Properties

Label 9200.2.a.cs.1.3
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(1\)
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: no (minimal twist has level 4600)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.336890\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.33689 −0.771854 −0.385927 0.922529i \(-0.626118\pi\)
−0.385927 + 0.922529i \(0.626118\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.16736 −1.19715 −0.598575 0.801067i \(-0.704266\pi\)
−0.598575 + 0.801067i \(0.704266\pi\)
\(8\) 0 0
\(9\) −1.21273 −0.404242
\(10\) 0 0
\(11\) 0.0955192 0.0288001 0.0144001 0.999896i \(-0.495416\pi\)
0.0144001 + 0.999896i \(0.495416\pi\)
\(12\) 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 \(-0.796968\pi\)
−0.803381 + 0.595466i \(0.796968\pi\)
\(20\) 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 \(-0.483285\pi\)
0.0524886 + 0.998622i \(0.483285\pi\)
\(32\) 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 \(-0.242058\pi\)
0.724527 + 0.689246i \(0.242058\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.09353 1.03470 0.517349 0.855775i \(-0.326919\pi\)
0.517349 + 0.855775i \(0.326919\pi\)
\(48\) 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 \(-0.847946\pi\)
−0.888059 + 0.459730i \(0.847946\pi\)
\(60\) 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 \(-0.348577\pi\)
0.457970 + 0.888968i \(0.348577\pi\)
\(68\) 0 0
\(69\) 1.33689 0.160943
\(70\) 0 0
\(71\) 5.18426 0.615258 0.307629 0.951506i \(-0.400464\pi\)
0.307629 + 0.951506i \(0.400464\pi\)
\(72\) 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 \(-0.445283\pi\)
0.171052 + 0.985262i \(0.445283\pi\)
\(80\) 0 0
\(81\) −3.89112 −0.432347
\(82\) 0 0
\(83\) −15.9909 −1.75523 −0.877613 0.479369i \(-0.840865\pi\)
−0.877613 + 0.479369i \(0.840865\pi\)
\(84\) 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 \(-0.836126\pi\)
−0.870378 + 0.492383i \(0.836126\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.83635 −0.564221 −0.282111 0.959382i \(-0.591035\pi\)
−0.282111 + 0.959382i \(0.591035\pi\)
\(108\) 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 \(-0.659143\pi\)
−0.479394 + 0.877600i \(0.659143\pi\)
\(128\) 0 0
\(129\) −12.7032 −1.11846
\(130\) 0 0
\(131\) 8.45211 0.738464 0.369232 0.929337i \(-0.379621\pi\)
0.369232 + 0.929337i \(0.379621\pi\)
\(132\) 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 \(-0.601984\pi\)
−0.314940 + 0.949112i \(0.601984\pi\)
\(140\) 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 \(-0.500087\pi\)
−0.000274803 1.00000i \(0.500087\pi\)
\(152\) 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 \(-0.209103\pi\)
0.791879 + 0.610677i \(0.209103\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.04709 0.622702 0.311351 0.950295i \(-0.399218\pi\)
0.311351 + 0.950295i \(0.399218\pi\)
\(168\) 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 \(-0.847978\pi\)
−0.888105 + 0.459641i \(0.847978\pi\)
\(180\) 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 \(-0.571727\pi\)
−0.223435 + 0.974719i \(0.571727\pi\)
\(192\) 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 \(-0.479213\pi\)
0.0652575 + 0.997868i \(0.479213\pi\)
\(200\) 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 \(-0.172711\pi\)
0.856375 + 0.516354i \(0.172711\pi\)
\(212\) 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 \(-0.543289\pi\)
−0.135579 + 0.990767i \(0.543289\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.3916 −1.15432 −0.577162 0.816630i \(-0.695840\pi\)
−0.577162 + 0.816630i \(0.695840\pi\)
\(228\) 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 \(-0.470417\pi\)
0.0928042 + 0.995684i \(0.470417\pi\)
\(240\) 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 \(-0.378756\pi\)
0.371755 + 0.928331i \(0.378756\pi\)
\(252\) 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 \(-0.693345\pi\)
−0.570745 + 0.821128i \(0.693345\pi\)
\(264\) 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 \(-0.358259\pi\)
0.430723 + 0.902484i \(0.358259\pi\)
\(272\) 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 \(-0.373345\pi\)
0.387483 + 0.921877i \(0.373345\pi\)
\(284\) 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 \(-0.647533\pi\)
−0.447071 + 0.894498i \(0.647533\pi\)
\(308\) 0 0
\(309\) 23.6185 1.34361
\(310\) 0 0
\(311\) −8.27922 −0.469472 −0.234736 0.972059i \(-0.575423\pi\)
−0.234736 + 0.972059i \(0.575423\pi\)
\(312\) 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 \(-0.488377\pi\)
0.0365067 + 0.999333i \(0.488377\pi\)
\(332\) 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 \(-0.639010\pi\)
−0.422963 + 0.906147i \(0.639010\pi\)
\(348\) 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 \(-0.501803\pi\)
−0.00566542 + 0.999984i \(0.501803\pi\)
\(360\) 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 \(-0.684843\pi\)
−0.548610 + 0.836079i \(0.684843\pi\)
\(368\) 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 \(-0.322274\pi\)
0.529780 + 0.848135i \(0.322274\pi\)
\(380\) 0 0
\(381\) 14.4451 0.740044
\(382\) 0 0
\(383\) −18.7419 −0.957667 −0.478833 0.877906i \(-0.658940\pi\)
−0.478833 + 0.877906i \(0.658940\pi\)
\(384\) 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 \(-0.505293\pi\)
−0.0166279 + 0.999862i \(0.505293\pi\)
\(420\) 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 \(-0.620026\pi\)
−0.368201 + 0.929746i \(0.620026\pi\)
\(432\) 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 \(-0.647870\pi\)
−0.448018 + 0.894025i \(0.647870\pi\)
\(440\) 0 0
\(441\) −3.67720 −0.175105
\(442\) 0 0
\(443\) −5.49270 −0.260966 −0.130483 0.991451i \(-0.541653\pi\)
−0.130483 + 0.991451i \(0.541653\pi\)
\(444\) 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 \(-0.429182\pi\)
0.220650 + 0.975353i \(0.429182\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.9066 0.643518 0.321759 0.946822i \(-0.395726\pi\)
0.321759 + 0.946822i \(0.395726\pi\)
\(468\) 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 \(-0.526663\pi\)
−0.0836652 + 0.996494i \(0.526663\pi\)
\(480\) 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 \(-0.272132\pi\)
0.656274 + 0.754523i \(0.272132\pi\)
\(488\) 0 0
\(489\) −27.0320 −1.22243
\(490\) 0 0
\(491\) 37.8991 1.71036 0.855182 0.518328i \(-0.173446\pi\)
0.855182 + 0.518328i \(0.173446\pi\)
\(492\) 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 \(-0.296186\pi\)
0.597436 + 0.801917i \(0.296186\pi\)
\(500\) 0 0
\(501\) −10.7581 −0.480635
\(502\) 0 0
\(503\) −18.2182 −0.812309 −0.406154 0.913804i \(-0.633130\pi\)
−0.406154 + 0.913804i \(0.633130\pi\)
\(504\) 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 \(-0.427619\pi\)
0.225437 + 0.974258i \(0.427619\pi\)
\(524\) 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 \(-0.483117\pi\)
0.0530156 + 0.998594i \(0.483117\pi\)
\(548\) 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 \(-0.627426\pi\)
−0.389713 + 0.920936i \(0.627426\pi\)
\(564\) 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 \(-0.641726\pi\)
−0.430680 + 0.902505i \(0.641726\pi\)
\(572\) 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 \(-0.451925\pi\)
0.150458 + 0.988616i \(0.451925\pi\)
\(588\) 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 \(-0.463273\pi\)
0.115124 + 0.993351i \(0.463273\pi\)
\(600\) 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 \(-0.351959\pi\)
0.448498 + 0.893784i \(0.351959\pi\)
\(608\) 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 \(-0.782205\pi\)
−0.774910 + 0.632072i \(0.782205\pi\)
\(620\) 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 \(-0.488165\pi\)
0.0371722 + 0.999309i \(0.488165\pi\)
\(632\) 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 \(-0.468146\pi\)
0.0999055 + 0.994997i \(0.468146\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 37.0429 1.45631 0.728153 0.685414i \(-0.240379\pi\)
0.728153 + 0.685414i \(0.240379\pi\)
\(648\) 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 \(-0.482476\pi\)
0.0550257 + 0.998485i \(0.482476\pi\)
\(660\) 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 \(-0.497703\pi\)
0.00721483 + 0.999974i \(0.497703\pi\)
\(684\) 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 \(-0.544020\pi\)
−0.137853 + 0.990453i \(0.544020\pi\)
\(692\) 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 \(-0.109305\pi\)
0.941619 + 0.336682i \(0.109305\pi\)
\(720\) 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 \(-0.385215\pi\)
0.352842 + 0.935683i \(0.385215\pi\)
\(728\) 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 \(-0.843402\pi\)
−0.881405 + 0.472361i \(0.843402\pi\)
\(740\) 0 0
\(741\) −13.5151 −0.496489
\(742\) 0 0
\(743\) −21.3492 −0.783225 −0.391613 0.920130i \(-0.628083\pi\)
−0.391613 + 0.920130i \(0.628083\pi\)
\(744\) 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 \(-0.330527\pi\)
0.507617 + 0.861583i \(0.330527\pi\)
\(752\) 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 \(-0.392616\pi\)
0.330995 + 0.943632i \(0.392616\pi\)
\(788\) 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 \(-0.522688\pi\)
−0.0712174 + 0.997461i \(0.522688\pi\)
\(812\) 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 \(-0.230481\pi\)
0.749111 + 0.662444i \(0.230481\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −51.6777 −1.79701 −0.898505 0.438963i \(-0.855346\pi\)
−0.898505 + 0.438963i \(0.855346\pi\)
\(828\) 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 \(-0.131857\pi\)
0.915422 + 0.402495i \(0.131857\pi\)
\(840\) 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 \(-0.755388\pi\)
−0.718973 + 0.695038i \(0.755388\pi\)
\(860\) 0 0
\(861\) −12.1331 −0.413493
\(862\) 0 0
\(863\) 15.2130 0.517856 0.258928 0.965897i \(-0.416631\pi\)
0.258928 + 0.965897i \(0.416631\pi\)
\(864\) 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 \(-0.390869\pi\)
0.336169 + 0.941802i \(0.390869\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −51.9251 −1.74347 −0.871737 0.489974i \(-0.837006\pi\)
−0.871737 + 0.489974i \(0.837006\pi\)
\(888\) 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 \(-0.464821\pi\)
0.110294 + 0.993899i \(0.464821\pi\)
\(908\) 0 0
\(909\) 8.07209 0.267734
\(910\) 0 0
\(911\) −15.2064 −0.503811 −0.251905 0.967752i \(-0.581057\pi\)
−0.251905 + 0.967752i \(0.581057\pi\)
\(912\) 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 \(-0.737866\pi\)
−0.679644 + 0.733542i \(0.737866\pi\)
\(920\) 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 \(-0.473215\pi\)
0.0840496 + 0.996462i \(0.473215\pi\)
\(948\) 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 \(-0.590818\pi\)
−0.281457 + 0.959574i \(0.590818\pi\)
\(968\) 0 0
\(969\) 21.5143 0.691139
\(970\) 0 0
\(971\) −35.9954 −1.15515 −0.577574 0.816338i \(-0.696001\pi\)
−0.577574 + 0.816338i \(0.696001\pi\)
\(972\) 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 \(-0.302698\pi\)
0.580908 + 0.813969i \(0.302698\pi\)
\(984\) 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 \(-0.531514\pi\)
−0.0988426 + 0.995103i \(0.531514\pi\)
\(992\) 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 9200.2.a.cs.1.3 5
4.3 odd 2 4600.2.a.bg.1.3 yes 5
5.4 even 2 9200.2.a.cw.1.3 5
20.3 even 4 4600.2.e.v.4049.7 10
20.7 even 4 4600.2.e.v.4049.4 10
20.19 odd 2 4600.2.a.bc.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bc.1.3 5 20.19 odd 2
4600.2.a.bg.1.3 yes 5 4.3 odd 2
4600.2.e.v.4049.4 10 20.7 even 4
4600.2.e.v.4049.7 10 20.3 even 4
9200.2.a.cs.1.3 5 1.1 even 1 trivial
9200.2.a.cw.1.3 5 5.4 even 2