Properties

Label 8008.2.a.u.1.4
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.55177\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.55177 q^{3} -0.910737 q^{5} -1.00000 q^{7} -0.592010 q^{9} +O(q^{10})\) \(q-1.55177 q^{3} -0.910737 q^{5} -1.00000 q^{7} -0.592010 q^{9} -1.00000 q^{11} -1.00000 q^{13} +1.41325 q^{15} +6.01520 q^{17} -0.663623 q^{19} +1.55177 q^{21} +5.85206 q^{23} -4.17056 q^{25} +5.57397 q^{27} -3.16099 q^{29} -9.74220 q^{31} +1.55177 q^{33} +0.910737 q^{35} -2.95353 q^{37} +1.55177 q^{39} -3.08433 q^{41} +5.25927 q^{43} +0.539165 q^{45} +6.11545 q^{47} +1.00000 q^{49} -9.33421 q^{51} +9.32092 q^{53} +0.910737 q^{55} +1.02979 q^{57} -5.66109 q^{59} +0.357389 q^{61} +0.592010 q^{63} +0.910737 q^{65} +6.56129 q^{67} -9.08105 q^{69} +5.46315 q^{71} -3.71538 q^{73} +6.47175 q^{75} +1.00000 q^{77} +1.33520 q^{79} -6.87350 q^{81} +10.5822 q^{83} -5.47826 q^{85} +4.90513 q^{87} +0.721451 q^{89} +1.00000 q^{91} +15.1177 q^{93} +0.604386 q^{95} +4.59096 q^{97} +0.592010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.55177 −0.895915 −0.447957 0.894055i \(-0.647848\pi\)
−0.447957 + 0.894055i \(0.647848\pi\)
\(4\) 0 0
\(5\) −0.910737 −0.407294 −0.203647 0.979044i \(-0.565279\pi\)
−0.203647 + 0.979044i \(0.565279\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.592010 −0.197337
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.41325 0.364901
\(16\) 0 0
\(17\) 6.01520 1.45890 0.729450 0.684034i \(-0.239776\pi\)
0.729450 + 0.684034i \(0.239776\pi\)
\(18\) 0 0
\(19\) −0.663623 −0.152246 −0.0761228 0.997098i \(-0.524254\pi\)
−0.0761228 + 0.997098i \(0.524254\pi\)
\(20\) 0 0
\(21\) 1.55177 0.338624
\(22\) 0 0
\(23\) 5.85206 1.22024 0.610120 0.792309i \(-0.291121\pi\)
0.610120 + 0.792309i \(0.291121\pi\)
\(24\) 0 0
\(25\) −4.17056 −0.834112
\(26\) 0 0
\(27\) 5.57397 1.07271
\(28\) 0 0
\(29\) −3.16099 −0.586982 −0.293491 0.955962i \(-0.594817\pi\)
−0.293491 + 0.955962i \(0.594817\pi\)
\(30\) 0 0
\(31\) −9.74220 −1.74975 −0.874876 0.484348i \(-0.839057\pi\)
−0.874876 + 0.484348i \(0.839057\pi\)
\(32\) 0 0
\(33\) 1.55177 0.270129
\(34\) 0 0
\(35\) 0.910737 0.153943
\(36\) 0 0
\(37\) −2.95353 −0.485558 −0.242779 0.970082i \(-0.578059\pi\)
−0.242779 + 0.970082i \(0.578059\pi\)
\(38\) 0 0
\(39\) 1.55177 0.248482
\(40\) 0 0
\(41\) −3.08433 −0.481692 −0.240846 0.970563i \(-0.577425\pi\)
−0.240846 + 0.970563i \(0.577425\pi\)
\(42\) 0 0
\(43\) 5.25927 0.802031 0.401016 0.916071i \(-0.368657\pi\)
0.401016 + 0.916071i \(0.368657\pi\)
\(44\) 0 0
\(45\) 0.539165 0.0803739
\(46\) 0 0
\(47\) 6.11545 0.892030 0.446015 0.895025i \(-0.352843\pi\)
0.446015 + 0.895025i \(0.352843\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −9.33421 −1.30705
\(52\) 0 0
\(53\) 9.32092 1.28033 0.640163 0.768239i \(-0.278867\pi\)
0.640163 + 0.768239i \(0.278867\pi\)
\(54\) 0 0
\(55\) 0.910737 0.122804
\(56\) 0 0
\(57\) 1.02979 0.136399
\(58\) 0 0
\(59\) −5.66109 −0.737011 −0.368505 0.929626i \(-0.620130\pi\)
−0.368505 + 0.929626i \(0.620130\pi\)
\(60\) 0 0
\(61\) 0.357389 0.0457590 0.0228795 0.999738i \(-0.492717\pi\)
0.0228795 + 0.999738i \(0.492717\pi\)
\(62\) 0 0
\(63\) 0.592010 0.0745862
\(64\) 0 0
\(65\) 0.910737 0.112963
\(66\) 0 0
\(67\) 6.56129 0.801589 0.400794 0.916168i \(-0.368734\pi\)
0.400794 + 0.916168i \(0.368734\pi\)
\(68\) 0 0
\(69\) −9.08105 −1.09323
\(70\) 0 0
\(71\) 5.46315 0.648356 0.324178 0.945996i \(-0.394912\pi\)
0.324178 + 0.945996i \(0.394912\pi\)
\(72\) 0 0
\(73\) −3.71538 −0.434853 −0.217426 0.976077i \(-0.569766\pi\)
−0.217426 + 0.976077i \(0.569766\pi\)
\(74\) 0 0
\(75\) 6.47175 0.747293
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 1.33520 0.150221 0.0751107 0.997175i \(-0.476069\pi\)
0.0751107 + 0.997175i \(0.476069\pi\)
\(80\) 0 0
\(81\) −6.87350 −0.763722
\(82\) 0 0
\(83\) 10.5822 1.16155 0.580774 0.814065i \(-0.302750\pi\)
0.580774 + 0.814065i \(0.302750\pi\)
\(84\) 0 0
\(85\) −5.47826 −0.594201
\(86\) 0 0
\(87\) 4.90513 0.525886
\(88\) 0 0
\(89\) 0.721451 0.0764736 0.0382368 0.999269i \(-0.487826\pi\)
0.0382368 + 0.999269i \(0.487826\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 15.1177 1.56763
\(94\) 0 0
\(95\) 0.604386 0.0620087
\(96\) 0 0
\(97\) 4.59096 0.466141 0.233071 0.972460i \(-0.425123\pi\)
0.233071 + 0.972460i \(0.425123\pi\)
\(98\) 0 0
\(99\) 0.592010 0.0594992
\(100\) 0 0
\(101\) 19.7528 1.96548 0.982741 0.184987i \(-0.0592243\pi\)
0.982741 + 0.184987i \(0.0592243\pi\)
\(102\) 0 0
\(103\) −3.25475 −0.320700 −0.160350 0.987060i \(-0.551262\pi\)
−0.160350 + 0.987060i \(0.551262\pi\)
\(104\) 0 0
\(105\) −1.41325 −0.137919
\(106\) 0 0
\(107\) −0.556211 −0.0537710 −0.0268855 0.999639i \(-0.508559\pi\)
−0.0268855 + 0.999639i \(0.508559\pi\)
\(108\) 0 0
\(109\) −12.7855 −1.22463 −0.612313 0.790615i \(-0.709761\pi\)
−0.612313 + 0.790615i \(0.709761\pi\)
\(110\) 0 0
\(111\) 4.58321 0.435019
\(112\) 0 0
\(113\) −12.8767 −1.21133 −0.605667 0.795718i \(-0.707094\pi\)
−0.605667 + 0.795718i \(0.707094\pi\)
\(114\) 0 0
\(115\) −5.32969 −0.496996
\(116\) 0 0
\(117\) 0.592010 0.0547313
\(118\) 0 0
\(119\) −6.01520 −0.551413
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 4.78618 0.431555
\(124\) 0 0
\(125\) 8.35196 0.747022
\(126\) 0 0
\(127\) −1.08433 −0.0962187 −0.0481094 0.998842i \(-0.515320\pi\)
−0.0481094 + 0.998842i \(0.515320\pi\)
\(128\) 0 0
\(129\) −8.16118 −0.718552
\(130\) 0 0
\(131\) 19.7048 1.72162 0.860808 0.508930i \(-0.169959\pi\)
0.860808 + 0.508930i \(0.169959\pi\)
\(132\) 0 0
\(133\) 0.663623 0.0575434
\(134\) 0 0
\(135\) −5.07642 −0.436909
\(136\) 0 0
\(137\) −7.21187 −0.616152 −0.308076 0.951362i \(-0.599685\pi\)
−0.308076 + 0.951362i \(0.599685\pi\)
\(138\) 0 0
\(139\) 2.26144 0.191813 0.0959063 0.995390i \(-0.469425\pi\)
0.0959063 + 0.995390i \(0.469425\pi\)
\(140\) 0 0
\(141\) −9.48978 −0.799183
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 2.87883 0.239074
\(146\) 0 0
\(147\) −1.55177 −0.127988
\(148\) 0 0
\(149\) −11.7786 −0.964937 −0.482468 0.875913i \(-0.660260\pi\)
−0.482468 + 0.875913i \(0.660260\pi\)
\(150\) 0 0
\(151\) −11.9791 −0.974849 −0.487424 0.873165i \(-0.662063\pi\)
−0.487424 + 0.873165i \(0.662063\pi\)
\(152\) 0 0
\(153\) −3.56106 −0.287894
\(154\) 0 0
\(155\) 8.87258 0.712663
\(156\) 0 0
\(157\) 9.73669 0.777072 0.388536 0.921433i \(-0.372981\pi\)
0.388536 + 0.921433i \(0.372981\pi\)
\(158\) 0 0
\(159\) −14.4639 −1.14706
\(160\) 0 0
\(161\) −5.85206 −0.461207
\(162\) 0 0
\(163\) 19.5025 1.52756 0.763778 0.645479i \(-0.223342\pi\)
0.763778 + 0.645479i \(0.223342\pi\)
\(164\) 0 0
\(165\) −1.41325 −0.110022
\(166\) 0 0
\(167\) 2.49870 0.193355 0.0966775 0.995316i \(-0.469178\pi\)
0.0966775 + 0.995316i \(0.469178\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.392871 0.0300436
\(172\) 0 0
\(173\) −1.99039 −0.151326 −0.0756632 0.997133i \(-0.524107\pi\)
−0.0756632 + 0.997133i \(0.524107\pi\)
\(174\) 0 0
\(175\) 4.17056 0.315265
\(176\) 0 0
\(177\) 8.78471 0.660299
\(178\) 0 0
\(179\) 0.215428 0.0161018 0.00805092 0.999968i \(-0.497437\pi\)
0.00805092 + 0.999968i \(0.497437\pi\)
\(180\) 0 0
\(181\) −17.5955 −1.30786 −0.653931 0.756554i \(-0.726881\pi\)
−0.653931 + 0.756554i \(0.726881\pi\)
\(182\) 0 0
\(183\) −0.554586 −0.0409962
\(184\) 0 0
\(185\) 2.68989 0.197765
\(186\) 0 0
\(187\) −6.01520 −0.439875
\(188\) 0 0
\(189\) −5.57397 −0.405447
\(190\) 0 0
\(191\) −8.46661 −0.612622 −0.306311 0.951931i \(-0.599095\pi\)
−0.306311 + 0.951931i \(0.599095\pi\)
\(192\) 0 0
\(193\) −3.52127 −0.253467 −0.126733 0.991937i \(-0.540449\pi\)
−0.126733 + 0.991937i \(0.540449\pi\)
\(194\) 0 0
\(195\) −1.41325 −0.101205
\(196\) 0 0
\(197\) −16.1657 −1.15176 −0.575878 0.817536i \(-0.695340\pi\)
−0.575878 + 0.817536i \(0.695340\pi\)
\(198\) 0 0
\(199\) −3.83654 −0.271965 −0.135983 0.990711i \(-0.543419\pi\)
−0.135983 + 0.990711i \(0.543419\pi\)
\(200\) 0 0
\(201\) −10.1816 −0.718155
\(202\) 0 0
\(203\) 3.16099 0.221858
\(204\) 0 0
\(205\) 2.80902 0.196190
\(206\) 0 0
\(207\) −3.46448 −0.240798
\(208\) 0 0
\(209\) 0.663623 0.0459038
\(210\) 0 0
\(211\) 13.9168 0.958070 0.479035 0.877796i \(-0.340987\pi\)
0.479035 + 0.877796i \(0.340987\pi\)
\(212\) 0 0
\(213\) −8.47755 −0.580872
\(214\) 0 0
\(215\) −4.78981 −0.326662
\(216\) 0 0
\(217\) 9.74220 0.661344
\(218\) 0 0
\(219\) 5.76542 0.389591
\(220\) 0 0
\(221\) −6.01520 −0.404626
\(222\) 0 0
\(223\) 2.90631 0.194621 0.0973104 0.995254i \(-0.468976\pi\)
0.0973104 + 0.995254i \(0.468976\pi\)
\(224\) 0 0
\(225\) 2.46901 0.164601
\(226\) 0 0
\(227\) −26.1433 −1.73519 −0.867597 0.497267i \(-0.834337\pi\)
−0.867597 + 0.497267i \(0.834337\pi\)
\(228\) 0 0
\(229\) −28.1783 −1.86207 −0.931037 0.364925i \(-0.881095\pi\)
−0.931037 + 0.364925i \(0.881095\pi\)
\(230\) 0 0
\(231\) −1.55177 −0.102099
\(232\) 0 0
\(233\) 6.22067 0.407530 0.203765 0.979020i \(-0.434682\pi\)
0.203765 + 0.979020i \(0.434682\pi\)
\(234\) 0 0
\(235\) −5.56957 −0.363318
\(236\) 0 0
\(237\) −2.07192 −0.134586
\(238\) 0 0
\(239\) −3.33334 −0.215616 −0.107808 0.994172i \(-0.534383\pi\)
−0.107808 + 0.994172i \(0.534383\pi\)
\(240\) 0 0
\(241\) −25.2296 −1.62518 −0.812589 0.582837i \(-0.801943\pi\)
−0.812589 + 0.582837i \(0.801943\pi\)
\(242\) 0 0
\(243\) −6.05583 −0.388482
\(244\) 0 0
\(245\) −0.910737 −0.0581848
\(246\) 0 0
\(247\) 0.663623 0.0422253
\(248\) 0 0
\(249\) −16.4212 −1.04065
\(250\) 0 0
\(251\) −16.9218 −1.06809 −0.534047 0.845455i \(-0.679330\pi\)
−0.534047 + 0.845455i \(0.679330\pi\)
\(252\) 0 0
\(253\) −5.85206 −0.367916
\(254\) 0 0
\(255\) 8.50101 0.532354
\(256\) 0 0
\(257\) −0.307446 −0.0191780 −0.00958898 0.999954i \(-0.503052\pi\)
−0.00958898 + 0.999954i \(0.503052\pi\)
\(258\) 0 0
\(259\) 2.95353 0.183524
\(260\) 0 0
\(261\) 1.87134 0.115833
\(262\) 0 0
\(263\) −0.767082 −0.0473003 −0.0236502 0.999720i \(-0.507529\pi\)
−0.0236502 + 0.999720i \(0.507529\pi\)
\(264\) 0 0
\(265\) −8.48890 −0.521469
\(266\) 0 0
\(267\) −1.11953 −0.0685138
\(268\) 0 0
\(269\) 13.1452 0.801478 0.400739 0.916192i \(-0.368753\pi\)
0.400739 + 0.916192i \(0.368753\pi\)
\(270\) 0 0
\(271\) −31.2845 −1.90040 −0.950199 0.311643i \(-0.899121\pi\)
−0.950199 + 0.311643i \(0.899121\pi\)
\(272\) 0 0
\(273\) −1.55177 −0.0939174
\(274\) 0 0
\(275\) 4.17056 0.251494
\(276\) 0 0
\(277\) 3.00937 0.180815 0.0904077 0.995905i \(-0.471183\pi\)
0.0904077 + 0.995905i \(0.471183\pi\)
\(278\) 0 0
\(279\) 5.76748 0.345290
\(280\) 0 0
\(281\) −27.8687 −1.66251 −0.831255 0.555892i \(-0.812377\pi\)
−0.831255 + 0.555892i \(0.812377\pi\)
\(282\) 0 0
\(283\) 5.88575 0.349871 0.174936 0.984580i \(-0.444028\pi\)
0.174936 + 0.984580i \(0.444028\pi\)
\(284\) 0 0
\(285\) −0.937868 −0.0555545
\(286\) 0 0
\(287\) 3.08433 0.182063
\(288\) 0 0
\(289\) 19.1827 1.12839
\(290\) 0 0
\(291\) −7.12411 −0.417623
\(292\) 0 0
\(293\) −3.91935 −0.228971 −0.114486 0.993425i \(-0.536522\pi\)
−0.114486 + 0.993425i \(0.536522\pi\)
\(294\) 0 0
\(295\) 5.15576 0.300180
\(296\) 0 0
\(297\) −5.57397 −0.323435
\(298\) 0 0
\(299\) −5.85206 −0.338433
\(300\) 0 0
\(301\) −5.25927 −0.303139
\(302\) 0 0
\(303\) −30.6519 −1.76090
\(304\) 0 0
\(305\) −0.325487 −0.0186374
\(306\) 0 0
\(307\) −8.36693 −0.477526 −0.238763 0.971078i \(-0.576742\pi\)
−0.238763 + 0.971078i \(0.576742\pi\)
\(308\) 0 0
\(309\) 5.05063 0.287320
\(310\) 0 0
\(311\) 9.90124 0.561448 0.280724 0.959789i \(-0.409426\pi\)
0.280724 + 0.959789i \(0.409426\pi\)
\(312\) 0 0
\(313\) 15.1521 0.856447 0.428224 0.903673i \(-0.359140\pi\)
0.428224 + 0.903673i \(0.359140\pi\)
\(314\) 0 0
\(315\) −0.539165 −0.0303785
\(316\) 0 0
\(317\) 8.50792 0.477852 0.238926 0.971038i \(-0.423205\pi\)
0.238926 + 0.971038i \(0.423205\pi\)
\(318\) 0 0
\(319\) 3.16099 0.176982
\(320\) 0 0
\(321\) 0.863112 0.0481742
\(322\) 0 0
\(323\) −3.99183 −0.222111
\(324\) 0 0
\(325\) 4.17056 0.231341
\(326\) 0 0
\(327\) 19.8401 1.09716
\(328\) 0 0
\(329\) −6.11545 −0.337156
\(330\) 0 0
\(331\) −26.3057 −1.44589 −0.722946 0.690904i \(-0.757213\pi\)
−0.722946 + 0.690904i \(0.757213\pi\)
\(332\) 0 0
\(333\) 1.74852 0.0958184
\(334\) 0 0
\(335\) −5.97560 −0.326482
\(336\) 0 0
\(337\) −17.4519 −0.950667 −0.475333 0.879806i \(-0.657673\pi\)
−0.475333 + 0.879806i \(0.657673\pi\)
\(338\) 0 0
\(339\) 19.9816 1.08525
\(340\) 0 0
\(341\) 9.74220 0.527570
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 8.27045 0.445266
\(346\) 0 0
\(347\) 14.6380 0.785808 0.392904 0.919580i \(-0.371470\pi\)
0.392904 + 0.919580i \(0.371470\pi\)
\(348\) 0 0
\(349\) 20.3827 1.09106 0.545530 0.838091i \(-0.316328\pi\)
0.545530 + 0.838091i \(0.316328\pi\)
\(350\) 0 0
\(351\) −5.57397 −0.297517
\(352\) 0 0
\(353\) 15.1450 0.806087 0.403044 0.915181i \(-0.367952\pi\)
0.403044 + 0.915181i \(0.367952\pi\)
\(354\) 0 0
\(355\) −4.97549 −0.264071
\(356\) 0 0
\(357\) 9.33421 0.494019
\(358\) 0 0
\(359\) 31.4828 1.66160 0.830799 0.556572i \(-0.187884\pi\)
0.830799 + 0.556572i \(0.187884\pi\)
\(360\) 0 0
\(361\) −18.5596 −0.976821
\(362\) 0 0
\(363\) −1.55177 −0.0814468
\(364\) 0 0
\(365\) 3.38374 0.177113
\(366\) 0 0
\(367\) −20.1120 −1.04984 −0.524918 0.851153i \(-0.675904\pi\)
−0.524918 + 0.851153i \(0.675904\pi\)
\(368\) 0 0
\(369\) 1.82596 0.0950555
\(370\) 0 0
\(371\) −9.32092 −0.483918
\(372\) 0 0
\(373\) −28.6679 −1.48437 −0.742185 0.670196i \(-0.766210\pi\)
−0.742185 + 0.670196i \(0.766210\pi\)
\(374\) 0 0
\(375\) −12.9603 −0.669268
\(376\) 0 0
\(377\) 3.16099 0.162799
\(378\) 0 0
\(379\) 27.9104 1.43366 0.716830 0.697248i \(-0.245592\pi\)
0.716830 + 0.697248i \(0.245592\pi\)
\(380\) 0 0
\(381\) 1.68263 0.0862038
\(382\) 0 0
\(383\) 4.84357 0.247495 0.123748 0.992314i \(-0.460509\pi\)
0.123748 + 0.992314i \(0.460509\pi\)
\(384\) 0 0
\(385\) −0.910737 −0.0464154
\(386\) 0 0
\(387\) −3.11354 −0.158270
\(388\) 0 0
\(389\) −32.5971 −1.65274 −0.826369 0.563130i \(-0.809597\pi\)
−0.826369 + 0.563130i \(0.809597\pi\)
\(390\) 0 0
\(391\) 35.2013 1.78021
\(392\) 0 0
\(393\) −30.5773 −1.54242
\(394\) 0 0
\(395\) −1.21601 −0.0611843
\(396\) 0 0
\(397\) 31.0179 1.55674 0.778371 0.627804i \(-0.216046\pi\)
0.778371 + 0.627804i \(0.216046\pi\)
\(398\) 0 0
\(399\) −1.02979 −0.0515540
\(400\) 0 0
\(401\) −3.17190 −0.158397 −0.0791986 0.996859i \(-0.525236\pi\)
−0.0791986 + 0.996859i \(0.525236\pi\)
\(402\) 0 0
\(403\) 9.74220 0.485294
\(404\) 0 0
\(405\) 6.25994 0.311059
\(406\) 0 0
\(407\) 2.95353 0.146401
\(408\) 0 0
\(409\) 2.89406 0.143102 0.0715511 0.997437i \(-0.477205\pi\)
0.0715511 + 0.997437i \(0.477205\pi\)
\(410\) 0 0
\(411\) 11.1912 0.552020
\(412\) 0 0
\(413\) 5.66109 0.278564
\(414\) 0 0
\(415\) −9.63761 −0.473092
\(416\) 0 0
\(417\) −3.50923 −0.171848
\(418\) 0 0
\(419\) −14.5879 −0.712666 −0.356333 0.934359i \(-0.615973\pi\)
−0.356333 + 0.934359i \(0.615973\pi\)
\(420\) 0 0
\(421\) −24.2602 −1.18237 −0.591184 0.806537i \(-0.701339\pi\)
−0.591184 + 0.806537i \(0.701339\pi\)
\(422\) 0 0
\(423\) −3.62041 −0.176030
\(424\) 0 0
\(425\) −25.0868 −1.21689
\(426\) 0 0
\(427\) −0.357389 −0.0172953
\(428\) 0 0
\(429\) −1.55177 −0.0749202
\(430\) 0 0
\(431\) −7.51492 −0.361981 −0.180990 0.983485i \(-0.557930\pi\)
−0.180990 + 0.983485i \(0.557930\pi\)
\(432\) 0 0
\(433\) −2.76319 −0.132790 −0.0663952 0.997793i \(-0.521150\pi\)
−0.0663952 + 0.997793i \(0.521150\pi\)
\(434\) 0 0
\(435\) −4.46729 −0.214190
\(436\) 0 0
\(437\) −3.88356 −0.185776
\(438\) 0 0
\(439\) 8.72133 0.416246 0.208123 0.978103i \(-0.433265\pi\)
0.208123 + 0.978103i \(0.433265\pi\)
\(440\) 0 0
\(441\) −0.592010 −0.0281909
\(442\) 0 0
\(443\) 14.0203 0.666126 0.333063 0.942905i \(-0.391918\pi\)
0.333063 + 0.942905i \(0.391918\pi\)
\(444\) 0 0
\(445\) −0.657051 −0.0311472
\(446\) 0 0
\(447\) 18.2776 0.864501
\(448\) 0 0
\(449\) −28.6336 −1.35131 −0.675653 0.737220i \(-0.736138\pi\)
−0.675653 + 0.737220i \(0.736138\pi\)
\(450\) 0 0
\(451\) 3.08433 0.145236
\(452\) 0 0
\(453\) 18.5889 0.873381
\(454\) 0 0
\(455\) −0.910737 −0.0426960
\(456\) 0 0
\(457\) −14.2467 −0.666434 −0.333217 0.942850i \(-0.608134\pi\)
−0.333217 + 0.942850i \(0.608134\pi\)
\(458\) 0 0
\(459\) 33.5286 1.56498
\(460\) 0 0
\(461\) −6.91724 −0.322168 −0.161084 0.986941i \(-0.551499\pi\)
−0.161084 + 0.986941i \(0.551499\pi\)
\(462\) 0 0
\(463\) −5.14642 −0.239175 −0.119587 0.992824i \(-0.538157\pi\)
−0.119587 + 0.992824i \(0.538157\pi\)
\(464\) 0 0
\(465\) −13.7682 −0.638485
\(466\) 0 0
\(467\) 21.4559 0.992861 0.496430 0.868077i \(-0.334644\pi\)
0.496430 + 0.868077i \(0.334644\pi\)
\(468\) 0 0
\(469\) −6.56129 −0.302972
\(470\) 0 0
\(471\) −15.1091 −0.696191
\(472\) 0 0
\(473\) −5.25927 −0.241821
\(474\) 0 0
\(475\) 2.76768 0.126990
\(476\) 0 0
\(477\) −5.51807 −0.252655
\(478\) 0 0
\(479\) −27.7159 −1.26637 −0.633186 0.774000i \(-0.718253\pi\)
−0.633186 + 0.774000i \(0.718253\pi\)
\(480\) 0 0
\(481\) 2.95353 0.134670
\(482\) 0 0
\(483\) 9.08105 0.413202
\(484\) 0 0
\(485\) −4.18116 −0.189856
\(486\) 0 0
\(487\) 11.3761 0.515500 0.257750 0.966212i \(-0.417019\pi\)
0.257750 + 0.966212i \(0.417019\pi\)
\(488\) 0 0
\(489\) −30.2634 −1.36856
\(490\) 0 0
\(491\) −22.1519 −0.999703 −0.499851 0.866111i \(-0.666612\pi\)
−0.499851 + 0.866111i \(0.666612\pi\)
\(492\) 0 0
\(493\) −19.0140 −0.856348
\(494\) 0 0
\(495\) −0.539165 −0.0242337
\(496\) 0 0
\(497\) −5.46315 −0.245056
\(498\) 0 0
\(499\) 28.6915 1.28441 0.642205 0.766533i \(-0.278020\pi\)
0.642205 + 0.766533i \(0.278020\pi\)
\(500\) 0 0
\(501\) −3.87740 −0.173230
\(502\) 0 0
\(503\) 2.21758 0.0988771 0.0494385 0.998777i \(-0.484257\pi\)
0.0494385 + 0.998777i \(0.484257\pi\)
\(504\) 0 0
\(505\) −17.9896 −0.800529
\(506\) 0 0
\(507\) −1.55177 −0.0689165
\(508\) 0 0
\(509\) 5.95624 0.264006 0.132003 0.991249i \(-0.457859\pi\)
0.132003 + 0.991249i \(0.457859\pi\)
\(510\) 0 0
\(511\) 3.71538 0.164359
\(512\) 0 0
\(513\) −3.69902 −0.163316
\(514\) 0 0
\(515\) 2.96422 0.130619
\(516\) 0 0
\(517\) −6.11545 −0.268957
\(518\) 0 0
\(519\) 3.08863 0.135576
\(520\) 0 0
\(521\) −20.0565 −0.878690 −0.439345 0.898318i \(-0.644789\pi\)
−0.439345 + 0.898318i \(0.644789\pi\)
\(522\) 0 0
\(523\) 26.1792 1.14474 0.572368 0.819997i \(-0.306025\pi\)
0.572368 + 0.819997i \(0.306025\pi\)
\(524\) 0 0
\(525\) −6.47175 −0.282450
\(526\) 0 0
\(527\) −58.6013 −2.55271
\(528\) 0 0
\(529\) 11.2466 0.488983
\(530\) 0 0
\(531\) 3.35142 0.145439
\(532\) 0 0
\(533\) 3.08433 0.133597
\(534\) 0 0
\(535\) 0.506562 0.0219006
\(536\) 0 0
\(537\) −0.334295 −0.0144259
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −31.4183 −1.35078 −0.675388 0.737462i \(-0.736024\pi\)
−0.675388 + 0.737462i \(0.736024\pi\)
\(542\) 0 0
\(543\) 27.3041 1.17173
\(544\) 0 0
\(545\) 11.6442 0.498783
\(546\) 0 0
\(547\) −42.2584 −1.80684 −0.903420 0.428757i \(-0.858952\pi\)
−0.903420 + 0.428757i \(0.858952\pi\)
\(548\) 0 0
\(549\) −0.211578 −0.00902992
\(550\) 0 0
\(551\) 2.09771 0.0893654
\(552\) 0 0
\(553\) −1.33520 −0.0567784
\(554\) 0 0
\(555\) −4.17409 −0.177180
\(556\) 0 0
\(557\) 19.1508 0.811446 0.405723 0.913996i \(-0.367020\pi\)
0.405723 + 0.913996i \(0.367020\pi\)
\(558\) 0 0
\(559\) −5.25927 −0.222443
\(560\) 0 0
\(561\) 9.33421 0.394091
\(562\) 0 0
\(563\) 14.4902 0.610690 0.305345 0.952242i \(-0.401228\pi\)
0.305345 + 0.952242i \(0.401228\pi\)
\(564\) 0 0
\(565\) 11.7273 0.493369
\(566\) 0 0
\(567\) 6.87350 0.288660
\(568\) 0 0
\(569\) −36.7574 −1.54095 −0.770475 0.637470i \(-0.779981\pi\)
−0.770475 + 0.637470i \(0.779981\pi\)
\(570\) 0 0
\(571\) 37.2205 1.55763 0.778815 0.627253i \(-0.215821\pi\)
0.778815 + 0.627253i \(0.215821\pi\)
\(572\) 0 0
\(573\) 13.1382 0.548857
\(574\) 0 0
\(575\) −24.4064 −1.01782
\(576\) 0 0
\(577\) −3.62361 −0.150853 −0.0754264 0.997151i \(-0.524032\pi\)
−0.0754264 + 0.997151i \(0.524032\pi\)
\(578\) 0 0
\(579\) 5.46421 0.227085
\(580\) 0 0
\(581\) −10.5822 −0.439024
\(582\) 0 0
\(583\) −9.32092 −0.386033
\(584\) 0 0
\(585\) −0.539165 −0.0222917
\(586\) 0 0
\(587\) −40.9191 −1.68891 −0.844455 0.535626i \(-0.820076\pi\)
−0.844455 + 0.535626i \(0.820076\pi\)
\(588\) 0 0
\(589\) 6.46515 0.266392
\(590\) 0 0
\(591\) 25.0854 1.03188
\(592\) 0 0
\(593\) −16.6109 −0.682129 −0.341064 0.940040i \(-0.610787\pi\)
−0.341064 + 0.940040i \(0.610787\pi\)
\(594\) 0 0
\(595\) 5.47826 0.224587
\(596\) 0 0
\(597\) 5.95343 0.243658
\(598\) 0 0
\(599\) −47.3606 −1.93510 −0.967551 0.252674i \(-0.918690\pi\)
−0.967551 + 0.252674i \(0.918690\pi\)
\(600\) 0 0
\(601\) 23.6736 0.965667 0.482833 0.875712i \(-0.339608\pi\)
0.482833 + 0.875712i \(0.339608\pi\)
\(602\) 0 0
\(603\) −3.88434 −0.158183
\(604\) 0 0
\(605\) −0.910737 −0.0370267
\(606\) 0 0
\(607\) 15.2312 0.618215 0.309107 0.951027i \(-0.399970\pi\)
0.309107 + 0.951027i \(0.399970\pi\)
\(608\) 0 0
\(609\) −4.90513 −0.198766
\(610\) 0 0
\(611\) −6.11545 −0.247405
\(612\) 0 0
\(613\) −30.5582 −1.23423 −0.617117 0.786871i \(-0.711700\pi\)
−0.617117 + 0.786871i \(0.711700\pi\)
\(614\) 0 0
\(615\) −4.35895 −0.175770
\(616\) 0 0
\(617\) 34.1300 1.37402 0.687011 0.726647i \(-0.258923\pi\)
0.687011 + 0.726647i \(0.258923\pi\)
\(618\) 0 0
\(619\) −40.2766 −1.61885 −0.809426 0.587221i \(-0.800222\pi\)
−0.809426 + 0.587221i \(0.800222\pi\)
\(620\) 0 0
\(621\) 32.6192 1.30896
\(622\) 0 0
\(623\) −0.721451 −0.0289043
\(624\) 0 0
\(625\) 13.2464 0.529854
\(626\) 0 0
\(627\) −1.02979 −0.0411259
\(628\) 0 0
\(629\) −17.7661 −0.708381
\(630\) 0 0
\(631\) −8.32938 −0.331587 −0.165794 0.986160i \(-0.553019\pi\)
−0.165794 + 0.986160i \(0.553019\pi\)
\(632\) 0 0
\(633\) −21.5956 −0.858349
\(634\) 0 0
\(635\) 0.987539 0.0391893
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −3.23423 −0.127944
\(640\) 0 0
\(641\) −11.3428 −0.448012 −0.224006 0.974588i \(-0.571914\pi\)
−0.224006 + 0.974588i \(0.571914\pi\)
\(642\) 0 0
\(643\) 24.7287 0.975205 0.487602 0.873066i \(-0.337872\pi\)
0.487602 + 0.873066i \(0.337872\pi\)
\(644\) 0 0
\(645\) 7.43268 0.292662
\(646\) 0 0
\(647\) −27.2257 −1.07035 −0.535177 0.844740i \(-0.679755\pi\)
−0.535177 + 0.844740i \(0.679755\pi\)
\(648\) 0 0
\(649\) 5.66109 0.222217
\(650\) 0 0
\(651\) −15.1177 −0.592508
\(652\) 0 0
\(653\) −40.3737 −1.57995 −0.789973 0.613141i \(-0.789906\pi\)
−0.789973 + 0.613141i \(0.789906\pi\)
\(654\) 0 0
\(655\) −17.9459 −0.701204
\(656\) 0 0
\(657\) 2.19954 0.0858123
\(658\) 0 0
\(659\) −17.0720 −0.665029 −0.332515 0.943098i \(-0.607897\pi\)
−0.332515 + 0.943098i \(0.607897\pi\)
\(660\) 0 0
\(661\) −43.2009 −1.68032 −0.840160 0.542338i \(-0.817539\pi\)
−0.840160 + 0.542338i \(0.817539\pi\)
\(662\) 0 0
\(663\) 9.33421 0.362511
\(664\) 0 0
\(665\) −0.604386 −0.0234371
\(666\) 0 0
\(667\) −18.4983 −0.716258
\(668\) 0 0
\(669\) −4.50992 −0.174364
\(670\) 0 0
\(671\) −0.357389 −0.0137969
\(672\) 0 0
\(673\) −17.7183 −0.682992 −0.341496 0.939883i \(-0.610934\pi\)
−0.341496 + 0.939883i \(0.610934\pi\)
\(674\) 0 0
\(675\) −23.2466 −0.894761
\(676\) 0 0
\(677\) 4.18372 0.160793 0.0803967 0.996763i \(-0.474381\pi\)
0.0803967 + 0.996763i \(0.474381\pi\)
\(678\) 0 0
\(679\) −4.59096 −0.176185
\(680\) 0 0
\(681\) 40.5685 1.55459
\(682\) 0 0
\(683\) −14.0585 −0.537933 −0.268967 0.963150i \(-0.586682\pi\)
−0.268967 + 0.963150i \(0.586682\pi\)
\(684\) 0 0
\(685\) 6.56812 0.250955
\(686\) 0 0
\(687\) 43.7262 1.66826
\(688\) 0 0
\(689\) −9.32092 −0.355099
\(690\) 0 0
\(691\) 41.1069 1.56378 0.781890 0.623416i \(-0.214256\pi\)
0.781890 + 0.623416i \(0.214256\pi\)
\(692\) 0 0
\(693\) −0.592010 −0.0224886
\(694\) 0 0
\(695\) −2.05957 −0.0781241
\(696\) 0 0
\(697\) −18.5529 −0.702741
\(698\) 0 0
\(699\) −9.65305 −0.365112
\(700\) 0 0
\(701\) 7.07558 0.267241 0.133621 0.991033i \(-0.457340\pi\)
0.133621 + 0.991033i \(0.457340\pi\)
\(702\) 0 0
\(703\) 1.96003 0.0739241
\(704\) 0 0
\(705\) 8.64269 0.325502
\(706\) 0 0
\(707\) −19.7528 −0.742882
\(708\) 0 0
\(709\) 33.9379 1.27456 0.637282 0.770631i \(-0.280059\pi\)
0.637282 + 0.770631i \(0.280059\pi\)
\(710\) 0 0
\(711\) −0.790450 −0.0296442
\(712\) 0 0
\(713\) −57.0120 −2.13511
\(714\) 0 0
\(715\) −0.910737 −0.0340596
\(716\) 0 0
\(717\) 5.17257 0.193173
\(718\) 0 0
\(719\) 39.4955 1.47294 0.736468 0.676473i \(-0.236492\pi\)
0.736468 + 0.676473i \(0.236492\pi\)
\(720\) 0 0
\(721\) 3.25475 0.121213
\(722\) 0 0
\(723\) 39.1505 1.45602
\(724\) 0 0
\(725\) 13.1831 0.489608
\(726\) 0 0
\(727\) 29.4815 1.09341 0.546704 0.837326i \(-0.315882\pi\)
0.546704 + 0.837326i \(0.315882\pi\)
\(728\) 0 0
\(729\) 30.0177 1.11177
\(730\) 0 0
\(731\) 31.6356 1.17008
\(732\) 0 0
\(733\) 25.5191 0.942569 0.471285 0.881981i \(-0.343791\pi\)
0.471285 + 0.881981i \(0.343791\pi\)
\(734\) 0 0
\(735\) 1.41325 0.0521287
\(736\) 0 0
\(737\) −6.56129 −0.241688
\(738\) 0 0
\(739\) 6.75547 0.248504 0.124252 0.992251i \(-0.460347\pi\)
0.124252 + 0.992251i \(0.460347\pi\)
\(740\) 0 0
\(741\) −1.02979 −0.0378303
\(742\) 0 0
\(743\) −20.8104 −0.763461 −0.381730 0.924274i \(-0.624672\pi\)
−0.381730 + 0.924274i \(0.624672\pi\)
\(744\) 0 0
\(745\) 10.7272 0.393013
\(746\) 0 0
\(747\) −6.26477 −0.229216
\(748\) 0 0
\(749\) 0.556211 0.0203235
\(750\) 0 0
\(751\) −10.7772 −0.393266 −0.196633 0.980477i \(-0.563001\pi\)
−0.196633 + 0.980477i \(0.563001\pi\)
\(752\) 0 0
\(753\) 26.2587 0.956922
\(754\) 0 0
\(755\) 10.9098 0.397050
\(756\) 0 0
\(757\) −35.3881 −1.28620 −0.643100 0.765782i \(-0.722352\pi\)
−0.643100 + 0.765782i \(0.722352\pi\)
\(758\) 0 0
\(759\) 9.08105 0.329621
\(760\) 0 0
\(761\) −26.2071 −0.950008 −0.475004 0.879984i \(-0.657553\pi\)
−0.475004 + 0.879984i \(0.657553\pi\)
\(762\) 0 0
\(763\) 12.7855 0.462865
\(764\) 0 0
\(765\) 3.24319 0.117258
\(766\) 0 0
\(767\) 5.66109 0.204410
\(768\) 0 0
\(769\) 10.2395 0.369244 0.184622 0.982810i \(-0.440894\pi\)
0.184622 + 0.982810i \(0.440894\pi\)
\(770\) 0 0
\(771\) 0.477085 0.0171818
\(772\) 0 0
\(773\) 24.1776 0.869607 0.434803 0.900525i \(-0.356818\pi\)
0.434803 + 0.900525i \(0.356818\pi\)
\(774\) 0 0
\(775\) 40.6304 1.45949
\(776\) 0 0
\(777\) −4.58321 −0.164422
\(778\) 0 0
\(779\) 2.04684 0.0733355
\(780\) 0 0
\(781\) −5.46315 −0.195487
\(782\) 0 0
\(783\) −17.6193 −0.629662
\(784\) 0 0
\(785\) −8.86756 −0.316497
\(786\) 0 0
\(787\) −38.7299 −1.38057 −0.690286 0.723537i \(-0.742515\pi\)
−0.690286 + 0.723537i \(0.742515\pi\)
\(788\) 0 0
\(789\) 1.19034 0.0423771
\(790\) 0 0
\(791\) 12.8767 0.457841
\(792\) 0 0
\(793\) −0.357389 −0.0126913
\(794\) 0 0
\(795\) 13.1728 0.467192
\(796\) 0 0
\(797\) −51.6082 −1.82806 −0.914028 0.405652i \(-0.867045\pi\)
−0.914028 + 0.405652i \(0.867045\pi\)
\(798\) 0 0
\(799\) 36.7857 1.30138
\(800\) 0 0
\(801\) −0.427106 −0.0150910
\(802\) 0 0
\(803\) 3.71538 0.131113
\(804\) 0 0
\(805\) 5.32969 0.187847
\(806\) 0 0
\(807\) −20.3983 −0.718056
\(808\) 0 0
\(809\) −33.3684 −1.17317 −0.586586 0.809887i \(-0.699528\pi\)
−0.586586 + 0.809887i \(0.699528\pi\)
\(810\) 0 0
\(811\) 32.3132 1.13467 0.567336 0.823487i \(-0.307974\pi\)
0.567336 + 0.823487i \(0.307974\pi\)
\(812\) 0 0
\(813\) 48.5464 1.70260
\(814\) 0 0
\(815\) −17.7617 −0.622164
\(816\) 0 0
\(817\) −3.49017 −0.122106
\(818\) 0 0
\(819\) −0.592010 −0.0206865
\(820\) 0 0
\(821\) −14.0297 −0.489639 −0.244819 0.969569i \(-0.578729\pi\)
−0.244819 + 0.969569i \(0.578729\pi\)
\(822\) 0 0
\(823\) −31.3080 −1.09133 −0.545663 0.838005i \(-0.683722\pi\)
−0.545663 + 0.838005i \(0.683722\pi\)
\(824\) 0 0
\(825\) −6.47175 −0.225317
\(826\) 0 0
\(827\) −0.588740 −0.0204725 −0.0102363 0.999948i \(-0.503258\pi\)
−0.0102363 + 0.999948i \(0.503258\pi\)
\(828\) 0 0
\(829\) −21.7058 −0.753874 −0.376937 0.926239i \(-0.623023\pi\)
−0.376937 + 0.926239i \(0.623023\pi\)
\(830\) 0 0
\(831\) −4.66985 −0.161995
\(832\) 0 0
\(833\) 6.01520 0.208414
\(834\) 0 0
\(835\) −2.27565 −0.0787523
\(836\) 0 0
\(837\) −54.3028 −1.87698
\(838\) 0 0
\(839\) 52.2530 1.80397 0.901987 0.431763i \(-0.142108\pi\)
0.901987 + 0.431763i \(0.142108\pi\)
\(840\) 0 0
\(841\) −19.0081 −0.655453
\(842\) 0 0
\(843\) 43.2459 1.48947
\(844\) 0 0
\(845\) −0.910737 −0.0313303
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −9.13333 −0.313455
\(850\) 0 0
\(851\) −17.2843 −0.592497
\(852\) 0 0
\(853\) 22.3651 0.765765 0.382883 0.923797i \(-0.374931\pi\)
0.382883 + 0.923797i \(0.374931\pi\)
\(854\) 0 0
\(855\) −0.357802 −0.0122366
\(856\) 0 0
\(857\) −39.8612 −1.36163 −0.680816 0.732455i \(-0.738375\pi\)
−0.680816 + 0.732455i \(0.738375\pi\)
\(858\) 0 0
\(859\) −10.8605 −0.370556 −0.185278 0.982686i \(-0.559319\pi\)
−0.185278 + 0.982686i \(0.559319\pi\)
\(860\) 0 0
\(861\) −4.78618 −0.163113
\(862\) 0 0
\(863\) −44.9094 −1.52873 −0.764367 0.644782i \(-0.776948\pi\)
−0.764367 + 0.644782i \(0.776948\pi\)
\(864\) 0 0
\(865\) 1.81272 0.0616343
\(866\) 0 0
\(867\) −29.7671 −1.01094
\(868\) 0 0
\(869\) −1.33520 −0.0452935
\(870\) 0 0
\(871\) −6.56129 −0.222321
\(872\) 0 0
\(873\) −2.71789 −0.0919867
\(874\) 0 0
\(875\) −8.35196 −0.282348
\(876\) 0 0
\(877\) −0.248085 −0.00837725 −0.00418862 0.999991i \(-0.501333\pi\)
−0.00418862 + 0.999991i \(0.501333\pi\)
\(878\) 0 0
\(879\) 6.08193 0.205139
\(880\) 0 0
\(881\) 12.4635 0.419907 0.209953 0.977711i \(-0.432669\pi\)
0.209953 + 0.977711i \(0.432669\pi\)
\(882\) 0 0
\(883\) 17.0192 0.572742 0.286371 0.958119i \(-0.407551\pi\)
0.286371 + 0.958119i \(0.407551\pi\)
\(884\) 0 0
\(885\) −8.00055 −0.268936
\(886\) 0 0
\(887\) −9.58989 −0.321997 −0.160998 0.986955i \(-0.551471\pi\)
−0.160998 + 0.986955i \(0.551471\pi\)
\(888\) 0 0
\(889\) 1.08433 0.0363673
\(890\) 0 0
\(891\) 6.87350 0.230271
\(892\) 0 0
\(893\) −4.05836 −0.135808
\(894\) 0 0
\(895\) −0.196198 −0.00655818
\(896\) 0 0
\(897\) 9.08105 0.303208
\(898\) 0 0
\(899\) 30.7950 1.02707
\(900\) 0 0
\(901\) 56.0672 1.86787
\(902\) 0 0
\(903\) 8.16118 0.271587
\(904\) 0 0
\(905\) 16.0248 0.532684
\(906\) 0 0
\(907\) −54.0186 −1.79366 −0.896830 0.442376i \(-0.854136\pi\)
−0.896830 + 0.442376i \(0.854136\pi\)
\(908\) 0 0
\(909\) −11.6939 −0.387861
\(910\) 0 0
\(911\) −5.85266 −0.193907 −0.0969536 0.995289i \(-0.530910\pi\)
−0.0969536 + 0.995289i \(0.530910\pi\)
\(912\) 0 0
\(913\) −10.5822 −0.350220
\(914\) 0 0
\(915\) 0.505082 0.0166975
\(916\) 0 0
\(917\) −19.7048 −0.650710
\(918\) 0 0
\(919\) 29.1772 0.962466 0.481233 0.876593i \(-0.340189\pi\)
0.481233 + 0.876593i \(0.340189\pi\)
\(920\) 0 0
\(921\) 12.9836 0.427823
\(922\) 0 0
\(923\) −5.46315 −0.179822
\(924\) 0 0
\(925\) 12.3179 0.405010
\(926\) 0 0
\(927\) 1.92684 0.0632859
\(928\) 0 0
\(929\) −27.8494 −0.913711 −0.456855 0.889541i \(-0.651024\pi\)
−0.456855 + 0.889541i \(0.651024\pi\)
\(930\) 0 0
\(931\) −0.663623 −0.0217494
\(932\) 0 0
\(933\) −15.3644 −0.503009
\(934\) 0 0
\(935\) 5.47826 0.179158
\(936\) 0 0
\(937\) 37.3007 1.21856 0.609280 0.792955i \(-0.291458\pi\)
0.609280 + 0.792955i \(0.291458\pi\)
\(938\) 0 0
\(939\) −23.5126 −0.767304
\(940\) 0 0
\(941\) 39.6822 1.29360 0.646801 0.762659i \(-0.276106\pi\)
0.646801 + 0.762659i \(0.276106\pi\)
\(942\) 0 0
\(943\) −18.0497 −0.587780
\(944\) 0 0
\(945\) 5.07642 0.165136
\(946\) 0 0
\(947\) 60.2975 1.95940 0.979702 0.200458i \(-0.0642429\pi\)
0.979702 + 0.200458i \(0.0642429\pi\)
\(948\) 0 0
\(949\) 3.71538 0.120606
\(950\) 0 0
\(951\) −13.2023 −0.428115
\(952\) 0 0
\(953\) 4.91672 0.159268 0.0796340 0.996824i \(-0.474625\pi\)
0.0796340 + 0.996824i \(0.474625\pi\)
\(954\) 0 0
\(955\) 7.71085 0.249517
\(956\) 0 0
\(957\) −4.90513 −0.158560
\(958\) 0 0
\(959\) 7.21187 0.232884
\(960\) 0 0
\(961\) 63.9105 2.06163
\(962\) 0 0
\(963\) 0.329282 0.0106110
\(964\) 0 0
\(965\) 3.20695 0.103236
\(966\) 0 0
\(967\) −5.83665 −0.187694 −0.0938470 0.995587i \(-0.529916\pi\)
−0.0938470 + 0.995587i \(0.529916\pi\)
\(968\) 0 0
\(969\) 6.19440 0.198993
\(970\) 0 0
\(971\) 27.4939 0.882320 0.441160 0.897428i \(-0.354567\pi\)
0.441160 + 0.897428i \(0.354567\pi\)
\(972\) 0 0
\(973\) −2.26144 −0.0724983
\(974\) 0 0
\(975\) −6.47175 −0.207262
\(976\) 0 0
\(977\) −18.8741 −0.603835 −0.301918 0.953334i \(-0.597627\pi\)
−0.301918 + 0.953334i \(0.597627\pi\)
\(978\) 0 0
\(979\) −0.721451 −0.0230577
\(980\) 0 0
\(981\) 7.56912 0.241664
\(982\) 0 0
\(983\) 14.3979 0.459220 0.229610 0.973283i \(-0.426255\pi\)
0.229610 + 0.973283i \(0.426255\pi\)
\(984\) 0 0
\(985\) 14.7227 0.469103
\(986\) 0 0
\(987\) 9.48978 0.302063
\(988\) 0 0
\(989\) 30.7776 0.978670
\(990\) 0 0
\(991\) 5.77395 0.183415 0.0917077 0.995786i \(-0.470767\pi\)
0.0917077 + 0.995786i \(0.470767\pi\)
\(992\) 0 0
\(993\) 40.8204 1.29540
\(994\) 0 0
\(995\) 3.49408 0.110770
\(996\) 0 0
\(997\) −41.5886 −1.31713 −0.658563 0.752526i \(-0.728835\pi\)
−0.658563 + 0.752526i \(0.728835\pi\)
\(998\) 0 0
\(999\) −16.4629 −0.520864
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 \(a_p\))