Properties

Label 8008.2.a.i.1.3
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 3
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: \(3\)
Coefficient field: 3.3.229.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.11491\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.47283 q^{3} -0.114908 q^{5} -1.00000 q^{7} +3.11491 q^{9} +O(q^{10})\) \(q+2.47283 q^{3} -0.114908 q^{5} -1.00000 q^{7} +3.11491 q^{9} -1.00000 q^{11} +1.00000 q^{13} -0.284147 q^{15} -5.83076 q^{17} +2.75698 q^{19} -2.47283 q^{21} +3.81756 q^{23} -4.98680 q^{25} +0.284147 q^{27} -5.17548 q^{29} -5.35793 q^{31} -2.47283 q^{33} +0.114908 q^{35} +2.64207 q^{37} +2.47283 q^{39} -8.79811 q^{41} +9.34472 q^{43} -0.357926 q^{45} -5.51396 q^{47} +1.00000 q^{49} -14.4185 q^{51} -13.0062 q^{53} +0.114908 q^{55} +6.81756 q^{57} +3.92622 q^{59} +5.11491 q^{61} -3.11491 q^{63} -0.114908 q^{65} -5.75698 q^{67} +9.44018 q^{69} -8.83076 q^{71} -14.4596 q^{73} -12.3315 q^{75} +1.00000 q^{77} +8.64832 q^{79} -8.64207 q^{81} +9.93246 q^{83} +0.669998 q^{85} -12.7981 q^{87} +11.9868 q^{89} -1.00000 q^{91} -13.2493 q^{93} -0.316798 q^{95} -1.73530 q^{97} -3.11491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 2q^{3} + 6q^{5} - 3q^{7} + 3q^{9} + O(q^{10}) \) \( 3q + 2q^{3} + 6q^{5} - 3q^{7} + 3q^{9} - 3q^{11} + 3q^{13} + q^{15} - 13q^{17} + q^{19} - 2q^{21} - 13q^{23} + 5q^{25} - q^{27} + 8q^{29} - 17q^{31} - 2q^{33} - 6q^{35} + 7q^{37} + 2q^{39} - 10q^{41} + 9q^{43} - 2q^{45} - 2q^{47} + 3q^{49} - 27q^{51} - 11q^{53} - 6q^{55} - 4q^{57} + 9q^{59} + 9q^{61} - 3q^{63} + 6q^{65} - 10q^{67} + 11q^{69} - 22q^{71} - 18q^{73} + 2q^{75} + 3q^{77} - 3q^{79} - 25q^{81} - q^{83} - 28q^{85} - 22q^{87} + 16q^{89} - 3q^{91} - 19q^{93} - 11q^{95} + q^{97} - 3q^{99} + O(q^{100}) \)

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
\(3\) 2.47283 1.42769 0.713846 0.700303i \(-0.246952\pi\)
0.713846 + 0.700303i \(0.246952\pi\)
\(4\) 0 0
\(5\) −0.114908 −0.0513882 −0.0256941 0.999670i \(-0.508180\pi\)
−0.0256941 + 0.999670i \(0.508180\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 3.11491 1.03830
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −0.284147 −0.0733665
\(16\) 0 0
\(17\) −5.83076 −1.41417 −0.707084 0.707130i \(-0.749990\pi\)
−0.707084 + 0.707130i \(0.749990\pi\)
\(18\) 0 0
\(19\) 2.75698 0.632495 0.316247 0.948677i \(-0.397577\pi\)
0.316247 + 0.948677i \(0.397577\pi\)
\(20\) 0 0
\(21\) −2.47283 −0.539617
\(22\) 0 0
\(23\) 3.81756 0.796016 0.398008 0.917382i \(-0.369702\pi\)
0.398008 + 0.917382i \(0.369702\pi\)
\(24\) 0 0
\(25\) −4.98680 −0.997359
\(26\) 0 0
\(27\) 0.284147 0.0546842
\(28\) 0 0
\(29\) −5.17548 −0.961063 −0.480532 0.876977i \(-0.659556\pi\)
−0.480532 + 0.876977i \(0.659556\pi\)
\(30\) 0 0
\(31\) −5.35793 −0.962312 −0.481156 0.876635i \(-0.659783\pi\)
−0.481156 + 0.876635i \(0.659783\pi\)
\(32\) 0 0
\(33\) −2.47283 −0.430465
\(34\) 0 0
\(35\) 0.114908 0.0194229
\(36\) 0 0
\(37\) 2.64207 0.434354 0.217177 0.976132i \(-0.430315\pi\)
0.217177 + 0.976132i \(0.430315\pi\)
\(38\) 0 0
\(39\) 2.47283 0.395970
\(40\) 0 0
\(41\) −8.79811 −1.37403 −0.687017 0.726641i \(-0.741080\pi\)
−0.687017 + 0.726641i \(0.741080\pi\)
\(42\) 0 0
\(43\) 9.34472 1.42506 0.712528 0.701643i \(-0.247550\pi\)
0.712528 + 0.701643i \(0.247550\pi\)
\(44\) 0 0
\(45\) −0.357926 −0.0533565
\(46\) 0 0
\(47\) −5.51396 −0.804294 −0.402147 0.915575i \(-0.631736\pi\)
−0.402147 + 0.915575i \(0.631736\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −14.4185 −2.01899
\(52\) 0 0
\(53\) −13.0062 −1.78654 −0.893272 0.449516i \(-0.851597\pi\)
−0.893272 + 0.449516i \(0.851597\pi\)
\(54\) 0 0
\(55\) 0.114908 0.0154941
\(56\) 0 0
\(57\) 6.81756 0.903007
\(58\) 0 0
\(59\) 3.92622 0.511150 0.255575 0.966789i \(-0.417735\pi\)
0.255575 + 0.966789i \(0.417735\pi\)
\(60\) 0 0
\(61\) 5.11491 0.654897 0.327448 0.944869i \(-0.393811\pi\)
0.327448 + 0.944869i \(0.393811\pi\)
\(62\) 0 0
\(63\) −3.11491 −0.392441
\(64\) 0 0
\(65\) −0.114908 −0.0142525
\(66\) 0 0
\(67\) −5.75698 −0.703327 −0.351664 0.936126i \(-0.614384\pi\)
−0.351664 + 0.936126i \(0.614384\pi\)
\(68\) 0 0
\(69\) 9.44018 1.13646
\(70\) 0 0
\(71\) −8.83076 −1.04802 −0.524009 0.851713i \(-0.675564\pi\)
−0.524009 + 0.851713i \(0.675564\pi\)
\(72\) 0 0
\(73\) −14.4596 −1.69237 −0.846186 0.532888i \(-0.821107\pi\)
−0.846186 + 0.532888i \(0.821107\pi\)
\(74\) 0 0
\(75\) −12.3315 −1.42392
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 8.64832 0.973012 0.486506 0.873677i \(-0.338271\pi\)
0.486506 + 0.873677i \(0.338271\pi\)
\(80\) 0 0
\(81\) −8.64207 −0.960230
\(82\) 0 0
\(83\) 9.93246 1.09023 0.545115 0.838361i \(-0.316486\pi\)
0.545115 + 0.838361i \(0.316486\pi\)
\(84\) 0 0
\(85\) 0.669998 0.0726715
\(86\) 0 0
\(87\) −12.7981 −1.37210
\(88\) 0 0
\(89\) 11.9868 1.27060 0.635299 0.772266i \(-0.280877\pi\)
0.635299 + 0.772266i \(0.280877\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −13.2493 −1.37388
\(94\) 0 0
\(95\) −0.316798 −0.0325028
\(96\) 0 0
\(97\) −1.73530 −0.176193 −0.0880965 0.996112i \(-0.528078\pi\)
−0.0880965 + 0.996112i \(0.528078\pi\)
\(98\) 0 0
\(99\) −3.11491 −0.313060
\(100\) 0 0
\(101\) −4.52717 −0.450470 −0.225235 0.974304i \(-0.572315\pi\)
−0.225235 + 0.974304i \(0.572315\pi\)
\(102\) 0 0
\(103\) −6.56829 −0.647193 −0.323597 0.946195i \(-0.604892\pi\)
−0.323597 + 0.946195i \(0.604892\pi\)
\(104\) 0 0
\(105\) 0.284147 0.0277299
\(106\) 0 0
\(107\) −14.7500 −1.42594 −0.712969 0.701195i \(-0.752650\pi\)
−0.712969 + 0.701195i \(0.752650\pi\)
\(108\) 0 0
\(109\) 14.9868 1.43547 0.717737 0.696314i \(-0.245178\pi\)
0.717737 + 0.696314i \(0.245178\pi\)
\(110\) 0 0
\(111\) 6.53341 0.620124
\(112\) 0 0
\(113\) −13.1692 −1.23886 −0.619429 0.785053i \(-0.712636\pi\)
−0.619429 + 0.785053i \(0.712636\pi\)
\(114\) 0 0
\(115\) −0.438666 −0.0409058
\(116\) 0 0
\(117\) 3.11491 0.287973
\(118\) 0 0
\(119\) 5.83076 0.534505
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −21.7563 −1.96170
\(124\) 0 0
\(125\) 1.14756 0.102641
\(126\) 0 0
\(127\) −11.8238 −1.04919 −0.524596 0.851351i \(-0.675784\pi\)
−0.524596 + 0.851351i \(0.675784\pi\)
\(128\) 0 0
\(129\) 23.1079 2.03454
\(130\) 0 0
\(131\) 8.60719 0.752014 0.376007 0.926617i \(-0.377297\pi\)
0.376007 + 0.926617i \(0.377297\pi\)
\(132\) 0 0
\(133\) −2.75698 −0.239061
\(134\) 0 0
\(135\) −0.0326507 −0.00281012
\(136\) 0 0
\(137\) −4.78963 −0.409206 −0.204603 0.978845i \(-0.565590\pi\)
−0.204603 + 0.978845i \(0.565590\pi\)
\(138\) 0 0
\(139\) 2.71585 0.230356 0.115178 0.993345i \(-0.463256\pi\)
0.115178 + 0.993345i \(0.463256\pi\)
\(140\) 0 0
\(141\) −13.6351 −1.14828
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 0.594702 0.0493873
\(146\) 0 0
\(147\) 2.47283 0.203956
\(148\) 0 0
\(149\) 13.9325 1.14139 0.570696 0.821161i \(-0.306673\pi\)
0.570696 + 0.821161i \(0.306673\pi\)
\(150\) 0 0
\(151\) −0.338479 −0.0275451 −0.0137725 0.999905i \(-0.504384\pi\)
−0.0137725 + 0.999905i \(0.504384\pi\)
\(152\) 0 0
\(153\) −18.1623 −1.46833
\(154\) 0 0
\(155\) 0.615666 0.0494515
\(156\) 0 0
\(157\) 16.4247 1.31084 0.655419 0.755266i \(-0.272492\pi\)
0.655419 + 0.755266i \(0.272492\pi\)
\(158\) 0 0
\(159\) −32.1623 −2.55063
\(160\) 0 0
\(161\) −3.81756 −0.300866
\(162\) 0 0
\(163\) −0.527166 −0.0412908 −0.0206454 0.999787i \(-0.506572\pi\)
−0.0206454 + 0.999787i \(0.506572\pi\)
\(164\) 0 0
\(165\) 0.284147 0.0221208
\(166\) 0 0
\(167\) −6.65528 −0.515001 −0.257500 0.966278i \(-0.582899\pi\)
−0.257500 + 0.966278i \(0.582899\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 8.58774 0.656721
\(172\) 0 0
\(173\) −20.1623 −1.53291 −0.766455 0.642298i \(-0.777981\pi\)
−0.766455 + 0.642298i \(0.777981\pi\)
\(174\) 0 0
\(175\) 4.98680 0.376966
\(176\) 0 0
\(177\) 9.70889 0.729765
\(178\) 0 0
\(179\) −25.7089 −1.92157 −0.960786 0.277290i \(-0.910564\pi\)
−0.960786 + 0.277290i \(0.910564\pi\)
\(180\) 0 0
\(181\) 17.3315 1.28824 0.644121 0.764924i \(-0.277223\pi\)
0.644121 + 0.764924i \(0.277223\pi\)
\(182\) 0 0
\(183\) 12.6483 0.934990
\(184\) 0 0
\(185\) −0.303594 −0.0223207
\(186\) 0 0
\(187\) 5.83076 0.426387
\(188\) 0 0
\(189\) −0.284147 −0.0206687
\(190\) 0 0
\(191\) 5.10170 0.369146 0.184573 0.982819i \(-0.440910\pi\)
0.184573 + 0.982819i \(0.440910\pi\)
\(192\) 0 0
\(193\) −8.96735 −0.645484 −0.322742 0.946487i \(-0.604605\pi\)
−0.322742 + 0.946487i \(0.604605\pi\)
\(194\) 0 0
\(195\) −0.284147 −0.0203482
\(196\) 0 0
\(197\) 12.3726 0.881515 0.440757 0.897626i \(-0.354710\pi\)
0.440757 + 0.897626i \(0.354710\pi\)
\(198\) 0 0
\(199\) −19.2555 −1.36499 −0.682493 0.730892i \(-0.739104\pi\)
−0.682493 + 0.730892i \(0.739104\pi\)
\(200\) 0 0
\(201\) −14.2361 −1.00413
\(202\) 0 0
\(203\) 5.17548 0.363248
\(204\) 0 0
\(205\) 1.01097 0.0706091
\(206\) 0 0
\(207\) 11.8913 0.826505
\(208\) 0 0
\(209\) −2.75698 −0.190704
\(210\) 0 0
\(211\) 15.5745 1.07220 0.536098 0.844156i \(-0.319898\pi\)
0.536098 + 0.844156i \(0.319898\pi\)
\(212\) 0 0
\(213\) −21.8370 −1.49625
\(214\) 0 0
\(215\) −1.07378 −0.0732311
\(216\) 0 0
\(217\) 5.35793 0.363720
\(218\) 0 0
\(219\) −35.7563 −2.41618
\(220\) 0 0
\(221\) −5.83076 −0.392219
\(222\) 0 0
\(223\) −0.680967 −0.0456010 −0.0228005 0.999740i \(-0.507258\pi\)
−0.0228005 + 0.999740i \(0.507258\pi\)
\(224\) 0 0
\(225\) −15.5334 −1.03556
\(226\) 0 0
\(227\) 19.6134 1.30179 0.650895 0.759168i \(-0.274394\pi\)
0.650895 + 0.759168i \(0.274394\pi\)
\(228\) 0 0
\(229\) −4.80435 −0.317481 −0.158740 0.987320i \(-0.550743\pi\)
−0.158740 + 0.987320i \(0.550743\pi\)
\(230\) 0 0
\(231\) 2.47283 0.162701
\(232\) 0 0
\(233\) −14.0823 −0.922559 −0.461280 0.887255i \(-0.652610\pi\)
−0.461280 + 0.887255i \(0.652610\pi\)
\(234\) 0 0
\(235\) 0.633596 0.0413312
\(236\) 0 0
\(237\) 21.3859 1.38916
\(238\) 0 0
\(239\) 20.8370 1.34783 0.673917 0.738807i \(-0.264611\pi\)
0.673917 + 0.738807i \(0.264611\pi\)
\(240\) 0 0
\(241\) −11.5140 −0.741680 −0.370840 0.928697i \(-0.620930\pi\)
−0.370840 + 0.928697i \(0.620930\pi\)
\(242\) 0 0
\(243\) −22.2229 −1.42560
\(244\) 0 0
\(245\) −0.114908 −0.00734117
\(246\) 0 0
\(247\) 2.75698 0.175423
\(248\) 0 0
\(249\) 24.5613 1.55651
\(250\) 0 0
\(251\) −18.4270 −1.16310 −0.581550 0.813510i \(-0.697554\pi\)
−0.581550 + 0.813510i \(0.697554\pi\)
\(252\) 0 0
\(253\) −3.81756 −0.240008
\(254\) 0 0
\(255\) 1.65679 0.103753
\(256\) 0 0
\(257\) −11.2966 −0.704665 −0.352332 0.935875i \(-0.614611\pi\)
−0.352332 + 0.935875i \(0.614611\pi\)
\(258\) 0 0
\(259\) −2.64207 −0.164170
\(260\) 0 0
\(261\) −16.1212 −0.997874
\(262\) 0 0
\(263\) 14.3921 0.887455 0.443727 0.896162i \(-0.353656\pi\)
0.443727 + 0.896162i \(0.353656\pi\)
\(264\) 0 0
\(265\) 1.49452 0.0918074
\(266\) 0 0
\(267\) 29.6414 1.81402
\(268\) 0 0
\(269\) 20.5683 1.25407 0.627036 0.778991i \(-0.284268\pi\)
0.627036 + 0.778991i \(0.284268\pi\)
\(270\) 0 0
\(271\) −0.694171 −0.0421679 −0.0210839 0.999778i \(-0.506712\pi\)
−0.0210839 + 0.999778i \(0.506712\pi\)
\(272\) 0 0
\(273\) −2.47283 −0.149663
\(274\) 0 0
\(275\) 4.98680 0.300715
\(276\) 0 0
\(277\) −23.4053 −1.40629 −0.703144 0.711047i \(-0.748221\pi\)
−0.703144 + 0.711047i \(0.748221\pi\)
\(278\) 0 0
\(279\) −16.6894 −0.999171
\(280\) 0 0
\(281\) −23.9255 −1.42728 −0.713638 0.700515i \(-0.752954\pi\)
−0.713638 + 0.700515i \(0.752954\pi\)
\(282\) 0 0
\(283\) 13.5264 0.804064 0.402032 0.915626i \(-0.368304\pi\)
0.402032 + 0.915626i \(0.368304\pi\)
\(284\) 0 0
\(285\) −0.783389 −0.0464039
\(286\) 0 0
\(287\) 8.79811 0.519336
\(288\) 0 0
\(289\) 16.9978 0.999869
\(290\) 0 0
\(291\) −4.29111 −0.251549
\(292\) 0 0
\(293\) −3.40530 −0.198940 −0.0994698 0.995041i \(-0.531715\pi\)
−0.0994698 + 0.995041i \(0.531715\pi\)
\(294\) 0 0
\(295\) −0.451152 −0.0262671
\(296\) 0 0
\(297\) −0.284147 −0.0164879
\(298\) 0 0
\(299\) 3.81756 0.220775
\(300\) 0 0
\(301\) −9.34472 −0.538621
\(302\) 0 0
\(303\) −11.1949 −0.643132
\(304\) 0 0
\(305\) −0.587741 −0.0336540
\(306\) 0 0
\(307\) −5.91302 −0.337474 −0.168737 0.985661i \(-0.553969\pi\)
−0.168737 + 0.985661i \(0.553969\pi\)
\(308\) 0 0
\(309\) −16.2423 −0.923992
\(310\) 0 0
\(311\) −26.0411 −1.47666 −0.738328 0.674441i \(-0.764385\pi\)
−0.738328 + 0.674441i \(0.764385\pi\)
\(312\) 0 0
\(313\) −12.6810 −0.716771 −0.358385 0.933574i \(-0.616673\pi\)
−0.358385 + 0.933574i \(0.616673\pi\)
\(314\) 0 0
\(315\) 0.357926 0.0201669
\(316\) 0 0
\(317\) −6.64207 −0.373056 −0.186528 0.982450i \(-0.559724\pi\)
−0.186528 + 0.982450i \(0.559724\pi\)
\(318\) 0 0
\(319\) 5.17548 0.289771
\(320\) 0 0
\(321\) −36.4744 −2.03580
\(322\) 0 0
\(323\) −16.0753 −0.894453
\(324\) 0 0
\(325\) −4.98680 −0.276618
\(326\) 0 0
\(327\) 37.0599 2.04941
\(328\) 0 0
\(329\) 5.51396 0.303995
\(330\) 0 0
\(331\) −3.88509 −0.213544 −0.106772 0.994284i \(-0.534051\pi\)
−0.106772 + 0.994284i \(0.534051\pi\)
\(332\) 0 0
\(333\) 8.22982 0.450991
\(334\) 0 0
\(335\) 0.661521 0.0361427
\(336\) 0 0
\(337\) 10.6506 0.580173 0.290086 0.957001i \(-0.406316\pi\)
0.290086 + 0.957001i \(0.406316\pi\)
\(338\) 0 0
\(339\) −32.5653 −1.76871
\(340\) 0 0
\(341\) 5.35793 0.290148
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −1.08475 −0.0584009
\(346\) 0 0
\(347\) 3.01320 0.161757 0.0808786 0.996724i \(-0.474227\pi\)
0.0808786 + 0.996724i \(0.474227\pi\)
\(348\) 0 0
\(349\) −7.16300 −0.383426 −0.191713 0.981451i \(-0.561404\pi\)
−0.191713 + 0.981451i \(0.561404\pi\)
\(350\) 0 0
\(351\) 0.284147 0.0151667
\(352\) 0 0
\(353\) 29.2229 1.55538 0.777688 0.628651i \(-0.216392\pi\)
0.777688 + 0.628651i \(0.216392\pi\)
\(354\) 0 0
\(355\) 1.01472 0.0538558
\(356\) 0 0
\(357\) 14.4185 0.763108
\(358\) 0 0
\(359\) 26.3246 1.38936 0.694679 0.719320i \(-0.255547\pi\)
0.694679 + 0.719320i \(0.255547\pi\)
\(360\) 0 0
\(361\) −11.3991 −0.599950
\(362\) 0 0
\(363\) 2.47283 0.129790
\(364\) 0 0
\(365\) 1.66152 0.0869680
\(366\) 0 0
\(367\) 2.85021 0.148780 0.0743898 0.997229i \(-0.476299\pi\)
0.0743898 + 0.997229i \(0.476299\pi\)
\(368\) 0 0
\(369\) −27.4053 −1.42666
\(370\) 0 0
\(371\) 13.0062 0.675251
\(372\) 0 0
\(373\) 31.1057 1.61059 0.805296 0.592872i \(-0.202006\pi\)
0.805296 + 0.592872i \(0.202006\pi\)
\(374\) 0 0
\(375\) 2.83772 0.146539
\(376\) 0 0
\(377\) −5.17548 −0.266551
\(378\) 0 0
\(379\) −15.9170 −0.817603 −0.408801 0.912623i \(-0.634053\pi\)
−0.408801 + 0.912623i \(0.634053\pi\)
\(380\) 0 0
\(381\) −29.2383 −1.49792
\(382\) 0 0
\(383\) 16.3983 0.837916 0.418958 0.908006i \(-0.362395\pi\)
0.418958 + 0.908006i \(0.362395\pi\)
\(384\) 0 0
\(385\) −0.114908 −0.00585623
\(386\) 0 0
\(387\) 29.1079 1.47964
\(388\) 0 0
\(389\) −26.4270 −1.33990 −0.669951 0.742406i \(-0.733685\pi\)
−0.669951 + 0.742406i \(0.733685\pi\)
\(390\) 0 0
\(391\) −22.2593 −1.12570
\(392\) 0 0
\(393\) 21.2841 1.07364
\(394\) 0 0
\(395\) −0.993757 −0.0500013
\(396\) 0 0
\(397\) 22.5202 1.13026 0.565128 0.825003i \(-0.308827\pi\)
0.565128 + 0.825003i \(0.308827\pi\)
\(398\) 0 0
\(399\) −6.81756 −0.341305
\(400\) 0 0
\(401\) −15.0404 −0.751082 −0.375541 0.926806i \(-0.622543\pi\)
−0.375541 + 0.926806i \(0.622543\pi\)
\(402\) 0 0
\(403\) −5.35793 −0.266897
\(404\) 0 0
\(405\) 0.993039 0.0493445
\(406\) 0 0
\(407\) −2.64207 −0.130963
\(408\) 0 0
\(409\) −21.3664 −1.05650 −0.528250 0.849089i \(-0.677152\pi\)
−0.528250 + 0.849089i \(0.677152\pi\)
\(410\) 0 0
\(411\) −11.8440 −0.584220
\(412\) 0 0
\(413\) −3.92622 −0.193197
\(414\) 0 0
\(415\) −1.14132 −0.0560250
\(416\) 0 0
\(417\) 6.71585 0.328877
\(418\) 0 0
\(419\) −5.69569 −0.278253 −0.139126 0.990275i \(-0.544429\pi\)
−0.139126 + 0.990275i \(0.544429\pi\)
\(420\) 0 0
\(421\) −20.0558 −0.977462 −0.488731 0.872434i \(-0.662540\pi\)
−0.488731 + 0.872434i \(0.662540\pi\)
\(422\) 0 0
\(423\) −17.1755 −0.835101
\(424\) 0 0
\(425\) 29.0768 1.41043
\(426\) 0 0
\(427\) −5.11491 −0.247528
\(428\) 0 0
\(429\) −2.47283 −0.119390
\(430\) 0 0
\(431\) 8.86341 0.426935 0.213468 0.976950i \(-0.431524\pi\)
0.213468 + 0.976950i \(0.431524\pi\)
\(432\) 0 0
\(433\) 28.2897 1.35951 0.679757 0.733437i \(-0.262085\pi\)
0.679757 + 0.733437i \(0.262085\pi\)
\(434\) 0 0
\(435\) 1.47060 0.0705098
\(436\) 0 0
\(437\) 10.5249 0.503476
\(438\) 0 0
\(439\) −4.33848 −0.207064 −0.103532 0.994626i \(-0.533014\pi\)
−0.103532 + 0.994626i \(0.533014\pi\)
\(440\) 0 0
\(441\) 3.11491 0.148329
\(442\) 0 0
\(443\) −8.57677 −0.407495 −0.203747 0.979023i \(-0.565312\pi\)
−0.203747 + 0.979023i \(0.565312\pi\)
\(444\) 0 0
\(445\) −1.37737 −0.0652938
\(446\) 0 0
\(447\) 34.4527 1.62956
\(448\) 0 0
\(449\) −34.3594 −1.62152 −0.810761 0.585377i \(-0.800946\pi\)
−0.810761 + 0.585377i \(0.800946\pi\)
\(450\) 0 0
\(451\) 8.79811 0.414287
\(452\) 0 0
\(453\) −0.837003 −0.0393259
\(454\) 0 0
\(455\) 0.114908 0.00538695
\(456\) 0 0
\(457\) −10.1234 −0.473552 −0.236776 0.971564i \(-0.576091\pi\)
−0.236776 + 0.971564i \(0.576091\pi\)
\(458\) 0 0
\(459\) −1.65679 −0.0773325
\(460\) 0 0
\(461\) 33.2577 1.54897 0.774484 0.632594i \(-0.218010\pi\)
0.774484 + 0.632594i \(0.218010\pi\)
\(462\) 0 0
\(463\) −31.1281 −1.44665 −0.723323 0.690510i \(-0.757386\pi\)
−0.723323 + 0.690510i \(0.757386\pi\)
\(464\) 0 0
\(465\) 1.52244 0.0706015
\(466\) 0 0
\(467\) −8.36417 −0.387048 −0.193524 0.981096i \(-0.561992\pi\)
−0.193524 + 0.981096i \(0.561992\pi\)
\(468\) 0 0
\(469\) 5.75698 0.265833
\(470\) 0 0
\(471\) 40.6157 1.87147
\(472\) 0 0
\(473\) −9.34472 −0.429671
\(474\) 0 0
\(475\) −13.7485 −0.630825
\(476\) 0 0
\(477\) −40.5132 −1.85497
\(478\) 0 0
\(479\) 12.9045 0.589623 0.294812 0.955555i \(-0.404743\pi\)
0.294812 + 0.955555i \(0.404743\pi\)
\(480\) 0 0
\(481\) 2.64207 0.120468
\(482\) 0 0
\(483\) −9.44018 −0.429543
\(484\) 0 0
\(485\) 0.199399 0.00905424
\(486\) 0 0
\(487\) −15.4402 −0.699661 −0.349831 0.936813i \(-0.613761\pi\)
−0.349831 + 0.936813i \(0.613761\pi\)
\(488\) 0 0
\(489\) −1.30359 −0.0589506
\(490\) 0 0
\(491\) 22.7159 1.02515 0.512576 0.858642i \(-0.328691\pi\)
0.512576 + 0.858642i \(0.328691\pi\)
\(492\) 0 0
\(493\) 30.1770 1.35910
\(494\) 0 0
\(495\) 0.357926 0.0160876
\(496\) 0 0
\(497\) 8.83076 0.396114
\(498\) 0 0
\(499\) 35.7974 1.60251 0.801256 0.598322i \(-0.204166\pi\)
0.801256 + 0.598322i \(0.204166\pi\)
\(500\) 0 0
\(501\) −16.4574 −0.735262
\(502\) 0 0
\(503\) −11.5264 −0.513939 −0.256969 0.966420i \(-0.582724\pi\)
−0.256969 + 0.966420i \(0.582724\pi\)
\(504\) 0 0
\(505\) 0.520206 0.0231488
\(506\) 0 0
\(507\) 2.47283 0.109822
\(508\) 0 0
\(509\) −0.373365 −0.0165491 −0.00827455 0.999966i \(-0.502634\pi\)
−0.00827455 + 0.999966i \(0.502634\pi\)
\(510\) 0 0
\(511\) 14.4596 0.639656
\(512\) 0 0
\(513\) 0.783389 0.0345875
\(514\) 0 0
\(515\) 0.754747 0.0332581
\(516\) 0 0
\(517\) 5.51396 0.242504
\(518\) 0 0
\(519\) −49.8580 −2.18852
\(520\) 0 0
\(521\) 27.8734 1.22116 0.610578 0.791956i \(-0.290937\pi\)
0.610578 + 0.791956i \(0.290937\pi\)
\(522\) 0 0
\(523\) −36.6894 −1.60432 −0.802159 0.597111i \(-0.796315\pi\)
−0.802159 + 0.597111i \(0.796315\pi\)
\(524\) 0 0
\(525\) 12.3315 0.538192
\(526\) 0 0
\(527\) 31.2408 1.36087
\(528\) 0 0
\(529\) −8.42626 −0.366359
\(530\) 0 0
\(531\) 12.2298 0.530729
\(532\) 0 0
\(533\) −8.79811 −0.381088
\(534\) 0 0
\(535\) 1.69489 0.0732764
\(536\) 0 0
\(537\) −63.5738 −2.74341
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 37.7827 1.62440 0.812202 0.583376i \(-0.198269\pi\)
0.812202 + 0.583376i \(0.198269\pi\)
\(542\) 0 0
\(543\) 42.8580 1.83921
\(544\) 0 0
\(545\) −1.72210 −0.0737665
\(546\) 0 0
\(547\) 0.754747 0.0322706 0.0161353 0.999870i \(-0.494864\pi\)
0.0161353 + 0.999870i \(0.494864\pi\)
\(548\) 0 0
\(549\) 15.9325 0.679981
\(550\) 0 0
\(551\) −14.2687 −0.607867
\(552\) 0 0
\(553\) −8.64832 −0.367764
\(554\) 0 0
\(555\) −0.750738 −0.0318671
\(556\) 0 0
\(557\) 13.1079 0.555402 0.277701 0.960668i \(-0.410428\pi\)
0.277701 + 0.960668i \(0.410428\pi\)
\(558\) 0 0
\(559\) 9.34472 0.395240
\(560\) 0 0
\(561\) 14.4185 0.608750
\(562\) 0 0
\(563\) −31.5918 −1.33143 −0.665717 0.746205i \(-0.731874\pi\)
−0.665717 + 0.746205i \(0.731874\pi\)
\(564\) 0 0
\(565\) 1.51324 0.0636627
\(566\) 0 0
\(567\) 8.64207 0.362933
\(568\) 0 0
\(569\) −6.59470 −0.276464 −0.138232 0.990400i \(-0.544142\pi\)
−0.138232 + 0.990400i \(0.544142\pi\)
\(570\) 0 0
\(571\) 30.8781 1.29221 0.646105 0.763249i \(-0.276397\pi\)
0.646105 + 0.763249i \(0.276397\pi\)
\(572\) 0 0
\(573\) 12.6157 0.527027
\(574\) 0 0
\(575\) −19.0374 −0.793913
\(576\) 0 0
\(577\) 3.28343 0.136691 0.0683455 0.997662i \(-0.478228\pi\)
0.0683455 + 0.997662i \(0.478228\pi\)
\(578\) 0 0
\(579\) −22.1748 −0.921552
\(580\) 0 0
\(581\) −9.93246 −0.412068
\(582\) 0 0
\(583\) 13.0062 0.538664
\(584\) 0 0
\(585\) −0.357926 −0.0147984
\(586\) 0 0
\(587\) 4.12115 0.170098 0.0850490 0.996377i \(-0.472895\pi\)
0.0850490 + 0.996377i \(0.472895\pi\)
\(588\) 0 0
\(589\) −14.7717 −0.608657
\(590\) 0 0
\(591\) 30.5955 1.25853
\(592\) 0 0
\(593\) −46.1600 −1.89557 −0.947783 0.318916i \(-0.896681\pi\)
−0.947783 + 0.318916i \(0.896681\pi\)
\(594\) 0 0
\(595\) −0.669998 −0.0274673
\(596\) 0 0
\(597\) −47.6157 −1.94878
\(598\) 0 0
\(599\) 24.3635 0.995464 0.497732 0.867331i \(-0.334166\pi\)
0.497732 + 0.867331i \(0.334166\pi\)
\(600\) 0 0
\(601\) −18.4115 −0.751022 −0.375511 0.926818i \(-0.622533\pi\)
−0.375511 + 0.926818i \(0.622533\pi\)
\(602\) 0 0
\(603\) −17.9325 −0.730266
\(604\) 0 0
\(605\) −0.114908 −0.00467166
\(606\) 0 0
\(607\) −22.6630 −0.919864 −0.459932 0.887954i \(-0.652126\pi\)
−0.459932 + 0.887954i \(0.652126\pi\)
\(608\) 0 0
\(609\) 12.7981 0.518606
\(610\) 0 0
\(611\) −5.51396 −0.223071
\(612\) 0 0
\(613\) 34.4068 1.38968 0.694839 0.719165i \(-0.255476\pi\)
0.694839 + 0.719165i \(0.255476\pi\)
\(614\) 0 0
\(615\) 2.49996 0.100808
\(616\) 0 0
\(617\) −26.6630 −1.07341 −0.536707 0.843769i \(-0.680332\pi\)
−0.536707 + 0.843769i \(0.680332\pi\)
\(618\) 0 0
\(619\) −34.2772 −1.37772 −0.688858 0.724896i \(-0.741888\pi\)
−0.688858 + 0.724896i \(0.741888\pi\)
\(620\) 0 0
\(621\) 1.08475 0.0435294
\(622\) 0 0
\(623\) −11.9868 −0.480241
\(624\) 0 0
\(625\) 24.8021 0.992085
\(626\) 0 0
\(627\) −6.81756 −0.272267
\(628\) 0 0
\(629\) −15.4053 −0.614249
\(630\) 0 0
\(631\) −11.9215 −0.474587 −0.237294 0.971438i \(-0.576260\pi\)
−0.237294 + 0.971438i \(0.576260\pi\)
\(632\) 0 0
\(633\) 38.5132 1.53076
\(634\) 0 0
\(635\) 1.35864 0.0539161
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −27.5070 −1.08816
\(640\) 0 0
\(641\) 43.9729 1.73682 0.868412 0.495843i \(-0.165141\pi\)
0.868412 + 0.495843i \(0.165141\pi\)
\(642\) 0 0
\(643\) 34.3983 1.35654 0.678269 0.734814i \(-0.262730\pi\)
0.678269 + 0.734814i \(0.262730\pi\)
\(644\) 0 0
\(645\) −2.65528 −0.104551
\(646\) 0 0
\(647\) −25.6964 −1.01023 −0.505115 0.863052i \(-0.668550\pi\)
−0.505115 + 0.863052i \(0.668550\pi\)
\(648\) 0 0
\(649\) −3.92622 −0.154118
\(650\) 0 0
\(651\) 13.2493 0.519280
\(652\) 0 0
\(653\) 44.1857 1.72912 0.864561 0.502528i \(-0.167597\pi\)
0.864561 + 0.502528i \(0.167597\pi\)
\(654\) 0 0
\(655\) −0.989031 −0.0386446
\(656\) 0 0
\(657\) −45.0404 −1.75719
\(658\) 0 0
\(659\) −41.7346 −1.62575 −0.812874 0.582439i \(-0.802098\pi\)
−0.812874 + 0.582439i \(0.802098\pi\)
\(660\) 0 0
\(661\) 34.1538 1.32843 0.664214 0.747542i \(-0.268766\pi\)
0.664214 + 0.747542i \(0.268766\pi\)
\(662\) 0 0
\(663\) −14.4185 −0.559968
\(664\) 0 0
\(665\) 0.316798 0.0122849
\(666\) 0 0
\(667\) −19.7577 −0.765021
\(668\) 0 0
\(669\) −1.68392 −0.0651041
\(670\) 0 0
\(671\) −5.11491 −0.197459
\(672\) 0 0
\(673\) −6.41627 −0.247329 −0.123664 0.992324i \(-0.539465\pi\)
−0.123664 + 0.992324i \(0.539465\pi\)
\(674\) 0 0
\(675\) −1.41698 −0.0545398
\(676\) 0 0
\(677\) 46.9798 1.80558 0.902791 0.430080i \(-0.141515\pi\)
0.902791 + 0.430080i \(0.141515\pi\)
\(678\) 0 0
\(679\) 1.73530 0.0665947
\(680\) 0 0
\(681\) 48.5008 1.85855
\(682\) 0 0
\(683\) −9.31832 −0.356555 −0.178278 0.983980i \(-0.557053\pi\)
−0.178278 + 0.983980i \(0.557053\pi\)
\(684\) 0 0
\(685\) 0.550365 0.0210284
\(686\) 0 0
\(687\) −11.8804 −0.453264
\(688\) 0 0
\(689\) −13.0062 −0.495498
\(690\) 0 0
\(691\) −3.93871 −0.149835 −0.0749177 0.997190i \(-0.523869\pi\)
−0.0749177 + 0.997190i \(0.523869\pi\)
\(692\) 0 0
\(693\) 3.11491 0.118326
\(694\) 0 0
\(695\) −0.312072 −0.0118376
\(696\) 0 0
\(697\) 51.2997 1.94311
\(698\) 0 0
\(699\) −34.8231 −1.31713
\(700\) 0 0
\(701\) −13.3928 −0.505840 −0.252920 0.967487i \(-0.581391\pi\)
−0.252920 + 0.967487i \(0.581391\pi\)
\(702\) 0 0
\(703\) 7.28415 0.274727
\(704\) 0 0
\(705\) 1.56678 0.0590082
\(706\) 0 0
\(707\) 4.52717 0.170262
\(708\) 0 0
\(709\) 37.3176 1.40149 0.700746 0.713411i \(-0.252851\pi\)
0.700746 + 0.713411i \(0.252851\pi\)
\(710\) 0 0
\(711\) 26.9387 1.01028
\(712\) 0 0
\(713\) −20.4542 −0.766015
\(714\) 0 0
\(715\) 0.114908 0.00429730
\(716\) 0 0
\(717\) 51.5264 1.92429
\(718\) 0 0
\(719\) 7.69168 0.286851 0.143426 0.989661i \(-0.454188\pi\)
0.143426 + 0.989661i \(0.454188\pi\)
\(720\) 0 0
\(721\) 6.56829 0.244616
\(722\) 0 0
\(723\) −28.4721 −1.05889
\(724\) 0 0
\(725\) 25.8091 0.958525
\(726\) 0 0
\(727\) 45.3587 1.68226 0.841131 0.540831i \(-0.181890\pi\)
0.841131 + 0.540831i \(0.181890\pi\)
\(728\) 0 0
\(729\) −29.0272 −1.07508
\(730\) 0 0
\(731\) −54.4868 −2.01527
\(732\) 0 0
\(733\) −3.75626 −0.138741 −0.0693704 0.997591i \(-0.522099\pi\)
−0.0693704 + 0.997591i \(0.522099\pi\)
\(734\) 0 0
\(735\) −0.284147 −0.0104809
\(736\) 0 0
\(737\) 5.75698 0.212061
\(738\) 0 0
\(739\) 26.3246 0.968365 0.484182 0.874967i \(-0.339117\pi\)
0.484182 + 0.874967i \(0.339117\pi\)
\(740\) 0 0
\(741\) 6.81756 0.250449
\(742\) 0 0
\(743\) 14.9193 0.547335 0.273667 0.961824i \(-0.411763\pi\)
0.273667 + 0.961824i \(0.411763\pi\)
\(744\) 0 0
\(745\) −1.60095 −0.0586541
\(746\) 0 0
\(747\) 30.9387 1.13199
\(748\) 0 0
\(749\) 14.7500 0.538954
\(750\) 0 0
\(751\) −34.3425 −1.25318 −0.626588 0.779351i \(-0.715549\pi\)
−0.626588 + 0.779351i \(0.715549\pi\)
\(752\) 0 0
\(753\) −45.5669 −1.66055
\(754\) 0 0
\(755\) 0.0388938 0.00141549
\(756\) 0 0
\(757\) −10.2320 −0.371890 −0.185945 0.982560i \(-0.559535\pi\)
−0.185945 + 0.982560i \(0.559535\pi\)
\(758\) 0 0
\(759\) −9.44018 −0.342657
\(760\) 0 0
\(761\) 26.9582 0.977232 0.488616 0.872499i \(-0.337502\pi\)
0.488616 + 0.872499i \(0.337502\pi\)
\(762\) 0 0
\(763\) −14.9868 −0.542558
\(764\) 0 0
\(765\) 2.08698 0.0754550
\(766\) 0 0
\(767\) 3.92622 0.141768
\(768\) 0 0
\(769\) 49.0265 1.76794 0.883970 0.467543i \(-0.154861\pi\)
0.883970 + 0.467543i \(0.154861\pi\)
\(770\) 0 0
\(771\) −27.9347 −1.00604
\(772\) 0 0
\(773\) 52.3587 1.88321 0.941606 0.336716i \(-0.109316\pi\)
0.941606 + 0.336716i \(0.109316\pi\)
\(774\) 0 0
\(775\) 26.7189 0.959771
\(776\) 0 0
\(777\) −6.53341 −0.234385
\(778\) 0 0
\(779\) −24.2562 −0.869069
\(780\) 0 0
\(781\) 8.83076 0.315989
\(782\) 0 0
\(783\) −1.47060 −0.0525549
\(784\) 0 0
\(785\) −1.88733 −0.0673616
\(786\) 0 0
\(787\) −18.6414 −0.664493 −0.332246 0.943193i \(-0.607807\pi\)
−0.332246 + 0.943193i \(0.607807\pi\)
\(788\) 0 0
\(789\) 35.5893 1.26701
\(790\) 0 0
\(791\) 13.1692 0.468244
\(792\) 0 0
\(793\) 5.11491 0.181636
\(794\) 0 0
\(795\) 3.69569 0.131073
\(796\) 0 0
\(797\) −16.1421 −0.571783 −0.285892 0.958262i \(-0.592290\pi\)
−0.285892 + 0.958262i \(0.592290\pi\)
\(798\) 0 0
\(799\) 32.1506 1.13741
\(800\) 0 0
\(801\) 37.3378 1.31926
\(802\) 0 0
\(803\) 14.4596 0.510269
\(804\) 0 0
\(805\) 0.438666 0.0154609
\(806\) 0 0
\(807\) 50.8620 1.79043
\(808\) 0 0
\(809\) 53.8121 1.89193 0.945967 0.324264i \(-0.105117\pi\)
0.945967 + 0.324264i \(0.105117\pi\)
\(810\) 0 0
\(811\) 28.7306 1.00887 0.504433 0.863451i \(-0.331701\pi\)
0.504433 + 0.863451i \(0.331701\pi\)
\(812\) 0 0
\(813\) −1.71657 −0.0602027
\(814\) 0 0
\(815\) 0.0605754 0.00212186
\(816\) 0 0
\(817\) 25.7632 0.901341
\(818\) 0 0
\(819\) −3.11491 −0.108844
\(820\) 0 0
\(821\) −9.87412 −0.344609 −0.172305 0.985044i \(-0.555121\pi\)
−0.172305 + 0.985044i \(0.555121\pi\)
\(822\) 0 0
\(823\) 14.5459 0.507038 0.253519 0.967330i \(-0.418412\pi\)
0.253519 + 0.967330i \(0.418412\pi\)
\(824\) 0 0
\(825\) 12.3315 0.429328
\(826\) 0 0
\(827\) 12.6894 0.441255 0.220628 0.975358i \(-0.429189\pi\)
0.220628 + 0.975358i \(0.429189\pi\)
\(828\) 0 0
\(829\) 15.2104 0.528278 0.264139 0.964485i \(-0.414912\pi\)
0.264139 + 0.964485i \(0.414912\pi\)
\(830\) 0 0
\(831\) −57.8774 −2.00775
\(832\) 0 0
\(833\) −5.83076 −0.202024
\(834\) 0 0
\(835\) 0.764742 0.0264650
\(836\) 0 0
\(837\) −1.52244 −0.0526232
\(838\) 0 0
\(839\) −9.14060 −0.315568 −0.157784 0.987474i \(-0.550435\pi\)
−0.157784 + 0.987474i \(0.550435\pi\)
\(840\) 0 0
\(841\) −2.21438 −0.0763578
\(842\) 0 0
\(843\) −59.1638 −2.03771
\(844\) 0 0
\(845\) −0.114908 −0.00395294
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 33.4487 1.14796
\(850\) 0 0
\(851\) 10.0863 0.345753
\(852\) 0 0
\(853\) 7.34000 0.251317 0.125658 0.992074i \(-0.459896\pi\)
0.125658 + 0.992074i \(0.459896\pi\)
\(854\) 0 0
\(855\) −0.986796 −0.0337477
\(856\) 0 0
\(857\) 38.7820 1.32477 0.662383 0.749165i \(-0.269545\pi\)
0.662383 + 0.749165i \(0.269545\pi\)
\(858\) 0 0
\(859\) −40.0474 −1.36640 −0.683199 0.730232i \(-0.739412\pi\)
−0.683199 + 0.730232i \(0.739412\pi\)
\(860\) 0 0
\(861\) 21.7563 0.741451
\(862\) 0 0
\(863\) −11.7827 −0.401087 −0.200543 0.979685i \(-0.564271\pi\)
−0.200543 + 0.979685i \(0.564271\pi\)
\(864\) 0 0
\(865\) 2.31680 0.0787735
\(866\) 0 0
\(867\) 42.0327 1.42750
\(868\) 0 0
\(869\) −8.64832 −0.293374
\(870\) 0 0
\(871\) −5.75698 −0.195068
\(872\) 0 0
\(873\) −5.40530 −0.182942
\(874\) 0 0
\(875\) −1.14756 −0.0387945
\(876\) 0 0
\(877\) −4.57302 −0.154420 −0.0772100 0.997015i \(-0.524601\pi\)
−0.0772100 + 0.997015i \(0.524601\pi\)
\(878\) 0 0
\(879\) −8.42074 −0.284024
\(880\) 0 0
\(881\) −7.31903 −0.246584 −0.123292 0.992370i \(-0.539345\pi\)
−0.123292 + 0.992370i \(0.539345\pi\)
\(882\) 0 0
\(883\) 38.0947 1.28199 0.640995 0.767545i \(-0.278522\pi\)
0.640995 + 0.767545i \(0.278522\pi\)
\(884\) 0 0
\(885\) −1.11562 −0.0375013
\(886\) 0 0
\(887\) −12.9721 −0.435560 −0.217780 0.975998i \(-0.569881\pi\)
−0.217780 + 0.975998i \(0.569881\pi\)
\(888\) 0 0
\(889\) 11.8238 0.396558
\(890\) 0 0
\(891\) 8.64207 0.289520
\(892\) 0 0
\(893\) −15.2019 −0.508712
\(894\) 0 0
\(895\) 2.95415 0.0987462
\(896\) 0 0
\(897\) 9.44018 0.315199
\(898\) 0 0
\(899\) 27.7299 0.924842
\(900\) 0 0
\(901\) 75.8363 2.52647
\(902\) 0 0
\(903\) −23.1079 −0.768984
\(904\) 0 0
\(905\) −1.99152 −0.0662004
\(906\) 0 0
\(907\) −41.3744 −1.37382 −0.686908 0.726745i \(-0.741032\pi\)
−0.686908 + 0.726745i \(0.741032\pi\)
\(908\) 0 0
\(909\) −14.1017 −0.467724
\(910\) 0 0
\(911\) 2.47212 0.0819049 0.0409524 0.999161i \(-0.486961\pi\)
0.0409524 + 0.999161i \(0.486961\pi\)
\(912\) 0 0
\(913\) −9.93246 −0.328717
\(914\) 0 0
\(915\) −1.45339 −0.0480475
\(916\) 0 0
\(917\) −8.60719 −0.284234
\(918\) 0 0
\(919\) 15.5885 0.514216 0.257108 0.966383i \(-0.417230\pi\)
0.257108 + 0.966383i \(0.417230\pi\)
\(920\) 0 0
\(921\) −14.6219 −0.481808
\(922\) 0 0
\(923\) −8.83076 −0.290668
\(924\) 0 0
\(925\) −13.1755 −0.433207
\(926\) 0 0
\(927\) −20.4596 −0.671982
\(928\) 0 0
\(929\) 31.7391 1.04132 0.520662 0.853763i \(-0.325685\pi\)
0.520662 + 0.853763i \(0.325685\pi\)
\(930\) 0 0
\(931\) 2.75698 0.0903564
\(932\) 0 0
\(933\) −64.3954 −2.10821
\(934\) 0 0
\(935\) −0.669998 −0.0219113
\(936\) 0 0
\(937\) −26.9993 −0.882028 −0.441014 0.897500i \(-0.645381\pi\)
−0.441014 + 0.897500i \(0.645381\pi\)
\(938\) 0 0
\(939\) −31.3579 −1.02333
\(940\) 0 0
\(941\) −7.40530 −0.241406 −0.120703 0.992689i \(-0.538515\pi\)
−0.120703 + 0.992689i \(0.538515\pi\)
\(942\) 0 0
\(943\) −33.5873 −1.09375
\(944\) 0 0
\(945\) 0.0326507 0.00106213
\(946\) 0 0
\(947\) −5.37514 −0.174669 −0.0873343 0.996179i \(-0.527835\pi\)
−0.0873343 + 0.996179i \(0.527835\pi\)
\(948\) 0 0
\(949\) −14.4596 −0.469379
\(950\) 0 0
\(951\) −16.4247 −0.532609
\(952\) 0 0
\(953\) −53.2577 −1.72519 −0.862594 0.505897i \(-0.831161\pi\)
−0.862594 + 0.505897i \(0.831161\pi\)
\(954\) 0 0
\(955\) −0.586224 −0.0189698
\(956\) 0 0
\(957\) 12.7981 0.413704
\(958\) 0 0
\(959\) 4.78963 0.154665
\(960\) 0 0
\(961\) −2.29263 −0.0739556
\(962\) 0 0
\(963\) −45.9450 −1.48056
\(964\) 0 0
\(965\) 1.03042 0.0331703
\(966\) 0 0
\(967\) −10.7019 −0.344151 −0.172075 0.985084i \(-0.555047\pi\)
−0.172075 + 0.985084i \(0.555047\pi\)
\(968\) 0 0
\(969\) −39.7515 −1.27700
\(970\) 0 0
\(971\) −57.5452 −1.84671 −0.923356 0.383944i \(-0.874566\pi\)
−0.923356 + 0.383944i \(0.874566\pi\)
\(972\) 0 0
\(973\) −2.71585 −0.0870662
\(974\) 0 0
\(975\) −12.3315 −0.394925
\(976\) 0 0
\(977\) 33.7214 1.07884 0.539421 0.842036i \(-0.318643\pi\)
0.539421 + 0.842036i \(0.318643\pi\)
\(978\) 0 0
\(979\) −11.9868 −0.383100
\(980\) 0 0
\(981\) 46.6825 1.49046
\(982\) 0 0
\(983\) −14.3734 −0.458439 −0.229220 0.973375i \(-0.573617\pi\)
−0.229220 + 0.973375i \(0.573617\pi\)
\(984\) 0 0
\(985\) −1.42171 −0.0452995
\(986\) 0 0
\(987\) 13.6351 0.434010
\(988\) 0 0
\(989\) 35.6740 1.13437
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 0 0
\(993\) −9.60719 −0.304875
\(994\) 0 0
\(995\) 2.21260 0.0701442
\(996\) 0 0
\(997\) 28.6050 0.905928 0.452964 0.891529i \(-0.350367\pi\)
0.452964 + 0.891529i \(0.350367\pi\)
\(998\) 0 0
\(999\) 0.750738 0.0237523
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 \(a_p\))