Properties

Label 4017.2.a.j.1.22
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.45725 q^{2} -1.00000 q^{3} +4.03807 q^{4} +1.82467 q^{5} -2.45725 q^{6} +1.71478 q^{7} +5.00803 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.45725 q^{2} -1.00000 q^{3} +4.03807 q^{4} +1.82467 q^{5} -2.45725 q^{6} +1.71478 q^{7} +5.00803 q^{8} +1.00000 q^{9} +4.48366 q^{10} -2.47217 q^{11} -4.03807 q^{12} +1.00000 q^{13} +4.21365 q^{14} -1.82467 q^{15} +4.22984 q^{16} +2.10209 q^{17} +2.45725 q^{18} +5.03790 q^{19} +7.36812 q^{20} -1.71478 q^{21} -6.07475 q^{22} -4.48018 q^{23} -5.00803 q^{24} -1.67059 q^{25} +2.45725 q^{26} -1.00000 q^{27} +6.92441 q^{28} +2.41624 q^{29} -4.48366 q^{30} +8.42140 q^{31} +0.377710 q^{32} +2.47217 q^{33} +5.16535 q^{34} +3.12891 q^{35} +4.03807 q^{36} +5.69321 q^{37} +12.3794 q^{38} -1.00000 q^{39} +9.13799 q^{40} +11.1071 q^{41} -4.21365 q^{42} -2.64739 q^{43} -9.98280 q^{44} +1.82467 q^{45} -11.0089 q^{46} +6.04114 q^{47} -4.22984 q^{48} -4.05952 q^{49} -4.10506 q^{50} -2.10209 q^{51} +4.03807 q^{52} -1.63456 q^{53} -2.45725 q^{54} -4.51089 q^{55} +8.58769 q^{56} -5.03790 q^{57} +5.93731 q^{58} +2.39601 q^{59} -7.36812 q^{60} -10.8292 q^{61} +20.6935 q^{62} +1.71478 q^{63} -7.53156 q^{64} +1.82467 q^{65} +6.07475 q^{66} -7.49568 q^{67} +8.48837 q^{68} +4.48018 q^{69} +7.68850 q^{70} -1.28480 q^{71} +5.00803 q^{72} +4.77967 q^{73} +13.9896 q^{74} +1.67059 q^{75} +20.3434 q^{76} -4.23924 q^{77} -2.45725 q^{78} +10.3906 q^{79} +7.71805 q^{80} +1.00000 q^{81} +27.2929 q^{82} +5.09703 q^{83} -6.92441 q^{84} +3.83561 q^{85} -6.50529 q^{86} -2.41624 q^{87} -12.3807 q^{88} -5.25191 q^{89} +4.48366 q^{90} +1.71478 q^{91} -18.0913 q^{92} -8.42140 q^{93} +14.8446 q^{94} +9.19248 q^{95} -0.377710 q^{96} -13.6887 q^{97} -9.97524 q^{98} -2.47217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45725 1.73754 0.868768 0.495219i \(-0.164912\pi\)
0.868768 + 0.495219i \(0.164912\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.03807 2.01903
\(5\) 1.82467 0.816016 0.408008 0.912978i \(-0.366224\pi\)
0.408008 + 0.912978i \(0.366224\pi\)
\(6\) −2.45725 −1.00317
\(7\) 1.71478 0.648127 0.324064 0.946035i \(-0.394951\pi\)
0.324064 + 0.946035i \(0.394951\pi\)
\(8\) 5.00803 1.77061
\(9\) 1.00000 0.333333
\(10\) 4.48366 1.41786
\(11\) −2.47217 −0.745389 −0.372694 0.927954i \(-0.621566\pi\)
−0.372694 + 0.927954i \(0.621566\pi\)
\(12\) −4.03807 −1.16569
\(13\) 1.00000 0.277350
\(14\) 4.21365 1.12614
\(15\) −1.82467 −0.471127
\(16\) 4.22984 1.05746
\(17\) 2.10209 0.509831 0.254916 0.966963i \(-0.417952\pi\)
0.254916 + 0.966963i \(0.417952\pi\)
\(18\) 2.45725 0.579179
\(19\) 5.03790 1.15577 0.577887 0.816117i \(-0.303878\pi\)
0.577887 + 0.816117i \(0.303878\pi\)
\(20\) 7.36812 1.64756
\(21\) −1.71478 −0.374196
\(22\) −6.07475 −1.29514
\(23\) −4.48018 −0.934183 −0.467091 0.884209i \(-0.654698\pi\)
−0.467091 + 0.884209i \(0.654698\pi\)
\(24\) −5.00803 −1.02226
\(25\) −1.67059 −0.334119
\(26\) 2.45725 0.481906
\(27\) −1.00000 −0.192450
\(28\) 6.92441 1.30859
\(29\) 2.41624 0.448685 0.224343 0.974510i \(-0.427977\pi\)
0.224343 + 0.974510i \(0.427977\pi\)
\(30\) −4.48366 −0.818600
\(31\) 8.42140 1.51253 0.756264 0.654266i \(-0.227022\pi\)
0.756264 + 0.654266i \(0.227022\pi\)
\(32\) 0.377710 0.0667704
\(33\) 2.47217 0.430350
\(34\) 5.16535 0.885850
\(35\) 3.12891 0.528882
\(36\) 4.03807 0.673011
\(37\) 5.69321 0.935957 0.467979 0.883740i \(-0.344982\pi\)
0.467979 + 0.883740i \(0.344982\pi\)
\(38\) 12.3794 2.00820
\(39\) −1.00000 −0.160128
\(40\) 9.13799 1.44484
\(41\) 11.1071 1.73464 0.867319 0.497752i \(-0.165841\pi\)
0.867319 + 0.497752i \(0.165841\pi\)
\(42\) −4.21365 −0.650180
\(43\) −2.64739 −0.403723 −0.201862 0.979414i \(-0.564699\pi\)
−0.201862 + 0.979414i \(0.564699\pi\)
\(44\) −9.98280 −1.50496
\(45\) 1.82467 0.272005
\(46\) −11.0089 −1.62318
\(47\) 6.04114 0.881190 0.440595 0.897706i \(-0.354767\pi\)
0.440595 + 0.897706i \(0.354767\pi\)
\(48\) −4.22984 −0.610525
\(49\) −4.05952 −0.579931
\(50\) −4.10506 −0.580543
\(51\) −2.10209 −0.294351
\(52\) 4.03807 0.559979
\(53\) −1.63456 −0.224525 −0.112262 0.993679i \(-0.535810\pi\)
−0.112262 + 0.993679i \(0.535810\pi\)
\(54\) −2.45725 −0.334389
\(55\) −4.51089 −0.608249
\(56\) 8.58769 1.14758
\(57\) −5.03790 −0.667286
\(58\) 5.93731 0.779607
\(59\) 2.39601 0.311934 0.155967 0.987762i \(-0.450151\pi\)
0.155967 + 0.987762i \(0.450151\pi\)
\(60\) −7.36812 −0.951221
\(61\) −10.8292 −1.38654 −0.693270 0.720678i \(-0.743831\pi\)
−0.693270 + 0.720678i \(0.743831\pi\)
\(62\) 20.6935 2.62807
\(63\) 1.71478 0.216042
\(64\) −7.53156 −0.941445
\(65\) 1.82467 0.226322
\(66\) 6.07475 0.747749
\(67\) −7.49568 −0.915743 −0.457872 0.889018i \(-0.651388\pi\)
−0.457872 + 0.889018i \(0.651388\pi\)
\(68\) 8.48837 1.02937
\(69\) 4.48018 0.539351
\(70\) 7.68850 0.918952
\(71\) −1.28480 −0.152478 −0.0762389 0.997090i \(-0.524291\pi\)
−0.0762389 + 0.997090i \(0.524291\pi\)
\(72\) 5.00803 0.590202
\(73\) 4.77967 0.559418 0.279709 0.960085i \(-0.409762\pi\)
0.279709 + 0.960085i \(0.409762\pi\)
\(74\) 13.9896 1.62626
\(75\) 1.67059 0.192903
\(76\) 20.3434 2.33354
\(77\) −4.23924 −0.483107
\(78\) −2.45725 −0.278229
\(79\) 10.3906 1.16904 0.584519 0.811380i \(-0.301283\pi\)
0.584519 + 0.811380i \(0.301283\pi\)
\(80\) 7.71805 0.862905
\(81\) 1.00000 0.111111
\(82\) 27.2929 3.01400
\(83\) 5.09703 0.559471 0.279736 0.960077i \(-0.409753\pi\)
0.279736 + 0.960077i \(0.409753\pi\)
\(84\) −6.92441 −0.755515
\(85\) 3.83561 0.416030
\(86\) −6.50529 −0.701484
\(87\) −2.41624 −0.259048
\(88\) −12.3807 −1.31979
\(89\) −5.25191 −0.556702 −0.278351 0.960479i \(-0.589788\pi\)
−0.278351 + 0.960479i \(0.589788\pi\)
\(90\) 4.48366 0.472619
\(91\) 1.71478 0.179758
\(92\) −18.0913 −1.88615
\(93\) −8.42140 −0.873259
\(94\) 14.8446 1.53110
\(95\) 9.19248 0.943129
\(96\) −0.377710 −0.0385499
\(97\) −13.6887 −1.38988 −0.694940 0.719068i \(-0.744569\pi\)
−0.694940 + 0.719068i \(0.744569\pi\)
\(98\) −9.97524 −1.00765
\(99\) −2.47217 −0.248463
\(100\) −6.74596 −0.674596
\(101\) −1.97292 −0.196313 −0.0981566 0.995171i \(-0.531295\pi\)
−0.0981566 + 0.995171i \(0.531295\pi\)
\(102\) −5.16535 −0.511446
\(103\) −1.00000 −0.0985329
\(104\) 5.00803 0.491078
\(105\) −3.12891 −0.305350
\(106\) −4.01653 −0.390120
\(107\) 15.1982 1.46927 0.734634 0.678463i \(-0.237354\pi\)
0.734634 + 0.678463i \(0.237354\pi\)
\(108\) −4.03807 −0.388563
\(109\) −18.2958 −1.75242 −0.876208 0.481933i \(-0.839935\pi\)
−0.876208 + 0.481933i \(0.839935\pi\)
\(110\) −11.0844 −1.05685
\(111\) −5.69321 −0.540375
\(112\) 7.25327 0.685369
\(113\) −10.9011 −1.02549 −0.512743 0.858542i \(-0.671371\pi\)
−0.512743 + 0.858542i \(0.671371\pi\)
\(114\) −12.3794 −1.15943
\(115\) −8.17484 −0.762308
\(116\) 9.75695 0.905910
\(117\) 1.00000 0.0924500
\(118\) 5.88758 0.541996
\(119\) 3.60463 0.330436
\(120\) −9.13799 −0.834180
\(121\) −4.88835 −0.444396
\(122\) −26.6101 −2.40916
\(123\) −11.1071 −1.00149
\(124\) 34.0062 3.05384
\(125\) −12.1716 −1.08866
\(126\) 4.21365 0.375382
\(127\) 18.0296 1.59987 0.799934 0.600088i \(-0.204868\pi\)
0.799934 + 0.600088i \(0.204868\pi\)
\(128\) −19.2623 −1.70257
\(129\) 2.64739 0.233090
\(130\) 4.48366 0.393243
\(131\) 7.05989 0.616826 0.308413 0.951253i \(-0.400202\pi\)
0.308413 + 0.951253i \(0.400202\pi\)
\(132\) 9.98280 0.868892
\(133\) 8.63891 0.749088
\(134\) −18.4187 −1.59114
\(135\) −1.82467 −0.157042
\(136\) 10.5273 0.902711
\(137\) 18.8311 1.60885 0.804424 0.594055i \(-0.202474\pi\)
0.804424 + 0.594055i \(0.202474\pi\)
\(138\) 11.0089 0.937141
\(139\) −15.2404 −1.29268 −0.646339 0.763051i \(-0.723701\pi\)
−0.646339 + 0.763051i \(0.723701\pi\)
\(140\) 12.6347 1.06783
\(141\) −6.04114 −0.508756
\(142\) −3.15707 −0.264936
\(143\) −2.47217 −0.206734
\(144\) 4.22984 0.352487
\(145\) 4.40884 0.366134
\(146\) 11.7448 0.972009
\(147\) 4.05952 0.334823
\(148\) 22.9895 1.88973
\(149\) −9.62177 −0.788246 −0.394123 0.919058i \(-0.628952\pi\)
−0.394123 + 0.919058i \(0.628952\pi\)
\(150\) 4.10506 0.335177
\(151\) −5.21999 −0.424797 −0.212398 0.977183i \(-0.568127\pi\)
−0.212398 + 0.977183i \(0.568127\pi\)
\(152\) 25.2300 2.04642
\(153\) 2.10209 0.169944
\(154\) −10.4169 −0.839416
\(155\) 15.3662 1.23425
\(156\) −4.03807 −0.323304
\(157\) 2.11215 0.168568 0.0842841 0.996442i \(-0.473140\pi\)
0.0842841 + 0.996442i \(0.473140\pi\)
\(158\) 25.5324 2.03125
\(159\) 1.63456 0.129629
\(160\) 0.689195 0.0544856
\(161\) −7.68254 −0.605469
\(162\) 2.45725 0.193060
\(163\) −22.7611 −1.78279 −0.891393 0.453231i \(-0.850271\pi\)
−0.891393 + 0.453231i \(0.850271\pi\)
\(164\) 44.8512 3.50229
\(165\) 4.51089 0.351173
\(166\) 12.5247 0.972102
\(167\) 6.01129 0.465168 0.232584 0.972576i \(-0.425282\pi\)
0.232584 + 0.972576i \(0.425282\pi\)
\(168\) −8.58769 −0.662555
\(169\) 1.00000 0.0769231
\(170\) 9.42504 0.722868
\(171\) 5.03790 0.385258
\(172\) −10.6903 −0.815131
\(173\) 2.03881 0.155008 0.0775038 0.996992i \(-0.475305\pi\)
0.0775038 + 0.996992i \(0.475305\pi\)
\(174\) −5.93731 −0.450106
\(175\) −2.86471 −0.216551
\(176\) −10.4569 −0.788220
\(177\) −2.39601 −0.180095
\(178\) −12.9053 −0.967290
\(179\) 25.5086 1.90661 0.953303 0.302016i \(-0.0976596\pi\)
0.953303 + 0.302016i \(0.0976596\pi\)
\(180\) 7.36812 0.549187
\(181\) 10.2267 0.760147 0.380073 0.924956i \(-0.375899\pi\)
0.380073 + 0.924956i \(0.375899\pi\)
\(182\) 4.21365 0.312336
\(183\) 10.8292 0.800519
\(184\) −22.4369 −1.65407
\(185\) 10.3882 0.763756
\(186\) −20.6935 −1.51732
\(187\) −5.19673 −0.380022
\(188\) 24.3945 1.77915
\(189\) −1.71478 −0.124732
\(190\) 22.5882 1.63872
\(191\) −8.37666 −0.606114 −0.303057 0.952972i \(-0.598007\pi\)
−0.303057 + 0.952972i \(0.598007\pi\)
\(192\) 7.53156 0.543544
\(193\) −15.6923 −1.12956 −0.564779 0.825242i \(-0.691039\pi\)
−0.564779 + 0.825242i \(0.691039\pi\)
\(194\) −33.6366 −2.41497
\(195\) −1.82467 −0.130667
\(196\) −16.3926 −1.17090
\(197\) −11.2707 −0.803001 −0.401501 0.915859i \(-0.631511\pi\)
−0.401501 + 0.915859i \(0.631511\pi\)
\(198\) −6.07475 −0.431713
\(199\) −0.778082 −0.0551567 −0.0275784 0.999620i \(-0.508780\pi\)
−0.0275784 + 0.999620i \(0.508780\pi\)
\(200\) −8.36638 −0.591593
\(201\) 7.49568 0.528705
\(202\) −4.84796 −0.341101
\(203\) 4.14333 0.290805
\(204\) −8.48837 −0.594305
\(205\) 20.2668 1.41549
\(206\) −2.45725 −0.171205
\(207\) −4.48018 −0.311394
\(208\) 4.22984 0.293287
\(209\) −12.4546 −0.861500
\(210\) −7.68850 −0.530557
\(211\) 27.4762 1.89154 0.945769 0.324840i \(-0.105311\pi\)
0.945769 + 0.324840i \(0.105311\pi\)
\(212\) −6.60047 −0.453322
\(213\) 1.28480 0.0880331
\(214\) 37.3458 2.55291
\(215\) −4.83060 −0.329444
\(216\) −5.00803 −0.340753
\(217\) 14.4409 0.980311
\(218\) −44.9572 −3.04489
\(219\) −4.77967 −0.322980
\(220\) −18.2153 −1.22807
\(221\) 2.10209 0.141402
\(222\) −13.9896 −0.938922
\(223\) 21.7022 1.45329 0.726643 0.687015i \(-0.241079\pi\)
0.726643 + 0.687015i \(0.241079\pi\)
\(224\) 0.647691 0.0432757
\(225\) −1.67059 −0.111373
\(226\) −26.7866 −1.78182
\(227\) −6.41324 −0.425662 −0.212831 0.977089i \(-0.568268\pi\)
−0.212831 + 0.977089i \(0.568268\pi\)
\(228\) −20.3434 −1.34727
\(229\) −18.9532 −1.25247 −0.626233 0.779636i \(-0.715404\pi\)
−0.626233 + 0.779636i \(0.715404\pi\)
\(230\) −20.0876 −1.32454
\(231\) 4.23924 0.278922
\(232\) 12.1006 0.794445
\(233\) −13.3023 −0.871460 −0.435730 0.900077i \(-0.643510\pi\)
−0.435730 + 0.900077i \(0.643510\pi\)
\(234\) 2.45725 0.160635
\(235\) 11.0231 0.719065
\(236\) 9.67524 0.629804
\(237\) −10.3906 −0.674944
\(238\) 8.85746 0.574144
\(239\) 3.37996 0.218631 0.109316 0.994007i \(-0.465134\pi\)
0.109316 + 0.994007i \(0.465134\pi\)
\(240\) −7.71805 −0.498198
\(241\) −6.02414 −0.388049 −0.194025 0.980997i \(-0.562154\pi\)
−0.194025 + 0.980997i \(0.562154\pi\)
\(242\) −12.0119 −0.772154
\(243\) −1.00000 −0.0641500
\(244\) −43.7291 −2.79947
\(245\) −7.40726 −0.473233
\(246\) −27.2929 −1.74013
\(247\) 5.03790 0.320554
\(248\) 42.1747 2.67809
\(249\) −5.09703 −0.323011
\(250\) −29.9087 −1.89159
\(251\) 6.55153 0.413529 0.206764 0.978391i \(-0.433707\pi\)
0.206764 + 0.978391i \(0.433707\pi\)
\(252\) 6.92441 0.436197
\(253\) 11.0758 0.696329
\(254\) 44.3032 2.77983
\(255\) −3.83561 −0.240195
\(256\) −32.2692 −2.01682
\(257\) 20.5033 1.27896 0.639482 0.768806i \(-0.279149\pi\)
0.639482 + 0.768806i \(0.279149\pi\)
\(258\) 6.50529 0.405002
\(259\) 9.76262 0.606619
\(260\) 7.36812 0.456952
\(261\) 2.41624 0.149562
\(262\) 17.3479 1.07176
\(263\) −17.7020 −1.09155 −0.545775 0.837932i \(-0.683765\pi\)
−0.545775 + 0.837932i \(0.683765\pi\)
\(264\) 12.3807 0.761981
\(265\) −2.98253 −0.183216
\(266\) 21.2279 1.30157
\(267\) 5.25191 0.321412
\(268\) −30.2681 −1.84892
\(269\) −24.5061 −1.49417 −0.747083 0.664731i \(-0.768546\pi\)
−0.747083 + 0.664731i \(0.768546\pi\)
\(270\) −4.48366 −0.272867
\(271\) −26.9728 −1.63848 −0.819240 0.573451i \(-0.805604\pi\)
−0.819240 + 0.573451i \(0.805604\pi\)
\(272\) 8.89151 0.539127
\(273\) −1.71478 −0.103783
\(274\) 46.2727 2.79543
\(275\) 4.13000 0.249048
\(276\) 18.0913 1.08897
\(277\) 24.0323 1.44396 0.721980 0.691914i \(-0.243232\pi\)
0.721980 + 0.691914i \(0.243232\pi\)
\(278\) −37.4495 −2.24607
\(279\) 8.42140 0.504176
\(280\) 15.6697 0.936442
\(281\) 12.5280 0.747359 0.373679 0.927558i \(-0.378096\pi\)
0.373679 + 0.927558i \(0.378096\pi\)
\(282\) −14.8446 −0.883981
\(283\) −30.3643 −1.80497 −0.902485 0.430721i \(-0.858259\pi\)
−0.902485 + 0.430721i \(0.858259\pi\)
\(284\) −5.18811 −0.307858
\(285\) −9.19248 −0.544516
\(286\) −6.07475 −0.359207
\(287\) 19.0463 1.12427
\(288\) 0.377710 0.0222568
\(289\) −12.5812 −0.740072
\(290\) 10.8336 0.636171
\(291\) 13.6887 0.802448
\(292\) 19.3006 1.12948
\(293\) −29.0186 −1.69529 −0.847644 0.530566i \(-0.821979\pi\)
−0.847644 + 0.530566i \(0.821979\pi\)
\(294\) 9.97524 0.581768
\(295\) 4.37191 0.254543
\(296\) 28.5118 1.65721
\(297\) 2.47217 0.143450
\(298\) −23.6431 −1.36961
\(299\) −4.48018 −0.259096
\(300\) 6.74596 0.389478
\(301\) −4.53970 −0.261664
\(302\) −12.8268 −0.738100
\(303\) 1.97292 0.113341
\(304\) 21.3095 1.22219
\(305\) −19.7597 −1.13144
\(306\) 5.16535 0.295283
\(307\) −30.0178 −1.71321 −0.856603 0.515976i \(-0.827429\pi\)
−0.856603 + 0.515976i \(0.827429\pi\)
\(308\) −17.1183 −0.975409
\(309\) 1.00000 0.0568880
\(310\) 37.7587 2.14455
\(311\) 17.9357 1.01704 0.508521 0.861050i \(-0.330192\pi\)
0.508521 + 0.861050i \(0.330192\pi\)
\(312\) −5.00803 −0.283524
\(313\) 5.61280 0.317254 0.158627 0.987339i \(-0.449293\pi\)
0.158627 + 0.987339i \(0.449293\pi\)
\(314\) 5.19009 0.292894
\(315\) 3.12891 0.176294
\(316\) 41.9581 2.36033
\(317\) 21.9236 1.23135 0.615677 0.787999i \(-0.288883\pi\)
0.615677 + 0.787999i \(0.288883\pi\)
\(318\) 4.01653 0.225236
\(319\) −5.97338 −0.334445
\(320\) −13.7426 −0.768234
\(321\) −15.1982 −0.848282
\(322\) −18.8779 −1.05202
\(323\) 10.5901 0.589249
\(324\) 4.03807 0.224337
\(325\) −1.67059 −0.0926678
\(326\) −55.9296 −3.09766
\(327\) 18.2958 1.01176
\(328\) 55.6247 3.07136
\(329\) 10.3592 0.571124
\(330\) 11.0844 0.610175
\(331\) −2.09911 −0.115377 −0.0576887 0.998335i \(-0.518373\pi\)
−0.0576887 + 0.998335i \(0.518373\pi\)
\(332\) 20.5821 1.12959
\(333\) 5.69321 0.311986
\(334\) 14.7712 0.808246
\(335\) −13.6771 −0.747261
\(336\) −7.25327 −0.395698
\(337\) −0.810195 −0.0441342 −0.0220671 0.999756i \(-0.507025\pi\)
−0.0220671 + 0.999756i \(0.507025\pi\)
\(338\) 2.45725 0.133657
\(339\) 10.9011 0.592065
\(340\) 15.4884 0.839979
\(341\) −20.8192 −1.12742
\(342\) 12.3794 0.669399
\(343\) −18.9647 −1.02400
\(344\) −13.2582 −0.714835
\(345\) 8.17484 0.440118
\(346\) 5.00986 0.269331
\(347\) −20.7820 −1.11564 −0.557818 0.829963i \(-0.688361\pi\)
−0.557818 + 0.829963i \(0.688361\pi\)
\(348\) −9.75695 −0.523027
\(349\) 11.4654 0.613731 0.306865 0.951753i \(-0.400720\pi\)
0.306865 + 0.951753i \(0.400720\pi\)
\(350\) −7.03929 −0.376266
\(351\) −1.00000 −0.0533761
\(352\) −0.933765 −0.0497699
\(353\) 16.0880 0.856278 0.428139 0.903713i \(-0.359169\pi\)
0.428139 + 0.903713i \(0.359169\pi\)
\(354\) −5.88758 −0.312922
\(355\) −2.34433 −0.124424
\(356\) −21.2076 −1.12400
\(357\) −3.60463 −0.190777
\(358\) 62.6811 3.31280
\(359\) −9.74393 −0.514265 −0.257133 0.966376i \(-0.582778\pi\)
−0.257133 + 0.966376i \(0.582778\pi\)
\(360\) 9.13799 0.481614
\(361\) 6.38042 0.335811
\(362\) 25.1296 1.32078
\(363\) 4.88835 0.256572
\(364\) 6.92441 0.362938
\(365\) 8.72130 0.456494
\(366\) 26.6101 1.39093
\(367\) 4.49956 0.234875 0.117437 0.993080i \(-0.462532\pi\)
0.117437 + 0.993080i \(0.462532\pi\)
\(368\) −18.9505 −0.987862
\(369\) 11.1071 0.578213
\(370\) 25.5264 1.32705
\(371\) −2.80292 −0.145520
\(372\) −34.0062 −1.76314
\(373\) 29.6861 1.53709 0.768543 0.639798i \(-0.220982\pi\)
0.768543 + 0.639798i \(0.220982\pi\)
\(374\) −12.7696 −0.660303
\(375\) 12.1716 0.628539
\(376\) 30.2542 1.56024
\(377\) 2.41624 0.124443
\(378\) −4.21365 −0.216727
\(379\) −24.5787 −1.26252 −0.631262 0.775569i \(-0.717463\pi\)
−0.631262 + 0.775569i \(0.717463\pi\)
\(380\) 37.1198 1.90421
\(381\) −18.0296 −0.923684
\(382\) −20.5835 −1.05314
\(383\) −18.1584 −0.927849 −0.463925 0.885875i \(-0.653559\pi\)
−0.463925 + 0.885875i \(0.653559\pi\)
\(384\) 19.2623 0.982977
\(385\) −7.73521 −0.394223
\(386\) −38.5599 −1.96265
\(387\) −2.64739 −0.134574
\(388\) −55.2760 −2.80621
\(389\) 0.0830578 0.00421120 0.00210560 0.999998i \(-0.499330\pi\)
0.00210560 + 0.999998i \(0.499330\pi\)
\(390\) −4.48366 −0.227039
\(391\) −9.41774 −0.476275
\(392\) −20.3302 −1.02683
\(393\) −7.05989 −0.356125
\(394\) −27.6948 −1.39524
\(395\) 18.9594 0.953953
\(396\) −9.98280 −0.501655
\(397\) 13.2343 0.664212 0.332106 0.943242i \(-0.392241\pi\)
0.332106 + 0.943242i \(0.392241\pi\)
\(398\) −1.91194 −0.0958368
\(399\) −8.63891 −0.432486
\(400\) −7.06635 −0.353317
\(401\) −9.78535 −0.488657 −0.244329 0.969693i \(-0.578568\pi\)
−0.244329 + 0.969693i \(0.578568\pi\)
\(402\) 18.4187 0.918644
\(403\) 8.42140 0.419500
\(404\) −7.96679 −0.396363
\(405\) 1.82467 0.0906684
\(406\) 10.1812 0.505284
\(407\) −14.0746 −0.697652
\(408\) −10.5273 −0.521180
\(409\) 32.2133 1.59284 0.796422 0.604742i \(-0.206724\pi\)
0.796422 + 0.604742i \(0.206724\pi\)
\(410\) 49.8004 2.45947
\(411\) −18.8311 −0.928869
\(412\) −4.03807 −0.198941
\(413\) 4.10863 0.202173
\(414\) −11.0089 −0.541059
\(415\) 9.30037 0.456537
\(416\) 0.377710 0.0185188
\(417\) 15.2404 0.746328
\(418\) −30.6039 −1.49689
\(419\) −20.8448 −1.01833 −0.509167 0.860668i \(-0.670046\pi\)
−0.509167 + 0.860668i \(0.670046\pi\)
\(420\) −12.6347 −0.616512
\(421\) −26.9078 −1.31141 −0.655704 0.755018i \(-0.727628\pi\)
−0.655704 + 0.755018i \(0.727628\pi\)
\(422\) 67.5158 3.28662
\(423\) 6.04114 0.293730
\(424\) −8.18595 −0.397545
\(425\) −3.51173 −0.170344
\(426\) 3.15707 0.152961
\(427\) −18.5698 −0.898654
\(428\) 61.3715 2.96650
\(429\) 2.47217 0.119358
\(430\) −11.8700 −0.572422
\(431\) 25.2765 1.21753 0.608763 0.793352i \(-0.291666\pi\)
0.608763 + 0.793352i \(0.291666\pi\)
\(432\) −4.22984 −0.203508
\(433\) −33.2750 −1.59909 −0.799547 0.600604i \(-0.794927\pi\)
−0.799547 + 0.600604i \(0.794927\pi\)
\(434\) 35.4848 1.70333
\(435\) −4.40884 −0.211388
\(436\) −73.8795 −3.53819
\(437\) −22.5707 −1.07970
\(438\) −11.7448 −0.561190
\(439\) −27.8343 −1.32846 −0.664230 0.747528i \(-0.731240\pi\)
−0.664230 + 0.747528i \(0.731240\pi\)
\(440\) −22.5907 −1.07697
\(441\) −4.05952 −0.193310
\(442\) 5.16535 0.245691
\(443\) 13.4728 0.640114 0.320057 0.947398i \(-0.396298\pi\)
0.320057 + 0.947398i \(0.396298\pi\)
\(444\) −22.9895 −1.09104
\(445\) −9.58299 −0.454277
\(446\) 53.3276 2.52514
\(447\) 9.62177 0.455094
\(448\) −12.9150 −0.610176
\(449\) −27.8246 −1.31312 −0.656561 0.754273i \(-0.727990\pi\)
−0.656561 + 0.754273i \(0.727990\pi\)
\(450\) −4.10506 −0.193514
\(451\) −27.4587 −1.29298
\(452\) −44.0192 −2.07049
\(453\) 5.21999 0.245257
\(454\) −15.7589 −0.739603
\(455\) 3.12891 0.146685
\(456\) −25.2300 −1.18150
\(457\) 4.15766 0.194487 0.0972435 0.995261i \(-0.468997\pi\)
0.0972435 + 0.995261i \(0.468997\pi\)
\(458\) −46.5728 −2.17620
\(459\) −2.10209 −0.0981171
\(460\) −33.0105 −1.53912
\(461\) −28.3340 −1.31964 −0.659822 0.751422i \(-0.729368\pi\)
−0.659822 + 0.751422i \(0.729368\pi\)
\(462\) 10.4169 0.484637
\(463\) −4.84265 −0.225057 −0.112529 0.993648i \(-0.535895\pi\)
−0.112529 + 0.993648i \(0.535895\pi\)
\(464\) 10.2203 0.474467
\(465\) −15.3662 −0.712593
\(466\) −32.6870 −1.51419
\(467\) 3.18012 0.147159 0.0735793 0.997289i \(-0.476558\pi\)
0.0735793 + 0.997289i \(0.476558\pi\)
\(468\) 4.03807 0.186660
\(469\) −12.8535 −0.593518
\(470\) 27.0864 1.24940
\(471\) −2.11215 −0.0973229
\(472\) 11.9993 0.552312
\(473\) 6.54481 0.300931
\(474\) −25.5324 −1.17274
\(475\) −8.41628 −0.386165
\(476\) 14.5557 0.667160
\(477\) −1.63456 −0.0748415
\(478\) 8.30540 0.379880
\(479\) 15.9757 0.729948 0.364974 0.931018i \(-0.381078\pi\)
0.364974 + 0.931018i \(0.381078\pi\)
\(480\) −0.689195 −0.0314573
\(481\) 5.69321 0.259588
\(482\) −14.8028 −0.674250
\(483\) 7.68254 0.349568
\(484\) −19.7395 −0.897250
\(485\) −24.9774 −1.13416
\(486\) −2.45725 −0.111463
\(487\) 6.70437 0.303804 0.151902 0.988396i \(-0.451460\pi\)
0.151902 + 0.988396i \(0.451460\pi\)
\(488\) −54.2331 −2.45502
\(489\) 22.7611 1.02929
\(490\) −18.2015 −0.822259
\(491\) 20.3061 0.916402 0.458201 0.888849i \(-0.348494\pi\)
0.458201 + 0.888849i \(0.348494\pi\)
\(492\) −44.8512 −2.02205
\(493\) 5.07916 0.228754
\(494\) 12.3794 0.556974
\(495\) −4.51089 −0.202750
\(496\) 35.6212 1.59944
\(497\) −2.20315 −0.0988250
\(498\) −12.5247 −0.561243
\(499\) 6.47947 0.290061 0.145030 0.989427i \(-0.453672\pi\)
0.145030 + 0.989427i \(0.453672\pi\)
\(500\) −49.1497 −2.19804
\(501\) −6.01129 −0.268565
\(502\) 16.0987 0.718521
\(503\) −23.7928 −1.06087 −0.530434 0.847726i \(-0.677971\pi\)
−0.530434 + 0.847726i \(0.677971\pi\)
\(504\) 8.58769 0.382526
\(505\) −3.59992 −0.160195
\(506\) 27.2160 1.20990
\(507\) −1.00000 −0.0444116
\(508\) 72.8047 3.23019
\(509\) 28.2482 1.25208 0.626040 0.779791i \(-0.284675\pi\)
0.626040 + 0.779791i \(0.284675\pi\)
\(510\) −9.42504 −0.417348
\(511\) 8.19610 0.362574
\(512\) −40.7687 −1.80174
\(513\) −5.03790 −0.222429
\(514\) 50.3818 2.22225
\(515\) −1.82467 −0.0804044
\(516\) 10.6903 0.470616
\(517\) −14.9347 −0.656829
\(518\) 23.9892 1.05402
\(519\) −2.03881 −0.0894937
\(520\) 9.13799 0.400727
\(521\) −44.1567 −1.93454 −0.967271 0.253746i \(-0.918337\pi\)
−0.967271 + 0.253746i \(0.918337\pi\)
\(522\) 5.93731 0.259869
\(523\) 31.6452 1.38375 0.691875 0.722017i \(-0.256785\pi\)
0.691875 + 0.722017i \(0.256785\pi\)
\(524\) 28.5083 1.24539
\(525\) 2.86471 0.125026
\(526\) −43.4981 −1.89661
\(527\) 17.7025 0.771134
\(528\) 10.4569 0.455079
\(529\) −2.92797 −0.127303
\(530\) −7.32882 −0.318344
\(531\) 2.39601 0.103978
\(532\) 34.8845 1.51243
\(533\) 11.1071 0.481102
\(534\) 12.9053 0.558465
\(535\) 27.7317 1.19895
\(536\) −37.5386 −1.62142
\(537\) −25.5086 −1.10078
\(538\) −60.2176 −2.59617
\(539\) 10.0358 0.432274
\(540\) −7.36812 −0.317074
\(541\) −42.7803 −1.83927 −0.919634 0.392775i \(-0.871515\pi\)
−0.919634 + 0.392775i \(0.871515\pi\)
\(542\) −66.2788 −2.84692
\(543\) −10.2267 −0.438871
\(544\) 0.793980 0.0340416
\(545\) −33.3837 −1.43000
\(546\) −4.21365 −0.180327
\(547\) 16.3747 0.700131 0.350066 0.936725i \(-0.386159\pi\)
0.350066 + 0.936725i \(0.386159\pi\)
\(548\) 76.0412 3.24832
\(549\) −10.8292 −0.462180
\(550\) 10.1484 0.432730
\(551\) 12.1728 0.518578
\(552\) 22.4369 0.954978
\(553\) 17.8177 0.757685
\(554\) 59.0533 2.50893
\(555\) −10.3882 −0.440955
\(556\) −61.5419 −2.60996
\(557\) 33.3832 1.41449 0.707245 0.706969i \(-0.249938\pi\)
0.707245 + 0.706969i \(0.249938\pi\)
\(558\) 20.6935 0.876024
\(559\) −2.64739 −0.111973
\(560\) 13.2348 0.559272
\(561\) 5.19673 0.219406
\(562\) 30.7844 1.29856
\(563\) 14.3656 0.605439 0.302719 0.953080i \(-0.402105\pi\)
0.302719 + 0.953080i \(0.402105\pi\)
\(564\) −24.3945 −1.02719
\(565\) −19.8908 −0.836813
\(566\) −74.6126 −3.13620
\(567\) 1.71478 0.0720141
\(568\) −6.43432 −0.269978
\(569\) 12.0211 0.503949 0.251975 0.967734i \(-0.418920\pi\)
0.251975 + 0.967734i \(0.418920\pi\)
\(570\) −22.5882 −0.946116
\(571\) 18.0344 0.754718 0.377359 0.926067i \(-0.376832\pi\)
0.377359 + 0.926067i \(0.376832\pi\)
\(572\) −9.98280 −0.417402
\(573\) 8.37666 0.349940
\(574\) 46.8014 1.95345
\(575\) 7.48456 0.312128
\(576\) −7.53156 −0.313815
\(577\) 10.8638 0.452266 0.226133 0.974096i \(-0.427392\pi\)
0.226133 + 0.974096i \(0.427392\pi\)
\(578\) −30.9152 −1.28590
\(579\) 15.6923 0.652151
\(580\) 17.8032 0.739237
\(581\) 8.74030 0.362609
\(582\) 33.6366 1.39428
\(583\) 4.04093 0.167358
\(584\) 23.9367 0.990509
\(585\) 1.82467 0.0754407
\(586\) −71.3060 −2.94562
\(587\) 4.52036 0.186575 0.0932877 0.995639i \(-0.470262\pi\)
0.0932877 + 0.995639i \(0.470262\pi\)
\(588\) 16.3926 0.676019
\(589\) 42.4262 1.74814
\(590\) 10.7429 0.442277
\(591\) 11.2707 0.463613
\(592\) 24.0814 0.989738
\(593\) −31.7623 −1.30432 −0.652160 0.758081i \(-0.726137\pi\)
−0.652160 + 0.758081i \(0.726137\pi\)
\(594\) 6.07475 0.249250
\(595\) 6.57724 0.269641
\(596\) −38.8534 −1.59150
\(597\) 0.778082 0.0318448
\(598\) −11.0089 −0.450188
\(599\) −22.3684 −0.913948 −0.456974 0.889480i \(-0.651067\pi\)
−0.456974 + 0.889480i \(0.651067\pi\)
\(600\) 8.36638 0.341556
\(601\) −12.7059 −0.518284 −0.259142 0.965839i \(-0.583440\pi\)
−0.259142 + 0.965839i \(0.583440\pi\)
\(602\) −11.1552 −0.454651
\(603\) −7.49568 −0.305248
\(604\) −21.0787 −0.857679
\(605\) −8.91961 −0.362634
\(606\) 4.84796 0.196935
\(607\) 13.8752 0.563176 0.281588 0.959535i \(-0.409139\pi\)
0.281588 + 0.959535i \(0.409139\pi\)
\(608\) 1.90287 0.0771714
\(609\) −4.14333 −0.167896
\(610\) −48.5545 −1.96591
\(611\) 6.04114 0.244398
\(612\) 8.48837 0.343122
\(613\) 20.2055 0.816094 0.408047 0.912961i \(-0.366210\pi\)
0.408047 + 0.912961i \(0.366210\pi\)
\(614\) −73.7612 −2.97676
\(615\) −20.2668 −0.817235
\(616\) −21.2303 −0.855392
\(617\) −25.7238 −1.03560 −0.517802 0.855501i \(-0.673249\pi\)
−0.517802 + 0.855501i \(0.673249\pi\)
\(618\) 2.45725 0.0988450
\(619\) −19.3588 −0.778094 −0.389047 0.921218i \(-0.627196\pi\)
−0.389047 + 0.921218i \(0.627196\pi\)
\(620\) 62.0499 2.49198
\(621\) 4.48018 0.179784
\(622\) 44.0725 1.76715
\(623\) −9.00590 −0.360814
\(624\) −4.22984 −0.169329
\(625\) −13.8562 −0.554246
\(626\) 13.7920 0.551241
\(627\) 12.4546 0.497387
\(628\) 8.52902 0.340345
\(629\) 11.9676 0.477180
\(630\) 7.68850 0.306317
\(631\) −30.4519 −1.21227 −0.606136 0.795361i \(-0.707281\pi\)
−0.606136 + 0.795361i \(0.707281\pi\)
\(632\) 52.0366 2.06991
\(633\) −27.4762 −1.09208
\(634\) 53.8718 2.13952
\(635\) 32.8980 1.30552
\(636\) 6.60047 0.261726
\(637\) −4.05952 −0.160844
\(638\) −14.6781 −0.581110
\(639\) −1.28480 −0.0508259
\(640\) −35.1473 −1.38932
\(641\) 8.91397 0.352081 0.176040 0.984383i \(-0.443671\pi\)
0.176040 + 0.984383i \(0.443671\pi\)
\(642\) −37.3458 −1.47392
\(643\) 11.9688 0.472005 0.236002 0.971752i \(-0.424163\pi\)
0.236002 + 0.971752i \(0.424163\pi\)
\(644\) −31.0226 −1.22246
\(645\) 4.83060 0.190205
\(646\) 26.0225 1.02384
\(647\) −4.78523 −0.188127 −0.0940634 0.995566i \(-0.529986\pi\)
−0.0940634 + 0.995566i \(0.529986\pi\)
\(648\) 5.00803 0.196734
\(649\) −5.92335 −0.232512
\(650\) −4.10506 −0.161014
\(651\) −14.4409 −0.565983
\(652\) −91.9108 −3.59950
\(653\) −24.9769 −0.977422 −0.488711 0.872446i \(-0.662533\pi\)
−0.488711 + 0.872446i \(0.662533\pi\)
\(654\) 44.9572 1.75797
\(655\) 12.8820 0.503339
\(656\) 46.9813 1.83431
\(657\) 4.77967 0.186473
\(658\) 25.4552 0.992348
\(659\) 10.8201 0.421490 0.210745 0.977541i \(-0.432411\pi\)
0.210745 + 0.977541i \(0.432411\pi\)
\(660\) 18.2153 0.709029
\(661\) −7.22917 −0.281182 −0.140591 0.990068i \(-0.544900\pi\)
−0.140591 + 0.990068i \(0.544900\pi\)
\(662\) −5.15802 −0.200472
\(663\) −2.10209 −0.0816383
\(664\) 25.5261 0.990604
\(665\) 15.7631 0.611268
\(666\) 13.9896 0.542087
\(667\) −10.8252 −0.419154
\(668\) 24.2740 0.939189
\(669\) −21.7022 −0.839055
\(670\) −33.6081 −1.29839
\(671\) 26.7717 1.03351
\(672\) −0.647691 −0.0249852
\(673\) 26.7146 1.02977 0.514886 0.857259i \(-0.327834\pi\)
0.514886 + 0.857259i \(0.327834\pi\)
\(674\) −1.99085 −0.0766847
\(675\) 1.67059 0.0643012
\(676\) 4.03807 0.155310
\(677\) 17.6487 0.678294 0.339147 0.940733i \(-0.389862\pi\)
0.339147 + 0.940733i \(0.389862\pi\)
\(678\) 26.7866 1.02873
\(679\) −23.4732 −0.900819
\(680\) 19.2089 0.736626
\(681\) 6.41324 0.245756
\(682\) −51.1579 −1.95894
\(683\) −22.1422 −0.847247 −0.423623 0.905838i \(-0.639242\pi\)
−0.423623 + 0.905838i \(0.639242\pi\)
\(684\) 20.3434 0.777848
\(685\) 34.3605 1.31285
\(686\) −46.6009 −1.77923
\(687\) 18.9532 0.723111
\(688\) −11.1981 −0.426922
\(689\) −1.63456 −0.0622719
\(690\) 20.0876 0.764722
\(691\) 26.0769 0.992011 0.496006 0.868319i \(-0.334800\pi\)
0.496006 + 0.868319i \(0.334800\pi\)
\(692\) 8.23284 0.312966
\(693\) −4.23924 −0.161036
\(694\) −51.0665 −1.93846
\(695\) −27.8087 −1.05484
\(696\) −12.1006 −0.458673
\(697\) 23.3481 0.884373
\(698\) 28.1734 1.06638
\(699\) 13.3023 0.503138
\(700\) −11.5679 −0.437224
\(701\) −13.9609 −0.527297 −0.263648 0.964619i \(-0.584926\pi\)
−0.263648 + 0.964619i \(0.584926\pi\)
\(702\) −2.45725 −0.0927428
\(703\) 28.6818 1.08175
\(704\) 18.6193 0.701743
\(705\) −11.0231 −0.415152
\(706\) 39.5322 1.48781
\(707\) −3.38313 −0.127236
\(708\) −9.67524 −0.363618
\(709\) −16.0197 −0.601632 −0.300816 0.953682i \(-0.597259\pi\)
−0.300816 + 0.953682i \(0.597259\pi\)
\(710\) −5.76060 −0.216192
\(711\) 10.3906 0.389679
\(712\) −26.3018 −0.985700
\(713\) −37.7294 −1.41298
\(714\) −8.85746 −0.331482
\(715\) −4.51089 −0.168698
\(716\) 103.006 3.84950
\(717\) −3.37996 −0.126227
\(718\) −23.9433 −0.893555
\(719\) −8.82899 −0.329266 −0.164633 0.986355i \(-0.552644\pi\)
−0.164633 + 0.986355i \(0.552644\pi\)
\(720\) 7.71805 0.287635
\(721\) −1.71478 −0.0638619
\(722\) 15.6783 0.583484
\(723\) 6.02414 0.224040
\(724\) 41.2962 1.53476
\(725\) −4.03656 −0.149914
\(726\) 12.0119 0.445803
\(727\) 19.1342 0.709649 0.354825 0.934933i \(-0.384541\pi\)
0.354825 + 0.934933i \(0.384541\pi\)
\(728\) 8.58769 0.318281
\(729\) 1.00000 0.0370370
\(730\) 21.4304 0.793174
\(731\) −5.56505 −0.205831
\(732\) 43.7291 1.61627
\(733\) −11.8488 −0.437644 −0.218822 0.975765i \(-0.570221\pi\)
−0.218822 + 0.975765i \(0.570221\pi\)
\(734\) 11.0565 0.408104
\(735\) 7.40726 0.273221
\(736\) −1.69221 −0.0623757
\(737\) 18.5306 0.682585
\(738\) 27.2929 1.00467
\(739\) 35.6420 1.31111 0.655555 0.755147i \(-0.272435\pi\)
0.655555 + 0.755147i \(0.272435\pi\)
\(740\) 41.9482 1.54205
\(741\) −5.03790 −0.185072
\(742\) −6.88748 −0.252847
\(743\) 32.2067 1.18155 0.590774 0.806837i \(-0.298823\pi\)
0.590774 + 0.806837i \(0.298823\pi\)
\(744\) −42.1747 −1.54620
\(745\) −17.5565 −0.643221
\(746\) 72.9460 2.67074
\(747\) 5.09703 0.186490
\(748\) −20.9847 −0.767278
\(749\) 26.0617 0.952273
\(750\) 29.9087 1.09211
\(751\) 24.8419 0.906494 0.453247 0.891385i \(-0.350266\pi\)
0.453247 + 0.891385i \(0.350266\pi\)
\(752\) 25.5531 0.931825
\(753\) −6.55153 −0.238751
\(754\) 5.93731 0.216224
\(755\) −9.52474 −0.346641
\(756\) −6.92441 −0.251838
\(757\) −15.3497 −0.557893 −0.278946 0.960307i \(-0.589985\pi\)
−0.278946 + 0.960307i \(0.589985\pi\)
\(758\) −60.3960 −2.19368
\(759\) −11.0758 −0.402026
\(760\) 46.0363 1.66991
\(761\) 6.52172 0.236412 0.118206 0.992989i \(-0.462286\pi\)
0.118206 + 0.992989i \(0.462286\pi\)
\(762\) −44.3032 −1.60493
\(763\) −31.3733 −1.13579
\(764\) −33.8255 −1.22376
\(765\) 3.83561 0.138677
\(766\) −44.6196 −1.61217
\(767\) 2.39601 0.0865148
\(768\) 32.2692 1.16441
\(769\) −21.7203 −0.783252 −0.391626 0.920124i \(-0.628087\pi\)
−0.391626 + 0.920124i \(0.628087\pi\)
\(770\) −19.0073 −0.684976
\(771\) −20.5033 −0.738410
\(772\) −63.3667 −2.28062
\(773\) −4.58871 −0.165045 −0.0825223 0.996589i \(-0.526298\pi\)
−0.0825223 + 0.996589i \(0.526298\pi\)
\(774\) −6.50529 −0.233828
\(775\) −14.0687 −0.505364
\(776\) −68.5536 −2.46093
\(777\) −9.76262 −0.350232
\(778\) 0.204094 0.00731711
\(779\) 55.9565 2.00485
\(780\) −7.36812 −0.263821
\(781\) 3.17625 0.113655
\(782\) −23.1417 −0.827546
\(783\) −2.41624 −0.0863495
\(784\) −17.1711 −0.613254
\(785\) 3.85398 0.137554
\(786\) −17.3479 −0.618779
\(787\) 10.4885 0.373873 0.186937 0.982372i \(-0.440144\pi\)
0.186937 + 0.982372i \(0.440144\pi\)
\(788\) −45.5117 −1.62129
\(789\) 17.7020 0.630207
\(790\) 46.5880 1.65753
\(791\) −18.6930 −0.664646
\(792\) −12.3807 −0.439930
\(793\) −10.8292 −0.384557
\(794\) 32.5200 1.15409
\(795\) 2.98253 0.105780
\(796\) −3.14194 −0.111363
\(797\) −19.4563 −0.689178 −0.344589 0.938754i \(-0.611982\pi\)
−0.344589 + 0.938754i \(0.611982\pi\)
\(798\) −21.2279 −0.751461
\(799\) 12.6990 0.449258
\(800\) −0.631000 −0.0223092
\(801\) −5.25191 −0.185567
\(802\) −24.0450 −0.849059
\(803\) −11.8162 −0.416984
\(804\) 30.2681 1.06747
\(805\) −14.0181 −0.494072
\(806\) 20.6935 0.728896
\(807\) 24.5061 0.862657
\(808\) −9.88046 −0.347593
\(809\) −33.2176 −1.16787 −0.583935 0.811800i \(-0.698488\pi\)
−0.583935 + 0.811800i \(0.698488\pi\)
\(810\) 4.48366 0.157540
\(811\) 20.0974 0.705715 0.352857 0.935677i \(-0.385210\pi\)
0.352857 + 0.935677i \(0.385210\pi\)
\(812\) 16.7311 0.587145
\(813\) 26.9728 0.945977
\(814\) −34.5848 −1.21220
\(815\) −41.5314 −1.45478
\(816\) −8.89151 −0.311265
\(817\) −13.3373 −0.466613
\(818\) 79.1560 2.76762
\(819\) 1.71478 0.0599194
\(820\) 81.8385 2.85792
\(821\) −9.75001 −0.340278 −0.170139 0.985420i \(-0.554422\pi\)
−0.170139 + 0.985420i \(0.554422\pi\)
\(822\) −46.2727 −1.61394
\(823\) −33.2226 −1.15807 −0.579033 0.815304i \(-0.696570\pi\)
−0.579033 + 0.815304i \(0.696570\pi\)
\(824\) −5.00803 −0.174463
\(825\) −4.13000 −0.143788
\(826\) 10.0959 0.351282
\(827\) −37.6560 −1.30943 −0.654714 0.755877i \(-0.727211\pi\)
−0.654714 + 0.755877i \(0.727211\pi\)
\(828\) −18.0913 −0.628715
\(829\) 28.5745 0.992433 0.496217 0.868199i \(-0.334722\pi\)
0.496217 + 0.868199i \(0.334722\pi\)
\(830\) 22.8533 0.793250
\(831\) −24.0323 −0.833670
\(832\) −7.53156 −0.261110
\(833\) −8.53346 −0.295667
\(834\) 37.4495 1.29677
\(835\) 10.9686 0.379584
\(836\) −50.2923 −1.73940
\(837\) −8.42140 −0.291086
\(838\) −51.2207 −1.76939
\(839\) 35.7276 1.23346 0.616728 0.787177i \(-0.288458\pi\)
0.616728 + 0.787177i \(0.288458\pi\)
\(840\) −15.6697 −0.540655
\(841\) −23.1618 −0.798682
\(842\) −66.1192 −2.27862
\(843\) −12.5280 −0.431488
\(844\) 110.951 3.81908
\(845\) 1.82467 0.0627704
\(846\) 14.8446 0.510367
\(847\) −8.38247 −0.288025
\(848\) −6.91395 −0.237426
\(849\) 30.3643 1.04210
\(850\) −8.62920 −0.295979
\(851\) −25.5066 −0.874355
\(852\) 5.18811 0.177742
\(853\) −44.9199 −1.53803 −0.769015 0.639231i \(-0.779253\pi\)
−0.769015 + 0.639231i \(0.779253\pi\)
\(854\) −45.6305 −1.56144
\(855\) 9.19248 0.314376
\(856\) 76.1132 2.60150
\(857\) 41.0855 1.40345 0.701726 0.712447i \(-0.252413\pi\)
0.701726 + 0.712447i \(0.252413\pi\)
\(858\) 6.07475 0.207388
\(859\) −50.4833 −1.72247 −0.861234 0.508209i \(-0.830308\pi\)
−0.861234 + 0.508209i \(0.830308\pi\)
\(860\) −19.5063 −0.665159
\(861\) −19.0463 −0.649096
\(862\) 62.1106 2.11550
\(863\) −36.8528 −1.25448 −0.627241 0.778825i \(-0.715816\pi\)
−0.627241 + 0.778825i \(0.715816\pi\)
\(864\) −0.377710 −0.0128500
\(865\) 3.72014 0.126489
\(866\) −81.7649 −2.77848
\(867\) 12.5812 0.427281
\(868\) 58.3132 1.97928
\(869\) −25.6875 −0.871387
\(870\) −10.8336 −0.367294
\(871\) −7.49568 −0.253982
\(872\) −91.6258 −3.10284
\(873\) −13.6887 −0.463293
\(874\) −55.4618 −1.87602
\(875\) −20.8717 −0.705591
\(876\) −19.3006 −0.652107
\(877\) 7.42795 0.250824 0.125412 0.992105i \(-0.459975\pi\)
0.125412 + 0.992105i \(0.459975\pi\)
\(878\) −68.3958 −2.30825
\(879\) 29.0186 0.978775
\(880\) −19.0804 −0.643199
\(881\) −23.2794 −0.784302 −0.392151 0.919901i \(-0.628269\pi\)
−0.392151 + 0.919901i \(0.628269\pi\)
\(882\) −9.97524 −0.335884
\(883\) 3.87577 0.130430 0.0652149 0.997871i \(-0.479227\pi\)
0.0652149 + 0.997871i \(0.479227\pi\)
\(884\) 8.48837 0.285495
\(885\) −4.37191 −0.146960
\(886\) 33.1061 1.11222
\(887\) 47.3370 1.58942 0.794711 0.606988i \(-0.207623\pi\)
0.794711 + 0.606988i \(0.207623\pi\)
\(888\) −28.5118 −0.956792
\(889\) 30.9168 1.03692
\(890\) −23.5478 −0.789323
\(891\) −2.47217 −0.0828210
\(892\) 87.6349 2.93423
\(893\) 30.4346 1.01846
\(894\) 23.6431 0.790743
\(895\) 46.5448 1.55582
\(896\) −33.0307 −1.10348
\(897\) 4.48018 0.149589
\(898\) −68.3719 −2.28160
\(899\) 20.3482 0.678649
\(900\) −6.74596 −0.224865
\(901\) −3.43600 −0.114470
\(902\) −67.4728 −2.24660
\(903\) 4.53970 0.151072
\(904\) −54.5929 −1.81573
\(905\) 18.6604 0.620292
\(906\) 12.8268 0.426142
\(907\) −33.1774 −1.10164 −0.550818 0.834625i \(-0.685684\pi\)
−0.550818 + 0.834625i \(0.685684\pi\)
\(908\) −25.8971 −0.859426
\(909\) −1.97292 −0.0654377
\(910\) 7.68850 0.254871
\(911\) 38.9751 1.29130 0.645651 0.763633i \(-0.276586\pi\)
0.645651 + 0.763633i \(0.276586\pi\)
\(912\) −21.3095 −0.705629
\(913\) −12.6007 −0.417024
\(914\) 10.2164 0.337928
\(915\) 19.7597 0.653236
\(916\) −76.5344 −2.52877
\(917\) 12.1062 0.399782
\(918\) −5.16535 −0.170482
\(919\) −33.4095 −1.10208 −0.551038 0.834480i \(-0.685768\pi\)
−0.551038 + 0.834480i \(0.685768\pi\)
\(920\) −40.9399 −1.34975
\(921\) 30.0178 0.989120
\(922\) −69.6236 −2.29293
\(923\) −1.28480 −0.0422897
\(924\) 17.1183 0.563152
\(925\) −9.51103 −0.312721
\(926\) −11.8996 −0.391045
\(927\) −1.00000 −0.0328443
\(928\) 0.912640 0.0299589
\(929\) 40.9112 1.34225 0.671126 0.741344i \(-0.265811\pi\)
0.671126 + 0.741344i \(0.265811\pi\)
\(930\) −37.7587 −1.23816
\(931\) −20.4514 −0.670269
\(932\) −53.7154 −1.75951
\(933\) −17.9357 −0.587189
\(934\) 7.81435 0.255693
\(935\) −9.48230 −0.310104
\(936\) 5.00803 0.163693
\(937\) 32.3748 1.05764 0.528820 0.848734i \(-0.322635\pi\)
0.528820 + 0.848734i \(0.322635\pi\)
\(938\) −31.5842 −1.03126
\(939\) −5.61280 −0.183167
\(940\) 44.5118 1.45182
\(941\) 2.27246 0.0740801 0.0370401 0.999314i \(-0.488207\pi\)
0.0370401 + 0.999314i \(0.488207\pi\)
\(942\) −5.19009 −0.169102
\(943\) −49.7619 −1.62047
\(944\) 10.1347 0.329858
\(945\) −3.12891 −0.101783
\(946\) 16.0822 0.522878
\(947\) 35.5665 1.15575 0.577877 0.816124i \(-0.303881\pi\)
0.577877 + 0.816124i \(0.303881\pi\)
\(948\) −41.9581 −1.36273
\(949\) 4.77967 0.155155
\(950\) −20.6809 −0.670976
\(951\) −21.9236 −0.710922
\(952\) 18.0521 0.585071
\(953\) 58.0872 1.88163 0.940814 0.338924i \(-0.110063\pi\)
0.940814 + 0.338924i \(0.110063\pi\)
\(954\) −4.01653 −0.130040
\(955\) −15.2846 −0.494598
\(956\) 13.6485 0.441424
\(957\) 5.97338 0.193092
\(958\) 39.2562 1.26831
\(959\) 32.2912 1.04274
\(960\) 13.7426 0.443540
\(961\) 39.9200 1.28774
\(962\) 13.9896 0.451043
\(963\) 15.1982 0.489756
\(964\) −24.3259 −0.783484
\(965\) −28.6333 −0.921737
\(966\) 18.8779 0.607387
\(967\) −31.2378 −1.00454 −0.502269 0.864711i \(-0.667501\pi\)
−0.502269 + 0.864711i \(0.667501\pi\)
\(968\) −24.4810 −0.786850
\(969\) −10.5901 −0.340203
\(970\) −61.3756 −1.97065
\(971\) −23.6040 −0.757487 −0.378743 0.925502i \(-0.623644\pi\)
−0.378743 + 0.925502i \(0.623644\pi\)
\(972\) −4.03807 −0.129521
\(973\) −26.1341 −0.837820
\(974\) 16.4743 0.527871
\(975\) 1.67059 0.0535018
\(976\) −45.8059 −1.46621
\(977\) −21.7135 −0.694678 −0.347339 0.937740i \(-0.612915\pi\)
−0.347339 + 0.937740i \(0.612915\pi\)
\(978\) 55.9296 1.78843
\(979\) 12.9836 0.414959
\(980\) −29.9110 −0.955472
\(981\) −18.2958 −0.584139
\(982\) 49.8971 1.59228
\(983\) 48.1433 1.53553 0.767766 0.640730i \(-0.221368\pi\)
0.767766 + 0.640730i \(0.221368\pi\)
\(984\) −55.6247 −1.77325
\(985\) −20.5652 −0.655262
\(986\) 12.4807 0.397468
\(987\) −10.3592 −0.329738
\(988\) 20.3434 0.647209
\(989\) 11.8608 0.377151
\(990\) −11.0844 −0.352285
\(991\) 12.3184 0.391308 0.195654 0.980673i \(-0.437317\pi\)
0.195654 + 0.980673i \(0.437317\pi\)
\(992\) 3.18085 0.100992
\(993\) 2.09911 0.0666131
\(994\) −5.41370 −0.171712
\(995\) −1.41974 −0.0450088
\(996\) −20.5821 −0.652170
\(997\) −9.40592 −0.297889 −0.148944 0.988846i \(-0.547588\pi\)
−0.148944 + 0.988846i \(0.547588\pi\)
\(998\) 15.9217 0.503991
\(999\) −5.69321 −0.180125
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 \(a_p\))