Properties

Label 6038.2.a.a.1.2
Level 6038
Weight 2
Character 6038.1
Self dual Yes
Analytic conductor 48.214
Analytic rank 2
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6038.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2136727404\)
Analytic rank: \(2\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\)
Character \(\chi\) = 6038.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.381966 q^{3}\) \(+1.00000 q^{4}\) \(-3.61803 q^{5}\) \(-0.381966 q^{6}\) \(-3.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.85410 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.381966 q^{3}\) \(+1.00000 q^{4}\) \(-3.61803 q^{5}\) \(-0.381966 q^{6}\) \(-3.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.85410 q^{9}\) \(-3.61803 q^{10}\) \(-4.61803 q^{11}\) \(-0.381966 q^{12}\) \(-3.00000 q^{13}\) \(-3.00000 q^{14}\) \(+1.38197 q^{15}\) \(+1.00000 q^{16}\) \(+1.47214 q^{17}\) \(-2.85410 q^{18}\) \(-3.00000 q^{19}\) \(-3.61803 q^{20}\) \(+1.14590 q^{21}\) \(-4.61803 q^{22}\) \(-7.47214 q^{23}\) \(-0.381966 q^{24}\) \(+8.09017 q^{25}\) \(-3.00000 q^{26}\) \(+2.23607 q^{27}\) \(-3.00000 q^{28}\) \(-4.76393 q^{29}\) \(+1.38197 q^{30}\) \(+5.09017 q^{31}\) \(+1.00000 q^{32}\) \(+1.76393 q^{33}\) \(+1.47214 q^{34}\) \(+10.8541 q^{35}\) \(-2.85410 q^{36}\) \(+4.85410 q^{37}\) \(-3.00000 q^{38}\) \(+1.14590 q^{39}\) \(-3.61803 q^{40}\) \(-11.1803 q^{41}\) \(+1.14590 q^{42}\) \(-4.76393 q^{43}\) \(-4.61803 q^{44}\) \(+10.3262 q^{45}\) \(-7.47214 q^{46}\) \(-8.56231 q^{47}\) \(-0.381966 q^{48}\) \(+2.00000 q^{49}\) \(+8.09017 q^{50}\) \(-0.562306 q^{51}\) \(-3.00000 q^{52}\) \(-9.00000 q^{53}\) \(+2.23607 q^{54}\) \(+16.7082 q^{55}\) \(-3.00000 q^{56}\) \(+1.14590 q^{57}\) \(-4.76393 q^{58}\) \(-14.2361 q^{59}\) \(+1.38197 q^{60}\) \(-4.61803 q^{61}\) \(+5.09017 q^{62}\) \(+8.56231 q^{63}\) \(+1.00000 q^{64}\) \(+10.8541 q^{65}\) \(+1.76393 q^{66}\) \(-4.85410 q^{67}\) \(+1.47214 q^{68}\) \(+2.85410 q^{69}\) \(+10.8541 q^{70}\) \(+5.94427 q^{71}\) \(-2.85410 q^{72}\) \(-12.7082 q^{73}\) \(+4.85410 q^{74}\) \(-3.09017 q^{75}\) \(-3.00000 q^{76}\) \(+13.8541 q^{77}\) \(+1.14590 q^{78}\) \(+4.85410 q^{79}\) \(-3.61803 q^{80}\) \(+7.70820 q^{81}\) \(-11.1803 q^{82}\) \(+15.9443 q^{83}\) \(+1.14590 q^{84}\) \(-5.32624 q^{85}\) \(-4.76393 q^{86}\) \(+1.81966 q^{87}\) \(-4.61803 q^{88}\) \(+7.79837 q^{89}\) \(+10.3262 q^{90}\) \(+9.00000 q^{91}\) \(-7.47214 q^{92}\) \(-1.94427 q^{93}\) \(-8.56231 q^{94}\) \(+10.8541 q^{95}\) \(-0.381966 q^{96}\) \(+18.2361 q^{97}\) \(+2.00000 q^{98}\) \(+13.1803 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 7q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 5q^{30} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 2q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut +\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 14q^{43} \) \(\mathstrut -\mathstrut 7q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 19q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 5q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut +\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 6q^{76} \) \(\mathstrut +\mathstrut 21q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 3q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 5q^{85} \) \(\mathstrut -\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 26q^{87} \) \(\mathstrut -\mathstrut 7q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut +\mathstrut 5q^{90} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut -\mathstrut 3q^{96} \) \(\mathstrut +\mathstrut 32q^{97} \) \(\mathstrut +\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.381966 −0.220528 −0.110264 0.993902i \(-0.535170\pi\)
−0.110264 + 0.993902i \(0.535170\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) −0.381966 −0.155937
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.85410 −0.951367
\(10\) −3.61803 −1.14412
\(11\) −4.61803 −1.39239 −0.696195 0.717853i \(-0.745125\pi\)
−0.696195 + 0.717853i \(0.745125\pi\)
\(12\) −0.381966 −0.110264
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) −3.00000 −0.801784
\(15\) 1.38197 0.356822
\(16\) 1.00000 0.250000
\(17\) 1.47214 0.357045 0.178523 0.983936i \(-0.442868\pi\)
0.178523 + 0.983936i \(0.442868\pi\)
\(18\) −2.85410 −0.672718
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) −3.61803 −0.809017
\(21\) 1.14590 0.250055
\(22\) −4.61803 −0.984568
\(23\) −7.47214 −1.55805 −0.779024 0.626994i \(-0.784285\pi\)
−0.779024 + 0.626994i \(0.784285\pi\)
\(24\) −0.381966 −0.0779685
\(25\) 8.09017 1.61803
\(26\) −3.00000 −0.588348
\(27\) 2.23607 0.430331
\(28\) −3.00000 −0.566947
\(29\) −4.76393 −0.884640 −0.442320 0.896857i \(-0.645844\pi\)
−0.442320 + 0.896857i \(0.645844\pi\)
\(30\) 1.38197 0.252311
\(31\) 5.09017 0.914222 0.457111 0.889410i \(-0.348884\pi\)
0.457111 + 0.889410i \(0.348884\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.76393 0.307061
\(34\) 1.47214 0.252469
\(35\) 10.8541 1.83468
\(36\) −2.85410 −0.475684
\(37\) 4.85410 0.798009 0.399005 0.916949i \(-0.369356\pi\)
0.399005 + 0.916949i \(0.369356\pi\)
\(38\) −3.00000 −0.486664
\(39\) 1.14590 0.183491
\(40\) −3.61803 −0.572061
\(41\) −11.1803 −1.74608 −0.873038 0.487652i \(-0.837853\pi\)
−0.873038 + 0.487652i \(0.837853\pi\)
\(42\) 1.14590 0.176816
\(43\) −4.76393 −0.726493 −0.363246 0.931693i \(-0.618332\pi\)
−0.363246 + 0.931693i \(0.618332\pi\)
\(44\) −4.61803 −0.696195
\(45\) 10.3262 1.53934
\(46\) −7.47214 −1.10171
\(47\) −8.56231 −1.24894 −0.624470 0.781049i \(-0.714685\pi\)
−0.624470 + 0.781049i \(0.714685\pi\)
\(48\) −0.381966 −0.0551320
\(49\) 2.00000 0.285714
\(50\) 8.09017 1.14412
\(51\) −0.562306 −0.0787386
\(52\) −3.00000 −0.416025
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 2.23607 0.304290
\(55\) 16.7082 2.25293
\(56\) −3.00000 −0.400892
\(57\) 1.14590 0.151778
\(58\) −4.76393 −0.625535
\(59\) −14.2361 −1.85338 −0.926689 0.375829i \(-0.877358\pi\)
−0.926689 + 0.375829i \(0.877358\pi\)
\(60\) 1.38197 0.178411
\(61\) −4.61803 −0.591279 −0.295639 0.955300i \(-0.595533\pi\)
−0.295639 + 0.955300i \(0.595533\pi\)
\(62\) 5.09017 0.646452
\(63\) 8.56231 1.07875
\(64\) 1.00000 0.125000
\(65\) 10.8541 1.34629
\(66\) 1.76393 0.217125
\(67\) −4.85410 −0.593023 −0.296511 0.955029i \(-0.595823\pi\)
−0.296511 + 0.955029i \(0.595823\pi\)
\(68\) 1.47214 0.178523
\(69\) 2.85410 0.343594
\(70\) 10.8541 1.29731
\(71\) 5.94427 0.705455 0.352728 0.935726i \(-0.385254\pi\)
0.352728 + 0.935726i \(0.385254\pi\)
\(72\) −2.85410 −0.336359
\(73\) −12.7082 −1.48738 −0.743691 0.668523i \(-0.766927\pi\)
−0.743691 + 0.668523i \(0.766927\pi\)
\(74\) 4.85410 0.564278
\(75\) −3.09017 −0.356822
\(76\) −3.00000 −0.344124
\(77\) 13.8541 1.57882
\(78\) 1.14590 0.129747
\(79\) 4.85410 0.546129 0.273065 0.961996i \(-0.411963\pi\)
0.273065 + 0.961996i \(0.411963\pi\)
\(80\) −3.61803 −0.404508
\(81\) 7.70820 0.856467
\(82\) −11.1803 −1.23466
\(83\) 15.9443 1.75011 0.875056 0.484022i \(-0.160825\pi\)
0.875056 + 0.484022i \(0.160825\pi\)
\(84\) 1.14590 0.125028
\(85\) −5.32624 −0.577712
\(86\) −4.76393 −0.513708
\(87\) 1.81966 0.195088
\(88\) −4.61803 −0.492284
\(89\) 7.79837 0.826626 0.413313 0.910589i \(-0.364372\pi\)
0.413313 + 0.910589i \(0.364372\pi\)
\(90\) 10.3262 1.08848
\(91\) 9.00000 0.943456
\(92\) −7.47214 −0.779024
\(93\) −1.94427 −0.201612
\(94\) −8.56231 −0.883134
\(95\) 10.8541 1.11361
\(96\) −0.381966 −0.0389842
\(97\) 18.2361 1.85159 0.925796 0.378023i \(-0.123396\pi\)
0.925796 + 0.378023i \(0.123396\pi\)
\(98\) 2.00000 0.202031
\(99\) 13.1803 1.32467
\(100\) 8.09017 0.809017
\(101\) 0.763932 0.0760141 0.0380070 0.999277i \(-0.487899\pi\)
0.0380070 + 0.999277i \(0.487899\pi\)
\(102\) −0.562306 −0.0556766
\(103\) 11.8541 1.16802 0.584010 0.811747i \(-0.301483\pi\)
0.584010 + 0.811747i \(0.301483\pi\)
\(104\) −3.00000 −0.294174
\(105\) −4.14590 −0.404598
\(106\) −9.00000 −0.874157
\(107\) −8.23607 −0.796211 −0.398105 0.917340i \(-0.630332\pi\)
−0.398105 + 0.917340i \(0.630332\pi\)
\(108\) 2.23607 0.215166
\(109\) −0.527864 −0.0505602 −0.0252801 0.999680i \(-0.508048\pi\)
−0.0252801 + 0.999680i \(0.508048\pi\)
\(110\) 16.7082 1.59306
\(111\) −1.85410 −0.175984
\(112\) −3.00000 −0.283473
\(113\) −6.61803 −0.622572 −0.311286 0.950316i \(-0.600760\pi\)
−0.311286 + 0.950316i \(0.600760\pi\)
\(114\) 1.14590 0.107323
\(115\) 27.0344 2.52097
\(116\) −4.76393 −0.442320
\(117\) 8.56231 0.791585
\(118\) −14.2361 −1.31054
\(119\) −4.41641 −0.404851
\(120\) 1.38197 0.126156
\(121\) 10.3262 0.938749
\(122\) −4.61803 −0.418097
\(123\) 4.27051 0.385059
\(124\) 5.09017 0.457111
\(125\) −11.1803 −1.00000
\(126\) 8.56231 0.762791
\(127\) 14.4164 1.27925 0.639625 0.768687i \(-0.279090\pi\)
0.639625 + 0.768687i \(0.279090\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.81966 0.160212
\(130\) 10.8541 0.951968
\(131\) 19.3820 1.69341 0.846705 0.532062i \(-0.178583\pi\)
0.846705 + 0.532062i \(0.178583\pi\)
\(132\) 1.76393 0.153531
\(133\) 9.00000 0.780399
\(134\) −4.85410 −0.419331
\(135\) −8.09017 −0.696291
\(136\) 1.47214 0.126235
\(137\) −11.5623 −0.987834 −0.493917 0.869509i \(-0.664435\pi\)
−0.493917 + 0.869509i \(0.664435\pi\)
\(138\) 2.85410 0.242957
\(139\) −6.52786 −0.553686 −0.276843 0.960915i \(-0.589288\pi\)
−0.276843 + 0.960915i \(0.589288\pi\)
\(140\) 10.8541 0.917339
\(141\) 3.27051 0.275427
\(142\) 5.94427 0.498832
\(143\) 13.8541 1.15854
\(144\) −2.85410 −0.237842
\(145\) 17.2361 1.43138
\(146\) −12.7082 −1.05174
\(147\) −0.763932 −0.0630081
\(148\) 4.85410 0.399005
\(149\) 2.23607 0.183186 0.0915929 0.995797i \(-0.470804\pi\)
0.0915929 + 0.995797i \(0.470804\pi\)
\(150\) −3.09017 −0.252311
\(151\) 14.7984 1.20427 0.602137 0.798393i \(-0.294316\pi\)
0.602137 + 0.798393i \(0.294316\pi\)
\(152\) −3.00000 −0.243332
\(153\) −4.20163 −0.339681
\(154\) 13.8541 1.11640
\(155\) −18.4164 −1.47924
\(156\) 1.14590 0.0917453
\(157\) −3.09017 −0.246622 −0.123311 0.992368i \(-0.539351\pi\)
−0.123311 + 0.992368i \(0.539351\pi\)
\(158\) 4.85410 0.386172
\(159\) 3.43769 0.272627
\(160\) −3.61803 −0.286031
\(161\) 22.4164 1.76666
\(162\) 7.70820 0.605614
\(163\) −5.85410 −0.458529 −0.229264 0.973364i \(-0.573632\pi\)
−0.229264 + 0.973364i \(0.573632\pi\)
\(164\) −11.1803 −0.873038
\(165\) −6.38197 −0.496835
\(166\) 15.9443 1.23752
\(167\) −0.763932 −0.0591148 −0.0295574 0.999563i \(-0.509410\pi\)
−0.0295574 + 0.999563i \(0.509410\pi\)
\(168\) 1.14590 0.0884080
\(169\) −4.00000 −0.307692
\(170\) −5.32624 −0.408504
\(171\) 8.56231 0.654776
\(172\) −4.76393 −0.363246
\(173\) −23.3262 −1.77346 −0.886731 0.462287i \(-0.847029\pi\)
−0.886731 + 0.462287i \(0.847029\pi\)
\(174\) 1.81966 0.137948
\(175\) −24.2705 −1.83468
\(176\) −4.61803 −0.348097
\(177\) 5.43769 0.408722
\(178\) 7.79837 0.584513
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 10.3262 0.769672
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 9.00000 0.667124
\(183\) 1.76393 0.130394
\(184\) −7.47214 −0.550853
\(185\) −17.5623 −1.29121
\(186\) −1.94427 −0.142561
\(187\) −6.79837 −0.497146
\(188\) −8.56231 −0.624470
\(189\) −6.70820 −0.487950
\(190\) 10.8541 0.787439
\(191\) −22.3607 −1.61796 −0.808981 0.587835i \(-0.799981\pi\)
−0.808981 + 0.587835i \(0.799981\pi\)
\(192\) −0.381966 −0.0275660
\(193\) 9.85410 0.709314 0.354657 0.934997i \(-0.384598\pi\)
0.354657 + 0.934997i \(0.384598\pi\)
\(194\) 18.2361 1.30927
\(195\) −4.14590 −0.296894
\(196\) 2.00000 0.142857
\(197\) 21.7984 1.55307 0.776535 0.630074i \(-0.216976\pi\)
0.776535 + 0.630074i \(0.216976\pi\)
\(198\) 13.1803 0.936686
\(199\) −12.2705 −0.869833 −0.434917 0.900471i \(-0.643222\pi\)
−0.434917 + 0.900471i \(0.643222\pi\)
\(200\) 8.09017 0.572061
\(201\) 1.85410 0.130778
\(202\) 0.763932 0.0537501
\(203\) 14.2918 1.00309
\(204\) −0.562306 −0.0393693
\(205\) 40.4508 2.82521
\(206\) 11.8541 0.825914
\(207\) 21.3262 1.48228
\(208\) −3.00000 −0.208013
\(209\) 13.8541 0.958308
\(210\) −4.14590 −0.286094
\(211\) 11.1459 0.767315 0.383658 0.923475i \(-0.374664\pi\)
0.383658 + 0.923475i \(0.374664\pi\)
\(212\) −9.00000 −0.618123
\(213\) −2.27051 −0.155573
\(214\) −8.23607 −0.563006
\(215\) 17.2361 1.17549
\(216\) 2.23607 0.152145
\(217\) −15.2705 −1.03663
\(218\) −0.527864 −0.0357515
\(219\) 4.85410 0.328010
\(220\) 16.7082 1.12647
\(221\) −4.41641 −0.297080
\(222\) −1.85410 −0.124439
\(223\) −28.4164 −1.90290 −0.951452 0.307798i \(-0.900408\pi\)
−0.951452 + 0.307798i \(0.900408\pi\)
\(224\) −3.00000 −0.200446
\(225\) −23.0902 −1.53934
\(226\) −6.61803 −0.440225
\(227\) 7.14590 0.474290 0.237145 0.971474i \(-0.423788\pi\)
0.237145 + 0.971474i \(0.423788\pi\)
\(228\) 1.14590 0.0758890
\(229\) −22.5967 −1.49324 −0.746618 0.665253i \(-0.768323\pi\)
−0.746618 + 0.665253i \(0.768323\pi\)
\(230\) 27.0344 1.78260
\(231\) −5.29180 −0.348175
\(232\) −4.76393 −0.312767
\(233\) 10.8541 0.711076 0.355538 0.934662i \(-0.384298\pi\)
0.355538 + 0.934662i \(0.384298\pi\)
\(234\) 8.56231 0.559735
\(235\) 30.9787 2.02083
\(236\) −14.2361 −0.926689
\(237\) −1.85410 −0.120437
\(238\) −4.41641 −0.286273
\(239\) −9.70820 −0.627972 −0.313986 0.949428i \(-0.601664\pi\)
−0.313986 + 0.949428i \(0.601664\pi\)
\(240\) 1.38197 0.0892055
\(241\) 16.4164 1.05747 0.528737 0.848786i \(-0.322666\pi\)
0.528737 + 0.848786i \(0.322666\pi\)
\(242\) 10.3262 0.663796
\(243\) −9.65248 −0.619207
\(244\) −4.61803 −0.295639
\(245\) −7.23607 −0.462295
\(246\) 4.27051 0.272278
\(247\) 9.00000 0.572656
\(248\) 5.09017 0.323226
\(249\) −6.09017 −0.385949
\(250\) −11.1803 −0.707107
\(251\) −16.9443 −1.06951 −0.534756 0.845006i \(-0.679597\pi\)
−0.534756 + 0.845006i \(0.679597\pi\)
\(252\) 8.56231 0.539375
\(253\) 34.5066 2.16941
\(254\) 14.4164 0.904566
\(255\) 2.03444 0.127402
\(256\) 1.00000 0.0625000
\(257\) −28.4164 −1.77257 −0.886283 0.463143i \(-0.846722\pi\)
−0.886283 + 0.463143i \(0.846722\pi\)
\(258\) 1.81966 0.113287
\(259\) −14.5623 −0.904858
\(260\) 10.8541 0.673143
\(261\) 13.5967 0.841618
\(262\) 19.3820 1.19742
\(263\) −26.3607 −1.62547 −0.812735 0.582634i \(-0.802022\pi\)
−0.812735 + 0.582634i \(0.802022\pi\)
\(264\) 1.76393 0.108563
\(265\) 32.5623 2.00029
\(266\) 9.00000 0.551825
\(267\) −2.97871 −0.182294
\(268\) −4.85410 −0.296511
\(269\) 14.5623 0.887879 0.443940 0.896057i \(-0.353580\pi\)
0.443940 + 0.896057i \(0.353580\pi\)
\(270\) −8.09017 −0.492352
\(271\) −4.38197 −0.266185 −0.133093 0.991104i \(-0.542491\pi\)
−0.133093 + 0.991104i \(0.542491\pi\)
\(272\) 1.47214 0.0892614
\(273\) −3.43769 −0.208059
\(274\) −11.5623 −0.698504
\(275\) −37.3607 −2.25293
\(276\) 2.85410 0.171797
\(277\) −0.437694 −0.0262985 −0.0131492 0.999914i \(-0.504186\pi\)
−0.0131492 + 0.999914i \(0.504186\pi\)
\(278\) −6.52786 −0.391515
\(279\) −14.5279 −0.869760
\(280\) 10.8541 0.648657
\(281\) 19.3607 1.15496 0.577481 0.816404i \(-0.304036\pi\)
0.577481 + 0.816404i \(0.304036\pi\)
\(282\) 3.27051 0.194756
\(283\) −2.70820 −0.160986 −0.0804930 0.996755i \(-0.525649\pi\)
−0.0804930 + 0.996755i \(0.525649\pi\)
\(284\) 5.94427 0.352728
\(285\) −4.14590 −0.245582
\(286\) 13.8541 0.819210
\(287\) 33.5410 1.97986
\(288\) −2.85410 −0.168180
\(289\) −14.8328 −0.872519
\(290\) 17.2361 1.01214
\(291\) −6.96556 −0.408328
\(292\) −12.7082 −0.743691
\(293\) −20.9098 −1.22157 −0.610783 0.791798i \(-0.709145\pi\)
−0.610783 + 0.791798i \(0.709145\pi\)
\(294\) −0.763932 −0.0445534
\(295\) 51.5066 2.99883
\(296\) 4.85410 0.282139
\(297\) −10.3262 −0.599189
\(298\) 2.23607 0.129532
\(299\) 22.4164 1.29637
\(300\) −3.09017 −0.178411
\(301\) 14.2918 0.823765
\(302\) 14.7984 0.851551
\(303\) −0.291796 −0.0167632
\(304\) −3.00000 −0.172062
\(305\) 16.7082 0.956709
\(306\) −4.20163 −0.240191
\(307\) 15.0902 0.861241 0.430621 0.902533i \(-0.358295\pi\)
0.430621 + 0.902533i \(0.358295\pi\)
\(308\) 13.8541 0.789411
\(309\) −4.52786 −0.257581
\(310\) −18.4164 −1.04598
\(311\) 29.2361 1.65783 0.828913 0.559378i \(-0.188960\pi\)
0.828913 + 0.559378i \(0.188960\pi\)
\(312\) 1.14590 0.0648737
\(313\) −9.74265 −0.550687 −0.275343 0.961346i \(-0.588792\pi\)
−0.275343 + 0.961346i \(0.588792\pi\)
\(314\) −3.09017 −0.174388
\(315\) −30.9787 −1.74545
\(316\) 4.85410 0.273065
\(317\) −8.38197 −0.470778 −0.235389 0.971901i \(-0.575636\pi\)
−0.235389 + 0.971901i \(0.575636\pi\)
\(318\) 3.43769 0.192776
\(319\) 22.0000 1.23176
\(320\) −3.61803 −0.202254
\(321\) 3.14590 0.175587
\(322\) 22.4164 1.24922
\(323\) −4.41641 −0.245736
\(324\) 7.70820 0.428234
\(325\) −24.2705 −1.34629
\(326\) −5.85410 −0.324229
\(327\) 0.201626 0.0111500
\(328\) −11.1803 −0.617331
\(329\) 25.6869 1.41617
\(330\) −6.38197 −0.351316
\(331\) −25.5623 −1.40503 −0.702516 0.711668i \(-0.747940\pi\)
−0.702516 + 0.711668i \(0.747940\pi\)
\(332\) 15.9443 0.875056
\(333\) −13.8541 −0.759200
\(334\) −0.763932 −0.0418005
\(335\) 17.5623 0.959531
\(336\) 1.14590 0.0625139
\(337\) 2.38197 0.129754 0.0648770 0.997893i \(-0.479335\pi\)
0.0648770 + 0.997893i \(0.479335\pi\)
\(338\) −4.00000 −0.217571
\(339\) 2.52786 0.137295
\(340\) −5.32624 −0.288856
\(341\) −23.5066 −1.27295
\(342\) 8.56231 0.462996
\(343\) 15.0000 0.809924
\(344\) −4.76393 −0.256854
\(345\) −10.3262 −0.555946
\(346\) −23.3262 −1.25403
\(347\) −24.3262 −1.30590 −0.652950 0.757401i \(-0.726469\pi\)
−0.652950 + 0.757401i \(0.726469\pi\)
\(348\) 1.81966 0.0975440
\(349\) −9.29180 −0.497378 −0.248689 0.968583i \(-0.580000\pi\)
−0.248689 + 0.968583i \(0.580000\pi\)
\(350\) −24.2705 −1.29731
\(351\) −6.70820 −0.358057
\(352\) −4.61803 −0.246142
\(353\) −29.1803 −1.55311 −0.776556 0.630048i \(-0.783035\pi\)
−0.776556 + 0.630048i \(0.783035\pi\)
\(354\) 5.43769 0.289010
\(355\) −21.5066 −1.14145
\(356\) 7.79837 0.413313
\(357\) 1.68692 0.0892812
\(358\) −9.00000 −0.475665
\(359\) 34.5967 1.82595 0.912973 0.408019i \(-0.133780\pi\)
0.912973 + 0.408019i \(0.133780\pi\)
\(360\) 10.3262 0.544241
\(361\) −10.0000 −0.526316
\(362\) −18.0000 −0.946059
\(363\) −3.94427 −0.207021
\(364\) 9.00000 0.471728
\(365\) 45.9787 2.40664
\(366\) 1.76393 0.0922022
\(367\) −30.8885 −1.61237 −0.806184 0.591664i \(-0.798471\pi\)
−0.806184 + 0.591664i \(0.798471\pi\)
\(368\) −7.47214 −0.389512
\(369\) 31.9098 1.66116
\(370\) −17.5623 −0.913021
\(371\) 27.0000 1.40177
\(372\) −1.94427 −0.100806
\(373\) −12.0000 −0.621336 −0.310668 0.950518i \(-0.600553\pi\)
−0.310668 + 0.950518i \(0.600553\pi\)
\(374\) −6.79837 −0.351536
\(375\) 4.27051 0.220528
\(376\) −8.56231 −0.441567
\(377\) 14.2918 0.736065
\(378\) −6.70820 −0.345033
\(379\) −30.8328 −1.58378 −0.791888 0.610667i \(-0.790901\pi\)
−0.791888 + 0.610667i \(0.790901\pi\)
\(380\) 10.8541 0.556804
\(381\) −5.50658 −0.282111
\(382\) −22.3607 −1.14407
\(383\) −15.7082 −0.802652 −0.401326 0.915935i \(-0.631451\pi\)
−0.401326 + 0.915935i \(0.631451\pi\)
\(384\) −0.381966 −0.0194921
\(385\) −50.1246 −2.55459
\(386\) 9.85410 0.501561
\(387\) 13.5967 0.691162
\(388\) 18.2361 0.925796
\(389\) −22.7639 −1.15418 −0.577089 0.816682i \(-0.695811\pi\)
−0.577089 + 0.816682i \(0.695811\pi\)
\(390\) −4.14590 −0.209936
\(391\) −11.0000 −0.556294
\(392\) 2.00000 0.101015
\(393\) −7.40325 −0.373445
\(394\) 21.7984 1.09819
\(395\) −17.5623 −0.883656
\(396\) 13.1803 0.662337
\(397\) 11.5623 0.580295 0.290148 0.956982i \(-0.406296\pi\)
0.290148 + 0.956982i \(0.406296\pi\)
\(398\) −12.2705 −0.615065
\(399\) −3.43769 −0.172100
\(400\) 8.09017 0.404508
\(401\) −31.9443 −1.59522 −0.797610 0.603173i \(-0.793903\pi\)
−0.797610 + 0.603173i \(0.793903\pi\)
\(402\) 1.85410 0.0924742
\(403\) −15.2705 −0.760678
\(404\) 0.763932 0.0380070
\(405\) −27.8885 −1.38579
\(406\) 14.2918 0.709290
\(407\) −22.4164 −1.11114
\(408\) −0.562306 −0.0278383
\(409\) −6.58359 −0.325538 −0.162769 0.986664i \(-0.552042\pi\)
−0.162769 + 0.986664i \(0.552042\pi\)
\(410\) 40.4508 1.99773
\(411\) 4.41641 0.217845
\(412\) 11.8541 0.584010
\(413\) 42.7082 2.10153
\(414\) 21.3262 1.04813
\(415\) −57.6869 −2.83174
\(416\) −3.00000 −0.147087
\(417\) 2.49342 0.122103
\(418\) 13.8541 0.677626
\(419\) 16.3262 0.797589 0.398794 0.917040i \(-0.369429\pi\)
0.398794 + 0.917040i \(0.369429\pi\)
\(420\) −4.14590 −0.202299
\(421\) −40.3951 −1.96874 −0.984369 0.176119i \(-0.943646\pi\)
−0.984369 + 0.176119i \(0.943646\pi\)
\(422\) 11.1459 0.542574
\(423\) 24.4377 1.18820
\(424\) −9.00000 −0.437079
\(425\) 11.9098 0.577712
\(426\) −2.27051 −0.110007
\(427\) 13.8541 0.670447
\(428\) −8.23607 −0.398105
\(429\) −5.29180 −0.255490
\(430\) 17.2361 0.831197
\(431\) −29.2361 −1.40825 −0.704126 0.710075i \(-0.748661\pi\)
−0.704126 + 0.710075i \(0.748661\pi\)
\(432\) 2.23607 0.107583
\(433\) 32.4164 1.55783 0.778917 0.627128i \(-0.215770\pi\)
0.778917 + 0.627128i \(0.215770\pi\)
\(434\) −15.2705 −0.733008
\(435\) −6.58359 −0.315659
\(436\) −0.527864 −0.0252801
\(437\) 22.4164 1.07232
\(438\) 4.85410 0.231938
\(439\) −13.0000 −0.620456 −0.310228 0.950662i \(-0.600405\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 16.7082 0.796532
\(441\) −5.70820 −0.271819
\(442\) −4.41641 −0.210067
\(443\) 13.4721 0.640080 0.320040 0.947404i \(-0.396304\pi\)
0.320040 + 0.947404i \(0.396304\pi\)
\(444\) −1.85410 −0.0879918
\(445\) −28.2148 −1.33751
\(446\) −28.4164 −1.34556
\(447\) −0.854102 −0.0403976
\(448\) −3.00000 −0.141737
\(449\) 27.3607 1.29123 0.645615 0.763663i \(-0.276601\pi\)
0.645615 + 0.763663i \(0.276601\pi\)
\(450\) −23.0902 −1.08848
\(451\) 51.6312 2.43122
\(452\) −6.61803 −0.311286
\(453\) −5.65248 −0.265576
\(454\) 7.14590 0.335374
\(455\) −32.5623 −1.52654
\(456\) 1.14590 0.0536616
\(457\) −11.9656 −0.559725 −0.279863 0.960040i \(-0.590289\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(458\) −22.5967 −1.05588
\(459\) 3.29180 0.153648
\(460\) 27.0344 1.26049
\(461\) −4.61803 −0.215083 −0.107542 0.994201i \(-0.534298\pi\)
−0.107542 + 0.994201i \(0.534298\pi\)
\(462\) −5.29180 −0.246197
\(463\) −18.3607 −0.853293 −0.426647 0.904418i \(-0.640305\pi\)
−0.426647 + 0.904418i \(0.640305\pi\)
\(464\) −4.76393 −0.221160
\(465\) 7.03444 0.326214
\(466\) 10.8541 0.502807
\(467\) 7.20163 0.333252 0.166626 0.986020i \(-0.446713\pi\)
0.166626 + 0.986020i \(0.446713\pi\)
\(468\) 8.56231 0.395793
\(469\) 14.5623 0.672425
\(470\) 30.9787 1.42894
\(471\) 1.18034 0.0543872
\(472\) −14.2361 −0.655268
\(473\) 22.0000 1.01156
\(474\) −1.85410 −0.0851617
\(475\) −24.2705 −1.11361
\(476\) −4.41641 −0.202426
\(477\) 25.6869 1.17612
\(478\) −9.70820 −0.444043
\(479\) −7.14590 −0.326504 −0.163252 0.986584i \(-0.552198\pi\)
−0.163252 + 0.986584i \(0.552198\pi\)
\(480\) 1.38197 0.0630778
\(481\) −14.5623 −0.663984
\(482\) 16.4164 0.747747
\(483\) −8.56231 −0.389598
\(484\) 10.3262 0.469374
\(485\) −65.9787 −2.99594
\(486\) −9.65248 −0.437845
\(487\) −19.8885 −0.901236 −0.450618 0.892717i \(-0.648796\pi\)
−0.450618 + 0.892717i \(0.648796\pi\)
\(488\) −4.61803 −0.209049
\(489\) 2.23607 0.101118
\(490\) −7.23607 −0.326892
\(491\) 27.2705 1.23070 0.615350 0.788254i \(-0.289015\pi\)
0.615350 + 0.788254i \(0.289015\pi\)
\(492\) 4.27051 0.192529
\(493\) −7.01316 −0.315857
\(494\) 9.00000 0.404929
\(495\) −47.6869 −2.14337
\(496\) 5.09017 0.228555
\(497\) −17.8328 −0.799911
\(498\) −6.09017 −0.272907
\(499\) 25.6525 1.14836 0.574181 0.818728i \(-0.305320\pi\)
0.574181 + 0.818728i \(0.305320\pi\)
\(500\) −11.1803 −0.500000
\(501\) 0.291796 0.0130365
\(502\) −16.9443 −0.756260
\(503\) 18.7082 0.834158 0.417079 0.908870i \(-0.363054\pi\)
0.417079 + 0.908870i \(0.363054\pi\)
\(504\) 8.56231 0.381395
\(505\) −2.76393 −0.122993
\(506\) 34.5066 1.53400
\(507\) 1.52786 0.0678548
\(508\) 14.4164 0.639625
\(509\) −1.58359 −0.0701915 −0.0350957 0.999384i \(-0.511174\pi\)
−0.0350957 + 0.999384i \(0.511174\pi\)
\(510\) 2.03444 0.0900866
\(511\) 38.1246 1.68653
\(512\) 1.00000 0.0441942
\(513\) −6.70820 −0.296174
\(514\) −28.4164 −1.25339
\(515\) −42.8885 −1.88990
\(516\) 1.81966 0.0801061
\(517\) 39.5410 1.73901
\(518\) −14.5623 −0.639831
\(519\) 8.90983 0.391098
\(520\) 10.8541 0.475984
\(521\) 18.6525 0.817180 0.408590 0.912718i \(-0.366021\pi\)
0.408590 + 0.912718i \(0.366021\pi\)
\(522\) 13.5967 0.595113
\(523\) 23.0344 1.00723 0.503613 0.863929i \(-0.332004\pi\)
0.503613 + 0.863929i \(0.332004\pi\)
\(524\) 19.3820 0.846705
\(525\) 9.27051 0.404598
\(526\) −26.3607 −1.14938
\(527\) 7.49342 0.326419
\(528\) 1.76393 0.0767653
\(529\) 32.8328 1.42751
\(530\) 32.5623 1.41442
\(531\) 40.6312 1.76324
\(532\) 9.00000 0.390199
\(533\) 33.5410 1.45282
\(534\) −2.97871 −0.128902
\(535\) 29.7984 1.28830
\(536\) −4.85410 −0.209665
\(537\) 3.43769 0.148347
\(538\) 14.5623 0.627826
\(539\) −9.23607 −0.397826
\(540\) −8.09017 −0.348145
\(541\) −18.2918 −0.786426 −0.393213 0.919447i \(-0.628636\pi\)
−0.393213 + 0.919447i \(0.628636\pi\)
\(542\) −4.38197 −0.188222
\(543\) 6.87539 0.295051
\(544\) 1.47214 0.0631173
\(545\) 1.90983 0.0818081
\(546\) −3.43769 −0.147120
\(547\) −7.94427 −0.339673 −0.169836 0.985472i \(-0.554324\pi\)
−0.169836 + 0.985472i \(0.554324\pi\)
\(548\) −11.5623 −0.493917
\(549\) 13.1803 0.562523
\(550\) −37.3607 −1.59306
\(551\) 14.2918 0.608851
\(552\) 2.85410 0.121479
\(553\) −14.5623 −0.619252
\(554\) −0.437694 −0.0185958
\(555\) 6.70820 0.284747
\(556\) −6.52786 −0.276843
\(557\) −12.2361 −0.518459 −0.259229 0.965816i \(-0.583469\pi\)
−0.259229 + 0.965816i \(0.583469\pi\)
\(558\) −14.5279 −0.615014
\(559\) 14.2918 0.604479
\(560\) 10.8541 0.458670
\(561\) 2.59675 0.109635
\(562\) 19.3607 0.816681
\(563\) 0.270510 0.0114006 0.00570032 0.999984i \(-0.498186\pi\)
0.00570032 + 0.999984i \(0.498186\pi\)
\(564\) 3.27051 0.137713
\(565\) 23.9443 1.00734
\(566\) −2.70820 −0.113834
\(567\) −23.1246 −0.971142
\(568\) 5.94427 0.249416
\(569\) −43.0344 −1.80410 −0.902049 0.431634i \(-0.857937\pi\)
−0.902049 + 0.431634i \(0.857937\pi\)
\(570\) −4.14590 −0.173653
\(571\) −25.0000 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(572\) 13.8541 0.579269
\(573\) 8.54102 0.356806
\(574\) 33.5410 1.39998
\(575\) −60.4508 −2.52097
\(576\) −2.85410 −0.118921
\(577\) 22.4164 0.933207 0.466604 0.884467i \(-0.345477\pi\)
0.466604 + 0.884467i \(0.345477\pi\)
\(578\) −14.8328 −0.616964
\(579\) −3.76393 −0.156424
\(580\) 17.2361 0.715689
\(581\) −47.8328 −1.98444
\(582\) −6.96556 −0.288732
\(583\) 41.5623 1.72133
\(584\) −12.7082 −0.525869
\(585\) −30.9787 −1.28081
\(586\) −20.9098 −0.863777
\(587\) −23.0557 −0.951612 −0.475806 0.879550i \(-0.657844\pi\)
−0.475806 + 0.879550i \(0.657844\pi\)
\(588\) −0.763932 −0.0315040
\(589\) −15.2705 −0.629210
\(590\) 51.5066 2.12049
\(591\) −8.32624 −0.342496
\(592\) 4.85410 0.199502
\(593\) −21.2148 −0.871187 −0.435593 0.900144i \(-0.643461\pi\)
−0.435593 + 0.900144i \(0.643461\pi\)
\(594\) −10.3262 −0.423691
\(595\) 15.9787 0.655063
\(596\) 2.23607 0.0915929
\(597\) 4.68692 0.191823
\(598\) 22.4164 0.916675
\(599\) −22.8541 −0.933793 −0.466897 0.884312i \(-0.654628\pi\)
−0.466897 + 0.884312i \(0.654628\pi\)
\(600\) −3.09017 −0.126156
\(601\) 16.2705 0.663688 0.331844 0.943334i \(-0.392329\pi\)
0.331844 + 0.943334i \(0.392329\pi\)
\(602\) 14.2918 0.582490
\(603\) 13.8541 0.564183
\(604\) 14.7984 0.602137
\(605\) −37.3607 −1.51893
\(606\) −0.291796 −0.0118534
\(607\) −20.4164 −0.828676 −0.414338 0.910123i \(-0.635987\pi\)
−0.414338 + 0.910123i \(0.635987\pi\)
\(608\) −3.00000 −0.121666
\(609\) −5.45898 −0.221209
\(610\) 16.7082 0.676495
\(611\) 25.6869 1.03918
\(612\) −4.20163 −0.169841
\(613\) −3.41641 −0.137987 −0.0689937 0.997617i \(-0.521979\pi\)
−0.0689937 + 0.997617i \(0.521979\pi\)
\(614\) 15.0902 0.608990
\(615\) −15.4508 −0.623038
\(616\) 13.8541 0.558198
\(617\) 5.67376 0.228417 0.114209 0.993457i \(-0.463567\pi\)
0.114209 + 0.993457i \(0.463567\pi\)
\(618\) −4.52786 −0.182137
\(619\) 38.1459 1.53321 0.766607 0.642117i \(-0.221944\pi\)
0.766607 + 0.642117i \(0.221944\pi\)
\(620\) −18.4164 −0.739621
\(621\) −16.7082 −0.670477
\(622\) 29.2361 1.17226
\(623\) −23.3951 −0.937306
\(624\) 1.14590 0.0458726
\(625\) 0 0
\(626\) −9.74265 −0.389394
\(627\) −5.29180 −0.211334
\(628\) −3.09017 −0.123311
\(629\) 7.14590 0.284926
\(630\) −30.9787 −1.23422
\(631\) −18.2705 −0.727338 −0.363669 0.931528i \(-0.618476\pi\)
−0.363669 + 0.931528i \(0.618476\pi\)
\(632\) 4.85410 0.193086
\(633\) −4.25735 −0.169215
\(634\) −8.38197 −0.332890
\(635\) −52.1591 −2.06987
\(636\) 3.43769 0.136313
\(637\) −6.00000 −0.237729
\(638\) 22.0000 0.870988
\(639\) −16.9656 −0.671147
\(640\) −3.61803 −0.143015
\(641\) 41.1803 1.62653 0.813263 0.581897i \(-0.197689\pi\)
0.813263 + 0.581897i \(0.197689\pi\)
\(642\) 3.14590 0.124159
\(643\) 32.3050 1.27398 0.636991 0.770871i \(-0.280179\pi\)
0.636991 + 0.770871i \(0.280179\pi\)
\(644\) 22.4164 0.883330
\(645\) −6.58359 −0.259229
\(646\) −4.41641 −0.173761
\(647\) 18.3262 0.720479 0.360239 0.932860i \(-0.382695\pi\)
0.360239 + 0.932860i \(0.382695\pi\)
\(648\) 7.70820 0.302807
\(649\) 65.7426 2.58062
\(650\) −24.2705 −0.951968
\(651\) 5.83282 0.228606
\(652\) −5.85410 −0.229264
\(653\) 6.90983 0.270403 0.135201 0.990818i \(-0.456832\pi\)
0.135201 + 0.990818i \(0.456832\pi\)
\(654\) 0.201626 0.00788421
\(655\) −70.1246 −2.74000
\(656\) −11.1803 −0.436519
\(657\) 36.2705 1.41505
\(658\) 25.6869 1.00138
\(659\) −6.47214 −0.252119 −0.126059 0.992023i \(-0.540233\pi\)
−0.126059 + 0.992023i \(0.540233\pi\)
\(660\) −6.38197 −0.248418
\(661\) 32.2918 1.25601 0.628003 0.778211i \(-0.283873\pi\)
0.628003 + 0.778211i \(0.283873\pi\)
\(662\) −25.5623 −0.993507
\(663\) 1.68692 0.0655145
\(664\) 15.9443 0.618758
\(665\) −32.5623 −1.26271
\(666\) −13.8541 −0.536836
\(667\) 35.5967 1.37831
\(668\) −0.763932 −0.0295574
\(669\) 10.8541 0.419644
\(670\) 17.5623 0.678491
\(671\) 21.3262 0.823290
\(672\) 1.14590 0.0442040
\(673\) 48.5410 1.87112 0.935559 0.353169i \(-0.114896\pi\)
0.935559 + 0.353169i \(0.114896\pi\)
\(674\) 2.38197 0.0917499
\(675\) 18.0902 0.696291
\(676\) −4.00000 −0.153846
\(677\) 12.8885 0.495347 0.247673 0.968844i \(-0.420334\pi\)
0.247673 + 0.968844i \(0.420334\pi\)
\(678\) 2.52786 0.0970820
\(679\) −54.7082 −2.09951
\(680\) −5.32624 −0.204252
\(681\) −2.72949 −0.104594
\(682\) −23.5066 −0.900113
\(683\) 11.6180 0.444552 0.222276 0.974984i \(-0.428651\pi\)
0.222276 + 0.974984i \(0.428651\pi\)
\(684\) 8.56231 0.327388
\(685\) 41.8328 1.59835
\(686\) 15.0000 0.572703
\(687\) 8.63119 0.329300
\(688\) −4.76393 −0.181623
\(689\) 27.0000 1.02862
\(690\) −10.3262 −0.393113
\(691\) −3.90983 −0.148737 −0.0743685 0.997231i \(-0.523694\pi\)
−0.0743685 + 0.997231i \(0.523694\pi\)
\(692\) −23.3262 −0.886731
\(693\) −39.5410 −1.50204
\(694\) −24.3262 −0.923411
\(695\) 23.6180 0.895883
\(696\) 1.81966 0.0689740
\(697\) −16.4590 −0.623428
\(698\) −9.29180 −0.351700
\(699\) −4.14590 −0.156812
\(700\) −24.2705 −0.917339
\(701\) 2.21478 0.0836512 0.0418256 0.999125i \(-0.486683\pi\)
0.0418256 + 0.999125i \(0.486683\pi\)
\(702\) −6.70820 −0.253185
\(703\) −14.5623 −0.549228
\(704\) −4.61803 −0.174049
\(705\) −11.8328 −0.445650
\(706\) −29.1803 −1.09822
\(707\) −2.29180 −0.0861919
\(708\) 5.43769 0.204361
\(709\) −34.9443 −1.31236 −0.656180 0.754605i \(-0.727829\pi\)
−0.656180 + 0.754605i \(0.727829\pi\)
\(710\) −21.5066 −0.807127
\(711\) −13.8541 −0.519569
\(712\) 7.79837 0.292256
\(713\) −38.0344 −1.42440
\(714\) 1.68692 0.0631313
\(715\) −50.1246 −1.87455
\(716\) −9.00000 −0.336346
\(717\) 3.70820 0.138485
\(718\) 34.5967 1.29114
\(719\) −32.9443 −1.22861 −0.614307 0.789067i \(-0.710564\pi\)
−0.614307 + 0.789067i \(0.710564\pi\)
\(720\) 10.3262 0.384836
\(721\) −35.5623 −1.32441
\(722\) −10.0000 −0.372161
\(723\) −6.27051 −0.233203
\(724\) −18.0000 −0.668965
\(725\) −38.5410 −1.43138
\(726\) −3.94427 −0.146386
\(727\) 6.47214 0.240038 0.120019 0.992772i \(-0.461704\pi\)
0.120019 + 0.992772i \(0.461704\pi\)
\(728\) 9.00000 0.333562
\(729\) −19.4377 −0.719915
\(730\) 45.9787 1.70175
\(731\) −7.01316 −0.259391
\(732\) 1.76393 0.0651968
\(733\) −36.8885 −1.36251 −0.681255 0.732046i \(-0.738565\pi\)
−0.681255 + 0.732046i \(0.738565\pi\)
\(734\) −30.8885 −1.14012
\(735\) 2.76393 0.101949
\(736\) −7.47214 −0.275427
\(737\) 22.4164 0.825719
\(738\) 31.9098 1.17462
\(739\) −29.5279 −1.08620 −0.543100 0.839668i \(-0.682750\pi\)
−0.543100 + 0.839668i \(0.682750\pi\)
\(740\) −17.5623 −0.645603
\(741\) −3.43769 −0.126287
\(742\) 27.0000 0.991201
\(743\) −17.2361 −0.632330 −0.316165 0.948704i \(-0.602395\pi\)
−0.316165 + 0.948704i \(0.602395\pi\)
\(744\) −1.94427 −0.0712805
\(745\) −8.09017 −0.296401
\(746\) −12.0000 −0.439351
\(747\) −45.5066 −1.66500
\(748\) −6.79837 −0.248573
\(749\) 24.7082 0.902818
\(750\) 4.27051 0.155937
\(751\) −3.43769 −0.125443 −0.0627216 0.998031i \(-0.519978\pi\)
−0.0627216 + 0.998031i \(0.519978\pi\)
\(752\) −8.56231 −0.312235
\(753\) 6.47214 0.235858
\(754\) 14.2918 0.520477
\(755\) −53.5410 −1.94856
\(756\) −6.70820 −0.243975
\(757\) −1.70820 −0.0620857 −0.0310429 0.999518i \(-0.509883\pi\)
−0.0310429 + 0.999518i \(0.509883\pi\)
\(758\) −30.8328 −1.11990
\(759\) −13.1803 −0.478416
\(760\) 10.8541 0.393720
\(761\) 26.0344 0.943748 0.471874 0.881666i \(-0.343578\pi\)
0.471874 + 0.881666i \(0.343578\pi\)
\(762\) −5.50658 −0.199482
\(763\) 1.58359 0.0573299
\(764\) −22.3607 −0.808981
\(765\) 15.2016 0.549616
\(766\) −15.7082 −0.567560
\(767\) 42.7082 1.54210
\(768\) −0.381966 −0.0137830
\(769\) 13.4164 0.483808 0.241904 0.970300i \(-0.422228\pi\)
0.241904 + 0.970300i \(0.422228\pi\)
\(770\) −50.1246 −1.80637
\(771\) 10.8541 0.390901
\(772\) 9.85410 0.354657
\(773\) −36.7639 −1.32231 −0.661153 0.750251i \(-0.729933\pi\)
−0.661153 + 0.750251i \(0.729933\pi\)
\(774\) 13.5967 0.488725
\(775\) 41.1803 1.47924
\(776\) 18.2361 0.654637
\(777\) 5.56231 0.199547
\(778\) −22.7639 −0.816127
\(779\) 33.5410 1.20173
\(780\) −4.14590 −0.148447
\(781\) −27.4508 −0.982269
\(782\) −11.0000 −0.393359
\(783\) −10.6525 −0.380688
\(784\) 2.00000 0.0714286
\(785\) 11.1803 0.399043
\(786\) −7.40325 −0.264065
\(787\) 9.94427 0.354475 0.177238 0.984168i \(-0.443284\pi\)
0.177238 + 0.984168i \(0.443284\pi\)
\(788\) 21.7984 0.776535
\(789\) 10.0689 0.358462
\(790\) −17.5623 −0.624839
\(791\) 19.8541 0.705931
\(792\) 13.1803 0.468343
\(793\) 13.8541 0.491974
\(794\) 11.5623 0.410331
\(795\) −12.4377 −0.441120
\(796\) −12.2705 −0.434917
\(797\) −13.0557 −0.462458 −0.231229 0.972899i \(-0.574275\pi\)
−0.231229 + 0.972899i \(0.574275\pi\)
\(798\) −3.43769 −0.121693
\(799\) −12.6049 −0.445929
\(800\) 8.09017 0.286031
\(801\) −22.2574 −0.786425
\(802\) −31.9443 −1.12799
\(803\) 58.6869 2.07102
\(804\) 1.85410 0.0653891
\(805\) −81.1033 −2.85852
\(806\) −15.2705 −0.537881
\(807\) −5.56231 −0.195802
\(808\) 0.763932 0.0268750
\(809\) 37.8541 1.33088 0.665440 0.746452i \(-0.268244\pi\)
0.665440 + 0.746452i \(0.268244\pi\)
\(810\) −27.8885 −0.979904
\(811\) −5.05573 −0.177531 −0.0887653 0.996053i \(-0.528292\pi\)
−0.0887653 + 0.996053i \(0.528292\pi\)
\(812\) 14.2918 0.501544
\(813\) 1.67376 0.0587014
\(814\) −22.4164 −0.785695
\(815\) 21.1803 0.741915
\(816\) −0.562306 −0.0196846
\(817\) 14.2918 0.500007
\(818\) −6.58359 −0.230190
\(819\) −25.6869 −0.897574
\(820\) 40.4508 1.41260
\(821\) −39.5066 −1.37879 −0.689395 0.724386i \(-0.742123\pi\)
−0.689395 + 0.724386i \(0.742123\pi\)
\(822\) 4.41641 0.154040
\(823\) −7.41641 −0.258520 −0.129260 0.991611i \(-0.541260\pi\)
−0.129260 + 0.991611i \(0.541260\pi\)
\(824\) 11.8541 0.412957
\(825\) 14.2705 0.496835
\(826\) 42.7082 1.48601
\(827\) 23.0557 0.801726 0.400863 0.916138i \(-0.368710\pi\)
0.400863 + 0.916138i \(0.368710\pi\)
\(828\) 21.3262 0.741138
\(829\) −20.7082 −0.719226 −0.359613 0.933102i \(-0.617091\pi\)
−0.359613 + 0.933102i \(0.617091\pi\)
\(830\) −57.6869 −2.00234
\(831\) 0.167184 0.00579956
\(832\) −3.00000 −0.104006
\(833\) 2.94427 0.102013
\(834\) 2.49342 0.0863401
\(835\) 2.76393 0.0956498
\(836\) 13.8541 0.479154
\(837\) 11.3820 0.393418
\(838\) 16.3262 0.563981
\(839\) 46.6525 1.61062 0.805311 0.592852i \(-0.201998\pi\)
0.805311 + 0.592852i \(0.201998\pi\)
\(840\) −4.14590 −0.143047
\(841\) −6.30495 −0.217412
\(842\) −40.3951 −1.39211
\(843\) −7.39512 −0.254702
\(844\) 11.1459 0.383658
\(845\) 14.4721 0.497857
\(846\) 24.4377 0.840185
\(847\) −30.9787 −1.06444
\(848\) −9.00000 −0.309061
\(849\) 1.03444 0.0355020
\(850\) 11.9098 0.408504
\(851\) −36.2705 −1.24334
\(852\) −2.27051 −0.0777864
\(853\) 33.5623 1.14915 0.574576 0.818451i \(-0.305167\pi\)
0.574576 + 0.818451i \(0.305167\pi\)
\(854\) 13.8541 0.474078
\(855\) −30.9787 −1.05945
\(856\) −8.23607 −0.281503
\(857\) −20.9098 −0.714266 −0.357133 0.934054i \(-0.616246\pi\)
−0.357133 + 0.934054i \(0.616246\pi\)
\(858\) −5.29180 −0.180659
\(859\) 33.9443 1.15816 0.579082 0.815269i \(-0.303411\pi\)
0.579082 + 0.815269i \(0.303411\pi\)
\(860\) 17.2361 0.587745
\(861\) −12.8115 −0.436616
\(862\) −29.2361 −0.995784
\(863\) 32.0132 1.08974 0.544870 0.838520i \(-0.316579\pi\)
0.544870 + 0.838520i \(0.316579\pi\)
\(864\) 2.23607 0.0760726
\(865\) 84.3951 2.86952
\(866\) 32.4164 1.10155
\(867\) 5.66563 0.192415
\(868\) −15.2705 −0.518315
\(869\) −22.4164 −0.760425
\(870\) −6.58359 −0.223205
\(871\) 14.5623 0.493425
\(872\) −0.527864 −0.0178757
\(873\) −52.0476 −1.76154
\(874\) 22.4164 0.758246
\(875\) 33.5410 1.13389
\(876\) 4.85410 0.164005
\(877\) 5.12461 0.173046 0.0865229 0.996250i \(-0.472424\pi\)
0.0865229 + 0.996250i \(0.472424\pi\)
\(878\) −13.0000 −0.438729
\(879\) 7.98684 0.269390
\(880\) 16.7082 0.563233
\(881\) 31.7214 1.06872 0.534360 0.845257i \(-0.320553\pi\)
0.534360 + 0.845257i \(0.320553\pi\)
\(882\) −5.70820 −0.192205
\(883\) −21.9656 −0.739200 −0.369600 0.929191i \(-0.620505\pi\)
−0.369600 + 0.929191i \(0.620505\pi\)
\(884\) −4.41641 −0.148540
\(885\) −19.6738 −0.661326
\(886\) 13.4721 0.452605
\(887\) 9.70820 0.325970 0.162985 0.986629i \(-0.447888\pi\)
0.162985 + 0.986629i \(0.447888\pi\)
\(888\) −1.85410 −0.0622196
\(889\) −43.2492 −1.45053
\(890\) −28.2148 −0.945762
\(891\) −35.5967 −1.19254
\(892\) −28.4164 −0.951452
\(893\) 25.6869 0.859580
\(894\) −0.854102 −0.0285654
\(895\) 32.5623 1.08844
\(896\) −3.00000 −0.100223
\(897\) −8.56231 −0.285887
\(898\) 27.3607 0.913038
\(899\) −24.2492 −0.808757
\(900\) −23.0902 −0.769672
\(901\) −13.2492 −0.441396
\(902\) 51.6312 1.71913
\(903\) −5.45898 −0.181663
\(904\) −6.61803 −0.220113
\(905\) 65.1246 2.16482
\(906\) −5.65248 −0.187791
\(907\) 5.41641 0.179849 0.0899244 0.995949i \(-0.471337\pi\)
0.0899244 + 0.995949i \(0.471337\pi\)
\(908\) 7.14590 0.237145
\(909\) −2.18034 −0.0723173
\(910\) −32.5623 −1.07943
\(911\) −11.5623 −0.383076 −0.191538 0.981485i \(-0.561348\pi\)
−0.191538 + 0.981485i \(0.561348\pi\)
\(912\) 1.14590 0.0379445
\(913\) −73.6312 −2.43684
\(914\) −11.9656 −0.395785
\(915\) −6.38197 −0.210981
\(916\) −22.5967 −0.746618
\(917\) −58.1459 −1.92015
\(918\) 3.29180 0.108645
\(919\) −45.7214 −1.50821 −0.754104 0.656755i \(-0.771929\pi\)
−0.754104 + 0.656755i \(0.771929\pi\)
\(920\) 27.0344 0.891299
\(921\) −5.76393 −0.189928
\(922\) −4.61803 −0.152087
\(923\) −17.8328 −0.586974
\(924\) −5.29180 −0.174087
\(925\) 39.2705 1.29121
\(926\) −18.3607 −0.603369
\(927\) −33.8328 −1.11122
\(928\) −4.76393 −0.156384
\(929\) −11.8328 −0.388222 −0.194111 0.980980i \(-0.562182\pi\)
−0.194111 + 0.980980i \(0.562182\pi\)
\(930\) 7.03444 0.230668
\(931\) −6.00000 −0.196642
\(932\) 10.8541 0.355538
\(933\) −11.1672 −0.365597
\(934\) 7.20163 0.235644
\(935\) 24.5967 0.804400
\(936\) 8.56231 0.279868
\(937\) 44.8328 1.46462 0.732312 0.680969i \(-0.238441\pi\)
0.732312 + 0.680969i \(0.238441\pi\)
\(938\) 14.5623 0.475476
\(939\) 3.72136 0.121442
\(940\) 30.9787 1.01041
\(941\) −22.7984 −0.743206 −0.371603 0.928392i \(-0.621192\pi\)
−0.371603 + 0.928392i \(0.621192\pi\)
\(942\) 1.18034 0.0384576
\(943\) 83.5410 2.72047
\(944\) −14.2361 −0.463345
\(945\) 24.2705 0.789520
\(946\) 22.0000 0.715282
\(947\) −40.7984 −1.32577 −0.662885 0.748722i \(-0.730668\pi\)
−0.662885 + 0.748722i \(0.730668\pi\)
\(948\) −1.85410 −0.0602184
\(949\) 38.1246 1.23758
\(950\) −24.2705 −0.787439
\(951\) 3.20163 0.103820
\(952\) −4.41641 −0.143137
\(953\) −57.6525 −1.86755 −0.933773 0.357865i \(-0.883505\pi\)
−0.933773 + 0.357865i \(0.883505\pi\)
\(954\) 25.6869 0.831645
\(955\) 80.9017 2.61792
\(956\) −9.70820 −0.313986
\(957\) −8.40325 −0.271639
\(958\) −7.14590 −0.230873
\(959\) 34.6869 1.12010
\(960\) 1.38197 0.0446028
\(961\) −5.09017 −0.164199
\(962\) −14.5623 −0.469508
\(963\) 23.5066 0.757489
\(964\) 16.4164 0.528737
\(965\) −35.6525 −1.14769
\(966\) −8.56231 −0.275488
\(967\) 5.16718 0.166165 0.0830827 0.996543i \(-0.473523\pi\)
0.0830827 + 0.996543i \(0.473523\pi\)
\(968\) 10.3262 0.331898
\(969\) 1.68692 0.0541916
\(970\) −65.9787 −2.11845
\(971\) 49.2492 1.58048 0.790241 0.612796i \(-0.209955\pi\)
0.790241 + 0.612796i \(0.209955\pi\)
\(972\) −9.65248 −0.309603
\(973\) 19.5836 0.627821
\(974\) −19.8885 −0.637270
\(975\) 9.27051 0.296894
\(976\) −4.61803 −0.147820
\(977\) −18.2361 −0.583424 −0.291712 0.956506i \(-0.594225\pi\)
−0.291712 + 0.956506i \(0.594225\pi\)
\(978\) 2.23607 0.0715016
\(979\) −36.0132 −1.15099
\(980\) −7.23607 −0.231148
\(981\) 1.50658 0.0481013
\(982\) 27.2705 0.870237
\(983\) 31.7426 1.01243 0.506217 0.862406i \(-0.331044\pi\)
0.506217 + 0.862406i \(0.331044\pi\)
\(984\) 4.27051 0.136139
\(985\) −78.8673 −2.51292
\(986\) −7.01316 −0.223344
\(987\) −9.81153 −0.312304
\(988\) 9.00000 0.286328
\(989\) 35.5967 1.13191
\(990\) −47.6869 −1.51559
\(991\) 53.3050 1.69329 0.846644 0.532160i \(-0.178620\pi\)
0.846644 + 0.532160i \(0.178620\pi\)
\(992\) 5.09017 0.161613
\(993\) 9.76393 0.309849
\(994\) −17.8328 −0.565623
\(995\) 44.3951 1.40742
\(996\) −6.09017 −0.192974
\(997\) 35.0000 1.10846 0.554231 0.832363i \(-0.313013\pi\)
0.554231 + 0.832363i \(0.313013\pi\)
\(998\) 25.6525 0.812015
\(999\) 10.8541 0.343409
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 \(a_p\))