Properties

Label 6008.2.a.e.1.14
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.38456 q^{3}\) \(-1.32143 q^{5}\) \(+2.39545 q^{7}\) \(-1.08299 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.38456 q^{3}\) \(-1.32143 q^{5}\) \(+2.39545 q^{7}\) \(-1.08299 q^{9}\) \(+3.31333 q^{11}\) \(-3.52800 q^{13}\) \(+1.82960 q^{15}\) \(+2.72465 q^{17}\) \(+6.86584 q^{19}\) \(-3.31664 q^{21}\) \(+6.61624 q^{23}\) \(-3.25383 q^{25}\) \(+5.65315 q^{27}\) \(-7.66755 q^{29}\) \(-1.56808 q^{31}\) \(-4.58751 q^{33}\) \(-3.16541 q^{35}\) \(+1.61416 q^{37}\) \(+4.88473 q^{39}\) \(+3.10413 q^{41}\) \(-2.57942 q^{43}\) \(+1.43109 q^{45}\) \(-2.66539 q^{47}\) \(-1.26184 q^{49}\) \(-3.77244 q^{51}\) \(+3.91075 q^{53}\) \(-4.37832 q^{55}\) \(-9.50618 q^{57}\) \(+1.25988 q^{59}\) \(+11.2785 q^{61}\) \(-2.59424 q^{63}\) \(+4.66199 q^{65}\) \(+9.01948 q^{67}\) \(-9.16060 q^{69}\) \(+6.20826 q^{71}\) \(-8.76402 q^{73}\) \(+4.50513 q^{75}\) \(+7.93691 q^{77}\) \(-10.5971 q^{79}\) \(-4.57817 q^{81}\) \(-10.8953 q^{83}\) \(-3.60042 q^{85}\) \(+10.6162 q^{87}\) \(-13.0225 q^{89}\) \(-8.45112 q^{91}\) \(+2.17110 q^{93}\) \(-9.07270 q^{95}\) \(+3.05044 q^{97}\) \(-3.58830 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.38456 −0.799377 −0.399689 0.916651i \(-0.630882\pi\)
−0.399689 + 0.916651i \(0.630882\pi\)
\(4\) 0 0
\(5\) −1.32143 −0.590960 −0.295480 0.955349i \(-0.595480\pi\)
−0.295480 + 0.955349i \(0.595480\pi\)
\(6\) 0 0
\(7\) 2.39545 0.905393 0.452697 0.891665i \(-0.350462\pi\)
0.452697 + 0.891665i \(0.350462\pi\)
\(8\) 0 0
\(9\) −1.08299 −0.360996
\(10\) 0 0
\(11\) 3.31333 0.999007 0.499504 0.866312i \(-0.333516\pi\)
0.499504 + 0.866312i \(0.333516\pi\)
\(12\) 0 0
\(13\) −3.52800 −0.978490 −0.489245 0.872146i \(-0.662728\pi\)
−0.489245 + 0.872146i \(0.662728\pi\)
\(14\) 0 0
\(15\) 1.82960 0.472400
\(16\) 0 0
\(17\) 2.72465 0.660824 0.330412 0.943837i \(-0.392812\pi\)
0.330412 + 0.943837i \(0.392812\pi\)
\(18\) 0 0
\(19\) 6.86584 1.57513 0.787566 0.616230i \(-0.211341\pi\)
0.787566 + 0.616230i \(0.211341\pi\)
\(20\) 0 0
\(21\) −3.31664 −0.723751
\(22\) 0 0
\(23\) 6.61624 1.37958 0.689791 0.724009i \(-0.257702\pi\)
0.689791 + 0.724009i \(0.257702\pi\)
\(24\) 0 0
\(25\) −3.25383 −0.650766
\(26\) 0 0
\(27\) 5.65315 1.08795
\(28\) 0 0
\(29\) −7.66755 −1.42383 −0.711915 0.702266i \(-0.752172\pi\)
−0.711915 + 0.702266i \(0.752172\pi\)
\(30\) 0 0
\(31\) −1.56808 −0.281635 −0.140818 0.990036i \(-0.544973\pi\)
−0.140818 + 0.990036i \(0.544973\pi\)
\(32\) 0 0
\(33\) −4.58751 −0.798583
\(34\) 0 0
\(35\) −3.16541 −0.535051
\(36\) 0 0
\(37\) 1.61416 0.265366 0.132683 0.991159i \(-0.457641\pi\)
0.132683 + 0.991159i \(0.457641\pi\)
\(38\) 0 0
\(39\) 4.88473 0.782182
\(40\) 0 0
\(41\) 3.10413 0.484783 0.242392 0.970178i \(-0.422068\pi\)
0.242392 + 0.970178i \(0.422068\pi\)
\(42\) 0 0
\(43\) −2.57942 −0.393358 −0.196679 0.980468i \(-0.563016\pi\)
−0.196679 + 0.980468i \(0.563016\pi\)
\(44\) 0 0
\(45\) 1.43109 0.213334
\(46\) 0 0
\(47\) −2.66539 −0.388787 −0.194394 0.980924i \(-0.562274\pi\)
−0.194394 + 0.980924i \(0.562274\pi\)
\(48\) 0 0
\(49\) −1.26184 −0.180263
\(50\) 0 0
\(51\) −3.77244 −0.528248
\(52\) 0 0
\(53\) 3.91075 0.537183 0.268592 0.963254i \(-0.413442\pi\)
0.268592 + 0.963254i \(0.413442\pi\)
\(54\) 0 0
\(55\) −4.37832 −0.590373
\(56\) 0 0
\(57\) −9.50618 −1.25912
\(58\) 0 0
\(59\) 1.25988 0.164022 0.0820112 0.996631i \(-0.473866\pi\)
0.0820112 + 0.996631i \(0.473866\pi\)
\(60\) 0 0
\(61\) 11.2785 1.44406 0.722030 0.691862i \(-0.243209\pi\)
0.722030 + 0.691862i \(0.243209\pi\)
\(62\) 0 0
\(63\) −2.59424 −0.326844
\(64\) 0 0
\(65\) 4.66199 0.578248
\(66\) 0 0
\(67\) 9.01948 1.10191 0.550953 0.834537i \(-0.314265\pi\)
0.550953 + 0.834537i \(0.314265\pi\)
\(68\) 0 0
\(69\) −9.16060 −1.10281
\(70\) 0 0
\(71\) 6.20826 0.736785 0.368392 0.929670i \(-0.379908\pi\)
0.368392 + 0.929670i \(0.379908\pi\)
\(72\) 0 0
\(73\) −8.76402 −1.02575 −0.512875 0.858463i \(-0.671420\pi\)
−0.512875 + 0.858463i \(0.671420\pi\)
\(74\) 0 0
\(75\) 4.50513 0.520208
\(76\) 0 0
\(77\) 7.93691 0.904495
\(78\) 0 0
\(79\) −10.5971 −1.19227 −0.596135 0.802884i \(-0.703298\pi\)
−0.596135 + 0.802884i \(0.703298\pi\)
\(80\) 0 0
\(81\) −4.57817 −0.508685
\(82\) 0 0
\(83\) −10.8953 −1.19591 −0.597955 0.801530i \(-0.704020\pi\)
−0.597955 + 0.801530i \(0.704020\pi\)
\(84\) 0 0
\(85\) −3.60042 −0.390521
\(86\) 0 0
\(87\) 10.6162 1.13818
\(88\) 0 0
\(89\) −13.0225 −1.38039 −0.690194 0.723625i \(-0.742475\pi\)
−0.690194 + 0.723625i \(0.742475\pi\)
\(90\) 0 0
\(91\) −8.45112 −0.885918
\(92\) 0 0
\(93\) 2.17110 0.225133
\(94\) 0 0
\(95\) −9.07270 −0.930840
\(96\) 0 0
\(97\) 3.05044 0.309725 0.154863 0.987936i \(-0.450507\pi\)
0.154863 + 0.987936i \(0.450507\pi\)
\(98\) 0 0
\(99\) −3.58830 −0.360638
\(100\) 0 0
\(101\) 0.567035 0.0564221 0.0282110 0.999602i \(-0.491019\pi\)
0.0282110 + 0.999602i \(0.491019\pi\)
\(102\) 0 0
\(103\) −7.62185 −0.751003 −0.375502 0.926822i \(-0.622530\pi\)
−0.375502 + 0.926822i \(0.622530\pi\)
\(104\) 0 0
\(105\) 4.38270 0.427708
\(106\) 0 0
\(107\) −0.433918 −0.0419484 −0.0209742 0.999780i \(-0.506677\pi\)
−0.0209742 + 0.999780i \(0.506677\pi\)
\(108\) 0 0
\(109\) 12.5223 1.19942 0.599710 0.800217i \(-0.295282\pi\)
0.599710 + 0.800217i \(0.295282\pi\)
\(110\) 0 0
\(111\) −2.23490 −0.212127
\(112\) 0 0
\(113\) 11.7364 1.10407 0.552034 0.833821i \(-0.313852\pi\)
0.552034 + 0.833821i \(0.313852\pi\)
\(114\) 0 0
\(115\) −8.74288 −0.815278
\(116\) 0 0
\(117\) 3.82078 0.353231
\(118\) 0 0
\(119\) 6.52675 0.598306
\(120\) 0 0
\(121\) −0.0218313 −0.00198467
\(122\) 0 0
\(123\) −4.29786 −0.387525
\(124\) 0 0
\(125\) 10.9068 0.975537
\(126\) 0 0
\(127\) −5.29959 −0.470262 −0.235131 0.971964i \(-0.575552\pi\)
−0.235131 + 0.971964i \(0.575552\pi\)
\(128\) 0 0
\(129\) 3.57136 0.314441
\(130\) 0 0
\(131\) −9.13635 −0.798246 −0.399123 0.916897i \(-0.630685\pi\)
−0.399123 + 0.916897i \(0.630685\pi\)
\(132\) 0 0
\(133\) 16.4468 1.42611
\(134\) 0 0
\(135\) −7.47022 −0.642934
\(136\) 0 0
\(137\) −12.2093 −1.04311 −0.521554 0.853218i \(-0.674648\pi\)
−0.521554 + 0.853218i \(0.674648\pi\)
\(138\) 0 0
\(139\) 17.2855 1.46614 0.733068 0.680156i \(-0.238088\pi\)
0.733068 + 0.680156i \(0.238088\pi\)
\(140\) 0 0
\(141\) 3.69040 0.310787
\(142\) 0 0
\(143\) −11.6894 −0.977518
\(144\) 0 0
\(145\) 10.1321 0.841426
\(146\) 0 0
\(147\) 1.74709 0.144098
\(148\) 0 0
\(149\) 11.7744 0.964595 0.482298 0.876007i \(-0.339802\pi\)
0.482298 + 0.876007i \(0.339802\pi\)
\(150\) 0 0
\(151\) 11.3961 0.927405 0.463702 0.885991i \(-0.346521\pi\)
0.463702 + 0.885991i \(0.346521\pi\)
\(152\) 0 0
\(153\) −2.95076 −0.238555
\(154\) 0 0
\(155\) 2.07210 0.166435
\(156\) 0 0
\(157\) 10.9795 0.876256 0.438128 0.898913i \(-0.355642\pi\)
0.438128 + 0.898913i \(0.355642\pi\)
\(158\) 0 0
\(159\) −5.41468 −0.429412
\(160\) 0 0
\(161\) 15.8489 1.24906
\(162\) 0 0
\(163\) −5.84552 −0.457857 −0.228928 0.973443i \(-0.573522\pi\)
−0.228928 + 0.973443i \(0.573522\pi\)
\(164\) 0 0
\(165\) 6.06206 0.471931
\(166\) 0 0
\(167\) 12.7460 0.986312 0.493156 0.869941i \(-0.335843\pi\)
0.493156 + 0.869941i \(0.335843\pi\)
\(168\) 0 0
\(169\) −0.553251 −0.0425578
\(170\) 0 0
\(171\) −7.43563 −0.568617
\(172\) 0 0
\(173\) 4.64420 0.353092 0.176546 0.984292i \(-0.443508\pi\)
0.176546 + 0.984292i \(0.443508\pi\)
\(174\) 0 0
\(175\) −7.79438 −0.589200
\(176\) 0 0
\(177\) −1.74438 −0.131116
\(178\) 0 0
\(179\) 1.76747 0.132107 0.0660536 0.997816i \(-0.478959\pi\)
0.0660536 + 0.997816i \(0.478959\pi\)
\(180\) 0 0
\(181\) 5.86495 0.435938 0.217969 0.975956i \(-0.430057\pi\)
0.217969 + 0.975956i \(0.430057\pi\)
\(182\) 0 0
\(183\) −15.6157 −1.15435
\(184\) 0 0
\(185\) −2.13299 −0.156820
\(186\) 0 0
\(187\) 9.02767 0.660168
\(188\) 0 0
\(189\) 13.5418 0.985022
\(190\) 0 0
\(191\) 13.5392 0.979662 0.489831 0.871817i \(-0.337058\pi\)
0.489831 + 0.871817i \(0.337058\pi\)
\(192\) 0 0
\(193\) 7.65319 0.550889 0.275444 0.961317i \(-0.411175\pi\)
0.275444 + 0.961317i \(0.411175\pi\)
\(194\) 0 0
\(195\) −6.45481 −0.462238
\(196\) 0 0
\(197\) −2.06922 −0.147426 −0.0737128 0.997280i \(-0.523485\pi\)
−0.0737128 + 0.997280i \(0.523485\pi\)
\(198\) 0 0
\(199\) −4.48651 −0.318040 −0.159020 0.987275i \(-0.550833\pi\)
−0.159020 + 0.987275i \(0.550833\pi\)
\(200\) 0 0
\(201\) −12.4880 −0.880838
\(202\) 0 0
\(203\) −18.3672 −1.28913
\(204\) 0 0
\(205\) −4.10188 −0.286488
\(206\) 0 0
\(207\) −7.16532 −0.498024
\(208\) 0 0
\(209\) 22.7488 1.57357
\(210\) 0 0
\(211\) 22.1253 1.52317 0.761583 0.648067i \(-0.224422\pi\)
0.761583 + 0.648067i \(0.224422\pi\)
\(212\) 0 0
\(213\) −8.59572 −0.588969
\(214\) 0 0
\(215\) 3.40851 0.232459
\(216\) 0 0
\(217\) −3.75625 −0.254991
\(218\) 0 0
\(219\) 12.1343 0.819961
\(220\) 0 0
\(221\) −9.61255 −0.646610
\(222\) 0 0
\(223\) 20.3020 1.35952 0.679760 0.733434i \(-0.262084\pi\)
0.679760 + 0.733434i \(0.262084\pi\)
\(224\) 0 0
\(225\) 3.52386 0.234924
\(226\) 0 0
\(227\) 14.9537 0.992509 0.496255 0.868177i \(-0.334708\pi\)
0.496255 + 0.868177i \(0.334708\pi\)
\(228\) 0 0
\(229\) 4.45255 0.294232 0.147116 0.989119i \(-0.453001\pi\)
0.147116 + 0.989119i \(0.453001\pi\)
\(230\) 0 0
\(231\) −10.9891 −0.723032
\(232\) 0 0
\(233\) −22.1365 −1.45021 −0.725104 0.688640i \(-0.758208\pi\)
−0.725104 + 0.688640i \(0.758208\pi\)
\(234\) 0 0
\(235\) 3.52212 0.229758
\(236\) 0 0
\(237\) 14.6724 0.953073
\(238\) 0 0
\(239\) 6.23974 0.403615 0.201808 0.979425i \(-0.435318\pi\)
0.201808 + 0.979425i \(0.435318\pi\)
\(240\) 0 0
\(241\) −23.1955 −1.49415 −0.747076 0.664738i \(-0.768543\pi\)
−0.747076 + 0.664738i \(0.768543\pi\)
\(242\) 0 0
\(243\) −10.6207 −0.681318
\(244\) 0 0
\(245\) 1.66743 0.106528
\(246\) 0 0
\(247\) −24.2227 −1.54125
\(248\) 0 0
\(249\) 15.0852 0.955983
\(250\) 0 0
\(251\) 11.7528 0.741833 0.370916 0.928666i \(-0.379044\pi\)
0.370916 + 0.928666i \(0.379044\pi\)
\(252\) 0 0
\(253\) 21.9218 1.37821
\(254\) 0 0
\(255\) 4.98501 0.312173
\(256\) 0 0
\(257\) −5.47590 −0.341577 −0.170789 0.985308i \(-0.554632\pi\)
−0.170789 + 0.985308i \(0.554632\pi\)
\(258\) 0 0
\(259\) 3.86662 0.240260
\(260\) 0 0
\(261\) 8.30388 0.513997
\(262\) 0 0
\(263\) 1.05628 0.0651333 0.0325666 0.999470i \(-0.489632\pi\)
0.0325666 + 0.999470i \(0.489632\pi\)
\(264\) 0 0
\(265\) −5.16777 −0.317454
\(266\) 0 0
\(267\) 18.0305 1.10345
\(268\) 0 0
\(269\) −2.37386 −0.144737 −0.0723683 0.997378i \(-0.523056\pi\)
−0.0723683 + 0.997378i \(0.523056\pi\)
\(270\) 0 0
\(271\) 24.6662 1.49837 0.749184 0.662362i \(-0.230446\pi\)
0.749184 + 0.662362i \(0.230446\pi\)
\(272\) 0 0
\(273\) 11.7011 0.708183
\(274\) 0 0
\(275\) −10.7810 −0.650120
\(276\) 0 0
\(277\) −0.680049 −0.0408602 −0.0204301 0.999791i \(-0.506504\pi\)
−0.0204301 + 0.999791i \(0.506504\pi\)
\(278\) 0 0
\(279\) 1.69821 0.101669
\(280\) 0 0
\(281\) 8.38448 0.500176 0.250088 0.968223i \(-0.419540\pi\)
0.250088 + 0.968223i \(0.419540\pi\)
\(282\) 0 0
\(283\) −17.8996 −1.06402 −0.532010 0.846738i \(-0.678563\pi\)
−0.532010 + 0.846738i \(0.678563\pi\)
\(284\) 0 0
\(285\) 12.5617 0.744092
\(286\) 0 0
\(287\) 7.43577 0.438920
\(288\) 0 0
\(289\) −9.57629 −0.563311
\(290\) 0 0
\(291\) −4.22352 −0.247587
\(292\) 0 0
\(293\) −9.05758 −0.529150 −0.264575 0.964365i \(-0.585232\pi\)
−0.264575 + 0.964365i \(0.585232\pi\)
\(294\) 0 0
\(295\) −1.66484 −0.0969306
\(296\) 0 0
\(297\) 18.7308 1.08687
\(298\) 0 0
\(299\) −23.3421 −1.34991
\(300\) 0 0
\(301\) −6.17886 −0.356143
\(302\) 0 0
\(303\) −0.785095 −0.0451025
\(304\) 0 0
\(305\) −14.9037 −0.853381
\(306\) 0 0
\(307\) 28.9617 1.65293 0.826465 0.562988i \(-0.190348\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(308\) 0 0
\(309\) 10.5529 0.600335
\(310\) 0 0
\(311\) −0.161250 −0.00914363 −0.00457181 0.999990i \(-0.501455\pi\)
−0.00457181 + 0.999990i \(0.501455\pi\)
\(312\) 0 0
\(313\) 26.0251 1.47102 0.735512 0.677512i \(-0.236942\pi\)
0.735512 + 0.677512i \(0.236942\pi\)
\(314\) 0 0
\(315\) 3.42810 0.193151
\(316\) 0 0
\(317\) −6.20573 −0.348548 −0.174274 0.984697i \(-0.555758\pi\)
−0.174274 + 0.984697i \(0.555758\pi\)
\(318\) 0 0
\(319\) −25.4052 −1.42242
\(320\) 0 0
\(321\) 0.600786 0.0335326
\(322\) 0 0
\(323\) 18.7070 1.04089
\(324\) 0 0
\(325\) 11.4795 0.636768
\(326\) 0 0
\(327\) −17.3379 −0.958789
\(328\) 0 0
\(329\) −6.38480 −0.352005
\(330\) 0 0
\(331\) −19.1181 −1.05083 −0.525414 0.850847i \(-0.676090\pi\)
−0.525414 + 0.850847i \(0.676090\pi\)
\(332\) 0 0
\(333\) −1.74811 −0.0957960
\(334\) 0 0
\(335\) −11.9186 −0.651182
\(336\) 0 0
\(337\) 1.33950 0.0729670 0.0364835 0.999334i \(-0.488384\pi\)
0.0364835 + 0.999334i \(0.488384\pi\)
\(338\) 0 0
\(339\) −16.2498 −0.882567
\(340\) 0 0
\(341\) −5.19557 −0.281356
\(342\) 0 0
\(343\) −19.7908 −1.06860
\(344\) 0 0
\(345\) 12.1051 0.651714
\(346\) 0 0
\(347\) −3.36148 −0.180454 −0.0902270 0.995921i \(-0.528759\pi\)
−0.0902270 + 0.995921i \(0.528759\pi\)
\(348\) 0 0
\(349\) 7.24629 0.387885 0.193942 0.981013i \(-0.437872\pi\)
0.193942 + 0.981013i \(0.437872\pi\)
\(350\) 0 0
\(351\) −19.9443 −1.06455
\(352\) 0 0
\(353\) 27.9330 1.48672 0.743361 0.668890i \(-0.233230\pi\)
0.743361 + 0.668890i \(0.233230\pi\)
\(354\) 0 0
\(355\) −8.20376 −0.435410
\(356\) 0 0
\(357\) −9.03669 −0.478272
\(358\) 0 0
\(359\) −14.0445 −0.741242 −0.370621 0.928784i \(-0.620855\pi\)
−0.370621 + 0.928784i \(0.620855\pi\)
\(360\) 0 0
\(361\) 28.1398 1.48104
\(362\) 0 0
\(363\) 0.0302268 0.00158650
\(364\) 0 0
\(365\) 11.5810 0.606177
\(366\) 0 0
\(367\) 26.7704 1.39740 0.698701 0.715413i \(-0.253762\pi\)
0.698701 + 0.715413i \(0.253762\pi\)
\(368\) 0 0
\(369\) −3.36174 −0.175005
\(370\) 0 0
\(371\) 9.36800 0.486362
\(372\) 0 0
\(373\) 9.20138 0.476429 0.238215 0.971213i \(-0.423438\pi\)
0.238215 + 0.971213i \(0.423438\pi\)
\(374\) 0 0
\(375\) −15.1012 −0.779822
\(376\) 0 0
\(377\) 27.0511 1.39320
\(378\) 0 0
\(379\) −1.97475 −0.101436 −0.0507182 0.998713i \(-0.516151\pi\)
−0.0507182 + 0.998713i \(0.516151\pi\)
\(380\) 0 0
\(381\) 7.33761 0.375917
\(382\) 0 0
\(383\) 36.7039 1.87548 0.937741 0.347336i \(-0.112914\pi\)
0.937741 + 0.347336i \(0.112914\pi\)
\(384\) 0 0
\(385\) −10.4880 −0.534520
\(386\) 0 0
\(387\) 2.79348 0.142001
\(388\) 0 0
\(389\) 20.2274 1.02557 0.512784 0.858518i \(-0.328614\pi\)
0.512784 + 0.858518i \(0.328614\pi\)
\(390\) 0 0
\(391\) 18.0269 0.911661
\(392\) 0 0
\(393\) 12.6498 0.638100
\(394\) 0 0
\(395\) 14.0033 0.704584
\(396\) 0 0
\(397\) −11.5935 −0.581859 −0.290929 0.956745i \(-0.593964\pi\)
−0.290929 + 0.956745i \(0.593964\pi\)
\(398\) 0 0
\(399\) −22.7715 −1.14000
\(400\) 0 0
\(401\) 17.1601 0.856932 0.428466 0.903558i \(-0.359054\pi\)
0.428466 + 0.903558i \(0.359054\pi\)
\(402\) 0 0
\(403\) 5.53217 0.275577
\(404\) 0 0
\(405\) 6.04971 0.300613
\(406\) 0 0
\(407\) 5.34824 0.265102
\(408\) 0 0
\(409\) −17.1798 −0.849486 −0.424743 0.905314i \(-0.639635\pi\)
−0.424743 + 0.905314i \(0.639635\pi\)
\(410\) 0 0
\(411\) 16.9045 0.833837
\(412\) 0 0
\(413\) 3.01797 0.148505
\(414\) 0 0
\(415\) 14.3973 0.706735
\(416\) 0 0
\(417\) −23.9328 −1.17200
\(418\) 0 0
\(419\) −17.5543 −0.857584 −0.428792 0.903403i \(-0.641061\pi\)
−0.428792 + 0.903403i \(0.641061\pi\)
\(420\) 0 0
\(421\) 36.9668 1.80165 0.900825 0.434183i \(-0.142963\pi\)
0.900825 + 0.434183i \(0.142963\pi\)
\(422\) 0 0
\(423\) 2.88659 0.140351
\(424\) 0 0
\(425\) −8.86555 −0.430042
\(426\) 0 0
\(427\) 27.0169 1.30744
\(428\) 0 0
\(429\) 16.1847 0.781406
\(430\) 0 0
\(431\) 15.4484 0.744122 0.372061 0.928208i \(-0.378651\pi\)
0.372061 + 0.928208i \(0.378651\pi\)
\(432\) 0 0
\(433\) 20.1095 0.966401 0.483200 0.875510i \(-0.339474\pi\)
0.483200 + 0.875510i \(0.339474\pi\)
\(434\) 0 0
\(435\) −14.0285 −0.672617
\(436\) 0 0
\(437\) 45.4261 2.17302
\(438\) 0 0
\(439\) 15.9474 0.761127 0.380564 0.924755i \(-0.375730\pi\)
0.380564 + 0.924755i \(0.375730\pi\)
\(440\) 0 0
\(441\) 1.36656 0.0650741
\(442\) 0 0
\(443\) 5.19141 0.246651 0.123326 0.992366i \(-0.460644\pi\)
0.123326 + 0.992366i \(0.460644\pi\)
\(444\) 0 0
\(445\) 17.2083 0.815754
\(446\) 0 0
\(447\) −16.3024 −0.771075
\(448\) 0 0
\(449\) −7.83939 −0.369964 −0.184982 0.982742i \(-0.559223\pi\)
−0.184982 + 0.982742i \(0.559223\pi\)
\(450\) 0 0
\(451\) 10.2850 0.484302
\(452\) 0 0
\(453\) −15.7787 −0.741346
\(454\) 0 0
\(455\) 11.1675 0.523542
\(456\) 0 0
\(457\) 38.0223 1.77861 0.889303 0.457318i \(-0.151190\pi\)
0.889303 + 0.457318i \(0.151190\pi\)
\(458\) 0 0
\(459\) 15.4028 0.718943
\(460\) 0 0
\(461\) −2.61241 −0.121672 −0.0608361 0.998148i \(-0.519377\pi\)
−0.0608361 + 0.998148i \(0.519377\pi\)
\(462\) 0 0
\(463\) −1.53825 −0.0714885 −0.0357443 0.999361i \(-0.511380\pi\)
−0.0357443 + 0.999361i \(0.511380\pi\)
\(464\) 0 0
\(465\) −2.86895 −0.133044
\(466\) 0 0
\(467\) −10.4328 −0.482774 −0.241387 0.970429i \(-0.577602\pi\)
−0.241387 + 0.970429i \(0.577602\pi\)
\(468\) 0 0
\(469\) 21.6057 0.997658
\(470\) 0 0
\(471\) −15.2017 −0.700459
\(472\) 0 0
\(473\) −8.54647 −0.392967
\(474\) 0 0
\(475\) −22.3403 −1.02504
\(476\) 0 0
\(477\) −4.23530 −0.193921
\(478\) 0 0
\(479\) −33.1317 −1.51382 −0.756912 0.653517i \(-0.773293\pi\)
−0.756912 + 0.653517i \(0.773293\pi\)
\(480\) 0 0
\(481\) −5.69474 −0.259658
\(482\) 0 0
\(483\) −21.9437 −0.998474
\(484\) 0 0
\(485\) −4.03093 −0.183035
\(486\) 0 0
\(487\) 12.7899 0.579564 0.289782 0.957093i \(-0.406417\pi\)
0.289782 + 0.957093i \(0.406417\pi\)
\(488\) 0 0
\(489\) 8.09349 0.366000
\(490\) 0 0
\(491\) 24.9775 1.12722 0.563610 0.826041i \(-0.309412\pi\)
0.563610 + 0.826041i \(0.309412\pi\)
\(492\) 0 0
\(493\) −20.8914 −0.940901
\(494\) 0 0
\(495\) 4.74168 0.213123
\(496\) 0 0
\(497\) 14.8715 0.667080
\(498\) 0 0
\(499\) −2.92974 −0.131153 −0.0655766 0.997848i \(-0.520889\pi\)
−0.0655766 + 0.997848i \(0.520889\pi\)
\(500\) 0 0
\(501\) −17.6476 −0.788435
\(502\) 0 0
\(503\) 15.3054 0.682433 0.341217 0.939985i \(-0.389161\pi\)
0.341217 + 0.939985i \(0.389161\pi\)
\(504\) 0 0
\(505\) −0.749295 −0.0333432
\(506\) 0 0
\(507\) 0.766011 0.0340197
\(508\) 0 0
\(509\) 4.14117 0.183554 0.0917772 0.995780i \(-0.470745\pi\)
0.0917772 + 0.995780i \(0.470745\pi\)
\(510\) 0 0
\(511\) −20.9937 −0.928708
\(512\) 0 0
\(513\) 38.8136 1.71366
\(514\) 0 0
\(515\) 10.0717 0.443813
\(516\) 0 0
\(517\) −8.83132 −0.388401
\(518\) 0 0
\(519\) −6.43018 −0.282254
\(520\) 0 0
\(521\) 25.3987 1.11274 0.556368 0.830936i \(-0.312195\pi\)
0.556368 + 0.830936i \(0.312195\pi\)
\(522\) 0 0
\(523\) 23.2162 1.01518 0.507588 0.861600i \(-0.330537\pi\)
0.507588 + 0.861600i \(0.330537\pi\)
\(524\) 0 0
\(525\) 10.7918 0.470993
\(526\) 0 0
\(527\) −4.27246 −0.186111
\(528\) 0 0
\(529\) 20.7747 0.903246
\(530\) 0 0
\(531\) −1.36444 −0.0592114
\(532\) 0 0
\(533\) −10.9513 −0.474356
\(534\) 0 0
\(535\) 0.573390 0.0247898
\(536\) 0 0
\(537\) −2.44718 −0.105603
\(538\) 0 0
\(539\) −4.18089 −0.180084
\(540\) 0 0
\(541\) 3.82144 0.164296 0.0821482 0.996620i \(-0.473822\pi\)
0.0821482 + 0.996620i \(0.473822\pi\)
\(542\) 0 0
\(543\) −8.12039 −0.348479
\(544\) 0 0
\(545\) −16.5473 −0.708810
\(546\) 0 0
\(547\) 41.2930 1.76556 0.882781 0.469784i \(-0.155668\pi\)
0.882781 + 0.469784i \(0.155668\pi\)
\(548\) 0 0
\(549\) −12.2144 −0.521300
\(550\) 0 0
\(551\) −52.6442 −2.24272
\(552\) 0 0
\(553\) −25.3848 −1.07947
\(554\) 0 0
\(555\) 2.95326 0.125359
\(556\) 0 0
\(557\) −24.5868 −1.04177 −0.520887 0.853626i \(-0.674399\pi\)
−0.520887 + 0.853626i \(0.674399\pi\)
\(558\) 0 0
\(559\) 9.10018 0.384896
\(560\) 0 0
\(561\) −12.4994 −0.527723
\(562\) 0 0
\(563\) −36.8816 −1.55437 −0.777187 0.629270i \(-0.783354\pi\)
−0.777187 + 0.629270i \(0.783354\pi\)
\(564\) 0 0
\(565\) −15.5088 −0.652460
\(566\) 0 0
\(567\) −10.9668 −0.460561
\(568\) 0 0
\(569\) −28.8053 −1.20758 −0.603790 0.797144i \(-0.706343\pi\)
−0.603790 + 0.797144i \(0.706343\pi\)
\(570\) 0 0
\(571\) 18.2124 0.762167 0.381084 0.924541i \(-0.375551\pi\)
0.381084 + 0.924541i \(0.375551\pi\)
\(572\) 0 0
\(573\) −18.7459 −0.783119
\(574\) 0 0
\(575\) −21.5281 −0.897785
\(576\) 0 0
\(577\) 31.8420 1.32560 0.662800 0.748796i \(-0.269368\pi\)
0.662800 + 0.748796i \(0.269368\pi\)
\(578\) 0 0
\(579\) −10.5963 −0.440368
\(580\) 0 0
\(581\) −26.0990 −1.08277
\(582\) 0 0
\(583\) 12.9576 0.536650
\(584\) 0 0
\(585\) −5.04888 −0.208745
\(586\) 0 0
\(587\) 34.8832 1.43978 0.719891 0.694087i \(-0.244192\pi\)
0.719891 + 0.694087i \(0.244192\pi\)
\(588\) 0 0
\(589\) −10.7662 −0.443613
\(590\) 0 0
\(591\) 2.86496 0.117849
\(592\) 0 0
\(593\) 20.4938 0.841581 0.420791 0.907158i \(-0.361753\pi\)
0.420791 + 0.907158i \(0.361753\pi\)
\(594\) 0 0
\(595\) −8.62462 −0.353575
\(596\) 0 0
\(597\) 6.21185 0.254234
\(598\) 0 0
\(599\) 16.0790 0.656972 0.328486 0.944509i \(-0.393462\pi\)
0.328486 + 0.944509i \(0.393462\pi\)
\(600\) 0 0
\(601\) −33.1585 −1.35256 −0.676282 0.736643i \(-0.736410\pi\)
−0.676282 + 0.736643i \(0.736410\pi\)
\(602\) 0 0
\(603\) −9.76800 −0.397784
\(604\) 0 0
\(605\) 0.0288485 0.00117286
\(606\) 0 0
\(607\) −20.9718 −0.851219 −0.425610 0.904907i \(-0.639940\pi\)
−0.425610 + 0.904907i \(0.639940\pi\)
\(608\) 0 0
\(609\) 25.4305 1.03050
\(610\) 0 0
\(611\) 9.40348 0.380424
\(612\) 0 0
\(613\) 31.6074 1.27661 0.638305 0.769784i \(-0.279636\pi\)
0.638305 + 0.769784i \(0.279636\pi\)
\(614\) 0 0
\(615\) 5.67930 0.229012
\(616\) 0 0
\(617\) −13.9619 −0.562086 −0.281043 0.959695i \(-0.590680\pi\)
−0.281043 + 0.959695i \(0.590680\pi\)
\(618\) 0 0
\(619\) 21.0375 0.845567 0.422784 0.906231i \(-0.361053\pi\)
0.422784 + 0.906231i \(0.361053\pi\)
\(620\) 0 0
\(621\) 37.4026 1.50092
\(622\) 0 0
\(623\) −31.1948 −1.24979
\(624\) 0 0
\(625\) 1.85658 0.0742632
\(626\) 0 0
\(627\) −31.4971 −1.25787
\(628\) 0 0
\(629\) 4.39801 0.175360
\(630\) 0 0
\(631\) −5.97501 −0.237861 −0.118931 0.992903i \(-0.537947\pi\)
−0.118931 + 0.992903i \(0.537947\pi\)
\(632\) 0 0
\(633\) −30.6338 −1.21758
\(634\) 0 0
\(635\) 7.00302 0.277906
\(636\) 0 0
\(637\) 4.45176 0.176385
\(638\) 0 0
\(639\) −6.72347 −0.265977
\(640\) 0 0
\(641\) −31.0723 −1.22728 −0.613642 0.789585i \(-0.710296\pi\)
−0.613642 + 0.789585i \(0.710296\pi\)
\(642\) 0 0
\(643\) 2.63610 0.103958 0.0519789 0.998648i \(-0.483447\pi\)
0.0519789 + 0.998648i \(0.483447\pi\)
\(644\) 0 0
\(645\) −4.71930 −0.185822
\(646\) 0 0
\(647\) −16.7314 −0.657781 −0.328890 0.944368i \(-0.606675\pi\)
−0.328890 + 0.944368i \(0.606675\pi\)
\(648\) 0 0
\(649\) 4.17440 0.163859
\(650\) 0 0
\(651\) 5.20076 0.203834
\(652\) 0 0
\(653\) 27.4451 1.07401 0.537005 0.843579i \(-0.319556\pi\)
0.537005 + 0.843579i \(0.319556\pi\)
\(654\) 0 0
\(655\) 12.0730 0.471732
\(656\) 0 0
\(657\) 9.49133 0.370292
\(658\) 0 0
\(659\) −19.9180 −0.775897 −0.387948 0.921681i \(-0.626816\pi\)
−0.387948 + 0.921681i \(0.626816\pi\)
\(660\) 0 0
\(661\) −12.4042 −0.482466 −0.241233 0.970467i \(-0.577552\pi\)
−0.241233 + 0.970467i \(0.577552\pi\)
\(662\) 0 0
\(663\) 13.3092 0.516885
\(664\) 0 0
\(665\) −21.7332 −0.842776
\(666\) 0 0
\(667\) −50.7304 −1.96429
\(668\) 0 0
\(669\) −28.1093 −1.08677
\(670\) 0 0
\(671\) 37.3693 1.44263
\(672\) 0 0
\(673\) −21.3201 −0.821828 −0.410914 0.911674i \(-0.634790\pi\)
−0.410914 + 0.911674i \(0.634790\pi\)
\(674\) 0 0
\(675\) −18.3944 −0.708001
\(676\) 0 0
\(677\) −7.87306 −0.302586 −0.151293 0.988489i \(-0.548344\pi\)
−0.151293 + 0.988489i \(0.548344\pi\)
\(678\) 0 0
\(679\) 7.30716 0.280423
\(680\) 0 0
\(681\) −20.7043 −0.793389
\(682\) 0 0
\(683\) 8.40307 0.321535 0.160767 0.986992i \(-0.448603\pi\)
0.160767 + 0.986992i \(0.448603\pi\)
\(684\) 0 0
\(685\) 16.1337 0.616435
\(686\) 0 0
\(687\) −6.16482 −0.235203
\(688\) 0 0
\(689\) −13.7971 −0.525628
\(690\) 0 0
\(691\) 36.4880 1.38807 0.694035 0.719941i \(-0.255831\pi\)
0.694035 + 0.719941i \(0.255831\pi\)
\(692\) 0 0
\(693\) −8.59558 −0.326519
\(694\) 0 0
\(695\) −22.8415 −0.866427
\(696\) 0 0
\(697\) 8.45766 0.320357
\(698\) 0 0
\(699\) 30.6493 1.15926
\(700\) 0 0
\(701\) −25.7402 −0.972195 −0.486098 0.873905i \(-0.661580\pi\)
−0.486098 + 0.873905i \(0.661580\pi\)
\(702\) 0 0
\(703\) 11.0825 0.417986
\(704\) 0 0
\(705\) −4.87659 −0.183663
\(706\) 0 0
\(707\) 1.35830 0.0510842
\(708\) 0 0
\(709\) 25.7008 0.965213 0.482606 0.875837i \(-0.339690\pi\)
0.482606 + 0.875837i \(0.339690\pi\)
\(710\) 0 0
\(711\) 11.4766 0.430405
\(712\) 0 0
\(713\) −10.3748 −0.388539
\(714\) 0 0
\(715\) 15.4467 0.577674
\(716\) 0 0
\(717\) −8.63931 −0.322641
\(718\) 0 0
\(719\) 16.8604 0.628787 0.314394 0.949293i \(-0.398199\pi\)
0.314394 + 0.949293i \(0.398199\pi\)
\(720\) 0 0
\(721\) −18.2577 −0.679953
\(722\) 0 0
\(723\) 32.1156 1.19439
\(724\) 0 0
\(725\) 24.9489 0.926580
\(726\) 0 0
\(727\) −43.7631 −1.62308 −0.811542 0.584295i \(-0.801371\pi\)
−0.811542 + 0.584295i \(0.801371\pi\)
\(728\) 0 0
\(729\) 28.4395 1.05332
\(730\) 0 0
\(731\) −7.02801 −0.259940
\(732\) 0 0
\(733\) 13.5934 0.502082 0.251041 0.967976i \(-0.419227\pi\)
0.251041 + 0.967976i \(0.419227\pi\)
\(734\) 0 0
\(735\) −2.30866 −0.0851560
\(736\) 0 0
\(737\) 29.8845 1.10081
\(738\) 0 0
\(739\) −8.69122 −0.319712 −0.159856 0.987140i \(-0.551103\pi\)
−0.159856 + 0.987140i \(0.551103\pi\)
\(740\) 0 0
\(741\) 33.5378 1.23204
\(742\) 0 0
\(743\) −33.8821 −1.24302 −0.621508 0.783408i \(-0.713480\pi\)
−0.621508 + 0.783408i \(0.713480\pi\)
\(744\) 0 0
\(745\) −15.5590 −0.570037
\(746\) 0 0
\(747\) 11.7994 0.431719
\(748\) 0 0
\(749\) −1.03943 −0.0379798
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −16.2725 −0.593004
\(754\) 0 0
\(755\) −15.0592 −0.548059
\(756\) 0 0
\(757\) 28.7758 1.04587 0.522937 0.852371i \(-0.324836\pi\)
0.522937 + 0.852371i \(0.324836\pi\)
\(758\) 0 0
\(759\) −30.3521 −1.10171
\(760\) 0 0
\(761\) −27.6680 −1.00297 −0.501483 0.865168i \(-0.667212\pi\)
−0.501483 + 0.865168i \(0.667212\pi\)
\(762\) 0 0
\(763\) 29.9965 1.08595
\(764\) 0 0
\(765\) 3.89922 0.140977
\(766\) 0 0
\(767\) −4.44485 −0.160494
\(768\) 0 0
\(769\) −32.8613 −1.18501 −0.592505 0.805567i \(-0.701861\pi\)
−0.592505 + 0.805567i \(0.701861\pi\)
\(770\) 0 0
\(771\) 7.58173 0.273049
\(772\) 0 0
\(773\) −23.7167 −0.853031 −0.426515 0.904480i \(-0.640259\pi\)
−0.426515 + 0.904480i \(0.640259\pi\)
\(774\) 0 0
\(775\) 5.10226 0.183279
\(776\) 0 0
\(777\) −5.35358 −0.192059
\(778\) 0 0
\(779\) 21.3125 0.763598
\(780\) 0 0
\(781\) 20.5700 0.736053
\(782\) 0 0
\(783\) −43.3458 −1.54905
\(784\) 0 0
\(785\) −14.5085 −0.517832
\(786\) 0 0
\(787\) 42.2466 1.50593 0.752964 0.658062i \(-0.228623\pi\)
0.752964 + 0.658062i \(0.228623\pi\)
\(788\) 0 0
\(789\) −1.46249 −0.0520661
\(790\) 0 0
\(791\) 28.1139 0.999616
\(792\) 0 0
\(793\) −39.7904 −1.41300
\(794\) 0 0
\(795\) 7.15510 0.253765
\(796\) 0 0
\(797\) −17.7775 −0.629710 −0.314855 0.949140i \(-0.601956\pi\)
−0.314855 + 0.949140i \(0.601956\pi\)
\(798\) 0 0
\(799\) −7.26225 −0.256920
\(800\) 0 0
\(801\) 14.1033 0.498315
\(802\) 0 0
\(803\) −29.0381 −1.02473
\(804\) 0 0
\(805\) −20.9431 −0.738147
\(806\) 0 0
\(807\) 3.28675 0.115699
\(808\) 0 0
\(809\) −31.0812 −1.09276 −0.546379 0.837538i \(-0.683994\pi\)
−0.546379 + 0.837538i \(0.683994\pi\)
\(810\) 0 0
\(811\) −27.3377 −0.959956 −0.479978 0.877281i \(-0.659355\pi\)
−0.479978 + 0.877281i \(0.659355\pi\)
\(812\) 0 0
\(813\) −34.1519 −1.19776
\(814\) 0 0
\(815\) 7.72443 0.270575
\(816\) 0 0
\(817\) −17.7099 −0.619590
\(818\) 0 0
\(819\) 9.15247 0.319813
\(820\) 0 0
\(821\) −15.7341 −0.549125 −0.274563 0.961569i \(-0.588533\pi\)
−0.274563 + 0.961569i \(0.588533\pi\)
\(822\) 0 0
\(823\) −10.0741 −0.351161 −0.175581 0.984465i \(-0.556180\pi\)
−0.175581 + 0.984465i \(0.556180\pi\)
\(824\) 0 0
\(825\) 14.9270 0.519691
\(826\) 0 0
\(827\) −33.8221 −1.17611 −0.588055 0.808821i \(-0.700106\pi\)
−0.588055 + 0.808821i \(0.700106\pi\)
\(828\) 0 0
\(829\) 10.3217 0.358487 0.179243 0.983805i \(-0.442635\pi\)
0.179243 + 0.983805i \(0.442635\pi\)
\(830\) 0 0
\(831\) 0.941570 0.0326627
\(832\) 0 0
\(833\) −3.43807 −0.119122
\(834\) 0 0
\(835\) −16.8428 −0.582871
\(836\) 0 0
\(837\) −8.86458 −0.306405
\(838\) 0 0
\(839\) −22.2506 −0.768175 −0.384088 0.923297i \(-0.625484\pi\)
−0.384088 + 0.923297i \(0.625484\pi\)
\(840\) 0 0
\(841\) 29.7914 1.02729
\(842\) 0 0
\(843\) −11.6088 −0.399829
\(844\) 0 0
\(845\) 0.731081 0.0251499
\(846\) 0 0
\(847\) −0.0522958 −0.00179690
\(848\) 0 0
\(849\) 24.7831 0.850552
\(850\) 0 0
\(851\) 10.6796 0.366094
\(852\) 0 0
\(853\) −1.80520 −0.0618090 −0.0309045 0.999522i \(-0.509839\pi\)
−0.0309045 + 0.999522i \(0.509839\pi\)
\(854\) 0 0
\(855\) 9.82564 0.336030
\(856\) 0 0
\(857\) 25.6244 0.875313 0.437657 0.899142i \(-0.355809\pi\)
0.437657 + 0.899142i \(0.355809\pi\)
\(858\) 0 0
\(859\) 25.2050 0.859982 0.429991 0.902833i \(-0.358517\pi\)
0.429991 + 0.902833i \(0.358517\pi\)
\(860\) 0 0
\(861\) −10.2953 −0.350862
\(862\) 0 0
\(863\) −30.5911 −1.04133 −0.520667 0.853760i \(-0.674317\pi\)
−0.520667 + 0.853760i \(0.674317\pi\)
\(864\) 0 0
\(865\) −6.13697 −0.208663
\(866\) 0 0
\(867\) 13.2590 0.450298
\(868\) 0 0
\(869\) −35.1118 −1.19109
\(870\) 0 0
\(871\) −31.8207 −1.07820
\(872\) 0 0
\(873\) −3.30359 −0.111810
\(874\) 0 0
\(875\) 26.1267 0.883245
\(876\) 0 0
\(877\) 2.41338 0.0814939 0.0407469 0.999169i \(-0.487026\pi\)
0.0407469 + 0.999169i \(0.487026\pi\)
\(878\) 0 0
\(879\) 12.5408 0.422990
\(880\) 0 0
\(881\) 50.8491 1.71315 0.856575 0.516022i \(-0.172588\pi\)
0.856575 + 0.516022i \(0.172588\pi\)
\(882\) 0 0
\(883\) −38.0832 −1.28160 −0.640801 0.767707i \(-0.721398\pi\)
−0.640801 + 0.767707i \(0.721398\pi\)
\(884\) 0 0
\(885\) 2.30507 0.0774841
\(886\) 0 0
\(887\) 16.1179 0.541188 0.270594 0.962694i \(-0.412780\pi\)
0.270594 + 0.962694i \(0.412780\pi\)
\(888\) 0 0
\(889\) −12.6949 −0.425773
\(890\) 0 0
\(891\) −15.1690 −0.508180
\(892\) 0 0
\(893\) −18.3001 −0.612391
\(894\) 0 0
\(895\) −2.33559 −0.0780701
\(896\) 0 0
\(897\) 32.3185 1.07908
\(898\) 0 0
\(899\) 12.0233 0.401001
\(900\) 0 0
\(901\) 10.6554 0.354984
\(902\) 0 0
\(903\) 8.55501 0.284693
\(904\) 0 0
\(905\) −7.75010 −0.257622
\(906\) 0 0
\(907\) 38.9490 1.29328 0.646640 0.762796i \(-0.276174\pi\)
0.646640 + 0.762796i \(0.276174\pi\)
\(908\) 0 0
\(909\) −0.614092 −0.0203682
\(910\) 0 0
\(911\) −41.5336 −1.37607 −0.688034 0.725678i \(-0.741526\pi\)
−0.688034 + 0.725678i \(0.741526\pi\)
\(912\) 0 0
\(913\) −36.0996 −1.19472
\(914\) 0 0
\(915\) 20.6350 0.682173
\(916\) 0 0
\(917\) −21.8856 −0.722727
\(918\) 0 0
\(919\) 11.7811 0.388621 0.194311 0.980940i \(-0.437753\pi\)
0.194311 + 0.980940i \(0.437753\pi\)
\(920\) 0 0
\(921\) −40.0992 −1.32131
\(922\) 0 0
\(923\) −21.9027 −0.720936
\(924\) 0 0
\(925\) −5.25219 −0.172691
\(926\) 0 0
\(927\) 8.25438 0.271109
\(928\) 0 0
\(929\) −45.5816 −1.49549 −0.747743 0.663989i \(-0.768862\pi\)
−0.747743 + 0.663989i \(0.768862\pi\)
\(930\) 0 0
\(931\) −8.66358 −0.283937
\(932\) 0 0
\(933\) 0.223260 0.00730921
\(934\) 0 0
\(935\) −11.9294 −0.390133
\(936\) 0 0
\(937\) 17.0635 0.557441 0.278720 0.960372i \(-0.410090\pi\)
0.278720 + 0.960372i \(0.410090\pi\)
\(938\) 0 0
\(939\) −36.0333 −1.17590
\(940\) 0 0
\(941\) 9.03747 0.294613 0.147306 0.989091i \(-0.452940\pi\)
0.147306 + 0.989091i \(0.452940\pi\)
\(942\) 0 0
\(943\) 20.5377 0.668798
\(944\) 0 0
\(945\) −17.8945 −0.582109
\(946\) 0 0
\(947\) −20.2044 −0.656556 −0.328278 0.944581i \(-0.606468\pi\)
−0.328278 + 0.944581i \(0.606468\pi\)
\(948\) 0 0
\(949\) 30.9194 1.00369
\(950\) 0 0
\(951\) 8.59221 0.278622
\(952\) 0 0
\(953\) 7.77078 0.251720 0.125860 0.992048i \(-0.459831\pi\)
0.125860 + 0.992048i \(0.459831\pi\)
\(954\) 0 0
\(955\) −17.8911 −0.578941
\(956\) 0 0
\(957\) 35.1750 1.13705
\(958\) 0 0
\(959\) −29.2467 −0.944424
\(960\) 0 0
\(961\) −28.5411 −0.920682
\(962\) 0 0
\(963\) 0.469928 0.0151432
\(964\) 0 0
\(965\) −10.1131 −0.325553
\(966\) 0 0
\(967\) 37.8630 1.21759 0.608795 0.793327i \(-0.291653\pi\)
0.608795 + 0.793327i \(0.291653\pi\)
\(968\) 0 0
\(969\) −25.9010 −0.832060
\(970\) 0 0
\(971\) −5.69990 −0.182919 −0.0914593 0.995809i \(-0.529153\pi\)
−0.0914593 + 0.995809i \(0.529153\pi\)
\(972\) 0 0
\(973\) 41.4064 1.32743
\(974\) 0 0
\(975\) −15.8941 −0.509018
\(976\) 0 0
\(977\) 0.107457 0.00343785 0.00171893 0.999999i \(-0.499453\pi\)
0.00171893 + 0.999999i \(0.499453\pi\)
\(978\) 0 0
\(979\) −43.1480 −1.37902
\(980\) 0 0
\(981\) −13.5615 −0.432986
\(982\) 0 0
\(983\) 0.277299 0.00884447 0.00442224 0.999990i \(-0.498592\pi\)
0.00442224 + 0.999990i \(0.498592\pi\)
\(984\) 0 0
\(985\) 2.73432 0.0871226
\(986\) 0 0
\(987\) 8.84015 0.281385
\(988\) 0 0
\(989\) −17.0661 −0.542669
\(990\) 0 0
\(991\) −16.8235 −0.534418 −0.267209 0.963639i \(-0.586101\pi\)
−0.267209 + 0.963639i \(0.586101\pi\)
\(992\) 0 0
\(993\) 26.4702 0.840008
\(994\) 0 0
\(995\) 5.92859 0.187949
\(996\) 0 0
\(997\) 1.20514 0.0381671 0.0190835 0.999818i \(-0.493925\pi\)
0.0190835 + 0.999818i \(0.493925\pi\)
\(998\) 0 0
\(999\) 9.12507 0.288704
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 \(a_p\))