Properties

Label 8040.2.a.t.1.4
Level 8040
Weight 2
Character 8040.1
Self dual Yes
Analytic conductor 64.200
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1997232251\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.05266\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -1.00000 q^{5} +0.670274 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -1.00000 q^{5} +0.670274 q^{7} +1.00000 q^{9} +3.78339 q^{11} +4.11429 q^{13} -1.00000 q^{15} +1.83923 q^{17} +5.73969 q^{19} +0.670274 q^{21} +7.13944 q^{23} +1.00000 q^{25} +1.00000 q^{27} -1.82187 q^{29} -5.12208 q^{31} +3.78339 q^{33} -0.670274 q^{35} +2.09121 q^{37} +4.11429 q^{39} +7.12208 q^{41} -3.02515 q^{43} -1.00000 q^{45} -5.47041 q^{47} -6.55073 q^{49} +1.83923 q^{51} +6.86073 q^{53} -3.78339 q^{55} +5.73969 q^{57} +1.63478 q^{59} +5.50889 q^{61} +0.670274 q^{63} -4.11429 q^{65} +1.00000 q^{67} +7.13944 q^{69} -12.4491 q^{71} -10.4317 q^{73} +1.00000 q^{75} +2.53591 q^{77} +7.01717 q^{79} +1.00000 q^{81} -5.16000 q^{83} -1.83923 q^{85} -1.82187 q^{87} +5.63153 q^{89} +2.75770 q^{91} -5.12208 q^{93} -5.73969 q^{95} -9.80937 q^{97} +3.78339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 7q^{3} - 7q^{5} + 10q^{7} + 7q^{9} + O(q^{10}) \) \( 7q + 7q^{3} - 7q^{5} + 10q^{7} + 7q^{9} - q^{13} - 7q^{15} - 2q^{17} + 9q^{19} + 10q^{21} + 2q^{23} + 7q^{25} + 7q^{27} - q^{29} + 9q^{31} - 10q^{35} + 23q^{37} - q^{39} + 5q^{41} - 3q^{43} - 7q^{45} + 11q^{47} + 13q^{49} - 2q^{51} + 13q^{53} + 9q^{57} + q^{59} + 4q^{61} + 10q^{63} + q^{65} + 7q^{67} + 2q^{69} + q^{71} + 14q^{73} + 7q^{75} + 18q^{77} + 25q^{79} + 7q^{81} - 29q^{83} + 2q^{85} - q^{87} + 7q^{89} + 27q^{91} + 9q^{93} - 9q^{95} + 38q^{97} + O(q^{100}) \)

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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.670274 0.253340 0.126670 0.991945i \(-0.459571\pi\)
0.126670 + 0.991945i \(0.459571\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.78339 1.14073 0.570367 0.821390i \(-0.306801\pi\)
0.570367 + 0.821390i \(0.306801\pi\)
\(12\) 0 0
\(13\) 4.11429 1.14110 0.570550 0.821263i \(-0.306730\pi\)
0.570550 + 0.821263i \(0.306730\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 1.83923 0.446080 0.223040 0.974809i \(-0.428402\pi\)
0.223040 + 0.974809i \(0.428402\pi\)
\(18\) 0 0
\(19\) 5.73969 1.31677 0.658387 0.752679i \(-0.271239\pi\)
0.658387 + 0.752679i \(0.271239\pi\)
\(20\) 0 0
\(21\) 0.670274 0.146266
\(22\) 0 0
\(23\) 7.13944 1.48868 0.744338 0.667803i \(-0.232765\pi\)
0.744338 + 0.667803i \(0.232765\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.82187 −0.338313 −0.169156 0.985589i \(-0.554104\pi\)
−0.169156 + 0.985589i \(0.554104\pi\)
\(30\) 0 0
\(31\) −5.12208 −0.919952 −0.459976 0.887931i \(-0.652142\pi\)
−0.459976 + 0.887931i \(0.652142\pi\)
\(32\) 0 0
\(33\) 3.78339 0.658603
\(34\) 0 0
\(35\) −0.670274 −0.113297
\(36\) 0 0
\(37\) 2.09121 0.343793 0.171896 0.985115i \(-0.445011\pi\)
0.171896 + 0.985115i \(0.445011\pi\)
\(38\) 0 0
\(39\) 4.11429 0.658814
\(40\) 0 0
\(41\) 7.12208 1.11228 0.556141 0.831088i \(-0.312282\pi\)
0.556141 + 0.831088i \(0.312282\pi\)
\(42\) 0 0
\(43\) −3.02515 −0.461331 −0.230665 0.973033i \(-0.574090\pi\)
−0.230665 + 0.973033i \(0.574090\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −5.47041 −0.797941 −0.398971 0.916964i \(-0.630632\pi\)
−0.398971 + 0.916964i \(0.630632\pi\)
\(48\) 0 0
\(49\) −6.55073 −0.935819
\(50\) 0 0
\(51\) 1.83923 0.257544
\(52\) 0 0
\(53\) 6.86073 0.942393 0.471197 0.882028i \(-0.343822\pi\)
0.471197 + 0.882028i \(0.343822\pi\)
\(54\) 0 0
\(55\) −3.78339 −0.510152
\(56\) 0 0
\(57\) 5.73969 0.760240
\(58\) 0 0
\(59\) 1.63478 0.212830 0.106415 0.994322i \(-0.466063\pi\)
0.106415 + 0.994322i \(0.466063\pi\)
\(60\) 0 0
\(61\) 5.50889 0.705341 0.352671 0.935748i \(-0.385274\pi\)
0.352671 + 0.935748i \(0.385274\pi\)
\(62\) 0 0
\(63\) 0.670274 0.0844466
\(64\) 0 0
\(65\) −4.11429 −0.510315
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) 7.13944 0.859488
\(70\) 0 0
\(71\) −12.4491 −1.47744 −0.738718 0.674015i \(-0.764568\pi\)
−0.738718 + 0.674015i \(0.764568\pi\)
\(72\) 0 0
\(73\) −10.4317 −1.22093 −0.610467 0.792042i \(-0.709018\pi\)
−0.610467 + 0.792042i \(0.709018\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 2.53591 0.288993
\(78\) 0 0
\(79\) 7.01717 0.789493 0.394746 0.918790i \(-0.370832\pi\)
0.394746 + 0.918790i \(0.370832\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.16000 −0.566383 −0.283192 0.959063i \(-0.591393\pi\)
−0.283192 + 0.959063i \(0.591393\pi\)
\(84\) 0 0
\(85\) −1.83923 −0.199493
\(86\) 0 0
\(87\) −1.82187 −0.195325
\(88\) 0 0
\(89\) 5.63153 0.596941 0.298470 0.954419i \(-0.403524\pi\)
0.298470 + 0.954419i \(0.403524\pi\)
\(90\) 0 0
\(91\) 2.75770 0.289086
\(92\) 0 0
\(93\) −5.12208 −0.531135
\(94\) 0 0
\(95\) −5.73969 −0.588879
\(96\) 0 0
\(97\) −9.80937 −0.995991 −0.497995 0.867180i \(-0.665930\pi\)
−0.497995 + 0.867180i \(0.665930\pi\)
\(98\) 0 0
\(99\) 3.78339 0.380245
\(100\) 0 0
\(101\) 3.47407 0.345683 0.172842 0.984950i \(-0.444705\pi\)
0.172842 + 0.984950i \(0.444705\pi\)
\(102\) 0 0
\(103\) 16.1717 1.59345 0.796723 0.604345i \(-0.206565\pi\)
0.796723 + 0.604345i \(0.206565\pi\)
\(104\) 0 0
\(105\) −0.670274 −0.0654121
\(106\) 0 0
\(107\) −17.9034 −1.73079 −0.865393 0.501093i \(-0.832931\pi\)
−0.865393 + 0.501093i \(0.832931\pi\)
\(108\) 0 0
\(109\) 17.3694 1.66369 0.831844 0.555009i \(-0.187285\pi\)
0.831844 + 0.555009i \(0.187285\pi\)
\(110\) 0 0
\(111\) 2.09121 0.198489
\(112\) 0 0
\(113\) −19.3577 −1.82102 −0.910508 0.413491i \(-0.864309\pi\)
−0.910508 + 0.413491i \(0.864309\pi\)
\(114\) 0 0
\(115\) −7.13944 −0.665756
\(116\) 0 0
\(117\) 4.11429 0.380366
\(118\) 0 0
\(119\) 1.23279 0.113010
\(120\) 0 0
\(121\) 3.31401 0.301274
\(122\) 0 0
\(123\) 7.12208 0.642176
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 12.6572 1.12315 0.561573 0.827427i \(-0.310196\pi\)
0.561573 + 0.827427i \(0.310196\pi\)
\(128\) 0 0
\(129\) −3.02515 −0.266349
\(130\) 0 0
\(131\) −13.7384 −1.20033 −0.600166 0.799876i \(-0.704899\pi\)
−0.600166 + 0.799876i \(0.704899\pi\)
\(132\) 0 0
\(133\) 3.84716 0.333591
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −10.2004 −0.871476 −0.435738 0.900074i \(-0.643513\pi\)
−0.435738 + 0.900074i \(0.643513\pi\)
\(138\) 0 0
\(139\) −12.0665 −1.02347 −0.511733 0.859144i \(-0.670996\pi\)
−0.511733 + 0.859144i \(0.670996\pi\)
\(140\) 0 0
\(141\) −5.47041 −0.460691
\(142\) 0 0
\(143\) 15.5660 1.30169
\(144\) 0 0
\(145\) 1.82187 0.151298
\(146\) 0 0
\(147\) −6.55073 −0.540295
\(148\) 0 0
\(149\) −1.31188 −0.107474 −0.0537368 0.998555i \(-0.517113\pi\)
−0.0537368 + 0.998555i \(0.517113\pi\)
\(150\) 0 0
\(151\) 3.61324 0.294041 0.147021 0.989133i \(-0.453032\pi\)
0.147021 + 0.989133i \(0.453032\pi\)
\(152\) 0 0
\(153\) 1.83923 0.148693
\(154\) 0 0
\(155\) 5.12208 0.411415
\(156\) 0 0
\(157\) 5.72452 0.456867 0.228433 0.973560i \(-0.426640\pi\)
0.228433 + 0.973560i \(0.426640\pi\)
\(158\) 0 0
\(159\) 6.86073 0.544091
\(160\) 0 0
\(161\) 4.78538 0.377141
\(162\) 0 0
\(163\) 14.8151 1.16041 0.580204 0.814471i \(-0.302973\pi\)
0.580204 + 0.814471i \(0.302973\pi\)
\(164\) 0 0
\(165\) −3.78339 −0.294536
\(166\) 0 0
\(167\) −3.97042 −0.307240 −0.153620 0.988130i \(-0.549093\pi\)
−0.153620 + 0.988130i \(0.549093\pi\)
\(168\) 0 0
\(169\) 3.92740 0.302107
\(170\) 0 0
\(171\) 5.73969 0.438925
\(172\) 0 0
\(173\) 24.2043 1.84022 0.920109 0.391662i \(-0.128100\pi\)
0.920109 + 0.391662i \(0.128100\pi\)
\(174\) 0 0
\(175\) 0.670274 0.0506680
\(176\) 0 0
\(177\) 1.63478 0.122877
\(178\) 0 0
\(179\) −9.26827 −0.692743 −0.346371 0.938097i \(-0.612586\pi\)
−0.346371 + 0.938097i \(0.612586\pi\)
\(180\) 0 0
\(181\) −24.7538 −1.83994 −0.919969 0.391991i \(-0.871786\pi\)
−0.919969 + 0.391991i \(0.871786\pi\)
\(182\) 0 0
\(183\) 5.50889 0.407229
\(184\) 0 0
\(185\) −2.09121 −0.153749
\(186\) 0 0
\(187\) 6.95853 0.508858
\(188\) 0 0
\(189\) 0.670274 0.0487553
\(190\) 0 0
\(191\) 1.65532 0.119775 0.0598875 0.998205i \(-0.480926\pi\)
0.0598875 + 0.998205i \(0.480926\pi\)
\(192\) 0 0
\(193\) −13.2421 −0.953191 −0.476595 0.879123i \(-0.658129\pi\)
−0.476595 + 0.879123i \(0.658129\pi\)
\(194\) 0 0
\(195\) −4.11429 −0.294631
\(196\) 0 0
\(197\) −3.51881 −0.250705 −0.125352 0.992112i \(-0.540006\pi\)
−0.125352 + 0.992112i \(0.540006\pi\)
\(198\) 0 0
\(199\) 13.9365 0.987933 0.493966 0.869481i \(-0.335547\pi\)
0.493966 + 0.869481i \(0.335547\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) −1.22115 −0.0857081
\(204\) 0 0
\(205\) −7.12208 −0.497427
\(206\) 0 0
\(207\) 7.13944 0.496225
\(208\) 0 0
\(209\) 21.7154 1.50209
\(210\) 0 0
\(211\) 24.8657 1.71183 0.855914 0.517118i \(-0.172995\pi\)
0.855914 + 0.517118i \(0.172995\pi\)
\(212\) 0 0
\(213\) −12.4491 −0.852998
\(214\) 0 0
\(215\) 3.02515 0.206313
\(216\) 0 0
\(217\) −3.43320 −0.233060
\(218\) 0 0
\(219\) −10.4317 −0.704906
\(220\) 0 0
\(221\) 7.56715 0.509021
\(222\) 0 0
\(223\) −9.60254 −0.643033 −0.321517 0.946904i \(-0.604193\pi\)
−0.321517 + 0.946904i \(0.604193\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 13.6064 0.903089 0.451545 0.892249i \(-0.350873\pi\)
0.451545 + 0.892249i \(0.350873\pi\)
\(228\) 0 0
\(229\) 3.78622 0.250200 0.125100 0.992144i \(-0.460075\pi\)
0.125100 + 0.992144i \(0.460075\pi\)
\(230\) 0 0
\(231\) 2.53591 0.166850
\(232\) 0 0
\(233\) 13.4793 0.883059 0.441530 0.897247i \(-0.354436\pi\)
0.441530 + 0.897247i \(0.354436\pi\)
\(234\) 0 0
\(235\) 5.47041 0.356850
\(236\) 0 0
\(237\) 7.01717 0.455814
\(238\) 0 0
\(239\) −7.81123 −0.505266 −0.252633 0.967562i \(-0.581297\pi\)
−0.252633 + 0.967562i \(0.581297\pi\)
\(240\) 0 0
\(241\) 13.8308 0.890923 0.445462 0.895301i \(-0.353040\pi\)
0.445462 + 0.895301i \(0.353040\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 6.55073 0.418511
\(246\) 0 0
\(247\) 23.6147 1.50257
\(248\) 0 0
\(249\) −5.16000 −0.327001
\(250\) 0 0
\(251\) −13.7731 −0.869352 −0.434676 0.900587i \(-0.643137\pi\)
−0.434676 + 0.900587i \(0.643137\pi\)
\(252\) 0 0
\(253\) 27.0113 1.69818
\(254\) 0 0
\(255\) −1.83923 −0.115177
\(256\) 0 0
\(257\) 20.1620 1.25767 0.628837 0.777538i \(-0.283531\pi\)
0.628837 + 0.777538i \(0.283531\pi\)
\(258\) 0 0
\(259\) 1.40168 0.0870964
\(260\) 0 0
\(261\) −1.82187 −0.112771
\(262\) 0 0
\(263\) 0.295696 0.0182334 0.00911671 0.999958i \(-0.497098\pi\)
0.00911671 + 0.999958i \(0.497098\pi\)
\(264\) 0 0
\(265\) −6.86073 −0.421451
\(266\) 0 0
\(267\) 5.63153 0.344644
\(268\) 0 0
\(269\) −19.4531 −1.18608 −0.593038 0.805175i \(-0.702071\pi\)
−0.593038 + 0.805175i \(0.702071\pi\)
\(270\) 0 0
\(271\) −10.8772 −0.660743 −0.330372 0.943851i \(-0.607174\pi\)
−0.330372 + 0.943851i \(0.607174\pi\)
\(272\) 0 0
\(273\) 2.75770 0.166904
\(274\) 0 0
\(275\) 3.78339 0.228147
\(276\) 0 0
\(277\) 25.1608 1.51177 0.755883 0.654707i \(-0.227208\pi\)
0.755883 + 0.654707i \(0.227208\pi\)
\(278\) 0 0
\(279\) −5.12208 −0.306651
\(280\) 0 0
\(281\) 8.91436 0.531786 0.265893 0.964003i \(-0.414333\pi\)
0.265893 + 0.964003i \(0.414333\pi\)
\(282\) 0 0
\(283\) −19.4711 −1.15744 −0.578720 0.815526i \(-0.696447\pi\)
−0.578720 + 0.815526i \(0.696447\pi\)
\(284\) 0 0
\(285\) −5.73969 −0.339990
\(286\) 0 0
\(287\) 4.77374 0.281785
\(288\) 0 0
\(289\) −13.6172 −0.801013
\(290\) 0 0
\(291\) −9.80937 −0.575035
\(292\) 0 0
\(293\) −10.3591 −0.605185 −0.302592 0.953120i \(-0.597852\pi\)
−0.302592 + 0.953120i \(0.597852\pi\)
\(294\) 0 0
\(295\) −1.63478 −0.0951803
\(296\) 0 0
\(297\) 3.78339 0.219534
\(298\) 0 0
\(299\) 29.3737 1.69873
\(300\) 0 0
\(301\) −2.02768 −0.116873
\(302\) 0 0
\(303\) 3.47407 0.199580
\(304\) 0 0
\(305\) −5.50889 −0.315438
\(306\) 0 0
\(307\) 25.7029 1.46694 0.733470 0.679721i \(-0.237899\pi\)
0.733470 + 0.679721i \(0.237899\pi\)
\(308\) 0 0
\(309\) 16.1717 0.919976
\(310\) 0 0
\(311\) −2.07146 −0.117462 −0.0587308 0.998274i \(-0.518705\pi\)
−0.0587308 + 0.998274i \(0.518705\pi\)
\(312\) 0 0
\(313\) 11.9262 0.674110 0.337055 0.941485i \(-0.390569\pi\)
0.337055 + 0.941485i \(0.390569\pi\)
\(314\) 0 0
\(315\) −0.670274 −0.0377657
\(316\) 0 0
\(317\) −32.0644 −1.80092 −0.900458 0.434943i \(-0.856769\pi\)
−0.900458 + 0.434943i \(0.856769\pi\)
\(318\) 0 0
\(319\) −6.89284 −0.385925
\(320\) 0 0
\(321\) −17.9034 −0.999270
\(322\) 0 0
\(323\) 10.5566 0.587386
\(324\) 0 0
\(325\) 4.11429 0.228220
\(326\) 0 0
\(327\) 17.3694 0.960531
\(328\) 0 0
\(329\) −3.66667 −0.202150
\(330\) 0 0
\(331\) 10.3465 0.568697 0.284349 0.958721i \(-0.408223\pi\)
0.284349 + 0.958721i \(0.408223\pi\)
\(332\) 0 0
\(333\) 2.09121 0.114598
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) 3.03793 0.165486 0.0827432 0.996571i \(-0.473632\pi\)
0.0827432 + 0.996571i \(0.473632\pi\)
\(338\) 0 0
\(339\) −19.3577 −1.05136
\(340\) 0 0
\(341\) −19.3788 −1.04942
\(342\) 0 0
\(343\) −9.08271 −0.490420
\(344\) 0 0
\(345\) −7.13944 −0.384375
\(346\) 0 0
\(347\) −14.1956 −0.762058 −0.381029 0.924563i \(-0.624430\pi\)
−0.381029 + 0.924563i \(0.624430\pi\)
\(348\) 0 0
\(349\) 29.5421 1.58135 0.790677 0.612234i \(-0.209729\pi\)
0.790677 + 0.612234i \(0.209729\pi\)
\(350\) 0 0
\(351\) 4.11429 0.219605
\(352\) 0 0
\(353\) 32.2119 1.71447 0.857234 0.514927i \(-0.172181\pi\)
0.857234 + 0.514927i \(0.172181\pi\)
\(354\) 0 0
\(355\) 12.4491 0.660729
\(356\) 0 0
\(357\) 1.23279 0.0652462
\(358\) 0 0
\(359\) 30.8548 1.62845 0.814226 0.580548i \(-0.197162\pi\)
0.814226 + 0.580548i \(0.197162\pi\)
\(360\) 0 0
\(361\) 13.9440 0.733894
\(362\) 0 0
\(363\) 3.31401 0.173941
\(364\) 0 0
\(365\) 10.4317 0.546018
\(366\) 0 0
\(367\) −30.8580 −1.61077 −0.805386 0.592750i \(-0.798042\pi\)
−0.805386 + 0.592750i \(0.798042\pi\)
\(368\) 0 0
\(369\) 7.12208 0.370760
\(370\) 0 0
\(371\) 4.59857 0.238746
\(372\) 0 0
\(373\) 15.4483 0.799881 0.399940 0.916541i \(-0.369031\pi\)
0.399940 + 0.916541i \(0.369031\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −7.49570 −0.386048
\(378\) 0 0
\(379\) 18.9680 0.974320 0.487160 0.873313i \(-0.338033\pi\)
0.487160 + 0.873313i \(0.338033\pi\)
\(380\) 0 0
\(381\) 12.6572 0.648449
\(382\) 0 0
\(383\) −10.5529 −0.539230 −0.269615 0.962968i \(-0.586896\pi\)
−0.269615 + 0.962968i \(0.586896\pi\)
\(384\) 0 0
\(385\) −2.53591 −0.129242
\(386\) 0 0
\(387\) −3.02515 −0.153777
\(388\) 0 0
\(389\) −5.90885 −0.299591 −0.149795 0.988717i \(-0.547861\pi\)
−0.149795 + 0.988717i \(0.547861\pi\)
\(390\) 0 0
\(391\) 13.1311 0.664068
\(392\) 0 0
\(393\) −13.7384 −0.693012
\(394\) 0 0
\(395\) −7.01717 −0.353072
\(396\) 0 0
\(397\) 19.2533 0.966295 0.483148 0.875539i \(-0.339493\pi\)
0.483148 + 0.875539i \(0.339493\pi\)
\(398\) 0 0
\(399\) 3.84716 0.192599
\(400\) 0 0
\(401\) 4.05547 0.202520 0.101260 0.994860i \(-0.467713\pi\)
0.101260 + 0.994860i \(0.467713\pi\)
\(402\) 0 0
\(403\) −21.0737 −1.04976
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 7.91185 0.392176
\(408\) 0 0
\(409\) 1.26712 0.0626550 0.0313275 0.999509i \(-0.490027\pi\)
0.0313275 + 0.999509i \(0.490027\pi\)
\(410\) 0 0
\(411\) −10.2004 −0.503147
\(412\) 0 0
\(413\) 1.09575 0.0539182
\(414\) 0 0
\(415\) 5.16000 0.253294
\(416\) 0 0
\(417\) −12.0665 −0.590899
\(418\) 0 0
\(419\) 31.0552 1.51714 0.758572 0.651589i \(-0.225897\pi\)
0.758572 + 0.651589i \(0.225897\pi\)
\(420\) 0 0
\(421\) −22.9337 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(422\) 0 0
\(423\) −5.47041 −0.265980
\(424\) 0 0
\(425\) 1.83923 0.0892160
\(426\) 0 0
\(427\) 3.69247 0.178691
\(428\) 0 0
\(429\) 15.5660 0.751531
\(430\) 0 0
\(431\) −10.8073 −0.520568 −0.260284 0.965532i \(-0.583816\pi\)
−0.260284 + 0.965532i \(0.583816\pi\)
\(432\) 0 0
\(433\) −39.1113 −1.87957 −0.939785 0.341766i \(-0.888975\pi\)
−0.939785 + 0.341766i \(0.888975\pi\)
\(434\) 0 0
\(435\) 1.82187 0.0873519
\(436\) 0 0
\(437\) 40.9781 1.96025
\(438\) 0 0
\(439\) −3.92985 −0.187561 −0.0937807 0.995593i \(-0.529895\pi\)
−0.0937807 + 0.995593i \(0.529895\pi\)
\(440\) 0 0
\(441\) −6.55073 −0.311940
\(442\) 0 0
\(443\) −21.6585 −1.02903 −0.514513 0.857483i \(-0.672027\pi\)
−0.514513 + 0.857483i \(0.672027\pi\)
\(444\) 0 0
\(445\) −5.63153 −0.266960
\(446\) 0 0
\(447\) −1.31188 −0.0620499
\(448\) 0 0
\(449\) −17.5401 −0.827770 −0.413885 0.910329i \(-0.635828\pi\)
−0.413885 + 0.910329i \(0.635828\pi\)
\(450\) 0 0
\(451\) 26.9456 1.26882
\(452\) 0 0
\(453\) 3.61324 0.169765
\(454\) 0 0
\(455\) −2.75770 −0.129283
\(456\) 0 0
\(457\) −12.1088 −0.566424 −0.283212 0.959057i \(-0.591400\pi\)
−0.283212 + 0.959057i \(0.591400\pi\)
\(458\) 0 0
\(459\) 1.83923 0.0858481
\(460\) 0 0
\(461\) −26.6861 −1.24290 −0.621448 0.783455i \(-0.713455\pi\)
−0.621448 + 0.783455i \(0.713455\pi\)
\(462\) 0 0
\(463\) 24.7128 1.14850 0.574250 0.818680i \(-0.305294\pi\)
0.574250 + 0.818680i \(0.305294\pi\)
\(464\) 0 0
\(465\) 5.12208 0.237531
\(466\) 0 0
\(467\) 0.926018 0.0428510 0.0214255 0.999770i \(-0.493180\pi\)
0.0214255 + 0.999770i \(0.493180\pi\)
\(468\) 0 0
\(469\) 0.670274 0.0309504
\(470\) 0 0
\(471\) 5.72452 0.263772
\(472\) 0 0
\(473\) −11.4453 −0.526256
\(474\) 0 0
\(475\) 5.73969 0.263355
\(476\) 0 0
\(477\) 6.86073 0.314131
\(478\) 0 0
\(479\) 31.8360 1.45462 0.727312 0.686307i \(-0.240769\pi\)
0.727312 + 0.686307i \(0.240769\pi\)
\(480\) 0 0
\(481\) 8.60384 0.392302
\(482\) 0 0
\(483\) 4.78538 0.217742
\(484\) 0 0
\(485\) 9.80937 0.445421
\(486\) 0 0
\(487\) 25.2782 1.14547 0.572733 0.819742i \(-0.305883\pi\)
0.572733 + 0.819742i \(0.305883\pi\)
\(488\) 0 0
\(489\) 14.8151 0.669962
\(490\) 0 0
\(491\) −15.9319 −0.718997 −0.359499 0.933146i \(-0.617052\pi\)
−0.359499 + 0.933146i \(0.617052\pi\)
\(492\) 0 0
\(493\) −3.35084 −0.150914
\(494\) 0 0
\(495\) −3.78339 −0.170051
\(496\) 0 0
\(497\) −8.34430 −0.374293
\(498\) 0 0
\(499\) −5.67237 −0.253930 −0.126965 0.991907i \(-0.540524\pi\)
−0.126965 + 0.991907i \(0.540524\pi\)
\(500\) 0 0
\(501\) −3.97042 −0.177385
\(502\) 0 0
\(503\) −15.2206 −0.678654 −0.339327 0.940668i \(-0.610199\pi\)
−0.339327 + 0.940668i \(0.610199\pi\)
\(504\) 0 0
\(505\) −3.47407 −0.154594
\(506\) 0 0
\(507\) 3.92740 0.174422
\(508\) 0 0
\(509\) −9.30717 −0.412533 −0.206266 0.978496i \(-0.566131\pi\)
−0.206266 + 0.978496i \(0.566131\pi\)
\(510\) 0 0
\(511\) −6.99207 −0.309311
\(512\) 0 0
\(513\) 5.73969 0.253413
\(514\) 0 0
\(515\) −16.1717 −0.712610
\(516\) 0 0
\(517\) −20.6967 −0.910238
\(518\) 0 0
\(519\) 24.2043 1.06245
\(520\) 0 0
\(521\) −11.3936 −0.499162 −0.249581 0.968354i \(-0.580293\pi\)
−0.249581 + 0.968354i \(0.580293\pi\)
\(522\) 0 0
\(523\) 21.3201 0.932261 0.466130 0.884716i \(-0.345648\pi\)
0.466130 + 0.884716i \(0.345648\pi\)
\(524\) 0 0
\(525\) 0.670274 0.0292532
\(526\) 0 0
\(527\) −9.42070 −0.410372
\(528\) 0 0
\(529\) 27.9716 1.21616
\(530\) 0 0
\(531\) 1.63478 0.0709432
\(532\) 0 0
\(533\) 29.3023 1.26922
\(534\) 0 0
\(535\) 17.9034 0.774031
\(536\) 0 0
\(537\) −9.26827 −0.399955
\(538\) 0 0
\(539\) −24.7840 −1.06752
\(540\) 0 0
\(541\) −29.2004 −1.25542 −0.627712 0.778446i \(-0.716008\pi\)
−0.627712 + 0.778446i \(0.716008\pi\)
\(542\) 0 0
\(543\) −24.7538 −1.06229
\(544\) 0 0
\(545\) −17.3694 −0.744024
\(546\) 0 0
\(547\) 34.0743 1.45691 0.728455 0.685093i \(-0.240239\pi\)
0.728455 + 0.685093i \(0.240239\pi\)
\(548\) 0 0
\(549\) 5.50889 0.235114
\(550\) 0 0
\(551\) −10.4570 −0.445481
\(552\) 0 0
\(553\) 4.70342 0.200010
\(554\) 0 0
\(555\) −2.09121 −0.0887669
\(556\) 0 0
\(557\) 37.7922 1.60131 0.800654 0.599127i \(-0.204486\pi\)
0.800654 + 0.599127i \(0.204486\pi\)
\(558\) 0 0
\(559\) −12.4463 −0.526424
\(560\) 0 0
\(561\) 6.95853 0.293789
\(562\) 0 0
\(563\) 26.1466 1.10195 0.550974 0.834522i \(-0.314256\pi\)
0.550974 + 0.834522i \(0.314256\pi\)
\(564\) 0 0
\(565\) 19.3577 0.814383
\(566\) 0 0
\(567\) 0.670274 0.0281489
\(568\) 0 0
\(569\) −37.3200 −1.56454 −0.782268 0.622942i \(-0.785937\pi\)
−0.782268 + 0.622942i \(0.785937\pi\)
\(570\) 0 0
\(571\) 1.81060 0.0757713 0.0378856 0.999282i \(-0.487938\pi\)
0.0378856 + 0.999282i \(0.487938\pi\)
\(572\) 0 0
\(573\) 1.65532 0.0691521
\(574\) 0 0
\(575\) 7.13944 0.297735
\(576\) 0 0
\(577\) −18.7019 −0.778568 −0.389284 0.921118i \(-0.627278\pi\)
−0.389284 + 0.921118i \(0.627278\pi\)
\(578\) 0 0
\(579\) −13.2421 −0.550325
\(580\) 0 0
\(581\) −3.45861 −0.143487
\(582\) 0 0
\(583\) 25.9568 1.07502
\(584\) 0 0
\(585\) −4.11429 −0.170105
\(586\) 0 0
\(587\) −1.91146 −0.0788944 −0.0394472 0.999222i \(-0.512560\pi\)
−0.0394472 + 0.999222i \(0.512560\pi\)
\(588\) 0 0
\(589\) −29.3991 −1.21137
\(590\) 0 0
\(591\) −3.51881 −0.144744
\(592\) 0 0
\(593\) 1.36025 0.0558588 0.0279294 0.999610i \(-0.491109\pi\)
0.0279294 + 0.999610i \(0.491109\pi\)
\(594\) 0 0
\(595\) −1.23279 −0.0505395
\(596\) 0 0
\(597\) 13.9365 0.570383
\(598\) 0 0
\(599\) 30.3993 1.24208 0.621040 0.783779i \(-0.286710\pi\)
0.621040 + 0.783779i \(0.286710\pi\)
\(600\) 0 0
\(601\) −25.6037 −1.04439 −0.522197 0.852825i \(-0.674888\pi\)
−0.522197 + 0.852825i \(0.674888\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) −3.31401 −0.134734
\(606\) 0 0
\(607\) 1.07196 0.0435094 0.0217547 0.999763i \(-0.493075\pi\)
0.0217547 + 0.999763i \(0.493075\pi\)
\(608\) 0 0
\(609\) −1.22115 −0.0494836
\(610\) 0 0
\(611\) −22.5069 −0.910530
\(612\) 0 0
\(613\) 19.7022 0.795765 0.397883 0.917436i \(-0.369745\pi\)
0.397883 + 0.917436i \(0.369745\pi\)
\(614\) 0 0
\(615\) −7.12208 −0.287190
\(616\) 0 0
\(617\) −9.84791 −0.396462 −0.198231 0.980155i \(-0.563520\pi\)
−0.198231 + 0.980155i \(0.563520\pi\)
\(618\) 0 0
\(619\) 5.39967 0.217031 0.108516 0.994095i \(-0.465390\pi\)
0.108516 + 0.994095i \(0.465390\pi\)
\(620\) 0 0
\(621\) 7.13944 0.286496
\(622\) 0 0
\(623\) 3.77467 0.151229
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 21.7154 0.867232
\(628\) 0 0
\(629\) 3.84622 0.153359
\(630\) 0 0
\(631\) 45.8600 1.82566 0.912829 0.408343i \(-0.133893\pi\)
0.912829 + 0.408343i \(0.133893\pi\)
\(632\) 0 0
\(633\) 24.8657 0.988324
\(634\) 0 0
\(635\) −12.6572 −0.502286
\(636\) 0 0
\(637\) −26.9516 −1.06786
\(638\) 0 0
\(639\) −12.4491 −0.492478
\(640\) 0 0
\(641\) −33.9181 −1.33969 −0.669843 0.742503i \(-0.733639\pi\)
−0.669843 + 0.742503i \(0.733639\pi\)
\(642\) 0 0
\(643\) −2.51361 −0.0991272 −0.0495636 0.998771i \(-0.515783\pi\)
−0.0495636 + 0.998771i \(0.515783\pi\)
\(644\) 0 0
\(645\) 3.02515 0.119115
\(646\) 0 0
\(647\) 27.6877 1.08852 0.544259 0.838917i \(-0.316811\pi\)
0.544259 + 0.838917i \(0.316811\pi\)
\(648\) 0 0
\(649\) 6.18499 0.242782
\(650\) 0 0
\(651\) −3.43320 −0.134558
\(652\) 0 0
\(653\) −39.6926 −1.55329 −0.776645 0.629938i \(-0.783080\pi\)
−0.776645 + 0.629938i \(0.783080\pi\)
\(654\) 0 0
\(655\) 13.7384 0.536805
\(656\) 0 0
\(657\) −10.4317 −0.406978
\(658\) 0 0
\(659\) −16.4133 −0.639370 −0.319685 0.947524i \(-0.603577\pi\)
−0.319685 + 0.947524i \(0.603577\pi\)
\(660\) 0 0
\(661\) 3.56972 0.138846 0.0694230 0.997587i \(-0.477884\pi\)
0.0694230 + 0.997587i \(0.477884\pi\)
\(662\) 0 0
\(663\) 7.56715 0.293884
\(664\) 0 0
\(665\) −3.84716 −0.149187
\(666\) 0 0
\(667\) −13.0071 −0.503638
\(668\) 0 0
\(669\) −9.60254 −0.371256
\(670\) 0 0
\(671\) 20.8423 0.804607
\(672\) 0 0
\(673\) −6.07992 −0.234364 −0.117182 0.993110i \(-0.537386\pi\)
−0.117182 + 0.993110i \(0.537386\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −32.9303 −1.26561 −0.632807 0.774310i \(-0.718097\pi\)
−0.632807 + 0.774310i \(0.718097\pi\)
\(678\) 0 0
\(679\) −6.57497 −0.252324
\(680\) 0 0
\(681\) 13.6064 0.521399
\(682\) 0 0
\(683\) 21.7093 0.830685 0.415342 0.909665i \(-0.363662\pi\)
0.415342 + 0.909665i \(0.363662\pi\)
\(684\) 0 0
\(685\) 10.2004 0.389736
\(686\) 0 0
\(687\) 3.78622 0.144453
\(688\) 0 0
\(689\) 28.2270 1.07536
\(690\) 0 0
\(691\) 48.7214 1.85345 0.926724 0.375742i \(-0.122612\pi\)
0.926724 + 0.375742i \(0.122612\pi\)
\(692\) 0 0
\(693\) 2.53591 0.0963311
\(694\) 0 0
\(695\) 12.0665 0.457708
\(696\) 0 0
\(697\) 13.0992 0.496166
\(698\) 0 0
\(699\) 13.4793 0.509835
\(700\) 0 0
\(701\) −11.2299 −0.424146 −0.212073 0.977254i \(-0.568021\pi\)
−0.212073 + 0.977254i \(0.568021\pi\)
\(702\) 0 0
\(703\) 12.0029 0.452697
\(704\) 0 0
\(705\) 5.47041 0.206027
\(706\) 0 0
\(707\) 2.32858 0.0875753
\(708\) 0 0
\(709\) −6.42425 −0.241268 −0.120634 0.992697i \(-0.538493\pi\)
−0.120634 + 0.992697i \(0.538493\pi\)
\(710\) 0 0
\(711\) 7.01717 0.263164
\(712\) 0 0
\(713\) −36.5688 −1.36951
\(714\) 0 0
\(715\) −15.5660 −0.582134
\(716\) 0 0
\(717\) −7.81123 −0.291716
\(718\) 0 0
\(719\) −14.1488 −0.527662 −0.263831 0.964569i \(-0.584986\pi\)
−0.263831 + 0.964569i \(0.584986\pi\)
\(720\) 0 0
\(721\) 10.8395 0.403683
\(722\) 0 0
\(723\) 13.8308 0.514375
\(724\) 0 0
\(725\) −1.82187 −0.0676625
\(726\) 0 0
\(727\) 0.0186600 0.000692059 0 0.000346030 1.00000i \(-0.499890\pi\)
0.000346030 1.00000i \(0.499890\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.56396 −0.205790
\(732\) 0 0
\(733\) −38.2015 −1.41101 −0.705503 0.708707i \(-0.749279\pi\)
−0.705503 + 0.708707i \(0.749279\pi\)
\(734\) 0 0
\(735\) 6.55073 0.241627
\(736\) 0 0
\(737\) 3.78339 0.139363
\(738\) 0 0
\(739\) −17.1980 −0.632640 −0.316320 0.948653i \(-0.602447\pi\)
−0.316320 + 0.948653i \(0.602447\pi\)
\(740\) 0 0
\(741\) 23.6147 0.867509
\(742\) 0 0
\(743\) −33.1297 −1.21541 −0.607705 0.794163i \(-0.707910\pi\)
−0.607705 + 0.794163i \(0.707910\pi\)
\(744\) 0 0
\(745\) 1.31188 0.0480636
\(746\) 0 0
\(747\) −5.16000 −0.188794
\(748\) 0 0
\(749\) −12.0002 −0.438477
\(750\) 0 0
\(751\) −31.0531 −1.13314 −0.566572 0.824012i \(-0.691731\pi\)
−0.566572 + 0.824012i \(0.691731\pi\)
\(752\) 0 0
\(753\) −13.7731 −0.501920
\(754\) 0 0
\(755\) −3.61324 −0.131499
\(756\) 0 0
\(757\) −23.1862 −0.842716 −0.421358 0.906894i \(-0.638446\pi\)
−0.421358 + 0.906894i \(0.638446\pi\)
\(758\) 0 0
\(759\) 27.0113 0.980447
\(760\) 0 0
\(761\) −2.58898 −0.0938503 −0.0469251 0.998898i \(-0.514942\pi\)
−0.0469251 + 0.998898i \(0.514942\pi\)
\(762\) 0 0
\(763\) 11.6423 0.421479
\(764\) 0 0
\(765\) −1.83923 −0.0664976
\(766\) 0 0
\(767\) 6.72594 0.242860
\(768\) 0 0
\(769\) −23.4029 −0.843929 −0.421964 0.906612i \(-0.638659\pi\)
−0.421964 + 0.906612i \(0.638659\pi\)
\(770\) 0 0
\(771\) 20.1620 0.726118
\(772\) 0 0
\(773\) −30.9422 −1.11292 −0.556458 0.830876i \(-0.687840\pi\)
−0.556458 + 0.830876i \(0.687840\pi\)
\(774\) 0 0
\(775\) −5.12208 −0.183990
\(776\) 0 0
\(777\) 1.40168 0.0502851
\(778\) 0 0
\(779\) 40.8785 1.46462
\(780\) 0 0
\(781\) −47.0997 −1.68536
\(782\) 0 0
\(783\) −1.82187 −0.0651083
\(784\) 0 0
\(785\) −5.72452 −0.204317
\(786\) 0 0
\(787\) −44.1093 −1.57233 −0.786163 0.618019i \(-0.787935\pi\)
−0.786163 + 0.618019i \(0.787935\pi\)
\(788\) 0 0
\(789\) 0.295696 0.0105271
\(790\) 0 0
\(791\) −12.9749 −0.461336
\(792\) 0 0
\(793\) 22.6652 0.804864
\(794\) 0 0
\(795\) −6.86073 −0.243325
\(796\) 0 0
\(797\) −30.2678 −1.07214 −0.536070 0.844173i \(-0.680092\pi\)
−0.536070 + 0.844173i \(0.680092\pi\)
\(798\) 0 0
\(799\) −10.0614 −0.355945
\(800\) 0 0
\(801\) 5.63153 0.198980
\(802\) 0 0
\(803\) −39.4670 −1.39276
\(804\) 0 0
\(805\) −4.78538 −0.168663
\(806\) 0 0
\(807\) −19.4531 −0.684781
\(808\) 0 0
\(809\) −20.5517 −0.722561 −0.361280 0.932457i \(-0.617660\pi\)
−0.361280 + 0.932457i \(0.617660\pi\)
\(810\) 0 0
\(811\) −23.4426 −0.823182 −0.411591 0.911369i \(-0.635027\pi\)
−0.411591 + 0.911369i \(0.635027\pi\)
\(812\) 0 0
\(813\) −10.8772 −0.381480
\(814\) 0 0
\(815\) −14.8151 −0.518951
\(816\) 0 0
\(817\) −17.3634 −0.607469
\(818\) 0 0
\(819\) 2.75770 0.0963620
\(820\) 0 0
\(821\) −27.1275 −0.946755 −0.473377 0.880860i \(-0.656965\pi\)
−0.473377 + 0.880860i \(0.656965\pi\)
\(822\) 0 0
\(823\) −13.6446 −0.475622 −0.237811 0.971311i \(-0.576430\pi\)
−0.237811 + 0.971311i \(0.576430\pi\)
\(824\) 0 0
\(825\) 3.78339 0.131721
\(826\) 0 0
\(827\) −37.5205 −1.30472 −0.652358 0.757911i \(-0.726220\pi\)
−0.652358 + 0.757911i \(0.726220\pi\)
\(828\) 0 0
\(829\) −9.84587 −0.341961 −0.170981 0.985274i \(-0.554694\pi\)
−0.170981 + 0.985274i \(0.554694\pi\)
\(830\) 0 0
\(831\) 25.1608 0.872818
\(832\) 0 0
\(833\) −12.0483 −0.417450
\(834\) 0 0
\(835\) 3.97042 0.137402
\(836\) 0 0
\(837\) −5.12208 −0.177045
\(838\) 0 0
\(839\) 0.762629 0.0263289 0.0131644 0.999913i \(-0.495810\pi\)
0.0131644 + 0.999913i \(0.495810\pi\)
\(840\) 0 0
\(841\) −25.6808 −0.885545
\(842\) 0 0
\(843\) 8.91436 0.307027
\(844\) 0 0
\(845\) −3.92740 −0.135107
\(846\) 0 0
\(847\) 2.22130 0.0763247
\(848\) 0 0
\(849\) −19.4711 −0.668248
\(850\) 0 0
\(851\) 14.9301 0.511796
\(852\) 0 0
\(853\) 42.8841 1.46832 0.734162 0.678974i \(-0.237575\pi\)
0.734162 + 0.678974i \(0.237575\pi\)
\(854\) 0 0
\(855\) −5.73969 −0.196293
\(856\) 0 0
\(857\) 35.6280 1.21703 0.608514 0.793543i \(-0.291766\pi\)
0.608514 + 0.793543i \(0.291766\pi\)
\(858\) 0 0
\(859\) 7.95039 0.271264 0.135632 0.990759i \(-0.456694\pi\)
0.135632 + 0.990759i \(0.456694\pi\)
\(860\) 0 0
\(861\) 4.77374 0.162689
\(862\) 0 0
\(863\) 54.3602 1.85044 0.925221 0.379430i \(-0.123880\pi\)
0.925221 + 0.379430i \(0.123880\pi\)
\(864\) 0 0
\(865\) −24.2043 −0.822971
\(866\) 0 0
\(867\) −13.6172 −0.462465
\(868\) 0 0
\(869\) 26.5486 0.900601
\(870\) 0 0
\(871\) 4.11429 0.139407
\(872\) 0 0
\(873\) −9.80937 −0.331997
\(874\) 0 0
\(875\) −0.670274 −0.0226594
\(876\) 0 0
\(877\) 10.3772 0.350413 0.175207 0.984532i \(-0.443941\pi\)
0.175207 + 0.984532i \(0.443941\pi\)
\(878\) 0 0
\(879\) −10.3591 −0.349404
\(880\) 0 0
\(881\) 25.8167 0.869786 0.434893 0.900482i \(-0.356786\pi\)
0.434893 + 0.900482i \(0.356786\pi\)
\(882\) 0 0
\(883\) 1.52466 0.0513088 0.0256544 0.999671i \(-0.491833\pi\)
0.0256544 + 0.999671i \(0.491833\pi\)
\(884\) 0 0
\(885\) −1.63478 −0.0549524
\(886\) 0 0
\(887\) 13.2881 0.446172 0.223086 0.974799i \(-0.428387\pi\)
0.223086 + 0.974799i \(0.428387\pi\)
\(888\) 0 0
\(889\) 8.48380 0.284538
\(890\) 0 0
\(891\) 3.78339 0.126748
\(892\) 0 0
\(893\) −31.3984 −1.05071
\(894\) 0 0
\(895\) 9.26827 0.309804
\(896\) 0 0
\(897\) 29.3737 0.980761
\(898\) 0 0
\(899\) 9.33175 0.311231
\(900\) 0 0
\(901\) 12.6185 0.420383
\(902\) 0 0
\(903\) −2.02768 −0.0674769
\(904\) 0 0
\(905\) 24.7538 0.822845
\(906\) 0 0
\(907\) −38.0633 −1.26387 −0.631936 0.775021i \(-0.717739\pi\)
−0.631936 + 0.775021i \(0.717739\pi\)
\(908\) 0 0
\(909\) 3.47407 0.115228
\(910\) 0 0
\(911\) −16.9805 −0.562589 −0.281295 0.959621i \(-0.590764\pi\)
−0.281295 + 0.959621i \(0.590764\pi\)
\(912\) 0 0
\(913\) −19.5223 −0.646093
\(914\) 0 0
\(915\) −5.50889 −0.182118
\(916\) 0 0
\(917\) −9.20851 −0.304092
\(918\) 0 0
\(919\) 19.4705 0.642272 0.321136 0.947033i \(-0.395935\pi\)
0.321136 + 0.947033i \(0.395935\pi\)
\(920\) 0 0
\(921\) 25.7029 0.846939
\(922\) 0 0
\(923\) −51.2192 −1.68590
\(924\) 0 0
\(925\) 2.09121 0.0687585
\(926\) 0 0
\(927\) 16.1717 0.531148
\(928\) 0 0
\(929\) −43.5080 −1.42745 −0.713725 0.700426i \(-0.752993\pi\)
−0.713725 + 0.700426i \(0.752993\pi\)
\(930\) 0 0
\(931\) −37.5991 −1.23226
\(932\) 0 0
\(933\) −2.07146 −0.0678165
\(934\) 0 0
\(935\) −6.95853 −0.227568
\(936\) 0 0
\(937\) 16.6446 0.543756 0.271878 0.962332i \(-0.412355\pi\)
0.271878 + 0.962332i \(0.412355\pi\)
\(938\) 0 0
\(939\) 11.9262 0.389198
\(940\) 0 0
\(941\) 5.64480 0.184015 0.0920077 0.995758i \(-0.470672\pi\)
0.0920077 + 0.995758i \(0.470672\pi\)
\(942\) 0 0
\(943\) 50.8476 1.65583
\(944\) 0 0
\(945\) −0.670274 −0.0218040
\(946\) 0 0
\(947\) −44.4840 −1.44553 −0.722767 0.691092i \(-0.757130\pi\)
−0.722767 + 0.691092i \(0.757130\pi\)
\(948\) 0 0
\(949\) −42.9189 −1.39321
\(950\) 0 0
\(951\) −32.0644 −1.03976
\(952\) 0 0
\(953\) −10.4655 −0.339012 −0.169506 0.985529i \(-0.554217\pi\)
−0.169506 + 0.985529i \(0.554217\pi\)
\(954\) 0 0
\(955\) −1.65532 −0.0535650
\(956\) 0 0
\(957\) −6.89284 −0.222814
\(958\) 0 0
\(959\) −6.83704 −0.220779
\(960\) 0 0
\(961\) −4.76434 −0.153688
\(962\) 0 0
\(963\) −17.9034 −0.576929
\(964\) 0 0
\(965\) 13.2421 0.426280
\(966\) 0 0
\(967\) 47.4772 1.52676 0.763382 0.645948i \(-0.223538\pi\)
0.763382 + 0.645948i \(0.223538\pi\)
\(968\) 0 0
\(969\) 10.5566 0.339128
\(970\) 0 0
\(971\) 38.5501 1.23713 0.618567 0.785732i \(-0.287714\pi\)
0.618567 + 0.785732i \(0.287714\pi\)
\(972\) 0 0
\(973\) −8.08786 −0.259285
\(974\) 0 0
\(975\) 4.11429 0.131763
\(976\) 0 0
\(977\) 18.3124 0.585866 0.292933 0.956133i \(-0.405369\pi\)
0.292933 + 0.956133i \(0.405369\pi\)
\(978\) 0 0
\(979\) 21.3063 0.680951
\(980\) 0 0
\(981\) 17.3694 0.554563
\(982\) 0 0
\(983\) 16.1671 0.515650 0.257825 0.966192i \(-0.416994\pi\)
0.257825 + 0.966192i \(0.416994\pi\)
\(984\) 0 0
\(985\) 3.51881 0.112118
\(986\) 0 0
\(987\) −3.66667 −0.116711
\(988\) 0 0
\(989\) −21.5979 −0.686772
\(990\) 0 0
\(991\) 57.2685 1.81919 0.909597 0.415492i \(-0.136391\pi\)
0.909597 + 0.415492i \(0.136391\pi\)
\(992\) 0 0
\(993\) 10.3465 0.328337
\(994\) 0 0
\(995\) −13.9365 −0.441817
\(996\) 0 0
\(997\) 43.2429 1.36952 0.684758 0.728771i \(-0.259908\pi\)
0.684758 + 0.728771i \(0.259908\pi\)
\(998\) 0 0
\(999\) 2.09121 0.0661629
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 \(a_p\))