Properties

Label 8024.2.a.y.1.10
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.29710 q^{3}\) \(-1.23439 q^{5}\) \(-2.46133 q^{7}\) \(-1.31752 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.29710 q^{3}\) \(-1.23439 q^{5}\) \(-2.46133 q^{7}\) \(-1.31752 q^{9}\) \(-0.0568786 q^{11}\) \(+4.73593 q^{13}\) \(+1.60113 q^{15}\) \(-1.00000 q^{17}\) \(-0.278794 q^{19}\) \(+3.19260 q^{21}\) \(+1.06619 q^{23}\) \(-3.47628 q^{25}\) \(+5.60027 q^{27}\) \(-6.61540 q^{29}\) \(+4.85624 q^{31}\) \(+0.0737774 q^{33}\) \(+3.03824 q^{35}\) \(+0.645264 q^{37}\) \(-6.14300 q^{39}\) \(+3.28997 q^{41}\) \(-2.78716 q^{43}\) \(+1.62634 q^{45}\) \(-4.10740 q^{47}\) \(-0.941872 q^{49}\) \(+1.29710 q^{51}\) \(+9.36717 q^{53}\) \(+0.0702104 q^{55}\) \(+0.361625 q^{57}\) \(-1.00000 q^{59}\) \(+9.88658 q^{61}\) \(+3.24285 q^{63}\) \(-5.84599 q^{65}\) \(-3.10620 q^{67}\) \(-1.38296 q^{69}\) \(+0.938212 q^{71}\) \(+5.16381 q^{73}\) \(+4.50909 q^{75}\) \(+0.139997 q^{77}\) \(-1.50059 q^{79}\) \(-3.31157 q^{81}\) \(+0.594577 q^{83}\) \(+1.23439 q^{85}\) \(+8.58086 q^{87}\) \(+16.4643 q^{89}\) \(-11.6567 q^{91}\) \(-6.29905 q^{93}\) \(+0.344141 q^{95}\) \(-3.06896 q^{97}\) \(+0.0749388 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.29710 −0.748883 −0.374442 0.927251i \(-0.622166\pi\)
−0.374442 + 0.927251i \(0.622166\pi\)
\(4\) 0 0
\(5\) −1.23439 −0.552036 −0.276018 0.961152i \(-0.589015\pi\)
−0.276018 + 0.961152i \(0.589015\pi\)
\(6\) 0 0
\(7\) −2.46133 −0.930294 −0.465147 0.885233i \(-0.653999\pi\)
−0.465147 + 0.885233i \(0.653999\pi\)
\(8\) 0 0
\(9\) −1.31752 −0.439174
\(10\) 0 0
\(11\) −0.0568786 −0.0171495 −0.00857477 0.999963i \(-0.502729\pi\)
−0.00857477 + 0.999963i \(0.502729\pi\)
\(12\) 0 0
\(13\) 4.73593 1.31351 0.656756 0.754103i \(-0.271928\pi\)
0.656756 + 0.754103i \(0.271928\pi\)
\(14\) 0 0
\(15\) 1.60113 0.413411
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −0.278794 −0.0639597 −0.0319799 0.999489i \(-0.510181\pi\)
−0.0319799 + 0.999489i \(0.510181\pi\)
\(20\) 0 0
\(21\) 3.19260 0.696681
\(22\) 0 0
\(23\) 1.06619 0.222317 0.111158 0.993803i \(-0.464544\pi\)
0.111158 + 0.993803i \(0.464544\pi\)
\(24\) 0 0
\(25\) −3.47628 −0.695256
\(26\) 0 0
\(27\) 5.60027 1.07777
\(28\) 0 0
\(29\) −6.61540 −1.22845 −0.614224 0.789131i \(-0.710531\pi\)
−0.614224 + 0.789131i \(0.710531\pi\)
\(30\) 0 0
\(31\) 4.85624 0.872206 0.436103 0.899897i \(-0.356358\pi\)
0.436103 + 0.899897i \(0.356358\pi\)
\(32\) 0 0
\(33\) 0.0737774 0.0128430
\(34\) 0 0
\(35\) 3.03824 0.513556
\(36\) 0 0
\(37\) 0.645264 0.106081 0.0530404 0.998592i \(-0.483109\pi\)
0.0530404 + 0.998592i \(0.483109\pi\)
\(38\) 0 0
\(39\) −6.14300 −0.983667
\(40\) 0 0
\(41\) 3.28997 0.513806 0.256903 0.966437i \(-0.417298\pi\)
0.256903 + 0.966437i \(0.417298\pi\)
\(42\) 0 0
\(43\) −2.78716 −0.425037 −0.212519 0.977157i \(-0.568167\pi\)
−0.212519 + 0.977157i \(0.568167\pi\)
\(44\) 0 0
\(45\) 1.62634 0.242440
\(46\) 0 0
\(47\) −4.10740 −0.599127 −0.299563 0.954076i \(-0.596841\pi\)
−0.299563 + 0.954076i \(0.596841\pi\)
\(48\) 0 0
\(49\) −0.941872 −0.134553
\(50\) 0 0
\(51\) 1.29710 0.181631
\(52\) 0 0
\(53\) 9.36717 1.28668 0.643340 0.765581i \(-0.277548\pi\)
0.643340 + 0.765581i \(0.277548\pi\)
\(54\) 0 0
\(55\) 0.0702104 0.00946717
\(56\) 0 0
\(57\) 0.361625 0.0478984
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 9.88658 1.26585 0.632924 0.774214i \(-0.281855\pi\)
0.632924 + 0.774214i \(0.281855\pi\)
\(62\) 0 0
\(63\) 3.24285 0.408561
\(64\) 0 0
\(65\) −5.84599 −0.725106
\(66\) 0 0
\(67\) −3.10620 −0.379483 −0.189742 0.981834i \(-0.560765\pi\)
−0.189742 + 0.981834i \(0.560765\pi\)
\(68\) 0 0
\(69\) −1.38296 −0.166489
\(70\) 0 0
\(71\) 0.938212 0.111345 0.0556727 0.998449i \(-0.482270\pi\)
0.0556727 + 0.998449i \(0.482270\pi\)
\(72\) 0 0
\(73\) 5.16381 0.604378 0.302189 0.953248i \(-0.402283\pi\)
0.302189 + 0.953248i \(0.402283\pi\)
\(74\) 0 0
\(75\) 4.50909 0.520665
\(76\) 0 0
\(77\) 0.139997 0.0159541
\(78\) 0 0
\(79\) −1.50059 −0.168829 −0.0844147 0.996431i \(-0.526902\pi\)
−0.0844147 + 0.996431i \(0.526902\pi\)
\(80\) 0 0
\(81\) −3.31157 −0.367952
\(82\) 0 0
\(83\) 0.594577 0.0652633 0.0326316 0.999467i \(-0.489611\pi\)
0.0326316 + 0.999467i \(0.489611\pi\)
\(84\) 0 0
\(85\) 1.23439 0.133888
\(86\) 0 0
\(87\) 8.58086 0.919965
\(88\) 0 0
\(89\) 16.4643 1.74521 0.872607 0.488424i \(-0.162428\pi\)
0.872607 + 0.488424i \(0.162428\pi\)
\(90\) 0 0
\(91\) −11.6567 −1.22195
\(92\) 0 0
\(93\) −6.29905 −0.653181
\(94\) 0 0
\(95\) 0.344141 0.0353081
\(96\) 0 0
\(97\) −3.06896 −0.311605 −0.155803 0.987788i \(-0.549796\pi\)
−0.155803 + 0.987788i \(0.549796\pi\)
\(98\) 0 0
\(99\) 0.0749388 0.00753163
\(100\) 0 0
\(101\) 9.78384 0.973529 0.486764 0.873533i \(-0.338177\pi\)
0.486764 + 0.873533i \(0.338177\pi\)
\(102\) 0 0
\(103\) 4.25123 0.418886 0.209443 0.977821i \(-0.432835\pi\)
0.209443 + 0.977821i \(0.432835\pi\)
\(104\) 0 0
\(105\) −3.94091 −0.384594
\(106\) 0 0
\(107\) −1.22464 −0.118390 −0.0591952 0.998246i \(-0.518853\pi\)
−0.0591952 + 0.998246i \(0.518853\pi\)
\(108\) 0 0
\(109\) 9.14796 0.876216 0.438108 0.898922i \(-0.355649\pi\)
0.438108 + 0.898922i \(0.355649\pi\)
\(110\) 0 0
\(111\) −0.836975 −0.0794421
\(112\) 0 0
\(113\) 4.34210 0.408471 0.204235 0.978922i \(-0.434529\pi\)
0.204235 + 0.978922i \(0.434529\pi\)
\(114\) 0 0
\(115\) −1.31610 −0.122727
\(116\) 0 0
\(117\) −6.23970 −0.576860
\(118\) 0 0
\(119\) 2.46133 0.225629
\(120\) 0 0
\(121\) −10.9968 −0.999706
\(122\) 0 0
\(123\) −4.26743 −0.384781
\(124\) 0 0
\(125\) 10.4630 0.935843
\(126\) 0 0
\(127\) −11.1112 −0.985963 −0.492982 0.870040i \(-0.664093\pi\)
−0.492982 + 0.870040i \(0.664093\pi\)
\(128\) 0 0
\(129\) 3.61523 0.318303
\(130\) 0 0
\(131\) −1.43243 −0.125152 −0.0625759 0.998040i \(-0.519932\pi\)
−0.0625759 + 0.998040i \(0.519932\pi\)
\(132\) 0 0
\(133\) 0.686203 0.0595014
\(134\) 0 0
\(135\) −6.91293 −0.594970
\(136\) 0 0
\(137\) 9.56972 0.817596 0.408798 0.912625i \(-0.365948\pi\)
0.408798 + 0.912625i \(0.365948\pi\)
\(138\) 0 0
\(139\) 18.7075 1.58675 0.793374 0.608735i \(-0.208323\pi\)
0.793374 + 0.608735i \(0.208323\pi\)
\(140\) 0 0
\(141\) 5.32773 0.448676
\(142\) 0 0
\(143\) −0.269373 −0.0225261
\(144\) 0 0
\(145\) 8.16599 0.678148
\(146\) 0 0
\(147\) 1.22171 0.100765
\(148\) 0 0
\(149\) 12.8792 1.05511 0.527553 0.849522i \(-0.323110\pi\)
0.527553 + 0.849522i \(0.323110\pi\)
\(150\) 0 0
\(151\) −13.6159 −1.10805 −0.554023 0.832502i \(-0.686908\pi\)
−0.554023 + 0.832502i \(0.686908\pi\)
\(152\) 0 0
\(153\) 1.31752 0.106515
\(154\) 0 0
\(155\) −5.99450 −0.481490
\(156\) 0 0
\(157\) −10.6662 −0.851257 −0.425629 0.904898i \(-0.639947\pi\)
−0.425629 + 0.904898i \(0.639947\pi\)
\(158\) 0 0
\(159\) −12.1502 −0.963573
\(160\) 0 0
\(161\) −2.62425 −0.206820
\(162\) 0 0
\(163\) −17.3746 −1.36089 −0.680443 0.732801i \(-0.738212\pi\)
−0.680443 + 0.732801i \(0.738212\pi\)
\(164\) 0 0
\(165\) −0.0910702 −0.00708981
\(166\) 0 0
\(167\) −14.3787 −1.11266 −0.556330 0.830961i \(-0.687791\pi\)
−0.556330 + 0.830961i \(0.687791\pi\)
\(168\) 0 0
\(169\) 9.42907 0.725313
\(170\) 0 0
\(171\) 0.367317 0.0280895
\(172\) 0 0
\(173\) 21.9374 1.66787 0.833936 0.551861i \(-0.186082\pi\)
0.833936 + 0.551861i \(0.186082\pi\)
\(174\) 0 0
\(175\) 8.55626 0.646792
\(176\) 0 0
\(177\) 1.29710 0.0974963
\(178\) 0 0
\(179\) −23.8613 −1.78348 −0.891740 0.452549i \(-0.850515\pi\)
−0.891740 + 0.452549i \(0.850515\pi\)
\(180\) 0 0
\(181\) −12.3488 −0.917877 −0.458939 0.888468i \(-0.651770\pi\)
−0.458939 + 0.888468i \(0.651770\pi\)
\(182\) 0 0
\(183\) −12.8239 −0.947972
\(184\) 0 0
\(185\) −0.796509 −0.0585605
\(186\) 0 0
\(187\) 0.0568786 0.00415937
\(188\) 0 0
\(189\) −13.7841 −1.00265
\(190\) 0 0
\(191\) −16.5135 −1.19488 −0.597439 0.801914i \(-0.703815\pi\)
−0.597439 + 0.801914i \(0.703815\pi\)
\(192\) 0 0
\(193\) −13.3093 −0.958026 −0.479013 0.877808i \(-0.659005\pi\)
−0.479013 + 0.877808i \(0.659005\pi\)
\(194\) 0 0
\(195\) 7.58286 0.543020
\(196\) 0 0
\(197\) −0.348682 −0.0248426 −0.0124213 0.999923i \(-0.503954\pi\)
−0.0124213 + 0.999923i \(0.503954\pi\)
\(198\) 0 0
\(199\) −8.45657 −0.599470 −0.299735 0.954022i \(-0.596898\pi\)
−0.299735 + 0.954022i \(0.596898\pi\)
\(200\) 0 0
\(201\) 4.02907 0.284188
\(202\) 0 0
\(203\) 16.2827 1.14282
\(204\) 0 0
\(205\) −4.06110 −0.283640
\(206\) 0 0
\(207\) −1.40473 −0.0976358
\(208\) 0 0
\(209\) 0.0158574 0.00109688
\(210\) 0 0
\(211\) 24.9053 1.71455 0.857276 0.514858i \(-0.172155\pi\)
0.857276 + 0.514858i \(0.172155\pi\)
\(212\) 0 0
\(213\) −1.21696 −0.0833846
\(214\) 0 0
\(215\) 3.44044 0.234636
\(216\) 0 0
\(217\) −11.9528 −0.811408
\(218\) 0 0
\(219\) −6.69800 −0.452609
\(220\) 0 0
\(221\) −4.73593 −0.318573
\(222\) 0 0
\(223\) 12.8729 0.862035 0.431018 0.902343i \(-0.358155\pi\)
0.431018 + 0.902343i \(0.358155\pi\)
\(224\) 0 0
\(225\) 4.58007 0.305338
\(226\) 0 0
\(227\) −10.6341 −0.705811 −0.352905 0.935659i \(-0.614806\pi\)
−0.352905 + 0.935659i \(0.614806\pi\)
\(228\) 0 0
\(229\) −25.3482 −1.67506 −0.837529 0.546393i \(-0.816000\pi\)
−0.837529 + 0.546393i \(0.816000\pi\)
\(230\) 0 0
\(231\) −0.181590 −0.0119478
\(232\) 0 0
\(233\) −0.903128 −0.0591659 −0.0295829 0.999562i \(-0.509418\pi\)
−0.0295829 + 0.999562i \(0.509418\pi\)
\(234\) 0 0
\(235\) 5.07014 0.330740
\(236\) 0 0
\(237\) 1.94642 0.126433
\(238\) 0 0
\(239\) 7.41826 0.479847 0.239924 0.970792i \(-0.422878\pi\)
0.239924 + 0.970792i \(0.422878\pi\)
\(240\) 0 0
\(241\) −15.4288 −0.993854 −0.496927 0.867792i \(-0.665538\pi\)
−0.496927 + 0.867792i \(0.665538\pi\)
\(242\) 0 0
\(243\) −12.5054 −0.802220
\(244\) 0 0
\(245\) 1.16264 0.0742783
\(246\) 0 0
\(247\) −1.32035 −0.0840119
\(248\) 0 0
\(249\) −0.771227 −0.0488746
\(250\) 0 0
\(251\) −15.4448 −0.974867 −0.487434 0.873160i \(-0.662067\pi\)
−0.487434 + 0.873160i \(0.662067\pi\)
\(252\) 0 0
\(253\) −0.0606436 −0.00381263
\(254\) 0 0
\(255\) −1.60113 −0.100267
\(256\) 0 0
\(257\) −2.64880 −0.165228 −0.0826138 0.996582i \(-0.526327\pi\)
−0.0826138 + 0.996582i \(0.526327\pi\)
\(258\) 0 0
\(259\) −1.58821 −0.0986863
\(260\) 0 0
\(261\) 8.71594 0.539503
\(262\) 0 0
\(263\) −8.40475 −0.518259 −0.259129 0.965843i \(-0.583436\pi\)
−0.259129 + 0.965843i \(0.583436\pi\)
\(264\) 0 0
\(265\) −11.5628 −0.710294
\(266\) 0 0
\(267\) −21.3559 −1.30696
\(268\) 0 0
\(269\) −10.8550 −0.661840 −0.330920 0.943659i \(-0.607359\pi\)
−0.330920 + 0.943659i \(0.607359\pi\)
\(270\) 0 0
\(271\) −3.96028 −0.240570 −0.120285 0.992739i \(-0.538381\pi\)
−0.120285 + 0.992739i \(0.538381\pi\)
\(272\) 0 0
\(273\) 15.1199 0.915099
\(274\) 0 0
\(275\) 0.197726 0.0119233
\(276\) 0 0
\(277\) −6.36631 −0.382515 −0.191257 0.981540i \(-0.561256\pi\)
−0.191257 + 0.981540i \(0.561256\pi\)
\(278\) 0 0
\(279\) −6.39820 −0.383050
\(280\) 0 0
\(281\) −28.4860 −1.69933 −0.849667 0.527319i \(-0.823197\pi\)
−0.849667 + 0.527319i \(0.823197\pi\)
\(282\) 0 0
\(283\) 2.61282 0.155316 0.0776579 0.996980i \(-0.475256\pi\)
0.0776579 + 0.996980i \(0.475256\pi\)
\(284\) 0 0
\(285\) −0.446386 −0.0264416
\(286\) 0 0
\(287\) −8.09768 −0.477991
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 3.98075 0.233356
\(292\) 0 0
\(293\) 12.1151 0.707770 0.353885 0.935289i \(-0.384860\pi\)
0.353885 + 0.935289i \(0.384860\pi\)
\(294\) 0 0
\(295\) 1.23439 0.0718690
\(296\) 0 0
\(297\) −0.318536 −0.0184833
\(298\) 0 0
\(299\) 5.04942 0.292016
\(300\) 0 0
\(301\) 6.86010 0.395410
\(302\) 0 0
\(303\) −12.6907 −0.729059
\(304\) 0 0
\(305\) −12.2039 −0.698794
\(306\) 0 0
\(307\) −30.3898 −1.73444 −0.867220 0.497926i \(-0.834095\pi\)
−0.867220 + 0.497926i \(0.834095\pi\)
\(308\) 0 0
\(309\) −5.51429 −0.313697
\(310\) 0 0
\(311\) 25.6621 1.45516 0.727582 0.686021i \(-0.240644\pi\)
0.727582 + 0.686021i \(0.240644\pi\)
\(312\) 0 0
\(313\) 13.3777 0.756152 0.378076 0.925775i \(-0.376586\pi\)
0.378076 + 0.925775i \(0.376586\pi\)
\(314\) 0 0
\(315\) −4.00295 −0.225541
\(316\) 0 0
\(317\) −26.4148 −1.48360 −0.741801 0.670620i \(-0.766028\pi\)
−0.741801 + 0.670620i \(0.766028\pi\)
\(318\) 0 0
\(319\) 0.376275 0.0210673
\(320\) 0 0
\(321\) 1.58849 0.0886606
\(322\) 0 0
\(323\) 0.278794 0.0155125
\(324\) 0 0
\(325\) −16.4634 −0.913227
\(326\) 0 0
\(327\) −11.8659 −0.656183
\(328\) 0 0
\(329\) 10.1097 0.557364
\(330\) 0 0
\(331\) 2.69457 0.148107 0.0740534 0.997254i \(-0.476406\pi\)
0.0740534 + 0.997254i \(0.476406\pi\)
\(332\) 0 0
\(333\) −0.850150 −0.0465879
\(334\) 0 0
\(335\) 3.83427 0.209488
\(336\) 0 0
\(337\) −12.4081 −0.675911 −0.337955 0.941162i \(-0.609735\pi\)
−0.337955 + 0.941162i \(0.609735\pi\)
\(338\) 0 0
\(339\) −5.63216 −0.305897
\(340\) 0 0
\(341\) −0.276216 −0.0149579
\(342\) 0 0
\(343\) 19.5475 1.05547
\(344\) 0 0
\(345\) 1.70712 0.0919082
\(346\) 0 0
\(347\) −1.95860 −0.105143 −0.0525715 0.998617i \(-0.516742\pi\)
−0.0525715 + 0.998617i \(0.516742\pi\)
\(348\) 0 0
\(349\) 13.4538 0.720167 0.360083 0.932920i \(-0.382748\pi\)
0.360083 + 0.932920i \(0.382748\pi\)
\(350\) 0 0
\(351\) 26.5225 1.41567
\(352\) 0 0
\(353\) 4.13084 0.219862 0.109931 0.993939i \(-0.464937\pi\)
0.109931 + 0.993939i \(0.464937\pi\)
\(354\) 0 0
\(355\) −1.15812 −0.0614667
\(356\) 0 0
\(357\) −3.19260 −0.168970
\(358\) 0 0
\(359\) 15.9796 0.843372 0.421686 0.906742i \(-0.361438\pi\)
0.421686 + 0.906742i \(0.361438\pi\)
\(360\) 0 0
\(361\) −18.9223 −0.995909
\(362\) 0 0
\(363\) 14.2639 0.748663
\(364\) 0 0
\(365\) −6.37416 −0.333639
\(366\) 0 0
\(367\) −4.20086 −0.219283 −0.109642 0.993971i \(-0.534970\pi\)
−0.109642 + 0.993971i \(0.534970\pi\)
\(368\) 0 0
\(369\) −4.33460 −0.225650
\(370\) 0 0
\(371\) −23.0557 −1.19699
\(372\) 0 0
\(373\) −18.1911 −0.941898 −0.470949 0.882161i \(-0.656088\pi\)
−0.470949 + 0.882161i \(0.656088\pi\)
\(374\) 0 0
\(375\) −13.5716 −0.700837
\(376\) 0 0
\(377\) −31.3301 −1.61358
\(378\) 0 0
\(379\) −36.3502 −1.86718 −0.933592 0.358339i \(-0.883343\pi\)
−0.933592 + 0.358339i \(0.883343\pi\)
\(380\) 0 0
\(381\) 14.4124 0.738371
\(382\) 0 0
\(383\) −20.8142 −1.06356 −0.531779 0.846883i \(-0.678476\pi\)
−0.531779 + 0.846883i \(0.678476\pi\)
\(384\) 0 0
\(385\) −0.172811 −0.00880725
\(386\) 0 0
\(387\) 3.67214 0.186665
\(388\) 0 0
\(389\) −1.10874 −0.0562156 −0.0281078 0.999605i \(-0.508948\pi\)
−0.0281078 + 0.999605i \(0.508948\pi\)
\(390\) 0 0
\(391\) −1.06619 −0.0539197
\(392\) 0 0
\(393\) 1.85801 0.0937240
\(394\) 0 0
\(395\) 1.85231 0.0931999
\(396\) 0 0
\(397\) 6.78384 0.340471 0.170236 0.985403i \(-0.445547\pi\)
0.170236 + 0.985403i \(0.445547\pi\)
\(398\) 0 0
\(399\) −0.890076 −0.0445596
\(400\) 0 0
\(401\) −18.4040 −0.919052 −0.459526 0.888164i \(-0.651981\pi\)
−0.459526 + 0.888164i \(0.651981\pi\)
\(402\) 0 0
\(403\) 22.9988 1.14565
\(404\) 0 0
\(405\) 4.08777 0.203123
\(406\) 0 0
\(407\) −0.0367017 −0.00181924
\(408\) 0 0
\(409\) 27.9777 1.38341 0.691704 0.722181i \(-0.256860\pi\)
0.691704 + 0.722181i \(0.256860\pi\)
\(410\) 0 0
\(411\) −12.4129 −0.612284
\(412\) 0 0
\(413\) 2.46133 0.121114
\(414\) 0 0
\(415\) −0.733940 −0.0360277
\(416\) 0 0
\(417\) −24.2655 −1.18829
\(418\) 0 0
\(419\) −9.68779 −0.473279 −0.236640 0.971597i \(-0.576046\pi\)
−0.236640 + 0.971597i \(0.576046\pi\)
\(420\) 0 0
\(421\) −36.2543 −1.76692 −0.883462 0.468503i \(-0.844794\pi\)
−0.883462 + 0.468503i \(0.844794\pi\)
\(422\) 0 0
\(423\) 5.41160 0.263121
\(424\) 0 0
\(425\) 3.47628 0.168624
\(426\) 0 0
\(427\) −24.3341 −1.17761
\(428\) 0 0
\(429\) 0.349405 0.0168694
\(430\) 0 0
\(431\) −20.9131 −1.00735 −0.503674 0.863894i \(-0.668019\pi\)
−0.503674 + 0.863894i \(0.668019\pi\)
\(432\) 0 0
\(433\) 33.7397 1.62143 0.810713 0.585443i \(-0.199080\pi\)
0.810713 + 0.585443i \(0.199080\pi\)
\(434\) 0 0
\(435\) −10.5921 −0.507854
\(436\) 0 0
\(437\) −0.297248 −0.0142193
\(438\) 0 0
\(439\) −21.2782 −1.01555 −0.507777 0.861488i \(-0.669533\pi\)
−0.507777 + 0.861488i \(0.669533\pi\)
\(440\) 0 0
\(441\) 1.24094 0.0590923
\(442\) 0 0
\(443\) −1.49998 −0.0712660 −0.0356330 0.999365i \(-0.511345\pi\)
−0.0356330 + 0.999365i \(0.511345\pi\)
\(444\) 0 0
\(445\) −20.3234 −0.963421
\(446\) 0 0
\(447\) −16.7057 −0.790151
\(448\) 0 0
\(449\) 28.5674 1.34818 0.674090 0.738649i \(-0.264536\pi\)
0.674090 + 0.738649i \(0.264536\pi\)
\(450\) 0 0
\(451\) −0.187129 −0.00881155
\(452\) 0 0
\(453\) 17.6612 0.829796
\(454\) 0 0
\(455\) 14.3889 0.674562
\(456\) 0 0
\(457\) 28.1463 1.31663 0.658315 0.752743i \(-0.271270\pi\)
0.658315 + 0.752743i \(0.271270\pi\)
\(458\) 0 0
\(459\) −5.60027 −0.261398
\(460\) 0 0
\(461\) 15.4758 0.720782 0.360391 0.932801i \(-0.382643\pi\)
0.360391 + 0.932801i \(0.382643\pi\)
\(462\) 0 0
\(463\) −20.0767 −0.933042 −0.466521 0.884510i \(-0.654493\pi\)
−0.466521 + 0.884510i \(0.654493\pi\)
\(464\) 0 0
\(465\) 7.77548 0.360579
\(466\) 0 0
\(467\) −27.8613 −1.28927 −0.644634 0.764491i \(-0.722990\pi\)
−0.644634 + 0.764491i \(0.722990\pi\)
\(468\) 0 0
\(469\) 7.64538 0.353031
\(470\) 0 0
\(471\) 13.8352 0.637492
\(472\) 0 0
\(473\) 0.158530 0.00728920
\(474\) 0 0
\(475\) 0.969166 0.0444684
\(476\) 0 0
\(477\) −12.3415 −0.565077
\(478\) 0 0
\(479\) 12.4137 0.567198 0.283599 0.958943i \(-0.408472\pi\)
0.283599 + 0.958943i \(0.408472\pi\)
\(480\) 0 0
\(481\) 3.05593 0.139338
\(482\) 0 0
\(483\) 3.40393 0.154884
\(484\) 0 0
\(485\) 3.78829 0.172017
\(486\) 0 0
\(487\) −8.51783 −0.385980 −0.192990 0.981201i \(-0.561818\pi\)
−0.192990 + 0.981201i \(0.561818\pi\)
\(488\) 0 0
\(489\) 22.5367 1.01914
\(490\) 0 0
\(491\) −21.1020 −0.952318 −0.476159 0.879359i \(-0.657971\pi\)
−0.476159 + 0.879359i \(0.657971\pi\)
\(492\) 0 0
\(493\) 6.61540 0.297943
\(494\) 0 0
\(495\) −0.0925038 −0.00415774
\(496\) 0 0
\(497\) −2.30925 −0.103584
\(498\) 0 0
\(499\) 35.6039 1.59385 0.796925 0.604078i \(-0.206458\pi\)
0.796925 + 0.604078i \(0.206458\pi\)
\(500\) 0 0
\(501\) 18.6507 0.833253
\(502\) 0 0
\(503\) −1.21833 −0.0543226 −0.0271613 0.999631i \(-0.508647\pi\)
−0.0271613 + 0.999631i \(0.508647\pi\)
\(504\) 0 0
\(505\) −12.0771 −0.537423
\(506\) 0 0
\(507\) −12.2305 −0.543175
\(508\) 0 0
\(509\) 29.1474 1.29194 0.645969 0.763364i \(-0.276454\pi\)
0.645969 + 0.763364i \(0.276454\pi\)
\(510\) 0 0
\(511\) −12.7098 −0.562250
\(512\) 0 0
\(513\) −1.56132 −0.0689341
\(514\) 0 0
\(515\) −5.24768 −0.231240
\(516\) 0 0
\(517\) 0.233623 0.0102747
\(518\) 0 0
\(519\) −28.4551 −1.24904
\(520\) 0 0
\(521\) 27.2902 1.19561 0.597803 0.801643i \(-0.296041\pi\)
0.597803 + 0.801643i \(0.296041\pi\)
\(522\) 0 0
\(523\) −29.9036 −1.30759 −0.653796 0.756671i \(-0.726825\pi\)
−0.653796 + 0.756671i \(0.726825\pi\)
\(524\) 0 0
\(525\) −11.0984 −0.484372
\(526\) 0 0
\(527\) −4.85624 −0.211541
\(528\) 0 0
\(529\) −21.8632 −0.950575
\(530\) 0 0
\(531\) 1.31752 0.0571756
\(532\) 0 0
\(533\) 15.5811 0.674891
\(534\) 0 0
\(535\) 1.51168 0.0653558
\(536\) 0 0
\(537\) 30.9506 1.33562
\(538\) 0 0
\(539\) 0.0535724 0.00230753
\(540\) 0 0
\(541\) −4.82213 −0.207319 −0.103660 0.994613i \(-0.533055\pi\)
−0.103660 + 0.994613i \(0.533055\pi\)
\(542\) 0 0
\(543\) 16.0176 0.687383
\(544\) 0 0
\(545\) −11.2922 −0.483703
\(546\) 0 0
\(547\) 31.3028 1.33841 0.669206 0.743077i \(-0.266634\pi\)
0.669206 + 0.743077i \(0.266634\pi\)
\(548\) 0 0
\(549\) −13.0258 −0.555927
\(550\) 0 0
\(551\) 1.84433 0.0785713
\(552\) 0 0
\(553\) 3.69344 0.157061
\(554\) 0 0
\(555\) 1.03315 0.0438549
\(556\) 0 0
\(557\) 0.301869 0.0127906 0.00639529 0.999980i \(-0.497964\pi\)
0.00639529 + 0.999980i \(0.497964\pi\)
\(558\) 0 0
\(559\) −13.1998 −0.558292
\(560\) 0 0
\(561\) −0.0737774 −0.00311489
\(562\) 0 0
\(563\) 4.21394 0.177596 0.0887981 0.996050i \(-0.471697\pi\)
0.0887981 + 0.996050i \(0.471697\pi\)
\(564\) 0 0
\(565\) −5.35985 −0.225491
\(566\) 0 0
\(567\) 8.15085 0.342304
\(568\) 0 0
\(569\) 39.7024 1.66441 0.832205 0.554468i \(-0.187078\pi\)
0.832205 + 0.554468i \(0.187078\pi\)
\(570\) 0 0
\(571\) −35.0906 −1.46850 −0.734248 0.678881i \(-0.762465\pi\)
−0.734248 + 0.678881i \(0.762465\pi\)
\(572\) 0 0
\(573\) 21.4198 0.894824
\(574\) 0 0
\(575\) −3.70639 −0.154567
\(576\) 0 0
\(577\) −15.0787 −0.627733 −0.313867 0.949467i \(-0.601624\pi\)
−0.313867 + 0.949467i \(0.601624\pi\)
\(578\) 0 0
\(579\) 17.2636 0.717449
\(580\) 0 0
\(581\) −1.46345 −0.0607140
\(582\) 0 0
\(583\) −0.532792 −0.0220660
\(584\) 0 0
\(585\) 7.70223 0.318448
\(586\) 0 0
\(587\) 21.0474 0.868718 0.434359 0.900740i \(-0.356975\pi\)
0.434359 + 0.900740i \(0.356975\pi\)
\(588\) 0 0
\(589\) −1.35389 −0.0557861
\(590\) 0 0
\(591\) 0.452277 0.0186042
\(592\) 0 0
\(593\) −46.2794 −1.90047 −0.950234 0.311538i \(-0.899156\pi\)
−0.950234 + 0.311538i \(0.899156\pi\)
\(594\) 0 0
\(595\) −3.03824 −0.124556
\(596\) 0 0
\(597\) 10.9690 0.448933
\(598\) 0 0
\(599\) −5.37923 −0.219789 −0.109895 0.993943i \(-0.535051\pi\)
−0.109895 + 0.993943i \(0.535051\pi\)
\(600\) 0 0
\(601\) 24.2604 0.989603 0.494801 0.869006i \(-0.335241\pi\)
0.494801 + 0.869006i \(0.335241\pi\)
\(602\) 0 0
\(603\) 4.09249 0.166659
\(604\) 0 0
\(605\) 13.5743 0.551874
\(606\) 0 0
\(607\) −5.00634 −0.203201 −0.101601 0.994825i \(-0.532396\pi\)
−0.101601 + 0.994825i \(0.532396\pi\)
\(608\) 0 0
\(609\) −21.1203 −0.855837
\(610\) 0 0
\(611\) −19.4524 −0.786960
\(612\) 0 0
\(613\) 14.1069 0.569771 0.284886 0.958562i \(-0.408044\pi\)
0.284886 + 0.958562i \(0.408044\pi\)
\(614\) 0 0
\(615\) 5.26767 0.212413
\(616\) 0 0
\(617\) 33.7805 1.35995 0.679976 0.733234i \(-0.261990\pi\)
0.679976 + 0.733234i \(0.261990\pi\)
\(618\) 0 0
\(619\) 13.2756 0.533591 0.266796 0.963753i \(-0.414035\pi\)
0.266796 + 0.963753i \(0.414035\pi\)
\(620\) 0 0
\(621\) 5.97098 0.239607
\(622\) 0 0
\(623\) −40.5240 −1.62356
\(624\) 0 0
\(625\) 4.46591 0.178636
\(626\) 0 0
\(627\) −0.0205687 −0.000821435 0
\(628\) 0 0
\(629\) −0.645264 −0.0257284
\(630\) 0 0
\(631\) −20.8175 −0.828731 −0.414366 0.910110i \(-0.635997\pi\)
−0.414366 + 0.910110i \(0.635997\pi\)
\(632\) 0 0
\(633\) −32.3048 −1.28400
\(634\) 0 0
\(635\) 13.7156 0.544288
\(636\) 0 0
\(637\) −4.46065 −0.176737
\(638\) 0 0
\(639\) −1.23612 −0.0489000
\(640\) 0 0
\(641\) 23.0983 0.912327 0.456164 0.889896i \(-0.349223\pi\)
0.456164 + 0.889896i \(0.349223\pi\)
\(642\) 0 0
\(643\) 10.1158 0.398927 0.199464 0.979905i \(-0.436080\pi\)
0.199464 + 0.979905i \(0.436080\pi\)
\(644\) 0 0
\(645\) −4.46261 −0.175715
\(646\) 0 0
\(647\) 3.05842 0.120239 0.0601195 0.998191i \(-0.480852\pi\)
0.0601195 + 0.998191i \(0.480852\pi\)
\(648\) 0 0
\(649\) 0.0568786 0.00223268
\(650\) 0 0
\(651\) 15.5040 0.607650
\(652\) 0 0
\(653\) −20.5635 −0.804713 −0.402356 0.915483i \(-0.631809\pi\)
−0.402356 + 0.915483i \(0.631809\pi\)
\(654\) 0 0
\(655\) 1.76818 0.0690883
\(656\) 0 0
\(657\) −6.80344 −0.265427
\(658\) 0 0
\(659\) −39.1876 −1.52653 −0.763266 0.646085i \(-0.776405\pi\)
−0.763266 + 0.646085i \(0.776405\pi\)
\(660\) 0 0
\(661\) −13.8958 −0.540483 −0.270241 0.962793i \(-0.587103\pi\)
−0.270241 + 0.962793i \(0.587103\pi\)
\(662\) 0 0
\(663\) 6.14300 0.238574
\(664\) 0 0
\(665\) −0.847043 −0.0328469
\(666\) 0 0
\(667\) −7.05330 −0.273105
\(668\) 0 0
\(669\) −16.6975 −0.645564
\(670\) 0 0
\(671\) −0.562335 −0.0217087
\(672\) 0 0
\(673\) 28.1016 1.08324 0.541619 0.840624i \(-0.317812\pi\)
0.541619 + 0.840624i \(0.317812\pi\)
\(674\) 0 0
\(675\) −19.4681 −0.749328
\(676\) 0 0
\(677\) −17.3079 −0.665197 −0.332599 0.943069i \(-0.607925\pi\)
−0.332599 + 0.943069i \(0.607925\pi\)
\(678\) 0 0
\(679\) 7.55370 0.289885
\(680\) 0 0
\(681\) 13.7935 0.528570
\(682\) 0 0
\(683\) 4.64602 0.177775 0.0888875 0.996042i \(-0.471669\pi\)
0.0888875 + 0.996042i \(0.471669\pi\)
\(684\) 0 0
\(685\) −11.8128 −0.451343
\(686\) 0 0
\(687\) 32.8793 1.25442
\(688\) 0 0
\(689\) 44.3623 1.69007
\(690\) 0 0
\(691\) 31.2186 1.18761 0.593806 0.804609i \(-0.297625\pi\)
0.593806 + 0.804609i \(0.297625\pi\)
\(692\) 0 0
\(693\) −0.184449 −0.00700663
\(694\) 0 0
\(695\) −23.0923 −0.875943
\(696\) 0 0
\(697\) −3.28997 −0.124616
\(698\) 0 0
\(699\) 1.17145 0.0443083
\(700\) 0 0
\(701\) 47.6324 1.79905 0.899525 0.436870i \(-0.143913\pi\)
0.899525 + 0.436870i \(0.143913\pi\)
\(702\) 0 0
\(703\) −0.179896 −0.00678490
\(704\) 0 0
\(705\) −6.57650 −0.247685
\(706\) 0 0
\(707\) −24.0812 −0.905668
\(708\) 0 0
\(709\) −34.7195 −1.30392 −0.651958 0.758255i \(-0.726052\pi\)
−0.651958 + 0.758255i \(0.726052\pi\)
\(710\) 0 0
\(711\) 1.97706 0.0741455
\(712\) 0 0
\(713\) 5.17769 0.193906
\(714\) 0 0
\(715\) 0.332512 0.0124352
\(716\) 0 0
\(717\) −9.62225 −0.359350
\(718\) 0 0
\(719\) −37.8312 −1.41087 −0.705433 0.708777i \(-0.749247\pi\)
−0.705433 + 0.708777i \(0.749247\pi\)
\(720\) 0 0
\(721\) −10.4637 −0.389687
\(722\) 0 0
\(723\) 20.0127 0.744280
\(724\) 0 0
\(725\) 22.9970 0.854086
\(726\) 0 0
\(727\) 24.6336 0.913610 0.456805 0.889567i \(-0.348994\pi\)
0.456805 + 0.889567i \(0.348994\pi\)
\(728\) 0 0
\(729\) 26.1555 0.968721
\(730\) 0 0
\(731\) 2.78716 0.103087
\(732\) 0 0
\(733\) −30.3216 −1.11995 −0.559977 0.828508i \(-0.689190\pi\)
−0.559977 + 0.828508i \(0.689190\pi\)
\(734\) 0 0
\(735\) −1.50806 −0.0556257
\(736\) 0 0
\(737\) 0.176676 0.00650796
\(738\) 0 0
\(739\) −15.2402 −0.560618 −0.280309 0.959910i \(-0.590437\pi\)
−0.280309 + 0.959910i \(0.590437\pi\)
\(740\) 0 0
\(741\) 1.71263 0.0629151
\(742\) 0 0
\(743\) 2.24737 0.0824480 0.0412240 0.999150i \(-0.486874\pi\)
0.0412240 + 0.999150i \(0.486874\pi\)
\(744\) 0 0
\(745\) −15.8980 −0.582457
\(746\) 0 0
\(747\) −0.783368 −0.0286619
\(748\) 0 0
\(749\) 3.01424 0.110138
\(750\) 0 0
\(751\) 12.1025 0.441625 0.220812 0.975316i \(-0.429129\pi\)
0.220812 + 0.975316i \(0.429129\pi\)
\(752\) 0 0
\(753\) 20.0335 0.730062
\(754\) 0 0
\(755\) 16.8073 0.611681
\(756\) 0 0
\(757\) −35.5942 −1.29369 −0.646846 0.762621i \(-0.723912\pi\)
−0.646846 + 0.762621i \(0.723912\pi\)
\(758\) 0 0
\(759\) 0.0786611 0.00285522
\(760\) 0 0
\(761\) −53.5622 −1.94163 −0.970815 0.239832i \(-0.922908\pi\)
−0.970815 + 0.239832i \(0.922908\pi\)
\(762\) 0 0
\(763\) −22.5161 −0.815138
\(764\) 0 0
\(765\) −1.62634 −0.0588004
\(766\) 0 0
\(767\) −4.73593 −0.171005
\(768\) 0 0
\(769\) −44.1430 −1.59184 −0.795918 0.605404i \(-0.793011\pi\)
−0.795918 + 0.605404i \(0.793011\pi\)
\(770\) 0 0
\(771\) 3.43577 0.123736
\(772\) 0 0
\(773\) −31.3459 −1.12743 −0.563717 0.825968i \(-0.690629\pi\)
−0.563717 + 0.825968i \(0.690629\pi\)
\(774\) 0 0
\(775\) −16.8816 −0.606407
\(776\) 0 0
\(777\) 2.06007 0.0739045
\(778\) 0 0
\(779\) −0.917223 −0.0328629
\(780\) 0 0
\(781\) −0.0533642 −0.00190952
\(782\) 0 0
\(783\) −37.0480 −1.32399
\(784\) 0 0
\(785\) 13.1663 0.469925
\(786\) 0 0
\(787\) 22.3412 0.796378 0.398189 0.917303i \(-0.369639\pi\)
0.398189 + 0.917303i \(0.369639\pi\)
\(788\) 0 0
\(789\) 10.9018 0.388115
\(790\) 0 0
\(791\) −10.6873 −0.379998
\(792\) 0 0
\(793\) 46.8222 1.66271
\(794\) 0 0
\(795\) 14.9981 0.531927
\(796\) 0 0
\(797\) 20.3273 0.720030 0.360015 0.932946i \(-0.382771\pi\)
0.360015 + 0.932946i \(0.382771\pi\)
\(798\) 0 0
\(799\) 4.10740 0.145310
\(800\) 0 0
\(801\) −21.6921 −0.766452
\(802\) 0 0
\(803\) −0.293710 −0.0103648
\(804\) 0 0
\(805\) 3.23935 0.114172
\(806\) 0 0
\(807\) 14.0800 0.495641
\(808\) 0 0
\(809\) −20.4906 −0.720410 −0.360205 0.932873i \(-0.617293\pi\)
−0.360205 + 0.932873i \(0.617293\pi\)
\(810\) 0 0
\(811\) −30.7105 −1.07839 −0.539196 0.842180i \(-0.681272\pi\)
−0.539196 + 0.842180i \(0.681272\pi\)
\(812\) 0 0
\(813\) 5.13689 0.180159
\(814\) 0 0
\(815\) 21.4471 0.751258
\(816\) 0 0
\(817\) 0.777043 0.0271853
\(818\) 0 0
\(819\) 15.3579 0.536650
\(820\) 0 0
\(821\) −23.1768 −0.808876 −0.404438 0.914566i \(-0.632533\pi\)
−0.404438 + 0.914566i \(0.632533\pi\)
\(822\) 0 0
\(823\) −1.00721 −0.0351093 −0.0175546 0.999846i \(-0.505588\pi\)
−0.0175546 + 0.999846i \(0.505588\pi\)
\(824\) 0 0
\(825\) −0.256471 −0.00892917
\(826\) 0 0
\(827\) −0.370447 −0.0128817 −0.00644085 0.999979i \(-0.502050\pi\)
−0.00644085 + 0.999979i \(0.502050\pi\)
\(828\) 0 0
\(829\) −8.66441 −0.300927 −0.150464 0.988616i \(-0.548077\pi\)
−0.150464 + 0.988616i \(0.548077\pi\)
\(830\) 0 0
\(831\) 8.25776 0.286459
\(832\) 0 0
\(833\) 0.941872 0.0326339
\(834\) 0 0
\(835\) 17.7490 0.614229
\(836\) 0 0
\(837\) 27.1963 0.940041
\(838\) 0 0
\(839\) −27.9570 −0.965184 −0.482592 0.875845i \(-0.660305\pi\)
−0.482592 + 0.875845i \(0.660305\pi\)
\(840\) 0 0
\(841\) 14.7635 0.509086
\(842\) 0 0
\(843\) 36.9493 1.27260
\(844\) 0 0
\(845\) −11.6392 −0.400399
\(846\) 0 0
\(847\) 27.0666 0.930020
\(848\) 0 0
\(849\) −3.38909 −0.116313
\(850\) 0 0
\(851\) 0.687977 0.0235835
\(852\) 0 0
\(853\) −16.9894 −0.581705 −0.290852 0.956768i \(-0.593939\pi\)
−0.290852 + 0.956768i \(0.593939\pi\)
\(854\) 0 0
\(855\) −0.453413 −0.0155064
\(856\) 0 0
\(857\) −2.37942 −0.0812794 −0.0406397 0.999174i \(-0.512940\pi\)
−0.0406397 + 0.999174i \(0.512940\pi\)
\(858\) 0 0
\(859\) −34.4718 −1.17616 −0.588082 0.808801i \(-0.700117\pi\)
−0.588082 + 0.808801i \(0.700117\pi\)
\(860\) 0 0
\(861\) 10.5035 0.357959
\(862\) 0 0
\(863\) −1.14835 −0.0390903 −0.0195452 0.999809i \(-0.506222\pi\)
−0.0195452 + 0.999809i \(0.506222\pi\)
\(864\) 0 0
\(865\) −27.0794 −0.920726
\(866\) 0 0
\(867\) −1.29710 −0.0440519
\(868\) 0 0
\(869\) 0.0853513 0.00289535
\(870\) 0 0
\(871\) −14.7108 −0.498456
\(872\) 0 0
\(873\) 4.04342 0.136849
\(874\) 0 0
\(875\) −25.7530 −0.870609
\(876\) 0 0
\(877\) −23.1612 −0.782099 −0.391050 0.920370i \(-0.627888\pi\)
−0.391050 + 0.920370i \(0.627888\pi\)
\(878\) 0 0
\(879\) −15.7145 −0.530037
\(880\) 0 0
\(881\) 33.9290 1.14310 0.571548 0.820569i \(-0.306343\pi\)
0.571548 + 0.820569i \(0.306343\pi\)
\(882\) 0 0
\(883\) 26.0128 0.875399 0.437699 0.899121i \(-0.355793\pi\)
0.437699 + 0.899121i \(0.355793\pi\)
\(884\) 0 0
\(885\) −1.60113 −0.0538215
\(886\) 0 0
\(887\) 28.4546 0.955414 0.477707 0.878519i \(-0.341468\pi\)
0.477707 + 0.878519i \(0.341468\pi\)
\(888\) 0 0
\(889\) 27.3484 0.917236
\(890\) 0 0
\(891\) 0.188357 0.00631021
\(892\) 0 0
\(893\) 1.14512 0.0383200
\(894\) 0 0
\(895\) 29.4542 0.984546
\(896\) 0 0
\(897\) −6.54963 −0.218686
\(898\) 0 0
\(899\) −32.1260 −1.07146
\(900\) 0 0
\(901\) −9.36717 −0.312066
\(902\) 0 0
\(903\) −8.89826 −0.296116
\(904\) 0 0
\(905\) 15.2432 0.506702
\(906\) 0 0
\(907\) −8.04234 −0.267041 −0.133521 0.991046i \(-0.542628\pi\)
−0.133521 + 0.991046i \(0.542628\pi\)
\(908\) 0 0
\(909\) −12.8904 −0.427549
\(910\) 0 0
\(911\) 42.6491 1.41303 0.706513 0.707700i \(-0.250267\pi\)
0.706513 + 0.707700i \(0.250267\pi\)
\(912\) 0 0
\(913\) −0.0338187 −0.00111924
\(914\) 0 0
\(915\) 15.8297 0.523315
\(916\) 0 0
\(917\) 3.52567 0.116428
\(918\) 0 0
\(919\) −46.8344 −1.54492 −0.772462 0.635061i \(-0.780975\pi\)
−0.772462 + 0.635061i \(0.780975\pi\)
\(920\) 0 0
\(921\) 39.4188 1.29889
\(922\) 0 0
\(923\) 4.44331 0.146253
\(924\) 0 0
\(925\) −2.24312 −0.0737533
\(926\) 0 0
\(927\) −5.60109 −0.183964
\(928\) 0 0
\(929\) 12.7665 0.418855 0.209428 0.977824i \(-0.432840\pi\)
0.209428 + 0.977824i \(0.432840\pi\)
\(930\) 0 0
\(931\) 0.262588 0.00860599
\(932\) 0 0
\(933\) −33.2864 −1.08975
\(934\) 0 0
\(935\) −0.0702104 −0.00229613
\(936\) 0 0
\(937\) 42.0096 1.37239 0.686197 0.727415i \(-0.259279\pi\)
0.686197 + 0.727415i \(0.259279\pi\)
\(938\) 0 0
\(939\) −17.3522 −0.566269
\(940\) 0 0
\(941\) −7.12858 −0.232385 −0.116193 0.993227i \(-0.537069\pi\)
−0.116193 + 0.993227i \(0.537069\pi\)
\(942\) 0 0
\(943\) 3.50774 0.114228
\(944\) 0 0
\(945\) 17.0150 0.553497
\(946\) 0 0
\(947\) 31.2060 1.01406 0.507029 0.861929i \(-0.330744\pi\)
0.507029 + 0.861929i \(0.330744\pi\)
\(948\) 0 0
\(949\) 24.4555 0.793858
\(950\) 0 0
\(951\) 34.2627 1.11104
\(952\) 0 0
\(953\) 26.9057 0.871562 0.435781 0.900053i \(-0.356472\pi\)
0.435781 + 0.900053i \(0.356472\pi\)
\(954\) 0 0
\(955\) 20.3842 0.659616
\(956\) 0 0
\(957\) −0.488067 −0.0157770
\(958\) 0 0
\(959\) −23.5542 −0.760605
\(960\) 0 0
\(961\) −7.41694 −0.239256
\(962\) 0 0
\(963\) 1.61349 0.0519940
\(964\) 0 0
\(965\) 16.4289 0.528865
\(966\) 0 0
\(967\) 55.0536 1.77040 0.885202 0.465208i \(-0.154020\pi\)
0.885202 + 0.465208i \(0.154020\pi\)
\(968\) 0 0
\(969\) −0.361625 −0.0116171
\(970\) 0 0
\(971\) −51.5144 −1.65317 −0.826587 0.562808i \(-0.809721\pi\)
−0.826587 + 0.562808i \(0.809721\pi\)
\(972\) 0 0
\(973\) −46.0452 −1.47614
\(974\) 0 0
\(975\) 21.3548 0.683900
\(976\) 0 0
\(977\) 6.46003 0.206675 0.103337 0.994646i \(-0.467048\pi\)
0.103337 + 0.994646i \(0.467048\pi\)
\(978\) 0 0
\(979\) −0.936467 −0.0299296
\(980\) 0 0
\(981\) −12.0526 −0.384811
\(982\) 0 0
\(983\) 8.87906 0.283198 0.141599 0.989924i \(-0.454776\pi\)
0.141599 + 0.989924i \(0.454776\pi\)
\(984\) 0 0
\(985\) 0.430410 0.0137140
\(986\) 0 0
\(987\) −13.1133 −0.417400
\(988\) 0 0
\(989\) −2.97165 −0.0944930
\(990\) 0 0
\(991\) −31.5625 −1.00261 −0.501307 0.865269i \(-0.667147\pi\)
−0.501307 + 0.865269i \(0.667147\pi\)
\(992\) 0 0
\(993\) −3.49513 −0.110915
\(994\) 0 0
\(995\) 10.4387 0.330929
\(996\) 0 0
\(997\) 30.7798 0.974806 0.487403 0.873177i \(-0.337944\pi\)
0.487403 + 0.873177i \(0.337944\pi\)
\(998\) 0 0
\(999\) 3.61366 0.114331
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 \(a_p\))