Properties

Label 6034.2.a.n.1.4
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.92027 q^{3}\) \(+1.00000 q^{4}\) \(-2.53143 q^{5}\) \(+1.92027 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+0.687441 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.92027 q^{3}\) \(+1.00000 q^{4}\) \(-2.53143 q^{5}\) \(+1.92027 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+0.687441 q^{9}\) \(+2.53143 q^{10}\) \(-3.57947 q^{11}\) \(-1.92027 q^{12}\) \(+3.61870 q^{13}\) \(+1.00000 q^{14}\) \(+4.86104 q^{15}\) \(+1.00000 q^{16}\) \(-0.257224 q^{17}\) \(-0.687441 q^{18}\) \(+0.598623 q^{19}\) \(-2.53143 q^{20}\) \(+1.92027 q^{21}\) \(+3.57947 q^{22}\) \(+8.37463 q^{23}\) \(+1.92027 q^{24}\) \(+1.40815 q^{25}\) \(-3.61870 q^{26}\) \(+4.44074 q^{27}\) \(-1.00000 q^{28}\) \(-4.10604 q^{29}\) \(-4.86104 q^{30}\) \(-10.1150 q^{31}\) \(-1.00000 q^{32}\) \(+6.87354 q^{33}\) \(+0.257224 q^{34}\) \(+2.53143 q^{35}\) \(+0.687441 q^{36}\) \(-4.11862 q^{37}\) \(-0.598623 q^{38}\) \(-6.94889 q^{39}\) \(+2.53143 q^{40}\) \(+2.61524 q^{41}\) \(-1.92027 q^{42}\) \(-2.17771 q^{43}\) \(-3.57947 q^{44}\) \(-1.74021 q^{45}\) \(-8.37463 q^{46}\) \(+4.93647 q^{47}\) \(-1.92027 q^{48}\) \(+1.00000 q^{49}\) \(-1.40815 q^{50}\) \(+0.493939 q^{51}\) \(+3.61870 q^{52}\) \(+1.94415 q^{53}\) \(-4.44074 q^{54}\) \(+9.06118 q^{55}\) \(+1.00000 q^{56}\) \(-1.14952 q^{57}\) \(+4.10604 q^{58}\) \(-8.21369 q^{59}\) \(+4.86104 q^{60}\) \(-15.5521 q^{61}\) \(+10.1150 q^{62}\) \(-0.687441 q^{63}\) \(+1.00000 q^{64}\) \(-9.16050 q^{65}\) \(-6.87354 q^{66}\) \(-8.51172 q^{67}\) \(-0.257224 q^{68}\) \(-16.0816 q^{69}\) \(-2.53143 q^{70}\) \(-4.42305 q^{71}\) \(-0.687441 q^{72}\) \(-9.04366 q^{73}\) \(+4.11862 q^{74}\) \(-2.70403 q^{75}\) \(+0.598623 q^{76}\) \(+3.57947 q^{77}\) \(+6.94889 q^{78}\) \(-2.43578 q^{79}\) \(-2.53143 q^{80}\) \(-10.5897 q^{81}\) \(-2.61524 q^{82}\) \(+1.85571 q^{83}\) \(+1.92027 q^{84}\) \(+0.651144 q^{85}\) \(+2.17771 q^{86}\) \(+7.88471 q^{87}\) \(+3.57947 q^{88}\) \(+15.7350 q^{89}\) \(+1.74021 q^{90}\) \(-3.61870 q^{91}\) \(+8.37463 q^{92}\) \(+19.4235 q^{93}\) \(-4.93647 q^{94}\) \(-1.51537 q^{95}\) \(+1.92027 q^{96}\) \(-11.1596 q^{97}\) \(-1.00000 q^{98}\) \(-2.46067 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.92027 −1.10867 −0.554334 0.832294i \(-0.687027\pi\)
−0.554334 + 0.832294i \(0.687027\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.53143 −1.13209 −0.566046 0.824374i \(-0.691527\pi\)
−0.566046 + 0.824374i \(0.691527\pi\)
\(6\) 1.92027 0.783947
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0.687441 0.229147
\(10\) 2.53143 0.800509
\(11\) −3.57947 −1.07925 −0.539625 0.841906i \(-0.681434\pi\)
−0.539625 + 0.841906i \(0.681434\pi\)
\(12\) −1.92027 −0.554334
\(13\) 3.61870 1.00365 0.501824 0.864970i \(-0.332663\pi\)
0.501824 + 0.864970i \(0.332663\pi\)
\(14\) 1.00000 0.267261
\(15\) 4.86104 1.25511
\(16\) 1.00000 0.250000
\(17\) −0.257224 −0.0623859 −0.0311929 0.999513i \(-0.509931\pi\)
−0.0311929 + 0.999513i \(0.509931\pi\)
\(18\) −0.687441 −0.162031
\(19\) 0.598623 0.137333 0.0686667 0.997640i \(-0.478125\pi\)
0.0686667 + 0.997640i \(0.478125\pi\)
\(20\) −2.53143 −0.566046
\(21\) 1.92027 0.419037
\(22\) 3.57947 0.763145
\(23\) 8.37463 1.74623 0.873116 0.487513i \(-0.162096\pi\)
0.873116 + 0.487513i \(0.162096\pi\)
\(24\) 1.92027 0.391974
\(25\) 1.40815 0.281630
\(26\) −3.61870 −0.709686
\(27\) 4.44074 0.854621
\(28\) −1.00000 −0.188982
\(29\) −4.10604 −0.762472 −0.381236 0.924478i \(-0.624502\pi\)
−0.381236 + 0.924478i \(0.624502\pi\)
\(30\) −4.86104 −0.887500
\(31\) −10.1150 −1.81671 −0.908353 0.418204i \(-0.862660\pi\)
−0.908353 + 0.418204i \(0.862660\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.87354 1.19653
\(34\) 0.257224 0.0441135
\(35\) 2.53143 0.427890
\(36\) 0.687441 0.114573
\(37\) −4.11862 −0.677096 −0.338548 0.940949i \(-0.609936\pi\)
−0.338548 + 0.940949i \(0.609936\pi\)
\(38\) −0.598623 −0.0971094
\(39\) −6.94889 −1.11271
\(40\) 2.53143 0.400255
\(41\) 2.61524 0.408432 0.204216 0.978926i \(-0.434535\pi\)
0.204216 + 0.978926i \(0.434535\pi\)
\(42\) −1.92027 −0.296304
\(43\) −2.17771 −0.332098 −0.166049 0.986118i \(-0.553101\pi\)
−0.166049 + 0.986118i \(0.553101\pi\)
\(44\) −3.57947 −0.539625
\(45\) −1.74021 −0.259415
\(46\) −8.37463 −1.23477
\(47\) 4.93647 0.720058 0.360029 0.932941i \(-0.382767\pi\)
0.360029 + 0.932941i \(0.382767\pi\)
\(48\) −1.92027 −0.277167
\(49\) 1.00000 0.142857
\(50\) −1.40815 −0.199143
\(51\) 0.493939 0.0691653
\(52\) 3.61870 0.501824
\(53\) 1.94415 0.267049 0.133525 0.991046i \(-0.457371\pi\)
0.133525 + 0.991046i \(0.457371\pi\)
\(54\) −4.44074 −0.604308
\(55\) 9.06118 1.22181
\(56\) 1.00000 0.133631
\(57\) −1.14952 −0.152257
\(58\) 4.10604 0.539149
\(59\) −8.21369 −1.06933 −0.534666 0.845064i \(-0.679563\pi\)
−0.534666 + 0.845064i \(0.679563\pi\)
\(60\) 4.86104 0.627557
\(61\) −15.5521 −1.99124 −0.995621 0.0934776i \(-0.970202\pi\)
−0.995621 + 0.0934776i \(0.970202\pi\)
\(62\) 10.1150 1.28461
\(63\) −0.687441 −0.0866094
\(64\) 1.00000 0.125000
\(65\) −9.16050 −1.13622
\(66\) −6.87354 −0.846075
\(67\) −8.51172 −1.03987 −0.519936 0.854205i \(-0.674044\pi\)
−0.519936 + 0.854205i \(0.674044\pi\)
\(68\) −0.257224 −0.0311929
\(69\) −16.0816 −1.93599
\(70\) −2.53143 −0.302564
\(71\) −4.42305 −0.524919 −0.262460 0.964943i \(-0.584534\pi\)
−0.262460 + 0.964943i \(0.584534\pi\)
\(72\) −0.687441 −0.0810157
\(73\) −9.04366 −1.05848 −0.529240 0.848472i \(-0.677523\pi\)
−0.529240 + 0.848472i \(0.677523\pi\)
\(74\) 4.11862 0.478779
\(75\) −2.70403 −0.312235
\(76\) 0.598623 0.0686667
\(77\) 3.57947 0.407918
\(78\) 6.94889 0.786807
\(79\) −2.43578 −0.274047 −0.137023 0.990568i \(-0.543754\pi\)
−0.137023 + 0.990568i \(0.543754\pi\)
\(80\) −2.53143 −0.283023
\(81\) −10.5897 −1.17664
\(82\) −2.61524 −0.288805
\(83\) 1.85571 0.203691 0.101845 0.994800i \(-0.467525\pi\)
0.101845 + 0.994800i \(0.467525\pi\)
\(84\) 1.92027 0.209519
\(85\) 0.651144 0.0706265
\(86\) 2.17771 0.234828
\(87\) 7.88471 0.845329
\(88\) 3.57947 0.381572
\(89\) 15.7350 1.66790 0.833952 0.551838i \(-0.186073\pi\)
0.833952 + 0.551838i \(0.186073\pi\)
\(90\) 1.74021 0.183434
\(91\) −3.61870 −0.379343
\(92\) 8.37463 0.873116
\(93\) 19.4235 2.01413
\(94\) −4.93647 −0.509158
\(95\) −1.51537 −0.155474
\(96\) 1.92027 0.195987
\(97\) −11.1596 −1.13309 −0.566545 0.824031i \(-0.691720\pi\)
−0.566545 + 0.824031i \(0.691720\pi\)
\(98\) −1.00000 −0.101015
\(99\) −2.46067 −0.247307
\(100\) 1.40815 0.140815
\(101\) −4.51337 −0.449097 −0.224548 0.974463i \(-0.572091\pi\)
−0.224548 + 0.974463i \(0.572091\pi\)
\(102\) −0.493939 −0.0489072
\(103\) −6.56636 −0.647003 −0.323502 0.946228i \(-0.604860\pi\)
−0.323502 + 0.946228i \(0.604860\pi\)
\(104\) −3.61870 −0.354843
\(105\) −4.86104 −0.474389
\(106\) −1.94415 −0.188832
\(107\) −8.62604 −0.833911 −0.416956 0.908927i \(-0.636903\pi\)
−0.416956 + 0.908927i \(0.636903\pi\)
\(108\) 4.44074 0.427310
\(109\) 9.73455 0.932400 0.466200 0.884679i \(-0.345623\pi\)
0.466200 + 0.884679i \(0.345623\pi\)
\(110\) −9.06118 −0.863949
\(111\) 7.90886 0.750676
\(112\) −1.00000 −0.0944911
\(113\) −12.9385 −1.21715 −0.608574 0.793497i \(-0.708258\pi\)
−0.608574 + 0.793497i \(0.708258\pi\)
\(114\) 1.14952 0.107662
\(115\) −21.1998 −1.97689
\(116\) −4.10604 −0.381236
\(117\) 2.48764 0.229983
\(118\) 8.21369 0.756132
\(119\) 0.257224 0.0235796
\(120\) −4.86104 −0.443750
\(121\) 1.81257 0.164779
\(122\) 15.5521 1.40802
\(123\) −5.02197 −0.452816
\(124\) −10.1150 −0.908353
\(125\) 9.09252 0.813260
\(126\) 0.687441 0.0612421
\(127\) −10.1471 −0.900411 −0.450206 0.892925i \(-0.648649\pi\)
−0.450206 + 0.892925i \(0.648649\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.18179 0.368186
\(130\) 9.16050 0.803429
\(131\) 11.9416 1.04334 0.521672 0.853146i \(-0.325309\pi\)
0.521672 + 0.853146i \(0.325309\pi\)
\(132\) 6.87354 0.598265
\(133\) −0.598623 −0.0519072
\(134\) 8.51172 0.735300
\(135\) −11.2414 −0.967509
\(136\) 0.257224 0.0220567
\(137\) 9.15383 0.782064 0.391032 0.920377i \(-0.372118\pi\)
0.391032 + 0.920377i \(0.372118\pi\)
\(138\) 16.0816 1.36895
\(139\) −0.332567 −0.0282079 −0.0141040 0.999901i \(-0.504490\pi\)
−0.0141040 + 0.999901i \(0.504490\pi\)
\(140\) 2.53143 0.213945
\(141\) −9.47935 −0.798306
\(142\) 4.42305 0.371174
\(143\) −12.9530 −1.08319
\(144\) 0.687441 0.0572867
\(145\) 10.3942 0.863188
\(146\) 9.04366 0.748459
\(147\) −1.92027 −0.158381
\(148\) −4.11862 −0.338548
\(149\) −6.88464 −0.564012 −0.282006 0.959413i \(-0.591000\pi\)
−0.282006 + 0.959413i \(0.591000\pi\)
\(150\) 2.70403 0.220783
\(151\) −1.65194 −0.134433 −0.0672165 0.997738i \(-0.521412\pi\)
−0.0672165 + 0.997738i \(0.521412\pi\)
\(152\) −0.598623 −0.0485547
\(153\) −0.176826 −0.0142955
\(154\) −3.57947 −0.288442
\(155\) 25.6054 2.05668
\(156\) −6.94889 −0.556357
\(157\) −8.97337 −0.716153 −0.358076 0.933692i \(-0.616567\pi\)
−0.358076 + 0.933692i \(0.616567\pi\)
\(158\) 2.43578 0.193780
\(159\) −3.73329 −0.296069
\(160\) 2.53143 0.200127
\(161\) −8.37463 −0.660013
\(162\) 10.5897 0.832009
\(163\) 12.9833 1.01693 0.508465 0.861083i \(-0.330213\pi\)
0.508465 + 0.861083i \(0.330213\pi\)
\(164\) 2.61524 0.204216
\(165\) −17.3999 −1.35458
\(166\) −1.85571 −0.144031
\(167\) 4.34910 0.336543 0.168272 0.985741i \(-0.446181\pi\)
0.168272 + 0.985741i \(0.446181\pi\)
\(168\) −1.92027 −0.148152
\(169\) 0.0950129 0.00730869
\(170\) −0.651144 −0.0499405
\(171\) 0.411518 0.0314695
\(172\) −2.17771 −0.166049
\(173\) 19.2037 1.46003 0.730013 0.683433i \(-0.239514\pi\)
0.730013 + 0.683433i \(0.239514\pi\)
\(174\) −7.88471 −0.597738
\(175\) −1.40815 −0.106446
\(176\) −3.57947 −0.269812
\(177\) 15.7725 1.18553
\(178\) −15.7350 −1.17939
\(179\) 12.8897 0.963424 0.481712 0.876330i \(-0.340015\pi\)
0.481712 + 0.876330i \(0.340015\pi\)
\(180\) −1.74021 −0.129708
\(181\) −19.4900 −1.44868 −0.724340 0.689443i \(-0.757855\pi\)
−0.724340 + 0.689443i \(0.757855\pi\)
\(182\) 3.61870 0.268236
\(183\) 29.8643 2.20763
\(184\) −8.37463 −0.617386
\(185\) 10.4260 0.766535
\(186\) −19.4235 −1.42420
\(187\) 0.920723 0.0673299
\(188\) 4.93647 0.360029
\(189\) −4.44074 −0.323016
\(190\) 1.51537 0.109937
\(191\) 21.3778 1.54684 0.773422 0.633891i \(-0.218543\pi\)
0.773422 + 0.633891i \(0.218543\pi\)
\(192\) −1.92027 −0.138584
\(193\) −3.51896 −0.253300 −0.126650 0.991947i \(-0.540423\pi\)
−0.126650 + 0.991947i \(0.540423\pi\)
\(194\) 11.1596 0.801216
\(195\) 17.5906 1.25969
\(196\) 1.00000 0.0714286
\(197\) −12.9752 −0.924443 −0.462222 0.886764i \(-0.652948\pi\)
−0.462222 + 0.886764i \(0.652948\pi\)
\(198\) 2.46067 0.174872
\(199\) 24.2163 1.71665 0.858325 0.513107i \(-0.171505\pi\)
0.858325 + 0.513107i \(0.171505\pi\)
\(200\) −1.40815 −0.0995714
\(201\) 16.3448 1.15287
\(202\) 4.51337 0.317559
\(203\) 4.10604 0.288187
\(204\) 0.493939 0.0345826
\(205\) −6.62031 −0.462383
\(206\) 6.56636 0.457500
\(207\) 5.75706 0.400143
\(208\) 3.61870 0.250912
\(209\) −2.14275 −0.148217
\(210\) 4.86104 0.335443
\(211\) −17.3419 −1.19387 −0.596933 0.802291i \(-0.703614\pi\)
−0.596933 + 0.802291i \(0.703614\pi\)
\(212\) 1.94415 0.133525
\(213\) 8.49345 0.581962
\(214\) 8.62604 0.589664
\(215\) 5.51272 0.375965
\(216\) −4.44074 −0.302154
\(217\) 10.1150 0.686650
\(218\) −9.73455 −0.659307
\(219\) 17.3663 1.17350
\(220\) 9.06118 0.610904
\(221\) −0.930816 −0.0626134
\(222\) −7.90886 −0.530808
\(223\) 16.5519 1.10840 0.554199 0.832384i \(-0.313025\pi\)
0.554199 + 0.832384i \(0.313025\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0.968021 0.0645347
\(226\) 12.9385 0.860653
\(227\) −4.67367 −0.310203 −0.155101 0.987899i \(-0.549570\pi\)
−0.155101 + 0.987899i \(0.549570\pi\)
\(228\) −1.14952 −0.0761287
\(229\) −22.0926 −1.45992 −0.729959 0.683491i \(-0.760461\pi\)
−0.729959 + 0.683491i \(0.760461\pi\)
\(230\) 21.1998 1.39787
\(231\) −6.87354 −0.452246
\(232\) 4.10604 0.269575
\(233\) −18.0457 −1.18221 −0.591106 0.806594i \(-0.701308\pi\)
−0.591106 + 0.806594i \(0.701308\pi\)
\(234\) −2.48764 −0.162622
\(235\) −12.4963 −0.815171
\(236\) −8.21369 −0.534666
\(237\) 4.67736 0.303827
\(238\) −0.257224 −0.0166733
\(239\) −22.6294 −1.46377 −0.731887 0.681426i \(-0.761360\pi\)
−0.731887 + 0.681426i \(0.761360\pi\)
\(240\) 4.86104 0.313779
\(241\) −4.88488 −0.314663 −0.157331 0.987546i \(-0.550289\pi\)
−0.157331 + 0.987546i \(0.550289\pi\)
\(242\) −1.81257 −0.116517
\(243\) 7.01296 0.449882
\(244\) −15.5521 −0.995621
\(245\) −2.53143 −0.161727
\(246\) 5.02197 0.320189
\(247\) 2.16624 0.137834
\(248\) 10.1150 0.642303
\(249\) −3.56347 −0.225826
\(250\) −9.09252 −0.575062
\(251\) 5.84078 0.368667 0.184333 0.982864i \(-0.440987\pi\)
0.184333 + 0.982864i \(0.440987\pi\)
\(252\) −0.687441 −0.0433047
\(253\) −29.9767 −1.88462
\(254\) 10.1471 0.636687
\(255\) −1.25037 −0.0783014
\(256\) 1.00000 0.0625000
\(257\) 5.57160 0.347547 0.173773 0.984786i \(-0.444404\pi\)
0.173773 + 0.984786i \(0.444404\pi\)
\(258\) −4.18179 −0.260347
\(259\) 4.11862 0.255918
\(260\) −9.16050 −0.568110
\(261\) −2.82266 −0.174718
\(262\) −11.9416 −0.737755
\(263\) −21.9048 −1.35071 −0.675353 0.737495i \(-0.736009\pi\)
−0.675353 + 0.737495i \(0.736009\pi\)
\(264\) −6.87354 −0.423037
\(265\) −4.92148 −0.302324
\(266\) 0.598623 0.0367039
\(267\) −30.2154 −1.84915
\(268\) −8.51172 −0.519936
\(269\) 15.3493 0.935866 0.467933 0.883764i \(-0.344999\pi\)
0.467933 + 0.883764i \(0.344999\pi\)
\(270\) 11.2414 0.684132
\(271\) 29.7738 1.80863 0.904315 0.426866i \(-0.140382\pi\)
0.904315 + 0.426866i \(0.140382\pi\)
\(272\) −0.257224 −0.0155965
\(273\) 6.94889 0.420566
\(274\) −9.15383 −0.553003
\(275\) −5.04043 −0.303949
\(276\) −16.0816 −0.967996
\(277\) −23.7870 −1.42922 −0.714610 0.699523i \(-0.753396\pi\)
−0.714610 + 0.699523i \(0.753396\pi\)
\(278\) 0.332567 0.0199460
\(279\) −6.95346 −0.416293
\(280\) −2.53143 −0.151282
\(281\) 1.87745 0.112000 0.0559998 0.998431i \(-0.482165\pi\)
0.0559998 + 0.998431i \(0.482165\pi\)
\(282\) 9.47935 0.564487
\(283\) −15.9527 −0.948290 −0.474145 0.880447i \(-0.657243\pi\)
−0.474145 + 0.880447i \(0.657243\pi\)
\(284\) −4.42305 −0.262460
\(285\) 2.90993 0.172369
\(286\) 12.9530 0.765928
\(287\) −2.61524 −0.154373
\(288\) −0.687441 −0.0405078
\(289\) −16.9338 −0.996108
\(290\) −10.3942 −0.610366
\(291\) 21.4295 1.25622
\(292\) −9.04366 −0.529240
\(293\) −6.31742 −0.369067 −0.184534 0.982826i \(-0.559077\pi\)
−0.184534 + 0.982826i \(0.559077\pi\)
\(294\) 1.92027 0.111992
\(295\) 20.7924 1.21058
\(296\) 4.11862 0.239390
\(297\) −15.8955 −0.922349
\(298\) 6.88464 0.398817
\(299\) 30.3053 1.75260
\(300\) −2.70403 −0.156117
\(301\) 2.17771 0.125521
\(302\) 1.65194 0.0950585
\(303\) 8.66689 0.497900
\(304\) 0.598623 0.0343334
\(305\) 39.3691 2.25427
\(306\) 0.176826 0.0101085
\(307\) 12.5877 0.718415 0.359208 0.933258i \(-0.383047\pi\)
0.359208 + 0.933258i \(0.383047\pi\)
\(308\) 3.57947 0.203959
\(309\) 12.6092 0.717312
\(310\) −25.6054 −1.45429
\(311\) −25.4835 −1.44504 −0.722519 0.691351i \(-0.757016\pi\)
−0.722519 + 0.691351i \(0.757016\pi\)
\(312\) 6.94889 0.393403
\(313\) 14.0108 0.791940 0.395970 0.918263i \(-0.370408\pi\)
0.395970 + 0.918263i \(0.370408\pi\)
\(314\) 8.97337 0.506397
\(315\) 1.74021 0.0980497
\(316\) −2.43578 −0.137023
\(317\) 30.6658 1.72236 0.861181 0.508299i \(-0.169726\pi\)
0.861181 + 0.508299i \(0.169726\pi\)
\(318\) 3.73329 0.209352
\(319\) 14.6974 0.822898
\(320\) −2.53143 −0.141511
\(321\) 16.5643 0.924531
\(322\) 8.37463 0.466700
\(323\) −0.153980 −0.00856767
\(324\) −10.5897 −0.588319
\(325\) 5.09568 0.282658
\(326\) −12.9833 −0.719078
\(327\) −18.6930 −1.03372
\(328\) −2.61524 −0.144403
\(329\) −4.93647 −0.272156
\(330\) 17.3999 0.957834
\(331\) −17.5804 −0.966306 −0.483153 0.875536i \(-0.660508\pi\)
−0.483153 + 0.875536i \(0.660508\pi\)
\(332\) 1.85571 0.101845
\(333\) −2.83130 −0.155155
\(334\) −4.34910 −0.237972
\(335\) 21.5468 1.17723
\(336\) 1.92027 0.104759
\(337\) 2.39027 0.130206 0.0651031 0.997879i \(-0.479262\pi\)
0.0651031 + 0.997879i \(0.479262\pi\)
\(338\) −0.0950129 −0.00516802
\(339\) 24.8453 1.34941
\(340\) 0.651144 0.0353132
\(341\) 36.2063 1.96068
\(342\) −0.411518 −0.0222523
\(343\) −1.00000 −0.0539949
\(344\) 2.17771 0.117414
\(345\) 40.7094 2.19172
\(346\) −19.2037 −1.03239
\(347\) −0.211265 −0.0113413 −0.00567064 0.999984i \(-0.501805\pi\)
−0.00567064 + 0.999984i \(0.501805\pi\)
\(348\) 7.88471 0.422665
\(349\) 3.91333 0.209476 0.104738 0.994500i \(-0.466600\pi\)
0.104738 + 0.994500i \(0.466600\pi\)
\(350\) 1.40815 0.0752689
\(351\) 16.0697 0.857738
\(352\) 3.57947 0.190786
\(353\) 9.57877 0.509827 0.254913 0.966964i \(-0.417953\pi\)
0.254913 + 0.966964i \(0.417953\pi\)
\(354\) −15.7725 −0.838300
\(355\) 11.1967 0.594257
\(356\) 15.7350 0.833952
\(357\) −0.493939 −0.0261420
\(358\) −12.8897 −0.681244
\(359\) 28.8694 1.52367 0.761834 0.647772i \(-0.224299\pi\)
0.761834 + 0.647772i \(0.224299\pi\)
\(360\) 1.74021 0.0917171
\(361\) −18.6417 −0.981140
\(362\) 19.4900 1.02437
\(363\) −3.48063 −0.182686
\(364\) −3.61870 −0.189672
\(365\) 22.8934 1.19830
\(366\) −29.8643 −1.56103
\(367\) 2.06116 0.107591 0.0537957 0.998552i \(-0.482868\pi\)
0.0537957 + 0.998552i \(0.482868\pi\)
\(368\) 8.37463 0.436558
\(369\) 1.79782 0.0935910
\(370\) −10.4260 −0.542022
\(371\) −1.94415 −0.100935
\(372\) 19.4235 1.00706
\(373\) −9.76150 −0.505431 −0.252716 0.967541i \(-0.581324\pi\)
−0.252716 + 0.967541i \(0.581324\pi\)
\(374\) −0.920723 −0.0476094
\(375\) −17.4601 −0.901636
\(376\) −4.93647 −0.254579
\(377\) −14.8585 −0.765253
\(378\) 4.44074 0.228407
\(379\) 36.6366 1.88189 0.940947 0.338554i \(-0.109938\pi\)
0.940947 + 0.338554i \(0.109938\pi\)
\(380\) −1.51537 −0.0777370
\(381\) 19.4852 0.998258
\(382\) −21.3778 −1.09378
\(383\) 11.9608 0.611166 0.305583 0.952165i \(-0.401149\pi\)
0.305583 + 0.952165i \(0.401149\pi\)
\(384\) 1.92027 0.0979934
\(385\) −9.06118 −0.461800
\(386\) 3.51896 0.179110
\(387\) −1.49705 −0.0760991
\(388\) −11.1596 −0.566545
\(389\) −19.3100 −0.979054 −0.489527 0.871988i \(-0.662831\pi\)
−0.489527 + 0.871988i \(0.662831\pi\)
\(390\) −17.5906 −0.890737
\(391\) −2.15415 −0.108940
\(392\) −1.00000 −0.0505076
\(393\) −22.9311 −1.15672
\(394\) 12.9752 0.653680
\(395\) 6.16601 0.310246
\(396\) −2.46067 −0.123653
\(397\) 21.5798 1.08306 0.541528 0.840683i \(-0.317846\pi\)
0.541528 + 0.840683i \(0.317846\pi\)
\(398\) −24.2163 −1.21385
\(399\) 1.14952 0.0575479
\(400\) 1.40815 0.0704076
\(401\) 17.0332 0.850598 0.425299 0.905053i \(-0.360169\pi\)
0.425299 + 0.905053i \(0.360169\pi\)
\(402\) −16.3448 −0.815205
\(403\) −36.6032 −1.82333
\(404\) −4.51337 −0.224548
\(405\) 26.8072 1.33206
\(406\) −4.10604 −0.203779
\(407\) 14.7424 0.730756
\(408\) −0.493939 −0.0244536
\(409\) 36.8660 1.82290 0.911452 0.411406i \(-0.134962\pi\)
0.911452 + 0.411406i \(0.134962\pi\)
\(410\) 6.62031 0.326954
\(411\) −17.5778 −0.867051
\(412\) −6.56636 −0.323502
\(413\) 8.21369 0.404169
\(414\) −5.75706 −0.282944
\(415\) −4.69761 −0.230596
\(416\) −3.61870 −0.177422
\(417\) 0.638618 0.0312733
\(418\) 2.14275 0.104805
\(419\) −36.8813 −1.80177 −0.900884 0.434060i \(-0.857081\pi\)
−0.900884 + 0.434060i \(0.857081\pi\)
\(420\) −4.86104 −0.237194
\(421\) −8.50994 −0.414749 −0.207375 0.978262i \(-0.566492\pi\)
−0.207375 + 0.978262i \(0.566492\pi\)
\(422\) 17.3419 0.844190
\(423\) 3.39353 0.164999
\(424\) −1.94415 −0.0944161
\(425\) −0.362210 −0.0175698
\(426\) −8.49345 −0.411509
\(427\) 15.5521 0.752619
\(428\) −8.62604 −0.416956
\(429\) 24.8733 1.20089
\(430\) −5.51272 −0.265847
\(431\) 1.00000 0.0481683
\(432\) 4.44074 0.213655
\(433\) 26.8256 1.28916 0.644578 0.764539i \(-0.277033\pi\)
0.644578 + 0.764539i \(0.277033\pi\)
\(434\) −10.1150 −0.485535
\(435\) −19.9596 −0.956990
\(436\) 9.73455 0.466200
\(437\) 5.01324 0.239816
\(438\) −17.3663 −0.829793
\(439\) 29.2805 1.39748 0.698741 0.715375i \(-0.253744\pi\)
0.698741 + 0.715375i \(0.253744\pi\)
\(440\) −9.06118 −0.431975
\(441\) 0.687441 0.0327353
\(442\) 0.930816 0.0442744
\(443\) −27.1409 −1.28950 −0.644752 0.764392i \(-0.723039\pi\)
−0.644752 + 0.764392i \(0.723039\pi\)
\(444\) 7.90886 0.375338
\(445\) −39.8320 −1.88822
\(446\) −16.5519 −0.783755
\(447\) 13.2204 0.625303
\(448\) −1.00000 −0.0472456
\(449\) −4.32527 −0.204122 −0.102061 0.994778i \(-0.532544\pi\)
−0.102061 + 0.994778i \(0.532544\pi\)
\(450\) −0.968021 −0.0456329
\(451\) −9.36117 −0.440800
\(452\) −12.9385 −0.608574
\(453\) 3.17217 0.149042
\(454\) 4.67367 0.219346
\(455\) 9.16050 0.429451
\(456\) 1.14952 0.0538311
\(457\) 28.1770 1.31806 0.659032 0.752115i \(-0.270966\pi\)
0.659032 + 0.752115i \(0.270966\pi\)
\(458\) 22.0926 1.03232
\(459\) −1.14226 −0.0533163
\(460\) −21.1998 −0.988446
\(461\) 11.8908 0.553808 0.276904 0.960898i \(-0.410692\pi\)
0.276904 + 0.960898i \(0.410692\pi\)
\(462\) 6.87354 0.319786
\(463\) 19.8802 0.923910 0.461955 0.886903i \(-0.347148\pi\)
0.461955 + 0.886903i \(0.347148\pi\)
\(464\) −4.10604 −0.190618
\(465\) −49.1694 −2.28017
\(466\) 18.0457 0.835949
\(467\) −18.2222 −0.843222 −0.421611 0.906777i \(-0.638535\pi\)
−0.421611 + 0.906777i \(0.638535\pi\)
\(468\) 2.48764 0.114991
\(469\) 8.51172 0.393035
\(470\) 12.4963 0.576413
\(471\) 17.2313 0.793976
\(472\) 8.21369 0.378066
\(473\) 7.79504 0.358416
\(474\) −4.67736 −0.214838
\(475\) 0.842951 0.0386773
\(476\) 0.257224 0.0117898
\(477\) 1.33649 0.0611935
\(478\) 22.6294 1.03504
\(479\) 33.3364 1.52318 0.761590 0.648059i \(-0.224419\pi\)
0.761590 + 0.648059i \(0.224419\pi\)
\(480\) −4.86104 −0.221875
\(481\) −14.9040 −0.679566
\(482\) 4.88488 0.222500
\(483\) 16.0816 0.731736
\(484\) 1.81257 0.0823896
\(485\) 28.2499 1.28276
\(486\) −7.01296 −0.318114
\(487\) 23.6231 1.07047 0.535233 0.844704i \(-0.320224\pi\)
0.535233 + 0.844704i \(0.320224\pi\)
\(488\) 15.5521 0.704011
\(489\) −24.9314 −1.12744
\(490\) 2.53143 0.114358
\(491\) 25.5752 1.15419 0.577097 0.816676i \(-0.304186\pi\)
0.577097 + 0.816676i \(0.304186\pi\)
\(492\) −5.02197 −0.226408
\(493\) 1.05617 0.0475675
\(494\) −2.16624 −0.0974636
\(495\) 6.22902 0.279974
\(496\) −10.1150 −0.454177
\(497\) 4.42305 0.198401
\(498\) 3.56347 0.159683
\(499\) 7.94164 0.355517 0.177758 0.984074i \(-0.443115\pi\)
0.177758 + 0.984074i \(0.443115\pi\)
\(500\) 9.09252 0.406630
\(501\) −8.35145 −0.373115
\(502\) −5.84078 −0.260687
\(503\) 13.3794 0.596558 0.298279 0.954479i \(-0.403587\pi\)
0.298279 + 0.954479i \(0.403587\pi\)
\(504\) 0.687441 0.0306210
\(505\) 11.4253 0.508418
\(506\) 29.9767 1.33263
\(507\) −0.182451 −0.00810292
\(508\) −10.1471 −0.450206
\(509\) −29.4965 −1.30741 −0.653705 0.756750i \(-0.726786\pi\)
−0.653705 + 0.756750i \(0.726786\pi\)
\(510\) 1.25037 0.0553675
\(511\) 9.04366 0.400068
\(512\) −1.00000 −0.0441942
\(513\) 2.65833 0.117368
\(514\) −5.57160 −0.245753
\(515\) 16.6223 0.732466
\(516\) 4.18179 0.184093
\(517\) −17.6699 −0.777122
\(518\) −4.11862 −0.180962
\(519\) −36.8762 −1.61869
\(520\) 9.16050 0.401715
\(521\) −3.49588 −0.153157 −0.0765787 0.997064i \(-0.524400\pi\)
−0.0765787 + 0.997064i \(0.524400\pi\)
\(522\) 2.82266 0.123544
\(523\) −37.7659 −1.65139 −0.825693 0.564120i \(-0.809216\pi\)
−0.825693 + 0.564120i \(0.809216\pi\)
\(524\) 11.9416 0.521672
\(525\) 2.70403 0.118014
\(526\) 21.9048 0.955093
\(527\) 2.60181 0.113337
\(528\) 6.87354 0.299133
\(529\) 47.1344 2.04932
\(530\) 4.92148 0.213775
\(531\) −5.64643 −0.245034
\(532\) −0.598623 −0.0259536
\(533\) 9.46379 0.409922
\(534\) 30.2154 1.30755
\(535\) 21.8362 0.944063
\(536\) 8.51172 0.367650
\(537\) −24.7518 −1.06812
\(538\) −15.3493 −0.661757
\(539\) −3.57947 −0.154178
\(540\) −11.2414 −0.483754
\(541\) −4.69716 −0.201947 −0.100973 0.994889i \(-0.532196\pi\)
−0.100973 + 0.994889i \(0.532196\pi\)
\(542\) −29.7738 −1.27889
\(543\) 37.4260 1.60611
\(544\) 0.257224 0.0110284
\(545\) −24.6423 −1.05556
\(546\) −6.94889 −0.297385
\(547\) 26.8344 1.14736 0.573679 0.819081i \(-0.305516\pi\)
0.573679 + 0.819081i \(0.305516\pi\)
\(548\) 9.15383 0.391032
\(549\) −10.6911 −0.456287
\(550\) 5.04043 0.214925
\(551\) −2.45797 −0.104713
\(552\) 16.0816 0.684477
\(553\) 2.43578 0.103580
\(554\) 23.7870 1.01061
\(555\) −20.0207 −0.849833
\(556\) −0.332567 −0.0141040
\(557\) −37.7660 −1.60020 −0.800098 0.599869i \(-0.795219\pi\)
−0.800098 + 0.599869i \(0.795219\pi\)
\(558\) 6.95346 0.294363
\(559\) −7.88048 −0.333309
\(560\) 2.53143 0.106973
\(561\) −1.76804 −0.0746466
\(562\) −1.87745 −0.0791956
\(563\) 44.6848 1.88324 0.941621 0.336676i \(-0.109303\pi\)
0.941621 + 0.336676i \(0.109303\pi\)
\(564\) −9.47935 −0.399153
\(565\) 32.7528 1.37792
\(566\) 15.9527 0.670543
\(567\) 10.5897 0.444728
\(568\) 4.42305 0.185587
\(569\) 44.7601 1.87644 0.938221 0.346037i \(-0.112473\pi\)
0.938221 + 0.346037i \(0.112473\pi\)
\(570\) −2.90993 −0.121883
\(571\) −12.0269 −0.503310 −0.251655 0.967817i \(-0.580975\pi\)
−0.251655 + 0.967817i \(0.580975\pi\)
\(572\) −12.9530 −0.541593
\(573\) −41.0512 −1.71494
\(574\) 2.61524 0.109158
\(575\) 11.7927 0.491792
\(576\) 0.687441 0.0286434
\(577\) −35.1423 −1.46299 −0.731497 0.681845i \(-0.761178\pi\)
−0.731497 + 0.681845i \(0.761178\pi\)
\(578\) 16.9338 0.704355
\(579\) 6.75736 0.280826
\(580\) 10.3942 0.431594
\(581\) −1.85571 −0.0769879
\(582\) −21.4295 −0.888283
\(583\) −6.95900 −0.288212
\(584\) 9.04366 0.374229
\(585\) −6.29730 −0.260361
\(586\) 6.31742 0.260970
\(587\) −29.4813 −1.21682 −0.608412 0.793621i \(-0.708193\pi\)
−0.608412 + 0.793621i \(0.708193\pi\)
\(588\) −1.92027 −0.0791906
\(589\) −6.05506 −0.249495
\(590\) −20.7924 −0.856010
\(591\) 24.9159 1.02490
\(592\) −4.11862 −0.169274
\(593\) 21.0135 0.862919 0.431460 0.902132i \(-0.357999\pi\)
0.431460 + 0.902132i \(0.357999\pi\)
\(594\) 15.8955 0.652199
\(595\) −0.651144 −0.0266943
\(596\) −6.88464 −0.282006
\(597\) −46.5019 −1.90320
\(598\) −30.3053 −1.23928
\(599\) −26.3189 −1.07536 −0.537680 0.843149i \(-0.680699\pi\)
−0.537680 + 0.843149i \(0.680699\pi\)
\(600\) 2.70403 0.110392
\(601\) −12.3216 −0.502610 −0.251305 0.967908i \(-0.580860\pi\)
−0.251305 + 0.967908i \(0.580860\pi\)
\(602\) −2.17771 −0.0887568
\(603\) −5.85130 −0.238283
\(604\) −1.65194 −0.0672165
\(605\) −4.58840 −0.186545
\(606\) −8.66689 −0.352068
\(607\) −16.6222 −0.674673 −0.337336 0.941384i \(-0.609526\pi\)
−0.337336 + 0.941384i \(0.609526\pi\)
\(608\) −0.598623 −0.0242774
\(609\) −7.88471 −0.319504
\(610\) −39.3691 −1.59401
\(611\) 17.8636 0.722684
\(612\) −0.176826 −0.00714776
\(613\) −44.6724 −1.80430 −0.902151 0.431420i \(-0.858013\pi\)
−0.902151 + 0.431420i \(0.858013\pi\)
\(614\) −12.5877 −0.507996
\(615\) 12.7128 0.512629
\(616\) −3.57947 −0.144221
\(617\) −19.8383 −0.798662 −0.399331 0.916807i \(-0.630758\pi\)
−0.399331 + 0.916807i \(0.630758\pi\)
\(618\) −12.6092 −0.507216
\(619\) 33.1395 1.33199 0.665994 0.745958i \(-0.268008\pi\)
0.665994 + 0.745958i \(0.268008\pi\)
\(620\) 25.6054 1.02834
\(621\) 37.1896 1.49237
\(622\) 25.4835 1.02180
\(623\) −15.7350 −0.630408
\(624\) −6.94889 −0.278178
\(625\) −30.0579 −1.20231
\(626\) −14.0108 −0.559986
\(627\) 4.11466 0.164324
\(628\) −8.97337 −0.358076
\(629\) 1.05941 0.0422412
\(630\) −1.74021 −0.0693316
\(631\) 35.8455 1.42699 0.713493 0.700662i \(-0.247112\pi\)
0.713493 + 0.700662i \(0.247112\pi\)
\(632\) 2.43578 0.0968901
\(633\) 33.3011 1.32360
\(634\) −30.6658 −1.21789
\(635\) 25.6867 1.01935
\(636\) −3.73329 −0.148034
\(637\) 3.61870 0.143378
\(638\) −14.6974 −0.581877
\(639\) −3.04058 −0.120284
\(640\) 2.53143 0.100064
\(641\) 23.4067 0.924508 0.462254 0.886748i \(-0.347041\pi\)
0.462254 + 0.886748i \(0.347041\pi\)
\(642\) −16.5643 −0.653742
\(643\) 28.1021 1.10824 0.554119 0.832437i \(-0.313055\pi\)
0.554119 + 0.832437i \(0.313055\pi\)
\(644\) −8.37463 −0.330007
\(645\) −10.5859 −0.416820
\(646\) 0.153980 0.00605825
\(647\) 28.8652 1.13481 0.567404 0.823440i \(-0.307948\pi\)
0.567404 + 0.823440i \(0.307948\pi\)
\(648\) 10.5897 0.416005
\(649\) 29.4006 1.15408
\(650\) −5.09568 −0.199869
\(651\) −19.4235 −0.761268
\(652\) 12.9833 0.508465
\(653\) 17.7438 0.694368 0.347184 0.937797i \(-0.387138\pi\)
0.347184 + 0.937797i \(0.387138\pi\)
\(654\) 18.6930 0.730953
\(655\) −30.2294 −1.18116
\(656\) 2.61524 0.102108
\(657\) −6.21698 −0.242548
\(658\) 4.93647 0.192443
\(659\) 27.0341 1.05310 0.526550 0.850144i \(-0.323485\pi\)
0.526550 + 0.850144i \(0.323485\pi\)
\(660\) −17.3999 −0.677291
\(661\) 11.8516 0.460973 0.230486 0.973076i \(-0.425968\pi\)
0.230486 + 0.973076i \(0.425968\pi\)
\(662\) 17.5804 0.683281
\(663\) 1.78742 0.0694176
\(664\) −1.85571 −0.0720156
\(665\) 1.51537 0.0587636
\(666\) 2.83130 0.109711
\(667\) −34.3866 −1.33145
\(668\) 4.34910 0.168272
\(669\) −31.7841 −1.22885
\(670\) −21.5468 −0.832427
\(671\) 55.6682 2.14905
\(672\) −1.92027 −0.0740761
\(673\) 3.23045 0.124525 0.0622624 0.998060i \(-0.480168\pi\)
0.0622624 + 0.998060i \(0.480168\pi\)
\(674\) −2.39027 −0.0920697
\(675\) 6.25324 0.240687
\(676\) 0.0950129 0.00365434
\(677\) −42.4144 −1.63012 −0.815059 0.579378i \(-0.803295\pi\)
−0.815059 + 0.579378i \(0.803295\pi\)
\(678\) −24.8453 −0.954180
\(679\) 11.1596 0.428268
\(680\) −0.651144 −0.0249702
\(681\) 8.97472 0.343912
\(682\) −36.2063 −1.38641
\(683\) −15.5111 −0.593514 −0.296757 0.954953i \(-0.595905\pi\)
−0.296757 + 0.954953i \(0.595905\pi\)
\(684\) 0.411518 0.0157348
\(685\) −23.1723 −0.885368
\(686\) 1.00000 0.0381802
\(687\) 42.4237 1.61857
\(688\) −2.17771 −0.0830244
\(689\) 7.03529 0.268023
\(690\) −40.7094 −1.54978
\(691\) 19.0728 0.725565 0.362782 0.931874i \(-0.381827\pi\)
0.362782 + 0.931874i \(0.381827\pi\)
\(692\) 19.2037 0.730013
\(693\) 2.46067 0.0934731
\(694\) 0.211265 0.00801949
\(695\) 0.841870 0.0319339
\(696\) −7.88471 −0.298869
\(697\) −0.672702 −0.0254804
\(698\) −3.91333 −0.148122
\(699\) 34.6526 1.31068
\(700\) −1.40815 −0.0532231
\(701\) 10.1492 0.383330 0.191665 0.981460i \(-0.438611\pi\)
0.191665 + 0.981460i \(0.438611\pi\)
\(702\) −16.0697 −0.606513
\(703\) −2.46550 −0.0929880
\(704\) −3.57947 −0.134906
\(705\) 23.9963 0.903755
\(706\) −9.57877 −0.360502
\(707\) 4.51337 0.169743
\(708\) 15.7725 0.592767
\(709\) −4.71016 −0.176894 −0.0884469 0.996081i \(-0.528190\pi\)
−0.0884469 + 0.996081i \(0.528190\pi\)
\(710\) −11.1967 −0.420203
\(711\) −1.67445 −0.0627969
\(712\) −15.7350 −0.589693
\(713\) −84.7093 −3.17239
\(714\) 0.493939 0.0184852
\(715\) 32.7897 1.22627
\(716\) 12.8897 0.481712
\(717\) 43.4546 1.62284
\(718\) −28.8694 −1.07740
\(719\) −27.4159 −1.02244 −0.511220 0.859450i \(-0.670806\pi\)
−0.511220 + 0.859450i \(0.670806\pi\)
\(720\) −1.74021 −0.0648538
\(721\) 6.56636 0.244544
\(722\) 18.6417 0.693770
\(723\) 9.38029 0.348857
\(724\) −19.4900 −0.724340
\(725\) −5.78193 −0.214735
\(726\) 3.48063 0.129178
\(727\) 12.8952 0.478256 0.239128 0.970988i \(-0.423139\pi\)
0.239128 + 0.970988i \(0.423139\pi\)
\(728\) 3.61870 0.134118
\(729\) 18.3025 0.677869
\(730\) −22.8934 −0.847324
\(731\) 0.560158 0.0207182
\(732\) 29.8643 1.10381
\(733\) 36.0673 1.33217 0.666087 0.745874i \(-0.267968\pi\)
0.666087 + 0.745874i \(0.267968\pi\)
\(734\) −2.06116 −0.0760787
\(735\) 4.86104 0.179302
\(736\) −8.37463 −0.308693
\(737\) 30.4674 1.12228
\(738\) −1.79782 −0.0661788
\(739\) 23.6268 0.869124 0.434562 0.900642i \(-0.356903\pi\)
0.434562 + 0.900642i \(0.356903\pi\)
\(740\) 10.4260 0.383267
\(741\) −4.15976 −0.152813
\(742\) 1.94415 0.0713719
\(743\) −47.4064 −1.73917 −0.869586 0.493782i \(-0.835614\pi\)
−0.869586 + 0.493782i \(0.835614\pi\)
\(744\) −19.4235 −0.712101
\(745\) 17.4280 0.638513
\(746\) 9.76150 0.357394
\(747\) 1.27569 0.0466751
\(748\) 0.920723 0.0336650
\(749\) 8.62604 0.315189
\(750\) 17.4601 0.637553
\(751\) −47.1565 −1.72076 −0.860382 0.509650i \(-0.829775\pi\)
−0.860382 + 0.509650i \(0.829775\pi\)
\(752\) 4.93647 0.180014
\(753\) −11.2159 −0.408730
\(754\) 14.8585 0.541116
\(755\) 4.18178 0.152190
\(756\) −4.44074 −0.161508
\(757\) 33.2278 1.20769 0.603843 0.797103i \(-0.293635\pi\)
0.603843 + 0.797103i \(0.293635\pi\)
\(758\) −36.6366 −1.33070
\(759\) 57.5634 2.08942
\(760\) 1.51537 0.0549683
\(761\) −24.4532 −0.886427 −0.443214 0.896416i \(-0.646162\pi\)
−0.443214 + 0.896416i \(0.646162\pi\)
\(762\) −19.4852 −0.705875
\(763\) −9.73455 −0.352414
\(764\) 21.3778 0.773422
\(765\) 0.447623 0.0161838
\(766\) −11.9608 −0.432160
\(767\) −29.7229 −1.07323
\(768\) −1.92027 −0.0692918
\(769\) 7.81428 0.281790 0.140895 0.990025i \(-0.455002\pi\)
0.140895 + 0.990025i \(0.455002\pi\)
\(770\) 9.06118 0.326542
\(771\) −10.6990 −0.385315
\(772\) −3.51896 −0.126650
\(773\) 50.5238 1.81721 0.908607 0.417653i \(-0.137147\pi\)
0.908607 + 0.417653i \(0.137147\pi\)
\(774\) 1.49705 0.0538102
\(775\) −14.2434 −0.511640
\(776\) 11.1596 0.400608
\(777\) −7.90886 −0.283729
\(778\) 19.3100 0.692296
\(779\) 1.56554 0.0560914
\(780\) 17.5906 0.629846
\(781\) 15.8322 0.566519
\(782\) 2.15415 0.0770323
\(783\) −18.2339 −0.651625
\(784\) 1.00000 0.0357143
\(785\) 22.7155 0.810750
\(786\) 22.9311 0.817926
\(787\) 23.8235 0.849217 0.424608 0.905377i \(-0.360412\pi\)
0.424608 + 0.905377i \(0.360412\pi\)
\(788\) −12.9752 −0.462222
\(789\) 42.0631 1.49749
\(790\) −6.16601 −0.219377
\(791\) 12.9385 0.460039
\(792\) 2.46067 0.0874361
\(793\) −56.2784 −1.99851
\(794\) −21.5798 −0.765837
\(795\) 9.45057 0.335177
\(796\) 24.2163 0.858325
\(797\) −6.73393 −0.238528 −0.119264 0.992863i \(-0.538054\pi\)
−0.119264 + 0.992863i \(0.538054\pi\)
\(798\) −1.14952 −0.0406925
\(799\) −1.26978 −0.0449214
\(800\) −1.40815 −0.0497857
\(801\) 10.8169 0.382195
\(802\) −17.0332 −0.601464
\(803\) 32.3715 1.14236
\(804\) 16.3448 0.576437
\(805\) 21.1998 0.747195
\(806\) 36.6032 1.28929
\(807\) −29.4749 −1.03757
\(808\) 4.51337 0.158780
\(809\) 11.4594 0.402892 0.201446 0.979500i \(-0.435436\pi\)
0.201446 + 0.979500i \(0.435436\pi\)
\(810\) −26.8072 −0.941910
\(811\) 42.2035 1.48196 0.740982 0.671525i \(-0.234360\pi\)
0.740982 + 0.671525i \(0.234360\pi\)
\(812\) 4.10604 0.144094
\(813\) −57.1738 −2.00517
\(814\) −14.7424 −0.516722
\(815\) −32.8663 −1.15126
\(816\) 0.493939 0.0172913
\(817\) −1.30363 −0.0456081
\(818\) −36.8660 −1.28899
\(819\) −2.48764 −0.0869253
\(820\) −6.62031 −0.231191
\(821\) −41.7478 −1.45701 −0.728504 0.685042i \(-0.759784\pi\)
−0.728504 + 0.685042i \(0.759784\pi\)
\(822\) 17.5778 0.613097
\(823\) −31.4625 −1.09671 −0.548357 0.836244i \(-0.684747\pi\)
−0.548357 + 0.836244i \(0.684747\pi\)
\(824\) 6.56636 0.228750
\(825\) 9.67899 0.336979
\(826\) −8.21369 −0.285791
\(827\) −31.4249 −1.09275 −0.546376 0.837540i \(-0.683993\pi\)
−0.546376 + 0.837540i \(0.683993\pi\)
\(828\) 5.75706 0.200072
\(829\) 28.0892 0.975580 0.487790 0.872961i \(-0.337803\pi\)
0.487790 + 0.872961i \(0.337803\pi\)
\(830\) 4.69761 0.163056
\(831\) 45.6774 1.58453
\(832\) 3.61870 0.125456
\(833\) −0.257224 −0.00891227
\(834\) −0.638618 −0.0221135
\(835\) −11.0094 −0.380998
\(836\) −2.14275 −0.0741085
\(837\) −44.9181 −1.55260
\(838\) 36.8813 1.27404
\(839\) 35.5109 1.22597 0.612987 0.790093i \(-0.289968\pi\)
0.612987 + 0.790093i \(0.289968\pi\)
\(840\) 4.86104 0.167722
\(841\) −12.1404 −0.418636
\(842\) 8.50994 0.293272
\(843\) −3.60522 −0.124170
\(844\) −17.3419 −0.596933
\(845\) −0.240519 −0.00827410
\(846\) −3.39353 −0.116672
\(847\) −1.81257 −0.0622807
\(848\) 1.94415 0.0667623
\(849\) 30.6335 1.05134
\(850\) 0.362210 0.0124237
\(851\) −34.4919 −1.18237
\(852\) 8.49345 0.290981
\(853\) 14.4060 0.493252 0.246626 0.969111i \(-0.420678\pi\)
0.246626 + 0.969111i \(0.420678\pi\)
\(854\) −15.5521 −0.532182
\(855\) −1.04173 −0.0356264
\(856\) 8.62604 0.294832
\(857\) −18.5416 −0.633370 −0.316685 0.948531i \(-0.602570\pi\)
−0.316685 + 0.948531i \(0.602570\pi\)
\(858\) −24.8733 −0.849161
\(859\) 47.9436 1.63582 0.817908 0.575349i \(-0.195134\pi\)
0.817908 + 0.575349i \(0.195134\pi\)
\(860\) 5.51272 0.187982
\(861\) 5.02197 0.171148
\(862\) −1.00000 −0.0340601
\(863\) −26.2151 −0.892371 −0.446185 0.894941i \(-0.647218\pi\)
−0.446185 + 0.894941i \(0.647218\pi\)
\(864\) −4.44074 −0.151077
\(865\) −48.6128 −1.65288
\(866\) −26.8256 −0.911571
\(867\) 32.5176 1.10435
\(868\) 10.1150 0.343325
\(869\) 8.71879 0.295765
\(870\) 19.9596 0.676694
\(871\) −30.8014 −1.04366
\(872\) −9.73455 −0.329653
\(873\) −7.67160 −0.259644
\(874\) −5.01324 −0.169575
\(875\) −9.09252 −0.307383
\(876\) 17.3663 0.586752
\(877\) −27.4345 −0.926396 −0.463198 0.886255i \(-0.653298\pi\)
−0.463198 + 0.886255i \(0.653298\pi\)
\(878\) −29.2805 −0.988169
\(879\) 12.1312 0.409174
\(880\) 9.06118 0.305452
\(881\) 19.5667 0.659218 0.329609 0.944118i \(-0.393083\pi\)
0.329609 + 0.944118i \(0.393083\pi\)
\(882\) −0.687441 −0.0231473
\(883\) −15.4238 −0.519054 −0.259527 0.965736i \(-0.583567\pi\)
−0.259527 + 0.965736i \(0.583567\pi\)
\(884\) −0.930816 −0.0313067
\(885\) −39.9271 −1.34213
\(886\) 27.1409 0.911817
\(887\) −24.2448 −0.814061 −0.407030 0.913415i \(-0.633436\pi\)
−0.407030 + 0.913415i \(0.633436\pi\)
\(888\) −7.90886 −0.265404
\(889\) 10.1471 0.340323
\(890\) 39.8320 1.33517
\(891\) 37.9056 1.26989
\(892\) 16.5519 0.554199
\(893\) 2.95508 0.0988880
\(894\) −13.2204 −0.442156
\(895\) −32.6295 −1.09068
\(896\) 1.00000 0.0334077
\(897\) −58.1944 −1.94305
\(898\) 4.32527 0.144336
\(899\) 41.5325 1.38519
\(900\) 0.968021 0.0322674
\(901\) −0.500080 −0.0166601
\(902\) 9.36117 0.311693
\(903\) −4.18179 −0.139161
\(904\) 12.9385 0.430327
\(905\) 49.3376 1.64004
\(906\) −3.17217 −0.105388
\(907\) 32.7706 1.08813 0.544066 0.839043i \(-0.316884\pi\)
0.544066 + 0.839043i \(0.316884\pi\)
\(908\) −4.67367 −0.155101
\(909\) −3.10267 −0.102909
\(910\) −9.16050 −0.303668
\(911\) −3.32266 −0.110085 −0.0550423 0.998484i \(-0.517529\pi\)
−0.0550423 + 0.998484i \(0.517529\pi\)
\(912\) −1.14952 −0.0380643
\(913\) −6.64245 −0.219833
\(914\) −28.1770 −0.932012
\(915\) −75.5993 −2.49924
\(916\) −22.0926 −0.729959
\(917\) −11.9416 −0.394347
\(918\) 1.14226 0.0377003
\(919\) 7.20609 0.237707 0.118853 0.992912i \(-0.462078\pi\)
0.118853 + 0.992912i \(0.462078\pi\)
\(920\) 21.1998 0.698937
\(921\) −24.1717 −0.796485
\(922\) −11.8908 −0.391602
\(923\) −16.0057 −0.526834
\(924\) −6.87354 −0.226123
\(925\) −5.79964 −0.190691
\(926\) −19.8802 −0.653303
\(927\) −4.51399 −0.148259
\(928\) 4.10604 0.134787
\(929\) −10.7846 −0.353832 −0.176916 0.984226i \(-0.556612\pi\)
−0.176916 + 0.984226i \(0.556612\pi\)
\(930\) 49.1694 1.61233
\(931\) 0.598623 0.0196191
\(932\) −18.0457 −0.591106
\(933\) 48.9353 1.60207
\(934\) 18.2222 0.596248
\(935\) −2.33075 −0.0762236
\(936\) −2.48764 −0.0813112
\(937\) −34.5629 −1.12912 −0.564560 0.825392i \(-0.690954\pi\)
−0.564560 + 0.825392i \(0.690954\pi\)
\(938\) −8.51172 −0.277917
\(939\) −26.9046 −0.877999
\(940\) −12.4963 −0.407585
\(941\) −38.3022 −1.24862 −0.624308 0.781179i \(-0.714619\pi\)
−0.624308 + 0.781179i \(0.714619\pi\)
\(942\) −17.2313 −0.561426
\(943\) 21.9017 0.713217
\(944\) −8.21369 −0.267333
\(945\) 11.2414 0.365684
\(946\) −7.79504 −0.253438
\(947\) −10.4257 −0.338789 −0.169395 0.985548i \(-0.554181\pi\)
−0.169395 + 0.985548i \(0.554181\pi\)
\(948\) 4.67736 0.151914
\(949\) −32.7263 −1.06234
\(950\) −0.842951 −0.0273490
\(951\) −58.8866 −1.90953
\(952\) −0.257224 −0.00833666
\(953\) −24.3620 −0.789162 −0.394581 0.918861i \(-0.629110\pi\)
−0.394581 + 0.918861i \(0.629110\pi\)
\(954\) −1.33649 −0.0432703
\(955\) −54.1165 −1.75117
\(956\) −22.6294 −0.731887
\(957\) −28.2230 −0.912321
\(958\) −33.3364 −1.07705
\(959\) −9.15383 −0.295593
\(960\) 4.86104 0.156889
\(961\) 71.3131 2.30042
\(962\) 14.9040 0.480526
\(963\) −5.92989 −0.191088
\(964\) −4.88488 −0.157331
\(965\) 8.90802 0.286759
\(966\) −16.0816 −0.517416
\(967\) 26.6509 0.857034 0.428517 0.903534i \(-0.359036\pi\)
0.428517 + 0.903534i \(0.359036\pi\)
\(968\) −1.81257 −0.0582583
\(969\) 0.295683 0.00949871
\(970\) −28.2499 −0.907050
\(971\) 39.9077 1.28070 0.640349 0.768084i \(-0.278790\pi\)
0.640349 + 0.768084i \(0.278790\pi\)
\(972\) 7.01296 0.224941
\(973\) 0.332567 0.0106616
\(974\) −23.6231 −0.756934
\(975\) −9.78509 −0.313374
\(976\) −15.5521 −0.497811
\(977\) 8.73674 0.279513 0.139757 0.990186i \(-0.455368\pi\)
0.139757 + 0.990186i \(0.455368\pi\)
\(978\) 24.9314 0.797219
\(979\) −56.3228 −1.80008
\(980\) −2.53143 −0.0808637
\(981\) 6.69192 0.213657
\(982\) −25.5752 −0.816138
\(983\) 22.3321 0.712283 0.356141 0.934432i \(-0.384092\pi\)
0.356141 + 0.934432i \(0.384092\pi\)
\(984\) 5.02197 0.160095
\(985\) 32.8458 1.04655
\(986\) −1.05617 −0.0336353
\(987\) 9.47935 0.301731
\(988\) 2.16624 0.0689172
\(989\) −18.2375 −0.579919
\(990\) −6.22902 −0.197971
\(991\) 0.307369 0.00976388 0.00488194 0.999988i \(-0.498446\pi\)
0.00488194 + 0.999988i \(0.498446\pi\)
\(992\) 10.1150 0.321151
\(993\) 33.7591 1.07131
\(994\) −4.42305 −0.140291
\(995\) −61.3020 −1.94340
\(996\) −3.56347 −0.112913
\(997\) −2.36172 −0.0747963 −0.0373982 0.999300i \(-0.511907\pi\)
−0.0373982 + 0.999300i \(0.511907\pi\)
\(998\) −7.94164 −0.251388
\(999\) −18.2897 −0.578661
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 \(a_p\))