Properties

Label 6008.2.a.e.1.50
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.50
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.42580 q^{3} +1.19116 q^{5} -1.06018 q^{7} +8.73609 q^{9} +O(q^{10})\) \(q+3.42580 q^{3} +1.19116 q^{5} -1.06018 q^{7} +8.73609 q^{9} +0.730687 q^{11} +5.49734 q^{13} +4.08066 q^{15} +0.933752 q^{17} +5.09856 q^{19} -3.63197 q^{21} -6.73974 q^{23} -3.58115 q^{25} +19.6507 q^{27} +5.95222 q^{29} +7.12567 q^{31} +2.50318 q^{33} -1.26284 q^{35} +7.45858 q^{37} +18.8328 q^{39} -11.8661 q^{41} -12.0255 q^{43} +10.4060 q^{45} -11.0394 q^{47} -5.87601 q^{49} +3.19885 q^{51} -7.95898 q^{53} +0.870361 q^{55} +17.4666 q^{57} -8.66266 q^{59} +11.6731 q^{61} -9.26185 q^{63} +6.54818 q^{65} +0.0992160 q^{67} -23.0890 q^{69} -0.301153 q^{71} +1.95916 q^{73} -12.2683 q^{75} -0.774662 q^{77} +0.440104 q^{79} +41.1110 q^{81} -10.9971 q^{83} +1.11224 q^{85} +20.3911 q^{87} +5.62519 q^{89} -5.82818 q^{91} +24.4111 q^{93} +6.07317 q^{95} +2.36384 q^{97} +6.38334 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.42580 1.97789 0.988943 0.148299i \(-0.0473798\pi\)
0.988943 + 0.148299i \(0.0473798\pi\)
\(4\) 0 0
\(5\) 1.19116 0.532701 0.266350 0.963876i \(-0.414182\pi\)
0.266350 + 0.963876i \(0.414182\pi\)
\(6\) 0 0
\(7\) −1.06018 −0.400712 −0.200356 0.979723i \(-0.564210\pi\)
−0.200356 + 0.979723i \(0.564210\pi\)
\(8\) 0 0
\(9\) 8.73609 2.91203
\(10\) 0 0
\(11\) 0.730687 0.220310 0.110155 0.993914i \(-0.464865\pi\)
0.110155 + 0.993914i \(0.464865\pi\)
\(12\) 0 0
\(13\) 5.49734 1.52469 0.762343 0.647173i \(-0.224049\pi\)
0.762343 + 0.647173i \(0.224049\pi\)
\(14\) 0 0
\(15\) 4.08066 1.05362
\(16\) 0 0
\(17\) 0.933752 0.226468 0.113234 0.993568i \(-0.463879\pi\)
0.113234 + 0.993568i \(0.463879\pi\)
\(18\) 0 0
\(19\) 5.09856 1.16969 0.584844 0.811145i \(-0.301156\pi\)
0.584844 + 0.811145i \(0.301156\pi\)
\(20\) 0 0
\(21\) −3.63197 −0.792561
\(22\) 0 0
\(23\) −6.73974 −1.40533 −0.702666 0.711520i \(-0.748007\pi\)
−0.702666 + 0.711520i \(0.748007\pi\)
\(24\) 0 0
\(25\) −3.58115 −0.716230
\(26\) 0 0
\(27\) 19.6507 3.78177
\(28\) 0 0
\(29\) 5.95222 1.10530 0.552650 0.833413i \(-0.313617\pi\)
0.552650 + 0.833413i \(0.313617\pi\)
\(30\) 0 0
\(31\) 7.12567 1.27981 0.639904 0.768455i \(-0.278974\pi\)
0.639904 + 0.768455i \(0.278974\pi\)
\(32\) 0 0
\(33\) 2.50318 0.435749
\(34\) 0 0
\(35\) −1.26284 −0.213459
\(36\) 0 0
\(37\) 7.45858 1.22618 0.613092 0.790012i \(-0.289926\pi\)
0.613092 + 0.790012i \(0.289926\pi\)
\(38\) 0 0
\(39\) 18.8328 3.01565
\(40\) 0 0
\(41\) −11.8661 −1.85318 −0.926589 0.376076i \(-0.877273\pi\)
−0.926589 + 0.376076i \(0.877273\pi\)
\(42\) 0 0
\(43\) −12.0255 −1.83388 −0.916939 0.399028i \(-0.869348\pi\)
−0.916939 + 0.399028i \(0.869348\pi\)
\(44\) 0 0
\(45\) 10.4060 1.55124
\(46\) 0 0
\(47\) −11.0394 −1.61026 −0.805131 0.593096i \(-0.797905\pi\)
−0.805131 + 0.593096i \(0.797905\pi\)
\(48\) 0 0
\(49\) −5.87601 −0.839430
\(50\) 0 0
\(51\) 3.19885 0.447928
\(52\) 0 0
\(53\) −7.95898 −1.09325 −0.546625 0.837378i \(-0.684088\pi\)
−0.546625 + 0.837378i \(0.684088\pi\)
\(54\) 0 0
\(55\) 0.870361 0.117359
\(56\) 0 0
\(57\) 17.4666 2.31351
\(58\) 0 0
\(59\) −8.66266 −1.12778 −0.563891 0.825849i \(-0.690696\pi\)
−0.563891 + 0.825849i \(0.690696\pi\)
\(60\) 0 0
\(61\) 11.6731 1.49459 0.747297 0.664490i \(-0.231351\pi\)
0.747297 + 0.664490i \(0.231351\pi\)
\(62\) 0 0
\(63\) −9.26185 −1.16688
\(64\) 0 0
\(65\) 6.54818 0.812202
\(66\) 0 0
\(67\) 0.0992160 0.0121212 0.00606058 0.999982i \(-0.498071\pi\)
0.00606058 + 0.999982i \(0.498071\pi\)
\(68\) 0 0
\(69\) −23.0890 −2.77959
\(70\) 0 0
\(71\) −0.301153 −0.0357403 −0.0178701 0.999840i \(-0.505689\pi\)
−0.0178701 + 0.999840i \(0.505689\pi\)
\(72\) 0 0
\(73\) 1.95916 0.229302 0.114651 0.993406i \(-0.463425\pi\)
0.114651 + 0.993406i \(0.463425\pi\)
\(74\) 0 0
\(75\) −12.2683 −1.41662
\(76\) 0 0
\(77\) −0.774662 −0.0882809
\(78\) 0 0
\(79\) 0.440104 0.0495155 0.0247578 0.999693i \(-0.492119\pi\)
0.0247578 + 0.999693i \(0.492119\pi\)
\(80\) 0 0
\(81\) 41.1110 4.56789
\(82\) 0 0
\(83\) −10.9971 −1.20709 −0.603543 0.797330i \(-0.706245\pi\)
−0.603543 + 0.797330i \(0.706245\pi\)
\(84\) 0 0
\(85\) 1.11224 0.120640
\(86\) 0 0
\(87\) 20.3911 2.18616
\(88\) 0 0
\(89\) 5.62519 0.596269 0.298134 0.954524i \(-0.403636\pi\)
0.298134 + 0.954524i \(0.403636\pi\)
\(90\) 0 0
\(91\) −5.82818 −0.610959
\(92\) 0 0
\(93\) 24.4111 2.53131
\(94\) 0 0
\(95\) 6.07317 0.623094
\(96\) 0 0
\(97\) 2.36384 0.240012 0.120006 0.992773i \(-0.461709\pi\)
0.120006 + 0.992773i \(0.461709\pi\)
\(98\) 0 0
\(99\) 6.38334 0.641550
\(100\) 0 0
\(101\) 0.990036 0.0985122 0.0492561 0.998786i \(-0.484315\pi\)
0.0492561 + 0.998786i \(0.484315\pi\)
\(102\) 0 0
\(103\) −7.92463 −0.780837 −0.390419 0.920637i \(-0.627670\pi\)
−0.390419 + 0.920637i \(0.627670\pi\)
\(104\) 0 0
\(105\) −4.32624 −0.422198
\(106\) 0 0
\(107\) 2.72000 0.262952 0.131476 0.991319i \(-0.458028\pi\)
0.131476 + 0.991319i \(0.458028\pi\)
\(108\) 0 0
\(109\) 2.88417 0.276254 0.138127 0.990415i \(-0.455892\pi\)
0.138127 + 0.990415i \(0.455892\pi\)
\(110\) 0 0
\(111\) 25.5516 2.42525
\(112\) 0 0
\(113\) 3.59853 0.338521 0.169261 0.985571i \(-0.445862\pi\)
0.169261 + 0.985571i \(0.445862\pi\)
\(114\) 0 0
\(115\) −8.02807 −0.748622
\(116\) 0 0
\(117\) 48.0252 4.43993
\(118\) 0 0
\(119\) −0.989948 −0.0907484
\(120\) 0 0
\(121\) −10.4661 −0.951463
\(122\) 0 0
\(123\) −40.6510 −3.66537
\(124\) 0 0
\(125\) −10.2215 −0.914237
\(126\) 0 0
\(127\) 19.5079 1.73104 0.865522 0.500871i \(-0.166987\pi\)
0.865522 + 0.500871i \(0.166987\pi\)
\(128\) 0 0
\(129\) −41.1971 −3.62720
\(130\) 0 0
\(131\) −6.57371 −0.574348 −0.287174 0.957878i \(-0.592716\pi\)
−0.287174 + 0.957878i \(0.592716\pi\)
\(132\) 0 0
\(133\) −5.40540 −0.468708
\(134\) 0 0
\(135\) 23.4070 2.01455
\(136\) 0 0
\(137\) −7.44055 −0.635689 −0.317845 0.948143i \(-0.602959\pi\)
−0.317845 + 0.948143i \(0.602959\pi\)
\(138\) 0 0
\(139\) −9.31538 −0.790120 −0.395060 0.918655i \(-0.629276\pi\)
−0.395060 + 0.918655i \(0.629276\pi\)
\(140\) 0 0
\(141\) −37.8188 −3.18491
\(142\) 0 0
\(143\) 4.01683 0.335904
\(144\) 0 0
\(145\) 7.09002 0.588794
\(146\) 0 0
\(147\) −20.1300 −1.66030
\(148\) 0 0
\(149\) −14.8200 −1.21410 −0.607050 0.794664i \(-0.707647\pi\)
−0.607050 + 0.794664i \(0.707647\pi\)
\(150\) 0 0
\(151\) 10.0357 0.816690 0.408345 0.912828i \(-0.366106\pi\)
0.408345 + 0.912828i \(0.366106\pi\)
\(152\) 0 0
\(153\) 8.15734 0.659482
\(154\) 0 0
\(155\) 8.48778 0.681755
\(156\) 0 0
\(157\) 13.3876 1.06845 0.534223 0.845344i \(-0.320604\pi\)
0.534223 + 0.845344i \(0.320604\pi\)
\(158\) 0 0
\(159\) −27.2659 −2.16232
\(160\) 0 0
\(161\) 7.14535 0.563133
\(162\) 0 0
\(163\) −18.0020 −1.41003 −0.705014 0.709194i \(-0.749059\pi\)
−0.705014 + 0.709194i \(0.749059\pi\)
\(164\) 0 0
\(165\) 2.98168 0.232124
\(166\) 0 0
\(167\) 10.5541 0.816702 0.408351 0.912825i \(-0.366104\pi\)
0.408351 + 0.912825i \(0.366104\pi\)
\(168\) 0 0
\(169\) 17.2207 1.32467
\(170\) 0 0
\(171\) 44.5414 3.40617
\(172\) 0 0
\(173\) −7.00754 −0.532773 −0.266387 0.963866i \(-0.585830\pi\)
−0.266387 + 0.963866i \(0.585830\pi\)
\(174\) 0 0
\(175\) 3.79667 0.287002
\(176\) 0 0
\(177\) −29.6765 −2.23062
\(178\) 0 0
\(179\) 19.4480 1.45362 0.726808 0.686841i \(-0.241003\pi\)
0.726808 + 0.686841i \(0.241003\pi\)
\(180\) 0 0
\(181\) 14.0724 1.04599 0.522996 0.852335i \(-0.324814\pi\)
0.522996 + 0.852335i \(0.324814\pi\)
\(182\) 0 0
\(183\) 39.9898 2.95613
\(184\) 0 0
\(185\) 8.88433 0.653189
\(186\) 0 0
\(187\) 0.682280 0.0498933
\(188\) 0 0
\(189\) −20.8333 −1.51540
\(190\) 0 0
\(191\) −23.1982 −1.67856 −0.839280 0.543700i \(-0.817023\pi\)
−0.839280 + 0.543700i \(0.817023\pi\)
\(192\) 0 0
\(193\) 12.5544 0.903688 0.451844 0.892097i \(-0.350766\pi\)
0.451844 + 0.892097i \(0.350766\pi\)
\(194\) 0 0
\(195\) 22.4327 1.60644
\(196\) 0 0
\(197\) −8.14448 −0.580270 −0.290135 0.956986i \(-0.593700\pi\)
−0.290135 + 0.956986i \(0.593700\pi\)
\(198\) 0 0
\(199\) 1.53179 0.108586 0.0542929 0.998525i \(-0.482710\pi\)
0.0542929 + 0.998525i \(0.482710\pi\)
\(200\) 0 0
\(201\) 0.339894 0.0239743
\(202\) 0 0
\(203\) −6.31044 −0.442906
\(204\) 0 0
\(205\) −14.1344 −0.987189
\(206\) 0 0
\(207\) −58.8789 −4.09237
\(208\) 0 0
\(209\) 3.72545 0.257695
\(210\) 0 0
\(211\) −1.59340 −0.109694 −0.0548471 0.998495i \(-0.517467\pi\)
−0.0548471 + 0.998495i \(0.517467\pi\)
\(212\) 0 0
\(213\) −1.03169 −0.0706902
\(214\) 0 0
\(215\) −14.3243 −0.976908
\(216\) 0 0
\(217\) −7.55451 −0.512834
\(218\) 0 0
\(219\) 6.71167 0.453533
\(220\) 0 0
\(221\) 5.13315 0.345293
\(222\) 0 0
\(223\) 15.2605 1.02192 0.510959 0.859605i \(-0.329290\pi\)
0.510959 + 0.859605i \(0.329290\pi\)
\(224\) 0 0
\(225\) −31.2852 −2.08568
\(226\) 0 0
\(227\) 28.8322 1.91366 0.956832 0.290643i \(-0.0938692\pi\)
0.956832 + 0.290643i \(0.0938692\pi\)
\(228\) 0 0
\(229\) 16.6559 1.10065 0.550327 0.834949i \(-0.314503\pi\)
0.550327 + 0.834949i \(0.314503\pi\)
\(230\) 0 0
\(231\) −2.65383 −0.174609
\(232\) 0 0
\(233\) 4.30821 0.282240 0.141120 0.989992i \(-0.454930\pi\)
0.141120 + 0.989992i \(0.454930\pi\)
\(234\) 0 0
\(235\) −13.1496 −0.857788
\(236\) 0 0
\(237\) 1.50771 0.0979360
\(238\) 0 0
\(239\) 15.4629 1.00021 0.500105 0.865965i \(-0.333295\pi\)
0.500105 + 0.865965i \(0.333295\pi\)
\(240\) 0 0
\(241\) −9.26533 −0.596832 −0.298416 0.954436i \(-0.596458\pi\)
−0.298416 + 0.954436i \(0.596458\pi\)
\(242\) 0 0
\(243\) 81.8859 5.25298
\(244\) 0 0
\(245\) −6.99924 −0.447165
\(246\) 0 0
\(247\) 28.0285 1.78341
\(248\) 0 0
\(249\) −37.6738 −2.38748
\(250\) 0 0
\(251\) −2.87265 −0.181320 −0.0906601 0.995882i \(-0.528898\pi\)
−0.0906601 + 0.995882i \(0.528898\pi\)
\(252\) 0 0
\(253\) −4.92464 −0.309609
\(254\) 0 0
\(255\) 3.81032 0.238612
\(256\) 0 0
\(257\) 25.1631 1.56963 0.784817 0.619728i \(-0.212757\pi\)
0.784817 + 0.619728i \(0.212757\pi\)
\(258\) 0 0
\(259\) −7.90746 −0.491346
\(260\) 0 0
\(261\) 51.9991 3.21867
\(262\) 0 0
\(263\) 21.7659 1.34214 0.671072 0.741392i \(-0.265834\pi\)
0.671072 + 0.741392i \(0.265834\pi\)
\(264\) 0 0
\(265\) −9.48038 −0.582375
\(266\) 0 0
\(267\) 19.2707 1.17935
\(268\) 0 0
\(269\) 16.4541 1.00322 0.501611 0.865093i \(-0.332741\pi\)
0.501611 + 0.865093i \(0.332741\pi\)
\(270\) 0 0
\(271\) −22.7471 −1.38179 −0.690895 0.722956i \(-0.742783\pi\)
−0.690895 + 0.722956i \(0.742783\pi\)
\(272\) 0 0
\(273\) −19.9662 −1.20841
\(274\) 0 0
\(275\) −2.61670 −0.157793
\(276\) 0 0
\(277\) −11.8828 −0.713967 −0.356983 0.934111i \(-0.616195\pi\)
−0.356983 + 0.934111i \(0.616195\pi\)
\(278\) 0 0
\(279\) 62.2505 3.72684
\(280\) 0 0
\(281\) −12.3086 −0.734268 −0.367134 0.930168i \(-0.619661\pi\)
−0.367134 + 0.930168i \(0.619661\pi\)
\(282\) 0 0
\(283\) −16.2708 −0.967199 −0.483599 0.875289i \(-0.660671\pi\)
−0.483599 + 0.875289i \(0.660671\pi\)
\(284\) 0 0
\(285\) 20.8055 1.23241
\(286\) 0 0
\(287\) 12.5803 0.742590
\(288\) 0 0
\(289\) −16.1281 −0.948712
\(290\) 0 0
\(291\) 8.09804 0.474716
\(292\) 0 0
\(293\) 30.3002 1.77016 0.885079 0.465441i \(-0.154104\pi\)
0.885079 + 0.465441i \(0.154104\pi\)
\(294\) 0 0
\(295\) −10.3186 −0.600770
\(296\) 0 0
\(297\) 14.3585 0.833164
\(298\) 0 0
\(299\) −37.0506 −2.14269
\(300\) 0 0
\(301\) 12.7493 0.734856
\(302\) 0 0
\(303\) 3.39166 0.194846
\(304\) 0 0
\(305\) 13.9045 0.796171
\(306\) 0 0
\(307\) −8.56308 −0.488721 −0.244360 0.969684i \(-0.578578\pi\)
−0.244360 + 0.969684i \(0.578578\pi\)
\(308\) 0 0
\(309\) −27.1482 −1.54441
\(310\) 0 0
\(311\) 2.09759 0.118944 0.0594718 0.998230i \(-0.481058\pi\)
0.0594718 + 0.998230i \(0.481058\pi\)
\(312\) 0 0
\(313\) 25.9664 1.46771 0.733854 0.679307i \(-0.237720\pi\)
0.733854 + 0.679307i \(0.237720\pi\)
\(314\) 0 0
\(315\) −11.0323 −0.621600
\(316\) 0 0
\(317\) −26.8548 −1.50832 −0.754158 0.656693i \(-0.771955\pi\)
−0.754158 + 0.656693i \(0.771955\pi\)
\(318\) 0 0
\(319\) 4.34921 0.243509
\(320\) 0 0
\(321\) 9.31817 0.520090
\(322\) 0 0
\(323\) 4.76079 0.264897
\(324\) 0 0
\(325\) −19.6868 −1.09203
\(326\) 0 0
\(327\) 9.88059 0.546398
\(328\) 0 0
\(329\) 11.7038 0.645251
\(330\) 0 0
\(331\) −4.73548 −0.260285 −0.130143 0.991495i \(-0.541544\pi\)
−0.130143 + 0.991495i \(0.541544\pi\)
\(332\) 0 0
\(333\) 65.1588 3.57068
\(334\) 0 0
\(335\) 0.118182 0.00645695
\(336\) 0 0
\(337\) −22.8801 −1.24636 −0.623179 0.782079i \(-0.714159\pi\)
−0.623179 + 0.782079i \(0.714159\pi\)
\(338\) 0 0
\(339\) 12.3278 0.669556
\(340\) 0 0
\(341\) 5.20663 0.281955
\(342\) 0 0
\(343\) 13.6509 0.737081
\(344\) 0 0
\(345\) −27.5025 −1.48069
\(346\) 0 0
\(347\) −32.3176 −1.73490 −0.867450 0.497525i \(-0.834242\pi\)
−0.867450 + 0.497525i \(0.834242\pi\)
\(348\) 0 0
\(349\) −16.7908 −0.898792 −0.449396 0.893333i \(-0.648361\pi\)
−0.449396 + 0.893333i \(0.648361\pi\)
\(350\) 0 0
\(351\) 108.026 5.76602
\(352\) 0 0
\(353\) −15.7745 −0.839591 −0.419795 0.907619i \(-0.637898\pi\)
−0.419795 + 0.907619i \(0.637898\pi\)
\(354\) 0 0
\(355\) −0.358720 −0.0190389
\(356\) 0 0
\(357\) −3.39136 −0.179490
\(358\) 0 0
\(359\) −2.54133 −0.134126 −0.0670630 0.997749i \(-0.521363\pi\)
−0.0670630 + 0.997749i \(0.521363\pi\)
\(360\) 0 0
\(361\) 6.99527 0.368172
\(362\) 0 0
\(363\) −35.8547 −1.88189
\(364\) 0 0
\(365\) 2.33366 0.122149
\(366\) 0 0
\(367\) −1.27115 −0.0663537 −0.0331768 0.999449i \(-0.510562\pi\)
−0.0331768 + 0.999449i \(0.510562\pi\)
\(368\) 0 0
\(369\) −103.664 −5.39651
\(370\) 0 0
\(371\) 8.43797 0.438078
\(372\) 0 0
\(373\) 12.2315 0.633323 0.316661 0.948539i \(-0.397438\pi\)
0.316661 + 0.948539i \(0.397438\pi\)
\(374\) 0 0
\(375\) −35.0167 −1.80826
\(376\) 0 0
\(377\) 32.7214 1.68524
\(378\) 0 0
\(379\) 7.81196 0.401273 0.200637 0.979666i \(-0.435699\pi\)
0.200637 + 0.979666i \(0.435699\pi\)
\(380\) 0 0
\(381\) 66.8300 3.42381
\(382\) 0 0
\(383\) −7.92385 −0.404890 −0.202445 0.979294i \(-0.564889\pi\)
−0.202445 + 0.979294i \(0.564889\pi\)
\(384\) 0 0
\(385\) −0.922742 −0.0470273
\(386\) 0 0
\(387\) −105.056 −5.34031
\(388\) 0 0
\(389\) −17.3213 −0.878223 −0.439111 0.898433i \(-0.644707\pi\)
−0.439111 + 0.898433i \(0.644707\pi\)
\(390\) 0 0
\(391\) −6.29324 −0.318263
\(392\) 0 0
\(393\) −22.5202 −1.13599
\(394\) 0 0
\(395\) 0.524232 0.0263770
\(396\) 0 0
\(397\) 1.16479 0.0584594 0.0292297 0.999573i \(-0.490695\pi\)
0.0292297 + 0.999573i \(0.490695\pi\)
\(398\) 0 0
\(399\) −18.5178 −0.927050
\(400\) 0 0
\(401\) −37.1501 −1.85519 −0.927594 0.373590i \(-0.878127\pi\)
−0.927594 + 0.373590i \(0.878127\pi\)
\(402\) 0 0
\(403\) 39.1722 1.95131
\(404\) 0 0
\(405\) 48.9696 2.43332
\(406\) 0 0
\(407\) 5.44989 0.270141
\(408\) 0 0
\(409\) −6.15989 −0.304587 −0.152293 0.988335i \(-0.548666\pi\)
−0.152293 + 0.988335i \(0.548666\pi\)
\(410\) 0 0
\(411\) −25.4898 −1.25732
\(412\) 0 0
\(413\) 9.18400 0.451915
\(414\) 0 0
\(415\) −13.0992 −0.643016
\(416\) 0 0
\(417\) −31.9126 −1.56277
\(418\) 0 0
\(419\) −5.25531 −0.256739 −0.128369 0.991726i \(-0.540974\pi\)
−0.128369 + 0.991726i \(0.540974\pi\)
\(420\) 0 0
\(421\) −24.2976 −1.18419 −0.592096 0.805867i \(-0.701699\pi\)
−0.592096 + 0.805867i \(0.701699\pi\)
\(422\) 0 0
\(423\) −96.4412 −4.68913
\(424\) 0 0
\(425\) −3.34391 −0.162203
\(426\) 0 0
\(427\) −12.3757 −0.598901
\(428\) 0 0
\(429\) 13.7608 0.664380
\(430\) 0 0
\(431\) 4.09597 0.197296 0.0986481 0.995122i \(-0.468548\pi\)
0.0986481 + 0.995122i \(0.468548\pi\)
\(432\) 0 0
\(433\) 14.4549 0.694657 0.347329 0.937743i \(-0.387089\pi\)
0.347329 + 0.937743i \(0.387089\pi\)
\(434\) 0 0
\(435\) 24.2890 1.16457
\(436\) 0 0
\(437\) −34.3629 −1.64380
\(438\) 0 0
\(439\) −37.0021 −1.76602 −0.883008 0.469358i \(-0.844485\pi\)
−0.883008 + 0.469358i \(0.844485\pi\)
\(440\) 0 0
\(441\) −51.3334 −2.44445
\(442\) 0 0
\(443\) 17.9905 0.854757 0.427378 0.904073i \(-0.359437\pi\)
0.427378 + 0.904073i \(0.359437\pi\)
\(444\) 0 0
\(445\) 6.70047 0.317633
\(446\) 0 0
\(447\) −50.7702 −2.40135
\(448\) 0 0
\(449\) 25.7971 1.21744 0.608721 0.793385i \(-0.291683\pi\)
0.608721 + 0.793385i \(0.291683\pi\)
\(450\) 0 0
\(451\) −8.67042 −0.408274
\(452\) 0 0
\(453\) 34.3801 1.61532
\(454\) 0 0
\(455\) −6.94227 −0.325459
\(456\) 0 0
\(457\) −38.1478 −1.78448 −0.892239 0.451564i \(-0.850866\pi\)
−0.892239 + 0.451564i \(0.850866\pi\)
\(458\) 0 0
\(459\) 18.3489 0.856452
\(460\) 0 0
\(461\) 14.7727 0.688034 0.344017 0.938963i \(-0.388212\pi\)
0.344017 + 0.938963i \(0.388212\pi\)
\(462\) 0 0
\(463\) 40.3241 1.87402 0.937011 0.349300i \(-0.113581\pi\)
0.937011 + 0.349300i \(0.113581\pi\)
\(464\) 0 0
\(465\) 29.0774 1.34843
\(466\) 0 0
\(467\) 3.59372 0.166298 0.0831488 0.996537i \(-0.473502\pi\)
0.0831488 + 0.996537i \(0.473502\pi\)
\(468\) 0 0
\(469\) −0.105187 −0.00485709
\(470\) 0 0
\(471\) 45.8631 2.11326
\(472\) 0 0
\(473\) −8.78690 −0.404022
\(474\) 0 0
\(475\) −18.2587 −0.837766
\(476\) 0 0
\(477\) −69.5303 −3.18358
\(478\) 0 0
\(479\) −28.6332 −1.30828 −0.654142 0.756372i \(-0.726970\pi\)
−0.654142 + 0.756372i \(0.726970\pi\)
\(480\) 0 0
\(481\) 41.0023 1.86955
\(482\) 0 0
\(483\) 24.4785 1.11381
\(484\) 0 0
\(485\) 2.81570 0.127854
\(486\) 0 0
\(487\) 6.67522 0.302483 0.151241 0.988497i \(-0.451673\pi\)
0.151241 + 0.988497i \(0.451673\pi\)
\(488\) 0 0
\(489\) −61.6713 −2.78887
\(490\) 0 0
\(491\) −37.0220 −1.67078 −0.835391 0.549656i \(-0.814759\pi\)
−0.835391 + 0.549656i \(0.814759\pi\)
\(492\) 0 0
\(493\) 5.55790 0.250315
\(494\) 0 0
\(495\) 7.60355 0.341754
\(496\) 0 0
\(497\) 0.319277 0.0143215
\(498\) 0 0
\(499\) 26.7752 1.19862 0.599310 0.800517i \(-0.295441\pi\)
0.599310 + 0.800517i \(0.295441\pi\)
\(500\) 0 0
\(501\) 36.1563 1.61534
\(502\) 0 0
\(503\) −26.4446 −1.17911 −0.589554 0.807729i \(-0.700697\pi\)
−0.589554 + 0.807729i \(0.700697\pi\)
\(504\) 0 0
\(505\) 1.17929 0.0524775
\(506\) 0 0
\(507\) 58.9946 2.62004
\(508\) 0 0
\(509\) −14.1788 −0.628466 −0.314233 0.949346i \(-0.601747\pi\)
−0.314233 + 0.949346i \(0.601747\pi\)
\(510\) 0 0
\(511\) −2.07706 −0.0918839
\(512\) 0 0
\(513\) 100.190 4.42350
\(514\) 0 0
\(515\) −9.43946 −0.415952
\(516\) 0 0
\(517\) −8.06635 −0.354758
\(518\) 0 0
\(519\) −24.0064 −1.05376
\(520\) 0 0
\(521\) −20.5358 −0.899692 −0.449846 0.893106i \(-0.648521\pi\)
−0.449846 + 0.893106i \(0.648521\pi\)
\(522\) 0 0
\(523\) 19.0514 0.833060 0.416530 0.909122i \(-0.363246\pi\)
0.416530 + 0.909122i \(0.363246\pi\)
\(524\) 0 0
\(525\) 13.0066 0.567656
\(526\) 0 0
\(527\) 6.65361 0.289836
\(528\) 0 0
\(529\) 22.4240 0.974959
\(530\) 0 0
\(531\) −75.6777 −3.28413
\(532\) 0 0
\(533\) −65.2321 −2.82552
\(534\) 0 0
\(535\) 3.23994 0.140075
\(536\) 0 0
\(537\) 66.6251 2.87508
\(538\) 0 0
\(539\) −4.29352 −0.184935
\(540\) 0 0
\(541\) −22.7414 −0.977730 −0.488865 0.872359i \(-0.662589\pi\)
−0.488865 + 0.872359i \(0.662589\pi\)
\(542\) 0 0
\(543\) 48.2091 2.06885
\(544\) 0 0
\(545\) 3.43550 0.147161
\(546\) 0 0
\(547\) −29.9724 −1.28153 −0.640763 0.767739i \(-0.721382\pi\)
−0.640763 + 0.767739i \(0.721382\pi\)
\(548\) 0 0
\(549\) 101.978 4.35230
\(550\) 0 0
\(551\) 30.3477 1.29286
\(552\) 0 0
\(553\) −0.466590 −0.0198414
\(554\) 0 0
\(555\) 30.4359 1.29193
\(556\) 0 0
\(557\) 6.85807 0.290586 0.145293 0.989389i \(-0.453588\pi\)
0.145293 + 0.989389i \(0.453588\pi\)
\(558\) 0 0
\(559\) −66.1084 −2.79609
\(560\) 0 0
\(561\) 2.33735 0.0986832
\(562\) 0 0
\(563\) −32.1397 −1.35453 −0.677263 0.735741i \(-0.736834\pi\)
−0.677263 + 0.735741i \(0.736834\pi\)
\(564\) 0 0
\(565\) 4.28641 0.180331
\(566\) 0 0
\(567\) −43.5852 −1.83040
\(568\) 0 0
\(569\) 40.0343 1.67832 0.839162 0.543881i \(-0.183046\pi\)
0.839162 + 0.543881i \(0.183046\pi\)
\(570\) 0 0
\(571\) −16.8499 −0.705145 −0.352572 0.935785i \(-0.614693\pi\)
−0.352572 + 0.935785i \(0.614693\pi\)
\(572\) 0 0
\(573\) −79.4722 −3.32000
\(574\) 0 0
\(575\) 24.1360 1.00654
\(576\) 0 0
\(577\) 13.0112 0.541662 0.270831 0.962627i \(-0.412702\pi\)
0.270831 + 0.962627i \(0.412702\pi\)
\(578\) 0 0
\(579\) 43.0090 1.78739
\(580\) 0 0
\(581\) 11.6589 0.483694
\(582\) 0 0
\(583\) −5.81552 −0.240854
\(584\) 0 0
\(585\) 57.2055 2.36516
\(586\) 0 0
\(587\) 28.2923 1.16775 0.583874 0.811844i \(-0.301536\pi\)
0.583874 + 0.811844i \(0.301536\pi\)
\(588\) 0 0
\(589\) 36.3306 1.49698
\(590\) 0 0
\(591\) −27.9013 −1.14771
\(592\) 0 0
\(593\) 43.0379 1.76735 0.883677 0.468098i \(-0.155060\pi\)
0.883677 + 0.468098i \(0.155060\pi\)
\(594\) 0 0
\(595\) −1.17918 −0.0483417
\(596\) 0 0
\(597\) 5.24761 0.214770
\(598\) 0 0
\(599\) −26.1921 −1.07018 −0.535090 0.844795i \(-0.679722\pi\)
−0.535090 + 0.844795i \(0.679722\pi\)
\(600\) 0 0
\(601\) 23.2334 0.947712 0.473856 0.880602i \(-0.342862\pi\)
0.473856 + 0.880602i \(0.342862\pi\)
\(602\) 0 0
\(603\) 0.866759 0.0352972
\(604\) 0 0
\(605\) −12.4667 −0.506845
\(606\) 0 0
\(607\) 32.3906 1.31469 0.657347 0.753588i \(-0.271678\pi\)
0.657347 + 0.753588i \(0.271678\pi\)
\(608\) 0 0
\(609\) −21.6183 −0.876018
\(610\) 0 0
\(611\) −60.6873 −2.45515
\(612\) 0 0
\(613\) −23.8610 −0.963737 −0.481869 0.876243i \(-0.660042\pi\)
−0.481869 + 0.876243i \(0.660042\pi\)
\(614\) 0 0
\(615\) −48.4216 −1.95255
\(616\) 0 0
\(617\) 37.2777 1.50074 0.750371 0.661017i \(-0.229875\pi\)
0.750371 + 0.661017i \(0.229875\pi\)
\(618\) 0 0
\(619\) −22.0151 −0.884862 −0.442431 0.896802i \(-0.645884\pi\)
−0.442431 + 0.896802i \(0.645884\pi\)
\(620\) 0 0
\(621\) −132.440 −5.31465
\(622\) 0 0
\(623\) −5.96373 −0.238932
\(624\) 0 0
\(625\) 5.73038 0.229215
\(626\) 0 0
\(627\) 12.7626 0.509690
\(628\) 0 0
\(629\) 6.96447 0.277692
\(630\) 0 0
\(631\) −21.9633 −0.874347 −0.437173 0.899377i \(-0.644020\pi\)
−0.437173 + 0.899377i \(0.644020\pi\)
\(632\) 0 0
\(633\) −5.45867 −0.216963
\(634\) 0 0
\(635\) 23.2369 0.922129
\(636\) 0 0
\(637\) −32.3024 −1.27987
\(638\) 0 0
\(639\) −2.63090 −0.104077
\(640\) 0 0
\(641\) 23.0944 0.912174 0.456087 0.889935i \(-0.349251\pi\)
0.456087 + 0.889935i \(0.349251\pi\)
\(642\) 0 0
\(643\) −11.1967 −0.441554 −0.220777 0.975324i \(-0.570859\pi\)
−0.220777 + 0.975324i \(0.570859\pi\)
\(644\) 0 0
\(645\) −49.0721 −1.93221
\(646\) 0 0
\(647\) −24.8744 −0.977914 −0.488957 0.872308i \(-0.662623\pi\)
−0.488957 + 0.872308i \(0.662623\pi\)
\(648\) 0 0
\(649\) −6.32969 −0.248462
\(650\) 0 0
\(651\) −25.8802 −1.01433
\(652\) 0 0
\(653\) 19.3616 0.757678 0.378839 0.925463i \(-0.376323\pi\)
0.378839 + 0.925463i \(0.376323\pi\)
\(654\) 0 0
\(655\) −7.83031 −0.305955
\(656\) 0 0
\(657\) 17.1154 0.667734
\(658\) 0 0
\(659\) −4.91374 −0.191412 −0.0957060 0.995410i \(-0.530511\pi\)
−0.0957060 + 0.995410i \(0.530511\pi\)
\(660\) 0 0
\(661\) −18.4510 −0.717662 −0.358831 0.933402i \(-0.616825\pi\)
−0.358831 + 0.933402i \(0.616825\pi\)
\(662\) 0 0
\(663\) 17.5851 0.682950
\(664\) 0 0
\(665\) −6.43867 −0.249681
\(666\) 0 0
\(667\) −40.1164 −1.55331
\(668\) 0 0
\(669\) 52.2794 2.02124
\(670\) 0 0
\(671\) 8.52941 0.329274
\(672\) 0 0
\(673\) −3.71530 −0.143214 −0.0716072 0.997433i \(-0.522813\pi\)
−0.0716072 + 0.997433i \(0.522813\pi\)
\(674\) 0 0
\(675\) −70.3720 −2.70862
\(676\) 0 0
\(677\) −11.7177 −0.450349 −0.225174 0.974318i \(-0.572295\pi\)
−0.225174 + 0.974318i \(0.572295\pi\)
\(678\) 0 0
\(679\) −2.50610 −0.0961754
\(680\) 0 0
\(681\) 98.7734 3.78501
\(682\) 0 0
\(683\) 33.8630 1.29573 0.647867 0.761754i \(-0.275661\pi\)
0.647867 + 0.761754i \(0.275661\pi\)
\(684\) 0 0
\(685\) −8.86285 −0.338632
\(686\) 0 0
\(687\) 57.0598 2.17697
\(688\) 0 0
\(689\) −43.7532 −1.66686
\(690\) 0 0
\(691\) 39.8390 1.51555 0.757773 0.652518i \(-0.226287\pi\)
0.757773 + 0.652518i \(0.226287\pi\)
\(692\) 0 0
\(693\) −6.76751 −0.257077
\(694\) 0 0
\(695\) −11.0961 −0.420898
\(696\) 0 0
\(697\) −11.0800 −0.419686
\(698\) 0 0
\(699\) 14.7591 0.558239
\(700\) 0 0
\(701\) 36.3350 1.37235 0.686177 0.727435i \(-0.259288\pi\)
0.686177 + 0.727435i \(0.259288\pi\)
\(702\) 0 0
\(703\) 38.0280 1.43425
\(704\) 0 0
\(705\) −45.0480 −1.69661
\(706\) 0 0
\(707\) −1.04962 −0.0394750
\(708\) 0 0
\(709\) 8.77864 0.329689 0.164844 0.986320i \(-0.447288\pi\)
0.164844 + 0.986320i \(0.447288\pi\)
\(710\) 0 0
\(711\) 3.84478 0.144191
\(712\) 0 0
\(713\) −48.0251 −1.79856
\(714\) 0 0
\(715\) 4.78467 0.178936
\(716\) 0 0
\(717\) 52.9727 1.97830
\(718\) 0 0
\(719\) 10.4227 0.388702 0.194351 0.980932i \(-0.437740\pi\)
0.194351 + 0.980932i \(0.437740\pi\)
\(720\) 0 0
\(721\) 8.40156 0.312890
\(722\) 0 0
\(723\) −31.7411 −1.18047
\(724\) 0 0
\(725\) −21.3158 −0.791649
\(726\) 0 0
\(727\) −33.4171 −1.23937 −0.619686 0.784850i \(-0.712740\pi\)
−0.619686 + 0.784850i \(0.712740\pi\)
\(728\) 0 0
\(729\) 157.191 5.82190
\(730\) 0 0
\(731\) −11.2289 −0.415315
\(732\) 0 0
\(733\) −19.6742 −0.726684 −0.363342 0.931656i \(-0.618364\pi\)
−0.363342 + 0.931656i \(0.618364\pi\)
\(734\) 0 0
\(735\) −23.9780 −0.884441
\(736\) 0 0
\(737\) 0.0724958 0.00267042
\(738\) 0 0
\(739\) 25.9998 0.956420 0.478210 0.878246i \(-0.341286\pi\)
0.478210 + 0.878246i \(0.341286\pi\)
\(740\) 0 0
\(741\) 96.0199 3.52738
\(742\) 0 0
\(743\) −6.01446 −0.220649 −0.110325 0.993896i \(-0.535189\pi\)
−0.110325 + 0.993896i \(0.535189\pi\)
\(744\) 0 0
\(745\) −17.6529 −0.646752
\(746\) 0 0
\(747\) −96.0715 −3.51507
\(748\) 0 0
\(749\) −2.88370 −0.105368
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −9.84113 −0.358631
\(754\) 0 0
\(755\) 11.9540 0.435051
\(756\) 0 0
\(757\) 28.1700 1.02386 0.511928 0.859029i \(-0.328932\pi\)
0.511928 + 0.859029i \(0.328932\pi\)
\(758\) 0 0
\(759\) −16.8708 −0.612371
\(760\) 0 0
\(761\) 4.22909 0.153304 0.0766521 0.997058i \(-0.475577\pi\)
0.0766521 + 0.997058i \(0.475577\pi\)
\(762\) 0 0
\(763\) −3.05775 −0.110698
\(764\) 0 0
\(765\) 9.71666 0.351307
\(766\) 0 0
\(767\) −47.6215 −1.71951
\(768\) 0 0
\(769\) −23.3601 −0.842386 −0.421193 0.906971i \(-0.638389\pi\)
−0.421193 + 0.906971i \(0.638389\pi\)
\(770\) 0 0
\(771\) 86.2038 3.10455
\(772\) 0 0
\(773\) 15.8859 0.571375 0.285687 0.958323i \(-0.407778\pi\)
0.285687 + 0.958323i \(0.407778\pi\)
\(774\) 0 0
\(775\) −25.5181 −0.916637
\(776\) 0 0
\(777\) −27.0894 −0.971825
\(778\) 0 0
\(779\) −60.5001 −2.16764
\(780\) 0 0
\(781\) −0.220048 −0.00787395
\(782\) 0 0
\(783\) 116.965 4.18000
\(784\) 0 0
\(785\) 15.9467 0.569162
\(786\) 0 0
\(787\) −3.77666 −0.134624 −0.0673118 0.997732i \(-0.521442\pi\)
−0.0673118 + 0.997732i \(0.521442\pi\)
\(788\) 0 0
\(789\) 74.5656 2.65461
\(790\) 0 0
\(791\) −3.81510 −0.135649
\(792\) 0 0
\(793\) 64.1712 2.27879
\(794\) 0 0
\(795\) −32.4779 −1.15187
\(796\) 0 0
\(797\) −10.8272 −0.383518 −0.191759 0.981442i \(-0.561419\pi\)
−0.191759 + 0.981442i \(0.561419\pi\)
\(798\) 0 0
\(799\) −10.3081 −0.364673
\(800\) 0 0
\(801\) 49.1421 1.73635
\(802\) 0 0
\(803\) 1.43153 0.0505176
\(804\) 0 0
\(805\) 8.51122 0.299981
\(806\) 0 0
\(807\) 56.3683 1.98426
\(808\) 0 0
\(809\) −42.2346 −1.48489 −0.742444 0.669908i \(-0.766333\pi\)
−0.742444 + 0.669908i \(0.766333\pi\)
\(810\) 0 0
\(811\) −54.3277 −1.90770 −0.953852 0.300278i \(-0.902920\pi\)
−0.953852 + 0.300278i \(0.902920\pi\)
\(812\) 0 0
\(813\) −77.9270 −2.73302
\(814\) 0 0
\(815\) −21.4432 −0.751123
\(816\) 0 0
\(817\) −61.3129 −2.14507
\(818\) 0 0
\(819\) −50.9155 −1.77913
\(820\) 0 0
\(821\) 7.15332 0.249653 0.124826 0.992179i \(-0.460163\pi\)
0.124826 + 0.992179i \(0.460163\pi\)
\(822\) 0 0
\(823\) −27.2663 −0.950443 −0.475221 0.879866i \(-0.657632\pi\)
−0.475221 + 0.879866i \(0.657632\pi\)
\(824\) 0 0
\(825\) −8.96428 −0.312096
\(826\) 0 0
\(827\) −40.2047 −1.39806 −0.699028 0.715095i \(-0.746384\pi\)
−0.699028 + 0.715095i \(0.746384\pi\)
\(828\) 0 0
\(829\) −39.6423 −1.37683 −0.688417 0.725315i \(-0.741694\pi\)
−0.688417 + 0.725315i \(0.741694\pi\)
\(830\) 0 0
\(831\) −40.7080 −1.41214
\(832\) 0 0
\(833\) −5.48674 −0.190104
\(834\) 0 0
\(835\) 12.5716 0.435058
\(836\) 0 0
\(837\) 140.024 4.83995
\(838\) 0 0
\(839\) −33.5662 −1.15883 −0.579417 0.815031i \(-0.696720\pi\)
−0.579417 + 0.815031i \(0.696720\pi\)
\(840\) 0 0
\(841\) 6.42895 0.221688
\(842\) 0 0
\(843\) −42.1667 −1.45230
\(844\) 0 0
\(845\) 20.5125 0.705652
\(846\) 0 0
\(847\) 11.0960 0.381262
\(848\) 0 0
\(849\) −55.7405 −1.91301
\(850\) 0 0
\(851\) −50.2689 −1.72319
\(852\) 0 0
\(853\) −38.7464 −1.32665 −0.663325 0.748331i \(-0.730855\pi\)
−0.663325 + 0.748331i \(0.730855\pi\)
\(854\) 0 0
\(855\) 53.0558 1.81447
\(856\) 0 0
\(857\) 21.4319 0.732099 0.366049 0.930595i \(-0.380710\pi\)
0.366049 + 0.930595i \(0.380710\pi\)
\(858\) 0 0
\(859\) −24.6465 −0.840929 −0.420464 0.907309i \(-0.638133\pi\)
−0.420464 + 0.907309i \(0.638133\pi\)
\(860\) 0 0
\(861\) 43.0974 1.46876
\(862\) 0 0
\(863\) 3.84033 0.130726 0.0653632 0.997862i \(-0.479179\pi\)
0.0653632 + 0.997862i \(0.479179\pi\)
\(864\) 0 0
\(865\) −8.34706 −0.283809
\(866\) 0 0
\(867\) −55.2516 −1.87644
\(868\) 0 0
\(869\) 0.321578 0.0109088
\(870\) 0 0
\(871\) 0.545423 0.0184810
\(872\) 0 0
\(873\) 20.6507 0.698921
\(874\) 0 0
\(875\) 10.8366 0.366345
\(876\) 0 0
\(877\) 10.9204 0.368756 0.184378 0.982855i \(-0.440973\pi\)
0.184378 + 0.982855i \(0.440973\pi\)
\(878\) 0 0
\(879\) 103.802 3.50117
\(880\) 0 0
\(881\) 14.9811 0.504727 0.252364 0.967632i \(-0.418792\pi\)
0.252364 + 0.967632i \(0.418792\pi\)
\(882\) 0 0
\(883\) 8.44415 0.284168 0.142084 0.989855i \(-0.454620\pi\)
0.142084 + 0.989855i \(0.454620\pi\)
\(884\) 0 0
\(885\) −35.3493 −1.18825
\(886\) 0 0
\(887\) −2.76937 −0.0929864 −0.0464932 0.998919i \(-0.514805\pi\)
−0.0464932 + 0.998919i \(0.514805\pi\)
\(888\) 0 0
\(889\) −20.6819 −0.693649
\(890\) 0 0
\(891\) 30.0392 1.00635
\(892\) 0 0
\(893\) −56.2850 −1.88351
\(894\) 0 0
\(895\) 23.1656 0.774342
\(896\) 0 0
\(897\) −126.928 −4.23800
\(898\) 0 0
\(899\) 42.4136 1.41457
\(900\) 0 0
\(901\) −7.43172 −0.247586
\(902\) 0 0
\(903\) 43.6764 1.45346
\(904\) 0 0
\(905\) 16.7624 0.557201
\(906\) 0 0
\(907\) 3.53360 0.117331 0.0586657 0.998278i \(-0.481315\pi\)
0.0586657 + 0.998278i \(0.481315\pi\)
\(908\) 0 0
\(909\) 8.64904 0.286871
\(910\) 0 0
\(911\) 36.2467 1.20091 0.600454 0.799659i \(-0.294987\pi\)
0.600454 + 0.799659i \(0.294987\pi\)
\(912\) 0 0
\(913\) −8.03542 −0.265934
\(914\) 0 0
\(915\) 47.6341 1.57473
\(916\) 0 0
\(917\) 6.96934 0.230148
\(918\) 0 0
\(919\) 0.698427 0.0230390 0.0115195 0.999934i \(-0.496333\pi\)
0.0115195 + 0.999934i \(0.496333\pi\)
\(920\) 0 0
\(921\) −29.3354 −0.966633
\(922\) 0 0
\(923\) −1.65554 −0.0544927
\(924\) 0 0
\(925\) −26.7103 −0.878229
\(926\) 0 0
\(927\) −69.2303 −2.27382
\(928\) 0 0
\(929\) 37.2289 1.22144 0.610720 0.791846i \(-0.290880\pi\)
0.610720 + 0.791846i \(0.290880\pi\)
\(930\) 0 0
\(931\) −29.9592 −0.981872
\(932\) 0 0
\(933\) 7.18593 0.235257
\(934\) 0 0
\(935\) 0.812702 0.0265782
\(936\) 0 0
\(937\) 28.1562 0.919822 0.459911 0.887965i \(-0.347881\pi\)
0.459911 + 0.887965i \(0.347881\pi\)
\(938\) 0 0
\(939\) 88.9557 2.90296
\(940\) 0 0
\(941\) −28.9329 −0.943186 −0.471593 0.881816i \(-0.656321\pi\)
−0.471593 + 0.881816i \(0.656321\pi\)
\(942\) 0 0
\(943\) 79.9746 2.60433
\(944\) 0 0
\(945\) −24.8157 −0.807255
\(946\) 0 0
\(947\) 38.6193 1.25496 0.627479 0.778633i \(-0.284087\pi\)
0.627479 + 0.778633i \(0.284087\pi\)
\(948\) 0 0
\(949\) 10.7701 0.349613
\(950\) 0 0
\(951\) −91.9991 −2.98328
\(952\) 0 0
\(953\) 40.2597 1.30414 0.652069 0.758160i \(-0.273901\pi\)
0.652069 + 0.758160i \(0.273901\pi\)
\(954\) 0 0
\(955\) −27.6326 −0.894170
\(956\) 0 0
\(957\) 14.8995 0.481633
\(958\) 0 0
\(959\) 7.88835 0.254728
\(960\) 0 0
\(961\) 19.7752 0.637909
\(962\) 0 0
\(963\) 23.7622 0.765725
\(964\) 0 0
\(965\) 14.9543 0.481395
\(966\) 0 0
\(967\) 16.6932 0.536818 0.268409 0.963305i \(-0.413502\pi\)
0.268409 + 0.963305i \(0.413502\pi\)
\(968\) 0 0
\(969\) 16.3095 0.523937
\(970\) 0 0
\(971\) −58.3243 −1.87172 −0.935858 0.352376i \(-0.885374\pi\)
−0.935858 + 0.352376i \(0.885374\pi\)
\(972\) 0 0
\(973\) 9.87601 0.316610
\(974\) 0 0
\(975\) −67.4429 −2.15990
\(976\) 0 0
\(977\) 29.0123 0.928185 0.464093 0.885787i \(-0.346381\pi\)
0.464093 + 0.885787i \(0.346381\pi\)
\(978\) 0 0
\(979\) 4.11025 0.131364
\(980\) 0 0
\(981\) 25.1964 0.804459
\(982\) 0 0
\(983\) 29.1448 0.929574 0.464787 0.885422i \(-0.346131\pi\)
0.464787 + 0.885422i \(0.346131\pi\)
\(984\) 0 0
\(985\) −9.70134 −0.309110
\(986\) 0 0
\(987\) 40.0948 1.27623
\(988\) 0 0
\(989\) 81.0490 2.57721
\(990\) 0 0
\(991\) −8.95498 −0.284464 −0.142232 0.989833i \(-0.545428\pi\)
−0.142232 + 0.989833i \(0.545428\pi\)
\(992\) 0 0
\(993\) −16.2228 −0.514814
\(994\) 0 0
\(995\) 1.82460 0.0578437
\(996\) 0 0
\(997\) −23.4520 −0.742732 −0.371366 0.928487i \(-0.621111\pi\)
−0.371366 + 0.928487i \(0.621111\pi\)
\(998\) 0 0
\(999\) 146.566 4.63715
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 \(a_p\))