Properties

Label 8004.2.a.j.1.11
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 1.11
Root \(1.63007\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+1.63007 q^{5}\) \(-0.577524 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+1.63007 q^{5}\) \(-0.577524 q^{7}\) \(+1.00000 q^{9}\) \(+5.51763 q^{11}\) \(+0.530107 q^{13}\) \(+1.63007 q^{15}\) \(+6.30808 q^{17}\) \(+0.869087 q^{19}\) \(-0.577524 q^{21}\) \(+1.00000 q^{23}\) \(-2.34288 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(-4.68209 q^{31}\) \(+5.51763 q^{33}\) \(-0.941403 q^{35}\) \(-2.51955 q^{37}\) \(+0.530107 q^{39}\) \(+7.33380 q^{41}\) \(+7.82962 q^{43}\) \(+1.63007 q^{45}\) \(+4.94492 q^{47}\) \(-6.66647 q^{49}\) \(+6.30808 q^{51}\) \(+2.53916 q^{53}\) \(+8.99412 q^{55}\) \(+0.869087 q^{57}\) \(+14.0049 q^{59}\) \(-5.51000 q^{61}\) \(-0.577524 q^{63}\) \(+0.864111 q^{65}\) \(-11.2304 q^{67}\) \(+1.00000 q^{69}\) \(-9.56805 q^{71}\) \(-3.25416 q^{73}\) \(-2.34288 q^{75}\) \(-3.18656 q^{77}\) \(+0.347989 q^{79}\) \(+1.00000 q^{81}\) \(+10.1590 q^{83}\) \(+10.2826 q^{85}\) \(-1.00000 q^{87}\) \(+14.8738 q^{89}\) \(-0.306149 q^{91}\) \(-4.68209 q^{93}\) \(+1.41667 q^{95}\) \(+2.03129 q^{97}\) \(+5.51763 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.63007 0.728989 0.364494 0.931206i \(-0.381242\pi\)
0.364494 + 0.931206i \(0.381242\pi\)
\(6\) 0 0
\(7\) −0.577524 −0.218283 −0.109142 0.994026i \(-0.534810\pi\)
−0.109142 + 0.994026i \(0.534810\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.51763 1.66363 0.831814 0.555054i \(-0.187302\pi\)
0.831814 + 0.555054i \(0.187302\pi\)
\(12\) 0 0
\(13\) 0.530107 0.147025 0.0735126 0.997294i \(-0.476579\pi\)
0.0735126 + 0.997294i \(0.476579\pi\)
\(14\) 0 0
\(15\) 1.63007 0.420882
\(16\) 0 0
\(17\) 6.30808 1.52993 0.764967 0.644069i \(-0.222755\pi\)
0.764967 + 0.644069i \(0.222755\pi\)
\(18\) 0 0
\(19\) 0.869087 0.199382 0.0996911 0.995018i \(-0.468215\pi\)
0.0996911 + 0.995018i \(0.468215\pi\)
\(20\) 0 0
\(21\) −0.577524 −0.126026
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.34288 −0.468575
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −4.68209 −0.840929 −0.420464 0.907309i \(-0.638133\pi\)
−0.420464 + 0.907309i \(0.638133\pi\)
\(32\) 0 0
\(33\) 5.51763 0.960497
\(34\) 0 0
\(35\) −0.941403 −0.159126
\(36\) 0 0
\(37\) −2.51955 −0.414211 −0.207106 0.978319i \(-0.566404\pi\)
−0.207106 + 0.978319i \(0.566404\pi\)
\(38\) 0 0
\(39\) 0.530107 0.0848850
\(40\) 0 0
\(41\) 7.33380 1.14535 0.572673 0.819784i \(-0.305906\pi\)
0.572673 + 0.819784i \(0.305906\pi\)
\(42\) 0 0
\(43\) 7.82962 1.19401 0.597003 0.802239i \(-0.296358\pi\)
0.597003 + 0.802239i \(0.296358\pi\)
\(44\) 0 0
\(45\) 1.63007 0.242996
\(46\) 0 0
\(47\) 4.94492 0.721290 0.360645 0.932703i \(-0.382557\pi\)
0.360645 + 0.932703i \(0.382557\pi\)
\(48\) 0 0
\(49\) −6.66647 −0.952352
\(50\) 0 0
\(51\) 6.30808 0.883308
\(52\) 0 0
\(53\) 2.53916 0.348780 0.174390 0.984677i \(-0.444205\pi\)
0.174390 + 0.984677i \(0.444205\pi\)
\(54\) 0 0
\(55\) 8.99412 1.21277
\(56\) 0 0
\(57\) 0.869087 0.115113
\(58\) 0 0
\(59\) 14.0049 1.82328 0.911642 0.410984i \(-0.134815\pi\)
0.911642 + 0.410984i \(0.134815\pi\)
\(60\) 0 0
\(61\) −5.51000 −0.705484 −0.352742 0.935721i \(-0.614751\pi\)
−0.352742 + 0.935721i \(0.614751\pi\)
\(62\) 0 0
\(63\) −0.577524 −0.0727612
\(64\) 0 0
\(65\) 0.864111 0.107180
\(66\) 0 0
\(67\) −11.2304 −1.37201 −0.686006 0.727596i \(-0.740638\pi\)
−0.686006 + 0.727596i \(0.740638\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −9.56805 −1.13552 −0.567759 0.823195i \(-0.692190\pi\)
−0.567759 + 0.823195i \(0.692190\pi\)
\(72\) 0 0
\(73\) −3.25416 −0.380871 −0.190435 0.981700i \(-0.560990\pi\)
−0.190435 + 0.981700i \(0.560990\pi\)
\(74\) 0 0
\(75\) −2.34288 −0.270532
\(76\) 0 0
\(77\) −3.18656 −0.363143
\(78\) 0 0
\(79\) 0.347989 0.0391518 0.0195759 0.999808i \(-0.493768\pi\)
0.0195759 + 0.999808i \(0.493768\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 10.1590 1.11509 0.557546 0.830146i \(-0.311743\pi\)
0.557546 + 0.830146i \(0.311743\pi\)
\(84\) 0 0
\(85\) 10.2826 1.11531
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 14.8738 1.57662 0.788309 0.615280i \(-0.210957\pi\)
0.788309 + 0.615280i \(0.210957\pi\)
\(90\) 0 0
\(91\) −0.306149 −0.0320932
\(92\) 0 0
\(93\) −4.68209 −0.485510
\(94\) 0 0
\(95\) 1.41667 0.145347
\(96\) 0 0
\(97\) 2.03129 0.206246 0.103123 0.994669i \(-0.467116\pi\)
0.103123 + 0.994669i \(0.467116\pi\)
\(98\) 0 0
\(99\) 5.51763 0.554543
\(100\) 0 0
\(101\) −7.88165 −0.784253 −0.392127 0.919911i \(-0.628260\pi\)
−0.392127 + 0.919911i \(0.628260\pi\)
\(102\) 0 0
\(103\) 3.55532 0.350316 0.175158 0.984540i \(-0.443956\pi\)
0.175158 + 0.984540i \(0.443956\pi\)
\(104\) 0 0
\(105\) −0.941403 −0.0918716
\(106\) 0 0
\(107\) −3.84295 −0.371512 −0.185756 0.982596i \(-0.559473\pi\)
−0.185756 + 0.982596i \(0.559473\pi\)
\(108\) 0 0
\(109\) 16.9800 1.62639 0.813195 0.581992i \(-0.197726\pi\)
0.813195 + 0.581992i \(0.197726\pi\)
\(110\) 0 0
\(111\) −2.51955 −0.239145
\(112\) 0 0
\(113\) −4.39778 −0.413708 −0.206854 0.978372i \(-0.566323\pi\)
−0.206854 + 0.978372i \(0.566323\pi\)
\(114\) 0 0
\(115\) 1.63007 0.152005
\(116\) 0 0
\(117\) 0.530107 0.0490084
\(118\) 0 0
\(119\) −3.64307 −0.333959
\(120\) 0 0
\(121\) 19.4443 1.76766
\(122\) 0 0
\(123\) 7.33380 0.661266
\(124\) 0 0
\(125\) −11.9694 −1.07058
\(126\) 0 0
\(127\) −12.8595 −1.14110 −0.570548 0.821264i \(-0.693269\pi\)
−0.570548 + 0.821264i \(0.693269\pi\)
\(128\) 0 0
\(129\) 7.82962 0.689360
\(130\) 0 0
\(131\) −12.0820 −1.05561 −0.527807 0.849365i \(-0.676985\pi\)
−0.527807 + 0.849365i \(0.676985\pi\)
\(132\) 0 0
\(133\) −0.501919 −0.0435219
\(134\) 0 0
\(135\) 1.63007 0.140294
\(136\) 0 0
\(137\) 1.50378 0.128477 0.0642383 0.997935i \(-0.479538\pi\)
0.0642383 + 0.997935i \(0.479538\pi\)
\(138\) 0 0
\(139\) −18.4802 −1.56747 −0.783735 0.621095i \(-0.786688\pi\)
−0.783735 + 0.621095i \(0.786688\pi\)
\(140\) 0 0
\(141\) 4.94492 0.416437
\(142\) 0 0
\(143\) 2.92494 0.244595
\(144\) 0 0
\(145\) −1.63007 −0.135370
\(146\) 0 0
\(147\) −6.66647 −0.549841
\(148\) 0 0
\(149\) 5.69566 0.466607 0.233304 0.972404i \(-0.425046\pi\)
0.233304 + 0.972404i \(0.425046\pi\)
\(150\) 0 0
\(151\) −11.4329 −0.930395 −0.465198 0.885207i \(-0.654017\pi\)
−0.465198 + 0.885207i \(0.654017\pi\)
\(152\) 0 0
\(153\) 6.30808 0.509978
\(154\) 0 0
\(155\) −7.63213 −0.613028
\(156\) 0 0
\(157\) −2.38936 −0.190691 −0.0953457 0.995444i \(-0.530396\pi\)
−0.0953457 + 0.995444i \(0.530396\pi\)
\(158\) 0 0
\(159\) 2.53916 0.201369
\(160\) 0 0
\(161\) −0.577524 −0.0455153
\(162\) 0 0
\(163\) −23.0628 −1.80642 −0.903208 0.429203i \(-0.858794\pi\)
−0.903208 + 0.429203i \(0.858794\pi\)
\(164\) 0 0
\(165\) 8.99412 0.700191
\(166\) 0 0
\(167\) −2.42660 −0.187776 −0.0938878 0.995583i \(-0.529930\pi\)
−0.0938878 + 0.995583i \(0.529930\pi\)
\(168\) 0 0
\(169\) −12.7190 −0.978384
\(170\) 0 0
\(171\) 0.869087 0.0664608
\(172\) 0 0
\(173\) −15.0262 −1.14242 −0.571209 0.820805i \(-0.693525\pi\)
−0.571209 + 0.820805i \(0.693525\pi\)
\(174\) 0 0
\(175\) 1.35307 0.102282
\(176\) 0 0
\(177\) 14.0049 1.05267
\(178\) 0 0
\(179\) 15.9353 1.19106 0.595531 0.803332i \(-0.296942\pi\)
0.595531 + 0.803332i \(0.296942\pi\)
\(180\) 0 0
\(181\) −12.1265 −0.901359 −0.450680 0.892686i \(-0.648818\pi\)
−0.450680 + 0.892686i \(0.648818\pi\)
\(182\) 0 0
\(183\) −5.51000 −0.407311
\(184\) 0 0
\(185\) −4.10704 −0.301955
\(186\) 0 0
\(187\) 34.8057 2.54524
\(188\) 0 0
\(189\) −0.577524 −0.0420087
\(190\) 0 0
\(191\) 2.12503 0.153762 0.0768808 0.997040i \(-0.475504\pi\)
0.0768808 + 0.997040i \(0.475504\pi\)
\(192\) 0 0
\(193\) −13.0166 −0.936959 −0.468479 0.883474i \(-0.655198\pi\)
−0.468479 + 0.883474i \(0.655198\pi\)
\(194\) 0 0
\(195\) 0.864111 0.0618802
\(196\) 0 0
\(197\) 11.2634 0.802483 0.401242 0.915972i \(-0.368579\pi\)
0.401242 + 0.915972i \(0.368579\pi\)
\(198\) 0 0
\(199\) −9.31732 −0.660487 −0.330244 0.943896i \(-0.607131\pi\)
−0.330244 + 0.943896i \(0.607131\pi\)
\(200\) 0 0
\(201\) −11.2304 −0.792132
\(202\) 0 0
\(203\) 0.577524 0.0405342
\(204\) 0 0
\(205\) 11.9546 0.834945
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 4.79530 0.331698
\(210\) 0 0
\(211\) 7.76189 0.534350 0.267175 0.963648i \(-0.413910\pi\)
0.267175 + 0.963648i \(0.413910\pi\)
\(212\) 0 0
\(213\) −9.56805 −0.655592
\(214\) 0 0
\(215\) 12.7628 0.870417
\(216\) 0 0
\(217\) 2.70402 0.183561
\(218\) 0 0
\(219\) −3.25416 −0.219896
\(220\) 0 0
\(221\) 3.34396 0.224939
\(222\) 0 0
\(223\) 9.00853 0.603256 0.301628 0.953426i \(-0.402470\pi\)
0.301628 + 0.953426i \(0.402470\pi\)
\(224\) 0 0
\(225\) −2.34288 −0.156192
\(226\) 0 0
\(227\) 18.9075 1.25493 0.627467 0.778643i \(-0.284092\pi\)
0.627467 + 0.778643i \(0.284092\pi\)
\(228\) 0 0
\(229\) 0.0153065 0.00101148 0.000505742 1.00000i \(-0.499839\pi\)
0.000505742 1.00000i \(0.499839\pi\)
\(230\) 0 0
\(231\) −3.18656 −0.209661
\(232\) 0 0
\(233\) 10.9974 0.720461 0.360230 0.932863i \(-0.382698\pi\)
0.360230 + 0.932863i \(0.382698\pi\)
\(234\) 0 0
\(235\) 8.06056 0.525813
\(236\) 0 0
\(237\) 0.347989 0.0226043
\(238\) 0 0
\(239\) 17.4397 1.12808 0.564039 0.825748i \(-0.309247\pi\)
0.564039 + 0.825748i \(0.309247\pi\)
\(240\) 0 0
\(241\) 30.6019 1.97124 0.985622 0.168967i \(-0.0540431\pi\)
0.985622 + 0.168967i \(0.0540431\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −10.8668 −0.694254
\(246\) 0 0
\(247\) 0.460709 0.0293142
\(248\) 0 0
\(249\) 10.1590 0.643799
\(250\) 0 0
\(251\) 13.7596 0.868497 0.434248 0.900793i \(-0.357014\pi\)
0.434248 + 0.900793i \(0.357014\pi\)
\(252\) 0 0
\(253\) 5.51763 0.346891
\(254\) 0 0
\(255\) 10.2826 0.643922
\(256\) 0 0
\(257\) 18.0156 1.12378 0.561890 0.827212i \(-0.310074\pi\)
0.561890 + 0.827212i \(0.310074\pi\)
\(258\) 0 0
\(259\) 1.45510 0.0904154
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −8.65502 −0.533691 −0.266846 0.963739i \(-0.585981\pi\)
−0.266846 + 0.963739i \(0.585981\pi\)
\(264\) 0 0
\(265\) 4.13901 0.254257
\(266\) 0 0
\(267\) 14.8738 0.910260
\(268\) 0 0
\(269\) −12.1540 −0.741043 −0.370521 0.928824i \(-0.620821\pi\)
−0.370521 + 0.928824i \(0.620821\pi\)
\(270\) 0 0
\(271\) 9.41238 0.571761 0.285881 0.958265i \(-0.407714\pi\)
0.285881 + 0.958265i \(0.407714\pi\)
\(272\) 0 0
\(273\) −0.306149 −0.0185290
\(274\) 0 0
\(275\) −12.9271 −0.779535
\(276\) 0 0
\(277\) −22.4479 −1.34877 −0.674383 0.738381i \(-0.735590\pi\)
−0.674383 + 0.738381i \(0.735590\pi\)
\(278\) 0 0
\(279\) −4.68209 −0.280310
\(280\) 0 0
\(281\) −4.81073 −0.286984 −0.143492 0.989651i \(-0.545833\pi\)
−0.143492 + 0.989651i \(0.545833\pi\)
\(282\) 0 0
\(283\) 15.2976 0.909349 0.454675 0.890658i \(-0.349756\pi\)
0.454675 + 0.890658i \(0.349756\pi\)
\(284\) 0 0
\(285\) 1.41667 0.0839164
\(286\) 0 0
\(287\) −4.23544 −0.250010
\(288\) 0 0
\(289\) 22.7919 1.34070
\(290\) 0 0
\(291\) 2.03129 0.119076
\(292\) 0 0
\(293\) 28.3226 1.65463 0.827313 0.561741i \(-0.189868\pi\)
0.827313 + 0.561741i \(0.189868\pi\)
\(294\) 0 0
\(295\) 22.8290 1.32915
\(296\) 0 0
\(297\) 5.51763 0.320166
\(298\) 0 0
\(299\) 0.530107 0.0306569
\(300\) 0 0
\(301\) −4.52179 −0.260632
\(302\) 0 0
\(303\) −7.88165 −0.452789
\(304\) 0 0
\(305\) −8.98169 −0.514290
\(306\) 0 0
\(307\) 9.67118 0.551963 0.275982 0.961163i \(-0.410997\pi\)
0.275982 + 0.961163i \(0.410997\pi\)
\(308\) 0 0
\(309\) 3.55532 0.202255
\(310\) 0 0
\(311\) −25.4302 −1.44202 −0.721008 0.692927i \(-0.756321\pi\)
−0.721008 + 0.692927i \(0.756321\pi\)
\(312\) 0 0
\(313\) −0.926444 −0.0523657 −0.0261829 0.999657i \(-0.508335\pi\)
−0.0261829 + 0.999657i \(0.508335\pi\)
\(314\) 0 0
\(315\) −0.941403 −0.0530421
\(316\) 0 0
\(317\) −5.52724 −0.310441 −0.155220 0.987880i \(-0.549609\pi\)
−0.155220 + 0.987880i \(0.549609\pi\)
\(318\) 0 0
\(319\) −5.51763 −0.308928
\(320\) 0 0
\(321\) −3.84295 −0.214492
\(322\) 0 0
\(323\) 5.48227 0.305042
\(324\) 0 0
\(325\) −1.24197 −0.0688924
\(326\) 0 0
\(327\) 16.9800 0.938996
\(328\) 0 0
\(329\) −2.85581 −0.157446
\(330\) 0 0
\(331\) 7.45576 0.409805 0.204903 0.978782i \(-0.434312\pi\)
0.204903 + 0.978782i \(0.434312\pi\)
\(332\) 0 0
\(333\) −2.51955 −0.138070
\(334\) 0 0
\(335\) −18.3063 −1.00018
\(336\) 0 0
\(337\) 8.64930 0.471157 0.235579 0.971855i \(-0.424301\pi\)
0.235579 + 0.971855i \(0.424301\pi\)
\(338\) 0 0
\(339\) −4.39778 −0.238854
\(340\) 0 0
\(341\) −25.8341 −1.39899
\(342\) 0 0
\(343\) 7.89271 0.426166
\(344\) 0 0
\(345\) 1.63007 0.0877600
\(346\) 0 0
\(347\) −13.9560 −0.749199 −0.374599 0.927187i \(-0.622220\pi\)
−0.374599 + 0.927187i \(0.622220\pi\)
\(348\) 0 0
\(349\) 27.1835 1.45510 0.727551 0.686054i \(-0.240659\pi\)
0.727551 + 0.686054i \(0.240659\pi\)
\(350\) 0 0
\(351\) 0.530107 0.0282950
\(352\) 0 0
\(353\) 24.2745 1.29200 0.646002 0.763336i \(-0.276440\pi\)
0.646002 + 0.763336i \(0.276440\pi\)
\(354\) 0 0
\(355\) −15.5966 −0.827781
\(356\) 0 0
\(357\) −3.64307 −0.192812
\(358\) 0 0
\(359\) −25.7342 −1.35820 −0.679099 0.734046i \(-0.737629\pi\)
−0.679099 + 0.734046i \(0.737629\pi\)
\(360\) 0 0
\(361\) −18.2447 −0.960247
\(362\) 0 0
\(363\) 19.4443 1.02056
\(364\) 0 0
\(365\) −5.30450 −0.277650
\(366\) 0 0
\(367\) 24.5849 1.28332 0.641661 0.766988i \(-0.278246\pi\)
0.641661 + 0.766988i \(0.278246\pi\)
\(368\) 0 0
\(369\) 7.33380 0.381782
\(370\) 0 0
\(371\) −1.46643 −0.0761330
\(372\) 0 0
\(373\) 11.4513 0.592927 0.296463 0.955044i \(-0.404193\pi\)
0.296463 + 0.955044i \(0.404193\pi\)
\(374\) 0 0
\(375\) −11.9694 −0.618097
\(376\) 0 0
\(377\) −0.530107 −0.0273019
\(378\) 0 0
\(379\) −27.8423 −1.43016 −0.715081 0.699042i \(-0.753610\pi\)
−0.715081 + 0.699042i \(0.753610\pi\)
\(380\) 0 0
\(381\) −12.8595 −0.658812
\(382\) 0 0
\(383\) −20.9540 −1.07070 −0.535349 0.844631i \(-0.679820\pi\)
−0.535349 + 0.844631i \(0.679820\pi\)
\(384\) 0 0
\(385\) −5.19432 −0.264727
\(386\) 0 0
\(387\) 7.82962 0.398002
\(388\) 0 0
\(389\) 15.5047 0.786122 0.393061 0.919512i \(-0.371416\pi\)
0.393061 + 0.919512i \(0.371416\pi\)
\(390\) 0 0
\(391\) 6.30808 0.319013
\(392\) 0 0
\(393\) −12.0820 −0.609459
\(394\) 0 0
\(395\) 0.567246 0.0285412
\(396\) 0 0
\(397\) 21.8236 1.09530 0.547649 0.836709i \(-0.315523\pi\)
0.547649 + 0.836709i \(0.315523\pi\)
\(398\) 0 0
\(399\) −0.501919 −0.0251274
\(400\) 0 0
\(401\) 26.5683 1.32676 0.663379 0.748283i \(-0.269122\pi\)
0.663379 + 0.748283i \(0.269122\pi\)
\(402\) 0 0
\(403\) −2.48201 −0.123638
\(404\) 0 0
\(405\) 1.63007 0.0809988
\(406\) 0 0
\(407\) −13.9019 −0.689093
\(408\) 0 0
\(409\) −8.65898 −0.428159 −0.214079 0.976816i \(-0.568675\pi\)
−0.214079 + 0.976816i \(0.568675\pi\)
\(410\) 0 0
\(411\) 1.50378 0.0741760
\(412\) 0 0
\(413\) −8.08817 −0.397993
\(414\) 0 0
\(415\) 16.5598 0.812890
\(416\) 0 0
\(417\) −18.4802 −0.904979
\(418\) 0 0
\(419\) −8.94615 −0.437048 −0.218524 0.975832i \(-0.570124\pi\)
−0.218524 + 0.975832i \(0.570124\pi\)
\(420\) 0 0
\(421\) 2.15954 0.105249 0.0526247 0.998614i \(-0.483241\pi\)
0.0526247 + 0.998614i \(0.483241\pi\)
\(422\) 0 0
\(423\) 4.94492 0.240430
\(424\) 0 0
\(425\) −14.7791 −0.716889
\(426\) 0 0
\(427\) 3.18216 0.153995
\(428\) 0 0
\(429\) 2.92494 0.141217
\(430\) 0 0
\(431\) 40.7851 1.96455 0.982275 0.187447i \(-0.0600212\pi\)
0.982275 + 0.187447i \(0.0600212\pi\)
\(432\) 0 0
\(433\) −15.8505 −0.761727 −0.380863 0.924631i \(-0.624373\pi\)
−0.380863 + 0.924631i \(0.624373\pi\)
\(434\) 0 0
\(435\) −1.63007 −0.0781558
\(436\) 0 0
\(437\) 0.869087 0.0415741
\(438\) 0 0
\(439\) −10.6378 −0.507713 −0.253856 0.967242i \(-0.581699\pi\)
−0.253856 + 0.967242i \(0.581699\pi\)
\(440\) 0 0
\(441\) −6.66647 −0.317451
\(442\) 0 0
\(443\) −36.4732 −1.73289 −0.866446 0.499271i \(-0.833601\pi\)
−0.866446 + 0.499271i \(0.833601\pi\)
\(444\) 0 0
\(445\) 24.2453 1.14934
\(446\) 0 0
\(447\) 5.69566 0.269396
\(448\) 0 0
\(449\) 16.9657 0.800661 0.400330 0.916371i \(-0.368895\pi\)
0.400330 + 0.916371i \(0.368895\pi\)
\(450\) 0 0
\(451\) 40.4652 1.90543
\(452\) 0 0
\(453\) −11.4329 −0.537164
\(454\) 0 0
\(455\) −0.499044 −0.0233956
\(456\) 0 0
\(457\) 9.34001 0.436907 0.218454 0.975847i \(-0.429899\pi\)
0.218454 + 0.975847i \(0.429899\pi\)
\(458\) 0 0
\(459\) 6.30808 0.294436
\(460\) 0 0
\(461\) 21.6088 1.00642 0.503210 0.864164i \(-0.332152\pi\)
0.503210 + 0.864164i \(0.332152\pi\)
\(462\) 0 0
\(463\) −17.4907 −0.812863 −0.406431 0.913681i \(-0.633227\pi\)
−0.406431 + 0.913681i \(0.633227\pi\)
\(464\) 0 0
\(465\) −7.63213 −0.353932
\(466\) 0 0
\(467\) 16.7098 0.773240 0.386620 0.922239i \(-0.373643\pi\)
0.386620 + 0.922239i \(0.373643\pi\)
\(468\) 0 0
\(469\) 6.48583 0.299488
\(470\) 0 0
\(471\) −2.38936 −0.110096
\(472\) 0 0
\(473\) 43.2010 1.98638
\(474\) 0 0
\(475\) −2.03616 −0.0934256
\(476\) 0 0
\(477\) 2.53916 0.116260
\(478\) 0 0
\(479\) −7.66553 −0.350247 −0.175123 0.984546i \(-0.556032\pi\)
−0.175123 + 0.984546i \(0.556032\pi\)
\(480\) 0 0
\(481\) −1.33563 −0.0608995
\(482\) 0 0
\(483\) −0.577524 −0.0262782
\(484\) 0 0
\(485\) 3.31115 0.150351
\(486\) 0 0
\(487\) 22.7388 1.03039 0.515196 0.857073i \(-0.327719\pi\)
0.515196 + 0.857073i \(0.327719\pi\)
\(488\) 0 0
\(489\) −23.0628 −1.04293
\(490\) 0 0
\(491\) −6.66675 −0.300866 −0.150433 0.988620i \(-0.548067\pi\)
−0.150433 + 0.988620i \(0.548067\pi\)
\(492\) 0 0
\(493\) −6.30808 −0.284102
\(494\) 0 0
\(495\) 8.99412 0.404256
\(496\) 0 0
\(497\) 5.52578 0.247865
\(498\) 0 0
\(499\) −36.1611 −1.61879 −0.809397 0.587262i \(-0.800206\pi\)
−0.809397 + 0.587262i \(0.800206\pi\)
\(500\) 0 0
\(501\) −2.42660 −0.108412
\(502\) 0 0
\(503\) 13.1400 0.585886 0.292943 0.956130i \(-0.405365\pi\)
0.292943 + 0.956130i \(0.405365\pi\)
\(504\) 0 0
\(505\) −12.8476 −0.571712
\(506\) 0 0
\(507\) −12.7190 −0.564870
\(508\) 0 0
\(509\) −33.1123 −1.46767 −0.733837 0.679325i \(-0.762273\pi\)
−0.733837 + 0.679325i \(0.762273\pi\)
\(510\) 0 0
\(511\) 1.87935 0.0831377
\(512\) 0 0
\(513\) 0.869087 0.0383711
\(514\) 0 0
\(515\) 5.79541 0.255376
\(516\) 0 0
\(517\) 27.2842 1.19996
\(518\) 0 0
\(519\) −15.0262 −0.659575
\(520\) 0 0
\(521\) −9.99806 −0.438023 −0.219012 0.975722i \(-0.570283\pi\)
−0.219012 + 0.975722i \(0.570283\pi\)
\(522\) 0 0
\(523\) 2.52154 0.110259 0.0551297 0.998479i \(-0.482443\pi\)
0.0551297 + 0.998479i \(0.482443\pi\)
\(524\) 0 0
\(525\) 1.35307 0.0590527
\(526\) 0 0
\(527\) −29.5350 −1.28657
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 14.0049 0.607762
\(532\) 0 0
\(533\) 3.88770 0.168395
\(534\) 0 0
\(535\) −6.26427 −0.270828
\(536\) 0 0
\(537\) 15.9353 0.687660
\(538\) 0 0
\(539\) −36.7831 −1.58436
\(540\) 0 0
\(541\) −13.5362 −0.581968 −0.290984 0.956728i \(-0.593983\pi\)
−0.290984 + 0.956728i \(0.593983\pi\)
\(542\) 0 0
\(543\) −12.1265 −0.520400
\(544\) 0 0
\(545\) 27.6786 1.18562
\(546\) 0 0
\(547\) −8.42273 −0.360130 −0.180065 0.983655i \(-0.557631\pi\)
−0.180065 + 0.983655i \(0.557631\pi\)
\(548\) 0 0
\(549\) −5.51000 −0.235161
\(550\) 0 0
\(551\) −0.869087 −0.0370244
\(552\) 0 0
\(553\) −0.200972 −0.00854619
\(554\) 0 0
\(555\) −4.10704 −0.174334
\(556\) 0 0
\(557\) −29.9001 −1.26691 −0.633454 0.773781i \(-0.718363\pi\)
−0.633454 + 0.773781i \(0.718363\pi\)
\(558\) 0 0
\(559\) 4.15054 0.175549
\(560\) 0 0
\(561\) 34.8057 1.46950
\(562\) 0 0
\(563\) −27.4066 −1.15505 −0.577526 0.816373i \(-0.695982\pi\)
−0.577526 + 0.816373i \(0.695982\pi\)
\(564\) 0 0
\(565\) −7.16868 −0.301588
\(566\) 0 0
\(567\) −0.577524 −0.0242537
\(568\) 0 0
\(569\) −19.5145 −0.818089 −0.409044 0.912514i \(-0.634138\pi\)
−0.409044 + 0.912514i \(0.634138\pi\)
\(570\) 0 0
\(571\) 32.2698 1.35045 0.675224 0.737613i \(-0.264047\pi\)
0.675224 + 0.737613i \(0.264047\pi\)
\(572\) 0 0
\(573\) 2.12503 0.0887743
\(574\) 0 0
\(575\) −2.34288 −0.0977047
\(576\) 0 0
\(577\) −11.5878 −0.482407 −0.241203 0.970475i \(-0.577542\pi\)
−0.241203 + 0.970475i \(0.577542\pi\)
\(578\) 0 0
\(579\) −13.0166 −0.540953
\(580\) 0 0
\(581\) −5.86705 −0.243406
\(582\) 0 0
\(583\) 14.0102 0.580241
\(584\) 0 0
\(585\) 0.864111 0.0357266
\(586\) 0 0
\(587\) 21.7791 0.898919 0.449460 0.893301i \(-0.351617\pi\)
0.449460 + 0.893301i \(0.351617\pi\)
\(588\) 0 0
\(589\) −4.06915 −0.167666
\(590\) 0 0
\(591\) 11.2634 0.463314
\(592\) 0 0
\(593\) −13.9266 −0.571898 −0.285949 0.958245i \(-0.592309\pi\)
−0.285949 + 0.958245i \(0.592309\pi\)
\(594\) 0 0
\(595\) −5.93845 −0.243453
\(596\) 0 0
\(597\) −9.31732 −0.381333
\(598\) 0 0
\(599\) −40.5647 −1.65743 −0.828714 0.559672i \(-0.810927\pi\)
−0.828714 + 0.559672i \(0.810927\pi\)
\(600\) 0 0
\(601\) 17.5871 0.717391 0.358695 0.933455i \(-0.383222\pi\)
0.358695 + 0.933455i \(0.383222\pi\)
\(602\) 0 0
\(603\) −11.2304 −0.457337
\(604\) 0 0
\(605\) 31.6955 1.28861
\(606\) 0 0
\(607\) −2.45923 −0.0998170 −0.0499085 0.998754i \(-0.515893\pi\)
−0.0499085 + 0.998754i \(0.515893\pi\)
\(608\) 0 0
\(609\) 0.577524 0.0234024
\(610\) 0 0
\(611\) 2.62134 0.106048
\(612\) 0 0
\(613\) 10.4024 0.420148 0.210074 0.977686i \(-0.432630\pi\)
0.210074 + 0.977686i \(0.432630\pi\)
\(614\) 0 0
\(615\) 11.9546 0.482056
\(616\) 0 0
\(617\) 37.0896 1.49317 0.746586 0.665288i \(-0.231691\pi\)
0.746586 + 0.665288i \(0.231691\pi\)
\(618\) 0 0
\(619\) 27.3901 1.10090 0.550451 0.834868i \(-0.314456\pi\)
0.550451 + 0.834868i \(0.314456\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −8.58996 −0.344149
\(624\) 0 0
\(625\) −7.79655 −0.311862
\(626\) 0 0
\(627\) 4.79530 0.191506
\(628\) 0 0
\(629\) −15.8935 −0.633716
\(630\) 0 0
\(631\) −21.7665 −0.866509 −0.433254 0.901272i \(-0.642635\pi\)
−0.433254 + 0.901272i \(0.642635\pi\)
\(632\) 0 0
\(633\) 7.76189 0.308507
\(634\) 0 0
\(635\) −20.9619 −0.831847
\(636\) 0 0
\(637\) −3.53394 −0.140020
\(638\) 0 0
\(639\) −9.56805 −0.378506
\(640\) 0 0
\(641\) −14.5732 −0.575605 −0.287802 0.957690i \(-0.592925\pi\)
−0.287802 + 0.957690i \(0.592925\pi\)
\(642\) 0 0
\(643\) −22.3695 −0.882166 −0.441083 0.897466i \(-0.645405\pi\)
−0.441083 + 0.897466i \(0.645405\pi\)
\(644\) 0 0
\(645\) 12.7628 0.502535
\(646\) 0 0
\(647\) −37.6735 −1.48110 −0.740550 0.672002i \(-0.765435\pi\)
−0.740550 + 0.672002i \(0.765435\pi\)
\(648\) 0 0
\(649\) 77.2740 3.03327
\(650\) 0 0
\(651\) 2.70402 0.105979
\(652\) 0 0
\(653\) 5.53979 0.216789 0.108394 0.994108i \(-0.465429\pi\)
0.108394 + 0.994108i \(0.465429\pi\)
\(654\) 0 0
\(655\) −19.6946 −0.769530
\(656\) 0 0
\(657\) −3.25416 −0.126957
\(658\) 0 0
\(659\) 1.64161 0.0639479 0.0319739 0.999489i \(-0.489821\pi\)
0.0319739 + 0.999489i \(0.489821\pi\)
\(660\) 0 0
\(661\) 21.5960 0.839986 0.419993 0.907527i \(-0.362033\pi\)
0.419993 + 0.907527i \(0.362033\pi\)
\(662\) 0 0
\(663\) 3.34396 0.129869
\(664\) 0 0
\(665\) −0.818162 −0.0317270
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 9.00853 0.348290
\(670\) 0 0
\(671\) −30.4022 −1.17366
\(672\) 0 0
\(673\) −19.1413 −0.737845 −0.368922 0.929460i \(-0.620273\pi\)
−0.368922 + 0.929460i \(0.620273\pi\)
\(674\) 0 0
\(675\) −2.34288 −0.0901773
\(676\) 0 0
\(677\) 41.5452 1.59671 0.798356 0.602185i \(-0.205703\pi\)
0.798356 + 0.602185i \(0.205703\pi\)
\(678\) 0 0
\(679\) −1.17312 −0.0450202
\(680\) 0 0
\(681\) 18.9075 0.724536
\(682\) 0 0
\(683\) −17.7308 −0.678450 −0.339225 0.940705i \(-0.610165\pi\)
−0.339225 + 0.940705i \(0.610165\pi\)
\(684\) 0 0
\(685\) 2.45127 0.0936580
\(686\) 0 0
\(687\) 0.0153065 0.000583981 0
\(688\) 0 0
\(689\) 1.34603 0.0512795
\(690\) 0 0
\(691\) 31.0918 1.18279 0.591393 0.806383i \(-0.298578\pi\)
0.591393 + 0.806383i \(0.298578\pi\)
\(692\) 0 0
\(693\) −3.18656 −0.121048
\(694\) 0 0
\(695\) −30.1240 −1.14267
\(696\) 0 0
\(697\) 46.2622 1.75231
\(698\) 0 0
\(699\) 10.9974 0.415958
\(700\) 0 0
\(701\) 14.1464 0.534301 0.267151 0.963655i \(-0.413918\pi\)
0.267151 + 0.963655i \(0.413918\pi\)
\(702\) 0 0
\(703\) −2.18971 −0.0825863
\(704\) 0 0
\(705\) 8.06056 0.303578
\(706\) 0 0
\(707\) 4.55184 0.171190
\(708\) 0 0
\(709\) −32.5729 −1.22330 −0.611650 0.791129i \(-0.709494\pi\)
−0.611650 + 0.791129i \(0.709494\pi\)
\(710\) 0 0
\(711\) 0.347989 0.0130506
\(712\) 0 0
\(713\) −4.68209 −0.175346
\(714\) 0 0
\(715\) 4.76785 0.178307
\(716\) 0 0
\(717\) 17.4397 0.651296
\(718\) 0 0
\(719\) 31.3035 1.16742 0.583712 0.811961i \(-0.301600\pi\)
0.583712 + 0.811961i \(0.301600\pi\)
\(720\) 0 0
\(721\) −2.05328 −0.0764682
\(722\) 0 0
\(723\) 30.6019 1.13810
\(724\) 0 0
\(725\) 2.34288 0.0870122
\(726\) 0 0
\(727\) −34.3196 −1.27284 −0.636421 0.771342i \(-0.719586\pi\)
−0.636421 + 0.771342i \(0.719586\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 49.3899 1.82675
\(732\) 0 0
\(733\) −26.2172 −0.968355 −0.484177 0.874970i \(-0.660881\pi\)
−0.484177 + 0.874970i \(0.660881\pi\)
\(734\) 0 0
\(735\) −10.8668 −0.400828
\(736\) 0 0
\(737\) −61.9653 −2.28252
\(738\) 0 0
\(739\) −37.3977 −1.37570 −0.687848 0.725855i \(-0.741444\pi\)
−0.687848 + 0.725855i \(0.741444\pi\)
\(740\) 0 0
\(741\) 0.460709 0.0169246
\(742\) 0 0
\(743\) 36.4872 1.33858 0.669292 0.742999i \(-0.266597\pi\)
0.669292 + 0.742999i \(0.266597\pi\)
\(744\) 0 0
\(745\) 9.28432 0.340151
\(746\) 0 0
\(747\) 10.1590 0.371698
\(748\) 0 0
\(749\) 2.21939 0.0810949
\(750\) 0 0
\(751\) 38.5428 1.40645 0.703223 0.710970i \(-0.251744\pi\)
0.703223 + 0.710970i \(0.251744\pi\)
\(752\) 0 0
\(753\) 13.7596 0.501427
\(754\) 0 0
\(755\) −18.6364 −0.678248
\(756\) 0 0
\(757\) 30.5679 1.11101 0.555505 0.831513i \(-0.312525\pi\)
0.555505 + 0.831513i \(0.312525\pi\)
\(758\) 0 0
\(759\) 5.51763 0.200277
\(760\) 0 0
\(761\) −13.3966 −0.485627 −0.242813 0.970073i \(-0.578070\pi\)
−0.242813 + 0.970073i \(0.578070\pi\)
\(762\) 0 0
\(763\) −9.80635 −0.355014
\(764\) 0 0
\(765\) 10.2826 0.371768
\(766\) 0 0
\(767\) 7.42410 0.268069
\(768\) 0 0
\(769\) −8.23363 −0.296912 −0.148456 0.988919i \(-0.547430\pi\)
−0.148456 + 0.988919i \(0.547430\pi\)
\(770\) 0 0
\(771\) 18.0156 0.648815
\(772\) 0 0
\(773\) 26.6397 0.958164 0.479082 0.877770i \(-0.340970\pi\)
0.479082 + 0.877770i \(0.340970\pi\)
\(774\) 0 0
\(775\) 10.9696 0.394038
\(776\) 0 0
\(777\) 1.45510 0.0522014
\(778\) 0 0
\(779\) 6.37371 0.228362
\(780\) 0 0
\(781\) −52.7930 −1.88908
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −3.89481 −0.139012
\(786\) 0 0
\(787\) 18.7171 0.667193 0.333597 0.942716i \(-0.391738\pi\)
0.333597 + 0.942716i \(0.391738\pi\)
\(788\) 0 0
\(789\) −8.65502 −0.308127
\(790\) 0 0
\(791\) 2.53982 0.0903056
\(792\) 0 0
\(793\) −2.92089 −0.103724
\(794\) 0 0
\(795\) 4.13901 0.146795
\(796\) 0 0
\(797\) −37.8850 −1.34196 −0.670978 0.741477i \(-0.734125\pi\)
−0.670978 + 0.741477i \(0.734125\pi\)
\(798\) 0 0
\(799\) 31.1929 1.10353
\(800\) 0 0
\(801\) 14.8738 0.525539
\(802\) 0 0
\(803\) −17.9553 −0.633627
\(804\) 0 0
\(805\) −0.941403 −0.0331801
\(806\) 0 0
\(807\) −12.1540 −0.427841
\(808\) 0 0
\(809\) −6.20298 −0.218085 −0.109043 0.994037i \(-0.534778\pi\)
−0.109043 + 0.994037i \(0.534778\pi\)
\(810\) 0 0
\(811\) −50.6931 −1.78008 −0.890038 0.455885i \(-0.849323\pi\)
−0.890038 + 0.455885i \(0.849323\pi\)
\(812\) 0 0
\(813\) 9.41238 0.330106
\(814\) 0 0
\(815\) −37.5939 −1.31686
\(816\) 0 0
\(817\) 6.80462 0.238064
\(818\) 0 0
\(819\) −0.306149 −0.0106977
\(820\) 0 0
\(821\) −23.1105 −0.806561 −0.403280 0.915076i \(-0.632130\pi\)
−0.403280 + 0.915076i \(0.632130\pi\)
\(822\) 0 0
\(823\) −9.83204 −0.342723 −0.171362 0.985208i \(-0.554817\pi\)
−0.171362 + 0.985208i \(0.554817\pi\)
\(824\) 0 0
\(825\) −12.9271 −0.450065
\(826\) 0 0
\(827\) −13.3080 −0.462766 −0.231383 0.972863i \(-0.574325\pi\)
−0.231383 + 0.972863i \(0.574325\pi\)
\(828\) 0 0
\(829\) −17.0463 −0.592043 −0.296021 0.955181i \(-0.595660\pi\)
−0.296021 + 0.955181i \(0.595660\pi\)
\(830\) 0 0
\(831\) −22.4479 −0.778711
\(832\) 0 0
\(833\) −42.0526 −1.45704
\(834\) 0 0
\(835\) −3.95552 −0.136886
\(836\) 0 0
\(837\) −4.68209 −0.161837
\(838\) 0 0
\(839\) 3.46221 0.119529 0.0597644 0.998213i \(-0.480965\pi\)
0.0597644 + 0.998213i \(0.480965\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −4.81073 −0.165690
\(844\) 0 0
\(845\) −20.7328 −0.713231
\(846\) 0 0
\(847\) −11.2295 −0.385851
\(848\) 0 0
\(849\) 15.2976 0.525013
\(850\) 0 0
\(851\) −2.51955 −0.0863690
\(852\) 0 0
\(853\) −23.8575 −0.816865 −0.408432 0.912789i \(-0.633924\pi\)
−0.408432 + 0.912789i \(0.633924\pi\)
\(854\) 0 0
\(855\) 1.41667 0.0484492
\(856\) 0 0
\(857\) 13.1060 0.447691 0.223846 0.974625i \(-0.428139\pi\)
0.223846 + 0.974625i \(0.428139\pi\)
\(858\) 0 0
\(859\) 20.8685 0.712024 0.356012 0.934481i \(-0.384136\pi\)
0.356012 + 0.934481i \(0.384136\pi\)
\(860\) 0 0
\(861\) −4.23544 −0.144343
\(862\) 0 0
\(863\) 54.2789 1.84767 0.923837 0.382785i \(-0.125035\pi\)
0.923837 + 0.382785i \(0.125035\pi\)
\(864\) 0 0
\(865\) −24.4937 −0.832810
\(866\) 0 0
\(867\) 22.7919 0.774053
\(868\) 0 0
\(869\) 1.92008 0.0651341
\(870\) 0 0
\(871\) −5.95332 −0.201720
\(872\) 0 0
\(873\) 2.03129 0.0687488
\(874\) 0 0
\(875\) 6.91261 0.233689
\(876\) 0 0
\(877\) −42.0972 −1.42152 −0.710761 0.703433i \(-0.751649\pi\)
−0.710761 + 0.703433i \(0.751649\pi\)
\(878\) 0 0
\(879\) 28.3226 0.955299
\(880\) 0 0
\(881\) 10.7828 0.363283 0.181642 0.983365i \(-0.441859\pi\)
0.181642 + 0.983365i \(0.441859\pi\)
\(882\) 0 0
\(883\) −48.5709 −1.63454 −0.817270 0.576255i \(-0.804514\pi\)
−0.817270 + 0.576255i \(0.804514\pi\)
\(884\) 0 0
\(885\) 22.8290 0.767388
\(886\) 0 0
\(887\) −30.2426 −1.01545 −0.507723 0.861520i \(-0.669513\pi\)
−0.507723 + 0.861520i \(0.669513\pi\)
\(888\) 0 0
\(889\) 7.42667 0.249083
\(890\) 0 0
\(891\) 5.51763 0.184848
\(892\) 0 0
\(893\) 4.29757 0.143813
\(894\) 0 0
\(895\) 25.9757 0.868271
\(896\) 0 0
\(897\) 0.530107 0.0176998
\(898\) 0 0
\(899\) 4.68209 0.156157
\(900\) 0 0
\(901\) 16.0172 0.533611
\(902\) 0 0
\(903\) −4.52179 −0.150476
\(904\) 0 0
\(905\) −19.7671 −0.657081
\(906\) 0 0
\(907\) −3.52279 −0.116972 −0.0584862 0.998288i \(-0.518627\pi\)
−0.0584862 + 0.998288i \(0.518627\pi\)
\(908\) 0 0
\(909\) −7.88165 −0.261418
\(910\) 0 0
\(911\) 34.7657 1.15184 0.575919 0.817507i \(-0.304644\pi\)
0.575919 + 0.817507i \(0.304644\pi\)
\(912\) 0 0
\(913\) 56.0535 1.85510
\(914\) 0 0
\(915\) −8.98169 −0.296925
\(916\) 0 0
\(917\) 6.97767 0.230423
\(918\) 0 0
\(919\) 36.2219 1.19485 0.597425 0.801925i \(-0.296191\pi\)
0.597425 + 0.801925i \(0.296191\pi\)
\(920\) 0 0
\(921\) 9.67118 0.318676
\(922\) 0 0
\(923\) −5.07209 −0.166950
\(924\) 0 0
\(925\) 5.90299 0.194089
\(926\) 0 0
\(927\) 3.55532 0.116772
\(928\) 0 0
\(929\) −1.45222 −0.0476458 −0.0238229 0.999716i \(-0.507584\pi\)
−0.0238229 + 0.999716i \(0.507584\pi\)
\(930\) 0 0
\(931\) −5.79374 −0.189882
\(932\) 0 0
\(933\) −25.4302 −0.832548
\(934\) 0 0
\(935\) 56.7356 1.85545
\(936\) 0 0
\(937\) 21.0101 0.686372 0.343186 0.939268i \(-0.388494\pi\)
0.343186 + 0.939268i \(0.388494\pi\)
\(938\) 0 0
\(939\) −0.926444 −0.0302334
\(940\) 0 0
\(941\) −34.7983 −1.13439 −0.567196 0.823583i \(-0.691972\pi\)
−0.567196 + 0.823583i \(0.691972\pi\)
\(942\) 0 0
\(943\) 7.33380 0.238821
\(944\) 0 0
\(945\) −0.941403 −0.0306239
\(946\) 0 0
\(947\) −49.7719 −1.61737 −0.808685 0.588242i \(-0.799820\pi\)
−0.808685 + 0.588242i \(0.799820\pi\)
\(948\) 0 0
\(949\) −1.72505 −0.0559976
\(950\) 0 0
\(951\) −5.52724 −0.179233
\(952\) 0 0
\(953\) −7.49439 −0.242767 −0.121384 0.992606i \(-0.538733\pi\)
−0.121384 + 0.992606i \(0.538733\pi\)
\(954\) 0 0
\(955\) 3.46394 0.112090
\(956\) 0 0
\(957\) −5.51763 −0.178360
\(958\) 0 0
\(959\) −0.868469 −0.0280443
\(960\) 0 0
\(961\) −9.07800 −0.292839
\(962\) 0 0
\(963\) −3.84295 −0.123837
\(964\) 0 0
\(965\) −21.2180 −0.683033
\(966\) 0 0
\(967\) 28.7907 0.925848 0.462924 0.886398i \(-0.346800\pi\)
0.462924 + 0.886398i \(0.346800\pi\)
\(968\) 0 0
\(969\) 5.48227 0.176116
\(970\) 0 0
\(971\) −28.6646 −0.919892 −0.459946 0.887947i \(-0.652131\pi\)
−0.459946 + 0.887947i \(0.652131\pi\)
\(972\) 0 0
\(973\) 10.6728 0.342153
\(974\) 0 0
\(975\) −1.24197 −0.0397750
\(976\) 0 0
\(977\) 13.1205 0.419761 0.209881 0.977727i \(-0.432692\pi\)
0.209881 + 0.977727i \(0.432692\pi\)
\(978\) 0 0
\(979\) 82.0680 2.62291
\(980\) 0 0
\(981\) 16.9800 0.542130
\(982\) 0 0
\(983\) 13.4989 0.430547 0.215273 0.976554i \(-0.430936\pi\)
0.215273 + 0.976554i \(0.430936\pi\)
\(984\) 0 0
\(985\) 18.3601 0.585001
\(986\) 0 0
\(987\) −2.85581 −0.0909014
\(988\) 0 0
\(989\) 7.82962 0.248967
\(990\) 0 0
\(991\) −26.8488 −0.852881 −0.426440 0.904516i \(-0.640233\pi\)
−0.426440 + 0.904516i \(0.640233\pi\)
\(992\) 0 0
\(993\) 7.45576 0.236601
\(994\) 0 0
\(995\) −15.1879 −0.481488
\(996\) 0 0
\(997\) 26.4714 0.838359 0.419179 0.907903i \(-0.362318\pi\)
0.419179 + 0.907903i \(0.362318\pi\)
\(998\) 0 0
\(999\) −2.51955 −0.0797150
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 \(a_p\))