Properties

Label 8004.2.a.j.1.7
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.812118\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.812118 q^{5}\) \(-4.94593 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.812118 q^{5}\) \(-4.94593 q^{7}\) \(+1.00000 q^{9}\) \(+1.85682 q^{11}\) \(-6.88102 q^{13}\) \(-0.812118 q^{15}\) \(-7.62412 q^{17}\) \(+0.765989 q^{19}\) \(-4.94593 q^{21}\) \(+1.00000 q^{23}\) \(-4.34046 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-7.16139 q^{31}\) \(+1.85682 q^{33}\) \(+4.01668 q^{35}\) \(-6.94133 q^{37}\) \(-6.88102 q^{39}\) \(-2.06531 q^{41}\) \(+12.9781 q^{43}\) \(-0.812118 q^{45}\) \(-3.03906 q^{47}\) \(+17.4622 q^{49}\) \(-7.62412 q^{51}\) \(+13.0836 q^{53}\) \(-1.50796 q^{55}\) \(+0.765989 q^{57}\) \(+6.09500 q^{59}\) \(-3.49906 q^{61}\) \(-4.94593 q^{63}\) \(+5.58820 q^{65}\) \(-9.90455 q^{67}\) \(+1.00000 q^{69}\) \(+13.9449 q^{71}\) \(-3.62415 q^{73}\) \(-4.34046 q^{75}\) \(-9.18370 q^{77}\) \(+15.4261 q^{79}\) \(+1.00000 q^{81}\) \(+0.720700 q^{83}\) \(+6.19168 q^{85}\) \(-1.00000 q^{87}\) \(+4.99841 q^{89}\) \(+34.0330 q^{91}\) \(-7.16139 q^{93}\) \(-0.622073 q^{95}\) \(-5.22122 q^{97}\) \(+1.85682 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −0.812118 −0.363190 −0.181595 0.983373i \(-0.558126\pi\)
−0.181595 + 0.983373i \(0.558126\pi\)
\(6\) 0 0
\(7\) −4.94593 −1.86939 −0.934693 0.355456i \(-0.884325\pi\)
−0.934693 + 0.355456i \(0.884325\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.85682 0.559852 0.279926 0.960022i \(-0.409690\pi\)
0.279926 + 0.960022i \(0.409690\pi\)
\(12\) 0 0
\(13\) −6.88102 −1.90845 −0.954226 0.299088i \(-0.903318\pi\)
−0.954226 + 0.299088i \(0.903318\pi\)
\(14\) 0 0
\(15\) −0.812118 −0.209688
\(16\) 0 0
\(17\) −7.62412 −1.84912 −0.924560 0.381037i \(-0.875567\pi\)
−0.924560 + 0.381037i \(0.875567\pi\)
\(18\) 0 0
\(19\) 0.765989 0.175730 0.0878650 0.996132i \(-0.471996\pi\)
0.0878650 + 0.996132i \(0.471996\pi\)
\(20\) 0 0
\(21\) −4.94593 −1.07929
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.34046 −0.868093
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −7.16139 −1.28622 −0.643112 0.765773i \(-0.722357\pi\)
−0.643112 + 0.765773i \(0.722357\pi\)
\(32\) 0 0
\(33\) 1.85682 0.323231
\(34\) 0 0
\(35\) 4.01668 0.678942
\(36\) 0 0
\(37\) −6.94133 −1.14115 −0.570574 0.821246i \(-0.693279\pi\)
−0.570574 + 0.821246i \(0.693279\pi\)
\(38\) 0 0
\(39\) −6.88102 −1.10184
\(40\) 0 0
\(41\) −2.06531 −0.322548 −0.161274 0.986910i \(-0.551560\pi\)
−0.161274 + 0.986910i \(0.551560\pi\)
\(42\) 0 0
\(43\) 12.9781 1.97914 0.989570 0.144051i \(-0.0460130\pi\)
0.989570 + 0.144051i \(0.0460130\pi\)
\(44\) 0 0
\(45\) −0.812118 −0.121063
\(46\) 0 0
\(47\) −3.03906 −0.443292 −0.221646 0.975127i \(-0.571143\pi\)
−0.221646 + 0.975127i \(0.571143\pi\)
\(48\) 0 0
\(49\) 17.4622 2.49460
\(50\) 0 0
\(51\) −7.62412 −1.06759
\(52\) 0 0
\(53\) 13.0836 1.79717 0.898586 0.438798i \(-0.144596\pi\)
0.898586 + 0.438798i \(0.144596\pi\)
\(54\) 0 0
\(55\) −1.50796 −0.203333
\(56\) 0 0
\(57\) 0.765989 0.101458
\(58\) 0 0
\(59\) 6.09500 0.793501 0.396750 0.917927i \(-0.370138\pi\)
0.396750 + 0.917927i \(0.370138\pi\)
\(60\) 0 0
\(61\) −3.49906 −0.448009 −0.224005 0.974588i \(-0.571913\pi\)
−0.224005 + 0.974588i \(0.571913\pi\)
\(62\) 0 0
\(63\) −4.94593 −0.623129
\(64\) 0 0
\(65\) 5.58820 0.693130
\(66\) 0 0
\(67\) −9.90455 −1.21003 −0.605016 0.796213i \(-0.706833\pi\)
−0.605016 + 0.796213i \(0.706833\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 13.9449 1.65495 0.827477 0.561500i \(-0.189775\pi\)
0.827477 + 0.561500i \(0.189775\pi\)
\(72\) 0 0
\(73\) −3.62415 −0.424175 −0.212088 0.977251i \(-0.568026\pi\)
−0.212088 + 0.977251i \(0.568026\pi\)
\(74\) 0 0
\(75\) −4.34046 −0.501194
\(76\) 0 0
\(77\) −9.18370 −1.04658
\(78\) 0 0
\(79\) 15.4261 1.73557 0.867783 0.496943i \(-0.165544\pi\)
0.867783 + 0.496943i \(0.165544\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.720700 0.0791071 0.0395535 0.999217i \(-0.487406\pi\)
0.0395535 + 0.999217i \(0.487406\pi\)
\(84\) 0 0
\(85\) 6.19168 0.671582
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 4.99841 0.529830 0.264915 0.964272i \(-0.414656\pi\)
0.264915 + 0.964272i \(0.414656\pi\)
\(90\) 0 0
\(91\) 34.0330 3.56763
\(92\) 0 0
\(93\) −7.16139 −0.742601
\(94\) 0 0
\(95\) −0.622073 −0.0638234
\(96\) 0 0
\(97\) −5.22122 −0.530134 −0.265067 0.964230i \(-0.585394\pi\)
−0.265067 + 0.964230i \(0.585394\pi\)
\(98\) 0 0
\(99\) 1.85682 0.186617
\(100\) 0 0
\(101\) 17.5973 1.75100 0.875499 0.483220i \(-0.160533\pi\)
0.875499 + 0.483220i \(0.160533\pi\)
\(102\) 0 0
\(103\) −9.42864 −0.929031 −0.464516 0.885565i \(-0.653772\pi\)
−0.464516 + 0.885565i \(0.653772\pi\)
\(104\) 0 0
\(105\) 4.01668 0.391988
\(106\) 0 0
\(107\) 6.07940 0.587717 0.293859 0.955849i \(-0.405060\pi\)
0.293859 + 0.955849i \(0.405060\pi\)
\(108\) 0 0
\(109\) −17.4110 −1.66767 −0.833834 0.552015i \(-0.813859\pi\)
−0.833834 + 0.552015i \(0.813859\pi\)
\(110\) 0 0
\(111\) −6.94133 −0.658842
\(112\) 0 0
\(113\) 2.07795 0.195477 0.0977386 0.995212i \(-0.468839\pi\)
0.0977386 + 0.995212i \(0.468839\pi\)
\(114\) 0 0
\(115\) −0.812118 −0.0757304
\(116\) 0 0
\(117\) −6.88102 −0.636150
\(118\) 0 0
\(119\) 37.7083 3.45672
\(120\) 0 0
\(121\) −7.55222 −0.686566
\(122\) 0 0
\(123\) −2.06531 −0.186223
\(124\) 0 0
\(125\) 7.58556 0.678473
\(126\) 0 0
\(127\) 9.91116 0.879473 0.439737 0.898127i \(-0.355072\pi\)
0.439737 + 0.898127i \(0.355072\pi\)
\(128\) 0 0
\(129\) 12.9781 1.14266
\(130\) 0 0
\(131\) −9.89560 −0.864583 −0.432291 0.901734i \(-0.642295\pi\)
−0.432291 + 0.901734i \(0.642295\pi\)
\(132\) 0 0
\(133\) −3.78853 −0.328507
\(134\) 0 0
\(135\) −0.812118 −0.0698960
\(136\) 0 0
\(137\) 12.4914 1.06721 0.533607 0.845733i \(-0.320836\pi\)
0.533607 + 0.845733i \(0.320836\pi\)
\(138\) 0 0
\(139\) 13.0653 1.10819 0.554093 0.832455i \(-0.313065\pi\)
0.554093 + 0.832455i \(0.313065\pi\)
\(140\) 0 0
\(141\) −3.03906 −0.255935
\(142\) 0 0
\(143\) −12.7768 −1.06845
\(144\) 0 0
\(145\) 0.812118 0.0674427
\(146\) 0 0
\(147\) 17.4622 1.44026
\(148\) 0 0
\(149\) −22.9919 −1.88357 −0.941786 0.336214i \(-0.890854\pi\)
−0.941786 + 0.336214i \(0.890854\pi\)
\(150\) 0 0
\(151\) −7.78139 −0.633240 −0.316620 0.948552i \(-0.602548\pi\)
−0.316620 + 0.948552i \(0.602548\pi\)
\(152\) 0 0
\(153\) −7.62412 −0.616373
\(154\) 0 0
\(155\) 5.81589 0.467143
\(156\) 0 0
\(157\) −4.12748 −0.329409 −0.164704 0.986343i \(-0.552667\pi\)
−0.164704 + 0.986343i \(0.552667\pi\)
\(158\) 0 0
\(159\) 13.0836 1.03760
\(160\) 0 0
\(161\) −4.94593 −0.389794
\(162\) 0 0
\(163\) −15.4265 −1.20829 −0.604147 0.796873i \(-0.706486\pi\)
−0.604147 + 0.796873i \(0.706486\pi\)
\(164\) 0 0
\(165\) −1.50796 −0.117394
\(166\) 0 0
\(167\) −9.47945 −0.733542 −0.366771 0.930311i \(-0.619537\pi\)
−0.366771 + 0.930311i \(0.619537\pi\)
\(168\) 0 0
\(169\) 34.3484 2.64219
\(170\) 0 0
\(171\) 0.765989 0.0585767
\(172\) 0 0
\(173\) −12.7240 −0.967385 −0.483692 0.875238i \(-0.660705\pi\)
−0.483692 + 0.875238i \(0.660705\pi\)
\(174\) 0 0
\(175\) 21.4676 1.62280
\(176\) 0 0
\(177\) 6.09500 0.458128
\(178\) 0 0
\(179\) 13.5450 1.01240 0.506200 0.862416i \(-0.331050\pi\)
0.506200 + 0.862416i \(0.331050\pi\)
\(180\) 0 0
\(181\) −18.9936 −1.41178 −0.705891 0.708320i \(-0.749453\pi\)
−0.705891 + 0.708320i \(0.749453\pi\)
\(182\) 0 0
\(183\) −3.49906 −0.258658
\(184\) 0 0
\(185\) 5.63718 0.414454
\(186\) 0 0
\(187\) −14.1566 −1.03523
\(188\) 0 0
\(189\) −4.94593 −0.359763
\(190\) 0 0
\(191\) −0.0249716 −0.00180688 −0.000903439 1.00000i \(-0.500288\pi\)
−0.000903439 1.00000i \(0.500288\pi\)
\(192\) 0 0
\(193\) 9.83124 0.707668 0.353834 0.935308i \(-0.384878\pi\)
0.353834 + 0.935308i \(0.384878\pi\)
\(194\) 0 0
\(195\) 5.58820 0.400179
\(196\) 0 0
\(197\) 4.42935 0.315578 0.157789 0.987473i \(-0.449563\pi\)
0.157789 + 0.987473i \(0.449563\pi\)
\(198\) 0 0
\(199\) −1.93109 −0.136891 −0.0684455 0.997655i \(-0.521804\pi\)
−0.0684455 + 0.997655i \(0.521804\pi\)
\(200\) 0 0
\(201\) −9.90455 −0.698613
\(202\) 0 0
\(203\) 4.94593 0.347136
\(204\) 0 0
\(205\) 1.67728 0.117146
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 1.42230 0.0983828
\(210\) 0 0
\(211\) 9.35328 0.643907 0.321953 0.946756i \(-0.395661\pi\)
0.321953 + 0.946756i \(0.395661\pi\)
\(212\) 0 0
\(213\) 13.9449 0.955488
\(214\) 0 0
\(215\) −10.5397 −0.718804
\(216\) 0 0
\(217\) 35.4197 2.40445
\(218\) 0 0
\(219\) −3.62415 −0.244898
\(220\) 0 0
\(221\) 52.4617 3.52895
\(222\) 0 0
\(223\) −1.62611 −0.108892 −0.0544462 0.998517i \(-0.517339\pi\)
−0.0544462 + 0.998517i \(0.517339\pi\)
\(224\) 0 0
\(225\) −4.34046 −0.289364
\(226\) 0 0
\(227\) −14.0590 −0.933126 −0.466563 0.884488i \(-0.654508\pi\)
−0.466563 + 0.884488i \(0.654508\pi\)
\(228\) 0 0
\(229\) 0.113933 0.00752890 0.00376445 0.999993i \(-0.498802\pi\)
0.00376445 + 0.999993i \(0.498802\pi\)
\(230\) 0 0
\(231\) −9.18370 −0.604243
\(232\) 0 0
\(233\) −5.05724 −0.331311 −0.165655 0.986184i \(-0.552974\pi\)
−0.165655 + 0.986184i \(0.552974\pi\)
\(234\) 0 0
\(235\) 2.46807 0.160999
\(236\) 0 0
\(237\) 15.4261 1.00203
\(238\) 0 0
\(239\) −9.38121 −0.606820 −0.303410 0.952860i \(-0.598125\pi\)
−0.303410 + 0.952860i \(0.598125\pi\)
\(240\) 0 0
\(241\) −19.7142 −1.26990 −0.634952 0.772551i \(-0.718980\pi\)
−0.634952 + 0.772551i \(0.718980\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −14.1814 −0.906015
\(246\) 0 0
\(247\) −5.27079 −0.335372
\(248\) 0 0
\(249\) 0.720700 0.0456725
\(250\) 0 0
\(251\) −20.4703 −1.29208 −0.646038 0.763305i \(-0.723575\pi\)
−0.646038 + 0.763305i \(0.723575\pi\)
\(252\) 0 0
\(253\) 1.85682 0.116737
\(254\) 0 0
\(255\) 6.19168 0.387738
\(256\) 0 0
\(257\) 6.14767 0.383481 0.191740 0.981446i \(-0.438587\pi\)
0.191740 + 0.981446i \(0.438587\pi\)
\(258\) 0 0
\(259\) 34.3313 2.13325
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −10.0386 −0.619005 −0.309503 0.950899i \(-0.600163\pi\)
−0.309503 + 0.950899i \(0.600163\pi\)
\(264\) 0 0
\(265\) −10.6254 −0.652715
\(266\) 0 0
\(267\) 4.99841 0.305898
\(268\) 0 0
\(269\) 28.5233 1.73910 0.869549 0.493847i \(-0.164410\pi\)
0.869549 + 0.493847i \(0.164410\pi\)
\(270\) 0 0
\(271\) 9.35548 0.568305 0.284152 0.958779i \(-0.408288\pi\)
0.284152 + 0.958779i \(0.408288\pi\)
\(272\) 0 0
\(273\) 34.0330 2.05977
\(274\) 0 0
\(275\) −8.05946 −0.486004
\(276\) 0 0
\(277\) 0.246488 0.0148100 0.00740502 0.999973i \(-0.497643\pi\)
0.00740502 + 0.999973i \(0.497643\pi\)
\(278\) 0 0
\(279\) −7.16139 −0.428741
\(280\) 0 0
\(281\) 26.4451 1.57758 0.788791 0.614662i \(-0.210708\pi\)
0.788791 + 0.614662i \(0.210708\pi\)
\(282\) 0 0
\(283\) 6.59503 0.392034 0.196017 0.980601i \(-0.437199\pi\)
0.196017 + 0.980601i \(0.437199\pi\)
\(284\) 0 0
\(285\) −0.622073 −0.0368485
\(286\) 0 0
\(287\) 10.2149 0.602966
\(288\) 0 0
\(289\) 41.1272 2.41924
\(290\) 0 0
\(291\) −5.22122 −0.306073
\(292\) 0 0
\(293\) 16.3626 0.955912 0.477956 0.878384i \(-0.341378\pi\)
0.477956 + 0.878384i \(0.341378\pi\)
\(294\) 0 0
\(295\) −4.94985 −0.288192
\(296\) 0 0
\(297\) 1.85682 0.107744
\(298\) 0 0
\(299\) −6.88102 −0.397940
\(300\) 0 0
\(301\) −64.1887 −3.69978
\(302\) 0 0
\(303\) 17.5973 1.01094
\(304\) 0 0
\(305\) 2.84165 0.162712
\(306\) 0 0
\(307\) −17.5073 −0.999197 −0.499599 0.866257i \(-0.666519\pi\)
−0.499599 + 0.866257i \(0.666519\pi\)
\(308\) 0 0
\(309\) −9.42864 −0.536377
\(310\) 0 0
\(311\) −10.0872 −0.571993 −0.285997 0.958231i \(-0.592325\pi\)
−0.285997 + 0.958231i \(0.592325\pi\)
\(312\) 0 0
\(313\) 21.6111 1.22153 0.610765 0.791812i \(-0.290862\pi\)
0.610765 + 0.791812i \(0.290862\pi\)
\(314\) 0 0
\(315\) 4.01668 0.226314
\(316\) 0 0
\(317\) −17.6316 −0.990288 −0.495144 0.868811i \(-0.664885\pi\)
−0.495144 + 0.868811i \(0.664885\pi\)
\(318\) 0 0
\(319\) −1.85682 −0.103962
\(320\) 0 0
\(321\) 6.07940 0.339319
\(322\) 0 0
\(323\) −5.83999 −0.324946
\(324\) 0 0
\(325\) 29.8668 1.65671
\(326\) 0 0
\(327\) −17.4110 −0.962829
\(328\) 0 0
\(329\) 15.0310 0.828684
\(330\) 0 0
\(331\) 18.2302 1.00202 0.501012 0.865440i \(-0.332961\pi\)
0.501012 + 0.865440i \(0.332961\pi\)
\(332\) 0 0
\(333\) −6.94133 −0.380383
\(334\) 0 0
\(335\) 8.04366 0.439472
\(336\) 0 0
\(337\) 16.5663 0.902423 0.451211 0.892417i \(-0.350992\pi\)
0.451211 + 0.892417i \(0.350992\pi\)
\(338\) 0 0
\(339\) 2.07795 0.112859
\(340\) 0 0
\(341\) −13.2974 −0.720094
\(342\) 0 0
\(343\) −51.7454 −2.79399
\(344\) 0 0
\(345\) −0.812118 −0.0437229
\(346\) 0 0
\(347\) −0.993493 −0.0533335 −0.0266668 0.999644i \(-0.508489\pi\)
−0.0266668 + 0.999644i \(0.508489\pi\)
\(348\) 0 0
\(349\) −15.2438 −0.815981 −0.407991 0.912986i \(-0.633770\pi\)
−0.407991 + 0.912986i \(0.633770\pi\)
\(350\) 0 0
\(351\) −6.88102 −0.367282
\(352\) 0 0
\(353\) 4.35780 0.231942 0.115971 0.993253i \(-0.463002\pi\)
0.115971 + 0.993253i \(0.463002\pi\)
\(354\) 0 0
\(355\) −11.3249 −0.601063
\(356\) 0 0
\(357\) 37.7083 1.99574
\(358\) 0 0
\(359\) −15.0026 −0.791808 −0.395904 0.918292i \(-0.629569\pi\)
−0.395904 + 0.918292i \(0.629569\pi\)
\(360\) 0 0
\(361\) −18.4133 −0.969119
\(362\) 0 0
\(363\) −7.55222 −0.396389
\(364\) 0 0
\(365\) 2.94324 0.154056
\(366\) 0 0
\(367\) 29.7494 1.55291 0.776454 0.630174i \(-0.217016\pi\)
0.776454 + 0.630174i \(0.217016\pi\)
\(368\) 0 0
\(369\) −2.06531 −0.107516
\(370\) 0 0
\(371\) −64.7106 −3.35961
\(372\) 0 0
\(373\) 14.3697 0.744036 0.372018 0.928226i \(-0.378666\pi\)
0.372018 + 0.928226i \(0.378666\pi\)
\(374\) 0 0
\(375\) 7.58556 0.391716
\(376\) 0 0
\(377\) 6.88102 0.354390
\(378\) 0 0
\(379\) −22.5341 −1.15750 −0.578749 0.815506i \(-0.696459\pi\)
−0.578749 + 0.815506i \(0.696459\pi\)
\(380\) 0 0
\(381\) 9.91116 0.507764
\(382\) 0 0
\(383\) 16.3663 0.836278 0.418139 0.908383i \(-0.362682\pi\)
0.418139 + 0.908383i \(0.362682\pi\)
\(384\) 0 0
\(385\) 7.45824 0.380107
\(386\) 0 0
\(387\) 12.9781 0.659713
\(388\) 0 0
\(389\) 17.6023 0.892470 0.446235 0.894916i \(-0.352764\pi\)
0.446235 + 0.894916i \(0.352764\pi\)
\(390\) 0 0
\(391\) −7.62412 −0.385568
\(392\) 0 0
\(393\) −9.89560 −0.499167
\(394\) 0 0
\(395\) −12.5278 −0.630340
\(396\) 0 0
\(397\) 23.5933 1.18411 0.592056 0.805897i \(-0.298316\pi\)
0.592056 + 0.805897i \(0.298316\pi\)
\(398\) 0 0
\(399\) −3.78853 −0.189664
\(400\) 0 0
\(401\) −17.5098 −0.874400 −0.437200 0.899364i \(-0.644030\pi\)
−0.437200 + 0.899364i \(0.644030\pi\)
\(402\) 0 0
\(403\) 49.2776 2.45469
\(404\) 0 0
\(405\) −0.812118 −0.0403544
\(406\) 0 0
\(407\) −12.8888 −0.638874
\(408\) 0 0
\(409\) 6.91708 0.342027 0.171014 0.985269i \(-0.445296\pi\)
0.171014 + 0.985269i \(0.445296\pi\)
\(410\) 0 0
\(411\) 12.4914 0.616156
\(412\) 0 0
\(413\) −30.1454 −1.48336
\(414\) 0 0
\(415\) −0.585293 −0.0287309
\(416\) 0 0
\(417\) 13.0653 0.639812
\(418\) 0 0
\(419\) 36.1660 1.76683 0.883413 0.468595i \(-0.155240\pi\)
0.883413 + 0.468595i \(0.155240\pi\)
\(420\) 0 0
\(421\) −5.14718 −0.250858 −0.125429 0.992103i \(-0.540031\pi\)
−0.125429 + 0.992103i \(0.540031\pi\)
\(422\) 0 0
\(423\) −3.03906 −0.147764
\(424\) 0 0
\(425\) 33.0922 1.60521
\(426\) 0 0
\(427\) 17.3061 0.837502
\(428\) 0 0
\(429\) −12.7768 −0.616870
\(430\) 0 0
\(431\) −5.24355 −0.252573 −0.126286 0.991994i \(-0.540306\pi\)
−0.126286 + 0.991994i \(0.540306\pi\)
\(432\) 0 0
\(433\) 25.0784 1.20519 0.602595 0.798047i \(-0.294133\pi\)
0.602595 + 0.798047i \(0.294133\pi\)
\(434\) 0 0
\(435\) 0.812118 0.0389381
\(436\) 0 0
\(437\) 0.765989 0.0366422
\(438\) 0 0
\(439\) 11.1658 0.532915 0.266457 0.963847i \(-0.414147\pi\)
0.266457 + 0.963847i \(0.414147\pi\)
\(440\) 0 0
\(441\) 17.4622 0.831534
\(442\) 0 0
\(443\) −6.99870 −0.332518 −0.166259 0.986082i \(-0.553169\pi\)
−0.166259 + 0.986082i \(0.553169\pi\)
\(444\) 0 0
\(445\) −4.05930 −0.192429
\(446\) 0 0
\(447\) −22.9919 −1.08748
\(448\) 0 0
\(449\) 35.6458 1.68223 0.841114 0.540857i \(-0.181900\pi\)
0.841114 + 0.540857i \(0.181900\pi\)
\(450\) 0 0
\(451\) −3.83491 −0.180579
\(452\) 0 0
\(453\) −7.78139 −0.365602
\(454\) 0 0
\(455\) −27.6388 −1.29573
\(456\) 0 0
\(457\) −2.92721 −0.136929 −0.0684647 0.997654i \(-0.521810\pi\)
−0.0684647 + 0.997654i \(0.521810\pi\)
\(458\) 0 0
\(459\) −7.62412 −0.355863
\(460\) 0 0
\(461\) −8.11556 −0.377979 −0.188990 0.981979i \(-0.560521\pi\)
−0.188990 + 0.981979i \(0.560521\pi\)
\(462\) 0 0
\(463\) 11.8955 0.552830 0.276415 0.961038i \(-0.410854\pi\)
0.276415 + 0.961038i \(0.410854\pi\)
\(464\) 0 0
\(465\) 5.81589 0.269705
\(466\) 0 0
\(467\) −27.3979 −1.26782 −0.633912 0.773405i \(-0.718552\pi\)
−0.633912 + 0.773405i \(0.718552\pi\)
\(468\) 0 0
\(469\) 48.9872 2.26202
\(470\) 0 0
\(471\) −4.12748 −0.190184
\(472\) 0 0
\(473\) 24.0980 1.10803
\(474\) 0 0
\(475\) −3.32475 −0.152550
\(476\) 0 0
\(477\) 13.0836 0.599057
\(478\) 0 0
\(479\) 18.2273 0.832827 0.416413 0.909175i \(-0.363287\pi\)
0.416413 + 0.909175i \(0.363287\pi\)
\(480\) 0 0
\(481\) 47.7634 2.17782
\(482\) 0 0
\(483\) −4.94593 −0.225048
\(484\) 0 0
\(485\) 4.24024 0.192539
\(486\) 0 0
\(487\) 12.2112 0.553344 0.276672 0.960964i \(-0.410769\pi\)
0.276672 + 0.960964i \(0.410769\pi\)
\(488\) 0 0
\(489\) −15.4265 −0.697608
\(490\) 0 0
\(491\) 24.7324 1.11616 0.558079 0.829788i \(-0.311539\pi\)
0.558079 + 0.829788i \(0.311539\pi\)
\(492\) 0 0
\(493\) 7.62412 0.343373
\(494\) 0 0
\(495\) −1.50796 −0.0677776
\(496\) 0 0
\(497\) −68.9704 −3.09375
\(498\) 0 0
\(499\) 41.7864 1.87062 0.935309 0.353832i \(-0.115121\pi\)
0.935309 + 0.353832i \(0.115121\pi\)
\(500\) 0 0
\(501\) −9.47945 −0.423511
\(502\) 0 0
\(503\) −26.4959 −1.18139 −0.590697 0.806894i \(-0.701147\pi\)
−0.590697 + 0.806894i \(0.701147\pi\)
\(504\) 0 0
\(505\) −14.2911 −0.635945
\(506\) 0 0
\(507\) 34.3484 1.52547
\(508\) 0 0
\(509\) −29.6337 −1.31349 −0.656746 0.754112i \(-0.728068\pi\)
−0.656746 + 0.754112i \(0.728068\pi\)
\(510\) 0 0
\(511\) 17.9248 0.792947
\(512\) 0 0
\(513\) 0.765989 0.0338193
\(514\) 0 0
\(515\) 7.65716 0.337415
\(516\) 0 0
\(517\) −5.64298 −0.248178
\(518\) 0 0
\(519\) −12.7240 −0.558520
\(520\) 0 0
\(521\) 5.07091 0.222160 0.111080 0.993811i \(-0.464569\pi\)
0.111080 + 0.993811i \(0.464569\pi\)
\(522\) 0 0
\(523\) −3.70485 −0.162002 −0.0810008 0.996714i \(-0.525812\pi\)
−0.0810008 + 0.996714i \(0.525812\pi\)
\(524\) 0 0
\(525\) 21.4676 0.936924
\(526\) 0 0
\(527\) 54.5993 2.37838
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 6.09500 0.264500
\(532\) 0 0
\(533\) 14.2114 0.615566
\(534\) 0 0
\(535\) −4.93719 −0.213453
\(536\) 0 0
\(537\) 13.5450 0.584509
\(538\) 0 0
\(539\) 32.4242 1.39661
\(540\) 0 0
\(541\) 4.15109 0.178469 0.0892347 0.996011i \(-0.471558\pi\)
0.0892347 + 0.996011i \(0.471558\pi\)
\(542\) 0 0
\(543\) −18.9936 −0.815093
\(544\) 0 0
\(545\) 14.1398 0.605681
\(546\) 0 0
\(547\) −13.2304 −0.565691 −0.282846 0.959165i \(-0.591278\pi\)
−0.282846 + 0.959165i \(0.591278\pi\)
\(548\) 0 0
\(549\) −3.49906 −0.149336
\(550\) 0 0
\(551\) −0.765989 −0.0326322
\(552\) 0 0
\(553\) −76.2962 −3.24444
\(554\) 0 0
\(555\) 5.63718 0.239285
\(556\) 0 0
\(557\) −36.6588 −1.55328 −0.776641 0.629943i \(-0.783078\pi\)
−0.776641 + 0.629943i \(0.783078\pi\)
\(558\) 0 0
\(559\) −89.3025 −3.77709
\(560\) 0 0
\(561\) −14.1566 −0.597692
\(562\) 0 0
\(563\) −19.0766 −0.803982 −0.401991 0.915644i \(-0.631682\pi\)
−0.401991 + 0.915644i \(0.631682\pi\)
\(564\) 0 0
\(565\) −1.68754 −0.0709953
\(566\) 0 0
\(567\) −4.94593 −0.207710
\(568\) 0 0
\(569\) −42.3700 −1.77624 −0.888121 0.459610i \(-0.847989\pi\)
−0.888121 + 0.459610i \(0.847989\pi\)
\(570\) 0 0
\(571\) 2.63564 0.110298 0.0551490 0.998478i \(-0.482437\pi\)
0.0551490 + 0.998478i \(0.482437\pi\)
\(572\) 0 0
\(573\) −0.0249716 −0.00104320
\(574\) 0 0
\(575\) −4.34046 −0.181010
\(576\) 0 0
\(577\) 0.740812 0.0308404 0.0154202 0.999881i \(-0.495091\pi\)
0.0154202 + 0.999881i \(0.495091\pi\)
\(578\) 0 0
\(579\) 9.83124 0.408573
\(580\) 0 0
\(581\) −3.56453 −0.147882
\(582\) 0 0
\(583\) 24.2939 1.00615
\(584\) 0 0
\(585\) 5.58820 0.231043
\(586\) 0 0
\(587\) −6.89109 −0.284426 −0.142213 0.989836i \(-0.545422\pi\)
−0.142213 + 0.989836i \(0.545422\pi\)
\(588\) 0 0
\(589\) −5.48555 −0.226028
\(590\) 0 0
\(591\) 4.42935 0.182199
\(592\) 0 0
\(593\) −44.3354 −1.82064 −0.910319 0.413907i \(-0.864164\pi\)
−0.910319 + 0.413907i \(0.864164\pi\)
\(594\) 0 0
\(595\) −30.6236 −1.25545
\(596\) 0 0
\(597\) −1.93109 −0.0790341
\(598\) 0 0
\(599\) −27.2406 −1.11302 −0.556509 0.830841i \(-0.687860\pi\)
−0.556509 + 0.830841i \(0.687860\pi\)
\(600\) 0 0
\(601\) −8.15062 −0.332471 −0.166235 0.986086i \(-0.553161\pi\)
−0.166235 + 0.986086i \(0.553161\pi\)
\(602\) 0 0
\(603\) −9.90455 −0.403344
\(604\) 0 0
\(605\) 6.13329 0.249354
\(606\) 0 0
\(607\) 26.6056 1.07989 0.539944 0.841701i \(-0.318446\pi\)
0.539944 + 0.841701i \(0.318446\pi\)
\(608\) 0 0
\(609\) 4.94593 0.200419
\(610\) 0 0
\(611\) 20.9118 0.846001
\(612\) 0 0
\(613\) −9.44054 −0.381300 −0.190650 0.981658i \(-0.561059\pi\)
−0.190650 + 0.981658i \(0.561059\pi\)
\(614\) 0 0
\(615\) 1.67728 0.0676343
\(616\) 0 0
\(617\) 9.95593 0.400811 0.200405 0.979713i \(-0.435774\pi\)
0.200405 + 0.979713i \(0.435774\pi\)
\(618\) 0 0
\(619\) 5.11351 0.205529 0.102765 0.994706i \(-0.467231\pi\)
0.102765 + 0.994706i \(0.467231\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −24.7218 −0.990457
\(624\) 0 0
\(625\) 15.5420 0.621678
\(626\) 0 0
\(627\) 1.42230 0.0568013
\(628\) 0 0
\(629\) 52.9215 2.11012
\(630\) 0 0
\(631\) −29.4493 −1.17236 −0.586179 0.810182i \(-0.699368\pi\)
−0.586179 + 0.810182i \(0.699368\pi\)
\(632\) 0 0
\(633\) 9.35328 0.371760
\(634\) 0 0
\(635\) −8.04903 −0.319416
\(636\) 0 0
\(637\) −120.158 −4.76083
\(638\) 0 0
\(639\) 13.9449 0.551651
\(640\) 0 0
\(641\) 15.3757 0.607303 0.303652 0.952783i \(-0.401794\pi\)
0.303652 + 0.952783i \(0.401794\pi\)
\(642\) 0 0
\(643\) 35.6822 1.40717 0.703585 0.710611i \(-0.251581\pi\)
0.703585 + 0.710611i \(0.251581\pi\)
\(644\) 0 0
\(645\) −10.5397 −0.415002
\(646\) 0 0
\(647\) 28.9106 1.13659 0.568297 0.822824i \(-0.307603\pi\)
0.568297 + 0.822824i \(0.307603\pi\)
\(648\) 0 0
\(649\) 11.3173 0.444243
\(650\) 0 0
\(651\) 35.4197 1.38821
\(652\) 0 0
\(653\) 6.58135 0.257548 0.128774 0.991674i \(-0.458896\pi\)
0.128774 + 0.991674i \(0.458896\pi\)
\(654\) 0 0
\(655\) 8.03639 0.314008
\(656\) 0 0
\(657\) −3.62415 −0.141392
\(658\) 0 0
\(659\) −48.8441 −1.90270 −0.951349 0.308115i \(-0.900302\pi\)
−0.951349 + 0.308115i \(0.900302\pi\)
\(660\) 0 0
\(661\) 40.9767 1.59381 0.796904 0.604106i \(-0.206470\pi\)
0.796904 + 0.604106i \(0.206470\pi\)
\(662\) 0 0
\(663\) 52.4617 2.03744
\(664\) 0 0
\(665\) 3.07673 0.119311
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −1.62611 −0.0628691
\(670\) 0 0
\(671\) −6.49713 −0.250819
\(672\) 0 0
\(673\) 42.6389 1.64361 0.821804 0.569770i \(-0.192968\pi\)
0.821804 + 0.569770i \(0.192968\pi\)
\(674\) 0 0
\(675\) −4.34046 −0.167065
\(676\) 0 0
\(677\) −27.8300 −1.06959 −0.534796 0.844981i \(-0.679612\pi\)
−0.534796 + 0.844981i \(0.679612\pi\)
\(678\) 0 0
\(679\) 25.8238 0.991025
\(680\) 0 0
\(681\) −14.0590 −0.538741
\(682\) 0 0
\(683\) 37.2516 1.42539 0.712697 0.701472i \(-0.247473\pi\)
0.712697 + 0.701472i \(0.247473\pi\)
\(684\) 0 0
\(685\) −10.1445 −0.387602
\(686\) 0 0
\(687\) 0.113933 0.00434681
\(688\) 0 0
\(689\) −90.0285 −3.42981
\(690\) 0 0
\(691\) −9.45465 −0.359672 −0.179836 0.983697i \(-0.557557\pi\)
−0.179836 + 0.983697i \(0.557557\pi\)
\(692\) 0 0
\(693\) −9.18370 −0.348860
\(694\) 0 0
\(695\) −10.6106 −0.402482
\(696\) 0 0
\(697\) 15.7462 0.596429
\(698\) 0 0
\(699\) −5.05724 −0.191282
\(700\) 0 0
\(701\) 37.6280 1.42119 0.710596 0.703601i \(-0.248426\pi\)
0.710596 + 0.703601i \(0.248426\pi\)
\(702\) 0 0
\(703\) −5.31699 −0.200534
\(704\) 0 0
\(705\) 2.46807 0.0929530
\(706\) 0 0
\(707\) −87.0351 −3.27329
\(708\) 0 0
\(709\) 25.0874 0.942177 0.471088 0.882086i \(-0.343861\pi\)
0.471088 + 0.882086i \(0.343861\pi\)
\(710\) 0 0
\(711\) 15.4261 0.578522
\(712\) 0 0
\(713\) −7.16139 −0.268196
\(714\) 0 0
\(715\) 10.3763 0.388050
\(716\) 0 0
\(717\) −9.38121 −0.350348
\(718\) 0 0
\(719\) −35.2087 −1.31306 −0.656531 0.754299i \(-0.727977\pi\)
−0.656531 + 0.754299i \(0.727977\pi\)
\(720\) 0 0
\(721\) 46.6334 1.73672
\(722\) 0 0
\(723\) −19.7142 −0.733180
\(724\) 0 0
\(725\) 4.34046 0.161201
\(726\) 0 0
\(727\) −18.7656 −0.695976 −0.347988 0.937499i \(-0.613135\pi\)
−0.347988 + 0.937499i \(0.613135\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −98.9465 −3.65967
\(732\) 0 0
\(733\) −38.4650 −1.42074 −0.710368 0.703830i \(-0.751471\pi\)
−0.710368 + 0.703830i \(0.751471\pi\)
\(734\) 0 0
\(735\) −14.1814 −0.523088
\(736\) 0 0
\(737\) −18.3909 −0.677439
\(738\) 0 0
\(739\) −19.5454 −0.718988 −0.359494 0.933147i \(-0.617051\pi\)
−0.359494 + 0.933147i \(0.617051\pi\)
\(740\) 0 0
\(741\) −5.27079 −0.193627
\(742\) 0 0
\(743\) −22.1029 −0.810878 −0.405439 0.914122i \(-0.632881\pi\)
−0.405439 + 0.914122i \(0.632881\pi\)
\(744\) 0 0
\(745\) 18.6721 0.684094
\(746\) 0 0
\(747\) 0.720700 0.0263690
\(748\) 0 0
\(749\) −30.0683 −1.09867
\(750\) 0 0
\(751\) −17.6098 −0.642590 −0.321295 0.946979i \(-0.604118\pi\)
−0.321295 + 0.946979i \(0.604118\pi\)
\(752\) 0 0
\(753\) −20.4703 −0.745981
\(754\) 0 0
\(755\) 6.31940 0.229987
\(756\) 0 0
\(757\) −44.3255 −1.61104 −0.805519 0.592570i \(-0.798113\pi\)
−0.805519 + 0.592570i \(0.798113\pi\)
\(758\) 0 0
\(759\) 1.85682 0.0673983
\(760\) 0 0
\(761\) −7.34078 −0.266103 −0.133052 0.991109i \(-0.542478\pi\)
−0.133052 + 0.991109i \(0.542478\pi\)
\(762\) 0 0
\(763\) 86.1135 3.11752
\(764\) 0 0
\(765\) 6.19168 0.223861
\(766\) 0 0
\(767\) −41.9398 −1.51436
\(768\) 0 0
\(769\) 17.0004 0.613050 0.306525 0.951863i \(-0.400834\pi\)
0.306525 + 0.951863i \(0.400834\pi\)
\(770\) 0 0
\(771\) 6.14767 0.221403
\(772\) 0 0
\(773\) −10.6061 −0.381476 −0.190738 0.981641i \(-0.561088\pi\)
−0.190738 + 0.981641i \(0.561088\pi\)
\(774\) 0 0
\(775\) 31.0837 1.11656
\(776\) 0 0
\(777\) 34.3313 1.23163
\(778\) 0 0
\(779\) −1.58201 −0.0566813
\(780\) 0 0
\(781\) 25.8931 0.926529
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 3.35200 0.119638
\(786\) 0 0
\(787\) −28.6736 −1.02210 −0.511052 0.859550i \(-0.670744\pi\)
−0.511052 + 0.859550i \(0.670744\pi\)
\(788\) 0 0
\(789\) −10.0386 −0.357383
\(790\) 0 0
\(791\) −10.2774 −0.365422
\(792\) 0 0
\(793\) 24.0771 0.855003
\(794\) 0 0
\(795\) −10.6254 −0.376845
\(796\) 0 0
\(797\) 5.69586 0.201758 0.100879 0.994899i \(-0.467835\pi\)
0.100879 + 0.994899i \(0.467835\pi\)
\(798\) 0 0
\(799\) 23.1701 0.819700
\(800\) 0 0
\(801\) 4.99841 0.176610
\(802\) 0 0
\(803\) −6.72940 −0.237475
\(804\) 0 0
\(805\) 4.01668 0.141569
\(806\) 0 0
\(807\) 28.5233 1.00407
\(808\) 0 0
\(809\) 30.2084 1.06207 0.531035 0.847350i \(-0.321803\pi\)
0.531035 + 0.847350i \(0.321803\pi\)
\(810\) 0 0
\(811\) 30.3134 1.06445 0.532224 0.846604i \(-0.321357\pi\)
0.532224 + 0.846604i \(0.321357\pi\)
\(812\) 0 0
\(813\) 9.35548 0.328111
\(814\) 0 0
\(815\) 12.5281 0.438840
\(816\) 0 0
\(817\) 9.94108 0.347794
\(818\) 0 0
\(819\) 34.0330 1.18921
\(820\) 0 0
\(821\) 24.8099 0.865871 0.432935 0.901425i \(-0.357478\pi\)
0.432935 + 0.901425i \(0.357478\pi\)
\(822\) 0 0
\(823\) 8.77313 0.305812 0.152906 0.988241i \(-0.451137\pi\)
0.152906 + 0.988241i \(0.451137\pi\)
\(824\) 0 0
\(825\) −8.05946 −0.280594
\(826\) 0 0
\(827\) −56.7440 −1.97318 −0.986592 0.163208i \(-0.947816\pi\)
−0.986592 + 0.163208i \(0.947816\pi\)
\(828\) 0 0
\(829\) −6.30091 −0.218840 −0.109420 0.993996i \(-0.534899\pi\)
−0.109420 + 0.993996i \(0.534899\pi\)
\(830\) 0 0
\(831\) 0.246488 0.00855058
\(832\) 0 0
\(833\) −133.134 −4.61282
\(834\) 0 0
\(835\) 7.69843 0.266415
\(836\) 0 0
\(837\) −7.16139 −0.247534
\(838\) 0 0
\(839\) −2.38808 −0.0824455 −0.0412228 0.999150i \(-0.513125\pi\)
−0.0412228 + 0.999150i \(0.513125\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 26.4451 0.910817
\(844\) 0 0
\(845\) −27.8950 −0.959615
\(846\) 0 0
\(847\) 37.3528 1.28346
\(848\) 0 0
\(849\) 6.59503 0.226341
\(850\) 0 0
\(851\) −6.94133 −0.237946
\(852\) 0 0
\(853\) −14.6922 −0.503051 −0.251526 0.967851i \(-0.580932\pi\)
−0.251526 + 0.967851i \(0.580932\pi\)
\(854\) 0 0
\(855\) −0.622073 −0.0212745
\(856\) 0 0
\(857\) −4.72578 −0.161430 −0.0807148 0.996737i \(-0.525720\pi\)
−0.0807148 + 0.996737i \(0.525720\pi\)
\(858\) 0 0
\(859\) −37.4858 −1.27900 −0.639500 0.768791i \(-0.720858\pi\)
−0.639500 + 0.768791i \(0.720858\pi\)
\(860\) 0 0
\(861\) 10.2149 0.348122
\(862\) 0 0
\(863\) −32.5637 −1.10848 −0.554240 0.832357i \(-0.686991\pi\)
−0.554240 + 0.832357i \(0.686991\pi\)
\(864\) 0 0
\(865\) 10.3334 0.351344
\(866\) 0 0
\(867\) 41.1272 1.39675
\(868\) 0 0
\(869\) 28.6434 0.971660
\(870\) 0 0
\(871\) 68.1534 2.30929
\(872\) 0 0
\(873\) −5.22122 −0.176711
\(874\) 0 0
\(875\) −37.5176 −1.26833
\(876\) 0 0
\(877\) 44.0063 1.48599 0.742994 0.669298i \(-0.233405\pi\)
0.742994 + 0.669298i \(0.233405\pi\)
\(878\) 0 0
\(879\) 16.3626 0.551896
\(880\) 0 0
\(881\) 32.2383 1.08614 0.543069 0.839688i \(-0.317262\pi\)
0.543069 + 0.839688i \(0.317262\pi\)
\(882\) 0 0
\(883\) 28.1619 0.947724 0.473862 0.880599i \(-0.342860\pi\)
0.473862 + 0.880599i \(0.342860\pi\)
\(884\) 0 0
\(885\) −4.94985 −0.166388
\(886\) 0 0
\(887\) 22.6636 0.760970 0.380485 0.924787i \(-0.375757\pi\)
0.380485 + 0.924787i \(0.375757\pi\)
\(888\) 0 0
\(889\) −49.0199 −1.64408
\(890\) 0 0
\(891\) 1.85682 0.0622058
\(892\) 0 0
\(893\) −2.32789 −0.0778997
\(894\) 0 0
\(895\) −11.0001 −0.367694
\(896\) 0 0
\(897\) −6.88102 −0.229751
\(898\) 0 0
\(899\) 7.16139 0.238846
\(900\) 0 0
\(901\) −99.7510 −3.32319
\(902\) 0 0
\(903\) −64.1887 −2.13607
\(904\) 0 0
\(905\) 15.4250 0.512745
\(906\) 0 0
\(907\) 17.9805 0.597033 0.298516 0.954404i \(-0.403508\pi\)
0.298516 + 0.954404i \(0.403508\pi\)
\(908\) 0 0
\(909\) 17.5973 0.583666
\(910\) 0 0
\(911\) −50.4635 −1.67193 −0.835965 0.548783i \(-0.815091\pi\)
−0.835965 + 0.548783i \(0.815091\pi\)
\(912\) 0 0
\(913\) 1.33821 0.0442882
\(914\) 0 0
\(915\) 2.84165 0.0939421
\(916\) 0 0
\(917\) 48.9430 1.61624
\(918\) 0 0
\(919\) 39.9767 1.31871 0.659355 0.751832i \(-0.270830\pi\)
0.659355 + 0.751832i \(0.270830\pi\)
\(920\) 0 0
\(921\) −17.5073 −0.576887
\(922\) 0 0
\(923\) −95.9550 −3.15840
\(924\) 0 0
\(925\) 30.1286 0.990622
\(926\) 0 0
\(927\) −9.42864 −0.309677
\(928\) 0 0
\(929\) 23.1825 0.760593 0.380297 0.924865i \(-0.375822\pi\)
0.380297 + 0.924865i \(0.375822\pi\)
\(930\) 0 0
\(931\) 13.3759 0.438377
\(932\) 0 0
\(933\) −10.0872 −0.330240
\(934\) 0 0
\(935\) 11.4968 0.375986
\(936\) 0 0
\(937\) −31.7331 −1.03668 −0.518338 0.855176i \(-0.673449\pi\)
−0.518338 + 0.855176i \(0.673449\pi\)
\(938\) 0 0
\(939\) 21.6111 0.705251
\(940\) 0 0
\(941\) 59.5878 1.94251 0.971254 0.238046i \(-0.0765069\pi\)
0.971254 + 0.238046i \(0.0765069\pi\)
\(942\) 0 0
\(943\) −2.06531 −0.0672558
\(944\) 0 0
\(945\) 4.01668 0.130663
\(946\) 0 0
\(947\) 33.4587 1.08726 0.543631 0.839324i \(-0.317049\pi\)
0.543631 + 0.839324i \(0.317049\pi\)
\(948\) 0 0
\(949\) 24.9379 0.809517
\(950\) 0 0
\(951\) −17.6316 −0.571743
\(952\) 0 0
\(953\) 15.4240 0.499632 0.249816 0.968293i \(-0.419630\pi\)
0.249816 + 0.968293i \(0.419630\pi\)
\(954\) 0 0
\(955\) 0.0202798 0.000656240 0
\(956\) 0 0
\(957\) −1.85682 −0.0600224
\(958\) 0 0
\(959\) −61.7817 −1.99503
\(960\) 0 0
\(961\) 20.2855 0.654370
\(962\) 0 0
\(963\) 6.07940 0.195906
\(964\) 0 0
\(965\) −7.98413 −0.257018
\(966\) 0 0
\(967\) −17.8301 −0.573376 −0.286688 0.958024i \(-0.592554\pi\)
−0.286688 + 0.958024i \(0.592554\pi\)
\(968\) 0 0
\(969\) −5.83999 −0.187608
\(970\) 0 0
\(971\) 50.1093 1.60809 0.804043 0.594571i \(-0.202678\pi\)
0.804043 + 0.594571i \(0.202678\pi\)
\(972\) 0 0
\(973\) −64.6202 −2.07163
\(974\) 0 0
\(975\) 29.8668 0.956504
\(976\) 0 0
\(977\) −41.2024 −1.31818 −0.659090 0.752064i \(-0.729058\pi\)
−0.659090 + 0.752064i \(0.729058\pi\)
\(978\) 0 0
\(979\) 9.28114 0.296626
\(980\) 0 0
\(981\) −17.4110 −0.555890
\(982\) 0 0
\(983\) 35.7778 1.14113 0.570567 0.821251i \(-0.306724\pi\)
0.570567 + 0.821251i \(0.306724\pi\)
\(984\) 0 0
\(985\) −3.59715 −0.114615
\(986\) 0 0
\(987\) 15.0310 0.478441
\(988\) 0 0
\(989\) 12.9781 0.412679
\(990\) 0 0
\(991\) −33.3072 −1.05804 −0.529019 0.848610i \(-0.677440\pi\)
−0.529019 + 0.848610i \(0.677440\pi\)
\(992\) 0 0
\(993\) 18.2302 0.578519
\(994\) 0 0
\(995\) 1.56827 0.0497175
\(996\) 0 0
\(997\) 12.0657 0.382123 0.191062 0.981578i \(-0.438807\pi\)
0.191062 + 0.981578i \(0.438807\pi\)
\(998\) 0 0
\(999\) −6.94133 −0.219614
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 \(a_p\))