Properties

Label 6004.2.a.g.1.12
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 1.12
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.604994 q^{3} +2.44978 q^{5} +2.35442 q^{7} -2.63398 q^{9} +O(q^{10})\) \(q-0.604994 q^{3} +2.44978 q^{5} +2.35442 q^{7} -2.63398 q^{9} +0.468519 q^{11} +3.50927 q^{13} -1.48210 q^{15} -6.18064 q^{17} +1.00000 q^{19} -1.42441 q^{21} -7.62373 q^{23} +1.00144 q^{25} +3.40852 q^{27} +1.30072 q^{29} -1.64624 q^{31} -0.283451 q^{33} +5.76782 q^{35} -9.36695 q^{37} -2.12309 q^{39} -0.982363 q^{41} -10.0121 q^{43} -6.45269 q^{45} -2.43534 q^{47} -1.45671 q^{49} +3.73925 q^{51} +2.13707 q^{53} +1.14777 q^{55} -0.604994 q^{57} -14.8492 q^{59} -6.19170 q^{61} -6.20150 q^{63} +8.59696 q^{65} +9.26754 q^{67} +4.61231 q^{69} -2.60754 q^{71} +4.21490 q^{73} -0.605863 q^{75} +1.10309 q^{77} -1.00000 q^{79} +5.83981 q^{81} -2.00505 q^{83} -15.1412 q^{85} -0.786928 q^{87} +3.76515 q^{89} +8.26231 q^{91} +0.995968 q^{93} +2.44978 q^{95} -4.45794 q^{97} -1.23407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −0.604994 −0.349293 −0.174647 0.984631i \(-0.555878\pi\)
−0.174647 + 0.984631i \(0.555878\pi\)
\(4\) 0 0
\(5\) 2.44978 1.09558 0.547788 0.836617i \(-0.315470\pi\)
0.547788 + 0.836617i \(0.315470\pi\)
\(6\) 0 0
\(7\) 2.35442 0.889887 0.444944 0.895559i \(-0.353224\pi\)
0.444944 + 0.895559i \(0.353224\pi\)
\(8\) 0 0
\(9\) −2.63398 −0.877994
\(10\) 0 0
\(11\) 0.468519 0.141264 0.0706318 0.997502i \(-0.477498\pi\)
0.0706318 + 0.997502i \(0.477498\pi\)
\(12\) 0 0
\(13\) 3.50927 0.973298 0.486649 0.873598i \(-0.338219\pi\)
0.486649 + 0.873598i \(0.338219\pi\)
\(14\) 0 0
\(15\) −1.48210 −0.382677
\(16\) 0 0
\(17\) −6.18064 −1.49902 −0.749512 0.661990i \(-0.769712\pi\)
−0.749512 + 0.661990i \(0.769712\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.42441 −0.310832
\(22\) 0 0
\(23\) −7.62373 −1.58966 −0.794829 0.606833i \(-0.792440\pi\)
−0.794829 + 0.606833i \(0.792440\pi\)
\(24\) 0 0
\(25\) 1.00144 0.200287
\(26\) 0 0
\(27\) 3.40852 0.655971
\(28\) 0 0
\(29\) 1.30072 0.241538 0.120769 0.992681i \(-0.461464\pi\)
0.120769 + 0.992681i \(0.461464\pi\)
\(30\) 0 0
\(31\) −1.64624 −0.295674 −0.147837 0.989012i \(-0.547231\pi\)
−0.147837 + 0.989012i \(0.547231\pi\)
\(32\) 0 0
\(33\) −0.283451 −0.0493424
\(34\) 0 0
\(35\) 5.76782 0.974939
\(36\) 0 0
\(37\) −9.36695 −1.53992 −0.769959 0.638093i \(-0.779723\pi\)
−0.769959 + 0.638093i \(0.779723\pi\)
\(38\) 0 0
\(39\) −2.12309 −0.339966
\(40\) 0 0
\(41\) −0.982363 −0.153419 −0.0767096 0.997053i \(-0.524441\pi\)
−0.0767096 + 0.997053i \(0.524441\pi\)
\(42\) 0 0
\(43\) −10.0121 −1.52683 −0.763416 0.645907i \(-0.776479\pi\)
−0.763416 + 0.645907i \(0.776479\pi\)
\(44\) 0 0
\(45\) −6.45269 −0.961910
\(46\) 0 0
\(47\) −2.43534 −0.355231 −0.177615 0.984100i \(-0.556838\pi\)
−0.177615 + 0.984100i \(0.556838\pi\)
\(48\) 0 0
\(49\) −1.45671 −0.208101
\(50\) 0 0
\(51\) 3.73925 0.523599
\(52\) 0 0
\(53\) 2.13707 0.293549 0.146774 0.989170i \(-0.453111\pi\)
0.146774 + 0.989170i \(0.453111\pi\)
\(54\) 0 0
\(55\) 1.14777 0.154765
\(56\) 0 0
\(57\) −0.604994 −0.0801334
\(58\) 0 0
\(59\) −14.8492 −1.93320 −0.966602 0.256283i \(-0.917502\pi\)
−0.966602 + 0.256283i \(0.917502\pi\)
\(60\) 0 0
\(61\) −6.19170 −0.792766 −0.396383 0.918085i \(-0.629735\pi\)
−0.396383 + 0.918085i \(0.629735\pi\)
\(62\) 0 0
\(63\) −6.20150 −0.781316
\(64\) 0 0
\(65\) 8.59696 1.06632
\(66\) 0 0
\(67\) 9.26754 1.13221 0.566105 0.824333i \(-0.308450\pi\)
0.566105 + 0.824333i \(0.308450\pi\)
\(68\) 0 0
\(69\) 4.61231 0.555257
\(70\) 0 0
\(71\) −2.60754 −0.309458 −0.154729 0.987957i \(-0.549450\pi\)
−0.154729 + 0.987957i \(0.549450\pi\)
\(72\) 0 0
\(73\) 4.21490 0.493316 0.246658 0.969103i \(-0.420668\pi\)
0.246658 + 0.969103i \(0.420668\pi\)
\(74\) 0 0
\(75\) −0.605863 −0.0699590
\(76\) 0 0
\(77\) 1.10309 0.125709
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 5.83981 0.648868
\(82\) 0 0
\(83\) −2.00505 −0.220083 −0.110041 0.993927i \(-0.535098\pi\)
−0.110041 + 0.993927i \(0.535098\pi\)
\(84\) 0 0
\(85\) −15.1412 −1.64230
\(86\) 0 0
\(87\) −0.786928 −0.0843675
\(88\) 0 0
\(89\) 3.76515 0.399105 0.199553 0.979887i \(-0.436051\pi\)
0.199553 + 0.979887i \(0.436051\pi\)
\(90\) 0 0
\(91\) 8.26231 0.866125
\(92\) 0 0
\(93\) 0.995968 0.103277
\(94\) 0 0
\(95\) 2.44978 0.251342
\(96\) 0 0
\(97\) −4.45794 −0.452635 −0.226318 0.974054i \(-0.572669\pi\)
−0.226318 + 0.974054i \(0.572669\pi\)
\(98\) 0 0
\(99\) −1.23407 −0.124029
\(100\) 0 0
\(101\) −4.81751 −0.479360 −0.239680 0.970852i \(-0.577043\pi\)
−0.239680 + 0.970852i \(0.577043\pi\)
\(102\) 0 0
\(103\) 13.7916 1.35892 0.679461 0.733712i \(-0.262214\pi\)
0.679461 + 0.733712i \(0.262214\pi\)
\(104\) 0 0
\(105\) −3.48949 −0.340540
\(106\) 0 0
\(107\) −14.6905 −1.42018 −0.710090 0.704111i \(-0.751346\pi\)
−0.710090 + 0.704111i \(0.751346\pi\)
\(108\) 0 0
\(109\) −5.54311 −0.530934 −0.265467 0.964120i \(-0.585526\pi\)
−0.265467 + 0.964120i \(0.585526\pi\)
\(110\) 0 0
\(111\) 5.66695 0.537883
\(112\) 0 0
\(113\) −8.12912 −0.764723 −0.382362 0.924013i \(-0.624889\pi\)
−0.382362 + 0.924013i \(0.624889\pi\)
\(114\) 0 0
\(115\) −18.6765 −1.74159
\(116\) 0 0
\(117\) −9.24337 −0.854550
\(118\) 0 0
\(119\) −14.5518 −1.33396
\(120\) 0 0
\(121\) −10.7805 −0.980045
\(122\) 0 0
\(123\) 0.594323 0.0535883
\(124\) 0 0
\(125\) −9.79561 −0.876146
\(126\) 0 0
\(127\) 2.64614 0.234807 0.117404 0.993084i \(-0.462543\pi\)
0.117404 + 0.993084i \(0.462543\pi\)
\(128\) 0 0
\(129\) 6.05726 0.533312
\(130\) 0 0
\(131\) −2.88210 −0.251810 −0.125905 0.992042i \(-0.540183\pi\)
−0.125905 + 0.992042i \(0.540183\pi\)
\(132\) 0 0
\(133\) 2.35442 0.204154
\(134\) 0 0
\(135\) 8.35014 0.718666
\(136\) 0 0
\(137\) 12.2618 1.04760 0.523799 0.851842i \(-0.324514\pi\)
0.523799 + 0.851842i \(0.324514\pi\)
\(138\) 0 0
\(139\) 11.9899 1.01697 0.508483 0.861072i \(-0.330206\pi\)
0.508483 + 0.861072i \(0.330206\pi\)
\(140\) 0 0
\(141\) 1.47336 0.124080
\(142\) 0 0
\(143\) 1.64416 0.137492
\(144\) 0 0
\(145\) 3.18648 0.264623
\(146\) 0 0
\(147\) 0.881298 0.0726882
\(148\) 0 0
\(149\) 12.4904 1.02325 0.511626 0.859208i \(-0.329043\pi\)
0.511626 + 0.859208i \(0.329043\pi\)
\(150\) 0 0
\(151\) −3.55007 −0.288900 −0.144450 0.989512i \(-0.546141\pi\)
−0.144450 + 0.989512i \(0.546141\pi\)
\(152\) 0 0
\(153\) 16.2797 1.31614
\(154\) 0 0
\(155\) −4.03294 −0.323934
\(156\) 0 0
\(157\) 2.25373 0.179867 0.0899336 0.995948i \(-0.471335\pi\)
0.0899336 + 0.995948i \(0.471335\pi\)
\(158\) 0 0
\(159\) −1.29291 −0.102535
\(160\) 0 0
\(161\) −17.9495 −1.41462
\(162\) 0 0
\(163\) 17.1560 1.34376 0.671881 0.740659i \(-0.265487\pi\)
0.671881 + 0.740659i \(0.265487\pi\)
\(164\) 0 0
\(165\) −0.694393 −0.0540584
\(166\) 0 0
\(167\) 4.87658 0.377361 0.188681 0.982038i \(-0.439579\pi\)
0.188681 + 0.982038i \(0.439579\pi\)
\(168\) 0 0
\(169\) −0.684990 −0.0526915
\(170\) 0 0
\(171\) −2.63398 −0.201426
\(172\) 0 0
\(173\) 0.524244 0.0398575 0.0199288 0.999801i \(-0.493656\pi\)
0.0199288 + 0.999801i \(0.493656\pi\)
\(174\) 0 0
\(175\) 2.35780 0.178233
\(176\) 0 0
\(177\) 8.98368 0.675255
\(178\) 0 0
\(179\) 6.19268 0.462863 0.231431 0.972851i \(-0.425659\pi\)
0.231431 + 0.972851i \(0.425659\pi\)
\(180\) 0 0
\(181\) 3.98028 0.295852 0.147926 0.988998i \(-0.452740\pi\)
0.147926 + 0.988998i \(0.452740\pi\)
\(182\) 0 0
\(183\) 3.74594 0.276908
\(184\) 0 0
\(185\) −22.9470 −1.68710
\(186\) 0 0
\(187\) −2.89574 −0.211758
\(188\) 0 0
\(189\) 8.02510 0.583740
\(190\) 0 0
\(191\) −10.4934 −0.759279 −0.379639 0.925135i \(-0.623952\pi\)
−0.379639 + 0.925135i \(0.623952\pi\)
\(192\) 0 0
\(193\) 10.8655 0.782115 0.391057 0.920366i \(-0.372109\pi\)
0.391057 + 0.920366i \(0.372109\pi\)
\(194\) 0 0
\(195\) −5.20111 −0.372459
\(196\) 0 0
\(197\) −10.6489 −0.758702 −0.379351 0.925253i \(-0.623853\pi\)
−0.379351 + 0.925253i \(0.623853\pi\)
\(198\) 0 0
\(199\) 22.1387 1.56937 0.784684 0.619895i \(-0.212825\pi\)
0.784684 + 0.619895i \(0.212825\pi\)
\(200\) 0 0
\(201\) −5.60680 −0.395473
\(202\) 0 0
\(203\) 3.06244 0.214941
\(204\) 0 0
\(205\) −2.40657 −0.168082
\(206\) 0 0
\(207\) 20.0808 1.39571
\(208\) 0 0
\(209\) 0.468519 0.0324081
\(210\) 0 0
\(211\) 4.53308 0.312070 0.156035 0.987752i \(-0.450129\pi\)
0.156035 + 0.987752i \(0.450129\pi\)
\(212\) 0 0
\(213\) 1.57754 0.108092
\(214\) 0 0
\(215\) −24.5275 −1.67276
\(216\) 0 0
\(217\) −3.87595 −0.263117
\(218\) 0 0
\(219\) −2.54999 −0.172312
\(220\) 0 0
\(221\) −21.6896 −1.45900
\(222\) 0 0
\(223\) 22.3393 1.49595 0.747976 0.663726i \(-0.231026\pi\)
0.747976 + 0.663726i \(0.231026\pi\)
\(224\) 0 0
\(225\) −2.63777 −0.175851
\(226\) 0 0
\(227\) 1.81604 0.120535 0.0602675 0.998182i \(-0.480805\pi\)
0.0602675 + 0.998182i \(0.480805\pi\)
\(228\) 0 0
\(229\) −17.0168 −1.12450 −0.562250 0.826967i \(-0.690064\pi\)
−0.562250 + 0.826967i \(0.690064\pi\)
\(230\) 0 0
\(231\) −0.667362 −0.0439092
\(232\) 0 0
\(233\) −3.65045 −0.239149 −0.119575 0.992825i \(-0.538153\pi\)
−0.119575 + 0.992825i \(0.538153\pi\)
\(234\) 0 0
\(235\) −5.96605 −0.389182
\(236\) 0 0
\(237\) 0.604994 0.0392986
\(238\) 0 0
\(239\) 19.3988 1.25481 0.627403 0.778694i \(-0.284118\pi\)
0.627403 + 0.778694i \(0.284118\pi\)
\(240\) 0 0
\(241\) −9.13327 −0.588326 −0.294163 0.955755i \(-0.595041\pi\)
−0.294163 + 0.955755i \(0.595041\pi\)
\(242\) 0 0
\(243\) −13.7586 −0.882616
\(244\) 0 0
\(245\) −3.56861 −0.227990
\(246\) 0 0
\(247\) 3.50927 0.223290
\(248\) 0 0
\(249\) 1.21304 0.0768734
\(250\) 0 0
\(251\) 1.08945 0.0687652 0.0343826 0.999409i \(-0.489054\pi\)
0.0343826 + 0.999409i \(0.489054\pi\)
\(252\) 0 0
\(253\) −3.57186 −0.224561
\(254\) 0 0
\(255\) 9.16034 0.573643
\(256\) 0 0
\(257\) 12.2335 0.763105 0.381553 0.924347i \(-0.375389\pi\)
0.381553 + 0.924347i \(0.375389\pi\)
\(258\) 0 0
\(259\) −22.0537 −1.37035
\(260\) 0 0
\(261\) −3.42608 −0.212069
\(262\) 0 0
\(263\) 19.6933 1.21434 0.607171 0.794571i \(-0.292304\pi\)
0.607171 + 0.794571i \(0.292304\pi\)
\(264\) 0 0
\(265\) 5.23535 0.321605
\(266\) 0 0
\(267\) −2.27789 −0.139405
\(268\) 0 0
\(269\) 1.74189 0.106205 0.0531025 0.998589i \(-0.483089\pi\)
0.0531025 + 0.998589i \(0.483089\pi\)
\(270\) 0 0
\(271\) 25.0149 1.51954 0.759772 0.650190i \(-0.225311\pi\)
0.759772 + 0.650190i \(0.225311\pi\)
\(272\) 0 0
\(273\) −4.99864 −0.302532
\(274\) 0 0
\(275\) 0.469192 0.0282933
\(276\) 0 0
\(277\) −5.35877 −0.321977 −0.160989 0.986956i \(-0.551468\pi\)
−0.160989 + 0.986956i \(0.551468\pi\)
\(278\) 0 0
\(279\) 4.33618 0.259600
\(280\) 0 0
\(281\) −8.35419 −0.498369 −0.249185 0.968456i \(-0.580163\pi\)
−0.249185 + 0.968456i \(0.580163\pi\)
\(282\) 0 0
\(283\) −7.65083 −0.454795 −0.227397 0.973802i \(-0.573022\pi\)
−0.227397 + 0.973802i \(0.573022\pi\)
\(284\) 0 0
\(285\) −1.48210 −0.0877922
\(286\) 0 0
\(287\) −2.31289 −0.136526
\(288\) 0 0
\(289\) 21.2003 1.24708
\(290\) 0 0
\(291\) 2.69703 0.158102
\(292\) 0 0
\(293\) −0.0471832 −0.00275647 −0.00137824 0.999999i \(-0.500439\pi\)
−0.00137824 + 0.999999i \(0.500439\pi\)
\(294\) 0 0
\(295\) −36.3774 −2.11797
\(296\) 0 0
\(297\) 1.59696 0.0926648
\(298\) 0 0
\(299\) −26.7538 −1.54721
\(300\) 0 0
\(301\) −23.5727 −1.35871
\(302\) 0 0
\(303\) 2.91456 0.167437
\(304\) 0 0
\(305\) −15.1683 −0.868536
\(306\) 0 0
\(307\) −24.7943 −1.41509 −0.707543 0.706670i \(-0.750196\pi\)
−0.707543 + 0.706670i \(0.750196\pi\)
\(308\) 0 0
\(309\) −8.34380 −0.474662
\(310\) 0 0
\(311\) −21.4159 −1.21439 −0.607193 0.794554i \(-0.707705\pi\)
−0.607193 + 0.794554i \(0.707705\pi\)
\(312\) 0 0
\(313\) −16.1755 −0.914295 −0.457147 0.889391i \(-0.651129\pi\)
−0.457147 + 0.889391i \(0.651129\pi\)
\(314\) 0 0
\(315\) −15.1923 −0.855991
\(316\) 0 0
\(317\) −20.2817 −1.13913 −0.569567 0.821945i \(-0.692889\pi\)
−0.569567 + 0.821945i \(0.692889\pi\)
\(318\) 0 0
\(319\) 0.609412 0.0341205
\(320\) 0 0
\(321\) 8.88764 0.496059
\(322\) 0 0
\(323\) −6.18064 −0.343900
\(324\) 0 0
\(325\) 3.51432 0.194939
\(326\) 0 0
\(327\) 3.35355 0.185452
\(328\) 0 0
\(329\) −5.73381 −0.316115
\(330\) 0 0
\(331\) 9.99691 0.549480 0.274740 0.961519i \(-0.411408\pi\)
0.274740 + 0.961519i \(0.411408\pi\)
\(332\) 0 0
\(333\) 24.6724 1.35204
\(334\) 0 0
\(335\) 22.7035 1.24042
\(336\) 0 0
\(337\) 2.14801 0.117009 0.0585047 0.998287i \(-0.481367\pi\)
0.0585047 + 0.998287i \(0.481367\pi\)
\(338\) 0 0
\(339\) 4.91807 0.267113
\(340\) 0 0
\(341\) −0.771296 −0.0417680
\(342\) 0 0
\(343\) −19.9106 −1.07507
\(344\) 0 0
\(345\) 11.2992 0.608326
\(346\) 0 0
\(347\) −3.67034 −0.197034 −0.0985170 0.995135i \(-0.531410\pi\)
−0.0985170 + 0.995135i \(0.531410\pi\)
\(348\) 0 0
\(349\) 18.2766 0.978322 0.489161 0.872193i \(-0.337303\pi\)
0.489161 + 0.872193i \(0.337303\pi\)
\(350\) 0 0
\(351\) 11.9614 0.638455
\(352\) 0 0
\(353\) −33.9309 −1.80596 −0.902980 0.429683i \(-0.858625\pi\)
−0.902980 + 0.429683i \(0.858625\pi\)
\(354\) 0 0
\(355\) −6.38790 −0.339035
\(356\) 0 0
\(357\) 8.80376 0.465944
\(358\) 0 0
\(359\) −7.97748 −0.421035 −0.210518 0.977590i \(-0.567515\pi\)
−0.210518 + 0.977590i \(0.567515\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 6.52213 0.342323
\(364\) 0 0
\(365\) 10.3256 0.540466
\(366\) 0 0
\(367\) 17.4424 0.910488 0.455244 0.890367i \(-0.349552\pi\)
0.455244 + 0.890367i \(0.349552\pi\)
\(368\) 0 0
\(369\) 2.58753 0.134701
\(370\) 0 0
\(371\) 5.03155 0.261225
\(372\) 0 0
\(373\) −17.3519 −0.898449 −0.449224 0.893419i \(-0.648300\pi\)
−0.449224 + 0.893419i \(0.648300\pi\)
\(374\) 0 0
\(375\) 5.92628 0.306032
\(376\) 0 0
\(377\) 4.56459 0.235088
\(378\) 0 0
\(379\) −16.4005 −0.842440 −0.421220 0.906959i \(-0.638398\pi\)
−0.421220 + 0.906959i \(0.638398\pi\)
\(380\) 0 0
\(381\) −1.60090 −0.0820166
\(382\) 0 0
\(383\) −25.2958 −1.29256 −0.646278 0.763102i \(-0.723675\pi\)
−0.646278 + 0.763102i \(0.723675\pi\)
\(384\) 0 0
\(385\) 2.70233 0.137723
\(386\) 0 0
\(387\) 26.3717 1.34055
\(388\) 0 0
\(389\) 0.142242 0.00721196 0.00360598 0.999993i \(-0.498852\pi\)
0.00360598 + 0.999993i \(0.498852\pi\)
\(390\) 0 0
\(391\) 47.1195 2.38294
\(392\) 0 0
\(393\) 1.74365 0.0879555
\(394\) 0 0
\(395\) −2.44978 −0.123262
\(396\) 0 0
\(397\) 16.7945 0.842893 0.421446 0.906853i \(-0.361523\pi\)
0.421446 + 0.906853i \(0.361523\pi\)
\(398\) 0 0
\(399\) −1.42441 −0.0713096
\(400\) 0 0
\(401\) 16.1890 0.808438 0.404219 0.914662i \(-0.367543\pi\)
0.404219 + 0.914662i \(0.367543\pi\)
\(402\) 0 0
\(403\) −5.77713 −0.287779
\(404\) 0 0
\(405\) 14.3063 0.710884
\(406\) 0 0
\(407\) −4.38859 −0.217534
\(408\) 0 0
\(409\) −21.0235 −1.03955 −0.519773 0.854304i \(-0.673984\pi\)
−0.519773 + 0.854304i \(0.673984\pi\)
\(410\) 0 0
\(411\) −7.41833 −0.365919
\(412\) 0 0
\(413\) −34.9613 −1.72033
\(414\) 0 0
\(415\) −4.91194 −0.241117
\(416\) 0 0
\(417\) −7.25379 −0.355220
\(418\) 0 0
\(419\) −27.5659 −1.34668 −0.673342 0.739331i \(-0.735142\pi\)
−0.673342 + 0.739331i \(0.735142\pi\)
\(420\) 0 0
\(421\) −7.54751 −0.367843 −0.183922 0.982941i \(-0.558879\pi\)
−0.183922 + 0.982941i \(0.558879\pi\)
\(422\) 0 0
\(423\) 6.41464 0.311890
\(424\) 0 0
\(425\) −6.18952 −0.300236
\(426\) 0 0
\(427\) −14.5779 −0.705473
\(428\) 0 0
\(429\) −0.994707 −0.0480249
\(430\) 0 0
\(431\) 20.8660 1.00508 0.502540 0.864554i \(-0.332399\pi\)
0.502540 + 0.864554i \(0.332399\pi\)
\(432\) 0 0
\(433\) −19.0135 −0.913731 −0.456865 0.889536i \(-0.651028\pi\)
−0.456865 + 0.889536i \(0.651028\pi\)
\(434\) 0 0
\(435\) −1.92780 −0.0924310
\(436\) 0 0
\(437\) −7.62373 −0.364693
\(438\) 0 0
\(439\) 19.8903 0.949312 0.474656 0.880171i \(-0.342572\pi\)
0.474656 + 0.880171i \(0.342572\pi\)
\(440\) 0 0
\(441\) 3.83694 0.182711
\(442\) 0 0
\(443\) 24.6162 1.16955 0.584776 0.811195i \(-0.301182\pi\)
0.584776 + 0.811195i \(0.301182\pi\)
\(444\) 0 0
\(445\) 9.22381 0.437250
\(446\) 0 0
\(447\) −7.55660 −0.357415
\(448\) 0 0
\(449\) −3.98532 −0.188079 −0.0940394 0.995568i \(-0.529978\pi\)
−0.0940394 + 0.995568i \(0.529978\pi\)
\(450\) 0 0
\(451\) −0.460255 −0.0216726
\(452\) 0 0
\(453\) 2.14777 0.100911
\(454\) 0 0
\(455\) 20.2409 0.948906
\(456\) 0 0
\(457\) −6.19826 −0.289942 −0.144971 0.989436i \(-0.546309\pi\)
−0.144971 + 0.989436i \(0.546309\pi\)
\(458\) 0 0
\(459\) −21.0669 −0.983316
\(460\) 0 0
\(461\) −10.1185 −0.471267 −0.235634 0.971842i \(-0.575716\pi\)
−0.235634 + 0.971842i \(0.575716\pi\)
\(462\) 0 0
\(463\) 27.4102 1.27386 0.636931 0.770921i \(-0.280204\pi\)
0.636931 + 0.770921i \(0.280204\pi\)
\(464\) 0 0
\(465\) 2.43990 0.113148
\(466\) 0 0
\(467\) −7.55393 −0.349554 −0.174777 0.984608i \(-0.555921\pi\)
−0.174777 + 0.984608i \(0.555921\pi\)
\(468\) 0 0
\(469\) 21.8197 1.00754
\(470\) 0 0
\(471\) −1.36349 −0.0628264
\(472\) 0 0
\(473\) −4.69086 −0.215686
\(474\) 0 0
\(475\) 1.00144 0.0459491
\(476\) 0 0
\(477\) −5.62899 −0.257734
\(478\) 0 0
\(479\) 19.6830 0.899340 0.449670 0.893195i \(-0.351542\pi\)
0.449670 + 0.893195i \(0.351542\pi\)
\(480\) 0 0
\(481\) −32.8712 −1.49880
\(482\) 0 0
\(483\) 10.8593 0.494116
\(484\) 0 0
\(485\) −10.9210 −0.495897
\(486\) 0 0
\(487\) −22.1199 −1.00235 −0.501175 0.865346i \(-0.667099\pi\)
−0.501175 + 0.865346i \(0.667099\pi\)
\(488\) 0 0
\(489\) −10.3793 −0.469367
\(490\) 0 0
\(491\) 8.54047 0.385426 0.192713 0.981255i \(-0.438271\pi\)
0.192713 + 0.981255i \(0.438271\pi\)
\(492\) 0 0
\(493\) −8.03928 −0.362071
\(494\) 0 0
\(495\) −3.02320 −0.135883
\(496\) 0 0
\(497\) −6.13924 −0.275383
\(498\) 0 0
\(499\) −31.9166 −1.42878 −0.714391 0.699746i \(-0.753296\pi\)
−0.714391 + 0.699746i \(0.753296\pi\)
\(500\) 0 0
\(501\) −2.95030 −0.131810
\(502\) 0 0
\(503\) 1.31642 0.0586964 0.0293482 0.999569i \(-0.490657\pi\)
0.0293482 + 0.999569i \(0.490657\pi\)
\(504\) 0 0
\(505\) −11.8018 −0.525175
\(506\) 0 0
\(507\) 0.414414 0.0184048
\(508\) 0 0
\(509\) −1.23657 −0.0548101 −0.0274050 0.999624i \(-0.508724\pi\)
−0.0274050 + 0.999624i \(0.508724\pi\)
\(510\) 0 0
\(511\) 9.92364 0.438996
\(512\) 0 0
\(513\) 3.40852 0.150490
\(514\) 0 0
\(515\) 33.7863 1.48880
\(516\) 0 0
\(517\) −1.14100 −0.0501812
\(518\) 0 0
\(519\) −0.317164 −0.0139220
\(520\) 0 0
\(521\) −19.1777 −0.840192 −0.420096 0.907480i \(-0.638004\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(522\) 0 0
\(523\) 16.4298 0.718427 0.359213 0.933255i \(-0.383045\pi\)
0.359213 + 0.933255i \(0.383045\pi\)
\(524\) 0 0
\(525\) −1.42646 −0.0622556
\(526\) 0 0
\(527\) 10.1748 0.443223
\(528\) 0 0
\(529\) 35.1213 1.52701
\(530\) 0 0
\(531\) 39.1126 1.69734
\(532\) 0 0
\(533\) −3.44738 −0.149323
\(534\) 0 0
\(535\) −35.9884 −1.55592
\(536\) 0 0
\(537\) −3.74653 −0.161675
\(538\) 0 0
\(539\) −0.682494 −0.0293971
\(540\) 0 0
\(541\) 2.33319 0.100311 0.0501557 0.998741i \(-0.484028\pi\)
0.0501557 + 0.998741i \(0.484028\pi\)
\(542\) 0 0
\(543\) −2.40804 −0.103339
\(544\) 0 0
\(545\) −13.5794 −0.581679
\(546\) 0 0
\(547\) 22.6740 0.969470 0.484735 0.874661i \(-0.338916\pi\)
0.484735 + 0.874661i \(0.338916\pi\)
\(548\) 0 0
\(549\) 16.3088 0.696044
\(550\) 0 0
\(551\) 1.30072 0.0554126
\(552\) 0 0
\(553\) −2.35442 −0.100120
\(554\) 0 0
\(555\) 13.8828 0.589292
\(556\) 0 0
\(557\) 6.16892 0.261386 0.130693 0.991423i \(-0.458280\pi\)
0.130693 + 0.991423i \(0.458280\pi\)
\(558\) 0 0
\(559\) −35.1352 −1.48606
\(560\) 0 0
\(561\) 1.75191 0.0739655
\(562\) 0 0
\(563\) 18.8505 0.794453 0.397227 0.917721i \(-0.369973\pi\)
0.397227 + 0.917721i \(0.369973\pi\)
\(564\) 0 0
\(565\) −19.9146 −0.837813
\(566\) 0 0
\(567\) 13.7494 0.577419
\(568\) 0 0
\(569\) −35.7486 −1.49866 −0.749331 0.662196i \(-0.769625\pi\)
−0.749331 + 0.662196i \(0.769625\pi\)
\(570\) 0 0
\(571\) −24.3618 −1.01951 −0.509755 0.860320i \(-0.670264\pi\)
−0.509755 + 0.860320i \(0.670264\pi\)
\(572\) 0 0
\(573\) 6.34847 0.265211
\(574\) 0 0
\(575\) −7.63469 −0.318388
\(576\) 0 0
\(577\) −35.5817 −1.48129 −0.740643 0.671899i \(-0.765479\pi\)
−0.740643 + 0.671899i \(0.765479\pi\)
\(578\) 0 0
\(579\) −6.57355 −0.273187
\(580\) 0 0
\(581\) −4.72073 −0.195849
\(582\) 0 0
\(583\) 1.00125 0.0414677
\(584\) 0 0
\(585\) −22.6442 −0.936224
\(586\) 0 0
\(587\) 4.65457 0.192115 0.0960574 0.995376i \(-0.469377\pi\)
0.0960574 + 0.995376i \(0.469377\pi\)
\(588\) 0 0
\(589\) −1.64624 −0.0678323
\(590\) 0 0
\(591\) 6.44251 0.265010
\(592\) 0 0
\(593\) −38.0844 −1.56394 −0.781970 0.623316i \(-0.785785\pi\)
−0.781970 + 0.623316i \(0.785785\pi\)
\(594\) 0 0
\(595\) −35.6488 −1.46146
\(596\) 0 0
\(597\) −13.3938 −0.548170
\(598\) 0 0
\(599\) 21.2478 0.868163 0.434082 0.900874i \(-0.357073\pi\)
0.434082 + 0.900874i \(0.357073\pi\)
\(600\) 0 0
\(601\) −27.2110 −1.10996 −0.554980 0.831863i \(-0.687274\pi\)
−0.554980 + 0.831863i \(0.687274\pi\)
\(602\) 0 0
\(603\) −24.4105 −0.994074
\(604\) 0 0
\(605\) −26.4099 −1.07371
\(606\) 0 0
\(607\) −20.8955 −0.848122 −0.424061 0.905634i \(-0.639396\pi\)
−0.424061 + 0.905634i \(0.639396\pi\)
\(608\) 0 0
\(609\) −1.85276 −0.0750776
\(610\) 0 0
\(611\) −8.54627 −0.345745
\(612\) 0 0
\(613\) −10.2749 −0.414999 −0.207499 0.978235i \(-0.566532\pi\)
−0.207499 + 0.978235i \(0.566532\pi\)
\(614\) 0 0
\(615\) 1.45596 0.0587101
\(616\) 0 0
\(617\) −2.43149 −0.0978881 −0.0489441 0.998802i \(-0.515586\pi\)
−0.0489441 + 0.998802i \(0.515586\pi\)
\(618\) 0 0
\(619\) −22.9624 −0.922937 −0.461468 0.887157i \(-0.652677\pi\)
−0.461468 + 0.887157i \(0.652677\pi\)
\(620\) 0 0
\(621\) −25.9857 −1.04277
\(622\) 0 0
\(623\) 8.86475 0.355159
\(624\) 0 0
\(625\) −29.0043 −1.16017
\(626\) 0 0
\(627\) −0.283451 −0.0113199
\(628\) 0 0
\(629\) 57.8938 2.30838
\(630\) 0 0
\(631\) −3.41002 −0.135751 −0.0678754 0.997694i \(-0.521622\pi\)
−0.0678754 + 0.997694i \(0.521622\pi\)
\(632\) 0 0
\(633\) −2.74248 −0.109004
\(634\) 0 0
\(635\) 6.48248 0.257249
\(636\) 0 0
\(637\) −5.11198 −0.202544
\(638\) 0 0
\(639\) 6.86821 0.271702
\(640\) 0 0
\(641\) −18.8334 −0.743876 −0.371938 0.928258i \(-0.621307\pi\)
−0.371938 + 0.928258i \(0.621307\pi\)
\(642\) 0 0
\(643\) 11.4571 0.451824 0.225912 0.974148i \(-0.427464\pi\)
0.225912 + 0.974148i \(0.427464\pi\)
\(644\) 0 0
\(645\) 14.8390 0.584284
\(646\) 0 0
\(647\) −18.3098 −0.719831 −0.359916 0.932985i \(-0.617195\pi\)
−0.359916 + 0.932985i \(0.617195\pi\)
\(648\) 0 0
\(649\) −6.95713 −0.273091
\(650\) 0 0
\(651\) 2.34493 0.0919049
\(652\) 0 0
\(653\) 50.0215 1.95749 0.978747 0.205072i \(-0.0657428\pi\)
0.978747 + 0.205072i \(0.0657428\pi\)
\(654\) 0 0
\(655\) −7.06051 −0.275877
\(656\) 0 0
\(657\) −11.1020 −0.433129
\(658\) 0 0
\(659\) 46.6649 1.81780 0.908902 0.417009i \(-0.136922\pi\)
0.908902 + 0.417009i \(0.136922\pi\)
\(660\) 0 0
\(661\) −44.0677 −1.71404 −0.857018 0.515287i \(-0.827685\pi\)
−0.857018 + 0.515287i \(0.827685\pi\)
\(662\) 0 0
\(663\) 13.1220 0.509618
\(664\) 0 0
\(665\) 5.76782 0.223666
\(666\) 0 0
\(667\) −9.91635 −0.383963
\(668\) 0 0
\(669\) −13.5151 −0.522526
\(670\) 0 0
\(671\) −2.90093 −0.111989
\(672\) 0 0
\(673\) −3.44752 −0.132892 −0.0664461 0.997790i \(-0.521166\pi\)
−0.0664461 + 0.997790i \(0.521166\pi\)
\(674\) 0 0
\(675\) 3.41342 0.131383
\(676\) 0 0
\(677\) −1.91135 −0.0734590 −0.0367295 0.999325i \(-0.511694\pi\)
−0.0367295 + 0.999325i \(0.511694\pi\)
\(678\) 0 0
\(679\) −10.4959 −0.402794
\(680\) 0 0
\(681\) −1.09869 −0.0421021
\(682\) 0 0
\(683\) −40.2721 −1.54097 −0.770485 0.637458i \(-0.779986\pi\)
−0.770485 + 0.637458i \(0.779986\pi\)
\(684\) 0 0
\(685\) 30.0388 1.14772
\(686\) 0 0
\(687\) 10.2950 0.392780
\(688\) 0 0
\(689\) 7.49955 0.285710
\(690\) 0 0
\(691\) −16.4765 −0.626795 −0.313397 0.949622i \(-0.601467\pi\)
−0.313397 + 0.949622i \(0.601467\pi\)
\(692\) 0 0
\(693\) −2.90552 −0.110372
\(694\) 0 0
\(695\) 29.3726 1.11416
\(696\) 0 0
\(697\) 6.07163 0.229979
\(698\) 0 0
\(699\) 2.20850 0.0835331
\(700\) 0 0
\(701\) 20.9375 0.790797 0.395398 0.918510i \(-0.370607\pi\)
0.395398 + 0.918510i \(0.370607\pi\)
\(702\) 0 0
\(703\) −9.36695 −0.353281
\(704\) 0 0
\(705\) 3.60942 0.135939
\(706\) 0 0
\(707\) −11.3424 −0.426576
\(708\) 0 0
\(709\) −38.1386 −1.43233 −0.716163 0.697934i \(-0.754103\pi\)
−0.716163 + 0.697934i \(0.754103\pi\)
\(710\) 0 0
\(711\) 2.63398 0.0987821
\(712\) 0 0
\(713\) 12.5505 0.470021
\(714\) 0 0
\(715\) 4.02784 0.150633
\(716\) 0 0
\(717\) −11.7362 −0.438296
\(718\) 0 0
\(719\) −18.0836 −0.674405 −0.337202 0.941432i \(-0.609481\pi\)
−0.337202 + 0.941432i \(0.609481\pi\)
\(720\) 0 0
\(721\) 32.4711 1.20929
\(722\) 0 0
\(723\) 5.52557 0.205498
\(724\) 0 0
\(725\) 1.30259 0.0483769
\(726\) 0 0
\(727\) 38.3635 1.42282 0.711412 0.702775i \(-0.248056\pi\)
0.711412 + 0.702775i \(0.248056\pi\)
\(728\) 0 0
\(729\) −9.19556 −0.340576
\(730\) 0 0
\(731\) 61.8812 2.28876
\(732\) 0 0
\(733\) 46.2166 1.70705 0.853524 0.521054i \(-0.174461\pi\)
0.853524 + 0.521054i \(0.174461\pi\)
\(734\) 0 0
\(735\) 2.15899 0.0796355
\(736\) 0 0
\(737\) 4.34201 0.159940
\(738\) 0 0
\(739\) 22.0464 0.810991 0.405496 0.914097i \(-0.367099\pi\)
0.405496 + 0.914097i \(0.367099\pi\)
\(740\) 0 0
\(741\) −2.12309 −0.0779936
\(742\) 0 0
\(743\) 17.7743 0.652077 0.326039 0.945356i \(-0.394286\pi\)
0.326039 + 0.945356i \(0.394286\pi\)
\(744\) 0 0
\(745\) 30.5987 1.12105
\(746\) 0 0
\(747\) 5.28127 0.193231
\(748\) 0 0
\(749\) −34.5875 −1.26380
\(750\) 0 0
\(751\) 40.5750 1.48060 0.740301 0.672275i \(-0.234683\pi\)
0.740301 + 0.672275i \(0.234683\pi\)
\(752\) 0 0
\(753\) −0.659108 −0.0240192
\(754\) 0 0
\(755\) −8.69689 −0.316512
\(756\) 0 0
\(757\) 46.5174 1.69070 0.845352 0.534210i \(-0.179391\pi\)
0.845352 + 0.534210i \(0.179391\pi\)
\(758\) 0 0
\(759\) 2.16095 0.0784376
\(760\) 0 0
\(761\) −36.6586 −1.32887 −0.664436 0.747345i \(-0.731328\pi\)
−0.664436 + 0.747345i \(0.731328\pi\)
\(762\) 0 0
\(763\) −13.0508 −0.472471
\(764\) 0 0
\(765\) 39.8817 1.44193
\(766\) 0 0
\(767\) −52.1100 −1.88158
\(768\) 0 0
\(769\) 13.5212 0.487588 0.243794 0.969827i \(-0.421608\pi\)
0.243794 + 0.969827i \(0.421608\pi\)
\(770\) 0 0
\(771\) −7.40120 −0.266548
\(772\) 0 0
\(773\) 27.5500 0.990906 0.495453 0.868635i \(-0.335002\pi\)
0.495453 + 0.868635i \(0.335002\pi\)
\(774\) 0 0
\(775\) −1.64861 −0.0592198
\(776\) 0 0
\(777\) 13.3424 0.478655
\(778\) 0 0
\(779\) −0.982363 −0.0351968
\(780\) 0 0
\(781\) −1.22168 −0.0437151
\(782\) 0 0
\(783\) 4.43354 0.158442
\(784\) 0 0
\(785\) 5.52115 0.197058
\(786\) 0 0
\(787\) −37.7891 −1.34704 −0.673518 0.739171i \(-0.735218\pi\)
−0.673518 + 0.739171i \(0.735218\pi\)
\(788\) 0 0
\(789\) −11.9143 −0.424161
\(790\) 0 0
\(791\) −19.1394 −0.680518
\(792\) 0 0
\(793\) −21.7284 −0.771598
\(794\) 0 0
\(795\) −3.16735 −0.112334
\(796\) 0 0
\(797\) 3.43431 0.121649 0.0608247 0.998148i \(-0.480627\pi\)
0.0608247 + 0.998148i \(0.480627\pi\)
\(798\) 0 0
\(799\) 15.0519 0.532499
\(800\) 0 0
\(801\) −9.91735 −0.350412
\(802\) 0 0
\(803\) 1.97476 0.0696877
\(804\) 0 0
\(805\) −43.9723 −1.54982
\(806\) 0 0
\(807\) −1.05383 −0.0370967
\(808\) 0 0
\(809\) 14.2673 0.501612 0.250806 0.968037i \(-0.419304\pi\)
0.250806 + 0.968037i \(0.419304\pi\)
\(810\) 0 0
\(811\) 6.73142 0.236372 0.118186 0.992991i \(-0.462292\pi\)
0.118186 + 0.992991i \(0.462292\pi\)
\(812\) 0 0
\(813\) −15.1338 −0.530766
\(814\) 0 0
\(815\) 42.0285 1.47219
\(816\) 0 0
\(817\) −10.0121 −0.350279
\(818\) 0 0
\(819\) −21.7628 −0.760453
\(820\) 0 0
\(821\) −2.86039 −0.0998282 −0.0499141 0.998754i \(-0.515895\pi\)
−0.0499141 + 0.998754i \(0.515895\pi\)
\(822\) 0 0
\(823\) −9.96452 −0.347341 −0.173671 0.984804i \(-0.555563\pi\)
−0.173671 + 0.984804i \(0.555563\pi\)
\(824\) 0 0
\(825\) −0.283858 −0.00988266
\(826\) 0 0
\(827\) −5.15974 −0.179422 −0.0897109 0.995968i \(-0.528594\pi\)
−0.0897109 + 0.995968i \(0.528594\pi\)
\(828\) 0 0
\(829\) 19.1798 0.666141 0.333070 0.942902i \(-0.391915\pi\)
0.333070 + 0.942902i \(0.391915\pi\)
\(830\) 0 0
\(831\) 3.24202 0.112464
\(832\) 0 0
\(833\) 9.00337 0.311948
\(834\) 0 0
\(835\) 11.9466 0.413428
\(836\) 0 0
\(837\) −5.61126 −0.193954
\(838\) 0 0
\(839\) −10.3056 −0.355790 −0.177895 0.984049i \(-0.556929\pi\)
−0.177895 + 0.984049i \(0.556929\pi\)
\(840\) 0 0
\(841\) −27.3081 −0.941660
\(842\) 0 0
\(843\) 5.05423 0.174077
\(844\) 0 0
\(845\) −1.67808 −0.0577276
\(846\) 0 0
\(847\) −25.3818 −0.872129
\(848\) 0 0
\(849\) 4.62871 0.158857
\(850\) 0 0
\(851\) 71.4112 2.44794
\(852\) 0 0
\(853\) 0.0629119 0.00215406 0.00107703 0.999999i \(-0.499657\pi\)
0.00107703 + 0.999999i \(0.499657\pi\)
\(854\) 0 0
\(855\) −6.45269 −0.220677
\(856\) 0 0
\(857\) 12.4923 0.426730 0.213365 0.976973i \(-0.431558\pi\)
0.213365 + 0.976973i \(0.431558\pi\)
\(858\) 0 0
\(859\) 23.2530 0.793383 0.396692 0.917952i \(-0.370158\pi\)
0.396692 + 0.917952i \(0.370158\pi\)
\(860\) 0 0
\(861\) 1.39929 0.0476875
\(862\) 0 0
\(863\) 18.0492 0.614402 0.307201 0.951645i \(-0.400608\pi\)
0.307201 + 0.951645i \(0.400608\pi\)
\(864\) 0 0
\(865\) 1.28428 0.0436669
\(866\) 0 0
\(867\) −12.8260 −0.435595
\(868\) 0 0
\(869\) −0.468519 −0.0158934
\(870\) 0 0
\(871\) 32.5223 1.10198
\(872\) 0 0
\(873\) 11.7421 0.397411
\(874\) 0 0
\(875\) −23.0630 −0.779671
\(876\) 0 0
\(877\) −34.3261 −1.15911 −0.579555 0.814933i \(-0.696774\pi\)
−0.579555 + 0.814933i \(0.696774\pi\)
\(878\) 0 0
\(879\) 0.0285456 0.000962818 0
\(880\) 0 0
\(881\) 28.3318 0.954522 0.477261 0.878762i \(-0.341630\pi\)
0.477261 + 0.878762i \(0.341630\pi\)
\(882\) 0 0
\(883\) −13.8750 −0.466931 −0.233466 0.972365i \(-0.575007\pi\)
−0.233466 + 0.972365i \(0.575007\pi\)
\(884\) 0 0
\(885\) 22.0081 0.739793
\(886\) 0 0
\(887\) 14.7425 0.495005 0.247502 0.968887i \(-0.420390\pi\)
0.247502 + 0.968887i \(0.420390\pi\)
\(888\) 0 0
\(889\) 6.23014 0.208952
\(890\) 0 0
\(891\) 2.73606 0.0916615
\(892\) 0 0
\(893\) −2.43534 −0.0814955
\(894\) 0 0
\(895\) 15.1707 0.507102
\(896\) 0 0
\(897\) 16.1859 0.540430
\(898\) 0 0
\(899\) −2.14130 −0.0714165
\(900\) 0 0
\(901\) −13.2084 −0.440037
\(902\) 0 0
\(903\) 14.2613 0.474587
\(904\) 0 0
\(905\) 9.75082 0.324128
\(906\) 0 0
\(907\) 3.40751 0.113144 0.0565722 0.998399i \(-0.481983\pi\)
0.0565722 + 0.998399i \(0.481983\pi\)
\(908\) 0 0
\(909\) 12.6892 0.420875
\(910\) 0 0
\(911\) −16.4500 −0.545014 −0.272507 0.962154i \(-0.587853\pi\)
−0.272507 + 0.962154i \(0.587853\pi\)
\(912\) 0 0
\(913\) −0.939403 −0.0310897
\(914\) 0 0
\(915\) 9.17674 0.303374
\(916\) 0 0
\(917\) −6.78567 −0.224083
\(918\) 0 0
\(919\) −6.53585 −0.215598 −0.107799 0.994173i \(-0.534380\pi\)
−0.107799 + 0.994173i \(0.534380\pi\)
\(920\) 0 0
\(921\) 15.0004 0.494280
\(922\) 0 0
\(923\) −9.15057 −0.301195
\(924\) 0 0
\(925\) −9.38041 −0.308426
\(926\) 0 0
\(927\) −36.3267 −1.19313
\(928\) 0 0
\(929\) 37.2527 1.22222 0.611111 0.791545i \(-0.290723\pi\)
0.611111 + 0.791545i \(0.290723\pi\)
\(930\) 0 0
\(931\) −1.45671 −0.0477416
\(932\) 0 0
\(933\) 12.9565 0.424177
\(934\) 0 0
\(935\) −7.09394 −0.231997
\(936\) 0 0
\(937\) 20.7557 0.678061 0.339030 0.940775i \(-0.389901\pi\)
0.339030 + 0.940775i \(0.389901\pi\)
\(938\) 0 0
\(939\) 9.78609 0.319357
\(940\) 0 0
\(941\) −44.0633 −1.43642 −0.718211 0.695825i \(-0.755039\pi\)
−0.718211 + 0.695825i \(0.755039\pi\)
\(942\) 0 0
\(943\) 7.48927 0.243884
\(944\) 0 0
\(945\) 19.6597 0.639532
\(946\) 0 0
\(947\) −13.0438 −0.423867 −0.211933 0.977284i \(-0.567976\pi\)
−0.211933 + 0.977284i \(0.567976\pi\)
\(948\) 0 0
\(949\) 14.7912 0.480144
\(950\) 0 0
\(951\) 12.2703 0.397892
\(952\) 0 0
\(953\) 9.95984 0.322631 0.161315 0.986903i \(-0.448426\pi\)
0.161315 + 0.986903i \(0.448426\pi\)
\(954\) 0 0
\(955\) −25.7067 −0.831848
\(956\) 0 0
\(957\) −0.368690 −0.0119181
\(958\) 0 0
\(959\) 28.8695 0.932245
\(960\) 0 0
\(961\) −28.2899 −0.912577
\(962\) 0 0
\(963\) 38.6944 1.24691
\(964\) 0 0
\(965\) 26.6181 0.856866
\(966\) 0 0
\(967\) 41.6459 1.33924 0.669620 0.742704i \(-0.266457\pi\)
0.669620 + 0.742704i \(0.266457\pi\)
\(968\) 0 0
\(969\) 3.73925 0.120122
\(970\) 0 0
\(971\) −25.5000 −0.818335 −0.409167 0.912459i \(-0.634181\pi\)
−0.409167 + 0.912459i \(0.634181\pi\)
\(972\) 0 0
\(973\) 28.2292 0.904985
\(974\) 0 0
\(975\) −2.12614 −0.0680909
\(976\) 0 0
\(977\) −56.5702 −1.80984 −0.904920 0.425581i \(-0.860070\pi\)
−0.904920 + 0.425581i \(0.860070\pi\)
\(978\) 0 0
\(979\) 1.76404 0.0563791
\(980\) 0 0
\(981\) 14.6005 0.466157
\(982\) 0 0
\(983\) 2.46370 0.0785798 0.0392899 0.999228i \(-0.487490\pi\)
0.0392899 + 0.999228i \(0.487490\pi\)
\(984\) 0 0
\(985\) −26.0875 −0.831216
\(986\) 0 0
\(987\) 3.46892 0.110417
\(988\) 0 0
\(989\) 76.3296 2.42714
\(990\) 0 0
\(991\) 10.4126 0.330767 0.165383 0.986229i \(-0.447114\pi\)
0.165383 + 0.986229i \(0.447114\pi\)
\(992\) 0 0
\(993\) −6.04807 −0.191930
\(994\) 0 0
\(995\) 54.2349 1.71936
\(996\) 0 0
\(997\) 34.3528 1.08797 0.543983 0.839096i \(-0.316916\pi\)
0.543983 + 0.839096i \(0.316916\pi\)
\(998\) 0 0
\(999\) −31.9275 −1.01014
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 \(a_p\))