Properties

Label 8008.2.a.u.1.6
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.398142\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.398142 q^{3} +3.53033 q^{5} -1.00000 q^{7} -2.84148 q^{9} +O(q^{10})\) \(q+0.398142 q^{3} +3.53033 q^{5} -1.00000 q^{7} -2.84148 q^{9} -1.00000 q^{11} -1.00000 q^{13} +1.40557 q^{15} -1.07861 q^{17} +5.12685 q^{19} -0.398142 q^{21} -5.71619 q^{23} +7.46325 q^{25} -2.32574 q^{27} -1.17565 q^{29} +1.41204 q^{31} -0.398142 q^{33} -3.53033 q^{35} -7.80593 q^{37} -0.398142 q^{39} -5.27856 q^{41} -2.86769 q^{43} -10.0314 q^{45} -2.62898 q^{47} +1.00000 q^{49} -0.429439 q^{51} -6.09517 q^{53} -3.53033 q^{55} +2.04121 q^{57} +4.25733 q^{59} -1.98172 q^{61} +2.84148 q^{63} -3.53033 q^{65} +13.4087 q^{67} -2.27585 q^{69} -8.91852 q^{71} -10.4436 q^{73} +2.97143 q^{75} +1.00000 q^{77} +5.29521 q^{79} +7.59848 q^{81} +2.00236 q^{83} -3.80785 q^{85} -0.468076 q^{87} -5.89528 q^{89} +1.00000 q^{91} +0.562193 q^{93} +18.0995 q^{95} +10.8363 q^{97} +2.84148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 0.398142 0.229867 0.114934 0.993373i \(-0.463334\pi\)
0.114934 + 0.993373i \(0.463334\pi\)
\(4\) 0 0
\(5\) 3.53033 1.57881 0.789406 0.613871i \(-0.210389\pi\)
0.789406 + 0.613871i \(0.210389\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.84148 −0.947161
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.40557 0.362917
\(16\) 0 0
\(17\) −1.07861 −0.261601 −0.130801 0.991409i \(-0.541755\pi\)
−0.130801 + 0.991409i \(0.541755\pi\)
\(18\) 0 0
\(19\) 5.12685 1.17618 0.588090 0.808796i \(-0.299880\pi\)
0.588090 + 0.808796i \(0.299880\pi\)
\(20\) 0 0
\(21\) −0.398142 −0.0868816
\(22\) 0 0
\(23\) −5.71619 −1.19191 −0.595954 0.803019i \(-0.703226\pi\)
−0.595954 + 0.803019i \(0.703226\pi\)
\(24\) 0 0
\(25\) 7.46325 1.49265
\(26\) 0 0
\(27\) −2.32574 −0.447588
\(28\) 0 0
\(29\) −1.17565 −0.218313 −0.109157 0.994025i \(-0.534815\pi\)
−0.109157 + 0.994025i \(0.534815\pi\)
\(30\) 0 0
\(31\) 1.41204 0.253611 0.126805 0.991928i \(-0.459528\pi\)
0.126805 + 0.991928i \(0.459528\pi\)
\(32\) 0 0
\(33\) −0.398142 −0.0693076
\(34\) 0 0
\(35\) −3.53033 −0.596735
\(36\) 0 0
\(37\) −7.80593 −1.28329 −0.641643 0.767003i \(-0.721747\pi\)
−0.641643 + 0.767003i \(0.721747\pi\)
\(38\) 0 0
\(39\) −0.398142 −0.0637537
\(40\) 0 0
\(41\) −5.27856 −0.824372 −0.412186 0.911100i \(-0.635235\pi\)
−0.412186 + 0.911100i \(0.635235\pi\)
\(42\) 0 0
\(43\) −2.86769 −0.437318 −0.218659 0.975801i \(-0.570168\pi\)
−0.218659 + 0.975801i \(0.570168\pi\)
\(44\) 0 0
\(45\) −10.0314 −1.49539
\(46\) 0 0
\(47\) −2.62898 −0.383476 −0.191738 0.981446i \(-0.561412\pi\)
−0.191738 + 0.981446i \(0.561412\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −0.429439 −0.0601335
\(52\) 0 0
\(53\) −6.09517 −0.837236 −0.418618 0.908163i \(-0.637485\pi\)
−0.418618 + 0.908163i \(0.637485\pi\)
\(54\) 0 0
\(55\) −3.53033 −0.476030
\(56\) 0 0
\(57\) 2.04121 0.270365
\(58\) 0 0
\(59\) 4.25733 0.554257 0.277129 0.960833i \(-0.410617\pi\)
0.277129 + 0.960833i \(0.410617\pi\)
\(60\) 0 0
\(61\) −1.98172 −0.253733 −0.126866 0.991920i \(-0.540492\pi\)
−0.126866 + 0.991920i \(0.540492\pi\)
\(62\) 0 0
\(63\) 2.84148 0.357993
\(64\) 0 0
\(65\) −3.53033 −0.437884
\(66\) 0 0
\(67\) 13.4087 1.63814 0.819068 0.573696i \(-0.194491\pi\)
0.819068 + 0.573696i \(0.194491\pi\)
\(68\) 0 0
\(69\) −2.27585 −0.273980
\(70\) 0 0
\(71\) −8.91852 −1.05843 −0.529217 0.848487i \(-0.677514\pi\)
−0.529217 + 0.848487i \(0.677514\pi\)
\(72\) 0 0
\(73\) −10.4436 −1.22233 −0.611164 0.791504i \(-0.709299\pi\)
−0.611164 + 0.791504i \(0.709299\pi\)
\(74\) 0 0
\(75\) 2.97143 0.343111
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 5.29521 0.595758 0.297879 0.954604i \(-0.403721\pi\)
0.297879 + 0.954604i \(0.403721\pi\)
\(80\) 0 0
\(81\) 7.59848 0.844275
\(82\) 0 0
\(83\) 2.00236 0.219787 0.109894 0.993943i \(-0.464949\pi\)
0.109894 + 0.993943i \(0.464949\pi\)
\(84\) 0 0
\(85\) −3.80785 −0.413019
\(86\) 0 0
\(87\) −0.468076 −0.0501830
\(88\) 0 0
\(89\) −5.89528 −0.624899 −0.312449 0.949934i \(-0.601149\pi\)
−0.312449 + 0.949934i \(0.601149\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0.562193 0.0582967
\(94\) 0 0
\(95\) 18.0995 1.85697
\(96\) 0 0
\(97\) 10.8363 1.10026 0.550129 0.835080i \(-0.314579\pi\)
0.550129 + 0.835080i \(0.314579\pi\)
\(98\) 0 0
\(99\) 2.84148 0.285580
\(100\) 0 0
\(101\) −6.40496 −0.637317 −0.318659 0.947870i \(-0.603232\pi\)
−0.318659 + 0.947870i \(0.603232\pi\)
\(102\) 0 0
\(103\) −2.99636 −0.295241 −0.147620 0.989044i \(-0.547161\pi\)
−0.147620 + 0.989044i \(0.547161\pi\)
\(104\) 0 0
\(105\) −1.40557 −0.137170
\(106\) 0 0
\(107\) −14.7546 −1.42638 −0.713189 0.700972i \(-0.752750\pi\)
−0.713189 + 0.700972i \(0.752750\pi\)
\(108\) 0 0
\(109\) 15.8020 1.51356 0.756780 0.653670i \(-0.226771\pi\)
0.756780 + 0.653670i \(0.226771\pi\)
\(110\) 0 0
\(111\) −3.10786 −0.294985
\(112\) 0 0
\(113\) −12.3822 −1.16482 −0.582408 0.812897i \(-0.697889\pi\)
−0.582408 + 0.812897i \(0.697889\pi\)
\(114\) 0 0
\(115\) −20.1800 −1.88180
\(116\) 0 0
\(117\) 2.84148 0.262695
\(118\) 0 0
\(119\) 1.07861 0.0988760
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −2.10161 −0.189496
\(124\) 0 0
\(125\) 8.69608 0.777801
\(126\) 0 0
\(127\) −14.1106 −1.25211 −0.626057 0.779777i \(-0.715332\pi\)
−0.626057 + 0.779777i \(0.715332\pi\)
\(128\) 0 0
\(129\) −1.14175 −0.100525
\(130\) 0 0
\(131\) −0.00489576 −0.000427744 0 −0.000213872 1.00000i \(-0.500068\pi\)
−0.000213872 1.00000i \(0.500068\pi\)
\(132\) 0 0
\(133\) −5.12685 −0.444554
\(134\) 0 0
\(135\) −8.21063 −0.706658
\(136\) 0 0
\(137\) −15.7889 −1.34894 −0.674470 0.738303i \(-0.735628\pi\)
−0.674470 + 0.738303i \(0.735628\pi\)
\(138\) 0 0
\(139\) 10.7834 0.914634 0.457317 0.889304i \(-0.348811\pi\)
0.457317 + 0.889304i \(0.348811\pi\)
\(140\) 0 0
\(141\) −1.04671 −0.0881486
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −4.15044 −0.344676
\(146\) 0 0
\(147\) 0.398142 0.0328382
\(148\) 0 0
\(149\) −0.489805 −0.0401264 −0.0200632 0.999799i \(-0.506387\pi\)
−0.0200632 + 0.999799i \(0.506387\pi\)
\(150\) 0 0
\(151\) −15.9015 −1.29405 −0.647023 0.762470i \(-0.723986\pi\)
−0.647023 + 0.762470i \(0.723986\pi\)
\(152\) 0 0
\(153\) 3.06485 0.247778
\(154\) 0 0
\(155\) 4.98498 0.400404
\(156\) 0 0
\(157\) −22.7567 −1.81619 −0.908093 0.418769i \(-0.862462\pi\)
−0.908093 + 0.418769i \(0.862462\pi\)
\(158\) 0 0
\(159\) −2.42674 −0.192453
\(160\) 0 0
\(161\) 5.71619 0.450499
\(162\) 0 0
\(163\) 14.7578 1.15592 0.577959 0.816066i \(-0.303849\pi\)
0.577959 + 0.816066i \(0.303849\pi\)
\(164\) 0 0
\(165\) −1.40557 −0.109424
\(166\) 0 0
\(167\) −5.64625 −0.436920 −0.218460 0.975846i \(-0.570103\pi\)
−0.218460 + 0.975846i \(0.570103\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −14.5679 −1.11403
\(172\) 0 0
\(173\) −19.2055 −1.46017 −0.730084 0.683357i \(-0.760519\pi\)
−0.730084 + 0.683357i \(0.760519\pi\)
\(174\) 0 0
\(175\) −7.46325 −0.564168
\(176\) 0 0
\(177\) 1.69502 0.127406
\(178\) 0 0
\(179\) −14.8267 −1.10820 −0.554101 0.832450i \(-0.686938\pi\)
−0.554101 + 0.832450i \(0.686938\pi\)
\(180\) 0 0
\(181\) −17.9259 −1.33242 −0.666210 0.745764i \(-0.732085\pi\)
−0.666210 + 0.745764i \(0.732085\pi\)
\(182\) 0 0
\(183\) −0.789004 −0.0583249
\(184\) 0 0
\(185\) −27.5575 −2.02607
\(186\) 0 0
\(187\) 1.07861 0.0788757
\(188\) 0 0
\(189\) 2.32574 0.169173
\(190\) 0 0
\(191\) 13.3986 0.969488 0.484744 0.874656i \(-0.338913\pi\)
0.484744 + 0.874656i \(0.338913\pi\)
\(192\) 0 0
\(193\) 13.2546 0.954088 0.477044 0.878879i \(-0.341708\pi\)
0.477044 + 0.878879i \(0.341708\pi\)
\(194\) 0 0
\(195\) −1.40557 −0.100655
\(196\) 0 0
\(197\) −9.52971 −0.678964 −0.339482 0.940613i \(-0.610252\pi\)
−0.339482 + 0.940613i \(0.610252\pi\)
\(198\) 0 0
\(199\) 16.0569 1.13824 0.569122 0.822253i \(-0.307283\pi\)
0.569122 + 0.822253i \(0.307283\pi\)
\(200\) 0 0
\(201\) 5.33857 0.376554
\(202\) 0 0
\(203\) 1.17565 0.0825146
\(204\) 0 0
\(205\) −18.6351 −1.30153
\(206\) 0 0
\(207\) 16.2424 1.12893
\(208\) 0 0
\(209\) −5.12685 −0.354631
\(210\) 0 0
\(211\) 10.3841 0.714869 0.357434 0.933938i \(-0.383652\pi\)
0.357434 + 0.933938i \(0.383652\pi\)
\(212\) 0 0
\(213\) −3.55083 −0.243299
\(214\) 0 0
\(215\) −10.1239 −0.690443
\(216\) 0 0
\(217\) −1.41204 −0.0958558
\(218\) 0 0
\(219\) −4.15802 −0.280973
\(220\) 0 0
\(221\) 1.07861 0.0725551
\(222\) 0 0
\(223\) 2.73987 0.183475 0.0917375 0.995783i \(-0.470758\pi\)
0.0917375 + 0.995783i \(0.470758\pi\)
\(224\) 0 0
\(225\) −21.2067 −1.41378
\(226\) 0 0
\(227\) −11.9545 −0.793447 −0.396724 0.917938i \(-0.629853\pi\)
−0.396724 + 0.917938i \(0.629853\pi\)
\(228\) 0 0
\(229\) −6.05664 −0.400234 −0.200117 0.979772i \(-0.564132\pi\)
−0.200117 + 0.979772i \(0.564132\pi\)
\(230\) 0 0
\(231\) 0.398142 0.0261958
\(232\) 0 0
\(233\) 6.31979 0.414023 0.207012 0.978338i \(-0.433626\pi\)
0.207012 + 0.978338i \(0.433626\pi\)
\(234\) 0 0
\(235\) −9.28118 −0.605437
\(236\) 0 0
\(237\) 2.10824 0.136945
\(238\) 0 0
\(239\) 26.2496 1.69795 0.848973 0.528436i \(-0.177221\pi\)
0.848973 + 0.528436i \(0.177221\pi\)
\(240\) 0 0
\(241\) −3.11783 −0.200837 −0.100419 0.994945i \(-0.532018\pi\)
−0.100419 + 0.994945i \(0.532018\pi\)
\(242\) 0 0
\(243\) 10.0025 0.641660
\(244\) 0 0
\(245\) 3.53033 0.225545
\(246\) 0 0
\(247\) −5.12685 −0.326213
\(248\) 0 0
\(249\) 0.797221 0.0505218
\(250\) 0 0
\(251\) −6.71557 −0.423883 −0.211942 0.977282i \(-0.567979\pi\)
−0.211942 + 0.977282i \(0.567979\pi\)
\(252\) 0 0
\(253\) 5.71619 0.359374
\(254\) 0 0
\(255\) −1.51606 −0.0949396
\(256\) 0 0
\(257\) −1.71946 −0.107257 −0.0536284 0.998561i \(-0.517079\pi\)
−0.0536284 + 0.998561i \(0.517079\pi\)
\(258\) 0 0
\(259\) 7.80593 0.485037
\(260\) 0 0
\(261\) 3.34060 0.206778
\(262\) 0 0
\(263\) 2.39328 0.147576 0.0737881 0.997274i \(-0.476491\pi\)
0.0737881 + 0.997274i \(0.476491\pi\)
\(264\) 0 0
\(265\) −21.5180 −1.32184
\(266\) 0 0
\(267\) −2.34716 −0.143644
\(268\) 0 0
\(269\) −23.2462 −1.41734 −0.708672 0.705538i \(-0.750705\pi\)
−0.708672 + 0.705538i \(0.750705\pi\)
\(270\) 0 0
\(271\) 9.13004 0.554610 0.277305 0.960782i \(-0.410559\pi\)
0.277305 + 0.960782i \(0.410559\pi\)
\(272\) 0 0
\(273\) 0.398142 0.0240966
\(274\) 0 0
\(275\) −7.46325 −0.450051
\(276\) 0 0
\(277\) 18.1440 1.09017 0.545084 0.838382i \(-0.316498\pi\)
0.545084 + 0.838382i \(0.316498\pi\)
\(278\) 0 0
\(279\) −4.01230 −0.240210
\(280\) 0 0
\(281\) 11.9833 0.714865 0.357433 0.933939i \(-0.383652\pi\)
0.357433 + 0.933939i \(0.383652\pi\)
\(282\) 0 0
\(283\) −14.4334 −0.857978 −0.428989 0.903310i \(-0.641130\pi\)
−0.428989 + 0.903310i \(0.641130\pi\)
\(284\) 0 0
\(285\) 7.20616 0.426856
\(286\) 0 0
\(287\) 5.27856 0.311583
\(288\) 0 0
\(289\) −15.8366 −0.931565
\(290\) 0 0
\(291\) 4.31438 0.252913
\(292\) 0 0
\(293\) −7.10073 −0.414829 −0.207414 0.978253i \(-0.566505\pi\)
−0.207414 + 0.978253i \(0.566505\pi\)
\(294\) 0 0
\(295\) 15.0298 0.875068
\(296\) 0 0
\(297\) 2.32574 0.134953
\(298\) 0 0
\(299\) 5.71619 0.330576
\(300\) 0 0
\(301\) 2.86769 0.165291
\(302\) 0 0
\(303\) −2.55008 −0.146498
\(304\) 0 0
\(305\) −6.99612 −0.400597
\(306\) 0 0
\(307\) 0.0952457 0.00543596 0.00271798 0.999996i \(-0.499135\pi\)
0.00271798 + 0.999996i \(0.499135\pi\)
\(308\) 0 0
\(309\) −1.19298 −0.0678661
\(310\) 0 0
\(311\) 31.5533 1.78923 0.894613 0.446842i \(-0.147451\pi\)
0.894613 + 0.446842i \(0.147451\pi\)
\(312\) 0 0
\(313\) 8.06515 0.455869 0.227935 0.973676i \(-0.426803\pi\)
0.227935 + 0.973676i \(0.426803\pi\)
\(314\) 0 0
\(315\) 10.0314 0.565204
\(316\) 0 0
\(317\) 18.6840 1.04940 0.524700 0.851287i \(-0.324177\pi\)
0.524700 + 0.851287i \(0.324177\pi\)
\(318\) 0 0
\(319\) 1.17565 0.0658239
\(320\) 0 0
\(321\) −5.87441 −0.327877
\(322\) 0 0
\(323\) −5.52987 −0.307690
\(324\) 0 0
\(325\) −7.46325 −0.413986
\(326\) 0 0
\(327\) 6.29145 0.347918
\(328\) 0 0
\(329\) 2.62898 0.144940
\(330\) 0 0
\(331\) −11.2983 −0.621011 −0.310506 0.950572i \(-0.600498\pi\)
−0.310506 + 0.950572i \(0.600498\pi\)
\(332\) 0 0
\(333\) 22.1804 1.21548
\(334\) 0 0
\(335\) 47.3373 2.58631
\(336\) 0 0
\(337\) −5.26007 −0.286534 −0.143267 0.989684i \(-0.545761\pi\)
−0.143267 + 0.989684i \(0.545761\pi\)
\(338\) 0 0
\(339\) −4.92985 −0.267753
\(340\) 0 0
\(341\) −1.41204 −0.0764665
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −8.03451 −0.432564
\(346\) 0 0
\(347\) −0.564314 −0.0302939 −0.0151470 0.999885i \(-0.504822\pi\)
−0.0151470 + 0.999885i \(0.504822\pi\)
\(348\) 0 0
\(349\) 11.8039 0.631849 0.315925 0.948784i \(-0.397685\pi\)
0.315925 + 0.948784i \(0.397685\pi\)
\(350\) 0 0
\(351\) 2.32574 0.124139
\(352\) 0 0
\(353\) 9.12891 0.485883 0.242942 0.970041i \(-0.421888\pi\)
0.242942 + 0.970041i \(0.421888\pi\)
\(354\) 0 0
\(355\) −31.4853 −1.67107
\(356\) 0 0
\(357\) 0.429439 0.0227283
\(358\) 0 0
\(359\) 28.4115 1.49950 0.749750 0.661721i \(-0.230174\pi\)
0.749750 + 0.661721i \(0.230174\pi\)
\(360\) 0 0
\(361\) 7.28457 0.383398
\(362\) 0 0
\(363\) 0.398142 0.0208970
\(364\) 0 0
\(365\) −36.8693 −1.92983
\(366\) 0 0
\(367\) −29.4820 −1.53895 −0.769475 0.638677i \(-0.779482\pi\)
−0.769475 + 0.638677i \(0.779482\pi\)
\(368\) 0 0
\(369\) 14.9989 0.780813
\(370\) 0 0
\(371\) 6.09517 0.316445
\(372\) 0 0
\(373\) −21.0819 −1.09158 −0.545790 0.837922i \(-0.683770\pi\)
−0.545790 + 0.837922i \(0.683770\pi\)
\(374\) 0 0
\(375\) 3.46227 0.178791
\(376\) 0 0
\(377\) 1.17565 0.0605492
\(378\) 0 0
\(379\) −16.1750 −0.830852 −0.415426 0.909627i \(-0.636368\pi\)
−0.415426 + 0.909627i \(0.636368\pi\)
\(380\) 0 0
\(381\) −5.61802 −0.287820
\(382\) 0 0
\(383\) 30.5596 1.56152 0.780761 0.624830i \(-0.214832\pi\)
0.780761 + 0.624830i \(0.214832\pi\)
\(384\) 0 0
\(385\) 3.53033 0.179922
\(386\) 0 0
\(387\) 8.14848 0.414211
\(388\) 0 0
\(389\) −11.0373 −0.559612 −0.279806 0.960057i \(-0.590270\pi\)
−0.279806 + 0.960057i \(0.590270\pi\)
\(390\) 0 0
\(391\) 6.16553 0.311804
\(392\) 0 0
\(393\) −0.00194921 −9.83244e−5 0
\(394\) 0 0
\(395\) 18.6938 0.940590
\(396\) 0 0
\(397\) −12.1409 −0.609335 −0.304668 0.952459i \(-0.598545\pi\)
−0.304668 + 0.952459i \(0.598545\pi\)
\(398\) 0 0
\(399\) −2.04121 −0.102188
\(400\) 0 0
\(401\) −34.0372 −1.69974 −0.849869 0.526994i \(-0.823319\pi\)
−0.849869 + 0.526994i \(0.823319\pi\)
\(402\) 0 0
\(403\) −1.41204 −0.0703389
\(404\) 0 0
\(405\) 26.8251 1.33295
\(406\) 0 0
\(407\) 7.80593 0.386925
\(408\) 0 0
\(409\) 19.7905 0.978575 0.489288 0.872122i \(-0.337257\pi\)
0.489288 + 0.872122i \(0.337257\pi\)
\(410\) 0 0
\(411\) −6.28623 −0.310077
\(412\) 0 0
\(413\) −4.25733 −0.209489
\(414\) 0 0
\(415\) 7.06898 0.347003
\(416\) 0 0
\(417\) 4.29331 0.210244
\(418\) 0 0
\(419\) −27.9759 −1.36671 −0.683357 0.730085i \(-0.739481\pi\)
−0.683357 + 0.730085i \(0.739481\pi\)
\(420\) 0 0
\(421\) 22.9430 1.11817 0.559086 0.829110i \(-0.311152\pi\)
0.559086 + 0.829110i \(0.311152\pi\)
\(422\) 0 0
\(423\) 7.47021 0.363214
\(424\) 0 0
\(425\) −8.04993 −0.390479
\(426\) 0 0
\(427\) 1.98172 0.0959020
\(428\) 0 0
\(429\) 0.398142 0.0192225
\(430\) 0 0
\(431\) −12.6261 −0.608176 −0.304088 0.952644i \(-0.598352\pi\)
−0.304088 + 0.952644i \(0.598352\pi\)
\(432\) 0 0
\(433\) −24.0580 −1.15616 −0.578078 0.815982i \(-0.696197\pi\)
−0.578078 + 0.815982i \(0.696197\pi\)
\(434\) 0 0
\(435\) −1.65246 −0.0792296
\(436\) 0 0
\(437\) −29.3060 −1.40190
\(438\) 0 0
\(439\) −20.4145 −0.974329 −0.487165 0.873310i \(-0.661969\pi\)
−0.487165 + 0.873310i \(0.661969\pi\)
\(440\) 0 0
\(441\) −2.84148 −0.135309
\(442\) 0 0
\(443\) −12.9202 −0.613858 −0.306929 0.951732i \(-0.599301\pi\)
−0.306929 + 0.951732i \(0.599301\pi\)
\(444\) 0 0
\(445\) −20.8123 −0.986598
\(446\) 0 0
\(447\) −0.195012 −0.00922374
\(448\) 0 0
\(449\) −24.2981 −1.14670 −0.573350 0.819311i \(-0.694356\pi\)
−0.573350 + 0.819311i \(0.694356\pi\)
\(450\) 0 0
\(451\) 5.27856 0.248558
\(452\) 0 0
\(453\) −6.33105 −0.297459
\(454\) 0 0
\(455\) 3.53033 0.165505
\(456\) 0 0
\(457\) 34.4161 1.60992 0.804958 0.593331i \(-0.202188\pi\)
0.804958 + 0.593331i \(0.202188\pi\)
\(458\) 0 0
\(459\) 2.50856 0.117090
\(460\) 0 0
\(461\) 18.6720 0.869642 0.434821 0.900517i \(-0.356812\pi\)
0.434821 + 0.900517i \(0.356812\pi\)
\(462\) 0 0
\(463\) 28.4013 1.31992 0.659960 0.751301i \(-0.270573\pi\)
0.659960 + 0.751301i \(0.270573\pi\)
\(464\) 0 0
\(465\) 1.98473 0.0920396
\(466\) 0 0
\(467\) −12.5181 −0.579269 −0.289635 0.957137i \(-0.593534\pi\)
−0.289635 + 0.957137i \(0.593534\pi\)
\(468\) 0 0
\(469\) −13.4087 −0.619157
\(470\) 0 0
\(471\) −9.06041 −0.417481
\(472\) 0 0
\(473\) 2.86769 0.131856
\(474\) 0 0
\(475\) 38.2629 1.75562
\(476\) 0 0
\(477\) 17.3193 0.792997
\(478\) 0 0
\(479\) −12.6426 −0.577657 −0.288829 0.957381i \(-0.593266\pi\)
−0.288829 + 0.957381i \(0.593266\pi\)
\(480\) 0 0
\(481\) 7.80593 0.355920
\(482\) 0 0
\(483\) 2.27585 0.103555
\(484\) 0 0
\(485\) 38.2557 1.73710
\(486\) 0 0
\(487\) −7.51778 −0.340663 −0.170332 0.985387i \(-0.554484\pi\)
−0.170332 + 0.985387i \(0.554484\pi\)
\(488\) 0 0
\(489\) 5.87568 0.265708
\(490\) 0 0
\(491\) 32.9453 1.48680 0.743399 0.668848i \(-0.233212\pi\)
0.743399 + 0.668848i \(0.233212\pi\)
\(492\) 0 0
\(493\) 1.26807 0.0571110
\(494\) 0 0
\(495\) 10.0314 0.450877
\(496\) 0 0
\(497\) 8.91852 0.400050
\(498\) 0 0
\(499\) 17.0446 0.763021 0.381511 0.924364i \(-0.375404\pi\)
0.381511 + 0.924364i \(0.375404\pi\)
\(500\) 0 0
\(501\) −2.24801 −0.100434
\(502\) 0 0
\(503\) −4.96500 −0.221378 −0.110689 0.993855i \(-0.535306\pi\)
−0.110689 + 0.993855i \(0.535306\pi\)
\(504\) 0 0
\(505\) −22.6116 −1.00620
\(506\) 0 0
\(507\) 0.398142 0.0176821
\(508\) 0 0
\(509\) 13.2498 0.587287 0.293643 0.955915i \(-0.405132\pi\)
0.293643 + 0.955915i \(0.405132\pi\)
\(510\) 0 0
\(511\) 10.4436 0.461997
\(512\) 0 0
\(513\) −11.9237 −0.526444
\(514\) 0 0
\(515\) −10.5782 −0.466130
\(516\) 0 0
\(517\) 2.62898 0.115622
\(518\) 0 0
\(519\) −7.64651 −0.335645
\(520\) 0 0
\(521\) 27.8348 1.21947 0.609733 0.792607i \(-0.291277\pi\)
0.609733 + 0.792607i \(0.291277\pi\)
\(522\) 0 0
\(523\) −14.2962 −0.625127 −0.312564 0.949897i \(-0.601188\pi\)
−0.312564 + 0.949897i \(0.601188\pi\)
\(524\) 0 0
\(525\) −2.97143 −0.129684
\(526\) 0 0
\(527\) −1.52304 −0.0663448
\(528\) 0 0
\(529\) 9.67478 0.420643
\(530\) 0 0
\(531\) −12.0971 −0.524971
\(532\) 0 0
\(533\) 5.27856 0.228640
\(534\) 0 0
\(535\) −52.0885 −2.25198
\(536\) 0 0
\(537\) −5.90314 −0.254739
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 27.6088 1.18700 0.593498 0.804835i \(-0.297746\pi\)
0.593498 + 0.804835i \(0.297746\pi\)
\(542\) 0 0
\(543\) −7.13704 −0.306280
\(544\) 0 0
\(545\) 55.7864 2.38963
\(546\) 0 0
\(547\) 9.11449 0.389707 0.194854 0.980832i \(-0.437577\pi\)
0.194854 + 0.980832i \(0.437577\pi\)
\(548\) 0 0
\(549\) 5.63102 0.240326
\(550\) 0 0
\(551\) −6.02739 −0.256776
\(552\) 0 0
\(553\) −5.29521 −0.225175
\(554\) 0 0
\(555\) −10.9718 −0.465727
\(556\) 0 0
\(557\) −31.3149 −1.32685 −0.663426 0.748242i \(-0.730898\pi\)
−0.663426 + 0.748242i \(0.730898\pi\)
\(558\) 0 0
\(559\) 2.86769 0.121290
\(560\) 0 0
\(561\) 0.429439 0.0181309
\(562\) 0 0
\(563\) −9.73574 −0.410313 −0.205156 0.978729i \(-0.565770\pi\)
−0.205156 + 0.978729i \(0.565770\pi\)
\(564\) 0 0
\(565\) −43.7131 −1.83903
\(566\) 0 0
\(567\) −7.59848 −0.319106
\(568\) 0 0
\(569\) 31.8199 1.33396 0.666980 0.745075i \(-0.267586\pi\)
0.666980 + 0.745075i \(0.267586\pi\)
\(570\) 0 0
\(571\) 0.0548895 0.00229705 0.00114853 0.999999i \(-0.499634\pi\)
0.00114853 + 0.999999i \(0.499634\pi\)
\(572\) 0 0
\(573\) 5.33454 0.222854
\(574\) 0 0
\(575\) −42.6613 −1.77910
\(576\) 0 0
\(577\) −34.0582 −1.41786 −0.708931 0.705278i \(-0.750822\pi\)
−0.708931 + 0.705278i \(0.750822\pi\)
\(578\) 0 0
\(579\) 5.27722 0.219314
\(580\) 0 0
\(581\) −2.00236 −0.0830717
\(582\) 0 0
\(583\) 6.09517 0.252436
\(584\) 0 0
\(585\) 10.0314 0.414747
\(586\) 0 0
\(587\) 27.5504 1.13713 0.568563 0.822639i \(-0.307499\pi\)
0.568563 + 0.822639i \(0.307499\pi\)
\(588\) 0 0
\(589\) 7.23933 0.298292
\(590\) 0 0
\(591\) −3.79417 −0.156071
\(592\) 0 0
\(593\) 9.95074 0.408628 0.204314 0.978905i \(-0.434504\pi\)
0.204314 + 0.978905i \(0.434504\pi\)
\(594\) 0 0
\(595\) 3.80785 0.156107
\(596\) 0 0
\(597\) 6.39293 0.261645
\(598\) 0 0
\(599\) −6.97062 −0.284812 −0.142406 0.989808i \(-0.545484\pi\)
−0.142406 + 0.989808i \(0.545484\pi\)
\(600\) 0 0
\(601\) 5.23766 0.213649 0.106824 0.994278i \(-0.465932\pi\)
0.106824 + 0.994278i \(0.465932\pi\)
\(602\) 0 0
\(603\) −38.1007 −1.55158
\(604\) 0 0
\(605\) 3.53033 0.143528
\(606\) 0 0
\(607\) 46.8643 1.90216 0.951082 0.308938i \(-0.0999736\pi\)
0.951082 + 0.308938i \(0.0999736\pi\)
\(608\) 0 0
\(609\) 0.468076 0.0189674
\(610\) 0 0
\(611\) 2.62898 0.106357
\(612\) 0 0
\(613\) −8.92271 −0.360385 −0.180192 0.983631i \(-0.557672\pi\)
−0.180192 + 0.983631i \(0.557672\pi\)
\(614\) 0 0
\(615\) −7.41940 −0.299179
\(616\) 0 0
\(617\) 33.8268 1.36182 0.680909 0.732368i \(-0.261585\pi\)
0.680909 + 0.732368i \(0.261585\pi\)
\(618\) 0 0
\(619\) −35.0850 −1.41018 −0.705092 0.709115i \(-0.749095\pi\)
−0.705092 + 0.709115i \(0.749095\pi\)
\(620\) 0 0
\(621\) 13.2943 0.533484
\(622\) 0 0
\(623\) 5.89528 0.236190
\(624\) 0 0
\(625\) −6.61617 −0.264647
\(626\) 0 0
\(627\) −2.04121 −0.0815181
\(628\) 0 0
\(629\) 8.41954 0.335709
\(630\) 0 0
\(631\) −10.7092 −0.426326 −0.213163 0.977017i \(-0.568377\pi\)
−0.213163 + 0.977017i \(0.568377\pi\)
\(632\) 0 0
\(633\) 4.13433 0.164325
\(634\) 0 0
\(635\) −49.8152 −1.97685
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 25.3418 1.00251
\(640\) 0 0
\(641\) 4.77153 0.188464 0.0942321 0.995550i \(-0.469960\pi\)
0.0942321 + 0.995550i \(0.469960\pi\)
\(642\) 0 0
\(643\) −10.1320 −0.399568 −0.199784 0.979840i \(-0.564024\pi\)
−0.199784 + 0.979840i \(0.564024\pi\)
\(644\) 0 0
\(645\) −4.03074 −0.158710
\(646\) 0 0
\(647\) −2.26281 −0.0889602 −0.0444801 0.999010i \(-0.514163\pi\)
−0.0444801 + 0.999010i \(0.514163\pi\)
\(648\) 0 0
\(649\) −4.25733 −0.167115
\(650\) 0 0
\(651\) −0.562193 −0.0220341
\(652\) 0 0
\(653\) −35.7172 −1.39772 −0.698862 0.715257i \(-0.746310\pi\)
−0.698862 + 0.715257i \(0.746310\pi\)
\(654\) 0 0
\(655\) −0.0172837 −0.000675328 0
\(656\) 0 0
\(657\) 29.6753 1.15774
\(658\) 0 0
\(659\) −11.6107 −0.452288 −0.226144 0.974094i \(-0.572612\pi\)
−0.226144 + 0.974094i \(0.572612\pi\)
\(660\) 0 0
\(661\) −18.6643 −0.725958 −0.362979 0.931797i \(-0.618240\pi\)
−0.362979 + 0.931797i \(0.618240\pi\)
\(662\) 0 0
\(663\) 0.429439 0.0166780
\(664\) 0 0
\(665\) −18.0995 −0.701868
\(666\) 0 0
\(667\) 6.72025 0.260209
\(668\) 0 0
\(669\) 1.09085 0.0421749
\(670\) 0 0
\(671\) 1.98172 0.0765033
\(672\) 0 0
\(673\) −47.3405 −1.82484 −0.912420 0.409255i \(-0.865789\pi\)
−0.912420 + 0.409255i \(0.865789\pi\)
\(674\) 0 0
\(675\) −17.3576 −0.668093
\(676\) 0 0
\(677\) −24.7467 −0.951094 −0.475547 0.879690i \(-0.657750\pi\)
−0.475547 + 0.879690i \(0.657750\pi\)
\(678\) 0 0
\(679\) −10.8363 −0.415858
\(680\) 0 0
\(681\) −4.75958 −0.182387
\(682\) 0 0
\(683\) 43.3261 1.65783 0.828914 0.559376i \(-0.188959\pi\)
0.828914 + 0.559376i \(0.188959\pi\)
\(684\) 0 0
\(685\) −55.7402 −2.12972
\(686\) 0 0
\(687\) −2.41140 −0.0920006
\(688\) 0 0
\(689\) 6.09517 0.232207
\(690\) 0 0
\(691\) 1.97337 0.0750707 0.0375353 0.999295i \(-0.488049\pi\)
0.0375353 + 0.999295i \(0.488049\pi\)
\(692\) 0 0
\(693\) −2.84148 −0.107939
\(694\) 0 0
\(695\) 38.0689 1.44404
\(696\) 0 0
\(697\) 5.69350 0.215657
\(698\) 0 0
\(699\) 2.51617 0.0951704
\(700\) 0 0
\(701\) 45.5082 1.71882 0.859410 0.511286i \(-0.170831\pi\)
0.859410 + 0.511286i \(0.170831\pi\)
\(702\) 0 0
\(703\) −40.0198 −1.50938
\(704\) 0 0
\(705\) −3.69522 −0.139170
\(706\) 0 0
\(707\) 6.40496 0.240883
\(708\) 0 0
\(709\) −29.0351 −1.09043 −0.545217 0.838295i \(-0.683553\pi\)
−0.545217 + 0.838295i \(0.683553\pi\)
\(710\) 0 0
\(711\) −15.0462 −0.564278
\(712\) 0 0
\(713\) −8.07151 −0.302280
\(714\) 0 0
\(715\) 3.53033 0.132027
\(716\) 0 0
\(717\) 10.4511 0.390302
\(718\) 0 0
\(719\) −4.14268 −0.154496 −0.0772480 0.997012i \(-0.524613\pi\)
−0.0772480 + 0.997012i \(0.524613\pi\)
\(720\) 0 0
\(721\) 2.99636 0.111590
\(722\) 0 0
\(723\) −1.24134 −0.0461659
\(724\) 0 0
\(725\) −8.77419 −0.325865
\(726\) 0 0
\(727\) −50.0070 −1.85466 −0.927329 0.374247i \(-0.877901\pi\)
−0.927329 + 0.374247i \(0.877901\pi\)
\(728\) 0 0
\(729\) −18.8130 −0.696779
\(730\) 0 0
\(731\) 3.09311 0.114403
\(732\) 0 0
\(733\) 8.24352 0.304481 0.152241 0.988343i \(-0.451351\pi\)
0.152241 + 0.988343i \(0.451351\pi\)
\(734\) 0 0
\(735\) 1.40557 0.0518453
\(736\) 0 0
\(737\) −13.4087 −0.493917
\(738\) 0 0
\(739\) −13.5649 −0.498993 −0.249496 0.968376i \(-0.580265\pi\)
−0.249496 + 0.968376i \(0.580265\pi\)
\(740\) 0 0
\(741\) −2.04121 −0.0749858
\(742\) 0 0
\(743\) 42.7226 1.56734 0.783670 0.621177i \(-0.213345\pi\)
0.783670 + 0.621177i \(0.213345\pi\)
\(744\) 0 0
\(745\) −1.72918 −0.0633521
\(746\) 0 0
\(747\) −5.68966 −0.208174
\(748\) 0 0
\(749\) 14.7546 0.539120
\(750\) 0 0
\(751\) −5.25317 −0.191691 −0.0958454 0.995396i \(-0.530555\pi\)
−0.0958454 + 0.995396i \(0.530555\pi\)
\(752\) 0 0
\(753\) −2.67375 −0.0974369
\(754\) 0 0
\(755\) −56.1376 −2.04306
\(756\) 0 0
\(757\) 9.55305 0.347211 0.173606 0.984815i \(-0.444458\pi\)
0.173606 + 0.984815i \(0.444458\pi\)
\(758\) 0 0
\(759\) 2.27585 0.0826082
\(760\) 0 0
\(761\) 17.8079 0.645536 0.322768 0.946478i \(-0.395387\pi\)
0.322768 + 0.946478i \(0.395387\pi\)
\(762\) 0 0
\(763\) −15.8020 −0.572072
\(764\) 0 0
\(765\) 10.8199 0.391196
\(766\) 0 0
\(767\) −4.25733 −0.153723
\(768\) 0 0
\(769\) 11.4396 0.412523 0.206261 0.978497i \(-0.433870\pi\)
0.206261 + 0.978497i \(0.433870\pi\)
\(770\) 0 0
\(771\) −0.684587 −0.0246548
\(772\) 0 0
\(773\) −47.5847 −1.71150 −0.855751 0.517387i \(-0.826905\pi\)
−0.855751 + 0.517387i \(0.826905\pi\)
\(774\) 0 0
\(775\) 10.5384 0.378552
\(776\) 0 0
\(777\) 3.10786 0.111494
\(778\) 0 0
\(779\) −27.0624 −0.969610
\(780\) 0 0
\(781\) 8.91852 0.319130
\(782\) 0 0
\(783\) 2.73426 0.0977145
\(784\) 0 0
\(785\) −80.3389 −2.86742
\(786\) 0 0
\(787\) 40.6405 1.44868 0.724339 0.689444i \(-0.242145\pi\)
0.724339 + 0.689444i \(0.242145\pi\)
\(788\) 0 0
\(789\) 0.952865 0.0339229
\(790\) 0 0
\(791\) 12.3822 0.440259
\(792\) 0 0
\(793\) 1.98172 0.0703728
\(794\) 0 0
\(795\) −8.56720 −0.303847
\(796\) 0 0
\(797\) 31.9673 1.13234 0.566169 0.824289i \(-0.308425\pi\)
0.566169 + 0.824289i \(0.308425\pi\)
\(798\) 0 0
\(799\) 2.83564 0.100318
\(800\) 0 0
\(801\) 16.7514 0.591880
\(802\) 0 0
\(803\) 10.4436 0.368546
\(804\) 0 0
\(805\) 20.1800 0.711253
\(806\) 0 0
\(807\) −9.25526 −0.325801
\(808\) 0 0
\(809\) 28.8693 1.01499 0.507494 0.861655i \(-0.330572\pi\)
0.507494 + 0.861655i \(0.330572\pi\)
\(810\) 0 0
\(811\) −18.9186 −0.664322 −0.332161 0.943223i \(-0.607778\pi\)
−0.332161 + 0.943223i \(0.607778\pi\)
\(812\) 0 0
\(813\) 3.63505 0.127487
\(814\) 0 0
\(815\) 52.0998 1.82498
\(816\) 0 0
\(817\) −14.7022 −0.514365
\(818\) 0 0
\(819\) −2.84148 −0.0992895
\(820\) 0 0
\(821\) −12.7775 −0.445938 −0.222969 0.974826i \(-0.571575\pi\)
−0.222969 + 0.974826i \(0.571575\pi\)
\(822\) 0 0
\(823\) 24.4311 0.851615 0.425808 0.904814i \(-0.359990\pi\)
0.425808 + 0.904814i \(0.359990\pi\)
\(824\) 0 0
\(825\) −2.97143 −0.103452
\(826\) 0 0
\(827\) 41.7407 1.45147 0.725733 0.687976i \(-0.241501\pi\)
0.725733 + 0.687976i \(0.241501\pi\)
\(828\) 0 0
\(829\) 0.530225 0.0184155 0.00920774 0.999958i \(-0.497069\pi\)
0.00920774 + 0.999958i \(0.497069\pi\)
\(830\) 0 0
\(831\) 7.22388 0.250594
\(832\) 0 0
\(833\) −1.07861 −0.0373716
\(834\) 0 0
\(835\) −19.9331 −0.689815
\(836\) 0 0
\(837\) −3.28404 −0.113513
\(838\) 0 0
\(839\) −26.0810 −0.900417 −0.450208 0.892924i \(-0.648650\pi\)
−0.450208 + 0.892924i \(0.648650\pi\)
\(840\) 0 0
\(841\) −27.6178 −0.952339
\(842\) 0 0
\(843\) 4.77106 0.164324
\(844\) 0 0
\(845\) 3.53033 0.121447
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −5.74655 −0.197221
\(850\) 0 0
\(851\) 44.6201 1.52956
\(852\) 0 0
\(853\) 27.1746 0.930441 0.465221 0.885195i \(-0.345975\pi\)
0.465221 + 0.885195i \(0.345975\pi\)
\(854\) 0 0
\(855\) −51.4294 −1.75885
\(856\) 0 0
\(857\) −39.8600 −1.36159 −0.680796 0.732473i \(-0.738366\pi\)
−0.680796 + 0.732473i \(0.738366\pi\)
\(858\) 0 0
\(859\) 6.99532 0.238677 0.119339 0.992854i \(-0.461923\pi\)
0.119339 + 0.992854i \(0.461923\pi\)
\(860\) 0 0
\(861\) 2.10161 0.0716228
\(862\) 0 0
\(863\) −34.9134 −1.18847 −0.594234 0.804292i \(-0.702545\pi\)
−0.594234 + 0.804292i \(0.702545\pi\)
\(864\) 0 0
\(865\) −67.8018 −2.30533
\(866\) 0 0
\(867\) −6.30521 −0.214136
\(868\) 0 0
\(869\) −5.29521 −0.179628
\(870\) 0 0
\(871\) −13.4087 −0.454337
\(872\) 0 0
\(873\) −30.7911 −1.04212
\(874\) 0 0
\(875\) −8.69608 −0.293981
\(876\) 0 0
\(877\) 31.5141 1.06416 0.532078 0.846695i \(-0.321411\pi\)
0.532078 + 0.846695i \(0.321411\pi\)
\(878\) 0 0
\(879\) −2.82710 −0.0953556
\(880\) 0 0
\(881\) −6.50910 −0.219297 −0.109649 0.993970i \(-0.534973\pi\)
−0.109649 + 0.993970i \(0.534973\pi\)
\(882\) 0 0
\(883\) 19.4828 0.655647 0.327824 0.944739i \(-0.393685\pi\)
0.327824 + 0.944739i \(0.393685\pi\)
\(884\) 0 0
\(885\) 5.98398 0.201149
\(886\) 0 0
\(887\) 5.79773 0.194669 0.0973344 0.995252i \(-0.468968\pi\)
0.0973344 + 0.995252i \(0.468968\pi\)
\(888\) 0 0
\(889\) 14.1106 0.473255
\(890\) 0 0
\(891\) −7.59848 −0.254559
\(892\) 0 0
\(893\) −13.4784 −0.451037
\(894\) 0 0
\(895\) −52.3433 −1.74964
\(896\) 0 0
\(897\) 2.27585 0.0759885
\(898\) 0 0
\(899\) −1.66007 −0.0553665
\(900\) 0 0
\(901\) 6.57430 0.219022
\(902\) 0 0
\(903\) 1.14175 0.0379949
\(904\) 0 0
\(905\) −63.2843 −2.10364
\(906\) 0 0
\(907\) −37.2381 −1.23647 −0.618236 0.785993i \(-0.712152\pi\)
−0.618236 + 0.785993i \(0.712152\pi\)
\(908\) 0 0
\(909\) 18.1996 0.603642
\(910\) 0 0
\(911\) −19.7431 −0.654120 −0.327060 0.945004i \(-0.606058\pi\)
−0.327060 + 0.945004i \(0.606058\pi\)
\(912\) 0 0
\(913\) −2.00236 −0.0662683
\(914\) 0 0
\(915\) −2.78545 −0.0920840
\(916\) 0 0
\(917\) 0.00489576 0.000161672 0
\(918\) 0 0
\(919\) 18.6009 0.613587 0.306794 0.951776i \(-0.400744\pi\)
0.306794 + 0.951776i \(0.400744\pi\)
\(920\) 0 0
\(921\) 0.0379213 0.00124955
\(922\) 0 0
\(923\) 8.91852 0.293557
\(924\) 0 0
\(925\) −58.2576 −1.91550
\(926\) 0 0
\(927\) 8.51412 0.279640
\(928\) 0 0
\(929\) 14.6458 0.480513 0.240256 0.970709i \(-0.422768\pi\)
0.240256 + 0.970709i \(0.422768\pi\)
\(930\) 0 0
\(931\) 5.12685 0.168026
\(932\) 0 0
\(933\) 12.5627 0.411284
\(934\) 0 0
\(935\) 3.80785 0.124530
\(936\) 0 0
\(937\) 8.68070 0.283586 0.141793 0.989896i \(-0.454713\pi\)
0.141793 + 0.989896i \(0.454713\pi\)
\(938\) 0 0
\(939\) 3.21107 0.104789
\(940\) 0 0
\(941\) −14.5399 −0.473987 −0.236994 0.971511i \(-0.576162\pi\)
−0.236994 + 0.971511i \(0.576162\pi\)
\(942\) 0 0
\(943\) 30.1732 0.982575
\(944\) 0 0
\(945\) 8.21063 0.267092
\(946\) 0 0
\(947\) −21.3164 −0.692690 −0.346345 0.938107i \(-0.612577\pi\)
−0.346345 + 0.938107i \(0.612577\pi\)
\(948\) 0 0
\(949\) 10.4436 0.339013
\(950\) 0 0
\(951\) 7.43889 0.241223
\(952\) 0 0
\(953\) 16.6026 0.537811 0.268906 0.963167i \(-0.413338\pi\)
0.268906 + 0.963167i \(0.413338\pi\)
\(954\) 0 0
\(955\) 47.3015 1.53064
\(956\) 0 0
\(957\) 0.468076 0.0151308
\(958\) 0 0
\(959\) 15.7889 0.509851
\(960\) 0 0
\(961\) −29.0061 −0.935682
\(962\) 0 0
\(963\) 41.9249 1.35101
\(964\) 0 0
\(965\) 46.7932 1.50633
\(966\) 0 0
\(967\) −29.3169 −0.942768 −0.471384 0.881928i \(-0.656245\pi\)
−0.471384 + 0.881928i \(0.656245\pi\)
\(968\) 0 0
\(969\) −2.20167 −0.0707278
\(970\) 0 0
\(971\) 50.6171 1.62438 0.812189 0.583394i \(-0.198276\pi\)
0.812189 + 0.583394i \(0.198276\pi\)
\(972\) 0 0
\(973\) −10.7834 −0.345699
\(974\) 0 0
\(975\) −2.97143 −0.0951619
\(976\) 0 0
\(977\) −28.4386 −0.909830 −0.454915 0.890535i \(-0.650330\pi\)
−0.454915 + 0.890535i \(0.650330\pi\)
\(978\) 0 0
\(979\) 5.89528 0.188414
\(980\) 0 0
\(981\) −44.9012 −1.43358
\(982\) 0 0
\(983\) 53.0478 1.69196 0.845980 0.533214i \(-0.179016\pi\)
0.845980 + 0.533214i \(0.179016\pi\)
\(984\) 0 0
\(985\) −33.6430 −1.07196
\(986\) 0 0
\(987\) 1.04671 0.0333170
\(988\) 0 0
\(989\) 16.3922 0.521243
\(990\) 0 0
\(991\) 37.2209 1.18236 0.591181 0.806539i \(-0.298662\pi\)
0.591181 + 0.806539i \(0.298662\pi\)
\(992\) 0 0
\(993\) −4.49833 −0.142750
\(994\) 0 0
\(995\) 56.6862 1.79707
\(996\) 0 0
\(997\) −19.5528 −0.619245 −0.309622 0.950860i \(-0.600203\pi\)
−0.309622 + 0.950860i \(0.600203\pi\)
\(998\) 0 0
\(999\) 18.1545 0.574384
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 \(a_p\))