Properties

Label 6040.2.a.p.1.10
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.237601\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.237601 q^{3} +1.00000 q^{5} +4.27350 q^{7} -2.94355 q^{9} +O(q^{10})\) \(q+0.237601 q^{3} +1.00000 q^{5} +4.27350 q^{7} -2.94355 q^{9} -2.02953 q^{11} -4.81969 q^{13} +0.237601 q^{15} -5.46461 q^{17} +3.56063 q^{19} +1.01539 q^{21} -0.164087 q^{23} +1.00000 q^{25} -1.41219 q^{27} -7.17670 q^{29} +8.23553 q^{31} -0.482219 q^{33} +4.27350 q^{35} +7.02949 q^{37} -1.14516 q^{39} -7.73949 q^{41} +3.47560 q^{43} -2.94355 q^{45} +7.39739 q^{47} +11.2628 q^{49} -1.29840 q^{51} -5.18979 q^{53} -2.02953 q^{55} +0.846010 q^{57} -13.8741 q^{59} -11.9562 q^{61} -12.5792 q^{63} -4.81969 q^{65} -8.08848 q^{67} -0.0389872 q^{69} -0.838605 q^{71} -4.52854 q^{73} +0.237601 q^{75} -8.67319 q^{77} +11.6713 q^{79} +8.49510 q^{81} -6.71143 q^{83} -5.46461 q^{85} -1.70519 q^{87} -7.26146 q^{89} -20.5969 q^{91} +1.95677 q^{93} +3.56063 q^{95} +3.11104 q^{97} +5.97401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 5q^{3} + 19q^{5} - 8q^{7} + 26q^{9} + O(q^{10}) \) \( 19q - 5q^{3} + 19q^{5} - 8q^{7} + 26q^{9} - 18q^{11} + 5q^{13} - 5q^{15} - 4q^{17} - 27q^{19} - 18q^{21} - 25q^{23} + 19q^{25} - 35q^{27} - 35q^{29} - 26q^{31} - 8q^{35} - 10q^{37} - 48q^{39} - 14q^{41} - 21q^{43} + 26q^{45} - 40q^{47} + 23q^{49} - 32q^{51} - 3q^{53} - 18q^{55} - 13q^{57} - 28q^{59} - 46q^{61} - 53q^{63} + 5q^{65} - 42q^{67} - 31q^{69} - 46q^{71} + 31q^{73} - 5q^{75} + 15q^{77} - 56q^{79} + 31q^{81} - 25q^{83} - 4q^{85} - 20q^{87} - 7q^{89} - 61q^{91} + 29q^{93} - 27q^{95} + 39q^{97} - 52q^{99} + O(q^{100}) \)

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
\(3\) 0.237601 0.137179 0.0685896 0.997645i \(-0.478150\pi\)
0.0685896 + 0.997645i \(0.478150\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 4.27350 1.61523 0.807615 0.589709i \(-0.200758\pi\)
0.807615 + 0.589709i \(0.200758\pi\)
\(8\) 0 0
\(9\) −2.94355 −0.981182
\(10\) 0 0
\(11\) −2.02953 −0.611926 −0.305963 0.952043i \(-0.598978\pi\)
−0.305963 + 0.952043i \(0.598978\pi\)
\(12\) 0 0
\(13\) −4.81969 −1.33674 −0.668371 0.743828i \(-0.733008\pi\)
−0.668371 + 0.743828i \(0.733008\pi\)
\(14\) 0 0
\(15\) 0.237601 0.0613484
\(16\) 0 0
\(17\) −5.46461 −1.32536 −0.662681 0.748902i \(-0.730581\pi\)
−0.662681 + 0.748902i \(0.730581\pi\)
\(18\) 0 0
\(19\) 3.56063 0.816864 0.408432 0.912789i \(-0.366076\pi\)
0.408432 + 0.912789i \(0.366076\pi\)
\(20\) 0 0
\(21\) 1.01539 0.221576
\(22\) 0 0
\(23\) −0.164087 −0.0342144 −0.0171072 0.999854i \(-0.505446\pi\)
−0.0171072 + 0.999854i \(0.505446\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.41219 −0.271777
\(28\) 0 0
\(29\) −7.17670 −1.33268 −0.666340 0.745648i \(-0.732140\pi\)
−0.666340 + 0.745648i \(0.732140\pi\)
\(30\) 0 0
\(31\) 8.23553 1.47914 0.739572 0.673077i \(-0.235028\pi\)
0.739572 + 0.673077i \(0.235028\pi\)
\(32\) 0 0
\(33\) −0.482219 −0.0839435
\(34\) 0 0
\(35\) 4.27350 0.722353
\(36\) 0 0
\(37\) 7.02949 1.15564 0.577821 0.816164i \(-0.303903\pi\)
0.577821 + 0.816164i \(0.303903\pi\)
\(38\) 0 0
\(39\) −1.14516 −0.183373
\(40\) 0 0
\(41\) −7.73949 −1.20871 −0.604353 0.796717i \(-0.706568\pi\)
−0.604353 + 0.796717i \(0.706568\pi\)
\(42\) 0 0
\(43\) 3.47560 0.530023 0.265012 0.964245i \(-0.414624\pi\)
0.265012 + 0.964245i \(0.414624\pi\)
\(44\) 0 0
\(45\) −2.94355 −0.438798
\(46\) 0 0
\(47\) 7.39739 1.07902 0.539510 0.841979i \(-0.318609\pi\)
0.539510 + 0.841979i \(0.318609\pi\)
\(48\) 0 0
\(49\) 11.2628 1.60897
\(50\) 0 0
\(51\) −1.29840 −0.181812
\(52\) 0 0
\(53\) −5.18979 −0.712872 −0.356436 0.934320i \(-0.616008\pi\)
−0.356436 + 0.934320i \(0.616008\pi\)
\(54\) 0 0
\(55\) −2.02953 −0.273662
\(56\) 0 0
\(57\) 0.846010 0.112057
\(58\) 0 0
\(59\) −13.8741 −1.80625 −0.903126 0.429377i \(-0.858733\pi\)
−0.903126 + 0.429377i \(0.858733\pi\)
\(60\) 0 0
\(61\) −11.9562 −1.53084 −0.765420 0.643531i \(-0.777469\pi\)
−0.765420 + 0.643531i \(0.777469\pi\)
\(62\) 0 0
\(63\) −12.5792 −1.58484
\(64\) 0 0
\(65\) −4.81969 −0.597809
\(66\) 0 0
\(67\) −8.08848 −0.988165 −0.494082 0.869415i \(-0.664496\pi\)
−0.494082 + 0.869415i \(0.664496\pi\)
\(68\) 0 0
\(69\) −0.0389872 −0.00469351
\(70\) 0 0
\(71\) −0.838605 −0.0995241 −0.0497621 0.998761i \(-0.515846\pi\)
−0.0497621 + 0.998761i \(0.515846\pi\)
\(72\) 0 0
\(73\) −4.52854 −0.530026 −0.265013 0.964245i \(-0.585376\pi\)
−0.265013 + 0.964245i \(0.585376\pi\)
\(74\) 0 0
\(75\) 0.237601 0.0274358
\(76\) 0 0
\(77\) −8.67319 −0.988402
\(78\) 0 0
\(79\) 11.6713 1.31312 0.656561 0.754273i \(-0.272011\pi\)
0.656561 + 0.754273i \(0.272011\pi\)
\(80\) 0 0
\(81\) 8.49510 0.943900
\(82\) 0 0
\(83\) −6.71143 −0.736675 −0.368337 0.929692i \(-0.620073\pi\)
−0.368337 + 0.929692i \(0.620073\pi\)
\(84\) 0 0
\(85\) −5.46461 −0.592720
\(86\) 0 0
\(87\) −1.70519 −0.182816
\(88\) 0 0
\(89\) −7.26146 −0.769713 −0.384856 0.922976i \(-0.625749\pi\)
−0.384856 + 0.922976i \(0.625749\pi\)
\(90\) 0 0
\(91\) −20.5969 −2.15915
\(92\) 0 0
\(93\) 1.95677 0.202908
\(94\) 0 0
\(95\) 3.56063 0.365313
\(96\) 0 0
\(97\) 3.11104 0.315878 0.157939 0.987449i \(-0.449515\pi\)
0.157939 + 0.987449i \(0.449515\pi\)
\(98\) 0 0
\(99\) 5.97401 0.600411
\(100\) 0 0
\(101\) 0.834076 0.0829937 0.0414969 0.999139i \(-0.486787\pi\)
0.0414969 + 0.999139i \(0.486787\pi\)
\(102\) 0 0
\(103\) −10.2189 −1.00690 −0.503448 0.864025i \(-0.667936\pi\)
−0.503448 + 0.864025i \(0.667936\pi\)
\(104\) 0 0
\(105\) 1.01539 0.0990918
\(106\) 0 0
\(107\) −12.3395 −1.19291 −0.596453 0.802648i \(-0.703424\pi\)
−0.596453 + 0.802648i \(0.703424\pi\)
\(108\) 0 0
\(109\) −6.18989 −0.592884 −0.296442 0.955051i \(-0.595800\pi\)
−0.296442 + 0.955051i \(0.595800\pi\)
\(110\) 0 0
\(111\) 1.67022 0.158530
\(112\) 0 0
\(113\) −19.4597 −1.83061 −0.915305 0.402761i \(-0.868050\pi\)
−0.915305 + 0.402761i \(0.868050\pi\)
\(114\) 0 0
\(115\) −0.164087 −0.0153012
\(116\) 0 0
\(117\) 14.1870 1.31159
\(118\) 0 0
\(119\) −23.3530 −2.14077
\(120\) 0 0
\(121\) −6.88101 −0.625547
\(122\) 0 0
\(123\) −1.83891 −0.165809
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −7.01836 −0.622779 −0.311389 0.950282i \(-0.600794\pi\)
−0.311389 + 0.950282i \(0.600794\pi\)
\(128\) 0 0
\(129\) 0.825806 0.0727082
\(130\) 0 0
\(131\) 2.02148 0.176618 0.0883090 0.996093i \(-0.471854\pi\)
0.0883090 + 0.996093i \(0.471854\pi\)
\(132\) 0 0
\(133\) 15.2163 1.31942
\(134\) 0 0
\(135\) −1.41219 −0.121542
\(136\) 0 0
\(137\) −5.48501 −0.468616 −0.234308 0.972162i \(-0.575282\pi\)
−0.234308 + 0.972162i \(0.575282\pi\)
\(138\) 0 0
\(139\) 21.0354 1.78420 0.892099 0.451840i \(-0.149232\pi\)
0.892099 + 0.451840i \(0.149232\pi\)
\(140\) 0 0
\(141\) 1.75763 0.148019
\(142\) 0 0
\(143\) 9.78170 0.817987
\(144\) 0 0
\(145\) −7.17670 −0.595993
\(146\) 0 0
\(147\) 2.67606 0.220717
\(148\) 0 0
\(149\) 6.61132 0.541620 0.270810 0.962633i \(-0.412708\pi\)
0.270810 + 0.962633i \(0.412708\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) 16.0853 1.30042
\(154\) 0 0
\(155\) 8.23553 0.661494
\(156\) 0 0
\(157\) 18.5833 1.48311 0.741555 0.670892i \(-0.234088\pi\)
0.741555 + 0.670892i \(0.234088\pi\)
\(158\) 0 0
\(159\) −1.23310 −0.0977912
\(160\) 0 0
\(161\) −0.701225 −0.0552642
\(162\) 0 0
\(163\) 2.12360 0.166333 0.0831666 0.996536i \(-0.473497\pi\)
0.0831666 + 0.996536i \(0.473497\pi\)
\(164\) 0 0
\(165\) −0.482219 −0.0375407
\(166\) 0 0
\(167\) −11.9362 −0.923650 −0.461825 0.886971i \(-0.652805\pi\)
−0.461825 + 0.886971i \(0.652805\pi\)
\(168\) 0 0
\(169\) 10.2294 0.786878
\(170\) 0 0
\(171\) −10.4809 −0.801492
\(172\) 0 0
\(173\) −4.81892 −0.366376 −0.183188 0.983078i \(-0.558642\pi\)
−0.183188 + 0.983078i \(0.558642\pi\)
\(174\) 0 0
\(175\) 4.27350 0.323046
\(176\) 0 0
\(177\) −3.29650 −0.247780
\(178\) 0 0
\(179\) −12.2951 −0.918975 −0.459488 0.888184i \(-0.651967\pi\)
−0.459488 + 0.888184i \(0.651967\pi\)
\(180\) 0 0
\(181\) −6.56893 −0.488264 −0.244132 0.969742i \(-0.578503\pi\)
−0.244132 + 0.969742i \(0.578503\pi\)
\(182\) 0 0
\(183\) −2.84082 −0.209999
\(184\) 0 0
\(185\) 7.02949 0.516818
\(186\) 0 0
\(187\) 11.0906 0.811023
\(188\) 0 0
\(189\) −6.03501 −0.438983
\(190\) 0 0
\(191\) 17.1704 1.24241 0.621205 0.783648i \(-0.286644\pi\)
0.621205 + 0.783648i \(0.286644\pi\)
\(192\) 0 0
\(193\) −15.9716 −1.14966 −0.574829 0.818274i \(-0.694931\pi\)
−0.574829 + 0.818274i \(0.694931\pi\)
\(194\) 0 0
\(195\) −1.14516 −0.0820070
\(196\) 0 0
\(197\) 5.95356 0.424173 0.212087 0.977251i \(-0.431974\pi\)
0.212087 + 0.977251i \(0.431974\pi\)
\(198\) 0 0
\(199\) −18.7828 −1.33148 −0.665739 0.746184i \(-0.731884\pi\)
−0.665739 + 0.746184i \(0.731884\pi\)
\(200\) 0 0
\(201\) −1.92183 −0.135556
\(202\) 0 0
\(203\) −30.6696 −2.15259
\(204\) 0 0
\(205\) −7.73949 −0.540550
\(206\) 0 0
\(207\) 0.482997 0.0335706
\(208\) 0 0
\(209\) −7.22639 −0.499860
\(210\) 0 0
\(211\) −15.9244 −1.09628 −0.548141 0.836386i \(-0.684664\pi\)
−0.548141 + 0.836386i \(0.684664\pi\)
\(212\) 0 0
\(213\) −0.199254 −0.0136526
\(214\) 0 0
\(215\) 3.47560 0.237034
\(216\) 0 0
\(217\) 35.1945 2.38916
\(218\) 0 0
\(219\) −1.07599 −0.0727085
\(220\) 0 0
\(221\) 26.3377 1.77167
\(222\) 0 0
\(223\) 7.63255 0.511113 0.255557 0.966794i \(-0.417741\pi\)
0.255557 + 0.966794i \(0.417741\pi\)
\(224\) 0 0
\(225\) −2.94355 −0.196236
\(226\) 0 0
\(227\) −10.2914 −0.683062 −0.341531 0.939871i \(-0.610945\pi\)
−0.341531 + 0.939871i \(0.610945\pi\)
\(228\) 0 0
\(229\) −14.5034 −0.958414 −0.479207 0.877702i \(-0.659076\pi\)
−0.479207 + 0.877702i \(0.659076\pi\)
\(230\) 0 0
\(231\) −2.06076 −0.135588
\(232\) 0 0
\(233\) −27.1081 −1.77591 −0.887954 0.459932i \(-0.847874\pi\)
−0.887954 + 0.459932i \(0.847874\pi\)
\(234\) 0 0
\(235\) 7.39739 0.482553
\(236\) 0 0
\(237\) 2.77311 0.180133
\(238\) 0 0
\(239\) 18.9948 1.22867 0.614335 0.789045i \(-0.289424\pi\)
0.614335 + 0.789045i \(0.289424\pi\)
\(240\) 0 0
\(241\) −7.70051 −0.496033 −0.248017 0.968756i \(-0.579779\pi\)
−0.248017 + 0.968756i \(0.579779\pi\)
\(242\) 0 0
\(243\) 6.25503 0.401260
\(244\) 0 0
\(245\) 11.2628 0.719554
\(246\) 0 0
\(247\) −17.1611 −1.09194
\(248\) 0 0
\(249\) −1.59464 −0.101056
\(250\) 0 0
\(251\) −1.17780 −0.0743422 −0.0371711 0.999309i \(-0.511835\pi\)
−0.0371711 + 0.999309i \(0.511835\pi\)
\(252\) 0 0
\(253\) 0.333019 0.0209367
\(254\) 0 0
\(255\) −1.29840 −0.0813088
\(256\) 0 0
\(257\) 20.8865 1.30286 0.651432 0.758707i \(-0.274169\pi\)
0.651432 + 0.758707i \(0.274169\pi\)
\(258\) 0 0
\(259\) 30.0405 1.86663
\(260\) 0 0
\(261\) 21.1250 1.30760
\(262\) 0 0
\(263\) 11.2224 0.692003 0.346001 0.938234i \(-0.387539\pi\)
0.346001 + 0.938234i \(0.387539\pi\)
\(264\) 0 0
\(265\) −5.18979 −0.318806
\(266\) 0 0
\(267\) −1.72533 −0.105589
\(268\) 0 0
\(269\) 12.8636 0.784307 0.392154 0.919900i \(-0.371730\pi\)
0.392154 + 0.919900i \(0.371730\pi\)
\(270\) 0 0
\(271\) 30.7540 1.86817 0.934085 0.357050i \(-0.116218\pi\)
0.934085 + 0.357050i \(0.116218\pi\)
\(272\) 0 0
\(273\) −4.89386 −0.296190
\(274\) 0 0
\(275\) −2.02953 −0.122385
\(276\) 0 0
\(277\) 0.904791 0.0543636 0.0271818 0.999631i \(-0.491347\pi\)
0.0271818 + 0.999631i \(0.491347\pi\)
\(278\) 0 0
\(279\) −24.2417 −1.45131
\(280\) 0 0
\(281\) 13.5608 0.808970 0.404485 0.914545i \(-0.367451\pi\)
0.404485 + 0.914545i \(0.367451\pi\)
\(282\) 0 0
\(283\) −3.26259 −0.193941 −0.0969705 0.995287i \(-0.530915\pi\)
−0.0969705 + 0.995287i \(0.530915\pi\)
\(284\) 0 0
\(285\) 0.846010 0.0501133
\(286\) 0 0
\(287\) −33.0747 −1.95234
\(288\) 0 0
\(289\) 12.8619 0.756584
\(290\) 0 0
\(291\) 0.739186 0.0433319
\(292\) 0 0
\(293\) 16.8087 0.981975 0.490987 0.871167i \(-0.336636\pi\)
0.490987 + 0.871167i \(0.336636\pi\)
\(294\) 0 0
\(295\) −13.8741 −0.807780
\(296\) 0 0
\(297\) 2.86609 0.166307
\(298\) 0 0
\(299\) 0.790847 0.0457359
\(300\) 0 0
\(301\) 14.8530 0.856110
\(302\) 0 0
\(303\) 0.198178 0.0113850
\(304\) 0 0
\(305\) −11.9562 −0.684613
\(306\) 0 0
\(307\) −19.9288 −1.13740 −0.568699 0.822546i \(-0.692553\pi\)
−0.568699 + 0.822546i \(0.692553\pi\)
\(308\) 0 0
\(309\) −2.42802 −0.138125
\(310\) 0 0
\(311\) 4.71747 0.267503 0.133752 0.991015i \(-0.457298\pi\)
0.133752 + 0.991015i \(0.457298\pi\)
\(312\) 0 0
\(313\) 18.7915 1.06216 0.531080 0.847322i \(-0.321786\pi\)
0.531080 + 0.847322i \(0.321786\pi\)
\(314\) 0 0
\(315\) −12.5792 −0.708760
\(316\) 0 0
\(317\) 24.1265 1.35508 0.677540 0.735486i \(-0.263046\pi\)
0.677540 + 0.735486i \(0.263046\pi\)
\(318\) 0 0
\(319\) 14.5653 0.815502
\(320\) 0 0
\(321\) −2.93189 −0.163642
\(322\) 0 0
\(323\) −19.4574 −1.08264
\(324\) 0 0
\(325\) −4.81969 −0.267348
\(326\) 0 0
\(327\) −1.47073 −0.0813313
\(328\) 0 0
\(329\) 31.6128 1.74287
\(330\) 0 0
\(331\) −23.6036 −1.29737 −0.648686 0.761056i \(-0.724681\pi\)
−0.648686 + 0.761056i \(0.724681\pi\)
\(332\) 0 0
\(333\) −20.6916 −1.13389
\(334\) 0 0
\(335\) −8.08848 −0.441921
\(336\) 0 0
\(337\) 2.47693 0.134927 0.0674634 0.997722i \(-0.478509\pi\)
0.0674634 + 0.997722i \(0.478509\pi\)
\(338\) 0 0
\(339\) −4.62364 −0.251122
\(340\) 0 0
\(341\) −16.7142 −0.905127
\(342\) 0 0
\(343\) 18.2171 0.983629
\(344\) 0 0
\(345\) −0.0389872 −0.00209900
\(346\) 0 0
\(347\) −15.0865 −0.809884 −0.404942 0.914342i \(-0.632708\pi\)
−0.404942 + 0.914342i \(0.632708\pi\)
\(348\) 0 0
\(349\) −32.7748 −1.75439 −0.877197 0.480131i \(-0.840589\pi\)
−0.877197 + 0.480131i \(0.840589\pi\)
\(350\) 0 0
\(351\) 6.80634 0.363296
\(352\) 0 0
\(353\) −12.4770 −0.664081 −0.332041 0.943265i \(-0.607737\pi\)
−0.332041 + 0.943265i \(0.607737\pi\)
\(354\) 0 0
\(355\) −0.838605 −0.0445085
\(356\) 0 0
\(357\) −5.54870 −0.293668
\(358\) 0 0
\(359\) 30.8290 1.62709 0.813546 0.581501i \(-0.197534\pi\)
0.813546 + 0.581501i \(0.197534\pi\)
\(360\) 0 0
\(361\) −6.32194 −0.332734
\(362\) 0 0
\(363\) −1.63494 −0.0858120
\(364\) 0 0
\(365\) −4.52854 −0.237035
\(366\) 0 0
\(367\) 8.44434 0.440791 0.220395 0.975411i \(-0.429265\pi\)
0.220395 + 0.975411i \(0.429265\pi\)
\(368\) 0 0
\(369\) 22.7815 1.18596
\(370\) 0 0
\(371\) −22.1786 −1.15145
\(372\) 0 0
\(373\) −30.2385 −1.56569 −0.782845 0.622217i \(-0.786232\pi\)
−0.782845 + 0.622217i \(0.786232\pi\)
\(374\) 0 0
\(375\) 0.237601 0.0122697
\(376\) 0 0
\(377\) 34.5895 1.78145
\(378\) 0 0
\(379\) −35.8112 −1.83950 −0.919748 0.392509i \(-0.871607\pi\)
−0.919748 + 0.392509i \(0.871607\pi\)
\(380\) 0 0
\(381\) −1.66757 −0.0854323
\(382\) 0 0
\(383\) −9.15450 −0.467773 −0.233887 0.972264i \(-0.575144\pi\)
−0.233887 + 0.972264i \(0.575144\pi\)
\(384\) 0 0
\(385\) −8.67319 −0.442027
\(386\) 0 0
\(387\) −10.2306 −0.520049
\(388\) 0 0
\(389\) −10.9144 −0.553382 −0.276691 0.960959i \(-0.589238\pi\)
−0.276691 + 0.960959i \(0.589238\pi\)
\(390\) 0 0
\(391\) 0.896669 0.0453465
\(392\) 0 0
\(393\) 0.480307 0.0242283
\(394\) 0 0
\(395\) 11.6713 0.587246
\(396\) 0 0
\(397\) 6.97111 0.349870 0.174935 0.984580i \(-0.444028\pi\)
0.174935 + 0.984580i \(0.444028\pi\)
\(398\) 0 0
\(399\) 3.61542 0.180997
\(400\) 0 0
\(401\) 13.2016 0.659256 0.329628 0.944111i \(-0.393077\pi\)
0.329628 + 0.944111i \(0.393077\pi\)
\(402\) 0 0
\(403\) −39.6927 −1.97723
\(404\) 0 0
\(405\) 8.49510 0.422125
\(406\) 0 0
\(407\) −14.2666 −0.707167
\(408\) 0 0
\(409\) −17.5141 −0.866018 −0.433009 0.901390i \(-0.642548\pi\)
−0.433009 + 0.901390i \(0.642548\pi\)
\(410\) 0 0
\(411\) −1.30325 −0.0642844
\(412\) 0 0
\(413\) −59.2909 −2.91751
\(414\) 0 0
\(415\) −6.71143 −0.329451
\(416\) 0 0
\(417\) 4.99803 0.244755
\(418\) 0 0
\(419\) 15.8073 0.772237 0.386119 0.922449i \(-0.373816\pi\)
0.386119 + 0.922449i \(0.373816\pi\)
\(420\) 0 0
\(421\) 17.6010 0.857819 0.428909 0.903347i \(-0.358898\pi\)
0.428909 + 0.903347i \(0.358898\pi\)
\(422\) 0 0
\(423\) −21.7746 −1.05872
\(424\) 0 0
\(425\) −5.46461 −0.265072
\(426\) 0 0
\(427\) −51.0950 −2.47266
\(428\) 0 0
\(429\) 2.32414 0.112211
\(430\) 0 0
\(431\) −3.38829 −0.163208 −0.0816041 0.996665i \(-0.526004\pi\)
−0.0816041 + 0.996665i \(0.526004\pi\)
\(432\) 0 0
\(433\) 9.89980 0.475754 0.237877 0.971295i \(-0.423548\pi\)
0.237877 + 0.971295i \(0.423548\pi\)
\(434\) 0 0
\(435\) −1.70519 −0.0817578
\(436\) 0 0
\(437\) −0.584251 −0.0279485
\(438\) 0 0
\(439\) 26.6328 1.27112 0.635558 0.772053i \(-0.280770\pi\)
0.635558 + 0.772053i \(0.280770\pi\)
\(440\) 0 0
\(441\) −33.1526 −1.57869
\(442\) 0 0
\(443\) 11.4998 0.546374 0.273187 0.961961i \(-0.411922\pi\)
0.273187 + 0.961961i \(0.411922\pi\)
\(444\) 0 0
\(445\) −7.26146 −0.344226
\(446\) 0 0
\(447\) 1.57086 0.0742990
\(448\) 0 0
\(449\) 25.0921 1.18417 0.592085 0.805876i \(-0.298305\pi\)
0.592085 + 0.805876i \(0.298305\pi\)
\(450\) 0 0
\(451\) 15.7075 0.739638
\(452\) 0 0
\(453\) 0.237601 0.0111635
\(454\) 0 0
\(455\) −20.5969 −0.965600
\(456\) 0 0
\(457\) 4.49466 0.210251 0.105126 0.994459i \(-0.466476\pi\)
0.105126 + 0.994459i \(0.466476\pi\)
\(458\) 0 0
\(459\) 7.71709 0.360203
\(460\) 0 0
\(461\) −29.1580 −1.35802 −0.679011 0.734128i \(-0.737591\pi\)
−0.679011 + 0.734128i \(0.737591\pi\)
\(462\) 0 0
\(463\) 6.97403 0.324110 0.162055 0.986782i \(-0.448188\pi\)
0.162055 + 0.986782i \(0.448188\pi\)
\(464\) 0 0
\(465\) 1.95677 0.0907432
\(466\) 0 0
\(467\) 31.6575 1.46493 0.732467 0.680802i \(-0.238369\pi\)
0.732467 + 0.680802i \(0.238369\pi\)
\(468\) 0 0
\(469\) −34.5661 −1.59611
\(470\) 0 0
\(471\) 4.41542 0.203452
\(472\) 0 0
\(473\) −7.05382 −0.324335
\(474\) 0 0
\(475\) 3.56063 0.163373
\(476\) 0 0
\(477\) 15.2764 0.699457
\(478\) 0 0
\(479\) −29.8506 −1.36391 −0.681954 0.731395i \(-0.738870\pi\)
−0.681954 + 0.731395i \(0.738870\pi\)
\(480\) 0 0
\(481\) −33.8800 −1.54479
\(482\) 0 0
\(483\) −0.166612 −0.00758110
\(484\) 0 0
\(485\) 3.11104 0.141265
\(486\) 0 0
\(487\) 17.7584 0.804709 0.402355 0.915484i \(-0.368192\pi\)
0.402355 + 0.915484i \(0.368192\pi\)
\(488\) 0 0
\(489\) 0.504570 0.0228174
\(490\) 0 0
\(491\) 3.08870 0.139391 0.0696955 0.997568i \(-0.477797\pi\)
0.0696955 + 0.997568i \(0.477797\pi\)
\(492\) 0 0
\(493\) 39.2179 1.76628
\(494\) 0 0
\(495\) 5.97401 0.268512
\(496\) 0 0
\(497\) −3.58378 −0.160754
\(498\) 0 0
\(499\) 38.0808 1.70473 0.852366 0.522945i \(-0.175167\pi\)
0.852366 + 0.522945i \(0.175167\pi\)
\(500\) 0 0
\(501\) −2.83605 −0.126706
\(502\) 0 0
\(503\) −37.5152 −1.67272 −0.836361 0.548180i \(-0.815321\pi\)
−0.836361 + 0.548180i \(0.815321\pi\)
\(504\) 0 0
\(505\) 0.834076 0.0371159
\(506\) 0 0
\(507\) 2.43052 0.107943
\(508\) 0 0
\(509\) 34.8821 1.54612 0.773061 0.634331i \(-0.218724\pi\)
0.773061 + 0.634331i \(0.218724\pi\)
\(510\) 0 0
\(511\) −19.3527 −0.856114
\(512\) 0 0
\(513\) −5.02830 −0.222005
\(514\) 0 0
\(515\) −10.2189 −0.450298
\(516\) 0 0
\(517\) −15.0132 −0.660281
\(518\) 0 0
\(519\) −1.14498 −0.0502591
\(520\) 0 0
\(521\) −44.4217 −1.94615 −0.973075 0.230490i \(-0.925967\pi\)
−0.973075 + 0.230490i \(0.925967\pi\)
\(522\) 0 0
\(523\) 23.2976 1.01873 0.509366 0.860550i \(-0.329880\pi\)
0.509366 + 0.860550i \(0.329880\pi\)
\(524\) 0 0
\(525\) 1.01539 0.0443152
\(526\) 0 0
\(527\) −45.0039 −1.96040
\(528\) 0 0
\(529\) −22.9731 −0.998829
\(530\) 0 0
\(531\) 40.8390 1.77226
\(532\) 0 0
\(533\) 37.3020 1.61573
\(534\) 0 0
\(535\) −12.3395 −0.533484
\(536\) 0 0
\(537\) −2.92132 −0.126064
\(538\) 0 0
\(539\) −22.8582 −0.984571
\(540\) 0 0
\(541\) −37.2569 −1.60180 −0.800899 0.598799i \(-0.795645\pi\)
−0.800899 + 0.598799i \(0.795645\pi\)
\(542\) 0 0
\(543\) −1.56079 −0.0669797
\(544\) 0 0
\(545\) −6.18989 −0.265146
\(546\) 0 0
\(547\) −9.59085 −0.410075 −0.205038 0.978754i \(-0.565732\pi\)
−0.205038 + 0.978754i \(0.565732\pi\)
\(548\) 0 0
\(549\) 35.1938 1.50203
\(550\) 0 0
\(551\) −25.5536 −1.08862
\(552\) 0 0
\(553\) 49.8772 2.12099
\(554\) 0 0
\(555\) 1.67022 0.0708967
\(556\) 0 0
\(557\) 18.3090 0.775777 0.387889 0.921706i \(-0.373205\pi\)
0.387889 + 0.921706i \(0.373205\pi\)
\(558\) 0 0
\(559\) −16.7513 −0.708504
\(560\) 0 0
\(561\) 2.63514 0.111256
\(562\) 0 0
\(563\) −13.2883 −0.560034 −0.280017 0.959995i \(-0.590340\pi\)
−0.280017 + 0.959995i \(0.590340\pi\)
\(564\) 0 0
\(565\) −19.4597 −0.818674
\(566\) 0 0
\(567\) 36.3038 1.52462
\(568\) 0 0
\(569\) 4.45598 0.186804 0.0934022 0.995628i \(-0.470226\pi\)
0.0934022 + 0.995628i \(0.470226\pi\)
\(570\) 0 0
\(571\) −35.1551 −1.47120 −0.735598 0.677418i \(-0.763099\pi\)
−0.735598 + 0.677418i \(0.763099\pi\)
\(572\) 0 0
\(573\) 4.07972 0.170433
\(574\) 0 0
\(575\) −0.164087 −0.00684289
\(576\) 0 0
\(577\) −25.5308 −1.06286 −0.531430 0.847102i \(-0.678345\pi\)
−0.531430 + 0.847102i \(0.678345\pi\)
\(578\) 0 0
\(579\) −3.79486 −0.157709
\(580\) 0 0
\(581\) −28.6813 −1.18990
\(582\) 0 0
\(583\) 10.5328 0.436225
\(584\) 0 0
\(585\) 14.1870 0.586559
\(586\) 0 0
\(587\) −25.1426 −1.03775 −0.518873 0.854852i \(-0.673648\pi\)
−0.518873 + 0.854852i \(0.673648\pi\)
\(588\) 0 0
\(589\) 29.3236 1.20826
\(590\) 0 0
\(591\) 1.41457 0.0581878
\(592\) 0 0
\(593\) 19.2215 0.789333 0.394667 0.918824i \(-0.370860\pi\)
0.394667 + 0.918824i \(0.370860\pi\)
\(594\) 0 0
\(595\) −23.3530 −0.957379
\(596\) 0 0
\(597\) −4.46282 −0.182651
\(598\) 0 0
\(599\) −46.5042 −1.90011 −0.950054 0.312084i \(-0.898973\pi\)
−0.950054 + 0.312084i \(0.898973\pi\)
\(600\) 0 0
\(601\) −14.9252 −0.608814 −0.304407 0.952542i \(-0.598458\pi\)
−0.304407 + 0.952542i \(0.598458\pi\)
\(602\) 0 0
\(603\) 23.8088 0.969569
\(604\) 0 0
\(605\) −6.88101 −0.279753
\(606\) 0 0
\(607\) 28.4843 1.15614 0.578070 0.815987i \(-0.303806\pi\)
0.578070 + 0.815987i \(0.303806\pi\)
\(608\) 0 0
\(609\) −7.28715 −0.295290
\(610\) 0 0
\(611\) −35.6531 −1.44237
\(612\) 0 0
\(613\) 3.66993 0.148227 0.0741135 0.997250i \(-0.476387\pi\)
0.0741135 + 0.997250i \(0.476387\pi\)
\(614\) 0 0
\(615\) −1.83891 −0.0741522
\(616\) 0 0
\(617\) −7.29051 −0.293505 −0.146752 0.989173i \(-0.546882\pi\)
−0.146752 + 0.989173i \(0.546882\pi\)
\(618\) 0 0
\(619\) 8.93223 0.359017 0.179508 0.983756i \(-0.442549\pi\)
0.179508 + 0.983756i \(0.442549\pi\)
\(620\) 0 0
\(621\) 0.231722 0.00929870
\(622\) 0 0
\(623\) −31.0318 −1.24326
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −1.71700 −0.0685704
\(628\) 0 0
\(629\) −38.4134 −1.53164
\(630\) 0 0
\(631\) 5.16658 0.205678 0.102839 0.994698i \(-0.467207\pi\)
0.102839 + 0.994698i \(0.467207\pi\)
\(632\) 0 0
\(633\) −3.78366 −0.150387
\(634\) 0 0
\(635\) −7.01836 −0.278515
\(636\) 0 0
\(637\) −54.2832 −2.15078
\(638\) 0 0
\(639\) 2.46847 0.0976513
\(640\) 0 0
\(641\) −19.5346 −0.771570 −0.385785 0.922589i \(-0.626069\pi\)
−0.385785 + 0.922589i \(0.626069\pi\)
\(642\) 0 0
\(643\) 30.9124 1.21907 0.609533 0.792761i \(-0.291357\pi\)
0.609533 + 0.792761i \(0.291357\pi\)
\(644\) 0 0
\(645\) 0.825806 0.0325161
\(646\) 0 0
\(647\) 33.2644 1.30776 0.653879 0.756599i \(-0.273140\pi\)
0.653879 + 0.756599i \(0.273140\pi\)
\(648\) 0 0
\(649\) 28.1578 1.10529
\(650\) 0 0
\(651\) 8.36227 0.327743
\(652\) 0 0
\(653\) 48.1848 1.88562 0.942808 0.333336i \(-0.108174\pi\)
0.942808 + 0.333336i \(0.108174\pi\)
\(654\) 0 0
\(655\) 2.02148 0.0789859
\(656\) 0 0
\(657\) 13.3300 0.520052
\(658\) 0 0
\(659\) 18.0500 0.703129 0.351565 0.936164i \(-0.385650\pi\)
0.351565 + 0.936164i \(0.385650\pi\)
\(660\) 0 0
\(661\) 14.7920 0.575342 0.287671 0.957729i \(-0.407119\pi\)
0.287671 + 0.957729i \(0.407119\pi\)
\(662\) 0 0
\(663\) 6.25788 0.243036
\(664\) 0 0
\(665\) 15.2163 0.590064
\(666\) 0 0
\(667\) 1.17760 0.0455969
\(668\) 0 0
\(669\) 1.81350 0.0701141
\(670\) 0 0
\(671\) 24.2655 0.936761
\(672\) 0 0
\(673\) 12.5320 0.483073 0.241537 0.970392i \(-0.422349\pi\)
0.241537 + 0.970392i \(0.422349\pi\)
\(674\) 0 0
\(675\) −1.41219 −0.0543554
\(676\) 0 0
\(677\) 13.5499 0.520765 0.260382 0.965506i \(-0.416151\pi\)
0.260382 + 0.965506i \(0.416151\pi\)
\(678\) 0 0
\(679\) 13.2950 0.510216
\(680\) 0 0
\(681\) −2.44524 −0.0937018
\(682\) 0 0
\(683\) −2.48253 −0.0949914 −0.0474957 0.998871i \(-0.515124\pi\)
−0.0474957 + 0.998871i \(0.515124\pi\)
\(684\) 0 0
\(685\) −5.48501 −0.209572
\(686\) 0 0
\(687\) −3.44604 −0.131475
\(688\) 0 0
\(689\) 25.0132 0.952926
\(690\) 0 0
\(691\) −11.2056 −0.426282 −0.213141 0.977021i \(-0.568369\pi\)
−0.213141 + 0.977021i \(0.568369\pi\)
\(692\) 0 0
\(693\) 25.5299 0.969802
\(694\) 0 0
\(695\) 21.0354 0.797917
\(696\) 0 0
\(697\) 42.2933 1.60197
\(698\) 0 0
\(699\) −6.44091 −0.243618
\(700\) 0 0
\(701\) 49.3595 1.86428 0.932141 0.362095i \(-0.117938\pi\)
0.932141 + 0.362095i \(0.117938\pi\)
\(702\) 0 0
\(703\) 25.0294 0.944001
\(704\) 0 0
\(705\) 1.75763 0.0661962
\(706\) 0 0
\(707\) 3.56442 0.134054
\(708\) 0 0
\(709\) 27.1001 1.01777 0.508883 0.860836i \(-0.330058\pi\)
0.508883 + 0.860836i \(0.330058\pi\)
\(710\) 0 0
\(711\) −34.3549 −1.28841
\(712\) 0 0
\(713\) −1.35134 −0.0506081
\(714\) 0 0
\(715\) 9.78170 0.365815
\(716\) 0 0
\(717\) 4.51319 0.168548
\(718\) 0 0
\(719\) 36.1601 1.34854 0.674272 0.738483i \(-0.264457\pi\)
0.674272 + 0.738483i \(0.264457\pi\)
\(720\) 0 0
\(721\) −43.6704 −1.62637
\(722\) 0 0
\(723\) −1.82965 −0.0680455
\(724\) 0 0
\(725\) −7.17670 −0.266536
\(726\) 0 0
\(727\) 19.4147 0.720053 0.360026 0.932942i \(-0.382768\pi\)
0.360026 + 0.932942i \(0.382768\pi\)
\(728\) 0 0
\(729\) −23.9991 −0.888855
\(730\) 0 0
\(731\) −18.9928 −0.702473
\(732\) 0 0
\(733\) 19.2990 0.712825 0.356413 0.934329i \(-0.384000\pi\)
0.356413 + 0.934329i \(0.384000\pi\)
\(734\) 0 0
\(735\) 2.67606 0.0987078
\(736\) 0 0
\(737\) 16.4158 0.604683
\(738\) 0 0
\(739\) 35.2703 1.29744 0.648720 0.761027i \(-0.275305\pi\)
0.648720 + 0.761027i \(0.275305\pi\)
\(740\) 0 0
\(741\) −4.07750 −0.149791
\(742\) 0 0
\(743\) 3.91163 0.143504 0.0717520 0.997423i \(-0.477141\pi\)
0.0717520 + 0.997423i \(0.477141\pi\)
\(744\) 0 0
\(745\) 6.61132 0.242220
\(746\) 0 0
\(747\) 19.7554 0.722812
\(748\) 0 0
\(749\) −52.7330 −1.92682
\(750\) 0 0
\(751\) −10.9269 −0.398727 −0.199364 0.979926i \(-0.563888\pi\)
−0.199364 + 0.979926i \(0.563888\pi\)
\(752\) 0 0
\(753\) −0.279847 −0.0101982
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −0.733083 −0.0266444 −0.0133222 0.999911i \(-0.504241\pi\)
−0.0133222 + 0.999911i \(0.504241\pi\)
\(758\) 0 0
\(759\) 0.0791257 0.00287208
\(760\) 0 0
\(761\) 0.956193 0.0346620 0.0173310 0.999850i \(-0.494483\pi\)
0.0173310 + 0.999850i \(0.494483\pi\)
\(762\) 0 0
\(763\) −26.4525 −0.957644
\(764\) 0 0
\(765\) 16.0853 0.581566
\(766\) 0 0
\(767\) 66.8688 2.41449
\(768\) 0 0
\(769\) 23.4489 0.845590 0.422795 0.906225i \(-0.361049\pi\)
0.422795 + 0.906225i \(0.361049\pi\)
\(770\) 0 0
\(771\) 4.96266 0.178726
\(772\) 0 0
\(773\) 11.0156 0.396205 0.198103 0.980181i \(-0.436522\pi\)
0.198103 + 0.980181i \(0.436522\pi\)
\(774\) 0 0
\(775\) 8.23553 0.295829
\(776\) 0 0
\(777\) 7.13767 0.256062
\(778\) 0 0
\(779\) −27.5574 −0.987348
\(780\) 0 0
\(781\) 1.70197 0.0609014
\(782\) 0 0
\(783\) 10.1349 0.362192
\(784\) 0 0
\(785\) 18.5833 0.663267
\(786\) 0 0
\(787\) −10.1718 −0.362584 −0.181292 0.983429i \(-0.558028\pi\)
−0.181292 + 0.983429i \(0.558028\pi\)
\(788\) 0 0
\(789\) 2.66646 0.0949284
\(790\) 0 0
\(791\) −83.1608 −2.95686
\(792\) 0 0
\(793\) 57.6254 2.04634
\(794\) 0 0
\(795\) −1.23310 −0.0437336
\(796\) 0 0
\(797\) 6.05676 0.214542 0.107271 0.994230i \(-0.465789\pi\)
0.107271 + 0.994230i \(0.465789\pi\)
\(798\) 0 0
\(799\) −40.4238 −1.43009
\(800\) 0 0
\(801\) 21.3744 0.755228
\(802\) 0 0
\(803\) 9.19081 0.324336
\(804\) 0 0
\(805\) −0.701225 −0.0247149
\(806\) 0 0
\(807\) 3.05641 0.107591
\(808\) 0 0
\(809\) 9.09326 0.319702 0.159851 0.987141i \(-0.448899\pi\)
0.159851 + 0.987141i \(0.448899\pi\)
\(810\) 0 0
\(811\) −6.31290 −0.221676 −0.110838 0.993838i \(-0.535353\pi\)
−0.110838 + 0.993838i \(0.535353\pi\)
\(812\) 0 0
\(813\) 7.30718 0.256274
\(814\) 0 0
\(815\) 2.12360 0.0743864
\(816\) 0 0
\(817\) 12.3753 0.432957
\(818\) 0 0
\(819\) 60.6280 2.11852
\(820\) 0 0
\(821\) −37.6187 −1.31290 −0.656450 0.754369i \(-0.727943\pi\)
−0.656450 + 0.754369i \(0.727943\pi\)
\(822\) 0 0
\(823\) 42.1888 1.47061 0.735305 0.677737i \(-0.237039\pi\)
0.735305 + 0.677737i \(0.237039\pi\)
\(824\) 0 0
\(825\) −0.482219 −0.0167887
\(826\) 0 0
\(827\) 4.72001 0.164131 0.0820655 0.996627i \(-0.473848\pi\)
0.0820655 + 0.996627i \(0.473848\pi\)
\(828\) 0 0
\(829\) −45.3958 −1.57666 −0.788330 0.615253i \(-0.789054\pi\)
−0.788330 + 0.615253i \(0.789054\pi\)
\(830\) 0 0
\(831\) 0.214980 0.00745756
\(832\) 0 0
\(833\) −61.5467 −2.13247
\(834\) 0 0
\(835\) −11.9362 −0.413069
\(836\) 0 0
\(837\) −11.6302 −0.401997
\(838\) 0 0
\(839\) 6.32046 0.218207 0.109103 0.994030i \(-0.465202\pi\)
0.109103 + 0.994030i \(0.465202\pi\)
\(840\) 0 0
\(841\) 22.5051 0.776037
\(842\) 0 0
\(843\) 3.22207 0.110974
\(844\) 0 0
\(845\) 10.2294 0.351903
\(846\) 0 0
\(847\) −29.4060 −1.01040
\(848\) 0 0
\(849\) −0.775197 −0.0266047
\(850\) 0 0
\(851\) −1.15345 −0.0395396
\(852\) 0 0
\(853\) −38.5429 −1.31968 −0.659842 0.751404i \(-0.729377\pi\)
−0.659842 + 0.751404i \(0.729377\pi\)
\(854\) 0 0
\(855\) −10.4809 −0.358438
\(856\) 0 0
\(857\) 38.4681 1.31405 0.657023 0.753871i \(-0.271816\pi\)
0.657023 + 0.753871i \(0.271816\pi\)
\(858\) 0 0
\(859\) −4.61818 −0.157570 −0.0787851 0.996892i \(-0.525104\pi\)
−0.0787851 + 0.996892i \(0.525104\pi\)
\(860\) 0 0
\(861\) −7.85860 −0.267820
\(862\) 0 0
\(863\) 2.05034 0.0697943 0.0348971 0.999391i \(-0.488890\pi\)
0.0348971 + 0.999391i \(0.488890\pi\)
\(864\) 0 0
\(865\) −4.81892 −0.163848
\(866\) 0 0
\(867\) 3.05601 0.103788
\(868\) 0 0
\(869\) −23.6872 −0.803533
\(870\) 0 0
\(871\) 38.9839 1.32092
\(872\) 0 0
\(873\) −9.15748 −0.309934
\(874\) 0 0
\(875\) 4.27350 0.144471
\(876\) 0 0
\(877\) −55.4576 −1.87267 −0.936335 0.351107i \(-0.885805\pi\)
−0.936335 + 0.351107i \(0.885805\pi\)
\(878\) 0 0
\(879\) 3.99377 0.134707
\(880\) 0 0
\(881\) −28.3974 −0.956734 −0.478367 0.878160i \(-0.658771\pi\)
−0.478367 + 0.878160i \(0.658771\pi\)
\(882\) 0 0
\(883\) 24.6982 0.831160 0.415580 0.909557i \(-0.363579\pi\)
0.415580 + 0.909557i \(0.363579\pi\)
\(884\) 0 0
\(885\) −3.29650 −0.110811
\(886\) 0 0
\(887\) −38.3374 −1.28724 −0.643622 0.765343i \(-0.722569\pi\)
−0.643622 + 0.765343i \(0.722569\pi\)
\(888\) 0 0
\(889\) −29.9929 −1.00593
\(890\) 0 0
\(891\) −17.2410 −0.577597
\(892\) 0 0
\(893\) 26.3393 0.881413
\(894\) 0 0
\(895\) −12.2951 −0.410978
\(896\) 0 0
\(897\) 0.187906 0.00627401
\(898\) 0 0
\(899\) −59.1039 −1.97123
\(900\) 0 0
\(901\) 28.3601 0.944813
\(902\) 0 0
\(903\) 3.52908 0.117440
\(904\) 0 0
\(905\) −6.56893 −0.218358
\(906\) 0 0
\(907\) 7.77151 0.258049 0.129024 0.991641i \(-0.458815\pi\)
0.129024 + 0.991641i \(0.458815\pi\)
\(908\) 0 0
\(909\) −2.45514 −0.0814319
\(910\) 0 0
\(911\) 19.3165 0.639984 0.319992 0.947420i \(-0.396320\pi\)
0.319992 + 0.947420i \(0.396320\pi\)
\(912\) 0 0
\(913\) 13.6210 0.450790
\(914\) 0 0
\(915\) −2.84082 −0.0939146
\(916\) 0 0
\(917\) 8.63881 0.285279
\(918\) 0 0
\(919\) −37.3484 −1.23201 −0.616005 0.787742i \(-0.711250\pi\)
−0.616005 + 0.787742i \(0.711250\pi\)
\(920\) 0 0
\(921\) −4.73512 −0.156027
\(922\) 0 0
\(923\) 4.04182 0.133038
\(924\) 0 0
\(925\) 7.02949 0.231128
\(926\) 0 0
\(927\) 30.0797 0.987948
\(928\) 0 0
\(929\) 13.9336 0.457146 0.228573 0.973527i \(-0.426594\pi\)
0.228573 + 0.973527i \(0.426594\pi\)
\(930\) 0 0
\(931\) 40.1026 1.31431
\(932\) 0 0
\(933\) 1.12088 0.0366959
\(934\) 0 0
\(935\) 11.0906 0.362701
\(936\) 0 0
\(937\) −32.3733 −1.05759 −0.528794 0.848750i \(-0.677356\pi\)
−0.528794 + 0.848750i \(0.677356\pi\)
\(938\) 0 0
\(939\) 4.46489 0.145706
\(940\) 0 0
\(941\) 23.7927 0.775621 0.387811 0.921739i \(-0.373231\pi\)
0.387811 + 0.921739i \(0.373231\pi\)
\(942\) 0 0
\(943\) 1.26995 0.0413552
\(944\) 0 0
\(945\) −6.03501 −0.196319
\(946\) 0 0
\(947\) −26.6485 −0.865961 −0.432981 0.901403i \(-0.642538\pi\)
−0.432981 + 0.901403i \(0.642538\pi\)
\(948\) 0 0
\(949\) 21.8262 0.708507
\(950\) 0 0
\(951\) 5.73249 0.185889
\(952\) 0 0
\(953\) 26.4232 0.855932 0.427966 0.903795i \(-0.359230\pi\)
0.427966 + 0.903795i \(0.359230\pi\)
\(954\) 0 0
\(955\) 17.1704 0.555622
\(956\) 0 0
\(957\) 3.46074 0.111870
\(958\) 0 0
\(959\) −23.4402 −0.756923
\(960\) 0 0
\(961\) 36.8240 1.18787
\(962\) 0 0
\(963\) 36.3220 1.17046
\(964\) 0 0
\(965\) −15.9716 −0.514143
\(966\) 0 0
\(967\) 50.5130 1.62439 0.812195 0.583386i \(-0.198273\pi\)
0.812195 + 0.583386i \(0.198273\pi\)
\(968\) 0 0
\(969\) −4.62311 −0.148516
\(970\) 0 0
\(971\) 33.7689 1.08370 0.541848 0.840476i \(-0.317725\pi\)
0.541848 + 0.840476i \(0.317725\pi\)
\(972\) 0 0
\(973\) 89.8947 2.88189
\(974\) 0 0
\(975\) −1.14516 −0.0366746
\(976\) 0 0
\(977\) 2.09686 0.0670844 0.0335422 0.999437i \(-0.489321\pi\)
0.0335422 + 0.999437i \(0.489321\pi\)
\(978\) 0 0
\(979\) 14.7373 0.471007
\(980\) 0 0
\(981\) 18.2202 0.581727
\(982\) 0 0
\(983\) 54.3369 1.73308 0.866540 0.499108i \(-0.166339\pi\)
0.866540 + 0.499108i \(0.166339\pi\)
\(984\) 0 0
\(985\) 5.95356 0.189696
\(986\) 0 0
\(987\) 7.51123 0.239085
\(988\) 0 0
\(989\) −0.570299 −0.0181345
\(990\) 0 0
\(991\) −57.9400 −1.84053 −0.920263 0.391300i \(-0.872025\pi\)
−0.920263 + 0.391300i \(0.872025\pi\)
\(992\) 0 0
\(993\) −5.60825 −0.177972
\(994\) 0 0
\(995\) −18.7828 −0.595455
\(996\) 0 0
\(997\) −28.5055 −0.902779 −0.451390 0.892327i \(-0.649072\pi\)
−0.451390 + 0.892327i \(0.649072\pi\)
\(998\) 0 0
\(999\) −9.92701 −0.314077
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 \(a_p\))