Properties

Label 6008.2.a.b.1.23
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 1.23
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.345669 q^{3} +2.40831 q^{5} -1.76498 q^{7} -2.88051 q^{9} +O(q^{10})\) \(q-0.345669 q^{3} +2.40831 q^{5} -1.76498 q^{7} -2.88051 q^{9} -2.38392 q^{11} +4.86705 q^{13} -0.832480 q^{15} +4.36266 q^{17} -4.69953 q^{19} +0.610099 q^{21} -1.71079 q^{23} +0.799972 q^{25} +2.03271 q^{27} +2.59945 q^{29} -0.727592 q^{31} +0.824049 q^{33} -4.25062 q^{35} -7.06065 q^{37} -1.68239 q^{39} -0.505625 q^{41} +5.98623 q^{43} -6.93718 q^{45} -8.49724 q^{47} -3.88485 q^{49} -1.50804 q^{51} +4.93839 q^{53} -5.74123 q^{55} +1.62448 q^{57} -7.80350 q^{59} +6.09511 q^{61} +5.08405 q^{63} +11.7214 q^{65} -0.910535 q^{67} +0.591367 q^{69} +12.5995 q^{71} +7.63460 q^{73} -0.276526 q^{75} +4.20758 q^{77} -12.0523 q^{79} +7.93889 q^{81} -15.9712 q^{83} +10.5067 q^{85} -0.898550 q^{87} -13.5797 q^{89} -8.59025 q^{91} +0.251506 q^{93} -11.3179 q^{95} +11.4638 q^{97} +6.86692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.345669 −0.199572 −0.0997861 0.995009i \(-0.531816\pi\)
−0.0997861 + 0.995009i \(0.531816\pi\)
\(4\) 0 0
\(5\) 2.40831 1.07703 0.538515 0.842616i \(-0.318985\pi\)
0.538515 + 0.842616i \(0.318985\pi\)
\(6\) 0 0
\(7\) −1.76498 −0.667099 −0.333550 0.942733i \(-0.608247\pi\)
−0.333550 + 0.942733i \(0.608247\pi\)
\(8\) 0 0
\(9\) −2.88051 −0.960171
\(10\) 0 0
\(11\) −2.38392 −0.718780 −0.359390 0.933187i \(-0.617015\pi\)
−0.359390 + 0.933187i \(0.617015\pi\)
\(12\) 0 0
\(13\) 4.86705 1.34988 0.674939 0.737874i \(-0.264170\pi\)
0.674939 + 0.737874i \(0.264170\pi\)
\(14\) 0 0
\(15\) −0.832480 −0.214945
\(16\) 0 0
\(17\) 4.36266 1.05810 0.529050 0.848590i \(-0.322548\pi\)
0.529050 + 0.848590i \(0.322548\pi\)
\(18\) 0 0
\(19\) −4.69953 −1.07815 −0.539073 0.842259i \(-0.681225\pi\)
−0.539073 + 0.842259i \(0.681225\pi\)
\(20\) 0 0
\(21\) 0.610099 0.133134
\(22\) 0 0
\(23\) −1.71079 −0.356724 −0.178362 0.983965i \(-0.557080\pi\)
−0.178362 + 0.983965i \(0.557080\pi\)
\(24\) 0 0
\(25\) 0.799972 0.159994
\(26\) 0 0
\(27\) 2.03271 0.391196
\(28\) 0 0
\(29\) 2.59945 0.482706 0.241353 0.970437i \(-0.422409\pi\)
0.241353 + 0.970437i \(0.422409\pi\)
\(30\) 0 0
\(31\) −0.727592 −0.130679 −0.0653397 0.997863i \(-0.520813\pi\)
−0.0653397 + 0.997863i \(0.520813\pi\)
\(32\) 0 0
\(33\) 0.824049 0.143448
\(34\) 0 0
\(35\) −4.25062 −0.718486
\(36\) 0 0
\(37\) −7.06065 −1.16076 −0.580382 0.814344i \(-0.697097\pi\)
−0.580382 + 0.814344i \(0.697097\pi\)
\(38\) 0 0
\(39\) −1.68239 −0.269398
\(40\) 0 0
\(41\) −0.505625 −0.0789653 −0.0394827 0.999220i \(-0.512571\pi\)
−0.0394827 + 0.999220i \(0.512571\pi\)
\(42\) 0 0
\(43\) 5.98623 0.912891 0.456445 0.889751i \(-0.349122\pi\)
0.456445 + 0.889751i \(0.349122\pi\)
\(44\) 0 0
\(45\) −6.93718 −1.03413
\(46\) 0 0
\(47\) −8.49724 −1.23945 −0.619725 0.784819i \(-0.712756\pi\)
−0.619725 + 0.784819i \(0.712756\pi\)
\(48\) 0 0
\(49\) −3.88485 −0.554978
\(50\) 0 0
\(51\) −1.50804 −0.211167
\(52\) 0 0
\(53\) 4.93839 0.678341 0.339170 0.940725i \(-0.389854\pi\)
0.339170 + 0.940725i \(0.389854\pi\)
\(54\) 0 0
\(55\) −5.74123 −0.774148
\(56\) 0 0
\(57\) 1.62448 0.215168
\(58\) 0 0
\(59\) −7.80350 −1.01593 −0.507965 0.861378i \(-0.669602\pi\)
−0.507965 + 0.861378i \(0.669602\pi\)
\(60\) 0 0
\(61\) 6.09511 0.780399 0.390200 0.920730i \(-0.372406\pi\)
0.390200 + 0.920730i \(0.372406\pi\)
\(62\) 0 0
\(63\) 5.08405 0.640530
\(64\) 0 0
\(65\) 11.7214 1.45386
\(66\) 0 0
\(67\) −0.910535 −0.111240 −0.0556198 0.998452i \(-0.517713\pi\)
−0.0556198 + 0.998452i \(0.517713\pi\)
\(68\) 0 0
\(69\) 0.591367 0.0711922
\(70\) 0 0
\(71\) 12.5995 1.49529 0.747643 0.664101i \(-0.231185\pi\)
0.747643 + 0.664101i \(0.231185\pi\)
\(72\) 0 0
\(73\) 7.63460 0.893563 0.446781 0.894643i \(-0.352570\pi\)
0.446781 + 0.894643i \(0.352570\pi\)
\(74\) 0 0
\(75\) −0.276526 −0.0319304
\(76\) 0 0
\(77\) 4.20758 0.479498
\(78\) 0 0
\(79\) −12.0523 −1.35599 −0.677993 0.735069i \(-0.737150\pi\)
−0.677993 + 0.735069i \(0.737150\pi\)
\(80\) 0 0
\(81\) 7.93889 0.882099
\(82\) 0 0
\(83\) −15.9712 −1.75307 −0.876534 0.481340i \(-0.840150\pi\)
−0.876534 + 0.481340i \(0.840150\pi\)
\(84\) 0 0
\(85\) 10.5067 1.13961
\(86\) 0 0
\(87\) −0.898550 −0.0963347
\(88\) 0 0
\(89\) −13.5797 −1.43945 −0.719725 0.694259i \(-0.755732\pi\)
−0.719725 + 0.694259i \(0.755732\pi\)
\(90\) 0 0
\(91\) −8.59025 −0.900503
\(92\) 0 0
\(93\) 0.251506 0.0260800
\(94\) 0 0
\(95\) −11.3179 −1.16120
\(96\) 0 0
\(97\) 11.4638 1.16398 0.581989 0.813197i \(-0.302275\pi\)
0.581989 + 0.813197i \(0.302275\pi\)
\(98\) 0 0
\(99\) 6.86692 0.690152
\(100\) 0 0
\(101\) −10.4579 −1.04060 −0.520298 0.853985i \(-0.674179\pi\)
−0.520298 + 0.853985i \(0.674179\pi\)
\(102\) 0 0
\(103\) 3.52747 0.347572 0.173786 0.984783i \(-0.444400\pi\)
0.173786 + 0.984783i \(0.444400\pi\)
\(104\) 0 0
\(105\) 1.46931 0.143390
\(106\) 0 0
\(107\) 16.3428 1.57992 0.789960 0.613159i \(-0.210101\pi\)
0.789960 + 0.613159i \(0.210101\pi\)
\(108\) 0 0
\(109\) −10.9336 −1.04725 −0.523623 0.851950i \(-0.675420\pi\)
−0.523623 + 0.851950i \(0.675420\pi\)
\(110\) 0 0
\(111\) 2.44065 0.231656
\(112\) 0 0
\(113\) −7.74781 −0.728853 −0.364426 0.931232i \(-0.618735\pi\)
−0.364426 + 0.931232i \(0.618735\pi\)
\(114\) 0 0
\(115\) −4.12012 −0.384203
\(116\) 0 0
\(117\) −14.0196 −1.29611
\(118\) 0 0
\(119\) −7.70001 −0.705858
\(120\) 0 0
\(121\) −5.31691 −0.483355
\(122\) 0 0
\(123\) 0.174779 0.0157593
\(124\) 0 0
\(125\) −10.1150 −0.904711
\(126\) 0 0
\(127\) −13.8641 −1.23024 −0.615122 0.788432i \(-0.710893\pi\)
−0.615122 + 0.788432i \(0.710893\pi\)
\(128\) 0 0
\(129\) −2.06925 −0.182188
\(130\) 0 0
\(131\) −11.2082 −0.979261 −0.489631 0.871930i \(-0.662868\pi\)
−0.489631 + 0.871930i \(0.662868\pi\)
\(132\) 0 0
\(133\) 8.29457 0.719230
\(134\) 0 0
\(135\) 4.89541 0.421330
\(136\) 0 0
\(137\) 1.43734 0.122801 0.0614003 0.998113i \(-0.480443\pi\)
0.0614003 + 0.998113i \(0.480443\pi\)
\(138\) 0 0
\(139\) −6.34126 −0.537858 −0.268929 0.963160i \(-0.586670\pi\)
−0.268929 + 0.963160i \(0.586670\pi\)
\(140\) 0 0
\(141\) 2.93724 0.247360
\(142\) 0 0
\(143\) −11.6027 −0.970265
\(144\) 0 0
\(145\) 6.26029 0.519889
\(146\) 0 0
\(147\) 1.34287 0.110758
\(148\) 0 0
\(149\) −22.0181 −1.80380 −0.901898 0.431950i \(-0.857826\pi\)
−0.901898 + 0.431950i \(0.857826\pi\)
\(150\) 0 0
\(151\) −0.489202 −0.0398107 −0.0199053 0.999802i \(-0.506336\pi\)
−0.0199053 + 0.999802i \(0.506336\pi\)
\(152\) 0 0
\(153\) −12.5667 −1.01596
\(154\) 0 0
\(155\) −1.75227 −0.140746
\(156\) 0 0
\(157\) −8.78075 −0.700781 −0.350390 0.936604i \(-0.613951\pi\)
−0.350390 + 0.936604i \(0.613951\pi\)
\(158\) 0 0
\(159\) −1.70705 −0.135378
\(160\) 0 0
\(161\) 3.01951 0.237970
\(162\) 0 0
\(163\) 5.90187 0.462270 0.231135 0.972922i \(-0.425756\pi\)
0.231135 + 0.972922i \(0.425756\pi\)
\(164\) 0 0
\(165\) 1.98457 0.154498
\(166\) 0 0
\(167\) 17.2549 1.33522 0.667612 0.744509i \(-0.267316\pi\)
0.667612 + 0.744509i \(0.267316\pi\)
\(168\) 0 0
\(169\) 10.6882 0.822170
\(170\) 0 0
\(171\) 13.5371 1.03520
\(172\) 0 0
\(173\) −21.5820 −1.64085 −0.820425 0.571754i \(-0.806263\pi\)
−0.820425 + 0.571754i \(0.806263\pi\)
\(174\) 0 0
\(175\) −1.41193 −0.106732
\(176\) 0 0
\(177\) 2.69743 0.202751
\(178\) 0 0
\(179\) 5.90335 0.441237 0.220619 0.975360i \(-0.429192\pi\)
0.220619 + 0.975360i \(0.429192\pi\)
\(180\) 0 0
\(181\) −0.0844297 −0.00627561 −0.00313780 0.999995i \(-0.500999\pi\)
−0.00313780 + 0.999995i \(0.500999\pi\)
\(182\) 0 0
\(183\) −2.10689 −0.155746
\(184\) 0 0
\(185\) −17.0043 −1.25018
\(186\) 0 0
\(187\) −10.4003 −0.760542
\(188\) 0 0
\(189\) −3.58769 −0.260966
\(190\) 0 0
\(191\) 8.02592 0.580735 0.290368 0.956915i \(-0.406222\pi\)
0.290368 + 0.956915i \(0.406222\pi\)
\(192\) 0 0
\(193\) −8.57717 −0.617398 −0.308699 0.951160i \(-0.599894\pi\)
−0.308699 + 0.951160i \(0.599894\pi\)
\(194\) 0 0
\(195\) −4.05172 −0.290150
\(196\) 0 0
\(197\) 23.4701 1.67217 0.836087 0.548597i \(-0.184838\pi\)
0.836087 + 0.548597i \(0.184838\pi\)
\(198\) 0 0
\(199\) −12.3839 −0.877872 −0.438936 0.898518i \(-0.644645\pi\)
−0.438936 + 0.898518i \(0.644645\pi\)
\(200\) 0 0
\(201\) 0.314744 0.0222003
\(202\) 0 0
\(203\) −4.58798 −0.322013
\(204\) 0 0
\(205\) −1.21770 −0.0850480
\(206\) 0 0
\(207\) 4.92795 0.342516
\(208\) 0 0
\(209\) 11.2033 0.774950
\(210\) 0 0
\(211\) −11.6398 −0.801314 −0.400657 0.916228i \(-0.631218\pi\)
−0.400657 + 0.916228i \(0.631218\pi\)
\(212\) 0 0
\(213\) −4.35526 −0.298417
\(214\) 0 0
\(215\) 14.4167 0.983211
\(216\) 0 0
\(217\) 1.28418 0.0871761
\(218\) 0 0
\(219\) −2.63905 −0.178330
\(220\) 0 0
\(221\) 21.2333 1.42831
\(222\) 0 0
\(223\) 16.8154 1.12604 0.563022 0.826442i \(-0.309639\pi\)
0.563022 + 0.826442i \(0.309639\pi\)
\(224\) 0 0
\(225\) −2.30433 −0.153622
\(226\) 0 0
\(227\) 7.84706 0.520828 0.260414 0.965497i \(-0.416141\pi\)
0.260414 + 0.965497i \(0.416141\pi\)
\(228\) 0 0
\(229\) 10.8878 0.719488 0.359744 0.933051i \(-0.382864\pi\)
0.359744 + 0.933051i \(0.382864\pi\)
\(230\) 0 0
\(231\) −1.45443 −0.0956944
\(232\) 0 0
\(233\) 5.41401 0.354684 0.177342 0.984149i \(-0.443250\pi\)
0.177342 + 0.984149i \(0.443250\pi\)
\(234\) 0 0
\(235\) −20.4640 −1.33493
\(236\) 0 0
\(237\) 4.16609 0.270617
\(238\) 0 0
\(239\) −28.0408 −1.81381 −0.906904 0.421338i \(-0.861561\pi\)
−0.906904 + 0.421338i \(0.861561\pi\)
\(240\) 0 0
\(241\) −9.82891 −0.633136 −0.316568 0.948570i \(-0.602530\pi\)
−0.316568 + 0.948570i \(0.602530\pi\)
\(242\) 0 0
\(243\) −8.84237 −0.567238
\(244\) 0 0
\(245\) −9.35593 −0.597729
\(246\) 0 0
\(247\) −22.8729 −1.45537
\(248\) 0 0
\(249\) 5.52076 0.349864
\(250\) 0 0
\(251\) −7.51782 −0.474521 −0.237260 0.971446i \(-0.576249\pi\)
−0.237260 + 0.971446i \(0.576249\pi\)
\(252\) 0 0
\(253\) 4.07839 0.256406
\(254\) 0 0
\(255\) −3.63183 −0.227434
\(256\) 0 0
\(257\) 25.7198 1.60436 0.802180 0.597083i \(-0.203674\pi\)
0.802180 + 0.597083i \(0.203674\pi\)
\(258\) 0 0
\(259\) 12.4619 0.774345
\(260\) 0 0
\(261\) −7.48775 −0.463480
\(262\) 0 0
\(263\) −10.6598 −0.657312 −0.328656 0.944450i \(-0.606596\pi\)
−0.328656 + 0.944450i \(0.606596\pi\)
\(264\) 0 0
\(265\) 11.8932 0.730594
\(266\) 0 0
\(267\) 4.69410 0.287274
\(268\) 0 0
\(269\) −31.6684 −1.93086 −0.965430 0.260664i \(-0.916058\pi\)
−0.965430 + 0.260664i \(0.916058\pi\)
\(270\) 0 0
\(271\) −10.9165 −0.663131 −0.331566 0.943432i \(-0.607577\pi\)
−0.331566 + 0.943432i \(0.607577\pi\)
\(272\) 0 0
\(273\) 2.96938 0.179715
\(274\) 0 0
\(275\) −1.90707 −0.115001
\(276\) 0 0
\(277\) −12.4127 −0.745805 −0.372903 0.927871i \(-0.621637\pi\)
−0.372903 + 0.927871i \(0.621637\pi\)
\(278\) 0 0
\(279\) 2.09584 0.125475
\(280\) 0 0
\(281\) −8.24750 −0.492004 −0.246002 0.969269i \(-0.579117\pi\)
−0.246002 + 0.969269i \(0.579117\pi\)
\(282\) 0 0
\(283\) −23.3593 −1.38857 −0.694283 0.719702i \(-0.744278\pi\)
−0.694283 + 0.719702i \(0.744278\pi\)
\(284\) 0 0
\(285\) 3.91226 0.231742
\(286\) 0 0
\(287\) 0.892417 0.0526777
\(288\) 0 0
\(289\) 2.03281 0.119577
\(290\) 0 0
\(291\) −3.96270 −0.232298
\(292\) 0 0
\(293\) 27.5343 1.60857 0.804286 0.594242i \(-0.202548\pi\)
0.804286 + 0.594242i \(0.202548\pi\)
\(294\) 0 0
\(295\) −18.7933 −1.09419
\(296\) 0 0
\(297\) −4.84583 −0.281184
\(298\) 0 0
\(299\) −8.32650 −0.481534
\(300\) 0 0
\(301\) −10.5656 −0.608989
\(302\) 0 0
\(303\) 3.61496 0.207674
\(304\) 0 0
\(305\) 14.6789 0.840514
\(306\) 0 0
\(307\) 9.65984 0.551316 0.275658 0.961256i \(-0.411104\pi\)
0.275658 + 0.961256i \(0.411104\pi\)
\(308\) 0 0
\(309\) −1.21934 −0.0693656
\(310\) 0 0
\(311\) −7.58513 −0.430113 −0.215057 0.976602i \(-0.568994\pi\)
−0.215057 + 0.976602i \(0.568994\pi\)
\(312\) 0 0
\(313\) 21.4572 1.21283 0.606415 0.795148i \(-0.292607\pi\)
0.606415 + 0.795148i \(0.292607\pi\)
\(314\) 0 0
\(315\) 12.2440 0.689870
\(316\) 0 0
\(317\) −24.8585 −1.39619 −0.698096 0.716004i \(-0.745969\pi\)
−0.698096 + 0.716004i \(0.745969\pi\)
\(318\) 0 0
\(319\) −6.19689 −0.346959
\(320\) 0 0
\(321\) −5.64921 −0.315308
\(322\) 0 0
\(323\) −20.5025 −1.14079
\(324\) 0 0
\(325\) 3.89351 0.215973
\(326\) 0 0
\(327\) 3.77940 0.209001
\(328\) 0 0
\(329\) 14.9975 0.826837
\(330\) 0 0
\(331\) 32.8366 1.80487 0.902433 0.430831i \(-0.141780\pi\)
0.902433 + 0.430831i \(0.141780\pi\)
\(332\) 0 0
\(333\) 20.3383 1.11453
\(334\) 0 0
\(335\) −2.19285 −0.119808
\(336\) 0 0
\(337\) 3.38650 0.184474 0.0922372 0.995737i \(-0.470598\pi\)
0.0922372 + 0.995737i \(0.470598\pi\)
\(338\) 0 0
\(339\) 2.67818 0.145459
\(340\) 0 0
\(341\) 1.73452 0.0939297
\(342\) 0 0
\(343\) 19.2115 1.03733
\(344\) 0 0
\(345\) 1.42420 0.0766762
\(346\) 0 0
\(347\) 34.6622 1.86077 0.930383 0.366588i \(-0.119474\pi\)
0.930383 + 0.366588i \(0.119474\pi\)
\(348\) 0 0
\(349\) −15.7339 −0.842215 −0.421108 0.907011i \(-0.638359\pi\)
−0.421108 + 0.907011i \(0.638359\pi\)
\(350\) 0 0
\(351\) 9.89332 0.528066
\(352\) 0 0
\(353\) −13.0604 −0.695133 −0.347567 0.937655i \(-0.612992\pi\)
−0.347567 + 0.937655i \(0.612992\pi\)
\(354\) 0 0
\(355\) 30.3435 1.61047
\(356\) 0 0
\(357\) 2.66165 0.140870
\(358\) 0 0
\(359\) −3.98010 −0.210062 −0.105031 0.994469i \(-0.533494\pi\)
−0.105031 + 0.994469i \(0.533494\pi\)
\(360\) 0 0
\(361\) 3.08557 0.162398
\(362\) 0 0
\(363\) 1.83789 0.0964643
\(364\) 0 0
\(365\) 18.3865 0.962394
\(366\) 0 0
\(367\) −11.0076 −0.574595 −0.287297 0.957841i \(-0.592757\pi\)
−0.287297 + 0.957841i \(0.592757\pi\)
\(368\) 0 0
\(369\) 1.45646 0.0758202
\(370\) 0 0
\(371\) −8.71616 −0.452521
\(372\) 0 0
\(373\) −18.2570 −0.945313 −0.472656 0.881247i \(-0.656705\pi\)
−0.472656 + 0.881247i \(0.656705\pi\)
\(374\) 0 0
\(375\) 3.49644 0.180555
\(376\) 0 0
\(377\) 12.6517 0.651594
\(378\) 0 0
\(379\) 6.83252 0.350963 0.175481 0.984483i \(-0.443852\pi\)
0.175481 + 0.984483i \(0.443852\pi\)
\(380\) 0 0
\(381\) 4.79241 0.245522
\(382\) 0 0
\(383\) −24.6179 −1.25792 −0.628958 0.777439i \(-0.716518\pi\)
−0.628958 + 0.777439i \(0.716518\pi\)
\(384\) 0 0
\(385\) 10.1332 0.516434
\(386\) 0 0
\(387\) −17.2434 −0.876531
\(388\) 0 0
\(389\) −18.6918 −0.947714 −0.473857 0.880602i \(-0.657139\pi\)
−0.473857 + 0.880602i \(0.657139\pi\)
\(390\) 0 0
\(391\) −7.46359 −0.377450
\(392\) 0 0
\(393\) 3.87432 0.195433
\(394\) 0 0
\(395\) −29.0256 −1.46044
\(396\) 0 0
\(397\) −3.74016 −0.187713 −0.0938566 0.995586i \(-0.529920\pi\)
−0.0938566 + 0.995586i \(0.529920\pi\)
\(398\) 0 0
\(399\) −2.86718 −0.143538
\(400\) 0 0
\(401\) 6.02949 0.301098 0.150549 0.988603i \(-0.451896\pi\)
0.150549 + 0.988603i \(0.451896\pi\)
\(402\) 0 0
\(403\) −3.54123 −0.176401
\(404\) 0 0
\(405\) 19.1193 0.950048
\(406\) 0 0
\(407\) 16.8321 0.834334
\(408\) 0 0
\(409\) 18.6504 0.922202 0.461101 0.887348i \(-0.347455\pi\)
0.461101 + 0.887348i \(0.347455\pi\)
\(410\) 0 0
\(411\) −0.496846 −0.0245076
\(412\) 0 0
\(413\) 13.7730 0.677726
\(414\) 0 0
\(415\) −38.4637 −1.88811
\(416\) 0 0
\(417\) 2.19198 0.107342
\(418\) 0 0
\(419\) −5.12097 −0.250176 −0.125088 0.992146i \(-0.539921\pi\)
−0.125088 + 0.992146i \(0.539921\pi\)
\(420\) 0 0
\(421\) 22.6013 1.10152 0.550759 0.834664i \(-0.314338\pi\)
0.550759 + 0.834664i \(0.314338\pi\)
\(422\) 0 0
\(423\) 24.4764 1.19008
\(424\) 0 0
\(425\) 3.49001 0.169290
\(426\) 0 0
\(427\) −10.7578 −0.520604
\(428\) 0 0
\(429\) 4.01069 0.193638
\(430\) 0 0
\(431\) −29.5884 −1.42522 −0.712612 0.701558i \(-0.752488\pi\)
−0.712612 + 0.701558i \(0.752488\pi\)
\(432\) 0 0
\(433\) −15.9988 −0.768852 −0.384426 0.923156i \(-0.625601\pi\)
−0.384426 + 0.923156i \(0.625601\pi\)
\(434\) 0 0
\(435\) −2.16399 −0.103755
\(436\) 0 0
\(437\) 8.03990 0.384601
\(438\) 0 0
\(439\) 26.8720 1.28253 0.641266 0.767319i \(-0.278410\pi\)
0.641266 + 0.767319i \(0.278410\pi\)
\(440\) 0 0
\(441\) 11.1904 0.532874
\(442\) 0 0
\(443\) −25.4164 −1.20757 −0.603786 0.797146i \(-0.706342\pi\)
−0.603786 + 0.797146i \(0.706342\pi\)
\(444\) 0 0
\(445\) −32.7043 −1.55033
\(446\) 0 0
\(447\) 7.61099 0.359987
\(448\) 0 0
\(449\) 6.13787 0.289664 0.144832 0.989456i \(-0.453736\pi\)
0.144832 + 0.989456i \(0.453736\pi\)
\(450\) 0 0
\(451\) 1.20537 0.0567587
\(452\) 0 0
\(453\) 0.169102 0.00794510
\(454\) 0 0
\(455\) −20.6880 −0.969869
\(456\) 0 0
\(457\) 18.9094 0.884543 0.442272 0.896881i \(-0.354173\pi\)
0.442272 + 0.896881i \(0.354173\pi\)
\(458\) 0 0
\(459\) 8.86803 0.413924
\(460\) 0 0
\(461\) −21.4986 −1.00129 −0.500646 0.865652i \(-0.666904\pi\)
−0.500646 + 0.865652i \(0.666904\pi\)
\(462\) 0 0
\(463\) 20.7435 0.964031 0.482016 0.876163i \(-0.339905\pi\)
0.482016 + 0.876163i \(0.339905\pi\)
\(464\) 0 0
\(465\) 0.605705 0.0280889
\(466\) 0 0
\(467\) −13.7390 −0.635765 −0.317883 0.948130i \(-0.602972\pi\)
−0.317883 + 0.948130i \(0.602972\pi\)
\(468\) 0 0
\(469\) 1.60708 0.0742079
\(470\) 0 0
\(471\) 3.03524 0.139856
\(472\) 0 0
\(473\) −14.2707 −0.656168
\(474\) 0 0
\(475\) −3.75949 −0.172497
\(476\) 0 0
\(477\) −14.2251 −0.651323
\(478\) 0 0
\(479\) 31.2040 1.42575 0.712873 0.701294i \(-0.247394\pi\)
0.712873 + 0.701294i \(0.247394\pi\)
\(480\) 0 0
\(481\) −34.3646 −1.56689
\(482\) 0 0
\(483\) −1.04375 −0.0474923
\(484\) 0 0
\(485\) 27.6085 1.25364
\(486\) 0 0
\(487\) −39.8122 −1.80406 −0.902031 0.431671i \(-0.857924\pi\)
−0.902031 + 0.431671i \(0.857924\pi\)
\(488\) 0 0
\(489\) −2.04009 −0.0922563
\(490\) 0 0
\(491\) 5.16131 0.232927 0.116463 0.993195i \(-0.462844\pi\)
0.116463 + 0.993195i \(0.462844\pi\)
\(492\) 0 0
\(493\) 11.3405 0.510752
\(494\) 0 0
\(495\) 16.5377 0.743314
\(496\) 0 0
\(497\) −22.2379 −0.997504
\(498\) 0 0
\(499\) −19.9568 −0.893391 −0.446696 0.894686i \(-0.647399\pi\)
−0.446696 + 0.894686i \(0.647399\pi\)
\(500\) 0 0
\(501\) −5.96449 −0.266474
\(502\) 0 0
\(503\) 16.6423 0.742044 0.371022 0.928624i \(-0.379007\pi\)
0.371022 + 0.928624i \(0.379007\pi\)
\(504\) 0 0
\(505\) −25.1858 −1.12075
\(506\) 0 0
\(507\) −3.69459 −0.164082
\(508\) 0 0
\(509\) 19.6290 0.870039 0.435019 0.900421i \(-0.356742\pi\)
0.435019 + 0.900421i \(0.356742\pi\)
\(510\) 0 0
\(511\) −13.4749 −0.596095
\(512\) 0 0
\(513\) −9.55279 −0.421766
\(514\) 0 0
\(515\) 8.49524 0.374345
\(516\) 0 0
\(517\) 20.2568 0.890892
\(518\) 0 0
\(519\) 7.46023 0.327468
\(520\) 0 0
\(521\) 34.8899 1.52855 0.764277 0.644889i \(-0.223096\pi\)
0.764277 + 0.644889i \(0.223096\pi\)
\(522\) 0 0
\(523\) 9.51450 0.416040 0.208020 0.978125i \(-0.433298\pi\)
0.208020 + 0.978125i \(0.433298\pi\)
\(524\) 0 0
\(525\) 0.488062 0.0213008
\(526\) 0 0
\(527\) −3.17424 −0.138272
\(528\) 0 0
\(529\) −20.0732 −0.872748
\(530\) 0 0
\(531\) 22.4781 0.975466
\(532\) 0 0
\(533\) −2.46090 −0.106594
\(534\) 0 0
\(535\) 39.3586 1.70162
\(536\) 0 0
\(537\) −2.04061 −0.0880587
\(538\) 0 0
\(539\) 9.26118 0.398907
\(540\) 0 0
\(541\) −1.90299 −0.0818158 −0.0409079 0.999163i \(-0.513025\pi\)
−0.0409079 + 0.999163i \(0.513025\pi\)
\(542\) 0 0
\(543\) 0.0291847 0.00125244
\(544\) 0 0
\(545\) −26.3315 −1.12792
\(546\) 0 0
\(547\) 1.14465 0.0489416 0.0244708 0.999701i \(-0.492210\pi\)
0.0244708 + 0.999701i \(0.492210\pi\)
\(548\) 0 0
\(549\) −17.5571 −0.749317
\(550\) 0 0
\(551\) −12.2162 −0.520427
\(552\) 0 0
\(553\) 21.2720 0.904577
\(554\) 0 0
\(555\) 5.87785 0.249501
\(556\) 0 0
\(557\) −4.16627 −0.176531 −0.0882653 0.996097i \(-0.528132\pi\)
−0.0882653 + 0.996097i \(0.528132\pi\)
\(558\) 0 0
\(559\) 29.1353 1.23229
\(560\) 0 0
\(561\) 3.59505 0.151783
\(562\) 0 0
\(563\) −30.1721 −1.27160 −0.635801 0.771853i \(-0.719330\pi\)
−0.635801 + 0.771853i \(0.719330\pi\)
\(564\) 0 0
\(565\) −18.6592 −0.784997
\(566\) 0 0
\(567\) −14.0120 −0.588448
\(568\) 0 0
\(569\) −11.0112 −0.461614 −0.230807 0.973000i \(-0.574137\pi\)
−0.230807 + 0.973000i \(0.574137\pi\)
\(570\) 0 0
\(571\) −2.87520 −0.120323 −0.0601617 0.998189i \(-0.519162\pi\)
−0.0601617 + 0.998189i \(0.519162\pi\)
\(572\) 0 0
\(573\) −2.77431 −0.115899
\(574\) 0 0
\(575\) −1.36858 −0.0570739
\(576\) 0 0
\(577\) −2.04004 −0.0849280 −0.0424640 0.999098i \(-0.513521\pi\)
−0.0424640 + 0.999098i \(0.513521\pi\)
\(578\) 0 0
\(579\) 2.96486 0.123215
\(580\) 0 0
\(581\) 28.1889 1.16947
\(582\) 0 0
\(583\) −11.7728 −0.487578
\(584\) 0 0
\(585\) −33.7636 −1.39595
\(586\) 0 0
\(587\) −18.9834 −0.783531 −0.391765 0.920065i \(-0.628135\pi\)
−0.391765 + 0.920065i \(0.628135\pi\)
\(588\) 0 0
\(589\) 3.41934 0.140891
\(590\) 0 0
\(591\) −8.11288 −0.333719
\(592\) 0 0
\(593\) 7.28178 0.299027 0.149513 0.988760i \(-0.452229\pi\)
0.149513 + 0.988760i \(0.452229\pi\)
\(594\) 0 0
\(595\) −18.5440 −0.760231
\(596\) 0 0
\(597\) 4.28074 0.175199
\(598\) 0 0
\(599\) −9.89664 −0.404366 −0.202183 0.979348i \(-0.564804\pi\)
−0.202183 + 0.979348i \(0.564804\pi\)
\(600\) 0 0
\(601\) −41.7579 −1.70334 −0.851669 0.524080i \(-0.824409\pi\)
−0.851669 + 0.524080i \(0.824409\pi\)
\(602\) 0 0
\(603\) 2.62281 0.106809
\(604\) 0 0
\(605\) −12.8048 −0.520588
\(606\) 0 0
\(607\) 10.5724 0.429121 0.214560 0.976711i \(-0.431168\pi\)
0.214560 + 0.976711i \(0.431168\pi\)
\(608\) 0 0
\(609\) 1.58592 0.0642648
\(610\) 0 0
\(611\) −41.3565 −1.67311
\(612\) 0 0
\(613\) −25.4068 −1.02617 −0.513085 0.858338i \(-0.671497\pi\)
−0.513085 + 0.858338i \(0.671497\pi\)
\(614\) 0 0
\(615\) 0.420922 0.0169732
\(616\) 0 0
\(617\) −13.1154 −0.528007 −0.264003 0.964522i \(-0.585043\pi\)
−0.264003 + 0.964522i \(0.585043\pi\)
\(618\) 0 0
\(619\) −25.6281 −1.03008 −0.515041 0.857166i \(-0.672223\pi\)
−0.515041 + 0.857166i \(0.672223\pi\)
\(620\) 0 0
\(621\) −3.47754 −0.139549
\(622\) 0 0
\(623\) 23.9680 0.960257
\(624\) 0 0
\(625\) −28.3599 −1.13440
\(626\) 0 0
\(627\) −3.87264 −0.154658
\(628\) 0 0
\(629\) −30.8032 −1.22821
\(630\) 0 0
\(631\) −11.0099 −0.438299 −0.219149 0.975691i \(-0.570328\pi\)
−0.219149 + 0.975691i \(0.570328\pi\)
\(632\) 0 0
\(633\) 4.02351 0.159920
\(634\) 0 0
\(635\) −33.3892 −1.32501
\(636\) 0 0
\(637\) −18.9078 −0.749153
\(638\) 0 0
\(639\) −36.2930 −1.43573
\(640\) 0 0
\(641\) 3.74422 0.147888 0.0739439 0.997262i \(-0.476441\pi\)
0.0739439 + 0.997262i \(0.476441\pi\)
\(642\) 0 0
\(643\) 5.38602 0.212404 0.106202 0.994345i \(-0.466131\pi\)
0.106202 + 0.994345i \(0.466131\pi\)
\(644\) 0 0
\(645\) −4.98341 −0.196222
\(646\) 0 0
\(647\) 16.2176 0.637579 0.318790 0.947825i \(-0.396724\pi\)
0.318790 + 0.947825i \(0.396724\pi\)
\(648\) 0 0
\(649\) 18.6030 0.730230
\(650\) 0 0
\(651\) −0.443903 −0.0173979
\(652\) 0 0
\(653\) 21.0560 0.823986 0.411993 0.911187i \(-0.364833\pi\)
0.411993 + 0.911187i \(0.364833\pi\)
\(654\) 0 0
\(655\) −26.9928 −1.05469
\(656\) 0 0
\(657\) −21.9916 −0.857973
\(658\) 0 0
\(659\) −35.7317 −1.39191 −0.695954 0.718086i \(-0.745018\pi\)
−0.695954 + 0.718086i \(0.745018\pi\)
\(660\) 0 0
\(661\) 6.06191 0.235781 0.117890 0.993027i \(-0.462387\pi\)
0.117890 + 0.993027i \(0.462387\pi\)
\(662\) 0 0
\(663\) −7.33970 −0.285050
\(664\) 0 0
\(665\) 19.9759 0.774633
\(666\) 0 0
\(667\) −4.44711 −0.172193
\(668\) 0 0
\(669\) −5.81257 −0.224727
\(670\) 0 0
\(671\) −14.5303 −0.560936
\(672\) 0 0
\(673\) 49.8548 1.92176 0.960881 0.276960i \(-0.0893271\pi\)
0.960881 + 0.276960i \(0.0893271\pi\)
\(674\) 0 0
\(675\) 1.62611 0.0625891
\(676\) 0 0
\(677\) 34.4365 1.32350 0.661750 0.749724i \(-0.269814\pi\)
0.661750 + 0.749724i \(0.269814\pi\)
\(678\) 0 0
\(679\) −20.2335 −0.776489
\(680\) 0 0
\(681\) −2.71249 −0.103943
\(682\) 0 0
\(683\) −9.65122 −0.369294 −0.184647 0.982805i \(-0.559114\pi\)
−0.184647 + 0.982805i \(0.559114\pi\)
\(684\) 0 0
\(685\) 3.46158 0.132260
\(686\) 0 0
\(687\) −3.76359 −0.143590
\(688\) 0 0
\(689\) 24.0354 0.915677
\(690\) 0 0
\(691\) −19.5886 −0.745184 −0.372592 0.927995i \(-0.621531\pi\)
−0.372592 + 0.927995i \(0.621531\pi\)
\(692\) 0 0
\(693\) −12.1200 −0.460400
\(694\) 0 0
\(695\) −15.2717 −0.579290
\(696\) 0 0
\(697\) −2.20587 −0.0835533
\(698\) 0 0
\(699\) −1.87146 −0.0707850
\(700\) 0 0
\(701\) 26.2854 0.992788 0.496394 0.868097i \(-0.334657\pi\)
0.496394 + 0.868097i \(0.334657\pi\)
\(702\) 0 0
\(703\) 33.1817 1.25147
\(704\) 0 0
\(705\) 7.07378 0.266414
\(706\) 0 0
\(707\) 18.4579 0.694181
\(708\) 0 0
\(709\) −1.38546 −0.0520321 −0.0260161 0.999662i \(-0.508282\pi\)
−0.0260161 + 0.999662i \(0.508282\pi\)
\(710\) 0 0
\(711\) 34.7167 1.30198
\(712\) 0 0
\(713\) 1.24476 0.0466165
\(714\) 0 0
\(715\) −27.9429 −1.04501
\(716\) 0 0
\(717\) 9.69284 0.361986
\(718\) 0 0
\(719\) 0.0270462 0.00100865 0.000504326 1.00000i \(-0.499839\pi\)
0.000504326 1.00000i \(0.499839\pi\)
\(720\) 0 0
\(721\) −6.22590 −0.231865
\(722\) 0 0
\(723\) 3.39755 0.126356
\(724\) 0 0
\(725\) 2.07949 0.0772303
\(726\) 0 0
\(727\) 27.6126 1.02409 0.512047 0.858957i \(-0.328887\pi\)
0.512047 + 0.858957i \(0.328887\pi\)
\(728\) 0 0
\(729\) −20.7601 −0.768894
\(730\) 0 0
\(731\) 26.1159 0.965930
\(732\) 0 0
\(733\) 23.5920 0.871390 0.435695 0.900094i \(-0.356503\pi\)
0.435695 + 0.900094i \(0.356503\pi\)
\(734\) 0 0
\(735\) 3.23406 0.119290
\(736\) 0 0
\(737\) 2.17065 0.0799568
\(738\) 0 0
\(739\) −6.67759 −0.245639 −0.122820 0.992429i \(-0.539194\pi\)
−0.122820 + 0.992429i \(0.539194\pi\)
\(740\) 0 0
\(741\) 7.90644 0.290450
\(742\) 0 0
\(743\) 24.0827 0.883509 0.441754 0.897136i \(-0.354356\pi\)
0.441754 + 0.897136i \(0.354356\pi\)
\(744\) 0 0
\(745\) −53.0266 −1.94274
\(746\) 0 0
\(747\) 46.0053 1.68325
\(748\) 0 0
\(749\) −28.8447 −1.05396
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 2.59868 0.0947011
\(754\) 0 0
\(755\) −1.17815 −0.0428773
\(756\) 0 0
\(757\) 15.7801 0.573536 0.286768 0.958000i \(-0.407419\pi\)
0.286768 + 0.958000i \(0.407419\pi\)
\(758\) 0 0
\(759\) −1.40977 −0.0511715
\(760\) 0 0
\(761\) −45.4764 −1.64852 −0.824260 0.566212i \(-0.808408\pi\)
−0.824260 + 0.566212i \(0.808408\pi\)
\(762\) 0 0
\(763\) 19.2975 0.698618
\(764\) 0 0
\(765\) −30.2646 −1.09422
\(766\) 0 0
\(767\) −37.9801 −1.37138
\(768\) 0 0
\(769\) 0.00267693 9.65325e−5 0 4.82663e−5 1.00000i \(-0.499985\pi\)
4.82663e−5 1.00000i \(0.499985\pi\)
\(770\) 0 0
\(771\) −8.89055 −0.320185
\(772\) 0 0
\(773\) −55.0852 −1.98128 −0.990639 0.136506i \(-0.956413\pi\)
−0.990639 + 0.136506i \(0.956413\pi\)
\(774\) 0 0
\(775\) −0.582053 −0.0209080
\(776\) 0 0
\(777\) −4.30770 −0.154538
\(778\) 0 0
\(779\) 2.37620 0.0851361
\(780\) 0 0
\(781\) −30.0363 −1.07478
\(782\) 0 0
\(783\) 5.28394 0.188832
\(784\) 0 0
\(785\) −21.1468 −0.754762
\(786\) 0 0
\(787\) 14.0275 0.500025 0.250012 0.968243i \(-0.419565\pi\)
0.250012 + 0.968243i \(0.419565\pi\)
\(788\) 0 0
\(789\) 3.68477 0.131181
\(790\) 0 0
\(791\) 13.6747 0.486217
\(792\) 0 0
\(793\) 29.6653 1.05344
\(794\) 0 0
\(795\) −4.11111 −0.145806
\(796\) 0 0
\(797\) 45.8671 1.62469 0.812347 0.583174i \(-0.198189\pi\)
0.812347 + 0.583174i \(0.198189\pi\)
\(798\) 0 0
\(799\) −37.0706 −1.31146
\(800\) 0 0
\(801\) 39.1166 1.38212
\(802\) 0 0
\(803\) −18.2003 −0.642275
\(804\) 0 0
\(805\) 7.27192 0.256301
\(806\) 0 0
\(807\) 10.9468 0.385346
\(808\) 0 0
\(809\) 25.8037 0.907209 0.453605 0.891203i \(-0.350138\pi\)
0.453605 + 0.891203i \(0.350138\pi\)
\(810\) 0 0
\(811\) 25.6603 0.901055 0.450527 0.892763i \(-0.351236\pi\)
0.450527 + 0.892763i \(0.351236\pi\)
\(812\) 0 0
\(813\) 3.77350 0.132343
\(814\) 0 0
\(815\) 14.2136 0.497879
\(816\) 0 0
\(817\) −28.1324 −0.984229
\(818\) 0 0
\(819\) 24.7443 0.864637
\(820\) 0 0
\(821\) 12.1493 0.424013 0.212006 0.977268i \(-0.432000\pi\)
0.212006 + 0.977268i \(0.432000\pi\)
\(822\) 0 0
\(823\) 27.6280 0.963050 0.481525 0.876432i \(-0.340083\pi\)
0.481525 + 0.876432i \(0.340083\pi\)
\(824\) 0 0
\(825\) 0.659216 0.0229510
\(826\) 0 0
\(827\) −0.328324 −0.0114169 −0.00570847 0.999984i \(-0.501817\pi\)
−0.00570847 + 0.999984i \(0.501817\pi\)
\(828\) 0 0
\(829\) 17.0126 0.590872 0.295436 0.955363i \(-0.404535\pi\)
0.295436 + 0.955363i \(0.404535\pi\)
\(830\) 0 0
\(831\) 4.29068 0.148842
\(832\) 0 0
\(833\) −16.9483 −0.587223
\(834\) 0 0
\(835\) 41.5552 1.43808
\(836\) 0 0
\(837\) −1.47898 −0.0511212
\(838\) 0 0
\(839\) 12.7710 0.440903 0.220452 0.975398i \(-0.429247\pi\)
0.220452 + 0.975398i \(0.429247\pi\)
\(840\) 0 0
\(841\) −22.2429 −0.766995
\(842\) 0 0
\(843\) 2.85091 0.0981904
\(844\) 0 0
\(845\) 25.7406 0.885502
\(846\) 0 0
\(847\) 9.38423 0.322446
\(848\) 0 0
\(849\) 8.07459 0.277119
\(850\) 0 0
\(851\) 12.0793 0.414072
\(852\) 0 0
\(853\) 20.0843 0.687673 0.343837 0.939030i \(-0.388273\pi\)
0.343837 + 0.939030i \(0.388273\pi\)
\(854\) 0 0
\(855\) 32.6015 1.11495
\(856\) 0 0
\(857\) −48.9693 −1.67276 −0.836380 0.548149i \(-0.815333\pi\)
−0.836380 + 0.548149i \(0.815333\pi\)
\(858\) 0 0
\(859\) 44.0865 1.50421 0.752106 0.659042i \(-0.229038\pi\)
0.752106 + 0.659042i \(0.229038\pi\)
\(860\) 0 0
\(861\) −0.308481 −0.0105130
\(862\) 0 0
\(863\) −8.68309 −0.295576 −0.147788 0.989019i \(-0.547215\pi\)
−0.147788 + 0.989019i \(0.547215\pi\)
\(864\) 0 0
\(865\) −51.9762 −1.76724
\(866\) 0 0
\(867\) −0.702680 −0.0238643
\(868\) 0 0
\(869\) 28.7317 0.974655
\(870\) 0 0
\(871\) −4.43162 −0.150160
\(872\) 0 0
\(873\) −33.0218 −1.11762
\(874\) 0 0
\(875\) 17.8527 0.603533
\(876\) 0 0
\(877\) 40.9696 1.38344 0.691722 0.722163i \(-0.256852\pi\)
0.691722 + 0.722163i \(0.256852\pi\)
\(878\) 0 0
\(879\) −9.51776 −0.321026
\(880\) 0 0
\(881\) 46.3948 1.56308 0.781540 0.623856i \(-0.214435\pi\)
0.781540 + 0.623856i \(0.214435\pi\)
\(882\) 0 0
\(883\) −44.8034 −1.50776 −0.753878 0.657014i \(-0.771819\pi\)
−0.753878 + 0.657014i \(0.771819\pi\)
\(884\) 0 0
\(885\) 6.49626 0.218369
\(886\) 0 0
\(887\) 11.1769 0.375283 0.187641 0.982238i \(-0.439916\pi\)
0.187641 + 0.982238i \(0.439916\pi\)
\(888\) 0 0
\(889\) 24.4699 0.820695
\(890\) 0 0
\(891\) −18.9257 −0.634035
\(892\) 0 0
\(893\) 39.9330 1.33631
\(894\) 0 0
\(895\) 14.2171 0.475226
\(896\) 0 0
\(897\) 2.87821 0.0961008
\(898\) 0 0
\(899\) −1.89134 −0.0630797
\(900\) 0 0
\(901\) 21.5445 0.717753
\(902\) 0 0
\(903\) 3.65219 0.121537
\(904\) 0 0
\(905\) −0.203333 −0.00675902
\(906\) 0 0
\(907\) −15.6769 −0.520542 −0.260271 0.965536i \(-0.583812\pi\)
−0.260271 + 0.965536i \(0.583812\pi\)
\(908\) 0 0
\(909\) 30.1240 0.999151
\(910\) 0 0
\(911\) 26.9282 0.892171 0.446085 0.894990i \(-0.352818\pi\)
0.446085 + 0.894990i \(0.352818\pi\)
\(912\) 0 0
\(913\) 38.0742 1.26007
\(914\) 0 0
\(915\) −5.07406 −0.167743
\(916\) 0 0
\(917\) 19.7822 0.653265
\(918\) 0 0
\(919\) −38.5863 −1.27284 −0.636422 0.771341i \(-0.719586\pi\)
−0.636422 + 0.771341i \(0.719586\pi\)
\(920\) 0 0
\(921\) −3.33911 −0.110027
\(922\) 0 0
\(923\) 61.3225 2.01845
\(924\) 0 0
\(925\) −5.64832 −0.185716
\(926\) 0 0
\(927\) −10.1609 −0.333728
\(928\) 0 0
\(929\) 13.6751 0.448665 0.224333 0.974513i \(-0.427980\pi\)
0.224333 + 0.974513i \(0.427980\pi\)
\(930\) 0 0
\(931\) 18.2570 0.598348
\(932\) 0 0
\(933\) 2.62195 0.0858387
\(934\) 0 0
\(935\) −25.0471 −0.819126
\(936\) 0 0
\(937\) 21.2200 0.693228 0.346614 0.938008i \(-0.387331\pi\)
0.346614 + 0.938008i \(0.387331\pi\)
\(938\) 0 0
\(939\) −7.41708 −0.242047
\(940\) 0 0
\(941\) −38.5181 −1.25565 −0.627827 0.778353i \(-0.716056\pi\)
−0.627827 + 0.778353i \(0.716056\pi\)
\(942\) 0 0
\(943\) 0.865017 0.0281688
\(944\) 0 0
\(945\) −8.64029 −0.281069
\(946\) 0 0
\(947\) 34.2716 1.11368 0.556838 0.830621i \(-0.312014\pi\)
0.556838 + 0.830621i \(0.312014\pi\)
\(948\) 0 0
\(949\) 37.1580 1.20620
\(950\) 0 0
\(951\) 8.59281 0.278641
\(952\) 0 0
\(953\) 5.72208 0.185356 0.0926782 0.995696i \(-0.470457\pi\)
0.0926782 + 0.995696i \(0.470457\pi\)
\(954\) 0 0
\(955\) 19.3289 0.625470
\(956\) 0 0
\(957\) 2.14207 0.0692434
\(958\) 0 0
\(959\) −2.53688 −0.0819202
\(960\) 0 0
\(961\) −30.4706 −0.982923
\(962\) 0 0
\(963\) −47.0757 −1.51699
\(964\) 0 0
\(965\) −20.6565 −0.664956
\(966\) 0 0
\(967\) 1.58868 0.0510885 0.0255442 0.999674i \(-0.491868\pi\)
0.0255442 + 0.999674i \(0.491868\pi\)
\(968\) 0 0
\(969\) 7.08706 0.227669
\(970\) 0 0
\(971\) 22.7801 0.731049 0.365524 0.930802i \(-0.380890\pi\)
0.365524 + 0.930802i \(0.380890\pi\)
\(972\) 0 0
\(973\) 11.1922 0.358805
\(974\) 0 0
\(975\) −1.34587 −0.0431022
\(976\) 0 0
\(977\) 9.62553 0.307948 0.153974 0.988075i \(-0.450793\pi\)
0.153974 + 0.988075i \(0.450793\pi\)
\(978\) 0 0
\(979\) 32.3731 1.03465
\(980\) 0 0
\(981\) 31.4943 1.00554
\(982\) 0 0
\(983\) 58.5987 1.86901 0.934504 0.355953i \(-0.115844\pi\)
0.934504 + 0.355953i \(0.115844\pi\)
\(984\) 0 0
\(985\) 56.5233 1.80098
\(986\) 0 0
\(987\) −5.18416 −0.165014
\(988\) 0 0
\(989\) −10.2412 −0.325650
\(990\) 0 0
\(991\) −21.1018 −0.670322 −0.335161 0.942161i \(-0.608791\pi\)
−0.335161 + 0.942161i \(0.608791\pi\)
\(992\) 0 0
\(993\) −11.3506 −0.360201
\(994\) 0 0
\(995\) −29.8243 −0.945495
\(996\) 0 0
\(997\) −8.70858 −0.275803 −0.137902 0.990446i \(-0.544036\pi\)
−0.137902 + 0.990446i \(0.544036\pi\)
\(998\) 0 0
\(999\) −14.3523 −0.454086
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.1.23 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.23 44 1.1 even 1 trivial