Properties

Label 8048.2.a.v.1.3
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.84528 q^{3}\) \(-2.72112 q^{5}\) \(+3.71681 q^{7}\) \(+5.09562 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.84528 q^{3}\) \(-2.72112 q^{5}\) \(+3.71681 q^{7}\) \(+5.09562 q^{9}\) \(+3.83632 q^{11}\) \(+2.85172 q^{13}\) \(+7.74235 q^{15}\) \(+8.15606 q^{17}\) \(-3.41495 q^{19}\) \(-10.5754 q^{21}\) \(-0.915770 q^{23}\) \(+2.40450 q^{25}\) \(-5.96262 q^{27}\) \(-9.16823 q^{29}\) \(-5.69042 q^{31}\) \(-10.9154 q^{33}\) \(-10.1139 q^{35}\) \(-8.85477 q^{37}\) \(-8.11396 q^{39}\) \(-10.6339 q^{41}\) \(+11.1515 q^{43}\) \(-13.8658 q^{45}\) \(+3.44500 q^{47}\) \(+6.81471 q^{49}\) \(-23.2063 q^{51}\) \(-4.95726 q^{53}\) \(-10.4391 q^{55}\) \(+9.71648 q^{57}\) \(-2.81555 q^{59}\) \(-3.59989 q^{61}\) \(+18.9395 q^{63}\) \(-7.75989 q^{65}\) \(+9.01369 q^{67}\) \(+2.60562 q^{69}\) \(+7.15270 q^{71}\) \(-7.82872 q^{73}\) \(-6.84147 q^{75}\) \(+14.2589 q^{77}\) \(-13.4571 q^{79}\) \(+1.67848 q^{81}\) \(+13.5797 q^{83}\) \(-22.1936 q^{85}\) \(+26.0862 q^{87}\) \(+6.47898 q^{89}\) \(+10.5993 q^{91}\) \(+16.1908 q^{93}\) \(+9.29248 q^{95}\) \(+16.0682 q^{97}\) \(+19.5484 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.84528 −1.64272 −0.821362 0.570408i \(-0.806785\pi\)
−0.821362 + 0.570408i \(0.806785\pi\)
\(4\) 0 0
\(5\) −2.72112 −1.21692 −0.608461 0.793584i \(-0.708213\pi\)
−0.608461 + 0.793584i \(0.708213\pi\)
\(6\) 0 0
\(7\) 3.71681 1.40482 0.702412 0.711771i \(-0.252106\pi\)
0.702412 + 0.711771i \(0.252106\pi\)
\(8\) 0 0
\(9\) 5.09562 1.69854
\(10\) 0 0
\(11\) 3.83632 1.15670 0.578348 0.815790i \(-0.303698\pi\)
0.578348 + 0.815790i \(0.303698\pi\)
\(12\) 0 0
\(13\) 2.85172 0.790926 0.395463 0.918482i \(-0.370584\pi\)
0.395463 + 0.918482i \(0.370584\pi\)
\(14\) 0 0
\(15\) 7.74235 1.99907
\(16\) 0 0
\(17\) 8.15606 1.97814 0.989068 0.147460i \(-0.0471098\pi\)
0.989068 + 0.147460i \(0.0471098\pi\)
\(18\) 0 0
\(19\) −3.41495 −0.783443 −0.391721 0.920084i \(-0.628120\pi\)
−0.391721 + 0.920084i \(0.628120\pi\)
\(20\) 0 0
\(21\) −10.5754 −2.30774
\(22\) 0 0
\(23\) −0.915770 −0.190951 −0.0954756 0.995432i \(-0.530437\pi\)
−0.0954756 + 0.995432i \(0.530437\pi\)
\(24\) 0 0
\(25\) 2.40450 0.480900
\(26\) 0 0
\(27\) −5.96262 −1.14751
\(28\) 0 0
\(29\) −9.16823 −1.70250 −0.851249 0.524763i \(-0.824154\pi\)
−0.851249 + 0.524763i \(0.824154\pi\)
\(30\) 0 0
\(31\) −5.69042 −1.02203 −0.511014 0.859572i \(-0.670730\pi\)
−0.511014 + 0.859572i \(0.670730\pi\)
\(32\) 0 0
\(33\) −10.9154 −1.90013
\(34\) 0 0
\(35\) −10.1139 −1.70956
\(36\) 0 0
\(37\) −8.85477 −1.45571 −0.727857 0.685729i \(-0.759484\pi\)
−0.727857 + 0.685729i \(0.759484\pi\)
\(38\) 0 0
\(39\) −8.11396 −1.29927
\(40\) 0 0
\(41\) −10.6339 −1.66074 −0.830368 0.557215i \(-0.811870\pi\)
−0.830368 + 0.557215i \(0.811870\pi\)
\(42\) 0 0
\(43\) 11.1515 1.70058 0.850292 0.526312i \(-0.176425\pi\)
0.850292 + 0.526312i \(0.176425\pi\)
\(44\) 0 0
\(45\) −13.8658 −2.06699
\(46\) 0 0
\(47\) 3.44500 0.502504 0.251252 0.967922i \(-0.419158\pi\)
0.251252 + 0.967922i \(0.419158\pi\)
\(48\) 0 0
\(49\) 6.81471 0.973530
\(50\) 0 0
\(51\) −23.2063 −3.24953
\(52\) 0 0
\(53\) −4.95726 −0.680932 −0.340466 0.940257i \(-0.610585\pi\)
−0.340466 + 0.940257i \(0.610585\pi\)
\(54\) 0 0
\(55\) −10.4391 −1.40761
\(56\) 0 0
\(57\) 9.71648 1.28698
\(58\) 0 0
\(59\) −2.81555 −0.366554 −0.183277 0.983061i \(-0.558671\pi\)
−0.183277 + 0.983061i \(0.558671\pi\)
\(60\) 0 0
\(61\) −3.59989 −0.460919 −0.230460 0.973082i \(-0.574023\pi\)
−0.230460 + 0.973082i \(0.574023\pi\)
\(62\) 0 0
\(63\) 18.9395 2.38615
\(64\) 0 0
\(65\) −7.75989 −0.962496
\(66\) 0 0
\(67\) 9.01369 1.10120 0.550598 0.834770i \(-0.314400\pi\)
0.550598 + 0.834770i \(0.314400\pi\)
\(68\) 0 0
\(69\) 2.60562 0.313680
\(70\) 0 0
\(71\) 7.15270 0.848869 0.424435 0.905459i \(-0.360473\pi\)
0.424435 + 0.905459i \(0.360473\pi\)
\(72\) 0 0
\(73\) −7.82872 −0.916282 −0.458141 0.888880i \(-0.651485\pi\)
−0.458141 + 0.888880i \(0.651485\pi\)
\(74\) 0 0
\(75\) −6.84147 −0.789985
\(76\) 0 0
\(77\) 14.2589 1.62495
\(78\) 0 0
\(79\) −13.4571 −1.51405 −0.757024 0.653387i \(-0.773347\pi\)
−0.757024 + 0.653387i \(0.773347\pi\)
\(80\) 0 0
\(81\) 1.67848 0.186497
\(82\) 0 0
\(83\) 13.5797 1.49056 0.745280 0.666751i \(-0.232316\pi\)
0.745280 + 0.666751i \(0.232316\pi\)
\(84\) 0 0
\(85\) −22.1936 −2.40724
\(86\) 0 0
\(87\) 26.0862 2.79673
\(88\) 0 0
\(89\) 6.47898 0.686770 0.343385 0.939195i \(-0.388426\pi\)
0.343385 + 0.939195i \(0.388426\pi\)
\(90\) 0 0
\(91\) 10.5993 1.11111
\(92\) 0 0
\(93\) 16.1908 1.67891
\(94\) 0 0
\(95\) 9.29248 0.953389
\(96\) 0 0
\(97\) 16.0682 1.63148 0.815741 0.578417i \(-0.196329\pi\)
0.815741 + 0.578417i \(0.196329\pi\)
\(98\) 0 0
\(99\) 19.5484 1.96469
\(100\) 0 0
\(101\) −19.2180 −1.91226 −0.956131 0.292940i \(-0.905366\pi\)
−0.956131 + 0.292940i \(0.905366\pi\)
\(102\) 0 0
\(103\) 0.857652 0.0845070 0.0422535 0.999107i \(-0.486546\pi\)
0.0422535 + 0.999107i \(0.486546\pi\)
\(104\) 0 0
\(105\) 28.7769 2.80834
\(106\) 0 0
\(107\) −17.7650 −1.71741 −0.858703 0.512474i \(-0.828729\pi\)
−0.858703 + 0.512474i \(0.828729\pi\)
\(108\) 0 0
\(109\) −17.5952 −1.68532 −0.842659 0.538448i \(-0.819011\pi\)
−0.842659 + 0.538448i \(0.819011\pi\)
\(110\) 0 0
\(111\) 25.1943 2.39134
\(112\) 0 0
\(113\) 8.81848 0.829573 0.414786 0.909919i \(-0.363856\pi\)
0.414786 + 0.909919i \(0.363856\pi\)
\(114\) 0 0
\(115\) 2.49192 0.232373
\(116\) 0 0
\(117\) 14.5313 1.34342
\(118\) 0 0
\(119\) 30.3146 2.77893
\(120\) 0 0
\(121\) 3.71739 0.337944
\(122\) 0 0
\(123\) 30.2564 2.72813
\(124\) 0 0
\(125\) 7.06267 0.631705
\(126\) 0 0
\(127\) −13.2789 −1.17831 −0.589155 0.808020i \(-0.700539\pi\)
−0.589155 + 0.808020i \(0.700539\pi\)
\(128\) 0 0
\(129\) −31.7291 −2.79359
\(130\) 0 0
\(131\) 2.42642 0.211997 0.105999 0.994366i \(-0.466196\pi\)
0.105999 + 0.994366i \(0.466196\pi\)
\(132\) 0 0
\(133\) −12.6927 −1.10060
\(134\) 0 0
\(135\) 16.2250 1.39643
\(136\) 0 0
\(137\) −3.65954 −0.312656 −0.156328 0.987705i \(-0.549966\pi\)
−0.156328 + 0.987705i \(0.549966\pi\)
\(138\) 0 0
\(139\) −3.40899 −0.289147 −0.144574 0.989494i \(-0.546181\pi\)
−0.144574 + 0.989494i \(0.546181\pi\)
\(140\) 0 0
\(141\) −9.80198 −0.825475
\(142\) 0 0
\(143\) 10.9401 0.914861
\(144\) 0 0
\(145\) 24.9479 2.07181
\(146\) 0 0
\(147\) −19.3898 −1.59924
\(148\) 0 0
\(149\) 10.7745 0.882678 0.441339 0.897340i \(-0.354504\pi\)
0.441339 + 0.897340i \(0.354504\pi\)
\(150\) 0 0
\(151\) −10.4733 −0.852309 −0.426154 0.904650i \(-0.640132\pi\)
−0.426154 + 0.904650i \(0.640132\pi\)
\(152\) 0 0
\(153\) 41.5602 3.35994
\(154\) 0 0
\(155\) 15.4843 1.24373
\(156\) 0 0
\(157\) 2.27873 0.181862 0.0909310 0.995857i \(-0.471016\pi\)
0.0909310 + 0.995857i \(0.471016\pi\)
\(158\) 0 0
\(159\) 14.1048 1.11858
\(160\) 0 0
\(161\) −3.40375 −0.268253
\(162\) 0 0
\(163\) −15.0950 −1.18233 −0.591166 0.806550i \(-0.701332\pi\)
−0.591166 + 0.806550i \(0.701332\pi\)
\(164\) 0 0
\(165\) 29.7022 2.31231
\(166\) 0 0
\(167\) 10.3361 0.799830 0.399915 0.916552i \(-0.369040\pi\)
0.399915 + 0.916552i \(0.369040\pi\)
\(168\) 0 0
\(169\) −4.86767 −0.374436
\(170\) 0 0
\(171\) −17.4013 −1.33071
\(172\) 0 0
\(173\) −15.6052 −1.18644 −0.593221 0.805040i \(-0.702144\pi\)
−0.593221 + 0.805040i \(0.702144\pi\)
\(174\) 0 0
\(175\) 8.93707 0.675579
\(176\) 0 0
\(177\) 8.01104 0.602147
\(178\) 0 0
\(179\) 5.86603 0.438448 0.219224 0.975675i \(-0.429648\pi\)
0.219224 + 0.975675i \(0.429648\pi\)
\(180\) 0 0
\(181\) −17.7534 −1.31960 −0.659802 0.751440i \(-0.729360\pi\)
−0.659802 + 0.751440i \(0.729360\pi\)
\(182\) 0 0
\(183\) 10.2427 0.757162
\(184\) 0 0
\(185\) 24.0949 1.77149
\(186\) 0 0
\(187\) 31.2893 2.28810
\(188\) 0 0
\(189\) −22.1620 −1.61205
\(190\) 0 0
\(191\) 17.9243 1.29695 0.648477 0.761234i \(-0.275406\pi\)
0.648477 + 0.761234i \(0.275406\pi\)
\(192\) 0 0
\(193\) −14.7427 −1.06120 −0.530600 0.847623i \(-0.678033\pi\)
−0.530600 + 0.847623i \(0.678033\pi\)
\(194\) 0 0
\(195\) 22.0791 1.58111
\(196\) 0 0
\(197\) −22.9129 −1.63248 −0.816239 0.577715i \(-0.803945\pi\)
−0.816239 + 0.577715i \(0.803945\pi\)
\(198\) 0 0
\(199\) 0.191759 0.0135934 0.00679672 0.999977i \(-0.497837\pi\)
0.00679672 + 0.999977i \(0.497837\pi\)
\(200\) 0 0
\(201\) −25.6465 −1.80896
\(202\) 0 0
\(203\) −34.0766 −2.39171
\(204\) 0 0
\(205\) 28.9361 2.02099
\(206\) 0 0
\(207\) −4.66641 −0.324338
\(208\) 0 0
\(209\) −13.1008 −0.906204
\(210\) 0 0
\(211\) −12.1248 −0.834705 −0.417353 0.908745i \(-0.637042\pi\)
−0.417353 + 0.908745i \(0.637042\pi\)
\(212\) 0 0
\(213\) −20.3514 −1.39446
\(214\) 0 0
\(215\) −30.3445 −2.06948
\(216\) 0 0
\(217\) −21.1502 −1.43577
\(218\) 0 0
\(219\) 22.2749 1.50520
\(220\) 0 0
\(221\) 23.2588 1.56456
\(222\) 0 0
\(223\) 8.86947 0.593944 0.296972 0.954886i \(-0.404023\pi\)
0.296972 + 0.954886i \(0.404023\pi\)
\(224\) 0 0
\(225\) 12.2524 0.816827
\(226\) 0 0
\(227\) −10.3823 −0.689096 −0.344548 0.938769i \(-0.611968\pi\)
−0.344548 + 0.938769i \(0.611968\pi\)
\(228\) 0 0
\(229\) −9.90139 −0.654303 −0.327151 0.944972i \(-0.606089\pi\)
−0.327151 + 0.944972i \(0.606089\pi\)
\(230\) 0 0
\(231\) −40.5706 −2.66935
\(232\) 0 0
\(233\) 9.12344 0.597697 0.298848 0.954301i \(-0.403398\pi\)
0.298848 + 0.954301i \(0.403398\pi\)
\(234\) 0 0
\(235\) −9.37425 −0.611509
\(236\) 0 0
\(237\) 38.2894 2.48716
\(238\) 0 0
\(239\) 13.2494 0.857034 0.428517 0.903534i \(-0.359036\pi\)
0.428517 + 0.903534i \(0.359036\pi\)
\(240\) 0 0
\(241\) −11.6605 −0.751116 −0.375558 0.926799i \(-0.622549\pi\)
−0.375558 + 0.926799i \(0.622549\pi\)
\(242\) 0 0
\(243\) 13.1121 0.841144
\(244\) 0 0
\(245\) −18.5436 −1.18471
\(246\) 0 0
\(247\) −9.73849 −0.619645
\(248\) 0 0
\(249\) −38.6379 −2.44858
\(250\) 0 0
\(251\) −6.89173 −0.435002 −0.217501 0.976060i \(-0.569791\pi\)
−0.217501 + 0.976060i \(0.569791\pi\)
\(252\) 0 0
\(253\) −3.51319 −0.220872
\(254\) 0 0
\(255\) 63.1471 3.95443
\(256\) 0 0
\(257\) −15.3937 −0.960230 −0.480115 0.877206i \(-0.659405\pi\)
−0.480115 + 0.877206i \(0.659405\pi\)
\(258\) 0 0
\(259\) −32.9115 −2.04502
\(260\) 0 0
\(261\) −46.7178 −2.89176
\(262\) 0 0
\(263\) −17.4022 −1.07306 −0.536532 0.843880i \(-0.680266\pi\)
−0.536532 + 0.843880i \(0.680266\pi\)
\(264\) 0 0
\(265\) 13.4893 0.828641
\(266\) 0 0
\(267\) −18.4345 −1.12817
\(268\) 0 0
\(269\) 26.1637 1.59523 0.797615 0.603166i \(-0.206095\pi\)
0.797615 + 0.603166i \(0.206095\pi\)
\(270\) 0 0
\(271\) −25.9428 −1.57592 −0.787958 0.615729i \(-0.788861\pi\)
−0.787958 + 0.615729i \(0.788861\pi\)
\(272\) 0 0
\(273\) −30.1581 −1.82525
\(274\) 0 0
\(275\) 9.22444 0.556254
\(276\) 0 0
\(277\) −4.55601 −0.273744 −0.136872 0.990589i \(-0.543705\pi\)
−0.136872 + 0.990589i \(0.543705\pi\)
\(278\) 0 0
\(279\) −28.9962 −1.73596
\(280\) 0 0
\(281\) 14.6290 0.872691 0.436346 0.899779i \(-0.356272\pi\)
0.436346 + 0.899779i \(0.356272\pi\)
\(282\) 0 0
\(283\) 0.505950 0.0300756 0.0150378 0.999887i \(-0.495213\pi\)
0.0150378 + 0.999887i \(0.495213\pi\)
\(284\) 0 0
\(285\) −26.4397 −1.56615
\(286\) 0 0
\(287\) −39.5242 −2.33304
\(288\) 0 0
\(289\) 49.5214 2.91302
\(290\) 0 0
\(291\) −45.7186 −2.68007
\(292\) 0 0
\(293\) 19.3805 1.13222 0.566109 0.824330i \(-0.308448\pi\)
0.566109 + 0.824330i \(0.308448\pi\)
\(294\) 0 0
\(295\) 7.66146 0.446068
\(296\) 0 0
\(297\) −22.8746 −1.32732
\(298\) 0 0
\(299\) −2.61152 −0.151028
\(300\) 0 0
\(301\) 41.4480 2.38902
\(302\) 0 0
\(303\) 54.6806 3.14132
\(304\) 0 0
\(305\) 9.79574 0.560903
\(306\) 0 0
\(307\) 30.6653 1.75016 0.875082 0.483975i \(-0.160807\pi\)
0.875082 + 0.483975i \(0.160807\pi\)
\(308\) 0 0
\(309\) −2.44026 −0.138822
\(310\) 0 0
\(311\) 11.5530 0.655112 0.327556 0.944832i \(-0.393775\pi\)
0.327556 + 0.944832i \(0.393775\pi\)
\(312\) 0 0
\(313\) 10.3272 0.583729 0.291864 0.956460i \(-0.405724\pi\)
0.291864 + 0.956460i \(0.405724\pi\)
\(314\) 0 0
\(315\) −51.5366 −2.90376
\(316\) 0 0
\(317\) −10.6406 −0.597636 −0.298818 0.954310i \(-0.596592\pi\)
−0.298818 + 0.954310i \(0.596592\pi\)
\(318\) 0 0
\(319\) −35.1723 −1.96927
\(320\) 0 0
\(321\) 50.5464 2.82122
\(322\) 0 0
\(323\) −27.8525 −1.54976
\(324\) 0 0
\(325\) 6.85697 0.380356
\(326\) 0 0
\(327\) 50.0634 2.76851
\(328\) 0 0
\(329\) 12.8044 0.705930
\(330\) 0 0
\(331\) −17.5605 −0.965215 −0.482608 0.875837i \(-0.660310\pi\)
−0.482608 + 0.875837i \(0.660310\pi\)
\(332\) 0 0
\(333\) −45.1205 −2.47259
\(334\) 0 0
\(335\) −24.5273 −1.34007
\(336\) 0 0
\(337\) 0.888584 0.0484043 0.0242021 0.999707i \(-0.492295\pi\)
0.0242021 + 0.999707i \(0.492295\pi\)
\(338\) 0 0
\(339\) −25.0910 −1.36276
\(340\) 0 0
\(341\) −21.8303 −1.18218
\(342\) 0 0
\(343\) −0.688696 −0.0371861
\(344\) 0 0
\(345\) −7.09021 −0.381724
\(346\) 0 0
\(347\) 9.13438 0.490359 0.245180 0.969478i \(-0.421153\pi\)
0.245180 + 0.969478i \(0.421153\pi\)
\(348\) 0 0
\(349\) 6.69512 0.358381 0.179191 0.983814i \(-0.442652\pi\)
0.179191 + 0.983814i \(0.442652\pi\)
\(350\) 0 0
\(351\) −17.0038 −0.907594
\(352\) 0 0
\(353\) −18.8389 −1.00269 −0.501346 0.865247i \(-0.667162\pi\)
−0.501346 + 0.865247i \(0.667162\pi\)
\(354\) 0 0
\(355\) −19.4634 −1.03301
\(356\) 0 0
\(357\) −86.2535 −4.56502
\(358\) 0 0
\(359\) −1.59151 −0.0839966 −0.0419983 0.999118i \(-0.513372\pi\)
−0.0419983 + 0.999118i \(0.513372\pi\)
\(360\) 0 0
\(361\) −7.33814 −0.386218
\(362\) 0 0
\(363\) −10.5770 −0.555149
\(364\) 0 0
\(365\) 21.3029 1.11504
\(366\) 0 0
\(367\) −34.5867 −1.80541 −0.902706 0.430258i \(-0.858423\pi\)
−0.902706 + 0.430258i \(0.858423\pi\)
\(368\) 0 0
\(369\) −54.1863 −2.82083
\(370\) 0 0
\(371\) −18.4252 −0.956589
\(372\) 0 0
\(373\) 17.0429 0.882449 0.441224 0.897397i \(-0.354544\pi\)
0.441224 + 0.897397i \(0.354544\pi\)
\(374\) 0 0
\(375\) −20.0953 −1.03772
\(376\) 0 0
\(377\) −26.1453 −1.34655
\(378\) 0 0
\(379\) 14.7397 0.757129 0.378565 0.925575i \(-0.376418\pi\)
0.378565 + 0.925575i \(0.376418\pi\)
\(380\) 0 0
\(381\) 37.7821 1.93564
\(382\) 0 0
\(383\) 13.3274 0.680999 0.340499 0.940245i \(-0.389404\pi\)
0.340499 + 0.940245i \(0.389404\pi\)
\(384\) 0 0
\(385\) −38.8002 −1.97744
\(386\) 0 0
\(387\) 56.8237 2.88851
\(388\) 0 0
\(389\) 14.8579 0.753326 0.376663 0.926350i \(-0.377071\pi\)
0.376663 + 0.926350i \(0.377071\pi\)
\(390\) 0 0
\(391\) −7.46908 −0.377728
\(392\) 0 0
\(393\) −6.90384 −0.348253
\(394\) 0 0
\(395\) 36.6185 1.84248
\(396\) 0 0
\(397\) 4.63286 0.232517 0.116258 0.993219i \(-0.462910\pi\)
0.116258 + 0.993219i \(0.462910\pi\)
\(398\) 0 0
\(399\) 36.1144 1.80798
\(400\) 0 0
\(401\) −20.4551 −1.02148 −0.510740 0.859735i \(-0.670629\pi\)
−0.510740 + 0.859735i \(0.670629\pi\)
\(402\) 0 0
\(403\) −16.2275 −0.808349
\(404\) 0 0
\(405\) −4.56734 −0.226953
\(406\) 0 0
\(407\) −33.9698 −1.68382
\(408\) 0 0
\(409\) 4.52690 0.223841 0.111920 0.993717i \(-0.464300\pi\)
0.111920 + 0.993717i \(0.464300\pi\)
\(410\) 0 0
\(411\) 10.4124 0.513607
\(412\) 0 0
\(413\) −10.4649 −0.514944
\(414\) 0 0
\(415\) −36.9519 −1.81390
\(416\) 0 0
\(417\) 9.69955 0.474989
\(418\) 0 0
\(419\) −2.10462 −0.102817 −0.0514086 0.998678i \(-0.516371\pi\)
−0.0514086 + 0.998678i \(0.516371\pi\)
\(420\) 0 0
\(421\) 38.7225 1.88722 0.943610 0.331058i \(-0.107406\pi\)
0.943610 + 0.331058i \(0.107406\pi\)
\(422\) 0 0
\(423\) 17.5544 0.853523
\(424\) 0 0
\(425\) 19.6112 0.951285
\(426\) 0 0
\(427\) −13.3801 −0.647510
\(428\) 0 0
\(429\) −31.1278 −1.50286
\(430\) 0 0
\(431\) −14.5749 −0.702047 −0.351024 0.936367i \(-0.614166\pi\)
−0.351024 + 0.936367i \(0.614166\pi\)
\(432\) 0 0
\(433\) 36.6936 1.76338 0.881691 0.471828i \(-0.156406\pi\)
0.881691 + 0.471828i \(0.156406\pi\)
\(434\) 0 0
\(435\) −70.9836 −3.40340
\(436\) 0 0
\(437\) 3.12731 0.149599
\(438\) 0 0
\(439\) 17.8012 0.849605 0.424803 0.905286i \(-0.360343\pi\)
0.424803 + 0.905286i \(0.360343\pi\)
\(440\) 0 0
\(441\) 34.7252 1.65358
\(442\) 0 0
\(443\) 8.35105 0.396770 0.198385 0.980124i \(-0.436430\pi\)
0.198385 + 0.980124i \(0.436430\pi\)
\(444\) 0 0
\(445\) −17.6301 −0.835746
\(446\) 0 0
\(447\) −30.6563 −1.45000
\(448\) 0 0
\(449\) −21.7497 −1.02643 −0.513216 0.858260i \(-0.671546\pi\)
−0.513216 + 0.858260i \(0.671546\pi\)
\(450\) 0 0
\(451\) −40.7951 −1.92097
\(452\) 0 0
\(453\) 29.7996 1.40011
\(454\) 0 0
\(455\) −28.8421 −1.35214
\(456\) 0 0
\(457\) 13.4414 0.628761 0.314381 0.949297i \(-0.398203\pi\)
0.314381 + 0.949297i \(0.398203\pi\)
\(458\) 0 0
\(459\) −48.6315 −2.26993
\(460\) 0 0
\(461\) 12.1681 0.566726 0.283363 0.959013i \(-0.408550\pi\)
0.283363 + 0.959013i \(0.408550\pi\)
\(462\) 0 0
\(463\) 7.02984 0.326704 0.163352 0.986568i \(-0.447769\pi\)
0.163352 + 0.986568i \(0.447769\pi\)
\(464\) 0 0
\(465\) −44.0572 −2.04310
\(466\) 0 0
\(467\) 7.89249 0.365221 0.182610 0.983185i \(-0.441545\pi\)
0.182610 + 0.983185i \(0.441545\pi\)
\(468\) 0 0
\(469\) 33.5022 1.54699
\(470\) 0 0
\(471\) −6.48361 −0.298749
\(472\) 0 0
\(473\) 42.7807 1.96706
\(474\) 0 0
\(475\) −8.21123 −0.376757
\(476\) 0 0
\(477\) −25.2603 −1.15659
\(478\) 0 0
\(479\) 11.7262 0.535782 0.267891 0.963449i \(-0.413673\pi\)
0.267891 + 0.963449i \(0.413673\pi\)
\(480\) 0 0
\(481\) −25.2514 −1.15136
\(482\) 0 0
\(483\) 9.68461 0.440665
\(484\) 0 0
\(485\) −43.7236 −1.98539
\(486\) 0 0
\(487\) −17.2492 −0.781637 −0.390818 0.920468i \(-0.627808\pi\)
−0.390818 + 0.920468i \(0.627808\pi\)
\(488\) 0 0
\(489\) 42.9495 1.94224
\(490\) 0 0
\(491\) −12.0401 −0.543363 −0.271681 0.962387i \(-0.587580\pi\)
−0.271681 + 0.962387i \(0.587580\pi\)
\(492\) 0 0
\(493\) −74.7766 −3.36777
\(494\) 0 0
\(495\) −53.1937 −2.39088
\(496\) 0 0
\(497\) 26.5853 1.19251
\(498\) 0 0
\(499\) 43.6442 1.95378 0.976891 0.213739i \(-0.0685642\pi\)
0.976891 + 0.213739i \(0.0685642\pi\)
\(500\) 0 0
\(501\) −29.4091 −1.31390
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 52.2945 2.32707
\(506\) 0 0
\(507\) 13.8499 0.615094
\(508\) 0 0
\(509\) 21.4932 0.952669 0.476334 0.879264i \(-0.341965\pi\)
0.476334 + 0.879264i \(0.341965\pi\)
\(510\) 0 0
\(511\) −29.0979 −1.28721
\(512\) 0 0
\(513\) 20.3620 0.899006
\(514\) 0 0
\(515\) −2.33377 −0.102838
\(516\) 0 0
\(517\) 13.2161 0.581244
\(518\) 0 0
\(519\) 44.4012 1.94900
\(520\) 0 0
\(521\) −5.27284 −0.231007 −0.115504 0.993307i \(-0.536848\pi\)
−0.115504 + 0.993307i \(0.536848\pi\)
\(522\) 0 0
\(523\) 22.2996 0.975093 0.487546 0.873097i \(-0.337892\pi\)
0.487546 + 0.873097i \(0.337892\pi\)
\(524\) 0 0
\(525\) −25.4285 −1.10979
\(526\) 0 0
\(527\) −46.4114 −2.02171
\(528\) 0 0
\(529\) −22.1614 −0.963538
\(530\) 0 0
\(531\) −14.3470 −0.622607
\(532\) 0 0
\(533\) −30.3250 −1.31352
\(534\) 0 0
\(535\) 48.3407 2.08995
\(536\) 0 0
\(537\) −16.6905 −0.720248
\(538\) 0 0
\(539\) 26.1434 1.12608
\(540\) 0 0
\(541\) 7.94842 0.341729 0.170865 0.985294i \(-0.445344\pi\)
0.170865 + 0.985294i \(0.445344\pi\)
\(542\) 0 0
\(543\) 50.5135 2.16774
\(544\) 0 0
\(545\) 47.8788 2.05090
\(546\) 0 0
\(547\) 19.5507 0.835925 0.417963 0.908464i \(-0.362744\pi\)
0.417963 + 0.908464i \(0.362744\pi\)
\(548\) 0 0
\(549\) −18.3437 −0.782889
\(550\) 0 0
\(551\) 31.3090 1.33381
\(552\) 0 0
\(553\) −50.0177 −2.12697
\(554\) 0 0
\(555\) −68.5567 −2.91007
\(556\) 0 0
\(557\) 5.55069 0.235190 0.117595 0.993062i \(-0.462481\pi\)
0.117595 + 0.993062i \(0.462481\pi\)
\(558\) 0 0
\(559\) 31.8009 1.34504
\(560\) 0 0
\(561\) −89.0269 −3.75872
\(562\) 0 0
\(563\) −8.19830 −0.345517 −0.172759 0.984964i \(-0.555268\pi\)
−0.172759 + 0.984964i \(0.555268\pi\)
\(564\) 0 0
\(565\) −23.9961 −1.00953
\(566\) 0 0
\(567\) 6.23858 0.261996
\(568\) 0 0
\(569\) 3.01819 0.126529 0.0632645 0.997997i \(-0.479849\pi\)
0.0632645 + 0.997997i \(0.479849\pi\)
\(570\) 0 0
\(571\) −34.0007 −1.42289 −0.711443 0.702744i \(-0.751958\pi\)
−0.711443 + 0.702744i \(0.751958\pi\)
\(572\) 0 0
\(573\) −50.9995 −2.13054
\(574\) 0 0
\(575\) −2.20197 −0.0918284
\(576\) 0 0
\(577\) −27.0544 −1.12629 −0.563144 0.826358i \(-0.690409\pi\)
−0.563144 + 0.826358i \(0.690409\pi\)
\(578\) 0 0
\(579\) 41.9470 1.74326
\(580\) 0 0
\(581\) 50.4731 2.09398
\(582\) 0 0
\(583\) −19.0177 −0.787631
\(584\) 0 0
\(585\) −39.5414 −1.63484
\(586\) 0 0
\(587\) 17.7581 0.732953 0.366477 0.930427i \(-0.380564\pi\)
0.366477 + 0.930427i \(0.380564\pi\)
\(588\) 0 0
\(589\) 19.4325 0.800701
\(590\) 0 0
\(591\) 65.1936 2.68171
\(592\) 0 0
\(593\) −43.5559 −1.78863 −0.894314 0.447441i \(-0.852336\pi\)
−0.894314 + 0.447441i \(0.852336\pi\)
\(594\) 0 0
\(595\) −82.4896 −3.38174
\(596\) 0 0
\(597\) −0.545608 −0.0223303
\(598\) 0 0
\(599\) −32.7236 −1.33705 −0.668524 0.743690i \(-0.733074\pi\)
−0.668524 + 0.743690i \(0.733074\pi\)
\(600\) 0 0
\(601\) −22.7206 −0.926792 −0.463396 0.886151i \(-0.653369\pi\)
−0.463396 + 0.886151i \(0.653369\pi\)
\(602\) 0 0
\(603\) 45.9303 1.87043
\(604\) 0 0
\(605\) −10.1155 −0.411252
\(606\) 0 0
\(607\) −10.2469 −0.415911 −0.207955 0.978138i \(-0.566681\pi\)
−0.207955 + 0.978138i \(0.566681\pi\)
\(608\) 0 0
\(609\) 96.9575 3.92891
\(610\) 0 0
\(611\) 9.82418 0.397444
\(612\) 0 0
\(613\) 22.3683 0.903449 0.451725 0.892157i \(-0.350809\pi\)
0.451725 + 0.892157i \(0.350809\pi\)
\(614\) 0 0
\(615\) −82.3314 −3.31992
\(616\) 0 0
\(617\) 6.86067 0.276200 0.138100 0.990418i \(-0.455900\pi\)
0.138100 + 0.990418i \(0.455900\pi\)
\(618\) 0 0
\(619\) −15.0206 −0.603729 −0.301865 0.953351i \(-0.597609\pi\)
−0.301865 + 0.953351i \(0.597609\pi\)
\(620\) 0 0
\(621\) 5.46039 0.219118
\(622\) 0 0
\(623\) 24.0811 0.964791
\(624\) 0 0
\(625\) −31.2409 −1.24964
\(626\) 0 0
\(627\) 37.2756 1.48864
\(628\) 0 0
\(629\) −72.2200 −2.87960
\(630\) 0 0
\(631\) −35.7080 −1.42151 −0.710756 0.703438i \(-0.751647\pi\)
−0.710756 + 0.703438i \(0.751647\pi\)
\(632\) 0 0
\(633\) 34.4984 1.37119
\(634\) 0 0
\(635\) 36.1334 1.43391
\(636\) 0 0
\(637\) 19.4337 0.769990
\(638\) 0 0
\(639\) 36.4474 1.44184
\(640\) 0 0
\(641\) −13.2969 −0.525197 −0.262599 0.964905i \(-0.584580\pi\)
−0.262599 + 0.964905i \(0.584580\pi\)
\(642\) 0 0
\(643\) −41.1855 −1.62420 −0.812099 0.583519i \(-0.801675\pi\)
−0.812099 + 0.583519i \(0.801675\pi\)
\(644\) 0 0
\(645\) 86.3386 3.39958
\(646\) 0 0
\(647\) 10.0464 0.394963 0.197482 0.980307i \(-0.436724\pi\)
0.197482 + 0.980307i \(0.436724\pi\)
\(648\) 0 0
\(649\) −10.8014 −0.423991
\(650\) 0 0
\(651\) 60.1783 2.35857
\(652\) 0 0
\(653\) −41.7793 −1.63495 −0.817476 0.575963i \(-0.804627\pi\)
−0.817476 + 0.575963i \(0.804627\pi\)
\(654\) 0 0
\(655\) −6.60258 −0.257984
\(656\) 0 0
\(657\) −39.8922 −1.55634
\(658\) 0 0
\(659\) −22.6672 −0.882991 −0.441495 0.897264i \(-0.645552\pi\)
−0.441495 + 0.897264i \(0.645552\pi\)
\(660\) 0 0
\(661\) 30.7091 1.19445 0.597224 0.802075i \(-0.296271\pi\)
0.597224 + 0.802075i \(0.296271\pi\)
\(662\) 0 0
\(663\) −66.1779 −2.57014
\(664\) 0 0
\(665\) 34.5384 1.33934
\(666\) 0 0
\(667\) 8.39599 0.325094
\(668\) 0 0
\(669\) −25.2361 −0.975685
\(670\) 0 0
\(671\) −13.8104 −0.533143
\(672\) 0 0
\(673\) −9.82187 −0.378605 −0.189303 0.981919i \(-0.560623\pi\)
−0.189303 + 0.981919i \(0.560623\pi\)
\(674\) 0 0
\(675\) −14.3371 −0.551836
\(676\) 0 0
\(677\) −4.41084 −0.169522 −0.0847611 0.996401i \(-0.527013\pi\)
−0.0847611 + 0.996401i \(0.527013\pi\)
\(678\) 0 0
\(679\) 59.7227 2.29195
\(680\) 0 0
\(681\) 29.5405 1.13199
\(682\) 0 0
\(683\) −8.09181 −0.309625 −0.154812 0.987944i \(-0.549477\pi\)
−0.154812 + 0.987944i \(0.549477\pi\)
\(684\) 0 0
\(685\) 9.95806 0.380478
\(686\) 0 0
\(687\) 28.1722 1.07484
\(688\) 0 0
\(689\) −14.1367 −0.538567
\(690\) 0 0
\(691\) −20.7906 −0.790914 −0.395457 0.918485i \(-0.629414\pi\)
−0.395457 + 0.918485i \(0.629414\pi\)
\(692\) 0 0
\(693\) 72.6580 2.76005
\(694\) 0 0
\(695\) 9.27629 0.351870
\(696\) 0 0
\(697\) −86.7308 −3.28516
\(698\) 0 0
\(699\) −25.9588 −0.981850
\(700\) 0 0
\(701\) 21.9468 0.828920 0.414460 0.910068i \(-0.363971\pi\)
0.414460 + 0.910068i \(0.363971\pi\)
\(702\) 0 0
\(703\) 30.2386 1.14047
\(704\) 0 0
\(705\) 26.6724 1.00454
\(706\) 0 0
\(707\) −71.4297 −2.68639
\(708\) 0 0
\(709\) −43.2940 −1.62594 −0.812970 0.582305i \(-0.802151\pi\)
−0.812970 + 0.582305i \(0.802151\pi\)
\(710\) 0 0
\(711\) −68.5725 −2.57167
\(712\) 0 0
\(713\) 5.21111 0.195158
\(714\) 0 0
\(715\) −29.7694 −1.11331
\(716\) 0 0
\(717\) −37.6983 −1.40787
\(718\) 0 0
\(719\) 38.3358 1.42968 0.714842 0.699286i \(-0.246499\pi\)
0.714842 + 0.699286i \(0.246499\pi\)
\(720\) 0 0
\(721\) 3.18773 0.118717
\(722\) 0 0
\(723\) 33.1773 1.23388
\(724\) 0 0
\(725\) −22.0450 −0.818730
\(726\) 0 0
\(727\) 47.6902 1.76873 0.884366 0.466794i \(-0.154591\pi\)
0.884366 + 0.466794i \(0.154591\pi\)
\(728\) 0 0
\(729\) −42.3431 −1.56826
\(730\) 0 0
\(731\) 90.9521 3.36399
\(732\) 0 0
\(733\) −1.46620 −0.0541553 −0.0270777 0.999633i \(-0.508620\pi\)
−0.0270777 + 0.999633i \(0.508620\pi\)
\(734\) 0 0
\(735\) 52.7619 1.94615
\(736\) 0 0
\(737\) 34.5794 1.27375
\(738\) 0 0
\(739\) −19.1867 −0.705793 −0.352896 0.935662i \(-0.614803\pi\)
−0.352896 + 0.935662i \(0.614803\pi\)
\(740\) 0 0
\(741\) 27.7087 1.01791
\(742\) 0 0
\(743\) 25.3389 0.929593 0.464796 0.885418i \(-0.346128\pi\)
0.464796 + 0.885418i \(0.346128\pi\)
\(744\) 0 0
\(745\) −29.3186 −1.07415
\(746\) 0 0
\(747\) 69.1967 2.53178
\(748\) 0 0
\(749\) −66.0291 −2.41265
\(750\) 0 0
\(751\) −1.45873 −0.0532296 −0.0266148 0.999646i \(-0.508473\pi\)
−0.0266148 + 0.999646i \(0.508473\pi\)
\(752\) 0 0
\(753\) 19.6089 0.714588
\(754\) 0 0
\(755\) 28.4992 1.03719
\(756\) 0 0
\(757\) −20.9421 −0.761154 −0.380577 0.924749i \(-0.624275\pi\)
−0.380577 + 0.924749i \(0.624275\pi\)
\(758\) 0 0
\(759\) 9.99601 0.362832
\(760\) 0 0
\(761\) −18.4858 −0.670110 −0.335055 0.942199i \(-0.608755\pi\)
−0.335055 + 0.942199i \(0.608755\pi\)
\(762\) 0 0
\(763\) −65.3982 −2.36757
\(764\) 0 0
\(765\) −113.090 −4.08879
\(766\) 0 0
\(767\) −8.02919 −0.289917
\(768\) 0 0
\(769\) −35.0896 −1.26536 −0.632682 0.774412i \(-0.718046\pi\)
−0.632682 + 0.774412i \(0.718046\pi\)
\(770\) 0 0
\(771\) 43.7993 1.57739
\(772\) 0 0
\(773\) 1.58201 0.0569009 0.0284504 0.999595i \(-0.490943\pi\)
0.0284504 + 0.999595i \(0.490943\pi\)
\(774\) 0 0
\(775\) −13.6826 −0.491493
\(776\) 0 0
\(777\) 93.6425 3.35941
\(778\) 0 0
\(779\) 36.3142 1.30109
\(780\) 0 0
\(781\) 27.4401 0.981883
\(782\) 0 0
\(783\) 54.6667 1.95363
\(784\) 0 0
\(785\) −6.20069 −0.221312
\(786\) 0 0
\(787\) −43.4639 −1.54932 −0.774660 0.632378i \(-0.782079\pi\)
−0.774660 + 0.632378i \(0.782079\pi\)
\(788\) 0 0
\(789\) 49.5141 1.76275
\(790\) 0 0
\(791\) 32.7766 1.16540
\(792\) 0 0
\(793\) −10.2659 −0.364553
\(794\) 0 0
\(795\) −38.3808 −1.36123
\(796\) 0 0
\(797\) −5.25945 −0.186299 −0.0931496 0.995652i \(-0.529693\pi\)
−0.0931496 + 0.995652i \(0.529693\pi\)
\(798\) 0 0
\(799\) 28.0976 0.994022
\(800\) 0 0
\(801\) 33.0144 1.16651
\(802\) 0 0
\(803\) −30.0335 −1.05986
\(804\) 0 0
\(805\) 9.26201 0.326443
\(806\) 0 0
\(807\) −74.4431 −2.62052
\(808\) 0 0
\(809\) 9.20469 0.323620 0.161810 0.986822i \(-0.448267\pi\)
0.161810 + 0.986822i \(0.448267\pi\)
\(810\) 0 0
\(811\) −4.18969 −0.147120 −0.0735600 0.997291i \(-0.523436\pi\)
−0.0735600 + 0.997291i \(0.523436\pi\)
\(812\) 0 0
\(813\) 73.8146 2.58879
\(814\) 0 0
\(815\) 41.0753 1.43881
\(816\) 0 0
\(817\) −38.0817 −1.33231
\(818\) 0 0
\(819\) 54.0102 1.88727
\(820\) 0 0
\(821\) −16.1785 −0.564635 −0.282317 0.959321i \(-0.591103\pi\)
−0.282317 + 0.959321i \(0.591103\pi\)
\(822\) 0 0
\(823\) −29.2609 −1.01997 −0.509985 0.860183i \(-0.670349\pi\)
−0.509985 + 0.860183i \(0.670349\pi\)
\(824\) 0 0
\(825\) −26.2461 −0.913772
\(826\) 0 0
\(827\) −22.9175 −0.796919 −0.398460 0.917186i \(-0.630455\pi\)
−0.398460 + 0.917186i \(0.630455\pi\)
\(828\) 0 0
\(829\) −8.02706 −0.278791 −0.139396 0.990237i \(-0.544516\pi\)
−0.139396 + 0.990237i \(0.544516\pi\)
\(830\) 0 0
\(831\) 12.9631 0.449686
\(832\) 0 0
\(833\) 55.5812 1.92577
\(834\) 0 0
\(835\) −28.1257 −0.973331
\(836\) 0 0
\(837\) 33.9298 1.17279
\(838\) 0 0
\(839\) 32.2797 1.11442 0.557209 0.830372i \(-0.311872\pi\)
0.557209 + 0.830372i \(0.311872\pi\)
\(840\) 0 0
\(841\) 55.0564 1.89850
\(842\) 0 0
\(843\) −41.6235 −1.43359
\(844\) 0 0
\(845\) 13.2455 0.455659
\(846\) 0 0
\(847\) 13.8168 0.474752
\(848\) 0 0
\(849\) −1.43957 −0.0494059
\(850\) 0 0
\(851\) 8.10893 0.277971
\(852\) 0 0
\(853\) −51.4452 −1.76145 −0.880726 0.473627i \(-0.842945\pi\)
−0.880726 + 0.473627i \(0.842945\pi\)
\(854\) 0 0
\(855\) 47.3509 1.61937
\(856\) 0 0
\(857\) −41.5405 −1.41900 −0.709498 0.704707i \(-0.751078\pi\)
−0.709498 + 0.704707i \(0.751078\pi\)
\(858\) 0 0
\(859\) 17.3381 0.591567 0.295784 0.955255i \(-0.404419\pi\)
0.295784 + 0.955255i \(0.404419\pi\)
\(860\) 0 0
\(861\) 112.458 3.83254
\(862\) 0 0
\(863\) −55.0368 −1.87347 −0.936737 0.350034i \(-0.886170\pi\)
−0.936737 + 0.350034i \(0.886170\pi\)
\(864\) 0 0
\(865\) 42.4636 1.44381
\(866\) 0 0
\(867\) −140.902 −4.78529
\(868\) 0 0
\(869\) −51.6260 −1.75129
\(870\) 0 0
\(871\) 25.7045 0.870965
\(872\) 0 0
\(873\) 81.8776 2.77114
\(874\) 0 0
\(875\) 26.2506 0.887434
\(876\) 0 0
\(877\) −19.9695 −0.674322 −0.337161 0.941447i \(-0.609467\pi\)
−0.337161 + 0.941447i \(0.609467\pi\)
\(878\) 0 0
\(879\) −55.1429 −1.85992
\(880\) 0 0
\(881\) 36.1829 1.21903 0.609517 0.792773i \(-0.291364\pi\)
0.609517 + 0.792773i \(0.291364\pi\)
\(882\) 0 0
\(883\) −3.33445 −0.112213 −0.0561066 0.998425i \(-0.517869\pi\)
−0.0561066 + 0.998425i \(0.517869\pi\)
\(884\) 0 0
\(885\) −21.7990 −0.732766
\(886\) 0 0
\(887\) 27.0791 0.909228 0.454614 0.890689i \(-0.349777\pi\)
0.454614 + 0.890689i \(0.349777\pi\)
\(888\) 0 0
\(889\) −49.3551 −1.65532
\(890\) 0 0
\(891\) 6.43918 0.215721
\(892\) 0 0
\(893\) −11.7645 −0.393683
\(894\) 0 0
\(895\) −15.9622 −0.533557
\(896\) 0 0
\(897\) 7.43052 0.248098
\(898\) 0 0
\(899\) 52.1710 1.74000
\(900\) 0 0
\(901\) −40.4317 −1.34698
\(902\) 0 0
\(903\) −117.931 −3.92450
\(904\) 0 0
\(905\) 48.3093 1.60585
\(906\) 0 0
\(907\) 25.6784 0.852636 0.426318 0.904573i \(-0.359810\pi\)
0.426318 + 0.904573i \(0.359810\pi\)
\(908\) 0 0
\(909\) −97.9276 −3.24805
\(910\) 0 0
\(911\) −26.3249 −0.872183 −0.436092 0.899902i \(-0.643638\pi\)
−0.436092 + 0.899902i \(0.643638\pi\)
\(912\) 0 0
\(913\) 52.0960 1.72412
\(914\) 0 0
\(915\) −27.8716 −0.921408
\(916\) 0 0
\(917\) 9.01854 0.297819
\(918\) 0 0
\(919\) −43.2092 −1.42534 −0.712670 0.701499i \(-0.752514\pi\)
−0.712670 + 0.701499i \(0.752514\pi\)
\(920\) 0 0
\(921\) −87.2515 −2.87503
\(922\) 0 0
\(923\) 20.3975 0.671393
\(924\) 0 0
\(925\) −21.2913 −0.700053
\(926\) 0 0
\(927\) 4.37027 0.143538
\(928\) 0 0
\(929\) 48.7540 1.59957 0.799784 0.600288i \(-0.204948\pi\)
0.799784 + 0.600288i \(0.204948\pi\)
\(930\) 0 0
\(931\) −23.2719 −0.762705
\(932\) 0 0
\(933\) −32.8716 −1.07617
\(934\) 0 0
\(935\) −85.1420 −2.78444
\(936\) 0 0
\(937\) 13.6113 0.444663 0.222332 0.974971i \(-0.428633\pi\)
0.222332 + 0.974971i \(0.428633\pi\)
\(938\) 0 0
\(939\) −29.3838 −0.958904
\(940\) 0 0
\(941\) −16.7996 −0.547652 −0.273826 0.961779i \(-0.588289\pi\)
−0.273826 + 0.961779i \(0.588289\pi\)
\(942\) 0 0
\(943\) 9.73821 0.317120
\(944\) 0 0
\(945\) 60.3054 1.96173
\(946\) 0 0
\(947\) −39.8921 −1.29632 −0.648159 0.761505i \(-0.724461\pi\)
−0.648159 + 0.761505i \(0.724461\pi\)
\(948\) 0 0
\(949\) −22.3253 −0.724711
\(950\) 0 0
\(951\) 30.2755 0.981750
\(952\) 0 0
\(953\) −8.71093 −0.282175 −0.141087 0.989997i \(-0.545060\pi\)
−0.141087 + 0.989997i \(0.545060\pi\)
\(954\) 0 0
\(955\) −48.7741 −1.57829
\(956\) 0 0
\(957\) 100.075 3.23497
\(958\) 0 0
\(959\) −13.6018 −0.439226
\(960\) 0 0
\(961\) 1.38083 0.0445430
\(962\) 0 0
\(963\) −90.5236 −2.91708
\(964\) 0 0
\(965\) 40.1165 1.29140
\(966\) 0 0
\(967\) −29.5255 −0.949476 −0.474738 0.880127i \(-0.657457\pi\)
−0.474738 + 0.880127i \(0.657457\pi\)
\(968\) 0 0
\(969\) 79.2482 2.54582
\(970\) 0 0
\(971\) −8.31884 −0.266964 −0.133482 0.991051i \(-0.542616\pi\)
−0.133482 + 0.991051i \(0.542616\pi\)
\(972\) 0 0
\(973\) −12.6706 −0.406201
\(974\) 0 0
\(975\) −19.5100 −0.624820
\(976\) 0 0
\(977\) −25.5361 −0.816972 −0.408486 0.912765i \(-0.633943\pi\)
−0.408486 + 0.912765i \(0.633943\pi\)
\(978\) 0 0
\(979\) 24.8555 0.794384
\(980\) 0 0
\(981\) −89.6586 −2.86258
\(982\) 0 0
\(983\) 44.6712 1.42479 0.712394 0.701779i \(-0.247611\pi\)
0.712394 + 0.701779i \(0.247611\pi\)
\(984\) 0 0
\(985\) 62.3488 1.98660
\(986\) 0 0
\(987\) −36.4321 −1.15965
\(988\) 0 0
\(989\) −10.2122 −0.324729
\(990\) 0 0
\(991\) −1.18270 −0.0375696 −0.0187848 0.999824i \(-0.505980\pi\)
−0.0187848 + 0.999824i \(0.505980\pi\)
\(992\) 0 0
\(993\) 49.9647 1.58558
\(994\) 0 0
\(995\) −0.521800 −0.0165422
\(996\) 0 0
\(997\) 6.46140 0.204635 0.102317 0.994752i \(-0.467374\pi\)
0.102317 + 0.994752i \(0.467374\pi\)
\(998\) 0 0
\(999\) 52.7976 1.67044
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 \(a_p\))