Properties

Label 8001.2.a.v.1.14
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 1.14
Root \(-1.30029\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.30029 q^{2}\) \(-0.309249 q^{4}\) \(-3.89453 q^{5}\) \(+1.00000 q^{7}\) \(-3.00269 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.30029 q^{2}\) \(-0.309249 q^{4}\) \(-3.89453 q^{5}\) \(+1.00000 q^{7}\) \(-3.00269 q^{8}\) \(-5.06401 q^{10}\) \(+2.39630 q^{11}\) \(+6.75130 q^{13}\) \(+1.30029 q^{14}\) \(-3.28587 q^{16}\) \(-2.21708 q^{17}\) \(+2.24339 q^{19}\) \(+1.20438 q^{20}\) \(+3.11588 q^{22}\) \(-6.95956 q^{23}\) \(+10.1673 q^{25}\) \(+8.77864 q^{26}\) \(-0.309249 q^{28}\) \(+4.13812 q^{29}\) \(-7.14764 q^{31}\) \(+1.73281 q^{32}\) \(-2.88284 q^{34}\) \(-3.89453 q^{35}\) \(-5.98607 q^{37}\) \(+2.91705 q^{38}\) \(+11.6941 q^{40}\) \(-4.17542 q^{41}\) \(-6.77459 q^{43}\) \(-0.741053 q^{44}\) \(-9.04944 q^{46}\) \(-8.85337 q^{47}\) \(+1.00000 q^{49}\) \(+13.2205 q^{50}\) \(-2.08783 q^{52}\) \(+1.24294 q^{53}\) \(-9.33245 q^{55}\) \(-3.00269 q^{56}\) \(+5.38076 q^{58}\) \(-0.805013 q^{59}\) \(+12.7164 q^{61}\) \(-9.29399 q^{62}\) \(+8.82488 q^{64}\) \(-26.2931 q^{65}\) \(+0.850802 q^{67}\) \(+0.685629 q^{68}\) \(-5.06401 q^{70}\) \(+11.0690 q^{71}\) \(-11.9131 q^{73}\) \(-7.78362 q^{74}\) \(-0.693765 q^{76}\) \(+2.39630 q^{77}\) \(+3.01636 q^{79}\) \(+12.7969 q^{80}\) \(-5.42926 q^{82}\) \(+9.71900 q^{83}\) \(+8.63446 q^{85}\) \(-8.80892 q^{86}\) \(-7.19534 q^{88}\) \(-2.24162 q^{89}\) \(+6.75130 q^{91}\) \(+2.15224 q^{92}\) \(-11.5119 q^{94}\) \(-8.73693 q^{95}\) \(-2.27268 q^{97}\) \(+1.30029 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30029 0.919443 0.459722 0.888063i \(-0.347949\pi\)
0.459722 + 0.888063i \(0.347949\pi\)
\(3\) 0 0
\(4\) −0.309249 −0.154625
\(5\) −3.89453 −1.74169 −0.870843 0.491562i \(-0.836426\pi\)
−0.870843 + 0.491562i \(0.836426\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −3.00269 −1.06161
\(9\) 0 0
\(10\) −5.06401 −1.60138
\(11\) 2.39630 0.722511 0.361256 0.932467i \(-0.382348\pi\)
0.361256 + 0.932467i \(0.382348\pi\)
\(12\) 0 0
\(13\) 6.75130 1.87247 0.936237 0.351370i \(-0.114284\pi\)
0.936237 + 0.351370i \(0.114284\pi\)
\(14\) 1.30029 0.347517
\(15\) 0 0
\(16\) −3.28587 −0.821467
\(17\) −2.21708 −0.537720 −0.268860 0.963179i \(-0.586647\pi\)
−0.268860 + 0.963179i \(0.586647\pi\)
\(18\) 0 0
\(19\) 2.24339 0.514668 0.257334 0.966322i \(-0.417156\pi\)
0.257334 + 0.966322i \(0.417156\pi\)
\(20\) 1.20438 0.269307
\(21\) 0 0
\(22\) 3.11588 0.664308
\(23\) −6.95956 −1.45117 −0.725584 0.688133i \(-0.758430\pi\)
−0.725584 + 0.688133i \(0.758430\pi\)
\(24\) 0 0
\(25\) 10.1673 2.03347
\(26\) 8.77864 1.72163
\(27\) 0 0
\(28\) −0.309249 −0.0584426
\(29\) 4.13812 0.768430 0.384215 0.923244i \(-0.374472\pi\)
0.384215 + 0.923244i \(0.374472\pi\)
\(30\) 0 0
\(31\) −7.14764 −1.28375 −0.641877 0.766808i \(-0.721844\pi\)
−0.641877 + 0.766808i \(0.721844\pi\)
\(32\) 1.73281 0.306320
\(33\) 0 0
\(34\) −2.88284 −0.494403
\(35\) −3.89453 −0.658295
\(36\) 0 0
\(37\) −5.98607 −0.984104 −0.492052 0.870566i \(-0.663753\pi\)
−0.492052 + 0.870566i \(0.663753\pi\)
\(38\) 2.91705 0.473208
\(39\) 0 0
\(40\) 11.6941 1.84899
\(41\) −4.17542 −0.652092 −0.326046 0.945354i \(-0.605716\pi\)
−0.326046 + 0.945354i \(0.605716\pi\)
\(42\) 0 0
\(43\) −6.77459 −1.03312 −0.516558 0.856252i \(-0.672787\pi\)
−0.516558 + 0.856252i \(0.672787\pi\)
\(44\) −0.741053 −0.111718
\(45\) 0 0
\(46\) −9.04944 −1.33427
\(47\) −8.85337 −1.29140 −0.645699 0.763592i \(-0.723434\pi\)
−0.645699 + 0.763592i \(0.723434\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 13.2205 1.86966
\(51\) 0 0
\(52\) −2.08783 −0.289530
\(53\) 1.24294 0.170731 0.0853654 0.996350i \(-0.472794\pi\)
0.0853654 + 0.996350i \(0.472794\pi\)
\(54\) 0 0
\(55\) −9.33245 −1.25839
\(56\) −3.00269 −0.401251
\(57\) 0 0
\(58\) 5.38076 0.706528
\(59\) −0.805013 −0.104804 −0.0524019 0.998626i \(-0.516688\pi\)
−0.0524019 + 0.998626i \(0.516688\pi\)
\(60\) 0 0
\(61\) 12.7164 1.62817 0.814085 0.580746i \(-0.197239\pi\)
0.814085 + 0.580746i \(0.197239\pi\)
\(62\) −9.29399 −1.18034
\(63\) 0 0
\(64\) 8.82488 1.10311
\(65\) −26.2931 −3.26126
\(66\) 0 0
\(67\) 0.850802 0.103942 0.0519710 0.998649i \(-0.483450\pi\)
0.0519710 + 0.998649i \(0.483450\pi\)
\(68\) 0.685629 0.0831447
\(69\) 0 0
\(70\) −5.06401 −0.605265
\(71\) 11.0690 1.31364 0.656822 0.754046i \(-0.271900\pi\)
0.656822 + 0.754046i \(0.271900\pi\)
\(72\) 0 0
\(73\) −11.9131 −1.39432 −0.697162 0.716914i \(-0.745554\pi\)
−0.697162 + 0.716914i \(0.745554\pi\)
\(74\) −7.78362 −0.904827
\(75\) 0 0
\(76\) −0.693765 −0.0795804
\(77\) 2.39630 0.273084
\(78\) 0 0
\(79\) 3.01636 0.339368 0.169684 0.985499i \(-0.445725\pi\)
0.169684 + 0.985499i \(0.445725\pi\)
\(80\) 12.7969 1.43074
\(81\) 0 0
\(82\) −5.42926 −0.599561
\(83\) 9.71900 1.06680 0.533399 0.845864i \(-0.320914\pi\)
0.533399 + 0.845864i \(0.320914\pi\)
\(84\) 0 0
\(85\) 8.63446 0.936539
\(86\) −8.80892 −0.949891
\(87\) 0 0
\(88\) −7.19534 −0.767026
\(89\) −2.24162 −0.237611 −0.118805 0.992918i \(-0.537906\pi\)
−0.118805 + 0.992918i \(0.537906\pi\)
\(90\) 0 0
\(91\) 6.75130 0.707728
\(92\) 2.15224 0.224386
\(93\) 0 0
\(94\) −11.5119 −1.18737
\(95\) −8.73693 −0.896390
\(96\) 0 0
\(97\) −2.27268 −0.230756 −0.115378 0.993322i \(-0.536808\pi\)
−0.115378 + 0.993322i \(0.536808\pi\)
\(98\) 1.30029 0.131349
\(99\) 0 0
\(100\) −3.14424 −0.314424
\(101\) 12.4450 1.23833 0.619163 0.785263i \(-0.287472\pi\)
0.619163 + 0.785263i \(0.287472\pi\)
\(102\) 0 0
\(103\) −5.58562 −0.550368 −0.275184 0.961392i \(-0.588739\pi\)
−0.275184 + 0.961392i \(0.588739\pi\)
\(104\) −20.2721 −1.98784
\(105\) 0 0
\(106\) 1.61618 0.156977
\(107\) 12.8657 1.24378 0.621888 0.783106i \(-0.286366\pi\)
0.621888 + 0.783106i \(0.286366\pi\)
\(108\) 0 0
\(109\) 0.699267 0.0669777 0.0334888 0.999439i \(-0.489338\pi\)
0.0334888 + 0.999439i \(0.489338\pi\)
\(110\) −12.1349 −1.15702
\(111\) 0 0
\(112\) −3.28587 −0.310485
\(113\) 14.3692 1.35174 0.675869 0.737022i \(-0.263769\pi\)
0.675869 + 0.737022i \(0.263769\pi\)
\(114\) 0 0
\(115\) 27.1042 2.52748
\(116\) −1.27971 −0.118818
\(117\) 0 0
\(118\) −1.04675 −0.0963611
\(119\) −2.21708 −0.203239
\(120\) 0 0
\(121\) −5.25775 −0.477977
\(122\) 16.5350 1.49701
\(123\) 0 0
\(124\) 2.21040 0.198500
\(125\) −20.1243 −1.79997
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 8.00928 0.707927
\(129\) 0 0
\(130\) −34.1886 −2.99854
\(131\) 20.2823 1.77207 0.886035 0.463618i \(-0.153449\pi\)
0.886035 + 0.463618i \(0.153449\pi\)
\(132\) 0 0
\(133\) 2.24339 0.194526
\(134\) 1.10629 0.0955687
\(135\) 0 0
\(136\) 6.65720 0.570850
\(137\) −3.96873 −0.339071 −0.169536 0.985524i \(-0.554227\pi\)
−0.169536 + 0.985524i \(0.554227\pi\)
\(138\) 0 0
\(139\) 14.6292 1.24084 0.620418 0.784271i \(-0.286963\pi\)
0.620418 + 0.784271i \(0.286963\pi\)
\(140\) 1.20438 0.101789
\(141\) 0 0
\(142\) 14.3928 1.20782
\(143\) 16.1781 1.35288
\(144\) 0 0
\(145\) −16.1160 −1.33836
\(146\) −15.4905 −1.28200
\(147\) 0 0
\(148\) 1.85119 0.152167
\(149\) 11.7970 0.966451 0.483225 0.875496i \(-0.339465\pi\)
0.483225 + 0.875496i \(0.339465\pi\)
\(150\) 0 0
\(151\) 15.8963 1.29362 0.646811 0.762650i \(-0.276102\pi\)
0.646811 + 0.762650i \(0.276102\pi\)
\(152\) −6.73620 −0.546378
\(153\) 0 0
\(154\) 3.11588 0.251085
\(155\) 27.8367 2.23589
\(156\) 0 0
\(157\) −7.53723 −0.601536 −0.300768 0.953697i \(-0.597243\pi\)
−0.300768 + 0.953697i \(0.597243\pi\)
\(158\) 3.92214 0.312029
\(159\) 0 0
\(160\) −6.74846 −0.533512
\(161\) −6.95956 −0.548490
\(162\) 0 0
\(163\) −5.04061 −0.394811 −0.197405 0.980322i \(-0.563252\pi\)
−0.197405 + 0.980322i \(0.563252\pi\)
\(164\) 1.29125 0.100829
\(165\) 0 0
\(166\) 12.6375 0.980861
\(167\) 15.1860 1.17513 0.587564 0.809178i \(-0.300087\pi\)
0.587564 + 0.809178i \(0.300087\pi\)
\(168\) 0 0
\(169\) 32.5800 2.50616
\(170\) 11.2273 0.861094
\(171\) 0 0
\(172\) 2.09504 0.159745
\(173\) −5.85526 −0.445167 −0.222584 0.974914i \(-0.571449\pi\)
−0.222584 + 0.974914i \(0.571449\pi\)
\(174\) 0 0
\(175\) 10.1673 0.768578
\(176\) −7.87392 −0.593519
\(177\) 0 0
\(178\) −2.91475 −0.218470
\(179\) −5.92007 −0.442487 −0.221243 0.975219i \(-0.571012\pi\)
−0.221243 + 0.975219i \(0.571012\pi\)
\(180\) 0 0
\(181\) 14.4113 1.07119 0.535593 0.844476i \(-0.320088\pi\)
0.535593 + 0.844476i \(0.320088\pi\)
\(182\) 8.77864 0.650716
\(183\) 0 0
\(184\) 20.8974 1.54058
\(185\) 23.3129 1.71400
\(186\) 0 0
\(187\) −5.31278 −0.388509
\(188\) 2.73790 0.199682
\(189\) 0 0
\(190\) −11.3605 −0.824180
\(191\) −14.9477 −1.08158 −0.540790 0.841158i \(-0.681875\pi\)
−0.540790 + 0.841158i \(0.681875\pi\)
\(192\) 0 0
\(193\) 12.1148 0.872045 0.436023 0.899936i \(-0.356387\pi\)
0.436023 + 0.899936i \(0.356387\pi\)
\(194\) −2.95515 −0.212167
\(195\) 0 0
\(196\) −0.309249 −0.0220892
\(197\) −19.7870 −1.40977 −0.704883 0.709324i \(-0.749000\pi\)
−0.704883 + 0.709324i \(0.749000\pi\)
\(198\) 0 0
\(199\) −4.83892 −0.343022 −0.171511 0.985182i \(-0.554865\pi\)
−0.171511 + 0.985182i \(0.554865\pi\)
\(200\) −30.5294 −2.15875
\(201\) 0 0
\(202\) 16.1821 1.13857
\(203\) 4.13812 0.290439
\(204\) 0 0
\(205\) 16.2613 1.13574
\(206\) −7.26292 −0.506032
\(207\) 0 0
\(208\) −22.1839 −1.53817
\(209\) 5.37583 0.371854
\(210\) 0 0
\(211\) 16.8744 1.16168 0.580840 0.814018i \(-0.302724\pi\)
0.580840 + 0.814018i \(0.302724\pi\)
\(212\) −0.384378 −0.0263992
\(213\) 0 0
\(214\) 16.7292 1.14358
\(215\) 26.3838 1.79936
\(216\) 0 0
\(217\) −7.14764 −0.485213
\(218\) 0.909249 0.0615821
\(219\) 0 0
\(220\) 2.88605 0.194578
\(221\) −14.9681 −1.00687
\(222\) 0 0
\(223\) −4.23308 −0.283468 −0.141734 0.989905i \(-0.545268\pi\)
−0.141734 + 0.989905i \(0.545268\pi\)
\(224\) 1.73281 0.115778
\(225\) 0 0
\(226\) 18.6841 1.24285
\(227\) −11.2253 −0.745048 −0.372524 0.928023i \(-0.621508\pi\)
−0.372524 + 0.928023i \(0.621508\pi\)
\(228\) 0 0
\(229\) 26.9780 1.78276 0.891379 0.453259i \(-0.149739\pi\)
0.891379 + 0.453259i \(0.149739\pi\)
\(230\) 35.2433 2.32387
\(231\) 0 0
\(232\) −12.4255 −0.815774
\(233\) 0.503531 0.0329874 0.0164937 0.999864i \(-0.494750\pi\)
0.0164937 + 0.999864i \(0.494750\pi\)
\(234\) 0 0
\(235\) 34.4797 2.24921
\(236\) 0.248950 0.0162052
\(237\) 0 0
\(238\) −2.88284 −0.186867
\(239\) 24.9528 1.61406 0.807032 0.590508i \(-0.201072\pi\)
0.807032 + 0.590508i \(0.201072\pi\)
\(240\) 0 0
\(241\) −9.47834 −0.610553 −0.305277 0.952264i \(-0.598749\pi\)
−0.305277 + 0.952264i \(0.598749\pi\)
\(242\) −6.83660 −0.439473
\(243\) 0 0
\(244\) −3.93254 −0.251755
\(245\) −3.89453 −0.248812
\(246\) 0 0
\(247\) 15.1458 0.963703
\(248\) 21.4621 1.36285
\(249\) 0 0
\(250\) −26.1674 −1.65497
\(251\) 10.6194 0.670288 0.335144 0.942167i \(-0.391215\pi\)
0.335144 + 0.942167i \(0.391215\pi\)
\(252\) 0 0
\(253\) −16.6772 −1.04849
\(254\) 1.30029 0.0815874
\(255\) 0 0
\(256\) −7.23538 −0.452211
\(257\) −25.5404 −1.59317 −0.796583 0.604530i \(-0.793361\pi\)
−0.796583 + 0.604530i \(0.793361\pi\)
\(258\) 0 0
\(259\) −5.98607 −0.371956
\(260\) 8.13112 0.504271
\(261\) 0 0
\(262\) 26.3728 1.62932
\(263\) 8.16149 0.503259 0.251629 0.967824i \(-0.419034\pi\)
0.251629 + 0.967824i \(0.419034\pi\)
\(264\) 0 0
\(265\) −4.84066 −0.297359
\(266\) 2.91705 0.178856
\(267\) 0 0
\(268\) −0.263110 −0.0160720
\(269\) −0.585453 −0.0356957 −0.0178478 0.999841i \(-0.505681\pi\)
−0.0178478 + 0.999841i \(0.505681\pi\)
\(270\) 0 0
\(271\) −3.75629 −0.228178 −0.114089 0.993471i \(-0.536395\pi\)
−0.114089 + 0.993471i \(0.536395\pi\)
\(272\) 7.28502 0.441719
\(273\) 0 0
\(274\) −5.16049 −0.311757
\(275\) 24.3640 1.46920
\(276\) 0 0
\(277\) 22.9533 1.37913 0.689565 0.724224i \(-0.257802\pi\)
0.689565 + 0.724224i \(0.257802\pi\)
\(278\) 19.0222 1.14088
\(279\) 0 0
\(280\) 11.6941 0.698854
\(281\) −12.5921 −0.751182 −0.375591 0.926785i \(-0.622560\pi\)
−0.375591 + 0.926785i \(0.622560\pi\)
\(282\) 0 0
\(283\) −17.5458 −1.04299 −0.521494 0.853255i \(-0.674625\pi\)
−0.521494 + 0.853255i \(0.674625\pi\)
\(284\) −3.42307 −0.203122
\(285\) 0 0
\(286\) 21.0362 1.24390
\(287\) −4.17542 −0.246468
\(288\) 0 0
\(289\) −12.0846 −0.710857
\(290\) −20.9555 −1.23055
\(291\) 0 0
\(292\) 3.68412 0.215597
\(293\) −7.11385 −0.415596 −0.207798 0.978172i \(-0.566630\pi\)
−0.207798 + 0.978172i \(0.566630\pi\)
\(294\) 0 0
\(295\) 3.13514 0.182535
\(296\) 17.9743 1.04474
\(297\) 0 0
\(298\) 15.3396 0.888597
\(299\) −46.9861 −2.71728
\(300\) 0 0
\(301\) −6.77459 −0.390481
\(302\) 20.6698 1.18941
\(303\) 0 0
\(304\) −7.37147 −0.422783
\(305\) −49.5244 −2.83576
\(306\) 0 0
\(307\) 9.70536 0.553914 0.276957 0.960882i \(-0.410674\pi\)
0.276957 + 0.960882i \(0.410674\pi\)
\(308\) −0.741053 −0.0422254
\(309\) 0 0
\(310\) 36.1957 2.05578
\(311\) 13.6173 0.772168 0.386084 0.922464i \(-0.373828\pi\)
0.386084 + 0.922464i \(0.373828\pi\)
\(312\) 0 0
\(313\) 10.9421 0.618485 0.309242 0.950983i \(-0.399925\pi\)
0.309242 + 0.950983i \(0.399925\pi\)
\(314\) −9.80057 −0.553078
\(315\) 0 0
\(316\) −0.932808 −0.0524745
\(317\) 4.23874 0.238071 0.119036 0.992890i \(-0.462020\pi\)
0.119036 + 0.992890i \(0.462020\pi\)
\(318\) 0 0
\(319\) 9.91618 0.555200
\(320\) −34.3687 −1.92127
\(321\) 0 0
\(322\) −9.04944 −0.504306
\(323\) −4.97376 −0.276748
\(324\) 0 0
\(325\) 68.6427 3.80761
\(326\) −6.55424 −0.363006
\(327\) 0 0
\(328\) 12.5375 0.692268
\(329\) −8.85337 −0.488102
\(330\) 0 0
\(331\) 15.8239 0.869759 0.434880 0.900489i \(-0.356791\pi\)
0.434880 + 0.900489i \(0.356791\pi\)
\(332\) −3.00559 −0.164953
\(333\) 0 0
\(334\) 19.7462 1.08046
\(335\) −3.31347 −0.181034
\(336\) 0 0
\(337\) −0.576223 −0.0313889 −0.0156944 0.999877i \(-0.504996\pi\)
−0.0156944 + 0.999877i \(0.504996\pi\)
\(338\) 42.3635 2.30427
\(339\) 0 0
\(340\) −2.67020 −0.144812
\(341\) −17.1279 −0.927526
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 20.3420 1.09677
\(345\) 0 0
\(346\) −7.61353 −0.409306
\(347\) 6.25612 0.335846 0.167923 0.985800i \(-0.446294\pi\)
0.167923 + 0.985800i \(0.446294\pi\)
\(348\) 0 0
\(349\) −16.1162 −0.862679 −0.431339 0.902190i \(-0.641959\pi\)
−0.431339 + 0.902190i \(0.641959\pi\)
\(350\) 13.2205 0.706664
\(351\) 0 0
\(352\) 4.15232 0.221319
\(353\) −23.0130 −1.22486 −0.612430 0.790525i \(-0.709808\pi\)
−0.612430 + 0.790525i \(0.709808\pi\)
\(354\) 0 0
\(355\) −43.1084 −2.28795
\(356\) 0.693218 0.0367405
\(357\) 0 0
\(358\) −7.69780 −0.406842
\(359\) −17.7747 −0.938115 −0.469058 0.883168i \(-0.655406\pi\)
−0.469058 + 0.883168i \(0.655406\pi\)
\(360\) 0 0
\(361\) −13.9672 −0.735117
\(362\) 18.7389 0.984894
\(363\) 0 0
\(364\) −2.08783 −0.109432
\(365\) 46.3959 2.42847
\(366\) 0 0
\(367\) −32.1389 −1.67764 −0.838819 0.544410i \(-0.816754\pi\)
−0.838819 + 0.544410i \(0.816754\pi\)
\(368\) 22.8682 1.19209
\(369\) 0 0
\(370\) 30.3135 1.57592
\(371\) 1.24294 0.0645302
\(372\) 0 0
\(373\) 16.5396 0.856390 0.428195 0.903686i \(-0.359150\pi\)
0.428195 + 0.903686i \(0.359150\pi\)
\(374\) −6.90815 −0.357212
\(375\) 0 0
\(376\) 26.5839 1.37096
\(377\) 27.9377 1.43887
\(378\) 0 0
\(379\) 20.6102 1.05867 0.529336 0.848412i \(-0.322441\pi\)
0.529336 + 0.848412i \(0.322441\pi\)
\(380\) 2.70189 0.138604
\(381\) 0 0
\(382\) −19.4364 −0.994451
\(383\) 37.1156 1.89652 0.948259 0.317498i \(-0.102843\pi\)
0.948259 + 0.317498i \(0.102843\pi\)
\(384\) 0 0
\(385\) −9.33245 −0.475626
\(386\) 15.7528 0.801796
\(387\) 0 0
\(388\) 0.702825 0.0356806
\(389\) 11.1761 0.566653 0.283327 0.959023i \(-0.408562\pi\)
0.283327 + 0.959023i \(0.408562\pi\)
\(390\) 0 0
\(391\) 15.4299 0.780323
\(392\) −3.00269 −0.151659
\(393\) 0 0
\(394\) −25.7288 −1.29620
\(395\) −11.7473 −0.591071
\(396\) 0 0
\(397\) −13.9354 −0.699396 −0.349698 0.936862i \(-0.613716\pi\)
−0.349698 + 0.936862i \(0.613716\pi\)
\(398\) −6.29200 −0.315389
\(399\) 0 0
\(400\) −33.4085 −1.67043
\(401\) −16.6189 −0.829907 −0.414954 0.909843i \(-0.636202\pi\)
−0.414954 + 0.909843i \(0.636202\pi\)
\(402\) 0 0
\(403\) −48.2558 −2.40379
\(404\) −3.84861 −0.191476
\(405\) 0 0
\(406\) 5.38076 0.267042
\(407\) −14.3444 −0.711026
\(408\) 0 0
\(409\) 39.1584 1.93626 0.968129 0.250451i \(-0.0805790\pi\)
0.968129 + 0.250451i \(0.0805790\pi\)
\(410\) 21.1444 1.04425
\(411\) 0 0
\(412\) 1.72735 0.0851004
\(413\) −0.805013 −0.0396121
\(414\) 0 0
\(415\) −37.8509 −1.85803
\(416\) 11.6987 0.573575
\(417\) 0 0
\(418\) 6.99013 0.341898
\(419\) 22.5455 1.10142 0.550709 0.834697i \(-0.314357\pi\)
0.550709 + 0.834697i \(0.314357\pi\)
\(420\) 0 0
\(421\) 28.2216 1.37544 0.687718 0.725978i \(-0.258613\pi\)
0.687718 + 0.725978i \(0.258613\pi\)
\(422\) 21.9416 1.06810
\(423\) 0 0
\(424\) −3.73216 −0.181250
\(425\) −22.5418 −1.09344
\(426\) 0 0
\(427\) 12.7164 0.615390
\(428\) −3.97871 −0.192318
\(429\) 0 0
\(430\) 34.3066 1.65441
\(431\) 18.9034 0.910544 0.455272 0.890352i \(-0.349542\pi\)
0.455272 + 0.890352i \(0.349542\pi\)
\(432\) 0 0
\(433\) −26.1024 −1.25440 −0.627201 0.778858i \(-0.715799\pi\)
−0.627201 + 0.778858i \(0.715799\pi\)
\(434\) −9.29399 −0.446126
\(435\) 0 0
\(436\) −0.216248 −0.0103564
\(437\) −15.6130 −0.746871
\(438\) 0 0
\(439\) −32.3492 −1.54394 −0.771972 0.635656i \(-0.780730\pi\)
−0.771972 + 0.635656i \(0.780730\pi\)
\(440\) 28.0225 1.33592
\(441\) 0 0
\(442\) −19.4629 −0.925756
\(443\) −39.6894 −1.88570 −0.942850 0.333218i \(-0.891865\pi\)
−0.942850 + 0.333218i \(0.891865\pi\)
\(444\) 0 0
\(445\) 8.73004 0.413843
\(446\) −5.50423 −0.260633
\(447\) 0 0
\(448\) 8.82488 0.416936
\(449\) 35.2431 1.66323 0.831613 0.555355i \(-0.187418\pi\)
0.831613 + 0.555355i \(0.187418\pi\)
\(450\) 0 0
\(451\) −10.0056 −0.471144
\(452\) −4.44365 −0.209012
\(453\) 0 0
\(454\) −14.5961 −0.685029
\(455\) −26.2931 −1.23264
\(456\) 0 0
\(457\) 33.0348 1.54530 0.772651 0.634831i \(-0.218930\pi\)
0.772651 + 0.634831i \(0.218930\pi\)
\(458\) 35.0792 1.63914
\(459\) 0 0
\(460\) −8.38195 −0.390810
\(461\) 34.4017 1.60225 0.801124 0.598499i \(-0.204236\pi\)
0.801124 + 0.598499i \(0.204236\pi\)
\(462\) 0 0
\(463\) −11.8834 −0.552270 −0.276135 0.961119i \(-0.589054\pi\)
−0.276135 + 0.961119i \(0.589054\pi\)
\(464\) −13.5973 −0.631240
\(465\) 0 0
\(466\) 0.654736 0.0303300
\(467\) 37.4363 1.73235 0.866173 0.499744i \(-0.166572\pi\)
0.866173 + 0.499744i \(0.166572\pi\)
\(468\) 0 0
\(469\) 0.850802 0.0392864
\(470\) 44.8336 2.06802
\(471\) 0 0
\(472\) 2.41721 0.111261
\(473\) −16.2339 −0.746437
\(474\) 0 0
\(475\) 22.8093 1.04656
\(476\) 0.685629 0.0314258
\(477\) 0 0
\(478\) 32.4459 1.48404
\(479\) 20.9968 0.959370 0.479685 0.877441i \(-0.340751\pi\)
0.479685 + 0.877441i \(0.340751\pi\)
\(480\) 0 0
\(481\) −40.4137 −1.84271
\(482\) −12.3246 −0.561369
\(483\) 0 0
\(484\) 1.62595 0.0739070
\(485\) 8.85103 0.401904
\(486\) 0 0
\(487\) 43.7964 1.98461 0.992303 0.123832i \(-0.0395185\pi\)
0.992303 + 0.123832i \(0.0395185\pi\)
\(488\) −38.1834 −1.72848
\(489\) 0 0
\(490\) −5.06401 −0.228769
\(491\) 34.9624 1.57783 0.788915 0.614502i \(-0.210643\pi\)
0.788915 + 0.614502i \(0.210643\pi\)
\(492\) 0 0
\(493\) −9.17454 −0.413200
\(494\) 19.6939 0.886070
\(495\) 0 0
\(496\) 23.4862 1.05456
\(497\) 11.0690 0.496511
\(498\) 0 0
\(499\) 25.9616 1.16220 0.581099 0.813833i \(-0.302623\pi\)
0.581099 + 0.813833i \(0.302623\pi\)
\(500\) 6.22343 0.278320
\(501\) 0 0
\(502\) 13.8082 0.616291
\(503\) −7.61057 −0.339338 −0.169669 0.985501i \(-0.554270\pi\)
−0.169669 + 0.985501i \(0.554270\pi\)
\(504\) 0 0
\(505\) −48.4675 −2.15677
\(506\) −21.6852 −0.964023
\(507\) 0 0
\(508\) −0.309249 −0.0137207
\(509\) −3.81286 −0.169002 −0.0845010 0.996423i \(-0.526930\pi\)
−0.0845010 + 0.996423i \(0.526930\pi\)
\(510\) 0 0
\(511\) −11.9131 −0.527005
\(512\) −25.4267 −1.12371
\(513\) 0 0
\(514\) −33.2099 −1.46482
\(515\) 21.7534 0.958567
\(516\) 0 0
\(517\) −21.2153 −0.933049
\(518\) −7.78362 −0.341993
\(519\) 0 0
\(520\) 78.9501 3.46219
\(521\) −39.4310 −1.72750 −0.863752 0.503917i \(-0.831892\pi\)
−0.863752 + 0.503917i \(0.831892\pi\)
\(522\) 0 0
\(523\) −31.8685 −1.39351 −0.696756 0.717308i \(-0.745374\pi\)
−0.696756 + 0.717308i \(0.745374\pi\)
\(524\) −6.27228 −0.274006
\(525\) 0 0
\(526\) 10.6123 0.462718
\(527\) 15.8469 0.690300
\(528\) 0 0
\(529\) 25.4355 1.10589
\(530\) −6.29426 −0.273405
\(531\) 0 0
\(532\) −0.693765 −0.0300785
\(533\) −28.1895 −1.22102
\(534\) 0 0
\(535\) −50.1059 −2.16627
\(536\) −2.55470 −0.110346
\(537\) 0 0
\(538\) −0.761258 −0.0328202
\(539\) 2.39630 0.103216
\(540\) 0 0
\(541\) 7.69149 0.330683 0.165342 0.986236i \(-0.447127\pi\)
0.165342 + 0.986236i \(0.447127\pi\)
\(542\) −4.88426 −0.209797
\(543\) 0 0
\(544\) −3.84176 −0.164714
\(545\) −2.72332 −0.116654
\(546\) 0 0
\(547\) 36.3675 1.55496 0.777481 0.628907i \(-0.216497\pi\)
0.777481 + 0.628907i \(0.216497\pi\)
\(548\) 1.22732 0.0524287
\(549\) 0 0
\(550\) 31.6802 1.35085
\(551\) 9.28341 0.395487
\(552\) 0 0
\(553\) 3.01636 0.128269
\(554\) 29.8459 1.26803
\(555\) 0 0
\(556\) −4.52408 −0.191864
\(557\) 32.7213 1.38645 0.693223 0.720723i \(-0.256190\pi\)
0.693223 + 0.720723i \(0.256190\pi\)
\(558\) 0 0
\(559\) −45.7373 −1.93448
\(560\) 12.7969 0.540768
\(561\) 0 0
\(562\) −16.3734 −0.690669
\(563\) −37.9585 −1.59976 −0.799881 0.600159i \(-0.795104\pi\)
−0.799881 + 0.600159i \(0.795104\pi\)
\(564\) 0 0
\(565\) −55.9611 −2.35430
\(566\) −22.8146 −0.958968
\(567\) 0 0
\(568\) −33.2367 −1.39458
\(569\) 34.6604 1.45304 0.726520 0.687145i \(-0.241136\pi\)
0.726520 + 0.687145i \(0.241136\pi\)
\(570\) 0 0
\(571\) 26.3412 1.10234 0.551171 0.834392i \(-0.314181\pi\)
0.551171 + 0.834392i \(0.314181\pi\)
\(572\) −5.00307 −0.209189
\(573\) 0 0
\(574\) −5.42926 −0.226613
\(575\) −70.7602 −2.95090
\(576\) 0 0
\(577\) −18.7461 −0.780411 −0.390206 0.920728i \(-0.627596\pi\)
−0.390206 + 0.920728i \(0.627596\pi\)
\(578\) −15.7134 −0.653593
\(579\) 0 0
\(580\) 4.98387 0.206944
\(581\) 9.71900 0.403212
\(582\) 0 0
\(583\) 2.97845 0.123355
\(584\) 35.7714 1.48023
\(585\) 0 0
\(586\) −9.25006 −0.382116
\(587\) −14.9451 −0.616850 −0.308425 0.951249i \(-0.599802\pi\)
−0.308425 + 0.951249i \(0.599802\pi\)
\(588\) 0 0
\(589\) −16.0349 −0.660707
\(590\) 4.07659 0.167831
\(591\) 0 0
\(592\) 19.6694 0.808409
\(593\) −24.1999 −0.993769 −0.496885 0.867817i \(-0.665523\pi\)
−0.496885 + 0.867817i \(0.665523\pi\)
\(594\) 0 0
\(595\) 8.63446 0.353979
\(596\) −3.64822 −0.149437
\(597\) 0 0
\(598\) −61.0955 −2.49838
\(599\) −23.1503 −0.945896 −0.472948 0.881090i \(-0.656810\pi\)
−0.472948 + 0.881090i \(0.656810\pi\)
\(600\) 0 0
\(601\) 2.39101 0.0975313 0.0487657 0.998810i \(-0.484471\pi\)
0.0487657 + 0.998810i \(0.484471\pi\)
\(602\) −8.80892 −0.359025
\(603\) 0 0
\(604\) −4.91591 −0.200026
\(605\) 20.4765 0.832486
\(606\) 0 0
\(607\) 18.0847 0.734037 0.367019 0.930214i \(-0.380379\pi\)
0.367019 + 0.930214i \(0.380379\pi\)
\(608\) 3.88735 0.157653
\(609\) 0 0
\(610\) −64.3960 −2.60732
\(611\) −59.7718 −2.41811
\(612\) 0 0
\(613\) −15.7792 −0.637316 −0.318658 0.947870i \(-0.603232\pi\)
−0.318658 + 0.947870i \(0.603232\pi\)
\(614\) 12.6198 0.509292
\(615\) 0 0
\(616\) −7.19534 −0.289909
\(617\) −18.0117 −0.725123 −0.362561 0.931960i \(-0.618098\pi\)
−0.362561 + 0.931960i \(0.618098\pi\)
\(618\) 0 0
\(619\) 34.9940 1.40653 0.703264 0.710928i \(-0.251725\pi\)
0.703264 + 0.710928i \(0.251725\pi\)
\(620\) −8.60846 −0.345724
\(621\) 0 0
\(622\) 17.7065 0.709964
\(623\) −2.24162 −0.0898085
\(624\) 0 0
\(625\) 27.5380 1.10152
\(626\) 14.2279 0.568661
\(627\) 0 0
\(628\) 2.33088 0.0930122
\(629\) 13.2716 0.529172
\(630\) 0 0
\(631\) −38.1719 −1.51960 −0.759799 0.650158i \(-0.774703\pi\)
−0.759799 + 0.650158i \(0.774703\pi\)
\(632\) −9.05721 −0.360276
\(633\) 0 0
\(634\) 5.51158 0.218893
\(635\) −3.89453 −0.154550
\(636\) 0 0
\(637\) 6.75130 0.267496
\(638\) 12.8939 0.510474
\(639\) 0 0
\(640\) −31.1924 −1.23299
\(641\) 3.57350 0.141145 0.0705724 0.997507i \(-0.477517\pi\)
0.0705724 + 0.997507i \(0.477517\pi\)
\(642\) 0 0
\(643\) −22.1182 −0.872255 −0.436127 0.899885i \(-0.643650\pi\)
−0.436127 + 0.899885i \(0.643650\pi\)
\(644\) 2.15224 0.0848101
\(645\) 0 0
\(646\) −6.46733 −0.254454
\(647\) 11.8343 0.465256 0.232628 0.972566i \(-0.425268\pi\)
0.232628 + 0.972566i \(0.425268\pi\)
\(648\) 0 0
\(649\) −1.92905 −0.0757219
\(650\) 89.2554 3.50088
\(651\) 0 0
\(652\) 1.55880 0.0610474
\(653\) 43.8013 1.71408 0.857038 0.515253i \(-0.172302\pi\)
0.857038 + 0.515253i \(0.172302\pi\)
\(654\) 0 0
\(655\) −78.9899 −3.08639
\(656\) 13.7199 0.535672
\(657\) 0 0
\(658\) −11.5119 −0.448782
\(659\) −14.9940 −0.584085 −0.292042 0.956405i \(-0.594335\pi\)
−0.292042 + 0.956405i \(0.594335\pi\)
\(660\) 0 0
\(661\) −17.0713 −0.663996 −0.331998 0.943280i \(-0.607723\pi\)
−0.331998 + 0.943280i \(0.607723\pi\)
\(662\) 20.5756 0.799694
\(663\) 0 0
\(664\) −29.1831 −1.13253
\(665\) −8.73693 −0.338804
\(666\) 0 0
\(667\) −28.7995 −1.11512
\(668\) −4.69626 −0.181704
\(669\) 0 0
\(670\) −4.30847 −0.166451
\(671\) 30.4723 1.17637
\(672\) 0 0
\(673\) 11.8232 0.455751 0.227876 0.973690i \(-0.426822\pi\)
0.227876 + 0.973690i \(0.426822\pi\)
\(674\) −0.749256 −0.0288603
\(675\) 0 0
\(676\) −10.0753 −0.387513
\(677\) 14.6156 0.561723 0.280861 0.959748i \(-0.409380\pi\)
0.280861 + 0.959748i \(0.409380\pi\)
\(678\) 0 0
\(679\) −2.27268 −0.0872176
\(680\) −25.9266 −0.994241
\(681\) 0 0
\(682\) −22.2712 −0.852808
\(683\) 36.1076 1.38162 0.690810 0.723036i \(-0.257254\pi\)
0.690810 + 0.723036i \(0.257254\pi\)
\(684\) 0 0
\(685\) 15.4563 0.590555
\(686\) 1.30029 0.0496453
\(687\) 0 0
\(688\) 22.2604 0.848670
\(689\) 8.39146 0.319689
\(690\) 0 0
\(691\) −5.86998 −0.223305 −0.111652 0.993747i \(-0.535614\pi\)
−0.111652 + 0.993747i \(0.535614\pi\)
\(692\) 1.81073 0.0688338
\(693\) 0 0
\(694\) 8.13476 0.308791
\(695\) −56.9739 −2.16114
\(696\) 0 0
\(697\) 9.25724 0.350643
\(698\) −20.9557 −0.793184
\(699\) 0 0
\(700\) −3.14424 −0.118841
\(701\) 5.04266 0.190459 0.0952293 0.995455i \(-0.469642\pi\)
0.0952293 + 0.995455i \(0.469642\pi\)
\(702\) 0 0
\(703\) −13.4291 −0.506487
\(704\) 21.1471 0.797010
\(705\) 0 0
\(706\) −29.9236 −1.12619
\(707\) 12.4450 0.468043
\(708\) 0 0
\(709\) −5.42957 −0.203912 −0.101956 0.994789i \(-0.532510\pi\)
−0.101956 + 0.994789i \(0.532510\pi\)
\(710\) −56.0533 −2.10364
\(711\) 0 0
\(712\) 6.73088 0.252251
\(713\) 49.7444 1.86294
\(714\) 0 0
\(715\) −63.0061 −2.35630
\(716\) 1.83078 0.0684193
\(717\) 0 0
\(718\) −23.1123 −0.862544
\(719\) −32.5836 −1.21516 −0.607581 0.794258i \(-0.707860\pi\)
−0.607581 + 0.794258i \(0.707860\pi\)
\(720\) 0 0
\(721\) −5.58562 −0.208019
\(722\) −18.1614 −0.675898
\(723\) 0 0
\(724\) −4.45669 −0.165632
\(725\) 42.0737 1.56258
\(726\) 0 0
\(727\) −45.1575 −1.67480 −0.837399 0.546592i \(-0.815925\pi\)
−0.837399 + 0.546592i \(0.815925\pi\)
\(728\) −20.2721 −0.751333
\(729\) 0 0
\(730\) 60.3281 2.23284
\(731\) 15.0198 0.555527
\(732\) 0 0
\(733\) 37.6362 1.39013 0.695063 0.718949i \(-0.255377\pi\)
0.695063 + 0.718949i \(0.255377\pi\)
\(734\) −41.7899 −1.54249
\(735\) 0 0
\(736\) −12.0596 −0.444522
\(737\) 2.03878 0.0750993
\(738\) 0 0
\(739\) 22.5159 0.828260 0.414130 0.910218i \(-0.364086\pi\)
0.414130 + 0.910218i \(0.364086\pi\)
\(740\) −7.20949 −0.265026
\(741\) 0 0
\(742\) 1.61618 0.0593319
\(743\) 18.0968 0.663907 0.331954 0.943296i \(-0.392292\pi\)
0.331954 + 0.943296i \(0.392292\pi\)
\(744\) 0 0
\(745\) −45.9439 −1.68325
\(746\) 21.5063 0.787402
\(747\) 0 0
\(748\) 1.64297 0.0600730
\(749\) 12.8657 0.470103
\(750\) 0 0
\(751\) −1.12758 −0.0411461 −0.0205730 0.999788i \(-0.506549\pi\)
−0.0205730 + 0.999788i \(0.506549\pi\)
\(752\) 29.0910 1.06084
\(753\) 0 0
\(754\) 36.3271 1.32295
\(755\) −61.9085 −2.25308
\(756\) 0 0
\(757\) −46.0347 −1.67316 −0.836580 0.547845i \(-0.815448\pi\)
−0.836580 + 0.547845i \(0.815448\pi\)
\(758\) 26.7992 0.973389
\(759\) 0 0
\(760\) 26.2343 0.951618
\(761\) 13.8335 0.501464 0.250732 0.968056i \(-0.419329\pi\)
0.250732 + 0.968056i \(0.419329\pi\)
\(762\) 0 0
\(763\) 0.699267 0.0253152
\(764\) 4.62257 0.167239
\(765\) 0 0
\(766\) 48.2610 1.74374
\(767\) −5.43488 −0.196242
\(768\) 0 0
\(769\) −36.3802 −1.31190 −0.655951 0.754803i \(-0.727732\pi\)
−0.655951 + 0.754803i \(0.727732\pi\)
\(770\) −12.1349 −0.437311
\(771\) 0 0
\(772\) −3.74650 −0.134840
\(773\) 42.2178 1.51847 0.759234 0.650818i \(-0.225574\pi\)
0.759234 + 0.650818i \(0.225574\pi\)
\(774\) 0 0
\(775\) −72.6724 −2.61047
\(776\) 6.82417 0.244973
\(777\) 0 0
\(778\) 14.5322 0.521005
\(779\) −9.36709 −0.335611
\(780\) 0 0
\(781\) 26.5245 0.949123
\(782\) 20.0633 0.717462
\(783\) 0 0
\(784\) −3.28587 −0.117352
\(785\) 29.3539 1.04769
\(786\) 0 0
\(787\) 1.65472 0.0589845 0.0294922 0.999565i \(-0.490611\pi\)
0.0294922 + 0.999565i \(0.490611\pi\)
\(788\) 6.11911 0.217984
\(789\) 0 0
\(790\) −15.2749 −0.543456
\(791\) 14.3692 0.510909
\(792\) 0 0
\(793\) 85.8523 3.04870
\(794\) −18.1200 −0.643055
\(795\) 0 0
\(796\) 1.49643 0.0530397
\(797\) −47.9433 −1.69824 −0.849120 0.528200i \(-0.822867\pi\)
−0.849120 + 0.528200i \(0.822867\pi\)
\(798\) 0 0
\(799\) 19.6286 0.694410
\(800\) 17.6180 0.622891
\(801\) 0 0
\(802\) −21.6093 −0.763052
\(803\) −28.5474 −1.00741
\(804\) 0 0
\(805\) 27.1042 0.955297
\(806\) −62.7465 −2.21015
\(807\) 0 0
\(808\) −37.3685 −1.31462
\(809\) 39.4320 1.38635 0.693177 0.720767i \(-0.256210\pi\)
0.693177 + 0.720767i \(0.256210\pi\)
\(810\) 0 0
\(811\) −4.35171 −0.152809 −0.0764046 0.997077i \(-0.524344\pi\)
−0.0764046 + 0.997077i \(0.524344\pi\)
\(812\) −1.27971 −0.0449091
\(813\) 0 0
\(814\) −18.6519 −0.653748
\(815\) 19.6308 0.687636
\(816\) 0 0
\(817\) −15.1980 −0.531712
\(818\) 50.9172 1.78028
\(819\) 0 0
\(820\) −5.02879 −0.175613
\(821\) −4.11893 −0.143752 −0.0718758 0.997414i \(-0.522899\pi\)
−0.0718758 + 0.997414i \(0.522899\pi\)
\(822\) 0 0
\(823\) 26.0370 0.907594 0.453797 0.891105i \(-0.350069\pi\)
0.453797 + 0.891105i \(0.350069\pi\)
\(824\) 16.7719 0.584277
\(825\) 0 0
\(826\) −1.04675 −0.0364211
\(827\) −2.07080 −0.0720087 −0.0360043 0.999352i \(-0.511463\pi\)
−0.0360043 + 0.999352i \(0.511463\pi\)
\(828\) 0 0
\(829\) −7.43778 −0.258325 −0.129162 0.991623i \(-0.541229\pi\)
−0.129162 + 0.991623i \(0.541229\pi\)
\(830\) −49.2171 −1.70835
\(831\) 0 0
\(832\) 59.5794 2.06554
\(833\) −2.21708 −0.0768172
\(834\) 0 0
\(835\) −59.1423 −2.04670
\(836\) −1.66247 −0.0574977
\(837\) 0 0
\(838\) 29.3156 1.01269
\(839\) 47.8725 1.65274 0.826371 0.563126i \(-0.190401\pi\)
0.826371 + 0.563126i \(0.190401\pi\)
\(840\) 0 0
\(841\) −11.8759 −0.409515
\(842\) 36.6962 1.26463
\(843\) 0 0
\(844\) −5.21839 −0.179624
\(845\) −126.884 −4.36494
\(846\) 0 0
\(847\) −5.25775 −0.180658
\(848\) −4.08413 −0.140250
\(849\) 0 0
\(850\) −29.3108 −1.00535
\(851\) 41.6604 1.42810
\(852\) 0 0
\(853\) 8.81553 0.301838 0.150919 0.988546i \(-0.451777\pi\)
0.150919 + 0.988546i \(0.451777\pi\)
\(854\) 16.5350 0.565816
\(855\) 0 0
\(856\) −38.6318 −1.32041
\(857\) 20.5103 0.700617 0.350309 0.936634i \(-0.386077\pi\)
0.350309 + 0.936634i \(0.386077\pi\)
\(858\) 0 0
\(859\) −31.8746 −1.08755 −0.543774 0.839232i \(-0.683005\pi\)
−0.543774 + 0.839232i \(0.683005\pi\)
\(860\) −8.15917 −0.278225
\(861\) 0 0
\(862\) 24.5799 0.837194
\(863\) −11.0761 −0.377036 −0.188518 0.982070i \(-0.560368\pi\)
−0.188518 + 0.982070i \(0.560368\pi\)
\(864\) 0 0
\(865\) 22.8035 0.775341
\(866\) −33.9407 −1.15335
\(867\) 0 0
\(868\) 2.21040 0.0750259
\(869\) 7.22811 0.245197
\(870\) 0 0
\(871\) 5.74402 0.194629
\(872\) −2.09968 −0.0711043
\(873\) 0 0
\(874\) −20.3014 −0.686705
\(875\) −20.1243 −0.680326
\(876\) 0 0
\(877\) −11.3099 −0.381907 −0.190954 0.981599i \(-0.561158\pi\)
−0.190954 + 0.981599i \(0.561158\pi\)
\(878\) −42.0633 −1.41957
\(879\) 0 0
\(880\) 30.6652 1.03372
\(881\) −18.9516 −0.638497 −0.319249 0.947671i \(-0.603430\pi\)
−0.319249 + 0.947671i \(0.603430\pi\)
\(882\) 0 0
\(883\) −3.33386 −0.112193 −0.0560967 0.998425i \(-0.517866\pi\)
−0.0560967 + 0.998425i \(0.517866\pi\)
\(884\) 4.62889 0.155686
\(885\) 0 0
\(886\) −51.6077 −1.73379
\(887\) −29.6371 −0.995117 −0.497558 0.867431i \(-0.665770\pi\)
−0.497558 + 0.867431i \(0.665770\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 11.3516 0.380506
\(891\) 0 0
\(892\) 1.30908 0.0438311
\(893\) −19.8615 −0.664641
\(894\) 0 0
\(895\) 23.0559 0.770673
\(896\) 8.00928 0.267571
\(897\) 0 0
\(898\) 45.8263 1.52924
\(899\) −29.5778 −0.986475
\(900\) 0 0
\(901\) −2.75569 −0.0918054
\(902\) −13.0101 −0.433190
\(903\) 0 0
\(904\) −43.1462 −1.43502
\(905\) −56.1253 −1.86567
\(906\) 0 0
\(907\) −46.4626 −1.54276 −0.771382 0.636372i \(-0.780434\pi\)
−0.771382 + 0.636372i \(0.780434\pi\)
\(908\) 3.47141 0.115203
\(909\) 0 0
\(910\) −34.1886 −1.13334
\(911\) 47.3404 1.56846 0.784230 0.620471i \(-0.213058\pi\)
0.784230 + 0.620471i \(0.213058\pi\)
\(912\) 0 0
\(913\) 23.2896 0.770774
\(914\) 42.9548 1.42082
\(915\) 0 0
\(916\) −8.34293 −0.275658
\(917\) 20.2823 0.669780
\(918\) 0 0
\(919\) 56.6974 1.87028 0.935138 0.354285i \(-0.115276\pi\)
0.935138 + 0.354285i \(0.115276\pi\)
\(920\) −81.3855 −2.68320
\(921\) 0 0
\(922\) 44.7322 1.47318
\(923\) 74.7299 2.45976
\(924\) 0 0
\(925\) −60.8624 −2.00114
\(926\) −15.4519 −0.507781
\(927\) 0 0
\(928\) 7.17056 0.235385
\(929\) 2.96293 0.0972105 0.0486053 0.998818i \(-0.484522\pi\)
0.0486053 + 0.998818i \(0.484522\pi\)
\(930\) 0 0
\(931\) 2.24339 0.0735240
\(932\) −0.155716 −0.00510066
\(933\) 0 0
\(934\) 48.6780 1.59279
\(935\) 20.6908 0.676660
\(936\) 0 0
\(937\) 34.0156 1.11124 0.555621 0.831436i \(-0.312481\pi\)
0.555621 + 0.831436i \(0.312481\pi\)
\(938\) 1.10629 0.0361216
\(939\) 0 0
\(940\) −10.6628 −0.347783
\(941\) 2.00963 0.0655120 0.0327560 0.999463i \(-0.489572\pi\)
0.0327560 + 0.999463i \(0.489572\pi\)
\(942\) 0 0
\(943\) 29.0591 0.946295
\(944\) 2.64517 0.0860928
\(945\) 0 0
\(946\) −21.1088 −0.686307
\(947\) 46.6335 1.51538 0.757692 0.652612i \(-0.226327\pi\)
0.757692 + 0.652612i \(0.226327\pi\)
\(948\) 0 0
\(949\) −80.4289 −2.61083
\(950\) 29.6586 0.962253
\(951\) 0 0
\(952\) 6.65720 0.215761
\(953\) 22.7758 0.737780 0.368890 0.929473i \(-0.379738\pi\)
0.368890 + 0.929473i \(0.379738\pi\)
\(954\) 0 0
\(955\) 58.2144 1.88377
\(956\) −7.71664 −0.249574
\(957\) 0 0
\(958\) 27.3020 0.882086
\(959\) −3.96873 −0.128157
\(960\) 0 0
\(961\) 20.0887 0.648023
\(962\) −52.5495 −1.69427
\(963\) 0 0
\(964\) 2.93117 0.0944065
\(965\) −47.1816 −1.51883
\(966\) 0 0
\(967\) 29.5952 0.951718 0.475859 0.879521i \(-0.342137\pi\)
0.475859 + 0.879521i \(0.342137\pi\)
\(968\) 15.7874 0.507426
\(969\) 0 0
\(970\) 11.5089 0.369528
\(971\) 2.54430 0.0816504 0.0408252 0.999166i \(-0.487001\pi\)
0.0408252 + 0.999166i \(0.487001\pi\)
\(972\) 0 0
\(973\) 14.6292 0.468992
\(974\) 56.9480 1.82473
\(975\) 0 0
\(976\) −41.7844 −1.33749
\(977\) 18.9346 0.605772 0.302886 0.953027i \(-0.402050\pi\)
0.302886 + 0.953027i \(0.402050\pi\)
\(978\) 0 0
\(979\) −5.37159 −0.171677
\(980\) 1.20438 0.0384725
\(981\) 0 0
\(982\) 45.4612 1.45072
\(983\) 22.7616 0.725984 0.362992 0.931792i \(-0.381755\pi\)
0.362992 + 0.931792i \(0.381755\pi\)
\(984\) 0 0
\(985\) 77.0610 2.45537
\(986\) −11.9295 −0.379914
\(987\) 0 0
\(988\) −4.68382 −0.149012
\(989\) 47.1482 1.49922
\(990\) 0 0
\(991\) −25.0866 −0.796902 −0.398451 0.917190i \(-0.630452\pi\)
−0.398451 + 0.917190i \(0.630452\pi\)
\(992\) −12.3855 −0.393239
\(993\) 0 0
\(994\) 14.3928 0.456513
\(995\) 18.8453 0.597437
\(996\) 0 0
\(997\) 7.30016 0.231198 0.115599 0.993296i \(-0.463121\pi\)
0.115599 + 0.993296i \(0.463121\pi\)
\(998\) 33.7575 1.06858
\(999\) 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 \(a_p\))