Properties

Label 6008.2.a.b.1.12
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.01203 q^{3} -4.06513 q^{5} -4.33062 q^{7} +1.04828 q^{9} +O(q^{10})\) \(q-2.01203 q^{3} -4.06513 q^{5} -4.33062 q^{7} +1.04828 q^{9} -3.72115 q^{11} -4.52461 q^{13} +8.17917 q^{15} -5.00387 q^{17} +2.88544 q^{19} +8.71335 q^{21} +3.74014 q^{23} +11.5253 q^{25} +3.92693 q^{27} +9.42990 q^{29} -6.53919 q^{31} +7.48708 q^{33} +17.6045 q^{35} -6.59101 q^{37} +9.10367 q^{39} -2.05963 q^{41} +7.35890 q^{43} -4.26138 q^{45} -2.80542 q^{47} +11.7543 q^{49} +10.0680 q^{51} +11.5157 q^{53} +15.1270 q^{55} -5.80560 q^{57} -13.0847 q^{59} +4.80037 q^{61} -4.53968 q^{63} +18.3931 q^{65} +1.53550 q^{67} -7.52527 q^{69} +8.02541 q^{71} -16.0058 q^{73} -23.1892 q^{75} +16.1149 q^{77} -7.19216 q^{79} -11.0459 q^{81} -13.5406 q^{83} +20.3414 q^{85} -18.9733 q^{87} +3.29563 q^{89} +19.5944 q^{91} +13.1571 q^{93} -11.7297 q^{95} +5.35746 q^{97} -3.90079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.01203 −1.16165 −0.580824 0.814029i \(-0.697269\pi\)
−0.580824 + 0.814029i \(0.697269\pi\)
\(4\) 0 0
\(5\) −4.06513 −1.81798 −0.908991 0.416817i \(-0.863146\pi\)
−0.908991 + 0.416817i \(0.863146\pi\)
\(6\) 0 0
\(7\) −4.33062 −1.63682 −0.818411 0.574634i \(-0.805145\pi\)
−0.818411 + 0.574634i \(0.805145\pi\)
\(8\) 0 0
\(9\) 1.04828 0.349425
\(10\) 0 0
\(11\) −3.72115 −1.12197 −0.560985 0.827826i \(-0.689577\pi\)
−0.560985 + 0.827826i \(0.689577\pi\)
\(12\) 0 0
\(13\) −4.52461 −1.25490 −0.627451 0.778656i \(-0.715902\pi\)
−0.627451 + 0.778656i \(0.715902\pi\)
\(14\) 0 0
\(15\) 8.17917 2.11185
\(16\) 0 0
\(17\) −5.00387 −1.21362 −0.606809 0.794848i \(-0.707551\pi\)
−0.606809 + 0.794848i \(0.707551\pi\)
\(18\) 0 0
\(19\) 2.88544 0.661965 0.330983 0.943637i \(-0.392620\pi\)
0.330983 + 0.943637i \(0.392620\pi\)
\(20\) 0 0
\(21\) 8.71335 1.90141
\(22\) 0 0
\(23\) 3.74014 0.779872 0.389936 0.920842i \(-0.372497\pi\)
0.389936 + 0.920842i \(0.372497\pi\)
\(24\) 0 0
\(25\) 11.5253 2.30506
\(26\) 0 0
\(27\) 3.92693 0.755739
\(28\) 0 0
\(29\) 9.42990 1.75109 0.875544 0.483139i \(-0.160503\pi\)
0.875544 + 0.483139i \(0.160503\pi\)
\(30\) 0 0
\(31\) −6.53919 −1.17447 −0.587237 0.809415i \(-0.699784\pi\)
−0.587237 + 0.809415i \(0.699784\pi\)
\(32\) 0 0
\(33\) 7.48708 1.30333
\(34\) 0 0
\(35\) 17.6045 2.97571
\(36\) 0 0
\(37\) −6.59101 −1.08355 −0.541777 0.840522i \(-0.682248\pi\)
−0.541777 + 0.840522i \(0.682248\pi\)
\(38\) 0 0
\(39\) 9.10367 1.45775
\(40\) 0 0
\(41\) −2.05963 −0.321661 −0.160830 0.986982i \(-0.551417\pi\)
−0.160830 + 0.986982i \(0.551417\pi\)
\(42\) 0 0
\(43\) 7.35890 1.12222 0.561111 0.827741i \(-0.310374\pi\)
0.561111 + 0.827741i \(0.310374\pi\)
\(44\) 0 0
\(45\) −4.26138 −0.635248
\(46\) 0 0
\(47\) −2.80542 −0.409213 −0.204606 0.978844i \(-0.565591\pi\)
−0.204606 + 0.978844i \(0.565591\pi\)
\(48\) 0 0
\(49\) 11.7543 1.67918
\(50\) 0 0
\(51\) 10.0680 1.40980
\(52\) 0 0
\(53\) 11.5157 1.58180 0.790899 0.611947i \(-0.209614\pi\)
0.790899 + 0.611947i \(0.209614\pi\)
\(54\) 0 0
\(55\) 15.1270 2.03972
\(56\) 0 0
\(57\) −5.80560 −0.768970
\(58\) 0 0
\(59\) −13.0847 −1.70348 −0.851741 0.523963i \(-0.824453\pi\)
−0.851741 + 0.523963i \(0.824453\pi\)
\(60\) 0 0
\(61\) 4.80037 0.614624 0.307312 0.951609i \(-0.400570\pi\)
0.307312 + 0.951609i \(0.400570\pi\)
\(62\) 0 0
\(63\) −4.53968 −0.571947
\(64\) 0 0
\(65\) 18.3931 2.28139
\(66\) 0 0
\(67\) 1.53550 0.187591 0.0937956 0.995591i \(-0.470100\pi\)
0.0937956 + 0.995591i \(0.470100\pi\)
\(68\) 0 0
\(69\) −7.52527 −0.905937
\(70\) 0 0
\(71\) 8.02541 0.952441 0.476220 0.879326i \(-0.342006\pi\)
0.476220 + 0.879326i \(0.342006\pi\)
\(72\) 0 0
\(73\) −16.0058 −1.87334 −0.936668 0.350218i \(-0.886108\pi\)
−0.936668 + 0.350218i \(0.886108\pi\)
\(74\) 0 0
\(75\) −23.1892 −2.67766
\(76\) 0 0
\(77\) 16.1149 1.83646
\(78\) 0 0
\(79\) −7.19216 −0.809181 −0.404591 0.914498i \(-0.632586\pi\)
−0.404591 + 0.914498i \(0.632586\pi\)
\(80\) 0 0
\(81\) −11.0459 −1.22733
\(82\) 0 0
\(83\) −13.5406 −1.48627 −0.743135 0.669141i \(-0.766662\pi\)
−0.743135 + 0.669141i \(0.766662\pi\)
\(84\) 0 0
\(85\) 20.3414 2.20633
\(86\) 0 0
\(87\) −18.9733 −2.03415
\(88\) 0 0
\(89\) 3.29563 0.349336 0.174668 0.984627i \(-0.444115\pi\)
0.174668 + 0.984627i \(0.444115\pi\)
\(90\) 0 0
\(91\) 19.5944 2.05405
\(92\) 0 0
\(93\) 13.1571 1.36432
\(94\) 0 0
\(95\) −11.7297 −1.20344
\(96\) 0 0
\(97\) 5.35746 0.543967 0.271984 0.962302i \(-0.412320\pi\)
0.271984 + 0.962302i \(0.412320\pi\)
\(98\) 0 0
\(99\) −3.90079 −0.392045
\(100\) 0 0
\(101\) 9.36154 0.931508 0.465754 0.884914i \(-0.345783\pi\)
0.465754 + 0.884914i \(0.345783\pi\)
\(102\) 0 0
\(103\) −12.5802 −1.23957 −0.619784 0.784772i \(-0.712780\pi\)
−0.619784 + 0.784772i \(0.712780\pi\)
\(104\) 0 0
\(105\) −35.4209 −3.45673
\(106\) 0 0
\(107\) −6.82691 −0.659982 −0.329991 0.943984i \(-0.607046\pi\)
−0.329991 + 0.943984i \(0.607046\pi\)
\(108\) 0 0
\(109\) 19.9318 1.90912 0.954558 0.298024i \(-0.0963275\pi\)
0.954558 + 0.298024i \(0.0963275\pi\)
\(110\) 0 0
\(111\) 13.2613 1.25871
\(112\) 0 0
\(113\) −17.6715 −1.66239 −0.831197 0.555979i \(-0.812344\pi\)
−0.831197 + 0.555979i \(0.812344\pi\)
\(114\) 0 0
\(115\) −15.2041 −1.41779
\(116\) 0 0
\(117\) −4.74304 −0.438494
\(118\) 0 0
\(119\) 21.6699 1.98648
\(120\) 0 0
\(121\) 2.84699 0.258817
\(122\) 0 0
\(123\) 4.14405 0.373657
\(124\) 0 0
\(125\) −26.5261 −2.37257
\(126\) 0 0
\(127\) 17.2539 1.53104 0.765519 0.643413i \(-0.222482\pi\)
0.765519 + 0.643413i \(0.222482\pi\)
\(128\) 0 0
\(129\) −14.8063 −1.30363
\(130\) 0 0
\(131\) −1.24720 −0.108968 −0.0544841 0.998515i \(-0.517351\pi\)
−0.0544841 + 0.998515i \(0.517351\pi\)
\(132\) 0 0
\(133\) −12.4957 −1.08352
\(134\) 0 0
\(135\) −15.9635 −1.37392
\(136\) 0 0
\(137\) 14.7331 1.25874 0.629368 0.777107i \(-0.283314\pi\)
0.629368 + 0.777107i \(0.283314\pi\)
\(138\) 0 0
\(139\) −7.02323 −0.595703 −0.297851 0.954612i \(-0.596270\pi\)
−0.297851 + 0.954612i \(0.596270\pi\)
\(140\) 0 0
\(141\) 5.64460 0.475361
\(142\) 0 0
\(143\) 16.8368 1.40796
\(144\) 0 0
\(145\) −38.3337 −3.18344
\(146\) 0 0
\(147\) −23.6500 −1.95062
\(148\) 0 0
\(149\) −8.92957 −0.731539 −0.365769 0.930706i \(-0.619194\pi\)
−0.365769 + 0.930706i \(0.619194\pi\)
\(150\) 0 0
\(151\) 11.7960 0.959948 0.479974 0.877283i \(-0.340646\pi\)
0.479974 + 0.877283i \(0.340646\pi\)
\(152\) 0 0
\(153\) −5.24544 −0.424069
\(154\) 0 0
\(155\) 26.5827 2.13517
\(156\) 0 0
\(157\) 18.6068 1.48498 0.742492 0.669855i \(-0.233644\pi\)
0.742492 + 0.669855i \(0.233644\pi\)
\(158\) 0 0
\(159\) −23.1699 −1.83749
\(160\) 0 0
\(161\) −16.1971 −1.27651
\(162\) 0 0
\(163\) −14.4336 −1.13052 −0.565262 0.824911i \(-0.691225\pi\)
−0.565262 + 0.824911i \(0.691225\pi\)
\(164\) 0 0
\(165\) −30.4360 −2.36944
\(166\) 0 0
\(167\) −14.2875 −1.10560 −0.552801 0.833313i \(-0.686441\pi\)
−0.552801 + 0.833313i \(0.686441\pi\)
\(168\) 0 0
\(169\) 7.47213 0.574779
\(170\) 0 0
\(171\) 3.02474 0.231307
\(172\) 0 0
\(173\) 10.7209 0.815092 0.407546 0.913185i \(-0.366385\pi\)
0.407546 + 0.913185i \(0.366385\pi\)
\(174\) 0 0
\(175\) −49.9116 −3.77296
\(176\) 0 0
\(177\) 26.3268 1.97885
\(178\) 0 0
\(179\) 9.18034 0.686171 0.343086 0.939304i \(-0.388528\pi\)
0.343086 + 0.939304i \(0.388528\pi\)
\(180\) 0 0
\(181\) 14.4585 1.07469 0.537344 0.843363i \(-0.319428\pi\)
0.537344 + 0.843363i \(0.319428\pi\)
\(182\) 0 0
\(183\) −9.65850 −0.713977
\(184\) 0 0
\(185\) 26.7933 1.96988
\(186\) 0 0
\(187\) 18.6202 1.36164
\(188\) 0 0
\(189\) −17.0061 −1.23701
\(190\) 0 0
\(191\) −15.1319 −1.09491 −0.547454 0.836836i \(-0.684403\pi\)
−0.547454 + 0.836836i \(0.684403\pi\)
\(192\) 0 0
\(193\) −16.2492 −1.16965 −0.584823 0.811161i \(-0.698836\pi\)
−0.584823 + 0.811161i \(0.698836\pi\)
\(194\) 0 0
\(195\) −37.0076 −2.65017
\(196\) 0 0
\(197\) 17.1791 1.22396 0.611982 0.790872i \(-0.290373\pi\)
0.611982 + 0.790872i \(0.290373\pi\)
\(198\) 0 0
\(199\) −1.27122 −0.0901147 −0.0450574 0.998984i \(-0.514347\pi\)
−0.0450574 + 0.998984i \(0.514347\pi\)
\(200\) 0 0
\(201\) −3.08948 −0.217915
\(202\) 0 0
\(203\) −40.8373 −2.86622
\(204\) 0 0
\(205\) 8.37268 0.584774
\(206\) 0 0
\(207\) 3.92069 0.272507
\(208\) 0 0
\(209\) −10.7372 −0.742705
\(210\) 0 0
\(211\) −1.65657 −0.114043 −0.0570214 0.998373i \(-0.518160\pi\)
−0.0570214 + 0.998373i \(0.518160\pi\)
\(212\) 0 0
\(213\) −16.1474 −1.10640
\(214\) 0 0
\(215\) −29.9149 −2.04018
\(216\) 0 0
\(217\) 28.3188 1.92240
\(218\) 0 0
\(219\) 32.2042 2.17616
\(220\) 0 0
\(221\) 22.6406 1.52297
\(222\) 0 0
\(223\) −7.49229 −0.501721 −0.250860 0.968023i \(-0.580713\pi\)
−0.250860 + 0.968023i \(0.580713\pi\)
\(224\) 0 0
\(225\) 12.0817 0.805444
\(226\) 0 0
\(227\) 26.6560 1.76922 0.884611 0.466329i \(-0.154424\pi\)
0.884611 + 0.466329i \(0.154424\pi\)
\(228\) 0 0
\(229\) 3.53397 0.233531 0.116766 0.993160i \(-0.462747\pi\)
0.116766 + 0.993160i \(0.462747\pi\)
\(230\) 0 0
\(231\) −32.4237 −2.13332
\(232\) 0 0
\(233\) 12.7696 0.836562 0.418281 0.908318i \(-0.362633\pi\)
0.418281 + 0.908318i \(0.362633\pi\)
\(234\) 0 0
\(235\) 11.4044 0.743941
\(236\) 0 0
\(237\) 14.4709 0.939983
\(238\) 0 0
\(239\) 19.3615 1.25239 0.626196 0.779666i \(-0.284611\pi\)
0.626196 + 0.779666i \(0.284611\pi\)
\(240\) 0 0
\(241\) 20.9352 1.34855 0.674276 0.738479i \(-0.264456\pi\)
0.674276 + 0.738479i \(0.264456\pi\)
\(242\) 0 0
\(243\) 10.4440 0.669983
\(244\) 0 0
\(245\) −47.7827 −3.05272
\(246\) 0 0
\(247\) −13.0555 −0.830701
\(248\) 0 0
\(249\) 27.2441 1.72652
\(250\) 0 0
\(251\) −13.5506 −0.855305 −0.427653 0.903943i \(-0.640659\pi\)
−0.427653 + 0.903943i \(0.640659\pi\)
\(252\) 0 0
\(253\) −13.9176 −0.874993
\(254\) 0 0
\(255\) −40.9276 −2.56298
\(256\) 0 0
\(257\) 7.38314 0.460548 0.230274 0.973126i \(-0.426038\pi\)
0.230274 + 0.973126i \(0.426038\pi\)
\(258\) 0 0
\(259\) 28.5432 1.77359
\(260\) 0 0
\(261\) 9.88513 0.611874
\(262\) 0 0
\(263\) 7.32908 0.451930 0.225965 0.974135i \(-0.427446\pi\)
0.225965 + 0.974135i \(0.427446\pi\)
\(264\) 0 0
\(265\) −46.8126 −2.87568
\(266\) 0 0
\(267\) −6.63091 −0.405805
\(268\) 0 0
\(269\) 31.1844 1.90135 0.950673 0.310195i \(-0.100394\pi\)
0.950673 + 0.310195i \(0.100394\pi\)
\(270\) 0 0
\(271\) −1.91872 −0.116554 −0.0582769 0.998300i \(-0.518561\pi\)
−0.0582769 + 0.998300i \(0.518561\pi\)
\(272\) 0 0
\(273\) −39.4246 −2.38608
\(274\) 0 0
\(275\) −42.8873 −2.58620
\(276\) 0 0
\(277\) −27.7014 −1.66442 −0.832208 0.554463i \(-0.812924\pi\)
−0.832208 + 0.554463i \(0.812924\pi\)
\(278\) 0 0
\(279\) −6.85487 −0.410391
\(280\) 0 0
\(281\) 22.5790 1.34695 0.673475 0.739210i \(-0.264801\pi\)
0.673475 + 0.739210i \(0.264801\pi\)
\(282\) 0 0
\(283\) −4.41452 −0.262416 −0.131208 0.991355i \(-0.541886\pi\)
−0.131208 + 0.991355i \(0.541886\pi\)
\(284\) 0 0
\(285\) 23.6005 1.39797
\(286\) 0 0
\(287\) 8.91950 0.526501
\(288\) 0 0
\(289\) 8.03876 0.472868
\(290\) 0 0
\(291\) −10.7794 −0.631898
\(292\) 0 0
\(293\) 29.1045 1.70031 0.850153 0.526536i \(-0.176509\pi\)
0.850153 + 0.526536i \(0.176509\pi\)
\(294\) 0 0
\(295\) 53.1910 3.09690
\(296\) 0 0
\(297\) −14.6127 −0.847916
\(298\) 0 0
\(299\) −16.9227 −0.978663
\(300\) 0 0
\(301\) −31.8686 −1.83688
\(302\) 0 0
\(303\) −18.8357 −1.08208
\(304\) 0 0
\(305\) −19.5141 −1.11738
\(306\) 0 0
\(307\) 7.42663 0.423860 0.211930 0.977285i \(-0.432025\pi\)
0.211930 + 0.977285i \(0.432025\pi\)
\(308\) 0 0
\(309\) 25.3119 1.43994
\(310\) 0 0
\(311\) 27.1458 1.53929 0.769647 0.638469i \(-0.220432\pi\)
0.769647 + 0.638469i \(0.220432\pi\)
\(312\) 0 0
\(313\) −34.5622 −1.95357 −0.976785 0.214221i \(-0.931279\pi\)
−0.976785 + 0.214221i \(0.931279\pi\)
\(314\) 0 0
\(315\) 18.4544 1.03979
\(316\) 0 0
\(317\) −30.4991 −1.71300 −0.856499 0.516149i \(-0.827365\pi\)
−0.856499 + 0.516149i \(0.827365\pi\)
\(318\) 0 0
\(319\) −35.0901 −1.96467
\(320\) 0 0
\(321\) 13.7360 0.766667
\(322\) 0 0
\(323\) −14.4384 −0.803373
\(324\) 0 0
\(325\) −52.1474 −2.89262
\(326\) 0 0
\(327\) −40.1034 −2.21772
\(328\) 0 0
\(329\) 12.1492 0.669808
\(330\) 0 0
\(331\) −17.9515 −0.986704 −0.493352 0.869830i \(-0.664229\pi\)
−0.493352 + 0.869830i \(0.664229\pi\)
\(332\) 0 0
\(333\) −6.90919 −0.378621
\(334\) 0 0
\(335\) −6.24201 −0.341037
\(336\) 0 0
\(337\) −3.65450 −0.199073 −0.0995367 0.995034i \(-0.531736\pi\)
−0.0995367 + 0.995034i \(0.531736\pi\)
\(338\) 0 0
\(339\) 35.5556 1.93112
\(340\) 0 0
\(341\) 24.3333 1.31772
\(342\) 0 0
\(343\) −20.5890 −1.11170
\(344\) 0 0
\(345\) 30.5912 1.64698
\(346\) 0 0
\(347\) 26.1616 1.40443 0.702215 0.711965i \(-0.252195\pi\)
0.702215 + 0.711965i \(0.252195\pi\)
\(348\) 0 0
\(349\) −6.43682 −0.344555 −0.172278 0.985048i \(-0.555113\pi\)
−0.172278 + 0.985048i \(0.555113\pi\)
\(350\) 0 0
\(351\) −17.7679 −0.948378
\(352\) 0 0
\(353\) 0.525688 0.0279795 0.0139898 0.999902i \(-0.495547\pi\)
0.0139898 + 0.999902i \(0.495547\pi\)
\(354\) 0 0
\(355\) −32.6243 −1.73152
\(356\) 0 0
\(357\) −43.6005 −2.30758
\(358\) 0 0
\(359\) −30.4177 −1.60538 −0.802692 0.596394i \(-0.796600\pi\)
−0.802692 + 0.596394i \(0.796600\pi\)
\(360\) 0 0
\(361\) −10.6742 −0.561802
\(362\) 0 0
\(363\) −5.72823 −0.300654
\(364\) 0 0
\(365\) 65.0656 3.40569
\(366\) 0 0
\(367\) 11.1794 0.583560 0.291780 0.956485i \(-0.405752\pi\)
0.291780 + 0.956485i \(0.405752\pi\)
\(368\) 0 0
\(369\) −2.15906 −0.112396
\(370\) 0 0
\(371\) −49.8700 −2.58912
\(372\) 0 0
\(373\) −9.66223 −0.500291 −0.250146 0.968208i \(-0.580479\pi\)
−0.250146 + 0.968208i \(0.580479\pi\)
\(374\) 0 0
\(375\) 53.3714 2.75609
\(376\) 0 0
\(377\) −42.6666 −2.19744
\(378\) 0 0
\(379\) −1.44402 −0.0741741 −0.0370871 0.999312i \(-0.511808\pi\)
−0.0370871 + 0.999312i \(0.511808\pi\)
\(380\) 0 0
\(381\) −34.7155 −1.77853
\(382\) 0 0
\(383\) 8.59068 0.438963 0.219482 0.975617i \(-0.429563\pi\)
0.219482 + 0.975617i \(0.429563\pi\)
\(384\) 0 0
\(385\) −65.5092 −3.33866
\(386\) 0 0
\(387\) 7.71415 0.392132
\(388\) 0 0
\(389\) 21.3765 1.08383 0.541916 0.840432i \(-0.317699\pi\)
0.541916 + 0.840432i \(0.317699\pi\)
\(390\) 0 0
\(391\) −18.7152 −0.946467
\(392\) 0 0
\(393\) 2.50940 0.126583
\(394\) 0 0
\(395\) 29.2371 1.47108
\(396\) 0 0
\(397\) 11.1524 0.559724 0.279862 0.960040i \(-0.409711\pi\)
0.279862 + 0.960040i \(0.409711\pi\)
\(398\) 0 0
\(399\) 25.1419 1.25867
\(400\) 0 0
\(401\) −18.8751 −0.942579 −0.471289 0.881979i \(-0.656211\pi\)
−0.471289 + 0.881979i \(0.656211\pi\)
\(402\) 0 0
\(403\) 29.5873 1.47385
\(404\) 0 0
\(405\) 44.9032 2.23126
\(406\) 0 0
\(407\) 24.5262 1.21572
\(408\) 0 0
\(409\) −12.0952 −0.598068 −0.299034 0.954242i \(-0.596664\pi\)
−0.299034 + 0.954242i \(0.596664\pi\)
\(410\) 0 0
\(411\) −29.6435 −1.46221
\(412\) 0 0
\(413\) 56.6649 2.78830
\(414\) 0 0
\(415\) 55.0442 2.70201
\(416\) 0 0
\(417\) 14.1310 0.691997
\(418\) 0 0
\(419\) 1.65757 0.0809776 0.0404888 0.999180i \(-0.487108\pi\)
0.0404888 + 0.999180i \(0.487108\pi\)
\(420\) 0 0
\(421\) 13.9205 0.678446 0.339223 0.940706i \(-0.389836\pi\)
0.339223 + 0.940706i \(0.389836\pi\)
\(422\) 0 0
\(423\) −2.94085 −0.142989
\(424\) 0 0
\(425\) −57.6710 −2.79746
\(426\) 0 0
\(427\) −20.7886 −1.00603
\(428\) 0 0
\(429\) −33.8762 −1.63556
\(430\) 0 0
\(431\) −11.5896 −0.558252 −0.279126 0.960255i \(-0.590045\pi\)
−0.279126 + 0.960255i \(0.590045\pi\)
\(432\) 0 0
\(433\) 3.97943 0.191239 0.0956196 0.995418i \(-0.469517\pi\)
0.0956196 + 0.995418i \(0.469517\pi\)
\(434\) 0 0
\(435\) 77.1287 3.69804
\(436\) 0 0
\(437\) 10.7919 0.516248
\(438\) 0 0
\(439\) −14.2532 −0.680266 −0.340133 0.940377i \(-0.610472\pi\)
−0.340133 + 0.940377i \(0.610472\pi\)
\(440\) 0 0
\(441\) 12.3217 0.586749
\(442\) 0 0
\(443\) 10.7195 0.509297 0.254649 0.967034i \(-0.418040\pi\)
0.254649 + 0.967034i \(0.418040\pi\)
\(444\) 0 0
\(445\) −13.3972 −0.635086
\(446\) 0 0
\(447\) 17.9666 0.849790
\(448\) 0 0
\(449\) −3.99923 −0.188735 −0.0943676 0.995537i \(-0.530083\pi\)
−0.0943676 + 0.995537i \(0.530083\pi\)
\(450\) 0 0
\(451\) 7.66422 0.360894
\(452\) 0 0
\(453\) −23.7340 −1.11512
\(454\) 0 0
\(455\) −79.6537 −3.73422
\(456\) 0 0
\(457\) 7.79687 0.364722 0.182361 0.983232i \(-0.441626\pi\)
0.182361 + 0.983232i \(0.441626\pi\)
\(458\) 0 0
\(459\) −19.6499 −0.917178
\(460\) 0 0
\(461\) 8.58359 0.399778 0.199889 0.979819i \(-0.435942\pi\)
0.199889 + 0.979819i \(0.435942\pi\)
\(462\) 0 0
\(463\) 14.6903 0.682714 0.341357 0.939934i \(-0.389114\pi\)
0.341357 + 0.939934i \(0.389114\pi\)
\(464\) 0 0
\(465\) −53.4852 −2.48032
\(466\) 0 0
\(467\) −21.9626 −1.01631 −0.508155 0.861266i \(-0.669672\pi\)
−0.508155 + 0.861266i \(0.669672\pi\)
\(468\) 0 0
\(469\) −6.64967 −0.307053
\(470\) 0 0
\(471\) −37.4375 −1.72503
\(472\) 0 0
\(473\) −27.3836 −1.25910
\(474\) 0 0
\(475\) 33.2555 1.52587
\(476\) 0 0
\(477\) 12.0716 0.552720
\(478\) 0 0
\(479\) −28.2867 −1.29245 −0.646225 0.763147i \(-0.723653\pi\)
−0.646225 + 0.763147i \(0.723653\pi\)
\(480\) 0 0
\(481\) 29.8218 1.35976
\(482\) 0 0
\(483\) 32.5891 1.48286
\(484\) 0 0
\(485\) −21.7787 −0.988922
\(486\) 0 0
\(487\) −14.6857 −0.665471 −0.332736 0.943020i \(-0.607972\pi\)
−0.332736 + 0.943020i \(0.607972\pi\)
\(488\) 0 0
\(489\) 29.0408 1.31327
\(490\) 0 0
\(491\) −11.9416 −0.538916 −0.269458 0.963012i \(-0.586844\pi\)
−0.269458 + 0.963012i \(0.586844\pi\)
\(492\) 0 0
\(493\) −47.1860 −2.12515
\(494\) 0 0
\(495\) 15.8572 0.712730
\(496\) 0 0
\(497\) −34.7550 −1.55898
\(498\) 0 0
\(499\) 19.1397 0.856811 0.428406 0.903586i \(-0.359075\pi\)
0.428406 + 0.903586i \(0.359075\pi\)
\(500\) 0 0
\(501\) 28.7470 1.28432
\(502\) 0 0
\(503\) −18.6493 −0.831531 −0.415765 0.909472i \(-0.636486\pi\)
−0.415765 + 0.909472i \(0.636486\pi\)
\(504\) 0 0
\(505\) −38.0559 −1.69346
\(506\) 0 0
\(507\) −15.0342 −0.667691
\(508\) 0 0
\(509\) 32.7192 1.45025 0.725126 0.688617i \(-0.241782\pi\)
0.725126 + 0.688617i \(0.241782\pi\)
\(510\) 0 0
\(511\) 69.3151 3.06632
\(512\) 0 0
\(513\) 11.3309 0.500273
\(514\) 0 0
\(515\) 51.1403 2.25351
\(516\) 0 0
\(517\) 10.4394 0.459124
\(518\) 0 0
\(519\) −21.5707 −0.946849
\(520\) 0 0
\(521\) 41.5230 1.81915 0.909577 0.415536i \(-0.136406\pi\)
0.909577 + 0.415536i \(0.136406\pi\)
\(522\) 0 0
\(523\) −10.1565 −0.444112 −0.222056 0.975034i \(-0.571277\pi\)
−0.222056 + 0.975034i \(0.571277\pi\)
\(524\) 0 0
\(525\) 100.424 4.38285
\(526\) 0 0
\(527\) 32.7213 1.42536
\(528\) 0 0
\(529\) −9.01139 −0.391799
\(530\) 0 0
\(531\) −13.7164 −0.595240
\(532\) 0 0
\(533\) 9.31905 0.403653
\(534\) 0 0
\(535\) 27.7523 1.19984
\(536\) 0 0
\(537\) −18.4712 −0.797089
\(538\) 0 0
\(539\) −43.7395 −1.88399
\(540\) 0 0
\(541\) −29.6609 −1.27522 −0.637611 0.770358i \(-0.720077\pi\)
−0.637611 + 0.770358i \(0.720077\pi\)
\(542\) 0 0
\(543\) −29.0909 −1.24841
\(544\) 0 0
\(545\) −81.0252 −3.47074
\(546\) 0 0
\(547\) −22.9225 −0.980093 −0.490047 0.871696i \(-0.663020\pi\)
−0.490047 + 0.871696i \(0.663020\pi\)
\(548\) 0 0
\(549\) 5.03211 0.214765
\(550\) 0 0
\(551\) 27.2094 1.15916
\(552\) 0 0
\(553\) 31.1465 1.32449
\(554\) 0 0
\(555\) −53.9090 −2.28831
\(556\) 0 0
\(557\) −38.3587 −1.62531 −0.812656 0.582744i \(-0.801979\pi\)
−0.812656 + 0.582744i \(0.801979\pi\)
\(558\) 0 0
\(559\) −33.2962 −1.40828
\(560\) 0 0
\(561\) −37.4644 −1.58175
\(562\) 0 0
\(563\) 23.0794 0.972682 0.486341 0.873769i \(-0.338331\pi\)
0.486341 + 0.873769i \(0.338331\pi\)
\(564\) 0 0
\(565\) 71.8369 3.02220
\(566\) 0 0
\(567\) 47.8358 2.00892
\(568\) 0 0
\(569\) −13.0016 −0.545056 −0.272528 0.962148i \(-0.587860\pi\)
−0.272528 + 0.962148i \(0.587860\pi\)
\(570\) 0 0
\(571\) −4.92912 −0.206277 −0.103139 0.994667i \(-0.532889\pi\)
−0.103139 + 0.994667i \(0.532889\pi\)
\(572\) 0 0
\(573\) 30.4459 1.27190
\(574\) 0 0
\(575\) 43.1061 1.79765
\(576\) 0 0
\(577\) −17.2166 −0.716737 −0.358369 0.933580i \(-0.616667\pi\)
−0.358369 + 0.933580i \(0.616667\pi\)
\(578\) 0 0
\(579\) 32.6940 1.35872
\(580\) 0 0
\(581\) 58.6391 2.43276
\(582\) 0 0
\(583\) −42.8515 −1.77473
\(584\) 0 0
\(585\) 19.2811 0.797174
\(586\) 0 0
\(587\) 26.1351 1.07871 0.539355 0.842079i \(-0.318668\pi\)
0.539355 + 0.842079i \(0.318668\pi\)
\(588\) 0 0
\(589\) −18.8684 −0.777461
\(590\) 0 0
\(591\) −34.5650 −1.42181
\(592\) 0 0
\(593\) 19.6410 0.806561 0.403280 0.915076i \(-0.367870\pi\)
0.403280 + 0.915076i \(0.367870\pi\)
\(594\) 0 0
\(595\) −88.0909 −3.61137
\(596\) 0 0
\(597\) 2.55775 0.104682
\(598\) 0 0
\(599\) −6.42881 −0.262674 −0.131337 0.991338i \(-0.541927\pi\)
−0.131337 + 0.991338i \(0.541927\pi\)
\(600\) 0 0
\(601\) −8.20805 −0.334813 −0.167407 0.985888i \(-0.553539\pi\)
−0.167407 + 0.985888i \(0.553539\pi\)
\(602\) 0 0
\(603\) 1.60963 0.0655491
\(604\) 0 0
\(605\) −11.5734 −0.470524
\(606\) 0 0
\(607\) −21.2459 −0.862345 −0.431172 0.902270i \(-0.641900\pi\)
−0.431172 + 0.902270i \(0.641900\pi\)
\(608\) 0 0
\(609\) 82.1660 3.32953
\(610\) 0 0
\(611\) 12.6934 0.513522
\(612\) 0 0
\(613\) 22.1014 0.892667 0.446333 0.894867i \(-0.352730\pi\)
0.446333 + 0.894867i \(0.352730\pi\)
\(614\) 0 0
\(615\) −16.8461 −0.679301
\(616\) 0 0
\(617\) 17.1066 0.688685 0.344342 0.938844i \(-0.388102\pi\)
0.344342 + 0.938844i \(0.388102\pi\)
\(618\) 0 0
\(619\) 17.7718 0.714308 0.357154 0.934045i \(-0.383747\pi\)
0.357154 + 0.934045i \(0.383747\pi\)
\(620\) 0 0
\(621\) 14.6873 0.589380
\(622\) 0 0
\(623\) −14.2721 −0.571801
\(624\) 0 0
\(625\) 50.2056 2.00822
\(626\) 0 0
\(627\) 21.6035 0.862762
\(628\) 0 0
\(629\) 32.9806 1.31502
\(630\) 0 0
\(631\) 8.81650 0.350979 0.175490 0.984481i \(-0.443849\pi\)
0.175490 + 0.984481i \(0.443849\pi\)
\(632\) 0 0
\(633\) 3.33307 0.132478
\(634\) 0 0
\(635\) −70.1395 −2.78340
\(636\) 0 0
\(637\) −53.1836 −2.10721
\(638\) 0 0
\(639\) 8.41284 0.332807
\(640\) 0 0
\(641\) 30.3490 1.19871 0.599357 0.800482i \(-0.295423\pi\)
0.599357 + 0.800482i \(0.295423\pi\)
\(642\) 0 0
\(643\) −12.3081 −0.485382 −0.242691 0.970104i \(-0.578030\pi\)
−0.242691 + 0.970104i \(0.578030\pi\)
\(644\) 0 0
\(645\) 60.1897 2.36997
\(646\) 0 0
\(647\) 14.4382 0.567623 0.283812 0.958880i \(-0.408401\pi\)
0.283812 + 0.958880i \(0.408401\pi\)
\(648\) 0 0
\(649\) 48.6902 1.91126
\(650\) 0 0
\(651\) −56.9783 −2.23316
\(652\) 0 0
\(653\) 14.0299 0.549034 0.274517 0.961582i \(-0.411482\pi\)
0.274517 + 0.961582i \(0.411482\pi\)
\(654\) 0 0
\(655\) 5.07002 0.198102
\(656\) 0 0
\(657\) −16.7785 −0.654591
\(658\) 0 0
\(659\) −15.1215 −0.589049 −0.294525 0.955644i \(-0.595161\pi\)
−0.294525 + 0.955644i \(0.595161\pi\)
\(660\) 0 0
\(661\) 35.8330 1.39374 0.696871 0.717197i \(-0.254575\pi\)
0.696871 + 0.717197i \(0.254575\pi\)
\(662\) 0 0
\(663\) −45.5536 −1.76916
\(664\) 0 0
\(665\) 50.7968 1.96982
\(666\) 0 0
\(667\) 35.2691 1.36562
\(668\) 0 0
\(669\) 15.0747 0.582823
\(670\) 0 0
\(671\) −17.8629 −0.689590
\(672\) 0 0
\(673\) −6.66821 −0.257041 −0.128520 0.991707i \(-0.541023\pi\)
−0.128520 + 0.991707i \(0.541023\pi\)
\(674\) 0 0
\(675\) 45.2590 1.74202
\(676\) 0 0
\(677\) 30.3557 1.16667 0.583333 0.812233i \(-0.301748\pi\)
0.583333 + 0.812233i \(0.301748\pi\)
\(678\) 0 0
\(679\) −23.2011 −0.890377
\(680\) 0 0
\(681\) −53.6328 −2.05521
\(682\) 0 0
\(683\) −38.4006 −1.46936 −0.734679 0.678415i \(-0.762667\pi\)
−0.734679 + 0.678415i \(0.762667\pi\)
\(684\) 0 0
\(685\) −59.8921 −2.28836
\(686\) 0 0
\(687\) −7.11045 −0.271281
\(688\) 0 0
\(689\) −52.1039 −1.98500
\(690\) 0 0
\(691\) 41.7687 1.58895 0.794477 0.607294i \(-0.207745\pi\)
0.794477 + 0.607294i \(0.207745\pi\)
\(692\) 0 0
\(693\) 16.8929 0.641707
\(694\) 0 0
\(695\) 28.5503 1.08298
\(696\) 0 0
\(697\) 10.3062 0.390373
\(698\) 0 0
\(699\) −25.6928 −0.971790
\(700\) 0 0
\(701\) −20.3777 −0.769655 −0.384827 0.922989i \(-0.625739\pi\)
−0.384827 + 0.922989i \(0.625739\pi\)
\(702\) 0 0
\(703\) −19.0180 −0.717276
\(704\) 0 0
\(705\) −22.9460 −0.864197
\(706\) 0 0
\(707\) −40.5413 −1.52471
\(708\) 0 0
\(709\) 34.6746 1.30223 0.651115 0.758979i \(-0.274301\pi\)
0.651115 + 0.758979i \(0.274301\pi\)
\(710\) 0 0
\(711\) −7.53936 −0.282748
\(712\) 0 0
\(713\) −24.4575 −0.915939
\(714\) 0 0
\(715\) −68.4437 −2.55965
\(716\) 0 0
\(717\) −38.9560 −1.45484
\(718\) 0 0
\(719\) 12.8307 0.478504 0.239252 0.970958i \(-0.423098\pi\)
0.239252 + 0.970958i \(0.423098\pi\)
\(720\) 0 0
\(721\) 54.4803 2.02895
\(722\) 0 0
\(723\) −42.1222 −1.56654
\(724\) 0 0
\(725\) 108.682 4.03635
\(726\) 0 0
\(727\) 28.3677 1.05210 0.526050 0.850454i \(-0.323673\pi\)
0.526050 + 0.850454i \(0.323673\pi\)
\(728\) 0 0
\(729\) 12.1242 0.449043
\(730\) 0 0
\(731\) −36.8230 −1.36195
\(732\) 0 0
\(733\) 33.4349 1.23495 0.617473 0.786592i \(-0.288157\pi\)
0.617473 + 0.786592i \(0.288157\pi\)
\(734\) 0 0
\(735\) 96.1404 3.54619
\(736\) 0 0
\(737\) −5.71383 −0.210472
\(738\) 0 0
\(739\) −2.44248 −0.0898481 −0.0449240 0.998990i \(-0.514305\pi\)
−0.0449240 + 0.998990i \(0.514305\pi\)
\(740\) 0 0
\(741\) 26.2681 0.964982
\(742\) 0 0
\(743\) 1.04852 0.0384664 0.0192332 0.999815i \(-0.493878\pi\)
0.0192332 + 0.999815i \(0.493878\pi\)
\(744\) 0 0
\(745\) 36.2998 1.32992
\(746\) 0 0
\(747\) −14.1942 −0.519340
\(748\) 0 0
\(749\) 29.5648 1.08027
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 27.2642 0.993563
\(754\) 0 0
\(755\) −47.9524 −1.74517
\(756\) 0 0
\(757\) −41.2173 −1.49807 −0.749034 0.662532i \(-0.769482\pi\)
−0.749034 + 0.662532i \(0.769482\pi\)
\(758\) 0 0
\(759\) 28.0027 1.01643
\(760\) 0 0
\(761\) 39.9421 1.44790 0.723950 0.689852i \(-0.242324\pi\)
0.723950 + 0.689852i \(0.242324\pi\)
\(762\) 0 0
\(763\) −86.3169 −3.12488
\(764\) 0 0
\(765\) 21.3234 0.770949
\(766\) 0 0
\(767\) 59.2032 2.13770
\(768\) 0 0
\(769\) 31.8890 1.14995 0.574973 0.818173i \(-0.305013\pi\)
0.574973 + 0.818173i \(0.305013\pi\)
\(770\) 0 0
\(771\) −14.8551 −0.534994
\(772\) 0 0
\(773\) 3.01425 0.108415 0.0542075 0.998530i \(-0.482737\pi\)
0.0542075 + 0.998530i \(0.482737\pi\)
\(774\) 0 0
\(775\) −75.3660 −2.70723
\(776\) 0 0
\(777\) −57.4298 −2.06028
\(778\) 0 0
\(779\) −5.94295 −0.212928
\(780\) 0 0
\(781\) −29.8638 −1.06861
\(782\) 0 0
\(783\) 37.0306 1.32336
\(784\) 0 0
\(785\) −75.6391 −2.69967
\(786\) 0 0
\(787\) −55.8741 −1.99170 −0.995848 0.0910319i \(-0.970983\pi\)
−0.995848 + 0.0910319i \(0.970983\pi\)
\(788\) 0 0
\(789\) −14.7463 −0.524984
\(790\) 0 0
\(791\) 76.5285 2.72104
\(792\) 0 0
\(793\) −21.7198 −0.771293
\(794\) 0 0
\(795\) 94.1886 3.34052
\(796\) 0 0
\(797\) −46.2623 −1.63870 −0.819348 0.573296i \(-0.805664\pi\)
−0.819348 + 0.573296i \(0.805664\pi\)
\(798\) 0 0
\(799\) 14.0380 0.496628
\(800\) 0 0
\(801\) 3.45473 0.122067
\(802\) 0 0
\(803\) 59.5600 2.10183
\(804\) 0 0
\(805\) 65.8434 2.32067
\(806\) 0 0
\(807\) −62.7440 −2.20869
\(808\) 0 0
\(809\) 38.6556 1.35906 0.679529 0.733649i \(-0.262184\pi\)
0.679529 + 0.733649i \(0.262184\pi\)
\(810\) 0 0
\(811\) 26.0213 0.913733 0.456866 0.889535i \(-0.348972\pi\)
0.456866 + 0.889535i \(0.348972\pi\)
\(812\) 0 0
\(813\) 3.86052 0.135394
\(814\) 0 0
\(815\) 58.6743 2.05527
\(816\) 0 0
\(817\) 21.2337 0.742872
\(818\) 0 0
\(819\) 20.5403 0.717737
\(820\) 0 0
\(821\) 15.8446 0.552980 0.276490 0.961017i \(-0.410829\pi\)
0.276490 + 0.961017i \(0.410829\pi\)
\(822\) 0 0
\(823\) 4.37684 0.152567 0.0762835 0.997086i \(-0.475695\pi\)
0.0762835 + 0.997086i \(0.475695\pi\)
\(824\) 0 0
\(825\) 86.2907 3.00426
\(826\) 0 0
\(827\) −36.3887 −1.26536 −0.632680 0.774413i \(-0.718045\pi\)
−0.632680 + 0.774413i \(0.718045\pi\)
\(828\) 0 0
\(829\) −15.8605 −0.550857 −0.275428 0.961322i \(-0.588820\pi\)
−0.275428 + 0.961322i \(0.588820\pi\)
\(830\) 0 0
\(831\) 55.7361 1.93347
\(832\) 0 0
\(833\) −58.8170 −2.03789
\(834\) 0 0
\(835\) 58.0806 2.00996
\(836\) 0 0
\(837\) −25.6790 −0.887595
\(838\) 0 0
\(839\) −6.07994 −0.209903 −0.104951 0.994477i \(-0.533469\pi\)
−0.104951 + 0.994477i \(0.533469\pi\)
\(840\) 0 0
\(841\) 59.9229 2.06631
\(842\) 0 0
\(843\) −45.4297 −1.56468
\(844\) 0 0
\(845\) −30.3752 −1.04494
\(846\) 0 0
\(847\) −12.3292 −0.423637
\(848\) 0 0
\(849\) 8.88215 0.304835
\(850\) 0 0
\(851\) −24.6513 −0.845034
\(852\) 0 0
\(853\) −0.709262 −0.0242847 −0.0121423 0.999926i \(-0.503865\pi\)
−0.0121423 + 0.999926i \(0.503865\pi\)
\(854\) 0 0
\(855\) −12.2959 −0.420512
\(856\) 0 0
\(857\) −29.8262 −1.01884 −0.509422 0.860517i \(-0.670141\pi\)
−0.509422 + 0.860517i \(0.670141\pi\)
\(858\) 0 0
\(859\) −19.8437 −0.677059 −0.338529 0.940956i \(-0.609929\pi\)
−0.338529 + 0.940956i \(0.609929\pi\)
\(860\) 0 0
\(861\) −17.9463 −0.611609
\(862\) 0 0
\(863\) −23.9648 −0.815771 −0.407886 0.913033i \(-0.633734\pi\)
−0.407886 + 0.913033i \(0.633734\pi\)
\(864\) 0 0
\(865\) −43.5817 −1.48182
\(866\) 0 0
\(867\) −16.1742 −0.549306
\(868\) 0 0
\(869\) 26.7631 0.907877
\(870\) 0 0
\(871\) −6.94754 −0.235409
\(872\) 0 0
\(873\) 5.61609 0.190076
\(874\) 0 0
\(875\) 114.874 3.88347
\(876\) 0 0
\(877\) −17.0095 −0.574369 −0.287184 0.957875i \(-0.592719\pi\)
−0.287184 + 0.957875i \(0.592719\pi\)
\(878\) 0 0
\(879\) −58.5593 −1.97516
\(880\) 0 0
\(881\) 50.4179 1.69862 0.849311 0.527893i \(-0.177018\pi\)
0.849311 + 0.527893i \(0.177018\pi\)
\(882\) 0 0
\(883\) 0.354567 0.0119321 0.00596607 0.999982i \(-0.498101\pi\)
0.00596607 + 0.999982i \(0.498101\pi\)
\(884\) 0 0
\(885\) −107.022 −3.59751
\(886\) 0 0
\(887\) −23.5670 −0.791303 −0.395651 0.918401i \(-0.629481\pi\)
−0.395651 + 0.918401i \(0.629481\pi\)
\(888\) 0 0
\(889\) −74.7203 −2.50604
\(890\) 0 0
\(891\) 41.1037 1.37702
\(892\) 0 0
\(893\) −8.09487 −0.270885
\(894\) 0 0
\(895\) −37.3193 −1.24745
\(896\) 0 0
\(897\) 34.0490 1.13686
\(898\) 0 0
\(899\) −61.6639 −2.05661
\(900\) 0 0
\(901\) −57.6229 −1.91970
\(902\) 0 0
\(903\) 64.1207 2.13380
\(904\) 0 0
\(905\) −58.7755 −1.95376
\(906\) 0 0
\(907\) −29.3173 −0.973464 −0.486732 0.873551i \(-0.661811\pi\)
−0.486732 + 0.873551i \(0.661811\pi\)
\(908\) 0 0
\(909\) 9.81347 0.325492
\(910\) 0 0
\(911\) −3.44606 −0.114173 −0.0570865 0.998369i \(-0.518181\pi\)
−0.0570865 + 0.998369i \(0.518181\pi\)
\(912\) 0 0
\(913\) 50.3865 1.66755
\(914\) 0 0
\(915\) 39.2631 1.29800
\(916\) 0 0
\(917\) 5.40114 0.178361
\(918\) 0 0
\(919\) −1.98958 −0.0656301 −0.0328150 0.999461i \(-0.510447\pi\)
−0.0328150 + 0.999461i \(0.510447\pi\)
\(920\) 0 0
\(921\) −14.9426 −0.492376
\(922\) 0 0
\(923\) −36.3119 −1.19522
\(924\) 0 0
\(925\) −75.9632 −2.49765
\(926\) 0 0
\(927\) −13.1876 −0.433136
\(928\) 0 0
\(929\) −12.7657 −0.418829 −0.209415 0.977827i \(-0.567156\pi\)
−0.209415 + 0.977827i \(0.567156\pi\)
\(930\) 0 0
\(931\) 33.9163 1.11156
\(932\) 0 0
\(933\) −54.6182 −1.78812
\(934\) 0 0
\(935\) −75.6935 −2.47544
\(936\) 0 0
\(937\) 22.5907 0.738005 0.369002 0.929428i \(-0.379699\pi\)
0.369002 + 0.929428i \(0.379699\pi\)
\(938\) 0 0
\(939\) 69.5403 2.26936
\(940\) 0 0
\(941\) −41.5944 −1.35594 −0.677970 0.735090i \(-0.737140\pi\)
−0.677970 + 0.735090i \(0.737140\pi\)
\(942\) 0 0
\(943\) −7.70331 −0.250854
\(944\) 0 0
\(945\) 69.1319 2.24886
\(946\) 0 0
\(947\) −52.4274 −1.70366 −0.851831 0.523817i \(-0.824507\pi\)
−0.851831 + 0.523817i \(0.824507\pi\)
\(948\) 0 0
\(949\) 72.4200 2.35085
\(950\) 0 0
\(951\) 61.3651 1.98990
\(952\) 0 0
\(953\) 46.8538 1.51774 0.758871 0.651240i \(-0.225751\pi\)
0.758871 + 0.651240i \(0.225751\pi\)
\(954\) 0 0
\(955\) 61.5132 1.99052
\(956\) 0 0
\(957\) 70.6024 2.28225
\(958\) 0 0
\(959\) −63.8036 −2.06033
\(960\) 0 0
\(961\) 11.7610 0.379388
\(962\) 0 0
\(963\) −7.15648 −0.230614
\(964\) 0 0
\(965\) 66.0553 2.12640
\(966\) 0 0
\(967\) 0.831883 0.0267515 0.0133758 0.999911i \(-0.495742\pi\)
0.0133758 + 0.999911i \(0.495742\pi\)
\(968\) 0 0
\(969\) 29.0505 0.933236
\(970\) 0 0
\(971\) 16.6297 0.533672 0.266836 0.963742i \(-0.414022\pi\)
0.266836 + 0.963742i \(0.414022\pi\)
\(972\) 0 0
\(973\) 30.4150 0.975059
\(974\) 0 0
\(975\) 104.922 3.36020
\(976\) 0 0
\(977\) −42.9995 −1.37568 −0.687839 0.725864i \(-0.741440\pi\)
−0.687839 + 0.725864i \(0.741440\pi\)
\(978\) 0 0
\(979\) −12.2635 −0.391945
\(980\) 0 0
\(981\) 20.8940 0.667093
\(982\) 0 0
\(983\) 45.4079 1.44829 0.724143 0.689650i \(-0.242235\pi\)
0.724143 + 0.689650i \(0.242235\pi\)
\(984\) 0 0
\(985\) −69.8354 −2.22514
\(986\) 0 0
\(987\) −24.4446 −0.778081
\(988\) 0 0
\(989\) 27.5233 0.875189
\(990\) 0 0
\(991\) −23.5008 −0.746527 −0.373264 0.927725i \(-0.621761\pi\)
−0.373264 + 0.927725i \(0.621761\pi\)
\(992\) 0 0
\(993\) 36.1190 1.14620
\(994\) 0 0
\(995\) 5.16769 0.163827
\(996\) 0 0
\(997\) −35.7127 −1.13103 −0.565517 0.824737i \(-0.691323\pi\)
−0.565517 + 0.824737i \(0.691323\pi\)
\(998\) 0 0
\(999\) −25.8824 −0.818884
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 6008.2.a.b.1.12 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.12 44 1.1 even 1 trivial