Properties

Label 8004.2.a.j.1.9
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
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 1.9
Root \(0.187793\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+0.187793 q^{5}\) \(+3.11113 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+0.187793 q^{5}\) \(+3.11113 q^{7}\) \(+1.00000 q^{9}\) \(+0.0152079 q^{11}\) \(+5.09199 q^{13}\) \(+0.187793 q^{15}\) \(+2.80593 q^{17}\) \(+4.44446 q^{19}\) \(+3.11113 q^{21}\) \(+1.00000 q^{23}\) \(-4.96473 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-3.85168 q^{31}\) \(+0.0152079 q^{33}\) \(+0.584250 q^{35}\) \(-2.44794 q^{37}\) \(+5.09199 q^{39}\) \(+4.07580 q^{41}\) \(-4.10517 q^{43}\) \(+0.187793 q^{45}\) \(+10.7652 q^{47}\) \(+2.67915 q^{49}\) \(+2.80593 q^{51}\) \(+8.69169 q^{53}\) \(+0.00285595 q^{55}\) \(+4.44446 q^{57}\) \(-8.68248 q^{59}\) \(+2.99638 q^{61}\) \(+3.11113 q^{63}\) \(+0.956242 q^{65}\) \(+11.2830 q^{67}\) \(+1.00000 q^{69}\) \(+4.10798 q^{71}\) \(+12.5759 q^{73}\) \(-4.96473 q^{75}\) \(+0.0473140 q^{77}\) \(+6.51135 q^{79}\) \(+1.00000 q^{81}\) \(-4.47591 q^{83}\) \(+0.526935 q^{85}\) \(-1.00000 q^{87}\) \(-9.25893 q^{89}\) \(+15.8419 q^{91}\) \(-3.85168 q^{93}\) \(+0.834639 q^{95}\) \(+7.78248 q^{97}\) \(+0.0152079 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.187793 0.0839837 0.0419919 0.999118i \(-0.486630\pi\)
0.0419919 + 0.999118i \(0.486630\pi\)
\(6\) 0 0
\(7\) 3.11113 1.17590 0.587949 0.808898i \(-0.299936\pi\)
0.587949 + 0.808898i \(0.299936\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.0152079 0.00458537 0.00229268 0.999997i \(-0.499270\pi\)
0.00229268 + 0.999997i \(0.499270\pi\)
\(12\) 0 0
\(13\) 5.09199 1.41226 0.706132 0.708080i \(-0.250438\pi\)
0.706132 + 0.708080i \(0.250438\pi\)
\(14\) 0 0
\(15\) 0.187793 0.0484880
\(16\) 0 0
\(17\) 2.80593 0.680538 0.340269 0.940328i \(-0.389482\pi\)
0.340269 + 0.940328i \(0.389482\pi\)
\(18\) 0 0
\(19\) 4.44446 1.01963 0.509814 0.860285i \(-0.329714\pi\)
0.509814 + 0.860285i \(0.329714\pi\)
\(20\) 0 0
\(21\) 3.11113 0.678905
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.96473 −0.992947
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −3.85168 −0.691783 −0.345891 0.938275i \(-0.612423\pi\)
−0.345891 + 0.938275i \(0.612423\pi\)
\(32\) 0 0
\(33\) 0.0152079 0.00264736
\(34\) 0 0
\(35\) 0.584250 0.0987563
\(36\) 0 0
\(37\) −2.44794 −0.402439 −0.201220 0.979546i \(-0.564491\pi\)
−0.201220 + 0.979546i \(0.564491\pi\)
\(38\) 0 0
\(39\) 5.09199 0.815371
\(40\) 0 0
\(41\) 4.07580 0.636533 0.318267 0.948001i \(-0.396899\pi\)
0.318267 + 0.948001i \(0.396899\pi\)
\(42\) 0 0
\(43\) −4.10517 −0.626032 −0.313016 0.949748i \(-0.601339\pi\)
−0.313016 + 0.949748i \(0.601339\pi\)
\(44\) 0 0
\(45\) 0.187793 0.0279946
\(46\) 0 0
\(47\) 10.7652 1.57026 0.785130 0.619331i \(-0.212596\pi\)
0.785130 + 0.619331i \(0.212596\pi\)
\(48\) 0 0
\(49\) 2.67915 0.382736
\(50\) 0 0
\(51\) 2.80593 0.392909
\(52\) 0 0
\(53\) 8.69169 1.19390 0.596948 0.802280i \(-0.296380\pi\)
0.596948 + 0.802280i \(0.296380\pi\)
\(54\) 0 0
\(55\) 0.00285595 0.000385096 0
\(56\) 0 0
\(57\) 4.44446 0.588683
\(58\) 0 0
\(59\) −8.68248 −1.13036 −0.565181 0.824967i \(-0.691194\pi\)
−0.565181 + 0.824967i \(0.691194\pi\)
\(60\) 0 0
\(61\) 2.99638 0.383647 0.191824 0.981429i \(-0.438560\pi\)
0.191824 + 0.981429i \(0.438560\pi\)
\(62\) 0 0
\(63\) 3.11113 0.391966
\(64\) 0 0
\(65\) 0.956242 0.118607
\(66\) 0 0
\(67\) 11.2830 1.37844 0.689220 0.724552i \(-0.257953\pi\)
0.689220 + 0.724552i \(0.257953\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 4.10798 0.487528 0.243764 0.969835i \(-0.421618\pi\)
0.243764 + 0.969835i \(0.421618\pi\)
\(72\) 0 0
\(73\) 12.5759 1.47190 0.735949 0.677037i \(-0.236737\pi\)
0.735949 + 0.677037i \(0.236737\pi\)
\(74\) 0 0
\(75\) −4.96473 −0.573278
\(76\) 0 0
\(77\) 0.0473140 0.00539193
\(78\) 0 0
\(79\) 6.51135 0.732584 0.366292 0.930500i \(-0.380627\pi\)
0.366292 + 0.930500i \(0.380627\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.47591 −0.491295 −0.245647 0.969359i \(-0.579001\pi\)
−0.245647 + 0.969359i \(0.579001\pi\)
\(84\) 0 0
\(85\) 0.526935 0.0571541
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −9.25893 −0.981444 −0.490722 0.871316i \(-0.663267\pi\)
−0.490722 + 0.871316i \(0.663267\pi\)
\(90\) 0 0
\(91\) 15.8419 1.66068
\(92\) 0 0
\(93\) −3.85168 −0.399401
\(94\) 0 0
\(95\) 0.834639 0.0856322
\(96\) 0 0
\(97\) 7.78248 0.790191 0.395095 0.918640i \(-0.370711\pi\)
0.395095 + 0.918640i \(0.370711\pi\)
\(98\) 0 0
\(99\) 0.0152079 0.00152846
\(100\) 0 0
\(101\) −6.72116 −0.668780 −0.334390 0.942435i \(-0.608530\pi\)
−0.334390 + 0.942435i \(0.608530\pi\)
\(102\) 0 0
\(103\) −14.4939 −1.42812 −0.714061 0.700083i \(-0.753146\pi\)
−0.714061 + 0.700083i \(0.753146\pi\)
\(104\) 0 0
\(105\) 0.584250 0.0570170
\(106\) 0 0
\(107\) −9.80146 −0.947543 −0.473771 0.880648i \(-0.657108\pi\)
−0.473771 + 0.880648i \(0.657108\pi\)
\(108\) 0 0
\(109\) −3.75215 −0.359391 −0.179695 0.983722i \(-0.557511\pi\)
−0.179695 + 0.983722i \(0.557511\pi\)
\(110\) 0 0
\(111\) −2.44794 −0.232348
\(112\) 0 0
\(113\) −12.1826 −1.14604 −0.573022 0.819540i \(-0.694229\pi\)
−0.573022 + 0.819540i \(0.694229\pi\)
\(114\) 0 0
\(115\) 0.187793 0.0175118
\(116\) 0 0
\(117\) 5.09199 0.470755
\(118\) 0 0
\(119\) 8.72962 0.800243
\(120\) 0 0
\(121\) −10.9998 −0.999979
\(122\) 0 0
\(123\) 4.07580 0.367503
\(124\) 0 0
\(125\) −1.87131 −0.167375
\(126\) 0 0
\(127\) −14.7848 −1.31194 −0.655968 0.754788i \(-0.727740\pi\)
−0.655968 + 0.754788i \(0.727740\pi\)
\(128\) 0 0
\(129\) −4.10517 −0.361440
\(130\) 0 0
\(131\) −21.0448 −1.83869 −0.919346 0.393449i \(-0.871282\pi\)
−0.919346 + 0.393449i \(0.871282\pi\)
\(132\) 0 0
\(133\) 13.8273 1.19898
\(134\) 0 0
\(135\) 0.187793 0.0161627
\(136\) 0 0
\(137\) −18.4369 −1.57517 −0.787583 0.616208i \(-0.788668\pi\)
−0.787583 + 0.616208i \(0.788668\pi\)
\(138\) 0 0
\(139\) 19.3555 1.64171 0.820856 0.571135i \(-0.193497\pi\)
0.820856 + 0.571135i \(0.193497\pi\)
\(140\) 0 0
\(141\) 10.7652 0.906590
\(142\) 0 0
\(143\) 0.0774388 0.00647575
\(144\) 0 0
\(145\) −0.187793 −0.0155954
\(146\) 0 0
\(147\) 2.67915 0.220973
\(148\) 0 0
\(149\) −5.36191 −0.439265 −0.219633 0.975583i \(-0.570486\pi\)
−0.219633 + 0.975583i \(0.570486\pi\)
\(150\) 0 0
\(151\) 4.92971 0.401174 0.200587 0.979676i \(-0.435715\pi\)
0.200587 + 0.979676i \(0.435715\pi\)
\(152\) 0 0
\(153\) 2.80593 0.226846
\(154\) 0 0
\(155\) −0.723321 −0.0580985
\(156\) 0 0
\(157\) 14.5834 1.16388 0.581942 0.813230i \(-0.302293\pi\)
0.581942 + 0.813230i \(0.302293\pi\)
\(158\) 0 0
\(159\) 8.69169 0.689296
\(160\) 0 0
\(161\) 3.11113 0.245192
\(162\) 0 0
\(163\) 9.81554 0.768813 0.384406 0.923164i \(-0.374406\pi\)
0.384406 + 0.923164i \(0.374406\pi\)
\(164\) 0 0
\(165\) 0.00285595 0.000222336 0
\(166\) 0 0
\(167\) 15.8044 1.22298 0.611490 0.791252i \(-0.290570\pi\)
0.611490 + 0.791252i \(0.290570\pi\)
\(168\) 0 0
\(169\) 12.9284 0.994491
\(170\) 0 0
\(171\) 4.44446 0.339876
\(172\) 0 0
\(173\) −3.48262 −0.264778 −0.132389 0.991198i \(-0.542265\pi\)
−0.132389 + 0.991198i \(0.542265\pi\)
\(174\) 0 0
\(175\) −15.4459 −1.16760
\(176\) 0 0
\(177\) −8.68248 −0.652615
\(178\) 0 0
\(179\) −20.9975 −1.56942 −0.784712 0.619860i \(-0.787189\pi\)
−0.784712 + 0.619860i \(0.787189\pi\)
\(180\) 0 0
\(181\) 10.3852 0.771927 0.385964 0.922514i \(-0.373869\pi\)
0.385964 + 0.922514i \(0.373869\pi\)
\(182\) 0 0
\(183\) 2.99638 0.221499
\(184\) 0 0
\(185\) −0.459707 −0.0337984
\(186\) 0 0
\(187\) 0.0426724 0.00312052
\(188\) 0 0
\(189\) 3.11113 0.226302
\(190\) 0 0
\(191\) 0.396221 0.0286695 0.0143348 0.999897i \(-0.495437\pi\)
0.0143348 + 0.999897i \(0.495437\pi\)
\(192\) 0 0
\(193\) 3.34476 0.240761 0.120381 0.992728i \(-0.461589\pi\)
0.120381 + 0.992728i \(0.461589\pi\)
\(194\) 0 0
\(195\) 0.956242 0.0684779
\(196\) 0 0
\(197\) −21.7540 −1.54991 −0.774955 0.632016i \(-0.782228\pi\)
−0.774955 + 0.632016i \(0.782228\pi\)
\(198\) 0 0
\(199\) −27.1091 −1.92172 −0.960858 0.277041i \(-0.910646\pi\)
−0.960858 + 0.277041i \(0.910646\pi\)
\(200\) 0 0
\(201\) 11.2830 0.795843
\(202\) 0 0
\(203\) −3.11113 −0.218359
\(204\) 0 0
\(205\) 0.765408 0.0534584
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 0.0675911 0.00467537
\(210\) 0 0
\(211\) 12.1121 0.833832 0.416916 0.908945i \(-0.363111\pi\)
0.416916 + 0.908945i \(0.363111\pi\)
\(212\) 0 0
\(213\) 4.10798 0.281474
\(214\) 0 0
\(215\) −0.770923 −0.0525765
\(216\) 0 0
\(217\) −11.9831 −0.813466
\(218\) 0 0
\(219\) 12.5759 0.849800
\(220\) 0 0
\(221\) 14.2878 0.961099
\(222\) 0 0
\(223\) 14.3444 0.960572 0.480286 0.877112i \(-0.340533\pi\)
0.480286 + 0.877112i \(0.340533\pi\)
\(224\) 0 0
\(225\) −4.96473 −0.330982
\(226\) 0 0
\(227\) 23.3773 1.55161 0.775804 0.630974i \(-0.217344\pi\)
0.775804 + 0.630974i \(0.217344\pi\)
\(228\) 0 0
\(229\) −1.31074 −0.0866164 −0.0433082 0.999062i \(-0.513790\pi\)
−0.0433082 + 0.999062i \(0.513790\pi\)
\(230\) 0 0
\(231\) 0.0473140 0.00311303
\(232\) 0 0
\(233\) 13.3088 0.871891 0.435945 0.899973i \(-0.356414\pi\)
0.435945 + 0.899973i \(0.356414\pi\)
\(234\) 0 0
\(235\) 2.02163 0.131876
\(236\) 0 0
\(237\) 6.51135 0.422958
\(238\) 0 0
\(239\) −6.21912 −0.402281 −0.201141 0.979562i \(-0.564465\pi\)
−0.201141 + 0.979562i \(0.564465\pi\)
\(240\) 0 0
\(241\) 13.0556 0.840984 0.420492 0.907296i \(-0.361858\pi\)
0.420492 + 0.907296i \(0.361858\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.503126 0.0321436
\(246\) 0 0
\(247\) 22.6311 1.43998
\(248\) 0 0
\(249\) −4.47591 −0.283649
\(250\) 0 0
\(251\) −6.35262 −0.400974 −0.200487 0.979696i \(-0.564252\pi\)
−0.200487 + 0.979696i \(0.564252\pi\)
\(252\) 0 0
\(253\) 0.0152079 0.000956116 0
\(254\) 0 0
\(255\) 0.526935 0.0329979
\(256\) 0 0
\(257\) −4.20856 −0.262523 −0.131261 0.991348i \(-0.541903\pi\)
−0.131261 + 0.991348i \(0.541903\pi\)
\(258\) 0 0
\(259\) −7.61588 −0.473228
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 9.56002 0.589496 0.294748 0.955575i \(-0.404764\pi\)
0.294748 + 0.955575i \(0.404764\pi\)
\(264\) 0 0
\(265\) 1.63224 0.100268
\(266\) 0 0
\(267\) −9.25893 −0.566637
\(268\) 0 0
\(269\) 14.6114 0.890872 0.445436 0.895314i \(-0.353049\pi\)
0.445436 + 0.895314i \(0.353049\pi\)
\(270\) 0 0
\(271\) −5.99455 −0.364143 −0.182071 0.983285i \(-0.558280\pi\)
−0.182071 + 0.983285i \(0.558280\pi\)
\(272\) 0 0
\(273\) 15.8419 0.958793
\(274\) 0 0
\(275\) −0.0755034 −0.00455303
\(276\) 0 0
\(277\) 13.5161 0.812102 0.406051 0.913850i \(-0.366906\pi\)
0.406051 + 0.913850i \(0.366906\pi\)
\(278\) 0 0
\(279\) −3.85168 −0.230594
\(280\) 0 0
\(281\) 21.8604 1.30408 0.652041 0.758184i \(-0.273913\pi\)
0.652041 + 0.758184i \(0.273913\pi\)
\(282\) 0 0
\(283\) 15.8875 0.944415 0.472208 0.881487i \(-0.343457\pi\)
0.472208 + 0.881487i \(0.343457\pi\)
\(284\) 0 0
\(285\) 0.834639 0.0494398
\(286\) 0 0
\(287\) 12.6804 0.748498
\(288\) 0 0
\(289\) −9.12676 −0.536868
\(290\) 0 0
\(291\) 7.78248 0.456217
\(292\) 0 0
\(293\) 21.9988 1.28518 0.642592 0.766209i \(-0.277859\pi\)
0.642592 + 0.766209i \(0.277859\pi\)
\(294\) 0 0
\(295\) −1.63051 −0.0949320
\(296\) 0 0
\(297\) 0.0152079 0.000882455 0
\(298\) 0 0
\(299\) 5.09199 0.294478
\(300\) 0 0
\(301\) −12.7717 −0.736150
\(302\) 0 0
\(303\) −6.72116 −0.386120
\(304\) 0 0
\(305\) 0.562700 0.0322201
\(306\) 0 0
\(307\) 6.94886 0.396592 0.198296 0.980142i \(-0.436459\pi\)
0.198296 + 0.980142i \(0.436459\pi\)
\(308\) 0 0
\(309\) −14.4939 −0.824527
\(310\) 0 0
\(311\) −24.1375 −1.36871 −0.684357 0.729147i \(-0.739917\pi\)
−0.684357 + 0.729147i \(0.739917\pi\)
\(312\) 0 0
\(313\) 12.5436 0.709004 0.354502 0.935055i \(-0.384650\pi\)
0.354502 + 0.935055i \(0.384650\pi\)
\(314\) 0 0
\(315\) 0.584250 0.0329188
\(316\) 0 0
\(317\) −10.6497 −0.598149 −0.299074 0.954230i \(-0.596678\pi\)
−0.299074 + 0.954230i \(0.596678\pi\)
\(318\) 0 0
\(319\) −0.0152079 −0.000851482 0
\(320\) 0 0
\(321\) −9.80146 −0.547064
\(322\) 0 0
\(323\) 12.4708 0.693895
\(324\) 0 0
\(325\) −25.2804 −1.40230
\(326\) 0 0
\(327\) −3.75215 −0.207494
\(328\) 0 0
\(329\) 33.4918 1.84647
\(330\) 0 0
\(331\) −32.5359 −1.78834 −0.894169 0.447730i \(-0.852232\pi\)
−0.894169 + 0.447730i \(0.852232\pi\)
\(332\) 0 0
\(333\) −2.44794 −0.134146
\(334\) 0 0
\(335\) 2.11887 0.115767
\(336\) 0 0
\(337\) 10.9431 0.596110 0.298055 0.954549i \(-0.403662\pi\)
0.298055 + 0.954549i \(0.403662\pi\)
\(338\) 0 0
\(339\) −12.1826 −0.661669
\(340\) 0 0
\(341\) −0.0585762 −0.00317208
\(342\) 0 0
\(343\) −13.4427 −0.725840
\(344\) 0 0
\(345\) 0.187793 0.0101105
\(346\) 0 0
\(347\) −25.5705 −1.37270 −0.686350 0.727272i \(-0.740788\pi\)
−0.686350 + 0.727272i \(0.740788\pi\)
\(348\) 0 0
\(349\) −24.9768 −1.33698 −0.668490 0.743721i \(-0.733059\pi\)
−0.668490 + 0.743721i \(0.733059\pi\)
\(350\) 0 0
\(351\) 5.09199 0.271790
\(352\) 0 0
\(353\) −3.60990 −0.192136 −0.0960678 0.995375i \(-0.530627\pi\)
−0.0960678 + 0.995375i \(0.530627\pi\)
\(354\) 0 0
\(355\) 0.771452 0.0409444
\(356\) 0 0
\(357\) 8.72962 0.462020
\(358\) 0 0
\(359\) 35.1320 1.85420 0.927098 0.374818i \(-0.122295\pi\)
0.927098 + 0.374818i \(0.122295\pi\)
\(360\) 0 0
\(361\) 0.753189 0.0396415
\(362\) 0 0
\(363\) −10.9998 −0.577338
\(364\) 0 0
\(365\) 2.36167 0.123615
\(366\) 0 0
\(367\) 30.0290 1.56750 0.783750 0.621077i \(-0.213305\pi\)
0.783750 + 0.621077i \(0.213305\pi\)
\(368\) 0 0
\(369\) 4.07580 0.212178
\(370\) 0 0
\(371\) 27.0410 1.40390
\(372\) 0 0
\(373\) 30.9812 1.60415 0.802073 0.597225i \(-0.203730\pi\)
0.802073 + 0.597225i \(0.203730\pi\)
\(374\) 0 0
\(375\) −1.87131 −0.0966341
\(376\) 0 0
\(377\) −5.09199 −0.262251
\(378\) 0 0
\(379\) 13.2264 0.679394 0.339697 0.940535i \(-0.389676\pi\)
0.339697 + 0.940535i \(0.389676\pi\)
\(380\) 0 0
\(381\) −14.7848 −0.757447
\(382\) 0 0
\(383\) 10.9631 0.560189 0.280094 0.959972i \(-0.409634\pi\)
0.280094 + 0.959972i \(0.409634\pi\)
\(384\) 0 0
\(385\) 0.00888525 0.000452834 0
\(386\) 0 0
\(387\) −4.10517 −0.208677
\(388\) 0 0
\(389\) −7.37047 −0.373698 −0.186849 0.982389i \(-0.559827\pi\)
−0.186849 + 0.982389i \(0.559827\pi\)
\(390\) 0 0
\(391\) 2.80593 0.141902
\(392\) 0 0
\(393\) −21.0448 −1.06157
\(394\) 0 0
\(395\) 1.22279 0.0615251
\(396\) 0 0
\(397\) 11.9862 0.601569 0.300785 0.953692i \(-0.402751\pi\)
0.300785 + 0.953692i \(0.402751\pi\)
\(398\) 0 0
\(399\) 13.8273 0.692231
\(400\) 0 0
\(401\) 3.73312 0.186423 0.0932115 0.995646i \(-0.470287\pi\)
0.0932115 + 0.995646i \(0.470287\pi\)
\(402\) 0 0
\(403\) −19.6127 −0.976981
\(404\) 0 0
\(405\) 0.187793 0.00933153
\(406\) 0 0
\(407\) −0.0372282 −0.00184533
\(408\) 0 0
\(409\) −6.21178 −0.307153 −0.153576 0.988137i \(-0.549079\pi\)
−0.153576 + 0.988137i \(0.549079\pi\)
\(410\) 0 0
\(411\) −18.4369 −0.909423
\(412\) 0 0
\(413\) −27.0123 −1.32919
\(414\) 0 0
\(415\) −0.840546 −0.0412608
\(416\) 0 0
\(417\) 19.3555 0.947843
\(418\) 0 0
\(419\) −13.5022 −0.659625 −0.329812 0.944047i \(-0.606985\pi\)
−0.329812 + 0.944047i \(0.606985\pi\)
\(420\) 0 0
\(421\) −34.2427 −1.66888 −0.834442 0.551095i \(-0.814210\pi\)
−0.834442 + 0.551095i \(0.814210\pi\)
\(422\) 0 0
\(423\) 10.7652 0.523420
\(424\) 0 0
\(425\) −13.9307 −0.675738
\(426\) 0 0
\(427\) 9.32214 0.451130
\(428\) 0 0
\(429\) 0.0774388 0.00373878
\(430\) 0 0
\(431\) −8.29898 −0.399748 −0.199874 0.979822i \(-0.564053\pi\)
−0.199874 + 0.979822i \(0.564053\pi\)
\(432\) 0 0
\(433\) −7.21981 −0.346962 −0.173481 0.984837i \(-0.555502\pi\)
−0.173481 + 0.984837i \(0.555502\pi\)
\(434\) 0 0
\(435\) −0.187793 −0.00900400
\(436\) 0 0
\(437\) 4.44446 0.212607
\(438\) 0 0
\(439\) 14.3686 0.685774 0.342887 0.939377i \(-0.388595\pi\)
0.342887 + 0.939377i \(0.388595\pi\)
\(440\) 0 0
\(441\) 2.67915 0.127579
\(442\) 0 0
\(443\) −27.6642 −1.31437 −0.657183 0.753731i \(-0.728252\pi\)
−0.657183 + 0.753731i \(0.728252\pi\)
\(444\) 0 0
\(445\) −1.73876 −0.0824253
\(446\) 0 0
\(447\) −5.36191 −0.253610
\(448\) 0 0
\(449\) −35.9054 −1.69448 −0.847240 0.531211i \(-0.821737\pi\)
−0.847240 + 0.531211i \(0.821737\pi\)
\(450\) 0 0
\(451\) 0.0619846 0.00291874
\(452\) 0 0
\(453\) 4.92971 0.231618
\(454\) 0 0
\(455\) 2.97500 0.139470
\(456\) 0 0
\(457\) 3.92186 0.183457 0.0917285 0.995784i \(-0.470761\pi\)
0.0917285 + 0.995784i \(0.470761\pi\)
\(458\) 0 0
\(459\) 2.80593 0.130970
\(460\) 0 0
\(461\) 9.40397 0.437986 0.218993 0.975726i \(-0.429723\pi\)
0.218993 + 0.975726i \(0.429723\pi\)
\(462\) 0 0
\(463\) 10.3463 0.480835 0.240418 0.970670i \(-0.422716\pi\)
0.240418 + 0.970670i \(0.422716\pi\)
\(464\) 0 0
\(465\) −0.723321 −0.0335432
\(466\) 0 0
\(467\) −7.31033 −0.338282 −0.169141 0.985592i \(-0.554099\pi\)
−0.169141 + 0.985592i \(0.554099\pi\)
\(468\) 0 0
\(469\) 35.1030 1.62090
\(470\) 0 0
\(471\) 14.5834 0.671969
\(472\) 0 0
\(473\) −0.0624312 −0.00287059
\(474\) 0 0
\(475\) −22.0655 −1.01244
\(476\) 0 0
\(477\) 8.69169 0.397965
\(478\) 0 0
\(479\) −12.1642 −0.555799 −0.277899 0.960610i \(-0.589638\pi\)
−0.277899 + 0.960610i \(0.589638\pi\)
\(480\) 0 0
\(481\) −12.4649 −0.568351
\(482\) 0 0
\(483\) 3.11113 0.141561
\(484\) 0 0
\(485\) 1.46150 0.0663632
\(486\) 0 0
\(487\) 15.1124 0.684806 0.342403 0.939553i \(-0.388759\pi\)
0.342403 + 0.939553i \(0.388759\pi\)
\(488\) 0 0
\(489\) 9.81554 0.443874
\(490\) 0 0
\(491\) 24.3352 1.09823 0.549116 0.835746i \(-0.314964\pi\)
0.549116 + 0.835746i \(0.314964\pi\)
\(492\) 0 0
\(493\) −2.80593 −0.126373
\(494\) 0 0
\(495\) 0.00285595 0.000128365 0
\(496\) 0 0
\(497\) 12.7805 0.573283
\(498\) 0 0
\(499\) 37.8616 1.69492 0.847458 0.530862i \(-0.178132\pi\)
0.847458 + 0.530862i \(0.178132\pi\)
\(500\) 0 0
\(501\) 15.8044 0.706088
\(502\) 0 0
\(503\) −3.15047 −0.140473 −0.0702364 0.997530i \(-0.522375\pi\)
−0.0702364 + 0.997530i \(0.522375\pi\)
\(504\) 0 0
\(505\) −1.26219 −0.0561667
\(506\) 0 0
\(507\) 12.9284 0.574170
\(508\) 0 0
\(509\) −7.42367 −0.329048 −0.164524 0.986373i \(-0.552609\pi\)
−0.164524 + 0.986373i \(0.552609\pi\)
\(510\) 0 0
\(511\) 39.1253 1.73080
\(512\) 0 0
\(513\) 4.44446 0.196228
\(514\) 0 0
\(515\) −2.72185 −0.119939
\(516\) 0 0
\(517\) 0.163716 0.00720022
\(518\) 0 0
\(519\) −3.48262 −0.152870
\(520\) 0 0
\(521\) −2.65840 −0.116467 −0.0582333 0.998303i \(-0.518547\pi\)
−0.0582333 + 0.998303i \(0.518547\pi\)
\(522\) 0 0
\(523\) −15.0408 −0.657686 −0.328843 0.944385i \(-0.606659\pi\)
−0.328843 + 0.944385i \(0.606659\pi\)
\(524\) 0 0
\(525\) −15.4459 −0.674116
\(526\) 0 0
\(527\) −10.8076 −0.470784
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −8.68248 −0.376787
\(532\) 0 0
\(533\) 20.7540 0.898954
\(534\) 0 0
\(535\) −1.84065 −0.0795782
\(536\) 0 0
\(537\) −20.9975 −0.906108
\(538\) 0 0
\(539\) 0.0407444 0.00175498
\(540\) 0 0
\(541\) 24.5939 1.05737 0.528686 0.848817i \(-0.322685\pi\)
0.528686 + 0.848817i \(0.322685\pi\)
\(542\) 0 0
\(543\) 10.3852 0.445672
\(544\) 0 0
\(545\) −0.704629 −0.0301830
\(546\) 0 0
\(547\) 6.45639 0.276055 0.138028 0.990428i \(-0.455924\pi\)
0.138028 + 0.990428i \(0.455924\pi\)
\(548\) 0 0
\(549\) 2.99638 0.127882
\(550\) 0 0
\(551\) −4.44446 −0.189340
\(552\) 0 0
\(553\) 20.2577 0.861444
\(554\) 0 0
\(555\) −0.459707 −0.0195135
\(556\) 0 0
\(557\) −15.5826 −0.660255 −0.330127 0.943936i \(-0.607092\pi\)
−0.330127 + 0.943936i \(0.607092\pi\)
\(558\) 0 0
\(559\) −20.9035 −0.884123
\(560\) 0 0
\(561\) 0.0426724 0.00180163
\(562\) 0 0
\(563\) 28.0751 1.18322 0.591612 0.806223i \(-0.298492\pi\)
0.591612 + 0.806223i \(0.298492\pi\)
\(564\) 0 0
\(565\) −2.28781 −0.0962490
\(566\) 0 0
\(567\) 3.11113 0.130655
\(568\) 0 0
\(569\) −5.35305 −0.224412 −0.112206 0.993685i \(-0.535792\pi\)
−0.112206 + 0.993685i \(0.535792\pi\)
\(570\) 0 0
\(571\) −37.6630 −1.57615 −0.788073 0.615582i \(-0.788921\pi\)
−0.788073 + 0.615582i \(0.788921\pi\)
\(572\) 0 0
\(573\) 0.396221 0.0165524
\(574\) 0 0
\(575\) −4.96473 −0.207044
\(576\) 0 0
\(577\) 26.2753 1.09385 0.546927 0.837180i \(-0.315797\pi\)
0.546927 + 0.837180i \(0.315797\pi\)
\(578\) 0 0
\(579\) 3.34476 0.139003
\(580\) 0 0
\(581\) −13.9252 −0.577713
\(582\) 0 0
\(583\) 0.132183 0.00547445
\(584\) 0 0
\(585\) 0.956242 0.0395358
\(586\) 0 0
\(587\) 32.8088 1.35417 0.677083 0.735907i \(-0.263244\pi\)
0.677083 + 0.735907i \(0.263244\pi\)
\(588\) 0 0
\(589\) −17.1186 −0.705361
\(590\) 0 0
\(591\) −21.7540 −0.894842
\(592\) 0 0
\(593\) 33.2183 1.36411 0.682056 0.731300i \(-0.261086\pi\)
0.682056 + 0.731300i \(0.261086\pi\)
\(594\) 0 0
\(595\) 1.63936 0.0672074
\(596\) 0 0
\(597\) −27.1091 −1.10950
\(598\) 0 0
\(599\) 15.8213 0.646441 0.323221 0.946324i \(-0.395234\pi\)
0.323221 + 0.946324i \(0.395234\pi\)
\(600\) 0 0
\(601\) −5.10952 −0.208422 −0.104211 0.994555i \(-0.533232\pi\)
−0.104211 + 0.994555i \(0.533232\pi\)
\(602\) 0 0
\(603\) 11.2830 0.459480
\(604\) 0 0
\(605\) −2.06568 −0.0839820
\(606\) 0 0
\(607\) −8.83452 −0.358582 −0.179291 0.983796i \(-0.557380\pi\)
−0.179291 + 0.983796i \(0.557380\pi\)
\(608\) 0 0
\(609\) −3.11113 −0.126069
\(610\) 0 0
\(611\) 54.8161 2.21762
\(612\) 0 0
\(613\) 13.7895 0.556954 0.278477 0.960443i \(-0.410170\pi\)
0.278477 + 0.960443i \(0.410170\pi\)
\(614\) 0 0
\(615\) 0.765408 0.0308642
\(616\) 0 0
\(617\) −6.49692 −0.261556 −0.130778 0.991412i \(-0.541748\pi\)
−0.130778 + 0.991412i \(0.541748\pi\)
\(618\) 0 0
\(619\) 27.9394 1.12298 0.561490 0.827484i \(-0.310228\pi\)
0.561490 + 0.827484i \(0.310228\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −28.8058 −1.15408
\(624\) 0 0
\(625\) 24.4722 0.978890
\(626\) 0 0
\(627\) 0.0675911 0.00269933
\(628\) 0 0
\(629\) −6.86876 −0.273875
\(630\) 0 0
\(631\) 11.8703 0.472548 0.236274 0.971686i \(-0.424074\pi\)
0.236274 + 0.971686i \(0.424074\pi\)
\(632\) 0 0
\(633\) 12.1121 0.481413
\(634\) 0 0
\(635\) −2.77648 −0.110181
\(636\) 0 0
\(637\) 13.6422 0.540524
\(638\) 0 0
\(639\) 4.10798 0.162509
\(640\) 0 0
\(641\) −14.8700 −0.587328 −0.293664 0.955909i \(-0.594875\pi\)
−0.293664 + 0.955909i \(0.594875\pi\)
\(642\) 0 0
\(643\) −36.4858 −1.43886 −0.719430 0.694565i \(-0.755597\pi\)
−0.719430 + 0.694565i \(0.755597\pi\)
\(644\) 0 0
\(645\) −0.770923 −0.0303551
\(646\) 0 0
\(647\) 22.8891 0.899863 0.449932 0.893063i \(-0.351448\pi\)
0.449932 + 0.893063i \(0.351448\pi\)
\(648\) 0 0
\(649\) −0.132043 −0.00518313
\(650\) 0 0
\(651\) −11.9831 −0.469655
\(652\) 0 0
\(653\) −36.1865 −1.41609 −0.708044 0.706168i \(-0.750422\pi\)
−0.708044 + 0.706168i \(0.750422\pi\)
\(654\) 0 0
\(655\) −3.95207 −0.154420
\(656\) 0 0
\(657\) 12.5759 0.490632
\(658\) 0 0
\(659\) −9.45417 −0.368282 −0.184141 0.982900i \(-0.558950\pi\)
−0.184141 + 0.982900i \(0.558950\pi\)
\(660\) 0 0
\(661\) −6.62737 −0.257775 −0.128887 0.991659i \(-0.541141\pi\)
−0.128887 + 0.991659i \(0.541141\pi\)
\(662\) 0 0
\(663\) 14.2878 0.554891
\(664\) 0 0
\(665\) 2.59667 0.100695
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 14.3444 0.554587
\(670\) 0 0
\(671\) 0.0455688 0.00175916
\(672\) 0 0
\(673\) −38.3436 −1.47804 −0.739018 0.673685i \(-0.764710\pi\)
−0.739018 + 0.673685i \(0.764710\pi\)
\(674\) 0 0
\(675\) −4.96473 −0.191093
\(676\) 0 0
\(677\) −5.45076 −0.209490 −0.104745 0.994499i \(-0.533403\pi\)
−0.104745 + 0.994499i \(0.533403\pi\)
\(678\) 0 0
\(679\) 24.2123 0.929184
\(680\) 0 0
\(681\) 23.3773 0.895822
\(682\) 0 0
\(683\) −18.1931 −0.696140 −0.348070 0.937469i \(-0.613163\pi\)
−0.348070 + 0.937469i \(0.613163\pi\)
\(684\) 0 0
\(685\) −3.46232 −0.132288
\(686\) 0 0
\(687\) −1.31074 −0.0500080
\(688\) 0 0
\(689\) 44.2580 1.68610
\(690\) 0 0
\(691\) 14.7569 0.561378 0.280689 0.959799i \(-0.409437\pi\)
0.280689 + 0.959799i \(0.409437\pi\)
\(692\) 0 0
\(693\) 0.0473140 0.00179731
\(694\) 0 0
\(695\) 3.63483 0.137877
\(696\) 0 0
\(697\) 11.4364 0.433185
\(698\) 0 0
\(699\) 13.3088 0.503386
\(700\) 0 0
\(701\) 4.42193 0.167014 0.0835069 0.996507i \(-0.473388\pi\)
0.0835069 + 0.996507i \(0.473388\pi\)
\(702\) 0 0
\(703\) −10.8798 −0.410339
\(704\) 0 0
\(705\) 2.02163 0.0761388
\(706\) 0 0
\(707\) −20.9104 −0.786417
\(708\) 0 0
\(709\) −21.3150 −0.800503 −0.400251 0.916405i \(-0.631077\pi\)
−0.400251 + 0.916405i \(0.631077\pi\)
\(710\) 0 0
\(711\) 6.51135 0.244195
\(712\) 0 0
\(713\) −3.85168 −0.144247
\(714\) 0 0
\(715\) 0.0145425 0.000543858 0
\(716\) 0 0
\(717\) −6.21912 −0.232257
\(718\) 0 0
\(719\) −12.5714 −0.468835 −0.234417 0.972136i \(-0.575318\pi\)
−0.234417 + 0.972136i \(0.575318\pi\)
\(720\) 0 0
\(721\) −45.0923 −1.67933
\(722\) 0 0
\(723\) 13.0556 0.485542
\(724\) 0 0
\(725\) 4.96473 0.184386
\(726\) 0 0
\(727\) −5.10913 −0.189487 −0.0947436 0.995502i \(-0.530203\pi\)
−0.0947436 + 0.995502i \(0.530203\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −11.5188 −0.426038
\(732\) 0 0
\(733\) 32.5291 1.20149 0.600745 0.799441i \(-0.294871\pi\)
0.600745 + 0.799441i \(0.294871\pi\)
\(734\) 0 0
\(735\) 0.503126 0.0185581
\(736\) 0 0
\(737\) 0.171592 0.00632065
\(738\) 0 0
\(739\) 32.3091 1.18851 0.594254 0.804277i \(-0.297447\pi\)
0.594254 + 0.804277i \(0.297447\pi\)
\(740\) 0 0
\(741\) 22.6311 0.831376
\(742\) 0 0
\(743\) −15.8188 −0.580337 −0.290168 0.956976i \(-0.593711\pi\)
−0.290168 + 0.956976i \(0.593711\pi\)
\(744\) 0 0
\(745\) −1.00693 −0.0368911
\(746\) 0 0
\(747\) −4.47591 −0.163765
\(748\) 0 0
\(749\) −30.4936 −1.11421
\(750\) 0 0
\(751\) −37.3597 −1.36328 −0.681638 0.731690i \(-0.738732\pi\)
−0.681638 + 0.731690i \(0.738732\pi\)
\(752\) 0 0
\(753\) −6.35262 −0.231502
\(754\) 0 0
\(755\) 0.925768 0.0336921
\(756\) 0 0
\(757\) −22.0675 −0.802056 −0.401028 0.916066i \(-0.631347\pi\)
−0.401028 + 0.916066i \(0.631347\pi\)
\(758\) 0 0
\(759\) 0.0152079 0.000552014 0
\(760\) 0 0
\(761\) 38.4308 1.39311 0.696557 0.717501i \(-0.254714\pi\)
0.696557 + 0.717501i \(0.254714\pi\)
\(762\) 0 0
\(763\) −11.6734 −0.422607
\(764\) 0 0
\(765\) 0.526935 0.0190514
\(766\) 0 0
\(767\) −44.2111 −1.59637
\(768\) 0 0
\(769\) 28.1201 1.01404 0.507019 0.861935i \(-0.330747\pi\)
0.507019 + 0.861935i \(0.330747\pi\)
\(770\) 0 0
\(771\) −4.20856 −0.151568
\(772\) 0 0
\(773\) 46.7516 1.68154 0.840769 0.541394i \(-0.182103\pi\)
0.840769 + 0.541394i \(0.182103\pi\)
\(774\) 0 0
\(775\) 19.1226 0.686904
\(776\) 0 0
\(777\) −7.61588 −0.273218
\(778\) 0 0
\(779\) 18.1147 0.649027
\(780\) 0 0
\(781\) 0.0624740 0.00223550
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 2.73867 0.0977474
\(786\) 0 0
\(787\) −22.7176 −0.809794 −0.404897 0.914362i \(-0.632693\pi\)
−0.404897 + 0.914362i \(0.632693\pi\)
\(788\) 0 0
\(789\) 9.56002 0.340346
\(790\) 0 0
\(791\) −37.9017 −1.34763
\(792\) 0 0
\(793\) 15.2575 0.541811
\(794\) 0 0
\(795\) 1.63224 0.0578897
\(796\) 0 0
\(797\) 21.2517 0.752773 0.376387 0.926463i \(-0.377166\pi\)
0.376387 + 0.926463i \(0.377166\pi\)
\(798\) 0 0
\(799\) 30.2063 1.06862
\(800\) 0 0
\(801\) −9.25893 −0.327148
\(802\) 0 0
\(803\) 0.191254 0.00674919
\(804\) 0 0
\(805\) 0.584250 0.0205921
\(806\) 0 0
\(807\) 14.6114 0.514345
\(808\) 0 0
\(809\) −32.3017 −1.13567 −0.567833 0.823144i \(-0.692218\pi\)
−0.567833 + 0.823144i \(0.692218\pi\)
\(810\) 0 0
\(811\) −10.5968 −0.372104 −0.186052 0.982540i \(-0.559569\pi\)
−0.186052 + 0.982540i \(0.559569\pi\)
\(812\) 0 0
\(813\) −5.99455 −0.210238
\(814\) 0 0
\(815\) 1.84329 0.0645678
\(816\) 0 0
\(817\) −18.2452 −0.638320
\(818\) 0 0
\(819\) 15.8419 0.553560
\(820\) 0 0
\(821\) −21.3525 −0.745208 −0.372604 0.927990i \(-0.621535\pi\)
−0.372604 + 0.927990i \(0.621535\pi\)
\(822\) 0 0
\(823\) 10.9692 0.382361 0.191181 0.981555i \(-0.438768\pi\)
0.191181 + 0.981555i \(0.438768\pi\)
\(824\) 0 0
\(825\) −0.0755034 −0.00262869
\(826\) 0 0
\(827\) −50.2907 −1.74878 −0.874390 0.485224i \(-0.838738\pi\)
−0.874390 + 0.485224i \(0.838738\pi\)
\(828\) 0 0
\(829\) 25.4590 0.884229 0.442114 0.896959i \(-0.354229\pi\)
0.442114 + 0.896959i \(0.354229\pi\)
\(830\) 0 0
\(831\) 13.5161 0.468867
\(832\) 0 0
\(833\) 7.51750 0.260466
\(834\) 0 0
\(835\) 2.96796 0.102710
\(836\) 0 0
\(837\) −3.85168 −0.133134
\(838\) 0 0
\(839\) −32.8811 −1.13518 −0.567590 0.823311i \(-0.692124\pi\)
−0.567590 + 0.823311i \(0.692124\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 21.8604 0.752912
\(844\) 0 0
\(845\) 2.42787 0.0835211
\(846\) 0 0
\(847\) −34.2217 −1.17587
\(848\) 0 0
\(849\) 15.8875 0.545259
\(850\) 0 0
\(851\) −2.44794 −0.0839144
\(852\) 0 0
\(853\) 47.4857 1.62588 0.812939 0.582349i \(-0.197866\pi\)
0.812939 + 0.582349i \(0.197866\pi\)
\(854\) 0 0
\(855\) 0.834639 0.0285441
\(856\) 0 0
\(857\) 2.90915 0.0993745 0.0496873 0.998765i \(-0.484178\pi\)
0.0496873 + 0.998765i \(0.484178\pi\)
\(858\) 0 0
\(859\) −33.1860 −1.13229 −0.566146 0.824305i \(-0.691566\pi\)
−0.566146 + 0.824305i \(0.691566\pi\)
\(860\) 0 0
\(861\) 12.6804 0.432146
\(862\) 0 0
\(863\) −32.7369 −1.11438 −0.557189 0.830386i \(-0.688120\pi\)
−0.557189 + 0.830386i \(0.688120\pi\)
\(864\) 0 0
\(865\) −0.654012 −0.0222371
\(866\) 0 0
\(867\) −9.12676 −0.309961
\(868\) 0 0
\(869\) 0.0990243 0.00335917
\(870\) 0 0
\(871\) 57.4530 1.94672
\(872\) 0 0
\(873\) 7.78248 0.263397
\(874\) 0 0
\(875\) −5.82190 −0.196816
\(876\) 0 0
\(877\) −25.6359 −0.865664 −0.432832 0.901474i \(-0.642486\pi\)
−0.432832 + 0.901474i \(0.642486\pi\)
\(878\) 0 0
\(879\) 21.9988 0.742001
\(880\) 0 0
\(881\) 4.12625 0.139017 0.0695084 0.997581i \(-0.477857\pi\)
0.0695084 + 0.997581i \(0.477857\pi\)
\(882\) 0 0
\(883\) 5.82512 0.196031 0.0980155 0.995185i \(-0.468751\pi\)
0.0980155 + 0.995185i \(0.468751\pi\)
\(884\) 0 0
\(885\) −1.63051 −0.0548090
\(886\) 0 0
\(887\) −9.53824 −0.320263 −0.160131 0.987096i \(-0.551192\pi\)
−0.160131 + 0.987096i \(0.551192\pi\)
\(888\) 0 0
\(889\) −45.9974 −1.54270
\(890\) 0 0
\(891\) 0.0152079 0.000509485 0
\(892\) 0 0
\(893\) 47.8453 1.60108
\(894\) 0 0
\(895\) −3.94319 −0.131806
\(896\) 0 0
\(897\) 5.09199 0.170017
\(898\) 0 0
\(899\) 3.85168 0.128461
\(900\) 0 0
\(901\) 24.3883 0.812491
\(902\) 0 0
\(903\) −12.7717 −0.425016
\(904\) 0 0
\(905\) 1.95027 0.0648293
\(906\) 0 0
\(907\) −48.0271 −1.59471 −0.797357 0.603507i \(-0.793769\pi\)
−0.797357 + 0.603507i \(0.793769\pi\)
\(908\) 0 0
\(909\) −6.72116 −0.222927
\(910\) 0 0
\(911\) −8.95354 −0.296644 −0.148322 0.988939i \(-0.547387\pi\)
−0.148322 + 0.988939i \(0.547387\pi\)
\(912\) 0 0
\(913\) −0.0680694 −0.00225277
\(914\) 0 0
\(915\) 0.562700 0.0186023
\(916\) 0 0
\(917\) −65.4732 −2.16211
\(918\) 0 0
\(919\) −43.9536 −1.44990 −0.724948 0.688804i \(-0.758136\pi\)
−0.724948 + 0.688804i \(0.758136\pi\)
\(920\) 0 0
\(921\) 6.94886 0.228973
\(922\) 0 0
\(923\) 20.9178 0.688519
\(924\) 0 0
\(925\) 12.1534 0.399601
\(926\) 0 0
\(927\) −14.4939 −0.476041
\(928\) 0 0
\(929\) 37.2230 1.22125 0.610623 0.791921i \(-0.290919\pi\)
0.610623 + 0.791921i \(0.290919\pi\)
\(930\) 0 0
\(931\) 11.9074 0.390248
\(932\) 0 0
\(933\) −24.1375 −0.790228
\(934\) 0 0
\(935\) 0.00801360 0.000262073 0
\(936\) 0 0
\(937\) 31.1645 1.01810 0.509049 0.860737i \(-0.329997\pi\)
0.509049 + 0.860737i \(0.329997\pi\)
\(938\) 0 0
\(939\) 12.5436 0.409344
\(940\) 0 0
\(941\) −42.5579 −1.38735 −0.693674 0.720289i \(-0.744009\pi\)
−0.693674 + 0.720289i \(0.744009\pi\)
\(942\) 0 0
\(943\) 4.07580 0.132726
\(944\) 0 0
\(945\) 0.584250 0.0190057
\(946\) 0 0
\(947\) 56.5593 1.83793 0.918966 0.394338i \(-0.129026\pi\)
0.918966 + 0.394338i \(0.129026\pi\)
\(948\) 0 0
\(949\) 64.0364 2.07871
\(950\) 0 0
\(951\) −10.6497 −0.345341
\(952\) 0 0
\(953\) −18.3682 −0.595003 −0.297501 0.954721i \(-0.596153\pi\)
−0.297501 + 0.954721i \(0.596153\pi\)
\(954\) 0 0
\(955\) 0.0744076 0.00240777
\(956\) 0 0
\(957\) −0.0152079 −0.000491603 0
\(958\) 0 0
\(959\) −57.3595 −1.85224
\(960\) 0 0
\(961\) −16.1645 −0.521436
\(962\) 0 0
\(963\) −9.80146 −0.315848
\(964\) 0 0
\(965\) 0.628123 0.0202200
\(966\) 0 0
\(967\) 10.7246 0.344880 0.172440 0.985020i \(-0.444835\pi\)
0.172440 + 0.985020i \(0.444835\pi\)
\(968\) 0 0
\(969\) 12.4708 0.400621
\(970\) 0 0
\(971\) −52.8094 −1.69474 −0.847368 0.531007i \(-0.821814\pi\)
−0.847368 + 0.531007i \(0.821814\pi\)
\(972\) 0 0
\(973\) 60.2175 1.93049
\(974\) 0 0
\(975\) −25.2804 −0.809620
\(976\) 0 0
\(977\) 7.04878 0.225510 0.112755 0.993623i \(-0.464032\pi\)
0.112755 + 0.993623i \(0.464032\pi\)
\(978\) 0 0
\(979\) −0.140809 −0.00450028
\(980\) 0 0
\(981\) −3.75215 −0.119797
\(982\) 0 0
\(983\) 6.66905 0.212710 0.106355 0.994328i \(-0.466082\pi\)
0.106355 + 0.994328i \(0.466082\pi\)
\(984\) 0 0
\(985\) −4.08526 −0.130167
\(986\) 0 0
\(987\) 33.4918 1.06606
\(988\) 0 0
\(989\) −4.10517 −0.130537
\(990\) 0 0
\(991\) −43.2315 −1.37330 −0.686648 0.726990i \(-0.740918\pi\)
−0.686648 + 0.726990i \(0.740918\pi\)
\(992\) 0 0
\(993\) −32.5359 −1.03250
\(994\) 0 0
\(995\) −5.09092 −0.161393
\(996\) 0 0
\(997\) 19.0251 0.602531 0.301266 0.953540i \(-0.402591\pi\)
0.301266 + 0.953540i \(0.402591\pi\)
\(998\) 0 0
\(999\) −2.44794 −0.0774495
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 \(a_p\))