Properties

Label 6004.2.a.g.1.21
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 1.21
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41553 q^{3} +0.642687 q^{5} +1.33052 q^{7} -0.996264 q^{9} +O(q^{10})\) \(q+1.41553 q^{3} +0.642687 q^{5} +1.33052 q^{7} -0.996264 q^{9} +1.93346 q^{11} -5.21530 q^{13} +0.909745 q^{15} -1.65264 q^{17} +1.00000 q^{19} +1.88340 q^{21} +1.45774 q^{23} -4.58695 q^{25} -5.65685 q^{27} -0.0964612 q^{29} -5.73913 q^{31} +2.73688 q^{33} +0.855108 q^{35} -7.59822 q^{37} -7.38243 q^{39} +5.41539 q^{41} -6.60481 q^{43} -0.640286 q^{45} +1.50562 q^{47} -5.22971 q^{49} -2.33937 q^{51} +0.0801188 q^{53} +1.24261 q^{55} +1.41553 q^{57} -7.20139 q^{59} +10.8769 q^{61} -1.32555 q^{63} -3.35181 q^{65} -14.7930 q^{67} +2.06348 q^{69} -8.01632 q^{71} +10.6504 q^{73} -6.49299 q^{75} +2.57251 q^{77} -1.00000 q^{79} -5.01867 q^{81} +7.39572 q^{83} -1.06213 q^{85} -0.136544 q^{87} -4.64376 q^{89} -6.93907 q^{91} -8.12394 q^{93} +0.642687 q^{95} -5.13964 q^{97} -1.92624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 1.41553 0.817259 0.408629 0.912700i \(-0.366007\pi\)
0.408629 + 0.912700i \(0.366007\pi\)
\(4\) 0 0
\(5\) 0.642687 0.287418 0.143709 0.989620i \(-0.454097\pi\)
0.143709 + 0.989620i \(0.454097\pi\)
\(6\) 0 0
\(7\) 1.33052 0.502890 0.251445 0.967872i \(-0.419094\pi\)
0.251445 + 0.967872i \(0.419094\pi\)
\(8\) 0 0
\(9\) −0.996264 −0.332088
\(10\) 0 0
\(11\) 1.93346 0.582960 0.291480 0.956577i \(-0.405852\pi\)
0.291480 + 0.956577i \(0.405852\pi\)
\(12\) 0 0
\(13\) −5.21530 −1.44646 −0.723232 0.690605i \(-0.757344\pi\)
−0.723232 + 0.690605i \(0.757344\pi\)
\(14\) 0 0
\(15\) 0.909745 0.234895
\(16\) 0 0
\(17\) −1.65264 −0.400824 −0.200412 0.979712i \(-0.564228\pi\)
−0.200412 + 0.979712i \(0.564228\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 1.88340 0.410991
\(22\) 0 0
\(23\) 1.45774 0.303960 0.151980 0.988384i \(-0.451435\pi\)
0.151980 + 0.988384i \(0.451435\pi\)
\(24\) 0 0
\(25\) −4.58695 −0.917391
\(26\) 0 0
\(27\) −5.65685 −1.08866
\(28\) 0 0
\(29\) −0.0964612 −0.0179124 −0.00895619 0.999960i \(-0.502851\pi\)
−0.00895619 + 0.999960i \(0.502851\pi\)
\(30\) 0 0
\(31\) −5.73913 −1.03078 −0.515389 0.856956i \(-0.672353\pi\)
−0.515389 + 0.856956i \(0.672353\pi\)
\(32\) 0 0
\(33\) 2.73688 0.476430
\(34\) 0 0
\(35\) 0.855108 0.144540
\(36\) 0 0
\(37\) −7.59822 −1.24914 −0.624570 0.780969i \(-0.714726\pi\)
−0.624570 + 0.780969i \(0.714726\pi\)
\(38\) 0 0
\(39\) −7.38243 −1.18214
\(40\) 0 0
\(41\) 5.41539 0.845741 0.422871 0.906190i \(-0.361022\pi\)
0.422871 + 0.906190i \(0.361022\pi\)
\(42\) 0 0
\(43\) −6.60481 −1.00722 −0.503612 0.863930i \(-0.667996\pi\)
−0.503612 + 0.863930i \(0.667996\pi\)
\(44\) 0 0
\(45\) −0.640286 −0.0954482
\(46\) 0 0
\(47\) 1.50562 0.219617 0.109809 0.993953i \(-0.464976\pi\)
0.109809 + 0.993953i \(0.464976\pi\)
\(48\) 0 0
\(49\) −5.22971 −0.747102
\(50\) 0 0
\(51\) −2.33937 −0.327577
\(52\) 0 0
\(53\) 0.0801188 0.0110052 0.00550258 0.999985i \(-0.498248\pi\)
0.00550258 + 0.999985i \(0.498248\pi\)
\(54\) 0 0
\(55\) 1.24261 0.167554
\(56\) 0 0
\(57\) 1.41553 0.187492
\(58\) 0 0
\(59\) −7.20139 −0.937540 −0.468770 0.883320i \(-0.655303\pi\)
−0.468770 + 0.883320i \(0.655303\pi\)
\(60\) 0 0
\(61\) 10.8769 1.39265 0.696324 0.717728i \(-0.254818\pi\)
0.696324 + 0.717728i \(0.254818\pi\)
\(62\) 0 0
\(63\) −1.32555 −0.167004
\(64\) 0 0
\(65\) −3.35181 −0.415740
\(66\) 0 0
\(67\) −14.7930 −1.80726 −0.903629 0.428315i \(-0.859107\pi\)
−0.903629 + 0.428315i \(0.859107\pi\)
\(68\) 0 0
\(69\) 2.06348 0.248414
\(70\) 0 0
\(71\) −8.01632 −0.951362 −0.475681 0.879618i \(-0.657798\pi\)
−0.475681 + 0.879618i \(0.657798\pi\)
\(72\) 0 0
\(73\) 10.6504 1.24654 0.623268 0.782008i \(-0.285804\pi\)
0.623268 + 0.782008i \(0.285804\pi\)
\(74\) 0 0
\(75\) −6.49299 −0.749746
\(76\) 0 0
\(77\) 2.57251 0.293165
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −5.01867 −0.557630
\(82\) 0 0
\(83\) 7.39572 0.811785 0.405893 0.913921i \(-0.366961\pi\)
0.405893 + 0.913921i \(0.366961\pi\)
\(84\) 0 0
\(85\) −1.06213 −0.115204
\(86\) 0 0
\(87\) −0.136544 −0.0146391
\(88\) 0 0
\(89\) −4.64376 −0.492238 −0.246119 0.969240i \(-0.579155\pi\)
−0.246119 + 0.969240i \(0.579155\pi\)
\(90\) 0 0
\(91\) −6.93907 −0.727412
\(92\) 0 0
\(93\) −8.12394 −0.842413
\(94\) 0 0
\(95\) 0.642687 0.0659383
\(96\) 0 0
\(97\) −5.13964 −0.521851 −0.260926 0.965359i \(-0.584028\pi\)
−0.260926 + 0.965359i \(0.584028\pi\)
\(98\) 0 0
\(99\) −1.92624 −0.193594
\(100\) 0 0
\(101\) 11.1457 1.10904 0.554520 0.832170i \(-0.312902\pi\)
0.554520 + 0.832170i \(0.312902\pi\)
\(102\) 0 0
\(103\) −7.15830 −0.705329 −0.352664 0.935750i \(-0.614724\pi\)
−0.352664 + 0.935750i \(0.614724\pi\)
\(104\) 0 0
\(105\) 1.21043 0.118126
\(106\) 0 0
\(107\) 13.4227 1.29762 0.648809 0.760951i \(-0.275267\pi\)
0.648809 + 0.760951i \(0.275267\pi\)
\(108\) 0 0
\(109\) −8.85953 −0.848589 −0.424294 0.905524i \(-0.639478\pi\)
−0.424294 + 0.905524i \(0.639478\pi\)
\(110\) 0 0
\(111\) −10.7555 −1.02087
\(112\) 0 0
\(113\) 17.2233 1.62024 0.810118 0.586267i \(-0.199403\pi\)
0.810118 + 0.586267i \(0.199403\pi\)
\(114\) 0 0
\(115\) 0.936872 0.0873638
\(116\) 0 0
\(117\) 5.19582 0.480353
\(118\) 0 0
\(119\) −2.19887 −0.201570
\(120\) 0 0
\(121\) −7.26173 −0.660157
\(122\) 0 0
\(123\) 7.66566 0.691190
\(124\) 0 0
\(125\) −6.16141 −0.551093
\(126\) 0 0
\(127\) −11.8815 −1.05431 −0.527157 0.849768i \(-0.676742\pi\)
−0.527157 + 0.849768i \(0.676742\pi\)
\(128\) 0 0
\(129\) −9.34933 −0.823163
\(130\) 0 0
\(131\) −16.7271 −1.46145 −0.730726 0.682671i \(-0.760818\pi\)
−0.730726 + 0.682671i \(0.760818\pi\)
\(132\) 0 0
\(133\) 1.33052 0.115371
\(134\) 0 0
\(135\) −3.63558 −0.312901
\(136\) 0 0
\(137\) −15.3185 −1.30875 −0.654373 0.756172i \(-0.727067\pi\)
−0.654373 + 0.756172i \(0.727067\pi\)
\(138\) 0 0
\(139\) 7.32048 0.620915 0.310457 0.950587i \(-0.399518\pi\)
0.310457 + 0.950587i \(0.399518\pi\)
\(140\) 0 0
\(141\) 2.13126 0.179484
\(142\) 0 0
\(143\) −10.0836 −0.843231
\(144\) 0 0
\(145\) −0.0619943 −0.00514835
\(146\) 0 0
\(147\) −7.40284 −0.610576
\(148\) 0 0
\(149\) 17.4219 1.42726 0.713631 0.700522i \(-0.247049\pi\)
0.713631 + 0.700522i \(0.247049\pi\)
\(150\) 0 0
\(151\) 8.53489 0.694559 0.347280 0.937762i \(-0.387105\pi\)
0.347280 + 0.937762i \(0.387105\pi\)
\(152\) 0 0
\(153\) 1.64647 0.133109
\(154\) 0 0
\(155\) −3.68847 −0.296265
\(156\) 0 0
\(157\) 22.6908 1.81093 0.905463 0.424425i \(-0.139524\pi\)
0.905463 + 0.424425i \(0.139524\pi\)
\(158\) 0 0
\(159\) 0.113411 0.00899407
\(160\) 0 0
\(161\) 1.93956 0.152859
\(162\) 0 0
\(163\) −16.3631 −1.28166 −0.640828 0.767684i \(-0.721409\pi\)
−0.640828 + 0.767684i \(0.721409\pi\)
\(164\) 0 0
\(165\) 1.75896 0.136935
\(166\) 0 0
\(167\) −23.4032 −1.81099 −0.905497 0.424353i \(-0.860501\pi\)
−0.905497 + 0.424353i \(0.860501\pi\)
\(168\) 0 0
\(169\) 14.1994 1.09226
\(170\) 0 0
\(171\) −0.996264 −0.0761862
\(172\) 0 0
\(173\) −22.0490 −1.67635 −0.838175 0.545401i \(-0.816377\pi\)
−0.838175 + 0.545401i \(0.816377\pi\)
\(174\) 0 0
\(175\) −6.10304 −0.461346
\(176\) 0 0
\(177\) −10.1938 −0.766213
\(178\) 0 0
\(179\) 8.45284 0.631795 0.315897 0.948793i \(-0.397694\pi\)
0.315897 + 0.948793i \(0.397694\pi\)
\(180\) 0 0
\(181\) −17.2964 −1.28563 −0.642817 0.766020i \(-0.722234\pi\)
−0.642817 + 0.766020i \(0.722234\pi\)
\(182\) 0 0
\(183\) 15.3967 1.13815
\(184\) 0 0
\(185\) −4.88328 −0.359026
\(186\) 0 0
\(187\) −3.19532 −0.233665
\(188\) 0 0
\(189\) −7.52655 −0.547476
\(190\) 0 0
\(191\) 11.6517 0.843089 0.421544 0.906808i \(-0.361488\pi\)
0.421544 + 0.906808i \(0.361488\pi\)
\(192\) 0 0
\(193\) 10.3297 0.743547 0.371773 0.928324i \(-0.378750\pi\)
0.371773 + 0.928324i \(0.378750\pi\)
\(194\) 0 0
\(195\) −4.74459 −0.339767
\(196\) 0 0
\(197\) −5.98534 −0.426437 −0.213219 0.977004i \(-0.568395\pi\)
−0.213219 + 0.977004i \(0.568395\pi\)
\(198\) 0 0
\(199\) −4.70869 −0.333790 −0.166895 0.985975i \(-0.553374\pi\)
−0.166895 + 0.985975i \(0.553374\pi\)
\(200\) 0 0
\(201\) −20.9401 −1.47700
\(202\) 0 0
\(203\) −0.128344 −0.00900795
\(204\) 0 0
\(205\) 3.48040 0.243082
\(206\) 0 0
\(207\) −1.45230 −0.100942
\(208\) 0 0
\(209\) 1.93346 0.133740
\(210\) 0 0
\(211\) 17.0324 1.17256 0.586278 0.810110i \(-0.300593\pi\)
0.586278 + 0.810110i \(0.300593\pi\)
\(212\) 0 0
\(213\) −11.3474 −0.777509
\(214\) 0 0
\(215\) −4.24483 −0.289495
\(216\) 0 0
\(217\) −7.63603 −0.518368
\(218\) 0 0
\(219\) 15.0760 1.01874
\(220\) 0 0
\(221\) 8.61902 0.579778
\(222\) 0 0
\(223\) 17.4741 1.17015 0.585075 0.810979i \(-0.301065\pi\)
0.585075 + 0.810979i \(0.301065\pi\)
\(224\) 0 0
\(225\) 4.56982 0.304654
\(226\) 0 0
\(227\) 20.2456 1.34375 0.671874 0.740665i \(-0.265489\pi\)
0.671874 + 0.740665i \(0.265489\pi\)
\(228\) 0 0
\(229\) −15.8439 −1.04700 −0.523499 0.852026i \(-0.675373\pi\)
−0.523499 + 0.852026i \(0.675373\pi\)
\(230\) 0 0
\(231\) 3.64147 0.239591
\(232\) 0 0
\(233\) 25.8263 1.69194 0.845969 0.533232i \(-0.179023\pi\)
0.845969 + 0.533232i \(0.179023\pi\)
\(234\) 0 0
\(235\) 0.967643 0.0631221
\(236\) 0 0
\(237\) −1.41553 −0.0919488
\(238\) 0 0
\(239\) −12.4909 −0.807972 −0.403986 0.914765i \(-0.632376\pi\)
−0.403986 + 0.914765i \(0.632376\pi\)
\(240\) 0 0
\(241\) −12.8050 −0.824840 −0.412420 0.910994i \(-0.635316\pi\)
−0.412420 + 0.910994i \(0.635316\pi\)
\(242\) 0 0
\(243\) 9.86645 0.632933
\(244\) 0 0
\(245\) −3.36107 −0.214731
\(246\) 0 0
\(247\) −5.21530 −0.331842
\(248\) 0 0
\(249\) 10.4689 0.663439
\(250\) 0 0
\(251\) −0.527481 −0.0332943 −0.0166472 0.999861i \(-0.505299\pi\)
−0.0166472 + 0.999861i \(0.505299\pi\)
\(252\) 0 0
\(253\) 2.81849 0.177197
\(254\) 0 0
\(255\) −1.50348 −0.0941517
\(256\) 0 0
\(257\) −3.54045 −0.220847 −0.110424 0.993885i \(-0.535221\pi\)
−0.110424 + 0.993885i \(0.535221\pi\)
\(258\) 0 0
\(259\) −10.1096 −0.628179
\(260\) 0 0
\(261\) 0.0961008 0.00594849
\(262\) 0 0
\(263\) 18.3694 1.13270 0.566352 0.824163i \(-0.308354\pi\)
0.566352 + 0.824163i \(0.308354\pi\)
\(264\) 0 0
\(265\) 0.0514913 0.00316309
\(266\) 0 0
\(267\) −6.57340 −0.402286
\(268\) 0 0
\(269\) −11.8957 −0.725295 −0.362647 0.931926i \(-0.618127\pi\)
−0.362647 + 0.931926i \(0.618127\pi\)
\(270\) 0 0
\(271\) −7.58733 −0.460898 −0.230449 0.973084i \(-0.574019\pi\)
−0.230449 + 0.973084i \(0.574019\pi\)
\(272\) 0 0
\(273\) −9.82248 −0.594484
\(274\) 0 0
\(275\) −8.86870 −0.534802
\(276\) 0 0
\(277\) 15.1353 0.909389 0.454695 0.890647i \(-0.349748\pi\)
0.454695 + 0.890647i \(0.349748\pi\)
\(278\) 0 0
\(279\) 5.71769 0.342309
\(280\) 0 0
\(281\) −7.86338 −0.469090 −0.234545 0.972105i \(-0.575360\pi\)
−0.234545 + 0.972105i \(0.575360\pi\)
\(282\) 0 0
\(283\) 20.3069 1.20712 0.603560 0.797318i \(-0.293748\pi\)
0.603560 + 0.797318i \(0.293748\pi\)
\(284\) 0 0
\(285\) 0.909745 0.0538887
\(286\) 0 0
\(287\) 7.20528 0.425314
\(288\) 0 0
\(289\) −14.2688 −0.839340
\(290\) 0 0
\(291\) −7.27533 −0.426488
\(292\) 0 0
\(293\) −11.2096 −0.654873 −0.327436 0.944873i \(-0.606185\pi\)
−0.327436 + 0.944873i \(0.606185\pi\)
\(294\) 0 0
\(295\) −4.62824 −0.269466
\(296\) 0 0
\(297\) −10.9373 −0.634646
\(298\) 0 0
\(299\) −7.60257 −0.439668
\(300\) 0 0
\(301\) −8.78784 −0.506523
\(302\) 0 0
\(303\) 15.7771 0.906373
\(304\) 0 0
\(305\) 6.99046 0.400272
\(306\) 0 0
\(307\) 8.11820 0.463330 0.231665 0.972796i \(-0.425583\pi\)
0.231665 + 0.972796i \(0.425583\pi\)
\(308\) 0 0
\(309\) −10.1328 −0.576436
\(310\) 0 0
\(311\) −3.83714 −0.217584 −0.108792 0.994065i \(-0.534698\pi\)
−0.108792 + 0.994065i \(0.534698\pi\)
\(312\) 0 0
\(313\) −4.88873 −0.276327 −0.138164 0.990409i \(-0.544120\pi\)
−0.138164 + 0.990409i \(0.544120\pi\)
\(314\) 0 0
\(315\) −0.851914 −0.0479999
\(316\) 0 0
\(317\) 9.36341 0.525901 0.262951 0.964809i \(-0.415304\pi\)
0.262951 + 0.964809i \(0.415304\pi\)
\(318\) 0 0
\(319\) −0.186504 −0.0104422
\(320\) 0 0
\(321\) 19.0002 1.06049
\(322\) 0 0
\(323\) −1.65264 −0.0919554
\(324\) 0 0
\(325\) 23.9223 1.32697
\(326\) 0 0
\(327\) −12.5410 −0.693517
\(328\) 0 0
\(329\) 2.00326 0.110443
\(330\) 0 0
\(331\) 1.04474 0.0574239 0.0287120 0.999588i \(-0.490859\pi\)
0.0287120 + 0.999588i \(0.490859\pi\)
\(332\) 0 0
\(333\) 7.56983 0.414824
\(334\) 0 0
\(335\) −9.50730 −0.519439
\(336\) 0 0
\(337\) 30.1550 1.64265 0.821324 0.570462i \(-0.193236\pi\)
0.821324 + 0.570462i \(0.193236\pi\)
\(338\) 0 0
\(339\) 24.3802 1.32415
\(340\) 0 0
\(341\) −11.0964 −0.600903
\(342\) 0 0
\(343\) −16.2719 −0.878599
\(344\) 0 0
\(345\) 1.32617 0.0713988
\(346\) 0 0
\(347\) −20.7269 −1.11268 −0.556340 0.830955i \(-0.687795\pi\)
−0.556340 + 0.830955i \(0.687795\pi\)
\(348\) 0 0
\(349\) −26.1358 −1.39902 −0.699509 0.714624i \(-0.746598\pi\)
−0.699509 + 0.714624i \(0.746598\pi\)
\(350\) 0 0
\(351\) 29.5022 1.57471
\(352\) 0 0
\(353\) 5.10887 0.271918 0.135959 0.990714i \(-0.456588\pi\)
0.135959 + 0.990714i \(0.456588\pi\)
\(354\) 0 0
\(355\) −5.15198 −0.273439
\(356\) 0 0
\(357\) −3.11258 −0.164735
\(358\) 0 0
\(359\) 11.7863 0.622059 0.311029 0.950400i \(-0.399326\pi\)
0.311029 + 0.950400i \(0.399326\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −10.2792 −0.539519
\(364\) 0 0
\(365\) 6.84488 0.358277
\(366\) 0 0
\(367\) −13.5919 −0.709494 −0.354747 0.934962i \(-0.615433\pi\)
−0.354747 + 0.934962i \(0.615433\pi\)
\(368\) 0 0
\(369\) −5.39515 −0.280861
\(370\) 0 0
\(371\) 0.106600 0.00553438
\(372\) 0 0
\(373\) 0.174924 0.00905722 0.00452861 0.999990i \(-0.498558\pi\)
0.00452861 + 0.999990i \(0.498558\pi\)
\(374\) 0 0
\(375\) −8.72168 −0.450386
\(376\) 0 0
\(377\) 0.503074 0.0259096
\(378\) 0 0
\(379\) 6.78000 0.348265 0.174133 0.984722i \(-0.444288\pi\)
0.174133 + 0.984722i \(0.444288\pi\)
\(380\) 0 0
\(381\) −16.8187 −0.861647
\(382\) 0 0
\(383\) −11.7147 −0.598591 −0.299296 0.954160i \(-0.596752\pi\)
−0.299296 + 0.954160i \(0.596752\pi\)
\(384\) 0 0
\(385\) 1.65332 0.0842609
\(386\) 0 0
\(387\) 6.58014 0.334487
\(388\) 0 0
\(389\) 25.3448 1.28503 0.642515 0.766273i \(-0.277891\pi\)
0.642515 + 0.766273i \(0.277891\pi\)
\(390\) 0 0
\(391\) −2.40913 −0.121835
\(392\) 0 0
\(393\) −23.6778 −1.19438
\(394\) 0 0
\(395\) −0.642687 −0.0323371
\(396\) 0 0
\(397\) −38.5061 −1.93257 −0.966284 0.257480i \(-0.917108\pi\)
−0.966284 + 0.257480i \(0.917108\pi\)
\(398\) 0 0
\(399\) 1.88340 0.0942878
\(400\) 0 0
\(401\) −34.1188 −1.70381 −0.851905 0.523697i \(-0.824552\pi\)
−0.851905 + 0.523697i \(0.824552\pi\)
\(402\) 0 0
\(403\) 29.9313 1.49098
\(404\) 0 0
\(405\) −3.22543 −0.160273
\(406\) 0 0
\(407\) −14.6909 −0.728199
\(408\) 0 0
\(409\) 14.6675 0.725260 0.362630 0.931933i \(-0.381879\pi\)
0.362630 + 0.931933i \(0.381879\pi\)
\(410\) 0 0
\(411\) −21.6838 −1.06958
\(412\) 0 0
\(413\) −9.58159 −0.471479
\(414\) 0 0
\(415\) 4.75313 0.233322
\(416\) 0 0
\(417\) 10.3624 0.507448
\(418\) 0 0
\(419\) −23.1940 −1.13310 −0.566550 0.824027i \(-0.691722\pi\)
−0.566550 + 0.824027i \(0.691722\pi\)
\(420\) 0 0
\(421\) −15.7906 −0.769588 −0.384794 0.923002i \(-0.625728\pi\)
−0.384794 + 0.923002i \(0.625728\pi\)
\(422\) 0 0
\(423\) −1.50000 −0.0729323
\(424\) 0 0
\(425\) 7.58059 0.367713
\(426\) 0 0
\(427\) 14.4720 0.700348
\(428\) 0 0
\(429\) −14.2736 −0.689138
\(430\) 0 0
\(431\) 3.55450 0.171214 0.0856072 0.996329i \(-0.472717\pi\)
0.0856072 + 0.996329i \(0.472717\pi\)
\(432\) 0 0
\(433\) 5.44653 0.261743 0.130872 0.991399i \(-0.458222\pi\)
0.130872 + 0.991399i \(0.458222\pi\)
\(434\) 0 0
\(435\) −0.0877551 −0.00420753
\(436\) 0 0
\(437\) 1.45774 0.0697333
\(438\) 0 0
\(439\) 17.1089 0.816565 0.408283 0.912856i \(-0.366128\pi\)
0.408283 + 0.912856i \(0.366128\pi\)
\(440\) 0 0
\(441\) 5.21018 0.248104
\(442\) 0 0
\(443\) −13.1017 −0.622482 −0.311241 0.950331i \(-0.600745\pi\)
−0.311241 + 0.950331i \(0.600745\pi\)
\(444\) 0 0
\(445\) −2.98449 −0.141478
\(446\) 0 0
\(447\) 24.6614 1.16644
\(448\) 0 0
\(449\) −27.0013 −1.27427 −0.637135 0.770752i \(-0.719881\pi\)
−0.637135 + 0.770752i \(0.719881\pi\)
\(450\) 0 0
\(451\) 10.4704 0.493034
\(452\) 0 0
\(453\) 12.0814 0.567635
\(454\) 0 0
\(455\) −4.45965 −0.209071
\(456\) 0 0
\(457\) 25.2455 1.18093 0.590467 0.807062i \(-0.298944\pi\)
0.590467 + 0.807062i \(0.298944\pi\)
\(458\) 0 0
\(459\) 9.34874 0.436362
\(460\) 0 0
\(461\) −33.3158 −1.55167 −0.775837 0.630934i \(-0.782672\pi\)
−0.775837 + 0.630934i \(0.782672\pi\)
\(462\) 0 0
\(463\) 16.6210 0.772444 0.386222 0.922406i \(-0.373780\pi\)
0.386222 + 0.922406i \(0.373780\pi\)
\(464\) 0 0
\(465\) −5.22115 −0.242125
\(466\) 0 0
\(467\) 2.87012 0.132813 0.0664067 0.997793i \(-0.478847\pi\)
0.0664067 + 0.997793i \(0.478847\pi\)
\(468\) 0 0
\(469\) −19.6825 −0.908852
\(470\) 0 0
\(471\) 32.1197 1.48000
\(472\) 0 0
\(473\) −12.7701 −0.587172
\(474\) 0 0
\(475\) −4.58695 −0.210464
\(476\) 0 0
\(477\) −0.0798195 −0.00365468
\(478\) 0 0
\(479\) −1.75270 −0.0800828 −0.0400414 0.999198i \(-0.512749\pi\)
−0.0400414 + 0.999198i \(0.512749\pi\)
\(480\) 0 0
\(481\) 39.6270 1.80684
\(482\) 0 0
\(483\) 2.74551 0.124925
\(484\) 0 0
\(485\) −3.30318 −0.149990
\(486\) 0 0
\(487\) −14.1357 −0.640551 −0.320276 0.947324i \(-0.603776\pi\)
−0.320276 + 0.947324i \(0.603776\pi\)
\(488\) 0 0
\(489\) −23.1625 −1.04745
\(490\) 0 0
\(491\) −20.8121 −0.939236 −0.469618 0.882870i \(-0.655608\pi\)
−0.469618 + 0.882870i \(0.655608\pi\)
\(492\) 0 0
\(493\) 0.159416 0.00717972
\(494\) 0 0
\(495\) −1.23797 −0.0556425
\(496\) 0 0
\(497\) −10.6659 −0.478430
\(498\) 0 0
\(499\) 43.2900 1.93793 0.968963 0.247205i \(-0.0795121\pi\)
0.968963 + 0.247205i \(0.0795121\pi\)
\(500\) 0 0
\(501\) −33.1280 −1.48005
\(502\) 0 0
\(503\) 32.5372 1.45076 0.725381 0.688348i \(-0.241664\pi\)
0.725381 + 0.688348i \(0.241664\pi\)
\(504\) 0 0
\(505\) 7.16321 0.318759
\(506\) 0 0
\(507\) 20.0997 0.892658
\(508\) 0 0
\(509\) 14.3895 0.637804 0.318902 0.947788i \(-0.396686\pi\)
0.318902 + 0.947788i \(0.396686\pi\)
\(510\) 0 0
\(511\) 14.1706 0.626870
\(512\) 0 0
\(513\) −5.65685 −0.249756
\(514\) 0 0
\(515\) −4.60055 −0.202724
\(516\) 0 0
\(517\) 2.91106 0.128028
\(518\) 0 0
\(519\) −31.2110 −1.37001
\(520\) 0 0
\(521\) −18.0622 −0.791319 −0.395659 0.918397i \(-0.629484\pi\)
−0.395659 + 0.918397i \(0.629484\pi\)
\(522\) 0 0
\(523\) −16.9305 −0.740319 −0.370160 0.928968i \(-0.620697\pi\)
−0.370160 + 0.928968i \(0.620697\pi\)
\(524\) 0 0
\(525\) −8.63906 −0.377039
\(526\) 0 0
\(527\) 9.48473 0.413161
\(528\) 0 0
\(529\) −20.8750 −0.907608
\(530\) 0 0
\(531\) 7.17448 0.311346
\(532\) 0 0
\(533\) −28.2429 −1.22333
\(534\) 0 0
\(535\) 8.62657 0.372959
\(536\) 0 0
\(537\) 11.9653 0.516340
\(538\) 0 0
\(539\) −10.1114 −0.435531
\(540\) 0 0
\(541\) −11.7390 −0.504700 −0.252350 0.967636i \(-0.581203\pi\)
−0.252350 + 0.967636i \(0.581203\pi\)
\(542\) 0 0
\(543\) −24.4837 −1.05070
\(544\) 0 0
\(545\) −5.69390 −0.243900
\(546\) 0 0
\(547\) −14.8322 −0.634177 −0.317089 0.948396i \(-0.602705\pi\)
−0.317089 + 0.948396i \(0.602705\pi\)
\(548\) 0 0
\(549\) −10.8363 −0.462481
\(550\) 0 0
\(551\) −0.0964612 −0.00410938
\(552\) 0 0
\(553\) −1.33052 −0.0565795
\(554\) 0 0
\(555\) −6.91244 −0.293417
\(556\) 0 0
\(557\) 39.0955 1.65653 0.828264 0.560338i \(-0.189329\pi\)
0.828264 + 0.560338i \(0.189329\pi\)
\(558\) 0 0
\(559\) 34.4461 1.45691
\(560\) 0 0
\(561\) −4.52308 −0.190965
\(562\) 0 0
\(563\) −1.43413 −0.0604413 −0.0302207 0.999543i \(-0.509621\pi\)
−0.0302207 + 0.999543i \(0.509621\pi\)
\(564\) 0 0
\(565\) 11.0692 0.465685
\(566\) 0 0
\(567\) −6.67744 −0.280426
\(568\) 0 0
\(569\) −36.7102 −1.53897 −0.769486 0.638664i \(-0.779487\pi\)
−0.769486 + 0.638664i \(0.779487\pi\)
\(570\) 0 0
\(571\) −39.6097 −1.65762 −0.828808 0.559534i \(-0.810980\pi\)
−0.828808 + 0.559534i \(0.810980\pi\)
\(572\) 0 0
\(573\) 16.4934 0.689022
\(574\) 0 0
\(575\) −6.68660 −0.278850
\(576\) 0 0
\(577\) 13.8492 0.576548 0.288274 0.957548i \(-0.406919\pi\)
0.288274 + 0.957548i \(0.406919\pi\)
\(578\) 0 0
\(579\) 14.6220 0.607670
\(580\) 0 0
\(581\) 9.84015 0.408238
\(582\) 0 0
\(583\) 0.154907 0.00641557
\(584\) 0 0
\(585\) 3.33928 0.138062
\(586\) 0 0
\(587\) 33.1456 1.36806 0.684032 0.729452i \(-0.260225\pi\)
0.684032 + 0.729452i \(0.260225\pi\)
\(588\) 0 0
\(589\) −5.73913 −0.236477
\(590\) 0 0
\(591\) −8.47244 −0.348510
\(592\) 0 0
\(593\) −23.5972 −0.969022 −0.484511 0.874785i \(-0.661002\pi\)
−0.484511 + 0.874785i \(0.661002\pi\)
\(594\) 0 0
\(595\) −1.41319 −0.0579350
\(596\) 0 0
\(597\) −6.66531 −0.272793
\(598\) 0 0
\(599\) −41.6611 −1.70223 −0.851114 0.524981i \(-0.824072\pi\)
−0.851114 + 0.524981i \(0.824072\pi\)
\(600\) 0 0
\(601\) −6.57740 −0.268298 −0.134149 0.990961i \(-0.542830\pi\)
−0.134149 + 0.990961i \(0.542830\pi\)
\(602\) 0 0
\(603\) 14.7378 0.600169
\(604\) 0 0
\(605\) −4.66702 −0.189741
\(606\) 0 0
\(607\) 28.3654 1.15132 0.575658 0.817690i \(-0.304746\pi\)
0.575658 + 0.817690i \(0.304746\pi\)
\(608\) 0 0
\(609\) −0.181675 −0.00736183
\(610\) 0 0
\(611\) −7.85226 −0.317669
\(612\) 0 0
\(613\) 7.06554 0.285374 0.142687 0.989768i \(-0.454426\pi\)
0.142687 + 0.989768i \(0.454426\pi\)
\(614\) 0 0
\(615\) 4.92662 0.198661
\(616\) 0 0
\(617\) 44.3501 1.78547 0.892733 0.450586i \(-0.148785\pi\)
0.892733 + 0.450586i \(0.148785\pi\)
\(618\) 0 0
\(619\) 18.5118 0.744050 0.372025 0.928223i \(-0.378664\pi\)
0.372025 + 0.928223i \(0.378664\pi\)
\(620\) 0 0
\(621\) −8.24623 −0.330910
\(622\) 0 0
\(623\) −6.17862 −0.247541
\(624\) 0 0
\(625\) 18.9749 0.758996
\(626\) 0 0
\(627\) 2.73688 0.109300
\(628\) 0 0
\(629\) 12.5571 0.500686
\(630\) 0 0
\(631\) 11.6945 0.465550 0.232775 0.972531i \(-0.425219\pi\)
0.232775 + 0.972531i \(0.425219\pi\)
\(632\) 0 0
\(633\) 24.1099 0.958282
\(634\) 0 0
\(635\) −7.63609 −0.303029
\(636\) 0 0
\(637\) 27.2745 1.08066
\(638\) 0 0
\(639\) 7.98637 0.315936
\(640\) 0 0
\(641\) 33.8803 1.33819 0.669095 0.743177i \(-0.266682\pi\)
0.669095 + 0.743177i \(0.266682\pi\)
\(642\) 0 0
\(643\) 43.1523 1.70176 0.850881 0.525359i \(-0.176069\pi\)
0.850881 + 0.525359i \(0.176069\pi\)
\(644\) 0 0
\(645\) −6.00869 −0.236592
\(646\) 0 0
\(647\) −35.4426 −1.39339 −0.696697 0.717366i \(-0.745348\pi\)
−0.696697 + 0.717366i \(0.745348\pi\)
\(648\) 0 0
\(649\) −13.9236 −0.546549
\(650\) 0 0
\(651\) −10.8091 −0.423641
\(652\) 0 0
\(653\) 39.0569 1.52841 0.764207 0.644971i \(-0.223130\pi\)
0.764207 + 0.644971i \(0.223130\pi\)
\(654\) 0 0
\(655\) −10.7503 −0.420048
\(656\) 0 0
\(657\) −10.6106 −0.413960
\(658\) 0 0
\(659\) 31.2655 1.21793 0.608965 0.793197i \(-0.291585\pi\)
0.608965 + 0.793197i \(0.291585\pi\)
\(660\) 0 0
\(661\) 20.8381 0.810510 0.405255 0.914204i \(-0.367183\pi\)
0.405255 + 0.914204i \(0.367183\pi\)
\(662\) 0 0
\(663\) 12.2005 0.473829
\(664\) 0 0
\(665\) 0.855108 0.0331597
\(666\) 0 0
\(667\) −0.140616 −0.00544466
\(668\) 0 0
\(669\) 24.7351 0.956315
\(670\) 0 0
\(671\) 21.0301 0.811858
\(672\) 0 0
\(673\) −39.2747 −1.51393 −0.756964 0.653456i \(-0.773318\pi\)
−0.756964 + 0.653456i \(0.773318\pi\)
\(674\) 0 0
\(675\) 25.9477 0.998727
\(676\) 0 0
\(677\) 3.38317 0.130026 0.0650129 0.997884i \(-0.479291\pi\)
0.0650129 + 0.997884i \(0.479291\pi\)
\(678\) 0 0
\(679\) −6.83840 −0.262434
\(680\) 0 0
\(681\) 28.6584 1.09819
\(682\) 0 0
\(683\) 21.2944 0.814809 0.407405 0.913248i \(-0.366434\pi\)
0.407405 + 0.913248i \(0.366434\pi\)
\(684\) 0 0
\(685\) −9.84499 −0.376158
\(686\) 0 0
\(687\) −22.4276 −0.855668
\(688\) 0 0
\(689\) −0.417844 −0.0159186
\(690\) 0 0
\(691\) −38.0941 −1.44917 −0.724584 0.689187i \(-0.757968\pi\)
−0.724584 + 0.689187i \(0.757968\pi\)
\(692\) 0 0
\(693\) −2.56290 −0.0973565
\(694\) 0 0
\(695\) 4.70478 0.178462
\(696\) 0 0
\(697\) −8.94969 −0.338994
\(698\) 0 0
\(699\) 36.5580 1.38275
\(700\) 0 0
\(701\) −4.91662 −0.185698 −0.0928490 0.995680i \(-0.529597\pi\)
−0.0928490 + 0.995680i \(0.529597\pi\)
\(702\) 0 0
\(703\) −7.59822 −0.286572
\(704\) 0 0
\(705\) 1.36973 0.0515871
\(706\) 0 0
\(707\) 14.8296 0.557725
\(708\) 0 0
\(709\) −26.0735 −0.979212 −0.489606 0.871944i \(-0.662859\pi\)
−0.489606 + 0.871944i \(0.662859\pi\)
\(710\) 0 0
\(711\) 0.996264 0.0373628
\(712\) 0 0
\(713\) −8.36618 −0.313316
\(714\) 0 0
\(715\) −6.48059 −0.242360
\(716\) 0 0
\(717\) −17.6813 −0.660322
\(718\) 0 0
\(719\) 4.73114 0.176442 0.0882209 0.996101i \(-0.471882\pi\)
0.0882209 + 0.996101i \(0.471882\pi\)
\(720\) 0 0
\(721\) −9.52427 −0.354702
\(722\) 0 0
\(723\) −18.1259 −0.674108
\(724\) 0 0
\(725\) 0.442463 0.0164327
\(726\) 0 0
\(727\) −45.3031 −1.68020 −0.840099 0.542434i \(-0.817503\pi\)
−0.840099 + 0.542434i \(0.817503\pi\)
\(728\) 0 0
\(729\) 29.0223 1.07490
\(730\) 0 0
\(731\) 10.9154 0.403720
\(732\) 0 0
\(733\) −52.7436 −1.94813 −0.974065 0.226268i \(-0.927347\pi\)
−0.974065 + 0.226268i \(0.927347\pi\)
\(734\) 0 0
\(735\) −4.75771 −0.175491
\(736\) 0 0
\(737\) −28.6018 −1.05356
\(738\) 0 0
\(739\) −18.6112 −0.684622 −0.342311 0.939587i \(-0.611210\pi\)
−0.342311 + 0.939587i \(0.611210\pi\)
\(740\) 0 0
\(741\) −7.38243 −0.271201
\(742\) 0 0
\(743\) 0.405748 0.0148855 0.00744273 0.999972i \(-0.497631\pi\)
0.00744273 + 0.999972i \(0.497631\pi\)
\(744\) 0 0
\(745\) 11.1969 0.410221
\(746\) 0 0
\(747\) −7.36808 −0.269584
\(748\) 0 0
\(749\) 17.8591 0.652558
\(750\) 0 0
\(751\) 17.4223 0.635749 0.317874 0.948133i \(-0.397031\pi\)
0.317874 + 0.948133i \(0.397031\pi\)
\(752\) 0 0
\(753\) −0.746668 −0.0272101
\(754\) 0 0
\(755\) 5.48526 0.199629
\(756\) 0 0
\(757\) −13.1639 −0.478450 −0.239225 0.970964i \(-0.576893\pi\)
−0.239225 + 0.970964i \(0.576893\pi\)
\(758\) 0 0
\(759\) 3.98967 0.144816
\(760\) 0 0
\(761\) 28.4807 1.03242 0.516212 0.856461i \(-0.327342\pi\)
0.516212 + 0.856461i \(0.327342\pi\)
\(762\) 0 0
\(763\) −11.7878 −0.426747
\(764\) 0 0
\(765\) 1.05816 0.0382580
\(766\) 0 0
\(767\) 37.5574 1.35612
\(768\) 0 0
\(769\) 40.7191 1.46837 0.734184 0.678951i \(-0.237565\pi\)
0.734184 + 0.678951i \(0.237565\pi\)
\(770\) 0 0
\(771\) −5.01163 −0.180489
\(772\) 0 0
\(773\) 25.7812 0.927286 0.463643 0.886022i \(-0.346542\pi\)
0.463643 + 0.886022i \(0.346542\pi\)
\(774\) 0 0
\(775\) 26.3251 0.945627
\(776\) 0 0
\(777\) −14.3105 −0.513385
\(778\) 0 0
\(779\) 5.41539 0.194026
\(780\) 0 0
\(781\) −15.4992 −0.554606
\(782\) 0 0
\(783\) 0.545666 0.0195005
\(784\) 0 0
\(785\) 14.5831 0.520493
\(786\) 0 0
\(787\) −5.38688 −0.192021 −0.0960107 0.995380i \(-0.530608\pi\)
−0.0960107 + 0.995380i \(0.530608\pi\)
\(788\) 0 0
\(789\) 26.0025 0.925713
\(790\) 0 0
\(791\) 22.9160 0.814800
\(792\) 0 0
\(793\) −56.7264 −2.01441
\(794\) 0 0
\(795\) 0.0728877 0.00258506
\(796\) 0 0
\(797\) −20.2002 −0.715526 −0.357763 0.933812i \(-0.616460\pi\)
−0.357763 + 0.933812i \(0.616460\pi\)
\(798\) 0 0
\(799\) −2.48825 −0.0880280
\(800\) 0 0
\(801\) 4.62641 0.163466
\(802\) 0 0
\(803\) 20.5922 0.726682
\(804\) 0 0
\(805\) 1.24653 0.0439343
\(806\) 0 0
\(807\) −16.8388 −0.592754
\(808\) 0 0
\(809\) 5.95846 0.209488 0.104744 0.994499i \(-0.466598\pi\)
0.104744 + 0.994499i \(0.466598\pi\)
\(810\) 0 0
\(811\) −15.1558 −0.532193 −0.266096 0.963946i \(-0.585734\pi\)
−0.266096 + 0.963946i \(0.585734\pi\)
\(812\) 0 0
\(813\) −10.7401 −0.376673
\(814\) 0 0
\(815\) −10.5163 −0.368372
\(816\) 0 0
\(817\) −6.60481 −0.231073
\(818\) 0 0
\(819\) 6.91314 0.241565
\(820\) 0 0
\(821\) 10.2340 0.357169 0.178584 0.983925i \(-0.442848\pi\)
0.178584 + 0.983925i \(0.442848\pi\)
\(822\) 0 0
\(823\) −39.1399 −1.36433 −0.682165 0.731199i \(-0.738961\pi\)
−0.682165 + 0.731199i \(0.738961\pi\)
\(824\) 0 0
\(825\) −12.5539 −0.437072
\(826\) 0 0
\(827\) −42.1583 −1.46599 −0.732994 0.680235i \(-0.761878\pi\)
−0.732994 + 0.680235i \(0.761878\pi\)
\(828\) 0 0
\(829\) 37.4950 1.30226 0.651128 0.758968i \(-0.274296\pi\)
0.651128 + 0.758968i \(0.274296\pi\)
\(830\) 0 0
\(831\) 21.4245 0.743207
\(832\) 0 0
\(833\) 8.64284 0.299457
\(834\) 0 0
\(835\) −15.0409 −0.520513
\(836\) 0 0
\(837\) 32.4654 1.12217
\(838\) 0 0
\(839\) −19.5279 −0.674178 −0.337089 0.941473i \(-0.609442\pi\)
−0.337089 + 0.941473i \(0.609442\pi\)
\(840\) 0 0
\(841\) −28.9907 −0.999679
\(842\) 0 0
\(843\) −11.1309 −0.383368
\(844\) 0 0
\(845\) 9.12574 0.313935
\(846\) 0 0
\(847\) −9.66188 −0.331986
\(848\) 0 0
\(849\) 28.7451 0.986529
\(850\) 0 0
\(851\) −11.0763 −0.379689
\(852\) 0 0
\(853\) 30.6923 1.05088 0.525442 0.850829i \(-0.323900\pi\)
0.525442 + 0.850829i \(0.323900\pi\)
\(854\) 0 0
\(855\) −0.640286 −0.0218973
\(856\) 0 0
\(857\) −12.2942 −0.419960 −0.209980 0.977706i \(-0.567340\pi\)
−0.209980 + 0.977706i \(0.567340\pi\)
\(858\) 0 0
\(859\) 24.4783 0.835190 0.417595 0.908633i \(-0.362873\pi\)
0.417595 + 0.908633i \(0.362873\pi\)
\(860\) 0 0
\(861\) 10.1993 0.347592
\(862\) 0 0
\(863\) −18.1764 −0.618731 −0.309366 0.950943i \(-0.600117\pi\)
−0.309366 + 0.950943i \(0.600117\pi\)
\(864\) 0 0
\(865\) −14.1706 −0.481814
\(866\) 0 0
\(867\) −20.1979 −0.685958
\(868\) 0 0
\(869\) −1.93346 −0.0655882
\(870\) 0 0
\(871\) 77.1502 2.61413
\(872\) 0 0
\(873\) 5.12044 0.173301
\(874\) 0 0
\(875\) −8.19788 −0.277139
\(876\) 0 0
\(877\) 32.2526 1.08909 0.544547 0.838730i \(-0.316702\pi\)
0.544547 + 0.838730i \(0.316702\pi\)
\(878\) 0 0
\(879\) −15.8676 −0.535201
\(880\) 0 0
\(881\) −45.3656 −1.52841 −0.764204 0.644975i \(-0.776868\pi\)
−0.764204 + 0.644975i \(0.776868\pi\)
\(882\) 0 0
\(883\) −20.3669 −0.685402 −0.342701 0.939444i \(-0.611342\pi\)
−0.342701 + 0.939444i \(0.611342\pi\)
\(884\) 0 0
\(885\) −6.55142 −0.220224
\(886\) 0 0
\(887\) −54.0111 −1.81351 −0.906757 0.421654i \(-0.861450\pi\)
−0.906757 + 0.421654i \(0.861450\pi\)
\(888\) 0 0
\(889\) −15.8086 −0.530203
\(890\) 0 0
\(891\) −9.70340 −0.325076
\(892\) 0 0
\(893\) 1.50562 0.0503837
\(894\) 0 0
\(895\) 5.43253 0.181589
\(896\) 0 0
\(897\) −10.7617 −0.359322
\(898\) 0 0
\(899\) 0.553603 0.0184637
\(900\) 0 0
\(901\) −0.132408 −0.00441114
\(902\) 0 0
\(903\) −12.4395 −0.413960
\(904\) 0 0
\(905\) −11.1162 −0.369515
\(906\) 0 0
\(907\) 8.58408 0.285030 0.142515 0.989793i \(-0.454481\pi\)
0.142515 + 0.989793i \(0.454481\pi\)
\(908\) 0 0
\(909\) −11.1041 −0.368299
\(910\) 0 0
\(911\) −55.7805 −1.84809 −0.924045 0.382283i \(-0.875138\pi\)
−0.924045 + 0.382283i \(0.875138\pi\)
\(912\) 0 0
\(913\) 14.2993 0.473239
\(914\) 0 0
\(915\) 9.89523 0.327126
\(916\) 0 0
\(917\) −22.2557 −0.734949
\(918\) 0 0
\(919\) 23.2970 0.768497 0.384248 0.923230i \(-0.374461\pi\)
0.384248 + 0.923230i \(0.374461\pi\)
\(920\) 0 0
\(921\) 11.4916 0.378660
\(922\) 0 0
\(923\) 41.8075 1.37611
\(924\) 0 0
\(925\) 34.8527 1.14595
\(926\) 0 0
\(927\) 7.13156 0.234231
\(928\) 0 0
\(929\) 30.7079 1.00749 0.503746 0.863852i \(-0.331955\pi\)
0.503746 + 0.863852i \(0.331955\pi\)
\(930\) 0 0
\(931\) −5.22971 −0.171397
\(932\) 0 0
\(933\) −5.43161 −0.177823
\(934\) 0 0
\(935\) −2.05359 −0.0671596
\(936\) 0 0
\(937\) 9.54260 0.311743 0.155872 0.987777i \(-0.450181\pi\)
0.155872 + 0.987777i \(0.450181\pi\)
\(938\) 0 0
\(939\) −6.92017 −0.225831
\(940\) 0 0
\(941\) 17.1446 0.558899 0.279450 0.960160i \(-0.409848\pi\)
0.279450 + 0.960160i \(0.409848\pi\)
\(942\) 0 0
\(943\) 7.89424 0.257072
\(944\) 0 0
\(945\) −4.83722 −0.157355
\(946\) 0 0
\(947\) 27.6790 0.899446 0.449723 0.893168i \(-0.351523\pi\)
0.449723 + 0.893168i \(0.351523\pi\)
\(948\) 0 0
\(949\) −55.5451 −1.80307
\(950\) 0 0
\(951\) 13.2542 0.429798
\(952\) 0 0
\(953\) 46.7690 1.51500 0.757498 0.652837i \(-0.226421\pi\)
0.757498 + 0.652837i \(0.226421\pi\)
\(954\) 0 0
\(955\) 7.48841 0.242319
\(956\) 0 0
\(957\) −0.264003 −0.00853399
\(958\) 0 0
\(959\) −20.3816 −0.658155
\(960\) 0 0
\(961\) 1.93764 0.0625045
\(962\) 0 0
\(963\) −13.3725 −0.430923
\(964\) 0 0
\(965\) 6.63875 0.213709
\(966\) 0 0
\(967\) 24.6617 0.793066 0.396533 0.918021i \(-0.370213\pi\)
0.396533 + 0.918021i \(0.370213\pi\)
\(968\) 0 0
\(969\) −2.33937 −0.0751514
\(970\) 0 0
\(971\) −34.9613 −1.12196 −0.560981 0.827828i \(-0.689576\pi\)
−0.560981 + 0.827828i \(0.689576\pi\)
\(972\) 0 0
\(973\) 9.74005 0.312252
\(974\) 0 0
\(975\) 33.8629 1.08448
\(976\) 0 0
\(977\) −39.8874 −1.27611 −0.638056 0.769990i \(-0.720261\pi\)
−0.638056 + 0.769990i \(0.720261\pi\)
\(978\) 0 0
\(979\) −8.97854 −0.286955
\(980\) 0 0
\(981\) 8.82643 0.281806
\(982\) 0 0
\(983\) 25.4845 0.812831 0.406415 0.913688i \(-0.366779\pi\)
0.406415 + 0.913688i \(0.366779\pi\)
\(984\) 0 0
\(985\) −3.84670 −0.122566
\(986\) 0 0
\(987\) 2.83568 0.0902607
\(988\) 0 0
\(989\) −9.62812 −0.306156
\(990\) 0 0
\(991\) −10.3321 −0.328211 −0.164106 0.986443i \(-0.552474\pi\)
−0.164106 + 0.986443i \(0.552474\pi\)
\(992\) 0 0
\(993\) 1.47886 0.0469302
\(994\) 0 0
\(995\) −3.02622 −0.0959375
\(996\) 0 0
\(997\) −34.1889 −1.08277 −0.541387 0.840774i \(-0.682100\pi\)
−0.541387 + 0.840774i \(0.682100\pi\)
\(998\) 0 0
\(999\) 42.9820 1.35989
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 \(a_p\))