Properties

Label 6004.2.a.g.1.23
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 1.23
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.40855 q^{3} +0.936776 q^{5} -3.55545 q^{7} +2.80113 q^{9} +O(q^{10})\) \(q+2.40855 q^{3} +0.936776 q^{5} -3.55545 q^{7} +2.80113 q^{9} -1.35047 q^{11} -2.20428 q^{13} +2.25627 q^{15} +1.19197 q^{17} +1.00000 q^{19} -8.56349 q^{21} -5.26841 q^{23} -4.12245 q^{25} -0.478999 q^{27} +9.37775 q^{29} +0.532765 q^{31} -3.25268 q^{33} -3.33066 q^{35} +4.51687 q^{37} -5.30913 q^{39} -8.05936 q^{41} +12.1234 q^{43} +2.62403 q^{45} -0.711383 q^{47} +5.64123 q^{49} +2.87092 q^{51} -12.0299 q^{53} -1.26509 q^{55} +2.40855 q^{57} -7.85491 q^{59} -11.6631 q^{61} -9.95926 q^{63} -2.06492 q^{65} +7.91918 q^{67} -12.6892 q^{69} -11.5274 q^{71} -7.79171 q^{73} -9.92914 q^{75} +4.80153 q^{77} -1.00000 q^{79} -9.55707 q^{81} -8.02598 q^{83} +1.11661 q^{85} +22.5868 q^{87} +14.4395 q^{89} +7.83722 q^{91} +1.28319 q^{93} +0.936776 q^{95} -15.0900 q^{97} -3.78284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 2.40855 1.39058 0.695289 0.718730i \(-0.255276\pi\)
0.695289 + 0.718730i \(0.255276\pi\)
\(4\) 0 0
\(5\) 0.936776 0.418939 0.209469 0.977815i \(-0.432826\pi\)
0.209469 + 0.977815i \(0.432826\pi\)
\(6\) 0 0
\(7\) −3.55545 −1.34383 −0.671917 0.740627i \(-0.734529\pi\)
−0.671917 + 0.740627i \(0.734529\pi\)
\(8\) 0 0
\(9\) 2.80113 0.933709
\(10\) 0 0
\(11\) −1.35047 −0.407182 −0.203591 0.979056i \(-0.565261\pi\)
−0.203591 + 0.979056i \(0.565261\pi\)
\(12\) 0 0
\(13\) −2.20428 −0.611358 −0.305679 0.952135i \(-0.598883\pi\)
−0.305679 + 0.952135i \(0.598883\pi\)
\(14\) 0 0
\(15\) 2.25627 0.582567
\(16\) 0 0
\(17\) 1.19197 0.289095 0.144547 0.989498i \(-0.453827\pi\)
0.144547 + 0.989498i \(0.453827\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −8.56349 −1.86871
\(22\) 0 0
\(23\) −5.26841 −1.09854 −0.549269 0.835645i \(-0.685094\pi\)
−0.549269 + 0.835645i \(0.685094\pi\)
\(24\) 0 0
\(25\) −4.12245 −0.824490
\(26\) 0 0
\(27\) −0.478999 −0.0921834
\(28\) 0 0
\(29\) 9.37775 1.74140 0.870702 0.491810i \(-0.163665\pi\)
0.870702 + 0.491810i \(0.163665\pi\)
\(30\) 0 0
\(31\) 0.532765 0.0956874 0.0478437 0.998855i \(-0.484765\pi\)
0.0478437 + 0.998855i \(0.484765\pi\)
\(32\) 0 0
\(33\) −3.25268 −0.566218
\(34\) 0 0
\(35\) −3.33066 −0.562984
\(36\) 0 0
\(37\) 4.51687 0.742568 0.371284 0.928519i \(-0.378918\pi\)
0.371284 + 0.928519i \(0.378918\pi\)
\(38\) 0 0
\(39\) −5.30913 −0.850142
\(40\) 0 0
\(41\) −8.05936 −1.25866 −0.629330 0.777138i \(-0.716671\pi\)
−0.629330 + 0.777138i \(0.716671\pi\)
\(42\) 0 0
\(43\) 12.1234 1.84881 0.924403 0.381418i \(-0.124564\pi\)
0.924403 + 0.381418i \(0.124564\pi\)
\(44\) 0 0
\(45\) 2.62403 0.391167
\(46\) 0 0
\(47\) −0.711383 −0.103766 −0.0518829 0.998653i \(-0.516522\pi\)
−0.0518829 + 0.998653i \(0.516522\pi\)
\(48\) 0 0
\(49\) 5.64123 0.805890
\(50\) 0 0
\(51\) 2.87092 0.402009
\(52\) 0 0
\(53\) −12.0299 −1.65243 −0.826215 0.563356i \(-0.809510\pi\)
−0.826215 + 0.563356i \(0.809510\pi\)
\(54\) 0 0
\(55\) −1.26509 −0.170584
\(56\) 0 0
\(57\) 2.40855 0.319021
\(58\) 0 0
\(59\) −7.85491 −1.02262 −0.511311 0.859396i \(-0.670840\pi\)
−0.511311 + 0.859396i \(0.670840\pi\)
\(60\) 0 0
\(61\) −11.6631 −1.49330 −0.746652 0.665215i \(-0.768340\pi\)
−0.746652 + 0.665215i \(0.768340\pi\)
\(62\) 0 0
\(63\) −9.95926 −1.25475
\(64\) 0 0
\(65\) −2.06492 −0.256122
\(66\) 0 0
\(67\) 7.91918 0.967481 0.483741 0.875211i \(-0.339278\pi\)
0.483741 + 0.875211i \(0.339278\pi\)
\(68\) 0 0
\(69\) −12.6892 −1.52760
\(70\) 0 0
\(71\) −11.5274 −1.36805 −0.684026 0.729458i \(-0.739773\pi\)
−0.684026 + 0.729458i \(0.739773\pi\)
\(72\) 0 0
\(73\) −7.79171 −0.911951 −0.455975 0.889992i \(-0.650710\pi\)
−0.455975 + 0.889992i \(0.650710\pi\)
\(74\) 0 0
\(75\) −9.92914 −1.14652
\(76\) 0 0
\(77\) 4.80153 0.547185
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −9.55707 −1.06190
\(82\) 0 0
\(83\) −8.02598 −0.880965 −0.440483 0.897761i \(-0.645193\pi\)
−0.440483 + 0.897761i \(0.645193\pi\)
\(84\) 0 0
\(85\) 1.11661 0.121113
\(86\) 0 0
\(87\) 22.5868 2.42156
\(88\) 0 0
\(89\) 14.4395 1.53059 0.765294 0.643681i \(-0.222593\pi\)
0.765294 + 0.643681i \(0.222593\pi\)
\(90\) 0 0
\(91\) 7.83722 0.821564
\(92\) 0 0
\(93\) 1.28319 0.133061
\(94\) 0 0
\(95\) 0.936776 0.0961112
\(96\) 0 0
\(97\) −15.0900 −1.53216 −0.766080 0.642745i \(-0.777796\pi\)
−0.766080 + 0.642745i \(0.777796\pi\)
\(98\) 0 0
\(99\) −3.78284 −0.380189
\(100\) 0 0
\(101\) −11.2921 −1.12361 −0.561805 0.827269i \(-0.689893\pi\)
−0.561805 + 0.827269i \(0.689893\pi\)
\(102\) 0 0
\(103\) −10.5594 −1.04044 −0.520222 0.854031i \(-0.674151\pi\)
−0.520222 + 0.854031i \(0.674151\pi\)
\(104\) 0 0
\(105\) −8.02207 −0.782874
\(106\) 0 0
\(107\) −7.75718 −0.749915 −0.374957 0.927042i \(-0.622343\pi\)
−0.374957 + 0.927042i \(0.622343\pi\)
\(108\) 0 0
\(109\) −17.2452 −1.65179 −0.825893 0.563827i \(-0.809329\pi\)
−0.825893 + 0.563827i \(0.809329\pi\)
\(110\) 0 0
\(111\) 10.8791 1.03260
\(112\) 0 0
\(113\) 12.0383 1.13247 0.566236 0.824243i \(-0.308399\pi\)
0.566236 + 0.824243i \(0.308399\pi\)
\(114\) 0 0
\(115\) −4.93532 −0.460221
\(116\) 0 0
\(117\) −6.17448 −0.570830
\(118\) 0 0
\(119\) −4.23798 −0.388495
\(120\) 0 0
\(121\) −9.17623 −0.834203
\(122\) 0 0
\(123\) −19.4114 −1.75027
\(124\) 0 0
\(125\) −8.54569 −0.764350
\(126\) 0 0
\(127\) 7.04160 0.624841 0.312420 0.949944i \(-0.398860\pi\)
0.312420 + 0.949944i \(0.398860\pi\)
\(128\) 0 0
\(129\) 29.1999 2.57091
\(130\) 0 0
\(131\) 11.8609 1.03629 0.518146 0.855292i \(-0.326622\pi\)
0.518146 + 0.855292i \(0.326622\pi\)
\(132\) 0 0
\(133\) −3.55545 −0.308297
\(134\) 0 0
\(135\) −0.448715 −0.0386192
\(136\) 0 0
\(137\) 2.92152 0.249602 0.124801 0.992182i \(-0.460171\pi\)
0.124801 + 0.992182i \(0.460171\pi\)
\(138\) 0 0
\(139\) −1.79325 −0.152101 −0.0760507 0.997104i \(-0.524231\pi\)
−0.0760507 + 0.997104i \(0.524231\pi\)
\(140\) 0 0
\(141\) −1.71340 −0.144295
\(142\) 0 0
\(143\) 2.97682 0.248934
\(144\) 0 0
\(145\) 8.78485 0.729542
\(146\) 0 0
\(147\) 13.5872 1.12065
\(148\) 0 0
\(149\) 10.6057 0.868851 0.434426 0.900708i \(-0.356951\pi\)
0.434426 + 0.900708i \(0.356951\pi\)
\(150\) 0 0
\(151\) 10.6241 0.864581 0.432290 0.901734i \(-0.357706\pi\)
0.432290 + 0.901734i \(0.357706\pi\)
\(152\) 0 0
\(153\) 3.33885 0.269930
\(154\) 0 0
\(155\) 0.499081 0.0400872
\(156\) 0 0
\(157\) −0.709557 −0.0566288 −0.0283144 0.999599i \(-0.509014\pi\)
−0.0283144 + 0.999599i \(0.509014\pi\)
\(158\) 0 0
\(159\) −28.9746 −2.29783
\(160\) 0 0
\(161\) 18.7316 1.47625
\(162\) 0 0
\(163\) −5.99174 −0.469310 −0.234655 0.972079i \(-0.575396\pi\)
−0.234655 + 0.972079i \(0.575396\pi\)
\(164\) 0 0
\(165\) −3.04703 −0.237211
\(166\) 0 0
\(167\) −1.48640 −0.115021 −0.0575107 0.998345i \(-0.518316\pi\)
−0.0575107 + 0.998345i \(0.518316\pi\)
\(168\) 0 0
\(169\) −8.14113 −0.626241
\(170\) 0 0
\(171\) 2.80113 0.214207
\(172\) 0 0
\(173\) −4.82189 −0.366601 −0.183301 0.983057i \(-0.558678\pi\)
−0.183301 + 0.983057i \(0.558678\pi\)
\(174\) 0 0
\(175\) 14.6572 1.10798
\(176\) 0 0
\(177\) −18.9190 −1.42204
\(178\) 0 0
\(179\) −3.48479 −0.260466 −0.130233 0.991483i \(-0.541572\pi\)
−0.130233 + 0.991483i \(0.541572\pi\)
\(180\) 0 0
\(181\) −7.53606 −0.560151 −0.280075 0.959978i \(-0.590359\pi\)
−0.280075 + 0.959978i \(0.590359\pi\)
\(182\) 0 0
\(183\) −28.0911 −2.07656
\(184\) 0 0
\(185\) 4.23129 0.311091
\(186\) 0 0
\(187\) −1.60972 −0.117714
\(188\) 0 0
\(189\) 1.70306 0.123879
\(190\) 0 0
\(191\) 8.70692 0.630011 0.315005 0.949090i \(-0.397994\pi\)
0.315005 + 0.949090i \(0.397994\pi\)
\(192\) 0 0
\(193\) −22.0259 −1.58546 −0.792730 0.609573i \(-0.791341\pi\)
−0.792730 + 0.609573i \(0.791341\pi\)
\(194\) 0 0
\(195\) −4.97347 −0.356157
\(196\) 0 0
\(197\) −24.7276 −1.76177 −0.880883 0.473335i \(-0.843050\pi\)
−0.880883 + 0.473335i \(0.843050\pi\)
\(198\) 0 0
\(199\) 10.6889 0.757716 0.378858 0.925455i \(-0.376317\pi\)
0.378858 + 0.925455i \(0.376317\pi\)
\(200\) 0 0
\(201\) 19.0738 1.34536
\(202\) 0 0
\(203\) −33.3421 −2.34016
\(204\) 0 0
\(205\) −7.54982 −0.527302
\(206\) 0 0
\(207\) −14.7575 −1.02572
\(208\) 0 0
\(209\) −1.35047 −0.0934139
\(210\) 0 0
\(211\) 16.3535 1.12582 0.562912 0.826517i \(-0.309681\pi\)
0.562912 + 0.826517i \(0.309681\pi\)
\(212\) 0 0
\(213\) −27.7644 −1.90238
\(214\) 0 0
\(215\) 11.3569 0.774537
\(216\) 0 0
\(217\) −1.89422 −0.128588
\(218\) 0 0
\(219\) −18.7667 −1.26814
\(220\) 0 0
\(221\) −2.62744 −0.176740
\(222\) 0 0
\(223\) −5.94491 −0.398101 −0.199050 0.979989i \(-0.563786\pi\)
−0.199050 + 0.979989i \(0.563786\pi\)
\(224\) 0 0
\(225\) −11.5475 −0.769834
\(226\) 0 0
\(227\) 17.8838 1.18699 0.593494 0.804838i \(-0.297748\pi\)
0.593494 + 0.804838i \(0.297748\pi\)
\(228\) 0 0
\(229\) −11.2213 −0.741528 −0.370764 0.928727i \(-0.620904\pi\)
−0.370764 + 0.928727i \(0.620904\pi\)
\(230\) 0 0
\(231\) 11.5647 0.760903
\(232\) 0 0
\(233\) −1.00557 −0.0658772 −0.0329386 0.999457i \(-0.510487\pi\)
−0.0329386 + 0.999457i \(0.510487\pi\)
\(234\) 0 0
\(235\) −0.666406 −0.0434716
\(236\) 0 0
\(237\) −2.40855 −0.156452
\(238\) 0 0
\(239\) −8.35601 −0.540506 −0.270253 0.962789i \(-0.587107\pi\)
−0.270253 + 0.962789i \(0.587107\pi\)
\(240\) 0 0
\(241\) −19.6842 −1.26797 −0.633987 0.773344i \(-0.718583\pi\)
−0.633987 + 0.773344i \(0.718583\pi\)
\(242\) 0 0
\(243\) −21.5817 −1.38447
\(244\) 0 0
\(245\) 5.28457 0.337619
\(246\) 0 0
\(247\) −2.20428 −0.140255
\(248\) 0 0
\(249\) −19.3310 −1.22505
\(250\) 0 0
\(251\) 28.7823 1.81672 0.908361 0.418187i \(-0.137334\pi\)
0.908361 + 0.418187i \(0.137334\pi\)
\(252\) 0 0
\(253\) 7.11482 0.447305
\(254\) 0 0
\(255\) 2.68941 0.168417
\(256\) 0 0
\(257\) 22.0606 1.37610 0.688050 0.725663i \(-0.258467\pi\)
0.688050 + 0.725663i \(0.258467\pi\)
\(258\) 0 0
\(259\) −16.0595 −0.997888
\(260\) 0 0
\(261\) 26.2683 1.62596
\(262\) 0 0
\(263\) 29.8473 1.84046 0.920232 0.391374i \(-0.128000\pi\)
0.920232 + 0.391374i \(0.128000\pi\)
\(264\) 0 0
\(265\) −11.2693 −0.692267
\(266\) 0 0
\(267\) 34.7784 2.12840
\(268\) 0 0
\(269\) 27.5517 1.67986 0.839929 0.542697i \(-0.182597\pi\)
0.839929 + 0.542697i \(0.182597\pi\)
\(270\) 0 0
\(271\) −26.2579 −1.59506 −0.797528 0.603282i \(-0.793859\pi\)
−0.797528 + 0.603282i \(0.793859\pi\)
\(272\) 0 0
\(273\) 18.8764 1.14245
\(274\) 0 0
\(275\) 5.56724 0.335717
\(276\) 0 0
\(277\) 7.00196 0.420707 0.210353 0.977625i \(-0.432539\pi\)
0.210353 + 0.977625i \(0.432539\pi\)
\(278\) 0 0
\(279\) 1.49234 0.0893441
\(280\) 0 0
\(281\) 10.5668 0.630364 0.315182 0.949031i \(-0.397934\pi\)
0.315182 + 0.949031i \(0.397934\pi\)
\(282\) 0 0
\(283\) 12.4334 0.739089 0.369544 0.929213i \(-0.379514\pi\)
0.369544 + 0.929213i \(0.379514\pi\)
\(284\) 0 0
\(285\) 2.25627 0.133650
\(286\) 0 0
\(287\) 28.6547 1.69143
\(288\) 0 0
\(289\) −15.5792 −0.916424
\(290\) 0 0
\(291\) −36.3451 −2.13059
\(292\) 0 0
\(293\) −4.15069 −0.242486 −0.121243 0.992623i \(-0.538688\pi\)
−0.121243 + 0.992623i \(0.538688\pi\)
\(294\) 0 0
\(295\) −7.35829 −0.428416
\(296\) 0 0
\(297\) 0.646874 0.0375354
\(298\) 0 0
\(299\) 11.6131 0.671601
\(300\) 0 0
\(301\) −43.1042 −2.48449
\(302\) 0 0
\(303\) −27.1977 −1.56247
\(304\) 0 0
\(305\) −10.9257 −0.625603
\(306\) 0 0
\(307\) 25.2948 1.44365 0.721825 0.692075i \(-0.243303\pi\)
0.721825 + 0.692075i \(0.243303\pi\)
\(308\) 0 0
\(309\) −25.4328 −1.44682
\(310\) 0 0
\(311\) 11.6910 0.662935 0.331467 0.943467i \(-0.392456\pi\)
0.331467 + 0.943467i \(0.392456\pi\)
\(312\) 0 0
\(313\) 18.3489 1.03714 0.518570 0.855035i \(-0.326465\pi\)
0.518570 + 0.855035i \(0.326465\pi\)
\(314\) 0 0
\(315\) −9.32960 −0.525663
\(316\) 0 0
\(317\) −20.9077 −1.17429 −0.587147 0.809480i \(-0.699749\pi\)
−0.587147 + 0.809480i \(0.699749\pi\)
\(318\) 0 0
\(319\) −12.6644 −0.709069
\(320\) 0 0
\(321\) −18.6836 −1.04282
\(322\) 0 0
\(323\) 1.19197 0.0663229
\(324\) 0 0
\(325\) 9.08705 0.504059
\(326\) 0 0
\(327\) −41.5359 −2.29694
\(328\) 0 0
\(329\) 2.52929 0.139444
\(330\) 0 0
\(331\) −12.0338 −0.661439 −0.330719 0.943729i \(-0.607291\pi\)
−0.330719 + 0.943729i \(0.607291\pi\)
\(332\) 0 0
\(333\) 12.6523 0.693342
\(334\) 0 0
\(335\) 7.41849 0.405316
\(336\) 0 0
\(337\) 34.6249 1.88614 0.943069 0.332596i \(-0.107925\pi\)
0.943069 + 0.332596i \(0.107925\pi\)
\(338\) 0 0
\(339\) 28.9950 1.57479
\(340\) 0 0
\(341\) −0.719482 −0.0389622
\(342\) 0 0
\(343\) 4.83105 0.260852
\(344\) 0 0
\(345\) −11.8870 −0.639973
\(346\) 0 0
\(347\) −22.9817 −1.23372 −0.616862 0.787071i \(-0.711596\pi\)
−0.616862 + 0.787071i \(0.711596\pi\)
\(348\) 0 0
\(349\) 26.7221 1.43040 0.715202 0.698918i \(-0.246335\pi\)
0.715202 + 0.698918i \(0.246335\pi\)
\(350\) 0 0
\(351\) 1.05585 0.0563571
\(352\) 0 0
\(353\) 28.4540 1.51445 0.757227 0.653151i \(-0.226554\pi\)
0.757227 + 0.653151i \(0.226554\pi\)
\(354\) 0 0
\(355\) −10.7986 −0.573130
\(356\) 0 0
\(357\) −10.2074 −0.540233
\(358\) 0 0
\(359\) 6.68284 0.352707 0.176354 0.984327i \(-0.443570\pi\)
0.176354 + 0.984327i \(0.443570\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −22.1014 −1.16002
\(364\) 0 0
\(365\) −7.29909 −0.382052
\(366\) 0 0
\(367\) −3.58609 −0.187192 −0.0935961 0.995610i \(-0.529836\pi\)
−0.0935961 + 0.995610i \(0.529836\pi\)
\(368\) 0 0
\(369\) −22.5753 −1.17522
\(370\) 0 0
\(371\) 42.7716 2.22059
\(372\) 0 0
\(373\) 17.1091 0.885876 0.442938 0.896552i \(-0.353936\pi\)
0.442938 + 0.896552i \(0.353936\pi\)
\(374\) 0 0
\(375\) −20.5827 −1.06289
\(376\) 0 0
\(377\) −20.6712 −1.06462
\(378\) 0 0
\(379\) 23.0695 1.18500 0.592500 0.805570i \(-0.298141\pi\)
0.592500 + 0.805570i \(0.298141\pi\)
\(380\) 0 0
\(381\) 16.9601 0.868890
\(382\) 0 0
\(383\) 10.6418 0.543768 0.271884 0.962330i \(-0.412353\pi\)
0.271884 + 0.962330i \(0.412353\pi\)
\(384\) 0 0
\(385\) 4.49796 0.229237
\(386\) 0 0
\(387\) 33.9592 1.72625
\(388\) 0 0
\(389\) −35.9357 −1.82201 −0.911006 0.412392i \(-0.864693\pi\)
−0.911006 + 0.412392i \(0.864693\pi\)
\(390\) 0 0
\(391\) −6.27977 −0.317582
\(392\) 0 0
\(393\) 28.5676 1.44105
\(394\) 0 0
\(395\) −0.936776 −0.0471343
\(396\) 0 0
\(397\) 15.8086 0.793413 0.396707 0.917945i \(-0.370153\pi\)
0.396707 + 0.917945i \(0.370153\pi\)
\(398\) 0 0
\(399\) −8.56349 −0.428711
\(400\) 0 0
\(401\) −8.62286 −0.430605 −0.215302 0.976547i \(-0.569074\pi\)
−0.215302 + 0.976547i \(0.569074\pi\)
\(402\) 0 0
\(403\) −1.17436 −0.0584993
\(404\) 0 0
\(405\) −8.95283 −0.444870
\(406\) 0 0
\(407\) −6.09989 −0.302360
\(408\) 0 0
\(409\) 6.61999 0.327338 0.163669 0.986515i \(-0.447667\pi\)
0.163669 + 0.986515i \(0.447667\pi\)
\(410\) 0 0
\(411\) 7.03663 0.347091
\(412\) 0 0
\(413\) 27.9277 1.37423
\(414\) 0 0
\(415\) −7.51854 −0.369071
\(416\) 0 0
\(417\) −4.31913 −0.211509
\(418\) 0 0
\(419\) 6.46135 0.315658 0.157829 0.987466i \(-0.449551\pi\)
0.157829 + 0.987466i \(0.449551\pi\)
\(420\) 0 0
\(421\) 12.3262 0.600740 0.300370 0.953823i \(-0.402890\pi\)
0.300370 + 0.953823i \(0.402890\pi\)
\(422\) 0 0
\(423\) −1.99267 −0.0968871
\(424\) 0 0
\(425\) −4.91383 −0.238356
\(426\) 0 0
\(427\) 41.4675 2.00675
\(428\) 0 0
\(429\) 7.16982 0.346162
\(430\) 0 0
\(431\) −7.70060 −0.370925 −0.185463 0.982651i \(-0.559378\pi\)
−0.185463 + 0.982651i \(0.559378\pi\)
\(432\) 0 0
\(433\) 40.6940 1.95563 0.977815 0.209472i \(-0.0671745\pi\)
0.977815 + 0.209472i \(0.0671745\pi\)
\(434\) 0 0
\(435\) 21.1588 1.01449
\(436\) 0 0
\(437\) −5.26841 −0.252022
\(438\) 0 0
\(439\) −0.756586 −0.0361099 −0.0180549 0.999837i \(-0.505747\pi\)
−0.0180549 + 0.999837i \(0.505747\pi\)
\(440\) 0 0
\(441\) 15.8018 0.752466
\(442\) 0 0
\(443\) −8.48277 −0.403029 −0.201514 0.979486i \(-0.564586\pi\)
−0.201514 + 0.979486i \(0.564586\pi\)
\(444\) 0 0
\(445\) 13.5266 0.641223
\(446\) 0 0
\(447\) 25.5443 1.20821
\(448\) 0 0
\(449\) 14.6460 0.691188 0.345594 0.938384i \(-0.387677\pi\)
0.345594 + 0.938384i \(0.387677\pi\)
\(450\) 0 0
\(451\) 10.8839 0.512504
\(452\) 0 0
\(453\) 25.5888 1.20227
\(454\) 0 0
\(455\) 7.34172 0.344185
\(456\) 0 0
\(457\) −24.2432 −1.13405 −0.567024 0.823701i \(-0.691905\pi\)
−0.567024 + 0.823701i \(0.691905\pi\)
\(458\) 0 0
\(459\) −0.570952 −0.0266497
\(460\) 0 0
\(461\) −7.26290 −0.338267 −0.169134 0.985593i \(-0.554097\pi\)
−0.169134 + 0.985593i \(0.554097\pi\)
\(462\) 0 0
\(463\) 8.47744 0.393980 0.196990 0.980405i \(-0.436883\pi\)
0.196990 + 0.980405i \(0.436883\pi\)
\(464\) 0 0
\(465\) 1.20206 0.0557443
\(466\) 0 0
\(467\) −3.96076 −0.183282 −0.0916411 0.995792i \(-0.529211\pi\)
−0.0916411 + 0.995792i \(0.529211\pi\)
\(468\) 0 0
\(469\) −28.1562 −1.30013
\(470\) 0 0
\(471\) −1.70900 −0.0787468
\(472\) 0 0
\(473\) −16.3723 −0.752800
\(474\) 0 0
\(475\) −4.12245 −0.189151
\(476\) 0 0
\(477\) −33.6972 −1.54289
\(478\) 0 0
\(479\) −19.2114 −0.877792 −0.438896 0.898538i \(-0.644630\pi\)
−0.438896 + 0.898538i \(0.644630\pi\)
\(480\) 0 0
\(481\) −9.95645 −0.453975
\(482\) 0 0
\(483\) 45.1159 2.05285
\(484\) 0 0
\(485\) −14.1360 −0.641882
\(486\) 0 0
\(487\) 39.5738 1.79326 0.896629 0.442783i \(-0.146009\pi\)
0.896629 + 0.442783i \(0.146009\pi\)
\(488\) 0 0
\(489\) −14.4314 −0.652612
\(490\) 0 0
\(491\) −38.1386 −1.72117 −0.860585 0.509308i \(-0.829902\pi\)
−0.860585 + 0.509308i \(0.829902\pi\)
\(492\) 0 0
\(493\) 11.1780 0.503431
\(494\) 0 0
\(495\) −3.54367 −0.159276
\(496\) 0 0
\(497\) 40.9851 1.83843
\(498\) 0 0
\(499\) 7.47262 0.334520 0.167260 0.985913i \(-0.446508\pi\)
0.167260 + 0.985913i \(0.446508\pi\)
\(500\) 0 0
\(501\) −3.58008 −0.159946
\(502\) 0 0
\(503\) −31.9768 −1.42578 −0.712888 0.701277i \(-0.752613\pi\)
−0.712888 + 0.701277i \(0.752613\pi\)
\(504\) 0 0
\(505\) −10.5782 −0.470724
\(506\) 0 0
\(507\) −19.6083 −0.870837
\(508\) 0 0
\(509\) 6.15479 0.272806 0.136403 0.990653i \(-0.456446\pi\)
0.136403 + 0.990653i \(0.456446\pi\)
\(510\) 0 0
\(511\) 27.7030 1.22551
\(512\) 0 0
\(513\) −0.478999 −0.0211483
\(514\) 0 0
\(515\) −9.89175 −0.435883
\(516\) 0 0
\(517\) 0.960701 0.0422516
\(518\) 0 0
\(519\) −11.6138 −0.509788
\(520\) 0 0
\(521\) −9.55471 −0.418599 −0.209300 0.977852i \(-0.567118\pi\)
−0.209300 + 0.977852i \(0.567118\pi\)
\(522\) 0 0
\(523\) −4.66319 −0.203907 −0.101954 0.994789i \(-0.532509\pi\)
−0.101954 + 0.994789i \(0.532509\pi\)
\(524\) 0 0
\(525\) 35.3026 1.54073
\(526\) 0 0
\(527\) 0.635038 0.0276627
\(528\) 0 0
\(529\) 4.75611 0.206787
\(530\) 0 0
\(531\) −22.0026 −0.954831
\(532\) 0 0
\(533\) 17.7651 0.769493
\(534\) 0 0
\(535\) −7.26674 −0.314169
\(536\) 0 0
\(537\) −8.39331 −0.362198
\(538\) 0 0
\(539\) −7.61830 −0.328144
\(540\) 0 0
\(541\) 12.9631 0.557326 0.278663 0.960389i \(-0.410109\pi\)
0.278663 + 0.960389i \(0.410109\pi\)
\(542\) 0 0
\(543\) −18.1510 −0.778934
\(544\) 0 0
\(545\) −16.1548 −0.691998
\(546\) 0 0
\(547\) −16.5915 −0.709403 −0.354701 0.934980i \(-0.615417\pi\)
−0.354701 + 0.934980i \(0.615417\pi\)
\(548\) 0 0
\(549\) −32.6697 −1.39431
\(550\) 0 0
\(551\) 9.37775 0.399506
\(552\) 0 0
\(553\) 3.55545 0.151193
\(554\) 0 0
\(555\) 10.1913 0.432596
\(556\) 0 0
\(557\) −4.94935 −0.209711 −0.104855 0.994487i \(-0.533438\pi\)
−0.104855 + 0.994487i \(0.533438\pi\)
\(558\) 0 0
\(559\) −26.7235 −1.13028
\(560\) 0 0
\(561\) −3.87709 −0.163691
\(562\) 0 0
\(563\) 35.4185 1.49271 0.746356 0.665547i \(-0.231802\pi\)
0.746356 + 0.665547i \(0.231802\pi\)
\(564\) 0 0
\(565\) 11.2772 0.474437
\(566\) 0 0
\(567\) 33.9797 1.42701
\(568\) 0 0
\(569\) −16.5398 −0.693385 −0.346693 0.937979i \(-0.612695\pi\)
−0.346693 + 0.937979i \(0.612695\pi\)
\(570\) 0 0
\(571\) 8.56503 0.358435 0.179218 0.983809i \(-0.442643\pi\)
0.179218 + 0.983809i \(0.442643\pi\)
\(572\) 0 0
\(573\) 20.9711 0.876080
\(574\) 0 0
\(575\) 21.7187 0.905734
\(576\) 0 0
\(577\) 19.7332 0.821503 0.410751 0.911747i \(-0.365266\pi\)
0.410751 + 0.911747i \(0.365266\pi\)
\(578\) 0 0
\(579\) −53.0506 −2.20471
\(580\) 0 0
\(581\) 28.5360 1.18387
\(582\) 0 0
\(583\) 16.2460 0.672839
\(584\) 0 0
\(585\) −5.78410 −0.239143
\(586\) 0 0
\(587\) 21.0990 0.870847 0.435423 0.900226i \(-0.356599\pi\)
0.435423 + 0.900226i \(0.356599\pi\)
\(588\) 0 0
\(589\) 0.532765 0.0219522
\(590\) 0 0
\(591\) −59.5576 −2.44987
\(592\) 0 0
\(593\) −22.0395 −0.905055 −0.452527 0.891751i \(-0.649477\pi\)
−0.452527 + 0.891751i \(0.649477\pi\)
\(594\) 0 0
\(595\) −3.97004 −0.162756
\(596\) 0 0
\(597\) 25.7448 1.05366
\(598\) 0 0
\(599\) −27.3069 −1.11573 −0.557866 0.829931i \(-0.688380\pi\)
−0.557866 + 0.829931i \(0.688380\pi\)
\(600\) 0 0
\(601\) 21.4409 0.874592 0.437296 0.899318i \(-0.355936\pi\)
0.437296 + 0.899318i \(0.355936\pi\)
\(602\) 0 0
\(603\) 22.1826 0.903346
\(604\) 0 0
\(605\) −8.59607 −0.349480
\(606\) 0 0
\(607\) −39.6812 −1.61061 −0.805305 0.592861i \(-0.797999\pi\)
−0.805305 + 0.592861i \(0.797999\pi\)
\(608\) 0 0
\(609\) −80.3063 −3.25417
\(610\) 0 0
\(611\) 1.56809 0.0634381
\(612\) 0 0
\(613\) −45.2810 −1.82888 −0.914441 0.404719i \(-0.867369\pi\)
−0.914441 + 0.404719i \(0.867369\pi\)
\(614\) 0 0
\(615\) −18.1841 −0.733255
\(616\) 0 0
\(617\) 29.4900 1.18722 0.593611 0.804752i \(-0.297702\pi\)
0.593611 + 0.804752i \(0.297702\pi\)
\(618\) 0 0
\(619\) 0.389269 0.0156460 0.00782302 0.999969i \(-0.497510\pi\)
0.00782302 + 0.999969i \(0.497510\pi\)
\(620\) 0 0
\(621\) 2.52356 0.101267
\(622\) 0 0
\(623\) −51.3391 −2.05686
\(624\) 0 0
\(625\) 12.6069 0.504274
\(626\) 0 0
\(627\) −3.25268 −0.129899
\(628\) 0 0
\(629\) 5.38396 0.214673
\(630\) 0 0
\(631\) 39.8486 1.58635 0.793174 0.608995i \(-0.208427\pi\)
0.793174 + 0.608995i \(0.208427\pi\)
\(632\) 0 0
\(633\) 39.3884 1.56555
\(634\) 0 0
\(635\) 6.59640 0.261770
\(636\) 0 0
\(637\) −12.4349 −0.492687
\(638\) 0 0
\(639\) −32.2897 −1.27736
\(640\) 0 0
\(641\) 48.5283 1.91675 0.958377 0.285506i \(-0.0921617\pi\)
0.958377 + 0.285506i \(0.0921617\pi\)
\(642\) 0 0
\(643\) 12.6395 0.498452 0.249226 0.968445i \(-0.419824\pi\)
0.249226 + 0.968445i \(0.419824\pi\)
\(644\) 0 0
\(645\) 27.3538 1.07705
\(646\) 0 0
\(647\) −1.24413 −0.0489117 −0.0244558 0.999701i \(-0.507785\pi\)
−0.0244558 + 0.999701i \(0.507785\pi\)
\(648\) 0 0
\(649\) 10.6078 0.416393
\(650\) 0 0
\(651\) −4.56232 −0.178812
\(652\) 0 0
\(653\) 9.93629 0.388837 0.194419 0.980919i \(-0.437718\pi\)
0.194419 + 0.980919i \(0.437718\pi\)
\(654\) 0 0
\(655\) 11.1110 0.434143
\(656\) 0 0
\(657\) −21.8256 −0.851496
\(658\) 0 0
\(659\) −7.53507 −0.293525 −0.146762 0.989172i \(-0.546885\pi\)
−0.146762 + 0.989172i \(0.546885\pi\)
\(660\) 0 0
\(661\) −12.8718 −0.500654 −0.250327 0.968161i \(-0.580538\pi\)
−0.250327 + 0.968161i \(0.580538\pi\)
\(662\) 0 0
\(663\) −6.32832 −0.245771
\(664\) 0 0
\(665\) −3.33066 −0.129157
\(666\) 0 0
\(667\) −49.4058 −1.91300
\(668\) 0 0
\(669\) −14.3186 −0.553590
\(670\) 0 0
\(671\) 15.7506 0.608046
\(672\) 0 0
\(673\) −30.4816 −1.17498 −0.587490 0.809231i \(-0.699884\pi\)
−0.587490 + 0.809231i \(0.699884\pi\)
\(674\) 0 0
\(675\) 1.97465 0.0760043
\(676\) 0 0
\(677\) 5.75782 0.221291 0.110646 0.993860i \(-0.464708\pi\)
0.110646 + 0.993860i \(0.464708\pi\)
\(678\) 0 0
\(679\) 53.6519 2.05897
\(680\) 0 0
\(681\) 43.0740 1.65060
\(682\) 0 0
\(683\) −27.0527 −1.03514 −0.517572 0.855640i \(-0.673164\pi\)
−0.517572 + 0.855640i \(0.673164\pi\)
\(684\) 0 0
\(685\) 2.73681 0.104568
\(686\) 0 0
\(687\) −27.0272 −1.03115
\(688\) 0 0
\(689\) 26.5172 1.01023
\(690\) 0 0
\(691\) −20.6559 −0.785787 −0.392894 0.919584i \(-0.628526\pi\)
−0.392894 + 0.919584i \(0.628526\pi\)
\(692\) 0 0
\(693\) 13.4497 0.510911
\(694\) 0 0
\(695\) −1.67987 −0.0637212
\(696\) 0 0
\(697\) −9.60650 −0.363872
\(698\) 0 0
\(699\) −2.42197 −0.0916074
\(700\) 0 0
\(701\) −37.0156 −1.39806 −0.699031 0.715092i \(-0.746385\pi\)
−0.699031 + 0.715092i \(0.746385\pi\)
\(702\) 0 0
\(703\) 4.51687 0.170357
\(704\) 0 0
\(705\) −1.60507 −0.0604506
\(706\) 0 0
\(707\) 40.1487 1.50995
\(708\) 0 0
\(709\) −32.2592 −1.21152 −0.605761 0.795647i \(-0.707131\pi\)
−0.605761 + 0.795647i \(0.707131\pi\)
\(710\) 0 0
\(711\) −2.80113 −0.105050
\(712\) 0 0
\(713\) −2.80682 −0.105116
\(714\) 0 0
\(715\) 2.78861 0.104288
\(716\) 0 0
\(717\) −20.1259 −0.751615
\(718\) 0 0
\(719\) −41.5279 −1.54873 −0.774365 0.632739i \(-0.781931\pi\)
−0.774365 + 0.632739i \(0.781931\pi\)
\(720\) 0 0
\(721\) 37.5433 1.39818
\(722\) 0 0
\(723\) −47.4105 −1.76322
\(724\) 0 0
\(725\) −38.6593 −1.43577
\(726\) 0 0
\(727\) −26.8936 −0.997428 −0.498714 0.866767i \(-0.666194\pi\)
−0.498714 + 0.866767i \(0.666194\pi\)
\(728\) 0 0
\(729\) −23.3095 −0.863314
\(730\) 0 0
\(731\) 14.4507 0.534480
\(732\) 0 0
\(733\) 25.5539 0.943856 0.471928 0.881637i \(-0.343558\pi\)
0.471928 + 0.881637i \(0.343558\pi\)
\(734\) 0 0
\(735\) 12.7282 0.469485
\(736\) 0 0
\(737\) −10.6946 −0.393941
\(738\) 0 0
\(739\) 50.0571 1.84138 0.920689 0.390297i \(-0.127628\pi\)
0.920689 + 0.390297i \(0.127628\pi\)
\(740\) 0 0
\(741\) −5.30913 −0.195036
\(742\) 0 0
\(743\) −37.9288 −1.39147 −0.695736 0.718297i \(-0.744922\pi\)
−0.695736 + 0.718297i \(0.744922\pi\)
\(744\) 0 0
\(745\) 9.93515 0.363996
\(746\) 0 0
\(747\) −22.4818 −0.822565
\(748\) 0 0
\(749\) 27.5803 1.00776
\(750\) 0 0
\(751\) −14.9353 −0.544998 −0.272499 0.962156i \(-0.587850\pi\)
−0.272499 + 0.962156i \(0.587850\pi\)
\(752\) 0 0
\(753\) 69.3237 2.52629
\(754\) 0 0
\(755\) 9.95244 0.362207
\(756\) 0 0
\(757\) 28.1795 1.02420 0.512100 0.858926i \(-0.328868\pi\)
0.512100 + 0.858926i \(0.328868\pi\)
\(758\) 0 0
\(759\) 17.1364 0.622013
\(760\) 0 0
\(761\) 14.9983 0.543687 0.271843 0.962342i \(-0.412367\pi\)
0.271843 + 0.962342i \(0.412367\pi\)
\(762\) 0 0
\(763\) 61.3143 2.21973
\(764\) 0 0
\(765\) 3.12776 0.113084
\(766\) 0 0
\(767\) 17.3144 0.625188
\(768\) 0 0
\(769\) 39.9234 1.43967 0.719837 0.694143i \(-0.244217\pi\)
0.719837 + 0.694143i \(0.244217\pi\)
\(770\) 0 0
\(771\) 53.1340 1.91358
\(772\) 0 0
\(773\) −38.7050 −1.39212 −0.696060 0.717983i \(-0.745065\pi\)
−0.696060 + 0.717983i \(0.745065\pi\)
\(774\) 0 0
\(775\) −2.19630 −0.0788933
\(776\) 0 0
\(777\) −38.6801 −1.38764
\(778\) 0 0
\(779\) −8.05936 −0.288757
\(780\) 0 0
\(781\) 15.5674 0.557046
\(782\) 0 0
\(783\) −4.49193 −0.160529
\(784\) 0 0
\(785\) −0.664696 −0.0237240
\(786\) 0 0
\(787\) −31.6872 −1.12953 −0.564763 0.825253i \(-0.691032\pi\)
−0.564763 + 0.825253i \(0.691032\pi\)
\(788\) 0 0
\(789\) 71.8888 2.55931
\(790\) 0 0
\(791\) −42.8017 −1.52185
\(792\) 0 0
\(793\) 25.7087 0.912944
\(794\) 0 0
\(795\) −27.1427 −0.962651
\(796\) 0 0
\(797\) 31.2900 1.10835 0.554175 0.832400i \(-0.313034\pi\)
0.554175 + 0.832400i \(0.313034\pi\)
\(798\) 0 0
\(799\) −0.847946 −0.0299982
\(800\) 0 0
\(801\) 40.4470 1.42912
\(802\) 0 0
\(803\) 10.5225 0.371330
\(804\) 0 0
\(805\) 17.5473 0.618460
\(806\) 0 0
\(807\) 66.3598 2.33597
\(808\) 0 0
\(809\) −2.39222 −0.0841060 −0.0420530 0.999115i \(-0.513390\pi\)
−0.0420530 + 0.999115i \(0.513390\pi\)
\(810\) 0 0
\(811\) −19.8488 −0.696984 −0.348492 0.937312i \(-0.613306\pi\)
−0.348492 + 0.937312i \(0.613306\pi\)
\(812\) 0 0
\(813\) −63.2436 −2.21805
\(814\) 0 0
\(815\) −5.61292 −0.196612
\(816\) 0 0
\(817\) 12.1234 0.424145
\(818\) 0 0
\(819\) 21.9530 0.767101
\(820\) 0 0
\(821\) −37.1381 −1.29613 −0.648064 0.761586i \(-0.724421\pi\)
−0.648064 + 0.761586i \(0.724421\pi\)
\(822\) 0 0
\(823\) −13.6028 −0.474165 −0.237082 0.971490i \(-0.576191\pi\)
−0.237082 + 0.971490i \(0.576191\pi\)
\(824\) 0 0
\(825\) 13.4090 0.466841
\(826\) 0 0
\(827\) 31.8329 1.10694 0.553469 0.832870i \(-0.313304\pi\)
0.553469 + 0.832870i \(0.313304\pi\)
\(828\) 0 0
\(829\) −36.8408 −1.27953 −0.639767 0.768569i \(-0.720969\pi\)
−0.639767 + 0.768569i \(0.720969\pi\)
\(830\) 0 0
\(831\) 16.8646 0.585026
\(832\) 0 0
\(833\) 6.72416 0.232978
\(834\) 0 0
\(835\) −1.39243 −0.0481869
\(836\) 0 0
\(837\) −0.255194 −0.00882079
\(838\) 0 0
\(839\) 18.1493 0.626584 0.313292 0.949657i \(-0.398568\pi\)
0.313292 + 0.949657i \(0.398568\pi\)
\(840\) 0 0
\(841\) 58.9422 2.03249
\(842\) 0 0
\(843\) 25.4508 0.876571
\(844\) 0 0
\(845\) −7.62642 −0.262357
\(846\) 0 0
\(847\) 32.6256 1.12103
\(848\) 0 0
\(849\) 29.9465 1.02776
\(850\) 0 0
\(851\) −23.7967 −0.815740
\(852\) 0 0
\(853\) 0.742831 0.0254341 0.0127170 0.999919i \(-0.495952\pi\)
0.0127170 + 0.999919i \(0.495952\pi\)
\(854\) 0 0
\(855\) 2.62403 0.0897398
\(856\) 0 0
\(857\) −6.22275 −0.212565 −0.106282 0.994336i \(-0.533895\pi\)
−0.106282 + 0.994336i \(0.533895\pi\)
\(858\) 0 0
\(859\) 14.9061 0.508589 0.254295 0.967127i \(-0.418157\pi\)
0.254295 + 0.967127i \(0.418157\pi\)
\(860\) 0 0
\(861\) 69.0163 2.35207
\(862\) 0 0
\(863\) 47.3403 1.61148 0.805742 0.592267i \(-0.201767\pi\)
0.805742 + 0.592267i \(0.201767\pi\)
\(864\) 0 0
\(865\) −4.51703 −0.153584
\(866\) 0 0
\(867\) −37.5234 −1.27436
\(868\) 0 0
\(869\) 1.35047 0.0458115
\(870\) 0 0
\(871\) −17.4561 −0.591478
\(872\) 0 0
\(873\) −42.2691 −1.43059
\(874\) 0 0
\(875\) 30.3838 1.02716
\(876\) 0 0
\(877\) −55.6779 −1.88011 −0.940054 0.341026i \(-0.889226\pi\)
−0.940054 + 0.341026i \(0.889226\pi\)
\(878\) 0 0
\(879\) −9.99715 −0.337196
\(880\) 0 0
\(881\) −23.9339 −0.806352 −0.403176 0.915122i \(-0.632094\pi\)
−0.403176 + 0.915122i \(0.632094\pi\)
\(882\) 0 0
\(883\) −41.9442 −1.41154 −0.705768 0.708444i \(-0.749398\pi\)
−0.705768 + 0.708444i \(0.749398\pi\)
\(884\) 0 0
\(885\) −17.7228 −0.595746
\(886\) 0 0
\(887\) 13.6209 0.457344 0.228672 0.973503i \(-0.426562\pi\)
0.228672 + 0.973503i \(0.426562\pi\)
\(888\) 0 0
\(889\) −25.0361 −0.839682
\(890\) 0 0
\(891\) 12.9065 0.432385
\(892\) 0 0
\(893\) −0.711383 −0.0238055
\(894\) 0 0
\(895\) −3.26447 −0.109119
\(896\) 0 0
\(897\) 27.9707 0.933914
\(898\) 0 0
\(899\) 4.99613 0.166630
\(900\) 0 0
\(901\) −14.3392 −0.477709
\(902\) 0 0
\(903\) −103.819 −3.45487
\(904\) 0 0
\(905\) −7.05960 −0.234669
\(906\) 0 0
\(907\) −17.6087 −0.584686 −0.292343 0.956313i \(-0.594435\pi\)
−0.292343 + 0.956313i \(0.594435\pi\)
\(908\) 0 0
\(909\) −31.6307 −1.04912
\(910\) 0 0
\(911\) −47.7812 −1.58306 −0.791531 0.611129i \(-0.790716\pi\)
−0.791531 + 0.611129i \(0.790716\pi\)
\(912\) 0 0
\(913\) 10.8388 0.358713
\(914\) 0 0
\(915\) −26.3151 −0.869950
\(916\) 0 0
\(917\) −42.1709 −1.39261
\(918\) 0 0
\(919\) −39.4394 −1.30099 −0.650493 0.759512i \(-0.725438\pi\)
−0.650493 + 0.759512i \(0.725438\pi\)
\(920\) 0 0
\(921\) 60.9238 2.00751
\(922\) 0 0
\(923\) 25.4097 0.836370
\(924\) 0 0
\(925\) −18.6206 −0.612240
\(926\) 0 0
\(927\) −29.5781 −0.971472
\(928\) 0 0
\(929\) 27.5847 0.905025 0.452513 0.891758i \(-0.350528\pi\)
0.452513 + 0.891758i \(0.350528\pi\)
\(930\) 0 0
\(931\) 5.64123 0.184884
\(932\) 0 0
\(933\) 28.1583 0.921863
\(934\) 0 0
\(935\) −1.50794 −0.0493150
\(936\) 0 0
\(937\) −58.3070 −1.90481 −0.952403 0.304841i \(-0.901397\pi\)
−0.952403 + 0.304841i \(0.901397\pi\)
\(938\) 0 0
\(939\) 44.1942 1.44222
\(940\) 0 0
\(941\) −32.4625 −1.05825 −0.529123 0.848545i \(-0.677479\pi\)
−0.529123 + 0.848545i \(0.677479\pi\)
\(942\) 0 0
\(943\) 42.4600 1.38269
\(944\) 0 0
\(945\) 1.59538 0.0518978
\(946\) 0 0
\(947\) 36.7606 1.19456 0.597279 0.802034i \(-0.296249\pi\)
0.597279 + 0.802034i \(0.296249\pi\)
\(948\) 0 0
\(949\) 17.1751 0.557529
\(950\) 0 0
\(951\) −50.3573 −1.63295
\(952\) 0 0
\(953\) −45.3134 −1.46784 −0.733922 0.679233i \(-0.762312\pi\)
−0.733922 + 0.679233i \(0.762312\pi\)
\(954\) 0 0
\(955\) 8.15644 0.263936
\(956\) 0 0
\(957\) −30.5028 −0.986015
\(958\) 0 0
\(959\) −10.3873 −0.335424
\(960\) 0 0
\(961\) −30.7162 −0.990844
\(962\) 0 0
\(963\) −21.7288 −0.700202
\(964\) 0 0
\(965\) −20.6333 −0.664211
\(966\) 0 0
\(967\) 8.36218 0.268909 0.134455 0.990920i \(-0.457072\pi\)
0.134455 + 0.990920i \(0.457072\pi\)
\(968\) 0 0
\(969\) 2.87092 0.0922272
\(970\) 0 0
\(971\) −41.6833 −1.33768 −0.668841 0.743405i \(-0.733209\pi\)
−0.668841 + 0.743405i \(0.733209\pi\)
\(972\) 0 0
\(973\) 6.37580 0.204399
\(974\) 0 0
\(975\) 21.8866 0.700933
\(976\) 0 0
\(977\) 10.4067 0.332939 0.166469 0.986047i \(-0.446763\pi\)
0.166469 + 0.986047i \(0.446763\pi\)
\(978\) 0 0
\(979\) −19.5002 −0.623228
\(980\) 0 0
\(981\) −48.3059 −1.54229
\(982\) 0 0
\(983\) 34.5652 1.10246 0.551229 0.834354i \(-0.314159\pi\)
0.551229 + 0.834354i \(0.314159\pi\)
\(984\) 0 0
\(985\) −23.1642 −0.738072
\(986\) 0 0
\(987\) 6.09192 0.193908
\(988\) 0 0
\(989\) −63.8711 −2.03098
\(990\) 0 0
\(991\) 45.4244 1.44295 0.721477 0.692438i \(-0.243464\pi\)
0.721477 + 0.692438i \(0.243464\pi\)
\(992\) 0 0
\(993\) −28.9841 −0.919782
\(994\) 0 0
\(995\) 10.0131 0.317437
\(996\) 0 0
\(997\) −46.4719 −1.47178 −0.735889 0.677102i \(-0.763236\pi\)
−0.735889 + 0.677102i \(0.763236\pi\)
\(998\) 0 0
\(999\) −2.16357 −0.0684525
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 \(a_p\))