Properties

Label 8016.2.a.bf.1.11
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(3.59055\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+3.59055 q^{5}\) \(-4.10828 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+3.59055 q^{5}\) \(-4.10828 q^{7}\) \(+1.00000 q^{9}\) \(-1.62131 q^{11}\) \(+5.55250 q^{13}\) \(-3.59055 q^{15}\) \(-5.51714 q^{17}\) \(+0.688902 q^{19}\) \(+4.10828 q^{21}\) \(+4.57662 q^{23}\) \(+7.89208 q^{25}\) \(-1.00000 q^{27}\) \(+3.57239 q^{29}\) \(-7.18724 q^{31}\) \(+1.62131 q^{33}\) \(-14.7510 q^{35}\) \(-10.0764 q^{37}\) \(-5.55250 q^{39}\) \(-9.17469 q^{41}\) \(-2.89063 q^{43}\) \(+3.59055 q^{45}\) \(+5.70322 q^{47}\) \(+9.87799 q^{49}\) \(+5.51714 q^{51}\) \(-0.787842 q^{53}\) \(-5.82139 q^{55}\) \(-0.688902 q^{57}\) \(+2.75855 q^{59}\) \(-1.60053 q^{61}\) \(-4.10828 q^{63}\) \(+19.9365 q^{65}\) \(-7.32502 q^{67}\) \(-4.57662 q^{69}\) \(+6.98319 q^{71}\) \(+0.181729 q^{73}\) \(-7.89208 q^{75}\) \(+6.66079 q^{77}\) \(+13.9222 q^{79}\) \(+1.00000 q^{81}\) \(-3.82200 q^{83}\) \(-19.8096 q^{85}\) \(-3.57239 q^{87}\) \(-6.78217 q^{89}\) \(-22.8112 q^{91}\) \(+7.18724 q^{93}\) \(+2.47354 q^{95}\) \(-7.41920 q^{97}\) \(-1.62131 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut -\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 3.59055 1.60574 0.802872 0.596151i \(-0.203304\pi\)
0.802872 + 0.596151i \(0.203304\pi\)
\(6\) 0 0
\(7\) −4.10828 −1.55279 −0.776393 0.630250i \(-0.782953\pi\)
−0.776393 + 0.630250i \(0.782953\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.62131 −0.488842 −0.244421 0.969669i \(-0.578598\pi\)
−0.244421 + 0.969669i \(0.578598\pi\)
\(12\) 0 0
\(13\) 5.55250 1.53999 0.769993 0.638052i \(-0.220260\pi\)
0.769993 + 0.638052i \(0.220260\pi\)
\(14\) 0 0
\(15\) −3.59055 −0.927077
\(16\) 0 0
\(17\) −5.51714 −1.33810 −0.669051 0.743216i \(-0.733299\pi\)
−0.669051 + 0.743216i \(0.733299\pi\)
\(18\) 0 0
\(19\) 0.688902 0.158045 0.0790225 0.996873i \(-0.474820\pi\)
0.0790225 + 0.996873i \(0.474820\pi\)
\(20\) 0 0
\(21\) 4.10828 0.896501
\(22\) 0 0
\(23\) 4.57662 0.954291 0.477145 0.878824i \(-0.341671\pi\)
0.477145 + 0.878824i \(0.341671\pi\)
\(24\) 0 0
\(25\) 7.89208 1.57842
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.57239 0.663376 0.331688 0.943389i \(-0.392382\pi\)
0.331688 + 0.943389i \(0.392382\pi\)
\(30\) 0 0
\(31\) −7.18724 −1.29087 −0.645433 0.763817i \(-0.723323\pi\)
−0.645433 + 0.763817i \(0.723323\pi\)
\(32\) 0 0
\(33\) 1.62131 0.282233
\(34\) 0 0
\(35\) −14.7510 −2.49338
\(36\) 0 0
\(37\) −10.0764 −1.65655 −0.828273 0.560325i \(-0.810676\pi\)
−0.828273 + 0.560325i \(0.810676\pi\)
\(38\) 0 0
\(39\) −5.55250 −0.889111
\(40\) 0 0
\(41\) −9.17469 −1.43285 −0.716423 0.697666i \(-0.754222\pi\)
−0.716423 + 0.697666i \(0.754222\pi\)
\(42\) 0 0
\(43\) −2.89063 −0.440817 −0.220408 0.975408i \(-0.570739\pi\)
−0.220408 + 0.975408i \(0.570739\pi\)
\(44\) 0 0
\(45\) 3.59055 0.535248
\(46\) 0 0
\(47\) 5.70322 0.831901 0.415950 0.909387i \(-0.363449\pi\)
0.415950 + 0.909387i \(0.363449\pi\)
\(48\) 0 0
\(49\) 9.87799 1.41114
\(50\) 0 0
\(51\) 5.51714 0.772554
\(52\) 0 0
\(53\) −0.787842 −0.108218 −0.0541092 0.998535i \(-0.517232\pi\)
−0.0541092 + 0.998535i \(0.517232\pi\)
\(54\) 0 0
\(55\) −5.82139 −0.784956
\(56\) 0 0
\(57\) −0.688902 −0.0912473
\(58\) 0 0
\(59\) 2.75855 0.359132 0.179566 0.983746i \(-0.442531\pi\)
0.179566 + 0.983746i \(0.442531\pi\)
\(60\) 0 0
\(61\) −1.60053 −0.204927 −0.102464 0.994737i \(-0.532673\pi\)
−0.102464 + 0.994737i \(0.532673\pi\)
\(62\) 0 0
\(63\) −4.10828 −0.517595
\(64\) 0 0
\(65\) 19.9365 2.47282
\(66\) 0 0
\(67\) −7.32502 −0.894893 −0.447447 0.894311i \(-0.647667\pi\)
−0.447447 + 0.894311i \(0.647667\pi\)
\(68\) 0 0
\(69\) −4.57662 −0.550960
\(70\) 0 0
\(71\) 6.98319 0.828752 0.414376 0.910106i \(-0.364000\pi\)
0.414376 + 0.910106i \(0.364000\pi\)
\(72\) 0 0
\(73\) 0.181729 0.0212698 0.0106349 0.999943i \(-0.496615\pi\)
0.0106349 + 0.999943i \(0.496615\pi\)
\(74\) 0 0
\(75\) −7.89208 −0.911299
\(76\) 0 0
\(77\) 6.66079 0.759067
\(78\) 0 0
\(79\) 13.9222 1.56637 0.783184 0.621790i \(-0.213594\pi\)
0.783184 + 0.621790i \(0.213594\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.82200 −0.419519 −0.209759 0.977753i \(-0.567268\pi\)
−0.209759 + 0.977753i \(0.567268\pi\)
\(84\) 0 0
\(85\) −19.8096 −2.14865
\(86\) 0 0
\(87\) −3.57239 −0.383000
\(88\) 0 0
\(89\) −6.78217 −0.718908 −0.359454 0.933163i \(-0.617037\pi\)
−0.359454 + 0.933163i \(0.617037\pi\)
\(90\) 0 0
\(91\) −22.8112 −2.39127
\(92\) 0 0
\(93\) 7.18724 0.745282
\(94\) 0 0
\(95\) 2.47354 0.253780
\(96\) 0 0
\(97\) −7.41920 −0.753306 −0.376653 0.926354i \(-0.622925\pi\)
−0.376653 + 0.926354i \(0.622925\pi\)
\(98\) 0 0
\(99\) −1.62131 −0.162947
\(100\) 0 0
\(101\) −19.3734 −1.92773 −0.963863 0.266399i \(-0.914166\pi\)
−0.963863 + 0.266399i \(0.914166\pi\)
\(102\) 0 0
\(103\) 2.04851 0.201846 0.100923 0.994894i \(-0.467820\pi\)
0.100923 + 0.994894i \(0.467820\pi\)
\(104\) 0 0
\(105\) 14.7510 1.43955
\(106\) 0 0
\(107\) −0.805768 −0.0778965 −0.0389482 0.999241i \(-0.512401\pi\)
−0.0389482 + 0.999241i \(0.512401\pi\)
\(108\) 0 0
\(109\) 8.62091 0.825733 0.412867 0.910791i \(-0.364528\pi\)
0.412867 + 0.910791i \(0.364528\pi\)
\(110\) 0 0
\(111\) 10.0764 0.956407
\(112\) 0 0
\(113\) 4.93599 0.464339 0.232169 0.972675i \(-0.425418\pi\)
0.232169 + 0.972675i \(0.425418\pi\)
\(114\) 0 0
\(115\) 16.4326 1.53235
\(116\) 0 0
\(117\) 5.55250 0.513329
\(118\) 0 0
\(119\) 22.6660 2.07778
\(120\) 0 0
\(121\) −8.37136 −0.761033
\(122\) 0 0
\(123\) 9.17469 0.827254
\(124\) 0 0
\(125\) 10.3842 0.928787
\(126\) 0 0
\(127\) 12.3106 1.09239 0.546196 0.837658i \(-0.316075\pi\)
0.546196 + 0.837658i \(0.316075\pi\)
\(128\) 0 0
\(129\) 2.89063 0.254506
\(130\) 0 0
\(131\) −16.4098 −1.43373 −0.716867 0.697210i \(-0.754424\pi\)
−0.716867 + 0.697210i \(0.754424\pi\)
\(132\) 0 0
\(133\) −2.83021 −0.245410
\(134\) 0 0
\(135\) −3.59055 −0.309026
\(136\) 0 0
\(137\) −16.2690 −1.38996 −0.694979 0.719030i \(-0.744586\pi\)
−0.694979 + 0.719030i \(0.744586\pi\)
\(138\) 0 0
\(139\) 5.33754 0.452724 0.226362 0.974043i \(-0.427317\pi\)
0.226362 + 0.974043i \(0.427317\pi\)
\(140\) 0 0
\(141\) −5.70322 −0.480298
\(142\) 0 0
\(143\) −9.00230 −0.752810
\(144\) 0 0
\(145\) 12.8269 1.06521
\(146\) 0 0
\(147\) −9.87799 −0.814723
\(148\) 0 0
\(149\) −9.27063 −0.759480 −0.379740 0.925093i \(-0.623986\pi\)
−0.379740 + 0.925093i \(0.623986\pi\)
\(150\) 0 0
\(151\) 20.4894 1.66741 0.833703 0.552213i \(-0.186216\pi\)
0.833703 + 0.552213i \(0.186216\pi\)
\(152\) 0 0
\(153\) −5.51714 −0.446034
\(154\) 0 0
\(155\) −25.8062 −2.07280
\(156\) 0 0
\(157\) −3.90511 −0.311662 −0.155831 0.987784i \(-0.549805\pi\)
−0.155831 + 0.987784i \(0.549805\pi\)
\(158\) 0 0
\(159\) 0.787842 0.0624799
\(160\) 0 0
\(161\) −18.8020 −1.48181
\(162\) 0 0
\(163\) 13.1543 1.03032 0.515161 0.857094i \(-0.327732\pi\)
0.515161 + 0.857094i \(0.327732\pi\)
\(164\) 0 0
\(165\) 5.82139 0.453195
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 17.8302 1.37156
\(170\) 0 0
\(171\) 0.688902 0.0526817
\(172\) 0 0
\(173\) 11.4082 0.867351 0.433676 0.901069i \(-0.357216\pi\)
0.433676 + 0.901069i \(0.357216\pi\)
\(174\) 0 0
\(175\) −32.4229 −2.45094
\(176\) 0 0
\(177\) −2.75855 −0.207345
\(178\) 0 0
\(179\) −19.7878 −1.47901 −0.739503 0.673153i \(-0.764940\pi\)
−0.739503 + 0.673153i \(0.764940\pi\)
\(180\) 0 0
\(181\) 5.54242 0.411965 0.205982 0.978556i \(-0.433961\pi\)
0.205982 + 0.978556i \(0.433961\pi\)
\(182\) 0 0
\(183\) 1.60053 0.118315
\(184\) 0 0
\(185\) −36.1798 −2.65999
\(186\) 0 0
\(187\) 8.94497 0.654121
\(188\) 0 0
\(189\) 4.10828 0.298834
\(190\) 0 0
\(191\) −17.3823 −1.25774 −0.628871 0.777510i \(-0.716483\pi\)
−0.628871 + 0.777510i \(0.716483\pi\)
\(192\) 0 0
\(193\) −10.1587 −0.731239 −0.365619 0.930765i \(-0.619143\pi\)
−0.365619 + 0.930765i \(0.619143\pi\)
\(194\) 0 0
\(195\) −19.9365 −1.42769
\(196\) 0 0
\(197\) 12.6909 0.904193 0.452096 0.891969i \(-0.350676\pi\)
0.452096 + 0.891969i \(0.350676\pi\)
\(198\) 0 0
\(199\) −27.3399 −1.93808 −0.969038 0.246913i \(-0.920584\pi\)
−0.969038 + 0.246913i \(0.920584\pi\)
\(200\) 0 0
\(201\) 7.32502 0.516667
\(202\) 0 0
\(203\) −14.6764 −1.03008
\(204\) 0 0
\(205\) −32.9422 −2.30078
\(206\) 0 0
\(207\) 4.57662 0.318097
\(208\) 0 0
\(209\) −1.11692 −0.0772591
\(210\) 0 0
\(211\) −17.6413 −1.21448 −0.607239 0.794519i \(-0.707723\pi\)
−0.607239 + 0.794519i \(0.707723\pi\)
\(212\) 0 0
\(213\) −6.98319 −0.478480
\(214\) 0 0
\(215\) −10.3790 −0.707839
\(216\) 0 0
\(217\) 29.5272 2.00444
\(218\) 0 0
\(219\) −0.181729 −0.0122801
\(220\) 0 0
\(221\) −30.6339 −2.06066
\(222\) 0 0
\(223\) −20.6260 −1.38122 −0.690608 0.723229i \(-0.742657\pi\)
−0.690608 + 0.723229i \(0.742657\pi\)
\(224\) 0 0
\(225\) 7.89208 0.526138
\(226\) 0 0
\(227\) 6.16425 0.409135 0.204568 0.978852i \(-0.434421\pi\)
0.204568 + 0.978852i \(0.434421\pi\)
\(228\) 0 0
\(229\) −19.4392 −1.28458 −0.642289 0.766462i \(-0.722015\pi\)
−0.642289 + 0.766462i \(0.722015\pi\)
\(230\) 0 0
\(231\) −6.66079 −0.438248
\(232\) 0 0
\(233\) 19.8065 1.29757 0.648783 0.760973i \(-0.275278\pi\)
0.648783 + 0.760973i \(0.275278\pi\)
\(234\) 0 0
\(235\) 20.4777 1.33582
\(236\) 0 0
\(237\) −13.9222 −0.904343
\(238\) 0 0
\(239\) −1.11360 −0.0720327 −0.0360164 0.999351i \(-0.511467\pi\)
−0.0360164 + 0.999351i \(0.511467\pi\)
\(240\) 0 0
\(241\) −26.4165 −1.70164 −0.850820 0.525458i \(-0.823894\pi\)
−0.850820 + 0.525458i \(0.823894\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 35.4675 2.26593
\(246\) 0 0
\(247\) 3.82513 0.243387
\(248\) 0 0
\(249\) 3.82200 0.242209
\(250\) 0 0
\(251\) −1.81268 −0.114415 −0.0572077 0.998362i \(-0.518220\pi\)
−0.0572077 + 0.998362i \(0.518220\pi\)
\(252\) 0 0
\(253\) −7.42010 −0.466498
\(254\) 0 0
\(255\) 19.8096 1.24052
\(256\) 0 0
\(257\) 1.84493 0.115084 0.0575418 0.998343i \(-0.481674\pi\)
0.0575418 + 0.998343i \(0.481674\pi\)
\(258\) 0 0
\(259\) 41.3966 2.57226
\(260\) 0 0
\(261\) 3.57239 0.221125
\(262\) 0 0
\(263\) 7.50485 0.462769 0.231384 0.972862i \(-0.425674\pi\)
0.231384 + 0.972862i \(0.425674\pi\)
\(264\) 0 0
\(265\) −2.82879 −0.173771
\(266\) 0 0
\(267\) 6.78217 0.415062
\(268\) 0 0
\(269\) −6.31805 −0.385218 −0.192609 0.981276i \(-0.561695\pi\)
−0.192609 + 0.981276i \(0.561695\pi\)
\(270\) 0 0
\(271\) −8.88653 −0.539818 −0.269909 0.962886i \(-0.586994\pi\)
−0.269909 + 0.962886i \(0.586994\pi\)
\(272\) 0 0
\(273\) 22.8112 1.38060
\(274\) 0 0
\(275\) −12.7955 −0.771596
\(276\) 0 0
\(277\) 30.3868 1.82576 0.912882 0.408223i \(-0.133851\pi\)
0.912882 + 0.408223i \(0.133851\pi\)
\(278\) 0 0
\(279\) −7.18724 −0.430289
\(280\) 0 0
\(281\) −15.0587 −0.898330 −0.449165 0.893449i \(-0.648278\pi\)
−0.449165 + 0.893449i \(0.648278\pi\)
\(282\) 0 0
\(283\) −19.8690 −1.18109 −0.590546 0.807004i \(-0.701088\pi\)
−0.590546 + 0.807004i \(0.701088\pi\)
\(284\) 0 0
\(285\) −2.47354 −0.146520
\(286\) 0 0
\(287\) 37.6922 2.22490
\(288\) 0 0
\(289\) 13.4388 0.790517
\(290\) 0 0
\(291\) 7.41920 0.434921
\(292\) 0 0
\(293\) 2.68694 0.156973 0.0784864 0.996915i \(-0.474991\pi\)
0.0784864 + 0.996915i \(0.474991\pi\)
\(294\) 0 0
\(295\) 9.90472 0.576675
\(296\) 0 0
\(297\) 1.62131 0.0940778
\(298\) 0 0
\(299\) 25.4117 1.46959
\(300\) 0 0
\(301\) 11.8755 0.684493
\(302\) 0 0
\(303\) 19.3734 1.11297
\(304\) 0 0
\(305\) −5.74680 −0.329061
\(306\) 0 0
\(307\) −20.8605 −1.19057 −0.595284 0.803515i \(-0.702961\pi\)
−0.595284 + 0.803515i \(0.702961\pi\)
\(308\) 0 0
\(309\) −2.04851 −0.116536
\(310\) 0 0
\(311\) 10.4158 0.590627 0.295313 0.955400i \(-0.404576\pi\)
0.295313 + 0.955400i \(0.404576\pi\)
\(312\) 0 0
\(313\) 30.9992 1.75218 0.876089 0.482149i \(-0.160144\pi\)
0.876089 + 0.482149i \(0.160144\pi\)
\(314\) 0 0
\(315\) −14.7510 −0.831125
\(316\) 0 0
\(317\) −24.8470 −1.39555 −0.697774 0.716318i \(-0.745826\pi\)
−0.697774 + 0.716318i \(0.745826\pi\)
\(318\) 0 0
\(319\) −5.79194 −0.324286
\(320\) 0 0
\(321\) 0.805768 0.0449736
\(322\) 0 0
\(323\) −3.80077 −0.211480
\(324\) 0 0
\(325\) 43.8207 2.43074
\(326\) 0 0
\(327\) −8.62091 −0.476737
\(328\) 0 0
\(329\) −23.4305 −1.29176
\(330\) 0 0
\(331\) 17.7919 0.977930 0.488965 0.872303i \(-0.337375\pi\)
0.488965 + 0.872303i \(0.337375\pi\)
\(332\) 0 0
\(333\) −10.0764 −0.552182
\(334\) 0 0
\(335\) −26.3009 −1.43697
\(336\) 0 0
\(337\) 30.5764 1.66560 0.832802 0.553570i \(-0.186735\pi\)
0.832802 + 0.553570i \(0.186735\pi\)
\(338\) 0 0
\(339\) −4.93599 −0.268086
\(340\) 0 0
\(341\) 11.6527 0.631030
\(342\) 0 0
\(343\) −11.8236 −0.638414
\(344\) 0 0
\(345\) −16.4326 −0.884701
\(346\) 0 0
\(347\) −17.2533 −0.926207 −0.463104 0.886304i \(-0.653264\pi\)
−0.463104 + 0.886304i \(0.653264\pi\)
\(348\) 0 0
\(349\) −10.6088 −0.567874 −0.283937 0.958843i \(-0.591641\pi\)
−0.283937 + 0.958843i \(0.591641\pi\)
\(350\) 0 0
\(351\) −5.55250 −0.296370
\(352\) 0 0
\(353\) −25.8287 −1.37472 −0.687362 0.726315i \(-0.741231\pi\)
−0.687362 + 0.726315i \(0.741231\pi\)
\(354\) 0 0
\(355\) 25.0735 1.33076
\(356\) 0 0
\(357\) −22.6660 −1.19961
\(358\) 0 0
\(359\) 16.5743 0.874759 0.437379 0.899277i \(-0.355907\pi\)
0.437379 + 0.899277i \(0.355907\pi\)
\(360\) 0 0
\(361\) −18.5254 −0.975022
\(362\) 0 0
\(363\) 8.37136 0.439383
\(364\) 0 0
\(365\) 0.652509 0.0341539
\(366\) 0 0
\(367\) −25.5959 −1.33610 −0.668049 0.744117i \(-0.732870\pi\)
−0.668049 + 0.744117i \(0.732870\pi\)
\(368\) 0 0
\(369\) −9.17469 −0.477615
\(370\) 0 0
\(371\) 3.23668 0.168040
\(372\) 0 0
\(373\) −23.5687 −1.22034 −0.610170 0.792270i \(-0.708899\pi\)
−0.610170 + 0.792270i \(0.708899\pi\)
\(374\) 0 0
\(375\) −10.3842 −0.536236
\(376\) 0 0
\(377\) 19.8357 1.02159
\(378\) 0 0
\(379\) −19.7128 −1.01258 −0.506289 0.862364i \(-0.668983\pi\)
−0.506289 + 0.862364i \(0.668983\pi\)
\(380\) 0 0
\(381\) −12.3106 −0.630693
\(382\) 0 0
\(383\) 10.8187 0.552811 0.276406 0.961041i \(-0.410857\pi\)
0.276406 + 0.961041i \(0.410857\pi\)
\(384\) 0 0
\(385\) 23.9159 1.21887
\(386\) 0 0
\(387\) −2.89063 −0.146939
\(388\) 0 0
\(389\) 36.8399 1.86786 0.933929 0.357458i \(-0.116356\pi\)
0.933929 + 0.357458i \(0.116356\pi\)
\(390\) 0 0
\(391\) −25.2498 −1.27694
\(392\) 0 0
\(393\) 16.4098 0.827767
\(394\) 0 0
\(395\) 49.9883 2.51519
\(396\) 0 0
\(397\) 29.3928 1.47518 0.737591 0.675247i \(-0.235963\pi\)
0.737591 + 0.675247i \(0.235963\pi\)
\(398\) 0 0
\(399\) 2.83021 0.141688
\(400\) 0 0
\(401\) 27.4047 1.36853 0.684263 0.729235i \(-0.260124\pi\)
0.684263 + 0.729235i \(0.260124\pi\)
\(402\) 0 0
\(403\) −39.9071 −1.98792
\(404\) 0 0
\(405\) 3.59055 0.178416
\(406\) 0 0
\(407\) 16.3369 0.809790
\(408\) 0 0
\(409\) 33.9808 1.68024 0.840120 0.542401i \(-0.182484\pi\)
0.840120 + 0.542401i \(0.182484\pi\)
\(410\) 0 0
\(411\) 16.2690 0.802492
\(412\) 0 0
\(413\) −11.3329 −0.557655
\(414\) 0 0
\(415\) −13.7231 −0.673640
\(416\) 0 0
\(417\) −5.33754 −0.261381
\(418\) 0 0
\(419\) −15.5038 −0.757408 −0.378704 0.925518i \(-0.623630\pi\)
−0.378704 + 0.925518i \(0.623630\pi\)
\(420\) 0 0
\(421\) 21.4215 1.04402 0.522010 0.852939i \(-0.325182\pi\)
0.522010 + 0.852939i \(0.325182\pi\)
\(422\) 0 0
\(423\) 5.70322 0.277300
\(424\) 0 0
\(425\) −43.5417 −2.11208
\(426\) 0 0
\(427\) 6.57545 0.318208
\(428\) 0 0
\(429\) 9.00230 0.434635
\(430\) 0 0
\(431\) −30.5013 −1.46920 −0.734598 0.678502i \(-0.762629\pi\)
−0.734598 + 0.678502i \(0.762629\pi\)
\(432\) 0 0
\(433\) −27.4355 −1.31847 −0.659234 0.751938i \(-0.729119\pi\)
−0.659234 + 0.751938i \(0.729119\pi\)
\(434\) 0 0
\(435\) −12.8269 −0.615000
\(436\) 0 0
\(437\) 3.15284 0.150821
\(438\) 0 0
\(439\) 0.281832 0.0134511 0.00672556 0.999977i \(-0.497859\pi\)
0.00672556 + 0.999977i \(0.497859\pi\)
\(440\) 0 0
\(441\) 9.87799 0.470380
\(442\) 0 0
\(443\) 11.9068 0.565708 0.282854 0.959163i \(-0.408719\pi\)
0.282854 + 0.959163i \(0.408719\pi\)
\(444\) 0 0
\(445\) −24.3517 −1.15438
\(446\) 0 0
\(447\) 9.27063 0.438486
\(448\) 0 0
\(449\) 18.2052 0.859158 0.429579 0.903029i \(-0.358662\pi\)
0.429579 + 0.903029i \(0.358662\pi\)
\(450\) 0 0
\(451\) 14.8750 0.700436
\(452\) 0 0
\(453\) −20.4894 −0.962678
\(454\) 0 0
\(455\) −81.9050 −3.83976
\(456\) 0 0
\(457\) −9.31943 −0.435945 −0.217972 0.975955i \(-0.569944\pi\)
−0.217972 + 0.975955i \(0.569944\pi\)
\(458\) 0 0
\(459\) 5.51714 0.257518
\(460\) 0 0
\(461\) −25.0465 −1.16653 −0.583266 0.812281i \(-0.698225\pi\)
−0.583266 + 0.812281i \(0.698225\pi\)
\(462\) 0 0
\(463\) −0.497940 −0.0231412 −0.0115706 0.999933i \(-0.503683\pi\)
−0.0115706 + 0.999933i \(0.503683\pi\)
\(464\) 0 0
\(465\) 25.8062 1.19673
\(466\) 0 0
\(467\) −22.1274 −1.02393 −0.511966 0.859006i \(-0.671083\pi\)
−0.511966 + 0.859006i \(0.671083\pi\)
\(468\) 0 0
\(469\) 30.0932 1.38958
\(470\) 0 0
\(471\) 3.90511 0.179938
\(472\) 0 0
\(473\) 4.68659 0.215490
\(474\) 0 0
\(475\) 5.43687 0.249461
\(476\) 0 0
\(477\) −0.787842 −0.0360728
\(478\) 0 0
\(479\) −28.8134 −1.31652 −0.658259 0.752792i \(-0.728707\pi\)
−0.658259 + 0.752792i \(0.728707\pi\)
\(480\) 0 0
\(481\) −55.9491 −2.55106
\(482\) 0 0
\(483\) 18.8020 0.855523
\(484\) 0 0
\(485\) −26.6390 −1.20962
\(486\) 0 0
\(487\) −3.03643 −0.137594 −0.0687968 0.997631i \(-0.521916\pi\)
−0.0687968 + 0.997631i \(0.521916\pi\)
\(488\) 0 0
\(489\) −13.1543 −0.594856
\(490\) 0 0
\(491\) −20.6390 −0.931425 −0.465713 0.884936i \(-0.654202\pi\)
−0.465713 + 0.884936i \(0.654202\pi\)
\(492\) 0 0
\(493\) −19.7094 −0.887665
\(494\) 0 0
\(495\) −5.82139 −0.261652
\(496\) 0 0
\(497\) −28.6889 −1.28687
\(498\) 0 0
\(499\) −24.8144 −1.11084 −0.555422 0.831568i \(-0.687443\pi\)
−0.555422 + 0.831568i \(0.687443\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 0.0868793 0.00387375 0.00193688 0.999998i \(-0.499383\pi\)
0.00193688 + 0.999998i \(0.499383\pi\)
\(504\) 0 0
\(505\) −69.5613 −3.09544
\(506\) 0 0
\(507\) −17.8302 −0.791869
\(508\) 0 0
\(509\) 35.2337 1.56170 0.780852 0.624716i \(-0.214785\pi\)
0.780852 + 0.624716i \(0.214785\pi\)
\(510\) 0 0
\(511\) −0.746596 −0.0330274
\(512\) 0 0
\(513\) −0.688902 −0.0304158
\(514\) 0 0
\(515\) 7.35530 0.324113
\(516\) 0 0
\(517\) −9.24667 −0.406668
\(518\) 0 0
\(519\) −11.4082 −0.500766
\(520\) 0 0
\(521\) −19.7270 −0.864257 −0.432129 0.901812i \(-0.642237\pi\)
−0.432129 + 0.901812i \(0.642237\pi\)
\(522\) 0 0
\(523\) −26.8934 −1.17597 −0.587984 0.808872i \(-0.700078\pi\)
−0.587984 + 0.808872i \(0.700078\pi\)
\(524\) 0 0
\(525\) 32.4229 1.41505
\(526\) 0 0
\(527\) 39.6530 1.72731
\(528\) 0 0
\(529\) −2.05457 −0.0893290
\(530\) 0 0
\(531\) 2.75855 0.119711
\(532\) 0 0
\(533\) −50.9425 −2.20656
\(534\) 0 0
\(535\) −2.89315 −0.125082
\(536\) 0 0
\(537\) 19.7878 0.853905
\(538\) 0 0
\(539\) −16.0153 −0.689826
\(540\) 0 0
\(541\) 16.5773 0.712712 0.356356 0.934350i \(-0.384019\pi\)
0.356356 + 0.934350i \(0.384019\pi\)
\(542\) 0 0
\(543\) −5.54242 −0.237848
\(544\) 0 0
\(545\) 30.9538 1.32592
\(546\) 0 0
\(547\) −23.8486 −1.01969 −0.509846 0.860266i \(-0.670298\pi\)
−0.509846 + 0.860266i \(0.670298\pi\)
\(548\) 0 0
\(549\) −1.60053 −0.0683091
\(550\) 0 0
\(551\) 2.46103 0.104843
\(552\) 0 0
\(553\) −57.1963 −2.43223
\(554\) 0 0
\(555\) 36.1798 1.53575
\(556\) 0 0
\(557\) −35.7962 −1.51673 −0.758367 0.651828i \(-0.774002\pi\)
−0.758367 + 0.651828i \(0.774002\pi\)
\(558\) 0 0
\(559\) −16.0502 −0.678851
\(560\) 0 0
\(561\) −8.94497 −0.377657
\(562\) 0 0
\(563\) 18.8666 0.795131 0.397565 0.917574i \(-0.369855\pi\)
0.397565 + 0.917574i \(0.369855\pi\)
\(564\) 0 0
\(565\) 17.7229 0.745609
\(566\) 0 0
\(567\) −4.10828 −0.172532
\(568\) 0 0
\(569\) −20.0694 −0.841353 −0.420677 0.907211i \(-0.638207\pi\)
−0.420677 + 0.907211i \(0.638207\pi\)
\(570\) 0 0
\(571\) −37.5976 −1.57341 −0.786706 0.617328i \(-0.788215\pi\)
−0.786706 + 0.617328i \(0.788215\pi\)
\(572\) 0 0
\(573\) 17.3823 0.726158
\(574\) 0 0
\(575\) 36.1190 1.50627
\(576\) 0 0
\(577\) −26.4397 −1.10070 −0.550349 0.834934i \(-0.685506\pi\)
−0.550349 + 0.834934i \(0.685506\pi\)
\(578\) 0 0
\(579\) 10.1587 0.422181
\(580\) 0 0
\(581\) 15.7018 0.651422
\(582\) 0 0
\(583\) 1.27733 0.0529017
\(584\) 0 0
\(585\) 19.9365 0.824275
\(586\) 0 0
\(587\) 36.6050 1.51085 0.755426 0.655234i \(-0.227430\pi\)
0.755426 + 0.655234i \(0.227430\pi\)
\(588\) 0 0
\(589\) −4.95130 −0.204015
\(590\) 0 0
\(591\) −12.6909 −0.522036
\(592\) 0 0
\(593\) −9.38597 −0.385436 −0.192718 0.981254i \(-0.561730\pi\)
−0.192718 + 0.981254i \(0.561730\pi\)
\(594\) 0 0
\(595\) 81.3833 3.33639
\(596\) 0 0
\(597\) 27.3399 1.11895
\(598\) 0 0
\(599\) −40.1060 −1.63869 −0.819344 0.573303i \(-0.805662\pi\)
−0.819344 + 0.573303i \(0.805662\pi\)
\(600\) 0 0
\(601\) 31.0025 1.26462 0.632309 0.774716i \(-0.282107\pi\)
0.632309 + 0.774716i \(0.282107\pi\)
\(602\) 0 0
\(603\) −7.32502 −0.298298
\(604\) 0 0
\(605\) −30.0578 −1.22202
\(606\) 0 0
\(607\) 20.5512 0.834147 0.417074 0.908873i \(-0.363056\pi\)
0.417074 + 0.908873i \(0.363056\pi\)
\(608\) 0 0
\(609\) 14.6764 0.594717
\(610\) 0 0
\(611\) 31.6671 1.28112
\(612\) 0 0
\(613\) 36.7012 1.48235 0.741174 0.671313i \(-0.234269\pi\)
0.741174 + 0.671313i \(0.234269\pi\)
\(614\) 0 0
\(615\) 32.9422 1.32836
\(616\) 0 0
\(617\) −7.21525 −0.290475 −0.145238 0.989397i \(-0.546395\pi\)
−0.145238 + 0.989397i \(0.546395\pi\)
\(618\) 0 0
\(619\) −1.96526 −0.0789904 −0.0394952 0.999220i \(-0.512575\pi\)
−0.0394952 + 0.999220i \(0.512575\pi\)
\(620\) 0 0
\(621\) −4.57662 −0.183653
\(622\) 0 0
\(623\) 27.8631 1.11631
\(624\) 0 0
\(625\) −2.17550 −0.0870202
\(626\) 0 0
\(627\) 1.11692 0.0446056
\(628\) 0 0
\(629\) 55.5927 2.21663
\(630\) 0 0
\(631\) 21.5520 0.857970 0.428985 0.903312i \(-0.358871\pi\)
0.428985 + 0.903312i \(0.358871\pi\)
\(632\) 0 0
\(633\) 17.6413 0.701180
\(634\) 0 0
\(635\) 44.2020 1.75410
\(636\) 0 0
\(637\) 54.8475 2.17314
\(638\) 0 0
\(639\) 6.98319 0.276251
\(640\) 0 0
\(641\) −16.4228 −0.648660 −0.324330 0.945944i \(-0.605139\pi\)
−0.324330 + 0.945944i \(0.605139\pi\)
\(642\) 0 0
\(643\) −1.24263 −0.0490045 −0.0245023 0.999700i \(-0.507800\pi\)
−0.0245023 + 0.999700i \(0.507800\pi\)
\(644\) 0 0
\(645\) 10.3790 0.408671
\(646\) 0 0
\(647\) −32.8033 −1.28963 −0.644816 0.764338i \(-0.723066\pi\)
−0.644816 + 0.764338i \(0.723066\pi\)
\(648\) 0 0
\(649\) −4.47245 −0.175559
\(650\) 0 0
\(651\) −29.5272 −1.15726
\(652\) 0 0
\(653\) 10.3674 0.405707 0.202854 0.979209i \(-0.434978\pi\)
0.202854 + 0.979209i \(0.434978\pi\)
\(654\) 0 0
\(655\) −58.9204 −2.30221
\(656\) 0 0
\(657\) 0.181729 0.00708994
\(658\) 0 0
\(659\) 39.4077 1.53511 0.767554 0.640984i \(-0.221474\pi\)
0.767554 + 0.640984i \(0.221474\pi\)
\(660\) 0 0
\(661\) −30.3055 −1.17875 −0.589374 0.807861i \(-0.700625\pi\)
−0.589374 + 0.807861i \(0.700625\pi\)
\(662\) 0 0
\(663\) 30.6339 1.18972
\(664\) 0 0
\(665\) −10.1620 −0.394066
\(666\) 0 0
\(667\) 16.3495 0.633053
\(668\) 0 0
\(669\) 20.6260 0.797445
\(670\) 0 0
\(671\) 2.59496 0.100177
\(672\) 0 0
\(673\) −13.8516 −0.533940 −0.266970 0.963705i \(-0.586022\pi\)
−0.266970 + 0.963705i \(0.586022\pi\)
\(674\) 0 0
\(675\) −7.89208 −0.303766
\(676\) 0 0
\(677\) −25.5715 −0.982791 −0.491396 0.870936i \(-0.663513\pi\)
−0.491396 + 0.870936i \(0.663513\pi\)
\(678\) 0 0
\(679\) 30.4802 1.16972
\(680\) 0 0
\(681\) −6.16425 −0.236214
\(682\) 0 0
\(683\) 44.9178 1.71873 0.859365 0.511362i \(-0.170859\pi\)
0.859365 + 0.511362i \(0.170859\pi\)
\(684\) 0 0
\(685\) −58.4148 −2.23192
\(686\) 0 0
\(687\) 19.4392 0.741652
\(688\) 0 0
\(689\) −4.37449 −0.166655
\(690\) 0 0
\(691\) −6.52688 −0.248294 −0.124147 0.992264i \(-0.539619\pi\)
−0.124147 + 0.992264i \(0.539619\pi\)
\(692\) 0 0
\(693\) 6.66079 0.253022
\(694\) 0 0
\(695\) 19.1647 0.726960
\(696\) 0 0
\(697\) 50.6180 1.91729
\(698\) 0 0
\(699\) −19.8065 −0.749151
\(700\) 0 0
\(701\) 5.51986 0.208482 0.104241 0.994552i \(-0.466759\pi\)
0.104241 + 0.994552i \(0.466759\pi\)
\(702\) 0 0
\(703\) −6.94164 −0.261809
\(704\) 0 0
\(705\) −20.4777 −0.771236
\(706\) 0 0
\(707\) 79.5914 2.99334
\(708\) 0 0
\(709\) −43.8699 −1.64757 −0.823785 0.566902i \(-0.808142\pi\)
−0.823785 + 0.566902i \(0.808142\pi\)
\(710\) 0 0
\(711\) 13.9222 0.522123
\(712\) 0 0
\(713\) −32.8932 −1.23186
\(714\) 0 0
\(715\) −32.3233 −1.20882
\(716\) 0 0
\(717\) 1.11360 0.0415881
\(718\) 0 0
\(719\) 16.0080 0.596997 0.298499 0.954410i \(-0.403514\pi\)
0.298499 + 0.954410i \(0.403514\pi\)
\(720\) 0 0
\(721\) −8.41587 −0.313423
\(722\) 0 0
\(723\) 26.4165 0.982442
\(724\) 0 0
\(725\) 28.1936 1.04708
\(726\) 0 0
\(727\) −35.8776 −1.33063 −0.665313 0.746565i \(-0.731702\pi\)
−0.665313 + 0.746565i \(0.731702\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.9480 0.589857
\(732\) 0 0
\(733\) −35.6831 −1.31798 −0.658992 0.752150i \(-0.729017\pi\)
−0.658992 + 0.752150i \(0.729017\pi\)
\(734\) 0 0
\(735\) −35.4675 −1.30824
\(736\) 0 0
\(737\) 11.8761 0.437462
\(738\) 0 0
\(739\) 36.9496 1.35921 0.679607 0.733577i \(-0.262150\pi\)
0.679607 + 0.733577i \(0.262150\pi\)
\(740\) 0 0
\(741\) −3.82513 −0.140520
\(742\) 0 0
\(743\) 16.8490 0.618131 0.309066 0.951041i \(-0.399984\pi\)
0.309066 + 0.951041i \(0.399984\pi\)
\(744\) 0 0
\(745\) −33.2867 −1.21953
\(746\) 0 0
\(747\) −3.82200 −0.139840
\(748\) 0 0
\(749\) 3.31032 0.120957
\(750\) 0 0
\(751\) −45.5008 −1.66035 −0.830174 0.557505i \(-0.811759\pi\)
−0.830174 + 0.557505i \(0.811759\pi\)
\(752\) 0 0
\(753\) 1.81268 0.0660578
\(754\) 0 0
\(755\) 73.5684 2.67743
\(756\) 0 0
\(757\) 3.61208 0.131283 0.0656417 0.997843i \(-0.479091\pi\)
0.0656417 + 0.997843i \(0.479091\pi\)
\(758\) 0 0
\(759\) 7.42010 0.269333
\(760\) 0 0
\(761\) 31.5545 1.14385 0.571924 0.820306i \(-0.306197\pi\)
0.571924 + 0.820306i \(0.306197\pi\)
\(762\) 0 0
\(763\) −35.4171 −1.28219
\(764\) 0 0
\(765\) −19.8096 −0.716217
\(766\) 0 0
\(767\) 15.3168 0.553059
\(768\) 0 0
\(769\) 14.4083 0.519577 0.259789 0.965665i \(-0.416347\pi\)
0.259789 + 0.965665i \(0.416347\pi\)
\(770\) 0 0
\(771\) −1.84493 −0.0664436
\(772\) 0 0
\(773\) 6.46104 0.232387 0.116194 0.993227i \(-0.462931\pi\)
0.116194 + 0.993227i \(0.462931\pi\)
\(774\) 0 0
\(775\) −56.7222 −2.03752
\(776\) 0 0
\(777\) −41.3966 −1.48510
\(778\) 0 0
\(779\) −6.32047 −0.226454
\(780\) 0 0
\(781\) −11.3219 −0.405129
\(782\) 0 0
\(783\) −3.57239 −0.127667
\(784\) 0 0
\(785\) −14.0215 −0.500449
\(786\) 0 0
\(787\) −15.9998 −0.570330 −0.285165 0.958479i \(-0.592048\pi\)
−0.285165 + 0.958479i \(0.592048\pi\)
\(788\) 0 0
\(789\) −7.50485 −0.267180
\(790\) 0 0
\(791\) −20.2784 −0.721018
\(792\) 0 0
\(793\) −8.88696 −0.315585
\(794\) 0 0
\(795\) 2.82879 0.100327
\(796\) 0 0
\(797\) 2.33123 0.0825765 0.0412883 0.999147i \(-0.486854\pi\)
0.0412883 + 0.999147i \(0.486854\pi\)
\(798\) 0 0
\(799\) −31.4655 −1.11317
\(800\) 0 0
\(801\) −6.78217 −0.239636
\(802\) 0 0
\(803\) −0.294639 −0.0103976
\(804\) 0 0
\(805\) −67.5097 −2.37941
\(806\) 0 0
\(807\) 6.31805 0.222406
\(808\) 0 0
\(809\) 16.0736 0.565117 0.282558 0.959250i \(-0.408817\pi\)
0.282558 + 0.959250i \(0.408817\pi\)
\(810\) 0 0
\(811\) −38.6082 −1.35572 −0.677859 0.735192i \(-0.737092\pi\)
−0.677859 + 0.735192i \(0.737092\pi\)
\(812\) 0 0
\(813\) 8.88653 0.311664
\(814\) 0 0
\(815\) 47.2311 1.65443
\(816\) 0 0
\(817\) −1.99136 −0.0696689
\(818\) 0 0
\(819\) −22.8112 −0.797089
\(820\) 0 0
\(821\) −8.49502 −0.296478 −0.148239 0.988952i \(-0.547361\pi\)
−0.148239 + 0.988952i \(0.547361\pi\)
\(822\) 0 0
\(823\) 20.2987 0.707567 0.353783 0.935327i \(-0.384895\pi\)
0.353783 + 0.935327i \(0.384895\pi\)
\(824\) 0 0
\(825\) 12.7955 0.445481
\(826\) 0 0
\(827\) −31.6081 −1.09912 −0.549561 0.835454i \(-0.685205\pi\)
−0.549561 + 0.835454i \(0.685205\pi\)
\(828\) 0 0
\(829\) 30.2482 1.05056 0.525282 0.850928i \(-0.323960\pi\)
0.525282 + 0.850928i \(0.323960\pi\)
\(830\) 0 0
\(831\) −30.3868 −1.05411
\(832\) 0 0
\(833\) −54.4982 −1.88825
\(834\) 0 0
\(835\) −3.59055 −0.124256
\(836\) 0 0
\(837\) 7.18724 0.248427
\(838\) 0 0
\(839\) 38.0441 1.31343 0.656715 0.754139i \(-0.271945\pi\)
0.656715 + 0.754139i \(0.271945\pi\)
\(840\) 0 0
\(841\) −16.2380 −0.559933
\(842\) 0 0
\(843\) 15.0587 0.518651
\(844\) 0 0
\(845\) 64.0204 2.20237
\(846\) 0 0
\(847\) 34.3919 1.18172
\(848\) 0 0
\(849\) 19.8690 0.681904
\(850\) 0 0
\(851\) −46.1157 −1.58083
\(852\) 0 0
\(853\) 14.8978 0.510091 0.255045 0.966929i \(-0.417910\pi\)
0.255045 + 0.966929i \(0.417910\pi\)
\(854\) 0 0
\(855\) 2.47354 0.0845933
\(856\) 0 0
\(857\) 17.2863 0.590487 0.295244 0.955422i \(-0.404599\pi\)
0.295244 + 0.955422i \(0.404599\pi\)
\(858\) 0 0
\(859\) −2.45168 −0.0836501 −0.0418250 0.999125i \(-0.513317\pi\)
−0.0418250 + 0.999125i \(0.513317\pi\)
\(860\) 0 0
\(861\) −37.6922 −1.28455
\(862\) 0 0
\(863\) −24.4142 −0.831070 −0.415535 0.909577i \(-0.636406\pi\)
−0.415535 + 0.909577i \(0.636406\pi\)
\(864\) 0 0
\(865\) 40.9618 1.39274
\(866\) 0 0
\(867\) −13.4388 −0.456405
\(868\) 0 0
\(869\) −22.5721 −0.765707
\(870\) 0 0
\(871\) −40.6721 −1.37812
\(872\) 0 0
\(873\) −7.41920 −0.251102
\(874\) 0 0
\(875\) −42.6611 −1.44221
\(876\) 0 0
\(877\) −21.2565 −0.717782 −0.358891 0.933380i \(-0.616845\pi\)
−0.358891 + 0.933380i \(0.616845\pi\)
\(878\) 0 0
\(879\) −2.68694 −0.0906282
\(880\) 0 0
\(881\) −22.9501 −0.773209 −0.386605 0.922246i \(-0.626352\pi\)
−0.386605 + 0.922246i \(0.626352\pi\)
\(882\) 0 0
\(883\) −5.97231 −0.200984 −0.100492 0.994938i \(-0.532042\pi\)
−0.100492 + 0.994938i \(0.532042\pi\)
\(884\) 0 0
\(885\) −9.90472 −0.332943
\(886\) 0 0
\(887\) 6.82725 0.229237 0.114618 0.993410i \(-0.463436\pi\)
0.114618 + 0.993410i \(0.463436\pi\)
\(888\) 0 0
\(889\) −50.5755 −1.69625
\(890\) 0 0
\(891\) −1.62131 −0.0543158
\(892\) 0 0
\(893\) 3.92896 0.131478
\(894\) 0 0
\(895\) −71.0490 −2.37491
\(896\) 0 0
\(897\) −25.4117 −0.848471
\(898\) 0 0
\(899\) −25.6756 −0.856329
\(900\) 0 0
\(901\) 4.34663 0.144807
\(902\) 0 0
\(903\) −11.8755 −0.395192
\(904\) 0 0
\(905\) 19.9004 0.661510
\(906\) 0 0
\(907\) −16.0600 −0.533263 −0.266632 0.963798i \(-0.585911\pi\)
−0.266632 + 0.963798i \(0.585911\pi\)
\(908\) 0 0
\(909\) −19.3734 −0.642575
\(910\) 0 0
\(911\) −31.0437 −1.02852 −0.514262 0.857633i \(-0.671934\pi\)
−0.514262 + 0.857633i \(0.671934\pi\)
\(912\) 0 0
\(913\) 6.19663 0.205079
\(914\) 0 0
\(915\) 5.74680 0.189983
\(916\) 0 0
\(917\) 67.4162 2.22628
\(918\) 0 0
\(919\) 37.2155 1.22762 0.613812 0.789452i \(-0.289635\pi\)
0.613812 + 0.789452i \(0.289635\pi\)
\(920\) 0 0
\(921\) 20.8605 0.687375
\(922\) 0 0
\(923\) 38.7741 1.27627
\(924\) 0 0
\(925\) −79.5235 −2.61472
\(926\) 0 0
\(927\) 2.04851 0.0672820
\(928\) 0 0
\(929\) −7.11946 −0.233582 −0.116791 0.993157i \(-0.537261\pi\)
−0.116791 + 0.993157i \(0.537261\pi\)
\(930\) 0 0
\(931\) 6.80497 0.223024
\(932\) 0 0
\(933\) −10.4158 −0.340999
\(934\) 0 0
\(935\) 32.1174 1.05035
\(936\) 0 0
\(937\) −14.9767 −0.489268 −0.244634 0.969616i \(-0.578668\pi\)
−0.244634 + 0.969616i \(0.578668\pi\)
\(938\) 0 0
\(939\) −30.9992 −1.01162
\(940\) 0 0
\(941\) −48.7595 −1.58951 −0.794756 0.606929i \(-0.792401\pi\)
−0.794756 + 0.606929i \(0.792401\pi\)
\(942\) 0 0
\(943\) −41.9891 −1.36735
\(944\) 0 0
\(945\) 14.7510 0.479850
\(946\) 0 0
\(947\) 18.6838 0.607142 0.303571 0.952809i \(-0.401821\pi\)
0.303571 + 0.952809i \(0.401821\pi\)
\(948\) 0 0
\(949\) 1.00905 0.0327552
\(950\) 0 0
\(951\) 24.8470 0.805720
\(952\) 0 0
\(953\) 57.8655 1.87445 0.937224 0.348729i \(-0.113387\pi\)
0.937224 + 0.348729i \(0.113387\pi\)
\(954\) 0 0
\(955\) −62.4122 −2.01961
\(956\) 0 0
\(957\) 5.79194 0.187227
\(958\) 0 0
\(959\) 66.8378 2.15831
\(960\) 0 0
\(961\) 20.6564 0.666335
\(962\) 0 0
\(963\) −0.805768 −0.0259655
\(964\) 0 0
\(965\) −36.4753 −1.17418
\(966\) 0 0
\(967\) 13.9913 0.449930 0.224965 0.974367i \(-0.427773\pi\)
0.224965 + 0.974367i \(0.427773\pi\)
\(968\) 0 0
\(969\) 3.80077 0.122098
\(970\) 0 0
\(971\) 45.1729 1.44967 0.724833 0.688924i \(-0.241917\pi\)
0.724833 + 0.688924i \(0.241917\pi\)
\(972\) 0 0
\(973\) −21.9281 −0.702984
\(974\) 0 0
\(975\) −43.8207 −1.40339
\(976\) 0 0
\(977\) 4.49820 0.143910 0.0719550 0.997408i \(-0.477076\pi\)
0.0719550 + 0.997408i \(0.477076\pi\)
\(978\) 0 0
\(979\) 10.9960 0.351433
\(980\) 0 0
\(981\) 8.62091 0.275244
\(982\) 0 0
\(983\) −6.41141 −0.204492 −0.102246 0.994759i \(-0.532603\pi\)
−0.102246 + 0.994759i \(0.532603\pi\)
\(984\) 0 0
\(985\) 45.5675 1.45190
\(986\) 0 0
\(987\) 23.4305 0.745800
\(988\) 0 0
\(989\) −13.2293 −0.420667
\(990\) 0 0
\(991\) 42.9219 1.36346 0.681730 0.731604i \(-0.261228\pi\)
0.681730 + 0.731604i \(0.261228\pi\)
\(992\) 0 0
\(993\) −17.7919 −0.564608
\(994\) 0 0
\(995\) −98.1655 −3.11205
\(996\) 0 0
\(997\) −0.859857 −0.0272319 −0.0136160 0.999907i \(-0.504334\pi\)
−0.0136160 + 0.999907i \(0.504334\pi\)
\(998\) 0 0
\(999\) 10.0764 0.318802
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 \(a_p\))