Properties

Label 8004.2.a.j.1.12
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 1.12
Root \(1.72426\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+1.72426 q^{5}\) \(+4.78449 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+1.72426 q^{5}\) \(+4.78449 q^{7}\) \(+1.00000 q^{9}\) \(-0.855035 q^{11}\) \(+0.789026 q^{13}\) \(+1.72426 q^{15}\) \(-0.187005 q^{17}\) \(+2.96694 q^{19}\) \(+4.78449 q^{21}\) \(+1.00000 q^{23}\) \(-2.02694 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+6.56119 q^{31}\) \(-0.855035 q^{33}\) \(+8.24969 q^{35}\) \(+6.29864 q^{37}\) \(+0.789026 q^{39}\) \(-5.32568 q^{41}\) \(+4.21930 q^{43}\) \(+1.72426 q^{45}\) \(-5.43940 q^{47}\) \(+15.8914 q^{49}\) \(-0.187005 q^{51}\) \(+0.912333 q^{53}\) \(-1.47430 q^{55}\) \(+2.96694 q^{57}\) \(-4.84785 q^{59}\) \(-7.62097 q^{61}\) \(+4.78449 q^{63}\) \(+1.36048 q^{65}\) \(-12.2144 q^{67}\) \(+1.00000 q^{69}\) \(-5.33636 q^{71}\) \(-1.62179 q^{73}\) \(-2.02694 q^{75}\) \(-4.09091 q^{77}\) \(+12.3349 q^{79}\) \(+1.00000 q^{81}\) \(+13.5924 q^{83}\) \(-0.322445 q^{85}\) \(-1.00000 q^{87}\) \(+8.62527 q^{89}\) \(+3.77509 q^{91}\) \(+6.56119 q^{93}\) \(+5.11577 q^{95}\) \(-6.23401 q^{97}\) \(-0.855035 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.72426 0.771111 0.385555 0.922685i \(-0.374010\pi\)
0.385555 + 0.922685i \(0.374010\pi\)
\(6\) 0 0
\(7\) 4.78449 1.80837 0.904184 0.427143i \(-0.140480\pi\)
0.904184 + 0.427143i \(0.140480\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.855035 −0.257803 −0.128901 0.991657i \(-0.541145\pi\)
−0.128901 + 0.991657i \(0.541145\pi\)
\(12\) 0 0
\(13\) 0.789026 0.218836 0.109418 0.993996i \(-0.465101\pi\)
0.109418 + 0.993996i \(0.465101\pi\)
\(14\) 0 0
\(15\) 1.72426 0.445201
\(16\) 0 0
\(17\) −0.187005 −0.0453555 −0.0226777 0.999743i \(-0.507219\pi\)
−0.0226777 + 0.999743i \(0.507219\pi\)
\(18\) 0 0
\(19\) 2.96694 0.680663 0.340332 0.940305i \(-0.389461\pi\)
0.340332 + 0.940305i \(0.389461\pi\)
\(20\) 0 0
\(21\) 4.78449 1.04406
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.02694 −0.405388
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 6.56119 1.17842 0.589212 0.807978i \(-0.299438\pi\)
0.589212 + 0.807978i \(0.299438\pi\)
\(32\) 0 0
\(33\) −0.855035 −0.148843
\(34\) 0 0
\(35\) 8.24969 1.39445
\(36\) 0 0
\(37\) 6.29864 1.03549 0.517745 0.855535i \(-0.326772\pi\)
0.517745 + 0.855535i \(0.326772\pi\)
\(38\) 0 0
\(39\) 0.789026 0.126345
\(40\) 0 0
\(41\) −5.32568 −0.831732 −0.415866 0.909426i \(-0.636521\pi\)
−0.415866 + 0.909426i \(0.636521\pi\)
\(42\) 0 0
\(43\) 4.21930 0.643437 0.321718 0.946835i \(-0.395740\pi\)
0.321718 + 0.946835i \(0.395740\pi\)
\(44\) 0 0
\(45\) 1.72426 0.257037
\(46\) 0 0
\(47\) −5.43940 −0.793418 −0.396709 0.917944i \(-0.629848\pi\)
−0.396709 + 0.917944i \(0.629848\pi\)
\(48\) 0 0
\(49\) 15.8914 2.27020
\(50\) 0 0
\(51\) −0.187005 −0.0261860
\(52\) 0 0
\(53\) 0.912333 0.125319 0.0626593 0.998035i \(-0.480042\pi\)
0.0626593 + 0.998035i \(0.480042\pi\)
\(54\) 0 0
\(55\) −1.47430 −0.198795
\(56\) 0 0
\(57\) 2.96694 0.392981
\(58\) 0 0
\(59\) −4.84785 −0.631137 −0.315568 0.948903i \(-0.602195\pi\)
−0.315568 + 0.948903i \(0.602195\pi\)
\(60\) 0 0
\(61\) −7.62097 −0.975765 −0.487883 0.872909i \(-0.662231\pi\)
−0.487883 + 0.872909i \(0.662231\pi\)
\(62\) 0 0
\(63\) 4.78449 0.602789
\(64\) 0 0
\(65\) 1.36048 0.168747
\(66\) 0 0
\(67\) −12.2144 −1.49223 −0.746114 0.665818i \(-0.768083\pi\)
−0.746114 + 0.665818i \(0.768083\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −5.33636 −0.633310 −0.316655 0.948541i \(-0.602560\pi\)
−0.316655 + 0.948541i \(0.602560\pi\)
\(72\) 0 0
\(73\) −1.62179 −0.189816 −0.0949080 0.995486i \(-0.530256\pi\)
−0.0949080 + 0.995486i \(0.530256\pi\)
\(74\) 0 0
\(75\) −2.02694 −0.234051
\(76\) 0 0
\(77\) −4.09091 −0.466202
\(78\) 0 0
\(79\) 12.3349 1.38779 0.693894 0.720077i \(-0.255894\pi\)
0.693894 + 0.720077i \(0.255894\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 13.5924 1.49196 0.745981 0.665967i \(-0.231981\pi\)
0.745981 + 0.665967i \(0.231981\pi\)
\(84\) 0 0
\(85\) −0.322445 −0.0349741
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 8.62527 0.914277 0.457138 0.889396i \(-0.348874\pi\)
0.457138 + 0.889396i \(0.348874\pi\)
\(90\) 0 0
\(91\) 3.77509 0.395737
\(92\) 0 0
\(93\) 6.56119 0.680364
\(94\) 0 0
\(95\) 5.11577 0.524867
\(96\) 0 0
\(97\) −6.23401 −0.632968 −0.316484 0.948598i \(-0.602502\pi\)
−0.316484 + 0.948598i \(0.602502\pi\)
\(98\) 0 0
\(99\) −0.855035 −0.0859343
\(100\) 0 0
\(101\) 3.94404 0.392447 0.196224 0.980559i \(-0.437132\pi\)
0.196224 + 0.980559i \(0.437132\pi\)
\(102\) 0 0
\(103\) 12.7156 1.25290 0.626452 0.779460i \(-0.284507\pi\)
0.626452 + 0.779460i \(0.284507\pi\)
\(104\) 0 0
\(105\) 8.24969 0.805087
\(106\) 0 0
\(107\) 5.38985 0.521056 0.260528 0.965466i \(-0.416103\pi\)
0.260528 + 0.965466i \(0.416103\pi\)
\(108\) 0 0
\(109\) 12.3483 1.18275 0.591375 0.806397i \(-0.298585\pi\)
0.591375 + 0.806397i \(0.298585\pi\)
\(110\) 0 0
\(111\) 6.29864 0.597840
\(112\) 0 0
\(113\) −9.88638 −0.930032 −0.465016 0.885302i \(-0.653951\pi\)
−0.465016 + 0.885302i \(0.653951\pi\)
\(114\) 0 0
\(115\) 1.72426 0.160788
\(116\) 0 0
\(117\) 0.789026 0.0729455
\(118\) 0 0
\(119\) −0.894726 −0.0820194
\(120\) 0 0
\(121\) −10.2689 −0.933538
\(122\) 0 0
\(123\) −5.32568 −0.480200
\(124\) 0 0
\(125\) −12.1162 −1.08371
\(126\) 0 0
\(127\) −0.375952 −0.0333604 −0.0166802 0.999861i \(-0.505310\pi\)
−0.0166802 + 0.999861i \(0.505310\pi\)
\(128\) 0 0
\(129\) 4.21930 0.371488
\(130\) 0 0
\(131\) 15.9504 1.39359 0.696795 0.717271i \(-0.254609\pi\)
0.696795 + 0.717271i \(0.254609\pi\)
\(132\) 0 0
\(133\) 14.1953 1.23089
\(134\) 0 0
\(135\) 1.72426 0.148400
\(136\) 0 0
\(137\) −1.97401 −0.168651 −0.0843256 0.996438i \(-0.526874\pi\)
−0.0843256 + 0.996438i \(0.526874\pi\)
\(138\) 0 0
\(139\) 15.1152 1.28205 0.641027 0.767518i \(-0.278509\pi\)
0.641027 + 0.767518i \(0.278509\pi\)
\(140\) 0 0
\(141\) −5.43940 −0.458080
\(142\) 0 0
\(143\) −0.674645 −0.0564166
\(144\) 0 0
\(145\) −1.72426 −0.143192
\(146\) 0 0
\(147\) 15.8914 1.31070
\(148\) 0 0
\(149\) −9.27676 −0.759982 −0.379991 0.924990i \(-0.624073\pi\)
−0.379991 + 0.924990i \(0.624073\pi\)
\(150\) 0 0
\(151\) 3.16741 0.257760 0.128880 0.991660i \(-0.458862\pi\)
0.128880 + 0.991660i \(0.458862\pi\)
\(152\) 0 0
\(153\) −0.187005 −0.0151185
\(154\) 0 0
\(155\) 11.3132 0.908696
\(156\) 0 0
\(157\) 3.77975 0.301657 0.150828 0.988560i \(-0.451806\pi\)
0.150828 + 0.988560i \(0.451806\pi\)
\(158\) 0 0
\(159\) 0.912333 0.0723527
\(160\) 0 0
\(161\) 4.78449 0.377071
\(162\) 0 0
\(163\) −16.4883 −1.29146 −0.645732 0.763565i \(-0.723447\pi\)
−0.645732 + 0.763565i \(0.723447\pi\)
\(164\) 0 0
\(165\) −1.47430 −0.114774
\(166\) 0 0
\(167\) −4.69469 −0.363286 −0.181643 0.983365i \(-0.558141\pi\)
−0.181643 + 0.983365i \(0.558141\pi\)
\(168\) 0 0
\(169\) −12.3774 −0.952111
\(170\) 0 0
\(171\) 2.96694 0.226888
\(172\) 0 0
\(173\) 9.84890 0.748798 0.374399 0.927268i \(-0.377849\pi\)
0.374399 + 0.927268i \(0.377849\pi\)
\(174\) 0 0
\(175\) −9.69788 −0.733091
\(176\) 0 0
\(177\) −4.84785 −0.364387
\(178\) 0 0
\(179\) −20.7742 −1.55274 −0.776370 0.630278i \(-0.782941\pi\)
−0.776370 + 0.630278i \(0.782941\pi\)
\(180\) 0 0
\(181\) −12.8267 −0.953403 −0.476701 0.879065i \(-0.658168\pi\)
−0.476701 + 0.879065i \(0.658168\pi\)
\(182\) 0 0
\(183\) −7.62097 −0.563358
\(184\) 0 0
\(185\) 10.8605 0.798477
\(186\) 0 0
\(187\) 0.159896 0.0116928
\(188\) 0 0
\(189\) 4.78449 0.348021
\(190\) 0 0
\(191\) 4.62227 0.334456 0.167228 0.985918i \(-0.446518\pi\)
0.167228 + 0.985918i \(0.446518\pi\)
\(192\) 0 0
\(193\) 9.93990 0.715489 0.357745 0.933819i \(-0.383546\pi\)
0.357745 + 0.933819i \(0.383546\pi\)
\(194\) 0 0
\(195\) 1.36048 0.0974262
\(196\) 0 0
\(197\) −0.958271 −0.0682740 −0.0341370 0.999417i \(-0.510868\pi\)
−0.0341370 + 0.999417i \(0.510868\pi\)
\(198\) 0 0
\(199\) 6.03481 0.427797 0.213898 0.976856i \(-0.431384\pi\)
0.213898 + 0.976856i \(0.431384\pi\)
\(200\) 0 0
\(201\) −12.2144 −0.861539
\(202\) 0 0
\(203\) −4.78449 −0.335806
\(204\) 0 0
\(205\) −9.18284 −0.641357
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −2.53684 −0.175477
\(210\) 0 0
\(211\) −20.4935 −1.41083 −0.705414 0.708796i \(-0.749239\pi\)
−0.705414 + 0.708796i \(0.749239\pi\)
\(212\) 0 0
\(213\) −5.33636 −0.365642
\(214\) 0 0
\(215\) 7.27515 0.496161
\(216\) 0 0
\(217\) 31.3920 2.13103
\(218\) 0 0
\(219\) −1.62179 −0.109590
\(220\) 0 0
\(221\) −0.147552 −0.00992542
\(222\) 0 0
\(223\) −2.12672 −0.142415 −0.0712077 0.997462i \(-0.522685\pi\)
−0.0712077 + 0.997462i \(0.522685\pi\)
\(224\) 0 0
\(225\) −2.02694 −0.135129
\(226\) 0 0
\(227\) −27.8931 −1.85133 −0.925666 0.378341i \(-0.876495\pi\)
−0.925666 + 0.378341i \(0.876495\pi\)
\(228\) 0 0
\(229\) 19.5863 1.29430 0.647150 0.762363i \(-0.275961\pi\)
0.647150 + 0.762363i \(0.275961\pi\)
\(230\) 0 0
\(231\) −4.09091 −0.269162
\(232\) 0 0
\(233\) −18.6241 −1.22011 −0.610053 0.792360i \(-0.708852\pi\)
−0.610053 + 0.792360i \(0.708852\pi\)
\(234\) 0 0
\(235\) −9.37892 −0.611814
\(236\) 0 0
\(237\) 12.3349 0.801240
\(238\) 0 0
\(239\) −0.990350 −0.0640604 −0.0320302 0.999487i \(-0.510197\pi\)
−0.0320302 + 0.999487i \(0.510197\pi\)
\(240\) 0 0
\(241\) 6.19931 0.399333 0.199666 0.979864i \(-0.436014\pi\)
0.199666 + 0.979864i \(0.436014\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 27.4008 1.75057
\(246\) 0 0
\(247\) 2.34099 0.148954
\(248\) 0 0
\(249\) 13.5924 0.861385
\(250\) 0 0
\(251\) −2.55696 −0.161394 −0.0806968 0.996739i \(-0.525715\pi\)
−0.0806968 + 0.996739i \(0.525715\pi\)
\(252\) 0 0
\(253\) −0.855035 −0.0537556
\(254\) 0 0
\(255\) −0.322445 −0.0201923
\(256\) 0 0
\(257\) −3.28746 −0.205066 −0.102533 0.994730i \(-0.532695\pi\)
−0.102533 + 0.994730i \(0.532695\pi\)
\(258\) 0 0
\(259\) 30.1358 1.87255
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 6.29116 0.387930 0.193965 0.981008i \(-0.437865\pi\)
0.193965 + 0.981008i \(0.437865\pi\)
\(264\) 0 0
\(265\) 1.57310 0.0966345
\(266\) 0 0
\(267\) 8.62527 0.527858
\(268\) 0 0
\(269\) −13.4159 −0.817983 −0.408991 0.912538i \(-0.634119\pi\)
−0.408991 + 0.912538i \(0.634119\pi\)
\(270\) 0 0
\(271\) 3.11664 0.189322 0.0946611 0.995510i \(-0.469823\pi\)
0.0946611 + 0.995510i \(0.469823\pi\)
\(272\) 0 0
\(273\) 3.77509 0.228479
\(274\) 0 0
\(275\) 1.73311 0.104510
\(276\) 0 0
\(277\) 28.7265 1.72601 0.863004 0.505197i \(-0.168580\pi\)
0.863004 + 0.505197i \(0.168580\pi\)
\(278\) 0 0
\(279\) 6.56119 0.392808
\(280\) 0 0
\(281\) −0.0574064 −0.00342458 −0.00171229 0.999999i \(-0.500545\pi\)
−0.00171229 + 0.999999i \(0.500545\pi\)
\(282\) 0 0
\(283\) −5.36549 −0.318945 −0.159473 0.987202i \(-0.550979\pi\)
−0.159473 + 0.987202i \(0.550979\pi\)
\(284\) 0 0
\(285\) 5.11577 0.303032
\(286\) 0 0
\(287\) −25.4807 −1.50408
\(288\) 0 0
\(289\) −16.9650 −0.997943
\(290\) 0 0
\(291\) −6.23401 −0.365444
\(292\) 0 0
\(293\) −8.53152 −0.498417 −0.249208 0.968450i \(-0.580170\pi\)
−0.249208 + 0.968450i \(0.580170\pi\)
\(294\) 0 0
\(295\) −8.35894 −0.486676
\(296\) 0 0
\(297\) −0.855035 −0.0496142
\(298\) 0 0
\(299\) 0.789026 0.0456305
\(300\) 0 0
\(301\) 20.1872 1.16357
\(302\) 0 0
\(303\) 3.94404 0.226579
\(304\) 0 0
\(305\) −13.1405 −0.752423
\(306\) 0 0
\(307\) −24.4870 −1.39755 −0.698774 0.715343i \(-0.746270\pi\)
−0.698774 + 0.715343i \(0.746270\pi\)
\(308\) 0 0
\(309\) 12.7156 0.723364
\(310\) 0 0
\(311\) 15.8095 0.896477 0.448238 0.893914i \(-0.352052\pi\)
0.448238 + 0.893914i \(0.352052\pi\)
\(312\) 0 0
\(313\) −1.65880 −0.0937610 −0.0468805 0.998901i \(-0.514928\pi\)
−0.0468805 + 0.998901i \(0.514928\pi\)
\(314\) 0 0
\(315\) 8.24969 0.464817
\(316\) 0 0
\(317\) −19.0431 −1.06957 −0.534785 0.844988i \(-0.679607\pi\)
−0.534785 + 0.844988i \(0.679607\pi\)
\(318\) 0 0
\(319\) 0.855035 0.0478728
\(320\) 0 0
\(321\) 5.38985 0.300832
\(322\) 0 0
\(323\) −0.554834 −0.0308718
\(324\) 0 0
\(325\) −1.59931 −0.0887137
\(326\) 0 0
\(327\) 12.3483 0.682861
\(328\) 0 0
\(329\) −26.0248 −1.43479
\(330\) 0 0
\(331\) −10.8932 −0.598744 −0.299372 0.954136i \(-0.596777\pi\)
−0.299372 + 0.954136i \(0.596777\pi\)
\(332\) 0 0
\(333\) 6.29864 0.345163
\(334\) 0 0
\(335\) −21.0608 −1.15067
\(336\) 0 0
\(337\) 24.5134 1.33533 0.667664 0.744463i \(-0.267294\pi\)
0.667664 + 0.744463i \(0.267294\pi\)
\(338\) 0 0
\(339\) −9.88638 −0.536954
\(340\) 0 0
\(341\) −5.61005 −0.303801
\(342\) 0 0
\(343\) 42.5407 2.29698
\(344\) 0 0
\(345\) 1.72426 0.0928308
\(346\) 0 0
\(347\) 5.01255 0.269088 0.134544 0.990908i \(-0.457043\pi\)
0.134544 + 0.990908i \(0.457043\pi\)
\(348\) 0 0
\(349\) −26.8924 −1.43952 −0.719760 0.694223i \(-0.755748\pi\)
−0.719760 + 0.694223i \(0.755748\pi\)
\(350\) 0 0
\(351\) 0.789026 0.0421151
\(352\) 0 0
\(353\) −6.79532 −0.361679 −0.180839 0.983513i \(-0.557881\pi\)
−0.180839 + 0.983513i \(0.557881\pi\)
\(354\) 0 0
\(355\) −9.20126 −0.488352
\(356\) 0 0
\(357\) −0.894726 −0.0473539
\(358\) 0 0
\(359\) −3.11426 −0.164364 −0.0821822 0.996617i \(-0.526189\pi\)
−0.0821822 + 0.996617i \(0.526189\pi\)
\(360\) 0 0
\(361\) −10.1973 −0.536698
\(362\) 0 0
\(363\) −10.2689 −0.538978
\(364\) 0 0
\(365\) −2.79638 −0.146369
\(366\) 0 0
\(367\) −19.5113 −1.01848 −0.509242 0.860624i \(-0.670074\pi\)
−0.509242 + 0.860624i \(0.670074\pi\)
\(368\) 0 0
\(369\) −5.32568 −0.277244
\(370\) 0 0
\(371\) 4.36505 0.226622
\(372\) 0 0
\(373\) −15.1686 −0.785400 −0.392700 0.919667i \(-0.628459\pi\)
−0.392700 + 0.919667i \(0.628459\pi\)
\(374\) 0 0
\(375\) −12.1162 −0.625680
\(376\) 0 0
\(377\) −0.789026 −0.0406369
\(378\) 0 0
\(379\) −15.3925 −0.790657 −0.395329 0.918540i \(-0.629369\pi\)
−0.395329 + 0.918540i \(0.629369\pi\)
\(380\) 0 0
\(381\) −0.375952 −0.0192606
\(382\) 0 0
\(383\) −13.6175 −0.695820 −0.347910 0.937528i \(-0.613109\pi\)
−0.347910 + 0.937528i \(0.613109\pi\)
\(384\) 0 0
\(385\) −7.05378 −0.359494
\(386\) 0 0
\(387\) 4.21930 0.214479
\(388\) 0 0
\(389\) 32.8638 1.66626 0.833130 0.553077i \(-0.186547\pi\)
0.833130 + 0.553077i \(0.186547\pi\)
\(390\) 0 0
\(391\) −0.187005 −0.00945727
\(392\) 0 0
\(393\) 15.9504 0.804589
\(394\) 0 0
\(395\) 21.2686 1.07014
\(396\) 0 0
\(397\) −3.54562 −0.177949 −0.0889747 0.996034i \(-0.528359\pi\)
−0.0889747 + 0.996034i \(0.528359\pi\)
\(398\) 0 0
\(399\) 14.1953 0.710654
\(400\) 0 0
\(401\) 24.1091 1.20395 0.601975 0.798515i \(-0.294381\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(402\) 0 0
\(403\) 5.17695 0.257882
\(404\) 0 0
\(405\) 1.72426 0.0856790
\(406\) 0 0
\(407\) −5.38556 −0.266952
\(408\) 0 0
\(409\) −9.70146 −0.479706 −0.239853 0.970809i \(-0.577099\pi\)
−0.239853 + 0.970809i \(0.577099\pi\)
\(410\) 0 0
\(411\) −1.97401 −0.0973708
\(412\) 0 0
\(413\) −23.1945 −1.14133
\(414\) 0 0
\(415\) 23.4368 1.15047
\(416\) 0 0
\(417\) 15.1152 0.740194
\(418\) 0 0
\(419\) 2.47064 0.120699 0.0603495 0.998177i \(-0.480778\pi\)
0.0603495 + 0.998177i \(0.480778\pi\)
\(420\) 0 0
\(421\) 33.7375 1.64426 0.822132 0.569297i \(-0.192785\pi\)
0.822132 + 0.569297i \(0.192785\pi\)
\(422\) 0 0
\(423\) −5.43940 −0.264473
\(424\) 0 0
\(425\) 0.379049 0.0183866
\(426\) 0 0
\(427\) −36.4625 −1.76454
\(428\) 0 0
\(429\) −0.674645 −0.0325722
\(430\) 0 0
\(431\) 27.6550 1.33209 0.666047 0.745910i \(-0.267985\pi\)
0.666047 + 0.745910i \(0.267985\pi\)
\(432\) 0 0
\(433\) 11.3758 0.546688 0.273344 0.961916i \(-0.411870\pi\)
0.273344 + 0.961916i \(0.411870\pi\)
\(434\) 0 0
\(435\) −1.72426 −0.0826718
\(436\) 0 0
\(437\) 2.96694 0.141928
\(438\) 0 0
\(439\) −8.93034 −0.426222 −0.213111 0.977028i \(-0.568360\pi\)
−0.213111 + 0.977028i \(0.568360\pi\)
\(440\) 0 0
\(441\) 15.8914 0.756732
\(442\) 0 0
\(443\) 40.3086 1.91512 0.957560 0.288233i \(-0.0930678\pi\)
0.957560 + 0.288233i \(0.0930678\pi\)
\(444\) 0 0
\(445\) 14.8722 0.705009
\(446\) 0 0
\(447\) −9.27676 −0.438776
\(448\) 0 0
\(449\) −0.878885 −0.0414772 −0.0207386 0.999785i \(-0.506602\pi\)
−0.0207386 + 0.999785i \(0.506602\pi\)
\(450\) 0 0
\(451\) 4.55364 0.214423
\(452\) 0 0
\(453\) 3.16741 0.148818
\(454\) 0 0
\(455\) 6.50922 0.305157
\(456\) 0 0
\(457\) −6.28449 −0.293976 −0.146988 0.989138i \(-0.546958\pi\)
−0.146988 + 0.989138i \(0.546958\pi\)
\(458\) 0 0
\(459\) −0.187005 −0.00872866
\(460\) 0 0
\(461\) 1.29120 0.0601373 0.0300686 0.999548i \(-0.490427\pi\)
0.0300686 + 0.999548i \(0.490427\pi\)
\(462\) 0 0
\(463\) −16.6541 −0.773981 −0.386990 0.922084i \(-0.626485\pi\)
−0.386990 + 0.922084i \(0.626485\pi\)
\(464\) 0 0
\(465\) 11.3132 0.524636
\(466\) 0 0
\(467\) 22.6947 1.05018 0.525092 0.851045i \(-0.324031\pi\)
0.525092 + 0.851045i \(0.324031\pi\)
\(468\) 0 0
\(469\) −58.4398 −2.69850
\(470\) 0 0
\(471\) 3.77975 0.174162
\(472\) 0 0
\(473\) −3.60765 −0.165880
\(474\) 0 0
\(475\) −6.01381 −0.275933
\(476\) 0 0
\(477\) 0.912333 0.0417729
\(478\) 0 0
\(479\) −37.6079 −1.71835 −0.859174 0.511684i \(-0.829022\pi\)
−0.859174 + 0.511684i \(0.829022\pi\)
\(480\) 0 0
\(481\) 4.96979 0.226603
\(482\) 0 0
\(483\) 4.78449 0.217702
\(484\) 0 0
\(485\) −10.7490 −0.488089
\(486\) 0 0
\(487\) 38.8011 1.75824 0.879122 0.476597i \(-0.158130\pi\)
0.879122 + 0.476597i \(0.158130\pi\)
\(488\) 0 0
\(489\) −16.4883 −0.745627
\(490\) 0 0
\(491\) −13.5077 −0.609596 −0.304798 0.952417i \(-0.598589\pi\)
−0.304798 + 0.952417i \(0.598589\pi\)
\(492\) 0 0
\(493\) 0.187005 0.00842230
\(494\) 0 0
\(495\) −1.47430 −0.0662649
\(496\) 0 0
\(497\) −25.5318 −1.14526
\(498\) 0 0
\(499\) −13.2207 −0.591838 −0.295919 0.955213i \(-0.595626\pi\)
−0.295919 + 0.955213i \(0.595626\pi\)
\(500\) 0 0
\(501\) −4.69469 −0.209743
\(502\) 0 0
\(503\) 30.6579 1.36697 0.683485 0.729965i \(-0.260464\pi\)
0.683485 + 0.729965i \(0.260464\pi\)
\(504\) 0 0
\(505\) 6.80054 0.302620
\(506\) 0 0
\(507\) −12.3774 −0.549701
\(508\) 0 0
\(509\) 21.3888 0.948044 0.474022 0.880513i \(-0.342802\pi\)
0.474022 + 0.880513i \(0.342802\pi\)
\(510\) 0 0
\(511\) −7.75943 −0.343257
\(512\) 0 0
\(513\) 2.96694 0.130994
\(514\) 0 0
\(515\) 21.9249 0.966127
\(516\) 0 0
\(517\) 4.65088 0.204546
\(518\) 0 0
\(519\) 9.84890 0.432319
\(520\) 0 0
\(521\) −10.4546 −0.458024 −0.229012 0.973424i \(-0.573549\pi\)
−0.229012 + 0.973424i \(0.573549\pi\)
\(522\) 0 0
\(523\) 22.7567 0.995082 0.497541 0.867440i \(-0.334236\pi\)
0.497541 + 0.867440i \(0.334236\pi\)
\(524\) 0 0
\(525\) −9.69788 −0.423250
\(526\) 0 0
\(527\) −1.22698 −0.0534480
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −4.84785 −0.210379
\(532\) 0 0
\(533\) −4.20210 −0.182013
\(534\) 0 0
\(535\) 9.29348 0.401792
\(536\) 0 0
\(537\) −20.7742 −0.896475
\(538\) 0 0
\(539\) −13.5877 −0.585263
\(540\) 0 0
\(541\) 10.2618 0.441188 0.220594 0.975366i \(-0.429200\pi\)
0.220594 + 0.975366i \(0.429200\pi\)
\(542\) 0 0
\(543\) −12.8267 −0.550447
\(544\) 0 0
\(545\) 21.2916 0.912031
\(546\) 0 0
\(547\) 30.4075 1.30013 0.650064 0.759879i \(-0.274742\pi\)
0.650064 + 0.759879i \(0.274742\pi\)
\(548\) 0 0
\(549\) −7.62097 −0.325255
\(550\) 0 0
\(551\) −2.96694 −0.126396
\(552\) 0 0
\(553\) 59.0164 2.50963
\(554\) 0 0
\(555\) 10.8605 0.461001
\(556\) 0 0
\(557\) 18.4155 0.780288 0.390144 0.920754i \(-0.372425\pi\)
0.390144 + 0.920754i \(0.372425\pi\)
\(558\) 0 0
\(559\) 3.32913 0.140807
\(560\) 0 0
\(561\) 0.159896 0.00675082
\(562\) 0 0
\(563\) 35.3898 1.49150 0.745752 0.666224i \(-0.232090\pi\)
0.745752 + 0.666224i \(0.232090\pi\)
\(564\) 0 0
\(565\) −17.0467 −0.717158
\(566\) 0 0
\(567\) 4.78449 0.200930
\(568\) 0 0
\(569\) −8.54102 −0.358058 −0.179029 0.983844i \(-0.557296\pi\)
−0.179029 + 0.983844i \(0.557296\pi\)
\(570\) 0 0
\(571\) −27.8102 −1.16382 −0.581910 0.813253i \(-0.697694\pi\)
−0.581910 + 0.813253i \(0.697694\pi\)
\(572\) 0 0
\(573\) 4.62227 0.193098
\(574\) 0 0
\(575\) −2.02694 −0.0845292
\(576\) 0 0
\(577\) −11.2146 −0.466869 −0.233435 0.972372i \(-0.574996\pi\)
−0.233435 + 0.972372i \(0.574996\pi\)
\(578\) 0 0
\(579\) 9.93990 0.413088
\(580\) 0 0
\(581\) 65.0328 2.69802
\(582\) 0 0
\(583\) −0.780077 −0.0323075
\(584\) 0 0
\(585\) 1.36048 0.0562490
\(586\) 0 0
\(587\) −34.7689 −1.43506 −0.717532 0.696525i \(-0.754728\pi\)
−0.717532 + 0.696525i \(0.754728\pi\)
\(588\) 0 0
\(589\) 19.4667 0.802110
\(590\) 0 0
\(591\) −0.958271 −0.0394180
\(592\) 0 0
\(593\) −46.3761 −1.90444 −0.952220 0.305414i \(-0.901205\pi\)
−0.952220 + 0.305414i \(0.901205\pi\)
\(594\) 0 0
\(595\) −1.54274 −0.0632460
\(596\) 0 0
\(597\) 6.03481 0.246988
\(598\) 0 0
\(599\) 24.1121 0.985192 0.492596 0.870258i \(-0.336048\pi\)
0.492596 + 0.870258i \(0.336048\pi\)
\(600\) 0 0
\(601\) 11.4601 0.467467 0.233733 0.972301i \(-0.424906\pi\)
0.233733 + 0.972301i \(0.424906\pi\)
\(602\) 0 0
\(603\) −12.2144 −0.497410
\(604\) 0 0
\(605\) −17.7062 −0.719861
\(606\) 0 0
\(607\) 20.7087 0.840540 0.420270 0.907399i \(-0.361935\pi\)
0.420270 + 0.907399i \(0.361935\pi\)
\(608\) 0 0
\(609\) −4.78449 −0.193877
\(610\) 0 0
\(611\) −4.29183 −0.173629
\(612\) 0 0
\(613\) 9.31303 0.376150 0.188075 0.982155i \(-0.439775\pi\)
0.188075 + 0.982155i \(0.439775\pi\)
\(614\) 0 0
\(615\) −9.18284 −0.370288
\(616\) 0 0
\(617\) 25.2876 1.01804 0.509021 0.860754i \(-0.330008\pi\)
0.509021 + 0.860754i \(0.330008\pi\)
\(618\) 0 0
\(619\) −18.2419 −0.733202 −0.366601 0.930378i \(-0.619479\pi\)
−0.366601 + 0.930378i \(0.619479\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 41.2675 1.65335
\(624\) 0 0
\(625\) −10.7568 −0.430273
\(626\) 0 0
\(627\) −2.53684 −0.101312
\(628\) 0 0
\(629\) −1.17788 −0.0469651
\(630\) 0 0
\(631\) −4.39633 −0.175015 −0.0875075 0.996164i \(-0.527890\pi\)
−0.0875075 + 0.996164i \(0.527890\pi\)
\(632\) 0 0
\(633\) −20.4935 −0.814542
\(634\) 0 0
\(635\) −0.648238 −0.0257245
\(636\) 0 0
\(637\) 12.5387 0.496801
\(638\) 0 0
\(639\) −5.33636 −0.211103
\(640\) 0 0
\(641\) −47.4049 −1.87238 −0.936190 0.351495i \(-0.885674\pi\)
−0.936190 + 0.351495i \(0.885674\pi\)
\(642\) 0 0
\(643\) −24.9620 −0.984407 −0.492203 0.870480i \(-0.663808\pi\)
−0.492203 + 0.870480i \(0.663808\pi\)
\(644\) 0 0
\(645\) 7.27515 0.286459
\(646\) 0 0
\(647\) 39.9094 1.56900 0.784501 0.620128i \(-0.212919\pi\)
0.784501 + 0.620128i \(0.212919\pi\)
\(648\) 0 0
\(649\) 4.14509 0.162709
\(650\) 0 0
\(651\) 31.3920 1.23035
\(652\) 0 0
\(653\) −37.5504 −1.46946 −0.734731 0.678359i \(-0.762692\pi\)
−0.734731 + 0.678359i \(0.762692\pi\)
\(654\) 0 0
\(655\) 27.5025 1.07461
\(656\) 0 0
\(657\) −1.62179 −0.0632720
\(658\) 0 0
\(659\) 8.63524 0.336381 0.168191 0.985755i \(-0.446208\pi\)
0.168191 + 0.985755i \(0.446208\pi\)
\(660\) 0 0
\(661\) 37.8152 1.47084 0.735421 0.677610i \(-0.236984\pi\)
0.735421 + 0.677610i \(0.236984\pi\)
\(662\) 0 0
\(663\) −0.147552 −0.00573045
\(664\) 0 0
\(665\) 24.4764 0.949152
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −2.12672 −0.0822236
\(670\) 0 0
\(671\) 6.51620 0.251555
\(672\) 0 0
\(673\) 0.773706 0.0298242 0.0149121 0.999889i \(-0.495253\pi\)
0.0149121 + 0.999889i \(0.495253\pi\)
\(674\) 0 0
\(675\) −2.02694 −0.0780170
\(676\) 0 0
\(677\) 26.1809 1.00621 0.503106 0.864225i \(-0.332191\pi\)
0.503106 + 0.864225i \(0.332191\pi\)
\(678\) 0 0
\(679\) −29.8266 −1.14464
\(680\) 0 0
\(681\) −27.8931 −1.06887
\(682\) 0 0
\(683\) −30.0959 −1.15159 −0.575793 0.817595i \(-0.695307\pi\)
−0.575793 + 0.817595i \(0.695307\pi\)
\(684\) 0 0
\(685\) −3.40370 −0.130049
\(686\) 0 0
\(687\) 19.5863 0.747264
\(688\) 0 0
\(689\) 0.719855 0.0274243
\(690\) 0 0
\(691\) 27.1835 1.03411 0.517054 0.855953i \(-0.327029\pi\)
0.517054 + 0.855953i \(0.327029\pi\)
\(692\) 0 0
\(693\) −4.09091 −0.155401
\(694\) 0 0
\(695\) 26.0625 0.988606
\(696\) 0 0
\(697\) 0.995931 0.0377236
\(698\) 0 0
\(699\) −18.6241 −0.704429
\(700\) 0 0
\(701\) 11.4391 0.432049 0.216025 0.976388i \(-0.430691\pi\)
0.216025 + 0.976388i \(0.430691\pi\)
\(702\) 0 0
\(703\) 18.6877 0.704819
\(704\) 0 0
\(705\) −9.37892 −0.353231
\(706\) 0 0
\(707\) 18.8703 0.709689
\(708\) 0 0
\(709\) 23.3696 0.877665 0.438833 0.898569i \(-0.355392\pi\)
0.438833 + 0.898569i \(0.355392\pi\)
\(710\) 0 0
\(711\) 12.3349 0.462596
\(712\) 0 0
\(713\) 6.56119 0.245719
\(714\) 0 0
\(715\) −1.16326 −0.0435035
\(716\) 0 0
\(717\) −0.990350 −0.0369853
\(718\) 0 0
\(719\) −29.9344 −1.11637 −0.558183 0.829718i \(-0.688501\pi\)
−0.558183 + 0.829718i \(0.688501\pi\)
\(720\) 0 0
\(721\) 60.8376 2.26571
\(722\) 0 0
\(723\) 6.19931 0.230555
\(724\) 0 0
\(725\) 2.02694 0.0752787
\(726\) 0 0
\(727\) −18.1607 −0.673542 −0.336771 0.941587i \(-0.609335\pi\)
−0.336771 + 0.941587i \(0.609335\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.789031 −0.0291834
\(732\) 0 0
\(733\) −20.1354 −0.743718 −0.371859 0.928289i \(-0.621280\pi\)
−0.371859 + 0.928289i \(0.621280\pi\)
\(734\) 0 0
\(735\) 27.4008 1.01069
\(736\) 0 0
\(737\) 10.4438 0.384701
\(738\) 0 0
\(739\) −41.6587 −1.53244 −0.766220 0.642578i \(-0.777865\pi\)
−0.766220 + 0.642578i \(0.777865\pi\)
\(740\) 0 0
\(741\) 2.34099 0.0859986
\(742\) 0 0
\(743\) −31.6571 −1.16138 −0.580692 0.814123i \(-0.697218\pi\)
−0.580692 + 0.814123i \(0.697218\pi\)
\(744\) 0 0
\(745\) −15.9955 −0.586030
\(746\) 0 0
\(747\) 13.5924 0.497321
\(748\) 0 0
\(749\) 25.7877 0.942262
\(750\) 0 0
\(751\) −1.73648 −0.0633652 −0.0316826 0.999498i \(-0.510087\pi\)
−0.0316826 + 0.999498i \(0.510087\pi\)
\(752\) 0 0
\(753\) −2.55696 −0.0931807
\(754\) 0 0
\(755\) 5.46142 0.198761
\(756\) 0 0
\(757\) 46.3917 1.68613 0.843067 0.537809i \(-0.180748\pi\)
0.843067 + 0.537809i \(0.180748\pi\)
\(758\) 0 0
\(759\) −0.855035 −0.0310358
\(760\) 0 0
\(761\) −0.568486 −0.0206076 −0.0103038 0.999947i \(-0.503280\pi\)
−0.0103038 + 0.999947i \(0.503280\pi\)
\(762\) 0 0
\(763\) 59.0802 2.13885
\(764\) 0 0
\(765\) −0.322445 −0.0116580
\(766\) 0 0
\(767\) −3.82508 −0.138116
\(768\) 0 0
\(769\) 2.39867 0.0864984 0.0432492 0.999064i \(-0.486229\pi\)
0.0432492 + 0.999064i \(0.486229\pi\)
\(770\) 0 0
\(771\) −3.28746 −0.118395
\(772\) 0 0
\(773\) 12.1579 0.437289 0.218645 0.975805i \(-0.429836\pi\)
0.218645 + 0.975805i \(0.429836\pi\)
\(774\) 0 0
\(775\) −13.2991 −0.477719
\(776\) 0 0
\(777\) 30.1358 1.08111
\(778\) 0 0
\(779\) −15.8010 −0.566129
\(780\) 0 0
\(781\) 4.56278 0.163269
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 6.51725 0.232611
\(786\) 0 0
\(787\) 20.6856 0.737362 0.368681 0.929556i \(-0.379809\pi\)
0.368681 + 0.929556i \(0.379809\pi\)
\(788\) 0 0
\(789\) 6.29116 0.223971
\(790\) 0 0
\(791\) −47.3013 −1.68184
\(792\) 0 0
\(793\) −6.01314 −0.213533
\(794\) 0 0
\(795\) 1.57310 0.0557920
\(796\) 0 0
\(797\) −42.1025 −1.49135 −0.745673 0.666312i \(-0.767872\pi\)
−0.745673 + 0.666312i \(0.767872\pi\)
\(798\) 0 0
\(799\) 1.01720 0.0359859
\(800\) 0 0
\(801\) 8.62527 0.304759
\(802\) 0 0
\(803\) 1.38669 0.0489351
\(804\) 0 0
\(805\) 8.24969 0.290763
\(806\) 0 0
\(807\) −13.4159 −0.472262
\(808\) 0 0
\(809\) −1.00091 −0.0351902 −0.0175951 0.999845i \(-0.505601\pi\)
−0.0175951 + 0.999845i \(0.505601\pi\)
\(810\) 0 0
\(811\) 16.0430 0.563345 0.281673 0.959511i \(-0.409111\pi\)
0.281673 + 0.959511i \(0.409111\pi\)
\(812\) 0 0
\(813\) 3.11664 0.109305
\(814\) 0 0
\(815\) −28.4301 −0.995861
\(816\) 0 0
\(817\) 12.5184 0.437964
\(818\) 0 0
\(819\) 3.77509 0.131912
\(820\) 0 0
\(821\) 28.6972 1.00154 0.500769 0.865581i \(-0.333051\pi\)
0.500769 + 0.865581i \(0.333051\pi\)
\(822\) 0 0
\(823\) −44.7762 −1.56080 −0.780400 0.625280i \(-0.784985\pi\)
−0.780400 + 0.625280i \(0.784985\pi\)
\(824\) 0 0
\(825\) 1.73311 0.0603390
\(826\) 0 0
\(827\) 2.69922 0.0938611 0.0469305 0.998898i \(-0.485056\pi\)
0.0469305 + 0.998898i \(0.485056\pi\)
\(828\) 0 0
\(829\) 49.0230 1.70264 0.851319 0.524648i \(-0.175803\pi\)
0.851319 + 0.524648i \(0.175803\pi\)
\(830\) 0 0
\(831\) 28.7265 0.996511
\(832\) 0 0
\(833\) −2.97177 −0.102966
\(834\) 0 0
\(835\) −8.09484 −0.280134
\(836\) 0 0
\(837\) 6.56119 0.226788
\(838\) 0 0
\(839\) −29.9215 −1.03300 −0.516502 0.856286i \(-0.672766\pi\)
−0.516502 + 0.856286i \(0.672766\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −0.0574064 −0.00197718
\(844\) 0 0
\(845\) −21.3419 −0.734183
\(846\) 0 0
\(847\) −49.1315 −1.68818
\(848\) 0 0
\(849\) −5.36549 −0.184143
\(850\) 0 0
\(851\) 6.29864 0.215914
\(852\) 0 0
\(853\) 9.79614 0.335414 0.167707 0.985837i \(-0.446364\pi\)
0.167707 + 0.985837i \(0.446364\pi\)
\(854\) 0 0
\(855\) 5.11577 0.174956
\(856\) 0 0
\(857\) −38.1628 −1.30362 −0.651809 0.758383i \(-0.725990\pi\)
−0.651809 + 0.758383i \(0.725990\pi\)
\(858\) 0 0
\(859\) −10.8970 −0.371801 −0.185900 0.982569i \(-0.559520\pi\)
−0.185900 + 0.982569i \(0.559520\pi\)
\(860\) 0 0
\(861\) −25.4807 −0.868379
\(862\) 0 0
\(863\) −33.0375 −1.12461 −0.562304 0.826930i \(-0.690085\pi\)
−0.562304 + 0.826930i \(0.690085\pi\)
\(864\) 0 0
\(865\) 16.9820 0.577406
\(866\) 0 0
\(867\) −16.9650 −0.576163
\(868\) 0 0
\(869\) −10.5468 −0.357776
\(870\) 0 0
\(871\) −9.63749 −0.326554
\(872\) 0 0
\(873\) −6.23401 −0.210989
\(874\) 0 0
\(875\) −57.9701 −1.95975
\(876\) 0 0
\(877\) −14.4941 −0.489431 −0.244716 0.969595i \(-0.578695\pi\)
−0.244716 + 0.969595i \(0.578695\pi\)
\(878\) 0 0
\(879\) −8.53152 −0.287761
\(880\) 0 0
\(881\) 33.5872 1.13158 0.565791 0.824549i \(-0.308571\pi\)
0.565791 + 0.824549i \(0.308571\pi\)
\(882\) 0 0
\(883\) −6.58717 −0.221676 −0.110838 0.993839i \(-0.535353\pi\)
−0.110838 + 0.993839i \(0.535353\pi\)
\(884\) 0 0
\(885\) −8.35894 −0.280983
\(886\) 0 0
\(887\) 43.3703 1.45623 0.728116 0.685454i \(-0.240396\pi\)
0.728116 + 0.685454i \(0.240396\pi\)
\(888\) 0 0
\(889\) −1.79874 −0.0603278
\(890\) 0 0
\(891\) −0.855035 −0.0286448
\(892\) 0 0
\(893\) −16.1384 −0.540051
\(894\) 0 0
\(895\) −35.8201 −1.19733
\(896\) 0 0
\(897\) 0.789026 0.0263448
\(898\) 0 0
\(899\) −6.56119 −0.218828
\(900\) 0 0
\(901\) −0.170611 −0.00568388
\(902\) 0 0
\(903\) 20.1872 0.671788
\(904\) 0 0
\(905\) −22.1166 −0.735179
\(906\) 0 0
\(907\) 12.5959 0.418240 0.209120 0.977890i \(-0.432940\pi\)
0.209120 + 0.977890i \(0.432940\pi\)
\(908\) 0 0
\(909\) 3.94404 0.130816
\(910\) 0 0
\(911\) −39.4043 −1.30552 −0.652762 0.757563i \(-0.726390\pi\)
−0.652762 + 0.757563i \(0.726390\pi\)
\(912\) 0 0
\(913\) −11.6220 −0.384632
\(914\) 0 0
\(915\) −13.1405 −0.434412
\(916\) 0 0
\(917\) 76.3144 2.52012
\(918\) 0 0
\(919\) −44.8385 −1.47909 −0.739544 0.673109i \(-0.764959\pi\)
−0.739544 + 0.673109i \(0.764959\pi\)
\(920\) 0 0
\(921\) −24.4870 −0.806874
\(922\) 0 0
\(923\) −4.21053 −0.138591
\(924\) 0 0
\(925\) −12.7670 −0.419775
\(926\) 0 0
\(927\) 12.7156 0.417634
\(928\) 0 0
\(929\) −54.9624 −1.80326 −0.901630 0.432509i \(-0.857628\pi\)
−0.901630 + 0.432509i \(0.857628\pi\)
\(930\) 0 0
\(931\) 47.1488 1.54524
\(932\) 0 0
\(933\) 15.8095 0.517581
\(934\) 0 0
\(935\) 0.275702 0.00901642
\(936\) 0 0
\(937\) −26.8384 −0.876771 −0.438385 0.898787i \(-0.644449\pi\)
−0.438385 + 0.898787i \(0.644449\pi\)
\(938\) 0 0
\(939\) −1.65880 −0.0541330
\(940\) 0 0
\(941\) 9.20204 0.299978 0.149989 0.988688i \(-0.452076\pi\)
0.149989 + 0.988688i \(0.452076\pi\)
\(942\) 0 0
\(943\) −5.32568 −0.173428
\(944\) 0 0
\(945\) 8.24969 0.268362
\(946\) 0 0
\(947\) −27.3168 −0.887677 −0.443838 0.896107i \(-0.646384\pi\)
−0.443838 + 0.896107i \(0.646384\pi\)
\(948\) 0 0
\(949\) −1.27963 −0.0415386
\(950\) 0 0
\(951\) −19.0431 −0.617516
\(952\) 0 0
\(953\) −15.6897 −0.508240 −0.254120 0.967173i \(-0.581786\pi\)
−0.254120 + 0.967173i \(0.581786\pi\)
\(954\) 0 0
\(955\) 7.96999 0.257903
\(956\) 0 0
\(957\) 0.855035 0.0276394
\(958\) 0 0
\(959\) −9.44464 −0.304983
\(960\) 0 0
\(961\) 12.0492 0.388684
\(962\) 0 0
\(963\) 5.38985 0.173685
\(964\) 0 0
\(965\) 17.1389 0.551722
\(966\) 0 0
\(967\) −42.0218 −1.35133 −0.675665 0.737209i \(-0.736143\pi\)
−0.675665 + 0.737209i \(0.736143\pi\)
\(968\) 0 0
\(969\) −0.554834 −0.0178238
\(970\) 0 0
\(971\) −37.8204 −1.21371 −0.606857 0.794811i \(-0.707570\pi\)
−0.606857 + 0.794811i \(0.707570\pi\)
\(972\) 0 0
\(973\) 72.3185 2.31843
\(974\) 0 0
\(975\) −1.59931 −0.0512189
\(976\) 0 0
\(977\) −52.9911 −1.69534 −0.847668 0.530526i \(-0.821994\pi\)
−0.847668 + 0.530526i \(0.821994\pi\)
\(978\) 0 0
\(979\) −7.37491 −0.235703
\(980\) 0 0
\(981\) 12.3483 0.394250
\(982\) 0 0
\(983\) −15.8026 −0.504026 −0.252013 0.967724i \(-0.581093\pi\)
−0.252013 + 0.967724i \(0.581093\pi\)
\(984\) 0 0
\(985\) −1.65230 −0.0526468
\(986\) 0 0
\(987\) −26.0248 −0.828378
\(988\) 0 0
\(989\) 4.21930 0.134166
\(990\) 0 0
\(991\) −27.4667 −0.872508 −0.436254 0.899824i \(-0.643695\pi\)
−0.436254 + 0.899824i \(0.643695\pi\)
\(992\) 0 0
\(993\) −10.8932 −0.345685
\(994\) 0 0
\(995\) 10.4056 0.329879
\(996\) 0 0
\(997\) 1.35585 0.0429403 0.0214702 0.999769i \(-0.493165\pi\)
0.0214702 + 0.999769i \(0.493165\pi\)
\(998\) 0 0
\(999\) 6.29864 0.199280
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 \(a_p\))