Properties

Label 3.39.b.a.2.5
Level 3
Weight 39
Character 3.2
Analytic conductor 27.439
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 39 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.4390407101\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 17353504902 x^{10} + 111006258614054318328 x^{8} + 323765701965839203118204176384 x^{6} + 420150309279704216298413492838082805760 x^{4} + 190068212511425710374530430459662273636990976000 x^{2} + 27342285412416035125187079526375866471795145886924800000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{75}\cdot 3^{91}\cdot 5^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.5
Root \(-18842.7i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.39.b.a.2.8

$q$-expansion

\(f(q)\) \(=\) \(q-226112. i q^{2} +(-8.54601e8 - 7.87723e8i) q^{3} +2.23751e11 q^{4} -6.89065e12i q^{5} +(-1.78114e14 + 1.93236e14i) q^{6} +1.19822e16 q^{7} -1.12746e17i q^{8} +(1.09835e17 + 1.34638e18i) q^{9} +O(q^{10})\) \(q-226112. i q^{2} +(-8.54601e8 - 7.87723e8i) q^{3} +2.23751e11 q^{4} -6.89065e12i q^{5} +(-1.78114e14 + 1.93236e14i) q^{6} +1.19822e16 q^{7} -1.12746e17i q^{8} +(1.09835e17 + 1.34638e18i) q^{9} -1.55806e18 q^{10} +1.21660e20i q^{11} +(-1.91218e20 - 1.76254e20i) q^{12} +1.57410e21 q^{13} -2.70934e21i q^{14} +(-5.42793e21 + 5.88876e21i) q^{15} +3.60109e22 q^{16} +2.37425e23i q^{17} +(3.04433e23 - 2.48351e22i) q^{18} -3.40129e23 q^{19} -1.54179e24i q^{20} +(-1.02400e25 - 9.43870e24i) q^{21} +2.75089e25 q^{22} -1.60682e25i q^{23} +(-8.88128e25 + 9.63531e25i) q^{24} +3.16317e26 q^{25} -3.55924e26i q^{26} +(9.66709e26 - 1.23714e27i) q^{27} +2.68104e27 q^{28} -5.04838e27i q^{29} +(1.33152e27 + 1.22732e27i) q^{30} +1.48522e28 q^{31} -3.91340e28i q^{32} +(9.58347e28 - 1.03971e29i) q^{33} +5.36847e28 q^{34} -8.25655e28i q^{35} +(2.45757e28 + 3.01254e29i) q^{36} +4.44215e29 q^{37} +7.69074e28i q^{38} +(-1.34523e30 - 1.23996e30i) q^{39} -7.76895e29 q^{40} +2.53393e30i q^{41} +(-2.13421e30 + 2.31540e30i) q^{42} -1.36439e31 q^{43} +2.72216e31i q^{44} +(9.27743e30 - 7.56836e29i) q^{45} -3.63323e30 q^{46} -1.20655e31i q^{47} +(-3.07750e31 - 2.83666e31i) q^{48} +1.36394e31 q^{49} -7.15232e31i q^{50} +(1.87025e32 - 2.02904e32i) q^{51} +3.52207e32 q^{52} +1.42820e32i q^{53} +(-2.79732e32 - 2.18585e32i) q^{54} +8.38319e32 q^{55} -1.35095e33i q^{56} +(2.90675e32 + 2.67928e32i) q^{57} -1.14150e33 q^{58} +5.18925e33i q^{59} +(-1.21450e33 + 1.31762e33i) q^{60} -1.25756e34 q^{61} -3.35826e33i q^{62} +(1.31607e33 + 1.61326e34i) q^{63} +1.04993e33 q^{64} -1.08466e34i q^{65} +(-2.35092e34 - 2.16694e34i) q^{66} +7.45504e34 q^{67} +5.31241e34i q^{68} +(-1.26573e34 + 1.37319e34i) q^{69} -1.86691e34 q^{70} -2.70192e35i q^{71} +(1.51799e35 - 1.23835e34i) q^{72} +1.76445e35 q^{73} -1.00443e35i q^{74} +(-2.70325e35 - 2.49170e35i) q^{75} -7.61043e34 q^{76} +1.45776e36i q^{77} +(-2.80369e35 + 3.04173e35i) q^{78} +4.16277e34 q^{79} -2.48139e35i q^{80} +(-1.80067e36 + 2.95759e35i) q^{81} +5.72953e35 q^{82} -4.66415e35i q^{83} +(-2.29122e36 - 2.11192e36i) q^{84} +1.63601e36 q^{85} +3.08505e36i q^{86} +(-3.97673e36 + 4.31435e36i) q^{87} +1.37167e37 q^{88} -1.44520e37i q^{89} +(-1.71130e35 - 2.09774e36i) q^{90} +1.88613e37 q^{91} -3.59529e36i q^{92} +(-1.26927e37 - 1.16994e37i) q^{93} -2.72815e36 q^{94} +2.34371e36i q^{95} +(-3.08267e37 + 3.34439e37i) q^{96} +4.27060e37 q^{97} -3.08405e36i q^{98} +(-1.63801e38 + 1.33626e37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + O(q^{10}) \) \( 12q - 114742404q^{3} - 1699274528448q^{4} - 483611204680128q^{6} + 8107872236538648q^{7} - 424319151461513940q^{9} + 8521437485093339520q^{10} - 2862564534392665536q^{12} + \)\(10\!\cdots\!52\)\(q^{13} + \)\(63\!\cdots\!80\)\(q^{15} + \)\(67\!\cdots\!56\)\(q^{16} + \)\(14\!\cdots\!20\)\(q^{18} - \)\(46\!\cdots\!60\)\(q^{19} + \)\(33\!\cdots\!52\)\(q^{21} - \)\(13\!\cdots\!60\)\(q^{22} + \)\(78\!\cdots\!84\)\(q^{24} - \)\(12\!\cdots\!20\)\(q^{25} + \)\(35\!\cdots\!04\)\(q^{27} - \)\(77\!\cdots\!68\)\(q^{28} - \)\(31\!\cdots\!40\)\(q^{30} + \)\(62\!\cdots\!84\)\(q^{31} - \)\(20\!\cdots\!40\)\(q^{33} + \)\(27\!\cdots\!04\)\(q^{34} + \)\(52\!\cdots\!44\)\(q^{36} - \)\(10\!\cdots\!52\)\(q^{37} + \)\(37\!\cdots\!68\)\(q^{39} - \)\(86\!\cdots\!40\)\(q^{40} + \)\(37\!\cdots\!80\)\(q^{42} + \)\(10\!\cdots\!92\)\(q^{43} - \)\(61\!\cdots\!20\)\(q^{45} + \)\(13\!\cdots\!64\)\(q^{46} - \)\(16\!\cdots\!64\)\(q^{48} - \)\(74\!\cdots\!52\)\(q^{49} + \)\(71\!\cdots\!72\)\(q^{51} - \)\(99\!\cdots\!32\)\(q^{52} + \)\(12\!\cdots\!12\)\(q^{54} - \)\(14\!\cdots\!40\)\(q^{55} - \)\(19\!\cdots\!12\)\(q^{57} + \)\(54\!\cdots\!20\)\(q^{58} - \)\(21\!\cdots\!80\)\(q^{60} + \)\(19\!\cdots\!24\)\(q^{61} - \)\(68\!\cdots\!88\)\(q^{63} - \)\(33\!\cdots\!44\)\(q^{64} + \)\(29\!\cdots\!20\)\(q^{66} - \)\(12\!\cdots\!52\)\(q^{67} + \)\(14\!\cdots\!32\)\(q^{69} + \)\(13\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!40\)\(q^{72} + \)\(90\!\cdots\!72\)\(q^{73} - \)\(19\!\cdots\!60\)\(q^{75} + \)\(37\!\cdots\!48\)\(q^{76} - \)\(47\!\cdots\!80\)\(q^{78} + \)\(33\!\cdots\!20\)\(q^{79} - \)\(38\!\cdots\!88\)\(q^{81} + \)\(97\!\cdots\!60\)\(q^{82} - \)\(23\!\cdots\!52\)\(q^{84} + \)\(16\!\cdots\!60\)\(q^{85} - \)\(46\!\cdots\!20\)\(q^{87} + \)\(11\!\cdots\!20\)\(q^{88} - \)\(16\!\cdots\!20\)\(q^{90} + \)\(12\!\cdots\!24\)\(q^{91} - \)\(17\!\cdots\!28\)\(q^{93} + \)\(32\!\cdots\!64\)\(q^{94} - \)\(45\!\cdots\!24\)\(q^{96} + \)\(24\!\cdots\!28\)\(q^{97} - \)\(34\!\cdots\!40\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 226112.i 0.431275i −0.976473 0.215638i \(-0.930817\pi\)
0.976473 0.215638i \(-0.0691830\pi\)
\(3\) −8.54601e8 7.87723e8i −0.735292 0.677751i
\(4\) 2.23751e11 0.814002
\(5\) 6.89065e12i 0.361269i −0.983550 0.180634i \(-0.942185\pi\)
0.983550 0.180634i \(-0.0578150\pi\)
\(6\) −1.78114e14 + 1.93236e14i −0.292297 + 0.317113i
\(7\) 1.19822e16 1.05118 0.525588 0.850739i \(-0.323845\pi\)
0.525588 + 0.850739i \(0.323845\pi\)
\(8\) 1.12746e17i 0.782334i
\(9\) 1.09835e17 + 1.34638e18i 0.0813080 + 0.996689i
\(10\) −1.55806e18 −0.155806
\(11\) 1.21660e20i 1.98924i 0.103572 + 0.994622i \(0.466973\pi\)
−0.103572 + 0.994622i \(0.533027\pi\)
\(12\) −1.91218e20 1.76254e20i −0.598529 0.551690i
\(13\) 1.57410e21 1.07673 0.538367 0.842710i \(-0.319041\pi\)
0.538367 + 0.842710i \(0.319041\pi\)
\(14\) 2.70934e21i 0.453346i
\(15\) −5.42793e21 + 5.88876e21i −0.244850 + 0.265638i
\(16\) 3.60109e22 0.476600
\(17\) 2.37425e23i 0.993108i 0.868006 + 0.496554i \(0.165402\pi\)
−0.868006 + 0.496554i \(0.834598\pi\)
\(18\) 3.04433e23 2.48351e22i 0.429847 0.0350661i
\(19\) −3.40129e23 −0.171920 −0.0859598 0.996299i \(-0.527396\pi\)
−0.0859598 + 0.996299i \(0.527396\pi\)
\(20\) 1.54179e24i 0.294073i
\(21\) −1.02400e25 9.43870e24i −0.772921 0.712435i
\(22\) 2.75089e25 0.857912
\(23\) 1.60682e25i 0.215347i −0.994186 0.107674i \(-0.965660\pi\)
0.994186 0.107674i \(-0.0343402\pi\)
\(24\) −8.88128e25 + 9.63531e25i −0.530227 + 0.575244i
\(25\) 3.16317e26 0.869485
\(26\) 3.55924e26i 0.464369i
\(27\) 9.66709e26 1.23714e27i 0.615722 0.787964i
\(28\) 2.68104e27 0.855659
\(29\) 5.04838e27i 0.827161i −0.910468 0.413581i \(-0.864278\pi\)
0.910468 0.413581i \(-0.135722\pi\)
\(30\) 1.33152e27 + 1.22732e27i 0.114563 + 0.105598i
\(31\) 1.48522e28 0.685358 0.342679 0.939452i \(-0.388666\pi\)
0.342679 + 0.939452i \(0.388666\pi\)
\(32\) 3.91340e28i 0.987880i
\(33\) 9.58347e28 1.03971e29i 1.34821 1.46267i
\(34\) 5.36847e28 0.428303
\(35\) 8.25655e28i 0.379757i
\(36\) 2.45757e28 + 3.01254e29i 0.0661849 + 0.811306i
\(37\) 4.44215e29 0.710822 0.355411 0.934710i \(-0.384341\pi\)
0.355411 + 0.934710i \(0.384341\pi\)
\(38\) 7.69074e28i 0.0741447i
\(39\) −1.34523e30 1.23996e30i −0.791714 0.729757i
\(40\) −7.76895e29 −0.282633
\(41\) 2.53393e30i 0.576635i 0.957535 + 0.288318i \(0.0930959\pi\)
−0.957535 + 0.288318i \(0.906904\pi\)
\(42\) −2.13421e30 + 2.31540e30i −0.307256 + 0.333342i
\(43\) −1.36439e31 −1.25614 −0.628069 0.778158i \(-0.716154\pi\)
−0.628069 + 0.778158i \(0.716154\pi\)
\(44\) 2.72216e31i 1.61925i
\(45\) 9.27743e30 7.56836e29i 0.360072 0.0293740i
\(46\) −3.63323e30 −0.0928740
\(47\) 1.20655e31i 0.204967i −0.994735 0.102484i \(-0.967321\pi\)
0.994735 0.102484i \(-0.0326789\pi\)
\(48\) −3.07750e31 2.83666e31i −0.350440 0.323016i
\(49\) 1.36394e31 0.104971
\(50\) 7.15232e31i 0.374987i
\(51\) 1.87025e32 2.02904e32i 0.673080 0.730224i
\(52\) 3.52207e32 0.876464
\(53\) 1.42820e32i 0.247484i 0.992314 + 0.123742i \(0.0394896\pi\)
−0.992314 + 0.123742i \(0.960510\pi\)
\(54\) −2.79732e32 2.18585e32i −0.339829 0.265545i
\(55\) 8.38319e32 0.718651
\(56\) 1.35095e33i 0.822371i
\(57\) 2.90675e32 + 2.67928e32i 0.126411 + 0.116519i
\(58\) −1.14150e33 −0.356734
\(59\) 5.18925e33i 1.17197i 0.810322 + 0.585984i \(0.199292\pi\)
−0.810322 + 0.585984i \(0.800708\pi\)
\(60\) −1.21450e33 + 1.31762e33i −0.199308 + 0.216230i
\(61\) −1.25756e34 −1.50751 −0.753755 0.657155i \(-0.771760\pi\)
−0.753755 + 0.657155i \(0.771760\pi\)
\(62\) 3.35826e33i 0.295578i
\(63\) 1.31607e33 + 1.61326e34i 0.0854691 + 1.04770i
\(64\) 1.04993e33 0.0505521
\(65\) 1.08466e34i 0.388990i
\(66\) −2.35092e34 2.16694e34i −0.630815 0.581450i
\(67\) 7.45504e34 1.50324 0.751621 0.659596i \(-0.229273\pi\)
0.751621 + 0.659596i \(0.229273\pi\)
\(68\) 5.31241e34i 0.808392i
\(69\) −1.26573e34 + 1.37319e34i −0.145952 + 0.158343i
\(70\) −1.86691e34 −0.163780
\(71\) 2.70192e35i 1.81035i −0.425035 0.905177i \(-0.639738\pi\)
0.425035 0.905177i \(-0.360262\pi\)
\(72\) 1.51799e35 1.23835e34i 0.779744 0.0636101i
\(73\) 1.76445e35 0.697389 0.348694 0.937236i \(-0.386625\pi\)
0.348694 + 0.937236i \(0.386625\pi\)
\(74\) 1.00443e35i 0.306560i
\(75\) −2.70325e35 2.49170e35i −0.639325 0.589294i
\(76\) −7.61043e34 −0.139943
\(77\) 1.45776e36i 2.09105i
\(78\) −2.80369e35 + 3.04173e35i −0.314726 + 0.341447i
\(79\) 4.16277e34 0.0366833 0.0183416 0.999832i \(-0.494161\pi\)
0.0183416 + 0.999832i \(0.494161\pi\)
\(80\) 2.48139e35i 0.172181i
\(81\) −1.80067e36 + 2.95759e35i −0.986778 + 0.162078i
\(82\) 5.72953e35 0.248689
\(83\) 4.66415e35i 0.160801i −0.996763 0.0804006i \(-0.974380\pi\)
0.996763 0.0804006i \(-0.0256199\pi\)
\(84\) −2.29122e36 2.11192e36i −0.629159 0.579924i
\(85\) 1.63601e36 0.358779
\(86\) 3.08505e36i 0.541741i
\(87\) −3.97673e36 + 4.31435e36i −0.560609 + 0.608205i
\(88\) 1.37167e37 1.55625
\(89\) 1.44520e37i 1.32287i −0.750002 0.661435i \(-0.769948\pi\)
0.750002 0.661435i \(-0.230052\pi\)
\(90\) −1.71130e35 2.09774e36i −0.0126683 0.155290i
\(91\) 1.88613e37 1.13184
\(92\) 3.59529e36i 0.175293i
\(93\) −1.26927e37 1.16994e37i −0.503938 0.464502i
\(94\) −2.72815e36 −0.0883973
\(95\) 2.34371e36i 0.0621092i
\(96\) −3.08267e37 + 3.34439e37i −0.669536 + 0.726380i
\(97\) 4.27060e37 0.761773 0.380887 0.924622i \(-0.375619\pi\)
0.380887 + 0.924622i \(0.375619\pi\)
\(98\) 3.08405e36i 0.0452716i
\(99\) −1.63801e38 + 1.33626e37i −1.98266 + 0.161742i
\(100\) 7.07762e37 0.707762
\(101\) 1.73179e38i 1.43347i 0.697343 + 0.716737i \(0.254365\pi\)
−0.697343 + 0.716737i \(0.745635\pi\)
\(102\) −4.58790e37 4.22887e37i −0.314928 0.290283i
\(103\) 4.09091e37 0.233299 0.116649 0.993173i \(-0.462785\pi\)
0.116649 + 0.993173i \(0.462785\pi\)
\(104\) 1.77474e38i 0.842366i
\(105\) −6.50388e37 + 7.05606e37i −0.257381 + 0.279232i
\(106\) 3.22934e37 0.106734
\(107\) 1.64293e38i 0.454283i 0.973862 + 0.227142i \(0.0729380\pi\)
−0.973862 + 0.227142i \(0.927062\pi\)
\(108\) 2.16302e38 2.76811e38i 0.501198 0.641404i
\(109\) 4.00261e38 0.778466 0.389233 0.921139i \(-0.372740\pi\)
0.389233 + 0.921139i \(0.372740\pi\)
\(110\) 1.89554e38i 0.309937i
\(111\) −3.79627e38 3.49919e38i −0.522662 0.481760i
\(112\) 4.31492e38 0.500991
\(113\) 3.79863e38i 0.372508i −0.982502 0.186254i \(-0.940365\pi\)
0.982502 0.186254i \(-0.0596348\pi\)
\(114\) 6.05818e37 6.57252e37i 0.0502516 0.0545180i
\(115\) −1.10721e38 −0.0777982
\(116\) 1.12958e39i 0.673310i
\(117\) 1.72891e38 + 2.11934e39i 0.0875472 + 1.07317i
\(118\) 1.17335e39 0.505441
\(119\) 2.84488e39i 1.04393i
\(120\) 6.63935e38 + 6.11978e38i 0.207818 + 0.191555i
\(121\) −1.10608e40 −2.95709
\(122\) 2.84349e39i 0.650152i
\(123\) 1.99604e39 2.16550e39i 0.390815 0.423995i
\(124\) 3.32319e39 0.557883
\(125\) 4.68643e39i 0.675386i
\(126\) 3.64779e39 2.97580e38i 0.451845 0.0368607i
\(127\) −6.98583e39 −0.744641 −0.372321 0.928104i \(-0.621438\pi\)
−0.372321 + 0.928104i \(0.621438\pi\)
\(128\) 1.09945e40i 1.00968i
\(129\) 1.16601e40 + 1.07476e40i 0.923628 + 0.851348i
\(130\) −2.45255e39 −0.167762
\(131\) 2.27888e40i 1.34762i 0.738906 + 0.673809i \(0.235343\pi\)
−0.738906 + 0.673809i \(0.764657\pi\)
\(132\) 2.14431e40 2.32636e40i 1.09745 1.19062i
\(133\) −4.07551e39 −0.180718
\(134\) 1.68568e40i 0.648311i
\(135\) −8.52468e39 6.66126e39i −0.284667 0.222441i
\(136\) 2.67688e40 0.776942
\(137\) 1.16139e40i 0.293283i −0.989190 0.146641i \(-0.953154\pi\)
0.989190 0.146641i \(-0.0468464\pi\)
\(138\) 3.10496e39 + 2.86198e39i 0.0682895 + 0.0629454i
\(139\) −4.81953e40 −0.924110 −0.462055 0.886851i \(-0.652888\pi\)
−0.462055 + 0.886851i \(0.652888\pi\)
\(140\) 1.84741e40i 0.309123i
\(141\) −9.50424e39 + 1.03112e40i −0.138917 + 0.150711i
\(142\) −6.10937e40 −0.780761
\(143\) 1.91506e41i 2.14189i
\(144\) 3.95526e39 + 4.84843e40i 0.0387514 + 0.475022i
\(145\) −3.47866e40 −0.298827
\(146\) 3.98964e40i 0.300767i
\(147\) −1.16563e40 1.07441e40i −0.0771846 0.0711444i
\(148\) 9.93937e40 0.578610
\(149\) 2.78035e41i 1.42416i −0.702096 0.712082i \(-0.747752\pi\)
0.702096 0.712082i \(-0.252248\pi\)
\(150\) −5.63405e40 + 6.11238e40i −0.254148 + 0.275725i
\(151\) 1.74842e41 0.695158 0.347579 0.937651i \(-0.387004\pi\)
0.347579 + 0.937651i \(0.387004\pi\)
\(152\) 3.83483e40i 0.134499i
\(153\) −3.19664e41 + 2.60776e40i −0.989820 + 0.0807477i
\(154\) 3.29619e41 0.901816
\(155\) 1.02341e41i 0.247598i
\(156\) −3.00996e41 2.77441e41i −0.644456 0.594024i
\(157\) 8.83711e41 1.67578 0.837890 0.545840i \(-0.183789\pi\)
0.837890 + 0.545840i \(0.183789\pi\)
\(158\) 9.41255e39i 0.0158206i
\(159\) 1.12503e41 1.22054e41i 0.167733 0.181973i
\(160\) −2.69658e41 −0.356890
\(161\) 1.92534e41i 0.226368i
\(162\) 6.68749e40 + 4.07155e41i 0.0699001 + 0.425573i
\(163\) −4.43978e41 −0.412855 −0.206427 0.978462i \(-0.566184\pi\)
−0.206427 + 0.978462i \(0.566184\pi\)
\(164\) 5.66969e41i 0.469382i
\(165\) −7.16429e41 6.60364e41i −0.528418 0.487066i
\(166\) −1.05462e41 −0.0693495
\(167\) 2.19556e42i 1.28805i 0.765006 + 0.644023i \(0.222736\pi\)
−0.765006 + 0.644023i \(0.777264\pi\)
\(168\) −1.06418e42 + 1.15453e42i −0.557362 + 0.604683i
\(169\) 3.40580e41 0.159357
\(170\) 3.69923e41i 0.154732i
\(171\) −3.73581e40 4.57943e41i −0.0139784 0.171350i
\(172\) −3.05283e42 −1.02250
\(173\) 3.70657e42i 1.11198i −0.831189 0.555990i \(-0.812339\pi\)
0.831189 0.555990i \(-0.187661\pi\)
\(174\) 9.75529e41 + 8.99188e41i 0.262304 + 0.241777i
\(175\) 3.79019e42 0.913982
\(176\) 4.38110e42i 0.948074i
\(177\) 4.08769e42 4.43474e42i 0.794303 0.861739i
\(178\) −3.26777e42 −0.570521
\(179\) 5.09144e42i 0.799159i −0.916699 0.399579i \(-0.869156\pi\)
0.916699 0.399579i \(-0.130844\pi\)
\(180\) 2.07583e42 1.69343e41i 0.293100 0.0239105i
\(181\) 3.83972e42 0.487985 0.243992 0.969777i \(-0.421543\pi\)
0.243992 + 0.969777i \(0.421543\pi\)
\(182\) 4.26476e42i 0.488134i
\(183\) 1.07471e43 + 9.90606e42i 1.10846 + 1.02172i
\(184\) −1.81163e42 −0.168474
\(185\) 3.06093e42i 0.256798i
\(186\) −2.64538e42 + 2.86997e42i −0.200328 + 0.217336i
\(187\) −2.88852e43 −1.97553
\(188\) 2.69966e42i 0.166844i
\(189\) 1.15833e43 1.48237e43i 0.647232 0.828289i
\(190\) 5.29942e41 0.0267861
\(191\) 2.81633e43i 1.28840i 0.764858 + 0.644199i \(0.222809\pi\)
−0.764858 + 0.644199i \(0.777191\pi\)
\(192\) −8.97268e41 8.27051e41i −0.0371705 0.0342617i
\(193\) −1.91865e43 −0.720124 −0.360062 0.932928i \(-0.617244\pi\)
−0.360062 + 0.932928i \(0.617244\pi\)
\(194\) 9.65635e42i 0.328534i
\(195\) −8.54410e42 + 9.26950e42i −0.263638 + 0.286021i
\(196\) 3.05184e42 0.0854469
\(197\) 5.56749e43i 1.41514i 0.706641 + 0.707572i \(0.250210\pi\)
−0.706641 + 0.707572i \(0.749790\pi\)
\(198\) 3.02145e42 + 3.70374e43i 0.0697551 + 0.855071i
\(199\) 3.53506e43 0.741631 0.370815 0.928707i \(-0.379078\pi\)
0.370815 + 0.928707i \(0.379078\pi\)
\(200\) 3.56635e43i 0.680228i
\(201\) −6.37109e43 5.87251e43i −1.10532 1.01882i
\(202\) 3.91580e43 0.618222
\(203\) 6.04909e43i 0.869492i
\(204\) 4.18471e43 4.53999e43i 0.547888 0.594404i
\(205\) 1.74604e43 0.208320
\(206\) 9.25005e42i 0.100616i
\(207\) 2.16339e43 1.76486e42i 0.214634 0.0175095i
\(208\) 5.66848e43 0.513172
\(209\) 4.13802e43i 0.341990i
\(210\) 1.59546e43 + 1.47061e43i 0.120426 + 0.111002i
\(211\) 1.99609e43 0.137662 0.0688311 0.997628i \(-0.478073\pi\)
0.0688311 + 0.997628i \(0.478073\pi\)
\(212\) 3.19561e43i 0.201453i
\(213\) −2.12836e44 + 2.30906e44i −1.22697 + 1.33114i
\(214\) 3.71487e43 0.195921
\(215\) 9.40153e43i 0.453803i
\(216\) −1.39483e44 1.08993e44i −0.616451 0.481700i
\(217\) 1.77962e44 0.720432
\(218\) 9.05039e43i 0.335733i
\(219\) −1.50790e44 1.38990e44i −0.512784 0.472656i
\(220\) 1.87575e44 0.584983
\(221\) 3.73730e44i 1.06931i
\(222\) −7.91210e43 + 8.58384e43i −0.207771 + 0.225411i
\(223\) −6.72519e44 −1.62148 −0.810741 0.585406i \(-0.800935\pi\)
−0.810741 + 0.585406i \(0.800935\pi\)
\(224\) 4.68913e44i 1.03844i
\(225\) 3.47427e43 + 4.25882e44i 0.0706961 + 0.866606i
\(226\) −8.58917e43 −0.160654
\(227\) 3.07937e44i 0.529628i 0.964299 + 0.264814i \(0.0853106\pi\)
−0.964299 + 0.264814i \(0.914689\pi\)
\(228\) 6.50388e43 + 5.99491e43i 0.102899 + 0.0948464i
\(229\) 7.63372e44 1.11138 0.555690 0.831390i \(-0.312454\pi\)
0.555690 + 0.831390i \(0.312454\pi\)
\(230\) 2.50353e43i 0.0335524i
\(231\) 1.14832e45 1.24581e45i 1.41721 1.53753i
\(232\) −5.69186e44 −0.647116
\(233\) 9.50715e44i 0.996066i −0.867158 0.498033i \(-0.834056\pi\)
0.867158 0.498033i \(-0.165944\pi\)
\(234\) 4.79208e44 3.90929e43i 0.462831 0.0377569i
\(235\) −8.31389e43 −0.0740482
\(236\) 1.16110e45i 0.953984i
\(237\) −3.55751e43 3.27911e43i −0.0269729 0.0248621i
\(238\) 6.43263e44 0.450222
\(239\) 1.64609e45i 1.06388i −0.846782 0.531940i \(-0.821463\pi\)
0.846782 0.531940i \(-0.178537\pi\)
\(240\) −1.95465e44 + 2.12060e44i −0.116696 + 0.126603i
\(241\) −1.63494e45 −0.901942 −0.450971 0.892539i \(-0.648922\pi\)
−0.450971 + 0.892539i \(0.648922\pi\)
\(242\) 2.50099e45i 1.27532i
\(243\) 1.77183e45 + 1.16568e45i 0.835418 + 0.549615i
\(244\) −2.81379e45 −1.22712
\(245\) 9.39846e43i 0.0379229i
\(246\) −4.89646e44 4.51329e44i −0.182859 0.168549i
\(247\) −5.35397e44 −0.185112
\(248\) 1.67453e45i 0.536179i
\(249\) −3.67406e44 + 3.98599e44i −0.108983 + 0.118236i
\(250\) −1.05966e45 −0.291277
\(251\) 5.46320e42i 0.00139202i 1.00000 0.000696012i \(0.000221547\pi\)
−1.00000 0.000696012i \(0.999778\pi\)
\(252\) 2.94472e44 + 3.60970e45i 0.0695720 + 0.852826i
\(253\) 1.95487e45 0.428378
\(254\) 1.57958e45i 0.321145i
\(255\) −1.39814e45 1.28872e45i −0.263807 0.243163i
\(256\) −2.19738e45 −0.384899
\(257\) 2.10252e45i 0.341988i 0.985272 + 0.170994i \(0.0546978\pi\)
−0.985272 + 0.170994i \(0.945302\pi\)
\(258\) 2.43017e45 2.63649e45i 0.367166 0.398338i
\(259\) 5.32270e45 0.747199
\(260\) 2.42693e45i 0.316639i
\(261\) 6.79703e45 5.54489e44i 0.824422 0.0672548i
\(262\) 5.15283e45 0.581194
\(263\) 1.06476e46i 1.11710i −0.829471 0.558550i \(-0.811358\pi\)
0.829471 0.558550i \(-0.188642\pi\)
\(264\) −1.17223e46 1.08050e46i −1.14430 1.05475i
\(265\) 9.84123e44 0.0894083
\(266\) 9.21524e44i 0.0779391i
\(267\) −1.13842e46 + 1.23507e46i −0.896576 + 0.972696i
\(268\) 1.66807e46 1.22364
\(269\) 2.91439e45i 0.199184i −0.995028 0.0995921i \(-0.968246\pi\)
0.995028 0.0995921i \(-0.0317538\pi\)
\(270\) −1.50619e45 + 1.92754e45i −0.0959332 + 0.122770i
\(271\) 9.28598e45 0.551329 0.275665 0.961254i \(-0.411102\pi\)
0.275665 + 0.961254i \(0.411102\pi\)
\(272\) 8.54988e45i 0.473316i
\(273\) −1.61189e46 1.48575e46i −0.832231 0.767104i
\(274\) −2.62604e45 −0.126486
\(275\) 3.84832e46i 1.72962i
\(276\) −2.83209e45 + 3.07254e45i −0.118805 + 0.128892i
\(277\) −1.19106e46 −0.466462 −0.233231 0.972421i \(-0.574930\pi\)
−0.233231 + 0.972421i \(0.574930\pi\)
\(278\) 1.08976e46i 0.398546i
\(279\) 1.63129e45 + 1.99967e46i 0.0557252 + 0.683089i
\(280\) −9.30895e45 −0.297097
\(281\) 2.75232e46i 0.820880i −0.911888 0.410440i \(-0.865375\pi\)
0.911888 0.410440i \(-0.134625\pi\)
\(282\) 2.33148e45 + 2.14903e45i 0.0649978 + 0.0599113i
\(283\) −4.47611e46 −1.16670 −0.583350 0.812221i \(-0.698258\pi\)
−0.583350 + 0.812221i \(0.698258\pi\)
\(284\) 6.04557e46i 1.47363i
\(285\) 1.84620e45 2.00294e45i 0.0420945 0.0456684i
\(286\) 4.33018e46 0.923743
\(287\) 3.03622e46i 0.606145i
\(288\) 5.26891e46 4.29828e45i 0.984609 0.0803226i
\(289\) 7.85087e44 0.0137360
\(290\) 7.86569e45i 0.128877i
\(291\) −3.64966e46 3.36405e46i −0.560126 0.516292i
\(292\) 3.94797e46 0.567676
\(293\) 9.08247e45i 0.122382i −0.998126 0.0611912i \(-0.980510\pi\)
0.998126 0.0611912i \(-0.0194899\pi\)
\(294\) −2.42938e45 + 2.63563e45i −0.0306828 + 0.0332878i
\(295\) 3.57573e46 0.423396
\(296\) 5.00836e46i 0.556100i
\(297\) 1.50511e47 + 1.17610e47i 1.56745 + 1.22482i
\(298\) −6.28672e46 −0.614207
\(299\) 2.52930e46i 0.231872i
\(300\) −6.04855e46 5.57521e46i −0.520412 0.479686i
\(301\) −1.63484e47 −1.32042
\(302\) 3.95339e46i 0.299804i
\(303\) 1.36417e47 1.47999e47i 0.971538 1.05402i
\(304\) −1.22484e46 −0.0819369
\(305\) 8.66538e46i 0.544616i
\(306\) 5.89647e45 + 7.22800e46i 0.0348245 + 0.426885i
\(307\) −2.10043e47 −1.16595 −0.582975 0.812490i \(-0.698111\pi\)
−0.582975 + 0.812490i \(0.698111\pi\)
\(308\) 3.26176e47i 1.70211i
\(309\) −3.49609e46 3.22250e46i −0.171543 0.158118i
\(310\) −2.31406e46 −0.106783
\(311\) 1.38306e47i 0.600334i 0.953887 + 0.300167i \(0.0970425\pi\)
−0.953887 + 0.300167i \(0.902958\pi\)
\(312\) −1.39800e47 + 1.51669e47i −0.570914 + 0.619385i
\(313\) −4.51251e46 −0.173411 −0.0867053 0.996234i \(-0.527634\pi\)
−0.0867053 + 0.996234i \(0.527634\pi\)
\(314\) 1.99818e47i 0.722722i
\(315\) 1.11164e47 9.06859e45i 0.378500 0.0308773i
\(316\) 9.31425e45 0.0298602
\(317\) 3.49554e47i 1.05533i −0.849453 0.527665i \(-0.823068\pi\)
0.849453 0.527665i \(-0.176932\pi\)
\(318\) −2.75980e46 2.54383e46i −0.0784805 0.0723390i
\(319\) 6.14188e47 1.64543
\(320\) 7.23467e45i 0.0182629i
\(321\) 1.29417e47 1.40405e47i 0.307891 0.334031i
\(322\) −4.35342e46 −0.0976269
\(323\) 8.07551e46i 0.170735i
\(324\) −4.02902e47 + 6.61765e46i −0.803239 + 0.131931i
\(325\) 4.97914e47 0.936204
\(326\) 1.00389e47i 0.178054i
\(327\) −3.42063e47 3.15295e47i −0.572400 0.527606i
\(328\) 2.85691e47 0.451121
\(329\) 1.44571e47i 0.215457i
\(330\) −1.49316e47 + 1.61993e47i −0.210060 + 0.227894i
\(331\) −8.82926e46 −0.117272 −0.0586358 0.998279i \(-0.518675\pi\)
−0.0586358 + 0.998279i \(0.518675\pi\)
\(332\) 1.04361e47i 0.130892i
\(333\) 4.87904e46 + 5.98082e47i 0.0577955 + 0.708468i
\(334\) 4.96442e47 0.555502
\(335\) 5.13701e47i 0.543074i
\(336\) −3.68753e47 3.39896e47i −0.368374 0.339547i
\(337\) −4.55217e47 −0.429784 −0.214892 0.976638i \(-0.568940\pi\)
−0.214892 + 0.976638i \(0.568940\pi\)
\(338\) 7.70093e46i 0.0687268i
\(339\) −2.99227e47 + 3.24631e47i −0.252468 + 0.273902i
\(340\) 3.66059e47 0.292047
\(341\) 1.80692e48i 1.36335i
\(342\) −1.03547e47 + 8.44714e45i −0.0738992 + 0.00602856i
\(343\) −1.39348e48 −0.940833
\(344\) 1.53830e48i 0.982720i
\(345\) 9.46220e46 + 8.72173e46i 0.0572044 + 0.0527278i
\(346\) −8.38103e47 −0.479569
\(347\) 9.80357e47i 0.531036i −0.964106 0.265518i \(-0.914457\pi\)
0.964106 0.265518i \(-0.0855430\pi\)
\(348\) −8.89797e47 + 9.65341e47i −0.456337 + 0.495080i
\(349\) −1.86070e47 −0.0903635 −0.0451817 0.998979i \(-0.514387\pi\)
−0.0451817 + 0.998979i \(0.514387\pi\)
\(350\) 8.57008e47i 0.394178i
\(351\) 1.52170e48 1.94738e48i 0.662969 0.848428i
\(352\) 4.76105e48 1.96513
\(353\) 2.13190e47i 0.0833773i 0.999131 + 0.0416886i \(0.0132738\pi\)
−0.999131 + 0.0416886i \(0.986726\pi\)
\(354\) −1.00275e48 9.24278e47i −0.371647 0.342563i
\(355\) −1.86180e48 −0.654024
\(356\) 3.23365e48i 1.07682i
\(357\) 2.24098e48 2.43124e48i 0.707525 0.767594i
\(358\) −1.15124e48 −0.344657
\(359\) 2.43115e48i 0.690267i 0.938554 + 0.345133i \(0.112166\pi\)
−0.938554 + 0.345133i \(0.887834\pi\)
\(360\) −8.53303e46 1.04600e48i −0.0229803 0.281697i
\(361\) −3.79846e48 −0.970444
\(362\) 8.68208e47i 0.210456i
\(363\) 9.45258e48 + 8.71286e48i 2.17433 + 2.00417i
\(364\) 4.22023e48 0.921318
\(365\) 1.21582e48i 0.251945i
\(366\) 2.23988e48 2.43005e48i 0.440641 0.478051i
\(367\) −9.76811e48 −1.82455 −0.912274 0.409580i \(-0.865675\pi\)
−0.912274 + 0.409580i \(0.865675\pi\)
\(368\) 5.78632e47i 0.102635i
\(369\) −3.41163e48 + 2.78314e47i −0.574726 + 0.0468851i
\(370\) −6.92115e47 −0.110750
\(371\) 1.71131e48i 0.260150i
\(372\) −2.84000e48 2.61775e48i −0.410207 0.378106i
\(373\) 6.19042e47 0.0849674 0.0424837 0.999097i \(-0.486473\pi\)
0.0424837 + 0.999097i \(0.486473\pi\)
\(374\) 6.53130e48i 0.851999i
\(375\) −3.69161e48 + 4.00503e48i −0.457743 + 0.496606i
\(376\) −1.36033e48 −0.160353
\(377\) 7.94665e48i 0.890633i
\(378\) −3.35182e48 2.61914e48i −0.357220 0.279135i
\(379\) −6.49689e48 −0.658507 −0.329254 0.944242i \(-0.606797\pi\)
−0.329254 + 0.944242i \(0.606797\pi\)
\(380\) 5.24408e47i 0.0505570i
\(381\) 5.97010e48 + 5.50290e48i 0.547529 + 0.504681i
\(382\) 6.36808e48 0.555654
\(383\) 6.98738e48i 0.580147i 0.957004 + 0.290073i \(0.0936797\pi\)
−0.957004 + 0.290073i \(0.906320\pi\)
\(384\) −8.66060e48 + 9.39588e48i −0.684313 + 0.742411i
\(385\) 1.00449e49 0.755429
\(386\) 4.33831e48i 0.310572i
\(387\) −1.49858e48 1.83698e49i −0.102134 1.25198i
\(388\) 9.55551e48 0.620085
\(389\) 8.22924e48i 0.508531i −0.967134 0.254266i \(-0.918166\pi\)
0.967134 0.254266i \(-0.0818337\pi\)
\(390\) 2.09595e48 + 1.93193e48i 0.123354 + 0.113701i
\(391\) 3.81500e48 0.213863
\(392\) 1.53779e48i 0.0821227i
\(393\) 1.79513e49 1.94753e49i 0.913349 0.990892i
\(394\) 1.25888e49 0.610317
\(395\) 2.86842e47i 0.0132525i
\(396\) −3.66506e49 + 2.98989e48i −1.61389 + 0.131658i
\(397\) −1.02385e47 −0.00429749 −0.00214875 0.999998i \(-0.500684\pi\)
−0.00214875 + 0.999998i \(0.500684\pi\)
\(398\) 7.99320e48i 0.319847i
\(399\) 3.48294e48 + 3.21038e48i 0.132880 + 0.122482i
\(400\) 1.13909e49 0.414397
\(401\) 4.44850e49i 1.54337i −0.636004 0.771686i \(-0.719414\pi\)
0.636004 0.771686i \(-0.280586\pi\)
\(402\) −1.32785e49 + 1.44058e49i −0.439393 + 0.476698i
\(403\) 2.33788e49 0.737949
\(404\) 3.87491e49i 1.16685i
\(405\) 2.03798e48 + 1.24078e49i 0.0585536 + 0.356492i
\(406\) −1.36778e49 −0.374990
\(407\) 5.40434e49i 1.41400i
\(408\) −2.28766e49 2.10864e49i −0.571279 0.526573i
\(409\) −4.50122e49 −1.07297 −0.536484 0.843910i \(-0.680248\pi\)
−0.536484 + 0.843910i \(0.680248\pi\)
\(410\) 3.94802e48i 0.0898434i
\(411\) −9.14853e48 + 9.92524e48i −0.198773 + 0.215649i
\(412\) 9.15345e48 0.189906
\(413\) 6.21788e49i 1.23195i
\(414\) −3.99056e47 4.89170e48i −0.00755140 0.0925665i
\(415\) −3.21391e48 −0.0580924
\(416\) 6.16008e49i 1.06368i
\(417\) 4.11878e49 + 3.79646e49i 0.679491 + 0.626316i
\(418\) −9.35659e48 −0.147492
\(419\) 1.20666e50i 1.81768i −0.417140 0.908842i \(-0.636967\pi\)
0.417140 0.908842i \(-0.363033\pi\)
\(420\) −1.45525e49 + 1.57880e49i −0.209508 + 0.227295i
\(421\) 8.94542e48 0.123095 0.0615475 0.998104i \(-0.480396\pi\)
0.0615475 + 0.998104i \(0.480396\pi\)
\(422\) 4.51342e48i 0.0593703i
\(423\) 1.62447e49 1.32521e48i 0.204289 0.0166655i
\(424\) 1.61024e49 0.193615
\(425\) 7.51015e49i 0.863493i
\(426\) 5.22108e49 + 4.81250e49i 0.574087 + 0.529161i
\(427\) −1.50683e50 −1.58466
\(428\) 3.67607e49i 0.369787i
\(429\) 1.50853e50 1.63661e50i 1.45167 1.57491i
\(430\) 2.12580e49 0.195714
\(431\) 5.54855e49i 0.488778i −0.969677 0.244389i \(-0.921413\pi\)
0.969677 0.244389i \(-0.0785874\pi\)
\(432\) 3.48121e49 4.45504e49i 0.293453 0.375544i
\(433\) −9.80377e48 −0.0790903 −0.0395451 0.999218i \(-0.512591\pi\)
−0.0395451 + 0.999218i \(0.512591\pi\)
\(434\) 4.02395e49i 0.310705i
\(435\) 2.97287e49 + 2.74022e49i 0.219725 + 0.202530i
\(436\) 8.95588e49 0.633672
\(437\) 5.46528e48i 0.0370224i
\(438\) −3.14273e49 + 3.40955e49i −0.203845 + 0.221151i
\(439\) −1.14042e50 −0.708336 −0.354168 0.935182i \(-0.615236\pi\)
−0.354168 + 0.935182i \(0.615236\pi\)
\(440\) 9.45173e49i 0.562225i
\(441\) 1.49809e48 + 1.83638e49i 0.00853502 + 0.104624i
\(442\) 8.45051e49 0.461169
\(443\) 2.75252e50i 1.43900i 0.694494 + 0.719499i \(0.255628\pi\)
−0.694494 + 0.719499i \(0.744372\pi\)
\(444\) −8.49420e49 7.82947e49i −0.425447 0.392153i
\(445\) −9.95836e49 −0.477912
\(446\) 1.52065e50i 0.699305i
\(447\) −2.19015e50 + 2.37609e50i −0.965229 + 1.04718i
\(448\) 1.25805e49 0.0531392
\(449\) 4.10948e49i 0.166382i 0.996534 + 0.0831910i \(0.0265112\pi\)
−0.996534 + 0.0831910i \(0.973489\pi\)
\(450\) 9.62973e49 7.85575e48i 0.373746 0.0304895i
\(451\) −3.08279e50 −1.14707
\(452\) 8.49947e49i 0.303223i
\(453\) −1.49420e50 1.37727e50i −0.511144 0.471144i
\(454\) 6.96285e49 0.228416
\(455\) 1.29966e50i 0.408897i
\(456\) 3.02078e49 3.27725e49i 0.0911565 0.0988957i
\(457\) 3.29920e50 0.954993 0.477497 0.878634i \(-0.341544\pi\)
0.477497 + 0.878634i \(0.341544\pi\)
\(458\) 1.72608e50i 0.479310i
\(459\) 2.93727e50 + 2.29521e50i 0.782533 + 0.611478i
\(460\) −2.47739e49 −0.0633279
\(461\) 2.19869e50i 0.539319i −0.962956 0.269660i \(-0.913089\pi\)
0.962956 0.269660i \(-0.0869112\pi\)
\(462\) −2.81693e50 2.59648e50i −0.663098 0.611207i
\(463\) 4.94759e50 1.11778 0.558888 0.829243i \(-0.311228\pi\)
0.558888 + 0.829243i \(0.311228\pi\)
\(464\) 1.81797e50i 0.394225i
\(465\) −8.06165e49 + 8.74609e49i −0.167810 + 0.182057i
\(466\) −2.14969e50 −0.429578
\(467\) 8.34023e50i 1.60014i 0.599908 + 0.800069i \(0.295204\pi\)
−0.599908 + 0.800069i \(0.704796\pi\)
\(468\) 3.86846e49 + 4.74204e50i 0.0712635 + 0.873562i
\(469\) 8.93281e50 1.58017
\(470\) 1.87987e49i 0.0319352i
\(471\) −7.55220e50 6.96120e50i −1.23219 1.13576i
\(472\) 5.85068e50 0.916871
\(473\) 1.65992e51i 2.49877i
\(474\) −7.41449e48 + 8.04398e48i −0.0107224 + 0.0116327i
\(475\) −1.07589e50 −0.149482
\(476\) 6.36546e50i 0.849762i
\(477\) −1.92290e50 + 1.56867e49i −0.246665 + 0.0201225i
\(478\) −3.72201e50 −0.458826
\(479\) 1.93838e50i 0.229649i 0.993386 + 0.114824i \(0.0366306\pi\)
−0.993386 + 0.114824i \(0.963369\pi\)
\(480\) 2.30450e50 + 2.12416e50i 0.262418 + 0.241882i
\(481\) 6.99239e50 0.765366
\(482\) 3.69681e50i 0.388985i
\(483\) −1.51663e50 + 1.64539e50i −0.153421 + 0.166446i
\(484\) −2.47487e51 −2.40708
\(485\) 2.94272e50i 0.275205i
\(486\) 2.63574e50 4.00634e50i 0.237035 0.360295i
\(487\) −7.70368e50 −0.666267 −0.333133 0.942880i \(-0.608106\pi\)
−0.333133 + 0.942880i \(0.608106\pi\)
\(488\) 1.41785e51i 1.17938i
\(489\) 3.79424e50 + 3.49732e50i 0.303569 + 0.279813i
\(490\) −2.12511e49 −0.0163552
\(491\) 2.08113e51i 1.54081i 0.637552 + 0.770407i \(0.279947\pi\)
−0.637552 + 0.770407i \(0.720053\pi\)
\(492\) 4.46615e50 4.84533e50i 0.318124 0.345133i
\(493\) 1.19861e51 0.821460
\(494\) 1.21060e50i 0.0798341i
\(495\) 9.20769e49 + 1.12870e51i 0.0584321 + 0.716272i
\(496\) 5.34840e50 0.326642
\(497\) 3.23750e51i 1.90300i
\(498\) 9.01282e49 + 8.30751e49i 0.0509921 + 0.0470017i
\(499\) −3.02207e51 −1.64586 −0.822932 0.568140i \(-0.807663\pi\)
−0.822932 + 0.568140i \(0.807663\pi\)
\(500\) 1.04859e51i 0.549766i
\(501\) 1.72949e51 1.87632e51i 0.872974 0.947090i
\(502\) 1.23530e48 0.000600345
\(503\) 2.14049e50i 0.100166i −0.998745 0.0500831i \(-0.984051\pi\)
0.998745 0.0500831i \(-0.0159486\pi\)
\(504\) 1.81889e51 1.48382e50i 0.819648 0.0668654i
\(505\) 1.19332e51 0.517869
\(506\) 4.42020e50i 0.184749i
\(507\) −2.91060e50 2.68283e50i −0.117174 0.108004i
\(508\) −1.56309e51 −0.606139
\(509\) 1.75144e51i 0.654272i 0.944977 + 0.327136i \(0.106083\pi\)
−0.944977 + 0.327136i \(0.893917\pi\)
\(510\) −2.91397e50 + 3.16136e50i −0.104870 + 0.113773i
\(511\) 2.11421e51 0.733078
\(512\) 2.52528e51i 0.843685i
\(513\) −3.28806e50 + 4.20786e50i −0.105855 + 0.135466i
\(514\) 4.75406e50 0.147491
\(515\) 2.81890e50i 0.0842835i
\(516\) 2.60896e51 + 2.40479e51i 0.751835 + 0.692999i
\(517\) 1.46789e51 0.407730
\(518\) 1.20353e51i 0.322249i
\(519\) −2.91976e51 + 3.16764e51i −0.753645 + 0.817629i
\(520\) −1.22291e51 −0.304320
\(521\) 5.56561e50i 0.133535i 0.997769 + 0.0667676i \(0.0212686\pi\)
−0.997769 + 0.0667676i \(0.978731\pi\)
\(522\) −1.25377e50 1.53689e51i −0.0290054 0.355553i
\(523\) −5.01335e51 −1.11840 −0.559198 0.829034i \(-0.688891\pi\)
−0.559198 + 0.829034i \(0.688891\pi\)
\(524\) 5.09902e51i 1.09696i
\(525\) −3.23910e51 2.98562e51i −0.672043 0.619452i
\(526\) −2.40755e51 −0.481778
\(527\) 3.52627e51i 0.680635i
\(528\) 3.45109e51 3.74409e51i 0.642558 0.697111i
\(529\) 5.30928e51 0.953626
\(530\) 2.22523e50i 0.0385596i
\(531\) −6.98669e51 + 5.69961e50i −1.16809 + 0.0952905i
\(532\) −9.11900e50 −0.147105
\(533\) 3.98866e51i 0.620883i
\(534\) 2.79264e51 + 2.57410e51i 0.419500 + 0.386671i
\(535\) 1.13208e51 0.164118
\(536\) 8.40527e51i 1.17604i
\(537\) −4.01065e51 + 4.35115e51i −0.541630 + 0.587615i
\(538\) −6.58981e50 −0.0859033
\(539\) 1.65938e51i 0.208814i
\(540\) −1.90741e51 1.49046e51i −0.231719 0.181067i
\(541\) 6.87237e51 0.806044 0.403022 0.915190i \(-0.367960\pi\)
0.403022 + 0.915190i \(0.367960\pi\)
\(542\) 2.09968e51i 0.237775i
\(543\) −3.28143e51 3.02464e51i −0.358811 0.330732i
\(544\) 9.29137e51 0.981072
\(545\) 2.75806e51i 0.281235i
\(546\) −3.35946e51 + 3.64467e51i −0.330833 + 0.358921i
\(547\) 1.32047e52 1.25594 0.627970 0.778237i \(-0.283886\pi\)
0.627970 + 0.778237i \(0.283886\pi\)
\(548\) 2.59862e51i 0.238733i
\(549\) −1.38124e51 1.69315e52i −0.122573 1.50252i
\(550\) 8.70153e51 0.745941
\(551\) 1.71710e51i 0.142205i
\(552\) 1.54822e51 + 1.42707e51i 0.123877 + 0.114183i
\(553\) 4.98794e50 0.0385606
\(554\) 2.69312e51i 0.201174i
\(555\) −2.41117e51 + 2.61588e51i −0.174045 + 0.188821i
\(556\) −1.07838e52 −0.752227
\(557\) 6.23704e51i 0.420465i −0.977651 0.210233i \(-0.932578\pi\)
0.977651 0.210233i \(-0.0674221\pi\)
\(558\) 4.52149e51 3.68855e50i 0.294599 0.0240329i
\(559\) −2.14768e52 −1.35253
\(560\) 2.97326e51i 0.180992i
\(561\) 2.46853e52 + 2.27535e52i 1.45259 + 1.33892i
\(562\) −6.22335e51 −0.354025
\(563\) 1.16923e52i 0.643043i 0.946902 + 0.321522i \(0.104194\pi\)
−0.946902 + 0.321522i \(0.895806\pi\)
\(564\) −2.12658e51 + 2.30713e51i −0.113078 + 0.122679i
\(565\) −2.61750e51 −0.134576
\(566\) 1.01211e52i 0.503168i
\(567\) −2.15761e52 + 3.54386e51i −1.03728 + 0.170372i
\(568\) −3.04631e52 −1.41630
\(569\) 3.70607e52i 1.66641i −0.552968 0.833203i \(-0.686505\pi\)
0.552968 0.833203i \(-0.313495\pi\)
\(570\) −4.52889e50 4.17448e50i −0.0196956 0.0181543i
\(571\) −1.98355e51 −0.0834367 −0.0417184 0.999129i \(-0.513283\pi\)
−0.0417184 + 0.999129i \(0.513283\pi\)
\(572\) 4.28496e52i 1.74350i
\(573\) 2.21849e52 2.40684e52i 0.873213 0.947349i
\(574\) 6.86526e51 0.261416
\(575\) 5.08265e51i 0.187241i
\(576\) 1.15319e50 + 1.41360e51i 0.00411029 + 0.0503847i
\(577\) 1.96715e52 0.678417 0.339209 0.940711i \(-0.389841\pi\)
0.339209 + 0.940711i \(0.389841\pi\)
\(578\) 1.77518e50i 0.00592398i
\(579\) 1.63968e52 + 1.51137e52i 0.529501 + 0.488065i
\(580\) −7.78355e51 −0.243246
\(581\) 5.58870e51i 0.169030i
\(582\) −7.60654e51 + 8.25233e51i −0.222664 + 0.241568i
\(583\) −1.73755e52 −0.492307
\(584\) 1.98935e52i 0.545591i
\(585\) 1.46036e52 1.19133e51i 0.387702 0.0316280i
\(586\) −2.05366e51 −0.0527805
\(587\) 4.11855e52i 1.02476i 0.858760 + 0.512379i \(0.171236\pi\)
−0.858760 + 0.512379i \(0.828764\pi\)
\(588\) −2.60810e51 2.40400e51i −0.0628284 0.0579117i
\(589\) −5.05166e51 −0.117827
\(590\) 8.08517e51i 0.182600i
\(591\) 4.38564e52 4.75798e52i 0.959115 1.04054i
\(592\) 1.59966e52 0.338778
\(593\) 3.40678e52i 0.698724i −0.936988 0.349362i \(-0.886398\pi\)
0.936988 0.349362i \(-0.113602\pi\)
\(594\) 2.65931e52 3.40323e52i 0.528235 0.676003i
\(595\) 1.96031e52 0.377140
\(596\) 6.22106e52i 1.15927i
\(597\) −3.02106e52 2.78465e52i −0.545315 0.502641i
\(598\) −5.71907e51 −0.100001
\(599\) 1.29821e52i 0.219904i 0.993937 + 0.109952i \(0.0350698\pi\)
−0.993937 + 0.109952i \(0.964930\pi\)
\(600\) −2.80930e52 + 3.04781e52i −0.461025 + 0.500166i
\(601\) −2.33958e52 −0.371983 −0.185992 0.982551i \(-0.559550\pi\)
−0.185992 + 0.982551i \(0.559550\pi\)
\(602\) 3.69659e52i 0.569466i
\(603\) 8.18825e51 + 1.00373e53i 0.122226 + 1.49826i
\(604\) 3.91210e52 0.565860
\(605\) 7.62162e52i 1.06830i
\(606\) −3.34645e52 3.08457e52i −0.454574 0.419000i
\(607\) −2.92954e52 −0.385668 −0.192834 0.981231i \(-0.561768\pi\)
−0.192834 + 0.981231i \(0.561768\pi\)
\(608\) 1.33106e52i 0.169836i
\(609\) −4.76501e52 + 5.16956e52i −0.589299 + 0.639330i
\(610\) 1.95935e52 0.234879
\(611\) 1.89922e52i 0.220695i
\(612\) −7.15251e52 + 5.83489e51i −0.805715 + 0.0657288i
\(613\) −1.95347e52 −0.213332 −0.106666 0.994295i \(-0.534018\pi\)
−0.106666 + 0.994295i \(0.534018\pi\)
\(614\) 4.74934e52i 0.502845i
\(615\) −1.49217e52 1.37540e52i −0.153176 0.141189i
\(616\) 1.64357e53 1.63590
\(617\) 2.89268e52i 0.279179i −0.990209 0.139589i \(-0.955422\pi\)
0.990209 0.139589i \(-0.0445783\pi\)
\(618\) −7.28648e51 + 7.90510e51i −0.0681925 + 0.0739821i
\(619\) −1.54732e53 −1.40430 −0.702148 0.712031i \(-0.747776\pi\)
−0.702148 + 0.712031i \(0.747776\pi\)
\(620\) 2.28989e52i 0.201546i
\(621\) −1.98786e52 1.55333e52i −0.169686 0.132594i
\(622\) 3.12727e52 0.258909
\(623\) 1.73167e53i 1.39057i
\(624\) −4.84429e52 4.46519e52i −0.377331 0.347803i
\(625\) 8.27828e52 0.625489
\(626\) 1.02033e52i 0.0747877i
\(627\) −3.25962e52 + 3.53636e52i −0.231784 + 0.251462i
\(628\) 1.97731e53 1.36409
\(629\) 1.05468e53i 0.705923i
\(630\) −2.05052e51 2.51357e52i −0.0133166 0.163238i
\(631\) 3.10238e52 0.195496 0.0977478 0.995211i \(-0.468836\pi\)
0.0977478 + 0.995211i \(0.468836\pi\)
\(632\) 4.69337e51i 0.0286986i
\(633\) −1.70586e52 1.57237e52i −0.101222 0.0933006i
\(634\) −7.90385e52 −0.455138
\(635\) 4.81369e52i 0.269016i
\(636\) 2.51726e52 2.73098e52i 0.136535 0.148126i
\(637\) 2.14698e52 0.113026
\(638\) 1.38875e53i 0.709631i
\(639\) 3.63780e53 2.96765e52i 1.80436 0.147196i
\(640\) −7.57590e52 −0.364766
\(641\) 9.53340e52i 0.445600i 0.974864 + 0.222800i \(0.0715197\pi\)
−0.974864 + 0.222800i \(0.928480\pi\)
\(642\) −3.17473e52 2.92629e52i −0.144059 0.132786i
\(643\) 9.32636e52 0.410869 0.205435 0.978671i \(-0.434139\pi\)
0.205435 + 0.978671i \(0.434139\pi\)
\(644\) 4.30796e52i 0.184264i
\(645\) 7.40580e52 8.03456e52i 0.307565 0.333678i
\(646\) −1.82597e52 −0.0736337
\(647\) 7.58255e52i 0.296916i −0.988919 0.148458i \(-0.952569\pi\)
0.988919 0.148458i \(-0.0474310\pi\)
\(648\) 3.33458e52 + 2.03019e53i 0.126799 + 0.771990i
\(649\) −6.31326e53 −2.33133
\(650\) 1.12585e53i 0.403762i
\(651\) −1.52087e53 1.40185e53i −0.529728 0.488274i
\(652\) −9.93406e52 −0.336064
\(653\) 4.34569e53i 1.42794i 0.700178 + 0.713968i \(0.253104\pi\)
−0.700178 + 0.713968i \(0.746896\pi\)
\(654\) −7.12921e52 + 7.73448e52i −0.227543 + 0.246862i
\(655\) 1.57030e53 0.486852
\(656\) 9.12491e52i 0.274825i
\(657\) 1.93799e52 + 2.37562e53i 0.0567033 + 0.695080i
\(658\) −3.26894e52 −0.0929211
\(659\) 1.35861e53i 0.375207i 0.982245 + 0.187603i \(0.0600720\pi\)
−0.982245 + 0.187603i \(0.939928\pi\)
\(660\) −1.60302e53 1.47757e53i −0.430134 0.396473i
\(661\) −1.47594e53 −0.384805 −0.192402 0.981316i \(-0.561628\pi\)
−0.192402 + 0.981316i \(0.561628\pi\)
\(662\) 1.99641e52i 0.0505763i
\(663\) 2.94396e53 3.19390e53i 0.724728 0.786258i
\(664\) −5.25866e52 −0.125800
\(665\) 2.80829e52i 0.0652877i
\(666\) 1.35234e53 1.10321e52i 0.305545 0.0249258i
\(667\) −8.11186e52 −0.178127
\(668\) 4.91258e53i 1.04847i
\(669\) 5.74735e53 + 5.29759e53i 1.19226 + 1.09896i
\(670\) −1.16154e53 −0.234214
\(671\) 1.52995e54i 2.99881i
\(672\) −3.69374e53 + 4.00733e53i −0.703801 + 0.763553i
\(673\) −9.61367e52 −0.178075 −0.0890375 0.996028i \(-0.528379\pi\)
−0.0890375 + 0.996028i \(0.528379\pi\)
\(674\) 1.02930e53i 0.185355i
\(675\) 3.05786e53 3.91327e53i 0.535361 0.685123i
\(676\) 7.62051e52 0.129717
\(677\) 6.32159e53i 1.04627i −0.852251 0.523133i \(-0.824763\pi\)
0.852251 0.523133i \(-0.175237\pi\)
\(678\) 7.34031e52 + 6.76589e52i 0.118127 + 0.108883i
\(679\) 5.11714e53 0.800758
\(680\) 1.84454e53i 0.280685i
\(681\) 2.42570e53 2.63164e53i 0.358956 0.389431i
\(682\) 4.08567e53 0.587977
\(683\) 1.06104e54i 1.48504i 0.669823 + 0.742521i \(0.266370\pi\)
−0.669823 + 0.742521i \(0.733630\pi\)
\(684\) −8.35892e51 1.02465e53i −0.0113785 0.139479i
\(685\) −8.00272e52 −0.105954
\(686\) 3.15083e53i 0.405758i
\(687\) −6.52379e53 6.01326e53i −0.817188 0.753238i
\(688\) −4.91329e53 −0.598676
\(689\) 2.24813e53i 0.266475i
\(690\) 1.97209e52 2.13952e52i 0.0227402 0.0246708i
\(691\) 1.68158e54 1.88640 0.943201 0.332224i \(-0.107799\pi\)
0.943201 + 0.332224i \(0.107799\pi\)
\(692\) 8.29350e53i 0.905153i
\(693\) −1.96270e54 + 1.60114e53i −2.08412 + 0.170019i
\(694\) −2.21671e53 −0.229023
\(695\) 3.32097e53i 0.333852i
\(696\) 4.86427e53 + 4.48361e53i 0.475819 + 0.438583i
\(697\) −6.01618e53 −0.572661
\(698\) 4.20727e52i 0.0389715i
\(699\) −7.48901e53 + 8.12483e53i −0.675084 + 0.732399i
\(700\) 8.48058e53 0.743983
\(701\) 1.79665e53i 0.153398i 0.997054 + 0.0766991i \(0.0244381\pi\)
−0.997054 + 0.0766991i \(0.975562\pi\)
\(702\) −4.40326e53 3.44075e53i −0.365906 0.285922i
\(703\) −1.51091e53 −0.122204
\(704\) 1.27734e53i 0.100560i
\(705\) 7.10506e52 + 6.54904e52i 0.0544471 + 0.0501862i
\(706\) 4.82049e52 0.0359586
\(707\) 2.07508e54i 1.50683i
\(708\) 9.14625e53 9.92277e53i 0.646564 0.701457i
\(709\) −1.48779e53 −0.102391 −0.0511955 0.998689i \(-0.516303\pi\)
−0.0511955 + 0.998689i \(0.516303\pi\)
\(710\) 4.20976e53i 0.282064i
\(711\) 4.57219e51 + 5.60467e52i 0.00298264 + 0.0365618i
\(712\) −1.62941e54 −1.03493
\(713\) 2.38648e53i 0.147590i
\(714\) −5.49734e53 5.06714e53i −0.331045 0.305138i
\(715\) 1.31960e54 0.773797
\(716\) 1.13922e54i 0.650517i
\(717\) −1.29666e54 + 1.40675e54i −0.721046 + 0.782263i
\(718\) 5.49713e53 0.297695
\(719\) 2.13138e54i 1.12412i −0.827097 0.562059i \(-0.810009\pi\)
0.827097 0.562059i \(-0.189991\pi\)
\(720\) 3.34089e53 2.72543e52i 0.171611 0.0139997i
\(721\) 4.90183e53 0.245238
\(722\) 8.58878e53i 0.418528i
\(723\) 1.39722e54 + 1.28788e54i 0.663191 + 0.611292i
\(724\) 8.59141e53 0.397220
\(725\) 1.59689e54i 0.719204i
\(726\) 1.97009e54 2.13735e54i 0.864349 0.937733i
\(727\) −1.08624e54 −0.464273 −0.232137 0.972683i \(-0.574572\pi\)
−0.232137 + 0.972683i \(0.574572\pi\)
\(728\) 2.12654e54i 0.885475i
\(729\) −5.95981e53 2.39190e54i −0.241774 0.970333i
\(730\) −2.74912e53 −0.108658
\(731\) 3.23940e54i 1.24748i
\(732\) 2.40467e54 + 2.21649e54i 0.902288 + 0.831679i
\(733\) 1.44131e54 0.526967 0.263483 0.964664i \(-0.415129\pi\)
0.263483 + 0.964664i \(0.415129\pi\)
\(734\) 2.20869e54i 0.786883i
\(735\) −7.40339e52 + 8.03194e52i −0.0257022 + 0.0278844i
\(736\) −6.28814e53 −0.212737
\(737\) 9.06983e54i 2.99031i
\(738\) 6.29304e52 + 7.71412e53i 0.0202204 + 0.247865i
\(739\) −3.45110e54 −1.08072 −0.540360 0.841434i \(-0.681712\pi\)
−0.540360 + 0.841434i \(0.681712\pi\)
\(740\) 6.84887e53i 0.209034i
\(741\) 4.57551e53 + 4.21745e53i 0.136111 + 0.125460i
\(742\) 3.86947e53 0.112196
\(743\) 4.33606e54i 1.22548i −0.790283 0.612742i \(-0.790066\pi\)
0.790283 0.612742i \(-0.209934\pi\)
\(744\) −1.31906e54 + 1.43105e54i −0.363396 + 0.394248i
\(745\) −1.91584e54 −0.514506
\(746\) 1.39973e53i 0.0366443i
\(747\) 6.27972e53 5.12288e52i 0.160269 0.0130744i
\(748\) −6.46309e54 −1.60809
\(749\) 1.96860e54i 0.477532i
\(750\) 9.05588e53 + 8.34720e53i 0.214174 + 0.197413i
\(751\) 4.67397e54 1.07777 0.538886 0.842379i \(-0.318845\pi\)
0.538886 + 0.842379i \(0.318845\pi\)
\(752\) 4.34488e53i 0.0976875i
\(753\) 4.30349e51 4.66886e51i 0.000943445 0.00102354i
\(754\) −1.79684e54 −0.384108
\(755\) 1.20477e54i 0.251139i
\(756\) 2.59179e54 3.31681e54i 0.526848 0.674228i
\(757\) −7.66727e54 −1.51991 −0.759957 0.649974i \(-0.774780\pi\)
−0.759957 + 0.649974i