Properties

Label 8008.2.a.y.1.8
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 1.8
Root \(-0.129238\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.129238 q^{3} -0.197815 q^{5} +1.00000 q^{7} -2.98330 q^{9} +O(q^{10})\) \(q+0.129238 q^{3} -0.197815 q^{5} +1.00000 q^{7} -2.98330 q^{9} -1.00000 q^{11} -1.00000 q^{13} -0.0255653 q^{15} +0.463619 q^{17} +3.51860 q^{19} +0.129238 q^{21} +8.53398 q^{23} -4.96087 q^{25} -0.773271 q^{27} -7.30410 q^{29} +9.67692 q^{31} -0.129238 q^{33} -0.197815 q^{35} -11.6566 q^{37} -0.129238 q^{39} +3.57023 q^{41} -0.592150 q^{43} +0.590141 q^{45} -3.21507 q^{47} +1.00000 q^{49} +0.0599174 q^{51} -11.5471 q^{53} +0.197815 q^{55} +0.454738 q^{57} -11.4632 q^{59} +4.83822 q^{61} -2.98330 q^{63} +0.197815 q^{65} +6.38548 q^{67} +1.10292 q^{69} +12.7342 q^{71} +3.76737 q^{73} -0.641134 q^{75} -1.00000 q^{77} -3.12052 q^{79} +8.84996 q^{81} -4.06752 q^{83} -0.0917109 q^{85} -0.943969 q^{87} +16.4935 q^{89} -1.00000 q^{91} +1.25063 q^{93} -0.696032 q^{95} +6.85661 q^{97} +2.98330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) 0.129238 0.0746158 0.0373079 0.999304i \(-0.488122\pi\)
0.0373079 + 0.999304i \(0.488122\pi\)
\(4\) 0 0
\(5\) −0.197815 −0.0884655 −0.0442328 0.999021i \(-0.514084\pi\)
−0.0442328 + 0.999021i \(0.514084\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.98330 −0.994432
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.0255653 −0.00660093
\(16\) 0 0
\(17\) 0.463619 0.112444 0.0562221 0.998418i \(-0.482095\pi\)
0.0562221 + 0.998418i \(0.482095\pi\)
\(18\) 0 0
\(19\) 3.51860 0.807223 0.403611 0.914931i \(-0.367755\pi\)
0.403611 + 0.914931i \(0.367755\pi\)
\(20\) 0 0
\(21\) 0.129238 0.0282021
\(22\) 0 0
\(23\) 8.53398 1.77946 0.889729 0.456489i \(-0.150893\pi\)
0.889729 + 0.456489i \(0.150893\pi\)
\(24\) 0 0
\(25\) −4.96087 −0.992174
\(26\) 0 0
\(27\) −0.773271 −0.148816
\(28\) 0 0
\(29\) −7.30410 −1.35634 −0.678168 0.734907i \(-0.737226\pi\)
−0.678168 + 0.734907i \(0.737226\pi\)
\(30\) 0 0
\(31\) 9.67692 1.73803 0.869013 0.494789i \(-0.164754\pi\)
0.869013 + 0.494789i \(0.164754\pi\)
\(32\) 0 0
\(33\) −0.129238 −0.0224975
\(34\) 0 0
\(35\) −0.197815 −0.0334368
\(36\) 0 0
\(37\) −11.6566 −1.91634 −0.958170 0.286201i \(-0.907608\pi\)
−0.958170 + 0.286201i \(0.907608\pi\)
\(38\) 0 0
\(39\) −0.129238 −0.0206947
\(40\) 0 0
\(41\) 3.57023 0.557577 0.278788 0.960353i \(-0.410067\pi\)
0.278788 + 0.960353i \(0.410067\pi\)
\(42\) 0 0
\(43\) −0.592150 −0.0903021 −0.0451510 0.998980i \(-0.514377\pi\)
−0.0451510 + 0.998980i \(0.514377\pi\)
\(44\) 0 0
\(45\) 0.590141 0.0879730
\(46\) 0 0
\(47\) −3.21507 −0.468966 −0.234483 0.972120i \(-0.575340\pi\)
−0.234483 + 0.972120i \(0.575340\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0.0599174 0.00839011
\(52\) 0 0
\(53\) −11.5471 −1.58612 −0.793059 0.609144i \(-0.791513\pi\)
−0.793059 + 0.609144i \(0.791513\pi\)
\(54\) 0 0
\(55\) 0.197815 0.0266734
\(56\) 0 0
\(57\) 0.454738 0.0602315
\(58\) 0 0
\(59\) −11.4632 −1.49238 −0.746190 0.665733i \(-0.768119\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(60\) 0 0
\(61\) 4.83822 0.619471 0.309735 0.950823i \(-0.399760\pi\)
0.309735 + 0.950823i \(0.399760\pi\)
\(62\) 0 0
\(63\) −2.98330 −0.375860
\(64\) 0 0
\(65\) 0.197815 0.0245359
\(66\) 0 0
\(67\) 6.38548 0.780111 0.390055 0.920791i \(-0.372456\pi\)
0.390055 + 0.920791i \(0.372456\pi\)
\(68\) 0 0
\(69\) 1.10292 0.132776
\(70\) 0 0
\(71\) 12.7342 1.51128 0.755638 0.654990i \(-0.227327\pi\)
0.755638 + 0.654990i \(0.227327\pi\)
\(72\) 0 0
\(73\) 3.76737 0.440938 0.220469 0.975394i \(-0.429241\pi\)
0.220469 + 0.975394i \(0.429241\pi\)
\(74\) 0 0
\(75\) −0.641134 −0.0740318
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −3.12052 −0.351086 −0.175543 0.984472i \(-0.556168\pi\)
−0.175543 + 0.984472i \(0.556168\pi\)
\(80\) 0 0
\(81\) 8.84996 0.983328
\(82\) 0 0
\(83\) −4.06752 −0.446469 −0.223234 0.974765i \(-0.571662\pi\)
−0.223234 + 0.974765i \(0.571662\pi\)
\(84\) 0 0
\(85\) −0.0917109 −0.00994744
\(86\) 0 0
\(87\) −0.943969 −0.101204
\(88\) 0 0
\(89\) 16.4935 1.74831 0.874156 0.485645i \(-0.161415\pi\)
0.874156 + 0.485645i \(0.161415\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 1.25063 0.129684
\(94\) 0 0
\(95\) −0.696032 −0.0714114
\(96\) 0 0
\(97\) 6.85661 0.696183 0.348091 0.937461i \(-0.386830\pi\)
0.348091 + 0.937461i \(0.386830\pi\)
\(98\) 0 0
\(99\) 2.98330 0.299833
\(100\) 0 0
\(101\) 6.17551 0.614486 0.307243 0.951631i \(-0.400594\pi\)
0.307243 + 0.951631i \(0.400594\pi\)
\(102\) 0 0
\(103\) −11.7101 −1.15383 −0.576916 0.816803i \(-0.695744\pi\)
−0.576916 + 0.816803i \(0.695744\pi\)
\(104\) 0 0
\(105\) −0.0255653 −0.00249492
\(106\) 0 0
\(107\) −16.9145 −1.63518 −0.817592 0.575798i \(-0.804692\pi\)
−0.817592 + 0.575798i \(0.804692\pi\)
\(108\) 0 0
\(109\) 3.58673 0.343547 0.171773 0.985136i \(-0.445050\pi\)
0.171773 + 0.985136i \(0.445050\pi\)
\(110\) 0 0
\(111\) −1.50648 −0.142989
\(112\) 0 0
\(113\) −18.5857 −1.74840 −0.874199 0.485568i \(-0.838613\pi\)
−0.874199 + 0.485568i \(0.838613\pi\)
\(114\) 0 0
\(115\) −1.68815 −0.157421
\(116\) 0 0
\(117\) 2.98330 0.275806
\(118\) 0 0
\(119\) 0.463619 0.0424999
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.461411 0.0416040
\(124\) 0 0
\(125\) 1.97041 0.176239
\(126\) 0 0
\(127\) −9.70036 −0.860768 −0.430384 0.902646i \(-0.641622\pi\)
−0.430384 + 0.902646i \(0.641622\pi\)
\(128\) 0 0
\(129\) −0.0765285 −0.00673796
\(130\) 0 0
\(131\) 7.86434 0.687111 0.343555 0.939132i \(-0.388369\pi\)
0.343555 + 0.939132i \(0.388369\pi\)
\(132\) 0 0
\(133\) 3.51860 0.305101
\(134\) 0 0
\(135\) 0.152965 0.0131651
\(136\) 0 0
\(137\) −9.63428 −0.823112 −0.411556 0.911385i \(-0.635015\pi\)
−0.411556 + 0.911385i \(0.635015\pi\)
\(138\) 0 0
\(139\) −17.6752 −1.49919 −0.749597 0.661895i \(-0.769752\pi\)
−0.749597 + 0.661895i \(0.769752\pi\)
\(140\) 0 0
\(141\) −0.415510 −0.0349922
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 1.44486 0.119989
\(146\) 0 0
\(147\) 0.129238 0.0106594
\(148\) 0 0
\(149\) −7.64328 −0.626162 −0.313081 0.949726i \(-0.601361\pi\)
−0.313081 + 0.949726i \(0.601361\pi\)
\(150\) 0 0
\(151\) 1.50772 0.122697 0.0613483 0.998116i \(-0.480460\pi\)
0.0613483 + 0.998116i \(0.480460\pi\)
\(152\) 0 0
\(153\) −1.38311 −0.111818
\(154\) 0 0
\(155\) −1.91424 −0.153755
\(156\) 0 0
\(157\) −13.4784 −1.07569 −0.537846 0.843043i \(-0.680762\pi\)
−0.537846 + 0.843043i \(0.680762\pi\)
\(158\) 0 0
\(159\) −1.49233 −0.118349
\(160\) 0 0
\(161\) 8.53398 0.672572
\(162\) 0 0
\(163\) −13.5795 −1.06363 −0.531813 0.846862i \(-0.678489\pi\)
−0.531813 + 0.846862i \(0.678489\pi\)
\(164\) 0 0
\(165\) 0.0255653 0.00199025
\(166\) 0 0
\(167\) −25.5007 −1.97331 −0.986653 0.162837i \(-0.947936\pi\)
−0.986653 + 0.162837i \(0.947936\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −10.4970 −0.802728
\(172\) 0 0
\(173\) 0.815582 0.0620076 0.0310038 0.999519i \(-0.490130\pi\)
0.0310038 + 0.999519i \(0.490130\pi\)
\(174\) 0 0
\(175\) −4.96087 −0.375006
\(176\) 0 0
\(177\) −1.48148 −0.111355
\(178\) 0 0
\(179\) −2.64452 −0.197661 −0.0988304 0.995104i \(-0.531510\pi\)
−0.0988304 + 0.995104i \(0.531510\pi\)
\(180\) 0 0
\(181\) −7.63681 −0.567640 −0.283820 0.958878i \(-0.591602\pi\)
−0.283820 + 0.958878i \(0.591602\pi\)
\(182\) 0 0
\(183\) 0.625283 0.0462223
\(184\) 0 0
\(185\) 2.30586 0.169530
\(186\) 0 0
\(187\) −0.463619 −0.0339032
\(188\) 0 0
\(189\) −0.773271 −0.0562472
\(190\) 0 0
\(191\) −1.33366 −0.0965001 −0.0482500 0.998835i \(-0.515364\pi\)
−0.0482500 + 0.998835i \(0.515364\pi\)
\(192\) 0 0
\(193\) −18.6730 −1.34411 −0.672056 0.740500i \(-0.734589\pi\)
−0.672056 + 0.740500i \(0.734589\pi\)
\(194\) 0 0
\(195\) 0.0255653 0.00183077
\(196\) 0 0
\(197\) −10.7298 −0.764464 −0.382232 0.924066i \(-0.624844\pi\)
−0.382232 + 0.924066i \(0.624844\pi\)
\(198\) 0 0
\(199\) 15.3283 1.08659 0.543296 0.839541i \(-0.317176\pi\)
0.543296 + 0.839541i \(0.317176\pi\)
\(200\) 0 0
\(201\) 0.825249 0.0582086
\(202\) 0 0
\(203\) −7.30410 −0.512647
\(204\) 0 0
\(205\) −0.706246 −0.0493263
\(206\) 0 0
\(207\) −25.4594 −1.76955
\(208\) 0 0
\(209\) −3.51860 −0.243387
\(210\) 0 0
\(211\) 19.5524 1.34604 0.673022 0.739623i \(-0.264996\pi\)
0.673022 + 0.739623i \(0.264996\pi\)
\(212\) 0 0
\(213\) 1.64575 0.112765
\(214\) 0 0
\(215\) 0.117136 0.00798862
\(216\) 0 0
\(217\) 9.67692 0.656912
\(218\) 0 0
\(219\) 0.486889 0.0329009
\(220\) 0 0
\(221\) −0.463619 −0.0311864
\(222\) 0 0
\(223\) 22.9532 1.53706 0.768529 0.639815i \(-0.220989\pi\)
0.768529 + 0.639815i \(0.220989\pi\)
\(224\) 0 0
\(225\) 14.7997 0.986650
\(226\) 0 0
\(227\) 8.82787 0.585926 0.292963 0.956124i \(-0.405359\pi\)
0.292963 + 0.956124i \(0.405359\pi\)
\(228\) 0 0
\(229\) −3.40257 −0.224848 −0.112424 0.993660i \(-0.535861\pi\)
−0.112424 + 0.993660i \(0.535861\pi\)
\(230\) 0 0
\(231\) −0.129238 −0.00850326
\(232\) 0 0
\(233\) 20.3013 1.32998 0.664991 0.746851i \(-0.268435\pi\)
0.664991 + 0.746851i \(0.268435\pi\)
\(234\) 0 0
\(235\) 0.635988 0.0414873
\(236\) 0 0
\(237\) −0.403291 −0.0261966
\(238\) 0 0
\(239\) −20.0550 −1.29725 −0.648626 0.761107i \(-0.724656\pi\)
−0.648626 + 0.761107i \(0.724656\pi\)
\(240\) 0 0
\(241\) −30.0276 −1.93425 −0.967125 0.254302i \(-0.918154\pi\)
−0.967125 + 0.254302i \(0.918154\pi\)
\(242\) 0 0
\(243\) 3.46357 0.222188
\(244\) 0 0
\(245\) −0.197815 −0.0126379
\(246\) 0 0
\(247\) −3.51860 −0.223883
\(248\) 0 0
\(249\) −0.525680 −0.0333136
\(250\) 0 0
\(251\) 1.05864 0.0668207 0.0334104 0.999442i \(-0.489363\pi\)
0.0334104 + 0.999442i \(0.489363\pi\)
\(252\) 0 0
\(253\) −8.53398 −0.536527
\(254\) 0 0
\(255\) −0.0118526 −0.000742236 0
\(256\) 0 0
\(257\) −1.44813 −0.0903321 −0.0451661 0.998979i \(-0.514382\pi\)
−0.0451661 + 0.998979i \(0.514382\pi\)
\(258\) 0 0
\(259\) −11.6566 −0.724308
\(260\) 0 0
\(261\) 21.7903 1.34879
\(262\) 0 0
\(263\) −9.33707 −0.575749 −0.287874 0.957668i \(-0.592949\pi\)
−0.287874 + 0.957668i \(0.592949\pi\)
\(264\) 0 0
\(265\) 2.28419 0.140317
\(266\) 0 0
\(267\) 2.13160 0.130452
\(268\) 0 0
\(269\) −25.1245 −1.53187 −0.765933 0.642921i \(-0.777722\pi\)
−0.765933 + 0.642921i \(0.777722\pi\)
\(270\) 0 0
\(271\) −31.0492 −1.88611 −0.943053 0.332641i \(-0.892060\pi\)
−0.943053 + 0.332641i \(0.892060\pi\)
\(272\) 0 0
\(273\) −0.129238 −0.00782186
\(274\) 0 0
\(275\) 4.96087 0.299152
\(276\) 0 0
\(277\) −10.2464 −0.615648 −0.307824 0.951443i \(-0.599601\pi\)
−0.307824 + 0.951443i \(0.599601\pi\)
\(278\) 0 0
\(279\) −28.8691 −1.72835
\(280\) 0 0
\(281\) 4.87123 0.290593 0.145297 0.989388i \(-0.453586\pi\)
0.145297 + 0.989388i \(0.453586\pi\)
\(282\) 0 0
\(283\) 17.8952 1.06376 0.531881 0.846819i \(-0.321486\pi\)
0.531881 + 0.846819i \(0.321486\pi\)
\(284\) 0 0
\(285\) −0.0899540 −0.00532842
\(286\) 0 0
\(287\) 3.57023 0.210744
\(288\) 0 0
\(289\) −16.7851 −0.987356
\(290\) 0 0
\(291\) 0.886136 0.0519462
\(292\) 0 0
\(293\) 9.38671 0.548378 0.274189 0.961676i \(-0.411591\pi\)
0.274189 + 0.961676i \(0.411591\pi\)
\(294\) 0 0
\(295\) 2.26759 0.132024
\(296\) 0 0
\(297\) 0.773271 0.0448698
\(298\) 0 0
\(299\) −8.53398 −0.493533
\(300\) 0 0
\(301\) −0.592150 −0.0341310
\(302\) 0 0
\(303\) 0.798112 0.0458504
\(304\) 0 0
\(305\) −0.957072 −0.0548018
\(306\) 0 0
\(307\) 22.0195 1.25672 0.628360 0.777923i \(-0.283727\pi\)
0.628360 + 0.777923i \(0.283727\pi\)
\(308\) 0 0
\(309\) −1.51340 −0.0860941
\(310\) 0 0
\(311\) 10.3593 0.587424 0.293712 0.955894i \(-0.405109\pi\)
0.293712 + 0.955894i \(0.405109\pi\)
\(312\) 0 0
\(313\) −14.9185 −0.843246 −0.421623 0.906771i \(-0.638539\pi\)
−0.421623 + 0.906771i \(0.638539\pi\)
\(314\) 0 0
\(315\) 0.590141 0.0332507
\(316\) 0 0
\(317\) 7.03657 0.395213 0.197607 0.980281i \(-0.436683\pi\)
0.197607 + 0.980281i \(0.436683\pi\)
\(318\) 0 0
\(319\) 7.30410 0.408951
\(320\) 0 0
\(321\) −2.18600 −0.122011
\(322\) 0 0
\(323\) 1.63129 0.0907675
\(324\) 0 0
\(325\) 4.96087 0.275180
\(326\) 0 0
\(327\) 0.463543 0.0256340
\(328\) 0 0
\(329\) −3.21507 −0.177252
\(330\) 0 0
\(331\) −22.6551 −1.24524 −0.622619 0.782525i \(-0.713932\pi\)
−0.622619 + 0.782525i \(0.713932\pi\)
\(332\) 0 0
\(333\) 34.7752 1.90567
\(334\) 0 0
\(335\) −1.26314 −0.0690129
\(336\) 0 0
\(337\) 0.129314 0.00704421 0.00352210 0.999994i \(-0.498879\pi\)
0.00352210 + 0.999994i \(0.498879\pi\)
\(338\) 0 0
\(339\) −2.40199 −0.130458
\(340\) 0 0
\(341\) −9.67692 −0.524035
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −0.218174 −0.0117461
\(346\) 0 0
\(347\) 24.2845 1.30366 0.651831 0.758365i \(-0.274001\pi\)
0.651831 + 0.758365i \(0.274001\pi\)
\(348\) 0 0
\(349\) −12.7579 −0.682917 −0.341458 0.939897i \(-0.610921\pi\)
−0.341458 + 0.939897i \(0.610921\pi\)
\(350\) 0 0
\(351\) 0.773271 0.0412742
\(352\) 0 0
\(353\) −4.18185 −0.222577 −0.111289 0.993788i \(-0.535498\pi\)
−0.111289 + 0.993788i \(0.535498\pi\)
\(354\) 0 0
\(355\) −2.51902 −0.133696
\(356\) 0 0
\(357\) 0.0599174 0.00317117
\(358\) 0 0
\(359\) −14.8519 −0.783851 −0.391925 0.919997i \(-0.628191\pi\)
−0.391925 + 0.919997i \(0.628191\pi\)
\(360\) 0 0
\(361\) −6.61944 −0.348392
\(362\) 0 0
\(363\) 0.129238 0.00678325
\(364\) 0 0
\(365\) −0.745243 −0.0390078
\(366\) 0 0
\(367\) 14.2893 0.745893 0.372947 0.927853i \(-0.378347\pi\)
0.372947 + 0.927853i \(0.378347\pi\)
\(368\) 0 0
\(369\) −10.6511 −0.554473
\(370\) 0 0
\(371\) −11.5471 −0.599496
\(372\) 0 0
\(373\) 17.3728 0.899530 0.449765 0.893147i \(-0.351508\pi\)
0.449765 + 0.893147i \(0.351508\pi\)
\(374\) 0 0
\(375\) 0.254652 0.0131502
\(376\) 0 0
\(377\) 7.30410 0.376180
\(378\) 0 0
\(379\) 35.1184 1.80391 0.901956 0.431827i \(-0.142131\pi\)
0.901956 + 0.431827i \(0.142131\pi\)
\(380\) 0 0
\(381\) −1.25366 −0.0642268
\(382\) 0 0
\(383\) −6.85740 −0.350397 −0.175198 0.984533i \(-0.556057\pi\)
−0.175198 + 0.984533i \(0.556057\pi\)
\(384\) 0 0
\(385\) 0.197815 0.0100816
\(386\) 0 0
\(387\) 1.76656 0.0897993
\(388\) 0 0
\(389\) −13.2971 −0.674192 −0.337096 0.941470i \(-0.609445\pi\)
−0.337096 + 0.941470i \(0.609445\pi\)
\(390\) 0 0
\(391\) 3.95652 0.200090
\(392\) 0 0
\(393\) 1.01637 0.0512693
\(394\) 0 0
\(395\) 0.617286 0.0310590
\(396\) 0 0
\(397\) 8.87501 0.445424 0.222712 0.974884i \(-0.428509\pi\)
0.222712 + 0.974884i \(0.428509\pi\)
\(398\) 0 0
\(399\) 0.454738 0.0227654
\(400\) 0 0
\(401\) 4.28868 0.214166 0.107083 0.994250i \(-0.465849\pi\)
0.107083 + 0.994250i \(0.465849\pi\)
\(402\) 0 0
\(403\) −9.67692 −0.482042
\(404\) 0 0
\(405\) −1.75065 −0.0869907
\(406\) 0 0
\(407\) 11.6566 0.577798
\(408\) 0 0
\(409\) 27.7036 1.36986 0.684928 0.728611i \(-0.259834\pi\)
0.684928 + 0.728611i \(0.259834\pi\)
\(410\) 0 0
\(411\) −1.24512 −0.0614171
\(412\) 0 0
\(413\) −11.4632 −0.564067
\(414\) 0 0
\(415\) 0.804617 0.0394971
\(416\) 0 0
\(417\) −2.28432 −0.111863
\(418\) 0 0
\(419\) −35.0857 −1.71405 −0.857025 0.515275i \(-0.827690\pi\)
−0.857025 + 0.515275i \(0.827690\pi\)
\(420\) 0 0
\(421\) 24.4136 1.18985 0.594923 0.803783i \(-0.297183\pi\)
0.594923 + 0.803783i \(0.297183\pi\)
\(422\) 0 0
\(423\) 9.59150 0.466355
\(424\) 0 0
\(425\) −2.29996 −0.111564
\(426\) 0 0
\(427\) 4.83822 0.234138
\(428\) 0 0
\(429\) 0.129238 0.00623968
\(430\) 0 0
\(431\) 18.6685 0.899231 0.449616 0.893222i \(-0.351561\pi\)
0.449616 + 0.893222i \(0.351561\pi\)
\(432\) 0 0
\(433\) −26.3454 −1.26608 −0.633040 0.774119i \(-0.718193\pi\)
−0.633040 + 0.774119i \(0.718193\pi\)
\(434\) 0 0
\(435\) 0.186731 0.00895308
\(436\) 0 0
\(437\) 30.0277 1.43642
\(438\) 0 0
\(439\) −37.2674 −1.77867 −0.889337 0.457252i \(-0.848834\pi\)
−0.889337 + 0.457252i \(0.848834\pi\)
\(440\) 0 0
\(441\) −2.98330 −0.142062
\(442\) 0 0
\(443\) −5.09049 −0.241856 −0.120928 0.992661i \(-0.538587\pi\)
−0.120928 + 0.992661i \(0.538587\pi\)
\(444\) 0 0
\(445\) −3.26267 −0.154665
\(446\) 0 0
\(447\) −0.987805 −0.0467216
\(448\) 0 0
\(449\) 25.8216 1.21860 0.609298 0.792941i \(-0.291451\pi\)
0.609298 + 0.792941i \(0.291451\pi\)
\(450\) 0 0
\(451\) −3.57023 −0.168116
\(452\) 0 0
\(453\) 0.194855 0.00915510
\(454\) 0 0
\(455\) 0.197815 0.00927371
\(456\) 0 0
\(457\) 4.16106 0.194646 0.0973230 0.995253i \(-0.468972\pi\)
0.0973230 + 0.995253i \(0.468972\pi\)
\(458\) 0 0
\(459\) −0.358504 −0.0167335
\(460\) 0 0
\(461\) 16.5909 0.772716 0.386358 0.922349i \(-0.373733\pi\)
0.386358 + 0.922349i \(0.373733\pi\)
\(462\) 0 0
\(463\) 0.786258 0.0365405 0.0182702 0.999833i \(-0.494184\pi\)
0.0182702 + 0.999833i \(0.494184\pi\)
\(464\) 0 0
\(465\) −0.247393 −0.0114726
\(466\) 0 0
\(467\) −30.7759 −1.42414 −0.712070 0.702108i \(-0.752242\pi\)
−0.712070 + 0.702108i \(0.752242\pi\)
\(468\) 0 0
\(469\) 6.38548 0.294854
\(470\) 0 0
\(471\) −1.74192 −0.0802636
\(472\) 0 0
\(473\) 0.592150 0.0272271
\(474\) 0 0
\(475\) −17.4553 −0.800905
\(476\) 0 0
\(477\) 34.4485 1.57729
\(478\) 0 0
\(479\) −9.72212 −0.444215 −0.222108 0.975022i \(-0.571294\pi\)
−0.222108 + 0.975022i \(0.571294\pi\)
\(480\) 0 0
\(481\) 11.6566 0.531497
\(482\) 0 0
\(483\) 1.10292 0.0501845
\(484\) 0 0
\(485\) −1.35634 −0.0615882
\(486\) 0 0
\(487\) −37.0498 −1.67889 −0.839443 0.543448i \(-0.817119\pi\)
−0.839443 + 0.543448i \(0.817119\pi\)
\(488\) 0 0
\(489\) −1.75499 −0.0793633
\(490\) 0 0
\(491\) −39.8480 −1.79832 −0.899159 0.437623i \(-0.855821\pi\)
−0.899159 + 0.437623i \(0.855821\pi\)
\(492\) 0 0
\(493\) −3.38632 −0.152512
\(494\) 0 0
\(495\) −0.590141 −0.0265249
\(496\) 0 0
\(497\) 12.7342 0.571208
\(498\) 0 0
\(499\) −31.5726 −1.41339 −0.706693 0.707521i \(-0.749814\pi\)
−0.706693 + 0.707521i \(0.749814\pi\)
\(500\) 0 0
\(501\) −3.29567 −0.147240
\(502\) 0 0
\(503\) −0.757184 −0.0337611 −0.0168806 0.999858i \(-0.505374\pi\)
−0.0168806 + 0.999858i \(0.505374\pi\)
\(504\) 0 0
\(505\) −1.22161 −0.0543608
\(506\) 0 0
\(507\) 0.129238 0.00573968
\(508\) 0 0
\(509\) −34.5366 −1.53081 −0.765405 0.643549i \(-0.777461\pi\)
−0.765405 + 0.643549i \(0.777461\pi\)
\(510\) 0 0
\(511\) 3.76737 0.166659
\(512\) 0 0
\(513\) −2.72083 −0.120128
\(514\) 0 0
\(515\) 2.31644 0.102074
\(516\) 0 0
\(517\) 3.21507 0.141398
\(518\) 0 0
\(519\) 0.105404 0.00462674
\(520\) 0 0
\(521\) 22.3012 0.977031 0.488516 0.872555i \(-0.337539\pi\)
0.488516 + 0.872555i \(0.337539\pi\)
\(522\) 0 0
\(523\) −23.6448 −1.03392 −0.516958 0.856011i \(-0.672936\pi\)
−0.516958 + 0.856011i \(0.672936\pi\)
\(524\) 0 0
\(525\) −0.641134 −0.0279814
\(526\) 0 0
\(527\) 4.48641 0.195431
\(528\) 0 0
\(529\) 49.8289 2.16647
\(530\) 0 0
\(531\) 34.1981 1.48407
\(532\) 0 0
\(533\) −3.57023 −0.154644
\(534\) 0 0
\(535\) 3.34594 0.144657
\(536\) 0 0
\(537\) −0.341773 −0.0147486
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 5.91067 0.254120 0.127060 0.991895i \(-0.459446\pi\)
0.127060 + 0.991895i \(0.459446\pi\)
\(542\) 0 0
\(543\) −0.986969 −0.0423549
\(544\) 0 0
\(545\) −0.709510 −0.0303921
\(546\) 0 0
\(547\) 43.0158 1.83922 0.919611 0.392830i \(-0.128504\pi\)
0.919611 + 0.392830i \(0.128504\pi\)
\(548\) 0 0
\(549\) −14.4339 −0.616022
\(550\) 0 0
\(551\) −25.7002 −1.09487
\(552\) 0 0
\(553\) −3.12052 −0.132698
\(554\) 0 0
\(555\) 0.298005 0.0126496
\(556\) 0 0
\(557\) −20.5286 −0.869824 −0.434912 0.900473i \(-0.643220\pi\)
−0.434912 + 0.900473i \(0.643220\pi\)
\(558\) 0 0
\(559\) 0.592150 0.0250453
\(560\) 0 0
\(561\) −0.0599174 −0.00252971
\(562\) 0 0
\(563\) −26.1386 −1.10161 −0.550805 0.834634i \(-0.685679\pi\)
−0.550805 + 0.834634i \(0.685679\pi\)
\(564\) 0 0
\(565\) 3.67653 0.154673
\(566\) 0 0
\(567\) 8.84996 0.371663
\(568\) 0 0
\(569\) −14.9992 −0.628798 −0.314399 0.949291i \(-0.601803\pi\)
−0.314399 + 0.949291i \(0.601803\pi\)
\(570\) 0 0
\(571\) −41.2778 −1.72742 −0.863711 0.503988i \(-0.831866\pi\)
−0.863711 + 0.503988i \(0.831866\pi\)
\(572\) 0 0
\(573\) −0.172360 −0.00720043
\(574\) 0 0
\(575\) −42.3360 −1.76553
\(576\) 0 0
\(577\) −20.4712 −0.852227 −0.426113 0.904670i \(-0.640118\pi\)
−0.426113 + 0.904670i \(0.640118\pi\)
\(578\) 0 0
\(579\) −2.41327 −0.100292
\(580\) 0 0
\(581\) −4.06752 −0.168749
\(582\) 0 0
\(583\) 11.5471 0.478233
\(584\) 0 0
\(585\) −0.590141 −0.0243993
\(586\) 0 0
\(587\) 0.224576 0.00926923 0.00463462 0.999989i \(-0.498525\pi\)
0.00463462 + 0.999989i \(0.498525\pi\)
\(588\) 0 0
\(589\) 34.0492 1.40297
\(590\) 0 0
\(591\) −1.38670 −0.0570411
\(592\) 0 0
\(593\) −30.9017 −1.26898 −0.634489 0.772932i \(-0.718790\pi\)
−0.634489 + 0.772932i \(0.718790\pi\)
\(594\) 0 0
\(595\) −0.0917109 −0.00375978
\(596\) 0 0
\(597\) 1.98100 0.0810769
\(598\) 0 0
\(599\) −30.9787 −1.26576 −0.632878 0.774252i \(-0.718126\pi\)
−0.632878 + 0.774252i \(0.718126\pi\)
\(600\) 0 0
\(601\) −8.10062 −0.330431 −0.165216 0.986257i \(-0.552832\pi\)
−0.165216 + 0.986257i \(0.552832\pi\)
\(602\) 0 0
\(603\) −19.0498 −0.775767
\(604\) 0 0
\(605\) −0.197815 −0.00804232
\(606\) 0 0
\(607\) 10.1091 0.410316 0.205158 0.978729i \(-0.434229\pi\)
0.205158 + 0.978729i \(0.434229\pi\)
\(608\) 0 0
\(609\) −0.943969 −0.0382516
\(610\) 0 0
\(611\) 3.21507 0.130068
\(612\) 0 0
\(613\) 45.2647 1.82822 0.914112 0.405463i \(-0.132890\pi\)
0.914112 + 0.405463i \(0.132890\pi\)
\(614\) 0 0
\(615\) −0.0912740 −0.00368052
\(616\) 0 0
\(617\) −37.7923 −1.52146 −0.760730 0.649069i \(-0.775159\pi\)
−0.760730 + 0.649069i \(0.775159\pi\)
\(618\) 0 0
\(619\) −7.97336 −0.320476 −0.160238 0.987078i \(-0.551226\pi\)
−0.160238 + 0.987078i \(0.551226\pi\)
\(620\) 0 0
\(621\) −6.59908 −0.264812
\(622\) 0 0
\(623\) 16.4935 0.660800
\(624\) 0 0
\(625\) 24.4146 0.976583
\(626\) 0 0
\(627\) −0.454738 −0.0181605
\(628\) 0 0
\(629\) −5.40424 −0.215481
\(630\) 0 0
\(631\) 34.8030 1.38549 0.692744 0.721184i \(-0.256402\pi\)
0.692744 + 0.721184i \(0.256402\pi\)
\(632\) 0 0
\(633\) 2.52692 0.100436
\(634\) 0 0
\(635\) 1.91888 0.0761483
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −37.9900 −1.50286
\(640\) 0 0
\(641\) −29.7880 −1.17655 −0.588277 0.808660i \(-0.700193\pi\)
−0.588277 + 0.808660i \(0.700193\pi\)
\(642\) 0 0
\(643\) −39.4302 −1.55497 −0.777487 0.628899i \(-0.783506\pi\)
−0.777487 + 0.628899i \(0.783506\pi\)
\(644\) 0 0
\(645\) 0.0151385 0.000596077 0
\(646\) 0 0
\(647\) 30.2219 1.18815 0.594073 0.804411i \(-0.297519\pi\)
0.594073 + 0.804411i \(0.297519\pi\)
\(648\) 0 0
\(649\) 11.4632 0.449970
\(650\) 0 0
\(651\) 1.25063 0.0490160
\(652\) 0 0
\(653\) −24.3605 −0.953300 −0.476650 0.879093i \(-0.658149\pi\)
−0.476650 + 0.879093i \(0.658149\pi\)
\(654\) 0 0
\(655\) −1.55568 −0.0607856
\(656\) 0 0
\(657\) −11.2392 −0.438483
\(658\) 0 0
\(659\) 17.3956 0.677638 0.338819 0.940852i \(-0.389973\pi\)
0.338819 + 0.940852i \(0.389973\pi\)
\(660\) 0 0
\(661\) 4.54600 0.176819 0.0884095 0.996084i \(-0.471822\pi\)
0.0884095 + 0.996084i \(0.471822\pi\)
\(662\) 0 0
\(663\) −0.0599174 −0.00232700
\(664\) 0 0
\(665\) −0.696032 −0.0269910
\(666\) 0 0
\(667\) −62.3330 −2.41354
\(668\) 0 0
\(669\) 2.96643 0.114689
\(670\) 0 0
\(671\) −4.83822 −0.186777
\(672\) 0 0
\(673\) 5.78292 0.222915 0.111458 0.993769i \(-0.464448\pi\)
0.111458 + 0.993769i \(0.464448\pi\)
\(674\) 0 0
\(675\) 3.83610 0.147651
\(676\) 0 0
\(677\) −17.6208 −0.677223 −0.338611 0.940926i \(-0.609957\pi\)
−0.338611 + 0.940926i \(0.609957\pi\)
\(678\) 0 0
\(679\) 6.85661 0.263132
\(680\) 0 0
\(681\) 1.14090 0.0437193
\(682\) 0 0
\(683\) −12.3506 −0.472582 −0.236291 0.971682i \(-0.575932\pi\)
−0.236291 + 0.971682i \(0.575932\pi\)
\(684\) 0 0
\(685\) 1.90580 0.0728170
\(686\) 0 0
\(687\) −0.439742 −0.0167772
\(688\) 0 0
\(689\) 11.5471 0.439910
\(690\) 0 0
\(691\) 26.9884 1.02669 0.513343 0.858184i \(-0.328407\pi\)
0.513343 + 0.858184i \(0.328407\pi\)
\(692\) 0 0
\(693\) 2.98330 0.113326
\(694\) 0 0
\(695\) 3.49642 0.132627
\(696\) 0 0
\(697\) 1.65523 0.0626963
\(698\) 0 0
\(699\) 2.62370 0.0992376
\(700\) 0 0
\(701\) −17.3943 −0.656975 −0.328488 0.944508i \(-0.606539\pi\)
−0.328488 + 0.944508i \(0.606539\pi\)
\(702\) 0 0
\(703\) −41.0151 −1.54691
\(704\) 0 0
\(705\) 0.0821941 0.00309561
\(706\) 0 0
\(707\) 6.17551 0.232254
\(708\) 0 0
\(709\) 6.22661 0.233845 0.116923 0.993141i \(-0.462697\pi\)
0.116923 + 0.993141i \(0.462697\pi\)
\(710\) 0 0
\(711\) 9.30945 0.349132
\(712\) 0 0
\(713\) 82.5827 3.09275
\(714\) 0 0
\(715\) −0.197815 −0.00739786
\(716\) 0 0
\(717\) −2.59188 −0.0967955
\(718\) 0 0
\(719\) 46.8678 1.74787 0.873936 0.486040i \(-0.161559\pi\)
0.873936 + 0.486040i \(0.161559\pi\)
\(720\) 0 0
\(721\) −11.7101 −0.436108
\(722\) 0 0
\(723\) −3.88072 −0.144326
\(724\) 0 0
\(725\) 36.2347 1.34572
\(726\) 0 0
\(727\) 30.3261 1.12473 0.562367 0.826888i \(-0.309891\pi\)
0.562367 + 0.826888i \(0.309891\pi\)
\(728\) 0 0
\(729\) −26.1022 −0.966750
\(730\) 0 0
\(731\) −0.274532 −0.0101539
\(732\) 0 0
\(733\) −23.4198 −0.865029 −0.432515 0.901627i \(-0.642374\pi\)
−0.432515 + 0.901627i \(0.642374\pi\)
\(734\) 0 0
\(735\) −0.0255653 −0.000942989 0
\(736\) 0 0
\(737\) −6.38548 −0.235212
\(738\) 0 0
\(739\) 20.8340 0.766391 0.383195 0.923667i \(-0.374824\pi\)
0.383195 + 0.923667i \(0.374824\pi\)
\(740\) 0 0
\(741\) −0.454738 −0.0167052
\(742\) 0 0
\(743\) −14.8540 −0.544942 −0.272471 0.962164i \(-0.587841\pi\)
−0.272471 + 0.962164i \(0.587841\pi\)
\(744\) 0 0
\(745\) 1.51196 0.0553938
\(746\) 0 0
\(747\) 12.1346 0.443983
\(748\) 0 0
\(749\) −16.9145 −0.618042
\(750\) 0 0
\(751\) −13.7415 −0.501434 −0.250717 0.968060i \(-0.580666\pi\)
−0.250717 + 0.968060i \(0.580666\pi\)
\(752\) 0 0
\(753\) 0.136817 0.00498588
\(754\) 0 0
\(755\) −0.298250 −0.0108544
\(756\) 0 0
\(757\) 31.5560 1.14692 0.573460 0.819233i \(-0.305601\pi\)
0.573460 + 0.819233i \(0.305601\pi\)
\(758\) 0 0
\(759\) −1.10292 −0.0400334
\(760\) 0 0
\(761\) 34.8483 1.26325 0.631626 0.775273i \(-0.282388\pi\)
0.631626 + 0.775273i \(0.282388\pi\)
\(762\) 0 0
\(763\) 3.58673 0.129848
\(764\) 0 0
\(765\) 0.273601 0.00989206
\(766\) 0 0
\(767\) 11.4632 0.413912
\(768\) 0 0
\(769\) −3.37451 −0.121688 −0.0608439 0.998147i \(-0.519379\pi\)
−0.0608439 + 0.998147i \(0.519379\pi\)
\(770\) 0 0
\(771\) −0.187154 −0.00674020
\(772\) 0 0
\(773\) 27.2462 0.979978 0.489989 0.871729i \(-0.337001\pi\)
0.489989 + 0.871729i \(0.337001\pi\)
\(774\) 0 0
\(775\) −48.0060 −1.72442
\(776\) 0 0
\(777\) −1.50648 −0.0540448
\(778\) 0 0
\(779\) 12.5622 0.450089
\(780\) 0 0
\(781\) −12.7342 −0.455667
\(782\) 0 0
\(783\) 5.64805 0.201845
\(784\) 0 0
\(785\) 2.66623 0.0951617
\(786\) 0 0
\(787\) −25.2627 −0.900519 −0.450259 0.892898i \(-0.648668\pi\)
−0.450259 + 0.892898i \(0.648668\pi\)
\(788\) 0 0
\(789\) −1.20671 −0.0429599
\(790\) 0 0
\(791\) −18.5857 −0.660832
\(792\) 0 0
\(793\) −4.83822 −0.171810
\(794\) 0 0
\(795\) 0.295205 0.0104699
\(796\) 0 0
\(797\) −7.48866 −0.265262 −0.132631 0.991165i \(-0.542343\pi\)
−0.132631 + 0.991165i \(0.542343\pi\)
\(798\) 0 0
\(799\) −1.49057 −0.0527325
\(800\) 0 0
\(801\) −49.2051 −1.73858
\(802\) 0 0
\(803\) −3.76737 −0.132948
\(804\) 0 0
\(805\) −1.68815 −0.0594995
\(806\) 0 0
\(807\) −3.24704 −0.114301
\(808\) 0 0
\(809\) −45.0334 −1.58329 −0.791644 0.610982i \(-0.790775\pi\)
−0.791644 + 0.610982i \(0.790775\pi\)
\(810\) 0 0
\(811\) 46.9347 1.64810 0.824051 0.566516i \(-0.191709\pi\)
0.824051 + 0.566516i \(0.191709\pi\)
\(812\) 0 0
\(813\) −4.01275 −0.140733
\(814\) 0 0
\(815\) 2.68622 0.0940943
\(816\) 0 0
\(817\) −2.08354 −0.0728939
\(818\) 0 0
\(819\) 2.98330 0.104245
\(820\) 0 0
\(821\) −21.9833 −0.767221 −0.383610 0.923495i \(-0.625319\pi\)
−0.383610 + 0.923495i \(0.625319\pi\)
\(822\) 0 0
\(823\) 17.0645 0.594832 0.297416 0.954748i \(-0.403875\pi\)
0.297416 + 0.954748i \(0.403875\pi\)
\(824\) 0 0
\(825\) 0.641134 0.0223214
\(826\) 0 0
\(827\) −4.90972 −0.170728 −0.0853639 0.996350i \(-0.527205\pi\)
−0.0853639 + 0.996350i \(0.527205\pi\)
\(828\) 0 0
\(829\) 45.3542 1.57522 0.787609 0.616176i \(-0.211319\pi\)
0.787609 + 0.616176i \(0.211319\pi\)
\(830\) 0 0
\(831\) −1.32423 −0.0459371
\(832\) 0 0
\(833\) 0.463619 0.0160635
\(834\) 0 0
\(835\) 5.04443 0.174570
\(836\) 0 0
\(837\) −7.48289 −0.258646
\(838\) 0 0
\(839\) 34.4830 1.19049 0.595243 0.803546i \(-0.297056\pi\)
0.595243 + 0.803546i \(0.297056\pi\)
\(840\) 0 0
\(841\) 24.3498 0.839649
\(842\) 0 0
\(843\) 0.629549 0.0216828
\(844\) 0 0
\(845\) −0.197815 −0.00680504
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 2.31275 0.0793734
\(850\) 0 0
\(851\) −99.4776 −3.41005
\(852\) 0 0
\(853\) 28.6014 0.979294 0.489647 0.871921i \(-0.337126\pi\)
0.489647 + 0.871921i \(0.337126\pi\)
\(854\) 0 0
\(855\) 2.07647 0.0710138
\(856\) 0 0
\(857\) 21.0580 0.719327 0.359663 0.933082i \(-0.382892\pi\)
0.359663 + 0.933082i \(0.382892\pi\)
\(858\) 0 0
\(859\) 24.0337 0.820018 0.410009 0.912081i \(-0.365526\pi\)
0.410009 + 0.912081i \(0.365526\pi\)
\(860\) 0 0
\(861\) 0.461411 0.0157248
\(862\) 0 0
\(863\) −5.97833 −0.203505 −0.101752 0.994810i \(-0.532445\pi\)
−0.101752 + 0.994810i \(0.532445\pi\)
\(864\) 0 0
\(865\) −0.161334 −0.00548553
\(866\) 0 0
\(867\) −2.16927 −0.0736724
\(868\) 0 0
\(869\) 3.12052 0.105857
\(870\) 0 0
\(871\) −6.38548 −0.216364
\(872\) 0 0
\(873\) −20.4553 −0.692307
\(874\) 0 0
\(875\) 1.97041 0.0666120
\(876\) 0 0
\(877\) −35.8481 −1.21050 −0.605252 0.796034i \(-0.706927\pi\)
−0.605252 + 0.796034i \(0.706927\pi\)
\(878\) 0 0
\(879\) 1.21312 0.0409176
\(880\) 0 0
\(881\) −12.5115 −0.421522 −0.210761 0.977538i \(-0.567594\pi\)
−0.210761 + 0.977538i \(0.567594\pi\)
\(882\) 0 0
\(883\) 8.13045 0.273611 0.136806 0.990598i \(-0.456316\pi\)
0.136806 + 0.990598i \(0.456316\pi\)
\(884\) 0 0
\(885\) 0.293060 0.00985110
\(886\) 0 0
\(887\) 31.2623 1.04969 0.524843 0.851199i \(-0.324124\pi\)
0.524843 + 0.851199i \(0.324124\pi\)
\(888\) 0 0
\(889\) −9.70036 −0.325340
\(890\) 0 0
\(891\) −8.84996 −0.296485
\(892\) 0 0
\(893\) −11.3125 −0.378560
\(894\) 0 0
\(895\) 0.523126 0.0174862
\(896\) 0 0
\(897\) −1.10292 −0.0368253
\(898\) 0 0
\(899\) −70.6812 −2.35735
\(900\) 0 0
\(901\) −5.35347 −0.178350
\(902\) 0 0
\(903\) −0.0765285 −0.00254671
\(904\) 0 0
\(905\) 1.51068 0.0502166
\(906\) 0 0
\(907\) −1.25210 −0.0415754 −0.0207877 0.999784i \(-0.506617\pi\)
−0.0207877 + 0.999784i \(0.506617\pi\)
\(908\) 0 0
\(909\) −18.4234 −0.611065
\(910\) 0 0
\(911\) 37.5407 1.24378 0.621890 0.783105i \(-0.286365\pi\)
0.621890 + 0.783105i \(0.286365\pi\)
\(912\) 0 0
\(913\) 4.06752 0.134615
\(914\) 0 0
\(915\) −0.123690 −0.00408908
\(916\) 0 0
\(917\) 7.86434 0.259703
\(918\) 0 0
\(919\) −36.8320 −1.21498 −0.607488 0.794329i \(-0.707823\pi\)
−0.607488 + 0.794329i \(0.707823\pi\)
\(920\) 0 0
\(921\) 2.84576 0.0937711
\(922\) 0 0
\(923\) −12.7342 −0.419152
\(924\) 0 0
\(925\) 57.8271 1.90134
\(926\) 0 0
\(927\) 34.9348 1.14741
\(928\) 0 0
\(929\) 35.2646 1.15699 0.578497 0.815684i \(-0.303639\pi\)
0.578497 + 0.815684i \(0.303639\pi\)
\(930\) 0 0
\(931\) 3.51860 0.115318
\(932\) 0 0
\(933\) 1.33882 0.0438311
\(934\) 0 0
\(935\) 0.0917109 0.00299927
\(936\) 0 0
\(937\) −28.0393 −0.916004 −0.458002 0.888951i \(-0.651435\pi\)
−0.458002 + 0.888951i \(0.651435\pi\)
\(938\) 0 0
\(939\) −1.92805 −0.0629195
\(940\) 0 0
\(941\) −22.7773 −0.742518 −0.371259 0.928529i \(-0.621074\pi\)
−0.371259 + 0.928529i \(0.621074\pi\)
\(942\) 0 0
\(943\) 30.4683 0.992185
\(944\) 0 0
\(945\) 0.152965 0.00497594
\(946\) 0 0
\(947\) −8.67793 −0.281995 −0.140997 0.990010i \(-0.545031\pi\)
−0.140997 + 0.990010i \(0.545031\pi\)
\(948\) 0 0
\(949\) −3.76737 −0.122294
\(950\) 0 0
\(951\) 0.909394 0.0294891
\(952\) 0 0
\(953\) −10.0415 −0.325275 −0.162637 0.986686i \(-0.552000\pi\)
−0.162637 + 0.986686i \(0.552000\pi\)
\(954\) 0 0
\(955\) 0.263817 0.00853693
\(956\) 0 0
\(957\) 0.943969 0.0305142
\(958\) 0 0
\(959\) −9.63428 −0.311107
\(960\) 0 0
\(961\) 62.6428 2.02074
\(962\) 0 0
\(963\) 50.4609 1.62608
\(964\) 0 0
\(965\) 3.69380 0.118908
\(966\) 0 0
\(967\) 48.2707 1.55228 0.776140 0.630560i \(-0.217175\pi\)
0.776140 + 0.630560i \(0.217175\pi\)
\(968\) 0 0
\(969\) 0.210825 0.00677269
\(970\) 0 0
\(971\) −15.6176 −0.501194 −0.250597 0.968091i \(-0.580627\pi\)
−0.250597 + 0.968091i \(0.580627\pi\)
\(972\) 0 0
\(973\) −17.6752 −0.566642
\(974\) 0 0
\(975\) 0.641134 0.0205327
\(976\) 0 0
\(977\) −24.2841 −0.776917 −0.388458 0.921466i \(-0.626992\pi\)
−0.388458 + 0.921466i \(0.626992\pi\)
\(978\) 0 0
\(979\) −16.4935 −0.527136
\(980\) 0 0
\(981\) −10.7003 −0.341634
\(982\) 0 0
\(983\) −10.5961 −0.337962 −0.168981 0.985619i \(-0.554048\pi\)
−0.168981 + 0.985619i \(0.554048\pi\)
\(984\) 0 0
\(985\) 2.12251 0.0676287
\(986\) 0 0
\(987\) −0.415510 −0.0132258
\(988\) 0 0
\(989\) −5.05340 −0.160689
\(990\) 0 0
\(991\) 12.1302 0.385328 0.192664 0.981265i \(-0.438287\pi\)
0.192664 + 0.981265i \(0.438287\pi\)
\(992\) 0 0
\(993\) −2.92791 −0.0929145
\(994\) 0 0
\(995\) −3.03216 −0.0961260
\(996\) 0 0
\(997\) 20.9439 0.663299 0.331649 0.943403i \(-0.392395\pi\)
0.331649 + 0.943403i \(0.392395\pi\)
\(998\) 0 0
\(999\) 9.01374 0.285182
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 \(a_p\))