Properties

Label 8004.2.a.j.1.3
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.45101\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-2.45101 q^{5}\) \(+3.23607 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-2.45101 q^{5}\) \(+3.23607 q^{7}\) \(+1.00000 q^{9}\) \(+0.0433085 q^{11}\) \(+3.92153 q^{13}\) \(-2.45101 q^{15}\) \(-6.01799 q^{17}\) \(-4.13344 q^{19}\) \(+3.23607 q^{21}\) \(+1.00000 q^{23}\) \(+1.00745 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+2.00117 q^{31}\) \(+0.0433085 q^{33}\) \(-7.93163 q^{35}\) \(+3.70187 q^{37}\) \(+3.92153 q^{39}\) \(+9.70980 q^{41}\) \(+9.70508 q^{43}\) \(-2.45101 q^{45}\) \(-2.20139 q^{47}\) \(+3.47213 q^{49}\) \(-6.01799 q^{51}\) \(-8.20613 q^{53}\) \(-0.106150 q^{55}\) \(-4.13344 q^{57}\) \(+11.1275 q^{59}\) \(+4.07501 q^{61}\) \(+3.23607 q^{63}\) \(-9.61171 q^{65}\) \(+0.00749010 q^{67}\) \(+1.00000 q^{69}\) \(+9.37725 q^{71}\) \(-3.48676 q^{73}\) \(+1.00745 q^{75}\) \(+0.140149 q^{77}\) \(+4.80589 q^{79}\) \(+1.00000 q^{81}\) \(-14.3903 q^{83}\) \(+14.7501 q^{85}\) \(-1.00000 q^{87}\) \(+2.96492 q^{89}\) \(+12.6903 q^{91}\) \(+2.00117 q^{93}\) \(+10.1311 q^{95}\) \(+3.26962 q^{97}\) \(+0.0433085 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −2.45101 −1.09612 −0.548062 0.836437i \(-0.684634\pi\)
−0.548062 + 0.836437i \(0.684634\pi\)
\(6\) 0 0
\(7\) 3.23607 1.22312 0.611559 0.791199i \(-0.290543\pi\)
0.611559 + 0.791199i \(0.290543\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.0433085 0.0130580 0.00652901 0.999979i \(-0.497922\pi\)
0.00652901 + 0.999979i \(0.497922\pi\)
\(12\) 0 0
\(13\) 3.92153 1.08764 0.543818 0.839203i \(-0.316978\pi\)
0.543818 + 0.839203i \(0.316978\pi\)
\(14\) 0 0
\(15\) −2.45101 −0.632848
\(16\) 0 0
\(17\) −6.01799 −1.45958 −0.729788 0.683674i \(-0.760381\pi\)
−0.729788 + 0.683674i \(0.760381\pi\)
\(18\) 0 0
\(19\) −4.13344 −0.948275 −0.474138 0.880451i \(-0.657240\pi\)
−0.474138 + 0.880451i \(0.657240\pi\)
\(20\) 0 0
\(21\) 3.23607 0.706168
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00745 0.201489
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 2.00117 0.359421 0.179711 0.983720i \(-0.442484\pi\)
0.179711 + 0.983720i \(0.442484\pi\)
\(32\) 0 0
\(33\) 0.0433085 0.00753905
\(34\) 0 0
\(35\) −7.93163 −1.34069
\(36\) 0 0
\(37\) 3.70187 0.608583 0.304291 0.952579i \(-0.401580\pi\)
0.304291 + 0.952579i \(0.401580\pi\)
\(38\) 0 0
\(39\) 3.92153 0.627947
\(40\) 0 0
\(41\) 9.70980 1.51642 0.758208 0.652013i \(-0.226075\pi\)
0.758208 + 0.652013i \(0.226075\pi\)
\(42\) 0 0
\(43\) 9.70508 1.48001 0.740005 0.672601i \(-0.234823\pi\)
0.740005 + 0.672601i \(0.234823\pi\)
\(44\) 0 0
\(45\) −2.45101 −0.365375
\(46\) 0 0
\(47\) −2.20139 −0.321106 −0.160553 0.987027i \(-0.551328\pi\)
−0.160553 + 0.987027i \(0.551328\pi\)
\(48\) 0 0
\(49\) 3.47213 0.496018
\(50\) 0 0
\(51\) −6.01799 −0.842687
\(52\) 0 0
\(53\) −8.20613 −1.12720 −0.563600 0.826048i \(-0.690584\pi\)
−0.563600 + 0.826048i \(0.690584\pi\)
\(54\) 0 0
\(55\) −0.106150 −0.0143132
\(56\) 0 0
\(57\) −4.13344 −0.547487
\(58\) 0 0
\(59\) 11.1275 1.44868 0.724339 0.689444i \(-0.242145\pi\)
0.724339 + 0.689444i \(0.242145\pi\)
\(60\) 0 0
\(61\) 4.07501 0.521751 0.260876 0.965372i \(-0.415989\pi\)
0.260876 + 0.965372i \(0.415989\pi\)
\(62\) 0 0
\(63\) 3.23607 0.407706
\(64\) 0 0
\(65\) −9.61171 −1.19219
\(66\) 0 0
\(67\) 0.00749010 0.000915062 0 0.000457531 1.00000i \(-0.499854\pi\)
0.000457531 1.00000i \(0.499854\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 9.37725 1.11287 0.556437 0.830889i \(-0.312168\pi\)
0.556437 + 0.830889i \(0.312168\pi\)
\(72\) 0 0
\(73\) −3.48676 −0.408095 −0.204047 0.978961i \(-0.565410\pi\)
−0.204047 + 0.978961i \(0.565410\pi\)
\(74\) 0 0
\(75\) 1.00745 0.116330
\(76\) 0 0
\(77\) 0.140149 0.0159715
\(78\) 0 0
\(79\) 4.80589 0.540705 0.270353 0.962761i \(-0.412860\pi\)
0.270353 + 0.962761i \(0.412860\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.3903 −1.57954 −0.789771 0.613402i \(-0.789801\pi\)
−0.789771 + 0.613402i \(0.789801\pi\)
\(84\) 0 0
\(85\) 14.7501 1.59988
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 2.96492 0.314281 0.157141 0.987576i \(-0.449772\pi\)
0.157141 + 0.987576i \(0.449772\pi\)
\(90\) 0 0
\(91\) 12.6903 1.33031
\(92\) 0 0
\(93\) 2.00117 0.207512
\(94\) 0 0
\(95\) 10.1311 1.03943
\(96\) 0 0
\(97\) 3.26962 0.331979 0.165990 0.986127i \(-0.446918\pi\)
0.165990 + 0.986127i \(0.446918\pi\)
\(98\) 0 0
\(99\) 0.0433085 0.00435267
\(100\) 0 0
\(101\) 12.7449 1.26816 0.634082 0.773266i \(-0.281378\pi\)
0.634082 + 0.773266i \(0.281378\pi\)
\(102\) 0 0
\(103\) −4.23760 −0.417544 −0.208772 0.977964i \(-0.566947\pi\)
−0.208772 + 0.977964i \(0.566947\pi\)
\(104\) 0 0
\(105\) −7.93163 −0.774048
\(106\) 0 0
\(107\) −12.6453 −1.22247 −0.611236 0.791448i \(-0.709327\pi\)
−0.611236 + 0.791448i \(0.709327\pi\)
\(108\) 0 0
\(109\) 11.3055 1.08287 0.541433 0.840744i \(-0.317882\pi\)
0.541433 + 0.840744i \(0.317882\pi\)
\(110\) 0 0
\(111\) 3.70187 0.351366
\(112\) 0 0
\(113\) 2.48791 0.234042 0.117021 0.993129i \(-0.462665\pi\)
0.117021 + 0.993129i \(0.462665\pi\)
\(114\) 0 0
\(115\) −2.45101 −0.228558
\(116\) 0 0
\(117\) 3.92153 0.362546
\(118\) 0 0
\(119\) −19.4746 −1.78523
\(120\) 0 0
\(121\) −10.9981 −0.999829
\(122\) 0 0
\(123\) 9.70980 0.875503
\(124\) 0 0
\(125\) 9.78578 0.875267
\(126\) 0 0
\(127\) 14.5282 1.28917 0.644586 0.764532i \(-0.277030\pi\)
0.644586 + 0.764532i \(0.277030\pi\)
\(128\) 0 0
\(129\) 9.70508 0.854484
\(130\) 0 0
\(131\) −5.41017 −0.472688 −0.236344 0.971669i \(-0.575949\pi\)
−0.236344 + 0.971669i \(0.575949\pi\)
\(132\) 0 0
\(133\) −13.3761 −1.15985
\(134\) 0 0
\(135\) −2.45101 −0.210949
\(136\) 0 0
\(137\) 1.81125 0.154745 0.0773727 0.997002i \(-0.475347\pi\)
0.0773727 + 0.997002i \(0.475347\pi\)
\(138\) 0 0
\(139\) 15.7711 1.33769 0.668844 0.743403i \(-0.266789\pi\)
0.668844 + 0.743403i \(0.266789\pi\)
\(140\) 0 0
\(141\) −2.20139 −0.185390
\(142\) 0 0
\(143\) 0.169836 0.0142024
\(144\) 0 0
\(145\) 2.45101 0.203545
\(146\) 0 0
\(147\) 3.47213 0.286376
\(148\) 0 0
\(149\) 19.6325 1.60836 0.804179 0.594387i \(-0.202605\pi\)
0.804179 + 0.594387i \(0.202605\pi\)
\(150\) 0 0
\(151\) 17.8481 1.45245 0.726227 0.687455i \(-0.241272\pi\)
0.726227 + 0.687455i \(0.241272\pi\)
\(152\) 0 0
\(153\) −6.01799 −0.486525
\(154\) 0 0
\(155\) −4.90489 −0.393970
\(156\) 0 0
\(157\) −9.30848 −0.742898 −0.371449 0.928453i \(-0.621139\pi\)
−0.371449 + 0.928453i \(0.621139\pi\)
\(158\) 0 0
\(159\) −8.20613 −0.650789
\(160\) 0 0
\(161\) 3.23607 0.255038
\(162\) 0 0
\(163\) 2.99734 0.234770 0.117385 0.993086i \(-0.462549\pi\)
0.117385 + 0.993086i \(0.462549\pi\)
\(164\) 0 0
\(165\) −0.106150 −0.00826374
\(166\) 0 0
\(167\) −0.321484 −0.0248771 −0.0124386 0.999923i \(-0.503959\pi\)
−0.0124386 + 0.999923i \(0.503959\pi\)
\(168\) 0 0
\(169\) 2.37840 0.182954
\(170\) 0 0
\(171\) −4.13344 −0.316092
\(172\) 0 0
\(173\) −23.6090 −1.79496 −0.897479 0.441058i \(-0.854603\pi\)
−0.897479 + 0.441058i \(0.854603\pi\)
\(174\) 0 0
\(175\) 3.26017 0.246445
\(176\) 0 0
\(177\) 11.1275 0.836394
\(178\) 0 0
\(179\) −7.13868 −0.533570 −0.266785 0.963756i \(-0.585961\pi\)
−0.266785 + 0.963756i \(0.585961\pi\)
\(180\) 0 0
\(181\) 3.12027 0.231928 0.115964 0.993253i \(-0.463004\pi\)
0.115964 + 0.993253i \(0.463004\pi\)
\(182\) 0 0
\(183\) 4.07501 0.301233
\(184\) 0 0
\(185\) −9.07331 −0.667083
\(186\) 0 0
\(187\) −0.260630 −0.0190592
\(188\) 0 0
\(189\) 3.23607 0.235389
\(190\) 0 0
\(191\) −14.1136 −1.02122 −0.510611 0.859812i \(-0.670581\pi\)
−0.510611 + 0.859812i \(0.670581\pi\)
\(192\) 0 0
\(193\) −16.7712 −1.20722 −0.603608 0.797281i \(-0.706271\pi\)
−0.603608 + 0.797281i \(0.706271\pi\)
\(194\) 0 0
\(195\) −9.61171 −0.688309
\(196\) 0 0
\(197\) 10.6105 0.755968 0.377984 0.925812i \(-0.376617\pi\)
0.377984 + 0.925812i \(0.376617\pi\)
\(198\) 0 0
\(199\) 16.3722 1.16059 0.580296 0.814405i \(-0.302937\pi\)
0.580296 + 0.814405i \(0.302937\pi\)
\(200\) 0 0
\(201\) 0.00749010 0.000528311 0
\(202\) 0 0
\(203\) −3.23607 −0.227127
\(204\) 0 0
\(205\) −23.7988 −1.66218
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −0.179013 −0.0123826
\(210\) 0 0
\(211\) 15.8071 1.08820 0.544102 0.839019i \(-0.316871\pi\)
0.544102 + 0.839019i \(0.316871\pi\)
\(212\) 0 0
\(213\) 9.37725 0.642519
\(214\) 0 0
\(215\) −23.7872 −1.62228
\(216\) 0 0
\(217\) 6.47593 0.439614
\(218\) 0 0
\(219\) −3.48676 −0.235614
\(220\) 0 0
\(221\) −23.5997 −1.58749
\(222\) 0 0
\(223\) 6.72822 0.450555 0.225277 0.974295i \(-0.427671\pi\)
0.225277 + 0.974295i \(0.427671\pi\)
\(224\) 0 0
\(225\) 1.00745 0.0671632
\(226\) 0 0
\(227\) 5.94100 0.394318 0.197159 0.980372i \(-0.436828\pi\)
0.197159 + 0.980372i \(0.436828\pi\)
\(228\) 0 0
\(229\) 1.95543 0.129219 0.0646094 0.997911i \(-0.479420\pi\)
0.0646094 + 0.997911i \(0.479420\pi\)
\(230\) 0 0
\(231\) 0.140149 0.00922115
\(232\) 0 0
\(233\) 3.50808 0.229822 0.114911 0.993376i \(-0.463342\pi\)
0.114911 + 0.993376i \(0.463342\pi\)
\(234\) 0 0
\(235\) 5.39563 0.351972
\(236\) 0 0
\(237\) 4.80589 0.312176
\(238\) 0 0
\(239\) 18.3546 1.18726 0.593632 0.804737i \(-0.297694\pi\)
0.593632 + 0.804737i \(0.297694\pi\)
\(240\) 0 0
\(241\) −22.4205 −1.44423 −0.722115 0.691773i \(-0.756830\pi\)
−0.722115 + 0.691773i \(0.756830\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −8.51022 −0.543698
\(246\) 0 0
\(247\) −16.2094 −1.03138
\(248\) 0 0
\(249\) −14.3903 −0.911949
\(250\) 0 0
\(251\) 26.2027 1.65390 0.826949 0.562276i \(-0.190074\pi\)
0.826949 + 0.562276i \(0.190074\pi\)
\(252\) 0 0
\(253\) 0.0433085 0.00272278
\(254\) 0 0
\(255\) 14.7501 0.923690
\(256\) 0 0
\(257\) 8.42715 0.525671 0.262836 0.964841i \(-0.415342\pi\)
0.262836 + 0.964841i \(0.415342\pi\)
\(258\) 0 0
\(259\) 11.9795 0.744369
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 4.14464 0.255570 0.127785 0.991802i \(-0.459213\pi\)
0.127785 + 0.991802i \(0.459213\pi\)
\(264\) 0 0
\(265\) 20.1133 1.23555
\(266\) 0 0
\(267\) 2.96492 0.181450
\(268\) 0 0
\(269\) −26.8824 −1.63905 −0.819526 0.573043i \(-0.805763\pi\)
−0.819526 + 0.573043i \(0.805763\pi\)
\(270\) 0 0
\(271\) 2.17448 0.132090 0.0660452 0.997817i \(-0.478962\pi\)
0.0660452 + 0.997817i \(0.478962\pi\)
\(272\) 0 0
\(273\) 12.6903 0.768054
\(274\) 0 0
\(275\) 0.0436311 0.00263105
\(276\) 0 0
\(277\) 8.82094 0.529999 0.265000 0.964249i \(-0.414628\pi\)
0.265000 + 0.964249i \(0.414628\pi\)
\(278\) 0 0
\(279\) 2.00117 0.119807
\(280\) 0 0
\(281\) −12.1754 −0.726325 −0.363163 0.931726i \(-0.618303\pi\)
−0.363163 + 0.931726i \(0.618303\pi\)
\(282\) 0 0
\(283\) 10.7446 0.638699 0.319350 0.947637i \(-0.396536\pi\)
0.319350 + 0.947637i \(0.396536\pi\)
\(284\) 0 0
\(285\) 10.1311 0.600114
\(286\) 0 0
\(287\) 31.4216 1.85476
\(288\) 0 0
\(289\) 19.2162 1.13036
\(290\) 0 0
\(291\) 3.26962 0.191668
\(292\) 0 0
\(293\) −8.55893 −0.500018 −0.250009 0.968243i \(-0.580434\pi\)
−0.250009 + 0.968243i \(0.580434\pi\)
\(294\) 0 0
\(295\) −27.2736 −1.58793
\(296\) 0 0
\(297\) 0.0433085 0.00251302
\(298\) 0 0
\(299\) 3.92153 0.226788
\(300\) 0 0
\(301\) 31.4063 1.81023
\(302\) 0 0
\(303\) 12.7449 0.732175
\(304\) 0 0
\(305\) −9.98788 −0.571904
\(306\) 0 0
\(307\) 11.0895 0.632910 0.316455 0.948607i \(-0.397507\pi\)
0.316455 + 0.948607i \(0.397507\pi\)
\(308\) 0 0
\(309\) −4.23760 −0.241069
\(310\) 0 0
\(311\) −23.2362 −1.31760 −0.658802 0.752316i \(-0.728936\pi\)
−0.658802 + 0.752316i \(0.728936\pi\)
\(312\) 0 0
\(313\) −27.0018 −1.52623 −0.763117 0.646261i \(-0.776332\pi\)
−0.763117 + 0.646261i \(0.776332\pi\)
\(314\) 0 0
\(315\) −7.93163 −0.446897
\(316\) 0 0
\(317\) 3.56947 0.200481 0.100241 0.994963i \(-0.468039\pi\)
0.100241 + 0.994963i \(0.468039\pi\)
\(318\) 0 0
\(319\) −0.0433085 −0.00242481
\(320\) 0 0
\(321\) −12.6453 −0.705794
\(322\) 0 0
\(323\) 24.8750 1.38408
\(324\) 0 0
\(325\) 3.95073 0.219147
\(326\) 0 0
\(327\) 11.3055 0.625194
\(328\) 0 0
\(329\) −7.12385 −0.392750
\(330\) 0 0
\(331\) 26.4725 1.45506 0.727530 0.686076i \(-0.240668\pi\)
0.727530 + 0.686076i \(0.240668\pi\)
\(332\) 0 0
\(333\) 3.70187 0.202861
\(334\) 0 0
\(335\) −0.0183583 −0.00100302
\(336\) 0 0
\(337\) 5.92885 0.322965 0.161482 0.986876i \(-0.448372\pi\)
0.161482 + 0.986876i \(0.448372\pi\)
\(338\) 0 0
\(339\) 2.48791 0.135124
\(340\) 0 0
\(341\) 0.0866678 0.00469333
\(342\) 0 0
\(343\) −11.4164 −0.616429
\(344\) 0 0
\(345\) −2.45101 −0.131958
\(346\) 0 0
\(347\) 26.8239 1.43998 0.719990 0.693984i \(-0.244146\pi\)
0.719990 + 0.693984i \(0.244146\pi\)
\(348\) 0 0
\(349\) 15.0061 0.803258 0.401629 0.915802i \(-0.368444\pi\)
0.401629 + 0.915802i \(0.368444\pi\)
\(350\) 0 0
\(351\) 3.92153 0.209316
\(352\) 0 0
\(353\) −1.89223 −0.100713 −0.0503567 0.998731i \(-0.516036\pi\)
−0.0503567 + 0.998731i \(0.516036\pi\)
\(354\) 0 0
\(355\) −22.9837 −1.21985
\(356\) 0 0
\(357\) −19.4746 −1.03071
\(358\) 0 0
\(359\) −3.78277 −0.199647 −0.0998234 0.995005i \(-0.531828\pi\)
−0.0998234 + 0.995005i \(0.531828\pi\)
\(360\) 0 0
\(361\) −1.91471 −0.100774
\(362\) 0 0
\(363\) −10.9981 −0.577252
\(364\) 0 0
\(365\) 8.54609 0.447323
\(366\) 0 0
\(367\) 15.2247 0.794724 0.397362 0.917662i \(-0.369926\pi\)
0.397362 + 0.917662i \(0.369926\pi\)
\(368\) 0 0
\(369\) 9.70980 0.505472
\(370\) 0 0
\(371\) −26.5556 −1.37870
\(372\) 0 0
\(373\) 2.64921 0.137171 0.0685854 0.997645i \(-0.478151\pi\)
0.0685854 + 0.997645i \(0.478151\pi\)
\(374\) 0 0
\(375\) 9.78578 0.505336
\(376\) 0 0
\(377\) −3.92153 −0.201969
\(378\) 0 0
\(379\) 23.7427 1.21958 0.609790 0.792563i \(-0.291254\pi\)
0.609790 + 0.792563i \(0.291254\pi\)
\(380\) 0 0
\(381\) 14.5282 0.744304
\(382\) 0 0
\(383\) 21.9829 1.12328 0.561638 0.827383i \(-0.310172\pi\)
0.561638 + 0.827383i \(0.310172\pi\)
\(384\) 0 0
\(385\) −0.343507 −0.0175068
\(386\) 0 0
\(387\) 9.70508 0.493337
\(388\) 0 0
\(389\) −21.3962 −1.08483 −0.542416 0.840110i \(-0.682490\pi\)
−0.542416 + 0.840110i \(0.682490\pi\)
\(390\) 0 0
\(391\) −6.01799 −0.304343
\(392\) 0 0
\(393\) −5.41017 −0.272907
\(394\) 0 0
\(395\) −11.7793 −0.592680
\(396\) 0 0
\(397\) 22.2187 1.11512 0.557561 0.830136i \(-0.311737\pi\)
0.557561 + 0.830136i \(0.311737\pi\)
\(398\) 0 0
\(399\) −13.3761 −0.669641
\(400\) 0 0
\(401\) 13.5530 0.676804 0.338402 0.941002i \(-0.390114\pi\)
0.338402 + 0.941002i \(0.390114\pi\)
\(402\) 0 0
\(403\) 7.84766 0.390920
\(404\) 0 0
\(405\) −2.45101 −0.121792
\(406\) 0 0
\(407\) 0.160322 0.00794689
\(408\) 0 0
\(409\) 27.7829 1.37378 0.686888 0.726763i \(-0.258976\pi\)
0.686888 + 0.726763i \(0.258976\pi\)
\(410\) 0 0
\(411\) 1.81125 0.0893423
\(412\) 0 0
\(413\) 36.0093 1.77190
\(414\) 0 0
\(415\) 35.2708 1.73137
\(416\) 0 0
\(417\) 15.7711 0.772315
\(418\) 0 0
\(419\) 5.04791 0.246606 0.123303 0.992369i \(-0.460651\pi\)
0.123303 + 0.992369i \(0.460651\pi\)
\(420\) 0 0
\(421\) −22.9103 −1.11658 −0.558289 0.829646i \(-0.688542\pi\)
−0.558289 + 0.829646i \(0.688542\pi\)
\(422\) 0 0
\(423\) −2.20139 −0.107035
\(424\) 0 0
\(425\) −6.06280 −0.294089
\(426\) 0 0
\(427\) 13.1870 0.638163
\(428\) 0 0
\(429\) 0.169836 0.00819975
\(430\) 0 0
\(431\) −3.95827 −0.190663 −0.0953315 0.995446i \(-0.530391\pi\)
−0.0953315 + 0.995446i \(0.530391\pi\)
\(432\) 0 0
\(433\) −11.3630 −0.546073 −0.273037 0.962004i \(-0.588028\pi\)
−0.273037 + 0.962004i \(0.588028\pi\)
\(434\) 0 0
\(435\) 2.45101 0.117517
\(436\) 0 0
\(437\) −4.13344 −0.197729
\(438\) 0 0
\(439\) −2.41117 −0.115079 −0.0575394 0.998343i \(-0.518325\pi\)
−0.0575394 + 0.998343i \(0.518325\pi\)
\(440\) 0 0
\(441\) 3.47213 0.165339
\(442\) 0 0
\(443\) 1.17519 0.0558349 0.0279174 0.999610i \(-0.491112\pi\)
0.0279174 + 0.999610i \(0.491112\pi\)
\(444\) 0 0
\(445\) −7.26705 −0.344491
\(446\) 0 0
\(447\) 19.6325 0.928586
\(448\) 0 0
\(449\) 24.5786 1.15993 0.579967 0.814640i \(-0.303065\pi\)
0.579967 + 0.814640i \(0.303065\pi\)
\(450\) 0 0
\(451\) 0.420517 0.0198014
\(452\) 0 0
\(453\) 17.8481 0.838575
\(454\) 0 0
\(455\) −31.1041 −1.45818
\(456\) 0 0
\(457\) 5.45575 0.255209 0.127605 0.991825i \(-0.459271\pi\)
0.127605 + 0.991825i \(0.459271\pi\)
\(458\) 0 0
\(459\) −6.01799 −0.280896
\(460\) 0 0
\(461\) 18.9263 0.881487 0.440744 0.897633i \(-0.354715\pi\)
0.440744 + 0.897633i \(0.354715\pi\)
\(462\) 0 0
\(463\) −0.985702 −0.0458094 −0.0229047 0.999738i \(-0.507291\pi\)
−0.0229047 + 0.999738i \(0.507291\pi\)
\(464\) 0 0
\(465\) −4.90489 −0.227459
\(466\) 0 0
\(467\) 9.85204 0.455898 0.227949 0.973673i \(-0.426798\pi\)
0.227949 + 0.973673i \(0.426798\pi\)
\(468\) 0 0
\(469\) 0.0242385 0.00111923
\(470\) 0 0
\(471\) −9.30848 −0.428912
\(472\) 0 0
\(473\) 0.420313 0.0193260
\(474\) 0 0
\(475\) −4.16422 −0.191067
\(476\) 0 0
\(477\) −8.20613 −0.375733
\(478\) 0 0
\(479\) −11.9225 −0.544754 −0.272377 0.962191i \(-0.587810\pi\)
−0.272377 + 0.962191i \(0.587810\pi\)
\(480\) 0 0
\(481\) 14.5170 0.661917
\(482\) 0 0
\(483\) 3.23607 0.147246
\(484\) 0 0
\(485\) −8.01386 −0.363891
\(486\) 0 0
\(487\) 5.45791 0.247322 0.123661 0.992325i \(-0.460537\pi\)
0.123661 + 0.992325i \(0.460537\pi\)
\(488\) 0 0
\(489\) 2.99734 0.135544
\(490\) 0 0
\(491\) −23.6192 −1.06592 −0.532960 0.846140i \(-0.678920\pi\)
−0.532960 + 0.846140i \(0.678920\pi\)
\(492\) 0 0
\(493\) 6.01799 0.271036
\(494\) 0 0
\(495\) −0.106150 −0.00477107
\(496\) 0 0
\(497\) 30.3454 1.36118
\(498\) 0 0
\(499\) −27.0659 −1.21164 −0.605819 0.795603i \(-0.707154\pi\)
−0.605819 + 0.795603i \(0.707154\pi\)
\(500\) 0 0
\(501\) −0.321484 −0.0143628
\(502\) 0 0
\(503\) 21.8800 0.975580 0.487790 0.872961i \(-0.337803\pi\)
0.487790 + 0.872961i \(0.337803\pi\)
\(504\) 0 0
\(505\) −31.2378 −1.39007
\(506\) 0 0
\(507\) 2.37840 0.105628
\(508\) 0 0
\(509\) 35.7019 1.58246 0.791230 0.611519i \(-0.209441\pi\)
0.791230 + 0.611519i \(0.209441\pi\)
\(510\) 0 0
\(511\) −11.2834 −0.499148
\(512\) 0 0
\(513\) −4.13344 −0.182496
\(514\) 0 0
\(515\) 10.3864 0.457680
\(516\) 0 0
\(517\) −0.0953390 −0.00419300
\(518\) 0 0
\(519\) −23.6090 −1.03632
\(520\) 0 0
\(521\) 30.9027 1.35387 0.676936 0.736042i \(-0.263307\pi\)
0.676936 + 0.736042i \(0.263307\pi\)
\(522\) 0 0
\(523\) 9.83309 0.429971 0.214985 0.976617i \(-0.431030\pi\)
0.214985 + 0.976617i \(0.431030\pi\)
\(524\) 0 0
\(525\) 3.26017 0.142285
\(526\) 0 0
\(527\) −12.0430 −0.524602
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 11.1275 0.482893
\(532\) 0 0
\(533\) 38.0773 1.64931
\(534\) 0 0
\(535\) 30.9939 1.33998
\(536\) 0 0
\(537\) −7.13868 −0.308057
\(538\) 0 0
\(539\) 0.150373 0.00647702
\(540\) 0 0
\(541\) −6.66173 −0.286410 −0.143205 0.989693i \(-0.545741\pi\)
−0.143205 + 0.989693i \(0.545741\pi\)
\(542\) 0 0
\(543\) 3.12027 0.133904
\(544\) 0 0
\(545\) −27.7098 −1.18696
\(546\) 0 0
\(547\) −32.3634 −1.38376 −0.691879 0.722013i \(-0.743217\pi\)
−0.691879 + 0.722013i \(0.743217\pi\)
\(548\) 0 0
\(549\) 4.07501 0.173917
\(550\) 0 0
\(551\) 4.13344 0.176090
\(552\) 0 0
\(553\) 15.5522 0.661346
\(554\) 0 0
\(555\) −9.07331 −0.385140
\(556\) 0 0
\(557\) 43.1353 1.82770 0.913850 0.406052i \(-0.133095\pi\)
0.913850 + 0.406052i \(0.133095\pi\)
\(558\) 0 0
\(559\) 38.0588 1.60971
\(560\) 0 0
\(561\) −0.260630 −0.0110038
\(562\) 0 0
\(563\) −19.3550 −0.815717 −0.407858 0.913045i \(-0.633724\pi\)
−0.407858 + 0.913045i \(0.633724\pi\)
\(564\) 0 0
\(565\) −6.09788 −0.256540
\(566\) 0 0
\(567\) 3.23607 0.135902
\(568\) 0 0
\(569\) 1.73354 0.0726736 0.0363368 0.999340i \(-0.488431\pi\)
0.0363368 + 0.999340i \(0.488431\pi\)
\(570\) 0 0
\(571\) 17.9638 0.751762 0.375881 0.926668i \(-0.377340\pi\)
0.375881 + 0.926668i \(0.377340\pi\)
\(572\) 0 0
\(573\) −14.1136 −0.589603
\(574\) 0 0
\(575\) 1.00745 0.0420135
\(576\) 0 0
\(577\) −30.9094 −1.28677 −0.643387 0.765541i \(-0.722471\pi\)
−0.643387 + 0.765541i \(0.722471\pi\)
\(578\) 0 0
\(579\) −16.7712 −0.696987
\(580\) 0 0
\(581\) −46.5680 −1.93197
\(582\) 0 0
\(583\) −0.355396 −0.0147190
\(584\) 0 0
\(585\) −9.61171 −0.397395
\(586\) 0 0
\(587\) −6.79515 −0.280466 −0.140233 0.990119i \(-0.544785\pi\)
−0.140233 + 0.990119i \(0.544785\pi\)
\(588\) 0 0
\(589\) −8.27172 −0.340830
\(590\) 0 0
\(591\) 10.6105 0.436459
\(592\) 0 0
\(593\) −8.95477 −0.367728 −0.183864 0.982952i \(-0.558861\pi\)
−0.183864 + 0.982952i \(0.558861\pi\)
\(594\) 0 0
\(595\) 47.7324 1.95684
\(596\) 0 0
\(597\) 16.3722 0.670069
\(598\) 0 0
\(599\) 32.8233 1.34112 0.670562 0.741854i \(-0.266053\pi\)
0.670562 + 0.741854i \(0.266053\pi\)
\(600\) 0 0
\(601\) 45.6404 1.86171 0.930855 0.365388i \(-0.119064\pi\)
0.930855 + 0.365388i \(0.119064\pi\)
\(602\) 0 0
\(603\) 0.00749010 0.000305021 0
\(604\) 0 0
\(605\) 26.9565 1.09594
\(606\) 0 0
\(607\) 27.0597 1.09832 0.549159 0.835718i \(-0.314948\pi\)
0.549159 + 0.835718i \(0.314948\pi\)
\(608\) 0 0
\(609\) −3.23607 −0.131132
\(610\) 0 0
\(611\) −8.63282 −0.349246
\(612\) 0 0
\(613\) 3.03264 0.122487 0.0612435 0.998123i \(-0.480493\pi\)
0.0612435 + 0.998123i \(0.480493\pi\)
\(614\) 0 0
\(615\) −23.7988 −0.959661
\(616\) 0 0
\(617\) 24.4944 0.986106 0.493053 0.869999i \(-0.335881\pi\)
0.493053 + 0.869999i \(0.335881\pi\)
\(618\) 0 0
\(619\) −8.27879 −0.332753 −0.166376 0.986062i \(-0.553207\pi\)
−0.166376 + 0.986062i \(0.553207\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 9.59469 0.384403
\(624\) 0 0
\(625\) −29.0223 −1.16089
\(626\) 0 0
\(627\) −0.179013 −0.00714909
\(628\) 0 0
\(629\) −22.2778 −0.888273
\(630\) 0 0
\(631\) −31.6197 −1.25876 −0.629381 0.777097i \(-0.716691\pi\)
−0.629381 + 0.777097i \(0.716691\pi\)
\(632\) 0 0
\(633\) 15.8071 0.628274
\(634\) 0 0
\(635\) −35.6088 −1.41309
\(636\) 0 0
\(637\) 13.6161 0.539488
\(638\) 0 0
\(639\) 9.37725 0.370958
\(640\) 0 0
\(641\) 10.7088 0.422971 0.211486 0.977381i \(-0.432170\pi\)
0.211486 + 0.977381i \(0.432170\pi\)
\(642\) 0 0
\(643\) −25.2129 −0.994300 −0.497150 0.867664i \(-0.665620\pi\)
−0.497150 + 0.867664i \(0.665620\pi\)
\(644\) 0 0
\(645\) −23.7872 −0.936621
\(646\) 0 0
\(647\) 22.0045 0.865085 0.432542 0.901614i \(-0.357617\pi\)
0.432542 + 0.901614i \(0.357617\pi\)
\(648\) 0 0
\(649\) 0.481916 0.0189169
\(650\) 0 0
\(651\) 6.47593 0.253812
\(652\) 0 0
\(653\) −23.3374 −0.913263 −0.456631 0.889656i \(-0.650944\pi\)
−0.456631 + 0.889656i \(0.650944\pi\)
\(654\) 0 0
\(655\) 13.2604 0.518125
\(656\) 0 0
\(657\) −3.48676 −0.136032
\(658\) 0 0
\(659\) 11.7470 0.457597 0.228799 0.973474i \(-0.426520\pi\)
0.228799 + 0.973474i \(0.426520\pi\)
\(660\) 0 0
\(661\) −13.6798 −0.532082 −0.266041 0.963962i \(-0.585716\pi\)
−0.266041 + 0.963962i \(0.585716\pi\)
\(662\) 0 0
\(663\) −23.5997 −0.916537
\(664\) 0 0
\(665\) 32.7849 1.27134
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 6.72822 0.260128
\(670\) 0 0
\(671\) 0.176483 0.00681304
\(672\) 0 0
\(673\) −22.7418 −0.876630 −0.438315 0.898821i \(-0.644425\pi\)
−0.438315 + 0.898821i \(0.644425\pi\)
\(674\) 0 0
\(675\) 1.00745 0.0387767
\(676\) 0 0
\(677\) −24.6704 −0.948161 −0.474080 0.880482i \(-0.657219\pi\)
−0.474080 + 0.880482i \(0.657219\pi\)
\(678\) 0 0
\(679\) 10.5807 0.406050
\(680\) 0 0
\(681\) 5.94100 0.227660
\(682\) 0 0
\(683\) 31.8716 1.21953 0.609767 0.792581i \(-0.291263\pi\)
0.609767 + 0.792581i \(0.291263\pi\)
\(684\) 0 0
\(685\) −4.43939 −0.169620
\(686\) 0 0
\(687\) 1.95543 0.0746045
\(688\) 0 0
\(689\) −32.1806 −1.22598
\(690\) 0 0
\(691\) −16.8968 −0.642784 −0.321392 0.946946i \(-0.604151\pi\)
−0.321392 + 0.946946i \(0.604151\pi\)
\(692\) 0 0
\(693\) 0.140149 0.00532383
\(694\) 0 0
\(695\) −38.6552 −1.46627
\(696\) 0 0
\(697\) −58.4334 −2.21332
\(698\) 0 0
\(699\) 3.50808 0.132688
\(700\) 0 0
\(701\) −36.5682 −1.38116 −0.690580 0.723256i \(-0.742645\pi\)
−0.690580 + 0.723256i \(0.742645\pi\)
\(702\) 0 0
\(703\) −15.3014 −0.577104
\(704\) 0 0
\(705\) 5.39563 0.203211
\(706\) 0 0
\(707\) 41.2433 1.55111
\(708\) 0 0
\(709\) 16.1769 0.607538 0.303769 0.952746i \(-0.401755\pi\)
0.303769 + 0.952746i \(0.401755\pi\)
\(710\) 0 0
\(711\) 4.80589 0.180235
\(712\) 0 0
\(713\) 2.00117 0.0749445
\(714\) 0 0
\(715\) −0.416269 −0.0155676
\(716\) 0 0
\(717\) 18.3546 0.685467
\(718\) 0 0
\(719\) −40.9437 −1.52694 −0.763472 0.645841i \(-0.776507\pi\)
−0.763472 + 0.645841i \(0.776507\pi\)
\(720\) 0 0
\(721\) −13.7132 −0.510705
\(722\) 0 0
\(723\) −22.4205 −0.833827
\(724\) 0 0
\(725\) −1.00745 −0.0374157
\(726\) 0 0
\(727\) −3.01933 −0.111981 −0.0559904 0.998431i \(-0.517832\pi\)
−0.0559904 + 0.998431i \(0.517832\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −58.4050 −2.16019
\(732\) 0 0
\(733\) −4.34400 −0.160449 −0.0802247 0.996777i \(-0.525564\pi\)
−0.0802247 + 0.996777i \(0.525564\pi\)
\(734\) 0 0
\(735\) −8.51022 −0.313904
\(736\) 0 0
\(737\) 0.000324386 0 1.19489e−5 0
\(738\) 0 0
\(739\) −25.6178 −0.942365 −0.471182 0.882036i \(-0.656173\pi\)
−0.471182 + 0.882036i \(0.656173\pi\)
\(740\) 0 0
\(741\) −16.2094 −0.595467
\(742\) 0 0
\(743\) −10.2924 −0.377592 −0.188796 0.982016i \(-0.560458\pi\)
−0.188796 + 0.982016i \(0.560458\pi\)
\(744\) 0 0
\(745\) −48.1195 −1.76296
\(746\) 0 0
\(747\) −14.3903 −0.526514
\(748\) 0 0
\(749\) −40.9212 −1.49523
\(750\) 0 0
\(751\) 27.1428 0.990457 0.495228 0.868763i \(-0.335084\pi\)
0.495228 + 0.868763i \(0.335084\pi\)
\(752\) 0 0
\(753\) 26.2027 0.954879
\(754\) 0 0
\(755\) −43.7458 −1.59207
\(756\) 0 0
\(757\) −24.4659 −0.889227 −0.444613 0.895723i \(-0.646659\pi\)
−0.444613 + 0.895723i \(0.646659\pi\)
\(758\) 0 0
\(759\) 0.0433085 0.00157200
\(760\) 0 0
\(761\) −19.0747 −0.691459 −0.345729 0.938334i \(-0.612369\pi\)
−0.345729 + 0.938334i \(0.612369\pi\)
\(762\) 0 0
\(763\) 36.5852 1.32447
\(764\) 0 0
\(765\) 14.7501 0.533292
\(766\) 0 0
\(767\) 43.6368 1.57564
\(768\) 0 0
\(769\) −11.9271 −0.430101 −0.215050 0.976603i \(-0.568992\pi\)
−0.215050 + 0.976603i \(0.568992\pi\)
\(770\) 0 0
\(771\) 8.42715 0.303496
\(772\) 0 0
\(773\) 4.25365 0.152993 0.0764966 0.997070i \(-0.475627\pi\)
0.0764966 + 0.997070i \(0.475627\pi\)
\(774\) 0 0
\(775\) 2.01608 0.0724196
\(776\) 0 0
\(777\) 11.9795 0.429762
\(778\) 0 0
\(779\) −40.1348 −1.43798
\(780\) 0 0
\(781\) 0.406115 0.0145319
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) 22.8152 0.814309
\(786\) 0 0
\(787\) −33.7249 −1.20216 −0.601081 0.799188i \(-0.705263\pi\)
−0.601081 + 0.799188i \(0.705263\pi\)
\(788\) 0 0
\(789\) 4.14464 0.147553
\(790\) 0 0
\(791\) 8.05103 0.286262
\(792\) 0 0
\(793\) 15.9803 0.567476
\(794\) 0 0
\(795\) 20.1133 0.713346
\(796\) 0 0
\(797\) 15.2192 0.539090 0.269545 0.962988i \(-0.413127\pi\)
0.269545 + 0.962988i \(0.413127\pi\)
\(798\) 0 0
\(799\) 13.2479 0.468678
\(800\) 0 0
\(801\) 2.96492 0.104760
\(802\) 0 0
\(803\) −0.151007 −0.00532891
\(804\) 0 0
\(805\) −7.93163 −0.279553
\(806\) 0 0
\(807\) −26.8824 −0.946307
\(808\) 0 0
\(809\) −13.6184 −0.478799 −0.239399 0.970921i \(-0.576951\pi\)
−0.239399 + 0.970921i \(0.576951\pi\)
\(810\) 0 0
\(811\) −22.8818 −0.803487 −0.401743 0.915752i \(-0.631596\pi\)
−0.401743 + 0.915752i \(0.631596\pi\)
\(812\) 0 0
\(813\) 2.17448 0.0762624
\(814\) 0 0
\(815\) −7.34651 −0.257337
\(816\) 0 0
\(817\) −40.1153 −1.40346
\(818\) 0 0
\(819\) 12.6903 0.443436
\(820\) 0 0
\(821\) −6.65639 −0.232310 −0.116155 0.993231i \(-0.537057\pi\)
−0.116155 + 0.993231i \(0.537057\pi\)
\(822\) 0 0
\(823\) −28.1354 −0.980739 −0.490369 0.871515i \(-0.663138\pi\)
−0.490369 + 0.871515i \(0.663138\pi\)
\(824\) 0 0
\(825\) 0.0436311 0.00151904
\(826\) 0 0
\(827\) 0.959061 0.0333498 0.0166749 0.999861i \(-0.494692\pi\)
0.0166749 + 0.999861i \(0.494692\pi\)
\(828\) 0 0
\(829\) 6.49176 0.225468 0.112734 0.993625i \(-0.464039\pi\)
0.112734 + 0.993625i \(0.464039\pi\)
\(830\) 0 0
\(831\) 8.82094 0.305995
\(832\) 0 0
\(833\) −20.8952 −0.723976
\(834\) 0 0
\(835\) 0.787959 0.0272685
\(836\) 0 0
\(837\) 2.00117 0.0691706
\(838\) 0 0
\(839\) −38.7495 −1.33778 −0.668890 0.743362i \(-0.733230\pi\)
−0.668890 + 0.743362i \(0.733230\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −12.1754 −0.419344
\(844\) 0 0
\(845\) −5.82948 −0.200540
\(846\) 0 0
\(847\) −35.5907 −1.22291
\(848\) 0 0
\(849\) 10.7446 0.368753
\(850\) 0 0
\(851\) 3.70187 0.126898
\(852\) 0 0
\(853\) −8.01211 −0.274329 −0.137165 0.990548i \(-0.543799\pi\)
−0.137165 + 0.990548i \(0.543799\pi\)
\(854\) 0 0
\(855\) 10.1311 0.346476
\(856\) 0 0
\(857\) −17.1595 −0.586157 −0.293078 0.956088i \(-0.594680\pi\)
−0.293078 + 0.956088i \(0.594680\pi\)
\(858\) 0 0
\(859\) 18.4425 0.629251 0.314626 0.949216i \(-0.398121\pi\)
0.314626 + 0.949216i \(0.398121\pi\)
\(860\) 0 0
\(861\) 31.4216 1.07084
\(862\) 0 0
\(863\) −56.5433 −1.92476 −0.962378 0.271713i \(-0.912410\pi\)
−0.962378 + 0.271713i \(0.912410\pi\)
\(864\) 0 0
\(865\) 57.8658 1.96750
\(866\) 0 0
\(867\) 19.2162 0.652615
\(868\) 0 0
\(869\) 0.208136 0.00706054
\(870\) 0 0
\(871\) 0.0293727 0.000995255 0
\(872\) 0 0
\(873\) 3.26962 0.110660
\(874\) 0 0
\(875\) 31.6675 1.07056
\(876\) 0 0
\(877\) 47.9689 1.61979 0.809897 0.586572i \(-0.199523\pi\)
0.809897 + 0.586572i \(0.199523\pi\)
\(878\) 0 0
\(879\) −8.55893 −0.288686
\(880\) 0 0
\(881\) 19.8070 0.667315 0.333658 0.942694i \(-0.391717\pi\)
0.333658 + 0.942694i \(0.391717\pi\)
\(882\) 0 0
\(883\) 5.11055 0.171984 0.0859918 0.996296i \(-0.472594\pi\)
0.0859918 + 0.996296i \(0.472594\pi\)
\(884\) 0 0
\(885\) −27.2736 −0.916793
\(886\) 0 0
\(887\) −36.5325 −1.22664 −0.613321 0.789834i \(-0.710167\pi\)
−0.613321 + 0.789834i \(0.710167\pi\)
\(888\) 0 0
\(889\) 47.0143 1.57681
\(890\) 0 0
\(891\) 0.0433085 0.00145089
\(892\) 0 0
\(893\) 9.09930 0.304497
\(894\) 0 0
\(895\) 17.4970 0.584860
\(896\) 0 0
\(897\) 3.92153 0.130936
\(898\) 0 0
\(899\) −2.00117 −0.0667428
\(900\) 0 0
\(901\) 49.3844 1.64523
\(902\) 0 0
\(903\) 31.4063 1.04514
\(904\) 0 0
\(905\) −7.64781 −0.254222
\(906\) 0 0
\(907\) 39.4816 1.31097 0.655483 0.755210i \(-0.272465\pi\)
0.655483 + 0.755210i \(0.272465\pi\)
\(908\) 0 0
\(909\) 12.7449 0.422721
\(910\) 0 0
\(911\) −23.5180 −0.779186 −0.389593 0.920987i \(-0.627384\pi\)
−0.389593 + 0.920987i \(0.627384\pi\)
\(912\) 0 0
\(913\) −0.623223 −0.0206257
\(914\) 0 0
\(915\) −9.98788 −0.330189
\(916\) 0 0
\(917\) −17.5077 −0.578154
\(918\) 0 0
\(919\) −48.1970 −1.58987 −0.794937 0.606692i \(-0.792496\pi\)
−0.794937 + 0.606692i \(0.792496\pi\)
\(920\) 0 0
\(921\) 11.0895 0.365411
\(922\) 0 0
\(923\) 36.7732 1.21040
\(924\) 0 0
\(925\) 3.72943 0.122623
\(926\) 0 0
\(927\) −4.23760 −0.139181
\(928\) 0 0
\(929\) 15.2944 0.501793 0.250896 0.968014i \(-0.419275\pi\)
0.250896 + 0.968014i \(0.419275\pi\)
\(930\) 0 0
\(931\) −14.3518 −0.470362
\(932\) 0 0
\(933\) −23.2362 −0.760719
\(934\) 0 0
\(935\) 0.638807 0.0208912
\(936\) 0 0
\(937\) 5.91415 0.193207 0.0966034 0.995323i \(-0.469202\pi\)
0.0966034 + 0.995323i \(0.469202\pi\)
\(938\) 0 0
\(939\) −27.0018 −0.881171
\(940\) 0 0
\(941\) 35.8328 1.16812 0.584058 0.811712i \(-0.301464\pi\)
0.584058 + 0.811712i \(0.301464\pi\)
\(942\) 0 0
\(943\) 9.70980 0.316195
\(944\) 0 0
\(945\) −7.93163 −0.258016
\(946\) 0 0
\(947\) 43.4015 1.41036 0.705180 0.709028i \(-0.250866\pi\)
0.705180 + 0.709028i \(0.250866\pi\)
\(948\) 0 0
\(949\) −13.6734 −0.443859
\(950\) 0 0
\(951\) 3.56947 0.115748
\(952\) 0 0
\(953\) 11.9380 0.386711 0.193356 0.981129i \(-0.438063\pi\)
0.193356 + 0.981129i \(0.438063\pi\)
\(954\) 0 0
\(955\) 34.5925 1.11939
\(956\) 0 0
\(957\) −0.0433085 −0.00139997
\(958\) 0 0
\(959\) 5.86132 0.189272
\(960\) 0 0
\(961\) −26.9953 −0.870816
\(962\) 0 0
\(963\) −12.6453 −0.407491
\(964\) 0 0
\(965\) 41.1064 1.32326
\(966\) 0 0
\(967\) 43.0916 1.38573 0.692866 0.721066i \(-0.256348\pi\)
0.692866 + 0.721066i \(0.256348\pi\)
\(968\) 0 0
\(969\) 24.8750 0.799099
\(970\) 0 0
\(971\) −22.6354 −0.726403 −0.363202 0.931711i \(-0.618316\pi\)
−0.363202 + 0.931711i \(0.618316\pi\)
\(972\) 0 0
\(973\) 51.0364 1.63615
\(974\) 0 0
\(975\) 3.95073 0.126525
\(976\) 0 0
\(977\) −6.76852 −0.216544 −0.108272 0.994121i \(-0.534532\pi\)
−0.108272 + 0.994121i \(0.534532\pi\)
\(978\) 0 0
\(979\) 0.128406 0.00410389
\(980\) 0 0
\(981\) 11.3055 0.360956
\(982\) 0 0
\(983\) −40.8744 −1.30369 −0.651846 0.758352i \(-0.726005\pi\)
−0.651846 + 0.758352i \(0.726005\pi\)
\(984\) 0 0
\(985\) −26.0065 −0.828636
\(986\) 0 0
\(987\) −7.12385 −0.226754
\(988\) 0 0
\(989\) 9.70508 0.308603
\(990\) 0 0
\(991\) −5.79598 −0.184115 −0.0920577 0.995754i \(-0.529344\pi\)
−0.0920577 + 0.995754i \(0.529344\pi\)
\(992\) 0 0
\(993\) 26.4725 0.840079
\(994\) 0 0
\(995\) −40.1284 −1.27215
\(996\) 0 0
\(997\) −33.8370 −1.07163 −0.535815 0.844336i \(-0.679995\pi\)
−0.535815 + 0.844336i \(0.679995\pi\)
\(998\) 0 0
\(999\) 3.70187 0.117122
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 \(a_p\))