Properties

Label 8001.2.a.v.1.16
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(-1.91759\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.91759 q^{2}\) \(+1.67713 q^{4}\) \(-1.63006 q^{5}\) \(+1.00000 q^{7}\) \(-0.619124 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.91759 q^{2}\) \(+1.67713 q^{4}\) \(-1.63006 q^{5}\) \(+1.00000 q^{7}\) \(-0.619124 q^{8}\) \(-3.12578 q^{10}\) \(-4.53723 q^{11}\) \(+0.785019 q^{13}\) \(+1.91759 q^{14}\) \(-4.54149 q^{16}\) \(+4.58625 q^{17}\) \(+7.32031 q^{19}\) \(-2.73383 q^{20}\) \(-8.70052 q^{22}\) \(-1.77992 q^{23}\) \(-2.34290 q^{25}\) \(+1.50534 q^{26}\) \(+1.67713 q^{28}\) \(-4.77456 q^{29}\) \(+5.06545 q^{31}\) \(-7.47045 q^{32}\) \(+8.79452 q^{34}\) \(-1.63006 q^{35}\) \(-1.03335 q^{37}\) \(+14.0373 q^{38}\) \(+1.00921 q^{40}\) \(+10.6489 q^{41}\) \(+8.26855 q^{43}\) \(-7.60954 q^{44}\) \(-3.41315 q^{46}\) \(-7.59560 q^{47}\) \(+1.00000 q^{49}\) \(-4.49271 q^{50}\) \(+1.31658 q^{52}\) \(-0.151205 q^{53}\) \(+7.39596 q^{55}\) \(-0.619124 q^{56}\) \(-9.15563 q^{58}\) \(-4.69350 q^{59}\) \(-12.1937 q^{61}\) \(+9.71343 q^{62}\) \(-5.24224 q^{64}\) \(-1.27963 q^{65}\) \(+1.56249 q^{67}\) \(+7.69175 q^{68}\) \(-3.12578 q^{70}\) \(+13.2252 q^{71}\) \(+5.59318 q^{73}\) \(-1.98153 q^{74}\) \(+12.2771 q^{76}\) \(-4.53723 q^{77}\) \(-3.81705 q^{79}\) \(+7.40291 q^{80}\) \(+20.4201 q^{82}\) \(-0.734264 q^{83}\) \(-7.47586 q^{85}\) \(+15.8556 q^{86}\) \(+2.80911 q^{88}\) \(+5.16974 q^{89}\) \(+0.785019 q^{91}\) \(-2.98516 q^{92}\) \(-14.5652 q^{94}\) \(-11.9326 q^{95}\) \(-5.35014 q^{97}\) \(+1.91759 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.91759 1.35594 0.677969 0.735091i \(-0.262860\pi\)
0.677969 + 0.735091i \(0.262860\pi\)
\(3\) 0 0
\(4\) 1.67713 0.838567
\(5\) −1.63006 −0.728986 −0.364493 0.931206i \(-0.618758\pi\)
−0.364493 + 0.931206i \(0.618758\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −0.619124 −0.218893
\(9\) 0 0
\(10\) −3.12578 −0.988459
\(11\) −4.53723 −1.36803 −0.684013 0.729470i \(-0.739767\pi\)
−0.684013 + 0.729470i \(0.739767\pi\)
\(12\) 0 0
\(13\) 0.785019 0.217725 0.108863 0.994057i \(-0.465279\pi\)
0.108863 + 0.994057i \(0.465279\pi\)
\(14\) 1.91759 0.512496
\(15\) 0 0
\(16\) −4.54149 −1.13537
\(17\) 4.58625 1.11233 0.556164 0.831073i \(-0.312273\pi\)
0.556164 + 0.831073i \(0.312273\pi\)
\(18\) 0 0
\(19\) 7.32031 1.67940 0.839698 0.543054i \(-0.182732\pi\)
0.839698 + 0.543054i \(0.182732\pi\)
\(20\) −2.73383 −0.611303
\(21\) 0 0
\(22\) −8.70052 −1.85496
\(23\) −1.77992 −0.371139 −0.185569 0.982631i \(-0.559413\pi\)
−0.185569 + 0.982631i \(0.559413\pi\)
\(24\) 0 0
\(25\) −2.34290 −0.468580
\(26\) 1.50534 0.295222
\(27\) 0 0
\(28\) 1.67713 0.316948
\(29\) −4.77456 −0.886614 −0.443307 0.896370i \(-0.646195\pi\)
−0.443307 + 0.896370i \(0.646195\pi\)
\(30\) 0 0
\(31\) 5.06545 0.909781 0.454891 0.890547i \(-0.349678\pi\)
0.454891 + 0.890547i \(0.349678\pi\)
\(32\) −7.47045 −1.32060
\(33\) 0 0
\(34\) 8.79452 1.50825
\(35\) −1.63006 −0.275531
\(36\) 0 0
\(37\) −1.03335 −0.169881 −0.0849407 0.996386i \(-0.527070\pi\)
−0.0849407 + 0.996386i \(0.527070\pi\)
\(38\) 14.0373 2.27716
\(39\) 0 0
\(40\) 1.00921 0.159570
\(41\) 10.6489 1.66307 0.831536 0.555471i \(-0.187462\pi\)
0.831536 + 0.555471i \(0.187462\pi\)
\(42\) 0 0
\(43\) 8.26855 1.26094 0.630471 0.776213i \(-0.282862\pi\)
0.630471 + 0.776213i \(0.282862\pi\)
\(44\) −7.60954 −1.14718
\(45\) 0 0
\(46\) −3.41315 −0.503241
\(47\) −7.59560 −1.10793 −0.553966 0.832539i \(-0.686886\pi\)
−0.553966 + 0.832539i \(0.686886\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −4.49271 −0.635365
\(51\) 0 0
\(52\) 1.31658 0.182577
\(53\) −0.151205 −0.0207696 −0.0103848 0.999946i \(-0.503306\pi\)
−0.0103848 + 0.999946i \(0.503306\pi\)
\(54\) 0 0
\(55\) 7.39596 0.997272
\(56\) −0.619124 −0.0827339
\(57\) 0 0
\(58\) −9.15563 −1.20219
\(59\) −4.69350 −0.611042 −0.305521 0.952185i \(-0.598831\pi\)
−0.305521 + 0.952185i \(0.598831\pi\)
\(60\) 0 0
\(61\) −12.1937 −1.56125 −0.780623 0.625002i \(-0.785098\pi\)
−0.780623 + 0.625002i \(0.785098\pi\)
\(62\) 9.71343 1.23361
\(63\) 0 0
\(64\) −5.24224 −0.655280
\(65\) −1.27963 −0.158718
\(66\) 0 0
\(67\) 1.56249 0.190889 0.0954444 0.995435i \(-0.469573\pi\)
0.0954444 + 0.995435i \(0.469573\pi\)
\(68\) 7.69175 0.932761
\(69\) 0 0
\(70\) −3.12578 −0.373602
\(71\) 13.2252 1.56954 0.784768 0.619789i \(-0.212782\pi\)
0.784768 + 0.619789i \(0.212782\pi\)
\(72\) 0 0
\(73\) 5.59318 0.654632 0.327316 0.944915i \(-0.393856\pi\)
0.327316 + 0.944915i \(0.393856\pi\)
\(74\) −1.98153 −0.230349
\(75\) 0 0
\(76\) 12.2771 1.40829
\(77\) −4.53723 −0.517065
\(78\) 0 0
\(79\) −3.81705 −0.429451 −0.214726 0.976674i \(-0.568886\pi\)
−0.214726 + 0.976674i \(0.568886\pi\)
\(80\) 7.40291 0.827670
\(81\) 0 0
\(82\) 20.4201 2.25502
\(83\) −0.734264 −0.0805960 −0.0402980 0.999188i \(-0.512831\pi\)
−0.0402980 + 0.999188i \(0.512831\pi\)
\(84\) 0 0
\(85\) −7.47586 −0.810871
\(86\) 15.8556 1.70976
\(87\) 0 0
\(88\) 2.80911 0.299452
\(89\) 5.16974 0.547991 0.273996 0.961731i \(-0.411655\pi\)
0.273996 + 0.961731i \(0.411655\pi\)
\(90\) 0 0
\(91\) 0.785019 0.0822923
\(92\) −2.98516 −0.311225
\(93\) 0 0
\(94\) −14.5652 −1.50229
\(95\) −11.9326 −1.22426
\(96\) 0 0
\(97\) −5.35014 −0.543224 −0.271612 0.962407i \(-0.587557\pi\)
−0.271612 + 0.962407i \(0.587557\pi\)
\(98\) 1.91759 0.193705
\(99\) 0 0
\(100\) −3.92935 −0.392935
\(101\) 13.8634 1.37946 0.689731 0.724065i \(-0.257729\pi\)
0.689731 + 0.724065i \(0.257729\pi\)
\(102\) 0 0
\(103\) 17.4513 1.71953 0.859764 0.510691i \(-0.170610\pi\)
0.859764 + 0.510691i \(0.170610\pi\)
\(104\) −0.486024 −0.0476586
\(105\) 0 0
\(106\) −0.289949 −0.0281623
\(107\) 7.09496 0.685896 0.342948 0.939354i \(-0.388575\pi\)
0.342948 + 0.939354i \(0.388575\pi\)
\(108\) 0 0
\(109\) 17.4311 1.66959 0.834796 0.550559i \(-0.185586\pi\)
0.834796 + 0.550559i \(0.185586\pi\)
\(110\) 14.1824 1.35224
\(111\) 0 0
\(112\) −4.54149 −0.429130
\(113\) 7.36358 0.692707 0.346353 0.938104i \(-0.387420\pi\)
0.346353 + 0.938104i \(0.387420\pi\)
\(114\) 0 0
\(115\) 2.90138 0.270555
\(116\) −8.00758 −0.743485
\(117\) 0 0
\(118\) −9.00019 −0.828534
\(119\) 4.58625 0.420420
\(120\) 0 0
\(121\) 9.58645 0.871495
\(122\) −23.3825 −2.11695
\(123\) 0 0
\(124\) 8.49543 0.762912
\(125\) 11.9694 1.07057
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 4.88845 0.432082
\(129\) 0 0
\(130\) −2.45380 −0.215212
\(131\) −3.42397 −0.299153 −0.149577 0.988750i \(-0.547791\pi\)
−0.149577 + 0.988750i \(0.547791\pi\)
\(132\) 0 0
\(133\) 7.32031 0.634752
\(134\) 2.99621 0.258833
\(135\) 0 0
\(136\) −2.83945 −0.243481
\(137\) 8.60770 0.735405 0.367703 0.929943i \(-0.380144\pi\)
0.367703 + 0.929943i \(0.380144\pi\)
\(138\) 0 0
\(139\) 11.1427 0.945108 0.472554 0.881302i \(-0.343332\pi\)
0.472554 + 0.881302i \(0.343332\pi\)
\(140\) −2.73383 −0.231051
\(141\) 0 0
\(142\) 25.3604 2.12819
\(143\) −3.56181 −0.297854
\(144\) 0 0
\(145\) 7.78283 0.646329
\(146\) 10.7254 0.887640
\(147\) 0 0
\(148\) −1.73306 −0.142457
\(149\) 20.6563 1.69223 0.846117 0.532997i \(-0.178934\pi\)
0.846117 + 0.532997i \(0.178934\pi\)
\(150\) 0 0
\(151\) 1.83421 0.149266 0.0746330 0.997211i \(-0.476221\pi\)
0.0746330 + 0.997211i \(0.476221\pi\)
\(152\) −4.53218 −0.367608
\(153\) 0 0
\(154\) −8.70052 −0.701108
\(155\) −8.25699 −0.663218
\(156\) 0 0
\(157\) 9.98994 0.797284 0.398642 0.917107i \(-0.369482\pi\)
0.398642 + 0.917107i \(0.369482\pi\)
\(158\) −7.31952 −0.582309
\(159\) 0 0
\(160\) 12.1773 0.962699
\(161\) −1.77992 −0.140277
\(162\) 0 0
\(163\) 5.49104 0.430092 0.215046 0.976604i \(-0.431010\pi\)
0.215046 + 0.976604i \(0.431010\pi\)
\(164\) 17.8596 1.39460
\(165\) 0 0
\(166\) −1.40801 −0.109283
\(167\) −1.35423 −0.104794 −0.0523969 0.998626i \(-0.516686\pi\)
−0.0523969 + 0.998626i \(0.516686\pi\)
\(168\) 0 0
\(169\) −12.3837 −0.952596
\(170\) −14.3356 −1.09949
\(171\) 0 0
\(172\) 13.8675 1.05738
\(173\) 5.51469 0.419274 0.209637 0.977779i \(-0.432772\pi\)
0.209637 + 0.977779i \(0.432772\pi\)
\(174\) 0 0
\(175\) −2.34290 −0.177106
\(176\) 20.6058 1.55322
\(177\) 0 0
\(178\) 9.91342 0.743042
\(179\) 9.88587 0.738904 0.369452 0.929250i \(-0.379545\pi\)
0.369452 + 0.929250i \(0.379545\pi\)
\(180\) 0 0
\(181\) 3.10026 0.230441 0.115220 0.993340i \(-0.463243\pi\)
0.115220 + 0.993340i \(0.463243\pi\)
\(182\) 1.50534 0.111583
\(183\) 0 0
\(184\) 1.10199 0.0812398
\(185\) 1.68442 0.123841
\(186\) 0 0
\(187\) −20.8088 −1.52169
\(188\) −12.7388 −0.929075
\(189\) 0 0
\(190\) −22.8817 −1.66001
\(191\) −5.18368 −0.375078 −0.187539 0.982257i \(-0.560051\pi\)
−0.187539 + 0.982257i \(0.560051\pi\)
\(192\) 0 0
\(193\) 7.06423 0.508494 0.254247 0.967139i \(-0.418172\pi\)
0.254247 + 0.967139i \(0.418172\pi\)
\(194\) −10.2594 −0.736578
\(195\) 0 0
\(196\) 1.67713 0.119795
\(197\) 4.38545 0.312450 0.156225 0.987721i \(-0.450067\pi\)
0.156225 + 0.987721i \(0.450067\pi\)
\(198\) 0 0
\(199\) 1.65748 0.117496 0.0587479 0.998273i \(-0.481289\pi\)
0.0587479 + 0.998273i \(0.481289\pi\)
\(200\) 1.45054 0.102569
\(201\) 0 0
\(202\) 26.5843 1.87047
\(203\) −4.77456 −0.335109
\(204\) 0 0
\(205\) −17.3583 −1.21236
\(206\) 33.4644 2.33157
\(207\) 0 0
\(208\) −3.56516 −0.247199
\(209\) −33.2139 −2.29746
\(210\) 0 0
\(211\) −23.9651 −1.64983 −0.824913 0.565259i \(-0.808776\pi\)
−0.824913 + 0.565259i \(0.808776\pi\)
\(212\) −0.253591 −0.0174167
\(213\) 0 0
\(214\) 13.6052 0.930032
\(215\) −13.4782 −0.919209
\(216\) 0 0
\(217\) 5.06545 0.343865
\(218\) 33.4255 2.26386
\(219\) 0 0
\(220\) 12.4040 0.836279
\(221\) 3.60029 0.242182
\(222\) 0 0
\(223\) −6.48293 −0.434129 −0.217065 0.976157i \(-0.569648\pi\)
−0.217065 + 0.976157i \(0.569648\pi\)
\(224\) −7.47045 −0.499140
\(225\) 0 0
\(226\) 14.1203 0.939267
\(227\) −10.4264 −0.692024 −0.346012 0.938230i \(-0.612464\pi\)
−0.346012 + 0.938230i \(0.612464\pi\)
\(228\) 0 0
\(229\) −21.8797 −1.44585 −0.722925 0.690926i \(-0.757203\pi\)
−0.722925 + 0.690926i \(0.757203\pi\)
\(230\) 5.56364 0.366855
\(231\) 0 0
\(232\) 2.95605 0.194074
\(233\) −19.7154 −1.29160 −0.645799 0.763508i \(-0.723476\pi\)
−0.645799 + 0.763508i \(0.723476\pi\)
\(234\) 0 0
\(235\) 12.3813 0.807667
\(236\) −7.87163 −0.512399
\(237\) 0 0
\(238\) 8.79452 0.570064
\(239\) 18.5429 1.19944 0.599721 0.800209i \(-0.295278\pi\)
0.599721 + 0.800209i \(0.295278\pi\)
\(240\) 0 0
\(241\) 28.9917 1.86752 0.933761 0.357897i \(-0.116506\pi\)
0.933761 + 0.357897i \(0.116506\pi\)
\(242\) 18.3828 1.18169
\(243\) 0 0
\(244\) −20.4505 −1.30921
\(245\) −1.63006 −0.104141
\(246\) 0 0
\(247\) 5.74658 0.365646
\(248\) −3.13614 −0.199145
\(249\) 0 0
\(250\) 22.9523 1.45163
\(251\) −28.0776 −1.77225 −0.886123 0.463451i \(-0.846611\pi\)
−0.886123 + 0.463451i \(0.846611\pi\)
\(252\) 0 0
\(253\) 8.07590 0.507727
\(254\) 1.91759 0.120320
\(255\) 0 0
\(256\) 19.8585 1.24116
\(257\) −3.12939 −0.195206 −0.0976029 0.995225i \(-0.531118\pi\)
−0.0976029 + 0.995225i \(0.531118\pi\)
\(258\) 0 0
\(259\) −1.03335 −0.0642092
\(260\) −2.14611 −0.133096
\(261\) 0 0
\(262\) −6.56575 −0.405633
\(263\) −23.7229 −1.46281 −0.731407 0.681941i \(-0.761136\pi\)
−0.731407 + 0.681941i \(0.761136\pi\)
\(264\) 0 0
\(265\) 0.246474 0.0151408
\(266\) 14.0373 0.860684
\(267\) 0 0
\(268\) 2.62051 0.160073
\(269\) −4.27831 −0.260853 −0.130427 0.991458i \(-0.541635\pi\)
−0.130427 + 0.991458i \(0.541635\pi\)
\(270\) 0 0
\(271\) 12.9618 0.787375 0.393687 0.919244i \(-0.371199\pi\)
0.393687 + 0.919244i \(0.371199\pi\)
\(272\) −20.8284 −1.26291
\(273\) 0 0
\(274\) 16.5060 0.997163
\(275\) 10.6303 0.641029
\(276\) 0 0
\(277\) 26.8719 1.61457 0.807287 0.590160i \(-0.200935\pi\)
0.807287 + 0.590160i \(0.200935\pi\)
\(278\) 21.3670 1.28151
\(279\) 0 0
\(280\) 1.00921 0.0603118
\(281\) −7.21075 −0.430157 −0.215079 0.976597i \(-0.569001\pi\)
−0.215079 + 0.976597i \(0.569001\pi\)
\(282\) 0 0
\(283\) 7.06754 0.420121 0.210061 0.977688i \(-0.432634\pi\)
0.210061 + 0.977688i \(0.432634\pi\)
\(284\) 22.1803 1.31616
\(285\) 0 0
\(286\) −6.83008 −0.403871
\(287\) 10.6489 0.628582
\(288\) 0 0
\(289\) 4.03365 0.237273
\(290\) 14.9242 0.876382
\(291\) 0 0
\(292\) 9.38050 0.548952
\(293\) −6.10993 −0.356946 −0.178473 0.983945i \(-0.557116\pi\)
−0.178473 + 0.983945i \(0.557116\pi\)
\(294\) 0 0
\(295\) 7.65070 0.445441
\(296\) 0.639771 0.0371859
\(297\) 0 0
\(298\) 39.6103 2.29456
\(299\) −1.39727 −0.0808062
\(300\) 0 0
\(301\) 8.26855 0.476591
\(302\) 3.51726 0.202395
\(303\) 0 0
\(304\) −33.2451 −1.90674
\(305\) 19.8765 1.13813
\(306\) 0 0
\(307\) −14.8475 −0.847389 −0.423695 0.905805i \(-0.639267\pi\)
−0.423695 + 0.905805i \(0.639267\pi\)
\(308\) −7.60954 −0.433594
\(309\) 0 0
\(310\) −15.8335 −0.899282
\(311\) 12.1323 0.687961 0.343981 0.938977i \(-0.388225\pi\)
0.343981 + 0.938977i \(0.388225\pi\)
\(312\) 0 0
\(313\) 0.476080 0.0269097 0.0134548 0.999909i \(-0.495717\pi\)
0.0134548 + 0.999909i \(0.495717\pi\)
\(314\) 19.1566 1.08107
\(315\) 0 0
\(316\) −6.40170 −0.360124
\(317\) 1.09825 0.0616840 0.0308420 0.999524i \(-0.490181\pi\)
0.0308420 + 0.999524i \(0.490181\pi\)
\(318\) 0 0
\(319\) 21.6633 1.21291
\(320\) 8.54518 0.477690
\(321\) 0 0
\(322\) −3.41315 −0.190207
\(323\) 33.5728 1.86804
\(324\) 0 0
\(325\) −1.83922 −0.102022
\(326\) 10.5295 0.583177
\(327\) 0 0
\(328\) −6.59296 −0.364035
\(329\) −7.59560 −0.418759
\(330\) 0 0
\(331\) 21.4769 1.18048 0.590239 0.807228i \(-0.299033\pi\)
0.590239 + 0.807228i \(0.299033\pi\)
\(332\) −1.23146 −0.0675851
\(333\) 0 0
\(334\) −2.59686 −0.142094
\(335\) −2.54696 −0.139155
\(336\) 0 0
\(337\) −2.56002 −0.139453 −0.0697267 0.997566i \(-0.522213\pi\)
−0.0697267 + 0.997566i \(0.522213\pi\)
\(338\) −23.7469 −1.29166
\(339\) 0 0
\(340\) −12.5380 −0.679970
\(341\) −22.9831 −1.24460
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −5.11926 −0.276012
\(345\) 0 0
\(346\) 10.5749 0.568509
\(347\) −17.8141 −0.956312 −0.478156 0.878275i \(-0.658695\pi\)
−0.478156 + 0.878275i \(0.658695\pi\)
\(348\) 0 0
\(349\) −9.98746 −0.534616 −0.267308 0.963611i \(-0.586134\pi\)
−0.267308 + 0.963611i \(0.586134\pi\)
\(350\) −4.49271 −0.240145
\(351\) 0 0
\(352\) 33.8951 1.80662
\(353\) 1.59328 0.0848018 0.0424009 0.999101i \(-0.486499\pi\)
0.0424009 + 0.999101i \(0.486499\pi\)
\(354\) 0 0
\(355\) −21.5578 −1.14417
\(356\) 8.67035 0.459527
\(357\) 0 0
\(358\) 18.9570 1.00191
\(359\) 15.8997 0.839153 0.419576 0.907720i \(-0.362179\pi\)
0.419576 + 0.907720i \(0.362179\pi\)
\(360\) 0 0
\(361\) 34.5870 1.82037
\(362\) 5.94501 0.312463
\(363\) 0 0
\(364\) 1.31658 0.0690076
\(365\) −9.11722 −0.477217
\(366\) 0 0
\(367\) 30.3461 1.58405 0.792027 0.610486i \(-0.209026\pi\)
0.792027 + 0.610486i \(0.209026\pi\)
\(368\) 8.08348 0.421381
\(369\) 0 0
\(370\) 3.23002 0.167921
\(371\) −0.151205 −0.00785017
\(372\) 0 0
\(373\) −0.699026 −0.0361942 −0.0180971 0.999836i \(-0.505761\pi\)
−0.0180971 + 0.999836i \(0.505761\pi\)
\(374\) −39.9027 −2.06332
\(375\) 0 0
\(376\) 4.70262 0.242519
\(377\) −3.74812 −0.193038
\(378\) 0 0
\(379\) 2.08955 0.107333 0.0536665 0.998559i \(-0.482909\pi\)
0.0536665 + 0.998559i \(0.482909\pi\)
\(380\) −20.0125 −1.02662
\(381\) 0 0
\(382\) −9.94015 −0.508583
\(383\) −7.36514 −0.376341 −0.188170 0.982136i \(-0.560256\pi\)
−0.188170 + 0.982136i \(0.560256\pi\)
\(384\) 0 0
\(385\) 7.39596 0.376933
\(386\) 13.5463 0.689486
\(387\) 0 0
\(388\) −8.97290 −0.455530
\(389\) −25.3382 −1.28470 −0.642348 0.766413i \(-0.722040\pi\)
−0.642348 + 0.766413i \(0.722040\pi\)
\(390\) 0 0
\(391\) −8.16314 −0.412828
\(392\) −0.619124 −0.0312705
\(393\) 0 0
\(394\) 8.40948 0.423663
\(395\) 6.22202 0.313064
\(396\) 0 0
\(397\) −22.4952 −1.12900 −0.564500 0.825433i \(-0.690931\pi\)
−0.564500 + 0.825433i \(0.690931\pi\)
\(398\) 3.17836 0.159317
\(399\) 0 0
\(400\) 10.6402 0.532012
\(401\) −16.0902 −0.803508 −0.401754 0.915748i \(-0.631599\pi\)
−0.401754 + 0.915748i \(0.631599\pi\)
\(402\) 0 0
\(403\) 3.97647 0.198082
\(404\) 23.2508 1.15677
\(405\) 0 0
\(406\) −9.15563 −0.454386
\(407\) 4.68854 0.232402
\(408\) 0 0
\(409\) −26.5315 −1.31190 −0.655949 0.754805i \(-0.727731\pi\)
−0.655949 + 0.754805i \(0.727731\pi\)
\(410\) −33.2860 −1.64388
\(411\) 0 0
\(412\) 29.2682 1.44194
\(413\) −4.69350 −0.230952
\(414\) 0 0
\(415\) 1.19690 0.0587533
\(416\) −5.86444 −0.287528
\(417\) 0 0
\(418\) −63.6906 −3.11521
\(419\) 13.0559 0.637821 0.318911 0.947785i \(-0.396683\pi\)
0.318911 + 0.947785i \(0.396683\pi\)
\(420\) 0 0
\(421\) −0.503178 −0.0245234 −0.0122617 0.999925i \(-0.503903\pi\)
−0.0122617 + 0.999925i \(0.503903\pi\)
\(422\) −45.9551 −2.23706
\(423\) 0 0
\(424\) 0.0936146 0.00454633
\(425\) −10.7451 −0.521214
\(426\) 0 0
\(427\) −12.1937 −0.590095
\(428\) 11.8992 0.575170
\(429\) 0 0
\(430\) −25.8457 −1.24639
\(431\) −19.3583 −0.932457 −0.466228 0.884664i \(-0.654388\pi\)
−0.466228 + 0.884664i \(0.654388\pi\)
\(432\) 0 0
\(433\) −32.9626 −1.58408 −0.792041 0.610468i \(-0.790982\pi\)
−0.792041 + 0.610468i \(0.790982\pi\)
\(434\) 9.71343 0.466260
\(435\) 0 0
\(436\) 29.2342 1.40006
\(437\) −13.0296 −0.623289
\(438\) 0 0
\(439\) 32.0599 1.53013 0.765067 0.643951i \(-0.222706\pi\)
0.765067 + 0.643951i \(0.222706\pi\)
\(440\) −4.57902 −0.218296
\(441\) 0 0
\(442\) 6.90386 0.328383
\(443\) 19.0080 0.903096 0.451548 0.892247i \(-0.350872\pi\)
0.451548 + 0.892247i \(0.350872\pi\)
\(444\) 0 0
\(445\) −8.42700 −0.399478
\(446\) −12.4316 −0.588652
\(447\) 0 0
\(448\) −5.24224 −0.247673
\(449\) −16.2304 −0.765960 −0.382980 0.923757i \(-0.625102\pi\)
−0.382980 + 0.923757i \(0.625102\pi\)
\(450\) 0 0
\(451\) −48.3163 −2.27513
\(452\) 12.3497 0.580881
\(453\) 0 0
\(454\) −19.9935 −0.938341
\(455\) −1.27963 −0.0599899
\(456\) 0 0
\(457\) 15.6324 0.731254 0.365627 0.930761i \(-0.380855\pi\)
0.365627 + 0.930761i \(0.380855\pi\)
\(458\) −41.9562 −1.96048
\(459\) 0 0
\(460\) 4.86600 0.226878
\(461\) 21.3891 0.996191 0.498096 0.867122i \(-0.334033\pi\)
0.498096 + 0.867122i \(0.334033\pi\)
\(462\) 0 0
\(463\) −18.8588 −0.876445 −0.438222 0.898867i \(-0.644392\pi\)
−0.438222 + 0.898867i \(0.644392\pi\)
\(464\) 21.6836 1.00664
\(465\) 0 0
\(466\) −37.8059 −1.75133
\(467\) −21.0632 −0.974689 −0.487344 0.873210i \(-0.662034\pi\)
−0.487344 + 0.873210i \(0.662034\pi\)
\(468\) 0 0
\(469\) 1.56249 0.0721492
\(470\) 23.7422 1.09515
\(471\) 0 0
\(472\) 2.90586 0.133753
\(473\) −37.5163 −1.72500
\(474\) 0 0
\(475\) −17.1508 −0.786930
\(476\) 7.69175 0.352551
\(477\) 0 0
\(478\) 35.5577 1.62637
\(479\) −23.6039 −1.07849 −0.539245 0.842149i \(-0.681290\pi\)
−0.539245 + 0.842149i \(0.681290\pi\)
\(480\) 0 0
\(481\) −0.811198 −0.0369875
\(482\) 55.5941 2.53224
\(483\) 0 0
\(484\) 16.0778 0.730807
\(485\) 8.72106 0.396003
\(486\) 0 0
\(487\) −16.2006 −0.734119 −0.367060 0.930197i \(-0.619636\pi\)
−0.367060 + 0.930197i \(0.619636\pi\)
\(488\) 7.54942 0.341746
\(489\) 0 0
\(490\) −3.12578 −0.141208
\(491\) 20.8074 0.939025 0.469512 0.882926i \(-0.344430\pi\)
0.469512 + 0.882926i \(0.344430\pi\)
\(492\) 0 0
\(493\) −21.8973 −0.986206
\(494\) 11.0196 0.495794
\(495\) 0 0
\(496\) −23.0047 −1.03294
\(497\) 13.2252 0.593229
\(498\) 0 0
\(499\) −6.17234 −0.276312 −0.138156 0.990410i \(-0.544118\pi\)
−0.138156 + 0.990410i \(0.544118\pi\)
\(500\) 20.0742 0.897748
\(501\) 0 0
\(502\) −53.8413 −2.40305
\(503\) 28.7432 1.28159 0.640797 0.767710i \(-0.278604\pi\)
0.640797 + 0.767710i \(0.278604\pi\)
\(504\) 0 0
\(505\) −22.5982 −1.00561
\(506\) 15.4862 0.688447
\(507\) 0 0
\(508\) 1.67713 0.0744108
\(509\) −13.2246 −0.586169 −0.293084 0.956087i \(-0.594682\pi\)
−0.293084 + 0.956087i \(0.594682\pi\)
\(510\) 0 0
\(511\) 5.59318 0.247428
\(512\) 28.3035 1.25085
\(513\) 0 0
\(514\) −6.00087 −0.264687
\(515\) −28.4467 −1.25351
\(516\) 0 0
\(517\) 34.4630 1.51568
\(518\) −1.98153 −0.0870636
\(519\) 0 0
\(520\) 0.792249 0.0347424
\(521\) 32.9614 1.44407 0.722033 0.691858i \(-0.243208\pi\)
0.722033 + 0.691858i \(0.243208\pi\)
\(522\) 0 0
\(523\) −3.22512 −0.141025 −0.0705123 0.997511i \(-0.522463\pi\)
−0.0705123 + 0.997511i \(0.522463\pi\)
\(524\) −5.74245 −0.250860
\(525\) 0 0
\(526\) −45.4906 −1.98349
\(527\) 23.2314 1.01198
\(528\) 0 0
\(529\) −19.8319 −0.862256
\(530\) 0.472634 0.0205299
\(531\) 0 0
\(532\) 12.2771 0.532282
\(533\) 8.35955 0.362092
\(534\) 0 0
\(535\) −11.5652 −0.500009
\(536\) −0.967376 −0.0417843
\(537\) 0 0
\(538\) −8.20403 −0.353701
\(539\) −4.53723 −0.195432
\(540\) 0 0
\(541\) −4.01886 −0.172784 −0.0863922 0.996261i \(-0.527534\pi\)
−0.0863922 + 0.996261i \(0.527534\pi\)
\(542\) 24.8554 1.06763
\(543\) 0 0
\(544\) −34.2613 −1.46894
\(545\) −28.4137 −1.21711
\(546\) 0 0
\(547\) −3.36285 −0.143785 −0.0718926 0.997412i \(-0.522904\pi\)
−0.0718926 + 0.997412i \(0.522904\pi\)
\(548\) 14.4363 0.616686
\(549\) 0 0
\(550\) 20.3844 0.869196
\(551\) −34.9513 −1.48898
\(552\) 0 0
\(553\) −3.81705 −0.162317
\(554\) 51.5291 2.18926
\(555\) 0 0
\(556\) 18.6877 0.792536
\(557\) 36.3729 1.54117 0.770584 0.637339i \(-0.219965\pi\)
0.770584 + 0.637339i \(0.219965\pi\)
\(558\) 0 0
\(559\) 6.49097 0.274539
\(560\) 7.40291 0.312830
\(561\) 0 0
\(562\) −13.8272 −0.583266
\(563\) 21.8814 0.922190 0.461095 0.887351i \(-0.347457\pi\)
0.461095 + 0.887351i \(0.347457\pi\)
\(564\) 0 0
\(565\) −12.0031 −0.504974
\(566\) 13.5526 0.569658
\(567\) 0 0
\(568\) −8.18801 −0.343561
\(569\) 1.52443 0.0639073 0.0319536 0.999489i \(-0.489827\pi\)
0.0319536 + 0.999489i \(0.489827\pi\)
\(570\) 0 0
\(571\) −0.407383 −0.0170485 −0.00852423 0.999964i \(-0.502713\pi\)
−0.00852423 + 0.999964i \(0.502713\pi\)
\(572\) −5.97363 −0.249770
\(573\) 0 0
\(574\) 20.4201 0.852318
\(575\) 4.17017 0.173908
\(576\) 0 0
\(577\) −9.40086 −0.391363 −0.195681 0.980668i \(-0.562692\pi\)
−0.195681 + 0.980668i \(0.562692\pi\)
\(578\) 7.73486 0.321728
\(579\) 0 0
\(580\) 13.0529 0.541990
\(581\) −0.734264 −0.0304624
\(582\) 0 0
\(583\) 0.686052 0.0284134
\(584\) −3.46287 −0.143295
\(585\) 0 0
\(586\) −11.7163 −0.483996
\(587\) −7.47968 −0.308719 −0.154360 0.988015i \(-0.549331\pi\)
−0.154360 + 0.988015i \(0.549331\pi\)
\(588\) 0 0
\(589\) 37.0807 1.52788
\(590\) 14.6709 0.603990
\(591\) 0 0
\(592\) 4.69294 0.192879
\(593\) −26.7023 −1.09653 −0.548266 0.836304i \(-0.684712\pi\)
−0.548266 + 0.836304i \(0.684712\pi\)
\(594\) 0 0
\(595\) −7.47586 −0.306481
\(596\) 34.6434 1.41905
\(597\) 0 0
\(598\) −2.67938 −0.109568
\(599\) 9.66950 0.395085 0.197543 0.980294i \(-0.436704\pi\)
0.197543 + 0.980294i \(0.436704\pi\)
\(600\) 0 0
\(601\) 21.1650 0.863340 0.431670 0.902032i \(-0.357925\pi\)
0.431670 + 0.902032i \(0.357925\pi\)
\(602\) 15.8556 0.646228
\(603\) 0 0
\(604\) 3.07622 0.125170
\(605\) −15.6265 −0.635308
\(606\) 0 0
\(607\) 16.3837 0.664993 0.332496 0.943105i \(-0.392109\pi\)
0.332496 + 0.943105i \(0.392109\pi\)
\(608\) −54.6860 −2.21781
\(609\) 0 0
\(610\) 38.1149 1.54323
\(611\) −5.96269 −0.241225
\(612\) 0 0
\(613\) −36.7506 −1.48434 −0.742171 0.670210i \(-0.766204\pi\)
−0.742171 + 0.670210i \(0.766204\pi\)
\(614\) −28.4713 −1.14901
\(615\) 0 0
\(616\) 2.80911 0.113182
\(617\) −27.8500 −1.12120 −0.560600 0.828087i \(-0.689429\pi\)
−0.560600 + 0.828087i \(0.689429\pi\)
\(618\) 0 0
\(619\) −26.3590 −1.05946 −0.529730 0.848167i \(-0.677707\pi\)
−0.529730 + 0.848167i \(0.677707\pi\)
\(620\) −13.8481 −0.556152
\(621\) 0 0
\(622\) 23.2648 0.932832
\(623\) 5.16974 0.207121
\(624\) 0 0
\(625\) −7.79634 −0.311853
\(626\) 0.912925 0.0364878
\(627\) 0 0
\(628\) 16.7545 0.668576
\(629\) −4.73919 −0.188964
\(630\) 0 0
\(631\) 24.1225 0.960303 0.480151 0.877186i \(-0.340582\pi\)
0.480151 + 0.877186i \(0.340582\pi\)
\(632\) 2.36323 0.0940041
\(633\) 0 0
\(634\) 2.10599 0.0836397
\(635\) −1.63006 −0.0646870
\(636\) 0 0
\(637\) 0.785019 0.0311036
\(638\) 41.5412 1.64463
\(639\) 0 0
\(640\) −7.96848 −0.314982
\(641\) 31.6483 1.25003 0.625017 0.780611i \(-0.285092\pi\)
0.625017 + 0.780611i \(0.285092\pi\)
\(642\) 0 0
\(643\) −36.3625 −1.43400 −0.716998 0.697075i \(-0.754484\pi\)
−0.716998 + 0.697075i \(0.754484\pi\)
\(644\) −2.98516 −0.117632
\(645\) 0 0
\(646\) 64.3786 2.53294
\(647\) 30.6486 1.20492 0.602460 0.798149i \(-0.294187\pi\)
0.602460 + 0.798149i \(0.294187\pi\)
\(648\) 0 0
\(649\) 21.2955 0.835921
\(650\) −3.52686 −0.138335
\(651\) 0 0
\(652\) 9.20921 0.360660
\(653\) 5.09863 0.199525 0.0997625 0.995011i \(-0.468192\pi\)
0.0997625 + 0.995011i \(0.468192\pi\)
\(654\) 0 0
\(655\) 5.58128 0.218078
\(656\) −48.3617 −1.88821
\(657\) 0 0
\(658\) −14.5652 −0.567811
\(659\) −25.9346 −1.01027 −0.505135 0.863041i \(-0.668557\pi\)
−0.505135 + 0.863041i \(0.668557\pi\)
\(660\) 0 0
\(661\) −27.2692 −1.06065 −0.530324 0.847795i \(-0.677930\pi\)
−0.530324 + 0.847795i \(0.677930\pi\)
\(662\) 41.1838 1.60065
\(663\) 0 0
\(664\) 0.454601 0.0176419
\(665\) −11.9326 −0.462725
\(666\) 0 0
\(667\) 8.49833 0.329057
\(668\) −2.27123 −0.0878766
\(669\) 0 0
\(670\) −4.88401 −0.188686
\(671\) 55.3257 2.13582
\(672\) 0 0
\(673\) −28.5849 −1.10187 −0.550933 0.834549i \(-0.685728\pi\)
−0.550933 + 0.834549i \(0.685728\pi\)
\(674\) −4.90906 −0.189090
\(675\) 0 0
\(676\) −20.7692 −0.798815
\(677\) −28.2536 −1.08588 −0.542938 0.839773i \(-0.682688\pi\)
−0.542938 + 0.839773i \(0.682688\pi\)
\(678\) 0 0
\(679\) −5.35014 −0.205320
\(680\) 4.62849 0.177494
\(681\) 0 0
\(682\) −44.0721 −1.68761
\(683\) 10.4079 0.398248 0.199124 0.979974i \(-0.436190\pi\)
0.199124 + 0.979974i \(0.436190\pi\)
\(684\) 0 0
\(685\) −14.0311 −0.536100
\(686\) 1.91759 0.0732137
\(687\) 0 0
\(688\) −37.5515 −1.43164
\(689\) −0.118699 −0.00452206
\(690\) 0 0
\(691\) −36.1483 −1.37515 −0.687574 0.726115i \(-0.741324\pi\)
−0.687574 + 0.726115i \(0.741324\pi\)
\(692\) 9.24887 0.351589
\(693\) 0 0
\(694\) −34.1601 −1.29670
\(695\) −18.1632 −0.688970
\(696\) 0 0
\(697\) 48.8383 1.84988
\(698\) −19.1518 −0.724906
\(699\) 0 0
\(700\) −3.92935 −0.148516
\(701\) 9.20252 0.347574 0.173787 0.984783i \(-0.444399\pi\)
0.173787 + 0.984783i \(0.444399\pi\)
\(702\) 0 0
\(703\) −7.56444 −0.285298
\(704\) 23.7852 0.896440
\(705\) 0 0
\(706\) 3.05525 0.114986
\(707\) 13.8634 0.521388
\(708\) 0 0
\(709\) 7.72738 0.290208 0.145104 0.989416i \(-0.453648\pi\)
0.145104 + 0.989416i \(0.453648\pi\)
\(710\) −41.3389 −1.55142
\(711\) 0 0
\(712\) −3.20071 −0.119952
\(713\) −9.01609 −0.337655
\(714\) 0 0
\(715\) 5.80597 0.217131
\(716\) 16.5799 0.619621
\(717\) 0 0
\(718\) 30.4890 1.13784
\(719\) 43.6917 1.62942 0.814712 0.579865i \(-0.196895\pi\)
0.814712 + 0.579865i \(0.196895\pi\)
\(720\) 0 0
\(721\) 17.4513 0.649921
\(722\) 66.3235 2.46831
\(723\) 0 0
\(724\) 5.19955 0.193240
\(725\) 11.1863 0.415449
\(726\) 0 0
\(727\) 12.4150 0.460447 0.230224 0.973138i \(-0.426054\pi\)
0.230224 + 0.973138i \(0.426054\pi\)
\(728\) −0.486024 −0.0180132
\(729\) 0 0
\(730\) −17.4831 −0.647077
\(731\) 37.9216 1.40258
\(732\) 0 0
\(733\) −15.8586 −0.585752 −0.292876 0.956150i \(-0.594612\pi\)
−0.292876 + 0.956150i \(0.594612\pi\)
\(734\) 58.1913 2.14788
\(735\) 0 0
\(736\) 13.2968 0.490126
\(737\) −7.08939 −0.261141
\(738\) 0 0
\(739\) −50.8373 −1.87008 −0.935040 0.354542i \(-0.884637\pi\)
−0.935040 + 0.354542i \(0.884637\pi\)
\(740\) 2.82500 0.103849
\(741\) 0 0
\(742\) −0.289949 −0.0106443
\(743\) −19.4170 −0.712341 −0.356170 0.934421i \(-0.615918\pi\)
−0.356170 + 0.934421i \(0.615918\pi\)
\(744\) 0 0
\(745\) −33.6711 −1.23361
\(746\) −1.34044 −0.0490771
\(747\) 0 0
\(748\) −34.8992 −1.27604
\(749\) 7.09496 0.259244
\(750\) 0 0
\(751\) 30.2814 1.10498 0.552491 0.833519i \(-0.313677\pi\)
0.552491 + 0.833519i \(0.313677\pi\)
\(752\) 34.4953 1.25792
\(753\) 0 0
\(754\) −7.18734 −0.261748
\(755\) −2.98988 −0.108813
\(756\) 0 0
\(757\) −7.73773 −0.281233 −0.140616 0.990064i \(-0.544908\pi\)
−0.140616 + 0.990064i \(0.544908\pi\)
\(758\) 4.00689 0.145537
\(759\) 0 0
\(760\) 7.38774 0.267981
\(761\) 42.4083 1.53730 0.768650 0.639669i \(-0.220929\pi\)
0.768650 + 0.639669i \(0.220929\pi\)
\(762\) 0 0
\(763\) 17.4311 0.631047
\(764\) −8.69373 −0.314528
\(765\) 0 0
\(766\) −14.1233 −0.510295
\(767\) −3.68449 −0.133039
\(768\) 0 0
\(769\) 40.9692 1.47739 0.738694 0.674041i \(-0.235443\pi\)
0.738694 + 0.674041i \(0.235443\pi\)
\(770\) 14.1824 0.511098
\(771\) 0 0
\(772\) 11.8477 0.426406
\(773\) −24.7232 −0.889232 −0.444616 0.895721i \(-0.646660\pi\)
−0.444616 + 0.895721i \(0.646660\pi\)
\(774\) 0 0
\(775\) −11.8678 −0.426305
\(776\) 3.31240 0.118908
\(777\) 0 0
\(778\) −48.5881 −1.74197
\(779\) 77.9530 2.79295
\(780\) 0 0
\(781\) −60.0055 −2.14717
\(782\) −15.6535 −0.559769
\(783\) 0 0
\(784\) −4.54149 −0.162196
\(785\) −16.2842 −0.581209
\(786\) 0 0
\(787\) 38.2059 1.36189 0.680946 0.732334i \(-0.261569\pi\)
0.680946 + 0.732334i \(0.261569\pi\)
\(788\) 7.35499 0.262011
\(789\) 0 0
\(790\) 11.9313 0.424495
\(791\) 7.36358 0.261819
\(792\) 0 0
\(793\) −9.57230 −0.339922
\(794\) −43.1364 −1.53085
\(795\) 0 0
\(796\) 2.77982 0.0985280
\(797\) 39.8094 1.41012 0.705061 0.709147i \(-0.250920\pi\)
0.705061 + 0.709147i \(0.250920\pi\)
\(798\) 0 0
\(799\) −34.8353 −1.23238
\(800\) 17.5025 0.618807
\(801\) 0 0
\(802\) −30.8544 −1.08951
\(803\) −25.3775 −0.895553
\(804\) 0 0
\(805\) 2.90138 0.102260
\(806\) 7.62523 0.268587
\(807\) 0 0
\(808\) −8.58318 −0.301955
\(809\) 19.8034 0.696250 0.348125 0.937448i \(-0.386818\pi\)
0.348125 + 0.937448i \(0.386818\pi\)
\(810\) 0 0
\(811\) −48.6032 −1.70669 −0.853344 0.521348i \(-0.825430\pi\)
−0.853344 + 0.521348i \(0.825430\pi\)
\(812\) −8.00758 −0.281011
\(813\) 0 0
\(814\) 8.99068 0.315123
\(815\) −8.95074 −0.313531
\(816\) 0 0
\(817\) 60.5284 2.11762
\(818\) −50.8764 −1.77885
\(819\) 0 0
\(820\) −29.1122 −1.01664
\(821\) 27.5660 0.962060 0.481030 0.876704i \(-0.340263\pi\)
0.481030 + 0.876704i \(0.340263\pi\)
\(822\) 0 0
\(823\) 50.5300 1.76136 0.880682 0.473708i \(-0.157085\pi\)
0.880682 + 0.473708i \(0.157085\pi\)
\(824\) −10.8045 −0.376393
\(825\) 0 0
\(826\) −9.00019 −0.313157
\(827\) 34.5514 1.20147 0.600735 0.799448i \(-0.294875\pi\)
0.600735 + 0.799448i \(0.294875\pi\)
\(828\) 0 0
\(829\) 45.2920 1.57305 0.786527 0.617555i \(-0.211877\pi\)
0.786527 + 0.617555i \(0.211877\pi\)
\(830\) 2.29515 0.0796658
\(831\) 0 0
\(832\) −4.11526 −0.142671
\(833\) 4.58625 0.158904
\(834\) 0 0
\(835\) 2.20749 0.0763932
\(836\) −55.7042 −1.92657
\(837\) 0 0
\(838\) 25.0358 0.864846
\(839\) 45.4572 1.56936 0.784679 0.619902i \(-0.212828\pi\)
0.784679 + 0.619902i \(0.212828\pi\)
\(840\) 0 0
\(841\) −6.20354 −0.213915
\(842\) −0.964886 −0.0332522
\(843\) 0 0
\(844\) −40.1927 −1.38349
\(845\) 20.1863 0.694429
\(846\) 0 0
\(847\) 9.58645 0.329394
\(848\) 0.686696 0.0235812
\(849\) 0 0
\(850\) −20.6047 −0.706734
\(851\) 1.83928 0.0630496
\(852\) 0 0
\(853\) 7.10046 0.243115 0.121558 0.992584i \(-0.461211\pi\)
0.121558 + 0.992584i \(0.461211\pi\)
\(854\) −23.3825 −0.800132
\(855\) 0 0
\(856\) −4.39266 −0.150138
\(857\) −38.1705 −1.30388 −0.651940 0.758270i \(-0.726045\pi\)
−0.651940 + 0.758270i \(0.726045\pi\)
\(858\) 0 0
\(859\) −0.939629 −0.0320597 −0.0160299 0.999872i \(-0.505103\pi\)
−0.0160299 + 0.999872i \(0.505103\pi\)
\(860\) −22.6048 −0.770818
\(861\) 0 0
\(862\) −37.1212 −1.26435
\(863\) −37.0524 −1.26128 −0.630639 0.776077i \(-0.717207\pi\)
−0.630639 + 0.776077i \(0.717207\pi\)
\(864\) 0 0
\(865\) −8.98928 −0.305645
\(866\) −63.2086 −2.14792
\(867\) 0 0
\(868\) 8.49543 0.288354
\(869\) 17.3188 0.587501
\(870\) 0 0
\(871\) 1.22659 0.0415613
\(872\) −10.7920 −0.365463
\(873\) 0 0
\(874\) −24.9853 −0.845140
\(875\) 11.9694 0.404639
\(876\) 0 0
\(877\) 8.41666 0.284210 0.142105 0.989852i \(-0.454613\pi\)
0.142105 + 0.989852i \(0.454613\pi\)
\(878\) 61.4775 2.07477
\(879\) 0 0
\(880\) −33.5887 −1.13227
\(881\) 16.1308 0.543462 0.271731 0.962373i \(-0.412404\pi\)
0.271731 + 0.962373i \(0.412404\pi\)
\(882\) 0 0
\(883\) −54.9590 −1.84952 −0.924759 0.380553i \(-0.875734\pi\)
−0.924759 + 0.380553i \(0.875734\pi\)
\(884\) 6.03817 0.203086
\(885\) 0 0
\(886\) 36.4494 1.22454
\(887\) 6.72375 0.225761 0.112881 0.993609i \(-0.463992\pi\)
0.112881 + 0.993609i \(0.463992\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −16.1595 −0.541667
\(891\) 0 0
\(892\) −10.8727 −0.364046
\(893\) −55.6022 −1.86066
\(894\) 0 0
\(895\) −16.1146 −0.538651
\(896\) 4.88845 0.163312
\(897\) 0 0
\(898\) −31.1232 −1.03859
\(899\) −24.1853 −0.806625
\(900\) 0 0
\(901\) −0.693463 −0.0231026
\(902\) −92.6506 −3.08493
\(903\) 0 0
\(904\) −4.55897 −0.151629
\(905\) −5.05362 −0.167988
\(906\) 0 0
\(907\) −44.3476 −1.47254 −0.736269 0.676689i \(-0.763414\pi\)
−0.736269 + 0.676689i \(0.763414\pi\)
\(908\) −17.4865 −0.580308
\(909\) 0 0
\(910\) −2.45380 −0.0813426
\(911\) 26.5885 0.880916 0.440458 0.897773i \(-0.354816\pi\)
0.440458 + 0.897773i \(0.354816\pi\)
\(912\) 0 0
\(913\) 3.33153 0.110257
\(914\) 29.9765 0.991535
\(915\) 0 0
\(916\) −36.6952 −1.21244
\(917\) −3.42397 −0.113069
\(918\) 0 0
\(919\) −6.91175 −0.227998 −0.113999 0.993481i \(-0.536366\pi\)
−0.113999 + 0.993481i \(0.536366\pi\)
\(920\) −1.79631 −0.0592227
\(921\) 0 0
\(922\) 41.0155 1.35077
\(923\) 10.3820 0.341727
\(924\) 0 0
\(925\) 2.42103 0.0796030
\(926\) −36.1634 −1.18840
\(927\) 0 0
\(928\) 35.6681 1.17086
\(929\) −50.6624 −1.66218 −0.831090 0.556138i \(-0.812283\pi\)
−0.831090 + 0.556138i \(0.812283\pi\)
\(930\) 0 0
\(931\) 7.32031 0.239914
\(932\) −33.0653 −1.08309
\(933\) 0 0
\(934\) −40.3905 −1.32162
\(935\) 33.9197 1.10929
\(936\) 0 0
\(937\) 27.0802 0.884671 0.442335 0.896850i \(-0.354150\pi\)
0.442335 + 0.896850i \(0.354150\pi\)
\(938\) 2.99621 0.0978298
\(939\) 0 0
\(940\) 20.7651 0.677283
\(941\) 53.5291 1.74500 0.872500 0.488614i \(-0.162497\pi\)
0.872500 + 0.488614i \(0.162497\pi\)
\(942\) 0 0
\(943\) −18.9541 −0.617230
\(944\) 21.3155 0.693760
\(945\) 0 0
\(946\) −71.9407 −2.33899
\(947\) −45.4863 −1.47811 −0.739053 0.673647i \(-0.764727\pi\)
−0.739053 + 0.673647i \(0.764727\pi\)
\(948\) 0 0
\(949\) 4.39075 0.142530
\(950\) −32.8880 −1.06703
\(951\) 0 0
\(952\) −2.83945 −0.0920272
\(953\) 32.2357 1.04422 0.522108 0.852880i \(-0.325146\pi\)
0.522108 + 0.852880i \(0.325146\pi\)
\(954\) 0 0
\(955\) 8.44972 0.273427
\(956\) 31.0990 1.00581
\(957\) 0 0
\(958\) −45.2625 −1.46237
\(959\) 8.60770 0.277957
\(960\) 0 0
\(961\) −5.34123 −0.172298
\(962\) −1.55554 −0.0501527
\(963\) 0 0
\(964\) 48.6230 1.56604
\(965\) −11.5151 −0.370685
\(966\) 0 0
\(967\) 25.3030 0.813690 0.406845 0.913497i \(-0.366629\pi\)
0.406845 + 0.913497i \(0.366629\pi\)
\(968\) −5.93520 −0.190765
\(969\) 0 0
\(970\) 16.7234 0.536955
\(971\) −20.9204 −0.671367 −0.335683 0.941975i \(-0.608967\pi\)
−0.335683 + 0.941975i \(0.608967\pi\)
\(972\) 0 0
\(973\) 11.1427 0.357217
\(974\) −31.0660 −0.995420
\(975\) 0 0
\(976\) 55.3776 1.77260
\(977\) 31.9865 1.02334 0.511669 0.859183i \(-0.329027\pi\)
0.511669 + 0.859183i \(0.329027\pi\)
\(978\) 0 0
\(979\) −23.4563 −0.749667
\(980\) −2.73383 −0.0873290
\(981\) 0 0
\(982\) 39.9000 1.27326
\(983\) 21.4363 0.683712 0.341856 0.939752i \(-0.388944\pi\)
0.341856 + 0.939752i \(0.388944\pi\)
\(984\) 0 0
\(985\) −7.14856 −0.227772
\(986\) −41.9900 −1.33723
\(987\) 0 0
\(988\) 9.63779 0.306619
\(989\) −14.7173 −0.467984
\(990\) 0 0
\(991\) −47.1601 −1.49809 −0.749044 0.662520i \(-0.769487\pi\)
−0.749044 + 0.662520i \(0.769487\pi\)
\(992\) −37.8412 −1.20146
\(993\) 0 0
\(994\) 25.3604 0.804382
\(995\) −2.70180 −0.0856527
\(996\) 0 0
\(997\) 50.2481 1.59137 0.795687 0.605708i \(-0.207110\pi\)
0.795687 + 0.605708i \(0.207110\pi\)
\(998\) −11.8360 −0.374662
\(999\) 0 0
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 \(a_p\))