Properties

Label 8004.2.a.j.1.2
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.2
Root \(-3.12066\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-3.12066 q^{5}\) \(-0.760812 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-3.12066 q^{5}\) \(-0.760812 q^{7}\) \(+1.00000 q^{9}\) \(+3.50921 q^{11}\) \(-3.64935 q^{13}\) \(-3.12066 q^{15}\) \(+6.89390 q^{17}\) \(-2.74332 q^{19}\) \(-0.760812 q^{21}\) \(+1.00000 q^{23}\) \(+4.73851 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-5.32027 q^{31}\) \(+3.50921 q^{33}\) \(+2.37424 q^{35}\) \(+5.93131 q^{37}\) \(-3.64935 q^{39}\) \(+6.52429 q^{41}\) \(-1.04224 q^{43}\) \(-3.12066 q^{45}\) \(-8.77868 q^{47}\) \(-6.42116 q^{49}\) \(+6.89390 q^{51}\) \(+6.18193 q^{53}\) \(-10.9510 q^{55}\) \(-2.74332 q^{57}\) \(-11.2513 q^{59}\) \(+0.576123 q^{61}\) \(-0.760812 q^{63}\) \(+11.3884 q^{65}\) \(+3.98419 q^{67}\) \(+1.00000 q^{69}\) \(-6.42449 q^{71}\) \(+7.28163 q^{73}\) \(+4.73851 q^{75}\) \(-2.66985 q^{77}\) \(+6.45544 q^{79}\) \(+1.00000 q^{81}\) \(+2.58965 q^{83}\) \(-21.5135 q^{85}\) \(-1.00000 q^{87}\) \(-10.7495 q^{89}\) \(+2.77647 q^{91}\) \(-5.32027 q^{93}\) \(+8.56096 q^{95}\) \(+17.1691 q^{97}\) \(+3.50921 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −3.12066 −1.39560 −0.697800 0.716292i \(-0.745838\pi\)
−0.697800 + 0.716292i \(0.745838\pi\)
\(6\) 0 0
\(7\) −0.760812 −0.287560 −0.143780 0.989610i \(-0.545926\pi\)
−0.143780 + 0.989610i \(0.545926\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.50921 1.05807 0.529033 0.848601i \(-0.322555\pi\)
0.529033 + 0.848601i \(0.322555\pi\)
\(12\) 0 0
\(13\) −3.64935 −1.01215 −0.506074 0.862490i \(-0.668904\pi\)
−0.506074 + 0.862490i \(0.668904\pi\)
\(14\) 0 0
\(15\) −3.12066 −0.805751
\(16\) 0 0
\(17\) 6.89390 1.67202 0.836008 0.548717i \(-0.184884\pi\)
0.836008 + 0.548717i \(0.184884\pi\)
\(18\) 0 0
\(19\) −2.74332 −0.629360 −0.314680 0.949198i \(-0.601897\pi\)
−0.314680 + 0.949198i \(0.601897\pi\)
\(20\) 0 0
\(21\) −0.760812 −0.166023
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 4.73851 0.947702
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −5.32027 −0.955549 −0.477774 0.878483i \(-0.658556\pi\)
−0.477774 + 0.878483i \(0.658556\pi\)
\(32\) 0 0
\(33\) 3.50921 0.610875
\(34\) 0 0
\(35\) 2.37424 0.401319
\(36\) 0 0
\(37\) 5.93131 0.975102 0.487551 0.873095i \(-0.337890\pi\)
0.487551 + 0.873095i \(0.337890\pi\)
\(38\) 0 0
\(39\) −3.64935 −0.584364
\(40\) 0 0
\(41\) 6.52429 1.01892 0.509462 0.860493i \(-0.329845\pi\)
0.509462 + 0.860493i \(0.329845\pi\)
\(42\) 0 0
\(43\) −1.04224 −0.158940 −0.0794702 0.996837i \(-0.525323\pi\)
−0.0794702 + 0.996837i \(0.525323\pi\)
\(44\) 0 0
\(45\) −3.12066 −0.465200
\(46\) 0 0
\(47\) −8.77868 −1.28050 −0.640251 0.768166i \(-0.721170\pi\)
−0.640251 + 0.768166i \(0.721170\pi\)
\(48\) 0 0
\(49\) −6.42116 −0.917309
\(50\) 0 0
\(51\) 6.89390 0.965339
\(52\) 0 0
\(53\) 6.18193 0.849153 0.424576 0.905392i \(-0.360423\pi\)
0.424576 + 0.905392i \(0.360423\pi\)
\(54\) 0 0
\(55\) −10.9510 −1.47664
\(56\) 0 0
\(57\) −2.74332 −0.363361
\(58\) 0 0
\(59\) −11.2513 −1.46480 −0.732398 0.680876i \(-0.761599\pi\)
−0.732398 + 0.680876i \(0.761599\pi\)
\(60\) 0 0
\(61\) 0.576123 0.0737650 0.0368825 0.999320i \(-0.488257\pi\)
0.0368825 + 0.999320i \(0.488257\pi\)
\(62\) 0 0
\(63\) −0.760812 −0.0958534
\(64\) 0 0
\(65\) 11.3884 1.41255
\(66\) 0 0
\(67\) 3.98419 0.486746 0.243373 0.969933i \(-0.421746\pi\)
0.243373 + 0.969933i \(0.421746\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −6.42449 −0.762447 −0.381224 0.924483i \(-0.624497\pi\)
−0.381224 + 0.924483i \(0.624497\pi\)
\(72\) 0 0
\(73\) 7.28163 0.852250 0.426125 0.904664i \(-0.359878\pi\)
0.426125 + 0.904664i \(0.359878\pi\)
\(74\) 0 0
\(75\) 4.73851 0.547156
\(76\) 0 0
\(77\) −2.66985 −0.304258
\(78\) 0 0
\(79\) 6.45544 0.726294 0.363147 0.931732i \(-0.381702\pi\)
0.363147 + 0.931732i \(0.381702\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.58965 0.284252 0.142126 0.989849i \(-0.454606\pi\)
0.142126 + 0.989849i \(0.454606\pi\)
\(84\) 0 0
\(85\) −21.5135 −2.33347
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −10.7495 −1.13944 −0.569722 0.821837i \(-0.692949\pi\)
−0.569722 + 0.821837i \(0.692949\pi\)
\(90\) 0 0
\(91\) 2.77647 0.291053
\(92\) 0 0
\(93\) −5.32027 −0.551686
\(94\) 0 0
\(95\) 8.56096 0.878336
\(96\) 0 0
\(97\) 17.1691 1.74326 0.871631 0.490163i \(-0.163063\pi\)
0.871631 + 0.490163i \(0.163063\pi\)
\(98\) 0 0
\(99\) 3.50921 0.352689
\(100\) 0 0
\(101\) 6.05636 0.602630 0.301315 0.953525i \(-0.402574\pi\)
0.301315 + 0.953525i \(0.402574\pi\)
\(102\) 0 0
\(103\) −10.3203 −1.01689 −0.508445 0.861094i \(-0.669780\pi\)
−0.508445 + 0.861094i \(0.669780\pi\)
\(104\) 0 0
\(105\) 2.37424 0.231702
\(106\) 0 0
\(107\) 12.8482 1.24208 0.621041 0.783778i \(-0.286710\pi\)
0.621041 + 0.783778i \(0.286710\pi\)
\(108\) 0 0
\(109\) −9.57760 −0.917368 −0.458684 0.888600i \(-0.651679\pi\)
−0.458684 + 0.888600i \(0.651679\pi\)
\(110\) 0 0
\(111\) 5.93131 0.562975
\(112\) 0 0
\(113\) −17.2072 −1.61872 −0.809359 0.587314i \(-0.800185\pi\)
−0.809359 + 0.587314i \(0.800185\pi\)
\(114\) 0 0
\(115\) −3.12066 −0.291003
\(116\) 0 0
\(117\) −3.64935 −0.337382
\(118\) 0 0
\(119\) −5.24497 −0.480805
\(120\) 0 0
\(121\) 1.31456 0.119506
\(122\) 0 0
\(123\) 6.52429 0.588276
\(124\) 0 0
\(125\) 0.816024 0.0729874
\(126\) 0 0
\(127\) 12.8327 1.13872 0.569360 0.822088i \(-0.307191\pi\)
0.569360 + 0.822088i \(0.307191\pi\)
\(128\) 0 0
\(129\) −1.04224 −0.0917643
\(130\) 0 0
\(131\) 19.1889 1.67654 0.838272 0.545252i \(-0.183566\pi\)
0.838272 + 0.545252i \(0.183566\pi\)
\(132\) 0 0
\(133\) 2.08715 0.180979
\(134\) 0 0
\(135\) −3.12066 −0.268584
\(136\) 0 0
\(137\) 17.2757 1.47596 0.737982 0.674821i \(-0.235779\pi\)
0.737982 + 0.674821i \(0.235779\pi\)
\(138\) 0 0
\(139\) 8.12399 0.689068 0.344534 0.938774i \(-0.388037\pi\)
0.344534 + 0.938774i \(0.388037\pi\)
\(140\) 0 0
\(141\) −8.77868 −0.739298
\(142\) 0 0
\(143\) −12.8063 −1.07092
\(144\) 0 0
\(145\) 3.12066 0.259157
\(146\) 0 0
\(147\) −6.42116 −0.529609
\(148\) 0 0
\(149\) −2.15116 −0.176230 −0.0881148 0.996110i \(-0.528084\pi\)
−0.0881148 + 0.996110i \(0.528084\pi\)
\(150\) 0 0
\(151\) 11.9382 0.971521 0.485760 0.874092i \(-0.338543\pi\)
0.485760 + 0.874092i \(0.338543\pi\)
\(152\) 0 0
\(153\) 6.89390 0.557339
\(154\) 0 0
\(155\) 16.6027 1.33356
\(156\) 0 0
\(157\) 4.17674 0.333340 0.166670 0.986013i \(-0.446699\pi\)
0.166670 + 0.986013i \(0.446699\pi\)
\(158\) 0 0
\(159\) 6.18193 0.490259
\(160\) 0 0
\(161\) −0.760812 −0.0599604
\(162\) 0 0
\(163\) 6.80419 0.532945 0.266473 0.963842i \(-0.414142\pi\)
0.266473 + 0.963842i \(0.414142\pi\)
\(164\) 0 0
\(165\) −10.9510 −0.852538
\(166\) 0 0
\(167\) −2.97280 −0.230042 −0.115021 0.993363i \(-0.536694\pi\)
−0.115021 + 0.993363i \(0.536694\pi\)
\(168\) 0 0
\(169\) 0.317749 0.0244423
\(170\) 0 0
\(171\) −2.74332 −0.209787
\(172\) 0 0
\(173\) 1.57666 0.119871 0.0599355 0.998202i \(-0.480911\pi\)
0.0599355 + 0.998202i \(0.480911\pi\)
\(174\) 0 0
\(175\) −3.60512 −0.272521
\(176\) 0 0
\(177\) −11.2513 −0.845701
\(178\) 0 0
\(179\) 1.09555 0.0818853 0.0409427 0.999161i \(-0.486964\pi\)
0.0409427 + 0.999161i \(0.486964\pi\)
\(180\) 0 0
\(181\) 15.7252 1.16885 0.584423 0.811449i \(-0.301321\pi\)
0.584423 + 0.811449i \(0.301321\pi\)
\(182\) 0 0
\(183\) 0.576123 0.0425882
\(184\) 0 0
\(185\) −18.5096 −1.36085
\(186\) 0 0
\(187\) 24.1922 1.76911
\(188\) 0 0
\(189\) −0.760812 −0.0553410
\(190\) 0 0
\(191\) 1.34219 0.0971173 0.0485586 0.998820i \(-0.484537\pi\)
0.0485586 + 0.998820i \(0.484537\pi\)
\(192\) 0 0
\(193\) 15.9686 1.14944 0.574722 0.818349i \(-0.305110\pi\)
0.574722 + 0.818349i \(0.305110\pi\)
\(194\) 0 0
\(195\) 11.3884 0.815538
\(196\) 0 0
\(197\) 10.8821 0.775317 0.387659 0.921803i \(-0.373284\pi\)
0.387659 + 0.921803i \(0.373284\pi\)
\(198\) 0 0
\(199\) 20.5109 1.45398 0.726990 0.686648i \(-0.240919\pi\)
0.726990 + 0.686648i \(0.240919\pi\)
\(200\) 0 0
\(201\) 3.98419 0.281023
\(202\) 0 0
\(203\) 0.760812 0.0533986
\(204\) 0 0
\(205\) −20.3601 −1.42201
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −9.62688 −0.665906
\(210\) 0 0
\(211\) −8.39339 −0.577825 −0.288912 0.957356i \(-0.593294\pi\)
−0.288912 + 0.957356i \(0.593294\pi\)
\(212\) 0 0
\(213\) −6.42449 −0.440199
\(214\) 0 0
\(215\) 3.25248 0.221817
\(216\) 0 0
\(217\) 4.04773 0.274778
\(218\) 0 0
\(219\) 7.28163 0.492047
\(220\) 0 0
\(221\) −25.1582 −1.69233
\(222\) 0 0
\(223\) −2.46867 −0.165314 −0.0826572 0.996578i \(-0.526341\pi\)
−0.0826572 + 0.996578i \(0.526341\pi\)
\(224\) 0 0
\(225\) 4.73851 0.315901
\(226\) 0 0
\(227\) −18.3394 −1.21723 −0.608615 0.793466i \(-0.708275\pi\)
−0.608615 + 0.793466i \(0.708275\pi\)
\(228\) 0 0
\(229\) 2.30393 0.152248 0.0761240 0.997098i \(-0.475746\pi\)
0.0761240 + 0.997098i \(0.475746\pi\)
\(230\) 0 0
\(231\) −2.66985 −0.175663
\(232\) 0 0
\(233\) −3.12350 −0.204627 −0.102314 0.994752i \(-0.532625\pi\)
−0.102314 + 0.994752i \(0.532625\pi\)
\(234\) 0 0
\(235\) 27.3953 1.78707
\(236\) 0 0
\(237\) 6.45544 0.419326
\(238\) 0 0
\(239\) −2.43709 −0.157642 −0.0788211 0.996889i \(-0.525116\pi\)
−0.0788211 + 0.996889i \(0.525116\pi\)
\(240\) 0 0
\(241\) −4.96582 −0.319877 −0.159938 0.987127i \(-0.551130\pi\)
−0.159938 + 0.987127i \(0.551130\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 20.0383 1.28020
\(246\) 0 0
\(247\) 10.0113 0.637006
\(248\) 0 0
\(249\) 2.58965 0.164113
\(250\) 0 0
\(251\) 9.69649 0.612037 0.306018 0.952026i \(-0.401003\pi\)
0.306018 + 0.952026i \(0.401003\pi\)
\(252\) 0 0
\(253\) 3.50921 0.220622
\(254\) 0 0
\(255\) −21.5135 −1.34723
\(256\) 0 0
\(257\) 19.9656 1.24542 0.622710 0.782453i \(-0.286032\pi\)
0.622710 + 0.782453i \(0.286032\pi\)
\(258\) 0 0
\(259\) −4.51262 −0.280400
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −12.3305 −0.760332 −0.380166 0.924918i \(-0.624133\pi\)
−0.380166 + 0.924918i \(0.624133\pi\)
\(264\) 0 0
\(265\) −19.2917 −1.18508
\(266\) 0 0
\(267\) −10.7495 −0.657859
\(268\) 0 0
\(269\) −16.4593 −1.00354 −0.501772 0.865000i \(-0.667318\pi\)
−0.501772 + 0.865000i \(0.667318\pi\)
\(270\) 0 0
\(271\) 0.668966 0.0406368 0.0203184 0.999794i \(-0.493532\pi\)
0.0203184 + 0.999794i \(0.493532\pi\)
\(272\) 0 0
\(273\) 2.77647 0.168040
\(274\) 0 0
\(275\) 16.6284 1.00273
\(276\) 0 0
\(277\) 4.27134 0.256640 0.128320 0.991733i \(-0.459042\pi\)
0.128320 + 0.991733i \(0.459042\pi\)
\(278\) 0 0
\(279\) −5.32027 −0.318516
\(280\) 0 0
\(281\) −0.0728644 −0.00434673 −0.00217336 0.999998i \(-0.500692\pi\)
−0.00217336 + 0.999998i \(0.500692\pi\)
\(282\) 0 0
\(283\) 2.10058 0.124867 0.0624334 0.998049i \(-0.480114\pi\)
0.0624334 + 0.998049i \(0.480114\pi\)
\(284\) 0 0
\(285\) 8.56096 0.507108
\(286\) 0 0
\(287\) −4.96376 −0.293002
\(288\) 0 0
\(289\) 30.5259 1.79564
\(290\) 0 0
\(291\) 17.1691 1.00647
\(292\) 0 0
\(293\) 19.0717 1.11418 0.557090 0.830452i \(-0.311918\pi\)
0.557090 + 0.830452i \(0.311918\pi\)
\(294\) 0 0
\(295\) 35.1115 2.04427
\(296\) 0 0
\(297\) 3.50921 0.203625
\(298\) 0 0
\(299\) −3.64935 −0.211047
\(300\) 0 0
\(301\) 0.792951 0.0457049
\(302\) 0 0
\(303\) 6.05636 0.347929
\(304\) 0 0
\(305\) −1.79788 −0.102946
\(306\) 0 0
\(307\) 26.6122 1.51884 0.759418 0.650603i \(-0.225484\pi\)
0.759418 + 0.650603i \(0.225484\pi\)
\(308\) 0 0
\(309\) −10.3203 −0.587102
\(310\) 0 0
\(311\) −3.92862 −0.222772 −0.111386 0.993777i \(-0.535529\pi\)
−0.111386 + 0.993777i \(0.535529\pi\)
\(312\) 0 0
\(313\) −10.1563 −0.574069 −0.287034 0.957920i \(-0.592669\pi\)
−0.287034 + 0.957920i \(0.592669\pi\)
\(314\) 0 0
\(315\) 2.37424 0.133773
\(316\) 0 0
\(317\) 21.2960 1.19610 0.598051 0.801458i \(-0.295942\pi\)
0.598051 + 0.801458i \(0.295942\pi\)
\(318\) 0 0
\(319\) −3.50921 −0.196478
\(320\) 0 0
\(321\) 12.8482 0.717116
\(322\) 0 0
\(323\) −18.9122 −1.05230
\(324\) 0 0
\(325\) −17.2925 −0.959214
\(326\) 0 0
\(327\) −9.57760 −0.529642
\(328\) 0 0
\(329\) 6.67893 0.368221
\(330\) 0 0
\(331\) 21.2770 1.16949 0.584745 0.811217i \(-0.301195\pi\)
0.584745 + 0.811217i \(0.301195\pi\)
\(332\) 0 0
\(333\) 5.93131 0.325034
\(334\) 0 0
\(335\) −12.4333 −0.679303
\(336\) 0 0
\(337\) 16.0286 0.873135 0.436567 0.899672i \(-0.356194\pi\)
0.436567 + 0.899672i \(0.356194\pi\)
\(338\) 0 0
\(339\) −17.2072 −0.934567
\(340\) 0 0
\(341\) −18.6699 −1.01103
\(342\) 0 0
\(343\) 10.2110 0.551342
\(344\) 0 0
\(345\) −3.12066 −0.168011
\(346\) 0 0
\(347\) 11.0678 0.594150 0.297075 0.954854i \(-0.403989\pi\)
0.297075 + 0.954854i \(0.403989\pi\)
\(348\) 0 0
\(349\) 34.6536 1.85496 0.927482 0.373869i \(-0.121969\pi\)
0.927482 + 0.373869i \(0.121969\pi\)
\(350\) 0 0
\(351\) −3.64935 −0.194788
\(352\) 0 0
\(353\) 22.7684 1.21184 0.605919 0.795527i \(-0.292806\pi\)
0.605919 + 0.795527i \(0.292806\pi\)
\(354\) 0 0
\(355\) 20.0487 1.06407
\(356\) 0 0
\(357\) −5.24497 −0.277593
\(358\) 0 0
\(359\) 17.5444 0.925960 0.462980 0.886369i \(-0.346780\pi\)
0.462980 + 0.886369i \(0.346780\pi\)
\(360\) 0 0
\(361\) −11.4742 −0.603905
\(362\) 0 0
\(363\) 1.31456 0.0689967
\(364\) 0 0
\(365\) −22.7235 −1.18940
\(366\) 0 0
\(367\) −9.26701 −0.483734 −0.241867 0.970309i \(-0.577760\pi\)
−0.241867 + 0.970309i \(0.577760\pi\)
\(368\) 0 0
\(369\) 6.52429 0.339641
\(370\) 0 0
\(371\) −4.70329 −0.244182
\(372\) 0 0
\(373\) 27.4289 1.42022 0.710108 0.704093i \(-0.248646\pi\)
0.710108 + 0.704093i \(0.248646\pi\)
\(374\) 0 0
\(375\) 0.816024 0.0421393
\(376\) 0 0
\(377\) 3.64935 0.187951
\(378\) 0 0
\(379\) 21.1334 1.08555 0.542776 0.839878i \(-0.317373\pi\)
0.542776 + 0.839878i \(0.317373\pi\)
\(380\) 0 0
\(381\) 12.8327 0.657441
\(382\) 0 0
\(383\) −15.9421 −0.814602 −0.407301 0.913294i \(-0.633530\pi\)
−0.407301 + 0.913294i \(0.633530\pi\)
\(384\) 0 0
\(385\) 8.33170 0.424623
\(386\) 0 0
\(387\) −1.04224 −0.0529801
\(388\) 0 0
\(389\) −4.34366 −0.220233 −0.110116 0.993919i \(-0.535122\pi\)
−0.110116 + 0.993919i \(0.535122\pi\)
\(390\) 0 0
\(391\) 6.89390 0.348640
\(392\) 0 0
\(393\) 19.1889 0.967953
\(394\) 0 0
\(395\) −20.1452 −1.01362
\(396\) 0 0
\(397\) −30.9210 −1.55188 −0.775941 0.630806i \(-0.782724\pi\)
−0.775941 + 0.630806i \(0.782724\pi\)
\(398\) 0 0
\(399\) 2.08715 0.104488
\(400\) 0 0
\(401\) −12.6909 −0.633754 −0.316877 0.948467i \(-0.602634\pi\)
−0.316877 + 0.948467i \(0.602634\pi\)
\(402\) 0 0
\(403\) 19.4155 0.967156
\(404\) 0 0
\(405\) −3.12066 −0.155067
\(406\) 0 0
\(407\) 20.8142 1.03172
\(408\) 0 0
\(409\) 7.13402 0.352754 0.176377 0.984323i \(-0.443562\pi\)
0.176377 + 0.984323i \(0.443562\pi\)
\(410\) 0 0
\(411\) 17.2757 0.852148
\(412\) 0 0
\(413\) 8.56014 0.421217
\(414\) 0 0
\(415\) −8.08143 −0.396702
\(416\) 0 0
\(417\) 8.12399 0.397834
\(418\) 0 0
\(419\) −38.3203 −1.87207 −0.936034 0.351909i \(-0.885533\pi\)
−0.936034 + 0.351909i \(0.885533\pi\)
\(420\) 0 0
\(421\) 15.7125 0.765779 0.382890 0.923794i \(-0.374929\pi\)
0.382890 + 0.923794i \(0.374929\pi\)
\(422\) 0 0
\(423\) −8.77868 −0.426834
\(424\) 0 0
\(425\) 32.6668 1.58457
\(426\) 0 0
\(427\) −0.438321 −0.0212119
\(428\) 0 0
\(429\) −12.8063 −0.618296
\(430\) 0 0
\(431\) −9.14367 −0.440435 −0.220217 0.975451i \(-0.570677\pi\)
−0.220217 + 0.975451i \(0.570677\pi\)
\(432\) 0 0
\(433\) −30.3032 −1.45628 −0.728139 0.685430i \(-0.759614\pi\)
−0.728139 + 0.685430i \(0.759614\pi\)
\(434\) 0 0
\(435\) 3.12066 0.149624
\(436\) 0 0
\(437\) −2.74332 −0.131231
\(438\) 0 0
\(439\) 20.9626 1.00049 0.500245 0.865884i \(-0.333243\pi\)
0.500245 + 0.865884i \(0.333243\pi\)
\(440\) 0 0
\(441\) −6.42116 −0.305770
\(442\) 0 0
\(443\) −5.54152 −0.263286 −0.131643 0.991297i \(-0.542025\pi\)
−0.131643 + 0.991297i \(0.542025\pi\)
\(444\) 0 0
\(445\) 33.5455 1.59021
\(446\) 0 0
\(447\) −2.15116 −0.101746
\(448\) 0 0
\(449\) −39.2609 −1.85284 −0.926418 0.376497i \(-0.877128\pi\)
−0.926418 + 0.376497i \(0.877128\pi\)
\(450\) 0 0
\(451\) 22.8951 1.07809
\(452\) 0 0
\(453\) 11.9382 0.560908
\(454\) 0 0
\(455\) −8.66442 −0.406194
\(456\) 0 0
\(457\) −0.674951 −0.0315729 −0.0157864 0.999875i \(-0.505025\pi\)
−0.0157864 + 0.999875i \(0.505025\pi\)
\(458\) 0 0
\(459\) 6.89390 0.321780
\(460\) 0 0
\(461\) −10.6701 −0.496956 −0.248478 0.968638i \(-0.579930\pi\)
−0.248478 + 0.968638i \(0.579930\pi\)
\(462\) 0 0
\(463\) 11.2011 0.520557 0.260279 0.965534i \(-0.416186\pi\)
0.260279 + 0.965534i \(0.416186\pi\)
\(464\) 0 0
\(465\) 16.6027 0.769934
\(466\) 0 0
\(467\) 35.2217 1.62987 0.814934 0.579554i \(-0.196773\pi\)
0.814934 + 0.579554i \(0.196773\pi\)
\(468\) 0 0
\(469\) −3.03122 −0.139969
\(470\) 0 0
\(471\) 4.17674 0.192454
\(472\) 0 0
\(473\) −3.65745 −0.168170
\(474\) 0 0
\(475\) −12.9992 −0.596446
\(476\) 0 0
\(477\) 6.18193 0.283051
\(478\) 0 0
\(479\) −31.8883 −1.45701 −0.728507 0.685038i \(-0.759785\pi\)
−0.728507 + 0.685038i \(0.759785\pi\)
\(480\) 0 0
\(481\) −21.6454 −0.986947
\(482\) 0 0
\(483\) −0.760812 −0.0346182
\(484\) 0 0
\(485\) −53.5790 −2.43290
\(486\) 0 0
\(487\) −4.29418 −0.194588 −0.0972939 0.995256i \(-0.531019\pi\)
−0.0972939 + 0.995256i \(0.531019\pi\)
\(488\) 0 0
\(489\) 6.80419 0.307696
\(490\) 0 0
\(491\) 21.3458 0.963320 0.481660 0.876358i \(-0.340034\pi\)
0.481660 + 0.876358i \(0.340034\pi\)
\(492\) 0 0
\(493\) −6.89390 −0.310486
\(494\) 0 0
\(495\) −10.9510 −0.492213
\(496\) 0 0
\(497\) 4.88784 0.219249
\(498\) 0 0
\(499\) 38.3671 1.71755 0.858774 0.512354i \(-0.171226\pi\)
0.858774 + 0.512354i \(0.171226\pi\)
\(500\) 0 0
\(501\) −2.97280 −0.132815
\(502\) 0 0
\(503\) 2.11484 0.0942959 0.0471480 0.998888i \(-0.484987\pi\)
0.0471480 + 0.998888i \(0.484987\pi\)
\(504\) 0 0
\(505\) −18.8998 −0.841031
\(506\) 0 0
\(507\) 0.317749 0.0141117
\(508\) 0 0
\(509\) 37.6267 1.66777 0.833887 0.551935i \(-0.186110\pi\)
0.833887 + 0.551935i \(0.186110\pi\)
\(510\) 0 0
\(511\) −5.53995 −0.245073
\(512\) 0 0
\(513\) −2.74332 −0.121120
\(514\) 0 0
\(515\) 32.2062 1.41917
\(516\) 0 0
\(517\) −30.8062 −1.35486
\(518\) 0 0
\(519\) 1.57666 0.0692075
\(520\) 0 0
\(521\) −12.1293 −0.531392 −0.265696 0.964057i \(-0.585602\pi\)
−0.265696 + 0.964057i \(0.585602\pi\)
\(522\) 0 0
\(523\) 31.5939 1.38151 0.690753 0.723091i \(-0.257279\pi\)
0.690753 + 0.723091i \(0.257279\pi\)
\(524\) 0 0
\(525\) −3.60512 −0.157340
\(526\) 0 0
\(527\) −36.6774 −1.59769
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −11.2513 −0.488266
\(532\) 0 0
\(533\) −23.8094 −1.03130
\(534\) 0 0
\(535\) −40.0948 −1.73345
\(536\) 0 0
\(537\) 1.09555 0.0472765
\(538\) 0 0
\(539\) −22.5332 −0.970575
\(540\) 0 0
\(541\) 26.3451 1.13266 0.566331 0.824178i \(-0.308362\pi\)
0.566331 + 0.824178i \(0.308362\pi\)
\(542\) 0 0
\(543\) 15.7252 0.674834
\(544\) 0 0
\(545\) 29.8884 1.28028
\(546\) 0 0
\(547\) 13.4948 0.576994 0.288497 0.957481i \(-0.406844\pi\)
0.288497 + 0.957481i \(0.406844\pi\)
\(548\) 0 0
\(549\) 0.576123 0.0245883
\(550\) 0 0
\(551\) 2.74332 0.116869
\(552\) 0 0
\(553\) −4.91138 −0.208853
\(554\) 0 0
\(555\) −18.5096 −0.785689
\(556\) 0 0
\(557\) −35.1330 −1.48863 −0.744317 0.667827i \(-0.767225\pi\)
−0.744317 + 0.667827i \(0.767225\pi\)
\(558\) 0 0
\(559\) 3.80351 0.160871
\(560\) 0 0
\(561\) 24.1922 1.02139
\(562\) 0 0
\(563\) −1.86137 −0.0784475 −0.0392237 0.999230i \(-0.512489\pi\)
−0.0392237 + 0.999230i \(0.512489\pi\)
\(564\) 0 0
\(565\) 53.6978 2.25908
\(566\) 0 0
\(567\) −0.760812 −0.0319511
\(568\) 0 0
\(569\) 33.6725 1.41163 0.705813 0.708399i \(-0.250582\pi\)
0.705813 + 0.708399i \(0.250582\pi\)
\(570\) 0 0
\(571\) 5.50754 0.230483 0.115242 0.993337i \(-0.463236\pi\)
0.115242 + 0.993337i \(0.463236\pi\)
\(572\) 0 0
\(573\) 1.34219 0.0560707
\(574\) 0 0
\(575\) 4.73851 0.197609
\(576\) 0 0
\(577\) −22.0105 −0.916309 −0.458154 0.888873i \(-0.651489\pi\)
−0.458154 + 0.888873i \(0.651489\pi\)
\(578\) 0 0
\(579\) 15.9686 0.663632
\(580\) 0 0
\(581\) −1.97024 −0.0817394
\(582\) 0 0
\(583\) 21.6937 0.898461
\(584\) 0 0
\(585\) 11.3884 0.470851
\(586\) 0 0
\(587\) −1.14883 −0.0474171 −0.0237086 0.999719i \(-0.507547\pi\)
−0.0237086 + 0.999719i \(0.507547\pi\)
\(588\) 0 0
\(589\) 14.5952 0.601384
\(590\) 0 0
\(591\) 10.8821 0.447630
\(592\) 0 0
\(593\) 4.59279 0.188603 0.0943017 0.995544i \(-0.469938\pi\)
0.0943017 + 0.995544i \(0.469938\pi\)
\(594\) 0 0
\(595\) 16.3677 0.671012
\(596\) 0 0
\(597\) 20.5109 0.839456
\(598\) 0 0
\(599\) −17.0701 −0.697465 −0.348733 0.937222i \(-0.613388\pi\)
−0.348733 + 0.937222i \(0.613388\pi\)
\(600\) 0 0
\(601\) 46.7860 1.90844 0.954220 0.299106i \(-0.0966883\pi\)
0.954220 + 0.299106i \(0.0966883\pi\)
\(602\) 0 0
\(603\) 3.98419 0.162249
\(604\) 0 0
\(605\) −4.10230 −0.166782
\(606\) 0 0
\(607\) 17.9793 0.729756 0.364878 0.931055i \(-0.381111\pi\)
0.364878 + 0.931055i \(0.381111\pi\)
\(608\) 0 0
\(609\) 0.760812 0.0308297
\(610\) 0 0
\(611\) 32.0365 1.29606
\(612\) 0 0
\(613\) 6.23189 0.251704 0.125852 0.992049i \(-0.459834\pi\)
0.125852 + 0.992049i \(0.459834\pi\)
\(614\) 0 0
\(615\) −20.3601 −0.820998
\(616\) 0 0
\(617\) −9.37601 −0.377464 −0.188732 0.982029i \(-0.560438\pi\)
−0.188732 + 0.982029i \(0.560438\pi\)
\(618\) 0 0
\(619\) −25.5678 −1.02766 −0.513828 0.857893i \(-0.671773\pi\)
−0.513828 + 0.857893i \(0.671773\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 8.17835 0.327659
\(624\) 0 0
\(625\) −26.2391 −1.04956
\(626\) 0 0
\(627\) −9.62688 −0.384461
\(628\) 0 0
\(629\) 40.8899 1.63039
\(630\) 0 0
\(631\) −19.5977 −0.780173 −0.390087 0.920778i \(-0.627555\pi\)
−0.390087 + 0.920778i \(0.627555\pi\)
\(632\) 0 0
\(633\) −8.39339 −0.333607
\(634\) 0 0
\(635\) −40.0466 −1.58920
\(636\) 0 0
\(637\) 23.4331 0.928452
\(638\) 0 0
\(639\) −6.42449 −0.254149
\(640\) 0 0
\(641\) 17.5793 0.694339 0.347169 0.937802i \(-0.387143\pi\)
0.347169 + 0.937802i \(0.387143\pi\)
\(642\) 0 0
\(643\) 6.21692 0.245171 0.122586 0.992458i \(-0.460881\pi\)
0.122586 + 0.992458i \(0.460881\pi\)
\(644\) 0 0
\(645\) 3.25248 0.128066
\(646\) 0 0
\(647\) −6.28683 −0.247161 −0.123580 0.992335i \(-0.539438\pi\)
−0.123580 + 0.992335i \(0.539438\pi\)
\(648\) 0 0
\(649\) −39.4832 −1.54985
\(650\) 0 0
\(651\) 4.04773 0.158643
\(652\) 0 0
\(653\) −0.335306 −0.0131215 −0.00656077 0.999978i \(-0.502088\pi\)
−0.00656077 + 0.999978i \(0.502088\pi\)
\(654\) 0 0
\(655\) −59.8821 −2.33979
\(656\) 0 0
\(657\) 7.28163 0.284083
\(658\) 0 0
\(659\) 38.7356 1.50892 0.754462 0.656343i \(-0.227898\pi\)
0.754462 + 0.656343i \(0.227898\pi\)
\(660\) 0 0
\(661\) −36.2085 −1.40835 −0.704174 0.710027i \(-0.748683\pi\)
−0.704174 + 0.710027i \(0.748683\pi\)
\(662\) 0 0
\(663\) −25.1582 −0.977065
\(664\) 0 0
\(665\) −6.51329 −0.252574
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −2.46867 −0.0954443
\(670\) 0 0
\(671\) 2.02174 0.0780483
\(672\) 0 0
\(673\) −25.6364 −0.988211 −0.494105 0.869402i \(-0.664504\pi\)
−0.494105 + 0.869402i \(0.664504\pi\)
\(674\) 0 0
\(675\) 4.73851 0.182385
\(676\) 0 0
\(677\) −36.2195 −1.39203 −0.696015 0.718027i \(-0.745045\pi\)
−0.696015 + 0.718027i \(0.745045\pi\)
\(678\) 0 0
\(679\) −13.0625 −0.501292
\(680\) 0 0
\(681\) −18.3394 −0.702768
\(682\) 0 0
\(683\) 0.374532 0.0143311 0.00716554 0.999974i \(-0.497719\pi\)
0.00716554 + 0.999974i \(0.497719\pi\)
\(684\) 0 0
\(685\) −53.9116 −2.05986
\(686\) 0 0
\(687\) 2.30393 0.0879004
\(688\) 0 0
\(689\) −22.5600 −0.859468
\(690\) 0 0
\(691\) −50.4676 −1.91988 −0.959938 0.280212i \(-0.909595\pi\)
−0.959938 + 0.280212i \(0.909595\pi\)
\(692\) 0 0
\(693\) −2.66985 −0.101419
\(694\) 0 0
\(695\) −25.3522 −0.961664
\(696\) 0 0
\(697\) 44.9778 1.70366
\(698\) 0 0
\(699\) −3.12350 −0.118142
\(700\) 0 0
\(701\) 28.2080 1.06540 0.532701 0.846304i \(-0.321177\pi\)
0.532701 + 0.846304i \(0.321177\pi\)
\(702\) 0 0
\(703\) −16.2715 −0.613690
\(704\) 0 0
\(705\) 27.3953 1.03177
\(706\) 0 0
\(707\) −4.60775 −0.173292
\(708\) 0 0
\(709\) 17.4552 0.655544 0.327772 0.944757i \(-0.393702\pi\)
0.327772 + 0.944757i \(0.393702\pi\)
\(710\) 0 0
\(711\) 6.45544 0.242098
\(712\) 0 0
\(713\) −5.32027 −0.199246
\(714\) 0 0
\(715\) 39.9642 1.49458
\(716\) 0 0
\(717\) −2.43709 −0.0910147
\(718\) 0 0
\(719\) −22.2018 −0.827986 −0.413993 0.910280i \(-0.635866\pi\)
−0.413993 + 0.910280i \(0.635866\pi\)
\(720\) 0 0
\(721\) 7.85182 0.292417
\(722\) 0 0
\(723\) −4.96582 −0.184681
\(724\) 0 0
\(725\) −4.73851 −0.175984
\(726\) 0 0
\(727\) −20.8883 −0.774706 −0.387353 0.921932i \(-0.626610\pi\)
−0.387353 + 0.921932i \(0.626610\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.18511 −0.265751
\(732\) 0 0
\(733\) −21.7263 −0.802480 −0.401240 0.915973i \(-0.631421\pi\)
−0.401240 + 0.915973i \(0.631421\pi\)
\(734\) 0 0
\(735\) 20.0383 0.739122
\(736\) 0 0
\(737\) 13.9814 0.515010
\(738\) 0 0
\(739\) −10.6222 −0.390742 −0.195371 0.980729i \(-0.562591\pi\)
−0.195371 + 0.980729i \(0.562591\pi\)
\(740\) 0 0
\(741\) 10.0113 0.367775
\(742\) 0 0
\(743\) −37.0613 −1.35965 −0.679825 0.733375i \(-0.737944\pi\)
−0.679825 + 0.733375i \(0.737944\pi\)
\(744\) 0 0
\(745\) 6.71302 0.245946
\(746\) 0 0
\(747\) 2.58965 0.0947505
\(748\) 0 0
\(749\) −9.77507 −0.357173
\(750\) 0 0
\(751\) 0.703673 0.0256774 0.0128387 0.999918i \(-0.495913\pi\)
0.0128387 + 0.999918i \(0.495913\pi\)
\(752\) 0 0
\(753\) 9.69649 0.353360
\(754\) 0 0
\(755\) −37.2552 −1.35586
\(756\) 0 0
\(757\) 10.9505 0.398001 0.199001 0.979999i \(-0.436230\pi\)
0.199001 + 0.979999i \(0.436230\pi\)
\(758\) 0 0
\(759\) 3.50921 0.127376
\(760\) 0 0
\(761\) 22.3228 0.809201 0.404600 0.914494i \(-0.367411\pi\)
0.404600 + 0.914494i \(0.367411\pi\)
\(762\) 0 0
\(763\) 7.28676 0.263798
\(764\) 0 0
\(765\) −21.5135 −0.777823
\(766\) 0 0
\(767\) 41.0600 1.48259
\(768\) 0 0
\(769\) −22.0265 −0.794297 −0.397149 0.917754i \(-0.630000\pi\)
−0.397149 + 0.917754i \(0.630000\pi\)
\(770\) 0 0
\(771\) 19.9656 0.719043
\(772\) 0 0
\(773\) 23.8648 0.858356 0.429178 0.903220i \(-0.358803\pi\)
0.429178 + 0.903220i \(0.358803\pi\)
\(774\) 0 0
\(775\) −25.2101 −0.905575
\(776\) 0 0
\(777\) −4.51262 −0.161889
\(778\) 0 0
\(779\) −17.8982 −0.641270
\(780\) 0 0
\(781\) −22.5449 −0.806720
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −13.0342 −0.465209
\(786\) 0 0
\(787\) −37.9888 −1.35415 −0.677077 0.735912i \(-0.736754\pi\)
−0.677077 + 0.735912i \(0.736754\pi\)
\(788\) 0 0
\(789\) −12.3305 −0.438978
\(790\) 0 0
\(791\) 13.0915 0.465479
\(792\) 0 0
\(793\) −2.10247 −0.0746610
\(794\) 0 0
\(795\) −19.2917 −0.684205
\(796\) 0 0
\(797\) −39.8803 −1.41263 −0.706317 0.707896i \(-0.749645\pi\)
−0.706317 + 0.707896i \(0.749645\pi\)
\(798\) 0 0
\(799\) −60.5194 −2.14102
\(800\) 0 0
\(801\) −10.7495 −0.379815
\(802\) 0 0
\(803\) 25.5528 0.901737
\(804\) 0 0
\(805\) 2.37424 0.0836808
\(806\) 0 0
\(807\) −16.4593 −0.579396
\(808\) 0 0
\(809\) 40.9930 1.44124 0.720618 0.693332i \(-0.243858\pi\)
0.720618 + 0.693332i \(0.243858\pi\)
\(810\) 0 0
\(811\) −3.05091 −0.107132 −0.0535659 0.998564i \(-0.517059\pi\)
−0.0535659 + 0.998564i \(0.517059\pi\)
\(812\) 0 0
\(813\) 0.668966 0.0234617
\(814\) 0 0
\(815\) −21.2336 −0.743779
\(816\) 0 0
\(817\) 2.85920 0.100031
\(818\) 0 0
\(819\) 2.77647 0.0970177
\(820\) 0 0
\(821\) 35.0548 1.22342 0.611710 0.791082i \(-0.290482\pi\)
0.611710 + 0.791082i \(0.290482\pi\)
\(822\) 0 0
\(823\) −10.3018 −0.359097 −0.179549 0.983749i \(-0.557464\pi\)
−0.179549 + 0.983749i \(0.557464\pi\)
\(824\) 0 0
\(825\) 16.6284 0.578928
\(826\) 0 0
\(827\) −20.8974 −0.726674 −0.363337 0.931658i \(-0.618363\pi\)
−0.363337 + 0.931658i \(0.618363\pi\)
\(828\) 0 0
\(829\) 4.34240 0.150818 0.0754089 0.997153i \(-0.475974\pi\)
0.0754089 + 0.997153i \(0.475974\pi\)
\(830\) 0 0
\(831\) 4.27134 0.148171
\(832\) 0 0
\(833\) −44.2669 −1.53376
\(834\) 0 0
\(835\) 9.27710 0.321047
\(836\) 0 0
\(837\) −5.32027 −0.183895
\(838\) 0 0
\(839\) −37.9123 −1.30888 −0.654439 0.756114i \(-0.727095\pi\)
−0.654439 + 0.756114i \(0.727095\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −0.0728644 −0.00250958
\(844\) 0 0
\(845\) −0.991587 −0.0341116
\(846\) 0 0
\(847\) −1.00014 −0.0343651
\(848\) 0 0
\(849\) 2.10058 0.0720919
\(850\) 0 0
\(851\) 5.93131 0.203323
\(852\) 0 0
\(853\) −17.6823 −0.605431 −0.302715 0.953081i \(-0.597893\pi\)
−0.302715 + 0.953081i \(0.597893\pi\)
\(854\) 0 0
\(855\) 8.56096 0.292779
\(856\) 0 0
\(857\) 0.407348 0.0139148 0.00695738 0.999976i \(-0.497785\pi\)
0.00695738 + 0.999976i \(0.497785\pi\)
\(858\) 0 0
\(859\) −22.5200 −0.768373 −0.384186 0.923256i \(-0.625518\pi\)
−0.384186 + 0.923256i \(0.625518\pi\)
\(860\) 0 0
\(861\) −4.96376 −0.169165
\(862\) 0 0
\(863\) 22.5349 0.767098 0.383549 0.923521i \(-0.374702\pi\)
0.383549 + 0.923521i \(0.374702\pi\)
\(864\) 0 0
\(865\) −4.92020 −0.167292
\(866\) 0 0
\(867\) 30.5259 1.03671
\(868\) 0 0
\(869\) 22.6535 0.768467
\(870\) 0 0
\(871\) −14.5397 −0.492659
\(872\) 0 0
\(873\) 17.1691 0.581087
\(874\) 0 0
\(875\) −0.620841 −0.0209883
\(876\) 0 0
\(877\) 15.0439 0.507997 0.253999 0.967205i \(-0.418254\pi\)
0.253999 + 0.967205i \(0.418254\pi\)
\(878\) 0 0
\(879\) 19.0717 0.643272
\(880\) 0 0
\(881\) 4.02843 0.135721 0.0678607 0.997695i \(-0.478383\pi\)
0.0678607 + 0.997695i \(0.478383\pi\)
\(882\) 0 0
\(883\) 26.3602 0.887092 0.443546 0.896252i \(-0.353720\pi\)
0.443546 + 0.896252i \(0.353720\pi\)
\(884\) 0 0
\(885\) 35.1115 1.18026
\(886\) 0 0
\(887\) −17.4075 −0.584486 −0.292243 0.956344i \(-0.594402\pi\)
−0.292243 + 0.956344i \(0.594402\pi\)
\(888\) 0 0
\(889\) −9.76330 −0.327451
\(890\) 0 0
\(891\) 3.50921 0.117563
\(892\) 0 0
\(893\) 24.0827 0.805898
\(894\) 0 0
\(895\) −3.41884 −0.114279
\(896\) 0 0
\(897\) −3.64935 −0.121848
\(898\) 0 0
\(899\) 5.32027 0.177441
\(900\) 0 0
\(901\) 42.6176 1.41980
\(902\) 0 0
\(903\) 0.792951 0.0263878
\(904\) 0 0
\(905\) −49.0730 −1.63124
\(906\) 0 0
\(907\) −36.5466 −1.21351 −0.606756 0.794889i \(-0.707529\pi\)
−0.606756 + 0.794889i \(0.707529\pi\)
\(908\) 0 0
\(909\) 6.05636 0.200877
\(910\) 0 0
\(911\) 32.4069 1.07369 0.536845 0.843681i \(-0.319616\pi\)
0.536845 + 0.843681i \(0.319616\pi\)
\(912\) 0 0
\(913\) 9.08765 0.300757
\(914\) 0 0
\(915\) −1.79788 −0.0594362
\(916\) 0 0
\(917\) −14.5992 −0.482107
\(918\) 0 0
\(919\) −4.49915 −0.148413 −0.0742066 0.997243i \(-0.523642\pi\)
−0.0742066 + 0.997243i \(0.523642\pi\)
\(920\) 0 0
\(921\) 26.6122 0.876900
\(922\) 0 0
\(923\) 23.4452 0.771709
\(924\) 0 0
\(925\) 28.1056 0.924106
\(926\) 0 0
\(927\) −10.3203 −0.338963
\(928\) 0 0
\(929\) −28.8104 −0.945240 −0.472620 0.881266i \(-0.656692\pi\)
−0.472620 + 0.881266i \(0.656692\pi\)
\(930\) 0 0
\(931\) 17.6153 0.577318
\(932\) 0 0
\(933\) −3.92862 −0.128617
\(934\) 0 0
\(935\) −75.4954 −2.46897
\(936\) 0 0
\(937\) −6.81247 −0.222554 −0.111277 0.993789i \(-0.535494\pi\)
−0.111277 + 0.993789i \(0.535494\pi\)
\(938\) 0 0
\(939\) −10.1563 −0.331439
\(940\) 0 0
\(941\) 3.27509 0.106765 0.0533824 0.998574i \(-0.483000\pi\)
0.0533824 + 0.998574i \(0.483000\pi\)
\(942\) 0 0
\(943\) 6.52429 0.212460
\(944\) 0 0
\(945\) 2.37424 0.0772339
\(946\) 0 0
\(947\) −26.3180 −0.855219 −0.427610 0.903964i \(-0.640644\pi\)
−0.427610 + 0.903964i \(0.640644\pi\)
\(948\) 0 0
\(949\) −26.5732 −0.862602
\(950\) 0 0
\(951\) 21.2960 0.690570
\(952\) 0 0
\(953\) 49.3912 1.59994 0.799968 0.600042i \(-0.204850\pi\)
0.799968 + 0.600042i \(0.204850\pi\)
\(954\) 0 0
\(955\) −4.18851 −0.135537
\(956\) 0 0
\(957\) −3.50921 −0.113437
\(958\) 0 0
\(959\) −13.1436 −0.424428
\(960\) 0 0
\(961\) −2.69473 −0.0869269
\(962\) 0 0
\(963\) 12.8482 0.414027
\(964\) 0 0
\(965\) −49.8325 −1.60417
\(966\) 0 0
\(967\) −32.0459 −1.03053 −0.515264 0.857031i \(-0.672306\pi\)
−0.515264 + 0.857031i \(0.672306\pi\)
\(968\) 0 0
\(969\) −18.9122 −0.607546
\(970\) 0 0
\(971\) 8.64105 0.277304 0.138652 0.990341i \(-0.455723\pi\)
0.138652 + 0.990341i \(0.455723\pi\)
\(972\) 0 0
\(973\) −6.18084 −0.198149
\(974\) 0 0
\(975\) −17.2925 −0.553802
\(976\) 0 0
\(977\) 6.10450 0.195300 0.0976502 0.995221i \(-0.468867\pi\)
0.0976502 + 0.995221i \(0.468867\pi\)
\(978\) 0 0
\(979\) −37.7223 −1.20561
\(980\) 0 0
\(981\) −9.57760 −0.305789
\(982\) 0 0
\(983\) −37.5267 −1.19692 −0.598458 0.801154i \(-0.704220\pi\)
−0.598458 + 0.801154i \(0.704220\pi\)
\(984\) 0 0
\(985\) −33.9593 −1.08203
\(986\) 0 0
\(987\) 6.67893 0.212593
\(988\) 0 0
\(989\) −1.04224 −0.0331414
\(990\) 0 0
\(991\) −21.9560 −0.697457 −0.348728 0.937224i \(-0.613386\pi\)
−0.348728 + 0.937224i \(0.613386\pi\)
\(992\) 0 0
\(993\) 21.2770 0.675205
\(994\) 0 0
\(995\) −64.0076 −2.02918
\(996\) 0 0
\(997\) −4.70970 −0.149158 −0.0745788 0.997215i \(-0.523761\pi\)
−0.0745788 + 0.997215i \(0.523761\pi\)
\(998\) 0 0
\(999\) 5.93131 0.187658
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 \(a_p\))