Properties

Label 5733.2.a.x.1.3
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.81361\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.81361 q^{2} +1.28917 q^{4} +2.81361 q^{5} -1.28917 q^{8} +O(q^{10})\) \(q+1.81361 q^{2} +1.28917 q^{4} +2.81361 q^{5} -1.28917 q^{8} +5.10278 q^{10} -3.10278 q^{11} -1.00000 q^{13} -4.91638 q^{16} -0.524438 q^{17} -0.813607 q^{19} +3.62721 q^{20} -5.62721 q^{22} -7.33804 q^{23} +2.91638 q^{25} -1.81361 q^{26} -8.28917 q^{29} -1.39194 q^{31} -6.33804 q^{32} -0.951124 q^{34} -6.15165 q^{37} -1.47556 q^{38} -3.62721 q^{40} -4.20555 q^{41} +6.75971 q^{43} -4.00000 q^{44} -13.3083 q^{46} -5.97028 q^{47} +5.28917 q^{50} -1.28917 q^{52} +2.49472 q^{53} -8.72999 q^{55} -15.0333 q^{58} -4.47054 q^{59} +2.00000 q^{61} -2.52444 q^{62} -1.66196 q^{64} -2.81361 q^{65} +10.0383 q^{67} -0.676089 q^{68} +8.72999 q^{71} +2.34307 q^{73} -11.1567 q^{74} -1.04888 q^{76} -13.5436 q^{79} -13.8328 q^{80} -7.62721 q^{82} +16.4791 q^{83} -1.47556 q^{85} +12.2594 q^{86} +4.00000 q^{88} -10.6464 q^{89} -9.45998 q^{92} -10.8277 q^{94} -2.28917 q^{95} +1.18639 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} + 3q^{4} + 2q^{5} - 3q^{8} + O(q^{10}) \) \( 3q - q^{2} + 3q^{4} + 2q^{5} - 3q^{8} + 8q^{10} - 2q^{11} - 3q^{13} - q^{16} + 4q^{17} + 4q^{19} - 2q^{20} - 4q^{22} - 10q^{23} - 5q^{25} + q^{26} - 24q^{29} + 4q^{31} - 7q^{32} - 14q^{34} - 10q^{38} + 2q^{40} + 2q^{41} + 10q^{43} - 12q^{44} - 18q^{46} - 8q^{47} + 15q^{50} - 3q^{52} - 8q^{53} - 6q^{55} + 12q^{58} - 4q^{59} + 6q^{61} - 2q^{62} - 17q^{64} - 2q^{65} - 12q^{67} + 22q^{68} + 6q^{71} + 10q^{73} - 30q^{74} + 8q^{76} - 14q^{79} - 14q^{80} - 10q^{82} - 12q^{83} - 10q^{85} + 26q^{86} + 12q^{88} + 2q^{89} + 12q^{92} + 10q^{94} - 6q^{95} + 10q^{97} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.81361 1.28241 0.641207 0.767368i \(-0.278434\pi\)
0.641207 + 0.767368i \(0.278434\pi\)
\(3\) 0 0
\(4\) 1.28917 0.644584
\(5\) 2.81361 1.25828 0.629142 0.777291i \(-0.283407\pi\)
0.629142 + 0.777291i \(0.283407\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.28917 −0.455790
\(9\) 0 0
\(10\) 5.10278 1.61364
\(11\) −3.10278 −0.935522 −0.467761 0.883855i \(-0.654939\pi\)
−0.467761 + 0.883855i \(0.654939\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) −4.91638 −1.22910
\(17\) −0.524438 −0.127195 −0.0635974 0.997976i \(-0.520257\pi\)
−0.0635974 + 0.997976i \(0.520257\pi\)
\(18\) 0 0
\(19\) −0.813607 −0.186654 −0.0933271 0.995636i \(-0.529750\pi\)
−0.0933271 + 0.995636i \(0.529750\pi\)
\(20\) 3.62721 0.811069
\(21\) 0 0
\(22\) −5.62721 −1.19973
\(23\) −7.33804 −1.53009 −0.765044 0.643978i \(-0.777283\pi\)
−0.765044 + 0.643978i \(0.777283\pi\)
\(24\) 0 0
\(25\) 2.91638 0.583276
\(26\) −1.81361 −0.355677
\(27\) 0 0
\(28\) 0 0
\(29\) −8.28917 −1.53926 −0.769630 0.638490i \(-0.779559\pi\)
−0.769630 + 0.638490i \(0.779559\pi\)
\(30\) 0 0
\(31\) −1.39194 −0.250000 −0.125000 0.992157i \(-0.539893\pi\)
−0.125000 + 0.992157i \(0.539893\pi\)
\(32\) −6.33804 −1.12042
\(33\) 0 0
\(34\) −0.951124 −0.163116
\(35\) 0 0
\(36\) 0 0
\(37\) −6.15165 −1.01133 −0.505663 0.862731i \(-0.668752\pi\)
−0.505663 + 0.862731i \(0.668752\pi\)
\(38\) −1.47556 −0.239368
\(39\) 0 0
\(40\) −3.62721 −0.573513
\(41\) −4.20555 −0.656797 −0.328398 0.944539i \(-0.606509\pi\)
−0.328398 + 0.944539i \(0.606509\pi\)
\(42\) 0 0
\(43\) 6.75971 1.03085 0.515423 0.856936i \(-0.327635\pi\)
0.515423 + 0.856936i \(0.327635\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) −13.3083 −1.96221
\(47\) −5.97028 −0.870855 −0.435427 0.900224i \(-0.643403\pi\)
−0.435427 + 0.900224i \(0.643403\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 5.28917 0.748001
\(51\) 0 0
\(52\) −1.28917 −0.178776
\(53\) 2.49472 0.342676 0.171338 0.985212i \(-0.445191\pi\)
0.171338 + 0.985212i \(0.445191\pi\)
\(54\) 0 0
\(55\) −8.72999 −1.17715
\(56\) 0 0
\(57\) 0 0
\(58\) −15.0333 −1.97397
\(59\) −4.47054 −0.582015 −0.291007 0.956721i \(-0.593990\pi\)
−0.291007 + 0.956721i \(0.593990\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −2.52444 −0.320604
\(63\) 0 0
\(64\) −1.66196 −0.207744
\(65\) −2.81361 −0.348985
\(66\) 0 0
\(67\) 10.0383 1.22638 0.613188 0.789937i \(-0.289887\pi\)
0.613188 + 0.789937i \(0.289887\pi\)
\(68\) −0.676089 −0.0819878
\(69\) 0 0
\(70\) 0 0
\(71\) 8.72999 1.03606 0.518029 0.855363i \(-0.326666\pi\)
0.518029 + 0.855363i \(0.326666\pi\)
\(72\) 0 0
\(73\) 2.34307 0.274235 0.137118 0.990555i \(-0.456216\pi\)
0.137118 + 0.990555i \(0.456216\pi\)
\(74\) −11.1567 −1.29694
\(75\) 0 0
\(76\) −1.04888 −0.120314
\(77\) 0 0
\(78\) 0 0
\(79\) −13.5436 −1.52377 −0.761887 0.647710i \(-0.775727\pi\)
−0.761887 + 0.647710i \(0.775727\pi\)
\(80\) −13.8328 −1.54655
\(81\) 0 0
\(82\) −7.62721 −0.842285
\(83\) 16.4791 1.80882 0.904410 0.426665i \(-0.140312\pi\)
0.904410 + 0.426665i \(0.140312\pi\)
\(84\) 0 0
\(85\) −1.47556 −0.160047
\(86\) 12.2594 1.32197
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) −10.6464 −1.12851 −0.564256 0.825600i \(-0.690837\pi\)
−0.564256 + 0.825600i \(0.690837\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −9.45998 −0.986271
\(93\) 0 0
\(94\) −10.8277 −1.11680
\(95\) −2.28917 −0.234864
\(96\) 0 0
\(97\) 1.18639 0.120460 0.0602300 0.998185i \(-0.480817\pi\)
0.0602300 + 0.998185i \(0.480817\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 3.75971 0.375971
\(101\) 13.1028 1.30377 0.651887 0.758316i \(-0.273977\pi\)
0.651887 + 0.758316i \(0.273977\pi\)
\(102\) 0 0
\(103\) −4.41110 −0.434639 −0.217319 0.976101i \(-0.569731\pi\)
−0.217319 + 0.976101i \(0.569731\pi\)
\(104\) 1.28917 0.126413
\(105\) 0 0
\(106\) 4.52444 0.439452
\(107\) −0.578337 −0.0559100 −0.0279550 0.999609i \(-0.508900\pi\)
−0.0279550 + 0.999609i \(0.508900\pi\)
\(108\) 0 0
\(109\) 5.57331 0.533827 0.266913 0.963721i \(-0.413996\pi\)
0.266913 + 0.963721i \(0.413996\pi\)
\(110\) −15.8328 −1.50959
\(111\) 0 0
\(112\) 0 0
\(113\) −5.44584 −0.512302 −0.256151 0.966637i \(-0.582454\pi\)
−0.256151 + 0.966637i \(0.582454\pi\)
\(114\) 0 0
\(115\) −20.6464 −1.92528
\(116\) −10.6861 −0.992183
\(117\) 0 0
\(118\) −8.10780 −0.746383
\(119\) 0 0
\(120\) 0 0
\(121\) −1.37279 −0.124799
\(122\) 3.62721 0.328392
\(123\) 0 0
\(124\) −1.79445 −0.161146
\(125\) −5.86248 −0.524356
\(126\) 0 0
\(127\) −12.8816 −1.14306 −0.571530 0.820581i \(-0.693650\pi\)
−0.571530 + 0.820581i \(0.693650\pi\)
\(128\) 9.66196 0.854004
\(129\) 0 0
\(130\) −5.10278 −0.447543
\(131\) 9.04888 0.790604 0.395302 0.918551i \(-0.370640\pi\)
0.395302 + 0.918551i \(0.370640\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 18.2056 1.57272
\(135\) 0 0
\(136\) 0.676089 0.0579741
\(137\) 6.25945 0.534781 0.267390 0.963588i \(-0.413839\pi\)
0.267390 + 0.963588i \(0.413839\pi\)
\(138\) 0 0
\(139\) 11.5733 0.981636 0.490818 0.871262i \(-0.336698\pi\)
0.490818 + 0.871262i \(0.336698\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 15.8328 1.32866
\(143\) 3.10278 0.259467
\(144\) 0 0
\(145\) −23.3225 −1.93682
\(146\) 4.24940 0.351683
\(147\) 0 0
\(148\) −7.93051 −0.651884
\(149\) −8.52444 −0.698349 −0.349175 0.937058i \(-0.613538\pi\)
−0.349175 + 0.937058i \(0.613538\pi\)
\(150\) 0 0
\(151\) −11.9844 −0.975278 −0.487639 0.873045i \(-0.662142\pi\)
−0.487639 + 0.873045i \(0.662142\pi\)
\(152\) 1.04888 0.0850751
\(153\) 0 0
\(154\) 0 0
\(155\) −3.91638 −0.314571
\(156\) 0 0
\(157\) 12.8277 1.02377 0.511883 0.859055i \(-0.328948\pi\)
0.511883 + 0.859055i \(0.328948\pi\)
\(158\) −24.5628 −1.95411
\(159\) 0 0
\(160\) −17.8328 −1.40980
\(161\) 0 0
\(162\) 0 0
\(163\) −13.4600 −1.05427 −0.527133 0.849783i \(-0.676733\pi\)
−0.527133 + 0.849783i \(0.676733\pi\)
\(164\) −5.42166 −0.423361
\(165\) 0 0
\(166\) 29.8867 2.31965
\(167\) −2.02972 −0.157064 −0.0785322 0.996912i \(-0.525023\pi\)
−0.0785322 + 0.996912i \(0.525023\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −2.67609 −0.205247
\(171\) 0 0
\(172\) 8.71440 0.664467
\(173\) 20.2978 1.54321 0.771605 0.636102i \(-0.219454\pi\)
0.771605 + 0.636102i \(0.219454\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 15.2544 1.14985
\(177\) 0 0
\(178\) −19.3083 −1.44722
\(179\) 11.0036 0.822445 0.411223 0.911535i \(-0.365102\pi\)
0.411223 + 0.911535i \(0.365102\pi\)
\(180\) 0 0
\(181\) −0.691675 −0.0514118 −0.0257059 0.999670i \(-0.508183\pi\)
−0.0257059 + 0.999670i \(0.508183\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 9.45998 0.697399
\(185\) −17.3083 −1.27253
\(186\) 0 0
\(187\) 1.62721 0.118994
\(188\) −7.69670 −0.561339
\(189\) 0 0
\(190\) −4.15165 −0.301192
\(191\) −7.83276 −0.566759 −0.283379 0.959008i \(-0.591456\pi\)
−0.283379 + 0.959008i \(0.591456\pi\)
\(192\) 0 0
\(193\) −12.2056 −0.878575 −0.439287 0.898347i \(-0.644769\pi\)
−0.439287 + 0.898347i \(0.644769\pi\)
\(194\) 2.15165 0.154480
\(195\) 0 0
\(196\) 0 0
\(197\) 18.8222 1.34103 0.670513 0.741898i \(-0.266074\pi\)
0.670513 + 0.741898i \(0.266074\pi\)
\(198\) 0 0
\(199\) −21.6116 −1.53201 −0.766004 0.642836i \(-0.777758\pi\)
−0.766004 + 0.642836i \(0.777758\pi\)
\(200\) −3.75971 −0.265851
\(201\) 0 0
\(202\) 23.7633 1.67198
\(203\) 0 0
\(204\) 0 0
\(205\) −11.8328 −0.826436
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 4.91638 0.340890
\(209\) 2.52444 0.174619
\(210\) 0 0
\(211\) −17.3764 −1.19624 −0.598119 0.801407i \(-0.704085\pi\)
−0.598119 + 0.801407i \(0.704085\pi\)
\(212\) 3.21611 0.220884
\(213\) 0 0
\(214\) −1.04888 −0.0716997
\(215\) 19.0192 1.29710
\(216\) 0 0
\(217\) 0 0
\(218\) 10.1078 0.684586
\(219\) 0 0
\(220\) −11.2544 −0.758773
\(221\) 0.524438 0.0352775
\(222\) 0 0
\(223\) 10.5486 0.706388 0.353194 0.935550i \(-0.385096\pi\)
0.353194 + 0.935550i \(0.385096\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −9.87662 −0.656983
\(227\) −6.95112 −0.461362 −0.230681 0.973029i \(-0.574095\pi\)
−0.230681 + 0.973029i \(0.574095\pi\)
\(228\) 0 0
\(229\) 21.0872 1.39348 0.696740 0.717323i \(-0.254633\pi\)
0.696740 + 0.717323i \(0.254633\pi\)
\(230\) −37.4444 −2.46901
\(231\) 0 0
\(232\) 10.6861 0.701579
\(233\) −6.08362 −0.398551 −0.199276 0.979943i \(-0.563859\pi\)
−0.199276 + 0.979943i \(0.563859\pi\)
\(234\) 0 0
\(235\) −16.7980 −1.09578
\(236\) −5.76328 −0.375157
\(237\) 0 0
\(238\) 0 0
\(239\) 14.2056 0.918881 0.459440 0.888209i \(-0.348050\pi\)
0.459440 + 0.888209i \(0.348050\pi\)
\(240\) 0 0
\(241\) −8.44082 −0.543721 −0.271860 0.962337i \(-0.587639\pi\)
−0.271860 + 0.962337i \(0.587639\pi\)
\(242\) −2.48970 −0.160044
\(243\) 0 0
\(244\) 2.57834 0.165061
\(245\) 0 0
\(246\) 0 0
\(247\) 0.813607 0.0517685
\(248\) 1.79445 0.113948
\(249\) 0 0
\(250\) −10.6322 −0.672442
\(251\) −23.9844 −1.51388 −0.756941 0.653483i \(-0.773307\pi\)
−0.756941 + 0.653483i \(0.773307\pi\)
\(252\) 0 0
\(253\) 22.7683 1.43143
\(254\) −23.3622 −1.46588
\(255\) 0 0
\(256\) 20.8469 1.30293
\(257\) 15.6116 0.973827 0.486913 0.873450i \(-0.338123\pi\)
0.486913 + 0.873450i \(0.338123\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.62721 −0.224950
\(261\) 0 0
\(262\) 16.4111 1.01388
\(263\) 15.1708 0.935472 0.467736 0.883868i \(-0.345070\pi\)
0.467736 + 0.883868i \(0.345070\pi\)
\(264\) 0 0
\(265\) 7.01916 0.431183
\(266\) 0 0
\(267\) 0 0
\(268\) 12.9411 0.790502
\(269\) 23.2927 1.42018 0.710092 0.704109i \(-0.248653\pi\)
0.710092 + 0.704109i \(0.248653\pi\)
\(270\) 0 0
\(271\) −12.7456 −0.774238 −0.387119 0.922030i \(-0.626530\pi\)
−0.387119 + 0.922030i \(0.626530\pi\)
\(272\) 2.57834 0.156335
\(273\) 0 0
\(274\) 11.3522 0.685810
\(275\) −9.04888 −0.545668
\(276\) 0 0
\(277\) 8.12193 0.488000 0.244000 0.969775i \(-0.421540\pi\)
0.244000 + 0.969775i \(0.421540\pi\)
\(278\) 20.9894 1.25886
\(279\) 0 0
\(280\) 0 0
\(281\) −19.0333 −1.13543 −0.567715 0.823225i \(-0.692173\pi\)
−0.567715 + 0.823225i \(0.692173\pi\)
\(282\) 0 0
\(283\) −11.1466 −0.662598 −0.331299 0.943526i \(-0.607487\pi\)
−0.331299 + 0.943526i \(0.607487\pi\)
\(284\) 11.2544 0.667827
\(285\) 0 0
\(286\) 5.62721 0.332744
\(287\) 0 0
\(288\) 0 0
\(289\) −16.7250 −0.983821
\(290\) −42.2978 −2.48381
\(291\) 0 0
\(292\) 3.02061 0.176768
\(293\) −14.1758 −0.828161 −0.414080 0.910240i \(-0.635897\pi\)
−0.414080 + 0.910240i \(0.635897\pi\)
\(294\) 0 0
\(295\) −12.5783 −0.732339
\(296\) 7.93051 0.460952
\(297\) 0 0
\(298\) −15.4600 −0.895572
\(299\) 7.33804 0.424370
\(300\) 0 0
\(301\) 0 0
\(302\) −21.7350 −1.25071
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 5.62721 0.322213
\(306\) 0 0
\(307\) −13.5592 −0.773863 −0.386932 0.922108i \(-0.626465\pi\)
−0.386932 + 0.922108i \(0.626465\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −7.10278 −0.403411
\(311\) 0.426686 0.0241952 0.0120976 0.999927i \(-0.496149\pi\)
0.0120976 + 0.999927i \(0.496149\pi\)
\(312\) 0 0
\(313\) 18.1517 1.02599 0.512996 0.858391i \(-0.328536\pi\)
0.512996 + 0.858391i \(0.328536\pi\)
\(314\) 23.2645 1.31289
\(315\) 0 0
\(316\) −17.4600 −0.982200
\(317\) −9.42166 −0.529173 −0.264587 0.964362i \(-0.585236\pi\)
−0.264587 + 0.964362i \(0.585236\pi\)
\(318\) 0 0
\(319\) 25.7194 1.44001
\(320\) −4.67609 −0.261401
\(321\) 0 0
\(322\) 0 0
\(323\) 0.426686 0.0237415
\(324\) 0 0
\(325\) −2.91638 −0.161772
\(326\) −24.4111 −1.35201
\(327\) 0 0
\(328\) 5.42166 0.299361
\(329\) 0 0
\(330\) 0 0
\(331\) −17.4005 −0.956420 −0.478210 0.878246i \(-0.658714\pi\)
−0.478210 + 0.878246i \(0.658714\pi\)
\(332\) 21.2444 1.16594
\(333\) 0 0
\(334\) −3.68111 −0.201421
\(335\) 28.2439 1.54313
\(336\) 0 0
\(337\) 22.0524 1.20127 0.600637 0.799522i \(-0.294914\pi\)
0.600637 + 0.799522i \(0.294914\pi\)
\(338\) 1.81361 0.0986472
\(339\) 0 0
\(340\) −1.90225 −0.103164
\(341\) 4.31889 0.233881
\(342\) 0 0
\(343\) 0 0
\(344\) −8.71440 −0.469849
\(345\) 0 0
\(346\) 36.8122 1.97903
\(347\) −25.3522 −1.36098 −0.680488 0.732759i \(-0.738232\pi\)
−0.680488 + 0.732759i \(0.738232\pi\)
\(348\) 0 0
\(349\) 5.70529 0.305397 0.152699 0.988273i \(-0.451204\pi\)
0.152699 + 0.988273i \(0.451204\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 19.6655 1.04818
\(353\) −28.6761 −1.52627 −0.763137 0.646237i \(-0.776342\pi\)
−0.763137 + 0.646237i \(0.776342\pi\)
\(354\) 0 0
\(355\) 24.5628 1.30366
\(356\) −13.7250 −0.727422
\(357\) 0 0
\(358\) 19.9561 1.05472
\(359\) −11.0433 −0.582845 −0.291423 0.956594i \(-0.594129\pi\)
−0.291423 + 0.956594i \(0.594129\pi\)
\(360\) 0 0
\(361\) −18.3380 −0.965160
\(362\) −1.25443 −0.0659312
\(363\) 0 0
\(364\) 0 0
\(365\) 6.59247 0.345066
\(366\) 0 0
\(367\) −27.3466 −1.42748 −0.713741 0.700409i \(-0.753001\pi\)
−0.713741 + 0.700409i \(0.753001\pi\)
\(368\) 36.0766 1.88062
\(369\) 0 0
\(370\) −31.3905 −1.63191
\(371\) 0 0
\(372\) 0 0
\(373\) 16.1461 0.836014 0.418007 0.908444i \(-0.362729\pi\)
0.418007 + 0.908444i \(0.362729\pi\)
\(374\) 2.95112 0.152599
\(375\) 0 0
\(376\) 7.69670 0.396927
\(377\) 8.28917 0.426914
\(378\) 0 0
\(379\) 26.1305 1.34223 0.671117 0.741351i \(-0.265815\pi\)
0.671117 + 0.741351i \(0.265815\pi\)
\(380\) −2.95112 −0.151389
\(381\) 0 0
\(382\) −14.2056 −0.726819
\(383\) −21.0489 −1.07555 −0.537774 0.843089i \(-0.680735\pi\)
−0.537774 + 0.843089i \(0.680735\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −22.1361 −1.12670
\(387\) 0 0
\(388\) 1.52946 0.0776466
\(389\) 21.6061 1.09547 0.547736 0.836651i \(-0.315490\pi\)
0.547736 + 0.836651i \(0.315490\pi\)
\(390\) 0 0
\(391\) 3.84835 0.194619
\(392\) 0 0
\(393\) 0 0
\(394\) 34.1361 1.71975
\(395\) −38.1063 −1.91734
\(396\) 0 0
\(397\) 27.6952 1.38998 0.694992 0.719017i \(-0.255408\pi\)
0.694992 + 0.719017i \(0.255408\pi\)
\(398\) −39.1950 −1.96467
\(399\) 0 0
\(400\) −14.3380 −0.716902
\(401\) 2.57834 0.128756 0.0643780 0.997926i \(-0.479494\pi\)
0.0643780 + 0.997926i \(0.479494\pi\)
\(402\) 0 0
\(403\) 1.39194 0.0693376
\(404\) 16.8917 0.840393
\(405\) 0 0
\(406\) 0 0
\(407\) 19.0872 0.946117
\(408\) 0 0
\(409\) −15.1169 −0.747483 −0.373742 0.927533i \(-0.621925\pi\)
−0.373742 + 0.927533i \(0.621925\pi\)
\(410\) −21.4600 −1.05983
\(411\) 0 0
\(412\) −5.68665 −0.280161
\(413\) 0 0
\(414\) 0 0
\(415\) 46.3658 2.27601
\(416\) 6.33804 0.310748
\(417\) 0 0
\(418\) 4.57834 0.223934
\(419\) −9.99446 −0.488261 −0.244131 0.969742i \(-0.578503\pi\)
−0.244131 + 0.969742i \(0.578503\pi\)
\(420\) 0 0
\(421\) −25.9250 −1.26351 −0.631753 0.775170i \(-0.717664\pi\)
−0.631753 + 0.775170i \(0.717664\pi\)
\(422\) −31.5139 −1.53407
\(423\) 0 0
\(424\) −3.21611 −0.156188
\(425\) −1.52946 −0.0741898
\(426\) 0 0
\(427\) 0 0
\(428\) −0.745574 −0.0360387
\(429\) 0 0
\(430\) 34.4933 1.66341
\(431\) −30.6761 −1.47762 −0.738808 0.673916i \(-0.764611\pi\)
−0.738808 + 0.673916i \(0.764611\pi\)
\(432\) 0 0
\(433\) 3.51941 0.169132 0.0845661 0.996418i \(-0.473050\pi\)
0.0845661 + 0.996418i \(0.473050\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.18494 0.344096
\(437\) 5.97028 0.285597
\(438\) 0 0
\(439\) −32.3517 −1.54406 −0.772030 0.635586i \(-0.780759\pi\)
−0.772030 + 0.635586i \(0.780759\pi\)
\(440\) 11.2544 0.536534
\(441\) 0 0
\(442\) 0.951124 0.0452404
\(443\) −15.4458 −0.733854 −0.366927 0.930250i \(-0.619590\pi\)
−0.366927 + 0.930250i \(0.619590\pi\)
\(444\) 0 0
\(445\) −29.9547 −1.41999
\(446\) 19.1310 0.905881
\(447\) 0 0
\(448\) 0 0
\(449\) 14.4705 0.682907 0.341453 0.939899i \(-0.389081\pi\)
0.341453 + 0.939899i \(0.389081\pi\)
\(450\) 0 0
\(451\) 13.0489 0.614448
\(452\) −7.02061 −0.330222
\(453\) 0 0
\(454\) −12.6066 −0.591657
\(455\) 0 0
\(456\) 0 0
\(457\) −34.6705 −1.62182 −0.810910 0.585171i \(-0.801027\pi\)
−0.810910 + 0.585171i \(0.801027\pi\)
\(458\) 38.2439 1.78702
\(459\) 0 0
\(460\) −26.6167 −1.24101
\(461\) 12.5400 0.584047 0.292024 0.956411i \(-0.405671\pi\)
0.292024 + 0.956411i \(0.405671\pi\)
\(462\) 0 0
\(463\) 12.1517 0.564735 0.282368 0.959306i \(-0.408880\pi\)
0.282368 + 0.959306i \(0.408880\pi\)
\(464\) 40.7527 1.89190
\(465\) 0 0
\(466\) −11.0333 −0.511107
\(467\) −37.0333 −1.71370 −0.856848 0.515569i \(-0.827581\pi\)
−0.856848 + 0.515569i \(0.827581\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −30.4650 −1.40525
\(471\) 0 0
\(472\) 5.76328 0.265276
\(473\) −20.9739 −0.964379
\(474\) 0 0
\(475\) −2.37279 −0.108871
\(476\) 0 0
\(477\) 0 0
\(478\) 25.7633 1.17838
\(479\) 12.0086 0.548687 0.274343 0.961632i \(-0.411540\pi\)
0.274343 + 0.961632i \(0.411540\pi\)
\(480\) 0 0
\(481\) 6.15165 0.280491
\(482\) −15.3083 −0.697275
\(483\) 0 0
\(484\) −1.76975 −0.0804434
\(485\) 3.33804 0.151573
\(486\) 0 0
\(487\) 11.1184 0.503821 0.251911 0.967751i \(-0.418941\pi\)
0.251911 + 0.967751i \(0.418941\pi\)
\(488\) −2.57834 −0.116716
\(489\) 0 0
\(490\) 0 0
\(491\) −0.0594386 −0.00268243 −0.00134121 0.999999i \(-0.500427\pi\)
−0.00134121 + 0.999999i \(0.500427\pi\)
\(492\) 0 0
\(493\) 4.34715 0.195786
\(494\) 1.47556 0.0663887
\(495\) 0 0
\(496\) 6.84333 0.307274
\(497\) 0 0
\(498\) 0 0
\(499\) 10.2978 0.460991 0.230496 0.973073i \(-0.425965\pi\)
0.230496 + 0.973073i \(0.425965\pi\)
\(500\) −7.55773 −0.337992
\(501\) 0 0
\(502\) −43.4983 −1.94142
\(503\) −9.32391 −0.415733 −0.207866 0.978157i \(-0.566652\pi\)
−0.207866 + 0.978157i \(0.566652\pi\)
\(504\) 0 0
\(505\) 36.8661 1.64052
\(506\) 41.2927 1.83569
\(507\) 0 0
\(508\) −16.6066 −0.736799
\(509\) 39.6952 1.75946 0.879730 0.475473i \(-0.157723\pi\)
0.879730 + 0.475473i \(0.157723\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 18.4842 0.816892
\(513\) 0 0
\(514\) 28.3133 1.24885
\(515\) −12.4111 −0.546898
\(516\) 0 0
\(517\) 18.5244 0.814704
\(518\) 0 0
\(519\) 0 0
\(520\) 3.62721 0.159064
\(521\) 22.3627 0.979729 0.489865 0.871798i \(-0.337046\pi\)
0.489865 + 0.871798i \(0.337046\pi\)
\(522\) 0 0
\(523\) 20.6550 0.903178 0.451589 0.892226i \(-0.350857\pi\)
0.451589 + 0.892226i \(0.350857\pi\)
\(524\) 11.6655 0.509611
\(525\) 0 0
\(526\) 27.5139 1.19966
\(527\) 0.729988 0.0317988
\(528\) 0 0
\(529\) 30.8469 1.34117
\(530\) 12.7300 0.552955
\(531\) 0 0
\(532\) 0 0
\(533\) 4.20555 0.182163
\(534\) 0 0
\(535\) −1.62721 −0.0703506
\(536\) −12.9411 −0.558969
\(537\) 0 0
\(538\) 42.2439 1.82126
\(539\) 0 0
\(540\) 0 0
\(541\) 5.62167 0.241695 0.120847 0.992671i \(-0.461439\pi\)
0.120847 + 0.992671i \(0.461439\pi\)
\(542\) −23.1155 −0.992894
\(543\) 0 0
\(544\) 3.32391 0.142512
\(545\) 15.6811 0.671705
\(546\) 0 0
\(547\) −10.3970 −0.444542 −0.222271 0.974985i \(-0.571347\pi\)
−0.222271 + 0.974985i \(0.571347\pi\)
\(548\) 8.06949 0.344711
\(549\) 0 0
\(550\) −16.4111 −0.699772
\(551\) 6.74412 0.287309
\(552\) 0 0
\(553\) 0 0
\(554\) 14.7300 0.625817
\(555\) 0 0
\(556\) 14.9200 0.632747
\(557\) −14.6550 −0.620951 −0.310475 0.950581i \(-0.600488\pi\)
−0.310475 + 0.950581i \(0.600488\pi\)
\(558\) 0 0
\(559\) −6.75971 −0.285905
\(560\) 0 0
\(561\) 0 0
\(562\) −34.5189 −1.45609
\(563\) −24.7456 −1.04290 −0.521451 0.853281i \(-0.674609\pi\)
−0.521451 + 0.853281i \(0.674609\pi\)
\(564\) 0 0
\(565\) −15.3225 −0.644621
\(566\) −20.2156 −0.849725
\(567\) 0 0
\(568\) −11.2544 −0.472225
\(569\) 20.5330 0.860789 0.430395 0.902641i \(-0.358374\pi\)
0.430395 + 0.902641i \(0.358374\pi\)
\(570\) 0 0
\(571\) −41.8953 −1.75326 −0.876631 0.481163i \(-0.840214\pi\)
−0.876631 + 0.481163i \(0.840214\pi\)
\(572\) 4.00000 0.167248
\(573\) 0 0
\(574\) 0 0
\(575\) −21.4005 −0.892464
\(576\) 0 0
\(577\) 20.1744 0.839870 0.419935 0.907554i \(-0.362053\pi\)
0.419935 + 0.907554i \(0.362053\pi\)
\(578\) −30.3325 −1.26167
\(579\) 0 0
\(580\) −30.0666 −1.24845
\(581\) 0 0
\(582\) 0 0
\(583\) −7.74055 −0.320581
\(584\) −3.02061 −0.124994
\(585\) 0 0
\(586\) −25.7094 −1.06204
\(587\) −18.7441 −0.773653 −0.386826 0.922153i \(-0.626429\pi\)
−0.386826 + 0.922153i \(0.626429\pi\)
\(588\) 0 0
\(589\) 1.13249 0.0466636
\(590\) −22.8122 −0.939162
\(591\) 0 0
\(592\) 30.2439 1.24302
\(593\) −2.98084 −0.122409 −0.0612043 0.998125i \(-0.519494\pi\)
−0.0612043 + 0.998125i \(0.519494\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10.9894 −0.450145
\(597\) 0 0
\(598\) 13.3083 0.544218
\(599\) −7.47411 −0.305384 −0.152692 0.988274i \(-0.548794\pi\)
−0.152692 + 0.988274i \(0.548794\pi\)
\(600\) 0 0
\(601\) −21.4700 −0.875780 −0.437890 0.899028i \(-0.644274\pi\)
−0.437890 + 0.899028i \(0.644274\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −15.4499 −0.628649
\(605\) −3.86248 −0.157032
\(606\) 0 0
\(607\) 22.9044 0.929660 0.464830 0.885400i \(-0.346116\pi\)
0.464830 + 0.885400i \(0.346116\pi\)
\(608\) 5.15667 0.209131
\(609\) 0 0
\(610\) 10.2056 0.413211
\(611\) 5.97028 0.241532
\(612\) 0 0
\(613\) −20.1461 −0.813694 −0.406847 0.913496i \(-0.633372\pi\)
−0.406847 + 0.913496i \(0.633372\pi\)
\(614\) −24.5910 −0.992413
\(615\) 0 0
\(616\) 0 0
\(617\) 13.7844 0.554939 0.277470 0.960734i \(-0.410504\pi\)
0.277470 + 0.960734i \(0.410504\pi\)
\(618\) 0 0
\(619\) 19.6655 0.790424 0.395212 0.918590i \(-0.370671\pi\)
0.395212 + 0.918590i \(0.370671\pi\)
\(620\) −5.04888 −0.202768
\(621\) 0 0
\(622\) 0.773841 0.0310282
\(623\) 0 0
\(624\) 0 0
\(625\) −31.0766 −1.24307
\(626\) 32.9200 1.31575
\(627\) 0 0
\(628\) 16.5371 0.659903
\(629\) 3.22616 0.128635
\(630\) 0 0
\(631\) −16.1672 −0.643608 −0.321804 0.946806i \(-0.604289\pi\)
−0.321804 + 0.946806i \(0.604289\pi\)
\(632\) 17.4600 0.694521
\(633\) 0 0
\(634\) −17.0872 −0.678619
\(635\) −36.2439 −1.43829
\(636\) 0 0
\(637\) 0 0
\(638\) 46.6449 1.84669
\(639\) 0 0
\(640\) 27.1849 1.07458
\(641\) 29.0036 1.14557 0.572786 0.819705i \(-0.305863\pi\)
0.572786 + 0.819705i \(0.305863\pi\)
\(642\) 0 0
\(643\) 39.2233 1.54681 0.773407 0.633910i \(-0.218551\pi\)
0.773407 + 0.633910i \(0.218551\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.773841 0.0304464
\(647\) −11.9844 −0.471156 −0.235578 0.971855i \(-0.575698\pi\)
−0.235578 + 0.971855i \(0.575698\pi\)
\(648\) 0 0
\(649\) 13.8711 0.544487
\(650\) −5.28917 −0.207458
\(651\) 0 0
\(652\) −17.3522 −0.679564
\(653\) −45.3311 −1.77394 −0.886971 0.461826i \(-0.847194\pi\)
−0.886971 + 0.461826i \(0.847194\pi\)
\(654\) 0 0
\(655\) 25.4600 0.994804
\(656\) 20.6761 0.807266
\(657\) 0 0
\(658\) 0 0
\(659\) −6.12193 −0.238477 −0.119238 0.992866i \(-0.538045\pi\)
−0.119238 + 0.992866i \(0.538045\pi\)
\(660\) 0 0
\(661\) 27.5280 1.07072 0.535358 0.844625i \(-0.320177\pi\)
0.535358 + 0.844625i \(0.320177\pi\)
\(662\) −31.5577 −1.22653
\(663\) 0 0
\(664\) −21.2444 −0.824442
\(665\) 0 0
\(666\) 0 0
\(667\) 60.8263 2.35520
\(668\) −2.61665 −0.101241
\(669\) 0 0
\(670\) 51.2233 1.97893
\(671\) −6.20555 −0.239563
\(672\) 0 0
\(673\) 27.9547 1.07757 0.538787 0.842442i \(-0.318883\pi\)
0.538787 + 0.842442i \(0.318883\pi\)
\(674\) 39.9945 1.54053
\(675\) 0 0
\(676\) 1.28917 0.0495834
\(677\) −12.6605 −0.486583 −0.243291 0.969953i \(-0.578227\pi\)
−0.243291 + 0.969953i \(0.578227\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.90225 0.0729479
\(681\) 0 0
\(682\) 7.83276 0.299932
\(683\) 28.3033 1.08300 0.541498 0.840702i \(-0.317857\pi\)
0.541498 + 0.840702i \(0.317857\pi\)
\(684\) 0 0
\(685\) 17.6116 0.672906
\(686\) 0 0
\(687\) 0 0
\(688\) −33.2333 −1.26701
\(689\) −2.49472 −0.0950412
\(690\) 0 0
\(691\) −12.2353 −0.465452 −0.232726 0.972542i \(-0.574764\pi\)
−0.232726 + 0.972542i \(0.574764\pi\)
\(692\) 26.1672 0.994729
\(693\) 0 0
\(694\) −45.9789 −1.74533
\(695\) 32.5628 1.23518
\(696\) 0 0
\(697\) 2.20555 0.0835412
\(698\) 10.3472 0.391646
\(699\) 0 0
\(700\) 0 0
\(701\) −51.0419 −1.92783 −0.963913 0.266219i \(-0.914226\pi\)
−0.963913 + 0.266219i \(0.914226\pi\)
\(702\) 0 0
\(703\) 5.00502 0.188768
\(704\) 5.15667 0.194349
\(705\) 0 0
\(706\) −52.0071 −1.95731
\(707\) 0 0
\(708\) 0 0
\(709\) 42.5910 1.59954 0.799770 0.600307i \(-0.204955\pi\)
0.799770 + 0.600307i \(0.204955\pi\)
\(710\) 44.5472 1.67183
\(711\) 0 0
\(712\) 13.7250 0.514365
\(713\) 10.2141 0.382523
\(714\) 0 0
\(715\) 8.72999 0.326483
\(716\) 14.1855 0.530135
\(717\) 0 0
\(718\) −20.0283 −0.747448
\(719\) −42.4933 −1.58473 −0.792366 0.610046i \(-0.791151\pi\)
−0.792366 + 0.610046i \(0.791151\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −33.2580 −1.23773
\(723\) 0 0
\(724\) −0.891685 −0.0331392
\(725\) −24.1744 −0.897814
\(726\) 0 0
\(727\) 3.75614 0.139307 0.0696537 0.997571i \(-0.477811\pi\)
0.0696537 + 0.997571i \(0.477811\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 11.9561 0.442517
\(731\) −3.54505 −0.131118
\(732\) 0 0
\(733\) −45.7819 −1.69099 −0.845497 0.533980i \(-0.820696\pi\)
−0.845497 + 0.533980i \(0.820696\pi\)
\(734\) −49.5960 −1.83062
\(735\) 0 0
\(736\) 46.5089 1.71434
\(737\) −31.1466 −1.14730
\(738\) 0 0
\(739\) −14.0539 −0.516981 −0.258491 0.966014i \(-0.583225\pi\)
−0.258491 + 0.966014i \(0.583225\pi\)
\(740\) −22.3133 −0.820255
\(741\) 0 0
\(742\) 0 0
\(743\) −4.74557 −0.174098 −0.0870491 0.996204i \(-0.527744\pi\)
−0.0870491 + 0.996204i \(0.527744\pi\)
\(744\) 0 0
\(745\) −23.9844 −0.878721
\(746\) 29.2827 1.07212
\(747\) 0 0
\(748\) 2.09775 0.0767014
\(749\) 0 0
\(750\) 0 0
\(751\) 36.1008 1.31734 0.658669 0.752433i \(-0.271120\pi\)
0.658669 + 0.752433i \(0.271120\pi\)
\(752\) 29.3522 1.07036
\(753\) 0 0
\(754\) 15.0333 0.547480
\(755\) −33.7194 −1.22718
\(756\) 0 0
\(757\) −1.03474 −0.0376084 −0.0188042 0.999823i \(-0.505986\pi\)
−0.0188042 + 0.999823i \(0.505986\pi\)
\(758\) 47.3905 1.72130
\(759\) 0 0
\(760\) 2.95112 0.107049
\(761\) 29.8414 1.08175 0.540874 0.841104i \(-0.318094\pi\)
0.540874 + 0.841104i \(0.318094\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −10.0978 −0.365324
\(765\) 0 0
\(766\) −38.1744 −1.37930
\(767\) 4.47054 0.161422
\(768\) 0 0
\(769\) −23.6358 −0.852329 −0.426164 0.904646i \(-0.640136\pi\)
−0.426164 + 0.904646i \(0.640136\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −15.7350 −0.566315
\(773\) 13.0278 0.468576 0.234288 0.972167i \(-0.424724\pi\)
0.234288 + 0.972167i \(0.424724\pi\)
\(774\) 0 0
\(775\) −4.05944 −0.145819
\(776\) −1.52946 −0.0549045
\(777\) 0 0
\(778\) 39.1849 1.40485
\(779\) 3.42166 0.122594
\(780\) 0 0
\(781\) −27.0872 −0.969256
\(782\) 6.97939 0.249583
\(783\) 0 0
\(784\) 0 0
\(785\) 36.0922 1.28819
\(786\) 0 0
\(787\) −46.2141 −1.64736 −0.823678 0.567058i \(-0.808082\pi\)
−0.823678 + 0.567058i \(0.808082\pi\)
\(788\) 24.2650 0.864404
\(789\) 0 0
\(790\) −69.1099 −2.45882
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) 50.2283 1.78253
\(795\) 0 0
\(796\) −27.8610 −0.987508
\(797\) 53.1155 1.88145 0.940723 0.339176i \(-0.110148\pi\)
0.940723 + 0.339176i \(0.110148\pi\)
\(798\) 0 0
\(799\) 3.13104 0.110768
\(800\) −18.4842 −0.653514
\(801\) 0 0
\(802\) 4.67609 0.165118
\(803\) −7.27001 −0.256553
\(804\) 0 0
\(805\) 0 0
\(806\) 2.52444 0.0889195
\(807\) 0 0
\(808\) −16.8917 −0.594247
\(809\) 54.4635 1.91484 0.957418 0.288705i \(-0.0932246\pi\)
0.957418 + 0.288705i \(0.0932246\pi\)
\(810\) 0 0
\(811\) −38.0978 −1.33779 −0.668897 0.743356i \(-0.733233\pi\)
−0.668897 + 0.743356i \(0.733233\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 34.6167 1.21331
\(815\) −37.8711 −1.32657
\(816\) 0 0
\(817\) −5.49974 −0.192412
\(818\) −27.4161 −0.958582
\(819\) 0 0
\(820\) −15.2544 −0.532708
\(821\) 2.30330 0.0803858 0.0401929 0.999192i \(-0.487203\pi\)
0.0401929 + 0.999192i \(0.487203\pi\)
\(822\) 0 0
\(823\) 23.6172 0.823243 0.411621 0.911355i \(-0.364963\pi\)
0.411621 + 0.911355i \(0.364963\pi\)
\(824\) 5.68665 0.198104
\(825\) 0 0
\(826\) 0 0
\(827\) 48.1643 1.67484 0.837419 0.546562i \(-0.184064\pi\)
0.837419 + 0.546562i \(0.184064\pi\)
\(828\) 0 0
\(829\) −13.0716 −0.453996 −0.226998 0.973895i \(-0.572891\pi\)
−0.226998 + 0.973895i \(0.572891\pi\)
\(830\) 84.0893 2.91878
\(831\) 0 0
\(832\) 1.66196 0.0576179
\(833\) 0 0
\(834\) 0 0
\(835\) −5.71083 −0.197631
\(836\) 3.25443 0.112557
\(837\) 0 0
\(838\) −18.1260 −0.626153
\(839\) −17.6756 −0.610229 −0.305114 0.952316i \(-0.598695\pi\)
−0.305114 + 0.952316i \(0.598695\pi\)
\(840\) 0 0
\(841\) 39.7103 1.36932
\(842\) −47.0177 −1.62034
\(843\) 0 0
\(844\) −22.4011 −0.771076
\(845\) 2.81361 0.0967910
\(846\) 0 0
\(847\) 0 0
\(848\) −12.2650 −0.421181
\(849\) 0 0
\(850\) −2.77384 −0.0951420
\(851\) 45.1411 1.54742
\(852\) 0 0
\(853\) 5.48970 0.187964 0.0939818 0.995574i \(-0.470040\pi\)
0.0939818 + 0.995574i \(0.470040\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.745574 0.0254832
\(857\) −11.0489 −0.377422 −0.188711 0.982033i \(-0.560431\pi\)
−0.188711 + 0.982033i \(0.560431\pi\)
\(858\) 0 0
\(859\) −45.2616 −1.54430 −0.772152 0.635437i \(-0.780820\pi\)
−0.772152 + 0.635437i \(0.780820\pi\)
\(860\) 24.5189 0.836087
\(861\) 0 0
\(862\) −55.6344 −1.89491
\(863\) 5.90225 0.200915 0.100457 0.994941i \(-0.467969\pi\)
0.100457 + 0.994941i \(0.467969\pi\)
\(864\) 0 0
\(865\) 57.1099 1.94180
\(866\) 6.38283 0.216898
\(867\) 0 0
\(868\) 0 0
\(869\) 42.0227 1.42552
\(870\) 0 0
\(871\) −10.0383 −0.340135
\(872\) −7.18494 −0.243313
\(873\) 0 0
\(874\) 10.8277 0.366254
\(875\) 0 0
\(876\) 0 0
\(877\) −4.90727 −0.165707 −0.0828534 0.996562i \(-0.526403\pi\)
−0.0828534 + 0.996562i \(0.526403\pi\)
\(878\) −58.6732 −1.98012
\(879\) 0 0
\(880\) 42.9200 1.44683
\(881\) 44.2822 1.49190 0.745952 0.665999i \(-0.231995\pi\)
0.745952 + 0.665999i \(0.231995\pi\)
\(882\) 0 0
\(883\) −58.8605 −1.98081 −0.990407 0.138181i \(-0.955874\pi\)
−0.990407 + 0.138181i \(0.955874\pi\)
\(884\) 0.676089 0.0227393
\(885\) 0 0
\(886\) −28.0127 −0.941104
\(887\) −10.1289 −0.340096 −0.170048 0.985436i \(-0.554392\pi\)
−0.170048 + 0.985436i \(0.554392\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −54.3260 −1.82101
\(891\) 0 0
\(892\) 13.5989 0.455326
\(893\) 4.85746 0.162549
\(894\) 0 0
\(895\) 30.9597 1.03487
\(896\) 0 0
\(897\) 0 0
\(898\) 26.2439 0.875769
\(899\) 11.5381 0.384816
\(900\) 0 0
\(901\) −1.30833 −0.0435866
\(902\) 23.6655 0.787976
\(903\) 0 0
\(904\) 7.02061 0.233502
\(905\) −1.94610 −0.0646906
\(906\) 0 0
\(907\) 37.9547 1.26026 0.630132 0.776488i \(-0.283001\pi\)
0.630132 + 0.776488i \(0.283001\pi\)
\(908\) −8.96117 −0.297387
\(909\) 0 0
\(910\) 0 0
\(911\) −5.57477 −0.184700 −0.0923501 0.995727i \(-0.529438\pi\)
−0.0923501 + 0.995727i \(0.529438\pi\)
\(912\) 0 0
\(913\) −51.1310 −1.69219
\(914\) −62.8787 −2.07984
\(915\) 0 0
\(916\) 27.1849 0.898216
\(917\) 0 0
\(918\) 0 0
\(919\) 15.7844 0.520679 0.260340 0.965517i \(-0.416165\pi\)
0.260340 + 0.965517i \(0.416165\pi\)
\(920\) 26.6167 0.877525
\(921\) 0 0
\(922\) 22.7427 0.748990
\(923\) −8.72999 −0.287351
\(924\) 0 0
\(925\) −17.9406 −0.589882
\(926\) 22.0383 0.724224
\(927\) 0 0
\(928\) 52.5371 1.72462
\(929\) −45.2630 −1.48503 −0.742516 0.669829i \(-0.766368\pi\)
−0.742516 + 0.669829i \(0.766368\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −7.84281 −0.256900
\(933\) 0 0
\(934\) −67.1638 −2.19767
\(935\) 4.57834 0.149728
\(936\) 0 0
\(937\) −53.6188 −1.75165 −0.875824 0.482630i \(-0.839682\pi\)
−0.875824 + 0.482630i \(0.839682\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −21.6555 −0.706324
\(941\) 20.7753 0.677255 0.338628 0.940920i \(-0.390037\pi\)
0.338628 + 0.940920i \(0.390037\pi\)
\(942\) 0 0
\(943\) 30.8605 1.00496
\(944\) 21.9789 0.715351
\(945\) 0 0
\(946\) −38.0383 −1.23673
\(947\) 10.8605 0.352919 0.176460 0.984308i \(-0.443535\pi\)
0.176460 + 0.984308i \(0.443535\pi\)
\(948\) 0 0
\(949\) −2.34307 −0.0760592
\(950\) −4.30330 −0.139618
\(951\) 0 0
\(952\) 0 0
\(953\) 25.7180 0.833087 0.416543 0.909116i \(-0.363241\pi\)
0.416543 + 0.909116i \(0.363241\pi\)
\(954\) 0 0
\(955\) −22.0383 −0.713143
\(956\) 18.3133 0.592296
\(957\) 0 0
\(958\) 21.7789 0.703643
\(959\) 0 0
\(960\) 0 0
\(961\) −29.0625 −0.937500
\(962\) 11.1567 0.359706
\(963\) 0 0
\(964\) −10.8816 −0.350474
\(965\) −34.3416 −1.10550
\(966\) 0 0
\(967\) 33.5038 1.07741 0.538705 0.842494i \(-0.318914\pi\)
0.538705 + 0.842494i \(0.318914\pi\)
\(968\) 1.76975 0.0568820
\(969\) 0 0
\(970\) 6.05390 0.194379
\(971\) 2.03831 0.0654126 0.0327063 0.999465i \(-0.489587\pi\)
0.0327063 + 0.999465i \(0.489587\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 20.1643 0.646107
\(975\) 0 0
\(976\) −9.83276 −0.314739
\(977\) −15.1411 −0.484406 −0.242203 0.970226i \(-0.577870\pi\)
−0.242203 + 0.970226i \(0.577870\pi\)
\(978\) 0 0
\(979\) 33.0333 1.05575
\(980\) 0 0
\(981\) 0 0
\(982\) −0.107798 −0.00343998
\(983\) 49.3124 1.57282 0.786411 0.617704i \(-0.211937\pi\)
0.786411 + 0.617704i \(0.211937\pi\)
\(984\) 0 0
\(985\) 52.9583 1.68739
\(986\) 7.88403 0.251079
\(987\) 0 0
\(988\) 1.04888 0.0333692
\(989\) −49.6030 −1.57728
\(990\) 0 0
\(991\) 5.43171 0.172544 0.0862720 0.996272i \(-0.472505\pi\)
0.0862720 + 0.996272i \(0.472505\pi\)
\(992\) 8.82220 0.280105
\(993\) 0 0
\(994\) 0 0
\(995\) −60.8066 −1.92770
\(996\) 0 0
\(997\) 53.6061 1.69772 0.848861 0.528616i \(-0.177289\pi\)
0.848861 + 0.528616i \(0.177289\pi\)
\(998\) 18.6761 0.591181
\(999\) 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 5733.2.a.x.1.3 3
3.2 odd 2 637.2.a.j.1.1 3
7.6 odd 2 819.2.a.i.1.3 3
21.2 odd 6 637.2.e.i.508.3 6
21.5 even 6 637.2.e.j.508.3 6
21.11 odd 6 637.2.e.i.79.3 6
21.17 even 6 637.2.e.j.79.3 6
21.20 even 2 91.2.a.d.1.1 3
39.38 odd 2 8281.2.a.bg.1.3 3
84.83 odd 2 1456.2.a.t.1.3 3
105.104 even 2 2275.2.a.m.1.3 3
168.83 odd 2 5824.2.a.bs.1.1 3
168.125 even 2 5824.2.a.by.1.3 3
273.83 odd 4 1183.2.c.f.337.5 6
273.125 odd 4 1183.2.c.f.337.2 6
273.272 even 2 1183.2.a.i.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.a.d.1.1 3 21.20 even 2
637.2.a.j.1.1 3 3.2 odd 2
637.2.e.i.79.3 6 21.11 odd 6
637.2.e.i.508.3 6 21.2 odd 6
637.2.e.j.79.3 6 21.17 even 6
637.2.e.j.508.3 6 21.5 even 6
819.2.a.i.1.3 3 7.6 odd 2
1183.2.a.i.1.3 3 273.272 even 2
1183.2.c.f.337.2 6 273.125 odd 4
1183.2.c.f.337.5 6 273.83 odd 4
1456.2.a.t.1.3 3 84.83 odd 2
2275.2.a.m.1.3 3 105.104 even 2
5733.2.a.x.1.3 3 1.1 even 1 trivial
5824.2.a.bs.1.1 3 168.83 odd 2
5824.2.a.by.1.3 3 168.125 even 2
8281.2.a.bg.1.3 3 39.38 odd 2