Properties

Label 6036.2.a.i.1.3
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -3.00702 q^{5} +4.42560 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -3.00702 q^{5} +4.42560 q^{7} +1.00000 q^{9} -1.26137 q^{11} -7.02573 q^{13} +3.00702 q^{15} +4.46748 q^{17} -6.47908 q^{19} -4.42560 q^{21} -5.72649 q^{23} +4.04214 q^{25} -1.00000 q^{27} -5.47114 q^{29} +3.83015 q^{31} +1.26137 q^{33} -13.3078 q^{35} +1.66867 q^{37} +7.02573 q^{39} +3.44867 q^{41} +7.06939 q^{43} -3.00702 q^{45} +2.66617 q^{47} +12.5859 q^{49} -4.46748 q^{51} -11.5714 q^{53} +3.79297 q^{55} +6.47908 q^{57} +8.23464 q^{59} +12.8932 q^{61} +4.42560 q^{63} +21.1265 q^{65} +7.21874 q^{67} +5.72649 q^{69} +3.73003 q^{71} -13.1020 q^{73} -4.04214 q^{75} -5.58233 q^{77} -5.90073 q^{79} +1.00000 q^{81} +2.99590 q^{83} -13.4338 q^{85} +5.47114 q^{87} -14.3130 q^{89} -31.0931 q^{91} -3.83015 q^{93} +19.4827 q^{95} -9.56984 q^{97} -1.26137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 26q^{3} + 6q^{5} + 5q^{7} + 26q^{9} + O(q^{10}) \) \( 26q - 26q^{3} + 6q^{5} + 5q^{7} + 26q^{9} - 11q^{11} + 13q^{13} - 6q^{15} + 12q^{17} - q^{19} - 5q^{21} - 22q^{23} + 48q^{25} - 26q^{27} + 6q^{29} + 19q^{31} + 11q^{33} - 21q^{35} + 20q^{37} - 13q^{39} + 25q^{41} + 4q^{43} + 6q^{45} + 8q^{47} + 67q^{49} - 12q^{51} - 5q^{53} + 20q^{55} + q^{57} - 18q^{59} + 43q^{61} + 5q^{63} + 41q^{65} + 5q^{67} + 22q^{69} - q^{71} + 22q^{73} - 48q^{75} + 23q^{77} + 16q^{79} + 26q^{81} - 19q^{83} + 29q^{85} - 6q^{87} + 49q^{89} - 13q^{91} - 19q^{93} - 26q^{95} + 25q^{97} - 11q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −3.00702 −1.34478 −0.672389 0.740198i \(-0.734732\pi\)
−0.672389 + 0.740198i \(0.734732\pi\)
\(6\) 0 0
\(7\) 4.42560 1.67272 0.836359 0.548182i \(-0.184680\pi\)
0.836359 + 0.548182i \(0.184680\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.26137 −0.380318 −0.190159 0.981753i \(-0.560900\pi\)
−0.190159 + 0.981753i \(0.560900\pi\)
\(12\) 0 0
\(13\) −7.02573 −1.94859 −0.974294 0.225281i \(-0.927670\pi\)
−0.974294 + 0.225281i \(0.927670\pi\)
\(14\) 0 0
\(15\) 3.00702 0.776408
\(16\) 0 0
\(17\) 4.46748 1.08352 0.541761 0.840533i \(-0.317758\pi\)
0.541761 + 0.840533i \(0.317758\pi\)
\(18\) 0 0
\(19\) −6.47908 −1.48640 −0.743202 0.669067i \(-0.766694\pi\)
−0.743202 + 0.669067i \(0.766694\pi\)
\(20\) 0 0
\(21\) −4.42560 −0.965744
\(22\) 0 0
\(23\) −5.72649 −1.19406 −0.597028 0.802221i \(-0.703652\pi\)
−0.597028 + 0.802221i \(0.703652\pi\)
\(24\) 0 0
\(25\) 4.04214 0.808428
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.47114 −1.01597 −0.507983 0.861367i \(-0.669609\pi\)
−0.507983 + 0.861367i \(0.669609\pi\)
\(30\) 0 0
\(31\) 3.83015 0.687915 0.343958 0.938985i \(-0.388232\pi\)
0.343958 + 0.938985i \(0.388232\pi\)
\(32\) 0 0
\(33\) 1.26137 0.219577
\(34\) 0 0
\(35\) −13.3078 −2.24943
\(36\) 0 0
\(37\) 1.66867 0.274328 0.137164 0.990548i \(-0.456201\pi\)
0.137164 + 0.990548i \(0.456201\pi\)
\(38\) 0 0
\(39\) 7.02573 1.12502
\(40\) 0 0
\(41\) 3.44867 0.538591 0.269296 0.963058i \(-0.413209\pi\)
0.269296 + 0.963058i \(0.413209\pi\)
\(42\) 0 0
\(43\) 7.06939 1.07807 0.539036 0.842283i \(-0.318789\pi\)
0.539036 + 0.842283i \(0.318789\pi\)
\(44\) 0 0
\(45\) −3.00702 −0.448259
\(46\) 0 0
\(47\) 2.66617 0.388900 0.194450 0.980912i \(-0.437708\pi\)
0.194450 + 0.980912i \(0.437708\pi\)
\(48\) 0 0
\(49\) 12.5859 1.79799
\(50\) 0 0
\(51\) −4.46748 −0.625572
\(52\) 0 0
\(53\) −11.5714 −1.58946 −0.794729 0.606964i \(-0.792387\pi\)
−0.794729 + 0.606964i \(0.792387\pi\)
\(54\) 0 0
\(55\) 3.79297 0.511444
\(56\) 0 0
\(57\) 6.47908 0.858176
\(58\) 0 0
\(59\) 8.23464 1.07206 0.536029 0.844199i \(-0.319924\pi\)
0.536029 + 0.844199i \(0.319924\pi\)
\(60\) 0 0
\(61\) 12.8932 1.65081 0.825403 0.564544i \(-0.190948\pi\)
0.825403 + 0.564544i \(0.190948\pi\)
\(62\) 0 0
\(63\) 4.42560 0.557573
\(64\) 0 0
\(65\) 21.1265 2.62042
\(66\) 0 0
\(67\) 7.21874 0.881909 0.440954 0.897529i \(-0.354640\pi\)
0.440954 + 0.897529i \(0.354640\pi\)
\(68\) 0 0
\(69\) 5.72649 0.689388
\(70\) 0 0
\(71\) 3.73003 0.442673 0.221336 0.975198i \(-0.428958\pi\)
0.221336 + 0.975198i \(0.428958\pi\)
\(72\) 0 0
\(73\) −13.1020 −1.53347 −0.766735 0.641964i \(-0.778120\pi\)
−0.766735 + 0.641964i \(0.778120\pi\)
\(74\) 0 0
\(75\) −4.04214 −0.466746
\(76\) 0 0
\(77\) −5.58233 −0.636165
\(78\) 0 0
\(79\) −5.90073 −0.663884 −0.331942 0.943300i \(-0.607704\pi\)
−0.331942 + 0.943300i \(0.607704\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.99590 0.328843 0.164421 0.986390i \(-0.447424\pi\)
0.164421 + 0.986390i \(0.447424\pi\)
\(84\) 0 0
\(85\) −13.4338 −1.45710
\(86\) 0 0
\(87\) 5.47114 0.586568
\(88\) 0 0
\(89\) −14.3130 −1.51717 −0.758586 0.651573i \(-0.774109\pi\)
−0.758586 + 0.651573i \(0.774109\pi\)
\(90\) 0 0
\(91\) −31.0931 −3.25944
\(92\) 0 0
\(93\) −3.83015 −0.397168
\(94\) 0 0
\(95\) 19.4827 1.99888
\(96\) 0 0
\(97\) −9.56984 −0.971670 −0.485835 0.874051i \(-0.661484\pi\)
−0.485835 + 0.874051i \(0.661484\pi\)
\(98\) 0 0
\(99\) −1.26137 −0.126773
\(100\) 0 0
\(101\) −11.6943 −1.16363 −0.581814 0.813322i \(-0.697657\pi\)
−0.581814 + 0.813322i \(0.697657\pi\)
\(102\) 0 0
\(103\) 0.703986 0.0693658 0.0346829 0.999398i \(-0.488958\pi\)
0.0346829 + 0.999398i \(0.488958\pi\)
\(104\) 0 0
\(105\) 13.3078 1.29871
\(106\) 0 0
\(107\) −9.02064 −0.872058 −0.436029 0.899933i \(-0.643615\pi\)
−0.436029 + 0.899933i \(0.643615\pi\)
\(108\) 0 0
\(109\) 16.0323 1.53561 0.767806 0.640683i \(-0.221349\pi\)
0.767806 + 0.640683i \(0.221349\pi\)
\(110\) 0 0
\(111\) −1.66867 −0.158383
\(112\) 0 0
\(113\) −9.36851 −0.881315 −0.440658 0.897675i \(-0.645255\pi\)
−0.440658 + 0.897675i \(0.645255\pi\)
\(114\) 0 0
\(115\) 17.2196 1.60574
\(116\) 0 0
\(117\) −7.02573 −0.649529
\(118\) 0 0
\(119\) 19.7712 1.81243
\(120\) 0 0
\(121\) −9.40894 −0.855358
\(122\) 0 0
\(123\) −3.44867 −0.310956
\(124\) 0 0
\(125\) 2.88030 0.257622
\(126\) 0 0
\(127\) 1.24996 0.110916 0.0554581 0.998461i \(-0.482338\pi\)
0.0554581 + 0.998461i \(0.482338\pi\)
\(128\) 0 0
\(129\) −7.06939 −0.622425
\(130\) 0 0
\(131\) 13.7936 1.20516 0.602578 0.798060i \(-0.294140\pi\)
0.602578 + 0.798060i \(0.294140\pi\)
\(132\) 0 0
\(133\) −28.6738 −2.48633
\(134\) 0 0
\(135\) 3.00702 0.258803
\(136\) 0 0
\(137\) −17.0579 −1.45735 −0.728676 0.684858i \(-0.759864\pi\)
−0.728676 + 0.684858i \(0.759864\pi\)
\(138\) 0 0
\(139\) −5.40359 −0.458327 −0.229163 0.973388i \(-0.573599\pi\)
−0.229163 + 0.973388i \(0.573599\pi\)
\(140\) 0 0
\(141\) −2.66617 −0.224532
\(142\) 0 0
\(143\) 8.86207 0.741084
\(144\) 0 0
\(145\) 16.4518 1.36625
\(146\) 0 0
\(147\) −12.5859 −1.03807
\(148\) 0 0
\(149\) 3.74723 0.306985 0.153492 0.988150i \(-0.450948\pi\)
0.153492 + 0.988150i \(0.450948\pi\)
\(150\) 0 0
\(151\) 23.7345 1.93149 0.965743 0.259500i \(-0.0835576\pi\)
0.965743 + 0.259500i \(0.0835576\pi\)
\(152\) 0 0
\(153\) 4.46748 0.361174
\(154\) 0 0
\(155\) −11.5173 −0.925093
\(156\) 0 0
\(157\) 23.3909 1.86679 0.933397 0.358846i \(-0.116830\pi\)
0.933397 + 0.358846i \(0.116830\pi\)
\(158\) 0 0
\(159\) 11.5714 0.917674
\(160\) 0 0
\(161\) −25.3431 −1.99732
\(162\) 0 0
\(163\) 13.5342 1.06008 0.530042 0.847971i \(-0.322176\pi\)
0.530042 + 0.847971i \(0.322176\pi\)
\(164\) 0 0
\(165\) −3.79297 −0.295282
\(166\) 0 0
\(167\) 10.5120 0.813445 0.406723 0.913552i \(-0.366672\pi\)
0.406723 + 0.913552i \(0.366672\pi\)
\(168\) 0 0
\(169\) 36.3609 2.79699
\(170\) 0 0
\(171\) −6.47908 −0.495468
\(172\) 0 0
\(173\) 11.4272 0.868796 0.434398 0.900721i \(-0.356961\pi\)
0.434398 + 0.900721i \(0.356961\pi\)
\(174\) 0 0
\(175\) 17.8889 1.35227
\(176\) 0 0
\(177\) −8.23464 −0.618953
\(178\) 0 0
\(179\) −22.8420 −1.70729 −0.853646 0.520854i \(-0.825614\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(180\) 0 0
\(181\) 6.70936 0.498703 0.249351 0.968413i \(-0.419783\pi\)
0.249351 + 0.968413i \(0.419783\pi\)
\(182\) 0 0
\(183\) −12.8932 −0.953093
\(184\) 0 0
\(185\) −5.01771 −0.368910
\(186\) 0 0
\(187\) −5.63516 −0.412083
\(188\) 0 0
\(189\) −4.42560 −0.321915
\(190\) 0 0
\(191\) −7.17863 −0.519427 −0.259714 0.965686i \(-0.583628\pi\)
−0.259714 + 0.965686i \(0.583628\pi\)
\(192\) 0 0
\(193\) 19.2715 1.38719 0.693596 0.720364i \(-0.256025\pi\)
0.693596 + 0.720364i \(0.256025\pi\)
\(194\) 0 0
\(195\) −21.1265 −1.51290
\(196\) 0 0
\(197\) 19.7295 1.40567 0.702833 0.711355i \(-0.251918\pi\)
0.702833 + 0.711355i \(0.251918\pi\)
\(198\) 0 0
\(199\) 10.7240 0.760204 0.380102 0.924945i \(-0.375889\pi\)
0.380102 + 0.924945i \(0.375889\pi\)
\(200\) 0 0
\(201\) −7.21874 −0.509170
\(202\) 0 0
\(203\) −24.2131 −1.69942
\(204\) 0 0
\(205\) −10.3702 −0.724285
\(206\) 0 0
\(207\) −5.72649 −0.398018
\(208\) 0 0
\(209\) 8.17254 0.565307
\(210\) 0 0
\(211\) −23.1655 −1.59478 −0.797391 0.603463i \(-0.793787\pi\)
−0.797391 + 0.603463i \(0.793787\pi\)
\(212\) 0 0
\(213\) −3.73003 −0.255577
\(214\) 0 0
\(215\) −21.2578 −1.44977
\(216\) 0 0
\(217\) 16.9507 1.15069
\(218\) 0 0
\(219\) 13.1020 0.885349
\(220\) 0 0
\(221\) −31.3873 −2.11134
\(222\) 0 0
\(223\) 19.5792 1.31112 0.655561 0.755142i \(-0.272432\pi\)
0.655561 + 0.755142i \(0.272432\pi\)
\(224\) 0 0
\(225\) 4.04214 0.269476
\(226\) 0 0
\(227\) 13.6014 0.902757 0.451379 0.892333i \(-0.350932\pi\)
0.451379 + 0.892333i \(0.350932\pi\)
\(228\) 0 0
\(229\) −12.4302 −0.821413 −0.410706 0.911768i \(-0.634718\pi\)
−0.410706 + 0.911768i \(0.634718\pi\)
\(230\) 0 0
\(231\) 5.58233 0.367290
\(232\) 0 0
\(233\) −11.2581 −0.737544 −0.368772 0.929520i \(-0.620222\pi\)
−0.368772 + 0.929520i \(0.620222\pi\)
\(234\) 0 0
\(235\) −8.01721 −0.522985
\(236\) 0 0
\(237\) 5.90073 0.383293
\(238\) 0 0
\(239\) 23.0467 1.49076 0.745382 0.666637i \(-0.232267\pi\)
0.745382 + 0.666637i \(0.232267\pi\)
\(240\) 0 0
\(241\) 25.7686 1.65990 0.829951 0.557836i \(-0.188368\pi\)
0.829951 + 0.557836i \(0.188368\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −37.8460 −2.41789
\(246\) 0 0
\(247\) 45.5203 2.89639
\(248\) 0 0
\(249\) −2.99590 −0.189857
\(250\) 0 0
\(251\) −4.22022 −0.266378 −0.133189 0.991091i \(-0.542522\pi\)
−0.133189 + 0.991091i \(0.542522\pi\)
\(252\) 0 0
\(253\) 7.22324 0.454121
\(254\) 0 0
\(255\) 13.4338 0.841255
\(256\) 0 0
\(257\) −15.8165 −0.986607 −0.493304 0.869857i \(-0.664211\pi\)
−0.493304 + 0.869857i \(0.664211\pi\)
\(258\) 0 0
\(259\) 7.38486 0.458873
\(260\) 0 0
\(261\) −5.47114 −0.338655
\(262\) 0 0
\(263\) 13.1279 0.809503 0.404752 0.914427i \(-0.367358\pi\)
0.404752 + 0.914427i \(0.367358\pi\)
\(264\) 0 0
\(265\) 34.7955 2.13747
\(266\) 0 0
\(267\) 14.3130 0.875939
\(268\) 0 0
\(269\) 7.27608 0.443630 0.221815 0.975089i \(-0.428802\pi\)
0.221815 + 0.975089i \(0.428802\pi\)
\(270\) 0 0
\(271\) 5.30166 0.322053 0.161026 0.986950i \(-0.448520\pi\)
0.161026 + 0.986950i \(0.448520\pi\)
\(272\) 0 0
\(273\) 31.0931 1.88184
\(274\) 0 0
\(275\) −5.09865 −0.307460
\(276\) 0 0
\(277\) −6.17368 −0.370940 −0.185470 0.982650i \(-0.559381\pi\)
−0.185470 + 0.982650i \(0.559381\pi\)
\(278\) 0 0
\(279\) 3.83015 0.229305
\(280\) 0 0
\(281\) 22.6254 1.34972 0.674860 0.737946i \(-0.264204\pi\)
0.674860 + 0.737946i \(0.264204\pi\)
\(282\) 0 0
\(283\) 6.53144 0.388254 0.194127 0.980976i \(-0.437813\pi\)
0.194127 + 0.980976i \(0.437813\pi\)
\(284\) 0 0
\(285\) −19.4827 −1.15406
\(286\) 0 0
\(287\) 15.2624 0.900911
\(288\) 0 0
\(289\) 2.95834 0.174020
\(290\) 0 0
\(291\) 9.56984 0.560994
\(292\) 0 0
\(293\) 31.2931 1.82816 0.914082 0.405530i \(-0.132913\pi\)
0.914082 + 0.405530i \(0.132913\pi\)
\(294\) 0 0
\(295\) −24.7617 −1.44168
\(296\) 0 0
\(297\) 1.26137 0.0731923
\(298\) 0 0
\(299\) 40.2328 2.32672
\(300\) 0 0
\(301\) 31.2863 1.80331
\(302\) 0 0
\(303\) 11.6943 0.671821
\(304\) 0 0
\(305\) −38.7701 −2.21997
\(306\) 0 0
\(307\) 22.9963 1.31247 0.656235 0.754557i \(-0.272148\pi\)
0.656235 + 0.754557i \(0.272148\pi\)
\(308\) 0 0
\(309\) −0.703986 −0.0400484
\(310\) 0 0
\(311\) −23.7421 −1.34629 −0.673147 0.739509i \(-0.735058\pi\)
−0.673147 + 0.739509i \(0.735058\pi\)
\(312\) 0 0
\(313\) 17.5847 0.993947 0.496974 0.867766i \(-0.334445\pi\)
0.496974 + 0.867766i \(0.334445\pi\)
\(314\) 0 0
\(315\) −13.3078 −0.749811
\(316\) 0 0
\(317\) −34.1952 −1.92060 −0.960298 0.278977i \(-0.910005\pi\)
−0.960298 + 0.278977i \(0.910005\pi\)
\(318\) 0 0
\(319\) 6.90115 0.386390
\(320\) 0 0
\(321\) 9.02064 0.503483
\(322\) 0 0
\(323\) −28.9451 −1.61055
\(324\) 0 0
\(325\) −28.3990 −1.57529
\(326\) 0 0
\(327\) −16.0323 −0.886586
\(328\) 0 0
\(329\) 11.7994 0.650521
\(330\) 0 0
\(331\) −12.7003 −0.698069 −0.349034 0.937110i \(-0.613490\pi\)
−0.349034 + 0.937110i \(0.613490\pi\)
\(332\) 0 0
\(333\) 1.66867 0.0914425
\(334\) 0 0
\(335\) −21.7068 −1.18597
\(336\) 0 0
\(337\) −17.8065 −0.969983 −0.484991 0.874519i \(-0.661177\pi\)
−0.484991 + 0.874519i \(0.661177\pi\)
\(338\) 0 0
\(339\) 9.36851 0.508828
\(340\) 0 0
\(341\) −4.83125 −0.261627
\(342\) 0 0
\(343\) 24.7209 1.33480
\(344\) 0 0
\(345\) −17.2196 −0.927074
\(346\) 0 0
\(347\) 36.7852 1.97473 0.987366 0.158454i \(-0.0506509\pi\)
0.987366 + 0.158454i \(0.0506509\pi\)
\(348\) 0 0
\(349\) −2.96397 −0.158658 −0.0793288 0.996849i \(-0.525278\pi\)
−0.0793288 + 0.996849i \(0.525278\pi\)
\(350\) 0 0
\(351\) 7.02573 0.375006
\(352\) 0 0
\(353\) 19.4758 1.03659 0.518297 0.855201i \(-0.326566\pi\)
0.518297 + 0.855201i \(0.326566\pi\)
\(354\) 0 0
\(355\) −11.2163 −0.595297
\(356\) 0 0
\(357\) −19.7712 −1.04641
\(358\) 0 0
\(359\) −27.6093 −1.45716 −0.728581 0.684960i \(-0.759820\pi\)
−0.728581 + 0.684960i \(0.759820\pi\)
\(360\) 0 0
\(361\) 22.9785 1.20940
\(362\) 0 0
\(363\) 9.40894 0.493841
\(364\) 0 0
\(365\) 39.3978 2.06218
\(366\) 0 0
\(367\) −5.26407 −0.274782 −0.137391 0.990517i \(-0.543872\pi\)
−0.137391 + 0.990517i \(0.543872\pi\)
\(368\) 0 0
\(369\) 3.44867 0.179530
\(370\) 0 0
\(371\) −51.2105 −2.65871
\(372\) 0 0
\(373\) 16.3581 0.846988 0.423494 0.905899i \(-0.360803\pi\)
0.423494 + 0.905899i \(0.360803\pi\)
\(374\) 0 0
\(375\) −2.88030 −0.148738
\(376\) 0 0
\(377\) 38.4388 1.97970
\(378\) 0 0
\(379\) 10.1367 0.520688 0.260344 0.965516i \(-0.416164\pi\)
0.260344 + 0.965516i \(0.416164\pi\)
\(380\) 0 0
\(381\) −1.24996 −0.0640375
\(382\) 0 0
\(383\) 5.44289 0.278119 0.139059 0.990284i \(-0.455592\pi\)
0.139059 + 0.990284i \(0.455592\pi\)
\(384\) 0 0
\(385\) 16.7861 0.855501
\(386\) 0 0
\(387\) 7.06939 0.359357
\(388\) 0 0
\(389\) 34.0346 1.72562 0.862811 0.505527i \(-0.168702\pi\)
0.862811 + 0.505527i \(0.168702\pi\)
\(390\) 0 0
\(391\) −25.5829 −1.29378
\(392\) 0 0
\(393\) −13.7936 −0.695797
\(394\) 0 0
\(395\) 17.7436 0.892776
\(396\) 0 0
\(397\) 9.82450 0.493078 0.246539 0.969133i \(-0.420707\pi\)
0.246539 + 0.969133i \(0.420707\pi\)
\(398\) 0 0
\(399\) 28.6738 1.43549
\(400\) 0 0
\(401\) 8.64054 0.431488 0.215744 0.976450i \(-0.430782\pi\)
0.215744 + 0.976450i \(0.430782\pi\)
\(402\) 0 0
\(403\) −26.9096 −1.34046
\(404\) 0 0
\(405\) −3.00702 −0.149420
\(406\) 0 0
\(407\) −2.10482 −0.104332
\(408\) 0 0
\(409\) 13.5588 0.670437 0.335219 0.942140i \(-0.391190\pi\)
0.335219 + 0.942140i \(0.391190\pi\)
\(410\) 0 0
\(411\) 17.0579 0.841403
\(412\) 0 0
\(413\) 36.4432 1.79325
\(414\) 0 0
\(415\) −9.00872 −0.442221
\(416\) 0 0
\(417\) 5.40359 0.264615
\(418\) 0 0
\(419\) −16.1540 −0.789173 −0.394586 0.918859i \(-0.629112\pi\)
−0.394586 + 0.918859i \(0.629112\pi\)
\(420\) 0 0
\(421\) −35.8761 −1.74850 −0.874248 0.485480i \(-0.838645\pi\)
−0.874248 + 0.485480i \(0.838645\pi\)
\(422\) 0 0
\(423\) 2.66617 0.129633
\(424\) 0 0
\(425\) 18.0582 0.875949
\(426\) 0 0
\(427\) 57.0601 2.76133
\(428\) 0 0
\(429\) −8.86207 −0.427865
\(430\) 0 0
\(431\) −18.6705 −0.899326 −0.449663 0.893198i \(-0.648456\pi\)
−0.449663 + 0.893198i \(0.648456\pi\)
\(432\) 0 0
\(433\) −7.53304 −0.362015 −0.181007 0.983482i \(-0.557936\pi\)
−0.181007 + 0.983482i \(0.557936\pi\)
\(434\) 0 0
\(435\) −16.4518 −0.788804
\(436\) 0 0
\(437\) 37.1024 1.77485
\(438\) 0 0
\(439\) 18.7912 0.896856 0.448428 0.893819i \(-0.351984\pi\)
0.448428 + 0.893819i \(0.351984\pi\)
\(440\) 0 0
\(441\) 12.5859 0.599328
\(442\) 0 0
\(443\) −31.1465 −1.47981 −0.739907 0.672709i \(-0.765131\pi\)
−0.739907 + 0.672709i \(0.765131\pi\)
\(444\) 0 0
\(445\) 43.0393 2.04026
\(446\) 0 0
\(447\) −3.74723 −0.177238
\(448\) 0 0
\(449\) 19.5780 0.923943 0.461971 0.886895i \(-0.347142\pi\)
0.461971 + 0.886895i \(0.347142\pi\)
\(450\) 0 0
\(451\) −4.35006 −0.204836
\(452\) 0 0
\(453\) −23.7345 −1.11514
\(454\) 0 0
\(455\) 93.4973 4.38322
\(456\) 0 0
\(457\) −12.1175 −0.566835 −0.283417 0.958997i \(-0.591468\pi\)
−0.283417 + 0.958997i \(0.591468\pi\)
\(458\) 0 0
\(459\) −4.46748 −0.208524
\(460\) 0 0
\(461\) 4.21556 0.196338 0.0981691 0.995170i \(-0.468701\pi\)
0.0981691 + 0.995170i \(0.468701\pi\)
\(462\) 0 0
\(463\) −16.7951 −0.780535 −0.390267 0.920702i \(-0.627617\pi\)
−0.390267 + 0.920702i \(0.627617\pi\)
\(464\) 0 0
\(465\) 11.5173 0.534103
\(466\) 0 0
\(467\) −22.3934 −1.03624 −0.518121 0.855307i \(-0.673368\pi\)
−0.518121 + 0.855307i \(0.673368\pi\)
\(468\) 0 0
\(469\) 31.9472 1.47518
\(470\) 0 0
\(471\) −23.3909 −1.07779
\(472\) 0 0
\(473\) −8.91714 −0.410011
\(474\) 0 0
\(475\) −26.1894 −1.20165
\(476\) 0 0
\(477\) −11.5714 −0.529819
\(478\) 0 0
\(479\) 12.4221 0.567582 0.283791 0.958886i \(-0.408408\pi\)
0.283791 + 0.958886i \(0.408408\pi\)
\(480\) 0 0
\(481\) −11.7236 −0.534551
\(482\) 0 0
\(483\) 25.3431 1.15315
\(484\) 0 0
\(485\) 28.7766 1.30668
\(486\) 0 0
\(487\) 14.5340 0.658597 0.329298 0.944226i \(-0.393188\pi\)
0.329298 + 0.944226i \(0.393188\pi\)
\(488\) 0 0
\(489\) −13.5342 −0.612040
\(490\) 0 0
\(491\) 5.49906 0.248169 0.124085 0.992272i \(-0.460401\pi\)
0.124085 + 0.992272i \(0.460401\pi\)
\(492\) 0 0
\(493\) −24.4422 −1.10082
\(494\) 0 0
\(495\) 3.79297 0.170481
\(496\) 0 0
\(497\) 16.5076 0.740467
\(498\) 0 0
\(499\) 39.2026 1.75495 0.877474 0.479623i \(-0.159227\pi\)
0.877474 + 0.479623i \(0.159227\pi\)
\(500\) 0 0
\(501\) −10.5120 −0.469643
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 35.1650 1.56482
\(506\) 0 0
\(507\) −36.3609 −1.61484
\(508\) 0 0
\(509\) −18.9641 −0.840567 −0.420284 0.907393i \(-0.638069\pi\)
−0.420284 + 0.907393i \(0.638069\pi\)
\(510\) 0 0
\(511\) −57.9840 −2.56506
\(512\) 0 0
\(513\) 6.47908 0.286059
\(514\) 0 0
\(515\) −2.11690 −0.0932816
\(516\) 0 0
\(517\) −3.36303 −0.147906
\(518\) 0 0
\(519\) −11.4272 −0.501600
\(520\) 0 0
\(521\) 8.14358 0.356777 0.178388 0.983960i \(-0.442912\pi\)
0.178388 + 0.983960i \(0.442912\pi\)
\(522\) 0 0
\(523\) 15.6543 0.684513 0.342257 0.939607i \(-0.388809\pi\)
0.342257 + 0.939607i \(0.388809\pi\)
\(524\) 0 0
\(525\) −17.8889 −0.780735
\(526\) 0 0
\(527\) 17.1111 0.745371
\(528\) 0 0
\(529\) 9.79265 0.425767
\(530\) 0 0
\(531\) 8.23464 0.357353
\(532\) 0 0
\(533\) −24.2294 −1.04949
\(534\) 0 0
\(535\) 27.1252 1.17272
\(536\) 0 0
\(537\) 22.8420 0.985705
\(538\) 0 0
\(539\) −15.8755 −0.683807
\(540\) 0 0
\(541\) 38.1085 1.63841 0.819206 0.573500i \(-0.194415\pi\)
0.819206 + 0.573500i \(0.194415\pi\)
\(542\) 0 0
\(543\) −6.70936 −0.287926
\(544\) 0 0
\(545\) −48.2092 −2.06506
\(546\) 0 0
\(547\) 8.73347 0.373416 0.186708 0.982415i \(-0.440218\pi\)
0.186708 + 0.982415i \(0.440218\pi\)
\(548\) 0 0
\(549\) 12.8932 0.550269
\(550\) 0 0
\(551\) 35.4480 1.51014
\(552\) 0 0
\(553\) −26.1142 −1.11049
\(554\) 0 0
\(555\) 5.01771 0.212990
\(556\) 0 0
\(557\) −0.442840 −0.0187637 −0.00938187 0.999956i \(-0.502986\pi\)
−0.00938187 + 0.999956i \(0.502986\pi\)
\(558\) 0 0
\(559\) −49.6676 −2.10072
\(560\) 0 0
\(561\) 5.63516 0.237916
\(562\) 0 0
\(563\) 10.1173 0.426395 0.213197 0.977009i \(-0.431612\pi\)
0.213197 + 0.977009i \(0.431612\pi\)
\(564\) 0 0
\(565\) 28.1713 1.18517
\(566\) 0 0
\(567\) 4.42560 0.185858
\(568\) 0 0
\(569\) −25.1697 −1.05517 −0.527585 0.849502i \(-0.676902\pi\)
−0.527585 + 0.849502i \(0.676902\pi\)
\(570\) 0 0
\(571\) −37.9163 −1.58675 −0.793375 0.608734i \(-0.791678\pi\)
−0.793375 + 0.608734i \(0.791678\pi\)
\(572\) 0 0
\(573\) 7.17863 0.299892
\(574\) 0 0
\(575\) −23.1473 −0.965307
\(576\) 0 0
\(577\) 12.8925 0.536724 0.268362 0.963318i \(-0.413518\pi\)
0.268362 + 0.963318i \(0.413518\pi\)
\(578\) 0 0
\(579\) −19.2715 −0.800896
\(580\) 0 0
\(581\) 13.2586 0.550061
\(582\) 0 0
\(583\) 14.5959 0.604500
\(584\) 0 0
\(585\) 21.1265 0.873473
\(586\) 0 0
\(587\) −38.5802 −1.59238 −0.796188 0.605050i \(-0.793153\pi\)
−0.796188 + 0.605050i \(0.793153\pi\)
\(588\) 0 0
\(589\) −24.8159 −1.02252
\(590\) 0 0
\(591\) −19.7295 −0.811561
\(592\) 0 0
\(593\) 12.6819 0.520785 0.260393 0.965503i \(-0.416148\pi\)
0.260393 + 0.965503i \(0.416148\pi\)
\(594\) 0 0
\(595\) −59.4524 −2.43731
\(596\) 0 0
\(597\) −10.7240 −0.438904
\(598\) 0 0
\(599\) 36.6373 1.49696 0.748479 0.663159i \(-0.230785\pi\)
0.748479 + 0.663159i \(0.230785\pi\)
\(600\) 0 0
\(601\) 20.4538 0.834327 0.417164 0.908831i \(-0.363024\pi\)
0.417164 + 0.908831i \(0.363024\pi\)
\(602\) 0 0
\(603\) 7.21874 0.293970
\(604\) 0 0
\(605\) 28.2928 1.15027
\(606\) 0 0
\(607\) −44.0882 −1.78949 −0.894743 0.446582i \(-0.852641\pi\)
−0.894743 + 0.446582i \(0.852641\pi\)
\(608\) 0 0
\(609\) 24.2131 0.981163
\(610\) 0 0
\(611\) −18.7318 −0.757807
\(612\) 0 0
\(613\) 1.54841 0.0625396 0.0312698 0.999511i \(-0.490045\pi\)
0.0312698 + 0.999511i \(0.490045\pi\)
\(614\) 0 0
\(615\) 10.3702 0.418166
\(616\) 0 0
\(617\) 33.6995 1.35669 0.678346 0.734743i \(-0.262697\pi\)
0.678346 + 0.734743i \(0.262697\pi\)
\(618\) 0 0
\(619\) −0.599738 −0.0241055 −0.0120528 0.999927i \(-0.503837\pi\)
−0.0120528 + 0.999927i \(0.503837\pi\)
\(620\) 0 0
\(621\) 5.72649 0.229796
\(622\) 0 0
\(623\) −63.3434 −2.53780
\(624\) 0 0
\(625\) −28.8718 −1.15487
\(626\) 0 0
\(627\) −8.17254 −0.326380
\(628\) 0 0
\(629\) 7.45474 0.297240
\(630\) 0 0
\(631\) 2.82660 0.112525 0.0562627 0.998416i \(-0.482082\pi\)
0.0562627 + 0.998416i \(0.482082\pi\)
\(632\) 0 0
\(633\) 23.1655 0.920747
\(634\) 0 0
\(635\) −3.75865 −0.149158
\(636\) 0 0
\(637\) −88.4251 −3.50353
\(638\) 0 0
\(639\) 3.73003 0.147558
\(640\) 0 0
\(641\) −10.0004 −0.394993 −0.197496 0.980304i \(-0.563281\pi\)
−0.197496 + 0.980304i \(0.563281\pi\)
\(642\) 0 0
\(643\) −32.5066 −1.28194 −0.640968 0.767567i \(-0.721467\pi\)
−0.640968 + 0.767567i \(0.721467\pi\)
\(644\) 0 0
\(645\) 21.2578 0.837024
\(646\) 0 0
\(647\) 38.0913 1.49752 0.748761 0.662840i \(-0.230649\pi\)
0.748761 + 0.662840i \(0.230649\pi\)
\(648\) 0 0
\(649\) −10.3870 −0.407724
\(650\) 0 0
\(651\) −16.9507 −0.664350
\(652\) 0 0
\(653\) 28.0839 1.09901 0.549504 0.835491i \(-0.314817\pi\)
0.549504 + 0.835491i \(0.314817\pi\)
\(654\) 0 0
\(655\) −41.4777 −1.62067
\(656\) 0 0
\(657\) −13.1020 −0.511157
\(658\) 0 0
\(659\) 20.8790 0.813329 0.406664 0.913578i \(-0.366692\pi\)
0.406664 + 0.913578i \(0.366692\pi\)
\(660\) 0 0
\(661\) 4.73847 0.184305 0.0921525 0.995745i \(-0.470625\pi\)
0.0921525 + 0.995745i \(0.470625\pi\)
\(662\) 0 0
\(663\) 31.3873 1.21898
\(664\) 0 0
\(665\) 86.2226 3.34357
\(666\) 0 0
\(667\) 31.3304 1.21312
\(668\) 0 0
\(669\) −19.5792 −0.756977
\(670\) 0 0
\(671\) −16.2631 −0.627832
\(672\) 0 0
\(673\) −32.5041 −1.25294 −0.626470 0.779446i \(-0.715501\pi\)
−0.626470 + 0.779446i \(0.715501\pi\)
\(674\) 0 0
\(675\) −4.04214 −0.155582
\(676\) 0 0
\(677\) 22.9804 0.883207 0.441604 0.897210i \(-0.354410\pi\)
0.441604 + 0.897210i \(0.354410\pi\)
\(678\) 0 0
\(679\) −42.3522 −1.62533
\(680\) 0 0
\(681\) −13.6014 −0.521207
\(682\) 0 0
\(683\) −14.9887 −0.573528 −0.286764 0.958001i \(-0.592580\pi\)
−0.286764 + 0.958001i \(0.592580\pi\)
\(684\) 0 0
\(685\) 51.2933 1.95982
\(686\) 0 0
\(687\) 12.4302 0.474243
\(688\) 0 0
\(689\) 81.2978 3.09720
\(690\) 0 0
\(691\) −23.7088 −0.901925 −0.450963 0.892543i \(-0.648919\pi\)
−0.450963 + 0.892543i \(0.648919\pi\)
\(692\) 0 0
\(693\) −5.58233 −0.212055
\(694\) 0 0
\(695\) 16.2487 0.616348
\(696\) 0 0
\(697\) 15.4068 0.583575
\(698\) 0 0
\(699\) 11.2581 0.425821
\(700\) 0 0
\(701\) 12.0436 0.454879 0.227440 0.973792i \(-0.426965\pi\)
0.227440 + 0.973792i \(0.426965\pi\)
\(702\) 0 0
\(703\) −10.8114 −0.407762
\(704\) 0 0
\(705\) 8.01721 0.301945
\(706\) 0 0
\(707\) −51.7543 −1.94642
\(708\) 0 0
\(709\) −23.2067 −0.871545 −0.435773 0.900057i \(-0.643525\pi\)
−0.435773 + 0.900057i \(0.643525\pi\)
\(710\) 0 0
\(711\) −5.90073 −0.221295
\(712\) 0 0
\(713\) −21.9333 −0.821409
\(714\) 0 0
\(715\) −26.6484 −0.996593
\(716\) 0 0
\(717\) −23.0467 −0.860693
\(718\) 0 0
\(719\) 2.51137 0.0936582 0.0468291 0.998903i \(-0.485088\pi\)
0.0468291 + 0.998903i \(0.485088\pi\)
\(720\) 0 0
\(721\) 3.11556 0.116029
\(722\) 0 0
\(723\) −25.7686 −0.958345
\(724\) 0 0
\(725\) −22.1151 −0.821335
\(726\) 0 0
\(727\) −7.34411 −0.272378 −0.136189 0.990683i \(-0.543485\pi\)
−0.136189 + 0.990683i \(0.543485\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 31.5823 1.16811
\(732\) 0 0
\(733\) −4.56543 −0.168628 −0.0843140 0.996439i \(-0.526870\pi\)
−0.0843140 + 0.996439i \(0.526870\pi\)
\(734\) 0 0
\(735\) 37.8460 1.39597
\(736\) 0 0
\(737\) −9.10552 −0.335406
\(738\) 0 0
\(739\) 0.437296 0.0160862 0.00804310 0.999968i \(-0.497440\pi\)
0.00804310 + 0.999968i \(0.497440\pi\)
\(740\) 0 0
\(741\) −45.5203 −1.67223
\(742\) 0 0
\(743\) 46.7944 1.71672 0.858361 0.513046i \(-0.171483\pi\)
0.858361 + 0.513046i \(0.171483\pi\)
\(744\) 0 0
\(745\) −11.2680 −0.412826
\(746\) 0 0
\(747\) 2.99590 0.109614
\(748\) 0 0
\(749\) −39.9217 −1.45871
\(750\) 0 0
\(751\) 5.60629 0.204576 0.102288 0.994755i \(-0.467384\pi\)
0.102288 + 0.994755i \(0.467384\pi\)
\(752\) 0 0
\(753\) 4.22022 0.153793
\(754\) 0 0
\(755\) −71.3700 −2.59742
\(756\) 0 0
\(757\) 29.2598 1.06347 0.531734 0.846912i \(-0.321541\pi\)
0.531734 + 0.846912i \(0.321541\pi\)
\(758\) 0 0
\(759\) −7.22324 −0.262187
\(760\) 0 0
\(761\) 35.1392 1.27379 0.636897 0.770949i \(-0.280218\pi\)
0.636897 + 0.770949i \(0.280218\pi\)
\(762\) 0 0
\(763\) 70.9523 2.56864
\(764\) 0 0
\(765\) −13.4338 −0.485699
\(766\) 0 0
\(767\) −57.8544 −2.08900
\(768\) 0 0
\(769\) −17.1973 −0.620152 −0.310076 0.950712i \(-0.600355\pi\)
−0.310076 + 0.950712i \(0.600355\pi\)
\(770\) 0 0
\(771\) 15.8165 0.569618
\(772\) 0 0
\(773\) −21.6372 −0.778237 −0.389119 0.921188i \(-0.627220\pi\)
−0.389119 + 0.921188i \(0.627220\pi\)
\(774\) 0 0
\(775\) 15.4820 0.556130
\(776\) 0 0
\(777\) −7.38486 −0.264930
\(778\) 0 0
\(779\) −22.3442 −0.800564
\(780\) 0 0
\(781\) −4.70496 −0.168357
\(782\) 0 0
\(783\) 5.47114 0.195523
\(784\) 0 0
\(785\) −70.3367 −2.51042
\(786\) 0 0
\(787\) 7.86308 0.280289 0.140144 0.990131i \(-0.455243\pi\)
0.140144 + 0.990131i \(0.455243\pi\)
\(788\) 0 0
\(789\) −13.1279 −0.467367
\(790\) 0 0
\(791\) −41.4612 −1.47419
\(792\) 0 0
\(793\) −90.5842 −3.21674
\(794\) 0 0
\(795\) −34.7955 −1.23407
\(796\) 0 0
\(797\) 6.02181 0.213304 0.106652 0.994296i \(-0.465987\pi\)
0.106652 + 0.994296i \(0.465987\pi\)
\(798\) 0 0
\(799\) 11.9110 0.421382
\(800\) 0 0
\(801\) −14.3130 −0.505724
\(802\) 0 0
\(803\) 16.5265 0.583207
\(804\) 0 0
\(805\) 76.2071 2.68595
\(806\) 0 0
\(807\) −7.27608 −0.256130
\(808\) 0 0
\(809\) −8.89558 −0.312752 −0.156376 0.987698i \(-0.549981\pi\)
−0.156376 + 0.987698i \(0.549981\pi\)
\(810\) 0 0
\(811\) −33.0037 −1.15892 −0.579459 0.815002i \(-0.696736\pi\)
−0.579459 + 0.815002i \(0.696736\pi\)
\(812\) 0 0
\(813\) −5.30166 −0.185937
\(814\) 0 0
\(815\) −40.6977 −1.42558
\(816\) 0 0
\(817\) −45.8032 −1.60245
\(818\) 0 0
\(819\) −31.0931 −1.08648
\(820\) 0 0
\(821\) −27.6415 −0.964695 −0.482347 0.875980i \(-0.660216\pi\)
−0.482347 + 0.875980i \(0.660216\pi\)
\(822\) 0 0
\(823\) −14.2051 −0.495159 −0.247579 0.968868i \(-0.579635\pi\)
−0.247579 + 0.968868i \(0.579635\pi\)
\(824\) 0 0
\(825\) 5.09865 0.177512
\(826\) 0 0
\(827\) 3.86280 0.134323 0.0671614 0.997742i \(-0.478606\pi\)
0.0671614 + 0.997742i \(0.478606\pi\)
\(828\) 0 0
\(829\) 50.8147 1.76487 0.882433 0.470438i \(-0.155904\pi\)
0.882433 + 0.470438i \(0.155904\pi\)
\(830\) 0 0
\(831\) 6.17368 0.214163
\(832\) 0 0
\(833\) 56.2272 1.94816
\(834\) 0 0
\(835\) −31.6098 −1.09390
\(836\) 0 0
\(837\) −3.83015 −0.132389
\(838\) 0 0
\(839\) −27.4864 −0.948935 −0.474468 0.880273i \(-0.657359\pi\)
−0.474468 + 0.880273i \(0.657359\pi\)
\(840\) 0 0
\(841\) 0.933398 0.0321861
\(842\) 0 0
\(843\) −22.6254 −0.779261
\(844\) 0 0
\(845\) −109.338 −3.76134
\(846\) 0 0
\(847\) −41.6402 −1.43077
\(848\) 0 0
\(849\) −6.53144 −0.224159
\(850\) 0 0
\(851\) −9.55561 −0.327562
\(852\) 0 0
\(853\) −3.12491 −0.106995 −0.0534974 0.998568i \(-0.517037\pi\)
−0.0534974 + 0.998568i \(0.517037\pi\)
\(854\) 0 0
\(855\) 19.4827 0.666294
\(856\) 0 0
\(857\) −7.14433 −0.244046 −0.122023 0.992527i \(-0.538938\pi\)
−0.122023 + 0.992527i \(0.538938\pi\)
\(858\) 0 0
\(859\) 43.1328 1.47167 0.735836 0.677159i \(-0.236789\pi\)
0.735836 + 0.677159i \(0.236789\pi\)
\(860\) 0 0
\(861\) −15.2624 −0.520141
\(862\) 0 0
\(863\) −51.4061 −1.74988 −0.874941 0.484229i \(-0.839100\pi\)
−0.874941 + 0.484229i \(0.839100\pi\)
\(864\) 0 0
\(865\) −34.3619 −1.16834
\(866\) 0 0
\(867\) −2.95834 −0.100470
\(868\) 0 0
\(869\) 7.44302 0.252487
\(870\) 0 0
\(871\) −50.7169 −1.71848
\(872\) 0 0
\(873\) −9.56984 −0.323890
\(874\) 0 0
\(875\) 12.7470 0.430929
\(876\) 0 0
\(877\) 15.9358 0.538113 0.269056 0.963124i \(-0.413288\pi\)
0.269056 + 0.963124i \(0.413288\pi\)
\(878\) 0 0
\(879\) −31.2931 −1.05549
\(880\) 0 0
\(881\) 7.57491 0.255205 0.127603 0.991825i \(-0.459272\pi\)
0.127603 + 0.991825i \(0.459272\pi\)
\(882\) 0 0
\(883\) 22.9900 0.773673 0.386837 0.922148i \(-0.373568\pi\)
0.386837 + 0.922148i \(0.373568\pi\)
\(884\) 0 0
\(885\) 24.7617 0.832355
\(886\) 0 0
\(887\) −19.1168 −0.641881 −0.320940 0.947099i \(-0.603999\pi\)
−0.320940 + 0.947099i \(0.603999\pi\)
\(888\) 0 0
\(889\) 5.53182 0.185531
\(890\) 0 0
\(891\) −1.26137 −0.0422576
\(892\) 0 0
\(893\) −17.2743 −0.578063
\(894\) 0 0
\(895\) 68.6863 2.29593
\(896\) 0 0
\(897\) −40.2328 −1.34333
\(898\) 0 0
\(899\) −20.9553 −0.698898
\(900\) 0 0
\(901\) −51.6951 −1.72221
\(902\) 0 0
\(903\) −31.2863 −1.04114
\(904\) 0 0
\(905\) −20.1752 −0.670645
\(906\) 0 0
\(907\) −7.37065 −0.244739 −0.122369 0.992485i \(-0.539049\pi\)
−0.122369 + 0.992485i \(0.539049\pi\)
\(908\) 0 0
\(909\) −11.6943 −0.387876
\(910\) 0 0
\(911\) −0.0486751 −0.00161268 −0.000806339 1.00000i \(-0.500257\pi\)
−0.000806339 1.00000i \(0.500257\pi\)
\(912\) 0 0
\(913\) −3.77895 −0.125065
\(914\) 0 0
\(915\) 38.7701 1.28170
\(916\) 0 0
\(917\) 61.0451 2.01589
\(918\) 0 0
\(919\) 27.6991 0.913709 0.456855 0.889541i \(-0.348976\pi\)
0.456855 + 0.889541i \(0.348976\pi\)
\(920\) 0 0
\(921\) −22.9963 −0.757755
\(922\) 0 0
\(923\) −26.2062 −0.862587
\(924\) 0 0
\(925\) 6.74500 0.221774
\(926\) 0 0
\(927\) 0.703986 0.0231219
\(928\) 0 0
\(929\) 30.4208 0.998073 0.499036 0.866581i \(-0.333687\pi\)
0.499036 + 0.866581i \(0.333687\pi\)
\(930\) 0 0
\(931\) −81.5451 −2.67253
\(932\) 0 0
\(933\) 23.7421 0.777283
\(934\) 0 0
\(935\) 16.9450 0.554161
\(936\) 0 0
\(937\) 34.6412 1.13168 0.565839 0.824516i \(-0.308552\pi\)
0.565839 + 0.824516i \(0.308552\pi\)
\(938\) 0 0
\(939\) −17.5847 −0.573856
\(940\) 0 0
\(941\) 51.4359 1.67676 0.838382 0.545083i \(-0.183502\pi\)
0.838382 + 0.545083i \(0.183502\pi\)
\(942\) 0 0
\(943\) −19.7487 −0.643107
\(944\) 0 0
\(945\) 13.3078 0.432904
\(946\) 0 0
\(947\) 23.8989 0.776610 0.388305 0.921531i \(-0.373061\pi\)
0.388305 + 0.921531i \(0.373061\pi\)
\(948\) 0 0
\(949\) 92.0510 2.98810
\(950\) 0 0
\(951\) 34.1952 1.10886
\(952\) 0 0
\(953\) 9.72615 0.315061 0.157531 0.987514i \(-0.449647\pi\)
0.157531 + 0.987514i \(0.449647\pi\)
\(954\) 0 0
\(955\) 21.5863 0.698515
\(956\) 0 0
\(957\) −6.90115 −0.223083
\(958\) 0 0
\(959\) −75.4913 −2.43774
\(960\) 0 0
\(961\) −16.3300 −0.526773
\(962\) 0 0
\(963\) −9.02064 −0.290686
\(964\) 0 0
\(965\) −57.9496 −1.86547
\(966\) 0 0
\(967\) 18.0681 0.581031 0.290516 0.956870i \(-0.406173\pi\)
0.290516 + 0.956870i \(0.406173\pi\)
\(968\) 0 0
\(969\) 28.9451 0.929852
\(970\) 0 0
\(971\) −26.1902 −0.840484 −0.420242 0.907412i \(-0.638055\pi\)
−0.420242 + 0.907412i \(0.638055\pi\)
\(972\) 0 0
\(973\) −23.9141 −0.766651
\(974\) 0 0
\(975\) 28.3990 0.909496
\(976\) 0 0
\(977\) −23.0168 −0.736374 −0.368187 0.929752i \(-0.620021\pi\)
−0.368187 + 0.929752i \(0.620021\pi\)
\(978\) 0 0
\(979\) 18.0540 0.577008
\(980\) 0 0
\(981\) 16.0323 0.511870
\(982\) 0 0
\(983\) 5.01061 0.159814 0.0799069 0.996802i \(-0.474538\pi\)
0.0799069 + 0.996802i \(0.474538\pi\)
\(984\) 0 0
\(985\) −59.3268 −1.89031
\(986\) 0 0
\(987\) −11.7994 −0.375578
\(988\) 0 0
\(989\) −40.4828 −1.28728
\(990\) 0 0
\(991\) 4.98445 0.158336 0.0791681 0.996861i \(-0.474774\pi\)
0.0791681 + 0.996861i \(0.474774\pi\)
\(992\) 0 0
\(993\) 12.7003 0.403030
\(994\) 0 0
\(995\) −32.2472 −1.02231
\(996\) 0 0
\(997\) 30.0604 0.952022 0.476011 0.879439i \(-0.342082\pi\)
0.476011 + 0.879439i \(0.342082\pi\)
\(998\) 0 0
\(999\) −1.66867 −0.0527944
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 \(a_p\))