Properties

Label 8036.2.a.q.1.2
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.10047\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.10047 q^{3} -3.31369 q^{5} +6.61290 q^{9} +O(q^{10})\) \(q-3.10047 q^{3} -3.31369 q^{5} +6.61290 q^{9} -0.792186 q^{11} +6.10265 q^{13} +10.2740 q^{15} +0.423014 q^{17} +0.177816 q^{19} +5.55791 q^{23} +5.98052 q^{25} -11.2017 q^{27} +6.87240 q^{29} +1.03742 q^{31} +2.45615 q^{33} +10.9371 q^{37} -18.9211 q^{39} -1.00000 q^{41} +7.60020 q^{43} -21.9131 q^{45} -0.719310 q^{47} -1.31154 q^{51} +9.70480 q^{53} +2.62506 q^{55} -0.551312 q^{57} +8.31526 q^{59} +9.24684 q^{61} -20.2223 q^{65} -14.6528 q^{67} -17.2321 q^{69} +6.50677 q^{71} +15.7518 q^{73} -18.5424 q^{75} +0.0105912 q^{79} +14.8917 q^{81} +7.04482 q^{83} -1.40174 q^{85} -21.3076 q^{87} -16.3892 q^{89} -3.21648 q^{93} -0.589225 q^{95} -12.9888 q^{97} -5.23864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −3.10047 −1.79006 −0.895028 0.446010i \(-0.852844\pi\)
−0.895028 + 0.446010i \(0.852844\pi\)
\(4\) 0 0
\(5\) −3.31369 −1.48193 −0.740963 0.671546i \(-0.765631\pi\)
−0.740963 + 0.671546i \(0.765631\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 6.61290 2.20430
\(10\) 0 0
\(11\) −0.792186 −0.238853 −0.119426 0.992843i \(-0.538106\pi\)
−0.119426 + 0.992843i \(0.538106\pi\)
\(12\) 0 0
\(13\) 6.10265 1.69257 0.846286 0.532729i \(-0.178834\pi\)
0.846286 + 0.532729i \(0.178834\pi\)
\(14\) 0 0
\(15\) 10.2740 2.65273
\(16\) 0 0
\(17\) 0.423014 0.102596 0.0512980 0.998683i \(-0.483664\pi\)
0.0512980 + 0.998683i \(0.483664\pi\)
\(18\) 0 0
\(19\) 0.177816 0.0407937 0.0203969 0.999792i \(-0.493507\pi\)
0.0203969 + 0.999792i \(0.493507\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.55791 1.15890 0.579452 0.815007i \(-0.303267\pi\)
0.579452 + 0.815007i \(0.303267\pi\)
\(24\) 0 0
\(25\) 5.98052 1.19610
\(26\) 0 0
\(27\) −11.2017 −2.15576
\(28\) 0 0
\(29\) 6.87240 1.27617 0.638086 0.769965i \(-0.279726\pi\)
0.638086 + 0.769965i \(0.279726\pi\)
\(30\) 0 0
\(31\) 1.03742 0.186326 0.0931630 0.995651i \(-0.470302\pi\)
0.0931630 + 0.995651i \(0.470302\pi\)
\(32\) 0 0
\(33\) 2.45615 0.427560
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.9371 1.79805 0.899026 0.437896i \(-0.144276\pi\)
0.899026 + 0.437896i \(0.144276\pi\)
\(38\) 0 0
\(39\) −18.9211 −3.02980
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 7.60020 1.15902 0.579509 0.814965i \(-0.303244\pi\)
0.579509 + 0.814965i \(0.303244\pi\)
\(44\) 0 0
\(45\) −21.9131 −3.26661
\(46\) 0 0
\(47\) −0.719310 −0.104922 −0.0524611 0.998623i \(-0.516707\pi\)
−0.0524611 + 0.998623i \(0.516707\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.31154 −0.183653
\(52\) 0 0
\(53\) 9.70480 1.33306 0.666529 0.745479i \(-0.267779\pi\)
0.666529 + 0.745479i \(0.267779\pi\)
\(54\) 0 0
\(55\) 2.62506 0.353962
\(56\) 0 0
\(57\) −0.551312 −0.0730230
\(58\) 0 0
\(59\) 8.31526 1.08255 0.541277 0.840844i \(-0.317941\pi\)
0.541277 + 0.840844i \(0.317941\pi\)
\(60\) 0 0
\(61\) 9.24684 1.18394 0.591968 0.805961i \(-0.298351\pi\)
0.591968 + 0.805961i \(0.298351\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −20.2223 −2.50827
\(66\) 0 0
\(67\) −14.6528 −1.79013 −0.895064 0.445937i \(-0.852870\pi\)
−0.895064 + 0.445937i \(0.852870\pi\)
\(68\) 0 0
\(69\) −17.2321 −2.07450
\(70\) 0 0
\(71\) 6.50677 0.772211 0.386106 0.922455i \(-0.373820\pi\)
0.386106 + 0.922455i \(0.373820\pi\)
\(72\) 0 0
\(73\) 15.7518 1.84360 0.921802 0.387661i \(-0.126717\pi\)
0.921802 + 0.387661i \(0.126717\pi\)
\(74\) 0 0
\(75\) −18.5424 −2.14109
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.0105912 0.00119160 0.000595801 1.00000i \(-0.499810\pi\)
0.000595801 1.00000i \(0.499810\pi\)
\(80\) 0 0
\(81\) 14.8917 1.65464
\(82\) 0 0
\(83\) 7.04482 0.773269 0.386635 0.922233i \(-0.373637\pi\)
0.386635 + 0.922233i \(0.373637\pi\)
\(84\) 0 0
\(85\) −1.40174 −0.152040
\(86\) 0 0
\(87\) −21.3076 −2.28442
\(88\) 0 0
\(89\) −16.3892 −1.73725 −0.868625 0.495470i \(-0.834996\pi\)
−0.868625 + 0.495470i \(0.834996\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.21648 −0.333534
\(94\) 0 0
\(95\) −0.589225 −0.0604533
\(96\) 0 0
\(97\) −12.9888 −1.31881 −0.659407 0.751786i \(-0.729192\pi\)
−0.659407 + 0.751786i \(0.729192\pi\)
\(98\) 0 0
\(99\) −5.23864 −0.526503
\(100\) 0 0
\(101\) −3.90959 −0.389019 −0.194510 0.980901i \(-0.562312\pi\)
−0.194510 + 0.980901i \(0.562312\pi\)
\(102\) 0 0
\(103\) −4.71318 −0.464403 −0.232202 0.972668i \(-0.574593\pi\)
−0.232202 + 0.972668i \(0.574593\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.411875 −0.0398174 −0.0199087 0.999802i \(-0.506338\pi\)
−0.0199087 + 0.999802i \(0.506338\pi\)
\(108\) 0 0
\(109\) 1.17123 0.112184 0.0560918 0.998426i \(-0.482136\pi\)
0.0560918 + 0.998426i \(0.482136\pi\)
\(110\) 0 0
\(111\) −33.9102 −3.21861
\(112\) 0 0
\(113\) −8.91233 −0.838401 −0.419201 0.907894i \(-0.637690\pi\)
−0.419201 + 0.907894i \(0.637690\pi\)
\(114\) 0 0
\(115\) −18.4172 −1.71741
\(116\) 0 0
\(117\) 40.3562 3.73093
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.3724 −0.942949
\(122\) 0 0
\(123\) 3.10047 0.279560
\(124\) 0 0
\(125\) −3.24914 −0.290612
\(126\) 0 0
\(127\) −11.1494 −0.989351 −0.494675 0.869078i \(-0.664713\pi\)
−0.494675 + 0.869078i \(0.664713\pi\)
\(128\) 0 0
\(129\) −23.5642 −2.07471
\(130\) 0 0
\(131\) −14.6291 −1.27815 −0.639074 0.769146i \(-0.720682\pi\)
−0.639074 + 0.769146i \(0.720682\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 37.1188 3.19468
\(136\) 0 0
\(137\) −0.269536 −0.0230280 −0.0115140 0.999934i \(-0.503665\pi\)
−0.0115140 + 0.999934i \(0.503665\pi\)
\(138\) 0 0
\(139\) 3.94454 0.334572 0.167286 0.985908i \(-0.446500\pi\)
0.167286 + 0.985908i \(0.446500\pi\)
\(140\) 0 0
\(141\) 2.23020 0.187817
\(142\) 0 0
\(143\) −4.83443 −0.404276
\(144\) 0 0
\(145\) −22.7730 −1.89119
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.84100 −0.478513 −0.239256 0.970956i \(-0.576904\pi\)
−0.239256 + 0.970956i \(0.576904\pi\)
\(150\) 0 0
\(151\) 3.95499 0.321853 0.160926 0.986966i \(-0.448552\pi\)
0.160926 + 0.986966i \(0.448552\pi\)
\(152\) 0 0
\(153\) 2.79735 0.226152
\(154\) 0 0
\(155\) −3.43768 −0.276121
\(156\) 0 0
\(157\) 12.1983 0.973527 0.486764 0.873534i \(-0.338177\pi\)
0.486764 + 0.873534i \(0.338177\pi\)
\(158\) 0 0
\(159\) −30.0894 −2.38625
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.2328 0.958151 0.479075 0.877774i \(-0.340972\pi\)
0.479075 + 0.877774i \(0.340972\pi\)
\(164\) 0 0
\(165\) −8.13890 −0.633612
\(166\) 0 0
\(167\) −9.89569 −0.765751 −0.382876 0.923800i \(-0.625066\pi\)
−0.382876 + 0.923800i \(0.625066\pi\)
\(168\) 0 0
\(169\) 24.2424 1.86480
\(170\) 0 0
\(171\) 1.17588 0.0899216
\(172\) 0 0
\(173\) 3.45189 0.262443 0.131221 0.991353i \(-0.458110\pi\)
0.131221 + 0.991353i \(0.458110\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −25.7812 −1.93783
\(178\) 0 0
\(179\) 23.3124 1.74245 0.871226 0.490881i \(-0.163325\pi\)
0.871226 + 0.490881i \(0.163325\pi\)
\(180\) 0 0
\(181\) 21.9722 1.63318 0.816591 0.577216i \(-0.195861\pi\)
0.816591 + 0.577216i \(0.195861\pi\)
\(182\) 0 0
\(183\) −28.6695 −2.11931
\(184\) 0 0
\(185\) −36.2422 −2.66458
\(186\) 0 0
\(187\) −0.335106 −0.0245054
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.4033 −0.969829 −0.484914 0.874562i \(-0.661149\pi\)
−0.484914 + 0.874562i \(0.661149\pi\)
\(192\) 0 0
\(193\) 13.4914 0.971130 0.485565 0.874200i \(-0.338614\pi\)
0.485565 + 0.874200i \(0.338614\pi\)
\(194\) 0 0
\(195\) 62.6985 4.48994
\(196\) 0 0
\(197\) 1.13551 0.0809021 0.0404510 0.999182i \(-0.487121\pi\)
0.0404510 + 0.999182i \(0.487121\pi\)
\(198\) 0 0
\(199\) 6.42701 0.455599 0.227799 0.973708i \(-0.426847\pi\)
0.227799 + 0.973708i \(0.426847\pi\)
\(200\) 0 0
\(201\) 45.4306 3.20443
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.31369 0.231438
\(206\) 0 0
\(207\) 36.7539 2.55457
\(208\) 0 0
\(209\) −0.140863 −0.00974370
\(210\) 0 0
\(211\) −6.69852 −0.461145 −0.230573 0.973055i \(-0.574060\pi\)
−0.230573 + 0.973055i \(0.574060\pi\)
\(212\) 0 0
\(213\) −20.1740 −1.38230
\(214\) 0 0
\(215\) −25.1847 −1.71758
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −48.8378 −3.30015
\(220\) 0 0
\(221\) 2.58151 0.173651
\(222\) 0 0
\(223\) 15.8949 1.06440 0.532201 0.846618i \(-0.321365\pi\)
0.532201 + 0.846618i \(0.321365\pi\)
\(224\) 0 0
\(225\) 39.5486 2.63657
\(226\) 0 0
\(227\) −26.1890 −1.73822 −0.869112 0.494614i \(-0.835309\pi\)
−0.869112 + 0.494614i \(0.835309\pi\)
\(228\) 0 0
\(229\) 9.66874 0.638929 0.319464 0.947598i \(-0.396497\pi\)
0.319464 + 0.947598i \(0.396497\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.61564 0.629942 0.314971 0.949101i \(-0.398005\pi\)
0.314971 + 0.949101i \(0.398005\pi\)
\(234\) 0 0
\(235\) 2.38357 0.155487
\(236\) 0 0
\(237\) −0.0328376 −0.00213303
\(238\) 0 0
\(239\) −11.3337 −0.733119 −0.366559 0.930395i \(-0.619464\pi\)
−0.366559 + 0.930395i \(0.619464\pi\)
\(240\) 0 0
\(241\) 13.4507 0.866435 0.433218 0.901289i \(-0.357378\pi\)
0.433218 + 0.901289i \(0.357378\pi\)
\(242\) 0 0
\(243\) −12.5663 −0.806129
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.08515 0.0690463
\(248\) 0 0
\(249\) −21.8422 −1.38420
\(250\) 0 0
\(251\) 23.7920 1.50174 0.750870 0.660450i \(-0.229635\pi\)
0.750870 + 0.660450i \(0.229635\pi\)
\(252\) 0 0
\(253\) −4.40289 −0.276808
\(254\) 0 0
\(255\) 4.34604 0.272159
\(256\) 0 0
\(257\) −10.8482 −0.676690 −0.338345 0.941022i \(-0.609867\pi\)
−0.338345 + 0.941022i \(0.609867\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 45.4465 2.81307
\(262\) 0 0
\(263\) 0.397372 0.0245030 0.0122515 0.999925i \(-0.496100\pi\)
0.0122515 + 0.999925i \(0.496100\pi\)
\(264\) 0 0
\(265\) −32.1587 −1.97549
\(266\) 0 0
\(267\) 50.8141 3.10977
\(268\) 0 0
\(269\) −20.4031 −1.24400 −0.622000 0.783017i \(-0.713680\pi\)
−0.622000 + 0.783017i \(0.713680\pi\)
\(270\) 0 0
\(271\) 8.26540 0.502087 0.251044 0.967976i \(-0.419226\pi\)
0.251044 + 0.967976i \(0.419226\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.73768 −0.285693
\(276\) 0 0
\(277\) 12.6537 0.760287 0.380143 0.924928i \(-0.375875\pi\)
0.380143 + 0.924928i \(0.375875\pi\)
\(278\) 0 0
\(279\) 6.86034 0.410718
\(280\) 0 0
\(281\) 4.90459 0.292583 0.146292 0.989242i \(-0.453266\pi\)
0.146292 + 0.989242i \(0.453266\pi\)
\(282\) 0 0
\(283\) 19.4702 1.15738 0.578692 0.815546i \(-0.303563\pi\)
0.578692 + 0.815546i \(0.303563\pi\)
\(284\) 0 0
\(285\) 1.82687 0.108215
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.8211 −0.989474
\(290\) 0 0
\(291\) 40.2714 2.36075
\(292\) 0 0
\(293\) 25.0432 1.46304 0.731521 0.681819i \(-0.238811\pi\)
0.731521 + 0.681819i \(0.238811\pi\)
\(294\) 0 0
\(295\) −27.5542 −1.60427
\(296\) 0 0
\(297\) 8.87380 0.514910
\(298\) 0 0
\(299\) 33.9180 1.96153
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 12.1216 0.696366
\(304\) 0 0
\(305\) −30.6411 −1.75451
\(306\) 0 0
\(307\) −18.1513 −1.03595 −0.517973 0.855397i \(-0.673313\pi\)
−0.517973 + 0.855397i \(0.673313\pi\)
\(308\) 0 0
\(309\) 14.6131 0.831308
\(310\) 0 0
\(311\) 33.4499 1.89677 0.948386 0.317119i \(-0.102715\pi\)
0.948386 + 0.317119i \(0.102715\pi\)
\(312\) 0 0
\(313\) −21.5440 −1.21774 −0.608869 0.793271i \(-0.708376\pi\)
−0.608869 + 0.793271i \(0.708376\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.64818 −0.429565 −0.214782 0.976662i \(-0.568904\pi\)
−0.214782 + 0.976662i \(0.568904\pi\)
\(318\) 0 0
\(319\) −5.44421 −0.304817
\(320\) 0 0
\(321\) 1.27700 0.0712754
\(322\) 0 0
\(323\) 0.0752185 0.00418527
\(324\) 0 0
\(325\) 36.4971 2.02449
\(326\) 0 0
\(327\) −3.63136 −0.200815
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.12802 −0.391791 −0.195896 0.980625i \(-0.562761\pi\)
−0.195896 + 0.980625i \(0.562761\pi\)
\(332\) 0 0
\(333\) 72.3261 3.96344
\(334\) 0 0
\(335\) 48.5549 2.65284
\(336\) 0 0
\(337\) −18.0930 −0.985589 −0.492795 0.870146i \(-0.664025\pi\)
−0.492795 + 0.870146i \(0.664025\pi\)
\(338\) 0 0
\(339\) 27.6324 1.50079
\(340\) 0 0
\(341\) −0.821828 −0.0445045
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 57.1018 3.07426
\(346\) 0 0
\(347\) −28.4867 −1.52925 −0.764624 0.644476i \(-0.777075\pi\)
−0.764624 + 0.644476i \(0.777075\pi\)
\(348\) 0 0
\(349\) 17.3830 0.930488 0.465244 0.885182i \(-0.345967\pi\)
0.465244 + 0.885182i \(0.345967\pi\)
\(350\) 0 0
\(351\) −68.3599 −3.64878
\(352\) 0 0
\(353\) −26.5923 −1.41537 −0.707683 0.706530i \(-0.750260\pi\)
−0.707683 + 0.706530i \(0.750260\pi\)
\(354\) 0 0
\(355\) −21.5614 −1.14436
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 21.5703 1.13843 0.569217 0.822187i \(-0.307246\pi\)
0.569217 + 0.822187i \(0.307246\pi\)
\(360\) 0 0
\(361\) −18.9684 −0.998336
\(362\) 0 0
\(363\) 32.1594 1.68793
\(364\) 0 0
\(365\) −52.1964 −2.73208
\(366\) 0 0
\(367\) −2.36326 −0.123361 −0.0616807 0.998096i \(-0.519646\pi\)
−0.0616807 + 0.998096i \(0.519646\pi\)
\(368\) 0 0
\(369\) −6.61290 −0.344254
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −17.0641 −0.883546 −0.441773 0.897127i \(-0.645650\pi\)
−0.441773 + 0.897127i \(0.645650\pi\)
\(374\) 0 0
\(375\) 10.0739 0.520212
\(376\) 0 0
\(377\) 41.9399 2.16001
\(378\) 0 0
\(379\) −12.0302 −0.617947 −0.308974 0.951071i \(-0.599985\pi\)
−0.308974 + 0.951071i \(0.599985\pi\)
\(380\) 0 0
\(381\) 34.5684 1.77099
\(382\) 0 0
\(383\) 8.73714 0.446447 0.223223 0.974767i \(-0.428342\pi\)
0.223223 + 0.974767i \(0.428342\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 50.2593 2.55482
\(388\) 0 0
\(389\) 23.2242 1.17752 0.588758 0.808310i \(-0.299617\pi\)
0.588758 + 0.808310i \(0.299617\pi\)
\(390\) 0 0
\(391\) 2.35107 0.118899
\(392\) 0 0
\(393\) 45.3569 2.28795
\(394\) 0 0
\(395\) −0.0350959 −0.00176587
\(396\) 0 0
\(397\) 34.9679 1.75499 0.877495 0.479585i \(-0.159213\pi\)
0.877495 + 0.479585i \(0.159213\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 28.0528 1.40089 0.700444 0.713707i \(-0.252985\pi\)
0.700444 + 0.713707i \(0.252985\pi\)
\(402\) 0 0
\(403\) 6.33101 0.315370
\(404\) 0 0
\(405\) −49.3465 −2.45205
\(406\) 0 0
\(407\) −8.66423 −0.429470
\(408\) 0 0
\(409\) 39.0591 1.93135 0.965675 0.259754i \(-0.0836414\pi\)
0.965675 + 0.259754i \(0.0836414\pi\)
\(410\) 0 0
\(411\) 0.835688 0.0412215
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −23.3443 −1.14593
\(416\) 0 0
\(417\) −12.2299 −0.598902
\(418\) 0 0
\(419\) −9.90234 −0.483761 −0.241880 0.970306i \(-0.577764\pi\)
−0.241880 + 0.970306i \(0.577764\pi\)
\(420\) 0 0
\(421\) 13.5351 0.659660 0.329830 0.944040i \(-0.393008\pi\)
0.329830 + 0.944040i \(0.393008\pi\)
\(422\) 0 0
\(423\) −4.75673 −0.231280
\(424\) 0 0
\(425\) 2.52984 0.122715
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 14.9890 0.723676
\(430\) 0 0
\(431\) 4.60848 0.221983 0.110991 0.993821i \(-0.464597\pi\)
0.110991 + 0.993821i \(0.464597\pi\)
\(432\) 0 0
\(433\) 12.0521 0.579188 0.289594 0.957150i \(-0.406480\pi\)
0.289594 + 0.957150i \(0.406480\pi\)
\(434\) 0 0
\(435\) 70.6069 3.38534
\(436\) 0 0
\(437\) 0.988283 0.0472760
\(438\) 0 0
\(439\) 30.9186 1.47566 0.737832 0.674984i \(-0.235850\pi\)
0.737832 + 0.674984i \(0.235850\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −16.6901 −0.792971 −0.396486 0.918041i \(-0.629770\pi\)
−0.396486 + 0.918041i \(0.629770\pi\)
\(444\) 0 0
\(445\) 54.3086 2.57448
\(446\) 0 0
\(447\) 18.1098 0.856565
\(448\) 0 0
\(449\) 20.5726 0.970883 0.485441 0.874269i \(-0.338659\pi\)
0.485441 + 0.874269i \(0.338659\pi\)
\(450\) 0 0
\(451\) 0.792186 0.0373026
\(452\) 0 0
\(453\) −12.2623 −0.576134
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 28.1632 1.31742 0.658709 0.752397i \(-0.271103\pi\)
0.658709 + 0.752397i \(0.271103\pi\)
\(458\) 0 0
\(459\) −4.73847 −0.221173
\(460\) 0 0
\(461\) −24.0754 −1.12130 −0.560651 0.828052i \(-0.689449\pi\)
−0.560651 + 0.828052i \(0.689449\pi\)
\(462\) 0 0
\(463\) −27.4976 −1.27792 −0.638960 0.769240i \(-0.720635\pi\)
−0.638960 + 0.769240i \(0.720635\pi\)
\(464\) 0 0
\(465\) 10.6584 0.494272
\(466\) 0 0
\(467\) −40.7584 −1.88608 −0.943038 0.332685i \(-0.892045\pi\)
−0.943038 + 0.332685i \(0.892045\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −37.8203 −1.74267
\(472\) 0 0
\(473\) −6.02077 −0.276835
\(474\) 0 0
\(475\) 1.06343 0.0487935
\(476\) 0 0
\(477\) 64.1769 2.93846
\(478\) 0 0
\(479\) 5.97986 0.273227 0.136613 0.990624i \(-0.456378\pi\)
0.136613 + 0.990624i \(0.456378\pi\)
\(480\) 0 0
\(481\) 66.7455 3.04333
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 43.0408 1.95438
\(486\) 0 0
\(487\) −17.2220 −0.780405 −0.390202 0.920729i \(-0.627595\pi\)
−0.390202 + 0.920729i \(0.627595\pi\)
\(488\) 0 0
\(489\) −37.9276 −1.71514
\(490\) 0 0
\(491\) −30.4029 −1.37207 −0.686033 0.727571i \(-0.740649\pi\)
−0.686033 + 0.727571i \(0.740649\pi\)
\(492\) 0 0
\(493\) 2.90712 0.130930
\(494\) 0 0
\(495\) 17.3592 0.780239
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.05907 0.136943 0.0684713 0.997653i \(-0.478188\pi\)
0.0684713 + 0.997653i \(0.478188\pi\)
\(500\) 0 0
\(501\) 30.6813 1.37074
\(502\) 0 0
\(503\) −13.3163 −0.593745 −0.296872 0.954917i \(-0.595944\pi\)
−0.296872 + 0.954917i \(0.595944\pi\)
\(504\) 0 0
\(505\) 12.9552 0.576498
\(506\) 0 0
\(507\) −75.1627 −3.33809
\(508\) 0 0
\(509\) −19.2352 −0.852585 −0.426293 0.904585i \(-0.640181\pi\)
−0.426293 + 0.904585i \(0.640181\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.99183 −0.0879416
\(514\) 0 0
\(515\) 15.6180 0.688211
\(516\) 0 0
\(517\) 0.569827 0.0250610
\(518\) 0 0
\(519\) −10.7025 −0.469787
\(520\) 0 0
\(521\) −23.8725 −1.04587 −0.522936 0.852372i \(-0.675163\pi\)
−0.522936 + 0.852372i \(0.675163\pi\)
\(522\) 0 0
\(523\) −32.9618 −1.44132 −0.720660 0.693288i \(-0.756161\pi\)
−0.720660 + 0.693288i \(0.756161\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.438843 0.0191163
\(528\) 0 0
\(529\) 7.89032 0.343057
\(530\) 0 0
\(531\) 54.9880 2.38628
\(532\) 0 0
\(533\) −6.10265 −0.264335
\(534\) 0 0
\(535\) 1.36482 0.0590065
\(536\) 0 0
\(537\) −72.2794 −3.11909
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 6.56283 0.282158 0.141079 0.989998i \(-0.454943\pi\)
0.141079 + 0.989998i \(0.454943\pi\)
\(542\) 0 0
\(543\) −68.1242 −2.92349
\(544\) 0 0
\(545\) −3.88109 −0.166248
\(546\) 0 0
\(547\) 9.98754 0.427036 0.213518 0.976939i \(-0.431508\pi\)
0.213518 + 0.976939i \(0.431508\pi\)
\(548\) 0 0
\(549\) 61.1484 2.60975
\(550\) 0 0
\(551\) 1.22202 0.0520598
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 112.368 4.76974
\(556\) 0 0
\(557\) −22.6717 −0.960632 −0.480316 0.877096i \(-0.659478\pi\)
−0.480316 + 0.877096i \(0.659478\pi\)
\(558\) 0 0
\(559\) 46.3814 1.96172
\(560\) 0 0
\(561\) 1.03898 0.0438659
\(562\) 0 0
\(563\) −6.55561 −0.276286 −0.138143 0.990412i \(-0.544113\pi\)
−0.138143 + 0.990412i \(0.544113\pi\)
\(564\) 0 0
\(565\) 29.5327 1.24245
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −10.7593 −0.451054 −0.225527 0.974237i \(-0.572410\pi\)
−0.225527 + 0.974237i \(0.572410\pi\)
\(570\) 0 0
\(571\) 25.3975 1.06285 0.531427 0.847104i \(-0.321656\pi\)
0.531427 + 0.847104i \(0.321656\pi\)
\(572\) 0 0
\(573\) 41.5565 1.73605
\(574\) 0 0
\(575\) 33.2392 1.38617
\(576\) 0 0
\(577\) −1.65595 −0.0689381 −0.0344690 0.999406i \(-0.510974\pi\)
−0.0344690 + 0.999406i \(0.510974\pi\)
\(578\) 0 0
\(579\) −41.8296 −1.73838
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −7.68801 −0.318405
\(584\) 0 0
\(585\) −133.728 −5.52897
\(586\) 0 0
\(587\) −39.9868 −1.65043 −0.825215 0.564818i \(-0.808946\pi\)
−0.825215 + 0.564818i \(0.808946\pi\)
\(588\) 0 0
\(589\) 0.184469 0.00760093
\(590\) 0 0
\(591\) −3.52063 −0.144819
\(592\) 0 0
\(593\) 1.35910 0.0558115 0.0279057 0.999611i \(-0.491116\pi\)
0.0279057 + 0.999611i \(0.491116\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −19.9267 −0.815547
\(598\) 0 0
\(599\) −28.6150 −1.16918 −0.584588 0.811330i \(-0.698744\pi\)
−0.584588 + 0.811330i \(0.698744\pi\)
\(600\) 0 0
\(601\) −20.9899 −0.856194 −0.428097 0.903733i \(-0.640816\pi\)
−0.428097 + 0.903733i \(0.640816\pi\)
\(602\) 0 0
\(603\) −96.8977 −3.94598
\(604\) 0 0
\(605\) 34.3710 1.39738
\(606\) 0 0
\(607\) 41.4598 1.68280 0.841401 0.540411i \(-0.181731\pi\)
0.841401 + 0.540411i \(0.181731\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.38970 −0.177588
\(612\) 0 0
\(613\) −3.80139 −0.153537 −0.0767683 0.997049i \(-0.524460\pi\)
−0.0767683 + 0.997049i \(0.524460\pi\)
\(614\) 0 0
\(615\) −10.2740 −0.414287
\(616\) 0 0
\(617\) 0.818128 0.0329366 0.0164683 0.999864i \(-0.494758\pi\)
0.0164683 + 0.999864i \(0.494758\pi\)
\(618\) 0 0
\(619\) −8.72606 −0.350730 −0.175365 0.984503i \(-0.556111\pi\)
−0.175365 + 0.984503i \(0.556111\pi\)
\(620\) 0 0
\(621\) −62.2578 −2.49832
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −19.1360 −0.765439
\(626\) 0 0
\(627\) 0.436741 0.0174418
\(628\) 0 0
\(629\) 4.62656 0.184473
\(630\) 0 0
\(631\) −32.1325 −1.27917 −0.639587 0.768719i \(-0.720895\pi\)
−0.639587 + 0.768719i \(0.720895\pi\)
\(632\) 0 0
\(633\) 20.7686 0.825476
\(634\) 0 0
\(635\) 36.9457 1.46614
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 43.0286 1.70218
\(640\) 0 0
\(641\) −12.9983 −0.513402 −0.256701 0.966491i \(-0.582636\pi\)
−0.256701 + 0.966491i \(0.582636\pi\)
\(642\) 0 0
\(643\) −3.06891 −0.121026 −0.0605131 0.998167i \(-0.519274\pi\)
−0.0605131 + 0.998167i \(0.519274\pi\)
\(644\) 0 0
\(645\) 78.0842 3.07456
\(646\) 0 0
\(647\) −13.2665 −0.521561 −0.260780 0.965398i \(-0.583980\pi\)
−0.260780 + 0.965398i \(0.583980\pi\)
\(648\) 0 0
\(649\) −6.58723 −0.258571
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.01002 0.196057 0.0980287 0.995184i \(-0.468746\pi\)
0.0980287 + 0.995184i \(0.468746\pi\)
\(654\) 0 0
\(655\) 48.4761 1.89412
\(656\) 0 0
\(657\) 104.165 4.06386
\(658\) 0 0
\(659\) −19.0067 −0.740397 −0.370198 0.928953i \(-0.620710\pi\)
−0.370198 + 0.928953i \(0.620710\pi\)
\(660\) 0 0
\(661\) −9.64577 −0.375177 −0.187588 0.982248i \(-0.560067\pi\)
−0.187588 + 0.982248i \(0.560067\pi\)
\(662\) 0 0
\(663\) −8.00388 −0.310845
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 38.1961 1.47896
\(668\) 0 0
\(669\) −49.2816 −1.90534
\(670\) 0 0
\(671\) −7.32521 −0.282787
\(672\) 0 0
\(673\) −18.4596 −0.711564 −0.355782 0.934569i \(-0.615785\pi\)
−0.355782 + 0.934569i \(0.615785\pi\)
\(674\) 0 0
\(675\) −66.9919 −2.57852
\(676\) 0 0
\(677\) 37.0226 1.42289 0.711447 0.702740i \(-0.248040\pi\)
0.711447 + 0.702740i \(0.248040\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 81.1981 3.11152
\(682\) 0 0
\(683\) −30.1788 −1.15476 −0.577380 0.816475i \(-0.695925\pi\)
−0.577380 + 0.816475i \(0.695925\pi\)
\(684\) 0 0
\(685\) 0.893159 0.0341258
\(686\) 0 0
\(687\) −29.9776 −1.14372
\(688\) 0 0
\(689\) 59.2251 2.25630
\(690\) 0 0
\(691\) 41.8766 1.59306 0.796530 0.604599i \(-0.206667\pi\)
0.796530 + 0.604599i \(0.206667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −13.0710 −0.495810
\(696\) 0 0
\(697\) −0.423014 −0.0160228
\(698\) 0 0
\(699\) −29.8130 −1.12763
\(700\) 0 0
\(701\) 4.68425 0.176922 0.0884609 0.996080i \(-0.471805\pi\)
0.0884609 + 0.996080i \(0.471805\pi\)
\(702\) 0 0
\(703\) 1.94479 0.0733492
\(704\) 0 0
\(705\) −7.39018 −0.278330
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13.6768 −0.513642 −0.256821 0.966459i \(-0.582675\pi\)
−0.256821 + 0.966459i \(0.582675\pi\)
\(710\) 0 0
\(711\) 0.0700385 0.00262665
\(712\) 0 0
\(713\) 5.76588 0.215934
\(714\) 0 0
\(715\) 16.0198 0.599107
\(716\) 0 0
\(717\) 35.1399 1.31232
\(718\) 0 0
\(719\) 31.4037 1.17116 0.585580 0.810614i \(-0.300867\pi\)
0.585580 + 0.810614i \(0.300867\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −41.7034 −1.55097
\(724\) 0 0
\(725\) 41.1005 1.52643
\(726\) 0 0
\(727\) 28.8878 1.07139 0.535694 0.844412i \(-0.320050\pi\)
0.535694 + 0.844412i \(0.320050\pi\)
\(728\) 0 0
\(729\) −5.71378 −0.211622
\(730\) 0 0
\(731\) 3.21499 0.118911
\(732\) 0 0
\(733\) 26.0897 0.963645 0.481822 0.876269i \(-0.339975\pi\)
0.481822 + 0.876269i \(0.339975\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11.6078 0.427577
\(738\) 0 0
\(739\) 50.5825 1.86071 0.930354 0.366662i \(-0.119499\pi\)
0.930354 + 0.366662i \(0.119499\pi\)
\(740\) 0 0
\(741\) −3.36446 −0.123597
\(742\) 0 0
\(743\) −32.2795 −1.18422 −0.592110 0.805857i \(-0.701705\pi\)
−0.592110 + 0.805857i \(0.701705\pi\)
\(744\) 0 0
\(745\) 19.3552 0.709121
\(746\) 0 0
\(747\) 46.5867 1.70452
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 27.2583 0.994669 0.497335 0.867559i \(-0.334312\pi\)
0.497335 + 0.867559i \(0.334312\pi\)
\(752\) 0 0
\(753\) −73.7664 −2.68820
\(754\) 0 0
\(755\) −13.1056 −0.476962
\(756\) 0 0
\(757\) −8.70767 −0.316486 −0.158243 0.987400i \(-0.550583\pi\)
−0.158243 + 0.987400i \(0.550583\pi\)
\(758\) 0 0
\(759\) 13.6510 0.495501
\(760\) 0 0
\(761\) −13.9333 −0.505081 −0.252540 0.967586i \(-0.581266\pi\)
−0.252540 + 0.967586i \(0.581266\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −9.26954 −0.335141
\(766\) 0 0
\(767\) 50.7452 1.83230
\(768\) 0 0
\(769\) −19.9808 −0.720528 −0.360264 0.932850i \(-0.617313\pi\)
−0.360264 + 0.932850i \(0.617313\pi\)
\(770\) 0 0
\(771\) 33.6344 1.21131
\(772\) 0 0
\(773\) 19.4581 0.699858 0.349929 0.936776i \(-0.386206\pi\)
0.349929 + 0.936776i \(0.386206\pi\)
\(774\) 0 0
\(775\) 6.20431 0.222865
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.177816 −0.00637091
\(780\) 0 0
\(781\) −5.15457 −0.184445
\(782\) 0 0
\(783\) −76.9823 −2.75112
\(784\) 0 0
\(785\) −40.4212 −1.44270
\(786\) 0 0
\(787\) −2.22135 −0.0791825 −0.0395913 0.999216i \(-0.512606\pi\)
−0.0395913 + 0.999216i \(0.512606\pi\)
\(788\) 0 0
\(789\) −1.23204 −0.0438617
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 56.4303 2.00390
\(794\) 0 0
\(795\) 99.7070 3.53624
\(796\) 0 0
\(797\) 44.0244 1.55942 0.779712 0.626139i \(-0.215366\pi\)
0.779712 + 0.626139i \(0.215366\pi\)
\(798\) 0 0
\(799\) −0.304278 −0.0107646
\(800\) 0 0
\(801\) −108.380 −3.82942
\(802\) 0 0
\(803\) −12.4783 −0.440350
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 63.2592 2.22683
\(808\) 0 0
\(809\) −12.5660 −0.441798 −0.220899 0.975297i \(-0.570899\pi\)
−0.220899 + 0.975297i \(0.570899\pi\)
\(810\) 0 0
\(811\) −36.4864 −1.28121 −0.640606 0.767870i \(-0.721317\pi\)
−0.640606 + 0.767870i \(0.721317\pi\)
\(812\) 0 0
\(813\) −25.6266 −0.898764
\(814\) 0 0
\(815\) −40.5358 −1.41991
\(816\) 0 0
\(817\) 1.35143 0.0472807
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.85719 0.0648164 0.0324082 0.999475i \(-0.489682\pi\)
0.0324082 + 0.999475i \(0.489682\pi\)
\(822\) 0 0
\(823\) −37.2988 −1.30016 −0.650078 0.759868i \(-0.725264\pi\)
−0.650078 + 0.759868i \(0.725264\pi\)
\(824\) 0 0
\(825\) 14.6890 0.511406
\(826\) 0 0
\(827\) −3.33099 −0.115830 −0.0579150 0.998322i \(-0.518445\pi\)
−0.0579150 + 0.998322i \(0.518445\pi\)
\(828\) 0 0
\(829\) −42.5501 −1.47783 −0.738913 0.673801i \(-0.764661\pi\)
−0.738913 + 0.673801i \(0.764661\pi\)
\(830\) 0 0
\(831\) −39.2324 −1.36096
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 32.7912 1.13479
\(836\) 0 0
\(837\) −11.6208 −0.401675
\(838\) 0 0
\(839\) −17.2324 −0.594929 −0.297465 0.954733i \(-0.596141\pi\)
−0.297465 + 0.954733i \(0.596141\pi\)
\(840\) 0 0
\(841\) 18.2298 0.628615
\(842\) 0 0
\(843\) −15.2065 −0.523740
\(844\) 0 0
\(845\) −80.3317 −2.76349
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −60.3668 −2.07178
\(850\) 0 0
\(851\) 60.7875 2.08377
\(852\) 0 0
\(853\) 14.8844 0.509633 0.254817 0.966989i \(-0.417985\pi\)
0.254817 + 0.966989i \(0.417985\pi\)
\(854\) 0 0
\(855\) −3.89649 −0.133257
\(856\) 0 0
\(857\) 42.7726 1.46108 0.730542 0.682868i \(-0.239268\pi\)
0.730542 + 0.682868i \(0.239268\pi\)
\(858\) 0 0
\(859\) 22.8541 0.779773 0.389886 0.920863i \(-0.372514\pi\)
0.389886 + 0.920863i \(0.372514\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 9.93663 0.338247 0.169123 0.985595i \(-0.445906\pi\)
0.169123 + 0.985595i \(0.445906\pi\)
\(864\) 0 0
\(865\) −11.4385 −0.388921
\(866\) 0 0
\(867\) 52.1531 1.77121
\(868\) 0 0
\(869\) −0.00839019 −0.000284618 0
\(870\) 0 0
\(871\) −89.4212 −3.02992
\(872\) 0 0
\(873\) −85.8936 −2.90706
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −4.22010 −0.142503 −0.0712514 0.997458i \(-0.522699\pi\)
−0.0712514 + 0.997458i \(0.522699\pi\)
\(878\) 0 0
\(879\) −77.6457 −2.61893
\(880\) 0 0
\(881\) 37.1986 1.25325 0.626626 0.779320i \(-0.284435\pi\)
0.626626 + 0.779320i \(0.284435\pi\)
\(882\) 0 0
\(883\) −5.39445 −0.181538 −0.0907689 0.995872i \(-0.528932\pi\)
−0.0907689 + 0.995872i \(0.528932\pi\)
\(884\) 0 0
\(885\) 85.4308 2.87173
\(886\) 0 0
\(887\) −22.7727 −0.764633 −0.382316 0.924031i \(-0.624874\pi\)
−0.382316 + 0.924031i \(0.624874\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −11.7970 −0.395215
\(892\) 0 0
\(893\) −0.127905 −0.00428017
\(894\) 0 0
\(895\) −77.2501 −2.58219
\(896\) 0 0
\(897\) −105.162 −3.51124
\(898\) 0 0
\(899\) 7.12955 0.237784
\(900\) 0 0
\(901\) 4.10527 0.136766
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −72.8091 −2.42026
\(906\) 0 0
\(907\) −37.2836 −1.23798 −0.618991 0.785398i \(-0.712458\pi\)
−0.618991 + 0.785398i \(0.712458\pi\)
\(908\) 0 0
\(909\) −25.8537 −0.857515
\(910\) 0 0
\(911\) −5.99739 −0.198703 −0.0993513 0.995052i \(-0.531677\pi\)
−0.0993513 + 0.995052i \(0.531677\pi\)
\(912\) 0 0
\(913\) −5.58080 −0.184698
\(914\) 0 0
\(915\) 95.0018 3.14066
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −32.4009 −1.06881 −0.534403 0.845230i \(-0.679464\pi\)
−0.534403 + 0.845230i \(0.679464\pi\)
\(920\) 0 0
\(921\) 56.2774 1.85440
\(922\) 0 0
\(923\) 39.7086 1.30702
\(924\) 0 0
\(925\) 65.4097 2.15066
\(926\) 0 0
\(927\) −31.1678 −1.02368
\(928\) 0 0
\(929\) −34.0590 −1.11744 −0.558721 0.829356i \(-0.688708\pi\)
−0.558721 + 0.829356i \(0.688708\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −103.710 −3.39533
\(934\) 0 0
\(935\) 1.11044 0.0363151
\(936\) 0 0
\(937\) 27.7733 0.907315 0.453658 0.891176i \(-0.350119\pi\)
0.453658 + 0.891176i \(0.350119\pi\)
\(938\) 0 0
\(939\) 66.7964 2.17982
\(940\) 0 0
\(941\) −54.4091 −1.77369 −0.886843 0.462072i \(-0.847106\pi\)
−0.886843 + 0.462072i \(0.847106\pi\)
\(942\) 0 0
\(943\) −5.55791 −0.180990
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 28.5414 0.927469 0.463735 0.885974i \(-0.346509\pi\)
0.463735 + 0.885974i \(0.346509\pi\)
\(948\) 0 0
\(949\) 96.1276 3.12043
\(950\) 0 0
\(951\) 23.7129 0.768945
\(952\) 0 0
\(953\) −16.2810 −0.527395 −0.263697 0.964605i \(-0.584942\pi\)
−0.263697 + 0.964605i \(0.584942\pi\)
\(954\) 0 0
\(955\) 44.4143 1.43721
\(956\) 0 0
\(957\) 16.8796 0.545640
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −29.9238 −0.965283
\(962\) 0 0
\(963\) −2.72369 −0.0877695
\(964\) 0 0
\(965\) −44.7062 −1.43914
\(966\) 0 0
\(967\) −29.7976 −0.958225 −0.479112 0.877754i \(-0.659041\pi\)
−0.479112 + 0.877754i \(0.659041\pi\)
\(968\) 0 0
\(969\) −0.233213 −0.00749187
\(970\) 0 0
\(971\) 15.4946 0.497245 0.248622 0.968601i \(-0.420022\pi\)
0.248622 + 0.968601i \(0.420022\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −113.158 −3.62395
\(976\) 0 0
\(977\) 34.8448 1.11478 0.557392 0.830249i \(-0.311802\pi\)
0.557392 + 0.830249i \(0.311802\pi\)
\(978\) 0 0
\(979\) 12.9833 0.414947
\(980\) 0 0
\(981\) 7.74523 0.247286
\(982\) 0 0
\(983\) 0.361484 0.0115296 0.00576478 0.999983i \(-0.498165\pi\)
0.00576478 + 0.999983i \(0.498165\pi\)
\(984\) 0 0
\(985\) −3.76274 −0.119891
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 42.2412 1.34319
\(990\) 0 0
\(991\) 28.3356 0.900110 0.450055 0.893001i \(-0.351404\pi\)
0.450055 + 0.893001i \(0.351404\pi\)
\(992\) 0 0
\(993\) 22.1002 0.701329
\(994\) 0 0
\(995\) −21.2971 −0.675163
\(996\) 0 0
\(997\) −31.3530 −0.992958 −0.496479 0.868049i \(-0.665374\pi\)
−0.496479 + 0.868049i \(0.665374\pi\)
\(998\) 0 0
\(999\) −122.514 −3.87617
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 \(a_p\))