Properties

Label 5184.2.f.e.2591.4
Level $5184$
Weight $2$
Character 5184.2591
Analytic conductor $41.394$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{37}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.4
Root \(0.367543 - 0.212201i\) of defining polynomial
Character \(\chi\) \(=\) 5184.2591
Dual form 5184.2.f.e.2591.3

$q$-expansion

\(f(q)\) \(=\) \(q-2.24254 q^{5} +3.77162i q^{7} +O(q^{10})\) \(q-2.24254 q^{5} +3.77162i q^{7} +2.57370i q^{11} -2.77162i q^{13} -4.81624i q^{17} +5.77162 q^{19} -1.91137 q^{23} +0.0289668 q^{25} +10.2533 q^{29} +6.22512i q^{31} -8.45799i q^{35} +1.96043i q^{37} -10.6118i q^{41} +5.01060 q^{43} -6.36915 q^{47} -7.22512 q^{49} +2.35856 q^{53} -5.77162i q^{55} +5.22196i q^{59} -2.26469i q^{61} +6.21546i q^{65} +12.5326 q^{67} +1.19446 q^{71} +8.57221 q^{73} -9.70703 q^{77} +2.39557i q^{79} -15.3593i q^{83} +10.8006i q^{85} +14.7111i q^{89} +10.4535 q^{91} -12.9431 q^{95} -13.7684 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 24 q^{19} + 16 q^{25} + 24 q^{43} - 48 q^{49} + 120 q^{67} + 16 q^{73} + 168 q^{91} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(5\) −2.24254 −1.00289 −0.501446 0.865189i \(-0.667198\pi\)
−0.501446 + 0.865189i \(0.667198\pi\)
\(6\) 0 0
\(7\) 3.77162i 1.42554i 0.701399 + 0.712769i \(0.252559\pi\)
−0.701399 + 0.712769i \(0.747441\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.57370i 0.776001i 0.921659 + 0.388000i \(0.126834\pi\)
−0.921659 + 0.388000i \(0.873166\pi\)
\(12\) 0 0
\(13\) − 2.77162i − 0.768709i −0.923186 0.384355i \(-0.874424\pi\)
0.923186 0.384355i \(-0.125576\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 4.81624i − 1.16811i −0.811714 0.584055i \(-0.801465\pi\)
0.811714 0.584055i \(-0.198535\pi\)
\(18\) 0 0
\(19\) 5.77162 1.32410 0.662050 0.749459i \(-0.269687\pi\)
0.662050 + 0.749459i \(0.269687\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.91137 −0.398548 −0.199274 0.979944i \(-0.563858\pi\)
−0.199274 + 0.979944i \(0.563858\pi\)
\(24\) 0 0
\(25\) 0.0289668 0.00579337
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 10.2533 1.90400 0.951999 0.306102i \(-0.0990250\pi\)
0.951999 + 0.306102i \(0.0990250\pi\)
\(30\) 0 0
\(31\) 6.22512i 1.11806i 0.829146 + 0.559032i \(0.188827\pi\)
−0.829146 + 0.559032i \(0.811173\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 8.45799i − 1.42966i
\(36\) 0 0
\(37\) 1.96043i 0.322293i 0.986931 + 0.161146i \(0.0515191\pi\)
−0.986931 + 0.161146i \(0.948481\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 10.6118i − 1.65728i −0.559779 0.828642i \(-0.689114\pi\)
0.559779 0.828642i \(-0.310886\pi\)
\(42\) 0 0
\(43\) 5.01060 0.764110 0.382055 0.924140i \(-0.375217\pi\)
0.382055 + 0.924140i \(0.375217\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.36915 −0.929036 −0.464518 0.885564i \(-0.653772\pi\)
−0.464518 + 0.885564i \(0.653772\pi\)
\(48\) 0 0
\(49\) −7.22512 −1.03216
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.35856 0.323973 0.161987 0.986793i \(-0.448210\pi\)
0.161987 + 0.986793i \(0.448210\pi\)
\(54\) 0 0
\(55\) − 5.77162i − 0.778245i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.22196i 0.679841i 0.940454 + 0.339920i \(0.110400\pi\)
−0.940454 + 0.339920i \(0.889600\pi\)
\(60\) 0 0
\(61\) − 2.26469i − 0.289964i −0.989434 0.144982i \(-0.953688\pi\)
0.989434 0.144982i \(-0.0463124\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.21546i 0.770933i
\(66\) 0 0
\(67\) 12.5326 1.53111 0.765553 0.643373i \(-0.222466\pi\)
0.765553 + 0.643373i \(0.222466\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.19446 0.141756 0.0708781 0.997485i \(-0.477420\pi\)
0.0708781 + 0.997485i \(0.477420\pi\)
\(72\) 0 0
\(73\) 8.57221 1.00330 0.501650 0.865070i \(-0.332726\pi\)
0.501650 + 0.865070i \(0.332726\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.70703 −1.10622
\(78\) 0 0
\(79\) 2.39557i 0.269522i 0.990878 + 0.134761i \(0.0430267\pi\)
−0.990878 + 0.134761i \(0.956973\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 15.3593i − 1.68590i −0.537993 0.842950i \(-0.680817\pi\)
0.537993 0.842950i \(-0.319183\pi\)
\(84\) 0 0
\(85\) 10.8006i 1.17149i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.7111i 1.55938i 0.626168 + 0.779688i \(0.284622\pi\)
−0.626168 + 0.779688i \(0.715378\pi\)
\(90\) 0 0
\(91\) 10.4535 1.09582
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −12.9431 −1.32793
\(96\) 0 0
\(97\) −13.7684 −1.39797 −0.698983 0.715139i \(-0.746364\pi\)
−0.698983 + 0.715139i \(0.746364\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.20106 0.219014 0.109507 0.993986i \(-0.465073\pi\)
0.109507 + 0.993986i \(0.465073\pi\)
\(102\) 0 0
\(103\) 2.00000i 0.197066i 0.995134 + 0.0985329i \(0.0314150\pi\)
−0.995134 + 0.0985329i \(0.968585\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.16717i 0.112835i 0.998407 + 0.0564174i \(0.0179677\pi\)
−0.998407 + 0.0564174i \(0.982032\pi\)
\(108\) 0 0
\(109\) 17.6118i 1.68690i 0.537206 + 0.843451i \(0.319480\pi\)
−0.537206 + 0.843451i \(0.680520\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 0.405719i − 0.0381668i −0.999818 0.0190834i \(-0.993925\pi\)
0.999818 0.0190834i \(-0.00607481\pi\)
\(114\) 0 0
\(115\) 4.28631 0.399701
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 18.1650 1.66518
\(120\) 0 0
\(121\) 4.37605 0.397823
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.1477 0.997082
\(126\) 0 0
\(127\) 14.1639i 1.25685i 0.777872 + 0.628423i \(0.216299\pi\)
−0.777872 + 0.628423i \(0.783701\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 21.2509i 1.85670i 0.371710 + 0.928349i \(0.378771\pi\)
−0.371710 + 0.928349i \(0.621229\pi\)
\(132\) 0 0
\(133\) 21.7684i 1.88756i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 7.62506i − 0.651453i −0.945464 0.325726i \(-0.894391\pi\)
0.945464 0.325726i \(-0.105609\pi\)
\(138\) 0 0
\(139\) −16.0726 −1.36326 −0.681631 0.731696i \(-0.738729\pi\)
−0.681631 + 0.731696i \(0.738729\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.13333 0.596519
\(144\) 0 0
\(145\) −22.9935 −1.90950
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −21.3596 −1.74985 −0.874923 0.484262i \(-0.839088\pi\)
−0.874923 + 0.484262i \(0.839088\pi\)
\(150\) 0 0
\(151\) − 7.54324i − 0.613860i −0.951732 0.306930i \(-0.900698\pi\)
0.951732 0.306930i \(-0.0993018\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 13.9601i − 1.12130i
\(156\) 0 0
\(157\) 16.2068i 1.29344i 0.762728 + 0.646720i \(0.223860\pi\)
−0.762728 + 0.646720i \(0.776140\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 7.20896i − 0.568145i
\(162\) 0 0
\(163\) −14.7545 −1.15566 −0.577831 0.816157i \(-0.696101\pi\)
−0.577831 + 0.816157i \(0.696101\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.5539 −1.59051 −0.795256 0.606274i \(-0.792663\pi\)
−0.795256 + 0.606274i \(0.792663\pi\)
\(168\) 0 0
\(169\) 5.31812 0.409086
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −11.0732 −0.841877 −0.420939 0.907089i \(-0.638299\pi\)
−0.420939 + 0.907089i \(0.638299\pi\)
\(174\) 0 0
\(175\) 0.109252i 0.00825867i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 0.232048i − 0.0173441i −0.999962 0.00867203i \(-0.997240\pi\)
0.999962 0.00867203i \(-0.00276043\pi\)
\(180\) 0 0
\(181\) 4.47796i 0.332844i 0.986055 + 0.166422i \(0.0532215\pi\)
−0.986055 + 0.166422i \(0.946779\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 4.39634i − 0.323225i
\(186\) 0 0
\(187\) 12.3956 0.906454
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.58521 0.693562 0.346781 0.937946i \(-0.387275\pi\)
0.346781 + 0.937946i \(0.387275\pi\)
\(192\) 0 0
\(193\) −12.0865 −0.870004 −0.435002 0.900430i \(-0.643252\pi\)
−0.435002 + 0.900430i \(0.643252\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.1477 0.794242 0.397121 0.917766i \(-0.370009\pi\)
0.397121 + 0.917766i \(0.370009\pi\)
\(198\) 0 0
\(199\) 13.5432i 0.960055i 0.877253 + 0.480027i \(0.159373\pi\)
−0.877253 + 0.480027i \(0.840627\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 38.6717i 2.71422i
\(204\) 0 0
\(205\) 23.7973i 1.66208i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 14.8544i 1.02750i
\(210\) 0 0
\(211\) 28.1639 1.93888 0.969442 0.245320i \(-0.0788929\pi\)
0.969442 + 0.245320i \(0.0788929\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.2365 −0.766320
\(216\) 0 0
\(217\) −23.4788 −1.59384
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −13.3488 −0.897936
\(222\) 0 0
\(223\) 21.9902i 1.47257i 0.676669 + 0.736287i \(0.263423\pi\)
−0.676669 + 0.736287i \(0.736577\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 12.7856i − 0.848608i −0.905520 0.424304i \(-0.860519\pi\)
0.905520 0.424304i \(-0.139481\pi\)
\(228\) 0 0
\(229\) 3.02447i 0.199862i 0.994994 + 0.0999312i \(0.0318623\pi\)
−0.994994 + 0.0999312i \(0.968138\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23.7558i 1.55630i 0.628081 + 0.778148i \(0.283840\pi\)
−0.628081 + 0.778148i \(0.716160\pi\)
\(234\) 0 0
\(235\) 14.2831 0.931724
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 29.4222 1.90317 0.951583 0.307391i \(-0.0994558\pi\)
0.951583 + 0.307391i \(0.0994558\pi\)
\(240\) 0 0
\(241\) −5.87803 −0.378637 −0.189319 0.981916i \(-0.560628\pi\)
−0.189319 + 0.981916i \(0.560628\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 16.2026 1.03515
\(246\) 0 0
\(247\) − 15.9967i − 1.01785i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 2.06886i − 0.130586i −0.997866 0.0652928i \(-0.979202\pi\)
0.997866 0.0652928i \(-0.0207981\pi\)
\(252\) 0 0
\(253\) − 4.91930i − 0.309273i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 7.19477i − 0.448798i −0.974497 0.224399i \(-0.927958\pi\)
0.974497 0.224399i \(-0.0720418\pi\)
\(258\) 0 0
\(259\) −7.39400 −0.459441
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 27.1625 1.67491 0.837454 0.546507i \(-0.184043\pi\)
0.837454 + 0.546507i \(0.184043\pi\)
\(264\) 0 0
\(265\) −5.28915 −0.324910
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.7078 0.652869 0.326434 0.945220i \(-0.394153\pi\)
0.326434 + 0.945220i \(0.394153\pi\)
\(270\) 0 0
\(271\) 3.24463i 0.197097i 0.995132 + 0.0985486i \(0.0314200\pi\)
−0.995132 + 0.0985486i \(0.968580\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.0745520i 0.00449566i
\(276\) 0 0
\(277\) − 23.0008i − 1.38199i −0.722862 0.690993i \(-0.757174\pi\)
0.722862 0.690993i \(-0.242826\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.1757i 1.44220i 0.692830 + 0.721101i \(0.256364\pi\)
−0.692830 + 0.721101i \(0.743636\pi\)
\(282\) 0 0
\(283\) 23.2236 1.38050 0.690248 0.723572i \(-0.257501\pi\)
0.690248 + 0.723572i \(0.257501\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 40.0237 2.36252
\(288\) 0 0
\(289\) −6.19615 −0.364480
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.7723 −0.921428 −0.460714 0.887549i \(-0.652407\pi\)
−0.460714 + 0.887549i \(0.652407\pi\)
\(294\) 0 0
\(295\) − 11.7104i − 0.681807i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.29759i 0.306367i
\(300\) 0 0
\(301\) 18.8981i 1.08927i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5.07865i 0.290802i
\(306\) 0 0
\(307\) 17.7104 1.01079 0.505394 0.862889i \(-0.331347\pi\)
0.505394 + 0.862889i \(0.331347\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −11.4336 −0.648341 −0.324170 0.945999i \(-0.605085\pi\)
−0.324170 + 0.945999i \(0.605085\pi\)
\(312\) 0 0
\(313\) 0.376055 0.0212559 0.0106279 0.999944i \(-0.496617\pi\)
0.0106279 + 0.999944i \(0.496617\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.7492 1.27772 0.638862 0.769322i \(-0.279406\pi\)
0.638862 + 0.769322i \(0.279406\pi\)
\(318\) 0 0
\(319\) 26.3890i 1.47750i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 27.7975i − 1.54669i
\(324\) 0 0
\(325\) − 0.0802851i − 0.00445341i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 24.0220i − 1.32438i
\(330\) 0 0
\(331\) 28.0670 1.54270 0.771350 0.636411i \(-0.219582\pi\)
0.771350 + 0.636411i \(0.219582\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −28.1049 −1.53553
\(336\) 0 0
\(337\) 12.9193 0.703759 0.351879 0.936045i \(-0.385543\pi\)
0.351879 + 0.936045i \(0.385543\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −16.0216 −0.867619
\(342\) 0 0
\(343\) − 0.849064i − 0.0458452i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 13.6800i 0.734378i 0.930146 + 0.367189i \(0.119680\pi\)
−0.930146 + 0.367189i \(0.880320\pi\)
\(348\) 0 0
\(349\) 17.1533i 0.918196i 0.888386 + 0.459098i \(0.151827\pi\)
−0.888386 + 0.459098i \(0.848173\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 6.63156i − 0.352962i −0.984304 0.176481i \(-0.943529\pi\)
0.984304 0.176481i \(-0.0564715\pi\)
\(354\) 0 0
\(355\) −2.67862 −0.142166
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.921669 −0.0486438 −0.0243219 0.999704i \(-0.507743\pi\)
−0.0243219 + 0.999704i \(0.507743\pi\)
\(360\) 0 0
\(361\) 14.3116 0.753242
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −19.2235 −1.00620
\(366\) 0 0
\(367\) 13.0162i 0.679443i 0.940526 + 0.339721i \(0.110333\pi\)
−0.940526 + 0.339721i \(0.889667\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.89559i 0.461836i
\(372\) 0 0
\(373\) 2.21282i 0.114576i 0.998358 + 0.0572878i \(0.0182453\pi\)
−0.998358 + 0.0572878i \(0.981755\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 28.4184i − 1.46362i
\(378\) 0 0
\(379\) −5.15332 −0.264708 −0.132354 0.991202i \(-0.542254\pi\)
−0.132354 + 0.991202i \(0.542254\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −33.0478 −1.68866 −0.844332 0.535820i \(-0.820003\pi\)
−0.844332 + 0.535820i \(0.820003\pi\)
\(384\) 0 0
\(385\) 21.7684 1.10942
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 30.5790 1.55042 0.775209 0.631705i \(-0.217644\pi\)
0.775209 + 0.631705i \(0.217644\pi\)
\(390\) 0 0
\(391\) 9.20561i 0.465548i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 5.37214i − 0.270302i
\(396\) 0 0
\(397\) − 5.10485i − 0.256205i −0.991761 0.128102i \(-0.959111\pi\)
0.991761 0.128102i \(-0.0408886\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.825622i 0.0412296i 0.999787 + 0.0206148i \(0.00656235\pi\)
−0.999787 + 0.0206148i \(0.993438\pi\)
\(402\) 0 0
\(403\) 17.2537 0.859466
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.04557 −0.250099
\(408\) 0 0
\(409\) −4.10315 −0.202888 −0.101444 0.994841i \(-0.532346\pi\)
−0.101444 + 0.994841i \(0.532346\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −19.6952 −0.969139
\(414\) 0 0
\(415\) 34.4437i 1.69078i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 24.9172i − 1.21728i −0.793445 0.608642i \(-0.791714\pi\)
0.793445 0.608642i \(-0.208286\pi\)
\(420\) 0 0
\(421\) 16.9176i 0.824513i 0.911068 + 0.412257i \(0.135259\pi\)
−0.911068 + 0.412257i \(0.864741\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 0.139511i − 0.00676729i
\(426\) 0 0
\(427\) 8.54155 0.413354
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.33455 −0.305125 −0.152562 0.988294i \(-0.548752\pi\)
−0.152562 + 0.988294i \(0.548752\pi\)
\(432\) 0 0
\(433\) 32.3695 1.55558 0.777790 0.628524i \(-0.216341\pi\)
0.777790 + 0.628524i \(0.216341\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −11.0317 −0.527718
\(438\) 0 0
\(439\) − 11.1321i − 0.531307i −0.964069 0.265653i \(-0.914412\pi\)
0.964069 0.265653i \(-0.0855877\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.80297i 0.370730i 0.982670 + 0.185365i \(0.0593468\pi\)
−0.982670 + 0.185365i \(0.940653\pi\)
\(444\) 0 0
\(445\) − 32.9902i − 1.56389i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.3258i 1.05362i 0.849983 + 0.526810i \(0.176612\pi\)
−0.849983 + 0.526810i \(0.823388\pi\)
\(450\) 0 0
\(451\) 27.3116 1.28605
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −23.4423 −1.09899
\(456\) 0 0
\(457\) −30.9768 −1.44903 −0.724517 0.689257i \(-0.757937\pi\)
−0.724517 + 0.689257i \(0.757937\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.18130 0.287892 0.143946 0.989586i \(-0.454021\pi\)
0.143946 + 0.989586i \(0.454021\pi\)
\(462\) 0 0
\(463\) 1.53094i 0.0711490i 0.999367 + 0.0355745i \(0.0113261\pi\)
−0.999367 + 0.0355745i \(0.988674\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.97014i 0.415089i 0.978226 + 0.207544i \(0.0665471\pi\)
−0.978226 + 0.207544i \(0.933453\pi\)
\(468\) 0 0
\(469\) 47.2684i 2.18265i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.8958i 0.592950i
\(474\) 0 0
\(475\) 0.167186 0.00767100
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −36.1253 −1.65061 −0.825303 0.564690i \(-0.808996\pi\)
−0.825303 + 0.564690i \(0.808996\pi\)
\(480\) 0 0
\(481\) 5.43357 0.247749
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 30.8760 1.40201
\(486\) 0 0
\(487\) − 42.1027i − 1.90786i −0.300034 0.953928i \(-0.596998\pi\)
0.300034 0.953928i \(-0.403002\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 2.64825i − 0.119514i −0.998213 0.0597570i \(-0.980967\pi\)
0.998213 0.0597570i \(-0.0190326\pi\)
\(492\) 0 0
\(493\) − 49.3825i − 2.22408i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.50505i 0.202079i
\(498\) 0 0
\(499\) −23.0253 −1.03075 −0.515377 0.856964i \(-0.672348\pi\)
−0.515377 + 0.856964i \(0.672348\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.0980 −0.985301 −0.492650 0.870227i \(-0.663972\pi\)
−0.492650 + 0.870227i \(0.663972\pi\)
\(504\) 0 0
\(505\) −4.93596 −0.219648
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.9064 −0.749363 −0.374681 0.927154i \(-0.622248\pi\)
−0.374681 + 0.927154i \(0.622248\pi\)
\(510\) 0 0
\(511\) 32.3311i 1.43024i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 4.48507i − 0.197636i
\(516\) 0 0
\(517\) − 16.3923i − 0.720933i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 17.5687i − 0.769700i −0.922979 0.384850i \(-0.874253\pi\)
0.922979 0.384850i \(-0.125747\pi\)
\(522\) 0 0
\(523\) 22.6354 0.989776 0.494888 0.868957i \(-0.335209\pi\)
0.494888 + 0.868957i \(0.335209\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.9817 1.30602
\(528\) 0 0
\(529\) −19.3467 −0.841160
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −29.4119 −1.27397
\(534\) 0 0
\(535\) − 2.61742i − 0.113161i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 18.5953i − 0.800957i
\(540\) 0 0
\(541\) − 9.86701i − 0.424216i −0.977246 0.212108i \(-0.931967\pi\)
0.977246 0.212108i \(-0.0680328\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 39.4950i − 1.69178i
\(546\) 0 0
\(547\) −12.5383 −0.536098 −0.268049 0.963405i \(-0.586379\pi\)
−0.268049 + 0.963405i \(0.586379\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 59.1784 2.52108
\(552\) 0 0
\(553\) −9.03516 −0.384214
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.93876 −0.166891 −0.0834453 0.996512i \(-0.526592\pi\)
−0.0834453 + 0.996512i \(0.526592\pi\)
\(558\) 0 0
\(559\) − 13.8875i − 0.587378i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 33.2250i 1.40027i 0.714012 + 0.700134i \(0.246876\pi\)
−0.714012 + 0.700134i \(0.753124\pi\)
\(564\) 0 0
\(565\) 0.909839i 0.0382772i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 3.82654i − 0.160417i −0.996778 0.0802084i \(-0.974441\pi\)
0.996778 0.0802084i \(-0.0255586\pi\)
\(570\) 0 0
\(571\) −9.63129 −0.403057 −0.201528 0.979483i \(-0.564591\pi\)
−0.201528 + 0.979483i \(0.564591\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.0553663 −0.00230893
\(576\) 0 0
\(577\) 13.6754 0.569313 0.284656 0.958630i \(-0.408121\pi\)
0.284656 + 0.958630i \(0.408121\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 57.9293 2.40331
\(582\) 0 0
\(583\) 6.07023i 0.251403i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 28.4598i − 1.17466i −0.809346 0.587332i \(-0.800178\pi\)
0.809346 0.587332i \(-0.199822\pi\)
\(588\) 0 0
\(589\) 35.9290i 1.48043i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.70103i 0.234113i 0.993125 + 0.117057i \(0.0373459\pi\)
−0.993125 + 0.117057i \(0.962654\pi\)
\(594\) 0 0
\(595\) −40.7357 −1.67000
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15.5997 0.637387 0.318693 0.947858i \(-0.396756\pi\)
0.318693 + 0.947858i \(0.396756\pi\)
\(600\) 0 0
\(601\) −15.1607 −0.618416 −0.309208 0.950994i \(-0.600064\pi\)
−0.309208 + 0.950994i \(0.600064\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.81346 −0.398974
\(606\) 0 0
\(607\) 35.9837i 1.46053i 0.683162 + 0.730267i \(0.260604\pi\)
−0.683162 + 0.730267i \(0.739396\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 17.6529i 0.714159i
\(612\) 0 0
\(613\) − 24.1003i − 0.973404i −0.873568 0.486702i \(-0.838200\pi\)
0.873568 0.486702i \(-0.161800\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 28.1317i 1.13254i 0.824219 + 0.566271i \(0.191614\pi\)
−0.824219 + 0.566271i \(0.808386\pi\)
\(618\) 0 0
\(619\) −36.0849 −1.45038 −0.725188 0.688551i \(-0.758247\pi\)
−0.725188 + 0.688551i \(0.758247\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −55.4848 −2.22295
\(624\) 0 0
\(625\) −25.1440 −1.00576
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.44190 0.376473
\(630\) 0 0
\(631\) − 35.5302i − 1.41443i −0.706996 0.707217i \(-0.749950\pi\)
0.706996 0.707217i \(-0.250050\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 31.7631i − 1.26048i
\(636\) 0 0
\(637\) 20.0253i 0.793431i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 30.4054i − 1.20094i −0.799647 0.600470i \(-0.794980\pi\)
0.799647 0.600470i \(-0.205020\pi\)
\(642\) 0 0
\(643\) 6.38578 0.251831 0.125915 0.992041i \(-0.459813\pi\)
0.125915 + 0.992041i \(0.459813\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.4730 −1.19802 −0.599009 0.800742i \(-0.704439\pi\)
−0.599009 + 0.800742i \(0.704439\pi\)
\(648\) 0 0
\(649\) −13.4398 −0.527557
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 35.7411 1.39866 0.699328 0.714801i \(-0.253483\pi\)
0.699328 + 0.714801i \(0.253483\pi\)
\(654\) 0 0
\(655\) − 47.6558i − 1.86207i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.0672402i 0.00261931i 0.999999 + 0.00130965i \(0.000416876\pi\)
−0.999999 + 0.00130965i \(0.999583\pi\)
\(660\) 0 0
\(661\) 9.61954i 0.374157i 0.982345 + 0.187078i \(0.0599018\pi\)
−0.982345 + 0.187078i \(0.940098\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 48.8163i − 1.89302i
\(666\) 0 0
\(667\) −19.5979 −0.758834
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.82864 0.225012
\(672\) 0 0
\(673\) 20.0800 0.774026 0.387013 0.922074i \(-0.373507\pi\)
0.387013 + 0.922074i \(0.373507\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −22.6332 −0.869864 −0.434932 0.900463i \(-0.643228\pi\)
−0.434932 + 0.900463i \(0.643228\pi\)
\(678\) 0 0
\(679\) − 51.9290i − 1.99285i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3.38622i 0.129570i 0.997899 + 0.0647851i \(0.0206362\pi\)
−0.997899 + 0.0647851i \(0.979364\pi\)
\(684\) 0 0
\(685\) 17.0995i 0.653337i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 6.53703i − 0.249041i
\(690\) 0 0
\(691\) −4.59057 −0.174634 −0.0873168 0.996181i \(-0.527829\pi\)
−0.0873168 + 0.996181i \(0.527829\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 36.0434 1.36720
\(696\) 0 0
\(697\) −51.1089 −1.93589
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 14.8717 0.561696 0.280848 0.959752i \(-0.409384\pi\)
0.280848 + 0.959752i \(0.409384\pi\)
\(702\) 0 0
\(703\) 11.3149i 0.426748i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.30158i 0.312213i
\(708\) 0 0
\(709\) 14.3851i 0.540243i 0.962826 + 0.270122i \(0.0870639\pi\)
−0.962826 + 0.270122i \(0.912936\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 11.8985i − 0.445602i
\(714\) 0 0
\(715\) −15.9967 −0.598244
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.35549 0.0878449 0.0439224 0.999035i \(-0.486015\pi\)
0.0439224 + 0.999035i \(0.486015\pi\)
\(720\) 0 0
\(721\) −7.54324 −0.280925
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.297007 0.0110306
\(726\) 0 0
\(727\) − 1.41182i − 0.0523613i −0.999657 0.0261807i \(-0.991665\pi\)
0.999657 0.0261807i \(-0.00833452\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 24.1323i − 0.892564i
\(732\) 0 0
\(733\) − 33.3784i − 1.23286i −0.787409 0.616430i \(-0.788578\pi\)
0.787409 0.616430i \(-0.211422\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 32.2553i 1.18814i
\(738\) 0 0
\(739\) 6.74220 0.248016 0.124008 0.992281i \(-0.460425\pi\)
0.124008 + 0.992281i \(0.460425\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.5581 −1.01101 −0.505505 0.862824i \(-0.668694\pi\)
−0.505505 + 0.862824i \(0.668694\pi\)
\(744\) 0 0
\(745\) 47.8996 1.75491
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.40213 −0.160850
\(750\) 0 0
\(751\) 9.01951i 0.329127i 0.986367 + 0.164563i \(0.0526215\pi\)
−0.986367 + 0.164563i \(0.947379\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 16.9160i 0.615636i
\(756\) 0 0
\(757\) − 20.8213i − 0.756764i −0.925649 0.378382i \(-0.876481\pi\)
0.925649 0.378382i \(-0.123519\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.1602i 1.52831i 0.645035 + 0.764153i \(0.276843\pi\)
−0.645035 + 0.764153i \(0.723157\pi\)
\(762\) 0 0
\(763\) −66.4249 −2.40474
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14.4733 0.522600
\(768\) 0 0
\(769\) 37.3279 1.34608 0.673038 0.739608i \(-0.264989\pi\)
0.673038 + 0.739608i \(0.264989\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.26180 0.117319 0.0586595 0.998278i \(-0.481317\pi\)
0.0586595 + 0.998278i \(0.481317\pi\)
\(774\) 0 0
\(775\) 0.180322i 0.00647736i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 61.2472i − 2.19441i
\(780\) 0 0
\(781\) 3.07418i 0.110003i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 36.3442i − 1.29718i
\(786\) 0 0
\(787\) −39.3172 −1.40151 −0.700754 0.713403i \(-0.747153\pi\)
−0.700754 + 0.713403i \(0.747153\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.53022 0.0544083
\(792\) 0 0
\(793\) −6.27686 −0.222898
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 33.9204 1.20152 0.600761 0.799428i \(-0.294864\pi\)
0.600761 + 0.799428i \(0.294864\pi\)
\(798\) 0 0
\(799\) 30.6754i 1.08522i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 22.0623i 0.778562i
\(804\) 0 0
\(805\) 16.1663i 0.569789i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.7361i 0.975148i 0.873082 + 0.487574i \(0.162118\pi\)
−0.873082 + 0.487574i \(0.837882\pi\)
\(810\) 0 0
\(811\) −41.1345 −1.44443 −0.722214 0.691670i \(-0.756875\pi\)
−0.722214 + 0.691670i \(0.756875\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 33.0875 1.15900
\(816\) 0 0
\(817\) 28.9193 1.01176
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −39.3502 −1.37333 −0.686666 0.726973i \(-0.740926\pi\)
−0.686666 + 0.726973i \(0.740926\pi\)
\(822\) 0 0
\(823\) − 42.3213i − 1.47523i −0.675222 0.737614i \(-0.735952\pi\)
0.675222 0.737614i \(-0.264048\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 31.7777i 1.10502i 0.833506 + 0.552510i \(0.186330\pi\)
−0.833506 + 0.552510i \(0.813670\pi\)
\(828\) 0 0
\(829\) 8.68766i 0.301735i 0.988554 + 0.150867i \(0.0482066\pi\)
−0.988554 + 0.150867i \(0.951793\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 34.7979i 1.20568i
\(834\) 0 0
\(835\) 46.0929 1.59511
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 12.9147 0.445865 0.222932 0.974834i \(-0.428437\pi\)
0.222932 + 0.974834i \(0.428437\pi\)
\(840\) 0 0
\(841\) 76.1310 2.62521
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −11.9261 −0.410270
\(846\) 0 0
\(847\) 16.5048i 0.567112i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 3.74711i − 0.128449i
\(852\) 0 0
\(853\) − 45.5644i − 1.56010i −0.625719 0.780048i \(-0.715194\pi\)
0.625719 0.780048i \(-0.284806\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6.19747i 0.211702i 0.994382 + 0.105851i \(0.0337566\pi\)
−0.994382 + 0.105851i \(0.966243\pi\)
\(858\) 0 0
\(859\) 22.3368 0.762120 0.381060 0.924550i \(-0.375559\pi\)
0.381060 + 0.924550i \(0.375559\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 51.2947 1.74609 0.873046 0.487638i \(-0.162141\pi\)
0.873046 + 0.487638i \(0.162141\pi\)
\(864\) 0 0
\(865\) 24.8320 0.844312
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −6.16547 −0.209149
\(870\) 0 0
\(871\) − 34.7357i − 1.17697i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 42.0450i 1.42138i
\(876\) 0 0
\(877\) − 23.0681i − 0.778955i −0.921036 0.389477i \(-0.872656\pi\)
0.921036 0.389477i \(-0.127344\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 1.79075i − 0.0603320i −0.999545 0.0301660i \(-0.990396\pi\)
0.999545 0.0301660i \(-0.00960360\pi\)
\(882\) 0 0
\(883\) −2.85559 −0.0960981 −0.0480490 0.998845i \(-0.515300\pi\)
−0.0480490 + 0.998845i \(0.515300\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11.8305 0.397228 0.198614 0.980078i \(-0.436356\pi\)
0.198614 + 0.980078i \(0.436356\pi\)
\(888\) 0 0
\(889\) −53.4209 −1.79168
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −36.7603 −1.23014
\(894\) 0 0
\(895\) 0.520375i 0.0173942i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 63.8283i 2.12879i
\(900\) 0 0
\(901\) − 11.3594i − 0.378436i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 10.0420i − 0.333807i
\(906\) 0 0
\(907\) 15.8198 0.525287 0.262643 0.964893i \(-0.415406\pi\)
0.262643 + 0.964893i \(0.415406\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −41.5047 −1.37511 −0.687557 0.726131i \(-0.741317\pi\)
−0.687557 + 0.726131i \(0.741317\pi\)
\(912\) 0 0
\(913\) 39.5302 1.30826
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −80.1502 −2.64679
\(918\) 0 0
\(919\) − 19.7014i − 0.649889i −0.945733 0.324944i \(-0.894654\pi\)
0.945733 0.324944i \(-0.105346\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 3.31059i − 0.108969i
\(924\) 0 0
\(925\) 0.0567875i 0.00186716i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 16.3128i 0.535206i 0.963529 + 0.267603i \(0.0862316\pi\)
−0.963529 + 0.267603i \(0.913768\pi\)
\(930\) 0 0
\(931\) −41.7006 −1.36668
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −27.7975 −0.909075
\(936\) 0 0
\(937\) 2.92325 0.0954983 0.0477492 0.998859i \(-0.484795\pi\)
0.0477492 + 0.998859i \(0.484795\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 25.0248 0.815786 0.407893 0.913030i \(-0.366264\pi\)
0.407893 + 0.913030i \(0.366264\pi\)
\(942\) 0 0
\(943\) 20.2831i 0.660507i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 44.9033i 1.45916i 0.683894 + 0.729581i \(0.260285\pi\)
−0.683894 + 0.729581i \(0.739715\pi\)
\(948\) 0 0
\(949\) − 23.7589i − 0.771247i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 30.6498i − 0.992844i −0.868081 0.496422i \(-0.834647\pi\)
0.868081 0.496422i \(-0.165353\pi\)
\(954\) 0 0
\(955\) −21.4952 −0.695568
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 28.7588 0.928671
\(960\) 0 0
\(961\) −7.75211 −0.250068
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 27.1044 0.872520
\(966\) 0 0
\(967\) − 1.63693i − 0.0526403i −0.999654 0.0263201i \(-0.991621\pi\)
0.999654 0.0263201i \(-0.00837893\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12.7448i 0.409001i 0.978866 + 0.204500i \(0.0655570\pi\)
−0.978866 + 0.204500i \(0.934443\pi\)
\(972\) 0 0
\(973\) − 60.6198i − 1.94338i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 28.1764i 0.901442i 0.892665 + 0.450721i \(0.148833\pi\)
−0.892665 + 0.450721i \(0.851167\pi\)
\(978\) 0 0
\(979\) −37.8621 −1.21008
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.53342 −0.144593 −0.0722967 0.997383i \(-0.523033\pi\)
−0.0722967 + 0.997383i \(0.523033\pi\)
\(984\) 0 0
\(985\) −24.9992 −0.796539
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.57711 −0.304534
\(990\) 0 0
\(991\) 32.4984i 1.03235i 0.856485 + 0.516173i \(0.172644\pi\)
−0.856485 + 0.516173i \(0.827356\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 30.3712i − 0.962832i
\(996\) 0 0
\(997\) 6.02966i 0.190961i 0.995431 + 0.0954806i \(0.0304388\pi\)
−0.995431 + 0.0954806i \(0.969561\pi\)
\(998\) 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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5184.2.f.e.2591.4 yes 16
3.2 odd 2 inner 5184.2.f.e.2591.14 yes 16
4.3 odd 2 5184.2.f.b.2591.3 16
8.3 odd 2 inner 5184.2.f.e.2591.13 yes 16
8.5 even 2 5184.2.f.b.2591.14 yes 16
12.11 even 2 5184.2.f.b.2591.13 yes 16
24.5 odd 2 5184.2.f.b.2591.4 yes 16
24.11 even 2 inner 5184.2.f.e.2591.3 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5184.2.f.b.2591.3 16 4.3 odd 2
5184.2.f.b.2591.4 yes 16 24.5 odd 2
5184.2.f.b.2591.13 yes 16 12.11 even 2
5184.2.f.b.2591.14 yes 16 8.5 even 2
5184.2.f.e.2591.3 yes 16 24.11 even 2 inner
5184.2.f.e.2591.4 yes 16 1.1 even 1 trivial
5184.2.f.e.2591.13 yes 16 8.3 odd 2 inner
5184.2.f.e.2591.14 yes 16 3.2 odd 2 inner