Properties

Label 6008.2.a.e.1.33
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 1.33
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.28833 q^{3} -3.57208 q^{5} -2.67571 q^{7} -1.34021 q^{9} +O(q^{10})\) \(q+1.28833 q^{3} -3.57208 q^{5} -2.67571 q^{7} -1.34021 q^{9} -2.04152 q^{11} -0.441037 q^{13} -4.60201 q^{15} -5.96418 q^{17} -6.28740 q^{19} -3.44720 q^{21} -5.22768 q^{23} +7.75974 q^{25} -5.59162 q^{27} +9.50063 q^{29} +0.189527 q^{31} -2.63015 q^{33} +9.55784 q^{35} -9.10273 q^{37} -0.568202 q^{39} +7.36637 q^{41} -2.12659 q^{43} +4.78732 q^{45} +0.117694 q^{47} +0.159424 q^{49} -7.68384 q^{51} -7.37578 q^{53} +7.29246 q^{55} -8.10024 q^{57} -6.95408 q^{59} +3.87058 q^{61} +3.58600 q^{63} +1.57542 q^{65} +13.8653 q^{67} -6.73497 q^{69} -8.22977 q^{71} -1.09521 q^{73} +9.99710 q^{75} +5.46251 q^{77} +13.2693 q^{79} -3.18323 q^{81} +5.72632 q^{83} +21.3045 q^{85} +12.2399 q^{87} -10.3226 q^{89} +1.18009 q^{91} +0.244173 q^{93} +22.4591 q^{95} +0.540681 q^{97} +2.73605 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 1.28833 0.743818 0.371909 0.928269i \(-0.378703\pi\)
0.371909 + 0.928269i \(0.378703\pi\)
\(4\) 0 0
\(5\) −3.57208 −1.59748 −0.798741 0.601675i \(-0.794500\pi\)
−0.798741 + 0.601675i \(0.794500\pi\)
\(6\) 0 0
\(7\) −2.67571 −1.01132 −0.505662 0.862732i \(-0.668752\pi\)
−0.505662 + 0.862732i \(0.668752\pi\)
\(8\) 0 0
\(9\) −1.34021 −0.446735
\(10\) 0 0
\(11\) −2.04152 −0.615541 −0.307770 0.951461i \(-0.599583\pi\)
−0.307770 + 0.951461i \(0.599583\pi\)
\(12\) 0 0
\(13\) −0.441037 −0.122322 −0.0611609 0.998128i \(-0.519480\pi\)
−0.0611609 + 0.998128i \(0.519480\pi\)
\(14\) 0 0
\(15\) −4.60201 −1.18824
\(16\) 0 0
\(17\) −5.96418 −1.44653 −0.723264 0.690572i \(-0.757359\pi\)
−0.723264 + 0.690572i \(0.757359\pi\)
\(18\) 0 0
\(19\) −6.28740 −1.44243 −0.721214 0.692712i \(-0.756416\pi\)
−0.721214 + 0.692712i \(0.756416\pi\)
\(20\) 0 0
\(21\) −3.44720 −0.752240
\(22\) 0 0
\(23\) −5.22768 −1.09005 −0.545023 0.838421i \(-0.683479\pi\)
−0.545023 + 0.838421i \(0.683479\pi\)
\(24\) 0 0
\(25\) 7.75974 1.55195
\(26\) 0 0
\(27\) −5.59162 −1.07611
\(28\) 0 0
\(29\) 9.50063 1.76422 0.882111 0.471041i \(-0.156122\pi\)
0.882111 + 0.471041i \(0.156122\pi\)
\(30\) 0 0
\(31\) 0.189527 0.0340400 0.0170200 0.999855i \(-0.494582\pi\)
0.0170200 + 0.999855i \(0.494582\pi\)
\(32\) 0 0
\(33\) −2.63015 −0.457850
\(34\) 0 0
\(35\) 9.55784 1.61557
\(36\) 0 0
\(37\) −9.10273 −1.49648 −0.748240 0.663429i \(-0.769101\pi\)
−0.748240 + 0.663429i \(0.769101\pi\)
\(38\) 0 0
\(39\) −0.568202 −0.0909851
\(40\) 0 0
\(41\) 7.36637 1.15043 0.575217 0.818001i \(-0.304918\pi\)
0.575217 + 0.818001i \(0.304918\pi\)
\(42\) 0 0
\(43\) −2.12659 −0.324303 −0.162151 0.986766i \(-0.551843\pi\)
−0.162151 + 0.986766i \(0.551843\pi\)
\(44\) 0 0
\(45\) 4.78732 0.713651
\(46\) 0 0
\(47\) 0.117694 0.0171674 0.00858372 0.999963i \(-0.497268\pi\)
0.00858372 + 0.999963i \(0.497268\pi\)
\(48\) 0 0
\(49\) 0.159424 0.0227749
\(50\) 0 0
\(51\) −7.68384 −1.07595
\(52\) 0 0
\(53\) −7.37578 −1.01314 −0.506570 0.862199i \(-0.669087\pi\)
−0.506570 + 0.862199i \(0.669087\pi\)
\(54\) 0 0
\(55\) 7.29246 0.983315
\(56\) 0 0
\(57\) −8.10024 −1.07290
\(58\) 0 0
\(59\) −6.95408 −0.905345 −0.452672 0.891677i \(-0.649529\pi\)
−0.452672 + 0.891677i \(0.649529\pi\)
\(60\) 0 0
\(61\) 3.87058 0.495577 0.247789 0.968814i \(-0.420296\pi\)
0.247789 + 0.968814i \(0.420296\pi\)
\(62\) 0 0
\(63\) 3.58600 0.451794
\(64\) 0 0
\(65\) 1.57542 0.195407
\(66\) 0 0
\(67\) 13.8653 1.69391 0.846957 0.531661i \(-0.178432\pi\)
0.846957 + 0.531661i \(0.178432\pi\)
\(68\) 0 0
\(69\) −6.73497 −0.810795
\(70\) 0 0
\(71\) −8.22977 −0.976693 −0.488347 0.872650i \(-0.662400\pi\)
−0.488347 + 0.872650i \(0.662400\pi\)
\(72\) 0 0
\(73\) −1.09521 −0.128184 −0.0640921 0.997944i \(-0.520415\pi\)
−0.0640921 + 0.997944i \(0.520415\pi\)
\(74\) 0 0
\(75\) 9.99710 1.15437
\(76\) 0 0
\(77\) 5.46251 0.622511
\(78\) 0 0
\(79\) 13.2693 1.49292 0.746459 0.665432i \(-0.231753\pi\)
0.746459 + 0.665432i \(0.231753\pi\)
\(80\) 0 0
\(81\) −3.18323 −0.353692
\(82\) 0 0
\(83\) 5.72632 0.628545 0.314273 0.949333i \(-0.398239\pi\)
0.314273 + 0.949333i \(0.398239\pi\)
\(84\) 0 0
\(85\) 21.3045 2.31080
\(86\) 0 0
\(87\) 12.2399 1.31226
\(88\) 0 0
\(89\) −10.3226 −1.09420 −0.547098 0.837069i \(-0.684267\pi\)
−0.547098 + 0.837069i \(0.684267\pi\)
\(90\) 0 0
\(91\) 1.18009 0.123707
\(92\) 0 0
\(93\) 0.244173 0.0253196
\(94\) 0 0
\(95\) 22.4591 2.30425
\(96\) 0 0
\(97\) 0.540681 0.0548979 0.0274489 0.999623i \(-0.491262\pi\)
0.0274489 + 0.999623i \(0.491262\pi\)
\(98\) 0 0
\(99\) 2.73605 0.274984
\(100\) 0 0
\(101\) 16.4337 1.63521 0.817605 0.575780i \(-0.195302\pi\)
0.817605 + 0.575780i \(0.195302\pi\)
\(102\) 0 0
\(103\) 0.333663 0.0328768 0.0164384 0.999865i \(-0.494767\pi\)
0.0164384 + 0.999865i \(0.494767\pi\)
\(104\) 0 0
\(105\) 12.3137 1.20169
\(106\) 0 0
\(107\) −6.64539 −0.642434 −0.321217 0.947006i \(-0.604092\pi\)
−0.321217 + 0.947006i \(0.604092\pi\)
\(108\) 0 0
\(109\) 1.23474 0.118267 0.0591334 0.998250i \(-0.481166\pi\)
0.0591334 + 0.998250i \(0.481166\pi\)
\(110\) 0 0
\(111\) −11.7273 −1.11311
\(112\) 0 0
\(113\) −1.14610 −0.107816 −0.0539081 0.998546i \(-0.517168\pi\)
−0.0539081 + 0.998546i \(0.517168\pi\)
\(114\) 0 0
\(115\) 18.6737 1.74133
\(116\) 0 0
\(117\) 0.591081 0.0546454
\(118\) 0 0
\(119\) 15.9584 1.46291
\(120\) 0 0
\(121\) −6.83220 −0.621110
\(122\) 0 0
\(123\) 9.49032 0.855713
\(124\) 0 0
\(125\) −9.85800 −0.881726
\(126\) 0 0
\(127\) 3.78518 0.335881 0.167940 0.985797i \(-0.446288\pi\)
0.167940 + 0.985797i \(0.446288\pi\)
\(128\) 0 0
\(129\) −2.73976 −0.241222
\(130\) 0 0
\(131\) −11.8910 −1.03892 −0.519460 0.854495i \(-0.673867\pi\)
−0.519460 + 0.854495i \(0.673867\pi\)
\(132\) 0 0
\(133\) 16.8233 1.45876
\(134\) 0 0
\(135\) 19.9737 1.71906
\(136\) 0 0
\(137\) −11.0472 −0.943828 −0.471914 0.881645i \(-0.656437\pi\)
−0.471914 + 0.881645i \(0.656437\pi\)
\(138\) 0 0
\(139\) −18.7836 −1.59320 −0.796602 0.604504i \(-0.793371\pi\)
−0.796602 + 0.604504i \(0.793371\pi\)
\(140\) 0 0
\(141\) 0.151629 0.0127694
\(142\) 0 0
\(143\) 0.900386 0.0752940
\(144\) 0 0
\(145\) −33.9370 −2.81831
\(146\) 0 0
\(147\) 0.205391 0.0169404
\(148\) 0 0
\(149\) 6.89079 0.564516 0.282258 0.959339i \(-0.408917\pi\)
0.282258 + 0.959339i \(0.408917\pi\)
\(150\) 0 0
\(151\) −9.38913 −0.764077 −0.382038 0.924146i \(-0.624778\pi\)
−0.382038 + 0.924146i \(0.624778\pi\)
\(152\) 0 0
\(153\) 7.99323 0.646215
\(154\) 0 0
\(155\) −0.677005 −0.0543783
\(156\) 0 0
\(157\) −5.47393 −0.436867 −0.218434 0.975852i \(-0.570095\pi\)
−0.218434 + 0.975852i \(0.570095\pi\)
\(158\) 0 0
\(159\) −9.50244 −0.753592
\(160\) 0 0
\(161\) 13.9877 1.10239
\(162\) 0 0
\(163\) 8.73015 0.683798 0.341899 0.939737i \(-0.388930\pi\)
0.341899 + 0.939737i \(0.388930\pi\)
\(164\) 0 0
\(165\) 9.39510 0.731407
\(166\) 0 0
\(167\) 25.0121 1.93550 0.967748 0.251920i \(-0.0810618\pi\)
0.967748 + 0.251920i \(0.0810618\pi\)
\(168\) 0 0
\(169\) −12.8055 −0.985037
\(170\) 0 0
\(171\) 8.42641 0.644383
\(172\) 0 0
\(173\) 3.35141 0.254803 0.127402 0.991851i \(-0.459336\pi\)
0.127402 + 0.991851i \(0.459336\pi\)
\(174\) 0 0
\(175\) −20.7628 −1.56952
\(176\) 0 0
\(177\) −8.95916 −0.673411
\(178\) 0 0
\(179\) −13.4195 −1.00302 −0.501509 0.865153i \(-0.667222\pi\)
−0.501509 + 0.865153i \(0.667222\pi\)
\(180\) 0 0
\(181\) −19.3756 −1.44018 −0.720089 0.693882i \(-0.755899\pi\)
−0.720089 + 0.693882i \(0.755899\pi\)
\(182\) 0 0
\(183\) 4.98659 0.368619
\(184\) 0 0
\(185\) 32.5156 2.39060
\(186\) 0 0
\(187\) 12.1760 0.890397
\(188\) 0 0
\(189\) 14.9615 1.08829
\(190\) 0 0
\(191\) −10.7892 −0.780676 −0.390338 0.920672i \(-0.627642\pi\)
−0.390338 + 0.920672i \(0.627642\pi\)
\(192\) 0 0
\(193\) 21.4166 1.54160 0.770800 0.637077i \(-0.219857\pi\)
0.770800 + 0.637077i \(0.219857\pi\)
\(194\) 0 0
\(195\) 2.02966 0.145347
\(196\) 0 0
\(197\) −7.24009 −0.515835 −0.257917 0.966167i \(-0.583036\pi\)
−0.257917 + 0.966167i \(0.583036\pi\)
\(198\) 0 0
\(199\) −9.36488 −0.663859 −0.331929 0.943304i \(-0.607700\pi\)
−0.331929 + 0.943304i \(0.607700\pi\)
\(200\) 0 0
\(201\) 17.8631 1.25996
\(202\) 0 0
\(203\) −25.4209 −1.78420
\(204\) 0 0
\(205\) −26.3133 −1.83780
\(206\) 0 0
\(207\) 7.00616 0.486962
\(208\) 0 0
\(209\) 12.8358 0.887873
\(210\) 0 0
\(211\) 6.86143 0.472360 0.236180 0.971709i \(-0.424104\pi\)
0.236180 + 0.971709i \(0.424104\pi\)
\(212\) 0 0
\(213\) −10.6027 −0.726482
\(214\) 0 0
\(215\) 7.59636 0.518068
\(216\) 0 0
\(217\) −0.507119 −0.0344255
\(218\) 0 0
\(219\) −1.41099 −0.0953456
\(220\) 0 0
\(221\) 2.63043 0.176942
\(222\) 0 0
\(223\) 18.8480 1.26215 0.631077 0.775720i \(-0.282613\pi\)
0.631077 + 0.775720i \(0.282613\pi\)
\(224\) 0 0
\(225\) −10.3996 −0.693310
\(226\) 0 0
\(227\) 22.4565 1.49049 0.745245 0.666791i \(-0.232332\pi\)
0.745245 + 0.666791i \(0.232332\pi\)
\(228\) 0 0
\(229\) 14.5681 0.962688 0.481344 0.876532i \(-0.340149\pi\)
0.481344 + 0.876532i \(0.340149\pi\)
\(230\) 0 0
\(231\) 7.03752 0.463035
\(232\) 0 0
\(233\) 3.57459 0.234179 0.117090 0.993121i \(-0.462644\pi\)
0.117090 + 0.993121i \(0.462644\pi\)
\(234\) 0 0
\(235\) −0.420412 −0.0274247
\(236\) 0 0
\(237\) 17.0953 1.11046
\(238\) 0 0
\(239\) −19.0399 −1.23159 −0.615796 0.787906i \(-0.711165\pi\)
−0.615796 + 0.787906i \(0.711165\pi\)
\(240\) 0 0
\(241\) 9.31092 0.599769 0.299885 0.953975i \(-0.403052\pi\)
0.299885 + 0.953975i \(0.403052\pi\)
\(242\) 0 0
\(243\) 12.6738 0.813025
\(244\) 0 0
\(245\) −0.569475 −0.0363824
\(246\) 0 0
\(247\) 2.77298 0.176440
\(248\) 0 0
\(249\) 7.37739 0.467523
\(250\) 0 0
\(251\) −15.3439 −0.968497 −0.484248 0.874931i \(-0.660907\pi\)
−0.484248 + 0.874931i \(0.660907\pi\)
\(252\) 0 0
\(253\) 10.6724 0.670968
\(254\) 0 0
\(255\) 27.4473 1.71881
\(256\) 0 0
\(257\) −11.1498 −0.695502 −0.347751 0.937587i \(-0.613055\pi\)
−0.347751 + 0.937587i \(0.613055\pi\)
\(258\) 0 0
\(259\) 24.3563 1.51342
\(260\) 0 0
\(261\) −12.7328 −0.788140
\(262\) 0 0
\(263\) 0.437878 0.0270007 0.0135004 0.999909i \(-0.495703\pi\)
0.0135004 + 0.999909i \(0.495703\pi\)
\(264\) 0 0
\(265\) 26.3468 1.61847
\(266\) 0 0
\(267\) −13.2989 −0.813882
\(268\) 0 0
\(269\) −9.06132 −0.552478 −0.276239 0.961089i \(-0.589088\pi\)
−0.276239 + 0.961089i \(0.589088\pi\)
\(270\) 0 0
\(271\) 20.8803 1.26839 0.634194 0.773174i \(-0.281332\pi\)
0.634194 + 0.773174i \(0.281332\pi\)
\(272\) 0 0
\(273\) 1.52034 0.0920153
\(274\) 0 0
\(275\) −15.8416 −0.955287
\(276\) 0 0
\(277\) 28.2179 1.69545 0.847725 0.530435i \(-0.177972\pi\)
0.847725 + 0.530435i \(0.177972\pi\)
\(278\) 0 0
\(279\) −0.254005 −0.0152069
\(280\) 0 0
\(281\) −29.2334 −1.74392 −0.871960 0.489577i \(-0.837151\pi\)
−0.871960 + 0.489577i \(0.837151\pi\)
\(282\) 0 0
\(283\) −18.3857 −1.09291 −0.546457 0.837487i \(-0.684024\pi\)
−0.546457 + 0.837487i \(0.684024\pi\)
\(284\) 0 0
\(285\) 28.9347 1.71394
\(286\) 0 0
\(287\) −19.7103 −1.16346
\(288\) 0 0
\(289\) 18.5715 1.09244
\(290\) 0 0
\(291\) 0.696576 0.0408340
\(292\) 0 0
\(293\) 13.7614 0.803951 0.401976 0.915650i \(-0.368324\pi\)
0.401976 + 0.915650i \(0.368324\pi\)
\(294\) 0 0
\(295\) 24.8405 1.44627
\(296\) 0 0
\(297\) 11.4154 0.662388
\(298\) 0 0
\(299\) 2.30560 0.133336
\(300\) 0 0
\(301\) 5.69015 0.327975
\(302\) 0 0
\(303\) 21.1720 1.21630
\(304\) 0 0
\(305\) −13.8260 −0.791676
\(306\) 0 0
\(307\) 10.7074 0.611102 0.305551 0.952176i \(-0.401159\pi\)
0.305551 + 0.952176i \(0.401159\pi\)
\(308\) 0 0
\(309\) 0.429868 0.0244543
\(310\) 0 0
\(311\) −15.8062 −0.896287 −0.448144 0.893962i \(-0.647915\pi\)
−0.448144 + 0.893962i \(0.647915\pi\)
\(312\) 0 0
\(313\) 9.60415 0.542859 0.271429 0.962458i \(-0.412504\pi\)
0.271429 + 0.962458i \(0.412504\pi\)
\(314\) 0 0
\(315\) −12.8095 −0.721732
\(316\) 0 0
\(317\) −5.15186 −0.289357 −0.144679 0.989479i \(-0.546215\pi\)
−0.144679 + 0.989479i \(0.546215\pi\)
\(318\) 0 0
\(319\) −19.3957 −1.08595
\(320\) 0 0
\(321\) −8.56146 −0.477854
\(322\) 0 0
\(323\) 37.4992 2.08651
\(324\) 0 0
\(325\) −3.42233 −0.189837
\(326\) 0 0
\(327\) 1.59075 0.0879689
\(328\) 0 0
\(329\) −0.314915 −0.0173618
\(330\) 0 0
\(331\) −19.9142 −1.09458 −0.547292 0.836942i \(-0.684341\pi\)
−0.547292 + 0.836942i \(0.684341\pi\)
\(332\) 0 0
\(333\) 12.1995 0.668530
\(334\) 0 0
\(335\) −49.5279 −2.70600
\(336\) 0 0
\(337\) −19.2990 −1.05128 −0.525642 0.850706i \(-0.676175\pi\)
−0.525642 + 0.850706i \(0.676175\pi\)
\(338\) 0 0
\(339\) −1.47656 −0.0801956
\(340\) 0 0
\(341\) −0.386923 −0.0209530
\(342\) 0 0
\(343\) 18.3034 0.988291
\(344\) 0 0
\(345\) 24.0578 1.29523
\(346\) 0 0
\(347\) −28.5554 −1.53293 −0.766466 0.642284i \(-0.777987\pi\)
−0.766466 + 0.642284i \(0.777987\pi\)
\(348\) 0 0
\(349\) 30.3217 1.62308 0.811542 0.584294i \(-0.198628\pi\)
0.811542 + 0.584294i \(0.198628\pi\)
\(350\) 0 0
\(351\) 2.46611 0.131631
\(352\) 0 0
\(353\) 36.8838 1.96313 0.981564 0.191133i \(-0.0612161\pi\)
0.981564 + 0.191133i \(0.0612161\pi\)
\(354\) 0 0
\(355\) 29.3974 1.56025
\(356\) 0 0
\(357\) 20.5597 1.08814
\(358\) 0 0
\(359\) −6.72062 −0.354701 −0.177350 0.984148i \(-0.556753\pi\)
−0.177350 + 0.984148i \(0.556753\pi\)
\(360\) 0 0
\(361\) 20.5314 1.08060
\(362\) 0 0
\(363\) −8.80213 −0.461992
\(364\) 0 0
\(365\) 3.91216 0.204772
\(366\) 0 0
\(367\) 22.6296 1.18125 0.590627 0.806945i \(-0.298881\pi\)
0.590627 + 0.806945i \(0.298881\pi\)
\(368\) 0 0
\(369\) −9.87245 −0.513939
\(370\) 0 0
\(371\) 19.7354 1.02461
\(372\) 0 0
\(373\) −11.5558 −0.598335 −0.299167 0.954201i \(-0.596709\pi\)
−0.299167 + 0.954201i \(0.596709\pi\)
\(374\) 0 0
\(375\) −12.7004 −0.655843
\(376\) 0 0
\(377\) −4.19013 −0.215803
\(378\) 0 0
\(379\) −0.357363 −0.0183565 −0.00917825 0.999958i \(-0.502922\pi\)
−0.00917825 + 0.999958i \(0.502922\pi\)
\(380\) 0 0
\(381\) 4.87656 0.249834
\(382\) 0 0
\(383\) −17.6556 −0.902161 −0.451080 0.892483i \(-0.648961\pi\)
−0.451080 + 0.892483i \(0.648961\pi\)
\(384\) 0 0
\(385\) −19.5125 −0.994450
\(386\) 0 0
\(387\) 2.85007 0.144877
\(388\) 0 0
\(389\) 14.7043 0.745536 0.372768 0.927924i \(-0.378409\pi\)
0.372768 + 0.927924i \(0.378409\pi\)
\(390\) 0 0
\(391\) 31.1788 1.57678
\(392\) 0 0
\(393\) −15.3195 −0.772768
\(394\) 0 0
\(395\) −47.3991 −2.38491
\(396\) 0 0
\(397\) −30.8735 −1.54949 −0.774747 0.632271i \(-0.782123\pi\)
−0.774747 + 0.632271i \(0.782123\pi\)
\(398\) 0 0
\(399\) 21.6739 1.08505
\(400\) 0 0
\(401\) −31.9447 −1.59524 −0.797621 0.603159i \(-0.793908\pi\)
−0.797621 + 0.603159i \(0.793908\pi\)
\(402\) 0 0
\(403\) −0.0835885 −0.00416384
\(404\) 0 0
\(405\) 11.3708 0.565017
\(406\) 0 0
\(407\) 18.5834 0.921144
\(408\) 0 0
\(409\) 15.9936 0.790831 0.395415 0.918502i \(-0.370601\pi\)
0.395415 + 0.918502i \(0.370601\pi\)
\(410\) 0 0
\(411\) −14.2325 −0.702036
\(412\) 0 0
\(413\) 18.6071 0.915596
\(414\) 0 0
\(415\) −20.4549 −1.00409
\(416\) 0 0
\(417\) −24.1995 −1.18505
\(418\) 0 0
\(419\) −21.3783 −1.04440 −0.522199 0.852824i \(-0.674888\pi\)
−0.522199 + 0.852824i \(0.674888\pi\)
\(420\) 0 0
\(421\) −8.70322 −0.424169 −0.212085 0.977251i \(-0.568025\pi\)
−0.212085 + 0.977251i \(0.568025\pi\)
\(422\) 0 0
\(423\) −0.157734 −0.00766930
\(424\) 0 0
\(425\) −46.2805 −2.24493
\(426\) 0 0
\(427\) −10.3566 −0.501189
\(428\) 0 0
\(429\) 1.15999 0.0560050
\(430\) 0 0
\(431\) 5.26757 0.253730 0.126865 0.991920i \(-0.459509\pi\)
0.126865 + 0.991920i \(0.459509\pi\)
\(432\) 0 0
\(433\) −24.0209 −1.15437 −0.577185 0.816613i \(-0.695849\pi\)
−0.577185 + 0.816613i \(0.695849\pi\)
\(434\) 0 0
\(435\) −43.7220 −2.09631
\(436\) 0 0
\(437\) 32.8685 1.57231
\(438\) 0 0
\(439\) 16.5337 0.789108 0.394554 0.918873i \(-0.370899\pi\)
0.394554 + 0.918873i \(0.370899\pi\)
\(440\) 0 0
\(441\) −0.213661 −0.0101743
\(442\) 0 0
\(443\) 32.2086 1.53028 0.765140 0.643864i \(-0.222670\pi\)
0.765140 + 0.643864i \(0.222670\pi\)
\(444\) 0 0
\(445\) 36.8732 1.74796
\(446\) 0 0
\(447\) 8.87761 0.419897
\(448\) 0 0
\(449\) −19.8216 −0.935441 −0.467721 0.883876i \(-0.654925\pi\)
−0.467721 + 0.883876i \(0.654925\pi\)
\(450\) 0 0
\(451\) −15.0386 −0.708139
\(452\) 0 0
\(453\) −12.0963 −0.568334
\(454\) 0 0
\(455\) −4.21537 −0.197619
\(456\) 0 0
\(457\) 11.8335 0.553549 0.276775 0.960935i \(-0.410734\pi\)
0.276775 + 0.960935i \(0.410734\pi\)
\(458\) 0 0
\(459\) 33.3494 1.55662
\(460\) 0 0
\(461\) 8.94646 0.416678 0.208339 0.978057i \(-0.433194\pi\)
0.208339 + 0.978057i \(0.433194\pi\)
\(462\) 0 0
\(463\) 1.04111 0.0483846 0.0241923 0.999707i \(-0.492299\pi\)
0.0241923 + 0.999707i \(0.492299\pi\)
\(464\) 0 0
\(465\) −0.872206 −0.0404476
\(466\) 0 0
\(467\) −19.2054 −0.888718 −0.444359 0.895849i \(-0.646569\pi\)
−0.444359 + 0.895849i \(0.646569\pi\)
\(468\) 0 0
\(469\) −37.0995 −1.71310
\(470\) 0 0
\(471\) −7.05223 −0.324950
\(472\) 0 0
\(473\) 4.34148 0.199622
\(474\) 0 0
\(475\) −48.7886 −2.23857
\(476\) 0 0
\(477\) 9.88506 0.452606
\(478\) 0 0
\(479\) −29.5634 −1.35079 −0.675394 0.737457i \(-0.736026\pi\)
−0.675394 + 0.737457i \(0.736026\pi\)
\(480\) 0 0
\(481\) 4.01464 0.183052
\(482\) 0 0
\(483\) 18.0208 0.819976
\(484\) 0 0
\(485\) −1.93136 −0.0876984
\(486\) 0 0
\(487\) −8.17355 −0.370379 −0.185189 0.982703i \(-0.559290\pi\)
−0.185189 + 0.982703i \(0.559290\pi\)
\(488\) 0 0
\(489\) 11.2473 0.508621
\(490\) 0 0
\(491\) −23.3728 −1.05480 −0.527400 0.849617i \(-0.676833\pi\)
−0.527400 + 0.849617i \(0.676833\pi\)
\(492\) 0 0
\(493\) −56.6635 −2.55200
\(494\) 0 0
\(495\) −9.77340 −0.439281
\(496\) 0 0
\(497\) 22.0205 0.987753
\(498\) 0 0
\(499\) 29.5228 1.32162 0.660812 0.750552i \(-0.270212\pi\)
0.660812 + 0.750552i \(0.270212\pi\)
\(500\) 0 0
\(501\) 32.2239 1.43966
\(502\) 0 0
\(503\) −20.8393 −0.929180 −0.464590 0.885526i \(-0.653798\pi\)
−0.464590 + 0.885526i \(0.653798\pi\)
\(504\) 0 0
\(505\) −58.7023 −2.61222
\(506\) 0 0
\(507\) −16.4977 −0.732688
\(508\) 0 0
\(509\) −10.5880 −0.469305 −0.234652 0.972079i \(-0.575395\pi\)
−0.234652 + 0.972079i \(0.575395\pi\)
\(510\) 0 0
\(511\) 2.93045 0.129636
\(512\) 0 0
\(513\) 35.1567 1.55221
\(514\) 0 0
\(515\) −1.19187 −0.0525201
\(516\) 0 0
\(517\) −0.240275 −0.0105673
\(518\) 0 0
\(519\) 4.31772 0.189527
\(520\) 0 0
\(521\) −15.9829 −0.700224 −0.350112 0.936708i \(-0.613856\pi\)
−0.350112 + 0.936708i \(0.613856\pi\)
\(522\) 0 0
\(523\) 32.8042 1.43443 0.717215 0.696852i \(-0.245417\pi\)
0.717215 + 0.696852i \(0.245417\pi\)
\(524\) 0 0
\(525\) −26.7493 −1.16744
\(526\) 0 0
\(527\) −1.13037 −0.0492398
\(528\) 0 0
\(529\) 4.32859 0.188200
\(530\) 0 0
\(531\) 9.31990 0.404449
\(532\) 0 0
\(533\) −3.24885 −0.140723
\(534\) 0 0
\(535\) 23.7379 1.02628
\(536\) 0 0
\(537\) −17.2887 −0.746062
\(538\) 0 0
\(539\) −0.325467 −0.0140189
\(540\) 0 0
\(541\) 12.5910 0.541328 0.270664 0.962674i \(-0.412757\pi\)
0.270664 + 0.962674i \(0.412757\pi\)
\(542\) 0 0
\(543\) −24.9622 −1.07123
\(544\) 0 0
\(545\) −4.41059 −0.188929
\(546\) 0 0
\(547\) −31.3205 −1.33917 −0.669584 0.742736i \(-0.733528\pi\)
−0.669584 + 0.742736i \(0.733528\pi\)
\(548\) 0 0
\(549\) −5.18738 −0.221392
\(550\) 0 0
\(551\) −59.7343 −2.54476
\(552\) 0 0
\(553\) −35.5049 −1.50982
\(554\) 0 0
\(555\) 41.8909 1.77817
\(556\) 0 0
\(557\) 29.6867 1.25787 0.628933 0.777460i \(-0.283492\pi\)
0.628933 + 0.777460i \(0.283492\pi\)
\(558\) 0 0
\(559\) 0.937908 0.0396693
\(560\) 0 0
\(561\) 15.6867 0.662293
\(562\) 0 0
\(563\) 6.37326 0.268601 0.134301 0.990941i \(-0.457121\pi\)
0.134301 + 0.990941i \(0.457121\pi\)
\(564\) 0 0
\(565\) 4.09397 0.172234
\(566\) 0 0
\(567\) 8.51741 0.357697
\(568\) 0 0
\(569\) 28.9920 1.21541 0.607703 0.794164i \(-0.292091\pi\)
0.607703 + 0.794164i \(0.292091\pi\)
\(570\) 0 0
\(571\) −26.1872 −1.09590 −0.547949 0.836511i \(-0.684591\pi\)
−0.547949 + 0.836511i \(0.684591\pi\)
\(572\) 0 0
\(573\) −13.9000 −0.580680
\(574\) 0 0
\(575\) −40.5654 −1.69169
\(576\) 0 0
\(577\) 34.8454 1.45063 0.725316 0.688416i \(-0.241694\pi\)
0.725316 + 0.688416i \(0.241694\pi\)
\(578\) 0 0
\(579\) 27.5916 1.14667
\(580\) 0 0
\(581\) −15.3220 −0.635662
\(582\) 0 0
\(583\) 15.0578 0.623630
\(584\) 0 0
\(585\) −2.11139 −0.0872951
\(586\) 0 0
\(587\) −44.7924 −1.84878 −0.924391 0.381447i \(-0.875426\pi\)
−0.924391 + 0.381447i \(0.875426\pi\)
\(588\) 0 0
\(589\) −1.19163 −0.0491003
\(590\) 0 0
\(591\) −9.32762 −0.383687
\(592\) 0 0
\(593\) 29.3237 1.20418 0.602091 0.798428i \(-0.294335\pi\)
0.602091 + 0.798428i \(0.294335\pi\)
\(594\) 0 0
\(595\) −57.0047 −2.33697
\(596\) 0 0
\(597\) −12.0651 −0.493790
\(598\) 0 0
\(599\) −10.6058 −0.433342 −0.216671 0.976245i \(-0.569520\pi\)
−0.216671 + 0.976245i \(0.569520\pi\)
\(600\) 0 0
\(601\) −17.5359 −0.715304 −0.357652 0.933855i \(-0.616423\pi\)
−0.357652 + 0.933855i \(0.616423\pi\)
\(602\) 0 0
\(603\) −18.5823 −0.756731
\(604\) 0 0
\(605\) 24.4052 0.992211
\(606\) 0 0
\(607\) −9.86097 −0.400245 −0.200122 0.979771i \(-0.564134\pi\)
−0.200122 + 0.979771i \(0.564134\pi\)
\(608\) 0 0
\(609\) −32.7506 −1.32712
\(610\) 0 0
\(611\) −0.0519075 −0.00209995
\(612\) 0 0
\(613\) 18.4422 0.744875 0.372438 0.928057i \(-0.378522\pi\)
0.372438 + 0.928057i \(0.378522\pi\)
\(614\) 0 0
\(615\) −33.9002 −1.36699
\(616\) 0 0
\(617\) −4.87178 −0.196130 −0.0980652 0.995180i \(-0.531265\pi\)
−0.0980652 + 0.995180i \(0.531265\pi\)
\(618\) 0 0
\(619\) 12.2177 0.491071 0.245536 0.969388i \(-0.421036\pi\)
0.245536 + 0.969388i \(0.421036\pi\)
\(620\) 0 0
\(621\) 29.2312 1.17301
\(622\) 0 0
\(623\) 27.6203 1.10659
\(624\) 0 0
\(625\) −3.58516 −0.143407
\(626\) 0 0
\(627\) 16.5368 0.660416
\(628\) 0 0
\(629\) 54.2903 2.16470
\(630\) 0 0
\(631\) −7.01178 −0.279135 −0.139567 0.990213i \(-0.544571\pi\)
−0.139567 + 0.990213i \(0.544571\pi\)
\(632\) 0 0
\(633\) 8.83979 0.351350
\(634\) 0 0
\(635\) −13.5210 −0.536563
\(636\) 0 0
\(637\) −0.0703120 −0.00278586
\(638\) 0 0
\(639\) 11.0296 0.436323
\(640\) 0 0
\(641\) −22.0216 −0.869800 −0.434900 0.900479i \(-0.643216\pi\)
−0.434900 + 0.900479i \(0.643216\pi\)
\(642\) 0 0
\(643\) 27.3253 1.07760 0.538802 0.842432i \(-0.318877\pi\)
0.538802 + 0.842432i \(0.318877\pi\)
\(644\) 0 0
\(645\) 9.78662 0.385348
\(646\) 0 0
\(647\) −42.8063 −1.68289 −0.841444 0.540344i \(-0.818294\pi\)
−0.841444 + 0.540344i \(0.818294\pi\)
\(648\) 0 0
\(649\) 14.1969 0.557277
\(650\) 0 0
\(651\) −0.653337 −0.0256063
\(652\) 0 0
\(653\) 31.8210 1.24525 0.622626 0.782520i \(-0.286066\pi\)
0.622626 + 0.782520i \(0.286066\pi\)
\(654\) 0 0
\(655\) 42.4755 1.65966
\(656\) 0 0
\(657\) 1.46780 0.0572644
\(658\) 0 0
\(659\) 8.80529 0.343005 0.171503 0.985184i \(-0.445138\pi\)
0.171503 + 0.985184i \(0.445138\pi\)
\(660\) 0 0
\(661\) 47.6268 1.85247 0.926234 0.376948i \(-0.123026\pi\)
0.926234 + 0.376948i \(0.123026\pi\)
\(662\) 0 0
\(663\) 3.38886 0.131612
\(664\) 0 0
\(665\) −60.0940 −2.33034
\(666\) 0 0
\(667\) −49.6662 −1.92308
\(668\) 0 0
\(669\) 24.2824 0.938813
\(670\) 0 0
\(671\) −7.90186 −0.305048
\(672\) 0 0
\(673\) 21.6638 0.835077 0.417538 0.908659i \(-0.362893\pi\)
0.417538 + 0.908659i \(0.362893\pi\)
\(674\) 0 0
\(675\) −43.3895 −1.67006
\(676\) 0 0
\(677\) 21.0477 0.808927 0.404463 0.914554i \(-0.367458\pi\)
0.404463 + 0.914554i \(0.367458\pi\)
\(678\) 0 0
\(679\) −1.44671 −0.0555195
\(680\) 0 0
\(681\) 28.9314 1.10865
\(682\) 0 0
\(683\) 2.07993 0.0795863 0.0397932 0.999208i \(-0.487330\pi\)
0.0397932 + 0.999208i \(0.487330\pi\)
\(684\) 0 0
\(685\) 39.4615 1.50775
\(686\) 0 0
\(687\) 18.7685 0.716064
\(688\) 0 0
\(689\) 3.25299 0.123929
\(690\) 0 0
\(691\) −14.0094 −0.532941 −0.266470 0.963843i \(-0.585857\pi\)
−0.266470 + 0.963843i \(0.585857\pi\)
\(692\) 0 0
\(693\) −7.32089 −0.278097
\(694\) 0 0
\(695\) 67.0965 2.54511
\(696\) 0 0
\(697\) −43.9344 −1.66413
\(698\) 0 0
\(699\) 4.60525 0.174187
\(700\) 0 0
\(701\) 37.8604 1.42997 0.714984 0.699141i \(-0.246434\pi\)
0.714984 + 0.699141i \(0.246434\pi\)
\(702\) 0 0
\(703\) 57.2325 2.15856
\(704\) 0 0
\(705\) −0.541630 −0.0203990
\(706\) 0 0
\(707\) −43.9717 −1.65373
\(708\) 0 0
\(709\) −25.5861 −0.960908 −0.480454 0.877020i \(-0.659528\pi\)
−0.480454 + 0.877020i \(0.659528\pi\)
\(710\) 0 0
\(711\) −17.7836 −0.666939
\(712\) 0 0
\(713\) −0.990785 −0.0371052
\(714\) 0 0
\(715\) −3.21625 −0.120281
\(716\) 0 0
\(717\) −24.5297 −0.916079
\(718\) 0 0
\(719\) −24.4381 −0.911386 −0.455693 0.890137i \(-0.650609\pi\)
−0.455693 + 0.890137i \(0.650609\pi\)
\(720\) 0 0
\(721\) −0.892785 −0.0332491
\(722\) 0 0
\(723\) 11.9955 0.446119
\(724\) 0 0
\(725\) 73.7224 2.73798
\(726\) 0 0
\(727\) −37.1717 −1.37862 −0.689311 0.724465i \(-0.742087\pi\)
−0.689311 + 0.724465i \(0.742087\pi\)
\(728\) 0 0
\(729\) 25.8777 0.958435
\(730\) 0 0
\(731\) 12.6834 0.469113
\(732\) 0 0
\(733\) −14.9168 −0.550964 −0.275482 0.961306i \(-0.588837\pi\)
−0.275482 + 0.961306i \(0.588837\pi\)
\(734\) 0 0
\(735\) −0.733672 −0.0270619
\(736\) 0 0
\(737\) −28.3062 −1.04267
\(738\) 0 0
\(739\) −27.4561 −1.00999 −0.504994 0.863123i \(-0.668505\pi\)
−0.504994 + 0.863123i \(0.668505\pi\)
\(740\) 0 0
\(741\) 3.57251 0.131239
\(742\) 0 0
\(743\) −9.07117 −0.332789 −0.166394 0.986059i \(-0.553212\pi\)
−0.166394 + 0.986059i \(0.553212\pi\)
\(744\) 0 0
\(745\) −24.6144 −0.901803
\(746\) 0 0
\(747\) −7.67445 −0.280793
\(748\) 0 0
\(749\) 17.7811 0.649709
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −19.7680 −0.720385
\(754\) 0 0
\(755\) 33.5387 1.22060
\(756\) 0 0
\(757\) 0.960844 0.0349225 0.0174612 0.999848i \(-0.494442\pi\)
0.0174612 + 0.999848i \(0.494442\pi\)
\(758\) 0 0
\(759\) 13.7496 0.499078
\(760\) 0 0
\(761\) −17.7673 −0.644064 −0.322032 0.946729i \(-0.604366\pi\)
−0.322032 + 0.946729i \(0.604366\pi\)
\(762\) 0 0
\(763\) −3.30381 −0.119606
\(764\) 0 0
\(765\) −28.5524 −1.03232
\(766\) 0 0
\(767\) 3.06701 0.110743
\(768\) 0 0
\(769\) 47.3537 1.70762 0.853809 0.520587i \(-0.174287\pi\)
0.853809 + 0.520587i \(0.174287\pi\)
\(770\) 0 0
\(771\) −14.3646 −0.517327
\(772\) 0 0
\(773\) 21.7897 0.783720 0.391860 0.920025i \(-0.371832\pi\)
0.391860 + 0.920025i \(0.371832\pi\)
\(774\) 0 0
\(775\) 1.47068 0.0528284
\(776\) 0 0
\(777\) 31.3789 1.12571
\(778\) 0 0
\(779\) −46.3153 −1.65942
\(780\) 0 0
\(781\) 16.8012 0.601195
\(782\) 0 0
\(783\) −53.1239 −1.89849
\(784\) 0 0
\(785\) 19.5533 0.697888
\(786\) 0 0
\(787\) −23.5080 −0.837971 −0.418985 0.907993i \(-0.637614\pi\)
−0.418985 + 0.907993i \(0.637614\pi\)
\(788\) 0 0
\(789\) 0.564131 0.0200836
\(790\) 0 0
\(791\) 3.06664 0.109037
\(792\) 0 0
\(793\) −1.70707 −0.0606199
\(794\) 0 0
\(795\) 33.9434 1.20385
\(796\) 0 0
\(797\) 34.0936 1.20766 0.603829 0.797114i \(-0.293641\pi\)
0.603829 + 0.797114i \(0.293641\pi\)
\(798\) 0 0
\(799\) −0.701949 −0.0248332
\(800\) 0 0
\(801\) 13.8344 0.488816
\(802\) 0 0
\(803\) 2.23588 0.0789026
\(804\) 0 0
\(805\) −49.9653 −1.76105
\(806\) 0 0
\(807\) −11.6740 −0.410943
\(808\) 0 0
\(809\) −0.128725 −0.00452575 −0.00226287 0.999997i \(-0.500720\pi\)
−0.00226287 + 0.999997i \(0.500720\pi\)
\(810\) 0 0
\(811\) −20.3188 −0.713490 −0.356745 0.934202i \(-0.616114\pi\)
−0.356745 + 0.934202i \(0.616114\pi\)
\(812\) 0 0
\(813\) 26.9007 0.943450
\(814\) 0 0
\(815\) −31.1848 −1.09236
\(816\) 0 0
\(817\) 13.3707 0.467783
\(818\) 0 0
\(819\) −1.58156 −0.0552642
\(820\) 0 0
\(821\) −35.9433 −1.25443 −0.627215 0.778846i \(-0.715805\pi\)
−0.627215 + 0.778846i \(0.715805\pi\)
\(822\) 0 0
\(823\) −15.5476 −0.541955 −0.270978 0.962586i \(-0.587347\pi\)
−0.270978 + 0.962586i \(0.587347\pi\)
\(824\) 0 0
\(825\) −20.4093 −0.710559
\(826\) 0 0
\(827\) 36.5751 1.27184 0.635921 0.771754i \(-0.280620\pi\)
0.635921 + 0.771754i \(0.280620\pi\)
\(828\) 0 0
\(829\) 24.3098 0.844313 0.422156 0.906523i \(-0.361273\pi\)
0.422156 + 0.906523i \(0.361273\pi\)
\(830\) 0 0
\(831\) 36.3540 1.26111
\(832\) 0 0
\(833\) −0.950835 −0.0329445
\(834\) 0 0
\(835\) −89.3452 −3.09192
\(836\) 0 0
\(837\) −1.05976 −0.0366307
\(838\) 0 0
\(839\) −13.0316 −0.449901 −0.224951 0.974370i \(-0.572222\pi\)
−0.224951 + 0.974370i \(0.572222\pi\)
\(840\) 0 0
\(841\) 61.2620 2.11248
\(842\) 0 0
\(843\) −37.6623 −1.29716
\(844\) 0 0
\(845\) 45.7422 1.57358
\(846\) 0 0
\(847\) 18.2810 0.628143
\(848\) 0 0
\(849\) −23.6868 −0.812929
\(850\) 0 0
\(851\) 47.5861 1.63123
\(852\) 0 0
\(853\) −41.0184 −1.40444 −0.702222 0.711958i \(-0.747809\pi\)
−0.702222 + 0.711958i \(0.747809\pi\)
\(854\) 0 0
\(855\) −30.0998 −1.02939
\(856\) 0 0
\(857\) −28.1492 −0.961557 −0.480779 0.876842i \(-0.659646\pi\)
−0.480779 + 0.876842i \(0.659646\pi\)
\(858\) 0 0
\(859\) 9.31891 0.317957 0.158979 0.987282i \(-0.449180\pi\)
0.158979 + 0.987282i \(0.449180\pi\)
\(860\) 0 0
\(861\) −25.3933 −0.865403
\(862\) 0 0
\(863\) −10.7485 −0.365882 −0.182941 0.983124i \(-0.558562\pi\)
−0.182941 + 0.983124i \(0.558562\pi\)
\(864\) 0 0
\(865\) −11.9715 −0.407043
\(866\) 0 0
\(867\) 23.9262 0.812577
\(868\) 0 0
\(869\) −27.0896 −0.918951
\(870\) 0 0
\(871\) −6.11511 −0.207203
\(872\) 0 0
\(873\) −0.724624 −0.0245248
\(874\) 0 0
\(875\) 26.3771 0.891710
\(876\) 0 0
\(877\) 11.9566 0.403747 0.201873 0.979412i \(-0.435297\pi\)
0.201873 + 0.979412i \(0.435297\pi\)
\(878\) 0 0
\(879\) 17.7293 0.597993
\(880\) 0 0
\(881\) 9.42127 0.317411 0.158705 0.987326i \(-0.449268\pi\)
0.158705 + 0.987326i \(0.449268\pi\)
\(882\) 0 0
\(883\) −52.3746 −1.76254 −0.881272 0.472609i \(-0.843312\pi\)
−0.881272 + 0.472609i \(0.843312\pi\)
\(884\) 0 0
\(885\) 32.0028 1.07576
\(886\) 0 0
\(887\) 32.9398 1.10601 0.553005 0.833178i \(-0.313481\pi\)
0.553005 + 0.833178i \(0.313481\pi\)
\(888\) 0 0
\(889\) −10.1280 −0.339684
\(890\) 0 0
\(891\) 6.49863 0.217712
\(892\) 0 0
\(893\) −0.739989 −0.0247628
\(894\) 0 0
\(895\) 47.9354 1.60230
\(896\) 0 0
\(897\) 2.97037 0.0991779
\(898\) 0 0
\(899\) 1.80063 0.0600542
\(900\) 0 0
\(901\) 43.9905 1.46554
\(902\) 0 0
\(903\) 7.33079 0.243954
\(904\) 0 0
\(905\) 69.2112 2.30066
\(906\) 0 0
\(907\) 2.14636 0.0712688 0.0356344 0.999365i \(-0.488655\pi\)
0.0356344 + 0.999365i \(0.488655\pi\)
\(908\) 0 0
\(909\) −22.0245 −0.730506
\(910\) 0 0
\(911\) −13.4623 −0.446026 −0.223013 0.974816i \(-0.571589\pi\)
−0.223013 + 0.974816i \(0.571589\pi\)
\(912\) 0 0
\(913\) −11.6904 −0.386895
\(914\) 0 0
\(915\) −17.8125 −0.588862
\(916\) 0 0
\(917\) 31.8168 1.05068
\(918\) 0 0
\(919\) −57.7851 −1.90615 −0.953077 0.302729i \(-0.902102\pi\)
−0.953077 + 0.302729i \(0.902102\pi\)
\(920\) 0 0
\(921\) 13.7946 0.454548
\(922\) 0 0
\(923\) 3.62963 0.119471
\(924\) 0 0
\(925\) −70.6348 −2.32246
\(926\) 0 0
\(927\) −0.447177 −0.0146872
\(928\) 0 0
\(929\) −0.800369 −0.0262592 −0.0131296 0.999914i \(-0.504179\pi\)
−0.0131296 + 0.999914i \(0.504179\pi\)
\(930\) 0 0
\(931\) −1.00236 −0.0328511
\(932\) 0 0
\(933\) −20.3636 −0.666674
\(934\) 0 0
\(935\) −43.4936 −1.42239
\(936\) 0 0
\(937\) 17.5708 0.574012 0.287006 0.957929i \(-0.407340\pi\)
0.287006 + 0.957929i \(0.407340\pi\)
\(938\) 0 0
\(939\) 12.3733 0.403788
\(940\) 0 0
\(941\) −43.3075 −1.41179 −0.705893 0.708319i \(-0.749454\pi\)
−0.705893 + 0.708319i \(0.749454\pi\)
\(942\) 0 0
\(943\) −38.5090 −1.25403
\(944\) 0 0
\(945\) −53.4438 −1.73853
\(946\) 0 0
\(947\) −28.8758 −0.938337 −0.469169 0.883109i \(-0.655446\pi\)
−0.469169 + 0.883109i \(0.655446\pi\)
\(948\) 0 0
\(949\) 0.483027 0.0156797
\(950\) 0 0
\(951\) −6.63729 −0.215229
\(952\) 0 0
\(953\) −47.3290 −1.53314 −0.766568 0.642163i \(-0.778037\pi\)
−0.766568 + 0.642163i \(0.778037\pi\)
\(954\) 0 0
\(955\) 38.5397 1.24712
\(956\) 0 0
\(957\) −24.9881 −0.807750
\(958\) 0 0
\(959\) 29.5592 0.954515
\(960\) 0 0
\(961\) −30.9641 −0.998841
\(962\) 0 0
\(963\) 8.90619 0.286998
\(964\) 0 0
\(965\) −76.5017 −2.46268
\(966\) 0 0
\(967\) 28.3284 0.910980 0.455490 0.890241i \(-0.349464\pi\)
0.455490 + 0.890241i \(0.349464\pi\)
\(968\) 0 0
\(969\) 48.3113 1.55198
\(970\) 0 0
\(971\) 1.74420 0.0559739 0.0279870 0.999608i \(-0.491090\pi\)
0.0279870 + 0.999608i \(0.491090\pi\)
\(972\) 0 0
\(973\) 50.2595 1.61124
\(974\) 0 0
\(975\) −4.40910 −0.141204
\(976\) 0 0
\(977\) −26.2490 −0.839779 −0.419889 0.907575i \(-0.637931\pi\)
−0.419889 + 0.907575i \(0.637931\pi\)
\(978\) 0 0
\(979\) 21.0738 0.673522
\(980\) 0 0
\(981\) −1.65481 −0.0528339
\(982\) 0 0
\(983\) 41.8706 1.33546 0.667732 0.744401i \(-0.267265\pi\)
0.667732 + 0.744401i \(0.267265\pi\)
\(984\) 0 0
\(985\) 25.8621 0.824037
\(986\) 0 0
\(987\) −0.405715 −0.0129140
\(988\) 0 0
\(989\) 11.1171 0.353505
\(990\) 0 0
\(991\) 11.0507 0.351038 0.175519 0.984476i \(-0.443840\pi\)
0.175519 + 0.984476i \(0.443840\pi\)
\(992\) 0 0
\(993\) −25.6561 −0.814171
\(994\) 0 0
\(995\) 33.4521 1.06050
\(996\) 0 0
\(997\) 33.5320 1.06197 0.530985 0.847381i \(-0.321822\pi\)
0.530985 + 0.847381i \(0.321822\pi\)
\(998\) 0 0
\(999\) 50.8990 1.61037
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 \(a_p\))