Properties

Label 8016.2.a.bg.1.2
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
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: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
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 1.2
Root \(-3.60065\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-3.60065 q^{5}\) \(+4.85776 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-3.60065 q^{5}\) \(+4.85776 q^{7}\) \(+1.00000 q^{9}\) \(-0.783405 q^{11}\) \(-2.28883 q^{13}\) \(+3.60065 q^{15}\) \(-3.64326 q^{17}\) \(+1.90236 q^{19}\) \(-4.85776 q^{21}\) \(-0.781756 q^{23}\) \(+7.96466 q^{25}\) \(-1.00000 q^{27}\) \(-5.79522 q^{29}\) \(+5.38959 q^{31}\) \(+0.783405 q^{33}\) \(-17.4911 q^{35}\) \(-7.39337 q^{37}\) \(+2.28883 q^{39}\) \(+1.19043 q^{41}\) \(-2.44687 q^{43}\) \(-3.60065 q^{45}\) \(+0.0708292 q^{47}\) \(+16.5979 q^{49}\) \(+3.64326 q^{51}\) \(+2.21252 q^{53}\) \(+2.82076 q^{55}\) \(-1.90236 q^{57}\) \(+3.50468 q^{59}\) \(+15.0468 q^{61}\) \(+4.85776 q^{63}\) \(+8.24127 q^{65}\) \(-2.58442 q^{67}\) \(+0.781756 q^{69}\) \(+6.82762 q^{71}\) \(+8.47077 q^{73}\) \(-7.96466 q^{75}\) \(-3.80559 q^{77}\) \(+10.1377 q^{79}\) \(+1.00000 q^{81}\) \(-16.5852 q^{83}\) \(+13.1181 q^{85}\) \(+5.79522 q^{87}\) \(+0.933406 q^{89}\) \(-11.1186 q^{91}\) \(-5.38959 q^{93}\) \(-6.84973 q^{95}\) \(-15.9639 q^{97}\) \(-0.783405 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −3.60065 −1.61026 −0.805129 0.593100i \(-0.797904\pi\)
−0.805129 + 0.593100i \(0.797904\pi\)
\(6\) 0 0
\(7\) 4.85776 1.83606 0.918031 0.396509i \(-0.129778\pi\)
0.918031 + 0.396509i \(0.129778\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.783405 −0.236205 −0.118103 0.993001i \(-0.537681\pi\)
−0.118103 + 0.993001i \(0.537681\pi\)
\(12\) 0 0
\(13\) −2.28883 −0.634808 −0.317404 0.948290i \(-0.602811\pi\)
−0.317404 + 0.948290i \(0.602811\pi\)
\(14\) 0 0
\(15\) 3.60065 0.929683
\(16\) 0 0
\(17\) −3.64326 −0.883619 −0.441810 0.897109i \(-0.645663\pi\)
−0.441810 + 0.897109i \(0.645663\pi\)
\(18\) 0 0
\(19\) 1.90236 0.436431 0.218216 0.975901i \(-0.429976\pi\)
0.218216 + 0.975901i \(0.429976\pi\)
\(20\) 0 0
\(21\) −4.85776 −1.06005
\(22\) 0 0
\(23\) −0.781756 −0.163007 −0.0815036 0.996673i \(-0.525972\pi\)
−0.0815036 + 0.996673i \(0.525972\pi\)
\(24\) 0 0
\(25\) 7.96466 1.59293
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.79522 −1.07615 −0.538073 0.842898i \(-0.680847\pi\)
−0.538073 + 0.842898i \(0.680847\pi\)
\(30\) 0 0
\(31\) 5.38959 0.967999 0.483999 0.875068i \(-0.339184\pi\)
0.483999 + 0.875068i \(0.339184\pi\)
\(32\) 0 0
\(33\) 0.783405 0.136373
\(34\) 0 0
\(35\) −17.4911 −2.95653
\(36\) 0 0
\(37\) −7.39337 −1.21546 −0.607731 0.794143i \(-0.707920\pi\)
−0.607731 + 0.794143i \(0.707920\pi\)
\(38\) 0 0
\(39\) 2.28883 0.366506
\(40\) 0 0
\(41\) 1.19043 0.185914 0.0929569 0.995670i \(-0.470368\pi\)
0.0929569 + 0.995670i \(0.470368\pi\)
\(42\) 0 0
\(43\) −2.44687 −0.373143 −0.186572 0.982441i \(-0.559738\pi\)
−0.186572 + 0.982441i \(0.559738\pi\)
\(44\) 0 0
\(45\) −3.60065 −0.536753
\(46\) 0 0
\(47\) 0.0708292 0.0103315 0.00516575 0.999987i \(-0.498356\pi\)
0.00516575 + 0.999987i \(0.498356\pi\)
\(48\) 0 0
\(49\) 16.5979 2.37112
\(50\) 0 0
\(51\) 3.64326 0.510158
\(52\) 0 0
\(53\) 2.21252 0.303913 0.151956 0.988387i \(-0.451443\pi\)
0.151956 + 0.988387i \(0.451443\pi\)
\(54\) 0 0
\(55\) 2.82076 0.380352
\(56\) 0 0
\(57\) −1.90236 −0.251974
\(58\) 0 0
\(59\) 3.50468 0.456270 0.228135 0.973630i \(-0.426737\pi\)
0.228135 + 0.973630i \(0.426737\pi\)
\(60\) 0 0
\(61\) 15.0468 1.92655 0.963273 0.268523i \(-0.0865356\pi\)
0.963273 + 0.268523i \(0.0865356\pi\)
\(62\) 0 0
\(63\) 4.85776 0.612021
\(64\) 0 0
\(65\) 8.24127 1.02220
\(66\) 0 0
\(67\) −2.58442 −0.315737 −0.157869 0.987460i \(-0.550462\pi\)
−0.157869 + 0.987460i \(0.550462\pi\)
\(68\) 0 0
\(69\) 0.781756 0.0941123
\(70\) 0 0
\(71\) 6.82762 0.810289 0.405145 0.914253i \(-0.367221\pi\)
0.405145 + 0.914253i \(0.367221\pi\)
\(72\) 0 0
\(73\) 8.47077 0.991429 0.495714 0.868486i \(-0.334906\pi\)
0.495714 + 0.868486i \(0.334906\pi\)
\(74\) 0 0
\(75\) −7.96466 −0.919680
\(76\) 0 0
\(77\) −3.80559 −0.433688
\(78\) 0 0
\(79\) 10.1377 1.14058 0.570291 0.821443i \(-0.306830\pi\)
0.570291 + 0.821443i \(0.306830\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −16.5852 −1.82046 −0.910232 0.414098i \(-0.864097\pi\)
−0.910232 + 0.414098i \(0.864097\pi\)
\(84\) 0 0
\(85\) 13.1181 1.42286
\(86\) 0 0
\(87\) 5.79522 0.621313
\(88\) 0 0
\(89\) 0.933406 0.0989408 0.0494704 0.998776i \(-0.484247\pi\)
0.0494704 + 0.998776i \(0.484247\pi\)
\(90\) 0 0
\(91\) −11.1186 −1.16555
\(92\) 0 0
\(93\) −5.38959 −0.558874
\(94\) 0 0
\(95\) −6.84973 −0.702767
\(96\) 0 0
\(97\) −15.9639 −1.62089 −0.810446 0.585813i \(-0.800775\pi\)
−0.810446 + 0.585813i \(0.800775\pi\)
\(98\) 0 0
\(99\) −0.783405 −0.0787351
\(100\) 0 0
\(101\) −6.69164 −0.665843 −0.332921 0.942955i \(-0.608034\pi\)
−0.332921 + 0.942955i \(0.608034\pi\)
\(102\) 0 0
\(103\) −15.7002 −1.54699 −0.773496 0.633802i \(-0.781493\pi\)
−0.773496 + 0.633802i \(0.781493\pi\)
\(104\) 0 0
\(105\) 17.4911 1.70696
\(106\) 0 0
\(107\) −1.29322 −0.125020 −0.0625102 0.998044i \(-0.519911\pi\)
−0.0625102 + 0.998044i \(0.519911\pi\)
\(108\) 0 0
\(109\) 0.00600031 0.000574726 0 0.000287363 1.00000i \(-0.499909\pi\)
0.000287363 1.00000i \(0.499909\pi\)
\(110\) 0 0
\(111\) 7.39337 0.701748
\(112\) 0 0
\(113\) −2.77121 −0.260694 −0.130347 0.991468i \(-0.541609\pi\)
−0.130347 + 0.991468i \(0.541609\pi\)
\(114\) 0 0
\(115\) 2.81483 0.262484
\(116\) 0 0
\(117\) −2.28883 −0.211603
\(118\) 0 0
\(119\) −17.6981 −1.62238
\(120\) 0 0
\(121\) −10.3863 −0.944207
\(122\) 0 0
\(123\) −1.19043 −0.107337
\(124\) 0 0
\(125\) −10.6747 −0.954773
\(126\) 0 0
\(127\) −20.0283 −1.77722 −0.888612 0.458660i \(-0.848330\pi\)
−0.888612 + 0.458660i \(0.848330\pi\)
\(128\) 0 0
\(129\) 2.44687 0.215434
\(130\) 0 0
\(131\) 13.2921 1.16134 0.580669 0.814140i \(-0.302791\pi\)
0.580669 + 0.814140i \(0.302791\pi\)
\(132\) 0 0
\(133\) 9.24121 0.801315
\(134\) 0 0
\(135\) 3.60065 0.309894
\(136\) 0 0
\(137\) 5.56619 0.475552 0.237776 0.971320i \(-0.423582\pi\)
0.237776 + 0.971320i \(0.423582\pi\)
\(138\) 0 0
\(139\) −14.5785 −1.23653 −0.618265 0.785970i \(-0.712164\pi\)
−0.618265 + 0.785970i \(0.712164\pi\)
\(140\) 0 0
\(141\) −0.0708292 −0.00596489
\(142\) 0 0
\(143\) 1.79308 0.149945
\(144\) 0 0
\(145\) 20.8665 1.73287
\(146\) 0 0
\(147\) −16.5979 −1.36897
\(148\) 0 0
\(149\) −0.839632 −0.0687854 −0.0343927 0.999408i \(-0.510950\pi\)
−0.0343927 + 0.999408i \(0.510950\pi\)
\(150\) 0 0
\(151\) −0.823210 −0.0669919 −0.0334959 0.999439i \(-0.510664\pi\)
−0.0334959 + 0.999439i \(0.510664\pi\)
\(152\) 0 0
\(153\) −3.64326 −0.294540
\(154\) 0 0
\(155\) −19.4060 −1.55873
\(156\) 0 0
\(157\) 8.27681 0.660561 0.330281 0.943883i \(-0.392857\pi\)
0.330281 + 0.943883i \(0.392857\pi\)
\(158\) 0 0
\(159\) −2.21252 −0.175464
\(160\) 0 0
\(161\) −3.79758 −0.299291
\(162\) 0 0
\(163\) 3.21987 0.252200 0.126100 0.992018i \(-0.459754\pi\)
0.126100 + 0.992018i \(0.459754\pi\)
\(164\) 0 0
\(165\) −2.82076 −0.219596
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −7.76125 −0.597019
\(170\) 0 0
\(171\) 1.90236 0.145477
\(172\) 0 0
\(173\) 8.74339 0.664748 0.332374 0.943148i \(-0.392150\pi\)
0.332374 + 0.943148i \(0.392150\pi\)
\(174\) 0 0
\(175\) 38.6904 2.92472
\(176\) 0 0
\(177\) −3.50468 −0.263428
\(178\) 0 0
\(179\) 20.6471 1.54323 0.771617 0.636087i \(-0.219448\pi\)
0.771617 + 0.636087i \(0.219448\pi\)
\(180\) 0 0
\(181\) 23.3686 1.73697 0.868487 0.495713i \(-0.165093\pi\)
0.868487 + 0.495713i \(0.165093\pi\)
\(182\) 0 0
\(183\) −15.0468 −1.11229
\(184\) 0 0
\(185\) 26.6209 1.95721
\(186\) 0 0
\(187\) 2.85414 0.208716
\(188\) 0 0
\(189\) −4.85776 −0.353350
\(190\) 0 0
\(191\) −18.3180 −1.32544 −0.662721 0.748866i \(-0.730599\pi\)
−0.662721 + 0.748866i \(0.730599\pi\)
\(192\) 0 0
\(193\) 8.36969 0.602463 0.301232 0.953551i \(-0.402602\pi\)
0.301232 + 0.953551i \(0.402602\pi\)
\(194\) 0 0
\(195\) −8.24127 −0.590170
\(196\) 0 0
\(197\) 12.1914 0.868599 0.434300 0.900768i \(-0.356996\pi\)
0.434300 + 0.900768i \(0.356996\pi\)
\(198\) 0 0
\(199\) −3.39186 −0.240443 −0.120221 0.992747i \(-0.538360\pi\)
−0.120221 + 0.992747i \(0.538360\pi\)
\(200\) 0 0
\(201\) 2.58442 0.182291
\(202\) 0 0
\(203\) −28.1518 −1.97587
\(204\) 0 0
\(205\) −4.28631 −0.299369
\(206\) 0 0
\(207\) −0.781756 −0.0543358
\(208\) 0 0
\(209\) −1.49032 −0.103087
\(210\) 0 0
\(211\) 19.3307 1.33078 0.665389 0.746497i \(-0.268266\pi\)
0.665389 + 0.746497i \(0.268266\pi\)
\(212\) 0 0
\(213\) −6.82762 −0.467821
\(214\) 0 0
\(215\) 8.81030 0.600857
\(216\) 0 0
\(217\) 26.1813 1.77731
\(218\) 0 0
\(219\) −8.47077 −0.572402
\(220\) 0 0
\(221\) 8.33880 0.560928
\(222\) 0 0
\(223\) −11.5418 −0.772896 −0.386448 0.922311i \(-0.626298\pi\)
−0.386448 + 0.922311i \(0.626298\pi\)
\(224\) 0 0
\(225\) 7.96466 0.530977
\(226\) 0 0
\(227\) 12.1495 0.806392 0.403196 0.915114i \(-0.367899\pi\)
0.403196 + 0.915114i \(0.367899\pi\)
\(228\) 0 0
\(229\) 23.6217 1.56097 0.780483 0.625177i \(-0.214973\pi\)
0.780483 + 0.625177i \(0.214973\pi\)
\(230\) 0 0
\(231\) 3.80559 0.250390
\(232\) 0 0
\(233\) 7.08707 0.464290 0.232145 0.972681i \(-0.425426\pi\)
0.232145 + 0.972681i \(0.425426\pi\)
\(234\) 0 0
\(235\) −0.255031 −0.0166364
\(236\) 0 0
\(237\) −10.1377 −0.658516
\(238\) 0 0
\(239\) 30.5104 1.97355 0.986776 0.162091i \(-0.0518239\pi\)
0.986776 + 0.162091i \(0.0518239\pi\)
\(240\) 0 0
\(241\) 10.7672 0.693578 0.346789 0.937943i \(-0.387272\pi\)
0.346789 + 0.937943i \(0.387272\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −59.7630 −3.81812
\(246\) 0 0
\(247\) −4.35418 −0.277050
\(248\) 0 0
\(249\) 16.5852 1.05105
\(250\) 0 0
\(251\) 16.4758 1.03994 0.519972 0.854183i \(-0.325942\pi\)
0.519972 + 0.854183i \(0.325942\pi\)
\(252\) 0 0
\(253\) 0.612431 0.0385032
\(254\) 0 0
\(255\) −13.1181 −0.821486
\(256\) 0 0
\(257\) −14.1522 −0.882790 −0.441395 0.897313i \(-0.645516\pi\)
−0.441395 + 0.897313i \(0.645516\pi\)
\(258\) 0 0
\(259\) −35.9153 −2.23167
\(260\) 0 0
\(261\) −5.79522 −0.358715
\(262\) 0 0
\(263\) 1.37436 0.0847469 0.0423734 0.999102i \(-0.486508\pi\)
0.0423734 + 0.999102i \(0.486508\pi\)
\(264\) 0 0
\(265\) −7.96650 −0.489378
\(266\) 0 0
\(267\) −0.933406 −0.0571235
\(268\) 0 0
\(269\) 1.22578 0.0747372 0.0373686 0.999302i \(-0.488102\pi\)
0.0373686 + 0.999302i \(0.488102\pi\)
\(270\) 0 0
\(271\) −19.2991 −1.17234 −0.586168 0.810189i \(-0.699364\pi\)
−0.586168 + 0.810189i \(0.699364\pi\)
\(272\) 0 0
\(273\) 11.1186 0.672928
\(274\) 0 0
\(275\) −6.23955 −0.376259
\(276\) 0 0
\(277\) 13.5577 0.814601 0.407301 0.913294i \(-0.366470\pi\)
0.407301 + 0.913294i \(0.366470\pi\)
\(278\) 0 0
\(279\) 5.38959 0.322666
\(280\) 0 0
\(281\) 16.5306 0.986134 0.493067 0.869991i \(-0.335876\pi\)
0.493067 + 0.869991i \(0.335876\pi\)
\(282\) 0 0
\(283\) 21.1153 1.25517 0.627587 0.778546i \(-0.284043\pi\)
0.627587 + 0.778546i \(0.284043\pi\)
\(284\) 0 0
\(285\) 6.84973 0.405743
\(286\) 0 0
\(287\) 5.78282 0.341349
\(288\) 0 0
\(289\) −3.72669 −0.219217
\(290\) 0 0
\(291\) 15.9639 0.935823
\(292\) 0 0
\(293\) −14.3562 −0.838698 −0.419349 0.907825i \(-0.637742\pi\)
−0.419349 + 0.907825i \(0.637742\pi\)
\(294\) 0 0
\(295\) −12.6191 −0.734712
\(296\) 0 0
\(297\) 0.783405 0.0454578
\(298\) 0 0
\(299\) 1.78931 0.103478
\(300\) 0 0
\(301\) −11.8863 −0.685114
\(302\) 0 0
\(303\) 6.69164 0.384424
\(304\) 0 0
\(305\) −54.1782 −3.10224
\(306\) 0 0
\(307\) 23.3658 1.33356 0.666778 0.745257i \(-0.267673\pi\)
0.666778 + 0.745257i \(0.267673\pi\)
\(308\) 0 0
\(309\) 15.7002 0.893156
\(310\) 0 0
\(311\) 12.7290 0.721794 0.360897 0.932606i \(-0.382471\pi\)
0.360897 + 0.932606i \(0.382471\pi\)
\(312\) 0 0
\(313\) 9.72833 0.549878 0.274939 0.961462i \(-0.411342\pi\)
0.274939 + 0.961462i \(0.411342\pi\)
\(314\) 0 0
\(315\) −17.4911 −0.985511
\(316\) 0 0
\(317\) −14.6156 −0.820892 −0.410446 0.911885i \(-0.634627\pi\)
−0.410446 + 0.911885i \(0.634627\pi\)
\(318\) 0 0
\(319\) 4.54000 0.254191
\(320\) 0 0
\(321\) 1.29322 0.0721806
\(322\) 0 0
\(323\) −6.93078 −0.385639
\(324\) 0 0
\(325\) −18.2298 −1.01121
\(326\) 0 0
\(327\) −0.00600031 −0.000331818 0
\(328\) 0 0
\(329\) 0.344071 0.0189693
\(330\) 0 0
\(331\) −7.54681 −0.414810 −0.207405 0.978255i \(-0.566502\pi\)
−0.207405 + 0.978255i \(0.566502\pi\)
\(332\) 0 0
\(333\) −7.39337 −0.405154
\(334\) 0 0
\(335\) 9.30559 0.508419
\(336\) 0 0
\(337\) 7.59790 0.413884 0.206942 0.978353i \(-0.433649\pi\)
0.206942 + 0.978353i \(0.433649\pi\)
\(338\) 0 0
\(339\) 2.77121 0.150512
\(340\) 0 0
\(341\) −4.22223 −0.228647
\(342\) 0 0
\(343\) 46.6241 2.51747
\(344\) 0 0
\(345\) −2.81483 −0.151545
\(346\) 0 0
\(347\) 18.8244 1.01055 0.505274 0.862959i \(-0.331391\pi\)
0.505274 + 0.862959i \(0.331391\pi\)
\(348\) 0 0
\(349\) 13.3873 0.716605 0.358303 0.933605i \(-0.383356\pi\)
0.358303 + 0.933605i \(0.383356\pi\)
\(350\) 0 0
\(351\) 2.28883 0.122169
\(352\) 0 0
\(353\) −9.06818 −0.482651 −0.241325 0.970444i \(-0.577582\pi\)
−0.241325 + 0.970444i \(0.577582\pi\)
\(354\) 0 0
\(355\) −24.5838 −1.30477
\(356\) 0 0
\(357\) 17.6981 0.936681
\(358\) 0 0
\(359\) 33.6393 1.77541 0.887707 0.460409i \(-0.152297\pi\)
0.887707 + 0.460409i \(0.152297\pi\)
\(360\) 0 0
\(361\) −15.3810 −0.809528
\(362\) 0 0
\(363\) 10.3863 0.545138
\(364\) 0 0
\(365\) −30.5003 −1.59646
\(366\) 0 0
\(367\) 0.524318 0.0273692 0.0136846 0.999906i \(-0.495644\pi\)
0.0136846 + 0.999906i \(0.495644\pi\)
\(368\) 0 0
\(369\) 1.19043 0.0619713
\(370\) 0 0
\(371\) 10.7479 0.558003
\(372\) 0 0
\(373\) 21.2711 1.10138 0.550688 0.834711i \(-0.314365\pi\)
0.550688 + 0.834711i \(0.314365\pi\)
\(374\) 0 0
\(375\) 10.6747 0.551238
\(376\) 0 0
\(377\) 13.2643 0.683145
\(378\) 0 0
\(379\) 15.1229 0.776813 0.388407 0.921488i \(-0.373026\pi\)
0.388407 + 0.921488i \(0.373026\pi\)
\(380\) 0 0
\(381\) 20.0283 1.02608
\(382\) 0 0
\(383\) 19.4932 0.996054 0.498027 0.867162i \(-0.334058\pi\)
0.498027 + 0.867162i \(0.334058\pi\)
\(384\) 0 0
\(385\) 13.7026 0.698349
\(386\) 0 0
\(387\) −2.44687 −0.124381
\(388\) 0 0
\(389\) −8.32263 −0.421974 −0.210987 0.977489i \(-0.567668\pi\)
−0.210987 + 0.977489i \(0.567668\pi\)
\(390\) 0 0
\(391\) 2.84814 0.144036
\(392\) 0 0
\(393\) −13.2921 −0.670499
\(394\) 0 0
\(395\) −36.5023 −1.83663
\(396\) 0 0
\(397\) −2.62043 −0.131516 −0.0657578 0.997836i \(-0.520946\pi\)
−0.0657578 + 0.997836i \(0.520946\pi\)
\(398\) 0 0
\(399\) −9.24121 −0.462639
\(400\) 0 0
\(401\) −18.1038 −0.904061 −0.452030 0.892003i \(-0.649300\pi\)
−0.452030 + 0.892003i \(0.649300\pi\)
\(402\) 0 0
\(403\) −12.3359 −0.614493
\(404\) 0 0
\(405\) −3.60065 −0.178918
\(406\) 0 0
\(407\) 5.79200 0.287099
\(408\) 0 0
\(409\) 12.4295 0.614600 0.307300 0.951613i \(-0.400574\pi\)
0.307300 + 0.951613i \(0.400574\pi\)
\(410\) 0 0
\(411\) −5.56619 −0.274560
\(412\) 0 0
\(413\) 17.0249 0.837740
\(414\) 0 0
\(415\) 59.7175 2.93142
\(416\) 0 0
\(417\) 14.5785 0.713910
\(418\) 0 0
\(419\) 5.91586 0.289009 0.144504 0.989504i \(-0.453841\pi\)
0.144504 + 0.989504i \(0.453841\pi\)
\(420\) 0 0
\(421\) −12.0216 −0.585896 −0.292948 0.956128i \(-0.594636\pi\)
−0.292948 + 0.956128i \(0.594636\pi\)
\(422\) 0 0
\(423\) 0.0708292 0.00344383
\(424\) 0 0
\(425\) −29.0173 −1.40755
\(426\) 0 0
\(427\) 73.0938 3.53726
\(428\) 0 0
\(429\) −1.79308 −0.0865708
\(430\) 0 0
\(431\) 14.6512 0.705724 0.352862 0.935675i \(-0.385209\pi\)
0.352862 + 0.935675i \(0.385209\pi\)
\(432\) 0 0
\(433\) 19.9063 0.956634 0.478317 0.878187i \(-0.341247\pi\)
0.478317 + 0.878187i \(0.341247\pi\)
\(434\) 0 0
\(435\) −20.8665 −1.00047
\(436\) 0 0
\(437\) −1.48718 −0.0711415
\(438\) 0 0
\(439\) 30.8325 1.47156 0.735778 0.677223i \(-0.236817\pi\)
0.735778 + 0.677223i \(0.236817\pi\)
\(440\) 0 0
\(441\) 16.5979 0.790374
\(442\) 0 0
\(443\) −30.0346 −1.42699 −0.713494 0.700661i \(-0.752889\pi\)
−0.713494 + 0.700661i \(0.752889\pi\)
\(444\) 0 0
\(445\) −3.36086 −0.159320
\(446\) 0 0
\(447\) 0.839632 0.0397133
\(448\) 0 0
\(449\) −5.30369 −0.250296 −0.125148 0.992138i \(-0.539941\pi\)
−0.125148 + 0.992138i \(0.539941\pi\)
\(450\) 0 0
\(451\) −0.932588 −0.0439138
\(452\) 0 0
\(453\) 0.823210 0.0386778
\(454\) 0 0
\(455\) 40.0342 1.87683
\(456\) 0 0
\(457\) 19.6992 0.921491 0.460745 0.887532i \(-0.347582\pi\)
0.460745 + 0.887532i \(0.347582\pi\)
\(458\) 0 0
\(459\) 3.64326 0.170053
\(460\) 0 0
\(461\) 24.4557 1.13901 0.569507 0.821986i \(-0.307134\pi\)
0.569507 + 0.821986i \(0.307134\pi\)
\(462\) 0 0
\(463\) −24.0218 −1.11639 −0.558194 0.829711i \(-0.688505\pi\)
−0.558194 + 0.829711i \(0.688505\pi\)
\(464\) 0 0
\(465\) 19.4060 0.899932
\(466\) 0 0
\(467\) −32.6160 −1.50929 −0.754644 0.656134i \(-0.772191\pi\)
−0.754644 + 0.656134i \(0.772191\pi\)
\(468\) 0 0
\(469\) −12.5545 −0.579713
\(470\) 0 0
\(471\) −8.27681 −0.381375
\(472\) 0 0
\(473\) 1.91689 0.0881385
\(474\) 0 0
\(475\) 15.1516 0.695205
\(476\) 0 0
\(477\) 2.21252 0.101304
\(478\) 0 0
\(479\) 11.9826 0.547500 0.273750 0.961801i \(-0.411736\pi\)
0.273750 + 0.961801i \(0.411736\pi\)
\(480\) 0 0
\(481\) 16.9222 0.771585
\(482\) 0 0
\(483\) 3.79758 0.172796
\(484\) 0 0
\(485\) 57.4805 2.61006
\(486\) 0 0
\(487\) −1.58389 −0.0717728 −0.0358864 0.999356i \(-0.511425\pi\)
−0.0358864 + 0.999356i \(0.511425\pi\)
\(488\) 0 0
\(489\) −3.21987 −0.145607
\(490\) 0 0
\(491\) −4.01554 −0.181219 −0.0906095 0.995887i \(-0.528881\pi\)
−0.0906095 + 0.995887i \(0.528881\pi\)
\(492\) 0 0
\(493\) 21.1135 0.950903
\(494\) 0 0
\(495\) 2.82076 0.126784
\(496\) 0 0
\(497\) 33.1669 1.48774
\(498\) 0 0
\(499\) 10.1751 0.455501 0.227751 0.973720i \(-0.426863\pi\)
0.227751 + 0.973720i \(0.426863\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 2.26034 0.100784 0.0503918 0.998730i \(-0.483953\pi\)
0.0503918 + 0.998730i \(0.483953\pi\)
\(504\) 0 0
\(505\) 24.0942 1.07218
\(506\) 0 0
\(507\) 7.76125 0.344689
\(508\) 0 0
\(509\) 32.1893 1.42677 0.713383 0.700774i \(-0.247162\pi\)
0.713383 + 0.700774i \(0.247162\pi\)
\(510\) 0 0
\(511\) 41.1490 1.82032
\(512\) 0 0
\(513\) −1.90236 −0.0839912
\(514\) 0 0
\(515\) 56.5310 2.49106
\(516\) 0 0
\(517\) −0.0554879 −0.00244036
\(518\) 0 0
\(519\) −8.74339 −0.383792
\(520\) 0 0
\(521\) 27.2358 1.19322 0.596611 0.802530i \(-0.296513\pi\)
0.596611 + 0.802530i \(0.296513\pi\)
\(522\) 0 0
\(523\) −0.145872 −0.00637853 −0.00318927 0.999995i \(-0.501015\pi\)
−0.00318927 + 0.999995i \(0.501015\pi\)
\(524\) 0 0
\(525\) −38.6904 −1.68859
\(526\) 0 0
\(527\) −19.6356 −0.855342
\(528\) 0 0
\(529\) −22.3889 −0.973429
\(530\) 0 0
\(531\) 3.50468 0.152090
\(532\) 0 0
\(533\) −2.72469 −0.118019
\(534\) 0 0
\(535\) 4.65643 0.201315
\(536\) 0 0
\(537\) −20.6471 −0.890987
\(538\) 0 0
\(539\) −13.0028 −0.560072
\(540\) 0 0
\(541\) −35.7512 −1.53707 −0.768533 0.639810i \(-0.779013\pi\)
−0.768533 + 0.639810i \(0.779013\pi\)
\(542\) 0 0
\(543\) −23.3686 −1.00284
\(544\) 0 0
\(545\) −0.0216050 −0.000925457 0
\(546\) 0 0
\(547\) −10.4338 −0.446116 −0.223058 0.974805i \(-0.571604\pi\)
−0.223058 + 0.974805i \(0.571604\pi\)
\(548\) 0 0
\(549\) 15.0468 0.642182
\(550\) 0 0
\(551\) −11.0246 −0.469664
\(552\) 0 0
\(553\) 49.2466 2.09418
\(554\) 0 0
\(555\) −26.6209 −1.13000
\(556\) 0 0
\(557\) −10.8646 −0.460350 −0.230175 0.973149i \(-0.573930\pi\)
−0.230175 + 0.973149i \(0.573930\pi\)
\(558\) 0 0
\(559\) 5.60046 0.236874
\(560\) 0 0
\(561\) −2.85414 −0.120502
\(562\) 0 0
\(563\) −24.8441 −1.04705 −0.523527 0.852009i \(-0.675384\pi\)
−0.523527 + 0.852009i \(0.675384\pi\)
\(564\) 0 0
\(565\) 9.97815 0.419784
\(566\) 0 0
\(567\) 4.85776 0.204007
\(568\) 0 0
\(569\) 6.52556 0.273566 0.136783 0.990601i \(-0.456324\pi\)
0.136783 + 0.990601i \(0.456324\pi\)
\(570\) 0 0
\(571\) −28.6005 −1.19689 −0.598446 0.801163i \(-0.704215\pi\)
−0.598446 + 0.801163i \(0.704215\pi\)
\(572\) 0 0
\(573\) 18.3180 0.765245
\(574\) 0 0
\(575\) −6.22642 −0.259659
\(576\) 0 0
\(577\) −9.16872 −0.381699 −0.190849 0.981619i \(-0.561124\pi\)
−0.190849 + 0.981619i \(0.561124\pi\)
\(578\) 0 0
\(579\) −8.36969 −0.347832
\(580\) 0 0
\(581\) −80.5671 −3.34249
\(582\) 0 0
\(583\) −1.73330 −0.0717859
\(584\) 0 0
\(585\) 8.24127 0.340735
\(586\) 0 0
\(587\) −29.9963 −1.23808 −0.619040 0.785359i \(-0.712478\pi\)
−0.619040 + 0.785359i \(0.712478\pi\)
\(588\) 0 0
\(589\) 10.2529 0.422465
\(590\) 0 0
\(591\) −12.1914 −0.501486
\(592\) 0 0
\(593\) 23.7026 0.973349 0.486675 0.873583i \(-0.338210\pi\)
0.486675 + 0.873583i \(0.338210\pi\)
\(594\) 0 0
\(595\) 63.7245 2.61245
\(596\) 0 0
\(597\) 3.39186 0.138820
\(598\) 0 0
\(599\) 35.0587 1.43246 0.716229 0.697865i \(-0.245867\pi\)
0.716229 + 0.697865i \(0.245867\pi\)
\(600\) 0 0
\(601\) 44.3852 1.81051 0.905254 0.424870i \(-0.139680\pi\)
0.905254 + 0.424870i \(0.139680\pi\)
\(602\) 0 0
\(603\) −2.58442 −0.105246
\(604\) 0 0
\(605\) 37.3973 1.52042
\(606\) 0 0
\(607\) 20.8130 0.844773 0.422386 0.906416i \(-0.361193\pi\)
0.422386 + 0.906416i \(0.361193\pi\)
\(608\) 0 0
\(609\) 28.1518 1.14077
\(610\) 0 0
\(611\) −0.162116 −0.00655851
\(612\) 0 0
\(613\) −17.3968 −0.702650 −0.351325 0.936254i \(-0.614269\pi\)
−0.351325 + 0.936254i \(0.614269\pi\)
\(614\) 0 0
\(615\) 4.28631 0.172841
\(616\) 0 0
\(617\) 36.8295 1.48270 0.741349 0.671119i \(-0.234186\pi\)
0.741349 + 0.671119i \(0.234186\pi\)
\(618\) 0 0
\(619\) −41.4504 −1.66603 −0.833016 0.553249i \(-0.813388\pi\)
−0.833016 + 0.553249i \(0.813388\pi\)
\(620\) 0 0
\(621\) 0.781756 0.0313708
\(622\) 0 0
\(623\) 4.53426 0.181661
\(624\) 0 0
\(625\) −1.38751 −0.0555004
\(626\) 0 0
\(627\) 1.49032 0.0595176
\(628\) 0 0
\(629\) 26.9359 1.07401
\(630\) 0 0
\(631\) 34.3932 1.36917 0.684586 0.728932i \(-0.259983\pi\)
0.684586 + 0.728932i \(0.259983\pi\)
\(632\) 0 0
\(633\) −19.3307 −0.768325
\(634\) 0 0
\(635\) 72.1148 2.86179
\(636\) 0 0
\(637\) −37.9897 −1.50521
\(638\) 0 0
\(639\) 6.82762 0.270096
\(640\) 0 0
\(641\) −50.1958 −1.98261 −0.991307 0.131567i \(-0.957999\pi\)
−0.991307 + 0.131567i \(0.957999\pi\)
\(642\) 0 0
\(643\) −22.1392 −0.873083 −0.436541 0.899684i \(-0.643797\pi\)
−0.436541 + 0.899684i \(0.643797\pi\)
\(644\) 0 0
\(645\) −8.81030 −0.346905
\(646\) 0 0
\(647\) 21.0276 0.826682 0.413341 0.910576i \(-0.364362\pi\)
0.413341 + 0.910576i \(0.364362\pi\)
\(648\) 0 0
\(649\) −2.74558 −0.107773
\(650\) 0 0
\(651\) −26.1813 −1.02613
\(652\) 0 0
\(653\) 32.1566 1.25838 0.629192 0.777250i \(-0.283386\pi\)
0.629192 + 0.777250i \(0.283386\pi\)
\(654\) 0 0
\(655\) −47.8602 −1.87005
\(656\) 0 0
\(657\) 8.47077 0.330476
\(658\) 0 0
\(659\) −17.7137 −0.690027 −0.345014 0.938598i \(-0.612126\pi\)
−0.345014 + 0.938598i \(0.612126\pi\)
\(660\) 0 0
\(661\) −32.5254 −1.26509 −0.632545 0.774524i \(-0.717990\pi\)
−0.632545 + 0.774524i \(0.717990\pi\)
\(662\) 0 0
\(663\) −8.33880 −0.323852
\(664\) 0 0
\(665\) −33.2743 −1.29032
\(666\) 0 0
\(667\) 4.53045 0.175420
\(668\) 0 0
\(669\) 11.5418 0.446232
\(670\) 0 0
\(671\) −11.7877 −0.455061
\(672\) 0 0
\(673\) 21.4777 0.827906 0.413953 0.910298i \(-0.364148\pi\)
0.413953 + 0.910298i \(0.364148\pi\)
\(674\) 0 0
\(675\) −7.96466 −0.306560
\(676\) 0 0
\(677\) 7.37246 0.283347 0.141673 0.989913i \(-0.454752\pi\)
0.141673 + 0.989913i \(0.454752\pi\)
\(678\) 0 0
\(679\) −77.5490 −2.97606
\(680\) 0 0
\(681\) −12.1495 −0.465571
\(682\) 0 0
\(683\) 14.6019 0.558727 0.279363 0.960185i \(-0.409877\pi\)
0.279363 + 0.960185i \(0.409877\pi\)
\(684\) 0 0
\(685\) −20.0419 −0.765761
\(686\) 0 0
\(687\) −23.6217 −0.901224
\(688\) 0 0
\(689\) −5.06408 −0.192926
\(690\) 0 0
\(691\) −9.88343 −0.375983 −0.187992 0.982171i \(-0.560198\pi\)
−0.187992 + 0.982171i \(0.560198\pi\)
\(692\) 0 0
\(693\) −3.80559 −0.144563
\(694\) 0 0
\(695\) 52.4919 1.99113
\(696\) 0 0
\(697\) −4.33704 −0.164277
\(698\) 0 0
\(699\) −7.08707 −0.268058
\(700\) 0 0
\(701\) −12.0603 −0.455512 −0.227756 0.973718i \(-0.573139\pi\)
−0.227756 + 0.973718i \(0.573139\pi\)
\(702\) 0 0
\(703\) −14.0649 −0.530466
\(704\) 0 0
\(705\) 0.255031 0.00960502
\(706\) 0 0
\(707\) −32.5064 −1.22253
\(708\) 0 0
\(709\) 31.8075 1.19456 0.597279 0.802034i \(-0.296249\pi\)
0.597279 + 0.802034i \(0.296249\pi\)
\(710\) 0 0
\(711\) 10.1377 0.380194
\(712\) 0 0
\(713\) −4.21334 −0.157791
\(714\) 0 0
\(715\) −6.45625 −0.241450
\(716\) 0 0
\(717\) −30.5104 −1.13943
\(718\) 0 0
\(719\) 27.9494 1.04234 0.521168 0.853454i \(-0.325496\pi\)
0.521168 + 0.853454i \(0.325496\pi\)
\(720\) 0 0
\(721\) −76.2681 −2.84037
\(722\) 0 0
\(723\) −10.7672 −0.400438
\(724\) 0 0
\(725\) −46.1570 −1.71423
\(726\) 0 0
\(727\) 20.6044 0.764173 0.382087 0.924127i \(-0.375206\pi\)
0.382087 + 0.924127i \(0.375206\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.91456 0.329717
\(732\) 0 0
\(733\) 23.2340 0.858168 0.429084 0.903265i \(-0.358836\pi\)
0.429084 + 0.903265i \(0.358836\pi\)
\(734\) 0 0
\(735\) 59.7630 2.20439
\(736\) 0 0
\(737\) 2.02465 0.0745789
\(738\) 0 0
\(739\) 12.2336 0.450022 0.225011 0.974356i \(-0.427758\pi\)
0.225011 + 0.974356i \(0.427758\pi\)
\(740\) 0 0
\(741\) 4.35418 0.159955
\(742\) 0 0
\(743\) 2.31177 0.0848105 0.0424053 0.999100i \(-0.486498\pi\)
0.0424053 + 0.999100i \(0.486498\pi\)
\(744\) 0 0
\(745\) 3.02322 0.110762
\(746\) 0 0
\(747\) −16.5852 −0.606822
\(748\) 0 0
\(749\) −6.28216 −0.229545
\(750\) 0 0
\(751\) −3.19637 −0.116637 −0.0583185 0.998298i \(-0.518574\pi\)
−0.0583185 + 0.998298i \(0.518574\pi\)
\(752\) 0 0
\(753\) −16.4758 −0.600412
\(754\) 0 0
\(755\) 2.96409 0.107874
\(756\) 0 0
\(757\) 39.6654 1.44167 0.720833 0.693109i \(-0.243760\pi\)
0.720833 + 0.693109i \(0.243760\pi\)
\(758\) 0 0
\(759\) −0.612431 −0.0222298
\(760\) 0 0
\(761\) −28.6313 −1.03788 −0.518941 0.854810i \(-0.673674\pi\)
−0.518941 + 0.854810i \(0.673674\pi\)
\(762\) 0 0
\(763\) 0.0291481 0.00105523
\(764\) 0 0
\(765\) 13.1181 0.474285
\(766\) 0 0
\(767\) −8.02161 −0.289644
\(768\) 0 0
\(769\) −13.9728 −0.503872 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(770\) 0 0
\(771\) 14.1522 0.509679
\(772\) 0 0
\(773\) 49.5495 1.78217 0.891086 0.453835i \(-0.149944\pi\)
0.891086 + 0.453835i \(0.149944\pi\)
\(774\) 0 0
\(775\) 42.9262 1.54196
\(776\) 0 0
\(777\) 35.9153 1.28845
\(778\) 0 0
\(779\) 2.26462 0.0811386
\(780\) 0 0
\(781\) −5.34879 −0.191395
\(782\) 0 0
\(783\) 5.79522 0.207104
\(784\) 0 0
\(785\) −29.8019 −1.06367
\(786\) 0 0
\(787\) 55.1125 1.96455 0.982275 0.187448i \(-0.0600216\pi\)
0.982275 + 0.187448i \(0.0600216\pi\)
\(788\) 0 0
\(789\) −1.37436 −0.0489286
\(790\) 0 0
\(791\) −13.4619 −0.478650
\(792\) 0 0
\(793\) −34.4396 −1.22299
\(794\) 0 0
\(795\) 7.96650 0.282543
\(796\) 0 0
\(797\) 47.0379 1.66617 0.833083 0.553148i \(-0.186573\pi\)
0.833083 + 0.553148i \(0.186573\pi\)
\(798\) 0 0
\(799\) −0.258049 −0.00912911
\(800\) 0 0
\(801\) 0.933406 0.0329803
\(802\) 0 0
\(803\) −6.63604 −0.234181
\(804\) 0 0
\(805\) 13.6738 0.481937
\(806\) 0 0
\(807\) −1.22578 −0.0431495
\(808\) 0 0
\(809\) 36.0404 1.26711 0.633557 0.773696i \(-0.281594\pi\)
0.633557 + 0.773696i \(0.281594\pi\)
\(810\) 0 0
\(811\) −9.87847 −0.346880 −0.173440 0.984844i \(-0.555488\pi\)
−0.173440 + 0.984844i \(0.555488\pi\)
\(812\) 0 0
\(813\) 19.2991 0.676849
\(814\) 0 0
\(815\) −11.5936 −0.406106
\(816\) 0 0
\(817\) −4.65482 −0.162851
\(818\) 0 0
\(819\) −11.1186 −0.388515
\(820\) 0 0
\(821\) 33.2827 1.16158 0.580788 0.814055i \(-0.302745\pi\)
0.580788 + 0.814055i \(0.302745\pi\)
\(822\) 0 0
\(823\) −50.0524 −1.74472 −0.872358 0.488867i \(-0.837410\pi\)
−0.872358 + 0.488867i \(0.837410\pi\)
\(824\) 0 0
\(825\) 6.23955 0.217233
\(826\) 0 0
\(827\) 40.7439 1.41680 0.708402 0.705809i \(-0.249416\pi\)
0.708402 + 0.705809i \(0.249416\pi\)
\(828\) 0 0
\(829\) 32.5331 1.12992 0.564961 0.825118i \(-0.308891\pi\)
0.564961 + 0.825118i \(0.308891\pi\)
\(830\) 0 0
\(831\) −13.5577 −0.470310
\(832\) 0 0
\(833\) −60.4702 −2.09517
\(834\) 0 0
\(835\) −3.60065 −0.124606
\(836\) 0 0
\(837\) −5.38959 −0.186291
\(838\) 0 0
\(839\) −14.9288 −0.515401 −0.257700 0.966225i \(-0.582965\pi\)
−0.257700 + 0.966225i \(0.582965\pi\)
\(840\) 0 0
\(841\) 4.58460 0.158090
\(842\) 0 0
\(843\) −16.5306 −0.569345
\(844\) 0 0
\(845\) 27.9455 0.961355
\(846\) 0 0
\(847\) −50.4541 −1.73362
\(848\) 0 0
\(849\) −21.1153 −0.724675
\(850\) 0 0
\(851\) 5.77981 0.198129
\(852\) 0 0
\(853\) 44.7233 1.53130 0.765648 0.643260i \(-0.222419\pi\)
0.765648 + 0.643260i \(0.222419\pi\)
\(854\) 0 0
\(855\) −6.84973 −0.234256
\(856\) 0 0
\(857\) −29.1460 −0.995608 −0.497804 0.867289i \(-0.665860\pi\)
−0.497804 + 0.867289i \(0.665860\pi\)
\(858\) 0 0
\(859\) −16.0575 −0.547873 −0.273937 0.961748i \(-0.588326\pi\)
−0.273937 + 0.961748i \(0.588326\pi\)
\(860\) 0 0
\(861\) −5.78282 −0.197078
\(862\) 0 0
\(863\) 37.7571 1.28527 0.642634 0.766174i \(-0.277842\pi\)
0.642634 + 0.766174i \(0.277842\pi\)
\(864\) 0 0
\(865\) −31.4819 −1.07042
\(866\) 0 0
\(867\) 3.72669 0.126565
\(868\) 0 0
\(869\) −7.94194 −0.269412
\(870\) 0 0
\(871\) 5.91531 0.200433
\(872\) 0 0
\(873\) −15.9639 −0.540298
\(874\) 0 0
\(875\) −51.8551 −1.75302
\(876\) 0 0
\(877\) 4.14356 0.139918 0.0699590 0.997550i \(-0.477713\pi\)
0.0699590 + 0.997550i \(0.477713\pi\)
\(878\) 0 0
\(879\) 14.3562 0.484223
\(880\) 0 0
\(881\) −15.5386 −0.523507 −0.261754 0.965135i \(-0.584301\pi\)
−0.261754 + 0.965135i \(0.584301\pi\)
\(882\) 0 0
\(883\) 39.8472 1.34097 0.670483 0.741925i \(-0.266087\pi\)
0.670483 + 0.741925i \(0.266087\pi\)
\(884\) 0 0
\(885\) 12.6191 0.424186
\(886\) 0 0
\(887\) 11.3968 0.382666 0.191333 0.981525i \(-0.438719\pi\)
0.191333 + 0.981525i \(0.438719\pi\)
\(888\) 0 0
\(889\) −97.2927 −3.26309
\(890\) 0 0
\(891\) −0.783405 −0.0262450
\(892\) 0 0
\(893\) 0.134743 0.00450899
\(894\) 0 0
\(895\) −74.3428 −2.48501
\(896\) 0 0
\(897\) −1.78931 −0.0597432
\(898\) 0 0
\(899\) −31.2339 −1.04171
\(900\) 0 0
\(901\) −8.06077 −0.268543
\(902\) 0 0
\(903\) 11.8863 0.395551
\(904\) 0 0
\(905\) −84.1420 −2.79698
\(906\) 0 0
\(907\) −33.3058 −1.10590 −0.552951 0.833214i \(-0.686498\pi\)
−0.552951 + 0.833214i \(0.686498\pi\)
\(908\) 0 0
\(909\) −6.69164 −0.221948
\(910\) 0 0
\(911\) 33.9755 1.12566 0.562830 0.826573i \(-0.309713\pi\)
0.562830 + 0.826573i \(0.309713\pi\)
\(912\) 0 0
\(913\) 12.9929 0.430004
\(914\) 0 0
\(915\) 54.1782 1.79108
\(916\) 0 0
\(917\) 64.5699 2.13229
\(918\) 0 0
\(919\) −23.2442 −0.766756 −0.383378 0.923592i \(-0.625239\pi\)
−0.383378 + 0.923592i \(0.625239\pi\)
\(920\) 0 0
\(921\) −23.3658 −0.769928
\(922\) 0 0
\(923\) −15.6273 −0.514378
\(924\) 0 0
\(925\) −58.8857 −1.93615
\(926\) 0 0
\(927\) −15.7002 −0.515664
\(928\) 0 0
\(929\) 9.87584 0.324016 0.162008 0.986789i \(-0.448203\pi\)
0.162008 + 0.986789i \(0.448203\pi\)
\(930\) 0 0
\(931\) 31.5751 1.03483
\(932\) 0 0
\(933\) −12.7290 −0.416728
\(934\) 0 0
\(935\) −10.2768 −0.336086
\(936\) 0 0
\(937\) 22.8528 0.746570 0.373285 0.927717i \(-0.378231\pi\)
0.373285 + 0.927717i \(0.378231\pi\)
\(938\) 0 0
\(939\) −9.72833 −0.317472
\(940\) 0 0
\(941\) −44.8358 −1.46161 −0.730803 0.682589i \(-0.760854\pi\)
−0.730803 + 0.682589i \(0.760854\pi\)
\(942\) 0 0
\(943\) −0.930624 −0.0303053
\(944\) 0 0
\(945\) 17.4911 0.568985
\(946\) 0 0
\(947\) 23.2347 0.755027 0.377513 0.926004i \(-0.376779\pi\)
0.377513 + 0.926004i \(0.376779\pi\)
\(948\) 0 0
\(949\) −19.3882 −0.629367
\(950\) 0 0
\(951\) 14.6156 0.473942
\(952\) 0 0
\(953\) 13.1951 0.427431 0.213715 0.976896i \(-0.431443\pi\)
0.213715 + 0.976896i \(0.431443\pi\)
\(954\) 0 0
\(955\) 65.9566 2.13430
\(956\) 0 0
\(957\) −4.54000 −0.146757
\(958\) 0 0
\(959\) 27.0392 0.873142
\(960\) 0 0
\(961\) −1.95233 −0.0629785
\(962\) 0 0
\(963\) −1.29322 −0.0416735
\(964\) 0 0
\(965\) −30.1363 −0.970122
\(966\) 0 0
\(967\) 18.7083 0.601618 0.300809 0.953684i \(-0.402743\pi\)
0.300809 + 0.953684i \(0.402743\pi\)
\(968\) 0 0
\(969\) 6.93078 0.222649
\(970\) 0 0
\(971\) 8.51320 0.273202 0.136601 0.990626i \(-0.456382\pi\)
0.136601 + 0.990626i \(0.456382\pi\)
\(972\) 0 0
\(973\) −70.8187 −2.27034
\(974\) 0 0
\(975\) 18.2298 0.583820
\(976\) 0 0
\(977\) 7.05179 0.225607 0.112803 0.993617i \(-0.464017\pi\)
0.112803 + 0.993617i \(0.464017\pi\)
\(978\) 0 0
\(979\) −0.731235 −0.0233704
\(980\) 0 0
\(981\) 0.00600031 0.000191575 0
\(982\) 0 0
\(983\) 10.4440 0.333112 0.166556 0.986032i \(-0.446735\pi\)
0.166556 + 0.986032i \(0.446735\pi\)
\(984\) 0 0
\(985\) −43.8968 −1.39867
\(986\) 0 0
\(987\) −0.344071 −0.0109519
\(988\) 0 0
\(989\) 1.91285 0.0608251
\(990\) 0 0
\(991\) 31.4692 0.999654 0.499827 0.866125i \(-0.333397\pi\)
0.499827 + 0.866125i \(0.333397\pi\)
\(992\) 0 0
\(993\) 7.54681 0.239491
\(994\) 0 0
\(995\) 12.2129 0.387175
\(996\) 0 0
\(997\) 28.6281 0.906661 0.453331 0.891342i \(-0.350236\pi\)
0.453331 + 0.891342i \(0.350236\pi\)
\(998\) 0 0
\(999\) 7.39337 0.233916
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 \(a_p\))