Properties

Label 4028.2.a.d.1.15
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(-1.67288\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.67288 q^{3} -0.778334 q^{5} +3.24553 q^{7} -0.201474 q^{9} +O(q^{10})\) \(q+1.67288 q^{3} -0.778334 q^{5} +3.24553 q^{7} -0.201474 q^{9} -5.19304 q^{11} -4.82763 q^{13} -1.30206 q^{15} +1.25277 q^{17} -1.00000 q^{19} +5.42938 q^{21} +8.02017 q^{23} -4.39420 q^{25} -5.35568 q^{27} -3.73699 q^{29} +8.22083 q^{31} -8.68733 q^{33} -2.52611 q^{35} -4.60720 q^{37} -8.07604 q^{39} -7.33839 q^{41} -7.17686 q^{43} +0.156814 q^{45} +2.69328 q^{47} +3.53345 q^{49} +2.09574 q^{51} +1.00000 q^{53} +4.04192 q^{55} -1.67288 q^{57} +3.81793 q^{59} -2.56764 q^{61} -0.653888 q^{63} +3.75751 q^{65} -6.53327 q^{67} +13.4168 q^{69} +5.85114 q^{71} -11.1689 q^{73} -7.35096 q^{75} -16.8542 q^{77} -2.01851 q^{79} -8.35499 q^{81} -8.37951 q^{83} -0.975075 q^{85} -6.25153 q^{87} -14.3217 q^{89} -15.6682 q^{91} +13.7525 q^{93} +0.778334 q^{95} +8.42831 q^{97} +1.04626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 1.67288 0.965838 0.482919 0.875665i \(-0.339577\pi\)
0.482919 + 0.875665i \(0.339577\pi\)
\(4\) 0 0
\(5\) −0.778334 −0.348082 −0.174041 0.984738i \(-0.555682\pi\)
−0.174041 + 0.984738i \(0.555682\pi\)
\(6\) 0 0
\(7\) 3.24553 1.22669 0.613347 0.789813i \(-0.289823\pi\)
0.613347 + 0.789813i \(0.289823\pi\)
\(8\) 0 0
\(9\) −0.201474 −0.0671579
\(10\) 0 0
\(11\) −5.19304 −1.56576 −0.782880 0.622173i \(-0.786250\pi\)
−0.782880 + 0.622173i \(0.786250\pi\)
\(12\) 0 0
\(13\) −4.82763 −1.33894 −0.669472 0.742838i \(-0.733479\pi\)
−0.669472 + 0.742838i \(0.733479\pi\)
\(14\) 0 0
\(15\) −1.30206 −0.336190
\(16\) 0 0
\(17\) 1.25277 0.303842 0.151921 0.988393i \(-0.451454\pi\)
0.151921 + 0.988393i \(0.451454\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 5.42938 1.18479
\(22\) 0 0
\(23\) 8.02017 1.67232 0.836161 0.548484i \(-0.184795\pi\)
0.836161 + 0.548484i \(0.184795\pi\)
\(24\) 0 0
\(25\) −4.39420 −0.878839
\(26\) 0 0
\(27\) −5.35568 −1.03070
\(28\) 0 0
\(29\) −3.73699 −0.693941 −0.346971 0.937876i \(-0.612790\pi\)
−0.346971 + 0.937876i \(0.612790\pi\)
\(30\) 0 0
\(31\) 8.22083 1.47651 0.738253 0.674524i \(-0.235651\pi\)
0.738253 + 0.674524i \(0.235651\pi\)
\(32\) 0 0
\(33\) −8.68733 −1.51227
\(34\) 0 0
\(35\) −2.52611 −0.426990
\(36\) 0 0
\(37\) −4.60720 −0.757419 −0.378710 0.925516i \(-0.623632\pi\)
−0.378710 + 0.925516i \(0.623632\pi\)
\(38\) 0 0
\(39\) −8.07604 −1.29320
\(40\) 0 0
\(41\) −7.33839 −1.14606 −0.573032 0.819533i \(-0.694233\pi\)
−0.573032 + 0.819533i \(0.694233\pi\)
\(42\) 0 0
\(43\) −7.17686 −1.09446 −0.547230 0.836982i \(-0.684318\pi\)
−0.547230 + 0.836982i \(0.684318\pi\)
\(44\) 0 0
\(45\) 0.156814 0.0233764
\(46\) 0 0
\(47\) 2.69328 0.392855 0.196427 0.980518i \(-0.437066\pi\)
0.196427 + 0.980518i \(0.437066\pi\)
\(48\) 0 0
\(49\) 3.53345 0.504779
\(50\) 0 0
\(51\) 2.09574 0.293462
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 4.04192 0.545012
\(56\) 0 0
\(57\) −1.67288 −0.221578
\(58\) 0 0
\(59\) 3.81793 0.497053 0.248526 0.968625i \(-0.420054\pi\)
0.248526 + 0.968625i \(0.420054\pi\)
\(60\) 0 0
\(61\) −2.56764 −0.328753 −0.164376 0.986398i \(-0.552561\pi\)
−0.164376 + 0.986398i \(0.552561\pi\)
\(62\) 0 0
\(63\) −0.653888 −0.0823822
\(64\) 0 0
\(65\) 3.75751 0.466061
\(66\) 0 0
\(67\) −6.53327 −0.798166 −0.399083 0.916915i \(-0.630671\pi\)
−0.399083 + 0.916915i \(0.630671\pi\)
\(68\) 0 0
\(69\) 13.4168 1.61519
\(70\) 0 0
\(71\) 5.85114 0.694403 0.347202 0.937791i \(-0.387132\pi\)
0.347202 + 0.937791i \(0.387132\pi\)
\(72\) 0 0
\(73\) −11.1689 −1.30722 −0.653609 0.756833i \(-0.726746\pi\)
−0.653609 + 0.756833i \(0.726746\pi\)
\(74\) 0 0
\(75\) −7.35096 −0.848816
\(76\) 0 0
\(77\) −16.8542 −1.92071
\(78\) 0 0
\(79\) −2.01851 −0.227100 −0.113550 0.993532i \(-0.536222\pi\)
−0.113550 + 0.993532i \(0.536222\pi\)
\(80\) 0 0
\(81\) −8.35499 −0.928332
\(82\) 0 0
\(83\) −8.37951 −0.919771 −0.459886 0.887978i \(-0.652110\pi\)
−0.459886 + 0.887978i \(0.652110\pi\)
\(84\) 0 0
\(85\) −0.975075 −0.105762
\(86\) 0 0
\(87\) −6.25153 −0.670235
\(88\) 0 0
\(89\) −14.3217 −1.51810 −0.759048 0.651035i \(-0.774335\pi\)
−0.759048 + 0.651035i \(0.774335\pi\)
\(90\) 0 0
\(91\) −15.6682 −1.64247
\(92\) 0 0
\(93\) 13.7525 1.42606
\(94\) 0 0
\(95\) 0.778334 0.0798554
\(96\) 0 0
\(97\) 8.42831 0.855766 0.427883 0.903834i \(-0.359260\pi\)
0.427883 + 0.903834i \(0.359260\pi\)
\(98\) 0 0
\(99\) 1.04626 0.105153
\(100\) 0 0
\(101\) −5.67029 −0.564215 −0.282108 0.959383i \(-0.591034\pi\)
−0.282108 + 0.959383i \(0.591034\pi\)
\(102\) 0 0
\(103\) −15.8524 −1.56199 −0.780994 0.624539i \(-0.785287\pi\)
−0.780994 + 0.624539i \(0.785287\pi\)
\(104\) 0 0
\(105\) −4.22587 −0.412403
\(106\) 0 0
\(107\) −10.7383 −1.03811 −0.519053 0.854742i \(-0.673715\pi\)
−0.519053 + 0.854742i \(0.673715\pi\)
\(108\) 0 0
\(109\) −14.5132 −1.39011 −0.695055 0.718957i \(-0.744620\pi\)
−0.695055 + 0.718957i \(0.744620\pi\)
\(110\) 0 0
\(111\) −7.70730 −0.731544
\(112\) 0 0
\(113\) 7.07224 0.665301 0.332650 0.943050i \(-0.392057\pi\)
0.332650 + 0.943050i \(0.392057\pi\)
\(114\) 0 0
\(115\) −6.24238 −0.582105
\(116\) 0 0
\(117\) 0.972640 0.0899206
\(118\) 0 0
\(119\) 4.06591 0.372721
\(120\) 0 0
\(121\) 15.9677 1.45161
\(122\) 0 0
\(123\) −12.2762 −1.10691
\(124\) 0 0
\(125\) 7.31182 0.653989
\(126\) 0 0
\(127\) 5.27496 0.468077 0.234039 0.972227i \(-0.424806\pi\)
0.234039 + 0.972227i \(0.424806\pi\)
\(128\) 0 0
\(129\) −12.0060 −1.05707
\(130\) 0 0
\(131\) 1.82656 0.159587 0.0797934 0.996811i \(-0.474574\pi\)
0.0797934 + 0.996811i \(0.474574\pi\)
\(132\) 0 0
\(133\) −3.24553 −0.281423
\(134\) 0 0
\(135\) 4.16851 0.358768
\(136\) 0 0
\(137\) −14.5688 −1.24470 −0.622348 0.782741i \(-0.713821\pi\)
−0.622348 + 0.782741i \(0.713821\pi\)
\(138\) 0 0
\(139\) 23.2106 1.96870 0.984348 0.176235i \(-0.0563919\pi\)
0.984348 + 0.176235i \(0.0563919\pi\)
\(140\) 0 0
\(141\) 4.50553 0.379434
\(142\) 0 0
\(143\) 25.0701 2.09646
\(144\) 0 0
\(145\) 2.90863 0.241548
\(146\) 0 0
\(147\) 5.91104 0.487534
\(148\) 0 0
\(149\) −5.00196 −0.409777 −0.204888 0.978785i \(-0.565683\pi\)
−0.204888 + 0.978785i \(0.565683\pi\)
\(150\) 0 0
\(151\) 15.5101 1.26219 0.631097 0.775704i \(-0.282605\pi\)
0.631097 + 0.775704i \(0.282605\pi\)
\(152\) 0 0
\(153\) −0.252400 −0.0204054
\(154\) 0 0
\(155\) −6.39855 −0.513944
\(156\) 0 0
\(157\) −19.4443 −1.55183 −0.775913 0.630840i \(-0.782710\pi\)
−0.775913 + 0.630840i \(0.782710\pi\)
\(158\) 0 0
\(159\) 1.67288 0.132668
\(160\) 0 0
\(161\) 26.0297 2.05143
\(162\) 0 0
\(163\) 11.9070 0.932630 0.466315 0.884619i \(-0.345581\pi\)
0.466315 + 0.884619i \(0.345581\pi\)
\(164\) 0 0
\(165\) 6.76165 0.526393
\(166\) 0 0
\(167\) 24.3850 1.88697 0.943485 0.331414i \(-0.107526\pi\)
0.943485 + 0.331414i \(0.107526\pi\)
\(168\) 0 0
\(169\) 10.3060 0.792768
\(170\) 0 0
\(171\) 0.201474 0.0154071
\(172\) 0 0
\(173\) 22.9883 1.74777 0.873883 0.486137i \(-0.161594\pi\)
0.873883 + 0.486137i \(0.161594\pi\)
\(174\) 0 0
\(175\) −14.2615 −1.07807
\(176\) 0 0
\(177\) 6.38694 0.480072
\(178\) 0 0
\(179\) 11.0530 0.826141 0.413070 0.910699i \(-0.364456\pi\)
0.413070 + 0.910699i \(0.364456\pi\)
\(180\) 0 0
\(181\) −20.7089 −1.53928 −0.769640 0.638478i \(-0.779564\pi\)
−0.769640 + 0.638478i \(0.779564\pi\)
\(182\) 0 0
\(183\) −4.29535 −0.317522
\(184\) 0 0
\(185\) 3.58594 0.263644
\(186\) 0 0
\(187\) −6.50569 −0.475743
\(188\) 0 0
\(189\) −17.3820 −1.26436
\(190\) 0 0
\(191\) −1.06309 −0.0769226 −0.0384613 0.999260i \(-0.512246\pi\)
−0.0384613 + 0.999260i \(0.512246\pi\)
\(192\) 0 0
\(193\) −11.2404 −0.809098 −0.404549 0.914516i \(-0.632572\pi\)
−0.404549 + 0.914516i \(0.632572\pi\)
\(194\) 0 0
\(195\) 6.28586 0.450140
\(196\) 0 0
\(197\) −10.5120 −0.748952 −0.374476 0.927237i \(-0.622177\pi\)
−0.374476 + 0.927237i \(0.622177\pi\)
\(198\) 0 0
\(199\) −6.37118 −0.451641 −0.225821 0.974169i \(-0.572506\pi\)
−0.225821 + 0.974169i \(0.572506\pi\)
\(200\) 0 0
\(201\) −10.9294 −0.770898
\(202\) 0 0
\(203\) −12.1285 −0.851254
\(204\) 0 0
\(205\) 5.71172 0.398924
\(206\) 0 0
\(207\) −1.61585 −0.112310
\(208\) 0 0
\(209\) 5.19304 0.359210
\(210\) 0 0
\(211\) −0.705035 −0.0485366 −0.0242683 0.999705i \(-0.507726\pi\)
−0.0242683 + 0.999705i \(0.507726\pi\)
\(212\) 0 0
\(213\) 9.78826 0.670681
\(214\) 0 0
\(215\) 5.58599 0.380961
\(216\) 0 0
\(217\) 26.6809 1.81122
\(218\) 0 0
\(219\) −18.6842 −1.26256
\(220\) 0 0
\(221\) −6.04791 −0.406827
\(222\) 0 0
\(223\) 13.3195 0.891940 0.445970 0.895048i \(-0.352859\pi\)
0.445970 + 0.895048i \(0.352859\pi\)
\(224\) 0 0
\(225\) 0.885315 0.0590210
\(226\) 0 0
\(227\) 2.89726 0.192298 0.0961490 0.995367i \(-0.469347\pi\)
0.0961490 + 0.995367i \(0.469347\pi\)
\(228\) 0 0
\(229\) −13.3336 −0.881111 −0.440556 0.897725i \(-0.645219\pi\)
−0.440556 + 0.897725i \(0.645219\pi\)
\(230\) 0 0
\(231\) −28.1950 −1.85509
\(232\) 0 0
\(233\) 12.8323 0.840671 0.420335 0.907369i \(-0.361912\pi\)
0.420335 + 0.907369i \(0.361912\pi\)
\(234\) 0 0
\(235\) −2.09627 −0.136745
\(236\) 0 0
\(237\) −3.37672 −0.219342
\(238\) 0 0
\(239\) 1.49143 0.0964724 0.0482362 0.998836i \(-0.484640\pi\)
0.0482362 + 0.998836i \(0.484640\pi\)
\(240\) 0 0
\(241\) 5.34389 0.344230 0.172115 0.985077i \(-0.444940\pi\)
0.172115 + 0.985077i \(0.444940\pi\)
\(242\) 0 0
\(243\) 2.09015 0.134083
\(244\) 0 0
\(245\) −2.75021 −0.175704
\(246\) 0 0
\(247\) 4.82763 0.307175
\(248\) 0 0
\(249\) −14.0179 −0.888349
\(250\) 0 0
\(251\) −19.1204 −1.20687 −0.603436 0.797411i \(-0.706202\pi\)
−0.603436 + 0.797411i \(0.706202\pi\)
\(252\) 0 0
\(253\) −41.6491 −2.61846
\(254\) 0 0
\(255\) −1.63118 −0.102149
\(256\) 0 0
\(257\) −12.5390 −0.782161 −0.391080 0.920357i \(-0.627899\pi\)
−0.391080 + 0.920357i \(0.627899\pi\)
\(258\) 0 0
\(259\) −14.9528 −0.929122
\(260\) 0 0
\(261\) 0.752905 0.0466036
\(262\) 0 0
\(263\) 15.6258 0.963530 0.481765 0.876300i \(-0.339996\pi\)
0.481765 + 0.876300i \(0.339996\pi\)
\(264\) 0 0
\(265\) −0.778334 −0.0478127
\(266\) 0 0
\(267\) −23.9585 −1.46623
\(268\) 0 0
\(269\) 25.4952 1.55447 0.777235 0.629211i \(-0.216622\pi\)
0.777235 + 0.629211i \(0.216622\pi\)
\(270\) 0 0
\(271\) 13.9737 0.848840 0.424420 0.905466i \(-0.360478\pi\)
0.424420 + 0.905466i \(0.360478\pi\)
\(272\) 0 0
\(273\) −26.2110 −1.58636
\(274\) 0 0
\(275\) 22.8192 1.37605
\(276\) 0 0
\(277\) 1.83060 0.109990 0.0549950 0.998487i \(-0.482486\pi\)
0.0549950 + 0.998487i \(0.482486\pi\)
\(278\) 0 0
\(279\) −1.65628 −0.0991589
\(280\) 0 0
\(281\) 5.13605 0.306391 0.153195 0.988196i \(-0.451044\pi\)
0.153195 + 0.988196i \(0.451044\pi\)
\(282\) 0 0
\(283\) 29.2044 1.73602 0.868010 0.496547i \(-0.165399\pi\)
0.868010 + 0.496547i \(0.165399\pi\)
\(284\) 0 0
\(285\) 1.30206 0.0771273
\(286\) 0 0
\(287\) −23.8169 −1.40587
\(288\) 0 0
\(289\) −15.4306 −0.907680
\(290\) 0 0
\(291\) 14.0996 0.826531
\(292\) 0 0
\(293\) 29.1212 1.70128 0.850638 0.525752i \(-0.176216\pi\)
0.850638 + 0.525752i \(0.176216\pi\)
\(294\) 0 0
\(295\) −2.97163 −0.173015
\(296\) 0 0
\(297\) 27.8123 1.61383
\(298\) 0 0
\(299\) −38.7184 −2.23914
\(300\) 0 0
\(301\) −23.2927 −1.34257
\(302\) 0 0
\(303\) −9.48572 −0.544940
\(304\) 0 0
\(305\) 1.99848 0.114433
\(306\) 0 0
\(307\) 2.49151 0.142198 0.0710991 0.997469i \(-0.477349\pi\)
0.0710991 + 0.997469i \(0.477349\pi\)
\(308\) 0 0
\(309\) −26.5192 −1.50863
\(310\) 0 0
\(311\) −2.81819 −0.159805 −0.0799025 0.996803i \(-0.525461\pi\)
−0.0799025 + 0.996803i \(0.525461\pi\)
\(312\) 0 0
\(313\) −33.3226 −1.88350 −0.941752 0.336309i \(-0.890821\pi\)
−0.941752 + 0.336309i \(0.890821\pi\)
\(314\) 0 0
\(315\) 0.508944 0.0286757
\(316\) 0 0
\(317\) −26.8703 −1.50919 −0.754593 0.656193i \(-0.772166\pi\)
−0.754593 + 0.656193i \(0.772166\pi\)
\(318\) 0 0
\(319\) 19.4063 1.08655
\(320\) 0 0
\(321\) −17.9638 −1.00264
\(322\) 0 0
\(323\) −1.25277 −0.0697061
\(324\) 0 0
\(325\) 21.2135 1.17672
\(326\) 0 0
\(327\) −24.2788 −1.34262
\(328\) 0 0
\(329\) 8.74110 0.481913
\(330\) 0 0
\(331\) 0.719643 0.0395552 0.0197776 0.999804i \(-0.493704\pi\)
0.0197776 + 0.999804i \(0.493704\pi\)
\(332\) 0 0
\(333\) 0.928230 0.0508667
\(334\) 0 0
\(335\) 5.08507 0.277827
\(336\) 0 0
\(337\) −1.71348 −0.0933392 −0.0466696 0.998910i \(-0.514861\pi\)
−0.0466696 + 0.998910i \(0.514861\pi\)
\(338\) 0 0
\(339\) 11.8310 0.642572
\(340\) 0 0
\(341\) −42.6911 −2.31185
\(342\) 0 0
\(343\) −11.2508 −0.607485
\(344\) 0 0
\(345\) −10.4427 −0.562218
\(346\) 0 0
\(347\) 19.6894 1.05698 0.528490 0.848940i \(-0.322758\pi\)
0.528490 + 0.848940i \(0.322758\pi\)
\(348\) 0 0
\(349\) −26.6881 −1.42858 −0.714291 0.699849i \(-0.753250\pi\)
−0.714291 + 0.699849i \(0.753250\pi\)
\(350\) 0 0
\(351\) 25.8552 1.38005
\(352\) 0 0
\(353\) 25.2447 1.34364 0.671819 0.740716i \(-0.265513\pi\)
0.671819 + 0.740716i \(0.265513\pi\)
\(354\) 0 0
\(355\) −4.55415 −0.241709
\(356\) 0 0
\(357\) 6.80177 0.359988
\(358\) 0 0
\(359\) 6.47017 0.341482 0.170741 0.985316i \(-0.445384\pi\)
0.170741 + 0.985316i \(0.445384\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 26.7120 1.40201
\(364\) 0 0
\(365\) 8.69312 0.455018
\(366\) 0 0
\(367\) −16.1206 −0.841487 −0.420744 0.907180i \(-0.638231\pi\)
−0.420744 + 0.907180i \(0.638231\pi\)
\(368\) 0 0
\(369\) 1.47849 0.0769672
\(370\) 0 0
\(371\) 3.24553 0.168499
\(372\) 0 0
\(373\) 31.3368 1.62256 0.811278 0.584660i \(-0.198772\pi\)
0.811278 + 0.584660i \(0.198772\pi\)
\(374\) 0 0
\(375\) 12.2318 0.631647
\(376\) 0 0
\(377\) 18.0408 0.929148
\(378\) 0 0
\(379\) −17.2986 −0.888571 −0.444286 0.895885i \(-0.646542\pi\)
−0.444286 + 0.895885i \(0.646542\pi\)
\(380\) 0 0
\(381\) 8.82437 0.452086
\(382\) 0 0
\(383\) −30.4824 −1.55758 −0.778789 0.627286i \(-0.784166\pi\)
−0.778789 + 0.627286i \(0.784166\pi\)
\(384\) 0 0
\(385\) 13.1182 0.668564
\(386\) 0 0
\(387\) 1.44595 0.0735016
\(388\) 0 0
\(389\) 17.3858 0.881495 0.440747 0.897631i \(-0.354713\pi\)
0.440747 + 0.897631i \(0.354713\pi\)
\(390\) 0 0
\(391\) 10.0474 0.508121
\(392\) 0 0
\(393\) 3.05561 0.154135
\(394\) 0 0
\(395\) 1.57107 0.0790494
\(396\) 0 0
\(397\) −26.2010 −1.31499 −0.657496 0.753458i \(-0.728384\pi\)
−0.657496 + 0.753458i \(0.728384\pi\)
\(398\) 0 0
\(399\) −5.42938 −0.271809
\(400\) 0 0
\(401\) 24.2367 1.21032 0.605161 0.796103i \(-0.293109\pi\)
0.605161 + 0.796103i \(0.293109\pi\)
\(402\) 0 0
\(403\) −39.6871 −1.97696
\(404\) 0 0
\(405\) 6.50297 0.323135
\(406\) 0 0
\(407\) 23.9254 1.18594
\(408\) 0 0
\(409\) −26.9488 −1.33253 −0.666266 0.745714i \(-0.732108\pi\)
−0.666266 + 0.745714i \(0.732108\pi\)
\(410\) 0 0
\(411\) −24.3718 −1.20217
\(412\) 0 0
\(413\) 12.3912 0.609732
\(414\) 0 0
\(415\) 6.52206 0.320155
\(416\) 0 0
\(417\) 38.8285 1.90144
\(418\) 0 0
\(419\) −16.0627 −0.784714 −0.392357 0.919813i \(-0.628340\pi\)
−0.392357 + 0.919813i \(0.628340\pi\)
\(420\) 0 0
\(421\) −10.9619 −0.534250 −0.267125 0.963662i \(-0.586074\pi\)
−0.267125 + 0.963662i \(0.586074\pi\)
\(422\) 0 0
\(423\) −0.542624 −0.0263833
\(424\) 0 0
\(425\) −5.50492 −0.267028
\(426\) 0 0
\(427\) −8.33335 −0.403279
\(428\) 0 0
\(429\) 41.9392 2.02484
\(430\) 0 0
\(431\) −14.3717 −0.692260 −0.346130 0.938187i \(-0.612504\pi\)
−0.346130 + 0.938187i \(0.612504\pi\)
\(432\) 0 0
\(433\) −10.0544 −0.483184 −0.241592 0.970378i \(-0.577670\pi\)
−0.241592 + 0.970378i \(0.577670\pi\)
\(434\) 0 0
\(435\) 4.86578 0.233296
\(436\) 0 0
\(437\) −8.02017 −0.383657
\(438\) 0 0
\(439\) −6.33631 −0.302416 −0.151208 0.988502i \(-0.548316\pi\)
−0.151208 + 0.988502i \(0.548316\pi\)
\(440\) 0 0
\(441\) −0.711897 −0.0338999
\(442\) 0 0
\(443\) −4.84937 −0.230401 −0.115200 0.993342i \(-0.536751\pi\)
−0.115200 + 0.993342i \(0.536751\pi\)
\(444\) 0 0
\(445\) 11.1471 0.528421
\(446\) 0 0
\(447\) −8.36768 −0.395778
\(448\) 0 0
\(449\) 24.0916 1.13695 0.568476 0.822700i \(-0.307533\pi\)
0.568476 + 0.822700i \(0.307533\pi\)
\(450\) 0 0
\(451\) 38.1085 1.79446
\(452\) 0 0
\(453\) 25.9465 1.21907
\(454\) 0 0
\(455\) 12.1951 0.571715
\(456\) 0 0
\(457\) 21.3811 1.00017 0.500084 0.865977i \(-0.333302\pi\)
0.500084 + 0.865977i \(0.333302\pi\)
\(458\) 0 0
\(459\) −6.70944 −0.313170
\(460\) 0 0
\(461\) 14.1902 0.660902 0.330451 0.943823i \(-0.392799\pi\)
0.330451 + 0.943823i \(0.392799\pi\)
\(462\) 0 0
\(463\) −13.1047 −0.609029 −0.304514 0.952508i \(-0.598494\pi\)
−0.304514 + 0.952508i \(0.598494\pi\)
\(464\) 0 0
\(465\) −10.7040 −0.496387
\(466\) 0 0
\(467\) −6.78909 −0.314161 −0.157081 0.987586i \(-0.550208\pi\)
−0.157081 + 0.987586i \(0.550208\pi\)
\(468\) 0 0
\(469\) −21.2039 −0.979105
\(470\) 0 0
\(471\) −32.5280 −1.49881
\(472\) 0 0
\(473\) 37.2697 1.71366
\(474\) 0 0
\(475\) 4.39420 0.201620
\(476\) 0 0
\(477\) −0.201474 −0.00922484
\(478\) 0 0
\(479\) −22.5334 −1.02958 −0.514789 0.857317i \(-0.672130\pi\)
−0.514789 + 0.857317i \(0.672130\pi\)
\(480\) 0 0
\(481\) 22.2419 1.01414
\(482\) 0 0
\(483\) 43.5446 1.98135
\(484\) 0 0
\(485\) −6.56004 −0.297876
\(486\) 0 0
\(487\) 10.7864 0.488780 0.244390 0.969677i \(-0.421412\pi\)
0.244390 + 0.969677i \(0.421412\pi\)
\(488\) 0 0
\(489\) 19.9190 0.900769
\(490\) 0 0
\(491\) 32.0432 1.44609 0.723045 0.690801i \(-0.242742\pi\)
0.723045 + 0.690801i \(0.242742\pi\)
\(492\) 0 0
\(493\) −4.68159 −0.210848
\(494\) 0 0
\(495\) −0.814340 −0.0366019
\(496\) 0 0
\(497\) 18.9901 0.851820
\(498\) 0 0
\(499\) −25.1862 −1.12749 −0.563743 0.825950i \(-0.690639\pi\)
−0.563743 + 0.825950i \(0.690639\pi\)
\(500\) 0 0
\(501\) 40.7932 1.82251
\(502\) 0 0
\(503\) 15.7313 0.701426 0.350713 0.936483i \(-0.385939\pi\)
0.350713 + 0.936483i \(0.385939\pi\)
\(504\) 0 0
\(505\) 4.41338 0.196393
\(506\) 0 0
\(507\) 17.2407 0.765685
\(508\) 0 0
\(509\) 26.0165 1.15316 0.576581 0.817040i \(-0.304386\pi\)
0.576581 + 0.817040i \(0.304386\pi\)
\(510\) 0 0
\(511\) −36.2489 −1.60356
\(512\) 0 0
\(513\) 5.35568 0.236459
\(514\) 0 0
\(515\) 12.3385 0.543699
\(516\) 0 0
\(517\) −13.9863 −0.615116
\(518\) 0 0
\(519\) 38.4566 1.68806
\(520\) 0 0
\(521\) −29.0583 −1.27307 −0.636533 0.771250i \(-0.719632\pi\)
−0.636533 + 0.771250i \(0.719632\pi\)
\(522\) 0 0
\(523\) −10.4208 −0.455668 −0.227834 0.973700i \(-0.573164\pi\)
−0.227834 + 0.973700i \(0.573164\pi\)
\(524\) 0 0
\(525\) −23.8578 −1.04124
\(526\) 0 0
\(527\) 10.2988 0.448624
\(528\) 0 0
\(529\) 41.3232 1.79666
\(530\) 0 0
\(531\) −0.769213 −0.0333810
\(532\) 0 0
\(533\) 35.4270 1.53451
\(534\) 0 0
\(535\) 8.35795 0.361346
\(536\) 0 0
\(537\) 18.4904 0.797918
\(538\) 0 0
\(539\) −18.3494 −0.790363
\(540\) 0 0
\(541\) −17.4953 −0.752183 −0.376091 0.926583i \(-0.622732\pi\)
−0.376091 + 0.926583i \(0.622732\pi\)
\(542\) 0 0
\(543\) −34.6435 −1.48669
\(544\) 0 0
\(545\) 11.2961 0.483872
\(546\) 0 0
\(547\) 1.69061 0.0722852 0.0361426 0.999347i \(-0.488493\pi\)
0.0361426 + 0.999347i \(0.488493\pi\)
\(548\) 0 0
\(549\) 0.517312 0.0220783
\(550\) 0 0
\(551\) 3.73699 0.159201
\(552\) 0 0
\(553\) −6.55113 −0.278582
\(554\) 0 0
\(555\) 5.99885 0.254637
\(556\) 0 0
\(557\) 7.27559 0.308277 0.154138 0.988049i \(-0.450740\pi\)
0.154138 + 0.988049i \(0.450740\pi\)
\(558\) 0 0
\(559\) 34.6472 1.46542
\(560\) 0 0
\(561\) −10.8832 −0.459491
\(562\) 0 0
\(563\) −23.0643 −0.972046 −0.486023 0.873946i \(-0.661553\pi\)
−0.486023 + 0.873946i \(0.661553\pi\)
\(564\) 0 0
\(565\) −5.50457 −0.231579
\(566\) 0 0
\(567\) −27.1163 −1.13878
\(568\) 0 0
\(569\) 9.16968 0.384413 0.192207 0.981355i \(-0.438436\pi\)
0.192207 + 0.981355i \(0.438436\pi\)
\(570\) 0 0
\(571\) −11.8650 −0.496535 −0.248268 0.968692i \(-0.579861\pi\)
−0.248268 + 0.968692i \(0.579861\pi\)
\(572\) 0 0
\(573\) −1.77842 −0.0742947
\(574\) 0 0
\(575\) −35.2422 −1.46970
\(576\) 0 0
\(577\) 11.6802 0.486252 0.243126 0.969995i \(-0.421827\pi\)
0.243126 + 0.969995i \(0.421827\pi\)
\(578\) 0 0
\(579\) −18.8038 −0.781457
\(580\) 0 0
\(581\) −27.1959 −1.12828
\(582\) 0 0
\(583\) −5.19304 −0.215074
\(584\) 0 0
\(585\) −0.757039 −0.0312997
\(586\) 0 0
\(587\) 38.8747 1.60453 0.802266 0.596967i \(-0.203628\pi\)
0.802266 + 0.596967i \(0.203628\pi\)
\(588\) 0 0
\(589\) −8.22083 −0.338734
\(590\) 0 0
\(591\) −17.5854 −0.723366
\(592\) 0 0
\(593\) 44.9056 1.84405 0.922025 0.387129i \(-0.126533\pi\)
0.922025 + 0.387129i \(0.126533\pi\)
\(594\) 0 0
\(595\) −3.16463 −0.129737
\(596\) 0 0
\(597\) −10.6582 −0.436212
\(598\) 0 0
\(599\) 14.3121 0.584778 0.292389 0.956299i \(-0.405550\pi\)
0.292389 + 0.956299i \(0.405550\pi\)
\(600\) 0 0
\(601\) −17.3112 −0.706140 −0.353070 0.935597i \(-0.614862\pi\)
−0.353070 + 0.935597i \(0.614862\pi\)
\(602\) 0 0
\(603\) 1.31628 0.0536031
\(604\) 0 0
\(605\) −12.4282 −0.505277
\(606\) 0 0
\(607\) −1.16252 −0.0471852 −0.0235926 0.999722i \(-0.507510\pi\)
−0.0235926 + 0.999722i \(0.507510\pi\)
\(608\) 0 0
\(609\) −20.2895 −0.822173
\(610\) 0 0
\(611\) −13.0021 −0.526010
\(612\) 0 0
\(613\) 0.545581 0.0220358 0.0110179 0.999939i \(-0.496493\pi\)
0.0110179 + 0.999939i \(0.496493\pi\)
\(614\) 0 0
\(615\) 9.55502 0.385295
\(616\) 0 0
\(617\) 15.1728 0.610834 0.305417 0.952219i \(-0.401204\pi\)
0.305417 + 0.952219i \(0.401204\pi\)
\(618\) 0 0
\(619\) −19.8771 −0.798930 −0.399465 0.916749i \(-0.630804\pi\)
−0.399465 + 0.916749i \(0.630804\pi\)
\(620\) 0 0
\(621\) −42.9535 −1.72366
\(622\) 0 0
\(623\) −46.4814 −1.86224
\(624\) 0 0
\(625\) 16.2799 0.651198
\(626\) 0 0
\(627\) 8.68733 0.346939
\(628\) 0 0
\(629\) −5.77177 −0.230136
\(630\) 0 0
\(631\) −45.5141 −1.81189 −0.905945 0.423396i \(-0.860838\pi\)
−0.905945 + 0.423396i \(0.860838\pi\)
\(632\) 0 0
\(633\) −1.17944 −0.0468785
\(634\) 0 0
\(635\) −4.10568 −0.162929
\(636\) 0 0
\(637\) −17.0582 −0.675870
\(638\) 0 0
\(639\) −1.17885 −0.0466346
\(640\) 0 0
\(641\) −43.8459 −1.73181 −0.865904 0.500210i \(-0.833256\pi\)
−0.865904 + 0.500210i \(0.833256\pi\)
\(642\) 0 0
\(643\) 35.2995 1.39208 0.696038 0.718005i \(-0.254945\pi\)
0.696038 + 0.718005i \(0.254945\pi\)
\(644\) 0 0
\(645\) 9.34469 0.367947
\(646\) 0 0
\(647\) −9.74852 −0.383254 −0.191627 0.981468i \(-0.561376\pi\)
−0.191627 + 0.981468i \(0.561376\pi\)
\(648\) 0 0
\(649\) −19.8267 −0.778265
\(650\) 0 0
\(651\) 44.6340 1.74934
\(652\) 0 0
\(653\) −18.6298 −0.729039 −0.364519 0.931196i \(-0.618767\pi\)
−0.364519 + 0.931196i \(0.618767\pi\)
\(654\) 0 0
\(655\) −1.42167 −0.0555493
\(656\) 0 0
\(657\) 2.25023 0.0877900
\(658\) 0 0
\(659\) −28.5798 −1.11331 −0.556655 0.830744i \(-0.687915\pi\)
−0.556655 + 0.830744i \(0.687915\pi\)
\(660\) 0 0
\(661\) 48.3257 1.87965 0.939827 0.341652i \(-0.110986\pi\)
0.939827 + 0.341652i \(0.110986\pi\)
\(662\) 0 0
\(663\) −10.1174 −0.392929
\(664\) 0 0
\(665\) 2.52611 0.0979582
\(666\) 0 0
\(667\) −29.9713 −1.16049
\(668\) 0 0
\(669\) 22.2819 0.861469
\(670\) 0 0
\(671\) 13.3339 0.514748
\(672\) 0 0
\(673\) 33.0602 1.27438 0.637189 0.770707i \(-0.280097\pi\)
0.637189 + 0.770707i \(0.280097\pi\)
\(674\) 0 0
\(675\) 23.5339 0.905821
\(676\) 0 0
\(677\) 37.7945 1.45256 0.726280 0.687399i \(-0.241247\pi\)
0.726280 + 0.687399i \(0.241247\pi\)
\(678\) 0 0
\(679\) 27.3543 1.04976
\(680\) 0 0
\(681\) 4.84677 0.185729
\(682\) 0 0
\(683\) 4.63831 0.177480 0.0887400 0.996055i \(-0.471716\pi\)
0.0887400 + 0.996055i \(0.471716\pi\)
\(684\) 0 0
\(685\) 11.3394 0.433256
\(686\) 0 0
\(687\) −22.3056 −0.851010
\(688\) 0 0
\(689\) −4.82763 −0.183918
\(690\) 0 0
\(691\) 29.2402 1.11235 0.556175 0.831065i \(-0.312268\pi\)
0.556175 + 0.831065i \(0.312268\pi\)
\(692\) 0 0
\(693\) 3.39567 0.128991
\(694\) 0 0
\(695\) −18.0656 −0.685267
\(696\) 0 0
\(697\) −9.19332 −0.348222
\(698\) 0 0
\(699\) 21.4669 0.811951
\(700\) 0 0
\(701\) −9.20118 −0.347524 −0.173762 0.984788i \(-0.555592\pi\)
−0.173762 + 0.984788i \(0.555592\pi\)
\(702\) 0 0
\(703\) 4.60720 0.173764
\(704\) 0 0
\(705\) −3.50681 −0.132074
\(706\) 0 0
\(707\) −18.4031 −0.692120
\(708\) 0 0
\(709\) 52.7394 1.98067 0.990336 0.138692i \(-0.0442899\pi\)
0.990336 + 0.138692i \(0.0442899\pi\)
\(710\) 0 0
\(711\) 0.406676 0.0152516
\(712\) 0 0
\(713\) 65.9325 2.46919
\(714\) 0 0
\(715\) −19.5129 −0.729740
\(716\) 0 0
\(717\) 2.49498 0.0931767
\(718\) 0 0
\(719\) 25.6194 0.955441 0.477720 0.878512i \(-0.341463\pi\)
0.477720 + 0.878512i \(0.341463\pi\)
\(720\) 0 0
\(721\) −51.4495 −1.91608
\(722\) 0 0
\(723\) 8.93968 0.332470
\(724\) 0 0
\(725\) 16.4211 0.609863
\(726\) 0 0
\(727\) 11.9483 0.443139 0.221569 0.975145i \(-0.428882\pi\)
0.221569 + 0.975145i \(0.428882\pi\)
\(728\) 0 0
\(729\) 28.5615 1.05783
\(730\) 0 0
\(731\) −8.99096 −0.332543
\(732\) 0 0
\(733\) −19.4962 −0.720108 −0.360054 0.932932i \(-0.617242\pi\)
−0.360054 + 0.932932i \(0.617242\pi\)
\(734\) 0 0
\(735\) −4.60077 −0.169702
\(736\) 0 0
\(737\) 33.9275 1.24974
\(738\) 0 0
\(739\) −22.5589 −0.829843 −0.414922 0.909857i \(-0.636191\pi\)
−0.414922 + 0.909857i \(0.636191\pi\)
\(740\) 0 0
\(741\) 8.07604 0.296681
\(742\) 0 0
\(743\) −51.4567 −1.88776 −0.943882 0.330282i \(-0.892856\pi\)
−0.943882 + 0.330282i \(0.892856\pi\)
\(744\) 0 0
\(745\) 3.89320 0.142636
\(746\) 0 0
\(747\) 1.68825 0.0617699
\(748\) 0 0
\(749\) −34.8513 −1.27344
\(750\) 0 0
\(751\) 43.6486 1.59276 0.796380 0.604796i \(-0.206746\pi\)
0.796380 + 0.604796i \(0.206746\pi\)
\(752\) 0 0
\(753\) −31.9862 −1.16564
\(754\) 0 0
\(755\) −12.0720 −0.439347
\(756\) 0 0
\(757\) 40.6663 1.47804 0.739021 0.673683i \(-0.235289\pi\)
0.739021 + 0.673683i \(0.235289\pi\)
\(758\) 0 0
\(759\) −69.6739 −2.52900
\(760\) 0 0
\(761\) −27.2693 −0.988511 −0.494256 0.869317i \(-0.664559\pi\)
−0.494256 + 0.869317i \(0.664559\pi\)
\(762\) 0 0
\(763\) −47.1029 −1.70524
\(764\) 0 0
\(765\) 0.196452 0.00710273
\(766\) 0 0
\(767\) −18.4316 −0.665525
\(768\) 0 0
\(769\) 10.2072 0.368081 0.184041 0.982919i \(-0.441082\pi\)
0.184041 + 0.982919i \(0.441082\pi\)
\(770\) 0 0
\(771\) −20.9762 −0.755440
\(772\) 0 0
\(773\) 29.1663 1.04904 0.524520 0.851398i \(-0.324245\pi\)
0.524520 + 0.851398i \(0.324245\pi\)
\(774\) 0 0
\(775\) −36.1239 −1.29761
\(776\) 0 0
\(777\) −25.0142 −0.897381
\(778\) 0 0
\(779\) 7.33839 0.262925
\(780\) 0 0
\(781\) −30.3852 −1.08727
\(782\) 0 0
\(783\) 20.0141 0.715246
\(784\) 0 0
\(785\) 15.1342 0.540162
\(786\) 0 0
\(787\) 2.45265 0.0874275 0.0437138 0.999044i \(-0.486081\pi\)
0.0437138 + 0.999044i \(0.486081\pi\)
\(788\) 0 0
\(789\) 26.1401 0.930613
\(790\) 0 0
\(791\) 22.9532 0.816121
\(792\) 0 0
\(793\) 12.3956 0.440181
\(794\) 0 0
\(795\) −1.30206 −0.0461793
\(796\) 0 0
\(797\) −31.7954 −1.12625 −0.563125 0.826371i \(-0.690401\pi\)
−0.563125 + 0.826371i \(0.690401\pi\)
\(798\) 0 0
\(799\) 3.37406 0.119366
\(800\) 0 0
\(801\) 2.88544 0.101952
\(802\) 0 0
\(803\) 58.0004 2.04679
\(804\) 0 0
\(805\) −20.2598 −0.714064
\(806\) 0 0
\(807\) 42.6504 1.50137
\(808\) 0 0
\(809\) −4.20199 −0.147734 −0.0738671 0.997268i \(-0.523534\pi\)
−0.0738671 + 0.997268i \(0.523534\pi\)
\(810\) 0 0
\(811\) 1.63821 0.0575252 0.0287626 0.999586i \(-0.490843\pi\)
0.0287626 + 0.999586i \(0.490843\pi\)
\(812\) 0 0
\(813\) 23.3763 0.819841
\(814\) 0 0
\(815\) −9.26764 −0.324631
\(816\) 0 0
\(817\) 7.17686 0.251086
\(818\) 0 0
\(819\) 3.15673 0.110305
\(820\) 0 0
\(821\) −49.7738 −1.73712 −0.868559 0.495585i \(-0.834954\pi\)
−0.868559 + 0.495585i \(0.834954\pi\)
\(822\) 0 0
\(823\) −39.2522 −1.36825 −0.684123 0.729367i \(-0.739815\pi\)
−0.684123 + 0.729367i \(0.739815\pi\)
\(824\) 0 0
\(825\) 38.1738 1.32904
\(826\) 0 0
\(827\) 13.0806 0.454858 0.227429 0.973795i \(-0.426968\pi\)
0.227429 + 0.973795i \(0.426968\pi\)
\(828\) 0 0
\(829\) −16.9126 −0.587398 −0.293699 0.955898i \(-0.594886\pi\)
−0.293699 + 0.955898i \(0.594886\pi\)
\(830\) 0 0
\(831\) 3.06237 0.106233
\(832\) 0 0
\(833\) 4.42661 0.153373
\(834\) 0 0
\(835\) −18.9797 −0.656820
\(836\) 0 0
\(837\) −44.0282 −1.52184
\(838\) 0 0
\(839\) 22.8199 0.787830 0.393915 0.919147i \(-0.371120\pi\)
0.393915 + 0.919147i \(0.371120\pi\)
\(840\) 0 0
\(841\) −15.0349 −0.518445
\(842\) 0 0
\(843\) 8.59199 0.295924
\(844\) 0 0
\(845\) −8.02150 −0.275948
\(846\) 0 0
\(847\) 51.8235 1.78068
\(848\) 0 0
\(849\) 48.8554 1.67671
\(850\) 0 0
\(851\) −36.9506 −1.26665
\(852\) 0 0
\(853\) −42.3169 −1.44890 −0.724451 0.689327i \(-0.757907\pi\)
−0.724451 + 0.689327i \(0.757907\pi\)
\(854\) 0 0
\(855\) −0.156814 −0.00536292
\(856\) 0 0
\(857\) 40.4513 1.38179 0.690895 0.722955i \(-0.257217\pi\)
0.690895 + 0.722955i \(0.257217\pi\)
\(858\) 0 0
\(859\) 33.4670 1.14188 0.570940 0.820992i \(-0.306579\pi\)
0.570940 + 0.820992i \(0.306579\pi\)
\(860\) 0 0
\(861\) −39.8429 −1.35784
\(862\) 0 0
\(863\) −8.18842 −0.278737 −0.139368 0.990241i \(-0.544507\pi\)
−0.139368 + 0.990241i \(0.544507\pi\)
\(864\) 0 0
\(865\) −17.8926 −0.608365
\(866\) 0 0
\(867\) −25.8135 −0.876672
\(868\) 0 0
\(869\) 10.4822 0.355584
\(870\) 0 0
\(871\) 31.5402 1.06870
\(872\) 0 0
\(873\) −1.69808 −0.0574714
\(874\) 0 0
\(875\) 23.7307 0.802245
\(876\) 0 0
\(877\) −5.91392 −0.199699 −0.0998495 0.995003i \(-0.531836\pi\)
−0.0998495 + 0.995003i \(0.531836\pi\)
\(878\) 0 0
\(879\) 48.7162 1.64316
\(880\) 0 0
\(881\) −52.5604 −1.77080 −0.885402 0.464826i \(-0.846117\pi\)
−0.885402 + 0.464826i \(0.846117\pi\)
\(882\) 0 0
\(883\) −18.9559 −0.637917 −0.318959 0.947769i \(-0.603333\pi\)
−0.318959 + 0.947769i \(0.603333\pi\)
\(884\) 0 0
\(885\) −4.97118 −0.167104
\(886\) 0 0
\(887\) −21.8842 −0.734799 −0.367399 0.930063i \(-0.619752\pi\)
−0.367399 + 0.930063i \(0.619752\pi\)
\(888\) 0 0
\(889\) 17.1200 0.574187
\(890\) 0 0
\(891\) 43.3878 1.45355
\(892\) 0 0
\(893\) −2.69328 −0.0901271
\(894\) 0 0
\(895\) −8.60293 −0.287564
\(896\) 0 0
\(897\) −64.7713 −2.16265
\(898\) 0 0
\(899\) −30.7212 −1.02461
\(900\) 0 0
\(901\) 1.25277 0.0417359
\(902\) 0 0
\(903\) −38.9659 −1.29670
\(904\) 0 0
\(905\) 16.1184 0.535795
\(906\) 0 0
\(907\) 35.5215 1.17947 0.589735 0.807597i \(-0.299232\pi\)
0.589735 + 0.807597i \(0.299232\pi\)
\(908\) 0 0
\(909\) 1.14241 0.0378915
\(910\) 0 0
\(911\) −16.4978 −0.546596 −0.273298 0.961929i \(-0.588114\pi\)
−0.273298 + 0.961929i \(0.588114\pi\)
\(912\) 0 0
\(913\) 43.5151 1.44014
\(914\) 0 0
\(915\) 3.34322 0.110523
\(916\) 0 0
\(917\) 5.92814 0.195764
\(918\) 0 0
\(919\) −26.4940 −0.873956 −0.436978 0.899472i \(-0.643951\pi\)
−0.436978 + 0.899472i \(0.643951\pi\)
\(920\) 0 0
\(921\) 4.16800 0.137340
\(922\) 0 0
\(923\) −28.2471 −0.929766
\(924\) 0 0
\(925\) 20.2450 0.665650
\(926\) 0 0
\(927\) 3.19385 0.104900
\(928\) 0 0
\(929\) −49.4200 −1.62142 −0.810709 0.585449i \(-0.800918\pi\)
−0.810709 + 0.585449i \(0.800918\pi\)
\(930\) 0 0
\(931\) −3.53345 −0.115804
\(932\) 0 0
\(933\) −4.71450 −0.154346
\(934\) 0 0
\(935\) 5.06360 0.165597
\(936\) 0 0
\(937\) −52.6725 −1.72073 −0.860367 0.509675i \(-0.829766\pi\)
−0.860367 + 0.509675i \(0.829766\pi\)
\(938\) 0 0
\(939\) −55.7447 −1.81916
\(940\) 0 0
\(941\) 12.5292 0.408441 0.204221 0.978925i \(-0.434534\pi\)
0.204221 + 0.978925i \(0.434534\pi\)
\(942\) 0 0
\(943\) −58.8552 −1.91659
\(944\) 0 0
\(945\) 13.5290 0.440099
\(946\) 0 0
\(947\) 40.5778 1.31860 0.659301 0.751879i \(-0.270852\pi\)
0.659301 + 0.751879i \(0.270852\pi\)
\(948\) 0 0
\(949\) 53.9192 1.75029
\(950\) 0 0
\(951\) −44.9508 −1.45763
\(952\) 0 0
\(953\) 1.78729 0.0578960 0.0289480 0.999581i \(-0.490784\pi\)
0.0289480 + 0.999581i \(0.490784\pi\)
\(954\) 0 0
\(955\) 0.827440 0.0267753
\(956\) 0 0
\(957\) 32.4645 1.04943
\(958\) 0 0
\(959\) −47.2834 −1.52686
\(960\) 0 0
\(961\) 36.5821 1.18007
\(962\) 0 0
\(963\) 2.16348 0.0697170
\(964\) 0 0
\(965\) 8.74875 0.281632
\(966\) 0 0
\(967\) −2.08006 −0.0668901 −0.0334450 0.999441i \(-0.510648\pi\)
−0.0334450 + 0.999441i \(0.510648\pi\)
\(968\) 0 0
\(969\) −2.09574 −0.0673247
\(970\) 0 0
\(971\) 19.3316 0.620379 0.310190 0.950675i \(-0.399607\pi\)
0.310190 + 0.950675i \(0.399607\pi\)
\(972\) 0 0
\(973\) 75.3306 2.41499
\(974\) 0 0
\(975\) 35.4877 1.13652
\(976\) 0 0
\(977\) −33.4729 −1.07089 −0.535447 0.844569i \(-0.679857\pi\)
−0.535447 + 0.844569i \(0.679857\pi\)
\(978\) 0 0
\(979\) 74.3731 2.37697
\(980\) 0 0
\(981\) 2.92402 0.0933568
\(982\) 0 0
\(983\) −46.4778 −1.48241 −0.741205 0.671279i \(-0.765745\pi\)
−0.741205 + 0.671279i \(0.765745\pi\)
\(984\) 0 0
\(985\) 8.18188 0.260696
\(986\) 0 0
\(987\) 14.6228 0.465449
\(988\) 0 0
\(989\) −57.5596 −1.83029
\(990\) 0 0
\(991\) 25.7412 0.817696 0.408848 0.912602i \(-0.365931\pi\)
0.408848 + 0.912602i \(0.365931\pi\)
\(992\) 0 0
\(993\) 1.20388 0.0382039
\(994\) 0 0
\(995\) 4.95891 0.157208
\(996\) 0 0
\(997\) 39.3208 1.24530 0.622650 0.782500i \(-0.286056\pi\)
0.622650 + 0.782500i \(0.286056\pi\)
\(998\) 0 0
\(999\) 24.6747 0.780673
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 \(a_p\))