Properties

Label 4004.2.a.j.1.8
Level 4004
Weight 2
Character 4004.1
Self dual Yes
Analytic conductor 31.972
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9721009693\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-1.59443\)
Character \(\chi\) = 4004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.59443 q^{3} +4.37026 q^{5} -1.00000 q^{7} -0.457782 q^{9} +O(q^{10})\) \(q+1.59443 q^{3} +4.37026 q^{5} -1.00000 q^{7} -0.457782 q^{9} -1.00000 q^{11} -1.00000 q^{13} +6.96809 q^{15} +5.00996 q^{17} +5.82903 q^{19} -1.59443 q^{21} +4.91986 q^{23} +14.0992 q^{25} -5.51320 q^{27} -0.0873354 q^{29} -10.3085 q^{31} -1.59443 q^{33} -4.37026 q^{35} -4.36576 q^{37} -1.59443 q^{39} +3.46920 q^{41} +10.3014 q^{43} -2.00063 q^{45} +5.16163 q^{47} +1.00000 q^{49} +7.98805 q^{51} +9.50483 q^{53} -4.37026 q^{55} +9.29399 q^{57} -12.3958 q^{59} -7.50512 q^{61} +0.457782 q^{63} -4.37026 q^{65} -5.26781 q^{67} +7.84439 q^{69} -15.1711 q^{71} +2.63392 q^{73} +22.4802 q^{75} +1.00000 q^{77} -4.66388 q^{79} -7.41709 q^{81} +18.1210 q^{83} +21.8948 q^{85} -0.139250 q^{87} +0.350510 q^{89} +1.00000 q^{91} -16.4362 q^{93} +25.4744 q^{95} +6.42082 q^{97} +0.457782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} + O(q^{10}) \) \( 10q - 2q^{3} - 2q^{5} - 10q^{7} + 10q^{9} - 10q^{11} - 10q^{13} - 4q^{15} + 9q^{17} + 3q^{19} + 2q^{21} - 4q^{23} + 22q^{25} - 8q^{27} + 13q^{29} - 17q^{31} + 2q^{33} + 2q^{35} + 11q^{37} + 2q^{39} + 8q^{41} + 21q^{43} - 15q^{45} + q^{47} + 10q^{49} + 19q^{51} + 22q^{53} + 2q^{55} + 8q^{57} - 24q^{59} + 16q^{61} - 10q^{63} + 2q^{65} + 19q^{67} + 51q^{69} - 25q^{71} + 22q^{73} + 28q^{75} + 10q^{77} + 41q^{79} + 54q^{81} + 8q^{83} + 9q^{85} - 5q^{87} + 36q^{89} + 10q^{91} + 12q^{93} + 13q^{95} - 5q^{97} - 10q^{99} + O(q^{100}) \)

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
\(3\) 1.59443 0.920546 0.460273 0.887777i \(-0.347751\pi\)
0.460273 + 0.887777i \(0.347751\pi\)
\(4\) 0 0
\(5\) 4.37026 1.95444 0.977221 0.212226i \(-0.0680712\pi\)
0.977221 + 0.212226i \(0.0680712\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.457782 −0.152594
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 6.96809 1.79915
\(16\) 0 0
\(17\) 5.00996 1.21509 0.607547 0.794284i \(-0.292154\pi\)
0.607547 + 0.794284i \(0.292154\pi\)
\(18\) 0 0
\(19\) 5.82903 1.33727 0.668635 0.743591i \(-0.266879\pi\)
0.668635 + 0.743591i \(0.266879\pi\)
\(20\) 0 0
\(21\) −1.59443 −0.347934
\(22\) 0 0
\(23\) 4.91986 1.02586 0.512931 0.858430i \(-0.328560\pi\)
0.512931 + 0.858430i \(0.328560\pi\)
\(24\) 0 0
\(25\) 14.0992 2.81984
\(26\) 0 0
\(27\) −5.51320 −1.06102
\(28\) 0 0
\(29\) −0.0873354 −0.0162178 −0.00810889 0.999967i \(-0.502581\pi\)
−0.00810889 + 0.999967i \(0.502581\pi\)
\(30\) 0 0
\(31\) −10.3085 −1.85146 −0.925732 0.378181i \(-0.876550\pi\)
−0.925732 + 0.378181i \(0.876550\pi\)
\(32\) 0 0
\(33\) −1.59443 −0.277555
\(34\) 0 0
\(35\) −4.37026 −0.738709
\(36\) 0 0
\(37\) −4.36576 −0.717727 −0.358863 0.933390i \(-0.616836\pi\)
−0.358863 + 0.933390i \(0.616836\pi\)
\(38\) 0 0
\(39\) −1.59443 −0.255314
\(40\) 0 0
\(41\) 3.46920 0.541797 0.270899 0.962608i \(-0.412679\pi\)
0.270899 + 0.962608i \(0.412679\pi\)
\(42\) 0 0
\(43\) 10.3014 1.57094 0.785471 0.618899i \(-0.212421\pi\)
0.785471 + 0.618899i \(0.212421\pi\)
\(44\) 0 0
\(45\) −2.00063 −0.298236
\(46\) 0 0
\(47\) 5.16163 0.752901 0.376451 0.926437i \(-0.377144\pi\)
0.376451 + 0.926437i \(0.377144\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 7.98805 1.11855
\(52\) 0 0
\(53\) 9.50483 1.30559 0.652794 0.757535i \(-0.273597\pi\)
0.652794 + 0.757535i \(0.273597\pi\)
\(54\) 0 0
\(55\) −4.37026 −0.589286
\(56\) 0 0
\(57\) 9.29399 1.23102
\(58\) 0 0
\(59\) −12.3958 −1.61380 −0.806901 0.590687i \(-0.798857\pi\)
−0.806901 + 0.590687i \(0.798857\pi\)
\(60\) 0 0
\(61\) −7.50512 −0.960932 −0.480466 0.877013i \(-0.659533\pi\)
−0.480466 + 0.877013i \(0.659533\pi\)
\(62\) 0 0
\(63\) 0.457782 0.0576752
\(64\) 0 0
\(65\) −4.37026 −0.542065
\(66\) 0 0
\(67\) −5.26781 −0.643565 −0.321783 0.946814i \(-0.604282\pi\)
−0.321783 + 0.946814i \(0.604282\pi\)
\(68\) 0 0
\(69\) 7.84439 0.944353
\(70\) 0 0
\(71\) −15.1711 −1.80048 −0.900242 0.435391i \(-0.856610\pi\)
−0.900242 + 0.435391i \(0.856610\pi\)
\(72\) 0 0
\(73\) 2.63392 0.308277 0.154139 0.988049i \(-0.450740\pi\)
0.154139 + 0.988049i \(0.450740\pi\)
\(74\) 0 0
\(75\) 22.4802 2.59579
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −4.66388 −0.524727 −0.262364 0.964969i \(-0.584502\pi\)
−0.262364 + 0.964969i \(0.584502\pi\)
\(80\) 0 0
\(81\) −7.41709 −0.824121
\(82\) 0 0
\(83\) 18.1210 1.98904 0.994521 0.104533i \(-0.0333346\pi\)
0.994521 + 0.104533i \(0.0333346\pi\)
\(84\) 0 0
\(85\) 21.8948 2.37483
\(86\) 0 0
\(87\) −0.139250 −0.0149292
\(88\) 0 0
\(89\) 0.350510 0.0371540 0.0185770 0.999827i \(-0.494086\pi\)
0.0185770 + 0.999827i \(0.494086\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −16.4362 −1.70436
\(94\) 0 0
\(95\) 25.4744 2.61362
\(96\) 0 0
\(97\) 6.42082 0.651935 0.325968 0.945381i \(-0.394310\pi\)
0.325968 + 0.945381i \(0.394310\pi\)
\(98\) 0 0
\(99\) 0.457782 0.0460089
\(100\) 0 0
\(101\) −7.32677 −0.729041 −0.364521 0.931195i \(-0.618767\pi\)
−0.364521 + 0.931195i \(0.618767\pi\)
\(102\) 0 0
\(103\) 8.18643 0.806633 0.403317 0.915061i \(-0.367857\pi\)
0.403317 + 0.915061i \(0.367857\pi\)
\(104\) 0 0
\(105\) −6.96809 −0.680016
\(106\) 0 0
\(107\) 15.9848 1.54531 0.772654 0.634827i \(-0.218929\pi\)
0.772654 + 0.634827i \(0.218929\pi\)
\(108\) 0 0
\(109\) −1.10632 −0.105967 −0.0529833 0.998595i \(-0.516873\pi\)
−0.0529833 + 0.998595i \(0.516873\pi\)
\(110\) 0 0
\(111\) −6.96092 −0.660701
\(112\) 0 0
\(113\) −1.18127 −0.111124 −0.0555621 0.998455i \(-0.517695\pi\)
−0.0555621 + 0.998455i \(0.517695\pi\)
\(114\) 0 0
\(115\) 21.5011 2.00499
\(116\) 0 0
\(117\) 0.457782 0.0423220
\(118\) 0 0
\(119\) −5.00996 −0.459262
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 5.53140 0.498750
\(124\) 0 0
\(125\) 39.7659 3.55677
\(126\) 0 0
\(127\) −3.32576 −0.295114 −0.147557 0.989054i \(-0.547141\pi\)
−0.147557 + 0.989054i \(0.547141\pi\)
\(128\) 0 0
\(129\) 16.4248 1.44612
\(130\) 0 0
\(131\) 2.00776 0.175419 0.0877093 0.996146i \(-0.472045\pi\)
0.0877093 + 0.996146i \(0.472045\pi\)
\(132\) 0 0
\(133\) −5.82903 −0.505441
\(134\) 0 0
\(135\) −24.0942 −2.07369
\(136\) 0 0
\(137\) 16.6995 1.42674 0.713368 0.700790i \(-0.247169\pi\)
0.713368 + 0.700790i \(0.247169\pi\)
\(138\) 0 0
\(139\) 1.13299 0.0960989 0.0480494 0.998845i \(-0.484699\pi\)
0.0480494 + 0.998845i \(0.484699\pi\)
\(140\) 0 0
\(141\) 8.22987 0.693080
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −0.381679 −0.0316967
\(146\) 0 0
\(147\) 1.59443 0.131507
\(148\) 0 0
\(149\) 12.7438 1.04401 0.522007 0.852941i \(-0.325183\pi\)
0.522007 + 0.852941i \(0.325183\pi\)
\(150\) 0 0
\(151\) −5.79298 −0.471426 −0.235713 0.971823i \(-0.575742\pi\)
−0.235713 + 0.971823i \(0.575742\pi\)
\(152\) 0 0
\(153\) −2.29347 −0.185416
\(154\) 0 0
\(155\) −45.0509 −3.61858
\(156\) 0 0
\(157\) −1.48499 −0.118515 −0.0592576 0.998243i \(-0.518873\pi\)
−0.0592576 + 0.998243i \(0.518873\pi\)
\(158\) 0 0
\(159\) 15.1548 1.20186
\(160\) 0 0
\(161\) −4.91986 −0.387739
\(162\) 0 0
\(163\) −16.0134 −1.25427 −0.627134 0.778911i \(-0.715772\pi\)
−0.627134 + 0.778911i \(0.715772\pi\)
\(164\) 0 0
\(165\) −6.96809 −0.542465
\(166\) 0 0
\(167\) −1.51840 −0.117497 −0.0587486 0.998273i \(-0.518711\pi\)
−0.0587486 + 0.998273i \(0.518711\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.66843 −0.204060
\(172\) 0 0
\(173\) 16.2659 1.23668 0.618339 0.785912i \(-0.287806\pi\)
0.618339 + 0.785912i \(0.287806\pi\)
\(174\) 0 0
\(175\) −14.0992 −1.06580
\(176\) 0 0
\(177\) −19.7644 −1.48558
\(178\) 0 0
\(179\) −20.1877 −1.50890 −0.754449 0.656358i \(-0.772096\pi\)
−0.754449 + 0.656358i \(0.772096\pi\)
\(180\) 0 0
\(181\) −8.44988 −0.628075 −0.314037 0.949411i \(-0.601682\pi\)
−0.314037 + 0.949411i \(0.601682\pi\)
\(182\) 0 0
\(183\) −11.9664 −0.884583
\(184\) 0 0
\(185\) −19.0795 −1.40276
\(186\) 0 0
\(187\) −5.00996 −0.366365
\(188\) 0 0
\(189\) 5.51320 0.401027
\(190\) 0 0
\(191\) −13.2739 −0.960465 −0.480233 0.877141i \(-0.659448\pi\)
−0.480233 + 0.877141i \(0.659448\pi\)
\(192\) 0 0
\(193\) −26.5622 −1.91199 −0.955995 0.293384i \(-0.905219\pi\)
−0.955995 + 0.293384i \(0.905219\pi\)
\(194\) 0 0
\(195\) −6.96809 −0.498996
\(196\) 0 0
\(197\) 2.65367 0.189066 0.0945332 0.995522i \(-0.469864\pi\)
0.0945332 + 0.995522i \(0.469864\pi\)
\(198\) 0 0
\(199\) −24.5382 −1.73947 −0.869734 0.493521i \(-0.835710\pi\)
−0.869734 + 0.493521i \(0.835710\pi\)
\(200\) 0 0
\(201\) −8.39917 −0.592432
\(202\) 0 0
\(203\) 0.0873354 0.00612974
\(204\) 0 0
\(205\) 15.1613 1.05891
\(206\) 0 0
\(207\) −2.25222 −0.156540
\(208\) 0 0
\(209\) −5.82903 −0.403202
\(210\) 0 0
\(211\) 2.83448 0.195134 0.0975669 0.995229i \(-0.468894\pi\)
0.0975669 + 0.995229i \(0.468894\pi\)
\(212\) 0 0
\(213\) −24.1894 −1.65743
\(214\) 0 0
\(215\) 45.0196 3.07031
\(216\) 0 0
\(217\) 10.3085 0.699787
\(218\) 0 0
\(219\) 4.19961 0.283784
\(220\) 0 0
\(221\) −5.00996 −0.337006
\(222\) 0 0
\(223\) −1.13256 −0.0758420 −0.0379210 0.999281i \(-0.512074\pi\)
−0.0379210 + 0.999281i \(0.512074\pi\)
\(224\) 0 0
\(225\) −6.45437 −0.430291
\(226\) 0 0
\(227\) −13.6316 −0.904763 −0.452381 0.891825i \(-0.649425\pi\)
−0.452381 + 0.891825i \(0.649425\pi\)
\(228\) 0 0
\(229\) 5.15726 0.340801 0.170401 0.985375i \(-0.445494\pi\)
0.170401 + 0.985375i \(0.445494\pi\)
\(230\) 0 0
\(231\) 1.59443 0.104906
\(232\) 0 0
\(233\) 9.22082 0.604076 0.302038 0.953296i \(-0.402333\pi\)
0.302038 + 0.953296i \(0.402333\pi\)
\(234\) 0 0
\(235\) 22.5577 1.47150
\(236\) 0 0
\(237\) −7.43624 −0.483036
\(238\) 0 0
\(239\) −2.08098 −0.134607 −0.0673037 0.997733i \(-0.521440\pi\)
−0.0673037 + 0.997733i \(0.521440\pi\)
\(240\) 0 0
\(241\) 6.84967 0.441226 0.220613 0.975361i \(-0.429194\pi\)
0.220613 + 0.975361i \(0.429194\pi\)
\(242\) 0 0
\(243\) 4.71356 0.302375
\(244\) 0 0
\(245\) 4.37026 0.279206
\(246\) 0 0
\(247\) −5.82903 −0.370892
\(248\) 0 0
\(249\) 28.8928 1.83101
\(250\) 0 0
\(251\) 4.53518 0.286258 0.143129 0.989704i \(-0.454284\pi\)
0.143129 + 0.989704i \(0.454284\pi\)
\(252\) 0 0
\(253\) −4.91986 −0.309309
\(254\) 0 0
\(255\) 34.9099 2.18614
\(256\) 0 0
\(257\) −21.4454 −1.33773 −0.668863 0.743385i \(-0.733219\pi\)
−0.668863 + 0.743385i \(0.733219\pi\)
\(258\) 0 0
\(259\) 4.36576 0.271275
\(260\) 0 0
\(261\) 0.0399806 0.00247474
\(262\) 0 0
\(263\) −5.32971 −0.328644 −0.164322 0.986407i \(-0.552544\pi\)
−0.164322 + 0.986407i \(0.552544\pi\)
\(264\) 0 0
\(265\) 41.5386 2.55170
\(266\) 0 0
\(267\) 0.558865 0.0342020
\(268\) 0 0
\(269\) 8.08626 0.493028 0.246514 0.969139i \(-0.420715\pi\)
0.246514 + 0.969139i \(0.420715\pi\)
\(270\) 0 0
\(271\) 6.76102 0.410703 0.205351 0.978688i \(-0.434166\pi\)
0.205351 + 0.978688i \(0.434166\pi\)
\(272\) 0 0
\(273\) 1.59443 0.0964995
\(274\) 0 0
\(275\) −14.0992 −0.850214
\(276\) 0 0
\(277\) −27.4920 −1.65184 −0.825918 0.563790i \(-0.809343\pi\)
−0.825918 + 0.563790i \(0.809343\pi\)
\(278\) 0 0
\(279\) 4.71906 0.282523
\(280\) 0 0
\(281\) −16.0366 −0.956661 −0.478330 0.878180i \(-0.658758\pi\)
−0.478330 + 0.878180i \(0.658758\pi\)
\(282\) 0 0
\(283\) −15.9216 −0.946440 −0.473220 0.880944i \(-0.656908\pi\)
−0.473220 + 0.880944i \(0.656908\pi\)
\(284\) 0 0
\(285\) 40.6172 2.40596
\(286\) 0 0
\(287\) −3.46920 −0.204780
\(288\) 0 0
\(289\) 8.09970 0.476453
\(290\) 0 0
\(291\) 10.2376 0.600137
\(292\) 0 0
\(293\) 19.9566 1.16588 0.582939 0.812516i \(-0.301902\pi\)
0.582939 + 0.812516i \(0.301902\pi\)
\(294\) 0 0
\(295\) −54.1731 −3.15408
\(296\) 0 0
\(297\) 5.51320 0.319909
\(298\) 0 0
\(299\) −4.91986 −0.284523
\(300\) 0 0
\(301\) −10.3014 −0.593760
\(302\) 0 0
\(303\) −11.6820 −0.671116
\(304\) 0 0
\(305\) −32.7994 −1.87809
\(306\) 0 0
\(307\) −27.0950 −1.54639 −0.773196 0.634168i \(-0.781343\pi\)
−0.773196 + 0.634168i \(0.781343\pi\)
\(308\) 0 0
\(309\) 13.0527 0.742543
\(310\) 0 0
\(311\) 23.8123 1.35027 0.675137 0.737693i \(-0.264085\pi\)
0.675137 + 0.737693i \(0.264085\pi\)
\(312\) 0 0
\(313\) −3.18696 −0.180138 −0.0900689 0.995936i \(-0.528709\pi\)
−0.0900689 + 0.995936i \(0.528709\pi\)
\(314\) 0 0
\(315\) 2.00063 0.112723
\(316\) 0 0
\(317\) 5.79545 0.325505 0.162752 0.986667i \(-0.447963\pi\)
0.162752 + 0.986667i \(0.447963\pi\)
\(318\) 0 0
\(319\) 0.0873354 0.00488984
\(320\) 0 0
\(321\) 25.4867 1.42253
\(322\) 0 0
\(323\) 29.2032 1.62491
\(324\) 0 0
\(325\) −14.0992 −0.782083
\(326\) 0 0
\(327\) −1.76396 −0.0975472
\(328\) 0 0
\(329\) −5.16163 −0.284570
\(330\) 0 0
\(331\) −1.58775 −0.0872707 −0.0436354 0.999048i \(-0.513894\pi\)
−0.0436354 + 0.999048i \(0.513894\pi\)
\(332\) 0 0
\(333\) 1.99857 0.109521
\(334\) 0 0
\(335\) −23.0217 −1.25781
\(336\) 0 0
\(337\) 34.1356 1.85948 0.929741 0.368214i \(-0.120030\pi\)
0.929741 + 0.368214i \(0.120030\pi\)
\(338\) 0 0
\(339\) −1.88345 −0.102295
\(340\) 0 0
\(341\) 10.3085 0.558237
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 34.2820 1.84568
\(346\) 0 0
\(347\) 15.2636 0.819393 0.409696 0.912222i \(-0.365635\pi\)
0.409696 + 0.912222i \(0.365635\pi\)
\(348\) 0 0
\(349\) −15.6193 −0.836080 −0.418040 0.908429i \(-0.637283\pi\)
−0.418040 + 0.908429i \(0.637283\pi\)
\(350\) 0 0
\(351\) 5.51320 0.294273
\(352\) 0 0
\(353\) 22.4801 1.19649 0.598247 0.801312i \(-0.295864\pi\)
0.598247 + 0.801312i \(0.295864\pi\)
\(354\) 0 0
\(355\) −66.3019 −3.51894
\(356\) 0 0
\(357\) −7.98805 −0.422772
\(358\) 0 0
\(359\) −30.3773 −1.60325 −0.801626 0.597826i \(-0.796031\pi\)
−0.801626 + 0.597826i \(0.796031\pi\)
\(360\) 0 0
\(361\) 14.9775 0.788292
\(362\) 0 0
\(363\) 1.59443 0.0836860
\(364\) 0 0
\(365\) 11.5109 0.602510
\(366\) 0 0
\(367\) −11.5608 −0.603468 −0.301734 0.953392i \(-0.597565\pi\)
−0.301734 + 0.953392i \(0.597565\pi\)
\(368\) 0 0
\(369\) −1.58814 −0.0826751
\(370\) 0 0
\(371\) −9.50483 −0.493466
\(372\) 0 0
\(373\) 9.41012 0.487238 0.243619 0.969871i \(-0.421665\pi\)
0.243619 + 0.969871i \(0.421665\pi\)
\(374\) 0 0
\(375\) 63.4041 3.27417
\(376\) 0 0
\(377\) 0.0873354 0.00449800
\(378\) 0 0
\(379\) −5.39466 −0.277105 −0.138553 0.990355i \(-0.544245\pi\)
−0.138553 + 0.990355i \(0.544245\pi\)
\(380\) 0 0
\(381\) −5.30271 −0.271666
\(382\) 0 0
\(383\) 6.86021 0.350540 0.175270 0.984520i \(-0.443920\pi\)
0.175270 + 0.984520i \(0.443920\pi\)
\(384\) 0 0
\(385\) 4.37026 0.222729
\(386\) 0 0
\(387\) −4.71578 −0.239717
\(388\) 0 0
\(389\) 1.84071 0.0933279 0.0466639 0.998911i \(-0.485141\pi\)
0.0466639 + 0.998911i \(0.485141\pi\)
\(390\) 0 0
\(391\) 24.6483 1.24652
\(392\) 0 0
\(393\) 3.20124 0.161481
\(394\) 0 0
\(395\) −20.3824 −1.02555
\(396\) 0 0
\(397\) −19.5268 −0.980024 −0.490012 0.871716i \(-0.663008\pi\)
−0.490012 + 0.871716i \(0.663008\pi\)
\(398\) 0 0
\(399\) −9.29399 −0.465282
\(400\) 0 0
\(401\) −10.6866 −0.533663 −0.266831 0.963743i \(-0.585977\pi\)
−0.266831 + 0.963743i \(0.585977\pi\)
\(402\) 0 0
\(403\) 10.3085 0.513504
\(404\) 0 0
\(405\) −32.4146 −1.61070
\(406\) 0 0
\(407\) 4.36576 0.216403
\(408\) 0 0
\(409\) 10.2901 0.508810 0.254405 0.967098i \(-0.418120\pi\)
0.254405 + 0.967098i \(0.418120\pi\)
\(410\) 0 0
\(411\) 26.6263 1.31338
\(412\) 0 0
\(413\) 12.3958 0.609960
\(414\) 0 0
\(415\) 79.1937 3.88747
\(416\) 0 0
\(417\) 1.80648 0.0884635
\(418\) 0 0
\(419\) −13.6990 −0.669238 −0.334619 0.942354i \(-0.608608\pi\)
−0.334619 + 0.942354i \(0.608608\pi\)
\(420\) 0 0
\(421\) −12.9608 −0.631669 −0.315834 0.948814i \(-0.602284\pi\)
−0.315834 + 0.948814i \(0.602284\pi\)
\(422\) 0 0
\(423\) −2.36290 −0.114888
\(424\) 0 0
\(425\) 70.6365 3.42637
\(426\) 0 0
\(427\) 7.50512 0.363198
\(428\) 0 0
\(429\) 1.59443 0.0769800
\(430\) 0 0
\(431\) −17.5057 −0.843221 −0.421611 0.906777i \(-0.638535\pi\)
−0.421611 + 0.906777i \(0.638535\pi\)
\(432\) 0 0
\(433\) −34.3398 −1.65027 −0.825134 0.564938i \(-0.808900\pi\)
−0.825134 + 0.564938i \(0.808900\pi\)
\(434\) 0 0
\(435\) −0.608561 −0.0291783
\(436\) 0 0
\(437\) 28.6780 1.37185
\(438\) 0 0
\(439\) 9.99675 0.477119 0.238559 0.971128i \(-0.423325\pi\)
0.238559 + 0.971128i \(0.423325\pi\)
\(440\) 0 0
\(441\) −0.457782 −0.0217992
\(442\) 0 0
\(443\) −32.9060 −1.56341 −0.781705 0.623649i \(-0.785650\pi\)
−0.781705 + 0.623649i \(0.785650\pi\)
\(444\) 0 0
\(445\) 1.53182 0.0726153
\(446\) 0 0
\(447\) 20.3192 0.961064
\(448\) 0 0
\(449\) 32.5993 1.53846 0.769228 0.638974i \(-0.220641\pi\)
0.769228 + 0.638974i \(0.220641\pi\)
\(450\) 0 0
\(451\) −3.46920 −0.163358
\(452\) 0 0
\(453\) −9.23651 −0.433969
\(454\) 0 0
\(455\) 4.37026 0.204881
\(456\) 0 0
\(457\) −31.6730 −1.48160 −0.740801 0.671724i \(-0.765554\pi\)
−0.740801 + 0.671724i \(0.765554\pi\)
\(458\) 0 0
\(459\) −27.6209 −1.28923
\(460\) 0 0
\(461\) −28.2165 −1.31418 −0.657088 0.753814i \(-0.728212\pi\)
−0.657088 + 0.753814i \(0.728212\pi\)
\(462\) 0 0
\(463\) 29.5157 1.37171 0.685855 0.727738i \(-0.259428\pi\)
0.685855 + 0.727738i \(0.259428\pi\)
\(464\) 0 0
\(465\) −71.8307 −3.33107
\(466\) 0 0
\(467\) 36.3702 1.68301 0.841505 0.540249i \(-0.181670\pi\)
0.841505 + 0.540249i \(0.181670\pi\)
\(468\) 0 0
\(469\) 5.26781 0.243245
\(470\) 0 0
\(471\) −2.36772 −0.109099
\(472\) 0 0
\(473\) −10.3014 −0.473657
\(474\) 0 0
\(475\) 82.1846 3.77089
\(476\) 0 0
\(477\) −4.35114 −0.199225
\(478\) 0 0
\(479\) 27.6354 1.26269 0.631346 0.775501i \(-0.282503\pi\)
0.631346 + 0.775501i \(0.282503\pi\)
\(480\) 0 0
\(481\) 4.36576 0.199062
\(482\) 0 0
\(483\) −7.84439 −0.356932
\(484\) 0 0
\(485\) 28.0607 1.27417
\(486\) 0 0
\(487\) −19.6605 −0.890902 −0.445451 0.895306i \(-0.646957\pi\)
−0.445451 + 0.895306i \(0.646957\pi\)
\(488\) 0 0
\(489\) −25.5323 −1.15461
\(490\) 0 0
\(491\) −22.4977 −1.01531 −0.507653 0.861562i \(-0.669487\pi\)
−0.507653 + 0.861562i \(0.669487\pi\)
\(492\) 0 0
\(493\) −0.437547 −0.0197061
\(494\) 0 0
\(495\) 2.00063 0.0899216
\(496\) 0 0
\(497\) 15.1711 0.680519
\(498\) 0 0
\(499\) 6.58842 0.294938 0.147469 0.989067i \(-0.452887\pi\)
0.147469 + 0.989067i \(0.452887\pi\)
\(500\) 0 0
\(501\) −2.42098 −0.108162
\(502\) 0 0
\(503\) 25.9999 1.15928 0.579639 0.814873i \(-0.303193\pi\)
0.579639 + 0.814873i \(0.303193\pi\)
\(504\) 0 0
\(505\) −32.0199 −1.42487
\(506\) 0 0
\(507\) 1.59443 0.0708113
\(508\) 0 0
\(509\) 0.198995 0.00882032 0.00441016 0.999990i \(-0.498596\pi\)
0.00441016 + 0.999990i \(0.498596\pi\)
\(510\) 0 0
\(511\) −2.63392 −0.116518
\(512\) 0 0
\(513\) −32.1366 −1.41887
\(514\) 0 0
\(515\) 35.7769 1.57652
\(516\) 0 0
\(517\) −5.16163 −0.227008
\(518\) 0 0
\(519\) 25.9350 1.13842
\(520\) 0 0
\(521\) 24.8049 1.08672 0.543361 0.839499i \(-0.317152\pi\)
0.543361 + 0.839499i \(0.317152\pi\)
\(522\) 0 0
\(523\) −23.3707 −1.02193 −0.510964 0.859602i \(-0.670711\pi\)
−0.510964 + 0.859602i \(0.670711\pi\)
\(524\) 0 0
\(525\) −22.4802 −0.981118
\(526\) 0 0
\(527\) −51.6452 −2.24970
\(528\) 0 0
\(529\) 1.20500 0.0523913
\(530\) 0 0
\(531\) 5.67460 0.246257
\(532\) 0 0
\(533\) −3.46920 −0.150268
\(534\) 0 0
\(535\) 69.8578 3.02022
\(536\) 0 0
\(537\) −32.1879 −1.38901
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 6.66279 0.286456 0.143228 0.989690i \(-0.454252\pi\)
0.143228 + 0.989690i \(0.454252\pi\)
\(542\) 0 0
\(543\) −13.4728 −0.578172
\(544\) 0 0
\(545\) −4.83493 −0.207105
\(546\) 0 0
\(547\) 36.9208 1.57862 0.789311 0.613994i \(-0.210438\pi\)
0.789311 + 0.613994i \(0.210438\pi\)
\(548\) 0 0
\(549\) 3.43571 0.146633
\(550\) 0 0
\(551\) −0.509080 −0.0216876
\(552\) 0 0
\(553\) 4.66388 0.198328
\(554\) 0 0
\(555\) −30.4210 −1.29130
\(556\) 0 0
\(557\) −5.99870 −0.254173 −0.127086 0.991892i \(-0.540563\pi\)
−0.127086 + 0.991892i \(0.540563\pi\)
\(558\) 0 0
\(559\) −10.3014 −0.435701
\(560\) 0 0
\(561\) −7.98805 −0.337256
\(562\) 0 0
\(563\) −19.3954 −0.817418 −0.408709 0.912665i \(-0.634021\pi\)
−0.408709 + 0.912665i \(0.634021\pi\)
\(564\) 0 0
\(565\) −5.16244 −0.217186
\(566\) 0 0
\(567\) 7.41709 0.311488
\(568\) 0 0
\(569\) 17.7023 0.742118 0.371059 0.928609i \(-0.378995\pi\)
0.371059 + 0.928609i \(0.378995\pi\)
\(570\) 0 0
\(571\) 1.84498 0.0772100 0.0386050 0.999255i \(-0.487709\pi\)
0.0386050 + 0.999255i \(0.487709\pi\)
\(572\) 0 0
\(573\) −21.1643 −0.884153
\(574\) 0 0
\(575\) 69.3661 2.89277
\(576\) 0 0
\(577\) 5.26948 0.219371 0.109686 0.993966i \(-0.465016\pi\)
0.109686 + 0.993966i \(0.465016\pi\)
\(578\) 0 0
\(579\) −42.3517 −1.76008
\(580\) 0 0
\(581\) −18.1210 −0.751788
\(582\) 0 0
\(583\) −9.50483 −0.393650
\(584\) 0 0
\(585\) 2.00063 0.0827159
\(586\) 0 0
\(587\) −18.4801 −0.762757 −0.381379 0.924419i \(-0.624551\pi\)
−0.381379 + 0.924419i \(0.624551\pi\)
\(588\) 0 0
\(589\) −60.0886 −2.47591
\(590\) 0 0
\(591\) 4.23111 0.174044
\(592\) 0 0
\(593\) 16.7446 0.687618 0.343809 0.939040i \(-0.388283\pi\)
0.343809 + 0.939040i \(0.388283\pi\)
\(594\) 0 0
\(595\) −21.8948 −0.897601
\(596\) 0 0
\(597\) −39.1245 −1.60126
\(598\) 0 0
\(599\) −0.670307 −0.0273880 −0.0136940 0.999906i \(-0.504359\pi\)
−0.0136940 + 0.999906i \(0.504359\pi\)
\(600\) 0 0
\(601\) −15.2148 −0.620623 −0.310311 0.950635i \(-0.600433\pi\)
−0.310311 + 0.950635i \(0.600433\pi\)
\(602\) 0 0
\(603\) 2.41151 0.0982043
\(604\) 0 0
\(605\) 4.37026 0.177676
\(606\) 0 0
\(607\) −13.0891 −0.531268 −0.265634 0.964074i \(-0.585581\pi\)
−0.265634 + 0.964074i \(0.585581\pi\)
\(608\) 0 0
\(609\) 0.139250 0.00564271
\(610\) 0 0
\(611\) −5.16163 −0.208817
\(612\) 0 0
\(613\) 28.8134 1.16376 0.581881 0.813274i \(-0.302317\pi\)
0.581881 + 0.813274i \(0.302317\pi\)
\(614\) 0 0
\(615\) 24.1737 0.974777
\(616\) 0 0
\(617\) −23.7648 −0.956733 −0.478367 0.878160i \(-0.658771\pi\)
−0.478367 + 0.878160i \(0.658771\pi\)
\(618\) 0 0
\(619\) −27.1544 −1.09143 −0.545714 0.837971i \(-0.683742\pi\)
−0.545714 + 0.837971i \(0.683742\pi\)
\(620\) 0 0
\(621\) −27.1242 −1.08846
\(622\) 0 0
\(623\) −0.350510 −0.0140429
\(624\) 0 0
\(625\) 103.292 4.13166
\(626\) 0 0
\(627\) −9.29399 −0.371166
\(628\) 0 0
\(629\) −21.8723 −0.872106
\(630\) 0 0
\(631\) −23.5102 −0.935927 −0.467964 0.883748i \(-0.655012\pi\)
−0.467964 + 0.883748i \(0.655012\pi\)
\(632\) 0 0
\(633\) 4.51939 0.179630
\(634\) 0 0
\(635\) −14.5345 −0.576783
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 6.94508 0.274743
\(640\) 0 0
\(641\) −23.5626 −0.930668 −0.465334 0.885135i \(-0.654066\pi\)
−0.465334 + 0.885135i \(0.654066\pi\)
\(642\) 0 0
\(643\) −5.51124 −0.217342 −0.108671 0.994078i \(-0.534659\pi\)
−0.108671 + 0.994078i \(0.534659\pi\)
\(644\) 0 0
\(645\) 71.7808 2.82637
\(646\) 0 0
\(647\) −21.6951 −0.852922 −0.426461 0.904506i \(-0.640240\pi\)
−0.426461 + 0.904506i \(0.640240\pi\)
\(648\) 0 0
\(649\) 12.3958 0.486580
\(650\) 0 0
\(651\) 16.4362 0.644187
\(652\) 0 0
\(653\) −32.3455 −1.26578 −0.632889 0.774243i \(-0.718131\pi\)
−0.632889 + 0.774243i \(0.718131\pi\)
\(654\) 0 0
\(655\) 8.77443 0.342846
\(656\) 0 0
\(657\) −1.20576 −0.0470413
\(658\) 0 0
\(659\) −44.8397 −1.74671 −0.873353 0.487087i \(-0.838059\pi\)
−0.873353 + 0.487087i \(0.838059\pi\)
\(660\) 0 0
\(661\) −37.4043 −1.45486 −0.727430 0.686182i \(-0.759285\pi\)
−0.727430 + 0.686182i \(0.759285\pi\)
\(662\) 0 0
\(663\) −7.98805 −0.310230
\(664\) 0 0
\(665\) −25.4744 −0.987854
\(666\) 0 0
\(667\) −0.429678 −0.0166372
\(668\) 0 0
\(669\) −1.80580 −0.0698161
\(670\) 0 0
\(671\) 7.50512 0.289732
\(672\) 0 0
\(673\) −13.0085 −0.501442 −0.250721 0.968059i \(-0.580668\pi\)
−0.250721 + 0.968059i \(0.580668\pi\)
\(674\) 0 0
\(675\) −77.7318 −2.99190
\(676\) 0 0
\(677\) −29.3502 −1.12802 −0.564009 0.825769i \(-0.690742\pi\)
−0.564009 + 0.825769i \(0.690742\pi\)
\(678\) 0 0
\(679\) −6.42082 −0.246408
\(680\) 0 0
\(681\) −21.7347 −0.832876
\(682\) 0 0
\(683\) 25.4697 0.974573 0.487286 0.873242i \(-0.337987\pi\)
0.487286 + 0.873242i \(0.337987\pi\)
\(684\) 0 0
\(685\) 72.9813 2.78847
\(686\) 0 0
\(687\) 8.22290 0.313723
\(688\) 0 0
\(689\) −9.50483 −0.362105
\(690\) 0 0
\(691\) −4.60340 −0.175121 −0.0875607 0.996159i \(-0.527907\pi\)
−0.0875607 + 0.996159i \(0.527907\pi\)
\(692\) 0 0
\(693\) −0.457782 −0.0173897
\(694\) 0 0
\(695\) 4.95146 0.187820
\(696\) 0 0
\(697\) 17.3805 0.658335
\(698\) 0 0
\(699\) 14.7020 0.556080
\(700\) 0 0
\(701\) −18.0383 −0.681299 −0.340649 0.940190i \(-0.610647\pi\)
−0.340649 + 0.940190i \(0.610647\pi\)
\(702\) 0 0
\(703\) −25.4481 −0.959795
\(704\) 0 0
\(705\) 35.9667 1.35459
\(706\) 0 0
\(707\) 7.32677 0.275552
\(708\) 0 0
\(709\) −29.0735 −1.09188 −0.545940 0.837824i \(-0.683827\pi\)
−0.545940 + 0.837824i \(0.683827\pi\)
\(710\) 0 0
\(711\) 2.13504 0.0800703
\(712\) 0 0
\(713\) −50.7164 −1.89934
\(714\) 0 0
\(715\) 4.37026 0.163439
\(716\) 0 0
\(717\) −3.31799 −0.123912
\(718\) 0 0
\(719\) 8.49859 0.316944 0.158472 0.987363i \(-0.449343\pi\)
0.158472 + 0.987363i \(0.449343\pi\)
\(720\) 0 0
\(721\) −8.18643 −0.304879
\(722\) 0 0
\(723\) 10.9213 0.406169
\(724\) 0 0
\(725\) −1.23136 −0.0457316
\(726\) 0 0
\(727\) 38.4840 1.42729 0.713647 0.700506i \(-0.247042\pi\)
0.713647 + 0.700506i \(0.247042\pi\)
\(728\) 0 0
\(729\) 29.7667 1.10247
\(730\) 0 0
\(731\) 51.6094 1.90884
\(732\) 0 0
\(733\) 31.2314 1.15356 0.576779 0.816900i \(-0.304309\pi\)
0.576779 + 0.816900i \(0.304309\pi\)
\(734\) 0 0
\(735\) 6.96809 0.257022
\(736\) 0 0
\(737\) 5.26781 0.194042
\(738\) 0 0
\(739\) 0.926502 0.0340819 0.0170410 0.999855i \(-0.494575\pi\)
0.0170410 + 0.999855i \(0.494575\pi\)
\(740\) 0 0
\(741\) −9.29399 −0.341423
\(742\) 0 0
\(743\) −46.6500 −1.71142 −0.855711 0.517454i \(-0.826880\pi\)
−0.855711 + 0.517454i \(0.826880\pi\)
\(744\) 0 0
\(745\) 55.6939 2.04047
\(746\) 0 0
\(747\) −8.29550 −0.303516
\(748\) 0 0
\(749\) −15.9848 −0.584072
\(750\) 0 0
\(751\) 52.6417 1.92092 0.960461 0.278414i \(-0.0898088\pi\)
0.960461 + 0.278414i \(0.0898088\pi\)
\(752\) 0 0
\(753\) 7.23104 0.263514
\(754\) 0 0
\(755\) −25.3168 −0.921374
\(756\) 0 0
\(757\) 27.9426 1.01559 0.507796 0.861477i \(-0.330460\pi\)
0.507796 + 0.861477i \(0.330460\pi\)
\(758\) 0 0
\(759\) −7.84439 −0.284733
\(760\) 0 0
\(761\) 3.15873 0.114504 0.0572520 0.998360i \(-0.481766\pi\)
0.0572520 + 0.998360i \(0.481766\pi\)
\(762\) 0 0
\(763\) 1.10632 0.0400516
\(764\) 0 0
\(765\) −10.0231 −0.362385
\(766\) 0 0
\(767\) 12.3958 0.447588
\(768\) 0 0
\(769\) −35.2104 −1.26972 −0.634859 0.772628i \(-0.718942\pi\)
−0.634859 + 0.772628i \(0.718942\pi\)
\(770\) 0 0
\(771\) −34.1932 −1.23144
\(772\) 0 0
\(773\) −4.25876 −0.153177 −0.0765885 0.997063i \(-0.524403\pi\)
−0.0765885 + 0.997063i \(0.524403\pi\)
\(774\) 0 0
\(775\) −145.342 −5.22083
\(776\) 0 0
\(777\) 6.96092 0.249722
\(778\) 0 0
\(779\) 20.2220 0.724530
\(780\) 0 0
\(781\) 15.1711 0.542866
\(782\) 0 0
\(783\) 0.481498 0.0172073
\(784\) 0 0
\(785\) −6.48981 −0.231631
\(786\) 0 0
\(787\) 14.1650 0.504926 0.252463 0.967607i \(-0.418759\pi\)
0.252463 + 0.967607i \(0.418759\pi\)
\(788\) 0 0
\(789\) −8.49787 −0.302532
\(790\) 0 0
\(791\) 1.18127 0.0420010
\(792\) 0 0
\(793\) 7.50512 0.266515
\(794\) 0 0
\(795\) 66.2306 2.34896
\(796\) 0 0
\(797\) 34.9117 1.23663 0.618317 0.785929i \(-0.287815\pi\)
0.618317 + 0.785929i \(0.287815\pi\)
\(798\) 0 0
\(799\) 25.8596 0.914845
\(800\) 0 0
\(801\) −0.160457 −0.00566948
\(802\) 0 0
\(803\) −2.63392 −0.0929491
\(804\) 0 0
\(805\) −21.5011 −0.757813
\(806\) 0 0
\(807\) 12.8930 0.453855
\(808\) 0 0
\(809\) 48.4361 1.70292 0.851461 0.524418i \(-0.175717\pi\)
0.851461 + 0.524418i \(0.175717\pi\)
\(810\) 0 0
\(811\) 11.9726 0.420417 0.210208 0.977657i \(-0.432586\pi\)
0.210208 + 0.977657i \(0.432586\pi\)
\(812\) 0 0
\(813\) 10.7800 0.378071
\(814\) 0 0
\(815\) −69.9829 −2.45139
\(816\) 0 0
\(817\) 60.0469 2.10077
\(818\) 0 0
\(819\) −0.457782 −0.0159962
\(820\) 0 0
\(821\) 3.06847 0.107090 0.0535451 0.998565i \(-0.482948\pi\)
0.0535451 + 0.998565i \(0.482948\pi\)
\(822\) 0 0
\(823\) −40.3991 −1.40823 −0.704113 0.710088i \(-0.748655\pi\)
−0.704113 + 0.710088i \(0.748655\pi\)
\(824\) 0 0
\(825\) −22.4802 −0.782662
\(826\) 0 0
\(827\) −42.8546 −1.49020 −0.745101 0.666952i \(-0.767599\pi\)
−0.745101 + 0.666952i \(0.767599\pi\)
\(828\) 0 0
\(829\) −39.6855 −1.37833 −0.689167 0.724603i \(-0.742023\pi\)
−0.689167 + 0.724603i \(0.742023\pi\)
\(830\) 0 0
\(831\) −43.8342 −1.52059
\(832\) 0 0
\(833\) 5.00996 0.173585
\(834\) 0 0
\(835\) −6.63580 −0.229641
\(836\) 0 0
\(837\) 56.8329 1.96443
\(838\) 0 0
\(839\) −27.1774 −0.938270 −0.469135 0.883127i \(-0.655434\pi\)
−0.469135 + 0.883127i \(0.655434\pi\)
\(840\) 0 0
\(841\) −28.9924 −0.999737
\(842\) 0 0
\(843\) −25.5692 −0.880651
\(844\) 0 0
\(845\) 4.37026 0.150342
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −25.3859 −0.871242
\(850\) 0 0
\(851\) −21.4789 −0.736288
\(852\) 0 0
\(853\) 1.87863 0.0643230 0.0321615 0.999483i \(-0.489761\pi\)
0.0321615 + 0.999483i \(0.489761\pi\)
\(854\) 0 0
\(855\) −11.6617 −0.398823
\(856\) 0 0
\(857\) 45.9573 1.56987 0.784936 0.619577i \(-0.212696\pi\)
0.784936 + 0.619577i \(0.212696\pi\)
\(858\) 0 0
\(859\) −19.6428 −0.670204 −0.335102 0.942182i \(-0.608771\pi\)
−0.335102 + 0.942182i \(0.608771\pi\)
\(860\) 0 0
\(861\) −5.53140 −0.188510
\(862\) 0 0
\(863\) −11.4940 −0.391260 −0.195630 0.980678i \(-0.562675\pi\)
−0.195630 + 0.980678i \(0.562675\pi\)
\(864\) 0 0
\(865\) 71.0865 2.41701
\(866\) 0 0
\(867\) 12.9144 0.438597
\(868\) 0 0
\(869\) 4.66388 0.158211
\(870\) 0 0
\(871\) 5.26781 0.178493
\(872\) 0 0
\(873\) −2.93934 −0.0994815
\(874\) 0 0
\(875\) −39.7659 −1.34433
\(876\) 0 0
\(877\) −35.5381 −1.20004 −0.600018 0.799986i \(-0.704840\pi\)
−0.600018 + 0.799986i \(0.704840\pi\)
\(878\) 0 0
\(879\) 31.8195 1.07325
\(880\) 0 0
\(881\) −1.88715 −0.0635797 −0.0317899 0.999495i \(-0.510121\pi\)
−0.0317899 + 0.999495i \(0.510121\pi\)
\(882\) 0 0
\(883\) 16.4260 0.552777 0.276389 0.961046i \(-0.410862\pi\)
0.276389 + 0.961046i \(0.410862\pi\)
\(884\) 0 0
\(885\) −86.3754 −2.90348
\(886\) 0 0
\(887\) 53.1774 1.78552 0.892761 0.450530i \(-0.148765\pi\)
0.892761 + 0.450530i \(0.148765\pi\)
\(888\) 0 0
\(889\) 3.32576 0.111543
\(890\) 0 0
\(891\) 7.41709 0.248482
\(892\) 0 0
\(893\) 30.0873 1.00683
\(894\) 0 0
\(895\) −88.2255 −2.94905
\(896\) 0 0
\(897\) −7.84439 −0.261916
\(898\) 0 0
\(899\) 0.900298 0.0300266
\(900\) 0 0
\(901\) 47.6188 1.58641
\(902\) 0 0
\(903\) −16.4248 −0.546584
\(904\) 0 0
\(905\) −36.9282 −1.22754
\(906\) 0 0
\(907\) 49.4232 1.64107 0.820536 0.571595i \(-0.193675\pi\)
0.820536 + 0.571595i \(0.193675\pi\)
\(908\) 0 0
\(909\) 3.35407 0.111247
\(910\) 0 0
\(911\) −9.65862 −0.320004 −0.160002 0.987117i \(-0.551150\pi\)
−0.160002 + 0.987117i \(0.551150\pi\)
\(912\) 0 0
\(913\) −18.1210 −0.599719
\(914\) 0 0
\(915\) −52.2964 −1.72887
\(916\) 0 0
\(917\) −2.00776 −0.0663020
\(918\) 0 0
\(919\) −4.92694 −0.162525 −0.0812624 0.996693i \(-0.525895\pi\)
−0.0812624 + 0.996693i \(0.525895\pi\)
\(920\) 0 0
\(921\) −43.2011 −1.42353
\(922\) 0 0
\(923\) 15.1711 0.499364
\(924\) 0 0
\(925\) −61.5538 −2.02388
\(926\) 0 0
\(927\) −3.74761 −0.123088
\(928\) 0 0
\(929\) 22.9980 0.754540 0.377270 0.926103i \(-0.376863\pi\)
0.377270 + 0.926103i \(0.376863\pi\)
\(930\) 0 0
\(931\) 5.82903 0.191039
\(932\) 0 0
\(933\) 37.9672 1.24299
\(934\) 0 0
\(935\) −21.8948 −0.716038
\(936\) 0 0
\(937\) 9.47482 0.309529 0.154764 0.987951i \(-0.450538\pi\)
0.154764 + 0.987951i \(0.450538\pi\)
\(938\) 0 0
\(939\) −5.08140 −0.165825
\(940\) 0 0
\(941\) −20.8949 −0.681154 −0.340577 0.940217i \(-0.610622\pi\)
−0.340577 + 0.940217i \(0.610622\pi\)
\(942\) 0 0
\(943\) 17.0680 0.555809
\(944\) 0 0
\(945\) 24.0942 0.783783
\(946\) 0 0
\(947\) −40.8100 −1.32615 −0.663074 0.748554i \(-0.730749\pi\)
−0.663074 + 0.748554i \(0.730749\pi\)
\(948\) 0 0
\(949\) −2.63392 −0.0855007
\(950\) 0 0
\(951\) 9.24046 0.299642
\(952\) 0 0
\(953\) −27.9634 −0.905824 −0.452912 0.891555i \(-0.649615\pi\)
−0.452912 + 0.891555i \(0.649615\pi\)
\(954\) 0 0
\(955\) −58.0104 −1.87717
\(956\) 0 0
\(957\) 0.139250 0.00450133
\(958\) 0 0
\(959\) −16.6995 −0.539255
\(960\) 0 0
\(961\) 75.2654 2.42792
\(962\) 0 0
\(963\) −7.31756 −0.235805
\(964\) 0 0
\(965\) −116.084 −3.73687
\(966\) 0 0
\(967\) −14.7327 −0.473772 −0.236886 0.971538i \(-0.576127\pi\)
−0.236886 + 0.971538i \(0.576127\pi\)
\(968\) 0 0
\(969\) 46.5625 1.49580
\(970\) 0 0
\(971\) −37.5031 −1.20353 −0.601766 0.798672i \(-0.705536\pi\)
−0.601766 + 0.798672i \(0.705536\pi\)
\(972\) 0 0
\(973\) −1.13299 −0.0363220
\(974\) 0 0
\(975\) −22.4802 −0.719944
\(976\) 0 0
\(977\) −4.71190 −0.150747 −0.0753735 0.997155i \(-0.524015\pi\)
−0.0753735 + 0.997155i \(0.524015\pi\)
\(978\) 0 0
\(979\) −0.350510 −0.0112023
\(980\) 0 0
\(981\) 0.506456 0.0161699
\(982\) 0 0
\(983\) −50.9941 −1.62646 −0.813229 0.581944i \(-0.802292\pi\)
−0.813229 + 0.581944i \(0.802292\pi\)
\(984\) 0 0
\(985\) 11.5973 0.369519
\(986\) 0 0
\(987\) −8.22987 −0.261960
\(988\) 0 0
\(989\) 50.6812 1.61157
\(990\) 0 0
\(991\) 30.9246 0.982354 0.491177 0.871060i \(-0.336567\pi\)
0.491177 + 0.871060i \(0.336567\pi\)
\(992\) 0 0
\(993\) −2.53156 −0.0803368
\(994\) 0 0
\(995\) −107.238 −3.39969
\(996\) 0 0
\(997\) 1.29052 0.0408711 0.0204356 0.999791i \(-0.493495\pi\)
0.0204356 + 0.999791i \(0.493495\pi\)
\(998\) 0 0
\(999\) 24.0693 0.761520
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 \(a_p\))