Properties

Label 8008.2.a.j.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 5
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: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.668973.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.376114\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.293231 q^{3} -3.94142 q^{5} +1.00000 q^{7} -2.91402 q^{9} +O(q^{10})\) \(q+0.293231 q^{3} -3.94142 q^{5} +1.00000 q^{7} -2.91402 q^{9} -1.00000 q^{11} -1.00000 q^{13} -1.15575 q^{15} +0.0585790 q^{17} -4.49244 q^{19} +0.293231 q^{21} -2.80394 q^{23} +10.5348 q^{25} -1.73417 q^{27} -7.01606 q^{29} -3.34473 q^{31} -0.293231 q^{33} -3.94142 q^{35} -9.50363 q^{37} -0.293231 q^{39} -9.75119 q^{41} -12.4521 q^{43} +11.4854 q^{45} +12.3205 q^{47} +1.00000 q^{49} +0.0171772 q^{51} +4.02741 q^{53} +3.94142 q^{55} -1.31732 q^{57} +11.9000 q^{59} +5.13748 q^{61} -2.91402 q^{63} +3.94142 q^{65} +9.12457 q^{67} -0.822202 q^{69} +13.5165 q^{71} -1.17401 q^{73} +3.08913 q^{75} -1.00000 q^{77} -10.3334 q^{79} +8.23353 q^{81} -8.10408 q^{83} -0.230884 q^{85} -2.05733 q^{87} -11.0789 q^{89} -1.00000 q^{91} -0.980779 q^{93} +17.7066 q^{95} -4.13149 q^{97} +2.91402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} + O(q^{10}) \) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} - 5q^{11} - 5q^{13} - 5q^{15} + 19q^{17} - 5q^{19} + q^{21} + 5q^{23} + 12q^{25} - 11q^{27} - 17q^{29} + 4q^{31} - q^{33} - q^{35} + 10q^{37} - q^{39} + 10q^{41} - 25q^{43} + q^{45} + 3q^{47} + 5q^{49} - q^{51} + 22q^{53} + q^{55} + 16q^{57} + 21q^{59} + 26q^{61} + 6q^{63} + q^{65} + 28q^{67} + 16q^{69} + 28q^{71} - 4q^{73} - 5q^{77} - 11q^{79} + 5q^{81} + 33q^{85} + 31q^{87} - 37q^{89} - 5q^{91} - 49q^{93} + 29q^{95} + 18q^{97} - 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.293231 0.169297 0.0846486 0.996411i \(-0.473023\pi\)
0.0846486 + 0.996411i \(0.473023\pi\)
\(4\) 0 0
\(5\) −3.94142 −1.76266 −0.881329 0.472504i \(-0.843350\pi\)
−0.881329 + 0.472504i \(0.843350\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.91402 −0.971338
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.15575 −0.298413
\(16\) 0 0
\(17\) 0.0585790 0.0142075 0.00710375 0.999975i \(-0.497739\pi\)
0.00710375 + 0.999975i \(0.497739\pi\)
\(18\) 0 0
\(19\) −4.49244 −1.03064 −0.515318 0.856999i \(-0.672326\pi\)
−0.515318 + 0.856999i \(0.672326\pi\)
\(20\) 0 0
\(21\) 0.293231 0.0639883
\(22\) 0 0
\(23\) −2.80394 −0.584661 −0.292331 0.956317i \(-0.594431\pi\)
−0.292331 + 0.956317i \(0.594431\pi\)
\(24\) 0 0
\(25\) 10.5348 2.10696
\(26\) 0 0
\(27\) −1.73417 −0.333742
\(28\) 0 0
\(29\) −7.01606 −1.30285 −0.651425 0.758713i \(-0.725828\pi\)
−0.651425 + 0.758713i \(0.725828\pi\)
\(30\) 0 0
\(31\) −3.34473 −0.600731 −0.300366 0.953824i \(-0.597109\pi\)
−0.300366 + 0.953824i \(0.597109\pi\)
\(32\) 0 0
\(33\) −0.293231 −0.0510450
\(34\) 0 0
\(35\) −3.94142 −0.666222
\(36\) 0 0
\(37\) −9.50363 −1.56239 −0.781193 0.624289i \(-0.785389\pi\)
−0.781193 + 0.624289i \(0.785389\pi\)
\(38\) 0 0
\(39\) −0.293231 −0.0469546
\(40\) 0 0
\(41\) −9.75119 −1.52288 −0.761440 0.648236i \(-0.775507\pi\)
−0.761440 + 0.648236i \(0.775507\pi\)
\(42\) 0 0
\(43\) −12.4521 −1.89893 −0.949466 0.313870i \(-0.898374\pi\)
−0.949466 + 0.313870i \(0.898374\pi\)
\(44\) 0 0
\(45\) 11.4854 1.71214
\(46\) 0 0
\(47\) 12.3205 1.79713 0.898563 0.438845i \(-0.144612\pi\)
0.898563 + 0.438845i \(0.144612\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0.0171772 0.00240529
\(52\) 0 0
\(53\) 4.02741 0.553207 0.276603 0.960984i \(-0.410791\pi\)
0.276603 + 0.960984i \(0.410791\pi\)
\(54\) 0 0
\(55\) 3.94142 0.531461
\(56\) 0 0
\(57\) −1.31732 −0.174484
\(58\) 0 0
\(59\) 11.9000 1.54925 0.774625 0.632421i \(-0.217938\pi\)
0.774625 + 0.632421i \(0.217938\pi\)
\(60\) 0 0
\(61\) 5.13748 0.657787 0.328894 0.944367i \(-0.393324\pi\)
0.328894 + 0.944367i \(0.393324\pi\)
\(62\) 0 0
\(63\) −2.91402 −0.367131
\(64\) 0 0
\(65\) 3.94142 0.488873
\(66\) 0 0
\(67\) 9.12457 1.11474 0.557372 0.830263i \(-0.311810\pi\)
0.557372 + 0.830263i \(0.311810\pi\)
\(68\) 0 0
\(69\) −0.822202 −0.0989815
\(70\) 0 0
\(71\) 13.5165 1.60412 0.802059 0.597245i \(-0.203738\pi\)
0.802059 + 0.597245i \(0.203738\pi\)
\(72\) 0 0
\(73\) −1.17401 −0.137408 −0.0687039 0.997637i \(-0.521886\pi\)
−0.0687039 + 0.997637i \(0.521886\pi\)
\(74\) 0 0
\(75\) 3.08913 0.356702
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −10.3334 −1.16260 −0.581298 0.813691i \(-0.697455\pi\)
−0.581298 + 0.813691i \(0.697455\pi\)
\(80\) 0 0
\(81\) 8.23353 0.914837
\(82\) 0 0
\(83\) −8.10408 −0.889539 −0.444769 0.895645i \(-0.646714\pi\)
−0.444769 + 0.895645i \(0.646714\pi\)
\(84\) 0 0
\(85\) −0.230884 −0.0250429
\(86\) 0 0
\(87\) −2.05733 −0.220569
\(88\) 0 0
\(89\) −11.0789 −1.17436 −0.587181 0.809456i \(-0.699762\pi\)
−0.587181 + 0.809456i \(0.699762\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −0.980779 −0.101702
\(94\) 0 0
\(95\) 17.7066 1.81666
\(96\) 0 0
\(97\) −4.13149 −0.419489 −0.209745 0.977756i \(-0.567263\pi\)
−0.209745 + 0.977756i \(0.567263\pi\)
\(98\) 0 0
\(99\) 2.91402 0.292870
\(100\) 0 0
\(101\) −9.53590 −0.948858 −0.474429 0.880294i \(-0.657345\pi\)
−0.474429 + 0.880294i \(0.657345\pi\)
\(102\) 0 0
\(103\) −7.64392 −0.753178 −0.376589 0.926380i \(-0.622903\pi\)
−0.376589 + 0.926380i \(0.622903\pi\)
\(104\) 0 0
\(105\) −1.15575 −0.112789
\(106\) 0 0
\(107\) 7.16472 0.692640 0.346320 0.938116i \(-0.387431\pi\)
0.346320 + 0.938116i \(0.387431\pi\)
\(108\) 0 0
\(109\) −18.7646 −1.79732 −0.898660 0.438647i \(-0.855458\pi\)
−0.898660 + 0.438647i \(0.855458\pi\)
\(110\) 0 0
\(111\) −2.78676 −0.264508
\(112\) 0 0
\(113\) −13.9273 −1.31017 −0.655083 0.755557i \(-0.727366\pi\)
−0.655083 + 0.755557i \(0.727366\pi\)
\(114\) 0 0
\(115\) 11.0515 1.03056
\(116\) 0 0
\(117\) 2.91402 0.269401
\(118\) 0 0
\(119\) 0.0585790 0.00536993
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −2.85935 −0.257819
\(124\) 0 0
\(125\) −21.8150 −1.95119
\(126\) 0 0
\(127\) 12.7443 1.13087 0.565435 0.824793i \(-0.308708\pi\)
0.565435 + 0.824793i \(0.308708\pi\)
\(128\) 0 0
\(129\) −3.65135 −0.321484
\(130\) 0 0
\(131\) −17.4397 −1.52371 −0.761856 0.647746i \(-0.775712\pi\)
−0.761856 + 0.647746i \(0.775712\pi\)
\(132\) 0 0
\(133\) −4.49244 −0.389544
\(134\) 0 0
\(135\) 6.83511 0.588273
\(136\) 0 0
\(137\) 12.4375 1.06260 0.531302 0.847182i \(-0.321703\pi\)
0.531302 + 0.847182i \(0.321703\pi\)
\(138\) 0 0
\(139\) 2.41133 0.204526 0.102263 0.994757i \(-0.467392\pi\)
0.102263 + 0.994757i \(0.467392\pi\)
\(140\) 0 0
\(141\) 3.61275 0.304248
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 27.6532 2.29648
\(146\) 0 0
\(147\) 0.293231 0.0241853
\(148\) 0 0
\(149\) 18.4118 1.50835 0.754177 0.656671i \(-0.228036\pi\)
0.754177 + 0.656671i \(0.228036\pi\)
\(150\) 0 0
\(151\) −17.6217 −1.43404 −0.717018 0.697055i \(-0.754493\pi\)
−0.717018 + 0.697055i \(0.754493\pi\)
\(152\) 0 0
\(153\) −0.170700 −0.0138003
\(154\) 0 0
\(155\) 13.1830 1.05888
\(156\) 0 0
\(157\) −13.4660 −1.07470 −0.537352 0.843358i \(-0.680575\pi\)
−0.537352 + 0.843358i \(0.680575\pi\)
\(158\) 0 0
\(159\) 1.18096 0.0936563
\(160\) 0 0
\(161\) −2.80394 −0.220981
\(162\) 0 0
\(163\) −14.8795 −1.16545 −0.582727 0.812668i \(-0.698014\pi\)
−0.582727 + 0.812668i \(0.698014\pi\)
\(164\) 0 0
\(165\) 1.15575 0.0899749
\(166\) 0 0
\(167\) 12.7765 0.988678 0.494339 0.869269i \(-0.335410\pi\)
0.494339 + 0.869269i \(0.335410\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 13.0910 1.00110
\(172\) 0 0
\(173\) −9.54394 −0.725612 −0.362806 0.931865i \(-0.618181\pi\)
−0.362806 + 0.931865i \(0.618181\pi\)
\(174\) 0 0
\(175\) 10.5348 0.796356
\(176\) 0 0
\(177\) 3.48946 0.262284
\(178\) 0 0
\(179\) 22.6135 1.69022 0.845108 0.534596i \(-0.179536\pi\)
0.845108 + 0.534596i \(0.179536\pi\)
\(180\) 0 0
\(181\) 5.42268 0.403065 0.201532 0.979482i \(-0.435408\pi\)
0.201532 + 0.979482i \(0.435408\pi\)
\(182\) 0 0
\(183\) 1.50647 0.111362
\(184\) 0 0
\(185\) 37.4578 2.75395
\(186\) 0 0
\(187\) −0.0585790 −0.00428372
\(188\) 0 0
\(189\) −1.73417 −0.126143
\(190\) 0 0
\(191\) 10.3973 0.752325 0.376162 0.926554i \(-0.377243\pi\)
0.376162 + 0.926554i \(0.377243\pi\)
\(192\) 0 0
\(193\) −16.9858 −1.22267 −0.611333 0.791373i \(-0.709366\pi\)
−0.611333 + 0.791373i \(0.709366\pi\)
\(194\) 0 0
\(195\) 1.15575 0.0827648
\(196\) 0 0
\(197\) −17.9413 −1.27826 −0.639131 0.769098i \(-0.720706\pi\)
−0.639131 + 0.769098i \(0.720706\pi\)
\(198\) 0 0
\(199\) 24.7269 1.75285 0.876423 0.481542i \(-0.159923\pi\)
0.876423 + 0.481542i \(0.159923\pi\)
\(200\) 0 0
\(201\) 2.67561 0.188723
\(202\) 0 0
\(203\) −7.01606 −0.492431
\(204\) 0 0
\(205\) 38.4335 2.68431
\(206\) 0 0
\(207\) 8.17072 0.567904
\(208\) 0 0
\(209\) 4.49244 0.310749
\(210\) 0 0
\(211\) −14.5148 −0.999241 −0.499620 0.866244i \(-0.666527\pi\)
−0.499620 + 0.866244i \(0.666527\pi\)
\(212\) 0 0
\(213\) 3.96347 0.271573
\(214\) 0 0
\(215\) 49.0791 3.34717
\(216\) 0 0
\(217\) −3.34473 −0.227055
\(218\) 0 0
\(219\) −0.344257 −0.0232627
\(220\) 0 0
\(221\) −0.0585790 −0.00394045
\(222\) 0 0
\(223\) 26.3731 1.76607 0.883036 0.469304i \(-0.155495\pi\)
0.883036 + 0.469304i \(0.155495\pi\)
\(224\) 0 0
\(225\) −30.6986 −2.04657
\(226\) 0 0
\(227\) 11.0509 0.733474 0.366737 0.930325i \(-0.380475\pi\)
0.366737 + 0.930325i \(0.380475\pi\)
\(228\) 0 0
\(229\) 16.9794 1.12203 0.561014 0.827806i \(-0.310411\pi\)
0.561014 + 0.827806i \(0.310411\pi\)
\(230\) 0 0
\(231\) −0.293231 −0.0192932
\(232\) 0 0
\(233\) 10.8630 0.711660 0.355830 0.934551i \(-0.384198\pi\)
0.355830 + 0.934551i \(0.384198\pi\)
\(234\) 0 0
\(235\) −48.5602 −3.16772
\(236\) 0 0
\(237\) −3.03007 −0.196824
\(238\) 0 0
\(239\) −2.97591 −0.192495 −0.0962477 0.995357i \(-0.530684\pi\)
−0.0962477 + 0.995357i \(0.530684\pi\)
\(240\) 0 0
\(241\) −8.60458 −0.554270 −0.277135 0.960831i \(-0.589385\pi\)
−0.277135 + 0.960831i \(0.589385\pi\)
\(242\) 0 0
\(243\) 7.61685 0.488621
\(244\) 0 0
\(245\) −3.94142 −0.251808
\(246\) 0 0
\(247\) 4.49244 0.285847
\(248\) 0 0
\(249\) −2.37637 −0.150596
\(250\) 0 0
\(251\) 6.40284 0.404143 0.202072 0.979371i \(-0.435233\pi\)
0.202072 + 0.979371i \(0.435233\pi\)
\(252\) 0 0
\(253\) 2.80394 0.176282
\(254\) 0 0
\(255\) −0.0677025 −0.00423970
\(256\) 0 0
\(257\) 13.0209 0.812223 0.406112 0.913823i \(-0.366884\pi\)
0.406112 + 0.913823i \(0.366884\pi\)
\(258\) 0 0
\(259\) −9.50363 −0.590527
\(260\) 0 0
\(261\) 20.4449 1.26551
\(262\) 0 0
\(263\) −3.01512 −0.185920 −0.0929600 0.995670i \(-0.529633\pi\)
−0.0929600 + 0.995670i \(0.529633\pi\)
\(264\) 0 0
\(265\) −15.8737 −0.975114
\(266\) 0 0
\(267\) −3.24868 −0.198816
\(268\) 0 0
\(269\) 5.67560 0.346047 0.173024 0.984918i \(-0.444646\pi\)
0.173024 + 0.984918i \(0.444646\pi\)
\(270\) 0 0
\(271\) 13.9693 0.848573 0.424286 0.905528i \(-0.360525\pi\)
0.424286 + 0.905528i \(0.360525\pi\)
\(272\) 0 0
\(273\) −0.293231 −0.0177472
\(274\) 0 0
\(275\) −10.5348 −0.635272
\(276\) 0 0
\(277\) 9.61164 0.577508 0.288754 0.957403i \(-0.406759\pi\)
0.288754 + 0.957403i \(0.406759\pi\)
\(278\) 0 0
\(279\) 9.74659 0.583513
\(280\) 0 0
\(281\) 30.1629 1.79936 0.899682 0.436545i \(-0.143798\pi\)
0.899682 + 0.436545i \(0.143798\pi\)
\(282\) 0 0
\(283\) 1.01338 0.0602390 0.0301195 0.999546i \(-0.490411\pi\)
0.0301195 + 0.999546i \(0.490411\pi\)
\(284\) 0 0
\(285\) 5.19213 0.307555
\(286\) 0 0
\(287\) −9.75119 −0.575594
\(288\) 0 0
\(289\) −16.9966 −0.999798
\(290\) 0 0
\(291\) −1.21148 −0.0710183
\(292\) 0 0
\(293\) 14.2404 0.831936 0.415968 0.909379i \(-0.363443\pi\)
0.415968 + 0.909379i \(0.363443\pi\)
\(294\) 0 0
\(295\) −46.9030 −2.73080
\(296\) 0 0
\(297\) 1.73417 0.100627
\(298\) 0 0
\(299\) 2.80394 0.162156
\(300\) 0 0
\(301\) −12.4521 −0.717729
\(302\) 0 0
\(303\) −2.79623 −0.160639
\(304\) 0 0
\(305\) −20.2490 −1.15945
\(306\) 0 0
\(307\) 3.73416 0.213120 0.106560 0.994306i \(-0.466016\pi\)
0.106560 + 0.994306i \(0.466016\pi\)
\(308\) 0 0
\(309\) −2.24144 −0.127511
\(310\) 0 0
\(311\) −0.962351 −0.0545699 −0.0272849 0.999628i \(-0.508686\pi\)
−0.0272849 + 0.999628i \(0.508686\pi\)
\(312\) 0 0
\(313\) 25.1345 1.42068 0.710342 0.703856i \(-0.248540\pi\)
0.710342 + 0.703856i \(0.248540\pi\)
\(314\) 0 0
\(315\) 11.4854 0.647127
\(316\) 0 0
\(317\) 27.7071 1.55619 0.778093 0.628149i \(-0.216187\pi\)
0.778093 + 0.628149i \(0.216187\pi\)
\(318\) 0 0
\(319\) 7.01606 0.392824
\(320\) 0 0
\(321\) 2.10092 0.117262
\(322\) 0 0
\(323\) −0.263163 −0.0146428
\(324\) 0 0
\(325\) −10.5348 −0.584366
\(326\) 0 0
\(327\) −5.50236 −0.304281
\(328\) 0 0
\(329\) 12.3205 0.679250
\(330\) 0 0
\(331\) −25.1882 −1.38447 −0.692234 0.721673i \(-0.743374\pi\)
−0.692234 + 0.721673i \(0.743374\pi\)
\(332\) 0 0
\(333\) 27.6937 1.51761
\(334\) 0 0
\(335\) −35.9638 −1.96491
\(336\) 0 0
\(337\) −24.8490 −1.35361 −0.676805 0.736163i \(-0.736636\pi\)
−0.676805 + 0.736163i \(0.736636\pi\)
\(338\) 0 0
\(339\) −4.08391 −0.221807
\(340\) 0 0
\(341\) 3.34473 0.181127
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 3.24065 0.174470
\(346\) 0 0
\(347\) −25.4035 −1.36373 −0.681865 0.731478i \(-0.738831\pi\)
−0.681865 + 0.731478i \(0.738831\pi\)
\(348\) 0 0
\(349\) 19.9449 1.06762 0.533812 0.845603i \(-0.320759\pi\)
0.533812 + 0.845603i \(0.320759\pi\)
\(350\) 0 0
\(351\) 1.73417 0.0925634
\(352\) 0 0
\(353\) 9.29638 0.494796 0.247398 0.968914i \(-0.420424\pi\)
0.247398 + 0.968914i \(0.420424\pi\)
\(354\) 0 0
\(355\) −53.2744 −2.82751
\(356\) 0 0
\(357\) 0.0171772 0.000909113 0
\(358\) 0 0
\(359\) 22.9714 1.21238 0.606191 0.795319i \(-0.292697\pi\)
0.606191 + 0.795319i \(0.292697\pi\)
\(360\) 0 0
\(361\) 1.18203 0.0622123
\(362\) 0 0
\(363\) 0.293231 0.0153907
\(364\) 0 0
\(365\) 4.62728 0.242203
\(366\) 0 0
\(367\) −17.2817 −0.902098 −0.451049 0.892499i \(-0.648950\pi\)
−0.451049 + 0.892499i \(0.648950\pi\)
\(368\) 0 0
\(369\) 28.4151 1.47923
\(370\) 0 0
\(371\) 4.02741 0.209092
\(372\) 0 0
\(373\) 12.7227 0.658754 0.329377 0.944198i \(-0.393161\pi\)
0.329377 + 0.944198i \(0.393161\pi\)
\(374\) 0 0
\(375\) −6.39683 −0.330331
\(376\) 0 0
\(377\) 7.01606 0.361345
\(378\) 0 0
\(379\) 12.9811 0.666794 0.333397 0.942786i \(-0.391805\pi\)
0.333397 + 0.942786i \(0.391805\pi\)
\(380\) 0 0
\(381\) 3.73701 0.191453
\(382\) 0 0
\(383\) 2.13971 0.109334 0.0546670 0.998505i \(-0.482590\pi\)
0.0546670 + 0.998505i \(0.482590\pi\)
\(384\) 0 0
\(385\) 3.94142 0.200873
\(386\) 0 0
\(387\) 36.2857 1.84451
\(388\) 0 0
\(389\) −14.2044 −0.720193 −0.360096 0.932915i \(-0.617256\pi\)
−0.360096 + 0.932915i \(0.617256\pi\)
\(390\) 0 0
\(391\) −0.164252 −0.00830657
\(392\) 0 0
\(393\) −5.11386 −0.257960
\(394\) 0 0
\(395\) 40.7282 2.04926
\(396\) 0 0
\(397\) −5.75387 −0.288778 −0.144389 0.989521i \(-0.546122\pi\)
−0.144389 + 0.989521i \(0.546122\pi\)
\(398\) 0 0
\(399\) −1.31732 −0.0659487
\(400\) 0 0
\(401\) 11.1493 0.556769 0.278384 0.960470i \(-0.410201\pi\)
0.278384 + 0.960470i \(0.410201\pi\)
\(402\) 0 0
\(403\) 3.34473 0.166613
\(404\) 0 0
\(405\) −32.4518 −1.61254
\(406\) 0 0
\(407\) 9.50363 0.471077
\(408\) 0 0
\(409\) 25.6577 1.26869 0.634345 0.773050i \(-0.281270\pi\)
0.634345 + 0.773050i \(0.281270\pi\)
\(410\) 0 0
\(411\) 3.64705 0.179896
\(412\) 0 0
\(413\) 11.9000 0.585562
\(414\) 0 0
\(415\) 31.9416 1.56795
\(416\) 0 0
\(417\) 0.707077 0.0346257
\(418\) 0 0
\(419\) 19.2479 0.940321 0.470160 0.882581i \(-0.344196\pi\)
0.470160 + 0.882581i \(0.344196\pi\)
\(420\) 0 0
\(421\) −7.70725 −0.375628 −0.187814 0.982205i \(-0.560140\pi\)
−0.187814 + 0.982205i \(0.560140\pi\)
\(422\) 0 0
\(423\) −35.9020 −1.74562
\(424\) 0 0
\(425\) 0.617118 0.0299346
\(426\) 0 0
\(427\) 5.13748 0.248620
\(428\) 0 0
\(429\) 0.293231 0.0141573
\(430\) 0 0
\(431\) −15.0825 −0.726500 −0.363250 0.931692i \(-0.618333\pi\)
−0.363250 + 0.931692i \(0.618333\pi\)
\(432\) 0 0
\(433\) 30.4403 1.46287 0.731434 0.681912i \(-0.238851\pi\)
0.731434 + 0.681912i \(0.238851\pi\)
\(434\) 0 0
\(435\) 8.10879 0.388787
\(436\) 0 0
\(437\) 12.5965 0.602574
\(438\) 0 0
\(439\) 18.4164 0.878965 0.439482 0.898251i \(-0.355162\pi\)
0.439482 + 0.898251i \(0.355162\pi\)
\(440\) 0 0
\(441\) −2.91402 −0.138763
\(442\) 0 0
\(443\) −10.0778 −0.478810 −0.239405 0.970920i \(-0.576952\pi\)
−0.239405 + 0.970920i \(0.576952\pi\)
\(444\) 0 0
\(445\) 43.6666 2.07000
\(446\) 0 0
\(447\) 5.39892 0.255360
\(448\) 0 0
\(449\) −22.2080 −1.04806 −0.524031 0.851699i \(-0.675572\pi\)
−0.524031 + 0.851699i \(0.675572\pi\)
\(450\) 0 0
\(451\) 9.75119 0.459165
\(452\) 0 0
\(453\) −5.16724 −0.242778
\(454\) 0 0
\(455\) 3.94142 0.184777
\(456\) 0 0
\(457\) 6.03167 0.282150 0.141075 0.989999i \(-0.454944\pi\)
0.141075 + 0.989999i \(0.454944\pi\)
\(458\) 0 0
\(459\) −0.101586 −0.00474164
\(460\) 0 0
\(461\) 36.3672 1.69379 0.846895 0.531760i \(-0.178469\pi\)
0.846895 + 0.531760i \(0.178469\pi\)
\(462\) 0 0
\(463\) −7.93119 −0.368594 −0.184297 0.982871i \(-0.559001\pi\)
−0.184297 + 0.982871i \(0.559001\pi\)
\(464\) 0 0
\(465\) 3.86566 0.179266
\(466\) 0 0
\(467\) −6.49546 −0.300574 −0.150287 0.988642i \(-0.548020\pi\)
−0.150287 + 0.988642i \(0.548020\pi\)
\(468\) 0 0
\(469\) 9.12457 0.421334
\(470\) 0 0
\(471\) −3.94865 −0.181944
\(472\) 0 0
\(473\) 12.4521 0.572549
\(474\) 0 0
\(475\) −47.3270 −2.17151
\(476\) 0 0
\(477\) −11.7359 −0.537351
\(478\) 0 0
\(479\) 13.3721 0.610988 0.305494 0.952194i \(-0.401178\pi\)
0.305494 + 0.952194i \(0.401178\pi\)
\(480\) 0 0
\(481\) 9.50363 0.433328
\(482\) 0 0
\(483\) −0.822202 −0.0374115
\(484\) 0 0
\(485\) 16.2839 0.739416
\(486\) 0 0
\(487\) −11.7625 −0.533010 −0.266505 0.963834i \(-0.585869\pi\)
−0.266505 + 0.963834i \(0.585869\pi\)
\(488\) 0 0
\(489\) −4.36314 −0.197308
\(490\) 0 0
\(491\) −17.3624 −0.783554 −0.391777 0.920060i \(-0.628139\pi\)
−0.391777 + 0.920060i \(0.628139\pi\)
\(492\) 0 0
\(493\) −0.410994 −0.0185102
\(494\) 0 0
\(495\) −11.4854 −0.516229
\(496\) 0 0
\(497\) 13.5165 0.606299
\(498\) 0 0
\(499\) 26.8540 1.20215 0.601075 0.799193i \(-0.294739\pi\)
0.601075 + 0.799193i \(0.294739\pi\)
\(500\) 0 0
\(501\) 3.74648 0.167380
\(502\) 0 0
\(503\) −11.4212 −0.509248 −0.254624 0.967040i \(-0.581952\pi\)
−0.254624 + 0.967040i \(0.581952\pi\)
\(504\) 0 0
\(505\) 37.5850 1.67251
\(506\) 0 0
\(507\) 0.293231 0.0130229
\(508\) 0 0
\(509\) −23.6340 −1.04756 −0.523780 0.851854i \(-0.675478\pi\)
−0.523780 + 0.851854i \(0.675478\pi\)
\(510\) 0 0
\(511\) −1.17401 −0.0519353
\(512\) 0 0
\(513\) 7.79068 0.343967
\(514\) 0 0
\(515\) 30.1279 1.32759
\(516\) 0 0
\(517\) −12.3205 −0.541854
\(518\) 0 0
\(519\) −2.79858 −0.122844
\(520\) 0 0
\(521\) −10.1277 −0.443704 −0.221852 0.975080i \(-0.571210\pi\)
−0.221852 + 0.975080i \(0.571210\pi\)
\(522\) 0 0
\(523\) −10.2101 −0.446456 −0.223228 0.974766i \(-0.571659\pi\)
−0.223228 + 0.974766i \(0.571659\pi\)
\(524\) 0 0
\(525\) 3.08913 0.134821
\(526\) 0 0
\(527\) −0.195931 −0.00853488
\(528\) 0 0
\(529\) −15.1379 −0.658171
\(530\) 0 0
\(531\) −34.6768 −1.50485
\(532\) 0 0
\(533\) 9.75119 0.422371
\(534\) 0 0
\(535\) −28.2392 −1.22089
\(536\) 0 0
\(537\) 6.63100 0.286149
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 13.5386 0.582069 0.291035 0.956713i \(-0.406001\pi\)
0.291035 + 0.956713i \(0.406001\pi\)
\(542\) 0 0
\(543\) 1.59010 0.0682377
\(544\) 0 0
\(545\) 73.9590 3.16806
\(546\) 0 0
\(547\) −42.2493 −1.80645 −0.903225 0.429167i \(-0.858807\pi\)
−0.903225 + 0.429167i \(0.858807\pi\)
\(548\) 0 0
\(549\) −14.9707 −0.638934
\(550\) 0 0
\(551\) 31.5192 1.34276
\(552\) 0 0
\(553\) −10.3334 −0.439420
\(554\) 0 0
\(555\) 10.9838 0.466236
\(556\) 0 0
\(557\) 22.7713 0.964853 0.482426 0.875936i \(-0.339756\pi\)
0.482426 + 0.875936i \(0.339756\pi\)
\(558\) 0 0
\(559\) 12.4521 0.526669
\(560\) 0 0
\(561\) −0.0171772 −0.000725222 0
\(562\) 0 0
\(563\) 16.9220 0.713179 0.356589 0.934261i \(-0.383940\pi\)
0.356589 + 0.934261i \(0.383940\pi\)
\(564\) 0 0
\(565\) 54.8932 2.30937
\(566\) 0 0
\(567\) 8.23353 0.345776
\(568\) 0 0
\(569\) −18.0905 −0.758395 −0.379198 0.925316i \(-0.623800\pi\)
−0.379198 + 0.925316i \(0.623800\pi\)
\(570\) 0 0
\(571\) 7.68784 0.321726 0.160863 0.986977i \(-0.448572\pi\)
0.160863 + 0.986977i \(0.448572\pi\)
\(572\) 0 0
\(573\) 3.04882 0.127366
\(574\) 0 0
\(575\) −29.5389 −1.23186
\(576\) 0 0
\(577\) −22.5674 −0.939493 −0.469746 0.882801i \(-0.655655\pi\)
−0.469746 + 0.882801i \(0.655655\pi\)
\(578\) 0 0
\(579\) −4.98077 −0.206994
\(580\) 0 0
\(581\) −8.10408 −0.336214
\(582\) 0 0
\(583\) −4.02741 −0.166798
\(584\) 0 0
\(585\) −11.4854 −0.474861
\(586\) 0 0
\(587\) 16.1376 0.666072 0.333036 0.942914i \(-0.391927\pi\)
0.333036 + 0.942914i \(0.391927\pi\)
\(588\) 0 0
\(589\) 15.0260 0.619136
\(590\) 0 0
\(591\) −5.26094 −0.216406
\(592\) 0 0
\(593\) −17.9139 −0.735634 −0.367817 0.929898i \(-0.619895\pi\)
−0.367817 + 0.929898i \(0.619895\pi\)
\(594\) 0 0
\(595\) −0.230884 −0.00946534
\(596\) 0 0
\(597\) 7.25071 0.296752
\(598\) 0 0
\(599\) −33.1029 −1.35255 −0.676273 0.736651i \(-0.736406\pi\)
−0.676273 + 0.736651i \(0.736406\pi\)
\(600\) 0 0
\(601\) −5.25939 −0.214535 −0.107268 0.994230i \(-0.534210\pi\)
−0.107268 + 0.994230i \(0.534210\pi\)
\(602\) 0 0
\(603\) −26.5892 −1.08279
\(604\) 0 0
\(605\) −3.94142 −0.160242
\(606\) 0 0
\(607\) −14.0776 −0.571394 −0.285697 0.958320i \(-0.592225\pi\)
−0.285697 + 0.958320i \(0.592225\pi\)
\(608\) 0 0
\(609\) −2.05733 −0.0833671
\(610\) 0 0
\(611\) −12.3205 −0.498433
\(612\) 0 0
\(613\) −10.2154 −0.412597 −0.206299 0.978489i \(-0.566142\pi\)
−0.206299 + 0.978489i \(0.566142\pi\)
\(614\) 0 0
\(615\) 11.2699 0.454447
\(616\) 0 0
\(617\) 18.2384 0.734251 0.367126 0.930171i \(-0.380342\pi\)
0.367126 + 0.930171i \(0.380342\pi\)
\(618\) 0 0
\(619\) 13.9994 0.562684 0.281342 0.959608i \(-0.409220\pi\)
0.281342 + 0.959608i \(0.409220\pi\)
\(620\) 0 0
\(621\) 4.86252 0.195126
\(622\) 0 0
\(623\) −11.0789 −0.443867
\(624\) 0 0
\(625\) 33.3080 1.33232
\(626\) 0 0
\(627\) 1.31732 0.0526089
\(628\) 0 0
\(629\) −0.556713 −0.0221976
\(630\) 0 0
\(631\) 14.6116 0.581679 0.290840 0.956772i \(-0.406065\pi\)
0.290840 + 0.956772i \(0.406065\pi\)
\(632\) 0 0
\(633\) −4.25620 −0.169169
\(634\) 0 0
\(635\) −50.2305 −1.99334
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −39.3874 −1.55814
\(640\) 0 0
\(641\) −27.9244 −1.10295 −0.551474 0.834192i \(-0.685934\pi\)
−0.551474 + 0.834192i \(0.685934\pi\)
\(642\) 0 0
\(643\) −2.57891 −0.101702 −0.0508512 0.998706i \(-0.516193\pi\)
−0.0508512 + 0.998706i \(0.516193\pi\)
\(644\) 0 0
\(645\) 14.3915 0.566666
\(646\) 0 0
\(647\) −20.4984 −0.805875 −0.402938 0.915227i \(-0.632011\pi\)
−0.402938 + 0.915227i \(0.632011\pi\)
\(648\) 0 0
\(649\) −11.9000 −0.467117
\(650\) 0 0
\(651\) −0.980779 −0.0384398
\(652\) 0 0
\(653\) 19.2756 0.754312 0.377156 0.926150i \(-0.376902\pi\)
0.377156 + 0.926150i \(0.376902\pi\)
\(654\) 0 0
\(655\) 68.7372 2.68578
\(656\) 0 0
\(657\) 3.42109 0.133469
\(658\) 0 0
\(659\) −9.95374 −0.387743 −0.193871 0.981027i \(-0.562104\pi\)
−0.193871 + 0.981027i \(0.562104\pi\)
\(660\) 0 0
\(661\) −20.3055 −0.789792 −0.394896 0.918726i \(-0.629219\pi\)
−0.394896 + 0.918726i \(0.629219\pi\)
\(662\) 0 0
\(663\) −0.0171772 −0.000667107 0
\(664\) 0 0
\(665\) 17.7066 0.686633
\(666\) 0 0
\(667\) 19.6726 0.761726
\(668\) 0 0
\(669\) 7.73342 0.298991
\(670\) 0 0
\(671\) −5.13748 −0.198330
\(672\) 0 0
\(673\) −34.9556 −1.34744 −0.673720 0.738987i \(-0.735305\pi\)
−0.673720 + 0.738987i \(0.735305\pi\)
\(674\) 0 0
\(675\) −18.2692 −0.703181
\(676\) 0 0
\(677\) −51.1105 −1.96434 −0.982169 0.188003i \(-0.939799\pi\)
−0.982169 + 0.188003i \(0.939799\pi\)
\(678\) 0 0
\(679\) −4.13149 −0.158552
\(680\) 0 0
\(681\) 3.24047 0.124175
\(682\) 0 0
\(683\) −19.9751 −0.764326 −0.382163 0.924095i \(-0.624821\pi\)
−0.382163 + 0.924095i \(0.624821\pi\)
\(684\) 0 0
\(685\) −49.0213 −1.87301
\(686\) 0 0
\(687\) 4.97888 0.189956
\(688\) 0 0
\(689\) −4.02741 −0.153432
\(690\) 0 0
\(691\) 19.7798 0.752460 0.376230 0.926526i \(-0.377220\pi\)
0.376230 + 0.926526i \(0.377220\pi\)
\(692\) 0 0
\(693\) 2.91402 0.110694
\(694\) 0 0
\(695\) −9.50407 −0.360510
\(696\) 0 0
\(697\) −0.571215 −0.0216363
\(698\) 0 0
\(699\) 3.18538 0.120482
\(700\) 0 0
\(701\) 32.5801 1.23054 0.615268 0.788318i \(-0.289048\pi\)
0.615268 + 0.788318i \(0.289048\pi\)
\(702\) 0 0
\(703\) 42.6945 1.61025
\(704\) 0 0
\(705\) −14.2394 −0.536285
\(706\) 0 0
\(707\) −9.53590 −0.358635
\(708\) 0 0
\(709\) −1.03903 −0.0390216 −0.0195108 0.999810i \(-0.506211\pi\)
−0.0195108 + 0.999810i \(0.506211\pi\)
\(710\) 0 0
\(711\) 30.1116 1.12927
\(712\) 0 0
\(713\) 9.37841 0.351224
\(714\) 0 0
\(715\) −3.94142 −0.147401
\(716\) 0 0
\(717\) −0.872629 −0.0325889
\(718\) 0 0
\(719\) −47.5876 −1.77472 −0.887359 0.461080i \(-0.847462\pi\)
−0.887359 + 0.461080i \(0.847462\pi\)
\(720\) 0 0
\(721\) −7.64392 −0.284675
\(722\) 0 0
\(723\) −2.52313 −0.0938363
\(724\) 0 0
\(725\) −73.9128 −2.74505
\(726\) 0 0
\(727\) 29.3405 1.08818 0.544089 0.839027i \(-0.316875\pi\)
0.544089 + 0.839027i \(0.316875\pi\)
\(728\) 0 0
\(729\) −22.4671 −0.832115
\(730\) 0 0
\(731\) −0.729433 −0.0269791
\(732\) 0 0
\(733\) −33.1850 −1.22572 −0.612859 0.790193i \(-0.709980\pi\)
−0.612859 + 0.790193i \(0.709980\pi\)
\(734\) 0 0
\(735\) −1.15575 −0.0426304
\(736\) 0 0
\(737\) −9.12457 −0.336108
\(738\) 0 0
\(739\) −36.9375 −1.35877 −0.679384 0.733783i \(-0.737753\pi\)
−0.679384 + 0.733783i \(0.737753\pi\)
\(740\) 0 0
\(741\) 1.31732 0.0483931
\(742\) 0 0
\(743\) −11.6592 −0.427736 −0.213868 0.976863i \(-0.568606\pi\)
−0.213868 + 0.976863i \(0.568606\pi\)
\(744\) 0 0
\(745\) −72.5687 −2.65871
\(746\) 0 0
\(747\) 23.6154 0.864043
\(748\) 0 0
\(749\) 7.16472 0.261793
\(750\) 0 0
\(751\) −31.6295 −1.15418 −0.577088 0.816682i \(-0.695811\pi\)
−0.577088 + 0.816682i \(0.695811\pi\)
\(752\) 0 0
\(753\) 1.87751 0.0684203
\(754\) 0 0
\(755\) 69.4546 2.52771
\(756\) 0 0
\(757\) 32.3590 1.17611 0.588055 0.808821i \(-0.299894\pi\)
0.588055 + 0.808821i \(0.299894\pi\)
\(758\) 0 0
\(759\) 0.822202 0.0298441
\(760\) 0 0
\(761\) 23.5517 0.853747 0.426874 0.904311i \(-0.359615\pi\)
0.426874 + 0.904311i \(0.359615\pi\)
\(762\) 0 0
\(763\) −18.7646 −0.679323
\(764\) 0 0
\(765\) 0.672801 0.0243252
\(766\) 0 0
\(767\) −11.9000 −0.429685
\(768\) 0 0
\(769\) 21.2055 0.764691 0.382346 0.924019i \(-0.375116\pi\)
0.382346 + 0.924019i \(0.375116\pi\)
\(770\) 0 0
\(771\) 3.81814 0.137507
\(772\) 0 0
\(773\) 43.9246 1.57986 0.789929 0.613198i \(-0.210117\pi\)
0.789929 + 0.613198i \(0.210117\pi\)
\(774\) 0 0
\(775\) −35.2361 −1.26572
\(776\) 0 0
\(777\) −2.78676 −0.0999745
\(778\) 0 0
\(779\) 43.8066 1.56954
\(780\) 0 0
\(781\) −13.5165 −0.483660
\(782\) 0 0
\(783\) 12.1671 0.434815
\(784\) 0 0
\(785\) 53.0751 1.89433
\(786\) 0 0
\(787\) −38.2548 −1.36364 −0.681819 0.731521i \(-0.738811\pi\)
−0.681819 + 0.731521i \(0.738811\pi\)
\(788\) 0 0
\(789\) −0.884126 −0.0314757
\(790\) 0 0
\(791\) −13.9273 −0.495196
\(792\) 0 0
\(793\) −5.13748 −0.182437
\(794\) 0 0
\(795\) −4.65467 −0.165084
\(796\) 0 0
\(797\) −54.6008 −1.93406 −0.967030 0.254663i \(-0.918035\pi\)
−0.967030 + 0.254663i \(0.918035\pi\)
\(798\) 0 0
\(799\) 0.721721 0.0255326
\(800\) 0 0
\(801\) 32.2841 1.14070
\(802\) 0 0
\(803\) 1.17401 0.0414300
\(804\) 0 0
\(805\) 11.0515 0.389514
\(806\) 0 0
\(807\) 1.66426 0.0585848
\(808\) 0 0
\(809\) 20.3682 0.716109 0.358055 0.933701i \(-0.383440\pi\)
0.358055 + 0.933701i \(0.383440\pi\)
\(810\) 0 0
\(811\) −45.3558 −1.59266 −0.796328 0.604864i \(-0.793227\pi\)
−0.796328 + 0.604864i \(0.793227\pi\)
\(812\) 0 0
\(813\) 4.09623 0.143661
\(814\) 0 0
\(815\) 58.6465 2.05430
\(816\) 0 0
\(817\) 55.9405 1.95711
\(818\) 0 0
\(819\) 2.91402 0.101824
\(820\) 0 0
\(821\) 26.1381 0.912226 0.456113 0.889922i \(-0.349241\pi\)
0.456113 + 0.889922i \(0.349241\pi\)
\(822\) 0 0
\(823\) 34.2998 1.19562 0.597809 0.801639i \(-0.296038\pi\)
0.597809 + 0.801639i \(0.296038\pi\)
\(824\) 0 0
\(825\) −3.08913 −0.107550
\(826\) 0 0
\(827\) −26.7159 −0.929004 −0.464502 0.885572i \(-0.653767\pi\)
−0.464502 + 0.885572i \(0.653767\pi\)
\(828\) 0 0
\(829\) 53.7968 1.86844 0.934221 0.356695i \(-0.116096\pi\)
0.934221 + 0.356695i \(0.116096\pi\)
\(830\) 0 0
\(831\) 2.81843 0.0977704
\(832\) 0 0
\(833\) 0.0585790 0.00202964
\(834\) 0 0
\(835\) −50.3577 −1.74270
\(836\) 0 0
\(837\) 5.80034 0.200489
\(838\) 0 0
\(839\) 49.8835 1.72217 0.861084 0.508463i \(-0.169786\pi\)
0.861084 + 0.508463i \(0.169786\pi\)
\(840\) 0 0
\(841\) 20.2251 0.697416
\(842\) 0 0
\(843\) 8.84469 0.304627
\(844\) 0 0
\(845\) −3.94142 −0.135589
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 0.297154 0.0101983
\(850\) 0 0
\(851\) 26.6476 0.913467
\(852\) 0 0
\(853\) −50.5409 −1.73049 −0.865244 0.501351i \(-0.832837\pi\)
−0.865244 + 0.501351i \(0.832837\pi\)
\(854\) 0 0
\(855\) −51.5973 −1.76459
\(856\) 0 0
\(857\) 37.2721 1.27319 0.636595 0.771198i \(-0.280342\pi\)
0.636595 + 0.771198i \(0.280342\pi\)
\(858\) 0 0
\(859\) −5.93782 −0.202596 −0.101298 0.994856i \(-0.532300\pi\)
−0.101298 + 0.994856i \(0.532300\pi\)
\(860\) 0 0
\(861\) −2.85935 −0.0974465
\(862\) 0 0
\(863\) −1.88803 −0.0642694 −0.0321347 0.999484i \(-0.510231\pi\)
−0.0321347 + 0.999484i \(0.510231\pi\)
\(864\) 0 0
\(865\) 37.6167 1.27901
\(866\) 0 0
\(867\) −4.98393 −0.169263
\(868\) 0 0
\(869\) 10.3334 0.350536
\(870\) 0 0
\(871\) −9.12457 −0.309174
\(872\) 0 0
\(873\) 12.0392 0.407466
\(874\) 0 0
\(875\) −21.8150 −0.737481
\(876\) 0 0
\(877\) −1.24217 −0.0419452 −0.0209726 0.999780i \(-0.506676\pi\)
−0.0209726 + 0.999780i \(0.506676\pi\)
\(878\) 0 0
\(879\) 4.17574 0.140844
\(880\) 0 0
\(881\) −39.2205 −1.32137 −0.660686 0.750663i \(-0.729734\pi\)
−0.660686 + 0.750663i \(0.729734\pi\)
\(882\) 0 0
\(883\) −33.6025 −1.13081 −0.565407 0.824812i \(-0.691281\pi\)
−0.565407 + 0.824812i \(0.691281\pi\)
\(884\) 0 0
\(885\) −13.7534 −0.462316
\(886\) 0 0
\(887\) 10.7323 0.360355 0.180177 0.983634i \(-0.442333\pi\)
0.180177 + 0.983634i \(0.442333\pi\)
\(888\) 0 0
\(889\) 12.7443 0.427429
\(890\) 0 0
\(891\) −8.23353 −0.275834
\(892\) 0 0
\(893\) −55.3490 −1.85218
\(894\) 0 0
\(895\) −89.1295 −2.97927
\(896\) 0 0
\(897\) 0.822202 0.0274525
\(898\) 0 0
\(899\) 23.4668 0.782662
\(900\) 0 0
\(901\) 0.235921 0.00785968
\(902\) 0 0
\(903\) −3.65135 −0.121509
\(904\) 0 0
\(905\) −21.3731 −0.710465
\(906\) 0 0
\(907\) 29.9491 0.994444 0.497222 0.867623i \(-0.334353\pi\)
0.497222 + 0.867623i \(0.334353\pi\)
\(908\) 0 0
\(909\) 27.7878 0.921662
\(910\) 0 0
\(911\) −3.20882 −0.106313 −0.0531565 0.998586i \(-0.516928\pi\)
−0.0531565 + 0.998586i \(0.516928\pi\)
\(912\) 0 0
\(913\) 8.10408 0.268206
\(914\) 0 0
\(915\) −5.93764 −0.196292
\(916\) 0 0
\(917\) −17.4397 −0.575909
\(918\) 0 0
\(919\) 0.777809 0.0256576 0.0128288 0.999918i \(-0.495916\pi\)
0.0128288 + 0.999918i \(0.495916\pi\)
\(920\) 0 0
\(921\) 1.09497 0.0360805
\(922\) 0 0
\(923\) −13.5165 −0.444902
\(924\) 0 0
\(925\) −100.119 −3.29189
\(926\) 0 0
\(927\) 22.2745 0.731591
\(928\) 0 0
\(929\) 8.12078 0.266434 0.133217 0.991087i \(-0.457469\pi\)
0.133217 + 0.991087i \(0.457469\pi\)
\(930\) 0 0
\(931\) −4.49244 −0.147234
\(932\) 0 0
\(933\) −0.282191 −0.00923853
\(934\) 0 0
\(935\) 0.230884 0.00755073
\(936\) 0 0
\(937\) 13.5167 0.441571 0.220786 0.975322i \(-0.429138\pi\)
0.220786 + 0.975322i \(0.429138\pi\)
\(938\) 0 0
\(939\) 7.37021 0.240518
\(940\) 0 0
\(941\) 53.5372 1.74526 0.872631 0.488380i \(-0.162412\pi\)
0.872631 + 0.488380i \(0.162412\pi\)
\(942\) 0 0
\(943\) 27.3417 0.890369
\(944\) 0 0
\(945\) 6.83511 0.222346
\(946\) 0 0
\(947\) −46.0746 −1.49722 −0.748612 0.663008i \(-0.769279\pi\)
−0.748612 + 0.663008i \(0.769279\pi\)
\(948\) 0 0
\(949\) 1.17401 0.0381101
\(950\) 0 0
\(951\) 8.12459 0.263458
\(952\) 0 0
\(953\) −16.9129 −0.547863 −0.273932 0.961749i \(-0.588324\pi\)
−0.273932 + 0.961749i \(0.588324\pi\)
\(954\) 0 0
\(955\) −40.9803 −1.32609
\(956\) 0 0
\(957\) 2.05733 0.0665039
\(958\) 0 0
\(959\) 12.4375 0.401627
\(960\) 0 0
\(961\) −19.8128 −0.639122
\(962\) 0 0
\(963\) −20.8781 −0.672788
\(964\) 0 0
\(965\) 66.9483 2.15514
\(966\) 0 0
\(967\) −3.07293 −0.0988187 −0.0494093 0.998779i \(-0.515734\pi\)
−0.0494093 + 0.998779i \(0.515734\pi\)
\(968\) 0 0
\(969\) −0.0771675 −0.00247898
\(970\) 0 0
\(971\) 48.1226 1.54433 0.772165 0.635423i \(-0.219174\pi\)
0.772165 + 0.635423i \(0.219174\pi\)
\(972\) 0 0
\(973\) 2.41133 0.0773037
\(974\) 0 0
\(975\) −3.08913 −0.0989314
\(976\) 0 0
\(977\) −5.07874 −0.162483 −0.0812416 0.996694i \(-0.525889\pi\)
−0.0812416 + 0.996694i \(0.525889\pi\)
\(978\) 0 0
\(979\) 11.0789 0.354083
\(980\) 0 0
\(981\) 54.6802 1.74581
\(982\) 0 0
\(983\) −7.44613 −0.237495 −0.118747 0.992924i \(-0.537888\pi\)
−0.118747 + 0.992924i \(0.537888\pi\)
\(984\) 0 0
\(985\) 70.7140 2.25314
\(986\) 0 0
\(987\) 3.61275 0.114995
\(988\) 0 0
\(989\) 34.9150 1.11023
\(990\) 0 0
\(991\) 11.1893 0.355439 0.177719 0.984081i \(-0.443128\pi\)
0.177719 + 0.984081i \(0.443128\pi\)
\(992\) 0 0
\(993\) −7.38597 −0.234387
\(994\) 0 0
\(995\) −97.4592 −3.08967
\(996\) 0 0
\(997\) −27.4077 −0.868012 −0.434006 0.900910i \(-0.642900\pi\)
−0.434006 + 0.900910i \(0.642900\pi\)
\(998\) 0 0
\(999\) 16.4809 0.521434
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 \(a_p\))