Properties

Label 8001.2.a.v.1.1
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 1.1
Root \(2.79341\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79341 q^{2}\) \(+5.80316 q^{4}\) \(+1.63704 q^{5}\) \(+1.00000 q^{7}\) \(-10.6238 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.79341 q^{2}\) \(+5.80316 q^{4}\) \(+1.63704 q^{5}\) \(+1.00000 q^{7}\) \(-10.6238 q^{8}\) \(-4.57293 q^{10}\) \(+6.47808 q^{11}\) \(+4.75000 q^{13}\) \(-2.79341 q^{14}\) \(+18.0703 q^{16}\) \(-0.645517 q^{17}\) \(+5.60124 q^{19}\) \(+9.50000 q^{20}\) \(-18.0960 q^{22}\) \(+0.0762406 q^{23}\) \(-2.32010 q^{25}\) \(-13.2687 q^{26}\) \(+5.80316 q^{28}\) \(-1.88240 q^{29}\) \(+2.27176 q^{31}\) \(-29.2303 q^{32}\) \(+1.80319 q^{34}\) \(+1.63704 q^{35}\) \(-5.95489 q^{37}\) \(-15.6466 q^{38}\) \(-17.3916 q^{40}\) \(+8.30140 q^{41}\) \(+0.409994 q^{43}\) \(+37.5934 q^{44}\) \(-0.212971 q^{46}\) \(-5.35216 q^{47}\) \(+1.00000 q^{49}\) \(+6.48100 q^{50}\) \(+27.5650 q^{52}\) \(+10.0642 q^{53}\) \(+10.6049 q^{55}\) \(-10.6238 q^{56}\) \(+5.25833 q^{58}\) \(+8.26943 q^{59}\) \(-4.31290 q^{61}\) \(-6.34596 q^{62}\) \(+45.5117 q^{64}\) \(+7.77594 q^{65}\) \(+7.25212 q^{67}\) \(-3.74604 q^{68}\) \(-4.57293 q^{70}\) \(-3.65756 q^{71}\) \(+11.6201 q^{73}\) \(+16.6345 q^{74}\) \(+32.5049 q^{76}\) \(+6.47808 q^{77}\) \(-12.8009 q^{79}\) \(+29.5818 q^{80}\) \(-23.1892 q^{82}\) \(-10.3550 q^{83}\) \(-1.05674 q^{85}\) \(-1.14528 q^{86}\) \(-68.8218 q^{88}\) \(+4.61148 q^{89}\) \(+4.75000 q^{91}\) \(+0.442436 q^{92}\) \(+14.9508 q^{94}\) \(+9.16946 q^{95}\) \(-8.08150 q^{97}\) \(-2.79341 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79341 −1.97524 −0.987621 0.156861i \(-0.949863\pi\)
−0.987621 + 0.156861i \(0.949863\pi\)
\(3\) 0 0
\(4\) 5.80316 2.90158
\(5\) 1.63704 0.732106 0.366053 0.930594i \(-0.380709\pi\)
0.366053 + 0.930594i \(0.380709\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −10.6238 −3.75608
\(9\) 0 0
\(10\) −4.57293 −1.44609
\(11\) 6.47808 1.95322 0.976608 0.215027i \(-0.0689840\pi\)
0.976608 + 0.215027i \(0.0689840\pi\)
\(12\) 0 0
\(13\) 4.75000 1.31741 0.658707 0.752400i \(-0.271104\pi\)
0.658707 + 0.752400i \(0.271104\pi\)
\(14\) −2.79341 −0.746571
\(15\) 0 0
\(16\) 18.0703 4.51758
\(17\) −0.645517 −0.156561 −0.0782804 0.996931i \(-0.524943\pi\)
−0.0782804 + 0.996931i \(0.524943\pi\)
\(18\) 0 0
\(19\) 5.60124 1.28501 0.642507 0.766280i \(-0.277895\pi\)
0.642507 + 0.766280i \(0.277895\pi\)
\(20\) 9.50000 2.12426
\(21\) 0 0
\(22\) −18.0960 −3.85807
\(23\) 0.0762406 0.0158973 0.00794863 0.999968i \(-0.497470\pi\)
0.00794863 + 0.999968i \(0.497470\pi\)
\(24\) 0 0
\(25\) −2.32010 −0.464020
\(26\) −13.2687 −2.60221
\(27\) 0 0
\(28\) 5.80316 1.09669
\(29\) −1.88240 −0.349553 −0.174777 0.984608i \(-0.555920\pi\)
−0.174777 + 0.984608i \(0.555920\pi\)
\(30\) 0 0
\(31\) 2.27176 0.408020 0.204010 0.978969i \(-0.434602\pi\)
0.204010 + 0.978969i \(0.434602\pi\)
\(32\) −29.2303 −5.16724
\(33\) 0 0
\(34\) 1.80319 0.309245
\(35\) 1.63704 0.276710
\(36\) 0 0
\(37\) −5.95489 −0.978978 −0.489489 0.872010i \(-0.662817\pi\)
−0.489489 + 0.872010i \(0.662817\pi\)
\(38\) −15.6466 −2.53821
\(39\) 0 0
\(40\) −17.3916 −2.74985
\(41\) 8.30140 1.29646 0.648230 0.761445i \(-0.275510\pi\)
0.648230 + 0.761445i \(0.275510\pi\)
\(42\) 0 0
\(43\) 0.409994 0.0625234 0.0312617 0.999511i \(-0.490047\pi\)
0.0312617 + 0.999511i \(0.490047\pi\)
\(44\) 37.5934 5.66741
\(45\) 0 0
\(46\) −0.212971 −0.0314009
\(47\) −5.35216 −0.780693 −0.390346 0.920668i \(-0.627645\pi\)
−0.390346 + 0.920668i \(0.627645\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 6.48100 0.916552
\(51\) 0 0
\(52\) 27.5650 3.82258
\(53\) 10.0642 1.38243 0.691214 0.722650i \(-0.257076\pi\)
0.691214 + 0.722650i \(0.257076\pi\)
\(54\) 0 0
\(55\) 10.6049 1.42996
\(56\) −10.6238 −1.41966
\(57\) 0 0
\(58\) 5.25833 0.690452
\(59\) 8.26943 1.07659 0.538294 0.842757i \(-0.319069\pi\)
0.538294 + 0.842757i \(0.319069\pi\)
\(60\) 0 0
\(61\) −4.31290 −0.552210 −0.276105 0.961128i \(-0.589044\pi\)
−0.276105 + 0.961128i \(0.589044\pi\)
\(62\) −6.34596 −0.805938
\(63\) 0 0
\(64\) 45.5117 5.68896
\(65\) 7.77594 0.964487
\(66\) 0 0
\(67\) 7.25212 0.885988 0.442994 0.896525i \(-0.353916\pi\)
0.442994 + 0.896525i \(0.353916\pi\)
\(68\) −3.74604 −0.454273
\(69\) 0 0
\(70\) −4.57293 −0.546569
\(71\) −3.65756 −0.434072 −0.217036 0.976164i \(-0.569639\pi\)
−0.217036 + 0.976164i \(0.569639\pi\)
\(72\) 0 0
\(73\) 11.6201 1.36003 0.680014 0.733199i \(-0.261974\pi\)
0.680014 + 0.733199i \(0.261974\pi\)
\(74\) 16.6345 1.93372
\(75\) 0 0
\(76\) 32.5049 3.72857
\(77\) 6.47808 0.738246
\(78\) 0 0
\(79\) −12.8009 −1.44021 −0.720105 0.693865i \(-0.755907\pi\)
−0.720105 + 0.693865i \(0.755907\pi\)
\(80\) 29.5818 3.30735
\(81\) 0 0
\(82\) −23.1892 −2.56082
\(83\) −10.3550 −1.13660 −0.568302 0.822820i \(-0.692400\pi\)
−0.568302 + 0.822820i \(0.692400\pi\)
\(84\) 0 0
\(85\) −1.05674 −0.114619
\(86\) −1.14528 −0.123499
\(87\) 0 0
\(88\) −68.8218 −7.33643
\(89\) 4.61148 0.488816 0.244408 0.969672i \(-0.421406\pi\)
0.244408 + 0.969672i \(0.421406\pi\)
\(90\) 0 0
\(91\) 4.75000 0.497936
\(92\) 0.442436 0.0461272
\(93\) 0 0
\(94\) 14.9508 1.54206
\(95\) 9.16946 0.940766
\(96\) 0 0
\(97\) −8.08150 −0.820552 −0.410276 0.911961i \(-0.634568\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(98\) −2.79341 −0.282177
\(99\) 0 0
\(100\) −13.4639 −1.34639
\(101\) 4.65231 0.462922 0.231461 0.972844i \(-0.425649\pi\)
0.231461 + 0.972844i \(0.425649\pi\)
\(102\) 0 0
\(103\) −5.57229 −0.549054 −0.274527 0.961579i \(-0.588521\pi\)
−0.274527 + 0.961579i \(0.588521\pi\)
\(104\) −50.4630 −4.94831
\(105\) 0 0
\(106\) −28.1136 −2.73063
\(107\) 14.8598 1.43655 0.718277 0.695757i \(-0.244931\pi\)
0.718277 + 0.695757i \(0.244931\pi\)
\(108\) 0 0
\(109\) −12.5572 −1.20276 −0.601382 0.798961i \(-0.705383\pi\)
−0.601382 + 0.798961i \(0.705383\pi\)
\(110\) −29.6238 −2.82452
\(111\) 0 0
\(112\) 18.0703 1.70749
\(113\) −1.79519 −0.168877 −0.0844385 0.996429i \(-0.526910\pi\)
−0.0844385 + 0.996429i \(0.526910\pi\)
\(114\) 0 0
\(115\) 0.124809 0.0116385
\(116\) −10.9239 −1.01426
\(117\) 0 0
\(118\) −23.0999 −2.12652
\(119\) −0.645517 −0.0591744
\(120\) 0 0
\(121\) 30.9656 2.81505
\(122\) 12.0477 1.09075
\(123\) 0 0
\(124\) 13.1834 1.18390
\(125\) −11.9833 −1.07182
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −68.6723 −6.06983
\(129\) 0 0
\(130\) −21.7214 −1.90509
\(131\) −0.419711 −0.0366703 −0.0183352 0.999832i \(-0.505837\pi\)
−0.0183352 + 0.999832i \(0.505837\pi\)
\(132\) 0 0
\(133\) 5.60124 0.485689
\(134\) −20.2582 −1.75004
\(135\) 0 0
\(136\) 6.85783 0.588054
\(137\) 17.1519 1.46539 0.732694 0.680559i \(-0.238263\pi\)
0.732694 + 0.680559i \(0.238263\pi\)
\(138\) 0 0
\(139\) 1.89367 0.160619 0.0803094 0.996770i \(-0.474409\pi\)
0.0803094 + 0.996770i \(0.474409\pi\)
\(140\) 9.50000 0.802897
\(141\) 0 0
\(142\) 10.2171 0.857398
\(143\) 30.7709 2.57319
\(144\) 0 0
\(145\) −3.08157 −0.255910
\(146\) −32.4597 −2.68638
\(147\) 0 0
\(148\) −34.5572 −2.84058
\(149\) 14.1732 1.16111 0.580556 0.814220i \(-0.302835\pi\)
0.580556 + 0.814220i \(0.302835\pi\)
\(150\) 0 0
\(151\) −6.99988 −0.569642 −0.284821 0.958581i \(-0.591934\pi\)
−0.284821 + 0.958581i \(0.591934\pi\)
\(152\) −59.5064 −4.82661
\(153\) 0 0
\(154\) −18.0960 −1.45821
\(155\) 3.71896 0.298714
\(156\) 0 0
\(157\) 6.59843 0.526612 0.263306 0.964712i \(-0.415187\pi\)
0.263306 + 0.964712i \(0.415187\pi\)
\(158\) 35.7581 2.84476
\(159\) 0 0
\(160\) −47.8512 −3.78297
\(161\) 0.0762406 0.00600860
\(162\) 0 0
\(163\) −19.4556 −1.52388 −0.761940 0.647647i \(-0.775753\pi\)
−0.761940 + 0.647647i \(0.775753\pi\)
\(164\) 48.1743 3.76178
\(165\) 0 0
\(166\) 28.9257 2.24507
\(167\) 22.4412 1.73655 0.868277 0.496079i \(-0.165227\pi\)
0.868277 + 0.496079i \(0.165227\pi\)
\(168\) 0 0
\(169\) 9.56252 0.735579
\(170\) 2.95190 0.226400
\(171\) 0 0
\(172\) 2.37926 0.181417
\(173\) −6.17908 −0.469786 −0.234893 0.972021i \(-0.575474\pi\)
−0.234893 + 0.972021i \(0.575474\pi\)
\(174\) 0 0
\(175\) −2.32010 −0.175383
\(176\) 117.061 8.82381
\(177\) 0 0
\(178\) −12.8818 −0.965530
\(179\) −10.6465 −0.795759 −0.397880 0.917438i \(-0.630254\pi\)
−0.397880 + 0.917438i \(0.630254\pi\)
\(180\) 0 0
\(181\) 22.0777 1.64102 0.820510 0.571632i \(-0.193690\pi\)
0.820510 + 0.571632i \(0.193690\pi\)
\(182\) −13.2687 −0.983543
\(183\) 0 0
\(184\) −0.809964 −0.0597113
\(185\) −9.74839 −0.716716
\(186\) 0 0
\(187\) −4.18171 −0.305797
\(188\) −31.0594 −2.26524
\(189\) 0 0
\(190\) −25.6141 −1.85824
\(191\) 25.1450 1.81943 0.909715 0.415233i \(-0.136300\pi\)
0.909715 + 0.415233i \(0.136300\pi\)
\(192\) 0 0
\(193\) −18.5403 −1.33456 −0.667279 0.744808i \(-0.732541\pi\)
−0.667279 + 0.744808i \(0.732541\pi\)
\(194\) 22.5750 1.62079
\(195\) 0 0
\(196\) 5.80316 0.414511
\(197\) −20.8774 −1.48745 −0.743726 0.668485i \(-0.766943\pi\)
−0.743726 + 0.668485i \(0.766943\pi\)
\(198\) 0 0
\(199\) 15.1555 1.07435 0.537173 0.843472i \(-0.319492\pi\)
0.537173 + 0.843472i \(0.319492\pi\)
\(200\) 24.6483 1.74290
\(201\) 0 0
\(202\) −12.9958 −0.914383
\(203\) −1.88240 −0.132119
\(204\) 0 0
\(205\) 13.5897 0.949147
\(206\) 15.5657 1.08451
\(207\) 0 0
\(208\) 85.8341 5.95152
\(209\) 36.2853 2.50991
\(210\) 0 0
\(211\) −2.41396 −0.166184 −0.0830919 0.996542i \(-0.526479\pi\)
−0.0830919 + 0.996542i \(0.526479\pi\)
\(212\) 58.4043 4.01123
\(213\) 0 0
\(214\) −41.5097 −2.83754
\(215\) 0.671176 0.0457738
\(216\) 0 0
\(217\) 2.27176 0.154217
\(218\) 35.0775 2.37575
\(219\) 0 0
\(220\) 61.5418 4.14915
\(221\) −3.06621 −0.206255
\(222\) 0 0
\(223\) −27.1479 −1.81796 −0.908979 0.416842i \(-0.863137\pi\)
−0.908979 + 0.416842i \(0.863137\pi\)
\(224\) −29.2303 −1.95303
\(225\) 0 0
\(226\) 5.01470 0.333573
\(227\) −20.6978 −1.37376 −0.686880 0.726771i \(-0.741020\pi\)
−0.686880 + 0.726771i \(0.741020\pi\)
\(228\) 0 0
\(229\) 9.38781 0.620364 0.310182 0.950677i \(-0.399610\pi\)
0.310182 + 0.950677i \(0.399610\pi\)
\(230\) −0.348643 −0.0229888
\(231\) 0 0
\(232\) 19.9982 1.31295
\(233\) −10.8180 −0.708713 −0.354357 0.935110i \(-0.615300\pi\)
−0.354357 + 0.935110i \(0.615300\pi\)
\(234\) 0 0
\(235\) −8.76170 −0.571550
\(236\) 47.9888 3.12381
\(237\) 0 0
\(238\) 1.80319 0.116884
\(239\) −18.6532 −1.20657 −0.603286 0.797525i \(-0.706142\pi\)
−0.603286 + 0.797525i \(0.706142\pi\)
\(240\) 0 0
\(241\) 5.88263 0.378934 0.189467 0.981887i \(-0.439324\pi\)
0.189467 + 0.981887i \(0.439324\pi\)
\(242\) −86.4997 −5.56041
\(243\) 0 0
\(244\) −25.0284 −1.60228
\(245\) 1.63704 0.104587
\(246\) 0 0
\(247\) 26.6059 1.69289
\(248\) −24.1347 −1.53255
\(249\) 0 0
\(250\) 33.4743 2.11710
\(251\) −17.2347 −1.08784 −0.543921 0.839136i \(-0.683061\pi\)
−0.543921 + 0.839136i \(0.683061\pi\)
\(252\) 0 0
\(253\) 0.493893 0.0310508
\(254\) −2.79341 −0.175274
\(255\) 0 0
\(256\) 100.807 6.30043
\(257\) −2.80843 −0.175185 −0.0875925 0.996156i \(-0.527917\pi\)
−0.0875925 + 0.996156i \(0.527917\pi\)
\(258\) 0 0
\(259\) −5.95489 −0.370019
\(260\) 45.1250 2.79854
\(261\) 0 0
\(262\) 1.17243 0.0724327
\(263\) −11.5545 −0.712478 −0.356239 0.934395i \(-0.615941\pi\)
−0.356239 + 0.934395i \(0.615941\pi\)
\(264\) 0 0
\(265\) 16.4755 1.01208
\(266\) −15.6466 −0.959354
\(267\) 0 0
\(268\) 42.0852 2.57076
\(269\) −2.77245 −0.169039 −0.0845196 0.996422i \(-0.526936\pi\)
−0.0845196 + 0.996422i \(0.526936\pi\)
\(270\) 0 0
\(271\) 31.7527 1.92884 0.964421 0.264372i \(-0.0851645\pi\)
0.964421 + 0.264372i \(0.0851645\pi\)
\(272\) −11.6647 −0.707276
\(273\) 0 0
\(274\) −47.9124 −2.89449
\(275\) −15.0298 −0.906332
\(276\) 0 0
\(277\) 11.0867 0.666135 0.333068 0.942903i \(-0.391916\pi\)
0.333068 + 0.942903i \(0.391916\pi\)
\(278\) −5.28980 −0.317261
\(279\) 0 0
\(280\) −17.3916 −1.03935
\(281\) −30.9985 −1.84921 −0.924607 0.380922i \(-0.875607\pi\)
−0.924607 + 0.380922i \(0.875607\pi\)
\(282\) 0 0
\(283\) −6.86487 −0.408074 −0.204037 0.978963i \(-0.565406\pi\)
−0.204037 + 0.978963i \(0.565406\pi\)
\(284\) −21.2254 −1.25950
\(285\) 0 0
\(286\) −85.9559 −5.08268
\(287\) 8.30140 0.490016
\(288\) 0 0
\(289\) −16.5833 −0.975489
\(290\) 8.60809 0.505484
\(291\) 0 0
\(292\) 67.4332 3.94623
\(293\) 23.5589 1.37632 0.688162 0.725557i \(-0.258418\pi\)
0.688162 + 0.725557i \(0.258418\pi\)
\(294\) 0 0
\(295\) 13.5374 0.788177
\(296\) 63.2635 3.67712
\(297\) 0 0
\(298\) −39.5916 −2.29348
\(299\) 0.362143 0.0209433
\(300\) 0 0
\(301\) 0.409994 0.0236316
\(302\) 19.5536 1.12518
\(303\) 0 0
\(304\) 101.216 5.80515
\(305\) −7.06038 −0.404276
\(306\) 0 0
\(307\) 14.6890 0.838345 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(308\) 37.5934 2.14208
\(309\) 0 0
\(310\) −10.3886 −0.590032
\(311\) 29.6569 1.68169 0.840845 0.541275i \(-0.182058\pi\)
0.840845 + 0.541275i \(0.182058\pi\)
\(312\) 0 0
\(313\) −9.14081 −0.516669 −0.258334 0.966056i \(-0.583174\pi\)
−0.258334 + 0.966056i \(0.583174\pi\)
\(314\) −18.4321 −1.04019
\(315\) 0 0
\(316\) −74.2855 −4.17888
\(317\) −13.1590 −0.739085 −0.369542 0.929214i \(-0.620486\pi\)
−0.369542 + 0.929214i \(0.620486\pi\)
\(318\) 0 0
\(319\) −12.1944 −0.682753
\(320\) 74.5044 4.16492
\(321\) 0 0
\(322\) −0.212971 −0.0118684
\(323\) −3.61570 −0.201183
\(324\) 0 0
\(325\) −11.0205 −0.611307
\(326\) 54.3475 3.01003
\(327\) 0 0
\(328\) −88.1923 −4.86961
\(329\) −5.35216 −0.295074
\(330\) 0 0
\(331\) −24.0050 −1.31944 −0.659718 0.751514i \(-0.729324\pi\)
−0.659718 + 0.751514i \(0.729324\pi\)
\(332\) −60.0915 −3.29795
\(333\) 0 0
\(334\) −62.6876 −3.43012
\(335\) 11.8720 0.648637
\(336\) 0 0
\(337\) 20.3680 1.10952 0.554758 0.832012i \(-0.312811\pi\)
0.554758 + 0.832012i \(0.312811\pi\)
\(338\) −26.7121 −1.45295
\(339\) 0 0
\(340\) −6.13241 −0.332577
\(341\) 14.7166 0.796951
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.35569 −0.234843
\(345\) 0 0
\(346\) 17.2607 0.927942
\(347\) −4.92725 −0.264509 −0.132254 0.991216i \(-0.542222\pi\)
−0.132254 + 0.991216i \(0.542222\pi\)
\(348\) 0 0
\(349\) −0.0921158 −0.00493084 −0.00246542 0.999997i \(-0.500785\pi\)
−0.00246542 + 0.999997i \(0.500785\pi\)
\(350\) 6.48100 0.346424
\(351\) 0 0
\(352\) −189.356 −10.0927
\(353\) −8.47294 −0.450969 −0.225484 0.974247i \(-0.572396\pi\)
−0.225484 + 0.974247i \(0.572396\pi\)
\(354\) 0 0
\(355\) −5.98757 −0.317787
\(356\) 26.7612 1.41834
\(357\) 0 0
\(358\) 29.7402 1.57182
\(359\) 18.1497 0.957906 0.478953 0.877840i \(-0.341016\pi\)
0.478953 + 0.877840i \(0.341016\pi\)
\(360\) 0 0
\(361\) 12.3739 0.651259
\(362\) −61.6720 −3.24141
\(363\) 0 0
\(364\) 27.5650 1.44480
\(365\) 19.0225 0.995686
\(366\) 0 0
\(367\) −19.3632 −1.01075 −0.505376 0.862899i \(-0.668646\pi\)
−0.505376 + 0.862899i \(0.668646\pi\)
\(368\) 1.37769 0.0718172
\(369\) 0 0
\(370\) 27.2313 1.41569
\(371\) 10.0642 0.522509
\(372\) 0 0
\(373\) 7.37194 0.381705 0.190852 0.981619i \(-0.438875\pi\)
0.190852 + 0.981619i \(0.438875\pi\)
\(374\) 11.6812 0.604023
\(375\) 0 0
\(376\) 56.8602 2.93234
\(377\) −8.94141 −0.460506
\(378\) 0 0
\(379\) 0.00612186 0.000314459 0 0.000157229 1.00000i \(-0.499950\pi\)
0.000157229 1.00000i \(0.499950\pi\)
\(380\) 53.2118 2.72971
\(381\) 0 0
\(382\) −70.2404 −3.59381
\(383\) −36.2288 −1.85121 −0.925603 0.378495i \(-0.876442\pi\)
−0.925603 + 0.378495i \(0.876442\pi\)
\(384\) 0 0
\(385\) 10.6049 0.540475
\(386\) 51.7907 2.63608
\(387\) 0 0
\(388\) −46.8982 −2.38090
\(389\) 17.0620 0.865080 0.432540 0.901615i \(-0.357617\pi\)
0.432540 + 0.901615i \(0.357617\pi\)
\(390\) 0 0
\(391\) −0.0492146 −0.00248889
\(392\) −10.6238 −0.536583
\(393\) 0 0
\(394\) 58.3192 2.93808
\(395\) −20.9555 −1.05439
\(396\) 0 0
\(397\) 28.3501 1.42285 0.711425 0.702762i \(-0.248050\pi\)
0.711425 + 0.702762i \(0.248050\pi\)
\(398\) −42.3356 −2.12209
\(399\) 0 0
\(400\) −41.9250 −2.09625
\(401\) −32.4139 −1.61867 −0.809336 0.587346i \(-0.800173\pi\)
−0.809336 + 0.587346i \(0.800173\pi\)
\(402\) 0 0
\(403\) 10.7909 0.537531
\(404\) 26.9981 1.34321
\(405\) 0 0
\(406\) 5.25833 0.260966
\(407\) −38.5763 −1.91215
\(408\) 0 0
\(409\) −34.2842 −1.69524 −0.847621 0.530602i \(-0.821966\pi\)
−0.847621 + 0.530602i \(0.821966\pi\)
\(410\) −37.9617 −1.87479
\(411\) 0 0
\(412\) −32.3369 −1.59312
\(413\) 8.26943 0.406912
\(414\) 0 0
\(415\) −16.9515 −0.832116
\(416\) −138.844 −6.80739
\(417\) 0 0
\(418\) −101.360 −4.95768
\(419\) −19.1663 −0.936333 −0.468167 0.883640i \(-0.655085\pi\)
−0.468167 + 0.883640i \(0.655085\pi\)
\(420\) 0 0
\(421\) 16.2901 0.793933 0.396966 0.917833i \(-0.370063\pi\)
0.396966 + 0.917833i \(0.370063\pi\)
\(422\) 6.74318 0.328253
\(423\) 0 0
\(424\) −106.920 −5.19251
\(425\) 1.49766 0.0726474
\(426\) 0 0
\(427\) −4.31290 −0.208716
\(428\) 86.2340 4.16828
\(429\) 0 0
\(430\) −1.87487 −0.0904143
\(431\) 11.5589 0.556770 0.278385 0.960469i \(-0.410201\pi\)
0.278385 + 0.960469i \(0.410201\pi\)
\(432\) 0 0
\(433\) −32.8944 −1.58080 −0.790401 0.612590i \(-0.790128\pi\)
−0.790401 + 0.612590i \(0.790128\pi\)
\(434\) −6.34596 −0.304616
\(435\) 0 0
\(436\) −72.8716 −3.48992
\(437\) 0.427042 0.0204282
\(438\) 0 0
\(439\) −34.9713 −1.66909 −0.834545 0.550939i \(-0.814270\pi\)
−0.834545 + 0.550939i \(0.814270\pi\)
\(440\) −112.664 −5.37105
\(441\) 0 0
\(442\) 8.56518 0.407404
\(443\) 1.22246 0.0580808 0.0290404 0.999578i \(-0.490755\pi\)
0.0290404 + 0.999578i \(0.490755\pi\)
\(444\) 0 0
\(445\) 7.54918 0.357865
\(446\) 75.8353 3.59091
\(447\) 0 0
\(448\) 45.5117 2.15022
\(449\) −32.8824 −1.55182 −0.775908 0.630846i \(-0.782708\pi\)
−0.775908 + 0.630846i \(0.782708\pi\)
\(450\) 0 0
\(451\) 53.7771 2.53227
\(452\) −10.4178 −0.490010
\(453\) 0 0
\(454\) 57.8175 2.71351
\(455\) 7.77594 0.364542
\(456\) 0 0
\(457\) 38.0040 1.77775 0.888876 0.458148i \(-0.151487\pi\)
0.888876 + 0.458148i \(0.151487\pi\)
\(458\) −26.2240 −1.22537
\(459\) 0 0
\(460\) 0.724285 0.0337700
\(461\) 13.1796 0.613837 0.306919 0.951736i \(-0.400702\pi\)
0.306919 + 0.951736i \(0.400702\pi\)
\(462\) 0 0
\(463\) 2.44809 0.113772 0.0568862 0.998381i \(-0.481883\pi\)
0.0568862 + 0.998381i \(0.481883\pi\)
\(464\) −34.0156 −1.57914
\(465\) 0 0
\(466\) 30.2192 1.39988
\(467\) 36.8115 1.70343 0.851716 0.524003i \(-0.175562\pi\)
0.851716 + 0.524003i \(0.175562\pi\)
\(468\) 0 0
\(469\) 7.25212 0.334872
\(470\) 24.4750 1.12895
\(471\) 0 0
\(472\) −87.8527 −4.04375
\(473\) 2.65597 0.122122
\(474\) 0 0
\(475\) −12.9955 −0.596272
\(476\) −3.74604 −0.171699
\(477\) 0 0
\(478\) 52.1060 2.38327
\(479\) −16.1423 −0.737560 −0.368780 0.929517i \(-0.620224\pi\)
−0.368780 + 0.929517i \(0.620224\pi\)
\(480\) 0 0
\(481\) −28.2857 −1.28972
\(482\) −16.4326 −0.748486
\(483\) 0 0
\(484\) 179.698 8.16810
\(485\) −13.2297 −0.600731
\(486\) 0 0
\(487\) −13.0028 −0.589214 −0.294607 0.955618i \(-0.595189\pi\)
−0.294607 + 0.955618i \(0.595189\pi\)
\(488\) 45.8193 2.07414
\(489\) 0 0
\(490\) −4.57293 −0.206584
\(491\) −24.8426 −1.12113 −0.560565 0.828111i \(-0.689416\pi\)
−0.560565 + 0.828111i \(0.689416\pi\)
\(492\) 0 0
\(493\) 1.21512 0.0547263
\(494\) −74.3213 −3.34387
\(495\) 0 0
\(496\) 41.0514 1.84326
\(497\) −3.65756 −0.164064
\(498\) 0 0
\(499\) −5.74183 −0.257040 −0.128520 0.991707i \(-0.541023\pi\)
−0.128520 + 0.991707i \(0.541023\pi\)
\(500\) −69.5410 −3.10997
\(501\) 0 0
\(502\) 48.1436 2.14875
\(503\) −7.36156 −0.328236 −0.164118 0.986441i \(-0.552478\pi\)
−0.164118 + 0.986441i \(0.552478\pi\)
\(504\) 0 0
\(505\) 7.61602 0.338908
\(506\) −1.37965 −0.0613328
\(507\) 0 0
\(508\) 5.80316 0.257474
\(509\) 25.0910 1.11214 0.556070 0.831136i \(-0.312309\pi\)
0.556070 + 0.831136i \(0.312309\pi\)
\(510\) 0 0
\(511\) 11.6201 0.514042
\(512\) −144.250 −6.37503
\(513\) 0 0
\(514\) 7.84511 0.346033
\(515\) −9.12206 −0.401966
\(516\) 0 0
\(517\) −34.6718 −1.52486
\(518\) 16.6345 0.730876
\(519\) 0 0
\(520\) −82.6100 −3.62269
\(521\) −9.28849 −0.406936 −0.203468 0.979082i \(-0.565221\pi\)
−0.203468 + 0.979082i \(0.565221\pi\)
\(522\) 0 0
\(523\) 2.49360 0.109038 0.0545188 0.998513i \(-0.482638\pi\)
0.0545188 + 0.998513i \(0.482638\pi\)
\(524\) −2.43565 −0.106402
\(525\) 0 0
\(526\) 32.2764 1.40732
\(527\) −1.46646 −0.0638799
\(528\) 0 0
\(529\) −22.9942 −0.999747
\(530\) −46.0230 −1.99911
\(531\) 0 0
\(532\) 32.5049 1.40927
\(533\) 39.4316 1.70797
\(534\) 0 0
\(535\) 24.3261 1.05171
\(536\) −77.0450 −3.32784
\(537\) 0 0
\(538\) 7.74459 0.333893
\(539\) 6.47808 0.279031
\(540\) 0 0
\(541\) 21.2860 0.915156 0.457578 0.889170i \(-0.348717\pi\)
0.457578 + 0.889170i \(0.348717\pi\)
\(542\) −88.6985 −3.80993
\(543\) 0 0
\(544\) 18.8687 0.808987
\(545\) −20.5567 −0.880552
\(546\) 0 0
\(547\) −6.21251 −0.265628 −0.132814 0.991141i \(-0.542401\pi\)
−0.132814 + 0.991141i \(0.542401\pi\)
\(548\) 99.5353 4.25194
\(549\) 0 0
\(550\) 41.9845 1.79022
\(551\) −10.5438 −0.449181
\(552\) 0 0
\(553\) −12.8009 −0.544348
\(554\) −30.9697 −1.31578
\(555\) 0 0
\(556\) 10.9893 0.466048
\(557\) −3.39391 −0.143804 −0.0719022 0.997412i \(-0.522907\pi\)
−0.0719022 + 0.997412i \(0.522907\pi\)
\(558\) 0 0
\(559\) 1.94747 0.0823692
\(560\) 29.5818 1.25006
\(561\) 0 0
\(562\) 86.5916 3.65265
\(563\) 26.3575 1.11084 0.555418 0.831571i \(-0.312558\pi\)
0.555418 + 0.831571i \(0.312558\pi\)
\(564\) 0 0
\(565\) −2.93879 −0.123636
\(566\) 19.1764 0.806046
\(567\) 0 0
\(568\) 38.8571 1.63041
\(569\) −36.8918 −1.54658 −0.773292 0.634050i \(-0.781392\pi\)
−0.773292 + 0.634050i \(0.781392\pi\)
\(570\) 0 0
\(571\) 5.78023 0.241895 0.120948 0.992659i \(-0.461407\pi\)
0.120948 + 0.992659i \(0.461407\pi\)
\(572\) 178.569 7.46632
\(573\) 0 0
\(574\) −23.1892 −0.967900
\(575\) −0.176886 −0.00737665
\(576\) 0 0
\(577\) −23.9133 −0.995524 −0.497762 0.867314i \(-0.665845\pi\)
−0.497762 + 0.867314i \(0.665845\pi\)
\(578\) 46.3240 1.92683
\(579\) 0 0
\(580\) −17.8828 −0.742544
\(581\) −10.3550 −0.429596
\(582\) 0 0
\(583\) 65.1969 2.70018
\(584\) −123.449 −5.10837
\(585\) 0 0
\(586\) −65.8096 −2.71857
\(587\) 6.21255 0.256419 0.128210 0.991747i \(-0.459077\pi\)
0.128210 + 0.991747i \(0.459077\pi\)
\(588\) 0 0
\(589\) 12.7247 0.524311
\(590\) −37.8155 −1.55684
\(591\) 0 0
\(592\) −107.607 −4.42261
\(593\) −3.72057 −0.152785 −0.0763927 0.997078i \(-0.524340\pi\)
−0.0763927 + 0.997078i \(0.524340\pi\)
\(594\) 0 0
\(595\) −1.05674 −0.0433220
\(596\) 82.2492 3.36906
\(597\) 0 0
\(598\) −1.01161 −0.0413680
\(599\) −2.35801 −0.0963457 −0.0481729 0.998839i \(-0.515340\pi\)
−0.0481729 + 0.998839i \(0.515340\pi\)
\(600\) 0 0
\(601\) 9.65719 0.393925 0.196963 0.980411i \(-0.436892\pi\)
0.196963 + 0.980411i \(0.436892\pi\)
\(602\) −1.14528 −0.0466782
\(603\) 0 0
\(604\) −40.6214 −1.65286
\(605\) 50.6919 2.06092
\(606\) 0 0
\(607\) −17.1890 −0.697681 −0.348841 0.937182i \(-0.613425\pi\)
−0.348841 + 0.937182i \(0.613425\pi\)
\(608\) −163.726 −6.63997
\(609\) 0 0
\(610\) 19.7226 0.798543
\(611\) −25.4228 −1.02850
\(612\) 0 0
\(613\) 5.98400 0.241691 0.120846 0.992671i \(-0.461439\pi\)
0.120846 + 0.992671i \(0.461439\pi\)
\(614\) −41.0324 −1.65593
\(615\) 0 0
\(616\) −68.8218 −2.77291
\(617\) 6.59582 0.265538 0.132769 0.991147i \(-0.457613\pi\)
0.132769 + 0.991147i \(0.457613\pi\)
\(618\) 0 0
\(619\) 16.8404 0.676873 0.338437 0.940989i \(-0.390102\pi\)
0.338437 + 0.940989i \(0.390102\pi\)
\(620\) 21.5817 0.866742
\(621\) 0 0
\(622\) −82.8441 −3.32175
\(623\) 4.61148 0.184755
\(624\) 0 0
\(625\) −8.01662 −0.320665
\(626\) 25.5341 1.02055
\(627\) 0 0
\(628\) 38.2917 1.52801
\(629\) 3.84398 0.153269
\(630\) 0 0
\(631\) 1.38194 0.0550144 0.0275072 0.999622i \(-0.491243\pi\)
0.0275072 + 0.999622i \(0.491243\pi\)
\(632\) 135.994 5.40954
\(633\) 0 0
\(634\) 36.7586 1.45987
\(635\) 1.63704 0.0649639
\(636\) 0 0
\(637\) 4.75000 0.188202
\(638\) 34.0639 1.34860
\(639\) 0 0
\(640\) −112.419 −4.44376
\(641\) −23.3835 −0.923593 −0.461796 0.886986i \(-0.652795\pi\)
−0.461796 + 0.886986i \(0.652795\pi\)
\(642\) 0 0
\(643\) −5.52497 −0.217884 −0.108942 0.994048i \(-0.534746\pi\)
−0.108942 + 0.994048i \(0.534746\pi\)
\(644\) 0.442436 0.0174344
\(645\) 0 0
\(646\) 10.1001 0.397384
\(647\) −32.3975 −1.27368 −0.636840 0.770996i \(-0.719759\pi\)
−0.636840 + 0.770996i \(0.719759\pi\)
\(648\) 0 0
\(649\) 53.5701 2.10281
\(650\) 30.7848 1.20748
\(651\) 0 0
\(652\) −112.904 −4.42166
\(653\) −32.9254 −1.28847 −0.644235 0.764828i \(-0.722824\pi\)
−0.644235 + 0.764828i \(0.722824\pi\)
\(654\) 0 0
\(655\) −0.687083 −0.0268466
\(656\) 150.009 5.85687
\(657\) 0 0
\(658\) 14.9508 0.582843
\(659\) 14.4822 0.564145 0.282072 0.959393i \(-0.408978\pi\)
0.282072 + 0.959393i \(0.408978\pi\)
\(660\) 0 0
\(661\) 1.90129 0.0739516 0.0369758 0.999316i \(-0.488228\pi\)
0.0369758 + 0.999316i \(0.488228\pi\)
\(662\) 67.0559 2.60620
\(663\) 0 0
\(664\) 110.009 4.26918
\(665\) 9.16946 0.355576
\(666\) 0 0
\(667\) −0.143515 −0.00555694
\(668\) 130.230 5.03875
\(669\) 0 0
\(670\) −33.1634 −1.28122
\(671\) −27.9393 −1.07858
\(672\) 0 0
\(673\) −16.2876 −0.627841 −0.313920 0.949449i \(-0.601643\pi\)
−0.313920 + 0.949449i \(0.601643\pi\)
\(674\) −56.8963 −2.19156
\(675\) 0 0
\(676\) 55.4928 2.13434
\(677\) −21.3059 −0.818850 −0.409425 0.912344i \(-0.634271\pi\)
−0.409425 + 0.912344i \(0.634271\pi\)
\(678\) 0 0
\(679\) −8.08150 −0.310140
\(680\) 11.2265 0.430518
\(681\) 0 0
\(682\) −41.1097 −1.57417
\(683\) −26.2565 −1.00468 −0.502338 0.864671i \(-0.667527\pi\)
−0.502338 + 0.864671i \(0.667527\pi\)
\(684\) 0 0
\(685\) 28.0784 1.07282
\(686\) −2.79341 −0.106653
\(687\) 0 0
\(688\) 7.40872 0.282455
\(689\) 47.8051 1.82123
\(690\) 0 0
\(691\) −9.62773 −0.366256 −0.183128 0.983089i \(-0.558622\pi\)
−0.183128 + 0.983089i \(0.558622\pi\)
\(692\) −35.8582 −1.36312
\(693\) 0 0
\(694\) 13.7638 0.522468
\(695\) 3.10001 0.117590
\(696\) 0 0
\(697\) −5.35869 −0.202975
\(698\) 0.257317 0.00973961
\(699\) 0 0
\(700\) −13.4639 −0.508888
\(701\) 18.5426 0.700344 0.350172 0.936685i \(-0.386123\pi\)
0.350172 + 0.936685i \(0.386123\pi\)
\(702\) 0 0
\(703\) −33.3548 −1.25800
\(704\) 294.829 11.1118
\(705\) 0 0
\(706\) 23.6684 0.890772
\(707\) 4.65231 0.174968
\(708\) 0 0
\(709\) 10.4568 0.392712 0.196356 0.980533i \(-0.437089\pi\)
0.196356 + 0.980533i \(0.437089\pi\)
\(710\) 16.7258 0.627706
\(711\) 0 0
\(712\) −48.9914 −1.83603
\(713\) 0.173200 0.00648640
\(714\) 0 0
\(715\) 50.3732 1.88385
\(716\) −61.7835 −2.30896
\(717\) 0 0
\(718\) −50.6997 −1.89210
\(719\) −32.2373 −1.20225 −0.601125 0.799155i \(-0.705280\pi\)
−0.601125 + 0.799155i \(0.705280\pi\)
\(720\) 0 0
\(721\) −5.57229 −0.207523
\(722\) −34.5655 −1.28639
\(723\) 0 0
\(724\) 128.120 4.76155
\(725\) 4.36736 0.162200
\(726\) 0 0
\(727\) 6.69881 0.248445 0.124223 0.992254i \(-0.460356\pi\)
0.124223 + 0.992254i \(0.460356\pi\)
\(728\) −50.4630 −1.87028
\(729\) 0 0
\(730\) −53.1378 −1.96672
\(731\) −0.264658 −0.00978872
\(732\) 0 0
\(733\) 28.6921 1.05977 0.529883 0.848070i \(-0.322236\pi\)
0.529883 + 0.848070i \(0.322236\pi\)
\(734\) 54.0895 1.99648
\(735\) 0 0
\(736\) −2.22854 −0.0821449
\(737\) 46.9799 1.73053
\(738\) 0 0
\(739\) 16.9397 0.623138 0.311569 0.950224i \(-0.399145\pi\)
0.311569 + 0.950224i \(0.399145\pi\)
\(740\) −56.5714 −2.07961
\(741\) 0 0
\(742\) −28.1136 −1.03208
\(743\) 7.74347 0.284081 0.142040 0.989861i \(-0.454634\pi\)
0.142040 + 0.989861i \(0.454634\pi\)
\(744\) 0 0
\(745\) 23.2021 0.850058
\(746\) −20.5929 −0.753959
\(747\) 0 0
\(748\) −24.2671 −0.887294
\(749\) 14.8598 0.542967
\(750\) 0 0
\(751\) 25.6251 0.935073 0.467537 0.883974i \(-0.345142\pi\)
0.467537 + 0.883974i \(0.345142\pi\)
\(752\) −96.7153 −3.52684
\(753\) 0 0
\(754\) 24.9771 0.909611
\(755\) −11.4591 −0.417039
\(756\) 0 0
\(757\) 15.7826 0.573629 0.286814 0.957986i \(-0.407404\pi\)
0.286814 + 0.957986i \(0.407404\pi\)
\(758\) −0.0171009 −0.000621132 0
\(759\) 0 0
\(760\) −97.4144 −3.53359
\(761\) −27.0152 −0.979301 −0.489650 0.871919i \(-0.662876\pi\)
−0.489650 + 0.871919i \(0.662876\pi\)
\(762\) 0 0
\(763\) −12.5572 −0.454602
\(764\) 145.921 5.27922
\(765\) 0 0
\(766\) 101.202 3.65658
\(767\) 39.2798 1.41831
\(768\) 0 0
\(769\) −12.5918 −0.454071 −0.227036 0.973886i \(-0.572903\pi\)
−0.227036 + 0.973886i \(0.572903\pi\)
\(770\) −29.6238 −1.06757
\(771\) 0 0
\(772\) −107.592 −3.87233
\(773\) −25.5403 −0.918621 −0.459311 0.888276i \(-0.651904\pi\)
−0.459311 + 0.888276i \(0.651904\pi\)
\(774\) 0 0
\(775\) −5.27071 −0.189330
\(776\) 85.8562 3.08206
\(777\) 0 0
\(778\) −47.6613 −1.70874
\(779\) 46.4981 1.66597
\(780\) 0 0
\(781\) −23.6940 −0.847837
\(782\) 0.137477 0.00491615
\(783\) 0 0
\(784\) 18.0703 0.645369
\(785\) 10.8019 0.385536
\(786\) 0 0
\(787\) 20.8753 0.744123 0.372061 0.928208i \(-0.378651\pi\)
0.372061 + 0.928208i \(0.378651\pi\)
\(788\) −121.155 −4.31596
\(789\) 0 0
\(790\) 58.5375 2.08267
\(791\) −1.79519 −0.0638295
\(792\) 0 0
\(793\) −20.4863 −0.727489
\(794\) −79.1935 −2.81047
\(795\) 0 0
\(796\) 87.9498 3.11730
\(797\) 37.7310 1.33650 0.668251 0.743936i \(-0.267043\pi\)
0.668251 + 0.743936i \(0.267043\pi\)
\(798\) 0 0
\(799\) 3.45491 0.122226
\(800\) 67.8173 2.39770
\(801\) 0 0
\(802\) 90.5454 3.19727
\(803\) 75.2759 2.65643
\(804\) 0 0
\(805\) 0.124809 0.00439893
\(806\) −30.1433 −1.06175
\(807\) 0 0
\(808\) −49.4252 −1.73877
\(809\) 40.8855 1.43746 0.718728 0.695291i \(-0.244724\pi\)
0.718728 + 0.695291i \(0.244724\pi\)
\(810\) 0 0
\(811\) 21.0579 0.739442 0.369721 0.929143i \(-0.379453\pi\)
0.369721 + 0.929143i \(0.379453\pi\)
\(812\) −10.9239 −0.383353
\(813\) 0 0
\(814\) 107.759 3.77697
\(815\) −31.8496 −1.11564
\(816\) 0 0
\(817\) 2.29647 0.0803434
\(818\) 95.7698 3.34851
\(819\) 0 0
\(820\) 78.8633 2.75402
\(821\) −11.9078 −0.415584 −0.207792 0.978173i \(-0.566628\pi\)
−0.207792 + 0.978173i \(0.566628\pi\)
\(822\) 0 0
\(823\) 23.9178 0.833721 0.416860 0.908971i \(-0.363130\pi\)
0.416860 + 0.908971i \(0.363130\pi\)
\(824\) 59.1988 2.06229
\(825\) 0 0
\(826\) −23.0999 −0.803750
\(827\) 20.4240 0.710212 0.355106 0.934826i \(-0.384445\pi\)
0.355106 + 0.934826i \(0.384445\pi\)
\(828\) 0 0
\(829\) −19.7342 −0.685396 −0.342698 0.939446i \(-0.611341\pi\)
−0.342698 + 0.939446i \(0.611341\pi\)
\(830\) 47.3525 1.64363
\(831\) 0 0
\(832\) 216.181 7.49471
\(833\) −0.645517 −0.0223658
\(834\) 0 0
\(835\) 36.7372 1.27134
\(836\) 210.569 7.28270
\(837\) 0 0
\(838\) 53.5393 1.84948
\(839\) 0.908480 0.0313642 0.0156821 0.999877i \(-0.495008\pi\)
0.0156821 + 0.999877i \(0.495008\pi\)
\(840\) 0 0
\(841\) −25.4566 −0.877813
\(842\) −45.5051 −1.56821
\(843\) 0 0
\(844\) −14.0086 −0.482195
\(845\) 15.6542 0.538522
\(846\) 0 0
\(847\) 30.9656 1.06399
\(848\) 181.864 6.24523
\(849\) 0 0
\(850\) −4.18359 −0.143496
\(851\) −0.454004 −0.0155631
\(852\) 0 0
\(853\) 9.77125 0.334561 0.167281 0.985909i \(-0.446501\pi\)
0.167281 + 0.985909i \(0.446501\pi\)
\(854\) 12.0477 0.412264
\(855\) 0 0
\(856\) −157.868 −5.39581
\(857\) 54.9123 1.87577 0.937884 0.346950i \(-0.112783\pi\)
0.937884 + 0.346950i \(0.112783\pi\)
\(858\) 0 0
\(859\) 33.3227 1.13696 0.568478 0.822698i \(-0.307532\pi\)
0.568478 + 0.822698i \(0.307532\pi\)
\(860\) 3.89494 0.132816
\(861\) 0 0
\(862\) −32.2887 −1.09976
\(863\) −13.4052 −0.456320 −0.228160 0.973624i \(-0.573271\pi\)
−0.228160 + 0.973624i \(0.573271\pi\)
\(864\) 0 0
\(865\) −10.1154 −0.343934
\(866\) 91.8875 3.12247
\(867\) 0 0
\(868\) 13.1834 0.447473
\(869\) −82.9251 −2.81304
\(870\) 0 0
\(871\) 34.4476 1.16721
\(872\) 133.405 4.51768
\(873\) 0 0
\(874\) −1.19290 −0.0403506
\(875\) −11.9833 −0.405109
\(876\) 0 0
\(877\) 24.6955 0.833909 0.416954 0.908927i \(-0.363097\pi\)
0.416954 + 0.908927i \(0.363097\pi\)
\(878\) 97.6894 3.29686
\(879\) 0 0
\(880\) 191.634 6.45997
\(881\) −43.6844 −1.47177 −0.735883 0.677109i \(-0.763233\pi\)
−0.735883 + 0.677109i \(0.763233\pi\)
\(882\) 0 0
\(883\) −22.9644 −0.772814 −0.386407 0.922328i \(-0.626284\pi\)
−0.386407 + 0.922328i \(0.626284\pi\)
\(884\) −17.7937 −0.598466
\(885\) 0 0
\(886\) −3.41483 −0.114724
\(887\) 35.8678 1.20432 0.602162 0.798374i \(-0.294306\pi\)
0.602162 + 0.798374i \(0.294306\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −21.0880 −0.706870
\(891\) 0 0
\(892\) −157.544 −5.27495
\(893\) −29.9788 −1.00320
\(894\) 0 0
\(895\) −17.4288 −0.582581
\(896\) −68.6723 −2.29418
\(897\) 0 0
\(898\) 91.8542 3.06521
\(899\) −4.27636 −0.142625
\(900\) 0 0
\(901\) −6.49663 −0.216434
\(902\) −150.222 −5.00184
\(903\) 0 0
\(904\) 19.0717 0.634315
\(905\) 36.1420 1.20140
\(906\) 0 0
\(907\) 46.3210 1.53806 0.769032 0.639210i \(-0.220739\pi\)
0.769032 + 0.639210i \(0.220739\pi\)
\(908\) −120.113 −3.98607
\(909\) 0 0
\(910\) −21.7214 −0.720058
\(911\) 12.2609 0.406221 0.203111 0.979156i \(-0.434895\pi\)
0.203111 + 0.979156i \(0.434895\pi\)
\(912\) 0 0
\(913\) −67.0803 −2.22004
\(914\) −106.161 −3.51149
\(915\) 0 0
\(916\) 54.4789 1.80004
\(917\) −0.419711 −0.0138601
\(918\) 0 0
\(919\) 16.5157 0.544803 0.272402 0.962184i \(-0.412182\pi\)
0.272402 + 0.962184i \(0.412182\pi\)
\(920\) −1.32594 −0.0437151
\(921\) 0 0
\(922\) −36.8162 −1.21248
\(923\) −17.3734 −0.571853
\(924\) 0 0
\(925\) 13.8159 0.454265
\(926\) −6.83852 −0.224728
\(927\) 0 0
\(928\) 55.0232 1.80622
\(929\) −45.0217 −1.47712 −0.738558 0.674190i \(-0.764493\pi\)
−0.738558 + 0.674190i \(0.764493\pi\)
\(930\) 0 0
\(931\) 5.60124 0.183573
\(932\) −62.7788 −2.05639
\(933\) 0 0
\(934\) −102.830 −3.36469
\(935\) −6.84563 −0.223876
\(936\) 0 0
\(937\) 41.6320 1.36006 0.680029 0.733185i \(-0.261967\pi\)
0.680029 + 0.733185i \(0.261967\pi\)
\(938\) −20.2582 −0.661453
\(939\) 0 0
\(940\) −50.8455 −1.65840
\(941\) −14.6293 −0.476902 −0.238451 0.971155i \(-0.576640\pi\)
−0.238451 + 0.971155i \(0.576640\pi\)
\(942\) 0 0
\(943\) 0.632903 0.0206102
\(944\) 149.431 4.86358
\(945\) 0 0
\(946\) −7.41923 −0.241220
\(947\) 48.5519 1.57772 0.788862 0.614570i \(-0.210671\pi\)
0.788862 + 0.614570i \(0.210671\pi\)
\(948\) 0 0
\(949\) 55.1955 1.79172
\(950\) 36.3017 1.17778
\(951\) 0 0
\(952\) 6.85783 0.222264
\(953\) −25.4440 −0.824211 −0.412106 0.911136i \(-0.635207\pi\)
−0.412106 + 0.911136i \(0.635207\pi\)
\(954\) 0 0
\(955\) 41.1634 1.33202
\(956\) −108.247 −3.50096
\(957\) 0 0
\(958\) 45.0921 1.45686
\(959\) 17.1519 0.553864
\(960\) 0 0
\(961\) −25.8391 −0.833520
\(962\) 79.0137 2.54751
\(963\) 0 0
\(964\) 34.1379 1.09951
\(965\) −30.3512 −0.977039
\(966\) 0 0
\(967\) −55.0393 −1.76995 −0.884973 0.465643i \(-0.845823\pi\)
−0.884973 + 0.465643i \(0.845823\pi\)
\(968\) −328.972 −10.5736
\(969\) 0 0
\(970\) 36.9561 1.18659
\(971\) −30.6876 −0.984813 −0.492406 0.870365i \(-0.663883\pi\)
−0.492406 + 0.870365i \(0.663883\pi\)
\(972\) 0 0
\(973\) 1.89367 0.0607082
\(974\) 36.3223 1.16384
\(975\) 0 0
\(976\) −77.9354 −2.49465
\(977\) 8.85827 0.283401 0.141701 0.989910i \(-0.454743\pi\)
0.141701 + 0.989910i \(0.454743\pi\)
\(978\) 0 0
\(979\) 29.8736 0.954763
\(980\) 9.50000 0.303466
\(981\) 0 0
\(982\) 69.3956 2.21450
\(983\) 31.5119 1.00507 0.502537 0.864556i \(-0.332400\pi\)
0.502537 + 0.864556i \(0.332400\pi\)
\(984\) 0 0
\(985\) −34.1771 −1.08897
\(986\) −3.39434 −0.108098
\(987\) 0 0
\(988\) 154.398 4.91207
\(989\) 0.0312581 0.000993951 0
\(990\) 0 0
\(991\) −9.28778 −0.295036 −0.147518 0.989059i \(-0.547128\pi\)
−0.147518 + 0.989059i \(0.547128\pi\)
\(992\) −66.4042 −2.10834
\(993\) 0 0
\(994\) 10.2171 0.324066
\(995\) 24.8102 0.786535
\(996\) 0 0
\(997\) −13.4491 −0.425937 −0.212969 0.977059i \(-0.568313\pi\)
−0.212969 + 0.977059i \(0.568313\pi\)
\(998\) 16.0393 0.507715
\(999\) 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 \(a_p\))