Properties

Label 8004.2.a.j.1.1
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 1.1
Root \(-4.29726\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -4.29726 q^{5} +3.54512 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -4.29726 q^{5} +3.54512 q^{7} +1.00000 q^{9} +0.161684 q^{11} +2.42045 q^{13} -4.29726 q^{15} +3.98980 q^{17} +7.43592 q^{19} +3.54512 q^{21} +1.00000 q^{23} +13.4665 q^{25} +1.00000 q^{27} -1.00000 q^{29} +2.05208 q^{31} +0.161684 q^{33} -15.2343 q^{35} -5.65285 q^{37} +2.42045 q^{39} -7.47256 q^{41} -2.80205 q^{43} -4.29726 q^{45} -5.80920 q^{47} +5.56789 q^{49} +3.98980 q^{51} +5.67820 q^{53} -0.694798 q^{55} +7.43592 q^{57} +14.1016 q^{59} +14.8564 q^{61} +3.54512 q^{63} -10.4013 q^{65} -9.34631 q^{67} +1.00000 q^{69} -11.6877 q^{71} +2.93865 q^{73} +13.4665 q^{75} +0.573189 q^{77} -0.741638 q^{79} +1.00000 q^{81} -7.89190 q^{83} -17.1452 q^{85} -1.00000 q^{87} +1.43329 q^{89} +8.58079 q^{91} +2.05208 q^{93} -31.9541 q^{95} -4.91986 q^{97} +0.161684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{3} + 3q^{5} + 4q^{7} + 16q^{9} + O(q^{10}) \) \( 16q + 16q^{3} + 3q^{5} + 4q^{7} + 16q^{9} + 5q^{11} + 6q^{13} + 3q^{15} + 3q^{17} + 11q^{19} + 4q^{21} + 16q^{23} + 27q^{25} + 16q^{27} - 16q^{29} + 14q^{31} + 5q^{33} + 11q^{35} + 4q^{37} + 6q^{39} + 11q^{41} + 23q^{43} + 3q^{45} - 2q^{47} + 34q^{49} + 3q^{51} + 19q^{53} + 31q^{55} + 11q^{57} + 32q^{59} + 19q^{61} + 4q^{63} + 6q^{65} + 33q^{67} + 16q^{69} - 5q^{71} + 23q^{73} + 27q^{75} + 42q^{77} + 24q^{79} + 16q^{81} + 7q^{83} - 16q^{87} - 2q^{89} + 25q^{91} + 14q^{93} + 7q^{95} + 33q^{97} + 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −4.29726 −1.92179 −0.960897 0.276905i \(-0.910691\pi\)
−0.960897 + 0.276905i \(0.910691\pi\)
\(6\) 0 0
\(7\) 3.54512 1.33993 0.669965 0.742393i \(-0.266309\pi\)
0.669965 + 0.742393i \(0.266309\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.161684 0.0487495 0.0243747 0.999703i \(-0.492241\pi\)
0.0243747 + 0.999703i \(0.492241\pi\)
\(12\) 0 0
\(13\) 2.42045 0.671312 0.335656 0.941985i \(-0.391042\pi\)
0.335656 + 0.941985i \(0.391042\pi\)
\(14\) 0 0
\(15\) −4.29726 −1.10955
\(16\) 0 0
\(17\) 3.98980 0.967669 0.483834 0.875160i \(-0.339244\pi\)
0.483834 + 0.875160i \(0.339244\pi\)
\(18\) 0 0
\(19\) 7.43592 1.70592 0.852959 0.521978i \(-0.174806\pi\)
0.852959 + 0.521978i \(0.174806\pi\)
\(20\) 0 0
\(21\) 3.54512 0.773609
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 13.4665 2.69329
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 2.05208 0.368565 0.184283 0.982873i \(-0.441004\pi\)
0.184283 + 0.982873i \(0.441004\pi\)
\(32\) 0 0
\(33\) 0.161684 0.0281455
\(34\) 0 0
\(35\) −15.2343 −2.57507
\(36\) 0 0
\(37\) −5.65285 −0.929322 −0.464661 0.885489i \(-0.653824\pi\)
−0.464661 + 0.885489i \(0.653824\pi\)
\(38\) 0 0
\(39\) 2.42045 0.387582
\(40\) 0 0
\(41\) −7.47256 −1.16702 −0.583509 0.812107i \(-0.698321\pi\)
−0.583509 + 0.812107i \(0.698321\pi\)
\(42\) 0 0
\(43\) −2.80205 −0.427309 −0.213655 0.976909i \(-0.568537\pi\)
−0.213655 + 0.976909i \(0.568537\pi\)
\(44\) 0 0
\(45\) −4.29726 −0.640598
\(46\) 0 0
\(47\) −5.80920 −0.847359 −0.423679 0.905812i \(-0.639262\pi\)
−0.423679 + 0.905812i \(0.639262\pi\)
\(48\) 0 0
\(49\) 5.56789 0.795412
\(50\) 0 0
\(51\) 3.98980 0.558684
\(52\) 0 0
\(53\) 5.67820 0.779960 0.389980 0.920823i \(-0.372482\pi\)
0.389980 + 0.920823i \(0.372482\pi\)
\(54\) 0 0
\(55\) −0.694798 −0.0936865
\(56\) 0 0
\(57\) 7.43592 0.984912
\(58\) 0 0
\(59\) 14.1016 1.83587 0.917936 0.396729i \(-0.129855\pi\)
0.917936 + 0.396729i \(0.129855\pi\)
\(60\) 0 0
\(61\) 14.8564 1.90217 0.951083 0.308936i \(-0.0999730\pi\)
0.951083 + 0.308936i \(0.0999730\pi\)
\(62\) 0 0
\(63\) 3.54512 0.446643
\(64\) 0 0
\(65\) −10.4013 −1.29012
\(66\) 0 0
\(67\) −9.34631 −1.14183 −0.570917 0.821008i \(-0.693412\pi\)
−0.570917 + 0.821008i \(0.693412\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −11.6877 −1.38707 −0.693536 0.720422i \(-0.743948\pi\)
−0.693536 + 0.720422i \(0.743948\pi\)
\(72\) 0 0
\(73\) 2.93865 0.343943 0.171972 0.985102i \(-0.444986\pi\)
0.171972 + 0.985102i \(0.444986\pi\)
\(74\) 0 0
\(75\) 13.4665 1.55497
\(76\) 0 0
\(77\) 0.573189 0.0653209
\(78\) 0 0
\(79\) −0.741638 −0.0834408 −0.0417204 0.999129i \(-0.513284\pi\)
−0.0417204 + 0.999129i \(0.513284\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.89190 −0.866249 −0.433124 0.901334i \(-0.642589\pi\)
−0.433124 + 0.901334i \(0.642589\pi\)
\(84\) 0 0
\(85\) −17.1452 −1.85966
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 1.43329 0.151928 0.0759640 0.997111i \(-0.475797\pi\)
0.0759640 + 0.997111i \(0.475797\pi\)
\(90\) 0 0
\(91\) 8.58079 0.899511
\(92\) 0 0
\(93\) 2.05208 0.212791
\(94\) 0 0
\(95\) −31.9541 −3.27842
\(96\) 0 0
\(97\) −4.91986 −0.499537 −0.249768 0.968306i \(-0.580354\pi\)
−0.249768 + 0.968306i \(0.580354\pi\)
\(98\) 0 0
\(99\) 0.161684 0.0162498
\(100\) 0 0
\(101\) −14.9474 −1.48732 −0.743659 0.668559i \(-0.766912\pi\)
−0.743659 + 0.668559i \(0.766912\pi\)
\(102\) 0 0
\(103\) 8.31164 0.818970 0.409485 0.912317i \(-0.365708\pi\)
0.409485 + 0.912317i \(0.365708\pi\)
\(104\) 0 0
\(105\) −15.2343 −1.48672
\(106\) 0 0
\(107\) 13.6226 1.31695 0.658473 0.752604i \(-0.271203\pi\)
0.658473 + 0.752604i \(0.271203\pi\)
\(108\) 0 0
\(109\) 1.79623 0.172047 0.0860237 0.996293i \(-0.472584\pi\)
0.0860237 + 0.996293i \(0.472584\pi\)
\(110\) 0 0
\(111\) −5.65285 −0.536544
\(112\) 0 0
\(113\) 7.84617 0.738106 0.369053 0.929408i \(-0.379682\pi\)
0.369053 + 0.929408i \(0.379682\pi\)
\(114\) 0 0
\(115\) −4.29726 −0.400722
\(116\) 0 0
\(117\) 2.42045 0.223771
\(118\) 0 0
\(119\) 14.1443 1.29661
\(120\) 0 0
\(121\) −10.9739 −0.997623
\(122\) 0 0
\(123\) −7.47256 −0.673778
\(124\) 0 0
\(125\) −36.3826 −3.25416
\(126\) 0 0
\(127\) 4.81437 0.427206 0.213603 0.976921i \(-0.431480\pi\)
0.213603 + 0.976921i \(0.431480\pi\)
\(128\) 0 0
\(129\) −2.80205 −0.246707
\(130\) 0 0
\(131\) 3.42938 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(132\) 0 0
\(133\) 26.3613 2.28581
\(134\) 0 0
\(135\) −4.29726 −0.369849
\(136\) 0 0
\(137\) 4.52628 0.386706 0.193353 0.981129i \(-0.438064\pi\)
0.193353 + 0.981129i \(0.438064\pi\)
\(138\) 0 0
\(139\) 12.9197 1.09583 0.547915 0.836534i \(-0.315422\pi\)
0.547915 + 0.836534i \(0.315422\pi\)
\(140\) 0 0
\(141\) −5.80920 −0.489223
\(142\) 0 0
\(143\) 0.391348 0.0327261
\(144\) 0 0
\(145\) 4.29726 0.356868
\(146\) 0 0
\(147\) 5.56789 0.459232
\(148\) 0 0
\(149\) 6.26844 0.513531 0.256765 0.966474i \(-0.417343\pi\)
0.256765 + 0.966474i \(0.417343\pi\)
\(150\) 0 0
\(151\) −22.1302 −1.80093 −0.900463 0.434932i \(-0.856772\pi\)
−0.900463 + 0.434932i \(0.856772\pi\)
\(152\) 0 0
\(153\) 3.98980 0.322556
\(154\) 0 0
\(155\) −8.81835 −0.708307
\(156\) 0 0
\(157\) −22.9965 −1.83532 −0.917662 0.397362i \(-0.869926\pi\)
−0.917662 + 0.397362i \(0.869926\pi\)
\(158\) 0 0
\(159\) 5.67820 0.450310
\(160\) 0 0
\(161\) 3.54512 0.279395
\(162\) 0 0
\(163\) 22.5673 1.76761 0.883805 0.467855i \(-0.154973\pi\)
0.883805 + 0.467855i \(0.154973\pi\)
\(164\) 0 0
\(165\) −0.694798 −0.0540899
\(166\) 0 0
\(167\) −15.3901 −1.19092 −0.595461 0.803385i \(-0.703030\pi\)
−0.595461 + 0.803385i \(0.703030\pi\)
\(168\) 0 0
\(169\) −7.14142 −0.549340
\(170\) 0 0
\(171\) 7.43592 0.568639
\(172\) 0 0
\(173\) 21.5562 1.63889 0.819443 0.573161i \(-0.194283\pi\)
0.819443 + 0.573161i \(0.194283\pi\)
\(174\) 0 0
\(175\) 47.7403 3.60882
\(176\) 0 0
\(177\) 14.1016 1.05994
\(178\) 0 0
\(179\) 24.5968 1.83845 0.919227 0.393729i \(-0.128815\pi\)
0.919227 + 0.393729i \(0.128815\pi\)
\(180\) 0 0
\(181\) 10.9273 0.812218 0.406109 0.913825i \(-0.366885\pi\)
0.406109 + 0.913825i \(0.366885\pi\)
\(182\) 0 0
\(183\) 14.8564 1.09822
\(184\) 0 0
\(185\) 24.2918 1.78597
\(186\) 0 0
\(187\) 0.645086 0.0471734
\(188\) 0 0
\(189\) 3.54512 0.257870
\(190\) 0 0
\(191\) 20.1377 1.45711 0.728557 0.684985i \(-0.240191\pi\)
0.728557 + 0.684985i \(0.240191\pi\)
\(192\) 0 0
\(193\) −11.2775 −0.811771 −0.405885 0.913924i \(-0.633037\pi\)
−0.405885 + 0.913924i \(0.633037\pi\)
\(194\) 0 0
\(195\) −10.4013 −0.744853
\(196\) 0 0
\(197\) −6.42258 −0.457590 −0.228795 0.973475i \(-0.573478\pi\)
−0.228795 + 0.973475i \(0.573478\pi\)
\(198\) 0 0
\(199\) 0.180557 0.0127993 0.00639967 0.999980i \(-0.497963\pi\)
0.00639967 + 0.999980i \(0.497963\pi\)
\(200\) 0 0
\(201\) −9.34631 −0.659238
\(202\) 0 0
\(203\) −3.54512 −0.248819
\(204\) 0 0
\(205\) 32.1115 2.24277
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 1.20227 0.0831626
\(210\) 0 0
\(211\) 13.5250 0.931099 0.465549 0.885022i \(-0.345857\pi\)
0.465549 + 0.885022i \(0.345857\pi\)
\(212\) 0 0
\(213\) −11.6877 −0.800827
\(214\) 0 0
\(215\) 12.0412 0.821200
\(216\) 0 0
\(217\) 7.27489 0.493852
\(218\) 0 0
\(219\) 2.93865 0.198576
\(220\) 0 0
\(221\) 9.65711 0.649608
\(222\) 0 0
\(223\) −0.118035 −0.00790420 −0.00395210 0.999992i \(-0.501258\pi\)
−0.00395210 + 0.999992i \(0.501258\pi\)
\(224\) 0 0
\(225\) 13.4665 0.897765
\(226\) 0 0
\(227\) 12.9065 0.856634 0.428317 0.903629i \(-0.359107\pi\)
0.428317 + 0.903629i \(0.359107\pi\)
\(228\) 0 0
\(229\) −13.2700 −0.876909 −0.438455 0.898753i \(-0.644474\pi\)
−0.438455 + 0.898753i \(0.644474\pi\)
\(230\) 0 0
\(231\) 0.573189 0.0377130
\(232\) 0 0
\(233\) 1.94230 0.127244 0.0636222 0.997974i \(-0.479735\pi\)
0.0636222 + 0.997974i \(0.479735\pi\)
\(234\) 0 0
\(235\) 24.9637 1.62845
\(236\) 0 0
\(237\) −0.741638 −0.0481746
\(238\) 0 0
\(239\) 17.3816 1.12432 0.562161 0.827028i \(-0.309970\pi\)
0.562161 + 0.827028i \(0.309970\pi\)
\(240\) 0 0
\(241\) 15.9745 1.02901 0.514504 0.857488i \(-0.327976\pi\)
0.514504 + 0.857488i \(0.327976\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −23.9267 −1.52862
\(246\) 0 0
\(247\) 17.9983 1.14520
\(248\) 0 0
\(249\) −7.89190 −0.500129
\(250\) 0 0
\(251\) 6.56916 0.414642 0.207321 0.978273i \(-0.433526\pi\)
0.207321 + 0.978273i \(0.433526\pi\)
\(252\) 0 0
\(253\) 0.161684 0.0101650
\(254\) 0 0
\(255\) −17.1452 −1.07368
\(256\) 0 0
\(257\) −22.8125 −1.42300 −0.711502 0.702684i \(-0.751985\pi\)
−0.711502 + 0.702684i \(0.751985\pi\)
\(258\) 0 0
\(259\) −20.0400 −1.24523
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −26.5281 −1.63579 −0.817896 0.575366i \(-0.804860\pi\)
−0.817896 + 0.575366i \(0.804860\pi\)
\(264\) 0 0
\(265\) −24.4007 −1.49892
\(266\) 0 0
\(267\) 1.43329 0.0877156
\(268\) 0 0
\(269\) 28.3257 1.72705 0.863525 0.504307i \(-0.168252\pi\)
0.863525 + 0.504307i \(0.168252\pi\)
\(270\) 0 0
\(271\) 32.1900 1.95540 0.977701 0.210002i \(-0.0673471\pi\)
0.977701 + 0.210002i \(0.0673471\pi\)
\(272\) 0 0
\(273\) 8.58079 0.519333
\(274\) 0 0
\(275\) 2.17731 0.131297
\(276\) 0 0
\(277\) 24.2130 1.45482 0.727409 0.686204i \(-0.240724\pi\)
0.727409 + 0.686204i \(0.240724\pi\)
\(278\) 0 0
\(279\) 2.05208 0.122855
\(280\) 0 0
\(281\) −11.0584 −0.659687 −0.329844 0.944036i \(-0.606996\pi\)
−0.329844 + 0.944036i \(0.606996\pi\)
\(282\) 0 0
\(283\) −18.1002 −1.07594 −0.537972 0.842963i \(-0.680809\pi\)
−0.537972 + 0.842963i \(0.680809\pi\)
\(284\) 0 0
\(285\) −31.9541 −1.89280
\(286\) 0 0
\(287\) −26.4911 −1.56372
\(288\) 0 0
\(289\) −1.08150 −0.0636175
\(290\) 0 0
\(291\) −4.91986 −0.288408
\(292\) 0 0
\(293\) 3.41385 0.199439 0.0997197 0.995016i \(-0.468205\pi\)
0.0997197 + 0.995016i \(0.468205\pi\)
\(294\) 0 0
\(295\) −60.5983 −3.52817
\(296\) 0 0
\(297\) 0.161684 0.00938184
\(298\) 0 0
\(299\) 2.42045 0.139978
\(300\) 0 0
\(301\) −9.93362 −0.572564
\(302\) 0 0
\(303\) −14.9474 −0.858704
\(304\) 0 0
\(305\) −63.8418 −3.65557
\(306\) 0 0
\(307\) 19.5836 1.11769 0.558846 0.829271i \(-0.311244\pi\)
0.558846 + 0.829271i \(0.311244\pi\)
\(308\) 0 0
\(309\) 8.31164 0.472833
\(310\) 0 0
\(311\) 18.5304 1.05076 0.525381 0.850867i \(-0.323923\pi\)
0.525381 + 0.850867i \(0.323923\pi\)
\(312\) 0 0
\(313\) −0.248252 −0.0140320 −0.00701602 0.999975i \(-0.502233\pi\)
−0.00701602 + 0.999975i \(0.502233\pi\)
\(314\) 0 0
\(315\) −15.2343 −0.858357
\(316\) 0 0
\(317\) 4.94475 0.277725 0.138862 0.990312i \(-0.455655\pi\)
0.138862 + 0.990312i \(0.455655\pi\)
\(318\) 0 0
\(319\) −0.161684 −0.00905255
\(320\) 0 0
\(321\) 13.6226 0.760339
\(322\) 0 0
\(323\) 29.6678 1.65076
\(324\) 0 0
\(325\) 32.5949 1.80804
\(326\) 0 0
\(327\) 1.79623 0.0993316
\(328\) 0 0
\(329\) −20.5943 −1.13540
\(330\) 0 0
\(331\) 31.6537 1.73984 0.869921 0.493191i \(-0.164170\pi\)
0.869921 + 0.493191i \(0.164170\pi\)
\(332\) 0 0
\(333\) −5.65285 −0.309774
\(334\) 0 0
\(335\) 40.1635 2.19437
\(336\) 0 0
\(337\) 0.331821 0.0180755 0.00903773 0.999959i \(-0.497123\pi\)
0.00903773 + 0.999959i \(0.497123\pi\)
\(338\) 0 0
\(339\) 7.84617 0.426146
\(340\) 0 0
\(341\) 0.331789 0.0179674
\(342\) 0 0
\(343\) −5.07701 −0.274133
\(344\) 0 0
\(345\) −4.29726 −0.231357
\(346\) 0 0
\(347\) −12.9088 −0.692978 −0.346489 0.938054i \(-0.612626\pi\)
−0.346489 + 0.938054i \(0.612626\pi\)
\(348\) 0 0
\(349\) 5.15461 0.275920 0.137960 0.990438i \(-0.455945\pi\)
0.137960 + 0.990438i \(0.455945\pi\)
\(350\) 0 0
\(351\) 2.42045 0.129194
\(352\) 0 0
\(353\) −25.7647 −1.37132 −0.685659 0.727923i \(-0.740486\pi\)
−0.685659 + 0.727923i \(0.740486\pi\)
\(354\) 0 0
\(355\) 50.2251 2.66567
\(356\) 0 0
\(357\) 14.1443 0.748597
\(358\) 0 0
\(359\) −37.3146 −1.96939 −0.984695 0.174286i \(-0.944238\pi\)
−0.984695 + 0.174286i \(0.944238\pi\)
\(360\) 0 0
\(361\) 36.2930 1.91016
\(362\) 0 0
\(363\) −10.9739 −0.575978
\(364\) 0 0
\(365\) −12.6282 −0.660988
\(366\) 0 0
\(367\) 14.9939 0.782673 0.391337 0.920248i \(-0.372013\pi\)
0.391337 + 0.920248i \(0.372013\pi\)
\(368\) 0 0
\(369\) −7.47256 −0.389006
\(370\) 0 0
\(371\) 20.1299 1.04509
\(372\) 0 0
\(373\) −10.0591 −0.520842 −0.260421 0.965495i \(-0.583861\pi\)
−0.260421 + 0.965495i \(0.583861\pi\)
\(374\) 0 0
\(375\) −36.3826 −1.87879
\(376\) 0 0
\(377\) −2.42045 −0.124660
\(378\) 0 0
\(379\) −36.5534 −1.87762 −0.938810 0.344435i \(-0.888070\pi\)
−0.938810 + 0.344435i \(0.888070\pi\)
\(380\) 0 0
\(381\) 4.81437 0.246647
\(382\) 0 0
\(383\) −3.76778 −0.192525 −0.0962623 0.995356i \(-0.530689\pi\)
−0.0962623 + 0.995356i \(0.530689\pi\)
\(384\) 0 0
\(385\) −2.46314 −0.125533
\(386\) 0 0
\(387\) −2.80205 −0.142436
\(388\) 0 0
\(389\) −17.8158 −0.903296 −0.451648 0.892196i \(-0.649164\pi\)
−0.451648 + 0.892196i \(0.649164\pi\)
\(390\) 0 0
\(391\) 3.98980 0.201773
\(392\) 0 0
\(393\) 3.42938 0.172989
\(394\) 0 0
\(395\) 3.18701 0.160356
\(396\) 0 0
\(397\) −36.0963 −1.81162 −0.905812 0.423681i \(-0.860738\pi\)
−0.905812 + 0.423681i \(0.860738\pi\)
\(398\) 0 0
\(399\) 26.3613 1.31971
\(400\) 0 0
\(401\) −25.7298 −1.28488 −0.642442 0.766334i \(-0.722079\pi\)
−0.642442 + 0.766334i \(0.722079\pi\)
\(402\) 0 0
\(403\) 4.96697 0.247422
\(404\) 0 0
\(405\) −4.29726 −0.213533
\(406\) 0 0
\(407\) −0.913974 −0.0453040
\(408\) 0 0
\(409\) −2.87957 −0.142386 −0.0711928 0.997463i \(-0.522681\pi\)
−0.0711928 + 0.997463i \(0.522681\pi\)
\(410\) 0 0
\(411\) 4.52628 0.223265
\(412\) 0 0
\(413\) 49.9919 2.45994
\(414\) 0 0
\(415\) 33.9136 1.66475
\(416\) 0 0
\(417\) 12.9197 0.632678
\(418\) 0 0
\(419\) 37.4858 1.83130 0.915651 0.401973i \(-0.131676\pi\)
0.915651 + 0.401973i \(0.131676\pi\)
\(420\) 0 0
\(421\) 23.1785 1.12965 0.564826 0.825210i \(-0.308943\pi\)
0.564826 + 0.825210i \(0.308943\pi\)
\(422\) 0 0
\(423\) −5.80920 −0.282453
\(424\) 0 0
\(425\) 53.7285 2.60622
\(426\) 0 0
\(427\) 52.6677 2.54877
\(428\) 0 0
\(429\) 0.391348 0.0188944
\(430\) 0 0
\(431\) 11.1831 0.538671 0.269335 0.963046i \(-0.413196\pi\)
0.269335 + 0.963046i \(0.413196\pi\)
\(432\) 0 0
\(433\) 14.3062 0.687514 0.343757 0.939059i \(-0.388300\pi\)
0.343757 + 0.939059i \(0.388300\pi\)
\(434\) 0 0
\(435\) 4.29726 0.206038
\(436\) 0 0
\(437\) 7.43592 0.355708
\(438\) 0 0
\(439\) 6.97421 0.332861 0.166431 0.986053i \(-0.446776\pi\)
0.166431 + 0.986053i \(0.446776\pi\)
\(440\) 0 0
\(441\) 5.56789 0.265137
\(442\) 0 0
\(443\) 15.1626 0.720396 0.360198 0.932876i \(-0.382709\pi\)
0.360198 + 0.932876i \(0.382709\pi\)
\(444\) 0 0
\(445\) −6.15920 −0.291974
\(446\) 0 0
\(447\) 6.26844 0.296487
\(448\) 0 0
\(449\) 16.0503 0.757460 0.378730 0.925507i \(-0.376361\pi\)
0.378730 + 0.925507i \(0.376361\pi\)
\(450\) 0 0
\(451\) −1.20819 −0.0568915
\(452\) 0 0
\(453\) −22.1302 −1.03977
\(454\) 0 0
\(455\) −36.8739 −1.72868
\(456\) 0 0
\(457\) −5.93598 −0.277673 −0.138837 0.990315i \(-0.544336\pi\)
−0.138837 + 0.990315i \(0.544336\pi\)
\(458\) 0 0
\(459\) 3.98980 0.186228
\(460\) 0 0
\(461\) 15.8202 0.736819 0.368410 0.929664i \(-0.379902\pi\)
0.368410 + 0.929664i \(0.379902\pi\)
\(462\) 0 0
\(463\) 21.4169 0.995330 0.497665 0.867369i \(-0.334191\pi\)
0.497665 + 0.867369i \(0.334191\pi\)
\(464\) 0 0
\(465\) −8.81835 −0.408941
\(466\) 0 0
\(467\) −10.0144 −0.463412 −0.231706 0.972786i \(-0.574431\pi\)
−0.231706 + 0.972786i \(0.574431\pi\)
\(468\) 0 0
\(469\) −33.1338 −1.52998
\(470\) 0 0
\(471\) −22.9965 −1.05962
\(472\) 0 0
\(473\) −0.453047 −0.0208311
\(474\) 0 0
\(475\) 100.136 4.59454
\(476\) 0 0
\(477\) 5.67820 0.259987
\(478\) 0 0
\(479\) 2.38039 0.108763 0.0543814 0.998520i \(-0.482681\pi\)
0.0543814 + 0.998520i \(0.482681\pi\)
\(480\) 0 0
\(481\) −13.6824 −0.623865
\(482\) 0 0
\(483\) 3.54512 0.161309
\(484\) 0 0
\(485\) 21.1420 0.960007
\(486\) 0 0
\(487\) 21.1654 0.959098 0.479549 0.877515i \(-0.340800\pi\)
0.479549 + 0.877515i \(0.340800\pi\)
\(488\) 0 0
\(489\) 22.5673 1.02053
\(490\) 0 0
\(491\) 26.1269 1.17909 0.589546 0.807735i \(-0.299307\pi\)
0.589546 + 0.807735i \(0.299307\pi\)
\(492\) 0 0
\(493\) −3.98980 −0.179692
\(494\) 0 0
\(495\) −0.694798 −0.0312288
\(496\) 0 0
\(497\) −41.4343 −1.85858
\(498\) 0 0
\(499\) 21.9600 0.983065 0.491533 0.870859i \(-0.336437\pi\)
0.491533 + 0.870859i \(0.336437\pi\)
\(500\) 0 0
\(501\) −15.3901 −0.687579
\(502\) 0 0
\(503\) −29.8753 −1.33207 −0.666037 0.745918i \(-0.732011\pi\)
−0.666037 + 0.745918i \(0.732011\pi\)
\(504\) 0 0
\(505\) 64.2328 2.85832
\(506\) 0 0
\(507\) −7.14142 −0.317162
\(508\) 0 0
\(509\) 1.76813 0.0783708 0.0391854 0.999232i \(-0.487524\pi\)
0.0391854 + 0.999232i \(0.487524\pi\)
\(510\) 0 0
\(511\) 10.4179 0.460860
\(512\) 0 0
\(513\) 7.43592 0.328304
\(514\) 0 0
\(515\) −35.7173 −1.57389
\(516\) 0 0
\(517\) −0.939253 −0.0413083
\(518\) 0 0
\(519\) 21.5562 0.946211
\(520\) 0 0
\(521\) 18.1591 0.795567 0.397783 0.917479i \(-0.369780\pi\)
0.397783 + 0.917479i \(0.369780\pi\)
\(522\) 0 0
\(523\) 18.5795 0.812425 0.406213 0.913779i \(-0.366849\pi\)
0.406213 + 0.913779i \(0.366849\pi\)
\(524\) 0 0
\(525\) 47.7403 2.08356
\(526\) 0 0
\(527\) 8.18741 0.356649
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 14.1016 0.611957
\(532\) 0 0
\(533\) −18.0870 −0.783433
\(534\) 0 0
\(535\) −58.5399 −2.53090
\(536\) 0 0
\(537\) 24.5968 1.06143
\(538\) 0 0
\(539\) 0.900237 0.0387760
\(540\) 0 0
\(541\) −33.9990 −1.46173 −0.730865 0.682522i \(-0.760883\pi\)
−0.730865 + 0.682522i \(0.760883\pi\)
\(542\) 0 0
\(543\) 10.9273 0.468934
\(544\) 0 0
\(545\) −7.71886 −0.330640
\(546\) 0 0
\(547\) −42.1184 −1.80085 −0.900427 0.435007i \(-0.856746\pi\)
−0.900427 + 0.435007i \(0.856746\pi\)
\(548\) 0 0
\(549\) 14.8564 0.634055
\(550\) 0 0
\(551\) −7.43592 −0.316781
\(552\) 0 0
\(553\) −2.62920 −0.111805
\(554\) 0 0
\(555\) 24.2918 1.03113
\(556\) 0 0
\(557\) −18.9780 −0.804122 −0.402061 0.915613i \(-0.631706\pi\)
−0.402061 + 0.915613i \(0.631706\pi\)
\(558\) 0 0
\(559\) −6.78223 −0.286858
\(560\) 0 0
\(561\) 0.645086 0.0272356
\(562\) 0 0
\(563\) −30.7441 −1.29571 −0.647854 0.761765i \(-0.724333\pi\)
−0.647854 + 0.761765i \(0.724333\pi\)
\(564\) 0 0
\(565\) −33.7171 −1.41849
\(566\) 0 0
\(567\) 3.54512 0.148881
\(568\) 0 0
\(569\) −20.8939 −0.875916 −0.437958 0.898995i \(-0.644298\pi\)
−0.437958 + 0.898995i \(0.644298\pi\)
\(570\) 0 0
\(571\) −37.3266 −1.56207 −0.781034 0.624488i \(-0.785308\pi\)
−0.781034 + 0.624488i \(0.785308\pi\)
\(572\) 0 0
\(573\) 20.1377 0.841265
\(574\) 0 0
\(575\) 13.4665 0.561591
\(576\) 0 0
\(577\) 9.26532 0.385720 0.192860 0.981226i \(-0.438224\pi\)
0.192860 + 0.981226i \(0.438224\pi\)
\(578\) 0 0
\(579\) −11.2775 −0.468676
\(580\) 0 0
\(581\) −27.9778 −1.16071
\(582\) 0 0
\(583\) 0.918072 0.0380227
\(584\) 0 0
\(585\) −10.4013 −0.430041
\(586\) 0 0
\(587\) 36.6545 1.51289 0.756447 0.654056i \(-0.226934\pi\)
0.756447 + 0.654056i \(0.226934\pi\)
\(588\) 0 0
\(589\) 15.2591 0.628742
\(590\) 0 0
\(591\) −6.42258 −0.264189
\(592\) 0 0
\(593\) 46.2980 1.90123 0.950616 0.310368i \(-0.100452\pi\)
0.950616 + 0.310368i \(0.100452\pi\)
\(594\) 0 0
\(595\) −60.7819 −2.49181
\(596\) 0 0
\(597\) 0.180557 0.00738970
\(598\) 0 0
\(599\) 22.9770 0.938813 0.469407 0.882982i \(-0.344468\pi\)
0.469407 + 0.882982i \(0.344468\pi\)
\(600\) 0 0
\(601\) −44.8715 −1.83035 −0.915173 0.403061i \(-0.867946\pi\)
−0.915173 + 0.403061i \(0.867946\pi\)
\(602\) 0 0
\(603\) −9.34631 −0.380611
\(604\) 0 0
\(605\) 47.1576 1.91723
\(606\) 0 0
\(607\) −17.5239 −0.711271 −0.355636 0.934625i \(-0.615736\pi\)
−0.355636 + 0.934625i \(0.615736\pi\)
\(608\) 0 0
\(609\) −3.54512 −0.143656
\(610\) 0 0
\(611\) −14.0609 −0.568842
\(612\) 0 0
\(613\) 13.7233 0.554279 0.277140 0.960830i \(-0.410614\pi\)
0.277140 + 0.960830i \(0.410614\pi\)
\(614\) 0 0
\(615\) 32.1115 1.29486
\(616\) 0 0
\(617\) −6.01447 −0.242133 −0.121067 0.992644i \(-0.538632\pi\)
−0.121067 + 0.992644i \(0.538632\pi\)
\(618\) 0 0
\(619\) −14.4997 −0.582792 −0.291396 0.956602i \(-0.594120\pi\)
−0.291396 + 0.956602i \(0.594120\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 5.08117 0.203573
\(624\) 0 0
\(625\) 89.0134 3.56054
\(626\) 0 0
\(627\) 1.20227 0.0480140
\(628\) 0 0
\(629\) −22.5537 −0.899276
\(630\) 0 0
\(631\) −8.13468 −0.323837 −0.161918 0.986804i \(-0.551768\pi\)
−0.161918 + 0.986804i \(0.551768\pi\)
\(632\) 0 0
\(633\) 13.5250 0.537570
\(634\) 0 0
\(635\) −20.6886 −0.821002
\(636\) 0 0
\(637\) 13.4768 0.533970
\(638\) 0 0
\(639\) −11.6877 −0.462358
\(640\) 0 0
\(641\) 34.3493 1.35672 0.678358 0.734732i \(-0.262692\pi\)
0.678358 + 0.734732i \(0.262692\pi\)
\(642\) 0 0
\(643\) 33.0356 1.30280 0.651399 0.758735i \(-0.274182\pi\)
0.651399 + 0.758735i \(0.274182\pi\)
\(644\) 0 0
\(645\) 12.0412 0.474120
\(646\) 0 0
\(647\) 11.7367 0.461417 0.230709 0.973023i \(-0.425896\pi\)
0.230709 + 0.973023i \(0.425896\pi\)
\(648\) 0 0
\(649\) 2.28000 0.0894978
\(650\) 0 0
\(651\) 7.27489 0.285125
\(652\) 0 0
\(653\) 15.8894 0.621801 0.310900 0.950443i \(-0.399369\pi\)
0.310900 + 0.950443i \(0.399369\pi\)
\(654\) 0 0
\(655\) −14.7369 −0.575819
\(656\) 0 0
\(657\) 2.93865 0.114648
\(658\) 0 0
\(659\) −7.06429 −0.275186 −0.137593 0.990489i \(-0.543937\pi\)
−0.137593 + 0.990489i \(0.543937\pi\)
\(660\) 0 0
\(661\) −48.1367 −1.87230 −0.936151 0.351599i \(-0.885638\pi\)
−0.936151 + 0.351599i \(0.885638\pi\)
\(662\) 0 0
\(663\) 9.65711 0.375051
\(664\) 0 0
\(665\) −113.281 −4.39286
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) −0.118035 −0.00456349
\(670\) 0 0
\(671\) 2.40204 0.0927296
\(672\) 0 0
\(673\) −11.0585 −0.426274 −0.213137 0.977022i \(-0.568368\pi\)
−0.213137 + 0.977022i \(0.568368\pi\)
\(674\) 0 0
\(675\) 13.4665 0.518325
\(676\) 0 0
\(677\) 14.2806 0.548849 0.274424 0.961609i \(-0.411513\pi\)
0.274424 + 0.961609i \(0.411513\pi\)
\(678\) 0 0
\(679\) −17.4415 −0.669344
\(680\) 0 0
\(681\) 12.9065 0.494578
\(682\) 0 0
\(683\) 15.7111 0.601169 0.300585 0.953755i \(-0.402818\pi\)
0.300585 + 0.953755i \(0.402818\pi\)
\(684\) 0 0
\(685\) −19.4506 −0.743169
\(686\) 0 0
\(687\) −13.2700 −0.506284
\(688\) 0 0
\(689\) 13.7438 0.523597
\(690\) 0 0
\(691\) −5.86530 −0.223126 −0.111563 0.993757i \(-0.535586\pi\)
−0.111563 + 0.993757i \(0.535586\pi\)
\(692\) 0 0
\(693\) 0.573189 0.0217736
\(694\) 0 0
\(695\) −55.5192 −2.10596
\(696\) 0 0
\(697\) −29.8140 −1.12929
\(698\) 0 0
\(699\) 1.94230 0.0734646
\(700\) 0 0
\(701\) −14.6443 −0.553109 −0.276555 0.960998i \(-0.589193\pi\)
−0.276555 + 0.960998i \(0.589193\pi\)
\(702\) 0 0
\(703\) −42.0341 −1.58535
\(704\) 0 0
\(705\) 24.9637 0.940186
\(706\) 0 0
\(707\) −52.9902 −1.99290
\(708\) 0 0
\(709\) −44.3384 −1.66516 −0.832582 0.553901i \(-0.813139\pi\)
−0.832582 + 0.553901i \(0.813139\pi\)
\(710\) 0 0
\(711\) −0.741638 −0.0278136
\(712\) 0 0
\(713\) 2.05208 0.0768512
\(714\) 0 0
\(715\) −1.68172 −0.0628929
\(716\) 0 0
\(717\) 17.3816 0.649128
\(718\) 0 0
\(719\) 1.77384 0.0661532 0.0330766 0.999453i \(-0.489469\pi\)
0.0330766 + 0.999453i \(0.489469\pi\)
\(720\) 0 0
\(721\) 29.4658 1.09736
\(722\) 0 0
\(723\) 15.9745 0.594099
\(724\) 0 0
\(725\) −13.4665 −0.500132
\(726\) 0 0
\(727\) 33.7989 1.25353 0.626766 0.779207i \(-0.284378\pi\)
0.626766 + 0.779207i \(0.284378\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −11.1796 −0.413494
\(732\) 0 0
\(733\) −4.74695 −0.175333 −0.0876664 0.996150i \(-0.527941\pi\)
−0.0876664 + 0.996150i \(0.527941\pi\)
\(734\) 0 0
\(735\) −23.9267 −0.882549
\(736\) 0 0
\(737\) −1.51115 −0.0556638
\(738\) 0 0
\(739\) −17.7880 −0.654342 −0.327171 0.944965i \(-0.606095\pi\)
−0.327171 + 0.944965i \(0.606095\pi\)
\(740\) 0 0
\(741\) 17.9983 0.661183
\(742\) 0 0
\(743\) −36.6763 −1.34552 −0.672762 0.739859i \(-0.734892\pi\)
−0.672762 + 0.739859i \(0.734892\pi\)
\(744\) 0 0
\(745\) −26.9371 −0.986901
\(746\) 0 0
\(747\) −7.89190 −0.288750
\(748\) 0 0
\(749\) 48.2938 1.76462
\(750\) 0 0
\(751\) −41.5848 −1.51745 −0.758726 0.651410i \(-0.774178\pi\)
−0.758726 + 0.651410i \(0.774178\pi\)
\(752\) 0 0
\(753\) 6.56916 0.239394
\(754\) 0 0
\(755\) 95.0991 3.46101
\(756\) 0 0
\(757\) 29.0852 1.05712 0.528559 0.848896i \(-0.322732\pi\)
0.528559 + 0.848896i \(0.322732\pi\)
\(758\) 0 0
\(759\) 0.161684 0.00586875
\(760\) 0 0
\(761\) 2.70655 0.0981123 0.0490562 0.998796i \(-0.484379\pi\)
0.0490562 + 0.998796i \(0.484379\pi\)
\(762\) 0 0
\(763\) 6.36784 0.230531
\(764\) 0 0
\(765\) −17.1452 −0.619887
\(766\) 0 0
\(767\) 34.1322 1.23244
\(768\) 0 0
\(769\) −3.47909 −0.125459 −0.0627295 0.998031i \(-0.519981\pi\)
−0.0627295 + 0.998031i \(0.519981\pi\)
\(770\) 0 0
\(771\) −22.8125 −0.821571
\(772\) 0 0
\(773\) −45.4744 −1.63560 −0.817800 0.575503i \(-0.804806\pi\)
−0.817800 + 0.575503i \(0.804806\pi\)
\(774\) 0 0
\(775\) 27.6343 0.992655
\(776\) 0 0
\(777\) −20.0400 −0.718932
\(778\) 0 0
\(779\) −55.5654 −1.99084
\(780\) 0 0
\(781\) −1.88971 −0.0676191
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 98.8222 3.52711
\(786\) 0 0
\(787\) 30.4430 1.08517 0.542587 0.840000i \(-0.317445\pi\)
0.542587 + 0.840000i \(0.317445\pi\)
\(788\) 0 0
\(789\) −26.5281 −0.944425
\(790\) 0 0
\(791\) 27.8156 0.989010
\(792\) 0 0
\(793\) 35.9592 1.27695
\(794\) 0 0
\(795\) −24.4007 −0.865404
\(796\) 0 0
\(797\) 8.83629 0.312997 0.156499 0.987678i \(-0.449979\pi\)
0.156499 + 0.987678i \(0.449979\pi\)
\(798\) 0 0
\(799\) −23.1775 −0.819963
\(800\) 0 0
\(801\) 1.43329 0.0506426
\(802\) 0 0
\(803\) 0.475132 0.0167671
\(804\) 0 0
\(805\) −15.2343 −0.536939
\(806\) 0 0
\(807\) 28.3257 0.997112
\(808\) 0 0
\(809\) 40.4858 1.42340 0.711702 0.702481i \(-0.247924\pi\)
0.711702 + 0.702481i \(0.247924\pi\)
\(810\) 0 0
\(811\) −14.4687 −0.508066 −0.254033 0.967196i \(-0.581757\pi\)
−0.254033 + 0.967196i \(0.581757\pi\)
\(812\) 0 0
\(813\) 32.1900 1.12895
\(814\) 0 0
\(815\) −96.9778 −3.39698
\(816\) 0 0
\(817\) −20.8359 −0.728954
\(818\) 0 0
\(819\) 8.58079 0.299837
\(820\) 0 0
\(821\) −7.96813 −0.278090 −0.139045 0.990286i \(-0.544403\pi\)
−0.139045 + 0.990286i \(0.544403\pi\)
\(822\) 0 0
\(823\) −21.2549 −0.740901 −0.370450 0.928852i \(-0.620797\pi\)
−0.370450 + 0.928852i \(0.620797\pi\)
\(824\) 0 0
\(825\) 2.17731 0.0758042
\(826\) 0 0
\(827\) −19.0576 −0.662697 −0.331349 0.943508i \(-0.607504\pi\)
−0.331349 + 0.943508i \(0.607504\pi\)
\(828\) 0 0
\(829\) −35.2113 −1.22294 −0.611469 0.791268i \(-0.709421\pi\)
−0.611469 + 0.791268i \(0.709421\pi\)
\(830\) 0 0
\(831\) 24.2130 0.839940
\(832\) 0 0
\(833\) 22.2148 0.769696
\(834\) 0 0
\(835\) 66.1353 2.28871
\(836\) 0 0
\(837\) 2.05208 0.0709304
\(838\) 0 0
\(839\) 2.68690 0.0927622 0.0463811 0.998924i \(-0.485231\pi\)
0.0463811 + 0.998924i \(0.485231\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −11.0584 −0.380871
\(844\) 0 0
\(845\) 30.6886 1.05572
\(846\) 0 0
\(847\) −38.9037 −1.33675
\(848\) 0 0
\(849\) −18.1002 −0.621197
\(850\) 0 0
\(851\) −5.65285 −0.193777
\(852\) 0 0
\(853\) 3.18917 0.109195 0.0545976 0.998508i \(-0.482612\pi\)
0.0545976 + 0.998508i \(0.482612\pi\)
\(854\) 0 0
\(855\) −31.9541 −1.09281
\(856\) 0 0
\(857\) 7.13026 0.243565 0.121782 0.992557i \(-0.461139\pi\)
0.121782 + 0.992557i \(0.461139\pi\)
\(858\) 0 0
\(859\) −36.2899 −1.23819 −0.619097 0.785314i \(-0.712501\pi\)
−0.619097 + 0.785314i \(0.712501\pi\)
\(860\) 0 0
\(861\) −26.4911 −0.902815
\(862\) 0 0
\(863\) 21.1719 0.720701 0.360350 0.932817i \(-0.382657\pi\)
0.360350 + 0.932817i \(0.382657\pi\)
\(864\) 0 0
\(865\) −92.6325 −3.14960
\(866\) 0 0
\(867\) −1.08150 −0.0367296
\(868\) 0 0
\(869\) −0.119911 −0.00406770
\(870\) 0 0
\(871\) −22.6223 −0.766527
\(872\) 0 0
\(873\) −4.91986 −0.166512
\(874\) 0 0
\(875\) −128.981 −4.36035
\(876\) 0 0
\(877\) 26.5380 0.896125 0.448063 0.894002i \(-0.352114\pi\)
0.448063 + 0.894002i \(0.352114\pi\)
\(878\) 0 0
\(879\) 3.41385 0.115146
\(880\) 0 0
\(881\) 2.83899 0.0956481 0.0478241 0.998856i \(-0.484771\pi\)
0.0478241 + 0.998856i \(0.484771\pi\)
\(882\) 0 0
\(883\) 34.7316 1.16881 0.584406 0.811461i \(-0.301327\pi\)
0.584406 + 0.811461i \(0.301327\pi\)
\(884\) 0 0
\(885\) −60.5983 −2.03699
\(886\) 0 0
\(887\) −45.9535 −1.54297 −0.771484 0.636249i \(-0.780485\pi\)
−0.771484 + 0.636249i \(0.780485\pi\)
\(888\) 0 0
\(889\) 17.0675 0.572426
\(890\) 0 0
\(891\) 0.161684 0.00541661
\(892\) 0 0
\(893\) −43.1968 −1.44552
\(894\) 0 0
\(895\) −105.699 −3.53313
\(896\) 0 0
\(897\) 2.42045 0.0808165
\(898\) 0 0
\(899\) −2.05208 −0.0684409
\(900\) 0 0
\(901\) 22.6549 0.754743
\(902\) 0 0
\(903\) −9.93362 −0.330570
\(904\) 0 0
\(905\) −46.9574 −1.56092
\(906\) 0 0
\(907\) 36.4184 1.20925 0.604626 0.796510i \(-0.293323\pi\)
0.604626 + 0.796510i \(0.293323\pi\)
\(908\) 0 0
\(909\) −14.9474 −0.495773
\(910\) 0 0
\(911\) 13.3952 0.443802 0.221901 0.975069i \(-0.428774\pi\)
0.221901 + 0.975069i \(0.428774\pi\)
\(912\) 0 0
\(913\) −1.27599 −0.0422292
\(914\) 0 0
\(915\) −63.8418 −2.11054
\(916\) 0 0
\(917\) 12.1576 0.401478
\(918\) 0 0
\(919\) 13.7689 0.454196 0.227098 0.973872i \(-0.427076\pi\)
0.227098 + 0.973872i \(0.427076\pi\)
\(920\) 0 0
\(921\) 19.5836 0.645300
\(922\) 0 0
\(923\) −28.2895 −0.931159
\(924\) 0 0
\(925\) −76.1239 −2.50294
\(926\) 0 0
\(927\) 8.31164 0.272990
\(928\) 0 0
\(929\) −9.33349 −0.306222 −0.153111 0.988209i \(-0.548929\pi\)
−0.153111 + 0.988209i \(0.548929\pi\)
\(930\) 0 0
\(931\) 41.4024 1.35691
\(932\) 0 0
\(933\) 18.5304 0.606658
\(934\) 0 0
\(935\) −2.77210 −0.0906575
\(936\) 0 0
\(937\) −4.55343 −0.148754 −0.0743770 0.997230i \(-0.523697\pi\)
−0.0743770 + 0.997230i \(0.523697\pi\)
\(938\) 0 0
\(939\) −0.248252 −0.00810140
\(940\) 0 0
\(941\) −6.31675 −0.205920 −0.102960 0.994685i \(-0.532831\pi\)
−0.102960 + 0.994685i \(0.532831\pi\)
\(942\) 0 0
\(943\) −7.47256 −0.243340
\(944\) 0 0
\(945\) −15.2343 −0.495572
\(946\) 0 0
\(947\) 36.0044 1.16999 0.584994 0.811038i \(-0.301097\pi\)
0.584994 + 0.811038i \(0.301097\pi\)
\(948\) 0 0
\(949\) 7.11286 0.230893
\(950\) 0 0
\(951\) 4.94475 0.160344
\(952\) 0 0
\(953\) 8.08380 0.261860 0.130930 0.991392i \(-0.458204\pi\)
0.130930 + 0.991392i \(0.458204\pi\)
\(954\) 0 0
\(955\) −86.5371 −2.80027
\(956\) 0 0
\(957\) −0.161684 −0.00522649
\(958\) 0 0
\(959\) 16.0462 0.518159
\(960\) 0 0
\(961\) −26.7889 −0.864160
\(962\) 0 0
\(963\) 13.6226 0.438982
\(964\) 0 0
\(965\) 48.4623 1.56006
\(966\) 0 0
\(967\) 44.6911 1.43717 0.718585 0.695439i \(-0.244790\pi\)
0.718585 + 0.695439i \(0.244790\pi\)
\(968\) 0 0
\(969\) 29.6678 0.953069
\(970\) 0 0
\(971\) 33.3864 1.07142 0.535710 0.844402i \(-0.320044\pi\)
0.535710 + 0.844402i \(0.320044\pi\)
\(972\) 0 0
\(973\) 45.8018 1.46834
\(974\) 0 0
\(975\) 32.5949 1.04387
\(976\) 0 0
\(977\) 54.3669 1.73935 0.869675 0.493624i \(-0.164328\pi\)
0.869675 + 0.493624i \(0.164328\pi\)
\(978\) 0 0
\(979\) 0.231739 0.00740641
\(980\) 0 0
\(981\) 1.79623 0.0573491
\(982\) 0 0
\(983\) −3.86378 −0.123236 −0.0616178 0.998100i \(-0.519626\pi\)
−0.0616178 + 0.998100i \(0.519626\pi\)
\(984\) 0 0
\(985\) 27.5995 0.879393
\(986\) 0 0
\(987\) −20.5943 −0.655524
\(988\) 0 0
\(989\) −2.80205 −0.0891001
\(990\) 0 0
\(991\) −16.0230 −0.508988 −0.254494 0.967074i \(-0.581909\pi\)
−0.254494 + 0.967074i \(0.581909\pi\)
\(992\) 0 0
\(993\) 31.6537 1.00450
\(994\) 0 0
\(995\) −0.775900 −0.0245977
\(996\) 0 0
\(997\) 7.95503 0.251938 0.125969 0.992034i \(-0.459796\pi\)
0.125969 + 0.992034i \(0.459796\pi\)
\(998\) 0 0
\(999\) −5.65285 −0.178848
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 \(a_p\))