Properties

Label 6008.2.a.b.1.20
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 1.20
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.753945 q^{3} -1.16579 q^{5} +1.19034 q^{7} -2.43157 q^{9} +O(q^{10})\) \(q-0.753945 q^{3} -1.16579 q^{5} +1.19034 q^{7} -2.43157 q^{9} -3.93174 q^{11} +2.90377 q^{13} +0.878938 q^{15} -1.93718 q^{17} +3.04157 q^{19} -0.897448 q^{21} +6.33561 q^{23} -3.64094 q^{25} +4.09510 q^{27} +3.20651 q^{29} +0.203587 q^{31} +2.96432 q^{33} -1.38768 q^{35} -5.22739 q^{37} -2.18928 q^{39} +10.5412 q^{41} -6.50559 q^{43} +2.83468 q^{45} -1.53219 q^{47} -5.58310 q^{49} +1.46053 q^{51} -0.0388220 q^{53} +4.58356 q^{55} -2.29318 q^{57} +4.00328 q^{59} +5.53333 q^{61} -2.89438 q^{63} -3.38517 q^{65} +12.0206 q^{67} -4.77670 q^{69} -2.94570 q^{71} +7.90151 q^{73} +2.74507 q^{75} -4.68009 q^{77} -10.4546 q^{79} +4.20722 q^{81} -4.73510 q^{83} +2.25834 q^{85} -2.41753 q^{87} -0.232387 q^{89} +3.45646 q^{91} -0.153493 q^{93} -3.54582 q^{95} +5.21513 q^{97} +9.56029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.753945 −0.435290 −0.217645 0.976028i \(-0.569838\pi\)
−0.217645 + 0.976028i \(0.569838\pi\)
\(4\) 0 0
\(5\) −1.16579 −0.521355 −0.260678 0.965426i \(-0.583946\pi\)
−0.260678 + 0.965426i \(0.583946\pi\)
\(6\) 0 0
\(7\) 1.19034 0.449905 0.224952 0.974370i \(-0.427777\pi\)
0.224952 + 0.974370i \(0.427777\pi\)
\(8\) 0 0
\(9\) −2.43157 −0.810522
\(10\) 0 0
\(11\) −3.93174 −1.18546 −0.592732 0.805400i \(-0.701951\pi\)
−0.592732 + 0.805400i \(0.701951\pi\)
\(12\) 0 0
\(13\) 2.90377 0.805361 0.402680 0.915341i \(-0.368079\pi\)
0.402680 + 0.915341i \(0.368079\pi\)
\(14\) 0 0
\(15\) 0.878938 0.226941
\(16\) 0 0
\(17\) −1.93718 −0.469836 −0.234918 0.972015i \(-0.575482\pi\)
−0.234918 + 0.972015i \(0.575482\pi\)
\(18\) 0 0
\(19\) 3.04157 0.697784 0.348892 0.937163i \(-0.386558\pi\)
0.348892 + 0.937163i \(0.386558\pi\)
\(20\) 0 0
\(21\) −0.897448 −0.195839
\(22\) 0 0
\(23\) 6.33561 1.32107 0.660533 0.750797i \(-0.270331\pi\)
0.660533 + 0.750797i \(0.270331\pi\)
\(24\) 0 0
\(25\) −3.64094 −0.728189
\(26\) 0 0
\(27\) 4.09510 0.788103
\(28\) 0 0
\(29\) 3.20651 0.595434 0.297717 0.954654i \(-0.403775\pi\)
0.297717 + 0.954654i \(0.403775\pi\)
\(30\) 0 0
\(31\) 0.203587 0.0365652 0.0182826 0.999833i \(-0.494180\pi\)
0.0182826 + 0.999833i \(0.494180\pi\)
\(32\) 0 0
\(33\) 2.96432 0.516021
\(34\) 0 0
\(35\) −1.38768 −0.234560
\(36\) 0 0
\(37\) −5.22739 −0.859378 −0.429689 0.902977i \(-0.641377\pi\)
−0.429689 + 0.902977i \(0.641377\pi\)
\(38\) 0 0
\(39\) −2.18928 −0.350566
\(40\) 0 0
\(41\) 10.5412 1.64626 0.823129 0.567855i \(-0.192227\pi\)
0.823129 + 0.567855i \(0.192227\pi\)
\(42\) 0 0
\(43\) −6.50559 −0.992093 −0.496046 0.868296i \(-0.665215\pi\)
−0.496046 + 0.868296i \(0.665215\pi\)
\(44\) 0 0
\(45\) 2.83468 0.422570
\(46\) 0 0
\(47\) −1.53219 −0.223492 −0.111746 0.993737i \(-0.535644\pi\)
−0.111746 + 0.993737i \(0.535644\pi\)
\(48\) 0 0
\(49\) −5.58310 −0.797586
\(50\) 0 0
\(51\) 1.46053 0.204515
\(52\) 0 0
\(53\) −0.0388220 −0.00533261 −0.00266630 0.999996i \(-0.500849\pi\)
−0.00266630 + 0.999996i \(0.500849\pi\)
\(54\) 0 0
\(55\) 4.58356 0.618048
\(56\) 0 0
\(57\) −2.29318 −0.303739
\(58\) 0 0
\(59\) 4.00328 0.521183 0.260591 0.965449i \(-0.416082\pi\)
0.260591 + 0.965449i \(0.416082\pi\)
\(60\) 0 0
\(61\) 5.53333 0.708470 0.354235 0.935156i \(-0.384741\pi\)
0.354235 + 0.935156i \(0.384741\pi\)
\(62\) 0 0
\(63\) −2.89438 −0.364658
\(64\) 0 0
\(65\) −3.38517 −0.419879
\(66\) 0 0
\(67\) 12.0206 1.46856 0.734278 0.678849i \(-0.237521\pi\)
0.734278 + 0.678849i \(0.237521\pi\)
\(68\) 0 0
\(69\) −4.77670 −0.575047
\(70\) 0 0
\(71\) −2.94570 −0.349590 −0.174795 0.984605i \(-0.555926\pi\)
−0.174795 + 0.984605i \(0.555926\pi\)
\(72\) 0 0
\(73\) 7.90151 0.924802 0.462401 0.886671i \(-0.346988\pi\)
0.462401 + 0.886671i \(0.346988\pi\)
\(74\) 0 0
\(75\) 2.74507 0.316974
\(76\) 0 0
\(77\) −4.68009 −0.533346
\(78\) 0 0
\(79\) −10.4546 −1.17624 −0.588119 0.808774i \(-0.700131\pi\)
−0.588119 + 0.808774i \(0.700131\pi\)
\(80\) 0 0
\(81\) 4.20722 0.467469
\(82\) 0 0
\(83\) −4.73510 −0.519745 −0.259873 0.965643i \(-0.583681\pi\)
−0.259873 + 0.965643i \(0.583681\pi\)
\(84\) 0 0
\(85\) 2.25834 0.244951
\(86\) 0 0
\(87\) −2.41753 −0.259187
\(88\) 0 0
\(89\) −0.232387 −0.0246330 −0.0123165 0.999924i \(-0.503921\pi\)
−0.0123165 + 0.999924i \(0.503921\pi\)
\(90\) 0 0
\(91\) 3.45646 0.362336
\(92\) 0 0
\(93\) −0.153493 −0.0159165
\(94\) 0 0
\(95\) −3.54582 −0.363793
\(96\) 0 0
\(97\) 5.21513 0.529516 0.264758 0.964315i \(-0.414708\pi\)
0.264758 + 0.964315i \(0.414708\pi\)
\(98\) 0 0
\(99\) 9.56029 0.960845
\(100\) 0 0
\(101\) −2.18327 −0.217244 −0.108622 0.994083i \(-0.534644\pi\)
−0.108622 + 0.994083i \(0.534644\pi\)
\(102\) 0 0
\(103\) −18.3295 −1.80606 −0.903028 0.429582i \(-0.858661\pi\)
−0.903028 + 0.429582i \(0.858661\pi\)
\(104\) 0 0
\(105\) 1.04623 0.102102
\(106\) 0 0
\(107\) −6.21563 −0.600887 −0.300444 0.953800i \(-0.597135\pi\)
−0.300444 + 0.953800i \(0.597135\pi\)
\(108\) 0 0
\(109\) −16.4967 −1.58010 −0.790048 0.613045i \(-0.789944\pi\)
−0.790048 + 0.613045i \(0.789944\pi\)
\(110\) 0 0
\(111\) 3.94116 0.374079
\(112\) 0 0
\(113\) 2.25911 0.212519 0.106260 0.994338i \(-0.466113\pi\)
0.106260 + 0.994338i \(0.466113\pi\)
\(114\) 0 0
\(115\) −7.38596 −0.688744
\(116\) 0 0
\(117\) −7.06071 −0.652763
\(118\) 0 0
\(119\) −2.30590 −0.211381
\(120\) 0 0
\(121\) 4.45857 0.405325
\(122\) 0 0
\(123\) −7.94748 −0.716600
\(124\) 0 0
\(125\) 10.0735 0.901000
\(126\) 0 0
\(127\) −17.1911 −1.52546 −0.762731 0.646715i \(-0.776142\pi\)
−0.762731 + 0.646715i \(0.776142\pi\)
\(128\) 0 0
\(129\) 4.90486 0.431849
\(130\) 0 0
\(131\) 17.2494 1.50709 0.753546 0.657396i \(-0.228342\pi\)
0.753546 + 0.657396i \(0.228342\pi\)
\(132\) 0 0
\(133\) 3.62049 0.313936
\(134\) 0 0
\(135\) −4.77401 −0.410881
\(136\) 0 0
\(137\) −17.4442 −1.49036 −0.745178 0.666866i \(-0.767635\pi\)
−0.745178 + 0.666866i \(0.767635\pi\)
\(138\) 0 0
\(139\) −7.39978 −0.627641 −0.313821 0.949482i \(-0.601609\pi\)
−0.313821 + 0.949482i \(0.601609\pi\)
\(140\) 0 0
\(141\) 1.15518 0.0972841
\(142\) 0 0
\(143\) −11.4169 −0.954726
\(144\) 0 0
\(145\) −3.73810 −0.310432
\(146\) 0 0
\(147\) 4.20935 0.347182
\(148\) 0 0
\(149\) −18.2348 −1.49385 −0.746925 0.664908i \(-0.768471\pi\)
−0.746925 + 0.664908i \(0.768471\pi\)
\(150\) 0 0
\(151\) −11.1641 −0.908521 −0.454261 0.890869i \(-0.650096\pi\)
−0.454261 + 0.890869i \(0.650096\pi\)
\(152\) 0 0
\(153\) 4.71039 0.380813
\(154\) 0 0
\(155\) −0.237338 −0.0190635
\(156\) 0 0
\(157\) 7.07285 0.564475 0.282238 0.959345i \(-0.408923\pi\)
0.282238 + 0.959345i \(0.408923\pi\)
\(158\) 0 0
\(159\) 0.0292696 0.00232123
\(160\) 0 0
\(161\) 7.54150 0.594353
\(162\) 0 0
\(163\) −15.3342 −1.20107 −0.600534 0.799599i \(-0.705045\pi\)
−0.600534 + 0.799599i \(0.705045\pi\)
\(164\) 0 0
\(165\) −3.45576 −0.269030
\(166\) 0 0
\(167\) 8.75536 0.677510 0.338755 0.940875i \(-0.389994\pi\)
0.338755 + 0.940875i \(0.389994\pi\)
\(168\) 0 0
\(169\) −4.56812 −0.351394
\(170\) 0 0
\(171\) −7.39578 −0.565570
\(172\) 0 0
\(173\) 9.81476 0.746202 0.373101 0.927791i \(-0.378294\pi\)
0.373101 + 0.927791i \(0.378294\pi\)
\(174\) 0 0
\(175\) −4.33395 −0.327615
\(176\) 0 0
\(177\) −3.01826 −0.226866
\(178\) 0 0
\(179\) −4.72461 −0.353134 −0.176567 0.984289i \(-0.556499\pi\)
−0.176567 + 0.984289i \(0.556499\pi\)
\(180\) 0 0
\(181\) 8.33219 0.619327 0.309664 0.950846i \(-0.399784\pi\)
0.309664 + 0.950846i \(0.399784\pi\)
\(182\) 0 0
\(183\) −4.17182 −0.308390
\(184\) 0 0
\(185\) 6.09401 0.448041
\(186\) 0 0
\(187\) 7.61650 0.556974
\(188\) 0 0
\(189\) 4.87455 0.354571
\(190\) 0 0
\(191\) −15.9022 −1.15064 −0.575321 0.817928i \(-0.695123\pi\)
−0.575321 + 0.817928i \(0.695123\pi\)
\(192\) 0 0
\(193\) 14.6714 1.05607 0.528036 0.849222i \(-0.322929\pi\)
0.528036 + 0.849222i \(0.322929\pi\)
\(194\) 0 0
\(195\) 2.55223 0.182769
\(196\) 0 0
\(197\) −6.47639 −0.461424 −0.230712 0.973022i \(-0.574105\pi\)
−0.230712 + 0.973022i \(0.574105\pi\)
\(198\) 0 0
\(199\) 0.905920 0.0642190 0.0321095 0.999484i \(-0.489777\pi\)
0.0321095 + 0.999484i \(0.489777\pi\)
\(200\) 0 0
\(201\) −9.06291 −0.639248
\(202\) 0 0
\(203\) 3.81682 0.267888
\(204\) 0 0
\(205\) −12.2888 −0.858284
\(206\) 0 0
\(207\) −15.4054 −1.07075
\(208\) 0 0
\(209\) −11.9587 −0.827198
\(210\) 0 0
\(211\) −8.14511 −0.560732 −0.280366 0.959893i \(-0.590456\pi\)
−0.280366 + 0.959893i \(0.590456\pi\)
\(212\) 0 0
\(213\) 2.22090 0.152173
\(214\) 0 0
\(215\) 7.58412 0.517233
\(216\) 0 0
\(217\) 0.242336 0.0164509
\(218\) 0 0
\(219\) −5.95730 −0.402557
\(220\) 0 0
\(221\) −5.62514 −0.378388
\(222\) 0 0
\(223\) 5.25390 0.351827 0.175913 0.984406i \(-0.443712\pi\)
0.175913 + 0.984406i \(0.443712\pi\)
\(224\) 0 0
\(225\) 8.85320 0.590213
\(226\) 0 0
\(227\) 26.0098 1.72633 0.863166 0.504921i \(-0.168478\pi\)
0.863166 + 0.504921i \(0.168478\pi\)
\(228\) 0 0
\(229\) 1.40548 0.0928767 0.0464383 0.998921i \(-0.485213\pi\)
0.0464383 + 0.998921i \(0.485213\pi\)
\(230\) 0 0
\(231\) 3.52853 0.232160
\(232\) 0 0
\(233\) 21.6290 1.41697 0.708483 0.705728i \(-0.249380\pi\)
0.708483 + 0.705728i \(0.249380\pi\)
\(234\) 0 0
\(235\) 1.78620 0.116519
\(236\) 0 0
\(237\) 7.88222 0.512005
\(238\) 0 0
\(239\) 20.7620 1.34298 0.671490 0.741014i \(-0.265655\pi\)
0.671490 + 0.741014i \(0.265655\pi\)
\(240\) 0 0
\(241\) −27.9928 −1.80317 −0.901586 0.432600i \(-0.857596\pi\)
−0.901586 + 0.432600i \(0.857596\pi\)
\(242\) 0 0
\(243\) −15.4573 −0.991588
\(244\) 0 0
\(245\) 6.50870 0.415825
\(246\) 0 0
\(247\) 8.83202 0.561968
\(248\) 0 0
\(249\) 3.57001 0.226240
\(250\) 0 0
\(251\) −24.8832 −1.57061 −0.785306 0.619108i \(-0.787494\pi\)
−0.785306 + 0.619108i \(0.787494\pi\)
\(252\) 0 0
\(253\) −24.9099 −1.56607
\(254\) 0 0
\(255\) −1.70266 −0.106625
\(256\) 0 0
\(257\) −17.0074 −1.06089 −0.530447 0.847718i \(-0.677976\pi\)
−0.530447 + 0.847718i \(0.677976\pi\)
\(258\) 0 0
\(259\) −6.22235 −0.386638
\(260\) 0 0
\(261\) −7.79684 −0.482612
\(262\) 0 0
\(263\) −1.51974 −0.0937113 −0.0468557 0.998902i \(-0.514920\pi\)
−0.0468557 + 0.998902i \(0.514920\pi\)
\(264\) 0 0
\(265\) 0.0452581 0.00278018
\(266\) 0 0
\(267\) 0.175207 0.0107225
\(268\) 0 0
\(269\) 14.8243 0.903856 0.451928 0.892054i \(-0.350736\pi\)
0.451928 + 0.892054i \(0.350736\pi\)
\(270\) 0 0
\(271\) −30.9026 −1.87720 −0.938599 0.345010i \(-0.887875\pi\)
−0.938599 + 0.345010i \(0.887875\pi\)
\(272\) 0 0
\(273\) −2.60598 −0.157721
\(274\) 0 0
\(275\) 14.3152 0.863242
\(276\) 0 0
\(277\) 2.52939 0.151976 0.0759881 0.997109i \(-0.475789\pi\)
0.0759881 + 0.997109i \(0.475789\pi\)
\(278\) 0 0
\(279\) −0.495034 −0.0296369
\(280\) 0 0
\(281\) 13.6965 0.817067 0.408534 0.912743i \(-0.366040\pi\)
0.408534 + 0.912743i \(0.366040\pi\)
\(282\) 0 0
\(283\) 20.0621 1.19257 0.596283 0.802774i \(-0.296643\pi\)
0.596283 + 0.802774i \(0.296643\pi\)
\(284\) 0 0
\(285\) 2.67335 0.158356
\(286\) 0 0
\(287\) 12.5476 0.740658
\(288\) 0 0
\(289\) −13.2473 −0.779254
\(290\) 0 0
\(291\) −3.93192 −0.230493
\(292\) 0 0
\(293\) −16.3008 −0.952303 −0.476151 0.879363i \(-0.657969\pi\)
−0.476151 + 0.879363i \(0.657969\pi\)
\(294\) 0 0
\(295\) −4.66697 −0.271721
\(296\) 0 0
\(297\) −16.1009 −0.934268
\(298\) 0 0
\(299\) 18.3971 1.06393
\(300\) 0 0
\(301\) −7.74383 −0.446347
\(302\) 0 0
\(303\) 1.64607 0.0945642
\(304\) 0 0
\(305\) −6.45067 −0.369364
\(306\) 0 0
\(307\) 5.53944 0.316152 0.158076 0.987427i \(-0.449471\pi\)
0.158076 + 0.987427i \(0.449471\pi\)
\(308\) 0 0
\(309\) 13.8194 0.786159
\(310\) 0 0
\(311\) 9.83496 0.557690 0.278845 0.960336i \(-0.410049\pi\)
0.278845 + 0.960336i \(0.410049\pi\)
\(312\) 0 0
\(313\) −34.3358 −1.94077 −0.970386 0.241560i \(-0.922341\pi\)
−0.970386 + 0.241560i \(0.922341\pi\)
\(314\) 0 0
\(315\) 3.37423 0.190116
\(316\) 0 0
\(317\) 8.19253 0.460138 0.230069 0.973174i \(-0.426105\pi\)
0.230069 + 0.973174i \(0.426105\pi\)
\(318\) 0 0
\(319\) −12.6072 −0.705865
\(320\) 0 0
\(321\) 4.68624 0.261561
\(322\) 0 0
\(323\) −5.89208 −0.327844
\(324\) 0 0
\(325\) −10.5725 −0.586455
\(326\) 0 0
\(327\) 12.4376 0.687800
\(328\) 0 0
\(329\) −1.82382 −0.100550
\(330\) 0 0
\(331\) −22.6716 −1.24614 −0.623072 0.782164i \(-0.714116\pi\)
−0.623072 + 0.782164i \(0.714116\pi\)
\(332\) 0 0
\(333\) 12.7107 0.696545
\(334\) 0 0
\(335\) −14.0135 −0.765639
\(336\) 0 0
\(337\) 31.8402 1.73445 0.867224 0.497918i \(-0.165902\pi\)
0.867224 + 0.497918i \(0.165902\pi\)
\(338\) 0 0
\(339\) −1.70325 −0.0925076
\(340\) 0 0
\(341\) −0.800449 −0.0433468
\(342\) 0 0
\(343\) −14.9781 −0.808742
\(344\) 0 0
\(345\) 5.56860 0.299804
\(346\) 0 0
\(347\) −31.9760 −1.71656 −0.858280 0.513182i \(-0.828467\pi\)
−0.858280 + 0.513182i \(0.828467\pi\)
\(348\) 0 0
\(349\) −0.326542 −0.0174794 −0.00873969 0.999962i \(-0.502782\pi\)
−0.00873969 + 0.999962i \(0.502782\pi\)
\(350\) 0 0
\(351\) 11.8912 0.634707
\(352\) 0 0
\(353\) 18.3671 0.977582 0.488791 0.872401i \(-0.337438\pi\)
0.488791 + 0.872401i \(0.337438\pi\)
\(354\) 0 0
\(355\) 3.43405 0.182261
\(356\) 0 0
\(357\) 1.73852 0.0920123
\(358\) 0 0
\(359\) −25.6775 −1.35520 −0.677602 0.735429i \(-0.736981\pi\)
−0.677602 + 0.735429i \(0.736981\pi\)
\(360\) 0 0
\(361\) −9.74885 −0.513097
\(362\) 0 0
\(363\) −3.36152 −0.176434
\(364\) 0 0
\(365\) −9.21146 −0.482150
\(366\) 0 0
\(367\) −9.03167 −0.471449 −0.235725 0.971820i \(-0.575746\pi\)
−0.235725 + 0.971820i \(0.575746\pi\)
\(368\) 0 0
\(369\) −25.6316 −1.33433
\(370\) 0 0
\(371\) −0.0462111 −0.00239916
\(372\) 0 0
\(373\) −5.16915 −0.267649 −0.133824 0.991005i \(-0.542726\pi\)
−0.133824 + 0.991005i \(0.542726\pi\)
\(374\) 0 0
\(375\) −7.59486 −0.392197
\(376\) 0 0
\(377\) 9.31096 0.479539
\(378\) 0 0
\(379\) −32.3359 −1.66098 −0.830492 0.557030i \(-0.811941\pi\)
−0.830492 + 0.557030i \(0.811941\pi\)
\(380\) 0 0
\(381\) 12.9611 0.664019
\(382\) 0 0
\(383\) −2.91126 −0.148758 −0.0743791 0.997230i \(-0.523697\pi\)
−0.0743791 + 0.997230i \(0.523697\pi\)
\(384\) 0 0
\(385\) 5.45598 0.278062
\(386\) 0 0
\(387\) 15.8188 0.804113
\(388\) 0 0
\(389\) 31.6507 1.60475 0.802376 0.596819i \(-0.203569\pi\)
0.802376 + 0.596819i \(0.203569\pi\)
\(390\) 0 0
\(391\) −12.2732 −0.620684
\(392\) 0 0
\(393\) −13.0051 −0.656022
\(394\) 0 0
\(395\) 12.1879 0.613238
\(396\) 0 0
\(397\) 17.6897 0.887818 0.443909 0.896072i \(-0.353591\pi\)
0.443909 + 0.896072i \(0.353591\pi\)
\(398\) 0 0
\(399\) −2.72965 −0.136653
\(400\) 0 0
\(401\) 26.5906 1.32787 0.663936 0.747789i \(-0.268885\pi\)
0.663936 + 0.747789i \(0.268885\pi\)
\(402\) 0 0
\(403\) 0.591169 0.0294482
\(404\) 0 0
\(405\) −4.90471 −0.243717
\(406\) 0 0
\(407\) 20.5527 1.01876
\(408\) 0 0
\(409\) −2.78936 −0.137925 −0.0689624 0.997619i \(-0.521969\pi\)
−0.0689624 + 0.997619i \(0.521969\pi\)
\(410\) 0 0
\(411\) 13.1519 0.648738
\(412\) 0 0
\(413\) 4.76525 0.234483
\(414\) 0 0
\(415\) 5.52011 0.270972
\(416\) 0 0
\(417\) 5.57903 0.273206
\(418\) 0 0
\(419\) 4.60858 0.225144 0.112572 0.993644i \(-0.464091\pi\)
0.112572 + 0.993644i \(0.464091\pi\)
\(420\) 0 0
\(421\) −39.8575 −1.94254 −0.971268 0.237989i \(-0.923512\pi\)
−0.971268 + 0.237989i \(0.923512\pi\)
\(422\) 0 0
\(423\) 3.72562 0.181146
\(424\) 0 0
\(425\) 7.05318 0.342129
\(426\) 0 0
\(427\) 6.58651 0.318744
\(428\) 0 0
\(429\) 8.60769 0.415583
\(430\) 0 0
\(431\) −17.5623 −0.845947 −0.422974 0.906142i \(-0.639014\pi\)
−0.422974 + 0.906142i \(0.639014\pi\)
\(432\) 0 0
\(433\) −18.3009 −0.879483 −0.439741 0.898124i \(-0.644930\pi\)
−0.439741 + 0.898124i \(0.644930\pi\)
\(434\) 0 0
\(435\) 2.81832 0.135128
\(436\) 0 0
\(437\) 19.2702 0.921818
\(438\) 0 0
\(439\) −41.1332 −1.96318 −0.981590 0.190998i \(-0.938828\pi\)
−0.981590 + 0.190998i \(0.938828\pi\)
\(440\) 0 0
\(441\) 13.5757 0.646461
\(442\) 0 0
\(443\) −29.3067 −1.39240 −0.696201 0.717847i \(-0.745128\pi\)
−0.696201 + 0.717847i \(0.745128\pi\)
\(444\) 0 0
\(445\) 0.270914 0.0128425
\(446\) 0 0
\(447\) 13.7480 0.650259
\(448\) 0 0
\(449\) 40.7352 1.92241 0.961206 0.275833i \(-0.0889536\pi\)
0.961206 + 0.275833i \(0.0889536\pi\)
\(450\) 0 0
\(451\) −41.4452 −1.95158
\(452\) 0 0
\(453\) 8.41711 0.395471
\(454\) 0 0
\(455\) −4.02949 −0.188905
\(456\) 0 0
\(457\) −21.9525 −1.02689 −0.513446 0.858122i \(-0.671631\pi\)
−0.513446 + 0.858122i \(0.671631\pi\)
\(458\) 0 0
\(459\) −7.93297 −0.370279
\(460\) 0 0
\(461\) 30.7593 1.43260 0.716302 0.697790i \(-0.245833\pi\)
0.716302 + 0.697790i \(0.245833\pi\)
\(462\) 0 0
\(463\) −34.6219 −1.60902 −0.804508 0.593941i \(-0.797571\pi\)
−0.804508 + 0.593941i \(0.797571\pi\)
\(464\) 0 0
\(465\) 0.178940 0.00829814
\(466\) 0 0
\(467\) −21.4310 −0.991706 −0.495853 0.868406i \(-0.665145\pi\)
−0.495853 + 0.868406i \(0.665145\pi\)
\(468\) 0 0
\(469\) 14.3086 0.660710
\(470\) 0 0
\(471\) −5.33254 −0.245711
\(472\) 0 0
\(473\) 25.5783 1.17609
\(474\) 0 0
\(475\) −11.0742 −0.508119
\(476\) 0 0
\(477\) 0.0943982 0.00432220
\(478\) 0 0
\(479\) −29.9036 −1.36633 −0.683164 0.730265i \(-0.739397\pi\)
−0.683164 + 0.730265i \(0.739397\pi\)
\(480\) 0 0
\(481\) −15.1791 −0.692109
\(482\) 0 0
\(483\) −5.68587 −0.258716
\(484\) 0 0
\(485\) −6.07972 −0.276066
\(486\) 0 0
\(487\) −15.2037 −0.688947 −0.344474 0.938796i \(-0.611943\pi\)
−0.344474 + 0.938796i \(0.611943\pi\)
\(488\) 0 0
\(489\) 11.5612 0.522814
\(490\) 0 0
\(491\) −39.4964 −1.78245 −0.891223 0.453566i \(-0.850152\pi\)
−0.891223 + 0.453566i \(0.850152\pi\)
\(492\) 0 0
\(493\) −6.21159 −0.279756
\(494\) 0 0
\(495\) −11.1452 −0.500941
\(496\) 0 0
\(497\) −3.50637 −0.157282
\(498\) 0 0
\(499\) −18.0985 −0.810202 −0.405101 0.914272i \(-0.632764\pi\)
−0.405101 + 0.914272i \(0.632764\pi\)
\(500\) 0 0
\(501\) −6.60106 −0.294914
\(502\) 0 0
\(503\) 9.34057 0.416475 0.208238 0.978078i \(-0.433227\pi\)
0.208238 + 0.978078i \(0.433227\pi\)
\(504\) 0 0
\(505\) 2.54523 0.113261
\(506\) 0 0
\(507\) 3.44411 0.152958
\(508\) 0 0
\(509\) −7.79856 −0.345665 −0.172833 0.984951i \(-0.555292\pi\)
−0.172833 + 0.984951i \(0.555292\pi\)
\(510\) 0 0
\(511\) 9.40545 0.416072
\(512\) 0 0
\(513\) 12.4555 0.549926
\(514\) 0 0
\(515\) 21.3682 0.941596
\(516\) 0 0
\(517\) 6.02416 0.264942
\(518\) 0 0
\(519\) −7.39979 −0.324815
\(520\) 0 0
\(521\) −42.1313 −1.84581 −0.922903 0.385031i \(-0.874191\pi\)
−0.922903 + 0.385031i \(0.874191\pi\)
\(522\) 0 0
\(523\) 40.1060 1.75371 0.876856 0.480753i \(-0.159637\pi\)
0.876856 + 0.480753i \(0.159637\pi\)
\(524\) 0 0
\(525\) 3.26756 0.142608
\(526\) 0 0
\(527\) −0.394385 −0.0171797
\(528\) 0 0
\(529\) 17.1399 0.745213
\(530\) 0 0
\(531\) −9.73425 −0.422430
\(532\) 0 0
\(533\) 30.6092 1.32583
\(534\) 0 0
\(535\) 7.24609 0.313276
\(536\) 0 0
\(537\) 3.56209 0.153716
\(538\) 0 0
\(539\) 21.9513 0.945509
\(540\) 0 0
\(541\) 29.7312 1.27824 0.639122 0.769105i \(-0.279298\pi\)
0.639122 + 0.769105i \(0.279298\pi\)
\(542\) 0 0
\(543\) −6.28202 −0.269587
\(544\) 0 0
\(545\) 19.2316 0.823791
\(546\) 0 0
\(547\) 23.9669 1.02475 0.512376 0.858761i \(-0.328765\pi\)
0.512376 + 0.858761i \(0.328765\pi\)
\(548\) 0 0
\(549\) −13.4547 −0.574231
\(550\) 0 0
\(551\) 9.75282 0.415484
\(552\) 0 0
\(553\) −12.4445 −0.529195
\(554\) 0 0
\(555\) −4.59455 −0.195028
\(556\) 0 0
\(557\) 0.749692 0.0317655 0.0158827 0.999874i \(-0.494944\pi\)
0.0158827 + 0.999874i \(0.494944\pi\)
\(558\) 0 0
\(559\) −18.8907 −0.798993
\(560\) 0 0
\(561\) −5.74242 −0.242445
\(562\) 0 0
\(563\) −2.73187 −0.115135 −0.0575673 0.998342i \(-0.518334\pi\)
−0.0575673 + 0.998342i \(0.518334\pi\)
\(564\) 0 0
\(565\) −2.63364 −0.110798
\(566\) 0 0
\(567\) 5.00800 0.210316
\(568\) 0 0
\(569\) −23.8731 −1.00081 −0.500406 0.865791i \(-0.666816\pi\)
−0.500406 + 0.865791i \(0.666816\pi\)
\(570\) 0 0
\(571\) 3.68911 0.154384 0.0771922 0.997016i \(-0.475404\pi\)
0.0771922 + 0.997016i \(0.475404\pi\)
\(572\) 0 0
\(573\) 11.9894 0.500863
\(574\) 0 0
\(575\) −23.0676 −0.961985
\(576\) 0 0
\(577\) −25.8555 −1.07638 −0.538189 0.842824i \(-0.680891\pi\)
−0.538189 + 0.842824i \(0.680891\pi\)
\(578\) 0 0
\(579\) −11.0614 −0.459698
\(580\) 0 0
\(581\) −5.63636 −0.233836
\(582\) 0 0
\(583\) 0.152638 0.00632161
\(584\) 0 0
\(585\) 8.23127 0.340321
\(586\) 0 0
\(587\) −18.0297 −0.744163 −0.372082 0.928200i \(-0.621356\pi\)
−0.372082 + 0.928200i \(0.621356\pi\)
\(588\) 0 0
\(589\) 0.619223 0.0255146
\(590\) 0 0
\(591\) 4.88284 0.200853
\(592\) 0 0
\(593\) −42.2040 −1.73311 −0.866555 0.499082i \(-0.833671\pi\)
−0.866555 + 0.499082i \(0.833671\pi\)
\(594\) 0 0
\(595\) 2.68818 0.110205
\(596\) 0 0
\(597\) −0.683014 −0.0279539
\(598\) 0 0
\(599\) −8.44815 −0.345182 −0.172591 0.984994i \(-0.555214\pi\)
−0.172591 + 0.984994i \(0.555214\pi\)
\(600\) 0 0
\(601\) 23.6713 0.965574 0.482787 0.875738i \(-0.339625\pi\)
0.482787 + 0.875738i \(0.339625\pi\)
\(602\) 0 0
\(603\) −29.2290 −1.19030
\(604\) 0 0
\(605\) −5.19774 −0.211318
\(606\) 0 0
\(607\) −12.3845 −0.502670 −0.251335 0.967900i \(-0.580870\pi\)
−0.251335 + 0.967900i \(0.580870\pi\)
\(608\) 0 0
\(609\) −2.87767 −0.116609
\(610\) 0 0
\(611\) −4.44912 −0.179992
\(612\) 0 0
\(613\) 21.1281 0.853355 0.426677 0.904404i \(-0.359684\pi\)
0.426677 + 0.904404i \(0.359684\pi\)
\(614\) 0 0
\(615\) 9.26505 0.373603
\(616\) 0 0
\(617\) −8.60266 −0.346330 −0.173165 0.984893i \(-0.555399\pi\)
−0.173165 + 0.984893i \(0.555399\pi\)
\(618\) 0 0
\(619\) 44.1235 1.77347 0.886736 0.462276i \(-0.152967\pi\)
0.886736 + 0.462276i \(0.152967\pi\)
\(620\) 0 0
\(621\) 25.9450 1.04114
\(622\) 0 0
\(623\) −0.276619 −0.0110825
\(624\) 0 0
\(625\) 6.46120 0.258448
\(626\) 0 0
\(627\) 9.01617 0.360071
\(628\) 0 0
\(629\) 10.1264 0.403767
\(630\) 0 0
\(631\) 44.8292 1.78462 0.892312 0.451420i \(-0.149082\pi\)
0.892312 + 0.451420i \(0.149082\pi\)
\(632\) 0 0
\(633\) 6.14096 0.244081
\(634\) 0 0
\(635\) 20.0411 0.795308
\(636\) 0 0
\(637\) −16.2120 −0.642345
\(638\) 0 0
\(639\) 7.16267 0.283351
\(640\) 0 0
\(641\) 1.38935 0.0548760 0.0274380 0.999624i \(-0.491265\pi\)
0.0274380 + 0.999624i \(0.491265\pi\)
\(642\) 0 0
\(643\) 13.5612 0.534802 0.267401 0.963585i \(-0.413835\pi\)
0.267401 + 0.963585i \(0.413835\pi\)
\(644\) 0 0
\(645\) −5.71801 −0.225146
\(646\) 0 0
\(647\) −18.7636 −0.737674 −0.368837 0.929494i \(-0.620244\pi\)
−0.368837 + 0.929494i \(0.620244\pi\)
\(648\) 0 0
\(649\) −15.7399 −0.617844
\(650\) 0 0
\(651\) −0.182708 −0.00716090
\(652\) 0 0
\(653\) −19.6968 −0.770797 −0.385399 0.922750i \(-0.625936\pi\)
−0.385399 + 0.922750i \(0.625936\pi\)
\(654\) 0 0
\(655\) −20.1092 −0.785730
\(656\) 0 0
\(657\) −19.2130 −0.749572
\(658\) 0 0
\(659\) −36.3069 −1.41432 −0.707159 0.707055i \(-0.750023\pi\)
−0.707159 + 0.707055i \(0.750023\pi\)
\(660\) 0 0
\(661\) 46.1595 1.79540 0.897698 0.440610i \(-0.145238\pi\)
0.897698 + 0.440610i \(0.145238\pi\)
\(662\) 0 0
\(663\) 4.24104 0.164708
\(664\) 0 0
\(665\) −4.22071 −0.163672
\(666\) 0 0
\(667\) 20.3152 0.786607
\(668\) 0 0
\(669\) −3.96115 −0.153147
\(670\) 0 0
\(671\) −21.7556 −0.839866
\(672\) 0 0
\(673\) −37.8370 −1.45851 −0.729254 0.684243i \(-0.760133\pi\)
−0.729254 + 0.684243i \(0.760133\pi\)
\(674\) 0 0
\(675\) −14.9100 −0.573888
\(676\) 0 0
\(677\) −17.1305 −0.658380 −0.329190 0.944264i \(-0.606776\pi\)
−0.329190 + 0.944264i \(0.606776\pi\)
\(678\) 0 0
\(679\) 6.20775 0.238232
\(680\) 0 0
\(681\) −19.6100 −0.751455
\(682\) 0 0
\(683\) −11.6402 −0.445401 −0.222701 0.974887i \(-0.571487\pi\)
−0.222701 + 0.974887i \(0.571487\pi\)
\(684\) 0 0
\(685\) 20.3362 0.777004
\(686\) 0 0
\(687\) −1.05965 −0.0404283
\(688\) 0 0
\(689\) −0.112730 −0.00429467
\(690\) 0 0
\(691\) −23.2923 −0.886079 −0.443040 0.896502i \(-0.646100\pi\)
−0.443040 + 0.896502i \(0.646100\pi\)
\(692\) 0 0
\(693\) 11.3799 0.432288
\(694\) 0 0
\(695\) 8.62655 0.327224
\(696\) 0 0
\(697\) −20.4202 −0.773471
\(698\) 0 0
\(699\) −16.3071 −0.616792
\(700\) 0 0
\(701\) 46.3984 1.75244 0.876222 0.481909i \(-0.160056\pi\)
0.876222 + 0.481909i \(0.160056\pi\)
\(702\) 0 0
\(703\) −15.8995 −0.599660
\(704\) 0 0
\(705\) −1.34670 −0.0507196
\(706\) 0 0
\(707\) −2.59883 −0.0977390
\(708\) 0 0
\(709\) 22.0094 0.826581 0.413290 0.910599i \(-0.364379\pi\)
0.413290 + 0.910599i \(0.364379\pi\)
\(710\) 0 0
\(711\) 25.4211 0.953367
\(712\) 0 0
\(713\) 1.28984 0.0483050
\(714\) 0 0
\(715\) 13.3096 0.497751
\(716\) 0 0
\(717\) −15.6534 −0.584586
\(718\) 0 0
\(719\) −42.0701 −1.56895 −0.784475 0.620160i \(-0.787068\pi\)
−0.784475 + 0.620160i \(0.787068\pi\)
\(720\) 0 0
\(721\) −21.8182 −0.812552
\(722\) 0 0
\(723\) 21.1050 0.784903
\(724\) 0 0
\(725\) −11.6747 −0.433588
\(726\) 0 0
\(727\) 19.3608 0.718053 0.359027 0.933327i \(-0.383109\pi\)
0.359027 + 0.933327i \(0.383109\pi\)
\(728\) 0 0
\(729\) −0.967681 −0.0358400
\(730\) 0 0
\(731\) 12.6025 0.466121
\(732\) 0 0
\(733\) 25.3443 0.936113 0.468057 0.883698i \(-0.344954\pi\)
0.468057 + 0.883698i \(0.344954\pi\)
\(734\) 0 0
\(735\) −4.90720 −0.181005
\(736\) 0 0
\(737\) −47.2620 −1.74092
\(738\) 0 0
\(739\) 13.4490 0.494731 0.247366 0.968922i \(-0.420435\pi\)
0.247366 + 0.968922i \(0.420435\pi\)
\(740\) 0 0
\(741\) −6.65886 −0.244619
\(742\) 0 0
\(743\) 36.2620 1.33032 0.665162 0.746699i \(-0.268363\pi\)
0.665162 + 0.746699i \(0.268363\pi\)
\(744\) 0 0
\(745\) 21.2578 0.778826
\(746\) 0 0
\(747\) 11.5137 0.421265
\(748\) 0 0
\(749\) −7.39868 −0.270342
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 18.7605 0.683672
\(754\) 0 0
\(755\) 13.0149 0.473662
\(756\) 0 0
\(757\) 19.3753 0.704206 0.352103 0.935961i \(-0.385467\pi\)
0.352103 + 0.935961i \(0.385467\pi\)
\(758\) 0 0
\(759\) 18.7807 0.681697
\(760\) 0 0
\(761\) 24.4960 0.887980 0.443990 0.896032i \(-0.353563\pi\)
0.443990 + 0.896032i \(0.353563\pi\)
\(762\) 0 0
\(763\) −19.6366 −0.710892
\(764\) 0 0
\(765\) −5.49130 −0.198539
\(766\) 0 0
\(767\) 11.6246 0.419740
\(768\) 0 0
\(769\) 25.4597 0.918101 0.459050 0.888410i \(-0.348190\pi\)
0.459050 + 0.888410i \(0.348190\pi\)
\(770\) 0 0
\(771\) 12.8227 0.461797
\(772\) 0 0
\(773\) 29.0973 1.04656 0.523279 0.852161i \(-0.324709\pi\)
0.523279 + 0.852161i \(0.324709\pi\)
\(774\) 0 0
\(775\) −0.741247 −0.0266264
\(776\) 0 0
\(777\) 4.69131 0.168300
\(778\) 0 0
\(779\) 32.0618 1.14873
\(780\) 0 0
\(781\) 11.5817 0.414427
\(782\) 0 0
\(783\) 13.1310 0.469263
\(784\) 0 0
\(785\) −8.24543 −0.294292
\(786\) 0 0
\(787\) 20.9705 0.747517 0.373758 0.927526i \(-0.378069\pi\)
0.373758 + 0.927526i \(0.378069\pi\)
\(788\) 0 0
\(789\) 1.14580 0.0407916
\(790\) 0 0
\(791\) 2.68910 0.0956134
\(792\) 0 0
\(793\) 16.0675 0.570574
\(794\) 0 0
\(795\) −0.0341221 −0.00121019
\(796\) 0 0
\(797\) 32.6754 1.15742 0.578712 0.815532i \(-0.303556\pi\)
0.578712 + 0.815532i \(0.303556\pi\)
\(798\) 0 0
\(799\) 2.96813 0.105005
\(800\) 0 0
\(801\) 0.565065 0.0199656
\(802\) 0 0
\(803\) −31.0667 −1.09632
\(804\) 0 0
\(805\) −8.79176 −0.309869
\(806\) 0 0
\(807\) −11.1767 −0.393440
\(808\) 0 0
\(809\) −19.7965 −0.696006 −0.348003 0.937493i \(-0.613140\pi\)
−0.348003 + 0.937493i \(0.613140\pi\)
\(810\) 0 0
\(811\) −8.18101 −0.287274 −0.143637 0.989630i \(-0.545880\pi\)
−0.143637 + 0.989630i \(0.545880\pi\)
\(812\) 0 0
\(813\) 23.2988 0.817126
\(814\) 0 0
\(815\) 17.8764 0.626183
\(816\) 0 0
\(817\) −19.7872 −0.692267
\(818\) 0 0
\(819\) −8.40462 −0.293681
\(820\) 0 0
\(821\) −54.0434 −1.88613 −0.943065 0.332610i \(-0.892071\pi\)
−0.943065 + 0.332610i \(0.892071\pi\)
\(822\) 0 0
\(823\) 4.14058 0.144331 0.0721657 0.997393i \(-0.477009\pi\)
0.0721657 + 0.997393i \(0.477009\pi\)
\(824\) 0 0
\(825\) −10.7929 −0.375761
\(826\) 0 0
\(827\) 37.5430 1.30550 0.652750 0.757574i \(-0.273615\pi\)
0.652750 + 0.757574i \(0.273615\pi\)
\(828\) 0 0
\(829\) 39.1228 1.35879 0.679395 0.733773i \(-0.262242\pi\)
0.679395 + 0.733773i \(0.262242\pi\)
\(830\) 0 0
\(831\) −1.90702 −0.0661537
\(832\) 0 0
\(833\) 10.8155 0.374735
\(834\) 0 0
\(835\) −10.2069 −0.353223
\(836\) 0 0
\(837\) 0.833708 0.0288172
\(838\) 0 0
\(839\) 48.6630 1.68003 0.840017 0.542560i \(-0.182545\pi\)
0.840017 + 0.542560i \(0.182545\pi\)
\(840\) 0 0
\(841\) −18.7183 −0.645459
\(842\) 0 0
\(843\) −10.3264 −0.355661
\(844\) 0 0
\(845\) 5.32545 0.183201
\(846\) 0 0
\(847\) 5.30720 0.182357
\(848\) 0 0
\(849\) −15.1257 −0.519113
\(850\) 0 0
\(851\) −33.1187 −1.13529
\(852\) 0 0
\(853\) −17.8323 −0.610567 −0.305284 0.952261i \(-0.598751\pi\)
−0.305284 + 0.952261i \(0.598751\pi\)
\(854\) 0 0
\(855\) 8.62189 0.294863
\(856\) 0 0
\(857\) 25.2337 0.861967 0.430984 0.902360i \(-0.358167\pi\)
0.430984 + 0.902360i \(0.358167\pi\)
\(858\) 0 0
\(859\) 8.85134 0.302004 0.151002 0.988533i \(-0.451750\pi\)
0.151002 + 0.988533i \(0.451750\pi\)
\(860\) 0 0
\(861\) −9.46016 −0.322402
\(862\) 0 0
\(863\) −20.4808 −0.697175 −0.348587 0.937276i \(-0.613339\pi\)
−0.348587 + 0.937276i \(0.613339\pi\)
\(864\) 0 0
\(865\) −11.4419 −0.389036
\(866\) 0 0
\(867\) 9.98775 0.339202
\(868\) 0 0
\(869\) 41.1049 1.39439
\(870\) 0 0
\(871\) 34.9052 1.18272
\(872\) 0 0
\(873\) −12.6809 −0.429185
\(874\) 0 0
\(875\) 11.9908 0.405364
\(876\) 0 0
\(877\) −5.50921 −0.186033 −0.0930164 0.995665i \(-0.529651\pi\)
−0.0930164 + 0.995665i \(0.529651\pi\)
\(878\) 0 0
\(879\) 12.2899 0.414528
\(880\) 0 0
\(881\) −32.6893 −1.10133 −0.550665 0.834726i \(-0.685626\pi\)
−0.550665 + 0.834726i \(0.685626\pi\)
\(882\) 0 0
\(883\) 4.87717 0.164130 0.0820650 0.996627i \(-0.473849\pi\)
0.0820650 + 0.996627i \(0.473849\pi\)
\(884\) 0 0
\(885\) 3.51864 0.118278
\(886\) 0 0
\(887\) −11.9276 −0.400491 −0.200245 0.979746i \(-0.564174\pi\)
−0.200245 + 0.979746i \(0.564174\pi\)
\(888\) 0 0
\(889\) −20.4632 −0.686313
\(890\) 0 0
\(891\) −16.5417 −0.554167
\(892\) 0 0
\(893\) −4.66025 −0.155949
\(894\) 0 0
\(895\) 5.50788 0.184108
\(896\) 0 0
\(897\) −13.8704 −0.463120
\(898\) 0 0
\(899\) 0.652802 0.0217722
\(900\) 0 0
\(901\) 0.0752052 0.00250545
\(902\) 0 0
\(903\) 5.83842 0.194291
\(904\) 0 0
\(905\) −9.71355 −0.322889
\(906\) 0 0
\(907\) 51.0492 1.69506 0.847531 0.530746i \(-0.178088\pi\)
0.847531 + 0.530746i \(0.178088\pi\)
\(908\) 0 0
\(909\) 5.30878 0.176081
\(910\) 0 0
\(911\) −1.23533 −0.0409283 −0.0204641 0.999791i \(-0.506514\pi\)
−0.0204641 + 0.999791i \(0.506514\pi\)
\(912\) 0 0
\(913\) 18.6172 0.616139
\(914\) 0 0
\(915\) 4.86345 0.160781
\(916\) 0 0
\(917\) 20.5326 0.678047
\(918\) 0 0
\(919\) 44.3490 1.46294 0.731470 0.681874i \(-0.238835\pi\)
0.731470 + 0.681874i \(0.238835\pi\)
\(920\) 0 0
\(921\) −4.17643 −0.137618
\(922\) 0 0
\(923\) −8.55364 −0.281546
\(924\) 0 0
\(925\) 19.0326 0.625789
\(926\) 0 0
\(927\) 44.5693 1.46385
\(928\) 0 0
\(929\) 28.1291 0.922885 0.461443 0.887170i \(-0.347332\pi\)
0.461443 + 0.887170i \(0.347332\pi\)
\(930\) 0 0
\(931\) −16.9814 −0.556543
\(932\) 0 0
\(933\) −7.41502 −0.242757
\(934\) 0 0
\(935\) −8.87920 −0.290381
\(936\) 0 0
\(937\) 43.0468 1.40628 0.703139 0.711053i \(-0.251781\pi\)
0.703139 + 0.711053i \(0.251781\pi\)
\(938\) 0 0
\(939\) 25.8873 0.844799
\(940\) 0 0
\(941\) −20.0151 −0.652473 −0.326236 0.945288i \(-0.605780\pi\)
−0.326236 + 0.945288i \(0.605780\pi\)
\(942\) 0 0
\(943\) 66.7848 2.17481
\(944\) 0 0
\(945\) −5.68267 −0.184857
\(946\) 0 0
\(947\) 1.31980 0.0428877 0.0214439 0.999770i \(-0.493174\pi\)
0.0214439 + 0.999770i \(0.493174\pi\)
\(948\) 0 0
\(949\) 22.9442 0.744799
\(950\) 0 0
\(951\) −6.17672 −0.200294
\(952\) 0 0
\(953\) 31.9537 1.03508 0.517541 0.855658i \(-0.326847\pi\)
0.517541 + 0.855658i \(0.326847\pi\)
\(954\) 0 0
\(955\) 18.5385 0.599893
\(956\) 0 0
\(957\) 9.50510 0.307256
\(958\) 0 0
\(959\) −20.7644 −0.670518
\(960\) 0 0
\(961\) −30.9586 −0.998663
\(962\) 0 0
\(963\) 15.1137 0.487033
\(964\) 0 0
\(965\) −17.1037 −0.550588
\(966\) 0 0
\(967\) −47.3793 −1.52362 −0.761808 0.647803i \(-0.775688\pi\)
−0.761808 + 0.647803i \(0.775688\pi\)
\(968\) 0 0
\(969\) 4.44230 0.142707
\(970\) 0 0
\(971\) 16.3405 0.524390 0.262195 0.965015i \(-0.415554\pi\)
0.262195 + 0.965015i \(0.415554\pi\)
\(972\) 0 0
\(973\) −8.80822 −0.282379
\(974\) 0 0
\(975\) 7.97106 0.255278
\(976\) 0 0
\(977\) 55.3239 1.76997 0.884984 0.465621i \(-0.154169\pi\)
0.884984 + 0.465621i \(0.154169\pi\)
\(978\) 0 0
\(979\) 0.913687 0.0292015
\(980\) 0 0
\(981\) 40.1128 1.28070
\(982\) 0 0
\(983\) 41.4214 1.32114 0.660569 0.750766i \(-0.270315\pi\)
0.660569 + 0.750766i \(0.270315\pi\)
\(984\) 0 0
\(985\) 7.55008 0.240565
\(986\) 0 0
\(987\) 1.37506 0.0437686
\(988\) 0 0
\(989\) −41.2168 −1.31062
\(990\) 0 0
\(991\) −42.8024 −1.35966 −0.679831 0.733369i \(-0.737947\pi\)
−0.679831 + 0.733369i \(0.737947\pi\)
\(992\) 0 0
\(993\) 17.0931 0.542435
\(994\) 0 0
\(995\) −1.05611 −0.0334809
\(996\) 0 0
\(997\) −39.8522 −1.26213 −0.631067 0.775729i \(-0.717383\pi\)
−0.631067 + 0.775729i \(0.717383\pi\)
\(998\) 0 0
\(999\) −21.4067 −0.677278
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.1.20 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.20 44 1.1 even 1 trivial