Properties

Label 6004.2.a.g.1.13
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.338800 q^{3} -3.08469 q^{5} -4.48412 q^{7} -2.88521 q^{9} +O(q^{10})\) \(q-0.338800 q^{3} -3.08469 q^{5} -4.48412 q^{7} -2.88521 q^{9} +5.90726 q^{11} +1.46463 q^{13} +1.04509 q^{15} -2.53371 q^{17} +1.00000 q^{19} +1.51922 q^{21} +2.61368 q^{23} +4.51532 q^{25} +1.99391 q^{27} +2.21728 q^{29} -8.75033 q^{31} -2.00138 q^{33} +13.8321 q^{35} -1.37694 q^{37} -0.496218 q^{39} +9.51019 q^{41} +10.4231 q^{43} +8.90000 q^{45} +4.08096 q^{47} +13.1073 q^{49} +0.858421 q^{51} -0.486802 q^{53} -18.2221 q^{55} -0.338800 q^{57} -11.1934 q^{59} +2.62780 q^{61} +12.9376 q^{63} -4.51794 q^{65} -10.4774 q^{67} -0.885514 q^{69} -3.34173 q^{71} +10.8433 q^{73} -1.52979 q^{75} -26.4889 q^{77} -1.00000 q^{79} +7.98011 q^{81} +5.71898 q^{83} +7.81571 q^{85} -0.751216 q^{87} -12.0355 q^{89} -6.56759 q^{91} +2.96461 q^{93} -3.08469 q^{95} +10.8032 q^{97} -17.0437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −0.338800 −0.195606 −0.0978032 0.995206i \(-0.531182\pi\)
−0.0978032 + 0.995206i \(0.531182\pi\)
\(4\) 0 0
\(5\) −3.08469 −1.37952 −0.689758 0.724040i \(-0.742283\pi\)
−0.689758 + 0.724040i \(0.742283\pi\)
\(6\) 0 0
\(7\) −4.48412 −1.69484 −0.847419 0.530925i \(-0.821845\pi\)
−0.847419 + 0.530925i \(0.821845\pi\)
\(8\) 0 0
\(9\) −2.88521 −0.961738
\(10\) 0 0
\(11\) 5.90726 1.78111 0.890553 0.454879i \(-0.150318\pi\)
0.890553 + 0.454879i \(0.150318\pi\)
\(12\) 0 0
\(13\) 1.46463 0.406216 0.203108 0.979156i \(-0.434896\pi\)
0.203108 + 0.979156i \(0.434896\pi\)
\(14\) 0 0
\(15\) 1.04509 0.269842
\(16\) 0 0
\(17\) −2.53371 −0.614514 −0.307257 0.951626i \(-0.599411\pi\)
−0.307257 + 0.951626i \(0.599411\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 1.51922 0.331521
\(22\) 0 0
\(23\) 2.61368 0.544989 0.272495 0.962157i \(-0.412151\pi\)
0.272495 + 0.962157i \(0.412151\pi\)
\(24\) 0 0
\(25\) 4.51532 0.903065
\(26\) 0 0
\(27\) 1.99391 0.383729
\(28\) 0 0
\(29\) 2.21728 0.411739 0.205869 0.978579i \(-0.433998\pi\)
0.205869 + 0.978579i \(0.433998\pi\)
\(30\) 0 0
\(31\) −8.75033 −1.57161 −0.785803 0.618477i \(-0.787750\pi\)
−0.785803 + 0.618477i \(0.787750\pi\)
\(32\) 0 0
\(33\) −2.00138 −0.348396
\(34\) 0 0
\(35\) 13.8321 2.33806
\(36\) 0 0
\(37\) −1.37694 −0.226368 −0.113184 0.993574i \(-0.536105\pi\)
−0.113184 + 0.993574i \(0.536105\pi\)
\(38\) 0 0
\(39\) −0.496218 −0.0794585
\(40\) 0 0
\(41\) 9.51019 1.48524 0.742621 0.669712i \(-0.233582\pi\)
0.742621 + 0.669712i \(0.233582\pi\)
\(42\) 0 0
\(43\) 10.4231 1.58950 0.794752 0.606934i \(-0.207601\pi\)
0.794752 + 0.606934i \(0.207601\pi\)
\(44\) 0 0
\(45\) 8.90000 1.32673
\(46\) 0 0
\(47\) 4.08096 0.595269 0.297635 0.954680i \(-0.403802\pi\)
0.297635 + 0.954680i \(0.403802\pi\)
\(48\) 0 0
\(49\) 13.1073 1.87248
\(50\) 0 0
\(51\) 0.858421 0.120203
\(52\) 0 0
\(53\) −0.486802 −0.0668675 −0.0334337 0.999441i \(-0.510644\pi\)
−0.0334337 + 0.999441i \(0.510644\pi\)
\(54\) 0 0
\(55\) −18.2221 −2.45706
\(56\) 0 0
\(57\) −0.338800 −0.0448752
\(58\) 0 0
\(59\) −11.1934 −1.45726 −0.728628 0.684909i \(-0.759842\pi\)
−0.728628 + 0.684909i \(0.759842\pi\)
\(60\) 0 0
\(61\) 2.62780 0.336455 0.168228 0.985748i \(-0.446196\pi\)
0.168228 + 0.985748i \(0.446196\pi\)
\(62\) 0 0
\(63\) 12.9376 1.62999
\(64\) 0 0
\(65\) −4.51794 −0.560382
\(66\) 0 0
\(67\) −10.4774 −1.28001 −0.640006 0.768370i \(-0.721068\pi\)
−0.640006 + 0.768370i \(0.721068\pi\)
\(68\) 0 0
\(69\) −0.885514 −0.106603
\(70\) 0 0
\(71\) −3.34173 −0.396590 −0.198295 0.980142i \(-0.563540\pi\)
−0.198295 + 0.980142i \(0.563540\pi\)
\(72\) 0 0
\(73\) 10.8433 1.26911 0.634554 0.772879i \(-0.281184\pi\)
0.634554 + 0.772879i \(0.281184\pi\)
\(74\) 0 0
\(75\) −1.52979 −0.176645
\(76\) 0 0
\(77\) −26.4889 −3.01869
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 7.98011 0.886678
\(82\) 0 0
\(83\) 5.71898 0.627740 0.313870 0.949466i \(-0.398374\pi\)
0.313870 + 0.949466i \(0.398374\pi\)
\(84\) 0 0
\(85\) 7.81571 0.847733
\(86\) 0 0
\(87\) −0.751216 −0.0805388
\(88\) 0 0
\(89\) −12.0355 −1.27576 −0.637878 0.770137i \(-0.720188\pi\)
−0.637878 + 0.770137i \(0.720188\pi\)
\(90\) 0 0
\(91\) −6.56759 −0.688471
\(92\) 0 0
\(93\) 2.96461 0.307416
\(94\) 0 0
\(95\) −3.08469 −0.316483
\(96\) 0 0
\(97\) 10.8032 1.09690 0.548449 0.836184i \(-0.315219\pi\)
0.548449 + 0.836184i \(0.315219\pi\)
\(98\) 0 0
\(99\) −17.0437 −1.71296
\(100\) 0 0
\(101\) 13.9850 1.39156 0.695782 0.718253i \(-0.255058\pi\)
0.695782 + 0.718253i \(0.255058\pi\)
\(102\) 0 0
\(103\) 15.0791 1.48579 0.742894 0.669410i \(-0.233453\pi\)
0.742894 + 0.669410i \(0.233453\pi\)
\(104\) 0 0
\(105\) −4.68633 −0.457339
\(106\) 0 0
\(107\) −6.29158 −0.608230 −0.304115 0.952635i \(-0.598361\pi\)
−0.304115 + 0.952635i \(0.598361\pi\)
\(108\) 0 0
\(109\) −20.2424 −1.93887 −0.969433 0.245356i \(-0.921095\pi\)
−0.969433 + 0.245356i \(0.921095\pi\)
\(110\) 0 0
\(111\) 0.466508 0.0442790
\(112\) 0 0
\(113\) 12.0917 1.13749 0.568747 0.822512i \(-0.307428\pi\)
0.568747 + 0.822512i \(0.307428\pi\)
\(114\) 0 0
\(115\) −8.06238 −0.751821
\(116\) 0 0
\(117\) −4.22578 −0.390674
\(118\) 0 0
\(119\) 11.3614 1.04150
\(120\) 0 0
\(121\) 23.8957 2.17234
\(122\) 0 0
\(123\) −3.22206 −0.290523
\(124\) 0 0
\(125\) 1.49508 0.133724
\(126\) 0 0
\(127\) −5.18235 −0.459859 −0.229930 0.973207i \(-0.573850\pi\)
−0.229930 + 0.973207i \(0.573850\pi\)
\(128\) 0 0
\(129\) −3.53134 −0.310917
\(130\) 0 0
\(131\) 18.8011 1.64266 0.821328 0.570456i \(-0.193233\pi\)
0.821328 + 0.570456i \(0.193233\pi\)
\(132\) 0 0
\(133\) −4.48412 −0.388822
\(134\) 0 0
\(135\) −6.15060 −0.529360
\(136\) 0 0
\(137\) −1.72878 −0.147700 −0.0738500 0.997269i \(-0.523529\pi\)
−0.0738500 + 0.997269i \(0.523529\pi\)
\(138\) 0 0
\(139\) −17.1941 −1.45838 −0.729190 0.684311i \(-0.760103\pi\)
−0.729190 + 0.684311i \(0.760103\pi\)
\(140\) 0 0
\(141\) −1.38263 −0.116439
\(142\) 0 0
\(143\) 8.65197 0.723514
\(144\) 0 0
\(145\) −6.83963 −0.568000
\(146\) 0 0
\(147\) −4.44077 −0.366268
\(148\) 0 0
\(149\) −1.98047 −0.162247 −0.0811233 0.996704i \(-0.525851\pi\)
−0.0811233 + 0.996704i \(0.525851\pi\)
\(150\) 0 0
\(151\) −16.5704 −1.34848 −0.674240 0.738512i \(-0.735529\pi\)
−0.674240 + 0.738512i \(0.735529\pi\)
\(152\) 0 0
\(153\) 7.31029 0.591002
\(154\) 0 0
\(155\) 26.9921 2.16806
\(156\) 0 0
\(157\) −19.2261 −1.53441 −0.767206 0.641401i \(-0.778354\pi\)
−0.767206 + 0.641401i \(0.778354\pi\)
\(158\) 0 0
\(159\) 0.164929 0.0130797
\(160\) 0 0
\(161\) −11.7200 −0.923668
\(162\) 0 0
\(163\) −9.35592 −0.732813 −0.366406 0.930455i \(-0.619412\pi\)
−0.366406 + 0.930455i \(0.619412\pi\)
\(164\) 0 0
\(165\) 6.17364 0.480618
\(166\) 0 0
\(167\) −6.03989 −0.467380 −0.233690 0.972311i \(-0.575080\pi\)
−0.233690 + 0.972311i \(0.575080\pi\)
\(168\) 0 0
\(169\) −10.8548 −0.834988
\(170\) 0 0
\(171\) −2.88521 −0.220638
\(172\) 0 0
\(173\) −16.6995 −1.26964 −0.634820 0.772660i \(-0.718926\pi\)
−0.634820 + 0.772660i \(0.718926\pi\)
\(174\) 0 0
\(175\) −20.2473 −1.53055
\(176\) 0 0
\(177\) 3.79233 0.285049
\(178\) 0 0
\(179\) 13.8403 1.03447 0.517236 0.855843i \(-0.326961\pi\)
0.517236 + 0.855843i \(0.326961\pi\)
\(180\) 0 0
\(181\) −16.7466 −1.24477 −0.622384 0.782712i \(-0.713836\pi\)
−0.622384 + 0.782712i \(0.713836\pi\)
\(182\) 0 0
\(183\) −0.890299 −0.0658128
\(184\) 0 0
\(185\) 4.24744 0.312278
\(186\) 0 0
\(187\) −14.9673 −1.09452
\(188\) 0 0
\(189\) −8.94094 −0.650358
\(190\) 0 0
\(191\) −0.352402 −0.0254989 −0.0127495 0.999919i \(-0.504058\pi\)
−0.0127495 + 0.999919i \(0.504058\pi\)
\(192\) 0 0
\(193\) −21.1203 −1.52027 −0.760137 0.649762i \(-0.774868\pi\)
−0.760137 + 0.649762i \(0.774868\pi\)
\(194\) 0 0
\(195\) 1.53068 0.109614
\(196\) 0 0
\(197\) −11.0954 −0.790512 −0.395256 0.918571i \(-0.629344\pi\)
−0.395256 + 0.918571i \(0.629344\pi\)
\(198\) 0 0
\(199\) 19.2457 1.36429 0.682144 0.731218i \(-0.261048\pi\)
0.682144 + 0.731218i \(0.261048\pi\)
\(200\) 0 0
\(201\) 3.54973 0.250379
\(202\) 0 0
\(203\) −9.94256 −0.697831
\(204\) 0 0
\(205\) −29.3360 −2.04892
\(206\) 0 0
\(207\) −7.54101 −0.524137
\(208\) 0 0
\(209\) 5.90726 0.408614
\(210\) 0 0
\(211\) −28.5102 −1.96272 −0.981361 0.192175i \(-0.938446\pi\)
−0.981361 + 0.192175i \(0.938446\pi\)
\(212\) 0 0
\(213\) 1.13218 0.0775756
\(214\) 0 0
\(215\) −32.1520 −2.19275
\(216\) 0 0
\(217\) 39.2375 2.66362
\(218\) 0 0
\(219\) −3.67370 −0.248246
\(220\) 0 0
\(221\) −3.71095 −0.249626
\(222\) 0 0
\(223\) −8.94778 −0.599188 −0.299594 0.954067i \(-0.596851\pi\)
−0.299594 + 0.954067i \(0.596851\pi\)
\(224\) 0 0
\(225\) −13.0277 −0.868512
\(226\) 0 0
\(227\) −1.57611 −0.104610 −0.0523052 0.998631i \(-0.516657\pi\)
−0.0523052 + 0.998631i \(0.516657\pi\)
\(228\) 0 0
\(229\) −17.5970 −1.16284 −0.581422 0.813602i \(-0.697504\pi\)
−0.581422 + 0.813602i \(0.697504\pi\)
\(230\) 0 0
\(231\) 8.97443 0.590474
\(232\) 0 0
\(233\) −26.6286 −1.74450 −0.872248 0.489063i \(-0.837339\pi\)
−0.872248 + 0.489063i \(0.837339\pi\)
\(234\) 0 0
\(235\) −12.5885 −0.821184
\(236\) 0 0
\(237\) 0.338800 0.0220074
\(238\) 0 0
\(239\) −22.4660 −1.45320 −0.726601 0.687059i \(-0.758901\pi\)
−0.726601 + 0.687059i \(0.758901\pi\)
\(240\) 0 0
\(241\) 15.2590 0.982921 0.491461 0.870900i \(-0.336463\pi\)
0.491461 + 0.870900i \(0.336463\pi\)
\(242\) 0 0
\(243\) −8.68540 −0.557169
\(244\) 0 0
\(245\) −40.4321 −2.58311
\(246\) 0 0
\(247\) 1.46463 0.0931924
\(248\) 0 0
\(249\) −1.93759 −0.122790
\(250\) 0 0
\(251\) 10.6697 0.673463 0.336732 0.941601i \(-0.390679\pi\)
0.336732 + 0.941601i \(0.390679\pi\)
\(252\) 0 0
\(253\) 15.4397 0.970683
\(254\) 0 0
\(255\) −2.64796 −0.165822
\(256\) 0 0
\(257\) 10.7725 0.671969 0.335984 0.941868i \(-0.390931\pi\)
0.335984 + 0.941868i \(0.390931\pi\)
\(258\) 0 0
\(259\) 6.17437 0.383656
\(260\) 0 0
\(261\) −6.39733 −0.395985
\(262\) 0 0
\(263\) 15.7910 0.973714 0.486857 0.873482i \(-0.338143\pi\)
0.486857 + 0.873482i \(0.338143\pi\)
\(264\) 0 0
\(265\) 1.50164 0.0922447
\(266\) 0 0
\(267\) 4.07762 0.249546
\(268\) 0 0
\(269\) −22.9870 −1.40154 −0.700770 0.713387i \(-0.747160\pi\)
−0.700770 + 0.713387i \(0.747160\pi\)
\(270\) 0 0
\(271\) 8.72036 0.529724 0.264862 0.964286i \(-0.414674\pi\)
0.264862 + 0.964286i \(0.414674\pi\)
\(272\) 0 0
\(273\) 2.22510 0.134669
\(274\) 0 0
\(275\) 26.6732 1.60845
\(276\) 0 0
\(277\) 4.41417 0.265222 0.132611 0.991168i \(-0.457664\pi\)
0.132611 + 0.991168i \(0.457664\pi\)
\(278\) 0 0
\(279\) 25.2466 1.51147
\(280\) 0 0
\(281\) −13.6091 −0.811848 −0.405924 0.913907i \(-0.633050\pi\)
−0.405924 + 0.913907i \(0.633050\pi\)
\(282\) 0 0
\(283\) −11.7878 −0.700714 −0.350357 0.936616i \(-0.613940\pi\)
−0.350357 + 0.936616i \(0.613940\pi\)
\(284\) 0 0
\(285\) 1.04509 0.0619060
\(286\) 0 0
\(287\) −42.6448 −2.51725
\(288\) 0 0
\(289\) −10.5803 −0.622372
\(290\) 0 0
\(291\) −3.66012 −0.214560
\(292\) 0 0
\(293\) 18.8709 1.10245 0.551224 0.834357i \(-0.314161\pi\)
0.551224 + 0.834357i \(0.314161\pi\)
\(294\) 0 0
\(295\) 34.5282 2.01031
\(296\) 0 0
\(297\) 11.7786 0.683461
\(298\) 0 0
\(299\) 3.82808 0.221383
\(300\) 0 0
\(301\) −46.7383 −2.69395
\(302\) 0 0
\(303\) −4.73814 −0.272199
\(304\) 0 0
\(305\) −8.10595 −0.464145
\(306\) 0 0
\(307\) 21.4752 1.22566 0.612828 0.790216i \(-0.290032\pi\)
0.612828 + 0.790216i \(0.290032\pi\)
\(308\) 0 0
\(309\) −5.10880 −0.290629
\(310\) 0 0
\(311\) 0.784787 0.0445012 0.0222506 0.999752i \(-0.492917\pi\)
0.0222506 + 0.999752i \(0.492917\pi\)
\(312\) 0 0
\(313\) 31.3559 1.77234 0.886169 0.463362i \(-0.153357\pi\)
0.886169 + 0.463362i \(0.153357\pi\)
\(314\) 0 0
\(315\) −39.9087 −2.24860
\(316\) 0 0
\(317\) 7.62243 0.428118 0.214059 0.976821i \(-0.431331\pi\)
0.214059 + 0.976821i \(0.431331\pi\)
\(318\) 0 0
\(319\) 13.0981 0.733351
\(320\) 0 0
\(321\) 2.13159 0.118974
\(322\) 0 0
\(323\) −2.53371 −0.140979
\(324\) 0 0
\(325\) 6.61330 0.366840
\(326\) 0 0
\(327\) 6.85812 0.379255
\(328\) 0 0
\(329\) −18.2995 −1.00889
\(330\) 0 0
\(331\) 15.5149 0.852774 0.426387 0.904541i \(-0.359786\pi\)
0.426387 + 0.904541i \(0.359786\pi\)
\(332\) 0 0
\(333\) 3.97277 0.217706
\(334\) 0 0
\(335\) 32.3194 1.76580
\(336\) 0 0
\(337\) 19.7990 1.07852 0.539259 0.842140i \(-0.318704\pi\)
0.539259 + 0.842140i \(0.318704\pi\)
\(338\) 0 0
\(339\) −4.09668 −0.222501
\(340\) 0 0
\(341\) −51.6905 −2.79920
\(342\) 0 0
\(343\) −27.3860 −1.47870
\(344\) 0 0
\(345\) 2.73154 0.147061
\(346\) 0 0
\(347\) −8.86787 −0.476052 −0.238026 0.971259i \(-0.576500\pi\)
−0.238026 + 0.971259i \(0.576500\pi\)
\(348\) 0 0
\(349\) 1.19957 0.0642115 0.0321058 0.999484i \(-0.489779\pi\)
0.0321058 + 0.999484i \(0.489779\pi\)
\(350\) 0 0
\(351\) 2.92035 0.155877
\(352\) 0 0
\(353\) −36.8592 −1.96182 −0.980909 0.194466i \(-0.937703\pi\)
−0.980909 + 0.194466i \(0.937703\pi\)
\(354\) 0 0
\(355\) 10.3082 0.547103
\(356\) 0 0
\(357\) −3.84926 −0.203725
\(358\) 0 0
\(359\) 32.8930 1.73602 0.868012 0.496542i \(-0.165397\pi\)
0.868012 + 0.496542i \(0.165397\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −8.09588 −0.424923
\(364\) 0 0
\(365\) −33.4481 −1.75075
\(366\) 0 0
\(367\) 17.9928 0.939219 0.469609 0.882874i \(-0.344395\pi\)
0.469609 + 0.882874i \(0.344395\pi\)
\(368\) 0 0
\(369\) −27.4389 −1.42841
\(370\) 0 0
\(371\) 2.18288 0.113330
\(372\) 0 0
\(373\) 16.2887 0.843396 0.421698 0.906736i \(-0.361434\pi\)
0.421698 + 0.906736i \(0.361434\pi\)
\(374\) 0 0
\(375\) −0.506533 −0.0261572
\(376\) 0 0
\(377\) 3.24751 0.167255
\(378\) 0 0
\(379\) −14.1494 −0.726805 −0.363402 0.931632i \(-0.618385\pi\)
−0.363402 + 0.931632i \(0.618385\pi\)
\(380\) 0 0
\(381\) 1.75578 0.0899514
\(382\) 0 0
\(383\) −31.8077 −1.62530 −0.812650 0.582752i \(-0.801976\pi\)
−0.812650 + 0.582752i \(0.801976\pi\)
\(384\) 0 0
\(385\) 81.7100 4.16433
\(386\) 0 0
\(387\) −30.0728 −1.52869
\(388\) 0 0
\(389\) −9.14502 −0.463671 −0.231835 0.972755i \(-0.574473\pi\)
−0.231835 + 0.972755i \(0.574473\pi\)
\(390\) 0 0
\(391\) −6.62229 −0.334904
\(392\) 0 0
\(393\) −6.36981 −0.321314
\(394\) 0 0
\(395\) 3.08469 0.155208
\(396\) 0 0
\(397\) 37.0203 1.85799 0.928997 0.370087i \(-0.120672\pi\)
0.928997 + 0.370087i \(0.120672\pi\)
\(398\) 0 0
\(399\) 1.51922 0.0760562
\(400\) 0 0
\(401\) −6.64571 −0.331871 −0.165935 0.986137i \(-0.553064\pi\)
−0.165935 + 0.986137i \(0.553064\pi\)
\(402\) 0 0
\(403\) −12.8160 −0.638412
\(404\) 0 0
\(405\) −24.6162 −1.22319
\(406\) 0 0
\(407\) −8.13395 −0.403185
\(408\) 0 0
\(409\) −30.4596 −1.50613 −0.753065 0.657946i \(-0.771425\pi\)
−0.753065 + 0.657946i \(0.771425\pi\)
\(410\) 0 0
\(411\) 0.585713 0.0288911
\(412\) 0 0
\(413\) 50.1926 2.46981
\(414\) 0 0
\(415\) −17.6413 −0.865977
\(416\) 0 0
\(417\) 5.82535 0.285269
\(418\) 0 0
\(419\) 9.79385 0.478461 0.239230 0.970963i \(-0.423105\pi\)
0.239230 + 0.970963i \(0.423105\pi\)
\(420\) 0 0
\(421\) −25.3652 −1.23622 −0.618111 0.786091i \(-0.712102\pi\)
−0.618111 + 0.786091i \(0.712102\pi\)
\(422\) 0 0
\(423\) −11.7744 −0.572493
\(424\) 0 0
\(425\) −11.4405 −0.554946
\(426\) 0 0
\(427\) −11.7834 −0.570237
\(428\) 0 0
\(429\) −2.93129 −0.141524
\(430\) 0 0
\(431\) −28.6505 −1.38005 −0.690023 0.723787i \(-0.742400\pi\)
−0.690023 + 0.723787i \(0.742400\pi\)
\(432\) 0 0
\(433\) −8.24308 −0.396137 −0.198069 0.980188i \(-0.563467\pi\)
−0.198069 + 0.980188i \(0.563467\pi\)
\(434\) 0 0
\(435\) 2.31727 0.111105
\(436\) 0 0
\(437\) 2.61368 0.125029
\(438\) 0 0
\(439\) 25.5811 1.22092 0.610461 0.792047i \(-0.290984\pi\)
0.610461 + 0.792047i \(0.290984\pi\)
\(440\) 0 0
\(441\) −37.8174 −1.80083
\(442\) 0 0
\(443\) 29.5111 1.40211 0.701056 0.713106i \(-0.252712\pi\)
0.701056 + 0.713106i \(0.252712\pi\)
\(444\) 0 0
\(445\) 37.1257 1.75993
\(446\) 0 0
\(447\) 0.670985 0.0317365
\(448\) 0 0
\(449\) −18.3951 −0.868121 −0.434060 0.900884i \(-0.642920\pi\)
−0.434060 + 0.900884i \(0.642920\pi\)
\(450\) 0 0
\(451\) 56.1792 2.64537
\(452\) 0 0
\(453\) 5.61405 0.263771
\(454\) 0 0
\(455\) 20.2590 0.949757
\(456\) 0 0
\(457\) −27.1112 −1.26821 −0.634104 0.773247i \(-0.718631\pi\)
−0.634104 + 0.773247i \(0.718631\pi\)
\(458\) 0 0
\(459\) −5.05199 −0.235807
\(460\) 0 0
\(461\) 37.5785 1.75021 0.875103 0.483937i \(-0.160793\pi\)
0.875103 + 0.483937i \(0.160793\pi\)
\(462\) 0 0
\(463\) 7.58950 0.352714 0.176357 0.984326i \(-0.443569\pi\)
0.176357 + 0.984326i \(0.443569\pi\)
\(464\) 0 0
\(465\) −9.14492 −0.424086
\(466\) 0 0
\(467\) 26.3208 1.21798 0.608991 0.793177i \(-0.291574\pi\)
0.608991 + 0.793177i \(0.291574\pi\)
\(468\) 0 0
\(469\) 46.9817 2.16941
\(470\) 0 0
\(471\) 6.51381 0.300141
\(472\) 0 0
\(473\) 61.5718 2.83108
\(474\) 0 0
\(475\) 4.51532 0.207177
\(476\) 0 0
\(477\) 1.40453 0.0643090
\(478\) 0 0
\(479\) −19.2534 −0.879709 −0.439855 0.898069i \(-0.644970\pi\)
−0.439855 + 0.898069i \(0.644970\pi\)
\(480\) 0 0
\(481\) −2.01671 −0.0919542
\(482\) 0 0
\(483\) 3.97075 0.180675
\(484\) 0 0
\(485\) −33.3245 −1.51319
\(486\) 0 0
\(487\) −7.52108 −0.340813 −0.170406 0.985374i \(-0.554508\pi\)
−0.170406 + 0.985374i \(0.554508\pi\)
\(488\) 0 0
\(489\) 3.16979 0.143343
\(490\) 0 0
\(491\) −1.14655 −0.0517431 −0.0258715 0.999665i \(-0.508236\pi\)
−0.0258715 + 0.999665i \(0.508236\pi\)
\(492\) 0 0
\(493\) −5.61794 −0.253020
\(494\) 0 0
\(495\) 52.5746 2.36305
\(496\) 0 0
\(497\) 14.9847 0.672156
\(498\) 0 0
\(499\) −23.6929 −1.06064 −0.530320 0.847797i \(-0.677928\pi\)
−0.530320 + 0.847797i \(0.677928\pi\)
\(500\) 0 0
\(501\) 2.04632 0.0914226
\(502\) 0 0
\(503\) 0.419221 0.0186921 0.00934606 0.999956i \(-0.497025\pi\)
0.00934606 + 0.999956i \(0.497025\pi\)
\(504\) 0 0
\(505\) −43.1396 −1.91968
\(506\) 0 0
\(507\) 3.67762 0.163329
\(508\) 0 0
\(509\) 17.1532 0.760302 0.380151 0.924924i \(-0.375872\pi\)
0.380151 + 0.924924i \(0.375872\pi\)
\(510\) 0 0
\(511\) −48.6225 −2.15093
\(512\) 0 0
\(513\) 1.99391 0.0880334
\(514\) 0 0
\(515\) −46.5144 −2.04967
\(516\) 0 0
\(517\) 24.1073 1.06024
\(518\) 0 0
\(519\) 5.65780 0.248350
\(520\) 0 0
\(521\) −35.7570 −1.56654 −0.783271 0.621680i \(-0.786450\pi\)
−0.783271 + 0.621680i \(0.786450\pi\)
\(522\) 0 0
\(523\) 37.9493 1.65941 0.829703 0.558205i \(-0.188510\pi\)
0.829703 + 0.558205i \(0.188510\pi\)
\(524\) 0 0
\(525\) 6.85977 0.299385
\(526\) 0 0
\(527\) 22.1708 0.965775
\(528\) 0 0
\(529\) −16.1687 −0.702987
\(530\) 0 0
\(531\) 32.2954 1.40150
\(532\) 0 0
\(533\) 13.9289 0.603330
\(534\) 0 0
\(535\) 19.4076 0.839063
\(536\) 0 0
\(537\) −4.68909 −0.202349
\(538\) 0 0
\(539\) 77.4284 3.33508
\(540\) 0 0
\(541\) 39.4666 1.69680 0.848401 0.529354i \(-0.177566\pi\)
0.848401 + 0.529354i \(0.177566\pi\)
\(542\) 0 0
\(543\) 5.67377 0.243485
\(544\) 0 0
\(545\) 62.4414 2.67470
\(546\) 0 0
\(547\) 31.0747 1.32866 0.664330 0.747440i \(-0.268717\pi\)
0.664330 + 0.747440i \(0.268717\pi\)
\(548\) 0 0
\(549\) −7.58176 −0.323582
\(550\) 0 0
\(551\) 2.21728 0.0944594
\(552\) 0 0
\(553\) 4.48412 0.190684
\(554\) 0 0
\(555\) −1.43903 −0.0610835
\(556\) 0 0
\(557\) 14.3467 0.607891 0.303945 0.952689i \(-0.401696\pi\)
0.303945 + 0.952689i \(0.401696\pi\)
\(558\) 0 0
\(559\) 15.2660 0.645682
\(560\) 0 0
\(561\) 5.07092 0.214094
\(562\) 0 0
\(563\) 34.7398 1.46411 0.732053 0.681248i \(-0.238562\pi\)
0.732053 + 0.681248i \(0.238562\pi\)
\(564\) 0 0
\(565\) −37.2993 −1.56919
\(566\) 0 0
\(567\) −35.7837 −1.50278
\(568\) 0 0
\(569\) 0.144869 0.00607321 0.00303660 0.999995i \(-0.499033\pi\)
0.00303660 + 0.999995i \(0.499033\pi\)
\(570\) 0 0
\(571\) −5.76371 −0.241204 −0.120602 0.992701i \(-0.538482\pi\)
−0.120602 + 0.992701i \(0.538482\pi\)
\(572\) 0 0
\(573\) 0.119394 0.00498775
\(574\) 0 0
\(575\) 11.8016 0.492160
\(576\) 0 0
\(577\) −2.07164 −0.0862434 −0.0431217 0.999070i \(-0.513730\pi\)
−0.0431217 + 0.999070i \(0.513730\pi\)
\(578\) 0 0
\(579\) 7.15557 0.297375
\(580\) 0 0
\(581\) −25.6446 −1.06392
\(582\) 0 0
\(583\) −2.87567 −0.119098
\(584\) 0 0
\(585\) 13.0352 0.538941
\(586\) 0 0
\(587\) −12.8255 −0.529367 −0.264683 0.964335i \(-0.585267\pi\)
−0.264683 + 0.964335i \(0.585267\pi\)
\(588\) 0 0
\(589\) −8.75033 −0.360551
\(590\) 0 0
\(591\) 3.75911 0.154629
\(592\) 0 0
\(593\) 20.5701 0.844714 0.422357 0.906430i \(-0.361203\pi\)
0.422357 + 0.906430i \(0.361203\pi\)
\(594\) 0 0
\(595\) −35.0466 −1.43677
\(596\) 0 0
\(597\) −6.52043 −0.266864
\(598\) 0 0
\(599\) 5.65119 0.230901 0.115451 0.993313i \(-0.463169\pi\)
0.115451 + 0.993313i \(0.463169\pi\)
\(600\) 0 0
\(601\) 26.9956 1.10117 0.550586 0.834779i \(-0.314404\pi\)
0.550586 + 0.834779i \(0.314404\pi\)
\(602\) 0 0
\(603\) 30.2294 1.23104
\(604\) 0 0
\(605\) −73.7109 −2.99678
\(606\) 0 0
\(607\) 22.9708 0.932356 0.466178 0.884691i \(-0.345631\pi\)
0.466178 + 0.884691i \(0.345631\pi\)
\(608\) 0 0
\(609\) 3.36854 0.136500
\(610\) 0 0
\(611\) 5.97711 0.241808
\(612\) 0 0
\(613\) −12.0176 −0.485388 −0.242694 0.970103i \(-0.578031\pi\)
−0.242694 + 0.970103i \(0.578031\pi\)
\(614\) 0 0
\(615\) 9.93905 0.400781
\(616\) 0 0
\(617\) −12.8926 −0.519038 −0.259519 0.965738i \(-0.583564\pi\)
−0.259519 + 0.965738i \(0.583564\pi\)
\(618\) 0 0
\(619\) −10.1606 −0.408390 −0.204195 0.978930i \(-0.565458\pi\)
−0.204195 + 0.978930i \(0.565458\pi\)
\(620\) 0 0
\(621\) 5.21144 0.209128
\(622\) 0 0
\(623\) 53.9685 2.16220
\(624\) 0 0
\(625\) −27.1885 −1.08754
\(626\) 0 0
\(627\) −2.00138 −0.0799275
\(628\) 0 0
\(629\) 3.48877 0.139106
\(630\) 0 0
\(631\) 28.3400 1.12820 0.564098 0.825708i \(-0.309224\pi\)
0.564098 + 0.825708i \(0.309224\pi\)
\(632\) 0 0
\(633\) 9.65925 0.383921
\(634\) 0 0
\(635\) 15.9860 0.634383
\(636\) 0 0
\(637\) 19.1974 0.760630
\(638\) 0 0
\(639\) 9.64161 0.381416
\(640\) 0 0
\(641\) 1.40962 0.0556767 0.0278384 0.999612i \(-0.491138\pi\)
0.0278384 + 0.999612i \(0.491138\pi\)
\(642\) 0 0
\(643\) −11.9832 −0.472573 −0.236287 0.971683i \(-0.575930\pi\)
−0.236287 + 0.971683i \(0.575930\pi\)
\(644\) 0 0
\(645\) 10.8931 0.428915
\(646\) 0 0
\(647\) −44.6259 −1.75443 −0.877213 0.480101i \(-0.840600\pi\)
−0.877213 + 0.480101i \(0.840600\pi\)
\(648\) 0 0
\(649\) −66.1223 −2.59553
\(650\) 0 0
\(651\) −13.2937 −0.521021
\(652\) 0 0
\(653\) −39.2720 −1.53683 −0.768416 0.639951i \(-0.778955\pi\)
−0.768416 + 0.639951i \(0.778955\pi\)
\(654\) 0 0
\(655\) −57.9955 −2.26607
\(656\) 0 0
\(657\) −31.2851 −1.22055
\(658\) 0 0
\(659\) −10.7789 −0.419884 −0.209942 0.977714i \(-0.567328\pi\)
−0.209942 + 0.977714i \(0.567328\pi\)
\(660\) 0 0
\(661\) −23.6337 −0.919243 −0.459621 0.888115i \(-0.652015\pi\)
−0.459621 + 0.888115i \(0.652015\pi\)
\(662\) 0 0
\(663\) 1.25727 0.0488284
\(664\) 0 0
\(665\) 13.8321 0.536387
\(666\) 0 0
\(667\) 5.79526 0.224393
\(668\) 0 0
\(669\) 3.03151 0.117205
\(670\) 0 0
\(671\) 15.5231 0.599262
\(672\) 0 0
\(673\) 9.51520 0.366784 0.183392 0.983040i \(-0.441292\pi\)
0.183392 + 0.983040i \(0.441292\pi\)
\(674\) 0 0
\(675\) 9.00316 0.346532
\(676\) 0 0
\(677\) −49.8809 −1.91708 −0.958539 0.284962i \(-0.908019\pi\)
−0.958539 + 0.284962i \(0.908019\pi\)
\(678\) 0 0
\(679\) −48.4428 −1.85906
\(680\) 0 0
\(681\) 0.533988 0.0204625
\(682\) 0 0
\(683\) −41.1571 −1.57483 −0.787417 0.616421i \(-0.788582\pi\)
−0.787417 + 0.616421i \(0.788582\pi\)
\(684\) 0 0
\(685\) 5.33277 0.203755
\(686\) 0 0
\(687\) 5.96188 0.227460
\(688\) 0 0
\(689\) −0.712987 −0.0271627
\(690\) 0 0
\(691\) 16.6379 0.632934 0.316467 0.948604i \(-0.397503\pi\)
0.316467 + 0.948604i \(0.397503\pi\)
\(692\) 0 0
\(693\) 76.4260 2.90319
\(694\) 0 0
\(695\) 53.0383 2.01186
\(696\) 0 0
\(697\) −24.0961 −0.912703
\(698\) 0 0
\(699\) 9.02177 0.341235
\(700\) 0 0
\(701\) −23.7052 −0.895332 −0.447666 0.894201i \(-0.647745\pi\)
−0.447666 + 0.894201i \(0.647745\pi\)
\(702\) 0 0
\(703\) −1.37694 −0.0519323
\(704\) 0 0
\(705\) 4.26499 0.160629
\(706\) 0 0
\(707\) −62.7106 −2.35848
\(708\) 0 0
\(709\) 30.5771 1.14835 0.574173 0.818734i \(-0.305324\pi\)
0.574173 + 0.818734i \(0.305324\pi\)
\(710\) 0 0
\(711\) 2.88521 0.108204
\(712\) 0 0
\(713\) −22.8705 −0.856508
\(714\) 0 0
\(715\) −26.6887 −0.998100
\(716\) 0 0
\(717\) 7.61148 0.284256
\(718\) 0 0
\(719\) −20.6191 −0.768963 −0.384482 0.923133i \(-0.625620\pi\)
−0.384482 + 0.923133i \(0.625620\pi\)
\(720\) 0 0
\(721\) −67.6164 −2.51817
\(722\) 0 0
\(723\) −5.16977 −0.192266
\(724\) 0 0
\(725\) 10.0117 0.371827
\(726\) 0 0
\(727\) −0.908317 −0.0336876 −0.0168438 0.999858i \(-0.505362\pi\)
−0.0168438 + 0.999858i \(0.505362\pi\)
\(728\) 0 0
\(729\) −20.9977 −0.777693
\(730\) 0 0
\(731\) −26.4090 −0.976773
\(732\) 0 0
\(733\) 51.9088 1.91730 0.958648 0.284595i \(-0.0918591\pi\)
0.958648 + 0.284595i \(0.0918591\pi\)
\(734\) 0 0
\(735\) 13.6984 0.505273
\(736\) 0 0
\(737\) −61.8925 −2.27984
\(738\) 0 0
\(739\) −2.64811 −0.0974123 −0.0487062 0.998813i \(-0.515510\pi\)
−0.0487062 + 0.998813i \(0.515510\pi\)
\(740\) 0 0
\(741\) −0.496218 −0.0182290
\(742\) 0 0
\(743\) −33.3942 −1.22511 −0.612557 0.790427i \(-0.709859\pi\)
−0.612557 + 0.790427i \(0.709859\pi\)
\(744\) 0 0
\(745\) 6.10915 0.223822
\(746\) 0 0
\(747\) −16.5005 −0.603721
\(748\) 0 0
\(749\) 28.2122 1.03085
\(750\) 0 0
\(751\) −4.63282 −0.169054 −0.0845270 0.996421i \(-0.526938\pi\)
−0.0845270 + 0.996421i \(0.526938\pi\)
\(752\) 0 0
\(753\) −3.61488 −0.131734
\(754\) 0 0
\(755\) 51.1146 1.86025
\(756\) 0 0
\(757\) −33.5146 −1.21811 −0.609055 0.793128i \(-0.708451\pi\)
−0.609055 + 0.793128i \(0.708451\pi\)
\(758\) 0 0
\(759\) −5.23096 −0.189872
\(760\) 0 0
\(761\) 6.94894 0.251899 0.125949 0.992037i \(-0.459802\pi\)
0.125949 + 0.992037i \(0.459802\pi\)
\(762\) 0 0
\(763\) 90.7692 3.28606
\(764\) 0 0
\(765\) −22.5500 −0.815297
\(766\) 0 0
\(767\) −16.3942 −0.591962
\(768\) 0 0
\(769\) 38.0036 1.37045 0.685223 0.728334i \(-0.259705\pi\)
0.685223 + 0.728334i \(0.259705\pi\)
\(770\) 0 0
\(771\) −3.64972 −0.131441
\(772\) 0 0
\(773\) −32.8033 −1.17985 −0.589926 0.807457i \(-0.700843\pi\)
−0.589926 + 0.807457i \(0.700843\pi\)
\(774\) 0 0
\(775\) −39.5106 −1.41926
\(776\) 0 0
\(777\) −2.09188 −0.0750457
\(778\) 0 0
\(779\) 9.51019 0.340738
\(780\) 0 0
\(781\) −19.7405 −0.706369
\(782\) 0 0
\(783\) 4.42106 0.157996
\(784\) 0 0
\(785\) 59.3067 2.11675
\(786\) 0 0
\(787\) 30.8568 1.09993 0.549963 0.835189i \(-0.314642\pi\)
0.549963 + 0.835189i \(0.314642\pi\)
\(788\) 0 0
\(789\) −5.34999 −0.190465
\(790\) 0 0
\(791\) −54.2208 −1.92787
\(792\) 0 0
\(793\) 3.84876 0.136674
\(794\) 0 0
\(795\) −0.508754 −0.0180437
\(796\) 0 0
\(797\) −23.6793 −0.838765 −0.419382 0.907810i \(-0.637753\pi\)
−0.419382 + 0.907810i \(0.637753\pi\)
\(798\) 0 0
\(799\) −10.3400 −0.365802
\(800\) 0 0
\(801\) 34.7249 1.22694
\(802\) 0 0
\(803\) 64.0539 2.26041
\(804\) 0 0
\(805\) 36.1527 1.27421
\(806\) 0 0
\(807\) 7.78799 0.274150
\(808\) 0 0
\(809\) −24.7466 −0.870044 −0.435022 0.900420i \(-0.643259\pi\)
−0.435022 + 0.900420i \(0.643259\pi\)
\(810\) 0 0
\(811\) 45.6336 1.60241 0.801206 0.598389i \(-0.204192\pi\)
0.801206 + 0.598389i \(0.204192\pi\)
\(812\) 0 0
\(813\) −2.95446 −0.103617
\(814\) 0 0
\(815\) 28.8601 1.01093
\(816\) 0 0
\(817\) 10.4231 0.364657
\(818\) 0 0
\(819\) 18.9489 0.662129
\(820\) 0 0
\(821\) −47.3053 −1.65097 −0.825484 0.564426i \(-0.809098\pi\)
−0.825484 + 0.564426i \(0.809098\pi\)
\(822\) 0 0
\(823\) 14.4445 0.503505 0.251753 0.967792i \(-0.418993\pi\)
0.251753 + 0.967792i \(0.418993\pi\)
\(824\) 0 0
\(825\) −9.03688 −0.314624
\(826\) 0 0
\(827\) 10.2502 0.356435 0.178218 0.983991i \(-0.442967\pi\)
0.178218 + 0.983991i \(0.442967\pi\)
\(828\) 0 0
\(829\) −46.0441 −1.59918 −0.799590 0.600547i \(-0.794950\pi\)
−0.799590 + 0.600547i \(0.794950\pi\)
\(830\) 0 0
\(831\) −1.49552 −0.0518791
\(832\) 0 0
\(833\) −33.2101 −1.15066
\(834\) 0 0
\(835\) 18.6312 0.644759
\(836\) 0 0
\(837\) −17.4474 −0.603070
\(838\) 0 0
\(839\) 2.67240 0.0922614 0.0461307 0.998935i \(-0.485311\pi\)
0.0461307 + 0.998935i \(0.485311\pi\)
\(840\) 0 0
\(841\) −24.0837 −0.830471
\(842\) 0 0
\(843\) 4.61075 0.158803
\(844\) 0 0
\(845\) 33.4839 1.15188
\(846\) 0 0
\(847\) −107.151 −3.68176
\(848\) 0 0
\(849\) 3.99372 0.137064
\(850\) 0 0
\(851\) −3.59888 −0.123368
\(852\) 0 0
\(853\) 28.0188 0.959345 0.479672 0.877448i \(-0.340755\pi\)
0.479672 + 0.877448i \(0.340755\pi\)
\(854\) 0 0
\(855\) 8.90000 0.304373
\(856\) 0 0
\(857\) 5.52577 0.188757 0.0943783 0.995536i \(-0.469914\pi\)
0.0943783 + 0.995536i \(0.469914\pi\)
\(858\) 0 0
\(859\) −44.3461 −1.51307 −0.756534 0.653954i \(-0.773109\pi\)
−0.756534 + 0.653954i \(0.773109\pi\)
\(860\) 0 0
\(861\) 14.4481 0.492389
\(862\) 0 0
\(863\) 0.737216 0.0250951 0.0125476 0.999921i \(-0.496006\pi\)
0.0125476 + 0.999921i \(0.496006\pi\)
\(864\) 0 0
\(865\) 51.5128 1.75149
\(866\) 0 0
\(867\) 3.58462 0.121740
\(868\) 0 0
\(869\) −5.90726 −0.200390
\(870\) 0 0
\(871\) −15.3455 −0.519962
\(872\) 0 0
\(873\) −31.1695 −1.05493
\(874\) 0 0
\(875\) −6.70411 −0.226640
\(876\) 0 0
\(877\) 8.07642 0.272721 0.136361 0.990659i \(-0.456459\pi\)
0.136361 + 0.990659i \(0.456459\pi\)
\(878\) 0 0
\(879\) −6.39346 −0.215646
\(880\) 0 0
\(881\) 44.8201 1.51003 0.755014 0.655708i \(-0.227630\pi\)
0.755014 + 0.655708i \(0.227630\pi\)
\(882\) 0 0
\(883\) −38.9580 −1.31104 −0.655521 0.755177i \(-0.727551\pi\)
−0.655521 + 0.755177i \(0.727551\pi\)
\(884\) 0 0
\(885\) −11.6982 −0.393229
\(886\) 0 0
\(887\) 37.9365 1.27378 0.636892 0.770953i \(-0.280220\pi\)
0.636892 + 0.770953i \(0.280220\pi\)
\(888\) 0 0
\(889\) 23.2383 0.779387
\(890\) 0 0
\(891\) 47.1406 1.57927
\(892\) 0 0
\(893\) 4.08096 0.136564
\(894\) 0 0
\(895\) −42.6930 −1.42707
\(896\) 0 0
\(897\) −1.29695 −0.0433040
\(898\) 0 0
\(899\) −19.4020 −0.647091
\(900\) 0 0
\(901\) 1.23342 0.0410910
\(902\) 0 0
\(903\) 15.8350 0.526954
\(904\) 0 0
\(905\) 51.6582 1.71718
\(906\) 0 0
\(907\) −10.9918 −0.364975 −0.182488 0.983208i \(-0.558415\pi\)
−0.182488 + 0.983208i \(0.558415\pi\)
\(908\) 0 0
\(909\) −40.3499 −1.33832
\(910\) 0 0
\(911\) −4.02940 −0.133500 −0.0667500 0.997770i \(-0.521263\pi\)
−0.0667500 + 0.997770i \(0.521263\pi\)
\(912\) 0 0
\(913\) 33.7835 1.11807
\(914\) 0 0
\(915\) 2.74630 0.0907898
\(916\) 0 0
\(917\) −84.3062 −2.78404
\(918\) 0 0
\(919\) 5.78258 0.190750 0.0953748 0.995441i \(-0.469595\pi\)
0.0953748 + 0.995441i \(0.469595\pi\)
\(920\) 0 0
\(921\) −7.27581 −0.239746
\(922\) 0 0
\(923\) −4.89441 −0.161101
\(924\) 0 0
\(925\) −6.21733 −0.204425
\(926\) 0 0
\(927\) −43.5064 −1.42894
\(928\) 0 0
\(929\) 16.5042 0.541484 0.270742 0.962652i \(-0.412731\pi\)
0.270742 + 0.962652i \(0.412731\pi\)
\(930\) 0 0
\(931\) 13.1073 0.429575
\(932\) 0 0
\(933\) −0.265886 −0.00870472
\(934\) 0 0
\(935\) 46.1694 1.50990
\(936\) 0 0
\(937\) −2.59864 −0.0848938 −0.0424469 0.999099i \(-0.513515\pi\)
−0.0424469 + 0.999099i \(0.513515\pi\)
\(938\) 0 0
\(939\) −10.6234 −0.346681
\(940\) 0 0
\(941\) −23.2239 −0.757079 −0.378540 0.925585i \(-0.623574\pi\)
−0.378540 + 0.925585i \(0.623574\pi\)
\(942\) 0 0
\(943\) 24.8566 0.809441
\(944\) 0 0
\(945\) 27.5800 0.897179
\(946\) 0 0
\(947\) −25.4744 −0.827808 −0.413904 0.910320i \(-0.635835\pi\)
−0.413904 + 0.910320i \(0.635835\pi\)
\(948\) 0 0
\(949\) 15.8814 0.515532
\(950\) 0 0
\(951\) −2.58248 −0.0837427
\(952\) 0 0
\(953\) −1.82084 −0.0589827 −0.0294914 0.999565i \(-0.509389\pi\)
−0.0294914 + 0.999565i \(0.509389\pi\)
\(954\) 0 0
\(955\) 1.08705 0.0351762
\(956\) 0 0
\(957\) −4.43763 −0.143448
\(958\) 0 0
\(959\) 7.75208 0.250328
\(960\) 0 0
\(961\) 45.5683 1.46995
\(962\) 0 0
\(963\) 18.1526 0.584958
\(964\) 0 0
\(965\) 65.1497 2.09724
\(966\) 0 0
\(967\) 16.9154 0.543962 0.271981 0.962303i \(-0.412321\pi\)
0.271981 + 0.962303i \(0.412321\pi\)
\(968\) 0 0
\(969\) 0.858421 0.0275765
\(970\) 0 0
\(971\) −23.9082 −0.767251 −0.383625 0.923489i \(-0.625325\pi\)
−0.383625 + 0.923489i \(0.625325\pi\)
\(972\) 0 0
\(973\) 77.1002 2.47172
\(974\) 0 0
\(975\) −2.24059 −0.0717562
\(976\) 0 0
\(977\) 5.22674 0.167218 0.0836092 0.996499i \(-0.473355\pi\)
0.0836092 + 0.996499i \(0.473355\pi\)
\(978\) 0 0
\(979\) −71.0966 −2.27226
\(980\) 0 0
\(981\) 58.4035 1.86468
\(982\) 0 0
\(983\) −28.0200 −0.893699 −0.446849 0.894609i \(-0.647454\pi\)
−0.446849 + 0.894609i \(0.647454\pi\)
\(984\) 0 0
\(985\) 34.2258 1.09052
\(986\) 0 0
\(987\) 6.19988 0.197344
\(988\) 0 0
\(989\) 27.2425 0.866262
\(990\) 0 0
\(991\) −5.85812 −0.186089 −0.0930446 0.995662i \(-0.529660\pi\)
−0.0930446 + 0.995662i \(0.529660\pi\)
\(992\) 0 0
\(993\) −5.25644 −0.166808
\(994\) 0 0
\(995\) −59.3669 −1.88206
\(996\) 0 0
\(997\) 5.23537 0.165806 0.0829029 0.996558i \(-0.473581\pi\)
0.0829029 + 0.996558i \(0.473581\pi\)
\(998\) 0 0
\(999\) −2.74550 −0.0868637
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 \(a_p\))