Properties

Label 8001.2.a.v.1.6
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 1.6
Root \(1.49024\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.49024 q^{2}\) \(+0.220813 q^{4}\) \(-2.04744 q^{5}\) \(+1.00000 q^{7}\) \(+2.65141 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.49024 q^{2}\) \(+0.220813 q^{4}\) \(-2.04744 q^{5}\) \(+1.00000 q^{7}\) \(+2.65141 q^{8}\) \(+3.05118 q^{10}\) \(+1.77527 q^{11}\) \(-4.05756 q^{13}\) \(-1.49024 q^{14}\) \(-4.39287 q^{16}\) \(-7.64794 q^{17}\) \(+3.24885 q^{19}\) \(-0.452102 q^{20}\) \(-2.64557 q^{22}\) \(-6.77465 q^{23}\) \(-0.807977 q^{25}\) \(+6.04673 q^{26}\) \(+0.220813 q^{28}\) \(-6.90210 q^{29}\) \(-1.66081 q^{31}\) \(+1.24359 q^{32}\) \(+11.3973 q^{34}\) \(-2.04744 q^{35}\) \(+9.03684 q^{37}\) \(-4.84157 q^{38}\) \(-5.42862 q^{40}\) \(-9.40281 q^{41}\) \(+2.27572 q^{43}\) \(+0.392001 q^{44}\) \(+10.0958 q^{46}\) \(+1.14335 q^{47}\) \(+1.00000 q^{49}\) \(+1.20408 q^{50}\) \(-0.895961 q^{52}\) \(-0.909120 q^{53}\) \(-3.63476 q^{55}\) \(+2.65141 q^{56}\) \(+10.2858 q^{58}\) \(+0.510997 q^{59}\) \(-14.6668 q^{61}\) \(+2.47501 q^{62}\) \(+6.93248 q^{64}\) \(+8.30762 q^{65}\) \(-0.730117 q^{67}\) \(-1.68876 q^{68}\) \(+3.05118 q^{70}\) \(+2.37985 q^{71}\) \(+3.42990 q^{73}\) \(-13.4671 q^{74}\) \(+0.717389 q^{76}\) \(+1.77527 q^{77}\) \(-7.04927 q^{79}\) \(+8.99415 q^{80}\) \(+14.0124 q^{82}\) \(-1.32633 q^{83}\) \(+15.6587 q^{85}\) \(-3.39137 q^{86}\) \(+4.70696 q^{88}\) \(+3.63475 q^{89}\) \(-4.05756 q^{91}\) \(-1.49593 q^{92}\) \(-1.70387 q^{94}\) \(-6.65185 q^{95}\) \(-9.35645 q^{97}\) \(-1.49024 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49024 −1.05376 −0.526879 0.849940i \(-0.676638\pi\)
−0.526879 + 0.849940i \(0.676638\pi\)
\(3\) 0 0
\(4\) 0.220813 0.110406
\(5\) −2.04744 −0.915644 −0.457822 0.889044i \(-0.651370\pi\)
−0.457822 + 0.889044i \(0.651370\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.65141 0.937417
\(9\) 0 0
\(10\) 3.05118 0.964868
\(11\) 1.77527 0.535263 0.267631 0.963521i \(-0.413759\pi\)
0.267631 + 0.963521i \(0.413759\pi\)
\(12\) 0 0
\(13\) −4.05756 −1.12536 −0.562682 0.826673i \(-0.690231\pi\)
−0.562682 + 0.826673i \(0.690231\pi\)
\(14\) −1.49024 −0.398283
\(15\) 0 0
\(16\) −4.39287 −1.09822
\(17\) −7.64794 −1.85490 −0.927449 0.373949i \(-0.878004\pi\)
−0.927449 + 0.373949i \(0.878004\pi\)
\(18\) 0 0
\(19\) 3.24885 0.745338 0.372669 0.927964i \(-0.378443\pi\)
0.372669 + 0.927964i \(0.378443\pi\)
\(20\) −0.452102 −0.101093
\(21\) 0 0
\(22\) −2.64557 −0.564037
\(23\) −6.77465 −1.41261 −0.706306 0.707906i \(-0.749640\pi\)
−0.706306 + 0.707906i \(0.749640\pi\)
\(24\) 0 0
\(25\) −0.807977 −0.161595
\(26\) 6.04673 1.18586
\(27\) 0 0
\(28\) 0.220813 0.0417297
\(29\) −6.90210 −1.28169 −0.640844 0.767671i \(-0.721415\pi\)
−0.640844 + 0.767671i \(0.721415\pi\)
\(30\) 0 0
\(31\) −1.66081 −0.298291 −0.149145 0.988815i \(-0.547652\pi\)
−0.149145 + 0.988815i \(0.547652\pi\)
\(32\) 1.24359 0.219838
\(33\) 0 0
\(34\) 11.3973 1.95461
\(35\) −2.04744 −0.346081
\(36\) 0 0
\(37\) 9.03684 1.48565 0.742824 0.669487i \(-0.233486\pi\)
0.742824 + 0.669487i \(0.233486\pi\)
\(38\) −4.84157 −0.785406
\(39\) 0 0
\(40\) −5.42862 −0.858340
\(41\) −9.40281 −1.46847 −0.734236 0.678894i \(-0.762460\pi\)
−0.734236 + 0.678894i \(0.762460\pi\)
\(42\) 0 0
\(43\) 2.27572 0.347045 0.173522 0.984830i \(-0.444485\pi\)
0.173522 + 0.984830i \(0.444485\pi\)
\(44\) 0.392001 0.0590964
\(45\) 0 0
\(46\) 10.0958 1.48855
\(47\) 1.14335 0.166775 0.0833875 0.996517i \(-0.473426\pi\)
0.0833875 + 0.996517i \(0.473426\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.20408 0.170282
\(51\) 0 0
\(52\) −0.895961 −0.124247
\(53\) −0.909120 −0.124877 −0.0624386 0.998049i \(-0.519888\pi\)
−0.0624386 + 0.998049i \(0.519888\pi\)
\(54\) 0 0
\(55\) −3.63476 −0.490110
\(56\) 2.65141 0.354310
\(57\) 0 0
\(58\) 10.2858 1.35059
\(59\) 0.510997 0.0665261 0.0332631 0.999447i \(-0.489410\pi\)
0.0332631 + 0.999447i \(0.489410\pi\)
\(60\) 0 0
\(61\) −14.6668 −1.87789 −0.938943 0.344074i \(-0.888193\pi\)
−0.938943 + 0.344074i \(0.888193\pi\)
\(62\) 2.47501 0.314326
\(63\) 0 0
\(64\) 6.93248 0.866560
\(65\) 8.30762 1.03043
\(66\) 0 0
\(67\) −0.730117 −0.0891980 −0.0445990 0.999005i \(-0.514201\pi\)
−0.0445990 + 0.999005i \(0.514201\pi\)
\(68\) −1.68876 −0.204793
\(69\) 0 0
\(70\) 3.05118 0.364686
\(71\) 2.37985 0.282437 0.141218 0.989978i \(-0.454898\pi\)
0.141218 + 0.989978i \(0.454898\pi\)
\(72\) 0 0
\(73\) 3.42990 0.401439 0.200720 0.979649i \(-0.435672\pi\)
0.200720 + 0.979649i \(0.435672\pi\)
\(74\) −13.4671 −1.56551
\(75\) 0 0
\(76\) 0.717389 0.0822901
\(77\) 1.77527 0.202310
\(78\) 0 0
\(79\) −7.04927 −0.793104 −0.396552 0.918012i \(-0.629793\pi\)
−0.396552 + 0.918012i \(0.629793\pi\)
\(80\) 8.99415 1.00558
\(81\) 0 0
\(82\) 14.0124 1.54741
\(83\) −1.32633 −0.145584 −0.0727920 0.997347i \(-0.523191\pi\)
−0.0727920 + 0.997347i \(0.523191\pi\)
\(84\) 0 0
\(85\) 15.6587 1.69843
\(86\) −3.39137 −0.365701
\(87\) 0 0
\(88\) 4.70696 0.501764
\(89\) 3.63475 0.385283 0.192641 0.981269i \(-0.438295\pi\)
0.192641 + 0.981269i \(0.438295\pi\)
\(90\) 0 0
\(91\) −4.05756 −0.425348
\(92\) −1.49593 −0.155961
\(93\) 0 0
\(94\) −1.70387 −0.175741
\(95\) −6.65185 −0.682465
\(96\) 0 0
\(97\) −9.35645 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(98\) −1.49024 −0.150537
\(99\) 0 0
\(100\) −0.178412 −0.0178412
\(101\) −1.21116 −0.120515 −0.0602573 0.998183i \(-0.519192\pi\)
−0.0602573 + 0.998183i \(0.519192\pi\)
\(102\) 0 0
\(103\) −8.69531 −0.856774 −0.428387 0.903595i \(-0.640918\pi\)
−0.428387 + 0.903595i \(0.640918\pi\)
\(104\) −10.7583 −1.05494
\(105\) 0 0
\(106\) 1.35481 0.131590
\(107\) 17.3884 1.68100 0.840499 0.541813i \(-0.182262\pi\)
0.840499 + 0.541813i \(0.182262\pi\)
\(108\) 0 0
\(109\) 13.0624 1.25115 0.625576 0.780164i \(-0.284864\pi\)
0.625576 + 0.780164i \(0.284864\pi\)
\(110\) 5.41665 0.516458
\(111\) 0 0
\(112\) −4.39287 −0.415087
\(113\) 12.6936 1.19411 0.597057 0.802199i \(-0.296337\pi\)
0.597057 + 0.802199i \(0.296337\pi\)
\(114\) 0 0
\(115\) 13.8707 1.29345
\(116\) −1.52407 −0.141506
\(117\) 0 0
\(118\) −0.761508 −0.0701025
\(119\) −7.64794 −0.701086
\(120\) 0 0
\(121\) −7.84843 −0.713494
\(122\) 21.8570 1.97884
\(123\) 0 0
\(124\) −0.366729 −0.0329332
\(125\) 11.8915 1.06361
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −12.8182 −1.13298
\(129\) 0 0
\(130\) −12.3803 −1.08583
\(131\) 10.1857 0.889928 0.444964 0.895548i \(-0.353216\pi\)
0.444964 + 0.895548i \(0.353216\pi\)
\(132\) 0 0
\(133\) 3.24885 0.281711
\(134\) 1.08805 0.0939931
\(135\) 0 0
\(136\) −20.2779 −1.73881
\(137\) −5.48349 −0.468486 −0.234243 0.972178i \(-0.575261\pi\)
−0.234243 + 0.972178i \(0.575261\pi\)
\(138\) 0 0
\(139\) −9.95792 −0.844620 −0.422310 0.906451i \(-0.638781\pi\)
−0.422310 + 0.906451i \(0.638781\pi\)
\(140\) −0.452102 −0.0382096
\(141\) 0 0
\(142\) −3.54655 −0.297620
\(143\) −7.20324 −0.602366
\(144\) 0 0
\(145\) 14.1317 1.17357
\(146\) −5.11137 −0.423020
\(147\) 0 0
\(148\) 1.99545 0.164025
\(149\) 4.47456 0.366571 0.183285 0.983060i \(-0.441327\pi\)
0.183285 + 0.983060i \(0.441327\pi\)
\(150\) 0 0
\(151\) −14.0817 −1.14595 −0.572977 0.819571i \(-0.694212\pi\)
−0.572977 + 0.819571i \(0.694212\pi\)
\(152\) 8.61406 0.698693
\(153\) 0 0
\(154\) −2.64557 −0.213186
\(155\) 3.40042 0.273128
\(156\) 0 0
\(157\) −5.58675 −0.445871 −0.222936 0.974833i \(-0.571564\pi\)
−0.222936 + 0.974833i \(0.571564\pi\)
\(158\) 10.5051 0.835740
\(159\) 0 0
\(160\) −2.54619 −0.201294
\(161\) −6.77465 −0.533917
\(162\) 0 0
\(163\) −12.1815 −0.954127 −0.477064 0.878869i \(-0.658299\pi\)
−0.477064 + 0.878869i \(0.658299\pi\)
\(164\) −2.07626 −0.162129
\(165\) 0 0
\(166\) 1.97655 0.153410
\(167\) −6.23754 −0.482676 −0.241338 0.970441i \(-0.577586\pi\)
−0.241338 + 0.970441i \(0.577586\pi\)
\(168\) 0 0
\(169\) 3.46378 0.266445
\(170\) −23.3353 −1.78973
\(171\) 0 0
\(172\) 0.502509 0.0383159
\(173\) 13.5405 1.02946 0.514731 0.857352i \(-0.327892\pi\)
0.514731 + 0.857352i \(0.327892\pi\)
\(174\) 0 0
\(175\) −0.807977 −0.0610773
\(176\) −7.79851 −0.587834
\(177\) 0 0
\(178\) −5.41664 −0.405995
\(179\) −10.0729 −0.752887 −0.376443 0.926440i \(-0.622853\pi\)
−0.376443 + 0.926440i \(0.622853\pi\)
\(180\) 0 0
\(181\) 15.0581 1.11926 0.559630 0.828742i \(-0.310943\pi\)
0.559630 + 0.828742i \(0.310943\pi\)
\(182\) 6.04673 0.448214
\(183\) 0 0
\(184\) −17.9624 −1.32421
\(185\) −18.5024 −1.36032
\(186\) 0 0
\(187\) −13.5771 −0.992858
\(188\) 0.252467 0.0184130
\(189\) 0 0
\(190\) 9.91284 0.719153
\(191\) −4.76684 −0.344916 −0.172458 0.985017i \(-0.555171\pi\)
−0.172458 + 0.985017i \(0.555171\pi\)
\(192\) 0 0
\(193\) −7.71655 −0.555449 −0.277725 0.960661i \(-0.589580\pi\)
−0.277725 + 0.960661i \(0.589580\pi\)
\(194\) 13.9434 1.00107
\(195\) 0 0
\(196\) 0.220813 0.0157723
\(197\) 2.00654 0.142960 0.0714799 0.997442i \(-0.477228\pi\)
0.0714799 + 0.997442i \(0.477228\pi\)
\(198\) 0 0
\(199\) 11.5326 0.817525 0.408762 0.912641i \(-0.365960\pi\)
0.408762 + 0.912641i \(0.365960\pi\)
\(200\) −2.14228 −0.151482
\(201\) 0 0
\(202\) 1.80491 0.126993
\(203\) −6.90210 −0.484432
\(204\) 0 0
\(205\) 19.2517 1.34460
\(206\) 12.9581 0.902833
\(207\) 0 0
\(208\) 17.8243 1.23589
\(209\) 5.76758 0.398952
\(210\) 0 0
\(211\) 20.5078 1.41181 0.705906 0.708306i \(-0.250540\pi\)
0.705906 + 0.708306i \(0.250540\pi\)
\(212\) −0.200745 −0.0137872
\(213\) 0 0
\(214\) −25.9129 −1.77137
\(215\) −4.65942 −0.317769
\(216\) 0 0
\(217\) −1.66081 −0.112743
\(218\) −19.4661 −1.31841
\(219\) 0 0
\(220\) −0.802600 −0.0541113
\(221\) 31.0320 2.08744
\(222\) 0 0
\(223\) −1.44549 −0.0967969 −0.0483985 0.998828i \(-0.515412\pi\)
−0.0483985 + 0.998828i \(0.515412\pi\)
\(224\) 1.24359 0.0830911
\(225\) 0 0
\(226\) −18.9165 −1.25831
\(227\) −23.4362 −1.55551 −0.777757 0.628565i \(-0.783643\pi\)
−0.777757 + 0.628565i \(0.783643\pi\)
\(228\) 0 0
\(229\) 17.5045 1.15673 0.578364 0.815779i \(-0.303691\pi\)
0.578364 + 0.815779i \(0.303691\pi\)
\(230\) −20.6707 −1.36298
\(231\) 0 0
\(232\) −18.3003 −1.20147
\(233\) −24.5272 −1.60683 −0.803415 0.595419i \(-0.796986\pi\)
−0.803415 + 0.595419i \(0.796986\pi\)
\(234\) 0 0
\(235\) −2.34095 −0.152707
\(236\) 0.112835 0.00734491
\(237\) 0 0
\(238\) 11.3973 0.738775
\(239\) −12.9074 −0.834908 −0.417454 0.908698i \(-0.637077\pi\)
−0.417454 + 0.908698i \(0.637077\pi\)
\(240\) 0 0
\(241\) −17.5870 −1.13288 −0.566440 0.824103i \(-0.691680\pi\)
−0.566440 + 0.824103i \(0.691680\pi\)
\(242\) 11.6960 0.751850
\(243\) 0 0
\(244\) −3.23861 −0.207330
\(245\) −2.04744 −0.130806
\(246\) 0 0
\(247\) −13.1824 −0.838777
\(248\) −4.40350 −0.279623
\(249\) 0 0
\(250\) −17.7212 −1.12079
\(251\) −10.2258 −0.645445 −0.322722 0.946494i \(-0.604598\pi\)
−0.322722 + 0.946494i \(0.604598\pi\)
\(252\) 0 0
\(253\) −12.0268 −0.756119
\(254\) −1.49024 −0.0935059
\(255\) 0 0
\(256\) 5.23728 0.327330
\(257\) −13.1251 −0.818723 −0.409361 0.912372i \(-0.634248\pi\)
−0.409361 + 0.912372i \(0.634248\pi\)
\(258\) 0 0
\(259\) 9.03684 0.561522
\(260\) 1.83443 0.113766
\(261\) 0 0
\(262\) −15.1791 −0.937769
\(263\) 6.65987 0.410665 0.205333 0.978692i \(-0.434172\pi\)
0.205333 + 0.978692i \(0.434172\pi\)
\(264\) 0 0
\(265\) 1.86137 0.114343
\(266\) −4.84157 −0.296856
\(267\) 0 0
\(268\) −0.161219 −0.00984802
\(269\) −7.74043 −0.471942 −0.235971 0.971760i \(-0.575827\pi\)
−0.235971 + 0.971760i \(0.575827\pi\)
\(270\) 0 0
\(271\) 6.03897 0.366842 0.183421 0.983034i \(-0.441283\pi\)
0.183421 + 0.983034i \(0.441283\pi\)
\(272\) 33.5964 2.03708
\(273\) 0 0
\(274\) 8.17171 0.493671
\(275\) −1.43437 −0.0864959
\(276\) 0 0
\(277\) −22.9334 −1.37794 −0.688968 0.724792i \(-0.741936\pi\)
−0.688968 + 0.724792i \(0.741936\pi\)
\(278\) 14.8397 0.890025
\(279\) 0 0
\(280\) −5.42862 −0.324422
\(281\) 25.2804 1.50810 0.754052 0.656814i \(-0.228096\pi\)
0.754052 + 0.656814i \(0.228096\pi\)
\(282\) 0 0
\(283\) −13.0595 −0.776308 −0.388154 0.921594i \(-0.626887\pi\)
−0.388154 + 0.921594i \(0.626887\pi\)
\(284\) 0.525502 0.0311828
\(285\) 0 0
\(286\) 10.7346 0.634748
\(287\) −9.40281 −0.555030
\(288\) 0 0
\(289\) 41.4910 2.44065
\(290\) −21.0595 −1.23666
\(291\) 0 0
\(292\) 0.757366 0.0443215
\(293\) 3.00348 0.175465 0.0877327 0.996144i \(-0.472038\pi\)
0.0877327 + 0.996144i \(0.472038\pi\)
\(294\) 0 0
\(295\) −1.04624 −0.0609143
\(296\) 23.9604 1.39267
\(297\) 0 0
\(298\) −6.66817 −0.386277
\(299\) 27.4885 1.58970
\(300\) 0 0
\(301\) 2.27572 0.131171
\(302\) 20.9851 1.20756
\(303\) 0 0
\(304\) −14.2718 −0.818543
\(305\) 30.0293 1.71947
\(306\) 0 0
\(307\) 2.33304 0.133153 0.0665767 0.997781i \(-0.478792\pi\)
0.0665767 + 0.997781i \(0.478792\pi\)
\(308\) 0.392001 0.0223363
\(309\) 0 0
\(310\) −5.06744 −0.287811
\(311\) 0.675512 0.0383047 0.0191524 0.999817i \(-0.493903\pi\)
0.0191524 + 0.999817i \(0.493903\pi\)
\(312\) 0 0
\(313\) −6.63228 −0.374879 −0.187439 0.982276i \(-0.560019\pi\)
−0.187439 + 0.982276i \(0.560019\pi\)
\(314\) 8.32560 0.469841
\(315\) 0 0
\(316\) −1.55657 −0.0875638
\(317\) 4.68652 0.263221 0.131611 0.991301i \(-0.457985\pi\)
0.131611 + 0.991301i \(0.457985\pi\)
\(318\) 0 0
\(319\) −12.2531 −0.686039
\(320\) −14.1939 −0.793461
\(321\) 0 0
\(322\) 10.0958 0.562620
\(323\) −24.8471 −1.38253
\(324\) 0 0
\(325\) 3.27841 0.181854
\(326\) 18.1533 1.00542
\(327\) 0 0
\(328\) −24.9308 −1.37657
\(329\) 1.14335 0.0630350
\(330\) 0 0
\(331\) −6.07509 −0.333917 −0.166959 0.985964i \(-0.553395\pi\)
−0.166959 + 0.985964i \(0.553395\pi\)
\(332\) −0.292871 −0.0160734
\(333\) 0 0
\(334\) 9.29543 0.508623
\(335\) 1.49487 0.0816736
\(336\) 0 0
\(337\) 5.31829 0.289706 0.144853 0.989453i \(-0.453729\pi\)
0.144853 + 0.989453i \(0.453729\pi\)
\(338\) −5.16187 −0.280769
\(339\) 0 0
\(340\) 3.45765 0.187517
\(341\) −2.94838 −0.159664
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 6.03389 0.325325
\(345\) 0 0
\(346\) −20.1785 −1.08480
\(347\) 14.5110 0.778993 0.389496 0.921028i \(-0.372649\pi\)
0.389496 + 0.921028i \(0.372649\pi\)
\(348\) 0 0
\(349\) 19.6940 1.05419 0.527097 0.849805i \(-0.323281\pi\)
0.527097 + 0.849805i \(0.323281\pi\)
\(350\) 1.20408 0.0643607
\(351\) 0 0
\(352\) 2.20771 0.117671
\(353\) −17.7743 −0.946033 −0.473016 0.881054i \(-0.656835\pi\)
−0.473016 + 0.881054i \(0.656835\pi\)
\(354\) 0 0
\(355\) −4.87262 −0.258612
\(356\) 0.802599 0.0425376
\(357\) 0 0
\(358\) 15.0111 0.793360
\(359\) 14.7077 0.776245 0.388123 0.921608i \(-0.373124\pi\)
0.388123 + 0.921608i \(0.373124\pi\)
\(360\) 0 0
\(361\) −8.44494 −0.444471
\(362\) −22.4402 −1.17943
\(363\) 0 0
\(364\) −0.895961 −0.0469611
\(365\) −7.02252 −0.367576
\(366\) 0 0
\(367\) −13.9272 −0.726995 −0.363498 0.931595i \(-0.618417\pi\)
−0.363498 + 0.931595i \(0.618417\pi\)
\(368\) 29.7601 1.55135
\(369\) 0 0
\(370\) 27.5730 1.43345
\(371\) −0.909120 −0.0471991
\(372\) 0 0
\(373\) 29.6120 1.53325 0.766627 0.642093i \(-0.221934\pi\)
0.766627 + 0.642093i \(0.221934\pi\)
\(374\) 20.2332 1.04623
\(375\) 0 0
\(376\) 3.03150 0.156338
\(377\) 28.0057 1.44237
\(378\) 0 0
\(379\) −16.3108 −0.837829 −0.418914 0.908026i \(-0.637589\pi\)
−0.418914 + 0.908026i \(0.637589\pi\)
\(380\) −1.46881 −0.0753485
\(381\) 0 0
\(382\) 7.10373 0.363458
\(383\) 30.7897 1.57328 0.786640 0.617412i \(-0.211819\pi\)
0.786640 + 0.617412i \(0.211819\pi\)
\(384\) 0 0
\(385\) −3.63476 −0.185244
\(386\) 11.4995 0.585309
\(387\) 0 0
\(388\) −2.06602 −0.104886
\(389\) −3.20667 −0.162585 −0.0812923 0.996690i \(-0.525905\pi\)
−0.0812923 + 0.996690i \(0.525905\pi\)
\(390\) 0 0
\(391\) 51.8121 2.62025
\(392\) 2.65141 0.133917
\(393\) 0 0
\(394\) −2.99022 −0.150645
\(395\) 14.4330 0.726202
\(396\) 0 0
\(397\) 34.4082 1.72690 0.863449 0.504435i \(-0.168299\pi\)
0.863449 + 0.504435i \(0.168299\pi\)
\(398\) −17.1863 −0.861474
\(399\) 0 0
\(400\) 3.54933 0.177467
\(401\) 6.69898 0.334531 0.167266 0.985912i \(-0.446506\pi\)
0.167266 + 0.985912i \(0.446506\pi\)
\(402\) 0 0
\(403\) 6.73884 0.335686
\(404\) −0.267439 −0.0133056
\(405\) 0 0
\(406\) 10.2858 0.510474
\(407\) 16.0428 0.795212
\(408\) 0 0
\(409\) −28.8318 −1.42564 −0.712820 0.701347i \(-0.752582\pi\)
−0.712820 + 0.701347i \(0.752582\pi\)
\(410\) −28.6897 −1.41688
\(411\) 0 0
\(412\) −1.92003 −0.0945933
\(413\) 0.510997 0.0251445
\(414\) 0 0
\(415\) 2.71559 0.133303
\(416\) −5.04595 −0.247398
\(417\) 0 0
\(418\) −8.59507 −0.420399
\(419\) −26.8706 −1.31272 −0.656358 0.754450i \(-0.727904\pi\)
−0.656358 + 0.754450i \(0.727904\pi\)
\(420\) 0 0
\(421\) 35.8612 1.74777 0.873884 0.486135i \(-0.161594\pi\)
0.873884 + 0.486135i \(0.161594\pi\)
\(422\) −30.5615 −1.48771
\(423\) 0 0
\(424\) −2.41045 −0.117062
\(425\) 6.17936 0.299743
\(426\) 0 0
\(427\) −14.6668 −0.709774
\(428\) 3.83958 0.185593
\(429\) 0 0
\(430\) 6.94364 0.334852
\(431\) 25.9119 1.24813 0.624066 0.781372i \(-0.285480\pi\)
0.624066 + 0.781372i \(0.285480\pi\)
\(432\) 0 0
\(433\) 17.2601 0.829468 0.414734 0.909943i \(-0.363875\pi\)
0.414734 + 0.909943i \(0.363875\pi\)
\(434\) 2.47501 0.118804
\(435\) 0 0
\(436\) 2.88434 0.138135
\(437\) −22.0099 −1.05287
\(438\) 0 0
\(439\) 32.7590 1.56350 0.781752 0.623590i \(-0.214327\pi\)
0.781752 + 0.623590i \(0.214327\pi\)
\(440\) −9.63724 −0.459438
\(441\) 0 0
\(442\) −46.2451 −2.19965
\(443\) 25.1899 1.19681 0.598404 0.801195i \(-0.295802\pi\)
0.598404 + 0.801195i \(0.295802\pi\)
\(444\) 0 0
\(445\) −7.44194 −0.352782
\(446\) 2.15412 0.102001
\(447\) 0 0
\(448\) 6.93248 0.327529
\(449\) 38.5015 1.81700 0.908500 0.417885i \(-0.137229\pi\)
0.908500 + 0.417885i \(0.137229\pi\)
\(450\) 0 0
\(451\) −16.6925 −0.786018
\(452\) 2.80291 0.131838
\(453\) 0 0
\(454\) 34.9255 1.63914
\(455\) 8.30762 0.389467
\(456\) 0 0
\(457\) −23.8848 −1.11729 −0.558643 0.829408i \(-0.688678\pi\)
−0.558643 + 0.829408i \(0.688678\pi\)
\(458\) −26.0859 −1.21891
\(459\) 0 0
\(460\) 3.06283 0.142805
\(461\) 22.5033 1.04808 0.524041 0.851693i \(-0.324424\pi\)
0.524041 + 0.851693i \(0.324424\pi\)
\(462\) 0 0
\(463\) −7.25600 −0.337215 −0.168607 0.985683i \(-0.553927\pi\)
−0.168607 + 0.985683i \(0.553927\pi\)
\(464\) 30.3200 1.40757
\(465\) 0 0
\(466\) 36.5514 1.69321
\(467\) 3.02312 0.139893 0.0699465 0.997551i \(-0.477717\pi\)
0.0699465 + 0.997551i \(0.477717\pi\)
\(468\) 0 0
\(469\) −0.730117 −0.0337137
\(470\) 3.48857 0.160916
\(471\) 0 0
\(472\) 1.35486 0.0623627
\(473\) 4.04001 0.185760
\(474\) 0 0
\(475\) −2.62500 −0.120443
\(476\) −1.68876 −0.0774043
\(477\) 0 0
\(478\) 19.2351 0.879791
\(479\) −12.8660 −0.587862 −0.293931 0.955827i \(-0.594964\pi\)
−0.293931 + 0.955827i \(0.594964\pi\)
\(480\) 0 0
\(481\) −36.6675 −1.67189
\(482\) 26.2089 1.19378
\(483\) 0 0
\(484\) −1.73303 −0.0787743
\(485\) 19.1568 0.869866
\(486\) 0 0
\(487\) −38.6527 −1.75152 −0.875761 0.482745i \(-0.839640\pi\)
−0.875761 + 0.482745i \(0.839640\pi\)
\(488\) −38.8876 −1.76036
\(489\) 0 0
\(490\) 3.05118 0.137838
\(491\) 17.5142 0.790404 0.395202 0.918594i \(-0.370675\pi\)
0.395202 + 0.918594i \(0.370675\pi\)
\(492\) 0 0
\(493\) 52.7869 2.37740
\(494\) 19.6450 0.883868
\(495\) 0 0
\(496\) 7.29573 0.327588
\(497\) 2.37985 0.106751
\(498\) 0 0
\(499\) 8.34272 0.373471 0.186736 0.982410i \(-0.440209\pi\)
0.186736 + 0.982410i \(0.440209\pi\)
\(500\) 2.62580 0.117429
\(501\) 0 0
\(502\) 15.2388 0.680143
\(503\) 20.6604 0.921203 0.460602 0.887607i \(-0.347634\pi\)
0.460602 + 0.887607i \(0.347634\pi\)
\(504\) 0 0
\(505\) 2.47977 0.110349
\(506\) 17.9228 0.796766
\(507\) 0 0
\(508\) 0.220813 0.00979698
\(509\) 23.3833 1.03644 0.518222 0.855246i \(-0.326594\pi\)
0.518222 + 0.855246i \(0.326594\pi\)
\(510\) 0 0
\(511\) 3.42990 0.151730
\(512\) 17.8317 0.788056
\(513\) 0 0
\(514\) 19.5596 0.862736
\(515\) 17.8031 0.784500
\(516\) 0 0
\(517\) 2.02975 0.0892684
\(518\) −13.4671 −0.591708
\(519\) 0 0
\(520\) 22.0269 0.965946
\(521\) −17.6114 −0.771568 −0.385784 0.922589i \(-0.626069\pi\)
−0.385784 + 0.922589i \(0.626069\pi\)
\(522\) 0 0
\(523\) −26.6248 −1.16422 −0.582110 0.813110i \(-0.697773\pi\)
−0.582110 + 0.813110i \(0.697773\pi\)
\(524\) 2.24913 0.0982538
\(525\) 0 0
\(526\) −9.92481 −0.432742
\(527\) 12.7018 0.553299
\(528\) 0 0
\(529\) 22.8959 0.995474
\(530\) −2.77389 −0.120490
\(531\) 0 0
\(532\) 0.717389 0.0311027
\(533\) 38.1525 1.65257
\(534\) 0 0
\(535\) −35.6017 −1.53920
\(536\) −1.93584 −0.0836157
\(537\) 0 0
\(538\) 11.5351 0.497313
\(539\) 1.77527 0.0764661
\(540\) 0 0
\(541\) 27.4985 1.18225 0.591126 0.806579i \(-0.298684\pi\)
0.591126 + 0.806579i \(0.298684\pi\)
\(542\) −8.99952 −0.386562
\(543\) 0 0
\(544\) −9.51094 −0.407778
\(545\) −26.7445 −1.14561
\(546\) 0 0
\(547\) 10.0299 0.428846 0.214423 0.976741i \(-0.431213\pi\)
0.214423 + 0.976741i \(0.431213\pi\)
\(548\) −1.21082 −0.0517239
\(549\) 0 0
\(550\) 2.13756 0.0911458
\(551\) −22.4239 −0.955291
\(552\) 0 0
\(553\) −7.04927 −0.299765
\(554\) 34.1763 1.45201
\(555\) 0 0
\(556\) −2.19884 −0.0932514
\(557\) 32.2636 1.36705 0.683527 0.729925i \(-0.260445\pi\)
0.683527 + 0.729925i \(0.260445\pi\)
\(558\) 0 0
\(559\) −9.23388 −0.390552
\(560\) 8.99415 0.380072
\(561\) 0 0
\(562\) −37.6739 −1.58918
\(563\) −5.87677 −0.247676 −0.123838 0.992302i \(-0.539520\pi\)
−0.123838 + 0.992302i \(0.539520\pi\)
\(564\) 0 0
\(565\) −25.9894 −1.09338
\(566\) 19.4618 0.818041
\(567\) 0 0
\(568\) 6.30998 0.264761
\(569\) 33.2432 1.39363 0.696813 0.717253i \(-0.254601\pi\)
0.696813 + 0.717253i \(0.254601\pi\)
\(570\) 0 0
\(571\) 43.6479 1.82661 0.913305 0.407277i \(-0.133522\pi\)
0.913305 + 0.407277i \(0.133522\pi\)
\(572\) −1.59057 −0.0665050
\(573\) 0 0
\(574\) 14.0124 0.584868
\(575\) 5.47376 0.228272
\(576\) 0 0
\(577\) −11.2681 −0.469099 −0.234549 0.972104i \(-0.575361\pi\)
−0.234549 + 0.972104i \(0.575361\pi\)
\(578\) −61.8316 −2.57185
\(579\) 0 0
\(580\) 3.12045 0.129570
\(581\) −1.32633 −0.0550256
\(582\) 0 0
\(583\) −1.61393 −0.0668421
\(584\) 9.09409 0.376316
\(585\) 0 0
\(586\) −4.47591 −0.184898
\(587\) 11.3396 0.468037 0.234018 0.972232i \(-0.424812\pi\)
0.234018 + 0.972232i \(0.424812\pi\)
\(588\) 0 0
\(589\) −5.39574 −0.222328
\(590\) 1.55914 0.0641889
\(591\) 0 0
\(592\) −39.6976 −1.63156
\(593\) −12.6697 −0.520283 −0.260141 0.965571i \(-0.583769\pi\)
−0.260141 + 0.965571i \(0.583769\pi\)
\(594\) 0 0
\(595\) 15.6587 0.641945
\(596\) 0.988041 0.0404717
\(597\) 0 0
\(598\) −40.9645 −1.67516
\(599\) −11.1486 −0.455520 −0.227760 0.973717i \(-0.573140\pi\)
−0.227760 + 0.973717i \(0.573140\pi\)
\(600\) 0 0
\(601\) 35.8081 1.46064 0.730322 0.683104i \(-0.239370\pi\)
0.730322 + 0.683104i \(0.239370\pi\)
\(602\) −3.39137 −0.138222
\(603\) 0 0
\(604\) −3.10942 −0.126521
\(605\) 16.0692 0.653307
\(606\) 0 0
\(607\) −5.95533 −0.241719 −0.120860 0.992670i \(-0.538565\pi\)
−0.120860 + 0.992670i \(0.538565\pi\)
\(608\) 4.04026 0.163854
\(609\) 0 0
\(610\) −44.7509 −1.81191
\(611\) −4.63922 −0.187683
\(612\) 0 0
\(613\) 17.0813 0.689908 0.344954 0.938620i \(-0.387894\pi\)
0.344954 + 0.938620i \(0.387894\pi\)
\(614\) −3.47678 −0.140311
\(615\) 0 0
\(616\) 4.70696 0.189649
\(617\) −23.2365 −0.935465 −0.467732 0.883870i \(-0.654929\pi\)
−0.467732 + 0.883870i \(0.654929\pi\)
\(618\) 0 0
\(619\) −48.1408 −1.93494 −0.967470 0.252984i \(-0.918588\pi\)
−0.967470 + 0.252984i \(0.918588\pi\)
\(620\) 0.750856 0.0301551
\(621\) 0 0
\(622\) −1.00667 −0.0403639
\(623\) 3.63475 0.145623
\(624\) 0 0
\(625\) −20.3073 −0.812292
\(626\) 9.88369 0.395032
\(627\) 0 0
\(628\) −1.23363 −0.0492270
\(629\) −69.1132 −2.75573
\(630\) 0 0
\(631\) −18.0853 −0.719963 −0.359982 0.932959i \(-0.617217\pi\)
−0.359982 + 0.932959i \(0.617217\pi\)
\(632\) −18.6905 −0.743469
\(633\) 0 0
\(634\) −6.98403 −0.277371
\(635\) −2.04744 −0.0812503
\(636\) 0 0
\(637\) −4.05756 −0.160766
\(638\) 18.2600 0.722920
\(639\) 0 0
\(640\) 26.2446 1.03741
\(641\) 12.7420 0.503280 0.251640 0.967821i \(-0.419030\pi\)
0.251640 + 0.967821i \(0.419030\pi\)
\(642\) 0 0
\(643\) −4.19773 −0.165542 −0.0827712 0.996569i \(-0.526377\pi\)
−0.0827712 + 0.996569i \(0.526377\pi\)
\(644\) −1.49593 −0.0589479
\(645\) 0 0
\(646\) 37.0281 1.45685
\(647\) 21.9409 0.862587 0.431293 0.902212i \(-0.358057\pi\)
0.431293 + 0.902212i \(0.358057\pi\)
\(648\) 0 0
\(649\) 0.907155 0.0356090
\(650\) −4.88562 −0.191630
\(651\) 0 0
\(652\) −2.68983 −0.105342
\(653\) 1.77511 0.0694654 0.0347327 0.999397i \(-0.488942\pi\)
0.0347327 + 0.999397i \(0.488942\pi\)
\(654\) 0 0
\(655\) −20.8546 −0.814858
\(656\) 41.3053 1.61270
\(657\) 0 0
\(658\) −1.70387 −0.0664237
\(659\) 14.8065 0.576780 0.288390 0.957513i \(-0.406880\pi\)
0.288390 + 0.957513i \(0.406880\pi\)
\(660\) 0 0
\(661\) −22.5004 −0.875164 −0.437582 0.899179i \(-0.644165\pi\)
−0.437582 + 0.899179i \(0.644165\pi\)
\(662\) 9.05334 0.351868
\(663\) 0 0
\(664\) −3.51666 −0.136473
\(665\) −6.65185 −0.257947
\(666\) 0 0
\(667\) 46.7593 1.81053
\(668\) −1.37733 −0.0532905
\(669\) 0 0
\(670\) −2.22772 −0.0860643
\(671\) −26.0374 −1.00516
\(672\) 0 0
\(673\) 32.2028 1.24133 0.620663 0.784077i \(-0.286864\pi\)
0.620663 + 0.784077i \(0.286864\pi\)
\(674\) −7.92553 −0.305280
\(675\) 0 0
\(676\) 0.764848 0.0294172
\(677\) −38.5853 −1.48296 −0.741478 0.670978i \(-0.765875\pi\)
−0.741478 + 0.670978i \(0.765875\pi\)
\(678\) 0 0
\(679\) −9.35645 −0.359068
\(680\) 41.5178 1.59213
\(681\) 0 0
\(682\) 4.39380 0.168247
\(683\) −37.7291 −1.44366 −0.721831 0.692069i \(-0.756699\pi\)
−0.721831 + 0.692069i \(0.756699\pi\)
\(684\) 0 0
\(685\) 11.2271 0.428967
\(686\) −1.49024 −0.0568976
\(687\) 0 0
\(688\) −9.99695 −0.381130
\(689\) 3.68881 0.140532
\(690\) 0 0
\(691\) 40.9255 1.55688 0.778439 0.627720i \(-0.216012\pi\)
0.778439 + 0.627720i \(0.216012\pi\)
\(692\) 2.98991 0.113659
\(693\) 0 0
\(694\) −21.6249 −0.820870
\(695\) 20.3883 0.773372
\(696\) 0 0
\(697\) 71.9122 2.72387
\(698\) −29.3487 −1.11087
\(699\) 0 0
\(700\) −0.178412 −0.00674332
\(701\) −18.9250 −0.714788 −0.357394 0.933954i \(-0.616335\pi\)
−0.357394 + 0.933954i \(0.616335\pi\)
\(702\) 0 0
\(703\) 29.3594 1.10731
\(704\) 12.3070 0.463837
\(705\) 0 0
\(706\) 26.4880 0.996890
\(707\) −1.21116 −0.0455502
\(708\) 0 0
\(709\) −9.73734 −0.365693 −0.182847 0.983141i \(-0.558531\pi\)
−0.182847 + 0.983141i \(0.558531\pi\)
\(710\) 7.26136 0.272514
\(711\) 0 0
\(712\) 9.63722 0.361170
\(713\) 11.2514 0.421369
\(714\) 0 0
\(715\) 14.7482 0.551553
\(716\) −2.22423 −0.0831235
\(717\) 0 0
\(718\) −21.9181 −0.817975
\(719\) 33.4897 1.24896 0.624478 0.781042i \(-0.285312\pi\)
0.624478 + 0.781042i \(0.285312\pi\)
\(720\) 0 0
\(721\) −8.69531 −0.323830
\(722\) 12.5850 0.468365
\(723\) 0 0
\(724\) 3.32502 0.123574
\(725\) 5.57673 0.207115
\(726\) 0 0
\(727\) 7.63222 0.283063 0.141532 0.989934i \(-0.454797\pi\)
0.141532 + 0.989934i \(0.454797\pi\)
\(728\) −10.7583 −0.398728
\(729\) 0 0
\(730\) 10.4652 0.387336
\(731\) −17.4046 −0.643733
\(732\) 0 0
\(733\) 41.0907 1.51772 0.758859 0.651254i \(-0.225757\pi\)
0.758859 + 0.651254i \(0.225757\pi\)
\(734\) 20.7549 0.766077
\(735\) 0 0
\(736\) −8.42491 −0.310546
\(737\) −1.29615 −0.0477443
\(738\) 0 0
\(739\) −40.6018 −1.49356 −0.746781 0.665070i \(-0.768402\pi\)
−0.746781 + 0.665070i \(0.768402\pi\)
\(740\) −4.08557 −0.150189
\(741\) 0 0
\(742\) 1.35481 0.0497365
\(743\) 18.3986 0.674977 0.337489 0.941330i \(-0.390423\pi\)
0.337489 + 0.941330i \(0.390423\pi\)
\(744\) 0 0
\(745\) −9.16141 −0.335648
\(746\) −44.1290 −1.61568
\(747\) 0 0
\(748\) −2.99800 −0.109618
\(749\) 17.3884 0.635358
\(750\) 0 0
\(751\) 32.7553 1.19526 0.597630 0.801772i \(-0.296109\pi\)
0.597630 + 0.801772i \(0.296109\pi\)
\(752\) −5.02259 −0.183155
\(753\) 0 0
\(754\) −41.7351 −1.51990
\(755\) 28.8315 1.04929
\(756\) 0 0
\(757\) −46.5385 −1.69147 −0.845735 0.533604i \(-0.820837\pi\)
−0.845735 + 0.533604i \(0.820837\pi\)
\(758\) 24.3070 0.882869
\(759\) 0 0
\(760\) −17.6368 −0.639754
\(761\) 11.4405 0.414718 0.207359 0.978265i \(-0.433513\pi\)
0.207359 + 0.978265i \(0.433513\pi\)
\(762\) 0 0
\(763\) 13.0624 0.472891
\(764\) −1.05258 −0.0380810
\(765\) 0 0
\(766\) −45.8840 −1.65786
\(767\) −2.07340 −0.0748662
\(768\) 0 0
\(769\) −1.29466 −0.0466867 −0.0233434 0.999728i \(-0.507431\pi\)
−0.0233434 + 0.999728i \(0.507431\pi\)
\(770\) 5.41665 0.195203
\(771\) 0 0
\(772\) −1.70391 −0.0613251
\(773\) −34.0700 −1.22541 −0.612706 0.790311i \(-0.709919\pi\)
−0.612706 + 0.790311i \(0.709919\pi\)
\(774\) 0 0
\(775\) 1.34190 0.0482024
\(776\) −24.8078 −0.890549
\(777\) 0 0
\(778\) 4.77870 0.171325
\(779\) −30.5484 −1.09451
\(780\) 0 0
\(781\) 4.22487 0.151178
\(782\) −77.2125 −2.76111
\(783\) 0 0
\(784\) −4.39287 −0.156888
\(785\) 11.4386 0.408260
\(786\) 0 0
\(787\) 33.5028 1.19424 0.597122 0.802150i \(-0.296311\pi\)
0.597122 + 0.802150i \(0.296311\pi\)
\(788\) 0.443069 0.0157837
\(789\) 0 0
\(790\) −21.5086 −0.765241
\(791\) 12.6936 0.451333
\(792\) 0 0
\(793\) 59.5112 2.11330
\(794\) −51.2765 −1.81973
\(795\) 0 0
\(796\) 2.54655 0.0902600
\(797\) −19.4492 −0.688927 −0.344464 0.938800i \(-0.611939\pi\)
−0.344464 + 0.938800i \(0.611939\pi\)
\(798\) 0 0
\(799\) −8.74429 −0.309351
\(800\) −1.00479 −0.0355249
\(801\) 0 0
\(802\) −9.98309 −0.352515
\(803\) 6.08898 0.214876
\(804\) 0 0
\(805\) 13.8707 0.488878
\(806\) −10.0425 −0.353732
\(807\) 0 0
\(808\) −3.21128 −0.112972
\(809\) 16.3351 0.574311 0.287156 0.957884i \(-0.407290\pi\)
0.287156 + 0.957884i \(0.407290\pi\)
\(810\) 0 0
\(811\) −32.0347 −1.12489 −0.562445 0.826835i \(-0.690139\pi\)
−0.562445 + 0.826835i \(0.690139\pi\)
\(812\) −1.52407 −0.0534844
\(813\) 0 0
\(814\) −23.9076 −0.837961
\(815\) 24.9409 0.873641
\(816\) 0 0
\(817\) 7.39350 0.258666
\(818\) 42.9663 1.50228
\(819\) 0 0
\(820\) 4.25103 0.148452
\(821\) −21.7526 −0.759171 −0.379586 0.925157i \(-0.623933\pi\)
−0.379586 + 0.925157i \(0.623933\pi\)
\(822\) 0 0
\(823\) −19.0673 −0.664643 −0.332322 0.943166i \(-0.607832\pi\)
−0.332322 + 0.943166i \(0.607832\pi\)
\(824\) −23.0549 −0.803154
\(825\) 0 0
\(826\) −0.761508 −0.0264962
\(827\) −16.0124 −0.556807 −0.278403 0.960464i \(-0.589805\pi\)
−0.278403 + 0.960464i \(0.589805\pi\)
\(828\) 0 0
\(829\) 8.10746 0.281584 0.140792 0.990039i \(-0.455035\pi\)
0.140792 + 0.990039i \(0.455035\pi\)
\(830\) −4.04688 −0.140469
\(831\) 0 0
\(832\) −28.1290 −0.975196
\(833\) −7.64794 −0.264986
\(834\) 0 0
\(835\) 12.7710 0.441959
\(836\) 1.27356 0.0440468
\(837\) 0 0
\(838\) 40.0436 1.38328
\(839\) −13.7923 −0.476161 −0.238081 0.971245i \(-0.576518\pi\)
−0.238081 + 0.971245i \(0.576518\pi\)
\(840\) 0 0
\(841\) 18.6389 0.642722
\(842\) −53.4418 −1.84172
\(843\) 0 0
\(844\) 4.52837 0.155873
\(845\) −7.09190 −0.243969
\(846\) 0 0
\(847\) −7.84843 −0.269675
\(848\) 3.99364 0.137142
\(849\) 0 0
\(850\) −9.20872 −0.315857
\(851\) −61.2214 −2.09864
\(852\) 0 0
\(853\) 0.711300 0.0243545 0.0121772 0.999926i \(-0.496124\pi\)
0.0121772 + 0.999926i \(0.496124\pi\)
\(854\) 21.8570 0.747930
\(855\) 0 0
\(856\) 46.1038 1.57580
\(857\) 7.40150 0.252831 0.126415 0.991977i \(-0.459653\pi\)
0.126415 + 0.991977i \(0.459653\pi\)
\(858\) 0 0
\(859\) −17.0089 −0.580335 −0.290167 0.956976i \(-0.593711\pi\)
−0.290167 + 0.956976i \(0.593711\pi\)
\(860\) −1.02886 −0.0350838
\(861\) 0 0
\(862\) −38.6149 −1.31523
\(863\) −18.4171 −0.626927 −0.313464 0.949600i \(-0.601489\pi\)
−0.313464 + 0.949600i \(0.601489\pi\)
\(864\) 0 0
\(865\) −27.7233 −0.942621
\(866\) −25.7217 −0.874059
\(867\) 0 0
\(868\) −0.366729 −0.0124476
\(869\) −12.5143 −0.424519
\(870\) 0 0
\(871\) 2.96249 0.100380
\(872\) 34.6338 1.17285
\(873\) 0 0
\(874\) 32.7999 1.10947
\(875\) 11.8915 0.402006
\(876\) 0 0
\(877\) 11.4975 0.388242 0.194121 0.980978i \(-0.437815\pi\)
0.194121 + 0.980978i \(0.437815\pi\)
\(878\) −48.8188 −1.64755
\(879\) 0 0
\(880\) 15.9670 0.538247
\(881\) −25.7078 −0.866119 −0.433060 0.901365i \(-0.642566\pi\)
−0.433060 + 0.901365i \(0.642566\pi\)
\(882\) 0 0
\(883\) −49.3302 −1.66009 −0.830047 0.557693i \(-0.811687\pi\)
−0.830047 + 0.557693i \(0.811687\pi\)
\(884\) 6.85226 0.230466
\(885\) 0 0
\(886\) −37.5390 −1.26115
\(887\) 9.71012 0.326034 0.163017 0.986623i \(-0.447877\pi\)
0.163017 + 0.986623i \(0.447877\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 11.0903 0.371747
\(891\) 0 0
\(892\) −0.319182 −0.0106870
\(893\) 3.71458 0.124304
\(894\) 0 0
\(895\) 20.6238 0.689376
\(896\) −12.8182 −0.428227
\(897\) 0 0
\(898\) −57.3765 −1.91468
\(899\) 11.4631 0.382315
\(900\) 0 0
\(901\) 6.95290 0.231635
\(902\) 24.8758 0.828273
\(903\) 0 0
\(904\) 33.6560 1.11938
\(905\) −30.8306 −1.02484
\(906\) 0 0
\(907\) 8.87266 0.294612 0.147306 0.989091i \(-0.452940\pi\)
0.147306 + 0.989091i \(0.452940\pi\)
\(908\) −5.17501 −0.171739
\(909\) 0 0
\(910\) −12.3803 −0.410404
\(911\) 16.3270 0.540938 0.270469 0.962729i \(-0.412821\pi\)
0.270469 + 0.962729i \(0.412821\pi\)
\(912\) 0 0
\(913\) −2.35459 −0.0779257
\(914\) 35.5941 1.17735
\(915\) 0 0
\(916\) 3.86521 0.127710
\(917\) 10.1857 0.336361
\(918\) 0 0
\(919\) −28.0448 −0.925111 −0.462556 0.886590i \(-0.653067\pi\)
−0.462556 + 0.886590i \(0.653067\pi\)
\(920\) 36.7770 1.21250
\(921\) 0 0
\(922\) −33.5353 −1.10442
\(923\) −9.65640 −0.317844
\(924\) 0 0
\(925\) −7.30156 −0.240074
\(926\) 10.8132 0.355343
\(927\) 0 0
\(928\) −8.58340 −0.281764
\(929\) 50.8036 1.66681 0.833406 0.552662i \(-0.186388\pi\)
0.833406 + 0.552662i \(0.186388\pi\)
\(930\) 0 0
\(931\) 3.24885 0.106477
\(932\) −5.41592 −0.177404
\(933\) 0 0
\(934\) −4.50516 −0.147413
\(935\) 27.7984 0.909105
\(936\) 0 0
\(937\) 30.2345 0.987719 0.493860 0.869542i \(-0.335586\pi\)
0.493860 + 0.869542i \(0.335586\pi\)
\(938\) 1.08805 0.0355261
\(939\) 0 0
\(940\) −0.516911 −0.0168598
\(941\) −22.7086 −0.740280 −0.370140 0.928976i \(-0.620690\pi\)
−0.370140 + 0.928976i \(0.620690\pi\)
\(942\) 0 0
\(943\) 63.7008 2.07438
\(944\) −2.24474 −0.0730601
\(945\) 0 0
\(946\) −6.02059 −0.195746
\(947\) −48.8988 −1.58900 −0.794499 0.607265i \(-0.792267\pi\)
−0.794499 + 0.607265i \(0.792267\pi\)
\(948\) 0 0
\(949\) −13.9170 −0.451766
\(950\) 3.91188 0.126918
\(951\) 0 0
\(952\) −20.2779 −0.657210
\(953\) 43.4704 1.40814 0.704072 0.710129i \(-0.251363\pi\)
0.704072 + 0.710129i \(0.251363\pi\)
\(954\) 0 0
\(955\) 9.75983 0.315821
\(956\) −2.85011 −0.0921792
\(957\) 0 0
\(958\) 19.1734 0.619464
\(959\) −5.48349 −0.177071
\(960\) 0 0
\(961\) −28.2417 −0.911023
\(962\) 54.6434 1.76177
\(963\) 0 0
\(964\) −3.88344 −0.125077
\(965\) 15.7992 0.508594
\(966\) 0 0
\(967\) 5.76371 0.185348 0.0926742 0.995696i \(-0.470458\pi\)
0.0926742 + 0.995696i \(0.470458\pi\)
\(968\) −20.8094 −0.668841
\(969\) 0 0
\(970\) −28.5482 −0.916628
\(971\) −42.8223 −1.37423 −0.687117 0.726547i \(-0.741124\pi\)
−0.687117 + 0.726547i \(0.741124\pi\)
\(972\) 0 0
\(973\) −9.95792 −0.319236
\(974\) 57.6018 1.84568
\(975\) 0 0
\(976\) 64.4291 2.06232
\(977\) 35.6861 1.14170 0.570850 0.821054i \(-0.306614\pi\)
0.570850 + 0.821054i \(0.306614\pi\)
\(978\) 0 0
\(979\) 6.45264 0.206227
\(980\) −0.452102 −0.0144419
\(981\) 0 0
\(982\) −26.1003 −0.832895
\(983\) −15.2090 −0.485092 −0.242546 0.970140i \(-0.577983\pi\)
−0.242546 + 0.970140i \(0.577983\pi\)
\(984\) 0 0
\(985\) −4.10827 −0.130900
\(986\) −78.6650 −2.50521
\(987\) 0 0
\(988\) −2.91085 −0.0926063
\(989\) −15.4172 −0.490240
\(990\) 0 0
\(991\) −12.7220 −0.404126 −0.202063 0.979373i \(-0.564765\pi\)
−0.202063 + 0.979373i \(0.564765\pi\)
\(992\) −2.06538 −0.0655757
\(993\) 0 0
\(994\) −3.54655 −0.112490
\(995\) −23.6124 −0.748562
\(996\) 0 0
\(997\) −15.9043 −0.503695 −0.251847 0.967767i \(-0.581038\pi\)
−0.251847 + 0.967767i \(0.581038\pi\)
\(998\) −12.4326 −0.393549
\(999\) 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 \(a_p\))