Properties

Label 6040.2.a.p.1.15
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 1.15
Root \(-1.76710\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.76710 q^{3}\) \(+1.00000 q^{5}\) \(+0.0387940 q^{7}\) \(+0.122653 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.76710 q^{3}\) \(+1.00000 q^{5}\) \(+0.0387940 q^{7}\) \(+0.122653 q^{9}\) \(-4.56985 q^{11}\) \(+2.95916 q^{13}\) \(+1.76710 q^{15}\) \(-3.20092 q^{17}\) \(+2.27921 q^{19}\) \(+0.0685530 q^{21}\) \(+5.32494 q^{23}\) \(+1.00000 q^{25}\) \(-5.08457 q^{27}\) \(-9.46209 q^{29}\) \(-8.25733 q^{31}\) \(-8.07539 q^{33}\) \(+0.0387940 q^{35}\) \(-8.02356 q^{37}\) \(+5.22914 q^{39}\) \(-1.45591 q^{41}\) \(-4.90058 q^{43}\) \(+0.122653 q^{45}\) \(-6.28585 q^{47}\) \(-6.99850 q^{49}\) \(-5.65636 q^{51}\) \(-0.800929 q^{53}\) \(-4.56985 q^{55}\) \(+4.02760 q^{57}\) \(-7.10666 q^{59}\) \(+12.2872 q^{61}\) \(+0.00475819 q^{63}\) \(+2.95916 q^{65}\) \(-11.7703 q^{67}\) \(+9.40972 q^{69}\) \(+13.1978 q^{71}\) \(+11.9471 q^{73}\) \(+1.76710 q^{75}\) \(-0.177283 q^{77}\) \(+10.5301 q^{79}\) \(-9.35291 q^{81}\) \(+2.60891 q^{83}\) \(-3.20092 q^{85}\) \(-16.7205 q^{87}\) \(-1.97946 q^{89}\) \(+0.114798 q^{91}\) \(-14.5915 q^{93}\) \(+2.27921 q^{95}\) \(+6.49362 q^{97}\) \(-0.560504 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.76710 1.02024 0.510119 0.860104i \(-0.329601\pi\)
0.510119 + 0.860104i \(0.329601\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.0387940 0.0146628 0.00733138 0.999973i \(-0.497666\pi\)
0.00733138 + 0.999973i \(0.497666\pi\)
\(8\) 0 0
\(9\) 0.122653 0.0408842
\(10\) 0 0
\(11\) −4.56985 −1.37786 −0.688931 0.724827i \(-0.741920\pi\)
−0.688931 + 0.724827i \(0.741920\pi\)
\(12\) 0 0
\(13\) 2.95916 0.820724 0.410362 0.911923i \(-0.365402\pi\)
0.410362 + 0.911923i \(0.365402\pi\)
\(14\) 0 0
\(15\) 1.76710 0.456264
\(16\) 0 0
\(17\) −3.20092 −0.776338 −0.388169 0.921588i \(-0.626892\pi\)
−0.388169 + 0.921588i \(0.626892\pi\)
\(18\) 0 0
\(19\) 2.27921 0.522886 0.261443 0.965219i \(-0.415802\pi\)
0.261443 + 0.965219i \(0.415802\pi\)
\(20\) 0 0
\(21\) 0.0685530 0.0149595
\(22\) 0 0
\(23\) 5.32494 1.11033 0.555163 0.831741i \(-0.312656\pi\)
0.555163 + 0.831741i \(0.312656\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.08457 −0.978526
\(28\) 0 0
\(29\) −9.46209 −1.75707 −0.878533 0.477682i \(-0.841477\pi\)
−0.878533 + 0.477682i \(0.841477\pi\)
\(30\) 0 0
\(31\) −8.25733 −1.48306 −0.741530 0.670920i \(-0.765899\pi\)
−0.741530 + 0.670920i \(0.765899\pi\)
\(32\) 0 0
\(33\) −8.07539 −1.40575
\(34\) 0 0
\(35\) 0.0387940 0.00655738
\(36\) 0 0
\(37\) −8.02356 −1.31906 −0.659532 0.751676i \(-0.729246\pi\)
−0.659532 + 0.751676i \(0.729246\pi\)
\(38\) 0 0
\(39\) 5.22914 0.837333
\(40\) 0 0
\(41\) −1.45591 −0.227375 −0.113688 0.993517i \(-0.536266\pi\)
−0.113688 + 0.993517i \(0.536266\pi\)
\(42\) 0 0
\(43\) −4.90058 −0.747332 −0.373666 0.927563i \(-0.621899\pi\)
−0.373666 + 0.927563i \(0.621899\pi\)
\(44\) 0 0
\(45\) 0.122653 0.0182840
\(46\) 0 0
\(47\) −6.28585 −0.916885 −0.458442 0.888724i \(-0.651592\pi\)
−0.458442 + 0.888724i \(0.651592\pi\)
\(48\) 0 0
\(49\) −6.99850 −0.999785
\(50\) 0 0
\(51\) −5.65636 −0.792049
\(52\) 0 0
\(53\) −0.800929 −0.110016 −0.0550080 0.998486i \(-0.517518\pi\)
−0.0550080 + 0.998486i \(0.517518\pi\)
\(54\) 0 0
\(55\) −4.56985 −0.616198
\(56\) 0 0
\(57\) 4.02760 0.533468
\(58\) 0 0
\(59\) −7.10666 −0.925208 −0.462604 0.886565i \(-0.653085\pi\)
−0.462604 + 0.886565i \(0.653085\pi\)
\(60\) 0 0
\(61\) 12.2872 1.57322 0.786608 0.617453i \(-0.211835\pi\)
0.786608 + 0.617453i \(0.211835\pi\)
\(62\) 0 0
\(63\) 0.00475819 0.000599475 0
\(64\) 0 0
\(65\) 2.95916 0.367039
\(66\) 0 0
\(67\) −11.7703 −1.43797 −0.718986 0.695024i \(-0.755394\pi\)
−0.718986 + 0.695024i \(0.755394\pi\)
\(68\) 0 0
\(69\) 9.40972 1.13280
\(70\) 0 0
\(71\) 13.1978 1.56629 0.783147 0.621837i \(-0.213613\pi\)
0.783147 + 0.621837i \(0.213613\pi\)
\(72\) 0 0
\(73\) 11.9471 1.39830 0.699150 0.714975i \(-0.253562\pi\)
0.699150 + 0.714975i \(0.253562\pi\)
\(74\) 0 0
\(75\) 1.76710 0.204047
\(76\) 0 0
\(77\) −0.177283 −0.0202032
\(78\) 0 0
\(79\) 10.5301 1.18473 0.592366 0.805669i \(-0.298194\pi\)
0.592366 + 0.805669i \(0.298194\pi\)
\(80\) 0 0
\(81\) −9.35291 −1.03921
\(82\) 0 0
\(83\) 2.60891 0.286365 0.143182 0.989696i \(-0.454266\pi\)
0.143182 + 0.989696i \(0.454266\pi\)
\(84\) 0 0
\(85\) −3.20092 −0.347189
\(86\) 0 0
\(87\) −16.7205 −1.79262
\(88\) 0 0
\(89\) −1.97946 −0.209822 −0.104911 0.994482i \(-0.533456\pi\)
−0.104911 + 0.994482i \(0.533456\pi\)
\(90\) 0 0
\(91\) 0.114798 0.0120341
\(92\) 0 0
\(93\) −14.5915 −1.51307
\(94\) 0 0
\(95\) 2.27921 0.233842
\(96\) 0 0
\(97\) 6.49362 0.659327 0.329664 0.944098i \(-0.393065\pi\)
0.329664 + 0.944098i \(0.393065\pi\)
\(98\) 0 0
\(99\) −0.560504 −0.0563328
\(100\) 0 0
\(101\) 5.67550 0.564733 0.282367 0.959307i \(-0.408881\pi\)
0.282367 + 0.959307i \(0.408881\pi\)
\(102\) 0 0
\(103\) 2.74080 0.270059 0.135030 0.990842i \(-0.456887\pi\)
0.135030 + 0.990842i \(0.456887\pi\)
\(104\) 0 0
\(105\) 0.0685530 0.00669009
\(106\) 0 0
\(107\) −9.83326 −0.950617 −0.475309 0.879819i \(-0.657664\pi\)
−0.475309 + 0.879819i \(0.657664\pi\)
\(108\) 0 0
\(109\) 6.08385 0.582728 0.291364 0.956612i \(-0.405891\pi\)
0.291364 + 0.956612i \(0.405891\pi\)
\(110\) 0 0
\(111\) −14.1785 −1.34576
\(112\) 0 0
\(113\) −5.26544 −0.495331 −0.247666 0.968846i \(-0.579663\pi\)
−0.247666 + 0.968846i \(0.579663\pi\)
\(114\) 0 0
\(115\) 5.32494 0.496553
\(116\) 0 0
\(117\) 0.362949 0.0335547
\(118\) 0 0
\(119\) −0.124177 −0.0113833
\(120\) 0 0
\(121\) 9.88353 0.898502
\(122\) 0 0
\(123\) −2.57275 −0.231977
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −17.8506 −1.58398 −0.791992 0.610531i \(-0.790956\pi\)
−0.791992 + 0.610531i \(0.790956\pi\)
\(128\) 0 0
\(129\) −8.65983 −0.762456
\(130\) 0 0
\(131\) −1.79650 −0.156961 −0.0784804 0.996916i \(-0.525007\pi\)
−0.0784804 + 0.996916i \(0.525007\pi\)
\(132\) 0 0
\(133\) 0.0884197 0.00766696
\(134\) 0 0
\(135\) −5.08457 −0.437610
\(136\) 0 0
\(137\) −2.61311 −0.223253 −0.111626 0.993750i \(-0.535606\pi\)
−0.111626 + 0.993750i \(0.535606\pi\)
\(138\) 0 0
\(139\) −15.3106 −1.29863 −0.649313 0.760521i \(-0.724944\pi\)
−0.649313 + 0.760521i \(0.724944\pi\)
\(140\) 0 0
\(141\) −11.1077 −0.935440
\(142\) 0 0
\(143\) −13.5229 −1.13084
\(144\) 0 0
\(145\) −9.46209 −0.785784
\(146\) 0 0
\(147\) −12.3671 −1.02002
\(148\) 0 0
\(149\) −6.28565 −0.514941 −0.257470 0.966286i \(-0.582889\pi\)
−0.257470 + 0.966286i \(0.582889\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −0.392602 −0.0317400
\(154\) 0 0
\(155\) −8.25733 −0.663244
\(156\) 0 0
\(157\) 17.1820 1.37127 0.685635 0.727946i \(-0.259525\pi\)
0.685635 + 0.727946i \(0.259525\pi\)
\(158\) 0 0
\(159\) −1.41532 −0.112242
\(160\) 0 0
\(161\) 0.206576 0.0162805
\(162\) 0 0
\(163\) 7.15053 0.560073 0.280036 0.959989i \(-0.409653\pi\)
0.280036 + 0.959989i \(0.409653\pi\)
\(164\) 0 0
\(165\) −8.07539 −0.628669
\(166\) 0 0
\(167\) −2.33831 −0.180944 −0.0904720 0.995899i \(-0.528838\pi\)
−0.0904720 + 0.995899i \(0.528838\pi\)
\(168\) 0 0
\(169\) −4.24336 −0.326412
\(170\) 0 0
\(171\) 0.279551 0.0213778
\(172\) 0 0
\(173\) −11.3007 −0.859179 −0.429589 0.903024i \(-0.641342\pi\)
−0.429589 + 0.903024i \(0.641342\pi\)
\(174\) 0 0
\(175\) 0.0387940 0.00293255
\(176\) 0 0
\(177\) −12.5582 −0.943932
\(178\) 0 0
\(179\) 13.0976 0.978964 0.489482 0.872013i \(-0.337186\pi\)
0.489482 + 0.872013i \(0.337186\pi\)
\(180\) 0 0
\(181\) −14.3326 −1.06533 −0.532667 0.846325i \(-0.678810\pi\)
−0.532667 + 0.846325i \(0.678810\pi\)
\(182\) 0 0
\(183\) 21.7128 1.60505
\(184\) 0 0
\(185\) −8.02356 −0.589904
\(186\) 0 0
\(187\) 14.6277 1.06969
\(188\) 0 0
\(189\) −0.197251 −0.0143479
\(190\) 0 0
\(191\) 6.61903 0.478936 0.239468 0.970904i \(-0.423027\pi\)
0.239468 + 0.970904i \(0.423027\pi\)
\(192\) 0 0
\(193\) −8.71813 −0.627545 −0.313772 0.949498i \(-0.601593\pi\)
−0.313772 + 0.949498i \(0.601593\pi\)
\(194\) 0 0
\(195\) 5.22914 0.374467
\(196\) 0 0
\(197\) −20.0485 −1.42840 −0.714198 0.699944i \(-0.753208\pi\)
−0.714198 + 0.699944i \(0.753208\pi\)
\(198\) 0 0
\(199\) −1.44127 −0.102169 −0.0510846 0.998694i \(-0.516268\pi\)
−0.0510846 + 0.998694i \(0.516268\pi\)
\(200\) 0 0
\(201\) −20.7993 −1.46707
\(202\) 0 0
\(203\) −0.367072 −0.0257634
\(204\) 0 0
\(205\) −1.45591 −0.101685
\(206\) 0 0
\(207\) 0.653118 0.0453949
\(208\) 0 0
\(209\) −10.4156 −0.720465
\(210\) 0 0
\(211\) 18.9084 1.30171 0.650855 0.759202i \(-0.274411\pi\)
0.650855 + 0.759202i \(0.274411\pi\)
\(212\) 0 0
\(213\) 23.3219 1.59799
\(214\) 0 0
\(215\) −4.90058 −0.334217
\(216\) 0 0
\(217\) −0.320335 −0.0217457
\(218\) 0 0
\(219\) 21.1117 1.42660
\(220\) 0 0
\(221\) −9.47205 −0.637159
\(222\) 0 0
\(223\) −5.41547 −0.362647 −0.181323 0.983424i \(-0.558038\pi\)
−0.181323 + 0.983424i \(0.558038\pi\)
\(224\) 0 0
\(225\) 0.122653 0.00817685
\(226\) 0 0
\(227\) −18.2785 −1.21319 −0.606594 0.795012i \(-0.707465\pi\)
−0.606594 + 0.795012i \(0.707465\pi\)
\(228\) 0 0
\(229\) −1.23060 −0.0813205 −0.0406602 0.999173i \(-0.512946\pi\)
−0.0406602 + 0.999173i \(0.512946\pi\)
\(230\) 0 0
\(231\) −0.313277 −0.0206121
\(232\) 0 0
\(233\) 25.6000 1.67711 0.838555 0.544817i \(-0.183401\pi\)
0.838555 + 0.544817i \(0.183401\pi\)
\(234\) 0 0
\(235\) −6.28585 −0.410043
\(236\) 0 0
\(237\) 18.6078 1.20871
\(238\) 0 0
\(239\) 12.4541 0.805590 0.402795 0.915290i \(-0.368039\pi\)
0.402795 + 0.915290i \(0.368039\pi\)
\(240\) 0 0
\(241\) 18.3219 1.18022 0.590108 0.807324i \(-0.299085\pi\)
0.590108 + 0.807324i \(0.299085\pi\)
\(242\) 0 0
\(243\) −1.27386 −0.0817179
\(244\) 0 0
\(245\) −6.99850 −0.447117
\(246\) 0 0
\(247\) 6.74455 0.429145
\(248\) 0 0
\(249\) 4.61021 0.292160
\(250\) 0 0
\(251\) −22.6627 −1.43046 −0.715230 0.698889i \(-0.753678\pi\)
−0.715230 + 0.698889i \(0.753678\pi\)
\(252\) 0 0
\(253\) −24.3342 −1.52988
\(254\) 0 0
\(255\) −5.65636 −0.354215
\(256\) 0 0
\(257\) −19.7215 −1.23019 −0.615096 0.788452i \(-0.710883\pi\)
−0.615096 + 0.788452i \(0.710883\pi\)
\(258\) 0 0
\(259\) −0.311266 −0.0193411
\(260\) 0 0
\(261\) −1.16055 −0.0718363
\(262\) 0 0
\(263\) −21.0741 −1.29948 −0.649741 0.760155i \(-0.725123\pi\)
−0.649741 + 0.760155i \(0.725123\pi\)
\(264\) 0 0
\(265\) −0.800929 −0.0492007
\(266\) 0 0
\(267\) −3.49791 −0.214068
\(268\) 0 0
\(269\) 1.51179 0.0921756 0.0460878 0.998937i \(-0.485325\pi\)
0.0460878 + 0.998937i \(0.485325\pi\)
\(270\) 0 0
\(271\) −15.5008 −0.941607 −0.470803 0.882238i \(-0.656036\pi\)
−0.470803 + 0.882238i \(0.656036\pi\)
\(272\) 0 0
\(273\) 0.202859 0.0122776
\(274\) 0 0
\(275\) −4.56985 −0.275572
\(276\) 0 0
\(277\) 23.5766 1.41658 0.708292 0.705920i \(-0.249466\pi\)
0.708292 + 0.705920i \(0.249466\pi\)
\(278\) 0 0
\(279\) −1.01278 −0.0606337
\(280\) 0 0
\(281\) 7.81071 0.465948 0.232974 0.972483i \(-0.425154\pi\)
0.232974 + 0.972483i \(0.425154\pi\)
\(282\) 0 0
\(283\) −3.56257 −0.211773 −0.105886 0.994378i \(-0.533768\pi\)
−0.105886 + 0.994378i \(0.533768\pi\)
\(284\) 0 0
\(285\) 4.02760 0.238574
\(286\) 0 0
\(287\) −0.0564807 −0.00333395
\(288\) 0 0
\(289\) −6.75409 −0.397299
\(290\) 0 0
\(291\) 11.4749 0.672670
\(292\) 0 0
\(293\) −6.02125 −0.351765 −0.175882 0.984411i \(-0.556278\pi\)
−0.175882 + 0.984411i \(0.556278\pi\)
\(294\) 0 0
\(295\) −7.10666 −0.413766
\(296\) 0 0
\(297\) 23.2357 1.34827
\(298\) 0 0
\(299\) 15.7574 0.911272
\(300\) 0 0
\(301\) −0.190113 −0.0109579
\(302\) 0 0
\(303\) 10.0292 0.576162
\(304\) 0 0
\(305\) 12.2872 0.703564
\(306\) 0 0
\(307\) 23.0560 1.31587 0.657936 0.753074i \(-0.271430\pi\)
0.657936 + 0.753074i \(0.271430\pi\)
\(308\) 0 0
\(309\) 4.84328 0.275524
\(310\) 0 0
\(311\) 20.3684 1.15498 0.577492 0.816396i \(-0.304032\pi\)
0.577492 + 0.816396i \(0.304032\pi\)
\(312\) 0 0
\(313\) 15.2529 0.862143 0.431072 0.902318i \(-0.358136\pi\)
0.431072 + 0.902318i \(0.358136\pi\)
\(314\) 0 0
\(315\) 0.00475819 0.000268094 0
\(316\) 0 0
\(317\) 3.23641 0.181775 0.0908874 0.995861i \(-0.471030\pi\)
0.0908874 + 0.995861i \(0.471030\pi\)
\(318\) 0 0
\(319\) 43.2403 2.42099
\(320\) 0 0
\(321\) −17.3764 −0.969855
\(322\) 0 0
\(323\) −7.29557 −0.405937
\(324\) 0 0
\(325\) 2.95916 0.164145
\(326\) 0 0
\(327\) 10.7508 0.594520
\(328\) 0 0
\(329\) −0.243853 −0.0134441
\(330\) 0 0
\(331\) −11.7991 −0.648537 −0.324268 0.945965i \(-0.605118\pi\)
−0.324268 + 0.945965i \(0.605118\pi\)
\(332\) 0 0
\(333\) −0.984111 −0.0539289
\(334\) 0 0
\(335\) −11.7703 −0.643081
\(336\) 0 0
\(337\) 20.3246 1.10715 0.553575 0.832799i \(-0.313263\pi\)
0.553575 + 0.832799i \(0.313263\pi\)
\(338\) 0 0
\(339\) −9.30458 −0.505355
\(340\) 0 0
\(341\) 37.7347 2.04345
\(342\) 0 0
\(343\) −0.543058 −0.0293224
\(344\) 0 0
\(345\) 9.40972 0.506602
\(346\) 0 0
\(347\) −5.62496 −0.301963 −0.150982 0.988537i \(-0.548243\pi\)
−0.150982 + 0.988537i \(0.548243\pi\)
\(348\) 0 0
\(349\) 20.0986 1.07585 0.537927 0.842991i \(-0.319207\pi\)
0.537927 + 0.842991i \(0.319207\pi\)
\(350\) 0 0
\(351\) −15.0461 −0.803100
\(352\) 0 0
\(353\) −12.6630 −0.673984 −0.336992 0.941508i \(-0.609410\pi\)
−0.336992 + 0.941508i \(0.609410\pi\)
\(354\) 0 0
\(355\) 13.1978 0.700468
\(356\) 0 0
\(357\) −0.219433 −0.0116136
\(358\) 0 0
\(359\) −19.1956 −1.01311 −0.506553 0.862209i \(-0.669081\pi\)
−0.506553 + 0.862209i \(0.669081\pi\)
\(360\) 0 0
\(361\) −13.8052 −0.726590
\(362\) 0 0
\(363\) 17.4652 0.916686
\(364\) 0 0
\(365\) 11.9471 0.625338
\(366\) 0 0
\(367\) −5.36036 −0.279809 −0.139904 0.990165i \(-0.544679\pi\)
−0.139904 + 0.990165i \(0.544679\pi\)
\(368\) 0 0
\(369\) −0.178572 −0.00929606
\(370\) 0 0
\(371\) −0.0310712 −0.00161314
\(372\) 0 0
\(373\) 2.61435 0.135366 0.0676831 0.997707i \(-0.478439\pi\)
0.0676831 + 0.997707i \(0.478439\pi\)
\(374\) 0 0
\(375\) 1.76710 0.0912528
\(376\) 0 0
\(377\) −27.9999 −1.44207
\(378\) 0 0
\(379\) −19.5377 −1.00359 −0.501793 0.864988i \(-0.667326\pi\)
−0.501793 + 0.864988i \(0.667326\pi\)
\(380\) 0 0
\(381\) −31.5438 −1.61604
\(382\) 0 0
\(383\) −21.6004 −1.10373 −0.551865 0.833933i \(-0.686084\pi\)
−0.551865 + 0.833933i \(0.686084\pi\)
\(384\) 0 0
\(385\) −0.177283 −0.00903517
\(386\) 0 0
\(387\) −0.601070 −0.0305541
\(388\) 0 0
\(389\) −10.8691 −0.551083 −0.275542 0.961289i \(-0.588857\pi\)
−0.275542 + 0.961289i \(0.588857\pi\)
\(390\) 0 0
\(391\) −17.0447 −0.861989
\(392\) 0 0
\(393\) −3.17460 −0.160137
\(394\) 0 0
\(395\) 10.5301 0.529828
\(396\) 0 0
\(397\) 5.11621 0.256775 0.128388 0.991724i \(-0.459020\pi\)
0.128388 + 0.991724i \(0.459020\pi\)
\(398\) 0 0
\(399\) 0.156247 0.00782212
\(400\) 0 0
\(401\) 10.6595 0.532308 0.266154 0.963930i \(-0.414247\pi\)
0.266154 + 0.963930i \(0.414247\pi\)
\(402\) 0 0
\(403\) −24.4348 −1.21718
\(404\) 0 0
\(405\) −9.35291 −0.464750
\(406\) 0 0
\(407\) 36.6665 1.81749
\(408\) 0 0
\(409\) 24.4102 1.20700 0.603502 0.797361i \(-0.293771\pi\)
0.603502 + 0.797361i \(0.293771\pi\)
\(410\) 0 0
\(411\) −4.61763 −0.227771
\(412\) 0 0
\(413\) −0.275696 −0.0135661
\(414\) 0 0
\(415\) 2.60891 0.128066
\(416\) 0 0
\(417\) −27.0554 −1.32491
\(418\) 0 0
\(419\) −9.51427 −0.464802 −0.232401 0.972620i \(-0.574658\pi\)
−0.232401 + 0.972620i \(0.574658\pi\)
\(420\) 0 0
\(421\) −9.28534 −0.452540 −0.226270 0.974065i \(-0.572653\pi\)
−0.226270 + 0.974065i \(0.572653\pi\)
\(422\) 0 0
\(423\) −0.770976 −0.0374861
\(424\) 0 0
\(425\) −3.20092 −0.155268
\(426\) 0 0
\(427\) 0.476670 0.0230677
\(428\) 0 0
\(429\) −23.8964 −1.15373
\(430\) 0 0
\(431\) 1.19193 0.0574132 0.0287066 0.999588i \(-0.490861\pi\)
0.0287066 + 0.999588i \(0.490861\pi\)
\(432\) 0 0
\(433\) −0.166866 −0.00801906 −0.00400953 0.999992i \(-0.501276\pi\)
−0.00400953 + 0.999992i \(0.501276\pi\)
\(434\) 0 0
\(435\) −16.7205 −0.801686
\(436\) 0 0
\(437\) 12.1367 0.580575
\(438\) 0 0
\(439\) −16.2855 −0.777263 −0.388632 0.921393i \(-0.627052\pi\)
−0.388632 + 0.921393i \(0.627052\pi\)
\(440\) 0 0
\(441\) −0.858384 −0.0408754
\(442\) 0 0
\(443\) −13.9686 −0.663666 −0.331833 0.943338i \(-0.607667\pi\)
−0.331833 + 0.943338i \(0.607667\pi\)
\(444\) 0 0
\(445\) −1.97946 −0.0938353
\(446\) 0 0
\(447\) −11.1074 −0.525362
\(448\) 0 0
\(449\) −13.7196 −0.647470 −0.323735 0.946148i \(-0.604939\pi\)
−0.323735 + 0.946148i \(0.604939\pi\)
\(450\) 0 0
\(451\) 6.65330 0.313292
\(452\) 0 0
\(453\) 1.76710 0.0830257
\(454\) 0 0
\(455\) 0.114798 0.00538180
\(456\) 0 0
\(457\) −17.9449 −0.839427 −0.419714 0.907657i \(-0.637869\pi\)
−0.419714 + 0.907657i \(0.637869\pi\)
\(458\) 0 0
\(459\) 16.2753 0.759667
\(460\) 0 0
\(461\) −30.8821 −1.43832 −0.719160 0.694844i \(-0.755473\pi\)
−0.719160 + 0.694844i \(0.755473\pi\)
\(462\) 0 0
\(463\) 15.9285 0.740262 0.370131 0.928979i \(-0.379313\pi\)
0.370131 + 0.928979i \(0.379313\pi\)
\(464\) 0 0
\(465\) −14.5915 −0.676667
\(466\) 0 0
\(467\) 1.60709 0.0743673 0.0371836 0.999308i \(-0.488161\pi\)
0.0371836 + 0.999308i \(0.488161\pi\)
\(468\) 0 0
\(469\) −0.456617 −0.0210846
\(470\) 0 0
\(471\) 30.3623 1.39902
\(472\) 0 0
\(473\) 22.3949 1.02972
\(474\) 0 0
\(475\) 2.27921 0.104577
\(476\) 0 0
\(477\) −0.0982360 −0.00449792
\(478\) 0 0
\(479\) −28.1231 −1.28498 −0.642489 0.766295i \(-0.722098\pi\)
−0.642489 + 0.766295i \(0.722098\pi\)
\(480\) 0 0
\(481\) −23.7430 −1.08259
\(482\) 0 0
\(483\) 0.365041 0.0166099
\(484\) 0 0
\(485\) 6.49362 0.294860
\(486\) 0 0
\(487\) −39.4637 −1.78827 −0.894135 0.447797i \(-0.852209\pi\)
−0.894135 + 0.447797i \(0.852209\pi\)
\(488\) 0 0
\(489\) 12.6357 0.571407
\(490\) 0 0
\(491\) −15.1021 −0.681549 −0.340775 0.940145i \(-0.610689\pi\)
−0.340775 + 0.940145i \(0.610689\pi\)
\(492\) 0 0
\(493\) 30.2874 1.36408
\(494\) 0 0
\(495\) −0.560504 −0.0251928
\(496\) 0 0
\(497\) 0.511996 0.0229662
\(498\) 0 0
\(499\) 24.1026 1.07898 0.539489 0.841993i \(-0.318617\pi\)
0.539489 + 0.841993i \(0.318617\pi\)
\(500\) 0 0
\(501\) −4.13204 −0.184606
\(502\) 0 0
\(503\) −6.77947 −0.302282 −0.151141 0.988512i \(-0.548295\pi\)
−0.151141 + 0.988512i \(0.548295\pi\)
\(504\) 0 0
\(505\) 5.67550 0.252556
\(506\) 0 0
\(507\) −7.49845 −0.333018
\(508\) 0 0
\(509\) 24.1741 1.07150 0.535748 0.844378i \(-0.320030\pi\)
0.535748 + 0.844378i \(0.320030\pi\)
\(510\) 0 0
\(511\) 0.463475 0.0205029
\(512\) 0 0
\(513\) −11.5888 −0.511658
\(514\) 0 0
\(515\) 2.74080 0.120774
\(516\) 0 0
\(517\) 28.7254 1.26334
\(518\) 0 0
\(519\) −19.9696 −0.876566
\(520\) 0 0
\(521\) 31.1397 1.36426 0.682129 0.731232i \(-0.261054\pi\)
0.682129 + 0.731232i \(0.261054\pi\)
\(522\) 0 0
\(523\) 22.7975 0.996867 0.498433 0.866928i \(-0.333909\pi\)
0.498433 + 0.866928i \(0.333909\pi\)
\(524\) 0 0
\(525\) 0.0685530 0.00299190
\(526\) 0 0
\(527\) 26.4311 1.15136
\(528\) 0 0
\(529\) 5.35499 0.232826
\(530\) 0 0
\(531\) −0.871651 −0.0378264
\(532\) 0 0
\(533\) −4.30828 −0.186612
\(534\) 0 0
\(535\) −9.83326 −0.425129
\(536\) 0 0
\(537\) 23.1449 0.998776
\(538\) 0 0
\(539\) 31.9821 1.37757
\(540\) 0 0
\(541\) −14.3365 −0.616374 −0.308187 0.951326i \(-0.599722\pi\)
−0.308187 + 0.951326i \(0.599722\pi\)
\(542\) 0 0
\(543\) −25.3272 −1.08689
\(544\) 0 0
\(545\) 6.08385 0.260604
\(546\) 0 0
\(547\) 3.02146 0.129188 0.0645941 0.997912i \(-0.479425\pi\)
0.0645941 + 0.997912i \(0.479425\pi\)
\(548\) 0 0
\(549\) 1.50706 0.0643197
\(550\) 0 0
\(551\) −21.5661 −0.918746
\(552\) 0 0
\(553\) 0.408506 0.0173714
\(554\) 0 0
\(555\) −14.1785 −0.601842
\(556\) 0 0
\(557\) 21.3291 0.903744 0.451872 0.892083i \(-0.350756\pi\)
0.451872 + 0.892083i \(0.350756\pi\)
\(558\) 0 0
\(559\) −14.5016 −0.613353
\(560\) 0 0
\(561\) 25.8487 1.09133
\(562\) 0 0
\(563\) −40.3960 −1.70249 −0.851245 0.524769i \(-0.824152\pi\)
−0.851245 + 0.524769i \(0.824152\pi\)
\(564\) 0 0
\(565\) −5.26544 −0.221519
\(566\) 0 0
\(567\) −0.362837 −0.0152377
\(568\) 0 0
\(569\) 32.3561 1.35644 0.678219 0.734860i \(-0.262752\pi\)
0.678219 + 0.734860i \(0.262752\pi\)
\(570\) 0 0
\(571\) −4.79143 −0.200515 −0.100258 0.994962i \(-0.531967\pi\)
−0.100258 + 0.994962i \(0.531967\pi\)
\(572\) 0 0
\(573\) 11.6965 0.488629
\(574\) 0 0
\(575\) 5.32494 0.222065
\(576\) 0 0
\(577\) 18.9158 0.787473 0.393737 0.919223i \(-0.371182\pi\)
0.393737 + 0.919223i \(0.371182\pi\)
\(578\) 0 0
\(579\) −15.4058 −0.640245
\(580\) 0 0
\(581\) 0.101210 0.00419890
\(582\) 0 0
\(583\) 3.66012 0.151587
\(584\) 0 0
\(585\) 0.362949 0.0150061
\(586\) 0 0
\(587\) 18.6739 0.770753 0.385376 0.922759i \(-0.374072\pi\)
0.385376 + 0.922759i \(0.374072\pi\)
\(588\) 0 0
\(589\) −18.8202 −0.775472
\(590\) 0 0
\(591\) −35.4277 −1.45730
\(592\) 0 0
\(593\) 25.9862 1.06712 0.533562 0.845761i \(-0.320853\pi\)
0.533562 + 0.845761i \(0.320853\pi\)
\(594\) 0 0
\(595\) −0.124177 −0.00509075
\(596\) 0 0
\(597\) −2.54688 −0.104237
\(598\) 0 0
\(599\) 20.3171 0.830134 0.415067 0.909791i \(-0.363758\pi\)
0.415067 + 0.909791i \(0.363758\pi\)
\(600\) 0 0
\(601\) 40.9972 1.67231 0.836155 0.548493i \(-0.184798\pi\)
0.836155 + 0.548493i \(0.184798\pi\)
\(602\) 0 0
\(603\) −1.44366 −0.0587904
\(604\) 0 0
\(605\) 9.88353 0.401823
\(606\) 0 0
\(607\) −9.75068 −0.395768 −0.197884 0.980225i \(-0.563407\pi\)
−0.197884 + 0.980225i \(0.563407\pi\)
\(608\) 0 0
\(609\) −0.648655 −0.0262848
\(610\) 0 0
\(611\) −18.6008 −0.752509
\(612\) 0 0
\(613\) 25.6381 1.03551 0.517756 0.855528i \(-0.326767\pi\)
0.517756 + 0.855528i \(0.326767\pi\)
\(614\) 0 0
\(615\) −2.57275 −0.103743
\(616\) 0 0
\(617\) −3.53450 −0.142294 −0.0711468 0.997466i \(-0.522666\pi\)
−0.0711468 + 0.997466i \(0.522666\pi\)
\(618\) 0 0
\(619\) 16.1241 0.648081 0.324041 0.946043i \(-0.394959\pi\)
0.324041 + 0.946043i \(0.394959\pi\)
\(620\) 0 0
\(621\) −27.0750 −1.08648
\(622\) 0 0
\(623\) −0.0767911 −0.00307657
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −18.4055 −0.735045
\(628\) 0 0
\(629\) 25.6828 1.02404
\(630\) 0 0
\(631\) −25.0961 −0.999060 −0.499530 0.866297i \(-0.666494\pi\)
−0.499530 + 0.866297i \(0.666494\pi\)
\(632\) 0 0
\(633\) 33.4131 1.32805
\(634\) 0 0
\(635\) −17.8506 −0.708379
\(636\) 0 0
\(637\) −20.7097 −0.820548
\(638\) 0 0
\(639\) 1.61875 0.0640367
\(640\) 0 0
\(641\) 5.65432 0.223332 0.111666 0.993746i \(-0.464381\pi\)
0.111666 + 0.993746i \(0.464381\pi\)
\(642\) 0 0
\(643\) 30.4400 1.20044 0.600218 0.799836i \(-0.295080\pi\)
0.600218 + 0.799836i \(0.295080\pi\)
\(644\) 0 0
\(645\) −8.65983 −0.340981
\(646\) 0 0
\(647\) 1.26228 0.0496254 0.0248127 0.999692i \(-0.492101\pi\)
0.0248127 + 0.999692i \(0.492101\pi\)
\(648\) 0 0
\(649\) 32.4764 1.27481
\(650\) 0 0
\(651\) −0.566065 −0.0221858
\(652\) 0 0
\(653\) 21.4840 0.840733 0.420366 0.907354i \(-0.361902\pi\)
0.420366 + 0.907354i \(0.361902\pi\)
\(654\) 0 0
\(655\) −1.79650 −0.0701950
\(656\) 0 0
\(657\) 1.46534 0.0571684
\(658\) 0 0
\(659\) 30.9084 1.20402 0.602010 0.798489i \(-0.294367\pi\)
0.602010 + 0.798489i \(0.294367\pi\)
\(660\) 0 0
\(661\) −24.2710 −0.944033 −0.472016 0.881590i \(-0.656474\pi\)
−0.472016 + 0.881590i \(0.656474\pi\)
\(662\) 0 0
\(663\) −16.7381 −0.650054
\(664\) 0 0
\(665\) 0.0884197 0.00342877
\(666\) 0 0
\(667\) −50.3851 −1.95092
\(668\) 0 0
\(669\) −9.56969 −0.369986
\(670\) 0 0
\(671\) −56.1507 −2.16767
\(672\) 0 0
\(673\) −28.0862 −1.08264 −0.541322 0.840815i \(-0.682076\pi\)
−0.541322 + 0.840815i \(0.682076\pi\)
\(674\) 0 0
\(675\) −5.08457 −0.195705
\(676\) 0 0
\(677\) 8.41113 0.323266 0.161633 0.986851i \(-0.448324\pi\)
0.161633 + 0.986851i \(0.448324\pi\)
\(678\) 0 0
\(679\) 0.251914 0.00966755
\(680\) 0 0
\(681\) −32.3000 −1.23774
\(682\) 0 0
\(683\) 46.8456 1.79250 0.896249 0.443551i \(-0.146282\pi\)
0.896249 + 0.443551i \(0.146282\pi\)
\(684\) 0 0
\(685\) −2.61311 −0.0998416
\(686\) 0 0
\(687\) −2.17460 −0.0829662
\(688\) 0 0
\(689\) −2.37008 −0.0902928
\(690\) 0 0
\(691\) 11.6065 0.441531 0.220766 0.975327i \(-0.429144\pi\)
0.220766 + 0.975327i \(0.429144\pi\)
\(692\) 0 0
\(693\) −0.0217442 −0.000825994 0
\(694\) 0 0
\(695\) −15.3106 −0.580764
\(696\) 0 0
\(697\) 4.66026 0.176520
\(698\) 0 0
\(699\) 45.2378 1.71105
\(700\) 0 0
\(701\) −24.3597 −0.920055 −0.460027 0.887905i \(-0.652160\pi\)
−0.460027 + 0.887905i \(0.652160\pi\)
\(702\) 0 0
\(703\) −18.2874 −0.689721
\(704\) 0 0
\(705\) −11.1077 −0.418342
\(706\) 0 0
\(707\) 0.220175 0.00828055
\(708\) 0 0
\(709\) −10.2668 −0.385579 −0.192789 0.981240i \(-0.561753\pi\)
−0.192789 + 0.981240i \(0.561753\pi\)
\(710\) 0 0
\(711\) 1.29155 0.0484368
\(712\) 0 0
\(713\) −43.9698 −1.64668
\(714\) 0 0
\(715\) −13.5229 −0.505729
\(716\) 0 0
\(717\) 22.0077 0.821893
\(718\) 0 0
\(719\) 12.1952 0.454806 0.227403 0.973801i \(-0.426977\pi\)
0.227403 + 0.973801i \(0.426977\pi\)
\(720\) 0 0
\(721\) 0.106327 0.00395981
\(722\) 0 0
\(723\) 32.3766 1.20410
\(724\) 0 0
\(725\) −9.46209 −0.351413
\(726\) 0 0
\(727\) −26.2674 −0.974203 −0.487102 0.873345i \(-0.661946\pi\)
−0.487102 + 0.873345i \(0.661946\pi\)
\(728\) 0 0
\(729\) 25.8077 0.955841
\(730\) 0 0
\(731\) 15.6864 0.580182
\(732\) 0 0
\(733\) 19.6577 0.726073 0.363036 0.931775i \(-0.381740\pi\)
0.363036 + 0.931775i \(0.381740\pi\)
\(734\) 0 0
\(735\) −12.3671 −0.456166
\(736\) 0 0
\(737\) 53.7885 1.98133
\(738\) 0 0
\(739\) 29.5196 1.08590 0.542948 0.839766i \(-0.317308\pi\)
0.542948 + 0.839766i \(0.317308\pi\)
\(740\) 0 0
\(741\) 11.9183 0.437830
\(742\) 0 0
\(743\) −50.9633 −1.86966 −0.934832 0.355091i \(-0.884450\pi\)
−0.934832 + 0.355091i \(0.884450\pi\)
\(744\) 0 0
\(745\) −6.28565 −0.230288
\(746\) 0 0
\(747\) 0.319990 0.0117078
\(748\) 0 0
\(749\) −0.381472 −0.0139387
\(750\) 0 0
\(751\) −18.0252 −0.657748 −0.328874 0.944374i \(-0.606669\pi\)
−0.328874 + 0.944374i \(0.606669\pi\)
\(752\) 0 0
\(753\) −40.0474 −1.45941
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 39.5850 1.43874 0.719370 0.694627i \(-0.244431\pi\)
0.719370 + 0.694627i \(0.244431\pi\)
\(758\) 0 0
\(759\) −43.0010 −1.56084
\(760\) 0 0
\(761\) 29.4089 1.06607 0.533036 0.846093i \(-0.321051\pi\)
0.533036 + 0.846093i \(0.321051\pi\)
\(762\) 0 0
\(763\) 0.236017 0.00854439
\(764\) 0 0
\(765\) −0.392602 −0.0141946
\(766\) 0 0
\(767\) −21.0298 −0.759340
\(768\) 0 0
\(769\) 0.506255 0.0182560 0.00912802 0.999958i \(-0.497094\pi\)
0.00912802 + 0.999958i \(0.497094\pi\)
\(770\) 0 0
\(771\) −34.8499 −1.25509
\(772\) 0 0
\(773\) 6.48236 0.233154 0.116577 0.993182i \(-0.462808\pi\)
0.116577 + 0.993182i \(0.462808\pi\)
\(774\) 0 0
\(775\) −8.25733 −0.296612
\(776\) 0 0
\(777\) −0.550039 −0.0197325
\(778\) 0 0
\(779\) −3.31833 −0.118891
\(780\) 0 0
\(781\) −60.3121 −2.15814
\(782\) 0 0
\(783\) 48.1106 1.71933
\(784\) 0 0
\(785\) 17.1820 0.613251
\(786\) 0 0
\(787\) 10.6830 0.380806 0.190403 0.981706i \(-0.439021\pi\)
0.190403 + 0.981706i \(0.439021\pi\)
\(788\) 0 0
\(789\) −37.2400 −1.32578
\(790\) 0 0
\(791\) −0.204268 −0.00726292
\(792\) 0 0
\(793\) 36.3599 1.29118
\(794\) 0 0
\(795\) −1.41532 −0.0501963
\(796\) 0 0
\(797\) −5.48024 −0.194120 −0.0970601 0.995279i \(-0.530944\pi\)
−0.0970601 + 0.995279i \(0.530944\pi\)
\(798\) 0 0
\(799\) 20.1205 0.711812
\(800\) 0 0
\(801\) −0.242786 −0.00857842
\(802\) 0 0
\(803\) −54.5963 −1.92666
\(804\) 0 0
\(805\) 0.206576 0.00728084
\(806\) 0 0
\(807\) 2.67149 0.0940410
\(808\) 0 0
\(809\) 50.0241 1.75876 0.879378 0.476125i \(-0.157959\pi\)
0.879378 + 0.476125i \(0.157959\pi\)
\(810\) 0 0
\(811\) −13.0612 −0.458641 −0.229320 0.973351i \(-0.573650\pi\)
−0.229320 + 0.973351i \(0.573650\pi\)
\(812\) 0 0
\(813\) −27.3915 −0.960662
\(814\) 0 0
\(815\) 7.15053 0.250472
\(816\) 0 0
\(817\) −11.1695 −0.390770
\(818\) 0 0
\(819\) 0.0140803 0.000492004 0
\(820\) 0 0
\(821\) −38.4173 −1.34077 −0.670386 0.742012i \(-0.733872\pi\)
−0.670386 + 0.742012i \(0.733872\pi\)
\(822\) 0 0
\(823\) −22.1835 −0.773269 −0.386635 0.922233i \(-0.626363\pi\)
−0.386635 + 0.922233i \(0.626363\pi\)
\(824\) 0 0
\(825\) −8.07539 −0.281149
\(826\) 0 0
\(827\) −40.7872 −1.41831 −0.709155 0.705053i \(-0.750923\pi\)
−0.709155 + 0.705053i \(0.750923\pi\)
\(828\) 0 0
\(829\) −45.8876 −1.59374 −0.796872 0.604149i \(-0.793513\pi\)
−0.796872 + 0.604149i \(0.793513\pi\)
\(830\) 0 0
\(831\) 41.6624 1.44525
\(832\) 0 0
\(833\) 22.4016 0.776171
\(834\) 0 0
\(835\) −2.33831 −0.0809206
\(836\) 0 0
\(837\) 41.9849 1.45121
\(838\) 0 0
\(839\) 49.4757 1.70809 0.854045 0.520199i \(-0.174142\pi\)
0.854045 + 0.520199i \(0.174142\pi\)
\(840\) 0 0
\(841\) 60.5311 2.08728
\(842\) 0 0
\(843\) 13.8023 0.475378
\(844\) 0 0
\(845\) −4.24336 −0.145976
\(846\) 0 0
\(847\) 0.383422 0.0131745
\(848\) 0 0
\(849\) −6.29543 −0.216059
\(850\) 0 0
\(851\) −42.7250 −1.46459
\(852\) 0 0
\(853\) 24.0309 0.822801 0.411401 0.911455i \(-0.365040\pi\)
0.411401 + 0.911455i \(0.365040\pi\)
\(854\) 0 0
\(855\) 0.279551 0.00956045
\(856\) 0 0
\(857\) −31.8225 −1.08704 −0.543518 0.839397i \(-0.682908\pi\)
−0.543518 + 0.839397i \(0.682908\pi\)
\(858\) 0 0
\(859\) −12.6715 −0.432346 −0.216173 0.976355i \(-0.569358\pi\)
−0.216173 + 0.976355i \(0.569358\pi\)
\(860\) 0 0
\(861\) −0.0998071 −0.00340142
\(862\) 0 0
\(863\) 0.669733 0.0227980 0.0113990 0.999935i \(-0.496372\pi\)
0.0113990 + 0.999935i \(0.496372\pi\)
\(864\) 0 0
\(865\) −11.3007 −0.384236
\(866\) 0 0
\(867\) −11.9352 −0.405340
\(868\) 0 0
\(869\) −48.1211 −1.63240
\(870\) 0 0
\(871\) −34.8303 −1.18018
\(872\) 0 0
\(873\) 0.796460 0.0269561
\(874\) 0 0
\(875\) 0.0387940 0.00131148
\(876\) 0 0
\(877\) −51.1381 −1.72681 −0.863406 0.504509i \(-0.831673\pi\)
−0.863406 + 0.504509i \(0.831673\pi\)
\(878\) 0 0
\(879\) −10.6402 −0.358884
\(880\) 0 0
\(881\) −6.38097 −0.214980 −0.107490 0.994206i \(-0.534281\pi\)
−0.107490 + 0.994206i \(0.534281\pi\)
\(882\) 0 0
\(883\) −11.6058 −0.390566 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(884\) 0 0
\(885\) −12.5582 −0.422139
\(886\) 0 0
\(887\) 36.1963 1.21535 0.607677 0.794184i \(-0.292102\pi\)
0.607677 + 0.794184i \(0.292102\pi\)
\(888\) 0 0
\(889\) −0.692496 −0.0232256
\(890\) 0 0
\(891\) 42.7414 1.43189
\(892\) 0 0
\(893\) −14.3268 −0.479427
\(894\) 0 0
\(895\) 13.0976 0.437806
\(896\) 0 0
\(897\) 27.8449 0.929714
\(898\) 0 0
\(899\) 78.1316 2.60583
\(900\) 0 0
\(901\) 2.56371 0.0854096
\(902\) 0 0
\(903\) −0.335950 −0.0111797
\(904\) 0 0
\(905\) −14.3326 −0.476431
\(906\) 0 0
\(907\) 40.1081 1.33177 0.665884 0.746055i \(-0.268055\pi\)
0.665884 + 0.746055i \(0.268055\pi\)
\(908\) 0 0
\(909\) 0.696115 0.0230887
\(910\) 0 0
\(911\) −37.6097 −1.24607 −0.623033 0.782196i \(-0.714100\pi\)
−0.623033 + 0.782196i \(0.714100\pi\)
\(912\) 0 0
\(913\) −11.9223 −0.394571
\(914\) 0 0
\(915\) 21.7128 0.717802
\(916\) 0 0
\(917\) −0.0696934 −0.00230148
\(918\) 0 0
\(919\) −20.3608 −0.671642 −0.335821 0.941926i \(-0.609014\pi\)
−0.335821 + 0.941926i \(0.609014\pi\)
\(920\) 0 0
\(921\) 40.7422 1.34250
\(922\) 0 0
\(923\) 39.0545 1.28549
\(924\) 0 0
\(925\) −8.02356 −0.263813
\(926\) 0 0
\(927\) 0.336167 0.0110412
\(928\) 0 0
\(929\) 15.2860 0.501518 0.250759 0.968050i \(-0.419320\pi\)
0.250759 + 0.968050i \(0.419320\pi\)
\(930\) 0 0
\(931\) −15.9510 −0.522774
\(932\) 0 0
\(933\) 35.9930 1.17836
\(934\) 0 0
\(935\) 14.6277 0.478378
\(936\) 0 0
\(937\) 33.6942 1.10074 0.550371 0.834920i \(-0.314486\pi\)
0.550371 + 0.834920i \(0.314486\pi\)
\(938\) 0 0
\(939\) 26.9534 0.879591
\(940\) 0 0
\(941\) 51.5975 1.68203 0.841014 0.541013i \(-0.181959\pi\)
0.841014 + 0.541013i \(0.181959\pi\)
\(942\) 0 0
\(943\) −7.75264 −0.252461
\(944\) 0 0
\(945\) −0.197251 −0.00641657
\(946\) 0 0
\(947\) 41.7964 1.35820 0.679100 0.734046i \(-0.262370\pi\)
0.679100 + 0.734046i \(0.262370\pi\)
\(948\) 0 0
\(949\) 35.3533 1.14762
\(950\) 0 0
\(951\) 5.71907 0.185453
\(952\) 0 0
\(953\) 45.4569 1.47249 0.736246 0.676714i \(-0.236596\pi\)
0.736246 + 0.676714i \(0.236596\pi\)
\(954\) 0 0
\(955\) 6.61903 0.214187
\(956\) 0 0
\(957\) 76.4101 2.46999
\(958\) 0 0
\(959\) −0.101373 −0.00327350
\(960\) 0 0
\(961\) 37.1834 1.19947
\(962\) 0 0
\(963\) −1.20608 −0.0388653
\(964\) 0 0
\(965\) −8.71813 −0.280647
\(966\) 0 0
\(967\) −25.7130 −0.826876 −0.413438 0.910532i \(-0.635672\pi\)
−0.413438 + 0.910532i \(0.635672\pi\)
\(968\) 0 0
\(969\) −12.8920 −0.414152
\(970\) 0 0
\(971\) −48.9973 −1.57240 −0.786199 0.617973i \(-0.787954\pi\)
−0.786199 + 0.617973i \(0.787954\pi\)
\(972\) 0 0
\(973\) −0.593959 −0.0190415
\(974\) 0 0
\(975\) 5.22914 0.167467
\(976\) 0 0
\(977\) 32.1109 1.02732 0.513659 0.857995i \(-0.328290\pi\)
0.513659 + 0.857995i \(0.328290\pi\)
\(978\) 0 0
\(979\) 9.04583 0.289106
\(980\) 0 0
\(981\) 0.746201 0.0238244
\(982\) 0 0
\(983\) −37.0689 −1.18232 −0.591158 0.806556i \(-0.701329\pi\)
−0.591158 + 0.806556i \(0.701329\pi\)
\(984\) 0 0
\(985\) −20.0485 −0.638798
\(986\) 0 0
\(987\) −0.430914 −0.0137161
\(988\) 0 0
\(989\) −26.0953 −0.829783
\(990\) 0 0
\(991\) 48.2142 1.53158 0.765788 0.643093i \(-0.222349\pi\)
0.765788 + 0.643093i \(0.222349\pi\)
\(992\) 0 0
\(993\) −20.8502 −0.661662
\(994\) 0 0
\(995\) −1.44127 −0.0456915
\(996\) 0 0
\(997\) −6.74238 −0.213533 −0.106767 0.994284i \(-0.534050\pi\)
−0.106767 + 0.994284i \(0.534050\pi\)
\(998\) 0 0
\(999\) 40.7963 1.29074
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 \(a_p\))