Properties

Label 8048.2.a.v.1.10
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.49100 q^{3}\) \(-1.09730 q^{5}\) \(+0.799854 q^{7}\) \(-0.776913 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.49100 q^{3}\) \(-1.09730 q^{5}\) \(+0.799854 q^{7}\) \(-0.776913 q^{9}\) \(+0.838888 q^{11}\) \(+2.03223 q^{13}\) \(+1.63608 q^{15}\) \(-1.82317 q^{17}\) \(-4.30282 q^{19}\) \(-1.19258 q^{21}\) \(+0.747572 q^{23}\) \(-3.79593 q^{25}\) \(+5.63138 q^{27}\) \(+2.79315 q^{29}\) \(+0.0226322 q^{31}\) \(-1.25078 q^{33}\) \(-0.877680 q^{35}\) \(+1.80488 q^{37}\) \(-3.03006 q^{39}\) \(+6.90939 q^{41}\) \(+8.84694 q^{43}\) \(+0.852507 q^{45}\) \(+6.50163 q^{47}\) \(-6.36023 q^{49}\) \(+2.71835 q^{51}\) \(-8.42159 q^{53}\) \(-0.920512 q^{55}\) \(+6.41551 q^{57}\) \(+1.81714 q^{59}\) \(-8.08359 q^{61}\) \(-0.621417 q^{63}\) \(-2.22997 q^{65}\) \(-11.6490 q^{67}\) \(-1.11463 q^{69}\) \(+1.18928 q^{71}\) \(+3.90124 q^{73}\) \(+5.65974 q^{75}\) \(+0.670988 q^{77}\) \(+8.22799 q^{79}\) \(-6.06567 q^{81}\) \(+5.12022 q^{83}\) \(+2.00056 q^{85}\) \(-4.16459 q^{87}\) \(-9.57753 q^{89}\) \(+1.62549 q^{91}\) \(-0.0337447 q^{93}\) \(+4.72149 q^{95}\) \(-0.843274 q^{97}\) \(-0.651742 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.49100 −0.860831 −0.430415 0.902631i \(-0.641633\pi\)
−0.430415 + 0.902631i \(0.641633\pi\)
\(4\) 0 0
\(5\) −1.09730 −0.490728 −0.245364 0.969431i \(-0.578907\pi\)
−0.245364 + 0.969431i \(0.578907\pi\)
\(6\) 0 0
\(7\) 0.799854 0.302316 0.151158 0.988510i \(-0.451700\pi\)
0.151158 + 0.988510i \(0.451700\pi\)
\(8\) 0 0
\(9\) −0.776913 −0.258971
\(10\) 0 0
\(11\) 0.838888 0.252934 0.126467 0.991971i \(-0.459636\pi\)
0.126467 + 0.991971i \(0.459636\pi\)
\(12\) 0 0
\(13\) 2.03223 0.563640 0.281820 0.959467i \(-0.409062\pi\)
0.281820 + 0.959467i \(0.409062\pi\)
\(14\) 0 0
\(15\) 1.63608 0.422433
\(16\) 0 0
\(17\) −1.82317 −0.442183 −0.221091 0.975253i \(-0.570962\pi\)
−0.221091 + 0.975253i \(0.570962\pi\)
\(18\) 0 0
\(19\) −4.30282 −0.987134 −0.493567 0.869708i \(-0.664307\pi\)
−0.493567 + 0.869708i \(0.664307\pi\)
\(20\) 0 0
\(21\) −1.19258 −0.260243
\(22\) 0 0
\(23\) 0.747572 0.155880 0.0779398 0.996958i \(-0.475166\pi\)
0.0779398 + 0.996958i \(0.475166\pi\)
\(24\) 0 0
\(25\) −3.79593 −0.759186
\(26\) 0 0
\(27\) 5.63138 1.08376
\(28\) 0 0
\(29\) 2.79315 0.518675 0.259337 0.965787i \(-0.416496\pi\)
0.259337 + 0.965787i \(0.416496\pi\)
\(30\) 0 0
\(31\) 0.0226322 0.00406487 0.00203243 0.999998i \(-0.499353\pi\)
0.00203243 + 0.999998i \(0.499353\pi\)
\(32\) 0 0
\(33\) −1.25078 −0.217733
\(34\) 0 0
\(35\) −0.877680 −0.148355
\(36\) 0 0
\(37\) 1.80488 0.296721 0.148360 0.988933i \(-0.452600\pi\)
0.148360 + 0.988933i \(0.452600\pi\)
\(38\) 0 0
\(39\) −3.03006 −0.485198
\(40\) 0 0
\(41\) 6.90939 1.07907 0.539533 0.841965i \(-0.318601\pi\)
0.539533 + 0.841965i \(0.318601\pi\)
\(42\) 0 0
\(43\) 8.84694 1.34914 0.674572 0.738209i \(-0.264328\pi\)
0.674572 + 0.738209i \(0.264328\pi\)
\(44\) 0 0
\(45\) 0.852507 0.127084
\(46\) 0 0
\(47\) 6.50163 0.948360 0.474180 0.880428i \(-0.342745\pi\)
0.474180 + 0.880428i \(0.342745\pi\)
\(48\) 0 0
\(49\) −6.36023 −0.908605
\(50\) 0 0
\(51\) 2.71835 0.380645
\(52\) 0 0
\(53\) −8.42159 −1.15679 −0.578397 0.815755i \(-0.696321\pi\)
−0.578397 + 0.815755i \(0.696321\pi\)
\(54\) 0 0
\(55\) −0.920512 −0.124122
\(56\) 0 0
\(57\) 6.41551 0.849755
\(58\) 0 0
\(59\) 1.81714 0.236572 0.118286 0.992980i \(-0.462260\pi\)
0.118286 + 0.992980i \(0.462260\pi\)
\(60\) 0 0
\(61\) −8.08359 −1.03500 −0.517499 0.855684i \(-0.673137\pi\)
−0.517499 + 0.855684i \(0.673137\pi\)
\(62\) 0 0
\(63\) −0.621417 −0.0782911
\(64\) 0 0
\(65\) −2.22997 −0.276594
\(66\) 0 0
\(67\) −11.6490 −1.42315 −0.711577 0.702608i \(-0.752019\pi\)
−0.711577 + 0.702608i \(0.752019\pi\)
\(68\) 0 0
\(69\) −1.11463 −0.134186
\(70\) 0 0
\(71\) 1.18928 0.141142 0.0705709 0.997507i \(-0.477518\pi\)
0.0705709 + 0.997507i \(0.477518\pi\)
\(72\) 0 0
\(73\) 3.90124 0.456605 0.228303 0.973590i \(-0.426682\pi\)
0.228303 + 0.973590i \(0.426682\pi\)
\(74\) 0 0
\(75\) 5.65974 0.653531
\(76\) 0 0
\(77\) 0.670988 0.0764661
\(78\) 0 0
\(79\) 8.22799 0.925721 0.462861 0.886431i \(-0.346823\pi\)
0.462861 + 0.886431i \(0.346823\pi\)
\(80\) 0 0
\(81\) −6.06567 −0.673963
\(82\) 0 0
\(83\) 5.12022 0.562017 0.281009 0.959705i \(-0.409331\pi\)
0.281009 + 0.959705i \(0.409331\pi\)
\(84\) 0 0
\(85\) 2.00056 0.216991
\(86\) 0 0
\(87\) −4.16459 −0.446491
\(88\) 0 0
\(89\) −9.57753 −1.01522 −0.507608 0.861588i \(-0.669470\pi\)
−0.507608 + 0.861588i \(0.669470\pi\)
\(90\) 0 0
\(91\) 1.62549 0.170398
\(92\) 0 0
\(93\) −0.0337447 −0.00349916
\(94\) 0 0
\(95\) 4.72149 0.484414
\(96\) 0 0
\(97\) −0.843274 −0.0856215 −0.0428108 0.999083i \(-0.513631\pi\)
−0.0428108 + 0.999083i \(0.513631\pi\)
\(98\) 0 0
\(99\) −0.651742 −0.0655026
\(100\) 0 0
\(101\) −14.2484 −1.41777 −0.708885 0.705324i \(-0.750802\pi\)
−0.708885 + 0.705324i \(0.750802\pi\)
\(102\) 0 0
\(103\) 17.0465 1.67964 0.839822 0.542862i \(-0.182660\pi\)
0.839822 + 0.542862i \(0.182660\pi\)
\(104\) 0 0
\(105\) 1.30862 0.127709
\(106\) 0 0
\(107\) −0.481214 −0.0465207 −0.0232604 0.999729i \(-0.507405\pi\)
−0.0232604 + 0.999729i \(0.507405\pi\)
\(108\) 0 0
\(109\) 17.2858 1.65568 0.827840 0.560964i \(-0.189569\pi\)
0.827840 + 0.560964i \(0.189569\pi\)
\(110\) 0 0
\(111\) −2.69108 −0.255426
\(112\) 0 0
\(113\) −5.97071 −0.561677 −0.280839 0.959755i \(-0.590613\pi\)
−0.280839 + 0.959755i \(0.590613\pi\)
\(114\) 0 0
\(115\) −0.820311 −0.0764944
\(116\) 0 0
\(117\) −1.57887 −0.145966
\(118\) 0 0
\(119\) −1.45827 −0.133679
\(120\) 0 0
\(121\) −10.2963 −0.936024
\(122\) 0 0
\(123\) −10.3019 −0.928892
\(124\) 0 0
\(125\) 9.65178 0.863282
\(126\) 0 0
\(127\) −0.211759 −0.0187906 −0.00939528 0.999956i \(-0.502991\pi\)
−0.00939528 + 0.999956i \(0.502991\pi\)
\(128\) 0 0
\(129\) −13.1908 −1.16139
\(130\) 0 0
\(131\) −13.0638 −1.14139 −0.570696 0.821161i \(-0.693327\pi\)
−0.570696 + 0.821161i \(0.693327\pi\)
\(132\) 0 0
\(133\) −3.44163 −0.298427
\(134\) 0 0
\(135\) −6.17932 −0.531831
\(136\) 0 0
\(137\) −3.99672 −0.341463 −0.170731 0.985318i \(-0.554613\pi\)
−0.170731 + 0.985318i \(0.554613\pi\)
\(138\) 0 0
\(139\) 0.0245475 0.00208209 0.00104104 0.999999i \(-0.499669\pi\)
0.00104104 + 0.999999i \(0.499669\pi\)
\(140\) 0 0
\(141\) −9.69394 −0.816377
\(142\) 0 0
\(143\) 1.70481 0.142564
\(144\) 0 0
\(145\) −3.06493 −0.254528
\(146\) 0 0
\(147\) 9.48312 0.782155
\(148\) 0 0
\(149\) −22.5192 −1.84485 −0.922423 0.386181i \(-0.873794\pi\)
−0.922423 + 0.386181i \(0.873794\pi\)
\(150\) 0 0
\(151\) 18.9657 1.54341 0.771703 0.635983i \(-0.219405\pi\)
0.771703 + 0.635983i \(0.219405\pi\)
\(152\) 0 0
\(153\) 1.41644 0.114512
\(154\) 0 0
\(155\) −0.0248343 −0.00199474
\(156\) 0 0
\(157\) 20.2221 1.61390 0.806951 0.590619i \(-0.201116\pi\)
0.806951 + 0.590619i \(0.201116\pi\)
\(158\) 0 0
\(159\) 12.5566 0.995803
\(160\) 0 0
\(161\) 0.597949 0.0471249
\(162\) 0 0
\(163\) −2.22151 −0.174002 −0.0870011 0.996208i \(-0.527728\pi\)
−0.0870011 + 0.996208i \(0.527728\pi\)
\(164\) 0 0
\(165\) 1.37249 0.106848
\(166\) 0 0
\(167\) 17.3196 1.34023 0.670117 0.742256i \(-0.266244\pi\)
0.670117 + 0.742256i \(0.266244\pi\)
\(168\) 0 0
\(169\) −8.87003 −0.682310
\(170\) 0 0
\(171\) 3.34291 0.255639
\(172\) 0 0
\(173\) 3.64302 0.276974 0.138487 0.990364i \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(174\) 0 0
\(175\) −3.03619 −0.229514
\(176\) 0 0
\(177\) −2.70936 −0.203648
\(178\) 0 0
\(179\) 13.8085 1.03210 0.516050 0.856559i \(-0.327402\pi\)
0.516050 + 0.856559i \(0.327402\pi\)
\(180\) 0 0
\(181\) −7.95829 −0.591535 −0.295768 0.955260i \(-0.595575\pi\)
−0.295768 + 0.955260i \(0.595575\pi\)
\(182\) 0 0
\(183\) 12.0527 0.890958
\(184\) 0 0
\(185\) −1.98050 −0.145609
\(186\) 0 0
\(187\) −1.52943 −0.111843
\(188\) 0 0
\(189\) 4.50429 0.327639
\(190\) 0 0
\(191\) 4.49411 0.325182 0.162591 0.986694i \(-0.448015\pi\)
0.162591 + 0.986694i \(0.448015\pi\)
\(192\) 0 0
\(193\) 26.8118 1.92996 0.964979 0.262328i \(-0.0844903\pi\)
0.964979 + 0.262328i \(0.0844903\pi\)
\(194\) 0 0
\(195\) 3.32489 0.238100
\(196\) 0 0
\(197\) −7.67895 −0.547103 −0.273551 0.961857i \(-0.588198\pi\)
−0.273551 + 0.961857i \(0.588198\pi\)
\(198\) 0 0
\(199\) 1.27465 0.0903578 0.0451789 0.998979i \(-0.485614\pi\)
0.0451789 + 0.998979i \(0.485614\pi\)
\(200\) 0 0
\(201\) 17.3687 1.22509
\(202\) 0 0
\(203\) 2.23411 0.156804
\(204\) 0 0
\(205\) −7.58168 −0.529527
\(206\) 0 0
\(207\) −0.580798 −0.0403683
\(208\) 0 0
\(209\) −3.60958 −0.249680
\(210\) 0 0
\(211\) −16.0159 −1.10258 −0.551291 0.834313i \(-0.685865\pi\)
−0.551291 + 0.834313i \(0.685865\pi\)
\(212\) 0 0
\(213\) −1.77322 −0.121499
\(214\) 0 0
\(215\) −9.70775 −0.662063
\(216\) 0 0
\(217\) 0.0181025 0.00122888
\(218\) 0 0
\(219\) −5.81675 −0.393060
\(220\) 0 0
\(221\) −3.70510 −0.249232
\(222\) 0 0
\(223\) −20.3323 −1.36155 −0.680775 0.732492i \(-0.738357\pi\)
−0.680775 + 0.732492i \(0.738357\pi\)
\(224\) 0 0
\(225\) 2.94911 0.196607
\(226\) 0 0
\(227\) −2.56302 −0.170113 −0.0850567 0.996376i \(-0.527107\pi\)
−0.0850567 + 0.996376i \(0.527107\pi\)
\(228\) 0 0
\(229\) −10.5606 −0.697865 −0.348932 0.937148i \(-0.613456\pi\)
−0.348932 + 0.937148i \(0.613456\pi\)
\(230\) 0 0
\(231\) −1.00044 −0.0658244
\(232\) 0 0
\(233\) 19.1168 1.25238 0.626192 0.779669i \(-0.284613\pi\)
0.626192 + 0.779669i \(0.284613\pi\)
\(234\) 0 0
\(235\) −7.13424 −0.465387
\(236\) 0 0
\(237\) −12.2680 −0.796889
\(238\) 0 0
\(239\) 8.24459 0.533298 0.266649 0.963794i \(-0.414084\pi\)
0.266649 + 0.963794i \(0.414084\pi\)
\(240\) 0 0
\(241\) 8.11563 0.522774 0.261387 0.965234i \(-0.415820\pi\)
0.261387 + 0.965234i \(0.415820\pi\)
\(242\) 0 0
\(243\) −7.85023 −0.503592
\(244\) 0 0
\(245\) 6.97909 0.445878
\(246\) 0 0
\(247\) −8.74433 −0.556388
\(248\) 0 0
\(249\) −7.63426 −0.483802
\(250\) 0 0
\(251\) −3.53539 −0.223152 −0.111576 0.993756i \(-0.535590\pi\)
−0.111576 + 0.993756i \(0.535590\pi\)
\(252\) 0 0
\(253\) 0.627129 0.0394273
\(254\) 0 0
\(255\) −2.98284 −0.186793
\(256\) 0 0
\(257\) −21.3707 −1.33307 −0.666535 0.745474i \(-0.732223\pi\)
−0.666535 + 0.745474i \(0.732223\pi\)
\(258\) 0 0
\(259\) 1.44364 0.0897036
\(260\) 0 0
\(261\) −2.17003 −0.134322
\(262\) 0 0
\(263\) −2.15569 −0.132925 −0.0664627 0.997789i \(-0.521171\pi\)
−0.0664627 + 0.997789i \(0.521171\pi\)
\(264\) 0 0
\(265\) 9.24101 0.567671
\(266\) 0 0
\(267\) 14.2801 0.873929
\(268\) 0 0
\(269\) −5.55734 −0.338837 −0.169419 0.985544i \(-0.554189\pi\)
−0.169419 + 0.985544i \(0.554189\pi\)
\(270\) 0 0
\(271\) −20.2990 −1.23307 −0.616537 0.787326i \(-0.711465\pi\)
−0.616537 + 0.787326i \(0.711465\pi\)
\(272\) 0 0
\(273\) −2.42361 −0.146683
\(274\) 0 0
\(275\) −3.18436 −0.192024
\(276\) 0 0
\(277\) −24.2147 −1.45492 −0.727461 0.686149i \(-0.759300\pi\)
−0.727461 + 0.686149i \(0.759300\pi\)
\(278\) 0 0
\(279\) −0.0175833 −0.00105268
\(280\) 0 0
\(281\) 32.0352 1.91106 0.955530 0.294894i \(-0.0952842\pi\)
0.955530 + 0.294894i \(0.0952842\pi\)
\(282\) 0 0
\(283\) −24.0778 −1.43128 −0.715638 0.698472i \(-0.753864\pi\)
−0.715638 + 0.698472i \(0.753864\pi\)
\(284\) 0 0
\(285\) −7.03975 −0.416999
\(286\) 0 0
\(287\) 5.52650 0.326219
\(288\) 0 0
\(289\) −13.6761 −0.804474
\(290\) 0 0
\(291\) 1.25732 0.0737056
\(292\) 0 0
\(293\) −0.373309 −0.0218089 −0.0109045 0.999941i \(-0.503471\pi\)
−0.0109045 + 0.999941i \(0.503471\pi\)
\(294\) 0 0
\(295\) −1.99395 −0.116092
\(296\) 0 0
\(297\) 4.72410 0.274120
\(298\) 0 0
\(299\) 1.51924 0.0878599
\(300\) 0 0
\(301\) 7.07626 0.407869
\(302\) 0 0
\(303\) 21.2444 1.22046
\(304\) 0 0
\(305\) 8.87013 0.507902
\(306\) 0 0
\(307\) −28.5239 −1.62795 −0.813974 0.580901i \(-0.802700\pi\)
−0.813974 + 0.580901i \(0.802700\pi\)
\(308\) 0 0
\(309\) −25.4164 −1.44589
\(310\) 0 0
\(311\) 21.2504 1.20500 0.602500 0.798119i \(-0.294171\pi\)
0.602500 + 0.798119i \(0.294171\pi\)
\(312\) 0 0
\(313\) −14.0831 −0.796022 −0.398011 0.917381i \(-0.630299\pi\)
−0.398011 + 0.917381i \(0.630299\pi\)
\(314\) 0 0
\(315\) 0.681881 0.0384196
\(316\) 0 0
\(317\) −27.0436 −1.51892 −0.759459 0.650555i \(-0.774536\pi\)
−0.759459 + 0.650555i \(0.774536\pi\)
\(318\) 0 0
\(319\) 2.34314 0.131191
\(320\) 0 0
\(321\) 0.717491 0.0400464
\(322\) 0 0
\(323\) 7.84476 0.436494
\(324\) 0 0
\(325\) −7.71421 −0.427908
\(326\) 0 0
\(327\) −25.7732 −1.42526
\(328\) 0 0
\(329\) 5.20035 0.286705
\(330\) 0 0
\(331\) −8.83232 −0.485468 −0.242734 0.970093i \(-0.578044\pi\)
−0.242734 + 0.970093i \(0.578044\pi\)
\(332\) 0 0
\(333\) −1.40224 −0.0768421
\(334\) 0 0
\(335\) 12.7825 0.698381
\(336\) 0 0
\(337\) 5.01026 0.272926 0.136463 0.990645i \(-0.456426\pi\)
0.136463 + 0.990645i \(0.456426\pi\)
\(338\) 0 0
\(339\) 8.90234 0.483509
\(340\) 0 0
\(341\) 0.0189859 0.00102814
\(342\) 0 0
\(343\) −10.6862 −0.577003
\(344\) 0 0
\(345\) 1.22309 0.0658487
\(346\) 0 0
\(347\) −18.1935 −0.976679 −0.488339 0.872654i \(-0.662397\pi\)
−0.488339 + 0.872654i \(0.662397\pi\)
\(348\) 0 0
\(349\) −19.8229 −1.06109 −0.530547 0.847656i \(-0.678013\pi\)
−0.530547 + 0.847656i \(0.678013\pi\)
\(350\) 0 0
\(351\) 11.4443 0.610851
\(352\) 0 0
\(353\) −25.7268 −1.36930 −0.684650 0.728872i \(-0.740045\pi\)
−0.684650 + 0.728872i \(0.740045\pi\)
\(354\) 0 0
\(355\) −1.30500 −0.0692622
\(356\) 0 0
\(357\) 2.17428 0.115075
\(358\) 0 0
\(359\) −32.6690 −1.72421 −0.862103 0.506733i \(-0.830853\pi\)
−0.862103 + 0.506733i \(0.830853\pi\)
\(360\) 0 0
\(361\) −0.485748 −0.0255657
\(362\) 0 0
\(363\) 15.3518 0.805758
\(364\) 0 0
\(365\) −4.28083 −0.224069
\(366\) 0 0
\(367\) −6.33622 −0.330748 −0.165374 0.986231i \(-0.552883\pi\)
−0.165374 + 0.986231i \(0.552883\pi\)
\(368\) 0 0
\(369\) −5.36799 −0.279446
\(370\) 0 0
\(371\) −6.73604 −0.349718
\(372\) 0 0
\(373\) 2.77574 0.143722 0.0718612 0.997415i \(-0.477106\pi\)
0.0718612 + 0.997415i \(0.477106\pi\)
\(374\) 0 0
\(375\) −14.3908 −0.743139
\(376\) 0 0
\(377\) 5.67633 0.292346
\(378\) 0 0
\(379\) −1.36981 −0.0703624 −0.0351812 0.999381i \(-0.511201\pi\)
−0.0351812 + 0.999381i \(0.511201\pi\)
\(380\) 0 0
\(381\) 0.315733 0.0161755
\(382\) 0 0
\(383\) −21.9702 −1.12262 −0.561312 0.827604i \(-0.689703\pi\)
−0.561312 + 0.827604i \(0.689703\pi\)
\(384\) 0 0
\(385\) −0.736275 −0.0375241
\(386\) 0 0
\(387\) −6.87329 −0.349389
\(388\) 0 0
\(389\) 8.99985 0.456310 0.228155 0.973625i \(-0.426731\pi\)
0.228155 + 0.973625i \(0.426731\pi\)
\(390\) 0 0
\(391\) −1.36295 −0.0689273
\(392\) 0 0
\(393\) 19.4782 0.982545
\(394\) 0 0
\(395\) −9.02858 −0.454277
\(396\) 0 0
\(397\) −6.02280 −0.302276 −0.151138 0.988513i \(-0.548294\pi\)
−0.151138 + 0.988513i \(0.548294\pi\)
\(398\) 0 0
\(399\) 5.13147 0.256895
\(400\) 0 0
\(401\) 21.1265 1.05501 0.527503 0.849553i \(-0.323128\pi\)
0.527503 + 0.849553i \(0.323128\pi\)
\(402\) 0 0
\(403\) 0.0459939 0.00229112
\(404\) 0 0
\(405\) 6.65586 0.330733
\(406\) 0 0
\(407\) 1.51409 0.0750508
\(408\) 0 0
\(409\) −31.2674 −1.54607 −0.773036 0.634363i \(-0.781263\pi\)
−0.773036 + 0.634363i \(0.781263\pi\)
\(410\) 0 0
\(411\) 5.95911 0.293941
\(412\) 0 0
\(413\) 1.45345 0.0715195
\(414\) 0 0
\(415\) −5.61842 −0.275798
\(416\) 0 0
\(417\) −0.0366003 −0.00179233
\(418\) 0 0
\(419\) 3.24693 0.158623 0.0793115 0.996850i \(-0.474728\pi\)
0.0793115 + 0.996850i \(0.474728\pi\)
\(420\) 0 0
\(421\) 17.2288 0.839680 0.419840 0.907598i \(-0.362086\pi\)
0.419840 + 0.907598i \(0.362086\pi\)
\(422\) 0 0
\(423\) −5.05120 −0.245598
\(424\) 0 0
\(425\) 6.92062 0.335699
\(426\) 0 0
\(427\) −6.46569 −0.312897
\(428\) 0 0
\(429\) −2.54188 −0.122723
\(430\) 0 0
\(431\) −16.4443 −0.792095 −0.396047 0.918230i \(-0.629618\pi\)
−0.396047 + 0.918230i \(0.629618\pi\)
\(432\) 0 0
\(433\) −13.2198 −0.635305 −0.317652 0.948207i \(-0.602895\pi\)
−0.317652 + 0.948207i \(0.602895\pi\)
\(434\) 0 0
\(435\) 4.56981 0.219106
\(436\) 0 0
\(437\) −3.21667 −0.153874
\(438\) 0 0
\(439\) −20.5145 −0.979106 −0.489553 0.871974i \(-0.662840\pi\)
−0.489553 + 0.871974i \(0.662840\pi\)
\(440\) 0 0
\(441\) 4.94135 0.235302
\(442\) 0 0
\(443\) −34.5081 −1.63953 −0.819764 0.572702i \(-0.805895\pi\)
−0.819764 + 0.572702i \(0.805895\pi\)
\(444\) 0 0
\(445\) 10.5094 0.498195
\(446\) 0 0
\(447\) 33.5762 1.58810
\(448\) 0 0
\(449\) 27.1657 1.28203 0.641014 0.767529i \(-0.278514\pi\)
0.641014 + 0.767529i \(0.278514\pi\)
\(450\) 0 0
\(451\) 5.79620 0.272932
\(452\) 0 0
\(453\) −28.2779 −1.32861
\(454\) 0 0
\(455\) −1.78365 −0.0836188
\(456\) 0 0
\(457\) −18.1314 −0.848153 −0.424077 0.905626i \(-0.639401\pi\)
−0.424077 + 0.905626i \(0.639401\pi\)
\(458\) 0 0
\(459\) −10.2670 −0.479220
\(460\) 0 0
\(461\) −24.1606 −1.12527 −0.562636 0.826705i \(-0.690213\pi\)
−0.562636 + 0.826705i \(0.690213\pi\)
\(462\) 0 0
\(463\) 25.8126 1.19961 0.599806 0.800146i \(-0.295245\pi\)
0.599806 + 0.800146i \(0.295245\pi\)
\(464\) 0 0
\(465\) 0.0370281 0.00171714
\(466\) 0 0
\(467\) 23.9669 1.10906 0.554528 0.832165i \(-0.312899\pi\)
0.554528 + 0.832165i \(0.312899\pi\)
\(468\) 0 0
\(469\) −9.31751 −0.430243
\(470\) 0 0
\(471\) −30.1512 −1.38930
\(472\) 0 0
\(473\) 7.42158 0.341245
\(474\) 0 0
\(475\) 16.3332 0.749419
\(476\) 0 0
\(477\) 6.54284 0.299576
\(478\) 0 0
\(479\) 2.97853 0.136092 0.0680462 0.997682i \(-0.478323\pi\)
0.0680462 + 0.997682i \(0.478323\pi\)
\(480\) 0 0
\(481\) 3.66794 0.167244
\(482\) 0 0
\(483\) −0.891543 −0.0405666
\(484\) 0 0
\(485\) 0.925325 0.0420169
\(486\) 0 0
\(487\) −31.0404 −1.40657 −0.703287 0.710906i \(-0.748285\pi\)
−0.703287 + 0.710906i \(0.748285\pi\)
\(488\) 0 0
\(489\) 3.31228 0.149786
\(490\) 0 0
\(491\) 6.52070 0.294275 0.147138 0.989116i \(-0.452994\pi\)
0.147138 + 0.989116i \(0.452994\pi\)
\(492\) 0 0
\(493\) −5.09238 −0.229349
\(494\) 0 0
\(495\) 0.715157 0.0321439
\(496\) 0 0
\(497\) 0.951252 0.0426695
\(498\) 0 0
\(499\) −34.8087 −1.55825 −0.779125 0.626869i \(-0.784336\pi\)
−0.779125 + 0.626869i \(0.784336\pi\)
\(500\) 0 0
\(501\) −25.8236 −1.15371
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 15.6348 0.695739
\(506\) 0 0
\(507\) 13.2252 0.587353
\(508\) 0 0
\(509\) 8.27277 0.366684 0.183342 0.983049i \(-0.441308\pi\)
0.183342 + 0.983049i \(0.441308\pi\)
\(510\) 0 0
\(511\) 3.12042 0.138039
\(512\) 0 0
\(513\) −24.2308 −1.06982
\(514\) 0 0
\(515\) −18.7052 −0.824248
\(516\) 0 0
\(517\) 5.45413 0.239873
\(518\) 0 0
\(519\) −5.43175 −0.238427
\(520\) 0 0
\(521\) 17.4742 0.765559 0.382779 0.923840i \(-0.374967\pi\)
0.382779 + 0.923840i \(0.374967\pi\)
\(522\) 0 0
\(523\) −3.26300 −0.142681 −0.0713404 0.997452i \(-0.522728\pi\)
−0.0713404 + 0.997452i \(0.522728\pi\)
\(524\) 0 0
\(525\) 4.52697 0.197573
\(526\) 0 0
\(527\) −0.0412623 −0.00179741
\(528\) 0 0
\(529\) −22.4411 −0.975702
\(530\) 0 0
\(531\) −1.41176 −0.0612651
\(532\) 0 0
\(533\) 14.0415 0.608204
\(534\) 0 0
\(535\) 0.528036 0.0228290
\(536\) 0 0
\(537\) −20.5886 −0.888462
\(538\) 0 0
\(539\) −5.33552 −0.229817
\(540\) 0 0
\(541\) −36.8792 −1.58556 −0.792781 0.609507i \(-0.791367\pi\)
−0.792781 + 0.609507i \(0.791367\pi\)
\(542\) 0 0
\(543\) 11.8658 0.509212
\(544\) 0 0
\(545\) −18.9677 −0.812489
\(546\) 0 0
\(547\) −3.57057 −0.152667 −0.0763334 0.997082i \(-0.524321\pi\)
−0.0763334 + 0.997082i \(0.524321\pi\)
\(548\) 0 0
\(549\) 6.28024 0.268034
\(550\) 0 0
\(551\) −12.0184 −0.512002
\(552\) 0 0
\(553\) 6.58119 0.279861
\(554\) 0 0
\(555\) 2.95293 0.125345
\(556\) 0 0
\(557\) −30.2578 −1.28206 −0.641032 0.767514i \(-0.721494\pi\)
−0.641032 + 0.767514i \(0.721494\pi\)
\(558\) 0 0
\(559\) 17.9790 0.760432
\(560\) 0 0
\(561\) 2.28039 0.0962780
\(562\) 0 0
\(563\) 22.4953 0.948062 0.474031 0.880508i \(-0.342798\pi\)
0.474031 + 0.880508i \(0.342798\pi\)
\(564\) 0 0
\(565\) 6.55166 0.275631
\(566\) 0 0
\(567\) −4.85165 −0.203750
\(568\) 0 0
\(569\) −36.4374 −1.52753 −0.763767 0.645492i \(-0.776652\pi\)
−0.763767 + 0.645492i \(0.776652\pi\)
\(570\) 0 0
\(571\) −23.2768 −0.974104 −0.487052 0.873373i \(-0.661928\pi\)
−0.487052 + 0.873373i \(0.661928\pi\)
\(572\) 0 0
\(573\) −6.70072 −0.279927
\(574\) 0 0
\(575\) −2.83773 −0.118342
\(576\) 0 0
\(577\) 15.7394 0.655241 0.327621 0.944809i \(-0.393753\pi\)
0.327621 + 0.944809i \(0.393753\pi\)
\(578\) 0 0
\(579\) −39.9765 −1.66137
\(580\) 0 0
\(581\) 4.09543 0.169907
\(582\) 0 0
\(583\) −7.06476 −0.292593
\(584\) 0 0
\(585\) 1.73249 0.0716297
\(586\) 0 0
\(587\) −19.7718 −0.816068 −0.408034 0.912967i \(-0.633786\pi\)
−0.408034 + 0.912967i \(0.633786\pi\)
\(588\) 0 0
\(589\) −0.0973823 −0.00401257
\(590\) 0 0
\(591\) 11.4493 0.470963
\(592\) 0 0
\(593\) 26.9384 1.10623 0.553114 0.833106i \(-0.313439\pi\)
0.553114 + 0.833106i \(0.313439\pi\)
\(594\) 0 0
\(595\) 1.60016 0.0656001
\(596\) 0 0
\(597\) −1.90051 −0.0777827
\(598\) 0 0
\(599\) 42.4760 1.73552 0.867761 0.496982i \(-0.165558\pi\)
0.867761 + 0.496982i \(0.165558\pi\)
\(600\) 0 0
\(601\) 33.6101 1.37099 0.685493 0.728080i \(-0.259587\pi\)
0.685493 + 0.728080i \(0.259587\pi\)
\(602\) 0 0
\(603\) 9.05027 0.368555
\(604\) 0 0
\(605\) 11.2981 0.459333
\(606\) 0 0
\(607\) −11.3897 −0.462295 −0.231147 0.972919i \(-0.574248\pi\)
−0.231147 + 0.972919i \(0.574248\pi\)
\(608\) 0 0
\(609\) −3.33107 −0.134982
\(610\) 0 0
\(611\) 13.2128 0.534533
\(612\) 0 0
\(613\) 1.30427 0.0526789 0.0263395 0.999653i \(-0.491615\pi\)
0.0263395 + 0.999653i \(0.491615\pi\)
\(614\) 0 0
\(615\) 11.3043 0.455833
\(616\) 0 0
\(617\) −18.4802 −0.743985 −0.371992 0.928236i \(-0.621325\pi\)
−0.371992 + 0.928236i \(0.621325\pi\)
\(618\) 0 0
\(619\) 31.5751 1.26911 0.634554 0.772878i \(-0.281184\pi\)
0.634554 + 0.772878i \(0.281184\pi\)
\(620\) 0 0
\(621\) 4.20987 0.168936
\(622\) 0 0
\(623\) −7.66063 −0.306917
\(624\) 0 0
\(625\) 8.38875 0.335550
\(626\) 0 0
\(627\) 5.38189 0.214932
\(628\) 0 0
\(629\) −3.29060 −0.131205
\(630\) 0 0
\(631\) −42.9916 −1.71147 −0.855734 0.517416i \(-0.826894\pi\)
−0.855734 + 0.517416i \(0.826894\pi\)
\(632\) 0 0
\(633\) 23.8798 0.949137
\(634\) 0 0
\(635\) 0.232363 0.00922105
\(636\) 0 0
\(637\) −12.9255 −0.512126
\(638\) 0 0
\(639\) −0.923968 −0.0365516
\(640\) 0 0
\(641\) −20.0209 −0.790779 −0.395390 0.918513i \(-0.629390\pi\)
−0.395390 + 0.918513i \(0.629390\pi\)
\(642\) 0 0
\(643\) 28.3527 1.11812 0.559060 0.829127i \(-0.311162\pi\)
0.559060 + 0.829127i \(0.311162\pi\)
\(644\) 0 0
\(645\) 14.4743 0.569924
\(646\) 0 0
\(647\) 25.7284 1.01149 0.505744 0.862683i \(-0.331218\pi\)
0.505744 + 0.862683i \(0.331218\pi\)
\(648\) 0 0
\(649\) 1.52438 0.0598370
\(650\) 0 0
\(651\) −0.0269908 −0.00105785
\(652\) 0 0
\(653\) 37.4989 1.46744 0.733722 0.679449i \(-0.237781\pi\)
0.733722 + 0.679449i \(0.237781\pi\)
\(654\) 0 0
\(655\) 14.3349 0.560113
\(656\) 0 0
\(657\) −3.03092 −0.118247
\(658\) 0 0
\(659\) 21.3066 0.829988 0.414994 0.909824i \(-0.363784\pi\)
0.414994 + 0.909824i \(0.363784\pi\)
\(660\) 0 0
\(661\) −23.3872 −0.909656 −0.454828 0.890579i \(-0.650299\pi\)
−0.454828 + 0.890579i \(0.650299\pi\)
\(662\) 0 0
\(663\) 5.52431 0.214546
\(664\) 0 0
\(665\) 3.77650 0.146446
\(666\) 0 0
\(667\) 2.08808 0.0808508
\(668\) 0 0
\(669\) 30.3155 1.17206
\(670\) 0 0
\(671\) −6.78123 −0.261786
\(672\) 0 0
\(673\) 20.6684 0.796706 0.398353 0.917232i \(-0.369582\pi\)
0.398353 + 0.917232i \(0.369582\pi\)
\(674\) 0 0
\(675\) −21.3763 −0.822776
\(676\) 0 0
\(677\) 26.0320 1.00049 0.500246 0.865883i \(-0.333243\pi\)
0.500246 + 0.865883i \(0.333243\pi\)
\(678\) 0 0
\(679\) −0.674496 −0.0258848
\(680\) 0 0
\(681\) 3.82147 0.146439
\(682\) 0 0
\(683\) 13.3035 0.509043 0.254522 0.967067i \(-0.418082\pi\)
0.254522 + 0.967067i \(0.418082\pi\)
\(684\) 0 0
\(685\) 4.38560 0.167565
\(686\) 0 0
\(687\) 15.7459 0.600743
\(688\) 0 0
\(689\) −17.1146 −0.652015
\(690\) 0 0
\(691\) 11.2943 0.429657 0.214828 0.976652i \(-0.431081\pi\)
0.214828 + 0.976652i \(0.431081\pi\)
\(692\) 0 0
\(693\) −0.521299 −0.0198025
\(694\) 0 0
\(695\) −0.0269359 −0.00102174
\(696\) 0 0
\(697\) −12.5970 −0.477144
\(698\) 0 0
\(699\) −28.5032 −1.07809
\(700\) 0 0
\(701\) −6.64761 −0.251077 −0.125538 0.992089i \(-0.540066\pi\)
−0.125538 + 0.992089i \(0.540066\pi\)
\(702\) 0 0
\(703\) −7.76608 −0.292903
\(704\) 0 0
\(705\) 10.6372 0.400619
\(706\) 0 0
\(707\) −11.3966 −0.428615
\(708\) 0 0
\(709\) −25.8987 −0.972648 −0.486324 0.873779i \(-0.661662\pi\)
−0.486324 + 0.873779i \(0.661662\pi\)
\(710\) 0 0
\(711\) −6.39243 −0.239735
\(712\) 0 0
\(713\) 0.0169192 0.000633630 0
\(714\) 0 0
\(715\) −1.87069 −0.0699600
\(716\) 0 0
\(717\) −12.2927 −0.459079
\(718\) 0 0
\(719\) 16.3355 0.609210 0.304605 0.952479i \(-0.401475\pi\)
0.304605 + 0.952479i \(0.401475\pi\)
\(720\) 0 0
\(721\) 13.6347 0.507784
\(722\) 0 0
\(723\) −12.1004 −0.450020
\(724\) 0 0
\(725\) −10.6026 −0.393771
\(726\) 0 0
\(727\) 19.6052 0.727117 0.363559 0.931571i \(-0.381562\pi\)
0.363559 + 0.931571i \(0.381562\pi\)
\(728\) 0 0
\(729\) 29.9017 1.10747
\(730\) 0 0
\(731\) −16.1294 −0.596569
\(732\) 0 0
\(733\) −34.6268 −1.27897 −0.639484 0.768804i \(-0.720852\pi\)
−0.639484 + 0.768804i \(0.720852\pi\)
\(734\) 0 0
\(735\) −10.4058 −0.383825
\(736\) 0 0
\(737\) −9.77221 −0.359964
\(738\) 0 0
\(739\) −51.1192 −1.88045 −0.940225 0.340554i \(-0.889385\pi\)
−0.940225 + 0.340554i \(0.889385\pi\)
\(740\) 0 0
\(741\) 13.0378 0.478956
\(742\) 0 0
\(743\) −18.3318 −0.672530 −0.336265 0.941767i \(-0.609164\pi\)
−0.336265 + 0.941767i \(0.609164\pi\)
\(744\) 0 0
\(745\) 24.7104 0.905317
\(746\) 0 0
\(747\) −3.97797 −0.145546
\(748\) 0 0
\(749\) −0.384901 −0.0140640
\(750\) 0 0
\(751\) −19.2142 −0.701136 −0.350568 0.936537i \(-0.614011\pi\)
−0.350568 + 0.936537i \(0.614011\pi\)
\(752\) 0 0
\(753\) 5.27127 0.192096
\(754\) 0 0
\(755\) −20.8111 −0.757392
\(756\) 0 0
\(757\) −25.5974 −0.930352 −0.465176 0.885218i \(-0.654009\pi\)
−0.465176 + 0.885218i \(0.654009\pi\)
\(758\) 0 0
\(759\) −0.935051 −0.0339402
\(760\) 0 0
\(761\) 28.0281 1.01602 0.508009 0.861352i \(-0.330382\pi\)
0.508009 + 0.861352i \(0.330382\pi\)
\(762\) 0 0
\(763\) 13.8261 0.500539
\(764\) 0 0
\(765\) −1.55426 −0.0561945
\(766\) 0 0
\(767\) 3.69285 0.133341
\(768\) 0 0
\(769\) 50.7564 1.83032 0.915162 0.403087i \(-0.132063\pi\)
0.915162 + 0.403087i \(0.132063\pi\)
\(770\) 0 0
\(771\) 31.8638 1.14755
\(772\) 0 0
\(773\) −55.0059 −1.97842 −0.989212 0.146494i \(-0.953201\pi\)
−0.989212 + 0.146494i \(0.953201\pi\)
\(774\) 0 0
\(775\) −0.0859103 −0.00308599
\(776\) 0 0
\(777\) −2.15247 −0.0772196
\(778\) 0 0
\(779\) −29.7299 −1.06518
\(780\) 0 0
\(781\) 0.997674 0.0356996
\(782\) 0 0
\(783\) 15.7293 0.562119
\(784\) 0 0
\(785\) −22.1898 −0.791986
\(786\) 0 0
\(787\) −6.78536 −0.241872 −0.120936 0.992660i \(-0.538590\pi\)
−0.120936 + 0.992660i \(0.538590\pi\)
\(788\) 0 0
\(789\) 3.21414 0.114426
\(790\) 0 0
\(791\) −4.77570 −0.169804
\(792\) 0 0
\(793\) −16.4277 −0.583366
\(794\) 0 0
\(795\) −13.7784 −0.488668
\(796\) 0 0
\(797\) −42.3449 −1.49993 −0.749967 0.661475i \(-0.769931\pi\)
−0.749967 + 0.661475i \(0.769931\pi\)
\(798\) 0 0
\(799\) −11.8536 −0.419349
\(800\) 0 0
\(801\) 7.44091 0.262911
\(802\) 0 0
\(803\) 3.27270 0.115491
\(804\) 0 0
\(805\) −0.656129 −0.0231255
\(806\) 0 0
\(807\) 8.28601 0.291681
\(808\) 0 0
\(809\) −25.3991 −0.892984 −0.446492 0.894788i \(-0.647327\pi\)
−0.446492 + 0.894788i \(0.647327\pi\)
\(810\) 0 0
\(811\) −20.0288 −0.703306 −0.351653 0.936130i \(-0.614380\pi\)
−0.351653 + 0.936130i \(0.614380\pi\)
\(812\) 0 0
\(813\) 30.2658 1.06147
\(814\) 0 0
\(815\) 2.43767 0.0853877
\(816\) 0 0
\(817\) −38.0668 −1.33179
\(818\) 0 0
\(819\) −1.26286 −0.0441280
\(820\) 0 0
\(821\) 12.1634 0.424506 0.212253 0.977215i \(-0.431920\pi\)
0.212253 + 0.977215i \(0.431920\pi\)
\(822\) 0 0
\(823\) 40.1250 1.39867 0.699335 0.714794i \(-0.253480\pi\)
0.699335 + 0.714794i \(0.253480\pi\)
\(824\) 0 0
\(825\) 4.74789 0.165300
\(826\) 0 0
\(827\) 37.2441 1.29510 0.647552 0.762022i \(-0.275793\pi\)
0.647552 + 0.762022i \(0.275793\pi\)
\(828\) 0 0
\(829\) 25.9066 0.899774 0.449887 0.893086i \(-0.351464\pi\)
0.449887 + 0.893086i \(0.351464\pi\)
\(830\) 0 0
\(831\) 36.1042 1.25244
\(832\) 0 0
\(833\) 11.5958 0.401770
\(834\) 0 0
\(835\) −19.0048 −0.657690
\(836\) 0 0
\(837\) 0.127451 0.00440534
\(838\) 0 0
\(839\) −5.02724 −0.173560 −0.0867798 0.996228i \(-0.527658\pi\)
−0.0867798 + 0.996228i \(0.527658\pi\)
\(840\) 0 0
\(841\) −21.1983 −0.730976
\(842\) 0 0
\(843\) −47.7646 −1.64510
\(844\) 0 0
\(845\) 9.73309 0.334829
\(846\) 0 0
\(847\) −8.23551 −0.282976
\(848\) 0 0
\(849\) 35.9000 1.23209
\(850\) 0 0
\(851\) 1.34928 0.0462527
\(852\) 0 0
\(853\) 26.7681 0.916524 0.458262 0.888817i \(-0.348472\pi\)
0.458262 + 0.888817i \(0.348472\pi\)
\(854\) 0 0
\(855\) −3.66818 −0.125449
\(856\) 0 0
\(857\) 48.8760 1.66957 0.834787 0.550574i \(-0.185591\pi\)
0.834787 + 0.550574i \(0.185591\pi\)
\(858\) 0 0
\(859\) −1.54729 −0.0527928 −0.0263964 0.999652i \(-0.508403\pi\)
−0.0263964 + 0.999652i \(0.508403\pi\)
\(860\) 0 0
\(861\) −8.24003 −0.280819
\(862\) 0 0
\(863\) 3.76724 0.128238 0.0641192 0.997942i \(-0.479576\pi\)
0.0641192 + 0.997942i \(0.479576\pi\)
\(864\) 0 0
\(865\) −3.99749 −0.135919
\(866\) 0 0
\(867\) 20.3910 0.692516
\(868\) 0 0
\(869\) 6.90236 0.234146
\(870\) 0 0
\(871\) −23.6735 −0.802146
\(872\) 0 0
\(873\) 0.655150 0.0221735
\(874\) 0 0
\(875\) 7.72002 0.260984
\(876\) 0 0
\(877\) −4.29648 −0.145082 −0.0725410 0.997365i \(-0.523111\pi\)
−0.0725410 + 0.997365i \(0.523111\pi\)
\(878\) 0 0
\(879\) 0.556604 0.0187738
\(880\) 0 0
\(881\) −27.7084 −0.933519 −0.466760 0.884384i \(-0.654579\pi\)
−0.466760 + 0.884384i \(0.654579\pi\)
\(882\) 0 0
\(883\) −37.4492 −1.26027 −0.630134 0.776487i \(-0.717000\pi\)
−0.630134 + 0.776487i \(0.717000\pi\)
\(884\) 0 0
\(885\) 2.97298 0.0999357
\(886\) 0 0
\(887\) −0.219360 −0.00736539 −0.00368270 0.999993i \(-0.501172\pi\)
−0.00368270 + 0.999993i \(0.501172\pi\)
\(888\) 0 0
\(889\) −0.169376 −0.00568070
\(890\) 0 0
\(891\) −5.08841 −0.170468
\(892\) 0 0
\(893\) −27.9753 −0.936159
\(894\) 0 0
\(895\) −15.1521 −0.506480
\(896\) 0 0
\(897\) −2.26519 −0.0756325
\(898\) 0 0
\(899\) 0.0632152 0.00210834
\(900\) 0 0
\(901\) 15.3540 0.511515
\(902\) 0 0
\(903\) −10.5507 −0.351106
\(904\) 0 0
\(905\) 8.73264 0.290283
\(906\) 0 0
\(907\) −52.0680 −1.72889 −0.864444 0.502729i \(-0.832330\pi\)
−0.864444 + 0.502729i \(0.832330\pi\)
\(908\) 0 0
\(909\) 11.0698 0.367161
\(910\) 0 0
\(911\) −41.6078 −1.37853 −0.689263 0.724511i \(-0.742066\pi\)
−0.689263 + 0.724511i \(0.742066\pi\)
\(912\) 0 0
\(913\) 4.29529 0.142153
\(914\) 0 0
\(915\) −13.2254 −0.437218
\(916\) 0 0
\(917\) −10.4492 −0.345062
\(918\) 0 0
\(919\) −54.3382 −1.79245 −0.896226 0.443597i \(-0.853702\pi\)
−0.896226 + 0.443597i \(0.853702\pi\)
\(920\) 0 0
\(921\) 42.5293 1.40139
\(922\) 0 0
\(923\) 2.41690 0.0795532
\(924\) 0 0
\(925\) −6.85121 −0.225266
\(926\) 0 0
\(927\) −13.2437 −0.434979
\(928\) 0 0
\(929\) 31.9579 1.04851 0.524253 0.851563i \(-0.324345\pi\)
0.524253 + 0.851563i \(0.324345\pi\)
\(930\) 0 0
\(931\) 27.3669 0.896915
\(932\) 0 0
\(933\) −31.6844 −1.03730
\(934\) 0 0
\(935\) 1.67825 0.0548845
\(936\) 0 0
\(937\) −52.6379 −1.71960 −0.859802 0.510627i \(-0.829413\pi\)
−0.859802 + 0.510627i \(0.829413\pi\)
\(938\) 0 0
\(939\) 20.9979 0.685240
\(940\) 0 0
\(941\) 7.74283 0.252409 0.126205 0.992004i \(-0.459720\pi\)
0.126205 + 0.992004i \(0.459720\pi\)
\(942\) 0 0
\(943\) 5.16527 0.168204
\(944\) 0 0
\(945\) −4.94256 −0.160781
\(946\) 0 0
\(947\) 54.5052 1.77118 0.885591 0.464467i \(-0.153754\pi\)
0.885591 + 0.464467i \(0.153754\pi\)
\(948\) 0 0
\(949\) 7.92822 0.257361
\(950\) 0 0
\(951\) 40.3220 1.30753
\(952\) 0 0
\(953\) 19.8770 0.643880 0.321940 0.946760i \(-0.395665\pi\)
0.321940 + 0.946760i \(0.395665\pi\)
\(954\) 0 0
\(955\) −4.93139 −0.159576
\(956\) 0 0
\(957\) −3.49362 −0.112933
\(958\) 0 0
\(959\) −3.19679 −0.103230
\(960\) 0 0
\(961\) −30.9995 −0.999983
\(962\) 0 0
\(963\) 0.373861 0.0120475
\(964\) 0 0
\(965\) −29.4206 −0.947084
\(966\) 0 0
\(967\) −18.0432 −0.580230 −0.290115 0.956992i \(-0.593694\pi\)
−0.290115 + 0.956992i \(0.593694\pi\)
\(968\) 0 0
\(969\) −11.6966 −0.375747
\(970\) 0 0
\(971\) 30.4956 0.978649 0.489324 0.872102i \(-0.337243\pi\)
0.489324 + 0.872102i \(0.337243\pi\)
\(972\) 0 0
\(973\) 0.0196344 0.000629450 0
\(974\) 0 0
\(975\) 11.5019 0.368356
\(976\) 0 0
\(977\) 37.3960 1.19640 0.598201 0.801346i \(-0.295882\pi\)
0.598201 + 0.801346i \(0.295882\pi\)
\(978\) 0 0
\(979\) −8.03447 −0.256783
\(980\) 0 0
\(981\) −13.4296 −0.428773
\(982\) 0 0
\(983\) 17.8473 0.569239 0.284620 0.958641i \(-0.408133\pi\)
0.284620 + 0.958641i \(0.408133\pi\)
\(984\) 0 0
\(985\) 8.42612 0.268479
\(986\) 0 0
\(987\) −7.75374 −0.246804
\(988\) 0 0
\(989\) 6.61372 0.210304
\(990\) 0 0
\(991\) 21.9819 0.698277 0.349138 0.937071i \(-0.386474\pi\)
0.349138 + 0.937071i \(0.386474\pi\)
\(992\) 0 0
\(993\) 13.1690 0.417906
\(994\) 0 0
\(995\) −1.39868 −0.0443411
\(996\) 0 0
\(997\) 31.0250 0.982571 0.491286 0.870999i \(-0.336527\pi\)
0.491286 + 0.870999i \(0.336527\pi\)
\(998\) 0 0
\(999\) 10.1640 0.321574
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 \(a_p\))