	0.0196947i
$926$			10838.7i			0.384645i
$927$	26795.0	−	19744.7i	0.949368	−	0.699569i
$928$	4035.09			0.142735
$929$			44128.4i			1.55846i	0.626740	+	0.779229i	$0.284389\pi$
$929$			44128.4i			1.55846i	−0.626740	+	0.779229i	$0.715611\pi$
$930$	29204.6	+	14756.9i	1.02974	+	0.520320i
$931$			15090.4i			0.531223i
$932$			21257.7i			0.747124i
$933$	9670.38	+	4886.38i	0.339329	+	0.171461i
$934$			23196.8i			0.812656i
$935$	−13175.7			−0.460845
$936$	9956.78	−	7336.94i	0.347700	−	0.256213i
$937$		−	27758.5i		−	0.967803i	−0.875122	−	0.483902i	$-0.839219\pi$
$937$		−	27758.5i		−	0.967803i	0.875122	−	0.483902i	$-0.160781\pi$
$938$		−	29309.8i		−	1.02026i
$939$	34925.5	+	17647.6i	1.21379	+	0.613321i
$940$			11080.0i			0.384459i
$941$	18461.1			0.639549			0.319774	−	0.947494i	$-0.396393\pi$
$941$	18461.1			0.639549			0.319774	+	0.947494i	$0.396393\pi$
$942$	3215.69	−	6364.00i	0.111224	−	0.220117i
$943$	−14170.6	+	29848.7i	−0.489351	+	1.03076i
$944$			4868.87i			0.167869i
$945$	5543.65	+	32850.9i	0.190831	+	1.13083i
$946$	7747.29			0.266264
$947$		−	3695.82i		−	0.126819i	−0.997988	−	0.0634097i	$-0.979803\pi$
$947$		−	3695.82i		−	0.126819i	0.997988	−	0.0634097i	$-0.0201975\pi$
$948$	−1459.18	−	737.313i	−0.0499915	−	0.0252604i
$949$	18403.5			0.629508
$950$	−1483.92			−0.0506787
$951$	27002.4	+	13644.1i	0.920728	+	0.465237i
$952$	−19936.2			−0.678716
$953$	−10904.7			−0.370658			−0.185329	−	0.982677i	$-0.559335\pi$
$953$	−10904.7			−0.370658			−0.185329	+	0.982677i	$0.559335\pi$
$954$	−20305.2	+	14962.5i	−0.689105	+	0.507786i
$955$	24855.4			0.842202
$956$		−	14073.0i		−	0.476102i
$957$	6198.05	+	3131.83i	0.209357	+	0.105787i
$958$			10748.7i			0.362500i
$959$			28850.3i			0.971454i
$960$	−1632.35	+	3230.50i	−0.0548790	+	0.108608i
$961$	53897.2			1.80918
$962$	9701.47			0.325143
$963$	−15994.2	−	21705.4i	−0.535210	−	0.726321i
$964$			18970.5i			0.633817i
$965$	−40398.9			−1.34765
$966$	19762.7	−	15327.9i	0.658236	−	0.510524i
$967$	34528.8			1.14827			0.574133	−	0.818762i	$-0.305339\pi$
$967$	34528.8			1.14827			0.574133	+	0.818762i	$0.305339\pi$
$968$			9749.36i			0.323715i
$969$	−60093.1	−	30364.6i	−1.99223	−	1.00666i
$970$	12049.0			0.398835
$971$	−41579.1			−1.37419			−0.687094	−	0.726568i	$-0.741114\pi$
$971$	−41579.1			−1.37419			−0.687094	+	0.726568i	$0.741114\pi$
$972$	−10892.8	−	10532.3i	−0.359453	−	0.347554i
$973$		−	14014.1i		−	0.461738i
$974$		−	13966.8i		−	0.459473i
$975$	877.597	−	1736.81i	0.0288263	−	0.0570486i
$976$			11166.7i			0.366226i
$977$	−4631.39			−0.151660			−0.0758298	−	0.997121i	$-0.524161\pi$
$977$	−4631.39			−0.151660			−0.0758298	+	0.997121i	$0.524161\pi$
$978$	23728.0	+	11989.6i	0.775806	+	0.392009i
$979$	−11896.2			−0.388360
$980$	5791.17			0.188768
$981$	−22661.3	+	16698.6i	−0.737531	+	0.543471i
$982$	17118.8			0.556297
$983$	−11223.2			−0.364155			−0.182077	−	0.983284i	$-0.558282\pi$
$983$	−11223.2			−0.364155			−0.182077	+	0.983284i	$0.558282\pi$
$984$	5615.75	−	11113.9i	0.181935	−	0.360058i
$985$		−	38648.6i		−	1.25020i
$986$	28805.4			0.930376
$987$	−13012.4	+	25752.2i	−0.419644	+	0.830497i
$988$		−	25982.8i		−	0.836664i
$989$	−17289.8	+	36419.0i	−0.555900	+	1.17094i
$990$	−5014.69	+	3695.22i	−0.160987	+	0.118628i
$991$	19975.4			0.640304			0.320152	−	0.947366i	$-0.396266\pi$
$991$	19975.4			0.640304			0.320152	+	0.947366i	$0.396266\pi$
$992$			9257.25i			0.296288i
$993$	21138.9	−	41834.9i	0.675550	−	1.33695i
$994$			15472.3i			0.493714i
$995$			5457.33i			0.173878i
$996$	−4751.83	+	9404.12i	−0.151172	+	0.299178i
$997$	22337.7			0.709571			0.354785	−	0.934948i	$-0.384554\pi$
$997$	22337.7			0.709571			0.354785	+	0.934948i	$0.384554\pi$
$998$		−	37991.6i		−	1.20501i
$999$	−1977.69	−	11719.5i	−0.0626340	−	0.371160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.d.a.137.20	yes	24
3.2	odd	2	inner	138.4.d.a.137.7	✓	24
23.22	odd	2	inner	138.4.d.a.137.19	yes	24
69.68	even	2	inner	138.4.d.a.137.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.d.a.137.7	✓	24	3.2	odd	2	inner
138.4.d.a.137.8	yes	24	69.68	even	2	inner
138.4.d.a.137.19	yes	24	23.22	odd	2	inner
138.4.d.a.137.20	yes	24	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(2.34341 - 4.63772i) q^{3} -4.00000 q^{4} +10.8839 q^{5} +(9.27544 + 4.68682i) q^{6} -21.8179i q^{7} -8.00000i q^{8} +(-16.0169 - 21.7361i) q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +(2.34341 - 4.63772i) q^{3} -4.00000 q^{4} +10.8839 q^{5} +(9.27544 + 4.68682i) q^{6} -21.8179i q^{7} -8.00000i q^{8} +(-16.0169 - 21.7361i) q^{9} +21.7678i q^{10} -10.5986 q^{11} +(-9.37363 + 18.5509i) q^{12} -57.2594 q^{13} +43.6358 q^{14} +(25.5055 - 50.4766i) q^{15} +16.0000 q^{16} +114.219 q^{17} +(43.4723 - 32.0338i) q^{18} -113.444i q^{19} -43.5357 q^{20} +(-101.185 - 51.1283i) q^{21} -21.1971i q^{22} +(99.6450 + 47.3062i) q^{23} +(-37.1018 - 18.7473i) q^{24} -6.54035 q^{25} -114.519i q^{26} +(-138.340 + 23.3452i) q^{27} +87.2717i q^{28} -126.097i q^{29} +(100.953 + 51.0109i) q^{30} +289.289 q^{31} +32.0000i q^{32} +(-24.8368 + 49.1532i) q^{33} +228.439i q^{34} -237.464i q^{35} +(64.0675 + 86.9445i) q^{36} +84.7151i q^{37} +226.887 q^{38} +(-134.182 + 265.553i) q^{39} -87.0713i q^{40} +299.551i q^{41} +(102.257 - 202.371i) q^{42} +365.488i q^{43} +42.3943 q^{44} +(-174.326 - 236.574i) q^{45} +(-94.6123 + 199.290i) q^{46} -254.505i q^{47} +(37.4945 - 74.2035i) q^{48} -133.021 q^{49} -13.0807i q^{50} +(267.663 - 529.718i) q^{51} +229.038 q^{52} -467.085 q^{53} +(-46.6904 - 276.680i) q^{54} -115.354 q^{55} -174.543 q^{56} +(-526.120 - 265.845i) q^{57} +252.193 q^{58} +304.305i q^{59} +(-102.022 + 201.906i) q^{60} +697.918i q^{61} +578.578i q^{62} +(-474.237 + 349.455i) q^{63} -64.0000 q^{64} -623.206 q^{65} +(-98.3063 - 49.6735i) q^{66} -671.692i q^{67} -456.878 q^{68} +(452.902 - 351.268i) q^{69} +474.929 q^{70} +354.578i q^{71} +(-173.889 + 128.135i) q^{72} -321.406 q^{73} -169.430 q^{74} +(-15.3267 + 30.3323i) q^{75} +453.774i q^{76} +231.239i q^{77} +(-531.106 - 268.364i) q^{78} +78.6582i q^{79} +174.143 q^{80} +(-215.919 + 696.290i) q^{81} -599.101 q^{82} +506.936 q^{83} +(404.741 + 204.513i) q^{84} +1243.16 q^{85} -730.976 q^{86} +(-584.801 - 295.496i) q^{87} +84.7885i q^{88} +1122.44 q^{89} +(473.149 - 348.653i) q^{90} +1249.28i q^{91} +(-398.580 - 189.225i) q^{92} +(677.922 - 1341.64i) q^{93} +509.010 q^{94} -1234.71i q^{95} +(148.407 + 74.9890i) q^{96} -553.523i q^{97} -266.043i q^{98} +(169.756 + 230.372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) \) 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9	\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) \) 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

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