Properties

Label 6004.2.a.g.1.14
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 1.14
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.338332 q^{3} +0.413944 q^{5} -1.61145 q^{7} -2.88553 q^{9} +O(q^{10})\) \(q-0.338332 q^{3} +0.413944 q^{5} -1.61145 q^{7} -2.88553 q^{9} +1.62423 q^{11} +1.42248 q^{13} -0.140051 q^{15} +0.598456 q^{17} +1.00000 q^{19} +0.545204 q^{21} -0.815594 q^{23} -4.82865 q^{25} +1.99126 q^{27} +7.29709 q^{29} -4.96239 q^{31} -0.549530 q^{33} -0.667050 q^{35} +5.22799 q^{37} -0.481270 q^{39} +2.10875 q^{41} -5.53106 q^{43} -1.19445 q^{45} +5.12276 q^{47} -4.40324 q^{49} -0.202477 q^{51} -5.32257 q^{53} +0.672341 q^{55} -0.338332 q^{57} +11.5040 q^{59} -12.2460 q^{61} +4.64988 q^{63} +0.588827 q^{65} -4.41080 q^{67} +0.275942 q^{69} +13.9441 q^{71} -6.82902 q^{73} +1.63369 q^{75} -2.61736 q^{77} -1.00000 q^{79} +7.98289 q^{81} -11.3773 q^{83} +0.247727 q^{85} -2.46884 q^{87} +0.614336 q^{89} -2.29225 q^{91} +1.67893 q^{93} +0.413944 q^{95} -2.40472 q^{97} -4.68677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −0.338332 −0.195336 −0.0976680 0.995219i \(-0.531138\pi\)
−0.0976680 + 0.995219i \(0.531138\pi\)
\(4\) 0 0
\(5\) 0.413944 0.185122 0.0925608 0.995707i \(-0.470495\pi\)
0.0925608 + 0.995707i \(0.470495\pi\)
\(6\) 0 0
\(7\) −1.61145 −0.609070 −0.304535 0.952501i \(-0.598501\pi\)
−0.304535 + 0.952501i \(0.598501\pi\)
\(8\) 0 0
\(9\) −2.88553 −0.961844
\(10\) 0 0
\(11\) 1.62423 0.489724 0.244862 0.969558i \(-0.421257\pi\)
0.244862 + 0.969558i \(0.421257\pi\)
\(12\) 0 0
\(13\) 1.42248 0.394525 0.197262 0.980351i \(-0.436795\pi\)
0.197262 + 0.980351i \(0.436795\pi\)
\(14\) 0 0
\(15\) −0.140051 −0.0361609
\(16\) 0 0
\(17\) 0.598456 0.145147 0.0725734 0.997363i \(-0.476879\pi\)
0.0725734 + 0.997363i \(0.476879\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0.545204 0.118973
\(22\) 0 0
\(23\) −0.815594 −0.170063 −0.0850315 0.996378i \(-0.527099\pi\)
−0.0850315 + 0.996378i \(0.527099\pi\)
\(24\) 0 0
\(25\) −4.82865 −0.965730
\(26\) 0 0
\(27\) 1.99126 0.383219
\(28\) 0 0
\(29\) 7.29709 1.35504 0.677518 0.735506i \(-0.263056\pi\)
0.677518 + 0.735506i \(0.263056\pi\)
\(30\) 0 0
\(31\) −4.96239 −0.891271 −0.445635 0.895215i \(-0.647022\pi\)
−0.445635 + 0.895215i \(0.647022\pi\)
\(32\) 0 0
\(33\) −0.549530 −0.0956608
\(34\) 0 0
\(35\) −0.667050 −0.112752
\(36\) 0 0
\(37\) 5.22799 0.859476 0.429738 0.902954i \(-0.358606\pi\)
0.429738 + 0.902954i \(0.358606\pi\)
\(38\) 0 0
\(39\) −0.481270 −0.0770649
\(40\) 0 0
\(41\) 2.10875 0.329332 0.164666 0.986349i \(-0.447345\pi\)
0.164666 + 0.986349i \(0.447345\pi\)
\(42\) 0 0
\(43\) −5.53106 −0.843478 −0.421739 0.906717i \(-0.638580\pi\)
−0.421739 + 0.906717i \(0.638580\pi\)
\(44\) 0 0
\(45\) −1.19445 −0.178058
\(46\) 0 0
\(47\) 5.12276 0.747231 0.373616 0.927584i \(-0.378118\pi\)
0.373616 + 0.927584i \(0.378118\pi\)
\(48\) 0 0
\(49\) −4.40324 −0.629034
\(50\) 0 0
\(51\) −0.202477 −0.0283524
\(52\) 0 0
\(53\) −5.32257 −0.731111 −0.365556 0.930790i \(-0.619121\pi\)
−0.365556 + 0.930790i \(0.619121\pi\)
\(54\) 0 0
\(55\) 0.672341 0.0906585
\(56\) 0 0
\(57\) −0.338332 −0.0448132
\(58\) 0 0
\(59\) 11.5040 1.49769 0.748846 0.662744i \(-0.230608\pi\)
0.748846 + 0.662744i \(0.230608\pi\)
\(60\) 0 0
\(61\) −12.2460 −1.56794 −0.783968 0.620802i \(-0.786807\pi\)
−0.783968 + 0.620802i \(0.786807\pi\)
\(62\) 0 0
\(63\) 4.64988 0.585830
\(64\) 0 0
\(65\) 0.588827 0.0730350
\(66\) 0 0
\(67\) −4.41080 −0.538865 −0.269433 0.963019i \(-0.586836\pi\)
−0.269433 + 0.963019i \(0.586836\pi\)
\(68\) 0 0
\(69\) 0.275942 0.0332195
\(70\) 0 0
\(71\) 13.9441 1.65487 0.827433 0.561565i \(-0.189801\pi\)
0.827433 + 0.561565i \(0.189801\pi\)
\(72\) 0 0
\(73\) −6.82902 −0.799276 −0.399638 0.916673i \(-0.630864\pi\)
−0.399638 + 0.916673i \(0.630864\pi\)
\(74\) 0 0
\(75\) 1.63369 0.188642
\(76\) 0 0
\(77\) −2.61736 −0.298276
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 7.98289 0.886987
\(82\) 0 0
\(83\) −11.3773 −1.24882 −0.624410 0.781097i \(-0.714661\pi\)
−0.624410 + 0.781097i \(0.714661\pi\)
\(84\) 0 0
\(85\) 0.247727 0.0268698
\(86\) 0 0
\(87\) −2.46884 −0.264687
\(88\) 0 0
\(89\) 0.614336 0.0651195 0.0325597 0.999470i \(-0.489634\pi\)
0.0325597 + 0.999470i \(0.489634\pi\)
\(90\) 0 0
\(91\) −2.29225 −0.240293
\(92\) 0 0
\(93\) 1.67893 0.174097
\(94\) 0 0
\(95\) 0.413944 0.0424698
\(96\) 0 0
\(97\) −2.40472 −0.244163 −0.122081 0.992520i \(-0.538957\pi\)
−0.122081 + 0.992520i \(0.538957\pi\)
\(98\) 0 0
\(99\) −4.68677 −0.471038
\(100\) 0 0
\(101\) −12.5520 −1.24897 −0.624484 0.781037i \(-0.714691\pi\)
−0.624484 + 0.781037i \(0.714691\pi\)
\(102\) 0 0
\(103\) 10.1972 1.00476 0.502381 0.864646i \(-0.332457\pi\)
0.502381 + 0.864646i \(0.332457\pi\)
\(104\) 0 0
\(105\) 0.225684 0.0220245
\(106\) 0 0
\(107\) 0.0950657 0.00919035 0.00459518 0.999989i \(-0.498537\pi\)
0.00459518 + 0.999989i \(0.498537\pi\)
\(108\) 0 0
\(109\) 1.49100 0.142811 0.0714057 0.997447i \(-0.477251\pi\)
0.0714057 + 0.997447i \(0.477251\pi\)
\(110\) 0 0
\(111\) −1.76880 −0.167887
\(112\) 0 0
\(113\) 2.10963 0.198457 0.0992285 0.995065i \(-0.468363\pi\)
0.0992285 + 0.995065i \(0.468363\pi\)
\(114\) 0 0
\(115\) −0.337610 −0.0314823
\(116\) 0 0
\(117\) −4.10461 −0.379471
\(118\) 0 0
\(119\) −0.964381 −0.0884046
\(120\) 0 0
\(121\) −8.36187 −0.760170
\(122\) 0 0
\(123\) −0.713459 −0.0643304
\(124\) 0 0
\(125\) −4.06851 −0.363899
\(126\) 0 0
\(127\) −8.22200 −0.729585 −0.364792 0.931089i \(-0.618860\pi\)
−0.364792 + 0.931089i \(0.618860\pi\)
\(128\) 0 0
\(129\) 1.87133 0.164762
\(130\) 0 0
\(131\) −15.0824 −1.31776 −0.658879 0.752249i \(-0.728969\pi\)
−0.658879 + 0.752249i \(0.728969\pi\)
\(132\) 0 0
\(133\) −1.61145 −0.139730
\(134\) 0 0
\(135\) 0.824272 0.0709421
\(136\) 0 0
\(137\) 9.71607 0.830100 0.415050 0.909799i \(-0.363764\pi\)
0.415050 + 0.909799i \(0.363764\pi\)
\(138\) 0 0
\(139\) −4.01186 −0.340281 −0.170141 0.985420i \(-0.554422\pi\)
−0.170141 + 0.985420i \(0.554422\pi\)
\(140\) 0 0
\(141\) −1.73319 −0.145961
\(142\) 0 0
\(143\) 2.31044 0.193208
\(144\) 0 0
\(145\) 3.02059 0.250846
\(146\) 0 0
\(147\) 1.48976 0.122873
\(148\) 0 0
\(149\) −14.7351 −1.20715 −0.603573 0.797308i \(-0.706257\pi\)
−0.603573 + 0.797308i \(0.706257\pi\)
\(150\) 0 0
\(151\) −14.2681 −1.16112 −0.580561 0.814217i \(-0.697167\pi\)
−0.580561 + 0.814217i \(0.697167\pi\)
\(152\) 0 0
\(153\) −1.72686 −0.139609
\(154\) 0 0
\(155\) −2.05415 −0.164993
\(156\) 0 0
\(157\) 20.7206 1.65368 0.826841 0.562436i \(-0.190136\pi\)
0.826841 + 0.562436i \(0.190136\pi\)
\(158\) 0 0
\(159\) 1.80080 0.142812
\(160\) 0 0
\(161\) 1.31429 0.103580
\(162\) 0 0
\(163\) −1.21351 −0.0950497 −0.0475248 0.998870i \(-0.515133\pi\)
−0.0475248 + 0.998870i \(0.515133\pi\)
\(164\) 0 0
\(165\) −0.227475 −0.0177089
\(166\) 0 0
\(167\) 10.8525 0.839789 0.419895 0.907573i \(-0.362067\pi\)
0.419895 + 0.907573i \(0.362067\pi\)
\(168\) 0 0
\(169\) −10.9766 −0.844350
\(170\) 0 0
\(171\) −2.88553 −0.220662
\(172\) 0 0
\(173\) −15.4950 −1.17806 −0.589031 0.808110i \(-0.700490\pi\)
−0.589031 + 0.808110i \(0.700490\pi\)
\(174\) 0 0
\(175\) 7.78112 0.588197
\(176\) 0 0
\(177\) −3.89217 −0.292553
\(178\) 0 0
\(179\) −9.59731 −0.717336 −0.358668 0.933465i \(-0.616769\pi\)
−0.358668 + 0.933465i \(0.616769\pi\)
\(180\) 0 0
\(181\) 12.6940 0.943538 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(182\) 0 0
\(183\) 4.14320 0.306274
\(184\) 0 0
\(185\) 2.16409 0.159107
\(186\) 0 0
\(187\) 0.972031 0.0710819
\(188\) 0 0
\(189\) −3.20882 −0.233407
\(190\) 0 0
\(191\) −15.1508 −1.09628 −0.548138 0.836388i \(-0.684663\pi\)
−0.548138 + 0.836388i \(0.684663\pi\)
\(192\) 0 0
\(193\) −16.2264 −1.16800 −0.584001 0.811753i \(-0.698514\pi\)
−0.584001 + 0.811753i \(0.698514\pi\)
\(194\) 0 0
\(195\) −0.199219 −0.0142664
\(196\) 0 0
\(197\) −12.6227 −0.899332 −0.449666 0.893197i \(-0.648457\pi\)
−0.449666 + 0.893197i \(0.648457\pi\)
\(198\) 0 0
\(199\) −13.8752 −0.983589 −0.491794 0.870711i \(-0.663659\pi\)
−0.491794 + 0.870711i \(0.663659\pi\)
\(200\) 0 0
\(201\) 1.49232 0.105260
\(202\) 0 0
\(203\) −11.7589 −0.825312
\(204\) 0 0
\(205\) 0.872906 0.0609664
\(206\) 0 0
\(207\) 2.35342 0.163574
\(208\) 0 0
\(209\) 1.62423 0.112350
\(210\) 0 0
\(211\) −8.91556 −0.613772 −0.306886 0.951746i \(-0.599287\pi\)
−0.306886 + 0.951746i \(0.599287\pi\)
\(212\) 0 0
\(213\) −4.71775 −0.323255
\(214\) 0 0
\(215\) −2.28955 −0.156146
\(216\) 0 0
\(217\) 7.99663 0.542846
\(218\) 0 0
\(219\) 2.31047 0.156127
\(220\) 0 0
\(221\) 0.851291 0.0572641
\(222\) 0 0
\(223\) −0.639245 −0.0428070 −0.0214035 0.999771i \(-0.506813\pi\)
−0.0214035 + 0.999771i \(0.506813\pi\)
\(224\) 0 0
\(225\) 13.9332 0.928881
\(226\) 0 0
\(227\) −6.83330 −0.453542 −0.226771 0.973948i \(-0.572817\pi\)
−0.226771 + 0.973948i \(0.572817\pi\)
\(228\) 0 0
\(229\) −8.01872 −0.529892 −0.264946 0.964263i \(-0.585354\pi\)
−0.264946 + 0.964263i \(0.585354\pi\)
\(230\) 0 0
\(231\) 0.885538 0.0582641
\(232\) 0 0
\(233\) 23.0368 1.50919 0.754594 0.656192i \(-0.227834\pi\)
0.754594 + 0.656192i \(0.227834\pi\)
\(234\) 0 0
\(235\) 2.12054 0.138329
\(236\) 0 0
\(237\) 0.338332 0.0219770
\(238\) 0 0
\(239\) 10.2334 0.661941 0.330971 0.943641i \(-0.392624\pi\)
0.330971 + 0.943641i \(0.392624\pi\)
\(240\) 0 0
\(241\) 13.6100 0.876699 0.438349 0.898805i \(-0.355563\pi\)
0.438349 + 0.898805i \(0.355563\pi\)
\(242\) 0 0
\(243\) −8.67466 −0.556480
\(244\) 0 0
\(245\) −1.82269 −0.116448
\(246\) 0 0
\(247\) 1.42248 0.0905102
\(248\) 0 0
\(249\) 3.84930 0.243940
\(250\) 0 0
\(251\) −21.9818 −1.38748 −0.693738 0.720227i \(-0.744037\pi\)
−0.693738 + 0.720227i \(0.744037\pi\)
\(252\) 0 0
\(253\) −1.32471 −0.0832840
\(254\) 0 0
\(255\) −0.0838141 −0.00524864
\(256\) 0 0
\(257\) −30.9121 −1.92825 −0.964123 0.265457i \(-0.914477\pi\)
−0.964123 + 0.265457i \(0.914477\pi\)
\(258\) 0 0
\(259\) −8.42463 −0.523481
\(260\) 0 0
\(261\) −21.0560 −1.30333
\(262\) 0 0
\(263\) 3.15646 0.194636 0.0973179 0.995253i \(-0.468974\pi\)
0.0973179 + 0.995253i \(0.468974\pi\)
\(264\) 0 0
\(265\) −2.20325 −0.135344
\(266\) 0 0
\(267\) −0.207849 −0.0127202
\(268\) 0 0
\(269\) −21.8955 −1.33499 −0.667497 0.744613i \(-0.732634\pi\)
−0.667497 + 0.744613i \(0.732634\pi\)
\(270\) 0 0
\(271\) −7.39092 −0.448966 −0.224483 0.974478i \(-0.572069\pi\)
−0.224483 + 0.974478i \(0.572069\pi\)
\(272\) 0 0
\(273\) 0.775542 0.0469380
\(274\) 0 0
\(275\) −7.84285 −0.472941
\(276\) 0 0
\(277\) −25.4178 −1.52721 −0.763605 0.645684i \(-0.776572\pi\)
−0.763605 + 0.645684i \(0.776572\pi\)
\(278\) 0 0
\(279\) 14.3191 0.857263
\(280\) 0 0
\(281\) −10.3840 −0.619457 −0.309729 0.950825i \(-0.600238\pi\)
−0.309729 + 0.950825i \(0.600238\pi\)
\(282\) 0 0
\(283\) 16.9184 1.00570 0.502849 0.864375i \(-0.332285\pi\)
0.502849 + 0.864375i \(0.332285\pi\)
\(284\) 0 0
\(285\) −0.140051 −0.00829588
\(286\) 0 0
\(287\) −3.39815 −0.200586
\(288\) 0 0
\(289\) −16.6419 −0.978932
\(290\) 0 0
\(291\) 0.813595 0.0476938
\(292\) 0 0
\(293\) −6.66743 −0.389515 −0.194758 0.980851i \(-0.562392\pi\)
−0.194758 + 0.980851i \(0.562392\pi\)
\(294\) 0 0
\(295\) 4.76201 0.277255
\(296\) 0 0
\(297\) 3.23427 0.187672
\(298\) 0 0
\(299\) −1.16017 −0.0670941
\(300\) 0 0
\(301\) 8.91301 0.513737
\(302\) 0 0
\(303\) 4.24674 0.243969
\(304\) 0 0
\(305\) −5.06915 −0.290259
\(306\) 0 0
\(307\) 13.4905 0.769945 0.384973 0.922928i \(-0.374211\pi\)
0.384973 + 0.922928i \(0.374211\pi\)
\(308\) 0 0
\(309\) −3.45005 −0.196266
\(310\) 0 0
\(311\) 27.7482 1.57346 0.786728 0.617300i \(-0.211773\pi\)
0.786728 + 0.617300i \(0.211773\pi\)
\(312\) 0 0
\(313\) 30.8571 1.74415 0.872074 0.489375i \(-0.162775\pi\)
0.872074 + 0.489375i \(0.162775\pi\)
\(314\) 0 0
\(315\) 1.92479 0.108450
\(316\) 0 0
\(317\) 22.6357 1.27135 0.635674 0.771957i \(-0.280722\pi\)
0.635674 + 0.771957i \(0.280722\pi\)
\(318\) 0 0
\(319\) 11.8522 0.663594
\(320\) 0 0
\(321\) −0.0321638 −0.00179521
\(322\) 0 0
\(323\) 0.598456 0.0332990
\(324\) 0 0
\(325\) −6.86866 −0.381004
\(326\) 0 0
\(327\) −0.504452 −0.0278962
\(328\) 0 0
\(329\) −8.25506 −0.455116
\(330\) 0 0
\(331\) 10.4160 0.572514 0.286257 0.958153i \(-0.407589\pi\)
0.286257 + 0.958153i \(0.407589\pi\)
\(332\) 0 0
\(333\) −15.0855 −0.826681
\(334\) 0 0
\(335\) −1.82583 −0.0997555
\(336\) 0 0
\(337\) −24.6952 −1.34523 −0.672615 0.739992i \(-0.734829\pi\)
−0.672615 + 0.739992i \(0.734829\pi\)
\(338\) 0 0
\(339\) −0.713754 −0.0387658
\(340\) 0 0
\(341\) −8.06006 −0.436477
\(342\) 0 0
\(343\) 18.3757 0.992196
\(344\) 0 0
\(345\) 0.114224 0.00614964
\(346\) 0 0
\(347\) −22.6736 −1.21718 −0.608590 0.793485i \(-0.708265\pi\)
−0.608590 + 0.793485i \(0.708265\pi\)
\(348\) 0 0
\(349\) 0.284829 0.0152466 0.00762328 0.999971i \(-0.497573\pi\)
0.00762328 + 0.999971i \(0.497573\pi\)
\(350\) 0 0
\(351\) 2.83253 0.151189
\(352\) 0 0
\(353\) −11.6885 −0.622115 −0.311057 0.950391i \(-0.600683\pi\)
−0.311057 + 0.950391i \(0.600683\pi\)
\(354\) 0 0
\(355\) 5.77210 0.306351
\(356\) 0 0
\(357\) 0.326281 0.0172686
\(358\) 0 0
\(359\) 13.3124 0.702604 0.351302 0.936262i \(-0.385739\pi\)
0.351302 + 0.936262i \(0.385739\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 2.82909 0.148489
\(364\) 0 0
\(365\) −2.82683 −0.147963
\(366\) 0 0
\(367\) −23.7394 −1.23919 −0.619594 0.784922i \(-0.712703\pi\)
−0.619594 + 0.784922i \(0.712703\pi\)
\(368\) 0 0
\(369\) −6.08487 −0.316766
\(370\) 0 0
\(371\) 8.57704 0.445298
\(372\) 0 0
\(373\) −21.4212 −1.10915 −0.554574 0.832134i \(-0.687119\pi\)
−0.554574 + 0.832134i \(0.687119\pi\)
\(374\) 0 0
\(375\) 1.37651 0.0710826
\(376\) 0 0
\(377\) 10.3800 0.534595
\(378\) 0 0
\(379\) 19.8946 1.02192 0.510960 0.859605i \(-0.329290\pi\)
0.510960 + 0.859605i \(0.329290\pi\)
\(380\) 0 0
\(381\) 2.78177 0.142514
\(382\) 0 0
\(383\) 25.0286 1.27890 0.639451 0.768832i \(-0.279162\pi\)
0.639451 + 0.768832i \(0.279162\pi\)
\(384\) 0 0
\(385\) −1.08344 −0.0552174
\(386\) 0 0
\(387\) 15.9600 0.811294
\(388\) 0 0
\(389\) 22.8639 1.15924 0.579622 0.814885i \(-0.303200\pi\)
0.579622 + 0.814885i \(0.303200\pi\)
\(390\) 0 0
\(391\) −0.488097 −0.0246841
\(392\) 0 0
\(393\) 5.10287 0.257406
\(394\) 0 0
\(395\) −0.413944 −0.0208278
\(396\) 0 0
\(397\) −22.0635 −1.10733 −0.553667 0.832738i \(-0.686772\pi\)
−0.553667 + 0.832738i \(0.686772\pi\)
\(398\) 0 0
\(399\) 0.545204 0.0272944
\(400\) 0 0
\(401\) −18.7571 −0.936685 −0.468342 0.883547i \(-0.655149\pi\)
−0.468342 + 0.883547i \(0.655149\pi\)
\(402\) 0 0
\(403\) −7.05889 −0.351629
\(404\) 0 0
\(405\) 3.30447 0.164200
\(406\) 0 0
\(407\) 8.49146 0.420906
\(408\) 0 0
\(409\) 28.6473 1.41652 0.708259 0.705953i \(-0.249481\pi\)
0.708259 + 0.705953i \(0.249481\pi\)
\(410\) 0 0
\(411\) −3.28726 −0.162149
\(412\) 0 0
\(413\) −18.5381 −0.912200
\(414\) 0 0
\(415\) −4.70957 −0.231184
\(416\) 0 0
\(417\) 1.35734 0.0664692
\(418\) 0 0
\(419\) 17.8953 0.874242 0.437121 0.899403i \(-0.355998\pi\)
0.437121 + 0.899403i \(0.355998\pi\)
\(420\) 0 0
\(421\) −27.9131 −1.36040 −0.680201 0.733026i \(-0.738107\pi\)
−0.680201 + 0.733026i \(0.738107\pi\)
\(422\) 0 0
\(423\) −14.7819 −0.718720
\(424\) 0 0
\(425\) −2.88973 −0.140173
\(426\) 0 0
\(427\) 19.7337 0.954983
\(428\) 0 0
\(429\) −0.781695 −0.0377406
\(430\) 0 0
\(431\) 20.2859 0.977136 0.488568 0.872526i \(-0.337519\pi\)
0.488568 + 0.872526i \(0.337519\pi\)
\(432\) 0 0
\(433\) −5.31006 −0.255185 −0.127593 0.991827i \(-0.540725\pi\)
−0.127593 + 0.991827i \(0.540725\pi\)
\(434\) 0 0
\(435\) −1.02196 −0.0489993
\(436\) 0 0
\(437\) −0.815594 −0.0390151
\(438\) 0 0
\(439\) −32.0477 −1.52955 −0.764777 0.644295i \(-0.777151\pi\)
−0.764777 + 0.644295i \(0.777151\pi\)
\(440\) 0 0
\(441\) 12.7057 0.605032
\(442\) 0 0
\(443\) −12.7242 −0.604543 −0.302271 0.953222i \(-0.597745\pi\)
−0.302271 + 0.953222i \(0.597745\pi\)
\(444\) 0 0
\(445\) 0.254301 0.0120550
\(446\) 0 0
\(447\) 4.98535 0.235799
\(448\) 0 0
\(449\) 27.6838 1.30648 0.653240 0.757151i \(-0.273409\pi\)
0.653240 + 0.757151i \(0.273409\pi\)
\(450\) 0 0
\(451\) 3.42510 0.161282
\(452\) 0 0
\(453\) 4.82736 0.226809
\(454\) 0 0
\(455\) −0.948865 −0.0444835
\(456\) 0 0
\(457\) −38.5568 −1.80361 −0.901806 0.432141i \(-0.857758\pi\)
−0.901806 + 0.432141i \(0.857758\pi\)
\(458\) 0 0
\(459\) 1.19168 0.0556230
\(460\) 0 0
\(461\) −20.1377 −0.937905 −0.468953 0.883223i \(-0.655369\pi\)
−0.468953 + 0.883223i \(0.655369\pi\)
\(462\) 0 0
\(463\) −3.29768 −0.153256 −0.0766280 0.997060i \(-0.524415\pi\)
−0.0766280 + 0.997060i \(0.524415\pi\)
\(464\) 0 0
\(465\) 0.694985 0.0322292
\(466\) 0 0
\(467\) −20.3525 −0.941803 −0.470902 0.882186i \(-0.656071\pi\)
−0.470902 + 0.882186i \(0.656071\pi\)
\(468\) 0 0
\(469\) 7.10778 0.328207
\(470\) 0 0
\(471\) −7.01043 −0.323024
\(472\) 0 0
\(473\) −8.98372 −0.413072
\(474\) 0 0
\(475\) −4.82865 −0.221554
\(476\) 0 0
\(477\) 15.3584 0.703215
\(478\) 0 0
\(479\) −2.45347 −0.112102 −0.0560509 0.998428i \(-0.517851\pi\)
−0.0560509 + 0.998428i \(0.517851\pi\)
\(480\) 0 0
\(481\) 7.43670 0.339084
\(482\) 0 0
\(483\) −0.444665 −0.0202330
\(484\) 0 0
\(485\) −0.995422 −0.0451998
\(486\) 0 0
\(487\) 33.9858 1.54004 0.770021 0.638019i \(-0.220246\pi\)
0.770021 + 0.638019i \(0.220246\pi\)
\(488\) 0 0
\(489\) 0.410570 0.0185666
\(490\) 0 0
\(491\) 29.1688 1.31637 0.658184 0.752857i \(-0.271325\pi\)
0.658184 + 0.752857i \(0.271325\pi\)
\(492\) 0 0
\(493\) 4.36699 0.196679
\(494\) 0 0
\(495\) −1.94006 −0.0871993
\(496\) 0 0
\(497\) −22.4703 −1.00793
\(498\) 0 0
\(499\) 17.0035 0.761181 0.380591 0.924744i \(-0.375721\pi\)
0.380591 + 0.924744i \(0.375721\pi\)
\(500\) 0 0
\(501\) −3.67174 −0.164041
\(502\) 0 0
\(503\) −0.648168 −0.0289004 −0.0144502 0.999896i \(-0.504600\pi\)
−0.0144502 + 0.999896i \(0.504600\pi\)
\(504\) 0 0
\(505\) −5.19582 −0.231211
\(506\) 0 0
\(507\) 3.71372 0.164932
\(508\) 0 0
\(509\) −25.1086 −1.11292 −0.556461 0.830874i \(-0.687841\pi\)
−0.556461 + 0.830874i \(0.687841\pi\)
\(510\) 0 0
\(511\) 11.0046 0.486815
\(512\) 0 0
\(513\) 1.99126 0.0879164
\(514\) 0 0
\(515\) 4.22108 0.186003
\(516\) 0 0
\(517\) 8.32055 0.365937
\(518\) 0 0
\(519\) 5.24245 0.230118
\(520\) 0 0
\(521\) −12.6135 −0.552609 −0.276305 0.961070i \(-0.589110\pi\)
−0.276305 + 0.961070i \(0.589110\pi\)
\(522\) 0 0
\(523\) 14.7001 0.642789 0.321394 0.946945i \(-0.395848\pi\)
0.321394 + 0.946945i \(0.395848\pi\)
\(524\) 0 0
\(525\) −2.63260 −0.114896
\(526\) 0 0
\(527\) −2.96977 −0.129365
\(528\) 0 0
\(529\) −22.3348 −0.971079
\(530\) 0 0
\(531\) −33.1951 −1.44055
\(532\) 0 0
\(533\) 2.99966 0.129930
\(534\) 0 0
\(535\) 0.0393519 0.00170133
\(536\) 0 0
\(537\) 3.24708 0.140122
\(538\) 0 0
\(539\) −7.15187 −0.308053
\(540\) 0 0
\(541\) −8.11654 −0.348957 −0.174479 0.984661i \(-0.555824\pi\)
−0.174479 + 0.984661i \(0.555824\pi\)
\(542\) 0 0
\(543\) −4.29479 −0.184307
\(544\) 0 0
\(545\) 0.617189 0.0264375
\(546\) 0 0
\(547\) −6.71606 −0.287158 −0.143579 0.989639i \(-0.545861\pi\)
−0.143579 + 0.989639i \(0.545861\pi\)
\(548\) 0 0
\(549\) 35.3361 1.50811
\(550\) 0 0
\(551\) 7.29709 0.310867
\(552\) 0 0
\(553\) 1.61145 0.0685257
\(554\) 0 0
\(555\) −0.732183 −0.0310794
\(556\) 0 0
\(557\) 5.80162 0.245823 0.122911 0.992418i \(-0.460777\pi\)
0.122911 + 0.992418i \(0.460777\pi\)
\(558\) 0 0
\(559\) −7.86782 −0.332773
\(560\) 0 0
\(561\) −0.328869 −0.0138849
\(562\) 0 0
\(563\) −6.42477 −0.270772 −0.135386 0.990793i \(-0.543227\pi\)
−0.135386 + 0.990793i \(0.543227\pi\)
\(564\) 0 0
\(565\) 0.873268 0.0367386
\(566\) 0 0
\(567\) −12.8640 −0.540237
\(568\) 0 0
\(569\) −15.4100 −0.646023 −0.323011 0.946395i \(-0.604695\pi\)
−0.323011 + 0.946395i \(0.604695\pi\)
\(570\) 0 0
\(571\) −23.3203 −0.975923 −0.487962 0.872865i \(-0.662259\pi\)
−0.487962 + 0.872865i \(0.662259\pi\)
\(572\) 0 0
\(573\) 5.12601 0.214142
\(574\) 0 0
\(575\) 3.93822 0.164235
\(576\) 0 0
\(577\) −10.5312 −0.438418 −0.219209 0.975678i \(-0.570348\pi\)
−0.219209 + 0.975678i \(0.570348\pi\)
\(578\) 0 0
\(579\) 5.48991 0.228153
\(580\) 0 0
\(581\) 18.3339 0.760619
\(582\) 0 0
\(583\) −8.64509 −0.358043
\(584\) 0 0
\(585\) −1.69908 −0.0702483
\(586\) 0 0
\(587\) 28.5141 1.17690 0.588451 0.808533i \(-0.299738\pi\)
0.588451 + 0.808533i \(0.299738\pi\)
\(588\) 0 0
\(589\) −4.96239 −0.204472
\(590\) 0 0
\(591\) 4.27067 0.175672
\(592\) 0 0
\(593\) −18.1479 −0.745246 −0.372623 0.927983i \(-0.621542\pi\)
−0.372623 + 0.927983i \(0.621542\pi\)
\(594\) 0 0
\(595\) −0.399200 −0.0163656
\(596\) 0 0
\(597\) 4.69443 0.192130
\(598\) 0 0
\(599\) −22.2881 −0.910665 −0.455333 0.890321i \(-0.650480\pi\)
−0.455333 + 0.890321i \(0.650480\pi\)
\(600\) 0 0
\(601\) −5.30668 −0.216464 −0.108232 0.994126i \(-0.534519\pi\)
−0.108232 + 0.994126i \(0.534519\pi\)
\(602\) 0 0
\(603\) 12.7275 0.518304
\(604\) 0 0
\(605\) −3.46135 −0.140724
\(606\) 0 0
\(607\) −29.7063 −1.20574 −0.602871 0.797838i \(-0.705977\pi\)
−0.602871 + 0.797838i \(0.705977\pi\)
\(608\) 0 0
\(609\) 3.97841 0.161213
\(610\) 0 0
\(611\) 7.28702 0.294801
\(612\) 0 0
\(613\) 20.1642 0.814426 0.407213 0.913333i \(-0.366501\pi\)
0.407213 + 0.913333i \(0.366501\pi\)
\(614\) 0 0
\(615\) −0.295332 −0.0119089
\(616\) 0 0
\(617\) −44.9895 −1.81121 −0.905605 0.424123i \(-0.860582\pi\)
−0.905605 + 0.424123i \(0.860582\pi\)
\(618\) 0 0
\(619\) −13.6631 −0.549166 −0.274583 0.961563i \(-0.588540\pi\)
−0.274583 + 0.961563i \(0.588540\pi\)
\(620\) 0 0
\(621\) −1.62406 −0.0651714
\(622\) 0 0
\(623\) −0.989970 −0.0396623
\(624\) 0 0
\(625\) 22.4591 0.898365
\(626\) 0 0
\(627\) −0.549530 −0.0219461
\(628\) 0 0
\(629\) 3.12872 0.124750
\(630\) 0 0
\(631\) −27.3683 −1.08951 −0.544756 0.838594i \(-0.683378\pi\)
−0.544756 + 0.838594i \(0.683378\pi\)
\(632\) 0 0
\(633\) 3.01642 0.119892
\(634\) 0 0
\(635\) −3.40345 −0.135062
\(636\) 0 0
\(637\) −6.26351 −0.248169
\(638\) 0 0
\(639\) −40.2363 −1.59172
\(640\) 0 0
\(641\) 47.0443 1.85814 0.929070 0.369905i \(-0.120610\pi\)
0.929070 + 0.369905i \(0.120610\pi\)
\(642\) 0 0
\(643\) 19.9980 0.788644 0.394322 0.918972i \(-0.370979\pi\)
0.394322 + 0.918972i \(0.370979\pi\)
\(644\) 0 0
\(645\) 0.774628 0.0305009
\(646\) 0 0
\(647\) −35.3485 −1.38969 −0.694847 0.719158i \(-0.744528\pi\)
−0.694847 + 0.719158i \(0.744528\pi\)
\(648\) 0 0
\(649\) 18.6852 0.733457
\(650\) 0 0
\(651\) −2.70552 −0.106038
\(652\) 0 0
\(653\) 26.1725 1.02421 0.512104 0.858923i \(-0.328866\pi\)
0.512104 + 0.858923i \(0.328866\pi\)
\(654\) 0 0
\(655\) −6.24329 −0.243945
\(656\) 0 0
\(657\) 19.7053 0.768778
\(658\) 0 0
\(659\) 32.9819 1.28479 0.642396 0.766373i \(-0.277941\pi\)
0.642396 + 0.766373i \(0.277941\pi\)
\(660\) 0 0
\(661\) −4.59821 −0.178850 −0.0894249 0.995994i \(-0.528503\pi\)
−0.0894249 + 0.995994i \(0.528503\pi\)
\(662\) 0 0
\(663\) −0.288019 −0.0111857
\(664\) 0 0
\(665\) −0.667050 −0.0258671
\(666\) 0 0
\(667\) −5.95146 −0.230442
\(668\) 0 0
\(669\) 0.216277 0.00836175
\(670\) 0 0
\(671\) −19.8903 −0.767856
\(672\) 0 0
\(673\) 21.6841 0.835861 0.417930 0.908479i \(-0.362756\pi\)
0.417930 + 0.908479i \(0.362756\pi\)
\(674\) 0 0
\(675\) −9.61512 −0.370086
\(676\) 0 0
\(677\) −37.1049 −1.42606 −0.713029 0.701135i \(-0.752677\pi\)
−0.713029 + 0.701135i \(0.752677\pi\)
\(678\) 0 0
\(679\) 3.87509 0.148712
\(680\) 0 0
\(681\) 2.31192 0.0885931
\(682\) 0 0
\(683\) −12.7002 −0.485960 −0.242980 0.970031i \(-0.578125\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(684\) 0 0
\(685\) 4.02191 0.153669
\(686\) 0 0
\(687\) 2.71299 0.103507
\(688\) 0 0
\(689\) −7.57125 −0.288442
\(690\) 0 0
\(691\) 30.1820 1.14818 0.574089 0.818793i \(-0.305356\pi\)
0.574089 + 0.818793i \(0.305356\pi\)
\(692\) 0 0
\(693\) 7.55249 0.286895
\(694\) 0 0
\(695\) −1.66069 −0.0629934
\(696\) 0 0
\(697\) 1.26200 0.0478015
\(698\) 0 0
\(699\) −7.79408 −0.294799
\(700\) 0 0
\(701\) 48.0683 1.81552 0.907758 0.419495i \(-0.137793\pi\)
0.907758 + 0.419495i \(0.137793\pi\)
\(702\) 0 0
\(703\) 5.22799 0.197177
\(704\) 0 0
\(705\) −0.717446 −0.0270206
\(706\) 0 0
\(707\) 20.2269 0.760710
\(708\) 0 0
\(709\) −14.7547 −0.554126 −0.277063 0.960852i \(-0.589361\pi\)
−0.277063 + 0.960852i \(0.589361\pi\)
\(710\) 0 0
\(711\) 2.88553 0.108216
\(712\) 0 0
\(713\) 4.04729 0.151572
\(714\) 0 0
\(715\) 0.956392 0.0357670
\(716\) 0 0
\(717\) −3.46227 −0.129301
\(718\) 0 0
\(719\) −27.8461 −1.03848 −0.519242 0.854627i \(-0.673786\pi\)
−0.519242 + 0.854627i \(0.673786\pi\)
\(720\) 0 0
\(721\) −16.4323 −0.611971
\(722\) 0 0
\(723\) −4.60471 −0.171251
\(724\) 0 0
\(725\) −35.2351 −1.30860
\(726\) 0 0
\(727\) −36.4582 −1.35216 −0.676081 0.736828i \(-0.736323\pi\)
−0.676081 + 0.736828i \(0.736323\pi\)
\(728\) 0 0
\(729\) −21.0137 −0.778287
\(730\) 0 0
\(731\) −3.31009 −0.122428
\(732\) 0 0
\(733\) −5.98155 −0.220933 −0.110467 0.993880i \(-0.535235\pi\)
−0.110467 + 0.993880i \(0.535235\pi\)
\(734\) 0 0
\(735\) 0.616676 0.0227464
\(736\) 0 0
\(737\) −7.16416 −0.263895
\(738\) 0 0
\(739\) −12.6232 −0.464351 −0.232175 0.972674i \(-0.574584\pi\)
−0.232175 + 0.972674i \(0.574584\pi\)
\(740\) 0 0
\(741\) −0.481270 −0.0176799
\(742\) 0 0
\(743\) 22.5942 0.828901 0.414450 0.910072i \(-0.363974\pi\)
0.414450 + 0.910072i \(0.363974\pi\)
\(744\) 0 0
\(745\) −6.09950 −0.223469
\(746\) 0 0
\(747\) 32.8295 1.20117
\(748\) 0 0
\(749\) −0.153193 −0.00559757
\(750\) 0 0
\(751\) 33.6398 1.22753 0.613767 0.789487i \(-0.289653\pi\)
0.613767 + 0.789487i \(0.289653\pi\)
\(752\) 0 0
\(753\) 7.43713 0.271024
\(754\) 0 0
\(755\) −5.90620 −0.214949
\(756\) 0 0
\(757\) −38.5796 −1.40220 −0.701100 0.713063i \(-0.747307\pi\)
−0.701100 + 0.713063i \(0.747307\pi\)
\(758\) 0 0
\(759\) 0.448193 0.0162684
\(760\) 0 0
\(761\) 0.701726 0.0254375 0.0127188 0.999919i \(-0.495951\pi\)
0.0127188 + 0.999919i \(0.495951\pi\)
\(762\) 0 0
\(763\) −2.40266 −0.0869822
\(764\) 0 0
\(765\) −0.714825 −0.0258446
\(766\) 0 0
\(767\) 16.3642 0.590877
\(768\) 0 0
\(769\) 0.0981808 0.00354049 0.00177024 0.999998i \(-0.499437\pi\)
0.00177024 + 0.999998i \(0.499437\pi\)
\(770\) 0 0
\(771\) 10.4586 0.376656
\(772\) 0 0
\(773\) 0.324378 0.0116671 0.00583354 0.999983i \(-0.498143\pi\)
0.00583354 + 0.999983i \(0.498143\pi\)
\(774\) 0 0
\(775\) 23.9616 0.860727
\(776\) 0 0
\(777\) 2.85032 0.102255
\(778\) 0 0
\(779\) 2.10875 0.0755539
\(780\) 0 0
\(781\) 22.6485 0.810428
\(782\) 0 0
\(783\) 14.5304 0.519275
\(784\) 0 0
\(785\) 8.57716 0.306132
\(786\) 0 0
\(787\) 20.4633 0.729438 0.364719 0.931118i \(-0.381165\pi\)
0.364719 + 0.931118i \(0.381165\pi\)
\(788\) 0 0
\(789\) −1.06793 −0.0380194
\(790\) 0 0
\(791\) −3.39955 −0.120874
\(792\) 0 0
\(793\) −17.4196 −0.618589
\(794\) 0 0
\(795\) 0.745429 0.0264376
\(796\) 0 0
\(797\) −35.0236 −1.24060 −0.620300 0.784365i \(-0.712989\pi\)
−0.620300 + 0.784365i \(0.712989\pi\)
\(798\) 0 0
\(799\) 3.06575 0.108458
\(800\) 0 0
\(801\) −1.77268 −0.0626347
\(802\) 0 0
\(803\) −11.0919 −0.391425
\(804\) 0 0
\(805\) 0.544042 0.0191749
\(806\) 0 0
\(807\) 7.40796 0.260772
\(808\) 0 0
\(809\) −31.2774 −1.09965 −0.549827 0.835278i \(-0.685306\pi\)
−0.549827 + 0.835278i \(0.685306\pi\)
\(810\) 0 0
\(811\) 27.2968 0.958521 0.479261 0.877673i \(-0.340905\pi\)
0.479261 + 0.877673i \(0.340905\pi\)
\(812\) 0 0
\(813\) 2.50058 0.0876993
\(814\) 0 0
\(815\) −0.502327 −0.0175957
\(816\) 0 0
\(817\) −5.53106 −0.193507
\(818\) 0 0
\(819\) 6.61436 0.231125
\(820\) 0 0
\(821\) −28.8166 −1.00571 −0.502854 0.864371i \(-0.667717\pi\)
−0.502854 + 0.864371i \(0.667717\pi\)
\(822\) 0 0
\(823\) 32.7428 1.14134 0.570671 0.821179i \(-0.306683\pi\)
0.570671 + 0.821179i \(0.306683\pi\)
\(824\) 0 0
\(825\) 2.65349 0.0923825
\(826\) 0 0
\(827\) −32.8914 −1.14375 −0.571873 0.820342i \(-0.693783\pi\)
−0.571873 + 0.820342i \(0.693783\pi\)
\(828\) 0 0
\(829\) −11.3646 −0.394708 −0.197354 0.980332i \(-0.563235\pi\)
−0.197354 + 0.980332i \(0.563235\pi\)
\(830\) 0 0
\(831\) 8.59967 0.298319
\(832\) 0 0
\(833\) −2.63514 −0.0913023
\(834\) 0 0
\(835\) 4.49232 0.155463
\(836\) 0 0
\(837\) −9.88142 −0.341552
\(838\) 0 0
\(839\) 26.1915 0.904230 0.452115 0.891960i \(-0.350670\pi\)
0.452115 + 0.891960i \(0.350670\pi\)
\(840\) 0 0
\(841\) 24.2475 0.836122
\(842\) 0 0
\(843\) 3.51324 0.121002
\(844\) 0 0
\(845\) −4.54368 −0.156307
\(846\) 0 0
\(847\) 13.4747 0.462997
\(848\) 0 0
\(849\) −5.72405 −0.196449
\(850\) 0 0
\(851\) −4.26391 −0.146165
\(852\) 0 0
\(853\) 42.6980 1.46195 0.730976 0.682403i \(-0.239065\pi\)
0.730976 + 0.682403i \(0.239065\pi\)
\(854\) 0 0
\(855\) −1.19445 −0.0408493
\(856\) 0 0
\(857\) −26.0061 −0.888352 −0.444176 0.895940i \(-0.646503\pi\)
−0.444176 + 0.895940i \(0.646503\pi\)
\(858\) 0 0
\(859\) −26.4047 −0.900915 −0.450458 0.892798i \(-0.648739\pi\)
−0.450458 + 0.892798i \(0.648739\pi\)
\(860\) 0 0
\(861\) 1.14970 0.0391817
\(862\) 0 0
\(863\) 49.3537 1.68002 0.840010 0.542570i \(-0.182549\pi\)
0.840010 + 0.542570i \(0.182549\pi\)
\(864\) 0 0
\(865\) −6.41406 −0.218085
\(866\) 0 0
\(867\) 5.63047 0.191221
\(868\) 0 0
\(869\) −1.62423 −0.0550983
\(870\) 0 0
\(871\) −6.27427 −0.212596
\(872\) 0 0
\(873\) 6.93891 0.234846
\(874\) 0 0
\(875\) 6.55620 0.221640
\(876\) 0 0
\(877\) 30.2291 1.02076 0.510382 0.859948i \(-0.329504\pi\)
0.510382 + 0.859948i \(0.329504\pi\)
\(878\) 0 0
\(879\) 2.25580 0.0760864
\(880\) 0 0
\(881\) −40.5269 −1.36539 −0.682693 0.730706i \(-0.739191\pi\)
−0.682693 + 0.730706i \(0.739191\pi\)
\(882\) 0 0
\(883\) 56.3441 1.89613 0.948064 0.318079i \(-0.103038\pi\)
0.948064 + 0.318079i \(0.103038\pi\)
\(884\) 0 0
\(885\) −1.61114 −0.0541579
\(886\) 0 0
\(887\) −41.9554 −1.40873 −0.704363 0.709840i \(-0.748767\pi\)
−0.704363 + 0.709840i \(0.748767\pi\)
\(888\) 0 0
\(889\) 13.2493 0.444368
\(890\) 0 0
\(891\) 12.9661 0.434379
\(892\) 0 0
\(893\) 5.12276 0.171427
\(894\) 0 0
\(895\) −3.97275 −0.132794
\(896\) 0 0
\(897\) 0.392521 0.0131059
\(898\) 0 0
\(899\) −36.2110 −1.20770
\(900\) 0 0
\(901\) −3.18532 −0.106119
\(902\) 0 0
\(903\) −3.01556 −0.100351
\(904\) 0 0
\(905\) 5.25461 0.174669
\(906\) 0 0
\(907\) 21.8127 0.724277 0.362139 0.932124i \(-0.382047\pi\)
0.362139 + 0.932124i \(0.382047\pi\)
\(908\) 0 0
\(909\) 36.2191 1.20131
\(910\) 0 0
\(911\) 32.3550 1.07197 0.535984 0.844228i \(-0.319941\pi\)
0.535984 + 0.844228i \(0.319941\pi\)
\(912\) 0 0
\(913\) −18.4794 −0.611578
\(914\) 0 0
\(915\) 1.71505 0.0566980
\(916\) 0 0
\(917\) 24.3046 0.802607
\(918\) 0 0
\(919\) 31.8658 1.05115 0.525577 0.850746i \(-0.323849\pi\)
0.525577 + 0.850746i \(0.323849\pi\)
\(920\) 0 0
\(921\) −4.56428 −0.150398
\(922\) 0 0
\(923\) 19.8353 0.652885
\(924\) 0 0
\(925\) −25.2441 −0.830021
\(926\) 0 0
\(927\) −29.4244 −0.966424
\(928\) 0 0
\(929\) 2.30025 0.0754686 0.0377343 0.999288i \(-0.487986\pi\)
0.0377343 + 0.999288i \(0.487986\pi\)
\(930\) 0 0
\(931\) −4.40324 −0.144310
\(932\) 0 0
\(933\) −9.38811 −0.307353
\(934\) 0 0
\(935\) 0.402367 0.0131588
\(936\) 0 0
\(937\) −1.41041 −0.0460761 −0.0230381 0.999735i \(-0.507334\pi\)
−0.0230381 + 0.999735i \(0.507334\pi\)
\(938\) 0 0
\(939\) −10.4399 −0.340695
\(940\) 0 0
\(941\) 21.0629 0.686632 0.343316 0.939220i \(-0.388450\pi\)
0.343316 + 0.939220i \(0.388450\pi\)
\(942\) 0 0
\(943\) −1.71989 −0.0560072
\(944\) 0 0
\(945\) −1.32827 −0.0432087
\(946\) 0 0
\(947\) 45.2127 1.46922 0.734608 0.678492i \(-0.237366\pi\)
0.734608 + 0.678492i \(0.237366\pi\)
\(948\) 0 0
\(949\) −9.71413 −0.315334
\(950\) 0 0
\(951\) −7.65839 −0.248340
\(952\) 0 0
\(953\) 3.57380 0.115767 0.0578834 0.998323i \(-0.481565\pi\)
0.0578834 + 0.998323i \(0.481565\pi\)
\(954\) 0 0
\(955\) −6.27160 −0.202944
\(956\) 0 0
\(957\) −4.00997 −0.129624
\(958\) 0 0
\(959\) −15.6569 −0.505589
\(960\) 0 0
\(961\) −6.37472 −0.205636
\(962\) 0 0
\(963\) −0.274315 −0.00883968
\(964\) 0 0
\(965\) −6.71683 −0.216222
\(966\) 0 0
\(967\) 48.5589 1.56155 0.780775 0.624813i \(-0.214825\pi\)
0.780775 + 0.624813i \(0.214825\pi\)
\(968\) 0 0
\(969\) −0.202477 −0.00650449
\(970\) 0 0
\(971\) 42.2841 1.35696 0.678481 0.734618i \(-0.262639\pi\)
0.678481 + 0.734618i \(0.262639\pi\)
\(972\) 0 0
\(973\) 6.46490 0.207255
\(974\) 0 0
\(975\) 2.32389 0.0744239
\(976\) 0 0
\(977\) −23.7753 −0.760639 −0.380320 0.924855i \(-0.624186\pi\)
−0.380320 + 0.924855i \(0.624186\pi\)
\(978\) 0 0
\(979\) 0.997823 0.0318906
\(980\) 0 0
\(981\) −4.30231 −0.137362
\(982\) 0 0
\(983\) 16.0244 0.511100 0.255550 0.966796i \(-0.417743\pi\)
0.255550 + 0.966796i \(0.417743\pi\)
\(984\) 0 0
\(985\) −5.22511 −0.166486
\(986\) 0 0
\(987\) 2.79295 0.0889006
\(988\) 0 0
\(989\) 4.51110 0.143445
\(990\) 0 0
\(991\) −50.7254 −1.61135 −0.805673 0.592360i \(-0.798196\pi\)
−0.805673 + 0.592360i \(0.798196\pi\)
\(992\) 0 0
\(993\) −3.52406 −0.111833
\(994\) 0 0
\(995\) −5.74357 −0.182083
\(996\) 0 0
\(997\) 11.6654 0.369447 0.184723 0.982791i \(-0.440861\pi\)
0.184723 + 0.982791i \(0.440861\pi\)
\(998\) 0 0
\(999\) 10.4103 0.329367
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 \(a_p\))