Properties

Label 8024.2.a.y.1.2
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 1.2
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.11439 q^{3}\) \(+4.12614 q^{5}\) \(+1.17263 q^{7}\) \(+6.69943 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.11439 q^{3}\) \(+4.12614 q^{5}\) \(+1.17263 q^{7}\) \(+6.69943 q^{9}\) \(-4.55495 q^{11}\) \(-2.99424 q^{13}\) \(-12.8504 q^{15}\) \(-1.00000 q^{17}\) \(-3.45676 q^{19}\) \(-3.65201 q^{21}\) \(-0.461059 q^{23}\) \(+12.0251 q^{25}\) \(-11.5215 q^{27}\) \(+5.51517 q^{29}\) \(+0.588605 q^{31}\) \(+14.1859 q^{33}\) \(+4.83842 q^{35}\) \(+3.02077 q^{37}\) \(+9.32522 q^{39}\) \(-4.05248 q^{41}\) \(+8.04701 q^{43}\) \(+27.6428 q^{45}\) \(+1.26780 q^{47}\) \(-5.62495 q^{49}\) \(+3.11439 q^{51}\) \(-5.96344 q^{53}\) \(-18.7944 q^{55}\) \(+10.7657 q^{57}\) \(-1.00000 q^{59}\) \(+6.85935 q^{61}\) \(+7.85592 q^{63}\) \(-12.3547 q^{65}\) \(-9.06822 q^{67}\) \(+1.43592 q^{69}\) \(-0.0811455 q^{71}\) \(-13.4210 q^{73}\) \(-37.4508 q^{75}\) \(-5.34125 q^{77}\) \(+0.604690 q^{79}\) \(+15.7841 q^{81}\) \(-1.82936 q^{83}\) \(-4.12614 q^{85}\) \(-17.1764 q^{87}\) \(+13.3031 q^{89}\) \(-3.51112 q^{91}\) \(-1.83315 q^{93}\) \(-14.2631 q^{95}\) \(-2.19162 q^{97}\) \(-30.5156 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.11439 −1.79809 −0.899047 0.437851i \(-0.855740\pi\)
−0.899047 + 0.437851i \(0.855740\pi\)
\(4\) 0 0
\(5\) 4.12614 1.84527 0.922634 0.385677i \(-0.126032\pi\)
0.922634 + 0.385677i \(0.126032\pi\)
\(6\) 0 0
\(7\) 1.17263 0.443211 0.221605 0.975136i \(-0.428870\pi\)
0.221605 + 0.975136i \(0.428870\pi\)
\(8\) 0 0
\(9\) 6.69943 2.23314
\(10\) 0 0
\(11\) −4.55495 −1.37337 −0.686685 0.726955i \(-0.740935\pi\)
−0.686685 + 0.726955i \(0.740935\pi\)
\(12\) 0 0
\(13\) −2.99424 −0.830452 −0.415226 0.909718i \(-0.636297\pi\)
−0.415226 + 0.909718i \(0.636297\pi\)
\(14\) 0 0
\(15\) −12.8504 −3.31797
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −3.45676 −0.793035 −0.396518 0.918027i \(-0.629781\pi\)
−0.396518 + 0.918027i \(0.629781\pi\)
\(20\) 0 0
\(21\) −3.65201 −0.796935
\(22\) 0 0
\(23\) −0.461059 −0.0961375 −0.0480688 0.998844i \(-0.515307\pi\)
−0.0480688 + 0.998844i \(0.515307\pi\)
\(24\) 0 0
\(25\) 12.0251 2.40501
\(26\) 0 0
\(27\) −11.5215 −2.21731
\(28\) 0 0
\(29\) 5.51517 1.02414 0.512071 0.858943i \(-0.328878\pi\)
0.512071 + 0.858943i \(0.328878\pi\)
\(30\) 0 0
\(31\) 0.588605 0.105717 0.0528583 0.998602i \(-0.483167\pi\)
0.0528583 + 0.998602i \(0.483167\pi\)
\(32\) 0 0
\(33\) 14.1859 2.46945
\(34\) 0 0
\(35\) 4.83842 0.817842
\(36\) 0 0
\(37\) 3.02077 0.496611 0.248306 0.968682i \(-0.420126\pi\)
0.248306 + 0.968682i \(0.420126\pi\)
\(38\) 0 0
\(39\) 9.32522 1.49323
\(40\) 0 0
\(41\) −4.05248 −0.632891 −0.316446 0.948611i \(-0.602490\pi\)
−0.316446 + 0.948611i \(0.602490\pi\)
\(42\) 0 0
\(43\) 8.04701 1.22716 0.613579 0.789634i \(-0.289729\pi\)
0.613579 + 0.789634i \(0.289729\pi\)
\(44\) 0 0
\(45\) 27.6428 4.12075
\(46\) 0 0
\(47\) 1.26780 0.184928 0.0924641 0.995716i \(-0.470526\pi\)
0.0924641 + 0.995716i \(0.470526\pi\)
\(48\) 0 0
\(49\) −5.62495 −0.803564
\(50\) 0 0
\(51\) 3.11439 0.436102
\(52\) 0 0
\(53\) −5.96344 −0.819142 −0.409571 0.912278i \(-0.634322\pi\)
−0.409571 + 0.912278i \(0.634322\pi\)
\(54\) 0 0
\(55\) −18.7944 −2.53423
\(56\) 0 0
\(57\) 10.7657 1.42595
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 6.85935 0.878250 0.439125 0.898426i \(-0.355289\pi\)
0.439125 + 0.898426i \(0.355289\pi\)
\(62\) 0 0
\(63\) 7.85592 0.989753
\(64\) 0 0
\(65\) −12.3547 −1.53241
\(66\) 0 0
\(67\) −9.06822 −1.10786 −0.553930 0.832563i \(-0.686872\pi\)
−0.553930 + 0.832563i \(0.686872\pi\)
\(68\) 0 0
\(69\) 1.43592 0.172864
\(70\) 0 0
\(71\) −0.0811455 −0.00963020 −0.00481510 0.999988i \(-0.501533\pi\)
−0.00481510 + 0.999988i \(0.501533\pi\)
\(72\) 0 0
\(73\) −13.4210 −1.57081 −0.785403 0.618984i \(-0.787544\pi\)
−0.785403 + 0.618984i \(0.787544\pi\)
\(74\) 0 0
\(75\) −37.4508 −4.32444
\(76\) 0 0
\(77\) −5.34125 −0.608692
\(78\) 0 0
\(79\) 0.604690 0.0680329 0.0340165 0.999421i \(-0.489170\pi\)
0.0340165 + 0.999421i \(0.489170\pi\)
\(80\) 0 0
\(81\) 15.7841 1.75379
\(82\) 0 0
\(83\) −1.82936 −0.200798 −0.100399 0.994947i \(-0.532012\pi\)
−0.100399 + 0.994947i \(0.532012\pi\)
\(84\) 0 0
\(85\) −4.12614 −0.447543
\(86\) 0 0
\(87\) −17.1764 −1.84150
\(88\) 0 0
\(89\) 13.3031 1.41012 0.705061 0.709146i \(-0.250919\pi\)
0.705061 + 0.709146i \(0.250919\pi\)
\(90\) 0 0
\(91\) −3.51112 −0.368065
\(92\) 0 0
\(93\) −1.83315 −0.190088
\(94\) 0 0
\(95\) −14.2631 −1.46336
\(96\) 0 0
\(97\) −2.19162 −0.222525 −0.111262 0.993791i \(-0.535489\pi\)
−0.111262 + 0.993791i \(0.535489\pi\)
\(98\) 0 0
\(99\) −30.5156 −3.06693
\(100\) 0 0
\(101\) −15.5982 −1.55208 −0.776039 0.630685i \(-0.782774\pi\)
−0.776039 + 0.630685i \(0.782774\pi\)
\(102\) 0 0
\(103\) −2.38971 −0.235466 −0.117733 0.993045i \(-0.537563\pi\)
−0.117733 + 0.993045i \(0.537563\pi\)
\(104\) 0 0
\(105\) −15.0687 −1.47056
\(106\) 0 0
\(107\) −2.18994 −0.211710 −0.105855 0.994382i \(-0.533758\pi\)
−0.105855 + 0.994382i \(0.533758\pi\)
\(108\) 0 0
\(109\) −18.0955 −1.73324 −0.866619 0.498971i \(-0.833711\pi\)
−0.866619 + 0.498971i \(0.833711\pi\)
\(110\) 0 0
\(111\) −9.40786 −0.892954
\(112\) 0 0
\(113\) 10.9603 1.03106 0.515528 0.856873i \(-0.327596\pi\)
0.515528 + 0.856873i \(0.327596\pi\)
\(114\) 0 0
\(115\) −1.90240 −0.177399
\(116\) 0 0
\(117\) −20.0597 −1.85452
\(118\) 0 0
\(119\) −1.17263 −0.107494
\(120\) 0 0
\(121\) 9.74758 0.886143
\(122\) 0 0
\(123\) 12.6210 1.13800
\(124\) 0 0
\(125\) 28.9864 2.59263
\(126\) 0 0
\(127\) 19.5601 1.73567 0.867837 0.496848i \(-0.165510\pi\)
0.867837 + 0.496848i \(0.165510\pi\)
\(128\) 0 0
\(129\) −25.0615 −2.20654
\(130\) 0 0
\(131\) 0.264375 0.0230985 0.0115493 0.999933i \(-0.496324\pi\)
0.0115493 + 0.999933i \(0.496324\pi\)
\(132\) 0 0
\(133\) −4.05348 −0.351482
\(134\) 0 0
\(135\) −47.5393 −4.09153
\(136\) 0 0
\(137\) 10.7900 0.921849 0.460925 0.887439i \(-0.347518\pi\)
0.460925 + 0.887439i \(0.347518\pi\)
\(138\) 0 0
\(139\) −10.8712 −0.922082 −0.461041 0.887379i \(-0.652524\pi\)
−0.461041 + 0.887379i \(0.652524\pi\)
\(140\) 0 0
\(141\) −3.94844 −0.332518
\(142\) 0 0
\(143\) 13.6386 1.14052
\(144\) 0 0
\(145\) 22.7564 1.88982
\(146\) 0 0
\(147\) 17.5183 1.44488
\(148\) 0 0
\(149\) −17.6464 −1.44565 −0.722823 0.691033i \(-0.757156\pi\)
−0.722823 + 0.691033i \(0.757156\pi\)
\(150\) 0 0
\(151\) 19.6472 1.59887 0.799435 0.600752i \(-0.205132\pi\)
0.799435 + 0.600752i \(0.205132\pi\)
\(152\) 0 0
\(153\) −6.69943 −0.541617
\(154\) 0 0
\(155\) 2.42867 0.195075
\(156\) 0 0
\(157\) 4.34965 0.347140 0.173570 0.984822i \(-0.444470\pi\)
0.173570 + 0.984822i \(0.444470\pi\)
\(158\) 0 0
\(159\) 18.5725 1.47289
\(160\) 0 0
\(161\) −0.540650 −0.0426092
\(162\) 0 0
\(163\) 0.633892 0.0496503 0.0248251 0.999692i \(-0.492097\pi\)
0.0248251 + 0.999692i \(0.492097\pi\)
\(164\) 0 0
\(165\) 58.5331 4.55679
\(166\) 0 0
\(167\) −22.0070 −1.70295 −0.851475 0.524394i \(-0.824292\pi\)
−0.851475 + 0.524394i \(0.824292\pi\)
\(168\) 0 0
\(169\) −4.03455 −0.310350
\(170\) 0 0
\(171\) −23.1583 −1.77096
\(172\) 0 0
\(173\) −6.34228 −0.482195 −0.241097 0.970501i \(-0.577507\pi\)
−0.241097 + 0.970501i \(0.577507\pi\)
\(174\) 0 0
\(175\) 14.1009 1.06593
\(176\) 0 0
\(177\) 3.11439 0.234092
\(178\) 0 0
\(179\) −13.7344 −1.02656 −0.513278 0.858222i \(-0.671569\pi\)
−0.513278 + 0.858222i \(0.671569\pi\)
\(180\) 0 0
\(181\) −16.7361 −1.24398 −0.621991 0.783025i \(-0.713676\pi\)
−0.621991 + 0.783025i \(0.713676\pi\)
\(182\) 0 0
\(183\) −21.3627 −1.57918
\(184\) 0 0
\(185\) 12.4641 0.916381
\(186\) 0 0
\(187\) 4.55495 0.333091
\(188\) 0 0
\(189\) −13.5104 −0.982736
\(190\) 0 0
\(191\) 16.3773 1.18502 0.592511 0.805562i \(-0.298137\pi\)
0.592511 + 0.805562i \(0.298137\pi\)
\(192\) 0 0
\(193\) −23.2060 −1.67041 −0.835203 0.549941i \(-0.814650\pi\)
−0.835203 + 0.549941i \(0.814650\pi\)
\(194\) 0 0
\(195\) 38.4772 2.75541
\(196\) 0 0
\(197\) 16.7561 1.19382 0.596910 0.802308i \(-0.296395\pi\)
0.596910 + 0.802308i \(0.296395\pi\)
\(198\) 0 0
\(199\) −11.4111 −0.808912 −0.404456 0.914558i \(-0.632539\pi\)
−0.404456 + 0.914558i \(0.632539\pi\)
\(200\) 0 0
\(201\) 28.2420 1.99204
\(202\) 0 0
\(203\) 6.46723 0.453911
\(204\) 0 0
\(205\) −16.7211 −1.16785
\(206\) 0 0
\(207\) −3.08884 −0.214689
\(208\) 0 0
\(209\) 15.7454 1.08913
\(210\) 0 0
\(211\) 15.0814 1.03825 0.519124 0.854699i \(-0.326258\pi\)
0.519124 + 0.854699i \(0.326258\pi\)
\(212\) 0 0
\(213\) 0.252719 0.0173160
\(214\) 0 0
\(215\) 33.2031 2.26443
\(216\) 0 0
\(217\) 0.690213 0.0468547
\(218\) 0 0
\(219\) 41.7982 2.82446
\(220\) 0 0
\(221\) 2.99424 0.201414
\(222\) 0 0
\(223\) −3.30334 −0.221208 −0.110604 0.993865i \(-0.535279\pi\)
−0.110604 + 0.993865i \(0.535279\pi\)
\(224\) 0 0
\(225\) 80.5611 5.37074
\(226\) 0 0
\(227\) 15.7175 1.04320 0.521602 0.853189i \(-0.325334\pi\)
0.521602 + 0.853189i \(0.325334\pi\)
\(228\) 0 0
\(229\) −5.92162 −0.391311 −0.195656 0.980673i \(-0.562684\pi\)
−0.195656 + 0.980673i \(0.562684\pi\)
\(230\) 0 0
\(231\) 16.6347 1.09449
\(232\) 0 0
\(233\) −4.46527 −0.292530 −0.146265 0.989245i \(-0.546725\pi\)
−0.146265 + 0.989245i \(0.546725\pi\)
\(234\) 0 0
\(235\) 5.23114 0.341242
\(236\) 0 0
\(237\) −1.88324 −0.122330
\(238\) 0 0
\(239\) −3.55971 −0.230259 −0.115129 0.993351i \(-0.536728\pi\)
−0.115129 + 0.993351i \(0.536728\pi\)
\(240\) 0 0
\(241\) 22.7638 1.46635 0.733174 0.680041i \(-0.238038\pi\)
0.733174 + 0.680041i \(0.238038\pi\)
\(242\) 0 0
\(243\) −14.5935 −0.936170
\(244\) 0 0
\(245\) −23.2094 −1.48279
\(246\) 0 0
\(247\) 10.3504 0.658578
\(248\) 0 0
\(249\) 5.69733 0.361054
\(250\) 0 0
\(251\) −5.85116 −0.369322 −0.184661 0.982802i \(-0.559119\pi\)
−0.184661 + 0.982802i \(0.559119\pi\)
\(252\) 0 0
\(253\) 2.10010 0.132032
\(254\) 0 0
\(255\) 12.8504 0.804725
\(256\) 0 0
\(257\) −6.93306 −0.432472 −0.216236 0.976341i \(-0.569378\pi\)
−0.216236 + 0.976341i \(0.569378\pi\)
\(258\) 0 0
\(259\) 3.54223 0.220103
\(260\) 0 0
\(261\) 36.9485 2.28706
\(262\) 0 0
\(263\) −29.8344 −1.83967 −0.919834 0.392309i \(-0.871676\pi\)
−0.919834 + 0.392309i \(0.871676\pi\)
\(264\) 0 0
\(265\) −24.6060 −1.51154
\(266\) 0 0
\(267\) −41.4310 −2.53553
\(268\) 0 0
\(269\) −24.2491 −1.47850 −0.739248 0.673433i \(-0.764819\pi\)
−0.739248 + 0.673433i \(0.764819\pi\)
\(270\) 0 0
\(271\) −24.8194 −1.50767 −0.753835 0.657064i \(-0.771798\pi\)
−0.753835 + 0.657064i \(0.771798\pi\)
\(272\) 0 0
\(273\) 10.9350 0.661816
\(274\) 0 0
\(275\) −54.7736 −3.30297
\(276\) 0 0
\(277\) 23.0008 1.38199 0.690993 0.722862i \(-0.257174\pi\)
0.690993 + 0.722862i \(0.257174\pi\)
\(278\) 0 0
\(279\) 3.94332 0.236080
\(280\) 0 0
\(281\) −31.3246 −1.86867 −0.934336 0.356394i \(-0.884006\pi\)
−0.934336 + 0.356394i \(0.884006\pi\)
\(282\) 0 0
\(283\) −16.5797 −0.985560 −0.492780 0.870154i \(-0.664019\pi\)
−0.492780 + 0.870154i \(0.664019\pi\)
\(284\) 0 0
\(285\) 44.4209 2.63126
\(286\) 0 0
\(287\) −4.75204 −0.280504
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 6.82555 0.400121
\(292\) 0 0
\(293\) −15.5910 −0.910836 −0.455418 0.890278i \(-0.650510\pi\)
−0.455418 + 0.890278i \(0.650510\pi\)
\(294\) 0 0
\(295\) −4.12614 −0.240233
\(296\) 0 0
\(297\) 52.4798 3.04519
\(298\) 0 0
\(299\) 1.38052 0.0798376
\(300\) 0 0
\(301\) 9.43612 0.543889
\(302\) 0 0
\(303\) 48.5789 2.79078
\(304\) 0 0
\(305\) 28.3027 1.62061
\(306\) 0 0
\(307\) −29.5457 −1.68626 −0.843132 0.537707i \(-0.819291\pi\)
−0.843132 + 0.537707i \(0.819291\pi\)
\(308\) 0 0
\(309\) 7.44251 0.423389
\(310\) 0 0
\(311\) 12.4271 0.704678 0.352339 0.935873i \(-0.385386\pi\)
0.352339 + 0.935873i \(0.385386\pi\)
\(312\) 0 0
\(313\) −2.14612 −0.121306 −0.0606530 0.998159i \(-0.519318\pi\)
−0.0606530 + 0.998159i \(0.519318\pi\)
\(314\) 0 0
\(315\) 32.4147 1.82636
\(316\) 0 0
\(317\) 0.262583 0.0147481 0.00737407 0.999973i \(-0.497653\pi\)
0.00737407 + 0.999973i \(0.497653\pi\)
\(318\) 0 0
\(319\) −25.1214 −1.40653
\(320\) 0 0
\(321\) 6.82034 0.380674
\(322\) 0 0
\(323\) 3.45676 0.192339
\(324\) 0 0
\(325\) −36.0059 −1.99725
\(326\) 0 0
\(327\) 56.3566 3.11652
\(328\) 0 0
\(329\) 1.48666 0.0819621
\(330\) 0 0
\(331\) −11.0540 −0.607584 −0.303792 0.952738i \(-0.598253\pi\)
−0.303792 + 0.952738i \(0.598253\pi\)
\(332\) 0 0
\(333\) 20.2374 1.10900
\(334\) 0 0
\(335\) −37.4168 −2.04430
\(336\) 0 0
\(337\) −2.23252 −0.121613 −0.0608065 0.998150i \(-0.519367\pi\)
−0.0608065 + 0.998150i \(0.519367\pi\)
\(338\) 0 0
\(339\) −34.1346 −1.85394
\(340\) 0 0
\(341\) −2.68107 −0.145188
\(342\) 0 0
\(343\) −14.8043 −0.799359
\(344\) 0 0
\(345\) 5.92481 0.318981
\(346\) 0 0
\(347\) −3.64605 −0.195730 −0.0978650 0.995200i \(-0.531201\pi\)
−0.0978650 + 0.995200i \(0.531201\pi\)
\(348\) 0 0
\(349\) 0.937629 0.0501901 0.0250951 0.999685i \(-0.492011\pi\)
0.0250951 + 0.999685i \(0.492011\pi\)
\(350\) 0 0
\(351\) 34.4981 1.84137
\(352\) 0 0
\(353\) 24.0257 1.27876 0.639379 0.768892i \(-0.279192\pi\)
0.639379 + 0.768892i \(0.279192\pi\)
\(354\) 0 0
\(355\) −0.334818 −0.0177703
\(356\) 0 0
\(357\) 3.65201 0.193285
\(358\) 0 0
\(359\) 27.6941 1.46164 0.730820 0.682570i \(-0.239138\pi\)
0.730820 + 0.682570i \(0.239138\pi\)
\(360\) 0 0
\(361\) −7.05081 −0.371095
\(362\) 0 0
\(363\) −30.3578 −1.59337
\(364\) 0 0
\(365\) −55.3769 −2.89856
\(366\) 0 0
\(367\) 9.07744 0.473838 0.236919 0.971529i \(-0.423862\pi\)
0.236919 + 0.971529i \(0.423862\pi\)
\(368\) 0 0
\(369\) −27.1493 −1.41334
\(370\) 0 0
\(371\) −6.99288 −0.363052
\(372\) 0 0
\(373\) −20.6744 −1.07048 −0.535240 0.844700i \(-0.679779\pi\)
−0.535240 + 0.844700i \(0.679779\pi\)
\(374\) 0 0
\(375\) −90.2751 −4.66179
\(376\) 0 0
\(377\) −16.5137 −0.850501
\(378\) 0 0
\(379\) 24.1185 1.23889 0.619443 0.785042i \(-0.287359\pi\)
0.619443 + 0.785042i \(0.287359\pi\)
\(380\) 0 0
\(381\) −60.9177 −3.12091
\(382\) 0 0
\(383\) 27.8429 1.42270 0.711352 0.702836i \(-0.248083\pi\)
0.711352 + 0.702836i \(0.248083\pi\)
\(384\) 0 0
\(385\) −22.0388 −1.12320
\(386\) 0 0
\(387\) 53.9104 2.74042
\(388\) 0 0
\(389\) 14.0303 0.711364 0.355682 0.934607i \(-0.384249\pi\)
0.355682 + 0.934607i \(0.384249\pi\)
\(390\) 0 0
\(391\) 0.461059 0.0233168
\(392\) 0 0
\(393\) −0.823366 −0.0415333
\(394\) 0 0
\(395\) 2.49504 0.125539
\(396\) 0 0
\(397\) 21.3589 1.07197 0.535986 0.844227i \(-0.319940\pi\)
0.535986 + 0.844227i \(0.319940\pi\)
\(398\) 0 0
\(399\) 12.6241 0.631997
\(400\) 0 0
\(401\) 25.8587 1.29132 0.645661 0.763624i \(-0.276582\pi\)
0.645661 + 0.763624i \(0.276582\pi\)
\(402\) 0 0
\(403\) −1.76242 −0.0877925
\(404\) 0 0
\(405\) 65.1275 3.23621
\(406\) 0 0
\(407\) −13.7595 −0.682031
\(408\) 0 0
\(409\) −2.18497 −0.108040 −0.0540199 0.998540i \(-0.517203\pi\)
−0.0540199 + 0.998540i \(0.517203\pi\)
\(410\) 0 0
\(411\) −33.6042 −1.65757
\(412\) 0 0
\(413\) −1.17263 −0.0577011
\(414\) 0 0
\(415\) −7.54819 −0.370526
\(416\) 0 0
\(417\) 33.8571 1.65799
\(418\) 0 0
\(419\) −19.8867 −0.971528 −0.485764 0.874090i \(-0.661459\pi\)
−0.485764 + 0.874090i \(0.661459\pi\)
\(420\) 0 0
\(421\) −5.67589 −0.276626 −0.138313 0.990389i \(-0.544168\pi\)
−0.138313 + 0.990389i \(0.544168\pi\)
\(422\) 0 0
\(423\) 8.49357 0.412971
\(424\) 0 0
\(425\) −12.0251 −0.583301
\(426\) 0 0
\(427\) 8.04345 0.389250
\(428\) 0 0
\(429\) −42.4759 −2.05076
\(430\) 0 0
\(431\) −2.12421 −0.102320 −0.0511599 0.998690i \(-0.516292\pi\)
−0.0511599 + 0.998690i \(0.516292\pi\)
\(432\) 0 0
\(433\) 24.0825 1.15733 0.578667 0.815564i \(-0.303573\pi\)
0.578667 + 0.815564i \(0.303573\pi\)
\(434\) 0 0
\(435\) −70.8724 −3.39807
\(436\) 0 0
\(437\) 1.59377 0.0762404
\(438\) 0 0
\(439\) −32.7727 −1.56416 −0.782078 0.623180i \(-0.785840\pi\)
−0.782078 + 0.623180i \(0.785840\pi\)
\(440\) 0 0
\(441\) −37.6840 −1.79448
\(442\) 0 0
\(443\) −19.3652 −0.920067 −0.460033 0.887902i \(-0.652163\pi\)
−0.460033 + 0.887902i \(0.652163\pi\)
\(444\) 0 0
\(445\) 54.8904 2.60205
\(446\) 0 0
\(447\) 54.9577 2.59941
\(448\) 0 0
\(449\) −24.7554 −1.16828 −0.584140 0.811653i \(-0.698568\pi\)
−0.584140 + 0.811653i \(0.698568\pi\)
\(450\) 0 0
\(451\) 18.4589 0.869194
\(452\) 0 0
\(453\) −61.1892 −2.87492
\(454\) 0 0
\(455\) −14.4874 −0.679179
\(456\) 0 0
\(457\) 13.6010 0.636230 0.318115 0.948052i \(-0.396950\pi\)
0.318115 + 0.948052i \(0.396950\pi\)
\(458\) 0 0
\(459\) 11.5215 0.537777
\(460\) 0 0
\(461\) −18.6549 −0.868844 −0.434422 0.900709i \(-0.643047\pi\)
−0.434422 + 0.900709i \(0.643047\pi\)
\(462\) 0 0
\(463\) 22.5423 1.04763 0.523814 0.851833i \(-0.324509\pi\)
0.523814 + 0.851833i \(0.324509\pi\)
\(464\) 0 0
\(465\) −7.56383 −0.350764
\(466\) 0 0
\(467\) 24.5657 1.13676 0.568382 0.822765i \(-0.307570\pi\)
0.568382 + 0.822765i \(0.307570\pi\)
\(468\) 0 0
\(469\) −10.6336 −0.491015
\(470\) 0 0
\(471\) −13.5465 −0.624190
\(472\) 0 0
\(473\) −36.6537 −1.68534
\(474\) 0 0
\(475\) −41.5678 −1.90726
\(476\) 0 0
\(477\) −39.9517 −1.82926
\(478\) 0 0
\(479\) −1.75100 −0.0800050 −0.0400025 0.999200i \(-0.512737\pi\)
−0.0400025 + 0.999200i \(0.512737\pi\)
\(480\) 0 0
\(481\) −9.04490 −0.412412
\(482\) 0 0
\(483\) 1.68379 0.0766153
\(484\) 0 0
\(485\) −9.04292 −0.410618
\(486\) 0 0
\(487\) 13.1349 0.595200 0.297600 0.954691i \(-0.403814\pi\)
0.297600 + 0.954691i \(0.403814\pi\)
\(488\) 0 0
\(489\) −1.97419 −0.0892759
\(490\) 0 0
\(491\) −3.28449 −0.148227 −0.0741135 0.997250i \(-0.523613\pi\)
−0.0741135 + 0.997250i \(0.523613\pi\)
\(492\) 0 0
\(493\) −5.51517 −0.248391
\(494\) 0 0
\(495\) −125.912 −5.65931
\(496\) 0 0
\(497\) −0.0951532 −0.00426821
\(498\) 0 0
\(499\) −43.7636 −1.95913 −0.979564 0.201134i \(-0.935537\pi\)
−0.979564 + 0.201134i \(0.935537\pi\)
\(500\) 0 0
\(501\) 68.5383 3.06207
\(502\) 0 0
\(503\) 9.74232 0.434389 0.217194 0.976128i \(-0.430309\pi\)
0.217194 + 0.976128i \(0.430309\pi\)
\(504\) 0 0
\(505\) −64.3604 −2.86400
\(506\) 0 0
\(507\) 12.5652 0.558038
\(508\) 0 0
\(509\) −29.9256 −1.32643 −0.663214 0.748430i \(-0.730808\pi\)
−0.663214 + 0.748430i \(0.730808\pi\)
\(510\) 0 0
\(511\) −15.7378 −0.696198
\(512\) 0 0
\(513\) 39.8270 1.75841
\(514\) 0 0
\(515\) −9.86031 −0.434497
\(516\) 0 0
\(517\) −5.77478 −0.253975
\(518\) 0 0
\(519\) 19.7523 0.867032
\(520\) 0 0
\(521\) −28.4691 −1.24725 −0.623627 0.781722i \(-0.714341\pi\)
−0.623627 + 0.781722i \(0.714341\pi\)
\(522\) 0 0
\(523\) −36.9677 −1.61649 −0.808243 0.588849i \(-0.799581\pi\)
−0.808243 + 0.588849i \(0.799581\pi\)
\(524\) 0 0
\(525\) −43.9157 −1.91664
\(526\) 0 0
\(527\) −0.588605 −0.0256400
\(528\) 0 0
\(529\) −22.7874 −0.990758
\(530\) 0 0
\(531\) −6.69943 −0.290731
\(532\) 0 0
\(533\) 12.1341 0.525586
\(534\) 0 0
\(535\) −9.03602 −0.390661
\(536\) 0 0
\(537\) 42.7742 1.84584
\(538\) 0 0
\(539\) 25.6214 1.10359
\(540\) 0 0
\(541\) 26.4418 1.13682 0.568412 0.822744i \(-0.307558\pi\)
0.568412 + 0.822744i \(0.307558\pi\)
\(542\) 0 0
\(543\) 52.1226 2.23680
\(544\) 0 0
\(545\) −74.6648 −3.19829
\(546\) 0 0
\(547\) −26.5755 −1.13629 −0.568143 0.822930i \(-0.692338\pi\)
−0.568143 + 0.822930i \(0.692338\pi\)
\(548\) 0 0
\(549\) 45.9538 1.96126
\(550\) 0 0
\(551\) −19.0646 −0.812181
\(552\) 0 0
\(553\) 0.709074 0.0301529
\(554\) 0 0
\(555\) −38.8182 −1.64774
\(556\) 0 0
\(557\) −17.3239 −0.734039 −0.367019 0.930213i \(-0.619622\pi\)
−0.367019 + 0.930213i \(0.619622\pi\)
\(558\) 0 0
\(559\) −24.0946 −1.01909
\(560\) 0 0
\(561\) −14.1859 −0.598929
\(562\) 0 0
\(563\) −13.0724 −0.550938 −0.275469 0.961310i \(-0.588833\pi\)
−0.275469 + 0.961310i \(0.588833\pi\)
\(564\) 0 0
\(565\) 45.2237 1.90257
\(566\) 0 0
\(567\) 18.5088 0.777299
\(568\) 0 0
\(569\) −9.49116 −0.397890 −0.198945 0.980011i \(-0.563752\pi\)
−0.198945 + 0.980011i \(0.563752\pi\)
\(570\) 0 0
\(571\) 21.5508 0.901872 0.450936 0.892556i \(-0.351090\pi\)
0.450936 + 0.892556i \(0.351090\pi\)
\(572\) 0 0
\(573\) −51.0054 −2.13078
\(574\) 0 0
\(575\) −5.54427 −0.231212
\(576\) 0 0
\(577\) 3.36917 0.140261 0.0701303 0.997538i \(-0.477659\pi\)
0.0701303 + 0.997538i \(0.477659\pi\)
\(578\) 0 0
\(579\) 72.2727 3.00355
\(580\) 0 0
\(581\) −2.14515 −0.0889958
\(582\) 0 0
\(583\) 27.1632 1.12498
\(584\) 0 0
\(585\) −82.7692 −3.42208
\(586\) 0 0
\(587\) −17.7700 −0.733447 −0.366723 0.930330i \(-0.619520\pi\)
−0.366723 + 0.930330i \(0.619520\pi\)
\(588\) 0 0
\(589\) −2.03467 −0.0838370
\(590\) 0 0
\(591\) −52.1849 −2.14660
\(592\) 0 0
\(593\) −23.7553 −0.975513 −0.487757 0.872980i \(-0.662185\pi\)
−0.487757 + 0.872980i \(0.662185\pi\)
\(594\) 0 0
\(595\) −4.83842 −0.198356
\(596\) 0 0
\(597\) 35.5386 1.45450
\(598\) 0 0
\(599\) 3.74074 0.152842 0.0764212 0.997076i \(-0.475651\pi\)
0.0764212 + 0.997076i \(0.475651\pi\)
\(600\) 0 0
\(601\) −8.54129 −0.348407 −0.174203 0.984710i \(-0.555735\pi\)
−0.174203 + 0.984710i \(0.555735\pi\)
\(602\) 0 0
\(603\) −60.7520 −2.47401
\(604\) 0 0
\(605\) 40.2199 1.63517
\(606\) 0 0
\(607\) −18.8510 −0.765139 −0.382569 0.923927i \(-0.624961\pi\)
−0.382569 + 0.923927i \(0.624961\pi\)
\(608\) 0 0
\(609\) −20.1415 −0.816174
\(610\) 0 0
\(611\) −3.79610 −0.153574
\(612\) 0 0
\(613\) 49.3590 1.99359 0.996796 0.0799889i \(-0.0254885\pi\)
0.996796 + 0.0799889i \(0.0254885\pi\)
\(614\) 0 0
\(615\) 52.0761 2.09991
\(616\) 0 0
\(617\) −27.3583 −1.10141 −0.550703 0.834702i \(-0.685640\pi\)
−0.550703 + 0.834702i \(0.685640\pi\)
\(618\) 0 0
\(619\) 23.3006 0.936531 0.468266 0.883588i \(-0.344879\pi\)
0.468266 + 0.883588i \(0.344879\pi\)
\(620\) 0 0
\(621\) 5.31209 0.213167
\(622\) 0 0
\(623\) 15.5995 0.624981
\(624\) 0 0
\(625\) 59.4769 2.37907
\(626\) 0 0
\(627\) −49.0373 −1.95836
\(628\) 0 0
\(629\) −3.02077 −0.120446
\(630\) 0 0
\(631\) −32.3083 −1.28617 −0.643086 0.765794i \(-0.722346\pi\)
−0.643086 + 0.765794i \(0.722346\pi\)
\(632\) 0 0
\(633\) −46.9694 −1.86687
\(634\) 0 0
\(635\) 80.7076 3.20278
\(636\) 0 0
\(637\) 16.8424 0.667321
\(638\) 0 0
\(639\) −0.543629 −0.0215056
\(640\) 0 0
\(641\) 16.4350 0.649143 0.324571 0.945861i \(-0.394780\pi\)
0.324571 + 0.945861i \(0.394780\pi\)
\(642\) 0 0
\(643\) −38.7344 −1.52754 −0.763768 0.645490i \(-0.776653\pi\)
−0.763768 + 0.645490i \(0.776653\pi\)
\(644\) 0 0
\(645\) −103.407 −4.07167
\(646\) 0 0
\(647\) 44.7163 1.75798 0.878989 0.476843i \(-0.158219\pi\)
0.878989 + 0.476843i \(0.158219\pi\)
\(648\) 0 0
\(649\) 4.55495 0.178797
\(650\) 0 0
\(651\) −2.14959 −0.0842492
\(652\) 0 0
\(653\) 5.26890 0.206188 0.103094 0.994672i \(-0.467126\pi\)
0.103094 + 0.994672i \(0.467126\pi\)
\(654\) 0 0
\(655\) 1.09085 0.0426229
\(656\) 0 0
\(657\) −89.9130 −3.50784
\(658\) 0 0
\(659\) −29.3417 −1.14299 −0.571495 0.820605i \(-0.693636\pi\)
−0.571495 + 0.820605i \(0.693636\pi\)
\(660\) 0 0
\(661\) 26.2952 1.02276 0.511382 0.859353i \(-0.329134\pi\)
0.511382 + 0.859353i \(0.329134\pi\)
\(662\) 0 0
\(663\) −9.32522 −0.362162
\(664\) 0 0
\(665\) −16.7253 −0.648578
\(666\) 0 0
\(667\) −2.54282 −0.0984585
\(668\) 0 0
\(669\) 10.2879 0.397753
\(670\) 0 0
\(671\) −31.2440 −1.20616
\(672\) 0 0
\(673\) −3.51890 −0.135644 −0.0678218 0.997697i \(-0.521605\pi\)
−0.0678218 + 0.997697i \(0.521605\pi\)
\(674\) 0 0
\(675\) −138.547 −5.33266
\(676\) 0 0
\(677\) −25.5634 −0.982483 −0.491241 0.871024i \(-0.663457\pi\)
−0.491241 + 0.871024i \(0.663457\pi\)
\(678\) 0 0
\(679\) −2.56994 −0.0986254
\(680\) 0 0
\(681\) −48.9503 −1.87578
\(682\) 0 0
\(683\) −4.34941 −0.166426 −0.0832128 0.996532i \(-0.526518\pi\)
−0.0832128 + 0.996532i \(0.526518\pi\)
\(684\) 0 0
\(685\) 44.5210 1.70106
\(686\) 0 0
\(687\) 18.4422 0.703615
\(688\) 0 0
\(689\) 17.8560 0.680258
\(690\) 0 0
\(691\) 48.4384 1.84269 0.921343 0.388752i \(-0.127094\pi\)
0.921343 + 0.388752i \(0.127094\pi\)
\(692\) 0 0
\(693\) −35.7834 −1.35930
\(694\) 0 0
\(695\) −44.8561 −1.70149
\(696\) 0 0
\(697\) 4.05248 0.153499
\(698\) 0 0
\(699\) 13.9066 0.525996
\(700\) 0 0
\(701\) 21.1163 0.797553 0.398777 0.917048i \(-0.369435\pi\)
0.398777 + 0.917048i \(0.369435\pi\)
\(702\) 0 0
\(703\) −10.4421 −0.393830
\(704\) 0 0
\(705\) −16.2918 −0.613586
\(706\) 0 0
\(707\) −18.2908 −0.687897
\(708\) 0 0
\(709\) 29.3265 1.10138 0.550690 0.834710i \(-0.314365\pi\)
0.550690 + 0.834710i \(0.314365\pi\)
\(710\) 0 0
\(711\) 4.05108 0.151927
\(712\) 0 0
\(713\) −0.271382 −0.0101633
\(714\) 0 0
\(715\) 56.2748 2.10456
\(716\) 0 0
\(717\) 11.0863 0.414027
\(718\) 0 0
\(719\) 34.8870 1.30107 0.650533 0.759478i \(-0.274545\pi\)
0.650533 + 0.759478i \(0.274545\pi\)
\(720\) 0 0
\(721\) −2.80224 −0.104361
\(722\) 0 0
\(723\) −70.8955 −2.63663
\(724\) 0 0
\(725\) 66.3203 2.46308
\(726\) 0 0
\(727\) 4.49022 0.166533 0.0832665 0.996527i \(-0.473465\pi\)
0.0832665 + 0.996527i \(0.473465\pi\)
\(728\) 0 0
\(729\) −1.90262 −0.0704674
\(730\) 0 0
\(731\) −8.04701 −0.297629
\(732\) 0 0
\(733\) −25.4027 −0.938271 −0.469135 0.883126i \(-0.655434\pi\)
−0.469135 + 0.883126i \(0.655434\pi\)
\(734\) 0 0
\(735\) 72.2830 2.66620
\(736\) 0 0
\(737\) 41.3053 1.52150
\(738\) 0 0
\(739\) −33.2763 −1.22409 −0.612045 0.790823i \(-0.709653\pi\)
−0.612045 + 0.790823i \(0.709653\pi\)
\(740\) 0 0
\(741\) −32.2351 −1.18418
\(742\) 0 0
\(743\) −10.8147 −0.396752 −0.198376 0.980126i \(-0.563567\pi\)
−0.198376 + 0.980126i \(0.563567\pi\)
\(744\) 0 0
\(745\) −72.8115 −2.66761
\(746\) 0 0
\(747\) −12.2557 −0.448411
\(748\) 0 0
\(749\) −2.56798 −0.0938320
\(750\) 0 0
\(751\) −4.67715 −0.170672 −0.0853358 0.996352i \(-0.527196\pi\)
−0.0853358 + 0.996352i \(0.527196\pi\)
\(752\) 0 0
\(753\) 18.2228 0.664075
\(754\) 0 0
\(755\) 81.0674 2.95034
\(756\) 0 0
\(757\) 3.85501 0.140113 0.0700564 0.997543i \(-0.477682\pi\)
0.0700564 + 0.997543i \(0.477682\pi\)
\(758\) 0 0
\(759\) −6.54054 −0.237407
\(760\) 0 0
\(761\) −17.4761 −0.633509 −0.316755 0.948507i \(-0.602593\pi\)
−0.316755 + 0.948507i \(0.602593\pi\)
\(762\) 0 0
\(763\) −21.2193 −0.768189
\(764\) 0 0
\(765\) −27.6428 −0.999429
\(766\) 0 0
\(767\) 2.99424 0.108116
\(768\) 0 0
\(769\) −33.4052 −1.20462 −0.602311 0.798262i \(-0.705753\pi\)
−0.602311 + 0.798262i \(0.705753\pi\)
\(770\) 0 0
\(771\) 21.5923 0.777626
\(772\) 0 0
\(773\) 5.47206 0.196816 0.0984081 0.995146i \(-0.468625\pi\)
0.0984081 + 0.995146i \(0.468625\pi\)
\(774\) 0 0
\(775\) 7.07802 0.254250
\(776\) 0 0
\(777\) −11.0319 −0.395767
\(778\) 0 0
\(779\) 14.0085 0.501905
\(780\) 0 0
\(781\) 0.369614 0.0132258
\(782\) 0 0
\(783\) −63.5430 −2.27084
\(784\) 0 0
\(785\) 17.9473 0.640566
\(786\) 0 0
\(787\) 24.8078 0.884303 0.442151 0.896940i \(-0.354215\pi\)
0.442151 + 0.896940i \(0.354215\pi\)
\(788\) 0 0
\(789\) 92.9160 3.30790
\(790\) 0 0
\(791\) 12.8523 0.456975
\(792\) 0 0
\(793\) −20.5385 −0.729344
\(794\) 0 0
\(795\) 76.6328 2.71788
\(796\) 0 0
\(797\) 7.73963 0.274152 0.137076 0.990561i \(-0.456230\pi\)
0.137076 + 0.990561i \(0.456230\pi\)
\(798\) 0 0
\(799\) −1.26780 −0.0448517
\(800\) 0 0
\(801\) 89.1231 3.14901
\(802\) 0 0
\(803\) 61.1319 2.15730
\(804\) 0 0
\(805\) −2.23080 −0.0786253
\(806\) 0 0
\(807\) 75.5213 2.65848
\(808\) 0 0
\(809\) 20.4809 0.720069 0.360034 0.932939i \(-0.382765\pi\)
0.360034 + 0.932939i \(0.382765\pi\)
\(810\) 0 0
\(811\) 29.8759 1.04909 0.524543 0.851384i \(-0.324236\pi\)
0.524543 + 0.851384i \(0.324236\pi\)
\(812\) 0 0
\(813\) 77.2972 2.71093
\(814\) 0 0
\(815\) 2.61553 0.0916180
\(816\) 0 0
\(817\) −27.8166 −0.973179
\(818\) 0 0
\(819\) −23.5225 −0.821943
\(820\) 0 0
\(821\) −14.5822 −0.508921 −0.254461 0.967083i \(-0.581898\pi\)
−0.254461 + 0.967083i \(0.581898\pi\)
\(822\) 0 0
\(823\) 48.8653 1.70334 0.851668 0.524082i \(-0.175591\pi\)
0.851668 + 0.524082i \(0.175591\pi\)
\(824\) 0 0
\(825\) 170.586 5.93906
\(826\) 0 0
\(827\) −20.7292 −0.720823 −0.360412 0.932793i \(-0.617364\pi\)
−0.360412 + 0.932793i \(0.617364\pi\)
\(828\) 0 0
\(829\) 4.78801 0.166295 0.0831473 0.996537i \(-0.473503\pi\)
0.0831473 + 0.996537i \(0.473503\pi\)
\(830\) 0 0
\(831\) −71.6335 −2.48494
\(832\) 0 0
\(833\) 5.62495 0.194893
\(834\) 0 0
\(835\) −90.8040 −3.14240
\(836\) 0 0
\(837\) −6.78161 −0.234407
\(838\) 0 0
\(839\) 6.32786 0.218462 0.109231 0.994016i \(-0.465161\pi\)
0.109231 + 0.994016i \(0.465161\pi\)
\(840\) 0 0
\(841\) 1.41715 0.0488673
\(842\) 0 0
\(843\) 97.5572 3.36005
\(844\) 0 0
\(845\) −16.6471 −0.572679
\(846\) 0 0
\(847\) 11.4303 0.392748
\(848\) 0 0
\(849\) 51.6356 1.77213
\(850\) 0 0
\(851\) −1.39275 −0.0477430
\(852\) 0 0
\(853\) −24.2047 −0.828752 −0.414376 0.910106i \(-0.636000\pi\)
−0.414376 + 0.910106i \(0.636000\pi\)
\(854\) 0 0
\(855\) −95.5546 −3.26790
\(856\) 0 0
\(857\) −7.42641 −0.253681 −0.126841 0.991923i \(-0.540484\pi\)
−0.126841 + 0.991923i \(0.540484\pi\)
\(858\) 0 0
\(859\) −35.5180 −1.21186 −0.605930 0.795518i \(-0.707199\pi\)
−0.605930 + 0.795518i \(0.707199\pi\)
\(860\) 0 0
\(861\) 14.7997 0.504373
\(862\) 0 0
\(863\) −29.1511 −0.992315 −0.496157 0.868233i \(-0.665256\pi\)
−0.496157 + 0.868233i \(0.665256\pi\)
\(864\) 0 0
\(865\) −26.1692 −0.889778
\(866\) 0 0
\(867\) −3.11439 −0.105770
\(868\) 0 0
\(869\) −2.75433 −0.0934343
\(870\) 0 0
\(871\) 27.1524 0.920024
\(872\) 0 0
\(873\) −14.6826 −0.496930
\(874\) 0 0
\(875\) 33.9902 1.14908
\(876\) 0 0
\(877\) −4.55632 −0.153856 −0.0769279 0.997037i \(-0.524511\pi\)
−0.0769279 + 0.997037i \(0.524511\pi\)
\(878\) 0 0
\(879\) 48.5565 1.63777
\(880\) 0 0
\(881\) 46.3799 1.56258 0.781289 0.624169i \(-0.214563\pi\)
0.781289 + 0.624169i \(0.214563\pi\)
\(882\) 0 0
\(883\) −37.9096 −1.27576 −0.637880 0.770136i \(-0.720188\pi\)
−0.637880 + 0.770136i \(0.720188\pi\)
\(884\) 0 0
\(885\) 12.8504 0.431962
\(886\) 0 0
\(887\) −35.4535 −1.19041 −0.595207 0.803573i \(-0.702930\pi\)
−0.595207 + 0.803573i \(0.702930\pi\)
\(888\) 0 0
\(889\) 22.9366 0.769269
\(890\) 0 0
\(891\) −71.8959 −2.40860
\(892\) 0 0
\(893\) −4.38249 −0.146655
\(894\) 0 0
\(895\) −56.6700 −1.89427
\(896\) 0 0
\(897\) −4.29948 −0.143555
\(898\) 0 0
\(899\) 3.24626 0.108269
\(900\) 0 0
\(901\) 5.96344 0.198671
\(902\) 0 0
\(903\) −29.3878 −0.977964
\(904\) 0 0
\(905\) −69.0554 −2.29548
\(906\) 0 0
\(907\) −18.4105 −0.611312 −0.305656 0.952142i \(-0.598876\pi\)
−0.305656 + 0.952142i \(0.598876\pi\)
\(908\) 0 0
\(909\) −104.499 −3.46601
\(910\) 0 0
\(911\) −4.31180 −0.142856 −0.0714281 0.997446i \(-0.522756\pi\)
−0.0714281 + 0.997446i \(0.522756\pi\)
\(912\) 0 0
\(913\) 8.33263 0.275770
\(914\) 0 0
\(915\) −88.1456 −2.91400
\(916\) 0 0
\(917\) 0.310012 0.0102375
\(918\) 0 0
\(919\) 11.7584 0.387873 0.193936 0.981014i \(-0.437874\pi\)
0.193936 + 0.981014i \(0.437874\pi\)
\(920\) 0 0
\(921\) 92.0169 3.03206
\(922\) 0 0
\(923\) 0.242969 0.00799742
\(924\) 0 0
\(925\) 36.3249 1.19436
\(926\) 0 0
\(927\) −16.0097 −0.525829
\(928\) 0 0
\(929\) −44.8861 −1.47267 −0.736333 0.676619i \(-0.763444\pi\)
−0.736333 + 0.676619i \(0.763444\pi\)
\(930\) 0 0
\(931\) 19.4441 0.637255
\(932\) 0 0
\(933\) −38.7029 −1.26708
\(934\) 0 0
\(935\) 18.7944 0.614642
\(936\) 0 0
\(937\) 18.6852 0.610420 0.305210 0.952285i \(-0.401273\pi\)
0.305210 + 0.952285i \(0.401273\pi\)
\(938\) 0 0
\(939\) 6.68387 0.218120
\(940\) 0 0
\(941\) −20.7971 −0.677966 −0.338983 0.940793i \(-0.610083\pi\)
−0.338983 + 0.940793i \(0.610083\pi\)
\(942\) 0 0
\(943\) 1.86843 0.0608446
\(944\) 0 0
\(945\) −55.7458 −1.81341
\(946\) 0 0
\(947\) 21.0334 0.683495 0.341747 0.939792i \(-0.388981\pi\)
0.341747 + 0.939792i \(0.388981\pi\)
\(948\) 0 0
\(949\) 40.1856 1.30448
\(950\) 0 0
\(951\) −0.817786 −0.0265185
\(952\) 0 0
\(953\) 21.1419 0.684855 0.342427 0.939544i \(-0.388751\pi\)
0.342427 + 0.939544i \(0.388751\pi\)
\(954\) 0 0
\(955\) 67.5752 2.18668
\(956\) 0 0
\(957\) 78.2377 2.52907
\(958\) 0 0
\(959\) 12.6526 0.408573
\(960\) 0 0
\(961\) −30.6535 −0.988824
\(962\) 0 0
\(963\) −14.6714 −0.472779
\(964\) 0 0
\(965\) −95.7514 −3.08235
\(966\) 0 0
\(967\) −2.17163 −0.0698350 −0.0349175 0.999390i \(-0.511117\pi\)
−0.0349175 + 0.999390i \(0.511117\pi\)
\(968\) 0 0
\(969\) −10.7657 −0.345844
\(970\) 0 0
\(971\) 13.0442 0.418608 0.209304 0.977851i \(-0.432880\pi\)
0.209304 + 0.977851i \(0.432880\pi\)
\(972\) 0 0
\(973\) −12.7478 −0.408677
\(974\) 0 0
\(975\) 112.136 3.59124
\(976\) 0 0
\(977\) −18.8436 −0.602862 −0.301431 0.953488i \(-0.597464\pi\)
−0.301431 + 0.953488i \(0.597464\pi\)
\(978\) 0 0
\(979\) −60.5948 −1.93662
\(980\) 0 0
\(981\) −121.230 −3.87057
\(982\) 0 0
\(983\) −0.300627 −0.00958853 −0.00479426 0.999989i \(-0.501526\pi\)
−0.00479426 + 0.999989i \(0.501526\pi\)
\(984\) 0 0
\(985\) 69.1379 2.20292
\(986\) 0 0
\(987\) −4.63004 −0.147376
\(988\) 0 0
\(989\) −3.71015 −0.117976
\(990\) 0 0
\(991\) −21.4890 −0.682622 −0.341311 0.939950i \(-0.610871\pi\)
−0.341311 + 0.939950i \(0.610871\pi\)
\(992\) 0 0
\(993\) 34.4265 1.09249
\(994\) 0 0
\(995\) −47.0838 −1.49266
\(996\) 0 0
\(997\) 36.3345 1.15072 0.575362 0.817899i \(-0.304861\pi\)
0.575362 + 0.817899i \(0.304861\pi\)
\(998\) 0 0
\(999\) −34.8037 −1.10114
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 \(a_p\))