Properties

Label 8024.2.a.y.1.12
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.725294 q^{3} -2.56147 q^{5} -0.934698 q^{7} -2.47395 q^{9} +O(q^{10})\) \(q-0.725294 q^{3} -2.56147 q^{5} -0.934698 q^{7} -2.47395 q^{9} +0.446734 q^{11} +5.91850 q^{13} +1.85782 q^{15} -1.00000 q^{17} -3.85324 q^{19} +0.677931 q^{21} -7.09996 q^{23} +1.56115 q^{25} +3.97022 q^{27} +9.38960 q^{29} -8.41148 q^{31} -0.324014 q^{33} +2.39421 q^{35} +5.65988 q^{37} -4.29266 q^{39} +8.92656 q^{41} +9.40875 q^{43} +6.33696 q^{45} +9.71641 q^{47} -6.12634 q^{49} +0.725294 q^{51} -4.68648 q^{53} -1.14430 q^{55} +2.79473 q^{57} -1.00000 q^{59} +3.41446 q^{61} +2.31240 q^{63} -15.1601 q^{65} +1.82375 q^{67} +5.14956 q^{69} +0.929049 q^{71} -12.9737 q^{73} -1.13230 q^{75} -0.417561 q^{77} +10.8484 q^{79} +4.54226 q^{81} -13.5254 q^{83} +2.56147 q^{85} -6.81023 q^{87} +8.98484 q^{89} -5.53202 q^{91} +6.10080 q^{93} +9.86997 q^{95} -0.541858 q^{97} -1.10520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

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
\(3\) −0.725294 −0.418749 −0.209374 0.977836i \(-0.567143\pi\)
−0.209374 + 0.977836i \(0.567143\pi\)
\(4\) 0 0
\(5\) −2.56147 −1.14553 −0.572763 0.819721i \(-0.694129\pi\)
−0.572763 + 0.819721i \(0.694129\pi\)
\(6\) 0 0
\(7\) −0.934698 −0.353283 −0.176641 0.984275i \(-0.556523\pi\)
−0.176641 + 0.984275i \(0.556523\pi\)
\(8\) 0 0
\(9\) −2.47395 −0.824649
\(10\) 0 0
\(11\) 0.446734 0.134695 0.0673477 0.997730i \(-0.478546\pi\)
0.0673477 + 0.997730i \(0.478546\pi\)
\(12\) 0 0
\(13\) 5.91850 1.64150 0.820749 0.571289i \(-0.193556\pi\)
0.820749 + 0.571289i \(0.193556\pi\)
\(14\) 0 0
\(15\) 1.85782 0.479688
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −3.85324 −0.883993 −0.441997 0.897017i \(-0.645730\pi\)
−0.441997 + 0.897017i \(0.645730\pi\)
\(20\) 0 0
\(21\) 0.677931 0.147937
\(22\) 0 0
\(23\) −7.09996 −1.48044 −0.740222 0.672362i \(-0.765280\pi\)
−0.740222 + 0.672362i \(0.765280\pi\)
\(24\) 0 0
\(25\) 1.56115 0.312231
\(26\) 0 0
\(27\) 3.97022 0.764070
\(28\) 0 0
\(29\) 9.38960 1.74361 0.871803 0.489857i \(-0.162951\pi\)
0.871803 + 0.489857i \(0.162951\pi\)
\(30\) 0 0
\(31\) −8.41148 −1.51075 −0.755373 0.655295i \(-0.772544\pi\)
−0.755373 + 0.655295i \(0.772544\pi\)
\(32\) 0 0
\(33\) −0.324014 −0.0564035
\(34\) 0 0
\(35\) 2.39421 0.404695
\(36\) 0 0
\(37\) 5.65988 0.930478 0.465239 0.885185i \(-0.345968\pi\)
0.465239 + 0.885185i \(0.345968\pi\)
\(38\) 0 0
\(39\) −4.29266 −0.687376
\(40\) 0 0
\(41\) 8.92656 1.39409 0.697047 0.717025i \(-0.254497\pi\)
0.697047 + 0.717025i \(0.254497\pi\)
\(42\) 0 0
\(43\) 9.40875 1.43482 0.717411 0.696651i \(-0.245327\pi\)
0.717411 + 0.696651i \(0.245327\pi\)
\(44\) 0 0
\(45\) 6.33696 0.944658
\(46\) 0 0
\(47\) 9.71641 1.41728 0.708642 0.705569i \(-0.249308\pi\)
0.708642 + 0.705569i \(0.249308\pi\)
\(48\) 0 0
\(49\) −6.12634 −0.875191
\(50\) 0 0
\(51\) 0.725294 0.101562
\(52\) 0 0
\(53\) −4.68648 −0.643738 −0.321869 0.946784i \(-0.604311\pi\)
−0.321869 + 0.946784i \(0.604311\pi\)
\(54\) 0 0
\(55\) −1.14430 −0.154297
\(56\) 0 0
\(57\) 2.79473 0.370171
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 3.41446 0.437176 0.218588 0.975817i \(-0.429855\pi\)
0.218588 + 0.975817i \(0.429855\pi\)
\(62\) 0 0
\(63\) 2.31240 0.291334
\(64\) 0 0
\(65\) −15.1601 −1.88038
\(66\) 0 0
\(67\) 1.82375 0.222807 0.111403 0.993775i \(-0.464465\pi\)
0.111403 + 0.993775i \(0.464465\pi\)
\(68\) 0 0
\(69\) 5.14956 0.619935
\(70\) 0 0
\(71\) 0.929049 0.110258 0.0551289 0.998479i \(-0.482443\pi\)
0.0551289 + 0.998479i \(0.482443\pi\)
\(72\) 0 0
\(73\) −12.9737 −1.51846 −0.759230 0.650822i \(-0.774424\pi\)
−0.759230 + 0.650822i \(0.774424\pi\)
\(74\) 0 0
\(75\) −1.13230 −0.130746
\(76\) 0 0
\(77\) −0.417561 −0.0475855
\(78\) 0 0
\(79\) 10.8484 1.22054 0.610268 0.792195i \(-0.291062\pi\)
0.610268 + 0.792195i \(0.291062\pi\)
\(80\) 0 0
\(81\) 4.54226 0.504696
\(82\) 0 0
\(83\) −13.5254 −1.48461 −0.742305 0.670062i \(-0.766267\pi\)
−0.742305 + 0.670062i \(0.766267\pi\)
\(84\) 0 0
\(85\) 2.56147 0.277831
\(86\) 0 0
\(87\) −6.81023 −0.730133
\(88\) 0 0
\(89\) 8.98484 0.952392 0.476196 0.879339i \(-0.342015\pi\)
0.476196 + 0.879339i \(0.342015\pi\)
\(90\) 0 0
\(91\) −5.53202 −0.579913
\(92\) 0 0
\(93\) 6.10080 0.632623
\(94\) 0 0
\(95\) 9.86997 1.01264
\(96\) 0 0
\(97\) −0.541858 −0.0550174 −0.0275087 0.999622i \(-0.508757\pi\)
−0.0275087 + 0.999622i \(0.508757\pi\)
\(98\) 0 0
\(99\) −1.10520 −0.111076
\(100\) 0 0
\(101\) −0.720239 −0.0716664 −0.0358332 0.999358i \(-0.511409\pi\)
−0.0358332 + 0.999358i \(0.511409\pi\)
\(102\) 0 0
\(103\) −0.458495 −0.0451769 −0.0225884 0.999745i \(-0.507191\pi\)
−0.0225884 + 0.999745i \(0.507191\pi\)
\(104\) 0 0
\(105\) −1.73650 −0.169465
\(106\) 0 0
\(107\) −8.74047 −0.844973 −0.422487 0.906369i \(-0.638843\pi\)
−0.422487 + 0.906369i \(0.638843\pi\)
\(108\) 0 0
\(109\) −5.58873 −0.535304 −0.267652 0.963516i \(-0.586248\pi\)
−0.267652 + 0.963516i \(0.586248\pi\)
\(110\) 0 0
\(111\) −4.10508 −0.389637
\(112\) 0 0
\(113\) 4.04937 0.380933 0.190466 0.981694i \(-0.439000\pi\)
0.190466 + 0.981694i \(0.439000\pi\)
\(114\) 0 0
\(115\) 18.1864 1.69589
\(116\) 0 0
\(117\) −14.6421 −1.35366
\(118\) 0 0
\(119\) 0.934698 0.0856837
\(120\) 0 0
\(121\) −10.8004 −0.981857
\(122\) 0 0
\(123\) −6.47439 −0.583776
\(124\) 0 0
\(125\) 8.80852 0.787858
\(126\) 0 0
\(127\) −4.01400 −0.356185 −0.178093 0.984014i \(-0.556993\pi\)
−0.178093 + 0.984014i \(0.556993\pi\)
\(128\) 0 0
\(129\) −6.82412 −0.600830
\(130\) 0 0
\(131\) 21.4968 1.87818 0.939092 0.343665i \(-0.111669\pi\)
0.939092 + 0.343665i \(0.111669\pi\)
\(132\) 0 0
\(133\) 3.60161 0.312300
\(134\) 0 0
\(135\) −10.1696 −0.875262
\(136\) 0 0
\(137\) −7.82761 −0.668758 −0.334379 0.942439i \(-0.608526\pi\)
−0.334379 + 0.942439i \(0.608526\pi\)
\(138\) 0 0
\(139\) −2.27916 −0.193316 −0.0966578 0.995318i \(-0.530815\pi\)
−0.0966578 + 0.995318i \(0.530815\pi\)
\(140\) 0 0
\(141\) −7.04725 −0.593486
\(142\) 0 0
\(143\) 2.64400 0.221102
\(144\) 0 0
\(145\) −24.0512 −1.99735
\(146\) 0 0
\(147\) 4.44340 0.366485
\(148\) 0 0
\(149\) −14.8308 −1.21499 −0.607493 0.794325i \(-0.707825\pi\)
−0.607493 + 0.794325i \(0.707825\pi\)
\(150\) 0 0
\(151\) −5.33764 −0.434371 −0.217186 0.976130i \(-0.569688\pi\)
−0.217186 + 0.976130i \(0.569688\pi\)
\(152\) 0 0
\(153\) 2.47395 0.200007
\(154\) 0 0
\(155\) 21.5458 1.73060
\(156\) 0 0
\(157\) 1.53179 0.122250 0.0611250 0.998130i \(-0.480531\pi\)
0.0611250 + 0.998130i \(0.480531\pi\)
\(158\) 0 0
\(159\) 3.39908 0.269565
\(160\) 0 0
\(161\) 6.63632 0.523016
\(162\) 0 0
\(163\) 20.2166 1.58348 0.791742 0.610855i \(-0.209174\pi\)
0.791742 + 0.610855i \(0.209174\pi\)
\(164\) 0 0
\(165\) 0.829953 0.0646117
\(166\) 0 0
\(167\) 0.942783 0.0729547 0.0364774 0.999334i \(-0.488386\pi\)
0.0364774 + 0.999334i \(0.488386\pi\)
\(168\) 0 0
\(169\) 22.0287 1.69452
\(170\) 0 0
\(171\) 9.53271 0.728985
\(172\) 0 0
\(173\) 7.22155 0.549045 0.274522 0.961581i \(-0.411480\pi\)
0.274522 + 0.961581i \(0.411480\pi\)
\(174\) 0 0
\(175\) −1.45921 −0.110306
\(176\) 0 0
\(177\) 0.725294 0.0545165
\(178\) 0 0
\(179\) 5.76976 0.431252 0.215626 0.976476i \(-0.430821\pi\)
0.215626 + 0.976476i \(0.430821\pi\)
\(180\) 0 0
\(181\) −12.5556 −0.933253 −0.466626 0.884454i \(-0.654531\pi\)
−0.466626 + 0.884454i \(0.654531\pi\)
\(182\) 0 0
\(183\) −2.47649 −0.183067
\(184\) 0 0
\(185\) −14.4976 −1.06589
\(186\) 0 0
\(187\) −0.446734 −0.0326684
\(188\) 0 0
\(189\) −3.71096 −0.269933
\(190\) 0 0
\(191\) −11.3447 −0.820876 −0.410438 0.911888i \(-0.634624\pi\)
−0.410438 + 0.911888i \(0.634624\pi\)
\(192\) 0 0
\(193\) 19.2719 1.38722 0.693612 0.720349i \(-0.256018\pi\)
0.693612 + 0.720349i \(0.256018\pi\)
\(194\) 0 0
\(195\) 10.9955 0.787407
\(196\) 0 0
\(197\) 23.7447 1.69174 0.845868 0.533392i \(-0.179083\pi\)
0.845868 + 0.533392i \(0.179083\pi\)
\(198\) 0 0
\(199\) 4.02230 0.285133 0.142567 0.989785i \(-0.454464\pi\)
0.142567 + 0.989785i \(0.454464\pi\)
\(200\) 0 0
\(201\) −1.32276 −0.0933001
\(202\) 0 0
\(203\) −8.77645 −0.615986
\(204\) 0 0
\(205\) −22.8652 −1.59697
\(206\) 0 0
\(207\) 17.5649 1.22085
\(208\) 0 0
\(209\) −1.72137 −0.119070
\(210\) 0 0
\(211\) −22.5620 −1.55323 −0.776614 0.629976i \(-0.783065\pi\)
−0.776614 + 0.629976i \(0.783065\pi\)
\(212\) 0 0
\(213\) −0.673834 −0.0461703
\(214\) 0 0
\(215\) −24.1003 −1.64363
\(216\) 0 0
\(217\) 7.86219 0.533720
\(218\) 0 0
\(219\) 9.40977 0.635854
\(220\) 0 0
\(221\) −5.91850 −0.398122
\(222\) 0 0
\(223\) −10.1726 −0.681207 −0.340603 0.940207i \(-0.610631\pi\)
−0.340603 + 0.940207i \(0.610631\pi\)
\(224\) 0 0
\(225\) −3.86221 −0.257481
\(226\) 0 0
\(227\) −15.1402 −1.00489 −0.502444 0.864610i \(-0.667566\pi\)
−0.502444 + 0.864610i \(0.667566\pi\)
\(228\) 0 0
\(229\) 17.4377 1.15231 0.576157 0.817339i \(-0.304552\pi\)
0.576157 + 0.817339i \(0.304552\pi\)
\(230\) 0 0
\(231\) 0.302855 0.0199264
\(232\) 0 0
\(233\) 19.8800 1.30238 0.651192 0.758913i \(-0.274269\pi\)
0.651192 + 0.758913i \(0.274269\pi\)
\(234\) 0 0
\(235\) −24.8883 −1.62354
\(236\) 0 0
\(237\) −7.86826 −0.511098
\(238\) 0 0
\(239\) −23.4315 −1.51566 −0.757830 0.652452i \(-0.773740\pi\)
−0.757830 + 0.652452i \(0.773740\pi\)
\(240\) 0 0
\(241\) −29.5422 −1.90298 −0.951491 0.307677i \(-0.900448\pi\)
−0.951491 + 0.307677i \(0.900448\pi\)
\(242\) 0 0
\(243\) −15.2051 −0.975411
\(244\) 0 0
\(245\) 15.6925 1.00255
\(246\) 0 0
\(247\) −22.8054 −1.45107
\(248\) 0 0
\(249\) 9.80993 0.621679
\(250\) 0 0
\(251\) 5.79689 0.365896 0.182948 0.983123i \(-0.441436\pi\)
0.182948 + 0.983123i \(0.441436\pi\)
\(252\) 0 0
\(253\) −3.17179 −0.199409
\(254\) 0 0
\(255\) −1.85782 −0.116341
\(256\) 0 0
\(257\) −18.0796 −1.12778 −0.563888 0.825851i \(-0.690695\pi\)
−0.563888 + 0.825851i \(0.690695\pi\)
\(258\) 0 0
\(259\) −5.29028 −0.328722
\(260\) 0 0
\(261\) −23.2294 −1.43786
\(262\) 0 0
\(263\) −26.5121 −1.63481 −0.817404 0.576065i \(-0.804588\pi\)
−0.817404 + 0.576065i \(0.804588\pi\)
\(264\) 0 0
\(265\) 12.0043 0.737419
\(266\) 0 0
\(267\) −6.51666 −0.398813
\(268\) 0 0
\(269\) 30.1028 1.83540 0.917699 0.397277i \(-0.130045\pi\)
0.917699 + 0.397277i \(0.130045\pi\)
\(270\) 0 0
\(271\) 10.0017 0.607560 0.303780 0.952742i \(-0.401751\pi\)
0.303780 + 0.952742i \(0.401751\pi\)
\(272\) 0 0
\(273\) 4.01234 0.242838
\(274\) 0 0
\(275\) 0.697420 0.0420560
\(276\) 0 0
\(277\) −14.0171 −0.842209 −0.421104 0.907012i \(-0.638357\pi\)
−0.421104 + 0.907012i \(0.638357\pi\)
\(278\) 0 0
\(279\) 20.8096 1.24584
\(280\) 0 0
\(281\) −1.81149 −0.108064 −0.0540322 0.998539i \(-0.517207\pi\)
−0.0540322 + 0.998539i \(0.517207\pi\)
\(282\) 0 0
\(283\) −18.5608 −1.10333 −0.551664 0.834067i \(-0.686007\pi\)
−0.551664 + 0.834067i \(0.686007\pi\)
\(284\) 0 0
\(285\) −7.15864 −0.424041
\(286\) 0 0
\(287\) −8.34364 −0.492510
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0.393007 0.0230385
\(292\) 0 0
\(293\) −19.6608 −1.14859 −0.574297 0.818647i \(-0.694724\pi\)
−0.574297 + 0.818647i \(0.694724\pi\)
\(294\) 0 0
\(295\) 2.56147 0.149135
\(296\) 0 0
\(297\) 1.77363 0.102917
\(298\) 0 0
\(299\) −42.0212 −2.43015
\(300\) 0 0
\(301\) −8.79435 −0.506898
\(302\) 0 0
\(303\) 0.522385 0.0300102
\(304\) 0 0
\(305\) −8.74605 −0.500797
\(306\) 0 0
\(307\) −16.5537 −0.944770 −0.472385 0.881392i \(-0.656607\pi\)
−0.472385 + 0.881392i \(0.656607\pi\)
\(308\) 0 0
\(309\) 0.332544 0.0189178
\(310\) 0 0
\(311\) −35.0470 −1.98733 −0.993667 0.112362i \(-0.964158\pi\)
−0.993667 + 0.112362i \(0.964158\pi\)
\(312\) 0 0
\(313\) 15.3844 0.869579 0.434790 0.900532i \(-0.356823\pi\)
0.434790 + 0.900532i \(0.356823\pi\)
\(314\) 0 0
\(315\) −5.92314 −0.333731
\(316\) 0 0
\(317\) 8.24780 0.463243 0.231621 0.972806i \(-0.425597\pi\)
0.231621 + 0.972806i \(0.425597\pi\)
\(318\) 0 0
\(319\) 4.19465 0.234856
\(320\) 0 0
\(321\) 6.33941 0.353832
\(322\) 0 0
\(323\) 3.85324 0.214400
\(324\) 0 0
\(325\) 9.23970 0.512526
\(326\) 0 0
\(327\) 4.05348 0.224158
\(328\) 0 0
\(329\) −9.08191 −0.500702
\(330\) 0 0
\(331\) −36.3521 −1.99809 −0.999046 0.0436765i \(-0.986093\pi\)
−0.999046 + 0.0436765i \(0.986093\pi\)
\(332\) 0 0
\(333\) −14.0022 −0.767318
\(334\) 0 0
\(335\) −4.67150 −0.255231
\(336\) 0 0
\(337\) −12.2859 −0.669255 −0.334627 0.942351i \(-0.608610\pi\)
−0.334627 + 0.942351i \(0.608610\pi\)
\(338\) 0 0
\(339\) −2.93698 −0.159515
\(340\) 0 0
\(341\) −3.75769 −0.203490
\(342\) 0 0
\(343\) 12.2692 0.662473
\(344\) 0 0
\(345\) −13.1905 −0.710152
\(346\) 0 0
\(347\) −8.40762 −0.451345 −0.225672 0.974203i \(-0.572458\pi\)
−0.225672 + 0.974203i \(0.572458\pi\)
\(348\) 0 0
\(349\) −17.6090 −0.942586 −0.471293 0.881977i \(-0.656213\pi\)
−0.471293 + 0.881977i \(0.656213\pi\)
\(350\) 0 0
\(351\) 23.4978 1.25422
\(352\) 0 0
\(353\) −2.29316 −0.122052 −0.0610262 0.998136i \(-0.519437\pi\)
−0.0610262 + 0.998136i \(0.519437\pi\)
\(354\) 0 0
\(355\) −2.37974 −0.126303
\(356\) 0 0
\(357\) −0.677931 −0.0358799
\(358\) 0 0
\(359\) 6.10348 0.322129 0.161065 0.986944i \(-0.448507\pi\)
0.161065 + 0.986944i \(0.448507\pi\)
\(360\) 0 0
\(361\) −4.15256 −0.218556
\(362\) 0 0
\(363\) 7.83349 0.411152
\(364\) 0 0
\(365\) 33.2319 1.73944
\(366\) 0 0
\(367\) −28.4841 −1.48686 −0.743428 0.668816i \(-0.766802\pi\)
−0.743428 + 0.668816i \(0.766802\pi\)
\(368\) 0 0
\(369\) −22.0839 −1.14964
\(370\) 0 0
\(371\) 4.38045 0.227421
\(372\) 0 0
\(373\) −32.6127 −1.68862 −0.844311 0.535854i \(-0.819990\pi\)
−0.844311 + 0.535854i \(0.819990\pi\)
\(374\) 0 0
\(375\) −6.38877 −0.329915
\(376\) 0 0
\(377\) 55.5724 2.86212
\(378\) 0 0
\(379\) 7.35687 0.377897 0.188948 0.981987i \(-0.439492\pi\)
0.188948 + 0.981987i \(0.439492\pi\)
\(380\) 0 0
\(381\) 2.91134 0.149152
\(382\) 0 0
\(383\) 24.4030 1.24693 0.623467 0.781850i \(-0.285724\pi\)
0.623467 + 0.781850i \(0.285724\pi\)
\(384\) 0 0
\(385\) 1.06957 0.0545105
\(386\) 0 0
\(387\) −23.2768 −1.18322
\(388\) 0 0
\(389\) 20.4230 1.03549 0.517744 0.855536i \(-0.326772\pi\)
0.517744 + 0.855536i \(0.326772\pi\)
\(390\) 0 0
\(391\) 7.09996 0.359061
\(392\) 0 0
\(393\) −15.5915 −0.786488
\(394\) 0 0
\(395\) −27.7878 −1.39816
\(396\) 0 0
\(397\) −38.1133 −1.91285 −0.956426 0.291975i \(-0.905688\pi\)
−0.956426 + 0.291975i \(0.905688\pi\)
\(398\) 0 0
\(399\) −2.61223 −0.130775
\(400\) 0 0
\(401\) −9.01541 −0.450208 −0.225104 0.974335i \(-0.572272\pi\)
−0.225104 + 0.974335i \(0.572272\pi\)
\(402\) 0 0
\(403\) −49.7834 −2.47989
\(404\) 0 0
\(405\) −11.6349 −0.578142
\(406\) 0 0
\(407\) 2.52846 0.125331
\(408\) 0 0
\(409\) 12.9479 0.640233 0.320116 0.947378i \(-0.396278\pi\)
0.320116 + 0.947378i \(0.396278\pi\)
\(410\) 0 0
\(411\) 5.67732 0.280042
\(412\) 0 0
\(413\) 0.934698 0.0459935
\(414\) 0 0
\(415\) 34.6451 1.70066
\(416\) 0 0
\(417\) 1.65306 0.0809507
\(418\) 0 0
\(419\) −17.1407 −0.837378 −0.418689 0.908130i \(-0.637510\pi\)
−0.418689 + 0.908130i \(0.637510\pi\)
\(420\) 0 0
\(421\) 11.0403 0.538073 0.269036 0.963130i \(-0.413295\pi\)
0.269036 + 0.963130i \(0.413295\pi\)
\(422\) 0 0
\(423\) −24.0379 −1.16876
\(424\) 0 0
\(425\) −1.56115 −0.0757271
\(426\) 0 0
\(427\) −3.19149 −0.154447
\(428\) 0 0
\(429\) −1.91768 −0.0925863
\(430\) 0 0
\(431\) 40.0431 1.92881 0.964404 0.264431i \(-0.0851843\pi\)
0.964404 + 0.264431i \(0.0851843\pi\)
\(432\) 0 0
\(433\) −13.6185 −0.654464 −0.327232 0.944944i \(-0.606116\pi\)
−0.327232 + 0.944944i \(0.606116\pi\)
\(434\) 0 0
\(435\) 17.4442 0.836387
\(436\) 0 0
\(437\) 27.3579 1.30870
\(438\) 0 0
\(439\) 3.86864 0.184640 0.0923200 0.995729i \(-0.470572\pi\)
0.0923200 + 0.995729i \(0.470572\pi\)
\(440\) 0 0
\(441\) 15.1562 0.721726
\(442\) 0 0
\(443\) −11.4390 −0.543486 −0.271743 0.962370i \(-0.587600\pi\)
−0.271743 + 0.962370i \(0.587600\pi\)
\(444\) 0 0
\(445\) −23.0145 −1.09099
\(446\) 0 0
\(447\) 10.7567 0.508774
\(448\) 0 0
\(449\) 8.08590 0.381597 0.190799 0.981629i \(-0.438892\pi\)
0.190799 + 0.981629i \(0.438892\pi\)
\(450\) 0 0
\(451\) 3.98780 0.187778
\(452\) 0 0
\(453\) 3.87136 0.181893
\(454\) 0 0
\(455\) 14.1701 0.664306
\(456\) 0 0
\(457\) −2.33261 −0.109115 −0.0545574 0.998511i \(-0.517375\pi\)
−0.0545574 + 0.998511i \(0.517375\pi\)
\(458\) 0 0
\(459\) −3.97022 −0.185314
\(460\) 0 0
\(461\) 0.470093 0.0218944 0.0109472 0.999940i \(-0.496515\pi\)
0.0109472 + 0.999940i \(0.496515\pi\)
\(462\) 0 0
\(463\) −13.4557 −0.625341 −0.312671 0.949862i \(-0.601224\pi\)
−0.312671 + 0.949862i \(0.601224\pi\)
\(464\) 0 0
\(465\) −15.6270 −0.724687
\(466\) 0 0
\(467\) 15.5956 0.721679 0.360839 0.932628i \(-0.382490\pi\)
0.360839 + 0.932628i \(0.382490\pi\)
\(468\) 0 0
\(469\) −1.70466 −0.0787138
\(470\) 0 0
\(471\) −1.11100 −0.0511921
\(472\) 0 0
\(473\) 4.20321 0.193264
\(474\) 0 0
\(475\) −6.01550 −0.276010
\(476\) 0 0
\(477\) 11.5941 0.530858
\(478\) 0 0
\(479\) −11.1953 −0.511528 −0.255764 0.966739i \(-0.582327\pi\)
−0.255764 + 0.966739i \(0.582327\pi\)
\(480\) 0 0
\(481\) 33.4980 1.52738
\(482\) 0 0
\(483\) −4.81329 −0.219012
\(484\) 0 0
\(485\) 1.38796 0.0630239
\(486\) 0 0
\(487\) −30.9430 −1.40216 −0.701080 0.713082i \(-0.747299\pi\)
−0.701080 + 0.713082i \(0.747299\pi\)
\(488\) 0 0
\(489\) −14.6630 −0.663083
\(490\) 0 0
\(491\) −15.1379 −0.683165 −0.341582 0.939852i \(-0.610963\pi\)
−0.341582 + 0.939852i \(0.610963\pi\)
\(492\) 0 0
\(493\) −9.38960 −0.422886
\(494\) 0 0
\(495\) 2.83093 0.127241
\(496\) 0 0
\(497\) −0.868380 −0.0389522
\(498\) 0 0
\(499\) −39.0950 −1.75013 −0.875065 0.484005i \(-0.839182\pi\)
−0.875065 + 0.484005i \(0.839182\pi\)
\(500\) 0 0
\(501\) −0.683795 −0.0305497
\(502\) 0 0
\(503\) −22.6860 −1.01152 −0.505759 0.862675i \(-0.668787\pi\)
−0.505759 + 0.862675i \(0.668787\pi\)
\(504\) 0 0
\(505\) 1.84487 0.0820958
\(506\) 0 0
\(507\) −15.9773 −0.709577
\(508\) 0 0
\(509\) −31.0842 −1.37778 −0.688891 0.724865i \(-0.741902\pi\)
−0.688891 + 0.724865i \(0.741902\pi\)
\(510\) 0 0
\(511\) 12.1265 0.536446
\(512\) 0 0
\(513\) −15.2982 −0.675433
\(514\) 0 0
\(515\) 1.17442 0.0517513
\(516\) 0 0
\(517\) 4.34065 0.190901
\(518\) 0 0
\(519\) −5.23775 −0.229912
\(520\) 0 0
\(521\) 41.9487 1.83780 0.918902 0.394486i \(-0.129077\pi\)
0.918902 + 0.394486i \(0.129077\pi\)
\(522\) 0 0
\(523\) 2.75418 0.120432 0.0602160 0.998185i \(-0.480821\pi\)
0.0602160 + 0.998185i \(0.480821\pi\)
\(524\) 0 0
\(525\) 1.05836 0.0461904
\(526\) 0 0
\(527\) 8.41148 0.366410
\(528\) 0 0
\(529\) 27.4095 1.19172
\(530\) 0 0
\(531\) 2.47395 0.107360
\(532\) 0 0
\(533\) 52.8319 2.28840
\(534\) 0 0
\(535\) 22.3885 0.967939
\(536\) 0 0
\(537\) −4.18477 −0.180586
\(538\) 0 0
\(539\) −2.73684 −0.117884
\(540\) 0 0
\(541\) −19.8206 −0.852153 −0.426076 0.904687i \(-0.640104\pi\)
−0.426076 + 0.904687i \(0.640104\pi\)
\(542\) 0 0
\(543\) 9.10653 0.390799
\(544\) 0 0
\(545\) 14.3154 0.613204
\(546\) 0 0
\(547\) −11.1238 −0.475619 −0.237809 0.971312i \(-0.576429\pi\)
−0.237809 + 0.971312i \(0.576429\pi\)
\(548\) 0 0
\(549\) −8.44719 −0.360517
\(550\) 0 0
\(551\) −36.1804 −1.54134
\(552\) 0 0
\(553\) −10.1399 −0.431194
\(554\) 0 0
\(555\) 10.5151 0.446339
\(556\) 0 0
\(557\) −15.3609 −0.650861 −0.325430 0.945566i \(-0.605509\pi\)
−0.325430 + 0.945566i \(0.605509\pi\)
\(558\) 0 0
\(559\) 55.6857 2.35526
\(560\) 0 0
\(561\) 0.324014 0.0136799
\(562\) 0 0
\(563\) 1.02740 0.0432996 0.0216498 0.999766i \(-0.493108\pi\)
0.0216498 + 0.999766i \(0.493108\pi\)
\(564\) 0 0
\(565\) −10.3724 −0.436368
\(566\) 0 0
\(567\) −4.24565 −0.178300
\(568\) 0 0
\(569\) −2.07739 −0.0870888 −0.0435444 0.999051i \(-0.513865\pi\)
−0.0435444 + 0.999051i \(0.513865\pi\)
\(570\) 0 0
\(571\) 23.5776 0.986690 0.493345 0.869834i \(-0.335774\pi\)
0.493345 + 0.869834i \(0.335774\pi\)
\(572\) 0 0
\(573\) 8.22828 0.343741
\(574\) 0 0
\(575\) −11.0841 −0.462240
\(576\) 0 0
\(577\) 10.1090 0.420843 0.210421 0.977611i \(-0.432516\pi\)
0.210421 + 0.977611i \(0.432516\pi\)
\(578\) 0 0
\(579\) −13.9778 −0.580898
\(580\) 0 0
\(581\) 12.6422 0.524487
\(582\) 0 0
\(583\) −2.09361 −0.0867085
\(584\) 0 0
\(585\) 37.5053 1.55065
\(586\) 0 0
\(587\) −31.6779 −1.30749 −0.653743 0.756717i \(-0.726802\pi\)
−0.653743 + 0.756717i \(0.726802\pi\)
\(588\) 0 0
\(589\) 32.4114 1.33549
\(590\) 0 0
\(591\) −17.2219 −0.708413
\(592\) 0 0
\(593\) 42.3183 1.73780 0.868902 0.494983i \(-0.164826\pi\)
0.868902 + 0.494983i \(0.164826\pi\)
\(594\) 0 0
\(595\) −2.39421 −0.0981529
\(596\) 0 0
\(597\) −2.91735 −0.119399
\(598\) 0 0
\(599\) −17.0153 −0.695225 −0.347613 0.937638i \(-0.613008\pi\)
−0.347613 + 0.937638i \(0.613008\pi\)
\(600\) 0 0
\(601\) −13.5937 −0.554499 −0.277250 0.960798i \(-0.589423\pi\)
−0.277250 + 0.960798i \(0.589423\pi\)
\(602\) 0 0
\(603\) −4.51187 −0.183738
\(604\) 0 0
\(605\) 27.6650 1.12474
\(606\) 0 0
\(607\) −33.1495 −1.34550 −0.672748 0.739872i \(-0.734886\pi\)
−0.672748 + 0.739872i \(0.734886\pi\)
\(608\) 0 0
\(609\) 6.36551 0.257943
\(610\) 0 0
\(611\) 57.5066 2.32647
\(612\) 0 0
\(613\) 0.654037 0.0264163 0.0132081 0.999913i \(-0.495796\pi\)
0.0132081 + 0.999913i \(0.495796\pi\)
\(614\) 0 0
\(615\) 16.5840 0.668731
\(616\) 0 0
\(617\) −3.54471 −0.142705 −0.0713524 0.997451i \(-0.522731\pi\)
−0.0713524 + 0.997451i \(0.522731\pi\)
\(618\) 0 0
\(619\) 37.2912 1.49886 0.749430 0.662084i \(-0.230328\pi\)
0.749430 + 0.662084i \(0.230328\pi\)
\(620\) 0 0
\(621\) −28.1884 −1.13116
\(622\) 0 0
\(623\) −8.39812 −0.336464
\(624\) 0 0
\(625\) −30.3686 −1.21474
\(626\) 0 0
\(627\) 1.24850 0.0498603
\(628\) 0 0
\(629\) −5.65988 −0.225674
\(630\) 0 0
\(631\) 32.2740 1.28481 0.642404 0.766366i \(-0.277937\pi\)
0.642404 + 0.766366i \(0.277937\pi\)
\(632\) 0 0
\(633\) 16.3641 0.650413
\(634\) 0 0
\(635\) 10.2818 0.408020
\(636\) 0 0
\(637\) −36.2588 −1.43662
\(638\) 0 0
\(639\) −2.29842 −0.0909240
\(640\) 0 0
\(641\) −4.17268 −0.164811 −0.0824055 0.996599i \(-0.526260\pi\)
−0.0824055 + 0.996599i \(0.526260\pi\)
\(642\) 0 0
\(643\) 6.73630 0.265654 0.132827 0.991139i \(-0.457595\pi\)
0.132827 + 0.991139i \(0.457595\pi\)
\(644\) 0 0
\(645\) 17.4798 0.688267
\(646\) 0 0
\(647\) 16.9090 0.664762 0.332381 0.943145i \(-0.392148\pi\)
0.332381 + 0.943145i \(0.392148\pi\)
\(648\) 0 0
\(649\) −0.446734 −0.0175358
\(650\) 0 0
\(651\) −5.70240 −0.223495
\(652\) 0 0
\(653\) 32.2794 1.26319 0.631595 0.775298i \(-0.282401\pi\)
0.631595 + 0.775298i \(0.282401\pi\)
\(654\) 0 0
\(655\) −55.0635 −2.15151
\(656\) 0 0
\(657\) 32.0963 1.25220
\(658\) 0 0
\(659\) 47.1252 1.83574 0.917869 0.396883i \(-0.129908\pi\)
0.917869 + 0.396883i \(0.129908\pi\)
\(660\) 0 0
\(661\) −47.4873 −1.84704 −0.923521 0.383549i \(-0.874702\pi\)
−0.923521 + 0.383549i \(0.874702\pi\)
\(662\) 0 0
\(663\) 4.29266 0.166713
\(664\) 0 0
\(665\) −9.22545 −0.357747
\(666\) 0 0
\(667\) −66.6658 −2.58131
\(668\) 0 0
\(669\) 7.37812 0.285255
\(670\) 0 0
\(671\) 1.52535 0.0588856
\(672\) 0 0
\(673\) 13.2602 0.511144 0.255572 0.966790i \(-0.417736\pi\)
0.255572 + 0.966790i \(0.417736\pi\)
\(674\) 0 0
\(675\) 6.19813 0.238566
\(676\) 0 0
\(677\) −26.9261 −1.03485 −0.517426 0.855728i \(-0.673110\pi\)
−0.517426 + 0.855728i \(0.673110\pi\)
\(678\) 0 0
\(679\) 0.506474 0.0194367
\(680\) 0 0
\(681\) 10.9811 0.420796
\(682\) 0 0
\(683\) 0.674417 0.0258059 0.0129029 0.999917i \(-0.495893\pi\)
0.0129029 + 0.999917i \(0.495893\pi\)
\(684\) 0 0
\(685\) 20.0502 0.766080
\(686\) 0 0
\(687\) −12.6474 −0.482530
\(688\) 0 0
\(689\) −27.7370 −1.05669
\(690\) 0 0
\(691\) −12.2692 −0.466744 −0.233372 0.972388i \(-0.574976\pi\)
−0.233372 + 0.972388i \(0.574976\pi\)
\(692\) 0 0
\(693\) 1.03303 0.0392414
\(694\) 0 0
\(695\) 5.83800 0.221448
\(696\) 0 0
\(697\) −8.92656 −0.338118
\(698\) 0 0
\(699\) −14.4189 −0.545372
\(700\) 0 0
\(701\) 10.7165 0.404758 0.202379 0.979307i \(-0.435133\pi\)
0.202379 + 0.979307i \(0.435133\pi\)
\(702\) 0 0
\(703\) −21.8089 −0.822537
\(704\) 0 0
\(705\) 18.0514 0.679854
\(706\) 0 0
\(707\) 0.673206 0.0253185
\(708\) 0 0
\(709\) 5.26472 0.197721 0.0988604 0.995101i \(-0.468480\pi\)
0.0988604 + 0.995101i \(0.468480\pi\)
\(710\) 0 0
\(711\) −26.8383 −1.00651
\(712\) 0 0
\(713\) 59.7212 2.23658
\(714\) 0 0
\(715\) −6.77253 −0.253278
\(716\) 0 0
\(717\) 16.9948 0.634681
\(718\) 0 0
\(719\) 7.34566 0.273947 0.136973 0.990575i \(-0.456262\pi\)
0.136973 + 0.990575i \(0.456262\pi\)
\(720\) 0 0
\(721\) 0.428555 0.0159602
\(722\) 0 0
\(723\) 21.4268 0.796872
\(724\) 0 0
\(725\) 14.6586 0.544407
\(726\) 0 0
\(727\) 5.05292 0.187403 0.0937013 0.995600i \(-0.470130\pi\)
0.0937013 + 0.995600i \(0.470130\pi\)
\(728\) 0 0
\(729\) −2.59858 −0.0962436
\(730\) 0 0
\(731\) −9.40875 −0.347995
\(732\) 0 0
\(733\) −26.3381 −0.972821 −0.486410 0.873730i \(-0.661694\pi\)
−0.486410 + 0.873730i \(0.661694\pi\)
\(734\) 0 0
\(735\) −11.3817 −0.419819
\(736\) 0 0
\(737\) 0.814732 0.0300110
\(738\) 0 0
\(739\) 12.0392 0.442870 0.221435 0.975175i \(-0.428926\pi\)
0.221435 + 0.975175i \(0.428926\pi\)
\(740\) 0 0
\(741\) 16.5406 0.607635
\(742\) 0 0
\(743\) −10.0430 −0.368442 −0.184221 0.982885i \(-0.558976\pi\)
−0.184221 + 0.982885i \(0.558976\pi\)
\(744\) 0 0
\(745\) 37.9887 1.39180
\(746\) 0 0
\(747\) 33.4612 1.22428
\(748\) 0 0
\(749\) 8.16970 0.298514
\(750\) 0 0
\(751\) −1.21544 −0.0443522 −0.0221761 0.999754i \(-0.507059\pi\)
−0.0221761 + 0.999754i \(0.507059\pi\)
\(752\) 0 0
\(753\) −4.20445 −0.153219
\(754\) 0 0
\(755\) 13.6722 0.497584
\(756\) 0 0
\(757\) 28.2954 1.02842 0.514208 0.857666i \(-0.328086\pi\)
0.514208 + 0.857666i \(0.328086\pi\)
\(758\) 0 0
\(759\) 2.30048 0.0835023
\(760\) 0 0
\(761\) −4.19969 −0.152239 −0.0761193 0.997099i \(-0.524253\pi\)
−0.0761193 + 0.997099i \(0.524253\pi\)
\(762\) 0 0
\(763\) 5.22378 0.189114
\(764\) 0 0
\(765\) −6.33696 −0.229113
\(766\) 0 0
\(767\) −5.91850 −0.213705
\(768\) 0 0
\(769\) 36.8364 1.32836 0.664178 0.747574i \(-0.268782\pi\)
0.664178 + 0.747574i \(0.268782\pi\)
\(770\) 0 0
\(771\) 13.1131 0.472255
\(772\) 0 0
\(773\) −14.6491 −0.526891 −0.263446 0.964674i \(-0.584859\pi\)
−0.263446 + 0.964674i \(0.584859\pi\)
\(774\) 0 0
\(775\) −13.1316 −0.471701
\(776\) 0 0
\(777\) 3.83701 0.137652
\(778\) 0 0
\(779\) −34.3962 −1.23237
\(780\) 0 0
\(781\) 0.415038 0.0148512
\(782\) 0 0
\(783\) 37.2788 1.33224
\(784\) 0 0
\(785\) −3.92364 −0.140041
\(786\) 0 0
\(787\) 31.7905 1.13321 0.566604 0.823990i \(-0.308257\pi\)
0.566604 + 0.823990i \(0.308257\pi\)
\(788\) 0 0
\(789\) 19.2291 0.684574
\(790\) 0 0
\(791\) −3.78494 −0.134577
\(792\) 0 0
\(793\) 20.2085 0.717624
\(794\) 0 0
\(795\) −8.70666 −0.308793
\(796\) 0 0
\(797\) −37.4627 −1.32700 −0.663498 0.748178i \(-0.730929\pi\)
−0.663498 + 0.748178i \(0.730929\pi\)
\(798\) 0 0
\(799\) −9.71641 −0.343742
\(800\) 0 0
\(801\) −22.2280 −0.785389
\(802\) 0 0
\(803\) −5.79580 −0.204529
\(804\) 0 0
\(805\) −16.9988 −0.599128
\(806\) 0 0
\(807\) −21.8334 −0.768571
\(808\) 0 0
\(809\) −40.8574 −1.43647 −0.718235 0.695801i \(-0.755050\pi\)
−0.718235 + 0.695801i \(0.755050\pi\)
\(810\) 0 0
\(811\) 15.1495 0.531970 0.265985 0.963977i \(-0.414303\pi\)
0.265985 + 0.963977i \(0.414303\pi\)
\(812\) 0 0
\(813\) −7.25418 −0.254415
\(814\) 0 0
\(815\) −51.7843 −1.81392
\(816\) 0 0
\(817\) −36.2542 −1.26837
\(818\) 0 0
\(819\) 13.6859 0.478225
\(820\) 0 0
\(821\) 15.7527 0.549772 0.274886 0.961477i \(-0.411360\pi\)
0.274886 + 0.961477i \(0.411360\pi\)
\(822\) 0 0
\(823\) 20.6716 0.720567 0.360284 0.932843i \(-0.382680\pi\)
0.360284 + 0.932843i \(0.382680\pi\)
\(824\) 0 0
\(825\) −0.505835 −0.0176109
\(826\) 0 0
\(827\) 4.44020 0.154401 0.0772004 0.997016i \(-0.475402\pi\)
0.0772004 + 0.997016i \(0.475402\pi\)
\(828\) 0 0
\(829\) −43.7937 −1.52102 −0.760510 0.649326i \(-0.775051\pi\)
−0.760510 + 0.649326i \(0.775051\pi\)
\(830\) 0 0
\(831\) 10.1666 0.352674
\(832\) 0 0
\(833\) 6.12634 0.212265
\(834\) 0 0
\(835\) −2.41491 −0.0835715
\(836\) 0 0
\(837\) −33.3954 −1.15432
\(838\) 0 0
\(839\) −4.32417 −0.149287 −0.0746435 0.997210i \(-0.523782\pi\)
−0.0746435 + 0.997210i \(0.523782\pi\)
\(840\) 0 0
\(841\) 59.1646 2.04016
\(842\) 0 0
\(843\) 1.31386 0.0452519
\(844\) 0 0
\(845\) −56.4260 −1.94111
\(846\) 0 0
\(847\) 10.0951 0.346873
\(848\) 0 0
\(849\) 13.4621 0.462017
\(850\) 0 0
\(851\) −40.1849 −1.37752
\(852\) 0 0
\(853\) 5.33669 0.182725 0.0913623 0.995818i \(-0.470878\pi\)
0.0913623 + 0.995818i \(0.470878\pi\)
\(854\) 0 0
\(855\) −24.4178 −0.835071
\(856\) 0 0
\(857\) 16.7413 0.571872 0.285936 0.958249i \(-0.407695\pi\)
0.285936 + 0.958249i \(0.407695\pi\)
\(858\) 0 0
\(859\) −44.1369 −1.50593 −0.752965 0.658060i \(-0.771377\pi\)
−0.752965 + 0.658060i \(0.771377\pi\)
\(860\) 0 0
\(861\) 6.05160 0.206238
\(862\) 0 0
\(863\) −6.59314 −0.224433 −0.112217 0.993684i \(-0.535795\pi\)
−0.112217 + 0.993684i \(0.535795\pi\)
\(864\) 0 0
\(865\) −18.4978 −0.628945
\(866\) 0 0
\(867\) −0.725294 −0.0246323
\(868\) 0 0
\(869\) 4.84633 0.164401
\(870\) 0 0
\(871\) 10.7939 0.365737
\(872\) 0 0
\(873\) 1.34053 0.0453700
\(874\) 0 0
\(875\) −8.23331 −0.278337
\(876\) 0 0
\(877\) 17.7407 0.599061 0.299530 0.954087i \(-0.403170\pi\)
0.299530 + 0.954087i \(0.403170\pi\)
\(878\) 0 0
\(879\) 14.2598 0.480972
\(880\) 0 0
\(881\) −28.6508 −0.965270 −0.482635 0.875822i \(-0.660320\pi\)
−0.482635 + 0.875822i \(0.660320\pi\)
\(882\) 0 0
\(883\) −15.7856 −0.531229 −0.265615 0.964079i \(-0.585575\pi\)
−0.265615 + 0.964079i \(0.585575\pi\)
\(884\) 0 0
\(885\) −1.85782 −0.0624501
\(886\) 0 0
\(887\) −19.4723 −0.653817 −0.326909 0.945056i \(-0.606007\pi\)
−0.326909 + 0.945056i \(0.606007\pi\)
\(888\) 0 0
\(889\) 3.75188 0.125834
\(890\) 0 0
\(891\) 2.02918 0.0679802
\(892\) 0 0
\(893\) −37.4396 −1.25287
\(894\) 0 0
\(895\) −14.7791 −0.494011
\(896\) 0 0
\(897\) 30.4777 1.01762
\(898\) 0 0
\(899\) −78.9804 −2.63414
\(900\) 0 0
\(901\) 4.68648 0.156129
\(902\) 0 0
\(903\) 6.37849 0.212263
\(904\) 0 0
\(905\) 32.1609 1.06907
\(906\) 0 0
\(907\) −11.4770 −0.381089 −0.190544 0.981679i \(-0.561025\pi\)
−0.190544 + 0.981679i \(0.561025\pi\)
\(908\) 0 0
\(909\) 1.78183 0.0590997
\(910\) 0 0
\(911\) −55.2982 −1.83211 −0.916056 0.401050i \(-0.868645\pi\)
−0.916056 + 0.401050i \(0.868645\pi\)
\(912\) 0 0
\(913\) −6.04227 −0.199970
\(914\) 0 0
\(915\) 6.34346 0.209708
\(916\) 0 0
\(917\) −20.0930 −0.663530
\(918\) 0 0
\(919\) −51.3671 −1.69444 −0.847222 0.531239i \(-0.821727\pi\)
−0.847222 + 0.531239i \(0.821727\pi\)
\(920\) 0 0
\(921\) 12.0063 0.395621
\(922\) 0 0
\(923\) 5.49858 0.180988
\(924\) 0 0
\(925\) 8.83594 0.290524
\(926\) 0 0
\(927\) 1.13429 0.0372551
\(928\) 0 0
\(929\) 24.9838 0.819693 0.409847 0.912154i \(-0.365582\pi\)
0.409847 + 0.912154i \(0.365582\pi\)
\(930\) 0 0
\(931\) 23.6062 0.773663
\(932\) 0 0
\(933\) 25.4194 0.832194
\(934\) 0 0
\(935\) 1.14430 0.0374225
\(936\) 0 0
\(937\) −33.0250 −1.07888 −0.539440 0.842024i \(-0.681364\pi\)
−0.539440 + 0.842024i \(0.681364\pi\)
\(938\) 0 0
\(939\) −11.1582 −0.364135
\(940\) 0 0
\(941\) 56.3908 1.83829 0.919144 0.393921i \(-0.128882\pi\)
0.919144 + 0.393921i \(0.128882\pi\)
\(942\) 0 0
\(943\) −63.3783 −2.06388
\(944\) 0 0
\(945\) 9.50554 0.309215
\(946\) 0 0
\(947\) 8.07846 0.262515 0.131257 0.991348i \(-0.458099\pi\)
0.131257 + 0.991348i \(0.458099\pi\)
\(948\) 0 0
\(949\) −76.7851 −2.49255
\(950\) 0 0
\(951\) −5.98209 −0.193982
\(952\) 0 0
\(953\) 43.6028 1.41243 0.706216 0.707997i \(-0.250401\pi\)
0.706216 + 0.707997i \(0.250401\pi\)
\(954\) 0 0
\(955\) 29.0593 0.940336
\(956\) 0 0
\(957\) −3.04236 −0.0983455
\(958\) 0 0
\(959\) 7.31645 0.236261
\(960\) 0 0
\(961\) 39.7529 1.28235
\(962\) 0 0
\(963\) 21.6235 0.696807
\(964\) 0 0
\(965\) −49.3646 −1.58910
\(966\) 0 0
\(967\) 29.9869 0.964314 0.482157 0.876085i \(-0.339853\pi\)
0.482157 + 0.876085i \(0.339853\pi\)
\(968\) 0 0
\(969\) −2.79473 −0.0897797
\(970\) 0 0
\(971\) −18.1930 −0.583841 −0.291920 0.956443i \(-0.594294\pi\)
−0.291920 + 0.956443i \(0.594294\pi\)
\(972\) 0 0
\(973\) 2.13032 0.0682950
\(974\) 0 0
\(975\) −6.70150 −0.214620
\(976\) 0 0
\(977\) −37.6344 −1.20403 −0.602015 0.798485i \(-0.705635\pi\)
−0.602015 + 0.798485i \(0.705635\pi\)
\(978\) 0 0
\(979\) 4.01383 0.128283
\(980\) 0 0
\(981\) 13.8262 0.441438
\(982\) 0 0
\(983\) 30.4375 0.970804 0.485402 0.874291i \(-0.338673\pi\)
0.485402 + 0.874291i \(0.338673\pi\)
\(984\) 0 0
\(985\) −60.8213 −1.93793
\(986\) 0 0
\(987\) 6.58706 0.209668
\(988\) 0 0
\(989\) −66.8018 −2.12417
\(990\) 0 0
\(991\) 35.7667 1.13617 0.568083 0.822971i \(-0.307685\pi\)
0.568083 + 0.822971i \(0.307685\pi\)
\(992\) 0 0
\(993\) 26.3660 0.836699
\(994\) 0 0
\(995\) −10.3030 −0.326628
\(996\) 0 0
\(997\) −50.7437 −1.60707 −0.803534 0.595259i \(-0.797050\pi\)
−0.803534 + 0.595259i \(0.797050\pi\)
\(998\) 0 0
\(999\) 22.4710 0.710951
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 \(a_p\))