Properties

Label 4600.2.a.bg.1.3
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.791953.1
Defining polynomial: \(x^{5} - 2 x^{4} - 7 x^{3} + 7 x^{2} + 9 x + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.336890\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.33689 q^{3} +3.16736 q^{7} -1.21273 q^{9} +O(q^{10})\) \(q+1.33689 q^{3} +3.16736 q^{7} -1.21273 q^{9} -0.0955192 q^{11} -1.44343 q^{13} +2.29775 q^{17} +7.00371 q^{19} +4.23441 q^{21} +1.00000 q^{23} -5.63195 q^{27} +5.39076 q^{29} -0.584488 q^{31} -0.127699 q^{33} +9.29985 q^{37} -1.92970 q^{39} -2.86534 q^{41} -9.50208 q^{43} -7.09353 q^{47} +3.03218 q^{49} +3.07184 q^{51} +7.73922 q^{53} +9.36319 q^{57} +13.6426 q^{59} +0.234413 q^{61} -3.84114 q^{63} -7.49729 q^{67} +1.33689 q^{69} -5.18426 q^{71} +1.52384 q^{73} -0.302544 q^{77} -3.04068 q^{79} -3.89112 q^{81} +15.9909 q^{83} +7.20685 q^{87} +5.53325 q^{89} -4.57186 q^{91} -0.781396 q^{93} -2.58305 q^{97} +0.115839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 3q^{3} - q^{7} + 4q^{9} + O(q^{10}) \) \( 5q + 3q^{3} - q^{7} + 4q^{9} - 4q^{11} - q^{13} + 5q^{17} + 4q^{19} - 6q^{21} + 5q^{23} + 6q^{27} - 11q^{29} + 4q^{31} + 13q^{33} + 6q^{37} + 31q^{39} - 8q^{41} + 3q^{43} + 2q^{47} - 2q^{49} - 5q^{51} + 18q^{53} + 27q^{57} + 23q^{59} - 26q^{61} + 5q^{63} + 3q^{67} + 3q^{69} - 2q^{71} + 4q^{73} + 15q^{77} + 43q^{79} - 3q^{81} + 30q^{83} + 27q^{87} + 15q^{89} - 19q^{91} - 15q^{93} + 8q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) 1.33689 0.771854 0.385927 0.922529i \(-0.373882\pi\)
0.385927 + 0.922529i \(0.373882\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.16736 1.19715 0.598575 0.801067i \(-0.295734\pi\)
0.598575 + 0.801067i \(0.295734\pi\)
\(8\) 0 0
\(9\) −1.21273 −0.404242
\(10\) 0 0
\(11\) −0.0955192 −0.0288001 −0.0144001 0.999896i \(-0.504584\pi\)
−0.0144001 + 0.999896i \(0.504584\pi\)
\(12\) 0 0
\(13\) −1.44343 −0.400335 −0.200167 0.979762i \(-0.564149\pi\)
−0.200167 + 0.979762i \(0.564149\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.29775 0.557287 0.278643 0.960395i \(-0.410115\pi\)
0.278643 + 0.960395i \(0.410115\pi\)
\(18\) 0 0
\(19\) 7.00371 1.60676 0.803381 0.595466i \(-0.203032\pi\)
0.803381 + 0.595466i \(0.203032\pi\)
\(20\) 0 0
\(21\) 4.23441 0.924025
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.63195 −1.08387
\(28\) 0 0
\(29\) 5.39076 1.00104 0.500519 0.865725i \(-0.333142\pi\)
0.500519 + 0.865725i \(0.333142\pi\)
\(30\) 0 0
\(31\) −0.584488 −0.104977 −0.0524886 0.998622i \(-0.516715\pi\)
−0.0524886 + 0.998622i \(0.516715\pi\)
\(32\) 0 0
\(33\) −0.127699 −0.0222295
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9.29985 1.52889 0.764443 0.644691i \(-0.223014\pi\)
0.764443 + 0.644691i \(0.223014\pi\)
\(38\) 0 0
\(39\) −1.92970 −0.309000
\(40\) 0 0
\(41\) −2.86534 −0.447492 −0.223746 0.974648i \(-0.571829\pi\)
−0.223746 + 0.974648i \(0.571829\pi\)
\(42\) 0 0
\(43\) −9.50208 −1.44905 −0.724527 0.689246i \(-0.757942\pi\)
−0.724527 + 0.689246i \(0.757942\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.09353 −1.03470 −0.517349 0.855775i \(-0.673081\pi\)
−0.517349 + 0.855775i \(0.673081\pi\)
\(48\) 0 0
\(49\) 3.03218 0.433168
\(50\) 0 0
\(51\) 3.07184 0.430144
\(52\) 0 0
\(53\) 7.73922 1.06306 0.531532 0.847038i \(-0.321617\pi\)
0.531532 + 0.847038i \(0.321617\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 9.36319 1.24018
\(58\) 0 0
\(59\) 13.6426 1.77612 0.888059 0.459730i \(-0.152054\pi\)
0.888059 + 0.459730i \(0.152054\pi\)
\(60\) 0 0
\(61\) 0.234413 0.0300135 0.0150068 0.999887i \(-0.495223\pi\)
0.0150068 + 0.999887i \(0.495223\pi\)
\(62\) 0 0
\(63\) −3.84114 −0.483938
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.49729 −0.915940 −0.457970 0.888968i \(-0.651423\pi\)
−0.457970 + 0.888968i \(0.651423\pi\)
\(68\) 0 0
\(69\) 1.33689 0.160943
\(70\) 0 0
\(71\) −5.18426 −0.615258 −0.307629 0.951506i \(-0.599536\pi\)
−0.307629 + 0.951506i \(0.599536\pi\)
\(72\) 0 0
\(73\) 1.52384 0.178352 0.0891760 0.996016i \(-0.471577\pi\)
0.0891760 + 0.996016i \(0.471577\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.302544 −0.0344781
\(78\) 0 0
\(79\) −3.04068 −0.342103 −0.171052 0.985262i \(-0.554717\pi\)
−0.171052 + 0.985262i \(0.554717\pi\)
\(80\) 0 0
\(81\) −3.89112 −0.432347
\(82\) 0 0
\(83\) 15.9909 1.75523 0.877613 0.479369i \(-0.159135\pi\)
0.877613 + 0.479369i \(0.159135\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 7.20685 0.772655
\(88\) 0 0
\(89\) 5.53325 0.586523 0.293261 0.956032i \(-0.405259\pi\)
0.293261 + 0.956032i \(0.405259\pi\)
\(90\) 0 0
\(91\) −4.57186 −0.479261
\(92\) 0 0
\(93\) −0.781396 −0.0810270
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.58305 −0.262269 −0.131135 0.991365i \(-0.541862\pi\)
−0.131135 + 0.991365i \(0.541862\pi\)
\(98\) 0 0
\(99\) 0.115839 0.0116422
\(100\) 0 0
\(101\) −6.65615 −0.662312 −0.331156 0.943576i \(-0.607439\pi\)
−0.331156 + 0.943576i \(0.607439\pi\)
\(102\) 0 0
\(103\) 17.6668 1.74076 0.870378 0.492383i \(-0.163874\pi\)
0.870378 + 0.492383i \(0.163874\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.83635 0.564221 0.282111 0.959382i \(-0.408965\pi\)
0.282111 + 0.959382i \(0.408965\pi\)
\(108\) 0 0
\(109\) 7.02096 0.672486 0.336243 0.941775i \(-0.390844\pi\)
0.336243 + 0.941775i \(0.390844\pi\)
\(110\) 0 0
\(111\) 12.4329 1.18008
\(112\) 0 0
\(113\) 17.1003 1.60866 0.804328 0.594185i \(-0.202525\pi\)
0.804328 + 0.594185i \(0.202525\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.75048 0.161832
\(118\) 0 0
\(119\) 7.27781 0.667156
\(120\) 0 0
\(121\) −10.9909 −0.999171
\(122\) 0 0
\(123\) −3.83065 −0.345398
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 10.8050 0.958787 0.479394 0.877600i \(-0.340857\pi\)
0.479394 + 0.877600i \(0.340857\pi\)
\(128\) 0 0
\(129\) −12.7032 −1.11846
\(130\) 0 0
\(131\) −8.45211 −0.738464 −0.369232 0.929337i \(-0.620379\pi\)
−0.369232 + 0.929337i \(0.620379\pi\)
\(132\) 0 0
\(133\) 22.1833 1.92354
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 18.5322 1.58331 0.791655 0.610969i \(-0.209220\pi\)
0.791655 + 0.610969i \(0.209220\pi\)
\(138\) 0 0
\(139\) 7.42618 0.629880 0.314940 0.949112i \(-0.398016\pi\)
0.314940 + 0.949112i \(0.398016\pi\)
\(140\) 0 0
\(141\) −9.48327 −0.798635
\(142\) 0 0
\(143\) 0.137875 0.0115297
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 4.05369 0.334343
\(148\) 0 0
\(149\) −4.53968 −0.371905 −0.185952 0.982559i \(-0.559537\pi\)
−0.185952 + 0.982559i \(0.559537\pi\)
\(150\) 0 0
\(151\) 0.00675366 0.000549605 0 0.000274803 1.00000i \(-0.499913\pi\)
0.000274803 1.00000i \(0.499913\pi\)
\(152\) 0 0
\(153\) −2.78654 −0.225279
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.1721 −0.971439 −0.485719 0.874115i \(-0.661442\pi\)
−0.485719 + 0.874115i \(0.661442\pi\)
\(158\) 0 0
\(159\) 10.3465 0.820529
\(160\) 0 0
\(161\) 3.16736 0.249623
\(162\) 0 0
\(163\) −20.2201 −1.58376 −0.791879 0.610677i \(-0.790897\pi\)
−0.791879 + 0.610677i \(0.790897\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.04709 −0.622702 −0.311351 0.950295i \(-0.600782\pi\)
−0.311351 + 0.950295i \(0.600782\pi\)
\(168\) 0 0
\(169\) −10.9165 −0.839732
\(170\) 0 0
\(171\) −8.49358 −0.649520
\(172\) 0 0
\(173\) −16.8394 −1.28028 −0.640139 0.768259i \(-0.721123\pi\)
−0.640139 + 0.768259i \(0.721123\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 18.2387 1.37090
\(178\) 0 0
\(179\) 23.7641 1.77621 0.888105 0.459641i \(-0.152022\pi\)
0.888105 + 0.459641i \(0.152022\pi\)
\(180\) 0 0
\(181\) −3.13518 −0.233036 −0.116518 0.993189i \(-0.537173\pi\)
−0.116518 + 0.993189i \(0.537173\pi\)
\(182\) 0 0
\(183\) 0.313385 0.0231661
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.219479 −0.0160499
\(188\) 0 0
\(189\) −17.8384 −1.29755
\(190\) 0 0
\(191\) 6.17586 0.446870 0.223435 0.974719i \(-0.428273\pi\)
0.223435 + 0.974719i \(0.428273\pi\)
\(192\) 0 0
\(193\) −7.22267 −0.519899 −0.259949 0.965622i \(-0.583706\pi\)
−0.259949 + 0.965622i \(0.583706\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.0019 0.926349 0.463174 0.886267i \(-0.346710\pi\)
0.463174 + 0.886267i \(0.346710\pi\)
\(198\) 0 0
\(199\) −1.84114 −0.130515 −0.0652575 0.997868i \(-0.520787\pi\)
−0.0652575 + 0.997868i \(0.520787\pi\)
\(200\) 0 0
\(201\) −10.0231 −0.706972
\(202\) 0 0
\(203\) 17.0745 1.19839
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.21273 −0.0842903
\(208\) 0 0
\(209\) −0.668989 −0.0462749
\(210\) 0 0
\(211\) −24.8791 −1.71275 −0.856375 0.516354i \(-0.827289\pi\)
−0.856375 + 0.516354i \(0.827289\pi\)
\(212\) 0 0
\(213\) −6.93078 −0.474889
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.85128 −0.125673
\(218\) 0 0
\(219\) 2.03721 0.137662
\(220\) 0 0
\(221\) −3.31664 −0.223101
\(222\) 0 0
\(223\) 4.04924 0.271157 0.135579 0.990767i \(-0.456711\pi\)
0.135579 + 0.990767i \(0.456711\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.3916 1.15432 0.577162 0.816630i \(-0.304160\pi\)
0.577162 + 0.816630i \(0.304160\pi\)
\(228\) 0 0
\(229\) −3.51761 −0.232450 −0.116225 0.993223i \(-0.537079\pi\)
−0.116225 + 0.993223i \(0.537079\pi\)
\(230\) 0 0
\(231\) −0.404468 −0.0266120
\(232\) 0 0
\(233\) −10.7910 −0.706941 −0.353471 0.935446i \(-0.614999\pi\)
−0.353471 + 0.935446i \(0.614999\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4.06506 −0.264054
\(238\) 0 0
\(239\) −2.86944 −0.185608 −0.0928042 0.995684i \(-0.529583\pi\)
−0.0928042 + 0.995684i \(0.529583\pi\)
\(240\) 0 0
\(241\) 27.0486 1.74235 0.871176 0.490972i \(-0.163358\pi\)
0.871176 + 0.490972i \(0.163358\pi\)
\(242\) 0 0
\(243\) 11.6939 0.750161
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −10.1093 −0.643242
\(248\) 0 0
\(249\) 21.3780 1.35478
\(250\) 0 0
\(251\) −11.7794 −0.743510 −0.371755 0.928331i \(-0.621244\pi\)
−0.371755 + 0.928331i \(0.621244\pi\)
\(252\) 0 0
\(253\) −0.0955192 −0.00600524
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.47742 0.528807 0.264404 0.964412i \(-0.414825\pi\)
0.264404 + 0.964412i \(0.414825\pi\)
\(258\) 0 0
\(259\) 29.4560 1.83031
\(260\) 0 0
\(261\) −6.53751 −0.404662
\(262\) 0 0
\(263\) 18.5118 1.14149 0.570745 0.821128i \(-0.306655\pi\)
0.570745 + 0.821128i \(0.306655\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.39734 0.452710
\(268\) 0 0
\(269\) −25.4583 −1.55222 −0.776109 0.630599i \(-0.782809\pi\)
−0.776109 + 0.630599i \(0.782809\pi\)
\(270\) 0 0
\(271\) −14.1812 −0.861446 −0.430723 0.902484i \(-0.641741\pi\)
−0.430723 + 0.902484i \(0.641741\pi\)
\(272\) 0 0
\(273\) −6.11207 −0.369919
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 21.4281 1.28749 0.643744 0.765241i \(-0.277380\pi\)
0.643744 + 0.765241i \(0.277380\pi\)
\(278\) 0 0
\(279\) 0.708823 0.0424361
\(280\) 0 0
\(281\) −8.90281 −0.531097 −0.265548 0.964098i \(-0.585553\pi\)
−0.265548 + 0.964098i \(0.585553\pi\)
\(282\) 0 0
\(283\) −13.0369 −0.774966 −0.387483 0.921877i \(-0.626655\pi\)
−0.387483 + 0.921877i \(0.626655\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.07558 −0.535715
\(288\) 0 0
\(289\) −11.7203 −0.689431
\(290\) 0 0
\(291\) −3.45325 −0.202433
\(292\) 0 0
\(293\) −6.74772 −0.394206 −0.197103 0.980383i \(-0.563153\pi\)
−0.197103 + 0.980383i \(0.563153\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0.537959 0.0312156
\(298\) 0 0
\(299\) −1.44343 −0.0834755
\(300\) 0 0
\(301\) −30.0965 −1.73474
\(302\) 0 0
\(303\) −8.89854 −0.511208
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 15.6667 0.894143 0.447071 0.894498i \(-0.352467\pi\)
0.447071 + 0.894498i \(0.352467\pi\)
\(308\) 0 0
\(309\) 23.6185 1.34361
\(310\) 0 0
\(311\) 8.27922 0.469472 0.234736 0.972059i \(-0.424577\pi\)
0.234736 + 0.972059i \(0.424577\pi\)
\(312\) 0 0
\(313\) 15.4898 0.875534 0.437767 0.899088i \(-0.355769\pi\)
0.437767 + 0.899088i \(0.355769\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.5803 −0.594251 −0.297125 0.954838i \(-0.596028\pi\)
−0.297125 + 0.954838i \(0.596028\pi\)
\(318\) 0 0
\(319\) −0.514921 −0.0288300
\(320\) 0 0
\(321\) 7.80256 0.435496
\(322\) 0 0
\(323\) 16.0928 0.895427
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 9.38625 0.519061
\(328\) 0 0
\(329\) −22.4678 −1.23869
\(330\) 0 0
\(331\) −1.32836 −0.0730133 −0.0365067 0.999333i \(-0.511623\pi\)
−0.0365067 + 0.999333i \(0.511623\pi\)
\(332\) 0 0
\(333\) −11.2782 −0.618040
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 33.1297 1.80469 0.902345 0.431014i \(-0.141844\pi\)
0.902345 + 0.431014i \(0.141844\pi\)
\(338\) 0 0
\(339\) 22.8611 1.24165
\(340\) 0 0
\(341\) 0.0558298 0.00302335
\(342\) 0 0
\(343\) −12.5675 −0.678582
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.7579 0.845926 0.422963 0.906147i \(-0.360990\pi\)
0.422963 + 0.906147i \(0.360990\pi\)
\(348\) 0 0
\(349\) −14.5904 −0.781004 −0.390502 0.920602i \(-0.627699\pi\)
−0.390502 + 0.920602i \(0.627699\pi\)
\(350\) 0 0
\(351\) 8.12931 0.433910
\(352\) 0 0
\(353\) −28.0097 −1.49080 −0.745402 0.666615i \(-0.767742\pi\)
−0.745402 + 0.666615i \(0.767742\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 9.72964 0.514947
\(358\) 0 0
\(359\) 0.214689 0.0113308 0.00566542 0.999984i \(-0.498197\pi\)
0.00566542 + 0.999984i \(0.498197\pi\)
\(360\) 0 0
\(361\) 30.0520 1.58168
\(362\) 0 0
\(363\) −14.6936 −0.771213
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 21.0197 1.09722 0.548610 0.836079i \(-0.315157\pi\)
0.548610 + 0.836079i \(0.315157\pi\)
\(368\) 0 0
\(369\) 3.47488 0.180895
\(370\) 0 0
\(371\) 24.5129 1.27265
\(372\) 0 0
\(373\) −10.2558 −0.531023 −0.265511 0.964108i \(-0.585541\pi\)
−0.265511 + 0.964108i \(0.585541\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.78116 −0.400750
\(378\) 0 0
\(379\) −20.6274 −1.05956 −0.529780 0.848135i \(-0.677726\pi\)
−0.529780 + 0.848135i \(0.677726\pi\)
\(380\) 0 0
\(381\) 14.4451 0.740044
\(382\) 0 0
\(383\) 18.7419 0.957667 0.478833 0.877906i \(-0.341060\pi\)
0.478833 + 0.877906i \(0.341060\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 11.5234 0.585769
\(388\) 0 0
\(389\) −3.07719 −0.156020 −0.0780100 0.996953i \(-0.524857\pi\)
−0.0780100 + 0.996953i \(0.524857\pi\)
\(390\) 0 0
\(391\) 2.29775 0.116202
\(392\) 0 0
\(393\) −11.2995 −0.569986
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 11.4670 0.575513 0.287756 0.957704i \(-0.407091\pi\)
0.287756 + 0.957704i \(0.407091\pi\)
\(398\) 0 0
\(399\) 29.6566 1.48469
\(400\) 0 0
\(401\) 14.1227 0.705252 0.352626 0.935764i \(-0.385289\pi\)
0.352626 + 0.935764i \(0.385289\pi\)
\(402\) 0 0
\(403\) 0.843666 0.0420260
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.888314 −0.0440321
\(408\) 0 0
\(409\) −0.851429 −0.0421005 −0.0210502 0.999778i \(-0.506701\pi\)
−0.0210502 + 0.999778i \(0.506701\pi\)
\(410\) 0 0
\(411\) 24.7755 1.22208
\(412\) 0 0
\(413\) 43.2111 2.12628
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 9.92799 0.486176
\(418\) 0 0
\(419\) 0.680728 0.0332557 0.0166279 0.999862i \(-0.494707\pi\)
0.0166279 + 0.999862i \(0.494707\pi\)
\(420\) 0 0
\(421\) −35.9671 −1.75293 −0.876466 0.481465i \(-0.840105\pi\)
−0.876466 + 0.481465i \(0.840105\pi\)
\(422\) 0 0
\(423\) 8.60251 0.418268
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.742472 0.0359307
\(428\) 0 0
\(429\) 0.184324 0.00889923
\(430\) 0 0
\(431\) 15.2881 0.736402 0.368201 0.929746i \(-0.379974\pi\)
0.368201 + 0.929746i \(0.379974\pi\)
\(432\) 0 0
\(433\) −13.2632 −0.637390 −0.318695 0.947857i \(-0.603245\pi\)
−0.318695 + 0.947857i \(0.603245\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.00371 0.335033
\(438\) 0 0
\(439\) 18.7740 0.896035 0.448018 0.894025i \(-0.352130\pi\)
0.448018 + 0.894025i \(0.352130\pi\)
\(440\) 0 0
\(441\) −3.67720 −0.175105
\(442\) 0 0
\(443\) 5.49270 0.260966 0.130483 0.991451i \(-0.458347\pi\)
0.130483 + 0.991451i \(0.458347\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −6.06905 −0.287056
\(448\) 0 0
\(449\) 13.1705 0.621553 0.310777 0.950483i \(-0.399411\pi\)
0.310777 + 0.950483i \(0.399411\pi\)
\(450\) 0 0
\(451\) 0.273695 0.0128878
\(452\) 0 0
\(453\) 0.00902890 0.000424215 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −20.9676 −0.980821 −0.490410 0.871492i \(-0.663153\pi\)
−0.490410 + 0.871492i \(0.663153\pi\)
\(458\) 0 0
\(459\) −12.9408 −0.604026
\(460\) 0 0
\(461\) 6.27335 0.292179 0.146089 0.989271i \(-0.453331\pi\)
0.146089 + 0.989271i \(0.453331\pi\)
\(462\) 0 0
\(463\) −9.49565 −0.441300 −0.220650 0.975353i \(-0.570818\pi\)
−0.220650 + 0.975353i \(0.570818\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.9066 −0.643518 −0.321759 0.946822i \(-0.604274\pi\)
−0.321759 + 0.946822i \(0.604274\pi\)
\(468\) 0 0
\(469\) −23.7466 −1.09652
\(470\) 0 0
\(471\) −16.2727 −0.749809
\(472\) 0 0
\(473\) 0.907631 0.0417329
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.38555 −0.429735
\(478\) 0 0
\(479\) 3.66220 0.167330 0.0836652 0.996494i \(-0.473337\pi\)
0.0836652 + 0.996494i \(0.473337\pi\)
\(480\) 0 0
\(481\) −13.4237 −0.612066
\(482\) 0 0
\(483\) 4.23441 0.192672
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −28.9654 −1.31255 −0.656274 0.754523i \(-0.727868\pi\)
−0.656274 + 0.754523i \(0.727868\pi\)
\(488\) 0 0
\(489\) −27.0320 −1.22243
\(490\) 0 0
\(491\) −37.8991 −1.71036 −0.855182 0.518328i \(-0.826554\pi\)
−0.855182 + 0.518328i \(0.826554\pi\)
\(492\) 0 0
\(493\) 12.3866 0.557866
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.4204 −0.736557
\(498\) 0 0
\(499\) −26.6914 −1.19487 −0.597436 0.801917i \(-0.703814\pi\)
−0.597436 + 0.801917i \(0.703814\pi\)
\(500\) 0 0
\(501\) −10.7581 −0.480635
\(502\) 0 0
\(503\) 18.2182 0.812309 0.406154 0.913804i \(-0.366870\pi\)
0.406154 + 0.913804i \(0.366870\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −14.5942 −0.648150
\(508\) 0 0
\(509\) −31.0138 −1.37466 −0.687332 0.726344i \(-0.741218\pi\)
−0.687332 + 0.726344i \(0.741218\pi\)
\(510\) 0 0
\(511\) 4.82655 0.213514
\(512\) 0 0
\(513\) −39.4446 −1.74152
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.677568 0.0297994
\(518\) 0 0
\(519\) −22.5125 −0.988188
\(520\) 0 0
\(521\) −39.9824 −1.75166 −0.875831 0.482618i \(-0.839686\pi\)
−0.875831 + 0.482618i \(0.839686\pi\)
\(522\) 0 0
\(523\) −10.3111 −0.450873 −0.225437 0.974258i \(-0.572381\pi\)
−0.225437 + 0.974258i \(0.572381\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.34301 −0.0585024
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −16.5448 −0.717981
\(532\) 0 0
\(533\) 4.13592 0.179146
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 31.7699 1.37097
\(538\) 0 0
\(539\) −0.289631 −0.0124753
\(540\) 0 0
\(541\) −42.5472 −1.82925 −0.914623 0.404307i \(-0.867513\pi\)
−0.914623 + 0.404307i \(0.867513\pi\)
\(542\) 0 0
\(543\) −4.19139 −0.179870
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.47986 −0.106031 −0.0530156 0.998594i \(-0.516883\pi\)
−0.0530156 + 0.998594i \(0.516883\pi\)
\(548\) 0 0
\(549\) −0.284279 −0.0121327
\(550\) 0 0
\(551\) 37.7553 1.60843
\(552\) 0 0
\(553\) −9.63094 −0.409549
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22.9814 −0.973755 −0.486877 0.873470i \(-0.661864\pi\)
−0.486877 + 0.873470i \(0.661864\pi\)
\(558\) 0 0
\(559\) 13.7156 0.580107
\(560\) 0 0
\(561\) −0.293420 −0.0123882
\(562\) 0 0
\(563\) 18.4939 0.779427 0.389713 0.920936i \(-0.372574\pi\)
0.389713 + 0.920936i \(0.372574\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −12.3246 −0.517584
\(568\) 0 0
\(569\) 35.6081 1.49277 0.746385 0.665514i \(-0.231788\pi\)
0.746385 + 0.665514i \(0.231788\pi\)
\(570\) 0 0
\(571\) 20.5827 0.861359 0.430680 0.902505i \(-0.358274\pi\)
0.430680 + 0.902505i \(0.358274\pi\)
\(572\) 0 0
\(573\) 8.25645 0.344918
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19.0378 0.792554 0.396277 0.918131i \(-0.370302\pi\)
0.396277 + 0.918131i \(0.370302\pi\)
\(578\) 0 0
\(579\) −9.65591 −0.401286
\(580\) 0 0
\(581\) 50.6489 2.10127
\(582\) 0 0
\(583\) −0.739244 −0.0306163
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.29062 −0.300916 −0.150458 0.988616i \(-0.548075\pi\)
−0.150458 + 0.988616i \(0.548075\pi\)
\(588\) 0 0
\(589\) −4.09358 −0.168673
\(590\) 0 0
\(591\) 17.3821 0.715006
\(592\) 0 0
\(593\) −10.5832 −0.434598 −0.217299 0.976105i \(-0.569725\pi\)
−0.217299 + 0.976105i \(0.569725\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.46140 −0.100739
\(598\) 0 0
\(599\) −5.63520 −0.230248 −0.115124 0.993351i \(-0.536727\pi\)
−0.115124 + 0.993351i \(0.536727\pi\)
\(600\) 0 0
\(601\) −17.7093 −0.722377 −0.361188 0.932493i \(-0.617629\pi\)
−0.361188 + 0.932493i \(0.617629\pi\)
\(602\) 0 0
\(603\) 9.09216 0.370261
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −22.0996 −0.896996 −0.448498 0.893784i \(-0.648041\pi\)
−0.448498 + 0.893784i \(0.648041\pi\)
\(608\) 0 0
\(609\) 22.8267 0.924984
\(610\) 0 0
\(611\) 10.2390 0.414225
\(612\) 0 0
\(613\) −5.08532 −0.205394 −0.102697 0.994713i \(-0.532747\pi\)
−0.102697 + 0.994713i \(0.532747\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.63073 −0.307202 −0.153601 0.988133i \(-0.549087\pi\)
−0.153601 + 0.988133i \(0.549087\pi\)
\(618\) 0 0
\(619\) 38.5591 1.54982 0.774910 0.632072i \(-0.217795\pi\)
0.774910 + 0.632072i \(0.217795\pi\)
\(620\) 0 0
\(621\) −5.63195 −0.226002
\(622\) 0 0
\(623\) 17.5258 0.702156
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.894364 −0.0357175
\(628\) 0 0
\(629\) 21.3688 0.852028
\(630\) 0 0
\(631\) −1.86751 −0.0743444 −0.0371722 0.999309i \(-0.511835\pi\)
−0.0371722 + 0.999309i \(0.511835\pi\)
\(632\) 0 0
\(633\) −33.2607 −1.32199
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −4.37673 −0.173412
\(638\) 0 0
\(639\) 6.28708 0.248713
\(640\) 0 0
\(641\) −1.91236 −0.0755338 −0.0377669 0.999287i \(-0.512024\pi\)
−0.0377669 + 0.999287i \(0.512024\pi\)
\(642\) 0 0
\(643\) −5.06670 −0.199811 −0.0999055 0.994997i \(-0.531854\pi\)
−0.0999055 + 0.994997i \(0.531854\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −37.0429 −1.45631 −0.728153 0.685414i \(-0.759621\pi\)
−0.728153 + 0.685414i \(0.759621\pi\)
\(648\) 0 0
\(649\) −1.30313 −0.0511524
\(650\) 0 0
\(651\) −2.47496 −0.0970014
\(652\) 0 0
\(653\) 11.9884 0.469143 0.234572 0.972099i \(-0.424631\pi\)
0.234572 + 0.972099i \(0.424631\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.84800 −0.0720974
\(658\) 0 0
\(659\) −2.82513 −0.110051 −0.0550257 0.998485i \(-0.517524\pi\)
−0.0550257 + 0.998485i \(0.517524\pi\)
\(660\) 0 0
\(661\) −26.5004 −1.03075 −0.515374 0.856965i \(-0.672347\pi\)
−0.515374 + 0.856965i \(0.672347\pi\)
\(662\) 0 0
\(663\) −4.43398 −0.172202
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.39076 0.208731
\(668\) 0 0
\(669\) 5.41339 0.209294
\(670\) 0 0
\(671\) −0.0223910 −0.000864393 0
\(672\) 0 0
\(673\) 19.0620 0.734784 0.367392 0.930066i \(-0.380251\pi\)
0.367392 + 0.930066i \(0.380251\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.54346 0.0977533 0.0488766 0.998805i \(-0.484436\pi\)
0.0488766 + 0.998805i \(0.484436\pi\)
\(678\) 0 0
\(679\) −8.18146 −0.313975
\(680\) 0 0
\(681\) 23.2507 0.890969
\(682\) 0 0
\(683\) −0.377109 −0.0144297 −0.00721483 0.999974i \(-0.502297\pi\)
−0.00721483 + 0.999974i \(0.502297\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −4.70266 −0.179418
\(688\) 0 0
\(689\) −11.1710 −0.425581
\(690\) 0 0
\(691\) 7.24743 0.275705 0.137853 0.990453i \(-0.455980\pi\)
0.137853 + 0.990453i \(0.455980\pi\)
\(692\) 0 0
\(693\) 0.366903 0.0139375
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.58385 −0.249381
\(698\) 0 0
\(699\) −14.4264 −0.545655
\(700\) 0 0
\(701\) −15.7381 −0.594420 −0.297210 0.954812i \(-0.596056\pi\)
−0.297210 + 0.954812i \(0.596056\pi\)
\(702\) 0 0
\(703\) 65.1335 2.45656
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21.0824 −0.792887
\(708\) 0 0
\(709\) −45.9062 −1.72404 −0.862022 0.506870i \(-0.830802\pi\)
−0.862022 + 0.506870i \(0.830802\pi\)
\(710\) 0 0
\(711\) 3.68751 0.138293
\(712\) 0 0
\(713\) −0.584488 −0.0218892
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.83612 −0.143263
\(718\) 0 0
\(719\) −50.4975 −1.88324 −0.941619 0.336682i \(-0.890695\pi\)
−0.941619 + 0.336682i \(0.890695\pi\)
\(720\) 0 0
\(721\) 55.9570 2.08395
\(722\) 0 0
\(723\) 36.1609 1.34484
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −19.0273 −0.705685 −0.352842 0.935683i \(-0.614785\pi\)
−0.352842 + 0.935683i \(0.614785\pi\)
\(728\) 0 0
\(729\) 27.3067 1.01136
\(730\) 0 0
\(731\) −21.8334 −0.807539
\(732\) 0 0
\(733\) −42.1027 −1.55510 −0.777549 0.628822i \(-0.783537\pi\)
−0.777549 + 0.628822i \(0.783537\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.716135 0.0263792
\(738\) 0 0
\(739\) 47.9212 1.76281 0.881405 0.472361i \(-0.156598\pi\)
0.881405 + 0.472361i \(0.156598\pi\)
\(740\) 0 0
\(741\) −13.5151 −0.496489
\(742\) 0 0
\(743\) 21.3492 0.783225 0.391613 0.920130i \(-0.371917\pi\)
0.391613 + 0.920130i \(0.371917\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −19.3925 −0.709536
\(748\) 0 0
\(749\) 18.4858 0.675458
\(750\) 0 0
\(751\) −27.8218 −1.01523 −0.507617 0.861583i \(-0.669473\pi\)
−0.507617 + 0.861583i \(0.669473\pi\)
\(752\) 0 0
\(753\) −15.7478 −0.573881
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 8.74990 0.318020 0.159010 0.987277i \(-0.449170\pi\)
0.159010 + 0.987277i \(0.449170\pi\)
\(758\) 0 0
\(759\) −0.127699 −0.00463517
\(760\) 0 0
\(761\) 21.9923 0.797221 0.398610 0.917120i \(-0.369493\pi\)
0.398610 + 0.917120i \(0.369493\pi\)
\(762\) 0 0
\(763\) 22.2379 0.805066
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −19.6921 −0.711041
\(768\) 0 0
\(769\) −31.3229 −1.12953 −0.564766 0.825251i \(-0.691034\pi\)
−0.564766 + 0.825251i \(0.691034\pi\)
\(770\) 0 0
\(771\) 11.3334 0.408162
\(772\) 0 0
\(773\) 32.3308 1.16286 0.581429 0.813597i \(-0.302494\pi\)
0.581429 + 0.813597i \(0.302494\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 39.3794 1.41273
\(778\) 0 0
\(779\) −20.0680 −0.719012
\(780\) 0 0
\(781\) 0.495196 0.0177195
\(782\) 0 0
\(783\) −30.3605 −1.08499
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −18.5712 −0.661990 −0.330995 0.943632i \(-0.607384\pi\)
−0.330995 + 0.943632i \(0.607384\pi\)
\(788\) 0 0
\(789\) 24.7483 0.881063
\(790\) 0 0
\(791\) 54.1627 1.92580
\(792\) 0 0
\(793\) −0.338358 −0.0120155
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24.1985 −0.857154 −0.428577 0.903505i \(-0.640985\pi\)
−0.428577 + 0.903505i \(0.640985\pi\)
\(798\) 0 0
\(799\) −16.2992 −0.576624
\(800\) 0 0
\(801\) −6.71031 −0.237097
\(802\) 0 0
\(803\) −0.145556 −0.00513656
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −34.0349 −1.19809
\(808\) 0 0
\(809\) −30.4574 −1.07082 −0.535412 0.844591i \(-0.679844\pi\)
−0.535412 + 0.844591i \(0.679844\pi\)
\(810\) 0 0
\(811\) 4.05626 0.142435 0.0712174 0.997461i \(-0.477312\pi\)
0.0712174 + 0.997461i \(0.477312\pi\)
\(812\) 0 0
\(813\) −18.9587 −0.664910
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −66.5499 −2.32829
\(818\) 0 0
\(819\) 5.54441 0.193737
\(820\) 0 0
\(821\) 19.0615 0.665252 0.332626 0.943059i \(-0.392065\pi\)
0.332626 + 0.943059i \(0.392065\pi\)
\(822\) 0 0
\(823\) −42.9810 −1.49822 −0.749111 0.662444i \(-0.769519\pi\)
−0.749111 + 0.662444i \(0.769519\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 51.6777 1.79701 0.898505 0.438963i \(-0.144654\pi\)
0.898505 + 0.438963i \(0.144654\pi\)
\(828\) 0 0
\(829\) 25.6228 0.889915 0.444958 0.895552i \(-0.353219\pi\)
0.444958 + 0.895552i \(0.353219\pi\)
\(830\) 0 0
\(831\) 28.6470 0.993753
\(832\) 0 0
\(833\) 6.96720 0.241399
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3.29181 0.113781
\(838\) 0 0
\(839\) −53.0313 −1.83084 −0.915422 0.402495i \(-0.868143\pi\)
−0.915422 + 0.402495i \(0.868143\pi\)
\(840\) 0 0
\(841\) 0.0602571 0.00207783
\(842\) 0 0
\(843\) −11.9021 −0.409929
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −34.8121 −1.19616
\(848\) 0 0
\(849\) −17.4290 −0.598160
\(850\) 0 0
\(851\) 9.29985 0.318795
\(852\) 0 0
\(853\) 13.8668 0.474791 0.237395 0.971413i \(-0.423706\pi\)
0.237395 + 0.971413i \(0.423706\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.3518 0.558567 0.279283 0.960209i \(-0.409903\pi\)
0.279283 + 0.960209i \(0.409903\pi\)
\(858\) 0 0
\(859\) 42.1443 1.43795 0.718973 0.695038i \(-0.244612\pi\)
0.718973 + 0.695038i \(0.244612\pi\)
\(860\) 0 0
\(861\) −12.1331 −0.413493
\(862\) 0 0
\(863\) −15.2130 −0.517856 −0.258928 0.965897i \(-0.583369\pi\)
−0.258928 + 0.965897i \(0.583369\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −15.6688 −0.532140
\(868\) 0 0
\(869\) 0.290443 0.00985262
\(870\) 0 0
\(871\) 10.8218 0.366683
\(872\) 0 0
\(873\) 3.13253 0.106020
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −53.6934 −1.81310 −0.906549 0.422101i \(-0.861293\pi\)
−0.906549 + 0.422101i \(0.861293\pi\)
\(878\) 0 0
\(879\) −9.02096 −0.304269
\(880\) 0 0
\(881\) 46.5787 1.56928 0.784638 0.619954i \(-0.212849\pi\)
0.784638 + 0.619954i \(0.212849\pi\)
\(882\) 0 0
\(883\) −19.9787 −0.672337 −0.336169 0.941802i \(-0.609131\pi\)
−0.336169 + 0.941802i \(0.609131\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 51.9251 1.74347 0.871737 0.489974i \(-0.162994\pi\)
0.871737 + 0.489974i \(0.162994\pi\)
\(888\) 0 0
\(889\) 34.2233 1.14781
\(890\) 0 0
\(891\) 0.371676 0.0124516
\(892\) 0 0
\(893\) −49.6810 −1.66251
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.92970 −0.0644309
\(898\) 0 0
\(899\) −3.15083 −0.105086
\(900\) 0 0
\(901\) 17.7828 0.592431
\(902\) 0 0
\(903\) −40.2358 −1.33896
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −6.64335 −0.220589 −0.110294 0.993899i \(-0.535179\pi\)
−0.110294 + 0.993899i \(0.535179\pi\)
\(908\) 0 0
\(909\) 8.07209 0.267734
\(910\) 0 0
\(911\) 15.2064 0.503811 0.251905 0.967752i \(-0.418943\pi\)
0.251905 + 0.967752i \(0.418943\pi\)
\(912\) 0 0
\(913\) −1.52744 −0.0505507
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −26.7709 −0.884052
\(918\) 0 0
\(919\) 41.2068 1.35929 0.679644 0.733542i \(-0.262134\pi\)
0.679644 + 0.733542i \(0.262134\pi\)
\(920\) 0 0
\(921\) 20.9446 0.690148
\(922\) 0 0
\(923\) 7.48310 0.246309
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −21.4249 −0.703687
\(928\) 0 0
\(929\) −4.86715 −0.159686 −0.0798431 0.996807i \(-0.525442\pi\)
−0.0798431 + 0.996807i \(0.525442\pi\)
\(930\) 0 0
\(931\) 21.2365 0.695999
\(932\) 0 0
\(933\) 11.0684 0.362364
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −3.44469 −0.112533 −0.0562666 0.998416i \(-0.517920\pi\)
−0.0562666 + 0.998416i \(0.517920\pi\)
\(938\) 0 0
\(939\) 20.7081 0.675784
\(940\) 0 0
\(941\) −34.8591 −1.13637 −0.568187 0.822900i \(-0.692355\pi\)
−0.568187 + 0.822900i \(0.692355\pi\)
\(942\) 0 0
\(943\) −2.86534 −0.0933084
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.17298 −0.168099 −0.0840496 0.996462i \(-0.526785\pi\)
−0.0840496 + 0.996462i \(0.526785\pi\)
\(948\) 0 0
\(949\) −2.19955 −0.0714005
\(950\) 0 0
\(951\) −14.1447 −0.458675
\(952\) 0 0
\(953\) 3.41090 0.110490 0.0552449 0.998473i \(-0.482406\pi\)
0.0552449 + 0.998473i \(0.482406\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −0.688392 −0.0222526
\(958\) 0 0
\(959\) 58.6981 1.89546
\(960\) 0 0
\(961\) −30.6584 −0.988980
\(962\) 0 0
\(963\) −7.07789 −0.228082
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 17.5047 0.562914 0.281457 0.959574i \(-0.409182\pi\)
0.281457 + 0.959574i \(0.409182\pi\)
\(968\) 0 0
\(969\) 21.5143 0.691139
\(970\) 0 0
\(971\) 35.9954 1.15515 0.577574 0.816338i \(-0.303999\pi\)
0.577574 + 0.816338i \(0.303999\pi\)
\(972\) 0 0
\(973\) 23.5214 0.754062
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −31.3634 −1.00340 −0.501702 0.865040i \(-0.667293\pi\)
−0.501702 + 0.865040i \(0.667293\pi\)
\(978\) 0 0
\(979\) −0.528531 −0.0168919
\(980\) 0 0
\(981\) −8.51450 −0.271847
\(982\) 0 0
\(983\) −36.4262 −1.16182 −0.580908 0.813969i \(-0.697302\pi\)
−0.580908 + 0.813969i \(0.697302\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −30.0369 −0.956086
\(988\) 0 0
\(989\) −9.50208 −0.302149
\(990\) 0 0
\(991\) 6.22316 0.197685 0.0988426 0.995103i \(-0.468486\pi\)
0.0988426 + 0.995103i \(0.468486\pi\)
\(992\) 0 0
\(993\) −1.77587 −0.0563556
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −24.0896 −0.762925 −0.381463 0.924384i \(-0.624580\pi\)
−0.381463 + 0.924384i \(0.624580\pi\)
\(998\) 0 0
\(999\) −52.3763 −1.65711
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 4600.2.a.bg.1.3 yes 5
4.3 odd 2 9200.2.a.cs.1.3 5
5.2 odd 4 4600.2.e.v.4049.4 10
5.3 odd 4 4600.2.e.v.4049.7 10
5.4 even 2 4600.2.a.bc.1.3 5
20.19 odd 2 9200.2.a.cw.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bc.1.3 5 5.4 even 2
4600.2.a.bg.1.3 yes 5 1.1 even 1 trivial
4600.2.e.v.4049.4 10 5.2 odd 4
4600.2.e.v.4049.7 10 5.3 odd 4
9200.2.a.cs.1.3 5 4.3 odd 2
9200.2.a.cw.1.3 5 20.19 odd 2