Properties

Label 4028.2.a.d.1.14
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 1.14
Root \(-0.755832\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.755832 q^{3} +4.26919 q^{5} -2.09147 q^{7} -2.42872 q^{9} +O(q^{10})\) \(q+0.755832 q^{3} +4.26919 q^{5} -2.09147 q^{7} -2.42872 q^{9} -4.58245 q^{11} +1.90593 q^{13} +3.22679 q^{15} -5.40460 q^{17} -1.00000 q^{19} -1.58080 q^{21} -4.46639 q^{23} +13.2260 q^{25} -4.10320 q^{27} +1.04048 q^{29} -6.77185 q^{31} -3.46356 q^{33} -8.92889 q^{35} -1.41651 q^{37} +1.44056 q^{39} +4.93319 q^{41} +1.29411 q^{43} -10.3687 q^{45} +8.54538 q^{47} -2.62575 q^{49} -4.08497 q^{51} +1.00000 q^{53} -19.5633 q^{55} -0.755832 q^{57} -10.5166 q^{59} +1.99109 q^{61} +5.07959 q^{63} +8.13676 q^{65} -9.79064 q^{67} -3.37584 q^{69} +4.71806 q^{71} -6.64663 q^{73} +9.99661 q^{75} +9.58406 q^{77} -5.80655 q^{79} +4.18482 q^{81} -14.1602 q^{83} -23.0733 q^{85} +0.786425 q^{87} -12.5773 q^{89} -3.98619 q^{91} -5.11838 q^{93} -4.26919 q^{95} -9.06337 q^{97} +11.1295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 0.755832 0.436380 0.218190 0.975906i \(-0.429985\pi\)
0.218190 + 0.975906i \(0.429985\pi\)
\(4\) 0 0
\(5\) 4.26919 1.90924 0.954619 0.297828i \(-0.0962623\pi\)
0.954619 + 0.297828i \(0.0962623\pi\)
\(6\) 0 0
\(7\) −2.09147 −0.790502 −0.395251 0.918573i \(-0.629342\pi\)
−0.395251 + 0.918573i \(0.629342\pi\)
\(8\) 0 0
\(9\) −2.42872 −0.809573
\(10\) 0 0
\(11\) −4.58245 −1.38166 −0.690830 0.723017i \(-0.742755\pi\)
−0.690830 + 0.723017i \(0.742755\pi\)
\(12\) 0 0
\(13\) 1.90593 0.528609 0.264305 0.964439i \(-0.414858\pi\)
0.264305 + 0.964439i \(0.414858\pi\)
\(14\) 0 0
\(15\) 3.22679 0.833153
\(16\) 0 0
\(17\) −5.40460 −1.31081 −0.655404 0.755278i \(-0.727502\pi\)
−0.655404 + 0.755278i \(0.727502\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −1.58080 −0.344959
\(22\) 0 0
\(23\) −4.46639 −0.931307 −0.465654 0.884967i \(-0.654181\pi\)
−0.465654 + 0.884967i \(0.654181\pi\)
\(24\) 0 0
\(25\) 13.2260 2.64519
\(26\) 0 0
\(27\) −4.10320 −0.789661
\(28\) 0 0
\(29\) 1.04048 0.193211 0.0966057 0.995323i \(-0.469201\pi\)
0.0966057 + 0.995323i \(0.469201\pi\)
\(30\) 0 0
\(31\) −6.77185 −1.21626 −0.608130 0.793837i \(-0.708080\pi\)
−0.608130 + 0.793837i \(0.708080\pi\)
\(32\) 0 0
\(33\) −3.46356 −0.602928
\(34\) 0 0
\(35\) −8.92889 −1.50926
\(36\) 0 0
\(37\) −1.41651 −0.232873 −0.116437 0.993198i \(-0.537147\pi\)
−0.116437 + 0.993198i \(0.537147\pi\)
\(38\) 0 0
\(39\) 1.44056 0.230674
\(40\) 0 0
\(41\) 4.93319 0.770435 0.385217 0.922826i \(-0.374126\pi\)
0.385217 + 0.922826i \(0.374126\pi\)
\(42\) 0 0
\(43\) 1.29411 0.197350 0.0986749 0.995120i \(-0.468540\pi\)
0.0986749 + 0.995120i \(0.468540\pi\)
\(44\) 0 0
\(45\) −10.3687 −1.54567
\(46\) 0 0
\(47\) 8.54538 1.24647 0.623236 0.782034i \(-0.285818\pi\)
0.623236 + 0.782034i \(0.285818\pi\)
\(48\) 0 0
\(49\) −2.62575 −0.375107
\(50\) 0 0
\(51\) −4.08497 −0.572010
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −19.5633 −2.63792
\(56\) 0 0
\(57\) −0.755832 −0.100112
\(58\) 0 0
\(59\) −10.5166 −1.36915 −0.684575 0.728942i \(-0.740012\pi\)
−0.684575 + 0.728942i \(0.740012\pi\)
\(60\) 0 0
\(61\) 1.99109 0.254932 0.127466 0.991843i \(-0.459316\pi\)
0.127466 + 0.991843i \(0.459316\pi\)
\(62\) 0 0
\(63\) 5.07959 0.639969
\(64\) 0 0
\(65\) 8.13676 1.00924
\(66\) 0 0
\(67\) −9.79064 −1.19612 −0.598059 0.801452i \(-0.704061\pi\)
−0.598059 + 0.801452i \(0.704061\pi\)
\(68\) 0 0
\(69\) −3.37584 −0.406404
\(70\) 0 0
\(71\) 4.71806 0.559931 0.279965 0.960010i \(-0.409677\pi\)
0.279965 + 0.960010i \(0.409677\pi\)
\(72\) 0 0
\(73\) −6.64663 −0.777929 −0.388965 0.921253i \(-0.627167\pi\)
−0.388965 + 0.921253i \(0.627167\pi\)
\(74\) 0 0
\(75\) 9.99661 1.15431
\(76\) 0 0
\(77\) 9.58406 1.09220
\(78\) 0 0
\(79\) −5.80655 −0.653287 −0.326644 0.945148i \(-0.605918\pi\)
−0.326644 + 0.945148i \(0.605918\pi\)
\(80\) 0 0
\(81\) 4.18482 0.464981
\(82\) 0 0
\(83\) −14.1602 −1.55428 −0.777142 0.629325i \(-0.783331\pi\)
−0.777142 + 0.629325i \(0.783331\pi\)
\(84\) 0 0
\(85\) −23.0733 −2.50265
\(86\) 0 0
\(87\) 0.786425 0.0843136
\(88\) 0 0
\(89\) −12.5773 −1.33319 −0.666595 0.745420i \(-0.732249\pi\)
−0.666595 + 0.745420i \(0.732249\pi\)
\(90\) 0 0
\(91\) −3.98619 −0.417866
\(92\) 0 0
\(93\) −5.11838 −0.530751
\(94\) 0 0
\(95\) −4.26919 −0.438009
\(96\) 0 0
\(97\) −9.06337 −0.920246 −0.460123 0.887855i \(-0.652195\pi\)
−0.460123 + 0.887855i \(0.652195\pi\)
\(98\) 0 0
\(99\) 11.1295 1.11855
\(100\) 0 0
\(101\) 6.13657 0.610612 0.305306 0.952254i \(-0.401241\pi\)
0.305306 + 0.952254i \(0.401241\pi\)
\(102\) 0 0
\(103\) 4.88502 0.481335 0.240667 0.970608i \(-0.422634\pi\)
0.240667 + 0.970608i \(0.422634\pi\)
\(104\) 0 0
\(105\) −6.74874 −0.658609
\(106\) 0 0
\(107\) −1.16312 −0.112443 −0.0562217 0.998418i \(-0.517905\pi\)
−0.0562217 + 0.998418i \(0.517905\pi\)
\(108\) 0 0
\(109\) −16.1455 −1.54646 −0.773229 0.634127i \(-0.781360\pi\)
−0.773229 + 0.634127i \(0.781360\pi\)
\(110\) 0 0
\(111\) −1.07065 −0.101621
\(112\) 0 0
\(113\) −1.12181 −0.105531 −0.0527654 0.998607i \(-0.516804\pi\)
−0.0527654 + 0.998607i \(0.516804\pi\)
\(114\) 0 0
\(115\) −19.0679 −1.77809
\(116\) 0 0
\(117\) −4.62896 −0.427947
\(118\) 0 0
\(119\) 11.3036 1.03620
\(120\) 0 0
\(121\) 9.99882 0.908984
\(122\) 0 0
\(123\) 3.72866 0.336202
\(124\) 0 0
\(125\) 35.1182 3.14107
\(126\) 0 0
\(127\) 12.4138 1.10154 0.550772 0.834656i \(-0.314334\pi\)
0.550772 + 0.834656i \(0.314334\pi\)
\(128\) 0 0
\(129\) 0.978129 0.0861194
\(130\) 0 0
\(131\) −3.81267 −0.333115 −0.166557 0.986032i \(-0.553265\pi\)
−0.166557 + 0.986032i \(0.553265\pi\)
\(132\) 0 0
\(133\) 2.09147 0.181354
\(134\) 0 0
\(135\) −17.5173 −1.50765
\(136\) 0 0
\(137\) −8.05715 −0.688369 −0.344184 0.938902i \(-0.611845\pi\)
−0.344184 + 0.938902i \(0.611845\pi\)
\(138\) 0 0
\(139\) 19.6871 1.66984 0.834918 0.550375i \(-0.185515\pi\)
0.834918 + 0.550375i \(0.185515\pi\)
\(140\) 0 0
\(141\) 6.45887 0.543935
\(142\) 0 0
\(143\) −8.73381 −0.730358
\(144\) 0 0
\(145\) 4.44198 0.368887
\(146\) 0 0
\(147\) −1.98462 −0.163689
\(148\) 0 0
\(149\) −12.7977 −1.04843 −0.524216 0.851586i \(-0.675641\pi\)
−0.524216 + 0.851586i \(0.675641\pi\)
\(150\) 0 0
\(151\) −21.7008 −1.76599 −0.882993 0.469387i \(-0.844475\pi\)
−0.882993 + 0.469387i \(0.844475\pi\)
\(152\) 0 0
\(153\) 13.1263 1.06119
\(154\) 0 0
\(155\) −28.9103 −2.32213
\(156\) 0 0
\(157\) 17.1131 1.36577 0.682886 0.730525i \(-0.260725\pi\)
0.682886 + 0.730525i \(0.260725\pi\)
\(158\) 0 0
\(159\) 0.755832 0.0599414
\(160\) 0 0
\(161\) 9.34133 0.736200
\(162\) 0 0
\(163\) −11.6452 −0.912119 −0.456059 0.889949i \(-0.650740\pi\)
−0.456059 + 0.889949i \(0.650740\pi\)
\(164\) 0 0
\(165\) −14.7866 −1.15113
\(166\) 0 0
\(167\) 16.8173 1.30136 0.650679 0.759353i \(-0.274484\pi\)
0.650679 + 0.759353i \(0.274484\pi\)
\(168\) 0 0
\(169\) −9.36744 −0.720572
\(170\) 0 0
\(171\) 2.42872 0.185729
\(172\) 0 0
\(173\) 10.8256 0.823054 0.411527 0.911397i \(-0.364996\pi\)
0.411527 + 0.911397i \(0.364996\pi\)
\(174\) 0 0
\(175\) −27.6617 −2.09103
\(176\) 0 0
\(177\) −7.94881 −0.597469
\(178\) 0 0
\(179\) 17.8683 1.33554 0.667770 0.744368i \(-0.267249\pi\)
0.667770 + 0.744368i \(0.267249\pi\)
\(180\) 0 0
\(181\) 18.5908 1.38184 0.690922 0.722929i \(-0.257205\pi\)
0.690922 + 0.722929i \(0.257205\pi\)
\(182\) 0 0
\(183\) 1.50493 0.111247
\(184\) 0 0
\(185\) −6.04736 −0.444611
\(186\) 0 0
\(187\) 24.7663 1.81109
\(188\) 0 0
\(189\) 8.58172 0.624229
\(190\) 0 0
\(191\) −2.06510 −0.149426 −0.0747128 0.997205i \(-0.523804\pi\)
−0.0747128 + 0.997205i \(0.523804\pi\)
\(192\) 0 0
\(193\) 13.4781 0.970178 0.485089 0.874465i \(-0.338787\pi\)
0.485089 + 0.874465i \(0.338787\pi\)
\(194\) 0 0
\(195\) 6.15002 0.440412
\(196\) 0 0
\(197\) 12.6889 0.904049 0.452025 0.892005i \(-0.350702\pi\)
0.452025 + 0.892005i \(0.350702\pi\)
\(198\) 0 0
\(199\) −0.932888 −0.0661306 −0.0330653 0.999453i \(-0.510527\pi\)
−0.0330653 + 0.999453i \(0.510527\pi\)
\(200\) 0 0
\(201\) −7.40008 −0.521962
\(202\) 0 0
\(203\) −2.17612 −0.152734
\(204\) 0 0
\(205\) 21.0607 1.47094
\(206\) 0 0
\(207\) 10.8476 0.753961
\(208\) 0 0
\(209\) 4.58245 0.316974
\(210\) 0 0
\(211\) 0.487907 0.0335889 0.0167945 0.999859i \(-0.494654\pi\)
0.0167945 + 0.999859i \(0.494654\pi\)
\(212\) 0 0
\(213\) 3.56606 0.244342
\(214\) 0 0
\(215\) 5.52479 0.376788
\(216\) 0 0
\(217\) 14.1631 0.961456
\(218\) 0 0
\(219\) −5.02374 −0.339473
\(220\) 0 0
\(221\) −10.3008 −0.692905
\(222\) 0 0
\(223\) −16.4800 −1.10358 −0.551791 0.833982i \(-0.686056\pi\)
−0.551791 + 0.833982i \(0.686056\pi\)
\(224\) 0 0
\(225\) −32.1221 −2.14148
\(226\) 0 0
\(227\) −13.7045 −0.909598 −0.454799 0.890594i \(-0.650289\pi\)
−0.454799 + 0.890594i \(0.650289\pi\)
\(228\) 0 0
\(229\) 13.8828 0.917404 0.458702 0.888590i \(-0.348314\pi\)
0.458702 + 0.888590i \(0.348314\pi\)
\(230\) 0 0
\(231\) 7.24394 0.476616
\(232\) 0 0
\(233\) −28.3208 −1.85536 −0.927680 0.373376i \(-0.878200\pi\)
−0.927680 + 0.373376i \(0.878200\pi\)
\(234\) 0 0
\(235\) 36.4818 2.37981
\(236\) 0 0
\(237\) −4.38877 −0.285081
\(238\) 0 0
\(239\) 20.1363 1.30251 0.651255 0.758859i \(-0.274243\pi\)
0.651255 + 0.758859i \(0.274243\pi\)
\(240\) 0 0
\(241\) −6.37249 −0.410488 −0.205244 0.978711i \(-0.565799\pi\)
−0.205244 + 0.978711i \(0.565799\pi\)
\(242\) 0 0
\(243\) 15.4726 0.992569
\(244\) 0 0
\(245\) −11.2098 −0.716168
\(246\) 0 0
\(247\) −1.90593 −0.121271
\(248\) 0 0
\(249\) −10.7027 −0.678258
\(250\) 0 0
\(251\) −6.33554 −0.399896 −0.199948 0.979807i \(-0.564077\pi\)
−0.199948 + 0.979807i \(0.564077\pi\)
\(252\) 0 0
\(253\) 20.4670 1.28675
\(254\) 0 0
\(255\) −17.4395 −1.09210
\(256\) 0 0
\(257\) 15.3878 0.959862 0.479931 0.877306i \(-0.340662\pi\)
0.479931 + 0.877306i \(0.340662\pi\)
\(258\) 0 0
\(259\) 2.96260 0.184087
\(260\) 0 0
\(261\) −2.52702 −0.156419
\(262\) 0 0
\(263\) 1.65417 0.102000 0.0510002 0.998699i \(-0.483759\pi\)
0.0510002 + 0.998699i \(0.483759\pi\)
\(264\) 0 0
\(265\) 4.26919 0.262254
\(266\) 0 0
\(267\) −9.50632 −0.581777
\(268\) 0 0
\(269\) 23.2770 1.41922 0.709612 0.704593i \(-0.248870\pi\)
0.709612 + 0.704593i \(0.248870\pi\)
\(270\) 0 0
\(271\) 8.81860 0.535692 0.267846 0.963462i \(-0.413688\pi\)
0.267846 + 0.963462i \(0.413688\pi\)
\(272\) 0 0
\(273\) −3.01289 −0.182349
\(274\) 0 0
\(275\) −60.6073 −3.65476
\(276\) 0 0
\(277\) 5.30805 0.318930 0.159465 0.987204i \(-0.449023\pi\)
0.159465 + 0.987204i \(0.449023\pi\)
\(278\) 0 0
\(279\) 16.4469 0.984651
\(280\) 0 0
\(281\) −5.32370 −0.317585 −0.158793 0.987312i \(-0.550760\pi\)
−0.158793 + 0.987312i \(0.550760\pi\)
\(282\) 0 0
\(283\) −31.0893 −1.84807 −0.924033 0.382313i \(-0.875128\pi\)
−0.924033 + 0.382313i \(0.875128\pi\)
\(284\) 0 0
\(285\) −3.22679 −0.191138
\(286\) 0 0
\(287\) −10.3176 −0.609030
\(288\) 0 0
\(289\) 12.2097 0.718218
\(290\) 0 0
\(291\) −6.85038 −0.401577
\(292\) 0 0
\(293\) −25.0297 −1.46225 −0.731127 0.682242i \(-0.761005\pi\)
−0.731127 + 0.682242i \(0.761005\pi\)
\(294\) 0 0
\(295\) −44.8975 −2.61403
\(296\) 0 0
\(297\) 18.8027 1.09104
\(298\) 0 0
\(299\) −8.51262 −0.492297
\(300\) 0 0
\(301\) −2.70659 −0.156005
\(302\) 0 0
\(303\) 4.63822 0.266459
\(304\) 0 0
\(305\) 8.50032 0.486727
\(306\) 0 0
\(307\) 26.9466 1.53793 0.768963 0.639293i \(-0.220773\pi\)
0.768963 + 0.639293i \(0.220773\pi\)
\(308\) 0 0
\(309\) 3.69225 0.210045
\(310\) 0 0
\(311\) 21.6551 1.22795 0.613974 0.789326i \(-0.289570\pi\)
0.613974 + 0.789326i \(0.289570\pi\)
\(312\) 0 0
\(313\) 2.58150 0.145915 0.0729574 0.997335i \(-0.476756\pi\)
0.0729574 + 0.997335i \(0.476756\pi\)
\(314\) 0 0
\(315\) 21.6857 1.22185
\(316\) 0 0
\(317\) 1.40108 0.0786926 0.0393463 0.999226i \(-0.487472\pi\)
0.0393463 + 0.999226i \(0.487472\pi\)
\(318\) 0 0
\(319\) −4.76792 −0.266952
\(320\) 0 0
\(321\) −0.879126 −0.0490680
\(322\) 0 0
\(323\) 5.40460 0.300720
\(324\) 0 0
\(325\) 25.2077 1.39827
\(326\) 0 0
\(327\) −12.2033 −0.674843
\(328\) 0 0
\(329\) −17.8724 −0.985338
\(330\) 0 0
\(331\) −11.7553 −0.646131 −0.323066 0.946377i \(-0.604713\pi\)
−0.323066 + 0.946377i \(0.604713\pi\)
\(332\) 0 0
\(333\) 3.44031 0.188528
\(334\) 0 0
\(335\) −41.7981 −2.28367
\(336\) 0 0
\(337\) 27.5609 1.50134 0.750669 0.660679i \(-0.229731\pi\)
0.750669 + 0.660679i \(0.229731\pi\)
\(338\) 0 0
\(339\) −0.847898 −0.0460515
\(340\) 0 0
\(341\) 31.0316 1.68046
\(342\) 0 0
\(343\) 20.1320 1.08702
\(344\) 0 0
\(345\) −14.4121 −0.775922
\(346\) 0 0
\(347\) −1.43946 −0.0772743 −0.0386372 0.999253i \(-0.512302\pi\)
−0.0386372 + 0.999253i \(0.512302\pi\)
\(348\) 0 0
\(349\) −7.49282 −0.401081 −0.200541 0.979685i \(-0.564270\pi\)
−0.200541 + 0.979685i \(0.564270\pi\)
\(350\) 0 0
\(351\) −7.82040 −0.417422
\(352\) 0 0
\(353\) −13.3430 −0.710178 −0.355089 0.934832i \(-0.615549\pi\)
−0.355089 + 0.934832i \(0.615549\pi\)
\(354\) 0 0
\(355\) 20.1423 1.06904
\(356\) 0 0
\(357\) 8.54360 0.452175
\(358\) 0 0
\(359\) 23.8047 1.25637 0.628183 0.778065i \(-0.283799\pi\)
0.628183 + 0.778065i \(0.283799\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 7.55743 0.396662
\(364\) 0 0
\(365\) −28.3757 −1.48525
\(366\) 0 0
\(367\) −8.11128 −0.423405 −0.211703 0.977334i \(-0.567901\pi\)
−0.211703 + 0.977334i \(0.567901\pi\)
\(368\) 0 0
\(369\) −11.9813 −0.623723
\(370\) 0 0
\(371\) −2.09147 −0.108584
\(372\) 0 0
\(373\) 35.9853 1.86325 0.931625 0.363421i \(-0.118391\pi\)
0.931625 + 0.363421i \(0.118391\pi\)
\(374\) 0 0
\(375\) 26.5435 1.37070
\(376\) 0 0
\(377\) 1.98307 0.102133
\(378\) 0 0
\(379\) −33.9515 −1.74397 −0.871986 0.489531i \(-0.837168\pi\)
−0.871986 + 0.489531i \(0.837168\pi\)
\(380\) 0 0
\(381\) 9.38272 0.480691
\(382\) 0 0
\(383\) −29.3988 −1.50221 −0.751105 0.660182i \(-0.770479\pi\)
−0.751105 + 0.660182i \(0.770479\pi\)
\(384\) 0 0
\(385\) 40.9161 2.08528
\(386\) 0 0
\(387\) −3.14303 −0.159769
\(388\) 0 0
\(389\) −4.31425 −0.218741 −0.109370 0.994001i \(-0.534883\pi\)
−0.109370 + 0.994001i \(0.534883\pi\)
\(390\) 0 0
\(391\) 24.1391 1.22076
\(392\) 0 0
\(393\) −2.88174 −0.145365
\(394\) 0 0
\(395\) −24.7892 −1.24728
\(396\) 0 0
\(397\) 0.996779 0.0500269 0.0250135 0.999687i \(-0.492037\pi\)
0.0250135 + 0.999687i \(0.492037\pi\)
\(398\) 0 0
\(399\) 1.58080 0.0791390
\(400\) 0 0
\(401\) −30.8397 −1.54006 −0.770030 0.638007i \(-0.779759\pi\)
−0.770030 + 0.638007i \(0.779759\pi\)
\(402\) 0 0
\(403\) −12.9067 −0.642926
\(404\) 0 0
\(405\) 17.8658 0.887759
\(406\) 0 0
\(407\) 6.49110 0.321752
\(408\) 0 0
\(409\) −29.2447 −1.44606 −0.723029 0.690818i \(-0.757251\pi\)
−0.723029 + 0.690818i \(0.757251\pi\)
\(410\) 0 0
\(411\) −6.08985 −0.300390
\(412\) 0 0
\(413\) 21.9953 1.08232
\(414\) 0 0
\(415\) −60.4526 −2.96750
\(416\) 0 0
\(417\) 14.8801 0.728683
\(418\) 0 0
\(419\) −24.5587 −1.19977 −0.599886 0.800086i \(-0.704787\pi\)
−0.599886 + 0.800086i \(0.704787\pi\)
\(420\) 0 0
\(421\) −13.6879 −0.667108 −0.333554 0.942731i \(-0.608248\pi\)
−0.333554 + 0.942731i \(0.608248\pi\)
\(422\) 0 0
\(423\) −20.7543 −1.00911
\(424\) 0 0
\(425\) −71.4811 −3.46734
\(426\) 0 0
\(427\) −4.16430 −0.201524
\(428\) 0 0
\(429\) −6.60129 −0.318713
\(430\) 0 0
\(431\) −8.76877 −0.422377 −0.211188 0.977445i \(-0.567733\pi\)
−0.211188 + 0.977445i \(0.567733\pi\)
\(432\) 0 0
\(433\) −22.3080 −1.07206 −0.536028 0.844200i \(-0.680076\pi\)
−0.536028 + 0.844200i \(0.680076\pi\)
\(434\) 0 0
\(435\) 3.35739 0.160975
\(436\) 0 0
\(437\) 4.46639 0.213657
\(438\) 0 0
\(439\) 27.9897 1.33587 0.667937 0.744218i \(-0.267178\pi\)
0.667937 + 0.744218i \(0.267178\pi\)
\(440\) 0 0
\(441\) 6.37720 0.303676
\(442\) 0 0
\(443\) −8.56270 −0.406826 −0.203413 0.979093i \(-0.565203\pi\)
−0.203413 + 0.979093i \(0.565203\pi\)
\(444\) 0 0
\(445\) −53.6948 −2.54538
\(446\) 0 0
\(447\) −9.67294 −0.457514
\(448\) 0 0
\(449\) −13.3613 −0.630559 −0.315279 0.948999i \(-0.602098\pi\)
−0.315279 + 0.948999i \(0.602098\pi\)
\(450\) 0 0
\(451\) −22.6061 −1.06448
\(452\) 0 0
\(453\) −16.4022 −0.770640
\(454\) 0 0
\(455\) −17.0178 −0.797807
\(456\) 0 0
\(457\) −30.5153 −1.42745 −0.713723 0.700428i \(-0.752992\pi\)
−0.713723 + 0.700428i \(0.752992\pi\)
\(458\) 0 0
\(459\) 22.1762 1.03509
\(460\) 0 0
\(461\) 28.0025 1.30421 0.652103 0.758130i \(-0.273887\pi\)
0.652103 + 0.758130i \(0.273887\pi\)
\(462\) 0 0
\(463\) −0.235147 −0.0109282 −0.00546411 0.999985i \(-0.501739\pi\)
−0.00546411 + 0.999985i \(0.501739\pi\)
\(464\) 0 0
\(465\) −21.8513 −1.01333
\(466\) 0 0
\(467\) 33.7515 1.56183 0.780917 0.624635i \(-0.214752\pi\)
0.780917 + 0.624635i \(0.214752\pi\)
\(468\) 0 0
\(469\) 20.4769 0.945533
\(470\) 0 0
\(471\) 12.9346 0.595995
\(472\) 0 0
\(473\) −5.93019 −0.272670
\(474\) 0 0
\(475\) −13.2260 −0.606849
\(476\) 0 0
\(477\) −2.42872 −0.111203
\(478\) 0 0
\(479\) −26.5955 −1.21518 −0.607591 0.794250i \(-0.707864\pi\)
−0.607591 + 0.794250i \(0.707864\pi\)
\(480\) 0 0
\(481\) −2.69977 −0.123099
\(482\) 0 0
\(483\) 7.06048 0.321263
\(484\) 0 0
\(485\) −38.6932 −1.75697
\(486\) 0 0
\(487\) 3.39782 0.153970 0.0769849 0.997032i \(-0.475471\pi\)
0.0769849 + 0.997032i \(0.475471\pi\)
\(488\) 0 0
\(489\) −8.80178 −0.398030
\(490\) 0 0
\(491\) 27.6717 1.24881 0.624403 0.781102i \(-0.285342\pi\)
0.624403 + 0.781102i \(0.285342\pi\)
\(492\) 0 0
\(493\) −5.62335 −0.253263
\(494\) 0 0
\(495\) 47.5138 2.13559
\(496\) 0 0
\(497\) −9.86769 −0.442626
\(498\) 0 0
\(499\) 15.9106 0.712255 0.356128 0.934437i \(-0.384097\pi\)
0.356128 + 0.934437i \(0.384097\pi\)
\(500\) 0 0
\(501\) 12.7110 0.567887
\(502\) 0 0
\(503\) −10.8530 −0.483912 −0.241956 0.970287i \(-0.577789\pi\)
−0.241956 + 0.970287i \(0.577789\pi\)
\(504\) 0 0
\(505\) 26.1982 1.16580
\(506\) 0 0
\(507\) −7.08021 −0.314443
\(508\) 0 0
\(509\) −10.9377 −0.484806 −0.242403 0.970176i \(-0.577936\pi\)
−0.242403 + 0.970176i \(0.577936\pi\)
\(510\) 0 0
\(511\) 13.9012 0.614955
\(512\) 0 0
\(513\) 4.10320 0.181161
\(514\) 0 0
\(515\) 20.8551 0.918983
\(516\) 0 0
\(517\) −39.1587 −1.72220
\(518\) 0 0
\(519\) 8.18233 0.359164
\(520\) 0 0
\(521\) −24.1315 −1.05722 −0.528609 0.848865i \(-0.677286\pi\)
−0.528609 + 0.848865i \(0.677286\pi\)
\(522\) 0 0
\(523\) 2.11348 0.0924159 0.0462079 0.998932i \(-0.485286\pi\)
0.0462079 + 0.998932i \(0.485286\pi\)
\(524\) 0 0
\(525\) −20.9076 −0.912483
\(526\) 0 0
\(527\) 36.5991 1.59428
\(528\) 0 0
\(529\) −3.05134 −0.132667
\(530\) 0 0
\(531\) 25.5420 1.10843
\(532\) 0 0
\(533\) 9.40230 0.407259
\(534\) 0 0
\(535\) −4.96559 −0.214681
\(536\) 0 0
\(537\) 13.5054 0.582803
\(538\) 0 0
\(539\) 12.0323 0.518270
\(540\) 0 0
\(541\) 8.28065 0.356013 0.178006 0.984029i \(-0.443035\pi\)
0.178006 + 0.984029i \(0.443035\pi\)
\(542\) 0 0
\(543\) 14.0515 0.603009
\(544\) 0 0
\(545\) −68.9282 −2.95256
\(546\) 0 0
\(547\) 5.35720 0.229057 0.114529 0.993420i \(-0.463464\pi\)
0.114529 + 0.993420i \(0.463464\pi\)
\(548\) 0 0
\(549\) −4.83578 −0.206386
\(550\) 0 0
\(551\) −1.04048 −0.0443257
\(552\) 0 0
\(553\) 12.1442 0.516425
\(554\) 0 0
\(555\) −4.57079 −0.194019
\(556\) 0 0
\(557\) 38.0926 1.61404 0.807018 0.590527i \(-0.201080\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(558\) 0 0
\(559\) 2.46648 0.104321
\(560\) 0 0
\(561\) 18.7192 0.790323
\(562\) 0 0
\(563\) −33.2774 −1.40247 −0.701237 0.712928i \(-0.747369\pi\)
−0.701237 + 0.712928i \(0.747369\pi\)
\(564\) 0 0
\(565\) −4.78921 −0.201483
\(566\) 0 0
\(567\) −8.75244 −0.367568
\(568\) 0 0
\(569\) 39.1870 1.64280 0.821402 0.570350i \(-0.193192\pi\)
0.821402 + 0.570350i \(0.193192\pi\)
\(570\) 0 0
\(571\) 32.2438 1.34936 0.674681 0.738110i \(-0.264281\pi\)
0.674681 + 0.738110i \(0.264281\pi\)
\(572\) 0 0
\(573\) −1.56087 −0.0652063
\(574\) 0 0
\(575\) −59.0723 −2.46349
\(576\) 0 0
\(577\) −13.8047 −0.574698 −0.287349 0.957826i \(-0.592774\pi\)
−0.287349 + 0.957826i \(0.592774\pi\)
\(578\) 0 0
\(579\) 10.1872 0.423366
\(580\) 0 0
\(581\) 29.6157 1.22866
\(582\) 0 0
\(583\) −4.58245 −0.189786
\(584\) 0 0
\(585\) −19.7619 −0.817054
\(586\) 0 0
\(587\) 14.5565 0.600811 0.300406 0.953812i \(-0.402878\pi\)
0.300406 + 0.953812i \(0.402878\pi\)
\(588\) 0 0
\(589\) 6.77185 0.279029
\(590\) 0 0
\(591\) 9.59070 0.394509
\(592\) 0 0
\(593\) 18.6298 0.765033 0.382517 0.923949i \(-0.375058\pi\)
0.382517 + 0.923949i \(0.375058\pi\)
\(594\) 0 0
\(595\) 48.2571 1.97835
\(596\) 0 0
\(597\) −0.705106 −0.0288581
\(598\) 0 0
\(599\) −13.5356 −0.553051 −0.276526 0.961007i \(-0.589183\pi\)
−0.276526 + 0.961007i \(0.589183\pi\)
\(600\) 0 0
\(601\) −39.8556 −1.62574 −0.812872 0.582443i \(-0.802097\pi\)
−0.812872 + 0.582443i \(0.802097\pi\)
\(602\) 0 0
\(603\) 23.7787 0.968344
\(604\) 0 0
\(605\) 42.6868 1.73547
\(606\) 0 0
\(607\) 23.8760 0.969097 0.484549 0.874764i \(-0.338984\pi\)
0.484549 + 0.874764i \(0.338984\pi\)
\(608\) 0 0
\(609\) −1.64478 −0.0666500
\(610\) 0 0
\(611\) 16.2869 0.658896
\(612\) 0 0
\(613\) −35.2215 −1.42258 −0.711291 0.702897i \(-0.751889\pi\)
−0.711291 + 0.702897i \(0.751889\pi\)
\(614\) 0 0
\(615\) 15.9184 0.641890
\(616\) 0 0
\(617\) −14.4938 −0.583496 −0.291748 0.956495i \(-0.594237\pi\)
−0.291748 + 0.956495i \(0.594237\pi\)
\(618\) 0 0
\(619\) 9.77791 0.393007 0.196504 0.980503i \(-0.437041\pi\)
0.196504 + 0.980503i \(0.437041\pi\)
\(620\) 0 0
\(621\) 18.3265 0.735417
\(622\) 0 0
\(623\) 26.3050 1.05389
\(624\) 0 0
\(625\) 83.7963 3.35185
\(626\) 0 0
\(627\) 3.46356 0.138321
\(628\) 0 0
\(629\) 7.65569 0.305252
\(630\) 0 0
\(631\) 24.9888 0.994789 0.497394 0.867525i \(-0.334290\pi\)
0.497394 + 0.867525i \(0.334290\pi\)
\(632\) 0 0
\(633\) 0.368776 0.0146575
\(634\) 0 0
\(635\) 52.9967 2.10311
\(636\) 0 0
\(637\) −5.00448 −0.198285
\(638\) 0 0
\(639\) −11.4588 −0.453305
\(640\) 0 0
\(641\) 3.11175 0.122907 0.0614533 0.998110i \(-0.480426\pi\)
0.0614533 + 0.998110i \(0.480426\pi\)
\(642\) 0 0
\(643\) 20.1805 0.795841 0.397921 0.917420i \(-0.369732\pi\)
0.397921 + 0.917420i \(0.369732\pi\)
\(644\) 0 0
\(645\) 4.17582 0.164423
\(646\) 0 0
\(647\) 7.61650 0.299436 0.149718 0.988729i \(-0.452163\pi\)
0.149718 + 0.988729i \(0.452163\pi\)
\(648\) 0 0
\(649\) 48.1920 1.89170
\(650\) 0 0
\(651\) 10.7049 0.419560
\(652\) 0 0
\(653\) 19.5573 0.765335 0.382667 0.923886i \(-0.375005\pi\)
0.382667 + 0.923886i \(0.375005\pi\)
\(654\) 0 0
\(655\) −16.2770 −0.635996
\(656\) 0 0
\(657\) 16.1428 0.629790
\(658\) 0 0
\(659\) −12.4315 −0.484263 −0.242132 0.970243i \(-0.577847\pi\)
−0.242132 + 0.970243i \(0.577847\pi\)
\(660\) 0 0
\(661\) 24.3990 0.949010 0.474505 0.880253i \(-0.342627\pi\)
0.474505 + 0.880253i \(0.342627\pi\)
\(662\) 0 0
\(663\) −7.78566 −0.302370
\(664\) 0 0
\(665\) 8.92889 0.346247
\(666\) 0 0
\(667\) −4.64717 −0.179939
\(668\) 0 0
\(669\) −12.4561 −0.481581
\(670\) 0 0
\(671\) −9.12404 −0.352230
\(672\) 0 0
\(673\) 31.3700 1.20923 0.604613 0.796520i \(-0.293328\pi\)
0.604613 + 0.796520i \(0.293328\pi\)
\(674\) 0 0
\(675\) −54.2688 −2.08881
\(676\) 0 0
\(677\) −20.8259 −0.800406 −0.400203 0.916427i \(-0.631060\pi\)
−0.400203 + 0.916427i \(0.631060\pi\)
\(678\) 0 0
\(679\) 18.9558 0.727456
\(680\) 0 0
\(681\) −10.3583 −0.396930
\(682\) 0 0
\(683\) 39.2654 1.50245 0.751224 0.660047i \(-0.229464\pi\)
0.751224 + 0.660047i \(0.229464\pi\)
\(684\) 0 0
\(685\) −34.3975 −1.31426
\(686\) 0 0
\(687\) 10.4931 0.400337
\(688\) 0 0
\(689\) 1.90593 0.0726100
\(690\) 0 0
\(691\) −15.1167 −0.575068 −0.287534 0.957770i \(-0.592835\pi\)
−0.287534 + 0.957770i \(0.592835\pi\)
\(692\) 0 0
\(693\) −23.2770 −0.884219
\(694\) 0 0
\(695\) 84.0478 3.18812
\(696\) 0 0
\(697\) −26.6619 −1.00989
\(698\) 0 0
\(699\) −21.4058 −0.809642
\(700\) 0 0
\(701\) −12.1392 −0.458493 −0.229246 0.973368i \(-0.573626\pi\)
−0.229246 + 0.973368i \(0.573626\pi\)
\(702\) 0 0
\(703\) 1.41651 0.0534248
\(704\) 0 0
\(705\) 27.5741 1.03850
\(706\) 0 0
\(707\) −12.8345 −0.482690
\(708\) 0 0
\(709\) −38.8422 −1.45875 −0.729374 0.684115i \(-0.760189\pi\)
−0.729374 + 0.684115i \(0.760189\pi\)
\(710\) 0 0
\(711\) 14.1025 0.528884
\(712\) 0 0
\(713\) 30.2457 1.13271
\(714\) 0 0
\(715\) −37.2863 −1.39443
\(716\) 0 0
\(717\) 15.2197 0.568389
\(718\) 0 0
\(719\) −8.63184 −0.321913 −0.160957 0.986961i \(-0.551458\pi\)
−0.160957 + 0.986961i \(0.551458\pi\)
\(720\) 0 0
\(721\) −10.2169 −0.380496
\(722\) 0 0
\(723\) −4.81653 −0.179129
\(724\) 0 0
\(725\) 13.7613 0.511082
\(726\) 0 0
\(727\) 8.11390 0.300928 0.150464 0.988615i \(-0.451923\pi\)
0.150464 + 0.988615i \(0.451923\pi\)
\(728\) 0 0
\(729\) −0.859772 −0.0318434
\(730\) 0 0
\(731\) −6.99414 −0.258688
\(732\) 0 0
\(733\) −25.7078 −0.949539 −0.474769 0.880110i \(-0.657469\pi\)
−0.474769 + 0.880110i \(0.657469\pi\)
\(734\) 0 0
\(735\) −8.47273 −0.312521
\(736\) 0 0
\(737\) 44.8651 1.65263
\(738\) 0 0
\(739\) −29.1335 −1.07169 −0.535846 0.844316i \(-0.680007\pi\)
−0.535846 + 0.844316i \(0.680007\pi\)
\(740\) 0 0
\(741\) −1.44056 −0.0529203
\(742\) 0 0
\(743\) −1.80153 −0.0660918 −0.0330459 0.999454i \(-0.510521\pi\)
−0.0330459 + 0.999454i \(0.510521\pi\)
\(744\) 0 0
\(745\) −54.6359 −2.00171
\(746\) 0 0
\(747\) 34.3911 1.25831
\(748\) 0 0
\(749\) 2.43264 0.0888868
\(750\) 0 0
\(751\) 36.4147 1.32879 0.664395 0.747381i \(-0.268689\pi\)
0.664395 + 0.747381i \(0.268689\pi\)
\(752\) 0 0
\(753\) −4.78861 −0.174507
\(754\) 0 0
\(755\) −92.6447 −3.37169
\(756\) 0 0
\(757\) 28.8853 1.04985 0.524926 0.851148i \(-0.324093\pi\)
0.524926 + 0.851148i \(0.324093\pi\)
\(758\) 0 0
\(759\) 15.4696 0.561512
\(760\) 0 0
\(761\) 8.04178 0.291514 0.145757 0.989320i \(-0.453438\pi\)
0.145757 + 0.989320i \(0.453438\pi\)
\(762\) 0 0
\(763\) 33.7679 1.22248
\(764\) 0 0
\(765\) 56.0384 2.02607
\(766\) 0 0
\(767\) −20.0440 −0.723745
\(768\) 0 0
\(769\) −33.6211 −1.21241 −0.606204 0.795309i \(-0.707308\pi\)
−0.606204 + 0.795309i \(0.707308\pi\)
\(770\) 0 0
\(771\) 11.6306 0.418864
\(772\) 0 0
\(773\) 42.3933 1.52478 0.762391 0.647117i \(-0.224026\pi\)
0.762391 + 0.647117i \(0.224026\pi\)
\(774\) 0 0
\(775\) −89.5643 −3.21724
\(776\) 0 0
\(777\) 2.23923 0.0803318
\(778\) 0 0
\(779\) −4.93319 −0.176750
\(780\) 0 0
\(781\) −21.6203 −0.773634
\(782\) 0 0
\(783\) −4.26928 −0.152572
\(784\) 0 0
\(785\) 73.0589 2.60759
\(786\) 0 0
\(787\) −37.4901 −1.33638 −0.668189 0.743992i \(-0.732930\pi\)
−0.668189 + 0.743992i \(0.732930\pi\)
\(788\) 0 0
\(789\) 1.25027 0.0445110
\(790\) 0 0
\(791\) 2.34623 0.0834223
\(792\) 0 0
\(793\) 3.79486 0.134760
\(794\) 0 0
\(795\) 3.22679 0.114442
\(796\) 0 0
\(797\) 37.4896 1.32795 0.663975 0.747755i \(-0.268868\pi\)
0.663975 + 0.747755i \(0.268868\pi\)
\(798\) 0 0
\(799\) −46.1844 −1.63389
\(800\) 0 0
\(801\) 30.5467 1.07931
\(802\) 0 0
\(803\) 30.4578 1.07483
\(804\) 0 0
\(805\) 39.8799 1.40558
\(806\) 0 0
\(807\) 17.5935 0.619321
\(808\) 0 0
\(809\) 30.0452 1.05633 0.528167 0.849141i \(-0.322880\pi\)
0.528167 + 0.849141i \(0.322880\pi\)
\(810\) 0 0
\(811\) 47.0199 1.65109 0.825546 0.564335i \(-0.190867\pi\)
0.825546 + 0.564335i \(0.190867\pi\)
\(812\) 0 0
\(813\) 6.66538 0.233765
\(814\) 0 0
\(815\) −49.7154 −1.74145
\(816\) 0 0
\(817\) −1.29411 −0.0452751
\(818\) 0 0
\(819\) 9.68134 0.338293
\(820\) 0 0
\(821\) 51.0087 1.78022 0.890108 0.455749i \(-0.150629\pi\)
0.890108 + 0.455749i \(0.150629\pi\)
\(822\) 0 0
\(823\) −25.2441 −0.879953 −0.439977 0.898009i \(-0.645013\pi\)
−0.439977 + 0.898009i \(0.645013\pi\)
\(824\) 0 0
\(825\) −45.8089 −1.59486
\(826\) 0 0
\(827\) 19.3992 0.674578 0.337289 0.941401i \(-0.390490\pi\)
0.337289 + 0.941401i \(0.390490\pi\)
\(828\) 0 0
\(829\) 44.5506 1.54731 0.773653 0.633610i \(-0.218427\pi\)
0.773653 + 0.633610i \(0.218427\pi\)
\(830\) 0 0
\(831\) 4.01200 0.139175
\(832\) 0 0
\(833\) 14.1911 0.491693
\(834\) 0 0
\(835\) 71.7960 2.48460
\(836\) 0 0
\(837\) 27.7862 0.960433
\(838\) 0 0
\(839\) −24.0866 −0.831563 −0.415781 0.909465i \(-0.636492\pi\)
−0.415781 + 0.909465i \(0.636492\pi\)
\(840\) 0 0
\(841\) −27.9174 −0.962669
\(842\) 0 0
\(843\) −4.02382 −0.138588
\(844\) 0 0
\(845\) −39.9914 −1.37574
\(846\) 0 0
\(847\) −20.9122 −0.718553
\(848\) 0 0
\(849\) −23.4983 −0.806459
\(850\) 0 0
\(851\) 6.32670 0.216877
\(852\) 0 0
\(853\) 21.7912 0.746115 0.373058 0.927808i \(-0.378309\pi\)
0.373058 + 0.927808i \(0.378309\pi\)
\(854\) 0 0
\(855\) 10.3687 0.354600
\(856\) 0 0
\(857\) −2.54144 −0.0868141 −0.0434070 0.999057i \(-0.513821\pi\)
−0.0434070 + 0.999057i \(0.513821\pi\)
\(858\) 0 0
\(859\) −40.7092 −1.38898 −0.694491 0.719502i \(-0.744370\pi\)
−0.694491 + 0.719502i \(0.744370\pi\)
\(860\) 0 0
\(861\) −7.79839 −0.265768
\(862\) 0 0
\(863\) −14.4803 −0.492916 −0.246458 0.969154i \(-0.579267\pi\)
−0.246458 + 0.969154i \(0.579267\pi\)
\(864\) 0 0
\(865\) 46.2165 1.57141
\(866\) 0 0
\(867\) 9.22849 0.313416
\(868\) 0 0
\(869\) 26.6082 0.902621
\(870\) 0 0
\(871\) −18.6603 −0.632279
\(872\) 0 0
\(873\) 22.0124 0.745006
\(874\) 0 0
\(875\) −73.4487 −2.48302
\(876\) 0 0
\(877\) −30.9769 −1.04601 −0.523007 0.852328i \(-0.675190\pi\)
−0.523007 + 0.852328i \(0.675190\pi\)
\(878\) 0 0
\(879\) −18.9183 −0.638098
\(880\) 0 0
\(881\) −47.1900 −1.58987 −0.794936 0.606693i \(-0.792496\pi\)
−0.794936 + 0.606693i \(0.792496\pi\)
\(882\) 0 0
\(883\) 6.60510 0.222279 0.111140 0.993805i \(-0.464550\pi\)
0.111140 + 0.993805i \(0.464550\pi\)
\(884\) 0 0
\(885\) −33.9350 −1.14071
\(886\) 0 0
\(887\) −4.64869 −0.156088 −0.0780439 0.996950i \(-0.524867\pi\)
−0.0780439 + 0.996950i \(0.524867\pi\)
\(888\) 0 0
\(889\) −25.9630 −0.870772
\(890\) 0 0
\(891\) −19.1767 −0.642445
\(892\) 0 0
\(893\) −8.54538 −0.285960
\(894\) 0 0
\(895\) 76.2831 2.54986
\(896\) 0 0
\(897\) −6.43411 −0.214829
\(898\) 0 0
\(899\) −7.04594 −0.234995
\(900\) 0 0
\(901\) −5.40460 −0.180053
\(902\) 0 0
\(903\) −2.04573 −0.0680776
\(904\) 0 0
\(905\) 79.3676 2.63827
\(906\) 0 0
\(907\) −50.9420 −1.69150 −0.845751 0.533577i \(-0.820847\pi\)
−0.845751 + 0.533577i \(0.820847\pi\)
\(908\) 0 0
\(909\) −14.9040 −0.494335
\(910\) 0 0
\(911\) −11.8612 −0.392979 −0.196490 0.980506i \(-0.562954\pi\)
−0.196490 + 0.980506i \(0.562954\pi\)
\(912\) 0 0
\(913\) 64.8884 2.14749
\(914\) 0 0
\(915\) 6.42481 0.212398
\(916\) 0 0
\(917\) 7.97410 0.263328
\(918\) 0 0
\(919\) −32.4608 −1.07078 −0.535392 0.844604i \(-0.679836\pi\)
−0.535392 + 0.844604i \(0.679836\pi\)
\(920\) 0 0
\(921\) 20.3671 0.671120
\(922\) 0 0
\(923\) 8.99228 0.295984
\(924\) 0 0
\(925\) −18.7348 −0.615995
\(926\) 0 0
\(927\) −11.8643 −0.389676
\(928\) 0 0
\(929\) −54.2865 −1.78108 −0.890542 0.454902i \(-0.849674\pi\)
−0.890542 + 0.454902i \(0.849674\pi\)
\(930\) 0 0
\(931\) 2.62575 0.0860554
\(932\) 0 0
\(933\) 16.3676 0.535852
\(934\) 0 0
\(935\) 105.732 3.45781
\(936\) 0 0
\(937\) 2.35844 0.0770468 0.0385234 0.999258i \(-0.487735\pi\)
0.0385234 + 0.999258i \(0.487735\pi\)
\(938\) 0 0
\(939\) 1.95118 0.0636743
\(940\) 0 0
\(941\) −4.54445 −0.148145 −0.0740724 0.997253i \(-0.523600\pi\)
−0.0740724 + 0.997253i \(0.523600\pi\)
\(942\) 0 0
\(943\) −22.0336 −0.717511
\(944\) 0 0
\(945\) 36.6370 1.19180
\(946\) 0 0
\(947\) 30.0143 0.975334 0.487667 0.873030i \(-0.337848\pi\)
0.487667 + 0.873030i \(0.337848\pi\)
\(948\) 0 0
\(949\) −12.6680 −0.411220
\(950\) 0 0
\(951\) 1.05898 0.0343399
\(952\) 0 0
\(953\) 1.85207 0.0599944 0.0299972 0.999550i \(-0.490450\pi\)
0.0299972 + 0.999550i \(0.490450\pi\)
\(954\) 0 0
\(955\) −8.81631 −0.285289
\(956\) 0 0
\(957\) −3.60375 −0.116493
\(958\) 0 0
\(959\) 16.8513 0.544157
\(960\) 0 0
\(961\) 14.8580 0.479289
\(962\) 0 0
\(963\) 2.82490 0.0910311
\(964\) 0 0
\(965\) 57.5408 1.85230
\(966\) 0 0
\(967\) −5.99575 −0.192810 −0.0964052 0.995342i \(-0.530734\pi\)
−0.0964052 + 0.995342i \(0.530734\pi\)
\(968\) 0 0
\(969\) 4.08497 0.131228
\(970\) 0 0
\(971\) −20.7011 −0.664329 −0.332165 0.943221i \(-0.607779\pi\)
−0.332165 + 0.943221i \(0.607779\pi\)
\(972\) 0 0
\(973\) −41.1750 −1.32001
\(974\) 0 0
\(975\) 19.0528 0.610178
\(976\) 0 0
\(977\) 19.9594 0.638556 0.319278 0.947661i \(-0.396560\pi\)
0.319278 + 0.947661i \(0.396560\pi\)
\(978\) 0 0
\(979\) 57.6348 1.84202
\(980\) 0 0
\(981\) 39.2129 1.25197
\(982\) 0 0
\(983\) −52.0436 −1.65993 −0.829966 0.557814i \(-0.811640\pi\)
−0.829966 + 0.557814i \(0.811640\pi\)
\(984\) 0 0
\(985\) 54.1715 1.72605
\(986\) 0 0
\(987\) −13.5085 −0.429982
\(988\) 0 0
\(989\) −5.78000 −0.183793
\(990\) 0 0
\(991\) 12.5003 0.397087 0.198543 0.980092i \(-0.436379\pi\)
0.198543 + 0.980092i \(0.436379\pi\)
\(992\) 0 0
\(993\) −8.88506 −0.281959
\(994\) 0 0
\(995\) −3.98267 −0.126259
\(996\) 0 0
\(997\) −54.9379 −1.73990 −0.869951 0.493139i \(-0.835849\pi\)
−0.869951 + 0.493139i \(0.835849\pi\)
\(998\) 0 0
\(999\) 5.81224 0.183891
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 \(a_p\))