Properties

Label 6048.2.a.ba.1.2
Level 6048
Weight 2
Character 6048.1
Self dual Yes
Analytic conductor 48.294
Analytic rank 1
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2935231425\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
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 1.2
Root \(1.41421\)
Character \(\chi\) = 6048.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.414214 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+0.414214 q^{5} +1.00000 q^{7} +0.414214 q^{11} -2.82843 q^{13} +2.82843 q^{17} -1.82843 q^{19} +3.24264 q^{23} -4.82843 q^{25} -2.82843 q^{29} -6.65685 q^{31} +0.414214 q^{35} +5.82843 q^{37} -12.0711 q^{41} -0.828427 q^{43} -11.6569 q^{47} +1.00000 q^{49} +4.00000 q^{53} +0.171573 q^{55} -7.65685 q^{59} +11.3137 q^{61} -1.17157 q^{65} +12.4853 q^{67} -8.41421 q^{71} -8.82843 q^{73} +0.414214 q^{77} +0.828427 q^{79} -5.17157 q^{83} +1.17157 q^{85} +7.24264 q^{89} -2.82843 q^{91} -0.757359 q^{95} +1.65685 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{5} + 2q^{7} + O(q^{10}) \) \( 2q - 2q^{5} + 2q^{7} - 2q^{11} + 2q^{19} - 2q^{23} - 4q^{25} - 2q^{31} - 2q^{35} + 6q^{37} - 10q^{41} + 4q^{43} - 12q^{47} + 2q^{49} + 8q^{53} + 6q^{55} - 4q^{59} - 8q^{65} + 8q^{67} - 14q^{71} - 12q^{73} - 2q^{77} - 4q^{79} - 16q^{83} + 8q^{85} + 6q^{89} - 10q^{95} - 8q^{97} + O(q^{100}) \)

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 0
\(4\) 0 0
\(5\) 0.414214 0.185242 0.0926210 0.995701i \(-0.470476\pi\)
0.0926210 + 0.995701i \(0.470476\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.414214 0.124890 0.0624450 0.998048i \(-0.480110\pi\)
0.0624450 + 0.998048i \(0.480110\pi\)
\(12\) 0 0
\(13\) −2.82843 −0.784465 −0.392232 0.919866i \(-0.628297\pi\)
−0.392232 + 0.919866i \(0.628297\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.82843 0.685994 0.342997 0.939336i \(-0.388558\pi\)
0.342997 + 0.939336i \(0.388558\pi\)
\(18\) 0 0
\(19\) −1.82843 −0.419470 −0.209735 0.977758i \(-0.567260\pi\)
−0.209735 + 0.977758i \(0.567260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.24264 0.676137 0.338069 0.941121i \(-0.390226\pi\)
0.338069 + 0.941121i \(0.390226\pi\)
\(24\) 0 0
\(25\) −4.82843 −0.965685
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.82843 −0.525226 −0.262613 0.964901i \(-0.584584\pi\)
−0.262613 + 0.964901i \(0.584584\pi\)
\(30\) 0 0
\(31\) −6.65685 −1.19561 −0.597803 0.801643i \(-0.703960\pi\)
−0.597803 + 0.801643i \(0.703960\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.414214 0.0700149
\(36\) 0 0
\(37\) 5.82843 0.958188 0.479094 0.877764i \(-0.340965\pi\)
0.479094 + 0.877764i \(0.340965\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12.0711 −1.88518 −0.942592 0.333946i \(-0.891620\pi\)
−0.942592 + 0.333946i \(0.891620\pi\)
\(42\) 0 0
\(43\) −0.828427 −0.126334 −0.0631670 0.998003i \(-0.520120\pi\)
−0.0631670 + 0.998003i \(0.520120\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.6569 −1.70033 −0.850163 0.526519i \(-0.823497\pi\)
−0.850163 + 0.526519i \(0.823497\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) 0.171573 0.0231349
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.65685 −0.996838 −0.498419 0.866936i \(-0.666086\pi\)
−0.498419 + 0.866936i \(0.666086\pi\)
\(60\) 0 0
\(61\) 11.3137 1.44857 0.724286 0.689500i \(-0.242170\pi\)
0.724286 + 0.689500i \(0.242170\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.17157 −0.145316
\(66\) 0 0
\(67\) 12.4853 1.52532 0.762660 0.646800i \(-0.223893\pi\)
0.762660 + 0.646800i \(0.223893\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.41421 −0.998583 −0.499292 0.866434i \(-0.666406\pi\)
−0.499292 + 0.866434i \(0.666406\pi\)
\(72\) 0 0
\(73\) −8.82843 −1.03329 −0.516645 0.856200i \(-0.672819\pi\)
−0.516645 + 0.856200i \(0.672819\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.414214 0.0472040
\(78\) 0 0
\(79\) 0.828427 0.0932053 0.0466027 0.998914i \(-0.485161\pi\)
0.0466027 + 0.998914i \(0.485161\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.17157 −0.567654 −0.283827 0.958876i \(-0.591604\pi\)
−0.283827 + 0.958876i \(0.591604\pi\)
\(84\) 0 0
\(85\) 1.17157 0.127075
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.24264 0.767718 0.383859 0.923392i \(-0.374595\pi\)
0.383859 + 0.923392i \(0.374595\pi\)
\(90\) 0 0
\(91\) −2.82843 −0.296500
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.757359 −0.0777034
\(96\) 0 0
\(97\) 1.65685 0.168228 0.0841140 0.996456i \(-0.473194\pi\)
0.0841140 + 0.996456i \(0.473194\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.48528 −0.446302 −0.223151 0.974784i \(-0.571634\pi\)
−0.223151 + 0.974784i \(0.571634\pi\)
\(102\) 0 0
\(103\) 4.65685 0.458853 0.229427 0.973326i \(-0.426315\pi\)
0.229427 + 0.973326i \(0.426315\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.3137 −1.67378 −0.836890 0.547372i \(-0.815628\pi\)
−0.836890 + 0.547372i \(0.815628\pi\)
\(108\) 0 0
\(109\) −4.31371 −0.413178 −0.206589 0.978428i \(-0.566236\pi\)
−0.206589 + 0.978428i \(0.566236\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 16.1421 1.51852 0.759262 0.650785i \(-0.225560\pi\)
0.759262 + 0.650785i \(0.225560\pi\)
\(114\) 0 0
\(115\) 1.34315 0.125249
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.82843 0.259281
\(120\) 0 0
\(121\) −10.8284 −0.984402
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.07107 −0.364127
\(126\) 0 0
\(127\) 2.82843 0.250982 0.125491 0.992095i \(-0.459949\pi\)
0.125491 + 0.992095i \(0.459949\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.00000 −0.174741 −0.0873704 0.996176i \(-0.527846\pi\)
−0.0873704 + 0.996176i \(0.527846\pi\)
\(132\) 0 0
\(133\) −1.82843 −0.158545
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.82843 −0.241649 −0.120824 0.992674i \(-0.538554\pi\)
−0.120824 + 0.992674i \(0.538554\pi\)
\(138\) 0 0
\(139\) −9.65685 −0.819084 −0.409542 0.912291i \(-0.634311\pi\)
−0.409542 + 0.912291i \(0.634311\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.17157 −0.0979718
\(144\) 0 0
\(145\) −1.17157 −0.0972938
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.82843 −0.723253 −0.361626 0.932323i \(-0.617778\pi\)
−0.361626 + 0.932323i \(0.617778\pi\)
\(150\) 0 0
\(151\) −17.3137 −1.40897 −0.704485 0.709719i \(-0.748822\pi\)
−0.704485 + 0.709719i \(0.748822\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.75736 −0.221476
\(156\) 0 0
\(157\) 14.1421 1.12867 0.564333 0.825547i \(-0.309134\pi\)
0.564333 + 0.825547i \(0.309134\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.24264 0.255556
\(162\) 0 0
\(163\) 0.485281 0.0380102 0.0190051 0.999819i \(-0.493950\pi\)
0.0190051 + 0.999819i \(0.493950\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −18.4853 −1.43043 −0.715217 0.698902i \(-0.753672\pi\)
−0.715217 + 0.698902i \(0.753672\pi\)
\(168\) 0 0
\(169\) −5.00000 −0.384615
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.757359 −0.0575810 −0.0287905 0.999585i \(-0.509166\pi\)
−0.0287905 + 0.999585i \(0.509166\pi\)
\(174\) 0 0
\(175\) −4.82843 −0.364995
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.34315 −0.623596 −0.311798 0.950148i \(-0.600931\pi\)
−0.311798 + 0.950148i \(0.600931\pi\)
\(180\) 0 0
\(181\) 8.34315 0.620141 0.310071 0.950714i \(-0.399647\pi\)
0.310071 + 0.950714i \(0.399647\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.41421 0.177497
\(186\) 0 0
\(187\) 1.17157 0.0856739
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.58579 −0.693603 −0.346802 0.937939i \(-0.612732\pi\)
−0.346802 + 0.937939i \(0.612732\pi\)
\(192\) 0 0
\(193\) 7.65685 0.551152 0.275576 0.961279i \(-0.411131\pi\)
0.275576 + 0.961279i \(0.411131\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.1716 1.36592 0.682959 0.730457i \(-0.260693\pi\)
0.682959 + 0.730457i \(0.260693\pi\)
\(198\) 0 0
\(199\) 13.4853 0.955946 0.477973 0.878374i \(-0.341372\pi\)
0.477973 + 0.878374i \(0.341372\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.82843 −0.198517
\(204\) 0 0
\(205\) −5.00000 −0.349215
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.757359 −0.0523876
\(210\) 0 0
\(211\) −6.00000 −0.413057 −0.206529 0.978441i \(-0.566217\pi\)
−0.206529 + 0.978441i \(0.566217\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.343146 −0.0234023
\(216\) 0 0
\(217\) −6.65685 −0.451897
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) 14.7990 0.991014 0.495507 0.868604i \(-0.334982\pi\)
0.495507 + 0.868604i \(0.334982\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −15.1716 −1.00697 −0.503486 0.864003i \(-0.667950\pi\)
−0.503486 + 0.864003i \(0.667950\pi\)
\(228\) 0 0
\(229\) −3.31371 −0.218976 −0.109488 0.993988i \(-0.534921\pi\)
−0.109488 + 0.993988i \(0.534921\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.17157 0.469825 0.234913 0.972016i \(-0.424520\pi\)
0.234913 + 0.972016i \(0.424520\pi\)
\(234\) 0 0
\(235\) −4.82843 −0.314972
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4.34315 −0.280935 −0.140467 0.990085i \(-0.544861\pi\)
−0.140467 + 0.990085i \(0.544861\pi\)
\(240\) 0 0
\(241\) 4.14214 0.266818 0.133409 0.991061i \(-0.457408\pi\)
0.133409 + 0.991061i \(0.457408\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.414214 0.0264631
\(246\) 0 0
\(247\) 5.17157 0.329059
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 8.97056 0.566217 0.283108 0.959088i \(-0.408634\pi\)
0.283108 + 0.959088i \(0.408634\pi\)
\(252\) 0 0
\(253\) 1.34315 0.0844428
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −31.7279 −1.97913 −0.989567 0.144075i \(-0.953979\pi\)
−0.989567 + 0.144075i \(0.953979\pi\)
\(258\) 0 0
\(259\) 5.82843 0.362161
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −23.3848 −1.44197 −0.720984 0.692952i \(-0.756310\pi\)
−0.720984 + 0.692952i \(0.756310\pi\)
\(264\) 0 0
\(265\) 1.65685 0.101780
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.4142 1.12273 0.561367 0.827567i \(-0.310276\pi\)
0.561367 + 0.827567i \(0.310276\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) 8.17157 0.490982 0.245491 0.969399i \(-0.421051\pi\)
0.245491 + 0.969399i \(0.421051\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 7.31371 0.434755 0.217377 0.976088i \(-0.430250\pi\)
0.217377 + 0.976088i \(0.430250\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0711 −0.712533
\(288\) 0 0
\(289\) −9.00000 −0.529412
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −14.8284 −0.866286 −0.433143 0.901325i \(-0.642595\pi\)
−0.433143 + 0.901325i \(0.642595\pi\)
\(294\) 0 0
\(295\) −3.17157 −0.184656
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.17157 −0.530406
\(300\) 0 0
\(301\) −0.828427 −0.0477497
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.68629 0.268336
\(306\) 0 0
\(307\) −8.17157 −0.466376 −0.233188 0.972432i \(-0.574916\pi\)
−0.233188 + 0.972432i \(0.574916\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.4853 −0.934795 −0.467397 0.884047i \(-0.654808\pi\)
−0.467397 + 0.884047i \(0.654808\pi\)
\(312\) 0 0
\(313\) −13.1716 −0.744501 −0.372251 0.928132i \(-0.621414\pi\)
−0.372251 + 0.928132i \(0.621414\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.2843 1.25161 0.625805 0.779980i \(-0.284771\pi\)
0.625805 + 0.779980i \(0.284771\pi\)
\(318\) 0 0
\(319\) −1.17157 −0.0655955
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.17157 −0.287754
\(324\) 0 0
\(325\) 13.6569 0.757546
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −11.6569 −0.642663
\(330\) 0 0
\(331\) 10.6274 0.584136 0.292068 0.956398i \(-0.405657\pi\)
0.292068 + 0.956398i \(0.405657\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.17157 0.282553
\(336\) 0 0
\(337\) −19.6274 −1.06917 −0.534587 0.845114i \(-0.679533\pi\)
−0.534587 + 0.845114i \(0.679533\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.75736 −0.149319
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.92893 −0.210916 −0.105458 0.994424i \(-0.533631\pi\)
−0.105458 + 0.994424i \(0.533631\pi\)
\(348\) 0 0
\(349\) 8.34315 0.446598 0.223299 0.974750i \(-0.428317\pi\)
0.223299 + 0.974750i \(0.428317\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.41421 0.128496 0.0642478 0.997934i \(-0.479535\pi\)
0.0642478 + 0.997934i \(0.479535\pi\)
\(354\) 0 0
\(355\) −3.48528 −0.184980
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.31371 0.0693349 0.0346674 0.999399i \(-0.488963\pi\)
0.0346674 + 0.999399i \(0.488963\pi\)
\(360\) 0 0
\(361\) −15.6569 −0.824045
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.65685 −0.191408
\(366\) 0 0
\(367\) −19.4853 −1.01712 −0.508562 0.861026i \(-0.669823\pi\)
−0.508562 + 0.861026i \(0.669823\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 26.3137 1.36247 0.681236 0.732064i \(-0.261443\pi\)
0.681236 + 0.732064i \(0.261443\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 2.48528 0.127660 0.0638302 0.997961i \(-0.479668\pi\)
0.0638302 + 0.997961i \(0.479668\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 15.4558 0.789757 0.394878 0.918733i \(-0.370787\pi\)
0.394878 + 0.918733i \(0.370787\pi\)
\(384\) 0 0
\(385\) 0.171573 0.00874416
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −11.3137 −0.573628 −0.286814 0.957986i \(-0.592596\pi\)
−0.286814 + 0.957986i \(0.592596\pi\)
\(390\) 0 0
\(391\) 9.17157 0.463826
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.343146 0.0172655
\(396\) 0 0
\(397\) 7.65685 0.384286 0.192143 0.981367i \(-0.438456\pi\)
0.192143 + 0.981367i \(0.438456\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.1716 −0.857507 −0.428754 0.903421i \(-0.641047\pi\)
−0.428754 + 0.903421i \(0.641047\pi\)
\(402\) 0 0
\(403\) 18.8284 0.937911
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.41421 0.119668
\(408\) 0 0
\(409\) −17.5147 −0.866047 −0.433024 0.901383i \(-0.642553\pi\)
−0.433024 + 0.901383i \(0.642553\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.65685 −0.376769
\(414\) 0 0
\(415\) −2.14214 −0.105153
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.1421 −1.37483 −0.687417 0.726263i \(-0.741255\pi\)
−0.687417 + 0.726263i \(0.741255\pi\)
\(420\) 0 0
\(421\) 27.4853 1.33955 0.669775 0.742564i \(-0.266390\pi\)
0.669775 + 0.742564i \(0.266390\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −13.6569 −0.662455
\(426\) 0 0
\(427\) 11.3137 0.547509
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −20.2132 −0.973636 −0.486818 0.873503i \(-0.661842\pi\)
−0.486818 + 0.873503i \(0.661842\pi\)
\(432\) 0 0
\(433\) −29.4558 −1.41556 −0.707779 0.706434i \(-0.750303\pi\)
−0.707779 + 0.706434i \(0.750303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.92893 −0.283619
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.0711 −0.668537 −0.334268 0.942478i \(-0.608489\pi\)
−0.334268 + 0.942478i \(0.608489\pi\)
\(444\) 0 0
\(445\) 3.00000 0.142214
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 23.1716 1.09353 0.546767 0.837285i \(-0.315858\pi\)
0.546767 + 0.837285i \(0.315858\pi\)
\(450\) 0 0
\(451\) −5.00000 −0.235441
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.17157 −0.0549242
\(456\) 0 0
\(457\) 2.65685 0.124282 0.0621412 0.998067i \(-0.480207\pi\)
0.0621412 + 0.998067i \(0.480207\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.7574 −0.780468 −0.390234 0.920716i \(-0.627606\pi\)
−0.390234 + 0.920716i \(0.627606\pi\)
\(462\) 0 0
\(463\) 23.6569 1.09943 0.549714 0.835353i \(-0.314737\pi\)
0.549714 + 0.835353i \(0.314737\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −28.6274 −1.32472 −0.662359 0.749186i \(-0.730445\pi\)
−0.662359 + 0.749186i \(0.730445\pi\)
\(468\) 0 0
\(469\) 12.4853 0.576517
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.343146 −0.0157779
\(474\) 0 0
\(475\) 8.82843 0.405076
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.02944 −0.138419 −0.0692093 0.997602i \(-0.522048\pi\)
−0.0692093 + 0.997602i \(0.522048\pi\)
\(480\) 0 0
\(481\) −16.4853 −0.751664
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.686292 0.0311629
\(486\) 0 0
\(487\) 5.51472 0.249896 0.124948 0.992163i \(-0.460124\pi\)
0.124948 + 0.992163i \(0.460124\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −25.8701 −1.16750 −0.583750 0.811934i \(-0.698415\pi\)
−0.583750 + 0.811934i \(0.698415\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.41421 −0.377429
\(498\) 0 0
\(499\) −38.7696 −1.73556 −0.867782 0.496945i \(-0.834455\pi\)
−0.867782 + 0.496945i \(0.834455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −18.1421 −0.808918 −0.404459 0.914556i \(-0.632540\pi\)
−0.404459 + 0.914556i \(0.632540\pi\)
\(504\) 0 0
\(505\) −1.85786 −0.0826739
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15.5147 −0.687678 −0.343839 0.939029i \(-0.611727\pi\)
−0.343839 + 0.939029i \(0.611727\pi\)
\(510\) 0 0
\(511\) −8.82843 −0.390547
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.92893 0.0849989
\(516\) 0 0
\(517\) −4.82843 −0.212354
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.7574 0.821775 0.410887 0.911686i \(-0.365219\pi\)
0.410887 + 0.911686i \(0.365219\pi\)
\(522\) 0 0
\(523\) −21.9706 −0.960706 −0.480353 0.877075i \(-0.659491\pi\)
−0.480353 + 0.877075i \(0.659491\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −18.8284 −0.820179
\(528\) 0 0
\(529\) −12.4853 −0.542838
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 34.1421 1.47886
\(534\) 0 0
\(535\) −7.17157 −0.310054
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.414214 0.0178414
\(540\) 0 0
\(541\) 14.7990 0.636258 0.318129 0.948047i \(-0.396945\pi\)
0.318129 + 0.948047i \(0.396945\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.78680 −0.0765380
\(546\) 0 0
\(547\) −16.9706 −0.725609 −0.362804 0.931865i \(-0.618181\pi\)
−0.362804 + 0.931865i \(0.618181\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.17157 0.220316
\(552\) 0 0
\(553\) 0.828427 0.0352283
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 42.7696 1.81220 0.906102 0.423059i \(-0.139044\pi\)
0.906102 + 0.423059i \(0.139044\pi\)
\(558\) 0 0
\(559\) 2.34315 0.0991045
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.7990 0.665848 0.332924 0.942954i \(-0.391965\pi\)
0.332924 + 0.942954i \(0.391965\pi\)
\(564\) 0 0
\(565\) 6.68629 0.281294
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −29.7990 −1.24924 −0.624619 0.780929i \(-0.714746\pi\)
−0.624619 + 0.780929i \(0.714746\pi\)
\(570\) 0 0
\(571\) −32.6274 −1.36541 −0.682707 0.730692i \(-0.739198\pi\)
−0.682707 + 0.730692i \(0.739198\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −15.6569 −0.652936
\(576\) 0 0
\(577\) 27.9411 1.16320 0.581602 0.813473i \(-0.302426\pi\)
0.581602 + 0.813473i \(0.302426\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.17157 −0.214553
\(582\) 0 0
\(583\) 1.65685 0.0686199
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19.4558 0.803029 0.401514 0.915853i \(-0.368484\pi\)
0.401514 + 0.915853i \(0.368484\pi\)
\(588\) 0 0
\(589\) 12.1716 0.501521
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10.7574 0.441752 0.220876 0.975302i \(-0.429108\pi\)
0.220876 + 0.975302i \(0.429108\pi\)
\(594\) 0 0
\(595\) 1.17157 0.0480298
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 21.0416 0.859738 0.429869 0.902891i \(-0.358560\pi\)
0.429869 + 0.902891i \(0.358560\pi\)
\(600\) 0 0
\(601\) −38.1421 −1.55585 −0.777925 0.628357i \(-0.783728\pi\)
−0.777925 + 0.628357i \(0.783728\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.48528 −0.182353
\(606\) 0 0
\(607\) −14.3431 −0.582170 −0.291085 0.956697i \(-0.594016\pi\)
−0.291085 + 0.956697i \(0.594016\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 32.9706 1.33385
\(612\) 0 0
\(613\) 41.9706 1.69518 0.847588 0.530656i \(-0.178054\pi\)
0.847588 + 0.530656i \(0.178054\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −10.2843 −0.414029 −0.207015 0.978338i \(-0.566375\pi\)
−0.207015 + 0.978338i \(0.566375\pi\)
\(618\) 0 0
\(619\) 17.6863 0.710872 0.355436 0.934701i \(-0.384332\pi\)
0.355436 + 0.934701i \(0.384332\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.24264 0.290170
\(624\) 0 0
\(625\) 22.4558 0.898234
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.4853 0.657311
\(630\) 0 0
\(631\) 32.1421 1.27956 0.639779 0.768559i \(-0.279026\pi\)
0.639779 + 0.768559i \(0.279026\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.17157 0.0464925
\(636\) 0 0
\(637\) −2.82843 −0.112066
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 22.4853 0.888115 0.444058 0.895998i \(-0.353539\pi\)
0.444058 + 0.895998i \(0.353539\pi\)
\(642\) 0 0
\(643\) 13.4853 0.531808 0.265904 0.964000i \(-0.414330\pi\)
0.265904 + 0.964000i \(0.414330\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 33.3137 1.30970 0.654849 0.755760i \(-0.272732\pi\)
0.654849 + 0.755760i \(0.272732\pi\)
\(648\) 0 0
\(649\) −3.17157 −0.124495
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −38.9706 −1.52504 −0.762518 0.646967i \(-0.776037\pi\)
−0.762518 + 0.646967i \(0.776037\pi\)
\(654\) 0 0
\(655\) −0.828427 −0.0323693
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17.1005 0.666141 0.333071 0.942902i \(-0.391915\pi\)
0.333071 + 0.942902i \(0.391915\pi\)
\(660\) 0 0
\(661\) 5.17157 0.201151 0.100575 0.994929i \(-0.467932\pi\)
0.100575 + 0.994929i \(0.467932\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.757359 −0.0293691
\(666\) 0 0
\(667\) −9.17157 −0.355125
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.68629 0.180912
\(672\) 0 0
\(673\) −22.2843 −0.858996 −0.429498 0.903068i \(-0.641309\pi\)
−0.429498 + 0.903068i \(0.641309\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −43.0416 −1.65422 −0.827112 0.562037i \(-0.810018\pi\)
−0.827112 + 0.562037i \(0.810018\pi\)
\(678\) 0 0
\(679\) 1.65685 0.0635842
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.89949 0.264002 0.132001 0.991250i \(-0.457860\pi\)
0.132001 + 0.991250i \(0.457860\pi\)
\(684\) 0 0
\(685\) −1.17157 −0.0447635
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −11.3137 −0.431018
\(690\) 0 0
\(691\) 47.3137 1.79990 0.899949 0.435995i \(-0.143603\pi\)
0.899949 + 0.435995i \(0.143603\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.00000 −0.151729
\(696\) 0 0
\(697\) −34.1421 −1.29323
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 48.4853 1.83126 0.915632 0.402018i \(-0.131691\pi\)
0.915632 + 0.402018i \(0.131691\pi\)
\(702\) 0 0
\(703\) −10.6569 −0.401931
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.48528 −0.168686
\(708\) 0 0
\(709\) 3.68629 0.138442 0.0692208 0.997601i \(-0.477949\pi\)
0.0692208 + 0.997601i \(0.477949\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −21.5858 −0.808394
\(714\) 0 0
\(715\) −0.485281 −0.0181485
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 3.65685 0.136378 0.0681888 0.997672i \(-0.478278\pi\)
0.0681888 + 0.997672i \(0.478278\pi\)
\(720\) 0 0
\(721\) 4.65685 0.173430
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 13.6569 0.507203
\(726\) 0 0
\(727\) −38.6274 −1.43261 −0.716306 0.697787i \(-0.754168\pi\)
−0.716306 + 0.697787i \(0.754168\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.34315 −0.0866644
\(732\) 0 0
\(733\) 4.82843 0.178342 0.0891710 0.996016i \(-0.471578\pi\)
0.0891710 + 0.996016i \(0.471578\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.17157 0.190497
\(738\) 0 0
\(739\) 2.97056 0.109274 0.0546370 0.998506i \(-0.482600\pi\)
0.0546370 + 0.998506i \(0.482600\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.89949 0.106372 0.0531861 0.998585i \(-0.483062\pi\)
0.0531861 + 0.998585i \(0.483062\pi\)
\(744\) 0 0
\(745\) −3.65685 −0.133977
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −17.3137 −0.632629
\(750\) 0 0
\(751\) 33.5147 1.22297 0.611485 0.791256i \(-0.290573\pi\)
0.611485 + 0.791256i \(0.290573\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.17157 −0.261000
\(756\) 0 0
\(757\) −26.2843 −0.955318 −0.477659 0.878545i \(-0.658515\pi\)
−0.477659 + 0.878545i \(0.658515\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.20101 −0.297286 −0.148643 0.988891i \(-0.547491\pi\)
−0.148643 + 0.988891i \(0.547491\pi\)
\(762\) 0 0
\(763\) −4.31371 −0.156167
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 21.6569 0.781984
\(768\) 0 0
\(769\) 30.1421 1.08695 0.543477 0.839424i \(-0.317108\pi\)
0.543477 + 0.839424i \(0.317108\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 35.5858 1.27993 0.639966 0.768403i \(-0.278948\pi\)
0.639966 + 0.768403i \(0.278948\pi\)
\(774\) 0 0
\(775\) 32.1421 1.15458
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22.0711 0.790778
\(780\) 0 0
\(781\) −3.48528 −0.124713
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.85786 0.209076
\(786\) 0 0
\(787\) 41.9411 1.49504 0.747520 0.664239i \(-0.231244\pi\)
0.747520 + 0.664239i \(0.231244\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 16.1421 0.573948
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.1005 −0.747418 −0.373709 0.927546i \(-0.621914\pi\)
−0.373709 + 0.927546i \(0.621914\pi\)
\(798\) 0 0
\(799\) −32.9706 −1.16641
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3.65685 −0.129048
\(804\) 0 0
\(805\) 1.34315 0.0473397
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 31.5147 1.10800 0.553999 0.832517i \(-0.313101\pi\)
0.553999 + 0.832517i \(0.313101\pi\)
\(810\) 0 0
\(811\) −20.6569 −0.725360 −0.362680 0.931914i \(-0.618138\pi\)
−0.362680 + 0.931914i \(0.618138\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.201010 0.00704108
\(816\) 0 0
\(817\) 1.51472 0.0529933
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −50.2843 −1.75493 −0.877467 0.479638i \(-0.840768\pi\)
−0.877467 + 0.479638i \(0.840768\pi\)
\(822\) 0 0
\(823\) −3.37258 −0.117561 −0.0587804 0.998271i \(-0.518721\pi\)
−0.0587804 + 0.998271i \(0.518721\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −10.4142 −0.362138 −0.181069 0.983470i \(-0.557956\pi\)
−0.181069 + 0.983470i \(0.557956\pi\)
\(828\) 0 0
\(829\) −20.1421 −0.699565 −0.349783 0.936831i \(-0.613745\pi\)
−0.349783 + 0.936831i \(0.613745\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.82843 0.0979992
\(834\) 0 0
\(835\) −7.65685 −0.264976
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 5.85786 0.202236 0.101118 0.994874i \(-0.467758\pi\)
0.101118 + 0.994874i \(0.467758\pi\)
\(840\) 0 0
\(841\) −21.0000 −0.724138
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.07107 −0.0712469
\(846\) 0 0
\(847\) −10.8284 −0.372069
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 18.8995 0.647866
\(852\) 0 0
\(853\) 44.9706 1.53976 0.769881 0.638187i \(-0.220315\pi\)
0.769881 + 0.638187i \(0.220315\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 38.5563 1.31706 0.658530 0.752555i \(-0.271179\pi\)
0.658530 + 0.752555i \(0.271179\pi\)
\(858\) 0 0
\(859\) 16.1127 0.549758 0.274879 0.961479i \(-0.411362\pi\)
0.274879 + 0.961479i \(0.411362\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 24.3431 0.828650 0.414325 0.910129i \(-0.364018\pi\)
0.414325 + 0.910129i \(0.364018\pi\)
\(864\) 0 0
\(865\) −0.313708 −0.0106664
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.343146 0.0116404
\(870\) 0 0
\(871\) −35.3137 −1.19656
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −4.07107 −0.137627
\(876\) 0 0
\(877\) −27.9411 −0.943505 −0.471752 0.881731i \(-0.656378\pi\)
−0.471752 + 0.881731i \(0.656378\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −6.27208 −0.211312 −0.105656 0.994403i \(-0.533694\pi\)
−0.105656 + 0.994403i \(0.533694\pi\)
\(882\) 0 0
\(883\) −39.3137 −1.32301 −0.661506 0.749940i \(-0.730082\pi\)
−0.661506 + 0.749940i \(0.730082\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40.7696 −1.36891 −0.684454 0.729056i \(-0.739959\pi\)
−0.684454 + 0.729056i \(0.739959\pi\)
\(888\) 0 0
\(889\) 2.82843 0.0948624
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 21.3137 0.713236
\(894\) 0 0
\(895\) −3.45584 −0.115516
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 18.8284 0.627963
\(900\) 0 0
\(901\) 11.3137 0.376914
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.45584 0.114876
\(906\) 0 0
\(907\) 33.3137 1.10616 0.553082 0.833127i \(-0.313452\pi\)
0.553082 + 0.833127i \(0.313452\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 42.9706 1.42368 0.711839 0.702343i \(-0.247863\pi\)
0.711839 + 0.702343i \(0.247863\pi\)
\(912\) 0 0
\(913\) −2.14214 −0.0708943
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2.00000 −0.0660458
\(918\) 0 0
\(919\) 41.6569 1.37413 0.687066 0.726595i \(-0.258898\pi\)
0.687066 + 0.726595i \(0.258898\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 23.7990 0.783353
\(924\) 0 0
\(925\) −28.1421 −0.925308
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −17.8579 −0.585898 −0.292949 0.956128i \(-0.594637\pi\)
−0.292949 + 0.956128i \(0.594637\pi\)
\(930\) 0 0
\(931\) −1.82843 −0.0599243
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.485281 0.0158704
\(936\) 0 0
\(937\) 11.3137 0.369603 0.184801 0.982776i \(-0.440836\pi\)
0.184801 + 0.982776i \(0.440836\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 29.3848 0.957916 0.478958 0.877838i \(-0.341015\pi\)
0.478958 + 0.877838i \(0.341015\pi\)
\(942\) 0 0
\(943\) −39.1421 −1.27464
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −21.7279 −0.706063 −0.353031 0.935612i \(-0.614849\pi\)
−0.353031 + 0.935612i \(0.614849\pi\)
\(948\) 0 0
\(949\) 24.9706 0.810579
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 58.8284 1.90564 0.952820 0.303536i \(-0.0981674\pi\)
0.952820 + 0.303536i \(0.0981674\pi\)
\(954\) 0 0
\(955\) −3.97056 −0.128484
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −2.82843 −0.0913347
\(960\) 0 0
\(961\) 13.3137 0.429474
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3.17157 0.102097
\(966\) 0 0
\(967\) −46.2843 −1.48840 −0.744201 0.667956i \(-0.767169\pi\)
−0.744201 + 0.667956i \(0.767169\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 46.8284 1.50280 0.751398 0.659849i \(-0.229380\pi\)
0.751398 + 0.659849i \(0.229380\pi\)
\(972\) 0 0
\(973\) −9.65685 −0.309585
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −48.9706 −1.56671 −0.783354 0.621576i \(-0.786493\pi\)
−0.783354 + 0.621576i \(0.786493\pi\)
\(978\) 0 0
\(979\) 3.00000 0.0958804
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −53.5980 −1.70951 −0.854755 0.519032i \(-0.826293\pi\)
−0.854755 + 0.519032i \(0.826293\pi\)
\(984\) 0 0
\(985\) 7.94113 0.253025
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.68629 −0.0854191
\(990\) 0 0
\(991\) 13.4558 0.427439 0.213719 0.976895i \(-0.431442\pi\)
0.213719 + 0.976895i \(0.431442\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 5.58579 0.177081
\(996\) 0 0
\(997\) 45.3137 1.43510 0.717550 0.696507i \(-0.245264\pi\)
0.717550 + 0.696507i \(0.245264\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))