Properties

Label 6004.2.a.g.1.10
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.57318 q^{3} -4.10446 q^{5} -3.99696 q^{7} -0.525101 q^{9} +O(q^{10})\) \(q-1.57318 q^{3} -4.10446 q^{5} -3.99696 q^{7} -0.525101 q^{9} -5.59278 q^{11} +0.327083 q^{13} +6.45706 q^{15} +1.21729 q^{17} +1.00000 q^{19} +6.28794 q^{21} +0.458737 q^{23} +11.8466 q^{25} +5.54562 q^{27} -2.71079 q^{29} +0.456065 q^{31} +8.79846 q^{33} +16.4053 q^{35} +0.0670418 q^{37} -0.514561 q^{39} -1.54655 q^{41} +8.95138 q^{43} +2.15525 q^{45} -0.548674 q^{47} +8.97566 q^{49} -1.91502 q^{51} -5.96699 q^{53} +22.9553 q^{55} -1.57318 q^{57} +4.29820 q^{59} +1.43055 q^{61} +2.09880 q^{63} -1.34250 q^{65} +2.85776 q^{67} -0.721677 q^{69} +5.48446 q^{71} -16.0364 q^{73} -18.6368 q^{75} +22.3541 q^{77} -1.00000 q^{79} -7.14897 q^{81} +3.71197 q^{83} -4.99633 q^{85} +4.26457 q^{87} -3.84532 q^{89} -1.30734 q^{91} -0.717473 q^{93} -4.10446 q^{95} -6.85022 q^{97} +2.93677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −1.57318 −0.908277 −0.454138 0.890931i \(-0.650053\pi\)
−0.454138 + 0.890931i \(0.650053\pi\)
\(4\) 0 0
\(5\) −4.10446 −1.83557 −0.917785 0.397078i \(-0.870024\pi\)
−0.917785 + 0.397078i \(0.870024\pi\)
\(6\) 0 0
\(7\) −3.99696 −1.51071 −0.755354 0.655317i \(-0.772535\pi\)
−0.755354 + 0.655317i \(0.772535\pi\)
\(8\) 0 0
\(9\) −0.525101 −0.175034
\(10\) 0 0
\(11\) −5.59278 −1.68629 −0.843144 0.537689i \(-0.819298\pi\)
−0.843144 + 0.537689i \(0.819298\pi\)
\(12\) 0 0
\(13\) 0.327083 0.0907165 0.0453583 0.998971i \(-0.485557\pi\)
0.0453583 + 0.998971i \(0.485557\pi\)
\(14\) 0 0
\(15\) 6.45706 1.66720
\(16\) 0 0
\(17\) 1.21729 0.295237 0.147618 0.989044i \(-0.452839\pi\)
0.147618 + 0.989044i \(0.452839\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 6.28794 1.37214
\(22\) 0 0
\(23\) 0.458737 0.0956534 0.0478267 0.998856i \(-0.484770\pi\)
0.0478267 + 0.998856i \(0.484770\pi\)
\(24\) 0 0
\(25\) 11.8466 2.36931
\(26\) 0 0
\(27\) 5.54562 1.06726
\(28\) 0 0
\(29\) −2.71079 −0.503381 −0.251691 0.967808i \(-0.580987\pi\)
−0.251691 + 0.967808i \(0.580987\pi\)
\(30\) 0 0
\(31\) 0.456065 0.0819117 0.0409559 0.999161i \(-0.486960\pi\)
0.0409559 + 0.999161i \(0.486960\pi\)
\(32\) 0 0
\(33\) 8.79846 1.53162
\(34\) 0 0
\(35\) 16.4053 2.77301
\(36\) 0 0
\(37\) 0.0670418 0.0110216 0.00551080 0.999985i \(-0.498246\pi\)
0.00551080 + 0.999985i \(0.498246\pi\)
\(38\) 0 0
\(39\) −0.514561 −0.0823957
\(40\) 0 0
\(41\) −1.54655 −0.241531 −0.120766 0.992681i \(-0.538535\pi\)
−0.120766 + 0.992681i \(0.538535\pi\)
\(42\) 0 0
\(43\) 8.95138 1.36507 0.682536 0.730852i \(-0.260877\pi\)
0.682536 + 0.730852i \(0.260877\pi\)
\(44\) 0 0
\(45\) 2.15525 0.321286
\(46\) 0 0
\(47\) −0.548674 −0.0800323 −0.0400162 0.999199i \(-0.512741\pi\)
−0.0400162 + 0.999199i \(0.512741\pi\)
\(48\) 0 0
\(49\) 8.97566 1.28224
\(50\) 0 0
\(51\) −1.91502 −0.268157
\(52\) 0 0
\(53\) −5.96699 −0.819629 −0.409815 0.912169i \(-0.634407\pi\)
−0.409815 + 0.912169i \(0.634407\pi\)
\(54\) 0 0
\(55\) 22.9553 3.09530
\(56\) 0 0
\(57\) −1.57318 −0.208373
\(58\) 0 0
\(59\) 4.29820 0.559578 0.279789 0.960062i \(-0.409736\pi\)
0.279789 + 0.960062i \(0.409736\pi\)
\(60\) 0 0
\(61\) 1.43055 0.183163 0.0915815 0.995798i \(-0.470808\pi\)
0.0915815 + 0.995798i \(0.470808\pi\)
\(62\) 0 0
\(63\) 2.09880 0.264425
\(64\) 0 0
\(65\) −1.34250 −0.166516
\(66\) 0 0
\(67\) 2.85776 0.349131 0.174565 0.984646i \(-0.444148\pi\)
0.174565 + 0.984646i \(0.444148\pi\)
\(68\) 0 0
\(69\) −0.721677 −0.0868797
\(70\) 0 0
\(71\) 5.48446 0.650886 0.325443 0.945562i \(-0.394487\pi\)
0.325443 + 0.945562i \(0.394487\pi\)
\(72\) 0 0
\(73\) −16.0364 −1.87691 −0.938457 0.345395i \(-0.887745\pi\)
−0.938457 + 0.345395i \(0.887745\pi\)
\(74\) 0 0
\(75\) −18.6368 −2.15199
\(76\) 0 0
\(77\) 22.3541 2.54749
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −7.14897 −0.794330
\(82\) 0 0
\(83\) 3.71197 0.407442 0.203721 0.979029i \(-0.434696\pi\)
0.203721 + 0.979029i \(0.434696\pi\)
\(84\) 0 0
\(85\) −4.99633 −0.541928
\(86\) 0 0
\(87\) 4.26457 0.457209
\(88\) 0 0
\(89\) −3.84532 −0.407603 −0.203801 0.979012i \(-0.565330\pi\)
−0.203801 + 0.979012i \(0.565330\pi\)
\(90\) 0 0
\(91\) −1.30734 −0.137046
\(92\) 0 0
\(93\) −0.717473 −0.0743985
\(94\) 0 0
\(95\) −4.10446 −0.421108
\(96\) 0 0
\(97\) −6.85022 −0.695535 −0.347767 0.937581i \(-0.613060\pi\)
−0.347767 + 0.937581i \(0.613060\pi\)
\(98\) 0 0
\(99\) 2.93677 0.295157
\(100\) 0 0
\(101\) 1.15331 0.114759 0.0573795 0.998352i \(-0.481725\pi\)
0.0573795 + 0.998352i \(0.481725\pi\)
\(102\) 0 0
\(103\) 3.32912 0.328028 0.164014 0.986458i \(-0.447556\pi\)
0.164014 + 0.986458i \(0.447556\pi\)
\(104\) 0 0
\(105\) −25.8086 −2.51866
\(106\) 0 0
\(107\) 5.16106 0.498938 0.249469 0.968383i \(-0.419744\pi\)
0.249469 + 0.968383i \(0.419744\pi\)
\(108\) 0 0
\(109\) 20.0741 1.92275 0.961374 0.275246i \(-0.0887593\pi\)
0.961374 + 0.275246i \(0.0887593\pi\)
\(110\) 0 0
\(111\) −0.105469 −0.0100107
\(112\) 0 0
\(113\) −13.5486 −1.27454 −0.637271 0.770639i \(-0.719937\pi\)
−0.637271 + 0.770639i \(0.719937\pi\)
\(114\) 0 0
\(115\) −1.88287 −0.175578
\(116\) 0 0
\(117\) −0.171752 −0.0158784
\(118\) 0 0
\(119\) −4.86547 −0.446017
\(120\) 0 0
\(121\) 20.2792 1.84356
\(122\) 0 0
\(123\) 2.43301 0.219377
\(124\) 0 0
\(125\) −28.1015 −2.51347
\(126\) 0 0
\(127\) −6.08976 −0.540379 −0.270190 0.962807i \(-0.587086\pi\)
−0.270190 + 0.962807i \(0.587086\pi\)
\(128\) 0 0
\(129\) −14.0821 −1.23986
\(130\) 0 0
\(131\) −3.53677 −0.309009 −0.154505 0.987992i \(-0.549378\pi\)
−0.154505 + 0.987992i \(0.549378\pi\)
\(132\) 0 0
\(133\) −3.99696 −0.346580
\(134\) 0 0
\(135\) −22.7618 −1.95902
\(136\) 0 0
\(137\) −11.4890 −0.981568 −0.490784 0.871281i \(-0.663290\pi\)
−0.490784 + 0.871281i \(0.663290\pi\)
\(138\) 0 0
\(139\) 15.3300 1.30027 0.650136 0.759818i \(-0.274712\pi\)
0.650136 + 0.759818i \(0.274712\pi\)
\(140\) 0 0
\(141\) 0.863164 0.0726915
\(142\) 0 0
\(143\) −1.82930 −0.152974
\(144\) 0 0
\(145\) 11.1263 0.923991
\(146\) 0 0
\(147\) −14.1203 −1.16463
\(148\) 0 0
\(149\) −11.3751 −0.931886 −0.465943 0.884815i \(-0.654285\pi\)
−0.465943 + 0.884815i \(0.654285\pi\)
\(150\) 0 0
\(151\) −0.817869 −0.0665572 −0.0332786 0.999446i \(-0.510595\pi\)
−0.0332786 + 0.999446i \(0.510595\pi\)
\(152\) 0 0
\(153\) −0.639201 −0.0516764
\(154\) 0 0
\(155\) −1.87190 −0.150355
\(156\) 0 0
\(157\) 5.21581 0.416267 0.208134 0.978100i \(-0.433261\pi\)
0.208134 + 0.978100i \(0.433261\pi\)
\(158\) 0 0
\(159\) 9.38716 0.744450
\(160\) 0 0
\(161\) −1.83355 −0.144504
\(162\) 0 0
\(163\) 1.59696 0.125083 0.0625416 0.998042i \(-0.480079\pi\)
0.0625416 + 0.998042i \(0.480079\pi\)
\(164\) 0 0
\(165\) −36.1129 −2.81139
\(166\) 0 0
\(167\) −9.60733 −0.743437 −0.371719 0.928345i \(-0.621231\pi\)
−0.371719 + 0.928345i \(0.621231\pi\)
\(168\) 0 0
\(169\) −12.8930 −0.991771
\(170\) 0 0
\(171\) −0.525101 −0.0401555
\(172\) 0 0
\(173\) 9.33646 0.709838 0.354919 0.934897i \(-0.384508\pi\)
0.354919 + 0.934897i \(0.384508\pi\)
\(174\) 0 0
\(175\) −47.3502 −3.57934
\(176\) 0 0
\(177\) −6.76185 −0.508252
\(178\) 0 0
\(179\) 23.2905 1.74081 0.870405 0.492336i \(-0.163857\pi\)
0.870405 + 0.492336i \(0.163857\pi\)
\(180\) 0 0
\(181\) 9.48778 0.705221 0.352611 0.935770i \(-0.385294\pi\)
0.352611 + 0.935770i \(0.385294\pi\)
\(182\) 0 0
\(183\) −2.25051 −0.166363
\(184\) 0 0
\(185\) −0.275170 −0.0202309
\(186\) 0 0
\(187\) −6.80805 −0.497854
\(188\) 0 0
\(189\) −22.1656 −1.61231
\(190\) 0 0
\(191\) −13.1823 −0.953840 −0.476920 0.878947i \(-0.658247\pi\)
−0.476920 + 0.878947i \(0.658247\pi\)
\(192\) 0 0
\(193\) 1.75206 0.126116 0.0630579 0.998010i \(-0.479915\pi\)
0.0630579 + 0.998010i \(0.479915\pi\)
\(194\) 0 0
\(195\) 2.11199 0.151243
\(196\) 0 0
\(197\) 17.1443 1.22148 0.610740 0.791831i \(-0.290872\pi\)
0.610740 + 0.791831i \(0.290872\pi\)
\(198\) 0 0
\(199\) −21.4873 −1.52320 −0.761598 0.648050i \(-0.775585\pi\)
−0.761598 + 0.648050i \(0.775585\pi\)
\(200\) 0 0
\(201\) −4.49577 −0.317107
\(202\) 0 0
\(203\) 10.8349 0.760462
\(204\) 0 0
\(205\) 6.34776 0.443347
\(206\) 0 0
\(207\) −0.240883 −0.0167425
\(208\) 0 0
\(209\) −5.59278 −0.386861
\(210\) 0 0
\(211\) 19.9611 1.37418 0.687091 0.726572i \(-0.258888\pi\)
0.687091 + 0.726572i \(0.258888\pi\)
\(212\) 0 0
\(213\) −8.62805 −0.591185
\(214\) 0 0
\(215\) −36.7405 −2.50568
\(216\) 0 0
\(217\) −1.82287 −0.123745
\(218\) 0 0
\(219\) 25.2281 1.70476
\(220\) 0 0
\(221\) 0.398156 0.0267828
\(222\) 0 0
\(223\) 8.61741 0.577064 0.288532 0.957470i \(-0.406833\pi\)
0.288532 + 0.957470i \(0.406833\pi\)
\(224\) 0 0
\(225\) −6.22064 −0.414710
\(226\) 0 0
\(227\) 14.7063 0.976089 0.488044 0.872819i \(-0.337710\pi\)
0.488044 + 0.872819i \(0.337710\pi\)
\(228\) 0 0
\(229\) −12.8146 −0.846810 −0.423405 0.905941i \(-0.639165\pi\)
−0.423405 + 0.905941i \(0.639165\pi\)
\(230\) 0 0
\(231\) −35.1671 −2.31382
\(232\) 0 0
\(233\) −2.57316 −0.168574 −0.0842868 0.996442i \(-0.526861\pi\)
−0.0842868 + 0.996442i \(0.526861\pi\)
\(234\) 0 0
\(235\) 2.25201 0.146905
\(236\) 0 0
\(237\) 1.57318 0.102189
\(238\) 0 0
\(239\) 2.55062 0.164986 0.0824930 0.996592i \(-0.473712\pi\)
0.0824930 + 0.996592i \(0.473712\pi\)
\(240\) 0 0
\(241\) 20.1862 1.30031 0.650154 0.759803i \(-0.274704\pi\)
0.650154 + 0.759803i \(0.274704\pi\)
\(242\) 0 0
\(243\) −5.39025 −0.345784
\(244\) 0 0
\(245\) −36.8402 −2.35364
\(246\) 0 0
\(247\) 0.327083 0.0208118
\(248\) 0 0
\(249\) −5.83961 −0.370070
\(250\) 0 0
\(251\) −8.67050 −0.547277 −0.273639 0.961833i \(-0.588227\pi\)
−0.273639 + 0.961833i \(0.588227\pi\)
\(252\) 0 0
\(253\) −2.56562 −0.161299
\(254\) 0 0
\(255\) 7.86013 0.492220
\(256\) 0 0
\(257\) 28.1081 1.75334 0.876669 0.481095i \(-0.159761\pi\)
0.876669 + 0.481095i \(0.159761\pi\)
\(258\) 0 0
\(259\) −0.267963 −0.0166504
\(260\) 0 0
\(261\) 1.42344 0.0881086
\(262\) 0 0
\(263\) −10.2321 −0.630936 −0.315468 0.948936i \(-0.602162\pi\)
−0.315468 + 0.948936i \(0.602162\pi\)
\(264\) 0 0
\(265\) 24.4913 1.50449
\(266\) 0 0
\(267\) 6.04938 0.370216
\(268\) 0 0
\(269\) −5.04045 −0.307322 −0.153661 0.988124i \(-0.549106\pi\)
−0.153661 + 0.988124i \(0.549106\pi\)
\(270\) 0 0
\(271\) 10.6297 0.645710 0.322855 0.946448i \(-0.395357\pi\)
0.322855 + 0.946448i \(0.395357\pi\)
\(272\) 0 0
\(273\) 2.05668 0.124476
\(274\) 0 0
\(275\) −66.2553 −3.99535
\(276\) 0 0
\(277\) −3.79054 −0.227751 −0.113876 0.993495i \(-0.536327\pi\)
−0.113876 + 0.993495i \(0.536327\pi\)
\(278\) 0 0
\(279\) −0.239480 −0.0143373
\(280\) 0 0
\(281\) 22.5635 1.34602 0.673012 0.739632i \(-0.265000\pi\)
0.673012 + 0.739632i \(0.265000\pi\)
\(282\) 0 0
\(283\) −5.59292 −0.332465 −0.166232 0.986087i \(-0.553160\pi\)
−0.166232 + 0.986087i \(0.553160\pi\)
\(284\) 0 0
\(285\) 6.45706 0.382483
\(286\) 0 0
\(287\) 6.18151 0.364883
\(288\) 0 0
\(289\) −15.5182 −0.912835
\(290\) 0 0
\(291\) 10.7766 0.631738
\(292\) 0 0
\(293\) −6.38464 −0.372994 −0.186497 0.982455i \(-0.559714\pi\)
−0.186497 + 0.982455i \(0.559714\pi\)
\(294\) 0 0
\(295\) −17.6418 −1.02714
\(296\) 0 0
\(297\) −31.0155 −1.79970
\(298\) 0 0
\(299\) 0.150045 0.00867734
\(300\) 0 0
\(301\) −35.7783 −2.06222
\(302\) 0 0
\(303\) −1.81437 −0.104233
\(304\) 0 0
\(305\) −5.87162 −0.336208
\(306\) 0 0
\(307\) 12.3165 0.702938 0.351469 0.936200i \(-0.385682\pi\)
0.351469 + 0.936200i \(0.385682\pi\)
\(308\) 0 0
\(309\) −5.23731 −0.297940
\(310\) 0 0
\(311\) 8.26184 0.468486 0.234243 0.972178i \(-0.424739\pi\)
0.234243 + 0.972178i \(0.424739\pi\)
\(312\) 0 0
\(313\) 23.8083 1.34573 0.672863 0.739767i \(-0.265064\pi\)
0.672863 + 0.739767i \(0.265064\pi\)
\(314\) 0 0
\(315\) −8.61446 −0.485370
\(316\) 0 0
\(317\) −24.3381 −1.36696 −0.683482 0.729968i \(-0.739535\pi\)
−0.683482 + 0.729968i \(0.739535\pi\)
\(318\) 0 0
\(319\) 15.1609 0.848845
\(320\) 0 0
\(321\) −8.11928 −0.453174
\(322\) 0 0
\(323\) 1.21729 0.0677320
\(324\) 0 0
\(325\) 3.87481 0.214936
\(326\) 0 0
\(327\) −31.5802 −1.74639
\(328\) 0 0
\(329\) 2.19303 0.120905
\(330\) 0 0
\(331\) 24.3429 1.33801 0.669003 0.743260i \(-0.266721\pi\)
0.669003 + 0.743260i \(0.266721\pi\)
\(332\) 0 0
\(333\) −0.0352037 −0.00192915
\(334\) 0 0
\(335\) −11.7295 −0.640854
\(336\) 0 0
\(337\) 12.9317 0.704433 0.352217 0.935918i \(-0.385428\pi\)
0.352217 + 0.935918i \(0.385428\pi\)
\(338\) 0 0
\(339\) 21.3144 1.15764
\(340\) 0 0
\(341\) −2.55067 −0.138127
\(342\) 0 0
\(343\) −7.89664 −0.426379
\(344\) 0 0
\(345\) 2.96209 0.159474
\(346\) 0 0
\(347\) 2.39723 0.128690 0.0643449 0.997928i \(-0.479504\pi\)
0.0643449 + 0.997928i \(0.479504\pi\)
\(348\) 0 0
\(349\) 24.1153 1.29086 0.645432 0.763818i \(-0.276678\pi\)
0.645432 + 0.763818i \(0.276678\pi\)
\(350\) 0 0
\(351\) 1.81388 0.0968177
\(352\) 0 0
\(353\) −22.4944 −1.19726 −0.598628 0.801027i \(-0.704287\pi\)
−0.598628 + 0.801027i \(0.704287\pi\)
\(354\) 0 0
\(355\) −22.5107 −1.19475
\(356\) 0 0
\(357\) 7.65426 0.405106
\(358\) 0 0
\(359\) 5.62800 0.297034 0.148517 0.988910i \(-0.452550\pi\)
0.148517 + 0.988910i \(0.452550\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −31.9029 −1.67447
\(364\) 0 0
\(365\) 65.8206 3.44521
\(366\) 0 0
\(367\) −23.1345 −1.20761 −0.603806 0.797131i \(-0.706350\pi\)
−0.603806 + 0.797131i \(0.706350\pi\)
\(368\) 0 0
\(369\) 0.812096 0.0422760
\(370\) 0 0
\(371\) 23.8498 1.23822
\(372\) 0 0
\(373\) 18.4809 0.956905 0.478453 0.878113i \(-0.341198\pi\)
0.478453 + 0.878113i \(0.341198\pi\)
\(374\) 0 0
\(375\) 44.2087 2.28293
\(376\) 0 0
\(377\) −0.886654 −0.0456650
\(378\) 0 0
\(379\) −23.6326 −1.21392 −0.606962 0.794731i \(-0.707612\pi\)
−0.606962 + 0.794731i \(0.707612\pi\)
\(380\) 0 0
\(381\) 9.58030 0.490814
\(382\) 0 0
\(383\) 28.7925 1.47123 0.735615 0.677400i \(-0.236893\pi\)
0.735615 + 0.677400i \(0.236893\pi\)
\(384\) 0 0
\(385\) −91.7515 −4.67609
\(386\) 0 0
\(387\) −4.70037 −0.238933
\(388\) 0 0
\(389\) −27.7952 −1.40927 −0.704635 0.709570i \(-0.748889\pi\)
−0.704635 + 0.709570i \(0.748889\pi\)
\(390\) 0 0
\(391\) 0.558418 0.0282404
\(392\) 0 0
\(393\) 5.56399 0.280666
\(394\) 0 0
\(395\) 4.10446 0.206518
\(396\) 0 0
\(397\) −31.4482 −1.57834 −0.789169 0.614176i \(-0.789489\pi\)
−0.789169 + 0.614176i \(0.789489\pi\)
\(398\) 0 0
\(399\) 6.28794 0.314791
\(400\) 0 0
\(401\) 12.0651 0.602502 0.301251 0.953545i \(-0.402596\pi\)
0.301251 + 0.953545i \(0.402596\pi\)
\(402\) 0 0
\(403\) 0.149171 0.00743074
\(404\) 0 0
\(405\) 29.3426 1.45805
\(406\) 0 0
\(407\) −0.374950 −0.0185856
\(408\) 0 0
\(409\) −11.1415 −0.550913 −0.275457 0.961313i \(-0.588829\pi\)
−0.275457 + 0.961313i \(0.588829\pi\)
\(410\) 0 0
\(411\) 18.0742 0.891535
\(412\) 0 0
\(413\) −17.1797 −0.845359
\(414\) 0 0
\(415\) −15.2356 −0.747888
\(416\) 0 0
\(417\) −24.1168 −1.18101
\(418\) 0 0
\(419\) 38.5351 1.88256 0.941281 0.337623i \(-0.109623\pi\)
0.941281 + 0.337623i \(0.109623\pi\)
\(420\) 0 0
\(421\) −28.6715 −1.39737 −0.698683 0.715432i \(-0.746230\pi\)
−0.698683 + 0.715432i \(0.746230\pi\)
\(422\) 0 0
\(423\) 0.288109 0.0140083
\(424\) 0 0
\(425\) 14.4207 0.699509
\(426\) 0 0
\(427\) −5.71784 −0.276706
\(428\) 0 0
\(429\) 2.87783 0.138943
\(430\) 0 0
\(431\) −29.4598 −1.41903 −0.709515 0.704690i \(-0.751086\pi\)
−0.709515 + 0.704690i \(0.751086\pi\)
\(432\) 0 0
\(433\) 34.1873 1.64294 0.821469 0.570253i \(-0.193155\pi\)
0.821469 + 0.570253i \(0.193155\pi\)
\(434\) 0 0
\(435\) −17.5037 −0.839240
\(436\) 0 0
\(437\) 0.458737 0.0219444
\(438\) 0 0
\(439\) −5.24743 −0.250446 −0.125223 0.992129i \(-0.539965\pi\)
−0.125223 + 0.992129i \(0.539965\pi\)
\(440\) 0 0
\(441\) −4.71313 −0.224435
\(442\) 0 0
\(443\) 14.8133 0.703801 0.351901 0.936037i \(-0.385536\pi\)
0.351901 + 0.936037i \(0.385536\pi\)
\(444\) 0 0
\(445\) 15.7829 0.748183
\(446\) 0 0
\(447\) 17.8951 0.846410
\(448\) 0 0
\(449\) 16.0530 0.757589 0.378794 0.925481i \(-0.376339\pi\)
0.378794 + 0.925481i \(0.376339\pi\)
\(450\) 0 0
\(451\) 8.64953 0.407291
\(452\) 0 0
\(453\) 1.28666 0.0604524
\(454\) 0 0
\(455\) 5.36591 0.251558
\(456\) 0 0
\(457\) −11.9869 −0.560723 −0.280362 0.959894i \(-0.590454\pi\)
−0.280362 + 0.959894i \(0.590454\pi\)
\(458\) 0 0
\(459\) 6.75064 0.315093
\(460\) 0 0
\(461\) −8.84746 −0.412067 −0.206034 0.978545i \(-0.566056\pi\)
−0.206034 + 0.978545i \(0.566056\pi\)
\(462\) 0 0
\(463\) 20.4226 0.949121 0.474560 0.880223i \(-0.342607\pi\)
0.474560 + 0.880223i \(0.342607\pi\)
\(464\) 0 0
\(465\) 2.94484 0.136564
\(466\) 0 0
\(467\) 1.59247 0.0736907 0.0368454 0.999321i \(-0.488269\pi\)
0.0368454 + 0.999321i \(0.488269\pi\)
\(468\) 0 0
\(469\) −11.4223 −0.527434
\(470\) 0 0
\(471\) −8.20542 −0.378086
\(472\) 0 0
\(473\) −50.0631 −2.30190
\(474\) 0 0
\(475\) 11.8466 0.543558
\(476\) 0 0
\(477\) 3.13327 0.143463
\(478\) 0 0
\(479\) 1.82798 0.0835226 0.0417613 0.999128i \(-0.486703\pi\)
0.0417613 + 0.999128i \(0.486703\pi\)
\(480\) 0 0
\(481\) 0.0219282 0.000999841 0
\(482\) 0 0
\(483\) 2.88451 0.131250
\(484\) 0 0
\(485\) 28.1165 1.27670
\(486\) 0 0
\(487\) 10.7337 0.486392 0.243196 0.969977i \(-0.421804\pi\)
0.243196 + 0.969977i \(0.421804\pi\)
\(488\) 0 0
\(489\) −2.51230 −0.113610
\(490\) 0 0
\(491\) −14.6342 −0.660433 −0.330217 0.943905i \(-0.607122\pi\)
−0.330217 + 0.943905i \(0.607122\pi\)
\(492\) 0 0
\(493\) −3.29983 −0.148617
\(494\) 0 0
\(495\) −12.0539 −0.541781
\(496\) 0 0
\(497\) −21.9212 −0.983299
\(498\) 0 0
\(499\) −30.7058 −1.37458 −0.687289 0.726384i \(-0.741199\pi\)
−0.687289 + 0.726384i \(0.741199\pi\)
\(500\) 0 0
\(501\) 15.1141 0.675247
\(502\) 0 0
\(503\) 21.1039 0.940975 0.470488 0.882407i \(-0.344078\pi\)
0.470488 + 0.882407i \(0.344078\pi\)
\(504\) 0 0
\(505\) −4.73373 −0.210648
\(506\) 0 0
\(507\) 20.2831 0.900802
\(508\) 0 0
\(509\) −35.3917 −1.56871 −0.784355 0.620313i \(-0.787006\pi\)
−0.784355 + 0.620313i \(0.787006\pi\)
\(510\) 0 0
\(511\) 64.0967 2.83547
\(512\) 0 0
\(513\) 5.54562 0.244845
\(514\) 0 0
\(515\) −13.6642 −0.602118
\(516\) 0 0
\(517\) 3.06861 0.134957
\(518\) 0 0
\(519\) −14.6879 −0.644729
\(520\) 0 0
\(521\) −37.6559 −1.64973 −0.824867 0.565327i \(-0.808750\pi\)
−0.824867 + 0.565327i \(0.808750\pi\)
\(522\) 0 0
\(523\) −14.6908 −0.642382 −0.321191 0.947014i \(-0.604083\pi\)
−0.321191 + 0.947014i \(0.604083\pi\)
\(524\) 0 0
\(525\) 74.4905 3.25103
\(526\) 0 0
\(527\) 0.555165 0.0241834
\(528\) 0 0
\(529\) −22.7896 −0.990850
\(530\) 0 0
\(531\) −2.25699 −0.0979449
\(532\) 0 0
\(533\) −0.505851 −0.0219108
\(534\) 0 0
\(535\) −21.1833 −0.915836
\(536\) 0 0
\(537\) −36.6401 −1.58114
\(538\) 0 0
\(539\) −50.1989 −2.16222
\(540\) 0 0
\(541\) 3.52639 0.151611 0.0758057 0.997123i \(-0.475847\pi\)
0.0758057 + 0.997123i \(0.475847\pi\)
\(542\) 0 0
\(543\) −14.9260 −0.640536
\(544\) 0 0
\(545\) −82.3932 −3.52934
\(546\) 0 0
\(547\) −1.70442 −0.0728757 −0.0364379 0.999336i \(-0.511601\pi\)
−0.0364379 + 0.999336i \(0.511601\pi\)
\(548\) 0 0
\(549\) −0.751182 −0.0320597
\(550\) 0 0
\(551\) −2.71079 −0.115484
\(552\) 0 0
\(553\) 3.99696 0.169968
\(554\) 0 0
\(555\) 0.432893 0.0183753
\(556\) 0 0
\(557\) 4.10169 0.173794 0.0868971 0.996217i \(-0.472305\pi\)
0.0868971 + 0.996217i \(0.472305\pi\)
\(558\) 0 0
\(559\) 2.92784 0.123835
\(560\) 0 0
\(561\) 10.7103 0.452189
\(562\) 0 0
\(563\) 31.2141 1.31552 0.657758 0.753229i \(-0.271505\pi\)
0.657758 + 0.753229i \(0.271505\pi\)
\(564\) 0 0
\(565\) 55.6096 2.33951
\(566\) 0 0
\(567\) 28.5741 1.20000
\(568\) 0 0
\(569\) −41.8722 −1.75537 −0.877687 0.479234i \(-0.840915\pi\)
−0.877687 + 0.479234i \(0.840915\pi\)
\(570\) 0 0
\(571\) 10.2242 0.427868 0.213934 0.976848i \(-0.431372\pi\)
0.213934 + 0.976848i \(0.431372\pi\)
\(572\) 0 0
\(573\) 20.7382 0.866351
\(574\) 0 0
\(575\) 5.43447 0.226633
\(576\) 0 0
\(577\) 25.7283 1.07108 0.535542 0.844509i \(-0.320107\pi\)
0.535542 + 0.844509i \(0.320107\pi\)
\(578\) 0 0
\(579\) −2.75630 −0.114548
\(580\) 0 0
\(581\) −14.8366 −0.615526
\(582\) 0 0
\(583\) 33.3721 1.38213
\(584\) 0 0
\(585\) 0.704947 0.0291460
\(586\) 0 0
\(587\) −29.5875 −1.22121 −0.610603 0.791937i \(-0.709073\pi\)
−0.610603 + 0.791937i \(0.709073\pi\)
\(588\) 0 0
\(589\) 0.456065 0.0187918
\(590\) 0 0
\(591\) −26.9711 −1.10944
\(592\) 0 0
\(593\) 25.7882 1.05899 0.529497 0.848312i \(-0.322381\pi\)
0.529497 + 0.848312i \(0.322381\pi\)
\(594\) 0 0
\(595\) 19.9701 0.818694
\(596\) 0 0
\(597\) 33.8035 1.38348
\(598\) 0 0
\(599\) −3.29197 −0.134506 −0.0672532 0.997736i \(-0.521424\pi\)
−0.0672532 + 0.997736i \(0.521424\pi\)
\(600\) 0 0
\(601\) 39.9851 1.63103 0.815514 0.578738i \(-0.196454\pi\)
0.815514 + 0.578738i \(0.196454\pi\)
\(602\) 0 0
\(603\) −1.50061 −0.0611096
\(604\) 0 0
\(605\) −83.2351 −3.38399
\(606\) 0 0
\(607\) −20.3498 −0.825971 −0.412986 0.910738i \(-0.635514\pi\)
−0.412986 + 0.910738i \(0.635514\pi\)
\(608\) 0 0
\(609\) −17.0453 −0.690710
\(610\) 0 0
\(611\) −0.179462 −0.00726025
\(612\) 0 0
\(613\) −9.75369 −0.393948 −0.196974 0.980409i \(-0.563111\pi\)
−0.196974 + 0.980409i \(0.563111\pi\)
\(614\) 0 0
\(615\) −9.98618 −0.402682
\(616\) 0 0
\(617\) 32.5216 1.30927 0.654635 0.755945i \(-0.272822\pi\)
0.654635 + 0.755945i \(0.272822\pi\)
\(618\) 0 0
\(619\) −3.57754 −0.143793 −0.0718967 0.997412i \(-0.522905\pi\)
−0.0718967 + 0.997412i \(0.522905\pi\)
\(620\) 0 0
\(621\) 2.54398 0.102087
\(622\) 0 0
\(623\) 15.3696 0.615769
\(624\) 0 0
\(625\) 56.1085 2.24434
\(626\) 0 0
\(627\) 8.79846 0.351377
\(628\) 0 0
\(629\) 0.0816094 0.00325398
\(630\) 0 0
\(631\) −2.08973 −0.0831910 −0.0415955 0.999135i \(-0.513244\pi\)
−0.0415955 + 0.999135i \(0.513244\pi\)
\(632\) 0 0
\(633\) −31.4025 −1.24814
\(634\) 0 0
\(635\) 24.9952 0.991904
\(636\) 0 0
\(637\) 2.93579 0.116320
\(638\) 0 0
\(639\) −2.87990 −0.113927
\(640\) 0 0
\(641\) −47.6336 −1.88141 −0.940706 0.339223i \(-0.889836\pi\)
−0.940706 + 0.339223i \(0.889836\pi\)
\(642\) 0 0
\(643\) −20.5481 −0.810338 −0.405169 0.914242i \(-0.632787\pi\)
−0.405169 + 0.914242i \(0.632787\pi\)
\(644\) 0 0
\(645\) 57.7995 2.27585
\(646\) 0 0
\(647\) 38.2271 1.50286 0.751431 0.659811i \(-0.229364\pi\)
0.751431 + 0.659811i \(0.229364\pi\)
\(648\) 0 0
\(649\) −24.0389 −0.943609
\(650\) 0 0
\(651\) 2.86771 0.112394
\(652\) 0 0
\(653\) 36.5122 1.42883 0.714416 0.699721i \(-0.246692\pi\)
0.714416 + 0.699721i \(0.246692\pi\)
\(654\) 0 0
\(655\) 14.5165 0.567208
\(656\) 0 0
\(657\) 8.42071 0.328523
\(658\) 0 0
\(659\) 43.1347 1.68029 0.840145 0.542362i \(-0.182470\pi\)
0.840145 + 0.542362i \(0.182470\pi\)
\(660\) 0 0
\(661\) 0.743732 0.0289278 0.0144639 0.999895i \(-0.495396\pi\)
0.0144639 + 0.999895i \(0.495396\pi\)
\(662\) 0 0
\(663\) −0.626371 −0.0243262
\(664\) 0 0
\(665\) 16.4053 0.636172
\(666\) 0 0
\(667\) −1.24354 −0.0481501
\(668\) 0 0
\(669\) −13.5567 −0.524134
\(670\) 0 0
\(671\) −8.00074 −0.308865
\(672\) 0 0
\(673\) 16.5488 0.637908 0.318954 0.947770i \(-0.396668\pi\)
0.318954 + 0.947770i \(0.396668\pi\)
\(674\) 0 0
\(675\) 65.6966 2.52866
\(676\) 0 0
\(677\) −22.7688 −0.875075 −0.437538 0.899200i \(-0.644149\pi\)
−0.437538 + 0.899200i \(0.644149\pi\)
\(678\) 0 0
\(679\) 27.3800 1.05075
\(680\) 0 0
\(681\) −23.1356 −0.886559
\(682\) 0 0
\(683\) −1.80440 −0.0690434 −0.0345217 0.999404i \(-0.510991\pi\)
−0.0345217 + 0.999404i \(0.510991\pi\)
\(684\) 0 0
\(685\) 47.1559 1.80174
\(686\) 0 0
\(687\) 20.1596 0.769137
\(688\) 0 0
\(689\) −1.95170 −0.0743539
\(690\) 0 0
\(691\) −37.8270 −1.43901 −0.719503 0.694490i \(-0.755630\pi\)
−0.719503 + 0.694490i \(0.755630\pi\)
\(692\) 0 0
\(693\) −11.7382 −0.445896
\(694\) 0 0
\(695\) −62.9212 −2.38674
\(696\) 0 0
\(697\) −1.88261 −0.0713088
\(698\) 0 0
\(699\) 4.04805 0.153111
\(700\) 0 0
\(701\) −21.2393 −0.802198 −0.401099 0.916035i \(-0.631372\pi\)
−0.401099 + 0.916035i \(0.631372\pi\)
\(702\) 0 0
\(703\) 0.0670418 0.00252853
\(704\) 0 0
\(705\) −3.54282 −0.133430
\(706\) 0 0
\(707\) −4.60975 −0.173367
\(708\) 0 0
\(709\) −27.0595 −1.01624 −0.508121 0.861286i \(-0.669660\pi\)
−0.508121 + 0.861286i \(0.669660\pi\)
\(710\) 0 0
\(711\) 0.525101 0.0196928
\(712\) 0 0
\(713\) 0.209214 0.00783513
\(714\) 0 0
\(715\) 7.50830 0.280794
\(716\) 0 0
\(717\) −4.01259 −0.149853
\(718\) 0 0
\(719\) −38.1345 −1.42218 −0.711088 0.703103i \(-0.751797\pi\)
−0.711088 + 0.703103i \(0.751797\pi\)
\(720\) 0 0
\(721\) −13.3063 −0.495554
\(722\) 0 0
\(723\) −31.7566 −1.18104
\(724\) 0 0
\(725\) −32.1136 −1.19267
\(726\) 0 0
\(727\) 9.39871 0.348579 0.174289 0.984694i \(-0.444237\pi\)
0.174289 + 0.984694i \(0.444237\pi\)
\(728\) 0 0
\(729\) 29.9267 1.10840
\(730\) 0 0
\(731\) 10.8964 0.403019
\(732\) 0 0
\(733\) −2.07265 −0.0765552 −0.0382776 0.999267i \(-0.512187\pi\)
−0.0382776 + 0.999267i \(0.512187\pi\)
\(734\) 0 0
\(735\) 57.9564 2.13775
\(736\) 0 0
\(737\) −15.9828 −0.588734
\(738\) 0 0
\(739\) 34.6647 1.27516 0.637582 0.770383i \(-0.279935\pi\)
0.637582 + 0.770383i \(0.279935\pi\)
\(740\) 0 0
\(741\) −0.514561 −0.0189029
\(742\) 0 0
\(743\) −12.2067 −0.447819 −0.223909 0.974610i \(-0.571882\pi\)
−0.223909 + 0.974610i \(0.571882\pi\)
\(744\) 0 0
\(745\) 46.6887 1.71054
\(746\) 0 0
\(747\) −1.94916 −0.0713161
\(748\) 0 0
\(749\) −20.6285 −0.753750
\(750\) 0 0
\(751\) 28.2478 1.03078 0.515389 0.856956i \(-0.327647\pi\)
0.515389 + 0.856956i \(0.327647\pi\)
\(752\) 0 0
\(753\) 13.6403 0.497079
\(754\) 0 0
\(755\) 3.35691 0.122170
\(756\) 0 0
\(757\) 3.67098 0.133424 0.0667120 0.997772i \(-0.478749\pi\)
0.0667120 + 0.997772i \(0.478749\pi\)
\(758\) 0 0
\(759\) 4.03618 0.146504
\(760\) 0 0
\(761\) −30.8374 −1.11786 −0.558928 0.829216i \(-0.688787\pi\)
−0.558928 + 0.829216i \(0.688787\pi\)
\(762\) 0 0
\(763\) −80.2352 −2.90471
\(764\) 0 0
\(765\) 2.62357 0.0948555
\(766\) 0 0
\(767\) 1.40587 0.0507629
\(768\) 0 0
\(769\) 18.3452 0.661547 0.330773 0.943710i \(-0.392690\pi\)
0.330773 + 0.943710i \(0.392690\pi\)
\(770\) 0 0
\(771\) −44.2192 −1.59252
\(772\) 0 0
\(773\) 40.3154 1.45005 0.725023 0.688725i \(-0.241829\pi\)
0.725023 + 0.688725i \(0.241829\pi\)
\(774\) 0 0
\(775\) 5.40281 0.194075
\(776\) 0 0
\(777\) 0.421554 0.0151232
\(778\) 0 0
\(779\) −1.54655 −0.0554110
\(780\) 0 0
\(781\) −30.6734 −1.09758
\(782\) 0 0
\(783\) −15.0330 −0.537236
\(784\) 0 0
\(785\) −21.4081 −0.764087
\(786\) 0 0
\(787\) 8.00664 0.285406 0.142703 0.989766i \(-0.454421\pi\)
0.142703 + 0.989766i \(0.454421\pi\)
\(788\) 0 0
\(789\) 16.0969 0.573065
\(790\) 0 0
\(791\) 54.1531 1.92546
\(792\) 0 0
\(793\) 0.467908 0.0166159
\(794\) 0 0
\(795\) −38.5292 −1.36649
\(796\) 0 0
\(797\) 35.5703 1.25996 0.629982 0.776610i \(-0.283062\pi\)
0.629982 + 0.776610i \(0.283062\pi\)
\(798\) 0 0
\(799\) −0.667897 −0.0236285
\(800\) 0 0
\(801\) 2.01918 0.0713442
\(802\) 0 0
\(803\) 89.6879 3.16502
\(804\) 0 0
\(805\) 7.52574 0.265248
\(806\) 0 0
\(807\) 7.92955 0.279133
\(808\) 0 0
\(809\) −19.4000 −0.682069 −0.341034 0.940051i \(-0.610777\pi\)
−0.341034 + 0.940051i \(0.610777\pi\)
\(810\) 0 0
\(811\) −24.2890 −0.852901 −0.426450 0.904511i \(-0.640236\pi\)
−0.426450 + 0.904511i \(0.640236\pi\)
\(812\) 0 0
\(813\) −16.7225 −0.586483
\(814\) 0 0
\(815\) −6.55464 −0.229599
\(816\) 0 0
\(817\) 8.95138 0.313169
\(818\) 0 0
\(819\) 0.686483 0.0239877
\(820\) 0 0
\(821\) 0.547649 0.0191131 0.00955654 0.999954i \(-0.496958\pi\)
0.00955654 + 0.999954i \(0.496958\pi\)
\(822\) 0 0
\(823\) 25.4942 0.888671 0.444336 0.895860i \(-0.353440\pi\)
0.444336 + 0.895860i \(0.353440\pi\)
\(824\) 0 0
\(825\) 104.232 3.62888
\(826\) 0 0
\(827\) −48.8677 −1.69930 −0.849648 0.527351i \(-0.823185\pi\)
−0.849648 + 0.527351i \(0.823185\pi\)
\(828\) 0 0
\(829\) 38.4309 1.33476 0.667380 0.744717i \(-0.267416\pi\)
0.667380 + 0.744717i \(0.267416\pi\)
\(830\) 0 0
\(831\) 5.96320 0.206861
\(832\) 0 0
\(833\) 10.9260 0.378564
\(834\) 0 0
\(835\) 39.4329 1.36463
\(836\) 0 0
\(837\) 2.52916 0.0874207
\(838\) 0 0
\(839\) 21.9842 0.758980 0.379490 0.925196i \(-0.376099\pi\)
0.379490 + 0.925196i \(0.376099\pi\)
\(840\) 0 0
\(841\) −21.6516 −0.746607
\(842\) 0 0
\(843\) −35.4964 −1.22256
\(844\) 0 0
\(845\) 52.9188 1.82046
\(846\) 0 0
\(847\) −81.0551 −2.78509
\(848\) 0 0
\(849\) 8.79868 0.301970
\(850\) 0 0
\(851\) 0.0307546 0.00105425
\(852\) 0 0
\(853\) −17.0540 −0.583919 −0.291960 0.956431i \(-0.594307\pi\)
−0.291960 + 0.956431i \(0.594307\pi\)
\(854\) 0 0
\(855\) 2.15525 0.0737081
\(856\) 0 0
\(857\) −22.4244 −0.766004 −0.383002 0.923747i \(-0.625110\pi\)
−0.383002 + 0.923747i \(0.625110\pi\)
\(858\) 0 0
\(859\) 19.6310 0.669801 0.334900 0.942254i \(-0.391297\pi\)
0.334900 + 0.942254i \(0.391297\pi\)
\(860\) 0 0
\(861\) −9.72463 −0.331414
\(862\) 0 0
\(863\) −23.1648 −0.788538 −0.394269 0.918995i \(-0.629002\pi\)
−0.394269 + 0.918995i \(0.629002\pi\)
\(864\) 0 0
\(865\) −38.3211 −1.30296
\(866\) 0 0
\(867\) 24.4129 0.829107
\(868\) 0 0
\(869\) 5.59278 0.189722
\(870\) 0 0
\(871\) 0.934724 0.0316719
\(872\) 0 0
\(873\) 3.59706 0.121742
\(874\) 0 0
\(875\) 112.320 3.79712
\(876\) 0 0
\(877\) −40.9242 −1.38191 −0.690956 0.722897i \(-0.742810\pi\)
−0.690956 + 0.722897i \(0.742810\pi\)
\(878\) 0 0
\(879\) 10.0442 0.338782
\(880\) 0 0
\(881\) −55.6472 −1.87480 −0.937401 0.348253i \(-0.886775\pi\)
−0.937401 + 0.348253i \(0.886775\pi\)
\(882\) 0 0
\(883\) −11.1100 −0.373880 −0.186940 0.982371i \(-0.559857\pi\)
−0.186940 + 0.982371i \(0.559857\pi\)
\(884\) 0 0
\(885\) 27.7537 0.932931
\(886\) 0 0
\(887\) 42.3166 1.42085 0.710426 0.703772i \(-0.248502\pi\)
0.710426 + 0.703772i \(0.248502\pi\)
\(888\) 0 0
\(889\) 24.3405 0.816355
\(890\) 0 0
\(891\) 39.9826 1.33947
\(892\) 0 0
\(893\) −0.548674 −0.0183607
\(894\) 0 0
\(895\) −95.5947 −3.19538
\(896\) 0 0
\(897\) −0.236048 −0.00788142
\(898\) 0 0
\(899\) −1.23630 −0.0412328
\(900\) 0 0
\(901\) −7.26357 −0.241985
\(902\) 0 0
\(903\) 56.2857 1.87307
\(904\) 0 0
\(905\) −38.9422 −1.29448
\(906\) 0 0
\(907\) 42.7786 1.42044 0.710220 0.703980i \(-0.248595\pi\)
0.710220 + 0.703980i \(0.248595\pi\)
\(908\) 0 0
\(909\) −0.605606 −0.0200867
\(910\) 0 0
\(911\) −10.3474 −0.342824 −0.171412 0.985199i \(-0.554833\pi\)
−0.171412 + 0.985199i \(0.554833\pi\)
\(912\) 0 0
\(913\) −20.7603 −0.687064
\(914\) 0 0
\(915\) 9.23713 0.305370
\(916\) 0 0
\(917\) 14.1363 0.466823
\(918\) 0 0
\(919\) −49.5599 −1.63483 −0.817415 0.576049i \(-0.804594\pi\)
−0.817415 + 0.576049i \(0.804594\pi\)
\(920\) 0 0
\(921\) −19.3760 −0.638462
\(922\) 0 0
\(923\) 1.79387 0.0590461
\(924\) 0 0
\(925\) 0.794215 0.0261136
\(926\) 0 0
\(927\) −1.74812 −0.0574159
\(928\) 0 0
\(929\) −41.6654 −1.36700 −0.683498 0.729952i \(-0.739542\pi\)
−0.683498 + 0.729952i \(0.739542\pi\)
\(930\) 0 0
\(931\) 8.97566 0.294165
\(932\) 0 0
\(933\) −12.9974 −0.425515
\(934\) 0 0
\(935\) 27.9434 0.913846
\(936\) 0 0
\(937\) −22.6064 −0.738518 −0.369259 0.929326i \(-0.620389\pi\)
−0.369259 + 0.929326i \(0.620389\pi\)
\(938\) 0 0
\(939\) −37.4548 −1.22229
\(940\) 0 0
\(941\) 37.4668 1.22138 0.610692 0.791868i \(-0.290891\pi\)
0.610692 + 0.791868i \(0.290891\pi\)
\(942\) 0 0
\(943\) −0.709462 −0.0231033
\(944\) 0 0
\(945\) 90.9778 2.95951
\(946\) 0 0
\(947\) 58.3077 1.89474 0.947372 0.320135i \(-0.103728\pi\)
0.947372 + 0.320135i \(0.103728\pi\)
\(948\) 0 0
\(949\) −5.24522 −0.170267
\(950\) 0 0
\(951\) 38.2882 1.24158
\(952\) 0 0
\(953\) 26.4350 0.856312 0.428156 0.903705i \(-0.359163\pi\)
0.428156 + 0.903705i \(0.359163\pi\)
\(954\) 0 0
\(955\) 54.1063 1.75084
\(956\) 0 0
\(957\) −23.8508 −0.770986
\(958\) 0 0
\(959\) 45.9209 1.48286
\(960\) 0 0
\(961\) −30.7920 −0.993290
\(962\) 0 0
\(963\) −2.71007 −0.0873309
\(964\) 0 0
\(965\) −7.19124 −0.231494
\(966\) 0 0
\(967\) 38.9051 1.25111 0.625553 0.780182i \(-0.284874\pi\)
0.625553 + 0.780182i \(0.284874\pi\)
\(968\) 0 0
\(969\) −1.91502 −0.0615194
\(970\) 0 0
\(971\) −26.8772 −0.862531 −0.431266 0.902225i \(-0.641933\pi\)
−0.431266 + 0.902225i \(0.641933\pi\)
\(972\) 0 0
\(973\) −61.2732 −1.96433
\(974\) 0 0
\(975\) −6.09578 −0.195221
\(976\) 0 0
\(977\) 14.6472 0.468607 0.234303 0.972163i \(-0.424719\pi\)
0.234303 + 0.972163i \(0.424719\pi\)
\(978\) 0 0
\(979\) 21.5060 0.687335
\(980\) 0 0
\(981\) −10.5409 −0.336545
\(982\) 0 0
\(983\) −15.5276 −0.495255 −0.247627 0.968855i \(-0.579651\pi\)
−0.247627 + 0.968855i \(0.579651\pi\)
\(984\) 0 0
\(985\) −70.3680 −2.24211
\(986\) 0 0
\(987\) −3.45003 −0.109816
\(988\) 0 0
\(989\) 4.10633 0.130574
\(990\) 0 0
\(991\) −25.8684 −0.821738 −0.410869 0.911694i \(-0.634775\pi\)
−0.410869 + 0.911694i \(0.634775\pi\)
\(992\) 0 0
\(993\) −38.2958 −1.21528
\(994\) 0 0
\(995\) 88.1938 2.79593
\(996\) 0 0
\(997\) 57.1565 1.81017 0.905083 0.425235i \(-0.139809\pi\)
0.905083 + 0.425235i \(0.139809\pi\)
\(998\) 0 0
\(999\) 0.371788 0.0117629
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 \(a_p\))