Properties

Label 8001.2.a.z.1.3
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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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: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.44637 q^{2}\) \(+3.98471 q^{4}\) \(+1.74324 q^{5}\) \(-1.00000 q^{7}\) \(-4.85534 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.44637 q^{2}\) \(+3.98471 q^{4}\) \(+1.74324 q^{5}\) \(-1.00000 q^{7}\) \(-4.85534 q^{8}\) \(-4.26460 q^{10}\) \(-0.135794 q^{11}\) \(-2.02529 q^{13}\) \(+2.44637 q^{14}\) \(+3.90851 q^{16}\) \(+0.659283 q^{17}\) \(-3.26306 q^{19}\) \(+6.94630 q^{20}\) \(+0.332202 q^{22}\) \(-2.00548 q^{23}\) \(-1.96113 q^{25}\) \(+4.95459 q^{26}\) \(-3.98471 q^{28}\) \(-6.31569 q^{29}\) \(+6.78434 q^{31}\) \(+0.149022 q^{32}\) \(-1.61285 q^{34}\) \(-1.74324 q^{35}\) \(+2.08417 q^{37}\) \(+7.98265 q^{38}\) \(-8.46400 q^{40}\) \(+2.96378 q^{41}\) \(-2.48820 q^{43}\) \(-0.541100 q^{44}\) \(+4.90615 q^{46}\) \(+12.8855 q^{47}\) \(+1.00000 q^{49}\) \(+4.79763 q^{50}\) \(-8.07018 q^{52}\) \(+1.28176 q^{53}\) \(-0.236721 q^{55}\) \(+4.85534 q^{56}\) \(+15.4505 q^{58}\) \(+12.3426 q^{59}\) \(-11.9997 q^{61}\) \(-16.5970 q^{62}\) \(-8.18158 q^{64}\) \(-3.53055 q^{65}\) \(-13.6878 q^{67}\) \(+2.62705 q^{68}\) \(+4.26460 q^{70}\) \(-0.817936 q^{71}\) \(+10.1195 q^{73}\) \(-5.09863 q^{74}\) \(-13.0024 q^{76}\) \(+0.135794 q^{77}\) \(+3.94496 q^{79}\) \(+6.81346 q^{80}\) \(-7.25051 q^{82}\) \(+17.3428 q^{83}\) \(+1.14929 q^{85}\) \(+6.08704 q^{86}\) \(+0.659325 q^{88}\) \(+12.4110 q^{89}\) \(+2.02529 q^{91}\) \(-7.99127 q^{92}\) \(-31.5227 q^{94}\) \(-5.68829 q^{95}\) \(+4.98004 q^{97}\) \(-2.44637 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44637 −1.72984 −0.864921 0.501907i \(-0.832632\pi\)
−0.864921 + 0.501907i \(0.832632\pi\)
\(3\) 0 0
\(4\) 3.98471 1.99236
\(5\) 1.74324 0.779599 0.389800 0.920900i \(-0.372544\pi\)
0.389800 + 0.920900i \(0.372544\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −4.85534 −1.71662
\(9\) 0 0
\(10\) −4.26460 −1.34858
\(11\) −0.135794 −0.0409434 −0.0204717 0.999790i \(-0.506517\pi\)
−0.0204717 + 0.999790i \(0.506517\pi\)
\(12\) 0 0
\(13\) −2.02529 −0.561713 −0.280857 0.959750i \(-0.590619\pi\)
−0.280857 + 0.959750i \(0.590619\pi\)
\(14\) 2.44637 0.653819
\(15\) 0 0
\(16\) 3.90851 0.977127
\(17\) 0.659283 0.159900 0.0799498 0.996799i \(-0.474524\pi\)
0.0799498 + 0.996799i \(0.474524\pi\)
\(18\) 0 0
\(19\) −3.26306 −0.748598 −0.374299 0.927308i \(-0.622117\pi\)
−0.374299 + 0.927308i \(0.622117\pi\)
\(20\) 6.94630 1.55324
\(21\) 0 0
\(22\) 0.332202 0.0708257
\(23\) −2.00548 −0.418172 −0.209086 0.977897i \(-0.567049\pi\)
−0.209086 + 0.977897i \(0.567049\pi\)
\(24\) 0 0
\(25\) −1.96113 −0.392225
\(26\) 4.95459 0.971676
\(27\) 0 0
\(28\) −3.98471 −0.753040
\(29\) −6.31569 −1.17279 −0.586397 0.810024i \(-0.699454\pi\)
−0.586397 + 0.810024i \(0.699454\pi\)
\(30\) 0 0
\(31\) 6.78434 1.21850 0.609252 0.792977i \(-0.291470\pi\)
0.609252 + 0.792977i \(0.291470\pi\)
\(32\) 0.149022 0.0263437
\(33\) 0 0
\(34\) −1.61285 −0.276601
\(35\) −1.74324 −0.294661
\(36\) 0 0
\(37\) 2.08417 0.342635 0.171317 0.985216i \(-0.445198\pi\)
0.171317 + 0.985216i \(0.445198\pi\)
\(38\) 7.98265 1.29496
\(39\) 0 0
\(40\) −8.46400 −1.33828
\(41\) 2.96378 0.462865 0.231433 0.972851i \(-0.425659\pi\)
0.231433 + 0.972851i \(0.425659\pi\)
\(42\) 0 0
\(43\) −2.48820 −0.379447 −0.189723 0.981838i \(-0.560759\pi\)
−0.189723 + 0.981838i \(0.560759\pi\)
\(44\) −0.541100 −0.0815739
\(45\) 0 0
\(46\) 4.90615 0.723372
\(47\) 12.8855 1.87955 0.939773 0.341801i \(-0.111037\pi\)
0.939773 + 0.341801i \(0.111037\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.79763 0.678488
\(51\) 0 0
\(52\) −8.07018 −1.11913
\(53\) 1.28176 0.176063 0.0880317 0.996118i \(-0.471942\pi\)
0.0880317 + 0.996118i \(0.471942\pi\)
\(54\) 0 0
\(55\) −0.236721 −0.0319195
\(56\) 4.85534 0.648822
\(57\) 0 0
\(58\) 15.4505 2.02875
\(59\) 12.3426 1.60687 0.803434 0.595394i \(-0.203004\pi\)
0.803434 + 0.595394i \(0.203004\pi\)
\(60\) 0 0
\(61\) −11.9997 −1.53640 −0.768201 0.640209i \(-0.778848\pi\)
−0.768201 + 0.640209i \(0.778848\pi\)
\(62\) −16.5970 −2.10782
\(63\) 0 0
\(64\) −8.18158 −1.02270
\(65\) −3.53055 −0.437911
\(66\) 0 0
\(67\) −13.6878 −1.67223 −0.836113 0.548557i \(-0.815177\pi\)
−0.836113 + 0.548557i \(0.815177\pi\)
\(68\) 2.62705 0.318577
\(69\) 0 0
\(70\) 4.26460 0.509717
\(71\) −0.817936 −0.0970712 −0.0485356 0.998821i \(-0.515455\pi\)
−0.0485356 + 0.998821i \(0.515455\pi\)
\(72\) 0 0
\(73\) 10.1195 1.18439 0.592196 0.805794i \(-0.298261\pi\)
0.592196 + 0.805794i \(0.298261\pi\)
\(74\) −5.09863 −0.592704
\(75\) 0 0
\(76\) −13.0024 −1.49147
\(77\) 0.135794 0.0154752
\(78\) 0 0
\(79\) 3.94496 0.443842 0.221921 0.975065i \(-0.428767\pi\)
0.221921 + 0.975065i \(0.428767\pi\)
\(80\) 6.81346 0.761768
\(81\) 0 0
\(82\) −7.25051 −0.800684
\(83\) 17.3428 1.90362 0.951812 0.306684i \(-0.0992193\pi\)
0.951812 + 0.306684i \(0.0992193\pi\)
\(84\) 0 0
\(85\) 1.14929 0.124658
\(86\) 6.08704 0.656383
\(87\) 0 0
\(88\) 0.659325 0.0702843
\(89\) 12.4110 1.31556 0.657781 0.753209i \(-0.271495\pi\)
0.657781 + 0.753209i \(0.271495\pi\)
\(90\) 0 0
\(91\) 2.02529 0.212308
\(92\) −7.99127 −0.833148
\(93\) 0 0
\(94\) −31.5227 −3.25132
\(95\) −5.68829 −0.583606
\(96\) 0 0
\(97\) 4.98004 0.505647 0.252823 0.967512i \(-0.418641\pi\)
0.252823 + 0.967512i \(0.418641\pi\)
\(98\) −2.44637 −0.247120
\(99\) 0 0
\(100\) −7.81452 −0.781452
\(101\) −3.77619 −0.375745 −0.187873 0.982193i \(-0.560159\pi\)
−0.187873 + 0.982193i \(0.560159\pi\)
\(102\) 0 0
\(103\) −3.75563 −0.370054 −0.185027 0.982733i \(-0.559237\pi\)
−0.185027 + 0.982733i \(0.559237\pi\)
\(104\) 9.83344 0.964249
\(105\) 0 0
\(106\) −3.13566 −0.304562
\(107\) −4.86491 −0.470308 −0.235154 0.971958i \(-0.575560\pi\)
−0.235154 + 0.971958i \(0.575560\pi\)
\(108\) 0 0
\(109\) −2.59574 −0.248627 −0.124313 0.992243i \(-0.539673\pi\)
−0.124313 + 0.992243i \(0.539673\pi\)
\(110\) 0.579107 0.0552156
\(111\) 0 0
\(112\) −3.90851 −0.369319
\(113\) −2.63918 −0.248274 −0.124137 0.992265i \(-0.539616\pi\)
−0.124137 + 0.992265i \(0.539616\pi\)
\(114\) 0 0
\(115\) −3.49603 −0.326007
\(116\) −25.1662 −2.33662
\(117\) 0 0
\(118\) −30.1945 −2.77963
\(119\) −0.659283 −0.0604363
\(120\) 0 0
\(121\) −10.9816 −0.998324
\(122\) 29.3556 2.65773
\(123\) 0 0
\(124\) 27.0336 2.42769
\(125\) −12.1349 −1.08538
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 19.7171 1.74276
\(129\) 0 0
\(130\) 8.63703 0.757518
\(131\) 12.4783 1.09023 0.545115 0.838361i \(-0.316486\pi\)
0.545115 + 0.838361i \(0.316486\pi\)
\(132\) 0 0
\(133\) 3.26306 0.282943
\(134\) 33.4853 2.89269
\(135\) 0 0
\(136\) −3.20104 −0.274487
\(137\) 12.4812 1.06634 0.533171 0.846007i \(-0.321000\pi\)
0.533171 + 0.846007i \(0.321000\pi\)
\(138\) 0 0
\(139\) 6.12288 0.519336 0.259668 0.965698i \(-0.416387\pi\)
0.259668 + 0.965698i \(0.416387\pi\)
\(140\) −6.94630 −0.587069
\(141\) 0 0
\(142\) 2.00097 0.167918
\(143\) 0.275022 0.0229985
\(144\) 0 0
\(145\) −11.0097 −0.914310
\(146\) −24.7559 −2.04881
\(147\) 0 0
\(148\) 8.30480 0.682650
\(149\) −3.76846 −0.308725 −0.154362 0.988014i \(-0.549332\pi\)
−0.154362 + 0.988014i \(0.549332\pi\)
\(150\) 0 0
\(151\) −13.0889 −1.06516 −0.532579 0.846381i \(-0.678777\pi\)
−0.532579 + 0.846381i \(0.678777\pi\)
\(152\) 15.8433 1.28506
\(153\) 0 0
\(154\) −0.332202 −0.0267696
\(155\) 11.8267 0.949944
\(156\) 0 0
\(157\) 16.1694 1.29046 0.645230 0.763988i \(-0.276762\pi\)
0.645230 + 0.763988i \(0.276762\pi\)
\(158\) −9.65081 −0.767777
\(159\) 0 0
\(160\) 0.259781 0.0205375
\(161\) 2.00548 0.158054
\(162\) 0 0
\(163\) −17.0079 −1.33216 −0.666080 0.745880i \(-0.732029\pi\)
−0.666080 + 0.745880i \(0.732029\pi\)
\(164\) 11.8098 0.922193
\(165\) 0 0
\(166\) −42.4269 −3.29297
\(167\) −6.66021 −0.515382 −0.257691 0.966227i \(-0.582962\pi\)
−0.257691 + 0.966227i \(0.582962\pi\)
\(168\) 0 0
\(169\) −8.89822 −0.684478
\(170\) −2.81158 −0.215638
\(171\) 0 0
\(172\) −9.91475 −0.755993
\(173\) −18.1392 −1.37910 −0.689548 0.724240i \(-0.742191\pi\)
−0.689548 + 0.724240i \(0.742191\pi\)
\(174\) 0 0
\(175\) 1.96113 0.148247
\(176\) −0.530752 −0.0400069
\(177\) 0 0
\(178\) −30.3618 −2.27572
\(179\) −18.5858 −1.38917 −0.694583 0.719413i \(-0.744411\pi\)
−0.694583 + 0.719413i \(0.744411\pi\)
\(180\) 0 0
\(181\) −21.8637 −1.62512 −0.812558 0.582880i \(-0.801926\pi\)
−0.812558 + 0.582880i \(0.801926\pi\)
\(182\) −4.95459 −0.367259
\(183\) 0 0
\(184\) 9.73729 0.717843
\(185\) 3.63319 0.267118
\(186\) 0 0
\(187\) −0.0895266 −0.00654684
\(188\) 51.3451 3.74472
\(189\) 0 0
\(190\) 13.9156 1.00955
\(191\) −18.6935 −1.35262 −0.676308 0.736619i \(-0.736421\pi\)
−0.676308 + 0.736619i \(0.736421\pi\)
\(192\) 0 0
\(193\) −16.7789 −1.20777 −0.603886 0.797071i \(-0.706382\pi\)
−0.603886 + 0.797071i \(0.706382\pi\)
\(194\) −12.1830 −0.874689
\(195\) 0 0
\(196\) 3.98471 0.284622
\(197\) −11.4210 −0.813709 −0.406855 0.913493i \(-0.633374\pi\)
−0.406855 + 0.913493i \(0.633374\pi\)
\(198\) 0 0
\(199\) −11.0173 −0.780992 −0.390496 0.920605i \(-0.627697\pi\)
−0.390496 + 0.920605i \(0.627697\pi\)
\(200\) 9.52193 0.673302
\(201\) 0 0
\(202\) 9.23795 0.649980
\(203\) 6.31569 0.443275
\(204\) 0 0
\(205\) 5.16658 0.360849
\(206\) 9.18766 0.640135
\(207\) 0 0
\(208\) −7.91585 −0.548865
\(209\) 0.443104 0.0306501
\(210\) 0 0
\(211\) 9.44988 0.650557 0.325278 0.945618i \(-0.394542\pi\)
0.325278 + 0.945618i \(0.394542\pi\)
\(212\) 5.10745 0.350781
\(213\) 0 0
\(214\) 11.9014 0.813560
\(215\) −4.33752 −0.295816
\(216\) 0 0
\(217\) −6.78434 −0.460551
\(218\) 6.35013 0.430085
\(219\) 0 0
\(220\) −0.943265 −0.0635949
\(221\) −1.33524 −0.0898177
\(222\) 0 0
\(223\) −14.9005 −0.997811 −0.498906 0.866656i \(-0.666265\pi\)
−0.498906 + 0.866656i \(0.666265\pi\)
\(224\) −0.149022 −0.00995698
\(225\) 0 0
\(226\) 6.45641 0.429474
\(227\) −10.5921 −0.703025 −0.351513 0.936183i \(-0.614333\pi\)
−0.351513 + 0.936183i \(0.614333\pi\)
\(228\) 0 0
\(229\) 21.6836 1.43289 0.716447 0.697641i \(-0.245767\pi\)
0.716447 + 0.697641i \(0.245767\pi\)
\(230\) 8.55258 0.563940
\(231\) 0 0
\(232\) 30.6648 2.01324
\(233\) −9.95372 −0.652090 −0.326045 0.945354i \(-0.605716\pi\)
−0.326045 + 0.945354i \(0.605716\pi\)
\(234\) 0 0
\(235\) 22.4625 1.46529
\(236\) 49.1816 3.20145
\(237\) 0 0
\(238\) 1.61285 0.104545
\(239\) −23.4606 −1.51754 −0.758771 0.651357i \(-0.774200\pi\)
−0.758771 + 0.651357i \(0.774200\pi\)
\(240\) 0 0
\(241\) 9.49046 0.611334 0.305667 0.952138i \(-0.401121\pi\)
0.305667 + 0.952138i \(0.401121\pi\)
\(242\) 26.8649 1.72694
\(243\) 0 0
\(244\) −47.8153 −3.06106
\(245\) 1.74324 0.111371
\(246\) 0 0
\(247\) 6.60863 0.420497
\(248\) −32.9403 −2.09171
\(249\) 0 0
\(250\) 29.6864 1.87753
\(251\) −12.1739 −0.768409 −0.384204 0.923248i \(-0.625524\pi\)
−0.384204 + 0.923248i \(0.625524\pi\)
\(252\) 0 0
\(253\) 0.272333 0.0171214
\(254\) 2.44637 0.153499
\(255\) 0 0
\(256\) −31.8721 −1.99201
\(257\) −5.54656 −0.345985 −0.172993 0.984923i \(-0.555344\pi\)
−0.172993 + 0.984923i \(0.555344\pi\)
\(258\) 0 0
\(259\) −2.08417 −0.129504
\(260\) −14.0682 −0.872475
\(261\) 0 0
\(262\) −30.5264 −1.88593
\(263\) −28.9806 −1.78702 −0.893509 0.449046i \(-0.851764\pi\)
−0.893509 + 0.449046i \(0.851764\pi\)
\(264\) 0 0
\(265\) 2.23441 0.137259
\(266\) −7.98265 −0.489447
\(267\) 0 0
\(268\) −54.5418 −3.33167
\(269\) −3.14968 −0.192039 −0.0960197 0.995379i \(-0.530611\pi\)
−0.0960197 + 0.995379i \(0.530611\pi\)
\(270\) 0 0
\(271\) −9.19663 −0.558655 −0.279328 0.960196i \(-0.590112\pi\)
−0.279328 + 0.960196i \(0.590112\pi\)
\(272\) 2.57681 0.156242
\(273\) 0 0
\(274\) −30.5336 −1.84460
\(275\) 0.266309 0.0160590
\(276\) 0 0
\(277\) 11.1167 0.667935 0.333967 0.942585i \(-0.391612\pi\)
0.333967 + 0.942585i \(0.391612\pi\)
\(278\) −14.9788 −0.898370
\(279\) 0 0
\(280\) 8.46400 0.505821
\(281\) −14.0895 −0.840511 −0.420255 0.907406i \(-0.638060\pi\)
−0.420255 + 0.907406i \(0.638060\pi\)
\(282\) 0 0
\(283\) 24.6269 1.46392 0.731960 0.681348i \(-0.238606\pi\)
0.731960 + 0.681348i \(0.238606\pi\)
\(284\) −3.25924 −0.193400
\(285\) 0 0
\(286\) −0.672804 −0.0397837
\(287\) −2.96378 −0.174947
\(288\) 0 0
\(289\) −16.5653 −0.974432
\(290\) 26.9339 1.58161
\(291\) 0 0
\(292\) 40.3231 2.35973
\(293\) −5.37284 −0.313884 −0.156942 0.987608i \(-0.550164\pi\)
−0.156942 + 0.987608i \(0.550164\pi\)
\(294\) 0 0
\(295\) 21.5160 1.25271
\(296\) −10.1193 −0.588174
\(297\) 0 0
\(298\) 9.21905 0.534045
\(299\) 4.06168 0.234893
\(300\) 0 0
\(301\) 2.48820 0.143417
\(302\) 32.0202 1.84255
\(303\) 0 0
\(304\) −12.7537 −0.731475
\(305\) −20.9183 −1.19778
\(306\) 0 0
\(307\) −10.1371 −0.578554 −0.289277 0.957245i \(-0.593415\pi\)
−0.289277 + 0.957245i \(0.593415\pi\)
\(308\) 0.541100 0.0308320
\(309\) 0 0
\(310\) −28.9325 −1.64325
\(311\) 7.81567 0.443186 0.221593 0.975139i \(-0.428874\pi\)
0.221593 + 0.975139i \(0.428874\pi\)
\(312\) 0 0
\(313\) −17.2066 −0.972574 −0.486287 0.873799i \(-0.661649\pi\)
−0.486287 + 0.873799i \(0.661649\pi\)
\(314\) −39.5563 −2.23229
\(315\) 0 0
\(316\) 15.7195 0.884292
\(317\) 19.2484 1.08110 0.540548 0.841313i \(-0.318217\pi\)
0.540548 + 0.841313i \(0.318217\pi\)
\(318\) 0 0
\(319\) 0.857633 0.0480182
\(320\) −14.2624 −0.797294
\(321\) 0 0
\(322\) −4.90615 −0.273409
\(323\) −2.15128 −0.119700
\(324\) 0 0
\(325\) 3.97184 0.220318
\(326\) 41.6075 2.30443
\(327\) 0 0
\(328\) −14.3902 −0.794564
\(329\) −12.8855 −0.710401
\(330\) 0 0
\(331\) 27.8190 1.52907 0.764536 0.644581i \(-0.222968\pi\)
0.764536 + 0.644581i \(0.222968\pi\)
\(332\) 69.1062 3.79270
\(333\) 0 0
\(334\) 16.2933 0.891530
\(335\) −23.8610 −1.30367
\(336\) 0 0
\(337\) 28.9358 1.57623 0.788115 0.615528i \(-0.211057\pi\)
0.788115 + 0.615528i \(0.211057\pi\)
\(338\) 21.7683 1.18404
\(339\) 0 0
\(340\) 4.57957 0.248362
\(341\) −0.921273 −0.0498897
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 12.0810 0.651366
\(345\) 0 0
\(346\) 44.3751 2.38562
\(347\) −20.6974 −1.11109 −0.555547 0.831485i \(-0.687491\pi\)
−0.555547 + 0.831485i \(0.687491\pi\)
\(348\) 0 0
\(349\) −25.7409 −1.37788 −0.688938 0.724820i \(-0.741923\pi\)
−0.688938 + 0.724820i \(0.741923\pi\)
\(350\) −4.79763 −0.256444
\(351\) 0 0
\(352\) −0.0202364 −0.00107860
\(353\) 28.8035 1.53306 0.766529 0.642210i \(-0.221982\pi\)
0.766529 + 0.642210i \(0.221982\pi\)
\(354\) 0 0
\(355\) −1.42586 −0.0756766
\(356\) 49.4542 2.62107
\(357\) 0 0
\(358\) 45.4676 2.40304
\(359\) −8.09394 −0.427182 −0.213591 0.976923i \(-0.568516\pi\)
−0.213591 + 0.976923i \(0.568516\pi\)
\(360\) 0 0
\(361\) −8.35243 −0.439602
\(362\) 53.4866 2.81120
\(363\) 0 0
\(364\) 8.07018 0.422993
\(365\) 17.6406 0.923351
\(366\) 0 0
\(367\) −16.7470 −0.874186 −0.437093 0.899416i \(-0.643992\pi\)
−0.437093 + 0.899416i \(0.643992\pi\)
\(368\) −7.83845 −0.408607
\(369\) 0 0
\(370\) −8.88812 −0.462072
\(371\) −1.28176 −0.0665457
\(372\) 0 0
\(373\) 19.6227 1.01603 0.508013 0.861349i \(-0.330380\pi\)
0.508013 + 0.861349i \(0.330380\pi\)
\(374\) 0.219015 0.0113250
\(375\) 0 0
\(376\) −62.5635 −3.22647
\(377\) 12.7911 0.658774
\(378\) 0 0
\(379\) −8.60545 −0.442032 −0.221016 0.975270i \(-0.570937\pi\)
−0.221016 + 0.975270i \(0.570937\pi\)
\(380\) −22.6662 −1.16275
\(381\) 0 0
\(382\) 45.7312 2.33981
\(383\) 36.7316 1.87690 0.938448 0.345420i \(-0.112264\pi\)
0.938448 + 0.345420i \(0.112264\pi\)
\(384\) 0 0
\(385\) 0.236721 0.0120644
\(386\) 41.0473 2.08925
\(387\) 0 0
\(388\) 19.8440 1.00743
\(389\) −5.24504 −0.265934 −0.132967 0.991120i \(-0.542450\pi\)
−0.132967 + 0.991120i \(0.542450\pi\)
\(390\) 0 0
\(391\) −1.32218 −0.0668655
\(392\) −4.85534 −0.245231
\(393\) 0 0
\(394\) 27.9398 1.40759
\(395\) 6.87699 0.346019
\(396\) 0 0
\(397\) 11.4181 0.573058 0.286529 0.958072i \(-0.407499\pi\)
0.286529 + 0.958072i \(0.407499\pi\)
\(398\) 26.9522 1.35099
\(399\) 0 0
\(400\) −7.66508 −0.383254
\(401\) 3.11844 0.155728 0.0778638 0.996964i \(-0.475190\pi\)
0.0778638 + 0.996964i \(0.475190\pi\)
\(402\) 0 0
\(403\) −13.7402 −0.684450
\(404\) −15.0470 −0.748618
\(405\) 0 0
\(406\) −15.4505 −0.766796
\(407\) −0.283017 −0.0140286
\(408\) 0 0
\(409\) −24.6880 −1.22075 −0.610373 0.792114i \(-0.708980\pi\)
−0.610373 + 0.792114i \(0.708980\pi\)
\(410\) −12.6393 −0.624213
\(411\) 0 0
\(412\) −14.9651 −0.737279
\(413\) −12.3426 −0.607339
\(414\) 0 0
\(415\) 30.2327 1.48406
\(416\) −0.301813 −0.0147976
\(417\) 0 0
\(418\) −1.08400 −0.0530199
\(419\) −0.509385 −0.0248851 −0.0124425 0.999923i \(-0.503961\pi\)
−0.0124425 + 0.999923i \(0.503961\pi\)
\(420\) 0 0
\(421\) 26.9127 1.31165 0.655823 0.754915i \(-0.272322\pi\)
0.655823 + 0.754915i \(0.272322\pi\)
\(422\) −23.1179 −1.12536
\(423\) 0 0
\(424\) −6.22338 −0.302234
\(425\) −1.29294 −0.0627166
\(426\) 0 0
\(427\) 11.9997 0.580705
\(428\) −19.3853 −0.937022
\(429\) 0 0
\(430\) 10.6112 0.511715
\(431\) −5.41933 −0.261040 −0.130520 0.991446i \(-0.541665\pi\)
−0.130520 + 0.991446i \(0.541665\pi\)
\(432\) 0 0
\(433\) −5.57950 −0.268134 −0.134067 0.990972i \(-0.542804\pi\)
−0.134067 + 0.990972i \(0.542804\pi\)
\(434\) 16.5970 0.796681
\(435\) 0 0
\(436\) −10.3433 −0.495353
\(437\) 6.54401 0.313043
\(438\) 0 0
\(439\) −32.5614 −1.55407 −0.777035 0.629457i \(-0.783277\pi\)
−0.777035 + 0.629457i \(0.783277\pi\)
\(440\) 1.14936 0.0547936
\(441\) 0 0
\(442\) 3.26648 0.155371
\(443\) 28.6399 1.36072 0.680361 0.732878i \(-0.261823\pi\)
0.680361 + 0.732878i \(0.261823\pi\)
\(444\) 0 0
\(445\) 21.6353 1.02561
\(446\) 36.4521 1.72606
\(447\) 0 0
\(448\) 8.18158 0.386543
\(449\) 40.1926 1.89681 0.948403 0.317066i \(-0.102698\pi\)
0.948403 + 0.317066i \(0.102698\pi\)
\(450\) 0 0
\(451\) −0.402464 −0.0189513
\(452\) −10.5164 −0.494649
\(453\) 0 0
\(454\) 25.9123 1.21612
\(455\) 3.53055 0.165515
\(456\) 0 0
\(457\) 21.1798 0.990750 0.495375 0.868679i \(-0.335031\pi\)
0.495375 + 0.868679i \(0.335031\pi\)
\(458\) −53.0461 −2.47868
\(459\) 0 0
\(460\) −13.9307 −0.649521
\(461\) −1.87919 −0.0875224 −0.0437612 0.999042i \(-0.513934\pi\)
−0.0437612 + 0.999042i \(0.513934\pi\)
\(462\) 0 0
\(463\) 5.08778 0.236449 0.118225 0.992987i \(-0.462280\pi\)
0.118225 + 0.992987i \(0.462280\pi\)
\(464\) −24.6849 −1.14597
\(465\) 0 0
\(466\) 24.3505 1.12801
\(467\) −7.80477 −0.361162 −0.180581 0.983560i \(-0.557798\pi\)
−0.180581 + 0.983560i \(0.557798\pi\)
\(468\) 0 0
\(469\) 13.6878 0.632042
\(470\) −54.9515 −2.53472
\(471\) 0 0
\(472\) −59.9274 −2.75838
\(473\) 0.337882 0.0155358
\(474\) 0 0
\(475\) 6.39927 0.293619
\(476\) −2.62705 −0.120411
\(477\) 0 0
\(478\) 57.3933 2.62511
\(479\) −11.7028 −0.534717 −0.267358 0.963597i \(-0.586151\pi\)
−0.267358 + 0.963597i \(0.586151\pi\)
\(480\) 0 0
\(481\) −4.22103 −0.192462
\(482\) −23.2172 −1.05751
\(483\) 0 0
\(484\) −43.7584 −1.98902
\(485\) 8.68139 0.394202
\(486\) 0 0
\(487\) −38.1856 −1.73035 −0.865177 0.501466i \(-0.832794\pi\)
−0.865177 + 0.501466i \(0.832794\pi\)
\(488\) 58.2625 2.63742
\(489\) 0 0
\(490\) −4.26460 −0.192655
\(491\) −26.7718 −1.20820 −0.604098 0.796910i \(-0.706466\pi\)
−0.604098 + 0.796910i \(0.706466\pi\)
\(492\) 0 0
\(493\) −4.16383 −0.187529
\(494\) −16.1671 −0.727394
\(495\) 0 0
\(496\) 26.5167 1.19063
\(497\) 0.817936 0.0366895
\(498\) 0 0
\(499\) −30.8339 −1.38032 −0.690158 0.723659i \(-0.742459\pi\)
−0.690158 + 0.723659i \(0.742459\pi\)
\(500\) −48.3540 −2.16246
\(501\) 0 0
\(502\) 29.7818 1.32923
\(503\) −34.5237 −1.53934 −0.769669 0.638444i \(-0.779579\pi\)
−0.769669 + 0.638444i \(0.779579\pi\)
\(504\) 0 0
\(505\) −6.58280 −0.292931
\(506\) −0.666225 −0.0296173
\(507\) 0 0
\(508\) −3.98471 −0.176793
\(509\) 9.52278 0.422090 0.211045 0.977476i \(-0.432313\pi\)
0.211045 + 0.977476i \(0.432313\pi\)
\(510\) 0 0
\(511\) −10.1195 −0.447658
\(512\) 38.5367 1.70310
\(513\) 0 0
\(514\) 13.5689 0.598500
\(515\) −6.54696 −0.288493
\(516\) 0 0
\(517\) −1.74977 −0.0769550
\(518\) 5.09863 0.224021
\(519\) 0 0
\(520\) 17.1420 0.751727
\(521\) −28.8103 −1.26220 −0.631102 0.775700i \(-0.717397\pi\)
−0.631102 + 0.775700i \(0.717397\pi\)
\(522\) 0 0
\(523\) 15.7577 0.689036 0.344518 0.938780i \(-0.388042\pi\)
0.344518 + 0.938780i \(0.388042\pi\)
\(524\) 49.7222 2.17213
\(525\) 0 0
\(526\) 70.8971 3.09126
\(527\) 4.47280 0.194838
\(528\) 0 0
\(529\) −18.9780 −0.825132
\(530\) −5.46620 −0.237436
\(531\) 0 0
\(532\) 13.0024 0.563724
\(533\) −6.00251 −0.259998
\(534\) 0 0
\(535\) −8.48069 −0.366652
\(536\) 66.4587 2.87058
\(537\) 0 0
\(538\) 7.70528 0.332198
\(539\) −0.135794 −0.00584906
\(540\) 0 0
\(541\) −8.14738 −0.350283 −0.175142 0.984543i \(-0.556038\pi\)
−0.175142 + 0.984543i \(0.556038\pi\)
\(542\) 22.4983 0.966386
\(543\) 0 0
\(544\) 0.0982479 0.00421235
\(545\) −4.52498 −0.193829
\(546\) 0 0
\(547\) 40.1907 1.71843 0.859215 0.511614i \(-0.170952\pi\)
0.859215 + 0.511614i \(0.170952\pi\)
\(548\) 49.7341 2.12453
\(549\) 0 0
\(550\) −0.651490 −0.0277796
\(551\) 20.6085 0.877951
\(552\) 0 0
\(553\) −3.94496 −0.167757
\(554\) −27.1954 −1.15542
\(555\) 0 0
\(556\) 24.3979 1.03470
\(557\) 40.1085 1.69945 0.849727 0.527223i \(-0.176767\pi\)
0.849727 + 0.527223i \(0.176767\pi\)
\(558\) 0 0
\(559\) 5.03931 0.213140
\(560\) −6.81346 −0.287921
\(561\) 0 0
\(562\) 34.4682 1.45395
\(563\) −28.1913 −1.18812 −0.594062 0.804419i \(-0.702477\pi\)
−0.594062 + 0.804419i \(0.702477\pi\)
\(564\) 0 0
\(565\) −4.60072 −0.193554
\(566\) −60.2465 −2.53235
\(567\) 0 0
\(568\) 3.97136 0.166634
\(569\) −1.73907 −0.0729056 −0.0364528 0.999335i \(-0.511606\pi\)
−0.0364528 + 0.999335i \(0.511606\pi\)
\(570\) 0 0
\(571\) −42.7736 −1.79002 −0.895009 0.446048i \(-0.852831\pi\)
−0.895009 + 0.446048i \(0.852831\pi\)
\(572\) 1.09588 0.0458211
\(573\) 0 0
\(574\) 7.25051 0.302630
\(575\) 3.93300 0.164018
\(576\) 0 0
\(577\) −12.7296 −0.529940 −0.264970 0.964257i \(-0.585362\pi\)
−0.264970 + 0.964257i \(0.585362\pi\)
\(578\) 40.5249 1.68561
\(579\) 0 0
\(580\) −43.8707 −1.82163
\(581\) −17.3428 −0.719502
\(582\) 0 0
\(583\) −0.174055 −0.00720864
\(584\) −49.1334 −2.03315
\(585\) 0 0
\(586\) 13.1439 0.542971
\(587\) 1.89439 0.0781898 0.0390949 0.999236i \(-0.487553\pi\)
0.0390949 + 0.999236i \(0.487553\pi\)
\(588\) 0 0
\(589\) −22.1377 −0.912169
\(590\) −52.6361 −2.16700
\(591\) 0 0
\(592\) 8.14598 0.334798
\(593\) 21.0493 0.864391 0.432196 0.901780i \(-0.357739\pi\)
0.432196 + 0.901780i \(0.357739\pi\)
\(594\) 0 0
\(595\) −1.14929 −0.0471161
\(596\) −15.0162 −0.615089
\(597\) 0 0
\(598\) −9.93635 −0.406328
\(599\) 11.2389 0.459208 0.229604 0.973284i \(-0.426257\pi\)
0.229604 + 0.973284i \(0.426257\pi\)
\(600\) 0 0
\(601\) −9.58370 −0.390927 −0.195464 0.980711i \(-0.562621\pi\)
−0.195464 + 0.980711i \(0.562621\pi\)
\(602\) −6.08704 −0.248089
\(603\) 0 0
\(604\) −52.1554 −2.12217
\(605\) −19.1435 −0.778292
\(606\) 0 0
\(607\) −9.46115 −0.384016 −0.192008 0.981393i \(-0.561500\pi\)
−0.192008 + 0.981393i \(0.561500\pi\)
\(608\) −0.486269 −0.0197208
\(609\) 0 0
\(610\) 51.1738 2.07197
\(611\) −26.0968 −1.05577
\(612\) 0 0
\(613\) 13.9848 0.564839 0.282420 0.959291i \(-0.408863\pi\)
0.282420 + 0.959291i \(0.408863\pi\)
\(614\) 24.7990 1.00081
\(615\) 0 0
\(616\) −0.659325 −0.0265650
\(617\) −33.5946 −1.35247 −0.676233 0.736688i \(-0.736389\pi\)
−0.676233 + 0.736688i \(0.736389\pi\)
\(618\) 0 0
\(619\) 18.8830 0.758971 0.379486 0.925198i \(-0.376101\pi\)
0.379486 + 0.925198i \(0.376101\pi\)
\(620\) 47.1260 1.89263
\(621\) 0 0
\(622\) −19.1200 −0.766642
\(623\) −12.4110 −0.497236
\(624\) 0 0
\(625\) −11.3484 −0.453934
\(626\) 42.0936 1.68240
\(627\) 0 0
\(628\) 64.4305 2.57106
\(629\) 1.37405 0.0547871
\(630\) 0 0
\(631\) −31.1723 −1.24095 −0.620474 0.784227i \(-0.713060\pi\)
−0.620474 + 0.784227i \(0.713060\pi\)
\(632\) −19.1541 −0.761909
\(633\) 0 0
\(634\) −47.0886 −1.87013
\(635\) −1.74324 −0.0691782
\(636\) 0 0
\(637\) −2.02529 −0.0802448
\(638\) −2.09809 −0.0830640
\(639\) 0 0
\(640\) 34.3716 1.35866
\(641\) −25.0094 −0.987812 −0.493906 0.869515i \(-0.664431\pi\)
−0.493906 + 0.869515i \(0.664431\pi\)
\(642\) 0 0
\(643\) 12.4838 0.492313 0.246157 0.969230i \(-0.420832\pi\)
0.246157 + 0.969230i \(0.420832\pi\)
\(644\) 7.99127 0.314900
\(645\) 0 0
\(646\) 5.26282 0.207063
\(647\) −9.50215 −0.373568 −0.186784 0.982401i \(-0.559806\pi\)
−0.186784 + 0.982401i \(0.559806\pi\)
\(648\) 0 0
\(649\) −1.67605 −0.0657907
\(650\) −9.71658 −0.381116
\(651\) 0 0
\(652\) −67.7715 −2.65414
\(653\) 1.75747 0.0687752 0.0343876 0.999409i \(-0.489052\pi\)
0.0343876 + 0.999409i \(0.489052\pi\)
\(654\) 0 0
\(655\) 21.7525 0.849942
\(656\) 11.5840 0.452278
\(657\) 0 0
\(658\) 31.5227 1.22888
\(659\) 28.7980 1.12181 0.560905 0.827880i \(-0.310453\pi\)
0.560905 + 0.827880i \(0.310453\pi\)
\(660\) 0 0
\(661\) −28.6135 −1.11293 −0.556467 0.830870i \(-0.687843\pi\)
−0.556467 + 0.830870i \(0.687843\pi\)
\(662\) −68.0556 −2.64506
\(663\) 0 0
\(664\) −84.2053 −3.26780
\(665\) 5.68829 0.220582
\(666\) 0 0
\(667\) 12.6660 0.490430
\(668\) −26.5390 −1.02683
\(669\) 0 0
\(670\) 58.3728 2.25514
\(671\) 1.62948 0.0629055
\(672\) 0 0
\(673\) 6.74566 0.260026 0.130013 0.991512i \(-0.458498\pi\)
0.130013 + 0.991512i \(0.458498\pi\)
\(674\) −70.7875 −2.72663
\(675\) 0 0
\(676\) −35.4568 −1.36372
\(677\) −6.45811 −0.248205 −0.124103 0.992269i \(-0.539605\pi\)
−0.124103 + 0.992269i \(0.539605\pi\)
\(678\) 0 0
\(679\) −4.98004 −0.191116
\(680\) −5.58017 −0.213990
\(681\) 0 0
\(682\) 2.25377 0.0863014
\(683\) −14.7524 −0.564485 −0.282243 0.959343i \(-0.591078\pi\)
−0.282243 + 0.959343i \(0.591078\pi\)
\(684\) 0 0
\(685\) 21.7577 0.831319
\(686\) 2.44637 0.0934027
\(687\) 0 0
\(688\) −9.72514 −0.370768
\(689\) −2.59593 −0.0988972
\(690\) 0 0
\(691\) 47.3145 1.79993 0.899963 0.435965i \(-0.143593\pi\)
0.899963 + 0.435965i \(0.143593\pi\)
\(692\) −72.2794 −2.74765
\(693\) 0 0
\(694\) 50.6335 1.92202
\(695\) 10.6736 0.404874
\(696\) 0 0
\(697\) 1.95397 0.0740120
\(698\) 62.9716 2.38351
\(699\) 0 0
\(700\) 7.81452 0.295361
\(701\) 31.6000 1.19352 0.596758 0.802421i \(-0.296455\pi\)
0.596758 + 0.802421i \(0.296455\pi\)
\(702\) 0 0
\(703\) −6.80076 −0.256495
\(704\) 1.11101 0.0418728
\(705\) 0 0
\(706\) −70.4640 −2.65195
\(707\) 3.77619 0.142018
\(708\) 0 0
\(709\) 36.2336 1.36078 0.680390 0.732850i \(-0.261810\pi\)
0.680390 + 0.732850i \(0.261810\pi\)
\(710\) 3.48817 0.130909
\(711\) 0 0
\(712\) −60.2595 −2.25832
\(713\) −13.6059 −0.509544
\(714\) 0 0
\(715\) 0.479428 0.0179296
\(716\) −74.0589 −2.76771
\(717\) 0 0
\(718\) 19.8008 0.738958
\(719\) −23.9301 −0.892441 −0.446221 0.894923i \(-0.647230\pi\)
−0.446221 + 0.894923i \(0.647230\pi\)
\(720\) 0 0
\(721\) 3.75563 0.139867
\(722\) 20.4331 0.760442
\(723\) 0 0
\(724\) −87.1206 −3.23781
\(725\) 12.3859 0.460000
\(726\) 0 0
\(727\) −11.7407 −0.435439 −0.217719 0.976011i \(-0.569862\pi\)
−0.217719 + 0.976011i \(0.569862\pi\)
\(728\) −9.83344 −0.364452
\(729\) 0 0
\(730\) −43.1554 −1.59725
\(731\) −1.64043 −0.0606733
\(732\) 0 0
\(733\) 17.6643 0.652446 0.326223 0.945293i \(-0.394224\pi\)
0.326223 + 0.945293i \(0.394224\pi\)
\(734\) 40.9693 1.51221
\(735\) 0 0
\(736\) −0.298862 −0.0110162
\(737\) 1.85872 0.0684667
\(738\) 0 0
\(739\) −40.3601 −1.48467 −0.742335 0.670029i \(-0.766282\pi\)
−0.742335 + 0.670029i \(0.766282\pi\)
\(740\) 14.4772 0.532194
\(741\) 0 0
\(742\) 3.13566 0.115114
\(743\) −31.8055 −1.16683 −0.583415 0.812174i \(-0.698284\pi\)
−0.583415 + 0.812174i \(0.698284\pi\)
\(744\) 0 0
\(745\) −6.56932 −0.240681
\(746\) −48.0044 −1.75756
\(747\) 0 0
\(748\) −0.356738 −0.0130436
\(749\) 4.86491 0.177760
\(750\) 0 0
\(751\) −18.5089 −0.675398 −0.337699 0.941254i \(-0.609649\pi\)
−0.337699 + 0.941254i \(0.609649\pi\)
\(752\) 50.3631 1.83655
\(753\) 0 0
\(754\) −31.2917 −1.13958
\(755\) −22.8170 −0.830396
\(756\) 0 0
\(757\) 14.3991 0.523343 0.261671 0.965157i \(-0.415726\pi\)
0.261671 + 0.965157i \(0.415726\pi\)
\(758\) 21.0521 0.764646
\(759\) 0 0
\(760\) 27.6185 1.00183
\(761\) −50.0061 −1.81272 −0.906360 0.422507i \(-0.861150\pi\)
−0.906360 + 0.422507i \(0.861150\pi\)
\(762\) 0 0
\(763\) 2.59574 0.0939720
\(764\) −74.4883 −2.69489
\(765\) 0 0
\(766\) −89.8589 −3.24674
\(767\) −24.9973 −0.902599
\(768\) 0 0
\(769\) −15.2862 −0.551233 −0.275617 0.961268i \(-0.588882\pi\)
−0.275617 + 0.961268i \(0.588882\pi\)
\(770\) −0.579107 −0.0208696
\(771\) 0 0
\(772\) −66.8591 −2.40631
\(773\) 16.9843 0.610884 0.305442 0.952211i \(-0.401196\pi\)
0.305442 + 0.952211i \(0.401196\pi\)
\(774\) 0 0
\(775\) −13.3049 −0.477928
\(776\) −24.1798 −0.868003
\(777\) 0 0
\(778\) 12.8313 0.460024
\(779\) −9.67101 −0.346500
\(780\) 0 0
\(781\) 0.111071 0.00397443
\(782\) 3.23454 0.115667
\(783\) 0 0
\(784\) 3.90851 0.139590
\(785\) 28.1871 1.00604
\(786\) 0 0
\(787\) −51.8926 −1.84977 −0.924885 0.380247i \(-0.875839\pi\)
−0.924885 + 0.380247i \(0.875839\pi\)
\(788\) −45.5092 −1.62120
\(789\) 0 0
\(790\) −16.8236 −0.598559
\(791\) 2.63918 0.0938386
\(792\) 0 0
\(793\) 24.3028 0.863017
\(794\) −27.9329 −0.991300
\(795\) 0 0
\(796\) −43.9006 −1.55601
\(797\) 7.38115 0.261454 0.130727 0.991418i \(-0.458269\pi\)
0.130727 + 0.991418i \(0.458269\pi\)
\(798\) 0 0
\(799\) 8.49520 0.300538
\(800\) −0.292252 −0.0103327
\(801\) 0 0
\(802\) −7.62885 −0.269384
\(803\) −1.37416 −0.0484931
\(804\) 0 0
\(805\) 3.49603 0.123219
\(806\) 33.6137 1.18399
\(807\) 0 0
\(808\) 18.3347 0.645012
\(809\) 3.29935 0.115999 0.0579995 0.998317i \(-0.481528\pi\)
0.0579995 + 0.998317i \(0.481528\pi\)
\(810\) 0 0
\(811\) −14.1011 −0.495157 −0.247579 0.968868i \(-0.579635\pi\)
−0.247579 + 0.968868i \(0.579635\pi\)
\(812\) 25.1662 0.883161
\(813\) 0 0
\(814\) 0.692364 0.0242673
\(815\) −29.6488 −1.03855
\(816\) 0 0
\(817\) 8.11914 0.284053
\(818\) 60.3960 2.11170
\(819\) 0 0
\(820\) 20.5873 0.718941
\(821\) 37.3111 1.30217 0.651084 0.759006i \(-0.274315\pi\)
0.651084 + 0.759006i \(0.274315\pi\)
\(822\) 0 0
\(823\) −4.25210 −0.148219 −0.0741094 0.997250i \(-0.523611\pi\)
−0.0741094 + 0.997250i \(0.523611\pi\)
\(824\) 18.2349 0.635242
\(825\) 0 0
\(826\) 30.1945 1.05060
\(827\) −25.0081 −0.869617 −0.434809 0.900523i \(-0.643184\pi\)
−0.434809 + 0.900523i \(0.643184\pi\)
\(828\) 0 0
\(829\) 48.7303 1.69247 0.846236 0.532808i \(-0.178863\pi\)
0.846236 + 0.532808i \(0.178863\pi\)
\(830\) −73.9602 −2.56720
\(831\) 0 0
\(832\) 16.5700 0.574463
\(833\) 0.659283 0.0228428
\(834\) 0 0
\(835\) −11.6103 −0.401792
\(836\) 1.76564 0.0610660
\(837\) 0 0
\(838\) 1.24614 0.0430473
\(839\) 1.50639 0.0520062 0.0260031 0.999662i \(-0.491722\pi\)
0.0260031 + 0.999662i \(0.491722\pi\)
\(840\) 0 0
\(841\) 10.8880 0.375447
\(842\) −65.8384 −2.26894
\(843\) 0 0
\(844\) 37.6551 1.29614
\(845\) −15.5117 −0.533619
\(846\) 0 0
\(847\) 10.9816 0.377331
\(848\) 5.00978 0.172036
\(849\) 0 0
\(850\) 3.16300 0.108490
\(851\) −4.17976 −0.143280
\(852\) 0 0
\(853\) −10.9103 −0.373562 −0.186781 0.982402i \(-0.559805\pi\)
−0.186781 + 0.982402i \(0.559805\pi\)
\(854\) −29.3556 −1.00453
\(855\) 0 0
\(856\) 23.6208 0.807341
\(857\) −34.0924 −1.16457 −0.582286 0.812984i \(-0.697842\pi\)
−0.582286 + 0.812984i \(0.697842\pi\)
\(858\) 0 0
\(859\) 49.9172 1.70315 0.851576 0.524230i \(-0.175647\pi\)
0.851576 + 0.524230i \(0.175647\pi\)
\(860\) −17.2838 −0.589371
\(861\) 0 0
\(862\) 13.2577 0.451558
\(863\) −31.8199 −1.08316 −0.541582 0.840648i \(-0.682174\pi\)
−0.541582 + 0.840648i \(0.682174\pi\)
\(864\) 0 0
\(865\) −31.6209 −1.07514
\(866\) 13.6495 0.463829
\(867\) 0 0
\(868\) −27.0336 −0.917582
\(869\) −0.535701 −0.0181724
\(870\) 0 0
\(871\) 27.7216 0.939312
\(872\) 12.6032 0.426797
\(873\) 0 0
\(874\) −16.0091 −0.541515
\(875\) 12.1349 0.410234
\(876\) 0 0
\(877\) 33.8062 1.14156 0.570778 0.821105i \(-0.306642\pi\)
0.570778 + 0.821105i \(0.306642\pi\)
\(878\) 79.6571 2.68830
\(879\) 0 0
\(880\) −0.925226 −0.0311894
\(881\) 42.2270 1.42266 0.711332 0.702856i \(-0.248092\pi\)
0.711332 + 0.702856i \(0.248092\pi\)
\(882\) 0 0
\(883\) −22.1525 −0.745492 −0.372746 0.927933i \(-0.621584\pi\)
−0.372746 + 0.927933i \(0.621584\pi\)
\(884\) −5.32053 −0.178949
\(885\) 0 0
\(886\) −70.0636 −2.35383
\(887\) 23.5438 0.790524 0.395262 0.918568i \(-0.370654\pi\)
0.395262 + 0.918568i \(0.370654\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −52.9279 −1.77415
\(891\) 0 0
\(892\) −59.3742 −1.98800
\(893\) −42.0462 −1.40702
\(894\) 0 0
\(895\) −32.3994 −1.08299
\(896\) −19.7171 −0.658702
\(897\) 0 0
\(898\) −98.3259 −3.28118
\(899\) −42.8478 −1.42905
\(900\) 0 0
\(901\) 0.845043 0.0281525
\(902\) 0.984575 0.0327828
\(903\) 0 0
\(904\) 12.8141 0.426191
\(905\) −38.1136 −1.26694
\(906\) 0 0
\(907\) −25.5277 −0.847633 −0.423817 0.905748i \(-0.639310\pi\)
−0.423817 + 0.905748i \(0.639310\pi\)
\(908\) −42.2067 −1.40068
\(909\) 0 0
\(910\) −8.63703 −0.286315
\(911\) 54.1250 1.79324 0.896621 0.442799i \(-0.146014\pi\)
0.896621 + 0.442799i \(0.146014\pi\)
\(912\) 0 0
\(913\) −2.35505 −0.0779408
\(914\) −51.8136 −1.71384
\(915\) 0 0
\(916\) 86.4031 2.85484
\(917\) −12.4783 −0.412068
\(918\) 0 0
\(919\) −51.2896 −1.69189 −0.845944 0.533272i \(-0.820962\pi\)
−0.845944 + 0.533272i \(0.820962\pi\)
\(920\) 16.9744 0.559630
\(921\) 0 0
\(922\) 4.59718 0.151400
\(923\) 1.65656 0.0545262
\(924\) 0 0
\(925\) −4.08731 −0.134390
\(926\) −12.4466 −0.409020
\(927\) 0 0
\(928\) −0.941180 −0.0308958
\(929\) 44.9274 1.47402 0.737011 0.675881i \(-0.236237\pi\)
0.737011 + 0.675881i \(0.236237\pi\)
\(930\) 0 0
\(931\) −3.26306 −0.106943
\(932\) −39.6627 −1.29920
\(933\) 0 0
\(934\) 19.0933 0.624753
\(935\) −0.156066 −0.00510391
\(936\) 0 0
\(937\) 23.4048 0.764603 0.382301 0.924038i \(-0.375132\pi\)
0.382301 + 0.924038i \(0.375132\pi\)
\(938\) −33.4853 −1.09333
\(939\) 0 0
\(940\) 89.5066 2.91938
\(941\) −18.7843 −0.612349 −0.306175 0.951975i \(-0.599049\pi\)
−0.306175 + 0.951975i \(0.599049\pi\)
\(942\) 0 0
\(943\) −5.94382 −0.193557
\(944\) 48.2411 1.57011
\(945\) 0 0
\(946\) −0.826584 −0.0268746
\(947\) −16.1089 −0.523468 −0.261734 0.965140i \(-0.584294\pi\)
−0.261734 + 0.965140i \(0.584294\pi\)
\(948\) 0 0
\(949\) −20.4948 −0.665289
\(950\) −15.6550 −0.507914
\(951\) 0 0
\(952\) 3.20104 0.103746
\(953\) −7.01631 −0.227280 −0.113640 0.993522i \(-0.536251\pi\)
−0.113640 + 0.993522i \(0.536251\pi\)
\(954\) 0 0
\(955\) −32.5872 −1.05450
\(956\) −93.4839 −3.02348
\(957\) 0 0
\(958\) 28.6295 0.924976
\(959\) −12.4812 −0.403039
\(960\) 0 0
\(961\) 15.0273 0.484751
\(962\) 10.3262 0.332930
\(963\) 0 0
\(964\) 37.8168 1.21800
\(965\) −29.2496 −0.941577
\(966\) 0 0
\(967\) −2.73407 −0.0879218 −0.0439609 0.999033i \(-0.513998\pi\)
−0.0439609 + 0.999033i \(0.513998\pi\)
\(968\) 53.3192 1.71374
\(969\) 0 0
\(970\) −21.2379 −0.681907
\(971\) −35.6649 −1.14454 −0.572271 0.820065i \(-0.693937\pi\)
−0.572271 + 0.820065i \(0.693937\pi\)
\(972\) 0 0
\(973\) −6.12288 −0.196291
\(974\) 93.4160 2.99324
\(975\) 0 0
\(976\) −46.9009 −1.50126
\(977\) −46.1434 −1.47626 −0.738129 0.674660i \(-0.764290\pi\)
−0.738129 + 0.674660i \(0.764290\pi\)
\(978\) 0 0
\(979\) −1.68534 −0.0538636
\(980\) 6.94630 0.221891
\(981\) 0 0
\(982\) 65.4937 2.08999
\(983\) 29.5575 0.942736 0.471368 0.881937i \(-0.343760\pi\)
0.471368 + 0.881937i \(0.343760\pi\)
\(984\) 0 0
\(985\) −19.9094 −0.634367
\(986\) 10.1863 0.324396
\(987\) 0 0
\(988\) 26.3335 0.837780
\(989\) 4.99004 0.158674
\(990\) 0 0
\(991\) 18.8251 0.597998 0.298999 0.954254i \(-0.403347\pi\)
0.298999 + 0.954254i \(0.403347\pi\)
\(992\) 1.01102 0.0320999
\(993\) 0 0
\(994\) −2.00097 −0.0634670
\(995\) −19.2057 −0.608861
\(996\) 0 0
\(997\) −8.27591 −0.262101 −0.131050 0.991376i \(-0.541835\pi\)
−0.131050 + 0.991376i \(0.541835\pi\)
\(998\) 75.4311 2.38773
\(999\) 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 \(a_p\))