Properties

Label 8024.2.a.y.1.20
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.41453 q^{3}\) \(+0.0537401 q^{5}\) \(+0.349134 q^{7}\) \(+2.82994 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.41453 q^{3}\) \(+0.0537401 q^{5}\) \(+0.349134 q^{7}\) \(+2.82994 q^{9}\) \(+1.73444 q^{11}\) \(-5.19703 q^{13}\) \(+0.129757 q^{15}\) \(-1.00000 q^{17}\) \(+6.66321 q^{19}\) \(+0.842993 q^{21}\) \(-8.08544 q^{23}\) \(-4.99711 q^{25}\) \(-0.410603 q^{27}\) \(-4.27135 q^{29}\) \(-9.11085 q^{31}\) \(+4.18784 q^{33}\) \(+0.0187625 q^{35}\) \(-1.81775 q^{37}\) \(-12.5484 q^{39}\) \(-5.44082 q^{41}\) \(+4.67981 q^{43}\) \(+0.152082 q^{45}\) \(+6.77792 q^{47}\) \(-6.87811 q^{49}\) \(-2.41453 q^{51}\) \(-4.55286 q^{53}\) \(+0.0932088 q^{55}\) \(+16.0885 q^{57}\) \(-1.00000 q^{59}\) \(-5.51837 q^{61}\) \(+0.988029 q^{63}\) \(-0.279289 q^{65}\) \(-1.57074 q^{67}\) \(-19.5225 q^{69}\) \(-9.26340 q^{71}\) \(-12.8838 q^{73}\) \(-12.0657 q^{75}\) \(+0.605550 q^{77}\) \(+1.61283 q^{79}\) \(-9.48125 q^{81}\) \(+13.9676 q^{83}\) \(-0.0537401 q^{85}\) \(-10.3133 q^{87}\) \(+4.80452 q^{89}\) \(-1.81446 q^{91}\) \(-21.9984 q^{93}\) \(+0.358082 q^{95}\) \(+17.1429 q^{97}\) \(+4.90836 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.41453 1.39403 0.697014 0.717057i \(-0.254511\pi\)
0.697014 + 0.717057i \(0.254511\pi\)
\(4\) 0 0
\(5\) 0.0537401 0.0240333 0.0120167 0.999928i \(-0.496175\pi\)
0.0120167 + 0.999928i \(0.496175\pi\)
\(6\) 0 0
\(7\) 0.349134 0.131960 0.0659801 0.997821i \(-0.478983\pi\)
0.0659801 + 0.997821i \(0.478983\pi\)
\(8\) 0 0
\(9\) 2.82994 0.943315
\(10\) 0 0
\(11\) 1.73444 0.522952 0.261476 0.965210i \(-0.415791\pi\)
0.261476 + 0.965210i \(0.415791\pi\)
\(12\) 0 0
\(13\) −5.19703 −1.44140 −0.720698 0.693249i \(-0.756179\pi\)
−0.720698 + 0.693249i \(0.756179\pi\)
\(14\) 0 0
\(15\) 0.129757 0.0335031
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 6.66321 1.52864 0.764322 0.644834i \(-0.223074\pi\)
0.764322 + 0.644834i \(0.223074\pi\)
\(20\) 0 0
\(21\) 0.842993 0.183956
\(22\) 0 0
\(23\) −8.08544 −1.68593 −0.842966 0.537967i \(-0.819192\pi\)
−0.842966 + 0.537967i \(0.819192\pi\)
\(24\) 0 0
\(25\) −4.99711 −0.999422
\(26\) 0 0
\(27\) −0.410603 −0.0790206
\(28\) 0 0
\(29\) −4.27135 −0.793170 −0.396585 0.917998i \(-0.629805\pi\)
−0.396585 + 0.917998i \(0.629805\pi\)
\(30\) 0 0
\(31\) −9.11085 −1.63636 −0.818179 0.574964i \(-0.805016\pi\)
−0.818179 + 0.574964i \(0.805016\pi\)
\(32\) 0 0
\(33\) 4.18784 0.729010
\(34\) 0 0
\(35\) 0.0187625 0.00317144
\(36\) 0 0
\(37\) −1.81775 −0.298837 −0.149418 0.988774i \(-0.547740\pi\)
−0.149418 + 0.988774i \(0.547740\pi\)
\(38\) 0 0
\(39\) −12.5484 −2.00935
\(40\) 0 0
\(41\) −5.44082 −0.849713 −0.424857 0.905261i \(-0.639676\pi\)
−0.424857 + 0.905261i \(0.639676\pi\)
\(42\) 0 0
\(43\) 4.67981 0.713665 0.356832 0.934168i \(-0.383857\pi\)
0.356832 + 0.934168i \(0.383857\pi\)
\(44\) 0 0
\(45\) 0.152082 0.0226710
\(46\) 0 0
\(47\) 6.77792 0.988661 0.494331 0.869274i \(-0.335413\pi\)
0.494331 + 0.869274i \(0.335413\pi\)
\(48\) 0 0
\(49\) −6.87811 −0.982587
\(50\) 0 0
\(51\) −2.41453 −0.338102
\(52\) 0 0
\(53\) −4.55286 −0.625383 −0.312692 0.949855i \(-0.601231\pi\)
−0.312692 + 0.949855i \(0.601231\pi\)
\(54\) 0 0
\(55\) 0.0932088 0.0125683
\(56\) 0 0
\(57\) 16.0885 2.13097
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −5.51837 −0.706554 −0.353277 0.935519i \(-0.614933\pi\)
−0.353277 + 0.935519i \(0.614933\pi\)
\(62\) 0 0
\(63\) 0.988029 0.124480
\(64\) 0 0
\(65\) −0.279289 −0.0346415
\(66\) 0 0
\(67\) −1.57074 −0.191896 −0.0959481 0.995386i \(-0.530588\pi\)
−0.0959481 + 0.995386i \(0.530588\pi\)
\(68\) 0 0
\(69\) −19.5225 −2.35024
\(70\) 0 0
\(71\) −9.26340 −1.09936 −0.549681 0.835374i \(-0.685251\pi\)
−0.549681 + 0.835374i \(0.685251\pi\)
\(72\) 0 0
\(73\) −12.8838 −1.50793 −0.753966 0.656914i \(-0.771861\pi\)
−0.753966 + 0.656914i \(0.771861\pi\)
\(74\) 0 0
\(75\) −12.0657 −1.39322
\(76\) 0 0
\(77\) 0.605550 0.0690088
\(78\) 0 0
\(79\) 1.61283 0.181457 0.0907285 0.995876i \(-0.471080\pi\)
0.0907285 + 0.995876i \(0.471080\pi\)
\(80\) 0 0
\(81\) −9.48125 −1.05347
\(82\) 0 0
\(83\) 13.9676 1.53314 0.766571 0.642159i \(-0.221961\pi\)
0.766571 + 0.642159i \(0.221961\pi\)
\(84\) 0 0
\(85\) −0.0537401 −0.00582894
\(86\) 0 0
\(87\) −10.3133 −1.10570
\(88\) 0 0
\(89\) 4.80452 0.509278 0.254639 0.967036i \(-0.418043\pi\)
0.254639 + 0.967036i \(0.418043\pi\)
\(90\) 0 0
\(91\) −1.81446 −0.190207
\(92\) 0 0
\(93\) −21.9984 −2.28113
\(94\) 0 0
\(95\) 0.358082 0.0367384
\(96\) 0 0
\(97\) 17.1429 1.74060 0.870301 0.492521i \(-0.163924\pi\)
0.870301 + 0.492521i \(0.163924\pi\)
\(98\) 0 0
\(99\) 4.90836 0.493309
\(100\) 0 0
\(101\) −2.13439 −0.212380 −0.106190 0.994346i \(-0.533865\pi\)
−0.106190 + 0.994346i \(0.533865\pi\)
\(102\) 0 0
\(103\) 4.99359 0.492033 0.246017 0.969266i \(-0.420878\pi\)
0.246017 + 0.969266i \(0.420878\pi\)
\(104\) 0 0
\(105\) 0.0453026 0.00442108
\(106\) 0 0
\(107\) 11.9023 1.15064 0.575321 0.817928i \(-0.304877\pi\)
0.575321 + 0.817928i \(0.304877\pi\)
\(108\) 0 0
\(109\) 12.1250 1.16136 0.580680 0.814132i \(-0.302787\pi\)
0.580680 + 0.814132i \(0.302787\pi\)
\(110\) 0 0
\(111\) −4.38902 −0.416587
\(112\) 0 0
\(113\) −15.6906 −1.47604 −0.738022 0.674777i \(-0.764240\pi\)
−0.738022 + 0.674777i \(0.764240\pi\)
\(114\) 0 0
\(115\) −0.434513 −0.0405185
\(116\) 0 0
\(117\) −14.7073 −1.35969
\(118\) 0 0
\(119\) −0.349134 −0.0320050
\(120\) 0 0
\(121\) −7.99173 −0.726521
\(122\) 0 0
\(123\) −13.1370 −1.18452
\(124\) 0 0
\(125\) −0.537246 −0.0480527
\(126\) 0 0
\(127\) −12.8016 −1.13596 −0.567981 0.823042i \(-0.692275\pi\)
−0.567981 + 0.823042i \(0.692275\pi\)
\(128\) 0 0
\(129\) 11.2995 0.994869
\(130\) 0 0
\(131\) 5.79213 0.506060 0.253030 0.967458i \(-0.418573\pi\)
0.253030 + 0.967458i \(0.418573\pi\)
\(132\) 0 0
\(133\) 2.32635 0.201720
\(134\) 0 0
\(135\) −0.0220658 −0.00189913
\(136\) 0 0
\(137\) −7.90806 −0.675632 −0.337816 0.941212i \(-0.609688\pi\)
−0.337816 + 0.941212i \(0.609688\pi\)
\(138\) 0 0
\(139\) 20.1594 1.70990 0.854950 0.518710i \(-0.173588\pi\)
0.854950 + 0.518710i \(0.173588\pi\)
\(140\) 0 0
\(141\) 16.3655 1.37822
\(142\) 0 0
\(143\) −9.01391 −0.753781
\(144\) 0 0
\(145\) −0.229543 −0.0190625
\(146\) 0 0
\(147\) −16.6074 −1.36975
\(148\) 0 0
\(149\) −13.8859 −1.13758 −0.568790 0.822483i \(-0.692588\pi\)
−0.568790 + 0.822483i \(0.692588\pi\)
\(150\) 0 0
\(151\) 5.03667 0.409878 0.204939 0.978775i \(-0.434300\pi\)
0.204939 + 0.978775i \(0.434300\pi\)
\(152\) 0 0
\(153\) −2.82994 −0.228787
\(154\) 0 0
\(155\) −0.489618 −0.0393271
\(156\) 0 0
\(157\) 5.43483 0.433747 0.216873 0.976200i \(-0.430414\pi\)
0.216873 + 0.976200i \(0.430414\pi\)
\(158\) 0 0
\(159\) −10.9930 −0.871802
\(160\) 0 0
\(161\) −2.82290 −0.222476
\(162\) 0 0
\(163\) 10.4295 0.816900 0.408450 0.912781i \(-0.366069\pi\)
0.408450 + 0.912781i \(0.366069\pi\)
\(164\) 0 0
\(165\) 0.225055 0.0175205
\(166\) 0 0
\(167\) −2.73934 −0.211976 −0.105988 0.994367i \(-0.533801\pi\)
−0.105988 + 0.994367i \(0.533801\pi\)
\(168\) 0 0
\(169\) 14.0091 1.07762
\(170\) 0 0
\(171\) 18.8565 1.44199
\(172\) 0 0
\(173\) 12.2123 0.928485 0.464243 0.885708i \(-0.346327\pi\)
0.464243 + 0.885708i \(0.346327\pi\)
\(174\) 0 0
\(175\) −1.74466 −0.131884
\(176\) 0 0
\(177\) −2.41453 −0.181487
\(178\) 0 0
\(179\) 22.6154 1.69035 0.845177 0.534486i \(-0.179495\pi\)
0.845177 + 0.534486i \(0.179495\pi\)
\(180\) 0 0
\(181\) 16.8215 1.25033 0.625166 0.780491i \(-0.285031\pi\)
0.625166 + 0.780491i \(0.285031\pi\)
\(182\) 0 0
\(183\) −13.3242 −0.984957
\(184\) 0 0
\(185\) −0.0976863 −0.00718204
\(186\) 0 0
\(187\) −1.73444 −0.126835
\(188\) 0 0
\(189\) −0.143355 −0.0104276
\(190\) 0 0
\(191\) −8.02871 −0.580937 −0.290469 0.956885i \(-0.593811\pi\)
−0.290469 + 0.956885i \(0.593811\pi\)
\(192\) 0 0
\(193\) −10.3011 −0.741491 −0.370745 0.928735i \(-0.620898\pi\)
−0.370745 + 0.928735i \(0.620898\pi\)
\(194\) 0 0
\(195\) −0.674351 −0.0482913
\(196\) 0 0
\(197\) −4.56841 −0.325486 −0.162743 0.986669i \(-0.552034\pi\)
−0.162743 + 0.986669i \(0.552034\pi\)
\(198\) 0 0
\(199\) 11.2585 0.798094 0.399047 0.916930i \(-0.369341\pi\)
0.399047 + 0.916930i \(0.369341\pi\)
\(200\) 0 0
\(201\) −3.79259 −0.267509
\(202\) 0 0
\(203\) −1.49127 −0.104667
\(204\) 0 0
\(205\) −0.292390 −0.0204214
\(206\) 0 0
\(207\) −22.8814 −1.59036
\(208\) 0 0
\(209\) 11.5569 0.799408
\(210\) 0 0
\(211\) −18.4911 −1.27298 −0.636490 0.771285i \(-0.719614\pi\)
−0.636490 + 0.771285i \(0.719614\pi\)
\(212\) 0 0
\(213\) −22.3667 −1.53254
\(214\) 0 0
\(215\) 0.251494 0.0171517
\(216\) 0 0
\(217\) −3.18091 −0.215934
\(218\) 0 0
\(219\) −31.1082 −2.10210
\(220\) 0 0
\(221\) 5.19703 0.349590
\(222\) 0 0
\(223\) −19.5691 −1.31044 −0.655221 0.755437i \(-0.727425\pi\)
−0.655221 + 0.755437i \(0.727425\pi\)
\(224\) 0 0
\(225\) −14.1416 −0.942770
\(226\) 0 0
\(227\) −10.9587 −0.727352 −0.363676 0.931526i \(-0.618478\pi\)
−0.363676 + 0.931526i \(0.618478\pi\)
\(228\) 0 0
\(229\) −25.0556 −1.65572 −0.827862 0.560933i \(-0.810443\pi\)
−0.827862 + 0.560933i \(0.810443\pi\)
\(230\) 0 0
\(231\) 1.46212 0.0962003
\(232\) 0 0
\(233\) 0.405513 0.0265661 0.0132830 0.999912i \(-0.495772\pi\)
0.0132830 + 0.999912i \(0.495772\pi\)
\(234\) 0 0
\(235\) 0.364246 0.0237608
\(236\) 0 0
\(237\) 3.89421 0.252956
\(238\) 0 0
\(239\) 27.0527 1.74989 0.874945 0.484222i \(-0.160897\pi\)
0.874945 + 0.484222i \(0.160897\pi\)
\(240\) 0 0
\(241\) 0.764113 0.0492209 0.0246104 0.999697i \(-0.492165\pi\)
0.0246104 + 0.999697i \(0.492165\pi\)
\(242\) 0 0
\(243\) −21.6609 −1.38955
\(244\) 0 0
\(245\) −0.369630 −0.0236148
\(246\) 0 0
\(247\) −34.6289 −2.20338
\(248\) 0 0
\(249\) 33.7251 2.13724
\(250\) 0 0
\(251\) 2.10180 0.132664 0.0663321 0.997798i \(-0.478870\pi\)
0.0663321 + 0.997798i \(0.478870\pi\)
\(252\) 0 0
\(253\) −14.0237 −0.881661
\(254\) 0 0
\(255\) −0.129757 −0.00812570
\(256\) 0 0
\(257\) −6.37208 −0.397480 −0.198740 0.980052i \(-0.563685\pi\)
−0.198740 + 0.980052i \(0.563685\pi\)
\(258\) 0 0
\(259\) −0.634639 −0.0394345
\(260\) 0 0
\(261\) −12.0877 −0.748209
\(262\) 0 0
\(263\) 12.0398 0.742408 0.371204 0.928551i \(-0.378945\pi\)
0.371204 + 0.928551i \(0.378945\pi\)
\(264\) 0 0
\(265\) −0.244671 −0.0150300
\(266\) 0 0
\(267\) 11.6006 0.709948
\(268\) 0 0
\(269\) 20.0423 1.22200 0.611002 0.791629i \(-0.290767\pi\)
0.611002 + 0.791629i \(0.290767\pi\)
\(270\) 0 0
\(271\) −23.0256 −1.39871 −0.699354 0.714776i \(-0.746529\pi\)
−0.699354 + 0.714776i \(0.746529\pi\)
\(272\) 0 0
\(273\) −4.38106 −0.265154
\(274\) 0 0
\(275\) −8.66717 −0.522650
\(276\) 0 0
\(277\) −6.41713 −0.385568 −0.192784 0.981241i \(-0.561752\pi\)
−0.192784 + 0.981241i \(0.561752\pi\)
\(278\) 0 0
\(279\) −25.7832 −1.54360
\(280\) 0 0
\(281\) −21.4305 −1.27844 −0.639219 0.769025i \(-0.720742\pi\)
−0.639219 + 0.769025i \(0.720742\pi\)
\(282\) 0 0
\(283\) 20.2515 1.20383 0.601914 0.798561i \(-0.294405\pi\)
0.601914 + 0.798561i \(0.294405\pi\)
\(284\) 0 0
\(285\) 0.864598 0.0512144
\(286\) 0 0
\(287\) −1.89957 −0.112128
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 41.3921 2.42645
\(292\) 0 0
\(293\) 1.64095 0.0958652 0.0479326 0.998851i \(-0.484737\pi\)
0.0479326 + 0.998851i \(0.484737\pi\)
\(294\) 0 0
\(295\) −0.0537401 −0.00312887
\(296\) 0 0
\(297\) −0.712164 −0.0413240
\(298\) 0 0
\(299\) 42.0203 2.43010
\(300\) 0 0
\(301\) 1.63388 0.0941753
\(302\) 0 0
\(303\) −5.15354 −0.296063
\(304\) 0 0
\(305\) −0.296558 −0.0169808
\(306\) 0 0
\(307\) −22.1243 −1.26270 −0.631350 0.775498i \(-0.717499\pi\)
−0.631350 + 0.775498i \(0.717499\pi\)
\(308\) 0 0
\(309\) 12.0572 0.685909
\(310\) 0 0
\(311\) 6.57081 0.372596 0.186298 0.982493i \(-0.440351\pi\)
0.186298 + 0.982493i \(0.440351\pi\)
\(312\) 0 0
\(313\) −3.06102 −0.173019 −0.0865096 0.996251i \(-0.527571\pi\)
−0.0865096 + 0.996251i \(0.527571\pi\)
\(314\) 0 0
\(315\) 0.0530968 0.00299167
\(316\) 0 0
\(317\) 10.4983 0.589643 0.294822 0.955552i \(-0.404740\pi\)
0.294822 + 0.955552i \(0.404740\pi\)
\(318\) 0 0
\(319\) −7.40839 −0.414790
\(320\) 0 0
\(321\) 28.7385 1.60403
\(322\) 0 0
\(323\) −6.66321 −0.370751
\(324\) 0 0
\(325\) 25.9701 1.44056
\(326\) 0 0
\(327\) 29.2761 1.61897
\(328\) 0 0
\(329\) 2.36640 0.130464
\(330\) 0 0
\(331\) −20.7618 −1.14117 −0.570586 0.821238i \(-0.693284\pi\)
−0.570586 + 0.821238i \(0.693284\pi\)
\(332\) 0 0
\(333\) −5.14414 −0.281897
\(334\) 0 0
\(335\) −0.0844116 −0.00461190
\(336\) 0 0
\(337\) 4.14981 0.226055 0.113027 0.993592i \(-0.463945\pi\)
0.113027 + 0.993592i \(0.463945\pi\)
\(338\) 0 0
\(339\) −37.8853 −2.05765
\(340\) 0 0
\(341\) −15.8022 −0.855737
\(342\) 0 0
\(343\) −4.84531 −0.261622
\(344\) 0 0
\(345\) −1.04914 −0.0564840
\(346\) 0 0
\(347\) −5.64556 −0.303069 −0.151535 0.988452i \(-0.548422\pi\)
−0.151535 + 0.988452i \(0.548422\pi\)
\(348\) 0 0
\(349\) −3.08264 −0.165010 −0.0825050 0.996591i \(-0.526292\pi\)
−0.0825050 + 0.996591i \(0.526292\pi\)
\(350\) 0 0
\(351\) 2.13391 0.113900
\(352\) 0 0
\(353\) 17.8925 0.952319 0.476160 0.879359i \(-0.342028\pi\)
0.476160 + 0.879359i \(0.342028\pi\)
\(354\) 0 0
\(355\) −0.497816 −0.0264213
\(356\) 0 0
\(357\) −0.842993 −0.0446159
\(358\) 0 0
\(359\) 9.36247 0.494132 0.247066 0.968999i \(-0.420534\pi\)
0.247066 + 0.968999i \(0.420534\pi\)
\(360\) 0 0
\(361\) 25.3983 1.33675
\(362\) 0 0
\(363\) −19.2963 −1.01279
\(364\) 0 0
\(365\) −0.692375 −0.0362406
\(366\) 0 0
\(367\) 22.6479 1.18221 0.591105 0.806594i \(-0.298692\pi\)
0.591105 + 0.806594i \(0.298692\pi\)
\(368\) 0 0
\(369\) −15.3972 −0.801547
\(370\) 0 0
\(371\) −1.58956 −0.0825257
\(372\) 0 0
\(373\) −17.9109 −0.927394 −0.463697 0.885994i \(-0.653477\pi\)
−0.463697 + 0.885994i \(0.653477\pi\)
\(374\) 0 0
\(375\) −1.29720 −0.0669869
\(376\) 0 0
\(377\) 22.1983 1.14327
\(378\) 0 0
\(379\) 22.5349 1.15754 0.578771 0.815490i \(-0.303532\pi\)
0.578771 + 0.815490i \(0.303532\pi\)
\(380\) 0 0
\(381\) −30.9099 −1.58356
\(382\) 0 0
\(383\) −30.1045 −1.53827 −0.769134 0.639088i \(-0.779312\pi\)
−0.769134 + 0.639088i \(0.779312\pi\)
\(384\) 0 0
\(385\) 0.0325423 0.00165851
\(386\) 0 0
\(387\) 13.2436 0.673210
\(388\) 0 0
\(389\) −27.7088 −1.40489 −0.702445 0.711738i \(-0.747908\pi\)
−0.702445 + 0.711738i \(0.747908\pi\)
\(390\) 0 0
\(391\) 8.08544 0.408898
\(392\) 0 0
\(393\) 13.9852 0.705463
\(394\) 0 0
\(395\) 0.0866735 0.00436102
\(396\) 0 0
\(397\) 31.6917 1.59056 0.795282 0.606240i \(-0.207323\pi\)
0.795282 + 0.606240i \(0.207323\pi\)
\(398\) 0 0
\(399\) 5.61704 0.281204
\(400\) 0 0
\(401\) −22.5677 −1.12698 −0.563490 0.826123i \(-0.690542\pi\)
−0.563490 + 0.826123i \(0.690542\pi\)
\(402\) 0 0
\(403\) 47.3494 2.35864
\(404\) 0 0
\(405\) −0.509523 −0.0253184
\(406\) 0 0
\(407\) −3.15278 −0.156277
\(408\) 0 0
\(409\) 2.18714 0.108147 0.0540735 0.998537i \(-0.482779\pi\)
0.0540735 + 0.998537i \(0.482779\pi\)
\(410\) 0 0
\(411\) −19.0942 −0.941850
\(412\) 0 0
\(413\) −0.349134 −0.0171797
\(414\) 0 0
\(415\) 0.750620 0.0368465
\(416\) 0 0
\(417\) 48.6755 2.38365
\(418\) 0 0
\(419\) −34.4929 −1.68509 −0.842544 0.538628i \(-0.818943\pi\)
−0.842544 + 0.538628i \(0.818943\pi\)
\(420\) 0 0
\(421\) −35.6128 −1.73566 −0.867831 0.496859i \(-0.834487\pi\)
−0.867831 + 0.496859i \(0.834487\pi\)
\(422\) 0 0
\(423\) 19.1811 0.932619
\(424\) 0 0
\(425\) 4.99711 0.242396
\(426\) 0 0
\(427\) −1.92665 −0.0932370
\(428\) 0 0
\(429\) −21.7643 −1.05079
\(430\) 0 0
\(431\) 14.0728 0.677864 0.338932 0.940811i \(-0.389934\pi\)
0.338932 + 0.940811i \(0.389934\pi\)
\(432\) 0 0
\(433\) −10.0740 −0.484126 −0.242063 0.970260i \(-0.577824\pi\)
−0.242063 + 0.970260i \(0.577824\pi\)
\(434\) 0 0
\(435\) −0.554238 −0.0265737
\(436\) 0 0
\(437\) −53.8750 −2.57719
\(438\) 0 0
\(439\) 8.47384 0.404434 0.202217 0.979341i \(-0.435185\pi\)
0.202217 + 0.979341i \(0.435185\pi\)
\(440\) 0 0
\(441\) −19.4647 −0.926889
\(442\) 0 0
\(443\) −20.8634 −0.991252 −0.495626 0.868536i \(-0.665061\pi\)
−0.495626 + 0.868536i \(0.665061\pi\)
\(444\) 0 0
\(445\) 0.258195 0.0122396
\(446\) 0 0
\(447\) −33.5279 −1.58582
\(448\) 0 0
\(449\) −33.8575 −1.59783 −0.798917 0.601441i \(-0.794594\pi\)
−0.798917 + 0.601441i \(0.794594\pi\)
\(450\) 0 0
\(451\) −9.43675 −0.444359
\(452\) 0 0
\(453\) 12.1612 0.571382
\(454\) 0 0
\(455\) −0.0975092 −0.00457130
\(456\) 0 0
\(457\) −11.9766 −0.560242 −0.280121 0.959965i \(-0.590375\pi\)
−0.280121 + 0.959965i \(0.590375\pi\)
\(458\) 0 0
\(459\) 0.410603 0.0191653
\(460\) 0 0
\(461\) 35.0328 1.63164 0.815820 0.578305i \(-0.196286\pi\)
0.815820 + 0.578305i \(0.196286\pi\)
\(462\) 0 0
\(463\) 37.1208 1.72515 0.862575 0.505928i \(-0.168850\pi\)
0.862575 + 0.505928i \(0.168850\pi\)
\(464\) 0 0
\(465\) −1.18220 −0.0548231
\(466\) 0 0
\(467\) 7.96690 0.368664 0.184332 0.982864i \(-0.440988\pi\)
0.184332 + 0.982864i \(0.440988\pi\)
\(468\) 0 0
\(469\) −0.548397 −0.0253226
\(470\) 0 0
\(471\) 13.1226 0.604655
\(472\) 0 0
\(473\) 8.11683 0.373212
\(474\) 0 0
\(475\) −33.2968 −1.52776
\(476\) 0 0
\(477\) −12.8843 −0.589933
\(478\) 0 0
\(479\) −16.3586 −0.747442 −0.373721 0.927541i \(-0.621918\pi\)
−0.373721 + 0.927541i \(0.621918\pi\)
\(480\) 0 0
\(481\) 9.44692 0.430742
\(482\) 0 0
\(483\) −6.81597 −0.310137
\(484\) 0 0
\(485\) 0.921264 0.0418324
\(486\) 0 0
\(487\) −2.15399 −0.0976064 −0.0488032 0.998808i \(-0.515541\pi\)
−0.0488032 + 0.998808i \(0.515541\pi\)
\(488\) 0 0
\(489\) 25.1823 1.13878
\(490\) 0 0
\(491\) 28.4834 1.28544 0.642719 0.766102i \(-0.277806\pi\)
0.642719 + 0.766102i \(0.277806\pi\)
\(492\) 0 0
\(493\) 4.27135 0.192372
\(494\) 0 0
\(495\) 0.263776 0.0118558
\(496\) 0 0
\(497\) −3.23416 −0.145072
\(498\) 0 0
\(499\) −25.9575 −1.16202 −0.581008 0.813898i \(-0.697342\pi\)
−0.581008 + 0.813898i \(0.697342\pi\)
\(500\) 0 0
\(501\) −6.61421 −0.295501
\(502\) 0 0
\(503\) 12.9092 0.575592 0.287796 0.957692i \(-0.407078\pi\)
0.287796 + 0.957692i \(0.407078\pi\)
\(504\) 0 0
\(505\) −0.114702 −0.00510418
\(506\) 0 0
\(507\) 33.8254 1.50224
\(508\) 0 0
\(509\) −18.1021 −0.802362 −0.401181 0.915999i \(-0.631400\pi\)
−0.401181 + 0.915999i \(0.631400\pi\)
\(510\) 0 0
\(511\) −4.49816 −0.198987
\(512\) 0 0
\(513\) −2.73593 −0.120794
\(514\) 0 0
\(515\) 0.268356 0.0118252
\(516\) 0 0
\(517\) 11.7559 0.517022
\(518\) 0 0
\(519\) 29.4870 1.29433
\(520\) 0 0
\(521\) −13.5318 −0.592838 −0.296419 0.955058i \(-0.595792\pi\)
−0.296419 + 0.955058i \(0.595792\pi\)
\(522\) 0 0
\(523\) 11.9232 0.521363 0.260681 0.965425i \(-0.416053\pi\)
0.260681 + 0.965425i \(0.416053\pi\)
\(524\) 0 0
\(525\) −4.21253 −0.183850
\(526\) 0 0
\(527\) 9.11085 0.396875
\(528\) 0 0
\(529\) 42.3744 1.84236
\(530\) 0 0
\(531\) −2.82994 −0.122809
\(532\) 0 0
\(533\) 28.2761 1.22477
\(534\) 0 0
\(535\) 0.639633 0.0276537
\(536\) 0 0
\(537\) 54.6055 2.35640
\(538\) 0 0
\(539\) −11.9296 −0.513846
\(540\) 0 0
\(541\) 3.59963 0.154760 0.0773800 0.997002i \(-0.475345\pi\)
0.0773800 + 0.997002i \(0.475345\pi\)
\(542\) 0 0
\(543\) 40.6160 1.74300
\(544\) 0 0
\(545\) 0.651597 0.0279113
\(546\) 0 0
\(547\) −11.5984 −0.495912 −0.247956 0.968771i \(-0.579759\pi\)
−0.247956 + 0.968771i \(0.579759\pi\)
\(548\) 0 0
\(549\) −15.6167 −0.666503
\(550\) 0 0
\(551\) −28.4609 −1.21248
\(552\) 0 0
\(553\) 0.563092 0.0239451
\(554\) 0 0
\(555\) −0.235866 −0.0100120
\(556\) 0 0
\(557\) −26.9875 −1.14350 −0.571748 0.820429i \(-0.693734\pi\)
−0.571748 + 0.820429i \(0.693734\pi\)
\(558\) 0 0
\(559\) −24.3211 −1.02867
\(560\) 0 0
\(561\) −4.18784 −0.176811
\(562\) 0 0
\(563\) 32.5175 1.37045 0.685226 0.728331i \(-0.259704\pi\)
0.685226 + 0.728331i \(0.259704\pi\)
\(564\) 0 0
\(565\) −0.843213 −0.0354742
\(566\) 0 0
\(567\) −3.31022 −0.139016
\(568\) 0 0
\(569\) −12.2343 −0.512887 −0.256444 0.966559i \(-0.582551\pi\)
−0.256444 + 0.966559i \(0.582551\pi\)
\(570\) 0 0
\(571\) −3.43087 −0.143577 −0.0717887 0.997420i \(-0.522871\pi\)
−0.0717887 + 0.997420i \(0.522871\pi\)
\(572\) 0 0
\(573\) −19.3856 −0.809843
\(574\) 0 0
\(575\) 40.4039 1.68496
\(576\) 0 0
\(577\) −44.1741 −1.83899 −0.919496 0.393099i \(-0.871403\pi\)
−0.919496 + 0.393099i \(0.871403\pi\)
\(578\) 0 0
\(579\) −24.8723 −1.03366
\(580\) 0 0
\(581\) 4.87656 0.202314
\(582\) 0 0
\(583\) −7.89664 −0.327046
\(584\) 0 0
\(585\) −0.790372 −0.0326779
\(586\) 0 0
\(587\) 18.4762 0.762595 0.381298 0.924452i \(-0.375477\pi\)
0.381298 + 0.924452i \(0.375477\pi\)
\(588\) 0 0
\(589\) −60.7075 −2.50141
\(590\) 0 0
\(591\) −11.0305 −0.453736
\(592\) 0 0
\(593\) 11.3726 0.467017 0.233509 0.972355i \(-0.424979\pi\)
0.233509 + 0.972355i \(0.424979\pi\)
\(594\) 0 0
\(595\) −0.0187625 −0.000769187 0
\(596\) 0 0
\(597\) 27.1840 1.11257
\(598\) 0 0
\(599\) −20.3972 −0.833408 −0.416704 0.909042i \(-0.636815\pi\)
−0.416704 + 0.909042i \(0.636815\pi\)
\(600\) 0 0
\(601\) −7.04262 −0.287274 −0.143637 0.989630i \(-0.545880\pi\)
−0.143637 + 0.989630i \(0.545880\pi\)
\(602\) 0 0
\(603\) −4.44510 −0.181018
\(604\) 0 0
\(605\) −0.429477 −0.0174607
\(606\) 0 0
\(607\) −17.3165 −0.702855 −0.351427 0.936215i \(-0.614304\pi\)
−0.351427 + 0.936215i \(0.614304\pi\)
\(608\) 0 0
\(609\) −3.60072 −0.145909
\(610\) 0 0
\(611\) −35.2250 −1.42505
\(612\) 0 0
\(613\) 34.5167 1.39412 0.697058 0.717015i \(-0.254492\pi\)
0.697058 + 0.717015i \(0.254492\pi\)
\(614\) 0 0
\(615\) −0.705985 −0.0284681
\(616\) 0 0
\(617\) −15.1052 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(618\) 0 0
\(619\) −0.359586 −0.0144530 −0.00722648 0.999974i \(-0.502300\pi\)
−0.00722648 + 0.999974i \(0.502300\pi\)
\(620\) 0 0
\(621\) 3.31991 0.133223
\(622\) 0 0
\(623\) 1.67742 0.0672044
\(624\) 0 0
\(625\) 24.9567 0.998268
\(626\) 0 0
\(627\) 27.9045 1.11440
\(628\) 0 0
\(629\) 1.81775 0.0724786
\(630\) 0 0
\(631\) 9.43418 0.375569 0.187784 0.982210i \(-0.439869\pi\)
0.187784 + 0.982210i \(0.439869\pi\)
\(632\) 0 0
\(633\) −44.6473 −1.77457
\(634\) 0 0
\(635\) −0.687962 −0.0273009
\(636\) 0 0
\(637\) 35.7457 1.41630
\(638\) 0 0
\(639\) −26.2149 −1.03705
\(640\) 0 0
\(641\) 6.44665 0.254627 0.127314 0.991863i \(-0.459365\pi\)
0.127314 + 0.991863i \(0.459365\pi\)
\(642\) 0 0
\(643\) −23.7865 −0.938047 −0.469024 0.883186i \(-0.655394\pi\)
−0.469024 + 0.883186i \(0.655394\pi\)
\(644\) 0 0
\(645\) 0.607238 0.0239100
\(646\) 0 0
\(647\) −5.81776 −0.228720 −0.114360 0.993439i \(-0.536482\pi\)
−0.114360 + 0.993439i \(0.536482\pi\)
\(648\) 0 0
\(649\) −1.73444 −0.0680826
\(650\) 0 0
\(651\) −7.68039 −0.301018
\(652\) 0 0
\(653\) 22.1633 0.867317 0.433658 0.901077i \(-0.357222\pi\)
0.433658 + 0.901077i \(0.357222\pi\)
\(654\) 0 0
\(655\) 0.311270 0.0121623
\(656\) 0 0
\(657\) −36.4604 −1.42245
\(658\) 0 0
\(659\) −19.8457 −0.773077 −0.386539 0.922273i \(-0.626329\pi\)
−0.386539 + 0.922273i \(0.626329\pi\)
\(660\) 0 0
\(661\) 20.1704 0.784538 0.392269 0.919851i \(-0.371690\pi\)
0.392269 + 0.919851i \(0.371690\pi\)
\(662\) 0 0
\(663\) 12.5484 0.487338
\(664\) 0 0
\(665\) 0.125018 0.00484800
\(666\) 0 0
\(667\) 34.5358 1.33723
\(668\) 0 0
\(669\) −47.2501 −1.82679
\(670\) 0 0
\(671\) −9.57125 −0.369494
\(672\) 0 0
\(673\) 18.1562 0.699870 0.349935 0.936774i \(-0.386204\pi\)
0.349935 + 0.936774i \(0.386204\pi\)
\(674\) 0 0
\(675\) 2.05183 0.0789749
\(676\) 0 0
\(677\) 10.7326 0.412489 0.206244 0.978501i \(-0.433876\pi\)
0.206244 + 0.978501i \(0.433876\pi\)
\(678\) 0 0
\(679\) 5.98518 0.229690
\(680\) 0 0
\(681\) −26.4600 −1.01395
\(682\) 0 0
\(683\) −23.2790 −0.890746 −0.445373 0.895345i \(-0.646929\pi\)
−0.445373 + 0.895345i \(0.646929\pi\)
\(684\) 0 0
\(685\) −0.424980 −0.0162377
\(686\) 0 0
\(687\) −60.4975 −2.30812
\(688\) 0 0
\(689\) 23.6613 0.901425
\(690\) 0 0
\(691\) 9.80026 0.372820 0.186410 0.982472i \(-0.440315\pi\)
0.186410 + 0.982472i \(0.440315\pi\)
\(692\) 0 0
\(693\) 1.71367 0.0650971
\(694\) 0 0
\(695\) 1.08337 0.0410946
\(696\) 0 0
\(697\) 5.44082 0.206086
\(698\) 0 0
\(699\) 0.979124 0.0370339
\(700\) 0 0
\(701\) 26.9483 1.01782 0.508912 0.860819i \(-0.330048\pi\)
0.508912 + 0.860819i \(0.330048\pi\)
\(702\) 0 0
\(703\) −12.1121 −0.456815
\(704\) 0 0
\(705\) 0.879483 0.0331232
\(706\) 0 0
\(707\) −0.745187 −0.0280256
\(708\) 0 0
\(709\) −32.0476 −1.20357 −0.601787 0.798657i \(-0.705544\pi\)
−0.601787 + 0.798657i \(0.705544\pi\)
\(710\) 0 0
\(711\) 4.56421 0.171171
\(712\) 0 0
\(713\) 73.6653 2.75879
\(714\) 0 0
\(715\) −0.484409 −0.0181159
\(716\) 0 0
\(717\) 65.3194 2.43940
\(718\) 0 0
\(719\) 15.6089 0.582114 0.291057 0.956706i \(-0.405993\pi\)
0.291057 + 0.956706i \(0.405993\pi\)
\(720\) 0 0
\(721\) 1.74343 0.0649288
\(722\) 0 0
\(723\) 1.84497 0.0686153
\(724\) 0 0
\(725\) 21.3444 0.792712
\(726\) 0 0
\(727\) 5.51700 0.204614 0.102307 0.994753i \(-0.467378\pi\)
0.102307 + 0.994753i \(0.467378\pi\)
\(728\) 0 0
\(729\) −23.8572 −0.883599
\(730\) 0 0
\(731\) −4.67981 −0.173089
\(732\) 0 0
\(733\) 34.1749 1.26228 0.631139 0.775670i \(-0.282588\pi\)
0.631139 + 0.775670i \(0.282588\pi\)
\(734\) 0 0
\(735\) −0.892483 −0.0329197
\(736\) 0 0
\(737\) −2.72434 −0.100352
\(738\) 0 0
\(739\) 8.66078 0.318592 0.159296 0.987231i \(-0.449078\pi\)
0.159296 + 0.987231i \(0.449078\pi\)
\(740\) 0 0
\(741\) −83.6124 −3.07158
\(742\) 0 0
\(743\) −26.9103 −0.987244 −0.493622 0.869676i \(-0.664327\pi\)
−0.493622 + 0.869676i \(0.664327\pi\)
\(744\) 0 0
\(745\) −0.746231 −0.0273398
\(746\) 0 0
\(747\) 39.5275 1.44624
\(748\) 0 0
\(749\) 4.15550 0.151839
\(750\) 0 0
\(751\) −24.6401 −0.899130 −0.449565 0.893248i \(-0.648421\pi\)
−0.449565 + 0.893248i \(0.648421\pi\)
\(752\) 0 0
\(753\) 5.07485 0.184938
\(754\) 0 0
\(755\) 0.270671 0.00985073
\(756\) 0 0
\(757\) −11.2517 −0.408950 −0.204475 0.978872i \(-0.565549\pi\)
−0.204475 + 0.978872i \(0.565549\pi\)
\(758\) 0 0
\(759\) −33.8606 −1.22906
\(760\) 0 0
\(761\) 13.3883 0.485325 0.242663 0.970111i \(-0.421979\pi\)
0.242663 + 0.970111i \(0.421979\pi\)
\(762\) 0 0
\(763\) 4.23323 0.153253
\(764\) 0 0
\(765\) −0.152082 −0.00549852
\(766\) 0 0
\(767\) 5.19703 0.187654
\(768\) 0 0
\(769\) −15.3465 −0.553407 −0.276704 0.960955i \(-0.589242\pi\)
−0.276704 + 0.960955i \(0.589242\pi\)
\(770\) 0 0
\(771\) −15.3856 −0.554098
\(772\) 0 0
\(773\) −7.93963 −0.285569 −0.142784 0.989754i \(-0.545606\pi\)
−0.142784 + 0.989754i \(0.545606\pi\)
\(774\) 0 0
\(775\) 45.5280 1.63541
\(776\) 0 0
\(777\) −1.53235 −0.0549729
\(778\) 0 0
\(779\) −36.2533 −1.29891
\(780\) 0 0
\(781\) −16.0668 −0.574914
\(782\) 0 0
\(783\) 1.75383 0.0626767
\(784\) 0 0
\(785\) 0.292069 0.0104244
\(786\) 0 0
\(787\) −21.2545 −0.757640 −0.378820 0.925470i \(-0.623670\pi\)
−0.378820 + 0.925470i \(0.623670\pi\)
\(788\) 0 0
\(789\) 29.0705 1.03494
\(790\) 0 0
\(791\) −5.47810 −0.194779
\(792\) 0 0
\(793\) 28.6791 1.01842
\(794\) 0 0
\(795\) −0.590765 −0.0209523
\(796\) 0 0
\(797\) 42.2136 1.49528 0.747641 0.664103i \(-0.231187\pi\)
0.747641 + 0.664103i \(0.231187\pi\)
\(798\) 0 0
\(799\) −6.77792 −0.239786
\(800\) 0 0
\(801\) 13.5965 0.480409
\(802\) 0 0
\(803\) −22.3461 −0.788576
\(804\) 0 0
\(805\) −0.151703 −0.00534683
\(806\) 0 0
\(807\) 48.3928 1.70351
\(808\) 0 0
\(809\) 49.0752 1.72539 0.862695 0.505724i \(-0.168775\pi\)
0.862695 + 0.505724i \(0.168775\pi\)
\(810\) 0 0
\(811\) 11.0126 0.386705 0.193353 0.981129i \(-0.438064\pi\)
0.193353 + 0.981129i \(0.438064\pi\)
\(812\) 0 0
\(813\) −55.5960 −1.94984
\(814\) 0 0
\(815\) 0.560482 0.0196328
\(816\) 0 0
\(817\) 31.1826 1.09094
\(818\) 0 0
\(819\) −5.13482 −0.179425
\(820\) 0 0
\(821\) 40.5380 1.41479 0.707394 0.706820i \(-0.249871\pi\)
0.707394 + 0.706820i \(0.249871\pi\)
\(822\) 0 0
\(823\) −0.946740 −0.0330013 −0.0165006 0.999864i \(-0.505253\pi\)
−0.0165006 + 0.999864i \(0.505253\pi\)
\(824\) 0 0
\(825\) −20.9271 −0.728589
\(826\) 0 0
\(827\) 19.5194 0.678758 0.339379 0.940650i \(-0.389783\pi\)
0.339379 + 0.940650i \(0.389783\pi\)
\(828\) 0 0
\(829\) 43.9129 1.52516 0.762579 0.646895i \(-0.223933\pi\)
0.762579 + 0.646895i \(0.223933\pi\)
\(830\) 0 0
\(831\) −15.4943 −0.537492
\(832\) 0 0
\(833\) 6.87811 0.238312
\(834\) 0 0
\(835\) −0.147212 −0.00509450
\(836\) 0 0
\(837\) 3.74094 0.129306
\(838\) 0 0
\(839\) 6.04587 0.208727 0.104363 0.994539i \(-0.466720\pi\)
0.104363 + 0.994539i \(0.466720\pi\)
\(840\) 0 0
\(841\) −10.7556 −0.370881
\(842\) 0 0
\(843\) −51.7446 −1.78218
\(844\) 0 0
\(845\) 0.752851 0.0258989
\(846\) 0 0
\(847\) −2.79018 −0.0958718
\(848\) 0 0
\(849\) 48.8979 1.67817
\(850\) 0 0
\(851\) 14.6973 0.503818
\(852\) 0 0
\(853\) 28.8950 0.989347 0.494673 0.869079i \(-0.335288\pi\)
0.494673 + 0.869079i \(0.335288\pi\)
\(854\) 0 0
\(855\) 1.01335 0.0346559
\(856\) 0 0
\(857\) −3.69170 −0.126106 −0.0630531 0.998010i \(-0.520084\pi\)
−0.0630531 + 0.998010i \(0.520084\pi\)
\(858\) 0 0
\(859\) −37.9888 −1.29616 −0.648080 0.761572i \(-0.724428\pi\)
−0.648080 + 0.761572i \(0.724428\pi\)
\(860\) 0 0
\(861\) −4.58657 −0.156310
\(862\) 0 0
\(863\) −36.3211 −1.23638 −0.618192 0.786027i \(-0.712135\pi\)
−0.618192 + 0.786027i \(0.712135\pi\)
\(864\) 0 0
\(865\) 0.656292 0.0223146
\(866\) 0 0
\(867\) 2.41453 0.0820017
\(868\) 0 0
\(869\) 2.79734 0.0948934
\(870\) 0 0
\(871\) 8.16317 0.276598
\(872\) 0 0
\(873\) 48.5136 1.64194
\(874\) 0 0
\(875\) −0.187571 −0.00634105
\(876\) 0 0
\(877\) −34.0447 −1.14961 −0.574804 0.818291i \(-0.694922\pi\)
−0.574804 + 0.818291i \(0.694922\pi\)
\(878\) 0 0
\(879\) 3.96211 0.133639
\(880\) 0 0
\(881\) −2.05354 −0.0691855 −0.0345927 0.999401i \(-0.511013\pi\)
−0.0345927 + 0.999401i \(0.511013\pi\)
\(882\) 0 0
\(883\) 17.4374 0.586816 0.293408 0.955987i \(-0.405211\pi\)
0.293408 + 0.955987i \(0.405211\pi\)
\(884\) 0 0
\(885\) −0.129757 −0.00436174
\(886\) 0 0
\(887\) −16.0174 −0.537812 −0.268906 0.963166i \(-0.586662\pi\)
−0.268906 + 0.963166i \(0.586662\pi\)
\(888\) 0 0
\(889\) −4.46948 −0.149902
\(890\) 0 0
\(891\) −16.4446 −0.550915
\(892\) 0 0
\(893\) 45.1627 1.51131
\(894\) 0 0
\(895\) 1.21535 0.0406248
\(896\) 0 0
\(897\) 101.459 3.38762
\(898\) 0 0
\(899\) 38.9157 1.29791
\(900\) 0 0
\(901\) 4.55286 0.151678
\(902\) 0 0
\(903\) 3.94505 0.131283
\(904\) 0 0
\(905\) 0.903990 0.0300496
\(906\) 0 0
\(907\) 24.6182 0.817435 0.408718 0.912661i \(-0.365976\pi\)
0.408718 + 0.912661i \(0.365976\pi\)
\(908\) 0 0
\(909\) −6.04020 −0.200341
\(910\) 0 0
\(911\) 20.9391 0.693742 0.346871 0.937913i \(-0.387244\pi\)
0.346871 + 0.937913i \(0.387244\pi\)
\(912\) 0 0
\(913\) 24.2259 0.801760
\(914\) 0 0
\(915\) −0.716047 −0.0236718
\(916\) 0 0
\(917\) 2.02223 0.0667798
\(918\) 0 0
\(919\) −41.5753 −1.37144 −0.685721 0.727864i \(-0.740513\pi\)
−0.685721 + 0.727864i \(0.740513\pi\)
\(920\) 0 0
\(921\) −53.4197 −1.76024
\(922\) 0 0
\(923\) 48.1421 1.58462
\(924\) 0 0
\(925\) 9.08352 0.298664
\(926\) 0 0
\(927\) 14.1316 0.464143
\(928\) 0 0
\(929\) 35.5445 1.16618 0.583088 0.812409i \(-0.301844\pi\)
0.583088 + 0.812409i \(0.301844\pi\)
\(930\) 0 0
\(931\) −45.8302 −1.50203
\(932\) 0 0
\(933\) 15.8654 0.519410
\(934\) 0 0
\(935\) −0.0932088 −0.00304825
\(936\) 0 0
\(937\) 8.27771 0.270421 0.135210 0.990817i \(-0.456829\pi\)
0.135210 + 0.990817i \(0.456829\pi\)
\(938\) 0 0
\(939\) −7.39092 −0.241194
\(940\) 0 0
\(941\) −4.50491 −0.146856 −0.0734279 0.997301i \(-0.523394\pi\)
−0.0734279 + 0.997301i \(0.523394\pi\)
\(942\) 0 0
\(943\) 43.9914 1.43256
\(944\) 0 0
\(945\) −0.00770393 −0.000250609 0
\(946\) 0 0
\(947\) 34.0978 1.10803 0.554015 0.832507i \(-0.313095\pi\)
0.554015 + 0.832507i \(0.313095\pi\)
\(948\) 0 0
\(949\) 66.9573 2.17353
\(950\) 0 0
\(951\) 25.3484 0.821979
\(952\) 0 0
\(953\) −18.9888 −0.615106 −0.307553 0.951531i \(-0.599510\pi\)
−0.307553 + 0.951531i \(0.599510\pi\)
\(954\) 0 0
\(955\) −0.431464 −0.0139618
\(956\) 0 0
\(957\) −17.8878 −0.578229
\(958\) 0 0
\(959\) −2.76097 −0.0891564
\(960\) 0 0
\(961\) 52.0076 1.67767
\(962\) 0 0
\(963\) 33.6829 1.08542
\(964\) 0 0
\(965\) −0.553583 −0.0178205
\(966\) 0 0
\(967\) −28.3110 −0.910421 −0.455211 0.890384i \(-0.650436\pi\)
−0.455211 + 0.890384i \(0.650436\pi\)
\(968\) 0 0
\(969\) −16.0885 −0.516837
\(970\) 0 0
\(971\) 5.06717 0.162613 0.0813066 0.996689i \(-0.474091\pi\)
0.0813066 + 0.996689i \(0.474091\pi\)
\(972\) 0 0
\(973\) 7.03834 0.225639
\(974\) 0 0
\(975\) 62.7056 2.00819
\(976\) 0 0
\(977\) 8.89827 0.284681 0.142340 0.989818i \(-0.454537\pi\)
0.142340 + 0.989818i \(0.454537\pi\)
\(978\) 0 0
\(979\) 8.33313 0.266328
\(980\) 0 0
\(981\) 34.3130 1.09553
\(982\) 0 0
\(983\) −24.9256 −0.795003 −0.397501 0.917602i \(-0.630123\pi\)
−0.397501 + 0.917602i \(0.630123\pi\)
\(984\) 0 0
\(985\) −0.245507 −0.00782250
\(986\) 0 0
\(987\) 5.71374 0.181870
\(988\) 0 0
\(989\) −37.8383 −1.20319
\(990\) 0 0
\(991\) −21.5978 −0.686076 −0.343038 0.939321i \(-0.611456\pi\)
−0.343038 + 0.939321i \(0.611456\pi\)
\(992\) 0 0
\(993\) −50.1300 −1.59083
\(994\) 0 0
\(995\) 0.605033 0.0191808
\(996\) 0 0
\(997\) −4.14487 −0.131269 −0.0656346 0.997844i \(-0.520907\pi\)
−0.0656346 + 0.997844i \(0.520907\pi\)
\(998\) 0 0
\(999\) 0.746375 0.0236143
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 \(a_p\))