Properties

Label 6008.2.a.e.1.11
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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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 1.11
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24563 q^{3} +3.86835 q^{5} -4.12735 q^{7} +2.04285 q^{9} +O(q^{10})\) \(q-2.24563 q^{3} +3.86835 q^{5} -4.12735 q^{7} +2.04285 q^{9} -3.58555 q^{11} -2.00933 q^{13} -8.68688 q^{15} -1.02183 q^{17} +2.57219 q^{19} +9.26850 q^{21} -6.19989 q^{23} +9.96413 q^{25} +2.14940 q^{27} -4.21182 q^{29} -3.01713 q^{31} +8.05182 q^{33} -15.9660 q^{35} -3.89792 q^{37} +4.51221 q^{39} -5.80696 q^{41} +0.0570193 q^{43} +7.90247 q^{45} +1.46241 q^{47} +10.0350 q^{49} +2.29465 q^{51} +1.31159 q^{53} -13.8702 q^{55} -5.77618 q^{57} -7.55313 q^{59} -0.242841 q^{61} -8.43157 q^{63} -7.77278 q^{65} +10.5525 q^{67} +13.9227 q^{69} +5.81735 q^{71} +15.2698 q^{73} -22.3757 q^{75} +14.7988 q^{77} +11.6962 q^{79} -10.9553 q^{81} -3.56219 q^{83} -3.95279 q^{85} +9.45819 q^{87} -15.0875 q^{89} +8.29320 q^{91} +6.77535 q^{93} +9.95013 q^{95} +10.9573 q^{97} -7.32475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.24563 −1.29651 −0.648257 0.761421i \(-0.724502\pi\)
−0.648257 + 0.761421i \(0.724502\pi\)
\(4\) 0 0
\(5\) 3.86835 1.72998 0.864989 0.501790i \(-0.167325\pi\)
0.864989 + 0.501790i \(0.167325\pi\)
\(6\) 0 0
\(7\) −4.12735 −1.55999 −0.779996 0.625784i \(-0.784779\pi\)
−0.779996 + 0.625784i \(0.784779\pi\)
\(8\) 0 0
\(9\) 2.04285 0.680951
\(10\) 0 0
\(11\) −3.58555 −1.08108 −0.540542 0.841317i \(-0.681781\pi\)
−0.540542 + 0.841317i \(0.681781\pi\)
\(12\) 0 0
\(13\) −2.00933 −0.557287 −0.278644 0.960395i \(-0.589885\pi\)
−0.278644 + 0.960395i \(0.589885\pi\)
\(14\) 0 0
\(15\) −8.68688 −2.24294
\(16\) 0 0
\(17\) −1.02183 −0.247830 −0.123915 0.992293i \(-0.539545\pi\)
−0.123915 + 0.992293i \(0.539545\pi\)
\(18\) 0 0
\(19\) 2.57219 0.590101 0.295050 0.955482i \(-0.404664\pi\)
0.295050 + 0.955482i \(0.404664\pi\)
\(20\) 0 0
\(21\) 9.26850 2.02255
\(22\) 0 0
\(23\) −6.19989 −1.29277 −0.646383 0.763013i \(-0.723719\pi\)
−0.646383 + 0.763013i \(0.723719\pi\)
\(24\) 0 0
\(25\) 9.96413 1.99283
\(26\) 0 0
\(27\) 2.14940 0.413652
\(28\) 0 0
\(29\) −4.21182 −0.782116 −0.391058 0.920366i \(-0.627891\pi\)
−0.391058 + 0.920366i \(0.627891\pi\)
\(30\) 0 0
\(31\) −3.01713 −0.541892 −0.270946 0.962595i \(-0.587336\pi\)
−0.270946 + 0.962595i \(0.587336\pi\)
\(32\) 0 0
\(33\) 8.05182 1.40164
\(34\) 0 0
\(35\) −15.9660 −2.69875
\(36\) 0 0
\(37\) −3.89792 −0.640813 −0.320407 0.947280i \(-0.603820\pi\)
−0.320407 + 0.947280i \(0.603820\pi\)
\(38\) 0 0
\(39\) 4.51221 0.722531
\(40\) 0 0
\(41\) −5.80696 −0.906894 −0.453447 0.891283i \(-0.649806\pi\)
−0.453447 + 0.891283i \(0.649806\pi\)
\(42\) 0 0
\(43\) 0.0570193 0.00869537 0.00434768 0.999991i \(-0.498616\pi\)
0.00434768 + 0.999991i \(0.498616\pi\)
\(44\) 0 0
\(45\) 7.90247 1.17803
\(46\) 0 0
\(47\) 1.46241 0.213314 0.106657 0.994296i \(-0.465985\pi\)
0.106657 + 0.994296i \(0.465985\pi\)
\(48\) 0 0
\(49\) 10.0350 1.43358
\(50\) 0 0
\(51\) 2.29465 0.321315
\(52\) 0 0
\(53\) 1.31159 0.180160 0.0900802 0.995935i \(-0.471288\pi\)
0.0900802 + 0.995935i \(0.471288\pi\)
\(54\) 0 0
\(55\) −13.8702 −1.87025
\(56\) 0 0
\(57\) −5.77618 −0.765074
\(58\) 0 0
\(59\) −7.55313 −0.983333 −0.491667 0.870784i \(-0.663612\pi\)
−0.491667 + 0.870784i \(0.663612\pi\)
\(60\) 0 0
\(61\) −0.242841 −0.0310927 −0.0155463 0.999879i \(-0.504949\pi\)
−0.0155463 + 0.999879i \(0.504949\pi\)
\(62\) 0 0
\(63\) −8.43157 −1.06228
\(64\) 0 0
\(65\) −7.77278 −0.964095
\(66\) 0 0
\(67\) 10.5525 1.28920 0.644598 0.764522i \(-0.277025\pi\)
0.644598 + 0.764522i \(0.277025\pi\)
\(68\) 0 0
\(69\) 13.9227 1.67609
\(70\) 0 0
\(71\) 5.81735 0.690392 0.345196 0.938531i \(-0.387812\pi\)
0.345196 + 0.938531i \(0.387812\pi\)
\(72\) 0 0
\(73\) 15.2698 1.78719 0.893597 0.448869i \(-0.148173\pi\)
0.893597 + 0.448869i \(0.148173\pi\)
\(74\) 0 0
\(75\) −22.3757 −2.58373
\(76\) 0 0
\(77\) 14.7988 1.68648
\(78\) 0 0
\(79\) 11.6962 1.31593 0.657965 0.753048i \(-0.271417\pi\)
0.657965 + 0.753048i \(0.271417\pi\)
\(80\) 0 0
\(81\) −10.9553 −1.21726
\(82\) 0 0
\(83\) −3.56219 −0.391001 −0.195500 0.980704i \(-0.562633\pi\)
−0.195500 + 0.980704i \(0.562633\pi\)
\(84\) 0 0
\(85\) −3.95279 −0.428741
\(86\) 0 0
\(87\) 9.45819 1.01402
\(88\) 0 0
\(89\) −15.0875 −1.59927 −0.799634 0.600488i \(-0.794973\pi\)
−0.799634 + 0.600488i \(0.794973\pi\)
\(90\) 0 0
\(91\) 8.29320 0.869364
\(92\) 0 0
\(93\) 6.77535 0.702571
\(94\) 0 0
\(95\) 9.95013 1.02086
\(96\) 0 0
\(97\) 10.9573 1.11255 0.556275 0.830998i \(-0.312230\pi\)
0.556275 + 0.830998i \(0.312230\pi\)
\(98\) 0 0
\(99\) −7.32475 −0.736165
\(100\) 0 0
\(101\) 2.94428 0.292966 0.146483 0.989213i \(-0.453205\pi\)
0.146483 + 0.989213i \(0.453205\pi\)
\(102\) 0 0
\(103\) −0.250675 −0.0246997 −0.0123499 0.999924i \(-0.503931\pi\)
−0.0123499 + 0.999924i \(0.503931\pi\)
\(104\) 0 0
\(105\) 35.8538 3.49897
\(106\) 0 0
\(107\) −18.9718 −1.83407 −0.917036 0.398803i \(-0.869426\pi\)
−0.917036 + 0.398803i \(0.869426\pi\)
\(108\) 0 0
\(109\) 0.387808 0.0371452 0.0185726 0.999828i \(-0.494088\pi\)
0.0185726 + 0.999828i \(0.494088\pi\)
\(110\) 0 0
\(111\) 8.75328 0.830824
\(112\) 0 0
\(113\) 4.86584 0.457740 0.228870 0.973457i \(-0.426497\pi\)
0.228870 + 0.973457i \(0.426497\pi\)
\(114\) 0 0
\(115\) −23.9833 −2.23646
\(116\) 0 0
\(117\) −4.10476 −0.379485
\(118\) 0 0
\(119\) 4.21745 0.386613
\(120\) 0 0
\(121\) 1.85617 0.168742
\(122\) 0 0
\(123\) 13.0403 1.17580
\(124\) 0 0
\(125\) 19.2030 1.71757
\(126\) 0 0
\(127\) 17.6795 1.56880 0.784402 0.620253i \(-0.212970\pi\)
0.784402 + 0.620253i \(0.212970\pi\)
\(128\) 0 0
\(129\) −0.128044 −0.0112737
\(130\) 0 0
\(131\) 7.53080 0.657969 0.328985 0.944335i \(-0.393294\pi\)
0.328985 + 0.944335i \(0.393294\pi\)
\(132\) 0 0
\(133\) −10.6163 −0.920553
\(134\) 0 0
\(135\) 8.31463 0.715609
\(136\) 0 0
\(137\) 1.03680 0.0885796 0.0442898 0.999019i \(-0.485898\pi\)
0.0442898 + 0.999019i \(0.485898\pi\)
\(138\) 0 0
\(139\) −0.219182 −0.0185907 −0.00929537 0.999957i \(-0.502959\pi\)
−0.00929537 + 0.999957i \(0.502959\pi\)
\(140\) 0 0
\(141\) −3.28402 −0.276564
\(142\) 0 0
\(143\) 7.20454 0.602474
\(144\) 0 0
\(145\) −16.2928 −1.35304
\(146\) 0 0
\(147\) −22.5350 −1.85865
\(148\) 0 0
\(149\) −20.6938 −1.69530 −0.847651 0.530554i \(-0.821984\pi\)
−0.847651 + 0.530554i \(0.821984\pi\)
\(150\) 0 0
\(151\) 1.09109 0.0887919 0.0443959 0.999014i \(-0.485864\pi\)
0.0443959 + 0.999014i \(0.485864\pi\)
\(152\) 0 0
\(153\) −2.08745 −0.168760
\(154\) 0 0
\(155\) −11.6713 −0.937461
\(156\) 0 0
\(157\) 19.3894 1.54744 0.773720 0.633528i \(-0.218394\pi\)
0.773720 + 0.633528i \(0.218394\pi\)
\(158\) 0 0
\(159\) −2.94534 −0.233581
\(160\) 0 0
\(161\) 25.5891 2.01671
\(162\) 0 0
\(163\) 8.33118 0.652548 0.326274 0.945275i \(-0.394207\pi\)
0.326274 + 0.945275i \(0.394207\pi\)
\(164\) 0 0
\(165\) 31.1472 2.42481
\(166\) 0 0
\(167\) 8.82303 0.682746 0.341373 0.939928i \(-0.389108\pi\)
0.341373 + 0.939928i \(0.389108\pi\)
\(168\) 0 0
\(169\) −8.96260 −0.689431
\(170\) 0 0
\(171\) 5.25460 0.401829
\(172\) 0 0
\(173\) 16.0022 1.21663 0.608314 0.793696i \(-0.291846\pi\)
0.608314 + 0.793696i \(0.291846\pi\)
\(174\) 0 0
\(175\) −41.1255 −3.10879
\(176\) 0 0
\(177\) 16.9615 1.27491
\(178\) 0 0
\(179\) 13.2053 0.987009 0.493505 0.869743i \(-0.335716\pi\)
0.493505 + 0.869743i \(0.335716\pi\)
\(180\) 0 0
\(181\) 9.72832 0.723101 0.361550 0.932353i \(-0.382248\pi\)
0.361550 + 0.932353i \(0.382248\pi\)
\(182\) 0 0
\(183\) 0.545332 0.0403121
\(184\) 0 0
\(185\) −15.0785 −1.10859
\(186\) 0 0
\(187\) 3.66382 0.267925
\(188\) 0 0
\(189\) −8.87133 −0.645294
\(190\) 0 0
\(191\) −5.04712 −0.365196 −0.182598 0.983188i \(-0.558451\pi\)
−0.182598 + 0.983188i \(0.558451\pi\)
\(192\) 0 0
\(193\) −1.49467 −0.107589 −0.0537943 0.998552i \(-0.517132\pi\)
−0.0537943 + 0.998552i \(0.517132\pi\)
\(194\) 0 0
\(195\) 17.4548 1.24996
\(196\) 0 0
\(197\) 10.7990 0.769400 0.384700 0.923042i \(-0.374305\pi\)
0.384700 + 0.923042i \(0.374305\pi\)
\(198\) 0 0
\(199\) −5.16057 −0.365823 −0.182911 0.983129i \(-0.558552\pi\)
−0.182911 + 0.983129i \(0.558552\pi\)
\(200\) 0 0
\(201\) −23.6971 −1.67146
\(202\) 0 0
\(203\) 17.3837 1.22009
\(204\) 0 0
\(205\) −22.4633 −1.56891
\(206\) 0 0
\(207\) −12.6655 −0.880310
\(208\) 0 0
\(209\) −9.22271 −0.637948
\(210\) 0 0
\(211\) −21.2776 −1.46481 −0.732407 0.680868i \(-0.761603\pi\)
−0.732407 + 0.680868i \(0.761603\pi\)
\(212\) 0 0
\(213\) −13.0636 −0.895104
\(214\) 0 0
\(215\) 0.220571 0.0150428
\(216\) 0 0
\(217\) 12.4527 0.845347
\(218\) 0 0
\(219\) −34.2903 −2.31712
\(220\) 0 0
\(221\) 2.05319 0.138113
\(222\) 0 0
\(223\) 7.27161 0.486943 0.243472 0.969908i \(-0.421714\pi\)
0.243472 + 0.969908i \(0.421714\pi\)
\(224\) 0 0
\(225\) 20.3552 1.35702
\(226\) 0 0
\(227\) −0.742723 −0.0492963 −0.0246481 0.999696i \(-0.507847\pi\)
−0.0246481 + 0.999696i \(0.507847\pi\)
\(228\) 0 0
\(229\) −9.08421 −0.600301 −0.300151 0.953892i \(-0.597037\pi\)
−0.300151 + 0.953892i \(0.597037\pi\)
\(230\) 0 0
\(231\) −33.2327 −2.18655
\(232\) 0 0
\(233\) 18.0901 1.18512 0.592560 0.805526i \(-0.298117\pi\)
0.592560 + 0.805526i \(0.298117\pi\)
\(234\) 0 0
\(235\) 5.65709 0.369028
\(236\) 0 0
\(237\) −26.2654 −1.70612
\(238\) 0 0
\(239\) −2.08622 −0.134946 −0.0674730 0.997721i \(-0.521494\pi\)
−0.0674730 + 0.997721i \(0.521494\pi\)
\(240\) 0 0
\(241\) −3.63280 −0.234009 −0.117004 0.993131i \(-0.537329\pi\)
−0.117004 + 0.993131i \(0.537329\pi\)
\(242\) 0 0
\(243\) 18.1534 1.16454
\(244\) 0 0
\(245\) 38.8190 2.48006
\(246\) 0 0
\(247\) −5.16837 −0.328856
\(248\) 0 0
\(249\) 7.99935 0.506938
\(250\) 0 0
\(251\) 5.95049 0.375592 0.187796 0.982208i \(-0.439866\pi\)
0.187796 + 0.982208i \(0.439866\pi\)
\(252\) 0 0
\(253\) 22.2300 1.39759
\(254\) 0 0
\(255\) 8.87651 0.555869
\(256\) 0 0
\(257\) −17.7496 −1.10719 −0.553594 0.832787i \(-0.686744\pi\)
−0.553594 + 0.832787i \(0.686744\pi\)
\(258\) 0 0
\(259\) 16.0881 0.999664
\(260\) 0 0
\(261\) −8.60413 −0.532582
\(262\) 0 0
\(263\) −20.0832 −1.23838 −0.619190 0.785241i \(-0.712539\pi\)
−0.619190 + 0.785241i \(0.712539\pi\)
\(264\) 0 0
\(265\) 5.07368 0.311674
\(266\) 0 0
\(267\) 33.8808 2.07347
\(268\) 0 0
\(269\) −31.1407 −1.89868 −0.949340 0.314251i \(-0.898247\pi\)
−0.949340 + 0.314251i \(0.898247\pi\)
\(270\) 0 0
\(271\) −6.52857 −0.396582 −0.198291 0.980143i \(-0.563539\pi\)
−0.198291 + 0.980143i \(0.563539\pi\)
\(272\) 0 0
\(273\) −18.6235 −1.12714
\(274\) 0 0
\(275\) −35.7269 −2.15441
\(276\) 0 0
\(277\) −0.196105 −0.0117828 −0.00589142 0.999983i \(-0.501875\pi\)
−0.00589142 + 0.999983i \(0.501875\pi\)
\(278\) 0 0
\(279\) −6.16354 −0.369001
\(280\) 0 0
\(281\) 14.6199 0.872152 0.436076 0.899910i \(-0.356368\pi\)
0.436076 + 0.899910i \(0.356368\pi\)
\(282\) 0 0
\(283\) −2.43022 −0.144462 −0.0722308 0.997388i \(-0.523012\pi\)
−0.0722308 + 0.997388i \(0.523012\pi\)
\(284\) 0 0
\(285\) −22.3443 −1.32356
\(286\) 0 0
\(287\) 23.9674 1.41475
\(288\) 0 0
\(289\) −15.9559 −0.938580
\(290\) 0 0
\(291\) −24.6061 −1.44244
\(292\) 0 0
\(293\) 8.69893 0.508197 0.254098 0.967178i \(-0.418221\pi\)
0.254098 + 0.967178i \(0.418221\pi\)
\(294\) 0 0
\(295\) −29.2181 −1.70115
\(296\) 0 0
\(297\) −7.70678 −0.447193
\(298\) 0 0
\(299\) 12.4576 0.720442
\(300\) 0 0
\(301\) −0.235339 −0.0135647
\(302\) 0 0
\(303\) −6.61175 −0.379835
\(304\) 0 0
\(305\) −0.939396 −0.0537896
\(306\) 0 0
\(307\) −30.3653 −1.73304 −0.866519 0.499144i \(-0.833648\pi\)
−0.866519 + 0.499144i \(0.833648\pi\)
\(308\) 0 0
\(309\) 0.562923 0.0320236
\(310\) 0 0
\(311\) 9.29032 0.526806 0.263403 0.964686i \(-0.415155\pi\)
0.263403 + 0.964686i \(0.415155\pi\)
\(312\) 0 0
\(313\) 21.6115 1.22156 0.610778 0.791802i \(-0.290857\pi\)
0.610778 + 0.791802i \(0.290857\pi\)
\(314\) 0 0
\(315\) −32.6163 −1.83772
\(316\) 0 0
\(317\) 2.00868 0.112819 0.0564095 0.998408i \(-0.482035\pi\)
0.0564095 + 0.998408i \(0.482035\pi\)
\(318\) 0 0
\(319\) 15.1017 0.845533
\(320\) 0 0
\(321\) 42.6036 2.37790
\(322\) 0 0
\(323\) −2.62834 −0.146245
\(324\) 0 0
\(325\) −20.0212 −1.11058
\(326\) 0 0
\(327\) −0.870872 −0.0481593
\(328\) 0 0
\(329\) −6.03586 −0.332768
\(330\) 0 0
\(331\) 29.0256 1.59539 0.797696 0.603060i \(-0.206052\pi\)
0.797696 + 0.603060i \(0.206052\pi\)
\(332\) 0 0
\(333\) −7.96287 −0.436362
\(334\) 0 0
\(335\) 40.8208 2.23028
\(336\) 0 0
\(337\) 9.06693 0.493907 0.246953 0.969027i \(-0.420571\pi\)
0.246953 + 0.969027i \(0.420571\pi\)
\(338\) 0 0
\(339\) −10.9269 −0.593466
\(340\) 0 0
\(341\) 10.8181 0.585830
\(342\) 0 0
\(343\) −12.5267 −0.676376
\(344\) 0 0
\(345\) 53.8577 2.89960
\(346\) 0 0
\(347\) 13.4505 0.722062 0.361031 0.932554i \(-0.382425\pi\)
0.361031 + 0.932554i \(0.382425\pi\)
\(348\) 0 0
\(349\) 21.2675 1.13842 0.569212 0.822191i \(-0.307248\pi\)
0.569212 + 0.822191i \(0.307248\pi\)
\(350\) 0 0
\(351\) −4.31885 −0.230523
\(352\) 0 0
\(353\) −19.4861 −1.03714 −0.518571 0.855034i \(-0.673536\pi\)
−0.518571 + 0.855034i \(0.673536\pi\)
\(354\) 0 0
\(355\) 22.5035 1.19436
\(356\) 0 0
\(357\) −9.47083 −0.501249
\(358\) 0 0
\(359\) 23.1068 1.21953 0.609765 0.792582i \(-0.291264\pi\)
0.609765 + 0.792582i \(0.291264\pi\)
\(360\) 0 0
\(361\) −12.3838 −0.651781
\(362\) 0 0
\(363\) −4.16826 −0.218777
\(364\) 0 0
\(365\) 59.0689 3.09181
\(366\) 0 0
\(367\) 30.6813 1.60155 0.800775 0.598965i \(-0.204421\pi\)
0.800775 + 0.598965i \(0.204421\pi\)
\(368\) 0 0
\(369\) −11.8628 −0.617550
\(370\) 0 0
\(371\) −5.41338 −0.281049
\(372\) 0 0
\(373\) 30.9162 1.60078 0.800390 0.599480i \(-0.204626\pi\)
0.800390 + 0.599480i \(0.204626\pi\)
\(374\) 0 0
\(375\) −43.1228 −2.22685
\(376\) 0 0
\(377\) 8.46293 0.435863
\(378\) 0 0
\(379\) 16.0759 0.825762 0.412881 0.910785i \(-0.364523\pi\)
0.412881 + 0.910785i \(0.364523\pi\)
\(380\) 0 0
\(381\) −39.7016 −2.03398
\(382\) 0 0
\(383\) 28.5450 1.45858 0.729290 0.684205i \(-0.239851\pi\)
0.729290 + 0.684205i \(0.239851\pi\)
\(384\) 0 0
\(385\) 57.2470 2.91758
\(386\) 0 0
\(387\) 0.116482 0.00592112
\(388\) 0 0
\(389\) 24.4058 1.23743 0.618713 0.785617i \(-0.287654\pi\)
0.618713 + 0.785617i \(0.287654\pi\)
\(390\) 0 0
\(391\) 6.33523 0.320386
\(392\) 0 0
\(393\) −16.9114 −0.853067
\(394\) 0 0
\(395\) 45.2452 2.27653
\(396\) 0 0
\(397\) −26.5858 −1.33430 −0.667150 0.744923i \(-0.732486\pi\)
−0.667150 + 0.744923i \(0.732486\pi\)
\(398\) 0 0
\(399\) 23.8403 1.19351
\(400\) 0 0
\(401\) 31.9310 1.59456 0.797278 0.603612i \(-0.206272\pi\)
0.797278 + 0.603612i \(0.206272\pi\)
\(402\) 0 0
\(403\) 6.06239 0.301989
\(404\) 0 0
\(405\) −42.3790 −2.10583
\(406\) 0 0
\(407\) 13.9762 0.692773
\(408\) 0 0
\(409\) 2.06458 0.102087 0.0510435 0.998696i \(-0.483745\pi\)
0.0510435 + 0.998696i \(0.483745\pi\)
\(410\) 0 0
\(411\) −2.32826 −0.114845
\(412\) 0 0
\(413\) 31.1744 1.53399
\(414\) 0 0
\(415\) −13.7798 −0.676423
\(416\) 0 0
\(417\) 0.492201 0.0241032
\(418\) 0 0
\(419\) 7.04738 0.344287 0.172144 0.985072i \(-0.444931\pi\)
0.172144 + 0.985072i \(0.444931\pi\)
\(420\) 0 0
\(421\) −9.18236 −0.447521 −0.223760 0.974644i \(-0.571833\pi\)
−0.223760 + 0.974644i \(0.571833\pi\)
\(422\) 0 0
\(423\) 2.98748 0.145256
\(424\) 0 0
\(425\) −10.1816 −0.493882
\(426\) 0 0
\(427\) 1.00229 0.0485043
\(428\) 0 0
\(429\) −16.1787 −0.781117
\(430\) 0 0
\(431\) 26.3927 1.27129 0.635646 0.771980i \(-0.280734\pi\)
0.635646 + 0.771980i \(0.280734\pi\)
\(432\) 0 0
\(433\) 29.5283 1.41904 0.709520 0.704685i \(-0.248912\pi\)
0.709520 + 0.704685i \(0.248912\pi\)
\(434\) 0 0
\(435\) 36.5876 1.75424
\(436\) 0 0
\(437\) −15.9473 −0.762862
\(438\) 0 0
\(439\) 9.83243 0.469276 0.234638 0.972083i \(-0.424610\pi\)
0.234638 + 0.972083i \(0.424610\pi\)
\(440\) 0 0
\(441\) 20.5001 0.976195
\(442\) 0 0
\(443\) 24.5381 1.16584 0.582921 0.812529i \(-0.301910\pi\)
0.582921 + 0.812529i \(0.301910\pi\)
\(444\) 0 0
\(445\) −58.3636 −2.76670
\(446\) 0 0
\(447\) 46.4706 2.19798
\(448\) 0 0
\(449\) −18.2902 −0.863170 −0.431585 0.902072i \(-0.642046\pi\)
−0.431585 + 0.902072i \(0.642046\pi\)
\(450\) 0 0
\(451\) 20.8211 0.980429
\(452\) 0 0
\(453\) −2.45019 −0.115120
\(454\) 0 0
\(455\) 32.0810 1.50398
\(456\) 0 0
\(457\) 5.87844 0.274982 0.137491 0.990503i \(-0.456096\pi\)
0.137491 + 0.990503i \(0.456096\pi\)
\(458\) 0 0
\(459\) −2.19632 −0.102515
\(460\) 0 0
\(461\) −25.6372 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(462\) 0 0
\(463\) −0.832038 −0.0386681 −0.0193340 0.999813i \(-0.506155\pi\)
−0.0193340 + 0.999813i \(0.506155\pi\)
\(464\) 0 0
\(465\) 26.2094 1.21543
\(466\) 0 0
\(467\) −26.3242 −1.21814 −0.609070 0.793117i \(-0.708457\pi\)
−0.609070 + 0.793117i \(0.708457\pi\)
\(468\) 0 0
\(469\) −43.5540 −2.01114
\(470\) 0 0
\(471\) −43.5413 −2.00628
\(472\) 0 0
\(473\) −0.204446 −0.00940042
\(474\) 0 0
\(475\) 25.6296 1.17597
\(476\) 0 0
\(477\) 2.67938 0.122680
\(478\) 0 0
\(479\) 17.0901 0.780865 0.390433 0.920631i \(-0.372325\pi\)
0.390433 + 0.920631i \(0.372325\pi\)
\(480\) 0 0
\(481\) 7.83219 0.357117
\(482\) 0 0
\(483\) −57.4637 −2.61469
\(484\) 0 0
\(485\) 42.3868 1.92469
\(486\) 0 0
\(487\) 7.95573 0.360509 0.180254 0.983620i \(-0.442308\pi\)
0.180254 + 0.983620i \(0.442308\pi\)
\(488\) 0 0
\(489\) −18.7087 −0.846039
\(490\) 0 0
\(491\) 35.0580 1.58215 0.791074 0.611721i \(-0.209522\pi\)
0.791074 + 0.611721i \(0.209522\pi\)
\(492\) 0 0
\(493\) 4.30377 0.193832
\(494\) 0 0
\(495\) −28.3347 −1.27355
\(496\) 0 0
\(497\) −24.0102 −1.07701
\(498\) 0 0
\(499\) 25.2841 1.13187 0.565935 0.824450i \(-0.308515\pi\)
0.565935 + 0.824450i \(0.308515\pi\)
\(500\) 0 0
\(501\) −19.8133 −0.885191
\(502\) 0 0
\(503\) 19.1981 0.855999 0.428000 0.903779i \(-0.359218\pi\)
0.428000 + 0.903779i \(0.359218\pi\)
\(504\) 0 0
\(505\) 11.3895 0.506825
\(506\) 0 0
\(507\) 20.1267 0.893857
\(508\) 0 0
\(509\) 17.3575 0.769359 0.384679 0.923050i \(-0.374312\pi\)
0.384679 + 0.923050i \(0.374312\pi\)
\(510\) 0 0
\(511\) −63.0238 −2.78801
\(512\) 0 0
\(513\) 5.52866 0.244096
\(514\) 0 0
\(515\) −0.969699 −0.0427300
\(516\) 0 0
\(517\) −5.24353 −0.230610
\(518\) 0 0
\(519\) −35.9351 −1.57738
\(520\) 0 0
\(521\) −40.5189 −1.77517 −0.887583 0.460647i \(-0.847617\pi\)
−0.887583 + 0.460647i \(0.847617\pi\)
\(522\) 0 0
\(523\) −13.4974 −0.590199 −0.295100 0.955466i \(-0.595353\pi\)
−0.295100 + 0.955466i \(0.595353\pi\)
\(524\) 0 0
\(525\) 92.3526 4.03060
\(526\) 0 0
\(527\) 3.08299 0.134297
\(528\) 0 0
\(529\) 15.4386 0.671245
\(530\) 0 0
\(531\) −15.4299 −0.669601
\(532\) 0 0
\(533\) 11.6681 0.505401
\(534\) 0 0
\(535\) −73.3895 −3.17291
\(536\) 0 0
\(537\) −29.6542 −1.27967
\(538\) 0 0
\(539\) −35.9811 −1.54982
\(540\) 0 0
\(541\) 1.94426 0.0835905 0.0417952 0.999126i \(-0.486692\pi\)
0.0417952 + 0.999126i \(0.486692\pi\)
\(542\) 0 0
\(543\) −21.8462 −0.937511
\(544\) 0 0
\(545\) 1.50018 0.0642604
\(546\) 0 0
\(547\) −4.07056 −0.174045 −0.0870223 0.996206i \(-0.527735\pi\)
−0.0870223 + 0.996206i \(0.527735\pi\)
\(548\) 0 0
\(549\) −0.496089 −0.0211726
\(550\) 0 0
\(551\) −10.8336 −0.461527
\(552\) 0 0
\(553\) −48.2745 −2.05284
\(554\) 0 0
\(555\) 33.8607 1.43731
\(556\) 0 0
\(557\) 43.8994 1.86008 0.930039 0.367460i \(-0.119772\pi\)
0.930039 + 0.367460i \(0.119772\pi\)
\(558\) 0 0
\(559\) −0.114571 −0.00484582
\(560\) 0 0
\(561\) −8.22758 −0.347369
\(562\) 0 0
\(563\) −22.4677 −0.946901 −0.473451 0.880820i \(-0.656992\pi\)
−0.473451 + 0.880820i \(0.656992\pi\)
\(564\) 0 0
\(565\) 18.8228 0.791880
\(566\) 0 0
\(567\) 45.2164 1.89891
\(568\) 0 0
\(569\) 20.7639 0.870467 0.435234 0.900318i \(-0.356666\pi\)
0.435234 + 0.900318i \(0.356666\pi\)
\(570\) 0 0
\(571\) −46.0109 −1.92549 −0.962747 0.270403i \(-0.912843\pi\)
−0.962747 + 0.270403i \(0.912843\pi\)
\(572\) 0 0
\(573\) 11.3340 0.473483
\(574\) 0 0
\(575\) −61.7765 −2.57626
\(576\) 0 0
\(577\) 8.66239 0.360620 0.180310 0.983610i \(-0.442290\pi\)
0.180310 + 0.983610i \(0.442290\pi\)
\(578\) 0 0
\(579\) 3.35647 0.139490
\(580\) 0 0
\(581\) 14.7024 0.609958
\(582\) 0 0
\(583\) −4.70276 −0.194769
\(584\) 0 0
\(585\) −15.8786 −0.656501
\(586\) 0 0
\(587\) 42.4086 1.75039 0.875195 0.483770i \(-0.160733\pi\)
0.875195 + 0.483770i \(0.160733\pi\)
\(588\) 0 0
\(589\) −7.76062 −0.319771
\(590\) 0 0
\(591\) −24.2507 −0.997539
\(592\) 0 0
\(593\) −41.2466 −1.69379 −0.846897 0.531756i \(-0.821532\pi\)
−0.846897 + 0.531756i \(0.821532\pi\)
\(594\) 0 0
\(595\) 16.3146 0.668832
\(596\) 0 0
\(597\) 11.5887 0.474295
\(598\) 0 0
\(599\) −16.7882 −0.685949 −0.342974 0.939345i \(-0.611434\pi\)
−0.342974 + 0.939345i \(0.611434\pi\)
\(600\) 0 0
\(601\) 17.7112 0.722455 0.361227 0.932478i \(-0.382358\pi\)
0.361227 + 0.932478i \(0.382358\pi\)
\(602\) 0 0
\(603\) 21.5572 0.877879
\(604\) 0 0
\(605\) 7.18030 0.291921
\(606\) 0 0
\(607\) −3.59364 −0.145861 −0.0729306 0.997337i \(-0.523235\pi\)
−0.0729306 + 0.997337i \(0.523235\pi\)
\(608\) 0 0
\(609\) −39.0373 −1.58187
\(610\) 0 0
\(611\) −2.93845 −0.118877
\(612\) 0 0
\(613\) −3.60604 −0.145647 −0.0728234 0.997345i \(-0.523201\pi\)
−0.0728234 + 0.997345i \(0.523201\pi\)
\(614\) 0 0
\(615\) 50.4443 2.03411
\(616\) 0 0
\(617\) −39.4534 −1.58833 −0.794167 0.607699i \(-0.792093\pi\)
−0.794167 + 0.607699i \(0.792093\pi\)
\(618\) 0 0
\(619\) 37.4639 1.50580 0.752900 0.658135i \(-0.228654\pi\)
0.752900 + 0.658135i \(0.228654\pi\)
\(620\) 0 0
\(621\) −13.3260 −0.534756
\(622\) 0 0
\(623\) 62.2712 2.49484
\(624\) 0 0
\(625\) 24.4632 0.978528
\(626\) 0 0
\(627\) 20.7108 0.827110
\(628\) 0 0
\(629\) 3.98301 0.158813
\(630\) 0 0
\(631\) 9.38680 0.373683 0.186841 0.982390i \(-0.440175\pi\)
0.186841 + 0.982390i \(0.440175\pi\)
\(632\) 0 0
\(633\) 47.7817 1.89915
\(634\) 0 0
\(635\) 68.3906 2.71400
\(636\) 0 0
\(637\) −20.1637 −0.798914
\(638\) 0 0
\(639\) 11.8840 0.470123
\(640\) 0 0
\(641\) 34.8033 1.37465 0.687323 0.726352i \(-0.258786\pi\)
0.687323 + 0.726352i \(0.258786\pi\)
\(642\) 0 0
\(643\) 46.7128 1.84217 0.921086 0.389360i \(-0.127304\pi\)
0.921086 + 0.389360i \(0.127304\pi\)
\(644\) 0 0
\(645\) −0.495320 −0.0195032
\(646\) 0 0
\(647\) −8.33210 −0.327568 −0.163784 0.986496i \(-0.552370\pi\)
−0.163784 + 0.986496i \(0.552370\pi\)
\(648\) 0 0
\(649\) 27.0821 1.06307
\(650\) 0 0
\(651\) −27.9642 −1.09600
\(652\) 0 0
\(653\) 25.5258 0.998903 0.499452 0.866342i \(-0.333535\pi\)
0.499452 + 0.866342i \(0.333535\pi\)
\(654\) 0 0
\(655\) 29.1318 1.13827
\(656\) 0 0
\(657\) 31.1939 1.21699
\(658\) 0 0
\(659\) 3.62485 0.141204 0.0706020 0.997505i \(-0.477508\pi\)
0.0706020 + 0.997505i \(0.477508\pi\)
\(660\) 0 0
\(661\) −46.9428 −1.82586 −0.912931 0.408113i \(-0.866187\pi\)
−0.912931 + 0.408113i \(0.866187\pi\)
\(662\) 0 0
\(663\) −4.61070 −0.179065
\(664\) 0 0
\(665\) −41.0677 −1.59254
\(666\) 0 0
\(667\) 26.1128 1.01109
\(668\) 0 0
\(669\) −16.3293 −0.631329
\(670\) 0 0
\(671\) 0.870720 0.0336138
\(672\) 0 0
\(673\) −25.3263 −0.976256 −0.488128 0.872772i \(-0.662320\pi\)
−0.488128 + 0.872772i \(0.662320\pi\)
\(674\) 0 0
\(675\) 21.4169 0.824337
\(676\) 0 0
\(677\) 7.06174 0.271405 0.135702 0.990750i \(-0.456671\pi\)
0.135702 + 0.990750i \(0.456671\pi\)
\(678\) 0 0
\(679\) −45.2248 −1.73557
\(680\) 0 0
\(681\) 1.66788 0.0639133
\(682\) 0 0
\(683\) 14.4159 0.551610 0.275805 0.961214i \(-0.411056\pi\)
0.275805 + 0.961214i \(0.411056\pi\)
\(684\) 0 0
\(685\) 4.01070 0.153241
\(686\) 0 0
\(687\) 20.3998 0.778300
\(688\) 0 0
\(689\) −2.63541 −0.100401
\(690\) 0 0
\(691\) −10.9622 −0.417021 −0.208511 0.978020i \(-0.566862\pi\)
−0.208511 + 0.978020i \(0.566862\pi\)
\(692\) 0 0
\(693\) 30.2318 1.14841
\(694\) 0 0
\(695\) −0.847871 −0.0321616
\(696\) 0 0
\(697\) 5.93372 0.224756
\(698\) 0 0
\(699\) −40.6236 −1.53653
\(700\) 0 0
\(701\) −22.9555 −0.867018 −0.433509 0.901149i \(-0.642725\pi\)
−0.433509 + 0.901149i \(0.642725\pi\)
\(702\) 0 0
\(703\) −10.0262 −0.378144
\(704\) 0 0
\(705\) −12.7037 −0.478450
\(706\) 0 0
\(707\) −12.1521 −0.457025
\(708\) 0 0
\(709\) 52.0170 1.95354 0.976770 0.214288i \(-0.0687432\pi\)
0.976770 + 0.214288i \(0.0687432\pi\)
\(710\) 0 0
\(711\) 23.8937 0.896084
\(712\) 0 0
\(713\) 18.7058 0.700539
\(714\) 0 0
\(715\) 27.8697 1.04227
\(716\) 0 0
\(717\) 4.68487 0.174960
\(718\) 0 0
\(719\) −47.6509 −1.77708 −0.888539 0.458801i \(-0.848279\pi\)
−0.888539 + 0.458801i \(0.848279\pi\)
\(720\) 0 0
\(721\) 1.03462 0.0385314
\(722\) 0 0
\(723\) 8.15791 0.303396
\(724\) 0 0
\(725\) −41.9671 −1.55862
\(726\) 0 0
\(727\) −45.2003 −1.67639 −0.838193 0.545374i \(-0.816387\pi\)
−0.838193 + 0.545374i \(0.816387\pi\)
\(728\) 0 0
\(729\) −7.89981 −0.292586
\(730\) 0 0
\(731\) −0.0582640 −0.00215497
\(732\) 0 0
\(733\) −11.4146 −0.421609 −0.210804 0.977528i \(-0.567608\pi\)
−0.210804 + 0.977528i \(0.567608\pi\)
\(734\) 0 0
\(735\) −87.1731 −3.21543
\(736\) 0 0
\(737\) −37.8366 −1.39373
\(738\) 0 0
\(739\) −43.0239 −1.58266 −0.791331 0.611388i \(-0.790611\pi\)
−0.791331 + 0.611388i \(0.790611\pi\)
\(740\) 0 0
\(741\) 11.6062 0.426366
\(742\) 0 0
\(743\) −40.9621 −1.50275 −0.751377 0.659873i \(-0.770610\pi\)
−0.751377 + 0.659873i \(0.770610\pi\)
\(744\) 0 0
\(745\) −80.0508 −2.93284
\(746\) 0 0
\(747\) −7.27702 −0.266252
\(748\) 0 0
\(749\) 78.3033 2.86114
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −13.3626 −0.486960
\(754\) 0 0
\(755\) 4.22073 0.153608
\(756\) 0 0
\(757\) 29.5531 1.07413 0.537063 0.843542i \(-0.319534\pi\)
0.537063 + 0.843542i \(0.319534\pi\)
\(758\) 0 0
\(759\) −49.9204 −1.81199
\(760\) 0 0
\(761\) −12.1186 −0.439299 −0.219649 0.975579i \(-0.570491\pi\)
−0.219649 + 0.975579i \(0.570491\pi\)
\(762\) 0 0
\(763\) −1.60062 −0.0579463
\(764\) 0 0
\(765\) −8.07497 −0.291951
\(766\) 0 0
\(767\) 15.1767 0.547999
\(768\) 0 0
\(769\) −31.9512 −1.15219 −0.576096 0.817382i \(-0.695424\pi\)
−0.576096 + 0.817382i \(0.695424\pi\)
\(770\) 0 0
\(771\) 39.8589 1.43548
\(772\) 0 0
\(773\) −29.9199 −1.07614 −0.538072 0.842899i \(-0.680847\pi\)
−0.538072 + 0.842899i \(0.680847\pi\)
\(774\) 0 0
\(775\) −30.0630 −1.07990
\(776\) 0 0
\(777\) −36.1278 −1.29608
\(778\) 0 0
\(779\) −14.9366 −0.535159
\(780\) 0 0
\(781\) −20.8584 −0.746372
\(782\) 0 0
\(783\) −9.05289 −0.323524
\(784\) 0 0
\(785\) 75.0048 2.67704
\(786\) 0 0
\(787\) 10.0271 0.357429 0.178714 0.983901i \(-0.442806\pi\)
0.178714 + 0.983901i \(0.442806\pi\)
\(788\) 0 0
\(789\) 45.0993 1.60558
\(790\) 0 0
\(791\) −20.0830 −0.714070
\(792\) 0 0
\(793\) 0.487948 0.0173275
\(794\) 0 0
\(795\) −11.3936 −0.404090
\(796\) 0 0
\(797\) 5.87150 0.207979 0.103990 0.994578i \(-0.466839\pi\)
0.103990 + 0.994578i \(0.466839\pi\)
\(798\) 0 0
\(799\) −1.49433 −0.0528655
\(800\) 0 0
\(801\) −30.8214 −1.08902
\(802\) 0 0
\(803\) −54.7506 −1.93211
\(804\) 0 0
\(805\) 98.9877 3.48886
\(806\) 0 0
\(807\) 69.9304 2.46167
\(808\) 0 0
\(809\) 44.5216 1.56530 0.782649 0.622464i \(-0.213868\pi\)
0.782649 + 0.622464i \(0.213868\pi\)
\(810\) 0 0
\(811\) 10.4644 0.367453 0.183727 0.982977i \(-0.441184\pi\)
0.183727 + 0.982977i \(0.441184\pi\)
\(812\) 0 0
\(813\) 14.6608 0.514175
\(814\) 0 0
\(815\) 32.2279 1.12889
\(816\) 0 0
\(817\) 0.146665 0.00513114
\(818\) 0 0
\(819\) 16.9418 0.591994
\(820\) 0 0
\(821\) −33.1807 −1.15801 −0.579007 0.815323i \(-0.696560\pi\)
−0.579007 + 0.815323i \(0.696560\pi\)
\(822\) 0 0
\(823\) −4.80329 −0.167432 −0.0837161 0.996490i \(-0.526679\pi\)
−0.0837161 + 0.996490i \(0.526679\pi\)
\(824\) 0 0
\(825\) 80.2293 2.79323
\(826\) 0 0
\(827\) 35.0800 1.21985 0.609926 0.792458i \(-0.291199\pi\)
0.609926 + 0.792458i \(0.291199\pi\)
\(828\) 0 0
\(829\) −3.49480 −0.121379 −0.0606897 0.998157i \(-0.519330\pi\)
−0.0606897 + 0.998157i \(0.519330\pi\)
\(830\) 0 0
\(831\) 0.440380 0.0152766
\(832\) 0 0
\(833\) −10.2541 −0.355283
\(834\) 0 0
\(835\) 34.1306 1.18114
\(836\) 0 0
\(837\) −6.48501 −0.224155
\(838\) 0 0
\(839\) −15.4940 −0.534913 −0.267457 0.963570i \(-0.586183\pi\)
−0.267457 + 0.963570i \(0.586183\pi\)
\(840\) 0 0
\(841\) −11.2605 −0.388295
\(842\) 0 0
\(843\) −32.8309 −1.13076
\(844\) 0 0
\(845\) −34.6705 −1.19270
\(846\) 0 0
\(847\) −7.66105 −0.263237
\(848\) 0 0
\(849\) 5.45737 0.187296
\(850\) 0 0
\(851\) 24.1666 0.828422
\(852\) 0 0
\(853\) 28.1189 0.962773 0.481386 0.876508i \(-0.340133\pi\)
0.481386 + 0.876508i \(0.340133\pi\)
\(854\) 0 0
\(855\) 20.3266 0.695156
\(856\) 0 0
\(857\) −1.44535 −0.0493723 −0.0246861 0.999695i \(-0.507859\pi\)
−0.0246861 + 0.999695i \(0.507859\pi\)
\(858\) 0 0
\(859\) −3.29259 −0.112342 −0.0561708 0.998421i \(-0.517889\pi\)
−0.0561708 + 0.998421i \(0.517889\pi\)
\(860\) 0 0
\(861\) −53.8218 −1.83424
\(862\) 0 0
\(863\) −30.7547 −1.04690 −0.523451 0.852056i \(-0.675356\pi\)
−0.523451 + 0.852056i \(0.675356\pi\)
\(864\) 0 0
\(865\) 61.9023 2.10474
\(866\) 0 0
\(867\) 35.8310 1.21688
\(868\) 0 0
\(869\) −41.9375 −1.42263
\(870\) 0 0
\(871\) −21.2035 −0.718452
\(872\) 0 0
\(873\) 22.3842 0.757591
\(874\) 0 0
\(875\) −79.2575 −2.67939
\(876\) 0 0
\(877\) 0.0561193 0.00189502 0.000947508 1.00000i \(-0.499698\pi\)
0.000947508 1.00000i \(0.499698\pi\)
\(878\) 0 0
\(879\) −19.5346 −0.658885
\(880\) 0 0
\(881\) 14.5293 0.489505 0.244752 0.969586i \(-0.421293\pi\)
0.244752 + 0.969586i \(0.421293\pi\)
\(882\) 0 0
\(883\) 22.2369 0.748332 0.374166 0.927362i \(-0.377929\pi\)
0.374166 + 0.927362i \(0.377929\pi\)
\(884\) 0 0
\(885\) 65.6131 2.20556
\(886\) 0 0
\(887\) −5.67185 −0.190442 −0.0952211 0.995456i \(-0.530356\pi\)
−0.0952211 + 0.995456i \(0.530356\pi\)
\(888\) 0 0
\(889\) −72.9696 −2.44732
\(890\) 0 0
\(891\) 39.2808 1.31596
\(892\) 0 0
\(893\) 3.76158 0.125877
\(894\) 0 0
\(895\) 51.0827 1.70751
\(896\) 0 0
\(897\) −27.9752 −0.934064
\(898\) 0 0
\(899\) 12.7076 0.423822
\(900\) 0 0
\(901\) −1.34022 −0.0446492
\(902\) 0 0
\(903\) 0.528484 0.0175868
\(904\) 0 0
\(905\) 37.6326 1.25095
\(906\) 0 0
\(907\) 10.0051 0.332215 0.166108 0.986108i \(-0.446880\pi\)
0.166108 + 0.986108i \(0.446880\pi\)
\(908\) 0 0
\(909\) 6.01472 0.199496
\(910\) 0 0
\(911\) 29.7482 0.985600 0.492800 0.870142i \(-0.335973\pi\)
0.492800 + 0.870142i \(0.335973\pi\)
\(912\) 0 0
\(913\) 12.7724 0.422705
\(914\) 0 0
\(915\) 2.10953 0.0697391
\(916\) 0 0
\(917\) −31.0823 −1.02643
\(918\) 0 0
\(919\) −50.5021 −1.66591 −0.832956 0.553340i \(-0.813353\pi\)
−0.832956 + 0.553340i \(0.813353\pi\)
\(920\) 0 0
\(921\) 68.1892 2.24691
\(922\) 0 0
\(923\) −11.6890 −0.384747
\(924\) 0 0
\(925\) −38.8393 −1.27703
\(926\) 0 0
\(927\) −0.512092 −0.0168193
\(928\) 0 0
\(929\) 8.62854 0.283093 0.141547 0.989932i \(-0.454792\pi\)
0.141547 + 0.989932i \(0.454792\pi\)
\(930\) 0 0
\(931\) 25.8120 0.845954
\(932\) 0 0
\(933\) −20.8626 −0.683011
\(934\) 0 0
\(935\) 14.1729 0.463505
\(936\) 0 0
\(937\) −0.825041 −0.0269529 −0.0134765 0.999909i \(-0.504290\pi\)
−0.0134765 + 0.999909i \(0.504290\pi\)
\(938\) 0 0
\(939\) −48.5315 −1.58377
\(940\) 0 0
\(941\) −33.8598 −1.10380 −0.551898 0.833911i \(-0.686096\pi\)
−0.551898 + 0.833911i \(0.686096\pi\)
\(942\) 0 0
\(943\) 36.0025 1.17240
\(944\) 0 0
\(945\) −34.3174 −1.11635
\(946\) 0 0
\(947\) −57.1115 −1.85588 −0.927938 0.372735i \(-0.878420\pi\)
−0.927938 + 0.372735i \(0.878420\pi\)
\(948\) 0 0
\(949\) −30.6820 −0.995981
\(950\) 0 0
\(951\) −4.51076 −0.146271
\(952\) 0 0
\(953\) 10.0768 0.326418 0.163209 0.986592i \(-0.447816\pi\)
0.163209 + 0.986592i \(0.447816\pi\)
\(954\) 0 0
\(955\) −19.5240 −0.631782
\(956\) 0 0
\(957\) −33.9128 −1.09625
\(958\) 0 0
\(959\) −4.27923 −0.138184
\(960\) 0 0
\(961\) −21.8970 −0.706353
\(962\) 0 0
\(963\) −38.7566 −1.24891
\(964\) 0 0
\(965\) −5.78191 −0.186126
\(966\) 0 0
\(967\) −38.6186 −1.24189 −0.620946 0.783853i \(-0.713251\pi\)
−0.620946 + 0.783853i \(0.713251\pi\)
\(968\) 0 0
\(969\) 5.90228 0.189608
\(970\) 0 0
\(971\) 12.5031 0.401244 0.200622 0.979669i \(-0.435704\pi\)
0.200622 + 0.979669i \(0.435704\pi\)
\(972\) 0 0
\(973\) 0.904640 0.0290014
\(974\) 0 0
\(975\) 44.9602 1.43988
\(976\) 0 0
\(977\) 12.1363 0.388276 0.194138 0.980974i \(-0.437809\pi\)
0.194138 + 0.980974i \(0.437809\pi\)
\(978\) 0 0
\(979\) 54.0968 1.72894
\(980\) 0 0
\(981\) 0.792233 0.0252941
\(982\) 0 0
\(983\) −35.8508 −1.14346 −0.571731 0.820441i \(-0.693728\pi\)
−0.571731 + 0.820441i \(0.693728\pi\)
\(984\) 0 0
\(985\) 41.7745 1.33105
\(986\) 0 0
\(987\) 13.5543 0.431438
\(988\) 0 0
\(989\) −0.353514 −0.0112411
\(990\) 0 0
\(991\) 40.9478 1.30075 0.650374 0.759614i \(-0.274612\pi\)
0.650374 + 0.759614i \(0.274612\pi\)
\(992\) 0 0
\(993\) −65.1807 −2.06845
\(994\) 0 0
\(995\) −19.9629 −0.632866
\(996\) 0 0
\(997\) 24.6576 0.780915 0.390457 0.920621i \(-0.372317\pi\)
0.390457 + 0.920621i \(0.372317\pi\)
\(998\) 0 0
\(999\) −8.37818 −0.265074
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 \(a_p\))