Properties

Label 8008.2.a.y.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.38813\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.38813 q^{3} -4.16385 q^{5} +1.00000 q^{7} +8.47945 q^{9} +O(q^{10})\) \(q-3.38813 q^{3} -4.16385 q^{5} +1.00000 q^{7} +8.47945 q^{9} -1.00000 q^{11} -1.00000 q^{13} +14.1077 q^{15} -4.56251 q^{17} -0.578129 q^{19} -3.38813 q^{21} -6.33270 q^{23} +12.3376 q^{25} -18.5651 q^{27} +2.97225 q^{29} +5.14700 q^{31} +3.38813 q^{33} -4.16385 q^{35} +3.64891 q^{37} +3.38813 q^{39} -8.27358 q^{41} -10.1989 q^{43} -35.3071 q^{45} -3.73854 q^{47} +1.00000 q^{49} +15.4584 q^{51} -7.91971 q^{53} +4.16385 q^{55} +1.95878 q^{57} +14.8556 q^{59} -2.44437 q^{61} +8.47945 q^{63} +4.16385 q^{65} -1.18087 q^{67} +21.4560 q^{69} +13.4792 q^{71} +1.09880 q^{73} -41.8016 q^{75} -1.00000 q^{77} +9.93914 q^{79} +37.4627 q^{81} -15.7239 q^{83} +18.9976 q^{85} -10.0704 q^{87} +8.11272 q^{89} -1.00000 q^{91} -17.4387 q^{93} +2.40724 q^{95} +10.1163 q^{97} -8.47945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.38813 −1.95614 −0.978070 0.208278i \(-0.933214\pi\)
−0.978070 + 0.208278i \(0.933214\pi\)
\(4\) 0 0
\(5\) −4.16385 −1.86213 −0.931065 0.364853i \(-0.881119\pi\)
−0.931065 + 0.364853i \(0.881119\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 8.47945 2.82648
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 14.1077 3.64259
\(16\) 0 0
\(17\) −4.56251 −1.10657 −0.553285 0.832992i \(-0.686626\pi\)
−0.553285 + 0.832992i \(0.686626\pi\)
\(18\) 0 0
\(19\) −0.578129 −0.132632 −0.0663159 0.997799i \(-0.521125\pi\)
−0.0663159 + 0.997799i \(0.521125\pi\)
\(20\) 0 0
\(21\) −3.38813 −0.739351
\(22\) 0 0
\(23\) −6.33270 −1.32046 −0.660230 0.751064i \(-0.729541\pi\)
−0.660230 + 0.751064i \(0.729541\pi\)
\(24\) 0 0
\(25\) 12.3376 2.46753
\(26\) 0 0
\(27\) −18.5651 −3.57285
\(28\) 0 0
\(29\) 2.97225 0.551933 0.275967 0.961167i \(-0.411002\pi\)
0.275967 + 0.961167i \(0.411002\pi\)
\(30\) 0 0
\(31\) 5.14700 0.924429 0.462214 0.886768i \(-0.347055\pi\)
0.462214 + 0.886768i \(0.347055\pi\)
\(32\) 0 0
\(33\) 3.38813 0.589798
\(34\) 0 0
\(35\) −4.16385 −0.703819
\(36\) 0 0
\(37\) 3.64891 0.599878 0.299939 0.953958i \(-0.403034\pi\)
0.299939 + 0.953958i \(0.403034\pi\)
\(38\) 0 0
\(39\) 3.38813 0.542535
\(40\) 0 0
\(41\) −8.27358 −1.29212 −0.646058 0.763288i \(-0.723584\pi\)
−0.646058 + 0.763288i \(0.723584\pi\)
\(42\) 0 0
\(43\) −10.1989 −1.55532 −0.777660 0.628685i \(-0.783594\pi\)
−0.777660 + 0.628685i \(0.783594\pi\)
\(44\) 0 0
\(45\) −35.3071 −5.26328
\(46\) 0 0
\(47\) −3.73854 −0.545322 −0.272661 0.962110i \(-0.587904\pi\)
−0.272661 + 0.962110i \(0.587904\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 15.4584 2.16461
\(52\) 0 0
\(53\) −7.91971 −1.08786 −0.543928 0.839132i \(-0.683063\pi\)
−0.543928 + 0.839132i \(0.683063\pi\)
\(54\) 0 0
\(55\) 4.16385 0.561453
\(56\) 0 0
\(57\) 1.95878 0.259446
\(58\) 0 0
\(59\) 14.8556 1.93404 0.967020 0.254701i \(-0.0819771\pi\)
0.967020 + 0.254701i \(0.0819771\pi\)
\(60\) 0 0
\(61\) −2.44437 −0.312970 −0.156485 0.987680i \(-0.550016\pi\)
−0.156485 + 0.987680i \(0.550016\pi\)
\(62\) 0 0
\(63\) 8.47945 1.06831
\(64\) 0 0
\(65\) 4.16385 0.516462
\(66\) 0 0
\(67\) −1.18087 −0.144266 −0.0721332 0.997395i \(-0.522981\pi\)
−0.0721332 + 0.997395i \(0.522981\pi\)
\(68\) 0 0
\(69\) 21.4560 2.58300
\(70\) 0 0
\(71\) 13.4792 1.59969 0.799844 0.600208i \(-0.204916\pi\)
0.799844 + 0.600208i \(0.204916\pi\)
\(72\) 0 0
\(73\) 1.09880 0.128605 0.0643024 0.997930i \(-0.479518\pi\)
0.0643024 + 0.997930i \(0.479518\pi\)
\(74\) 0 0
\(75\) −41.8016 −4.82683
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 9.93914 1.11824 0.559120 0.829087i \(-0.311139\pi\)
0.559120 + 0.829087i \(0.311139\pi\)
\(80\) 0 0
\(81\) 37.4627 4.16252
\(82\) 0 0
\(83\) −15.7239 −1.72592 −0.862960 0.505272i \(-0.831392\pi\)
−0.862960 + 0.505272i \(0.831392\pi\)
\(84\) 0 0
\(85\) 18.9976 2.06058
\(86\) 0 0
\(87\) −10.0704 −1.07966
\(88\) 0 0
\(89\) 8.11272 0.859947 0.429973 0.902842i \(-0.358523\pi\)
0.429973 + 0.902842i \(0.358523\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −17.4387 −1.80831
\(94\) 0 0
\(95\) 2.40724 0.246978
\(96\) 0 0
\(97\) 10.1163 1.02715 0.513575 0.858045i \(-0.328321\pi\)
0.513575 + 0.858045i \(0.328321\pi\)
\(98\) 0 0
\(99\) −8.47945 −0.852216
\(100\) 0 0
\(101\) 12.5130 1.24509 0.622544 0.782585i \(-0.286099\pi\)
0.622544 + 0.782585i \(0.286099\pi\)
\(102\) 0 0
\(103\) −6.10720 −0.601760 −0.300880 0.953662i \(-0.597280\pi\)
−0.300880 + 0.953662i \(0.597280\pi\)
\(104\) 0 0
\(105\) 14.1077 1.37677
\(106\) 0 0
\(107\) 4.32012 0.417642 0.208821 0.977954i \(-0.433037\pi\)
0.208821 + 0.977954i \(0.433037\pi\)
\(108\) 0 0
\(109\) 4.94475 0.473621 0.236810 0.971556i \(-0.423898\pi\)
0.236810 + 0.971556i \(0.423898\pi\)
\(110\) 0 0
\(111\) −12.3630 −1.17344
\(112\) 0 0
\(113\) 13.5510 1.27477 0.637385 0.770545i \(-0.280016\pi\)
0.637385 + 0.770545i \(0.280016\pi\)
\(114\) 0 0
\(115\) 26.3684 2.45887
\(116\) 0 0
\(117\) −8.47945 −0.783925
\(118\) 0 0
\(119\) −4.56251 −0.418244
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 28.0320 2.52756
\(124\) 0 0
\(125\) −30.5529 −2.73273
\(126\) 0 0
\(127\) −5.22621 −0.463751 −0.231875 0.972745i \(-0.574486\pi\)
−0.231875 + 0.972745i \(0.574486\pi\)
\(128\) 0 0
\(129\) 34.5553 3.04242
\(130\) 0 0
\(131\) 7.90049 0.690269 0.345135 0.938553i \(-0.387833\pi\)
0.345135 + 0.938553i \(0.387833\pi\)
\(132\) 0 0
\(133\) −0.578129 −0.0501301
\(134\) 0 0
\(135\) 77.3022 6.65312
\(136\) 0 0
\(137\) 12.1583 1.03876 0.519379 0.854544i \(-0.326163\pi\)
0.519379 + 0.854544i \(0.326163\pi\)
\(138\) 0 0
\(139\) 5.65024 0.479247 0.239624 0.970866i \(-0.422976\pi\)
0.239624 + 0.970866i \(0.422976\pi\)
\(140\) 0 0
\(141\) 12.6667 1.06673
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −12.3760 −1.02777
\(146\) 0 0
\(147\) −3.38813 −0.279448
\(148\) 0 0
\(149\) −8.36077 −0.684941 −0.342470 0.939529i \(-0.611264\pi\)
−0.342470 + 0.939529i \(0.611264\pi\)
\(150\) 0 0
\(151\) 1.72322 0.140233 0.0701167 0.997539i \(-0.477663\pi\)
0.0701167 + 0.997539i \(0.477663\pi\)
\(152\) 0 0
\(153\) −38.6875 −3.12770
\(154\) 0 0
\(155\) −21.4313 −1.72141
\(156\) 0 0
\(157\) 20.6885 1.65112 0.825561 0.564312i \(-0.190859\pi\)
0.825561 + 0.564312i \(0.190859\pi\)
\(158\) 0 0
\(159\) 26.8330 2.12800
\(160\) 0 0
\(161\) −6.33270 −0.499087
\(162\) 0 0
\(163\) −4.82463 −0.377894 −0.188947 0.981987i \(-0.560507\pi\)
−0.188947 + 0.981987i \(0.560507\pi\)
\(164\) 0 0
\(165\) −14.1077 −1.09828
\(166\) 0 0
\(167\) −0.413591 −0.0320046 −0.0160023 0.999872i \(-0.505094\pi\)
−0.0160023 + 0.999872i \(0.505094\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.90221 −0.374882
\(172\) 0 0
\(173\) −6.38148 −0.485175 −0.242588 0.970129i \(-0.577996\pi\)
−0.242588 + 0.970129i \(0.577996\pi\)
\(174\) 0 0
\(175\) 12.3376 0.932638
\(176\) 0 0
\(177\) −50.3329 −3.78325
\(178\) 0 0
\(179\) −21.3150 −1.59316 −0.796580 0.604533i \(-0.793360\pi\)
−0.796580 + 0.604533i \(0.793360\pi\)
\(180\) 0 0
\(181\) −10.9922 −0.817044 −0.408522 0.912749i \(-0.633956\pi\)
−0.408522 + 0.912749i \(0.633956\pi\)
\(182\) 0 0
\(183\) 8.28186 0.612212
\(184\) 0 0
\(185\) −15.1935 −1.11705
\(186\) 0 0
\(187\) 4.56251 0.333644
\(188\) 0 0
\(189\) −18.5651 −1.35041
\(190\) 0 0
\(191\) −14.4677 −1.04684 −0.523422 0.852074i \(-0.675345\pi\)
−0.523422 + 0.852074i \(0.675345\pi\)
\(192\) 0 0
\(193\) 17.8784 1.28692 0.643459 0.765481i \(-0.277499\pi\)
0.643459 + 0.765481i \(0.277499\pi\)
\(194\) 0 0
\(195\) −14.1077 −1.01027
\(196\) 0 0
\(197\) 13.7107 0.976844 0.488422 0.872608i \(-0.337573\pi\)
0.488422 + 0.872608i \(0.337573\pi\)
\(198\) 0 0
\(199\) −1.64030 −0.116277 −0.0581387 0.998309i \(-0.518517\pi\)
−0.0581387 + 0.998309i \(0.518517\pi\)
\(200\) 0 0
\(201\) 4.00095 0.282205
\(202\) 0 0
\(203\) 2.97225 0.208611
\(204\) 0 0
\(205\) 34.4500 2.40609
\(206\) 0 0
\(207\) −53.6978 −3.73226
\(208\) 0 0
\(209\) 0.578129 0.0399900
\(210\) 0 0
\(211\) 25.1395 1.73068 0.865338 0.501188i \(-0.167104\pi\)
0.865338 + 0.501188i \(0.167104\pi\)
\(212\) 0 0
\(213\) −45.6694 −3.12921
\(214\) 0 0
\(215\) 42.4668 2.89621
\(216\) 0 0
\(217\) 5.14700 0.349401
\(218\) 0 0
\(219\) −3.72288 −0.251569
\(220\) 0 0
\(221\) 4.56251 0.306907
\(222\) 0 0
\(223\) 4.50169 0.301456 0.150728 0.988575i \(-0.451838\pi\)
0.150728 + 0.988575i \(0.451838\pi\)
\(224\) 0 0
\(225\) 104.616 6.97443
\(226\) 0 0
\(227\) 6.91855 0.459201 0.229600 0.973285i \(-0.426258\pi\)
0.229600 + 0.973285i \(0.426258\pi\)
\(228\) 0 0
\(229\) 22.2406 1.46970 0.734851 0.678229i \(-0.237252\pi\)
0.734851 + 0.678229i \(0.237252\pi\)
\(230\) 0 0
\(231\) 3.38813 0.222923
\(232\) 0 0
\(233\) −4.54086 −0.297482 −0.148741 0.988876i \(-0.547522\pi\)
−0.148741 + 0.988876i \(0.547522\pi\)
\(234\) 0 0
\(235\) 15.5667 1.01546
\(236\) 0 0
\(237\) −33.6751 −2.18743
\(238\) 0 0
\(239\) −23.6439 −1.52940 −0.764700 0.644387i \(-0.777113\pi\)
−0.764700 + 0.644387i \(0.777113\pi\)
\(240\) 0 0
\(241\) 18.5134 1.19255 0.596277 0.802779i \(-0.296646\pi\)
0.596277 + 0.802779i \(0.296646\pi\)
\(242\) 0 0
\(243\) −71.2332 −4.56961
\(244\) 0 0
\(245\) −4.16385 −0.266019
\(246\) 0 0
\(247\) 0.578129 0.0367855
\(248\) 0 0
\(249\) 53.2746 3.37614
\(250\) 0 0
\(251\) 0.345313 0.0217960 0.0108980 0.999941i \(-0.496531\pi\)
0.0108980 + 0.999941i \(0.496531\pi\)
\(252\) 0 0
\(253\) 6.33270 0.398134
\(254\) 0 0
\(255\) −64.3664 −4.03078
\(256\) 0 0
\(257\) 6.59696 0.411507 0.205754 0.978604i \(-0.434035\pi\)
0.205754 + 0.978604i \(0.434035\pi\)
\(258\) 0 0
\(259\) 3.64891 0.226732
\(260\) 0 0
\(261\) 25.2030 1.56003
\(262\) 0 0
\(263\) 18.8188 1.16042 0.580210 0.814467i \(-0.302971\pi\)
0.580210 + 0.814467i \(0.302971\pi\)
\(264\) 0 0
\(265\) 32.9765 2.02573
\(266\) 0 0
\(267\) −27.4870 −1.68218
\(268\) 0 0
\(269\) −18.8982 −1.15224 −0.576121 0.817364i \(-0.695434\pi\)
−0.576121 + 0.817364i \(0.695434\pi\)
\(270\) 0 0
\(271\) −30.2005 −1.83455 −0.917274 0.398257i \(-0.869615\pi\)
−0.917274 + 0.398257i \(0.869615\pi\)
\(272\) 0 0
\(273\) 3.38813 0.205059
\(274\) 0 0
\(275\) −12.3376 −0.743988
\(276\) 0 0
\(277\) 22.0964 1.32764 0.663821 0.747892i \(-0.268934\pi\)
0.663821 + 0.747892i \(0.268934\pi\)
\(278\) 0 0
\(279\) 43.6437 2.61288
\(280\) 0 0
\(281\) −28.1117 −1.67700 −0.838500 0.544901i \(-0.816567\pi\)
−0.838500 + 0.544901i \(0.816567\pi\)
\(282\) 0 0
\(283\) −7.10241 −0.422194 −0.211097 0.977465i \(-0.567704\pi\)
−0.211097 + 0.977465i \(0.567704\pi\)
\(284\) 0 0
\(285\) −8.15606 −0.483123
\(286\) 0 0
\(287\) −8.27358 −0.488374
\(288\) 0 0
\(289\) 3.81647 0.224499
\(290\) 0 0
\(291\) −34.2752 −2.00925
\(292\) 0 0
\(293\) −7.05751 −0.412304 −0.206152 0.978520i \(-0.566094\pi\)
−0.206152 + 0.978520i \(0.566094\pi\)
\(294\) 0 0
\(295\) −61.8567 −3.60143
\(296\) 0 0
\(297\) 18.5651 1.07726
\(298\) 0 0
\(299\) 6.33270 0.366230
\(300\) 0 0
\(301\) −10.1989 −0.587856
\(302\) 0 0
\(303\) −42.3956 −2.43556
\(304\) 0 0
\(305\) 10.1780 0.582790
\(306\) 0 0
\(307\) 9.77610 0.557951 0.278976 0.960298i \(-0.410005\pi\)
0.278976 + 0.960298i \(0.410005\pi\)
\(308\) 0 0
\(309\) 20.6920 1.17713
\(310\) 0 0
\(311\) −2.63596 −0.149472 −0.0747358 0.997203i \(-0.523811\pi\)
−0.0747358 + 0.997203i \(0.523811\pi\)
\(312\) 0 0
\(313\) 3.11565 0.176107 0.0880534 0.996116i \(-0.471935\pi\)
0.0880534 + 0.996116i \(0.471935\pi\)
\(314\) 0 0
\(315\) −35.3071 −1.98933
\(316\) 0 0
\(317\) 26.3543 1.48020 0.740102 0.672495i \(-0.234777\pi\)
0.740102 + 0.672495i \(0.234777\pi\)
\(318\) 0 0
\(319\) −2.97225 −0.166414
\(320\) 0 0
\(321\) −14.6371 −0.816966
\(322\) 0 0
\(323\) 2.63772 0.146767
\(324\) 0 0
\(325\) −12.3376 −0.684369
\(326\) 0 0
\(327\) −16.7535 −0.926469
\(328\) 0 0
\(329\) −3.73854 −0.206113
\(330\) 0 0
\(331\) −32.3193 −1.77643 −0.888215 0.459428i \(-0.848054\pi\)
−0.888215 + 0.459428i \(0.848054\pi\)
\(332\) 0 0
\(333\) 30.9408 1.69554
\(334\) 0 0
\(335\) 4.91697 0.268643
\(336\) 0 0
\(337\) 24.9855 1.36105 0.680525 0.732725i \(-0.261752\pi\)
0.680525 + 0.732725i \(0.261752\pi\)
\(338\) 0 0
\(339\) −45.9126 −2.49363
\(340\) 0 0
\(341\) −5.14700 −0.278726
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −89.3397 −4.80989
\(346\) 0 0
\(347\) 0.828424 0.0444721 0.0222361 0.999753i \(-0.492921\pi\)
0.0222361 + 0.999753i \(0.492921\pi\)
\(348\) 0 0
\(349\) −1.41117 −0.0755381 −0.0377691 0.999286i \(-0.512025\pi\)
−0.0377691 + 0.999286i \(0.512025\pi\)
\(350\) 0 0
\(351\) 18.5651 0.990931
\(352\) 0 0
\(353\) 13.0527 0.694725 0.347363 0.937731i \(-0.387077\pi\)
0.347363 + 0.937731i \(0.387077\pi\)
\(354\) 0 0
\(355\) −56.1254 −2.97883
\(356\) 0 0
\(357\) 15.4584 0.818144
\(358\) 0 0
\(359\) −4.03934 −0.213188 −0.106594 0.994303i \(-0.533995\pi\)
−0.106594 + 0.994303i \(0.533995\pi\)
\(360\) 0 0
\(361\) −18.6658 −0.982409
\(362\) 0 0
\(363\) −3.38813 −0.177831
\(364\) 0 0
\(365\) −4.57524 −0.239479
\(366\) 0 0
\(367\) −25.1989 −1.31537 −0.657686 0.753292i \(-0.728465\pi\)
−0.657686 + 0.753292i \(0.728465\pi\)
\(368\) 0 0
\(369\) −70.1554 −3.65214
\(370\) 0 0
\(371\) −7.91971 −0.411171
\(372\) 0 0
\(373\) −10.8836 −0.563530 −0.281765 0.959483i \(-0.590920\pi\)
−0.281765 + 0.959483i \(0.590920\pi\)
\(374\) 0 0
\(375\) 103.517 5.34560
\(376\) 0 0
\(377\) −2.97225 −0.153079
\(378\) 0 0
\(379\) −0.232332 −0.0119341 −0.00596706 0.999982i \(-0.501899\pi\)
−0.00596706 + 0.999982i \(0.501899\pi\)
\(380\) 0 0
\(381\) 17.7071 0.907162
\(382\) 0 0
\(383\) −34.9499 −1.78586 −0.892928 0.450200i \(-0.851353\pi\)
−0.892928 + 0.450200i \(0.851353\pi\)
\(384\) 0 0
\(385\) 4.16385 0.212209
\(386\) 0 0
\(387\) −86.4812 −4.39608
\(388\) 0 0
\(389\) 3.22161 0.163342 0.0816710 0.996659i \(-0.473974\pi\)
0.0816710 + 0.996659i \(0.473974\pi\)
\(390\) 0 0
\(391\) 28.8930 1.46118
\(392\) 0 0
\(393\) −26.7679 −1.35026
\(394\) 0 0
\(395\) −41.3851 −2.08231
\(396\) 0 0
\(397\) −5.31581 −0.266793 −0.133396 0.991063i \(-0.542588\pi\)
−0.133396 + 0.991063i \(0.542588\pi\)
\(398\) 0 0
\(399\) 1.95878 0.0980615
\(400\) 0 0
\(401\) −1.24669 −0.0622566 −0.0311283 0.999515i \(-0.509910\pi\)
−0.0311283 + 0.999515i \(0.509910\pi\)
\(402\) 0 0
\(403\) −5.14700 −0.256390
\(404\) 0 0
\(405\) −155.989 −7.75115
\(406\) 0 0
\(407\) −3.64891 −0.180870
\(408\) 0 0
\(409\) 15.8690 0.784670 0.392335 0.919822i \(-0.371667\pi\)
0.392335 + 0.919822i \(0.371667\pi\)
\(410\) 0 0
\(411\) −41.1941 −2.03195
\(412\) 0 0
\(413\) 14.8556 0.730998
\(414\) 0 0
\(415\) 65.4719 3.21389
\(416\) 0 0
\(417\) −19.1438 −0.937474
\(418\) 0 0
\(419\) 11.4891 0.561282 0.280641 0.959813i \(-0.409453\pi\)
0.280641 + 0.959813i \(0.409453\pi\)
\(420\) 0 0
\(421\) −22.7327 −1.10792 −0.553962 0.832542i \(-0.686885\pi\)
−0.553962 + 0.832542i \(0.686885\pi\)
\(422\) 0 0
\(423\) −31.7008 −1.54134
\(424\) 0 0
\(425\) −56.2906 −2.73050
\(426\) 0 0
\(427\) −2.44437 −0.118291
\(428\) 0 0
\(429\) −3.38813 −0.163581
\(430\) 0 0
\(431\) 26.4519 1.27414 0.637071 0.770805i \(-0.280146\pi\)
0.637071 + 0.770805i \(0.280146\pi\)
\(432\) 0 0
\(433\) −27.1072 −1.30269 −0.651344 0.758782i \(-0.725795\pi\)
−0.651344 + 0.758782i \(0.725795\pi\)
\(434\) 0 0
\(435\) 41.9316 2.01046
\(436\) 0 0
\(437\) 3.66112 0.175135
\(438\) 0 0
\(439\) 18.9418 0.904043 0.452022 0.892007i \(-0.350703\pi\)
0.452022 + 0.892007i \(0.350703\pi\)
\(440\) 0 0
\(441\) 8.47945 0.403783
\(442\) 0 0
\(443\) −34.3524 −1.63213 −0.816065 0.577960i \(-0.803849\pi\)
−0.816065 + 0.577960i \(0.803849\pi\)
\(444\) 0 0
\(445\) −33.7802 −1.60133
\(446\) 0 0
\(447\) 28.3274 1.33984
\(448\) 0 0
\(449\) −11.5809 −0.546535 −0.273267 0.961938i \(-0.588104\pi\)
−0.273267 + 0.961938i \(0.588104\pi\)
\(450\) 0 0
\(451\) 8.27358 0.389588
\(452\) 0 0
\(453\) −5.83849 −0.274316
\(454\) 0 0
\(455\) 4.16385 0.195204
\(456\) 0 0
\(457\) 15.5678 0.728230 0.364115 0.931354i \(-0.381372\pi\)
0.364115 + 0.931354i \(0.381372\pi\)
\(458\) 0 0
\(459\) 84.7034 3.95361
\(460\) 0 0
\(461\) 13.2297 0.616169 0.308084 0.951359i \(-0.400312\pi\)
0.308084 + 0.951359i \(0.400312\pi\)
\(462\) 0 0
\(463\) −23.1636 −1.07651 −0.538253 0.842783i \(-0.680915\pi\)
−0.538253 + 0.842783i \(0.680915\pi\)
\(464\) 0 0
\(465\) 72.6122 3.36731
\(466\) 0 0
\(467\) −22.0130 −1.01864 −0.509319 0.860578i \(-0.670103\pi\)
−0.509319 + 0.860578i \(0.670103\pi\)
\(468\) 0 0
\(469\) −1.18087 −0.0545276
\(470\) 0 0
\(471\) −70.0954 −3.22983
\(472\) 0 0
\(473\) 10.1989 0.468947
\(474\) 0 0
\(475\) −7.13275 −0.327273
\(476\) 0 0
\(477\) −67.1547 −3.07480
\(478\) 0 0
\(479\) −4.80906 −0.219731 −0.109866 0.993946i \(-0.535042\pi\)
−0.109866 + 0.993946i \(0.535042\pi\)
\(480\) 0 0
\(481\) −3.64891 −0.166376
\(482\) 0 0
\(483\) 21.4560 0.976284
\(484\) 0 0
\(485\) −42.1226 −1.91269
\(486\) 0 0
\(487\) 16.4710 0.746373 0.373187 0.927756i \(-0.378265\pi\)
0.373187 + 0.927756i \(0.378265\pi\)
\(488\) 0 0
\(489\) 16.3465 0.739213
\(490\) 0 0
\(491\) −18.1439 −0.818825 −0.409412 0.912349i \(-0.634266\pi\)
−0.409412 + 0.912349i \(0.634266\pi\)
\(492\) 0 0
\(493\) −13.5609 −0.610753
\(494\) 0 0
\(495\) 35.3071 1.58694
\(496\) 0 0
\(497\) 13.4792 0.604625
\(498\) 0 0
\(499\) −16.6272 −0.744334 −0.372167 0.928166i \(-0.621385\pi\)
−0.372167 + 0.928166i \(0.621385\pi\)
\(500\) 0 0
\(501\) 1.40130 0.0626055
\(502\) 0 0
\(503\) −31.8164 −1.41862 −0.709311 0.704896i \(-0.750994\pi\)
−0.709311 + 0.704896i \(0.750994\pi\)
\(504\) 0 0
\(505\) −52.1021 −2.31851
\(506\) 0 0
\(507\) −3.38813 −0.150472
\(508\) 0 0
\(509\) 24.8265 1.10042 0.550209 0.835027i \(-0.314548\pi\)
0.550209 + 0.835027i \(0.314548\pi\)
\(510\) 0 0
\(511\) 1.09880 0.0486081
\(512\) 0 0
\(513\) 10.7330 0.473874
\(514\) 0 0
\(515\) 25.4295 1.12056
\(516\) 0 0
\(517\) 3.73854 0.164421
\(518\) 0 0
\(519\) 21.6213 0.949071
\(520\) 0 0
\(521\) 20.2143 0.885605 0.442803 0.896619i \(-0.353984\pi\)
0.442803 + 0.896619i \(0.353984\pi\)
\(522\) 0 0
\(523\) 32.5433 1.42302 0.711509 0.702677i \(-0.248012\pi\)
0.711509 + 0.702677i \(0.248012\pi\)
\(524\) 0 0
\(525\) −41.8016 −1.82437
\(526\) 0 0
\(527\) −23.4832 −1.02295
\(528\) 0 0
\(529\) 17.1031 0.743614
\(530\) 0 0
\(531\) 125.968 5.46653
\(532\) 0 0
\(533\) 8.27358 0.358369
\(534\) 0 0
\(535\) −17.9883 −0.777704
\(536\) 0 0
\(537\) 72.2181 3.11644
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 0.876603 0.0376881 0.0188440 0.999822i \(-0.494001\pi\)
0.0188440 + 0.999822i \(0.494001\pi\)
\(542\) 0 0
\(543\) 37.2430 1.59825
\(544\) 0 0
\(545\) −20.5892 −0.881944
\(546\) 0 0
\(547\) −10.7936 −0.461502 −0.230751 0.973013i \(-0.574118\pi\)
−0.230751 + 0.973013i \(0.574118\pi\)
\(548\) 0 0
\(549\) −20.7269 −0.884603
\(550\) 0 0
\(551\) −1.71834 −0.0732039
\(552\) 0 0
\(553\) 9.93914 0.422655
\(554\) 0 0
\(555\) 51.4777 2.18511
\(556\) 0 0
\(557\) 28.3459 1.20105 0.600526 0.799605i \(-0.294958\pi\)
0.600526 + 0.799605i \(0.294958\pi\)
\(558\) 0 0
\(559\) 10.1989 0.431368
\(560\) 0 0
\(561\) −15.4584 −0.652653
\(562\) 0 0
\(563\) 18.2804 0.770428 0.385214 0.922827i \(-0.374128\pi\)
0.385214 + 0.922827i \(0.374128\pi\)
\(564\) 0 0
\(565\) −56.4243 −2.37379
\(566\) 0 0
\(567\) 37.4627 1.57328
\(568\) 0 0
\(569\) −29.4714 −1.23551 −0.617753 0.786372i \(-0.711957\pi\)
−0.617753 + 0.786372i \(0.711957\pi\)
\(570\) 0 0
\(571\) −45.3596 −1.89824 −0.949120 0.314915i \(-0.898024\pi\)
−0.949120 + 0.314915i \(0.898024\pi\)
\(572\) 0 0
\(573\) 49.0184 2.04777
\(574\) 0 0
\(575\) −78.1306 −3.25827
\(576\) 0 0
\(577\) −14.8665 −0.618901 −0.309450 0.950916i \(-0.600145\pi\)
−0.309450 + 0.950916i \(0.600145\pi\)
\(578\) 0 0
\(579\) −60.5745 −2.51739
\(580\) 0 0
\(581\) −15.7239 −0.652337
\(582\) 0 0
\(583\) 7.91971 0.328001
\(584\) 0 0
\(585\) 35.3071 1.45977
\(586\) 0 0
\(587\) 19.3463 0.798509 0.399254 0.916840i \(-0.369269\pi\)
0.399254 + 0.916840i \(0.369269\pi\)
\(588\) 0 0
\(589\) −2.97563 −0.122609
\(590\) 0 0
\(591\) −46.4535 −1.91084
\(592\) 0 0
\(593\) −11.1479 −0.457789 −0.228895 0.973451i \(-0.573511\pi\)
−0.228895 + 0.973451i \(0.573511\pi\)
\(594\) 0 0
\(595\) 18.9976 0.778826
\(596\) 0 0
\(597\) 5.55754 0.227455
\(598\) 0 0
\(599\) 13.1330 0.536601 0.268301 0.963335i \(-0.413538\pi\)
0.268301 + 0.963335i \(0.413538\pi\)
\(600\) 0 0
\(601\) −27.5749 −1.12480 −0.562401 0.826864i \(-0.690122\pi\)
−0.562401 + 0.826864i \(0.690122\pi\)
\(602\) 0 0
\(603\) −10.0131 −0.407767
\(604\) 0 0
\(605\) −4.16385 −0.169285
\(606\) 0 0
\(607\) 33.5137 1.36028 0.680140 0.733082i \(-0.261919\pi\)
0.680140 + 0.733082i \(0.261919\pi\)
\(608\) 0 0
\(609\) −10.0704 −0.408073
\(610\) 0 0
\(611\) 3.73854 0.151245
\(612\) 0 0
\(613\) 40.8801 1.65113 0.825566 0.564305i \(-0.190856\pi\)
0.825566 + 0.564305i \(0.190856\pi\)
\(614\) 0 0
\(615\) −116.721 −4.70665
\(616\) 0 0
\(617\) −24.4563 −0.984572 −0.492286 0.870433i \(-0.663839\pi\)
−0.492286 + 0.870433i \(0.663839\pi\)
\(618\) 0 0
\(619\) 10.8443 0.435870 0.217935 0.975963i \(-0.430068\pi\)
0.217935 + 0.975963i \(0.430068\pi\)
\(620\) 0 0
\(621\) 117.567 4.71781
\(622\) 0 0
\(623\) 8.11272 0.325029
\(624\) 0 0
\(625\) 65.5293 2.62117
\(626\) 0 0
\(627\) −1.95878 −0.0782260
\(628\) 0 0
\(629\) −16.6482 −0.663807
\(630\) 0 0
\(631\) −24.5019 −0.975405 −0.487702 0.873010i \(-0.662165\pi\)
−0.487702 + 0.873010i \(0.662165\pi\)
\(632\) 0 0
\(633\) −85.1761 −3.38544
\(634\) 0 0
\(635\) 21.7611 0.863565
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 114.296 4.52149
\(640\) 0 0
\(641\) −36.0544 −1.42406 −0.712031 0.702148i \(-0.752225\pi\)
−0.712031 + 0.702148i \(0.752225\pi\)
\(642\) 0 0
\(643\) −40.1974 −1.58523 −0.792616 0.609721i \(-0.791281\pi\)
−0.792616 + 0.609721i \(0.791281\pi\)
\(644\) 0 0
\(645\) −143.883 −5.66539
\(646\) 0 0
\(647\) 25.7746 1.01330 0.506652 0.862151i \(-0.330883\pi\)
0.506652 + 0.862151i \(0.330883\pi\)
\(648\) 0 0
\(649\) −14.8556 −0.583135
\(650\) 0 0
\(651\) −17.4387 −0.683477
\(652\) 0 0
\(653\) 23.7994 0.931341 0.465671 0.884958i \(-0.345813\pi\)
0.465671 + 0.884958i \(0.345813\pi\)
\(654\) 0 0
\(655\) −32.8965 −1.28537
\(656\) 0 0
\(657\) 9.31722 0.363499
\(658\) 0 0
\(659\) 11.0585 0.430780 0.215390 0.976528i \(-0.430898\pi\)
0.215390 + 0.976528i \(0.430898\pi\)
\(660\) 0 0
\(661\) 9.20167 0.357904 0.178952 0.983858i \(-0.442729\pi\)
0.178952 + 0.983858i \(0.442729\pi\)
\(662\) 0 0
\(663\) −15.4584 −0.600354
\(664\) 0 0
\(665\) 2.40724 0.0933488
\(666\) 0 0
\(667\) −18.8224 −0.728806
\(668\) 0 0
\(669\) −15.2523 −0.589689
\(670\) 0 0
\(671\) 2.44437 0.0943639
\(672\) 0 0
\(673\) 26.7574 1.03142 0.515711 0.856762i \(-0.327528\pi\)
0.515711 + 0.856762i \(0.327528\pi\)
\(674\) 0 0
\(675\) −229.049 −8.81612
\(676\) 0 0
\(677\) 46.1583 1.77401 0.887004 0.461761i \(-0.152782\pi\)
0.887004 + 0.461761i \(0.152782\pi\)
\(678\) 0 0
\(679\) 10.1163 0.388226
\(680\) 0 0
\(681\) −23.4410 −0.898260
\(682\) 0 0
\(683\) 23.2642 0.890179 0.445090 0.895486i \(-0.353172\pi\)
0.445090 + 0.895486i \(0.353172\pi\)
\(684\) 0 0
\(685\) −50.6255 −1.93430
\(686\) 0 0
\(687\) −75.3542 −2.87494
\(688\) 0 0
\(689\) 7.91971 0.301717
\(690\) 0 0
\(691\) −3.09564 −0.117764 −0.0588819 0.998265i \(-0.518754\pi\)
−0.0588819 + 0.998265i \(0.518754\pi\)
\(692\) 0 0
\(693\) −8.47945 −0.322107
\(694\) 0 0
\(695\) −23.5267 −0.892420
\(696\) 0 0
\(697\) 37.7483 1.42982
\(698\) 0 0
\(699\) 15.3850 0.581916
\(700\) 0 0
\(701\) 31.7833 1.20044 0.600220 0.799835i \(-0.295080\pi\)
0.600220 + 0.799835i \(0.295080\pi\)
\(702\) 0 0
\(703\) −2.10954 −0.0795629
\(704\) 0 0
\(705\) −52.7422 −1.98638
\(706\) 0 0
\(707\) 12.5130 0.470599
\(708\) 0 0
\(709\) −37.4506 −1.40649 −0.703244 0.710948i \(-0.748266\pi\)
−0.703244 + 0.710948i \(0.748266\pi\)
\(710\) 0 0
\(711\) 84.2784 3.16069
\(712\) 0 0
\(713\) −32.5944 −1.22067
\(714\) 0 0
\(715\) −4.16385 −0.155719
\(716\) 0 0
\(717\) 80.1088 2.99172
\(718\) 0 0
\(719\) 29.0398 1.08300 0.541500 0.840700i \(-0.317856\pi\)
0.541500 + 0.840700i \(0.317856\pi\)
\(720\) 0 0
\(721\) −6.10720 −0.227444
\(722\) 0 0
\(723\) −62.7259 −2.33280
\(724\) 0 0
\(725\) 36.6706 1.36191
\(726\) 0 0
\(727\) 17.5015 0.649094 0.324547 0.945870i \(-0.394788\pi\)
0.324547 + 0.945870i \(0.394788\pi\)
\(728\) 0 0
\(729\) 128.960 4.77628
\(730\) 0 0
\(731\) 46.5326 1.72107
\(732\) 0 0
\(733\) −30.7054 −1.13413 −0.567066 0.823673i \(-0.691921\pi\)
−0.567066 + 0.823673i \(0.691921\pi\)
\(734\) 0 0
\(735\) 14.1077 0.520370
\(736\) 0 0
\(737\) 1.18087 0.0434980
\(738\) 0 0
\(739\) −15.9903 −0.588211 −0.294106 0.955773i \(-0.595022\pi\)
−0.294106 + 0.955773i \(0.595022\pi\)
\(740\) 0 0
\(741\) −1.95878 −0.0719575
\(742\) 0 0
\(743\) 35.6528 1.30798 0.653988 0.756505i \(-0.273095\pi\)
0.653988 + 0.756505i \(0.273095\pi\)
\(744\) 0 0
\(745\) 34.8130 1.27545
\(746\) 0 0
\(747\) −133.330 −4.87828
\(748\) 0 0
\(749\) 4.32012 0.157854
\(750\) 0 0
\(751\) 7.26334 0.265043 0.132521 0.991180i \(-0.457693\pi\)
0.132521 + 0.991180i \(0.457693\pi\)
\(752\) 0 0
\(753\) −1.16997 −0.0426359
\(754\) 0 0
\(755\) −7.17522 −0.261133
\(756\) 0 0
\(757\) 48.8018 1.77373 0.886865 0.462028i \(-0.152878\pi\)
0.886865 + 0.462028i \(0.152878\pi\)
\(758\) 0 0
\(759\) −21.4560 −0.778805
\(760\) 0 0
\(761\) −37.9565 −1.37592 −0.687961 0.725748i \(-0.741494\pi\)
−0.687961 + 0.725748i \(0.741494\pi\)
\(762\) 0 0
\(763\) 4.94475 0.179012
\(764\) 0 0
\(765\) 161.089 5.82419
\(766\) 0 0
\(767\) −14.8556 −0.536406
\(768\) 0 0
\(769\) −52.9477 −1.90934 −0.954672 0.297660i \(-0.903794\pi\)
−0.954672 + 0.297660i \(0.903794\pi\)
\(770\) 0 0
\(771\) −22.3514 −0.804965
\(772\) 0 0
\(773\) −35.4012 −1.27329 −0.636647 0.771155i \(-0.719679\pi\)
−0.636647 + 0.771155i \(0.719679\pi\)
\(774\) 0 0
\(775\) 63.5019 2.28105
\(776\) 0 0
\(777\) −12.3630 −0.443520
\(778\) 0 0
\(779\) 4.78320 0.171376
\(780\) 0 0
\(781\) −13.4792 −0.482324
\(782\) 0 0
\(783\) −55.1801 −1.97198
\(784\) 0 0
\(785\) −86.1438 −3.07461
\(786\) 0 0
\(787\) −6.57573 −0.234400 −0.117200 0.993108i \(-0.537392\pi\)
−0.117200 + 0.993108i \(0.537392\pi\)
\(788\) 0 0
\(789\) −63.7607 −2.26994
\(790\) 0 0
\(791\) 13.5510 0.481818
\(792\) 0 0
\(793\) 2.44437 0.0868022
\(794\) 0 0
\(795\) −111.729 −3.96261
\(796\) 0 0
\(797\) 37.3458 1.32286 0.661429 0.750008i \(-0.269950\pi\)
0.661429 + 0.750008i \(0.269950\pi\)
\(798\) 0 0
\(799\) 17.0571 0.603438
\(800\) 0 0
\(801\) 68.7914 2.43062
\(802\) 0 0
\(803\) −1.09880 −0.0387758
\(804\) 0 0
\(805\) 26.3684 0.929365
\(806\) 0 0
\(807\) 64.0295 2.25395
\(808\) 0 0
\(809\) 0.109808 0.00386065 0.00193032 0.999998i \(-0.499386\pi\)
0.00193032 + 0.999998i \(0.499386\pi\)
\(810\) 0 0
\(811\) 37.4524 1.31513 0.657566 0.753397i \(-0.271586\pi\)
0.657566 + 0.753397i \(0.271586\pi\)
\(812\) 0 0
\(813\) 102.323 3.58863
\(814\) 0 0
\(815\) 20.0890 0.703688
\(816\) 0 0
\(817\) 5.89629 0.206285
\(818\) 0 0
\(819\) −8.47945 −0.296296
\(820\) 0 0
\(821\) −52.5790 −1.83502 −0.917510 0.397712i \(-0.869804\pi\)
−0.917510 + 0.397712i \(0.869804\pi\)
\(822\) 0 0
\(823\) −44.9995 −1.56858 −0.784292 0.620392i \(-0.786973\pi\)
−0.784292 + 0.620392i \(0.786973\pi\)
\(824\) 0 0
\(825\) 41.8016 1.45534
\(826\) 0 0
\(827\) −23.4245 −0.814550 −0.407275 0.913306i \(-0.633521\pi\)
−0.407275 + 0.913306i \(0.633521\pi\)
\(828\) 0 0
\(829\) −5.98216 −0.207769 −0.103885 0.994589i \(-0.533127\pi\)
−0.103885 + 0.994589i \(0.533127\pi\)
\(830\) 0 0
\(831\) −74.8654 −2.59705
\(832\) 0 0
\(833\) −4.56251 −0.158082
\(834\) 0 0
\(835\) 1.72213 0.0595968
\(836\) 0 0
\(837\) −95.5545 −3.30285
\(838\) 0 0
\(839\) 20.9921 0.724728 0.362364 0.932037i \(-0.381970\pi\)
0.362364 + 0.932037i \(0.381970\pi\)
\(840\) 0 0
\(841\) −20.1657 −0.695370
\(842\) 0 0
\(843\) 95.2460 3.28045
\(844\) 0 0
\(845\) −4.16385 −0.143241
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 24.0639 0.825871
\(850\) 0 0
\(851\) −23.1075 −0.792114
\(852\) 0 0
\(853\) 10.9772 0.375853 0.187926 0.982183i \(-0.439823\pi\)
0.187926 + 0.982183i \(0.439823\pi\)
\(854\) 0 0
\(855\) 20.4121 0.698078
\(856\) 0 0
\(857\) 10.1129 0.345449 0.172725 0.984970i \(-0.444743\pi\)
0.172725 + 0.984970i \(0.444743\pi\)
\(858\) 0 0
\(859\) −25.4516 −0.868396 −0.434198 0.900817i \(-0.642968\pi\)
−0.434198 + 0.900817i \(0.642968\pi\)
\(860\) 0 0
\(861\) 28.0320 0.955328
\(862\) 0 0
\(863\) 0.579248 0.0197178 0.00985892 0.999951i \(-0.496862\pi\)
0.00985892 + 0.999951i \(0.496862\pi\)
\(864\) 0 0
\(865\) 26.5715 0.903460
\(866\) 0 0
\(867\) −12.9307 −0.439150
\(868\) 0 0
\(869\) −9.93914 −0.337162
\(870\) 0 0
\(871\) 1.18087 0.0400123
\(872\) 0 0
\(873\) 85.7803 2.90322
\(874\) 0 0
\(875\) −30.5529 −1.03288
\(876\) 0 0
\(877\) 18.5639 0.626860 0.313430 0.949611i \(-0.398522\pi\)
0.313430 + 0.949611i \(0.398522\pi\)
\(878\) 0 0
\(879\) 23.9118 0.806525
\(880\) 0 0
\(881\) 11.8188 0.398187 0.199094 0.979980i \(-0.436200\pi\)
0.199094 + 0.979980i \(0.436200\pi\)
\(882\) 0 0
\(883\) 41.9213 1.41076 0.705382 0.708827i \(-0.250775\pi\)
0.705382 + 0.708827i \(0.250775\pi\)
\(884\) 0 0
\(885\) 209.579 7.04491
\(886\) 0 0
\(887\) 18.8509 0.632950 0.316475 0.948601i \(-0.397501\pi\)
0.316475 + 0.948601i \(0.397501\pi\)
\(888\) 0 0
\(889\) −5.22621 −0.175281
\(890\) 0 0
\(891\) −37.4627 −1.25505
\(892\) 0 0
\(893\) 2.16136 0.0723271
\(894\) 0 0
\(895\) 88.7526 2.96667
\(896\) 0 0
\(897\) −21.4560 −0.716396
\(898\) 0 0
\(899\) 15.2982 0.510223
\(900\) 0 0
\(901\) 36.1337 1.20379
\(902\) 0 0
\(903\) 34.5553 1.14993
\(904\) 0 0
\(905\) 45.7699 1.52144
\(906\) 0 0
\(907\) −47.6986 −1.58381 −0.791903 0.610647i \(-0.790910\pi\)
−0.791903 + 0.610647i \(0.790910\pi\)
\(908\) 0 0
\(909\) 106.103 3.51922
\(910\) 0 0
\(911\) −18.1443 −0.601148 −0.300574 0.953758i \(-0.597178\pi\)
−0.300574 + 0.953758i \(0.597178\pi\)
\(912\) 0 0
\(913\) 15.7239 0.520385
\(914\) 0 0
\(915\) −34.4844 −1.14002
\(916\) 0 0
\(917\) 7.90049 0.260897
\(918\) 0 0
\(919\) 20.8502 0.687786 0.343893 0.939009i \(-0.388254\pi\)
0.343893 + 0.939009i \(0.388254\pi\)
\(920\) 0 0
\(921\) −33.1227 −1.09143
\(922\) 0 0
\(923\) −13.4792 −0.443674
\(924\) 0 0
\(925\) 45.0190 1.48022
\(926\) 0 0
\(927\) −51.7857 −1.70086
\(928\) 0 0
\(929\) 22.6593 0.743429 0.371714 0.928347i \(-0.378770\pi\)
0.371714 + 0.928347i \(0.378770\pi\)
\(930\) 0 0
\(931\) −0.578129 −0.0189474
\(932\) 0 0
\(933\) 8.93099 0.292387
\(934\) 0 0
\(935\) −18.9976 −0.621288
\(936\) 0 0
\(937\) −2.69027 −0.0878873 −0.0439437 0.999034i \(-0.513992\pi\)
−0.0439437 + 0.999034i \(0.513992\pi\)
\(938\) 0 0
\(939\) −10.5562 −0.344489
\(940\) 0 0
\(941\) −35.6464 −1.16204 −0.581020 0.813889i \(-0.697346\pi\)
−0.581020 + 0.813889i \(0.697346\pi\)
\(942\) 0 0
\(943\) 52.3941 1.70619
\(944\) 0 0
\(945\) 77.3022 2.51464
\(946\) 0 0
\(947\) 11.8507 0.385097 0.192548 0.981287i \(-0.438325\pi\)
0.192548 + 0.981287i \(0.438325\pi\)
\(948\) 0 0
\(949\) −1.09880 −0.0356686
\(950\) 0 0
\(951\) −89.2918 −2.89549
\(952\) 0 0
\(953\) −30.4931 −0.987768 −0.493884 0.869528i \(-0.664423\pi\)
−0.493884 + 0.869528i \(0.664423\pi\)
\(954\) 0 0
\(955\) 60.2412 1.94936
\(956\) 0 0
\(957\) 10.0704 0.325529
\(958\) 0 0
\(959\) 12.1583 0.392613
\(960\) 0 0
\(961\) −4.50839 −0.145432
\(962\) 0 0
\(963\) 36.6322 1.18046
\(964\) 0 0
\(965\) −74.4431 −2.39641
\(966\) 0 0
\(967\) 8.05417 0.259005 0.129502 0.991579i \(-0.458662\pi\)
0.129502 + 0.991579i \(0.458662\pi\)
\(968\) 0 0
\(969\) −8.93694 −0.287096
\(970\) 0 0
\(971\) 40.5052 1.29987 0.649936 0.759989i \(-0.274796\pi\)
0.649936 + 0.759989i \(0.274796\pi\)
\(972\) 0 0
\(973\) 5.65024 0.181138
\(974\) 0 0
\(975\) 41.8016 1.33872
\(976\) 0 0
\(977\) −15.4470 −0.494194 −0.247097 0.968991i \(-0.579477\pi\)
−0.247097 + 0.968991i \(0.579477\pi\)
\(978\) 0 0
\(979\) −8.11272 −0.259284
\(980\) 0 0
\(981\) 41.9287 1.33868
\(982\) 0 0
\(983\) 1.70663 0.0544332 0.0272166 0.999630i \(-0.491336\pi\)
0.0272166 + 0.999630i \(0.491336\pi\)
\(984\) 0 0
\(985\) −57.0891 −1.81901
\(986\) 0 0
\(987\) 12.6667 0.403185
\(988\) 0 0
\(989\) 64.5867 2.05374
\(990\) 0 0
\(991\) 27.0360 0.858828 0.429414 0.903108i \(-0.358720\pi\)
0.429414 + 0.903108i \(0.358720\pi\)
\(992\) 0 0
\(993\) 109.502 3.47494
\(994\) 0 0
\(995\) 6.82995 0.216524
\(996\) 0 0
\(997\) −60.0098 −1.90053 −0.950265 0.311441i \(-0.899188\pi\)
−0.950265 + 0.311441i \(0.899188\pi\)
\(998\) 0 0
\(999\) −67.7424 −2.14327
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 \(a_p\))