Properties

Label 6004.2.a.g.1.9
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.59467 q^{3}\) \(+2.11777 q^{5}\) \(+0.323115 q^{7}\) \(-0.457036 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.59467 q^{3}\) \(+2.11777 q^{5}\) \(+0.323115 q^{7}\) \(-0.457036 q^{9}\) \(-2.74648 q^{11}\) \(-4.84536 q^{13}\) \(-3.37714 q^{15}\) \(+4.66010 q^{17}\) \(+1.00000 q^{19}\) \(-0.515261 q^{21}\) \(+1.81055 q^{23}\) \(-0.515054 q^{25}\) \(+5.51282 q^{27}\) \(-3.81219 q^{29}\) \(+3.28850 q^{31}\) \(+4.37973 q^{33}\) \(+0.684283 q^{35}\) \(+7.27671 q^{37}\) \(+7.72674 q^{39}\) \(+3.37353 q^{41}\) \(-7.47612 q^{43}\) \(-0.967896 q^{45}\) \(+10.2596 q^{47}\) \(-6.89560 q^{49}\) \(-7.43131 q^{51}\) \(-1.33093 q^{53}\) \(-5.81642 q^{55}\) \(-1.59467 q^{57}\) \(+5.58694 q^{59}\) \(+2.74082 q^{61}\) \(-0.147675 q^{63}\) \(-10.2614 q^{65}\) \(+5.70222 q^{67}\) \(-2.88723 q^{69}\) \(-0.576483 q^{71}\) \(-12.9394 q^{73}\) \(+0.821339 q^{75}\) \(-0.887431 q^{77}\) \(-1.00000 q^{79}\) \(-7.42001 q^{81}\) \(-9.16280 q^{83}\) \(+9.86901 q^{85}\) \(+6.07918 q^{87}\) \(-5.29079 q^{89}\) \(-1.56561 q^{91}\) \(-5.24407 q^{93}\) \(+2.11777 q^{95}\) \(-13.8529 q^{97}\) \(+1.25524 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.59467 −0.920682 −0.460341 0.887742i \(-0.652273\pi\)
−0.460341 + 0.887742i \(0.652273\pi\)
\(4\) 0 0
\(5\) 2.11777 0.947095 0.473548 0.880768i \(-0.342973\pi\)
0.473548 + 0.880768i \(0.342973\pi\)
\(6\) 0 0
\(7\) 0.323115 0.122126 0.0610630 0.998134i \(-0.480551\pi\)
0.0610630 + 0.998134i \(0.480551\pi\)
\(8\) 0 0
\(9\) −0.457036 −0.152345
\(10\) 0 0
\(11\) −2.74648 −0.828096 −0.414048 0.910255i \(-0.635885\pi\)
−0.414048 + 0.910255i \(0.635885\pi\)
\(12\) 0 0
\(13\) −4.84536 −1.34386 −0.671931 0.740614i \(-0.734535\pi\)
−0.671931 + 0.740614i \(0.734535\pi\)
\(14\) 0 0
\(15\) −3.37714 −0.871973
\(16\) 0 0
\(17\) 4.66010 1.13024 0.565120 0.825009i \(-0.308830\pi\)
0.565120 + 0.825009i \(0.308830\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −0.515261 −0.112439
\(22\) 0 0
\(23\) 1.81055 0.377526 0.188763 0.982023i \(-0.439552\pi\)
0.188763 + 0.982023i \(0.439552\pi\)
\(24\) 0 0
\(25\) −0.515054 −0.103011
\(26\) 0 0
\(27\) 5.51282 1.06094
\(28\) 0 0
\(29\) −3.81219 −0.707906 −0.353953 0.935263i \(-0.615163\pi\)
−0.353953 + 0.935263i \(0.615163\pi\)
\(30\) 0 0
\(31\) 3.28850 0.590632 0.295316 0.955400i \(-0.404575\pi\)
0.295316 + 0.955400i \(0.404575\pi\)
\(32\) 0 0
\(33\) 4.37973 0.762413
\(34\) 0 0
\(35\) 0.684283 0.115665
\(36\) 0 0
\(37\) 7.27671 1.19628 0.598142 0.801390i \(-0.295906\pi\)
0.598142 + 0.801390i \(0.295906\pi\)
\(38\) 0 0
\(39\) 7.72674 1.23727
\(40\) 0 0
\(41\) 3.37353 0.526856 0.263428 0.964679i \(-0.415147\pi\)
0.263428 + 0.964679i \(0.415147\pi\)
\(42\) 0 0
\(43\) −7.47612 −1.14010 −0.570049 0.821611i \(-0.693076\pi\)
−0.570049 + 0.821611i \(0.693076\pi\)
\(44\) 0 0
\(45\) −0.967896 −0.144285
\(46\) 0 0
\(47\) 10.2596 1.49652 0.748260 0.663406i \(-0.230890\pi\)
0.748260 + 0.663406i \(0.230890\pi\)
\(48\) 0 0
\(49\) −6.89560 −0.985085
\(50\) 0 0
\(51\) −7.43131 −1.04059
\(52\) 0 0
\(53\) −1.33093 −0.182817 −0.0914086 0.995813i \(-0.529137\pi\)
−0.0914086 + 0.995813i \(0.529137\pi\)
\(54\) 0 0
\(55\) −5.81642 −0.784286
\(56\) 0 0
\(57\) −1.59467 −0.211219
\(58\) 0 0
\(59\) 5.58694 0.727358 0.363679 0.931524i \(-0.381521\pi\)
0.363679 + 0.931524i \(0.381521\pi\)
\(60\) 0 0
\(61\) 2.74082 0.350926 0.175463 0.984486i \(-0.443858\pi\)
0.175463 + 0.984486i \(0.443858\pi\)
\(62\) 0 0
\(63\) −0.147675 −0.0186053
\(64\) 0 0
\(65\) −10.2614 −1.27277
\(66\) 0 0
\(67\) 5.70222 0.696637 0.348318 0.937376i \(-0.386753\pi\)
0.348318 + 0.937376i \(0.386753\pi\)
\(68\) 0 0
\(69\) −2.88723 −0.347581
\(70\) 0 0
\(71\) −0.576483 −0.0684159 −0.0342080 0.999415i \(-0.510891\pi\)
−0.0342080 + 0.999415i \(0.510891\pi\)
\(72\) 0 0
\(73\) −12.9394 −1.51444 −0.757218 0.653162i \(-0.773442\pi\)
−0.757218 + 0.653162i \(0.773442\pi\)
\(74\) 0 0
\(75\) 0.821339 0.0948401
\(76\) 0 0
\(77\) −0.887431 −0.101132
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −7.42001 −0.824446
\(82\) 0 0
\(83\) −9.16280 −1.00575 −0.502874 0.864360i \(-0.667724\pi\)
−0.502874 + 0.864360i \(0.667724\pi\)
\(84\) 0 0
\(85\) 9.86901 1.07044
\(86\) 0 0
\(87\) 6.07918 0.651756
\(88\) 0 0
\(89\) −5.29079 −0.560823 −0.280412 0.959880i \(-0.590471\pi\)
−0.280412 + 0.959880i \(0.590471\pi\)
\(90\) 0 0
\(91\) −1.56561 −0.164121
\(92\) 0 0
\(93\) −5.24407 −0.543785
\(94\) 0 0
\(95\) 2.11777 0.217279
\(96\) 0 0
\(97\) −13.8529 −1.40655 −0.703274 0.710919i \(-0.748279\pi\)
−0.703274 + 0.710919i \(0.748279\pi\)
\(98\) 0 0
\(99\) 1.25524 0.126156
\(100\) 0 0
\(101\) −6.11741 −0.608705 −0.304353 0.952559i \(-0.598440\pi\)
−0.304353 + 0.952559i \(0.598440\pi\)
\(102\) 0 0
\(103\) −9.31022 −0.917363 −0.458682 0.888601i \(-0.651678\pi\)
−0.458682 + 0.888601i \(0.651678\pi\)
\(104\) 0 0
\(105\) −1.09120 −0.106491
\(106\) 0 0
\(107\) −0.658953 −0.0637034 −0.0318517 0.999493i \(-0.510140\pi\)
−0.0318517 + 0.999493i \(0.510140\pi\)
\(108\) 0 0
\(109\) 8.90670 0.853107 0.426553 0.904462i \(-0.359728\pi\)
0.426553 + 0.904462i \(0.359728\pi\)
\(110\) 0 0
\(111\) −11.6039 −1.10140
\(112\) 0 0
\(113\) −14.4760 −1.36179 −0.680895 0.732381i \(-0.738409\pi\)
−0.680895 + 0.732381i \(0.738409\pi\)
\(114\) 0 0
\(115\) 3.83433 0.357553
\(116\) 0 0
\(117\) 2.21450 0.204731
\(118\) 0 0
\(119\) 1.50575 0.138032
\(120\) 0 0
\(121\) −3.45682 −0.314257
\(122\) 0 0
\(123\) −5.37965 −0.485067
\(124\) 0 0
\(125\) −11.6796 −1.04466
\(126\) 0 0
\(127\) −10.2914 −0.913218 −0.456609 0.889668i \(-0.650936\pi\)
−0.456609 + 0.889668i \(0.650936\pi\)
\(128\) 0 0
\(129\) 11.9219 1.04967
\(130\) 0 0
\(131\) −1.15233 −0.100680 −0.0503399 0.998732i \(-0.516030\pi\)
−0.0503399 + 0.998732i \(0.516030\pi\)
\(132\) 0 0
\(133\) 0.323115 0.0280176
\(134\) 0 0
\(135\) 11.6749 1.00481
\(136\) 0 0
\(137\) −3.30339 −0.282227 −0.141114 0.989993i \(-0.545068\pi\)
−0.141114 + 0.989993i \(0.545068\pi\)
\(138\) 0 0
\(139\) 9.86153 0.836444 0.418222 0.908345i \(-0.362653\pi\)
0.418222 + 0.908345i \(0.362653\pi\)
\(140\) 0 0
\(141\) −16.3607 −1.37782
\(142\) 0 0
\(143\) 13.3077 1.11285
\(144\) 0 0
\(145\) −8.07334 −0.670455
\(146\) 0 0
\(147\) 10.9962 0.906950
\(148\) 0 0
\(149\) 18.6577 1.52850 0.764251 0.644919i \(-0.223109\pi\)
0.764251 + 0.644919i \(0.223109\pi\)
\(150\) 0 0
\(151\) −21.0737 −1.71495 −0.857477 0.514522i \(-0.827969\pi\)
−0.857477 + 0.514522i \(0.827969\pi\)
\(152\) 0 0
\(153\) −2.12983 −0.172187
\(154\) 0 0
\(155\) 6.96429 0.559385
\(156\) 0 0
\(157\) −15.4633 −1.23410 −0.617052 0.786922i \(-0.711673\pi\)
−0.617052 + 0.786922i \(0.711673\pi\)
\(158\) 0 0
\(159\) 2.12239 0.168316
\(160\) 0 0
\(161\) 0.585017 0.0461058
\(162\) 0 0
\(163\) 15.2557 1.19492 0.597458 0.801900i \(-0.296177\pi\)
0.597458 + 0.801900i \(0.296177\pi\)
\(164\) 0 0
\(165\) 9.27526 0.722078
\(166\) 0 0
\(167\) −4.44396 −0.343884 −0.171942 0.985107i \(-0.555004\pi\)
−0.171942 + 0.985107i \(0.555004\pi\)
\(168\) 0 0
\(169\) 10.4775 0.805965
\(170\) 0 0
\(171\) −0.457036 −0.0349504
\(172\) 0 0
\(173\) 12.6175 0.959289 0.479645 0.877463i \(-0.340766\pi\)
0.479645 + 0.877463i \(0.340766\pi\)
\(174\) 0 0
\(175\) −0.166422 −0.0125803
\(176\) 0 0
\(177\) −8.90932 −0.669665
\(178\) 0 0
\(179\) 2.96773 0.221819 0.110909 0.993831i \(-0.464624\pi\)
0.110909 + 0.993831i \(0.464624\pi\)
\(180\) 0 0
\(181\) −19.3583 −1.43889 −0.719444 0.694550i \(-0.755603\pi\)
−0.719444 + 0.694550i \(0.755603\pi\)
\(182\) 0 0
\(183\) −4.37070 −0.323091
\(184\) 0 0
\(185\) 15.4104 1.13299
\(186\) 0 0
\(187\) −12.7989 −0.935947
\(188\) 0 0
\(189\) 1.78128 0.129569
\(190\) 0 0
\(191\) 7.02208 0.508100 0.254050 0.967191i \(-0.418237\pi\)
0.254050 + 0.967191i \(0.418237\pi\)
\(192\) 0 0
\(193\) −21.4943 −1.54719 −0.773596 0.633679i \(-0.781544\pi\)
−0.773596 + 0.633679i \(0.781544\pi\)
\(194\) 0 0
\(195\) 16.3635 1.17181
\(196\) 0 0
\(197\) 5.72539 0.407917 0.203959 0.978980i \(-0.434619\pi\)
0.203959 + 0.978980i \(0.434619\pi\)
\(198\) 0 0
\(199\) 12.6059 0.893608 0.446804 0.894632i \(-0.352562\pi\)
0.446804 + 0.894632i \(0.352562\pi\)
\(200\) 0 0
\(201\) −9.09314 −0.641381
\(202\) 0 0
\(203\) −1.23178 −0.0864538
\(204\) 0 0
\(205\) 7.14435 0.498983
\(206\) 0 0
\(207\) −0.827487 −0.0575143
\(208\) 0 0
\(209\) −2.74648 −0.189978
\(210\) 0 0
\(211\) 12.3083 0.847337 0.423669 0.905817i \(-0.360742\pi\)
0.423669 + 0.905817i \(0.360742\pi\)
\(212\) 0 0
\(213\) 0.919299 0.0629893
\(214\) 0 0
\(215\) −15.8327 −1.07978
\(216\) 0 0
\(217\) 1.06257 0.0721316
\(218\) 0 0
\(219\) 20.6340 1.39431
\(220\) 0 0
\(221\) −22.5799 −1.51889
\(222\) 0 0
\(223\) −10.9471 −0.733074 −0.366537 0.930403i \(-0.619457\pi\)
−0.366537 + 0.930403i \(0.619457\pi\)
\(224\) 0 0
\(225\) 0.235398 0.0156932
\(226\) 0 0
\(227\) −21.5844 −1.43261 −0.716304 0.697789i \(-0.754167\pi\)
−0.716304 + 0.697789i \(0.754167\pi\)
\(228\) 0 0
\(229\) 6.83177 0.451456 0.225728 0.974190i \(-0.427524\pi\)
0.225728 + 0.974190i \(0.427524\pi\)
\(230\) 0 0
\(231\) 1.41516 0.0931105
\(232\) 0 0
\(233\) 7.96517 0.521816 0.260908 0.965364i \(-0.415978\pi\)
0.260908 + 0.965364i \(0.415978\pi\)
\(234\) 0 0
\(235\) 21.7275 1.41735
\(236\) 0 0
\(237\) 1.59467 0.103585
\(238\) 0 0
\(239\) −15.5380 −1.00507 −0.502533 0.864558i \(-0.667599\pi\)
−0.502533 + 0.864558i \(0.667599\pi\)
\(240\) 0 0
\(241\) 0.188665 0.0121530 0.00607649 0.999982i \(-0.498066\pi\)
0.00607649 + 0.999982i \(0.498066\pi\)
\(242\) 0 0
\(243\) −4.70601 −0.301891
\(244\) 0 0
\(245\) −14.6033 −0.932969
\(246\) 0 0
\(247\) −4.84536 −0.308303
\(248\) 0 0
\(249\) 14.6116 0.925974
\(250\) 0 0
\(251\) 23.9445 1.51136 0.755682 0.654939i \(-0.227306\pi\)
0.755682 + 0.654939i \(0.227306\pi\)
\(252\) 0 0
\(253\) −4.97265 −0.312628
\(254\) 0 0
\(255\) −15.7378 −0.985539
\(256\) 0 0
\(257\) −5.21562 −0.325341 −0.162671 0.986680i \(-0.552011\pi\)
−0.162671 + 0.986680i \(0.552011\pi\)
\(258\) 0 0
\(259\) 2.35122 0.146097
\(260\) 0 0
\(261\) 1.74231 0.107846
\(262\) 0 0
\(263\) 25.3965 1.56602 0.783008 0.622011i \(-0.213684\pi\)
0.783008 + 0.622011i \(0.213684\pi\)
\(264\) 0 0
\(265\) −2.81860 −0.173145
\(266\) 0 0
\(267\) 8.43706 0.516340
\(268\) 0 0
\(269\) −10.5565 −0.643641 −0.321821 0.946801i \(-0.604295\pi\)
−0.321821 + 0.946801i \(0.604295\pi\)
\(270\) 0 0
\(271\) −9.38280 −0.569964 −0.284982 0.958533i \(-0.591988\pi\)
−0.284982 + 0.958533i \(0.591988\pi\)
\(272\) 0 0
\(273\) 2.49663 0.151103
\(274\) 0 0
\(275\) 1.41459 0.0853028
\(276\) 0 0
\(277\) 11.6843 0.702042 0.351021 0.936368i \(-0.385835\pi\)
0.351021 + 0.936368i \(0.385835\pi\)
\(278\) 0 0
\(279\) −1.50296 −0.0899800
\(280\) 0 0
\(281\) −22.9348 −1.36817 −0.684087 0.729400i \(-0.739799\pi\)
−0.684087 + 0.729400i \(0.739799\pi\)
\(282\) 0 0
\(283\) 1.20607 0.0716936 0.0358468 0.999357i \(-0.488587\pi\)
0.0358468 + 0.999357i \(0.488587\pi\)
\(284\) 0 0
\(285\) −3.37714 −0.200044
\(286\) 0 0
\(287\) 1.09004 0.0643429
\(288\) 0 0
\(289\) 4.71650 0.277441
\(290\) 0 0
\(291\) 22.0907 1.29498
\(292\) 0 0
\(293\) −25.3863 −1.48308 −0.741541 0.670908i \(-0.765905\pi\)
−0.741541 + 0.670908i \(0.765905\pi\)
\(294\) 0 0
\(295\) 11.8319 0.688877
\(296\) 0 0
\(297\) −15.1409 −0.878563
\(298\) 0 0
\(299\) −8.77278 −0.507343
\(300\) 0 0
\(301\) −2.41565 −0.139236
\(302\) 0 0
\(303\) 9.75523 0.560424
\(304\) 0 0
\(305\) 5.80443 0.332360
\(306\) 0 0
\(307\) −1.59655 −0.0911202 −0.0455601 0.998962i \(-0.514507\pi\)
−0.0455601 + 0.998962i \(0.514507\pi\)
\(308\) 0 0
\(309\) 14.8467 0.844600
\(310\) 0 0
\(311\) −23.3100 −1.32179 −0.660893 0.750480i \(-0.729822\pi\)
−0.660893 + 0.750480i \(0.729822\pi\)
\(312\) 0 0
\(313\) −12.3906 −0.700356 −0.350178 0.936683i \(-0.613879\pi\)
−0.350178 + 0.936683i \(0.613879\pi\)
\(314\) 0 0
\(315\) −0.312742 −0.0176210
\(316\) 0 0
\(317\) 5.44994 0.306099 0.153050 0.988219i \(-0.451091\pi\)
0.153050 + 0.988219i \(0.451091\pi\)
\(318\) 0 0
\(319\) 10.4701 0.586214
\(320\) 0 0
\(321\) 1.05081 0.0586505
\(322\) 0 0
\(323\) 4.66010 0.259295
\(324\) 0 0
\(325\) 2.49562 0.138432
\(326\) 0 0
\(327\) −14.2032 −0.785440
\(328\) 0 0
\(329\) 3.31504 0.182764
\(330\) 0 0
\(331\) 4.97989 0.273720 0.136860 0.990590i \(-0.456299\pi\)
0.136860 + 0.990590i \(0.456299\pi\)
\(332\) 0 0
\(333\) −3.32572 −0.182248
\(334\) 0 0
\(335\) 12.0760 0.659781
\(336\) 0 0
\(337\) 7.12073 0.387891 0.193945 0.981012i \(-0.437872\pi\)
0.193945 + 0.981012i \(0.437872\pi\)
\(338\) 0 0
\(339\) 23.0844 1.25377
\(340\) 0 0
\(341\) −9.03182 −0.489100
\(342\) 0 0
\(343\) −4.48988 −0.242431
\(344\) 0 0
\(345\) −6.11448 −0.329193
\(346\) 0 0
\(347\) −4.42469 −0.237530 −0.118765 0.992922i \(-0.537893\pi\)
−0.118765 + 0.992922i \(0.537893\pi\)
\(348\) 0 0
\(349\) −26.4416 −1.41539 −0.707694 0.706519i \(-0.750264\pi\)
−0.707694 + 0.706519i \(0.750264\pi\)
\(350\) 0 0
\(351\) −26.7116 −1.42576
\(352\) 0 0
\(353\) −13.8394 −0.736599 −0.368300 0.929707i \(-0.620060\pi\)
−0.368300 + 0.929707i \(0.620060\pi\)
\(354\) 0 0
\(355\) −1.22086 −0.0647964
\(356\) 0 0
\(357\) −2.40117 −0.127083
\(358\) 0 0
\(359\) 22.3630 1.18027 0.590137 0.807303i \(-0.299074\pi\)
0.590137 + 0.807303i \(0.299074\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 5.51249 0.289330
\(364\) 0 0
\(365\) −27.4026 −1.43432
\(366\) 0 0
\(367\) 20.6459 1.07771 0.538854 0.842399i \(-0.318858\pi\)
0.538854 + 0.842399i \(0.318858\pi\)
\(368\) 0 0
\(369\) −1.54182 −0.0802640
\(370\) 0 0
\(371\) −0.430044 −0.0223267
\(372\) 0 0
\(373\) 0.868107 0.0449489 0.0224745 0.999747i \(-0.492846\pi\)
0.0224745 + 0.999747i \(0.492846\pi\)
\(374\) 0 0
\(375\) 18.6251 0.961796
\(376\) 0 0
\(377\) 18.4715 0.951328
\(378\) 0 0
\(379\) −25.5120 −1.31047 −0.655233 0.755427i \(-0.727429\pi\)
−0.655233 + 0.755427i \(0.727429\pi\)
\(380\) 0 0
\(381\) 16.4114 0.840783
\(382\) 0 0
\(383\) −23.3575 −1.19351 −0.596756 0.802423i \(-0.703544\pi\)
−0.596756 + 0.802423i \(0.703544\pi\)
\(384\) 0 0
\(385\) −1.87937 −0.0957817
\(386\) 0 0
\(387\) 3.41685 0.173688
\(388\) 0 0
\(389\) −17.5571 −0.890180 −0.445090 0.895486i \(-0.646828\pi\)
−0.445090 + 0.895486i \(0.646828\pi\)
\(390\) 0 0
\(391\) 8.43735 0.426695
\(392\) 0 0
\(393\) 1.83759 0.0926941
\(394\) 0 0
\(395\) −2.11777 −0.106557
\(396\) 0 0
\(397\) 28.3117 1.42092 0.710462 0.703736i \(-0.248486\pi\)
0.710462 + 0.703736i \(0.248486\pi\)
\(398\) 0 0
\(399\) −0.515261 −0.0257953
\(400\) 0 0
\(401\) 19.9971 0.998607 0.499303 0.866427i \(-0.333589\pi\)
0.499303 + 0.866427i \(0.333589\pi\)
\(402\) 0 0
\(403\) −15.9340 −0.793728
\(404\) 0 0
\(405\) −15.7139 −0.780829
\(406\) 0 0
\(407\) −19.9854 −0.990638
\(408\) 0 0
\(409\) −16.8900 −0.835158 −0.417579 0.908641i \(-0.637121\pi\)
−0.417579 + 0.908641i \(0.637121\pi\)
\(410\) 0 0
\(411\) 5.26780 0.259842
\(412\) 0 0
\(413\) 1.80523 0.0888294
\(414\) 0 0
\(415\) −19.4047 −0.952539
\(416\) 0 0
\(417\) −15.7259 −0.770099
\(418\) 0 0
\(419\) −8.61500 −0.420870 −0.210435 0.977608i \(-0.567488\pi\)
−0.210435 + 0.977608i \(0.567488\pi\)
\(420\) 0 0
\(421\) −24.0975 −1.17444 −0.587221 0.809427i \(-0.699778\pi\)
−0.587221 + 0.809427i \(0.699778\pi\)
\(422\) 0 0
\(423\) −4.68901 −0.227988
\(424\) 0 0
\(425\) −2.40020 −0.116427
\(426\) 0 0
\(427\) 0.885601 0.0428572
\(428\) 0 0
\(429\) −21.2214 −1.02458
\(430\) 0 0
\(431\) −1.64339 −0.0791594 −0.0395797 0.999216i \(-0.512602\pi\)
−0.0395797 + 0.999216i \(0.512602\pi\)
\(432\) 0 0
\(433\) −33.6046 −1.61493 −0.807466 0.589914i \(-0.799162\pi\)
−0.807466 + 0.589914i \(0.799162\pi\)
\(434\) 0 0
\(435\) 12.8743 0.617275
\(436\) 0 0
\(437\) 1.81055 0.0866105
\(438\) 0 0
\(439\) −20.6851 −0.987244 −0.493622 0.869677i \(-0.664327\pi\)
−0.493622 + 0.869677i \(0.664327\pi\)
\(440\) 0 0
\(441\) 3.15153 0.150073
\(442\) 0 0
\(443\) −8.89239 −0.422490 −0.211245 0.977433i \(-0.567752\pi\)
−0.211245 + 0.977433i \(0.567752\pi\)
\(444\) 0 0
\(445\) −11.2047 −0.531153
\(446\) 0 0
\(447\) −29.7529 −1.40726
\(448\) 0 0
\(449\) −24.4988 −1.15617 −0.578086 0.815976i \(-0.696200\pi\)
−0.578086 + 0.815976i \(0.696200\pi\)
\(450\) 0 0
\(451\) −9.26534 −0.436288
\(452\) 0 0
\(453\) 33.6056 1.57893
\(454\) 0 0
\(455\) −3.31560 −0.155438
\(456\) 0 0
\(457\) 1.44191 0.0674497 0.0337249 0.999431i \(-0.489263\pi\)
0.0337249 + 0.999431i \(0.489263\pi\)
\(458\) 0 0
\(459\) 25.6903 1.19912
\(460\) 0 0
\(461\) 4.91043 0.228702 0.114351 0.993440i \(-0.463521\pi\)
0.114351 + 0.993440i \(0.463521\pi\)
\(462\) 0 0
\(463\) 21.5919 1.00346 0.501730 0.865024i \(-0.332697\pi\)
0.501730 + 0.865024i \(0.332697\pi\)
\(464\) 0 0
\(465\) −11.1057 −0.515016
\(466\) 0 0
\(467\) −9.06547 −0.419500 −0.209750 0.977755i \(-0.567265\pi\)
−0.209750 + 0.977755i \(0.567265\pi\)
\(468\) 0 0
\(469\) 1.84247 0.0850775
\(470\) 0 0
\(471\) 24.6588 1.13622
\(472\) 0 0
\(473\) 20.5330 0.944110
\(474\) 0 0
\(475\) −0.515054 −0.0236323
\(476\) 0 0
\(477\) 0.608282 0.0278513
\(478\) 0 0
\(479\) −24.3371 −1.11199 −0.555995 0.831186i \(-0.687663\pi\)
−0.555995 + 0.831186i \(0.687663\pi\)
\(480\) 0 0
\(481\) −35.2583 −1.60764
\(482\) 0 0
\(483\) −0.932907 −0.0424488
\(484\) 0 0
\(485\) −29.3372 −1.33213
\(486\) 0 0
\(487\) −41.4169 −1.87678 −0.938389 0.345580i \(-0.887682\pi\)
−0.938389 + 0.345580i \(0.887682\pi\)
\(488\) 0 0
\(489\) −24.3277 −1.10014
\(490\) 0 0
\(491\) −16.5948 −0.748915 −0.374457 0.927244i \(-0.622171\pi\)
−0.374457 + 0.927244i \(0.622171\pi\)
\(492\) 0 0
\(493\) −17.7652 −0.800104
\(494\) 0 0
\(495\) 2.65831 0.119482
\(496\) 0 0
\(497\) −0.186270 −0.00835537
\(498\) 0 0
\(499\) −27.9869 −1.25287 −0.626434 0.779475i \(-0.715486\pi\)
−0.626434 + 0.779475i \(0.715486\pi\)
\(500\) 0 0
\(501\) 7.08665 0.316608
\(502\) 0 0
\(503\) 3.84514 0.171447 0.0857233 0.996319i \(-0.472680\pi\)
0.0857233 + 0.996319i \(0.472680\pi\)
\(504\) 0 0
\(505\) −12.9553 −0.576502
\(506\) 0 0
\(507\) −16.7082 −0.742037
\(508\) 0 0
\(509\) 18.0894 0.801800 0.400900 0.916122i \(-0.368697\pi\)
0.400900 + 0.916122i \(0.368697\pi\)
\(510\) 0 0
\(511\) −4.18090 −0.184952
\(512\) 0 0
\(513\) 5.51282 0.243397
\(514\) 0 0
\(515\) −19.7169 −0.868830
\(516\) 0 0
\(517\) −28.1779 −1.23926
\(518\) 0 0
\(519\) −20.1207 −0.883200
\(520\) 0 0
\(521\) 26.5432 1.16288 0.581439 0.813590i \(-0.302490\pi\)
0.581439 + 0.813590i \(0.302490\pi\)
\(522\) 0 0
\(523\) −12.0736 −0.527942 −0.263971 0.964531i \(-0.585032\pi\)
−0.263971 + 0.964531i \(0.585032\pi\)
\(524\) 0 0
\(525\) 0.265387 0.0115824
\(526\) 0 0
\(527\) 15.3247 0.667556
\(528\) 0 0
\(529\) −19.7219 −0.857474
\(530\) 0 0
\(531\) −2.55343 −0.110809
\(532\) 0 0
\(533\) −16.3460 −0.708022
\(534\) 0 0
\(535\) −1.39551 −0.0603332
\(536\) 0 0
\(537\) −4.73255 −0.204225
\(538\) 0 0
\(539\) 18.9386 0.815745
\(540\) 0 0
\(541\) 6.21111 0.267036 0.133518 0.991046i \(-0.457373\pi\)
0.133518 + 0.991046i \(0.457373\pi\)
\(542\) 0 0
\(543\) 30.8700 1.32476
\(544\) 0 0
\(545\) 18.8623 0.807974
\(546\) 0 0
\(547\) 2.17549 0.0930172 0.0465086 0.998918i \(-0.485191\pi\)
0.0465086 + 0.998918i \(0.485191\pi\)
\(548\) 0 0
\(549\) −1.25265 −0.0534619
\(550\) 0 0
\(551\) −3.81219 −0.162405
\(552\) 0 0
\(553\) −0.323115 −0.0137403
\(554\) 0 0
\(555\) −24.5745 −1.04313
\(556\) 0 0
\(557\) 29.3130 1.24203 0.621016 0.783798i \(-0.286720\pi\)
0.621016 + 0.783798i \(0.286720\pi\)
\(558\) 0 0
\(559\) 36.2245 1.53213
\(560\) 0 0
\(561\) 20.4100 0.861709
\(562\) 0 0
\(563\) −34.6181 −1.45898 −0.729490 0.683992i \(-0.760242\pi\)
−0.729490 + 0.683992i \(0.760242\pi\)
\(564\) 0 0
\(565\) −30.6569 −1.28974
\(566\) 0 0
\(567\) −2.39752 −0.100686
\(568\) 0 0
\(569\) −5.81835 −0.243918 −0.121959 0.992535i \(-0.538918\pi\)
−0.121959 + 0.992535i \(0.538918\pi\)
\(570\) 0 0
\(571\) 8.46730 0.354346 0.177173 0.984180i \(-0.443305\pi\)
0.177173 + 0.984180i \(0.443305\pi\)
\(572\) 0 0
\(573\) −11.1979 −0.467798
\(574\) 0 0
\(575\) −0.932531 −0.0388892
\(576\) 0 0
\(577\) 6.68430 0.278271 0.139135 0.990273i \(-0.455568\pi\)
0.139135 + 0.990273i \(0.455568\pi\)
\(578\) 0 0
\(579\) 34.2762 1.42447
\(580\) 0 0
\(581\) −2.96064 −0.122828
\(582\) 0 0
\(583\) 3.65538 0.151390
\(584\) 0 0
\(585\) 4.68981 0.193900
\(586\) 0 0
\(587\) 25.0857 1.03540 0.517699 0.855563i \(-0.326789\pi\)
0.517699 + 0.855563i \(0.326789\pi\)
\(588\) 0 0
\(589\) 3.28850 0.135500
\(590\) 0 0
\(591\) −9.13009 −0.375562
\(592\) 0 0
\(593\) −0.566761 −0.0232741 −0.0116370 0.999932i \(-0.503704\pi\)
−0.0116370 + 0.999932i \(0.503704\pi\)
\(594\) 0 0
\(595\) 3.18883 0.130729
\(596\) 0 0
\(597\) −20.1022 −0.822728
\(598\) 0 0
\(599\) −12.5388 −0.512320 −0.256160 0.966634i \(-0.582457\pi\)
−0.256160 + 0.966634i \(0.582457\pi\)
\(600\) 0 0
\(601\) 7.16822 0.292398 0.146199 0.989255i \(-0.453296\pi\)
0.146199 + 0.989255i \(0.453296\pi\)
\(602\) 0 0
\(603\) −2.60612 −0.106129
\(604\) 0 0
\(605\) −7.32076 −0.297631
\(606\) 0 0
\(607\) 39.4870 1.60273 0.801363 0.598178i \(-0.204109\pi\)
0.801363 + 0.598178i \(0.204109\pi\)
\(608\) 0 0
\(609\) 1.96427 0.0795964
\(610\) 0 0
\(611\) −49.7116 −2.01112
\(612\) 0 0
\(613\) −5.66030 −0.228617 −0.114309 0.993445i \(-0.536465\pi\)
−0.114309 + 0.993445i \(0.536465\pi\)
\(614\) 0 0
\(615\) −11.3929 −0.459405
\(616\) 0 0
\(617\) 38.2467 1.53975 0.769876 0.638193i \(-0.220318\pi\)
0.769876 + 0.638193i \(0.220318\pi\)
\(618\) 0 0
\(619\) 21.2732 0.855040 0.427520 0.904006i \(-0.359387\pi\)
0.427520 + 0.904006i \(0.359387\pi\)
\(620\) 0 0
\(621\) 9.98125 0.400534
\(622\) 0 0
\(623\) −1.70954 −0.0684911
\(624\) 0 0
\(625\) −22.1595 −0.886378
\(626\) 0 0
\(627\) 4.37973 0.174910
\(628\) 0 0
\(629\) 33.9102 1.35209
\(630\) 0 0
\(631\) 37.4546 1.49104 0.745522 0.666481i \(-0.232200\pi\)
0.745522 + 0.666481i \(0.232200\pi\)
\(632\) 0 0
\(633\) −19.6276 −0.780128
\(634\) 0 0
\(635\) −21.7949 −0.864904
\(636\) 0 0
\(637\) 33.4117 1.32382
\(638\) 0 0
\(639\) 0.263473 0.0104228
\(640\) 0 0
\(641\) −16.8514 −0.665591 −0.332795 0.942999i \(-0.607992\pi\)
−0.332795 + 0.942999i \(0.607992\pi\)
\(642\) 0 0
\(643\) 31.0714 1.22534 0.612668 0.790340i \(-0.290096\pi\)
0.612668 + 0.790340i \(0.290096\pi\)
\(644\) 0 0
\(645\) 25.2479 0.994134
\(646\) 0 0
\(647\) 39.7376 1.56224 0.781122 0.624378i \(-0.214647\pi\)
0.781122 + 0.624378i \(0.214647\pi\)
\(648\) 0 0
\(649\) −15.3444 −0.602322
\(650\) 0 0
\(651\) −1.69444 −0.0664103
\(652\) 0 0
\(653\) −30.6653 −1.20002 −0.600012 0.799991i \(-0.704838\pi\)
−0.600012 + 0.799991i \(0.704838\pi\)
\(654\) 0 0
\(655\) −2.44038 −0.0953534
\(656\) 0 0
\(657\) 5.91374 0.230717
\(658\) 0 0
\(659\) −29.5922 −1.15275 −0.576374 0.817186i \(-0.695533\pi\)
−0.576374 + 0.817186i \(0.695533\pi\)
\(660\) 0 0
\(661\) −25.6256 −0.996719 −0.498359 0.866971i \(-0.666064\pi\)
−0.498359 + 0.866971i \(0.666064\pi\)
\(662\) 0 0
\(663\) 36.0074 1.39841
\(664\) 0 0
\(665\) 0.684283 0.0265354
\(666\) 0 0
\(667\) −6.90217 −0.267253
\(668\) 0 0
\(669\) 17.4570 0.674928
\(670\) 0 0
\(671\) −7.52762 −0.290601
\(672\) 0 0
\(673\) −50.9893 −1.96549 −0.982746 0.184959i \(-0.940785\pi\)
−0.982746 + 0.184959i \(0.940785\pi\)
\(674\) 0 0
\(675\) −2.83940 −0.109289
\(676\) 0 0
\(677\) 6.80318 0.261467 0.130734 0.991418i \(-0.458267\pi\)
0.130734 + 0.991418i \(0.458267\pi\)
\(678\) 0 0
\(679\) −4.47608 −0.171776
\(680\) 0 0
\(681\) 34.4199 1.31898
\(682\) 0 0
\(683\) 37.1993 1.42339 0.711696 0.702488i \(-0.247927\pi\)
0.711696 + 0.702488i \(0.247927\pi\)
\(684\) 0 0
\(685\) −6.99581 −0.267296
\(686\) 0 0
\(687\) −10.8944 −0.415647
\(688\) 0 0
\(689\) 6.44884 0.245681
\(690\) 0 0
\(691\) 27.2064 1.03498 0.517491 0.855689i \(-0.326866\pi\)
0.517491 + 0.855689i \(0.326866\pi\)
\(692\) 0 0
\(693\) 0.405587 0.0154070
\(694\) 0 0
\(695\) 20.8844 0.792192
\(696\) 0 0
\(697\) 15.7210 0.595474
\(698\) 0 0
\(699\) −12.7018 −0.480426
\(700\) 0 0
\(701\) −50.6399 −1.91264 −0.956321 0.292320i \(-0.905573\pi\)
−0.956321 + 0.292320i \(0.905573\pi\)
\(702\) 0 0
\(703\) 7.27671 0.274446
\(704\) 0 0
\(705\) −34.6482 −1.30493
\(706\) 0 0
\(707\) −1.97663 −0.0743387
\(708\) 0 0
\(709\) 7.84863 0.294761 0.147381 0.989080i \(-0.452916\pi\)
0.147381 + 0.989080i \(0.452916\pi\)
\(710\) 0 0
\(711\) 0.457036 0.0171402
\(712\) 0 0
\(713\) 5.95401 0.222979
\(714\) 0 0
\(715\) 28.1827 1.05397
\(716\) 0 0
\(717\) 24.7779 0.925347
\(718\) 0 0
\(719\) −18.2128 −0.679222 −0.339611 0.940566i \(-0.610295\pi\)
−0.339611 + 0.940566i \(0.610295\pi\)
\(720\) 0 0
\(721\) −3.00827 −0.112034
\(722\) 0 0
\(723\) −0.300858 −0.0111890
\(724\) 0 0
\(725\) 1.96348 0.0729219
\(726\) 0 0
\(727\) −10.3058 −0.382221 −0.191110 0.981569i \(-0.561209\pi\)
−0.191110 + 0.981569i \(0.561209\pi\)
\(728\) 0 0
\(729\) 29.7646 1.10239
\(730\) 0 0
\(731\) −34.8394 −1.28858
\(732\) 0 0
\(733\) −26.1499 −0.965868 −0.482934 0.875657i \(-0.660429\pi\)
−0.482934 + 0.875657i \(0.660429\pi\)
\(734\) 0 0
\(735\) 23.2874 0.858968
\(736\) 0 0
\(737\) −15.6611 −0.576882
\(738\) 0 0
\(739\) 28.2626 1.03966 0.519829 0.854270i \(-0.325996\pi\)
0.519829 + 0.854270i \(0.325996\pi\)
\(740\) 0 0
\(741\) 7.72674 0.283849
\(742\) 0 0
\(743\) 47.8847 1.75672 0.878359 0.478001i \(-0.158638\pi\)
0.878359 + 0.478001i \(0.158638\pi\)
\(744\) 0 0
\(745\) 39.5128 1.44764
\(746\) 0 0
\(747\) 4.18773 0.153221
\(748\) 0 0
\(749\) −0.212918 −0.00777984
\(750\) 0 0
\(751\) 27.6887 1.01037 0.505187 0.863010i \(-0.331424\pi\)
0.505187 + 0.863010i \(0.331424\pi\)
\(752\) 0 0
\(753\) −38.1835 −1.39148
\(754\) 0 0
\(755\) −44.6293 −1.62422
\(756\) 0 0
\(757\) 39.4259 1.43296 0.716479 0.697609i \(-0.245753\pi\)
0.716479 + 0.697609i \(0.245753\pi\)
\(758\) 0 0
\(759\) 7.92973 0.287831
\(760\) 0 0
\(761\) −31.3218 −1.13541 −0.567707 0.823231i \(-0.692169\pi\)
−0.567707 + 0.823231i \(0.692169\pi\)
\(762\) 0 0
\(763\) 2.87789 0.104187
\(764\) 0 0
\(765\) −4.51049 −0.163077
\(766\) 0 0
\(767\) −27.0708 −0.977469
\(768\) 0 0
\(769\) 8.33522 0.300576 0.150288 0.988642i \(-0.451980\pi\)
0.150288 + 0.988642i \(0.451980\pi\)
\(770\) 0 0
\(771\) 8.31718 0.299536
\(772\) 0 0
\(773\) 9.92025 0.356807 0.178403 0.983957i \(-0.442907\pi\)
0.178403 + 0.983957i \(0.442907\pi\)
\(774\) 0 0
\(775\) −1.69375 −0.0608415
\(776\) 0 0
\(777\) −3.74941 −0.134509
\(778\) 0 0
\(779\) 3.37353 0.120869
\(780\) 0 0
\(781\) 1.58330 0.0566550
\(782\) 0 0
\(783\) −21.0159 −0.751048
\(784\) 0 0
\(785\) −32.7476 −1.16881
\(786\) 0 0
\(787\) 0.203720 0.00726184 0.00363092 0.999993i \(-0.498844\pi\)
0.00363092 + 0.999993i \(0.498844\pi\)
\(788\) 0 0
\(789\) −40.4990 −1.44180
\(790\) 0 0
\(791\) −4.67742 −0.166310
\(792\) 0 0
\(793\) −13.2803 −0.471596
\(794\) 0 0
\(795\) 4.49473 0.159412
\(796\) 0 0
\(797\) 11.3088 0.400577 0.200288 0.979737i \(-0.435812\pi\)
0.200288 + 0.979737i \(0.435812\pi\)
\(798\) 0 0
\(799\) 47.8108 1.69143
\(800\) 0 0
\(801\) 2.41808 0.0854387
\(802\) 0 0
\(803\) 35.5377 1.25410
\(804\) 0 0
\(805\) 1.23893 0.0436666
\(806\) 0 0
\(807\) 16.8341 0.592589
\(808\) 0 0
\(809\) −2.84585 −0.100055 −0.0500274 0.998748i \(-0.515931\pi\)
−0.0500274 + 0.998748i \(0.515931\pi\)
\(810\) 0 0
\(811\) −21.1837 −0.743859 −0.371930 0.928261i \(-0.621304\pi\)
−0.371930 + 0.928261i \(0.621304\pi\)
\(812\) 0 0
\(813\) 14.9624 0.524756
\(814\) 0 0
\(815\) 32.3080 1.13170
\(816\) 0 0
\(817\) −7.47612 −0.261556
\(818\) 0 0
\(819\) 0.715540 0.0250030
\(820\) 0 0
\(821\) 33.7164 1.17671 0.588355 0.808603i \(-0.299776\pi\)
0.588355 + 0.808603i \(0.299776\pi\)
\(822\) 0 0
\(823\) 23.6129 0.823093 0.411547 0.911389i \(-0.364989\pi\)
0.411547 + 0.911389i \(0.364989\pi\)
\(824\) 0 0
\(825\) −2.25580 −0.0785367
\(826\) 0 0
\(827\) 16.3631 0.569000 0.284500 0.958676i \(-0.408172\pi\)
0.284500 + 0.958676i \(0.408172\pi\)
\(828\) 0 0
\(829\) −3.67950 −0.127794 −0.0638971 0.997956i \(-0.520353\pi\)
−0.0638971 + 0.997956i \(0.520353\pi\)
\(830\) 0 0
\(831\) −18.6326 −0.646358
\(832\) 0 0
\(833\) −32.1341 −1.11338
\(834\) 0 0
\(835\) −9.41129 −0.325691
\(836\) 0 0
\(837\) 18.1289 0.626627
\(838\) 0 0
\(839\) −55.1408 −1.90367 −0.951835 0.306610i \(-0.900805\pi\)
−0.951835 + 0.306610i \(0.900805\pi\)
\(840\) 0 0
\(841\) −14.4672 −0.498869
\(842\) 0 0
\(843\) 36.5733 1.25965
\(844\) 0 0
\(845\) 22.1890 0.763325
\(846\) 0 0
\(847\) −1.11695 −0.0383789
\(848\) 0 0
\(849\) −1.92329 −0.0660070
\(850\) 0 0
\(851\) 13.1749 0.451629
\(852\) 0 0
\(853\) 30.6120 1.04813 0.524067 0.851677i \(-0.324414\pi\)
0.524067 + 0.851677i \(0.324414\pi\)
\(854\) 0 0
\(855\) −0.967896 −0.0331013
\(856\) 0 0
\(857\) 33.3005 1.13752 0.568762 0.822502i \(-0.307422\pi\)
0.568762 + 0.822502i \(0.307422\pi\)
\(858\) 0 0
\(859\) 5.33281 0.181953 0.0909765 0.995853i \(-0.471001\pi\)
0.0909765 + 0.995853i \(0.471001\pi\)
\(860\) 0 0
\(861\) −1.73825 −0.0592393
\(862\) 0 0
\(863\) 44.8075 1.52527 0.762633 0.646831i \(-0.223906\pi\)
0.762633 + 0.646831i \(0.223906\pi\)
\(864\) 0 0
\(865\) 26.7209 0.908538
\(866\) 0 0
\(867\) −7.52126 −0.255435
\(868\) 0 0
\(869\) 2.74648 0.0931681
\(870\) 0 0
\(871\) −27.6293 −0.936184
\(872\) 0 0
\(873\) 6.33126 0.214281
\(874\) 0 0
\(875\) −3.77386 −0.127580
\(876\) 0 0
\(877\) 6.94902 0.234652 0.117326 0.993093i \(-0.462568\pi\)
0.117326 + 0.993093i \(0.462568\pi\)
\(878\) 0 0
\(879\) 40.4826 1.36545
\(880\) 0 0
\(881\) 12.5697 0.423484 0.211742 0.977326i \(-0.432086\pi\)
0.211742 + 0.977326i \(0.432086\pi\)
\(882\) 0 0
\(883\) 14.4749 0.487120 0.243560 0.969886i \(-0.421685\pi\)
0.243560 + 0.969886i \(0.421685\pi\)
\(884\) 0 0
\(885\) −18.8679 −0.634237
\(886\) 0 0
\(887\) 7.66035 0.257209 0.128605 0.991696i \(-0.458950\pi\)
0.128605 + 0.991696i \(0.458950\pi\)
\(888\) 0 0
\(889\) −3.32532 −0.111528
\(890\) 0 0
\(891\) 20.3789 0.682720
\(892\) 0 0
\(893\) 10.2596 0.343325
\(894\) 0 0
\(895\) 6.28498 0.210084
\(896\) 0 0
\(897\) 13.9897 0.467101
\(898\) 0 0
\(899\) −12.5364 −0.418112
\(900\) 0 0
\(901\) −6.20226 −0.206627
\(902\) 0 0
\(903\) 3.85215 0.128192
\(904\) 0 0
\(905\) −40.9963 −1.36276
\(906\) 0 0
\(907\) 19.9321 0.661834 0.330917 0.943660i \(-0.392642\pi\)
0.330917 + 0.943660i \(0.392642\pi\)
\(908\) 0 0
\(909\) 2.79587 0.0927333
\(910\) 0 0
\(911\) 23.4198 0.775932 0.387966 0.921674i \(-0.373178\pi\)
0.387966 + 0.921674i \(0.373178\pi\)
\(912\) 0 0
\(913\) 25.1655 0.832856
\(914\) 0 0
\(915\) −9.25613 −0.305998
\(916\) 0 0
\(917\) −0.372336 −0.0122956
\(918\) 0 0
\(919\) −13.6098 −0.448945 −0.224473 0.974480i \(-0.572066\pi\)
−0.224473 + 0.974480i \(0.572066\pi\)
\(920\) 0 0
\(921\) 2.54597 0.0838927
\(922\) 0 0
\(923\) 2.79327 0.0919416
\(924\) 0 0
\(925\) −3.74790 −0.123230
\(926\) 0 0
\(927\) 4.25510 0.139756
\(928\) 0 0
\(929\) 10.8982 0.357557 0.178778 0.983889i \(-0.442785\pi\)
0.178778 + 0.983889i \(0.442785\pi\)
\(930\) 0 0
\(931\) −6.89560 −0.225994
\(932\) 0 0
\(933\) 37.1716 1.21694
\(934\) 0 0
\(935\) −27.1051 −0.886431
\(936\) 0 0
\(937\) −9.35143 −0.305498 −0.152749 0.988265i \(-0.548813\pi\)
−0.152749 + 0.988265i \(0.548813\pi\)
\(938\) 0 0
\(939\) 19.7588 0.644805
\(940\) 0 0
\(941\) 35.1171 1.14478 0.572392 0.819980i \(-0.306016\pi\)
0.572392 + 0.819980i \(0.306016\pi\)
\(942\) 0 0
\(943\) 6.10795 0.198902
\(944\) 0 0
\(945\) 3.77233 0.122714
\(946\) 0 0
\(947\) −58.1433 −1.88940 −0.944702 0.327931i \(-0.893649\pi\)
−0.944702 + 0.327931i \(0.893649\pi\)
\(948\) 0 0
\(949\) 62.6958 2.03519
\(950\) 0 0
\(951\) −8.69084 −0.281820
\(952\) 0 0
\(953\) −35.7717 −1.15876 −0.579380 0.815057i \(-0.696705\pi\)
−0.579380 + 0.815057i \(0.696705\pi\)
\(954\) 0 0
\(955\) 14.8711 0.481219
\(956\) 0 0
\(957\) −16.6964 −0.539717
\(958\) 0 0
\(959\) −1.06737 −0.0344673
\(960\) 0 0
\(961\) −20.1858 −0.651153
\(962\) 0 0
\(963\) 0.301165 0.00970490
\(964\) 0 0
\(965\) −45.5199 −1.46534
\(966\) 0 0
\(967\) 2.78169 0.0894530 0.0447265 0.998999i \(-0.485758\pi\)
0.0447265 + 0.998999i \(0.485758\pi\)
\(968\) 0 0
\(969\) −7.43131 −0.238728
\(970\) 0 0
\(971\) −45.7553 −1.46836 −0.734179 0.678956i \(-0.762432\pi\)
−0.734179 + 0.678956i \(0.762432\pi\)
\(972\) 0 0
\(973\) 3.18641 0.102152
\(974\) 0 0
\(975\) −3.97969 −0.127452
\(976\) 0 0
\(977\) 2.78690 0.0891607 0.0445804 0.999006i \(-0.485805\pi\)
0.0445804 + 0.999006i \(0.485805\pi\)
\(978\) 0 0
\(979\) 14.5311 0.464415
\(980\) 0 0
\(981\) −4.07068 −0.129967
\(982\) 0 0
\(983\) 22.5512 0.719272 0.359636 0.933093i \(-0.382901\pi\)
0.359636 + 0.933093i \(0.382901\pi\)
\(984\) 0 0
\(985\) 12.1251 0.386336
\(986\) 0 0
\(987\) −5.28639 −0.168268
\(988\) 0 0
\(989\) −13.5359 −0.430417
\(990\) 0 0
\(991\) −21.8924 −0.695437 −0.347718 0.937599i \(-0.613043\pi\)
−0.347718 + 0.937599i \(0.613043\pi\)
\(992\) 0 0
\(993\) −7.94127 −0.252009
\(994\) 0 0
\(995\) 26.6964 0.846332
\(996\) 0 0
\(997\) −33.0148 −1.04559 −0.522795 0.852459i \(-0.675111\pi\)
−0.522795 + 0.852459i \(0.675111\pi\)
\(998\) 0 0
\(999\) 40.1152 1.26919
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 \(a_p\))