Properties

Label 8024.2.a.y.1.9
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.40425 q^{3}\) \(+3.37446 q^{5}\) \(-3.92495 q^{7}\) \(-1.02809 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.40425 q^{3}\) \(+3.37446 q^{5}\) \(-3.92495 q^{7}\) \(-1.02809 q^{9}\) \(+1.19459 q^{11}\) \(+1.76914 q^{13}\) \(-4.73858 q^{15}\) \(-1.00000 q^{17}\) \(-5.97168 q^{19}\) \(+5.51160 q^{21}\) \(-1.06460 q^{23}\) \(+6.38698 q^{25}\) \(+5.65643 q^{27}\) \(+5.79547 q^{29}\) \(+0.924101 q^{31}\) \(-1.67751 q^{33}\) \(-13.2446 q^{35}\) \(-6.65188 q^{37}\) \(-2.48431 q^{39}\) \(+8.89664 q^{41}\) \(+8.28892 q^{43}\) \(-3.46925 q^{45}\) \(-1.68499 q^{47}\) \(+8.40520 q^{49}\) \(+1.40425 q^{51}\) \(+3.41618 q^{53}\) \(+4.03111 q^{55}\) \(+8.38571 q^{57}\) \(-1.00000 q^{59}\) \(-6.47999 q^{61}\) \(+4.03519 q^{63}\) \(+5.96988 q^{65}\) \(-1.63189 q^{67}\) \(+1.49497 q^{69}\) \(-11.1438 q^{71}\) \(+12.4653 q^{73}\) \(-8.96890 q^{75}\) \(-4.68872 q^{77}\) \(-11.1434 q^{79}\) \(-4.85877 q^{81}\) \(+9.00811 q^{83}\) \(-3.37446 q^{85}\) \(-8.13827 q^{87}\) \(-11.8666 q^{89}\) \(-6.94377 q^{91}\) \(-1.29767 q^{93}\) \(-20.1512 q^{95}\) \(-17.1397 q^{97}\) \(-1.22815 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.40425 −0.810743 −0.405371 0.914152i \(-0.632858\pi\)
−0.405371 + 0.914152i \(0.632858\pi\)
\(4\) 0 0
\(5\) 3.37446 1.50910 0.754552 0.656240i \(-0.227854\pi\)
0.754552 + 0.656240i \(0.227854\pi\)
\(6\) 0 0
\(7\) −3.92495 −1.48349 −0.741745 0.670682i \(-0.766002\pi\)
−0.741745 + 0.670682i \(0.766002\pi\)
\(8\) 0 0
\(9\) −1.02809 −0.342696
\(10\) 0 0
\(11\) 1.19459 0.360184 0.180092 0.983650i \(-0.442360\pi\)
0.180092 + 0.983650i \(0.442360\pi\)
\(12\) 0 0
\(13\) 1.76914 0.490670 0.245335 0.969438i \(-0.421102\pi\)
0.245335 + 0.969438i \(0.421102\pi\)
\(14\) 0 0
\(15\) −4.73858 −1.22350
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −5.97168 −1.37000 −0.684998 0.728545i \(-0.740197\pi\)
−0.684998 + 0.728545i \(0.740197\pi\)
\(20\) 0 0
\(21\) 5.51160 1.20273
\(22\) 0 0
\(23\) −1.06460 −0.221985 −0.110993 0.993821i \(-0.535403\pi\)
−0.110993 + 0.993821i \(0.535403\pi\)
\(24\) 0 0
\(25\) 6.38698 1.27740
\(26\) 0 0
\(27\) 5.65643 1.08858
\(28\) 0 0
\(29\) 5.79547 1.07619 0.538096 0.842884i \(-0.319144\pi\)
0.538096 + 0.842884i \(0.319144\pi\)
\(30\) 0 0
\(31\) 0.924101 0.165973 0.0829867 0.996551i \(-0.473554\pi\)
0.0829867 + 0.996551i \(0.473554\pi\)
\(32\) 0 0
\(33\) −1.67751 −0.292016
\(34\) 0 0
\(35\) −13.2446 −2.23874
\(36\) 0 0
\(37\) −6.65188 −1.09356 −0.546781 0.837275i \(-0.684147\pi\)
−0.546781 + 0.837275i \(0.684147\pi\)
\(38\) 0 0
\(39\) −2.48431 −0.397807
\(40\) 0 0
\(41\) 8.89664 1.38942 0.694711 0.719289i \(-0.255532\pi\)
0.694711 + 0.719289i \(0.255532\pi\)
\(42\) 0 0
\(43\) 8.28892 1.26405 0.632024 0.774949i \(-0.282224\pi\)
0.632024 + 0.774949i \(0.282224\pi\)
\(44\) 0 0
\(45\) −3.46925 −0.517165
\(46\) 0 0
\(47\) −1.68499 −0.245781 −0.122891 0.992420i \(-0.539216\pi\)
−0.122891 + 0.992420i \(0.539216\pi\)
\(48\) 0 0
\(49\) 8.40520 1.20074
\(50\) 0 0
\(51\) 1.40425 0.196634
\(52\) 0 0
\(53\) 3.41618 0.469249 0.234624 0.972086i \(-0.424614\pi\)
0.234624 + 0.972086i \(0.424614\pi\)
\(54\) 0 0
\(55\) 4.03111 0.543555
\(56\) 0 0
\(57\) 8.38571 1.11071
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −6.47999 −0.829677 −0.414839 0.909895i \(-0.636162\pi\)
−0.414839 + 0.909895i \(0.636162\pi\)
\(62\) 0 0
\(63\) 4.03519 0.508387
\(64\) 0 0
\(65\) 5.96988 0.740473
\(66\) 0 0
\(67\) −1.63189 −0.199368 −0.0996838 0.995019i \(-0.531783\pi\)
−0.0996838 + 0.995019i \(0.531783\pi\)
\(68\) 0 0
\(69\) 1.49497 0.179973
\(70\) 0 0
\(71\) −11.1438 −1.32253 −0.661265 0.750152i \(-0.729980\pi\)
−0.661265 + 0.750152i \(0.729980\pi\)
\(72\) 0 0
\(73\) 12.4653 1.45896 0.729478 0.684005i \(-0.239763\pi\)
0.729478 + 0.684005i \(0.239763\pi\)
\(74\) 0 0
\(75\) −8.96890 −1.03564
\(76\) 0 0
\(77\) −4.68872 −0.534329
\(78\) 0 0
\(79\) −11.1434 −1.25373 −0.626863 0.779129i \(-0.715662\pi\)
−0.626863 + 0.779129i \(0.715662\pi\)
\(80\) 0 0
\(81\) −4.85877 −0.539863
\(82\) 0 0
\(83\) 9.00811 0.988768 0.494384 0.869244i \(-0.335394\pi\)
0.494384 + 0.869244i \(0.335394\pi\)
\(84\) 0 0
\(85\) −3.37446 −0.366012
\(86\) 0 0
\(87\) −8.13827 −0.872515
\(88\) 0 0
\(89\) −11.8666 −1.25786 −0.628928 0.777464i \(-0.716506\pi\)
−0.628928 + 0.777464i \(0.716506\pi\)
\(90\) 0 0
\(91\) −6.94377 −0.727905
\(92\) 0 0
\(93\) −1.29767 −0.134562
\(94\) 0 0
\(95\) −20.1512 −2.06747
\(96\) 0 0
\(97\) −17.1397 −1.74028 −0.870138 0.492808i \(-0.835970\pi\)
−0.870138 + 0.492808i \(0.835970\pi\)
\(98\) 0 0
\(99\) −1.22815 −0.123434
\(100\) 0 0
\(101\) 6.12710 0.609670 0.304835 0.952405i \(-0.401399\pi\)
0.304835 + 0.952405i \(0.401399\pi\)
\(102\) 0 0
\(103\) −18.7949 −1.85191 −0.925957 0.377629i \(-0.876740\pi\)
−0.925957 + 0.377629i \(0.876740\pi\)
\(104\) 0 0
\(105\) 18.5987 1.81504
\(106\) 0 0
\(107\) 7.62309 0.736952 0.368476 0.929637i \(-0.379880\pi\)
0.368476 + 0.929637i \(0.379880\pi\)
\(108\) 0 0
\(109\) 17.8941 1.71394 0.856970 0.515367i \(-0.172344\pi\)
0.856970 + 0.515367i \(0.172344\pi\)
\(110\) 0 0
\(111\) 9.34089 0.886598
\(112\) 0 0
\(113\) −0.957182 −0.0900441 −0.0450220 0.998986i \(-0.514336\pi\)
−0.0450220 + 0.998986i \(0.514336\pi\)
\(114\) 0 0
\(115\) −3.59246 −0.334999
\(116\) 0 0
\(117\) −1.81883 −0.168151
\(118\) 0 0
\(119\) 3.92495 0.359799
\(120\) 0 0
\(121\) −9.57294 −0.870268
\(122\) 0 0
\(123\) −12.4931 −1.12646
\(124\) 0 0
\(125\) 4.68031 0.418619
\(126\) 0 0
\(127\) 16.1541 1.43345 0.716723 0.697358i \(-0.245641\pi\)
0.716723 + 0.697358i \(0.245641\pi\)
\(128\) 0 0
\(129\) −11.6397 −1.02482
\(130\) 0 0
\(131\) −4.95328 −0.432770 −0.216385 0.976308i \(-0.569427\pi\)
−0.216385 + 0.976308i \(0.569427\pi\)
\(132\) 0 0
\(133\) 23.4385 2.03238
\(134\) 0 0
\(135\) 19.0874 1.64278
\(136\) 0 0
\(137\) −3.57758 −0.305653 −0.152827 0.988253i \(-0.548838\pi\)
−0.152827 + 0.988253i \(0.548838\pi\)
\(138\) 0 0
\(139\) 7.16757 0.607946 0.303973 0.952681i \(-0.401687\pi\)
0.303973 + 0.952681i \(0.401687\pi\)
\(140\) 0 0
\(141\) 2.36615 0.199265
\(142\) 0 0
\(143\) 2.11340 0.176732
\(144\) 0 0
\(145\) 19.5566 1.62409
\(146\) 0 0
\(147\) −11.8030 −0.973494
\(148\) 0 0
\(149\) −13.3050 −1.08998 −0.544992 0.838441i \(-0.683467\pi\)
−0.544992 + 0.838441i \(0.683467\pi\)
\(150\) 0 0
\(151\) −4.88886 −0.397850 −0.198925 0.980015i \(-0.563745\pi\)
−0.198925 + 0.980015i \(0.563745\pi\)
\(152\) 0 0
\(153\) 1.02809 0.0831161
\(154\) 0 0
\(155\) 3.11834 0.250471
\(156\) 0 0
\(157\) 2.47404 0.197450 0.0987251 0.995115i \(-0.468524\pi\)
0.0987251 + 0.995115i \(0.468524\pi\)
\(158\) 0 0
\(159\) −4.79716 −0.380440
\(160\) 0 0
\(161\) 4.17851 0.329313
\(162\) 0 0
\(163\) −5.17630 −0.405439 −0.202719 0.979237i \(-0.564978\pi\)
−0.202719 + 0.979237i \(0.564978\pi\)
\(164\) 0 0
\(165\) −5.66068 −0.440683
\(166\) 0 0
\(167\) −21.3190 −1.64971 −0.824857 0.565342i \(-0.808744\pi\)
−0.824857 + 0.565342i \(0.808744\pi\)
\(168\) 0 0
\(169\) −9.87015 −0.759243
\(170\) 0 0
\(171\) 6.13941 0.469493
\(172\) 0 0
\(173\) −23.9668 −1.82217 −0.911083 0.412223i \(-0.864752\pi\)
−0.911083 + 0.412223i \(0.864752\pi\)
\(174\) 0 0
\(175\) −25.0686 −1.89500
\(176\) 0 0
\(177\) 1.40425 0.105550
\(178\) 0 0
\(179\) 9.00636 0.673167 0.336583 0.941654i \(-0.390729\pi\)
0.336583 + 0.941654i \(0.390729\pi\)
\(180\) 0 0
\(181\) 6.12584 0.455330 0.227665 0.973740i \(-0.426891\pi\)
0.227665 + 0.973740i \(0.426891\pi\)
\(182\) 0 0
\(183\) 9.09950 0.672655
\(184\) 0 0
\(185\) −22.4465 −1.65030
\(186\) 0 0
\(187\) −1.19459 −0.0873574
\(188\) 0 0
\(189\) −22.2012 −1.61490
\(190\) 0 0
\(191\) 9.98130 0.722222 0.361111 0.932523i \(-0.382398\pi\)
0.361111 + 0.932523i \(0.382398\pi\)
\(192\) 0 0
\(193\) −24.5420 −1.76657 −0.883286 0.468835i \(-0.844674\pi\)
−0.883286 + 0.468835i \(0.844674\pi\)
\(194\) 0 0
\(195\) −8.38319 −0.600333
\(196\) 0 0
\(197\) 0.312390 0.0222569 0.0111284 0.999938i \(-0.496458\pi\)
0.0111284 + 0.999938i \(0.496458\pi\)
\(198\) 0 0
\(199\) −21.0450 −1.49184 −0.745919 0.666037i \(-0.767989\pi\)
−0.745919 + 0.666037i \(0.767989\pi\)
\(200\) 0 0
\(201\) 2.29158 0.161636
\(202\) 0 0
\(203\) −22.7469 −1.59652
\(204\) 0 0
\(205\) 30.0213 2.09678
\(206\) 0 0
\(207\) 1.09451 0.0760736
\(208\) 0 0
\(209\) −7.13373 −0.493451
\(210\) 0 0
\(211\) −19.7315 −1.35837 −0.679187 0.733965i \(-0.737668\pi\)
−0.679187 + 0.733965i \(0.737668\pi\)
\(212\) 0 0
\(213\) 15.6487 1.07223
\(214\) 0 0
\(215\) 27.9706 1.90758
\(216\) 0 0
\(217\) −3.62705 −0.246220
\(218\) 0 0
\(219\) −17.5044 −1.18284
\(220\) 0 0
\(221\) −1.76914 −0.119005
\(222\) 0 0
\(223\) −3.67333 −0.245984 −0.122992 0.992408i \(-0.539249\pi\)
−0.122992 + 0.992408i \(0.539249\pi\)
\(224\) 0 0
\(225\) −6.56638 −0.437759
\(226\) 0 0
\(227\) −10.6693 −0.708147 −0.354073 0.935218i \(-0.615204\pi\)
−0.354073 + 0.935218i \(0.615204\pi\)
\(228\) 0 0
\(229\) 25.7563 1.70203 0.851014 0.525144i \(-0.175988\pi\)
0.851014 + 0.525144i \(0.175988\pi\)
\(230\) 0 0
\(231\) 6.58412 0.433204
\(232\) 0 0
\(233\) 14.6812 0.961800 0.480900 0.876776i \(-0.340310\pi\)
0.480900 + 0.876776i \(0.340310\pi\)
\(234\) 0 0
\(235\) −5.68594 −0.370910
\(236\) 0 0
\(237\) 15.6480 1.01645
\(238\) 0 0
\(239\) −1.22425 −0.0791900 −0.0395950 0.999216i \(-0.512607\pi\)
−0.0395950 + 0.999216i \(0.512607\pi\)
\(240\) 0 0
\(241\) −8.75573 −0.564006 −0.282003 0.959414i \(-0.590999\pi\)
−0.282003 + 0.959414i \(0.590999\pi\)
\(242\) 0 0
\(243\) −10.1464 −0.650891
\(244\) 0 0
\(245\) 28.3630 1.81205
\(246\) 0 0
\(247\) −10.5647 −0.672217
\(248\) 0 0
\(249\) −12.6496 −0.801637
\(250\) 0 0
\(251\) 0.410423 0.0259057 0.0129528 0.999916i \(-0.495877\pi\)
0.0129528 + 0.999916i \(0.495877\pi\)
\(252\) 0 0
\(253\) −1.27177 −0.0799555
\(254\) 0 0
\(255\) 4.73858 0.296741
\(256\) 0 0
\(257\) −16.6060 −1.03585 −0.517927 0.855425i \(-0.673296\pi\)
−0.517927 + 0.855425i \(0.673296\pi\)
\(258\) 0 0
\(259\) 26.1083 1.62229
\(260\) 0 0
\(261\) −5.95826 −0.368807
\(262\) 0 0
\(263\) −26.8406 −1.65506 −0.827531 0.561419i \(-0.810255\pi\)
−0.827531 + 0.561419i \(0.810255\pi\)
\(264\) 0 0
\(265\) 11.5278 0.708145
\(266\) 0 0
\(267\) 16.6636 1.01980
\(268\) 0 0
\(269\) −26.6572 −1.62532 −0.812659 0.582739i \(-0.801981\pi\)
−0.812659 + 0.582739i \(0.801981\pi\)
\(270\) 0 0
\(271\) 11.6422 0.707216 0.353608 0.935394i \(-0.384955\pi\)
0.353608 + 0.935394i \(0.384955\pi\)
\(272\) 0 0
\(273\) 9.75077 0.590143
\(274\) 0 0
\(275\) 7.62985 0.460097
\(276\) 0 0
\(277\) −4.23304 −0.254339 −0.127169 0.991881i \(-0.540589\pi\)
−0.127169 + 0.991881i \(0.540589\pi\)
\(278\) 0 0
\(279\) −0.950058 −0.0568785
\(280\) 0 0
\(281\) −5.87365 −0.350392 −0.175196 0.984534i \(-0.556056\pi\)
−0.175196 + 0.984534i \(0.556056\pi\)
\(282\) 0 0
\(283\) 28.2391 1.67864 0.839321 0.543637i \(-0.182953\pi\)
0.839321 + 0.543637i \(0.182953\pi\)
\(284\) 0 0
\(285\) 28.2972 1.67618
\(286\) 0 0
\(287\) −34.9188 −2.06119
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 24.0684 1.41092
\(292\) 0 0
\(293\) 20.2227 1.18142 0.590712 0.806882i \(-0.298847\pi\)
0.590712 + 0.806882i \(0.298847\pi\)
\(294\) 0 0
\(295\) −3.37446 −0.196469
\(296\) 0 0
\(297\) 6.75715 0.392089
\(298\) 0 0
\(299\) −1.88343 −0.108922
\(300\) 0 0
\(301\) −32.5336 −1.87520
\(302\) 0 0
\(303\) −8.60397 −0.494285
\(304\) 0 0
\(305\) −21.8665 −1.25207
\(306\) 0 0
\(307\) −14.1471 −0.807418 −0.403709 0.914887i \(-0.632279\pi\)
−0.403709 + 0.914887i \(0.632279\pi\)
\(308\) 0 0
\(309\) 26.3927 1.50143
\(310\) 0 0
\(311\) 8.64731 0.490344 0.245172 0.969480i \(-0.421156\pi\)
0.245172 + 0.969480i \(0.421156\pi\)
\(312\) 0 0
\(313\) 30.9936 1.75186 0.875932 0.482435i \(-0.160247\pi\)
0.875932 + 0.482435i \(0.160247\pi\)
\(314\) 0 0
\(315\) 13.6166 0.767209
\(316\) 0 0
\(317\) 33.6027 1.88732 0.943659 0.330919i \(-0.107359\pi\)
0.943659 + 0.330919i \(0.107359\pi\)
\(318\) 0 0
\(319\) 6.92324 0.387627
\(320\) 0 0
\(321\) −10.7047 −0.597479
\(322\) 0 0
\(323\) 5.97168 0.332273
\(324\) 0 0
\(325\) 11.2994 0.626780
\(326\) 0 0
\(327\) −25.1277 −1.38956
\(328\) 0 0
\(329\) 6.61351 0.364614
\(330\) 0 0
\(331\) −4.02899 −0.221453 −0.110727 0.993851i \(-0.535318\pi\)
−0.110727 + 0.993851i \(0.535318\pi\)
\(332\) 0 0
\(333\) 6.83873 0.374760
\(334\) 0 0
\(335\) −5.50676 −0.300866
\(336\) 0 0
\(337\) −21.0390 −1.14607 −0.573033 0.819533i \(-0.694233\pi\)
−0.573033 + 0.819533i \(0.694233\pi\)
\(338\) 0 0
\(339\) 1.34412 0.0730026
\(340\) 0 0
\(341\) 1.10393 0.0597810
\(342\) 0 0
\(343\) −5.51535 −0.297801
\(344\) 0 0
\(345\) 5.04471 0.271598
\(346\) 0 0
\(347\) −9.33028 −0.500876 −0.250438 0.968133i \(-0.580575\pi\)
−0.250438 + 0.968133i \(0.580575\pi\)
\(348\) 0 0
\(349\) 12.8849 0.689710 0.344855 0.938656i \(-0.387928\pi\)
0.344855 + 0.938656i \(0.387928\pi\)
\(350\) 0 0
\(351\) 10.0070 0.534135
\(352\) 0 0
\(353\) −15.0103 −0.798916 −0.399458 0.916752i \(-0.630802\pi\)
−0.399458 + 0.916752i \(0.630802\pi\)
\(354\) 0 0
\(355\) −37.6044 −1.99584
\(356\) 0 0
\(357\) −5.51160 −0.291705
\(358\) 0 0
\(359\) −34.9933 −1.84688 −0.923438 0.383748i \(-0.874633\pi\)
−0.923438 + 0.383748i \(0.874633\pi\)
\(360\) 0 0
\(361\) 16.6609 0.876890
\(362\) 0 0
\(363\) 13.4428 0.705563
\(364\) 0 0
\(365\) 42.0637 2.20172
\(366\) 0 0
\(367\) 11.5208 0.601381 0.300690 0.953722i \(-0.402783\pi\)
0.300690 + 0.953722i \(0.402783\pi\)
\(368\) 0 0
\(369\) −9.14653 −0.476150
\(370\) 0 0
\(371\) −13.4083 −0.696126
\(372\) 0 0
\(373\) 28.4863 1.47497 0.737483 0.675366i \(-0.236014\pi\)
0.737483 + 0.675366i \(0.236014\pi\)
\(374\) 0 0
\(375\) −6.57231 −0.339393
\(376\) 0 0
\(377\) 10.2530 0.528055
\(378\) 0 0
\(379\) 27.4443 1.40972 0.704859 0.709348i \(-0.251010\pi\)
0.704859 + 0.709348i \(0.251010\pi\)
\(380\) 0 0
\(381\) −22.6844 −1.16216
\(382\) 0 0
\(383\) 1.47669 0.0754552 0.0377276 0.999288i \(-0.487988\pi\)
0.0377276 + 0.999288i \(0.487988\pi\)
\(384\) 0 0
\(385\) −15.8219 −0.806359
\(386\) 0 0
\(387\) −8.52174 −0.433185
\(388\) 0 0
\(389\) −28.5353 −1.44680 −0.723399 0.690430i \(-0.757421\pi\)
−0.723399 + 0.690430i \(0.757421\pi\)
\(390\) 0 0
\(391\) 1.06460 0.0538393
\(392\) 0 0
\(393\) 6.95563 0.350865
\(394\) 0 0
\(395\) −37.6028 −1.89200
\(396\) 0 0
\(397\) −15.7144 −0.788681 −0.394341 0.918964i \(-0.629027\pi\)
−0.394341 + 0.918964i \(0.629027\pi\)
\(398\) 0 0
\(399\) −32.9135 −1.64773
\(400\) 0 0
\(401\) −10.3684 −0.517772 −0.258886 0.965908i \(-0.583355\pi\)
−0.258886 + 0.965908i \(0.583355\pi\)
\(402\) 0 0
\(403\) 1.63486 0.0814383
\(404\) 0 0
\(405\) −16.3957 −0.814709
\(406\) 0 0
\(407\) −7.94630 −0.393884
\(408\) 0 0
\(409\) −26.6310 −1.31682 −0.658408 0.752661i \(-0.728770\pi\)
−0.658408 + 0.752661i \(0.728770\pi\)
\(410\) 0 0
\(411\) 5.02381 0.247806
\(412\) 0 0
\(413\) 3.92495 0.193134
\(414\) 0 0
\(415\) 30.3975 1.49215
\(416\) 0 0
\(417\) −10.0650 −0.492887
\(418\) 0 0
\(419\) 31.6397 1.54570 0.772850 0.634589i \(-0.218831\pi\)
0.772850 + 0.634589i \(0.218831\pi\)
\(420\) 0 0
\(421\) 17.3788 0.846990 0.423495 0.905898i \(-0.360803\pi\)
0.423495 + 0.905898i \(0.360803\pi\)
\(422\) 0 0
\(423\) 1.73232 0.0842284
\(424\) 0 0
\(425\) −6.38698 −0.309814
\(426\) 0 0
\(427\) 25.4336 1.23082
\(428\) 0 0
\(429\) −2.96774 −0.143284
\(430\) 0 0
\(431\) −25.2679 −1.21711 −0.608557 0.793510i \(-0.708251\pi\)
−0.608557 + 0.793510i \(0.708251\pi\)
\(432\) 0 0
\(433\) 7.42428 0.356788 0.178394 0.983959i \(-0.442910\pi\)
0.178394 + 0.983959i \(0.442910\pi\)
\(434\) 0 0
\(435\) −27.4623 −1.31672
\(436\) 0 0
\(437\) 6.35747 0.304119
\(438\) 0 0
\(439\) −21.8827 −1.04440 −0.522201 0.852822i \(-0.674889\pi\)
−0.522201 + 0.852822i \(0.674889\pi\)
\(440\) 0 0
\(441\) −8.64130 −0.411490
\(442\) 0 0
\(443\) 10.7859 0.512455 0.256227 0.966617i \(-0.417520\pi\)
0.256227 + 0.966617i \(0.417520\pi\)
\(444\) 0 0
\(445\) −40.0433 −1.89824
\(446\) 0 0
\(447\) 18.6835 0.883697
\(448\) 0 0
\(449\) 8.13970 0.384136 0.192068 0.981382i \(-0.438481\pi\)
0.192068 + 0.981382i \(0.438481\pi\)
\(450\) 0 0
\(451\) 10.6279 0.500447
\(452\) 0 0
\(453\) 6.86517 0.322554
\(454\) 0 0
\(455\) −23.4315 −1.09848
\(456\) 0 0
\(457\) −0.343927 −0.0160882 −0.00804411 0.999968i \(-0.502561\pi\)
−0.00804411 + 0.999968i \(0.502561\pi\)
\(458\) 0 0
\(459\) −5.65643 −0.264020
\(460\) 0 0
\(461\) 5.70741 0.265821 0.132910 0.991128i \(-0.457568\pi\)
0.132910 + 0.991128i \(0.457568\pi\)
\(462\) 0 0
\(463\) 16.0862 0.747589 0.373795 0.927512i \(-0.378057\pi\)
0.373795 + 0.927512i \(0.378057\pi\)
\(464\) 0 0
\(465\) −4.37892 −0.203068
\(466\) 0 0
\(467\) −9.27233 −0.429072 −0.214536 0.976716i \(-0.568824\pi\)
−0.214536 + 0.976716i \(0.568824\pi\)
\(468\) 0 0
\(469\) 6.40510 0.295760
\(470\) 0 0
\(471\) −3.47417 −0.160081
\(472\) 0 0
\(473\) 9.90190 0.455290
\(474\) 0 0
\(475\) −38.1410 −1.75003
\(476\) 0 0
\(477\) −3.51214 −0.160810
\(478\) 0 0
\(479\) −24.6333 −1.12552 −0.562761 0.826619i \(-0.690261\pi\)
−0.562761 + 0.826619i \(0.690261\pi\)
\(480\) 0 0
\(481\) −11.7681 −0.536579
\(482\) 0 0
\(483\) −5.86767 −0.266988
\(484\) 0 0
\(485\) −57.8373 −2.62626
\(486\) 0 0
\(487\) 6.32303 0.286524 0.143262 0.989685i \(-0.454241\pi\)
0.143262 + 0.989685i \(0.454241\pi\)
\(488\) 0 0
\(489\) 7.26880 0.328707
\(490\) 0 0
\(491\) −19.7251 −0.890183 −0.445092 0.895485i \(-0.646829\pi\)
−0.445092 + 0.895485i \(0.646829\pi\)
\(492\) 0 0
\(493\) −5.79547 −0.261015
\(494\) 0 0
\(495\) −4.14434 −0.186274
\(496\) 0 0
\(497\) 43.7390 1.96196
\(498\) 0 0
\(499\) 18.0540 0.808206 0.404103 0.914713i \(-0.367584\pi\)
0.404103 + 0.914713i \(0.367584\pi\)
\(500\) 0 0
\(501\) 29.9371 1.33749
\(502\) 0 0
\(503\) −3.00127 −0.133820 −0.0669099 0.997759i \(-0.521314\pi\)
−0.0669099 + 0.997759i \(0.521314\pi\)
\(504\) 0 0
\(505\) 20.6757 0.920055
\(506\) 0 0
\(507\) 13.8601 0.615550
\(508\) 0 0
\(509\) −42.9672 −1.90449 −0.952244 0.305339i \(-0.901230\pi\)
−0.952244 + 0.305339i \(0.901230\pi\)
\(510\) 0 0
\(511\) −48.9257 −2.16435
\(512\) 0 0
\(513\) −33.7784 −1.49135
\(514\) 0 0
\(515\) −63.4226 −2.79473
\(516\) 0 0
\(517\) −2.01288 −0.0885265
\(518\) 0 0
\(519\) 33.6554 1.47731
\(520\) 0 0
\(521\) −34.9603 −1.53164 −0.765819 0.643056i \(-0.777666\pi\)
−0.765819 + 0.643056i \(0.777666\pi\)
\(522\) 0 0
\(523\) −3.07882 −0.134628 −0.0673138 0.997732i \(-0.521443\pi\)
−0.0673138 + 0.997732i \(0.521443\pi\)
\(524\) 0 0
\(525\) 35.2024 1.53636
\(526\) 0 0
\(527\) −0.924101 −0.0402545
\(528\) 0 0
\(529\) −21.8666 −0.950723
\(530\) 0 0
\(531\) 1.02809 0.0446153
\(532\) 0 0
\(533\) 15.7394 0.681748
\(534\) 0 0
\(535\) 25.7238 1.11214
\(536\) 0 0
\(537\) −12.6472 −0.545765
\(538\) 0 0
\(539\) 10.0408 0.432488
\(540\) 0 0
\(541\) −26.6997 −1.14791 −0.573955 0.818887i \(-0.694592\pi\)
−0.573955 + 0.818887i \(0.694592\pi\)
\(542\) 0 0
\(543\) −8.60219 −0.369155
\(544\) 0 0
\(545\) 60.3828 2.58651
\(546\) 0 0
\(547\) 8.39937 0.359131 0.179566 0.983746i \(-0.442531\pi\)
0.179566 + 0.983746i \(0.442531\pi\)
\(548\) 0 0
\(549\) 6.66200 0.284327
\(550\) 0 0
\(551\) −34.6087 −1.47438
\(552\) 0 0
\(553\) 43.7371 1.85989
\(554\) 0 0
\(555\) 31.5204 1.33797
\(556\) 0 0
\(557\) −39.2640 −1.66367 −0.831834 0.555024i \(-0.812709\pi\)
−0.831834 + 0.555024i \(0.812709\pi\)
\(558\) 0 0
\(559\) 14.6642 0.620231
\(560\) 0 0
\(561\) 1.67751 0.0708244
\(562\) 0 0
\(563\) −31.7135 −1.33657 −0.668283 0.743907i \(-0.732971\pi\)
−0.668283 + 0.743907i \(0.732971\pi\)
\(564\) 0 0
\(565\) −3.22997 −0.135886
\(566\) 0 0
\(567\) 19.0704 0.800881
\(568\) 0 0
\(569\) −3.99799 −0.167604 −0.0838021 0.996482i \(-0.526706\pi\)
−0.0838021 + 0.996482i \(0.526706\pi\)
\(570\) 0 0
\(571\) −3.72745 −0.155989 −0.0779945 0.996954i \(-0.524852\pi\)
−0.0779945 + 0.996954i \(0.524852\pi\)
\(572\) 0 0
\(573\) −14.0162 −0.585536
\(574\) 0 0
\(575\) −6.79961 −0.283563
\(576\) 0 0
\(577\) −41.5054 −1.72789 −0.863945 0.503586i \(-0.832014\pi\)
−0.863945 + 0.503586i \(0.832014\pi\)
\(578\) 0 0
\(579\) 34.4630 1.43223
\(580\) 0 0
\(581\) −35.3563 −1.46683
\(582\) 0 0
\(583\) 4.08095 0.169016
\(584\) 0 0
\(585\) −6.13757 −0.253757
\(586\) 0 0
\(587\) −29.9602 −1.23659 −0.618294 0.785947i \(-0.712176\pi\)
−0.618294 + 0.785947i \(0.712176\pi\)
\(588\) 0 0
\(589\) −5.51843 −0.227383
\(590\) 0 0
\(591\) −0.438673 −0.0180446
\(592\) 0 0
\(593\) 23.1764 0.951741 0.475870 0.879515i \(-0.342133\pi\)
0.475870 + 0.879515i \(0.342133\pi\)
\(594\) 0 0
\(595\) 13.2446 0.542975
\(596\) 0 0
\(597\) 29.5523 1.20950
\(598\) 0 0
\(599\) 17.7787 0.726418 0.363209 0.931708i \(-0.381681\pi\)
0.363209 + 0.931708i \(0.381681\pi\)
\(600\) 0 0
\(601\) −3.03049 −0.123616 −0.0618081 0.998088i \(-0.519687\pi\)
−0.0618081 + 0.998088i \(0.519687\pi\)
\(602\) 0 0
\(603\) 1.67773 0.0683225
\(604\) 0 0
\(605\) −32.3035 −1.31332
\(606\) 0 0
\(607\) −18.8912 −0.766769 −0.383385 0.923589i \(-0.625242\pi\)
−0.383385 + 0.923589i \(0.625242\pi\)
\(608\) 0 0
\(609\) 31.9423 1.29437
\(610\) 0 0
\(611\) −2.98098 −0.120598
\(612\) 0 0
\(613\) 4.81066 0.194301 0.0971504 0.995270i \(-0.469027\pi\)
0.0971504 + 0.995270i \(0.469027\pi\)
\(614\) 0 0
\(615\) −42.1574 −1.69995
\(616\) 0 0
\(617\) 29.9632 1.20627 0.603137 0.797638i \(-0.293917\pi\)
0.603137 + 0.797638i \(0.293917\pi\)
\(618\) 0 0
\(619\) 32.7428 1.31605 0.658023 0.752998i \(-0.271393\pi\)
0.658023 + 0.752998i \(0.271393\pi\)
\(620\) 0 0
\(621\) −6.02186 −0.241649
\(622\) 0 0
\(623\) 46.5757 1.86602
\(624\) 0 0
\(625\) −16.1414 −0.645656
\(626\) 0 0
\(627\) 10.0175 0.400062
\(628\) 0 0
\(629\) 6.65188 0.265228
\(630\) 0 0
\(631\) 33.5903 1.33721 0.668605 0.743618i \(-0.266892\pi\)
0.668605 + 0.743618i \(0.266892\pi\)
\(632\) 0 0
\(633\) 27.7080 1.10129
\(634\) 0 0
\(635\) 54.5114 2.16322
\(636\) 0 0
\(637\) 14.8700 0.589169
\(638\) 0 0
\(639\) 11.4569 0.453226
\(640\) 0 0
\(641\) −13.3976 −0.529175 −0.264587 0.964362i \(-0.585236\pi\)
−0.264587 + 0.964362i \(0.585236\pi\)
\(642\) 0 0
\(643\) 10.2416 0.403890 0.201945 0.979397i \(-0.435274\pi\)
0.201945 + 0.979397i \(0.435274\pi\)
\(644\) 0 0
\(645\) −39.2777 −1.54656
\(646\) 0 0
\(647\) 34.3309 1.34969 0.674843 0.737961i \(-0.264211\pi\)
0.674843 + 0.737961i \(0.264211\pi\)
\(648\) 0 0
\(649\) −1.19459 −0.0468920
\(650\) 0 0
\(651\) 5.09327 0.199621
\(652\) 0 0
\(653\) −17.8490 −0.698487 −0.349243 0.937032i \(-0.613561\pi\)
−0.349243 + 0.937032i \(0.613561\pi\)
\(654\) 0 0
\(655\) −16.7147 −0.653095
\(656\) 0 0
\(657\) −12.8155 −0.499979
\(658\) 0 0
\(659\) −9.67092 −0.376726 −0.188363 0.982100i \(-0.560318\pi\)
−0.188363 + 0.982100i \(0.560318\pi\)
\(660\) 0 0
\(661\) −14.4194 −0.560848 −0.280424 0.959876i \(-0.590475\pi\)
−0.280424 + 0.959876i \(0.590475\pi\)
\(662\) 0 0
\(663\) 2.48431 0.0964825
\(664\) 0 0
\(665\) 79.0923 3.06707
\(666\) 0 0
\(667\) −6.16988 −0.238899
\(668\) 0 0
\(669\) 5.15826 0.199430
\(670\) 0 0
\(671\) −7.74096 −0.298836
\(672\) 0 0
\(673\) −21.4315 −0.826125 −0.413063 0.910703i \(-0.635541\pi\)
−0.413063 + 0.910703i \(0.635541\pi\)
\(674\) 0 0
\(675\) 36.1275 1.39055
\(676\) 0 0
\(677\) 48.9977 1.88313 0.941567 0.336827i \(-0.109354\pi\)
0.941567 + 0.336827i \(0.109354\pi\)
\(678\) 0 0
\(679\) 67.2725 2.58168
\(680\) 0 0
\(681\) 14.9824 0.574125
\(682\) 0 0
\(683\) 5.38815 0.206172 0.103086 0.994672i \(-0.467128\pi\)
0.103086 + 0.994672i \(0.467128\pi\)
\(684\) 0 0
\(685\) −12.0724 −0.461262
\(686\) 0 0
\(687\) −36.1683 −1.37991
\(688\) 0 0
\(689\) 6.04369 0.230246
\(690\) 0 0
\(691\) −16.8920 −0.642602 −0.321301 0.946977i \(-0.604120\pi\)
−0.321301 + 0.946977i \(0.604120\pi\)
\(692\) 0 0
\(693\) 4.82042 0.183113
\(694\) 0 0
\(695\) 24.1867 0.917453
\(696\) 0 0
\(697\) −8.89664 −0.336984
\(698\) 0 0
\(699\) −20.6161 −0.779772
\(700\) 0 0
\(701\) −47.6074 −1.79811 −0.899053 0.437841i \(-0.855743\pi\)
−0.899053 + 0.437841i \(0.855743\pi\)
\(702\) 0 0
\(703\) 39.7229 1.49818
\(704\) 0 0
\(705\) 7.98447 0.300712
\(706\) 0 0
\(707\) −24.0486 −0.904439
\(708\) 0 0
\(709\) −37.3586 −1.40303 −0.701516 0.712654i \(-0.747493\pi\)
−0.701516 + 0.712654i \(0.747493\pi\)
\(710\) 0 0
\(711\) 11.4564 0.429648
\(712\) 0 0
\(713\) −0.983802 −0.0368437
\(714\) 0 0
\(715\) 7.13159 0.266706
\(716\) 0 0
\(717\) 1.71915 0.0642027
\(718\) 0 0
\(719\) 1.01318 0.0377852 0.0188926 0.999822i \(-0.493986\pi\)
0.0188926 + 0.999822i \(0.493986\pi\)
\(720\) 0 0
\(721\) 73.7689 2.74730
\(722\) 0 0
\(723\) 12.2952 0.457264
\(724\) 0 0
\(725\) 37.0155 1.37472
\(726\) 0 0
\(727\) −41.6767 −1.54570 −0.772851 0.634587i \(-0.781170\pi\)
−0.772851 + 0.634587i \(0.781170\pi\)
\(728\) 0 0
\(729\) 28.8243 1.06757
\(730\) 0 0
\(731\) −8.28892 −0.306577
\(732\) 0 0
\(733\) 45.0442 1.66375 0.831873 0.554967i \(-0.187269\pi\)
0.831873 + 0.554967i \(0.187269\pi\)
\(734\) 0 0
\(735\) −39.8287 −1.46910
\(736\) 0 0
\(737\) −1.94945 −0.0718090
\(738\) 0 0
\(739\) 14.9186 0.548789 0.274394 0.961617i \(-0.411523\pi\)
0.274394 + 0.961617i \(0.411523\pi\)
\(740\) 0 0
\(741\) 14.8355 0.544995
\(742\) 0 0
\(743\) 19.0492 0.698847 0.349424 0.936965i \(-0.386377\pi\)
0.349424 + 0.936965i \(0.386377\pi\)
\(744\) 0 0
\(745\) −44.8970 −1.64490
\(746\) 0 0
\(747\) −9.26114 −0.338847
\(748\) 0 0
\(749\) −29.9202 −1.09326
\(750\) 0 0
\(751\) −42.6468 −1.55621 −0.778103 0.628137i \(-0.783818\pi\)
−0.778103 + 0.628137i \(0.783818\pi\)
\(752\) 0 0
\(753\) −0.576336 −0.0210028
\(754\) 0 0
\(755\) −16.4973 −0.600397
\(756\) 0 0
\(757\) −29.5878 −1.07539 −0.537693 0.843141i \(-0.680704\pi\)
−0.537693 + 0.843141i \(0.680704\pi\)
\(758\) 0 0
\(759\) 1.78588 0.0648234
\(760\) 0 0
\(761\) −8.80505 −0.319183 −0.159591 0.987183i \(-0.551018\pi\)
−0.159591 + 0.987183i \(0.551018\pi\)
\(762\) 0 0
\(763\) −70.2332 −2.54261
\(764\) 0 0
\(765\) 3.46925 0.125431
\(766\) 0 0
\(767\) −1.76914 −0.0638798
\(768\) 0 0
\(769\) −23.6237 −0.851892 −0.425946 0.904749i \(-0.640059\pi\)
−0.425946 + 0.904749i \(0.640059\pi\)
\(770\) 0 0
\(771\) 23.3190 0.839812
\(772\) 0 0
\(773\) 6.83478 0.245830 0.122915 0.992417i \(-0.460776\pi\)
0.122915 + 0.992417i \(0.460776\pi\)
\(774\) 0 0
\(775\) 5.90221 0.212014
\(776\) 0 0
\(777\) −36.6625 −1.31526
\(778\) 0 0
\(779\) −53.1278 −1.90350
\(780\) 0 0
\(781\) −13.3124 −0.476354
\(782\) 0 0
\(783\) 32.7817 1.17152
\(784\) 0 0
\(785\) 8.34856 0.297973
\(786\) 0 0
\(787\) −1.88497 −0.0671918 −0.0335959 0.999435i \(-0.510696\pi\)
−0.0335959 + 0.999435i \(0.510696\pi\)
\(788\) 0 0
\(789\) 37.6909 1.34183
\(790\) 0 0
\(791\) 3.75689 0.133580
\(792\) 0 0
\(793\) −11.4640 −0.407098
\(794\) 0 0
\(795\) −16.1878 −0.574123
\(796\) 0 0
\(797\) −21.5434 −0.763108 −0.381554 0.924347i \(-0.624611\pi\)
−0.381554 + 0.924347i \(0.624611\pi\)
\(798\) 0 0
\(799\) 1.68499 0.0596108
\(800\) 0 0
\(801\) 12.1999 0.431063
\(802\) 0 0
\(803\) 14.8910 0.525492
\(804\) 0 0
\(805\) 14.1002 0.496968
\(806\) 0 0
\(807\) 37.4333 1.31771
\(808\) 0 0
\(809\) 6.69530 0.235394 0.117697 0.993050i \(-0.462449\pi\)
0.117697 + 0.993050i \(0.462449\pi\)
\(810\) 0 0
\(811\) −25.8625 −0.908156 −0.454078 0.890962i \(-0.650031\pi\)
−0.454078 + 0.890962i \(0.650031\pi\)
\(812\) 0 0
\(813\) −16.3486 −0.573370
\(814\) 0 0
\(815\) −17.4672 −0.611849
\(816\) 0 0
\(817\) −49.4987 −1.73174
\(818\) 0 0
\(819\) 7.13881 0.249450
\(820\) 0 0
\(821\) −39.2418 −1.36955 −0.684773 0.728756i \(-0.740099\pi\)
−0.684773 + 0.728756i \(0.740099\pi\)
\(822\) 0 0
\(823\) −6.96178 −0.242672 −0.121336 0.992611i \(-0.538718\pi\)
−0.121336 + 0.992611i \(0.538718\pi\)
\(824\) 0 0
\(825\) −10.7142 −0.373021
\(826\) 0 0
\(827\) −6.82120 −0.237196 −0.118598 0.992942i \(-0.537840\pi\)
−0.118598 + 0.992942i \(0.537840\pi\)
\(828\) 0 0
\(829\) 1.33307 0.0462994 0.0231497 0.999732i \(-0.492631\pi\)
0.0231497 + 0.999732i \(0.492631\pi\)
\(830\) 0 0
\(831\) 5.94424 0.206203
\(832\) 0 0
\(833\) −8.40520 −0.291223
\(834\) 0 0
\(835\) −71.9401 −2.48959
\(836\) 0 0
\(837\) 5.22712 0.180676
\(838\) 0 0
\(839\) −29.1530 −1.00647 −0.503237 0.864148i \(-0.667858\pi\)
−0.503237 + 0.864148i \(0.667858\pi\)
\(840\) 0 0
\(841\) 4.58747 0.158189
\(842\) 0 0
\(843\) 8.24805 0.284078
\(844\) 0 0
\(845\) −33.3064 −1.14578
\(846\) 0 0
\(847\) 37.5733 1.29103
\(848\) 0 0
\(849\) −39.6547 −1.36095
\(850\) 0 0
\(851\) 7.08162 0.242755
\(852\) 0 0
\(853\) −16.0424 −0.549281 −0.274641 0.961547i \(-0.588559\pi\)
−0.274641 + 0.961547i \(0.588559\pi\)
\(854\) 0 0
\(855\) 20.7172 0.708514
\(856\) 0 0
\(857\) −7.48834 −0.255797 −0.127898 0.991787i \(-0.540823\pi\)
−0.127898 + 0.991787i \(0.540823\pi\)
\(858\) 0 0
\(859\) −25.4552 −0.868519 −0.434259 0.900788i \(-0.642990\pi\)
−0.434259 + 0.900788i \(0.642990\pi\)
\(860\) 0 0
\(861\) 49.0347 1.67110
\(862\) 0 0
\(863\) 31.5577 1.07424 0.537118 0.843507i \(-0.319513\pi\)
0.537118 + 0.843507i \(0.319513\pi\)
\(864\) 0 0
\(865\) −80.8752 −2.74984
\(866\) 0 0
\(867\) −1.40425 −0.0476907
\(868\) 0 0
\(869\) −13.3118 −0.451572
\(870\) 0 0
\(871\) −2.88704 −0.0978238
\(872\) 0 0
\(873\) 17.6212 0.596386
\(874\) 0 0
\(875\) −18.3700 −0.621018
\(876\) 0 0
\(877\) 12.6969 0.428744 0.214372 0.976752i \(-0.431230\pi\)
0.214372 + 0.976752i \(0.431230\pi\)
\(878\) 0 0
\(879\) −28.3977 −0.957832
\(880\) 0 0
\(881\) −30.8661 −1.03991 −0.519953 0.854195i \(-0.674051\pi\)
−0.519953 + 0.854195i \(0.674051\pi\)
\(882\) 0 0
\(883\) 39.9064 1.34296 0.671479 0.741024i \(-0.265660\pi\)
0.671479 + 0.741024i \(0.265660\pi\)
\(884\) 0 0
\(885\) 4.73858 0.159286
\(886\) 0 0
\(887\) 36.6940 1.23207 0.616033 0.787721i \(-0.288739\pi\)
0.616033 + 0.787721i \(0.288739\pi\)
\(888\) 0 0
\(889\) −63.4040 −2.12650
\(890\) 0 0
\(891\) −5.80426 −0.194450
\(892\) 0 0
\(893\) 10.0622 0.336720
\(894\) 0 0
\(895\) 30.3916 1.01588
\(896\) 0 0
\(897\) 2.64480 0.0883074
\(898\) 0 0
\(899\) 5.35560 0.178619
\(900\) 0 0
\(901\) −3.41618 −0.113809
\(902\) 0 0
\(903\) 45.6852 1.52031
\(904\) 0 0
\(905\) 20.6714 0.687140
\(906\) 0 0
\(907\) 32.5219 1.07987 0.539936 0.841706i \(-0.318448\pi\)
0.539936 + 0.841706i \(0.318448\pi\)
\(908\) 0 0
\(909\) −6.29921 −0.208932
\(910\) 0 0
\(911\) −42.9944 −1.42447 −0.712233 0.701943i \(-0.752316\pi\)
−0.712233 + 0.701943i \(0.752316\pi\)
\(912\) 0 0
\(913\) 10.7610 0.356138
\(914\) 0 0
\(915\) 30.7059 1.01511
\(916\) 0 0
\(917\) 19.4414 0.642010
\(918\) 0 0
\(919\) 45.3225 1.49505 0.747526 0.664233i \(-0.231242\pi\)
0.747526 + 0.664233i \(0.231242\pi\)
\(920\) 0 0
\(921\) 19.8660 0.654608
\(922\) 0 0
\(923\) −19.7150 −0.648927
\(924\) 0 0
\(925\) −42.4854 −1.39691
\(926\) 0 0
\(927\) 19.3228 0.634644
\(928\) 0 0
\(929\) −5.76911 −0.189278 −0.0946392 0.995512i \(-0.530170\pi\)
−0.0946392 + 0.995512i \(0.530170\pi\)
\(930\) 0 0
\(931\) −50.1932 −1.64501
\(932\) 0 0
\(933\) −12.1430 −0.397543
\(934\) 0 0
\(935\) −4.03111 −0.131831
\(936\) 0 0
\(937\) 14.7630 0.482286 0.241143 0.970490i \(-0.422478\pi\)
0.241143 + 0.970490i \(0.422478\pi\)
\(938\) 0 0
\(939\) −43.5227 −1.42031
\(940\) 0 0
\(941\) 44.1338 1.43872 0.719361 0.694636i \(-0.244435\pi\)
0.719361 + 0.694636i \(0.244435\pi\)
\(942\) 0 0
\(943\) −9.47140 −0.308431
\(944\) 0 0
\(945\) −74.9171 −2.43705
\(946\) 0 0
\(947\) −54.8411 −1.78210 −0.891048 0.453909i \(-0.850029\pi\)
−0.891048 + 0.453909i \(0.850029\pi\)
\(948\) 0 0
\(949\) 22.0529 0.715866
\(950\) 0 0
\(951\) −47.1866 −1.53013
\(952\) 0 0
\(953\) −7.64403 −0.247615 −0.123807 0.992306i \(-0.539510\pi\)
−0.123807 + 0.992306i \(0.539510\pi\)
\(954\) 0 0
\(955\) 33.6815 1.08991
\(956\) 0 0
\(957\) −9.72194 −0.314266
\(958\) 0 0
\(959\) 14.0418 0.453433
\(960\) 0 0
\(961\) −30.1460 −0.972453
\(962\) 0 0
\(963\) −7.83722 −0.252551
\(964\) 0 0
\(965\) −82.8160 −2.66594
\(966\) 0 0
\(967\) 26.0353 0.837240 0.418620 0.908161i \(-0.362514\pi\)
0.418620 + 0.908161i \(0.362514\pi\)
\(968\) 0 0
\(969\) −8.38571 −0.269388
\(970\) 0 0
\(971\) 55.6088 1.78457 0.892285 0.451472i \(-0.149101\pi\)
0.892285 + 0.451472i \(0.149101\pi\)
\(972\) 0 0
\(973\) −28.1323 −0.901881
\(974\) 0 0
\(975\) −15.8672 −0.508158
\(976\) 0 0
\(977\) 33.1632 1.06098 0.530492 0.847690i \(-0.322007\pi\)
0.530492 + 0.847690i \(0.322007\pi\)
\(978\) 0 0
\(979\) −14.1758 −0.453060
\(980\) 0 0
\(981\) −18.3967 −0.587361
\(982\) 0 0
\(983\) −31.0265 −0.989592 −0.494796 0.869009i \(-0.664757\pi\)
−0.494796 + 0.869009i \(0.664757\pi\)
\(984\) 0 0
\(985\) 1.05415 0.0335879
\(986\) 0 0
\(987\) −9.28700 −0.295608
\(988\) 0 0
\(989\) −8.82442 −0.280600
\(990\) 0 0
\(991\) −5.28206 −0.167790 −0.0838950 0.996475i \(-0.526736\pi\)
−0.0838950 + 0.996475i \(0.526736\pi\)
\(992\) 0 0
\(993\) 5.65770 0.179542
\(994\) 0 0
\(995\) −71.0154 −2.25134
\(996\) 0 0
\(997\) −1.97901 −0.0626759 −0.0313379 0.999509i \(-0.509977\pi\)
−0.0313379 + 0.999509i \(0.509977\pi\)
\(998\) 0 0
\(999\) −37.6259 −1.19043
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 \(a_p\))