Properties

Label 6036.2.a.i.1.12
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-0.244833 q^{5}\) \(+2.69533 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-0.244833 q^{5}\) \(+2.69533 q^{7}\) \(+1.00000 q^{9}\) \(+4.17525 q^{11}\) \(-4.50565 q^{13}\) \(+0.244833 q^{15}\) \(+1.19780 q^{17}\) \(+2.55525 q^{19}\) \(-2.69533 q^{21}\) \(+4.82577 q^{23}\) \(-4.94006 q^{25}\) \(-1.00000 q^{27}\) \(-2.33354 q^{29}\) \(+8.83643 q^{31}\) \(-4.17525 q^{33}\) \(-0.659904 q^{35}\) \(+6.02074 q^{37}\) \(+4.50565 q^{39}\) \(-9.45996 q^{41}\) \(+7.71148 q^{43}\) \(-0.244833 q^{45}\) \(+2.80134 q^{47}\) \(+0.264777 q^{49}\) \(-1.19780 q^{51}\) \(+3.72490 q^{53}\) \(-1.02224 q^{55}\) \(-2.55525 q^{57}\) \(+6.71732 q^{59}\) \(-10.0509 q^{61}\) \(+2.69533 q^{63}\) \(+1.10313 q^{65}\) \(-5.48628 q^{67}\) \(-4.82577 q^{69}\) \(+2.35862 q^{71}\) \(+10.1415 q^{73}\) \(+4.94006 q^{75}\) \(+11.2536 q^{77}\) \(+1.84247 q^{79}\) \(+1.00000 q^{81}\) \(-6.03637 q^{83}\) \(-0.293261 q^{85}\) \(+2.33354 q^{87}\) \(-0.866842 q^{89}\) \(-12.1442 q^{91}\) \(-8.83643 q^{93}\) \(-0.625608 q^{95}\) \(+7.72995 q^{97}\) \(+4.17525 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.244833 −0.109493 −0.0547463 0.998500i \(-0.517435\pi\)
−0.0547463 + 0.998500i \(0.517435\pi\)
\(6\) 0 0
\(7\) 2.69533 1.01874 0.509369 0.860548i \(-0.329879\pi\)
0.509369 + 0.860548i \(0.329879\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.17525 1.25888 0.629442 0.777047i \(-0.283283\pi\)
0.629442 + 0.777047i \(0.283283\pi\)
\(12\) 0 0
\(13\) −4.50565 −1.24964 −0.624822 0.780768i \(-0.714828\pi\)
−0.624822 + 0.780768i \(0.714828\pi\)
\(14\) 0 0
\(15\) 0.244833 0.0632156
\(16\) 0 0
\(17\) 1.19780 0.290509 0.145255 0.989394i \(-0.453600\pi\)
0.145255 + 0.989394i \(0.453600\pi\)
\(18\) 0 0
\(19\) 2.55525 0.586214 0.293107 0.956080i \(-0.405311\pi\)
0.293107 + 0.956080i \(0.405311\pi\)
\(20\) 0 0
\(21\) −2.69533 −0.588168
\(22\) 0 0
\(23\) 4.82577 1.00624 0.503122 0.864216i \(-0.332185\pi\)
0.503122 + 0.864216i \(0.332185\pi\)
\(24\) 0 0
\(25\) −4.94006 −0.988011
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.33354 −0.433328 −0.216664 0.976246i \(-0.569518\pi\)
−0.216664 + 0.976246i \(0.569518\pi\)
\(30\) 0 0
\(31\) 8.83643 1.58707 0.793535 0.608525i \(-0.208238\pi\)
0.793535 + 0.608525i \(0.208238\pi\)
\(32\) 0 0
\(33\) −4.17525 −0.726817
\(34\) 0 0
\(35\) −0.659904 −0.111544
\(36\) 0 0
\(37\) 6.02074 0.989803 0.494902 0.868949i \(-0.335204\pi\)
0.494902 + 0.868949i \(0.335204\pi\)
\(38\) 0 0
\(39\) 4.50565 0.721482
\(40\) 0 0
\(41\) −9.45996 −1.47740 −0.738699 0.674036i \(-0.764559\pi\)
−0.738699 + 0.674036i \(0.764559\pi\)
\(42\) 0 0
\(43\) 7.71148 1.17599 0.587995 0.808864i \(-0.299917\pi\)
0.587995 + 0.808864i \(0.299917\pi\)
\(44\) 0 0
\(45\) −0.244833 −0.0364975
\(46\) 0 0
\(47\) 2.80134 0.408618 0.204309 0.978906i \(-0.434505\pi\)
0.204309 + 0.978906i \(0.434505\pi\)
\(48\) 0 0
\(49\) 0.264777 0.0378253
\(50\) 0 0
\(51\) −1.19780 −0.167725
\(52\) 0 0
\(53\) 3.72490 0.511655 0.255827 0.966722i \(-0.417652\pi\)
0.255827 + 0.966722i \(0.417652\pi\)
\(54\) 0 0
\(55\) −1.02224 −0.137839
\(56\) 0 0
\(57\) −2.55525 −0.338451
\(58\) 0 0
\(59\) 6.71732 0.874520 0.437260 0.899335i \(-0.355949\pi\)
0.437260 + 0.899335i \(0.355949\pi\)
\(60\) 0 0
\(61\) −10.0509 −1.28689 −0.643443 0.765494i \(-0.722495\pi\)
−0.643443 + 0.765494i \(0.722495\pi\)
\(62\) 0 0
\(63\) 2.69533 0.339579
\(64\) 0 0
\(65\) 1.10313 0.136827
\(66\) 0 0
\(67\) −5.48628 −0.670256 −0.335128 0.942173i \(-0.608780\pi\)
−0.335128 + 0.942173i \(0.608780\pi\)
\(68\) 0 0
\(69\) −4.82577 −0.580955
\(70\) 0 0
\(71\) 2.35862 0.279916 0.139958 0.990157i \(-0.455303\pi\)
0.139958 + 0.990157i \(0.455303\pi\)
\(72\) 0 0
\(73\) 10.1415 1.18697 0.593485 0.804845i \(-0.297752\pi\)
0.593485 + 0.804845i \(0.297752\pi\)
\(74\) 0 0
\(75\) 4.94006 0.570429
\(76\) 0 0
\(77\) 11.2536 1.28247
\(78\) 0 0
\(79\) 1.84247 0.207294 0.103647 0.994614i \(-0.466949\pi\)
0.103647 + 0.994614i \(0.466949\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.03637 −0.662578 −0.331289 0.943529i \(-0.607483\pi\)
−0.331289 + 0.943529i \(0.607483\pi\)
\(84\) 0 0
\(85\) −0.293261 −0.0318086
\(86\) 0 0
\(87\) 2.33354 0.250182
\(88\) 0 0
\(89\) −0.866842 −0.0918851 −0.0459425 0.998944i \(-0.514629\pi\)
−0.0459425 + 0.998944i \(0.514629\pi\)
\(90\) 0 0
\(91\) −12.1442 −1.27306
\(92\) 0 0
\(93\) −8.83643 −0.916295
\(94\) 0 0
\(95\) −0.625608 −0.0641861
\(96\) 0 0
\(97\) 7.72995 0.784858 0.392429 0.919782i \(-0.371635\pi\)
0.392429 + 0.919782i \(0.371635\pi\)
\(98\) 0 0
\(99\) 4.17525 0.419628
\(100\) 0 0
\(101\) −0.545900 −0.0543191 −0.0271595 0.999631i \(-0.508646\pi\)
−0.0271595 + 0.999631i \(0.508646\pi\)
\(102\) 0 0
\(103\) −3.90518 −0.384789 −0.192394 0.981318i \(-0.561625\pi\)
−0.192394 + 0.981318i \(0.561625\pi\)
\(104\) 0 0
\(105\) 0.659904 0.0644001
\(106\) 0 0
\(107\) 9.18330 0.887783 0.443891 0.896081i \(-0.353598\pi\)
0.443891 + 0.896081i \(0.353598\pi\)
\(108\) 0 0
\(109\) −9.00728 −0.862741 −0.431371 0.902175i \(-0.641970\pi\)
−0.431371 + 0.902175i \(0.641970\pi\)
\(110\) 0 0
\(111\) −6.02074 −0.571463
\(112\) 0 0
\(113\) 4.71190 0.443258 0.221629 0.975131i \(-0.428863\pi\)
0.221629 + 0.975131i \(0.428863\pi\)
\(114\) 0 0
\(115\) −1.18151 −0.110176
\(116\) 0 0
\(117\) −4.50565 −0.416548
\(118\) 0 0
\(119\) 3.22846 0.295952
\(120\) 0 0
\(121\) 6.43268 0.584790
\(122\) 0 0
\(123\) 9.45996 0.852976
\(124\) 0 0
\(125\) 2.43365 0.217673
\(126\) 0 0
\(127\) −11.6498 −1.03375 −0.516877 0.856060i \(-0.672906\pi\)
−0.516877 + 0.856060i \(0.672906\pi\)
\(128\) 0 0
\(129\) −7.71148 −0.678958
\(130\) 0 0
\(131\) −1.83085 −0.159962 −0.0799809 0.996796i \(-0.525486\pi\)
−0.0799809 + 0.996796i \(0.525486\pi\)
\(132\) 0 0
\(133\) 6.88722 0.597198
\(134\) 0 0
\(135\) 0.244833 0.0210719
\(136\) 0 0
\(137\) 13.4853 1.15213 0.576065 0.817404i \(-0.304587\pi\)
0.576065 + 0.817404i \(0.304587\pi\)
\(138\) 0 0
\(139\) 11.1740 0.947769 0.473885 0.880587i \(-0.342851\pi\)
0.473885 + 0.880587i \(0.342851\pi\)
\(140\) 0 0
\(141\) −2.80134 −0.235916
\(142\) 0 0
\(143\) −18.8122 −1.57316
\(144\) 0 0
\(145\) 0.571328 0.0474462
\(146\) 0 0
\(147\) −0.264777 −0.0218385
\(148\) 0 0
\(149\) −23.8442 −1.95339 −0.976696 0.214629i \(-0.931146\pi\)
−0.976696 + 0.214629i \(0.931146\pi\)
\(150\) 0 0
\(151\) −7.56968 −0.616011 −0.308006 0.951385i \(-0.599662\pi\)
−0.308006 + 0.951385i \(0.599662\pi\)
\(152\) 0 0
\(153\) 1.19780 0.0968363
\(154\) 0 0
\(155\) −2.16345 −0.173772
\(156\) 0 0
\(157\) 21.6508 1.72792 0.863960 0.503561i \(-0.167977\pi\)
0.863960 + 0.503561i \(0.167977\pi\)
\(158\) 0 0
\(159\) −3.72490 −0.295404
\(160\) 0 0
\(161\) 13.0070 1.02510
\(162\) 0 0
\(163\) −16.0454 −1.25677 −0.628386 0.777902i \(-0.716284\pi\)
−0.628386 + 0.777902i \(0.716284\pi\)
\(164\) 0 0
\(165\) 1.02224 0.0795811
\(166\) 0 0
\(167\) 9.20314 0.712160 0.356080 0.934455i \(-0.384113\pi\)
0.356080 + 0.934455i \(0.384113\pi\)
\(168\) 0 0
\(169\) 7.30091 0.561608
\(170\) 0 0
\(171\) 2.55525 0.195405
\(172\) 0 0
\(173\) −9.14157 −0.695021 −0.347510 0.937676i \(-0.612973\pi\)
−0.347510 + 0.937676i \(0.612973\pi\)
\(174\) 0 0
\(175\) −13.3151 −1.00652
\(176\) 0 0
\(177\) −6.71732 −0.504904
\(178\) 0 0
\(179\) −5.68254 −0.424733 −0.212366 0.977190i \(-0.568117\pi\)
−0.212366 + 0.977190i \(0.568117\pi\)
\(180\) 0 0
\(181\) 22.5449 1.67575 0.837874 0.545864i \(-0.183798\pi\)
0.837874 + 0.545864i \(0.183798\pi\)
\(182\) 0 0
\(183\) 10.0509 0.742984
\(184\) 0 0
\(185\) −1.47407 −0.108376
\(186\) 0 0
\(187\) 5.00111 0.365717
\(188\) 0 0
\(189\) −2.69533 −0.196056
\(190\) 0 0
\(191\) −13.8900 −1.00504 −0.502521 0.864565i \(-0.667594\pi\)
−0.502521 + 0.864565i \(0.667594\pi\)
\(192\) 0 0
\(193\) −11.8571 −0.853491 −0.426745 0.904372i \(-0.640340\pi\)
−0.426745 + 0.904372i \(0.640340\pi\)
\(194\) 0 0
\(195\) −1.10313 −0.0789969
\(196\) 0 0
\(197\) −7.71344 −0.549560 −0.274780 0.961507i \(-0.588605\pi\)
−0.274780 + 0.961507i \(0.588605\pi\)
\(198\) 0 0
\(199\) 11.8647 0.841068 0.420534 0.907277i \(-0.361843\pi\)
0.420534 + 0.907277i \(0.361843\pi\)
\(200\) 0 0
\(201\) 5.48628 0.386972
\(202\) 0 0
\(203\) −6.28965 −0.441447
\(204\) 0 0
\(205\) 2.31611 0.161764
\(206\) 0 0
\(207\) 4.82577 0.335415
\(208\) 0 0
\(209\) 10.6688 0.737975
\(210\) 0 0
\(211\) 12.8342 0.883545 0.441773 0.897127i \(-0.354350\pi\)
0.441773 + 0.897127i \(0.354350\pi\)
\(212\) 0 0
\(213\) −2.35862 −0.161610
\(214\) 0 0
\(215\) −1.88803 −0.128762
\(216\) 0 0
\(217\) 23.8171 1.61681
\(218\) 0 0
\(219\) −10.1415 −0.685298
\(220\) 0 0
\(221\) −5.39687 −0.363033
\(222\) 0 0
\(223\) 20.5846 1.37844 0.689222 0.724550i \(-0.257953\pi\)
0.689222 + 0.724550i \(0.257953\pi\)
\(224\) 0 0
\(225\) −4.94006 −0.329337
\(226\) 0 0
\(227\) −25.9870 −1.72482 −0.862410 0.506211i \(-0.831046\pi\)
−0.862410 + 0.506211i \(0.831046\pi\)
\(228\) 0 0
\(229\) 16.2462 1.07358 0.536791 0.843715i \(-0.319636\pi\)
0.536791 + 0.843715i \(0.319636\pi\)
\(230\) 0 0
\(231\) −11.2536 −0.740436
\(232\) 0 0
\(233\) 8.61228 0.564209 0.282104 0.959384i \(-0.408968\pi\)
0.282104 + 0.959384i \(0.408968\pi\)
\(234\) 0 0
\(235\) −0.685861 −0.0447406
\(236\) 0 0
\(237\) −1.84247 −0.119681
\(238\) 0 0
\(239\) 27.0577 1.75022 0.875110 0.483924i \(-0.160789\pi\)
0.875110 + 0.483924i \(0.160789\pi\)
\(240\) 0 0
\(241\) 4.99854 0.321985 0.160992 0.986956i \(-0.448531\pi\)
0.160992 + 0.986956i \(0.448531\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −0.0648262 −0.00414160
\(246\) 0 0
\(247\) −11.5131 −0.732558
\(248\) 0 0
\(249\) 6.03637 0.382539
\(250\) 0 0
\(251\) 8.14507 0.514113 0.257056 0.966396i \(-0.417247\pi\)
0.257056 + 0.966396i \(0.417247\pi\)
\(252\) 0 0
\(253\) 20.1488 1.26674
\(254\) 0 0
\(255\) 0.293261 0.0183647
\(256\) 0 0
\(257\) 8.67847 0.541348 0.270674 0.962671i \(-0.412753\pi\)
0.270674 + 0.962671i \(0.412753\pi\)
\(258\) 0 0
\(259\) 16.2278 1.00835
\(260\) 0 0
\(261\) −2.33354 −0.144443
\(262\) 0 0
\(263\) −15.7470 −0.971003 −0.485501 0.874236i \(-0.661363\pi\)
−0.485501 + 0.874236i \(0.661363\pi\)
\(264\) 0 0
\(265\) −0.911979 −0.0560224
\(266\) 0 0
\(267\) 0.866842 0.0530499
\(268\) 0 0
\(269\) 13.5710 0.827440 0.413720 0.910404i \(-0.364229\pi\)
0.413720 + 0.910404i \(0.364229\pi\)
\(270\) 0 0
\(271\) 25.8147 1.56813 0.784064 0.620679i \(-0.213143\pi\)
0.784064 + 0.620679i \(0.213143\pi\)
\(272\) 0 0
\(273\) 12.1442 0.735000
\(274\) 0 0
\(275\) −20.6260 −1.24379
\(276\) 0 0
\(277\) −15.9744 −0.959809 −0.479905 0.877321i \(-0.659329\pi\)
−0.479905 + 0.877321i \(0.659329\pi\)
\(278\) 0 0
\(279\) 8.83643 0.529023
\(280\) 0 0
\(281\) −3.06969 −0.183122 −0.0915611 0.995799i \(-0.529186\pi\)
−0.0915611 + 0.995799i \(0.529186\pi\)
\(282\) 0 0
\(283\) 31.9714 1.90050 0.950250 0.311487i \(-0.100827\pi\)
0.950250 + 0.311487i \(0.100827\pi\)
\(284\) 0 0
\(285\) 0.625608 0.0370578
\(286\) 0 0
\(287\) −25.4977 −1.50508
\(288\) 0 0
\(289\) −15.5653 −0.915605
\(290\) 0 0
\(291\) −7.72995 −0.453138
\(292\) 0 0
\(293\) −19.2704 −1.12579 −0.562893 0.826530i \(-0.690312\pi\)
−0.562893 + 0.826530i \(0.690312\pi\)
\(294\) 0 0
\(295\) −1.64462 −0.0957535
\(296\) 0 0
\(297\) −4.17525 −0.242272
\(298\) 0 0
\(299\) −21.7433 −1.25745
\(300\) 0 0
\(301\) 20.7850 1.19803
\(302\) 0 0
\(303\) 0.545900 0.0313611
\(304\) 0 0
\(305\) 2.46079 0.140905
\(306\) 0 0
\(307\) 6.36581 0.363316 0.181658 0.983362i \(-0.441854\pi\)
0.181658 + 0.983362i \(0.441854\pi\)
\(308\) 0 0
\(309\) 3.90518 0.222158
\(310\) 0 0
\(311\) 29.4669 1.67092 0.835458 0.549554i \(-0.185202\pi\)
0.835458 + 0.549554i \(0.185202\pi\)
\(312\) 0 0
\(313\) 22.9018 1.29448 0.647242 0.762285i \(-0.275922\pi\)
0.647242 + 0.762285i \(0.275922\pi\)
\(314\) 0 0
\(315\) −0.659904 −0.0371814
\(316\) 0 0
\(317\) −29.7613 −1.67156 −0.835780 0.549065i \(-0.814984\pi\)
−0.835780 + 0.549065i \(0.814984\pi\)
\(318\) 0 0
\(319\) −9.74311 −0.545510
\(320\) 0 0
\(321\) −9.18330 −0.512562
\(322\) 0 0
\(323\) 3.06067 0.170300
\(324\) 0 0
\(325\) 22.2582 1.23466
\(326\) 0 0
\(327\) 9.00728 0.498104
\(328\) 0 0
\(329\) 7.55053 0.416274
\(330\) 0 0
\(331\) −6.56891 −0.361060 −0.180530 0.983569i \(-0.557781\pi\)
−0.180530 + 0.983569i \(0.557781\pi\)
\(332\) 0 0
\(333\) 6.02074 0.329934
\(334\) 0 0
\(335\) 1.34322 0.0733881
\(336\) 0 0
\(337\) 7.65801 0.417159 0.208579 0.978005i \(-0.433116\pi\)
0.208579 + 0.978005i \(0.433116\pi\)
\(338\) 0 0
\(339\) −4.71190 −0.255915
\(340\) 0 0
\(341\) 36.8943 1.99794
\(342\) 0 0
\(343\) −18.1536 −0.980203
\(344\) 0 0
\(345\) 1.18151 0.0636103
\(346\) 0 0
\(347\) −13.1422 −0.705512 −0.352756 0.935715i \(-0.614755\pi\)
−0.352756 + 0.935715i \(0.614755\pi\)
\(348\) 0 0
\(349\) 5.85668 0.313501 0.156750 0.987638i \(-0.449898\pi\)
0.156750 + 0.987638i \(0.449898\pi\)
\(350\) 0 0
\(351\) 4.50565 0.240494
\(352\) 0 0
\(353\) −9.81238 −0.522260 −0.261130 0.965304i \(-0.584095\pi\)
−0.261130 + 0.965304i \(0.584095\pi\)
\(354\) 0 0
\(355\) −0.577467 −0.0306488
\(356\) 0 0
\(357\) −3.22846 −0.170868
\(358\) 0 0
\(359\) 23.9807 1.26565 0.632825 0.774295i \(-0.281895\pi\)
0.632825 + 0.774295i \(0.281895\pi\)
\(360\) 0 0
\(361\) −12.4707 −0.656354
\(362\) 0 0
\(363\) −6.43268 −0.337628
\(364\) 0 0
\(365\) −2.48297 −0.129964
\(366\) 0 0
\(367\) 27.4318 1.43193 0.715963 0.698138i \(-0.245988\pi\)
0.715963 + 0.698138i \(0.245988\pi\)
\(368\) 0 0
\(369\) −9.45996 −0.492466
\(370\) 0 0
\(371\) 10.0398 0.521242
\(372\) 0 0
\(373\) 16.9189 0.876028 0.438014 0.898968i \(-0.355682\pi\)
0.438014 + 0.898968i \(0.355682\pi\)
\(374\) 0 0
\(375\) −2.43365 −0.125673
\(376\) 0 0
\(377\) 10.5141 0.541505
\(378\) 0 0
\(379\) 36.6865 1.88446 0.942229 0.334968i \(-0.108726\pi\)
0.942229 + 0.334968i \(0.108726\pi\)
\(380\) 0 0
\(381\) 11.6498 0.596838
\(382\) 0 0
\(383\) −1.57033 −0.0802403 −0.0401201 0.999195i \(-0.512774\pi\)
−0.0401201 + 0.999195i \(0.512774\pi\)
\(384\) 0 0
\(385\) −2.75526 −0.140421
\(386\) 0 0
\(387\) 7.71148 0.391997
\(388\) 0 0
\(389\) 9.54858 0.484132 0.242066 0.970260i \(-0.422175\pi\)
0.242066 + 0.970260i \(0.422175\pi\)
\(390\) 0 0
\(391\) 5.78031 0.292323
\(392\) 0 0
\(393\) 1.83085 0.0923540
\(394\) 0 0
\(395\) −0.451096 −0.0226971
\(396\) 0 0
\(397\) 5.85597 0.293903 0.146951 0.989144i \(-0.453054\pi\)
0.146951 + 0.989144i \(0.453054\pi\)
\(398\) 0 0
\(399\) −6.88722 −0.344792
\(400\) 0 0
\(401\) 7.88455 0.393735 0.196868 0.980430i \(-0.436923\pi\)
0.196868 + 0.980430i \(0.436923\pi\)
\(402\) 0 0
\(403\) −39.8139 −1.98327
\(404\) 0 0
\(405\) −0.244833 −0.0121658
\(406\) 0 0
\(407\) 25.1381 1.24605
\(408\) 0 0
\(409\) 30.8972 1.52777 0.763884 0.645353i \(-0.223290\pi\)
0.763884 + 0.645353i \(0.223290\pi\)
\(410\) 0 0
\(411\) −13.4853 −0.665183
\(412\) 0 0
\(413\) 18.1054 0.890906
\(414\) 0 0
\(415\) 1.47790 0.0725474
\(416\) 0 0
\(417\) −11.1740 −0.547195
\(418\) 0 0
\(419\) 34.8669 1.70336 0.851679 0.524063i \(-0.175585\pi\)
0.851679 + 0.524063i \(0.175585\pi\)
\(420\) 0 0
\(421\) 24.2800 1.18334 0.591668 0.806182i \(-0.298470\pi\)
0.591668 + 0.806182i \(0.298470\pi\)
\(422\) 0 0
\(423\) 2.80134 0.136206
\(424\) 0 0
\(425\) −5.91720 −0.287026
\(426\) 0 0
\(427\) −27.0905 −1.31100
\(428\) 0 0
\(429\) 18.8122 0.908262
\(430\) 0 0
\(431\) −31.0586 −1.49604 −0.748020 0.663676i \(-0.768995\pi\)
−0.748020 + 0.663676i \(0.768995\pi\)
\(432\) 0 0
\(433\) 2.40142 0.115405 0.0577025 0.998334i \(-0.481623\pi\)
0.0577025 + 0.998334i \(0.481623\pi\)
\(434\) 0 0
\(435\) −0.571328 −0.0273931
\(436\) 0 0
\(437\) 12.3310 0.589874
\(438\) 0 0
\(439\) 15.0664 0.719081 0.359540 0.933129i \(-0.382933\pi\)
0.359540 + 0.933129i \(0.382933\pi\)
\(440\) 0 0
\(441\) 0.264777 0.0126084
\(442\) 0 0
\(443\) −3.31651 −0.157572 −0.0787861 0.996892i \(-0.525104\pi\)
−0.0787861 + 0.996892i \(0.525104\pi\)
\(444\) 0 0
\(445\) 0.212231 0.0100607
\(446\) 0 0
\(447\) 23.8442 1.12779
\(448\) 0 0
\(449\) 20.9427 0.988347 0.494174 0.869363i \(-0.335471\pi\)
0.494174 + 0.869363i \(0.335471\pi\)
\(450\) 0 0
\(451\) −39.4977 −1.85987
\(452\) 0 0
\(453\) 7.56968 0.355654
\(454\) 0 0
\(455\) 2.97330 0.139390
\(456\) 0 0
\(457\) 10.5175 0.491988 0.245994 0.969271i \(-0.420886\pi\)
0.245994 + 0.969271i \(0.420886\pi\)
\(458\) 0 0
\(459\) −1.19780 −0.0559085
\(460\) 0 0
\(461\) −17.6364 −0.821408 −0.410704 0.911769i \(-0.634717\pi\)
−0.410704 + 0.911769i \(0.634717\pi\)
\(462\) 0 0
\(463\) 3.71983 0.172875 0.0864375 0.996257i \(-0.472452\pi\)
0.0864375 + 0.996257i \(0.472452\pi\)
\(464\) 0 0
\(465\) 2.16345 0.100328
\(466\) 0 0
\(467\) −29.4817 −1.36425 −0.682125 0.731236i \(-0.738944\pi\)
−0.682125 + 0.731236i \(0.738944\pi\)
\(468\) 0 0
\(469\) −14.7873 −0.682815
\(470\) 0 0
\(471\) −21.6508 −0.997615
\(472\) 0 0
\(473\) 32.1974 1.48044
\(474\) 0 0
\(475\) −12.6231 −0.579186
\(476\) 0 0
\(477\) 3.72490 0.170552
\(478\) 0 0
\(479\) 35.4820 1.62122 0.810608 0.585590i \(-0.199137\pi\)
0.810608 + 0.585590i \(0.199137\pi\)
\(480\) 0 0
\(481\) −27.1274 −1.23690
\(482\) 0 0
\(483\) −13.0070 −0.591840
\(484\) 0 0
\(485\) −1.89255 −0.0859361
\(486\) 0 0
\(487\) 2.19988 0.0996862 0.0498431 0.998757i \(-0.484128\pi\)
0.0498431 + 0.998757i \(0.484128\pi\)
\(488\) 0 0
\(489\) 16.0454 0.725598
\(490\) 0 0
\(491\) 2.81164 0.126888 0.0634438 0.997985i \(-0.479792\pi\)
0.0634438 + 0.997985i \(0.479792\pi\)
\(492\) 0 0
\(493\) −2.79511 −0.125886
\(494\) 0 0
\(495\) −1.02224 −0.0459462
\(496\) 0 0
\(497\) 6.35724 0.285161
\(498\) 0 0
\(499\) 25.4483 1.13922 0.569612 0.821914i \(-0.307094\pi\)
0.569612 + 0.821914i \(0.307094\pi\)
\(500\) 0 0
\(501\) −9.20314 −0.411166
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 0.133654 0.00594754
\(506\) 0 0
\(507\) −7.30091 −0.324245
\(508\) 0 0
\(509\) 3.89029 0.172434 0.0862170 0.996276i \(-0.472522\pi\)
0.0862170 + 0.996276i \(0.472522\pi\)
\(510\) 0 0
\(511\) 27.3346 1.20921
\(512\) 0 0
\(513\) −2.55525 −0.112817
\(514\) 0 0
\(515\) 0.956116 0.0421315
\(516\) 0 0
\(517\) 11.6963 0.514402
\(518\) 0 0
\(519\) 9.14157 0.401270
\(520\) 0 0
\(521\) −2.72429 −0.119353 −0.0596767 0.998218i \(-0.519007\pi\)
−0.0596767 + 0.998218i \(0.519007\pi\)
\(522\) 0 0
\(523\) −27.6255 −1.20798 −0.603990 0.796992i \(-0.706423\pi\)
−0.603990 + 0.796992i \(0.706423\pi\)
\(524\) 0 0
\(525\) 13.3151 0.581117
\(526\) 0 0
\(527\) 10.5843 0.461058
\(528\) 0 0
\(529\) 0.288101 0.0125261
\(530\) 0 0
\(531\) 6.71732 0.291507
\(532\) 0 0
\(533\) 42.6233 1.84622
\(534\) 0 0
\(535\) −2.24837 −0.0972057
\(536\) 0 0
\(537\) 5.68254 0.245220
\(538\) 0 0
\(539\) 1.10551 0.0476177
\(540\) 0 0
\(541\) −21.0276 −0.904048 −0.452024 0.892006i \(-0.649298\pi\)
−0.452024 + 0.892006i \(0.649298\pi\)
\(542\) 0 0
\(543\) −22.5449 −0.967493
\(544\) 0 0
\(545\) 2.20528 0.0944638
\(546\) 0 0
\(547\) −16.1019 −0.688470 −0.344235 0.938884i \(-0.611862\pi\)
−0.344235 + 0.938884i \(0.611862\pi\)
\(548\) 0 0
\(549\) −10.0509 −0.428962
\(550\) 0 0
\(551\) −5.96277 −0.254023
\(552\) 0 0
\(553\) 4.96605 0.211178
\(554\) 0 0
\(555\) 1.47407 0.0625710
\(556\) 0 0
\(557\) 24.8272 1.05196 0.525981 0.850496i \(-0.323698\pi\)
0.525981 + 0.850496i \(0.323698\pi\)
\(558\) 0 0
\(559\) −34.7453 −1.46957
\(560\) 0 0
\(561\) −5.00111 −0.211147
\(562\) 0 0
\(563\) −18.5378 −0.781276 −0.390638 0.920544i \(-0.627746\pi\)
−0.390638 + 0.920544i \(0.627746\pi\)
\(564\) 0 0
\(565\) −1.15363 −0.0485335
\(566\) 0 0
\(567\) 2.69533 0.113193
\(568\) 0 0
\(569\) 1.86399 0.0781424 0.0390712 0.999236i \(-0.487560\pi\)
0.0390712 + 0.999236i \(0.487560\pi\)
\(570\) 0 0
\(571\) 4.01062 0.167839 0.0839197 0.996473i \(-0.473256\pi\)
0.0839197 + 0.996473i \(0.473256\pi\)
\(572\) 0 0
\(573\) 13.8900 0.580262
\(574\) 0 0
\(575\) −23.8396 −0.994180
\(576\) 0 0
\(577\) 1.58184 0.0658527 0.0329264 0.999458i \(-0.489517\pi\)
0.0329264 + 0.999458i \(0.489517\pi\)
\(578\) 0 0
\(579\) 11.8571 0.492763
\(580\) 0 0
\(581\) −16.2700 −0.674993
\(582\) 0 0
\(583\) 15.5524 0.644114
\(584\) 0 0
\(585\) 1.10313 0.0456089
\(586\) 0 0
\(587\) −29.5921 −1.22140 −0.610698 0.791863i \(-0.709111\pi\)
−0.610698 + 0.791863i \(0.709111\pi\)
\(588\) 0 0
\(589\) 22.5793 0.930362
\(590\) 0 0
\(591\) 7.71344 0.317289
\(592\) 0 0
\(593\) −25.9349 −1.06502 −0.532510 0.846424i \(-0.678751\pi\)
−0.532510 + 0.846424i \(0.678751\pi\)
\(594\) 0 0
\(595\) −0.790433 −0.0324046
\(596\) 0 0
\(597\) −11.8647 −0.485591
\(598\) 0 0
\(599\) 35.9091 1.46721 0.733604 0.679578i \(-0.237837\pi\)
0.733604 + 0.679578i \(0.237837\pi\)
\(600\) 0 0
\(601\) 9.35909 0.381765 0.190883 0.981613i \(-0.438865\pi\)
0.190883 + 0.981613i \(0.438865\pi\)
\(602\) 0 0
\(603\) −5.48628 −0.223419
\(604\) 0 0
\(605\) −1.57493 −0.0640301
\(606\) 0 0
\(607\) 24.5857 0.997902 0.498951 0.866630i \(-0.333719\pi\)
0.498951 + 0.866630i \(0.333719\pi\)
\(608\) 0 0
\(609\) 6.28965 0.254870
\(610\) 0 0
\(611\) −12.6219 −0.510626
\(612\) 0 0
\(613\) −26.5654 −1.07297 −0.536483 0.843911i \(-0.680248\pi\)
−0.536483 + 0.843911i \(0.680248\pi\)
\(614\) 0 0
\(615\) −2.31611 −0.0933945
\(616\) 0 0
\(617\) −27.2929 −1.09877 −0.549385 0.835570i \(-0.685138\pi\)
−0.549385 + 0.835570i \(0.685138\pi\)
\(618\) 0 0
\(619\) 17.6654 0.710032 0.355016 0.934860i \(-0.384475\pi\)
0.355016 + 0.934860i \(0.384475\pi\)
\(620\) 0 0
\(621\) −4.82577 −0.193652
\(622\) 0 0
\(623\) −2.33642 −0.0936067
\(624\) 0 0
\(625\) 24.1044 0.964178
\(626\) 0 0
\(627\) −10.6688 −0.426070
\(628\) 0 0
\(629\) 7.21164 0.287547
\(630\) 0 0
\(631\) 43.3134 1.72428 0.862139 0.506672i \(-0.169124\pi\)
0.862139 + 0.506672i \(0.169124\pi\)
\(632\) 0 0
\(633\) −12.8342 −0.510115
\(634\) 0 0
\(635\) 2.85226 0.113188
\(636\) 0 0
\(637\) −1.19300 −0.0472682
\(638\) 0 0
\(639\) 2.35862 0.0933054
\(640\) 0 0
\(641\) 11.0104 0.434884 0.217442 0.976073i \(-0.430229\pi\)
0.217442 + 0.976073i \(0.430229\pi\)
\(642\) 0 0
\(643\) 22.4543 0.885513 0.442756 0.896642i \(-0.354001\pi\)
0.442756 + 0.896642i \(0.354001\pi\)
\(644\) 0 0
\(645\) 1.88803 0.0743409
\(646\) 0 0
\(647\) −4.60853 −0.181180 −0.0905900 0.995888i \(-0.528875\pi\)
−0.0905900 + 0.995888i \(0.528875\pi\)
\(648\) 0 0
\(649\) 28.0465 1.10092
\(650\) 0 0
\(651\) −23.8171 −0.933464
\(652\) 0 0
\(653\) 6.19941 0.242602 0.121301 0.992616i \(-0.461293\pi\)
0.121301 + 0.992616i \(0.461293\pi\)
\(654\) 0 0
\(655\) 0.448251 0.0175146
\(656\) 0 0
\(657\) 10.1415 0.395657
\(658\) 0 0
\(659\) −45.6675 −1.77895 −0.889477 0.456980i \(-0.848931\pi\)
−0.889477 + 0.456980i \(0.848931\pi\)
\(660\) 0 0
\(661\) −40.1949 −1.56340 −0.781701 0.623654i \(-0.785648\pi\)
−0.781701 + 0.623654i \(0.785648\pi\)
\(662\) 0 0
\(663\) 5.39687 0.209597
\(664\) 0 0
\(665\) −1.68622 −0.0653887
\(666\) 0 0
\(667\) −11.2611 −0.436033
\(668\) 0 0
\(669\) −20.5846 −0.795845
\(670\) 0 0
\(671\) −41.9650 −1.62004
\(672\) 0 0
\(673\) −13.7682 −0.530727 −0.265363 0.964148i \(-0.585492\pi\)
−0.265363 + 0.964148i \(0.585492\pi\)
\(674\) 0 0
\(675\) 4.94006 0.190143
\(676\) 0 0
\(677\) −48.3502 −1.85825 −0.929124 0.369768i \(-0.879437\pi\)
−0.929124 + 0.369768i \(0.879437\pi\)
\(678\) 0 0
\(679\) 20.8347 0.799564
\(680\) 0 0
\(681\) 25.9870 0.995825
\(682\) 0 0
\(683\) −39.3798 −1.50683 −0.753414 0.657547i \(-0.771594\pi\)
−0.753414 + 0.657547i \(0.771594\pi\)
\(684\) 0 0
\(685\) −3.30166 −0.126150
\(686\) 0 0
\(687\) −16.2462 −0.619833
\(688\) 0 0
\(689\) −16.7831 −0.639386
\(690\) 0 0
\(691\) −39.0610 −1.48595 −0.742975 0.669319i \(-0.766586\pi\)
−0.742975 + 0.669319i \(0.766586\pi\)
\(692\) 0 0
\(693\) 11.2536 0.427491
\(694\) 0 0
\(695\) −2.73577 −0.103774
\(696\) 0 0
\(697\) −11.3311 −0.429197
\(698\) 0 0
\(699\) −8.61228 −0.325746
\(700\) 0 0
\(701\) −47.4853 −1.79349 −0.896747 0.442543i \(-0.854076\pi\)
−0.896747 + 0.442543i \(0.854076\pi\)
\(702\) 0 0
\(703\) 15.3845 0.580236
\(704\) 0 0
\(705\) 0.685861 0.0258310
\(706\) 0 0
\(707\) −1.47138 −0.0553369
\(708\) 0 0
\(709\) 11.0321 0.414319 0.207160 0.978307i \(-0.433578\pi\)
0.207160 + 0.978307i \(0.433578\pi\)
\(710\) 0 0
\(711\) 1.84247 0.0690979
\(712\) 0 0
\(713\) 42.6426 1.59698
\(714\) 0 0
\(715\) 4.60585 0.172249
\(716\) 0 0
\(717\) −27.0577 −1.01049
\(718\) 0 0
\(719\) 15.9644 0.595371 0.297686 0.954664i \(-0.403785\pi\)
0.297686 + 0.954664i \(0.403785\pi\)
\(720\) 0 0
\(721\) −10.5257 −0.391998
\(722\) 0 0
\(723\) −4.99854 −0.185898
\(724\) 0 0
\(725\) 11.5278 0.428133
\(726\) 0 0
\(727\) −44.5597 −1.65263 −0.826315 0.563209i \(-0.809567\pi\)
−0.826315 + 0.563209i \(0.809567\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 9.23681 0.341636
\(732\) 0 0
\(733\) −45.4408 −1.67839 −0.839196 0.543828i \(-0.816974\pi\)
−0.839196 + 0.543828i \(0.816974\pi\)
\(734\) 0 0
\(735\) 0.0648262 0.00239115
\(736\) 0 0
\(737\) −22.9066 −0.843775
\(738\) 0 0
\(739\) 7.70406 0.283398 0.141699 0.989910i \(-0.454743\pi\)
0.141699 + 0.989910i \(0.454743\pi\)
\(740\) 0 0
\(741\) 11.5131 0.422943
\(742\) 0 0
\(743\) −11.0135 −0.404047 −0.202024 0.979381i \(-0.564752\pi\)
−0.202024 + 0.979381i \(0.564752\pi\)
\(744\) 0 0
\(745\) 5.83784 0.213882
\(746\) 0 0
\(747\) −6.03637 −0.220859
\(748\) 0 0
\(749\) 24.7520 0.904417
\(750\) 0 0
\(751\) −22.3053 −0.813933 −0.406967 0.913443i \(-0.633413\pi\)
−0.406967 + 0.913443i \(0.633413\pi\)
\(752\) 0 0
\(753\) −8.14507 −0.296823
\(754\) 0 0
\(755\) 1.85331 0.0674487
\(756\) 0 0
\(757\) 6.29421 0.228767 0.114383 0.993437i \(-0.463511\pi\)
0.114383 + 0.993437i \(0.463511\pi\)
\(758\) 0 0
\(759\) −20.1488 −0.731355
\(760\) 0 0
\(761\) 14.7260 0.533817 0.266909 0.963722i \(-0.413998\pi\)
0.266909 + 0.963722i \(0.413998\pi\)
\(762\) 0 0
\(763\) −24.2776 −0.878906
\(764\) 0 0
\(765\) −0.293261 −0.0106029
\(766\) 0 0
\(767\) −30.2659 −1.09284
\(768\) 0 0
\(769\) 31.6883 1.14271 0.571354 0.820704i \(-0.306418\pi\)
0.571354 + 0.820704i \(0.306418\pi\)
\(770\) 0 0
\(771\) −8.67847 −0.312547
\(772\) 0 0
\(773\) 33.7530 1.21401 0.607005 0.794698i \(-0.292371\pi\)
0.607005 + 0.794698i \(0.292371\pi\)
\(774\) 0 0
\(775\) −43.6525 −1.56804
\(776\) 0 0
\(777\) −16.2278 −0.582171
\(778\) 0 0
\(779\) −24.1725 −0.866071
\(780\) 0 0
\(781\) 9.84781 0.352382
\(782\) 0 0
\(783\) 2.33354 0.0833940
\(784\) 0 0
\(785\) −5.30082 −0.189194
\(786\) 0 0
\(787\) 9.27299 0.330546 0.165273 0.986248i \(-0.447149\pi\)
0.165273 + 0.986248i \(0.447149\pi\)
\(788\) 0 0
\(789\) 15.7470 0.560609
\(790\) 0 0
\(791\) 12.7001 0.451564
\(792\) 0 0
\(793\) 45.2859 1.60815
\(794\) 0 0
\(795\) 0.911979 0.0323446
\(796\) 0 0
\(797\) 41.7808 1.47995 0.739976 0.672633i \(-0.234837\pi\)
0.739976 + 0.672633i \(0.234837\pi\)
\(798\) 0 0
\(799\) 3.35545 0.118707
\(800\) 0 0
\(801\) −0.866842 −0.0306284
\(802\) 0 0
\(803\) 42.3432 1.49426
\(804\) 0 0
\(805\) −3.18455 −0.112241
\(806\) 0 0
\(807\) −13.5710 −0.477723
\(808\) 0 0
\(809\) 5.07013 0.178256 0.0891282 0.996020i \(-0.471592\pi\)
0.0891282 + 0.996020i \(0.471592\pi\)
\(810\) 0 0
\(811\) −18.4918 −0.649334 −0.324667 0.945828i \(-0.605252\pi\)
−0.324667 + 0.945828i \(0.605252\pi\)
\(812\) 0 0
\(813\) −25.8147 −0.905360
\(814\) 0 0
\(815\) 3.92844 0.137607
\(816\) 0 0
\(817\) 19.7047 0.689382
\(818\) 0 0
\(819\) −12.1442 −0.424353
\(820\) 0 0
\(821\) 8.55963 0.298733 0.149367 0.988782i \(-0.452277\pi\)
0.149367 + 0.988782i \(0.452277\pi\)
\(822\) 0 0
\(823\) 0.229162 0.00798809 0.00399405 0.999992i \(-0.498729\pi\)
0.00399405 + 0.999992i \(0.498729\pi\)
\(824\) 0 0
\(825\) 20.6260 0.718104
\(826\) 0 0
\(827\) −10.2949 −0.357987 −0.178994 0.983850i \(-0.557284\pi\)
−0.178994 + 0.983850i \(0.557284\pi\)
\(828\) 0 0
\(829\) 4.42281 0.153611 0.0768053 0.997046i \(-0.475528\pi\)
0.0768053 + 0.997046i \(0.475528\pi\)
\(830\) 0 0
\(831\) 15.9744 0.554146
\(832\) 0 0
\(833\) 0.317150 0.0109886
\(834\) 0 0
\(835\) −2.25323 −0.0779763
\(836\) 0 0
\(837\) −8.83643 −0.305432
\(838\) 0 0
\(839\) −30.2460 −1.04421 −0.522103 0.852882i \(-0.674852\pi\)
−0.522103 + 0.852882i \(0.674852\pi\)
\(840\) 0 0
\(841\) −23.5546 −0.812227
\(842\) 0 0
\(843\) 3.06969 0.105726
\(844\) 0 0
\(845\) −1.78750 −0.0614920
\(846\) 0 0
\(847\) 17.3382 0.595747
\(848\) 0 0
\(849\) −31.9714 −1.09725
\(850\) 0 0
\(851\) 29.0547 0.995983
\(852\) 0 0
\(853\) 23.7512 0.813227 0.406613 0.913600i \(-0.366710\pi\)
0.406613 + 0.913600i \(0.366710\pi\)
\(854\) 0 0
\(855\) −0.625608 −0.0213954
\(856\) 0 0
\(857\) −26.2245 −0.895813 −0.447906 0.894080i \(-0.647830\pi\)
−0.447906 + 0.894080i \(0.647830\pi\)
\(858\) 0 0
\(859\) 35.5067 1.21147 0.605736 0.795665i \(-0.292879\pi\)
0.605736 + 0.795665i \(0.292879\pi\)
\(860\) 0 0
\(861\) 25.4977 0.868958
\(862\) 0 0
\(863\) −24.2621 −0.825891 −0.412945 0.910756i \(-0.635500\pi\)
−0.412945 + 0.910756i \(0.635500\pi\)
\(864\) 0 0
\(865\) 2.23816 0.0760996
\(866\) 0 0
\(867\) 15.5653 0.528625
\(868\) 0 0
\(869\) 7.69275 0.260959
\(870\) 0 0
\(871\) 24.7193 0.837581
\(872\) 0 0
\(873\) 7.72995 0.261619
\(874\) 0 0
\(875\) 6.55949 0.221751
\(876\) 0 0
\(877\) −9.06096 −0.305967 −0.152983 0.988229i \(-0.548888\pi\)
−0.152983 + 0.988229i \(0.548888\pi\)
\(878\) 0 0
\(879\) 19.2704 0.649973
\(880\) 0 0
\(881\) −45.6812 −1.53904 −0.769519 0.638624i \(-0.779504\pi\)
−0.769519 + 0.638624i \(0.779504\pi\)
\(882\) 0 0
\(883\) −41.1800 −1.38582 −0.692909 0.721025i \(-0.743671\pi\)
−0.692909 + 0.721025i \(0.743671\pi\)
\(884\) 0 0
\(885\) 1.64462 0.0552833
\(886\) 0 0
\(887\) 21.3278 0.716119 0.358059 0.933699i \(-0.383438\pi\)
0.358059 + 0.933699i \(0.383438\pi\)
\(888\) 0 0
\(889\) −31.4000 −1.05312
\(890\) 0 0
\(891\) 4.17525 0.139876
\(892\) 0 0
\(893\) 7.15812 0.239537
\(894\) 0 0
\(895\) 1.39127 0.0465051
\(896\) 0 0
\(897\) 21.7433 0.725987
\(898\) 0 0
\(899\) −20.6202 −0.687721
\(900\) 0 0
\(901\) 4.46169 0.148640
\(902\) 0 0
\(903\) −20.7850 −0.691680
\(904\) 0 0
\(905\) −5.51973 −0.183482
\(906\) 0 0
\(907\) 52.9012 1.75656 0.878278 0.478151i \(-0.158693\pi\)
0.878278 + 0.478151i \(0.158693\pi\)
\(908\) 0 0
\(909\) −0.545900 −0.0181064
\(910\) 0 0
\(911\) −16.5751 −0.549159 −0.274579 0.961564i \(-0.588539\pi\)
−0.274579 + 0.961564i \(0.588539\pi\)
\(912\) 0 0
\(913\) −25.2033 −0.834109
\(914\) 0 0
\(915\) −2.46079 −0.0813513
\(916\) 0 0
\(917\) −4.93473 −0.162959
\(918\) 0 0
\(919\) −34.8122 −1.14835 −0.574174 0.818733i \(-0.694677\pi\)
−0.574174 + 0.818733i \(0.694677\pi\)
\(920\) 0 0
\(921\) −6.36581 −0.209761
\(922\) 0 0
\(923\) −10.6271 −0.349796
\(924\) 0 0
\(925\) −29.7428 −0.977937
\(926\) 0 0
\(927\) −3.90518 −0.128263
\(928\) 0 0
\(929\) 50.6853 1.66293 0.831466 0.555576i \(-0.187502\pi\)
0.831466 + 0.555576i \(0.187502\pi\)
\(930\) 0 0
\(931\) 0.676571 0.0221737
\(932\) 0 0
\(933\) −29.4669 −0.964704
\(934\) 0 0
\(935\) −1.22444 −0.0400433
\(936\) 0 0
\(937\) 11.2435 0.367310 0.183655 0.982991i \(-0.441207\pi\)
0.183655 + 0.982991i \(0.441207\pi\)
\(938\) 0 0
\(939\) −22.9018 −0.747371
\(940\) 0 0
\(941\) −5.98689 −0.195167 −0.0975836 0.995227i \(-0.531111\pi\)
−0.0975836 + 0.995227i \(0.531111\pi\)
\(942\) 0 0
\(943\) −45.6516 −1.48662
\(944\) 0 0
\(945\) 0.659904 0.0214667
\(946\) 0 0
\(947\) 5.43436 0.176593 0.0882965 0.996094i \(-0.471858\pi\)
0.0882965 + 0.996094i \(0.471858\pi\)
\(948\) 0 0
\(949\) −45.6940 −1.48329
\(950\) 0 0
\(951\) 29.7613 0.965075
\(952\) 0 0
\(953\) −6.33785 −0.205303 −0.102652 0.994717i \(-0.532733\pi\)
−0.102652 + 0.994717i \(0.532733\pi\)
\(954\) 0 0
\(955\) 3.40072 0.110045
\(956\) 0 0
\(957\) 9.74311 0.314950
\(958\) 0 0
\(959\) 36.3474 1.17372
\(960\) 0 0
\(961\) 47.0825 1.51879
\(962\) 0 0
\(963\) 9.18330 0.295928
\(964\) 0 0
\(965\) 2.90300 0.0934509
\(966\) 0 0
\(967\) 12.8182 0.412206 0.206103 0.978530i \(-0.433922\pi\)
0.206103 + 0.978530i \(0.433922\pi\)
\(968\) 0 0
\(969\) −3.06067 −0.0983230
\(970\) 0 0
\(971\) −44.2204 −1.41910 −0.709549 0.704656i \(-0.751101\pi\)
−0.709549 + 0.704656i \(0.751101\pi\)
\(972\) 0 0
\(973\) 30.1177 0.965528
\(974\) 0 0
\(975\) −22.2582 −0.712832
\(976\) 0 0
\(977\) −11.9512 −0.382354 −0.191177 0.981556i \(-0.561230\pi\)
−0.191177 + 0.981556i \(0.561230\pi\)
\(978\) 0 0
\(979\) −3.61928 −0.115673
\(980\) 0 0
\(981\) −9.00728 −0.287580
\(982\) 0 0
\(983\) −15.5494 −0.495950 −0.247975 0.968766i \(-0.579765\pi\)
−0.247975 + 0.968766i \(0.579765\pi\)
\(984\) 0 0
\(985\) 1.88850 0.0601728
\(986\) 0 0
\(987\) −7.55053 −0.240336
\(988\) 0 0
\(989\) 37.2139 1.18333
\(990\) 0 0
\(991\) 14.6255 0.464594 0.232297 0.972645i \(-0.425376\pi\)
0.232297 + 0.972645i \(0.425376\pi\)
\(992\) 0 0
\(993\) 6.56891 0.208458
\(994\) 0 0
\(995\) −2.90488 −0.0920908
\(996\) 0 0
\(997\) −20.0004 −0.633420 −0.316710 0.948522i \(-0.602578\pi\)
−0.316710 + 0.948522i \(0.602578\pi\)
\(998\) 0 0
\(999\) −6.02074 −0.190488
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 \(a_p\))