Properties

Label 8004.2.a.d.1.1
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.85152\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-3.41642 q^{5}\) \(+2.05098 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-3.41642 q^{5}\) \(+2.05098 q^{7}\) \(+1.00000 q^{9}\) \(+1.14688 q^{11}\) \(-4.51492 q^{13}\) \(-3.41642 q^{15}\) \(+0.446852 q^{17}\) \(-2.11134 q^{19}\) \(+2.05098 q^{21}\) \(+1.00000 q^{23}\) \(+6.67190 q^{25}\) \(+1.00000 q^{27}\) \(+1.00000 q^{29}\) \(+6.57178 q^{31}\) \(+1.14688 q^{33}\) \(-7.00700 q^{35}\) \(-4.89567 q^{37}\) \(-4.51492 q^{39}\) \(+3.92571 q^{41}\) \(+3.16338 q^{43}\) \(-3.41642 q^{45}\) \(-0.451968 q^{47}\) \(-2.79348 q^{49}\) \(+0.446852 q^{51}\) \(+4.11866 q^{53}\) \(-3.91820 q^{55}\) \(-2.11134 q^{57}\) \(-6.31529 q^{59}\) \(-8.75827 q^{61}\) \(+2.05098 q^{63}\) \(+15.4248 q^{65}\) \(-10.6292 q^{67}\) \(+1.00000 q^{69}\) \(+13.3216 q^{71}\) \(-12.6838 q^{73}\) \(+6.67190 q^{75}\) \(+2.35222 q^{77}\) \(+2.30778 q^{79}\) \(+1.00000 q^{81}\) \(-4.59898 q^{83}\) \(-1.52663 q^{85}\) \(+1.00000 q^{87}\) \(+14.8381 q^{89}\) \(-9.26001 q^{91}\) \(+6.57178 q^{93}\) \(+7.21320 q^{95}\) \(+8.14524 q^{97}\) \(+1.14688 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 11q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 5q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −3.41642 −1.52787 −0.763934 0.645294i \(-0.776735\pi\)
−0.763934 + 0.645294i \(0.776735\pi\)
\(6\) 0 0
\(7\) 2.05098 0.775198 0.387599 0.921828i \(-0.373305\pi\)
0.387599 + 0.921828i \(0.373305\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.14688 0.345796 0.172898 0.984940i \(-0.444687\pi\)
0.172898 + 0.984940i \(0.444687\pi\)
\(12\) 0 0
\(13\) −4.51492 −1.25221 −0.626106 0.779738i \(-0.715352\pi\)
−0.626106 + 0.779738i \(0.715352\pi\)
\(14\) 0 0
\(15\) −3.41642 −0.882115
\(16\) 0 0
\(17\) 0.446852 0.108377 0.0541887 0.998531i \(-0.482743\pi\)
0.0541887 + 0.998531i \(0.482743\pi\)
\(18\) 0 0
\(19\) −2.11134 −0.484374 −0.242187 0.970230i \(-0.577865\pi\)
−0.242187 + 0.970230i \(0.577865\pi\)
\(20\) 0 0
\(21\) 2.05098 0.447561
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 6.67190 1.33438
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 6.57178 1.18033 0.590163 0.807284i \(-0.299063\pi\)
0.590163 + 0.807284i \(0.299063\pi\)
\(32\) 0 0
\(33\) 1.14688 0.199645
\(34\) 0 0
\(35\) −7.00700 −1.18440
\(36\) 0 0
\(37\) −4.89567 −0.804843 −0.402421 0.915455i \(-0.631831\pi\)
−0.402421 + 0.915455i \(0.631831\pi\)
\(38\) 0 0
\(39\) −4.51492 −0.722965
\(40\) 0 0
\(41\) 3.92571 0.613093 0.306547 0.951856i \(-0.400826\pi\)
0.306547 + 0.951856i \(0.400826\pi\)
\(42\) 0 0
\(43\) 3.16338 0.482410 0.241205 0.970474i \(-0.422457\pi\)
0.241205 + 0.970474i \(0.422457\pi\)
\(44\) 0 0
\(45\) −3.41642 −0.509289
\(46\) 0 0
\(47\) −0.451968 −0.0659262 −0.0329631 0.999457i \(-0.510494\pi\)
−0.0329631 + 0.999457i \(0.510494\pi\)
\(48\) 0 0
\(49\) −2.79348 −0.399068
\(50\) 0 0
\(51\) 0.446852 0.0625717
\(52\) 0 0
\(53\) 4.11866 0.565742 0.282871 0.959158i \(-0.408713\pi\)
0.282871 + 0.959158i \(0.408713\pi\)
\(54\) 0 0
\(55\) −3.91820 −0.528330
\(56\) 0 0
\(57\) −2.11134 −0.279653
\(58\) 0 0
\(59\) −6.31529 −0.822180 −0.411090 0.911595i \(-0.634852\pi\)
−0.411090 + 0.911595i \(0.634852\pi\)
\(60\) 0 0
\(61\) −8.75827 −1.12138 −0.560690 0.828025i \(-0.689464\pi\)
−0.560690 + 0.828025i \(0.689464\pi\)
\(62\) 0 0
\(63\) 2.05098 0.258399
\(64\) 0 0
\(65\) 15.4248 1.91322
\(66\) 0 0
\(67\) −10.6292 −1.29856 −0.649280 0.760549i \(-0.724930\pi\)
−0.649280 + 0.760549i \(0.724930\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 13.3216 1.58099 0.790494 0.612469i \(-0.209824\pi\)
0.790494 + 0.612469i \(0.209824\pi\)
\(72\) 0 0
\(73\) −12.6838 −1.48452 −0.742262 0.670110i \(-0.766247\pi\)
−0.742262 + 0.670110i \(0.766247\pi\)
\(74\) 0 0
\(75\) 6.67190 0.770405
\(76\) 0 0
\(77\) 2.35222 0.268060
\(78\) 0 0
\(79\) 2.30778 0.259646 0.129823 0.991537i \(-0.458559\pi\)
0.129823 + 0.991537i \(0.458559\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.59898 −0.504804 −0.252402 0.967622i \(-0.581221\pi\)
−0.252402 + 0.967622i \(0.581221\pi\)
\(84\) 0 0
\(85\) −1.52663 −0.165586
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) 14.8381 1.57284 0.786418 0.617695i \(-0.211933\pi\)
0.786418 + 0.617695i \(0.211933\pi\)
\(90\) 0 0
\(91\) −9.26001 −0.970713
\(92\) 0 0
\(93\) 6.57178 0.681462
\(94\) 0 0
\(95\) 7.21320 0.740059
\(96\) 0 0
\(97\) 8.14524 0.827024 0.413512 0.910499i \(-0.364302\pi\)
0.413512 + 0.910499i \(0.364302\pi\)
\(98\) 0 0
\(99\) 1.14688 0.115265
\(100\) 0 0
\(101\) −10.8719 −1.08180 −0.540899 0.841088i \(-0.681916\pi\)
−0.540899 + 0.841088i \(0.681916\pi\)
\(102\) 0 0
\(103\) 14.4916 1.42790 0.713950 0.700196i \(-0.246904\pi\)
0.713950 + 0.700196i \(0.246904\pi\)
\(104\) 0 0
\(105\) −7.00700 −0.683814
\(106\) 0 0
\(107\) −11.0590 −1.06912 −0.534558 0.845132i \(-0.679522\pi\)
−0.534558 + 0.845132i \(0.679522\pi\)
\(108\) 0 0
\(109\) −5.38049 −0.515358 −0.257679 0.966231i \(-0.582958\pi\)
−0.257679 + 0.966231i \(0.582958\pi\)
\(110\) 0 0
\(111\) −4.89567 −0.464676
\(112\) 0 0
\(113\) −2.54011 −0.238954 −0.119477 0.992837i \(-0.538122\pi\)
−0.119477 + 0.992837i \(0.538122\pi\)
\(114\) 0 0
\(115\) −3.41642 −0.318582
\(116\) 0 0
\(117\) −4.51492 −0.417404
\(118\) 0 0
\(119\) 0.916484 0.0840139
\(120\) 0 0
\(121\) −9.68468 −0.880425
\(122\) 0 0
\(123\) 3.92571 0.353969
\(124\) 0 0
\(125\) −5.71192 −0.510889
\(126\) 0 0
\(127\) −7.41710 −0.658161 −0.329080 0.944302i \(-0.606739\pi\)
−0.329080 + 0.944302i \(0.606739\pi\)
\(128\) 0 0
\(129\) 3.16338 0.278520
\(130\) 0 0
\(131\) −6.83180 −0.596897 −0.298448 0.954426i \(-0.596469\pi\)
−0.298448 + 0.954426i \(0.596469\pi\)
\(132\) 0 0
\(133\) −4.33031 −0.375486
\(134\) 0 0
\(135\) −3.41642 −0.294038
\(136\) 0 0
\(137\) −14.7282 −1.25832 −0.629159 0.777276i \(-0.716601\pi\)
−0.629159 + 0.777276i \(0.716601\pi\)
\(138\) 0 0
\(139\) −20.3372 −1.72497 −0.862487 0.506079i \(-0.831095\pi\)
−0.862487 + 0.506079i \(0.831095\pi\)
\(140\) 0 0
\(141\) −0.451968 −0.0380625
\(142\) 0 0
\(143\) −5.17805 −0.433010
\(144\) 0 0
\(145\) −3.41642 −0.283718
\(146\) 0 0
\(147\) −2.79348 −0.230402
\(148\) 0 0
\(149\) 1.98828 0.162887 0.0814433 0.996678i \(-0.474047\pi\)
0.0814433 + 0.996678i \(0.474047\pi\)
\(150\) 0 0
\(151\) −0.688066 −0.0559940 −0.0279970 0.999608i \(-0.508913\pi\)
−0.0279970 + 0.999608i \(0.508913\pi\)
\(152\) 0 0
\(153\) 0.446852 0.0361258
\(154\) 0 0
\(155\) −22.4519 −1.80338
\(156\) 0 0
\(157\) 7.26724 0.579989 0.289994 0.957028i \(-0.406347\pi\)
0.289994 + 0.957028i \(0.406347\pi\)
\(158\) 0 0
\(159\) 4.11866 0.326631
\(160\) 0 0
\(161\) 2.05098 0.161640
\(162\) 0 0
\(163\) −21.3903 −1.67542 −0.837711 0.546114i \(-0.816106\pi\)
−0.837711 + 0.546114i \(0.816106\pi\)
\(164\) 0 0
\(165\) −3.91820 −0.305032
\(166\) 0 0
\(167\) 3.78952 0.293242 0.146621 0.989193i \(-0.453160\pi\)
0.146621 + 0.989193i \(0.453160\pi\)
\(168\) 0 0
\(169\) 7.38447 0.568036
\(170\) 0 0
\(171\) −2.11134 −0.161458
\(172\) 0 0
\(173\) 21.3538 1.62350 0.811750 0.584005i \(-0.198515\pi\)
0.811750 + 0.584005i \(0.198515\pi\)
\(174\) 0 0
\(175\) 13.6839 1.03441
\(176\) 0 0
\(177\) −6.31529 −0.474686
\(178\) 0 0
\(179\) −19.0982 −1.42746 −0.713732 0.700418i \(-0.752997\pi\)
−0.713732 + 0.700418i \(0.752997\pi\)
\(180\) 0 0
\(181\) 10.7729 0.800747 0.400374 0.916352i \(-0.368880\pi\)
0.400374 + 0.916352i \(0.368880\pi\)
\(182\) 0 0
\(183\) −8.75827 −0.647430
\(184\) 0 0
\(185\) 16.7256 1.22969
\(186\) 0 0
\(187\) 0.512483 0.0374765
\(188\) 0 0
\(189\) 2.05098 0.149187
\(190\) 0 0
\(191\) −13.8685 −1.00349 −0.501746 0.865015i \(-0.667309\pi\)
−0.501746 + 0.865015i \(0.667309\pi\)
\(192\) 0 0
\(193\) 24.4103 1.75709 0.878545 0.477659i \(-0.158515\pi\)
0.878545 + 0.477659i \(0.158515\pi\)
\(194\) 0 0
\(195\) 15.4248 1.10460
\(196\) 0 0
\(197\) −15.9348 −1.13531 −0.567655 0.823267i \(-0.692149\pi\)
−0.567655 + 0.823267i \(0.692149\pi\)
\(198\) 0 0
\(199\) −22.3201 −1.58223 −0.791115 0.611667i \(-0.790499\pi\)
−0.791115 + 0.611667i \(0.790499\pi\)
\(200\) 0 0
\(201\) −10.6292 −0.749724
\(202\) 0 0
\(203\) 2.05098 0.143951
\(204\) 0 0
\(205\) −13.4119 −0.936725
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −2.42144 −0.167494
\(210\) 0 0
\(211\) −3.36302 −0.231520 −0.115760 0.993277i \(-0.536930\pi\)
−0.115760 + 0.993277i \(0.536930\pi\)
\(212\) 0 0
\(213\) 13.3216 0.912784
\(214\) 0 0
\(215\) −10.8074 −0.737060
\(216\) 0 0
\(217\) 13.4786 0.914987
\(218\) 0 0
\(219\) −12.6838 −0.857090
\(220\) 0 0
\(221\) −2.01750 −0.135712
\(222\) 0 0
\(223\) −16.0725 −1.07629 −0.538147 0.842851i \(-0.680875\pi\)
−0.538147 + 0.842851i \(0.680875\pi\)
\(224\) 0 0
\(225\) 6.67190 0.444794
\(226\) 0 0
\(227\) 18.1471 1.20447 0.602233 0.798320i \(-0.294278\pi\)
0.602233 + 0.798320i \(0.294278\pi\)
\(228\) 0 0
\(229\) −7.11132 −0.469929 −0.234965 0.972004i \(-0.575497\pi\)
−0.234965 + 0.972004i \(0.575497\pi\)
\(230\) 0 0
\(231\) 2.35222 0.154765
\(232\) 0 0
\(233\) 3.07312 0.201327 0.100663 0.994921i \(-0.467903\pi\)
0.100663 + 0.994921i \(0.467903\pi\)
\(234\) 0 0
\(235\) 1.54411 0.100727
\(236\) 0 0
\(237\) 2.30778 0.149906
\(238\) 0 0
\(239\) 7.61297 0.492442 0.246221 0.969214i \(-0.420811\pi\)
0.246221 + 0.969214i \(0.420811\pi\)
\(240\) 0 0
\(241\) −20.4791 −1.31917 −0.659587 0.751629i \(-0.729269\pi\)
−0.659587 + 0.751629i \(0.729269\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 9.54368 0.609724
\(246\) 0 0
\(247\) 9.53251 0.606539
\(248\) 0 0
\(249\) −4.59898 −0.291449
\(250\) 0 0
\(251\) 10.7623 0.679313 0.339656 0.940550i \(-0.389689\pi\)
0.339656 + 0.940550i \(0.389689\pi\)
\(252\) 0 0
\(253\) 1.14688 0.0721034
\(254\) 0 0
\(255\) −1.52663 −0.0956014
\(256\) 0 0
\(257\) −19.2212 −1.19899 −0.599493 0.800380i \(-0.704631\pi\)
−0.599493 + 0.800380i \(0.704631\pi\)
\(258\) 0 0
\(259\) −10.0409 −0.623913
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) 8.85390 0.545955 0.272978 0.962020i \(-0.411992\pi\)
0.272978 + 0.962020i \(0.411992\pi\)
\(264\) 0 0
\(265\) −14.0711 −0.864379
\(266\) 0 0
\(267\) 14.8381 0.908077
\(268\) 0 0
\(269\) 9.97519 0.608198 0.304099 0.952640i \(-0.401645\pi\)
0.304099 + 0.952640i \(0.401645\pi\)
\(270\) 0 0
\(271\) −14.7260 −0.894541 −0.447270 0.894399i \(-0.647604\pi\)
−0.447270 + 0.894399i \(0.647604\pi\)
\(272\) 0 0
\(273\) −9.26001 −0.560441
\(274\) 0 0
\(275\) 7.65184 0.461423
\(276\) 0 0
\(277\) 0.848598 0.0509873 0.0254937 0.999675i \(-0.491884\pi\)
0.0254937 + 0.999675i \(0.491884\pi\)
\(278\) 0 0
\(279\) 6.57178 0.393442
\(280\) 0 0
\(281\) −22.8691 −1.36426 −0.682128 0.731233i \(-0.738945\pi\)
−0.682128 + 0.731233i \(0.738945\pi\)
\(282\) 0 0
\(283\) −8.10218 −0.481624 −0.240812 0.970572i \(-0.577414\pi\)
−0.240812 + 0.970572i \(0.577414\pi\)
\(284\) 0 0
\(285\) 7.21320 0.427273
\(286\) 0 0
\(287\) 8.05156 0.475268
\(288\) 0 0
\(289\) −16.8003 −0.988254
\(290\) 0 0
\(291\) 8.14524 0.477482
\(292\) 0 0
\(293\) 24.6949 1.44269 0.721344 0.692577i \(-0.243525\pi\)
0.721344 + 0.692577i \(0.243525\pi\)
\(294\) 0 0
\(295\) 21.5757 1.25618
\(296\) 0 0
\(297\) 1.14688 0.0665485
\(298\) 0 0
\(299\) −4.51492 −0.261104
\(300\) 0 0
\(301\) 6.48803 0.373964
\(302\) 0 0
\(303\) −10.8719 −0.624576
\(304\) 0 0
\(305\) 29.9219 1.71332
\(306\) 0 0
\(307\) −7.75138 −0.442395 −0.221197 0.975229i \(-0.570997\pi\)
−0.221197 + 0.975229i \(0.570997\pi\)
\(308\) 0 0
\(309\) 14.4916 0.824399
\(310\) 0 0
\(311\) 11.2388 0.637292 0.318646 0.947874i \(-0.396772\pi\)
0.318646 + 0.947874i \(0.396772\pi\)
\(312\) 0 0
\(313\) 12.3629 0.698794 0.349397 0.936975i \(-0.386386\pi\)
0.349397 + 0.936975i \(0.386386\pi\)
\(314\) 0 0
\(315\) −7.00700 −0.394800
\(316\) 0 0
\(317\) −10.5402 −0.591994 −0.295997 0.955189i \(-0.595652\pi\)
−0.295997 + 0.955189i \(0.595652\pi\)
\(318\) 0 0
\(319\) 1.14688 0.0642127
\(320\) 0 0
\(321\) −11.0590 −0.617254
\(322\) 0 0
\(323\) −0.943454 −0.0524952
\(324\) 0 0
\(325\) −30.1231 −1.67093
\(326\) 0 0
\(327\) −5.38049 −0.297542
\(328\) 0 0
\(329\) −0.926977 −0.0511059
\(330\) 0 0
\(331\) −26.4647 −1.45463 −0.727316 0.686303i \(-0.759233\pi\)
−0.727316 + 0.686303i \(0.759233\pi\)
\(332\) 0 0
\(333\) −4.89567 −0.268281
\(334\) 0 0
\(335\) 36.3137 1.98403
\(336\) 0 0
\(337\) −24.0080 −1.30780 −0.653901 0.756580i \(-0.726869\pi\)
−0.653901 + 0.756580i \(0.726869\pi\)
\(338\) 0 0
\(339\) −2.54011 −0.137960
\(340\) 0 0
\(341\) 7.53701 0.408152
\(342\) 0 0
\(343\) −20.0862 −1.08455
\(344\) 0 0
\(345\) −3.41642 −0.183934
\(346\) 0 0
\(347\) −14.2863 −0.766929 −0.383465 0.923556i \(-0.625269\pi\)
−0.383465 + 0.923556i \(0.625269\pi\)
\(348\) 0 0
\(349\) 31.7682 1.70051 0.850257 0.526368i \(-0.176446\pi\)
0.850257 + 0.526368i \(0.176446\pi\)
\(350\) 0 0
\(351\) −4.51492 −0.240988
\(352\) 0 0
\(353\) 19.4300 1.03416 0.517078 0.855938i \(-0.327020\pi\)
0.517078 + 0.855938i \(0.327020\pi\)
\(354\) 0 0
\(355\) −45.5123 −2.41554
\(356\) 0 0
\(357\) 0.916484 0.0485055
\(358\) 0 0
\(359\) 13.6319 0.719465 0.359733 0.933055i \(-0.382868\pi\)
0.359733 + 0.933055i \(0.382868\pi\)
\(360\) 0 0
\(361\) −14.5423 −0.765382
\(362\) 0 0
\(363\) −9.68468 −0.508314
\(364\) 0 0
\(365\) 43.3331 2.26816
\(366\) 0 0
\(367\) −27.1439 −1.41690 −0.708450 0.705761i \(-0.750605\pi\)
−0.708450 + 0.705761i \(0.750605\pi\)
\(368\) 0 0
\(369\) 3.92571 0.204364
\(370\) 0 0
\(371\) 8.44730 0.438562
\(372\) 0 0
\(373\) 38.3540 1.98589 0.992947 0.118562i \(-0.0378284\pi\)
0.992947 + 0.118562i \(0.0378284\pi\)
\(374\) 0 0
\(375\) −5.71192 −0.294962
\(376\) 0 0
\(377\) −4.51492 −0.232530
\(378\) 0 0
\(379\) −35.1885 −1.80751 −0.903757 0.428046i \(-0.859202\pi\)
−0.903757 + 0.428046i \(0.859202\pi\)
\(380\) 0 0
\(381\) −7.41710 −0.379989
\(382\) 0 0
\(383\) −11.7678 −0.601307 −0.300653 0.953733i \(-0.597205\pi\)
−0.300653 + 0.953733i \(0.597205\pi\)
\(384\) 0 0
\(385\) −8.03616 −0.409561
\(386\) 0 0
\(387\) 3.16338 0.160803
\(388\) 0 0
\(389\) −16.4904 −0.836096 −0.418048 0.908425i \(-0.637286\pi\)
−0.418048 + 0.908425i \(0.637286\pi\)
\(390\) 0 0
\(391\) 0.446852 0.0225983
\(392\) 0 0
\(393\) −6.83180 −0.344618
\(394\) 0 0
\(395\) −7.88434 −0.396704
\(396\) 0 0
\(397\) 7.18614 0.360662 0.180331 0.983606i \(-0.442283\pi\)
0.180331 + 0.983606i \(0.442283\pi\)
\(398\) 0 0
\(399\) −4.33031 −0.216787
\(400\) 0 0
\(401\) −0.904789 −0.0451830 −0.0225915 0.999745i \(-0.507192\pi\)
−0.0225915 + 0.999745i \(0.507192\pi\)
\(402\) 0 0
\(403\) −29.6710 −1.47802
\(404\) 0 0
\(405\) −3.41642 −0.169763
\(406\) 0 0
\(407\) −5.61472 −0.278311
\(408\) 0 0
\(409\) 35.7504 1.76774 0.883872 0.467730i \(-0.154928\pi\)
0.883872 + 0.467730i \(0.154928\pi\)
\(410\) 0 0
\(411\) −14.7282 −0.726491
\(412\) 0 0
\(413\) −12.9525 −0.637353
\(414\) 0 0
\(415\) 15.7120 0.771274
\(416\) 0 0
\(417\) −20.3372 −0.995915
\(418\) 0 0
\(419\) 38.9086 1.90081 0.950404 0.311018i \(-0.100670\pi\)
0.950404 + 0.311018i \(0.100670\pi\)
\(420\) 0 0
\(421\) −28.3864 −1.38347 −0.691735 0.722151i \(-0.743154\pi\)
−0.691735 + 0.722151i \(0.743154\pi\)
\(422\) 0 0
\(423\) −0.451968 −0.0219754
\(424\) 0 0
\(425\) 2.98135 0.144617
\(426\) 0 0
\(427\) −17.9630 −0.869292
\(428\) 0 0
\(429\) −5.17805 −0.249998
\(430\) 0 0
\(431\) −0.922354 −0.0444282 −0.0222141 0.999753i \(-0.507072\pi\)
−0.0222141 + 0.999753i \(0.507072\pi\)
\(432\) 0 0
\(433\) 11.8030 0.567217 0.283608 0.958940i \(-0.408468\pi\)
0.283608 + 0.958940i \(0.408468\pi\)
\(434\) 0 0
\(435\) −3.41642 −0.163805
\(436\) 0 0
\(437\) −2.11134 −0.100999
\(438\) 0 0
\(439\) 21.5722 1.02958 0.514791 0.857315i \(-0.327869\pi\)
0.514791 + 0.857315i \(0.327869\pi\)
\(440\) 0 0
\(441\) −2.79348 −0.133023
\(442\) 0 0
\(443\) 8.00039 0.380110 0.190055 0.981773i \(-0.439133\pi\)
0.190055 + 0.981773i \(0.439133\pi\)
\(444\) 0 0
\(445\) −50.6931 −2.40309
\(446\) 0 0
\(447\) 1.98828 0.0940426
\(448\) 0 0
\(449\) −15.4319 −0.728277 −0.364138 0.931345i \(-0.618637\pi\)
−0.364138 + 0.931345i \(0.618637\pi\)
\(450\) 0 0
\(451\) 4.50230 0.212005
\(452\) 0 0
\(453\) −0.688066 −0.0323281
\(454\) 0 0
\(455\) 31.6360 1.48312
\(456\) 0 0
\(457\) −35.0563 −1.63987 −0.819933 0.572460i \(-0.805989\pi\)
−0.819933 + 0.572460i \(0.805989\pi\)
\(458\) 0 0
\(459\) 0.446852 0.0208572
\(460\) 0 0
\(461\) −34.9727 −1.62884 −0.814420 0.580276i \(-0.802945\pi\)
−0.814420 + 0.580276i \(0.802945\pi\)
\(462\) 0 0
\(463\) −17.9578 −0.834569 −0.417284 0.908776i \(-0.637018\pi\)
−0.417284 + 0.908776i \(0.637018\pi\)
\(464\) 0 0
\(465\) −22.4519 −1.04118
\(466\) 0 0
\(467\) −22.6365 −1.04749 −0.523747 0.851874i \(-0.675466\pi\)
−0.523747 + 0.851874i \(0.675466\pi\)
\(468\) 0 0
\(469\) −21.8002 −1.00664
\(470\) 0 0
\(471\) 7.26724 0.334857
\(472\) 0 0
\(473\) 3.62800 0.166816
\(474\) 0 0
\(475\) −14.0866 −0.646339
\(476\) 0 0
\(477\) 4.11866 0.188581
\(478\) 0 0
\(479\) 3.26212 0.149050 0.0745250 0.997219i \(-0.476256\pi\)
0.0745250 + 0.997219i \(0.476256\pi\)
\(480\) 0 0
\(481\) 22.1035 1.00783
\(482\) 0 0
\(483\) 2.05098 0.0933229
\(484\) 0 0
\(485\) −27.8275 −1.26358
\(486\) 0 0
\(487\) −36.0283 −1.63260 −0.816300 0.577628i \(-0.803978\pi\)
−0.816300 + 0.577628i \(0.803978\pi\)
\(488\) 0 0
\(489\) −21.3903 −0.967305
\(490\) 0 0
\(491\) −31.4507 −1.41935 −0.709674 0.704530i \(-0.751158\pi\)
−0.709674 + 0.704530i \(0.751158\pi\)
\(492\) 0 0
\(493\) 0.446852 0.0201252
\(494\) 0 0
\(495\) −3.91820 −0.176110
\(496\) 0 0
\(497\) 27.3224 1.22558
\(498\) 0 0
\(499\) 16.5170 0.739402 0.369701 0.929151i \(-0.379460\pi\)
0.369701 + 0.929151i \(0.379460\pi\)
\(500\) 0 0
\(501\) 3.78952 0.169303
\(502\) 0 0
\(503\) −30.9673 −1.38076 −0.690381 0.723446i \(-0.742557\pi\)
−0.690381 + 0.723446i \(0.742557\pi\)
\(504\) 0 0
\(505\) 37.1430 1.65284
\(506\) 0 0
\(507\) 7.38447 0.327956
\(508\) 0 0
\(509\) −14.5132 −0.643287 −0.321644 0.946861i \(-0.604235\pi\)
−0.321644 + 0.946861i \(0.604235\pi\)
\(510\) 0 0
\(511\) −26.0142 −1.15080
\(512\) 0 0
\(513\) −2.11134 −0.0932178
\(514\) 0 0
\(515\) −49.5094 −2.18164
\(516\) 0 0
\(517\) −0.518350 −0.0227970
\(518\) 0 0
\(519\) 21.3538 0.937329
\(520\) 0 0
\(521\) −4.08813 −0.179104 −0.0895522 0.995982i \(-0.528544\pi\)
−0.0895522 + 0.995982i \(0.528544\pi\)
\(522\) 0 0
\(523\) 21.1992 0.926976 0.463488 0.886103i \(-0.346598\pi\)
0.463488 + 0.886103i \(0.346598\pi\)
\(524\) 0 0
\(525\) 13.6839 0.597216
\(526\) 0 0
\(527\) 2.93661 0.127921
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −6.31529 −0.274060
\(532\) 0 0
\(533\) −17.7243 −0.767723
\(534\) 0 0
\(535\) 37.7822 1.63347
\(536\) 0 0
\(537\) −19.0982 −0.824147
\(538\) 0 0
\(539\) −3.20377 −0.137996
\(540\) 0 0
\(541\) 12.4030 0.533245 0.266622 0.963801i \(-0.414092\pi\)
0.266622 + 0.963801i \(0.414092\pi\)
\(542\) 0 0
\(543\) 10.7729 0.462312
\(544\) 0 0
\(545\) 18.3820 0.787399
\(546\) 0 0
\(547\) 13.8751 0.593255 0.296627 0.954993i \(-0.404138\pi\)
0.296627 + 0.954993i \(0.404138\pi\)
\(548\) 0 0
\(549\) −8.75827 −0.373794
\(550\) 0 0
\(551\) −2.11134 −0.0899460
\(552\) 0 0
\(553\) 4.73321 0.201277
\(554\) 0 0
\(555\) 16.7256 0.709964
\(556\) 0 0
\(557\) 9.49572 0.402347 0.201173 0.979556i \(-0.435525\pi\)
0.201173 + 0.979556i \(0.435525\pi\)
\(558\) 0 0
\(559\) −14.2824 −0.604080
\(560\) 0 0
\(561\) 0.512483 0.0216370
\(562\) 0 0
\(563\) 6.34046 0.267219 0.133609 0.991034i \(-0.457343\pi\)
0.133609 + 0.991034i \(0.457343\pi\)
\(564\) 0 0
\(565\) 8.67809 0.365090
\(566\) 0 0
\(567\) 2.05098 0.0861331
\(568\) 0 0
\(569\) −11.6377 −0.487876 −0.243938 0.969791i \(-0.578439\pi\)
−0.243938 + 0.969791i \(0.578439\pi\)
\(570\) 0 0
\(571\) −25.7525 −1.07771 −0.538854 0.842399i \(-0.681143\pi\)
−0.538854 + 0.842399i \(0.681143\pi\)
\(572\) 0 0
\(573\) −13.8685 −0.579367
\(574\) 0 0
\(575\) 6.67190 0.278238
\(576\) 0 0
\(577\) −0.196347 −0.00817405 −0.00408702 0.999992i \(-0.501301\pi\)
−0.00408702 + 0.999992i \(0.501301\pi\)
\(578\) 0 0
\(579\) 24.4103 1.01446
\(580\) 0 0
\(581\) −9.43243 −0.391323
\(582\) 0 0
\(583\) 4.72359 0.195631
\(584\) 0 0
\(585\) 15.4248 0.637739
\(586\) 0 0
\(587\) 3.75537 0.155001 0.0775003 0.996992i \(-0.475306\pi\)
0.0775003 + 0.996992i \(0.475306\pi\)
\(588\) 0 0
\(589\) −13.8752 −0.571719
\(590\) 0 0
\(591\) −15.9348 −0.655471
\(592\) 0 0
\(593\) −22.7741 −0.935219 −0.467609 0.883935i \(-0.654885\pi\)
−0.467609 + 0.883935i \(0.654885\pi\)
\(594\) 0 0
\(595\) −3.13109 −0.128362
\(596\) 0 0
\(597\) −22.3201 −0.913501
\(598\) 0 0
\(599\) 0.514422 0.0210187 0.0105093 0.999945i \(-0.496655\pi\)
0.0105093 + 0.999945i \(0.496655\pi\)
\(600\) 0 0
\(601\) −18.2236 −0.743358 −0.371679 0.928361i \(-0.621218\pi\)
−0.371679 + 0.928361i \(0.621218\pi\)
\(602\) 0 0
\(603\) −10.6292 −0.432854
\(604\) 0 0
\(605\) 33.0869 1.34517
\(606\) 0 0
\(607\) −12.4283 −0.504449 −0.252224 0.967669i \(-0.581162\pi\)
−0.252224 + 0.967669i \(0.581162\pi\)
\(608\) 0 0
\(609\) 2.05098 0.0831099
\(610\) 0 0
\(611\) 2.04060 0.0825537
\(612\) 0 0
\(613\) −22.1624 −0.895131 −0.447566 0.894251i \(-0.647709\pi\)
−0.447566 + 0.894251i \(0.647709\pi\)
\(614\) 0 0
\(615\) −13.4119 −0.540819
\(616\) 0 0
\(617\) −12.4373 −0.500705 −0.250352 0.968155i \(-0.580547\pi\)
−0.250352 + 0.968155i \(0.580547\pi\)
\(618\) 0 0
\(619\) 31.1769 1.25311 0.626553 0.779379i \(-0.284465\pi\)
0.626553 + 0.779379i \(0.284465\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 30.4327 1.21926
\(624\) 0 0
\(625\) −13.8452 −0.553809
\(626\) 0 0
\(627\) −2.42144 −0.0967030
\(628\) 0 0
\(629\) −2.18764 −0.0872268
\(630\) 0 0
\(631\) −23.1401 −0.921191 −0.460596 0.887610i \(-0.652364\pi\)
−0.460596 + 0.887610i \(0.652364\pi\)
\(632\) 0 0
\(633\) −3.36302 −0.133668
\(634\) 0 0
\(635\) 25.3399 1.00558
\(636\) 0 0
\(637\) 12.6123 0.499718
\(638\) 0 0
\(639\) 13.3216 0.526996
\(640\) 0 0
\(641\) 26.5718 1.04952 0.524761 0.851250i \(-0.324155\pi\)
0.524761 + 0.851250i \(0.324155\pi\)
\(642\) 0 0
\(643\) 14.2684 0.562691 0.281345 0.959607i \(-0.409219\pi\)
0.281345 + 0.959607i \(0.409219\pi\)
\(644\) 0 0
\(645\) −10.8074 −0.425542
\(646\) 0 0
\(647\) 21.4489 0.843242 0.421621 0.906772i \(-0.361461\pi\)
0.421621 + 0.906772i \(0.361461\pi\)
\(648\) 0 0
\(649\) −7.24285 −0.284307
\(650\) 0 0
\(651\) 13.4786 0.528268
\(652\) 0 0
\(653\) −26.4337 −1.03443 −0.517216 0.855855i \(-0.673032\pi\)
−0.517216 + 0.855855i \(0.673032\pi\)
\(654\) 0 0
\(655\) 23.3403 0.911979
\(656\) 0 0
\(657\) −12.6838 −0.494841
\(658\) 0 0
\(659\) 26.2186 1.02133 0.510666 0.859779i \(-0.329399\pi\)
0.510666 + 0.859779i \(0.329399\pi\)
\(660\) 0 0
\(661\) 29.9343 1.16431 0.582154 0.813078i \(-0.302210\pi\)
0.582154 + 0.813078i \(0.302210\pi\)
\(662\) 0 0
\(663\) −2.01750 −0.0783531
\(664\) 0 0
\(665\) 14.7941 0.573692
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) −16.0725 −0.621398
\(670\) 0 0
\(671\) −10.0446 −0.387769
\(672\) 0 0
\(673\) −10.9988 −0.423971 −0.211986 0.977273i \(-0.567993\pi\)
−0.211986 + 0.977273i \(0.567993\pi\)
\(674\) 0 0
\(675\) 6.67190 0.256802
\(676\) 0 0
\(677\) 24.7102 0.949688 0.474844 0.880070i \(-0.342504\pi\)
0.474844 + 0.880070i \(0.342504\pi\)
\(678\) 0 0
\(679\) 16.7057 0.641107
\(680\) 0 0
\(681\) 18.1471 0.695399
\(682\) 0 0
\(683\) 8.25274 0.315782 0.157891 0.987457i \(-0.449530\pi\)
0.157891 + 0.987457i \(0.449530\pi\)
\(684\) 0 0
\(685\) 50.3178 1.92254
\(686\) 0 0
\(687\) −7.11132 −0.271314
\(688\) 0 0
\(689\) −18.5954 −0.708429
\(690\) 0 0
\(691\) −10.9738 −0.417463 −0.208732 0.977973i \(-0.566934\pi\)
−0.208732 + 0.977973i \(0.566934\pi\)
\(692\) 0 0
\(693\) 2.35222 0.0893534
\(694\) 0 0
\(695\) 69.4802 2.63553
\(696\) 0 0
\(697\) 1.75421 0.0664455
\(698\) 0 0
\(699\) 3.07312 0.116236
\(700\) 0 0
\(701\) −43.2229 −1.63251 −0.816254 0.577694i \(-0.803953\pi\)
−0.816254 + 0.577694i \(0.803953\pi\)
\(702\) 0 0
\(703\) 10.3364 0.389845
\(704\) 0 0
\(705\) 1.54411 0.0581545
\(706\) 0 0
\(707\) −22.2981 −0.838607
\(708\) 0 0
\(709\) 7.16787 0.269195 0.134598 0.990900i \(-0.457026\pi\)
0.134598 + 0.990900i \(0.457026\pi\)
\(710\) 0 0
\(711\) 2.30778 0.0865485
\(712\) 0 0
\(713\) 6.57178 0.246115
\(714\) 0 0
\(715\) 17.6904 0.661582
\(716\) 0 0
\(717\) 7.61297 0.284312
\(718\) 0 0
\(719\) 8.57336 0.319732 0.159866 0.987139i \(-0.448894\pi\)
0.159866 + 0.987139i \(0.448894\pi\)
\(720\) 0 0
\(721\) 29.7220 1.10691
\(722\) 0 0
\(723\) −20.4791 −0.761625
\(724\) 0 0
\(725\) 6.67190 0.247788
\(726\) 0 0
\(727\) −6.72086 −0.249263 −0.124631 0.992203i \(-0.539775\pi\)
−0.124631 + 0.992203i \(0.539775\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.41356 0.0522824
\(732\) 0 0
\(733\) 24.5994 0.908601 0.454301 0.890848i \(-0.349889\pi\)
0.454301 + 0.890848i \(0.349889\pi\)
\(734\) 0 0
\(735\) 9.54368 0.352024
\(736\) 0 0
\(737\) −12.1903 −0.449037
\(738\) 0 0
\(739\) 22.8595 0.840901 0.420450 0.907316i \(-0.361872\pi\)
0.420450 + 0.907316i \(0.361872\pi\)
\(740\) 0 0
\(741\) 9.53251 0.350185
\(742\) 0 0
\(743\) −25.5707 −0.938099 −0.469050 0.883172i \(-0.655403\pi\)
−0.469050 + 0.883172i \(0.655403\pi\)
\(744\) 0 0
\(745\) −6.79280 −0.248869
\(746\) 0 0
\(747\) −4.59898 −0.168268
\(748\) 0 0
\(749\) −22.6818 −0.828776
\(750\) 0 0
\(751\) −7.27611 −0.265509 −0.132754 0.991149i \(-0.542382\pi\)
−0.132754 + 0.991149i \(0.542382\pi\)
\(752\) 0 0
\(753\) 10.7623 0.392201
\(754\) 0 0
\(755\) 2.35072 0.0855514
\(756\) 0 0
\(757\) 18.9497 0.688738 0.344369 0.938834i \(-0.388093\pi\)
0.344369 + 0.938834i \(0.388093\pi\)
\(758\) 0 0
\(759\) 1.14688 0.0416289
\(760\) 0 0
\(761\) 11.2163 0.406591 0.203295 0.979117i \(-0.434835\pi\)
0.203295 + 0.979117i \(0.434835\pi\)
\(762\) 0 0
\(763\) −11.0353 −0.399504
\(764\) 0 0
\(765\) −1.52663 −0.0551955
\(766\) 0 0
\(767\) 28.5130 1.02954
\(768\) 0 0
\(769\) −37.2889 −1.34467 −0.672337 0.740245i \(-0.734709\pi\)
−0.672337 + 0.740245i \(0.734709\pi\)
\(770\) 0 0
\(771\) −19.2212 −0.692234
\(772\) 0 0
\(773\) 54.5495 1.96201 0.981005 0.193983i \(-0.0621408\pi\)
0.981005 + 0.193983i \(0.0621408\pi\)
\(774\) 0 0
\(775\) 43.8463 1.57501
\(776\) 0 0
\(777\) −10.0409 −0.360216
\(778\) 0 0
\(779\) −8.28850 −0.296966
\(780\) 0 0
\(781\) 15.2783 0.546699
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) −24.8279 −0.886146
\(786\) 0 0
\(787\) 27.0718 0.965004 0.482502 0.875895i \(-0.339728\pi\)
0.482502 + 0.875895i \(0.339728\pi\)
\(788\) 0 0
\(789\) 8.85390 0.315207
\(790\) 0 0
\(791\) −5.20973 −0.185236
\(792\) 0 0
\(793\) 39.5428 1.40421
\(794\) 0 0
\(795\) −14.0711 −0.499049
\(796\) 0 0
\(797\) 4.74869 0.168207 0.0841036 0.996457i \(-0.473197\pi\)
0.0841036 + 0.996457i \(0.473197\pi\)
\(798\) 0 0
\(799\) −0.201962 −0.00714492
\(800\) 0 0
\(801\) 14.8381 0.524279
\(802\) 0 0
\(803\) −14.5467 −0.513342
\(804\) 0 0
\(805\) −7.00700 −0.246964
\(806\) 0 0
\(807\) 9.97519 0.351143
\(808\) 0 0
\(809\) 28.8430 1.01407 0.507033 0.861927i \(-0.330742\pi\)
0.507033 + 0.861927i \(0.330742\pi\)
\(810\) 0 0
\(811\) 3.47894 0.122162 0.0610810 0.998133i \(-0.480545\pi\)
0.0610810 + 0.998133i \(0.480545\pi\)
\(812\) 0 0
\(813\) −14.7260 −0.516463
\(814\) 0 0
\(815\) 73.0783 2.55982
\(816\) 0 0
\(817\) −6.67895 −0.233667
\(818\) 0 0
\(819\) −9.26001 −0.323571
\(820\) 0 0
\(821\) −34.1095 −1.19043 −0.595216 0.803566i \(-0.702933\pi\)
−0.595216 + 0.803566i \(0.702933\pi\)
\(822\) 0 0
\(823\) 44.6176 1.55527 0.777636 0.628715i \(-0.216419\pi\)
0.777636 + 0.628715i \(0.216419\pi\)
\(824\) 0 0
\(825\) 7.65184 0.266403
\(826\) 0 0
\(827\) 33.0174 1.14813 0.574064 0.818810i \(-0.305366\pi\)
0.574064 + 0.818810i \(0.305366\pi\)
\(828\) 0 0
\(829\) −40.4901 −1.40628 −0.703139 0.711052i \(-0.748219\pi\)
−0.703139 + 0.711052i \(0.748219\pi\)
\(830\) 0 0
\(831\) 0.848598 0.0294376
\(832\) 0 0
\(833\) −1.24827 −0.0432500
\(834\) 0 0
\(835\) −12.9466 −0.448035
\(836\) 0 0
\(837\) 6.57178 0.227154
\(838\) 0 0
\(839\) −41.3358 −1.42707 −0.713536 0.700619i \(-0.752907\pi\)
−0.713536 + 0.700619i \(0.752907\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −22.8691 −0.787654
\(844\) 0 0
\(845\) −25.2284 −0.867885
\(846\) 0 0
\(847\) −19.8631 −0.682504
\(848\) 0 0
\(849\) −8.10218 −0.278066
\(850\) 0 0
\(851\) −4.89567 −0.167821
\(852\) 0 0
\(853\) −13.0312 −0.446179 −0.223090 0.974798i \(-0.571614\pi\)
−0.223090 + 0.974798i \(0.571614\pi\)
\(854\) 0 0
\(855\) 7.21320 0.246686
\(856\) 0 0
\(857\) −5.49480 −0.187699 −0.0938494 0.995586i \(-0.529917\pi\)
−0.0938494 + 0.995586i \(0.529917\pi\)
\(858\) 0 0
\(859\) −21.8403 −0.745180 −0.372590 0.927996i \(-0.621530\pi\)
−0.372590 + 0.927996i \(0.621530\pi\)
\(860\) 0 0
\(861\) 8.05156 0.274396
\(862\) 0 0
\(863\) 7.67863 0.261384 0.130692 0.991423i \(-0.458280\pi\)
0.130692 + 0.991423i \(0.458280\pi\)
\(864\) 0 0
\(865\) −72.9535 −2.48049
\(866\) 0 0
\(867\) −16.8003 −0.570569
\(868\) 0 0
\(869\) 2.64674 0.0897844
\(870\) 0 0
\(871\) 47.9899 1.62607
\(872\) 0 0
\(873\) 8.14524 0.275675
\(874\) 0 0
\(875\) −11.7150 −0.396040
\(876\) 0 0
\(877\) 32.3068 1.09092 0.545461 0.838136i \(-0.316355\pi\)
0.545461 + 0.838136i \(0.316355\pi\)
\(878\) 0 0
\(879\) 24.6949 0.832937
\(880\) 0 0
\(881\) −24.7489 −0.833812 −0.416906 0.908950i \(-0.636886\pi\)
−0.416906 + 0.908950i \(0.636886\pi\)
\(882\) 0 0
\(883\) −23.2435 −0.782207 −0.391103 0.920347i \(-0.627907\pi\)
−0.391103 + 0.920347i \(0.627907\pi\)
\(884\) 0 0
\(885\) 21.5757 0.725258
\(886\) 0 0
\(887\) 26.2844 0.882544 0.441272 0.897374i \(-0.354527\pi\)
0.441272 + 0.897374i \(0.354527\pi\)
\(888\) 0 0
\(889\) −15.2123 −0.510205
\(890\) 0 0
\(891\) 1.14688 0.0384218
\(892\) 0 0
\(893\) 0.954255 0.0319329
\(894\) 0 0
\(895\) 65.2473 2.18098
\(896\) 0 0
\(897\) −4.51492 −0.150749
\(898\) 0 0
\(899\) 6.57178 0.219181
\(900\) 0 0
\(901\) 1.84043 0.0613136
\(902\) 0 0
\(903\) 6.48803 0.215908
\(904\) 0 0
\(905\) −36.8049 −1.22344
\(906\) 0 0
\(907\) 54.1109 1.79672 0.898361 0.439258i \(-0.144759\pi\)
0.898361 + 0.439258i \(0.144759\pi\)
\(908\) 0 0
\(909\) −10.8719 −0.360599
\(910\) 0 0
\(911\) −14.6064 −0.483932 −0.241966 0.970285i \(-0.577792\pi\)
−0.241966 + 0.970285i \(0.577792\pi\)
\(912\) 0 0
\(913\) −5.27446 −0.174559
\(914\) 0 0
\(915\) 29.9219 0.989187
\(916\) 0 0
\(917\) −14.0119 −0.462713
\(918\) 0 0
\(919\) −3.49205 −0.115192 −0.0575961 0.998340i \(-0.518344\pi\)
−0.0575961 + 0.998340i \(0.518344\pi\)
\(920\) 0 0
\(921\) −7.75138 −0.255417
\(922\) 0 0
\(923\) −60.1461 −1.97973
\(924\) 0 0
\(925\) −32.6634 −1.07397
\(926\) 0 0
\(927\) 14.4916 0.475967
\(928\) 0 0
\(929\) −12.6091 −0.413690 −0.206845 0.978374i \(-0.566320\pi\)
−0.206845 + 0.978374i \(0.566320\pi\)
\(930\) 0 0
\(931\) 5.89797 0.193298
\(932\) 0 0
\(933\) 11.2388 0.367941
\(934\) 0 0
\(935\) −1.75086 −0.0572591
\(936\) 0 0
\(937\) 21.6562 0.707477 0.353739 0.935344i \(-0.384910\pi\)
0.353739 + 0.935344i \(0.384910\pi\)
\(938\) 0 0
\(939\) 12.3629 0.403449
\(940\) 0 0
\(941\) 44.3084 1.44441 0.722206 0.691678i \(-0.243128\pi\)
0.722206 + 0.691678i \(0.243128\pi\)
\(942\) 0 0
\(943\) 3.92571 0.127839
\(944\) 0 0
\(945\) −7.00700 −0.227938
\(946\) 0 0
\(947\) 57.6519 1.87344 0.936718 0.350085i \(-0.113847\pi\)
0.936718 + 0.350085i \(0.113847\pi\)
\(948\) 0 0
\(949\) 57.2662 1.85894
\(950\) 0 0
\(951\) −10.5402 −0.341788
\(952\) 0 0
\(953\) 14.3695 0.465472 0.232736 0.972540i \(-0.425232\pi\)
0.232736 + 0.972540i \(0.425232\pi\)
\(954\) 0 0
\(955\) 47.3807 1.53320
\(956\) 0 0
\(957\) 1.14688 0.0370732
\(958\) 0 0
\(959\) −30.2073 −0.975446
\(960\) 0 0
\(961\) 12.1883 0.393172
\(962\) 0 0
\(963\) −11.0590 −0.356372
\(964\) 0 0
\(965\) −83.3957 −2.68460
\(966\) 0 0
\(967\) 10.7620 0.346082 0.173041 0.984915i \(-0.444641\pi\)
0.173041 + 0.984915i \(0.444641\pi\)
\(968\) 0 0
\(969\) −0.943454 −0.0303081
\(970\) 0 0
\(971\) −30.9320 −0.992656 −0.496328 0.868135i \(-0.665319\pi\)
−0.496328 + 0.868135i \(0.665319\pi\)
\(972\) 0 0
\(973\) −41.7111 −1.33720
\(974\) 0 0
\(975\) −30.1231 −0.964711
\(976\) 0 0
\(977\) 27.4813 0.879204 0.439602 0.898193i \(-0.355120\pi\)
0.439602 + 0.898193i \(0.355120\pi\)
\(978\) 0 0
\(979\) 17.0175 0.543880
\(980\) 0 0
\(981\) −5.38049 −0.171786
\(982\) 0 0
\(983\) 14.6830 0.468316 0.234158 0.972199i \(-0.424767\pi\)
0.234158 + 0.972199i \(0.424767\pi\)
\(984\) 0 0
\(985\) 54.4400 1.73460
\(986\) 0 0
\(987\) −0.926977 −0.0295060
\(988\) 0 0
\(989\) 3.16338 0.100590
\(990\) 0 0
\(991\) 8.32406 0.264422 0.132211 0.991222i \(-0.457792\pi\)
0.132211 + 0.991222i \(0.457792\pi\)
\(992\) 0 0
\(993\) −26.4647 −0.839832
\(994\) 0 0
\(995\) 76.2548 2.41744
\(996\) 0 0
\(997\) 20.9269 0.662762 0.331381 0.943497i \(-0.392486\pi\)
0.331381 + 0.943497i \(0.392486\pi\)
\(998\) 0 0
\(999\) −4.89567 −0.154892
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 \(a_p\))