Properties

Label 8008.2.a.v.1.9
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.62645\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.62645 q^{3} +1.90839 q^{5} -1.00000 q^{7} -0.354663 q^{9} +O(q^{10})\) \(q+1.62645 q^{3} +1.90839 q^{5} -1.00000 q^{7} -0.354663 q^{9} +1.00000 q^{11} -1.00000 q^{13} +3.10390 q^{15} -3.20781 q^{17} -1.68037 q^{19} -1.62645 q^{21} -6.28937 q^{23} -1.35805 q^{25} -5.45619 q^{27} -10.4085 q^{29} +10.9694 q^{31} +1.62645 q^{33} -1.90839 q^{35} +7.50885 q^{37} -1.62645 q^{39} +4.62709 q^{41} +6.59107 q^{43} -0.676835 q^{45} -6.28937 q^{47} +1.00000 q^{49} -5.21734 q^{51} -0.328865 q^{53} +1.90839 q^{55} -2.73303 q^{57} -0.221452 q^{59} -2.97164 q^{61} +0.354663 q^{63} -1.90839 q^{65} +5.06539 q^{67} -10.2293 q^{69} -4.48919 q^{71} -11.4302 q^{73} -2.20880 q^{75} -1.00000 q^{77} -8.26940 q^{79} -7.81023 q^{81} -16.2131 q^{83} -6.12175 q^{85} -16.9288 q^{87} -12.3083 q^{89} +1.00000 q^{91} +17.8412 q^{93} -3.20679 q^{95} +17.9739 q^{97} -0.354663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) 1.62645 0.939031 0.469515 0.882924i \(-0.344429\pi\)
0.469515 + 0.882924i \(0.344429\pi\)
\(4\) 0 0
\(5\) 1.90839 0.853458 0.426729 0.904380i \(-0.359666\pi\)
0.426729 + 0.904380i \(0.359666\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.354663 −0.118221
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 3.10390 0.801423
\(16\) 0 0
\(17\) −3.20781 −0.778009 −0.389004 0.921236i \(-0.627181\pi\)
−0.389004 + 0.921236i \(0.627181\pi\)
\(18\) 0 0
\(19\) −1.68037 −0.385502 −0.192751 0.981248i \(-0.561741\pi\)
−0.192751 + 0.981248i \(0.561741\pi\)
\(20\) 0 0
\(21\) −1.62645 −0.354920
\(22\) 0 0
\(23\) −6.28937 −1.31142 −0.655712 0.755011i \(-0.727631\pi\)
−0.655712 + 0.755011i \(0.727631\pi\)
\(24\) 0 0
\(25\) −1.35805 −0.271610
\(26\) 0 0
\(27\) −5.45619 −1.05004
\(28\) 0 0
\(29\) −10.4085 −1.93280 −0.966402 0.257034i \(-0.917255\pi\)
−0.966402 + 0.257034i \(0.917255\pi\)
\(30\) 0 0
\(31\) 10.9694 1.97016 0.985080 0.172095i \(-0.0550536\pi\)
0.985080 + 0.172095i \(0.0550536\pi\)
\(32\) 0 0
\(33\) 1.62645 0.283128
\(34\) 0 0
\(35\) −1.90839 −0.322577
\(36\) 0 0
\(37\) 7.50885 1.23445 0.617224 0.786788i \(-0.288257\pi\)
0.617224 + 0.786788i \(0.288257\pi\)
\(38\) 0 0
\(39\) −1.62645 −0.260440
\(40\) 0 0
\(41\) 4.62709 0.722631 0.361315 0.932444i \(-0.382328\pi\)
0.361315 + 0.932444i \(0.382328\pi\)
\(42\) 0 0
\(43\) 6.59107 1.00513 0.502564 0.864540i \(-0.332390\pi\)
0.502564 + 0.864540i \(0.332390\pi\)
\(44\) 0 0
\(45\) −0.676835 −0.100897
\(46\) 0 0
\(47\) −6.28937 −0.917399 −0.458699 0.888592i \(-0.651685\pi\)
−0.458699 + 0.888592i \(0.651685\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −5.21734 −0.730574
\(52\) 0 0
\(53\) −0.328865 −0.0451730 −0.0225865 0.999745i \(-0.507190\pi\)
−0.0225865 + 0.999745i \(0.507190\pi\)
\(54\) 0 0
\(55\) 1.90839 0.257327
\(56\) 0 0
\(57\) −2.73303 −0.361999
\(58\) 0 0
\(59\) −0.221452 −0.0288306 −0.0144153 0.999896i \(-0.504589\pi\)
−0.0144153 + 0.999896i \(0.504589\pi\)
\(60\) 0 0
\(61\) −2.97164 −0.380479 −0.190240 0.981738i \(-0.560927\pi\)
−0.190240 + 0.981738i \(0.560927\pi\)
\(62\) 0 0
\(63\) 0.354663 0.0446833
\(64\) 0 0
\(65\) −1.90839 −0.236707
\(66\) 0 0
\(67\) 5.06539 0.618836 0.309418 0.950926i \(-0.399866\pi\)
0.309418 + 0.950926i \(0.399866\pi\)
\(68\) 0 0
\(69\) −10.2293 −1.23147
\(70\) 0 0
\(71\) −4.48919 −0.532768 −0.266384 0.963867i \(-0.585829\pi\)
−0.266384 + 0.963867i \(0.585829\pi\)
\(72\) 0 0
\(73\) −11.4302 −1.33780 −0.668901 0.743352i \(-0.733235\pi\)
−0.668901 + 0.743352i \(0.733235\pi\)
\(74\) 0 0
\(75\) −2.20880 −0.255050
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −8.26940 −0.930381 −0.465190 0.885211i \(-0.654014\pi\)
−0.465190 + 0.885211i \(0.654014\pi\)
\(80\) 0 0
\(81\) −7.81023 −0.867803
\(82\) 0 0
\(83\) −16.2131 −1.77962 −0.889809 0.456333i \(-0.849162\pi\)
−0.889809 + 0.456333i \(0.849162\pi\)
\(84\) 0 0
\(85\) −6.12175 −0.663997
\(86\) 0 0
\(87\) −16.9288 −1.81496
\(88\) 0 0
\(89\) −12.3083 −1.30467 −0.652336 0.757930i \(-0.726211\pi\)
−0.652336 + 0.757930i \(0.726211\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 17.8412 1.85004
\(94\) 0 0
\(95\) −3.20679 −0.329010
\(96\) 0 0
\(97\) 17.9739 1.82498 0.912489 0.409102i \(-0.134158\pi\)
0.912489 + 0.409102i \(0.134158\pi\)
\(98\) 0 0
\(99\) −0.354663 −0.0356450
\(100\) 0 0
\(101\) −8.68705 −0.864394 −0.432197 0.901779i \(-0.642261\pi\)
−0.432197 + 0.901779i \(0.642261\pi\)
\(102\) 0 0
\(103\) 5.75825 0.567377 0.283689 0.958916i \(-0.408442\pi\)
0.283689 + 0.958916i \(0.408442\pi\)
\(104\) 0 0
\(105\) −3.10390 −0.302909
\(106\) 0 0
\(107\) −9.54635 −0.922881 −0.461440 0.887171i \(-0.652667\pi\)
−0.461440 + 0.887171i \(0.652667\pi\)
\(108\) 0 0
\(109\) −6.11737 −0.585938 −0.292969 0.956122i \(-0.594643\pi\)
−0.292969 + 0.956122i \(0.594643\pi\)
\(110\) 0 0
\(111\) 12.2128 1.15918
\(112\) 0 0
\(113\) −18.5097 −1.74125 −0.870623 0.491952i \(-0.836284\pi\)
−0.870623 + 0.491952i \(0.836284\pi\)
\(114\) 0 0
\(115\) −12.0026 −1.11924
\(116\) 0 0
\(117\) 0.354663 0.0327886
\(118\) 0 0
\(119\) 3.20781 0.294060
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 7.52573 0.678572
\(124\) 0 0
\(125\) −12.1336 −1.08527
\(126\) 0 0
\(127\) −19.8363 −1.76019 −0.880094 0.474800i \(-0.842520\pi\)
−0.880094 + 0.474800i \(0.842520\pi\)
\(128\) 0 0
\(129\) 10.7200 0.943846
\(130\) 0 0
\(131\) −20.9949 −1.83433 −0.917166 0.398506i \(-0.869529\pi\)
−0.917166 + 0.398506i \(0.869529\pi\)
\(132\) 0 0
\(133\) 1.68037 0.145706
\(134\) 0 0
\(135\) −10.4125 −0.896168
\(136\) 0 0
\(137\) 15.4984 1.32412 0.662059 0.749451i \(-0.269683\pi\)
0.662059 + 0.749451i \(0.269683\pi\)
\(138\) 0 0
\(139\) 10.7559 0.912305 0.456152 0.889902i \(-0.349227\pi\)
0.456152 + 0.889902i \(0.349227\pi\)
\(140\) 0 0
\(141\) −10.2293 −0.861466
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −19.8634 −1.64957
\(146\) 0 0
\(147\) 1.62645 0.134147
\(148\) 0 0
\(149\) 13.2011 1.08147 0.540737 0.841192i \(-0.318145\pi\)
0.540737 + 0.841192i \(0.318145\pi\)
\(150\) 0 0
\(151\) 23.8811 1.94342 0.971709 0.236179i \(-0.0758953\pi\)
0.971709 + 0.236179i \(0.0758953\pi\)
\(152\) 0 0
\(153\) 1.13769 0.0919769
\(154\) 0 0
\(155\) 20.9339 1.68145
\(156\) 0 0
\(157\) 9.74555 0.777779 0.388890 0.921284i \(-0.372859\pi\)
0.388890 + 0.921284i \(0.372859\pi\)
\(158\) 0 0
\(159\) −0.534882 −0.0424189
\(160\) 0 0
\(161\) 6.28937 0.495672
\(162\) 0 0
\(163\) −13.3341 −1.04441 −0.522205 0.852820i \(-0.674891\pi\)
−0.522205 + 0.852820i \(0.674891\pi\)
\(164\) 0 0
\(165\) 3.10390 0.241638
\(166\) 0 0
\(167\) 4.73134 0.366122 0.183061 0.983102i \(-0.441399\pi\)
0.183061 + 0.983102i \(0.441399\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.595963 0.0455745
\(172\) 0 0
\(173\) 11.2925 0.858552 0.429276 0.903173i \(-0.358769\pi\)
0.429276 + 0.903173i \(0.358769\pi\)
\(174\) 0 0
\(175\) 1.35805 0.102659
\(176\) 0 0
\(177\) −0.360181 −0.0270729
\(178\) 0 0
\(179\) −8.24817 −0.616497 −0.308249 0.951306i \(-0.599743\pi\)
−0.308249 + 0.951306i \(0.599743\pi\)
\(180\) 0 0
\(181\) −22.3944 −1.66456 −0.832280 0.554356i \(-0.812965\pi\)
−0.832280 + 0.554356i \(0.812965\pi\)
\(182\) 0 0
\(183\) −4.83322 −0.357282
\(184\) 0 0
\(185\) 14.3298 1.05355
\(186\) 0 0
\(187\) −3.20781 −0.234578
\(188\) 0 0
\(189\) 5.45619 0.396879
\(190\) 0 0
\(191\) −1.54463 −0.111765 −0.0558826 0.998437i \(-0.517797\pi\)
−0.0558826 + 0.998437i \(0.517797\pi\)
\(192\) 0 0
\(193\) 5.32671 0.383425 0.191712 0.981451i \(-0.438596\pi\)
0.191712 + 0.981451i \(0.438596\pi\)
\(194\) 0 0
\(195\) −3.10390 −0.222275
\(196\) 0 0
\(197\) 1.62108 0.115497 0.0577486 0.998331i \(-0.481608\pi\)
0.0577486 + 0.998331i \(0.481608\pi\)
\(198\) 0 0
\(199\) −19.2275 −1.36300 −0.681501 0.731817i \(-0.738672\pi\)
−0.681501 + 0.731817i \(0.738672\pi\)
\(200\) 0 0
\(201\) 8.23860 0.581106
\(202\) 0 0
\(203\) 10.4085 0.730531
\(204\) 0 0
\(205\) 8.83030 0.616735
\(206\) 0 0
\(207\) 2.23061 0.155038
\(208\) 0 0
\(209\) −1.68037 −0.116233
\(210\) 0 0
\(211\) 9.32059 0.641656 0.320828 0.947137i \(-0.396039\pi\)
0.320828 + 0.947137i \(0.396039\pi\)
\(212\) 0 0
\(213\) −7.30144 −0.500286
\(214\) 0 0
\(215\) 12.5783 0.857834
\(216\) 0 0
\(217\) −10.9694 −0.744651
\(218\) 0 0
\(219\) −18.5906 −1.25624
\(220\) 0 0
\(221\) 3.20781 0.215781
\(222\) 0 0
\(223\) −2.96696 −0.198682 −0.0993410 0.995053i \(-0.531673\pi\)
−0.0993410 + 0.995053i \(0.531673\pi\)
\(224\) 0 0
\(225\) 0.481650 0.0321100
\(226\) 0 0
\(227\) −8.46137 −0.561601 −0.280801 0.959766i \(-0.590600\pi\)
−0.280801 + 0.959766i \(0.590600\pi\)
\(228\) 0 0
\(229\) 21.6566 1.43111 0.715553 0.698559i \(-0.246175\pi\)
0.715553 + 0.698559i \(0.246175\pi\)
\(230\) 0 0
\(231\) −1.62645 −0.107013
\(232\) 0 0
\(233\) 5.37369 0.352042 0.176021 0.984386i \(-0.443677\pi\)
0.176021 + 0.984386i \(0.443677\pi\)
\(234\) 0 0
\(235\) −12.0026 −0.782961
\(236\) 0 0
\(237\) −13.4498 −0.873656
\(238\) 0 0
\(239\) −21.3666 −1.38209 −0.691045 0.722811i \(-0.742850\pi\)
−0.691045 + 0.722811i \(0.742850\pi\)
\(240\) 0 0
\(241\) 15.6292 1.00677 0.503383 0.864063i \(-0.332088\pi\)
0.503383 + 0.864063i \(0.332088\pi\)
\(242\) 0 0
\(243\) 3.66563 0.235150
\(244\) 0 0
\(245\) 1.90839 0.121923
\(246\) 0 0
\(247\) 1.68037 0.106919
\(248\) 0 0
\(249\) −26.3698 −1.67112
\(250\) 0 0
\(251\) −2.52299 −0.159250 −0.0796249 0.996825i \(-0.525372\pi\)
−0.0796249 + 0.996825i \(0.525372\pi\)
\(252\) 0 0
\(253\) −6.28937 −0.395409
\(254\) 0 0
\(255\) −9.95672 −0.623514
\(256\) 0 0
\(257\) −12.3572 −0.770824 −0.385412 0.922745i \(-0.625941\pi\)
−0.385412 + 0.922745i \(0.625941\pi\)
\(258\) 0 0
\(259\) −7.50885 −0.466577
\(260\) 0 0
\(261\) 3.69150 0.228498
\(262\) 0 0
\(263\) −4.69085 −0.289250 −0.144625 0.989487i \(-0.546198\pi\)
−0.144625 + 0.989487i \(0.546198\pi\)
\(264\) 0 0
\(265\) −0.627602 −0.0385533
\(266\) 0 0
\(267\) −20.0187 −1.22513
\(268\) 0 0
\(269\) −17.6895 −1.07855 −0.539274 0.842131i \(-0.681301\pi\)
−0.539274 + 0.842131i \(0.681301\pi\)
\(270\) 0 0
\(271\) −11.0560 −0.671604 −0.335802 0.941933i \(-0.609007\pi\)
−0.335802 + 0.941933i \(0.609007\pi\)
\(272\) 0 0
\(273\) 1.62645 0.0984372
\(274\) 0 0
\(275\) −1.35805 −0.0818935
\(276\) 0 0
\(277\) −12.3411 −0.741506 −0.370753 0.928732i \(-0.620900\pi\)
−0.370753 + 0.928732i \(0.620900\pi\)
\(278\) 0 0
\(279\) −3.89044 −0.232914
\(280\) 0 0
\(281\) 14.8951 0.888569 0.444285 0.895886i \(-0.353458\pi\)
0.444285 + 0.895886i \(0.353458\pi\)
\(282\) 0 0
\(283\) −3.76843 −0.224010 −0.112005 0.993708i \(-0.535727\pi\)
−0.112005 + 0.993708i \(0.535727\pi\)
\(284\) 0 0
\(285\) −5.21568 −0.308951
\(286\) 0 0
\(287\) −4.62709 −0.273129
\(288\) 0 0
\(289\) −6.70995 −0.394703
\(290\) 0 0
\(291\) 29.2337 1.71371
\(292\) 0 0
\(293\) 32.3057 1.88732 0.943659 0.330921i \(-0.107359\pi\)
0.943659 + 0.330921i \(0.107359\pi\)
\(294\) 0 0
\(295\) −0.422617 −0.0246057
\(296\) 0 0
\(297\) −5.45619 −0.316600
\(298\) 0 0
\(299\) 6.28937 0.363724
\(300\) 0 0
\(301\) −6.59107 −0.379903
\(302\) 0 0
\(303\) −14.1290 −0.811693
\(304\) 0 0
\(305\) −5.67104 −0.324723
\(306\) 0 0
\(307\) −5.08741 −0.290354 −0.145177 0.989406i \(-0.546375\pi\)
−0.145177 + 0.989406i \(0.546375\pi\)
\(308\) 0 0
\(309\) 9.36550 0.532785
\(310\) 0 0
\(311\) 32.4132 1.83799 0.918993 0.394275i \(-0.129004\pi\)
0.918993 + 0.394275i \(0.129004\pi\)
\(312\) 0 0
\(313\) 3.62197 0.204726 0.102363 0.994747i \(-0.467360\pi\)
0.102363 + 0.994747i \(0.467360\pi\)
\(314\) 0 0
\(315\) 0.676835 0.0381353
\(316\) 0 0
\(317\) −7.84224 −0.440464 −0.220232 0.975448i \(-0.570681\pi\)
−0.220232 + 0.975448i \(0.570681\pi\)
\(318\) 0 0
\(319\) −10.4085 −0.582762
\(320\) 0 0
\(321\) −15.5267 −0.866614
\(322\) 0 0
\(323\) 5.39030 0.299924
\(324\) 0 0
\(325\) 1.35805 0.0753310
\(326\) 0 0
\(327\) −9.94959 −0.550214
\(328\) 0 0
\(329\) 6.28937 0.346744
\(330\) 0 0
\(331\) 21.0271 1.15575 0.577876 0.816125i \(-0.303882\pi\)
0.577876 + 0.816125i \(0.303882\pi\)
\(332\) 0 0
\(333\) −2.66311 −0.145938
\(334\) 0 0
\(335\) 9.66674 0.528150
\(336\) 0 0
\(337\) 15.8491 0.863358 0.431679 0.902027i \(-0.357921\pi\)
0.431679 + 0.902027i \(0.357921\pi\)
\(338\) 0 0
\(339\) −30.1051 −1.63508
\(340\) 0 0
\(341\) 10.9694 0.594026
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −19.5216 −1.05101
\(346\) 0 0
\(347\) 5.88971 0.316176 0.158088 0.987425i \(-0.449467\pi\)
0.158088 + 0.987425i \(0.449467\pi\)
\(348\) 0 0
\(349\) 2.11752 0.113348 0.0566740 0.998393i \(-0.481950\pi\)
0.0566740 + 0.998393i \(0.481950\pi\)
\(350\) 0 0
\(351\) 5.45619 0.291230
\(352\) 0 0
\(353\) −27.8744 −1.48361 −0.741804 0.670617i \(-0.766029\pi\)
−0.741804 + 0.670617i \(0.766029\pi\)
\(354\) 0 0
\(355\) −8.56712 −0.454695
\(356\) 0 0
\(357\) 5.21734 0.276131
\(358\) 0 0
\(359\) −15.6143 −0.824091 −0.412046 0.911163i \(-0.635186\pi\)
−0.412046 + 0.911163i \(0.635186\pi\)
\(360\) 0 0
\(361\) −16.1764 −0.851388
\(362\) 0 0
\(363\) 1.62645 0.0853664
\(364\) 0 0
\(365\) −21.8132 −1.14176
\(366\) 0 0
\(367\) −6.96368 −0.363501 −0.181750 0.983345i \(-0.558176\pi\)
−0.181750 + 0.983345i \(0.558176\pi\)
\(368\) 0 0
\(369\) −1.64106 −0.0854301
\(370\) 0 0
\(371\) 0.328865 0.0170738
\(372\) 0 0
\(373\) 4.80581 0.248835 0.124418 0.992230i \(-0.460294\pi\)
0.124418 + 0.992230i \(0.460294\pi\)
\(374\) 0 0
\(375\) −19.7347 −1.01910
\(376\) 0 0
\(377\) 10.4085 0.536064
\(378\) 0 0
\(379\) 18.9190 0.971804 0.485902 0.874013i \(-0.338491\pi\)
0.485902 + 0.874013i \(0.338491\pi\)
\(380\) 0 0
\(381\) −32.2627 −1.65287
\(382\) 0 0
\(383\) −25.3652 −1.29610 −0.648049 0.761598i \(-0.724415\pi\)
−0.648049 + 0.761598i \(0.724415\pi\)
\(384\) 0 0
\(385\) −1.90839 −0.0972605
\(386\) 0 0
\(387\) −2.33761 −0.118827
\(388\) 0 0
\(389\) 8.12911 0.412162 0.206081 0.978535i \(-0.433929\pi\)
0.206081 + 0.978535i \(0.433929\pi\)
\(390\) 0 0
\(391\) 20.1751 1.02030
\(392\) 0 0
\(393\) −34.1471 −1.72249
\(394\) 0 0
\(395\) −15.7812 −0.794040
\(396\) 0 0
\(397\) 12.1618 0.610384 0.305192 0.952291i \(-0.401279\pi\)
0.305192 + 0.952291i \(0.401279\pi\)
\(398\) 0 0
\(399\) 2.73303 0.136823
\(400\) 0 0
\(401\) 9.41398 0.470112 0.235056 0.971982i \(-0.424473\pi\)
0.235056 + 0.971982i \(0.424473\pi\)
\(402\) 0 0
\(403\) −10.9694 −0.546424
\(404\) 0 0
\(405\) −14.9050 −0.740633
\(406\) 0 0
\(407\) 7.50885 0.372200
\(408\) 0 0
\(409\) −36.1693 −1.78845 −0.894227 0.447613i \(-0.852274\pi\)
−0.894227 + 0.447613i \(0.852274\pi\)
\(410\) 0 0
\(411\) 25.2074 1.24339
\(412\) 0 0
\(413\) 0.221452 0.0108970
\(414\) 0 0
\(415\) −30.9409 −1.51883
\(416\) 0 0
\(417\) 17.4939 0.856682
\(418\) 0 0
\(419\) 15.3781 0.751269 0.375635 0.926768i \(-0.377425\pi\)
0.375635 + 0.926768i \(0.377425\pi\)
\(420\) 0 0
\(421\) 35.7258 1.74117 0.870585 0.492019i \(-0.163741\pi\)
0.870585 + 0.492019i \(0.163741\pi\)
\(422\) 0 0
\(423\) 2.23061 0.108456
\(424\) 0 0
\(425\) 4.35637 0.211315
\(426\) 0 0
\(427\) 2.97164 0.143808
\(428\) 0 0
\(429\) −1.62645 −0.0785257
\(430\) 0 0
\(431\) 21.5530 1.03817 0.519087 0.854722i \(-0.326272\pi\)
0.519087 + 0.854722i \(0.326272\pi\)
\(432\) 0 0
\(433\) 40.1197 1.92803 0.964015 0.265849i \(-0.0856522\pi\)
0.964015 + 0.265849i \(0.0856522\pi\)
\(434\) 0 0
\(435\) −32.3068 −1.54899
\(436\) 0 0
\(437\) 10.5684 0.505557
\(438\) 0 0
\(439\) 6.52565 0.311452 0.155726 0.987800i \(-0.450228\pi\)
0.155726 + 0.987800i \(0.450228\pi\)
\(440\) 0 0
\(441\) −0.354663 −0.0168887
\(442\) 0 0
\(443\) 18.9523 0.900450 0.450225 0.892915i \(-0.351344\pi\)
0.450225 + 0.892915i \(0.351344\pi\)
\(444\) 0 0
\(445\) −23.4889 −1.11348
\(446\) 0 0
\(447\) 21.4709 1.01554
\(448\) 0 0
\(449\) −10.9854 −0.518431 −0.259215 0.965820i \(-0.583464\pi\)
−0.259215 + 0.965820i \(0.583464\pi\)
\(450\) 0 0
\(451\) 4.62709 0.217881
\(452\) 0 0
\(453\) 38.8414 1.82493
\(454\) 0 0
\(455\) 1.90839 0.0894667
\(456\) 0 0
\(457\) −15.3708 −0.719018 −0.359509 0.933142i \(-0.617056\pi\)
−0.359509 + 0.933142i \(0.617056\pi\)
\(458\) 0 0
\(459\) 17.5024 0.816943
\(460\) 0 0
\(461\) 26.3819 1.22873 0.614363 0.789023i \(-0.289413\pi\)
0.614363 + 0.789023i \(0.289413\pi\)
\(462\) 0 0
\(463\) −33.4206 −1.55319 −0.776594 0.630002i \(-0.783054\pi\)
−0.776594 + 0.630002i \(0.783054\pi\)
\(464\) 0 0
\(465\) 34.0479 1.57893
\(466\) 0 0
\(467\) 22.1787 1.02631 0.513155 0.858296i \(-0.328477\pi\)
0.513155 + 0.858296i \(0.328477\pi\)
\(468\) 0 0
\(469\) −5.06539 −0.233898
\(470\) 0 0
\(471\) 15.8506 0.730359
\(472\) 0 0
\(473\) 6.59107 0.303057
\(474\) 0 0
\(475\) 2.28202 0.104706
\(476\) 0 0
\(477\) 0.116636 0.00534040
\(478\) 0 0
\(479\) −6.06107 −0.276937 −0.138469 0.990367i \(-0.544218\pi\)
−0.138469 + 0.990367i \(0.544218\pi\)
\(480\) 0 0
\(481\) −7.50885 −0.342374
\(482\) 0 0
\(483\) 10.2293 0.465451
\(484\) 0 0
\(485\) 34.3013 1.55754
\(486\) 0 0
\(487\) 32.6068 1.47756 0.738779 0.673948i \(-0.235403\pi\)
0.738779 + 0.673948i \(0.235403\pi\)
\(488\) 0 0
\(489\) −21.6873 −0.980734
\(490\) 0 0
\(491\) −19.8647 −0.896480 −0.448240 0.893913i \(-0.647949\pi\)
−0.448240 + 0.893913i \(0.647949\pi\)
\(492\) 0 0
\(493\) 33.3884 1.50374
\(494\) 0 0
\(495\) −0.676835 −0.0304215
\(496\) 0 0
\(497\) 4.48919 0.201368
\(498\) 0 0
\(499\) 27.3571 1.22467 0.612336 0.790598i \(-0.290230\pi\)
0.612336 + 0.790598i \(0.290230\pi\)
\(500\) 0 0
\(501\) 7.69528 0.343800
\(502\) 0 0
\(503\) −2.15428 −0.0960548 −0.0480274 0.998846i \(-0.515293\pi\)
−0.0480274 + 0.998846i \(0.515293\pi\)
\(504\) 0 0
\(505\) −16.5783 −0.737724
\(506\) 0 0
\(507\) 1.62645 0.0722331
\(508\) 0 0
\(509\) 21.7700 0.964940 0.482470 0.875913i \(-0.339740\pi\)
0.482470 + 0.875913i \(0.339740\pi\)
\(510\) 0 0
\(511\) 11.4302 0.505642
\(512\) 0 0
\(513\) 9.16839 0.404794
\(514\) 0 0
\(515\) 10.9890 0.484232
\(516\) 0 0
\(517\) −6.28937 −0.276606
\(518\) 0 0
\(519\) 18.3667 0.806207
\(520\) 0 0
\(521\) 13.5638 0.594242 0.297121 0.954840i \(-0.403973\pi\)
0.297121 + 0.954840i \(0.403973\pi\)
\(522\) 0 0
\(523\) −25.1645 −1.10037 −0.550184 0.835043i \(-0.685443\pi\)
−0.550184 + 0.835043i \(0.685443\pi\)
\(524\) 0 0
\(525\) 2.20880 0.0963999
\(526\) 0 0
\(527\) −35.1877 −1.53280
\(528\) 0 0
\(529\) 16.5562 0.719833
\(530\) 0 0
\(531\) 0.0785409 0.00340839
\(532\) 0 0
\(533\) −4.62709 −0.200422
\(534\) 0 0
\(535\) −18.2182 −0.787640
\(536\) 0 0
\(537\) −13.4152 −0.578910
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 22.5108 0.967814 0.483907 0.875119i \(-0.339217\pi\)
0.483907 + 0.875119i \(0.339217\pi\)
\(542\) 0 0
\(543\) −36.4233 −1.56307
\(544\) 0 0
\(545\) −11.6743 −0.500073
\(546\) 0 0
\(547\) −39.3456 −1.68230 −0.841148 0.540805i \(-0.818120\pi\)
−0.841148 + 0.540805i \(0.818120\pi\)
\(548\) 0 0
\(549\) 1.05393 0.0449806
\(550\) 0 0
\(551\) 17.4900 0.745101
\(552\) 0 0
\(553\) 8.26940 0.351651
\(554\) 0 0
\(555\) 23.3067 0.989315
\(556\) 0 0
\(557\) 32.4826 1.37633 0.688166 0.725553i \(-0.258416\pi\)
0.688166 + 0.725553i \(0.258416\pi\)
\(558\) 0 0
\(559\) −6.59107 −0.278772
\(560\) 0 0
\(561\) −5.21734 −0.220276
\(562\) 0 0
\(563\) 20.7341 0.873839 0.436919 0.899501i \(-0.356069\pi\)
0.436919 + 0.899501i \(0.356069\pi\)
\(564\) 0 0
\(565\) −35.3237 −1.48608
\(566\) 0 0
\(567\) 7.81023 0.327999
\(568\) 0 0
\(569\) 10.7869 0.452212 0.226106 0.974103i \(-0.427400\pi\)
0.226106 + 0.974103i \(0.427400\pi\)
\(570\) 0 0
\(571\) −34.7841 −1.45567 −0.727834 0.685753i \(-0.759473\pi\)
−0.727834 + 0.685753i \(0.759473\pi\)
\(572\) 0 0
\(573\) −2.51226 −0.104951
\(574\) 0 0
\(575\) 8.54127 0.356196
\(576\) 0 0
\(577\) 22.2344 0.925630 0.462815 0.886455i \(-0.346839\pi\)
0.462815 + 0.886455i \(0.346839\pi\)
\(578\) 0 0
\(579\) 8.66362 0.360048
\(580\) 0 0
\(581\) 16.2131 0.672632
\(582\) 0 0
\(583\) −0.328865 −0.0136202
\(584\) 0 0
\(585\) 0.676835 0.0279837
\(586\) 0 0
\(587\) −10.1767 −0.420035 −0.210018 0.977698i \(-0.567352\pi\)
−0.210018 + 0.977698i \(0.567352\pi\)
\(588\) 0 0
\(589\) −18.4326 −0.759502
\(590\) 0 0
\(591\) 2.63660 0.108455
\(592\) 0 0
\(593\) −41.8268 −1.71762 −0.858810 0.512294i \(-0.828796\pi\)
−0.858810 + 0.512294i \(0.828796\pi\)
\(594\) 0 0
\(595\) 6.12175 0.250967
\(596\) 0 0
\(597\) −31.2726 −1.27990
\(598\) 0 0
\(599\) −0.652628 −0.0266657 −0.0133328 0.999911i \(-0.504244\pi\)
−0.0133328 + 0.999911i \(0.504244\pi\)
\(600\) 0 0
\(601\) −39.8032 −1.62361 −0.811803 0.583932i \(-0.801513\pi\)
−0.811803 + 0.583932i \(0.801513\pi\)
\(602\) 0 0
\(603\) −1.79651 −0.0731594
\(604\) 0 0
\(605\) 1.90839 0.0775871
\(606\) 0 0
\(607\) −42.4068 −1.72124 −0.860620 0.509247i \(-0.829924\pi\)
−0.860620 + 0.509247i \(0.829924\pi\)
\(608\) 0 0
\(609\) 16.9288 0.685992
\(610\) 0 0
\(611\) 6.28937 0.254441
\(612\) 0 0
\(613\) 30.4682 1.23060 0.615299 0.788294i \(-0.289035\pi\)
0.615299 + 0.788294i \(0.289035\pi\)
\(614\) 0 0
\(615\) 14.3620 0.579133
\(616\) 0 0
\(617\) −22.8378 −0.919415 −0.459708 0.888070i \(-0.652046\pi\)
−0.459708 + 0.888070i \(0.652046\pi\)
\(618\) 0 0
\(619\) −17.0595 −0.685681 −0.342840 0.939394i \(-0.611389\pi\)
−0.342840 + 0.939394i \(0.611389\pi\)
\(620\) 0 0
\(621\) 34.3160 1.37705
\(622\) 0 0
\(623\) 12.3083 0.493120
\(624\) 0 0
\(625\) −16.3655 −0.654618
\(626\) 0 0
\(627\) −2.73303 −0.109147
\(628\) 0 0
\(629\) −24.0870 −0.960411
\(630\) 0 0
\(631\) 14.1943 0.565065 0.282533 0.959258i \(-0.408825\pi\)
0.282533 + 0.959258i \(0.408825\pi\)
\(632\) 0 0
\(633\) 15.1595 0.602535
\(634\) 0 0
\(635\) −37.8554 −1.50225
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 1.59215 0.0629844
\(640\) 0 0
\(641\) 0.566058 0.0223579 0.0111790 0.999938i \(-0.496442\pi\)
0.0111790 + 0.999938i \(0.496442\pi\)
\(642\) 0 0
\(643\) −36.6769 −1.44639 −0.723197 0.690642i \(-0.757328\pi\)
−0.723197 + 0.690642i \(0.757328\pi\)
\(644\) 0 0
\(645\) 20.4580 0.805533
\(646\) 0 0
\(647\) 13.0002 0.511089 0.255544 0.966797i \(-0.417745\pi\)
0.255544 + 0.966797i \(0.417745\pi\)
\(648\) 0 0
\(649\) −0.221452 −0.00869277
\(650\) 0 0
\(651\) −17.8412 −0.699250
\(652\) 0 0
\(653\) −26.0183 −1.01817 −0.509087 0.860715i \(-0.670017\pi\)
−0.509087 + 0.860715i \(0.670017\pi\)
\(654\) 0 0
\(655\) −40.0664 −1.56552
\(656\) 0 0
\(657\) 4.05386 0.158156
\(658\) 0 0
\(659\) 15.5829 0.607023 0.303512 0.952828i \(-0.401841\pi\)
0.303512 + 0.952828i \(0.401841\pi\)
\(660\) 0 0
\(661\) −24.9084 −0.968824 −0.484412 0.874840i \(-0.660966\pi\)
−0.484412 + 0.874840i \(0.660966\pi\)
\(662\) 0 0
\(663\) 5.21734 0.202625
\(664\) 0 0
\(665\) 3.20679 0.124354
\(666\) 0 0
\(667\) 65.4627 2.53473
\(668\) 0 0
\(669\) −4.82560 −0.186569
\(670\) 0 0
\(671\) −2.97164 −0.114719
\(672\) 0 0
\(673\) −13.9389 −0.537307 −0.268653 0.963237i \(-0.586579\pi\)
−0.268653 + 0.963237i \(0.586579\pi\)
\(674\) 0 0
\(675\) 7.40977 0.285202
\(676\) 0 0
\(677\) 33.8055 1.29925 0.649625 0.760254i \(-0.274926\pi\)
0.649625 + 0.760254i \(0.274926\pi\)
\(678\) 0 0
\(679\) −17.9739 −0.689777
\(680\) 0 0
\(681\) −13.7620 −0.527361
\(682\) 0 0
\(683\) 27.6884 1.05947 0.529733 0.848164i \(-0.322292\pi\)
0.529733 + 0.848164i \(0.322292\pi\)
\(684\) 0 0
\(685\) 29.5770 1.13008
\(686\) 0 0
\(687\) 35.2233 1.34385
\(688\) 0 0
\(689\) 0.328865 0.0125287
\(690\) 0 0
\(691\) −41.2388 −1.56880 −0.784398 0.620257i \(-0.787028\pi\)
−0.784398 + 0.620257i \(0.787028\pi\)
\(692\) 0 0
\(693\) 0.354663 0.0134725
\(694\) 0 0
\(695\) 20.5265 0.778613
\(696\) 0 0
\(697\) −14.8428 −0.562213
\(698\) 0 0
\(699\) 8.74004 0.330579
\(700\) 0 0
\(701\) −2.89724 −0.109427 −0.0547136 0.998502i \(-0.517425\pi\)
−0.0547136 + 0.998502i \(0.517425\pi\)
\(702\) 0 0
\(703\) −12.6176 −0.475882
\(704\) 0 0
\(705\) −19.5216 −0.735225
\(706\) 0 0
\(707\) 8.68705 0.326710
\(708\) 0 0
\(709\) 0.752342 0.0282548 0.0141274 0.999900i \(-0.495503\pi\)
0.0141274 + 0.999900i \(0.495503\pi\)
\(710\) 0 0
\(711\) 2.93285 0.109990
\(712\) 0 0
\(713\) −68.9905 −2.58372
\(714\) 0 0
\(715\) −1.90839 −0.0713697
\(716\) 0 0
\(717\) −34.7517 −1.29783
\(718\) 0 0
\(719\) 32.2782 1.20377 0.601887 0.798582i \(-0.294416\pi\)
0.601887 + 0.798582i \(0.294416\pi\)
\(720\) 0 0
\(721\) −5.75825 −0.214448
\(722\) 0 0
\(723\) 25.4201 0.945385
\(724\) 0 0
\(725\) 14.1352 0.524969
\(726\) 0 0
\(727\) −32.1520 −1.19245 −0.596225 0.802817i \(-0.703333\pi\)
−0.596225 + 0.802817i \(0.703333\pi\)
\(728\) 0 0
\(729\) 29.3926 1.08862
\(730\) 0 0
\(731\) −21.1429 −0.781998
\(732\) 0 0
\(733\) −47.1623 −1.74198 −0.870989 0.491303i \(-0.836521\pi\)
−0.870989 + 0.491303i \(0.836521\pi\)
\(734\) 0 0
\(735\) 3.10390 0.114489
\(736\) 0 0
\(737\) 5.06539 0.186586
\(738\) 0 0
\(739\) −20.9921 −0.772205 −0.386103 0.922456i \(-0.626179\pi\)
−0.386103 + 0.922456i \(0.626179\pi\)
\(740\) 0 0
\(741\) 2.73303 0.100400
\(742\) 0 0
\(743\) 21.4532 0.787042 0.393521 0.919316i \(-0.371257\pi\)
0.393521 + 0.919316i \(0.371257\pi\)
\(744\) 0 0
\(745\) 25.1928 0.922992
\(746\) 0 0
\(747\) 5.75018 0.210388
\(748\) 0 0
\(749\) 9.54635 0.348816
\(750\) 0 0
\(751\) 42.7022 1.55822 0.779112 0.626885i \(-0.215670\pi\)
0.779112 + 0.626885i \(0.215670\pi\)
\(752\) 0 0
\(753\) −4.10352 −0.149541
\(754\) 0 0
\(755\) 45.5745 1.65863
\(756\) 0 0
\(757\) −14.3034 −0.519865 −0.259933 0.965627i \(-0.583700\pi\)
−0.259933 + 0.965627i \(0.583700\pi\)
\(758\) 0 0
\(759\) −10.2293 −0.371301
\(760\) 0 0
\(761\) −11.3615 −0.411856 −0.205928 0.978567i \(-0.566021\pi\)
−0.205928 + 0.978567i \(0.566021\pi\)
\(762\) 0 0
\(763\) 6.11737 0.221464
\(764\) 0 0
\(765\) 2.17116 0.0784984
\(766\) 0 0
\(767\) 0.221452 0.00799618
\(768\) 0 0
\(769\) −13.1967 −0.475886 −0.237943 0.971279i \(-0.576473\pi\)
−0.237943 + 0.971279i \(0.576473\pi\)
\(770\) 0 0
\(771\) −20.0984 −0.723827
\(772\) 0 0
\(773\) −16.8654 −0.606608 −0.303304 0.952894i \(-0.598090\pi\)
−0.303304 + 0.952894i \(0.598090\pi\)
\(774\) 0 0
\(775\) −14.8970 −0.535115
\(776\) 0 0
\(777\) −12.2128 −0.438130
\(778\) 0 0
\(779\) −7.77521 −0.278576
\(780\) 0 0
\(781\) −4.48919 −0.160636
\(782\) 0 0
\(783\) 56.7906 2.02953
\(784\) 0 0
\(785\) 18.5983 0.663802
\(786\) 0 0
\(787\) 10.9273 0.389517 0.194758 0.980851i \(-0.437608\pi\)
0.194758 + 0.980851i \(0.437608\pi\)
\(788\) 0 0
\(789\) −7.62943 −0.271615
\(790\) 0 0
\(791\) 18.5097 0.658129
\(792\) 0 0
\(793\) 2.97164 0.105526
\(794\) 0 0
\(795\) −1.02076 −0.0362027
\(796\) 0 0
\(797\) 36.6358 1.29771 0.648853 0.760914i \(-0.275249\pi\)
0.648853 + 0.760914i \(0.275249\pi\)
\(798\) 0 0
\(799\) 20.1751 0.713744
\(800\) 0 0
\(801\) 4.36528 0.154240
\(802\) 0 0
\(803\) −11.4302 −0.403362
\(804\) 0 0
\(805\) 12.0026 0.423035
\(806\) 0 0
\(807\) −28.7711 −1.01279
\(808\) 0 0
\(809\) 24.3012 0.854386 0.427193 0.904161i \(-0.359503\pi\)
0.427193 + 0.904161i \(0.359503\pi\)
\(810\) 0 0
\(811\) −9.44196 −0.331552 −0.165776 0.986163i \(-0.553013\pi\)
−0.165776 + 0.986163i \(0.553013\pi\)
\(812\) 0 0
\(813\) −17.9820 −0.630657
\(814\) 0 0
\(815\) −25.4467 −0.891360
\(816\) 0 0
\(817\) −11.0754 −0.387479
\(818\) 0 0
\(819\) −0.354663 −0.0123929
\(820\) 0 0
\(821\) −1.07471 −0.0375075 −0.0187537 0.999824i \(-0.505970\pi\)
−0.0187537 + 0.999824i \(0.505970\pi\)
\(822\) 0 0
\(823\) 2.51409 0.0876357 0.0438179 0.999040i \(-0.486048\pi\)
0.0438179 + 0.999040i \(0.486048\pi\)
\(824\) 0 0
\(825\) −2.20880 −0.0769005
\(826\) 0 0
\(827\) −42.0323 −1.46161 −0.730803 0.682588i \(-0.760854\pi\)
−0.730803 + 0.682588i \(0.760854\pi\)
\(828\) 0 0
\(829\) 31.2998 1.08709 0.543544 0.839381i \(-0.317082\pi\)
0.543544 + 0.839381i \(0.317082\pi\)
\(830\) 0 0
\(831\) −20.0722 −0.696297
\(832\) 0 0
\(833\) −3.20781 −0.111144
\(834\) 0 0
\(835\) 9.02924 0.312470
\(836\) 0 0
\(837\) −59.8511 −2.06876
\(838\) 0 0
\(839\) 36.5575 1.26210 0.631052 0.775741i \(-0.282624\pi\)
0.631052 + 0.775741i \(0.282624\pi\)
\(840\) 0 0
\(841\) 79.3363 2.73573
\(842\) 0 0
\(843\) 24.2262 0.834394
\(844\) 0 0
\(845\) 1.90839 0.0656506
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −6.12917 −0.210352
\(850\) 0 0
\(851\) −47.2259 −1.61888
\(852\) 0 0
\(853\) 39.2306 1.34323 0.671614 0.740901i \(-0.265601\pi\)
0.671614 + 0.740901i \(0.265601\pi\)
\(854\) 0 0
\(855\) 1.13733 0.0388959
\(856\) 0 0
\(857\) −9.97742 −0.340822 −0.170411 0.985373i \(-0.554510\pi\)
−0.170411 + 0.985373i \(0.554510\pi\)
\(858\) 0 0
\(859\) −37.6856 −1.28581 −0.642907 0.765944i \(-0.722272\pi\)
−0.642907 + 0.765944i \(0.722272\pi\)
\(860\) 0 0
\(861\) −7.52573 −0.256476
\(862\) 0 0
\(863\) −41.7315 −1.42056 −0.710278 0.703922i \(-0.751431\pi\)
−0.710278 + 0.703922i \(0.751431\pi\)
\(864\) 0 0
\(865\) 21.5505 0.732738
\(866\) 0 0
\(867\) −10.9134 −0.370638
\(868\) 0 0
\(869\) −8.26940 −0.280520
\(870\) 0 0
\(871\) −5.06539 −0.171634
\(872\) 0 0
\(873\) −6.37469 −0.215751
\(874\) 0 0
\(875\) 12.1336 0.410192
\(876\) 0 0
\(877\) 15.4493 0.521686 0.260843 0.965381i \(-0.415999\pi\)
0.260843 + 0.965381i \(0.415999\pi\)
\(878\) 0 0
\(879\) 52.5435 1.77225
\(880\) 0 0
\(881\) −33.1321 −1.11625 −0.558124 0.829757i \(-0.688479\pi\)
−0.558124 + 0.829757i \(0.688479\pi\)
\(882\) 0 0
\(883\) −4.68098 −0.157528 −0.0787638 0.996893i \(-0.525097\pi\)
−0.0787638 + 0.996893i \(0.525097\pi\)
\(884\) 0 0
\(885\) −0.687366 −0.0231055
\(886\) 0 0
\(887\) −19.5205 −0.655434 −0.327717 0.944776i \(-0.606279\pi\)
−0.327717 + 0.944776i \(0.606279\pi\)
\(888\) 0 0
\(889\) 19.8363 0.665288
\(890\) 0 0
\(891\) −7.81023 −0.261652
\(892\) 0 0
\(893\) 10.5684 0.353659
\(894\) 0 0
\(895\) −15.7407 −0.526154
\(896\) 0 0
\(897\) 10.2293 0.341548
\(898\) 0 0
\(899\) −114.175 −3.80794
\(900\) 0 0
\(901\) 1.05494 0.0351450
\(902\) 0 0
\(903\) −10.7200 −0.356740
\(904\) 0 0
\(905\) −42.7372 −1.42063
\(906\) 0 0
\(907\) 40.2283 1.33576 0.667880 0.744269i \(-0.267202\pi\)
0.667880 + 0.744269i \(0.267202\pi\)
\(908\) 0 0
\(909\) 3.08097 0.102189
\(910\) 0 0
\(911\) −56.3698 −1.86762 −0.933808 0.357775i \(-0.883536\pi\)
−0.933808 + 0.357775i \(0.883536\pi\)
\(912\) 0 0
\(913\) −16.2131 −0.536575
\(914\) 0 0
\(915\) −9.22366 −0.304925
\(916\) 0 0
\(917\) 20.9949 0.693312
\(918\) 0 0
\(919\) 36.0996 1.19082 0.595408 0.803423i \(-0.296990\pi\)
0.595408 + 0.803423i \(0.296990\pi\)
\(920\) 0 0
\(921\) −8.27441 −0.272651
\(922\) 0 0
\(923\) 4.48919 0.147763
\(924\) 0 0
\(925\) −10.1974 −0.335288
\(926\) 0 0
\(927\) −2.04224 −0.0670759
\(928\) 0 0
\(929\) 40.4748 1.32793 0.663967 0.747762i \(-0.268871\pi\)
0.663967 + 0.747762i \(0.268871\pi\)
\(930\) 0 0
\(931\) −1.68037 −0.0550718
\(932\) 0 0
\(933\) 52.7185 1.72592
\(934\) 0 0
\(935\) −6.12175 −0.200203
\(936\) 0 0
\(937\) −22.2900 −0.728181 −0.364091 0.931364i \(-0.618620\pi\)
−0.364091 + 0.931364i \(0.618620\pi\)
\(938\) 0 0
\(939\) 5.89094 0.192244
\(940\) 0 0
\(941\) 6.05858 0.197504 0.0987520 0.995112i \(-0.468515\pi\)
0.0987520 + 0.995112i \(0.468515\pi\)
\(942\) 0 0
\(943\) −29.1015 −0.947675
\(944\) 0 0
\(945\) 10.4125 0.338720
\(946\) 0 0
\(947\) 14.9044 0.484329 0.242164 0.970235i \(-0.422143\pi\)
0.242164 + 0.970235i \(0.422143\pi\)
\(948\) 0 0
\(949\) 11.4302 0.371039
\(950\) 0 0
\(951\) −12.7550 −0.413609
\(952\) 0 0
\(953\) −5.45099 −0.176575 −0.0882875 0.996095i \(-0.528139\pi\)
−0.0882875 + 0.996095i \(0.528139\pi\)
\(954\) 0 0
\(955\) −2.94775 −0.0953870
\(956\) 0 0
\(957\) −16.9288 −0.547232
\(958\) 0 0
\(959\) −15.4984 −0.500470
\(960\) 0 0
\(961\) 89.3275 2.88153
\(962\) 0 0
\(963\) 3.38574 0.109104
\(964\) 0 0
\(965\) 10.1654 0.327237
\(966\) 0 0
\(967\) −47.0978 −1.51456 −0.757282 0.653088i \(-0.773473\pi\)
−0.757282 + 0.653088i \(0.773473\pi\)
\(968\) 0 0
\(969\) 8.76704 0.281638
\(970\) 0 0
\(971\) −18.1878 −0.583675 −0.291838 0.956468i \(-0.594267\pi\)
−0.291838 + 0.956468i \(0.594267\pi\)
\(972\) 0 0
\(973\) −10.7559 −0.344819
\(974\) 0 0
\(975\) 2.20880 0.0707382
\(976\) 0 0
\(977\) 6.87450 0.219935 0.109967 0.993935i \(-0.464925\pi\)
0.109967 + 0.993935i \(0.464925\pi\)
\(978\) 0 0
\(979\) −12.3083 −0.393373
\(980\) 0 0
\(981\) 2.16960 0.0692701
\(982\) 0 0
\(983\) 2.05390 0.0655094 0.0327547 0.999463i \(-0.489572\pi\)
0.0327547 + 0.999463i \(0.489572\pi\)
\(984\) 0 0
\(985\) 3.09365 0.0985719
\(986\) 0 0
\(987\) 10.2293 0.325603
\(988\) 0 0
\(989\) −41.4536 −1.31815
\(990\) 0 0
\(991\) 9.80179 0.311364 0.155682 0.987807i \(-0.450242\pi\)
0.155682 + 0.987807i \(0.450242\pi\)
\(992\) 0 0
\(993\) 34.1995 1.08529
\(994\) 0 0
\(995\) −36.6936 −1.16326
\(996\) 0 0
\(997\) 44.7483 1.41719 0.708596 0.705615i \(-0.249329\pi\)
0.708596 + 0.705615i \(0.249329\pi\)
\(998\) 0 0
\(999\) −40.9697 −1.29622
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 \(a_p\))