Properties

Label 6008.2.a.b.1.28
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 1.28
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.320895 q^{3} +1.20543 q^{5} +2.62503 q^{7} -2.89703 q^{9} +O(q^{10})\) \(q+0.320895 q^{3} +1.20543 q^{5} +2.62503 q^{7} -2.89703 q^{9} +1.62663 q^{11} -3.31735 q^{13} +0.386816 q^{15} -2.66730 q^{17} +4.21646 q^{19} +0.842357 q^{21} -1.23332 q^{23} -3.54694 q^{25} -1.89232 q^{27} -9.10559 q^{29} +5.03784 q^{31} +0.521975 q^{33} +3.16428 q^{35} -8.64255 q^{37} -1.06452 q^{39} -6.06053 q^{41} -5.22644 q^{43} -3.49216 q^{45} -2.33691 q^{47} -0.109239 q^{49} -0.855921 q^{51} +1.51550 q^{53} +1.96078 q^{55} +1.35304 q^{57} +9.59427 q^{59} +7.73345 q^{61} -7.60477 q^{63} -3.99883 q^{65} -11.1614 q^{67} -0.395764 q^{69} -7.47848 q^{71} -3.57210 q^{73} -1.13819 q^{75} +4.26993 q^{77} +2.62845 q^{79} +8.08384 q^{81} -13.9519 q^{83} -3.21523 q^{85} -2.92193 q^{87} +11.3260 q^{89} -8.70812 q^{91} +1.61662 q^{93} +5.08265 q^{95} -16.2165 q^{97} -4.71238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 0.320895 0.185269 0.0926343 0.995700i \(-0.470471\pi\)
0.0926343 + 0.995700i \(0.470471\pi\)
\(4\) 0 0
\(5\) 1.20543 0.539084 0.269542 0.962989i \(-0.413128\pi\)
0.269542 + 0.962989i \(0.413128\pi\)
\(6\) 0 0
\(7\) 2.62503 0.992166 0.496083 0.868275i \(-0.334771\pi\)
0.496083 + 0.868275i \(0.334771\pi\)
\(8\) 0 0
\(9\) −2.89703 −0.965676
\(10\) 0 0
\(11\) 1.62663 0.490446 0.245223 0.969467i \(-0.421139\pi\)
0.245223 + 0.969467i \(0.421139\pi\)
\(12\) 0 0
\(13\) −3.31735 −0.920067 −0.460033 0.887902i \(-0.652163\pi\)
−0.460033 + 0.887902i \(0.652163\pi\)
\(14\) 0 0
\(15\) 0.386816 0.0998753
\(16\) 0 0
\(17\) −2.66730 −0.646914 −0.323457 0.946243i \(-0.604845\pi\)
−0.323457 + 0.946243i \(0.604845\pi\)
\(18\) 0 0
\(19\) 4.21646 0.967323 0.483661 0.875255i \(-0.339307\pi\)
0.483661 + 0.875255i \(0.339307\pi\)
\(20\) 0 0
\(21\) 0.842357 0.183817
\(22\) 0 0
\(23\) −1.23332 −0.257164 −0.128582 0.991699i \(-0.541043\pi\)
−0.128582 + 0.991699i \(0.541043\pi\)
\(24\) 0 0
\(25\) −3.54694 −0.709388
\(26\) 0 0
\(27\) −1.89232 −0.364178
\(28\) 0 0
\(29\) −9.10559 −1.69086 −0.845432 0.534082i \(-0.820657\pi\)
−0.845432 + 0.534082i \(0.820657\pi\)
\(30\) 0 0
\(31\) 5.03784 0.904823 0.452412 0.891809i \(-0.350564\pi\)
0.452412 + 0.891809i \(0.350564\pi\)
\(32\) 0 0
\(33\) 0.521975 0.0908642
\(34\) 0 0
\(35\) 3.16428 0.534861
\(36\) 0 0
\(37\) −8.64255 −1.42083 −0.710414 0.703784i \(-0.751492\pi\)
−0.710414 + 0.703784i \(0.751492\pi\)
\(38\) 0 0
\(39\) −1.06452 −0.170459
\(40\) 0 0
\(41\) −6.06053 −0.946496 −0.473248 0.880929i \(-0.656919\pi\)
−0.473248 + 0.880929i \(0.656919\pi\)
\(42\) 0 0
\(43\) −5.22644 −0.797025 −0.398513 0.917163i \(-0.630473\pi\)
−0.398513 + 0.917163i \(0.630473\pi\)
\(44\) 0 0
\(45\) −3.49216 −0.520580
\(46\) 0 0
\(47\) −2.33691 −0.340874 −0.170437 0.985369i \(-0.554518\pi\)
−0.170437 + 0.985369i \(0.554518\pi\)
\(48\) 0 0
\(49\) −0.109239 −0.0156056
\(50\) 0 0
\(51\) −0.855921 −0.119853
\(52\) 0 0
\(53\) 1.51550 0.208170 0.104085 0.994568i \(-0.466809\pi\)
0.104085 + 0.994568i \(0.466809\pi\)
\(54\) 0 0
\(55\) 1.96078 0.264392
\(56\) 0 0
\(57\) 1.35304 0.179215
\(58\) 0 0
\(59\) 9.59427 1.24907 0.624534 0.780998i \(-0.285289\pi\)
0.624534 + 0.780998i \(0.285289\pi\)
\(60\) 0 0
\(61\) 7.73345 0.990167 0.495083 0.868845i \(-0.335138\pi\)
0.495083 + 0.868845i \(0.335138\pi\)
\(62\) 0 0
\(63\) −7.60477 −0.958111
\(64\) 0 0
\(65\) −3.99883 −0.495993
\(66\) 0 0
\(67\) −11.1614 −1.36358 −0.681792 0.731546i \(-0.738799\pi\)
−0.681792 + 0.731546i \(0.738799\pi\)
\(68\) 0 0
\(69\) −0.395764 −0.0476444
\(70\) 0 0
\(71\) −7.47848 −0.887532 −0.443766 0.896143i \(-0.646358\pi\)
−0.443766 + 0.896143i \(0.646358\pi\)
\(72\) 0 0
\(73\) −3.57210 −0.418083 −0.209042 0.977907i \(-0.567034\pi\)
−0.209042 + 0.977907i \(0.567034\pi\)
\(74\) 0 0
\(75\) −1.13819 −0.131427
\(76\) 0 0
\(77\) 4.26993 0.486604
\(78\) 0 0
\(79\) 2.62845 0.295723 0.147862 0.989008i \(-0.452761\pi\)
0.147862 + 0.989008i \(0.452761\pi\)
\(80\) 0 0
\(81\) 8.08384 0.898205
\(82\) 0 0
\(83\) −13.9519 −1.53142 −0.765709 0.643187i \(-0.777612\pi\)
−0.765709 + 0.643187i \(0.777612\pi\)
\(84\) 0 0
\(85\) −3.21523 −0.348741
\(86\) 0 0
\(87\) −2.92193 −0.313264
\(88\) 0 0
\(89\) 11.3260 1.20055 0.600276 0.799793i \(-0.295057\pi\)
0.600276 + 0.799793i \(0.295057\pi\)
\(90\) 0 0
\(91\) −8.70812 −0.912859
\(92\) 0 0
\(93\) 1.61662 0.167635
\(94\) 0 0
\(95\) 5.08265 0.521468
\(96\) 0 0
\(97\) −16.2165 −1.64654 −0.823269 0.567651i \(-0.807852\pi\)
−0.823269 + 0.567651i \(0.807852\pi\)
\(98\) 0 0
\(99\) −4.71238 −0.473612
\(100\) 0 0
\(101\) 3.00960 0.299467 0.149733 0.988726i \(-0.452158\pi\)
0.149733 + 0.988726i \(0.452158\pi\)
\(102\) 0 0
\(103\) 3.21638 0.316919 0.158460 0.987365i \(-0.449347\pi\)
0.158460 + 0.987365i \(0.449347\pi\)
\(104\) 0 0
\(105\) 1.01540 0.0990930
\(106\) 0 0
\(107\) 13.5902 1.31381 0.656907 0.753972i \(-0.271864\pi\)
0.656907 + 0.753972i \(0.271864\pi\)
\(108\) 0 0
\(109\) 1.40152 0.134241 0.0671205 0.997745i \(-0.478619\pi\)
0.0671205 + 0.997745i \(0.478619\pi\)
\(110\) 0 0
\(111\) −2.77335 −0.263235
\(112\) 0 0
\(113\) 5.17404 0.486733 0.243366 0.969934i \(-0.421748\pi\)
0.243366 + 0.969934i \(0.421748\pi\)
\(114\) 0 0
\(115\) −1.48667 −0.138633
\(116\) 0 0
\(117\) 9.61044 0.888486
\(118\) 0 0
\(119\) −7.00172 −0.641847
\(120\) 0 0
\(121\) −8.35409 −0.759463
\(122\) 0 0
\(123\) −1.94479 −0.175356
\(124\) 0 0
\(125\) −10.3027 −0.921504
\(126\) 0 0
\(127\) −14.5742 −1.29325 −0.646624 0.762809i \(-0.723820\pi\)
−0.646624 + 0.762809i \(0.723820\pi\)
\(128\) 0 0
\(129\) −1.67714 −0.147664
\(130\) 0 0
\(131\) 5.71162 0.499027 0.249513 0.968371i \(-0.419729\pi\)
0.249513 + 0.968371i \(0.419729\pi\)
\(132\) 0 0
\(133\) 11.0683 0.959745
\(134\) 0 0
\(135\) −2.28106 −0.196323
\(136\) 0 0
\(137\) 0.504909 0.0431373 0.0215686 0.999767i \(-0.493134\pi\)
0.0215686 + 0.999767i \(0.493134\pi\)
\(138\) 0 0
\(139\) 0.0652126 0.00553126 0.00276563 0.999996i \(-0.499120\pi\)
0.00276563 + 0.999996i \(0.499120\pi\)
\(140\) 0 0
\(141\) −0.749903 −0.0631532
\(142\) 0 0
\(143\) −5.39608 −0.451243
\(144\) 0 0
\(145\) −10.9761 −0.911518
\(146\) 0 0
\(147\) −0.0350544 −0.00289124
\(148\) 0 0
\(149\) −15.1474 −1.24092 −0.620461 0.784238i \(-0.713054\pi\)
−0.620461 + 0.784238i \(0.713054\pi\)
\(150\) 0 0
\(151\) −7.53357 −0.613074 −0.306537 0.951859i \(-0.599170\pi\)
−0.306537 + 0.951859i \(0.599170\pi\)
\(152\) 0 0
\(153\) 7.72723 0.624709
\(154\) 0 0
\(155\) 6.07276 0.487776
\(156\) 0 0
\(157\) 2.54733 0.203299 0.101650 0.994820i \(-0.467588\pi\)
0.101650 + 0.994820i \(0.467588\pi\)
\(158\) 0 0
\(159\) 0.486316 0.0385674
\(160\) 0 0
\(161\) −3.23749 −0.255150
\(162\) 0 0
\(163\) −22.3582 −1.75123 −0.875614 0.483011i \(-0.839543\pi\)
−0.875614 + 0.483011i \(0.839543\pi\)
\(164\) 0 0
\(165\) 0.629204 0.0489835
\(166\) 0 0
\(167\) 4.90327 0.379427 0.189713 0.981840i \(-0.439244\pi\)
0.189713 + 0.981840i \(0.439244\pi\)
\(168\) 0 0
\(169\) −1.99521 −0.153478
\(170\) 0 0
\(171\) −12.2152 −0.934120
\(172\) 0 0
\(173\) 4.74521 0.360771 0.180386 0.983596i \(-0.442265\pi\)
0.180386 + 0.983596i \(0.442265\pi\)
\(174\) 0 0
\(175\) −9.31081 −0.703831
\(176\) 0 0
\(177\) 3.07875 0.231413
\(178\) 0 0
\(179\) 12.1050 0.904770 0.452385 0.891823i \(-0.350573\pi\)
0.452385 + 0.891823i \(0.350573\pi\)
\(180\) 0 0
\(181\) −3.83231 −0.284853 −0.142427 0.989805i \(-0.545491\pi\)
−0.142427 + 0.989805i \(0.545491\pi\)
\(182\) 0 0
\(183\) 2.48162 0.183447
\(184\) 0 0
\(185\) −10.4180 −0.765945
\(186\) 0 0
\(187\) −4.33869 −0.317277
\(188\) 0 0
\(189\) −4.96740 −0.361325
\(190\) 0 0
\(191\) 19.9858 1.44612 0.723060 0.690786i \(-0.242735\pi\)
0.723060 + 0.690786i \(0.242735\pi\)
\(192\) 0 0
\(193\) 18.4999 1.33165 0.665825 0.746108i \(-0.268080\pi\)
0.665825 + 0.746108i \(0.268080\pi\)
\(194\) 0 0
\(195\) −1.28320 −0.0918920
\(196\) 0 0
\(197\) −19.7677 −1.40839 −0.704196 0.710006i \(-0.748692\pi\)
−0.704196 + 0.710006i \(0.748692\pi\)
\(198\) 0 0
\(199\) 13.2396 0.938527 0.469264 0.883058i \(-0.344519\pi\)
0.469264 + 0.883058i \(0.344519\pi\)
\(200\) 0 0
\(201\) −3.58164 −0.252629
\(202\) 0 0
\(203\) −23.9024 −1.67762
\(204\) 0 0
\(205\) −7.30554 −0.510241
\(206\) 0 0
\(207\) 3.57295 0.248337
\(208\) 0 0
\(209\) 6.85861 0.474420
\(210\) 0 0
\(211\) 14.0915 0.970099 0.485050 0.874487i \(-0.338802\pi\)
0.485050 + 0.874487i \(0.338802\pi\)
\(212\) 0 0
\(213\) −2.39980 −0.164432
\(214\) 0 0
\(215\) −6.30010 −0.429663
\(216\) 0 0
\(217\) 13.2245 0.897736
\(218\) 0 0
\(219\) −1.14627 −0.0774577
\(220\) 0 0
\(221\) 8.84834 0.595204
\(222\) 0 0
\(223\) −4.51822 −0.302563 −0.151281 0.988491i \(-0.548340\pi\)
−0.151281 + 0.988491i \(0.548340\pi\)
\(224\) 0 0
\(225\) 10.2756 0.685039
\(226\) 0 0
\(227\) −8.24400 −0.547174 −0.273587 0.961847i \(-0.588210\pi\)
−0.273587 + 0.961847i \(0.588210\pi\)
\(228\) 0 0
\(229\) 24.4909 1.61840 0.809201 0.587532i \(-0.199900\pi\)
0.809201 + 0.587532i \(0.199900\pi\)
\(230\) 0 0
\(231\) 1.37020 0.0901525
\(232\) 0 0
\(233\) 14.5272 0.951706 0.475853 0.879525i \(-0.342139\pi\)
0.475853 + 0.879525i \(0.342139\pi\)
\(234\) 0 0
\(235\) −2.81698 −0.183760
\(236\) 0 0
\(237\) 0.843454 0.0547882
\(238\) 0 0
\(239\) −17.7484 −1.14805 −0.574026 0.818837i \(-0.694619\pi\)
−0.574026 + 0.818837i \(0.694619\pi\)
\(240\) 0 0
\(241\) 21.6534 1.39482 0.697409 0.716674i \(-0.254336\pi\)
0.697409 + 0.716674i \(0.254336\pi\)
\(242\) 0 0
\(243\) 8.27103 0.530587
\(244\) 0 0
\(245\) −0.131680 −0.00841275
\(246\) 0 0
\(247\) −13.9875 −0.890002
\(248\) 0 0
\(249\) −4.47708 −0.283724
\(250\) 0 0
\(251\) 0.705326 0.0445198 0.0222599 0.999752i \(-0.492914\pi\)
0.0222599 + 0.999752i \(0.492914\pi\)
\(252\) 0 0
\(253\) −2.00614 −0.126125
\(254\) 0 0
\(255\) −1.03175 −0.0646108
\(256\) 0 0
\(257\) −0.809803 −0.0505141 −0.0252571 0.999681i \(-0.508040\pi\)
−0.0252571 + 0.999681i \(0.508040\pi\)
\(258\) 0 0
\(259\) −22.6869 −1.40970
\(260\) 0 0
\(261\) 26.3791 1.63283
\(262\) 0 0
\(263\) −14.1848 −0.874672 −0.437336 0.899298i \(-0.644078\pi\)
−0.437336 + 0.899298i \(0.644078\pi\)
\(264\) 0 0
\(265\) 1.82683 0.112221
\(266\) 0 0
\(267\) 3.63445 0.222425
\(268\) 0 0
\(269\) 0.154171 0.00939995 0.00469997 0.999989i \(-0.498504\pi\)
0.00469997 + 0.999989i \(0.498504\pi\)
\(270\) 0 0
\(271\) 16.4281 0.997934 0.498967 0.866621i \(-0.333713\pi\)
0.498967 + 0.866621i \(0.333713\pi\)
\(272\) 0 0
\(273\) −2.79439 −0.169124
\(274\) 0 0
\(275\) −5.76955 −0.347917
\(276\) 0 0
\(277\) −29.8540 −1.79375 −0.896877 0.442281i \(-0.854170\pi\)
−0.896877 + 0.442281i \(0.854170\pi\)
\(278\) 0 0
\(279\) −14.5948 −0.873766
\(280\) 0 0
\(281\) 14.8895 0.888233 0.444117 0.895969i \(-0.353518\pi\)
0.444117 + 0.895969i \(0.353518\pi\)
\(282\) 0 0
\(283\) 25.5236 1.51722 0.758610 0.651545i \(-0.225879\pi\)
0.758610 + 0.651545i \(0.225879\pi\)
\(284\) 0 0
\(285\) 1.63099 0.0966117
\(286\) 0 0
\(287\) −15.9091 −0.939082
\(288\) 0 0
\(289\) −9.88554 −0.581502
\(290\) 0 0
\(291\) −5.20380 −0.305052
\(292\) 0 0
\(293\) 6.46654 0.377780 0.188890 0.981998i \(-0.439511\pi\)
0.188890 + 0.981998i \(0.439511\pi\)
\(294\) 0 0
\(295\) 11.5652 0.673352
\(296\) 0 0
\(297\) −3.07810 −0.178610
\(298\) 0 0
\(299\) 4.09134 0.236608
\(300\) 0 0
\(301\) −13.7195 −0.790782
\(302\) 0 0
\(303\) 0.965765 0.0554818
\(304\) 0 0
\(305\) 9.32212 0.533783
\(306\) 0 0
\(307\) −18.9859 −1.08358 −0.541791 0.840513i \(-0.682254\pi\)
−0.541791 + 0.840513i \(0.682254\pi\)
\(308\) 0 0
\(309\) 1.03212 0.0587152
\(310\) 0 0
\(311\) 6.11973 0.347018 0.173509 0.984832i \(-0.444489\pi\)
0.173509 + 0.984832i \(0.444489\pi\)
\(312\) 0 0
\(313\) 5.73279 0.324037 0.162018 0.986788i \(-0.448200\pi\)
0.162018 + 0.986788i \(0.448200\pi\)
\(314\) 0 0
\(315\) −9.16701 −0.516502
\(316\) 0 0
\(317\) −16.8637 −0.947158 −0.473579 0.880751i \(-0.657038\pi\)
−0.473579 + 0.880751i \(0.657038\pi\)
\(318\) 0 0
\(319\) −14.8114 −0.829278
\(320\) 0 0
\(321\) 4.36102 0.243408
\(322\) 0 0
\(323\) −11.2466 −0.625775
\(324\) 0 0
\(325\) 11.7664 0.652684
\(326\) 0 0
\(327\) 0.449739 0.0248706
\(328\) 0 0
\(329\) −6.13446 −0.338204
\(330\) 0 0
\(331\) 13.6510 0.750325 0.375162 0.926959i \(-0.377587\pi\)
0.375162 + 0.926959i \(0.377587\pi\)
\(332\) 0 0
\(333\) 25.0377 1.37206
\(334\) 0 0
\(335\) −13.4543 −0.735087
\(336\) 0 0
\(337\) −18.3359 −0.998821 −0.499410 0.866366i \(-0.666450\pi\)
−0.499410 + 0.866366i \(0.666450\pi\)
\(338\) 0 0
\(339\) 1.66032 0.0901763
\(340\) 0 0
\(341\) 8.19469 0.443767
\(342\) 0 0
\(343\) −18.6619 −1.00765
\(344\) 0 0
\(345\) −0.477066 −0.0256844
\(346\) 0 0
\(347\) 30.0533 1.61335 0.806673 0.590998i \(-0.201266\pi\)
0.806673 + 0.590998i \(0.201266\pi\)
\(348\) 0 0
\(349\) 14.3946 0.770527 0.385263 0.922807i \(-0.374111\pi\)
0.385263 + 0.922807i \(0.374111\pi\)
\(350\) 0 0
\(351\) 6.27750 0.335068
\(352\) 0 0
\(353\) −29.3940 −1.56448 −0.782241 0.622975i \(-0.785924\pi\)
−0.782241 + 0.622975i \(0.785924\pi\)
\(354\) 0 0
\(355\) −9.01477 −0.478454
\(356\) 0 0
\(357\) −2.24681 −0.118914
\(358\) 0 0
\(359\) −20.1770 −1.06490 −0.532450 0.846462i \(-0.678728\pi\)
−0.532450 + 0.846462i \(0.678728\pi\)
\(360\) 0 0
\(361\) −1.22144 −0.0642862
\(362\) 0 0
\(363\) −2.68078 −0.140705
\(364\) 0 0
\(365\) −4.30592 −0.225382
\(366\) 0 0
\(367\) 0.0988134 0.00515801 0.00257901 0.999997i \(-0.499179\pi\)
0.00257901 + 0.999997i \(0.499179\pi\)
\(368\) 0 0
\(369\) 17.5575 0.914008
\(370\) 0 0
\(371\) 3.97823 0.206539
\(372\) 0 0
\(373\) −23.1809 −1.20026 −0.600130 0.799902i \(-0.704885\pi\)
−0.600130 + 0.799902i \(0.704885\pi\)
\(374\) 0 0
\(375\) −3.30609 −0.170726
\(376\) 0 0
\(377\) 30.2064 1.55571
\(378\) 0 0
\(379\) −25.1812 −1.29347 −0.646735 0.762715i \(-0.723866\pi\)
−0.646735 + 0.762715i \(0.723866\pi\)
\(380\) 0 0
\(381\) −4.67677 −0.239598
\(382\) 0 0
\(383\) −4.72699 −0.241538 −0.120769 0.992681i \(-0.538536\pi\)
−0.120769 + 0.992681i \(0.538536\pi\)
\(384\) 0 0
\(385\) 5.14710 0.262321
\(386\) 0 0
\(387\) 15.1411 0.769668
\(388\) 0 0
\(389\) 2.41392 0.122390 0.0611952 0.998126i \(-0.480509\pi\)
0.0611952 + 0.998126i \(0.480509\pi\)
\(390\) 0 0
\(391\) 3.28962 0.166363
\(392\) 0 0
\(393\) 1.83283 0.0924540
\(394\) 0 0
\(395\) 3.16840 0.159420
\(396\) 0 0
\(397\) 17.1842 0.862451 0.431226 0.902244i \(-0.358081\pi\)
0.431226 + 0.902244i \(0.358081\pi\)
\(398\) 0 0
\(399\) 3.55177 0.177811
\(400\) 0 0
\(401\) −1.65099 −0.0824465 −0.0412233 0.999150i \(-0.513125\pi\)
−0.0412233 + 0.999150i \(0.513125\pi\)
\(402\) 0 0
\(403\) −16.7123 −0.832498
\(404\) 0 0
\(405\) 9.74450 0.484208
\(406\) 0 0
\(407\) −14.0582 −0.696839
\(408\) 0 0
\(409\) 5.54443 0.274155 0.137077 0.990560i \(-0.456229\pi\)
0.137077 + 0.990560i \(0.456229\pi\)
\(410\) 0 0
\(411\) 0.162022 0.00799198
\(412\) 0 0
\(413\) 25.1852 1.23928
\(414\) 0 0
\(415\) −16.8180 −0.825563
\(416\) 0 0
\(417\) 0.0209264 0.00102477
\(418\) 0 0
\(419\) −16.5645 −0.809228 −0.404614 0.914487i \(-0.632594\pi\)
−0.404614 + 0.914487i \(0.632594\pi\)
\(420\) 0 0
\(421\) −35.0445 −1.70797 −0.853983 0.520302i \(-0.825820\pi\)
−0.853983 + 0.520302i \(0.825820\pi\)
\(422\) 0 0
\(423\) 6.77010 0.329174
\(424\) 0 0
\(425\) 9.46074 0.458913
\(426\) 0 0
\(427\) 20.3005 0.982410
\(428\) 0 0
\(429\) −1.73157 −0.0836012
\(430\) 0 0
\(431\) −13.1111 −0.631542 −0.315771 0.948836i \(-0.602263\pi\)
−0.315771 + 0.948836i \(0.602263\pi\)
\(432\) 0 0
\(433\) −6.73845 −0.323829 −0.161915 0.986805i \(-0.551767\pi\)
−0.161915 + 0.986805i \(0.551767\pi\)
\(434\) 0 0
\(435\) −3.52218 −0.168876
\(436\) 0 0
\(437\) −5.20023 −0.248761
\(438\) 0 0
\(439\) 28.3510 1.35312 0.676560 0.736387i \(-0.263470\pi\)
0.676560 + 0.736387i \(0.263470\pi\)
\(440\) 0 0
\(441\) 0.316470 0.0150700
\(442\) 0 0
\(443\) 30.8531 1.46588 0.732939 0.680295i \(-0.238148\pi\)
0.732939 + 0.680295i \(0.238148\pi\)
\(444\) 0 0
\(445\) 13.6527 0.647198
\(446\) 0 0
\(447\) −4.86071 −0.229904
\(448\) 0 0
\(449\) −34.1984 −1.61392 −0.806962 0.590603i \(-0.798890\pi\)
−0.806962 + 0.590603i \(0.798890\pi\)
\(450\) 0 0
\(451\) −9.85822 −0.464205
\(452\) 0 0
\(453\) −2.41748 −0.113583
\(454\) 0 0
\(455\) −10.4970 −0.492108
\(456\) 0 0
\(457\) 13.8695 0.648787 0.324394 0.945922i \(-0.394840\pi\)
0.324394 + 0.945922i \(0.394840\pi\)
\(458\) 0 0
\(459\) 5.04739 0.235592
\(460\) 0 0
\(461\) −29.4101 −1.36976 −0.684882 0.728654i \(-0.740146\pi\)
−0.684882 + 0.728654i \(0.740146\pi\)
\(462\) 0 0
\(463\) 10.1122 0.469953 0.234976 0.972001i \(-0.424499\pi\)
0.234976 + 0.972001i \(0.424499\pi\)
\(464\) 0 0
\(465\) 1.94872 0.0903695
\(466\) 0 0
\(467\) −14.1149 −0.653161 −0.326581 0.945169i \(-0.605897\pi\)
−0.326581 + 0.945169i \(0.605897\pi\)
\(468\) 0 0
\(469\) −29.2990 −1.35290
\(470\) 0 0
\(471\) 0.817425 0.0376650
\(472\) 0 0
\(473\) −8.50147 −0.390898
\(474\) 0 0
\(475\) −14.9555 −0.686208
\(476\) 0 0
\(477\) −4.39045 −0.201025
\(478\) 0 0
\(479\) 7.59718 0.347124 0.173562 0.984823i \(-0.444472\pi\)
0.173562 + 0.984823i \(0.444472\pi\)
\(480\) 0 0
\(481\) 28.6704 1.30726
\(482\) 0 0
\(483\) −1.03889 −0.0472712
\(484\) 0 0
\(485\) −19.5479 −0.887623
\(486\) 0 0
\(487\) −25.6079 −1.16040 −0.580202 0.814473i \(-0.697026\pi\)
−0.580202 + 0.814473i \(0.697026\pi\)
\(488\) 0 0
\(489\) −7.17462 −0.324448
\(490\) 0 0
\(491\) −0.943905 −0.0425978 −0.0212989 0.999773i \(-0.506780\pi\)
−0.0212989 + 0.999773i \(0.506780\pi\)
\(492\) 0 0
\(493\) 24.2873 1.09384
\(494\) 0 0
\(495\) −5.68044 −0.255317
\(496\) 0 0
\(497\) −19.6312 −0.880580
\(498\) 0 0
\(499\) −32.2486 −1.44364 −0.721822 0.692078i \(-0.756695\pi\)
−0.721822 + 0.692078i \(0.756695\pi\)
\(500\) 0 0
\(501\) 1.57343 0.0702959
\(502\) 0 0
\(503\) 25.0618 1.11745 0.558726 0.829352i \(-0.311290\pi\)
0.558726 + 0.829352i \(0.311290\pi\)
\(504\) 0 0
\(505\) 3.62786 0.161438
\(506\) 0 0
\(507\) −0.640252 −0.0284346
\(508\) 0 0
\(509\) 13.8515 0.613958 0.306979 0.951716i \(-0.400682\pi\)
0.306979 + 0.951716i \(0.400682\pi\)
\(510\) 0 0
\(511\) −9.37687 −0.414808
\(512\) 0 0
\(513\) −7.97891 −0.352278
\(514\) 0 0
\(515\) 3.87712 0.170846
\(516\) 0 0
\(517\) −3.80129 −0.167180
\(518\) 0 0
\(519\) 1.52271 0.0668396
\(520\) 0 0
\(521\) −5.29758 −0.232091 −0.116046 0.993244i \(-0.537022\pi\)
−0.116046 + 0.993244i \(0.537022\pi\)
\(522\) 0 0
\(523\) −2.42411 −0.105999 −0.0529994 0.998595i \(-0.516878\pi\)
−0.0529994 + 0.998595i \(0.516878\pi\)
\(524\) 0 0
\(525\) −2.98779 −0.130398
\(526\) 0 0
\(527\) −13.4374 −0.585343
\(528\) 0 0
\(529\) −21.4789 −0.933867
\(530\) 0 0
\(531\) −27.7949 −1.20619
\(532\) 0 0
\(533\) 20.1049 0.870839
\(534\) 0 0
\(535\) 16.3820 0.708256
\(536\) 0 0
\(537\) 3.88443 0.167626
\(538\) 0 0
\(539\) −0.177692 −0.00765373
\(540\) 0 0
\(541\) −10.2679 −0.441453 −0.220727 0.975336i \(-0.570843\pi\)
−0.220727 + 0.975336i \(0.570843\pi\)
\(542\) 0 0
\(543\) −1.22977 −0.0527744
\(544\) 0 0
\(545\) 1.68943 0.0723671
\(546\) 0 0
\(547\) −40.1700 −1.71755 −0.858773 0.512356i \(-0.828773\pi\)
−0.858773 + 0.512356i \(0.828773\pi\)
\(548\) 0 0
\(549\) −22.4040 −0.956180
\(550\) 0 0
\(551\) −38.3934 −1.63561
\(552\) 0 0
\(553\) 6.89974 0.293407
\(554\) 0 0
\(555\) −3.34307 −0.141906
\(556\) 0 0
\(557\) 1.69529 0.0718317 0.0359159 0.999355i \(-0.488565\pi\)
0.0359159 + 0.999355i \(0.488565\pi\)
\(558\) 0 0
\(559\) 17.3379 0.733316
\(560\) 0 0
\(561\) −1.39226 −0.0587814
\(562\) 0 0
\(563\) −0.796711 −0.0335774 −0.0167887 0.999859i \(-0.505344\pi\)
−0.0167887 + 0.999859i \(0.505344\pi\)
\(564\) 0 0
\(565\) 6.23694 0.262390
\(566\) 0 0
\(567\) 21.2203 0.891169
\(568\) 0 0
\(569\) −34.3408 −1.43964 −0.719820 0.694161i \(-0.755776\pi\)
−0.719820 + 0.694161i \(0.755776\pi\)
\(570\) 0 0
\(571\) −13.1193 −0.549027 −0.274513 0.961583i \(-0.588517\pi\)
−0.274513 + 0.961583i \(0.588517\pi\)
\(572\) 0 0
\(573\) 6.41333 0.267921
\(574\) 0 0
\(575\) 4.37450 0.182429
\(576\) 0 0
\(577\) −33.1973 −1.38202 −0.691011 0.722844i \(-0.742834\pi\)
−0.691011 + 0.722844i \(0.742834\pi\)
\(578\) 0 0
\(579\) 5.93651 0.246713
\(580\) 0 0
\(581\) −36.6240 −1.51942
\(582\) 0 0
\(583\) 2.46515 0.102096
\(584\) 0 0
\(585\) 11.5847 0.478969
\(586\) 0 0
\(587\) 45.0798 1.86064 0.930321 0.366745i \(-0.119528\pi\)
0.930321 + 0.366745i \(0.119528\pi\)
\(588\) 0 0
\(589\) 21.2419 0.875257
\(590\) 0 0
\(591\) −6.34336 −0.260931
\(592\) 0 0
\(593\) −35.5467 −1.45973 −0.729865 0.683592i \(-0.760417\pi\)
−0.729865 + 0.683592i \(0.760417\pi\)
\(594\) 0 0
\(595\) −8.44007 −0.346009
\(596\) 0 0
\(597\) 4.24850 0.173880
\(598\) 0 0
\(599\) 2.70384 0.110476 0.0552379 0.998473i \(-0.482408\pi\)
0.0552379 + 0.998473i \(0.482408\pi\)
\(600\) 0 0
\(601\) −11.1644 −0.455406 −0.227703 0.973731i \(-0.573122\pi\)
−0.227703 + 0.973731i \(0.573122\pi\)
\(602\) 0 0
\(603\) 32.3349 1.31678
\(604\) 0 0
\(605\) −10.0703 −0.409414
\(606\) 0 0
\(607\) −13.2066 −0.536038 −0.268019 0.963414i \(-0.586369\pi\)
−0.268019 + 0.963414i \(0.586369\pi\)
\(608\) 0 0
\(609\) −7.67015 −0.310810
\(610\) 0 0
\(611\) 7.75236 0.313627
\(612\) 0 0
\(613\) 4.14238 0.167309 0.0836546 0.996495i \(-0.473341\pi\)
0.0836546 + 0.996495i \(0.473341\pi\)
\(614\) 0 0
\(615\) −2.34431 −0.0945316
\(616\) 0 0
\(617\) −13.2622 −0.533915 −0.266958 0.963708i \(-0.586018\pi\)
−0.266958 + 0.963708i \(0.586018\pi\)
\(618\) 0 0
\(619\) −22.7925 −0.916107 −0.458053 0.888925i \(-0.651453\pi\)
−0.458053 + 0.888925i \(0.651453\pi\)
\(620\) 0 0
\(621\) 2.33383 0.0936535
\(622\) 0 0
\(623\) 29.7310 1.19115
\(624\) 0 0
\(625\) 5.31551 0.212620
\(626\) 0 0
\(627\) 2.20089 0.0878951
\(628\) 0 0
\(629\) 23.0522 0.919153
\(630\) 0 0
\(631\) 20.5766 0.819143 0.409572 0.912278i \(-0.365678\pi\)
0.409572 + 0.912278i \(0.365678\pi\)
\(632\) 0 0
\(633\) 4.52189 0.179729
\(634\) 0 0
\(635\) −17.5681 −0.697169
\(636\) 0 0
\(637\) 0.362385 0.0143582
\(638\) 0 0
\(639\) 21.6654 0.857068
\(640\) 0 0
\(641\) 44.1596 1.74420 0.872099 0.489329i \(-0.162758\pi\)
0.872099 + 0.489329i \(0.162758\pi\)
\(642\) 0 0
\(643\) 24.0553 0.948650 0.474325 0.880350i \(-0.342692\pi\)
0.474325 + 0.880350i \(0.342692\pi\)
\(644\) 0 0
\(645\) −2.02167 −0.0796031
\(646\) 0 0
\(647\) 14.9928 0.589426 0.294713 0.955586i \(-0.404776\pi\)
0.294713 + 0.955586i \(0.404776\pi\)
\(648\) 0 0
\(649\) 15.6063 0.612600
\(650\) 0 0
\(651\) 4.24366 0.166322
\(652\) 0 0
\(653\) 13.9919 0.547545 0.273773 0.961794i \(-0.411728\pi\)
0.273773 + 0.961794i \(0.411728\pi\)
\(654\) 0 0
\(655\) 6.88496 0.269018
\(656\) 0 0
\(657\) 10.3485 0.403733
\(658\) 0 0
\(659\) 37.9086 1.47671 0.738354 0.674413i \(-0.235603\pi\)
0.738354 + 0.674413i \(0.235603\pi\)
\(660\) 0 0
\(661\) 24.0458 0.935273 0.467637 0.883921i \(-0.345106\pi\)
0.467637 + 0.883921i \(0.345106\pi\)
\(662\) 0 0
\(663\) 2.83939 0.110273
\(664\) 0 0
\(665\) 13.3421 0.517383
\(666\) 0 0
\(667\) 11.2301 0.434830
\(668\) 0 0
\(669\) −1.44987 −0.0560553
\(670\) 0 0
\(671\) 12.5794 0.485623
\(672\) 0 0
\(673\) 43.8276 1.68943 0.844714 0.535217i \(-0.179770\pi\)
0.844714 + 0.535217i \(0.179770\pi\)
\(674\) 0 0
\(675\) 6.71196 0.258344
\(676\) 0 0
\(677\) 4.73446 0.181960 0.0909801 0.995853i \(-0.471000\pi\)
0.0909801 + 0.995853i \(0.471000\pi\)
\(678\) 0 0
\(679\) −42.5688 −1.63364
\(680\) 0 0
\(681\) −2.64546 −0.101374
\(682\) 0 0
\(683\) −27.1872 −1.04029 −0.520144 0.854079i \(-0.674122\pi\)
−0.520144 + 0.854079i \(0.674122\pi\)
\(684\) 0 0
\(685\) 0.608631 0.0232546
\(686\) 0 0
\(687\) 7.85899 0.299839
\(688\) 0 0
\(689\) −5.02744 −0.191530
\(690\) 0 0
\(691\) 16.2101 0.616663 0.308331 0.951279i \(-0.400229\pi\)
0.308331 + 0.951279i \(0.400229\pi\)
\(692\) 0 0
\(693\) −12.3701 −0.469902
\(694\) 0 0
\(695\) 0.0786092 0.00298182
\(696\) 0 0
\(697\) 16.1652 0.612302
\(698\) 0 0
\(699\) 4.66169 0.176321
\(700\) 0 0
\(701\) 34.7625 1.31296 0.656481 0.754343i \(-0.272044\pi\)
0.656481 + 0.754343i \(0.272044\pi\)
\(702\) 0 0
\(703\) −36.4410 −1.37440
\(704\) 0 0
\(705\) −0.903955 −0.0340449
\(706\) 0 0
\(707\) 7.90028 0.297121
\(708\) 0 0
\(709\) 0.560357 0.0210447 0.0105223 0.999945i \(-0.496651\pi\)
0.0105223 + 0.999945i \(0.496651\pi\)
\(710\) 0 0
\(711\) −7.61468 −0.285573
\(712\) 0 0
\(713\) −6.21325 −0.232688
\(714\) 0 0
\(715\) −6.50459 −0.243258
\(716\) 0 0
\(717\) −5.69538 −0.212698
\(718\) 0 0
\(719\) −10.7798 −0.402020 −0.201010 0.979589i \(-0.564422\pi\)
−0.201010 + 0.979589i \(0.564422\pi\)
\(720\) 0 0
\(721\) 8.44308 0.314437
\(722\) 0 0
\(723\) 6.94845 0.258416
\(724\) 0 0
\(725\) 32.2970 1.19948
\(726\) 0 0
\(727\) −25.5181 −0.946413 −0.473207 0.880951i \(-0.656904\pi\)
−0.473207 + 0.880951i \(0.656904\pi\)
\(728\) 0 0
\(729\) −21.5974 −0.799904
\(730\) 0 0
\(731\) 13.9405 0.515607
\(732\) 0 0
\(733\) 49.6083 1.83233 0.916163 0.400806i \(-0.131270\pi\)
0.916163 + 0.400806i \(0.131270\pi\)
\(734\) 0 0
\(735\) −0.0422555 −0.00155862
\(736\) 0 0
\(737\) −18.1554 −0.668765
\(738\) 0 0
\(739\) 0.0908565 0.00334221 0.00167111 0.999999i \(-0.499468\pi\)
0.00167111 + 0.999999i \(0.499468\pi\)
\(740\) 0 0
\(741\) −4.48850 −0.164889
\(742\) 0 0
\(743\) −31.7804 −1.16591 −0.582955 0.812504i \(-0.698104\pi\)
−0.582955 + 0.812504i \(0.698104\pi\)
\(744\) 0 0
\(745\) −18.2591 −0.668961
\(746\) 0 0
\(747\) 40.4190 1.47885
\(748\) 0 0
\(749\) 35.6746 1.30352
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 0.226335 0.00824812
\(754\) 0 0
\(755\) −9.08118 −0.330498
\(756\) 0 0
\(757\) −11.3038 −0.410842 −0.205421 0.978674i \(-0.565856\pi\)
−0.205421 + 0.978674i \(0.565856\pi\)
\(758\) 0 0
\(759\) −0.643760 −0.0233670
\(760\) 0 0
\(761\) −41.9436 −1.52045 −0.760227 0.649657i \(-0.774912\pi\)
−0.760227 + 0.649657i \(0.774912\pi\)
\(762\) 0 0
\(763\) 3.67902 0.133189
\(764\) 0 0
\(765\) 9.31462 0.336771
\(766\) 0 0
\(767\) −31.8275 −1.14923
\(768\) 0 0
\(769\) 19.6203 0.707526 0.353763 0.935335i \(-0.384902\pi\)
0.353763 + 0.935335i \(0.384902\pi\)
\(770\) 0 0
\(771\) −0.259861 −0.00935868
\(772\) 0 0
\(773\) 47.1732 1.69670 0.848352 0.529433i \(-0.177595\pi\)
0.848352 + 0.529433i \(0.177595\pi\)
\(774\) 0 0
\(775\) −17.8689 −0.641871
\(776\) 0 0
\(777\) −7.28011 −0.261173
\(778\) 0 0
\(779\) −25.5540 −0.915567
\(780\) 0 0
\(781\) −12.1647 −0.435287
\(782\) 0 0
\(783\) 17.2307 0.615776
\(784\) 0 0
\(785\) 3.07063 0.109595
\(786\) 0 0
\(787\) −25.8127 −0.920123 −0.460062 0.887887i \(-0.652173\pi\)
−0.460062 + 0.887887i \(0.652173\pi\)
\(788\) 0 0
\(789\) −4.55182 −0.162049
\(790\) 0 0
\(791\) 13.5820 0.482920
\(792\) 0 0
\(793\) −25.6545 −0.911019
\(794\) 0 0
\(795\) 0.586220 0.0207911
\(796\) 0 0
\(797\) 14.9003 0.527796 0.263898 0.964551i \(-0.414992\pi\)
0.263898 + 0.964551i \(0.414992\pi\)
\(798\) 0 0
\(799\) 6.23324 0.220516
\(800\) 0 0
\(801\) −32.8117 −1.15934
\(802\) 0 0
\(803\) −5.81048 −0.205047
\(804\) 0 0
\(805\) −3.90256 −0.137547
\(806\) 0 0
\(807\) 0.0494725 0.00174152
\(808\) 0 0
\(809\) −35.2734 −1.24015 −0.620073 0.784544i \(-0.712897\pi\)
−0.620073 + 0.784544i \(0.712897\pi\)
\(810\) 0 0
\(811\) 4.72789 0.166019 0.0830093 0.996549i \(-0.473547\pi\)
0.0830093 + 0.996549i \(0.473547\pi\)
\(812\) 0 0
\(813\) 5.27168 0.184886
\(814\) 0 0
\(815\) −26.9512 −0.944059
\(816\) 0 0
\(817\) −22.0371 −0.770981
\(818\) 0 0
\(819\) 25.2277 0.881526
\(820\) 0 0
\(821\) 31.0676 1.08427 0.542133 0.840293i \(-0.317617\pi\)
0.542133 + 0.840293i \(0.317617\pi\)
\(822\) 0 0
\(823\) −30.6842 −1.06958 −0.534792 0.844984i \(-0.679610\pi\)
−0.534792 + 0.844984i \(0.679610\pi\)
\(824\) 0 0
\(825\) −1.85142 −0.0644580
\(826\) 0 0
\(827\) 38.1091 1.32518 0.662592 0.748981i \(-0.269456\pi\)
0.662592 + 0.748981i \(0.269456\pi\)
\(828\) 0 0
\(829\) −2.36830 −0.0822546 −0.0411273 0.999154i \(-0.513095\pi\)
−0.0411273 + 0.999154i \(0.513095\pi\)
\(830\) 0 0
\(831\) −9.57999 −0.332326
\(832\) 0 0
\(833\) 0.291374 0.0100955
\(834\) 0 0
\(835\) 5.91055 0.204543
\(836\) 0 0
\(837\) −9.53323 −0.329517
\(838\) 0 0
\(839\) −27.9016 −0.963271 −0.481636 0.876372i \(-0.659957\pi\)
−0.481636 + 0.876372i \(0.659957\pi\)
\(840\) 0 0
\(841\) 53.9117 1.85902
\(842\) 0 0
\(843\) 4.77796 0.164562
\(844\) 0 0
\(845\) −2.40508 −0.0827373
\(846\) 0 0
\(847\) −21.9297 −0.753513
\(848\) 0 0
\(849\) 8.19039 0.281093
\(850\) 0 0
\(851\) 10.6590 0.365386
\(852\) 0 0
\(853\) −20.7080 −0.709028 −0.354514 0.935051i \(-0.615354\pi\)
−0.354514 + 0.935051i \(0.615354\pi\)
\(854\) 0 0
\(855\) −14.7246 −0.503569
\(856\) 0 0
\(857\) 35.7308 1.22054 0.610271 0.792193i \(-0.291061\pi\)
0.610271 + 0.792193i \(0.291061\pi\)
\(858\) 0 0
\(859\) 31.5548 1.07663 0.538317 0.842742i \(-0.319060\pi\)
0.538317 + 0.842742i \(0.319060\pi\)
\(860\) 0 0
\(861\) −5.10513 −0.173982
\(862\) 0 0
\(863\) 21.9392 0.746819 0.373410 0.927667i \(-0.378189\pi\)
0.373410 + 0.927667i \(0.378189\pi\)
\(864\) 0 0
\(865\) 5.72001 0.194486
\(866\) 0 0
\(867\) −3.17221 −0.107734
\(868\) 0 0
\(869\) 4.27550 0.145036
\(870\) 0 0
\(871\) 37.0263 1.25459
\(872\) 0 0
\(873\) 46.9797 1.59002
\(874\) 0 0
\(875\) −27.0449 −0.914285
\(876\) 0 0
\(877\) −28.2204 −0.952934 −0.476467 0.879192i \(-0.658083\pi\)
−0.476467 + 0.879192i \(0.658083\pi\)
\(878\) 0 0
\(879\) 2.07508 0.0699907
\(880\) 0 0
\(881\) −31.1430 −1.04924 −0.524618 0.851338i \(-0.675792\pi\)
−0.524618 + 0.851338i \(0.675792\pi\)
\(882\) 0 0
\(883\) −7.77388 −0.261612 −0.130806 0.991408i \(-0.541756\pi\)
−0.130806 + 0.991408i \(0.541756\pi\)
\(884\) 0 0
\(885\) 3.71121 0.124751
\(886\) 0 0
\(887\) 31.4694 1.05664 0.528319 0.849046i \(-0.322823\pi\)
0.528319 + 0.849046i \(0.322823\pi\)
\(888\) 0 0
\(889\) −38.2576 −1.28312
\(890\) 0 0
\(891\) 13.1494 0.440521
\(892\) 0 0
\(893\) −9.85351 −0.329735
\(894\) 0 0
\(895\) 14.5917 0.487747
\(896\) 0 0
\(897\) 1.31289 0.0438360
\(898\) 0 0
\(899\) −45.8725 −1.52993
\(900\) 0 0
\(901\) −4.04229 −0.134668
\(902\) 0 0
\(903\) −4.40253 −0.146507
\(904\) 0 0
\(905\) −4.61958 −0.153560
\(906\) 0 0
\(907\) 21.8828 0.726608 0.363304 0.931671i \(-0.381649\pi\)
0.363304 + 0.931671i \(0.381649\pi\)
\(908\) 0 0
\(909\) −8.71890 −0.289188
\(910\) 0 0
\(911\) 31.3720 1.03940 0.519700 0.854349i \(-0.326044\pi\)
0.519700 + 0.854349i \(0.326044\pi\)
\(912\) 0 0
\(913\) −22.6945 −0.751078
\(914\) 0 0
\(915\) 2.99142 0.0988932
\(916\) 0 0
\(917\) 14.9932 0.495118
\(918\) 0 0
\(919\) 22.7351 0.749962 0.374981 0.927033i \(-0.377649\pi\)
0.374981 + 0.927033i \(0.377649\pi\)
\(920\) 0 0
\(921\) −6.09247 −0.200754
\(922\) 0 0
\(923\) 24.8087 0.816589
\(924\) 0 0
\(925\) 30.6546 1.00792
\(926\) 0 0
\(927\) −9.31794 −0.306041
\(928\) 0 0
\(929\) 22.3903 0.734603 0.367302 0.930102i \(-0.380282\pi\)
0.367302 + 0.930102i \(0.380282\pi\)
\(930\) 0 0
\(931\) −0.460604 −0.0150957
\(932\) 0 0
\(933\) 1.96379 0.0642916
\(934\) 0 0
\(935\) −5.22998 −0.171039
\(936\) 0 0
\(937\) 9.34736 0.305365 0.152682 0.988275i \(-0.451209\pi\)
0.152682 + 0.988275i \(0.451209\pi\)
\(938\) 0 0
\(939\) 1.83962 0.0600338
\(940\) 0 0
\(941\) 44.7622 1.45921 0.729603 0.683871i \(-0.239705\pi\)
0.729603 + 0.683871i \(0.239705\pi\)
\(942\) 0 0
\(943\) 7.47455 0.243405
\(944\) 0 0
\(945\) −5.98785 −0.194785
\(946\) 0 0
\(947\) −26.9382 −0.875374 −0.437687 0.899127i \(-0.644202\pi\)
−0.437687 + 0.899127i \(0.644202\pi\)
\(948\) 0 0
\(949\) 11.8499 0.384664
\(950\) 0 0
\(951\) −5.41146 −0.175479
\(952\) 0 0
\(953\) −8.50412 −0.275475 −0.137738 0.990469i \(-0.543983\pi\)
−0.137738 + 0.990469i \(0.543983\pi\)
\(954\) 0 0
\(955\) 24.0914 0.779580
\(956\) 0 0
\(957\) −4.75289 −0.153639
\(958\) 0 0
\(959\) 1.32540 0.0427993
\(960\) 0 0
\(961\) −5.62013 −0.181295
\(962\) 0 0
\(963\) −39.3712 −1.26872
\(964\) 0 0
\(965\) 22.3003 0.717871
\(966\) 0 0
\(967\) −35.3831 −1.13784 −0.568921 0.822392i \(-0.692639\pi\)
−0.568921 + 0.822392i \(0.692639\pi\)
\(968\) 0 0
\(969\) −3.60896 −0.115936
\(970\) 0 0
\(971\) −14.2839 −0.458392 −0.229196 0.973380i \(-0.573610\pi\)
−0.229196 + 0.973380i \(0.573610\pi\)
\(972\) 0 0
\(973\) 0.171185 0.00548793
\(974\) 0 0
\(975\) 3.77579 0.120922
\(976\) 0 0
\(977\) 37.7758 1.20856 0.604278 0.796774i \(-0.293462\pi\)
0.604278 + 0.796774i \(0.293462\pi\)
\(978\) 0 0
\(979\) 18.4231 0.588806
\(980\) 0 0
\(981\) −4.06023 −0.129633
\(982\) 0 0
\(983\) −25.7633 −0.821723 −0.410861 0.911698i \(-0.634772\pi\)
−0.410861 + 0.911698i \(0.634772\pi\)
\(984\) 0 0
\(985\) −23.8286 −0.759242
\(986\) 0 0
\(987\) −1.96852 −0.0626585
\(988\) 0 0
\(989\) 6.44585 0.204966
\(990\) 0 0
\(991\) 44.0197 1.39833 0.699167 0.714959i \(-0.253555\pi\)
0.699167 + 0.714959i \(0.253555\pi\)
\(992\) 0 0
\(993\) 4.38052 0.139012
\(994\) 0 0
\(995\) 15.9593 0.505945
\(996\) 0 0
\(997\) 47.0752 1.49089 0.745443 0.666569i \(-0.232238\pi\)
0.745443 + 0.666569i \(0.232238\pi\)
\(998\) 0 0
\(999\) 16.3545 0.517434
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.1.28 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.28 44 1.1 even 1 trivial