Properties

Label 8042.2.a.c.1.17
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.02152 q^{3}\) \(+1.00000 q^{4}\) \(+3.49725 q^{5}\) \(+2.02152 q^{6}\) \(-2.15386 q^{7}\) \(-1.00000 q^{8}\) \(+1.08655 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.02152 q^{3}\) \(+1.00000 q^{4}\) \(+3.49725 q^{5}\) \(+2.02152 q^{6}\) \(-2.15386 q^{7}\) \(-1.00000 q^{8}\) \(+1.08655 q^{9}\) \(-3.49725 q^{10}\) \(+0.642902 q^{11}\) \(-2.02152 q^{12}\) \(-2.94242 q^{13}\) \(+2.15386 q^{14}\) \(-7.06976 q^{15}\) \(+1.00000 q^{16}\) \(+1.73141 q^{17}\) \(-1.08655 q^{18}\) \(+2.22670 q^{19}\) \(+3.49725 q^{20}\) \(+4.35408 q^{21}\) \(-0.642902 q^{22}\) \(+7.43269 q^{23}\) \(+2.02152 q^{24}\) \(+7.23075 q^{25}\) \(+2.94242 q^{26}\) \(+3.86809 q^{27}\) \(-2.15386 q^{28}\) \(-4.41638 q^{29}\) \(+7.06976 q^{30}\) \(-1.19527 q^{31}\) \(-1.00000 q^{32}\) \(-1.29964 q^{33}\) \(-1.73141 q^{34}\) \(-7.53260 q^{35}\) \(+1.08655 q^{36}\) \(+0.585059 q^{37}\) \(-2.22670 q^{38}\) \(+5.94816 q^{39}\) \(-3.49725 q^{40}\) \(+9.41374 q^{41}\) \(-4.35408 q^{42}\) \(+0.549585 q^{43}\) \(+0.642902 q^{44}\) \(+3.79992 q^{45}\) \(-7.43269 q^{46}\) \(+4.47659 q^{47}\) \(-2.02152 q^{48}\) \(-2.36087 q^{49}\) \(-7.23075 q^{50}\) \(-3.50008 q^{51}\) \(-2.94242 q^{52}\) \(-0.998661 q^{53}\) \(-3.86809 q^{54}\) \(+2.24839 q^{55}\) \(+2.15386 q^{56}\) \(-4.50133 q^{57}\) \(+4.41638 q^{58}\) \(+1.72800 q^{59}\) \(-7.06976 q^{60}\) \(-2.52227 q^{61}\) \(+1.19527 q^{62}\) \(-2.34027 q^{63}\) \(+1.00000 q^{64}\) \(-10.2904 q^{65}\) \(+1.29964 q^{66}\) \(-7.72287 q^{67}\) \(+1.73141 q^{68}\) \(-15.0253 q^{69}\) \(+7.53260 q^{70}\) \(+1.70003 q^{71}\) \(-1.08655 q^{72}\) \(-10.7477 q^{73}\) \(-0.585059 q^{74}\) \(-14.6171 q^{75}\) \(+2.22670 q^{76}\) \(-1.38472 q^{77}\) \(-5.94816 q^{78}\) \(-4.59092 q^{79}\) \(+3.49725 q^{80}\) \(-11.0791 q^{81}\) \(-9.41374 q^{82}\) \(+4.17517 q^{83}\) \(+4.35408 q^{84}\) \(+6.05518 q^{85}\) \(-0.549585 q^{86}\) \(+8.92781 q^{87}\) \(-0.642902 q^{88}\) \(-12.7294 q^{89}\) \(-3.79992 q^{90}\) \(+6.33757 q^{91}\) \(+7.43269 q^{92}\) \(+2.41627 q^{93}\) \(-4.47659 q^{94}\) \(+7.78734 q^{95}\) \(+2.02152 q^{96}\) \(-8.89877 q^{97}\) \(+2.36087 q^{98}\) \(+0.698543 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.02152 −1.16713 −0.583563 0.812068i \(-0.698342\pi\)
−0.583563 + 0.812068i \(0.698342\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.49725 1.56402 0.782009 0.623267i \(-0.214195\pi\)
0.782009 + 0.623267i \(0.214195\pi\)
\(6\) 2.02152 0.825282
\(7\) −2.15386 −0.814084 −0.407042 0.913409i \(-0.633440\pi\)
−0.407042 + 0.913409i \(0.633440\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.08655 0.362182
\(10\) −3.49725 −1.10593
\(11\) 0.642902 0.193842 0.0969211 0.995292i \(-0.469101\pi\)
0.0969211 + 0.995292i \(0.469101\pi\)
\(12\) −2.02152 −0.583563
\(13\) −2.94242 −0.816081 −0.408040 0.912964i \(-0.633788\pi\)
−0.408040 + 0.912964i \(0.633788\pi\)
\(14\) 2.15386 0.575644
\(15\) −7.06976 −1.82540
\(16\) 1.00000 0.250000
\(17\) 1.73141 0.419929 0.209964 0.977709i \(-0.432665\pi\)
0.209964 + 0.977709i \(0.432665\pi\)
\(18\) −1.08655 −0.256102
\(19\) 2.22670 0.510841 0.255420 0.966830i \(-0.417786\pi\)
0.255420 + 0.966830i \(0.417786\pi\)
\(20\) 3.49725 0.782009
\(21\) 4.35408 0.950138
\(22\) −0.642902 −0.137067
\(23\) 7.43269 1.54982 0.774911 0.632070i \(-0.217795\pi\)
0.774911 + 0.632070i \(0.217795\pi\)
\(24\) 2.02152 0.412641
\(25\) 7.23075 1.44615
\(26\) 2.94242 0.577056
\(27\) 3.86809 0.744413
\(28\) −2.15386 −0.407042
\(29\) −4.41638 −0.820101 −0.410051 0.912063i \(-0.634489\pi\)
−0.410051 + 0.912063i \(0.634489\pi\)
\(30\) 7.06976 1.29076
\(31\) −1.19527 −0.214677 −0.107339 0.994223i \(-0.534233\pi\)
−0.107339 + 0.994223i \(0.534233\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.29964 −0.226238
\(34\) −1.73141 −0.296935
\(35\) −7.53260 −1.27324
\(36\) 1.08655 0.181091
\(37\) 0.585059 0.0961831 0.0480916 0.998843i \(-0.484686\pi\)
0.0480916 + 0.998843i \(0.484686\pi\)
\(38\) −2.22670 −0.361219
\(39\) 5.94816 0.952469
\(40\) −3.49725 −0.552964
\(41\) 9.41374 1.47018 0.735089 0.677970i \(-0.237140\pi\)
0.735089 + 0.677970i \(0.237140\pi\)
\(42\) −4.35408 −0.671849
\(43\) 0.549585 0.0838109 0.0419054 0.999122i \(-0.486657\pi\)
0.0419054 + 0.999122i \(0.486657\pi\)
\(44\) 0.642902 0.0969211
\(45\) 3.79992 0.566459
\(46\) −7.43269 −1.09589
\(47\) 4.47659 0.652978 0.326489 0.945201i \(-0.394134\pi\)
0.326489 + 0.945201i \(0.394134\pi\)
\(48\) −2.02152 −0.291781
\(49\) −2.36087 −0.337267
\(50\) −7.23075 −1.02258
\(51\) −3.50008 −0.490110
\(52\) −2.94242 −0.408040
\(53\) −0.998661 −0.137177 −0.0685883 0.997645i \(-0.521849\pi\)
−0.0685883 + 0.997645i \(0.521849\pi\)
\(54\) −3.86809 −0.526380
\(55\) 2.24839 0.303173
\(56\) 2.15386 0.287822
\(57\) −4.50133 −0.596216
\(58\) 4.41638 0.579899
\(59\) 1.72800 0.224966 0.112483 0.993654i \(-0.464120\pi\)
0.112483 + 0.993654i \(0.464120\pi\)
\(60\) −7.06976 −0.912702
\(61\) −2.52227 −0.322944 −0.161472 0.986877i \(-0.551624\pi\)
−0.161472 + 0.986877i \(0.551624\pi\)
\(62\) 1.19527 0.151800
\(63\) −2.34027 −0.294847
\(64\) 1.00000 0.125000
\(65\) −10.2904 −1.27636
\(66\) 1.29964 0.159975
\(67\) −7.72287 −0.943499 −0.471750 0.881733i \(-0.656377\pi\)
−0.471750 + 0.881733i \(0.656377\pi\)
\(68\) 1.73141 0.209964
\(69\) −15.0253 −1.80884
\(70\) 7.53260 0.900318
\(71\) 1.70003 0.201757 0.100879 0.994899i \(-0.467835\pi\)
0.100879 + 0.994899i \(0.467835\pi\)
\(72\) −1.08655 −0.128051
\(73\) −10.7477 −1.25793 −0.628964 0.777434i \(-0.716521\pi\)
−0.628964 + 0.777434i \(0.716521\pi\)
\(74\) −0.585059 −0.0680118
\(75\) −14.6171 −1.68784
\(76\) 2.22670 0.255420
\(77\) −1.38472 −0.157804
\(78\) −5.94816 −0.673497
\(79\) −4.59092 −0.516518 −0.258259 0.966076i \(-0.583149\pi\)
−0.258259 + 0.966076i \(0.583149\pi\)
\(80\) 3.49725 0.391004
\(81\) −11.0791 −1.23101
\(82\) −9.41374 −1.03957
\(83\) 4.17517 0.458284 0.229142 0.973393i \(-0.426408\pi\)
0.229142 + 0.973393i \(0.426408\pi\)
\(84\) 4.35408 0.475069
\(85\) 6.05518 0.656776
\(86\) −0.549585 −0.0592632
\(87\) 8.92781 0.957161
\(88\) −0.642902 −0.0685336
\(89\) −12.7294 −1.34932 −0.674658 0.738130i \(-0.735709\pi\)
−0.674658 + 0.738130i \(0.735709\pi\)
\(90\) −3.79992 −0.400547
\(91\) 6.33757 0.664358
\(92\) 7.43269 0.774911
\(93\) 2.41627 0.250555
\(94\) −4.47659 −0.461725
\(95\) 7.78734 0.798964
\(96\) 2.02152 0.206321
\(97\) −8.89877 −0.903534 −0.451767 0.892136i \(-0.649206\pi\)
−0.451767 + 0.892136i \(0.649206\pi\)
\(98\) 2.36087 0.238484
\(99\) 0.698543 0.0702062
\(100\) 7.23075 0.723075
\(101\) 19.9193 1.98204 0.991020 0.133716i \(-0.0426909\pi\)
0.991020 + 0.133716i \(0.0426909\pi\)
\(102\) 3.50008 0.346560
\(103\) 11.6970 1.15254 0.576272 0.817258i \(-0.304507\pi\)
0.576272 + 0.817258i \(0.304507\pi\)
\(104\) 2.94242 0.288528
\(105\) 15.2273 1.48603
\(106\) 0.998661 0.0969985
\(107\) 11.7161 1.13264 0.566320 0.824186i \(-0.308367\pi\)
0.566320 + 0.824186i \(0.308367\pi\)
\(108\) 3.86809 0.372207
\(109\) −6.28371 −0.601870 −0.300935 0.953645i \(-0.597299\pi\)
−0.300935 + 0.953645i \(0.597299\pi\)
\(110\) −2.24839 −0.214375
\(111\) −1.18271 −0.112258
\(112\) −2.15386 −0.203521
\(113\) 10.5949 0.996688 0.498344 0.866980i \(-0.333942\pi\)
0.498344 + 0.866980i \(0.333942\pi\)
\(114\) 4.50133 0.421588
\(115\) 25.9940 2.42395
\(116\) −4.41638 −0.410051
\(117\) −3.19708 −0.295570
\(118\) −1.72800 −0.159075
\(119\) −3.72922 −0.341857
\(120\) 7.06976 0.645378
\(121\) −10.5867 −0.962425
\(122\) 2.52227 0.228356
\(123\) −19.0301 −1.71588
\(124\) −1.19527 −0.107339
\(125\) 7.80151 0.697788
\(126\) 2.34027 0.208488
\(127\) 12.9073 1.14534 0.572668 0.819787i \(-0.305908\pi\)
0.572668 + 0.819787i \(0.305908\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.11100 −0.0978178
\(130\) 10.2904 0.902526
\(131\) −2.00531 −0.175204 −0.0876022 0.996156i \(-0.527920\pi\)
−0.0876022 + 0.996156i \(0.527920\pi\)
\(132\) −1.29964 −0.113119
\(133\) −4.79602 −0.415867
\(134\) 7.72287 0.667155
\(135\) 13.5277 1.16428
\(136\) −1.73141 −0.148467
\(137\) −6.16772 −0.526944 −0.263472 0.964667i \(-0.584868\pi\)
−0.263472 + 0.964667i \(0.584868\pi\)
\(138\) 15.0253 1.27904
\(139\) −8.87306 −0.752603 −0.376301 0.926497i \(-0.622804\pi\)
−0.376301 + 0.926497i \(0.622804\pi\)
\(140\) −7.53260 −0.636621
\(141\) −9.04953 −0.762108
\(142\) −1.70003 −0.142664
\(143\) −1.89169 −0.158191
\(144\) 1.08655 0.0905456
\(145\) −15.4452 −1.28265
\(146\) 10.7477 0.889490
\(147\) 4.77255 0.393633
\(148\) 0.585059 0.0480916
\(149\) −1.59975 −0.131057 −0.0655284 0.997851i \(-0.520873\pi\)
−0.0655284 + 0.997851i \(0.520873\pi\)
\(150\) 14.6171 1.19348
\(151\) 15.3028 1.24533 0.622664 0.782490i \(-0.286051\pi\)
0.622664 + 0.782490i \(0.286051\pi\)
\(152\) −2.22670 −0.180610
\(153\) 1.88126 0.152091
\(154\) 1.38472 0.111584
\(155\) −4.18016 −0.335759
\(156\) 5.94816 0.476234
\(157\) −3.45824 −0.275998 −0.137999 0.990432i \(-0.544067\pi\)
−0.137999 + 0.990432i \(0.544067\pi\)
\(158\) 4.59092 0.365234
\(159\) 2.01881 0.160102
\(160\) −3.49725 −0.276482
\(161\) −16.0090 −1.26169
\(162\) 11.0791 0.870453
\(163\) 6.03012 0.472315 0.236158 0.971715i \(-0.424112\pi\)
0.236158 + 0.971715i \(0.424112\pi\)
\(164\) 9.41374 0.735089
\(165\) −4.54517 −0.353841
\(166\) −4.17517 −0.324056
\(167\) 12.0460 0.932151 0.466075 0.884745i \(-0.345668\pi\)
0.466075 + 0.884745i \(0.345668\pi\)
\(168\) −4.35408 −0.335925
\(169\) −4.34216 −0.334012
\(170\) −6.05518 −0.464411
\(171\) 2.41942 0.185018
\(172\) 0.549585 0.0419054
\(173\) 23.1769 1.76211 0.881054 0.473015i \(-0.156834\pi\)
0.881054 + 0.473015i \(0.156834\pi\)
\(174\) −8.92781 −0.676815
\(175\) −15.5741 −1.17729
\(176\) 0.642902 0.0484606
\(177\) −3.49318 −0.262564
\(178\) 12.7294 0.954111
\(179\) −15.5092 −1.15921 −0.579607 0.814896i \(-0.696794\pi\)
−0.579607 + 0.814896i \(0.696794\pi\)
\(180\) 3.79992 0.283230
\(181\) −20.2179 −1.50278 −0.751392 0.659856i \(-0.770617\pi\)
−0.751392 + 0.659856i \(0.770617\pi\)
\(182\) −6.33757 −0.469772
\(183\) 5.09882 0.376916
\(184\) −7.43269 −0.547945
\(185\) 2.04610 0.150432
\(186\) −2.41627 −0.177169
\(187\) 1.11313 0.0814000
\(188\) 4.47659 0.326489
\(189\) −8.33133 −0.606015
\(190\) −7.78734 −0.564953
\(191\) 1.46415 0.105942 0.0529709 0.998596i \(-0.483131\pi\)
0.0529709 + 0.998596i \(0.483131\pi\)
\(192\) −2.02152 −0.145891
\(193\) 16.3124 1.17419 0.587097 0.809516i \(-0.300271\pi\)
0.587097 + 0.809516i \(0.300271\pi\)
\(194\) 8.89877 0.638895
\(195\) 20.8022 1.48968
\(196\) −2.36087 −0.168634
\(197\) 7.21408 0.513982 0.256991 0.966414i \(-0.417269\pi\)
0.256991 + 0.966414i \(0.417269\pi\)
\(198\) −0.698543 −0.0496433
\(199\) 3.36486 0.238529 0.119264 0.992863i \(-0.461946\pi\)
0.119264 + 0.992863i \(0.461946\pi\)
\(200\) −7.23075 −0.511292
\(201\) 15.6119 1.10118
\(202\) −19.9193 −1.40151
\(203\) 9.51228 0.667631
\(204\) −3.50008 −0.245055
\(205\) 32.9222 2.29939
\(206\) −11.6970 −0.814971
\(207\) 8.07596 0.561318
\(208\) −2.94242 −0.204020
\(209\) 1.43155 0.0990226
\(210\) −15.2273 −1.05078
\(211\) 27.3162 1.88053 0.940263 0.340448i \(-0.110579\pi\)
0.940263 + 0.340448i \(0.110579\pi\)
\(212\) −0.998661 −0.0685883
\(213\) −3.43666 −0.235476
\(214\) −11.7161 −0.800897
\(215\) 1.92203 0.131082
\(216\) −3.86809 −0.263190
\(217\) 2.57445 0.174765
\(218\) 6.28371 0.425587
\(219\) 21.7268 1.46816
\(220\) 2.24839 0.151586
\(221\) −5.09454 −0.342696
\(222\) 1.18271 0.0793783
\(223\) 16.7863 1.12410 0.562048 0.827105i \(-0.310014\pi\)
0.562048 + 0.827105i \(0.310014\pi\)
\(224\) 2.15386 0.143911
\(225\) 7.85655 0.523770
\(226\) −10.5949 −0.704765
\(227\) 24.7395 1.64202 0.821008 0.570916i \(-0.193412\pi\)
0.821008 + 0.570916i \(0.193412\pi\)
\(228\) −4.50133 −0.298108
\(229\) 4.21112 0.278279 0.139139 0.990273i \(-0.455566\pi\)
0.139139 + 0.990273i \(0.455566\pi\)
\(230\) −25.9940 −1.71399
\(231\) 2.79925 0.184177
\(232\) 4.41638 0.289950
\(233\) −15.6618 −1.02604 −0.513018 0.858378i \(-0.671473\pi\)
−0.513018 + 0.858378i \(0.671473\pi\)
\(234\) 3.19708 0.208999
\(235\) 15.6558 1.02127
\(236\) 1.72800 0.112483
\(237\) 9.28063 0.602842
\(238\) 3.72922 0.241730
\(239\) −19.5755 −1.26623 −0.633117 0.774056i \(-0.718225\pi\)
−0.633117 + 0.774056i \(0.718225\pi\)
\(240\) −7.06976 −0.456351
\(241\) −24.5795 −1.58331 −0.791653 0.610971i \(-0.790779\pi\)
−0.791653 + 0.610971i \(0.790779\pi\)
\(242\) 10.5867 0.680537
\(243\) 10.7923 0.692325
\(244\) −2.52227 −0.161472
\(245\) −8.25656 −0.527492
\(246\) 19.0301 1.21331
\(247\) −6.55190 −0.416887
\(248\) 1.19527 0.0758998
\(249\) −8.44019 −0.534876
\(250\) −7.80151 −0.493411
\(251\) −15.1881 −0.958667 −0.479333 0.877633i \(-0.659122\pi\)
−0.479333 + 0.877633i \(0.659122\pi\)
\(252\) −2.34027 −0.147423
\(253\) 4.77849 0.300421
\(254\) −12.9073 −0.809875
\(255\) −12.2407 −0.766540
\(256\) 1.00000 0.0625000
\(257\) 5.16747 0.322338 0.161169 0.986927i \(-0.448474\pi\)
0.161169 + 0.986927i \(0.448474\pi\)
\(258\) 1.11100 0.0691676
\(259\) −1.26014 −0.0783012
\(260\) −10.2904 −0.638182
\(261\) −4.79860 −0.297026
\(262\) 2.00531 0.123888
\(263\) 2.16179 0.133301 0.0666507 0.997776i \(-0.478769\pi\)
0.0666507 + 0.997776i \(0.478769\pi\)
\(264\) 1.29964 0.0799873
\(265\) −3.49257 −0.214547
\(266\) 4.79602 0.294063
\(267\) 25.7328 1.57482
\(268\) −7.72287 −0.471750
\(269\) 30.1665 1.83928 0.919642 0.392757i \(-0.128478\pi\)
0.919642 + 0.392757i \(0.128478\pi\)
\(270\) −13.5277 −0.823267
\(271\) −19.3988 −1.17839 −0.589196 0.807990i \(-0.700555\pi\)
−0.589196 + 0.807990i \(0.700555\pi\)
\(272\) 1.73141 0.104982
\(273\) −12.8115 −0.775389
\(274\) 6.16772 0.372606
\(275\) 4.64867 0.280325
\(276\) −15.0253 −0.904419
\(277\) −16.0873 −0.966590 −0.483295 0.875458i \(-0.660560\pi\)
−0.483295 + 0.875458i \(0.660560\pi\)
\(278\) 8.87306 0.532171
\(279\) −1.29872 −0.0777522
\(280\) 7.53260 0.450159
\(281\) 19.9018 1.18724 0.593620 0.804746i \(-0.297698\pi\)
0.593620 + 0.804746i \(0.297698\pi\)
\(282\) 9.04953 0.538892
\(283\) −11.3099 −0.672302 −0.336151 0.941808i \(-0.609125\pi\)
−0.336151 + 0.941808i \(0.609125\pi\)
\(284\) 1.70003 0.100879
\(285\) −15.7423 −0.932492
\(286\) 1.89169 0.111858
\(287\) −20.2759 −1.19685
\(288\) −1.08655 −0.0640254
\(289\) −14.0022 −0.823660
\(290\) 15.4452 0.906972
\(291\) 17.9891 1.05454
\(292\) −10.7477 −0.628964
\(293\) 5.95670 0.347994 0.173997 0.984746i \(-0.444332\pi\)
0.173997 + 0.984746i \(0.444332\pi\)
\(294\) −4.77255 −0.278341
\(295\) 6.04324 0.351851
\(296\) −0.585059 −0.0340059
\(297\) 2.48680 0.144299
\(298\) 1.59975 0.0926712
\(299\) −21.8701 −1.26478
\(300\) −14.6171 −0.843920
\(301\) −1.18373 −0.0682291
\(302\) −15.3028 −0.880579
\(303\) −40.2672 −2.31329
\(304\) 2.22670 0.127710
\(305\) −8.82101 −0.505090
\(306\) −1.88126 −0.107544
\(307\) −15.4762 −0.883273 −0.441636 0.897194i \(-0.645602\pi\)
−0.441636 + 0.897194i \(0.645602\pi\)
\(308\) −1.38472 −0.0789019
\(309\) −23.6458 −1.34516
\(310\) 4.18016 0.237417
\(311\) 25.7236 1.45865 0.729326 0.684166i \(-0.239834\pi\)
0.729326 + 0.684166i \(0.239834\pi\)
\(312\) −5.94816 −0.336749
\(313\) −8.70889 −0.492256 −0.246128 0.969237i \(-0.579158\pi\)
−0.246128 + 0.969237i \(0.579158\pi\)
\(314\) 3.45824 0.195160
\(315\) −8.18452 −0.461145
\(316\) −4.59092 −0.258259
\(317\) −2.20990 −0.124120 −0.0620601 0.998072i \(-0.519767\pi\)
−0.0620601 + 0.998072i \(0.519767\pi\)
\(318\) −2.01881 −0.113209
\(319\) −2.83930 −0.158970
\(320\) 3.49725 0.195502
\(321\) −23.6844 −1.32193
\(322\) 16.0090 0.892146
\(323\) 3.85534 0.214517
\(324\) −11.0791 −0.615503
\(325\) −21.2759 −1.18018
\(326\) −6.03012 −0.333977
\(327\) 12.7027 0.702458
\(328\) −9.41374 −0.519787
\(329\) −9.64197 −0.531579
\(330\) 4.54517 0.250203
\(331\) −24.1651 −1.32824 −0.664118 0.747628i \(-0.731193\pi\)
−0.664118 + 0.747628i \(0.731193\pi\)
\(332\) 4.17517 0.229142
\(333\) 0.635694 0.0348358
\(334\) −12.0460 −0.659130
\(335\) −27.0088 −1.47565
\(336\) 4.35408 0.237535
\(337\) −25.3401 −1.38036 −0.690181 0.723637i \(-0.742469\pi\)
−0.690181 + 0.723637i \(0.742469\pi\)
\(338\) 4.34216 0.236182
\(339\) −21.4179 −1.16326
\(340\) 6.05518 0.328388
\(341\) −0.768442 −0.0416135
\(342\) −2.41942 −0.130827
\(343\) 20.1620 1.08865
\(344\) −0.549585 −0.0296316
\(345\) −52.5473 −2.82905
\(346\) −23.1769 −1.24600
\(347\) 13.7829 0.739903 0.369951 0.929051i \(-0.379374\pi\)
0.369951 + 0.929051i \(0.379374\pi\)
\(348\) 8.92781 0.478581
\(349\) 2.28502 0.122314 0.0611572 0.998128i \(-0.480521\pi\)
0.0611572 + 0.998128i \(0.480521\pi\)
\(350\) 15.5741 0.832469
\(351\) −11.3815 −0.607501
\(352\) −0.642902 −0.0342668
\(353\) 3.99082 0.212410 0.106205 0.994344i \(-0.466130\pi\)
0.106205 + 0.994344i \(0.466130\pi\)
\(354\) 3.49318 0.185660
\(355\) 5.94545 0.315551
\(356\) −12.7294 −0.674658
\(357\) 7.53871 0.398991
\(358\) 15.5092 0.819688
\(359\) 12.2982 0.649072 0.324536 0.945873i \(-0.394792\pi\)
0.324536 + 0.945873i \(0.394792\pi\)
\(360\) −3.79992 −0.200274
\(361\) −14.0418 −0.739041
\(362\) 20.2179 1.06263
\(363\) 21.4012 1.12327
\(364\) 6.33757 0.332179
\(365\) −37.5876 −1.96742
\(366\) −5.09882 −0.266520
\(367\) −13.9872 −0.730128 −0.365064 0.930982i \(-0.618953\pi\)
−0.365064 + 0.930982i \(0.618953\pi\)
\(368\) 7.43269 0.387456
\(369\) 10.2285 0.532473
\(370\) −2.04610 −0.106372
\(371\) 2.15098 0.111673
\(372\) 2.41627 0.125278
\(373\) 29.8800 1.54713 0.773563 0.633719i \(-0.218473\pi\)
0.773563 + 0.633719i \(0.218473\pi\)
\(374\) −1.11313 −0.0575585
\(375\) −15.7709 −0.814406
\(376\) −4.47659 −0.230863
\(377\) 12.9948 0.669269
\(378\) 8.33133 0.428517
\(379\) 4.37390 0.224672 0.112336 0.993670i \(-0.464167\pi\)
0.112336 + 0.993670i \(0.464167\pi\)
\(380\) 7.78734 0.399482
\(381\) −26.0923 −1.33675
\(382\) −1.46415 −0.0749122
\(383\) 32.4114 1.65615 0.828074 0.560619i \(-0.189437\pi\)
0.828074 + 0.560619i \(0.189437\pi\)
\(384\) 2.02152 0.103160
\(385\) −4.84272 −0.246808
\(386\) −16.3124 −0.830281
\(387\) 0.597149 0.0303548
\(388\) −8.89877 −0.451767
\(389\) 29.9822 1.52016 0.760078 0.649832i \(-0.225161\pi\)
0.760078 + 0.649832i \(0.225161\pi\)
\(390\) −20.8022 −1.05336
\(391\) 12.8690 0.650815
\(392\) 2.36087 0.119242
\(393\) 4.05377 0.204486
\(394\) −7.21408 −0.363440
\(395\) −16.0556 −0.807844
\(396\) 0.698543 0.0351031
\(397\) 29.9500 1.50315 0.751574 0.659649i \(-0.229295\pi\)
0.751574 + 0.659649i \(0.229295\pi\)
\(398\) −3.36486 −0.168665
\(399\) 9.69525 0.485370
\(400\) 7.23075 0.361538
\(401\) 15.5388 0.775969 0.387985 0.921666i \(-0.373171\pi\)
0.387985 + 0.921666i \(0.373171\pi\)
\(402\) −15.6119 −0.778653
\(403\) 3.51699 0.175194
\(404\) 19.9193 0.991020
\(405\) −38.7462 −1.92532
\(406\) −9.51228 −0.472087
\(407\) 0.376136 0.0186444
\(408\) 3.50008 0.173280
\(409\) 13.7670 0.680733 0.340367 0.940293i \(-0.389449\pi\)
0.340367 + 0.940293i \(0.389449\pi\)
\(410\) −32.9222 −1.62591
\(411\) 12.4682 0.615010
\(412\) 11.6970 0.576272
\(413\) −3.72187 −0.183141
\(414\) −8.07596 −0.396912
\(415\) 14.6016 0.716765
\(416\) 2.94242 0.144264
\(417\) 17.9371 0.878382
\(418\) −1.43155 −0.0700195
\(419\) 27.8301 1.35959 0.679794 0.733404i \(-0.262069\pi\)
0.679794 + 0.733404i \(0.262069\pi\)
\(420\) 15.2273 0.743016
\(421\) 24.6876 1.20320 0.601600 0.798798i \(-0.294530\pi\)
0.601600 + 0.798798i \(0.294530\pi\)
\(422\) −27.3162 −1.32973
\(423\) 4.86403 0.236497
\(424\) 0.998661 0.0484993
\(425\) 12.5194 0.607281
\(426\) 3.43666 0.166507
\(427\) 5.43263 0.262903
\(428\) 11.7161 0.566320
\(429\) 3.82409 0.184629
\(430\) −1.92203 −0.0926887
\(431\) 4.81017 0.231698 0.115849 0.993267i \(-0.463041\pi\)
0.115849 + 0.993267i \(0.463041\pi\)
\(432\) 3.86809 0.186103
\(433\) 19.9556 0.959004 0.479502 0.877541i \(-0.340817\pi\)
0.479502 + 0.877541i \(0.340817\pi\)
\(434\) −2.57445 −0.123578
\(435\) 31.2228 1.49702
\(436\) −6.28371 −0.300935
\(437\) 16.5504 0.791713
\(438\) −21.7268 −1.03815
\(439\) −21.6464 −1.03313 −0.516563 0.856249i \(-0.672789\pi\)
−0.516563 + 0.856249i \(0.672789\pi\)
\(440\) −2.24839 −0.107188
\(441\) −2.56520 −0.122152
\(442\) 5.09454 0.242323
\(443\) −31.3307 −1.48857 −0.744284 0.667863i \(-0.767209\pi\)
−0.744284 + 0.667863i \(0.767209\pi\)
\(444\) −1.18271 −0.0561289
\(445\) −44.5180 −2.11035
\(446\) −16.7863 −0.794856
\(447\) 3.23393 0.152960
\(448\) −2.15386 −0.101760
\(449\) 1.16615 0.0550341 0.0275171 0.999621i \(-0.491240\pi\)
0.0275171 + 0.999621i \(0.491240\pi\)
\(450\) −7.85655 −0.370361
\(451\) 6.05211 0.284983
\(452\) 10.5949 0.498344
\(453\) −30.9350 −1.45345
\(454\) −24.7395 −1.16108
\(455\) 22.1641 1.03907
\(456\) 4.50133 0.210794
\(457\) 4.73128 0.221320 0.110660 0.993858i \(-0.464704\pi\)
0.110660 + 0.993858i \(0.464704\pi\)
\(458\) −4.21112 −0.196773
\(459\) 6.69725 0.312601
\(460\) 25.9940 1.21197
\(461\) −8.73944 −0.407036 −0.203518 0.979071i \(-0.565238\pi\)
−0.203518 + 0.979071i \(0.565238\pi\)
\(462\) −2.79925 −0.130233
\(463\) −41.3562 −1.92199 −0.960993 0.276572i \(-0.910802\pi\)
−0.960993 + 0.276572i \(0.910802\pi\)
\(464\) −4.41638 −0.205025
\(465\) 8.45028 0.391873
\(466\) 15.6618 0.725517
\(467\) −19.6447 −0.909047 −0.454524 0.890735i \(-0.650191\pi\)
−0.454524 + 0.890735i \(0.650191\pi\)
\(468\) −3.19708 −0.147785
\(469\) 16.6340 0.768087
\(470\) −15.6558 −0.722147
\(471\) 6.99091 0.322124
\(472\) −1.72800 −0.0795375
\(473\) 0.353329 0.0162461
\(474\) −9.28063 −0.426274
\(475\) 16.1008 0.738753
\(476\) −3.72922 −0.170929
\(477\) −1.08509 −0.0496829
\(478\) 19.5755 0.895363
\(479\) 28.5291 1.30353 0.651763 0.758422i \(-0.274030\pi\)
0.651763 + 0.758422i \(0.274030\pi\)
\(480\) 7.06976 0.322689
\(481\) −1.72149 −0.0784932
\(482\) 24.5795 1.11957
\(483\) 32.3625 1.47255
\(484\) −10.5867 −0.481213
\(485\) −31.1212 −1.41314
\(486\) −10.7923 −0.489548
\(487\) 7.51487 0.340531 0.170266 0.985398i \(-0.445537\pi\)
0.170266 + 0.985398i \(0.445537\pi\)
\(488\) 2.52227 0.114178
\(489\) −12.1900 −0.551251
\(490\) 8.25656 0.372993
\(491\) 12.2338 0.552106 0.276053 0.961142i \(-0.410974\pi\)
0.276053 + 0.961142i \(0.410974\pi\)
\(492\) −19.0301 −0.857942
\(493\) −7.64657 −0.344384
\(494\) 6.55190 0.294784
\(495\) 2.44298 0.109804
\(496\) −1.19527 −0.0536693
\(497\) −3.66164 −0.164247
\(498\) 8.44019 0.378214
\(499\) −27.7120 −1.24056 −0.620279 0.784381i \(-0.712981\pi\)
−0.620279 + 0.784381i \(0.712981\pi\)
\(500\) 7.80151 0.348894
\(501\) −24.3513 −1.08794
\(502\) 15.1881 0.677880
\(503\) 16.9979 0.757898 0.378949 0.925417i \(-0.376285\pi\)
0.378949 + 0.925417i \(0.376285\pi\)
\(504\) 2.34027 0.104244
\(505\) 69.6626 3.09994
\(506\) −4.77849 −0.212430
\(507\) 8.77777 0.389834
\(508\) 12.9073 0.572668
\(509\) −6.84593 −0.303440 −0.151720 0.988423i \(-0.548481\pi\)
−0.151720 + 0.988423i \(0.548481\pi\)
\(510\) 12.2407 0.542026
\(511\) 23.1492 1.02406
\(512\) −1.00000 −0.0441942
\(513\) 8.61308 0.380277
\(514\) −5.16747 −0.227927
\(515\) 40.9075 1.80260
\(516\) −1.11100 −0.0489089
\(517\) 2.87801 0.126575
\(518\) 1.26014 0.0553673
\(519\) −46.8526 −2.05660
\(520\) 10.2904 0.451263
\(521\) 36.6421 1.60532 0.802659 0.596438i \(-0.203418\pi\)
0.802659 + 0.596438i \(0.203418\pi\)
\(522\) 4.79860 0.210029
\(523\) −6.38212 −0.279071 −0.139535 0.990217i \(-0.544561\pi\)
−0.139535 + 0.990217i \(0.544561\pi\)
\(524\) −2.00531 −0.0876022
\(525\) 31.4833 1.37404
\(526\) −2.16179 −0.0942584
\(527\) −2.06951 −0.0901491
\(528\) −1.29964 −0.0565596
\(529\) 32.2448 1.40195
\(530\) 3.49257 0.151707
\(531\) 1.87755 0.0814787
\(532\) −4.79602 −0.207934
\(533\) −27.6992 −1.19978
\(534\) −25.7328 −1.11357
\(535\) 40.9742 1.77147
\(536\) 7.72287 0.333577
\(537\) 31.3522 1.35295
\(538\) −30.1665 −1.30057
\(539\) −1.51781 −0.0653767
\(540\) 13.5277 0.582138
\(541\) 1.38998 0.0597599 0.0298800 0.999553i \(-0.490487\pi\)
0.0298800 + 0.999553i \(0.490487\pi\)
\(542\) 19.3988 0.833248
\(543\) 40.8709 1.75394
\(544\) −1.73141 −0.0742337
\(545\) −21.9757 −0.941336
\(546\) 12.8115 0.548283
\(547\) 8.78084 0.375441 0.187721 0.982222i \(-0.439890\pi\)
0.187721 + 0.982222i \(0.439890\pi\)
\(548\) −6.16772 −0.263472
\(549\) −2.74056 −0.116964
\(550\) −4.64867 −0.198220
\(551\) −9.83397 −0.418941
\(552\) 15.0253 0.639520
\(553\) 9.88821 0.420489
\(554\) 16.0873 0.683482
\(555\) −4.13623 −0.175573
\(556\) −8.87306 −0.376301
\(557\) −11.1523 −0.472538 −0.236269 0.971688i \(-0.575925\pi\)
−0.236269 + 0.971688i \(0.575925\pi\)
\(558\) 1.29872 0.0549791
\(559\) −1.61711 −0.0683964
\(560\) −7.53260 −0.318310
\(561\) −2.25021 −0.0950040
\(562\) −19.9018 −0.839505
\(563\) 32.2555 1.35941 0.679704 0.733487i \(-0.262108\pi\)
0.679704 + 0.733487i \(0.262108\pi\)
\(564\) −9.04953 −0.381054
\(565\) 37.0531 1.55884
\(566\) 11.3099 0.475390
\(567\) 23.8628 1.00214
\(568\) −1.70003 −0.0713319
\(569\) −0.577039 −0.0241907 −0.0120954 0.999927i \(-0.503850\pi\)
−0.0120954 + 0.999927i \(0.503850\pi\)
\(570\) 15.7423 0.659371
\(571\) 27.0027 1.13003 0.565015 0.825081i \(-0.308870\pi\)
0.565015 + 0.825081i \(0.308870\pi\)
\(572\) −1.89169 −0.0790955
\(573\) −2.95980 −0.123647
\(574\) 20.2759 0.846300
\(575\) 53.7439 2.24128
\(576\) 1.08655 0.0452728
\(577\) −0.178303 −0.00742286 −0.00371143 0.999993i \(-0.501181\pi\)
−0.00371143 + 0.999993i \(0.501181\pi\)
\(578\) 14.0022 0.582415
\(579\) −32.9759 −1.37043
\(580\) −15.4452 −0.641326
\(581\) −8.99275 −0.373082
\(582\) −17.9891 −0.745670
\(583\) −0.642041 −0.0265906
\(584\) 10.7477 0.444745
\(585\) −11.1810 −0.462277
\(586\) −5.95670 −0.246069
\(587\) 6.00843 0.247994 0.123997 0.992283i \(-0.460429\pi\)
0.123997 + 0.992283i \(0.460429\pi\)
\(588\) 4.77255 0.196817
\(589\) −2.66152 −0.109666
\(590\) −6.04324 −0.248796
\(591\) −14.5834 −0.599882
\(592\) 0.585059 0.0240458
\(593\) 12.2715 0.503929 0.251965 0.967736i \(-0.418923\pi\)
0.251965 + 0.967736i \(0.418923\pi\)
\(594\) −2.48680 −0.102035
\(595\) −13.0420 −0.534671
\(596\) −1.59975 −0.0655284
\(597\) −6.80214 −0.278393
\(598\) 21.8701 0.894334
\(599\) 10.8323 0.442597 0.221298 0.975206i \(-0.428971\pi\)
0.221298 + 0.975206i \(0.428971\pi\)
\(600\) 14.6171 0.596741
\(601\) 4.39264 0.179179 0.0895897 0.995979i \(-0.471444\pi\)
0.0895897 + 0.995979i \(0.471444\pi\)
\(602\) 1.18373 0.0482452
\(603\) −8.39126 −0.341719
\(604\) 15.3028 0.622664
\(605\) −37.0243 −1.50525
\(606\) 40.2672 1.63574
\(607\) 16.0262 0.650482 0.325241 0.945631i \(-0.394555\pi\)
0.325241 + 0.945631i \(0.394555\pi\)
\(608\) −2.22670 −0.0903048
\(609\) −19.2293 −0.779210
\(610\) 8.82101 0.357152
\(611\) −13.1720 −0.532883
\(612\) 1.88126 0.0760454
\(613\) 31.4899 1.27186 0.635932 0.771745i \(-0.280616\pi\)
0.635932 + 0.771745i \(0.280616\pi\)
\(614\) 15.4762 0.624568
\(615\) −66.5529 −2.68367
\(616\) 1.38472 0.0557921
\(617\) 47.1116 1.89664 0.948321 0.317313i \(-0.102781\pi\)
0.948321 + 0.317313i \(0.102781\pi\)
\(618\) 23.6458 0.951174
\(619\) 18.2981 0.735464 0.367732 0.929932i \(-0.380134\pi\)
0.367732 + 0.929932i \(0.380134\pi\)
\(620\) −4.18016 −0.167879
\(621\) 28.7503 1.15371
\(622\) −25.7236 −1.03142
\(623\) 27.4174 1.09846
\(624\) 5.94816 0.238117
\(625\) −8.86996 −0.354798
\(626\) 8.70889 0.348077
\(627\) −2.89391 −0.115572
\(628\) −3.45824 −0.137999
\(629\) 1.01298 0.0403901
\(630\) 8.18452 0.326079
\(631\) 11.3852 0.453238 0.226619 0.973983i \(-0.427233\pi\)
0.226619 + 0.973983i \(0.427233\pi\)
\(632\) 4.59092 0.182617
\(633\) −55.2203 −2.19481
\(634\) 2.20990 0.0877662
\(635\) 45.1400 1.79133
\(636\) 2.01881 0.0800512
\(637\) 6.94668 0.275237
\(638\) 2.83930 0.112409
\(639\) 1.84717 0.0730728
\(640\) −3.49725 −0.138241
\(641\) 41.5729 1.64203 0.821016 0.570906i \(-0.193408\pi\)
0.821016 + 0.570906i \(0.193408\pi\)
\(642\) 23.6844 0.934747
\(643\) 27.1837 1.07202 0.536011 0.844211i \(-0.319931\pi\)
0.536011 + 0.844211i \(0.319931\pi\)
\(644\) −16.0090 −0.630843
\(645\) −3.88543 −0.152989
\(646\) −3.85534 −0.151686
\(647\) −47.4397 −1.86505 −0.932523 0.361110i \(-0.882398\pi\)
−0.932523 + 0.361110i \(0.882398\pi\)
\(648\) 11.0791 0.435226
\(649\) 1.11093 0.0436079
\(650\) 21.2759 0.834510
\(651\) −5.20431 −0.203973
\(652\) 6.03012 0.236158
\(653\) −34.6478 −1.35587 −0.677936 0.735121i \(-0.737126\pi\)
−0.677936 + 0.735121i \(0.737126\pi\)
\(654\) −12.7027 −0.496713
\(655\) −7.01306 −0.274023
\(656\) 9.41374 0.367545
\(657\) −11.6779 −0.455599
\(658\) 9.64197 0.375883
\(659\) 33.6518 1.31089 0.655444 0.755244i \(-0.272482\pi\)
0.655444 + 0.755244i \(0.272482\pi\)
\(660\) −4.54517 −0.176920
\(661\) −43.4029 −1.68818 −0.844089 0.536203i \(-0.819858\pi\)
−0.844089 + 0.536203i \(0.819858\pi\)
\(662\) 24.1651 0.939204
\(663\) 10.2987 0.399969
\(664\) −4.17517 −0.162028
\(665\) −16.7729 −0.650424
\(666\) −0.635694 −0.0246326
\(667\) −32.8256 −1.27101
\(668\) 12.0460 0.466075
\(669\) −33.9339 −1.31196
\(670\) 27.0088 1.04344
\(671\) −1.62157 −0.0626001
\(672\) −4.35408 −0.167962
\(673\) 12.9572 0.499464 0.249732 0.968315i \(-0.419657\pi\)
0.249732 + 0.968315i \(0.419657\pi\)
\(674\) 25.3401 0.976063
\(675\) 27.9692 1.07653
\(676\) −4.34216 −0.167006
\(677\) −2.48900 −0.0956600 −0.0478300 0.998855i \(-0.515231\pi\)
−0.0478300 + 0.998855i \(0.515231\pi\)
\(678\) 21.4179 0.822549
\(679\) 19.1667 0.735552
\(680\) −6.05518 −0.232205
\(681\) −50.0114 −1.91644
\(682\) 0.768442 0.0294252
\(683\) 21.3476 0.816843 0.408421 0.912794i \(-0.366079\pi\)
0.408421 + 0.912794i \(0.366079\pi\)
\(684\) 2.41942 0.0925088
\(685\) −21.5701 −0.824150
\(686\) −20.1620 −0.769790
\(687\) −8.51286 −0.324786
\(688\) 0.549585 0.0209527
\(689\) 2.93848 0.111947
\(690\) 52.5473 2.00044
\(691\) 11.7815 0.448188 0.224094 0.974568i \(-0.428058\pi\)
0.224094 + 0.974568i \(0.428058\pi\)
\(692\) 23.1769 0.881054
\(693\) −1.50457 −0.0571538
\(694\) −13.7829 −0.523190
\(695\) −31.0313 −1.17708
\(696\) −8.92781 −0.338408
\(697\) 16.2991 0.617371
\(698\) −2.28502 −0.0864894
\(699\) 31.6606 1.19751
\(700\) −15.5741 −0.588644
\(701\) −4.72292 −0.178382 −0.0891911 0.996015i \(-0.528428\pi\)
−0.0891911 + 0.996015i \(0.528428\pi\)
\(702\) 11.3815 0.429568
\(703\) 1.30275 0.0491343
\(704\) 0.642902 0.0242303
\(705\) −31.6485 −1.19195
\(706\) −3.99082 −0.150196
\(707\) −42.9034 −1.61355
\(708\) −3.49318 −0.131282
\(709\) 26.8042 1.00665 0.503326 0.864097i \(-0.332110\pi\)
0.503326 + 0.864097i \(0.332110\pi\)
\(710\) −5.94545 −0.223129
\(711\) −4.98824 −0.187074
\(712\) 12.7294 0.477055
\(713\) −8.88408 −0.332711
\(714\) −7.53871 −0.282129
\(715\) −6.61571 −0.247413
\(716\) −15.5092 −0.579607
\(717\) 39.5723 1.47785
\(718\) −12.2982 −0.458964
\(719\) −21.7152 −0.809841 −0.404920 0.914352i \(-0.632701\pi\)
−0.404920 + 0.914352i \(0.632701\pi\)
\(720\) 3.79992 0.141615
\(721\) −25.1938 −0.938267
\(722\) 14.0418 0.522581
\(723\) 49.6880 1.84792
\(724\) −20.2179 −0.751392
\(725\) −31.9338 −1.18599
\(726\) −21.4012 −0.794273
\(727\) 28.7190 1.06513 0.532564 0.846390i \(-0.321228\pi\)
0.532564 + 0.846390i \(0.321228\pi\)
\(728\) −6.33757 −0.234886
\(729\) 11.4203 0.422975
\(730\) 37.5876 1.39118
\(731\) 0.951557 0.0351946
\(732\) 5.09882 0.188458
\(733\) 26.4461 0.976810 0.488405 0.872617i \(-0.337579\pi\)
0.488405 + 0.872617i \(0.337579\pi\)
\(734\) 13.9872 0.516278
\(735\) 16.6908 0.615649
\(736\) −7.43269 −0.273972
\(737\) −4.96505 −0.182890
\(738\) −10.2285 −0.376515
\(739\) −16.1899 −0.595555 −0.297777 0.954635i \(-0.596245\pi\)
−0.297777 + 0.954635i \(0.596245\pi\)
\(740\) 2.04610 0.0752161
\(741\) 13.2448 0.486560
\(742\) −2.15098 −0.0789649
\(743\) −23.8998 −0.876799 −0.438399 0.898780i \(-0.644454\pi\)
−0.438399 + 0.898780i \(0.644454\pi\)
\(744\) −2.41627 −0.0885846
\(745\) −5.59474 −0.204975
\(746\) −29.8800 −1.09398
\(747\) 4.53652 0.165982
\(748\) 1.11313 0.0407000
\(749\) −25.2349 −0.922064
\(750\) 15.7709 0.575872
\(751\) −15.6871 −0.572431 −0.286215 0.958165i \(-0.592397\pi\)
−0.286215 + 0.958165i \(0.592397\pi\)
\(752\) 4.47659 0.163245
\(753\) 30.7031 1.11888
\(754\) −12.9948 −0.473244
\(755\) 53.5178 1.94771
\(756\) −8.33133 −0.303008
\(757\) 1.45948 0.0530456 0.0265228 0.999648i \(-0.491557\pi\)
0.0265228 + 0.999648i \(0.491557\pi\)
\(758\) −4.37390 −0.158867
\(759\) −9.65982 −0.350629
\(760\) −7.78734 −0.282477
\(761\) 26.5007 0.960649 0.480324 0.877091i \(-0.340519\pi\)
0.480324 + 0.877091i \(0.340519\pi\)
\(762\) 26.0923 0.945226
\(763\) 13.5343 0.489973
\(764\) 1.46415 0.0529709
\(765\) 6.57923 0.237873
\(766\) −32.4114 −1.17107
\(767\) −5.08449 −0.183590
\(768\) −2.02152 −0.0729454
\(769\) −6.55064 −0.236222 −0.118111 0.993000i \(-0.537684\pi\)
−0.118111 + 0.993000i \(0.537684\pi\)
\(770\) 4.84272 0.174520
\(771\) −10.4461 −0.376209
\(772\) 16.3124 0.587097
\(773\) −25.9131 −0.932028 −0.466014 0.884777i \(-0.654310\pi\)
−0.466014 + 0.884777i \(0.654310\pi\)
\(774\) −0.597149 −0.0214641
\(775\) −8.64271 −0.310455
\(776\) 8.89877 0.319447
\(777\) 2.54740 0.0913873
\(778\) −29.9822 −1.07491
\(779\) 20.9616 0.751028
\(780\) 20.8022 0.744839
\(781\) 1.09296 0.0391090
\(782\) −12.8690 −0.460196
\(783\) −17.0829 −0.610494
\(784\) −2.36087 −0.0843168
\(785\) −12.0943 −0.431665
\(786\) −4.05377 −0.144593
\(787\) −10.4513 −0.372548 −0.186274 0.982498i \(-0.559641\pi\)
−0.186274 + 0.982498i \(0.559641\pi\)
\(788\) 7.21408 0.256991
\(789\) −4.37010 −0.155580
\(790\) 16.0556 0.571232
\(791\) −22.8200 −0.811387
\(792\) −0.698543 −0.0248216
\(793\) 7.42158 0.263548
\(794\) −29.9500 −1.06289
\(795\) 7.06029 0.250403
\(796\) 3.36486 0.119264
\(797\) 23.5546 0.834347 0.417174 0.908827i \(-0.363021\pi\)
0.417174 + 0.908827i \(0.363021\pi\)
\(798\) −9.69525 −0.343208
\(799\) 7.75083 0.274205
\(800\) −7.23075 −0.255646
\(801\) −13.8311 −0.488698
\(802\) −15.5388 −0.548693
\(803\) −6.90975 −0.243840
\(804\) 15.6119 0.550591
\(805\) −55.9874 −1.97330
\(806\) −3.51699 −0.123881
\(807\) −60.9822 −2.14668
\(808\) −19.9193 −0.700757
\(809\) −16.7190 −0.587810 −0.293905 0.955835i \(-0.594955\pi\)
−0.293905 + 0.955835i \(0.594955\pi\)
\(810\) 38.7462 1.36140
\(811\) 41.2526 1.44857 0.724287 0.689499i \(-0.242169\pi\)
0.724287 + 0.689499i \(0.242169\pi\)
\(812\) 9.51228 0.333816
\(813\) 39.2150 1.37533
\(814\) −0.376136 −0.0131836
\(815\) 21.0888 0.738709
\(816\) −3.50008 −0.122527
\(817\) 1.22376 0.0428140
\(818\) −13.7670 −0.481351
\(819\) 6.88607 0.240619
\(820\) 32.9222 1.14969
\(821\) −41.9822 −1.46519 −0.732595 0.680665i \(-0.761691\pi\)
−0.732595 + 0.680665i \(0.761691\pi\)
\(822\) −12.4682 −0.434878
\(823\) 27.0241 0.942000 0.471000 0.882133i \(-0.343893\pi\)
0.471000 + 0.882133i \(0.343893\pi\)
\(824\) −11.6970 −0.407486
\(825\) −9.39738 −0.327175
\(826\) 3.72187 0.129500
\(827\) 56.1442 1.95233 0.976163 0.217040i \(-0.0696403\pi\)
0.976163 + 0.217040i \(0.0696403\pi\)
\(828\) 8.07596 0.280659
\(829\) 44.9217 1.56020 0.780098 0.625657i \(-0.215169\pi\)
0.780098 + 0.625657i \(0.215169\pi\)
\(830\) −14.6016 −0.506829
\(831\) 32.5207 1.12813
\(832\) −2.94242 −0.102010
\(833\) −4.08764 −0.141628
\(834\) −17.9371 −0.621110
\(835\) 42.1280 1.45790
\(836\) 1.43155 0.0495113
\(837\) −4.62341 −0.159808
\(838\) −27.8301 −0.961373
\(839\) 55.8999 1.92988 0.964940 0.262472i \(-0.0845378\pi\)
0.964940 + 0.262472i \(0.0845378\pi\)
\(840\) −15.2273 −0.525392
\(841\) −9.49558 −0.327434
\(842\) −24.6876 −0.850790
\(843\) −40.2318 −1.38566
\(844\) 27.3162 0.940263
\(845\) −15.1856 −0.522401
\(846\) −4.86403 −0.167229
\(847\) 22.8023 0.783495
\(848\) −0.998661 −0.0342942
\(849\) 22.8632 0.784661
\(850\) −12.5194 −0.429412
\(851\) 4.34856 0.149067
\(852\) −3.43666 −0.117738
\(853\) −18.9295 −0.648133 −0.324067 0.946034i \(-0.605050\pi\)
−0.324067 + 0.946034i \(0.605050\pi\)
\(854\) −5.43263 −0.185901
\(855\) 8.46131 0.289371
\(856\) −11.7161 −0.400449
\(857\) 4.72972 0.161564 0.0807821 0.996732i \(-0.474258\pi\)
0.0807821 + 0.996732i \(0.474258\pi\)
\(858\) −3.82409 −0.130552
\(859\) −29.1923 −0.996027 −0.498014 0.867169i \(-0.665937\pi\)
−0.498014 + 0.867169i \(0.665937\pi\)
\(860\) 1.92203 0.0655408
\(861\) 40.9882 1.39687
\(862\) −4.81017 −0.163835
\(863\) 2.90882 0.0990173 0.0495087 0.998774i \(-0.484234\pi\)
0.0495087 + 0.998774i \(0.484234\pi\)
\(864\) −3.86809 −0.131595
\(865\) 81.0555 2.75597
\(866\) −19.9556 −0.678119
\(867\) 28.3058 0.961314
\(868\) 2.57445 0.0873826
\(869\) −2.95151 −0.100123
\(870\) −31.2228 −1.05855
\(871\) 22.7239 0.769971
\(872\) 6.28371 0.212793
\(873\) −9.66893 −0.327244
\(874\) −16.5504 −0.559825
\(875\) −16.8034 −0.568058
\(876\) 21.7268 0.734080
\(877\) −5.43104 −0.183393 −0.0916966 0.995787i \(-0.529229\pi\)
−0.0916966 + 0.995787i \(0.529229\pi\)
\(878\) 21.6464 0.730530
\(879\) −12.0416 −0.406153
\(880\) 2.24839 0.0757932
\(881\) −3.91856 −0.132020 −0.0660099 0.997819i \(-0.521027\pi\)
−0.0660099 + 0.997819i \(0.521027\pi\)
\(882\) 2.56520 0.0863747
\(883\) 23.4133 0.787919 0.393960 0.919128i \(-0.371105\pi\)
0.393960 + 0.919128i \(0.371105\pi\)
\(884\) −5.09454 −0.171348
\(885\) −12.2165 −0.410654
\(886\) 31.3307 1.05258
\(887\) −9.36886 −0.314575 −0.157288 0.987553i \(-0.550275\pi\)
−0.157288 + 0.987553i \(0.550275\pi\)
\(888\) 1.18271 0.0396891
\(889\) −27.8005 −0.932400
\(890\) 44.5180 1.49225
\(891\) −7.12275 −0.238621
\(892\) 16.7863 0.562048
\(893\) 9.96805 0.333568
\(894\) −3.23393 −0.108159
\(895\) −54.2396 −1.81303
\(896\) 2.15386 0.0719555
\(897\) 44.2108 1.47616
\(898\) −1.16615 −0.0389150
\(899\) 5.27877 0.176057
\(900\) 7.85655 0.261885
\(901\) −1.72909 −0.0576044
\(902\) −6.05211 −0.201513
\(903\) 2.39294 0.0796319
\(904\) −10.5949 −0.352382
\(905\) −70.7070 −2.35038
\(906\) 30.9350 1.02775
\(907\) −2.74371 −0.0911036 −0.0455518 0.998962i \(-0.514505\pi\)
−0.0455518 + 0.998962i \(0.514505\pi\)
\(908\) 24.7395 0.821008
\(909\) 21.6432 0.717859
\(910\) −22.1641 −0.734732
\(911\) −6.33790 −0.209984 −0.104992 0.994473i \(-0.533482\pi\)
−0.104992 + 0.994473i \(0.533482\pi\)
\(912\) −4.50133 −0.149054
\(913\) 2.68423 0.0888349
\(914\) −4.73128 −0.156497
\(915\) 17.8319 0.589503
\(916\) 4.21112 0.139139
\(917\) 4.31916 0.142631
\(918\) −6.69725 −0.221042
\(919\) 31.5485 1.04069 0.520345 0.853956i \(-0.325803\pi\)
0.520345 + 0.853956i \(0.325803\pi\)
\(920\) −25.9940 −0.856995
\(921\) 31.2854 1.03089
\(922\) 8.73944 0.287818
\(923\) −5.00222 −0.164650
\(924\) 2.79925 0.0920885
\(925\) 4.23042 0.139095
\(926\) 41.3562 1.35905
\(927\) 12.7094 0.417431
\(928\) 4.41638 0.144975
\(929\) −31.1375 −1.02159 −0.510795 0.859703i \(-0.670649\pi\)
−0.510795 + 0.859703i \(0.670649\pi\)
\(930\) −8.45028 −0.277096
\(931\) −5.25696 −0.172290
\(932\) −15.6618 −0.513018
\(933\) −52.0008 −1.70243
\(934\) 19.6447 0.642794
\(935\) 3.89289 0.127311
\(936\) 3.19708 0.104500
\(937\) 14.5876 0.476555 0.238278 0.971197i \(-0.423417\pi\)
0.238278 + 0.971197i \(0.423417\pi\)
\(938\) −16.6340 −0.543120
\(939\) 17.6052 0.574524
\(940\) 15.6558 0.510635
\(941\) 14.6477 0.477501 0.238750 0.971081i \(-0.423262\pi\)
0.238750 + 0.971081i \(0.423262\pi\)
\(942\) −6.99091 −0.227776
\(943\) 69.9694 2.27852
\(944\) 1.72800 0.0562415
\(945\) −29.1367 −0.947818
\(946\) −0.353329 −0.0114877
\(947\) −24.6723 −0.801742 −0.400871 0.916135i \(-0.631292\pi\)
−0.400871 + 0.916135i \(0.631292\pi\)
\(948\) 9.28063 0.301421
\(949\) 31.6244 1.02657
\(950\) −16.1008 −0.522377
\(951\) 4.46735 0.144864
\(952\) 3.72922 0.120865
\(953\) −21.4461 −0.694706 −0.347353 0.937734i \(-0.612919\pi\)
−0.347353 + 0.937734i \(0.612919\pi\)
\(954\) 1.08509 0.0351311
\(955\) 5.12048 0.165695
\(956\) −19.5755 −0.633117
\(957\) 5.73970 0.185538
\(958\) −28.5291 −0.921733
\(959\) 13.2844 0.428977
\(960\) −7.06976 −0.228176
\(961\) −29.5713 −0.953914
\(962\) 1.72149 0.0555031
\(963\) 12.7301 0.410222
\(964\) −24.5795 −0.791653
\(965\) 57.0486 1.83646
\(966\) −32.3625 −1.04125
\(967\) 21.3306 0.685947 0.342973 0.939345i \(-0.388566\pi\)
0.342973 + 0.939345i \(0.388566\pi\)
\(968\) 10.5867 0.340269
\(969\) −7.79365 −0.250368
\(970\) 31.1212 0.999243
\(971\) 1.34944 0.0433054 0.0216527 0.999766i \(-0.493107\pi\)
0.0216527 + 0.999766i \(0.493107\pi\)
\(972\) 10.7923 0.346163
\(973\) 19.1114 0.612682
\(974\) −7.51487 −0.240792
\(975\) 43.0097 1.37741
\(976\) −2.52227 −0.0807359
\(977\) 41.0832 1.31437 0.657184 0.753730i \(-0.271747\pi\)
0.657184 + 0.753730i \(0.271747\pi\)
\(978\) 12.1900 0.389794
\(979\) −8.18377 −0.261555
\(980\) −8.25656 −0.263746
\(981\) −6.82754 −0.217987
\(982\) −12.2338 −0.390398
\(983\) −57.3111 −1.82794 −0.913970 0.405781i \(-0.866999\pi\)
−0.913970 + 0.405781i \(0.866999\pi\)
\(984\) 19.0301 0.606656
\(985\) 25.2294 0.803877
\(986\) 7.64657 0.243516
\(987\) 19.4914 0.620420
\(988\) −6.55190 −0.208444
\(989\) 4.08489 0.129892
\(990\) −2.44298 −0.0776430
\(991\) 12.5766 0.399508 0.199754 0.979846i \(-0.435986\pi\)
0.199754 + 0.979846i \(0.435986\pi\)
\(992\) 1.19527 0.0379499
\(993\) 48.8503 1.55022
\(994\) 3.66164 0.116140
\(995\) 11.7678 0.373063
\(996\) −8.44019 −0.267438
\(997\) −7.11949 −0.225477 −0.112738 0.993625i \(-0.535962\pi\)
−0.112738 + 0.993625i \(0.535962\pi\)
\(998\) 27.7120 0.877207
\(999\) 2.26306 0.0716000
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 \(a_p\))