Properties

Label 8008.2.a.p.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.37534\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37534 q^{3} -0.155697 q^{5} -1.00000 q^{7} +2.64224 q^{9} +O(q^{10})\) \(q-2.37534 q^{3} -0.155697 q^{5} -1.00000 q^{7} +2.64224 q^{9} +1.00000 q^{11} +1.00000 q^{13} +0.369832 q^{15} -3.88828 q^{17} -3.56736 q^{19} +2.37534 q^{21} +5.09749 q^{23} -4.97576 q^{25} +0.849810 q^{27} -6.55351 q^{29} +4.73339 q^{31} -2.37534 q^{33} +0.155697 q^{35} +7.33877 q^{37} -2.37534 q^{39} +11.7869 q^{41} +7.29212 q^{43} -0.411387 q^{45} -9.56368 q^{47} +1.00000 q^{49} +9.23598 q^{51} -8.39852 q^{53} -0.155697 q^{55} +8.47369 q^{57} +13.2210 q^{59} -8.66669 q^{61} -2.64224 q^{63} -0.155697 q^{65} -9.49672 q^{67} -12.1083 q^{69} -10.5347 q^{71} +1.56114 q^{73} +11.8191 q^{75} -1.00000 q^{77} -3.14222 q^{79} -9.94530 q^{81} +7.49797 q^{83} +0.605391 q^{85} +15.5668 q^{87} +0.972221 q^{89} -1.00000 q^{91} -11.2434 q^{93} +0.555426 q^{95} -4.23436 q^{97} +2.64224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + O(q^{10}) \) \( 9q + q^{3} - 4q^{5} - 9q^{7} + 4q^{9} + 9q^{11} + 9q^{13} - 9q^{15} - 11q^{17} + 10q^{19} - q^{21} - 14q^{23} - q^{25} - 5q^{27} - 10q^{29} + 5q^{31} + q^{33} + 4q^{35} - 16q^{37} + q^{39} + 2q^{41} + 4q^{43} - 30q^{45} + 9q^{49} + 3q^{51} - 23q^{53} - 4q^{55} + 14q^{57} + 9q^{59} - 14q^{61} - 4q^{63} - 4q^{65} + 8q^{67} - 26q^{69} - 20q^{71} - 23q^{73} + 32q^{75} - 9q^{77} + 2q^{79} - 11q^{81} - 9q^{83} - 3q^{85} - 7q^{87} - 6q^{89} - 9q^{91} - 19q^{93} - 4q^{95} - 3q^{97} + 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.37534 −1.37140 −0.685701 0.727883i \(-0.740504\pi\)
−0.685701 + 0.727883i \(0.740504\pi\)
\(4\) 0 0
\(5\) −0.155697 −0.0696296 −0.0348148 0.999394i \(-0.511084\pi\)
−0.0348148 + 0.999394i \(0.511084\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 2.64224 0.880745
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0.369832 0.0954902
\(16\) 0 0
\(17\) −3.88828 −0.943046 −0.471523 0.881854i \(-0.656296\pi\)
−0.471523 + 0.881854i \(0.656296\pi\)
\(18\) 0 0
\(19\) −3.56736 −0.818409 −0.409204 0.912443i \(-0.634194\pi\)
−0.409204 + 0.912443i \(0.634194\pi\)
\(20\) 0 0
\(21\) 2.37534 0.518342
\(22\) 0 0
\(23\) 5.09749 1.06290 0.531451 0.847089i \(-0.321647\pi\)
0.531451 + 0.847089i \(0.321647\pi\)
\(24\) 0 0
\(25\) −4.97576 −0.995152
\(26\) 0 0
\(27\) 0.849810 0.163546
\(28\) 0 0
\(29\) −6.55351 −1.21696 −0.608478 0.793571i \(-0.708220\pi\)
−0.608478 + 0.793571i \(0.708220\pi\)
\(30\) 0 0
\(31\) 4.73339 0.850141 0.425071 0.905160i \(-0.360249\pi\)
0.425071 + 0.905160i \(0.360249\pi\)
\(32\) 0 0
\(33\) −2.37534 −0.413493
\(34\) 0 0
\(35\) 0.155697 0.0263175
\(36\) 0 0
\(37\) 7.33877 1.20649 0.603243 0.797557i \(-0.293875\pi\)
0.603243 + 0.797557i \(0.293875\pi\)
\(38\) 0 0
\(39\) −2.37534 −0.380359
\(40\) 0 0
\(41\) 11.7869 1.84080 0.920399 0.390980i \(-0.127864\pi\)
0.920399 + 0.390980i \(0.127864\pi\)
\(42\) 0 0
\(43\) 7.29212 1.11204 0.556019 0.831170i \(-0.312328\pi\)
0.556019 + 0.831170i \(0.312328\pi\)
\(44\) 0 0
\(45\) −0.411387 −0.0613260
\(46\) 0 0
\(47\) −9.56368 −1.39501 −0.697503 0.716582i \(-0.745705\pi\)
−0.697503 + 0.716582i \(0.745705\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 9.23598 1.29330
\(52\) 0 0
\(53\) −8.39852 −1.15363 −0.576813 0.816876i \(-0.695704\pi\)
−0.576813 + 0.816876i \(0.695704\pi\)
\(54\) 0 0
\(55\) −0.155697 −0.0209941
\(56\) 0 0
\(57\) 8.47369 1.12237
\(58\) 0 0
\(59\) 13.2210 1.72122 0.860612 0.509262i \(-0.170081\pi\)
0.860612 + 0.509262i \(0.170081\pi\)
\(60\) 0 0
\(61\) −8.66669 −1.10966 −0.554828 0.831965i \(-0.687216\pi\)
−0.554828 + 0.831965i \(0.687216\pi\)
\(62\) 0 0
\(63\) −2.64224 −0.332890
\(64\) 0 0
\(65\) −0.155697 −0.0193118
\(66\) 0 0
\(67\) −9.49672 −1.16021 −0.580105 0.814542i \(-0.696988\pi\)
−0.580105 + 0.814542i \(0.696988\pi\)
\(68\) 0 0
\(69\) −12.1083 −1.45767
\(70\) 0 0
\(71\) −10.5347 −1.25024 −0.625118 0.780530i \(-0.714949\pi\)
−0.625118 + 0.780530i \(0.714949\pi\)
\(72\) 0 0
\(73\) 1.56114 0.182717 0.0913587 0.995818i \(-0.470879\pi\)
0.0913587 + 0.995818i \(0.470879\pi\)
\(74\) 0 0
\(75\) 11.8191 1.36475
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −3.14222 −0.353528 −0.176764 0.984253i \(-0.556563\pi\)
−0.176764 + 0.984253i \(0.556563\pi\)
\(80\) 0 0
\(81\) −9.94530 −1.10503
\(82\) 0 0
\(83\) 7.49797 0.823009 0.411505 0.911408i \(-0.365003\pi\)
0.411505 + 0.911408i \(0.365003\pi\)
\(84\) 0 0
\(85\) 0.605391 0.0656639
\(86\) 0 0
\(87\) 15.5668 1.66894
\(88\) 0 0
\(89\) 0.972221 0.103055 0.0515276 0.998672i \(-0.483591\pi\)
0.0515276 + 0.998672i \(0.483591\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −11.2434 −1.16589
\(94\) 0 0
\(95\) 0.555426 0.0569855
\(96\) 0 0
\(97\) −4.23436 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(98\) 0 0
\(99\) 2.64224 0.265555
\(100\) 0 0
\(101\) 14.4247 1.43531 0.717656 0.696398i \(-0.245215\pi\)
0.717656 + 0.696398i \(0.245215\pi\)
\(102\) 0 0
\(103\) 12.1967 1.20178 0.600888 0.799334i \(-0.294814\pi\)
0.600888 + 0.799334i \(0.294814\pi\)
\(104\) 0 0
\(105\) −0.369832 −0.0360919
\(106\) 0 0
\(107\) −0.424447 −0.0410329 −0.0205164 0.999790i \(-0.506531\pi\)
−0.0205164 + 0.999790i \(0.506531\pi\)
\(108\) 0 0
\(109\) −9.89917 −0.948169 −0.474084 0.880479i \(-0.657221\pi\)
−0.474084 + 0.880479i \(0.657221\pi\)
\(110\) 0 0
\(111\) −17.4321 −1.65458
\(112\) 0 0
\(113\) −3.41243 −0.321014 −0.160507 0.987035i \(-0.551313\pi\)
−0.160507 + 0.987035i \(0.551313\pi\)
\(114\) 0 0
\(115\) −0.793662 −0.0740094
\(116\) 0 0
\(117\) 2.64224 0.244275
\(118\) 0 0
\(119\) 3.88828 0.356438
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −27.9978 −2.52448
\(124\) 0 0
\(125\) 1.55319 0.138922
\(126\) 0 0
\(127\) 1.51328 0.134282 0.0671409 0.997744i \(-0.478612\pi\)
0.0671409 + 0.997744i \(0.478612\pi\)
\(128\) 0 0
\(129\) −17.3213 −1.52505
\(130\) 0 0
\(131\) 9.27572 0.810424 0.405212 0.914223i \(-0.367198\pi\)
0.405212 + 0.914223i \(0.367198\pi\)
\(132\) 0 0
\(133\) 3.56736 0.309329
\(134\) 0 0
\(135\) −0.132313 −0.0113877
\(136\) 0 0
\(137\) 1.71427 0.146460 0.0732298 0.997315i \(-0.476669\pi\)
0.0732298 + 0.997315i \(0.476669\pi\)
\(138\) 0 0
\(139\) 18.9472 1.60708 0.803539 0.595253i \(-0.202948\pi\)
0.803539 + 0.595253i \(0.202948\pi\)
\(140\) 0 0
\(141\) 22.7170 1.91311
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.02036 0.0847362
\(146\) 0 0
\(147\) −2.37534 −0.195915
\(148\) 0 0
\(149\) −13.9638 −1.14396 −0.571980 0.820268i \(-0.693824\pi\)
−0.571980 + 0.820268i \(0.693824\pi\)
\(150\) 0 0
\(151\) 12.5553 1.02173 0.510867 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(152\) 0 0
\(153\) −10.2737 −0.830583
\(154\) 0 0
\(155\) −0.736972 −0.0591950
\(156\) 0 0
\(157\) −8.43133 −0.672894 −0.336447 0.941702i \(-0.609225\pi\)
−0.336447 + 0.941702i \(0.609225\pi\)
\(158\) 0 0
\(159\) 19.9493 1.58209
\(160\) 0 0
\(161\) −5.09749 −0.401739
\(162\) 0 0
\(163\) 21.1518 1.65674 0.828369 0.560183i \(-0.189269\pi\)
0.828369 + 0.560183i \(0.189269\pi\)
\(164\) 0 0
\(165\) 0.369832 0.0287914
\(166\) 0 0
\(167\) 2.78684 0.215652 0.107826 0.994170i \(-0.465611\pi\)
0.107826 + 0.994170i \(0.465611\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −9.42581 −0.720810
\(172\) 0 0
\(173\) 12.6991 0.965491 0.482745 0.875761i \(-0.339640\pi\)
0.482745 + 0.875761i \(0.339640\pi\)
\(174\) 0 0
\(175\) 4.97576 0.376132
\(176\) 0 0
\(177\) −31.4043 −2.36049
\(178\) 0 0
\(179\) 1.25028 0.0934504 0.0467252 0.998908i \(-0.485121\pi\)
0.0467252 + 0.998908i \(0.485121\pi\)
\(180\) 0 0
\(181\) 19.4953 1.44907 0.724537 0.689236i \(-0.242054\pi\)
0.724537 + 0.689236i \(0.242054\pi\)
\(182\) 0 0
\(183\) 20.5863 1.52179
\(184\) 0 0
\(185\) −1.14262 −0.0840072
\(186\) 0 0
\(187\) −3.88828 −0.284339
\(188\) 0 0
\(189\) −0.849810 −0.0618146
\(190\) 0 0
\(191\) 10.2040 0.738339 0.369169 0.929362i \(-0.379642\pi\)
0.369169 + 0.929362i \(0.379642\pi\)
\(192\) 0 0
\(193\) −27.3089 −1.96574 −0.982868 0.184308i \(-0.940995\pi\)
−0.982868 + 0.184308i \(0.940995\pi\)
\(194\) 0 0
\(195\) 0.369832 0.0264842
\(196\) 0 0
\(197\) −8.40970 −0.599166 −0.299583 0.954070i \(-0.596848\pi\)
−0.299583 + 0.954070i \(0.596848\pi\)
\(198\) 0 0
\(199\) 13.4922 0.956437 0.478218 0.878241i \(-0.341283\pi\)
0.478218 + 0.878241i \(0.341283\pi\)
\(200\) 0 0
\(201\) 22.5579 1.59111
\(202\) 0 0
\(203\) 6.55351 0.459966
\(204\) 0 0
\(205\) −1.83517 −0.128174
\(206\) 0 0
\(207\) 13.4688 0.936145
\(208\) 0 0
\(209\) −3.56736 −0.246759
\(210\) 0 0
\(211\) 7.26113 0.499877 0.249938 0.968262i \(-0.419590\pi\)
0.249938 + 0.968262i \(0.419590\pi\)
\(212\) 0 0
\(213\) 25.0234 1.71458
\(214\) 0 0
\(215\) −1.13536 −0.0774307
\(216\) 0 0
\(217\) −4.73339 −0.321323
\(218\) 0 0
\(219\) −3.70823 −0.250579
\(220\) 0 0
\(221\) −3.88828 −0.261554
\(222\) 0 0
\(223\) 16.9737 1.13664 0.568321 0.822807i \(-0.307593\pi\)
0.568321 + 0.822807i \(0.307593\pi\)
\(224\) 0 0
\(225\) −13.1471 −0.876475
\(226\) 0 0
\(227\) −29.2374 −1.94056 −0.970278 0.241994i \(-0.922199\pi\)
−0.970278 + 0.241994i \(0.922199\pi\)
\(228\) 0 0
\(229\) −9.40858 −0.621736 −0.310868 0.950453i \(-0.600620\pi\)
−0.310868 + 0.950453i \(0.600620\pi\)
\(230\) 0 0
\(231\) 2.37534 0.156286
\(232\) 0 0
\(233\) −23.9028 −1.56593 −0.782964 0.622067i \(-0.786293\pi\)
−0.782964 + 0.622067i \(0.786293\pi\)
\(234\) 0 0
\(235\) 1.48903 0.0971337
\(236\) 0 0
\(237\) 7.46385 0.484829
\(238\) 0 0
\(239\) −12.5337 −0.810738 −0.405369 0.914153i \(-0.632857\pi\)
−0.405369 + 0.914153i \(0.632857\pi\)
\(240\) 0 0
\(241\) −13.7248 −0.884094 −0.442047 0.896992i \(-0.645748\pi\)
−0.442047 + 0.896992i \(0.645748\pi\)
\(242\) 0 0
\(243\) 21.0740 1.35190
\(244\) 0 0
\(245\) −0.155697 −0.00994709
\(246\) 0 0
\(247\) −3.56736 −0.226986
\(248\) 0 0
\(249\) −17.8102 −1.12868
\(250\) 0 0
\(251\) −24.3090 −1.53437 −0.767185 0.641426i \(-0.778343\pi\)
−0.767185 + 0.641426i \(0.778343\pi\)
\(252\) 0 0
\(253\) 5.09749 0.320477
\(254\) 0 0
\(255\) −1.43801 −0.0900517
\(256\) 0 0
\(257\) 7.93945 0.495249 0.247625 0.968856i \(-0.420350\pi\)
0.247625 + 0.968856i \(0.420350\pi\)
\(258\) 0 0
\(259\) −7.33877 −0.456009
\(260\) 0 0
\(261\) −17.3159 −1.07183
\(262\) 0 0
\(263\) 3.45539 0.213069 0.106534 0.994309i \(-0.466025\pi\)
0.106534 + 0.994309i \(0.466025\pi\)
\(264\) 0 0
\(265\) 1.30762 0.0803265
\(266\) 0 0
\(267\) −2.30935 −0.141330
\(268\) 0 0
\(269\) −12.9495 −0.789546 −0.394773 0.918779i \(-0.629177\pi\)
−0.394773 + 0.918779i \(0.629177\pi\)
\(270\) 0 0
\(271\) −28.2217 −1.71435 −0.857173 0.515029i \(-0.827781\pi\)
−0.857173 + 0.515029i \(0.827781\pi\)
\(272\) 0 0
\(273\) 2.37534 0.143762
\(274\) 0 0
\(275\) −4.97576 −0.300050
\(276\) 0 0
\(277\) 20.7906 1.24919 0.624595 0.780949i \(-0.285264\pi\)
0.624595 + 0.780949i \(0.285264\pi\)
\(278\) 0 0
\(279\) 12.5067 0.748758
\(280\) 0 0
\(281\) 12.9860 0.774680 0.387340 0.921937i \(-0.373394\pi\)
0.387340 + 0.921937i \(0.373394\pi\)
\(282\) 0 0
\(283\) −29.3499 −1.74467 −0.872334 0.488911i \(-0.837394\pi\)
−0.872334 + 0.488911i \(0.837394\pi\)
\(284\) 0 0
\(285\) −1.31932 −0.0781500
\(286\) 0 0
\(287\) −11.7869 −0.695756
\(288\) 0 0
\(289\) −1.88130 −0.110665
\(290\) 0 0
\(291\) 10.0580 0.589612
\(292\) 0 0
\(293\) 4.84940 0.283305 0.141652 0.989916i \(-0.454758\pi\)
0.141652 + 0.989916i \(0.454758\pi\)
\(294\) 0 0
\(295\) −2.05846 −0.119848
\(296\) 0 0
\(297\) 0.849810 0.0493110
\(298\) 0 0
\(299\) 5.09749 0.294796
\(300\) 0 0
\(301\) −7.29212 −0.420311
\(302\) 0 0
\(303\) −34.2636 −1.96839
\(304\) 0 0
\(305\) 1.34937 0.0772649
\(306\) 0 0
\(307\) −15.7972 −0.901593 −0.450797 0.892627i \(-0.648860\pi\)
−0.450797 + 0.892627i \(0.648860\pi\)
\(308\) 0 0
\(309\) −28.9713 −1.64812
\(310\) 0 0
\(311\) −6.90723 −0.391673 −0.195837 0.980637i \(-0.562742\pi\)
−0.195837 + 0.980637i \(0.562742\pi\)
\(312\) 0 0
\(313\) −32.8682 −1.85782 −0.928911 0.370303i \(-0.879254\pi\)
−0.928911 + 0.370303i \(0.879254\pi\)
\(314\) 0 0
\(315\) 0.411387 0.0231790
\(316\) 0 0
\(317\) 11.0127 0.618537 0.309269 0.950975i \(-0.399916\pi\)
0.309269 + 0.950975i \(0.399916\pi\)
\(318\) 0 0
\(319\) −6.55351 −0.366926
\(320\) 0 0
\(321\) 1.00821 0.0562726
\(322\) 0 0
\(323\) 13.8709 0.771797
\(324\) 0 0
\(325\) −4.97576 −0.276005
\(326\) 0 0
\(327\) 23.5139 1.30032
\(328\) 0 0
\(329\) 9.56368 0.527262
\(330\) 0 0
\(331\) 13.5598 0.745313 0.372657 0.927969i \(-0.378447\pi\)
0.372657 + 0.927969i \(0.378447\pi\)
\(332\) 0 0
\(333\) 19.3908 1.06261
\(334\) 0 0
\(335\) 1.47861 0.0807849
\(336\) 0 0
\(337\) −18.5865 −1.01247 −0.506237 0.862395i \(-0.668964\pi\)
−0.506237 + 0.862395i \(0.668964\pi\)
\(338\) 0 0
\(339\) 8.10567 0.440240
\(340\) 0 0
\(341\) 4.73339 0.256327
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 1.88522 0.101497
\(346\) 0 0
\(347\) −1.27970 −0.0686981 −0.0343491 0.999410i \(-0.510936\pi\)
−0.0343491 + 0.999410i \(0.510936\pi\)
\(348\) 0 0
\(349\) 14.3981 0.770712 0.385356 0.922768i \(-0.374079\pi\)
0.385356 + 0.922768i \(0.374079\pi\)
\(350\) 0 0
\(351\) 0.849810 0.0453595
\(352\) 0 0
\(353\) 21.6983 1.15489 0.577443 0.816431i \(-0.304051\pi\)
0.577443 + 0.816431i \(0.304051\pi\)
\(354\) 0 0
\(355\) 1.64021 0.0870534
\(356\) 0 0
\(357\) −9.23598 −0.488820
\(358\) 0 0
\(359\) −16.9334 −0.893709 −0.446854 0.894607i \(-0.647456\pi\)
−0.446854 + 0.894607i \(0.647456\pi\)
\(360\) 0 0
\(361\) −6.27394 −0.330207
\(362\) 0 0
\(363\) −2.37534 −0.124673
\(364\) 0 0
\(365\) −0.243064 −0.0127225
\(366\) 0 0
\(367\) −1.98179 −0.103449 −0.0517244 0.998661i \(-0.516472\pi\)
−0.0517244 + 0.998661i \(0.516472\pi\)
\(368\) 0 0
\(369\) 31.1437 1.62127
\(370\) 0 0
\(371\) 8.39852 0.436029
\(372\) 0 0
\(373\) −9.69086 −0.501774 −0.250887 0.968016i \(-0.580722\pi\)
−0.250887 + 0.968016i \(0.580722\pi\)
\(374\) 0 0
\(375\) −3.68936 −0.190518
\(376\) 0 0
\(377\) −6.55351 −0.337523
\(378\) 0 0
\(379\) −21.2624 −1.09218 −0.546088 0.837728i \(-0.683883\pi\)
−0.546088 + 0.837728i \(0.683883\pi\)
\(380\) 0 0
\(381\) −3.59455 −0.184154
\(382\) 0 0
\(383\) −23.1456 −1.18269 −0.591343 0.806420i \(-0.701402\pi\)
−0.591343 + 0.806420i \(0.701402\pi\)
\(384\) 0 0
\(385\) 0.155697 0.00793503
\(386\) 0 0
\(387\) 19.2675 0.979422
\(388\) 0 0
\(389\) 0.385464 0.0195438 0.00977191 0.999952i \(-0.496889\pi\)
0.00977191 + 0.999952i \(0.496889\pi\)
\(390\) 0 0
\(391\) −19.8205 −1.00236
\(392\) 0 0
\(393\) −22.0330 −1.11142
\(394\) 0 0
\(395\) 0.489234 0.0246160
\(396\) 0 0
\(397\) −27.9397 −1.40225 −0.701127 0.713036i \(-0.747319\pi\)
−0.701127 + 0.713036i \(0.747319\pi\)
\(398\) 0 0
\(399\) −8.47369 −0.424215
\(400\) 0 0
\(401\) −23.2228 −1.15969 −0.579845 0.814727i \(-0.696887\pi\)
−0.579845 + 0.814727i \(0.696887\pi\)
\(402\) 0 0
\(403\) 4.73339 0.235787
\(404\) 0 0
\(405\) 1.54845 0.0769430
\(406\) 0 0
\(407\) 7.33877 0.363769
\(408\) 0 0
\(409\) −39.7964 −1.96780 −0.983902 0.178709i \(-0.942808\pi\)
−0.983902 + 0.178709i \(0.942808\pi\)
\(410\) 0 0
\(411\) −4.07196 −0.200855
\(412\) 0 0
\(413\) −13.2210 −0.650561
\(414\) 0 0
\(415\) −1.16741 −0.0573058
\(416\) 0 0
\(417\) −45.0059 −2.20395
\(418\) 0 0
\(419\) −9.29641 −0.454159 −0.227080 0.973876i \(-0.572918\pi\)
−0.227080 + 0.973876i \(0.572918\pi\)
\(420\) 0 0
\(421\) 5.57715 0.271814 0.135907 0.990722i \(-0.456605\pi\)
0.135907 + 0.990722i \(0.456605\pi\)
\(422\) 0 0
\(423\) −25.2695 −1.22864
\(424\) 0 0
\(425\) 19.3471 0.938474
\(426\) 0 0
\(427\) 8.66669 0.419411
\(428\) 0 0
\(429\) −2.37534 −0.114682
\(430\) 0 0
\(431\) 7.30870 0.352048 0.176024 0.984386i \(-0.443676\pi\)
0.176024 + 0.984386i \(0.443676\pi\)
\(432\) 0 0
\(433\) 4.11611 0.197808 0.0989039 0.995097i \(-0.468466\pi\)
0.0989039 + 0.995097i \(0.468466\pi\)
\(434\) 0 0
\(435\) −2.42370 −0.116207
\(436\) 0 0
\(437\) −18.1846 −0.869887
\(438\) 0 0
\(439\) −3.78511 −0.180653 −0.0903267 0.995912i \(-0.528791\pi\)
−0.0903267 + 0.995912i \(0.528791\pi\)
\(440\) 0 0
\(441\) 2.64224 0.125821
\(442\) 0 0
\(443\) −26.8005 −1.27333 −0.636665 0.771141i \(-0.719687\pi\)
−0.636665 + 0.771141i \(0.719687\pi\)
\(444\) 0 0
\(445\) −0.151371 −0.00717569
\(446\) 0 0
\(447\) 33.1688 1.56883
\(448\) 0 0
\(449\) −6.99476 −0.330103 −0.165052 0.986285i \(-0.552779\pi\)
−0.165052 + 0.986285i \(0.552779\pi\)
\(450\) 0 0
\(451\) 11.7869 0.555022
\(452\) 0 0
\(453\) −29.8231 −1.40121
\(454\) 0 0
\(455\) 0.155697 0.00729917
\(456\) 0 0
\(457\) 23.9860 1.12202 0.561008 0.827810i \(-0.310414\pi\)
0.561008 + 0.827810i \(0.310414\pi\)
\(458\) 0 0
\(459\) −3.30430 −0.154231
\(460\) 0 0
\(461\) −3.90000 −0.181641 −0.0908205 0.995867i \(-0.528949\pi\)
−0.0908205 + 0.995867i \(0.528949\pi\)
\(462\) 0 0
\(463\) −10.4740 −0.486766 −0.243383 0.969930i \(-0.578257\pi\)
−0.243383 + 0.969930i \(0.578257\pi\)
\(464\) 0 0
\(465\) 1.75056 0.0811802
\(466\) 0 0
\(467\) 5.41240 0.250456 0.125228 0.992128i \(-0.460034\pi\)
0.125228 + 0.992128i \(0.460034\pi\)
\(468\) 0 0
\(469\) 9.49672 0.438518
\(470\) 0 0
\(471\) 20.0273 0.922808
\(472\) 0 0
\(473\) 7.29212 0.335292
\(474\) 0 0
\(475\) 17.7503 0.814441
\(476\) 0 0
\(477\) −22.1909 −1.01605
\(478\) 0 0
\(479\) −29.3013 −1.33881 −0.669405 0.742897i \(-0.733451\pi\)
−0.669405 + 0.742897i \(0.733451\pi\)
\(480\) 0 0
\(481\) 7.33877 0.334619
\(482\) 0 0
\(483\) 12.1083 0.550946
\(484\) 0 0
\(485\) 0.659275 0.0299361
\(486\) 0 0
\(487\) −16.2675 −0.737151 −0.368575 0.929598i \(-0.620154\pi\)
−0.368575 + 0.929598i \(0.620154\pi\)
\(488\) 0 0
\(489\) −50.2427 −2.27205
\(490\) 0 0
\(491\) 6.97369 0.314718 0.157359 0.987541i \(-0.449702\pi\)
0.157359 + 0.987541i \(0.449702\pi\)
\(492\) 0 0
\(493\) 25.4819 1.14765
\(494\) 0 0
\(495\) −0.411387 −0.0184905
\(496\) 0 0
\(497\) 10.5347 0.472545
\(498\) 0 0
\(499\) −18.9588 −0.848714 −0.424357 0.905495i \(-0.639500\pi\)
−0.424357 + 0.905495i \(0.639500\pi\)
\(500\) 0 0
\(501\) −6.61969 −0.295746
\(502\) 0 0
\(503\) −14.8464 −0.661970 −0.330985 0.943636i \(-0.607381\pi\)
−0.330985 + 0.943636i \(0.607381\pi\)
\(504\) 0 0
\(505\) −2.24588 −0.0999402
\(506\) 0 0
\(507\) −2.37534 −0.105493
\(508\) 0 0
\(509\) 28.2305 1.25129 0.625647 0.780107i \(-0.284835\pi\)
0.625647 + 0.780107i \(0.284835\pi\)
\(510\) 0 0
\(511\) −1.56114 −0.0690607
\(512\) 0 0
\(513\) −3.03158 −0.133848
\(514\) 0 0
\(515\) −1.89898 −0.0836792
\(516\) 0 0
\(517\) −9.56368 −0.420610
\(518\) 0 0
\(519\) −30.1646 −1.32408
\(520\) 0 0
\(521\) 8.27617 0.362585 0.181293 0.983429i \(-0.441972\pi\)
0.181293 + 0.983429i \(0.441972\pi\)
\(522\) 0 0
\(523\) 9.62287 0.420779 0.210389 0.977618i \(-0.432527\pi\)
0.210389 + 0.977618i \(0.432527\pi\)
\(524\) 0 0
\(525\) −11.8191 −0.515828
\(526\) 0 0
\(527\) −18.4047 −0.801722
\(528\) 0 0
\(529\) 2.98445 0.129759
\(530\) 0 0
\(531\) 34.9329 1.51596
\(532\) 0 0
\(533\) 11.7869 0.510546
\(534\) 0 0
\(535\) 0.0660850 0.00285710
\(536\) 0 0
\(537\) −2.96984 −0.128158
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −15.8296 −0.680567 −0.340283 0.940323i \(-0.610523\pi\)
−0.340283 + 0.940323i \(0.610523\pi\)
\(542\) 0 0
\(543\) −46.3080 −1.98726
\(544\) 0 0
\(545\) 1.54127 0.0660206
\(546\) 0 0
\(547\) −27.6597 −1.18264 −0.591322 0.806435i \(-0.701394\pi\)
−0.591322 + 0.806435i \(0.701394\pi\)
\(548\) 0 0
\(549\) −22.8994 −0.977325
\(550\) 0 0
\(551\) 23.3787 0.995967
\(552\) 0 0
\(553\) 3.14222 0.133621
\(554\) 0 0
\(555\) 2.71411 0.115208
\(556\) 0 0
\(557\) −41.4013 −1.75423 −0.877115 0.480281i \(-0.840535\pi\)
−0.877115 + 0.480281i \(0.840535\pi\)
\(558\) 0 0
\(559\) 7.29212 0.308424
\(560\) 0 0
\(561\) 9.23598 0.389943
\(562\) 0 0
\(563\) 13.7090 0.577764 0.288882 0.957365i \(-0.406716\pi\)
0.288882 + 0.957365i \(0.406716\pi\)
\(564\) 0 0
\(565\) 0.531303 0.0223521
\(566\) 0 0
\(567\) 9.94530 0.417663
\(568\) 0 0
\(569\) 25.1585 1.05470 0.527350 0.849648i \(-0.323186\pi\)
0.527350 + 0.849648i \(0.323186\pi\)
\(570\) 0 0
\(571\) 17.5647 0.735062 0.367531 0.930011i \(-0.380203\pi\)
0.367531 + 0.930011i \(0.380203\pi\)
\(572\) 0 0
\(573\) −24.2381 −1.01256
\(574\) 0 0
\(575\) −25.3639 −1.05775
\(576\) 0 0
\(577\) −27.3590 −1.13897 −0.569485 0.822002i \(-0.692857\pi\)
−0.569485 + 0.822002i \(0.692857\pi\)
\(578\) 0 0
\(579\) 64.8679 2.69582
\(580\) 0 0
\(581\) −7.49797 −0.311068
\(582\) 0 0
\(583\) −8.39852 −0.347831
\(584\) 0 0
\(585\) −0.411387 −0.0170088
\(586\) 0 0
\(587\) 37.9183 1.56505 0.782527 0.622617i \(-0.213930\pi\)
0.782527 + 0.622617i \(0.213930\pi\)
\(588\) 0 0
\(589\) −16.8857 −0.695763
\(590\) 0 0
\(591\) 19.9759 0.821698
\(592\) 0 0
\(593\) −9.92325 −0.407499 −0.203750 0.979023i \(-0.565313\pi\)
−0.203750 + 0.979023i \(0.565313\pi\)
\(594\) 0 0
\(595\) −0.605391 −0.0248186
\(596\) 0 0
\(597\) −32.0486 −1.31166
\(598\) 0 0
\(599\) −37.3898 −1.52771 −0.763853 0.645390i \(-0.776695\pi\)
−0.763853 + 0.645390i \(0.776695\pi\)
\(600\) 0 0
\(601\) 12.2992 0.501693 0.250847 0.968027i \(-0.419291\pi\)
0.250847 + 0.968027i \(0.419291\pi\)
\(602\) 0 0
\(603\) −25.0926 −1.02185
\(604\) 0 0
\(605\) −0.155697 −0.00632997
\(606\) 0 0
\(607\) 28.8733 1.17193 0.585967 0.810335i \(-0.300715\pi\)
0.585967 + 0.810335i \(0.300715\pi\)
\(608\) 0 0
\(609\) −15.5668 −0.630799
\(610\) 0 0
\(611\) −9.56368 −0.386905
\(612\) 0 0
\(613\) −32.0818 −1.29577 −0.647886 0.761737i \(-0.724347\pi\)
−0.647886 + 0.761737i \(0.724347\pi\)
\(614\) 0 0
\(615\) 4.35916 0.175778
\(616\) 0 0
\(617\) 5.82622 0.234555 0.117277 0.993099i \(-0.462583\pi\)
0.117277 + 0.993099i \(0.462583\pi\)
\(618\) 0 0
\(619\) 2.61388 0.105061 0.0525304 0.998619i \(-0.483271\pi\)
0.0525304 + 0.998619i \(0.483271\pi\)
\(620\) 0 0
\(621\) 4.33190 0.173833
\(622\) 0 0
\(623\) −0.972221 −0.0389512
\(624\) 0 0
\(625\) 24.6370 0.985479
\(626\) 0 0
\(627\) 8.47369 0.338407
\(628\) 0 0
\(629\) −28.5352 −1.13777
\(630\) 0 0
\(631\) 33.0163 1.31436 0.657180 0.753734i \(-0.271749\pi\)
0.657180 + 0.753734i \(0.271749\pi\)
\(632\) 0 0
\(633\) −17.2476 −0.685532
\(634\) 0 0
\(635\) −0.235612 −0.00934999
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −27.8351 −1.10114
\(640\) 0 0
\(641\) −23.6023 −0.932234 −0.466117 0.884723i \(-0.654347\pi\)
−0.466117 + 0.884723i \(0.654347\pi\)
\(642\) 0 0
\(643\) −7.39921 −0.291796 −0.145898 0.989300i \(-0.546607\pi\)
−0.145898 + 0.989300i \(0.546607\pi\)
\(644\) 0 0
\(645\) 2.69686 0.106189
\(646\) 0 0
\(647\) −27.3205 −1.07408 −0.537040 0.843557i \(-0.680458\pi\)
−0.537040 + 0.843557i \(0.680458\pi\)
\(648\) 0 0
\(649\) 13.2210 0.518968
\(650\) 0 0
\(651\) 11.2434 0.440663
\(652\) 0 0
\(653\) −2.75952 −0.107988 −0.0539942 0.998541i \(-0.517195\pi\)
−0.0539942 + 0.998541i \(0.517195\pi\)
\(654\) 0 0
\(655\) −1.44420 −0.0564295
\(656\) 0 0
\(657\) 4.12490 0.160928
\(658\) 0 0
\(659\) 28.3338 1.10373 0.551864 0.833934i \(-0.313917\pi\)
0.551864 + 0.833934i \(0.313917\pi\)
\(660\) 0 0
\(661\) 7.82911 0.304517 0.152258 0.988341i \(-0.451345\pi\)
0.152258 + 0.988341i \(0.451345\pi\)
\(662\) 0 0
\(663\) 9.23598 0.358696
\(664\) 0 0
\(665\) −0.555426 −0.0215385
\(666\) 0 0
\(667\) −33.4065 −1.29350
\(668\) 0 0
\(669\) −40.3183 −1.55879
\(670\) 0 0
\(671\) −8.66669 −0.334574
\(672\) 0 0
\(673\) −42.8793 −1.65287 −0.826437 0.563029i \(-0.809636\pi\)
−0.826437 + 0.563029i \(0.809636\pi\)
\(674\) 0 0
\(675\) −4.22845 −0.162753
\(676\) 0 0
\(677\) 8.79087 0.337861 0.168930 0.985628i \(-0.445969\pi\)
0.168930 + 0.985628i \(0.445969\pi\)
\(678\) 0 0
\(679\) 4.23436 0.162500
\(680\) 0 0
\(681\) 69.4488 2.66128
\(682\) 0 0
\(683\) 2.01042 0.0769266 0.0384633 0.999260i \(-0.487754\pi\)
0.0384633 + 0.999260i \(0.487754\pi\)
\(684\) 0 0
\(685\) −0.266905 −0.0101979
\(686\) 0 0
\(687\) 22.3486 0.852651
\(688\) 0 0
\(689\) −8.39852 −0.319958
\(690\) 0 0
\(691\) 22.0670 0.839469 0.419734 0.907647i \(-0.362123\pi\)
0.419734 + 0.907647i \(0.362123\pi\)
\(692\) 0 0
\(693\) −2.64224 −0.100370
\(694\) 0 0
\(695\) −2.95001 −0.111900
\(696\) 0 0
\(697\) −45.8306 −1.73596
\(698\) 0 0
\(699\) 56.7774 2.14752
\(700\) 0 0
\(701\) −21.1876 −0.800244 −0.400122 0.916462i \(-0.631032\pi\)
−0.400122 + 0.916462i \(0.631032\pi\)
\(702\) 0 0
\(703\) −26.1800 −0.987399
\(704\) 0 0
\(705\) −3.53695 −0.133209
\(706\) 0 0
\(707\) −14.4247 −0.542497
\(708\) 0 0
\(709\) 38.7172 1.45405 0.727027 0.686609i \(-0.240901\pi\)
0.727027 + 0.686609i \(0.240901\pi\)
\(710\) 0 0
\(711\) −8.30250 −0.311368
\(712\) 0 0
\(713\) 24.1284 0.903616
\(714\) 0 0
\(715\) −0.155697 −0.00582272
\(716\) 0 0
\(717\) 29.7718 1.11185
\(718\) 0 0
\(719\) 3.28910 0.122663 0.0613314 0.998117i \(-0.480465\pi\)
0.0613314 + 0.998117i \(0.480465\pi\)
\(720\) 0 0
\(721\) −12.1967 −0.454228
\(722\) 0 0
\(723\) 32.6011 1.21245
\(724\) 0 0
\(725\) 32.6087 1.21106
\(726\) 0 0
\(727\) −39.9534 −1.48179 −0.740895 0.671621i \(-0.765598\pi\)
−0.740895 + 0.671621i \(0.765598\pi\)
\(728\) 0 0
\(729\) −20.2221 −0.748965
\(730\) 0 0
\(731\) −28.3538 −1.04870
\(732\) 0 0
\(733\) −38.4587 −1.42050 −0.710252 0.703947i \(-0.751419\pi\)
−0.710252 + 0.703947i \(0.751419\pi\)
\(734\) 0 0
\(735\) 0.369832 0.0136415
\(736\) 0 0
\(737\) −9.49672 −0.349816
\(738\) 0 0
\(739\) 35.8084 1.31723 0.658617 0.752478i \(-0.271142\pi\)
0.658617 + 0.752478i \(0.271142\pi\)
\(740\) 0 0
\(741\) 8.47369 0.311289
\(742\) 0 0
\(743\) −16.7900 −0.615966 −0.307983 0.951392i \(-0.599654\pi\)
−0.307983 + 0.951392i \(0.599654\pi\)
\(744\) 0 0
\(745\) 2.17412 0.0796535
\(746\) 0 0
\(747\) 19.8114 0.724861
\(748\) 0 0
\(749\) 0.424447 0.0155090
\(750\) 0 0
\(751\) 17.4085 0.635244 0.317622 0.948217i \(-0.397116\pi\)
0.317622 + 0.948217i \(0.397116\pi\)
\(752\) 0 0
\(753\) 57.7421 2.10424
\(754\) 0 0
\(755\) −1.95481 −0.0711430
\(756\) 0 0
\(757\) 29.6453 1.07748 0.538739 0.842473i \(-0.318901\pi\)
0.538739 + 0.842473i \(0.318901\pi\)
\(758\) 0 0
\(759\) −12.1083 −0.439503
\(760\) 0 0
\(761\) 15.4943 0.561668 0.280834 0.959756i \(-0.409389\pi\)
0.280834 + 0.959756i \(0.409389\pi\)
\(762\) 0 0
\(763\) 9.89917 0.358374
\(764\) 0 0
\(765\) 1.59959 0.0578332
\(766\) 0 0
\(767\) 13.2210 0.477382
\(768\) 0 0
\(769\) 19.3434 0.697542 0.348771 0.937208i \(-0.386599\pi\)
0.348771 + 0.937208i \(0.386599\pi\)
\(770\) 0 0
\(771\) −18.8589 −0.679186
\(772\) 0 0
\(773\) 5.07363 0.182486 0.0912429 0.995829i \(-0.470916\pi\)
0.0912429 + 0.995829i \(0.470916\pi\)
\(774\) 0 0
\(775\) −23.5522 −0.846019
\(776\) 0 0
\(777\) 17.4321 0.625372
\(778\) 0 0
\(779\) −42.0480 −1.50653
\(780\) 0 0
\(781\) −10.5347 −0.376960
\(782\) 0 0
\(783\) −5.56924 −0.199028
\(784\) 0 0
\(785\) 1.31273 0.0468533
\(786\) 0 0
\(787\) 29.8975 1.06573 0.532865 0.846200i \(-0.321115\pi\)
0.532865 + 0.846200i \(0.321115\pi\)
\(788\) 0 0
\(789\) −8.20773 −0.292203
\(790\) 0 0
\(791\) 3.41243 0.121332
\(792\) 0 0
\(793\) −8.66669 −0.307763
\(794\) 0 0
\(795\) −3.10604 −0.110160
\(796\) 0 0
\(797\) −31.3867 −1.11177 −0.555886 0.831258i \(-0.687621\pi\)
−0.555886 + 0.831258i \(0.687621\pi\)
\(798\) 0 0
\(799\) 37.1862 1.31555
\(800\) 0 0
\(801\) 2.56884 0.0907654
\(802\) 0 0
\(803\) 1.56114 0.0550914
\(804\) 0 0
\(805\) 0.793662 0.0279729
\(806\) 0 0
\(807\) 30.7595 1.08279
\(808\) 0 0
\(809\) −50.0341 −1.75911 −0.879553 0.475801i \(-0.842158\pi\)
−0.879553 + 0.475801i \(0.842158\pi\)
\(810\) 0 0
\(811\) −4.96642 −0.174395 −0.0871973 0.996191i \(-0.527791\pi\)
−0.0871973 + 0.996191i \(0.527791\pi\)
\(812\) 0 0
\(813\) 67.0361 2.35106
\(814\) 0 0
\(815\) −3.29326 −0.115358
\(816\) 0 0
\(817\) −26.0136 −0.910101
\(818\) 0 0
\(819\) −2.64224 −0.0923272
\(820\) 0 0
\(821\) −43.5112 −1.51855 −0.759275 0.650769i \(-0.774446\pi\)
−0.759275 + 0.650769i \(0.774446\pi\)
\(822\) 0 0
\(823\) 26.6089 0.927527 0.463764 0.885959i \(-0.346499\pi\)
0.463764 + 0.885959i \(0.346499\pi\)
\(824\) 0 0
\(825\) 11.8191 0.411489
\(826\) 0 0
\(827\) −2.23030 −0.0775550 −0.0387775 0.999248i \(-0.512346\pi\)
−0.0387775 + 0.999248i \(0.512346\pi\)
\(828\) 0 0
\(829\) 36.3144 1.26125 0.630626 0.776087i \(-0.282798\pi\)
0.630626 + 0.776087i \(0.282798\pi\)
\(830\) 0 0
\(831\) −49.3848 −1.71314
\(832\) 0 0
\(833\) −3.88828 −0.134721
\(834\) 0 0
\(835\) −0.433901 −0.0150158
\(836\) 0 0
\(837\) 4.02248 0.139037
\(838\) 0 0
\(839\) −18.4590 −0.637275 −0.318637 0.947877i \(-0.603225\pi\)
−0.318637 + 0.947877i \(0.603225\pi\)
\(840\) 0 0
\(841\) 13.9485 0.480982
\(842\) 0 0
\(843\) −30.8462 −1.06240
\(844\) 0 0
\(845\) −0.155697 −0.00535612
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 69.7159 2.39264
\(850\) 0 0
\(851\) 37.4093 1.28238
\(852\) 0 0
\(853\) 37.8311 1.29531 0.647657 0.761932i \(-0.275749\pi\)
0.647657 + 0.761932i \(0.275749\pi\)
\(854\) 0 0
\(855\) 1.46757 0.0501897
\(856\) 0 0
\(857\) 6.04652 0.206545 0.103273 0.994653i \(-0.467069\pi\)
0.103273 + 0.994653i \(0.467069\pi\)
\(858\) 0 0
\(859\) 43.7958 1.49429 0.747147 0.664659i \(-0.231423\pi\)
0.747147 + 0.664659i \(0.231423\pi\)
\(860\) 0 0
\(861\) 27.9978 0.954162
\(862\) 0 0
\(863\) −0.882293 −0.0300336 −0.0150168 0.999887i \(-0.504780\pi\)
−0.0150168 + 0.999887i \(0.504780\pi\)
\(864\) 0 0
\(865\) −1.97720 −0.0672268
\(866\) 0 0
\(867\) 4.46872 0.151766
\(868\) 0 0
\(869\) −3.14222 −0.106593
\(870\) 0 0
\(871\) −9.49672 −0.321784
\(872\) 0 0
\(873\) −11.1882 −0.378662
\(874\) 0 0
\(875\) −1.55319 −0.0525074
\(876\) 0 0
\(877\) 19.1733 0.647435 0.323717 0.946154i \(-0.395067\pi\)
0.323717 + 0.946154i \(0.395067\pi\)
\(878\) 0 0
\(879\) −11.5190 −0.388525
\(880\) 0 0
\(881\) 10.0578 0.338855 0.169427 0.985543i \(-0.445808\pi\)
0.169427 + 0.985543i \(0.445808\pi\)
\(882\) 0 0
\(883\) −13.6610 −0.459729 −0.229864 0.973223i \(-0.573828\pi\)
−0.229864 + 0.973223i \(0.573828\pi\)
\(884\) 0 0
\(885\) 4.88954 0.164360
\(886\) 0 0
\(887\) −34.7724 −1.16754 −0.583772 0.811918i \(-0.698424\pi\)
−0.583772 + 0.811918i \(0.698424\pi\)
\(888\) 0 0
\(889\) −1.51328 −0.0507537
\(890\) 0 0
\(891\) −9.94530 −0.333180
\(892\) 0 0
\(893\) 34.1171 1.14168
\(894\) 0 0
\(895\) −0.194664 −0.00650691
\(896\) 0 0
\(897\) −12.1083 −0.404284
\(898\) 0 0
\(899\) −31.0203 −1.03458
\(900\) 0 0
\(901\) 32.6558 1.08792
\(902\) 0 0
\(903\) 17.3213 0.576415
\(904\) 0 0
\(905\) −3.03535 −0.100898
\(906\) 0 0
\(907\) −44.6162 −1.48146 −0.740729 0.671804i \(-0.765520\pi\)
−0.740729 + 0.671804i \(0.765520\pi\)
\(908\) 0 0
\(909\) 38.1135 1.26414
\(910\) 0 0
\(911\) −50.2029 −1.66330 −0.831648 0.555303i \(-0.812602\pi\)
−0.831648 + 0.555303i \(0.812602\pi\)
\(912\) 0 0
\(913\) 7.49797 0.248147
\(914\) 0 0
\(915\) −3.20522 −0.105961
\(916\) 0 0
\(917\) −9.27572 −0.306311
\(918\) 0 0
\(919\) 20.5136 0.676680 0.338340 0.941024i \(-0.390135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(920\) 0 0
\(921\) 37.5237 1.23645
\(922\) 0 0
\(923\) −10.5347 −0.346753
\(924\) 0 0
\(925\) −36.5160 −1.20064
\(926\) 0 0
\(927\) 32.2265 1.05846
\(928\) 0 0
\(929\) 31.5289 1.03443 0.517214 0.855856i \(-0.326969\pi\)
0.517214 + 0.855856i \(0.326969\pi\)
\(930\) 0 0
\(931\) −3.56736 −0.116916
\(932\) 0 0
\(933\) 16.4070 0.537141
\(934\) 0 0
\(935\) 0.605391 0.0197984
\(936\) 0 0
\(937\) −36.1696 −1.18161 −0.590805 0.806814i \(-0.701190\pi\)
−0.590805 + 0.806814i \(0.701190\pi\)
\(938\) 0 0
\(939\) 78.0732 2.54782
\(940\) 0 0
\(941\) −14.8955 −0.485578 −0.242789 0.970079i \(-0.578062\pi\)
−0.242789 + 0.970079i \(0.578062\pi\)
\(942\) 0 0
\(943\) 60.0835 1.95659
\(944\) 0 0
\(945\) 0.132313 0.00430413
\(946\) 0 0
\(947\) −59.3637 −1.92906 −0.964530 0.263973i \(-0.914967\pi\)
−0.964530 + 0.263973i \(0.914967\pi\)
\(948\) 0 0
\(949\) 1.56114 0.0506767
\(950\) 0 0
\(951\) −26.1590 −0.848264
\(952\) 0 0
\(953\) −10.6151 −0.343857 −0.171929 0.985109i \(-0.555000\pi\)
−0.171929 + 0.985109i \(0.555000\pi\)
\(954\) 0 0
\(955\) −1.58873 −0.0514102
\(956\) 0 0
\(957\) 15.5668 0.503203
\(958\) 0 0
\(959\) −1.71427 −0.0553566
\(960\) 0 0
\(961\) −8.59506 −0.277260
\(962\) 0 0
\(963\) −1.12149 −0.0361395
\(964\) 0 0
\(965\) 4.25190 0.136874
\(966\) 0 0
\(967\) −2.18758 −0.0703477 −0.0351739 0.999381i \(-0.511199\pi\)
−0.0351739 + 0.999381i \(0.511199\pi\)
\(968\) 0 0
\(969\) −32.9481 −1.05844
\(970\) 0 0
\(971\) −0.568205 −0.0182346 −0.00911729 0.999958i \(-0.502902\pi\)
−0.00911729 + 0.999958i \(0.502902\pi\)
\(972\) 0 0
\(973\) −18.9472 −0.607418
\(974\) 0 0
\(975\) 11.8191 0.378515
\(976\) 0 0
\(977\) −45.1230 −1.44361 −0.721806 0.692096i \(-0.756688\pi\)
−0.721806 + 0.692096i \(0.756688\pi\)
\(978\) 0 0
\(979\) 0.972221 0.0310723
\(980\) 0 0
\(981\) −26.1560 −0.835095
\(982\) 0 0
\(983\) −3.95602 −0.126178 −0.0630888 0.998008i \(-0.520095\pi\)
−0.0630888 + 0.998008i \(0.520095\pi\)
\(984\) 0 0
\(985\) 1.30936 0.0417197
\(986\) 0 0
\(987\) −22.7170 −0.723089
\(988\) 0 0
\(989\) 37.1715 1.18199
\(990\) 0 0
\(991\) 33.4691 1.06318 0.531590 0.847002i \(-0.321595\pi\)
0.531590 + 0.847002i \(0.321595\pi\)
\(992\) 0 0
\(993\) −32.2091 −1.02212
\(994\) 0 0
\(995\) −2.10069 −0.0665963
\(996\) 0 0
\(997\) −13.8410 −0.438350 −0.219175 0.975686i \(-0.570337\pi\)
−0.219175 + 0.975686i \(0.570337\pi\)
\(998\) 0 0
\(999\) 6.23656 0.197316
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 \(a_p\))