Properties

Label 8004.2.a.j.1.16
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(4.22634\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+4.22634 q^{5}\) \(+0.695618 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+4.22634 q^{5}\) \(+0.695618 q^{7}\) \(+1.00000 q^{9}\) \(+0.705979 q^{11}\) \(+2.93006 q^{13}\) \(+4.22634 q^{15}\) \(-6.80181 q^{17}\) \(+1.49499 q^{19}\) \(+0.695618 q^{21}\) \(+1.00000 q^{23}\) \(+12.8620 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-9.11330 q^{31}\) \(+0.705979 q^{33}\) \(+2.93992 q^{35}\) \(+10.9094 q^{37}\) \(+2.93006 q^{39}\) \(-2.16716 q^{41}\) \(+10.9369 q^{43}\) \(+4.22634 q^{45}\) \(-2.16821 q^{47}\) \(-6.51612 q^{49}\) \(-6.80181 q^{51}\) \(-1.12487 q^{53}\) \(+2.98371 q^{55}\) \(+1.49499 q^{57}\) \(-5.06726 q^{59}\) \(+13.4066 q^{61}\) \(+0.695618 q^{63}\) \(+12.3834 q^{65}\) \(+2.02926 q^{67}\) \(+1.00000 q^{69}\) \(-11.3044 q^{71}\) \(+9.21704 q^{73}\) \(+12.8620 q^{75}\) \(+0.491092 q^{77}\) \(+2.34097 q^{79}\) \(+1.00000 q^{81}\) \(+12.9043 q^{83}\) \(-28.7468 q^{85}\) \(-1.00000 q^{87}\) \(+6.64596 q^{89}\) \(+2.03820 q^{91}\) \(-9.11330 q^{93}\) \(+6.31836 q^{95}\) \(+9.49623 q^{97}\) \(+0.705979 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 4.22634 1.89008 0.945039 0.326958i \(-0.106023\pi\)
0.945039 + 0.326958i \(0.106023\pi\)
\(6\) 0 0
\(7\) 0.695618 0.262919 0.131459 0.991322i \(-0.458034\pi\)
0.131459 + 0.991322i \(0.458034\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.705979 0.212861 0.106430 0.994320i \(-0.466058\pi\)
0.106430 + 0.994320i \(0.466058\pi\)
\(12\) 0 0
\(13\) 2.93006 0.812651 0.406326 0.913728i \(-0.366810\pi\)
0.406326 + 0.913728i \(0.366810\pi\)
\(14\) 0 0
\(15\) 4.22634 1.09124
\(16\) 0 0
\(17\) −6.80181 −1.64968 −0.824840 0.565366i \(-0.808735\pi\)
−0.824840 + 0.565366i \(0.808735\pi\)
\(18\) 0 0
\(19\) 1.49499 0.342975 0.171488 0.985186i \(-0.445143\pi\)
0.171488 + 0.985186i \(0.445143\pi\)
\(20\) 0 0
\(21\) 0.695618 0.151796
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 12.8620 2.57240
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −9.11330 −1.63680 −0.818399 0.574651i \(-0.805138\pi\)
−0.818399 + 0.574651i \(0.805138\pi\)
\(32\) 0 0
\(33\) 0.705979 0.122895
\(34\) 0 0
\(35\) 2.93992 0.496937
\(36\) 0 0
\(37\) 10.9094 1.79349 0.896744 0.442550i \(-0.145926\pi\)
0.896744 + 0.442550i \(0.145926\pi\)
\(38\) 0 0
\(39\) 2.93006 0.469184
\(40\) 0 0
\(41\) −2.16716 −0.338453 −0.169226 0.985577i \(-0.554127\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(42\) 0 0
\(43\) 10.9369 1.66785 0.833927 0.551875i \(-0.186087\pi\)
0.833927 + 0.551875i \(0.186087\pi\)
\(44\) 0 0
\(45\) 4.22634 0.630026
\(46\) 0 0
\(47\) −2.16821 −0.316267 −0.158133 0.987418i \(-0.550548\pi\)
−0.158133 + 0.987418i \(0.550548\pi\)
\(48\) 0 0
\(49\) −6.51612 −0.930874
\(50\) 0 0
\(51\) −6.80181 −0.952444
\(52\) 0 0
\(53\) −1.12487 −0.154513 −0.0772564 0.997011i \(-0.524616\pi\)
−0.0772564 + 0.997011i \(0.524616\pi\)
\(54\) 0 0
\(55\) 2.98371 0.402323
\(56\) 0 0
\(57\) 1.49499 0.198017
\(58\) 0 0
\(59\) −5.06726 −0.659702 −0.329851 0.944033i \(-0.606998\pi\)
−0.329851 + 0.944033i \(0.606998\pi\)
\(60\) 0 0
\(61\) 13.4066 1.71655 0.858273 0.513194i \(-0.171538\pi\)
0.858273 + 0.513194i \(0.171538\pi\)
\(62\) 0 0
\(63\) 0.695618 0.0876396
\(64\) 0 0
\(65\) 12.3834 1.53597
\(66\) 0 0
\(67\) 2.02926 0.247914 0.123957 0.992288i \(-0.460442\pi\)
0.123957 + 0.992288i \(0.460442\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −11.3044 −1.34159 −0.670794 0.741644i \(-0.734046\pi\)
−0.670794 + 0.741644i \(0.734046\pi\)
\(72\) 0 0
\(73\) 9.21704 1.07877 0.539387 0.842058i \(-0.318656\pi\)
0.539387 + 0.842058i \(0.318656\pi\)
\(74\) 0 0
\(75\) 12.8620 1.48517
\(76\) 0 0
\(77\) 0.491092 0.0559651
\(78\) 0 0
\(79\) 2.34097 0.263380 0.131690 0.991291i \(-0.457960\pi\)
0.131690 + 0.991291i \(0.457960\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.9043 1.41643 0.708215 0.705996i \(-0.249501\pi\)
0.708215 + 0.705996i \(0.249501\pi\)
\(84\) 0 0
\(85\) −28.7468 −3.11803
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 6.64596 0.704471 0.352235 0.935911i \(-0.385422\pi\)
0.352235 + 0.935911i \(0.385422\pi\)
\(90\) 0 0
\(91\) 2.03820 0.213661
\(92\) 0 0
\(93\) −9.11330 −0.945006
\(94\) 0 0
\(95\) 6.31836 0.648250
\(96\) 0 0
\(97\) 9.49623 0.964196 0.482098 0.876117i \(-0.339875\pi\)
0.482098 + 0.876117i \(0.339875\pi\)
\(98\) 0 0
\(99\) 0.705979 0.0709535
\(100\) 0 0
\(101\) −3.11003 −0.309460 −0.154730 0.987957i \(-0.549451\pi\)
−0.154730 + 0.987957i \(0.549451\pi\)
\(102\) 0 0
\(103\) −2.89095 −0.284854 −0.142427 0.989805i \(-0.545491\pi\)
−0.142427 + 0.989805i \(0.545491\pi\)
\(104\) 0 0
\(105\) 2.93992 0.286907
\(106\) 0 0
\(107\) 9.92832 0.959807 0.479904 0.877321i \(-0.340672\pi\)
0.479904 + 0.877321i \(0.340672\pi\)
\(108\) 0 0
\(109\) −7.37977 −0.706854 −0.353427 0.935462i \(-0.614984\pi\)
−0.353427 + 0.935462i \(0.614984\pi\)
\(110\) 0 0
\(111\) 10.9094 1.03547
\(112\) 0 0
\(113\) 11.1473 1.04865 0.524325 0.851518i \(-0.324318\pi\)
0.524325 + 0.851518i \(0.324318\pi\)
\(114\) 0 0
\(115\) 4.22634 0.394109
\(116\) 0 0
\(117\) 2.93006 0.270884
\(118\) 0 0
\(119\) −4.73146 −0.433732
\(120\) 0 0
\(121\) −10.5016 −0.954690
\(122\) 0 0
\(123\) −2.16716 −0.195406
\(124\) 0 0
\(125\) 33.2274 2.97195
\(126\) 0 0
\(127\) 15.1490 1.34426 0.672130 0.740433i \(-0.265380\pi\)
0.672130 + 0.740433i \(0.265380\pi\)
\(128\) 0 0
\(129\) 10.9369 0.962936
\(130\) 0 0
\(131\) −20.2752 −1.77145 −0.885725 0.464210i \(-0.846338\pi\)
−0.885725 + 0.464210i \(0.846338\pi\)
\(132\) 0 0
\(133\) 1.03995 0.0901747
\(134\) 0 0
\(135\) 4.22634 0.363746
\(136\) 0 0
\(137\) 15.6266 1.33507 0.667536 0.744577i \(-0.267349\pi\)
0.667536 + 0.744577i \(0.267349\pi\)
\(138\) 0 0
\(139\) −18.6584 −1.58258 −0.791290 0.611440i \(-0.790590\pi\)
−0.791290 + 0.611440i \(0.790590\pi\)
\(140\) 0 0
\(141\) −2.16821 −0.182597
\(142\) 0 0
\(143\) 2.06856 0.172981
\(144\) 0 0
\(145\) −4.22634 −0.350979
\(146\) 0 0
\(147\) −6.51612 −0.537440
\(148\) 0 0
\(149\) 10.1880 0.834634 0.417317 0.908761i \(-0.362970\pi\)
0.417317 + 0.908761i \(0.362970\pi\)
\(150\) 0 0
\(151\) 6.23078 0.507054 0.253527 0.967328i \(-0.418409\pi\)
0.253527 + 0.967328i \(0.418409\pi\)
\(152\) 0 0
\(153\) −6.80181 −0.549894
\(154\) 0 0
\(155\) −38.5159 −3.09368
\(156\) 0 0
\(157\) −7.78900 −0.621630 −0.310815 0.950470i \(-0.600602\pi\)
−0.310815 + 0.950470i \(0.600602\pi\)
\(158\) 0 0
\(159\) −1.12487 −0.0892080
\(160\) 0 0
\(161\) 0.695618 0.0548224
\(162\) 0 0
\(163\) 22.8277 1.78800 0.894000 0.448066i \(-0.147887\pi\)
0.894000 + 0.448066i \(0.147887\pi\)
\(164\) 0 0
\(165\) 2.98371 0.232281
\(166\) 0 0
\(167\) 8.77045 0.678678 0.339339 0.940664i \(-0.389797\pi\)
0.339339 + 0.940664i \(0.389797\pi\)
\(168\) 0 0
\(169\) −4.41477 −0.339598
\(170\) 0 0
\(171\) 1.49499 0.114325
\(172\) 0 0
\(173\) −7.72555 −0.587363 −0.293681 0.955903i \(-0.594880\pi\)
−0.293681 + 0.955903i \(0.594880\pi\)
\(174\) 0 0
\(175\) 8.94702 0.676331
\(176\) 0 0
\(177\) −5.06726 −0.380879
\(178\) 0 0
\(179\) −14.1011 −1.05397 −0.526983 0.849876i \(-0.676677\pi\)
−0.526983 + 0.849876i \(0.676677\pi\)
\(180\) 0 0
\(181\) −6.96073 −0.517387 −0.258694 0.965959i \(-0.583292\pi\)
−0.258694 + 0.965959i \(0.583292\pi\)
\(182\) 0 0
\(183\) 13.4066 0.991048
\(184\) 0 0
\(185\) 46.1067 3.38983
\(186\) 0 0
\(187\) −4.80193 −0.351152
\(188\) 0 0
\(189\) 0.695618 0.0505988
\(190\) 0 0
\(191\) 6.81656 0.493229 0.246615 0.969114i \(-0.420682\pi\)
0.246615 + 0.969114i \(0.420682\pi\)
\(192\) 0 0
\(193\) −14.8527 −1.06912 −0.534559 0.845131i \(-0.679522\pi\)
−0.534559 + 0.845131i \(0.679522\pi\)
\(194\) 0 0
\(195\) 12.3834 0.886795
\(196\) 0 0
\(197\) 3.40123 0.242328 0.121164 0.992633i \(-0.461337\pi\)
0.121164 + 0.992633i \(0.461337\pi\)
\(198\) 0 0
\(199\) 12.0542 0.854498 0.427249 0.904134i \(-0.359483\pi\)
0.427249 + 0.904134i \(0.359483\pi\)
\(200\) 0 0
\(201\) 2.02926 0.143133
\(202\) 0 0
\(203\) −0.695618 −0.0488228
\(204\) 0 0
\(205\) −9.15914 −0.639702
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 1.05543 0.0730059
\(210\) 0 0
\(211\) 2.91873 0.200934 0.100467 0.994940i \(-0.467966\pi\)
0.100467 + 0.994940i \(0.467966\pi\)
\(212\) 0 0
\(213\) −11.3044 −0.774566
\(214\) 0 0
\(215\) 46.2229 3.15237
\(216\) 0 0
\(217\) −6.33938 −0.430345
\(218\) 0 0
\(219\) 9.21704 0.622830
\(220\) 0 0
\(221\) −19.9297 −1.34061
\(222\) 0 0
\(223\) 0.890415 0.0596266 0.0298133 0.999555i \(-0.490509\pi\)
0.0298133 + 0.999555i \(0.490509\pi\)
\(224\) 0 0
\(225\) 12.8620 0.857465
\(226\) 0 0
\(227\) −2.10706 −0.139851 −0.0699254 0.997552i \(-0.522276\pi\)
−0.0699254 + 0.997552i \(0.522276\pi\)
\(228\) 0 0
\(229\) −18.5927 −1.22864 −0.614319 0.789058i \(-0.710569\pi\)
−0.614319 + 0.789058i \(0.710569\pi\)
\(230\) 0 0
\(231\) 0.491092 0.0323115
\(232\) 0 0
\(233\) −25.9081 −1.69730 −0.848649 0.528956i \(-0.822584\pi\)
−0.848649 + 0.528956i \(0.822584\pi\)
\(234\) 0 0
\(235\) −9.16362 −0.597768
\(236\) 0 0
\(237\) 2.34097 0.152063
\(238\) 0 0
\(239\) −21.7029 −1.40384 −0.701921 0.712255i \(-0.747674\pi\)
−0.701921 + 0.712255i \(0.747674\pi\)
\(240\) 0 0
\(241\) 9.64217 0.621107 0.310553 0.950556i \(-0.399486\pi\)
0.310553 + 0.950556i \(0.399486\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −27.5393 −1.75942
\(246\) 0 0
\(247\) 4.38042 0.278719
\(248\) 0 0
\(249\) 12.9043 0.817777
\(250\) 0 0
\(251\) −23.9646 −1.51263 −0.756315 0.654208i \(-0.773002\pi\)
−0.756315 + 0.654208i \(0.773002\pi\)
\(252\) 0 0
\(253\) 0.705979 0.0443845
\(254\) 0 0
\(255\) −28.7468 −1.80019
\(256\) 0 0
\(257\) −19.5614 −1.22021 −0.610104 0.792321i \(-0.708873\pi\)
−0.610104 + 0.792321i \(0.708873\pi\)
\(258\) 0 0
\(259\) 7.58875 0.471542
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 2.55052 0.157272 0.0786361 0.996903i \(-0.474943\pi\)
0.0786361 + 0.996903i \(0.474943\pi\)
\(264\) 0 0
\(265\) −4.75409 −0.292041
\(266\) 0 0
\(267\) 6.64596 0.406726
\(268\) 0 0
\(269\) 29.4270 1.79420 0.897099 0.441829i \(-0.145670\pi\)
0.897099 + 0.441829i \(0.145670\pi\)
\(270\) 0 0
\(271\) −12.7498 −0.774498 −0.387249 0.921975i \(-0.626575\pi\)
−0.387249 + 0.921975i \(0.626575\pi\)
\(272\) 0 0
\(273\) 2.03820 0.123357
\(274\) 0 0
\(275\) 9.08028 0.547562
\(276\) 0 0
\(277\) −0.598050 −0.0359333 −0.0179667 0.999839i \(-0.505719\pi\)
−0.0179667 + 0.999839i \(0.505719\pi\)
\(278\) 0 0
\(279\) −9.11330 −0.545599
\(280\) 0 0
\(281\) −16.9309 −1.01001 −0.505005 0.863116i \(-0.668509\pi\)
−0.505005 + 0.863116i \(0.668509\pi\)
\(282\) 0 0
\(283\) −4.54766 −0.270330 −0.135165 0.990823i \(-0.543157\pi\)
−0.135165 + 0.990823i \(0.543157\pi\)
\(284\) 0 0
\(285\) 6.31836 0.374267
\(286\) 0 0
\(287\) −1.50751 −0.0889857
\(288\) 0 0
\(289\) 29.2646 1.72145
\(290\) 0 0
\(291\) 9.49623 0.556679
\(292\) 0 0
\(293\) 1.42438 0.0832132 0.0416066 0.999134i \(-0.486752\pi\)
0.0416066 + 0.999134i \(0.486752\pi\)
\(294\) 0 0
\(295\) −21.4160 −1.24689
\(296\) 0 0
\(297\) 0.705979 0.0409650
\(298\) 0 0
\(299\) 2.93006 0.169449
\(300\) 0 0
\(301\) 7.60787 0.438510
\(302\) 0 0
\(303\) −3.11003 −0.178667
\(304\) 0 0
\(305\) 56.6611 3.24440
\(306\) 0 0
\(307\) −24.9384 −1.42331 −0.711655 0.702529i \(-0.752054\pi\)
−0.711655 + 0.702529i \(0.752054\pi\)
\(308\) 0 0
\(309\) −2.89095 −0.164460
\(310\) 0 0
\(311\) −17.1542 −0.972727 −0.486364 0.873757i \(-0.661677\pi\)
−0.486364 + 0.873757i \(0.661677\pi\)
\(312\) 0 0
\(313\) 19.1772 1.08396 0.541979 0.840392i \(-0.317675\pi\)
0.541979 + 0.840392i \(0.317675\pi\)
\(314\) 0 0
\(315\) 2.93992 0.165646
\(316\) 0 0
\(317\) 26.0404 1.46258 0.731288 0.682069i \(-0.238920\pi\)
0.731288 + 0.682069i \(0.238920\pi\)
\(318\) 0 0
\(319\) −0.705979 −0.0395272
\(320\) 0 0
\(321\) 9.92832 0.554145
\(322\) 0 0
\(323\) −10.1687 −0.565800
\(324\) 0 0
\(325\) 37.6863 2.09046
\(326\) 0 0
\(327\) −7.37977 −0.408102
\(328\) 0 0
\(329\) −1.50825 −0.0831525
\(330\) 0 0
\(331\) −31.0116 −1.70455 −0.852276 0.523092i \(-0.824779\pi\)
−0.852276 + 0.523092i \(0.824779\pi\)
\(332\) 0 0
\(333\) 10.9094 0.597829
\(334\) 0 0
\(335\) 8.57635 0.468576
\(336\) 0 0
\(337\) −24.2760 −1.32240 −0.661200 0.750209i \(-0.729953\pi\)
−0.661200 + 0.750209i \(0.729953\pi\)
\(338\) 0 0
\(339\) 11.1473 0.605439
\(340\) 0 0
\(341\) −6.43380 −0.348410
\(342\) 0 0
\(343\) −9.40205 −0.507663
\(344\) 0 0
\(345\) 4.22634 0.227539
\(346\) 0 0
\(347\) 12.5571 0.674098 0.337049 0.941487i \(-0.390571\pi\)
0.337049 + 0.941487i \(0.390571\pi\)
\(348\) 0 0
\(349\) 26.5819 1.42289 0.711447 0.702740i \(-0.248040\pi\)
0.711447 + 0.702740i \(0.248040\pi\)
\(350\) 0 0
\(351\) 2.93006 0.156395
\(352\) 0 0
\(353\) 2.94759 0.156884 0.0784422 0.996919i \(-0.475005\pi\)
0.0784422 + 0.996919i \(0.475005\pi\)
\(354\) 0 0
\(355\) −47.7763 −2.53570
\(356\) 0 0
\(357\) −4.73146 −0.250415
\(358\) 0 0
\(359\) −10.4319 −0.550573 −0.275286 0.961362i \(-0.588773\pi\)
−0.275286 + 0.961362i \(0.588773\pi\)
\(360\) 0 0
\(361\) −16.7650 −0.882368
\(362\) 0 0
\(363\) −10.5016 −0.551191
\(364\) 0 0
\(365\) 38.9544 2.03897
\(366\) 0 0
\(367\) −5.00509 −0.261263 −0.130632 0.991431i \(-0.541701\pi\)
−0.130632 + 0.991431i \(0.541701\pi\)
\(368\) 0 0
\(369\) −2.16716 −0.112818
\(370\) 0 0
\(371\) −0.782480 −0.0406243
\(372\) 0 0
\(373\) 8.76104 0.453630 0.226815 0.973938i \(-0.427169\pi\)
0.226815 + 0.973938i \(0.427169\pi\)
\(374\) 0 0
\(375\) 33.2274 1.71586
\(376\) 0 0
\(377\) −2.93006 −0.150906
\(378\) 0 0
\(379\) −5.18877 −0.266529 −0.133265 0.991081i \(-0.542546\pi\)
−0.133265 + 0.991081i \(0.542546\pi\)
\(380\) 0 0
\(381\) 15.1490 0.776109
\(382\) 0 0
\(383\) 15.1249 0.772847 0.386424 0.922321i \(-0.373710\pi\)
0.386424 + 0.922321i \(0.373710\pi\)
\(384\) 0 0
\(385\) 2.07552 0.105778
\(386\) 0 0
\(387\) 10.9369 0.555951
\(388\) 0 0
\(389\) 20.1526 1.02178 0.510888 0.859648i \(-0.329317\pi\)
0.510888 + 0.859648i \(0.329317\pi\)
\(390\) 0 0
\(391\) −6.80181 −0.343982
\(392\) 0 0
\(393\) −20.2752 −1.02275
\(394\) 0 0
\(395\) 9.89376 0.497809
\(396\) 0 0
\(397\) −32.7190 −1.64212 −0.821060 0.570842i \(-0.806617\pi\)
−0.821060 + 0.570842i \(0.806617\pi\)
\(398\) 0 0
\(399\) 1.03995 0.0520624
\(400\) 0 0
\(401\) −29.6852 −1.48241 −0.741203 0.671280i \(-0.765745\pi\)
−0.741203 + 0.671280i \(0.765745\pi\)
\(402\) 0 0
\(403\) −26.7025 −1.33015
\(404\) 0 0
\(405\) 4.22634 0.210009
\(406\) 0 0
\(407\) 7.70178 0.381763
\(408\) 0 0
\(409\) 0.692258 0.0342299 0.0171150 0.999854i \(-0.494552\pi\)
0.0171150 + 0.999854i \(0.494552\pi\)
\(410\) 0 0
\(411\) 15.6266 0.770804
\(412\) 0 0
\(413\) −3.52488 −0.173448
\(414\) 0 0
\(415\) 54.5380 2.67717
\(416\) 0 0
\(417\) −18.6584 −0.913704
\(418\) 0 0
\(419\) −37.2573 −1.82014 −0.910070 0.414454i \(-0.863972\pi\)
−0.910070 + 0.414454i \(0.863972\pi\)
\(420\) 0 0
\(421\) −19.2567 −0.938514 −0.469257 0.883062i \(-0.655478\pi\)
−0.469257 + 0.883062i \(0.655478\pi\)
\(422\) 0 0
\(423\) −2.16821 −0.105422
\(424\) 0 0
\(425\) −87.4847 −4.24363
\(426\) 0 0
\(427\) 9.32591 0.451312
\(428\) 0 0
\(429\) 2.06856 0.0998709
\(430\) 0 0
\(431\) 4.74403 0.228512 0.114256 0.993451i \(-0.463552\pi\)
0.114256 + 0.993451i \(0.463552\pi\)
\(432\) 0 0
\(433\) 18.8800 0.907313 0.453657 0.891177i \(-0.350119\pi\)
0.453657 + 0.891177i \(0.350119\pi\)
\(434\) 0 0
\(435\) −4.22634 −0.202638
\(436\) 0 0
\(437\) 1.49499 0.0715153
\(438\) 0 0
\(439\) −10.2819 −0.490730 −0.245365 0.969431i \(-0.578908\pi\)
−0.245365 + 0.969431i \(0.578908\pi\)
\(440\) 0 0
\(441\) −6.51612 −0.310291
\(442\) 0 0
\(443\) 0.989031 0.0469903 0.0234951 0.999724i \(-0.492521\pi\)
0.0234951 + 0.999724i \(0.492521\pi\)
\(444\) 0 0
\(445\) 28.0881 1.33150
\(446\) 0 0
\(447\) 10.1880 0.481876
\(448\) 0 0
\(449\) 28.5709 1.34834 0.674171 0.738575i \(-0.264501\pi\)
0.674171 + 0.738575i \(0.264501\pi\)
\(450\) 0 0
\(451\) −1.52997 −0.0720433
\(452\) 0 0
\(453\) 6.23078 0.292748
\(454\) 0 0
\(455\) 8.61413 0.403837
\(456\) 0 0
\(457\) 8.16371 0.381882 0.190941 0.981601i \(-0.438846\pi\)
0.190941 + 0.981601i \(0.438846\pi\)
\(458\) 0 0
\(459\) −6.80181 −0.317481
\(460\) 0 0
\(461\) −2.15436 −0.100338 −0.0501692 0.998741i \(-0.515976\pi\)
−0.0501692 + 0.998741i \(0.515976\pi\)
\(462\) 0 0
\(463\) −4.28392 −0.199091 −0.0995453 0.995033i \(-0.531739\pi\)
−0.0995453 + 0.995033i \(0.531739\pi\)
\(464\) 0 0
\(465\) −38.5159 −1.78613
\(466\) 0 0
\(467\) −34.8913 −1.61458 −0.807289 0.590156i \(-0.799066\pi\)
−0.807289 + 0.590156i \(0.799066\pi\)
\(468\) 0 0
\(469\) 1.41159 0.0651812
\(470\) 0 0
\(471\) −7.78900 −0.358898
\(472\) 0 0
\(473\) 7.72119 0.355020
\(474\) 0 0
\(475\) 19.2286 0.882268
\(476\) 0 0
\(477\) −1.12487 −0.0515043
\(478\) 0 0
\(479\) −36.2133 −1.65463 −0.827314 0.561739i \(-0.810132\pi\)
−0.827314 + 0.561739i \(0.810132\pi\)
\(480\) 0 0
\(481\) 31.9650 1.45748
\(482\) 0 0
\(483\) 0.695618 0.0316517
\(484\) 0 0
\(485\) 40.1343 1.82241
\(486\) 0 0
\(487\) −7.38649 −0.334714 −0.167357 0.985896i \(-0.553523\pi\)
−0.167357 + 0.985896i \(0.553523\pi\)
\(488\) 0 0
\(489\) 22.8277 1.03230
\(490\) 0 0
\(491\) 29.6416 1.33771 0.668853 0.743395i \(-0.266786\pi\)
0.668853 + 0.743395i \(0.266786\pi\)
\(492\) 0 0
\(493\) 6.80181 0.306338
\(494\) 0 0
\(495\) 2.98371 0.134108
\(496\) 0 0
\(497\) −7.86356 −0.352729
\(498\) 0 0
\(499\) 6.54447 0.292971 0.146485 0.989213i \(-0.453204\pi\)
0.146485 + 0.989213i \(0.453204\pi\)
\(500\) 0 0
\(501\) 8.77045 0.391835
\(502\) 0 0
\(503\) −34.4277 −1.53505 −0.767527 0.641017i \(-0.778513\pi\)
−0.767527 + 0.641017i \(0.778513\pi\)
\(504\) 0 0
\(505\) −13.1441 −0.584903
\(506\) 0 0
\(507\) −4.41477 −0.196067
\(508\) 0 0
\(509\) 10.4694 0.464048 0.232024 0.972710i \(-0.425465\pi\)
0.232024 + 0.972710i \(0.425465\pi\)
\(510\) 0 0
\(511\) 6.41154 0.283630
\(512\) 0 0
\(513\) 1.49499 0.0660056
\(514\) 0 0
\(515\) −12.2181 −0.538396
\(516\) 0 0
\(517\) −1.53071 −0.0673207
\(518\) 0 0
\(519\) −7.72555 −0.339114
\(520\) 0 0
\(521\) −14.6679 −0.642614 −0.321307 0.946975i \(-0.604122\pi\)
−0.321307 + 0.946975i \(0.604122\pi\)
\(522\) 0 0
\(523\) −33.5365 −1.46645 −0.733224 0.679987i \(-0.761985\pi\)
−0.733224 + 0.679987i \(0.761985\pi\)
\(524\) 0 0
\(525\) 8.94702 0.390480
\(526\) 0 0
\(527\) 61.9869 2.70019
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −5.06726 −0.219901
\(532\) 0 0
\(533\) −6.34989 −0.275044
\(534\) 0 0
\(535\) 41.9605 1.81411
\(536\) 0 0
\(537\) −14.1011 −0.608507
\(538\) 0 0
\(539\) −4.60024 −0.198146
\(540\) 0 0
\(541\) −19.8448 −0.853195 −0.426597 0.904442i \(-0.640288\pi\)
−0.426597 + 0.904442i \(0.640288\pi\)
\(542\) 0 0
\(543\) −6.96073 −0.298714
\(544\) 0 0
\(545\) −31.1894 −1.33601
\(546\) 0 0
\(547\) −0.592763 −0.0253447 −0.0126724 0.999920i \(-0.504034\pi\)
−0.0126724 + 0.999920i \(0.504034\pi\)
\(548\) 0 0
\(549\) 13.4066 0.572182
\(550\) 0 0
\(551\) −1.49499 −0.0636889
\(552\) 0 0
\(553\) 1.62842 0.0692476
\(554\) 0 0
\(555\) 46.1067 1.95712
\(556\) 0 0
\(557\) −6.32303 −0.267915 −0.133958 0.990987i \(-0.542769\pi\)
−0.133958 + 0.990987i \(0.542769\pi\)
\(558\) 0 0
\(559\) 32.0456 1.35538
\(560\) 0 0
\(561\) −4.80193 −0.202738
\(562\) 0 0
\(563\) −22.8228 −0.961867 −0.480933 0.876757i \(-0.659702\pi\)
−0.480933 + 0.876757i \(0.659702\pi\)
\(564\) 0 0
\(565\) 47.1123 1.98203
\(566\) 0 0
\(567\) 0.695618 0.0292132
\(568\) 0 0
\(569\) 35.8006 1.50084 0.750419 0.660962i \(-0.229852\pi\)
0.750419 + 0.660962i \(0.229852\pi\)
\(570\) 0 0
\(571\) 24.1526 1.01075 0.505377 0.862899i \(-0.331354\pi\)
0.505377 + 0.862899i \(0.331354\pi\)
\(572\) 0 0
\(573\) 6.81656 0.284766
\(574\) 0 0
\(575\) 12.8620 0.536381
\(576\) 0 0
\(577\) 34.2863 1.42736 0.713678 0.700474i \(-0.247028\pi\)
0.713678 + 0.700474i \(0.247028\pi\)
\(578\) 0 0
\(579\) −14.8527 −0.617255
\(580\) 0 0
\(581\) 8.97646 0.372406
\(582\) 0 0
\(583\) −0.794134 −0.0328897
\(584\) 0 0
\(585\) 12.3834 0.511991
\(586\) 0 0
\(587\) −23.0081 −0.949648 −0.474824 0.880081i \(-0.657488\pi\)
−0.474824 + 0.880081i \(0.657488\pi\)
\(588\) 0 0
\(589\) −13.6243 −0.561381
\(590\) 0 0
\(591\) 3.40123 0.139908
\(592\) 0 0
\(593\) −14.1127 −0.579539 −0.289770 0.957096i \(-0.593579\pi\)
−0.289770 + 0.957096i \(0.593579\pi\)
\(594\) 0 0
\(595\) −19.9968 −0.819788
\(596\) 0 0
\(597\) 12.0542 0.493344
\(598\) 0 0
\(599\) −2.50251 −0.102250 −0.0511249 0.998692i \(-0.516281\pi\)
−0.0511249 + 0.998692i \(0.516281\pi\)
\(600\) 0 0
\(601\) −14.0139 −0.571640 −0.285820 0.958283i \(-0.592266\pi\)
−0.285820 + 0.958283i \(0.592266\pi\)
\(602\) 0 0
\(603\) 2.02926 0.0826379
\(604\) 0 0
\(605\) −44.3833 −1.80444
\(606\) 0 0
\(607\) −25.3436 −1.02866 −0.514332 0.857591i \(-0.671960\pi\)
−0.514332 + 0.857591i \(0.671960\pi\)
\(608\) 0 0
\(609\) −0.695618 −0.0281879
\(610\) 0 0
\(611\) −6.35299 −0.257014
\(612\) 0 0
\(613\) −18.6346 −0.752644 −0.376322 0.926489i \(-0.622811\pi\)
−0.376322 + 0.926489i \(0.622811\pi\)
\(614\) 0 0
\(615\) −9.15914 −0.369332
\(616\) 0 0
\(617\) 24.2469 0.976143 0.488072 0.872804i \(-0.337700\pi\)
0.488072 + 0.872804i \(0.337700\pi\)
\(618\) 0 0
\(619\) 44.6116 1.79309 0.896546 0.442950i \(-0.146068\pi\)
0.896546 + 0.442950i \(0.146068\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 4.62305 0.185219
\(624\) 0 0
\(625\) 76.1205 3.04482
\(626\) 0 0
\(627\) 1.05543 0.0421500
\(628\) 0 0
\(629\) −74.2034 −2.95868
\(630\) 0 0
\(631\) 31.6825 1.26126 0.630631 0.776083i \(-0.282796\pi\)
0.630631 + 0.776083i \(0.282796\pi\)
\(632\) 0 0
\(633\) 2.91873 0.116009
\(634\) 0 0
\(635\) 64.0250 2.54076
\(636\) 0 0
\(637\) −19.0926 −0.756476
\(638\) 0 0
\(639\) −11.3044 −0.447196
\(640\) 0 0
\(641\) 35.9623 1.42043 0.710213 0.703987i \(-0.248599\pi\)
0.710213 + 0.703987i \(0.248599\pi\)
\(642\) 0 0
\(643\) −31.4634 −1.24079 −0.620397 0.784288i \(-0.713028\pi\)
−0.620397 + 0.784288i \(0.713028\pi\)
\(644\) 0 0
\(645\) 46.2229 1.82002
\(646\) 0 0
\(647\) −11.8638 −0.466414 −0.233207 0.972427i \(-0.574922\pi\)
−0.233207 + 0.972427i \(0.574922\pi\)
\(648\) 0 0
\(649\) −3.57738 −0.140424
\(650\) 0 0
\(651\) −6.33938 −0.248460
\(652\) 0 0
\(653\) 15.5072 0.606844 0.303422 0.952856i \(-0.401871\pi\)
0.303422 + 0.952856i \(0.401871\pi\)
\(654\) 0 0
\(655\) −85.6899 −3.34818
\(656\) 0 0
\(657\) 9.21704 0.359591
\(658\) 0 0
\(659\) 5.80769 0.226235 0.113118 0.993582i \(-0.463916\pi\)
0.113118 + 0.993582i \(0.463916\pi\)
\(660\) 0 0
\(661\) 8.82689 0.343326 0.171663 0.985156i \(-0.445086\pi\)
0.171663 + 0.985156i \(0.445086\pi\)
\(662\) 0 0
\(663\) −19.9297 −0.774004
\(664\) 0 0
\(665\) 4.39517 0.170437
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 0.890415 0.0344254
\(670\) 0 0
\(671\) 9.46481 0.365385
\(672\) 0 0
\(673\) 21.3368 0.822473 0.411237 0.911529i \(-0.365097\pi\)
0.411237 + 0.911529i \(0.365097\pi\)
\(674\) 0 0
\(675\) 12.8620 0.495058
\(676\) 0 0
\(677\) 0.748433 0.0287646 0.0143823 0.999897i \(-0.495422\pi\)
0.0143823 + 0.999897i \(0.495422\pi\)
\(678\) 0 0
\(679\) 6.60575 0.253505
\(680\) 0 0
\(681\) −2.10706 −0.0807429
\(682\) 0 0
\(683\) −13.8840 −0.531258 −0.265629 0.964075i \(-0.585580\pi\)
−0.265629 + 0.964075i \(0.585580\pi\)
\(684\) 0 0
\(685\) 66.0434 2.52339
\(686\) 0 0
\(687\) −18.5927 −0.709355
\(688\) 0 0
\(689\) −3.29593 −0.125565
\(690\) 0 0
\(691\) −0.657470 −0.0250113 −0.0125057 0.999922i \(-0.503981\pi\)
−0.0125057 + 0.999922i \(0.503981\pi\)
\(692\) 0 0
\(693\) 0.491092 0.0186550
\(694\) 0 0
\(695\) −78.8566 −2.99120
\(696\) 0 0
\(697\) 14.7406 0.558339
\(698\) 0 0
\(699\) −25.9081 −0.979936
\(700\) 0 0
\(701\) −17.4436 −0.658836 −0.329418 0.944184i \(-0.606852\pi\)
−0.329418 + 0.944184i \(0.606852\pi\)
\(702\) 0 0
\(703\) 16.3094 0.615122
\(704\) 0 0
\(705\) −9.16362 −0.345122
\(706\) 0 0
\(707\) −2.16340 −0.0813629
\(708\) 0 0
\(709\) −28.3024 −1.06292 −0.531460 0.847083i \(-0.678356\pi\)
−0.531460 + 0.847083i \(0.678356\pi\)
\(710\) 0 0
\(711\) 2.34097 0.0877934
\(712\) 0 0
\(713\) −9.11330 −0.341296
\(714\) 0 0
\(715\) 8.74243 0.326948
\(716\) 0 0
\(717\) −21.7029 −0.810508
\(718\) 0 0
\(719\) −31.1323 −1.16104 −0.580520 0.814246i \(-0.697151\pi\)
−0.580520 + 0.814246i \(0.697151\pi\)
\(720\) 0 0
\(721\) −2.01100 −0.0748934
\(722\) 0 0
\(723\) 9.64217 0.358596
\(724\) 0 0
\(725\) −12.8620 −0.477682
\(726\) 0 0
\(727\) 11.0340 0.409227 0.204613 0.978843i \(-0.434406\pi\)
0.204613 + 0.978843i \(0.434406\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −74.3904 −2.75143
\(732\) 0 0
\(733\) 29.5537 1.09159 0.545796 0.837918i \(-0.316228\pi\)
0.545796 + 0.837918i \(0.316228\pi\)
\(734\) 0 0
\(735\) −27.5393 −1.01580
\(736\) 0 0
\(737\) 1.43262 0.0527711
\(738\) 0 0
\(739\) 48.7783 1.79434 0.897169 0.441688i \(-0.145620\pi\)
0.897169 + 0.441688i \(0.145620\pi\)
\(740\) 0 0
\(741\) 4.38042 0.160919
\(742\) 0 0
\(743\) −23.7435 −0.871063 −0.435531 0.900174i \(-0.643440\pi\)
−0.435531 + 0.900174i \(0.643440\pi\)
\(744\) 0 0
\(745\) 43.0580 1.57752
\(746\) 0 0
\(747\) 12.9043 0.472144
\(748\) 0 0
\(749\) 6.90632 0.252352
\(750\) 0 0
\(751\) 5.16660 0.188532 0.0942659 0.995547i \(-0.469950\pi\)
0.0942659 + 0.995547i \(0.469950\pi\)
\(752\) 0 0
\(753\) −23.9646 −0.873317
\(754\) 0 0
\(755\) 26.3334 0.958372
\(756\) 0 0
\(757\) 0.538380 0.0195678 0.00978389 0.999952i \(-0.496886\pi\)
0.00978389 + 0.999952i \(0.496886\pi\)
\(758\) 0 0
\(759\) 0.705979 0.0256254
\(760\) 0 0
\(761\) −50.1455 −1.81777 −0.908886 0.417044i \(-0.863066\pi\)
−0.908886 + 0.417044i \(0.863066\pi\)
\(762\) 0 0
\(763\) −5.13350 −0.185845
\(764\) 0 0
\(765\) −28.7468 −1.03934
\(766\) 0 0
\(767\) −14.8474 −0.536107
\(768\) 0 0
\(769\) 36.1197 1.30251 0.651255 0.758859i \(-0.274243\pi\)
0.651255 + 0.758859i \(0.274243\pi\)
\(770\) 0 0
\(771\) −19.5614 −0.704488
\(772\) 0 0
\(773\) −6.42381 −0.231048 −0.115524 0.993305i \(-0.536855\pi\)
−0.115524 + 0.993305i \(0.536855\pi\)
\(774\) 0 0
\(775\) −117.215 −4.21049
\(776\) 0 0
\(777\) 7.58875 0.272245
\(778\) 0 0
\(779\) −3.23989 −0.116081
\(780\) 0 0
\(781\) −7.98068 −0.285571
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −32.9190 −1.17493
\(786\) 0 0
\(787\) −12.1635 −0.433582 −0.216791 0.976218i \(-0.569559\pi\)
−0.216791 + 0.976218i \(0.569559\pi\)
\(788\) 0 0
\(789\) 2.55052 0.0908011
\(790\) 0 0
\(791\) 7.75427 0.275710
\(792\) 0 0
\(793\) 39.2822 1.39495
\(794\) 0 0
\(795\) −4.75409 −0.168610
\(796\) 0 0
\(797\) −0.452690 −0.0160351 −0.00801755 0.999968i \(-0.502552\pi\)
−0.00801755 + 0.999968i \(0.502552\pi\)
\(798\) 0 0
\(799\) 14.7478 0.521739
\(800\) 0 0
\(801\) 6.64596 0.234824
\(802\) 0 0
\(803\) 6.50704 0.229628
\(804\) 0 0
\(805\) 2.93992 0.103619
\(806\) 0 0
\(807\) 29.4270 1.03588
\(808\) 0 0
\(809\) −34.7499 −1.22174 −0.610871 0.791730i \(-0.709181\pi\)
−0.610871 + 0.791730i \(0.709181\pi\)
\(810\) 0 0
\(811\) −12.8338 −0.450657 −0.225328 0.974283i \(-0.572345\pi\)
−0.225328 + 0.974283i \(0.572345\pi\)
\(812\) 0 0
\(813\) −12.7498 −0.447157
\(814\) 0 0
\(815\) 96.4775 3.37946
\(816\) 0 0
\(817\) 16.3505 0.572033
\(818\) 0 0
\(819\) 2.03820 0.0712205
\(820\) 0 0
\(821\) −8.09811 −0.282626 −0.141313 0.989965i \(-0.545132\pi\)
−0.141313 + 0.989965i \(0.545132\pi\)
\(822\) 0 0
\(823\) 52.1215 1.81684 0.908421 0.418056i \(-0.137288\pi\)
0.908421 + 0.418056i \(0.137288\pi\)
\(824\) 0 0
\(825\) 9.08028 0.316135
\(826\) 0 0
\(827\) −10.4426 −0.363125 −0.181562 0.983379i \(-0.558115\pi\)
−0.181562 + 0.983379i \(0.558115\pi\)
\(828\) 0 0
\(829\) 49.4044 1.71588 0.857942 0.513746i \(-0.171743\pi\)
0.857942 + 0.513746i \(0.171743\pi\)
\(830\) 0 0
\(831\) −0.598050 −0.0207461
\(832\) 0 0
\(833\) 44.3214 1.53564
\(834\) 0 0
\(835\) 37.0669 1.28275
\(836\) 0 0
\(837\) −9.11330 −0.315002
\(838\) 0 0
\(839\) 14.1529 0.488611 0.244306 0.969698i \(-0.421440\pi\)
0.244306 + 0.969698i \(0.421440\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −16.9309 −0.583130
\(844\) 0 0
\(845\) −18.6584 −0.641867
\(846\) 0 0
\(847\) −7.30510 −0.251006
\(848\) 0 0
\(849\) −4.54766 −0.156075
\(850\) 0 0
\(851\) 10.9094 0.373968
\(852\) 0 0
\(853\) −47.2167 −1.61667 −0.808334 0.588724i \(-0.799630\pi\)
−0.808334 + 0.588724i \(0.799630\pi\)
\(854\) 0 0
\(855\) 6.31836 0.216083
\(856\) 0 0
\(857\) 26.4901 0.904884 0.452442 0.891794i \(-0.350553\pi\)
0.452442 + 0.891794i \(0.350553\pi\)
\(858\) 0 0
\(859\) 5.24114 0.178825 0.0894127 0.995995i \(-0.471501\pi\)
0.0894127 + 0.995995i \(0.471501\pi\)
\(860\) 0 0
\(861\) −1.50751 −0.0513759
\(862\) 0 0
\(863\) 21.8415 0.743492 0.371746 0.928335i \(-0.378759\pi\)
0.371746 + 0.928335i \(0.378759\pi\)
\(864\) 0 0
\(865\) −32.6508 −1.11016
\(866\) 0 0
\(867\) 29.2646 0.993878
\(868\) 0 0
\(869\) 1.65268 0.0560633
\(870\) 0 0
\(871\) 5.94585 0.201467
\(872\) 0 0
\(873\) 9.49623 0.321399
\(874\) 0 0
\(875\) 23.1136 0.781382
\(876\) 0 0
\(877\) −22.8446 −0.771408 −0.385704 0.922623i \(-0.626041\pi\)
−0.385704 + 0.922623i \(0.626041\pi\)
\(878\) 0 0
\(879\) 1.42438 0.0480432
\(880\) 0 0
\(881\) 18.3047 0.616703 0.308351 0.951273i \(-0.400223\pi\)
0.308351 + 0.951273i \(0.400223\pi\)
\(882\) 0 0
\(883\) −37.2872 −1.25481 −0.627406 0.778692i \(-0.715883\pi\)
−0.627406 + 0.778692i \(0.715883\pi\)
\(884\) 0 0
\(885\) −21.4160 −0.719891
\(886\) 0 0
\(887\) 12.5057 0.419901 0.209950 0.977712i \(-0.432670\pi\)
0.209950 + 0.977712i \(0.432670\pi\)
\(888\) 0 0
\(889\) 10.5379 0.353431
\(890\) 0 0
\(891\) 0.705979 0.0236512
\(892\) 0 0
\(893\) −3.24147 −0.108472
\(894\) 0 0
\(895\) −59.5961 −1.99208
\(896\) 0 0
\(897\) 2.93006 0.0978317
\(898\) 0 0
\(899\) 9.11330 0.303946
\(900\) 0 0
\(901\) 7.65115 0.254897
\(902\) 0 0
\(903\) 7.60787 0.253174
\(904\) 0 0
\(905\) −29.4184 −0.977902
\(906\) 0 0
\(907\) 38.9299 1.29265 0.646323 0.763064i \(-0.276306\pi\)
0.646323 + 0.763064i \(0.276306\pi\)
\(908\) 0 0
\(909\) −3.11003 −0.103153
\(910\) 0 0
\(911\) 45.3851 1.50367 0.751837 0.659349i \(-0.229168\pi\)
0.751837 + 0.659349i \(0.229168\pi\)
\(912\) 0 0
\(913\) 9.11016 0.301502
\(914\) 0 0
\(915\) 56.6611 1.87316
\(916\) 0 0
\(917\) −14.1038 −0.465748
\(918\) 0 0
\(919\) −37.3191 −1.23104 −0.615521 0.788120i \(-0.711055\pi\)
−0.615521 + 0.788120i \(0.711055\pi\)
\(920\) 0 0
\(921\) −24.9384 −0.821748
\(922\) 0 0
\(923\) −33.1226 −1.09024
\(924\) 0 0
\(925\) 140.316 4.61356
\(926\) 0 0
\(927\) −2.89095 −0.0949512
\(928\) 0 0
\(929\) −8.78075 −0.288087 −0.144043 0.989571i \(-0.546011\pi\)
−0.144043 + 0.989571i \(0.546011\pi\)
\(930\) 0 0
\(931\) −9.74156 −0.319267
\(932\) 0 0
\(933\) −17.1542 −0.561604
\(934\) 0 0
\(935\) −20.2946 −0.663705
\(936\) 0 0
\(937\) 21.3335 0.696936 0.348468 0.937321i \(-0.386702\pi\)
0.348468 + 0.937321i \(0.386702\pi\)
\(938\) 0 0
\(939\) 19.1772 0.625823
\(940\) 0 0
\(941\) 52.5356 1.71261 0.856305 0.516470i \(-0.172754\pi\)
0.856305 + 0.516470i \(0.172754\pi\)
\(942\) 0 0
\(943\) −2.16716 −0.0705723
\(944\) 0 0
\(945\) 2.93992 0.0956356
\(946\) 0 0
\(947\) 32.4135 1.05330 0.526648 0.850083i \(-0.323448\pi\)
0.526648 + 0.850083i \(0.323448\pi\)
\(948\) 0 0
\(949\) 27.0064 0.876666
\(950\) 0 0
\(951\) 26.0404 0.844419
\(952\) 0 0
\(953\) 0.738966 0.0239375 0.0119687 0.999928i \(-0.496190\pi\)
0.0119687 + 0.999928i \(0.496190\pi\)
\(954\) 0 0
\(955\) 28.8091 0.932242
\(956\) 0 0
\(957\) −0.705979 −0.0228211
\(958\) 0 0
\(959\) 10.8702 0.351016
\(960\) 0 0
\(961\) 52.0523 1.67911
\(962\) 0 0
\(963\) 9.92832 0.319936
\(964\) 0 0
\(965\) −62.7724 −2.02072
\(966\) 0 0
\(967\) 15.5013 0.498490 0.249245 0.968441i \(-0.419818\pi\)
0.249245 + 0.968441i \(0.419818\pi\)
\(968\) 0 0
\(969\) −10.1687 −0.326665
\(970\) 0 0
\(971\) −5.20909 −0.167168 −0.0835838 0.996501i \(-0.526637\pi\)
−0.0835838 + 0.996501i \(0.526637\pi\)
\(972\) 0 0
\(973\) −12.9791 −0.416090
\(974\) 0 0
\(975\) 37.6863 1.20693
\(976\) 0 0
\(977\) −35.1132 −1.12337 −0.561685 0.827351i \(-0.689847\pi\)
−0.561685 + 0.827351i \(0.689847\pi\)
\(978\) 0 0
\(979\) 4.69191 0.149954
\(980\) 0 0
\(981\) −7.37977 −0.235618
\(982\) 0 0
\(983\) 45.7961 1.46067 0.730335 0.683089i \(-0.239364\pi\)
0.730335 + 0.683089i \(0.239364\pi\)
\(984\) 0 0
\(985\) 14.3748 0.458019
\(986\) 0 0
\(987\) −1.50825 −0.0480081
\(988\) 0 0
\(989\) 10.9369 0.347772
\(990\) 0 0
\(991\) 34.3591 1.09145 0.545726 0.837964i \(-0.316254\pi\)
0.545726 + 0.837964i \(0.316254\pi\)
\(992\) 0 0
\(993\) −31.0116 −0.984124
\(994\) 0 0
\(995\) 50.9451 1.61507
\(996\) 0 0
\(997\) −59.7134 −1.89114 −0.945571 0.325415i \(-0.894496\pi\)
−0.945571 + 0.325415i \(0.894496\pi\)
\(998\) 0 0
\(999\) 10.9094 0.345157
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 \(a_p\))