Properties

Label 6040.2.a.p.1.8
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.40330\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.40330 q^{3}\) \(+1.00000 q^{5}\) \(+3.27194 q^{7}\) \(-1.03074 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.40330 q^{3}\) \(+1.00000 q^{5}\) \(+3.27194 q^{7}\) \(-1.03074 q^{9}\) \(+3.84502 q^{11}\) \(-5.20094 q^{13}\) \(-1.40330 q^{15}\) \(+0.810350 q^{17}\) \(-4.07576 q^{19}\) \(-4.59153 q^{21}\) \(+6.38337 q^{23}\) \(+1.00000 q^{25}\) \(+5.65635 q^{27}\) \(-7.98360 q^{29}\) \(-4.89556 q^{31}\) \(-5.39573 q^{33}\) \(+3.27194 q^{35}\) \(-7.95385 q^{37}\) \(+7.29849 q^{39}\) \(+10.5930 q^{41}\) \(-7.64500 q^{43}\) \(-1.03074 q^{45}\) \(-6.83414 q^{47}\) \(+3.70561 q^{49}\) \(-1.13717 q^{51}\) \(+1.56738 q^{53}\) \(+3.84502 q^{55}\) \(+5.71952 q^{57}\) \(+10.0522 q^{59}\) \(-7.68791 q^{61}\) \(-3.37252 q^{63}\) \(-5.20094 q^{65}\) \(-14.1120 q^{67}\) \(-8.95780 q^{69}\) \(-10.6571 q^{71}\) \(-8.04489 q^{73}\) \(-1.40330 q^{75}\) \(+12.5807 q^{77}\) \(-5.13669 q^{79}\) \(-4.84535 q^{81}\) \(+0.0490305 q^{83}\) \(+0.810350 q^{85}\) \(+11.2034 q^{87}\) \(+7.75451 q^{89}\) \(-17.0172 q^{91}\) \(+6.86996 q^{93}\) \(-4.07576 q^{95}\) \(+12.6883 q^{97}\) \(-3.96322 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.40330 −0.810197 −0.405099 0.914273i \(-0.632763\pi\)
−0.405099 + 0.914273i \(0.632763\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 3.27194 1.23668 0.618339 0.785911i \(-0.287806\pi\)
0.618339 + 0.785911i \(0.287806\pi\)
\(8\) 0 0
\(9\) −1.03074 −0.343580
\(10\) 0 0
\(11\) 3.84502 1.15932 0.579659 0.814859i \(-0.303186\pi\)
0.579659 + 0.814859i \(0.303186\pi\)
\(12\) 0 0
\(13\) −5.20094 −1.44248 −0.721240 0.692685i \(-0.756428\pi\)
−0.721240 + 0.692685i \(0.756428\pi\)
\(14\) 0 0
\(15\) −1.40330 −0.362331
\(16\) 0 0
\(17\) 0.810350 0.196539 0.0982694 0.995160i \(-0.468669\pi\)
0.0982694 + 0.995160i \(0.468669\pi\)
\(18\) 0 0
\(19\) −4.07576 −0.935043 −0.467521 0.883982i \(-0.654853\pi\)
−0.467521 + 0.883982i \(0.654853\pi\)
\(20\) 0 0
\(21\) −4.59153 −1.00195
\(22\) 0 0
\(23\) 6.38337 1.33102 0.665512 0.746387i \(-0.268213\pi\)
0.665512 + 0.746387i \(0.268213\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.65635 1.08857
\(28\) 0 0
\(29\) −7.98360 −1.48252 −0.741258 0.671220i \(-0.765771\pi\)
−0.741258 + 0.671220i \(0.765771\pi\)
\(30\) 0 0
\(31\) −4.89556 −0.879269 −0.439634 0.898177i \(-0.644892\pi\)
−0.439634 + 0.898177i \(0.644892\pi\)
\(32\) 0 0
\(33\) −5.39573 −0.939276
\(34\) 0 0
\(35\) 3.27194 0.553059
\(36\) 0 0
\(37\) −7.95385 −1.30760 −0.653802 0.756665i \(-0.726827\pi\)
−0.653802 + 0.756665i \(0.726827\pi\)
\(38\) 0 0
\(39\) 7.29849 1.16869
\(40\) 0 0
\(41\) 10.5930 1.65434 0.827172 0.561949i \(-0.189948\pi\)
0.827172 + 0.561949i \(0.189948\pi\)
\(42\) 0 0
\(43\) −7.64500 −1.16585 −0.582926 0.812525i \(-0.698092\pi\)
−0.582926 + 0.812525i \(0.698092\pi\)
\(44\) 0 0
\(45\) −1.03074 −0.153654
\(46\) 0 0
\(47\) −6.83414 −0.996862 −0.498431 0.866929i \(-0.666090\pi\)
−0.498431 + 0.866929i \(0.666090\pi\)
\(48\) 0 0
\(49\) 3.70561 0.529373
\(50\) 0 0
\(51\) −1.13717 −0.159235
\(52\) 0 0
\(53\) 1.56738 0.215296 0.107648 0.994189i \(-0.465668\pi\)
0.107648 + 0.994189i \(0.465668\pi\)
\(54\) 0 0
\(55\) 3.84502 0.518463
\(56\) 0 0
\(57\) 5.71952 0.757569
\(58\) 0 0
\(59\) 10.0522 1.30869 0.654345 0.756196i \(-0.272944\pi\)
0.654345 + 0.756196i \(0.272944\pi\)
\(60\) 0 0
\(61\) −7.68791 −0.984336 −0.492168 0.870500i \(-0.663796\pi\)
−0.492168 + 0.870500i \(0.663796\pi\)
\(62\) 0 0
\(63\) −3.37252 −0.424898
\(64\) 0 0
\(65\) −5.20094 −0.645097
\(66\) 0 0
\(67\) −14.1120 −1.72405 −0.862025 0.506866i \(-0.830804\pi\)
−0.862025 + 0.506866i \(0.830804\pi\)
\(68\) 0 0
\(69\) −8.95780 −1.07839
\(70\) 0 0
\(71\) −10.6571 −1.26476 −0.632381 0.774658i \(-0.717922\pi\)
−0.632381 + 0.774658i \(0.717922\pi\)
\(72\) 0 0
\(73\) −8.04489 −0.941583 −0.470792 0.882244i \(-0.656032\pi\)
−0.470792 + 0.882244i \(0.656032\pi\)
\(74\) 0 0
\(75\) −1.40330 −0.162039
\(76\) 0 0
\(77\) 12.5807 1.43370
\(78\) 0 0
\(79\) −5.13669 −0.577922 −0.288961 0.957341i \(-0.593310\pi\)
−0.288961 + 0.957341i \(0.593310\pi\)
\(80\) 0 0
\(81\) −4.84535 −0.538373
\(82\) 0 0
\(83\) 0.0490305 0.00538180 0.00269090 0.999996i \(-0.499143\pi\)
0.00269090 + 0.999996i \(0.499143\pi\)
\(84\) 0 0
\(85\) 0.810350 0.0878948
\(86\) 0 0
\(87\) 11.2034 1.20113
\(88\) 0 0
\(89\) 7.75451 0.821976 0.410988 0.911641i \(-0.365184\pi\)
0.410988 + 0.911641i \(0.365184\pi\)
\(90\) 0 0
\(91\) −17.0172 −1.78388
\(92\) 0 0
\(93\) 6.86996 0.712381
\(94\) 0 0
\(95\) −4.07576 −0.418164
\(96\) 0 0
\(97\) 12.6883 1.28830 0.644152 0.764898i \(-0.277211\pi\)
0.644152 + 0.764898i \(0.277211\pi\)
\(98\) 0 0
\(99\) −3.96322 −0.398319
\(100\) 0 0
\(101\) −11.4164 −1.13598 −0.567988 0.823037i \(-0.692278\pi\)
−0.567988 + 0.823037i \(0.692278\pi\)
\(102\) 0 0
\(103\) −13.2005 −1.30069 −0.650344 0.759640i \(-0.725375\pi\)
−0.650344 + 0.759640i \(0.725375\pi\)
\(104\) 0 0
\(105\) −4.59153 −0.448087
\(106\) 0 0
\(107\) 4.57558 0.442338 0.221169 0.975236i \(-0.429013\pi\)
0.221169 + 0.975236i \(0.429013\pi\)
\(108\) 0 0
\(109\) 13.2630 1.27037 0.635184 0.772361i \(-0.280924\pi\)
0.635184 + 0.772361i \(0.280924\pi\)
\(110\) 0 0
\(111\) 11.1617 1.05942
\(112\) 0 0
\(113\) −0.00584044 −0.000549422 0 −0.000274711 1.00000i \(-0.500087\pi\)
−0.000274711 1.00000i \(0.500087\pi\)
\(114\) 0 0
\(115\) 6.38337 0.595252
\(116\) 0 0
\(117\) 5.36082 0.495608
\(118\) 0 0
\(119\) 2.65142 0.243055
\(120\) 0 0
\(121\) 3.78419 0.344018
\(122\) 0 0
\(123\) −14.8651 −1.34035
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 6.40279 0.568156 0.284078 0.958801i \(-0.408313\pi\)
0.284078 + 0.958801i \(0.408313\pi\)
\(128\) 0 0
\(129\) 10.7283 0.944570
\(130\) 0 0
\(131\) 14.6034 1.27591 0.637953 0.770075i \(-0.279781\pi\)
0.637953 + 0.770075i \(0.279781\pi\)
\(132\) 0 0
\(133\) −13.3356 −1.15635
\(134\) 0 0
\(135\) 5.65635 0.486821
\(136\) 0 0
\(137\) 21.5765 1.84341 0.921704 0.387893i \(-0.126797\pi\)
0.921704 + 0.387893i \(0.126797\pi\)
\(138\) 0 0
\(139\) −7.42104 −0.629444 −0.314722 0.949184i \(-0.601911\pi\)
−0.314722 + 0.949184i \(0.601911\pi\)
\(140\) 0 0
\(141\) 9.59037 0.807655
\(142\) 0 0
\(143\) −19.9977 −1.67229
\(144\) 0 0
\(145\) −7.98360 −0.663002
\(146\) 0 0
\(147\) −5.20009 −0.428897
\(148\) 0 0
\(149\) −23.4817 −1.92369 −0.961847 0.273588i \(-0.911790\pi\)
−0.961847 + 0.273588i \(0.911790\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −0.835260 −0.0675268
\(154\) 0 0
\(155\) −4.89556 −0.393221
\(156\) 0 0
\(157\) 15.4023 1.22924 0.614619 0.788824i \(-0.289310\pi\)
0.614619 + 0.788824i \(0.289310\pi\)
\(158\) 0 0
\(159\) −2.19951 −0.174432
\(160\) 0 0
\(161\) 20.8860 1.64605
\(162\) 0 0
\(163\) −5.19282 −0.406733 −0.203367 0.979103i \(-0.565188\pi\)
−0.203367 + 0.979103i \(0.565188\pi\)
\(164\) 0 0
\(165\) −5.39573 −0.420057
\(166\) 0 0
\(167\) −16.4222 −1.27078 −0.635392 0.772190i \(-0.719162\pi\)
−0.635392 + 0.772190i \(0.719162\pi\)
\(168\) 0 0
\(169\) 14.0498 1.08075
\(170\) 0 0
\(171\) 4.20105 0.321262
\(172\) 0 0
\(173\) −14.6971 −1.11740 −0.558701 0.829369i \(-0.688700\pi\)
−0.558701 + 0.829369i \(0.688700\pi\)
\(174\) 0 0
\(175\) 3.27194 0.247336
\(176\) 0 0
\(177\) −14.1063 −1.06030
\(178\) 0 0
\(179\) −5.69508 −0.425670 −0.212835 0.977088i \(-0.568270\pi\)
−0.212835 + 0.977088i \(0.568270\pi\)
\(180\) 0 0
\(181\) −21.1956 −1.57546 −0.787729 0.616022i \(-0.788743\pi\)
−0.787729 + 0.616022i \(0.788743\pi\)
\(182\) 0 0
\(183\) 10.7885 0.797507
\(184\) 0 0
\(185\) −7.95385 −0.584779
\(186\) 0 0
\(187\) 3.11581 0.227851
\(188\) 0 0
\(189\) 18.5073 1.34620
\(190\) 0 0
\(191\) 1.74064 0.125948 0.0629742 0.998015i \(-0.479941\pi\)
0.0629742 + 0.998015i \(0.479941\pi\)
\(192\) 0 0
\(193\) 20.8045 1.49754 0.748772 0.662828i \(-0.230644\pi\)
0.748772 + 0.662828i \(0.230644\pi\)
\(194\) 0 0
\(195\) 7.29849 0.522656
\(196\) 0 0
\(197\) 13.1987 0.940372 0.470186 0.882567i \(-0.344187\pi\)
0.470186 + 0.882567i \(0.344187\pi\)
\(198\) 0 0
\(199\) −6.29581 −0.446298 −0.223149 0.974784i \(-0.571634\pi\)
−0.223149 + 0.974784i \(0.571634\pi\)
\(200\) 0 0
\(201\) 19.8034 1.39682
\(202\) 0 0
\(203\) −26.1219 −1.83340
\(204\) 0 0
\(205\) 10.5930 0.739845
\(206\) 0 0
\(207\) −6.57960 −0.457314
\(208\) 0 0
\(209\) −15.6714 −1.08401
\(210\) 0 0
\(211\) −9.48657 −0.653082 −0.326541 0.945183i \(-0.605883\pi\)
−0.326541 + 0.945183i \(0.605883\pi\)
\(212\) 0 0
\(213\) 14.9551 1.02471
\(214\) 0 0
\(215\) −7.64500 −0.521385
\(216\) 0 0
\(217\) −16.0180 −1.08737
\(218\) 0 0
\(219\) 11.2894 0.762868
\(220\) 0 0
\(221\) −4.21458 −0.283503
\(222\) 0 0
\(223\) 14.5509 0.974401 0.487200 0.873290i \(-0.338018\pi\)
0.487200 + 0.873290i \(0.338018\pi\)
\(224\) 0 0
\(225\) −1.03074 −0.0687160
\(226\) 0 0
\(227\) 9.07610 0.602402 0.301201 0.953561i \(-0.402613\pi\)
0.301201 + 0.953561i \(0.402613\pi\)
\(228\) 0 0
\(229\) −12.5140 −0.826945 −0.413473 0.910517i \(-0.635684\pi\)
−0.413473 + 0.910517i \(0.635684\pi\)
\(230\) 0 0
\(231\) −17.6545 −1.16158
\(232\) 0 0
\(233\) 4.53632 0.297184 0.148592 0.988899i \(-0.452526\pi\)
0.148592 + 0.988899i \(0.452526\pi\)
\(234\) 0 0
\(235\) −6.83414 −0.445810
\(236\) 0 0
\(237\) 7.20833 0.468231
\(238\) 0 0
\(239\) 1.41068 0.0912491 0.0456245 0.998959i \(-0.485472\pi\)
0.0456245 + 0.998959i \(0.485472\pi\)
\(240\) 0 0
\(241\) −15.6998 −1.01131 −0.505657 0.862735i \(-0.668750\pi\)
−0.505657 + 0.862735i \(0.668750\pi\)
\(242\) 0 0
\(243\) −10.1696 −0.652377
\(244\) 0 0
\(245\) 3.70561 0.236743
\(246\) 0 0
\(247\) 21.1978 1.34878
\(248\) 0 0
\(249\) −0.0688047 −0.00436032
\(250\) 0 0
\(251\) 25.7100 1.62280 0.811399 0.584493i \(-0.198706\pi\)
0.811399 + 0.584493i \(0.198706\pi\)
\(252\) 0 0
\(253\) 24.5442 1.54308
\(254\) 0 0
\(255\) −1.13717 −0.0712121
\(256\) 0 0
\(257\) −10.3265 −0.644150 −0.322075 0.946714i \(-0.604380\pi\)
−0.322075 + 0.946714i \(0.604380\pi\)
\(258\) 0 0
\(259\) −26.0245 −1.61709
\(260\) 0 0
\(261\) 8.22902 0.509363
\(262\) 0 0
\(263\) −6.04732 −0.372894 −0.186447 0.982465i \(-0.559697\pi\)
−0.186447 + 0.982465i \(0.559697\pi\)
\(264\) 0 0
\(265\) 1.56738 0.0962832
\(266\) 0 0
\(267\) −10.8819 −0.665963
\(268\) 0 0
\(269\) 22.8039 1.39038 0.695189 0.718827i \(-0.255321\pi\)
0.695189 + 0.718827i \(0.255321\pi\)
\(270\) 0 0
\(271\) 7.21320 0.438170 0.219085 0.975706i \(-0.429693\pi\)
0.219085 + 0.975706i \(0.429693\pi\)
\(272\) 0 0
\(273\) 23.8803 1.44530
\(274\) 0 0
\(275\) 3.84502 0.231864
\(276\) 0 0
\(277\) 5.93640 0.356684 0.178342 0.983969i \(-0.442927\pi\)
0.178342 + 0.983969i \(0.442927\pi\)
\(278\) 0 0
\(279\) 5.04605 0.302099
\(280\) 0 0
\(281\) −25.9424 −1.54759 −0.773796 0.633435i \(-0.781644\pi\)
−0.773796 + 0.633435i \(0.781644\pi\)
\(282\) 0 0
\(283\) −27.1237 −1.61234 −0.806168 0.591687i \(-0.798462\pi\)
−0.806168 + 0.591687i \(0.798462\pi\)
\(284\) 0 0
\(285\) 5.71952 0.338795
\(286\) 0 0
\(287\) 34.6596 2.04589
\(288\) 0 0
\(289\) −16.3433 −0.961373
\(290\) 0 0
\(291\) −17.8056 −1.04378
\(292\) 0 0
\(293\) −10.1144 −0.590891 −0.295446 0.955360i \(-0.595468\pi\)
−0.295446 + 0.955360i \(0.595468\pi\)
\(294\) 0 0
\(295\) 10.0522 0.585264
\(296\) 0 0
\(297\) 21.7488 1.26199
\(298\) 0 0
\(299\) −33.1995 −1.91998
\(300\) 0 0
\(301\) −25.0140 −1.44178
\(302\) 0 0
\(303\) 16.0207 0.920365
\(304\) 0 0
\(305\) −7.68791 −0.440209
\(306\) 0 0
\(307\) 25.2546 1.44135 0.720677 0.693271i \(-0.243831\pi\)
0.720677 + 0.693271i \(0.243831\pi\)
\(308\) 0 0
\(309\) 18.5244 1.05381
\(310\) 0 0
\(311\) −21.4464 −1.21611 −0.608056 0.793894i \(-0.708050\pi\)
−0.608056 + 0.793894i \(0.708050\pi\)
\(312\) 0 0
\(313\) −5.28376 −0.298656 −0.149328 0.988788i \(-0.547711\pi\)
−0.149328 + 0.988788i \(0.547711\pi\)
\(314\) 0 0
\(315\) −3.37252 −0.190020
\(316\) 0 0
\(317\) 23.3760 1.31292 0.656462 0.754359i \(-0.272052\pi\)
0.656462 + 0.754359i \(0.272052\pi\)
\(318\) 0 0
\(319\) −30.6971 −1.71871
\(320\) 0 0
\(321\) −6.42092 −0.358381
\(322\) 0 0
\(323\) −3.30279 −0.183772
\(324\) 0 0
\(325\) −5.20094 −0.288496
\(326\) 0 0
\(327\) −18.6121 −1.02925
\(328\) 0 0
\(329\) −22.3609 −1.23280
\(330\) 0 0
\(331\) −24.7162 −1.35853 −0.679263 0.733895i \(-0.737700\pi\)
−0.679263 + 0.733895i \(0.737700\pi\)
\(332\) 0 0
\(333\) 8.19835 0.449267
\(334\) 0 0
\(335\) −14.1120 −0.771019
\(336\) 0 0
\(337\) −11.6223 −0.633106 −0.316553 0.948575i \(-0.602525\pi\)
−0.316553 + 0.948575i \(0.602525\pi\)
\(338\) 0 0
\(339\) 0.00819590 0.000445140 0
\(340\) 0 0
\(341\) −18.8235 −1.01935
\(342\) 0 0
\(343\) −10.7791 −0.582014
\(344\) 0 0
\(345\) −8.95780 −0.482272
\(346\) 0 0
\(347\) −7.21844 −0.387506 −0.193753 0.981050i \(-0.562066\pi\)
−0.193753 + 0.981050i \(0.562066\pi\)
\(348\) 0 0
\(349\) 23.6872 1.26795 0.633975 0.773354i \(-0.281422\pi\)
0.633975 + 0.773354i \(0.281422\pi\)
\(350\) 0 0
\(351\) −29.4183 −1.57023
\(352\) 0 0
\(353\) −7.95333 −0.423313 −0.211657 0.977344i \(-0.567886\pi\)
−0.211657 + 0.977344i \(0.567886\pi\)
\(354\) 0 0
\(355\) −10.6571 −0.565619
\(356\) 0 0
\(357\) −3.72074 −0.196923
\(358\) 0 0
\(359\) −23.7509 −1.25352 −0.626762 0.779211i \(-0.715620\pi\)
−0.626762 + 0.779211i \(0.715620\pi\)
\(360\) 0 0
\(361\) −2.38820 −0.125695
\(362\) 0 0
\(363\) −5.31037 −0.278722
\(364\) 0 0
\(365\) −8.04489 −0.421089
\(366\) 0 0
\(367\) −6.27946 −0.327785 −0.163893 0.986478i \(-0.552405\pi\)
−0.163893 + 0.986478i \(0.552405\pi\)
\(368\) 0 0
\(369\) −10.9186 −0.568400
\(370\) 0 0
\(371\) 5.12837 0.266252
\(372\) 0 0
\(373\) 7.67701 0.397501 0.198750 0.980050i \(-0.436312\pi\)
0.198750 + 0.980050i \(0.436312\pi\)
\(374\) 0 0
\(375\) −1.40330 −0.0724663
\(376\) 0 0
\(377\) 41.5222 2.13850
\(378\) 0 0
\(379\) −30.8889 −1.58666 −0.793328 0.608795i \(-0.791653\pi\)
−0.793328 + 0.608795i \(0.791653\pi\)
\(380\) 0 0
\(381\) −8.98506 −0.460319
\(382\) 0 0
\(383\) −30.3203 −1.54930 −0.774648 0.632392i \(-0.782073\pi\)
−0.774648 + 0.632392i \(0.782073\pi\)
\(384\) 0 0
\(385\) 12.5807 0.641171
\(386\) 0 0
\(387\) 7.88001 0.400563
\(388\) 0 0
\(389\) −19.4655 −0.986939 −0.493469 0.869763i \(-0.664272\pi\)
−0.493469 + 0.869763i \(0.664272\pi\)
\(390\) 0 0
\(391\) 5.17276 0.261598
\(392\) 0 0
\(393\) −20.4930 −1.03374
\(394\) 0 0
\(395\) −5.13669 −0.258455
\(396\) 0 0
\(397\) −4.70594 −0.236185 −0.118092 0.993003i \(-0.537678\pi\)
−0.118092 + 0.993003i \(0.537678\pi\)
\(398\) 0 0
\(399\) 18.7140 0.936870
\(400\) 0 0
\(401\) 15.1758 0.757842 0.378921 0.925429i \(-0.376295\pi\)
0.378921 + 0.925429i \(0.376295\pi\)
\(402\) 0 0
\(403\) 25.4615 1.26833
\(404\) 0 0
\(405\) −4.84535 −0.240768
\(406\) 0 0
\(407\) −30.5827 −1.51593
\(408\) 0 0
\(409\) 14.4829 0.716132 0.358066 0.933696i \(-0.383436\pi\)
0.358066 + 0.933696i \(0.383436\pi\)
\(410\) 0 0
\(411\) −30.2784 −1.49353
\(412\) 0 0
\(413\) 32.8904 1.61843
\(414\) 0 0
\(415\) 0.0490305 0.00240681
\(416\) 0 0
\(417\) 10.4140 0.509974
\(418\) 0 0
\(419\) −31.2731 −1.52779 −0.763897 0.645339i \(-0.776716\pi\)
−0.763897 + 0.645339i \(0.776716\pi\)
\(420\) 0 0
\(421\) −20.6704 −1.00741 −0.503706 0.863875i \(-0.668031\pi\)
−0.503706 + 0.863875i \(0.668031\pi\)
\(422\) 0 0
\(423\) 7.04422 0.342502
\(424\) 0 0
\(425\) 0.810350 0.0393077
\(426\) 0 0
\(427\) −25.1544 −1.21731
\(428\) 0 0
\(429\) 28.0629 1.35489
\(430\) 0 0
\(431\) −20.6994 −0.997056 −0.498528 0.866874i \(-0.666126\pi\)
−0.498528 + 0.866874i \(0.666126\pi\)
\(432\) 0 0
\(433\) −0.0645117 −0.00310023 −0.00155012 0.999999i \(-0.500493\pi\)
−0.00155012 + 0.999999i \(0.500493\pi\)
\(434\) 0 0
\(435\) 11.2034 0.537162
\(436\) 0 0
\(437\) −26.0171 −1.24457
\(438\) 0 0
\(439\) −24.3477 −1.16205 −0.581026 0.813885i \(-0.697349\pi\)
−0.581026 + 0.813885i \(0.697349\pi\)
\(440\) 0 0
\(441\) −3.81952 −0.181882
\(442\) 0 0
\(443\) −3.21879 −0.152929 −0.0764647 0.997072i \(-0.524363\pi\)
−0.0764647 + 0.997072i \(0.524363\pi\)
\(444\) 0 0
\(445\) 7.75451 0.367599
\(446\) 0 0
\(447\) 32.9519 1.55857
\(448\) 0 0
\(449\) 3.15584 0.148933 0.0744667 0.997224i \(-0.476275\pi\)
0.0744667 + 0.997224i \(0.476275\pi\)
\(450\) 0 0
\(451\) 40.7302 1.91791
\(452\) 0 0
\(453\) −1.40330 −0.0659329
\(454\) 0 0
\(455\) −17.0172 −0.797777
\(456\) 0 0
\(457\) 12.1301 0.567424 0.283712 0.958910i \(-0.408434\pi\)
0.283712 + 0.958910i \(0.408434\pi\)
\(458\) 0 0
\(459\) 4.58362 0.213945
\(460\) 0 0
\(461\) 22.5679 1.05109 0.525546 0.850765i \(-0.323861\pi\)
0.525546 + 0.850765i \(0.323861\pi\)
\(462\) 0 0
\(463\) 18.6841 0.868322 0.434161 0.900835i \(-0.357045\pi\)
0.434161 + 0.900835i \(0.357045\pi\)
\(464\) 0 0
\(465\) 6.86996 0.318587
\(466\) 0 0
\(467\) −14.2947 −0.661481 −0.330740 0.943722i \(-0.607298\pi\)
−0.330740 + 0.943722i \(0.607298\pi\)
\(468\) 0 0
\(469\) −46.1735 −2.13210
\(470\) 0 0
\(471\) −21.6141 −0.995926
\(472\) 0 0
\(473\) −29.3952 −1.35159
\(474\) 0 0
\(475\) −4.07576 −0.187009
\(476\) 0 0
\(477\) −1.61556 −0.0739714
\(478\) 0 0
\(479\) 31.2260 1.42675 0.713377 0.700780i \(-0.247165\pi\)
0.713377 + 0.700780i \(0.247165\pi\)
\(480\) 0 0
\(481\) 41.3675 1.88620
\(482\) 0 0
\(483\) −29.3094 −1.33362
\(484\) 0 0
\(485\) 12.6883 0.576147
\(486\) 0 0
\(487\) 2.68911 0.121855 0.0609276 0.998142i \(-0.480594\pi\)
0.0609276 + 0.998142i \(0.480594\pi\)
\(488\) 0 0
\(489\) 7.28710 0.329534
\(490\) 0 0
\(491\) 14.2689 0.643948 0.321974 0.946749i \(-0.395654\pi\)
0.321974 + 0.946749i \(0.395654\pi\)
\(492\) 0 0
\(493\) −6.46951 −0.291372
\(494\) 0 0
\(495\) −3.96322 −0.178133
\(496\) 0 0
\(497\) −34.8693 −1.56410
\(498\) 0 0
\(499\) 8.96012 0.401110 0.200555 0.979682i \(-0.435725\pi\)
0.200555 + 0.979682i \(0.435725\pi\)
\(500\) 0 0
\(501\) 23.0453 1.02959
\(502\) 0 0
\(503\) 30.5544 1.36236 0.681178 0.732118i \(-0.261468\pi\)
0.681178 + 0.732118i \(0.261468\pi\)
\(504\) 0 0
\(505\) −11.4164 −0.508024
\(506\) 0 0
\(507\) −19.7161 −0.875622
\(508\) 0 0
\(509\) −29.3372 −1.30035 −0.650174 0.759785i \(-0.725304\pi\)
−0.650174 + 0.759785i \(0.725304\pi\)
\(510\) 0 0
\(511\) −26.3224 −1.16444
\(512\) 0 0
\(513\) −23.0539 −1.01786
\(514\) 0 0
\(515\) −13.2005 −0.581685
\(516\) 0 0
\(517\) −26.2774 −1.15568
\(518\) 0 0
\(519\) 20.6245 0.905317
\(520\) 0 0
\(521\) −39.1930 −1.71707 −0.858537 0.512751i \(-0.828626\pi\)
−0.858537 + 0.512751i \(0.828626\pi\)
\(522\) 0 0
\(523\) −6.88164 −0.300913 −0.150456 0.988617i \(-0.548074\pi\)
−0.150456 + 0.988617i \(0.548074\pi\)
\(524\) 0 0
\(525\) −4.59153 −0.200391
\(526\) 0 0
\(527\) −3.96712 −0.172810
\(528\) 0 0
\(529\) 17.7474 0.771627
\(530\) 0 0
\(531\) −10.3613 −0.449640
\(532\) 0 0
\(533\) −55.0934 −2.38636
\(534\) 0 0
\(535\) 4.57558 0.197820
\(536\) 0 0
\(537\) 7.99192 0.344877
\(538\) 0 0
\(539\) 14.2482 0.613711
\(540\) 0 0
\(541\) −0.545100 −0.0234357 −0.0117178 0.999931i \(-0.503730\pi\)
−0.0117178 + 0.999931i \(0.503730\pi\)
\(542\) 0 0
\(543\) 29.7439 1.27643
\(544\) 0 0
\(545\) 13.2630 0.568126
\(546\) 0 0
\(547\) −9.61966 −0.411307 −0.205653 0.978625i \(-0.565932\pi\)
−0.205653 + 0.978625i \(0.565932\pi\)
\(548\) 0 0
\(549\) 7.92424 0.338198
\(550\) 0 0
\(551\) 32.5392 1.38622
\(552\) 0 0
\(553\) −16.8069 −0.714704
\(554\) 0 0
\(555\) 11.1617 0.473786
\(556\) 0 0
\(557\) −22.9413 −0.972054 −0.486027 0.873944i \(-0.661554\pi\)
−0.486027 + 0.873944i \(0.661554\pi\)
\(558\) 0 0
\(559\) 39.7612 1.68172
\(560\) 0 0
\(561\) −4.37243 −0.184604
\(562\) 0 0
\(563\) −15.8451 −0.667790 −0.333895 0.942610i \(-0.608363\pi\)
−0.333895 + 0.942610i \(0.608363\pi\)
\(564\) 0 0
\(565\) −0.00584044 −0.000245709 0
\(566\) 0 0
\(567\) −15.8537 −0.665794
\(568\) 0 0
\(569\) −19.0538 −0.798776 −0.399388 0.916782i \(-0.630777\pi\)
−0.399388 + 0.916782i \(0.630777\pi\)
\(570\) 0 0
\(571\) 20.5077 0.858219 0.429110 0.903252i \(-0.358827\pi\)
0.429110 + 0.903252i \(0.358827\pi\)
\(572\) 0 0
\(573\) −2.44265 −0.102043
\(574\) 0 0
\(575\) 6.38337 0.266205
\(576\) 0 0
\(577\) 6.35981 0.264762 0.132381 0.991199i \(-0.457738\pi\)
0.132381 + 0.991199i \(0.457738\pi\)
\(578\) 0 0
\(579\) −29.1951 −1.21331
\(580\) 0 0
\(581\) 0.160425 0.00665556
\(582\) 0 0
\(583\) 6.02660 0.249596
\(584\) 0 0
\(585\) 5.36082 0.221643
\(586\) 0 0
\(587\) 32.1029 1.32503 0.662515 0.749049i \(-0.269489\pi\)
0.662515 + 0.749049i \(0.269489\pi\)
\(588\) 0 0
\(589\) 19.9531 0.822154
\(590\) 0 0
\(591\) −18.5218 −0.761887
\(592\) 0 0
\(593\) 18.5175 0.760424 0.380212 0.924899i \(-0.375851\pi\)
0.380212 + 0.924899i \(0.375851\pi\)
\(594\) 0 0
\(595\) 2.65142 0.108698
\(596\) 0 0
\(597\) 8.83493 0.361589
\(598\) 0 0
\(599\) −5.55831 −0.227107 −0.113553 0.993532i \(-0.536223\pi\)
−0.113553 + 0.993532i \(0.536223\pi\)
\(600\) 0 0
\(601\) −23.2149 −0.946954 −0.473477 0.880806i \(-0.657001\pi\)
−0.473477 + 0.880806i \(0.657001\pi\)
\(602\) 0 0
\(603\) 14.5458 0.592349
\(604\) 0 0
\(605\) 3.78419 0.153849
\(606\) 0 0
\(607\) 3.25348 0.132055 0.0660273 0.997818i \(-0.478968\pi\)
0.0660273 + 0.997818i \(0.478968\pi\)
\(608\) 0 0
\(609\) 36.6569 1.48541
\(610\) 0 0
\(611\) 35.5439 1.43795
\(612\) 0 0
\(613\) −15.4078 −0.622315 −0.311158 0.950358i \(-0.600717\pi\)
−0.311158 + 0.950358i \(0.600717\pi\)
\(614\) 0 0
\(615\) −14.8651 −0.599421
\(616\) 0 0
\(617\) 38.1339 1.53521 0.767606 0.640922i \(-0.221448\pi\)
0.767606 + 0.640922i \(0.221448\pi\)
\(618\) 0 0
\(619\) 42.1189 1.69290 0.846451 0.532466i \(-0.178735\pi\)
0.846451 + 0.532466i \(0.178735\pi\)
\(620\) 0 0
\(621\) 36.1066 1.44891
\(622\) 0 0
\(623\) 25.3723 1.01652
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 21.9917 0.878264
\(628\) 0 0
\(629\) −6.44540 −0.256995
\(630\) 0 0
\(631\) −29.8991 −1.19027 −0.595133 0.803627i \(-0.702901\pi\)
−0.595133 + 0.803627i \(0.702901\pi\)
\(632\) 0 0
\(633\) 13.3125 0.529126
\(634\) 0 0
\(635\) 6.40279 0.254087
\(636\) 0 0
\(637\) −19.2727 −0.763610
\(638\) 0 0
\(639\) 10.9847 0.434547
\(640\) 0 0
\(641\) −31.8436 −1.25775 −0.628874 0.777507i \(-0.716484\pi\)
−0.628874 + 0.777507i \(0.716484\pi\)
\(642\) 0 0
\(643\) −16.3952 −0.646564 −0.323282 0.946303i \(-0.604786\pi\)
−0.323282 + 0.946303i \(0.604786\pi\)
\(644\) 0 0
\(645\) 10.7283 0.422425
\(646\) 0 0
\(647\) −8.62054 −0.338908 −0.169454 0.985538i \(-0.554200\pi\)
−0.169454 + 0.985538i \(0.554200\pi\)
\(648\) 0 0
\(649\) 38.6511 1.51719
\(650\) 0 0
\(651\) 22.4781 0.880986
\(652\) 0 0
\(653\) −27.1705 −1.06326 −0.531632 0.846975i \(-0.678421\pi\)
−0.531632 + 0.846975i \(0.678421\pi\)
\(654\) 0 0
\(655\) 14.6034 0.570603
\(656\) 0 0
\(657\) 8.29219 0.323509
\(658\) 0 0
\(659\) −20.8605 −0.812609 −0.406304 0.913738i \(-0.633183\pi\)
−0.406304 + 0.913738i \(0.633183\pi\)
\(660\) 0 0
\(661\) 19.2152 0.747383 0.373692 0.927553i \(-0.378092\pi\)
0.373692 + 0.927553i \(0.378092\pi\)
\(662\) 0 0
\(663\) 5.91433 0.229694
\(664\) 0 0
\(665\) −13.3356 −0.517134
\(666\) 0 0
\(667\) −50.9623 −1.97327
\(668\) 0 0
\(669\) −20.4193 −0.789457
\(670\) 0 0
\(671\) −29.5602 −1.14116
\(672\) 0 0
\(673\) −29.6437 −1.14268 −0.571341 0.820713i \(-0.693576\pi\)
−0.571341 + 0.820713i \(0.693576\pi\)
\(674\) 0 0
\(675\) 5.65635 0.217713
\(676\) 0 0
\(677\) 10.0487 0.386204 0.193102 0.981179i \(-0.438145\pi\)
0.193102 + 0.981179i \(0.438145\pi\)
\(678\) 0 0
\(679\) 41.5154 1.59322
\(680\) 0 0
\(681\) −12.7365 −0.488064
\(682\) 0 0
\(683\) −1.27859 −0.0489238 −0.0244619 0.999701i \(-0.507787\pi\)
−0.0244619 + 0.999701i \(0.507787\pi\)
\(684\) 0 0
\(685\) 21.5765 0.824397
\(686\) 0 0
\(687\) 17.5609 0.669989
\(688\) 0 0
\(689\) −8.15184 −0.310560
\(690\) 0 0
\(691\) 38.6689 1.47103 0.735517 0.677506i \(-0.236939\pi\)
0.735517 + 0.677506i \(0.236939\pi\)
\(692\) 0 0
\(693\) −12.9674 −0.492592
\(694\) 0 0
\(695\) −7.42104 −0.281496
\(696\) 0 0
\(697\) 8.58401 0.325143
\(698\) 0 0
\(699\) −6.36583 −0.240778
\(700\) 0 0
\(701\) 20.4895 0.773877 0.386938 0.922106i \(-0.373533\pi\)
0.386938 + 0.922106i \(0.373533\pi\)
\(702\) 0 0
\(703\) 32.4180 1.22267
\(704\) 0 0
\(705\) 9.59037 0.361194
\(706\) 0 0
\(707\) −37.3539 −1.40484
\(708\) 0 0
\(709\) 6.92461 0.260059 0.130030 0.991510i \(-0.458493\pi\)
0.130030 + 0.991510i \(0.458493\pi\)
\(710\) 0 0
\(711\) 5.29459 0.198563
\(712\) 0 0
\(713\) −31.2502 −1.17033
\(714\) 0 0
\(715\) −19.9977 −0.747872
\(716\) 0 0
\(717\) −1.97961 −0.0739297
\(718\) 0 0
\(719\) 7.56860 0.282261 0.141131 0.989991i \(-0.454926\pi\)
0.141131 + 0.989991i \(0.454926\pi\)
\(720\) 0 0
\(721\) −43.1914 −1.60853
\(722\) 0 0
\(723\) 22.0316 0.819364
\(724\) 0 0
\(725\) −7.98360 −0.296503
\(726\) 0 0
\(727\) 21.7850 0.807960 0.403980 0.914768i \(-0.367627\pi\)
0.403980 + 0.914768i \(0.367627\pi\)
\(728\) 0 0
\(729\) 28.8070 1.06693
\(730\) 0 0
\(731\) −6.19513 −0.229135
\(732\) 0 0
\(733\) −37.2890 −1.37730 −0.688651 0.725093i \(-0.741797\pi\)
−0.688651 + 0.725093i \(0.741797\pi\)
\(734\) 0 0
\(735\) −5.20009 −0.191808
\(736\) 0 0
\(737\) −54.2608 −1.99872
\(738\) 0 0
\(739\) −52.9735 −1.94866 −0.974330 0.225123i \(-0.927722\pi\)
−0.974330 + 0.225123i \(0.927722\pi\)
\(740\) 0 0
\(741\) −29.7469 −1.09278
\(742\) 0 0
\(743\) 39.6643 1.45514 0.727571 0.686032i \(-0.240649\pi\)
0.727571 + 0.686032i \(0.240649\pi\)
\(744\) 0 0
\(745\) −23.4817 −0.860302
\(746\) 0 0
\(747\) −0.0505378 −0.00184908
\(748\) 0 0
\(749\) 14.9710 0.547030
\(750\) 0 0
\(751\) 34.0092 1.24101 0.620507 0.784201i \(-0.286927\pi\)
0.620507 + 0.784201i \(0.286927\pi\)
\(752\) 0 0
\(753\) −36.0789 −1.31479
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −9.21701 −0.334998 −0.167499 0.985872i \(-0.553569\pi\)
−0.167499 + 0.985872i \(0.553569\pi\)
\(758\) 0 0
\(759\) −34.4429 −1.25020
\(760\) 0 0
\(761\) 31.3311 1.13575 0.567875 0.823115i \(-0.307766\pi\)
0.567875 + 0.823115i \(0.307766\pi\)
\(762\) 0 0
\(763\) 43.3959 1.57104
\(764\) 0 0
\(765\) −0.835260 −0.0301989
\(766\) 0 0
\(767\) −52.2811 −1.88776
\(768\) 0 0
\(769\) 7.21347 0.260124 0.130062 0.991506i \(-0.458482\pi\)
0.130062 + 0.991506i \(0.458482\pi\)
\(770\) 0 0
\(771\) 14.4912 0.521888
\(772\) 0 0
\(773\) 55.0219 1.97900 0.989499 0.144536i \(-0.0461691\pi\)
0.989499 + 0.144536i \(0.0461691\pi\)
\(774\) 0 0
\(775\) −4.89556 −0.175854
\(776\) 0 0
\(777\) 36.5203 1.31016
\(778\) 0 0
\(779\) −43.1744 −1.54688
\(780\) 0 0
\(781\) −40.9767 −1.46626
\(782\) 0 0
\(783\) −45.1580 −1.61382
\(784\) 0 0
\(785\) 15.4023 0.549732
\(786\) 0 0
\(787\) −1.86384 −0.0664387 −0.0332193 0.999448i \(-0.510576\pi\)
−0.0332193 + 0.999448i \(0.510576\pi\)
\(788\) 0 0
\(789\) 8.48623 0.302118
\(790\) 0 0
\(791\) −0.0191096 −0.000679458 0
\(792\) 0 0
\(793\) 39.9844 1.41989
\(794\) 0 0
\(795\) −2.19951 −0.0780084
\(796\) 0 0
\(797\) 48.3216 1.71164 0.855820 0.517274i \(-0.173053\pi\)
0.855820 + 0.517274i \(0.173053\pi\)
\(798\) 0 0
\(799\) −5.53805 −0.195922
\(800\) 0 0
\(801\) −7.99288 −0.282415
\(802\) 0 0
\(803\) −30.9328 −1.09159
\(804\) 0 0
\(805\) 20.8860 0.736136
\(806\) 0 0
\(807\) −32.0008 −1.12648
\(808\) 0 0
\(809\) −27.8708 −0.979884 −0.489942 0.871755i \(-0.662982\pi\)
−0.489942 + 0.871755i \(0.662982\pi\)
\(810\) 0 0
\(811\) −16.7951 −0.589756 −0.294878 0.955535i \(-0.595279\pi\)
−0.294878 + 0.955535i \(0.595279\pi\)
\(812\) 0 0
\(813\) −10.1223 −0.355005
\(814\) 0 0
\(815\) −5.19282 −0.181897
\(816\) 0 0
\(817\) 31.1592 1.09012
\(818\) 0 0
\(819\) 17.5403 0.612907
\(820\) 0 0
\(821\) −41.9196 −1.46300 −0.731502 0.681839i \(-0.761180\pi\)
−0.731502 + 0.681839i \(0.761180\pi\)
\(822\) 0 0
\(823\) 42.9448 1.49696 0.748480 0.663157i \(-0.230784\pi\)
0.748480 + 0.663157i \(0.230784\pi\)
\(824\) 0 0
\(825\) −5.39573 −0.187855
\(826\) 0 0
\(827\) −13.8783 −0.482596 −0.241298 0.970451i \(-0.577573\pi\)
−0.241298 + 0.970451i \(0.577573\pi\)
\(828\) 0 0
\(829\) −9.64561 −0.335006 −0.167503 0.985872i \(-0.553570\pi\)
−0.167503 + 0.985872i \(0.553570\pi\)
\(830\) 0 0
\(831\) −8.33057 −0.288984
\(832\) 0 0
\(833\) 3.00284 0.104042
\(834\) 0 0
\(835\) −16.4222 −0.568312
\(836\) 0 0
\(837\) −27.6910 −0.957141
\(838\) 0 0
\(839\) −42.6996 −1.47415 −0.737077 0.675808i \(-0.763795\pi\)
−0.737077 + 0.675808i \(0.763795\pi\)
\(840\) 0 0
\(841\) 34.7378 1.19786
\(842\) 0 0
\(843\) 36.4050 1.25386
\(844\) 0 0
\(845\) 14.0498 0.483327
\(846\) 0 0
\(847\) 12.3817 0.425439
\(848\) 0 0
\(849\) 38.0628 1.30631
\(850\) 0 0
\(851\) −50.7724 −1.74045
\(852\) 0 0
\(853\) 47.9867 1.64303 0.821517 0.570184i \(-0.193128\pi\)
0.821517 + 0.570184i \(0.193128\pi\)
\(854\) 0 0
\(855\) 4.20105 0.143673
\(856\) 0 0
\(857\) 35.4416 1.21066 0.605331 0.795974i \(-0.293041\pi\)
0.605331 + 0.795974i \(0.293041\pi\)
\(858\) 0 0
\(859\) 22.5526 0.769486 0.384743 0.923024i \(-0.374290\pi\)
0.384743 + 0.923024i \(0.374290\pi\)
\(860\) 0 0
\(861\) −48.6379 −1.65758
\(862\) 0 0
\(863\) 12.5448 0.427028 0.213514 0.976940i \(-0.431509\pi\)
0.213514 + 0.976940i \(0.431509\pi\)
\(864\) 0 0
\(865\) −14.6971 −0.499718
\(866\) 0 0
\(867\) 22.9347 0.778902
\(868\) 0 0
\(869\) −19.7507 −0.669996
\(870\) 0 0
\(871\) 73.3954 2.48691
\(872\) 0 0
\(873\) −13.0784 −0.442635
\(874\) 0 0
\(875\) 3.27194 0.110612
\(876\) 0 0
\(877\) 30.5541 1.03174 0.515869 0.856668i \(-0.327469\pi\)
0.515869 + 0.856668i \(0.327469\pi\)
\(878\) 0 0
\(879\) 14.1936 0.478738
\(880\) 0 0
\(881\) 48.4175 1.63123 0.815614 0.578597i \(-0.196399\pi\)
0.815614 + 0.578597i \(0.196399\pi\)
\(882\) 0 0
\(883\) 3.78906 0.127512 0.0637560 0.997966i \(-0.479692\pi\)
0.0637560 + 0.997966i \(0.479692\pi\)
\(884\) 0 0
\(885\) −14.1063 −0.474180
\(886\) 0 0
\(887\) −12.4598 −0.418361 −0.209180 0.977877i \(-0.567080\pi\)
−0.209180 + 0.977877i \(0.567080\pi\)
\(888\) 0 0
\(889\) 20.9496 0.702626
\(890\) 0 0
\(891\) −18.6305 −0.624145
\(892\) 0 0
\(893\) 27.8543 0.932109
\(894\) 0 0
\(895\) −5.69508 −0.190365
\(896\) 0 0
\(897\) 46.5890 1.55556
\(898\) 0 0
\(899\) 39.0842 1.30353
\(900\) 0 0
\(901\) 1.27012 0.0423140
\(902\) 0 0
\(903\) 35.1022 1.16813
\(904\) 0 0
\(905\) −21.1956 −0.704566
\(906\) 0 0
\(907\) −26.7569 −0.888447 −0.444223 0.895916i \(-0.646520\pi\)
−0.444223 + 0.895916i \(0.646520\pi\)
\(908\) 0 0
\(909\) 11.7674 0.390299
\(910\) 0 0
\(911\) 48.1522 1.59535 0.797677 0.603085i \(-0.206062\pi\)
0.797677 + 0.603085i \(0.206062\pi\)
\(912\) 0 0
\(913\) 0.188524 0.00623922
\(914\) 0 0
\(915\) 10.7885 0.356656
\(916\) 0 0
\(917\) 47.7815 1.57789
\(918\) 0 0
\(919\) 33.8920 1.11799 0.558996 0.829170i \(-0.311187\pi\)
0.558996 + 0.829170i \(0.311187\pi\)
\(920\) 0 0
\(921\) −35.4398 −1.16778
\(922\) 0 0
\(923\) 55.4268 1.82439
\(924\) 0 0
\(925\) −7.95385 −0.261521
\(926\) 0 0
\(927\) 13.6063 0.446890
\(928\) 0 0
\(929\) −40.4302 −1.32647 −0.663236 0.748410i \(-0.730817\pi\)
−0.663236 + 0.748410i \(0.730817\pi\)
\(930\) 0 0
\(931\) −15.1032 −0.494986
\(932\) 0 0
\(933\) 30.0957 0.985290
\(934\) 0 0
\(935\) 3.11581 0.101898
\(936\) 0 0
\(937\) 22.6483 0.739888 0.369944 0.929054i \(-0.379377\pi\)
0.369944 + 0.929054i \(0.379377\pi\)
\(938\) 0 0
\(939\) 7.41472 0.241970
\(940\) 0 0
\(941\) 25.0363 0.816160 0.408080 0.912946i \(-0.366198\pi\)
0.408080 + 0.912946i \(0.366198\pi\)
\(942\) 0 0
\(943\) 67.6188 2.20197
\(944\) 0 0
\(945\) 18.5073 0.602041
\(946\) 0 0
\(947\) −22.6428 −0.735792 −0.367896 0.929867i \(-0.619922\pi\)
−0.367896 + 0.929867i \(0.619922\pi\)
\(948\) 0 0
\(949\) 41.8410 1.35822
\(950\) 0 0
\(951\) −32.8036 −1.06373
\(952\) 0 0
\(953\) 1.93946 0.0628253 0.0314126 0.999507i \(-0.489999\pi\)
0.0314126 + 0.999507i \(0.489999\pi\)
\(954\) 0 0
\(955\) 1.74064 0.0563258
\(956\) 0 0
\(957\) 43.0773 1.39249
\(958\) 0 0
\(959\) 70.5972 2.27970
\(960\) 0 0
\(961\) −7.03349 −0.226887
\(962\) 0 0
\(963\) −4.71623 −0.151979
\(964\) 0 0
\(965\) 20.8045 0.669722
\(966\) 0 0
\(967\) −11.8997 −0.382669 −0.191335 0.981525i \(-0.561282\pi\)
−0.191335 + 0.981525i \(0.561282\pi\)
\(968\) 0 0
\(969\) 4.63482 0.148892
\(970\) 0 0
\(971\) 19.5792 0.628327 0.314163 0.949369i \(-0.398276\pi\)
0.314163 + 0.949369i \(0.398276\pi\)
\(972\) 0 0
\(973\) −24.2812 −0.778420
\(974\) 0 0
\(975\) 7.29849 0.233739
\(976\) 0 0
\(977\) 60.3027 1.92925 0.964626 0.263621i \(-0.0849168\pi\)
0.964626 + 0.263621i \(0.0849168\pi\)
\(978\) 0 0
\(979\) 29.8162 0.952931
\(980\) 0 0
\(981\) −13.6707 −0.436473
\(982\) 0 0
\(983\) −49.9657 −1.59366 −0.796829 0.604205i \(-0.793491\pi\)
−0.796829 + 0.604205i \(0.793491\pi\)
\(984\) 0 0
\(985\) 13.1987 0.420547
\(986\) 0 0
\(987\) 31.3791 0.998809
\(988\) 0 0
\(989\) −48.8009 −1.55178
\(990\) 0 0
\(991\) 37.4437 1.18944 0.594720 0.803933i \(-0.297263\pi\)
0.594720 + 0.803933i \(0.297263\pi\)
\(992\) 0 0
\(993\) 34.6843 1.10067
\(994\) 0 0
\(995\) −6.29581 −0.199591
\(996\) 0 0
\(997\) −47.5262 −1.50517 −0.752585 0.658495i \(-0.771193\pi\)
−0.752585 + 0.658495i \(0.771193\pi\)
\(998\) 0 0
\(999\) −44.9898 −1.42341
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 \(a_p\))