Properties

Label 8036.2.a.t.1.12
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(0.538932\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.538932 q^{3}\) \(+0.810745 q^{5}\) \(-2.70955 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.538932 q^{3}\) \(+0.810745 q^{5}\) \(-2.70955 q^{9}\) \(+4.92893 q^{11}\) \(+0.0654121 q^{13}\) \(+0.436937 q^{15}\) \(-1.24015 q^{17}\) \(+3.82383 q^{19}\) \(-1.71957 q^{23}\) \(-4.34269 q^{25}\) \(-3.07706 q^{27}\) \(+3.89893 q^{29}\) \(+3.19907 q^{31}\) \(+2.65636 q^{33}\) \(-0.0930044 q^{37}\) \(+0.0352527 q^{39}\) \(-1.00000 q^{41}\) \(+10.5630 q^{43}\) \(-2.19676 q^{45}\) \(-0.959640 q^{47}\) \(-0.668359 q^{51}\) \(-2.72668 q^{53}\) \(+3.99611 q^{55}\) \(+2.06078 q^{57}\) \(+11.1898 q^{59}\) \(-10.8004 q^{61}\) \(+0.0530326 q^{65}\) \(+10.3531 q^{67}\) \(-0.926733 q^{69}\) \(-5.60052 q^{71}\) \(+2.76947 q^{73}\) \(-2.34041 q^{75}\) \(-16.2539 q^{79}\) \(+6.47033 q^{81}\) \(+9.99122 q^{83}\) \(-1.00545 q^{85}\) \(+2.10126 q^{87}\) \(+11.8641 q^{89}\) \(+1.72408 q^{93}\) \(+3.10015 q^{95}\) \(+6.31445 q^{97}\) \(-13.3552 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.538932 0.311152 0.155576 0.987824i \(-0.450277\pi\)
0.155576 + 0.987824i \(0.450277\pi\)
\(4\) 0 0
\(5\) 0.810745 0.362576 0.181288 0.983430i \(-0.441973\pi\)
0.181288 + 0.983430i \(0.441973\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.70955 −0.903184
\(10\) 0 0
\(11\) 4.92893 1.48613 0.743064 0.669220i \(-0.233372\pi\)
0.743064 + 0.669220i \(0.233372\pi\)
\(12\) 0 0
\(13\) 0.0654121 0.0181421 0.00907103 0.999959i \(-0.497113\pi\)
0.00907103 + 0.999959i \(0.497113\pi\)
\(14\) 0 0
\(15\) 0.436937 0.112817
\(16\) 0 0
\(17\) −1.24015 −0.300782 −0.150391 0.988627i \(-0.548053\pi\)
−0.150391 + 0.988627i \(0.548053\pi\)
\(18\) 0 0
\(19\) 3.82383 0.877247 0.438623 0.898671i \(-0.355466\pi\)
0.438623 + 0.898671i \(0.355466\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.71957 −0.358556 −0.179278 0.983798i \(-0.557376\pi\)
−0.179278 + 0.983798i \(0.557376\pi\)
\(24\) 0 0
\(25\) −4.34269 −0.868538
\(26\) 0 0
\(27\) −3.07706 −0.592180
\(28\) 0 0
\(29\) 3.89893 0.724014 0.362007 0.932175i \(-0.382092\pi\)
0.362007 + 0.932175i \(0.382092\pi\)
\(30\) 0 0
\(31\) 3.19907 0.574570 0.287285 0.957845i \(-0.407247\pi\)
0.287285 + 0.957845i \(0.407247\pi\)
\(32\) 0 0
\(33\) 2.65636 0.462413
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.0930044 −0.0152898 −0.00764492 0.999971i \(-0.502433\pi\)
−0.00764492 + 0.999971i \(0.502433\pi\)
\(38\) 0 0
\(39\) 0.0352527 0.00564495
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 10.5630 1.61084 0.805421 0.592703i \(-0.201939\pi\)
0.805421 + 0.592703i \(0.201939\pi\)
\(44\) 0 0
\(45\) −2.19676 −0.327473
\(46\) 0 0
\(47\) −0.959640 −0.139978 −0.0699889 0.997548i \(-0.522296\pi\)
−0.0699889 + 0.997548i \(0.522296\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.668359 −0.0935890
\(52\) 0 0
\(53\) −2.72668 −0.374539 −0.187269 0.982309i \(-0.559964\pi\)
−0.187269 + 0.982309i \(0.559964\pi\)
\(54\) 0 0
\(55\) 3.99611 0.538835
\(56\) 0 0
\(57\) 2.06078 0.272958
\(58\) 0 0
\(59\) 11.1898 1.45679 0.728393 0.685160i \(-0.240268\pi\)
0.728393 + 0.685160i \(0.240268\pi\)
\(60\) 0 0
\(61\) −10.8004 −1.38285 −0.691423 0.722450i \(-0.743016\pi\)
−0.691423 + 0.722450i \(0.743016\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.0530326 0.00657788
\(66\) 0 0
\(67\) 10.3531 1.26483 0.632414 0.774630i \(-0.282064\pi\)
0.632414 + 0.774630i \(0.282064\pi\)
\(68\) 0 0
\(69\) −0.926733 −0.111566
\(70\) 0 0
\(71\) −5.60052 −0.664659 −0.332330 0.943163i \(-0.607835\pi\)
−0.332330 + 0.943163i \(0.607835\pi\)
\(72\) 0 0
\(73\) 2.76947 0.324141 0.162071 0.986779i \(-0.448183\pi\)
0.162071 + 0.986779i \(0.448183\pi\)
\(74\) 0 0
\(75\) −2.34041 −0.270248
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −16.2539 −1.82870 −0.914352 0.404921i \(-0.867299\pi\)
−0.914352 + 0.404921i \(0.867299\pi\)
\(80\) 0 0
\(81\) 6.47033 0.718926
\(82\) 0 0
\(83\) 9.99122 1.09668 0.548340 0.836256i \(-0.315260\pi\)
0.548340 + 0.836256i \(0.315260\pi\)
\(84\) 0 0
\(85\) −1.00545 −0.109056
\(86\) 0 0
\(87\) 2.10126 0.225279
\(88\) 0 0
\(89\) 11.8641 1.25760 0.628799 0.777568i \(-0.283547\pi\)
0.628799 + 0.777568i \(0.283547\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1.72408 0.178779
\(94\) 0 0
\(95\) 3.10015 0.318069
\(96\) 0 0
\(97\) 6.31445 0.641136 0.320568 0.947226i \(-0.396126\pi\)
0.320568 + 0.947226i \(0.396126\pi\)
\(98\) 0 0
\(99\) −13.3552 −1.34225
\(100\) 0 0
\(101\) −12.5369 −1.24747 −0.623735 0.781636i \(-0.714386\pi\)
−0.623735 + 0.781636i \(0.714386\pi\)
\(102\) 0 0
\(103\) 18.0340 1.77695 0.888473 0.458929i \(-0.151767\pi\)
0.888473 + 0.458929i \(0.151767\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.09750 0.879488 0.439744 0.898123i \(-0.355069\pi\)
0.439744 + 0.898123i \(0.355069\pi\)
\(108\) 0 0
\(109\) 9.88562 0.946870 0.473435 0.880829i \(-0.343014\pi\)
0.473435 + 0.880829i \(0.343014\pi\)
\(110\) 0 0
\(111\) −0.0501230 −0.00475747
\(112\) 0 0
\(113\) −8.45002 −0.794911 −0.397455 0.917622i \(-0.630107\pi\)
−0.397455 + 0.917622i \(0.630107\pi\)
\(114\) 0 0
\(115\) −1.39414 −0.130004
\(116\) 0 0
\(117\) −0.177238 −0.0163856
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 13.2944 1.20858
\(122\) 0 0
\(123\) −0.538932 −0.0485938
\(124\) 0 0
\(125\) −7.57454 −0.677488
\(126\) 0 0
\(127\) 6.19115 0.549376 0.274688 0.961533i \(-0.411425\pi\)
0.274688 + 0.961533i \(0.411425\pi\)
\(128\) 0 0
\(129\) 5.69274 0.501218
\(130\) 0 0
\(131\) 0.990027 0.0864990 0.0432495 0.999064i \(-0.486229\pi\)
0.0432495 + 0.999064i \(0.486229\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.49471 −0.214711
\(136\) 0 0
\(137\) 3.78181 0.323102 0.161551 0.986864i \(-0.448350\pi\)
0.161551 + 0.986864i \(0.448350\pi\)
\(138\) 0 0
\(139\) −18.3431 −1.55584 −0.777920 0.628364i \(-0.783725\pi\)
−0.777920 + 0.628364i \(0.783725\pi\)
\(140\) 0 0
\(141\) −0.517181 −0.0435545
\(142\) 0 0
\(143\) 0.322412 0.0269614
\(144\) 0 0
\(145\) 3.16104 0.262510
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.01195 −0.410595 −0.205297 0.978700i \(-0.565816\pi\)
−0.205297 + 0.978700i \(0.565816\pi\)
\(150\) 0 0
\(151\) 21.4822 1.74819 0.874097 0.485751i \(-0.161454\pi\)
0.874097 + 0.485751i \(0.161454\pi\)
\(152\) 0 0
\(153\) 3.36026 0.271661
\(154\) 0 0
\(155\) 2.59363 0.208325
\(156\) 0 0
\(157\) −10.8416 −0.865255 −0.432627 0.901573i \(-0.642413\pi\)
−0.432627 + 0.901573i \(0.642413\pi\)
\(158\) 0 0
\(159\) −1.46950 −0.116539
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −19.1435 −1.49943 −0.749717 0.661759i \(-0.769810\pi\)
−0.749717 + 0.661759i \(0.769810\pi\)
\(164\) 0 0
\(165\) 2.15363 0.167660
\(166\) 0 0
\(167\) 21.3883 1.65508 0.827538 0.561409i \(-0.189741\pi\)
0.827538 + 0.561409i \(0.189741\pi\)
\(168\) 0 0
\(169\) −12.9957 −0.999671
\(170\) 0 0
\(171\) −10.3609 −0.792316
\(172\) 0 0
\(173\) 8.49170 0.645612 0.322806 0.946465i \(-0.395374\pi\)
0.322806 + 0.946465i \(0.395374\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.03053 0.453282
\(178\) 0 0
\(179\) 4.17881 0.312339 0.156169 0.987730i \(-0.450085\pi\)
0.156169 + 0.987730i \(0.450085\pi\)
\(180\) 0 0
\(181\) 7.46457 0.554837 0.277418 0.960749i \(-0.410521\pi\)
0.277418 + 0.960749i \(0.410521\pi\)
\(182\) 0 0
\(183\) −5.82066 −0.430276
\(184\) 0 0
\(185\) −0.0754029 −0.00554373
\(186\) 0 0
\(187\) −6.11264 −0.447000
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.0481 0.799413 0.399706 0.916643i \(-0.369112\pi\)
0.399706 + 0.916643i \(0.369112\pi\)
\(192\) 0 0
\(193\) 2.37310 0.170819 0.0854097 0.996346i \(-0.472780\pi\)
0.0854097 + 0.996346i \(0.472780\pi\)
\(194\) 0 0
\(195\) 0.0285809 0.00204672
\(196\) 0 0
\(197\) −23.9369 −1.70543 −0.852717 0.522374i \(-0.825047\pi\)
−0.852717 + 0.522374i \(0.825047\pi\)
\(198\) 0 0
\(199\) 5.28061 0.374333 0.187166 0.982328i \(-0.440070\pi\)
0.187166 + 0.982328i \(0.440070\pi\)
\(200\) 0 0
\(201\) 5.57960 0.393555
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.810745 −0.0566249
\(206\) 0 0
\(207\) 4.65928 0.323842
\(208\) 0 0
\(209\) 18.8474 1.30370
\(210\) 0 0
\(211\) −3.31065 −0.227915 −0.113957 0.993486i \(-0.536353\pi\)
−0.113957 + 0.993486i \(0.536353\pi\)
\(212\) 0 0
\(213\) −3.01830 −0.206810
\(214\) 0 0
\(215\) 8.56390 0.584053
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.49255 0.100857
\(220\) 0 0
\(221\) −0.0811212 −0.00545680
\(222\) 0 0
\(223\) −21.6139 −1.44738 −0.723688 0.690127i \(-0.757555\pi\)
−0.723688 + 0.690127i \(0.757555\pi\)
\(224\) 0 0
\(225\) 11.7668 0.784450
\(226\) 0 0
\(227\) 8.01651 0.532074 0.266037 0.963963i \(-0.414286\pi\)
0.266037 + 0.963963i \(0.414286\pi\)
\(228\) 0 0
\(229\) 1.03296 0.0682598 0.0341299 0.999417i \(-0.489134\pi\)
0.0341299 + 0.999417i \(0.489134\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 20.7626 1.36020 0.680100 0.733119i \(-0.261936\pi\)
0.680100 + 0.733119i \(0.261936\pi\)
\(234\) 0 0
\(235\) −0.778024 −0.0507527
\(236\) 0 0
\(237\) −8.75973 −0.569005
\(238\) 0 0
\(239\) −7.91757 −0.512145 −0.256073 0.966658i \(-0.582429\pi\)
−0.256073 + 0.966658i \(0.582429\pi\)
\(240\) 0 0
\(241\) 20.2523 1.30457 0.652283 0.757975i \(-0.273811\pi\)
0.652283 + 0.757975i \(0.273811\pi\)
\(242\) 0 0
\(243\) 12.7182 0.815876
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.250125 0.0159151
\(248\) 0 0
\(249\) 5.38459 0.341234
\(250\) 0 0
\(251\) −1.28654 −0.0812058 −0.0406029 0.999175i \(-0.512928\pi\)
−0.0406029 + 0.999175i \(0.512928\pi\)
\(252\) 0 0
\(253\) −8.47567 −0.532861
\(254\) 0 0
\(255\) −0.541869 −0.0339331
\(256\) 0 0
\(257\) 6.86057 0.427951 0.213975 0.976839i \(-0.431359\pi\)
0.213975 + 0.976839i \(0.431359\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −10.5644 −0.653918
\(262\) 0 0
\(263\) 4.28050 0.263947 0.131974 0.991253i \(-0.457869\pi\)
0.131974 + 0.991253i \(0.457869\pi\)
\(264\) 0 0
\(265\) −2.21065 −0.135799
\(266\) 0 0
\(267\) 6.39397 0.391304
\(268\) 0 0
\(269\) 8.24205 0.502527 0.251263 0.967919i \(-0.419154\pi\)
0.251263 + 0.967919i \(0.419154\pi\)
\(270\) 0 0
\(271\) 26.4651 1.60764 0.803820 0.594873i \(-0.202797\pi\)
0.803820 + 0.594873i \(0.202797\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −21.4048 −1.29076
\(276\) 0 0
\(277\) 15.1377 0.909537 0.454769 0.890610i \(-0.349722\pi\)
0.454769 + 0.890610i \(0.349722\pi\)
\(278\) 0 0
\(279\) −8.66805 −0.518942
\(280\) 0 0
\(281\) −4.51773 −0.269505 −0.134753 0.990879i \(-0.543024\pi\)
−0.134753 + 0.990879i \(0.543024\pi\)
\(282\) 0 0
\(283\) 30.9377 1.83906 0.919529 0.393022i \(-0.128571\pi\)
0.919529 + 0.393022i \(0.128571\pi\)
\(284\) 0 0
\(285\) 1.67077 0.0989679
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.4620 −0.909530
\(290\) 0 0
\(291\) 3.40306 0.199491
\(292\) 0 0
\(293\) 12.5755 0.734667 0.367334 0.930089i \(-0.380271\pi\)
0.367334 + 0.930089i \(0.380271\pi\)
\(294\) 0 0
\(295\) 9.07206 0.528196
\(296\) 0 0
\(297\) −15.1666 −0.880056
\(298\) 0 0
\(299\) −0.112481 −0.00650495
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −6.75655 −0.388154
\(304\) 0 0
\(305\) −8.75635 −0.501387
\(306\) 0 0
\(307\) 13.0695 0.745919 0.372959 0.927848i \(-0.378343\pi\)
0.372959 + 0.927848i \(0.378343\pi\)
\(308\) 0 0
\(309\) 9.71911 0.552901
\(310\) 0 0
\(311\) 17.9072 1.01542 0.507712 0.861527i \(-0.330492\pi\)
0.507712 + 0.861527i \(0.330492\pi\)
\(312\) 0 0
\(313\) −12.1024 −0.684070 −0.342035 0.939687i \(-0.611116\pi\)
−0.342035 + 0.939687i \(0.611116\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −15.9366 −0.895089 −0.447544 0.894262i \(-0.647701\pi\)
−0.447544 + 0.894262i \(0.647701\pi\)
\(318\) 0 0
\(319\) 19.2176 1.07598
\(320\) 0 0
\(321\) 4.90293 0.273655
\(322\) 0 0
\(323\) −4.74214 −0.263860
\(324\) 0 0
\(325\) −0.284065 −0.0157571
\(326\) 0 0
\(327\) 5.32767 0.294621
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.4334 0.573473 0.286737 0.958009i \(-0.407430\pi\)
0.286737 + 0.958009i \(0.407430\pi\)
\(332\) 0 0
\(333\) 0.252000 0.0138095
\(334\) 0 0
\(335\) 8.39370 0.458597
\(336\) 0 0
\(337\) −7.66374 −0.417470 −0.208735 0.977972i \(-0.566935\pi\)
−0.208735 + 0.977972i \(0.566935\pi\)
\(338\) 0 0
\(339\) −4.55398 −0.247338
\(340\) 0 0
\(341\) 15.7680 0.853885
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.751345 −0.0404510
\(346\) 0 0
\(347\) −23.4021 −1.25629 −0.628146 0.778095i \(-0.716186\pi\)
−0.628146 + 0.778095i \(0.716186\pi\)
\(348\) 0 0
\(349\) 14.4181 0.771781 0.385891 0.922545i \(-0.373894\pi\)
0.385891 + 0.922545i \(0.373894\pi\)
\(350\) 0 0
\(351\) −0.201277 −0.0107434
\(352\) 0 0
\(353\) 34.4990 1.83619 0.918097 0.396355i \(-0.129725\pi\)
0.918097 + 0.396355i \(0.129725\pi\)
\(354\) 0 0
\(355\) −4.54060 −0.240990
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.75593 −0.198231 −0.0991153 0.995076i \(-0.531601\pi\)
−0.0991153 + 0.995076i \(0.531601\pi\)
\(360\) 0 0
\(361\) −4.37832 −0.230438
\(362\) 0 0
\(363\) 7.16476 0.376052
\(364\) 0 0
\(365\) 2.24533 0.117526
\(366\) 0 0
\(367\) 19.7801 1.03251 0.516255 0.856435i \(-0.327326\pi\)
0.516255 + 0.856435i \(0.327326\pi\)
\(368\) 0 0
\(369\) 2.70955 0.141054
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −25.5124 −1.32098 −0.660490 0.750835i \(-0.729651\pi\)
−0.660490 + 0.750835i \(0.729651\pi\)
\(374\) 0 0
\(375\) −4.08216 −0.210802
\(376\) 0 0
\(377\) 0.255038 0.0131351
\(378\) 0 0
\(379\) 13.1317 0.674529 0.337264 0.941410i \(-0.390498\pi\)
0.337264 + 0.941410i \(0.390498\pi\)
\(380\) 0 0
\(381\) 3.33661 0.170940
\(382\) 0 0
\(383\) −21.2494 −1.08579 −0.542897 0.839799i \(-0.682673\pi\)
−0.542897 + 0.839799i \(0.682673\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −28.6210 −1.45489
\(388\) 0 0
\(389\) 37.7262 1.91280 0.956398 0.292068i \(-0.0943432\pi\)
0.956398 + 0.292068i \(0.0943432\pi\)
\(390\) 0 0
\(391\) 2.13254 0.107847
\(392\) 0 0
\(393\) 0.533557 0.0269144
\(394\) 0 0
\(395\) −13.1777 −0.663045
\(396\) 0 0
\(397\) 9.20513 0.461992 0.230996 0.972955i \(-0.425802\pi\)
0.230996 + 0.972955i \(0.425802\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.2942 0.813694 0.406847 0.913496i \(-0.366628\pi\)
0.406847 + 0.913496i \(0.366628\pi\)
\(402\) 0 0
\(403\) 0.209258 0.0104239
\(404\) 0 0
\(405\) 5.24579 0.260666
\(406\) 0 0
\(407\) −0.458413 −0.0227227
\(408\) 0 0
\(409\) −0.569169 −0.0281436 −0.0140718 0.999901i \(-0.504479\pi\)
−0.0140718 + 0.999901i \(0.504479\pi\)
\(410\) 0 0
\(411\) 2.03814 0.100534
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 8.10034 0.397630
\(416\) 0 0
\(417\) −9.88567 −0.484103
\(418\) 0 0
\(419\) −3.91313 −0.191169 −0.0955845 0.995421i \(-0.530472\pi\)
−0.0955845 + 0.995421i \(0.530472\pi\)
\(420\) 0 0
\(421\) 13.6649 0.665985 0.332992 0.942930i \(-0.391942\pi\)
0.332992 + 0.942930i \(0.391942\pi\)
\(422\) 0 0
\(423\) 2.60020 0.126426
\(424\) 0 0
\(425\) 5.38561 0.261240
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.173758 0.00838912
\(430\) 0 0
\(431\) 6.84032 0.329487 0.164743 0.986336i \(-0.447320\pi\)
0.164743 + 0.986336i \(0.447320\pi\)
\(432\) 0 0
\(433\) −1.46375 −0.0703434 −0.0351717 0.999381i \(-0.511198\pi\)
−0.0351717 + 0.999381i \(0.511198\pi\)
\(434\) 0 0
\(435\) 1.70359 0.0816807
\(436\) 0 0
\(437\) −6.57536 −0.314542
\(438\) 0 0
\(439\) −1.39866 −0.0667542 −0.0333771 0.999443i \(-0.510626\pi\)
−0.0333771 + 0.999443i \(0.510626\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.1620 −0.862902 −0.431451 0.902136i \(-0.641998\pi\)
−0.431451 + 0.902136i \(0.641998\pi\)
\(444\) 0 0
\(445\) 9.61880 0.455975
\(446\) 0 0
\(447\) −2.70110 −0.127758
\(448\) 0 0
\(449\) −38.4896 −1.81644 −0.908219 0.418495i \(-0.862558\pi\)
−0.908219 + 0.418495i \(0.862558\pi\)
\(450\) 0 0
\(451\) −4.92893 −0.232094
\(452\) 0 0
\(453\) 11.5774 0.543955
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −19.6702 −0.920135 −0.460067 0.887884i \(-0.652175\pi\)
−0.460067 + 0.887884i \(0.652175\pi\)
\(458\) 0 0
\(459\) 3.81603 0.178117
\(460\) 0 0
\(461\) 21.3526 0.994488 0.497244 0.867611i \(-0.334345\pi\)
0.497244 + 0.867611i \(0.334345\pi\)
\(462\) 0 0
\(463\) −11.5941 −0.538823 −0.269412 0.963025i \(-0.586829\pi\)
−0.269412 + 0.963025i \(0.586829\pi\)
\(464\) 0 0
\(465\) 1.39779 0.0648210
\(466\) 0 0
\(467\) −15.4316 −0.714087 −0.357044 0.934088i \(-0.616215\pi\)
−0.357044 + 0.934088i \(0.616215\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5.84289 −0.269226
\(472\) 0 0
\(473\) 52.0643 2.39392
\(474\) 0 0
\(475\) −16.6057 −0.761923
\(476\) 0 0
\(477\) 7.38809 0.338278
\(478\) 0 0
\(479\) 20.3619 0.930361 0.465180 0.885216i \(-0.345989\pi\)
0.465180 + 0.885216i \(0.345989\pi\)
\(480\) 0 0
\(481\) −0.00608362 −0.000277389 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.11942 0.232461
\(486\) 0 0
\(487\) −9.90723 −0.448939 −0.224470 0.974481i \(-0.572065\pi\)
−0.224470 + 0.974481i \(0.572065\pi\)
\(488\) 0 0
\(489\) −10.3170 −0.466552
\(490\) 0 0
\(491\) −9.11988 −0.411574 −0.205787 0.978597i \(-0.565975\pi\)
−0.205787 + 0.978597i \(0.565975\pi\)
\(492\) 0 0
\(493\) −4.83528 −0.217770
\(494\) 0 0
\(495\) −10.8277 −0.486667
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −13.1763 −0.589852 −0.294926 0.955520i \(-0.595295\pi\)
−0.294926 + 0.955520i \(0.595295\pi\)
\(500\) 0 0
\(501\) 11.5268 0.514981
\(502\) 0 0
\(503\) −33.6192 −1.49901 −0.749504 0.662000i \(-0.769708\pi\)
−0.749504 + 0.662000i \(0.769708\pi\)
\(504\) 0 0
\(505\) −10.1643 −0.452303
\(506\) 0 0
\(507\) −7.00381 −0.311050
\(508\) 0 0
\(509\) 29.7381 1.31812 0.659059 0.752091i \(-0.270955\pi\)
0.659059 + 0.752091i \(0.270955\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −11.7662 −0.519488
\(514\) 0 0
\(515\) 14.6210 0.644279
\(516\) 0 0
\(517\) −4.73000 −0.208025
\(518\) 0 0
\(519\) 4.57645 0.200884
\(520\) 0 0
\(521\) −0.710103 −0.0311102 −0.0155551 0.999879i \(-0.504952\pi\)
−0.0155551 + 0.999879i \(0.504952\pi\)
\(522\) 0 0
\(523\) 3.85319 0.168488 0.0842441 0.996445i \(-0.473152\pi\)
0.0842441 + 0.996445i \(0.473152\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.96734 −0.172820
\(528\) 0 0
\(529\) −20.0431 −0.871438
\(530\) 0 0
\(531\) −30.3193 −1.31575
\(532\) 0 0
\(533\) −0.0654121 −0.00283331
\(534\) 0 0
\(535\) 7.37575 0.318882
\(536\) 0 0
\(537\) 2.25209 0.0971849
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −15.9199 −0.684448 −0.342224 0.939618i \(-0.611180\pi\)
−0.342224 + 0.939618i \(0.611180\pi\)
\(542\) 0 0
\(543\) 4.02289 0.172639
\(544\) 0 0
\(545\) 8.01472 0.343313
\(546\) 0 0
\(547\) 4.91366 0.210093 0.105047 0.994467i \(-0.466501\pi\)
0.105047 + 0.994467i \(0.466501\pi\)
\(548\) 0 0
\(549\) 29.2642 1.24896
\(550\) 0 0
\(551\) 14.9089 0.635139
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.0406370 −0.00172495
\(556\) 0 0
\(557\) −26.2303 −1.11141 −0.555706 0.831379i \(-0.687552\pi\)
−0.555706 + 0.831379i \(0.687552\pi\)
\(558\) 0 0
\(559\) 0.690948 0.0292240
\(560\) 0 0
\(561\) −3.29430 −0.139085
\(562\) 0 0
\(563\) 4.73653 0.199621 0.0998105 0.995006i \(-0.468176\pi\)
0.0998105 + 0.995006i \(0.468176\pi\)
\(564\) 0 0
\(565\) −6.85081 −0.288216
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16.8284 0.705482 0.352741 0.935721i \(-0.385250\pi\)
0.352741 + 0.935721i \(0.385250\pi\)
\(570\) 0 0
\(571\) −20.4408 −0.855420 −0.427710 0.903916i \(-0.640680\pi\)
−0.427710 + 0.903916i \(0.640680\pi\)
\(572\) 0 0
\(573\) 5.95417 0.248739
\(574\) 0 0
\(575\) 7.46758 0.311420
\(576\) 0 0
\(577\) −15.1297 −0.629859 −0.314930 0.949115i \(-0.601981\pi\)
−0.314930 + 0.949115i \(0.601981\pi\)
\(578\) 0 0
\(579\) 1.27894 0.0531509
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −13.4396 −0.556613
\(584\) 0 0
\(585\) −0.143695 −0.00594104
\(586\) 0 0
\(587\) −44.9665 −1.85597 −0.927984 0.372620i \(-0.878459\pi\)
−0.927984 + 0.372620i \(0.878459\pi\)
\(588\) 0 0
\(589\) 12.2327 0.504040
\(590\) 0 0
\(591\) −12.9004 −0.530650
\(592\) 0 0
\(593\) 21.8232 0.896171 0.448085 0.893991i \(-0.352106\pi\)
0.448085 + 0.893991i \(0.352106\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 2.84589 0.116474
\(598\) 0 0
\(599\) 22.1256 0.904028 0.452014 0.892011i \(-0.350706\pi\)
0.452014 + 0.892011i \(0.350706\pi\)
\(600\) 0 0
\(601\) 41.2542 1.68279 0.841396 0.540418i \(-0.181734\pi\)
0.841396 + 0.540418i \(0.181734\pi\)
\(602\) 0 0
\(603\) −28.0522 −1.14237
\(604\) 0 0
\(605\) 10.7784 0.438202
\(606\) 0 0
\(607\) −2.98200 −0.121036 −0.0605178 0.998167i \(-0.519275\pi\)
−0.0605178 + 0.998167i \(0.519275\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.0627721 −0.00253949
\(612\) 0 0
\(613\) −22.1475 −0.894527 −0.447264 0.894402i \(-0.647601\pi\)
−0.447264 + 0.894402i \(0.647601\pi\)
\(614\) 0 0
\(615\) −0.436937 −0.0176190
\(616\) 0 0
\(617\) −4.94230 −0.198970 −0.0994848 0.995039i \(-0.531719\pi\)
−0.0994848 + 0.995039i \(0.531719\pi\)
\(618\) 0 0
\(619\) −35.4913 −1.42651 −0.713257 0.700902i \(-0.752781\pi\)
−0.713257 + 0.700902i \(0.752781\pi\)
\(620\) 0 0
\(621\) 5.29123 0.212330
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5724 0.622897
\(626\) 0 0
\(627\) 10.1575 0.405650
\(628\) 0 0
\(629\) 0.115340 0.00459890
\(630\) 0 0
\(631\) −40.6549 −1.61844 −0.809222 0.587503i \(-0.800111\pi\)
−0.809222 + 0.587503i \(0.800111\pi\)
\(632\) 0 0
\(633\) −1.78422 −0.0709163
\(634\) 0 0
\(635\) 5.01945 0.199191
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 15.1749 0.600310
\(640\) 0 0
\(641\) 41.3461 1.63307 0.816536 0.577295i \(-0.195892\pi\)
0.816536 + 0.577295i \(0.195892\pi\)
\(642\) 0 0
\(643\) 24.9995 0.985883 0.492942 0.870062i \(-0.335922\pi\)
0.492942 + 0.870062i \(0.335922\pi\)
\(644\) 0 0
\(645\) 4.61536 0.181730
\(646\) 0 0
\(647\) −25.1819 −0.990003 −0.495002 0.868892i \(-0.664832\pi\)
−0.495002 + 0.868892i \(0.664832\pi\)
\(648\) 0 0
\(649\) 55.1537 2.16497
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.3606 1.50117 0.750583 0.660776i \(-0.229773\pi\)
0.750583 + 0.660776i \(0.229773\pi\)
\(654\) 0 0
\(655\) 0.802660 0.0313625
\(656\) 0 0
\(657\) −7.50401 −0.292759
\(658\) 0 0
\(659\) 38.7750 1.51046 0.755230 0.655459i \(-0.227525\pi\)
0.755230 + 0.655459i \(0.227525\pi\)
\(660\) 0 0
\(661\) 37.8665 1.47284 0.736419 0.676526i \(-0.236515\pi\)
0.736419 + 0.676526i \(0.236515\pi\)
\(662\) 0 0
\(663\) −0.0437188 −0.00169790
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.70451 −0.259600
\(668\) 0 0
\(669\) −11.6484 −0.450355
\(670\) 0 0
\(671\) −53.2343 −2.05509
\(672\) 0 0
\(673\) −5.05883 −0.195004 −0.0975018 0.995235i \(-0.531085\pi\)
−0.0975018 + 0.995235i \(0.531085\pi\)
\(674\) 0 0
\(675\) 13.3627 0.514331
\(676\) 0 0
\(677\) −44.1411 −1.69648 −0.848241 0.529611i \(-0.822338\pi\)
−0.848241 + 0.529611i \(0.822338\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 4.32035 0.165556
\(682\) 0 0
\(683\) 10.5732 0.404572 0.202286 0.979326i \(-0.435163\pi\)
0.202286 + 0.979326i \(0.435163\pi\)
\(684\) 0 0
\(685\) 3.06609 0.117149
\(686\) 0 0
\(687\) 0.556694 0.0212392
\(688\) 0 0
\(689\) −0.178358 −0.00679491
\(690\) 0 0
\(691\) −28.1100 −1.06936 −0.534678 0.845056i \(-0.679567\pi\)
−0.534678 + 0.845056i \(0.679567\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.8716 −0.564111
\(696\) 0 0
\(697\) 1.24015 0.0469742
\(698\) 0 0
\(699\) 11.1896 0.423230
\(700\) 0 0
\(701\) −3.99389 −0.150847 −0.0754236 0.997152i \(-0.524031\pi\)
−0.0754236 + 0.997152i \(0.524031\pi\)
\(702\) 0 0
\(703\) −0.355633 −0.0134130
\(704\) 0 0
\(705\) −0.419302 −0.0157918
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.43794 0.0540028 0.0270014 0.999635i \(-0.491404\pi\)
0.0270014 + 0.999635i \(0.491404\pi\)
\(710\) 0 0
\(711\) 44.0407 1.65166
\(712\) 0 0
\(713\) −5.50104 −0.206016
\(714\) 0 0
\(715\) 0.261394 0.00977558
\(716\) 0 0
\(717\) −4.26703 −0.159355
\(718\) 0 0
\(719\) 4.38732 0.163619 0.0818097 0.996648i \(-0.473930\pi\)
0.0818097 + 0.996648i \(0.473930\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 10.9146 0.405919
\(724\) 0 0
\(725\) −16.9319 −0.628834
\(726\) 0 0
\(727\) −5.95216 −0.220753 −0.110377 0.993890i \(-0.535206\pi\)
−0.110377 + 0.993890i \(0.535206\pi\)
\(728\) 0 0
\(729\) −12.5567 −0.465064
\(730\) 0 0
\(731\) −13.0998 −0.484512
\(732\) 0 0
\(733\) 31.7441 1.17249 0.586247 0.810132i \(-0.300605\pi\)
0.586247 + 0.810132i \(0.300605\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 51.0296 1.87970
\(738\) 0 0
\(739\) 1.49001 0.0548109 0.0274055 0.999624i \(-0.491275\pi\)
0.0274055 + 0.999624i \(0.491275\pi\)
\(740\) 0 0
\(741\) 0.134800 0.00495201
\(742\) 0 0
\(743\) −2.63999 −0.0968519 −0.0484259 0.998827i \(-0.515420\pi\)
−0.0484259 + 0.998827i \(0.515420\pi\)
\(744\) 0 0
\(745\) −4.06341 −0.148872
\(746\) 0 0
\(747\) −27.0717 −0.990503
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.58728 −0.0579206 −0.0289603 0.999581i \(-0.509220\pi\)
−0.0289603 + 0.999581i \(0.509220\pi\)
\(752\) 0 0
\(753\) −0.693358 −0.0252674
\(754\) 0 0
\(755\) 17.4166 0.633854
\(756\) 0 0
\(757\) −1.41445 −0.0514090 −0.0257045 0.999670i \(-0.508183\pi\)
−0.0257045 + 0.999670i \(0.508183\pi\)
\(758\) 0 0
\(759\) −4.56781 −0.165801
\(760\) 0 0
\(761\) 34.5791 1.25349 0.626746 0.779224i \(-0.284387\pi\)
0.626746 + 0.779224i \(0.284387\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.72432 0.0984980
\(766\) 0 0
\(767\) 0.731947 0.0264291
\(768\) 0 0
\(769\) 45.3841 1.63659 0.818297 0.574796i \(-0.194919\pi\)
0.818297 + 0.574796i \(0.194919\pi\)
\(770\) 0 0
\(771\) 3.69738 0.133158
\(772\) 0 0
\(773\) −9.04090 −0.325179 −0.162589 0.986694i \(-0.551985\pi\)
−0.162589 + 0.986694i \(0.551985\pi\)
\(774\) 0 0
\(775\) −13.8926 −0.499036
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.82383 −0.137003
\(780\) 0 0
\(781\) −27.6046 −0.987770
\(782\) 0 0
\(783\) −11.9973 −0.428747
\(784\) 0 0
\(785\) −8.78979 −0.313721
\(786\) 0 0
\(787\) 14.1214 0.503372 0.251686 0.967809i \(-0.419015\pi\)
0.251686 + 0.967809i \(0.419015\pi\)
\(788\) 0 0
\(789\) 2.30690 0.0821278
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.706475 −0.0250877
\(794\) 0 0
\(795\) −1.19139 −0.0422542
\(796\) 0 0
\(797\) −52.9069 −1.87406 −0.937029 0.349252i \(-0.886436\pi\)
−0.937029 + 0.349252i \(0.886436\pi\)
\(798\) 0 0
\(799\) 1.19010 0.0421028
\(800\) 0 0
\(801\) −32.1465 −1.13584
\(802\) 0 0
\(803\) 13.6505 0.481716
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 4.44190 0.156362
\(808\) 0 0
\(809\) −38.4156 −1.35062 −0.675311 0.737533i \(-0.735991\pi\)
−0.675311 + 0.737533i \(0.735991\pi\)
\(810\) 0 0
\(811\) 10.9375 0.384068 0.192034 0.981388i \(-0.438492\pi\)
0.192034 + 0.981388i \(0.438492\pi\)
\(812\) 0 0
\(813\) 14.2629 0.500221
\(814\) 0 0
\(815\) −15.5205 −0.543659
\(816\) 0 0
\(817\) 40.3911 1.41311
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −52.1638 −1.82053 −0.910265 0.414027i \(-0.864122\pi\)
−0.910265 + 0.414027i \(0.864122\pi\)
\(822\) 0 0
\(823\) 23.4953 0.818995 0.409498 0.912311i \(-0.365704\pi\)
0.409498 + 0.912311i \(0.365704\pi\)
\(824\) 0 0
\(825\) −11.5357 −0.401623
\(826\) 0 0
\(827\) 2.66381 0.0926298 0.0463149 0.998927i \(-0.485252\pi\)
0.0463149 + 0.998927i \(0.485252\pi\)
\(828\) 0 0
\(829\) 39.4035 1.36854 0.684270 0.729229i \(-0.260121\pi\)
0.684270 + 0.729229i \(0.260121\pi\)
\(830\) 0 0
\(831\) 8.15820 0.283005
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 17.3405 0.600092
\(836\) 0 0
\(837\) −9.84373 −0.340249
\(838\) 0 0
\(839\) 23.2979 0.804334 0.402167 0.915566i \(-0.368257\pi\)
0.402167 + 0.915566i \(0.368257\pi\)
\(840\) 0 0
\(841\) −13.7983 −0.475804
\(842\) 0 0
\(843\) −2.43475 −0.0838572
\(844\) 0 0
\(845\) −10.5362 −0.362457
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 16.6733 0.572227
\(850\) 0 0
\(851\) 0.159928 0.00548226
\(852\) 0 0
\(853\) −34.1155 −1.16809 −0.584047 0.811720i \(-0.698532\pi\)
−0.584047 + 0.811720i \(0.698532\pi\)
\(854\) 0 0
\(855\) −8.40003 −0.287275
\(856\) 0 0
\(857\) −17.7004 −0.604633 −0.302317 0.953208i \(-0.597760\pi\)
−0.302317 + 0.953208i \(0.597760\pi\)
\(858\) 0 0
\(859\) 20.5431 0.700922 0.350461 0.936577i \(-0.386025\pi\)
0.350461 + 0.936577i \(0.386025\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 14.0834 0.479404 0.239702 0.970847i \(-0.422950\pi\)
0.239702 + 0.970847i \(0.422950\pi\)
\(864\) 0 0
\(865\) 6.88460 0.234084
\(866\) 0 0
\(867\) −8.33297 −0.283003
\(868\) 0 0
\(869\) −80.1142 −2.71769
\(870\) 0 0
\(871\) 0.677216 0.0229466
\(872\) 0 0
\(873\) −17.1093 −0.579064
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6.75794 −0.228199 −0.114100 0.993469i \(-0.536398\pi\)
−0.114100 + 0.993469i \(0.536398\pi\)
\(878\) 0 0
\(879\) 6.77733 0.228594
\(880\) 0 0
\(881\) 30.5704 1.02994 0.514972 0.857207i \(-0.327802\pi\)
0.514972 + 0.857207i \(0.327802\pi\)
\(882\) 0 0
\(883\) 55.0224 1.85165 0.925825 0.377952i \(-0.123372\pi\)
0.925825 + 0.377952i \(0.123372\pi\)
\(884\) 0 0
\(885\) 4.88922 0.164349
\(886\) 0 0
\(887\) −28.5153 −0.957450 −0.478725 0.877965i \(-0.658901\pi\)
−0.478725 + 0.877965i \(0.658901\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 31.8918 1.06842
\(892\) 0 0
\(893\) −3.66950 −0.122795
\(894\) 0 0
\(895\) 3.38795 0.113247
\(896\) 0 0
\(897\) −0.0606196 −0.00202403
\(898\) 0 0
\(899\) 12.4730 0.415997
\(900\) 0 0
\(901\) 3.38151 0.112654
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.05186 0.201171
\(906\) 0 0
\(907\) −30.7081 −1.01965 −0.509823 0.860279i \(-0.670289\pi\)
−0.509823 + 0.860279i \(0.670289\pi\)
\(908\) 0 0
\(909\) 33.9695 1.12670
\(910\) 0 0
\(911\) −24.7191 −0.818981 −0.409491 0.912314i \(-0.634294\pi\)
−0.409491 + 0.912314i \(0.634294\pi\)
\(912\) 0 0
\(913\) 49.2461 1.62981
\(914\) 0 0
\(915\) −4.71907 −0.156008
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −36.6530 −1.20907 −0.604535 0.796579i \(-0.706641\pi\)
−0.604535 + 0.796579i \(0.706641\pi\)
\(920\) 0 0
\(921\) 7.04360 0.232094
\(922\) 0 0
\(923\) −0.366342 −0.0120583
\(924\) 0 0
\(925\) 0.403890 0.0132798
\(926\) 0 0
\(927\) −48.8642 −1.60491
\(928\) 0 0
\(929\) 31.8880 1.04621 0.523105 0.852268i \(-0.324774\pi\)
0.523105 + 0.852268i \(0.324774\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 9.65075 0.315951
\(934\) 0 0
\(935\) −4.95579 −0.162072
\(936\) 0 0
\(937\) 49.5949 1.62019 0.810097 0.586295i \(-0.199414\pi\)
0.810097 + 0.586295i \(0.199414\pi\)
\(938\) 0 0
\(939\) −6.52238 −0.212850
\(940\) 0 0
\(941\) −1.24569 −0.0406084 −0.0203042 0.999794i \(-0.506463\pi\)
−0.0203042 + 0.999794i \(0.506463\pi\)
\(942\) 0 0
\(943\) 1.71957 0.0559971
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −14.8351 −0.482076 −0.241038 0.970516i \(-0.577488\pi\)
−0.241038 + 0.970516i \(0.577488\pi\)
\(948\) 0 0
\(949\) 0.181157 0.00588059
\(950\) 0 0
\(951\) −8.58874 −0.278509
\(952\) 0 0
\(953\) 31.5263 1.02124 0.510618 0.859808i \(-0.329417\pi\)
0.510618 + 0.859808i \(0.329417\pi\)
\(954\) 0 0
\(955\) 8.95720 0.289848
\(956\) 0 0
\(957\) 10.3570 0.334793
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −20.7660 −0.669869
\(962\) 0 0
\(963\) −24.6501 −0.794340
\(964\) 0 0
\(965\) 1.92398 0.0619351
\(966\) 0 0
\(967\) 7.43038 0.238945 0.119472 0.992838i \(-0.461880\pi\)
0.119472 + 0.992838i \(0.461880\pi\)
\(968\) 0 0
\(969\) −2.55569 −0.0821006
\(970\) 0 0
\(971\) −20.3316 −0.652472 −0.326236 0.945288i \(-0.605780\pi\)
−0.326236 + 0.945288i \(0.605780\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −0.153092 −0.00490285
\(976\) 0 0
\(977\) −9.88193 −0.316151 −0.158076 0.987427i \(-0.550529\pi\)
−0.158076 + 0.987427i \(0.550529\pi\)
\(978\) 0 0
\(979\) 58.4776 1.86895
\(980\) 0 0
\(981\) −26.7856 −0.855198
\(982\) 0 0
\(983\) 30.4507 0.971225 0.485612 0.874174i \(-0.338597\pi\)
0.485612 + 0.874174i \(0.338597\pi\)
\(984\) 0 0
\(985\) −19.4067 −0.618350
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −18.1639 −0.577577
\(990\) 0 0
\(991\) 37.0806 1.17791 0.588953 0.808167i \(-0.299540\pi\)
0.588953 + 0.808167i \(0.299540\pi\)
\(992\) 0 0
\(993\) 5.62291 0.178438
\(994\) 0 0
\(995\) 4.28123 0.135724
\(996\) 0 0
\(997\) −1.49925 −0.0474818 −0.0237409 0.999718i \(-0.507558\pi\)
−0.0237409 + 0.999718i \(0.507558\pi\)
\(998\) 0 0
\(999\) 0.286180 0.00905434
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 \(a_p\))