Properties

Label 8001.2.a.o.1.1
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
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: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.70878\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70878 q^{2}\) \(+5.33747 q^{4}\) \(-2.87857 q^{5}\) \(+1.00000 q^{7}\) \(-9.04047 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.70878 q^{2}\) \(+5.33747 q^{4}\) \(-2.87857 q^{5}\) \(+1.00000 q^{7}\) \(-9.04047 q^{8}\) \(+7.79741 q^{10}\) \(+1.50105 q^{11}\) \(+5.43745 q^{13}\) \(-2.70878 q^{14}\) \(+13.8137 q^{16}\) \(-1.68422 q^{17}\) \(-3.30288 q^{19}\) \(-15.3643 q^{20}\) \(-4.06601 q^{22}\) \(+5.07189 q^{23}\) \(+3.28617 q^{25}\) \(-14.7288 q^{26}\) \(+5.33747 q^{28}\) \(+8.28010 q^{29}\) \(-9.29635 q^{31}\) \(-19.3372 q^{32}\) \(+4.56218 q^{34}\) \(-2.87857 q^{35}\) \(-7.22083 q^{37}\) \(+8.94677 q^{38}\) \(+26.0237 q^{40}\) \(+2.03090 q^{41}\) \(+0.859629 q^{43}\) \(+8.01182 q^{44}\) \(-13.7386 q^{46}\) \(+6.92288 q^{47}\) \(+1.00000 q^{49}\) \(-8.90151 q^{50}\) \(+29.0223 q^{52}\) \(-8.32870 q^{53}\) \(-4.32088 q^{55}\) \(-9.04047 q^{56}\) \(-22.4289 q^{58}\) \(-8.94067 q^{59}\) \(+9.99896 q^{61}\) \(+25.1817 q^{62}\) \(+24.7529 q^{64}\) \(-15.6521 q^{65}\) \(-15.7116 q^{67}\) \(-8.98949 q^{68}\) \(+7.79741 q^{70}\) \(-5.53761 q^{71}\) \(+6.56437 q^{73}\) \(+19.5596 q^{74}\) \(-17.6290 q^{76}\) \(+1.50105 q^{77}\) \(-9.27964 q^{79}\) \(-39.7637 q^{80}\) \(-5.50124 q^{82}\) \(-7.17857 q^{83}\) \(+4.84815 q^{85}\) \(-2.32854 q^{86}\) \(-13.5702 q^{88}\) \(-9.76491 q^{89}\) \(+5.43745 q^{91}\) \(+27.0711 q^{92}\) \(-18.7525 q^{94}\) \(+9.50758 q^{95}\) \(-9.08877 q^{97}\) \(-2.70878 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70878 −1.91539 −0.957697 0.287777i \(-0.907084\pi\)
−0.957697 + 0.287777i \(0.907084\pi\)
\(3\) 0 0
\(4\) 5.33747 2.66874
\(5\) −2.87857 −1.28734 −0.643668 0.765305i \(-0.722588\pi\)
−0.643668 + 0.765305i \(0.722588\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −9.04047 −3.19629
\(9\) 0 0
\(10\) 7.79741 2.46576
\(11\) 1.50105 0.452584 0.226292 0.974060i \(-0.427340\pi\)
0.226292 + 0.974060i \(0.427340\pi\)
\(12\) 0 0
\(13\) 5.43745 1.50808 0.754039 0.656830i \(-0.228103\pi\)
0.754039 + 0.656830i \(0.228103\pi\)
\(14\) −2.70878 −0.723951
\(15\) 0 0
\(16\) 13.8137 3.45342
\(17\) −1.68422 −0.408484 −0.204242 0.978920i \(-0.565473\pi\)
−0.204242 + 0.978920i \(0.565473\pi\)
\(18\) 0 0
\(19\) −3.30288 −0.757733 −0.378867 0.925451i \(-0.623686\pi\)
−0.378867 + 0.925451i \(0.623686\pi\)
\(20\) −15.3643 −3.43556
\(21\) 0 0
\(22\) −4.06601 −0.866877
\(23\) 5.07189 1.05756 0.528781 0.848758i \(-0.322649\pi\)
0.528781 + 0.848758i \(0.322649\pi\)
\(24\) 0 0
\(25\) 3.28617 0.657235
\(26\) −14.7288 −2.88856
\(27\) 0 0
\(28\) 5.33747 1.00869
\(29\) 8.28010 1.53758 0.768788 0.639504i \(-0.220860\pi\)
0.768788 + 0.639504i \(0.220860\pi\)
\(30\) 0 0
\(31\) −9.29635 −1.66967 −0.834837 0.550498i \(-0.814438\pi\)
−0.834837 + 0.550498i \(0.814438\pi\)
\(32\) −19.3372 −3.41837
\(33\) 0 0
\(34\) 4.56218 0.782408
\(35\) −2.87857 −0.486567
\(36\) 0 0
\(37\) −7.22083 −1.18710 −0.593548 0.804798i \(-0.702273\pi\)
−0.593548 + 0.804798i \(0.702273\pi\)
\(38\) 8.94677 1.45136
\(39\) 0 0
\(40\) 26.0237 4.11470
\(41\) 2.03090 0.317173 0.158586 0.987345i \(-0.449306\pi\)
0.158586 + 0.987345i \(0.449306\pi\)
\(42\) 0 0
\(43\) 0.859629 0.131092 0.0655461 0.997850i \(-0.479121\pi\)
0.0655461 + 0.997850i \(0.479121\pi\)
\(44\) 8.01182 1.20783
\(45\) 0 0
\(46\) −13.7386 −2.02565
\(47\) 6.92288 1.00981 0.504903 0.863176i \(-0.331528\pi\)
0.504903 + 0.863176i \(0.331528\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −8.90151 −1.25886
\(51\) 0 0
\(52\) 29.0223 4.02466
\(53\) −8.32870 −1.14404 −0.572018 0.820241i \(-0.693839\pi\)
−0.572018 + 0.820241i \(0.693839\pi\)
\(54\) 0 0
\(55\) −4.32088 −0.582628
\(56\) −9.04047 −1.20808
\(57\) 0 0
\(58\) −22.4289 −2.94506
\(59\) −8.94067 −1.16398 −0.581988 0.813197i \(-0.697725\pi\)
−0.581988 + 0.813197i \(0.697725\pi\)
\(60\) 0 0
\(61\) 9.99896 1.28024 0.640118 0.768277i \(-0.278886\pi\)
0.640118 + 0.768277i \(0.278886\pi\)
\(62\) 25.1817 3.19808
\(63\) 0 0
\(64\) 24.7529 3.09411
\(65\) −15.6521 −1.94140
\(66\) 0 0
\(67\) −15.7116 −1.91947 −0.959736 0.280903i \(-0.909366\pi\)
−0.959736 + 0.280903i \(0.909366\pi\)
\(68\) −8.98949 −1.09014
\(69\) 0 0
\(70\) 7.79741 0.931969
\(71\) −5.53761 −0.657194 −0.328597 0.944470i \(-0.606576\pi\)
−0.328597 + 0.944470i \(0.606576\pi\)
\(72\) 0 0
\(73\) 6.56437 0.768302 0.384151 0.923270i \(-0.374494\pi\)
0.384151 + 0.923270i \(0.374494\pi\)
\(74\) 19.5596 2.27376
\(75\) 0 0
\(76\) −17.6290 −2.02219
\(77\) 1.50105 0.171061
\(78\) 0 0
\(79\) −9.27964 −1.04404 −0.522021 0.852933i \(-0.674822\pi\)
−0.522021 + 0.852933i \(0.674822\pi\)
\(80\) −39.7637 −4.44571
\(81\) 0 0
\(82\) −5.50124 −0.607511
\(83\) −7.17857 −0.787950 −0.393975 0.919121i \(-0.628900\pi\)
−0.393975 + 0.919121i \(0.628900\pi\)
\(84\) 0 0
\(85\) 4.84815 0.525856
\(86\) −2.32854 −0.251093
\(87\) 0 0
\(88\) −13.5702 −1.44659
\(89\) −9.76491 −1.03508 −0.517539 0.855660i \(-0.673152\pi\)
−0.517539 + 0.855660i \(0.673152\pi\)
\(90\) 0 0
\(91\) 5.43745 0.570000
\(92\) 27.0711 2.82235
\(93\) 0 0
\(94\) −18.7525 −1.93418
\(95\) 9.50758 0.975457
\(96\) 0 0
\(97\) −9.08877 −0.922825 −0.461412 0.887186i \(-0.652657\pi\)
−0.461412 + 0.887186i \(0.652657\pi\)
\(98\) −2.70878 −0.273628
\(99\) 0 0
\(100\) 17.5399 1.75399
\(101\) 2.25398 0.224279 0.112140 0.993692i \(-0.464230\pi\)
0.112140 + 0.993692i \(0.464230\pi\)
\(102\) 0 0
\(103\) 17.1074 1.68564 0.842820 0.538195i \(-0.180894\pi\)
0.842820 + 0.538195i \(0.180894\pi\)
\(104\) −49.1571 −4.82025
\(105\) 0 0
\(106\) 22.5606 2.19128
\(107\) 3.37485 0.326259 0.163130 0.986605i \(-0.447841\pi\)
0.163130 + 0.986605i \(0.447841\pi\)
\(108\) 0 0
\(109\) 8.18665 0.784139 0.392069 0.919936i \(-0.371759\pi\)
0.392069 + 0.919936i \(0.371759\pi\)
\(110\) 11.7043 1.11596
\(111\) 0 0
\(112\) 13.8137 1.30527
\(113\) 13.4635 1.26654 0.633269 0.773932i \(-0.281713\pi\)
0.633269 + 0.773932i \(0.281713\pi\)
\(114\) 0 0
\(115\) −14.5998 −1.36144
\(116\) 44.1948 4.10338
\(117\) 0 0
\(118\) 24.2183 2.22947
\(119\) −1.68422 −0.154392
\(120\) 0 0
\(121\) −8.74685 −0.795168
\(122\) −27.0850 −2.45216
\(123\) 0 0
\(124\) −49.6190 −4.45592
\(125\) 4.93337 0.441254
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −28.3756 −2.50808
\(129\) 0 0
\(130\) 42.3980 3.71855
\(131\) 0.496098 0.0433443 0.0216721 0.999765i \(-0.493101\pi\)
0.0216721 + 0.999765i \(0.493101\pi\)
\(132\) 0 0
\(133\) −3.30288 −0.286396
\(134\) 42.5591 3.67655
\(135\) 0 0
\(136\) 15.2262 1.30563
\(137\) −20.7815 −1.77548 −0.887741 0.460343i \(-0.847726\pi\)
−0.887741 + 0.460343i \(0.847726\pi\)
\(138\) 0 0
\(139\) 0.210195 0.0178285 0.00891424 0.999960i \(-0.497162\pi\)
0.00891424 + 0.999960i \(0.497162\pi\)
\(140\) −15.3643 −1.29852
\(141\) 0 0
\(142\) 15.0002 1.25879
\(143\) 8.16189 0.682531
\(144\) 0 0
\(145\) −23.8349 −1.97938
\(146\) −17.7814 −1.47160
\(147\) 0 0
\(148\) −38.5410 −3.16805
\(149\) 9.61526 0.787713 0.393857 0.919172i \(-0.371141\pi\)
0.393857 + 0.919172i \(0.371141\pi\)
\(150\) 0 0
\(151\) 4.39942 0.358020 0.179010 0.983847i \(-0.442711\pi\)
0.179010 + 0.983847i \(0.442711\pi\)
\(152\) 29.8596 2.42194
\(153\) 0 0
\(154\) −4.06601 −0.327649
\(155\) 26.7602 2.14943
\(156\) 0 0
\(157\) −1.08882 −0.0868971 −0.0434486 0.999056i \(-0.513834\pi\)
−0.0434486 + 0.999056i \(0.513834\pi\)
\(158\) 25.1365 1.99975
\(159\) 0 0
\(160\) 55.6636 4.40060
\(161\) 5.07189 0.399721
\(162\) 0 0
\(163\) −13.7282 −1.07528 −0.537638 0.843176i \(-0.680683\pi\)
−0.537638 + 0.843176i \(0.680683\pi\)
\(164\) 10.8398 0.846450
\(165\) 0 0
\(166\) 19.4451 1.50924
\(167\) −10.7070 −0.828536 −0.414268 0.910155i \(-0.635962\pi\)
−0.414268 + 0.910155i \(0.635962\pi\)
\(168\) 0 0
\(169\) 16.5659 1.27430
\(170\) −13.1326 −1.00722
\(171\) 0 0
\(172\) 4.58825 0.349851
\(173\) 5.28100 0.401507 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(174\) 0 0
\(175\) 3.28617 0.248411
\(176\) 20.7350 1.56296
\(177\) 0 0
\(178\) 26.4510 1.98258
\(179\) 3.05114 0.228053 0.114026 0.993478i \(-0.463625\pi\)
0.114026 + 0.993478i \(0.463625\pi\)
\(180\) 0 0
\(181\) 19.8363 1.47442 0.737209 0.675664i \(-0.236143\pi\)
0.737209 + 0.675664i \(0.236143\pi\)
\(182\) −14.7288 −1.09177
\(183\) 0 0
\(184\) −45.8523 −3.38027
\(185\) 20.7857 1.52819
\(186\) 0 0
\(187\) −2.52810 −0.184873
\(188\) 36.9507 2.69491
\(189\) 0 0
\(190\) −25.7539 −1.86839
\(191\) −26.8779 −1.94482 −0.972410 0.233280i \(-0.925054\pi\)
−0.972410 + 0.233280i \(0.925054\pi\)
\(192\) 0 0
\(193\) 11.4021 0.820739 0.410369 0.911919i \(-0.365400\pi\)
0.410369 + 0.911919i \(0.365400\pi\)
\(194\) 24.6194 1.76757
\(195\) 0 0
\(196\) 5.33747 0.381248
\(197\) 11.0512 0.787368 0.393684 0.919246i \(-0.371200\pi\)
0.393684 + 0.919246i \(0.371200\pi\)
\(198\) 0 0
\(199\) 4.37619 0.310220 0.155110 0.987897i \(-0.450427\pi\)
0.155110 + 0.987897i \(0.450427\pi\)
\(200\) −29.7086 −2.10071
\(201\) 0 0
\(202\) −6.10553 −0.429583
\(203\) 8.28010 0.581149
\(204\) 0 0
\(205\) −5.84608 −0.408308
\(206\) −46.3401 −3.22867
\(207\) 0 0
\(208\) 75.1112 5.20803
\(209\) −4.95779 −0.342938
\(210\) 0 0
\(211\) −4.47388 −0.307994 −0.153997 0.988071i \(-0.549215\pi\)
−0.153997 + 0.988071i \(0.549215\pi\)
\(212\) −44.4542 −3.05313
\(213\) 0 0
\(214\) −9.14172 −0.624915
\(215\) −2.47450 −0.168760
\(216\) 0 0
\(217\) −9.29635 −0.631077
\(218\) −22.1758 −1.50193
\(219\) 0 0
\(220\) −23.0626 −1.55488
\(221\) −9.15787 −0.616025
\(222\) 0 0
\(223\) 24.4884 1.63986 0.819932 0.572461i \(-0.194011\pi\)
0.819932 + 0.572461i \(0.194011\pi\)
\(224\) −19.3372 −1.29202
\(225\) 0 0
\(226\) −36.4696 −2.42592
\(227\) 0.513152 0.0340591 0.0170296 0.999855i \(-0.494579\pi\)
0.0170296 + 0.999855i \(0.494579\pi\)
\(228\) 0 0
\(229\) −19.6982 −1.30169 −0.650847 0.759209i \(-0.725586\pi\)
−0.650847 + 0.759209i \(0.725586\pi\)
\(230\) 39.5476 2.60769
\(231\) 0 0
\(232\) −74.8560 −4.91454
\(233\) 1.36091 0.0891564 0.0445782 0.999006i \(-0.485806\pi\)
0.0445782 + 0.999006i \(0.485806\pi\)
\(234\) 0 0
\(235\) −19.9280 −1.29996
\(236\) −47.7206 −3.10635
\(237\) 0 0
\(238\) 4.56218 0.295722
\(239\) −25.4879 −1.64867 −0.824336 0.566100i \(-0.808451\pi\)
−0.824336 + 0.566100i \(0.808451\pi\)
\(240\) 0 0
\(241\) 23.9835 1.54492 0.772458 0.635066i \(-0.219027\pi\)
0.772458 + 0.635066i \(0.219027\pi\)
\(242\) 23.6933 1.52306
\(243\) 0 0
\(244\) 53.3692 3.41661
\(245\) −2.87857 −0.183905
\(246\) 0 0
\(247\) −17.9593 −1.14272
\(248\) 84.0434 5.33676
\(249\) 0 0
\(250\) −13.3634 −0.845176
\(251\) −10.4969 −0.662558 −0.331279 0.943533i \(-0.607480\pi\)
−0.331279 + 0.943533i \(0.607480\pi\)
\(252\) 0 0
\(253\) 7.61316 0.478635
\(254\) 2.70878 0.169964
\(255\) 0 0
\(256\) 27.3575 1.70984
\(257\) −3.96662 −0.247431 −0.123716 0.992318i \(-0.539481\pi\)
−0.123716 + 0.992318i \(0.539481\pi\)
\(258\) 0 0
\(259\) −7.22083 −0.448680
\(260\) −83.5426 −5.18109
\(261\) 0 0
\(262\) −1.34382 −0.0830214
\(263\) 5.02765 0.310018 0.155009 0.987913i \(-0.450459\pi\)
0.155009 + 0.987913i \(0.450459\pi\)
\(264\) 0 0
\(265\) 23.9748 1.47276
\(266\) 8.94677 0.548562
\(267\) 0 0
\(268\) −83.8600 −5.12257
\(269\) −16.7702 −1.02250 −0.511249 0.859432i \(-0.670817\pi\)
−0.511249 + 0.859432i \(0.670817\pi\)
\(270\) 0 0
\(271\) −24.8503 −1.50955 −0.754773 0.655986i \(-0.772253\pi\)
−0.754773 + 0.655986i \(0.772253\pi\)
\(272\) −23.2653 −1.41067
\(273\) 0 0
\(274\) 56.2924 3.40075
\(275\) 4.93271 0.297454
\(276\) 0 0
\(277\) −5.45207 −0.327583 −0.163791 0.986495i \(-0.552372\pi\)
−0.163791 + 0.986495i \(0.552372\pi\)
\(278\) −0.569371 −0.0341486
\(279\) 0 0
\(280\) 26.0237 1.55521
\(281\) 9.96730 0.594600 0.297300 0.954784i \(-0.403914\pi\)
0.297300 + 0.954784i \(0.403914\pi\)
\(282\) 0 0
\(283\) −6.38116 −0.379320 −0.189660 0.981850i \(-0.560739\pi\)
−0.189660 + 0.981850i \(0.560739\pi\)
\(284\) −29.5569 −1.75388
\(285\) 0 0
\(286\) −22.1087 −1.30732
\(287\) 2.03090 0.119880
\(288\) 0 0
\(289\) −14.1634 −0.833141
\(290\) 64.5633 3.79129
\(291\) 0 0
\(292\) 35.0372 2.05040
\(293\) 26.0774 1.52346 0.761728 0.647896i \(-0.224351\pi\)
0.761728 + 0.647896i \(0.224351\pi\)
\(294\) 0 0
\(295\) 25.7364 1.49843
\(296\) 65.2797 3.79431
\(297\) 0 0
\(298\) −26.0456 −1.50878
\(299\) 27.5781 1.59489
\(300\) 0 0
\(301\) 0.859629 0.0495482
\(302\) −11.9171 −0.685750
\(303\) 0 0
\(304\) −45.6250 −2.61677
\(305\) −28.7827 −1.64809
\(306\) 0 0
\(307\) −6.03900 −0.344664 −0.172332 0.985039i \(-0.555130\pi\)
−0.172332 + 0.985039i \(0.555130\pi\)
\(308\) 8.01182 0.456516
\(309\) 0 0
\(310\) −72.4874 −4.11701
\(311\) 27.0222 1.53229 0.766144 0.642669i \(-0.222173\pi\)
0.766144 + 0.642669i \(0.222173\pi\)
\(312\) 0 0
\(313\) −24.2532 −1.37087 −0.685435 0.728134i \(-0.740388\pi\)
−0.685435 + 0.728134i \(0.740388\pi\)
\(314\) 2.94937 0.166442
\(315\) 0 0
\(316\) −49.5298 −2.78627
\(317\) −8.83443 −0.496191 −0.248095 0.968736i \(-0.579805\pi\)
−0.248095 + 0.968736i \(0.579805\pi\)
\(318\) 0 0
\(319\) 12.4288 0.695882
\(320\) −71.2530 −3.98317
\(321\) 0 0
\(322\) −13.7386 −0.765623
\(323\) 5.56279 0.309522
\(324\) 0 0
\(325\) 17.8684 0.991161
\(326\) 37.1867 2.05958
\(327\) 0 0
\(328\) −18.3603 −1.01378
\(329\) 6.92288 0.381671
\(330\) 0 0
\(331\) −16.9974 −0.934261 −0.467130 0.884188i \(-0.654712\pi\)
−0.467130 + 0.884188i \(0.654712\pi\)
\(332\) −38.3154 −2.10283
\(333\) 0 0
\(334\) 29.0030 1.58697
\(335\) 45.2268 2.47101
\(336\) 0 0
\(337\) 12.4361 0.677435 0.338718 0.940888i \(-0.390007\pi\)
0.338718 + 0.940888i \(0.390007\pi\)
\(338\) −44.8733 −2.44078
\(339\) 0 0
\(340\) 25.8769 1.40337
\(341\) −13.9543 −0.755667
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −7.77146 −0.419009
\(345\) 0 0
\(346\) −14.3051 −0.769045
\(347\) −10.2559 −0.550567 −0.275283 0.961363i \(-0.588772\pi\)
−0.275283 + 0.961363i \(0.588772\pi\)
\(348\) 0 0
\(349\) 28.0536 1.50167 0.750836 0.660488i \(-0.229651\pi\)
0.750836 + 0.660488i \(0.229651\pi\)
\(350\) −8.90151 −0.475806
\(351\) 0 0
\(352\) −29.0262 −1.54710
\(353\) 0.120411 0.00640881 0.00320440 0.999995i \(-0.498980\pi\)
0.00320440 + 0.999995i \(0.498980\pi\)
\(354\) 0 0
\(355\) 15.9404 0.846029
\(356\) −52.1199 −2.76235
\(357\) 0 0
\(358\) −8.26485 −0.436811
\(359\) −15.5091 −0.818542 −0.409271 0.912413i \(-0.634217\pi\)
−0.409271 + 0.912413i \(0.634217\pi\)
\(360\) 0 0
\(361\) −8.09097 −0.425840
\(362\) −53.7320 −2.82409
\(363\) 0 0
\(364\) 29.0223 1.52118
\(365\) −18.8960 −0.989063
\(366\) 0 0
\(367\) 0.278621 0.0145439 0.00727195 0.999974i \(-0.497685\pi\)
0.00727195 + 0.999974i \(0.497685\pi\)
\(368\) 70.0615 3.65221
\(369\) 0 0
\(370\) −56.3038 −2.92709
\(371\) −8.32870 −0.432405
\(372\) 0 0
\(373\) 25.5201 1.32138 0.660691 0.750658i \(-0.270263\pi\)
0.660691 + 0.750658i \(0.270263\pi\)
\(374\) 6.84807 0.354105
\(375\) 0 0
\(376\) −62.5861 −3.22763
\(377\) 45.0226 2.31878
\(378\) 0 0
\(379\) −10.1849 −0.523161 −0.261580 0.965182i \(-0.584244\pi\)
−0.261580 + 0.965182i \(0.584244\pi\)
\(380\) 50.7465 2.60324
\(381\) 0 0
\(382\) 72.8063 3.72510
\(383\) 27.7594 1.41844 0.709220 0.704987i \(-0.249047\pi\)
0.709220 + 0.704987i \(0.249047\pi\)
\(384\) 0 0
\(385\) −4.32088 −0.220213
\(386\) −30.8857 −1.57204
\(387\) 0 0
\(388\) −48.5111 −2.46278
\(389\) −26.1982 −1.32830 −0.664151 0.747598i \(-0.731207\pi\)
−0.664151 + 0.747598i \(0.731207\pi\)
\(390\) 0 0
\(391\) −8.54219 −0.431997
\(392\) −9.04047 −0.456613
\(393\) 0 0
\(394\) −29.9353 −1.50812
\(395\) 26.7121 1.34403
\(396\) 0 0
\(397\) 8.93868 0.448620 0.224310 0.974518i \(-0.427987\pi\)
0.224310 + 0.974518i \(0.427987\pi\)
\(398\) −11.8541 −0.594193
\(399\) 0 0
\(400\) 45.3942 2.26971
\(401\) 35.2875 1.76217 0.881086 0.472956i \(-0.156813\pi\)
0.881086 + 0.472956i \(0.156813\pi\)
\(402\) 0 0
\(403\) −50.5484 −2.51800
\(404\) 12.0306 0.598542
\(405\) 0 0
\(406\) −22.4289 −1.11313
\(407\) −10.8388 −0.537261
\(408\) 0 0
\(409\) −6.33933 −0.313460 −0.156730 0.987642i \(-0.550095\pi\)
−0.156730 + 0.987642i \(0.550095\pi\)
\(410\) 15.8357 0.782070
\(411\) 0 0
\(412\) 91.3102 4.49853
\(413\) −8.94067 −0.439942
\(414\) 0 0
\(415\) 20.6640 1.01436
\(416\) −105.145 −5.15517
\(417\) 0 0
\(418\) 13.4296 0.656861
\(419\) −36.2997 −1.77335 −0.886677 0.462388i \(-0.846993\pi\)
−0.886677 + 0.462388i \(0.846993\pi\)
\(420\) 0 0
\(421\) −8.45931 −0.412282 −0.206141 0.978522i \(-0.566091\pi\)
−0.206141 + 0.978522i \(0.566091\pi\)
\(422\) 12.1187 0.589931
\(423\) 0 0
\(424\) 75.2954 3.65667
\(425\) −5.53465 −0.268470
\(426\) 0 0
\(427\) 9.99896 0.483884
\(428\) 18.0132 0.870700
\(429\) 0 0
\(430\) 6.70288 0.323242
\(431\) 29.6930 1.43026 0.715130 0.698991i \(-0.246367\pi\)
0.715130 + 0.698991i \(0.246367\pi\)
\(432\) 0 0
\(433\) 29.0121 1.39423 0.697116 0.716958i \(-0.254466\pi\)
0.697116 + 0.716958i \(0.254466\pi\)
\(434\) 25.1817 1.20876
\(435\) 0 0
\(436\) 43.6960 2.09266
\(437\) −16.7519 −0.801350
\(438\) 0 0
\(439\) −15.1917 −0.725058 −0.362529 0.931972i \(-0.618087\pi\)
−0.362529 + 0.931972i \(0.618087\pi\)
\(440\) 39.0628 1.86225
\(441\) 0 0
\(442\) 24.8066 1.17993
\(443\) −21.9474 −1.04275 −0.521377 0.853327i \(-0.674581\pi\)
−0.521377 + 0.853327i \(0.674581\pi\)
\(444\) 0 0
\(445\) 28.1090 1.33249
\(446\) −66.3336 −3.14099
\(447\) 0 0
\(448\) 24.7529 1.16947
\(449\) −10.5308 −0.496979 −0.248490 0.968635i \(-0.579934\pi\)
−0.248490 + 0.968635i \(0.579934\pi\)
\(450\) 0 0
\(451\) 3.04848 0.143547
\(452\) 71.8610 3.38006
\(453\) 0 0
\(454\) −1.39002 −0.0652366
\(455\) −15.6521 −0.733781
\(456\) 0 0
\(457\) −26.7062 −1.24926 −0.624632 0.780920i \(-0.714751\pi\)
−0.624632 + 0.780920i \(0.714751\pi\)
\(458\) 53.3580 2.49326
\(459\) 0 0
\(460\) −77.9260 −3.63332
\(461\) −5.08320 −0.236748 −0.118374 0.992969i \(-0.537768\pi\)
−0.118374 + 0.992969i \(0.537768\pi\)
\(462\) 0 0
\(463\) −2.56483 −0.119198 −0.0595988 0.998222i \(-0.518982\pi\)
−0.0595988 + 0.998222i \(0.518982\pi\)
\(464\) 114.379 5.30990
\(465\) 0 0
\(466\) −3.68641 −0.170770
\(467\) 38.3764 1.77585 0.887925 0.459989i \(-0.152147\pi\)
0.887925 + 0.459989i \(0.152147\pi\)
\(468\) 0 0
\(469\) −15.7116 −0.725492
\(470\) 53.9805 2.48994
\(471\) 0 0
\(472\) 80.8279 3.72041
\(473\) 1.29035 0.0593302
\(474\) 0 0
\(475\) −10.8538 −0.498009
\(476\) −8.98949 −0.412033
\(477\) 0 0
\(478\) 69.0409 3.15786
\(479\) 9.38202 0.428675 0.214338 0.976760i \(-0.431241\pi\)
0.214338 + 0.976760i \(0.431241\pi\)
\(480\) 0 0
\(481\) −39.2629 −1.79023
\(482\) −64.9661 −2.95912
\(483\) 0 0
\(484\) −46.6861 −2.12209
\(485\) 26.1627 1.18799
\(486\) 0 0
\(487\) 30.0828 1.36318 0.681591 0.731733i \(-0.261288\pi\)
0.681591 + 0.731733i \(0.261288\pi\)
\(488\) −90.3953 −4.09200
\(489\) 0 0
\(490\) 7.79741 0.352251
\(491\) −39.3902 −1.77765 −0.888827 0.458244i \(-0.848479\pi\)
−0.888827 + 0.458244i \(0.848479\pi\)
\(492\) 0 0
\(493\) −13.9455 −0.628075
\(494\) 48.6476 2.18876
\(495\) 0 0
\(496\) −128.417 −5.76609
\(497\) −5.53761 −0.248396
\(498\) 0 0
\(499\) 19.4929 0.872624 0.436312 0.899795i \(-0.356284\pi\)
0.436312 + 0.899795i \(0.356284\pi\)
\(500\) 26.3317 1.17759
\(501\) 0 0
\(502\) 28.4337 1.26906
\(503\) 25.0033 1.11484 0.557421 0.830230i \(-0.311791\pi\)
0.557421 + 0.830230i \(0.311791\pi\)
\(504\) 0 0
\(505\) −6.48824 −0.288723
\(506\) −20.6224 −0.916776
\(507\) 0 0
\(508\) −5.33747 −0.236812
\(509\) −0.817857 −0.0362509 −0.0181254 0.999836i \(-0.505770\pi\)
−0.0181254 + 0.999836i \(0.505770\pi\)
\(510\) 0 0
\(511\) 6.56437 0.290391
\(512\) −17.3540 −0.766947
\(513\) 0 0
\(514\) 10.7447 0.473928
\(515\) −49.2448 −2.16999
\(516\) 0 0
\(517\) 10.3916 0.457022
\(518\) 19.5596 0.859400
\(519\) 0 0
\(520\) 141.502 6.20529
\(521\) −23.7258 −1.03945 −0.519723 0.854335i \(-0.673965\pi\)
−0.519723 + 0.854335i \(0.673965\pi\)
\(522\) 0 0
\(523\) −12.8646 −0.562530 −0.281265 0.959630i \(-0.590754\pi\)
−0.281265 + 0.959630i \(0.590754\pi\)
\(524\) 2.64791 0.115674
\(525\) 0 0
\(526\) −13.6188 −0.593807
\(527\) 15.6571 0.682035
\(528\) 0 0
\(529\) 2.72405 0.118437
\(530\) −64.9423 −2.82091
\(531\) 0 0
\(532\) −17.6290 −0.764316
\(533\) 11.0429 0.478321
\(534\) 0 0
\(535\) −9.71475 −0.420005
\(536\) 142.040 6.13519
\(537\) 0 0
\(538\) 45.4268 1.95849
\(539\) 1.50105 0.0646548
\(540\) 0 0
\(541\) −27.7136 −1.19150 −0.595751 0.803170i \(-0.703145\pi\)
−0.595751 + 0.803170i \(0.703145\pi\)
\(542\) 67.3139 2.89138
\(543\) 0 0
\(544\) 32.5682 1.39635
\(545\) −23.5658 −1.00945
\(546\) 0 0
\(547\) 41.1078 1.75764 0.878821 0.477152i \(-0.158331\pi\)
0.878821 + 0.477152i \(0.158331\pi\)
\(548\) −110.921 −4.73829
\(549\) 0 0
\(550\) −13.3616 −0.569742
\(551\) −27.3482 −1.16507
\(552\) 0 0
\(553\) −9.27964 −0.394610
\(554\) 14.7684 0.627451
\(555\) 0 0
\(556\) 1.12191 0.0475795
\(557\) 1.86702 0.0791083 0.0395541 0.999217i \(-0.487406\pi\)
0.0395541 + 0.999217i \(0.487406\pi\)
\(558\) 0 0
\(559\) 4.67419 0.197697
\(560\) −39.7637 −1.68032
\(561\) 0 0
\(562\) −26.9992 −1.13889
\(563\) 8.31194 0.350306 0.175153 0.984541i \(-0.443958\pi\)
0.175153 + 0.984541i \(0.443958\pi\)
\(564\) 0 0
\(565\) −38.7556 −1.63046
\(566\) 17.2851 0.726548
\(567\) 0 0
\(568\) 50.0626 2.10058
\(569\) −36.1817 −1.51681 −0.758407 0.651781i \(-0.774022\pi\)
−0.758407 + 0.651781i \(0.774022\pi\)
\(570\) 0 0
\(571\) 12.8415 0.537398 0.268699 0.963224i \(-0.413406\pi\)
0.268699 + 0.963224i \(0.413406\pi\)
\(572\) 43.5639 1.82150
\(573\) 0 0
\(574\) −5.50124 −0.229617
\(575\) 16.6671 0.695066
\(576\) 0 0
\(577\) −4.22429 −0.175860 −0.0879298 0.996127i \(-0.528025\pi\)
−0.0879298 + 0.996127i \(0.528025\pi\)
\(578\) 38.3655 1.59579
\(579\) 0 0
\(580\) −127.218 −5.28244
\(581\) −7.17857 −0.297817
\(582\) 0 0
\(583\) −12.5018 −0.517772
\(584\) −59.3451 −2.45572
\(585\) 0 0
\(586\) −70.6378 −2.91802
\(587\) 11.3497 0.468454 0.234227 0.972182i \(-0.424744\pi\)
0.234227 + 0.972182i \(0.424744\pi\)
\(588\) 0 0
\(589\) 30.7047 1.26517
\(590\) −69.7141 −2.87008
\(591\) 0 0
\(592\) −99.7462 −4.09955
\(593\) 40.4494 1.66106 0.830528 0.556977i \(-0.188039\pi\)
0.830528 + 0.556977i \(0.188039\pi\)
\(594\) 0 0
\(595\) 4.84815 0.198755
\(596\) 51.3212 2.10220
\(597\) 0 0
\(598\) −74.7031 −3.05484
\(599\) −25.7241 −1.05106 −0.525530 0.850775i \(-0.676133\pi\)
−0.525530 + 0.850775i \(0.676133\pi\)
\(600\) 0 0
\(601\) −7.07077 −0.288423 −0.144211 0.989547i \(-0.546065\pi\)
−0.144211 + 0.989547i \(0.546065\pi\)
\(602\) −2.32854 −0.0949044
\(603\) 0 0
\(604\) 23.4818 0.955461
\(605\) 25.1784 1.02365
\(606\) 0 0
\(607\) −23.7490 −0.963940 −0.481970 0.876188i \(-0.660079\pi\)
−0.481970 + 0.876188i \(0.660079\pi\)
\(608\) 63.8686 2.59021
\(609\) 0 0
\(610\) 77.9660 3.15675
\(611\) 37.6428 1.52287
\(612\) 0 0
\(613\) −36.8791 −1.48953 −0.744767 0.667325i \(-0.767439\pi\)
−0.744767 + 0.667325i \(0.767439\pi\)
\(614\) 16.3583 0.660167
\(615\) 0 0
\(616\) −13.5702 −0.546759
\(617\) −42.2547 −1.70111 −0.850555 0.525886i \(-0.823734\pi\)
−0.850555 + 0.525886i \(0.823734\pi\)
\(618\) 0 0
\(619\) 32.0800 1.28941 0.644703 0.764433i \(-0.276981\pi\)
0.644703 + 0.764433i \(0.276981\pi\)
\(620\) 142.832 5.73627
\(621\) 0 0
\(622\) −73.1971 −2.93494
\(623\) −9.76491 −0.391223
\(624\) 0 0
\(625\) −30.6319 −1.22528
\(626\) 65.6964 2.62576
\(627\) 0 0
\(628\) −5.81154 −0.231906
\(629\) 12.1615 0.484910
\(630\) 0 0
\(631\) −12.8436 −0.511294 −0.255647 0.966770i \(-0.582288\pi\)
−0.255647 + 0.966770i \(0.582288\pi\)
\(632\) 83.8924 3.33706
\(633\) 0 0
\(634\) 23.9305 0.950401
\(635\) 2.87857 0.114233
\(636\) 0 0
\(637\) 5.43745 0.215440
\(638\) −33.6670 −1.33289
\(639\) 0 0
\(640\) 81.6813 3.22874
\(641\) 20.1359 0.795322 0.397661 0.917532i \(-0.369822\pi\)
0.397661 + 0.917532i \(0.369822\pi\)
\(642\) 0 0
\(643\) 36.9635 1.45770 0.728848 0.684675i \(-0.240056\pi\)
0.728848 + 0.684675i \(0.240056\pi\)
\(644\) 27.0711 1.06675
\(645\) 0 0
\(646\) −15.0684 −0.592856
\(647\) −12.1948 −0.479426 −0.239713 0.970844i \(-0.577053\pi\)
−0.239713 + 0.970844i \(0.577053\pi\)
\(648\) 0 0
\(649\) −13.4204 −0.526797
\(650\) −48.4015 −1.89846
\(651\) 0 0
\(652\) −73.2740 −2.86963
\(653\) 11.5419 0.451669 0.225834 0.974166i \(-0.427489\pi\)
0.225834 + 0.974166i \(0.427489\pi\)
\(654\) 0 0
\(655\) −1.42805 −0.0557987
\(656\) 28.0541 1.09533
\(657\) 0 0
\(658\) −18.7525 −0.731050
\(659\) −13.9433 −0.543156 −0.271578 0.962416i \(-0.587545\pi\)
−0.271578 + 0.962416i \(0.587545\pi\)
\(660\) 0 0
\(661\) −46.7279 −1.81751 −0.908753 0.417335i \(-0.862964\pi\)
−0.908753 + 0.417335i \(0.862964\pi\)
\(662\) 46.0421 1.78948
\(663\) 0 0
\(664\) 64.8976 2.51852
\(665\) 9.50758 0.368688
\(666\) 0 0
\(667\) 41.9957 1.62608
\(668\) −57.1486 −2.21114
\(669\) 0 0
\(670\) −122.509 −4.73295
\(671\) 15.0089 0.579414
\(672\) 0 0
\(673\) −46.4878 −1.79197 −0.895986 0.444083i \(-0.853530\pi\)
−0.895986 + 0.444083i \(0.853530\pi\)
\(674\) −33.6865 −1.29756
\(675\) 0 0
\(676\) 88.4199 3.40077
\(677\) 17.3432 0.666555 0.333278 0.942829i \(-0.391845\pi\)
0.333278 + 0.942829i \(0.391845\pi\)
\(678\) 0 0
\(679\) −9.08877 −0.348795
\(680\) −43.8296 −1.68079
\(681\) 0 0
\(682\) 37.7991 1.44740
\(683\) −16.4433 −0.629185 −0.314593 0.949227i \(-0.601868\pi\)
−0.314593 + 0.949227i \(0.601868\pi\)
\(684\) 0 0
\(685\) 59.8210 2.28564
\(686\) −2.70878 −0.103422
\(687\) 0 0
\(688\) 11.8746 0.452717
\(689\) −45.2869 −1.72529
\(690\) 0 0
\(691\) −8.28341 −0.315116 −0.157558 0.987510i \(-0.550362\pi\)
−0.157558 + 0.987510i \(0.550362\pi\)
\(692\) 28.1872 1.07152
\(693\) 0 0
\(694\) 27.7810 1.05455
\(695\) −0.605061 −0.0229513
\(696\) 0 0
\(697\) −3.42048 −0.129560
\(698\) −75.9908 −2.87630
\(699\) 0 0
\(700\) 17.5399 0.662945
\(701\) 24.0456 0.908190 0.454095 0.890953i \(-0.349963\pi\)
0.454095 + 0.890953i \(0.349963\pi\)
\(702\) 0 0
\(703\) 23.8495 0.899503
\(704\) 37.1554 1.40035
\(705\) 0 0
\(706\) −0.326165 −0.0122754
\(707\) 2.25398 0.0847696
\(708\) 0 0
\(709\) −16.4417 −0.617480 −0.308740 0.951146i \(-0.599907\pi\)
−0.308740 + 0.951146i \(0.599907\pi\)
\(710\) −43.1790 −1.62048
\(711\) 0 0
\(712\) 88.2794 3.30841
\(713\) −47.1500 −1.76578
\(714\) 0 0
\(715\) −23.4946 −0.878648
\(716\) 16.2854 0.608612
\(717\) 0 0
\(718\) 42.0108 1.56783
\(719\) 12.7441 0.475276 0.237638 0.971354i \(-0.423627\pi\)
0.237638 + 0.971354i \(0.423627\pi\)
\(720\) 0 0
\(721\) 17.1074 0.637112
\(722\) 21.9166 0.815653
\(723\) 0 0
\(724\) 105.876 3.93484
\(725\) 27.2098 1.01055
\(726\) 0 0
\(727\) −51.9453 −1.92654 −0.963272 0.268528i \(-0.913463\pi\)
−0.963272 + 0.268528i \(0.913463\pi\)
\(728\) −49.1571 −1.82188
\(729\) 0 0
\(730\) 51.1851 1.89445
\(731\) −1.44781 −0.0535491
\(732\) 0 0
\(733\) 25.2902 0.934115 0.467057 0.884227i \(-0.345314\pi\)
0.467057 + 0.884227i \(0.345314\pi\)
\(734\) −0.754722 −0.0278573
\(735\) 0 0
\(736\) −98.0763 −3.61514
\(737\) −23.5838 −0.868722
\(738\) 0 0
\(739\) −17.4581 −0.642207 −0.321103 0.947044i \(-0.604054\pi\)
−0.321103 + 0.947044i \(0.604054\pi\)
\(740\) 110.943 4.07835
\(741\) 0 0
\(742\) 22.5606 0.828226
\(743\) −21.0345 −0.771680 −0.385840 0.922566i \(-0.626088\pi\)
−0.385840 + 0.922566i \(0.626088\pi\)
\(744\) 0 0
\(745\) −27.6782 −1.01405
\(746\) −69.1283 −2.53097
\(747\) 0 0
\(748\) −13.4937 −0.493378
\(749\) 3.37485 0.123314
\(750\) 0 0
\(751\) 31.0063 1.13144 0.565718 0.824599i \(-0.308599\pi\)
0.565718 + 0.824599i \(0.308599\pi\)
\(752\) 95.6305 3.48729
\(753\) 0 0
\(754\) −121.956 −4.44139
\(755\) −12.6641 −0.460892
\(756\) 0 0
\(757\) −2.88141 −0.104727 −0.0523633 0.998628i \(-0.516675\pi\)
−0.0523633 + 0.998628i \(0.516675\pi\)
\(758\) 27.5885 1.00206
\(759\) 0 0
\(760\) −85.9531 −3.11785
\(761\) −52.1088 −1.88894 −0.944470 0.328597i \(-0.893424\pi\)
−0.944470 + 0.328597i \(0.893424\pi\)
\(762\) 0 0
\(763\) 8.18665 0.296377
\(764\) −143.460 −5.19021
\(765\) 0 0
\(766\) −75.1941 −2.71687
\(767\) −48.6144 −1.75537
\(768\) 0 0
\(769\) 22.2692 0.803048 0.401524 0.915849i \(-0.368481\pi\)
0.401524 + 0.915849i \(0.368481\pi\)
\(770\) 11.7043 0.421794
\(771\) 0 0
\(772\) 60.8582 2.19034
\(773\) −33.9532 −1.22121 −0.610605 0.791935i \(-0.709074\pi\)
−0.610605 + 0.791935i \(0.709074\pi\)
\(774\) 0 0
\(775\) −30.5494 −1.09737
\(776\) 82.1668 2.94962
\(777\) 0 0
\(778\) 70.9652 2.54422
\(779\) −6.70781 −0.240332
\(780\) 0 0
\(781\) −8.31224 −0.297435
\(782\) 23.1389 0.827445
\(783\) 0 0
\(784\) 13.8137 0.493346
\(785\) 3.13424 0.111866
\(786\) 0 0
\(787\) 23.0039 0.820002 0.410001 0.912085i \(-0.365528\pi\)
0.410001 + 0.912085i \(0.365528\pi\)
\(788\) 58.9857 2.10128
\(789\) 0 0
\(790\) −72.3572 −2.57435
\(791\) 13.4635 0.478706
\(792\) 0 0
\(793\) 54.3689 1.93069
\(794\) −24.2129 −0.859284
\(795\) 0 0
\(796\) 23.3578 0.827895
\(797\) 3.18430 0.112794 0.0563968 0.998408i \(-0.482039\pi\)
0.0563968 + 0.998408i \(0.482039\pi\)
\(798\) 0 0
\(799\) −11.6597 −0.412490
\(800\) −63.5455 −2.24667
\(801\) 0 0
\(802\) −95.5859 −3.37526
\(803\) 9.85346 0.347721
\(804\) 0 0
\(805\) −14.5998 −0.514575
\(806\) 136.924 4.82296
\(807\) 0 0
\(808\) −20.3770 −0.716862
\(809\) −0.519198 −0.0182540 −0.00912701 0.999958i \(-0.502905\pi\)
−0.00912701 + 0.999958i \(0.502905\pi\)
\(810\) 0 0
\(811\) 17.7425 0.623023 0.311511 0.950242i \(-0.399165\pi\)
0.311511 + 0.950242i \(0.399165\pi\)
\(812\) 44.1948 1.55093
\(813\) 0 0
\(814\) 29.3600 1.02907
\(815\) 39.5176 1.38424
\(816\) 0 0
\(817\) −2.83925 −0.0993329
\(818\) 17.1718 0.600399
\(819\) 0 0
\(820\) −31.2033 −1.08967
\(821\) −13.1810 −0.460021 −0.230011 0.973188i \(-0.573876\pi\)
−0.230011 + 0.973188i \(0.573876\pi\)
\(822\) 0 0
\(823\) 16.7749 0.584736 0.292368 0.956306i \(-0.405557\pi\)
0.292368 + 0.956306i \(0.405557\pi\)
\(824\) −154.659 −5.38780
\(825\) 0 0
\(826\) 24.2183 0.842662
\(827\) −8.15970 −0.283740 −0.141870 0.989885i \(-0.545312\pi\)
−0.141870 + 0.989885i \(0.545312\pi\)
\(828\) 0 0
\(829\) −4.84768 −0.168367 −0.0841834 0.996450i \(-0.526828\pi\)
−0.0841834 + 0.996450i \(0.526828\pi\)
\(830\) −55.9742 −1.94289
\(831\) 0 0
\(832\) 134.593 4.66616
\(833\) −1.68422 −0.0583548
\(834\) 0 0
\(835\) 30.8210 1.06660
\(836\) −26.4621 −0.915211
\(837\) 0 0
\(838\) 98.3277 3.39667
\(839\) −35.2043 −1.21539 −0.607693 0.794172i \(-0.707905\pi\)
−0.607693 + 0.794172i \(0.707905\pi\)
\(840\) 0 0
\(841\) 39.5600 1.36414
\(842\) 22.9144 0.789682
\(843\) 0 0
\(844\) −23.8792 −0.821956
\(845\) −47.6861 −1.64045
\(846\) 0 0
\(847\) −8.74685 −0.300545
\(848\) −115.050 −3.95083
\(849\) 0 0
\(850\) 14.9921 0.514226
\(851\) −36.6232 −1.25543
\(852\) 0 0
\(853\) −30.9868 −1.06097 −0.530484 0.847695i \(-0.677990\pi\)
−0.530484 + 0.847695i \(0.677990\pi\)
\(854\) −27.0850 −0.926828
\(855\) 0 0
\(856\) −30.5102 −1.04282
\(857\) −30.4958 −1.04172 −0.520858 0.853643i \(-0.674388\pi\)
−0.520858 + 0.853643i \(0.674388\pi\)
\(858\) 0 0
\(859\) −24.8062 −0.846376 −0.423188 0.906042i \(-0.639089\pi\)
−0.423188 + 0.906042i \(0.639089\pi\)
\(860\) −13.2076 −0.450376
\(861\) 0 0
\(862\) −80.4317 −2.73951
\(863\) −45.5391 −1.55017 −0.775084 0.631858i \(-0.782293\pi\)
−0.775084 + 0.631858i \(0.782293\pi\)
\(864\) 0 0
\(865\) −15.2017 −0.516875
\(866\) −78.5873 −2.67050
\(867\) 0 0
\(868\) −49.6190 −1.68418
\(869\) −13.9292 −0.472516
\(870\) 0 0
\(871\) −85.4308 −2.89471
\(872\) −74.0112 −2.50633
\(873\) 0 0
\(874\) 45.3770 1.53490
\(875\) 4.93337 0.166778
\(876\) 0 0
\(877\) 38.0252 1.28402 0.642010 0.766697i \(-0.278101\pi\)
0.642010 + 0.766697i \(0.278101\pi\)
\(878\) 41.1508 1.38877
\(879\) 0 0
\(880\) −59.6873 −2.01206
\(881\) 18.1199 0.610476 0.305238 0.952276i \(-0.401264\pi\)
0.305238 + 0.952276i \(0.401264\pi\)
\(882\) 0 0
\(883\) −40.1982 −1.35278 −0.676388 0.736546i \(-0.736456\pi\)
−0.676388 + 0.736546i \(0.736456\pi\)
\(884\) −48.8799 −1.64401
\(885\) 0 0
\(886\) 59.4507 1.99728
\(887\) −43.6325 −1.46504 −0.732518 0.680748i \(-0.761655\pi\)
−0.732518 + 0.680748i \(0.761655\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) −76.1410 −2.55225
\(891\) 0 0
\(892\) 130.706 4.37637
\(893\) −22.8655 −0.765164
\(894\) 0 0
\(895\) −8.78291 −0.293580
\(896\) −28.3756 −0.947964
\(897\) 0 0
\(898\) 28.5256 0.951911
\(899\) −76.9747 −2.56725
\(900\) 0 0
\(901\) 14.0274 0.467320
\(902\) −8.25764 −0.274949
\(903\) 0 0
\(904\) −121.716 −4.04822
\(905\) −57.1001 −1.89807
\(906\) 0 0
\(907\) −14.8276 −0.492341 −0.246170 0.969227i \(-0.579172\pi\)
−0.246170 + 0.969227i \(0.579172\pi\)
\(908\) 2.73894 0.0908948
\(909\) 0 0
\(910\) 42.3980 1.40548
\(911\) −48.2909 −1.59995 −0.799975 0.600034i \(-0.795154\pi\)
−0.799975 + 0.600034i \(0.795154\pi\)
\(912\) 0 0
\(913\) −10.7754 −0.356613
\(914\) 72.3411 2.39283
\(915\) 0 0
\(916\) −105.139 −3.47388
\(917\) 0.496098 0.0163826
\(918\) 0 0
\(919\) −46.0061 −1.51760 −0.758801 0.651322i \(-0.774215\pi\)
−0.758801 + 0.651322i \(0.774215\pi\)
\(920\) 131.989 4.35155
\(921\) 0 0
\(922\) 13.7693 0.453466
\(923\) −30.1105 −0.991099
\(924\) 0 0
\(925\) −23.7289 −0.780201
\(926\) 6.94754 0.228310
\(927\) 0 0
\(928\) −160.114 −5.25601
\(929\) −15.8115 −0.518759 −0.259379 0.965776i \(-0.583518\pi\)
−0.259379 + 0.965776i \(0.583518\pi\)
\(930\) 0 0
\(931\) −3.30288 −0.108248
\(932\) 7.26384 0.237935
\(933\) 0 0
\(934\) −103.953 −3.40145
\(935\) 7.27732 0.237994
\(936\) 0 0
\(937\) 22.8913 0.747825 0.373913 0.927464i \(-0.378016\pi\)
0.373913 + 0.927464i \(0.378016\pi\)
\(938\) 42.5591 1.38960
\(939\) 0 0
\(940\) −106.365 −3.46925
\(941\) −58.6620 −1.91233 −0.956163 0.292836i \(-0.905401\pi\)
−0.956163 + 0.292836i \(0.905401\pi\)
\(942\) 0 0
\(943\) 10.3005 0.335430
\(944\) −123.504 −4.01970
\(945\) 0 0
\(946\) −3.49526 −0.113641
\(947\) 35.5721 1.15594 0.577969 0.816058i \(-0.303845\pi\)
0.577969 + 0.816058i \(0.303845\pi\)
\(948\) 0 0
\(949\) 35.6935 1.15866
\(950\) 29.4007 0.953883
\(951\) 0 0
\(952\) 15.2262 0.493483
\(953\) 56.3625 1.82576 0.912880 0.408229i \(-0.133853\pi\)
0.912880 + 0.408229i \(0.133853\pi\)
\(954\) 0 0
\(955\) 77.3701 2.50364
\(956\) −136.041 −4.39987
\(957\) 0 0
\(958\) −25.4138 −0.821082
\(959\) −20.7815 −0.671069
\(960\) 0 0
\(961\) 55.4221 1.78781
\(962\) 106.354 3.42901
\(963\) 0 0
\(964\) 128.012 4.12297
\(965\) −32.8217 −1.05657
\(966\) 0 0
\(967\) −32.3294 −1.03964 −0.519822 0.854275i \(-0.674002\pi\)
−0.519822 + 0.854275i \(0.674002\pi\)
\(968\) 79.0756 2.54159
\(969\) 0 0
\(970\) −70.8688 −2.27546
\(971\) −18.2980 −0.587210 −0.293605 0.955927i \(-0.594855\pi\)
−0.293605 + 0.955927i \(0.594855\pi\)
\(972\) 0 0
\(973\) 0.210195 0.00673853
\(974\) −81.4876 −2.61103
\(975\) 0 0
\(976\) 138.122 4.42119
\(977\) −35.5195 −1.13637 −0.568185 0.822901i \(-0.692354\pi\)
−0.568185 + 0.822901i \(0.692354\pi\)
\(978\) 0 0
\(979\) −14.6576 −0.468460
\(980\) −15.3643 −0.490795
\(981\) 0 0
\(982\) 106.699 3.40491
\(983\) −19.4569 −0.620578 −0.310289 0.950642i \(-0.600426\pi\)
−0.310289 + 0.950642i \(0.600426\pi\)
\(984\) 0 0
\(985\) −31.8118 −1.01361
\(986\) 37.7753 1.20301
\(987\) 0 0
\(988\) −95.8571 −3.04962
\(989\) 4.35994 0.138638
\(990\) 0 0
\(991\) 39.5095 1.25506 0.627531 0.778592i \(-0.284066\pi\)
0.627531 + 0.778592i \(0.284066\pi\)
\(992\) 179.766 5.70757
\(993\) 0 0
\(994\) 15.0002 0.475776
\(995\) −12.5972 −0.399357
\(996\) 0 0
\(997\) −48.2009 −1.52654 −0.763269 0.646080i \(-0.776407\pi\)
−0.763269 + 0.646080i \(0.776407\pi\)
\(998\) −52.8020 −1.67142
\(999\) 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 \(a_p\))