Properties

Label 8016.2.a.bf.1.4
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.14709\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-1.14709 q^{5}\) \(+3.32442 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-1.14709 q^{5}\) \(+3.32442 q^{7}\) \(+1.00000 q^{9}\) \(+2.04384 q^{11}\) \(+5.67233 q^{13}\) \(+1.14709 q^{15}\) \(-4.44387 q^{17}\) \(-4.57483 q^{19}\) \(-3.32442 q^{21}\) \(+8.33021 q^{23}\) \(-3.68419 q^{25}\) \(-1.00000 q^{27}\) \(-6.09591 q^{29}\) \(-10.8446 q^{31}\) \(-2.04384 q^{33}\) \(-3.81340 q^{35}\) \(+3.37692 q^{37}\) \(-5.67233 q^{39}\) \(+3.28441 q^{41}\) \(-10.1171 q^{43}\) \(-1.14709 q^{45}\) \(-7.22397 q^{47}\) \(+4.05178 q^{49}\) \(+4.44387 q^{51}\) \(+8.07461 q^{53}\) \(-2.34446 q^{55}\) \(+4.57483 q^{57}\) \(+0.491745 q^{59}\) \(-1.93432 q^{61}\) \(+3.32442 q^{63}\) \(-6.50665 q^{65}\) \(-5.76932 q^{67}\) \(-8.33021 q^{69}\) \(-8.42446 q^{71}\) \(-14.6540 q^{73}\) \(+3.68419 q^{75}\) \(+6.79458 q^{77}\) \(-0.640102 q^{79}\) \(+1.00000 q^{81}\) \(-12.9891 q^{83}\) \(+5.09750 q^{85}\) \(+6.09591 q^{87}\) \(-13.8518 q^{89}\) \(+18.8572 q^{91}\) \(+10.8446 q^{93}\) \(+5.24773 q^{95}\) \(-14.0653 q^{97}\) \(+2.04384 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut -\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −1.14709 −0.512993 −0.256496 0.966545i \(-0.582568\pi\)
−0.256496 + 0.966545i \(0.582568\pi\)
\(6\) 0 0
\(7\) 3.32442 1.25651 0.628257 0.778006i \(-0.283769\pi\)
0.628257 + 0.778006i \(0.283769\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.04384 0.616240 0.308120 0.951347i \(-0.400300\pi\)
0.308120 + 0.951347i \(0.400300\pi\)
\(12\) 0 0
\(13\) 5.67233 1.57322 0.786610 0.617450i \(-0.211834\pi\)
0.786610 + 0.617450i \(0.211834\pi\)
\(14\) 0 0
\(15\) 1.14709 0.296176
\(16\) 0 0
\(17\) −4.44387 −1.07780 −0.538898 0.842371i \(-0.681159\pi\)
−0.538898 + 0.842371i \(0.681159\pi\)
\(18\) 0 0
\(19\) −4.57483 −1.04954 −0.524769 0.851245i \(-0.675848\pi\)
−0.524769 + 0.851245i \(0.675848\pi\)
\(20\) 0 0
\(21\) −3.32442 −0.725448
\(22\) 0 0
\(23\) 8.33021 1.73697 0.868484 0.495717i \(-0.165095\pi\)
0.868484 + 0.495717i \(0.165095\pi\)
\(24\) 0 0
\(25\) −3.68419 −0.736839
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.09591 −1.13198 −0.565991 0.824411i \(-0.691506\pi\)
−0.565991 + 0.824411i \(0.691506\pi\)
\(30\) 0 0
\(31\) −10.8446 −1.94774 −0.973871 0.227100i \(-0.927076\pi\)
−0.973871 + 0.227100i \(0.927076\pi\)
\(32\) 0 0
\(33\) −2.04384 −0.355786
\(34\) 0 0
\(35\) −3.81340 −0.644582
\(36\) 0 0
\(37\) 3.37692 0.555162 0.277581 0.960702i \(-0.410467\pi\)
0.277581 + 0.960702i \(0.410467\pi\)
\(38\) 0 0
\(39\) −5.67233 −0.908299
\(40\) 0 0
\(41\) 3.28441 0.512939 0.256469 0.966552i \(-0.417441\pi\)
0.256469 + 0.966552i \(0.417441\pi\)
\(42\) 0 0
\(43\) −10.1171 −1.54285 −0.771423 0.636322i \(-0.780455\pi\)
−0.771423 + 0.636322i \(0.780455\pi\)
\(44\) 0 0
\(45\) −1.14709 −0.170998
\(46\) 0 0
\(47\) −7.22397 −1.05372 −0.526862 0.849951i \(-0.676632\pi\)
−0.526862 + 0.849951i \(0.676632\pi\)
\(48\) 0 0
\(49\) 4.05178 0.578826
\(50\) 0 0
\(51\) 4.44387 0.622266
\(52\) 0 0
\(53\) 8.07461 1.10913 0.554567 0.832139i \(-0.312884\pi\)
0.554567 + 0.832139i \(0.312884\pi\)
\(54\) 0 0
\(55\) −2.34446 −0.316127
\(56\) 0 0
\(57\) 4.57483 0.605951
\(58\) 0 0
\(59\) 0.491745 0.0640198 0.0320099 0.999488i \(-0.489809\pi\)
0.0320099 + 0.999488i \(0.489809\pi\)
\(60\) 0 0
\(61\) −1.93432 −0.247665 −0.123832 0.992303i \(-0.539518\pi\)
−0.123832 + 0.992303i \(0.539518\pi\)
\(62\) 0 0
\(63\) 3.32442 0.418838
\(64\) 0 0
\(65\) −6.50665 −0.807051
\(66\) 0 0
\(67\) −5.76932 −0.704835 −0.352417 0.935843i \(-0.614640\pi\)
−0.352417 + 0.935843i \(0.614640\pi\)
\(68\) 0 0
\(69\) −8.33021 −1.00284
\(70\) 0 0
\(71\) −8.42446 −0.999799 −0.499900 0.866083i \(-0.666630\pi\)
−0.499900 + 0.866083i \(0.666630\pi\)
\(72\) 0 0
\(73\) −14.6540 −1.71512 −0.857560 0.514384i \(-0.828021\pi\)
−0.857560 + 0.514384i \(0.828021\pi\)
\(74\) 0 0
\(75\) 3.68419 0.425414
\(76\) 0 0
\(77\) 6.79458 0.774314
\(78\) 0 0
\(79\) −0.640102 −0.0720171 −0.0360085 0.999351i \(-0.511464\pi\)
−0.0360085 + 0.999351i \(0.511464\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.9891 −1.42574 −0.712871 0.701296i \(-0.752605\pi\)
−0.712871 + 0.701296i \(0.752605\pi\)
\(84\) 0 0
\(85\) 5.09750 0.552902
\(86\) 0 0
\(87\) 6.09591 0.653550
\(88\) 0 0
\(89\) −13.8518 −1.46828 −0.734142 0.678996i \(-0.762415\pi\)
−0.734142 + 0.678996i \(0.762415\pi\)
\(90\) 0 0
\(91\) 18.8572 1.97677
\(92\) 0 0
\(93\) 10.8446 1.12453
\(94\) 0 0
\(95\) 5.24773 0.538406
\(96\) 0 0
\(97\) −14.0653 −1.42811 −0.714056 0.700089i \(-0.753144\pi\)
−0.714056 + 0.700089i \(0.753144\pi\)
\(98\) 0 0
\(99\) 2.04384 0.205413
\(100\) 0 0
\(101\) 9.38072 0.933417 0.466708 0.884411i \(-0.345440\pi\)
0.466708 + 0.884411i \(0.345440\pi\)
\(102\) 0 0
\(103\) −13.9780 −1.37729 −0.688645 0.725099i \(-0.741794\pi\)
−0.688645 + 0.725099i \(0.741794\pi\)
\(104\) 0 0
\(105\) 3.81340 0.372150
\(106\) 0 0
\(107\) 8.32030 0.804353 0.402177 0.915562i \(-0.368254\pi\)
0.402177 + 0.915562i \(0.368254\pi\)
\(108\) 0 0
\(109\) 16.2370 1.55522 0.777610 0.628748i \(-0.216432\pi\)
0.777610 + 0.628748i \(0.216432\pi\)
\(110\) 0 0
\(111\) −3.37692 −0.320523
\(112\) 0 0
\(113\) 10.0624 0.946595 0.473297 0.880903i \(-0.343064\pi\)
0.473297 + 0.880903i \(0.343064\pi\)
\(114\) 0 0
\(115\) −9.55547 −0.891052
\(116\) 0 0
\(117\) 5.67233 0.524407
\(118\) 0 0
\(119\) −14.7733 −1.35427
\(120\) 0 0
\(121\) −6.82273 −0.620248
\(122\) 0 0
\(123\) −3.28441 −0.296145
\(124\) 0 0
\(125\) 9.96152 0.890985
\(126\) 0 0
\(127\) 6.58874 0.584656 0.292328 0.956318i \(-0.405570\pi\)
0.292328 + 0.956318i \(0.405570\pi\)
\(128\) 0 0
\(129\) 10.1171 0.890763
\(130\) 0 0
\(131\) 3.88569 0.339494 0.169747 0.985488i \(-0.445705\pi\)
0.169747 + 0.985488i \(0.445705\pi\)
\(132\) 0 0
\(133\) −15.2087 −1.31876
\(134\) 0 0
\(135\) 1.14709 0.0987255
\(136\) 0 0
\(137\) 20.3679 1.74015 0.870075 0.492919i \(-0.164070\pi\)
0.870075 + 0.492919i \(0.164070\pi\)
\(138\) 0 0
\(139\) −14.2985 −1.21278 −0.606390 0.795168i \(-0.707383\pi\)
−0.606390 + 0.795168i \(0.707383\pi\)
\(140\) 0 0
\(141\) 7.22397 0.608368
\(142\) 0 0
\(143\) 11.5933 0.969482
\(144\) 0 0
\(145\) 6.99254 0.580699
\(146\) 0 0
\(147\) −4.05178 −0.334185
\(148\) 0 0
\(149\) 13.5233 1.10787 0.553936 0.832559i \(-0.313125\pi\)
0.553936 + 0.832559i \(0.313125\pi\)
\(150\) 0 0
\(151\) −2.39755 −0.195110 −0.0975549 0.995230i \(-0.531102\pi\)
−0.0975549 + 0.995230i \(0.531102\pi\)
\(152\) 0 0
\(153\) −4.44387 −0.359265
\(154\) 0 0
\(155\) 12.4397 0.999178
\(156\) 0 0
\(157\) −1.40129 −0.111835 −0.0559174 0.998435i \(-0.517808\pi\)
−0.0559174 + 0.998435i \(0.517808\pi\)
\(158\) 0 0
\(159\) −8.07461 −0.640358
\(160\) 0 0
\(161\) 27.6931 2.18252
\(162\) 0 0
\(163\) −13.9978 −1.09639 −0.548197 0.836350i \(-0.684685\pi\)
−0.548197 + 0.836350i \(0.684685\pi\)
\(164\) 0 0
\(165\) 2.34446 0.182516
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 19.1753 1.47502
\(170\) 0 0
\(171\) −4.57483 −0.349846
\(172\) 0 0
\(173\) 2.70111 0.205361 0.102681 0.994714i \(-0.467258\pi\)
0.102681 + 0.994714i \(0.467258\pi\)
\(174\) 0 0
\(175\) −12.2478 −0.925848
\(176\) 0 0
\(177\) −0.491745 −0.0369618
\(178\) 0 0
\(179\) 2.99486 0.223846 0.111923 0.993717i \(-0.464299\pi\)
0.111923 + 0.993717i \(0.464299\pi\)
\(180\) 0 0
\(181\) 13.5390 1.00634 0.503171 0.864187i \(-0.332166\pi\)
0.503171 + 0.864187i \(0.332166\pi\)
\(182\) 0 0
\(183\) 1.93432 0.142989
\(184\) 0 0
\(185\) −3.87362 −0.284794
\(186\) 0 0
\(187\) −9.08254 −0.664181
\(188\) 0 0
\(189\) −3.32442 −0.241816
\(190\) 0 0
\(191\) 18.3703 1.32923 0.664613 0.747188i \(-0.268596\pi\)
0.664613 + 0.747188i \(0.268596\pi\)
\(192\) 0 0
\(193\) −8.15030 −0.586671 −0.293336 0.956010i \(-0.594765\pi\)
−0.293336 + 0.956010i \(0.594765\pi\)
\(194\) 0 0
\(195\) 6.50665 0.465951
\(196\) 0 0
\(197\) 9.56487 0.681469 0.340734 0.940160i \(-0.389324\pi\)
0.340734 + 0.940160i \(0.389324\pi\)
\(198\) 0 0
\(199\) 24.9138 1.76609 0.883045 0.469289i \(-0.155490\pi\)
0.883045 + 0.469289i \(0.155490\pi\)
\(200\) 0 0
\(201\) 5.76932 0.406937
\(202\) 0 0
\(203\) −20.2654 −1.42235
\(204\) 0 0
\(205\) −3.76750 −0.263134
\(206\) 0 0
\(207\) 8.33021 0.578989
\(208\) 0 0
\(209\) −9.35021 −0.646768
\(210\) 0 0
\(211\) −21.2970 −1.46615 −0.733073 0.680150i \(-0.761915\pi\)
−0.733073 + 0.680150i \(0.761915\pi\)
\(212\) 0 0
\(213\) 8.42446 0.577234
\(214\) 0 0
\(215\) 11.6052 0.791469
\(216\) 0 0
\(217\) −36.0519 −2.44737
\(218\) 0 0
\(219\) 14.6540 0.990225
\(220\) 0 0
\(221\) −25.2071 −1.69561
\(222\) 0 0
\(223\) −21.5679 −1.44430 −0.722148 0.691738i \(-0.756845\pi\)
−0.722148 + 0.691738i \(0.756845\pi\)
\(224\) 0 0
\(225\) −3.68419 −0.245613
\(226\) 0 0
\(227\) −23.9038 −1.58655 −0.793275 0.608863i \(-0.791626\pi\)
−0.793275 + 0.608863i \(0.791626\pi\)
\(228\) 0 0
\(229\) 5.37332 0.355079 0.177539 0.984114i \(-0.443186\pi\)
0.177539 + 0.984114i \(0.443186\pi\)
\(230\) 0 0
\(231\) −6.79458 −0.447050
\(232\) 0 0
\(233\) −22.0472 −1.44436 −0.722179 0.691706i \(-0.756859\pi\)
−0.722179 + 0.691706i \(0.756859\pi\)
\(234\) 0 0
\(235\) 8.28652 0.540553
\(236\) 0 0
\(237\) 0.640102 0.0415791
\(238\) 0 0
\(239\) 11.1537 0.721473 0.360737 0.932668i \(-0.382525\pi\)
0.360737 + 0.932668i \(0.382525\pi\)
\(240\) 0 0
\(241\) −6.82085 −0.439370 −0.219685 0.975571i \(-0.570503\pi\)
−0.219685 + 0.975571i \(0.570503\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −4.64775 −0.296934
\(246\) 0 0
\(247\) −25.9500 −1.65116
\(248\) 0 0
\(249\) 12.9891 0.823152
\(250\) 0 0
\(251\) 14.3413 0.905216 0.452608 0.891710i \(-0.350494\pi\)
0.452608 + 0.891710i \(0.350494\pi\)
\(252\) 0 0
\(253\) 17.0256 1.07039
\(254\) 0 0
\(255\) −5.09750 −0.319218
\(256\) 0 0
\(257\) −6.18565 −0.385850 −0.192925 0.981213i \(-0.561797\pi\)
−0.192925 + 0.981213i \(0.561797\pi\)
\(258\) 0 0
\(259\) 11.2263 0.697569
\(260\) 0 0
\(261\) −6.09591 −0.377327
\(262\) 0 0
\(263\) −31.0969 −1.91752 −0.958760 0.284218i \(-0.908266\pi\)
−0.958760 + 0.284218i \(0.908266\pi\)
\(264\) 0 0
\(265\) −9.26228 −0.568977
\(266\) 0 0
\(267\) 13.8518 0.847714
\(268\) 0 0
\(269\) −1.23733 −0.0754411 −0.0377205 0.999288i \(-0.512010\pi\)
−0.0377205 + 0.999288i \(0.512010\pi\)
\(270\) 0 0
\(271\) 9.24471 0.561576 0.280788 0.959770i \(-0.409404\pi\)
0.280788 + 0.959770i \(0.409404\pi\)
\(272\) 0 0
\(273\) −18.8572 −1.14129
\(274\) 0 0
\(275\) −7.52989 −0.454069
\(276\) 0 0
\(277\) 6.13491 0.368611 0.184305 0.982869i \(-0.440996\pi\)
0.184305 + 0.982869i \(0.440996\pi\)
\(278\) 0 0
\(279\) −10.8446 −0.649248
\(280\) 0 0
\(281\) 9.93658 0.592766 0.296383 0.955069i \(-0.404219\pi\)
0.296383 + 0.955069i \(0.404219\pi\)
\(282\) 0 0
\(283\) −4.55893 −0.271000 −0.135500 0.990777i \(-0.543264\pi\)
−0.135500 + 0.990777i \(0.543264\pi\)
\(284\) 0 0
\(285\) −5.24773 −0.310849
\(286\) 0 0
\(287\) 10.9188 0.644514
\(288\) 0 0
\(289\) 2.74796 0.161645
\(290\) 0 0
\(291\) 14.0653 0.824521
\(292\) 0 0
\(293\) −20.4630 −1.19546 −0.597731 0.801696i \(-0.703931\pi\)
−0.597731 + 0.801696i \(0.703931\pi\)
\(294\) 0 0
\(295\) −0.564074 −0.0328417
\(296\) 0 0
\(297\) −2.04384 −0.118595
\(298\) 0 0
\(299\) 47.2517 2.73263
\(300\) 0 0
\(301\) −33.6336 −1.93861
\(302\) 0 0
\(303\) −9.38072 −0.538908
\(304\) 0 0
\(305\) 2.21883 0.127050
\(306\) 0 0
\(307\) −9.39972 −0.536470 −0.268235 0.963353i \(-0.586440\pi\)
−0.268235 + 0.963353i \(0.586440\pi\)
\(308\) 0 0
\(309\) 13.9780 0.795178
\(310\) 0 0
\(311\) −9.83249 −0.557549 −0.278775 0.960357i \(-0.589928\pi\)
−0.278775 + 0.960357i \(0.589928\pi\)
\(312\) 0 0
\(313\) 17.3580 0.981133 0.490567 0.871404i \(-0.336790\pi\)
0.490567 + 0.871404i \(0.336790\pi\)
\(314\) 0 0
\(315\) −3.81340 −0.214861
\(316\) 0 0
\(317\) −6.84251 −0.384314 −0.192157 0.981364i \(-0.561548\pi\)
−0.192157 + 0.981364i \(0.561548\pi\)
\(318\) 0 0
\(319\) −12.4591 −0.697573
\(320\) 0 0
\(321\) −8.32030 −0.464394
\(322\) 0 0
\(323\) 20.3299 1.13119
\(324\) 0 0
\(325\) −20.8980 −1.15921
\(326\) 0 0
\(327\) −16.2370 −0.897906
\(328\) 0 0
\(329\) −24.0155 −1.32402
\(330\) 0 0
\(331\) 8.53876 0.469333 0.234666 0.972076i \(-0.424600\pi\)
0.234666 + 0.972076i \(0.424600\pi\)
\(332\) 0 0
\(333\) 3.37692 0.185054
\(334\) 0 0
\(335\) 6.61791 0.361575
\(336\) 0 0
\(337\) 13.5786 0.739675 0.369838 0.929096i \(-0.379413\pi\)
0.369838 + 0.929096i \(0.379413\pi\)
\(338\) 0 0
\(339\) −10.0624 −0.546517
\(340\) 0 0
\(341\) −22.1645 −1.20028
\(342\) 0 0
\(343\) −9.80112 −0.529211
\(344\) 0 0
\(345\) 9.55547 0.514449
\(346\) 0 0
\(347\) 29.8672 1.60335 0.801677 0.597757i \(-0.203941\pi\)
0.801677 + 0.597757i \(0.203941\pi\)
\(348\) 0 0
\(349\) 19.2769 1.03187 0.515935 0.856627i \(-0.327444\pi\)
0.515935 + 0.856627i \(0.327444\pi\)
\(350\) 0 0
\(351\) −5.67233 −0.302766
\(352\) 0 0
\(353\) 21.4419 1.14124 0.570618 0.821215i \(-0.306704\pi\)
0.570618 + 0.821215i \(0.306704\pi\)
\(354\) 0 0
\(355\) 9.66358 0.512890
\(356\) 0 0
\(357\) 14.7733 0.781886
\(358\) 0 0
\(359\) −33.2799 −1.75645 −0.878223 0.478251i \(-0.841271\pi\)
−0.878223 + 0.478251i \(0.841271\pi\)
\(360\) 0 0
\(361\) 1.92909 0.101531
\(362\) 0 0
\(363\) 6.82273 0.358100
\(364\) 0 0
\(365\) 16.8094 0.879844
\(366\) 0 0
\(367\) −13.9046 −0.725814 −0.362907 0.931825i \(-0.618216\pi\)
−0.362907 + 0.931825i \(0.618216\pi\)
\(368\) 0 0
\(369\) 3.28441 0.170980
\(370\) 0 0
\(371\) 26.8434 1.39364
\(372\) 0 0
\(373\) 33.5870 1.73907 0.869535 0.493871i \(-0.164418\pi\)
0.869535 + 0.493871i \(0.164418\pi\)
\(374\) 0 0
\(375\) −9.96152 −0.514411
\(376\) 0 0
\(377\) −34.5780 −1.78086
\(378\) 0 0
\(379\) 5.30400 0.272448 0.136224 0.990678i \(-0.456503\pi\)
0.136224 + 0.990678i \(0.456503\pi\)
\(380\) 0 0
\(381\) −6.58874 −0.337551
\(382\) 0 0
\(383\) −15.4562 −0.789777 −0.394889 0.918729i \(-0.629217\pi\)
−0.394889 + 0.918729i \(0.629217\pi\)
\(384\) 0 0
\(385\) −7.79397 −0.397217
\(386\) 0 0
\(387\) −10.1171 −0.514282
\(388\) 0 0
\(389\) −30.0960 −1.52593 −0.762964 0.646441i \(-0.776256\pi\)
−0.762964 + 0.646441i \(0.776256\pi\)
\(390\) 0 0
\(391\) −37.0183 −1.87210
\(392\) 0 0
\(393\) −3.88569 −0.196007
\(394\) 0 0
\(395\) 0.734252 0.0369442
\(396\) 0 0
\(397\) −32.4774 −1.62999 −0.814997 0.579465i \(-0.803262\pi\)
−0.814997 + 0.579465i \(0.803262\pi\)
\(398\) 0 0
\(399\) 15.2087 0.761386
\(400\) 0 0
\(401\) 4.25313 0.212391 0.106196 0.994345i \(-0.466133\pi\)
0.106196 + 0.994345i \(0.466133\pi\)
\(402\) 0 0
\(403\) −61.5140 −3.06423
\(404\) 0 0
\(405\) −1.14709 −0.0569992
\(406\) 0 0
\(407\) 6.90187 0.342113
\(408\) 0 0
\(409\) −27.5145 −1.36050 −0.680252 0.732979i \(-0.738129\pi\)
−0.680252 + 0.732979i \(0.738129\pi\)
\(410\) 0 0
\(411\) −20.3679 −1.00468
\(412\) 0 0
\(413\) 1.63477 0.0804417
\(414\) 0 0
\(415\) 14.8996 0.731395
\(416\) 0 0
\(417\) 14.2985 0.700199
\(418\) 0 0
\(419\) −2.53824 −0.124001 −0.0620005 0.998076i \(-0.519748\pi\)
−0.0620005 + 0.998076i \(0.519748\pi\)
\(420\) 0 0
\(421\) −28.9312 −1.41002 −0.705009 0.709198i \(-0.749057\pi\)
−0.705009 + 0.709198i \(0.749057\pi\)
\(422\) 0 0
\(423\) −7.22397 −0.351242
\(424\) 0 0
\(425\) 16.3721 0.794162
\(426\) 0 0
\(427\) −6.43050 −0.311194
\(428\) 0 0
\(429\) −11.5933 −0.559731
\(430\) 0 0
\(431\) −18.5039 −0.891301 −0.445651 0.895207i \(-0.647028\pi\)
−0.445651 + 0.895207i \(0.647028\pi\)
\(432\) 0 0
\(433\) −19.0976 −0.917773 −0.458886 0.888495i \(-0.651752\pi\)
−0.458886 + 0.888495i \(0.651752\pi\)
\(434\) 0 0
\(435\) −6.99254 −0.335267
\(436\) 0 0
\(437\) −38.1093 −1.82301
\(438\) 0 0
\(439\) 38.8543 1.85441 0.927207 0.374548i \(-0.122202\pi\)
0.927207 + 0.374548i \(0.122202\pi\)
\(440\) 0 0
\(441\) 4.05178 0.192942
\(442\) 0 0
\(443\) −11.4378 −0.543426 −0.271713 0.962378i \(-0.587590\pi\)
−0.271713 + 0.962378i \(0.587590\pi\)
\(444\) 0 0
\(445\) 15.8892 0.753219
\(446\) 0 0
\(447\) −13.5233 −0.639631
\(448\) 0 0
\(449\) −13.7933 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(450\) 0 0
\(451\) 6.71280 0.316093
\(452\) 0 0
\(453\) 2.39755 0.112647
\(454\) 0 0
\(455\) −21.6309 −1.01407
\(456\) 0 0
\(457\) −6.78493 −0.317386 −0.158693 0.987328i \(-0.550728\pi\)
−0.158693 + 0.987328i \(0.550728\pi\)
\(458\) 0 0
\(459\) 4.44387 0.207422
\(460\) 0 0
\(461\) −34.5307 −1.60826 −0.804128 0.594457i \(-0.797367\pi\)
−0.804128 + 0.594457i \(0.797367\pi\)
\(462\) 0 0
\(463\) −3.97269 −0.184627 −0.0923133 0.995730i \(-0.529426\pi\)
−0.0923133 + 0.995730i \(0.529426\pi\)
\(464\) 0 0
\(465\) −12.4397 −0.576876
\(466\) 0 0
\(467\) 26.7295 1.23690 0.618448 0.785826i \(-0.287762\pi\)
0.618448 + 0.785826i \(0.287762\pi\)
\(468\) 0 0
\(469\) −19.1797 −0.885635
\(470\) 0 0
\(471\) 1.40129 0.0645679
\(472\) 0 0
\(473\) −20.6778 −0.950764
\(474\) 0 0
\(475\) 16.8546 0.773340
\(476\) 0 0
\(477\) 8.07461 0.369711
\(478\) 0 0
\(479\) 6.79972 0.310687 0.155343 0.987861i \(-0.450352\pi\)
0.155343 + 0.987861i \(0.450352\pi\)
\(480\) 0 0
\(481\) 19.1550 0.873392
\(482\) 0 0
\(483\) −27.6931 −1.26008
\(484\) 0 0
\(485\) 16.1341 0.732611
\(486\) 0 0
\(487\) 7.75129 0.351244 0.175622 0.984458i \(-0.443806\pi\)
0.175622 + 0.984458i \(0.443806\pi\)
\(488\) 0 0
\(489\) 13.9978 0.633003
\(490\) 0 0
\(491\) −25.4942 −1.15054 −0.575269 0.817964i \(-0.695103\pi\)
−0.575269 + 0.817964i \(0.695103\pi\)
\(492\) 0 0
\(493\) 27.0894 1.22005
\(494\) 0 0
\(495\) −2.34446 −0.105376
\(496\) 0 0
\(497\) −28.0065 −1.25626
\(498\) 0 0
\(499\) −10.0719 −0.450879 −0.225440 0.974257i \(-0.572382\pi\)
−0.225440 + 0.974257i \(0.572382\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −27.6005 −1.23065 −0.615323 0.788275i \(-0.710974\pi\)
−0.615323 + 0.788275i \(0.710974\pi\)
\(504\) 0 0
\(505\) −10.7605 −0.478836
\(506\) 0 0
\(507\) −19.1753 −0.851605
\(508\) 0 0
\(509\) 6.46064 0.286363 0.143181 0.989696i \(-0.454267\pi\)
0.143181 + 0.989696i \(0.454267\pi\)
\(510\) 0 0
\(511\) −48.7161 −2.15507
\(512\) 0 0
\(513\) 4.57483 0.201984
\(514\) 0 0
\(515\) 16.0339 0.706539
\(516\) 0 0
\(517\) −14.7646 −0.649348
\(518\) 0 0
\(519\) −2.70111 −0.118565
\(520\) 0 0
\(521\) −1.33945 −0.0586822 −0.0293411 0.999569i \(-0.509341\pi\)
−0.0293411 + 0.999569i \(0.509341\pi\)
\(522\) 0 0
\(523\) 32.4828 1.42037 0.710187 0.704013i \(-0.248610\pi\)
0.710187 + 0.704013i \(0.248610\pi\)
\(524\) 0 0
\(525\) 12.2478 0.534538
\(526\) 0 0
\(527\) 48.1918 2.09927
\(528\) 0 0
\(529\) 46.3923 2.01706
\(530\) 0 0
\(531\) 0.491745 0.0213399
\(532\) 0 0
\(533\) 18.6302 0.806966
\(534\) 0 0
\(535\) −9.54410 −0.412627
\(536\) 0 0
\(537\) −2.99486 −0.129238
\(538\) 0 0
\(539\) 8.28119 0.356696
\(540\) 0 0
\(541\) 6.51171 0.279960 0.139980 0.990154i \(-0.455296\pi\)
0.139980 + 0.990154i \(0.455296\pi\)
\(542\) 0 0
\(543\) −13.5390 −0.581012
\(544\) 0 0
\(545\) −18.6252 −0.797816
\(546\) 0 0
\(547\) −16.4574 −0.703669 −0.351835 0.936062i \(-0.614442\pi\)
−0.351835 + 0.936062i \(0.614442\pi\)
\(548\) 0 0
\(549\) −1.93432 −0.0825548
\(550\) 0 0
\(551\) 27.8878 1.18806
\(552\) 0 0
\(553\) −2.12797 −0.0904905
\(554\) 0 0
\(555\) 3.87362 0.164426
\(556\) 0 0
\(557\) 23.1395 0.980453 0.490226 0.871595i \(-0.336914\pi\)
0.490226 + 0.871595i \(0.336914\pi\)
\(558\) 0 0
\(559\) −57.3877 −2.42724
\(560\) 0 0
\(561\) 9.08254 0.383465
\(562\) 0 0
\(563\) 18.7483 0.790146 0.395073 0.918650i \(-0.370719\pi\)
0.395073 + 0.918650i \(0.370719\pi\)
\(564\) 0 0
\(565\) −11.5425 −0.485596
\(566\) 0 0
\(567\) 3.32442 0.139613
\(568\) 0 0
\(569\) −30.0098 −1.25808 −0.629038 0.777375i \(-0.716551\pi\)
−0.629038 + 0.777375i \(0.716551\pi\)
\(570\) 0 0
\(571\) 26.4171 1.10552 0.552760 0.833341i \(-0.313575\pi\)
0.552760 + 0.833341i \(0.313575\pi\)
\(572\) 0 0
\(573\) −18.3703 −0.767429
\(574\) 0 0
\(575\) −30.6901 −1.27986
\(576\) 0 0
\(577\) −4.92377 −0.204979 −0.102490 0.994734i \(-0.532681\pi\)
−0.102490 + 0.994734i \(0.532681\pi\)
\(578\) 0 0
\(579\) 8.15030 0.338715
\(580\) 0 0
\(581\) −43.1813 −1.79146
\(582\) 0 0
\(583\) 16.5032 0.683493
\(584\) 0 0
\(585\) −6.50665 −0.269017
\(586\) 0 0
\(587\) 10.1452 0.418738 0.209369 0.977837i \(-0.432859\pi\)
0.209369 + 0.977837i \(0.432859\pi\)
\(588\) 0 0
\(589\) 49.6121 2.04423
\(590\) 0 0
\(591\) −9.56487 −0.393446
\(592\) 0 0
\(593\) 2.97336 0.122101 0.0610507 0.998135i \(-0.480555\pi\)
0.0610507 + 0.998135i \(0.480555\pi\)
\(594\) 0 0
\(595\) 16.9462 0.694728
\(596\) 0 0
\(597\) −24.9138 −1.01965
\(598\) 0 0
\(599\) 1.29605 0.0529553 0.0264777 0.999649i \(-0.491571\pi\)
0.0264777 + 0.999649i \(0.491571\pi\)
\(600\) 0 0
\(601\) −19.8043 −0.807836 −0.403918 0.914795i \(-0.632352\pi\)
−0.403918 + 0.914795i \(0.632352\pi\)
\(602\) 0 0
\(603\) −5.76932 −0.234945
\(604\) 0 0
\(605\) 7.82626 0.318183
\(606\) 0 0
\(607\) 34.9075 1.41685 0.708425 0.705786i \(-0.249406\pi\)
0.708425 + 0.705786i \(0.249406\pi\)
\(608\) 0 0
\(609\) 20.2654 0.821195
\(610\) 0 0
\(611\) −40.9767 −1.65774
\(612\) 0 0
\(613\) 8.54783 0.345244 0.172622 0.984988i \(-0.444776\pi\)
0.172622 + 0.984988i \(0.444776\pi\)
\(614\) 0 0
\(615\) 3.76750 0.151920
\(616\) 0 0
\(617\) −31.5796 −1.27135 −0.635673 0.771958i \(-0.719277\pi\)
−0.635673 + 0.771958i \(0.719277\pi\)
\(618\) 0 0
\(619\) 8.99449 0.361519 0.180760 0.983527i \(-0.442144\pi\)
0.180760 + 0.983527i \(0.442144\pi\)
\(620\) 0 0
\(621\) −8.33021 −0.334280
\(622\) 0 0
\(623\) −46.0491 −1.84492
\(624\) 0 0
\(625\) 6.99424 0.279770
\(626\) 0 0
\(627\) 9.35021 0.373412
\(628\) 0 0
\(629\) −15.0066 −0.598352
\(630\) 0 0
\(631\) 27.2504 1.08482 0.542411 0.840114i \(-0.317512\pi\)
0.542411 + 0.840114i \(0.317512\pi\)
\(632\) 0 0
\(633\) 21.2970 0.846480
\(634\) 0 0
\(635\) −7.55786 −0.299924
\(636\) 0 0
\(637\) 22.9830 0.910621
\(638\) 0 0
\(639\) −8.42446 −0.333266
\(640\) 0 0
\(641\) 40.2440 1.58954 0.794772 0.606909i \(-0.207591\pi\)
0.794772 + 0.606909i \(0.207591\pi\)
\(642\) 0 0
\(643\) −7.20369 −0.284086 −0.142043 0.989861i \(-0.545367\pi\)
−0.142043 + 0.989861i \(0.545367\pi\)
\(644\) 0 0
\(645\) −11.6052 −0.456955
\(646\) 0 0
\(647\) 19.8491 0.780349 0.390175 0.920741i \(-0.372415\pi\)
0.390175 + 0.920741i \(0.372415\pi\)
\(648\) 0 0
\(649\) 1.00505 0.0394516
\(650\) 0 0
\(651\) 36.0519 1.41299
\(652\) 0 0
\(653\) 27.0947 1.06030 0.530149 0.847905i \(-0.322136\pi\)
0.530149 + 0.847905i \(0.322136\pi\)
\(654\) 0 0
\(655\) −4.45722 −0.174158
\(656\) 0 0
\(657\) −14.6540 −0.571707
\(658\) 0 0
\(659\) 0.316737 0.0123383 0.00616916 0.999981i \(-0.498036\pi\)
0.00616916 + 0.999981i \(0.498036\pi\)
\(660\) 0 0
\(661\) 4.11685 0.160127 0.0800635 0.996790i \(-0.474488\pi\)
0.0800635 + 0.996790i \(0.474488\pi\)
\(662\) 0 0
\(663\) 25.2071 0.978962
\(664\) 0 0
\(665\) 17.4457 0.676514
\(666\) 0 0
\(667\) −50.7802 −1.96622
\(668\) 0 0
\(669\) 21.5679 0.833865
\(670\) 0 0
\(671\) −3.95344 −0.152621
\(672\) 0 0
\(673\) −18.6970 −0.720718 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(674\) 0 0
\(675\) 3.68419 0.141805
\(676\) 0 0
\(677\) 7.14151 0.274470 0.137235 0.990538i \(-0.456178\pi\)
0.137235 + 0.990538i \(0.456178\pi\)
\(678\) 0 0
\(679\) −46.7589 −1.79444
\(680\) 0 0
\(681\) 23.9038 0.915995
\(682\) 0 0
\(683\) 17.6229 0.674323 0.337162 0.941447i \(-0.390533\pi\)
0.337162 + 0.941447i \(0.390533\pi\)
\(684\) 0 0
\(685\) −23.3638 −0.892685
\(686\) 0 0
\(687\) −5.37332 −0.205005
\(688\) 0 0
\(689\) 45.8019 1.74491
\(690\) 0 0
\(691\) 12.2885 0.467476 0.233738 0.972300i \(-0.424904\pi\)
0.233738 + 0.972300i \(0.424904\pi\)
\(692\) 0 0
\(693\) 6.79458 0.258105
\(694\) 0 0
\(695\) 16.4016 0.622147
\(696\) 0 0
\(697\) −14.5955 −0.552843
\(698\) 0 0
\(699\) 22.0472 0.833900
\(700\) 0 0
\(701\) 3.27369 0.123646 0.0618229 0.998087i \(-0.480309\pi\)
0.0618229 + 0.998087i \(0.480309\pi\)
\(702\) 0 0
\(703\) −15.4488 −0.582664
\(704\) 0 0
\(705\) −8.28652 −0.312088
\(706\) 0 0
\(707\) 31.1855 1.17285
\(708\) 0 0
\(709\) −33.5377 −1.25953 −0.629767 0.776784i \(-0.716850\pi\)
−0.629767 + 0.776784i \(0.716850\pi\)
\(710\) 0 0
\(711\) −0.640102 −0.0240057
\(712\) 0 0
\(713\) −90.3375 −3.38317
\(714\) 0 0
\(715\) −13.2985 −0.497337
\(716\) 0 0
\(717\) −11.1537 −0.416543
\(718\) 0 0
\(719\) −42.1058 −1.57028 −0.785141 0.619317i \(-0.787410\pi\)
−0.785141 + 0.619317i \(0.787410\pi\)
\(720\) 0 0
\(721\) −46.4686 −1.73058
\(722\) 0 0
\(723\) 6.82085 0.253670
\(724\) 0 0
\(725\) 22.4585 0.834088
\(726\) 0 0
\(727\) 31.1152 1.15400 0.576999 0.816745i \(-0.304224\pi\)
0.576999 + 0.816745i \(0.304224\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 44.9592 1.66287
\(732\) 0 0
\(733\) 17.6036 0.650202 0.325101 0.945679i \(-0.394602\pi\)
0.325101 + 0.945679i \(0.394602\pi\)
\(734\) 0 0
\(735\) 4.64775 0.171435
\(736\) 0 0
\(737\) −11.7916 −0.434348
\(738\) 0 0
\(739\) −31.9083 −1.17377 −0.586883 0.809672i \(-0.699645\pi\)
−0.586883 + 0.809672i \(0.699645\pi\)
\(740\) 0 0
\(741\) 25.9500 0.953295
\(742\) 0 0
\(743\) −43.2538 −1.58683 −0.793415 0.608681i \(-0.791699\pi\)
−0.793415 + 0.608681i \(0.791699\pi\)
\(744\) 0 0
\(745\) −15.5124 −0.568331
\(746\) 0 0
\(747\) −12.9891 −0.475247
\(748\) 0 0
\(749\) 27.6602 1.01068
\(750\) 0 0
\(751\) −24.4441 −0.891978 −0.445989 0.895038i \(-0.647148\pi\)
−0.445989 + 0.895038i \(0.647148\pi\)
\(752\) 0 0
\(753\) −14.3413 −0.522627
\(754\) 0 0
\(755\) 2.75020 0.100090
\(756\) 0 0
\(757\) −6.19894 −0.225304 −0.112652 0.993634i \(-0.535935\pi\)
−0.112652 + 0.993634i \(0.535935\pi\)
\(758\) 0 0
\(759\) −17.0256 −0.617990
\(760\) 0 0
\(761\) 9.28311 0.336512 0.168256 0.985743i \(-0.446186\pi\)
0.168256 + 0.985743i \(0.446186\pi\)
\(762\) 0 0
\(763\) 53.9785 1.95415
\(764\) 0 0
\(765\) 5.09750 0.184301
\(766\) 0 0
\(767\) 2.78934 0.100717
\(768\) 0 0
\(769\) 0.140927 0.00508195 0.00254098 0.999997i \(-0.499191\pi\)
0.00254098 + 0.999997i \(0.499191\pi\)
\(770\) 0 0
\(771\) 6.18565 0.222771
\(772\) 0 0
\(773\) 18.1051 0.651193 0.325597 0.945509i \(-0.394435\pi\)
0.325597 + 0.945509i \(0.394435\pi\)
\(774\) 0 0
\(775\) 39.9535 1.43517
\(776\) 0 0
\(777\) −11.2263 −0.402741
\(778\) 0 0
\(779\) −15.0256 −0.538349
\(780\) 0 0
\(781\) −17.2182 −0.616117
\(782\) 0 0
\(783\) 6.09591 0.217850
\(784\) 0 0
\(785\) 1.60740 0.0573705
\(786\) 0 0
\(787\) 18.1360 0.646478 0.323239 0.946317i \(-0.395228\pi\)
0.323239 + 0.946317i \(0.395228\pi\)
\(788\) 0 0
\(789\) 31.0969 1.10708
\(790\) 0 0
\(791\) 33.4518 1.18941
\(792\) 0 0
\(793\) −10.9721 −0.389631
\(794\) 0 0
\(795\) 9.26228 0.328499
\(796\) 0 0
\(797\) 3.43944 0.121831 0.0609157 0.998143i \(-0.480598\pi\)
0.0609157 + 0.998143i \(0.480598\pi\)
\(798\) 0 0
\(799\) 32.1024 1.13570
\(800\) 0 0
\(801\) −13.8518 −0.489428
\(802\) 0 0
\(803\) −29.9504 −1.05693
\(804\) 0 0
\(805\) −31.7664 −1.11962
\(806\) 0 0
\(807\) 1.23733 0.0435559
\(808\) 0 0
\(809\) −34.3884 −1.20903 −0.604516 0.796593i \(-0.706633\pi\)
−0.604516 + 0.796593i \(0.706633\pi\)
\(810\) 0 0
\(811\) 30.4085 1.06779 0.533894 0.845552i \(-0.320728\pi\)
0.533894 + 0.845552i \(0.320728\pi\)
\(812\) 0 0
\(813\) −9.24471 −0.324226
\(814\) 0 0
\(815\) 16.0567 0.562442
\(816\) 0 0
\(817\) 46.2841 1.61928
\(818\) 0 0
\(819\) 18.8572 0.658924
\(820\) 0 0
\(821\) 8.43876 0.294515 0.147257 0.989098i \(-0.452955\pi\)
0.147257 + 0.989098i \(0.452955\pi\)
\(822\) 0 0
\(823\) 49.0541 1.70992 0.854960 0.518694i \(-0.173582\pi\)
0.854960 + 0.518694i \(0.173582\pi\)
\(824\) 0 0
\(825\) 7.52989 0.262157
\(826\) 0 0
\(827\) 52.8282 1.83702 0.918508 0.395401i \(-0.129394\pi\)
0.918508 + 0.395401i \(0.129394\pi\)
\(828\) 0 0
\(829\) 45.6094 1.58408 0.792041 0.610468i \(-0.209019\pi\)
0.792041 + 0.610468i \(0.209019\pi\)
\(830\) 0 0
\(831\) −6.13491 −0.212818
\(832\) 0 0
\(833\) −18.0056 −0.623857
\(834\) 0 0
\(835\) 1.14709 0.0396966
\(836\) 0 0
\(837\) 10.8446 0.374843
\(838\) 0 0
\(839\) −7.63655 −0.263643 −0.131821 0.991273i \(-0.542083\pi\)
−0.131821 + 0.991273i \(0.542083\pi\)
\(840\) 0 0
\(841\) 8.16013 0.281384
\(842\) 0 0
\(843\) −9.93658 −0.342234
\(844\) 0 0
\(845\) −21.9957 −0.756676
\(846\) 0 0
\(847\) −22.6816 −0.779350
\(848\) 0 0
\(849\) 4.55893 0.156462
\(850\) 0 0
\(851\) 28.1304 0.964299
\(852\) 0 0
\(853\) −41.6725 −1.42684 −0.713420 0.700737i \(-0.752855\pi\)
−0.713420 + 0.700737i \(0.752855\pi\)
\(854\) 0 0
\(855\) 5.24773 0.179469
\(856\) 0 0
\(857\) 35.6503 1.21779 0.608895 0.793251i \(-0.291613\pi\)
0.608895 + 0.793251i \(0.291613\pi\)
\(858\) 0 0
\(859\) −25.6619 −0.875574 −0.437787 0.899079i \(-0.644238\pi\)
−0.437787 + 0.899079i \(0.644238\pi\)
\(860\) 0 0
\(861\) −10.9188 −0.372110
\(862\) 0 0
\(863\) −37.4463 −1.27469 −0.637344 0.770580i \(-0.719967\pi\)
−0.637344 + 0.770580i \(0.719967\pi\)
\(864\) 0 0
\(865\) −3.09840 −0.105349
\(866\) 0 0
\(867\) −2.74796 −0.0933257
\(868\) 0 0
\(869\) −1.30826 −0.0443798
\(870\) 0 0
\(871\) −32.7255 −1.10886
\(872\) 0 0
\(873\) −14.0653 −0.476037
\(874\) 0 0
\(875\) 33.1163 1.11954
\(876\) 0 0
\(877\) −29.5206 −0.996839 −0.498420 0.866936i \(-0.666086\pi\)
−0.498420 + 0.866936i \(0.666086\pi\)
\(878\) 0 0
\(879\) 20.4630 0.690201
\(880\) 0 0
\(881\) 24.7820 0.834927 0.417464 0.908694i \(-0.362919\pi\)
0.417464 + 0.908694i \(0.362919\pi\)
\(882\) 0 0
\(883\) −51.0962 −1.71952 −0.859762 0.510695i \(-0.829388\pi\)
−0.859762 + 0.510695i \(0.829388\pi\)
\(884\) 0 0
\(885\) 0.564074 0.0189611
\(886\) 0 0
\(887\) 1.22606 0.0411671 0.0205836 0.999788i \(-0.493448\pi\)
0.0205836 + 0.999788i \(0.493448\pi\)
\(888\) 0 0
\(889\) 21.9038 0.734628
\(890\) 0 0
\(891\) 2.04384 0.0684711
\(892\) 0 0
\(893\) 33.0485 1.10592
\(894\) 0 0
\(895\) −3.43536 −0.114832
\(896\) 0 0
\(897\) −47.2517 −1.57769
\(898\) 0 0
\(899\) 66.1076 2.20481
\(900\) 0 0
\(901\) −35.8825 −1.19542
\(902\) 0 0
\(903\) 33.6336 1.11926
\(904\) 0 0
\(905\) −15.5304 −0.516246
\(906\) 0 0
\(907\) −36.2593 −1.20397 −0.601985 0.798508i \(-0.705623\pi\)
−0.601985 + 0.798508i \(0.705623\pi\)
\(908\) 0 0
\(909\) 9.38072 0.311139
\(910\) 0 0
\(911\) −2.31720 −0.0767724 −0.0383862 0.999263i \(-0.512222\pi\)
−0.0383862 + 0.999263i \(0.512222\pi\)
\(912\) 0 0
\(913\) −26.5477 −0.878599
\(914\) 0 0
\(915\) −2.21883 −0.0733524
\(916\) 0 0
\(917\) 12.9177 0.426579
\(918\) 0 0
\(919\) 26.6598 0.879427 0.439714 0.898138i \(-0.355080\pi\)
0.439714 + 0.898138i \(0.355080\pi\)
\(920\) 0 0
\(921\) 9.39972 0.309731
\(922\) 0 0
\(923\) −47.7863 −1.57291
\(924\) 0 0
\(925\) −12.4412 −0.409065
\(926\) 0 0
\(927\) −13.9780 −0.459096
\(928\) 0 0
\(929\) −14.5860 −0.478553 −0.239276 0.970952i \(-0.576910\pi\)
−0.239276 + 0.970952i \(0.576910\pi\)
\(930\) 0 0
\(931\) −18.5362 −0.607500
\(932\) 0 0
\(933\) 9.83249 0.321901
\(934\) 0 0
\(935\) 10.4185 0.340720
\(936\) 0 0
\(937\) 52.2258 1.70614 0.853071 0.521794i \(-0.174737\pi\)
0.853071 + 0.521794i \(0.174737\pi\)
\(938\) 0 0
\(939\) −17.3580 −0.566458
\(940\) 0 0
\(941\) 35.7136 1.16423 0.582115 0.813106i \(-0.302225\pi\)
0.582115 + 0.813106i \(0.302225\pi\)
\(942\) 0 0
\(943\) 27.3598 0.890958
\(944\) 0 0
\(945\) 3.81340 0.124050
\(946\) 0 0
\(947\) −25.9066 −0.841851 −0.420926 0.907095i \(-0.638295\pi\)
−0.420926 + 0.907095i \(0.638295\pi\)
\(948\) 0 0
\(949\) −83.1222 −2.69826
\(950\) 0 0
\(951\) 6.84251 0.221884
\(952\) 0 0
\(953\) 37.1660 1.20393 0.601963 0.798524i \(-0.294386\pi\)
0.601963 + 0.798524i \(0.294386\pi\)
\(954\) 0 0
\(955\) −21.0723 −0.681883
\(956\) 0 0
\(957\) 12.4591 0.402744
\(958\) 0 0
\(959\) 67.7116 2.18652
\(960\) 0 0
\(961\) 86.6048 2.79370
\(962\) 0 0
\(963\) 8.32030 0.268118
\(964\) 0 0
\(965\) 9.34910 0.300958
\(966\) 0 0
\(967\) 2.00936 0.0646165 0.0323083 0.999478i \(-0.489714\pi\)
0.0323083 + 0.999478i \(0.489714\pi\)
\(968\) 0 0
\(969\) −20.3299 −0.653092
\(970\) 0 0
\(971\) 60.4891 1.94119 0.970594 0.240722i \(-0.0773841\pi\)
0.970594 + 0.240722i \(0.0773841\pi\)
\(972\) 0 0
\(973\) −47.5341 −1.52387
\(974\) 0 0
\(975\) 20.8980 0.669270
\(976\) 0 0
\(977\) −12.8429 −0.410880 −0.205440 0.978670i \(-0.565863\pi\)
−0.205440 + 0.978670i \(0.565863\pi\)
\(978\) 0 0
\(979\) −28.3107 −0.904815
\(980\) 0 0
\(981\) 16.2370 0.518406
\(982\) 0 0
\(983\) −53.1897 −1.69649 −0.848243 0.529607i \(-0.822339\pi\)
−0.848243 + 0.529607i \(0.822339\pi\)
\(984\) 0 0
\(985\) −10.9717 −0.349589
\(986\) 0 0
\(987\) 24.0155 0.764423
\(988\) 0 0
\(989\) −84.2777 −2.67988
\(990\) 0 0
\(991\) −21.7567 −0.691124 −0.345562 0.938396i \(-0.612312\pi\)
−0.345562 + 0.938396i \(0.612312\pi\)
\(992\) 0 0
\(993\) −8.53876 −0.270969
\(994\) 0 0
\(995\) −28.5782 −0.905991
\(996\) 0 0
\(997\) −1.56973 −0.0497137 −0.0248569 0.999691i \(-0.507913\pi\)
−0.0248569 + 0.999691i \(0.507913\pi\)
\(998\) 0 0
\(999\) −3.37692 −0.106841
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 \(a_p\))