Properties

Label 8046.2.a.l.1.8
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.09665\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.09665 q^{5}\) \(-2.72925 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.09665 q^{5}\) \(-2.72925 q^{7}\) \(-1.00000 q^{8}\) \(-1.09665 q^{10}\) \(-4.35836 q^{11}\) \(-3.83892 q^{13}\) \(+2.72925 q^{14}\) \(+1.00000 q^{16}\) \(-4.52192 q^{17}\) \(-1.46202 q^{19}\) \(+1.09665 q^{20}\) \(+4.35836 q^{22}\) \(-2.47990 q^{23}\) \(-3.79736 q^{25}\) \(+3.83892 q^{26}\) \(-2.72925 q^{28}\) \(+9.77560 q^{29}\) \(-0.816654 q^{31}\) \(-1.00000 q^{32}\) \(+4.52192 q^{34}\) \(-2.99302 q^{35}\) \(+3.29988 q^{37}\) \(+1.46202 q^{38}\) \(-1.09665 q^{40}\) \(-6.03409 q^{41}\) \(+2.88226 q^{43}\) \(-4.35836 q^{44}\) \(+2.47990 q^{46}\) \(-1.80668 q^{47}\) \(+0.448781 q^{49}\) \(+3.79736 q^{50}\) \(-3.83892 q^{52}\) \(+9.70841 q^{53}\) \(-4.77958 q^{55}\) \(+2.72925 q^{56}\) \(-9.77560 q^{58}\) \(-11.7716 q^{59}\) \(-12.5328 q^{61}\) \(+0.816654 q^{62}\) \(+1.00000 q^{64}\) \(-4.20994 q^{65}\) \(-9.19967 q^{67}\) \(-4.52192 q^{68}\) \(+2.99302 q^{70}\) \(-12.1052 q^{71}\) \(-9.35826 q^{73}\) \(-3.29988 q^{74}\) \(-1.46202 q^{76}\) \(+11.8950 q^{77}\) \(+6.85287 q^{79}\) \(+1.09665 q^{80}\) \(+6.03409 q^{82}\) \(+3.17103 q^{83}\) \(-4.95895 q^{85}\) \(-2.88226 q^{86}\) \(+4.35836 q^{88}\) \(+12.3920 q^{89}\) \(+10.4774 q^{91}\) \(-2.47990 q^{92}\) \(+1.80668 q^{94}\) \(-1.60332 q^{95}\) \(+6.62366 q^{97}\) \(-0.448781 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 1.09665 0.490436 0.245218 0.969468i \(-0.421141\pi\)
0.245218 + 0.969468i \(0.421141\pi\)
\(6\) 0 0
\(7\) −2.72925 −1.03156 −0.515779 0.856722i \(-0.672497\pi\)
−0.515779 + 0.856722i \(0.672497\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.09665 −0.346790
\(11\) −4.35836 −1.31409 −0.657047 0.753850i \(-0.728195\pi\)
−0.657047 + 0.753850i \(0.728195\pi\)
\(12\) 0 0
\(13\) −3.83892 −1.06472 −0.532362 0.846517i \(-0.678696\pi\)
−0.532362 + 0.846517i \(0.678696\pi\)
\(14\) 2.72925 0.729422
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.52192 −1.09673 −0.548364 0.836240i \(-0.684749\pi\)
−0.548364 + 0.836240i \(0.684749\pi\)
\(18\) 0 0
\(19\) −1.46202 −0.335411 −0.167706 0.985837i \(-0.553636\pi\)
−0.167706 + 0.985837i \(0.553636\pi\)
\(20\) 1.09665 0.245218
\(21\) 0 0
\(22\) 4.35836 0.929205
\(23\) −2.47990 −0.517094 −0.258547 0.965999i \(-0.583244\pi\)
−0.258547 + 0.965999i \(0.583244\pi\)
\(24\) 0 0
\(25\) −3.79736 −0.759473
\(26\) 3.83892 0.752874
\(27\) 0 0
\(28\) −2.72925 −0.515779
\(29\) 9.77560 1.81528 0.907642 0.419745i \(-0.137881\pi\)
0.907642 + 0.419745i \(0.137881\pi\)
\(30\) 0 0
\(31\) −0.816654 −0.146675 −0.0733377 0.997307i \(-0.523365\pi\)
−0.0733377 + 0.997307i \(0.523365\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 4.52192 0.775503
\(35\) −2.99302 −0.505913
\(36\) 0 0
\(37\) 3.29988 0.542498 0.271249 0.962509i \(-0.412563\pi\)
0.271249 + 0.962509i \(0.412563\pi\)
\(38\) 1.46202 0.237172
\(39\) 0 0
\(40\) −1.09665 −0.173395
\(41\) −6.03409 −0.942366 −0.471183 0.882035i \(-0.656173\pi\)
−0.471183 + 0.882035i \(0.656173\pi\)
\(42\) 0 0
\(43\) 2.88226 0.439540 0.219770 0.975552i \(-0.429469\pi\)
0.219770 + 0.975552i \(0.429469\pi\)
\(44\) −4.35836 −0.657047
\(45\) 0 0
\(46\) 2.47990 0.365641
\(47\) −1.80668 −0.263531 −0.131765 0.991281i \(-0.542065\pi\)
−0.131765 + 0.991281i \(0.542065\pi\)
\(48\) 0 0
\(49\) 0.448781 0.0641115
\(50\) 3.79736 0.537028
\(51\) 0 0
\(52\) −3.83892 −0.532362
\(53\) 9.70841 1.33355 0.666776 0.745258i \(-0.267674\pi\)
0.666776 + 0.745258i \(0.267674\pi\)
\(54\) 0 0
\(55\) −4.77958 −0.644479
\(56\) 2.72925 0.364711
\(57\) 0 0
\(58\) −9.77560 −1.28360
\(59\) −11.7716 −1.53253 −0.766265 0.642525i \(-0.777887\pi\)
−0.766265 + 0.642525i \(0.777887\pi\)
\(60\) 0 0
\(61\) −12.5328 −1.60466 −0.802332 0.596878i \(-0.796408\pi\)
−0.802332 + 0.596878i \(0.796408\pi\)
\(62\) 0.816654 0.103715
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.20994 −0.522179
\(66\) 0 0
\(67\) −9.19967 −1.12392 −0.561959 0.827165i \(-0.689952\pi\)
−0.561959 + 0.827165i \(0.689952\pi\)
\(68\) −4.52192 −0.548364
\(69\) 0 0
\(70\) 2.99302 0.357734
\(71\) −12.1052 −1.43662 −0.718310 0.695723i \(-0.755084\pi\)
−0.718310 + 0.695723i \(0.755084\pi\)
\(72\) 0 0
\(73\) −9.35826 −1.09530 −0.547651 0.836707i \(-0.684478\pi\)
−0.547651 + 0.836707i \(0.684478\pi\)
\(74\) −3.29988 −0.383604
\(75\) 0 0
\(76\) −1.46202 −0.167706
\(77\) 11.8950 1.35556
\(78\) 0 0
\(79\) 6.85287 0.771008 0.385504 0.922706i \(-0.374028\pi\)
0.385504 + 0.922706i \(0.374028\pi\)
\(80\) 1.09665 0.122609
\(81\) 0 0
\(82\) 6.03409 0.666353
\(83\) 3.17103 0.348066 0.174033 0.984740i \(-0.444320\pi\)
0.174033 + 0.984740i \(0.444320\pi\)
\(84\) 0 0
\(85\) −4.95895 −0.537874
\(86\) −2.88226 −0.310802
\(87\) 0 0
\(88\) 4.35836 0.464602
\(89\) 12.3920 1.31355 0.656776 0.754085i \(-0.271920\pi\)
0.656776 + 0.754085i \(0.271920\pi\)
\(90\) 0 0
\(91\) 10.4774 1.09833
\(92\) −2.47990 −0.258547
\(93\) 0 0
\(94\) 1.80668 0.186344
\(95\) −1.60332 −0.164498
\(96\) 0 0
\(97\) 6.62366 0.672531 0.336266 0.941767i \(-0.390836\pi\)
0.336266 + 0.941767i \(0.390836\pi\)
\(98\) −0.448781 −0.0453337
\(99\) 0 0
\(100\) −3.79736 −0.379736
\(101\) 18.9994 1.89051 0.945256 0.326328i \(-0.105812\pi\)
0.945256 + 0.326328i \(0.105812\pi\)
\(102\) 0 0
\(103\) 2.86431 0.282229 0.141114 0.989993i \(-0.454931\pi\)
0.141114 + 0.989993i \(0.454931\pi\)
\(104\) 3.83892 0.376437
\(105\) 0 0
\(106\) −9.70841 −0.942964
\(107\) 16.8994 1.63372 0.816862 0.576833i \(-0.195712\pi\)
0.816862 + 0.576833i \(0.195712\pi\)
\(108\) 0 0
\(109\) 0.752058 0.0720341 0.0360170 0.999351i \(-0.488533\pi\)
0.0360170 + 0.999351i \(0.488533\pi\)
\(110\) 4.77958 0.455715
\(111\) 0 0
\(112\) −2.72925 −0.257889
\(113\) −14.1817 −1.33410 −0.667052 0.745011i \(-0.732444\pi\)
−0.667052 + 0.745011i \(0.732444\pi\)
\(114\) 0 0
\(115\) −2.71957 −0.253601
\(116\) 9.77560 0.907642
\(117\) 0 0
\(118\) 11.7716 1.08366
\(119\) 12.3414 1.13134
\(120\) 0 0
\(121\) 7.99528 0.726844
\(122\) 12.5328 1.13467
\(123\) 0 0
\(124\) −0.816654 −0.0733377
\(125\) −9.64761 −0.862908
\(126\) 0 0
\(127\) 4.60414 0.408551 0.204276 0.978913i \(-0.434516\pi\)
0.204276 + 0.978913i \(0.434516\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 4.20994 0.369236
\(131\) −0.536620 −0.0468847 −0.0234423 0.999725i \(-0.507463\pi\)
−0.0234423 + 0.999725i \(0.507463\pi\)
\(132\) 0 0
\(133\) 3.99022 0.345996
\(134\) 9.19967 0.794730
\(135\) 0 0
\(136\) 4.52192 0.387752
\(137\) 20.2425 1.72944 0.864718 0.502259i \(-0.167497\pi\)
0.864718 + 0.502259i \(0.167497\pi\)
\(138\) 0 0
\(139\) −3.15773 −0.267835 −0.133918 0.990992i \(-0.542756\pi\)
−0.133918 + 0.990992i \(0.542756\pi\)
\(140\) −2.99302 −0.252956
\(141\) 0 0
\(142\) 12.1052 1.01584
\(143\) 16.7314 1.39915
\(144\) 0 0
\(145\) 10.7204 0.890280
\(146\) 9.35826 0.774495
\(147\) 0 0
\(148\) 3.29988 0.271249
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −24.1133 −1.96231 −0.981155 0.193222i \(-0.938106\pi\)
−0.981155 + 0.193222i \(0.938106\pi\)
\(152\) 1.46202 0.118586
\(153\) 0 0
\(154\) −11.8950 −0.958529
\(155\) −0.895581 −0.0719348
\(156\) 0 0
\(157\) −6.00350 −0.479131 −0.239566 0.970880i \(-0.577005\pi\)
−0.239566 + 0.970880i \(0.577005\pi\)
\(158\) −6.85287 −0.545185
\(159\) 0 0
\(160\) −1.09665 −0.0866976
\(161\) 6.76824 0.533412
\(162\) 0 0
\(163\) −19.2994 −1.51165 −0.755825 0.654774i \(-0.772764\pi\)
−0.755825 + 0.654774i \(0.772764\pi\)
\(164\) −6.03409 −0.471183
\(165\) 0 0
\(166\) −3.17103 −0.246120
\(167\) −16.5548 −1.28105 −0.640524 0.767938i \(-0.721283\pi\)
−0.640524 + 0.767938i \(0.721283\pi\)
\(168\) 0 0
\(169\) 1.73730 0.133639
\(170\) 4.95895 0.380334
\(171\) 0 0
\(172\) 2.88226 0.219770
\(173\) −11.9508 −0.908605 −0.454302 0.890848i \(-0.650111\pi\)
−0.454302 + 0.890848i \(0.650111\pi\)
\(174\) 0 0
\(175\) 10.3639 0.783440
\(176\) −4.35836 −0.328524
\(177\) 0 0
\(178\) −12.3920 −0.928822
\(179\) 18.9136 1.41367 0.706833 0.707380i \(-0.250123\pi\)
0.706833 + 0.707380i \(0.250123\pi\)
\(180\) 0 0
\(181\) 21.8386 1.62325 0.811624 0.584181i \(-0.198584\pi\)
0.811624 + 0.584181i \(0.198584\pi\)
\(182\) −10.4774 −0.776633
\(183\) 0 0
\(184\) 2.47990 0.182820
\(185\) 3.61881 0.266060
\(186\) 0 0
\(187\) 19.7082 1.44120
\(188\) −1.80668 −0.131765
\(189\) 0 0
\(190\) 1.60332 0.116317
\(191\) 16.5320 1.19621 0.598105 0.801418i \(-0.295920\pi\)
0.598105 + 0.801418i \(0.295920\pi\)
\(192\) 0 0
\(193\) 11.8366 0.852014 0.426007 0.904720i \(-0.359920\pi\)
0.426007 + 0.904720i \(0.359920\pi\)
\(194\) −6.62366 −0.475551
\(195\) 0 0
\(196\) 0.448781 0.0320558
\(197\) 17.0473 1.21457 0.607287 0.794483i \(-0.292258\pi\)
0.607287 + 0.794483i \(0.292258\pi\)
\(198\) 0 0
\(199\) 4.59160 0.325490 0.162745 0.986668i \(-0.447965\pi\)
0.162745 + 0.986668i \(0.447965\pi\)
\(200\) 3.79736 0.268514
\(201\) 0 0
\(202\) −18.9994 −1.33679
\(203\) −26.6800 −1.87257
\(204\) 0 0
\(205\) −6.61726 −0.462170
\(206\) −2.86431 −0.199566
\(207\) 0 0
\(208\) −3.83892 −0.266181
\(209\) 6.37202 0.440762
\(210\) 0 0
\(211\) 9.98312 0.687267 0.343633 0.939104i \(-0.388342\pi\)
0.343633 + 0.939104i \(0.388342\pi\)
\(212\) 9.70841 0.666776
\(213\) 0 0
\(214\) −16.8994 −1.15522
\(215\) 3.16082 0.215566
\(216\) 0 0
\(217\) 2.22885 0.151304
\(218\) −0.752058 −0.0509358
\(219\) 0 0
\(220\) −4.77958 −0.322239
\(221\) 17.3593 1.16771
\(222\) 0 0
\(223\) −12.4741 −0.835326 −0.417663 0.908602i \(-0.637151\pi\)
−0.417663 + 0.908602i \(0.637151\pi\)
\(224\) 2.72925 0.182355
\(225\) 0 0
\(226\) 14.1817 0.943354
\(227\) 4.41661 0.293141 0.146570 0.989200i \(-0.453176\pi\)
0.146570 + 0.989200i \(0.453176\pi\)
\(228\) 0 0
\(229\) −21.1109 −1.39505 −0.697524 0.716561i \(-0.745715\pi\)
−0.697524 + 0.716561i \(0.745715\pi\)
\(230\) 2.71957 0.179323
\(231\) 0 0
\(232\) −9.77560 −0.641800
\(233\) −3.50298 −0.229488 −0.114744 0.993395i \(-0.536605\pi\)
−0.114744 + 0.993395i \(0.536605\pi\)
\(234\) 0 0
\(235\) −1.98129 −0.129245
\(236\) −11.7716 −0.766265
\(237\) 0 0
\(238\) −12.3414 −0.799976
\(239\) 27.2008 1.75947 0.879736 0.475463i \(-0.157719\pi\)
0.879736 + 0.475463i \(0.157719\pi\)
\(240\) 0 0
\(241\) 6.93758 0.446889 0.223444 0.974717i \(-0.428270\pi\)
0.223444 + 0.974717i \(0.428270\pi\)
\(242\) −7.99528 −0.513956
\(243\) 0 0
\(244\) −12.5328 −0.802332
\(245\) 0.492154 0.0314426
\(246\) 0 0
\(247\) 5.61259 0.357121
\(248\) 0.816654 0.0518576
\(249\) 0 0
\(250\) 9.64761 0.610168
\(251\) 18.5290 1.16954 0.584771 0.811199i \(-0.301185\pi\)
0.584771 + 0.811199i \(0.301185\pi\)
\(252\) 0 0
\(253\) 10.8083 0.679510
\(254\) −4.60414 −0.288889
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −28.3360 −1.76755 −0.883776 0.467911i \(-0.845007\pi\)
−0.883776 + 0.467911i \(0.845007\pi\)
\(258\) 0 0
\(259\) −9.00619 −0.559618
\(260\) −4.20994 −0.261089
\(261\) 0 0
\(262\) 0.536620 0.0331525
\(263\) 13.0188 0.802773 0.401386 0.915909i \(-0.368528\pi\)
0.401386 + 0.915909i \(0.368528\pi\)
\(264\) 0 0
\(265\) 10.6467 0.654022
\(266\) −3.99022 −0.244656
\(267\) 0 0
\(268\) −9.19967 −0.561959
\(269\) 27.1713 1.65666 0.828331 0.560239i \(-0.189291\pi\)
0.828331 + 0.560239i \(0.189291\pi\)
\(270\) 0 0
\(271\) 0.154348 0.00937599 0.00468800 0.999989i \(-0.498508\pi\)
0.00468800 + 0.999989i \(0.498508\pi\)
\(272\) −4.52192 −0.274182
\(273\) 0 0
\(274\) −20.2425 −1.22290
\(275\) 16.5503 0.998019
\(276\) 0 0
\(277\) 28.6038 1.71864 0.859319 0.511440i \(-0.170888\pi\)
0.859319 + 0.511440i \(0.170888\pi\)
\(278\) 3.15773 0.189388
\(279\) 0 0
\(280\) 2.99302 0.178867
\(281\) 5.48687 0.327319 0.163660 0.986517i \(-0.447670\pi\)
0.163660 + 0.986517i \(0.447670\pi\)
\(282\) 0 0
\(283\) 18.3381 1.09008 0.545042 0.838408i \(-0.316514\pi\)
0.545042 + 0.838408i \(0.316514\pi\)
\(284\) −12.1052 −0.718310
\(285\) 0 0
\(286\) −16.7314 −0.989347
\(287\) 16.4685 0.972105
\(288\) 0 0
\(289\) 3.44778 0.202811
\(290\) −10.7204 −0.629523
\(291\) 0 0
\(292\) −9.35826 −0.547651
\(293\) 31.7560 1.85520 0.927602 0.373569i \(-0.121866\pi\)
0.927602 + 0.373569i \(0.121866\pi\)
\(294\) 0 0
\(295\) −12.9093 −0.751607
\(296\) −3.29988 −0.191802
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 9.52012 0.550563
\(300\) 0 0
\(301\) −7.86639 −0.453411
\(302\) 24.1133 1.38756
\(303\) 0 0
\(304\) −1.46202 −0.0838528
\(305\) −13.7441 −0.786984
\(306\) 0 0
\(307\) −34.4876 −1.96831 −0.984155 0.177310i \(-0.943261\pi\)
−0.984155 + 0.177310i \(0.943261\pi\)
\(308\) 11.8950 0.677782
\(309\) 0 0
\(310\) 0.895581 0.0508656
\(311\) 7.52575 0.426746 0.213373 0.976971i \(-0.431555\pi\)
0.213373 + 0.976971i \(0.431555\pi\)
\(312\) 0 0
\(313\) −28.0840 −1.58740 −0.793700 0.608310i \(-0.791848\pi\)
−0.793700 + 0.608310i \(0.791848\pi\)
\(314\) 6.00350 0.338797
\(315\) 0 0
\(316\) 6.85287 0.385504
\(317\) 25.6207 1.43900 0.719501 0.694492i \(-0.244371\pi\)
0.719501 + 0.694492i \(0.244371\pi\)
\(318\) 0 0
\(319\) −42.6056 −2.38545
\(320\) 1.09665 0.0613044
\(321\) 0 0
\(322\) −6.76824 −0.377180
\(323\) 6.61116 0.367855
\(324\) 0 0
\(325\) 14.5778 0.808630
\(326\) 19.2994 1.06890
\(327\) 0 0
\(328\) 6.03409 0.333177
\(329\) 4.93086 0.271847
\(330\) 0 0
\(331\) 1.31125 0.0720727 0.0360363 0.999350i \(-0.488527\pi\)
0.0360363 + 0.999350i \(0.488527\pi\)
\(332\) 3.17103 0.174033
\(333\) 0 0
\(334\) 16.5548 0.905838
\(335\) −10.0888 −0.551210
\(336\) 0 0
\(337\) −18.4513 −1.00511 −0.502553 0.864547i \(-0.667606\pi\)
−0.502553 + 0.864547i \(0.667606\pi\)
\(338\) −1.73730 −0.0944969
\(339\) 0 0
\(340\) −4.95895 −0.268937
\(341\) 3.55927 0.192745
\(342\) 0 0
\(343\) 17.8799 0.965423
\(344\) −2.88226 −0.155401
\(345\) 0 0
\(346\) 11.9508 0.642481
\(347\) 7.23732 0.388520 0.194260 0.980950i \(-0.437770\pi\)
0.194260 + 0.980950i \(0.437770\pi\)
\(348\) 0 0
\(349\) −16.0951 −0.861549 −0.430774 0.902460i \(-0.641760\pi\)
−0.430774 + 0.902460i \(0.641760\pi\)
\(350\) −10.3639 −0.553976
\(351\) 0 0
\(352\) 4.35836 0.232301
\(353\) −26.2451 −1.39689 −0.698443 0.715666i \(-0.746123\pi\)
−0.698443 + 0.715666i \(0.746123\pi\)
\(354\) 0 0
\(355\) −13.2751 −0.704570
\(356\) 12.3920 0.656776
\(357\) 0 0
\(358\) −18.9136 −0.999613
\(359\) −35.3204 −1.86414 −0.932071 0.362277i \(-0.881999\pi\)
−0.932071 + 0.362277i \(0.881999\pi\)
\(360\) 0 0
\(361\) −16.8625 −0.887499
\(362\) −21.8386 −1.14781
\(363\) 0 0
\(364\) 10.4774 0.549163
\(365\) −10.2627 −0.537175
\(366\) 0 0
\(367\) 17.7864 0.928443 0.464222 0.885719i \(-0.346334\pi\)
0.464222 + 0.885719i \(0.346334\pi\)
\(368\) −2.47990 −0.129274
\(369\) 0 0
\(370\) −3.61881 −0.188133
\(371\) −26.4966 −1.37564
\(372\) 0 0
\(373\) 5.38565 0.278858 0.139429 0.990232i \(-0.455473\pi\)
0.139429 + 0.990232i \(0.455473\pi\)
\(374\) −19.7082 −1.01908
\(375\) 0 0
\(376\) 1.80668 0.0931722
\(377\) −37.5278 −1.93278
\(378\) 0 0
\(379\) −2.50892 −0.128875 −0.0644373 0.997922i \(-0.520525\pi\)
−0.0644373 + 0.997922i \(0.520525\pi\)
\(380\) −1.60332 −0.0822488
\(381\) 0 0
\(382\) −16.5320 −0.845849
\(383\) −13.1237 −0.670591 −0.335296 0.942113i \(-0.608836\pi\)
−0.335296 + 0.942113i \(0.608836\pi\)
\(384\) 0 0
\(385\) 13.0446 0.664817
\(386\) −11.8366 −0.602465
\(387\) 0 0
\(388\) 6.62366 0.336266
\(389\) 16.8554 0.854601 0.427301 0.904110i \(-0.359465\pi\)
0.427301 + 0.904110i \(0.359465\pi\)
\(390\) 0 0
\(391\) 11.2139 0.567111
\(392\) −0.448781 −0.0226669
\(393\) 0 0
\(394\) −17.0473 −0.858833
\(395\) 7.51518 0.378130
\(396\) 0 0
\(397\) −28.5551 −1.43314 −0.716571 0.697514i \(-0.754289\pi\)
−0.716571 + 0.697514i \(0.754289\pi\)
\(398\) −4.59160 −0.230156
\(399\) 0 0
\(400\) −3.79736 −0.189868
\(401\) −26.0083 −1.29879 −0.649397 0.760450i \(-0.724979\pi\)
−0.649397 + 0.760450i \(0.724979\pi\)
\(402\) 0 0
\(403\) 3.13507 0.156169
\(404\) 18.9994 0.945256
\(405\) 0 0
\(406\) 26.6800 1.32411
\(407\) −14.3821 −0.712893
\(408\) 0 0
\(409\) 9.62454 0.475903 0.237951 0.971277i \(-0.423524\pi\)
0.237951 + 0.971277i \(0.423524\pi\)
\(410\) 6.61726 0.326803
\(411\) 0 0
\(412\) 2.86431 0.141114
\(413\) 32.1275 1.58089
\(414\) 0 0
\(415\) 3.47750 0.170704
\(416\) 3.83892 0.188219
\(417\) 0 0
\(418\) −6.37202 −0.311666
\(419\) 17.5251 0.856157 0.428078 0.903742i \(-0.359191\pi\)
0.428078 + 0.903742i \(0.359191\pi\)
\(420\) 0 0
\(421\) 31.8934 1.55439 0.777195 0.629260i \(-0.216642\pi\)
0.777195 + 0.629260i \(0.216642\pi\)
\(422\) −9.98312 −0.485971
\(423\) 0 0
\(424\) −9.70841 −0.471482
\(425\) 17.1714 0.832935
\(426\) 0 0
\(427\) 34.2052 1.65530
\(428\) 16.8994 0.816862
\(429\) 0 0
\(430\) −3.16082 −0.152428
\(431\) 6.40574 0.308553 0.154277 0.988028i \(-0.450695\pi\)
0.154277 + 0.988028i \(0.450695\pi\)
\(432\) 0 0
\(433\) 12.4910 0.600281 0.300141 0.953895i \(-0.402966\pi\)
0.300141 + 0.953895i \(0.402966\pi\)
\(434\) −2.22885 −0.106988
\(435\) 0 0
\(436\) 0.752058 0.0360170
\(437\) 3.62567 0.173439
\(438\) 0 0
\(439\) 31.2958 1.49367 0.746834 0.665010i \(-0.231573\pi\)
0.746834 + 0.665010i \(0.231573\pi\)
\(440\) 4.77958 0.227858
\(441\) 0 0
\(442\) −17.3593 −0.825698
\(443\) −39.4216 −1.87298 −0.936488 0.350700i \(-0.885944\pi\)
−0.936488 + 0.350700i \(0.885944\pi\)
\(444\) 0 0
\(445\) 13.5897 0.644213
\(446\) 12.4741 0.590665
\(447\) 0 0
\(448\) −2.72925 −0.128945
\(449\) 3.51295 0.165787 0.0828933 0.996558i \(-0.473584\pi\)
0.0828933 + 0.996558i \(0.473584\pi\)
\(450\) 0 0
\(451\) 26.2987 1.23836
\(452\) −14.1817 −0.667052
\(453\) 0 0
\(454\) −4.41661 −0.207282
\(455\) 11.4900 0.538658
\(456\) 0 0
\(457\) 13.0035 0.608278 0.304139 0.952628i \(-0.401631\pi\)
0.304139 + 0.952628i \(0.401631\pi\)
\(458\) 21.1109 0.986448
\(459\) 0 0
\(460\) −2.71957 −0.126801
\(461\) 7.06541 0.329069 0.164534 0.986371i \(-0.447388\pi\)
0.164534 + 0.986371i \(0.447388\pi\)
\(462\) 0 0
\(463\) −20.9332 −0.972847 −0.486423 0.873723i \(-0.661699\pi\)
−0.486423 + 0.873723i \(0.661699\pi\)
\(464\) 9.77560 0.453821
\(465\) 0 0
\(466\) 3.50298 0.162272
\(467\) −28.2094 −1.30538 −0.652688 0.757627i \(-0.726359\pi\)
−0.652688 + 0.757627i \(0.726359\pi\)
\(468\) 0 0
\(469\) 25.1082 1.15939
\(470\) 1.98129 0.0913899
\(471\) 0 0
\(472\) 11.7716 0.541831
\(473\) −12.5619 −0.577597
\(474\) 0 0
\(475\) 5.55184 0.254736
\(476\) 12.3414 0.565669
\(477\) 0 0
\(478\) −27.2008 −1.24413
\(479\) 19.7500 0.902399 0.451200 0.892423i \(-0.350996\pi\)
0.451200 + 0.892423i \(0.350996\pi\)
\(480\) 0 0
\(481\) −12.6680 −0.577611
\(482\) −6.93758 −0.315998
\(483\) 0 0
\(484\) 7.99528 0.363422
\(485\) 7.26382 0.329833
\(486\) 0 0
\(487\) −22.8585 −1.03582 −0.517908 0.855437i \(-0.673289\pi\)
−0.517908 + 0.855437i \(0.673289\pi\)
\(488\) 12.5328 0.567334
\(489\) 0 0
\(490\) −0.492154 −0.0222333
\(491\) −9.36712 −0.422732 −0.211366 0.977407i \(-0.567791\pi\)
−0.211366 + 0.977407i \(0.567791\pi\)
\(492\) 0 0
\(493\) −44.2045 −1.99087
\(494\) −5.61259 −0.252522
\(495\) 0 0
\(496\) −0.816654 −0.0366689
\(497\) 33.0380 1.48196
\(498\) 0 0
\(499\) −10.1322 −0.453580 −0.226790 0.973944i \(-0.572823\pi\)
−0.226790 + 0.973944i \(0.572823\pi\)
\(500\) −9.64761 −0.431454
\(501\) 0 0
\(502\) −18.5290 −0.826991
\(503\) −15.1255 −0.674413 −0.337206 0.941431i \(-0.609482\pi\)
−0.337206 + 0.941431i \(0.609482\pi\)
\(504\) 0 0
\(505\) 20.8357 0.927175
\(506\) −10.8083 −0.480486
\(507\) 0 0
\(508\) 4.60414 0.204276
\(509\) 6.98576 0.309638 0.154819 0.987943i \(-0.450521\pi\)
0.154819 + 0.987943i \(0.450521\pi\)
\(510\) 0 0
\(511\) 25.5410 1.12987
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 28.3360 1.24985
\(515\) 3.14114 0.138415
\(516\) 0 0
\(517\) 7.87414 0.346304
\(518\) 9.00619 0.395709
\(519\) 0 0
\(520\) 4.20994 0.184618
\(521\) −40.9358 −1.79343 −0.896714 0.442611i \(-0.854052\pi\)
−0.896714 + 0.442611i \(0.854052\pi\)
\(522\) 0 0
\(523\) −19.9444 −0.872109 −0.436055 0.899920i \(-0.643625\pi\)
−0.436055 + 0.899920i \(0.643625\pi\)
\(524\) −0.536620 −0.0234423
\(525\) 0 0
\(526\) −13.0188 −0.567646
\(527\) 3.69285 0.160863
\(528\) 0 0
\(529\) −16.8501 −0.732614
\(530\) −10.6467 −0.462463
\(531\) 0 0
\(532\) 3.99022 0.172998
\(533\) 23.1644 1.00336
\(534\) 0 0
\(535\) 18.5327 0.801237
\(536\) 9.19967 0.397365
\(537\) 0 0
\(538\) −27.1713 −1.17144
\(539\) −1.95595 −0.0842486
\(540\) 0 0
\(541\) 27.8738 1.19839 0.599195 0.800603i \(-0.295487\pi\)
0.599195 + 0.800603i \(0.295487\pi\)
\(542\) −0.154348 −0.00662983
\(543\) 0 0
\(544\) 4.52192 0.193876
\(545\) 0.824742 0.0353281
\(546\) 0 0
\(547\) 8.04603 0.344023 0.172012 0.985095i \(-0.444973\pi\)
0.172012 + 0.985095i \(0.444973\pi\)
\(548\) 20.2425 0.864718
\(549\) 0 0
\(550\) −16.5503 −0.705706
\(551\) −14.2922 −0.608867
\(552\) 0 0
\(553\) −18.7032 −0.795339
\(554\) −28.6038 −1.21526
\(555\) 0 0
\(556\) −3.15773 −0.133918
\(557\) 18.9214 0.801726 0.400863 0.916138i \(-0.368710\pi\)
0.400863 + 0.916138i \(0.368710\pi\)
\(558\) 0 0
\(559\) −11.0648 −0.467989
\(560\) −2.99302 −0.126478
\(561\) 0 0
\(562\) −5.48687 −0.231450
\(563\) −28.7214 −1.21046 −0.605232 0.796049i \(-0.706920\pi\)
−0.605232 + 0.796049i \(0.706920\pi\)
\(564\) 0 0
\(565\) −15.5523 −0.654292
\(566\) −18.3381 −0.770806
\(567\) 0 0
\(568\) 12.1052 0.507922
\(569\) 27.6719 1.16007 0.580033 0.814593i \(-0.303040\pi\)
0.580033 + 0.814593i \(0.303040\pi\)
\(570\) 0 0
\(571\) 8.38536 0.350916 0.175458 0.984487i \(-0.443859\pi\)
0.175458 + 0.984487i \(0.443859\pi\)
\(572\) 16.7314 0.699574
\(573\) 0 0
\(574\) −16.4685 −0.687382
\(575\) 9.41707 0.392719
\(576\) 0 0
\(577\) 34.4251 1.43314 0.716568 0.697517i \(-0.245712\pi\)
0.716568 + 0.697517i \(0.245712\pi\)
\(578\) −3.44778 −0.143409
\(579\) 0 0
\(580\) 10.7204 0.445140
\(581\) −8.65452 −0.359050
\(582\) 0 0
\(583\) −42.3127 −1.75241
\(584\) 9.35826 0.387248
\(585\) 0 0
\(586\) −31.7560 −1.31183
\(587\) −38.9122 −1.60608 −0.803039 0.595927i \(-0.796785\pi\)
−0.803039 + 0.595927i \(0.796785\pi\)
\(588\) 0 0
\(589\) 1.19397 0.0491966
\(590\) 12.9093 0.531467
\(591\) 0 0
\(592\) 3.29988 0.135624
\(593\) 9.78088 0.401653 0.200826 0.979627i \(-0.435637\pi\)
0.200826 + 0.979627i \(0.435637\pi\)
\(594\) 0 0
\(595\) 13.5342 0.554848
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −9.52012 −0.389307
\(599\) 37.3040 1.52420 0.762100 0.647459i \(-0.224168\pi\)
0.762100 + 0.647459i \(0.224168\pi\)
\(600\) 0 0
\(601\) 24.1603 0.985520 0.492760 0.870165i \(-0.335988\pi\)
0.492760 + 0.870165i \(0.335988\pi\)
\(602\) 7.86639 0.320610
\(603\) 0 0
\(604\) −24.1133 −0.981155
\(605\) 8.76800 0.356470
\(606\) 0 0
\(607\) −42.8379 −1.73874 −0.869369 0.494164i \(-0.835474\pi\)
−0.869369 + 0.494164i \(0.835474\pi\)
\(608\) 1.46202 0.0592929
\(609\) 0 0
\(610\) 13.7441 0.556482
\(611\) 6.93569 0.280588
\(612\) 0 0
\(613\) 30.7697 1.24278 0.621389 0.783502i \(-0.286569\pi\)
0.621389 + 0.783502i \(0.286569\pi\)
\(614\) 34.4876 1.39181
\(615\) 0 0
\(616\) −11.8950 −0.479264
\(617\) 35.1120 1.41356 0.706778 0.707435i \(-0.250148\pi\)
0.706778 + 0.707435i \(0.250148\pi\)
\(618\) 0 0
\(619\) 21.8156 0.876842 0.438421 0.898770i \(-0.355538\pi\)
0.438421 + 0.898770i \(0.355538\pi\)
\(620\) −0.895581 −0.0359674
\(621\) 0 0
\(622\) −7.52575 −0.301755
\(623\) −33.8209 −1.35501
\(624\) 0 0
\(625\) 8.40680 0.336272
\(626\) 28.0840 1.12246
\(627\) 0 0
\(628\) −6.00350 −0.239566
\(629\) −14.9218 −0.594972
\(630\) 0 0
\(631\) −12.1031 −0.481815 −0.240907 0.970548i \(-0.577445\pi\)
−0.240907 + 0.970548i \(0.577445\pi\)
\(632\) −6.85287 −0.272592
\(633\) 0 0
\(634\) −25.6207 −1.01753
\(635\) 5.04912 0.200368
\(636\) 0 0
\(637\) −1.72283 −0.0682611
\(638\) 42.6056 1.68677
\(639\) 0 0
\(640\) −1.09665 −0.0433488
\(641\) −13.1368 −0.518873 −0.259437 0.965760i \(-0.583537\pi\)
−0.259437 + 0.965760i \(0.583537\pi\)
\(642\) 0 0
\(643\) −11.8722 −0.468195 −0.234097 0.972213i \(-0.575213\pi\)
−0.234097 + 0.972213i \(0.575213\pi\)
\(644\) 6.76824 0.266706
\(645\) 0 0
\(646\) −6.61116 −0.260113
\(647\) −11.6314 −0.457279 −0.228639 0.973511i \(-0.573428\pi\)
−0.228639 + 0.973511i \(0.573428\pi\)
\(648\) 0 0
\(649\) 51.3048 2.01389
\(650\) −14.5778 −0.571788
\(651\) 0 0
\(652\) −19.2994 −0.755825
\(653\) −47.2362 −1.84850 −0.924248 0.381793i \(-0.875307\pi\)
−0.924248 + 0.381793i \(0.875307\pi\)
\(654\) 0 0
\(655\) −0.588483 −0.0229939
\(656\) −6.03409 −0.235591
\(657\) 0 0
\(658\) −4.93086 −0.192225
\(659\) 43.1846 1.68223 0.841117 0.540853i \(-0.181899\pi\)
0.841117 + 0.540853i \(0.181899\pi\)
\(660\) 0 0
\(661\) 40.8820 1.59013 0.795063 0.606526i \(-0.207438\pi\)
0.795063 + 0.606526i \(0.207438\pi\)
\(662\) −1.31125 −0.0509631
\(663\) 0 0
\(664\) −3.17103 −0.123060
\(665\) 4.37587 0.169689
\(666\) 0 0
\(667\) −24.2425 −0.938673
\(668\) −16.5548 −0.640524
\(669\) 0 0
\(670\) 10.0888 0.389764
\(671\) 54.6225 2.10868
\(672\) 0 0
\(673\) −5.77879 −0.222756 −0.111378 0.993778i \(-0.535526\pi\)
−0.111378 + 0.993778i \(0.535526\pi\)
\(674\) 18.4513 0.710717
\(675\) 0 0
\(676\) 1.73730 0.0668194
\(677\) −34.1968 −1.31429 −0.657146 0.753764i \(-0.728236\pi\)
−0.657146 + 0.753764i \(0.728236\pi\)
\(678\) 0 0
\(679\) −18.0776 −0.693755
\(680\) 4.95895 0.190167
\(681\) 0 0
\(682\) −3.55927 −0.136292
\(683\) −6.45987 −0.247180 −0.123590 0.992333i \(-0.539441\pi\)
−0.123590 + 0.992333i \(0.539441\pi\)
\(684\) 0 0
\(685\) 22.1989 0.848176
\(686\) −17.8799 −0.682657
\(687\) 0 0
\(688\) 2.88226 0.109885
\(689\) −37.2698 −1.41987
\(690\) 0 0
\(691\) −13.7970 −0.524863 −0.262432 0.964951i \(-0.584524\pi\)
−0.262432 + 0.964951i \(0.584524\pi\)
\(692\) −11.9508 −0.454302
\(693\) 0 0
\(694\) −7.23732 −0.274725
\(695\) −3.46292 −0.131356
\(696\) 0 0
\(697\) 27.2857 1.03352
\(698\) 16.0951 0.609207
\(699\) 0 0
\(700\) 10.3639 0.391720
\(701\) 28.5634 1.07882 0.539412 0.842042i \(-0.318646\pi\)
0.539412 + 0.842042i \(0.318646\pi\)
\(702\) 0 0
\(703\) −4.82451 −0.181960
\(704\) −4.35836 −0.164262
\(705\) 0 0
\(706\) 26.2451 0.987748
\(707\) −51.8541 −1.95017
\(708\) 0 0
\(709\) −28.6004 −1.07411 −0.537055 0.843547i \(-0.680463\pi\)
−0.537055 + 0.843547i \(0.680463\pi\)
\(710\) 13.2751 0.498206
\(711\) 0 0
\(712\) −12.3920 −0.464411
\(713\) 2.02522 0.0758450
\(714\) 0 0
\(715\) 18.3484 0.686192
\(716\) 18.9136 0.706833
\(717\) 0 0
\(718\) 35.3204 1.31815
\(719\) 18.5267 0.690931 0.345465 0.938432i \(-0.387721\pi\)
0.345465 + 0.938432i \(0.387721\pi\)
\(720\) 0 0
\(721\) −7.81741 −0.291135
\(722\) 16.8625 0.627557
\(723\) 0 0
\(724\) 21.8386 0.811624
\(725\) −37.1215 −1.37866
\(726\) 0 0
\(727\) −23.9428 −0.887989 −0.443995 0.896029i \(-0.646439\pi\)
−0.443995 + 0.896029i \(0.646439\pi\)
\(728\) −10.4774 −0.388317
\(729\) 0 0
\(730\) 10.2627 0.379840
\(731\) −13.0333 −0.482056
\(732\) 0 0
\(733\) −25.7865 −0.952444 −0.476222 0.879325i \(-0.657994\pi\)
−0.476222 + 0.879325i \(0.657994\pi\)
\(734\) −17.7864 −0.656508
\(735\) 0 0
\(736\) 2.47990 0.0914102
\(737\) 40.0955 1.47693
\(738\) 0 0
\(739\) 24.5497 0.903077 0.451538 0.892252i \(-0.350875\pi\)
0.451538 + 0.892252i \(0.350875\pi\)
\(740\) 3.61881 0.133030
\(741\) 0 0
\(742\) 26.4966 0.972722
\(743\) 9.44491 0.346500 0.173250 0.984878i \(-0.444573\pi\)
0.173250 + 0.984878i \(0.444573\pi\)
\(744\) 0 0
\(745\) 1.09665 0.0401780
\(746\) −5.38565 −0.197183
\(747\) 0 0
\(748\) 19.7082 0.720601
\(749\) −46.1226 −1.68528
\(750\) 0 0
\(751\) 24.0856 0.878895 0.439447 0.898268i \(-0.355174\pi\)
0.439447 + 0.898268i \(0.355174\pi\)
\(752\) −1.80668 −0.0658827
\(753\) 0 0
\(754\) 37.5278 1.36668
\(755\) −26.4438 −0.962387
\(756\) 0 0
\(757\) 40.5109 1.47240 0.736198 0.676767i \(-0.236619\pi\)
0.736198 + 0.676767i \(0.236619\pi\)
\(758\) 2.50892 0.0911281
\(759\) 0 0
\(760\) 1.60332 0.0581587
\(761\) −20.8544 −0.755972 −0.377986 0.925811i \(-0.623383\pi\)
−0.377986 + 0.925811i \(0.623383\pi\)
\(762\) 0 0
\(763\) −2.05255 −0.0743073
\(764\) 16.5320 0.598105
\(765\) 0 0
\(766\) 13.1237 0.474180
\(767\) 45.1902 1.63172
\(768\) 0 0
\(769\) 45.6339 1.64560 0.822800 0.568331i \(-0.192411\pi\)
0.822800 + 0.568331i \(0.192411\pi\)
\(770\) −13.0446 −0.470097
\(771\) 0 0
\(772\) 11.8366 0.426007
\(773\) 12.8727 0.462997 0.231499 0.972835i \(-0.425637\pi\)
0.231499 + 0.972835i \(0.425637\pi\)
\(774\) 0 0
\(775\) 3.10113 0.111396
\(776\) −6.62366 −0.237776
\(777\) 0 0
\(778\) −16.8554 −0.604294
\(779\) 8.82198 0.316080
\(780\) 0 0
\(781\) 52.7587 1.88785
\(782\) −11.2139 −0.401008
\(783\) 0 0
\(784\) 0.448781 0.0160279
\(785\) −6.58372 −0.234983
\(786\) 0 0
\(787\) 49.3025 1.75745 0.878723 0.477332i \(-0.158396\pi\)
0.878723 + 0.477332i \(0.158396\pi\)
\(788\) 17.0473 0.607287
\(789\) 0 0
\(790\) −7.51518 −0.267378
\(791\) 38.7054 1.37621
\(792\) 0 0
\(793\) 48.1125 1.70853
\(794\) 28.5551 1.01338
\(795\) 0 0
\(796\) 4.59160 0.162745
\(797\) 4.83675 0.171326 0.0856632 0.996324i \(-0.472699\pi\)
0.0856632 + 0.996324i \(0.472699\pi\)
\(798\) 0 0
\(799\) 8.16965 0.289021
\(800\) 3.79736 0.134257
\(801\) 0 0
\(802\) 26.0083 0.918386
\(803\) 40.7866 1.43933
\(804\) 0 0
\(805\) 7.42238 0.261604
\(806\) −3.13507 −0.110428
\(807\) 0 0
\(808\) −18.9994 −0.668397
\(809\) −16.3692 −0.575510 −0.287755 0.957704i \(-0.592909\pi\)
−0.287755 + 0.957704i \(0.592909\pi\)
\(810\) 0 0
\(811\) −38.7722 −1.36147 −0.680737 0.732528i \(-0.738340\pi\)
−0.680737 + 0.732528i \(0.738340\pi\)
\(812\) −26.6800 −0.936285
\(813\) 0 0
\(814\) 14.3821 0.504091
\(815\) −21.1647 −0.741366
\(816\) 0 0
\(817\) −4.21393 −0.147427
\(818\) −9.62454 −0.336514
\(819\) 0 0
\(820\) −6.61726 −0.231085
\(821\) 29.6576 1.03506 0.517529 0.855666i \(-0.326852\pi\)
0.517529 + 0.855666i \(0.326852\pi\)
\(822\) 0 0
\(823\) 29.6906 1.03495 0.517474 0.855699i \(-0.326872\pi\)
0.517474 + 0.855699i \(0.326872\pi\)
\(824\) −2.86431 −0.0997830
\(825\) 0 0
\(826\) −32.1275 −1.11786
\(827\) −13.8789 −0.482618 −0.241309 0.970448i \(-0.577577\pi\)
−0.241309 + 0.970448i \(0.577577\pi\)
\(828\) 0 0
\(829\) 39.1836 1.36090 0.680451 0.732793i \(-0.261784\pi\)
0.680451 + 0.732793i \(0.261784\pi\)
\(830\) −3.47750 −0.120706
\(831\) 0 0
\(832\) −3.83892 −0.133091
\(833\) −2.02935 −0.0703129
\(834\) 0 0
\(835\) −18.1548 −0.628271
\(836\) 6.37202 0.220381
\(837\) 0 0
\(838\) −17.5251 −0.605394
\(839\) −4.43681 −0.153176 −0.0765879 0.997063i \(-0.524403\pi\)
−0.0765879 + 0.997063i \(0.524403\pi\)
\(840\) 0 0
\(841\) 66.5624 2.29526
\(842\) −31.8934 −1.09912
\(843\) 0 0
\(844\) 9.98312 0.343633
\(845\) 1.90521 0.0655412
\(846\) 0 0
\(847\) −21.8211 −0.749781
\(848\) 9.70841 0.333388
\(849\) 0 0
\(850\) −17.1714 −0.588974
\(851\) −8.18337 −0.280522
\(852\) 0 0
\(853\) −53.3902 −1.82804 −0.914022 0.405664i \(-0.867040\pi\)
−0.914022 + 0.405664i \(0.867040\pi\)
\(854\) −34.2052 −1.17048
\(855\) 0 0
\(856\) −16.8994 −0.577609
\(857\) 34.9541 1.19401 0.597004 0.802238i \(-0.296358\pi\)
0.597004 + 0.802238i \(0.296358\pi\)
\(858\) 0 0
\(859\) 8.50093 0.290048 0.145024 0.989428i \(-0.453674\pi\)
0.145024 + 0.989428i \(0.453674\pi\)
\(860\) 3.16082 0.107783
\(861\) 0 0
\(862\) −6.40574 −0.218180
\(863\) −20.3417 −0.692440 −0.346220 0.938153i \(-0.612535\pi\)
−0.346220 + 0.938153i \(0.612535\pi\)
\(864\) 0 0
\(865\) −13.1058 −0.445612
\(866\) −12.4910 −0.424463
\(867\) 0 0
\(868\) 2.22885 0.0756521
\(869\) −29.8672 −1.01318
\(870\) 0 0
\(871\) 35.3168 1.19666
\(872\) −0.752058 −0.0254679
\(873\) 0 0
\(874\) −3.62567 −0.122640
\(875\) 26.3307 0.890140
\(876\) 0 0
\(877\) −11.1783 −0.377466 −0.188733 0.982028i \(-0.560438\pi\)
−0.188733 + 0.982028i \(0.560438\pi\)
\(878\) −31.2958 −1.05618
\(879\) 0 0
\(880\) −4.77958 −0.161120
\(881\) 13.5491 0.456480 0.228240 0.973605i \(-0.426703\pi\)
0.228240 + 0.973605i \(0.426703\pi\)
\(882\) 0 0
\(883\) 31.6753 1.06596 0.532979 0.846129i \(-0.321073\pi\)
0.532979 + 0.846129i \(0.321073\pi\)
\(884\) 17.3593 0.583856
\(885\) 0 0
\(886\) 39.4216 1.32439
\(887\) 2.92676 0.0982710 0.0491355 0.998792i \(-0.484353\pi\)
0.0491355 + 0.998792i \(0.484353\pi\)
\(888\) 0 0
\(889\) −12.5658 −0.421444
\(890\) −13.5897 −0.455527
\(891\) 0 0
\(892\) −12.4741 −0.417663
\(893\) 2.64140 0.0883912
\(894\) 0 0
\(895\) 20.7415 0.693312
\(896\) 2.72925 0.0911777
\(897\) 0 0
\(898\) −3.51295 −0.117229
\(899\) −7.98329 −0.266258
\(900\) 0 0
\(901\) −43.9007 −1.46254
\(902\) −26.2987 −0.875651
\(903\) 0 0
\(904\) 14.1817 0.471677
\(905\) 23.9492 0.796098
\(906\) 0 0
\(907\) −8.72412 −0.289680 −0.144840 0.989455i \(-0.546267\pi\)
−0.144840 + 0.989455i \(0.546267\pi\)
\(908\) 4.41661 0.146570
\(909\) 0 0
\(910\) −11.4900 −0.380889
\(911\) −18.4481 −0.611214 −0.305607 0.952158i \(-0.598859\pi\)
−0.305607 + 0.952158i \(0.598859\pi\)
\(912\) 0 0
\(913\) −13.8205 −0.457391
\(914\) −13.0035 −0.430118
\(915\) 0 0
\(916\) −21.1109 −0.697524
\(917\) 1.46457 0.0483643
\(918\) 0 0
\(919\) −33.8809 −1.11763 −0.558814 0.829293i \(-0.688743\pi\)
−0.558814 + 0.829293i \(0.688743\pi\)
\(920\) 2.71957 0.0896616
\(921\) 0 0
\(922\) −7.06541 −0.232687
\(923\) 46.4708 1.52960
\(924\) 0 0
\(925\) −12.5309 −0.412012
\(926\) 20.9332 0.687906
\(927\) 0 0
\(928\) −9.77560 −0.320900
\(929\) −6.69462 −0.219643 −0.109822 0.993951i \(-0.535028\pi\)
−0.109822 + 0.993951i \(0.535028\pi\)
\(930\) 0 0
\(931\) −0.656128 −0.0215037
\(932\) −3.50298 −0.114744
\(933\) 0 0
\(934\) 28.2094 0.923040
\(935\) 21.6129 0.706817
\(936\) 0 0
\(937\) 11.4433 0.373836 0.186918 0.982375i \(-0.440150\pi\)
0.186918 + 0.982375i \(0.440150\pi\)
\(938\) −25.1082 −0.819810
\(939\) 0 0
\(940\) −1.98129 −0.0646225
\(941\) −30.0674 −0.980171 −0.490085 0.871674i \(-0.663034\pi\)
−0.490085 + 0.871674i \(0.663034\pi\)
\(942\) 0 0
\(943\) 14.9639 0.487292
\(944\) −11.7716 −0.383132
\(945\) 0 0
\(946\) 12.5619 0.408423
\(947\) 18.9500 0.615793 0.307896 0.951420i \(-0.400375\pi\)
0.307896 + 0.951420i \(0.400375\pi\)
\(948\) 0 0
\(949\) 35.9256 1.16619
\(950\) −5.55184 −0.180125
\(951\) 0 0
\(952\) −12.3414 −0.399988
\(953\) 43.1005 1.39616 0.698081 0.716019i \(-0.254038\pi\)
0.698081 + 0.716019i \(0.254038\pi\)
\(954\) 0 0
\(955\) 18.1297 0.586664
\(956\) 27.2008 0.879736
\(957\) 0 0
\(958\) −19.7500 −0.638093
\(959\) −55.2468 −1.78401
\(960\) 0 0
\(961\) −30.3331 −0.978486
\(962\) 12.6680 0.408432
\(963\) 0 0
\(964\) 6.93758 0.223444
\(965\) 12.9805 0.417858
\(966\) 0 0
\(967\) 59.9741 1.92864 0.964319 0.264743i \(-0.0852870\pi\)
0.964319 + 0.264743i \(0.0852870\pi\)
\(968\) −7.99528 −0.256978
\(969\) 0 0
\(970\) −7.26382 −0.233227
\(971\) −22.6541 −0.727006 −0.363503 0.931593i \(-0.618419\pi\)
−0.363503 + 0.931593i \(0.618419\pi\)
\(972\) 0 0
\(973\) 8.61822 0.276287
\(974\) 22.8585 0.732432
\(975\) 0 0
\(976\) −12.5328 −0.401166
\(977\) −23.1749 −0.741430 −0.370715 0.928747i \(-0.620887\pi\)
−0.370715 + 0.928747i \(0.620887\pi\)
\(978\) 0 0
\(979\) −54.0089 −1.72613
\(980\) 0.492154 0.0157213
\(981\) 0 0
\(982\) 9.36712 0.298917
\(983\) 24.3734 0.777390 0.388695 0.921367i \(-0.372926\pi\)
0.388695 + 0.921367i \(0.372926\pi\)
\(984\) 0 0
\(985\) 18.6949 0.595670
\(986\) 44.2045 1.40776
\(987\) 0 0
\(988\) 5.61259 0.178560
\(989\) −7.14770 −0.227284
\(990\) 0 0
\(991\) 7.73172 0.245606 0.122803 0.992431i \(-0.460812\pi\)
0.122803 + 0.992431i \(0.460812\pi\)
\(992\) 0.816654 0.0259288
\(993\) 0 0
\(994\) −33.0380 −1.04790
\(995\) 5.03537 0.159632
\(996\) 0 0
\(997\) 5.46445 0.173061 0.0865305 0.996249i \(-0.472422\pi\)
0.0865305 + 0.996249i \(0.472422\pi\)
\(998\) 10.1322 0.320729
\(999\) 0 0
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 \(a_p\))