Properties

Label 6008.2.a.e.1.1
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.22705 q^{3} +2.92731 q^{5} +0.525757 q^{7} +7.41384 q^{9} +O(q^{10})\) \(q-3.22705 q^{3} +2.92731 q^{5} +0.525757 q^{7} +7.41384 q^{9} -1.19339 q^{11} -1.45885 q^{13} -9.44658 q^{15} +4.32149 q^{17} +2.66853 q^{19} -1.69664 q^{21} -0.287634 q^{23} +3.56917 q^{25} -14.2437 q^{27} +4.93433 q^{29} -5.71935 q^{31} +3.85112 q^{33} +1.53906 q^{35} -3.78706 q^{37} +4.70777 q^{39} +10.2624 q^{41} +3.99765 q^{43} +21.7026 q^{45} +1.23518 q^{47} -6.72358 q^{49} -13.9457 q^{51} +12.0361 q^{53} -3.49342 q^{55} -8.61147 q^{57} +12.3670 q^{59} -3.71482 q^{61} +3.89788 q^{63} -4.27050 q^{65} +2.87365 q^{67} +0.928209 q^{69} -4.40772 q^{71} +1.18677 q^{73} -11.5179 q^{75} -0.627433 q^{77} -8.82191 q^{79} +23.7235 q^{81} +14.4423 q^{83} +12.6504 q^{85} -15.9233 q^{87} -7.97365 q^{89} -0.767000 q^{91} +18.4566 q^{93} +7.81162 q^{95} -10.5153 q^{97} -8.84759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −3.22705 −1.86314 −0.931568 0.363566i \(-0.881559\pi\)
−0.931568 + 0.363566i \(0.881559\pi\)
\(4\) 0 0
\(5\) 2.92731 1.30913 0.654567 0.756004i \(-0.272851\pi\)
0.654567 + 0.756004i \(0.272851\pi\)
\(6\) 0 0
\(7\) 0.525757 0.198718 0.0993588 0.995052i \(-0.468321\pi\)
0.0993588 + 0.995052i \(0.468321\pi\)
\(8\) 0 0
\(9\) 7.41384 2.47128
\(10\) 0 0
\(11\) −1.19339 −0.359820 −0.179910 0.983683i \(-0.557581\pi\)
−0.179910 + 0.983683i \(0.557581\pi\)
\(12\) 0 0
\(13\) −1.45885 −0.404611 −0.202306 0.979322i \(-0.564843\pi\)
−0.202306 + 0.979322i \(0.564843\pi\)
\(14\) 0 0
\(15\) −9.44658 −2.43910
\(16\) 0 0
\(17\) 4.32149 1.04812 0.524058 0.851683i \(-0.324418\pi\)
0.524058 + 0.851683i \(0.324418\pi\)
\(18\) 0 0
\(19\) 2.66853 0.612202 0.306101 0.951999i \(-0.400975\pi\)
0.306101 + 0.951999i \(0.400975\pi\)
\(20\) 0 0
\(21\) −1.69664 −0.370238
\(22\) 0 0
\(23\) −0.287634 −0.0599758 −0.0299879 0.999550i \(-0.509547\pi\)
−0.0299879 + 0.999550i \(0.509547\pi\)
\(24\) 0 0
\(25\) 3.56917 0.713833
\(26\) 0 0
\(27\) −14.2437 −2.74119
\(28\) 0 0
\(29\) 4.93433 0.916282 0.458141 0.888880i \(-0.348516\pi\)
0.458141 + 0.888880i \(0.348516\pi\)
\(30\) 0 0
\(31\) −5.71935 −1.02723 −0.513613 0.858022i \(-0.671693\pi\)
−0.513613 + 0.858022i \(0.671693\pi\)
\(32\) 0 0
\(33\) 3.85112 0.670394
\(34\) 0 0
\(35\) 1.53906 0.260148
\(36\) 0 0
\(37\) −3.78706 −0.622588 −0.311294 0.950314i \(-0.600762\pi\)
−0.311294 + 0.950314i \(0.600762\pi\)
\(38\) 0 0
\(39\) 4.70777 0.753846
\(40\) 0 0
\(41\) 10.2624 1.60271 0.801355 0.598189i \(-0.204113\pi\)
0.801355 + 0.598189i \(0.204113\pi\)
\(42\) 0 0
\(43\) 3.99765 0.609636 0.304818 0.952411i \(-0.401404\pi\)
0.304818 + 0.952411i \(0.401404\pi\)
\(44\) 0 0
\(45\) 21.7026 3.23524
\(46\) 0 0
\(47\) 1.23518 0.180169 0.0900846 0.995934i \(-0.471286\pi\)
0.0900846 + 0.995934i \(0.471286\pi\)
\(48\) 0 0
\(49\) −6.72358 −0.960511
\(50\) 0 0
\(51\) −13.9457 −1.95278
\(52\) 0 0
\(53\) 12.0361 1.65329 0.826643 0.562727i \(-0.190248\pi\)
0.826643 + 0.562727i \(0.190248\pi\)
\(54\) 0 0
\(55\) −3.49342 −0.471053
\(56\) 0 0
\(57\) −8.61147 −1.14062
\(58\) 0 0
\(59\) 12.3670 1.61004 0.805022 0.593245i \(-0.202154\pi\)
0.805022 + 0.593245i \(0.202154\pi\)
\(60\) 0 0
\(61\) −3.71482 −0.475634 −0.237817 0.971310i \(-0.576432\pi\)
−0.237817 + 0.971310i \(0.576432\pi\)
\(62\) 0 0
\(63\) 3.89788 0.491087
\(64\) 0 0
\(65\) −4.27050 −0.529691
\(66\) 0 0
\(67\) 2.87365 0.351072 0.175536 0.984473i \(-0.443834\pi\)
0.175536 + 0.984473i \(0.443834\pi\)
\(68\) 0 0
\(69\) 0.928209 0.111743
\(70\) 0 0
\(71\) −4.40772 −0.523100 −0.261550 0.965190i \(-0.584234\pi\)
−0.261550 + 0.965190i \(0.584234\pi\)
\(72\) 0 0
\(73\) 1.18677 0.138901 0.0694504 0.997585i \(-0.477875\pi\)
0.0694504 + 0.997585i \(0.477875\pi\)
\(74\) 0 0
\(75\) −11.5179 −1.32997
\(76\) 0 0
\(77\) −0.627433 −0.0715026
\(78\) 0 0
\(79\) −8.82191 −0.992542 −0.496271 0.868168i \(-0.665298\pi\)
−0.496271 + 0.868168i \(0.665298\pi\)
\(80\) 0 0
\(81\) 23.7235 2.63594
\(82\) 0 0
\(83\) 14.4423 1.58525 0.792625 0.609709i \(-0.208714\pi\)
0.792625 + 0.609709i \(0.208714\pi\)
\(84\) 0 0
\(85\) 12.6504 1.37212
\(86\) 0 0
\(87\) −15.9233 −1.70716
\(88\) 0 0
\(89\) −7.97365 −0.845205 −0.422603 0.906315i \(-0.638883\pi\)
−0.422603 + 0.906315i \(0.638883\pi\)
\(90\) 0 0
\(91\) −0.767000 −0.0804034
\(92\) 0 0
\(93\) 18.4566 1.91386
\(94\) 0 0
\(95\) 7.81162 0.801455
\(96\) 0 0
\(97\) −10.5153 −1.06767 −0.533835 0.845588i \(-0.679250\pi\)
−0.533835 + 0.845588i \(0.679250\pi\)
\(98\) 0 0
\(99\) −8.84759 −0.889216
\(100\) 0 0
\(101\) −8.56150 −0.851901 −0.425950 0.904747i \(-0.640060\pi\)
−0.425950 + 0.904747i \(0.640060\pi\)
\(102\) 0 0
\(103\) 10.0164 0.986950 0.493475 0.869760i \(-0.335726\pi\)
0.493475 + 0.869760i \(0.335726\pi\)
\(104\) 0 0
\(105\) −4.96661 −0.484691
\(106\) 0 0
\(107\) 13.4499 1.30025 0.650125 0.759827i \(-0.274716\pi\)
0.650125 + 0.759827i \(0.274716\pi\)
\(108\) 0 0
\(109\) 18.3512 1.75773 0.878865 0.477070i \(-0.158301\pi\)
0.878865 + 0.477070i \(0.158301\pi\)
\(110\) 0 0
\(111\) 12.2210 1.15997
\(112\) 0 0
\(113\) −4.46354 −0.419895 −0.209947 0.977713i \(-0.567329\pi\)
−0.209947 + 0.977713i \(0.567329\pi\)
\(114\) 0 0
\(115\) −0.841995 −0.0785164
\(116\) 0 0
\(117\) −10.8157 −0.999908
\(118\) 0 0
\(119\) 2.27206 0.208279
\(120\) 0 0
\(121\) −9.57582 −0.870529
\(122\) 0 0
\(123\) −33.1171 −2.98607
\(124\) 0 0
\(125\) −4.18850 −0.374631
\(126\) 0 0
\(127\) −10.9047 −0.967635 −0.483817 0.875169i \(-0.660750\pi\)
−0.483817 + 0.875169i \(0.660750\pi\)
\(128\) 0 0
\(129\) −12.9006 −1.13583
\(130\) 0 0
\(131\) −12.7298 −1.11221 −0.556106 0.831112i \(-0.687705\pi\)
−0.556106 + 0.831112i \(0.687705\pi\)
\(132\) 0 0
\(133\) 1.40300 0.121655
\(134\) 0 0
\(135\) −41.6957 −3.58859
\(136\) 0 0
\(137\) −9.35071 −0.798885 −0.399443 0.916758i \(-0.630796\pi\)
−0.399443 + 0.916758i \(0.630796\pi\)
\(138\) 0 0
\(139\) −18.3516 −1.55656 −0.778281 0.627916i \(-0.783908\pi\)
−0.778281 + 0.627916i \(0.783908\pi\)
\(140\) 0 0
\(141\) −3.98598 −0.335680
\(142\) 0 0
\(143\) 1.74097 0.145587
\(144\) 0 0
\(145\) 14.4443 1.19954
\(146\) 0 0
\(147\) 21.6973 1.78956
\(148\) 0 0
\(149\) −3.53933 −0.289953 −0.144977 0.989435i \(-0.546311\pi\)
−0.144977 + 0.989435i \(0.546311\pi\)
\(150\) 0 0
\(151\) 2.32285 0.189031 0.0945153 0.995523i \(-0.469870\pi\)
0.0945153 + 0.995523i \(0.469870\pi\)
\(152\) 0 0
\(153\) 32.0388 2.59019
\(154\) 0 0
\(155\) −16.7423 −1.34478
\(156\) 0 0
\(157\) −2.35205 −0.187714 −0.0938569 0.995586i \(-0.529920\pi\)
−0.0938569 + 0.995586i \(0.529920\pi\)
\(158\) 0 0
\(159\) −38.8411 −3.08030
\(160\) 0 0
\(161\) −0.151226 −0.0119183
\(162\) 0 0
\(163\) 6.41777 0.502678 0.251339 0.967899i \(-0.419129\pi\)
0.251339 + 0.967899i \(0.419129\pi\)
\(164\) 0 0
\(165\) 11.2734 0.877637
\(166\) 0 0
\(167\) 22.5965 1.74857 0.874287 0.485410i \(-0.161330\pi\)
0.874287 + 0.485410i \(0.161330\pi\)
\(168\) 0 0
\(169\) −10.8718 −0.836290
\(170\) 0 0
\(171\) 19.7840 1.51292
\(172\) 0 0
\(173\) 10.4379 0.793577 0.396788 0.917910i \(-0.370125\pi\)
0.396788 + 0.917910i \(0.370125\pi\)
\(174\) 0 0
\(175\) 1.87652 0.141851
\(176\) 0 0
\(177\) −39.9088 −2.99973
\(178\) 0 0
\(179\) 7.49285 0.560042 0.280021 0.959994i \(-0.409659\pi\)
0.280021 + 0.959994i \(0.409659\pi\)
\(180\) 0 0
\(181\) 18.7890 1.39657 0.698287 0.715818i \(-0.253946\pi\)
0.698287 + 0.715818i \(0.253946\pi\)
\(182\) 0 0
\(183\) 11.9879 0.886171
\(184\) 0 0
\(185\) −11.0859 −0.815052
\(186\) 0 0
\(187\) −5.15722 −0.377133
\(188\) 0 0
\(189\) −7.48871 −0.544724
\(190\) 0 0
\(191\) −10.1590 −0.735080 −0.367540 0.930008i \(-0.619800\pi\)
−0.367540 + 0.930008i \(0.619800\pi\)
\(192\) 0 0
\(193\) 8.59068 0.618370 0.309185 0.951002i \(-0.399944\pi\)
0.309185 + 0.951002i \(0.399944\pi\)
\(194\) 0 0
\(195\) 13.7811 0.986886
\(196\) 0 0
\(197\) 17.9621 1.27975 0.639875 0.768479i \(-0.278986\pi\)
0.639875 + 0.768479i \(0.278986\pi\)
\(198\) 0 0
\(199\) −4.24759 −0.301104 −0.150552 0.988602i \(-0.548105\pi\)
−0.150552 + 0.988602i \(0.548105\pi\)
\(200\) 0 0
\(201\) −9.27341 −0.654096
\(202\) 0 0
\(203\) 2.59426 0.182081
\(204\) 0 0
\(205\) 30.0411 2.09816
\(206\) 0 0
\(207\) −2.13247 −0.148217
\(208\) 0 0
\(209\) −3.18459 −0.220283
\(210\) 0 0
\(211\) −15.0398 −1.03538 −0.517690 0.855568i \(-0.673208\pi\)
−0.517690 + 0.855568i \(0.673208\pi\)
\(212\) 0 0
\(213\) 14.2239 0.974608
\(214\) 0 0
\(215\) 11.7024 0.798095
\(216\) 0 0
\(217\) −3.00699 −0.204128
\(218\) 0 0
\(219\) −3.82976 −0.258791
\(220\) 0 0
\(221\) −6.30439 −0.424079
\(222\) 0 0
\(223\) −10.0775 −0.674842 −0.337421 0.941354i \(-0.609555\pi\)
−0.337421 + 0.941354i \(0.609555\pi\)
\(224\) 0 0
\(225\) 26.4612 1.76408
\(226\) 0 0
\(227\) −12.0629 −0.800642 −0.400321 0.916375i \(-0.631101\pi\)
−0.400321 + 0.916375i \(0.631101\pi\)
\(228\) 0 0
\(229\) −9.47307 −0.625998 −0.312999 0.949753i \(-0.601334\pi\)
−0.312999 + 0.949753i \(0.601334\pi\)
\(230\) 0 0
\(231\) 2.02476 0.133219
\(232\) 0 0
\(233\) 1.99752 0.130862 0.0654308 0.997857i \(-0.479158\pi\)
0.0654308 + 0.997857i \(0.479158\pi\)
\(234\) 0 0
\(235\) 3.61575 0.235866
\(236\) 0 0
\(237\) 28.4687 1.84924
\(238\) 0 0
\(239\) 14.2781 0.923572 0.461786 0.886991i \(-0.347209\pi\)
0.461786 + 0.886991i \(0.347209\pi\)
\(240\) 0 0
\(241\) 12.4854 0.804254 0.402127 0.915584i \(-0.368271\pi\)
0.402127 + 0.915584i \(0.368271\pi\)
\(242\) 0 0
\(243\) −33.8258 −2.16993
\(244\) 0 0
\(245\) −19.6820 −1.25744
\(246\) 0 0
\(247\) −3.89297 −0.247704
\(248\) 0 0
\(249\) −46.6061 −2.95354
\(250\) 0 0
\(251\) −20.1642 −1.27275 −0.636376 0.771379i \(-0.719567\pi\)
−0.636376 + 0.771379i \(0.719567\pi\)
\(252\) 0 0
\(253\) 0.343259 0.0215805
\(254\) 0 0
\(255\) −40.8233 −2.55646
\(256\) 0 0
\(257\) −6.96476 −0.434450 −0.217225 0.976122i \(-0.569700\pi\)
−0.217225 + 0.976122i \(0.569700\pi\)
\(258\) 0 0
\(259\) −1.99107 −0.123719
\(260\) 0 0
\(261\) 36.5823 2.26439
\(262\) 0 0
\(263\) 16.4273 1.01295 0.506475 0.862255i \(-0.330948\pi\)
0.506475 + 0.862255i \(0.330948\pi\)
\(264\) 0 0
\(265\) 35.2334 2.16437
\(266\) 0 0
\(267\) 25.7313 1.57473
\(268\) 0 0
\(269\) 11.1581 0.680323 0.340162 0.940367i \(-0.389518\pi\)
0.340162 + 0.940367i \(0.389518\pi\)
\(270\) 0 0
\(271\) 27.0322 1.64209 0.821046 0.570862i \(-0.193391\pi\)
0.821046 + 0.570862i \(0.193391\pi\)
\(272\) 0 0
\(273\) 2.47514 0.149803
\(274\) 0 0
\(275\) −4.25940 −0.256852
\(276\) 0 0
\(277\) 10.2355 0.614990 0.307495 0.951550i \(-0.400509\pi\)
0.307495 + 0.951550i \(0.400509\pi\)
\(278\) 0 0
\(279\) −42.4023 −2.53856
\(280\) 0 0
\(281\) 6.72767 0.401339 0.200670 0.979659i \(-0.435688\pi\)
0.200670 + 0.979659i \(0.435688\pi\)
\(282\) 0 0
\(283\) 6.08609 0.361780 0.180890 0.983503i \(-0.442102\pi\)
0.180890 + 0.983503i \(0.442102\pi\)
\(284\) 0 0
\(285\) −25.2085 −1.49322
\(286\) 0 0
\(287\) 5.39551 0.318487
\(288\) 0 0
\(289\) 1.67528 0.0985458
\(290\) 0 0
\(291\) 33.9335 1.98922
\(292\) 0 0
\(293\) −13.4113 −0.783498 −0.391749 0.920072i \(-0.628130\pi\)
−0.391749 + 0.920072i \(0.628130\pi\)
\(294\) 0 0
\(295\) 36.2020 2.10776
\(296\) 0 0
\(297\) 16.9982 0.986337
\(298\) 0 0
\(299\) 0.419614 0.0242669
\(300\) 0 0
\(301\) 2.10179 0.121145
\(302\) 0 0
\(303\) 27.6284 1.58721
\(304\) 0 0
\(305\) −10.8744 −0.622669
\(306\) 0 0
\(307\) 29.6956 1.69482 0.847408 0.530943i \(-0.178162\pi\)
0.847408 + 0.530943i \(0.178162\pi\)
\(308\) 0 0
\(309\) −32.3236 −1.83882
\(310\) 0 0
\(311\) −2.85559 −0.161926 −0.0809629 0.996717i \(-0.525800\pi\)
−0.0809629 + 0.996717i \(0.525800\pi\)
\(312\) 0 0
\(313\) 6.24002 0.352707 0.176353 0.984327i \(-0.443570\pi\)
0.176353 + 0.984327i \(0.443570\pi\)
\(314\) 0 0
\(315\) 11.4103 0.642899
\(316\) 0 0
\(317\) 2.52438 0.141783 0.0708915 0.997484i \(-0.477416\pi\)
0.0708915 + 0.997484i \(0.477416\pi\)
\(318\) 0 0
\(319\) −5.88857 −0.329697
\(320\) 0 0
\(321\) −43.4034 −2.42254
\(322\) 0 0
\(323\) 11.5320 0.641659
\(324\) 0 0
\(325\) −5.20687 −0.288825
\(326\) 0 0
\(327\) −59.2204 −3.27489
\(328\) 0 0
\(329\) 0.649404 0.0358028
\(330\) 0 0
\(331\) −10.7439 −0.590538 −0.295269 0.955414i \(-0.595409\pi\)
−0.295269 + 0.955414i \(0.595409\pi\)
\(332\) 0 0
\(333\) −28.0766 −1.53859
\(334\) 0 0
\(335\) 8.41208 0.459601
\(336\) 0 0
\(337\) 19.8614 1.08192 0.540959 0.841049i \(-0.318061\pi\)
0.540959 + 0.841049i \(0.318061\pi\)
\(338\) 0 0
\(339\) 14.4041 0.782321
\(340\) 0 0
\(341\) 6.82541 0.369616
\(342\) 0 0
\(343\) −7.21527 −0.389588
\(344\) 0 0
\(345\) 2.71716 0.146287
\(346\) 0 0
\(347\) 18.4429 0.990068 0.495034 0.868874i \(-0.335156\pi\)
0.495034 + 0.868874i \(0.335156\pi\)
\(348\) 0 0
\(349\) 21.6946 1.16129 0.580643 0.814159i \(-0.302801\pi\)
0.580643 + 0.814159i \(0.302801\pi\)
\(350\) 0 0
\(351\) 20.7793 1.10912
\(352\) 0 0
\(353\) 1.41973 0.0755645 0.0377823 0.999286i \(-0.487971\pi\)
0.0377823 + 0.999286i \(0.487971\pi\)
\(354\) 0 0
\(355\) −12.9028 −0.684809
\(356\) 0 0
\(357\) −7.33203 −0.388052
\(358\) 0 0
\(359\) −0.356449 −0.0188127 −0.00940633 0.999956i \(-0.502994\pi\)
−0.00940633 + 0.999956i \(0.502994\pi\)
\(360\) 0 0
\(361\) −11.8790 −0.625208
\(362\) 0 0
\(363\) 30.9016 1.62192
\(364\) 0 0
\(365\) 3.47405 0.181840
\(366\) 0 0
\(367\) 2.71839 0.141899 0.0709495 0.997480i \(-0.477397\pi\)
0.0709495 + 0.997480i \(0.477397\pi\)
\(368\) 0 0
\(369\) 76.0834 3.96074
\(370\) 0 0
\(371\) 6.32807 0.328537
\(372\) 0 0
\(373\) −30.0894 −1.55797 −0.778986 0.627041i \(-0.784266\pi\)
−0.778986 + 0.627041i \(0.784266\pi\)
\(374\) 0 0
\(375\) 13.5165 0.697988
\(376\) 0 0
\(377\) −7.19843 −0.370738
\(378\) 0 0
\(379\) −18.6583 −0.958412 −0.479206 0.877703i \(-0.659075\pi\)
−0.479206 + 0.877703i \(0.659075\pi\)
\(380\) 0 0
\(381\) 35.1900 1.80284
\(382\) 0 0
\(383\) 12.0271 0.614556 0.307278 0.951620i \(-0.400582\pi\)
0.307278 + 0.951620i \(0.400582\pi\)
\(384\) 0 0
\(385\) −1.83669 −0.0936065
\(386\) 0 0
\(387\) 29.6379 1.50658
\(388\) 0 0
\(389\) 25.8206 1.30916 0.654578 0.755994i \(-0.272846\pi\)
0.654578 + 0.755994i \(0.272846\pi\)
\(390\) 0 0
\(391\) −1.24301 −0.0628616
\(392\) 0 0
\(393\) 41.0798 2.07220
\(394\) 0 0
\(395\) −25.8245 −1.29937
\(396\) 0 0
\(397\) 8.09867 0.406461 0.203230 0.979131i \(-0.434856\pi\)
0.203230 + 0.979131i \(0.434856\pi\)
\(398\) 0 0
\(399\) −4.52754 −0.226661
\(400\) 0 0
\(401\) 7.64427 0.381736 0.190868 0.981616i \(-0.438870\pi\)
0.190868 + 0.981616i \(0.438870\pi\)
\(402\) 0 0
\(403\) 8.34365 0.415627
\(404\) 0 0
\(405\) 69.4461 3.45080
\(406\) 0 0
\(407\) 4.51943 0.224020
\(408\) 0 0
\(409\) −2.12008 −0.104831 −0.0524157 0.998625i \(-0.516692\pi\)
−0.0524157 + 0.998625i \(0.516692\pi\)
\(410\) 0 0
\(411\) 30.1752 1.48843
\(412\) 0 0
\(413\) 6.50203 0.319944
\(414\) 0 0
\(415\) 42.2772 2.07531
\(416\) 0 0
\(417\) 59.2215 2.90009
\(418\) 0 0
\(419\) 16.3561 0.799049 0.399525 0.916722i \(-0.369175\pi\)
0.399525 + 0.916722i \(0.369175\pi\)
\(420\) 0 0
\(421\) 9.23960 0.450310 0.225155 0.974323i \(-0.427711\pi\)
0.225155 + 0.974323i \(0.427711\pi\)
\(422\) 0 0
\(423\) 9.15741 0.445248
\(424\) 0 0
\(425\) 15.4241 0.748180
\(426\) 0 0
\(427\) −1.95309 −0.0945169
\(428\) 0 0
\(429\) −5.61820 −0.271249
\(430\) 0 0
\(431\) 29.4110 1.41668 0.708339 0.705872i \(-0.249445\pi\)
0.708339 + 0.705872i \(0.249445\pi\)
\(432\) 0 0
\(433\) 20.3634 0.978602 0.489301 0.872115i \(-0.337252\pi\)
0.489301 + 0.872115i \(0.337252\pi\)
\(434\) 0 0
\(435\) −46.6125 −2.23490
\(436\) 0 0
\(437\) −0.767559 −0.0367173
\(438\) 0 0
\(439\) −19.8359 −0.946718 −0.473359 0.880870i \(-0.656959\pi\)
−0.473359 + 0.880870i \(0.656959\pi\)
\(440\) 0 0
\(441\) −49.8475 −2.37369
\(442\) 0 0
\(443\) −8.27690 −0.393247 −0.196624 0.980479i \(-0.562998\pi\)
−0.196624 + 0.980479i \(0.562998\pi\)
\(444\) 0 0
\(445\) −23.3414 −1.10649
\(446\) 0 0
\(447\) 11.4216 0.540223
\(448\) 0 0
\(449\) 34.5329 1.62971 0.814854 0.579666i \(-0.196817\pi\)
0.814854 + 0.579666i \(0.196817\pi\)
\(450\) 0 0
\(451\) −12.2470 −0.576687
\(452\) 0 0
\(453\) −7.49594 −0.352190
\(454\) 0 0
\(455\) −2.24525 −0.105259
\(456\) 0 0
\(457\) 8.26068 0.386418 0.193209 0.981158i \(-0.438110\pi\)
0.193209 + 0.981158i \(0.438110\pi\)
\(458\) 0 0
\(459\) −61.5539 −2.87309
\(460\) 0 0
\(461\) 22.0892 1.02880 0.514399 0.857551i \(-0.328015\pi\)
0.514399 + 0.857551i \(0.328015\pi\)
\(462\) 0 0
\(463\) 25.8766 1.20259 0.601293 0.799029i \(-0.294653\pi\)
0.601293 + 0.799029i \(0.294653\pi\)
\(464\) 0 0
\(465\) 54.0283 2.50550
\(466\) 0 0
\(467\) 24.6592 1.14109 0.570545 0.821266i \(-0.306732\pi\)
0.570545 + 0.821266i \(0.306732\pi\)
\(468\) 0 0
\(469\) 1.51084 0.0697643
\(470\) 0 0
\(471\) 7.59017 0.349736
\(472\) 0 0
\(473\) −4.77075 −0.219359
\(474\) 0 0
\(475\) 9.52442 0.437010
\(476\) 0 0
\(477\) 89.2337 4.08573
\(478\) 0 0
\(479\) 12.5245 0.572260 0.286130 0.958191i \(-0.407631\pi\)
0.286130 + 0.958191i \(0.407631\pi\)
\(480\) 0 0
\(481\) 5.52474 0.251906
\(482\) 0 0
\(483\) 0.488012 0.0222053
\(484\) 0 0
\(485\) −30.7817 −1.39772
\(486\) 0 0
\(487\) −4.53327 −0.205422 −0.102711 0.994711i \(-0.532752\pi\)
−0.102711 + 0.994711i \(0.532752\pi\)
\(488\) 0 0
\(489\) −20.7104 −0.936558
\(490\) 0 0
\(491\) 31.9573 1.44221 0.721106 0.692825i \(-0.243634\pi\)
0.721106 + 0.692825i \(0.243634\pi\)
\(492\) 0 0
\(493\) 21.3237 0.960369
\(494\) 0 0
\(495\) −25.8997 −1.16410
\(496\) 0 0
\(497\) −2.31739 −0.103949
\(498\) 0 0
\(499\) 14.2081 0.636043 0.318021 0.948084i \(-0.396982\pi\)
0.318021 + 0.948084i \(0.396982\pi\)
\(500\) 0 0
\(501\) −72.9201 −3.25783
\(502\) 0 0
\(503\) −26.5276 −1.18281 −0.591404 0.806375i \(-0.701426\pi\)
−0.591404 + 0.806375i \(0.701426\pi\)
\(504\) 0 0
\(505\) −25.0622 −1.11525
\(506\) 0 0
\(507\) 35.0837 1.55812
\(508\) 0 0
\(509\) −0.689637 −0.0305676 −0.0152838 0.999883i \(-0.504865\pi\)
−0.0152838 + 0.999883i \(0.504865\pi\)
\(510\) 0 0
\(511\) 0.623952 0.0276020
\(512\) 0 0
\(513\) −38.0096 −1.67817
\(514\) 0 0
\(515\) 29.3213 1.29205
\(516\) 0 0
\(517\) −1.47405 −0.0648285
\(518\) 0 0
\(519\) −33.6835 −1.47854
\(520\) 0 0
\(521\) −3.32412 −0.145632 −0.0728161 0.997345i \(-0.523199\pi\)
−0.0728161 + 0.997345i \(0.523199\pi\)
\(522\) 0 0
\(523\) 10.3850 0.454104 0.227052 0.973883i \(-0.427091\pi\)
0.227052 + 0.973883i \(0.427091\pi\)
\(524\) 0 0
\(525\) −6.05561 −0.264288
\(526\) 0 0
\(527\) −24.7161 −1.07665
\(528\) 0 0
\(529\) −22.9173 −0.996403
\(530\) 0 0
\(531\) 91.6868 3.97887
\(532\) 0 0
\(533\) −14.9712 −0.648475
\(534\) 0 0
\(535\) 39.3721 1.70220
\(536\) 0 0
\(537\) −24.1798 −1.04343
\(538\) 0 0
\(539\) 8.02384 0.345611
\(540\) 0 0
\(541\) 20.9154 0.899224 0.449612 0.893224i \(-0.351562\pi\)
0.449612 + 0.893224i \(0.351562\pi\)
\(542\) 0 0
\(543\) −60.6329 −2.60201
\(544\) 0 0
\(545\) 53.7199 2.30111
\(546\) 0 0
\(547\) −5.89179 −0.251915 −0.125957 0.992036i \(-0.540200\pi\)
−0.125957 + 0.992036i \(0.540200\pi\)
\(548\) 0 0
\(549\) −27.5411 −1.17542
\(550\) 0 0
\(551\) 13.1674 0.560950
\(552\) 0 0
\(553\) −4.63818 −0.197236
\(554\) 0 0
\(555\) 35.7747 1.51855
\(556\) 0 0
\(557\) −31.9487 −1.35371 −0.676855 0.736116i \(-0.736658\pi\)
−0.676855 + 0.736116i \(0.736658\pi\)
\(558\) 0 0
\(559\) −5.83196 −0.246665
\(560\) 0 0
\(561\) 16.6426 0.702651
\(562\) 0 0
\(563\) 9.73827 0.410419 0.205210 0.978718i \(-0.434212\pi\)
0.205210 + 0.978718i \(0.434212\pi\)
\(564\) 0 0
\(565\) −13.0662 −0.549699
\(566\) 0 0
\(567\) 12.4728 0.523808
\(568\) 0 0
\(569\) 26.7550 1.12163 0.560813 0.827942i \(-0.310489\pi\)
0.560813 + 0.827942i \(0.310489\pi\)
\(570\) 0 0
\(571\) 13.4914 0.564599 0.282299 0.959326i \(-0.408903\pi\)
0.282299 + 0.959326i \(0.408903\pi\)
\(572\) 0 0
\(573\) 32.7836 1.36955
\(574\) 0 0
\(575\) −1.02661 −0.0428128
\(576\) 0 0
\(577\) −9.05659 −0.377031 −0.188515 0.982070i \(-0.560368\pi\)
−0.188515 + 0.982070i \(0.560368\pi\)
\(578\) 0 0
\(579\) −27.7225 −1.15211
\(580\) 0 0
\(581\) 7.59316 0.315017
\(582\) 0 0
\(583\) −14.3637 −0.594886
\(584\) 0 0
\(585\) −31.6608 −1.30901
\(586\) 0 0
\(587\) 2.57333 0.106212 0.0531062 0.998589i \(-0.483088\pi\)
0.0531062 + 0.998589i \(0.483088\pi\)
\(588\) 0 0
\(589\) −15.2622 −0.628870
\(590\) 0 0
\(591\) −57.9647 −2.38435
\(592\) 0 0
\(593\) 7.58695 0.311559 0.155779 0.987792i \(-0.450211\pi\)
0.155779 + 0.987792i \(0.450211\pi\)
\(594\) 0 0
\(595\) 6.65102 0.272665
\(596\) 0 0
\(597\) 13.7072 0.560998
\(598\) 0 0
\(599\) −24.5537 −1.00324 −0.501619 0.865089i \(-0.667262\pi\)
−0.501619 + 0.865089i \(0.667262\pi\)
\(600\) 0 0
\(601\) 38.8086 1.58304 0.791518 0.611145i \(-0.209291\pi\)
0.791518 + 0.611145i \(0.209291\pi\)
\(602\) 0 0
\(603\) 21.3048 0.867598
\(604\) 0 0
\(605\) −28.0314 −1.13964
\(606\) 0 0
\(607\) 15.1125 0.613395 0.306698 0.951807i \(-0.400776\pi\)
0.306698 + 0.951807i \(0.400776\pi\)
\(608\) 0 0
\(609\) −8.37180 −0.339242
\(610\) 0 0
\(611\) −1.80193 −0.0728985
\(612\) 0 0
\(613\) −45.8408 −1.85149 −0.925746 0.378147i \(-0.876562\pi\)
−0.925746 + 0.378147i \(0.876562\pi\)
\(614\) 0 0
\(615\) −96.9441 −3.90916
\(616\) 0 0
\(617\) −27.0879 −1.09052 −0.545259 0.838268i \(-0.683569\pi\)
−0.545259 + 0.838268i \(0.683569\pi\)
\(618\) 0 0
\(619\) 16.4472 0.661069 0.330535 0.943794i \(-0.392771\pi\)
0.330535 + 0.943794i \(0.392771\pi\)
\(620\) 0 0
\(621\) 4.09696 0.164405
\(622\) 0 0
\(623\) −4.19220 −0.167957
\(624\) 0 0
\(625\) −30.1069 −1.20428
\(626\) 0 0
\(627\) 10.2768 0.410417
\(628\) 0 0
\(629\) −16.3657 −0.652544
\(630\) 0 0
\(631\) −21.0499 −0.837984 −0.418992 0.907990i \(-0.637617\pi\)
−0.418992 + 0.907990i \(0.637617\pi\)
\(632\) 0 0
\(633\) 48.5340 1.92906
\(634\) 0 0
\(635\) −31.9214 −1.26676
\(636\) 0 0
\(637\) 9.80867 0.388634
\(638\) 0 0
\(639\) −32.6781 −1.29273
\(640\) 0 0
\(641\) −45.6273 −1.80217 −0.901086 0.433641i \(-0.857229\pi\)
−0.901086 + 0.433641i \(0.857229\pi\)
\(642\) 0 0
\(643\) −8.74422 −0.344838 −0.172419 0.985024i \(-0.555158\pi\)
−0.172419 + 0.985024i \(0.555158\pi\)
\(644\) 0 0
\(645\) −37.7641 −1.48696
\(646\) 0 0
\(647\) 19.6773 0.773596 0.386798 0.922165i \(-0.373581\pi\)
0.386798 + 0.922165i \(0.373581\pi\)
\(648\) 0 0
\(649\) −14.7586 −0.579326
\(650\) 0 0
\(651\) 9.70370 0.380318
\(652\) 0 0
\(653\) 38.8950 1.52208 0.761039 0.648706i \(-0.224689\pi\)
0.761039 + 0.648706i \(0.224689\pi\)
\(654\) 0 0
\(655\) −37.2642 −1.45603
\(656\) 0 0
\(657\) 8.79851 0.343263
\(658\) 0 0
\(659\) −22.0282 −0.858095 −0.429048 0.903282i \(-0.641151\pi\)
−0.429048 + 0.903282i \(0.641151\pi\)
\(660\) 0 0
\(661\) −37.6441 −1.46419 −0.732093 0.681205i \(-0.761456\pi\)
−0.732093 + 0.681205i \(0.761456\pi\)
\(662\) 0 0
\(663\) 20.3446 0.790118
\(664\) 0 0
\(665\) 4.10702 0.159263
\(666\) 0 0
\(667\) −1.41928 −0.0549548
\(668\) 0 0
\(669\) 32.5207 1.25732
\(670\) 0 0
\(671\) 4.43323 0.171143
\(672\) 0 0
\(673\) 42.9416 1.65528 0.827638 0.561262i \(-0.189684\pi\)
0.827638 + 0.561262i \(0.189684\pi\)
\(674\) 0 0
\(675\) −50.8380 −1.95676
\(676\) 0 0
\(677\) 37.4409 1.43897 0.719486 0.694507i \(-0.244377\pi\)
0.719486 + 0.694507i \(0.244377\pi\)
\(678\) 0 0
\(679\) −5.52852 −0.212165
\(680\) 0 0
\(681\) 38.9275 1.49171
\(682\) 0 0
\(683\) 1.08390 0.0414743 0.0207372 0.999785i \(-0.493399\pi\)
0.0207372 + 0.999785i \(0.493399\pi\)
\(684\) 0 0
\(685\) −27.3725 −1.04585
\(686\) 0 0
\(687\) 30.5701 1.16632
\(688\) 0 0
\(689\) −17.5588 −0.668938
\(690\) 0 0
\(691\) 22.2008 0.844559 0.422279 0.906466i \(-0.361230\pi\)
0.422279 + 0.906466i \(0.361230\pi\)
\(692\) 0 0
\(693\) −4.65169 −0.176703
\(694\) 0 0
\(695\) −53.7209 −2.03775
\(696\) 0 0
\(697\) 44.3486 1.67982
\(698\) 0 0
\(699\) −6.44608 −0.243813
\(700\) 0 0
\(701\) 1.43258 0.0541078 0.0270539 0.999634i \(-0.491387\pi\)
0.0270539 + 0.999634i \(0.491387\pi\)
\(702\) 0 0
\(703\) −10.1059 −0.381150
\(704\) 0 0
\(705\) −11.6682 −0.439450
\(706\) 0 0
\(707\) −4.50127 −0.169288
\(708\) 0 0
\(709\) −35.2484 −1.32378 −0.661891 0.749600i \(-0.730246\pi\)
−0.661891 + 0.749600i \(0.730246\pi\)
\(710\) 0 0
\(711\) −65.4042 −2.45285
\(712\) 0 0
\(713\) 1.64508 0.0616087
\(714\) 0 0
\(715\) 5.09637 0.190593
\(716\) 0 0
\(717\) −46.0761 −1.72074
\(718\) 0 0
\(719\) 29.9828 1.11817 0.559086 0.829110i \(-0.311152\pi\)
0.559086 + 0.829110i \(0.311152\pi\)
\(720\) 0 0
\(721\) 5.26622 0.196124
\(722\) 0 0
\(723\) −40.2909 −1.49844
\(724\) 0 0
\(725\) 17.6114 0.654073
\(726\) 0 0
\(727\) −18.2631 −0.677342 −0.338671 0.940905i \(-0.609977\pi\)
−0.338671 + 0.940905i \(0.609977\pi\)
\(728\) 0 0
\(729\) 37.9871 1.40693
\(730\) 0 0
\(731\) 17.2758 0.638968
\(732\) 0 0
\(733\) −32.3017 −1.19309 −0.596545 0.802579i \(-0.703460\pi\)
−0.596545 + 0.802579i \(0.703460\pi\)
\(734\) 0 0
\(735\) 63.5148 2.34278
\(736\) 0 0
\(737\) −3.42938 −0.126323
\(738\) 0 0
\(739\) 28.5787 1.05128 0.525642 0.850706i \(-0.323825\pi\)
0.525642 + 0.850706i \(0.323825\pi\)
\(740\) 0 0
\(741\) 12.5628 0.461506
\(742\) 0 0
\(743\) 30.2706 1.11052 0.555260 0.831677i \(-0.312619\pi\)
0.555260 + 0.831677i \(0.312619\pi\)
\(744\) 0 0
\(745\) −10.3607 −0.379588
\(746\) 0 0
\(747\) 107.073 3.91760
\(748\) 0 0
\(749\) 7.07138 0.258383
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 65.0708 2.37131
\(754\) 0 0
\(755\) 6.79970 0.247466
\(756\) 0 0
\(757\) 17.5444 0.637660 0.318830 0.947812i \(-0.396710\pi\)
0.318830 + 0.947812i \(0.396710\pi\)
\(758\) 0 0
\(759\) −1.10771 −0.0402075
\(760\) 0 0
\(761\) −5.01959 −0.181960 −0.0909800 0.995853i \(-0.529000\pi\)
−0.0909800 + 0.995853i \(0.529000\pi\)
\(762\) 0 0
\(763\) 9.64830 0.349292
\(764\) 0 0
\(765\) 93.7877 3.39090
\(766\) 0 0
\(767\) −18.0415 −0.651442
\(768\) 0 0
\(769\) −30.0687 −1.08431 −0.542153 0.840280i \(-0.682391\pi\)
−0.542153 + 0.840280i \(0.682391\pi\)
\(770\) 0 0
\(771\) 22.4756 0.809439
\(772\) 0 0
\(773\) 19.7999 0.712154 0.356077 0.934457i \(-0.384114\pi\)
0.356077 + 0.934457i \(0.384114\pi\)
\(774\) 0 0
\(775\) −20.4133 −0.733268
\(776\) 0 0
\(777\) 6.42529 0.230506
\(778\) 0 0
\(779\) 27.3854 0.981183
\(780\) 0 0
\(781\) 5.26013 0.188222
\(782\) 0 0
\(783\) −70.2829 −2.51171
\(784\) 0 0
\(785\) −6.88518 −0.245743
\(786\) 0 0
\(787\) −29.1549 −1.03926 −0.519630 0.854391i \(-0.673930\pi\)
−0.519630 + 0.854391i \(0.673930\pi\)
\(788\) 0 0
\(789\) −53.0116 −1.88726
\(790\) 0 0
\(791\) −2.34674 −0.0834405
\(792\) 0 0
\(793\) 5.41936 0.192447
\(794\) 0 0
\(795\) −113.700 −4.03252
\(796\) 0 0
\(797\) 2.81614 0.0997529 0.0498765 0.998755i \(-0.484117\pi\)
0.0498765 + 0.998755i \(0.484117\pi\)
\(798\) 0 0
\(799\) 5.33781 0.188838
\(800\) 0 0
\(801\) −59.1153 −2.08874
\(802\) 0 0
\(803\) −1.41628 −0.0499793
\(804\) 0 0
\(805\) −0.442685 −0.0156026
\(806\) 0 0
\(807\) −36.0078 −1.26754
\(808\) 0 0
\(809\) −40.6062 −1.42764 −0.713819 0.700331i \(-0.753036\pi\)
−0.713819 + 0.700331i \(0.753036\pi\)
\(810\) 0 0
\(811\) −25.4202 −0.892623 −0.446312 0.894878i \(-0.647263\pi\)
−0.446312 + 0.894878i \(0.647263\pi\)
\(812\) 0 0
\(813\) −87.2343 −3.05944
\(814\) 0 0
\(815\) 18.7868 0.658073
\(816\) 0 0
\(817\) 10.6678 0.373220
\(818\) 0 0
\(819\) −5.68641 −0.198699
\(820\) 0 0
\(821\) 25.6224 0.894227 0.447113 0.894477i \(-0.352452\pi\)
0.447113 + 0.894477i \(0.352452\pi\)
\(822\) 0 0
\(823\) −7.71419 −0.268900 −0.134450 0.990920i \(-0.542927\pi\)
−0.134450 + 0.990920i \(0.542927\pi\)
\(824\) 0 0
\(825\) 13.7453 0.478550
\(826\) 0 0
\(827\) −13.4859 −0.468951 −0.234475 0.972122i \(-0.575337\pi\)
−0.234475 + 0.972122i \(0.575337\pi\)
\(828\) 0 0
\(829\) −8.19326 −0.284564 −0.142282 0.989826i \(-0.545444\pi\)
−0.142282 + 0.989826i \(0.545444\pi\)
\(830\) 0 0
\(831\) −33.0304 −1.14581
\(832\) 0 0
\(833\) −29.0559 −1.00673
\(834\) 0 0
\(835\) 66.1472 2.28912
\(836\) 0 0
\(837\) 81.4645 2.81582
\(838\) 0 0
\(839\) −29.2073 −1.00835 −0.504175 0.863602i \(-0.668203\pi\)
−0.504175 + 0.863602i \(0.668203\pi\)
\(840\) 0 0
\(841\) −4.65240 −0.160428
\(842\) 0 0
\(843\) −21.7105 −0.747750
\(844\) 0 0
\(845\) −31.8251 −1.09482
\(846\) 0 0
\(847\) −5.03456 −0.172989
\(848\) 0 0
\(849\) −19.6401 −0.674047
\(850\) 0 0
\(851\) 1.08929 0.0373402
\(852\) 0 0
\(853\) −45.3761 −1.55365 −0.776825 0.629717i \(-0.783171\pi\)
−0.776825 + 0.629717i \(0.783171\pi\)
\(854\) 0 0
\(855\) 57.9141 1.98062
\(856\) 0 0
\(857\) −1.17185 −0.0400296 −0.0200148 0.999800i \(-0.506371\pi\)
−0.0200148 + 0.999800i \(0.506371\pi\)
\(858\) 0 0
\(859\) 43.4863 1.48373 0.741867 0.670547i \(-0.233940\pi\)
0.741867 + 0.670547i \(0.233940\pi\)
\(860\) 0 0
\(861\) −17.4116 −0.593384
\(862\) 0 0
\(863\) −14.6408 −0.498378 −0.249189 0.968455i \(-0.580164\pi\)
−0.249189 + 0.968455i \(0.580164\pi\)
\(864\) 0 0
\(865\) 30.5549 1.03890
\(866\) 0 0
\(867\) −5.40620 −0.183604
\(868\) 0 0
\(869\) 10.5280 0.357137
\(870\) 0 0
\(871\) −4.19222 −0.142048
\(872\) 0 0
\(873\) −77.9590 −2.63851
\(874\) 0 0
\(875\) −2.20213 −0.0744457
\(876\) 0 0
\(877\) 21.7239 0.733562 0.366781 0.930307i \(-0.380460\pi\)
0.366781 + 0.930307i \(0.380460\pi\)
\(878\) 0 0
\(879\) 43.2790 1.45976
\(880\) 0 0
\(881\) −50.2337 −1.69242 −0.846209 0.532852i \(-0.821120\pi\)
−0.846209 + 0.532852i \(0.821120\pi\)
\(882\) 0 0
\(883\) 25.5432 0.859598 0.429799 0.902925i \(-0.358584\pi\)
0.429799 + 0.902925i \(0.358584\pi\)
\(884\) 0 0
\(885\) −116.826 −3.92705
\(886\) 0 0
\(887\) 41.6041 1.39693 0.698465 0.715644i \(-0.253867\pi\)
0.698465 + 0.715644i \(0.253867\pi\)
\(888\) 0 0
\(889\) −5.73322 −0.192286
\(890\) 0 0
\(891\) −28.3113 −0.948465
\(892\) 0 0
\(893\) 3.29611 0.110300
\(894\) 0 0
\(895\) 21.9339 0.733170
\(896\) 0 0
\(897\) −1.35411 −0.0452126
\(898\) 0 0
\(899\) −28.2211 −0.941228
\(900\) 0 0
\(901\) 52.0139 1.73283
\(902\) 0 0
\(903\) −6.78259 −0.225710
\(904\) 0 0
\(905\) 55.0012 1.82830
\(906\) 0 0
\(907\) 50.3438 1.67164 0.835819 0.549006i \(-0.184993\pi\)
0.835819 + 0.549006i \(0.184993\pi\)
\(908\) 0 0
\(909\) −63.4735 −2.10528
\(910\) 0 0
\(911\) 52.2663 1.73166 0.865830 0.500338i \(-0.166791\pi\)
0.865830 + 0.500338i \(0.166791\pi\)
\(912\) 0 0
\(913\) −17.2353 −0.570405
\(914\) 0 0
\(915\) 35.0924 1.16012
\(916\) 0 0
\(917\) −6.69280 −0.221016
\(918\) 0 0
\(919\) 5.31746 0.175407 0.0877034 0.996147i \(-0.472047\pi\)
0.0877034 + 0.996147i \(0.472047\pi\)
\(920\) 0 0
\(921\) −95.8290 −3.15767
\(922\) 0 0
\(923\) 6.43019 0.211652
\(924\) 0 0
\(925\) −13.5166 −0.444424
\(926\) 0 0
\(927\) 74.2603 2.43903
\(928\) 0 0
\(929\) −54.8514 −1.79961 −0.899807 0.436287i \(-0.856293\pi\)
−0.899807 + 0.436287i \(0.856293\pi\)
\(930\) 0 0
\(931\) −17.9421 −0.588027
\(932\) 0 0
\(933\) 9.21513 0.301690
\(934\) 0 0
\(935\) −15.0968 −0.493718
\(936\) 0 0
\(937\) 36.6600 1.19763 0.598815 0.800887i \(-0.295638\pi\)
0.598815 + 0.800887i \(0.295638\pi\)
\(938\) 0 0
\(939\) −20.1368 −0.657141
\(940\) 0 0
\(941\) 34.1635 1.11370 0.556849 0.830614i \(-0.312010\pi\)
0.556849 + 0.830614i \(0.312010\pi\)
\(942\) 0 0
\(943\) −2.95180 −0.0961239
\(944\) 0 0
\(945\) −21.9218 −0.713117
\(946\) 0 0
\(947\) 13.9428 0.453081 0.226541 0.974002i \(-0.427258\pi\)
0.226541 + 0.974002i \(0.427258\pi\)
\(948\) 0 0
\(949\) −1.73131 −0.0562008
\(950\) 0 0
\(951\) −8.14628 −0.264161
\(952\) 0 0
\(953\) −56.1061 −1.81745 −0.908727 0.417391i \(-0.862945\pi\)
−0.908727 + 0.417391i \(0.862945\pi\)
\(954\) 0 0
\(955\) −29.7386 −0.962318
\(956\) 0 0
\(957\) 19.0027 0.614270
\(958\) 0 0
\(959\) −4.91621 −0.158753
\(960\) 0 0
\(961\) 1.71095 0.0551919
\(962\) 0 0
\(963\) 99.7153 3.21328
\(964\) 0 0
\(965\) 25.1476 0.809530
\(966\) 0 0
\(967\) −48.0536 −1.54530 −0.772651 0.634832i \(-0.781070\pi\)
−0.772651 + 0.634832i \(0.781070\pi\)
\(968\) 0 0
\(969\) −37.2144 −1.19550
\(970\) 0 0
\(971\) 11.9474 0.383409 0.191705 0.981453i \(-0.438598\pi\)
0.191705 + 0.981453i \(0.438598\pi\)
\(972\) 0 0
\(973\) −9.64849 −0.309316
\(974\) 0 0
\(975\) 16.8028 0.538121
\(976\) 0 0
\(977\) −36.7336 −1.17521 −0.587606 0.809147i \(-0.699930\pi\)
−0.587606 + 0.809147i \(0.699930\pi\)
\(978\) 0 0
\(979\) 9.51566 0.304122
\(980\) 0 0
\(981\) 136.053 4.34384
\(982\) 0 0
\(983\) 6.39913 0.204100 0.102050 0.994779i \(-0.467460\pi\)
0.102050 + 0.994779i \(0.467460\pi\)
\(984\) 0 0
\(985\) 52.5808 1.67536
\(986\) 0 0
\(987\) −2.09566 −0.0667055
\(988\) 0 0
\(989\) −1.14986 −0.0365634
\(990\) 0 0
\(991\) 8.26235 0.262462 0.131231 0.991352i \(-0.458107\pi\)
0.131231 + 0.991352i \(0.458107\pi\)
\(992\) 0 0
\(993\) 34.6711 1.10025
\(994\) 0 0
\(995\) −12.4340 −0.394185
\(996\) 0 0
\(997\) 4.66972 0.147892 0.0739458 0.997262i \(-0.476441\pi\)
0.0739458 + 0.997262i \(0.476441\pi\)
\(998\) 0 0
\(999\) 53.9416 1.70664
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 \(a_p\))