Properties

Label 8007.2.a.f.1.4
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46582 q^{2} -1.00000 q^{3} +4.08028 q^{4} +3.93570 q^{5} +2.46582 q^{6} -1.94268 q^{7} -5.12960 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.46582 q^{2} -1.00000 q^{3} +4.08028 q^{4} +3.93570 q^{5} +2.46582 q^{6} -1.94268 q^{7} -5.12960 q^{8} +1.00000 q^{9} -9.70474 q^{10} +2.09500 q^{11} -4.08028 q^{12} +1.26904 q^{13} +4.79030 q^{14} -3.93570 q^{15} +4.48813 q^{16} -1.00000 q^{17} -2.46582 q^{18} +6.20060 q^{19} +16.0588 q^{20} +1.94268 q^{21} -5.16591 q^{22} -3.25118 q^{23} +5.12960 q^{24} +10.4897 q^{25} -3.12923 q^{26} -1.00000 q^{27} -7.92668 q^{28} -0.821135 q^{29} +9.70474 q^{30} -6.07544 q^{31} -0.807730 q^{32} -2.09500 q^{33} +2.46582 q^{34} -7.64580 q^{35} +4.08028 q^{36} -5.69979 q^{37} -15.2896 q^{38} -1.26904 q^{39} -20.1886 q^{40} -5.88604 q^{41} -4.79030 q^{42} -3.21323 q^{43} +8.54820 q^{44} +3.93570 q^{45} +8.01683 q^{46} +6.01116 q^{47} -4.48813 q^{48} -3.22599 q^{49} -25.8658 q^{50} +1.00000 q^{51} +5.17804 q^{52} -12.3838 q^{53} +2.46582 q^{54} +8.24530 q^{55} +9.96518 q^{56} -6.20060 q^{57} +2.02477 q^{58} +1.39896 q^{59} -16.0588 q^{60} -0.577604 q^{61} +14.9810 q^{62} -1.94268 q^{63} -6.98455 q^{64} +4.99456 q^{65} +5.16591 q^{66} +10.3105 q^{67} -4.08028 q^{68} +3.25118 q^{69} +18.8532 q^{70} -8.11871 q^{71} -5.12960 q^{72} -12.1451 q^{73} +14.0547 q^{74} -10.4897 q^{75} +25.3002 q^{76} -4.06992 q^{77} +3.12923 q^{78} +15.1150 q^{79} +17.6639 q^{80} +1.00000 q^{81} +14.5139 q^{82} -14.8563 q^{83} +7.92668 q^{84} -3.93570 q^{85} +7.92326 q^{86} +0.821135 q^{87} -10.7465 q^{88} +9.36477 q^{89} -9.70474 q^{90} -2.46534 q^{91} -13.2657 q^{92} +6.07544 q^{93} -14.8224 q^{94} +24.4037 q^{95} +0.807730 q^{96} -13.6990 q^{97} +7.95473 q^{98} +2.09500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46582 −1.74360 −0.871800 0.489862i \(-0.837047\pi\)
−0.871800 + 0.489862i \(0.837047\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.08028 2.04014
\(5\) 3.93570 1.76010 0.880049 0.474883i \(-0.157510\pi\)
0.880049 + 0.474883i \(0.157510\pi\)
\(6\) 2.46582 1.00667
\(7\) −1.94268 −0.734264 −0.367132 0.930169i \(-0.619660\pi\)
−0.367132 + 0.930169i \(0.619660\pi\)
\(8\) −5.12960 −1.81359
\(9\) 1.00000 0.333333
\(10\) −9.70474 −3.06891
\(11\) 2.09500 0.631667 0.315834 0.948815i \(-0.397716\pi\)
0.315834 + 0.948815i \(0.397716\pi\)
\(12\) −4.08028 −1.17788
\(13\) 1.26904 0.351968 0.175984 0.984393i \(-0.443689\pi\)
0.175984 + 0.984393i \(0.443689\pi\)
\(14\) 4.79030 1.28026
\(15\) −3.93570 −1.01619
\(16\) 4.48813 1.12203
\(17\) −1.00000 −0.242536
\(18\) −2.46582 −0.581200
\(19\) 6.20060 1.42252 0.711258 0.702931i \(-0.248126\pi\)
0.711258 + 0.702931i \(0.248126\pi\)
\(20\) 16.0588 3.59085
\(21\) 1.94268 0.423928
\(22\) −5.16591 −1.10138
\(23\) −3.25118 −0.677917 −0.338959 0.940801i \(-0.610075\pi\)
−0.338959 + 0.940801i \(0.610075\pi\)
\(24\) 5.12960 1.04708
\(25\) 10.4897 2.09795
\(26\) −3.12923 −0.613692
\(27\) −1.00000 −0.192450
\(28\) −7.92668 −1.49800
\(29\) −0.821135 −0.152481 −0.0762405 0.997089i \(-0.524292\pi\)
−0.0762405 + 0.997089i \(0.524292\pi\)
\(30\) 9.70474 1.77183
\(31\) −6.07544 −1.09118 −0.545590 0.838052i \(-0.683695\pi\)
−0.545590 + 0.838052i \(0.683695\pi\)
\(32\) −0.807730 −0.142788
\(33\) −2.09500 −0.364693
\(34\) 2.46582 0.422885
\(35\) −7.64580 −1.29238
\(36\) 4.08028 0.680047
\(37\) −5.69979 −0.937039 −0.468520 0.883453i \(-0.655212\pi\)
−0.468520 + 0.883453i \(0.655212\pi\)
\(38\) −15.2896 −2.48030
\(39\) −1.26904 −0.203209
\(40\) −20.1886 −3.19209
\(41\) −5.88604 −0.919246 −0.459623 0.888114i \(-0.652015\pi\)
−0.459623 + 0.888114i \(0.652015\pi\)
\(42\) −4.79030 −0.739160
\(43\) −3.21323 −0.490013 −0.245007 0.969521i \(-0.578790\pi\)
−0.245007 + 0.969521i \(0.578790\pi\)
\(44\) 8.54820 1.28869
\(45\) 3.93570 0.586699
\(46\) 8.01683 1.18202
\(47\) 6.01116 0.876817 0.438409 0.898776i \(-0.355542\pi\)
0.438409 + 0.898776i \(0.355542\pi\)
\(48\) −4.48813 −0.647806
\(49\) −3.22599 −0.460856
\(50\) −25.8658 −3.65798
\(51\) 1.00000 0.140028
\(52\) 5.17804 0.718065
\(53\) −12.3838 −1.70105 −0.850523 0.525937i \(-0.823715\pi\)
−0.850523 + 0.525937i \(0.823715\pi\)
\(54\) 2.46582 0.335556
\(55\) 8.24530 1.11180
\(56\) 9.96518 1.33165
\(57\) −6.20060 −0.821290
\(58\) 2.02477 0.265866
\(59\) 1.39896 0.182130 0.0910649 0.995845i \(-0.470973\pi\)
0.0910649 + 0.995845i \(0.470973\pi\)
\(60\) −16.0588 −2.07318
\(61\) −0.577604 −0.0739547 −0.0369773 0.999316i \(-0.511773\pi\)
−0.0369773 + 0.999316i \(0.511773\pi\)
\(62\) 14.9810 1.90258
\(63\) −1.94268 −0.244755
\(64\) −6.98455 −0.873068
\(65\) 4.99456 0.619499
\(66\) 5.16591 0.635879
\(67\) 10.3105 1.25962 0.629812 0.776748i \(-0.283132\pi\)
0.629812 + 0.776748i \(0.283132\pi\)
\(68\) −4.08028 −0.494807
\(69\) 3.25118 0.391396
\(70\) 18.8532 2.25339
\(71\) −8.11871 −0.963514 −0.481757 0.876305i \(-0.660001\pi\)
−0.481757 + 0.876305i \(0.660001\pi\)
\(72\) −5.12960 −0.604530
\(73\) −12.1451 −1.42148 −0.710739 0.703455i \(-0.751640\pi\)
−0.710739 + 0.703455i \(0.751640\pi\)
\(74\) 14.0547 1.63382
\(75\) −10.4897 −1.21125
\(76\) 25.3002 2.90213
\(77\) −4.06992 −0.463811
\(78\) 3.12923 0.354315
\(79\) 15.1150 1.70057 0.850284 0.526324i \(-0.176430\pi\)
0.850284 + 0.526324i \(0.176430\pi\)
\(80\) 17.6639 1.97489
\(81\) 1.00000 0.111111
\(82\) 14.5139 1.60280
\(83\) −14.8563 −1.63069 −0.815344 0.578977i \(-0.803452\pi\)
−0.815344 + 0.578977i \(0.803452\pi\)
\(84\) 7.92668 0.864872
\(85\) −3.93570 −0.426887
\(86\) 7.92326 0.854387
\(87\) 0.821135 0.0880349
\(88\) −10.7465 −1.14559
\(89\) 9.36477 0.992663 0.496332 0.868133i \(-0.334680\pi\)
0.496332 + 0.868133i \(0.334680\pi\)
\(90\) −9.70474 −1.02297
\(91\) −2.46534 −0.258438
\(92\) −13.2657 −1.38305
\(93\) 6.07544 0.629994
\(94\) −14.8224 −1.52882
\(95\) 24.4037 2.50377
\(96\) 0.807730 0.0824386
\(97\) −13.6990 −1.39092 −0.695461 0.718564i \(-0.744800\pi\)
−0.695461 + 0.718564i \(0.744800\pi\)
\(98\) 7.95473 0.803549
\(99\) 2.09500 0.210556
\(100\) 42.8010 4.28010
\(101\) −12.5294 −1.24672 −0.623358 0.781936i \(-0.714232\pi\)
−0.623358 + 0.781936i \(0.714232\pi\)
\(102\) −2.46582 −0.244153
\(103\) −4.34464 −0.428090 −0.214045 0.976824i \(-0.568664\pi\)
−0.214045 + 0.976824i \(0.568664\pi\)
\(104\) −6.50967 −0.638326
\(105\) 7.64580 0.746154
\(106\) 30.5363 2.96595
\(107\) 6.34145 0.613051 0.306526 0.951862i \(-0.400834\pi\)
0.306526 + 0.951862i \(0.400834\pi\)
\(108\) −4.08028 −0.392625
\(109\) −0.667254 −0.0639113 −0.0319557 0.999489i \(-0.510174\pi\)
−0.0319557 + 0.999489i \(0.510174\pi\)
\(110\) −20.3315 −1.93853
\(111\) 5.69979 0.541000
\(112\) −8.71901 −0.823869
\(113\) −5.41124 −0.509046 −0.254523 0.967067i \(-0.581919\pi\)
−0.254523 + 0.967067i \(0.581919\pi\)
\(114\) 15.2896 1.43200
\(115\) −12.7957 −1.19320
\(116\) −3.35046 −0.311083
\(117\) 1.26904 0.117323
\(118\) −3.44960 −0.317561
\(119\) 1.94268 0.178085
\(120\) 20.1886 1.84296
\(121\) −6.61096 −0.600996
\(122\) 1.42427 0.128947
\(123\) 5.88604 0.530727
\(124\) −24.7895 −2.22616
\(125\) 21.6059 1.93249
\(126\) 4.79030 0.426754
\(127\) −16.3485 −1.45069 −0.725347 0.688383i \(-0.758321\pi\)
−0.725347 + 0.688383i \(0.758321\pi\)
\(128\) 18.8381 1.66507
\(129\) 3.21323 0.282909
\(130\) −12.3157 −1.08016
\(131\) 3.15110 0.275313 0.137656 0.990480i \(-0.456043\pi\)
0.137656 + 0.990480i \(0.456043\pi\)
\(132\) −8.54820 −0.744026
\(133\) −12.0458 −1.04450
\(134\) −25.4238 −2.19628
\(135\) −3.93570 −0.338731
\(136\) 5.12960 0.439860
\(137\) 6.04604 0.516548 0.258274 0.966072i \(-0.416846\pi\)
0.258274 + 0.966072i \(0.416846\pi\)
\(138\) −8.01683 −0.682438
\(139\) −10.2273 −0.867472 −0.433736 0.901040i \(-0.642805\pi\)
−0.433736 + 0.901040i \(0.642805\pi\)
\(140\) −31.1970 −2.63663
\(141\) −6.01116 −0.506231
\(142\) 20.0193 1.67998
\(143\) 2.65864 0.222327
\(144\) 4.48813 0.374011
\(145\) −3.23174 −0.268381
\(146\) 29.9477 2.47849
\(147\) 3.22599 0.266075
\(148\) −23.2567 −1.91169
\(149\) −12.8668 −1.05409 −0.527044 0.849838i \(-0.676700\pi\)
−0.527044 + 0.849838i \(0.676700\pi\)
\(150\) 25.8658 2.11193
\(151\) −1.25253 −0.101929 −0.0509646 0.998700i \(-0.516230\pi\)
−0.0509646 + 0.998700i \(0.516230\pi\)
\(152\) −31.8066 −2.57986
\(153\) −1.00000 −0.0808452
\(154\) 10.0357 0.808700
\(155\) −23.9111 −1.92059
\(156\) −5.17804 −0.414575
\(157\) −1.00000 −0.0798087
\(158\) −37.2709 −2.96511
\(159\) 12.3838 0.982100
\(160\) −3.17898 −0.251321
\(161\) 6.31600 0.497770
\(162\) −2.46582 −0.193733
\(163\) −18.4392 −1.44427 −0.722135 0.691752i \(-0.756839\pi\)
−0.722135 + 0.691752i \(0.756839\pi\)
\(164\) −24.0167 −1.87539
\(165\) −8.24530 −0.641896
\(166\) 36.6329 2.84327
\(167\) −15.0426 −1.16403 −0.582016 0.813177i \(-0.697736\pi\)
−0.582016 + 0.813177i \(0.697736\pi\)
\(168\) −9.96518 −0.768830
\(169\) −11.3895 −0.876118
\(170\) 9.70474 0.744319
\(171\) 6.20060 0.474172
\(172\) −13.1109 −0.999696
\(173\) 8.63339 0.656385 0.328192 0.944611i \(-0.393561\pi\)
0.328192 + 0.944611i \(0.393561\pi\)
\(174\) −2.02477 −0.153498
\(175\) −20.3782 −1.54045
\(176\) 9.40266 0.708752
\(177\) −1.39896 −0.105153
\(178\) −23.0919 −1.73081
\(179\) 22.8232 1.70589 0.852943 0.522004i \(-0.174816\pi\)
0.852943 + 0.522004i \(0.174816\pi\)
\(180\) 16.0588 1.19695
\(181\) −5.37203 −0.399300 −0.199650 0.979867i \(-0.563980\pi\)
−0.199650 + 0.979867i \(0.563980\pi\)
\(182\) 6.07909 0.450612
\(183\) 0.577604 0.0426977
\(184\) 16.6773 1.22946
\(185\) −22.4327 −1.64928
\(186\) −14.9810 −1.09846
\(187\) −2.09500 −0.153202
\(188\) 24.5272 1.78883
\(189\) 1.94268 0.141309
\(190\) −60.1752 −4.36557
\(191\) 1.40332 0.101541 0.0507705 0.998710i \(-0.483832\pi\)
0.0507705 + 0.998710i \(0.483832\pi\)
\(192\) 6.98455 0.504066
\(193\) −21.2256 −1.52785 −0.763924 0.645306i \(-0.776730\pi\)
−0.763924 + 0.645306i \(0.776730\pi\)
\(194\) 33.7793 2.42521
\(195\) −4.99456 −0.357668
\(196\) −13.1630 −0.940211
\(197\) 19.9176 1.41907 0.709534 0.704672i \(-0.248906\pi\)
0.709534 + 0.704672i \(0.248906\pi\)
\(198\) −5.16591 −0.367125
\(199\) −24.5012 −1.73684 −0.868420 0.495829i \(-0.834864\pi\)
−0.868420 + 0.495829i \(0.834864\pi\)
\(200\) −53.8082 −3.80481
\(201\) −10.3105 −0.727244
\(202\) 30.8952 2.17378
\(203\) 1.59520 0.111961
\(204\) 4.08028 0.285677
\(205\) −23.1657 −1.61796
\(206\) 10.7131 0.746418
\(207\) −3.25118 −0.225972
\(208\) 5.69562 0.394920
\(209\) 12.9903 0.898557
\(210\) −18.8532 −1.30099
\(211\) 3.88948 0.267763 0.133881 0.990997i \(-0.457256\pi\)
0.133881 + 0.990997i \(0.457256\pi\)
\(212\) −50.5294 −3.47037
\(213\) 8.11871 0.556285
\(214\) −15.6369 −1.06892
\(215\) −12.6463 −0.862471
\(216\) 5.12960 0.349025
\(217\) 11.8026 0.801215
\(218\) 1.64533 0.111436
\(219\) 12.1451 0.820691
\(220\) 33.6432 2.26822
\(221\) −1.26904 −0.0853649
\(222\) −14.0547 −0.943287
\(223\) −2.47405 −0.165675 −0.0828373 0.996563i \(-0.526398\pi\)
−0.0828373 + 0.996563i \(0.526398\pi\)
\(224\) 1.56916 0.104844
\(225\) 10.4897 0.699315
\(226\) 13.3431 0.887573
\(227\) −3.58147 −0.237710 −0.118855 0.992912i \(-0.537922\pi\)
−0.118855 + 0.992912i \(0.537922\pi\)
\(228\) −25.3002 −1.67555
\(229\) −25.5136 −1.68598 −0.842992 0.537926i \(-0.819208\pi\)
−0.842992 + 0.537926i \(0.819208\pi\)
\(230\) 31.5518 2.08046
\(231\) 4.06992 0.267781
\(232\) 4.21210 0.276538
\(233\) −17.3310 −1.13539 −0.567694 0.823239i \(-0.692164\pi\)
−0.567694 + 0.823239i \(0.692164\pi\)
\(234\) −3.12923 −0.204564
\(235\) 23.6581 1.54328
\(236\) 5.70817 0.371570
\(237\) −15.1150 −0.981823
\(238\) −4.79030 −0.310509
\(239\) −1.09864 −0.0710650 −0.0355325 0.999369i \(-0.511313\pi\)
−0.0355325 + 0.999369i \(0.511313\pi\)
\(240\) −17.6639 −1.14020
\(241\) 15.8369 1.02014 0.510072 0.860132i \(-0.329619\pi\)
0.510072 + 0.860132i \(0.329619\pi\)
\(242\) 16.3015 1.04790
\(243\) −1.00000 −0.0641500
\(244\) −2.35679 −0.150878
\(245\) −12.6965 −0.811152
\(246\) −14.5139 −0.925375
\(247\) 7.86881 0.500681
\(248\) 31.1646 1.97895
\(249\) 14.8563 0.941478
\(250\) −53.2764 −3.36949
\(251\) 13.2834 0.838441 0.419220 0.907885i \(-0.362303\pi\)
0.419220 + 0.907885i \(0.362303\pi\)
\(252\) −7.92668 −0.499334
\(253\) −6.81123 −0.428218
\(254\) 40.3125 2.52943
\(255\) 3.93570 0.246463
\(256\) −32.4824 −2.03015
\(257\) 25.5220 1.59202 0.796010 0.605284i \(-0.206940\pi\)
0.796010 + 0.605284i \(0.206940\pi\)
\(258\) −7.92326 −0.493281
\(259\) 11.0729 0.688034
\(260\) 20.3792 1.26386
\(261\) −0.821135 −0.0508270
\(262\) −7.77005 −0.480035
\(263\) −13.7209 −0.846067 −0.423033 0.906114i \(-0.639035\pi\)
−0.423033 + 0.906114i \(0.639035\pi\)
\(264\) 10.7465 0.661404
\(265\) −48.7389 −2.99401
\(266\) 29.7028 1.82119
\(267\) −9.36477 −0.573114
\(268\) 42.0696 2.56981
\(269\) 24.0416 1.46584 0.732922 0.680313i \(-0.238156\pi\)
0.732922 + 0.680313i \(0.238156\pi\)
\(270\) 9.70474 0.590611
\(271\) 14.7868 0.898237 0.449118 0.893472i \(-0.351738\pi\)
0.449118 + 0.893472i \(0.351738\pi\)
\(272\) −4.48813 −0.272133
\(273\) 2.46534 0.149209
\(274\) −14.9085 −0.900653
\(275\) 21.9760 1.32520
\(276\) 13.2657 0.798502
\(277\) 3.69899 0.222251 0.111125 0.993806i \(-0.464555\pi\)
0.111125 + 0.993806i \(0.464555\pi\)
\(278\) 25.2188 1.51252
\(279\) −6.07544 −0.363727
\(280\) 39.2200 2.34384
\(281\) −5.31177 −0.316873 −0.158437 0.987369i \(-0.550645\pi\)
−0.158437 + 0.987369i \(0.550645\pi\)
\(282\) 14.8224 0.882664
\(283\) 5.29973 0.315036 0.157518 0.987516i \(-0.449651\pi\)
0.157518 + 0.987516i \(0.449651\pi\)
\(284\) −33.1266 −1.96570
\(285\) −24.4037 −1.44555
\(286\) −6.55574 −0.387649
\(287\) 11.4347 0.674969
\(288\) −0.807730 −0.0475959
\(289\) 1.00000 0.0588235
\(290\) 7.96890 0.467950
\(291\) 13.6990 0.803049
\(292\) −49.5555 −2.90002
\(293\) 7.19362 0.420256 0.210128 0.977674i \(-0.432612\pi\)
0.210128 + 0.977674i \(0.432612\pi\)
\(294\) −7.95473 −0.463929
\(295\) 5.50591 0.320566
\(296\) 29.2377 1.69940
\(297\) −2.09500 −0.121564
\(298\) 31.7272 1.83791
\(299\) −4.12587 −0.238605
\(300\) −42.8010 −2.47112
\(301\) 6.24228 0.359799
\(302\) 3.08851 0.177724
\(303\) 12.5294 0.719792
\(304\) 27.8291 1.59611
\(305\) −2.27328 −0.130167
\(306\) 2.46582 0.140962
\(307\) 23.9532 1.36708 0.683540 0.729913i \(-0.260440\pi\)
0.683540 + 0.729913i \(0.260440\pi\)
\(308\) −16.6064 −0.946239
\(309\) 4.34464 0.247158
\(310\) 58.9605 3.34873
\(311\) −15.8399 −0.898198 −0.449099 0.893482i \(-0.648255\pi\)
−0.449099 + 0.893482i \(0.648255\pi\)
\(312\) 6.50967 0.368538
\(313\) −17.1781 −0.970966 −0.485483 0.874246i \(-0.661356\pi\)
−0.485483 + 0.874246i \(0.661356\pi\)
\(314\) 2.46582 0.139154
\(315\) −7.64580 −0.430792
\(316\) 61.6734 3.46940
\(317\) 9.30425 0.522579 0.261289 0.965261i \(-0.415852\pi\)
0.261289 + 0.965261i \(0.415852\pi\)
\(318\) −30.5363 −1.71239
\(319\) −1.72028 −0.0963173
\(320\) −27.4891 −1.53669
\(321\) −6.34145 −0.353945
\(322\) −15.5741 −0.867912
\(323\) −6.20060 −0.345011
\(324\) 4.08028 0.226682
\(325\) 13.3119 0.738410
\(326\) 45.4678 2.51823
\(327\) 0.667254 0.0368992
\(328\) 30.1931 1.66713
\(329\) −11.6778 −0.643815
\(330\) 20.3315 1.11921
\(331\) 14.6559 0.805559 0.402779 0.915297i \(-0.368044\pi\)
0.402779 + 0.915297i \(0.368044\pi\)
\(332\) −60.6178 −3.32683
\(333\) −5.69979 −0.312346
\(334\) 37.0924 2.02961
\(335\) 40.5789 2.21706
\(336\) 8.71901 0.475661
\(337\) −26.1001 −1.42176 −0.710882 0.703312i \(-0.751704\pi\)
−0.710882 + 0.703312i \(0.751704\pi\)
\(338\) 28.0846 1.52760
\(339\) 5.41124 0.293898
\(340\) −16.0588 −0.870909
\(341\) −12.7281 −0.689263
\(342\) −15.2896 −0.826766
\(343\) 19.8658 1.07265
\(344\) 16.4826 0.888683
\(345\) 12.7957 0.688895
\(346\) −21.2884 −1.14447
\(347\) −17.4252 −0.935435 −0.467717 0.883878i \(-0.654923\pi\)
−0.467717 + 0.883878i \(0.654923\pi\)
\(348\) 3.35046 0.179604
\(349\) 6.91286 0.370037 0.185019 0.982735i \(-0.440765\pi\)
0.185019 + 0.982735i \(0.440765\pi\)
\(350\) 50.2490 2.68592
\(351\) −1.26904 −0.0677363
\(352\) −1.69220 −0.0901944
\(353\) 4.07980 0.217146 0.108573 0.994089i \(-0.465372\pi\)
0.108573 + 0.994089i \(0.465372\pi\)
\(354\) 3.44960 0.183344
\(355\) −31.9528 −1.69588
\(356\) 38.2109 2.02517
\(357\) −1.94268 −0.102818
\(358\) −56.2779 −2.97438
\(359\) 37.4720 1.97770 0.988849 0.148920i \(-0.0475796\pi\)
0.988849 + 0.148920i \(0.0475796\pi\)
\(360\) −20.1886 −1.06403
\(361\) 19.4475 1.02355
\(362\) 13.2465 0.696219
\(363\) 6.61096 0.346985
\(364\) −10.0593 −0.527249
\(365\) −47.7995 −2.50194
\(366\) −1.42427 −0.0744478
\(367\) −26.3985 −1.37799 −0.688995 0.724767i \(-0.741948\pi\)
−0.688995 + 0.724767i \(0.741948\pi\)
\(368\) −14.5917 −0.760646
\(369\) −5.88604 −0.306415
\(370\) 55.3149 2.87569
\(371\) 24.0578 1.24902
\(372\) 24.7895 1.28528
\(373\) 7.28160 0.377027 0.188513 0.982071i \(-0.439633\pi\)
0.188513 + 0.982071i \(0.439633\pi\)
\(374\) 5.16591 0.267123
\(375\) −21.6059 −1.11572
\(376\) −30.8349 −1.59019
\(377\) −1.04205 −0.0536685
\(378\) −4.79030 −0.246387
\(379\) 15.9189 0.817699 0.408849 0.912602i \(-0.365930\pi\)
0.408849 + 0.912602i \(0.365930\pi\)
\(380\) 99.5740 5.10804
\(381\) 16.3485 0.837559
\(382\) −3.46035 −0.177047
\(383\) 8.72967 0.446065 0.223033 0.974811i \(-0.428404\pi\)
0.223033 + 0.974811i \(0.428404\pi\)
\(384\) −18.8381 −0.961328
\(385\) −16.0180 −0.816352
\(386\) 52.3385 2.66396
\(387\) −3.21323 −0.163338
\(388\) −55.8957 −2.83768
\(389\) −10.1002 −0.512100 −0.256050 0.966664i \(-0.582421\pi\)
−0.256050 + 0.966664i \(0.582421\pi\)
\(390\) 12.3157 0.623630
\(391\) 3.25118 0.164419
\(392\) 16.5481 0.835804
\(393\) −3.15110 −0.158952
\(394\) −49.1132 −2.47429
\(395\) 59.4880 2.99317
\(396\) 8.54820 0.429563
\(397\) 26.5414 1.33208 0.666038 0.745918i \(-0.267989\pi\)
0.666038 + 0.745918i \(0.267989\pi\)
\(398\) 60.4155 3.02836
\(399\) 12.0458 0.603044
\(400\) 47.0793 2.35396
\(401\) −23.6062 −1.17884 −0.589419 0.807827i \(-0.700643\pi\)
−0.589419 + 0.807827i \(0.700643\pi\)
\(402\) 25.4238 1.26802
\(403\) −7.70997 −0.384061
\(404\) −51.1233 −2.54348
\(405\) 3.93570 0.195566
\(406\) −3.93349 −0.195216
\(407\) −11.9411 −0.591897
\(408\) −5.12960 −0.253953
\(409\) 30.0177 1.48428 0.742141 0.670244i \(-0.233811\pi\)
0.742141 + 0.670244i \(0.233811\pi\)
\(410\) 57.1225 2.82108
\(411\) −6.04604 −0.298229
\(412\) −17.7274 −0.873364
\(413\) −2.71774 −0.133731
\(414\) 8.01683 0.394005
\(415\) −58.4698 −2.87017
\(416\) −1.02504 −0.0502568
\(417\) 10.2273 0.500835
\(418\) −32.0318 −1.56672
\(419\) 27.6615 1.35135 0.675676 0.737199i \(-0.263852\pi\)
0.675676 + 0.737199i \(0.263852\pi\)
\(420\) 31.1970 1.52226
\(421\) −23.2516 −1.13321 −0.566607 0.823988i \(-0.691744\pi\)
−0.566607 + 0.823988i \(0.691744\pi\)
\(422\) −9.59076 −0.466871
\(423\) 6.01116 0.292272
\(424\) 63.5240 3.08500
\(425\) −10.4897 −0.508827
\(426\) −20.0193 −0.969939
\(427\) 1.12210 0.0543022
\(428\) 25.8749 1.25071
\(429\) −2.65864 −0.128361
\(430\) 31.1836 1.50381
\(431\) 33.2075 1.59955 0.799775 0.600300i \(-0.204952\pi\)
0.799775 + 0.600300i \(0.204952\pi\)
\(432\) −4.48813 −0.215935
\(433\) −16.8929 −0.811821 −0.405911 0.913913i \(-0.633046\pi\)
−0.405911 + 0.913913i \(0.633046\pi\)
\(434\) −29.1032 −1.39700
\(435\) 3.23174 0.154950
\(436\) −2.72258 −0.130388
\(437\) −20.1593 −0.964348
\(438\) −29.9477 −1.43096
\(439\) 15.2542 0.728043 0.364022 0.931390i \(-0.381403\pi\)
0.364022 + 0.931390i \(0.381403\pi\)
\(440\) −42.2952 −2.01634
\(441\) −3.22599 −0.153619
\(442\) 3.12923 0.148842
\(443\) −3.06259 −0.145508 −0.0727539 0.997350i \(-0.523179\pi\)
−0.0727539 + 0.997350i \(0.523179\pi\)
\(444\) 23.2567 1.10372
\(445\) 36.8569 1.74718
\(446\) 6.10057 0.288870
\(447\) 12.8668 0.608578
\(448\) 13.5687 0.641063
\(449\) −33.1299 −1.56350 −0.781748 0.623594i \(-0.785672\pi\)
−0.781748 + 0.623594i \(0.785672\pi\)
\(450\) −25.8658 −1.21933
\(451\) −12.3313 −0.580658
\(452\) −22.0794 −1.03853
\(453\) 1.25253 0.0588489
\(454\) 8.83126 0.414471
\(455\) −9.70283 −0.454876
\(456\) 31.8066 1.48948
\(457\) 0.285102 0.0133365 0.00666826 0.999978i \(-0.497877\pi\)
0.00666826 + 0.999978i \(0.497877\pi\)
\(458\) 62.9119 2.93968
\(459\) 1.00000 0.0466760
\(460\) −52.2099 −2.43430
\(461\) −5.25587 −0.244790 −0.122395 0.992481i \(-0.539058\pi\)
−0.122395 + 0.992481i \(0.539058\pi\)
\(462\) −10.0357 −0.466903
\(463\) 33.8046 1.57103 0.785517 0.618840i \(-0.212397\pi\)
0.785517 + 0.618840i \(0.212397\pi\)
\(464\) −3.68536 −0.171089
\(465\) 23.9111 1.10885
\(466\) 42.7351 1.97966
\(467\) −27.4259 −1.26912 −0.634560 0.772874i \(-0.718818\pi\)
−0.634560 + 0.772874i \(0.718818\pi\)
\(468\) 5.17804 0.239355
\(469\) −20.0299 −0.924897
\(470\) −58.3367 −2.69087
\(471\) 1.00000 0.0460776
\(472\) −7.17614 −0.330308
\(473\) −6.73173 −0.309525
\(474\) 37.2709 1.71191
\(475\) 65.0426 2.98436
\(476\) 7.92668 0.363319
\(477\) −12.3838 −0.567016
\(478\) 2.70905 0.123909
\(479\) 4.87246 0.222628 0.111314 0.993785i \(-0.464494\pi\)
0.111314 + 0.993785i \(0.464494\pi\)
\(480\) 3.17898 0.145100
\(481\) −7.23326 −0.329808
\(482\) −39.0510 −1.77872
\(483\) −6.31600 −0.287388
\(484\) −26.9746 −1.22612
\(485\) −53.9151 −2.44816
\(486\) 2.46582 0.111852
\(487\) −24.0036 −1.08771 −0.543853 0.839181i \(-0.683035\pi\)
−0.543853 + 0.839181i \(0.683035\pi\)
\(488\) 2.96288 0.134123
\(489\) 18.4392 0.833850
\(490\) 31.3074 1.41432
\(491\) 14.5635 0.657242 0.328621 0.944462i \(-0.393416\pi\)
0.328621 + 0.944462i \(0.393416\pi\)
\(492\) 24.0167 1.08276
\(493\) 0.821135 0.0369821
\(494\) −19.4031 −0.872987
\(495\) 8.24530 0.370599
\(496\) −27.2674 −1.22434
\(497\) 15.7721 0.707474
\(498\) −36.6329 −1.64156
\(499\) −20.4267 −0.914424 −0.457212 0.889358i \(-0.651152\pi\)
−0.457212 + 0.889358i \(0.651152\pi\)
\(500\) 88.1582 3.94256
\(501\) 15.0426 0.672055
\(502\) −32.7545 −1.46191
\(503\) 12.4664 0.555849 0.277924 0.960603i \(-0.410354\pi\)
0.277924 + 0.960603i \(0.410354\pi\)
\(504\) 9.96518 0.443884
\(505\) −49.3118 −2.19434
\(506\) 16.7953 0.746641
\(507\) 11.3895 0.505827
\(508\) −66.7065 −2.95962
\(509\) −5.06355 −0.224438 −0.112219 0.993684i \(-0.535796\pi\)
−0.112219 + 0.993684i \(0.535796\pi\)
\(510\) −9.70474 −0.429733
\(511\) 23.5941 1.04374
\(512\) 42.4195 1.87469
\(513\) −6.20060 −0.273763
\(514\) −62.9328 −2.77584
\(515\) −17.0992 −0.753481
\(516\) 13.1109 0.577175
\(517\) 12.5934 0.553857
\(518\) −27.3037 −1.19966
\(519\) −8.63339 −0.378964
\(520\) −25.6201 −1.12352
\(521\) 29.1125 1.27544 0.637721 0.770268i \(-0.279877\pi\)
0.637721 + 0.770268i \(0.279877\pi\)
\(522\) 2.02477 0.0886219
\(523\) 6.22075 0.272014 0.136007 0.990708i \(-0.456573\pi\)
0.136007 + 0.990708i \(0.456573\pi\)
\(524\) 12.8574 0.561676
\(525\) 20.3782 0.889377
\(526\) 33.8333 1.47520
\(527\) 6.07544 0.264650
\(528\) −9.40266 −0.409198
\(529\) −12.4298 −0.540428
\(530\) 120.182 5.22035
\(531\) 1.39896 0.0607099
\(532\) −49.1502 −2.13093
\(533\) −7.46962 −0.323545
\(534\) 23.0919 0.999282
\(535\) 24.9580 1.07903
\(536\) −52.8886 −2.28444
\(537\) −22.8232 −0.984894
\(538\) −59.2824 −2.55585
\(539\) −6.75847 −0.291108
\(540\) −16.0588 −0.691059
\(541\) −7.22076 −0.310445 −0.155222 0.987880i \(-0.549609\pi\)
−0.155222 + 0.987880i \(0.549609\pi\)
\(542\) −36.4617 −1.56617
\(543\) 5.37203 0.230536
\(544\) 0.807730 0.0346311
\(545\) −2.62611 −0.112490
\(546\) −6.07909 −0.260161
\(547\) 15.4167 0.659173 0.329586 0.944125i \(-0.393091\pi\)
0.329586 + 0.944125i \(0.393091\pi\)
\(548\) 24.6695 1.05383
\(549\) −0.577604 −0.0246516
\(550\) −54.1890 −2.31063
\(551\) −5.09153 −0.216907
\(552\) −16.6773 −0.709831
\(553\) −29.3636 −1.24867
\(554\) −9.12105 −0.387516
\(555\) 22.4327 0.952213
\(556\) −41.7305 −1.76977
\(557\) 5.61421 0.237882 0.118941 0.992901i \(-0.462050\pi\)
0.118941 + 0.992901i \(0.462050\pi\)
\(558\) 14.9810 0.634194
\(559\) −4.07772 −0.172469
\(560\) −34.3154 −1.45009
\(561\) 2.09500 0.0884511
\(562\) 13.0979 0.552500
\(563\) 23.9854 1.01086 0.505431 0.862867i \(-0.331333\pi\)
0.505431 + 0.862867i \(0.331333\pi\)
\(564\) −24.5272 −1.03278
\(565\) −21.2970 −0.895971
\(566\) −13.0682 −0.549297
\(567\) −1.94268 −0.0815849
\(568\) 41.6458 1.74742
\(569\) 32.3260 1.35518 0.677589 0.735441i \(-0.263025\pi\)
0.677589 + 0.735441i \(0.263025\pi\)
\(570\) 60.1752 2.52046
\(571\) −25.9609 −1.08643 −0.543215 0.839593i \(-0.682793\pi\)
−0.543215 + 0.839593i \(0.682793\pi\)
\(572\) 10.8480 0.453578
\(573\) −1.40332 −0.0586247
\(574\) −28.1959 −1.17688
\(575\) −34.1040 −1.42223
\(576\) −6.98455 −0.291023
\(577\) 11.9944 0.499334 0.249667 0.968332i \(-0.419679\pi\)
0.249667 + 0.968332i \(0.419679\pi\)
\(578\) −2.46582 −0.102565
\(579\) 21.2256 0.882104
\(580\) −13.1864 −0.547536
\(581\) 28.8610 1.19736
\(582\) −33.7793 −1.40020
\(583\) −25.9441 −1.07450
\(584\) 62.2997 2.57798
\(585\) 4.99456 0.206500
\(586\) −17.7382 −0.732758
\(587\) 25.1159 1.03665 0.518323 0.855185i \(-0.326557\pi\)
0.518323 + 0.855185i \(0.326557\pi\)
\(588\) 13.1630 0.542831
\(589\) −37.6714 −1.55222
\(590\) −13.5766 −0.558939
\(591\) −19.9176 −0.819299
\(592\) −25.5814 −1.05139
\(593\) 21.3427 0.876438 0.438219 0.898868i \(-0.355609\pi\)
0.438219 + 0.898868i \(0.355609\pi\)
\(594\) 5.16591 0.211960
\(595\) 7.64580 0.313447
\(596\) −52.5001 −2.15049
\(597\) 24.5012 1.00277
\(598\) 10.1737 0.416032
\(599\) 35.9593 1.46926 0.734629 0.678469i \(-0.237356\pi\)
0.734629 + 0.678469i \(0.237356\pi\)
\(600\) 53.8082 2.19671
\(601\) −17.8433 −0.727842 −0.363921 0.931430i \(-0.618562\pi\)
−0.363921 + 0.931430i \(0.618562\pi\)
\(602\) −15.3924 −0.627346
\(603\) 10.3105 0.419875
\(604\) −5.11067 −0.207950
\(605\) −26.0187 −1.05781
\(606\) −30.8952 −1.25503
\(607\) 42.1682 1.71155 0.855777 0.517345i \(-0.173080\pi\)
0.855777 + 0.517345i \(0.173080\pi\)
\(608\) −5.00841 −0.203118
\(609\) −1.59520 −0.0646409
\(610\) 5.60550 0.226960
\(611\) 7.62840 0.308612
\(612\) −4.08028 −0.164936
\(613\) 0.581216 0.0234751 0.0117375 0.999931i \(-0.496264\pi\)
0.0117375 + 0.999931i \(0.496264\pi\)
\(614\) −59.0643 −2.38364
\(615\) 23.1657 0.934131
\(616\) 20.8771 0.841162
\(617\) −39.8146 −1.60288 −0.801438 0.598077i \(-0.795931\pi\)
−0.801438 + 0.598077i \(0.795931\pi\)
\(618\) −10.7131 −0.430945
\(619\) −42.6835 −1.71559 −0.857797 0.513989i \(-0.828167\pi\)
−0.857797 + 0.513989i \(0.828167\pi\)
\(620\) −97.5640 −3.91826
\(621\) 3.25118 0.130465
\(622\) 39.0584 1.56610
\(623\) −18.1927 −0.728877
\(624\) −5.69562 −0.228007
\(625\) 32.5857 1.30343
\(626\) 42.3583 1.69298
\(627\) −12.9903 −0.518782
\(628\) −4.08028 −0.162821
\(629\) 5.69979 0.227265
\(630\) 18.8532 0.751129
\(631\) 3.55088 0.141358 0.0706791 0.997499i \(-0.477483\pi\)
0.0706791 + 0.997499i \(0.477483\pi\)
\(632\) −77.5339 −3.08413
\(633\) −3.88948 −0.154593
\(634\) −22.9426 −0.911168
\(635\) −64.3428 −2.55336
\(636\) 50.5294 2.00362
\(637\) −4.09391 −0.162207
\(638\) 4.24191 0.167939
\(639\) −8.11871 −0.321171
\(640\) 74.1411 2.93069
\(641\) 28.4712 1.12454 0.562272 0.826952i \(-0.309927\pi\)
0.562272 + 0.826952i \(0.309927\pi\)
\(642\) 15.6369 0.617139
\(643\) −12.7686 −0.503544 −0.251772 0.967787i \(-0.581013\pi\)
−0.251772 + 0.967787i \(0.581013\pi\)
\(644\) 25.7710 1.01552
\(645\) 12.6463 0.497948
\(646\) 15.2896 0.601561
\(647\) 16.6629 0.655088 0.327544 0.944836i \(-0.393779\pi\)
0.327544 + 0.944836i \(0.393779\pi\)
\(648\) −5.12960 −0.201510
\(649\) 2.93084 0.115045
\(650\) −32.8247 −1.28749
\(651\) −11.8026 −0.462582
\(652\) −75.2372 −2.94652
\(653\) 20.8416 0.815596 0.407798 0.913072i \(-0.366297\pi\)
0.407798 + 0.913072i \(0.366297\pi\)
\(654\) −1.64533 −0.0643375
\(655\) 12.4018 0.484577
\(656\) −26.4173 −1.03142
\(657\) −12.1451 −0.473826
\(658\) 28.7953 1.12256
\(659\) 21.8267 0.850247 0.425124 0.905135i \(-0.360231\pi\)
0.425124 + 0.905135i \(0.360231\pi\)
\(660\) −33.6432 −1.30956
\(661\) −16.0059 −0.622558 −0.311279 0.950319i \(-0.600757\pi\)
−0.311279 + 0.950319i \(0.600757\pi\)
\(662\) −36.1388 −1.40457
\(663\) 1.26904 0.0492854
\(664\) 76.2068 2.95740
\(665\) −47.4086 −1.83843
\(666\) 14.0547 0.544607
\(667\) 2.66966 0.103369
\(668\) −61.3781 −2.37479
\(669\) 2.47405 0.0956523
\(670\) −100.060 −3.86567
\(671\) −1.21008 −0.0467147
\(672\) −1.56916 −0.0605317
\(673\) 12.3941 0.477758 0.238879 0.971049i \(-0.423220\pi\)
0.238879 + 0.971049i \(0.423220\pi\)
\(674\) 64.3582 2.47899
\(675\) −10.4897 −0.403750
\(676\) −46.4725 −1.78740
\(677\) −39.1474 −1.50456 −0.752278 0.658846i \(-0.771045\pi\)
−0.752278 + 0.658846i \(0.771045\pi\)
\(678\) −13.3431 −0.512441
\(679\) 26.6127 1.02130
\(680\) 20.1886 0.774197
\(681\) 3.58147 0.137242
\(682\) 31.3852 1.20180
\(683\) 11.8618 0.453878 0.226939 0.973909i \(-0.427128\pi\)
0.226939 + 0.973909i \(0.427128\pi\)
\(684\) 25.3002 0.967378
\(685\) 23.7954 0.909175
\(686\) −48.9856 −1.87028
\(687\) 25.5136 0.973404
\(688\) −14.4214 −0.549811
\(689\) −15.7155 −0.598715
\(690\) −31.5518 −1.20116
\(691\) −5.90943 −0.224805 −0.112403 0.993663i \(-0.535855\pi\)
−0.112403 + 0.993663i \(0.535855\pi\)
\(692\) 35.2267 1.33912
\(693\) −4.06992 −0.154604
\(694\) 42.9675 1.63102
\(695\) −40.2518 −1.52684
\(696\) −4.21210 −0.159659
\(697\) 5.88604 0.222950
\(698\) −17.0459 −0.645197
\(699\) 17.3310 0.655517
\(700\) −83.1487 −3.14273
\(701\) 3.44614 0.130159 0.0650794 0.997880i \(-0.479270\pi\)
0.0650794 + 0.997880i \(0.479270\pi\)
\(702\) 3.12923 0.118105
\(703\) −35.3421 −1.33295
\(704\) −14.6327 −0.551489
\(705\) −23.6581 −0.891016
\(706\) −10.0601 −0.378615
\(707\) 24.3405 0.915419
\(708\) −5.70817 −0.214526
\(709\) −30.8882 −1.16003 −0.580015 0.814606i \(-0.696953\pi\)
−0.580015 + 0.814606i \(0.696953\pi\)
\(710\) 78.7900 2.95694
\(711\) 15.1150 0.566856
\(712\) −48.0376 −1.80028
\(713\) 19.7523 0.739730
\(714\) 4.79030 0.179273
\(715\) 10.4636 0.391317
\(716\) 93.1251 3.48025
\(717\) 1.09864 0.0410294
\(718\) −92.3994 −3.44832
\(719\) 10.9851 0.409677 0.204838 0.978796i \(-0.434333\pi\)
0.204838 + 0.978796i \(0.434333\pi\)
\(720\) 17.6639 0.658296
\(721\) 8.44025 0.314331
\(722\) −47.9541 −1.78467
\(723\) −15.8369 −0.588980
\(724\) −21.9194 −0.814628
\(725\) −8.61348 −0.319897
\(726\) −16.3015 −0.605004
\(727\) −39.5232 −1.46583 −0.732916 0.680319i \(-0.761841\pi\)
−0.732916 + 0.680319i \(0.761841\pi\)
\(728\) 12.6462 0.468700
\(729\) 1.00000 0.0370370
\(730\) 117.865 4.36239
\(731\) 3.21323 0.118846
\(732\) 2.35679 0.0871094
\(733\) 7.05150 0.260453 0.130227 0.991484i \(-0.458430\pi\)
0.130227 + 0.991484i \(0.458430\pi\)
\(734\) 65.0940 2.40266
\(735\) 12.6965 0.468319
\(736\) 2.62607 0.0967983
\(737\) 21.6005 0.795663
\(738\) 14.5139 0.534266
\(739\) −26.3589 −0.969627 −0.484813 0.874618i \(-0.661113\pi\)
−0.484813 + 0.874618i \(0.661113\pi\)
\(740\) −91.5315 −3.36477
\(741\) −7.86881 −0.289068
\(742\) −59.3222 −2.17779
\(743\) −18.9592 −0.695545 −0.347773 0.937579i \(-0.613062\pi\)
−0.347773 + 0.937579i \(0.613062\pi\)
\(744\) −31.1646 −1.14255
\(745\) −50.6398 −1.85530
\(746\) −17.9551 −0.657384
\(747\) −14.8563 −0.543563
\(748\) −8.54820 −0.312553
\(749\) −12.3194 −0.450141
\(750\) 53.2764 1.94538
\(751\) 34.6987 1.26618 0.633088 0.774080i \(-0.281787\pi\)
0.633088 + 0.774080i \(0.281787\pi\)
\(752\) 26.9789 0.983818
\(753\) −13.2834 −0.484074
\(754\) 2.56952 0.0935763
\(755\) −4.92957 −0.179406
\(756\) 7.92668 0.288291
\(757\) −6.45257 −0.234523 −0.117261 0.993101i \(-0.537412\pi\)
−0.117261 + 0.993101i \(0.537412\pi\)
\(758\) −39.2532 −1.42574
\(759\) 6.81123 0.247232
\(760\) −125.181 −4.54081
\(761\) −7.67557 −0.278239 −0.139120 0.990276i \(-0.544427\pi\)
−0.139120 + 0.990276i \(0.544427\pi\)
\(762\) −40.3125 −1.46037
\(763\) 1.29626 0.0469278
\(764\) 5.72596 0.207158
\(765\) −3.93570 −0.142296
\(766\) −21.5258 −0.777759
\(767\) 1.77534 0.0641039
\(768\) 32.4824 1.17211
\(769\) 54.5833 1.96833 0.984163 0.177268i \(-0.0567259\pi\)
0.984163 + 0.177268i \(0.0567259\pi\)
\(770\) 39.4975 1.42339
\(771\) −25.5220 −0.919153
\(772\) −86.6062 −3.11703
\(773\) −38.0567 −1.36880 −0.684402 0.729105i \(-0.739937\pi\)
−0.684402 + 0.729105i \(0.739937\pi\)
\(774\) 7.92326 0.284796
\(775\) −63.7297 −2.28924
\(776\) 70.2704 2.52256
\(777\) −11.0729 −0.397237
\(778\) 24.9053 0.892897
\(779\) −36.4970 −1.30764
\(780\) −20.3792 −0.729693
\(781\) −17.0087 −0.608621
\(782\) −8.01683 −0.286681
\(783\) 0.821135 0.0293450
\(784\) −14.4787 −0.517096
\(785\) −3.93570 −0.140471
\(786\) 7.77005 0.277148
\(787\) −44.8200 −1.59766 −0.798830 0.601557i \(-0.794547\pi\)
−0.798830 + 0.601557i \(0.794547\pi\)
\(788\) 81.2692 2.89510
\(789\) 13.7209 0.488477
\(790\) −146.687 −5.21889
\(791\) 10.5123 0.373774
\(792\) −10.7465 −0.381862
\(793\) −0.733003 −0.0260297
\(794\) −65.4465 −2.32261
\(795\) 48.7389 1.72859
\(796\) −99.9716 −3.54340
\(797\) −4.98944 −0.176735 −0.0883675 0.996088i \(-0.528165\pi\)
−0.0883675 + 0.996088i \(0.528165\pi\)
\(798\) −29.7028 −1.05147
\(799\) −6.01116 −0.212659
\(800\) −8.47286 −0.299561
\(801\) 9.36477 0.330888
\(802\) 58.2087 2.05542
\(803\) −25.4441 −0.897902
\(804\) −42.0696 −1.48368
\(805\) 24.8579 0.876125
\(806\) 19.0114 0.669649
\(807\) −24.0416 −0.846305
\(808\) 64.2706 2.26103
\(809\) −18.0208 −0.633576 −0.316788 0.948496i \(-0.602604\pi\)
−0.316788 + 0.948496i \(0.602604\pi\)
\(810\) −9.70474 −0.340990
\(811\) −28.4350 −0.998486 −0.499243 0.866462i \(-0.666389\pi\)
−0.499243 + 0.866462i \(0.666389\pi\)
\(812\) 6.50888 0.228417
\(813\) −14.7868 −0.518597
\(814\) 29.4446 1.03203
\(815\) −72.5712 −2.54206
\(816\) 4.48813 0.157116
\(817\) −19.9240 −0.697052
\(818\) −74.0184 −2.58799
\(819\) −2.46534 −0.0861459
\(820\) −94.5226 −3.30087
\(821\) −19.3232 −0.674384 −0.337192 0.941436i \(-0.609477\pi\)
−0.337192 + 0.941436i \(0.609477\pi\)
\(822\) 14.9085 0.519992
\(823\) 52.8260 1.84140 0.920699 0.390273i \(-0.127619\pi\)
0.920699 + 0.390273i \(0.127619\pi\)
\(824\) 22.2863 0.776380
\(825\) −21.9760 −0.765107
\(826\) 6.70147 0.233174
\(827\) −46.0677 −1.60193 −0.800966 0.598710i \(-0.795680\pi\)
−0.800966 + 0.598710i \(0.795680\pi\)
\(828\) −13.2657 −0.461016
\(829\) 0.186629 0.00648190 0.00324095 0.999995i \(-0.498968\pi\)
0.00324095 + 0.999995i \(0.498968\pi\)
\(830\) 144.176 5.00443
\(831\) −3.69899 −0.128316
\(832\) −8.86367 −0.307292
\(833\) 3.22599 0.111774
\(834\) −25.2188 −0.873256
\(835\) −59.2032 −2.04881
\(836\) 53.0040 1.83318
\(837\) 6.07544 0.209998
\(838\) −68.2083 −2.35622
\(839\) 20.0225 0.691255 0.345627 0.938372i \(-0.387666\pi\)
0.345627 + 0.938372i \(0.387666\pi\)
\(840\) −39.2200 −1.35322
\(841\) −28.3257 −0.976750
\(842\) 57.3344 1.97587
\(843\) 5.31177 0.182947
\(844\) 15.8702 0.546273
\(845\) −44.8258 −1.54205
\(846\) −14.8224 −0.509606
\(847\) 12.8430 0.441290
\(848\) −55.5802 −1.90863
\(849\) −5.29973 −0.181886
\(850\) 25.8658 0.887190
\(851\) 18.5310 0.635235
\(852\) 33.1266 1.13490
\(853\) −12.8222 −0.439025 −0.219513 0.975610i \(-0.570447\pi\)
−0.219513 + 0.975610i \(0.570447\pi\)
\(854\) −2.76690 −0.0946814
\(855\) 24.4037 0.834589
\(856\) −32.5291 −1.11182
\(857\) −1.72140 −0.0588019 −0.0294010 0.999568i \(-0.509360\pi\)
−0.0294010 + 0.999568i \(0.509360\pi\)
\(858\) 6.55574 0.223809
\(859\) 7.52678 0.256810 0.128405 0.991722i \(-0.459014\pi\)
0.128405 + 0.991722i \(0.459014\pi\)
\(860\) −51.6005 −1.75956
\(861\) −11.4347 −0.389694
\(862\) −81.8838 −2.78897
\(863\) −57.4116 −1.95431 −0.977157 0.212517i \(-0.931834\pi\)
−0.977157 + 0.212517i \(0.931834\pi\)
\(864\) 0.807730 0.0274795
\(865\) 33.9784 1.15530
\(866\) 41.6549 1.41549
\(867\) −1.00000 −0.0339618
\(868\) 48.1581 1.63459
\(869\) 31.6659 1.07419
\(870\) −7.96890 −0.270171
\(871\) 13.0844 0.443348
\(872\) 3.42275 0.115909
\(873\) −13.6990 −0.463640
\(874\) 49.7092 1.68144
\(875\) −41.9734 −1.41896
\(876\) 49.5555 1.67433
\(877\) 23.6136 0.797375 0.398687 0.917087i \(-0.369466\pi\)
0.398687 + 0.917087i \(0.369466\pi\)
\(878\) −37.6142 −1.26942
\(879\) −7.19362 −0.242635
\(880\) 37.0060 1.24747
\(881\) −28.2491 −0.951736 −0.475868 0.879517i \(-0.657866\pi\)
−0.475868 + 0.879517i \(0.657866\pi\)
\(882\) 7.95473 0.267850
\(883\) 14.9807 0.504142 0.252071 0.967709i \(-0.418888\pi\)
0.252071 + 0.967709i \(0.418888\pi\)
\(884\) −5.17804 −0.174156
\(885\) −5.50591 −0.185079
\(886\) 7.55179 0.253707
\(887\) 52.4711 1.76181 0.880903 0.473297i \(-0.156936\pi\)
0.880903 + 0.473297i \(0.156936\pi\)
\(888\) −29.2377 −0.981152
\(889\) 31.7599 1.06519
\(890\) −90.8826 −3.04639
\(891\) 2.09500 0.0701853
\(892\) −10.0948 −0.338000
\(893\) 37.2728 1.24729
\(894\) −31.7272 −1.06112
\(895\) 89.8252 3.00253
\(896\) −36.5964 −1.22260
\(897\) 4.12587 0.137759
\(898\) 81.6924 2.72611
\(899\) 4.98875 0.166384
\(900\) 42.8010 1.42670
\(901\) 12.3838 0.412564
\(902\) 30.4068 1.01243
\(903\) −6.24228 −0.207730
\(904\) 27.7575 0.923201
\(905\) −21.1427 −0.702807
\(906\) −3.08851 −0.102609
\(907\) −1.65676 −0.0550117 −0.0275059 0.999622i \(-0.508756\pi\)
−0.0275059 + 0.999622i \(0.508756\pi\)
\(908\) −14.6134 −0.484962
\(909\) −12.5294 −0.415572
\(910\) 23.9255 0.793121
\(911\) −3.39647 −0.112530 −0.0562651 0.998416i \(-0.517919\pi\)
−0.0562651 + 0.998416i \(0.517919\pi\)
\(912\) −27.8291 −0.921515
\(913\) −31.1240 −1.03005
\(914\) −0.703011 −0.0232535
\(915\) 2.27328 0.0751522
\(916\) −104.103 −3.43965
\(917\) −6.12157 −0.202152
\(918\) −2.46582 −0.0813843
\(919\) 4.41358 0.145591 0.0727954 0.997347i \(-0.476808\pi\)
0.0727954 + 0.997347i \(0.476808\pi\)
\(920\) 65.6366 2.16398
\(921\) −23.9532 −0.789284
\(922\) 12.9601 0.426817
\(923\) −10.3030 −0.339126
\(924\) 16.6064 0.546311
\(925\) −59.7892 −1.96586
\(926\) −83.3562 −2.73926
\(927\) −4.34464 −0.142697
\(928\) 0.663255 0.0217724
\(929\) −6.46101 −0.211979 −0.105990 0.994367i \(-0.533801\pi\)
−0.105990 + 0.994367i \(0.533801\pi\)
\(930\) −58.9605 −1.93339
\(931\) −20.0031 −0.655575
\(932\) −70.7152 −2.31635
\(933\) 15.8399 0.518575
\(934\) 67.6274 2.21284
\(935\) −8.24530 −0.269650
\(936\) −6.50967 −0.212775
\(937\) −58.0645 −1.89689 −0.948443 0.316948i \(-0.897342\pi\)
−0.948443 + 0.316948i \(0.897342\pi\)
\(938\) 49.3903 1.61265
\(939\) 17.1781 0.560588
\(940\) 96.5317 3.14852
\(941\) 9.28817 0.302786 0.151393 0.988474i \(-0.451624\pi\)
0.151393 + 0.988474i \(0.451624\pi\)
\(942\) −2.46582 −0.0803408
\(943\) 19.1366 0.623172
\(944\) 6.27874 0.204356
\(945\) 7.64580 0.248718
\(946\) 16.5993 0.539688
\(947\) −44.6439 −1.45073 −0.725365 0.688364i \(-0.758329\pi\)
−0.725365 + 0.688364i \(0.758329\pi\)
\(948\) −61.6734 −2.00306
\(949\) −15.4126 −0.500316
\(950\) −160.384 −5.20353
\(951\) −9.30425 −0.301711
\(952\) −9.96518 −0.322973
\(953\) 40.4899 1.31160 0.655799 0.754936i \(-0.272332\pi\)
0.655799 + 0.754936i \(0.272332\pi\)
\(954\) 30.5363 0.988648
\(955\) 5.52306 0.178722
\(956\) −4.48275 −0.144983
\(957\) 1.72028 0.0556088
\(958\) −12.0146 −0.388175
\(959\) −11.7455 −0.379283
\(960\) 27.4891 0.887206
\(961\) 5.91094 0.190676
\(962\) 17.8359 0.575053
\(963\) 6.34145 0.204350
\(964\) 64.6189 2.08124
\(965\) −83.5374 −2.68916
\(966\) 15.5741 0.501089
\(967\) −21.5682 −0.693586 −0.346793 0.937942i \(-0.612729\pi\)
−0.346793 + 0.937942i \(0.612729\pi\)
\(968\) 33.9116 1.08996
\(969\) 6.20060 0.199192
\(970\) 132.945 4.26861
\(971\) −46.8893 −1.50475 −0.752374 0.658736i \(-0.771092\pi\)
−0.752374 + 0.658736i \(0.771092\pi\)
\(972\) −4.08028 −0.130875
\(973\) 19.8685 0.636954
\(974\) 59.1886 1.89652
\(975\) −13.3119 −0.426321
\(976\) −2.59236 −0.0829796
\(977\) −3.52393 −0.112741 −0.0563703 0.998410i \(-0.517953\pi\)
−0.0563703 + 0.998410i \(0.517953\pi\)
\(978\) −45.4678 −1.45390
\(979\) 19.6192 0.627033
\(980\) −51.8055 −1.65486
\(981\) −0.667254 −0.0213038
\(982\) −35.9110 −1.14597
\(983\) 18.8358 0.600770 0.300385 0.953818i \(-0.402885\pi\)
0.300385 + 0.953818i \(0.402885\pi\)
\(984\) −30.1931 −0.962520
\(985\) 78.3895 2.49770
\(986\) −2.02477 −0.0644819
\(987\) 11.6778 0.371707
\(988\) 32.1070 1.02146
\(989\) 10.4468 0.332188
\(990\) −20.3315 −0.646176
\(991\) 1.08870 0.0345838 0.0172919 0.999850i \(-0.494496\pi\)
0.0172919 + 0.999850i \(0.494496\pi\)
\(992\) 4.90731 0.155807
\(993\) −14.6559 −0.465090
\(994\) −38.8911 −1.23355
\(995\) −96.4292 −3.05701
\(996\) 60.6178 1.92075
\(997\) −20.2724 −0.642034 −0.321017 0.947073i \(-0.604025\pi\)
−0.321017 + 0.947073i \(0.604025\pi\)
\(998\) 50.3686 1.59439
\(999\) 5.69979 0.180333
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 \(a_p\))