Properties

Label 8008.2.a.j.1.2
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 1.2
Root \(3.50189\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.830554 q^{3} +3.93077 q^{5} +1.00000 q^{7} -2.31018 q^{9} +O(q^{10})\) \(q-0.830554 q^{3} +3.93077 q^{5} +1.00000 q^{7} -2.31018 q^{9} -1.00000 q^{11} -1.00000 q^{13} -3.26471 q^{15} +7.93077 q^{17} +4.36492 q^{19} -0.830554 q^{21} +1.83550 q^{23} +10.4509 q^{25} +4.41039 q^{27} -4.44186 q^{29} +1.61564 q^{31} +0.830554 q^{33} +3.93077 q^{35} +5.72080 q^{37} +0.830554 q^{39} +4.67038 q^{41} -1.06429 q^{43} -9.08078 q^{45} +2.25544 q^{47} +1.00000 q^{49} -6.58693 q^{51} -3.24095 q^{53} -3.93077 q^{55} -3.62530 q^{57} -10.4485 q^{59} +1.90473 q^{61} -2.31018 q^{63} -3.93077 q^{65} -3.90700 q^{67} -1.52448 q^{69} +8.09094 q^{71} -8.62469 q^{73} -8.68005 q^{75} -1.00000 q^{77} -10.0672 q^{79} +3.26747 q^{81} -12.3767 q^{83} +31.1740 q^{85} +3.68921 q^{87} +0.0260316 q^{89} -1.00000 q^{91} -1.34188 q^{93} +17.1575 q^{95} -1.13579 q^{97} +2.31018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} + O(q^{10}) \) \( 5q + q^{3} - q^{5} + 5q^{7} + 6q^{9} - 5q^{11} - 5q^{13} - 5q^{15} + 19q^{17} - 5q^{19} + q^{21} + 5q^{23} + 12q^{25} - 11q^{27} - 17q^{29} + 4q^{31} - q^{33} - q^{35} + 10q^{37} - q^{39} + 10q^{41} - 25q^{43} + q^{45} + 3q^{47} + 5q^{49} - q^{51} + 22q^{53} + q^{55} + 16q^{57} + 21q^{59} + 26q^{61} + 6q^{63} + q^{65} + 28q^{67} + 16q^{69} + 28q^{71} - 4q^{73} - 5q^{77} - 11q^{79} + 5q^{81} + 33q^{85} + 31q^{87} - 37q^{89} - 5q^{91} - 49q^{93} + 29q^{95} + 18q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) −0.830554 −0.479521 −0.239760 0.970832i \(-0.577069\pi\)
−0.239760 + 0.970832i \(0.577069\pi\)
\(4\) 0 0
\(5\) 3.93077 1.75789 0.878946 0.476922i \(-0.158247\pi\)
0.878946 + 0.476922i \(0.158247\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.31018 −0.770060
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.26471 −0.842945
\(16\) 0 0
\(17\) 7.93077 1.92349 0.961747 0.273941i \(-0.0883273\pi\)
0.961747 + 0.273941i \(0.0883273\pi\)
\(18\) 0 0
\(19\) 4.36492 1.00138 0.500691 0.865626i \(-0.333079\pi\)
0.500691 + 0.865626i \(0.333079\pi\)
\(20\) 0 0
\(21\) −0.830554 −0.181242
\(22\) 0 0
\(23\) 1.83550 0.382728 0.191364 0.981519i \(-0.438709\pi\)
0.191364 + 0.981519i \(0.438709\pi\)
\(24\) 0 0
\(25\) 10.4509 2.09018
\(26\) 0 0
\(27\) 4.41039 0.848780
\(28\) 0 0
\(29\) −4.44186 −0.824833 −0.412417 0.910995i \(-0.635315\pi\)
−0.412417 + 0.910995i \(0.635315\pi\)
\(30\) 0 0
\(31\) 1.61564 0.290178 0.145089 0.989419i \(-0.453653\pi\)
0.145089 + 0.989419i \(0.453653\pi\)
\(32\) 0 0
\(33\) 0.830554 0.144581
\(34\) 0 0
\(35\) 3.93077 0.664421
\(36\) 0 0
\(37\) 5.72080 0.940493 0.470247 0.882535i \(-0.344165\pi\)
0.470247 + 0.882535i \(0.344165\pi\)
\(38\) 0 0
\(39\) 0.830554 0.132995
\(40\) 0 0
\(41\) 4.67038 0.729391 0.364696 0.931127i \(-0.381173\pi\)
0.364696 + 0.931127i \(0.381173\pi\)
\(42\) 0 0
\(43\) −1.06429 −0.162303 −0.0811514 0.996702i \(-0.525860\pi\)
−0.0811514 + 0.996702i \(0.525860\pi\)
\(44\) 0 0
\(45\) −9.08078 −1.35368
\(46\) 0 0
\(47\) 2.25544 0.328989 0.164495 0.986378i \(-0.447401\pi\)
0.164495 + 0.986378i \(0.447401\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −6.58693 −0.922354
\(52\) 0 0
\(53\) −3.24095 −0.445178 −0.222589 0.974912i \(-0.571451\pi\)
−0.222589 + 0.974912i \(0.571451\pi\)
\(54\) 0 0
\(55\) −3.93077 −0.530024
\(56\) 0 0
\(57\) −3.62530 −0.480183
\(58\) 0 0
\(59\) −10.4485 −1.36027 −0.680137 0.733085i \(-0.738080\pi\)
−0.680137 + 0.733085i \(0.738080\pi\)
\(60\) 0 0
\(61\) 1.90473 0.243876 0.121938 0.992538i \(-0.461089\pi\)
0.121938 + 0.992538i \(0.461089\pi\)
\(62\) 0 0
\(63\) −2.31018 −0.291055
\(64\) 0 0
\(65\) −3.93077 −0.487551
\(66\) 0 0
\(67\) −3.90700 −0.477316 −0.238658 0.971104i \(-0.576707\pi\)
−0.238658 + 0.971104i \(0.576707\pi\)
\(68\) 0 0
\(69\) −1.52448 −0.183526
\(70\) 0 0
\(71\) 8.09094 0.960217 0.480109 0.877209i \(-0.340597\pi\)
0.480109 + 0.877209i \(0.340597\pi\)
\(72\) 0 0
\(73\) −8.62469 −1.00944 −0.504722 0.863282i \(-0.668405\pi\)
−0.504722 + 0.863282i \(0.668405\pi\)
\(74\) 0 0
\(75\) −8.68005 −1.00229
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −10.0672 −1.13264 −0.566322 0.824184i \(-0.691634\pi\)
−0.566322 + 0.824184i \(0.691634\pi\)
\(80\) 0 0
\(81\) 3.26747 0.363052
\(82\) 0 0
\(83\) −12.3767 −1.35852 −0.679262 0.733896i \(-0.737700\pi\)
−0.679262 + 0.733896i \(0.737700\pi\)
\(84\) 0 0
\(85\) 31.1740 3.38129
\(86\) 0 0
\(87\) 3.68921 0.395524
\(88\) 0 0
\(89\) 0.0260316 0.00275935 0.00137967 0.999999i \(-0.499561\pi\)
0.00137967 + 0.999999i \(0.499561\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −1.34188 −0.139146
\(94\) 0 0
\(95\) 17.1575 1.76032
\(96\) 0 0
\(97\) −1.13579 −0.115322 −0.0576610 0.998336i \(-0.518364\pi\)
−0.0576610 + 0.998336i \(0.518364\pi\)
\(98\) 0 0
\(99\) 2.31018 0.232182
\(100\) 0 0
\(101\) 9.16401 0.911853 0.455926 0.890018i \(-0.349308\pi\)
0.455926 + 0.890018i \(0.349308\pi\)
\(102\) 0 0
\(103\) −17.2984 −1.70447 −0.852233 0.523162i \(-0.824752\pi\)
−0.852233 + 0.523162i \(0.824752\pi\)
\(104\) 0 0
\(105\) −3.26471 −0.318603
\(106\) 0 0
\(107\) −5.00928 −0.484265 −0.242132 0.970243i \(-0.577847\pi\)
−0.242132 + 0.970243i \(0.577847\pi\)
\(108\) 0 0
\(109\) 8.69427 0.832760 0.416380 0.909191i \(-0.363299\pi\)
0.416380 + 0.909191i \(0.363299\pi\)
\(110\) 0 0
\(111\) −4.75143 −0.450986
\(112\) 0 0
\(113\) 17.3625 1.63332 0.816662 0.577117i \(-0.195822\pi\)
0.816662 + 0.577117i \(0.195822\pi\)
\(114\) 0 0
\(115\) 7.21491 0.672794
\(116\) 0 0
\(117\) 2.31018 0.213576
\(118\) 0 0
\(119\) 7.93077 0.727012
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −3.87901 −0.349758
\(124\) 0 0
\(125\) 21.4263 1.91642
\(126\) 0 0
\(127\) 18.8487 1.67255 0.836274 0.548312i \(-0.184729\pi\)
0.836274 + 0.548312i \(0.184729\pi\)
\(128\) 0 0
\(129\) 0.883951 0.0778275
\(130\) 0 0
\(131\) 1.19981 0.104828 0.0524139 0.998625i \(-0.483308\pi\)
0.0524139 + 0.998625i \(0.483308\pi\)
\(132\) 0 0
\(133\) 4.36492 0.378487
\(134\) 0 0
\(135\) 17.3362 1.49206
\(136\) 0 0
\(137\) 16.4439 1.40490 0.702449 0.711734i \(-0.252090\pi\)
0.702449 + 0.711734i \(0.252090\pi\)
\(138\) 0 0
\(139\) −3.25701 −0.276256 −0.138128 0.990414i \(-0.544109\pi\)
−0.138128 + 0.990414i \(0.544109\pi\)
\(140\) 0 0
\(141\) −1.87326 −0.157757
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −17.4599 −1.44997
\(146\) 0 0
\(147\) −0.830554 −0.0685029
\(148\) 0 0
\(149\) 4.49350 0.368122 0.184061 0.982915i \(-0.441076\pi\)
0.184061 + 0.982915i \(0.441076\pi\)
\(150\) 0 0
\(151\) 2.14725 0.174741 0.0873704 0.996176i \(-0.472154\pi\)
0.0873704 + 0.996176i \(0.472154\pi\)
\(152\) 0 0
\(153\) −18.3215 −1.48121
\(154\) 0 0
\(155\) 6.35070 0.510101
\(156\) 0 0
\(157\) −6.17417 −0.492752 −0.246376 0.969174i \(-0.579240\pi\)
−0.246376 + 0.969174i \(0.579240\pi\)
\(158\) 0 0
\(159\) 2.69178 0.213472
\(160\) 0 0
\(161\) 1.83550 0.144658
\(162\) 0 0
\(163\) −9.83527 −0.770358 −0.385179 0.922842i \(-0.625860\pi\)
−0.385179 + 0.922842i \(0.625860\pi\)
\(164\) 0 0
\(165\) 3.26471 0.254158
\(166\) 0 0
\(167\) 15.4054 1.19211 0.596055 0.802944i \(-0.296734\pi\)
0.596055 + 0.802944i \(0.296734\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −10.0838 −0.771124
\(172\) 0 0
\(173\) 3.15001 0.239491 0.119745 0.992805i \(-0.461792\pi\)
0.119745 + 0.992805i \(0.461792\pi\)
\(174\) 0 0
\(175\) 10.4509 0.790015
\(176\) 0 0
\(177\) 8.67801 0.652279
\(178\) 0 0
\(179\) 9.75182 0.728885 0.364443 0.931226i \(-0.381260\pi\)
0.364443 + 0.931226i \(0.381260\pi\)
\(180\) 0 0
\(181\) −4.93982 −0.367174 −0.183587 0.983003i \(-0.558771\pi\)
−0.183587 + 0.983003i \(0.558771\pi\)
\(182\) 0 0
\(183\) −1.58198 −0.116944
\(184\) 0 0
\(185\) 22.4871 1.65328
\(186\) 0 0
\(187\) −7.93077 −0.579955
\(188\) 0 0
\(189\) 4.41039 0.320809
\(190\) 0 0
\(191\) −17.0156 −1.23121 −0.615605 0.788055i \(-0.711088\pi\)
−0.615605 + 0.788055i \(0.711088\pi\)
\(192\) 0 0
\(193\) 21.0178 1.51290 0.756448 0.654053i \(-0.226933\pi\)
0.756448 + 0.654053i \(0.226933\pi\)
\(194\) 0 0
\(195\) 3.26471 0.233791
\(196\) 0 0
\(197\) −8.39617 −0.598202 −0.299101 0.954221i \(-0.596687\pi\)
−0.299101 + 0.954221i \(0.596687\pi\)
\(198\) 0 0
\(199\) 5.20069 0.368667 0.184334 0.982864i \(-0.440987\pi\)
0.184334 + 0.982864i \(0.440987\pi\)
\(200\) 0 0
\(201\) 3.24497 0.228883
\(202\) 0 0
\(203\) −4.44186 −0.311758
\(204\) 0 0
\(205\) 18.3582 1.28219
\(206\) 0 0
\(207\) −4.24033 −0.294723
\(208\) 0 0
\(209\) −4.36492 −0.301928
\(210\) 0 0
\(211\) 7.07667 0.487178 0.243589 0.969879i \(-0.421675\pi\)
0.243589 + 0.969879i \(0.421675\pi\)
\(212\) 0 0
\(213\) −6.71996 −0.460444
\(214\) 0 0
\(215\) −4.18348 −0.285311
\(216\) 0 0
\(217\) 1.61564 0.109677
\(218\) 0 0
\(219\) 7.16327 0.484049
\(220\) 0 0
\(221\) −7.93077 −0.533481
\(222\) 0 0
\(223\) 8.44156 0.565289 0.282644 0.959225i \(-0.408788\pi\)
0.282644 + 0.959225i \(0.408788\pi\)
\(224\) 0 0
\(225\) −24.1435 −1.60957
\(226\) 0 0
\(227\) −12.9815 −0.861611 −0.430806 0.902445i \(-0.641771\pi\)
−0.430806 + 0.902445i \(0.641771\pi\)
\(228\) 0 0
\(229\) 2.04884 0.135391 0.0676956 0.997706i \(-0.478435\pi\)
0.0676956 + 0.997706i \(0.478435\pi\)
\(230\) 0 0
\(231\) 0.830554 0.0546464
\(232\) 0 0
\(233\) −24.7160 −1.61920 −0.809601 0.586980i \(-0.800317\pi\)
−0.809601 + 0.586980i \(0.800317\pi\)
\(234\) 0 0
\(235\) 8.86559 0.578327
\(236\) 0 0
\(237\) 8.36133 0.543126
\(238\) 0 0
\(239\) 0.455859 0.0294870 0.0147435 0.999891i \(-0.495307\pi\)
0.0147435 + 0.999891i \(0.495307\pi\)
\(240\) 0 0
\(241\) 20.5360 1.32284 0.661421 0.750015i \(-0.269954\pi\)
0.661421 + 0.750015i \(0.269954\pi\)
\(242\) 0 0
\(243\) −15.9450 −1.02287
\(244\) 0 0
\(245\) 3.93077 0.251127
\(246\) 0 0
\(247\) −4.36492 −0.277733
\(248\) 0 0
\(249\) 10.2795 0.651440
\(250\) 0 0
\(251\) 6.76749 0.427160 0.213580 0.976926i \(-0.431488\pi\)
0.213580 + 0.976926i \(0.431488\pi\)
\(252\) 0 0
\(253\) −1.83550 −0.115397
\(254\) 0 0
\(255\) −25.8917 −1.62140
\(256\) 0 0
\(257\) 14.2396 0.888242 0.444121 0.895967i \(-0.353516\pi\)
0.444121 + 0.895967i \(0.353516\pi\)
\(258\) 0 0
\(259\) 5.72080 0.355473
\(260\) 0 0
\(261\) 10.2615 0.635171
\(262\) 0 0
\(263\) −20.7298 −1.27826 −0.639129 0.769100i \(-0.720705\pi\)
−0.639129 + 0.769100i \(0.720705\pi\)
\(264\) 0 0
\(265\) −12.7394 −0.782575
\(266\) 0 0
\(267\) −0.0216207 −0.00132316
\(268\) 0 0
\(269\) −8.34116 −0.508569 −0.254285 0.967129i \(-0.581840\pi\)
−0.254285 + 0.967129i \(0.581840\pi\)
\(270\) 0 0
\(271\) 17.3516 1.05404 0.527018 0.849854i \(-0.323310\pi\)
0.527018 + 0.849854i \(0.323310\pi\)
\(272\) 0 0
\(273\) 0.830554 0.0502674
\(274\) 0 0
\(275\) −10.4509 −0.630214
\(276\) 0 0
\(277\) 22.7417 1.36641 0.683207 0.730225i \(-0.260585\pi\)
0.683207 + 0.730225i \(0.260585\pi\)
\(278\) 0 0
\(279\) −3.73242 −0.223454
\(280\) 0 0
\(281\) −30.4118 −1.81421 −0.907107 0.420900i \(-0.861714\pi\)
−0.907107 + 0.420900i \(0.861714\pi\)
\(282\) 0 0
\(283\) −12.0239 −0.714746 −0.357373 0.933962i \(-0.616327\pi\)
−0.357373 + 0.933962i \(0.616327\pi\)
\(284\) 0 0
\(285\) −14.2502 −0.844110
\(286\) 0 0
\(287\) 4.67038 0.275684
\(288\) 0 0
\(289\) 45.8970 2.69983
\(290\) 0 0
\(291\) 0.943335 0.0552992
\(292\) 0 0
\(293\) 19.3103 1.12812 0.564059 0.825735i \(-0.309239\pi\)
0.564059 + 0.825735i \(0.309239\pi\)
\(294\) 0 0
\(295\) −41.0704 −2.39121
\(296\) 0 0
\(297\) −4.41039 −0.255917
\(298\) 0 0
\(299\) −1.83550 −0.106150
\(300\) 0 0
\(301\) −1.06429 −0.0613447
\(302\) 0 0
\(303\) −7.61120 −0.437252
\(304\) 0 0
\(305\) 7.48706 0.428708
\(306\) 0 0
\(307\) 28.1514 1.60669 0.803344 0.595516i \(-0.203052\pi\)
0.803344 + 0.595516i \(0.203052\pi\)
\(308\) 0 0
\(309\) 14.3673 0.817327
\(310\) 0 0
\(311\) 5.69117 0.322716 0.161358 0.986896i \(-0.448413\pi\)
0.161358 + 0.986896i \(0.448413\pi\)
\(312\) 0 0
\(313\) 8.09286 0.457435 0.228718 0.973493i \(-0.426547\pi\)
0.228718 + 0.973493i \(0.426547\pi\)
\(314\) 0 0
\(315\) −9.08078 −0.511644
\(316\) 0 0
\(317\) −11.6538 −0.654544 −0.327272 0.944930i \(-0.606129\pi\)
−0.327272 + 0.944930i \(0.606129\pi\)
\(318\) 0 0
\(319\) 4.44186 0.248697
\(320\) 0 0
\(321\) 4.16047 0.232215
\(322\) 0 0
\(323\) 34.6172 1.92615
\(324\) 0 0
\(325\) −10.4509 −0.579712
\(326\) 0 0
\(327\) −7.22106 −0.399326
\(328\) 0 0
\(329\) 2.25544 0.124346
\(330\) 0 0
\(331\) 18.3359 1.00783 0.503917 0.863752i \(-0.331892\pi\)
0.503917 + 0.863752i \(0.331892\pi\)
\(332\) 0 0
\(333\) −13.2161 −0.724236
\(334\) 0 0
\(335\) −15.3575 −0.839069
\(336\) 0 0
\(337\) −24.8600 −1.35421 −0.677104 0.735887i \(-0.736765\pi\)
−0.677104 + 0.735887i \(0.736765\pi\)
\(338\) 0 0
\(339\) −14.4205 −0.783212
\(340\) 0 0
\(341\) −1.61564 −0.0874918
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −5.99238 −0.322619
\(346\) 0 0
\(347\) 13.8423 0.743095 0.371547 0.928414i \(-0.378827\pi\)
0.371547 + 0.928414i \(0.378827\pi\)
\(348\) 0 0
\(349\) 0.573934 0.0307220 0.0153610 0.999882i \(-0.495110\pi\)
0.0153610 + 0.999882i \(0.495110\pi\)
\(350\) 0 0
\(351\) −4.41039 −0.235409
\(352\) 0 0
\(353\) −4.20042 −0.223566 −0.111783 0.993733i \(-0.535656\pi\)
−0.111783 + 0.993733i \(0.535656\pi\)
\(354\) 0 0
\(355\) 31.8036 1.68796
\(356\) 0 0
\(357\) −6.58693 −0.348617
\(358\) 0 0
\(359\) −24.7380 −1.30562 −0.652810 0.757522i \(-0.726410\pi\)
−0.652810 + 0.757522i \(0.726410\pi\)
\(360\) 0 0
\(361\) 0.0525588 0.00276625
\(362\) 0 0
\(363\) −0.830554 −0.0435928
\(364\) 0 0
\(365\) −33.9016 −1.77449
\(366\) 0 0
\(367\) −19.1792 −1.00115 −0.500573 0.865694i \(-0.666877\pi\)
−0.500573 + 0.865694i \(0.666877\pi\)
\(368\) 0 0
\(369\) −10.7894 −0.561675
\(370\) 0 0
\(371\) −3.24095 −0.168261
\(372\) 0 0
\(373\) 9.59935 0.497036 0.248518 0.968627i \(-0.420057\pi\)
0.248518 + 0.968627i \(0.420057\pi\)
\(374\) 0 0
\(375\) −17.7957 −0.918964
\(376\) 0 0
\(377\) 4.44186 0.228768
\(378\) 0 0
\(379\) 3.41932 0.175639 0.0878195 0.996136i \(-0.472010\pi\)
0.0878195 + 0.996136i \(0.472010\pi\)
\(380\) 0 0
\(381\) −15.6548 −0.802021
\(382\) 0 0
\(383\) −23.7390 −1.21301 −0.606503 0.795082i \(-0.707428\pi\)
−0.606503 + 0.795082i \(0.707428\pi\)
\(384\) 0 0
\(385\) −3.93077 −0.200330
\(386\) 0 0
\(387\) 2.45870 0.124983
\(388\) 0 0
\(389\) 30.2210 1.53227 0.766133 0.642682i \(-0.222178\pi\)
0.766133 + 0.642682i \(0.222178\pi\)
\(390\) 0 0
\(391\) 14.5569 0.736174
\(392\) 0 0
\(393\) −0.996506 −0.0502671
\(394\) 0 0
\(395\) −39.5717 −1.99107
\(396\) 0 0
\(397\) −1.79536 −0.0901067 −0.0450534 0.998985i \(-0.514346\pi\)
−0.0450534 + 0.998985i \(0.514346\pi\)
\(398\) 0 0
\(399\) −3.62530 −0.181492
\(400\) 0 0
\(401\) 36.3314 1.81430 0.907151 0.420804i \(-0.138252\pi\)
0.907151 + 0.420804i \(0.138252\pi\)
\(402\) 0 0
\(403\) −1.61564 −0.0804808
\(404\) 0 0
\(405\) 12.8437 0.638207
\(406\) 0 0
\(407\) −5.72080 −0.283569
\(408\) 0 0
\(409\) −34.1855 −1.69036 −0.845182 0.534478i \(-0.820508\pi\)
−0.845182 + 0.534478i \(0.820508\pi\)
\(410\) 0 0
\(411\) −13.6575 −0.673677
\(412\) 0 0
\(413\) −10.4485 −0.514135
\(414\) 0 0
\(415\) −48.6500 −2.38814
\(416\) 0 0
\(417\) 2.70512 0.132470
\(418\) 0 0
\(419\) −35.0201 −1.71084 −0.855422 0.517932i \(-0.826702\pi\)
−0.855422 + 0.517932i \(0.826702\pi\)
\(420\) 0 0
\(421\) −0.581067 −0.0283195 −0.0141597 0.999900i \(-0.504507\pi\)
−0.0141597 + 0.999900i \(0.504507\pi\)
\(422\) 0 0
\(423\) −5.21046 −0.253341
\(424\) 0 0
\(425\) 82.8837 4.02045
\(426\) 0 0
\(427\) 1.90473 0.0921765
\(428\) 0 0
\(429\) −0.830554 −0.0400995
\(430\) 0 0
\(431\) 5.84827 0.281701 0.140851 0.990031i \(-0.455016\pi\)
0.140851 + 0.990031i \(0.455016\pi\)
\(432\) 0 0
\(433\) 21.1995 1.01878 0.509391 0.860535i \(-0.329871\pi\)
0.509391 + 0.860535i \(0.329871\pi\)
\(434\) 0 0
\(435\) 14.5014 0.695289
\(436\) 0 0
\(437\) 8.01181 0.383257
\(438\) 0 0
\(439\) 4.94511 0.236017 0.118009 0.993013i \(-0.462349\pi\)
0.118009 + 0.993013i \(0.462349\pi\)
\(440\) 0 0
\(441\) −2.31018 −0.110009
\(442\) 0 0
\(443\) −3.00276 −0.142665 −0.0713327 0.997453i \(-0.522725\pi\)
−0.0713327 + 0.997453i \(0.522725\pi\)
\(444\) 0 0
\(445\) 0.102324 0.00485064
\(446\) 0 0
\(447\) −3.73210 −0.176522
\(448\) 0 0
\(449\) 1.48142 0.0699127 0.0349563 0.999389i \(-0.488871\pi\)
0.0349563 + 0.999389i \(0.488871\pi\)
\(450\) 0 0
\(451\) −4.67038 −0.219920
\(452\) 0 0
\(453\) −1.78341 −0.0837918
\(454\) 0 0
\(455\) −3.93077 −0.184277
\(456\) 0 0
\(457\) −17.6396 −0.825146 −0.412573 0.910925i \(-0.635370\pi\)
−0.412573 + 0.910925i \(0.635370\pi\)
\(458\) 0 0
\(459\) 34.9778 1.63262
\(460\) 0 0
\(461\) 36.3214 1.69166 0.845828 0.533456i \(-0.179107\pi\)
0.845828 + 0.533456i \(0.179107\pi\)
\(462\) 0 0
\(463\) −0.723252 −0.0336124 −0.0168062 0.999859i \(-0.505350\pi\)
−0.0168062 + 0.999859i \(0.505350\pi\)
\(464\) 0 0
\(465\) −5.27460 −0.244604
\(466\) 0 0
\(467\) 32.3836 1.49853 0.749266 0.662269i \(-0.230406\pi\)
0.749266 + 0.662269i \(0.230406\pi\)
\(468\) 0 0
\(469\) −3.90700 −0.180408
\(470\) 0 0
\(471\) 5.12798 0.236285
\(472\) 0 0
\(473\) 1.06429 0.0489361
\(474\) 0 0
\(475\) 45.6174 2.09307
\(476\) 0 0
\(477\) 7.48717 0.342814
\(478\) 0 0
\(479\) 1.14341 0.0522439 0.0261220 0.999659i \(-0.491684\pi\)
0.0261220 + 0.999659i \(0.491684\pi\)
\(480\) 0 0
\(481\) −5.72080 −0.260846
\(482\) 0 0
\(483\) −1.52448 −0.0693663
\(484\) 0 0
\(485\) −4.46452 −0.202723
\(486\) 0 0
\(487\) −8.62251 −0.390723 −0.195362 0.980731i \(-0.562588\pi\)
−0.195362 + 0.980731i \(0.562588\pi\)
\(488\) 0 0
\(489\) 8.16873 0.369403
\(490\) 0 0
\(491\) 2.45206 0.110660 0.0553299 0.998468i \(-0.482379\pi\)
0.0553299 + 0.998468i \(0.482379\pi\)
\(492\) 0 0
\(493\) −35.2274 −1.58656
\(494\) 0 0
\(495\) 9.08078 0.408150
\(496\) 0 0
\(497\) 8.09094 0.362928
\(498\) 0 0
\(499\) 19.0621 0.853336 0.426668 0.904408i \(-0.359687\pi\)
0.426668 + 0.904408i \(0.359687\pi\)
\(500\) 0 0
\(501\) −12.7951 −0.571641
\(502\) 0 0
\(503\) −16.3290 −0.728073 −0.364037 0.931385i \(-0.618602\pi\)
−0.364037 + 0.931385i \(0.618602\pi\)
\(504\) 0 0
\(505\) 36.0216 1.60294
\(506\) 0 0
\(507\) −0.830554 −0.0368862
\(508\) 0 0
\(509\) −24.0299 −1.06511 −0.532554 0.846396i \(-0.678768\pi\)
−0.532554 + 0.846396i \(0.678768\pi\)
\(510\) 0 0
\(511\) −8.62469 −0.381534
\(512\) 0 0
\(513\) 19.2510 0.849953
\(514\) 0 0
\(515\) −67.9961 −2.99627
\(516\) 0 0
\(517\) −2.25544 −0.0991940
\(518\) 0 0
\(519\) −2.61625 −0.114841
\(520\) 0 0
\(521\) 15.2769 0.669292 0.334646 0.942344i \(-0.391383\pi\)
0.334646 + 0.942344i \(0.391383\pi\)
\(522\) 0 0
\(523\) 4.76481 0.208351 0.104175 0.994559i \(-0.466780\pi\)
0.104175 + 0.994559i \(0.466780\pi\)
\(524\) 0 0
\(525\) −8.68005 −0.378828
\(526\) 0 0
\(527\) 12.8133 0.558155
\(528\) 0 0
\(529\) −19.6309 −0.853519
\(530\) 0 0
\(531\) 24.1378 1.04749
\(532\) 0 0
\(533\) −4.67038 −0.202297
\(534\) 0 0
\(535\) −19.6903 −0.851285
\(536\) 0 0
\(537\) −8.09941 −0.349515
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 5.30174 0.227940 0.113970 0.993484i \(-0.463643\pi\)
0.113970 + 0.993484i \(0.463643\pi\)
\(542\) 0 0
\(543\) 4.10278 0.176067
\(544\) 0 0
\(545\) 34.1751 1.46390
\(546\) 0 0
\(547\) 25.9714 1.11046 0.555229 0.831697i \(-0.312631\pi\)
0.555229 + 0.831697i \(0.312631\pi\)
\(548\) 0 0
\(549\) −4.40028 −0.187799
\(550\) 0 0
\(551\) −19.3884 −0.825973
\(552\) 0 0
\(553\) −10.0672 −0.428100
\(554\) 0 0
\(555\) −18.6768 −0.792784
\(556\) 0 0
\(557\) −12.3002 −0.521178 −0.260589 0.965450i \(-0.583917\pi\)
−0.260589 + 0.965450i \(0.583917\pi\)
\(558\) 0 0
\(559\) 1.06429 0.0450147
\(560\) 0 0
\(561\) 6.58693 0.278100
\(562\) 0 0
\(563\) 7.73805 0.326120 0.163060 0.986616i \(-0.447864\pi\)
0.163060 + 0.986616i \(0.447864\pi\)
\(564\) 0 0
\(565\) 68.2478 2.87121
\(566\) 0 0
\(567\) 3.26747 0.137221
\(568\) 0 0
\(569\) 11.4204 0.478768 0.239384 0.970925i \(-0.423054\pi\)
0.239384 + 0.970925i \(0.423054\pi\)
\(570\) 0 0
\(571\) 40.6088 1.69943 0.849713 0.527245i \(-0.176775\pi\)
0.849713 + 0.527245i \(0.176775\pi\)
\(572\) 0 0
\(573\) 14.1324 0.590390
\(574\) 0 0
\(575\) 19.1826 0.799971
\(576\) 0 0
\(577\) −19.8823 −0.827710 −0.413855 0.910343i \(-0.635818\pi\)
−0.413855 + 0.910343i \(0.635818\pi\)
\(578\) 0 0
\(579\) −17.4564 −0.725465
\(580\) 0 0
\(581\) −12.3767 −0.513473
\(582\) 0 0
\(583\) 3.24095 0.134226
\(584\) 0 0
\(585\) 9.08078 0.375444
\(586\) 0 0
\(587\) −43.8388 −1.80942 −0.904711 0.426025i \(-0.859913\pi\)
−0.904711 + 0.426025i \(0.859913\pi\)
\(588\) 0 0
\(589\) 7.05215 0.290579
\(590\) 0 0
\(591\) 6.97347 0.286850
\(592\) 0 0
\(593\) 14.9247 0.612884 0.306442 0.951889i \(-0.400861\pi\)
0.306442 + 0.951889i \(0.400861\pi\)
\(594\) 0 0
\(595\) 31.1740 1.27801
\(596\) 0 0
\(597\) −4.31946 −0.176784
\(598\) 0 0
\(599\) 17.6022 0.719206 0.359603 0.933105i \(-0.382912\pi\)
0.359603 + 0.933105i \(0.382912\pi\)
\(600\) 0 0
\(601\) 6.88188 0.280718 0.140359 0.990101i \(-0.455174\pi\)
0.140359 + 0.990101i \(0.455174\pi\)
\(602\) 0 0
\(603\) 9.02587 0.367562
\(604\) 0 0
\(605\) 3.93077 0.159808
\(606\) 0 0
\(607\) 25.2321 1.02414 0.512070 0.858944i \(-0.328879\pi\)
0.512070 + 0.858944i \(0.328879\pi\)
\(608\) 0 0
\(609\) 3.68921 0.149494
\(610\) 0 0
\(611\) −2.25544 −0.0912452
\(612\) 0 0
\(613\) −46.7285 −1.88735 −0.943673 0.330878i \(-0.892655\pi\)
−0.943673 + 0.330878i \(0.892655\pi\)
\(614\) 0 0
\(615\) −15.2475 −0.614837
\(616\) 0 0
\(617\) 31.6513 1.27423 0.637117 0.770767i \(-0.280127\pi\)
0.637117 + 0.770767i \(0.280127\pi\)
\(618\) 0 0
\(619\) −36.7582 −1.47744 −0.738719 0.674014i \(-0.764569\pi\)
−0.738719 + 0.674014i \(0.764569\pi\)
\(620\) 0 0
\(621\) 8.09527 0.324852
\(622\) 0 0
\(623\) 0.0260316 0.00104294
\(624\) 0 0
\(625\) 31.9670 1.27868
\(626\) 0 0
\(627\) 3.62530 0.144781
\(628\) 0 0
\(629\) 45.3703 1.80903
\(630\) 0 0
\(631\) 43.7174 1.74036 0.870180 0.492734i \(-0.164002\pi\)
0.870180 + 0.492734i \(0.164002\pi\)
\(632\) 0 0
\(633\) −5.87756 −0.233612
\(634\) 0 0
\(635\) 74.0896 2.94016
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −18.6915 −0.739425
\(640\) 0 0
\(641\) 15.5013 0.612264 0.306132 0.951989i \(-0.400965\pi\)
0.306132 + 0.951989i \(0.400965\pi\)
\(642\) 0 0
\(643\) −11.4587 −0.451885 −0.225943 0.974141i \(-0.572546\pi\)
−0.225943 + 0.974141i \(0.572546\pi\)
\(644\) 0 0
\(645\) 3.47460 0.136812
\(646\) 0 0
\(647\) −27.3797 −1.07641 −0.538204 0.842815i \(-0.680897\pi\)
−0.538204 + 0.842815i \(0.680897\pi\)
\(648\) 0 0
\(649\) 10.4485 0.410138
\(650\) 0 0
\(651\) −1.34188 −0.0525923
\(652\) 0 0
\(653\) 22.2087 0.869095 0.434548 0.900649i \(-0.356908\pi\)
0.434548 + 0.900649i \(0.356908\pi\)
\(654\) 0 0
\(655\) 4.71617 0.184276
\(656\) 0 0
\(657\) 19.9246 0.777332
\(658\) 0 0
\(659\) 38.8773 1.51444 0.757221 0.653158i \(-0.226556\pi\)
0.757221 + 0.653158i \(0.226556\pi\)
\(660\) 0 0
\(661\) −10.1744 −0.395736 −0.197868 0.980229i \(-0.563402\pi\)
−0.197868 + 0.980229i \(0.563402\pi\)
\(662\) 0 0
\(663\) 6.58693 0.255815
\(664\) 0 0
\(665\) 17.1575 0.665339
\(666\) 0 0
\(667\) −8.15303 −0.315687
\(668\) 0 0
\(669\) −7.01117 −0.271067
\(670\) 0 0
\(671\) −1.90473 −0.0735314
\(672\) 0 0
\(673\) −21.2566 −0.819380 −0.409690 0.912225i \(-0.634363\pi\)
−0.409690 + 0.912225i \(0.634363\pi\)
\(674\) 0 0
\(675\) 46.0926 1.77411
\(676\) 0 0
\(677\) −29.8385 −1.14679 −0.573393 0.819280i \(-0.694373\pi\)
−0.573393 + 0.819280i \(0.694373\pi\)
\(678\) 0 0
\(679\) −1.13579 −0.0435876
\(680\) 0 0
\(681\) 10.7818 0.413160
\(682\) 0 0
\(683\) −36.0336 −1.37879 −0.689394 0.724386i \(-0.742123\pi\)
−0.689394 + 0.724386i \(0.742123\pi\)
\(684\) 0 0
\(685\) 64.6371 2.46966
\(686\) 0 0
\(687\) −1.70167 −0.0649229
\(688\) 0 0
\(689\) 3.24095 0.123470
\(690\) 0 0
\(691\) 42.2705 1.60804 0.804022 0.594599i \(-0.202689\pi\)
0.804022 + 0.594599i \(0.202689\pi\)
\(692\) 0 0
\(693\) 2.31018 0.0877565
\(694\) 0 0
\(695\) −12.8025 −0.485628
\(696\) 0 0
\(697\) 37.0397 1.40298
\(698\) 0 0
\(699\) 20.5280 0.776441
\(700\) 0 0
\(701\) −17.9241 −0.676985 −0.338493 0.940969i \(-0.609917\pi\)
−0.338493 + 0.940969i \(0.609917\pi\)
\(702\) 0 0
\(703\) 24.9708 0.941793
\(704\) 0 0
\(705\) −7.36335 −0.277320
\(706\) 0 0
\(707\) 9.16401 0.344648
\(708\) 0 0
\(709\) −5.92651 −0.222575 −0.111287 0.993788i \(-0.535497\pi\)
−0.111287 + 0.993788i \(0.535497\pi\)
\(710\) 0 0
\(711\) 23.2570 0.872205
\(712\) 0 0
\(713\) 2.96551 0.111059
\(714\) 0 0
\(715\) 3.93077 0.147002
\(716\) 0 0
\(717\) −0.378615 −0.0141396
\(718\) 0 0
\(719\) −28.0414 −1.04577 −0.522884 0.852404i \(-0.675144\pi\)
−0.522884 + 0.852404i \(0.675144\pi\)
\(720\) 0 0
\(721\) −17.2984 −0.644228
\(722\) 0 0
\(723\) −17.0563 −0.634330
\(724\) 0 0
\(725\) −46.4215 −1.72405
\(726\) 0 0
\(727\) −33.6093 −1.24650 −0.623250 0.782022i \(-0.714188\pi\)
−0.623250 + 0.782022i \(0.714188\pi\)
\(728\) 0 0
\(729\) 3.44075 0.127435
\(730\) 0 0
\(731\) −8.44064 −0.312188
\(732\) 0 0
\(733\) 12.5522 0.463626 0.231813 0.972760i \(-0.425534\pi\)
0.231813 + 0.972760i \(0.425534\pi\)
\(734\) 0 0
\(735\) −3.26471 −0.120421
\(736\) 0 0
\(737\) 3.90700 0.143916
\(738\) 0 0
\(739\) −19.5696 −0.719881 −0.359940 0.932975i \(-0.617203\pi\)
−0.359940 + 0.932975i \(0.617203\pi\)
\(740\) 0 0
\(741\) 3.62530 0.133179
\(742\) 0 0
\(743\) 19.1048 0.700889 0.350444 0.936584i \(-0.386031\pi\)
0.350444 + 0.936584i \(0.386031\pi\)
\(744\) 0 0
\(745\) 17.6629 0.647119
\(746\) 0 0
\(747\) 28.5925 1.04614
\(748\) 0 0
\(749\) −5.00928 −0.183035
\(750\) 0 0
\(751\) 42.8140 1.56231 0.781153 0.624340i \(-0.214632\pi\)
0.781153 + 0.624340i \(0.214632\pi\)
\(752\) 0 0
\(753\) −5.62077 −0.204832
\(754\) 0 0
\(755\) 8.44034 0.307175
\(756\) 0 0
\(757\) −5.92751 −0.215439 −0.107720 0.994181i \(-0.534355\pi\)
−0.107720 + 0.994181i \(0.534355\pi\)
\(758\) 0 0
\(759\) 1.52448 0.0553351
\(760\) 0 0
\(761\) −17.0440 −0.617843 −0.308922 0.951087i \(-0.599968\pi\)
−0.308922 + 0.951087i \(0.599968\pi\)
\(762\) 0 0
\(763\) 8.69427 0.314754
\(764\) 0 0
\(765\) −72.0175 −2.60380
\(766\) 0 0
\(767\) 10.4485 0.377272
\(768\) 0 0
\(769\) −27.2498 −0.982653 −0.491327 0.870975i \(-0.663488\pi\)
−0.491327 + 0.870975i \(0.663488\pi\)
\(770\) 0 0
\(771\) −11.8268 −0.425930
\(772\) 0 0
\(773\) −28.3900 −1.02112 −0.510559 0.859842i \(-0.670562\pi\)
−0.510559 + 0.859842i \(0.670562\pi\)
\(774\) 0 0
\(775\) 16.8849 0.606524
\(776\) 0 0
\(777\) −4.75143 −0.170457
\(778\) 0 0
\(779\) 20.3859 0.730400
\(780\) 0 0
\(781\) −8.09094 −0.289516
\(782\) 0 0
\(783\) −19.5904 −0.700102
\(784\) 0 0
\(785\) −24.2692 −0.866205
\(786\) 0 0
\(787\) −23.1949 −0.826811 −0.413405 0.910547i \(-0.635661\pi\)
−0.413405 + 0.910547i \(0.635661\pi\)
\(788\) 0 0
\(789\) 17.2173 0.612951
\(790\) 0 0
\(791\) 17.3625 0.617338
\(792\) 0 0
\(793\) −1.90473 −0.0676391
\(794\) 0 0
\(795\) 10.5808 0.375261
\(796\) 0 0
\(797\) 10.2174 0.361917 0.180959 0.983491i \(-0.442080\pi\)
0.180959 + 0.983491i \(0.442080\pi\)
\(798\) 0 0
\(799\) 17.8873 0.632808
\(800\) 0 0
\(801\) −0.0601378 −0.00212486
\(802\) 0 0
\(803\) 8.62469 0.304359
\(804\) 0 0
\(805\) 7.21491 0.254292
\(806\) 0 0
\(807\) 6.92778 0.243869
\(808\) 0 0
\(809\) −31.9180 −1.12218 −0.561089 0.827756i \(-0.689617\pi\)
−0.561089 + 0.827756i \(0.689617\pi\)
\(810\) 0 0
\(811\) −16.3797 −0.575170 −0.287585 0.957755i \(-0.592852\pi\)
−0.287585 + 0.957755i \(0.592852\pi\)
\(812\) 0 0
\(813\) −14.4115 −0.505432
\(814\) 0 0
\(815\) −38.6602 −1.35421
\(816\) 0 0
\(817\) −4.64555 −0.162527
\(818\) 0 0
\(819\) 2.31018 0.0807242
\(820\) 0 0
\(821\) 13.8567 0.483604 0.241802 0.970326i \(-0.422262\pi\)
0.241802 + 0.970326i \(0.422262\pi\)
\(822\) 0 0
\(823\) −1.49284 −0.0520372 −0.0260186 0.999661i \(-0.508283\pi\)
−0.0260186 + 0.999661i \(0.508283\pi\)
\(824\) 0 0
\(825\) 8.68005 0.302200
\(826\) 0 0
\(827\) −29.8158 −1.03680 −0.518398 0.855140i \(-0.673471\pi\)
−0.518398 + 0.855140i \(0.673471\pi\)
\(828\) 0 0
\(829\) 24.1800 0.839805 0.419903 0.907569i \(-0.362064\pi\)
0.419903 + 0.907569i \(0.362064\pi\)
\(830\) 0 0
\(831\) −18.8882 −0.655224
\(832\) 0 0
\(833\) 7.93077 0.274785
\(834\) 0 0
\(835\) 60.5552 2.09560
\(836\) 0 0
\(837\) 7.12561 0.246297
\(838\) 0 0
\(839\) 10.5044 0.362651 0.181325 0.983423i \(-0.441961\pi\)
0.181325 + 0.983423i \(0.441961\pi\)
\(840\) 0 0
\(841\) −9.26985 −0.319650
\(842\) 0 0
\(843\) 25.2586 0.869953
\(844\) 0 0
\(845\) 3.93077 0.135222
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 9.98649 0.342735
\(850\) 0 0
\(851\) 10.5005 0.359953
\(852\) 0 0
\(853\) −9.45198 −0.323630 −0.161815 0.986821i \(-0.551735\pi\)
−0.161815 + 0.986821i \(0.551735\pi\)
\(854\) 0 0
\(855\) −39.6369 −1.35555
\(856\) 0 0
\(857\) 34.6464 1.18350 0.591748 0.806123i \(-0.298438\pi\)
0.591748 + 0.806123i \(0.298438\pi\)
\(858\) 0 0
\(859\) 22.6704 0.773503 0.386751 0.922184i \(-0.373597\pi\)
0.386751 + 0.922184i \(0.373597\pi\)
\(860\) 0 0
\(861\) −3.87901 −0.132196
\(862\) 0 0
\(863\) 19.9863 0.680343 0.340172 0.940363i \(-0.389515\pi\)
0.340172 + 0.940363i \(0.389515\pi\)
\(864\) 0 0
\(865\) 12.3819 0.420999
\(866\) 0 0
\(867\) −38.1200 −1.29462
\(868\) 0 0
\(869\) 10.0672 0.341505
\(870\) 0 0
\(871\) 3.90700 0.132384
\(872\) 0 0
\(873\) 2.62388 0.0888048
\(874\) 0 0
\(875\) 21.4263 0.724340
\(876\) 0 0
\(877\) −22.4779 −0.759024 −0.379512 0.925187i \(-0.623908\pi\)
−0.379512 + 0.925187i \(0.623908\pi\)
\(878\) 0 0
\(879\) −16.0382 −0.540955
\(880\) 0 0
\(881\) 7.77915 0.262086 0.131043 0.991377i \(-0.458167\pi\)
0.131043 + 0.991377i \(0.458167\pi\)
\(882\) 0 0
\(883\) −28.7808 −0.968550 −0.484275 0.874916i \(-0.660916\pi\)
−0.484275 + 0.874916i \(0.660916\pi\)
\(884\) 0 0
\(885\) 34.1112 1.14664
\(886\) 0 0
\(887\) 30.5794 1.02676 0.513379 0.858162i \(-0.328394\pi\)
0.513379 + 0.858162i \(0.328394\pi\)
\(888\) 0 0
\(889\) 18.8487 0.632164
\(890\) 0 0
\(891\) −3.26747 −0.109464
\(892\) 0 0
\(893\) 9.84481 0.329444
\(894\) 0 0
\(895\) 38.3321 1.28130
\(896\) 0 0
\(897\) 1.52448 0.0509009
\(898\) 0 0
\(899\) −7.17645 −0.239348
\(900\) 0 0
\(901\) −25.7032 −0.856297
\(902\) 0 0
\(903\) 0.883951 0.0294160
\(904\) 0 0
\(905\) −19.4173 −0.645451
\(906\) 0 0
\(907\) 24.7371 0.821382 0.410691 0.911775i \(-0.365288\pi\)
0.410691 + 0.911775i \(0.365288\pi\)
\(908\) 0 0
\(909\) −21.1705 −0.702181
\(910\) 0 0
\(911\) 14.5877 0.483311 0.241655 0.970362i \(-0.422310\pi\)
0.241655 + 0.970362i \(0.422310\pi\)
\(912\) 0 0
\(913\) 12.3767 0.409610
\(914\) 0 0
\(915\) −6.21841 −0.205574
\(916\) 0 0
\(917\) 1.19981 0.0396212
\(918\) 0 0
\(919\) −57.3669 −1.89236 −0.946180 0.323641i \(-0.895093\pi\)
−0.946180 + 0.323641i \(0.895093\pi\)
\(920\) 0 0
\(921\) −23.3813 −0.770440
\(922\) 0 0
\(923\) −8.09094 −0.266316
\(924\) 0 0
\(925\) 59.7875 1.96580
\(926\) 0 0
\(927\) 39.9625 1.31254
\(928\) 0 0
\(929\) 14.0393 0.460614 0.230307 0.973118i \(-0.426027\pi\)
0.230307 + 0.973118i \(0.426027\pi\)
\(930\) 0 0
\(931\) 4.36492 0.143055
\(932\) 0 0
\(933\) −4.72682 −0.154749
\(934\) 0 0
\(935\) −31.1740 −1.01950
\(936\) 0 0
\(937\) 9.76400 0.318976 0.159488 0.987200i \(-0.449016\pi\)
0.159488 + 0.987200i \(0.449016\pi\)
\(938\) 0 0
\(939\) −6.72155 −0.219350
\(940\) 0 0
\(941\) −25.9364 −0.845501 −0.422751 0.906246i \(-0.638935\pi\)
−0.422751 + 0.906246i \(0.638935\pi\)
\(942\) 0 0
\(943\) 8.57248 0.279158
\(944\) 0 0
\(945\) 17.3362 0.563947
\(946\) 0 0
\(947\) 7.04401 0.228900 0.114450 0.993429i \(-0.463490\pi\)
0.114450 + 0.993429i \(0.463490\pi\)
\(948\) 0 0
\(949\) 8.62469 0.279969
\(950\) 0 0
\(951\) 9.67913 0.313867
\(952\) 0 0
\(953\) −49.5112 −1.60383 −0.801913 0.597441i \(-0.796184\pi\)
−0.801913 + 0.597441i \(0.796184\pi\)
\(954\) 0 0
\(955\) −66.8845 −2.16433
\(956\) 0 0
\(957\) −3.68921 −0.119255
\(958\) 0 0
\(959\) 16.4439 0.531001
\(960\) 0 0
\(961\) −28.3897 −0.915797
\(962\) 0 0
\(963\) 11.5723 0.372913
\(964\) 0 0
\(965\) 82.6162 2.65951
\(966\) 0 0
\(967\) −6.79115 −0.218389 −0.109194 0.994020i \(-0.534827\pi\)
−0.109194 + 0.994020i \(0.534827\pi\)
\(968\) 0 0
\(969\) −28.7514 −0.923629
\(970\) 0 0
\(971\) 44.0252 1.41283 0.706417 0.707796i \(-0.250310\pi\)
0.706417 + 0.707796i \(0.250310\pi\)
\(972\) 0 0
\(973\) −3.25701 −0.104415
\(974\) 0 0
\(975\) 8.68005 0.277984
\(976\) 0 0
\(977\) 7.69910 0.246316 0.123158 0.992387i \(-0.460698\pi\)
0.123158 + 0.992387i \(0.460698\pi\)
\(978\) 0 0
\(979\) −0.0260316 −0.000831975 0
\(980\) 0 0
\(981\) −20.0853 −0.641275
\(982\) 0 0
\(983\) 3.70465 0.118160 0.0590800 0.998253i \(-0.481183\pi\)
0.0590800 + 0.998253i \(0.481183\pi\)
\(984\) 0 0
\(985\) −33.0034 −1.05157
\(986\) 0 0
\(987\) −1.87326 −0.0596266
\(988\) 0 0
\(989\) −1.95350 −0.0621178
\(990\) 0 0
\(991\) 54.0033 1.71547 0.857736 0.514091i \(-0.171871\pi\)
0.857736 + 0.514091i \(0.171871\pi\)
\(992\) 0 0
\(993\) −15.2290 −0.483277
\(994\) 0 0
\(995\) 20.4427 0.648077
\(996\) 0 0
\(997\) −15.5895 −0.493725 −0.246863 0.969050i \(-0.579400\pi\)
−0.246863 + 0.969050i \(0.579400\pi\)
\(998\) 0 0
\(999\) 25.2309 0.798272
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 \(a_p\))