Properties

Label 6008.2.a.b.1.35
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 1.35
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.65156 q^{3} +2.02555 q^{5} -1.52092 q^{7} -0.272343 q^{9} +O(q^{10})\) \(q+1.65156 q^{3} +2.02555 q^{5} -1.52092 q^{7} -0.272343 q^{9} -3.27838 q^{11} +0.0809580 q^{13} +3.34532 q^{15} +5.20822 q^{17} -4.81722 q^{19} -2.51190 q^{21} -0.265548 q^{23} -0.897146 q^{25} -5.40448 q^{27} -7.75756 q^{29} -1.01023 q^{31} -5.41445 q^{33} -3.08070 q^{35} +8.64694 q^{37} +0.133707 q^{39} +6.42334 q^{41} -7.71123 q^{43} -0.551644 q^{45} -6.87795 q^{47} -4.68680 q^{49} +8.60170 q^{51} -4.57105 q^{53} -6.64052 q^{55} -7.95594 q^{57} +3.22742 q^{59} -3.60539 q^{61} +0.414212 q^{63} +0.163985 q^{65} +5.12386 q^{67} -0.438569 q^{69} -8.35316 q^{71} +1.23424 q^{73} -1.48169 q^{75} +4.98616 q^{77} -12.3509 q^{79} -8.10880 q^{81} -4.33943 q^{83} +10.5495 q^{85} -12.8121 q^{87} +6.77024 q^{89} -0.123131 q^{91} -1.66846 q^{93} -9.75753 q^{95} -5.92247 q^{97} +0.892843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.65156 0.953530 0.476765 0.879031i \(-0.341809\pi\)
0.476765 + 0.879031i \(0.341809\pi\)
\(4\) 0 0
\(5\) 2.02555 0.905854 0.452927 0.891548i \(-0.350380\pi\)
0.452927 + 0.891548i \(0.350380\pi\)
\(6\) 0 0
\(7\) −1.52092 −0.574855 −0.287427 0.957802i \(-0.592800\pi\)
−0.287427 + 0.957802i \(0.592800\pi\)
\(8\) 0 0
\(9\) −0.272343 −0.0907809
\(10\) 0 0
\(11\) −3.27838 −0.988469 −0.494234 0.869329i \(-0.664552\pi\)
−0.494234 + 0.869329i \(0.664552\pi\)
\(12\) 0 0
\(13\) 0.0809580 0.0224537 0.0112269 0.999937i \(-0.496426\pi\)
0.0112269 + 0.999937i \(0.496426\pi\)
\(14\) 0 0
\(15\) 3.34532 0.863758
\(16\) 0 0
\(17\) 5.20822 1.26318 0.631590 0.775303i \(-0.282403\pi\)
0.631590 + 0.775303i \(0.282403\pi\)
\(18\) 0 0
\(19\) −4.81722 −1.10515 −0.552573 0.833464i \(-0.686354\pi\)
−0.552573 + 0.833464i \(0.686354\pi\)
\(20\) 0 0
\(21\) −2.51190 −0.548141
\(22\) 0 0
\(23\) −0.265548 −0.0553706 −0.0276853 0.999617i \(-0.508814\pi\)
−0.0276853 + 0.999617i \(0.508814\pi\)
\(24\) 0 0
\(25\) −0.897146 −0.179429
\(26\) 0 0
\(27\) −5.40448 −1.04009
\(28\) 0 0
\(29\) −7.75756 −1.44054 −0.720272 0.693692i \(-0.755983\pi\)
−0.720272 + 0.693692i \(0.755983\pi\)
\(30\) 0 0
\(31\) −1.01023 −0.181443 −0.0907215 0.995876i \(-0.528917\pi\)
−0.0907215 + 0.995876i \(0.528917\pi\)
\(32\) 0 0
\(33\) −5.41445 −0.942535
\(34\) 0 0
\(35\) −3.08070 −0.520734
\(36\) 0 0
\(37\) 8.64694 1.42155 0.710774 0.703420i \(-0.248345\pi\)
0.710774 + 0.703420i \(0.248345\pi\)
\(38\) 0 0
\(39\) 0.133707 0.0214103
\(40\) 0 0
\(41\) 6.42334 1.00316 0.501579 0.865112i \(-0.332753\pi\)
0.501579 + 0.865112i \(0.332753\pi\)
\(42\) 0 0
\(43\) −7.71123 −1.17595 −0.587976 0.808878i \(-0.700075\pi\)
−0.587976 + 0.808878i \(0.700075\pi\)
\(44\) 0 0
\(45\) −0.551644 −0.0822342
\(46\) 0 0
\(47\) −6.87795 −1.00325 −0.501626 0.865085i \(-0.667265\pi\)
−0.501626 + 0.865085i \(0.667265\pi\)
\(48\) 0 0
\(49\) −4.68680 −0.669542
\(50\) 0 0
\(51\) 8.60170 1.20448
\(52\) 0 0
\(53\) −4.57105 −0.627883 −0.313941 0.949442i \(-0.601650\pi\)
−0.313941 + 0.949442i \(0.601650\pi\)
\(54\) 0 0
\(55\) −6.64052 −0.895408
\(56\) 0 0
\(57\) −7.95594 −1.05379
\(58\) 0 0
\(59\) 3.22742 0.420175 0.210087 0.977683i \(-0.432625\pi\)
0.210087 + 0.977683i \(0.432625\pi\)
\(60\) 0 0
\(61\) −3.60539 −0.461623 −0.230812 0.972998i \(-0.574138\pi\)
−0.230812 + 0.972998i \(0.574138\pi\)
\(62\) 0 0
\(63\) 0.414212 0.0521858
\(64\) 0 0
\(65\) 0.163985 0.0203398
\(66\) 0 0
\(67\) 5.12386 0.625979 0.312989 0.949757i \(-0.398670\pi\)
0.312989 + 0.949757i \(0.398670\pi\)
\(68\) 0 0
\(69\) −0.438569 −0.0527975
\(70\) 0 0
\(71\) −8.35316 −0.991338 −0.495669 0.868511i \(-0.665077\pi\)
−0.495669 + 0.868511i \(0.665077\pi\)
\(72\) 0 0
\(73\) 1.23424 0.144457 0.0722287 0.997388i \(-0.476989\pi\)
0.0722287 + 0.997388i \(0.476989\pi\)
\(74\) 0 0
\(75\) −1.48169 −0.171091
\(76\) 0 0
\(77\) 4.98616 0.568226
\(78\) 0 0
\(79\) −12.3509 −1.38959 −0.694793 0.719209i \(-0.744504\pi\)
−0.694793 + 0.719209i \(0.744504\pi\)
\(80\) 0 0
\(81\) −8.10880 −0.900978
\(82\) 0 0
\(83\) −4.33943 −0.476315 −0.238157 0.971227i \(-0.576543\pi\)
−0.238157 + 0.971227i \(0.576543\pi\)
\(84\) 0 0
\(85\) 10.5495 1.14426
\(86\) 0 0
\(87\) −12.8121 −1.37360
\(88\) 0 0
\(89\) 6.77024 0.717644 0.358822 0.933406i \(-0.383178\pi\)
0.358822 + 0.933406i \(0.383178\pi\)
\(90\) 0 0
\(91\) −0.123131 −0.0129076
\(92\) 0 0
\(93\) −1.66846 −0.173011
\(94\) 0 0
\(95\) −9.75753 −1.00110
\(96\) 0 0
\(97\) −5.92247 −0.601336 −0.300668 0.953729i \(-0.597210\pi\)
−0.300668 + 0.953729i \(0.597210\pi\)
\(98\) 0 0
\(99\) 0.892843 0.0897341
\(100\) 0 0
\(101\) −7.50709 −0.746984 −0.373492 0.927633i \(-0.621840\pi\)
−0.373492 + 0.927633i \(0.621840\pi\)
\(102\) 0 0
\(103\) 8.31877 0.819673 0.409836 0.912159i \(-0.365586\pi\)
0.409836 + 0.912159i \(0.365586\pi\)
\(104\) 0 0
\(105\) −5.08797 −0.496535
\(106\) 0 0
\(107\) −1.90024 −0.183703 −0.0918516 0.995773i \(-0.529279\pi\)
−0.0918516 + 0.995773i \(0.529279\pi\)
\(108\) 0 0
\(109\) 15.2695 1.46256 0.731279 0.682079i \(-0.238924\pi\)
0.731279 + 0.682079i \(0.238924\pi\)
\(110\) 0 0
\(111\) 14.2810 1.35549
\(112\) 0 0
\(113\) 2.06287 0.194058 0.0970292 0.995282i \(-0.469066\pi\)
0.0970292 + 0.995282i \(0.469066\pi\)
\(114\) 0 0
\(115\) −0.537881 −0.0501576
\(116\) 0 0
\(117\) −0.0220483 −0.00203837
\(118\) 0 0
\(119\) −7.92130 −0.726145
\(120\) 0 0
\(121\) −0.252220 −0.0229291
\(122\) 0 0
\(123\) 10.6085 0.956541
\(124\) 0 0
\(125\) −11.9450 −1.06839
\(126\) 0 0
\(127\) −2.46083 −0.218363 −0.109182 0.994022i \(-0.534823\pi\)
−0.109182 + 0.994022i \(0.534823\pi\)
\(128\) 0 0
\(129\) −12.7356 −1.12131
\(130\) 0 0
\(131\) −0.745435 −0.0651290 −0.0325645 0.999470i \(-0.510367\pi\)
−0.0325645 + 0.999470i \(0.510367\pi\)
\(132\) 0 0
\(133\) 7.32662 0.635299
\(134\) 0 0
\(135\) −10.9470 −0.942171
\(136\) 0 0
\(137\) −5.48007 −0.468194 −0.234097 0.972213i \(-0.575213\pi\)
−0.234097 + 0.972213i \(0.575213\pi\)
\(138\) 0 0
\(139\) 19.6900 1.67009 0.835044 0.550183i \(-0.185442\pi\)
0.835044 + 0.550183i \(0.185442\pi\)
\(140\) 0 0
\(141\) −11.3594 −0.956630
\(142\) 0 0
\(143\) −0.265411 −0.0221948
\(144\) 0 0
\(145\) −15.7133 −1.30492
\(146\) 0 0
\(147\) −7.74053 −0.638428
\(148\) 0 0
\(149\) −7.53611 −0.617382 −0.308691 0.951162i \(-0.599891\pi\)
−0.308691 + 0.951162i \(0.599891\pi\)
\(150\) 0 0
\(151\) 0.725528 0.0590426 0.0295213 0.999564i \(-0.490602\pi\)
0.0295213 + 0.999564i \(0.490602\pi\)
\(152\) 0 0
\(153\) −1.41842 −0.114673
\(154\) 0 0
\(155\) −2.04628 −0.164361
\(156\) 0 0
\(157\) 15.4379 1.23208 0.616039 0.787716i \(-0.288736\pi\)
0.616039 + 0.787716i \(0.288736\pi\)
\(158\) 0 0
\(159\) −7.54938 −0.598705
\(160\) 0 0
\(161\) 0.403878 0.0318300
\(162\) 0 0
\(163\) −2.41843 −0.189426 −0.0947129 0.995505i \(-0.530193\pi\)
−0.0947129 + 0.995505i \(0.530193\pi\)
\(164\) 0 0
\(165\) −10.9672 −0.853798
\(166\) 0 0
\(167\) −4.10299 −0.317499 −0.158749 0.987319i \(-0.550746\pi\)
−0.158749 + 0.987319i \(0.550746\pi\)
\(168\) 0 0
\(169\) −12.9934 −0.999496
\(170\) 0 0
\(171\) 1.31194 0.100326
\(172\) 0 0
\(173\) 11.4448 0.870134 0.435067 0.900398i \(-0.356725\pi\)
0.435067 + 0.900398i \(0.356725\pi\)
\(174\) 0 0
\(175\) 1.36449 0.103146
\(176\) 0 0
\(177\) 5.33029 0.400649
\(178\) 0 0
\(179\) −20.5989 −1.53963 −0.769817 0.638265i \(-0.779653\pi\)
−0.769817 + 0.638265i \(0.779653\pi\)
\(180\) 0 0
\(181\) −9.01334 −0.669956 −0.334978 0.942226i \(-0.608729\pi\)
−0.334978 + 0.942226i \(0.608729\pi\)
\(182\) 0 0
\(183\) −5.95453 −0.440171
\(184\) 0 0
\(185\) 17.5148 1.28771
\(186\) 0 0
\(187\) −17.0745 −1.24861
\(188\) 0 0
\(189\) 8.21979 0.597902
\(190\) 0 0
\(191\) −7.13853 −0.516526 −0.258263 0.966075i \(-0.583150\pi\)
−0.258263 + 0.966075i \(0.583150\pi\)
\(192\) 0 0
\(193\) −8.12956 −0.585178 −0.292589 0.956238i \(-0.594517\pi\)
−0.292589 + 0.956238i \(0.594517\pi\)
\(194\) 0 0
\(195\) 0.270831 0.0193946
\(196\) 0 0
\(197\) −11.0465 −0.787031 −0.393516 0.919318i \(-0.628741\pi\)
−0.393516 + 0.919318i \(0.628741\pi\)
\(198\) 0 0
\(199\) −27.8421 −1.97367 −0.986836 0.161723i \(-0.948295\pi\)
−0.986836 + 0.161723i \(0.948295\pi\)
\(200\) 0 0
\(201\) 8.46237 0.596889
\(202\) 0 0
\(203\) 11.7986 0.828103
\(204\) 0 0
\(205\) 13.0108 0.908714
\(206\) 0 0
\(207\) 0.0723201 0.00502659
\(208\) 0 0
\(209\) 15.7927 1.09240
\(210\) 0 0
\(211\) 3.89496 0.268140 0.134070 0.990972i \(-0.457195\pi\)
0.134070 + 0.990972i \(0.457195\pi\)
\(212\) 0 0
\(213\) −13.7958 −0.945270
\(214\) 0 0
\(215\) −15.6195 −1.06524
\(216\) 0 0
\(217\) 1.53648 0.104303
\(218\) 0 0
\(219\) 2.03843 0.137744
\(220\) 0 0
\(221\) 0.421647 0.0283631
\(222\) 0 0
\(223\) −2.27199 −0.152144 −0.0760718 0.997102i \(-0.524238\pi\)
−0.0760718 + 0.997102i \(0.524238\pi\)
\(224\) 0 0
\(225\) 0.244331 0.0162888
\(226\) 0 0
\(227\) −4.95870 −0.329120 −0.164560 0.986367i \(-0.552620\pi\)
−0.164560 + 0.986367i \(0.552620\pi\)
\(228\) 0 0
\(229\) −9.60292 −0.634579 −0.317289 0.948329i \(-0.602773\pi\)
−0.317289 + 0.948329i \(0.602773\pi\)
\(230\) 0 0
\(231\) 8.23496 0.541820
\(232\) 0 0
\(233\) 10.5066 0.688309 0.344155 0.938913i \(-0.388166\pi\)
0.344155 + 0.938913i \(0.388166\pi\)
\(234\) 0 0
\(235\) −13.9316 −0.908799
\(236\) 0 0
\(237\) −20.3983 −1.32501
\(238\) 0 0
\(239\) 20.8737 1.35021 0.675105 0.737722i \(-0.264098\pi\)
0.675105 + 0.737722i \(0.264098\pi\)
\(240\) 0 0
\(241\) −19.8148 −1.27638 −0.638192 0.769877i \(-0.720317\pi\)
−0.638192 + 0.769877i \(0.720317\pi\)
\(242\) 0 0
\(243\) 2.82124 0.180983
\(244\) 0 0
\(245\) −9.49334 −0.606507
\(246\) 0 0
\(247\) −0.389993 −0.0248146
\(248\) 0 0
\(249\) −7.16684 −0.454180
\(250\) 0 0
\(251\) 3.33357 0.210413 0.105206 0.994450i \(-0.466450\pi\)
0.105206 + 0.994450i \(0.466450\pi\)
\(252\) 0 0
\(253\) 0.870567 0.0547321
\(254\) 0 0
\(255\) 17.4232 1.09108
\(256\) 0 0
\(257\) −11.7012 −0.729902 −0.364951 0.931027i \(-0.618914\pi\)
−0.364951 + 0.931027i \(0.618914\pi\)
\(258\) 0 0
\(259\) −13.1513 −0.817183
\(260\) 0 0
\(261\) 2.11272 0.130774
\(262\) 0 0
\(263\) 9.19127 0.566758 0.283379 0.959008i \(-0.408545\pi\)
0.283379 + 0.959008i \(0.408545\pi\)
\(264\) 0 0
\(265\) −9.25890 −0.568770
\(266\) 0 0
\(267\) 11.1815 0.684295
\(268\) 0 0
\(269\) −3.63385 −0.221560 −0.110780 0.993845i \(-0.535335\pi\)
−0.110780 + 0.993845i \(0.535335\pi\)
\(270\) 0 0
\(271\) −0.180685 −0.0109758 −0.00548792 0.999985i \(-0.501747\pi\)
−0.00548792 + 0.999985i \(0.501747\pi\)
\(272\) 0 0
\(273\) −0.203358 −0.0123078
\(274\) 0 0
\(275\) 2.94119 0.177360
\(276\) 0 0
\(277\) 11.5231 0.692358 0.346179 0.938168i \(-0.387479\pi\)
0.346179 + 0.938168i \(0.387479\pi\)
\(278\) 0 0
\(279\) 0.275130 0.0164716
\(280\) 0 0
\(281\) −12.7358 −0.759757 −0.379878 0.925036i \(-0.624034\pi\)
−0.379878 + 0.925036i \(0.624034\pi\)
\(282\) 0 0
\(283\) 14.5097 0.862513 0.431257 0.902229i \(-0.358070\pi\)
0.431257 + 0.902229i \(0.358070\pi\)
\(284\) 0 0
\(285\) −16.1152 −0.954580
\(286\) 0 0
\(287\) −9.76940 −0.576670
\(288\) 0 0
\(289\) 10.1256 0.595623
\(290\) 0 0
\(291\) −9.78133 −0.573392
\(292\) 0 0
\(293\) 5.15572 0.301200 0.150600 0.988595i \(-0.451879\pi\)
0.150600 + 0.988595i \(0.451879\pi\)
\(294\) 0 0
\(295\) 6.53731 0.380617
\(296\) 0 0
\(297\) 17.7179 1.02810
\(298\) 0 0
\(299\) −0.0214982 −0.00124328
\(300\) 0 0
\(301\) 11.7282 0.676001
\(302\) 0 0
\(303\) −12.3984 −0.712271
\(304\) 0 0
\(305\) −7.30290 −0.418163
\(306\) 0 0
\(307\) −6.52933 −0.372648 −0.186324 0.982488i \(-0.559657\pi\)
−0.186324 + 0.982488i \(0.559657\pi\)
\(308\) 0 0
\(309\) 13.7390 0.781583
\(310\) 0 0
\(311\) 28.4650 1.61410 0.807052 0.590480i \(-0.201062\pi\)
0.807052 + 0.590480i \(0.201062\pi\)
\(312\) 0 0
\(313\) 25.3691 1.43395 0.716974 0.697100i \(-0.245527\pi\)
0.716974 + 0.697100i \(0.245527\pi\)
\(314\) 0 0
\(315\) 0.839008 0.0472727
\(316\) 0 0
\(317\) 11.6306 0.653240 0.326620 0.945156i \(-0.394090\pi\)
0.326620 + 0.945156i \(0.394090\pi\)
\(318\) 0 0
\(319\) 25.4322 1.42393
\(320\) 0 0
\(321\) −3.13836 −0.175166
\(322\) 0 0
\(323\) −25.0892 −1.39600
\(324\) 0 0
\(325\) −0.0726312 −0.00402885
\(326\) 0 0
\(327\) 25.2186 1.39459
\(328\) 0 0
\(329\) 10.4608 0.576724
\(330\) 0 0
\(331\) 24.2703 1.33402 0.667008 0.745050i \(-0.267574\pi\)
0.667008 + 0.745050i \(0.267574\pi\)
\(332\) 0 0
\(333\) −2.35493 −0.129049
\(334\) 0 0
\(335\) 10.3786 0.567045
\(336\) 0 0
\(337\) −18.5276 −1.00926 −0.504632 0.863335i \(-0.668372\pi\)
−0.504632 + 0.863335i \(0.668372\pi\)
\(338\) 0 0
\(339\) 3.40696 0.185040
\(340\) 0 0
\(341\) 3.31193 0.179351
\(342\) 0 0
\(343\) 17.7747 0.959744
\(344\) 0 0
\(345\) −0.888343 −0.0478268
\(346\) 0 0
\(347\) 12.2744 0.658923 0.329462 0.944169i \(-0.393133\pi\)
0.329462 + 0.944169i \(0.393133\pi\)
\(348\) 0 0
\(349\) 15.5611 0.832966 0.416483 0.909144i \(-0.363263\pi\)
0.416483 + 0.909144i \(0.363263\pi\)
\(350\) 0 0
\(351\) −0.437536 −0.0233539
\(352\) 0 0
\(353\) 20.7158 1.10259 0.551296 0.834310i \(-0.314133\pi\)
0.551296 + 0.834310i \(0.314133\pi\)
\(354\) 0 0
\(355\) −16.9198 −0.898007
\(356\) 0 0
\(357\) −13.0825 −0.692400
\(358\) 0 0
\(359\) 9.42963 0.497677 0.248838 0.968545i \(-0.419951\pi\)
0.248838 + 0.968545i \(0.419951\pi\)
\(360\) 0 0
\(361\) 4.20564 0.221349
\(362\) 0 0
\(363\) −0.416558 −0.0218636
\(364\) 0 0
\(365\) 2.50002 0.130857
\(366\) 0 0
\(367\) 23.5343 1.22848 0.614240 0.789119i \(-0.289463\pi\)
0.614240 + 0.789119i \(0.289463\pi\)
\(368\) 0 0
\(369\) −1.74935 −0.0910676
\(370\) 0 0
\(371\) 6.95222 0.360941
\(372\) 0 0
\(373\) 17.7774 0.920478 0.460239 0.887795i \(-0.347764\pi\)
0.460239 + 0.887795i \(0.347764\pi\)
\(374\) 0 0
\(375\) −19.7279 −1.01874
\(376\) 0 0
\(377\) −0.628037 −0.0323455
\(378\) 0 0
\(379\) −28.6316 −1.47071 −0.735353 0.677685i \(-0.762983\pi\)
−0.735353 + 0.677685i \(0.762983\pi\)
\(380\) 0 0
\(381\) −4.06421 −0.208216
\(382\) 0 0
\(383\) 14.2635 0.728832 0.364416 0.931236i \(-0.381269\pi\)
0.364416 + 0.931236i \(0.381269\pi\)
\(384\) 0 0
\(385\) 10.0997 0.514729
\(386\) 0 0
\(387\) 2.10010 0.106754
\(388\) 0 0
\(389\) 6.81876 0.345725 0.172862 0.984946i \(-0.444698\pi\)
0.172862 + 0.984946i \(0.444698\pi\)
\(390\) 0 0
\(391\) −1.38303 −0.0699430
\(392\) 0 0
\(393\) −1.23113 −0.0621024
\(394\) 0 0
\(395\) −25.0174 −1.25876
\(396\) 0 0
\(397\) 8.87183 0.445264 0.222632 0.974903i \(-0.428535\pi\)
0.222632 + 0.974903i \(0.428535\pi\)
\(398\) 0 0
\(399\) 12.1004 0.605776
\(400\) 0 0
\(401\) −10.2486 −0.511792 −0.255896 0.966704i \(-0.582370\pi\)
−0.255896 + 0.966704i \(0.582370\pi\)
\(402\) 0 0
\(403\) −0.0817864 −0.00407407
\(404\) 0 0
\(405\) −16.4248 −0.816154
\(406\) 0 0
\(407\) −28.3480 −1.40516
\(408\) 0 0
\(409\) 8.48827 0.419718 0.209859 0.977732i \(-0.432700\pi\)
0.209859 + 0.977732i \(0.432700\pi\)
\(410\) 0 0
\(411\) −9.05067 −0.446437
\(412\) 0 0
\(413\) −4.90866 −0.241539
\(414\) 0 0
\(415\) −8.78974 −0.431471
\(416\) 0 0
\(417\) 32.5193 1.59248
\(418\) 0 0
\(419\) −31.8502 −1.55598 −0.777992 0.628274i \(-0.783762\pi\)
−0.777992 + 0.628274i \(0.783762\pi\)
\(420\) 0 0
\(421\) 6.65712 0.324448 0.162224 0.986754i \(-0.448133\pi\)
0.162224 + 0.986754i \(0.448133\pi\)
\(422\) 0 0
\(423\) 1.87316 0.0910761
\(424\) 0 0
\(425\) −4.67254 −0.226651
\(426\) 0 0
\(427\) 5.48352 0.265366
\(428\) 0 0
\(429\) −0.438343 −0.0211634
\(430\) 0 0
\(431\) 6.25257 0.301176 0.150588 0.988597i \(-0.451883\pi\)
0.150588 + 0.988597i \(0.451883\pi\)
\(432\) 0 0
\(433\) 14.5819 0.700761 0.350381 0.936607i \(-0.386052\pi\)
0.350381 + 0.936607i \(0.386052\pi\)
\(434\) 0 0
\(435\) −25.9515 −1.24428
\(436\) 0 0
\(437\) 1.27920 0.0611926
\(438\) 0 0
\(439\) −13.8347 −0.660293 −0.330147 0.943930i \(-0.607098\pi\)
−0.330147 + 0.943930i \(0.607098\pi\)
\(440\) 0 0
\(441\) 1.27642 0.0607817
\(442\) 0 0
\(443\) −6.68785 −0.317749 −0.158875 0.987299i \(-0.550787\pi\)
−0.158875 + 0.987299i \(0.550787\pi\)
\(444\) 0 0
\(445\) 13.7135 0.650081
\(446\) 0 0
\(447\) −12.4464 −0.588692
\(448\) 0 0
\(449\) −31.8338 −1.50233 −0.751164 0.660116i \(-0.770507\pi\)
−0.751164 + 0.660116i \(0.770507\pi\)
\(450\) 0 0
\(451\) −21.0582 −0.991590
\(452\) 0 0
\(453\) 1.19825 0.0562989
\(454\) 0 0
\(455\) −0.249408 −0.0116924
\(456\) 0 0
\(457\) 36.5502 1.70975 0.854874 0.518836i \(-0.173634\pi\)
0.854874 + 0.518836i \(0.173634\pi\)
\(458\) 0 0
\(459\) −28.1477 −1.31382
\(460\) 0 0
\(461\) 10.6315 0.495159 0.247580 0.968868i \(-0.420365\pi\)
0.247580 + 0.968868i \(0.420365\pi\)
\(462\) 0 0
\(463\) 13.0731 0.607560 0.303780 0.952742i \(-0.401751\pi\)
0.303780 + 0.952742i \(0.401751\pi\)
\(464\) 0 0
\(465\) −3.37955 −0.156723
\(466\) 0 0
\(467\) 23.0024 1.06442 0.532212 0.846611i \(-0.321361\pi\)
0.532212 + 0.846611i \(0.321361\pi\)
\(468\) 0 0
\(469\) −7.79299 −0.359847
\(470\) 0 0
\(471\) 25.4966 1.17482
\(472\) 0 0
\(473\) 25.2804 1.16239
\(474\) 0 0
\(475\) 4.32175 0.198296
\(476\) 0 0
\(477\) 1.24489 0.0569998
\(478\) 0 0
\(479\) −36.5372 −1.66943 −0.834713 0.550685i \(-0.814367\pi\)
−0.834713 + 0.550685i \(0.814367\pi\)
\(480\) 0 0
\(481\) 0.700039 0.0319190
\(482\) 0 0
\(483\) 0.667029 0.0303509
\(484\) 0 0
\(485\) −11.9963 −0.544722
\(486\) 0 0
\(487\) 6.14639 0.278519 0.139260 0.990256i \(-0.455528\pi\)
0.139260 + 0.990256i \(0.455528\pi\)
\(488\) 0 0
\(489\) −3.99418 −0.180623
\(490\) 0 0
\(491\) −21.1480 −0.954396 −0.477198 0.878796i \(-0.658348\pi\)
−0.477198 + 0.878796i \(0.658348\pi\)
\(492\) 0 0
\(493\) −40.4031 −1.81966
\(494\) 0 0
\(495\) 1.80850 0.0812860
\(496\) 0 0
\(497\) 12.7045 0.569875
\(498\) 0 0
\(499\) −12.2945 −0.550376 −0.275188 0.961390i \(-0.588740\pi\)
−0.275188 + 0.961390i \(0.588740\pi\)
\(500\) 0 0
\(501\) −6.77634 −0.302745
\(502\) 0 0
\(503\) 2.97430 0.132617 0.0663086 0.997799i \(-0.478878\pi\)
0.0663086 + 0.997799i \(0.478878\pi\)
\(504\) 0 0
\(505\) −15.2060 −0.676658
\(506\) 0 0
\(507\) −21.4595 −0.953049
\(508\) 0 0
\(509\) −29.8990 −1.32525 −0.662625 0.748952i \(-0.730557\pi\)
−0.662625 + 0.748952i \(0.730557\pi\)
\(510\) 0 0
\(511\) −1.87719 −0.0830420
\(512\) 0 0
\(513\) 26.0346 1.14945
\(514\) 0 0
\(515\) 16.8501 0.742504
\(516\) 0 0
\(517\) 22.5485 0.991683
\(518\) 0 0
\(519\) 18.9018 0.829699
\(520\) 0 0
\(521\) −10.8845 −0.476861 −0.238430 0.971160i \(-0.576633\pi\)
−0.238430 + 0.971160i \(0.576633\pi\)
\(522\) 0 0
\(523\) −28.3864 −1.24125 −0.620624 0.784108i \(-0.713121\pi\)
−0.620624 + 0.784108i \(0.713121\pi\)
\(524\) 0 0
\(525\) 2.25354 0.0983525
\(526\) 0 0
\(527\) −5.26151 −0.229195
\(528\) 0 0
\(529\) −22.9295 −0.996934
\(530\) 0 0
\(531\) −0.878966 −0.0381439
\(532\) 0 0
\(533\) 0.520021 0.0225246
\(534\) 0 0
\(535\) −3.84903 −0.166408
\(536\) 0 0
\(537\) −34.0204 −1.46809
\(538\) 0 0
\(539\) 15.3651 0.661822
\(540\) 0 0
\(541\) 4.36222 0.187547 0.0937733 0.995594i \(-0.470107\pi\)
0.0937733 + 0.995594i \(0.470107\pi\)
\(542\) 0 0
\(543\) −14.8861 −0.638823
\(544\) 0 0
\(545\) 30.9292 1.32486
\(546\) 0 0
\(547\) −33.1092 −1.41565 −0.707823 0.706390i \(-0.750323\pi\)
−0.707823 + 0.706390i \(0.750323\pi\)
\(548\) 0 0
\(549\) 0.981903 0.0419066
\(550\) 0 0
\(551\) 37.3699 1.59201
\(552\) 0 0
\(553\) 18.7848 0.798810
\(554\) 0 0
\(555\) 28.9268 1.22787
\(556\) 0 0
\(557\) 2.09450 0.0887466 0.0443733 0.999015i \(-0.485871\pi\)
0.0443733 + 0.999015i \(0.485871\pi\)
\(558\) 0 0
\(559\) −0.624286 −0.0264045
\(560\) 0 0
\(561\) −28.1997 −1.19059
\(562\) 0 0
\(563\) −5.42252 −0.228532 −0.114266 0.993450i \(-0.536452\pi\)
−0.114266 + 0.993450i \(0.536452\pi\)
\(564\) 0 0
\(565\) 4.17844 0.175788
\(566\) 0 0
\(567\) 12.3329 0.517931
\(568\) 0 0
\(569\) 9.82849 0.412032 0.206016 0.978549i \(-0.433950\pi\)
0.206016 + 0.978549i \(0.433950\pi\)
\(570\) 0 0
\(571\) −6.01362 −0.251662 −0.125831 0.992052i \(-0.540160\pi\)
−0.125831 + 0.992052i \(0.540160\pi\)
\(572\) 0 0
\(573\) −11.7897 −0.492523
\(574\) 0 0
\(575\) 0.238235 0.00993510
\(576\) 0 0
\(577\) −17.7537 −0.739098 −0.369549 0.929211i \(-0.620488\pi\)
−0.369549 + 0.929211i \(0.620488\pi\)
\(578\) 0 0
\(579\) −13.4265 −0.557985
\(580\) 0 0
\(581\) 6.59994 0.273812
\(582\) 0 0
\(583\) 14.9857 0.620643
\(584\) 0 0
\(585\) −0.0446600 −0.00184646
\(586\) 0 0
\(587\) 27.2355 1.12413 0.562065 0.827093i \(-0.310007\pi\)
0.562065 + 0.827093i \(0.310007\pi\)
\(588\) 0 0
\(589\) 4.86651 0.200521
\(590\) 0 0
\(591\) −18.2440 −0.750458
\(592\) 0 0
\(593\) −18.7228 −0.768851 −0.384426 0.923156i \(-0.625601\pi\)
−0.384426 + 0.923156i \(0.625601\pi\)
\(594\) 0 0
\(595\) −16.0450 −0.657781
\(596\) 0 0
\(597\) −45.9829 −1.88196
\(598\) 0 0
\(599\) −14.5647 −0.595099 −0.297549 0.954706i \(-0.596169\pi\)
−0.297549 + 0.954706i \(0.596169\pi\)
\(600\) 0 0
\(601\) −4.82199 −0.196693 −0.0983465 0.995152i \(-0.531355\pi\)
−0.0983465 + 0.995152i \(0.531355\pi\)
\(602\) 0 0
\(603\) −1.39545 −0.0568269
\(604\) 0 0
\(605\) −0.510885 −0.0207704
\(606\) 0 0
\(607\) 38.8119 1.57532 0.787662 0.616107i \(-0.211291\pi\)
0.787662 + 0.616107i \(0.211291\pi\)
\(608\) 0 0
\(609\) 19.4862 0.789621
\(610\) 0 0
\(611\) −0.556825 −0.0225267
\(612\) 0 0
\(613\) −1.16083 −0.0468855 −0.0234427 0.999725i \(-0.507463\pi\)
−0.0234427 + 0.999725i \(0.507463\pi\)
\(614\) 0 0
\(615\) 21.4881 0.866486
\(616\) 0 0
\(617\) 23.7024 0.954222 0.477111 0.878843i \(-0.341684\pi\)
0.477111 + 0.878843i \(0.341684\pi\)
\(618\) 0 0
\(619\) 15.1857 0.610364 0.305182 0.952294i \(-0.401283\pi\)
0.305182 + 0.952294i \(0.401283\pi\)
\(620\) 0 0
\(621\) 1.43515 0.0575905
\(622\) 0 0
\(623\) −10.2970 −0.412541
\(624\) 0 0
\(625\) −19.7094 −0.788376
\(626\) 0 0
\(627\) 26.0826 1.04164
\(628\) 0 0
\(629\) 45.0352 1.79567
\(630\) 0 0
\(631\) −32.9269 −1.31080 −0.655400 0.755282i \(-0.727500\pi\)
−0.655400 + 0.755282i \(0.727500\pi\)
\(632\) 0 0
\(633\) 6.43277 0.255680
\(634\) 0 0
\(635\) −4.98453 −0.197805
\(636\) 0 0
\(637\) −0.379434 −0.0150337
\(638\) 0 0
\(639\) 2.27492 0.0899946
\(640\) 0 0
\(641\) −26.8032 −1.05866 −0.529332 0.848415i \(-0.677557\pi\)
−0.529332 + 0.848415i \(0.677557\pi\)
\(642\) 0 0
\(643\) 5.89363 0.232422 0.116211 0.993225i \(-0.462925\pi\)
0.116211 + 0.993225i \(0.462925\pi\)
\(644\) 0 0
\(645\) −25.7966 −1.01574
\(646\) 0 0
\(647\) 13.4327 0.528096 0.264048 0.964510i \(-0.414942\pi\)
0.264048 + 0.964510i \(0.414942\pi\)
\(648\) 0 0
\(649\) −10.5807 −0.415330
\(650\) 0 0
\(651\) 2.53760 0.0994564
\(652\) 0 0
\(653\) −25.3103 −0.990470 −0.495235 0.868759i \(-0.664918\pi\)
−0.495235 + 0.868759i \(0.664918\pi\)
\(654\) 0 0
\(655\) −1.50992 −0.0589973
\(656\) 0 0
\(657\) −0.336138 −0.0131140
\(658\) 0 0
\(659\) −41.0118 −1.59759 −0.798796 0.601603i \(-0.794529\pi\)
−0.798796 + 0.601603i \(0.794529\pi\)
\(660\) 0 0
\(661\) −23.8401 −0.927271 −0.463636 0.886026i \(-0.653455\pi\)
−0.463636 + 0.886026i \(0.653455\pi\)
\(662\) 0 0
\(663\) 0.696377 0.0270450
\(664\) 0 0
\(665\) 14.8404 0.575488
\(666\) 0 0
\(667\) 2.06000 0.0797637
\(668\) 0 0
\(669\) −3.75233 −0.145073
\(670\) 0 0
\(671\) 11.8198 0.456300
\(672\) 0 0
\(673\) 11.2906 0.435220 0.217610 0.976036i \(-0.430174\pi\)
0.217610 + 0.976036i \(0.430174\pi\)
\(674\) 0 0
\(675\) 4.84860 0.186623
\(676\) 0 0
\(677\) 31.2844 1.20236 0.601178 0.799115i \(-0.294698\pi\)
0.601178 + 0.799115i \(0.294698\pi\)
\(678\) 0 0
\(679\) 9.00762 0.345681
\(680\) 0 0
\(681\) −8.18960 −0.313826
\(682\) 0 0
\(683\) 13.3600 0.511204 0.255602 0.966782i \(-0.417726\pi\)
0.255602 + 0.966782i \(0.417726\pi\)
\(684\) 0 0
\(685\) −11.1001 −0.424115
\(686\) 0 0
\(687\) −15.8598 −0.605090
\(688\) 0 0
\(689\) −0.370064 −0.0140983
\(690\) 0 0
\(691\) −19.4304 −0.739166 −0.369583 0.929198i \(-0.620499\pi\)
−0.369583 + 0.929198i \(0.620499\pi\)
\(692\) 0 0
\(693\) −1.35795 −0.0515841
\(694\) 0 0
\(695\) 39.8832 1.51285
\(696\) 0 0
\(697\) 33.4542 1.26717
\(698\) 0 0
\(699\) 17.3523 0.656323
\(700\) 0 0
\(701\) 20.2429 0.764563 0.382281 0.924046i \(-0.375139\pi\)
0.382281 + 0.924046i \(0.375139\pi\)
\(702\) 0 0
\(703\) −41.6542 −1.57102
\(704\) 0 0
\(705\) −23.0089 −0.866567
\(706\) 0 0
\(707\) 11.4177 0.429407
\(708\) 0 0
\(709\) 28.9129 1.08585 0.542924 0.839782i \(-0.317317\pi\)
0.542924 + 0.839782i \(0.317317\pi\)
\(710\) 0 0
\(711\) 3.36368 0.126148
\(712\) 0 0
\(713\) 0.268265 0.0100466
\(714\) 0 0
\(715\) −0.537604 −0.0201052
\(716\) 0 0
\(717\) 34.4743 1.28747
\(718\) 0 0
\(719\) −26.6620 −0.994325 −0.497162 0.867657i \(-0.665625\pi\)
−0.497162 + 0.867657i \(0.665625\pi\)
\(720\) 0 0
\(721\) −12.6522 −0.471193
\(722\) 0 0
\(723\) −32.7254 −1.21707
\(724\) 0 0
\(725\) 6.95967 0.258475
\(726\) 0 0
\(727\) −29.2675 −1.08547 −0.542735 0.839904i \(-0.682611\pi\)
−0.542735 + 0.839904i \(0.682611\pi\)
\(728\) 0 0
\(729\) 28.9859 1.07355
\(730\) 0 0
\(731\) −40.1618 −1.48544
\(732\) 0 0
\(733\) −31.8329 −1.17578 −0.587888 0.808943i \(-0.700040\pi\)
−0.587888 + 0.808943i \(0.700040\pi\)
\(734\) 0 0
\(735\) −15.6788 −0.578323
\(736\) 0 0
\(737\) −16.7980 −0.618761
\(738\) 0 0
\(739\) 1.67685 0.0616838 0.0308419 0.999524i \(-0.490181\pi\)
0.0308419 + 0.999524i \(0.490181\pi\)
\(740\) 0 0
\(741\) −0.644097 −0.0236615
\(742\) 0 0
\(743\) −20.3345 −0.746002 −0.373001 0.927831i \(-0.621671\pi\)
−0.373001 + 0.927831i \(0.621671\pi\)
\(744\) 0 0
\(745\) −15.2648 −0.559258
\(746\) 0 0
\(747\) 1.18181 0.0432403
\(748\) 0 0
\(749\) 2.89012 0.105603
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 5.50559 0.200635
\(754\) 0 0
\(755\) 1.46959 0.0534840
\(756\) 0 0
\(757\) 24.1189 0.876615 0.438308 0.898825i \(-0.355578\pi\)
0.438308 + 0.898825i \(0.355578\pi\)
\(758\) 0 0
\(759\) 1.43780 0.0521887
\(760\) 0 0
\(761\) 0.454644 0.0164808 0.00824042 0.999966i \(-0.497377\pi\)
0.00824042 + 0.999966i \(0.497377\pi\)
\(762\) 0 0
\(763\) −23.2238 −0.840758
\(764\) 0 0
\(765\) −2.87309 −0.103877
\(766\) 0 0
\(767\) 0.261286 0.00943448
\(768\) 0 0
\(769\) 12.2703 0.442479 0.221240 0.975219i \(-0.428990\pi\)
0.221240 + 0.975219i \(0.428990\pi\)
\(770\) 0 0
\(771\) −19.3253 −0.695983
\(772\) 0 0
\(773\) 18.1483 0.652751 0.326375 0.945240i \(-0.394173\pi\)
0.326375 + 0.945240i \(0.394173\pi\)
\(774\) 0 0
\(775\) 0.906326 0.0325562
\(776\) 0 0
\(777\) −21.7202 −0.779209
\(778\) 0 0
\(779\) −30.9427 −1.10864
\(780\) 0 0
\(781\) 27.3848 0.979907
\(782\) 0 0
\(783\) 41.9256 1.49830
\(784\) 0 0
\(785\) 31.2702 1.11608
\(786\) 0 0
\(787\) 32.1092 1.14457 0.572285 0.820055i \(-0.306057\pi\)
0.572285 + 0.820055i \(0.306057\pi\)
\(788\) 0 0
\(789\) 15.1800 0.540421
\(790\) 0 0
\(791\) −3.13746 −0.111555
\(792\) 0 0
\(793\) −0.291885 −0.0103652
\(794\) 0 0
\(795\) −15.2917 −0.542339
\(796\) 0 0
\(797\) −17.8073 −0.630768 −0.315384 0.948964i \(-0.602133\pi\)
−0.315384 + 0.948964i \(0.602133\pi\)
\(798\) 0 0
\(799\) −35.8219 −1.26729
\(800\) 0 0
\(801\) −1.84383 −0.0651484
\(802\) 0 0
\(803\) −4.04632 −0.142792
\(804\) 0 0
\(805\) 0.818075 0.0288333
\(806\) 0 0
\(807\) −6.00153 −0.211264
\(808\) 0 0
\(809\) −25.3856 −0.892511 −0.446255 0.894906i \(-0.647243\pi\)
−0.446255 + 0.894906i \(0.647243\pi\)
\(810\) 0 0
\(811\) 35.7235 1.25442 0.627211 0.778849i \(-0.284196\pi\)
0.627211 + 0.778849i \(0.284196\pi\)
\(812\) 0 0
\(813\) −0.298413 −0.0104658
\(814\) 0 0
\(815\) −4.89865 −0.171592
\(816\) 0 0
\(817\) 37.1467 1.29960
\(818\) 0 0
\(819\) 0.0335338 0.00117177
\(820\) 0 0
\(821\) 12.8050 0.446897 0.223448 0.974716i \(-0.428269\pi\)
0.223448 + 0.974716i \(0.428269\pi\)
\(822\) 0 0
\(823\) −40.6550 −1.41715 −0.708573 0.705638i \(-0.750661\pi\)
−0.708573 + 0.705638i \(0.750661\pi\)
\(824\) 0 0
\(825\) 4.85755 0.169118
\(826\) 0 0
\(827\) 17.3910 0.604745 0.302372 0.953190i \(-0.402221\pi\)
0.302372 + 0.953190i \(0.402221\pi\)
\(828\) 0 0
\(829\) 34.1291 1.18535 0.592676 0.805441i \(-0.298071\pi\)
0.592676 + 0.805441i \(0.298071\pi\)
\(830\) 0 0
\(831\) 19.0312 0.660184
\(832\) 0 0
\(833\) −24.4099 −0.845752
\(834\) 0 0
\(835\) −8.31081 −0.287608
\(836\) 0 0
\(837\) 5.45978 0.188718
\(838\) 0 0
\(839\) 40.5944 1.40147 0.700737 0.713420i \(-0.252855\pi\)
0.700737 + 0.713420i \(0.252855\pi\)
\(840\) 0 0
\(841\) 31.1798 1.07516
\(842\) 0 0
\(843\) −21.0340 −0.724451
\(844\) 0 0
\(845\) −26.3189 −0.905397
\(846\) 0 0
\(847\) 0.383608 0.0131809
\(848\) 0 0
\(849\) 23.9637 0.822432
\(850\) 0 0
\(851\) −2.29618 −0.0787119
\(852\) 0 0
\(853\) −29.2136 −1.00026 −0.500128 0.865952i \(-0.666714\pi\)
−0.500128 + 0.865952i \(0.666714\pi\)
\(854\) 0 0
\(855\) 2.65739 0.0908809
\(856\) 0 0
\(857\) 53.3210 1.82141 0.910706 0.413055i \(-0.135538\pi\)
0.910706 + 0.413055i \(0.135538\pi\)
\(858\) 0 0
\(859\) −44.1761 −1.50727 −0.753635 0.657294i \(-0.771701\pi\)
−0.753635 + 0.657294i \(0.771701\pi\)
\(860\) 0 0
\(861\) −16.1348 −0.549872
\(862\) 0 0
\(863\) 12.5556 0.427398 0.213699 0.976900i \(-0.431449\pi\)
0.213699 + 0.976900i \(0.431449\pi\)
\(864\) 0 0
\(865\) 23.1821 0.788214
\(866\) 0 0
\(867\) 16.7230 0.567944
\(868\) 0 0
\(869\) 40.4910 1.37356
\(870\) 0 0
\(871\) 0.414817 0.0140555
\(872\) 0 0
\(873\) 1.61294 0.0545898
\(874\) 0 0
\(875\) 18.1674 0.614169
\(876\) 0 0
\(877\) 25.1403 0.848926 0.424463 0.905445i \(-0.360463\pi\)
0.424463 + 0.905445i \(0.360463\pi\)
\(878\) 0 0
\(879\) 8.51499 0.287204
\(880\) 0 0
\(881\) −0.517665 −0.0174406 −0.00872029 0.999962i \(-0.502776\pi\)
−0.00872029 + 0.999962i \(0.502776\pi\)
\(882\) 0 0
\(883\) −41.9585 −1.41202 −0.706009 0.708203i \(-0.749506\pi\)
−0.706009 + 0.708203i \(0.749506\pi\)
\(884\) 0 0
\(885\) 10.7968 0.362929
\(886\) 0 0
\(887\) −14.4419 −0.484911 −0.242455 0.970163i \(-0.577953\pi\)
−0.242455 + 0.970163i \(0.577953\pi\)
\(888\) 0 0
\(889\) 3.74273 0.125527
\(890\) 0 0
\(891\) 26.5837 0.890589
\(892\) 0 0
\(893\) 33.1326 1.10874
\(894\) 0 0
\(895\) −41.7241 −1.39468
\(896\) 0 0
\(897\) −0.0355057 −0.00118550
\(898\) 0 0
\(899\) 7.83694 0.261377
\(900\) 0 0
\(901\) −23.8071 −0.793129
\(902\) 0 0
\(903\) 19.3698 0.644587
\(904\) 0 0
\(905\) −18.2570 −0.606882
\(906\) 0 0
\(907\) −16.0472 −0.532837 −0.266418 0.963857i \(-0.585840\pi\)
−0.266418 + 0.963857i \(0.585840\pi\)
\(908\) 0 0
\(909\) 2.04450 0.0678119
\(910\) 0 0
\(911\) 40.2080 1.33215 0.666075 0.745885i \(-0.267973\pi\)
0.666075 + 0.745885i \(0.267973\pi\)
\(912\) 0 0
\(913\) 14.2263 0.470822
\(914\) 0 0
\(915\) −12.0612 −0.398731
\(916\) 0 0
\(917\) 1.13375 0.0374397
\(918\) 0 0
\(919\) −39.3644 −1.29851 −0.649256 0.760570i \(-0.724920\pi\)
−0.649256 + 0.760570i \(0.724920\pi\)
\(920\) 0 0
\(921\) −10.7836 −0.355331
\(922\) 0 0
\(923\) −0.676255 −0.0222592
\(924\) 0 0
\(925\) −7.75757 −0.255067
\(926\) 0 0
\(927\) −2.26556 −0.0744107
\(928\) 0 0
\(929\) 42.8018 1.40428 0.702141 0.712038i \(-0.252228\pi\)
0.702141 + 0.712038i \(0.252228\pi\)
\(930\) 0 0
\(931\) 22.5773 0.739942
\(932\) 0 0
\(933\) 47.0118 1.53910
\(934\) 0 0
\(935\) −34.5853 −1.13106
\(936\) 0 0
\(937\) −13.8128 −0.451243 −0.225622 0.974215i \(-0.572441\pi\)
−0.225622 + 0.974215i \(0.572441\pi\)
\(938\) 0 0
\(939\) 41.8987 1.36731
\(940\) 0 0
\(941\) −7.82865 −0.255207 −0.127603 0.991825i \(-0.540728\pi\)
−0.127603 + 0.991825i \(0.540728\pi\)
\(942\) 0 0
\(943\) −1.70571 −0.0555454
\(944\) 0 0
\(945\) 16.6496 0.541611
\(946\) 0 0
\(947\) −31.0874 −1.01021 −0.505103 0.863059i \(-0.668545\pi\)
−0.505103 + 0.863059i \(0.668545\pi\)
\(948\) 0 0
\(949\) 0.0999220 0.00324360
\(950\) 0 0
\(951\) 19.2087 0.622884
\(952\) 0 0
\(953\) 16.6169 0.538276 0.269138 0.963102i \(-0.413261\pi\)
0.269138 + 0.963102i \(0.413261\pi\)
\(954\) 0 0
\(955\) −14.4595 −0.467897
\(956\) 0 0
\(957\) 42.0029 1.35776
\(958\) 0 0
\(959\) 8.33475 0.269143
\(960\) 0 0
\(961\) −29.9794 −0.967078
\(962\) 0 0
\(963\) 0.517517 0.0166767
\(964\) 0 0
\(965\) −16.4668 −0.530086
\(966\) 0 0
\(967\) 37.5255 1.20674 0.603369 0.797462i \(-0.293825\pi\)
0.603369 + 0.797462i \(0.293825\pi\)
\(968\) 0 0
\(969\) −41.4363 −1.33113
\(970\) 0 0
\(971\) 21.7506 0.698010 0.349005 0.937121i \(-0.386520\pi\)
0.349005 + 0.937121i \(0.386520\pi\)
\(972\) 0 0
\(973\) −29.9470 −0.960057
\(974\) 0 0
\(975\) −0.119955 −0.00384163
\(976\) 0 0
\(977\) 8.46868 0.270937 0.135469 0.990782i \(-0.456746\pi\)
0.135469 + 0.990782i \(0.456746\pi\)
\(978\) 0 0
\(979\) −22.1954 −0.709369
\(980\) 0 0
\(981\) −4.15855 −0.132772
\(982\) 0 0
\(983\) −3.60789 −0.115074 −0.0575369 0.998343i \(-0.518325\pi\)
−0.0575369 + 0.998343i \(0.518325\pi\)
\(984\) 0 0
\(985\) −22.3753 −0.712935
\(986\) 0 0
\(987\) 17.2767 0.549923
\(988\) 0 0
\(989\) 2.04770 0.0651131
\(990\) 0 0
\(991\) 10.3797 0.329721 0.164860 0.986317i \(-0.447283\pi\)
0.164860 + 0.986317i \(0.447283\pi\)
\(992\) 0 0
\(993\) 40.0839 1.27202
\(994\) 0 0
\(995\) −56.3955 −1.78786
\(996\) 0 0
\(997\) 8.81127 0.279056 0.139528 0.990218i \(-0.455442\pi\)
0.139528 + 0.990218i \(0.455442\pi\)
\(998\) 0 0
\(999\) −46.7322 −1.47854
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.1.35 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.35 44 1.1 even 1 trivial