Properties

Label 8008.2.a.y.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.22236\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.22236 q^{3} +1.94503 q^{5} +1.00000 q^{7} +7.38359 q^{9} +O(q^{10})\) \(q-3.22236 q^{3} +1.94503 q^{5} +1.00000 q^{7} +7.38359 q^{9} -1.00000 q^{11} -1.00000 q^{13} -6.26757 q^{15} +4.63936 q^{17} -4.17867 q^{19} -3.22236 q^{21} +6.50523 q^{23} -1.21688 q^{25} -14.1255 q^{27} +3.35077 q^{29} -7.82311 q^{31} +3.22236 q^{33} +1.94503 q^{35} +3.35205 q^{37} +3.22236 q^{39} -5.66737 q^{41} -1.16924 q^{43} +14.3613 q^{45} +10.7539 q^{47} +1.00000 q^{49} -14.9497 q^{51} -11.5881 q^{53} -1.94503 q^{55} +13.4652 q^{57} -10.3841 q^{59} -4.96940 q^{61} +7.38359 q^{63} -1.94503 q^{65} -10.1690 q^{67} -20.9622 q^{69} -0.157313 q^{71} +1.45524 q^{73} +3.92121 q^{75} -1.00000 q^{77} -15.4350 q^{79} +23.3666 q^{81} -4.26464 q^{83} +9.02367 q^{85} -10.7974 q^{87} +14.4609 q^{89} -1.00000 q^{91} +25.2089 q^{93} -8.12762 q^{95} -6.52587 q^{97} -7.38359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) −3.22236 −1.86043 −0.930215 0.367016i \(-0.880379\pi\)
−0.930215 + 0.367016i \(0.880379\pi\)
\(4\) 0 0
\(5\) 1.94503 0.869842 0.434921 0.900469i \(-0.356776\pi\)
0.434921 + 0.900469i \(0.356776\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 7.38359 2.46120
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −6.26757 −1.61828
\(16\) 0 0
\(17\) 4.63936 1.12521 0.562605 0.826726i \(-0.309799\pi\)
0.562605 + 0.826726i \(0.309799\pi\)
\(18\) 0 0
\(19\) −4.17867 −0.958652 −0.479326 0.877637i \(-0.659119\pi\)
−0.479326 + 0.877637i \(0.659119\pi\)
\(20\) 0 0
\(21\) −3.22236 −0.703176
\(22\) 0 0
\(23\) 6.50523 1.35643 0.678217 0.734862i \(-0.262753\pi\)
0.678217 + 0.734862i \(0.262753\pi\)
\(24\) 0 0
\(25\) −1.21688 −0.243375
\(26\) 0 0
\(27\) −14.1255 −2.71845
\(28\) 0 0
\(29\) 3.35077 0.622222 0.311111 0.950374i \(-0.399299\pi\)
0.311111 + 0.950374i \(0.399299\pi\)
\(30\) 0 0
\(31\) −7.82311 −1.40507 −0.702536 0.711648i \(-0.747949\pi\)
−0.702536 + 0.711648i \(0.747949\pi\)
\(32\) 0 0
\(33\) 3.22236 0.560940
\(34\) 0 0
\(35\) 1.94503 0.328769
\(36\) 0 0
\(37\) 3.35205 0.551074 0.275537 0.961290i \(-0.411144\pi\)
0.275537 + 0.961290i \(0.411144\pi\)
\(38\) 0 0
\(39\) 3.22236 0.515990
\(40\) 0 0
\(41\) −5.66737 −0.885094 −0.442547 0.896745i \(-0.645925\pi\)
−0.442547 + 0.896745i \(0.645925\pi\)
\(42\) 0 0
\(43\) −1.16924 −0.178307 −0.0891534 0.996018i \(-0.528416\pi\)
−0.0891534 + 0.996018i \(0.528416\pi\)
\(44\) 0 0
\(45\) 14.3613 2.14085
\(46\) 0 0
\(47\) 10.7539 1.56861 0.784305 0.620375i \(-0.213020\pi\)
0.784305 + 0.620375i \(0.213020\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −14.9497 −2.09337
\(52\) 0 0
\(53\) −11.5881 −1.59174 −0.795872 0.605465i \(-0.792987\pi\)
−0.795872 + 0.605465i \(0.792987\pi\)
\(54\) 0 0
\(55\) −1.94503 −0.262267
\(56\) 0 0
\(57\) 13.4652 1.78350
\(58\) 0 0
\(59\) −10.3841 −1.35190 −0.675948 0.736949i \(-0.736266\pi\)
−0.675948 + 0.736949i \(0.736266\pi\)
\(60\) 0 0
\(61\) −4.96940 −0.636266 −0.318133 0.948046i \(-0.603056\pi\)
−0.318133 + 0.948046i \(0.603056\pi\)
\(62\) 0 0
\(63\) 7.38359 0.930245
\(64\) 0 0
\(65\) −1.94503 −0.241251
\(66\) 0 0
\(67\) −10.1690 −1.24234 −0.621170 0.783676i \(-0.713342\pi\)
−0.621170 + 0.783676i \(0.713342\pi\)
\(68\) 0 0
\(69\) −20.9622 −2.52355
\(70\) 0 0
\(71\) −0.157313 −0.0186696 −0.00933479 0.999956i \(-0.502971\pi\)
−0.00933479 + 0.999956i \(0.502971\pi\)
\(72\) 0 0
\(73\) 1.45524 0.170323 0.0851617 0.996367i \(-0.472859\pi\)
0.0851617 + 0.996367i \(0.472859\pi\)
\(74\) 0 0
\(75\) 3.92121 0.452782
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −15.4350 −1.73657 −0.868284 0.496067i \(-0.834777\pi\)
−0.868284 + 0.496067i \(0.834777\pi\)
\(80\) 0 0
\(81\) 23.3666 2.59629
\(82\) 0 0
\(83\) −4.26464 −0.468105 −0.234052 0.972224i \(-0.575199\pi\)
−0.234052 + 0.972224i \(0.575199\pi\)
\(84\) 0 0
\(85\) 9.02367 0.978755
\(86\) 0 0
\(87\) −10.7974 −1.15760
\(88\) 0 0
\(89\) 14.4609 1.53286 0.766429 0.642329i \(-0.222032\pi\)
0.766429 + 0.642329i \(0.222032\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 25.2089 2.61404
\(94\) 0 0
\(95\) −8.12762 −0.833876
\(96\) 0 0
\(97\) −6.52587 −0.662602 −0.331301 0.943525i \(-0.607488\pi\)
−0.331301 + 0.943525i \(0.607488\pi\)
\(98\) 0 0
\(99\) −7.38359 −0.742079
\(100\) 0 0
\(101\) −11.6419 −1.15841 −0.579205 0.815182i \(-0.696637\pi\)
−0.579205 + 0.815182i \(0.696637\pi\)
\(102\) 0 0
\(103\) −17.3242 −1.70701 −0.853503 0.521088i \(-0.825526\pi\)
−0.853503 + 0.521088i \(0.825526\pi\)
\(104\) 0 0
\(105\) −6.26757 −0.611652
\(106\) 0 0
\(107\) 16.0034 1.54710 0.773552 0.633733i \(-0.218478\pi\)
0.773552 + 0.633733i \(0.218478\pi\)
\(108\) 0 0
\(109\) 7.34207 0.703243 0.351622 0.936142i \(-0.385630\pi\)
0.351622 + 0.936142i \(0.385630\pi\)
\(110\) 0 0
\(111\) −10.8015 −1.02523
\(112\) 0 0
\(113\) −2.90102 −0.272905 −0.136453 0.990647i \(-0.543570\pi\)
−0.136453 + 0.990647i \(0.543570\pi\)
\(114\) 0 0
\(115\) 12.6528 1.17988
\(116\) 0 0
\(117\) −7.38359 −0.682613
\(118\) 0 0
\(119\) 4.63936 0.425289
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 18.2623 1.64665
\(124\) 0 0
\(125\) −12.0920 −1.08154
\(126\) 0 0
\(127\) −7.84033 −0.695716 −0.347858 0.937547i \(-0.613091\pi\)
−0.347858 + 0.937547i \(0.613091\pi\)
\(128\) 0 0
\(129\) 3.76770 0.331727
\(130\) 0 0
\(131\) 8.68015 0.758389 0.379194 0.925317i \(-0.376201\pi\)
0.379194 + 0.925317i \(0.376201\pi\)
\(132\) 0 0
\(133\) −4.17867 −0.362336
\(134\) 0 0
\(135\) −27.4744 −2.36462
\(136\) 0 0
\(137\) 14.3959 1.22992 0.614960 0.788558i \(-0.289172\pi\)
0.614960 + 0.788558i \(0.289172\pi\)
\(138\) 0 0
\(139\) −9.55146 −0.810144 −0.405072 0.914285i \(-0.632754\pi\)
−0.405072 + 0.914285i \(0.632754\pi\)
\(140\) 0 0
\(141\) −34.6528 −2.91829
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 6.51733 0.541235
\(146\) 0 0
\(147\) −3.22236 −0.265776
\(148\) 0 0
\(149\) 10.1897 0.834773 0.417387 0.908729i \(-0.362946\pi\)
0.417387 + 0.908729i \(0.362946\pi\)
\(150\) 0 0
\(151\) 14.0177 1.14074 0.570372 0.821386i \(-0.306799\pi\)
0.570372 + 0.821386i \(0.306799\pi\)
\(152\) 0 0
\(153\) 34.2551 2.76936
\(154\) 0 0
\(155\) −15.2162 −1.22219
\(156\) 0 0
\(157\) 14.0025 1.11752 0.558760 0.829330i \(-0.311277\pi\)
0.558760 + 0.829330i \(0.311277\pi\)
\(158\) 0 0
\(159\) 37.3409 2.96133
\(160\) 0 0
\(161\) 6.50523 0.512684
\(162\) 0 0
\(163\) −8.73365 −0.684073 −0.342036 0.939687i \(-0.611117\pi\)
−0.342036 + 0.939687i \(0.611117\pi\)
\(164\) 0 0
\(165\) 6.26757 0.487929
\(166\) 0 0
\(167\) 16.1896 1.25279 0.626396 0.779505i \(-0.284529\pi\)
0.626396 + 0.779505i \(0.284529\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −30.8536 −2.35943
\(172\) 0 0
\(173\) −4.08100 −0.310273 −0.155136 0.987893i \(-0.549582\pi\)
−0.155136 + 0.987893i \(0.549582\pi\)
\(174\) 0 0
\(175\) −1.21688 −0.0919872
\(176\) 0 0
\(177\) 33.4613 2.51511
\(178\) 0 0
\(179\) 4.02007 0.300474 0.150237 0.988650i \(-0.451996\pi\)
0.150237 + 0.988650i \(0.451996\pi\)
\(180\) 0 0
\(181\) 17.4718 1.29867 0.649333 0.760504i \(-0.275048\pi\)
0.649333 + 0.760504i \(0.275048\pi\)
\(182\) 0 0
\(183\) 16.0132 1.18373
\(184\) 0 0
\(185\) 6.51983 0.479347
\(186\) 0 0
\(187\) −4.63936 −0.339264
\(188\) 0 0
\(189\) −14.1255 −1.02748
\(190\) 0 0
\(191\) 24.8214 1.79602 0.898008 0.439979i \(-0.145014\pi\)
0.898008 + 0.439979i \(0.145014\pi\)
\(192\) 0 0
\(193\) −22.8332 −1.64357 −0.821785 0.569798i \(-0.807021\pi\)
−0.821785 + 0.569798i \(0.807021\pi\)
\(194\) 0 0
\(195\) 6.26757 0.448830
\(196\) 0 0
\(197\) −11.4540 −0.816062 −0.408031 0.912968i \(-0.633784\pi\)
−0.408031 + 0.912968i \(0.633784\pi\)
\(198\) 0 0
\(199\) −6.24629 −0.442788 −0.221394 0.975184i \(-0.571061\pi\)
−0.221394 + 0.975184i \(0.571061\pi\)
\(200\) 0 0
\(201\) 32.7681 2.31128
\(202\) 0 0
\(203\) 3.35077 0.235178
\(204\) 0 0
\(205\) −11.0232 −0.769892
\(206\) 0 0
\(207\) 48.0319 3.33845
\(208\) 0 0
\(209\) 4.17867 0.289045
\(210\) 0 0
\(211\) −0.237993 −0.0163841 −0.00819205 0.999966i \(-0.502608\pi\)
−0.00819205 + 0.999966i \(0.502608\pi\)
\(212\) 0 0
\(213\) 0.506918 0.0347334
\(214\) 0 0
\(215\) −2.27419 −0.155099
\(216\) 0 0
\(217\) −7.82311 −0.531067
\(218\) 0 0
\(219\) −4.68932 −0.316875
\(220\) 0 0
\(221\) −4.63936 −0.312077
\(222\) 0 0
\(223\) −12.4008 −0.830420 −0.415210 0.909726i \(-0.636292\pi\)
−0.415210 + 0.909726i \(0.636292\pi\)
\(224\) 0 0
\(225\) −8.98491 −0.598994
\(226\) 0 0
\(227\) −2.58726 −0.171723 −0.0858613 0.996307i \(-0.527364\pi\)
−0.0858613 + 0.996307i \(0.527364\pi\)
\(228\) 0 0
\(229\) −11.3218 −0.748164 −0.374082 0.927396i \(-0.622042\pi\)
−0.374082 + 0.927396i \(0.622042\pi\)
\(230\) 0 0
\(231\) 3.22236 0.212016
\(232\) 0 0
\(233\) 6.54283 0.428635 0.214317 0.976764i \(-0.431247\pi\)
0.214317 + 0.976764i \(0.431247\pi\)
\(234\) 0 0
\(235\) 20.9165 1.36444
\(236\) 0 0
\(237\) 49.7369 3.23076
\(238\) 0 0
\(239\) 14.9464 0.966802 0.483401 0.875399i \(-0.339401\pi\)
0.483401 + 0.875399i \(0.339401\pi\)
\(240\) 0 0
\(241\) −25.2096 −1.62389 −0.811946 0.583733i \(-0.801592\pi\)
−0.811946 + 0.583733i \(0.801592\pi\)
\(242\) 0 0
\(243\) −32.9191 −2.11176
\(244\) 0 0
\(245\) 1.94503 0.124263
\(246\) 0 0
\(247\) 4.17867 0.265882
\(248\) 0 0
\(249\) 13.7422 0.870876
\(250\) 0 0
\(251\) −21.9195 −1.38355 −0.691773 0.722115i \(-0.743170\pi\)
−0.691773 + 0.722115i \(0.743170\pi\)
\(252\) 0 0
\(253\) −6.50523 −0.408980
\(254\) 0 0
\(255\) −29.0775 −1.82090
\(256\) 0 0
\(257\) −10.7181 −0.668576 −0.334288 0.942471i \(-0.608496\pi\)
−0.334288 + 0.942471i \(0.608496\pi\)
\(258\) 0 0
\(259\) 3.35205 0.208286
\(260\) 0 0
\(261\) 24.7407 1.53141
\(262\) 0 0
\(263\) −12.0053 −0.740281 −0.370141 0.928976i \(-0.620691\pi\)
−0.370141 + 0.928976i \(0.620691\pi\)
\(264\) 0 0
\(265\) −22.5391 −1.38457
\(266\) 0 0
\(267\) −46.5984 −2.85177
\(268\) 0 0
\(269\) 23.5986 1.43884 0.719418 0.694578i \(-0.244409\pi\)
0.719418 + 0.694578i \(0.244409\pi\)
\(270\) 0 0
\(271\) 5.73470 0.348358 0.174179 0.984714i \(-0.444273\pi\)
0.174179 + 0.984714i \(0.444273\pi\)
\(272\) 0 0
\(273\) 3.22236 0.195026
\(274\) 0 0
\(275\) 1.21688 0.0733804
\(276\) 0 0
\(277\) −7.88845 −0.473971 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(278\) 0 0
\(279\) −57.7626 −3.45816
\(280\) 0 0
\(281\) −7.68971 −0.458730 −0.229365 0.973341i \(-0.573665\pi\)
−0.229365 + 0.973341i \(0.573665\pi\)
\(282\) 0 0
\(283\) −5.38009 −0.319813 −0.159907 0.987132i \(-0.551119\pi\)
−0.159907 + 0.987132i \(0.551119\pi\)
\(284\) 0 0
\(285\) 26.1901 1.55137
\(286\) 0 0
\(287\) −5.66737 −0.334534
\(288\) 0 0
\(289\) 4.52365 0.266097
\(290\) 0 0
\(291\) 21.0287 1.23272
\(292\) 0 0
\(293\) −20.4984 −1.19753 −0.598764 0.800925i \(-0.704341\pi\)
−0.598764 + 0.800925i \(0.704341\pi\)
\(294\) 0 0
\(295\) −20.1974 −1.17594
\(296\) 0 0
\(297\) 14.1255 0.819644
\(298\) 0 0
\(299\) −6.50523 −0.376207
\(300\) 0 0
\(301\) −1.16924 −0.0673937
\(302\) 0 0
\(303\) 37.5143 2.15514
\(304\) 0 0
\(305\) −9.66561 −0.553451
\(306\) 0 0
\(307\) 21.9361 1.25196 0.625980 0.779839i \(-0.284699\pi\)
0.625980 + 0.779839i \(0.284699\pi\)
\(308\) 0 0
\(309\) 55.8248 3.17576
\(310\) 0 0
\(311\) −32.9098 −1.86614 −0.933072 0.359691i \(-0.882882\pi\)
−0.933072 + 0.359691i \(0.882882\pi\)
\(312\) 0 0
\(313\) 12.0173 0.679260 0.339630 0.940559i \(-0.389698\pi\)
0.339630 + 0.940559i \(0.389698\pi\)
\(314\) 0 0
\(315\) 14.3613 0.809166
\(316\) 0 0
\(317\) 1.89263 0.106301 0.0531503 0.998587i \(-0.483074\pi\)
0.0531503 + 0.998587i \(0.483074\pi\)
\(318\) 0 0
\(319\) −3.35077 −0.187607
\(320\) 0 0
\(321\) −51.5685 −2.87828
\(322\) 0 0
\(323\) −19.3863 −1.07869
\(324\) 0 0
\(325\) 1.21688 0.0675001
\(326\) 0 0
\(327\) −23.6588 −1.30833
\(328\) 0 0
\(329\) 10.7539 0.592879
\(330\) 0 0
\(331\) −8.84884 −0.486376 −0.243188 0.969979i \(-0.578193\pi\)
−0.243188 + 0.969979i \(0.578193\pi\)
\(332\) 0 0
\(333\) 24.7502 1.35630
\(334\) 0 0
\(335\) −19.7789 −1.08064
\(336\) 0 0
\(337\) −0.977482 −0.0532469 −0.0266234 0.999646i \(-0.508476\pi\)
−0.0266234 + 0.999646i \(0.508476\pi\)
\(338\) 0 0
\(339\) 9.34814 0.507721
\(340\) 0 0
\(341\) 7.82311 0.423645
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −40.7720 −2.19509
\(346\) 0 0
\(347\) 4.22496 0.226808 0.113404 0.993549i \(-0.463825\pi\)
0.113404 + 0.993549i \(0.463825\pi\)
\(348\) 0 0
\(349\) 3.94318 0.211074 0.105537 0.994415i \(-0.466344\pi\)
0.105537 + 0.994415i \(0.466344\pi\)
\(350\) 0 0
\(351\) 14.1255 0.753963
\(352\) 0 0
\(353\) −12.6355 −0.672522 −0.336261 0.941769i \(-0.609162\pi\)
−0.336261 + 0.941769i \(0.609162\pi\)
\(354\) 0 0
\(355\) −0.305977 −0.0162396
\(356\) 0 0
\(357\) −14.9497 −0.791221
\(358\) 0 0
\(359\) 25.3450 1.33766 0.668829 0.743416i \(-0.266796\pi\)
0.668829 + 0.743416i \(0.266796\pi\)
\(360\) 0 0
\(361\) −1.53873 −0.0809858
\(362\) 0 0
\(363\) −3.22236 −0.169130
\(364\) 0 0
\(365\) 2.83049 0.148154
\(366\) 0 0
\(367\) 6.08499 0.317634 0.158817 0.987308i \(-0.449232\pi\)
0.158817 + 0.987308i \(0.449232\pi\)
\(368\) 0 0
\(369\) −41.8455 −2.17839
\(370\) 0 0
\(371\) −11.5881 −0.601623
\(372\) 0 0
\(373\) −22.8749 −1.18442 −0.592209 0.805785i \(-0.701744\pi\)
−0.592209 + 0.805785i \(0.701744\pi\)
\(374\) 0 0
\(375\) 38.9647 2.01213
\(376\) 0 0
\(377\) −3.35077 −0.172573
\(378\) 0 0
\(379\) 6.64036 0.341093 0.170546 0.985350i \(-0.445447\pi\)
0.170546 + 0.985350i \(0.445447\pi\)
\(380\) 0 0
\(381\) 25.2643 1.29433
\(382\) 0 0
\(383\) 8.43826 0.431175 0.215587 0.976485i \(-0.430833\pi\)
0.215587 + 0.976485i \(0.430833\pi\)
\(384\) 0 0
\(385\) −1.94503 −0.0991277
\(386\) 0 0
\(387\) −8.63316 −0.438848
\(388\) 0 0
\(389\) −1.62741 −0.0825132 −0.0412566 0.999149i \(-0.513136\pi\)
−0.0412566 + 0.999149i \(0.513136\pi\)
\(390\) 0 0
\(391\) 30.1801 1.52627
\(392\) 0 0
\(393\) −27.9706 −1.41093
\(394\) 0 0
\(395\) −30.0214 −1.51054
\(396\) 0 0
\(397\) −33.9426 −1.70353 −0.851764 0.523925i \(-0.824467\pi\)
−0.851764 + 0.523925i \(0.824467\pi\)
\(398\) 0 0
\(399\) 13.4652 0.674101
\(400\) 0 0
\(401\) −30.2735 −1.51179 −0.755894 0.654694i \(-0.772797\pi\)
−0.755894 + 0.654694i \(0.772797\pi\)
\(402\) 0 0
\(403\) 7.82311 0.389697
\(404\) 0 0
\(405\) 45.4487 2.25836
\(406\) 0 0
\(407\) −3.35205 −0.166155
\(408\) 0 0
\(409\) 13.0225 0.643920 0.321960 0.946753i \(-0.395658\pi\)
0.321960 + 0.946753i \(0.395658\pi\)
\(410\) 0 0
\(411\) −46.3886 −2.28818
\(412\) 0 0
\(413\) −10.3841 −0.510969
\(414\) 0 0
\(415\) −8.29483 −0.407177
\(416\) 0 0
\(417\) 30.7782 1.50722
\(418\) 0 0
\(419\) 30.3550 1.48294 0.741469 0.670988i \(-0.234130\pi\)
0.741469 + 0.670988i \(0.234130\pi\)
\(420\) 0 0
\(421\) −17.6664 −0.861005 −0.430503 0.902589i \(-0.641664\pi\)
−0.430503 + 0.902589i \(0.641664\pi\)
\(422\) 0 0
\(423\) 79.4020 3.86066
\(424\) 0 0
\(425\) −5.64552 −0.273848
\(426\) 0 0
\(427\) −4.96940 −0.240486
\(428\) 0 0
\(429\) −3.22236 −0.155577
\(430\) 0 0
\(431\) 4.88937 0.235513 0.117756 0.993043i \(-0.462430\pi\)
0.117756 + 0.993043i \(0.462430\pi\)
\(432\) 0 0
\(433\) −9.53941 −0.458435 −0.229217 0.973375i \(-0.573617\pi\)
−0.229217 + 0.973375i \(0.573617\pi\)
\(434\) 0 0
\(435\) −21.0012 −1.00693
\(436\) 0 0
\(437\) −27.1832 −1.30035
\(438\) 0 0
\(439\) −40.0531 −1.91163 −0.955815 0.293968i \(-0.905024\pi\)
−0.955815 + 0.293968i \(0.905024\pi\)
\(440\) 0 0
\(441\) 7.38359 0.351599
\(442\) 0 0
\(443\) 8.19609 0.389408 0.194704 0.980862i \(-0.437625\pi\)
0.194704 + 0.980862i \(0.437625\pi\)
\(444\) 0 0
\(445\) 28.1269 1.33334
\(446\) 0 0
\(447\) −32.8349 −1.55304
\(448\) 0 0
\(449\) 39.4518 1.86185 0.930924 0.365214i \(-0.119004\pi\)
0.930924 + 0.365214i \(0.119004\pi\)
\(450\) 0 0
\(451\) 5.66737 0.266866
\(452\) 0 0
\(453\) −45.1701 −2.12227
\(454\) 0 0
\(455\) −1.94503 −0.0911842
\(456\) 0 0
\(457\) 10.3862 0.485848 0.242924 0.970045i \(-0.421893\pi\)
0.242924 + 0.970045i \(0.421893\pi\)
\(458\) 0 0
\(459\) −65.5332 −3.05883
\(460\) 0 0
\(461\) −36.5107 −1.70047 −0.850236 0.526402i \(-0.823541\pi\)
−0.850236 + 0.526402i \(0.823541\pi\)
\(462\) 0 0
\(463\) −4.84715 −0.225266 −0.112633 0.993637i \(-0.535928\pi\)
−0.112633 + 0.993637i \(0.535928\pi\)
\(464\) 0 0
\(465\) 49.0319 2.27380
\(466\) 0 0
\(467\) −3.94525 −0.182564 −0.0912822 0.995825i \(-0.529097\pi\)
−0.0912822 + 0.995825i \(0.529097\pi\)
\(468\) 0 0
\(469\) −10.1690 −0.469560
\(470\) 0 0
\(471\) −45.1210 −2.07907
\(472\) 0 0
\(473\) 1.16924 0.0537616
\(474\) 0 0
\(475\) 5.08492 0.233312
\(476\) 0 0
\(477\) −85.5616 −3.91760
\(478\) 0 0
\(479\) 25.7591 1.17696 0.588482 0.808511i \(-0.299726\pi\)
0.588482 + 0.808511i \(0.299726\pi\)
\(480\) 0 0
\(481\) −3.35205 −0.152840
\(482\) 0 0
\(483\) −20.9622 −0.953812
\(484\) 0 0
\(485\) −12.6930 −0.576359
\(486\) 0 0
\(487\) −28.5178 −1.29226 −0.646132 0.763225i \(-0.723615\pi\)
−0.646132 + 0.763225i \(0.723615\pi\)
\(488\) 0 0
\(489\) 28.1430 1.27267
\(490\) 0 0
\(491\) 15.7401 0.710343 0.355171 0.934801i \(-0.384423\pi\)
0.355171 + 0.934801i \(0.384423\pi\)
\(492\) 0 0
\(493\) 15.5454 0.700130
\(494\) 0 0
\(495\) −14.3613 −0.645491
\(496\) 0 0
\(497\) −0.157313 −0.00705644
\(498\) 0 0
\(499\) −30.3096 −1.35684 −0.678422 0.734672i \(-0.737336\pi\)
−0.678422 + 0.734672i \(0.737336\pi\)
\(500\) 0 0
\(501\) −52.1688 −2.33073
\(502\) 0 0
\(503\) −40.1739 −1.79126 −0.895632 0.444795i \(-0.853276\pi\)
−0.895632 + 0.444795i \(0.853276\pi\)
\(504\) 0 0
\(505\) −22.6437 −1.00763
\(506\) 0 0
\(507\) −3.22236 −0.143110
\(508\) 0 0
\(509\) −11.0293 −0.488866 −0.244433 0.969666i \(-0.578602\pi\)
−0.244433 + 0.969666i \(0.578602\pi\)
\(510\) 0 0
\(511\) 1.45524 0.0643762
\(512\) 0 0
\(513\) 59.0257 2.60605
\(514\) 0 0
\(515\) −33.6960 −1.48482
\(516\) 0 0
\(517\) −10.7539 −0.472954
\(518\) 0 0
\(519\) 13.1504 0.577241
\(520\) 0 0
\(521\) 30.4186 1.33266 0.666331 0.745656i \(-0.267864\pi\)
0.666331 + 0.745656i \(0.267864\pi\)
\(522\) 0 0
\(523\) 6.58986 0.288154 0.144077 0.989566i \(-0.453979\pi\)
0.144077 + 0.989566i \(0.453979\pi\)
\(524\) 0 0
\(525\) 3.92121 0.171136
\(526\) 0 0
\(527\) −36.2942 −1.58100
\(528\) 0 0
\(529\) 19.3180 0.839914
\(530\) 0 0
\(531\) −76.6720 −3.32728
\(532\) 0 0
\(533\) 5.66737 0.245481
\(534\) 0 0
\(535\) 31.1269 1.34573
\(536\) 0 0
\(537\) −12.9541 −0.559011
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 1.97756 0.0850219 0.0425109 0.999096i \(-0.486464\pi\)
0.0425109 + 0.999096i \(0.486464\pi\)
\(542\) 0 0
\(543\) −56.3003 −2.41608
\(544\) 0 0
\(545\) 14.2805 0.611710
\(546\) 0 0
\(547\) −24.0239 −1.02719 −0.513594 0.858033i \(-0.671686\pi\)
−0.513594 + 0.858033i \(0.671686\pi\)
\(548\) 0 0
\(549\) −36.6920 −1.56598
\(550\) 0 0
\(551\) −14.0017 −0.596494
\(552\) 0 0
\(553\) −15.4350 −0.656361
\(554\) 0 0
\(555\) −21.0092 −0.891792
\(556\) 0 0
\(557\) 17.3072 0.733331 0.366666 0.930353i \(-0.380499\pi\)
0.366666 + 0.930353i \(0.380499\pi\)
\(558\) 0 0
\(559\) 1.16924 0.0494534
\(560\) 0 0
\(561\) 14.9497 0.631176
\(562\) 0 0
\(563\) 15.0087 0.632541 0.316270 0.948669i \(-0.397569\pi\)
0.316270 + 0.948669i \(0.397569\pi\)
\(564\) 0 0
\(565\) −5.64257 −0.237385
\(566\) 0 0
\(567\) 23.3666 0.981306
\(568\) 0 0
\(569\) −23.4750 −0.984124 −0.492062 0.870560i \(-0.663757\pi\)
−0.492062 + 0.870560i \(0.663757\pi\)
\(570\) 0 0
\(571\) 16.6163 0.695370 0.347685 0.937611i \(-0.386968\pi\)
0.347685 + 0.937611i \(0.386968\pi\)
\(572\) 0 0
\(573\) −79.9836 −3.34136
\(574\) 0 0
\(575\) −7.91606 −0.330122
\(576\) 0 0
\(577\) 10.6288 0.442485 0.221242 0.975219i \(-0.428989\pi\)
0.221242 + 0.975219i \(0.428989\pi\)
\(578\) 0 0
\(579\) 73.5767 3.05774
\(580\) 0 0
\(581\) −4.26464 −0.176927
\(582\) 0 0
\(583\) 11.5881 0.479929
\(584\) 0 0
\(585\) −14.3613 −0.593765
\(586\) 0 0
\(587\) −20.4802 −0.845309 −0.422654 0.906291i \(-0.638902\pi\)
−0.422654 + 0.906291i \(0.638902\pi\)
\(588\) 0 0
\(589\) 32.6902 1.34698
\(590\) 0 0
\(591\) 36.9088 1.51823
\(592\) 0 0
\(593\) −6.92003 −0.284172 −0.142086 0.989854i \(-0.545381\pi\)
−0.142086 + 0.989854i \(0.545381\pi\)
\(594\) 0 0
\(595\) 9.02367 0.369934
\(596\) 0 0
\(597\) 20.1278 0.823776
\(598\) 0 0
\(599\) −8.64848 −0.353367 −0.176684 0.984268i \(-0.556537\pi\)
−0.176684 + 0.984268i \(0.556537\pi\)
\(600\) 0 0
\(601\) 37.7783 1.54101 0.770505 0.637434i \(-0.220004\pi\)
0.770505 + 0.637434i \(0.220004\pi\)
\(602\) 0 0
\(603\) −75.0836 −3.05764
\(604\) 0 0
\(605\) 1.94503 0.0790765
\(606\) 0 0
\(607\) −15.8501 −0.643335 −0.321668 0.946853i \(-0.604243\pi\)
−0.321668 + 0.946853i \(0.604243\pi\)
\(608\) 0 0
\(609\) −10.7974 −0.437532
\(610\) 0 0
\(611\) −10.7539 −0.435054
\(612\) 0 0
\(613\) −15.8053 −0.638368 −0.319184 0.947693i \(-0.603409\pi\)
−0.319184 + 0.947693i \(0.603409\pi\)
\(614\) 0 0
\(615\) 35.5206 1.43233
\(616\) 0 0
\(617\) −18.0325 −0.725963 −0.362981 0.931796i \(-0.618241\pi\)
−0.362981 + 0.931796i \(0.618241\pi\)
\(618\) 0 0
\(619\) −39.9213 −1.60457 −0.802287 0.596938i \(-0.796384\pi\)
−0.802287 + 0.596938i \(0.796384\pi\)
\(620\) 0 0
\(621\) −91.8896 −3.68740
\(622\) 0 0
\(623\) 14.4609 0.579366
\(624\) 0 0
\(625\) −17.4348 −0.697393
\(626\) 0 0
\(627\) −13.4652 −0.537747
\(628\) 0 0
\(629\) 15.5514 0.620074
\(630\) 0 0
\(631\) 14.1986 0.565238 0.282619 0.959232i \(-0.408797\pi\)
0.282619 + 0.959232i \(0.408797\pi\)
\(632\) 0 0
\(633\) 0.766898 0.0304815
\(634\) 0 0
\(635\) −15.2496 −0.605163
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −1.16153 −0.0459495
\(640\) 0 0
\(641\) 9.31133 0.367776 0.183888 0.982947i \(-0.441132\pi\)
0.183888 + 0.982947i \(0.441132\pi\)
\(642\) 0 0
\(643\) 23.9067 0.942787 0.471394 0.881923i \(-0.343751\pi\)
0.471394 + 0.881923i \(0.343751\pi\)
\(644\) 0 0
\(645\) 7.32827 0.288550
\(646\) 0 0
\(647\) −42.3172 −1.66366 −0.831830 0.555031i \(-0.812707\pi\)
−0.831830 + 0.555031i \(0.812707\pi\)
\(648\) 0 0
\(649\) 10.3841 0.407612
\(650\) 0 0
\(651\) 25.2089 0.988013
\(652\) 0 0
\(653\) −31.5512 −1.23469 −0.617346 0.786692i \(-0.711792\pi\)
−0.617346 + 0.786692i \(0.711792\pi\)
\(654\) 0 0
\(655\) 16.8831 0.659678
\(656\) 0 0
\(657\) 10.7449 0.419199
\(658\) 0 0
\(659\) −33.6398 −1.31042 −0.655211 0.755446i \(-0.727420\pi\)
−0.655211 + 0.755446i \(0.727420\pi\)
\(660\) 0 0
\(661\) 14.6140 0.568420 0.284210 0.958762i \(-0.408269\pi\)
0.284210 + 0.958762i \(0.408269\pi\)
\(662\) 0 0
\(663\) 14.9497 0.580597
\(664\) 0 0
\(665\) −8.12762 −0.315175
\(666\) 0 0
\(667\) 21.7975 0.844003
\(668\) 0 0
\(669\) 39.9599 1.54494
\(670\) 0 0
\(671\) 4.96940 0.191842
\(672\) 0 0
\(673\) −5.91195 −0.227889 −0.113945 0.993487i \(-0.536349\pi\)
−0.113945 + 0.993487i \(0.536349\pi\)
\(674\) 0 0
\(675\) 17.1890 0.661604
\(676\) 0 0
\(677\) 33.4033 1.28379 0.641897 0.766791i \(-0.278148\pi\)
0.641897 + 0.766791i \(0.278148\pi\)
\(678\) 0 0
\(679\) −6.52587 −0.250440
\(680\) 0 0
\(681\) 8.33709 0.319478
\(682\) 0 0
\(683\) −28.0098 −1.07177 −0.535883 0.844292i \(-0.680021\pi\)
−0.535883 + 0.844292i \(0.680021\pi\)
\(684\) 0 0
\(685\) 28.0003 1.06984
\(686\) 0 0
\(687\) 36.4828 1.39191
\(688\) 0 0
\(689\) 11.5881 0.441471
\(690\) 0 0
\(691\) −24.2259 −0.921596 −0.460798 0.887505i \(-0.652437\pi\)
−0.460798 + 0.887505i \(0.652437\pi\)
\(692\) 0 0
\(693\) −7.38359 −0.280479
\(694\) 0 0
\(695\) −18.5778 −0.704697
\(696\) 0 0
\(697\) −26.2930 −0.995917
\(698\) 0 0
\(699\) −21.0833 −0.797445
\(700\) 0 0
\(701\) −27.2779 −1.03027 −0.515137 0.857108i \(-0.672259\pi\)
−0.515137 + 0.857108i \(0.672259\pi\)
\(702\) 0 0
\(703\) −14.0071 −0.528288
\(704\) 0 0
\(705\) −67.4005 −2.53845
\(706\) 0 0
\(707\) −11.6419 −0.437837
\(708\) 0 0
\(709\) −35.9001 −1.34826 −0.674129 0.738614i \(-0.735481\pi\)
−0.674129 + 0.738614i \(0.735481\pi\)
\(710\) 0 0
\(711\) −113.965 −4.27403
\(712\) 0 0
\(713\) −50.8911 −1.90589
\(714\) 0 0
\(715\) 1.94503 0.0727398
\(716\) 0 0
\(717\) −48.1626 −1.79867
\(718\) 0 0
\(719\) −48.5196 −1.80948 −0.904738 0.425968i \(-0.859933\pi\)
−0.904738 + 0.425968i \(0.859933\pi\)
\(720\) 0 0
\(721\) −17.3242 −0.645187
\(722\) 0 0
\(723\) 81.2343 3.02113
\(724\) 0 0
\(725\) −4.07747 −0.151433
\(726\) 0 0
\(727\) 38.9907 1.44609 0.723043 0.690803i \(-0.242743\pi\)
0.723043 + 0.690803i \(0.242743\pi\)
\(728\) 0 0
\(729\) 35.9774 1.33250
\(730\) 0 0
\(731\) −5.42451 −0.200633
\(732\) 0 0
\(733\) −39.9311 −1.47489 −0.737444 0.675409i \(-0.763967\pi\)
−0.737444 + 0.675409i \(0.763967\pi\)
\(734\) 0 0
\(735\) −6.26757 −0.231183
\(736\) 0 0
\(737\) 10.1690 0.374579
\(738\) 0 0
\(739\) 13.2190 0.486270 0.243135 0.969992i \(-0.421824\pi\)
0.243135 + 0.969992i \(0.421824\pi\)
\(740\) 0 0
\(741\) −13.4652 −0.494655
\(742\) 0 0
\(743\) 13.1167 0.481204 0.240602 0.970624i \(-0.422655\pi\)
0.240602 + 0.970624i \(0.422655\pi\)
\(744\) 0 0
\(745\) 19.8192 0.726121
\(746\) 0 0
\(747\) −31.4883 −1.15210
\(748\) 0 0
\(749\) 16.0034 0.584750
\(750\) 0 0
\(751\) 35.1996 1.28445 0.642225 0.766516i \(-0.278011\pi\)
0.642225 + 0.766516i \(0.278011\pi\)
\(752\) 0 0
\(753\) 70.6324 2.57399
\(754\) 0 0
\(755\) 27.2648 0.992267
\(756\) 0 0
\(757\) 18.9669 0.689365 0.344683 0.938719i \(-0.387987\pi\)
0.344683 + 0.938719i \(0.387987\pi\)
\(758\) 0 0
\(759\) 20.9622 0.760879
\(760\) 0 0
\(761\) −29.0247 −1.05214 −0.526072 0.850440i \(-0.676336\pi\)
−0.526072 + 0.850440i \(0.676336\pi\)
\(762\) 0 0
\(763\) 7.34207 0.265801
\(764\) 0 0
\(765\) 66.6271 2.40891
\(766\) 0 0
\(767\) 10.3841 0.374949
\(768\) 0 0
\(769\) −6.90811 −0.249113 −0.124556 0.992213i \(-0.539751\pi\)
−0.124556 + 0.992213i \(0.539751\pi\)
\(770\) 0 0
\(771\) 34.5375 1.24384
\(772\) 0 0
\(773\) −26.4291 −0.950589 −0.475294 0.879827i \(-0.657658\pi\)
−0.475294 + 0.879827i \(0.657658\pi\)
\(774\) 0 0
\(775\) 9.51976 0.341960
\(776\) 0 0
\(777\) −10.8015 −0.387502
\(778\) 0 0
\(779\) 23.6820 0.848497
\(780\) 0 0
\(781\) 0.157313 0.00562909
\(782\) 0 0
\(783\) −47.3312 −1.69148
\(784\) 0 0
\(785\) 27.2352 0.972065
\(786\) 0 0
\(787\) 27.1502 0.967802 0.483901 0.875123i \(-0.339220\pi\)
0.483901 + 0.875123i \(0.339220\pi\)
\(788\) 0 0
\(789\) 38.6855 1.37724
\(790\) 0 0
\(791\) −2.90102 −0.103149
\(792\) 0 0
\(793\) 4.96940 0.176469
\(794\) 0 0
\(795\) 72.6290 2.57589
\(796\) 0 0
\(797\) −28.9697 −1.02616 −0.513080 0.858341i \(-0.671496\pi\)
−0.513080 + 0.858341i \(0.671496\pi\)
\(798\) 0 0
\(799\) 49.8910 1.76502
\(800\) 0 0
\(801\) 106.774 3.77266
\(802\) 0 0
\(803\) −1.45524 −0.0513545
\(804\) 0 0
\(805\) 12.6528 0.445954
\(806\) 0 0
\(807\) −76.0433 −2.67685
\(808\) 0 0
\(809\) 45.6503 1.60498 0.802489 0.596667i \(-0.203509\pi\)
0.802489 + 0.596667i \(0.203509\pi\)
\(810\) 0 0
\(811\) −33.2250 −1.16669 −0.583344 0.812225i \(-0.698256\pi\)
−0.583344 + 0.812225i \(0.698256\pi\)
\(812\) 0 0
\(813\) −18.4792 −0.648095
\(814\) 0 0
\(815\) −16.9872 −0.595035
\(816\) 0 0
\(817\) 4.88585 0.170934
\(818\) 0 0
\(819\) −7.38359 −0.258003
\(820\) 0 0
\(821\) −6.17463 −0.215496 −0.107748 0.994178i \(-0.534364\pi\)
−0.107748 + 0.994178i \(0.534364\pi\)
\(822\) 0 0
\(823\) −17.2372 −0.600849 −0.300425 0.953806i \(-0.597128\pi\)
−0.300425 + 0.953806i \(0.597128\pi\)
\(824\) 0 0
\(825\) −3.92121 −0.136519
\(826\) 0 0
\(827\) 53.2678 1.85230 0.926151 0.377152i \(-0.123096\pi\)
0.926151 + 0.377152i \(0.123096\pi\)
\(828\) 0 0
\(829\) 37.7052 1.30955 0.654777 0.755822i \(-0.272762\pi\)
0.654777 + 0.755822i \(0.272762\pi\)
\(830\) 0 0
\(831\) 25.4194 0.881789
\(832\) 0 0
\(833\) 4.63936 0.160744
\(834\) 0 0
\(835\) 31.4893 1.08973
\(836\) 0 0
\(837\) 110.505 3.81962
\(838\) 0 0
\(839\) −38.2253 −1.31968 −0.659842 0.751405i \(-0.729377\pi\)
−0.659842 + 0.751405i \(0.729377\pi\)
\(840\) 0 0
\(841\) −17.7724 −0.612840
\(842\) 0 0
\(843\) 24.7790 0.853434
\(844\) 0 0
\(845\) 1.94503 0.0669109
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 17.3366 0.594990
\(850\) 0 0
\(851\) 21.8059 0.747496
\(852\) 0 0
\(853\) −21.8945 −0.749655 −0.374827 0.927095i \(-0.622298\pi\)
−0.374827 + 0.927095i \(0.622298\pi\)
\(854\) 0 0
\(855\) −60.0110 −2.05233
\(856\) 0 0
\(857\) 15.3307 0.523688 0.261844 0.965110i \(-0.415669\pi\)
0.261844 + 0.965110i \(0.415669\pi\)
\(858\) 0 0
\(859\) 38.1887 1.30298 0.651491 0.758656i \(-0.274144\pi\)
0.651491 + 0.758656i \(0.274144\pi\)
\(860\) 0 0
\(861\) 18.2623 0.622377
\(862\) 0 0
\(863\) −56.8779 −1.93615 −0.968073 0.250668i \(-0.919350\pi\)
−0.968073 + 0.250668i \(0.919350\pi\)
\(864\) 0 0
\(865\) −7.93765 −0.269888
\(866\) 0 0
\(867\) −14.5768 −0.495055
\(868\) 0 0
\(869\) 15.4350 0.523595
\(870\) 0 0
\(871\) 10.1690 0.344563
\(872\) 0 0
\(873\) −48.1844 −1.63079
\(874\) 0 0
\(875\) −12.0920 −0.408784
\(876\) 0 0
\(877\) 49.6981 1.67818 0.839092 0.543990i \(-0.183087\pi\)
0.839092 + 0.543990i \(0.183087\pi\)
\(878\) 0 0
\(879\) 66.0532 2.22792
\(880\) 0 0
\(881\) 47.7356 1.60825 0.804127 0.594457i \(-0.202633\pi\)
0.804127 + 0.594457i \(0.202633\pi\)
\(882\) 0 0
\(883\) −39.9529 −1.34452 −0.672261 0.740314i \(-0.734677\pi\)
−0.672261 + 0.740314i \(0.734677\pi\)
\(884\) 0 0
\(885\) 65.0831 2.18775
\(886\) 0 0
\(887\) −52.1489 −1.75099 −0.875495 0.483227i \(-0.839465\pi\)
−0.875495 + 0.483227i \(0.839465\pi\)
\(888\) 0 0
\(889\) −7.84033 −0.262956
\(890\) 0 0
\(891\) −23.3666 −0.782811
\(892\) 0 0
\(893\) −44.9368 −1.50375
\(894\) 0 0
\(895\) 7.81914 0.261365
\(896\) 0 0
\(897\) 20.9622 0.699907
\(898\) 0 0
\(899\) −26.2134 −0.874267
\(900\) 0 0
\(901\) −53.7612 −1.79105
\(902\) 0 0
\(903\) 3.76770 0.125381
\(904\) 0 0
\(905\) 33.9830 1.12963
\(906\) 0 0
\(907\) −0.574022 −0.0190601 −0.00953004 0.999955i \(-0.503034\pi\)
−0.00953004 + 0.999955i \(0.503034\pi\)
\(908\) 0 0
\(909\) −85.9588 −2.85107
\(910\) 0 0
\(911\) 24.5841 0.814509 0.407254 0.913315i \(-0.366486\pi\)
0.407254 + 0.913315i \(0.366486\pi\)
\(912\) 0 0
\(913\) 4.26464 0.141139
\(914\) 0 0
\(915\) 31.1460 1.02966
\(916\) 0 0
\(917\) 8.68015 0.286644
\(918\) 0 0
\(919\) 18.1925 0.600115 0.300057 0.953921i \(-0.402994\pi\)
0.300057 + 0.953921i \(0.402994\pi\)
\(920\) 0 0
\(921\) −70.6860 −2.32918
\(922\) 0 0
\(923\) 0.157313 0.00517801
\(924\) 0 0
\(925\) −4.07903 −0.134118
\(926\) 0 0
\(927\) −127.915 −4.20128
\(928\) 0 0
\(929\) −31.3954 −1.03005 −0.515026 0.857175i \(-0.672218\pi\)
−0.515026 + 0.857175i \(0.672218\pi\)
\(930\) 0 0
\(931\) −4.17867 −0.136950
\(932\) 0 0
\(933\) 106.047 3.47183
\(934\) 0 0
\(935\) −9.02367 −0.295106
\(936\) 0 0
\(937\) −27.5483 −0.899964 −0.449982 0.893038i \(-0.648570\pi\)
−0.449982 + 0.893038i \(0.648570\pi\)
\(938\) 0 0
\(939\) −38.7242 −1.26371
\(940\) 0 0
\(941\) 15.9189 0.518943 0.259471 0.965751i \(-0.416452\pi\)
0.259471 + 0.965751i \(0.416452\pi\)
\(942\) 0 0
\(943\) −36.8675 −1.20057
\(944\) 0 0
\(945\) −27.4744 −0.893744
\(946\) 0 0
\(947\) 19.4282 0.631330 0.315665 0.948871i \(-0.397772\pi\)
0.315665 + 0.948871i \(0.397772\pi\)
\(948\) 0 0
\(949\) −1.45524 −0.0472392
\(950\) 0 0
\(951\) −6.09873 −0.197765
\(952\) 0 0
\(953\) −10.8945 −0.352907 −0.176454 0.984309i \(-0.556463\pi\)
−0.176454 + 0.984309i \(0.556463\pi\)
\(954\) 0 0
\(955\) 48.2783 1.56225
\(956\) 0 0
\(957\) 10.7974 0.349029
\(958\) 0 0
\(959\) 14.3959 0.464866
\(960\) 0 0
\(961\) 30.2011 0.974228
\(962\) 0 0
\(963\) 118.162 3.80772
\(964\) 0 0
\(965\) −44.4112 −1.42965
\(966\) 0 0
\(967\) 33.8901 1.08983 0.544916 0.838491i \(-0.316562\pi\)
0.544916 + 0.838491i \(0.316562\pi\)
\(968\) 0 0
\(969\) 62.4697 2.00682
\(970\) 0 0
\(971\) 31.6814 1.01670 0.508352 0.861149i \(-0.330255\pi\)
0.508352 + 0.861149i \(0.330255\pi\)
\(972\) 0 0
\(973\) −9.55146 −0.306206
\(974\) 0 0
\(975\) −3.92121 −0.125579
\(976\) 0 0
\(977\) −50.8388 −1.62648 −0.813239 0.581929i \(-0.802298\pi\)
−0.813239 + 0.581929i \(0.802298\pi\)
\(978\) 0 0
\(979\) −14.4609 −0.462174
\(980\) 0 0
\(981\) 54.2108 1.73082
\(982\) 0 0
\(983\) −3.74912 −0.119578 −0.0597891 0.998211i \(-0.519043\pi\)
−0.0597891 + 0.998211i \(0.519043\pi\)
\(984\) 0 0
\(985\) −22.2783 −0.709845
\(986\) 0 0
\(987\) −34.6528 −1.10301
\(988\) 0 0
\(989\) −7.60615 −0.241862
\(990\) 0 0
\(991\) −14.5433 −0.461982 −0.230991 0.972956i \(-0.574197\pi\)
−0.230991 + 0.972956i \(0.574197\pi\)
\(992\) 0 0
\(993\) 28.5141 0.904868
\(994\) 0 0
\(995\) −12.1492 −0.385156
\(996\) 0 0
\(997\) −20.5492 −0.650800 −0.325400 0.945576i \(-0.605499\pi\)
−0.325400 + 0.945576i \(0.605499\pi\)
\(998\) 0 0
\(999\) −47.3494 −1.49807
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 \(a_p\))