Properties

Label 8048.2.a.v.1.19
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 1.19
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.893789 q^{3}\) \(-3.85908 q^{5}\) \(-3.77625 q^{7}\) \(-2.20114 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.893789 q^{3}\) \(-3.85908 q^{5}\) \(-3.77625 q^{7}\) \(-2.20114 q^{9}\) \(+4.71894 q^{11}\) \(-0.511554 q^{13}\) \(-3.44921 q^{15}\) \(+5.63108 q^{17}\) \(-0.0695678 q^{19}\) \(-3.37517 q^{21}\) \(-5.20252 q^{23}\) \(+9.89252 q^{25}\) \(-4.64872 q^{27}\) \(-1.66971 q^{29}\) \(+0.370767 q^{31}\) \(+4.21774 q^{33}\) \(+14.5729 q^{35}\) \(+0.932872 q^{37}\) \(-0.457221 q^{39}\) \(+5.06469 q^{41}\) \(+6.38770 q^{43}\) \(+8.49438 q^{45}\) \(+4.19872 q^{47}\) \(+7.26006 q^{49}\) \(+5.03300 q^{51}\) \(+1.31018 q^{53}\) \(-18.2108 q^{55}\) \(-0.0621790 q^{57}\) \(+13.0216 q^{59}\) \(+10.4141 q^{61}\) \(+8.31206 q^{63}\) \(+1.97413 q^{65}\) \(-2.09964 q^{67}\) \(-4.64996 q^{69}\) \(-3.30951 q^{71}\) \(+1.07644 q^{73}\) \(+8.84182 q^{75}\) \(-17.8199 q^{77}\) \(-10.1610 q^{79}\) \(+2.44844 q^{81}\) \(-11.7519 q^{83}\) \(-21.7308 q^{85}\) \(-1.49237 q^{87}\) \(-16.5010 q^{89}\) \(+1.93176 q^{91}\) \(+0.331388 q^{93}\) \(+0.268468 q^{95}\) \(-12.5981 q^{97}\) \(-10.3871 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.893789 0.516029 0.258015 0.966141i \(-0.416932\pi\)
0.258015 + 0.966141i \(0.416932\pi\)
\(4\) 0 0
\(5\) −3.85908 −1.72583 −0.862917 0.505346i \(-0.831365\pi\)
−0.862917 + 0.505346i \(0.831365\pi\)
\(6\) 0 0
\(7\) −3.77625 −1.42729 −0.713644 0.700509i \(-0.752957\pi\)
−0.713644 + 0.700509i \(0.752957\pi\)
\(8\) 0 0
\(9\) −2.20114 −0.733714
\(10\) 0 0
\(11\) 4.71894 1.42281 0.711407 0.702780i \(-0.248058\pi\)
0.711407 + 0.702780i \(0.248058\pi\)
\(12\) 0 0
\(13\) −0.511554 −0.141880 −0.0709398 0.997481i \(-0.522600\pi\)
−0.0709398 + 0.997481i \(0.522600\pi\)
\(14\) 0 0
\(15\) −3.44921 −0.890581
\(16\) 0 0
\(17\) 5.63108 1.36574 0.682869 0.730541i \(-0.260732\pi\)
0.682869 + 0.730541i \(0.260732\pi\)
\(18\) 0 0
\(19\) −0.0695678 −0.0159600 −0.00797998 0.999968i \(-0.502540\pi\)
−0.00797998 + 0.999968i \(0.502540\pi\)
\(20\) 0 0
\(21\) −3.37517 −0.736523
\(22\) 0 0
\(23\) −5.20252 −1.08480 −0.542401 0.840120i \(-0.682485\pi\)
−0.542401 + 0.840120i \(0.682485\pi\)
\(24\) 0 0
\(25\) 9.89252 1.97850
\(26\) 0 0
\(27\) −4.64872 −0.894647
\(28\) 0 0
\(29\) −1.66971 −0.310057 −0.155028 0.987910i \(-0.549547\pi\)
−0.155028 + 0.987910i \(0.549547\pi\)
\(30\) 0 0
\(31\) 0.370767 0.0665918 0.0332959 0.999446i \(-0.489400\pi\)
0.0332959 + 0.999446i \(0.489400\pi\)
\(32\) 0 0
\(33\) 4.21774 0.734214
\(34\) 0 0
\(35\) 14.5729 2.46326
\(36\) 0 0
\(37\) 0.932872 0.153363 0.0766816 0.997056i \(-0.475568\pi\)
0.0766816 + 0.997056i \(0.475568\pi\)
\(38\) 0 0
\(39\) −0.457221 −0.0732140
\(40\) 0 0
\(41\) 5.06469 0.790972 0.395486 0.918472i \(-0.370576\pi\)
0.395486 + 0.918472i \(0.370576\pi\)
\(42\) 0 0
\(43\) 6.38770 0.974115 0.487058 0.873370i \(-0.338070\pi\)
0.487058 + 0.873370i \(0.338070\pi\)
\(44\) 0 0
\(45\) 8.49438 1.26627
\(46\) 0 0
\(47\) 4.19872 0.612447 0.306223 0.951960i \(-0.400935\pi\)
0.306223 + 0.951960i \(0.400935\pi\)
\(48\) 0 0
\(49\) 7.26006 1.03715
\(50\) 0 0
\(51\) 5.03300 0.704761
\(52\) 0 0
\(53\) 1.31018 0.179968 0.0899839 0.995943i \(-0.471318\pi\)
0.0899839 + 0.995943i \(0.471318\pi\)
\(54\) 0 0
\(55\) −18.2108 −2.45554
\(56\) 0 0
\(57\) −0.0621790 −0.00823581
\(58\) 0 0
\(59\) 13.0216 1.69527 0.847635 0.530579i \(-0.178026\pi\)
0.847635 + 0.530579i \(0.178026\pi\)
\(60\) 0 0
\(61\) 10.4141 1.33339 0.666696 0.745330i \(-0.267708\pi\)
0.666696 + 0.745330i \(0.267708\pi\)
\(62\) 0 0
\(63\) 8.31206 1.04722
\(64\) 0 0
\(65\) 1.97413 0.244861
\(66\) 0 0
\(67\) −2.09964 −0.256512 −0.128256 0.991741i \(-0.540938\pi\)
−0.128256 + 0.991741i \(0.540938\pi\)
\(68\) 0 0
\(69\) −4.64996 −0.559789
\(70\) 0 0
\(71\) −3.30951 −0.392767 −0.196383 0.980527i \(-0.562920\pi\)
−0.196383 + 0.980527i \(0.562920\pi\)
\(72\) 0 0
\(73\) 1.07644 0.125987 0.0629937 0.998014i \(-0.479935\pi\)
0.0629937 + 0.998014i \(0.479935\pi\)
\(74\) 0 0
\(75\) 8.84182 1.02097
\(76\) 0 0
\(77\) −17.8199 −2.03077
\(78\) 0 0
\(79\) −10.1610 −1.14320 −0.571598 0.820534i \(-0.693676\pi\)
−0.571598 + 0.820534i \(0.693676\pi\)
\(80\) 0 0
\(81\) 2.44844 0.272049
\(82\) 0 0
\(83\) −11.7519 −1.28993 −0.644967 0.764210i \(-0.723129\pi\)
−0.644967 + 0.764210i \(0.723129\pi\)
\(84\) 0 0
\(85\) −21.7308 −2.35704
\(86\) 0 0
\(87\) −1.49237 −0.159999
\(88\) 0 0
\(89\) −16.5010 −1.74910 −0.874551 0.484933i \(-0.838844\pi\)
−0.874551 + 0.484933i \(0.838844\pi\)
\(90\) 0 0
\(91\) 1.93176 0.202503
\(92\) 0 0
\(93\) 0.331388 0.0343633
\(94\) 0 0
\(95\) 0.268468 0.0275442
\(96\) 0 0
\(97\) −12.5981 −1.27914 −0.639572 0.768731i \(-0.720889\pi\)
−0.639572 + 0.768731i \(0.720889\pi\)
\(98\) 0 0
\(99\) −10.3871 −1.04394
\(100\) 0 0
\(101\) −16.9935 −1.69091 −0.845457 0.534044i \(-0.820672\pi\)
−0.845457 + 0.534044i \(0.820672\pi\)
\(102\) 0 0
\(103\) 15.7173 1.54867 0.774336 0.632775i \(-0.218084\pi\)
0.774336 + 0.632775i \(0.218084\pi\)
\(104\) 0 0
\(105\) 13.0251 1.27112
\(106\) 0 0
\(107\) 7.81103 0.755121 0.377561 0.925985i \(-0.376763\pi\)
0.377561 + 0.925985i \(0.376763\pi\)
\(108\) 0 0
\(109\) −1.47716 −0.141486 −0.0707430 0.997495i \(-0.522537\pi\)
−0.0707430 + 0.997495i \(0.522537\pi\)
\(110\) 0 0
\(111\) 0.833791 0.0791399
\(112\) 0 0
\(113\) −4.93874 −0.464598 −0.232299 0.972644i \(-0.574625\pi\)
−0.232299 + 0.972644i \(0.574625\pi\)
\(114\) 0 0
\(115\) 20.0770 1.87219
\(116\) 0 0
\(117\) 1.12600 0.104099
\(118\) 0 0
\(119\) −21.2644 −1.94930
\(120\) 0 0
\(121\) 11.2684 1.02440
\(122\) 0 0
\(123\) 4.52677 0.408165
\(124\) 0 0
\(125\) −18.8806 −1.68873
\(126\) 0 0
\(127\) 12.0431 1.06865 0.534325 0.845279i \(-0.320566\pi\)
0.534325 + 0.845279i \(0.320566\pi\)
\(128\) 0 0
\(129\) 5.70926 0.502672
\(130\) 0 0
\(131\) −0.173395 −0.0151496 −0.00757479 0.999971i \(-0.502411\pi\)
−0.00757479 + 0.999971i \(0.502411\pi\)
\(132\) 0 0
\(133\) 0.262705 0.0227795
\(134\) 0 0
\(135\) 17.9398 1.54401
\(136\) 0 0
\(137\) −10.3811 −0.886914 −0.443457 0.896296i \(-0.646248\pi\)
−0.443457 + 0.896296i \(0.646248\pi\)
\(138\) 0 0
\(139\) −14.1517 −1.20033 −0.600166 0.799875i \(-0.704899\pi\)
−0.600166 + 0.799875i \(0.704899\pi\)
\(140\) 0 0
\(141\) 3.75277 0.316041
\(142\) 0 0
\(143\) −2.41399 −0.201868
\(144\) 0 0
\(145\) 6.44354 0.535107
\(146\) 0 0
\(147\) 6.48896 0.535201
\(148\) 0 0
\(149\) 19.1922 1.57228 0.786142 0.618046i \(-0.212076\pi\)
0.786142 + 0.618046i \(0.212076\pi\)
\(150\) 0 0
\(151\) 7.33354 0.596795 0.298397 0.954442i \(-0.403548\pi\)
0.298397 + 0.954442i \(0.403548\pi\)
\(152\) 0 0
\(153\) −12.3948 −1.00206
\(154\) 0 0
\(155\) −1.43082 −0.114926
\(156\) 0 0
\(157\) 20.3956 1.62775 0.813873 0.581043i \(-0.197355\pi\)
0.813873 + 0.581043i \(0.197355\pi\)
\(158\) 0 0
\(159\) 1.17103 0.0928687
\(160\) 0 0
\(161\) 19.6460 1.54832
\(162\) 0 0
\(163\) −1.52868 −0.119735 −0.0598677 0.998206i \(-0.519068\pi\)
−0.0598677 + 0.998206i \(0.519068\pi\)
\(164\) 0 0
\(165\) −16.2766 −1.26713
\(166\) 0 0
\(167\) −6.89472 −0.533530 −0.266765 0.963762i \(-0.585955\pi\)
−0.266765 + 0.963762i \(0.585955\pi\)
\(168\) 0 0
\(169\) −12.7383 −0.979870
\(170\) 0 0
\(171\) 0.153129 0.0117100
\(172\) 0 0
\(173\) −24.2254 −1.84182 −0.920912 0.389770i \(-0.872555\pi\)
−0.920912 + 0.389770i \(0.872555\pi\)
\(174\) 0 0
\(175\) −37.3566 −2.82389
\(176\) 0 0
\(177\) 11.6386 0.874810
\(178\) 0 0
\(179\) −17.5123 −1.30893 −0.654467 0.756091i \(-0.727107\pi\)
−0.654467 + 0.756091i \(0.727107\pi\)
\(180\) 0 0
\(181\) −14.0756 −1.04623 −0.523115 0.852262i \(-0.675230\pi\)
−0.523115 + 0.852262i \(0.675230\pi\)
\(182\) 0 0
\(183\) 9.30803 0.688069
\(184\) 0 0
\(185\) −3.60003 −0.264679
\(186\) 0 0
\(187\) 26.5728 1.94319
\(188\) 0 0
\(189\) 17.5547 1.27692
\(190\) 0 0
\(191\) 18.0871 1.30874 0.654370 0.756175i \(-0.272934\pi\)
0.654370 + 0.756175i \(0.272934\pi\)
\(192\) 0 0
\(193\) −4.16569 −0.299853 −0.149926 0.988697i \(-0.547904\pi\)
−0.149926 + 0.988697i \(0.547904\pi\)
\(194\) 0 0
\(195\) 1.76446 0.126355
\(196\) 0 0
\(197\) −17.9008 −1.27538 −0.637689 0.770294i \(-0.720109\pi\)
−0.637689 + 0.770294i \(0.720109\pi\)
\(198\) 0 0
\(199\) −18.8700 −1.33766 −0.668830 0.743415i \(-0.733205\pi\)
−0.668830 + 0.743415i \(0.733205\pi\)
\(200\) 0 0
\(201\) −1.87664 −0.132368
\(202\) 0 0
\(203\) 6.30523 0.442541
\(204\) 0 0
\(205\) −19.5451 −1.36509
\(206\) 0 0
\(207\) 11.4515 0.795933
\(208\) 0 0
\(209\) −0.328287 −0.0227081
\(210\) 0 0
\(211\) −18.2052 −1.25330 −0.626649 0.779302i \(-0.715574\pi\)
−0.626649 + 0.779302i \(0.715574\pi\)
\(212\) 0 0
\(213\) −2.95801 −0.202679
\(214\) 0 0
\(215\) −24.6507 −1.68116
\(216\) 0 0
\(217\) −1.40011 −0.0950457
\(218\) 0 0
\(219\) 0.962107 0.0650132
\(220\) 0 0
\(221\) −2.88060 −0.193770
\(222\) 0 0
\(223\) −3.04587 −0.203967 −0.101983 0.994786i \(-0.532519\pi\)
−0.101983 + 0.994786i \(0.532519\pi\)
\(224\) 0 0
\(225\) −21.7748 −1.45165
\(226\) 0 0
\(227\) 7.06816 0.469130 0.234565 0.972100i \(-0.424633\pi\)
0.234565 + 0.972100i \(0.424633\pi\)
\(228\) 0 0
\(229\) 3.43621 0.227071 0.113536 0.993534i \(-0.463782\pi\)
0.113536 + 0.993534i \(0.463782\pi\)
\(230\) 0 0
\(231\) −15.9272 −1.04794
\(232\) 0 0
\(233\) −19.0437 −1.24759 −0.623797 0.781586i \(-0.714411\pi\)
−0.623797 + 0.781586i \(0.714411\pi\)
\(234\) 0 0
\(235\) −16.2032 −1.05698
\(236\) 0 0
\(237\) −9.08175 −0.589923
\(238\) 0 0
\(239\) 20.8015 1.34553 0.672767 0.739854i \(-0.265106\pi\)
0.672767 + 0.739854i \(0.265106\pi\)
\(240\) 0 0
\(241\) 4.43572 0.285730 0.142865 0.989742i \(-0.454369\pi\)
0.142865 + 0.989742i \(0.454369\pi\)
\(242\) 0 0
\(243\) 16.1346 1.03503
\(244\) 0 0
\(245\) −28.0172 −1.78995
\(246\) 0 0
\(247\) 0.0355877 0.00226439
\(248\) 0 0
\(249\) −10.5037 −0.665644
\(250\) 0 0
\(251\) 22.4720 1.41842 0.709210 0.704997i \(-0.249052\pi\)
0.709210 + 0.704997i \(0.249052\pi\)
\(252\) 0 0
\(253\) −24.5504 −1.54347
\(254\) 0 0
\(255\) −19.4228 −1.21630
\(256\) 0 0
\(257\) 0.369671 0.0230595 0.0115297 0.999934i \(-0.496330\pi\)
0.0115297 + 0.999934i \(0.496330\pi\)
\(258\) 0 0
\(259\) −3.52276 −0.218893
\(260\) 0 0
\(261\) 3.67526 0.227493
\(262\) 0 0
\(263\) −2.44589 −0.150820 −0.0754099 0.997153i \(-0.524027\pi\)
−0.0754099 + 0.997153i \(0.524027\pi\)
\(264\) 0 0
\(265\) −5.05611 −0.310594
\(266\) 0 0
\(267\) −14.7484 −0.902588
\(268\) 0 0
\(269\) −3.85067 −0.234780 −0.117390 0.993086i \(-0.537453\pi\)
−0.117390 + 0.993086i \(0.537453\pi\)
\(270\) 0 0
\(271\) 29.7078 1.80462 0.902310 0.431087i \(-0.141870\pi\)
0.902310 + 0.431087i \(0.141870\pi\)
\(272\) 0 0
\(273\) 1.72658 0.104498
\(274\) 0 0
\(275\) 46.6822 2.81504
\(276\) 0 0
\(277\) 21.6836 1.30284 0.651420 0.758717i \(-0.274173\pi\)
0.651420 + 0.758717i \(0.274173\pi\)
\(278\) 0 0
\(279\) −0.816111 −0.0488593
\(280\) 0 0
\(281\) −2.96764 −0.177035 −0.0885174 0.996075i \(-0.528213\pi\)
−0.0885174 + 0.996075i \(0.528213\pi\)
\(282\) 0 0
\(283\) 0.541058 0.0321626 0.0160813 0.999871i \(-0.494881\pi\)
0.0160813 + 0.999871i \(0.494881\pi\)
\(284\) 0 0
\(285\) 0.239954 0.0142136
\(286\) 0 0
\(287\) −19.1255 −1.12894
\(288\) 0 0
\(289\) 14.7091 0.865241
\(290\) 0 0
\(291\) −11.2601 −0.660076
\(292\) 0 0
\(293\) −11.3653 −0.663966 −0.331983 0.943285i \(-0.607718\pi\)
−0.331983 + 0.943285i \(0.607718\pi\)
\(294\) 0 0
\(295\) −50.2515 −2.92576
\(296\) 0 0
\(297\) −21.9371 −1.27292
\(298\) 0 0
\(299\) 2.66137 0.153911
\(300\) 0 0
\(301\) −24.1216 −1.39034
\(302\) 0 0
\(303\) −15.1886 −0.872561
\(304\) 0 0
\(305\) −40.1889 −2.30121
\(306\) 0 0
\(307\) −8.95952 −0.511347 −0.255674 0.966763i \(-0.582297\pi\)
−0.255674 + 0.966763i \(0.582297\pi\)
\(308\) 0 0
\(309\) 14.0480 0.799160
\(310\) 0 0
\(311\) 22.9435 1.30101 0.650503 0.759504i \(-0.274558\pi\)
0.650503 + 0.759504i \(0.274558\pi\)
\(312\) 0 0
\(313\) −29.0611 −1.64263 −0.821314 0.570477i \(-0.806759\pi\)
−0.821314 + 0.570477i \(0.806759\pi\)
\(314\) 0 0
\(315\) −32.0769 −1.80733
\(316\) 0 0
\(317\) 22.3051 1.25278 0.626390 0.779510i \(-0.284532\pi\)
0.626390 + 0.779510i \(0.284532\pi\)
\(318\) 0 0
\(319\) −7.87926 −0.441154
\(320\) 0 0
\(321\) 6.98142 0.389665
\(322\) 0 0
\(323\) −0.391742 −0.0217971
\(324\) 0 0
\(325\) −5.06056 −0.280709
\(326\) 0 0
\(327\) −1.32027 −0.0730109
\(328\) 0 0
\(329\) −15.8554 −0.874138
\(330\) 0 0
\(331\) −16.7757 −0.922076 −0.461038 0.887380i \(-0.652523\pi\)
−0.461038 + 0.887380i \(0.652523\pi\)
\(332\) 0 0
\(333\) −2.05338 −0.112525
\(334\) 0 0
\(335\) 8.10269 0.442697
\(336\) 0 0
\(337\) −27.7893 −1.51378 −0.756890 0.653542i \(-0.773282\pi\)
−0.756890 + 0.653542i \(0.773282\pi\)
\(338\) 0 0
\(339\) −4.41420 −0.239746
\(340\) 0 0
\(341\) 1.74963 0.0947478
\(342\) 0 0
\(343\) −0.982048 −0.0530256
\(344\) 0 0
\(345\) 17.9446 0.966104
\(346\) 0 0
\(347\) −1.80385 −0.0968359 −0.0484179 0.998827i \(-0.515418\pi\)
−0.0484179 + 0.998827i \(0.515418\pi\)
\(348\) 0 0
\(349\) 24.4308 1.30775 0.653876 0.756602i \(-0.273142\pi\)
0.653876 + 0.756602i \(0.273142\pi\)
\(350\) 0 0
\(351\) 2.37807 0.126932
\(352\) 0 0
\(353\) −9.08469 −0.483530 −0.241765 0.970335i \(-0.577726\pi\)
−0.241765 + 0.970335i \(0.577726\pi\)
\(354\) 0 0
\(355\) 12.7717 0.677850
\(356\) 0 0
\(357\) −19.0059 −1.00590
\(358\) 0 0
\(359\) 24.4405 1.28992 0.644961 0.764215i \(-0.276873\pi\)
0.644961 + 0.764215i \(0.276873\pi\)
\(360\) 0 0
\(361\) −18.9952 −0.999745
\(362\) 0 0
\(363\) 10.0716 0.528622
\(364\) 0 0
\(365\) −4.15406 −0.217433
\(366\) 0 0
\(367\) −34.6446 −1.80843 −0.904216 0.427075i \(-0.859544\pi\)
−0.904216 + 0.427075i \(0.859544\pi\)
\(368\) 0 0
\(369\) −11.1481 −0.580347
\(370\) 0 0
\(371\) −4.94758 −0.256866
\(372\) 0 0
\(373\) −28.5395 −1.47772 −0.738859 0.673860i \(-0.764635\pi\)
−0.738859 + 0.673860i \(0.764635\pi\)
\(374\) 0 0
\(375\) −16.8753 −0.871437
\(376\) 0 0
\(377\) 0.854146 0.0439907
\(378\) 0 0
\(379\) −5.70976 −0.293291 −0.146645 0.989189i \(-0.546848\pi\)
−0.146645 + 0.989189i \(0.546848\pi\)
\(380\) 0 0
\(381\) 10.7640 0.551455
\(382\) 0 0
\(383\) −20.8571 −1.06575 −0.532873 0.846195i \(-0.678888\pi\)
−0.532873 + 0.846195i \(0.678888\pi\)
\(384\) 0 0
\(385\) 68.7685 3.50477
\(386\) 0 0
\(387\) −14.0602 −0.714722
\(388\) 0 0
\(389\) −23.3177 −1.18225 −0.591126 0.806579i \(-0.701316\pi\)
−0.591126 + 0.806579i \(0.701316\pi\)
\(390\) 0 0
\(391\) −29.2958 −1.48155
\(392\) 0 0
\(393\) −0.154979 −0.00781763
\(394\) 0 0
\(395\) 39.2120 1.97297
\(396\) 0 0
\(397\) −33.4612 −1.67937 −0.839684 0.543076i \(-0.817260\pi\)
−0.839684 + 0.543076i \(0.817260\pi\)
\(398\) 0 0
\(399\) 0.234803 0.0117549
\(400\) 0 0
\(401\) −27.3510 −1.36584 −0.682922 0.730491i \(-0.739291\pi\)
−0.682922 + 0.730491i \(0.739291\pi\)
\(402\) 0 0
\(403\) −0.189668 −0.00944801
\(404\) 0 0
\(405\) −9.44874 −0.469512
\(406\) 0 0
\(407\) 4.40217 0.218207
\(408\) 0 0
\(409\) −2.71339 −0.134169 −0.0670843 0.997747i \(-0.521370\pi\)
−0.0670843 + 0.997747i \(0.521370\pi\)
\(410\) 0 0
\(411\) −9.27848 −0.457674
\(412\) 0 0
\(413\) −49.1729 −2.41964
\(414\) 0 0
\(415\) 45.3514 2.22621
\(416\) 0 0
\(417\) −12.6487 −0.619407
\(418\) 0 0
\(419\) 4.86004 0.237428 0.118714 0.992928i \(-0.462123\pi\)
0.118714 + 0.992928i \(0.462123\pi\)
\(420\) 0 0
\(421\) 13.2128 0.643952 0.321976 0.946748i \(-0.395653\pi\)
0.321976 + 0.946748i \(0.395653\pi\)
\(422\) 0 0
\(423\) −9.24198 −0.449360
\(424\) 0 0
\(425\) 55.7056 2.70212
\(426\) 0 0
\(427\) −39.3263 −1.90313
\(428\) 0 0
\(429\) −2.15760 −0.104170
\(430\) 0 0
\(431\) −23.1046 −1.11291 −0.556455 0.830878i \(-0.687839\pi\)
−0.556455 + 0.830878i \(0.687839\pi\)
\(432\) 0 0
\(433\) 2.97652 0.143043 0.0715213 0.997439i \(-0.477215\pi\)
0.0715213 + 0.997439i \(0.477215\pi\)
\(434\) 0 0
\(435\) 5.75917 0.276131
\(436\) 0 0
\(437\) 0.361928 0.0173134
\(438\) 0 0
\(439\) −26.2388 −1.25231 −0.626155 0.779699i \(-0.715372\pi\)
−0.626155 + 0.779699i \(0.715372\pi\)
\(440\) 0 0
\(441\) −15.9804 −0.760972
\(442\) 0 0
\(443\) 28.1621 1.33802 0.669012 0.743252i \(-0.266718\pi\)
0.669012 + 0.743252i \(0.266718\pi\)
\(444\) 0 0
\(445\) 63.6787 3.01866
\(446\) 0 0
\(447\) 17.1537 0.811344
\(448\) 0 0
\(449\) 14.4204 0.680541 0.340271 0.940328i \(-0.389481\pi\)
0.340271 + 0.940328i \(0.389481\pi\)
\(450\) 0 0
\(451\) 23.9000 1.12541
\(452\) 0 0
\(453\) 6.55464 0.307964
\(454\) 0 0
\(455\) −7.45480 −0.349487
\(456\) 0 0
\(457\) 3.73893 0.174900 0.0874499 0.996169i \(-0.472128\pi\)
0.0874499 + 0.996169i \(0.472128\pi\)
\(458\) 0 0
\(459\) −26.1774 −1.22185
\(460\) 0 0
\(461\) −12.1666 −0.566654 −0.283327 0.959023i \(-0.591438\pi\)
−0.283327 + 0.959023i \(0.591438\pi\)
\(462\) 0 0
\(463\) 25.0242 1.16298 0.581488 0.813555i \(-0.302471\pi\)
0.581488 + 0.813555i \(0.302471\pi\)
\(464\) 0 0
\(465\) −1.27885 −0.0593054
\(466\) 0 0
\(467\) 2.41158 0.111594 0.0557972 0.998442i \(-0.482230\pi\)
0.0557972 + 0.998442i \(0.482230\pi\)
\(468\) 0 0
\(469\) 7.92877 0.366117
\(470\) 0 0
\(471\) 18.2294 0.839965
\(472\) 0 0
\(473\) 30.1432 1.38599
\(474\) 0 0
\(475\) −0.688201 −0.0315768
\(476\) 0 0
\(477\) −2.88390 −0.132045
\(478\) 0 0
\(479\) 12.3217 0.562992 0.281496 0.959562i \(-0.409169\pi\)
0.281496 + 0.959562i \(0.409169\pi\)
\(480\) 0 0
\(481\) −0.477214 −0.0217591
\(482\) 0 0
\(483\) 17.5594 0.798981
\(484\) 0 0
\(485\) 48.6172 2.20759
\(486\) 0 0
\(487\) 34.7800 1.57603 0.788016 0.615655i \(-0.211109\pi\)
0.788016 + 0.615655i \(0.211109\pi\)
\(488\) 0 0
\(489\) −1.36632 −0.0617870
\(490\) 0 0
\(491\) 6.56397 0.296228 0.148114 0.988970i \(-0.452680\pi\)
0.148114 + 0.988970i \(0.452680\pi\)
\(492\) 0 0
\(493\) −9.40226 −0.423457
\(494\) 0 0
\(495\) 40.0845 1.80166
\(496\) 0 0
\(497\) 12.4975 0.560591
\(498\) 0 0
\(499\) −27.2924 −1.22178 −0.610888 0.791717i \(-0.709187\pi\)
−0.610888 + 0.791717i \(0.709187\pi\)
\(500\) 0 0
\(501\) −6.16243 −0.275317
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 65.5792 2.91824
\(506\) 0 0
\(507\) −11.3854 −0.505642
\(508\) 0 0
\(509\) 3.54941 0.157325 0.0786625 0.996901i \(-0.474935\pi\)
0.0786625 + 0.996901i \(0.474935\pi\)
\(510\) 0 0
\(511\) −4.06489 −0.179820
\(512\) 0 0
\(513\) 0.323402 0.0142785
\(514\) 0 0
\(515\) −60.6544 −2.67275
\(516\) 0 0
\(517\) 19.8135 0.871398
\(518\) 0 0
\(519\) −21.6524 −0.950436
\(520\) 0 0
\(521\) 10.8364 0.474751 0.237376 0.971418i \(-0.423713\pi\)
0.237376 + 0.971418i \(0.423713\pi\)
\(522\) 0 0
\(523\) −11.3289 −0.495377 −0.247689 0.968840i \(-0.579671\pi\)
−0.247689 + 0.968840i \(0.579671\pi\)
\(524\) 0 0
\(525\) −33.3889 −1.45721
\(526\) 0 0
\(527\) 2.08782 0.0909470
\(528\) 0 0
\(529\) 4.06626 0.176794
\(530\) 0 0
\(531\) −28.6624 −1.24384
\(532\) 0 0
\(533\) −2.59086 −0.112223
\(534\) 0 0
\(535\) −30.1434 −1.30321
\(536\) 0 0
\(537\) −15.6523 −0.675449
\(538\) 0 0
\(539\) 34.2598 1.47567
\(540\) 0 0
\(541\) −20.4018 −0.877140 −0.438570 0.898697i \(-0.644515\pi\)
−0.438570 + 0.898697i \(0.644515\pi\)
\(542\) 0 0
\(543\) −12.5806 −0.539886
\(544\) 0 0
\(545\) 5.70047 0.244181
\(546\) 0 0
\(547\) −24.3885 −1.04278 −0.521388 0.853319i \(-0.674586\pi\)
−0.521388 + 0.853319i \(0.674586\pi\)
\(548\) 0 0
\(549\) −22.9229 −0.978327
\(550\) 0 0
\(551\) 0.116158 0.00494849
\(552\) 0 0
\(553\) 38.3703 1.63167
\(554\) 0 0
\(555\) −3.21767 −0.136582
\(556\) 0 0
\(557\) −12.3148 −0.521793 −0.260897 0.965367i \(-0.584018\pi\)
−0.260897 + 0.965367i \(0.584018\pi\)
\(558\) 0 0
\(559\) −3.26765 −0.138207
\(560\) 0 0
\(561\) 23.7505 1.00274
\(562\) 0 0
\(563\) −29.9321 −1.26149 −0.630745 0.775990i \(-0.717250\pi\)
−0.630745 + 0.775990i \(0.717250\pi\)
\(564\) 0 0
\(565\) 19.0590 0.801819
\(566\) 0 0
\(567\) −9.24593 −0.388293
\(568\) 0 0
\(569\) 19.1154 0.801360 0.400680 0.916218i \(-0.368774\pi\)
0.400680 + 0.916218i \(0.368774\pi\)
\(570\) 0 0
\(571\) −15.4172 −0.645191 −0.322595 0.946537i \(-0.604555\pi\)
−0.322595 + 0.946537i \(0.604555\pi\)
\(572\) 0 0
\(573\) 16.1661 0.675348
\(574\) 0 0
\(575\) −51.4661 −2.14628
\(576\) 0 0
\(577\) 4.37226 0.182019 0.0910097 0.995850i \(-0.470991\pi\)
0.0910097 + 0.995850i \(0.470991\pi\)
\(578\) 0 0
\(579\) −3.72325 −0.154733
\(580\) 0 0
\(581\) 44.3780 1.84111
\(582\) 0 0
\(583\) 6.18269 0.256061
\(584\) 0 0
\(585\) −4.34534 −0.179657
\(586\) 0 0
\(587\) −16.8749 −0.696500 −0.348250 0.937402i \(-0.613224\pi\)
−0.348250 + 0.937402i \(0.613224\pi\)
\(588\) 0 0
\(589\) −0.0257935 −0.00106280
\(590\) 0 0
\(591\) −15.9995 −0.658133
\(592\) 0 0
\(593\) 25.1993 1.03481 0.517405 0.855741i \(-0.326898\pi\)
0.517405 + 0.855741i \(0.326898\pi\)
\(594\) 0 0
\(595\) 82.0610 3.36417
\(596\) 0 0
\(597\) −16.8658 −0.690272
\(598\) 0 0
\(599\) −33.5870 −1.37233 −0.686165 0.727446i \(-0.740707\pi\)
−0.686165 + 0.727446i \(0.740707\pi\)
\(600\) 0 0
\(601\) 19.6769 0.802636 0.401318 0.915939i \(-0.368552\pi\)
0.401318 + 0.915939i \(0.368552\pi\)
\(602\) 0 0
\(603\) 4.62161 0.188206
\(604\) 0 0
\(605\) −43.4858 −1.76795
\(606\) 0 0
\(607\) 0.481239 0.0195329 0.00976644 0.999952i \(-0.496891\pi\)
0.00976644 + 0.999952i \(0.496891\pi\)
\(608\) 0 0
\(609\) 5.63555 0.228364
\(610\) 0 0
\(611\) −2.14787 −0.0868937
\(612\) 0 0
\(613\) −7.08677 −0.286232 −0.143116 0.989706i \(-0.545712\pi\)
−0.143116 + 0.989706i \(0.545712\pi\)
\(614\) 0 0
\(615\) −17.4692 −0.704425
\(616\) 0 0
\(617\) 5.30571 0.213600 0.106800 0.994281i \(-0.465940\pi\)
0.106800 + 0.994281i \(0.465940\pi\)
\(618\) 0 0
\(619\) −30.7918 −1.23763 −0.618813 0.785539i \(-0.712386\pi\)
−0.618813 + 0.785539i \(0.712386\pi\)
\(620\) 0 0
\(621\) 24.1851 0.970515
\(622\) 0 0
\(623\) 62.3119 2.49647
\(624\) 0 0
\(625\) 23.3993 0.935972
\(626\) 0 0
\(627\) −0.293419 −0.0117180
\(628\) 0 0
\(629\) 5.25308 0.209454
\(630\) 0 0
\(631\) 35.2732 1.40421 0.702103 0.712076i \(-0.252245\pi\)
0.702103 + 0.712076i \(0.252245\pi\)
\(632\) 0 0
\(633\) −16.2716 −0.646739
\(634\) 0 0
\(635\) −46.4752 −1.84431
\(636\) 0 0
\(637\) −3.71391 −0.147151
\(638\) 0 0
\(639\) 7.28470 0.288178
\(640\) 0 0
\(641\) 17.8655 0.705644 0.352822 0.935690i \(-0.385222\pi\)
0.352822 + 0.935690i \(0.385222\pi\)
\(642\) 0 0
\(643\) 8.61818 0.339868 0.169934 0.985455i \(-0.445645\pi\)
0.169934 + 0.985455i \(0.445645\pi\)
\(644\) 0 0
\(645\) −22.0325 −0.867529
\(646\) 0 0
\(647\) −15.4910 −0.609016 −0.304508 0.952510i \(-0.598492\pi\)
−0.304508 + 0.952510i \(0.598492\pi\)
\(648\) 0 0
\(649\) 61.4483 2.41206
\(650\) 0 0
\(651\) −1.25140 −0.0490464
\(652\) 0 0
\(653\) 21.5939 0.845035 0.422517 0.906355i \(-0.361147\pi\)
0.422517 + 0.906355i \(0.361147\pi\)
\(654\) 0 0
\(655\) 0.669145 0.0261457
\(656\) 0 0
\(657\) −2.36939 −0.0924386
\(658\) 0 0
\(659\) −25.2479 −0.983517 −0.491759 0.870731i \(-0.663646\pi\)
−0.491759 + 0.870731i \(0.663646\pi\)
\(660\) 0 0
\(661\) −26.7554 −1.04067 −0.520333 0.853964i \(-0.674192\pi\)
−0.520333 + 0.853964i \(0.674192\pi\)
\(662\) 0 0
\(663\) −2.57465 −0.0999912
\(664\) 0 0
\(665\) −1.01380 −0.0393136
\(666\) 0 0
\(667\) 8.68670 0.336350
\(668\) 0 0
\(669\) −2.72237 −0.105253
\(670\) 0 0
\(671\) 49.1436 1.89717
\(672\) 0 0
\(673\) 44.1952 1.70360 0.851801 0.523866i \(-0.175511\pi\)
0.851801 + 0.523866i \(0.175511\pi\)
\(674\) 0 0
\(675\) −45.9876 −1.77006
\(676\) 0 0
\(677\) −25.5496 −0.981952 −0.490976 0.871173i \(-0.663360\pi\)
−0.490976 + 0.871173i \(0.663360\pi\)
\(678\) 0 0
\(679\) 47.5736 1.82571
\(680\) 0 0
\(681\) 6.31745 0.242085
\(682\) 0 0
\(683\) 4.16513 0.159374 0.0796872 0.996820i \(-0.474608\pi\)
0.0796872 + 0.996820i \(0.474608\pi\)
\(684\) 0 0
\(685\) 40.0614 1.53067
\(686\) 0 0
\(687\) 3.07125 0.117175
\(688\) 0 0
\(689\) −0.670230 −0.0255337
\(690\) 0 0
\(691\) −34.4452 −1.31036 −0.655179 0.755474i \(-0.727407\pi\)
−0.655179 + 0.755474i \(0.727407\pi\)
\(692\) 0 0
\(693\) 39.2241 1.49000
\(694\) 0 0
\(695\) 54.6126 2.07158
\(696\) 0 0
\(697\) 28.5197 1.08026
\(698\) 0 0
\(699\) −17.0210 −0.643795
\(700\) 0 0
\(701\) −19.9463 −0.753363 −0.376682 0.926343i \(-0.622935\pi\)
−0.376682 + 0.926343i \(0.622935\pi\)
\(702\) 0 0
\(703\) −0.0648979 −0.00244767
\(704\) 0 0
\(705\) −14.4823 −0.545434
\(706\) 0 0
\(707\) 64.1716 2.41342
\(708\) 0 0
\(709\) −42.3849 −1.59180 −0.795900 0.605429i \(-0.793002\pi\)
−0.795900 + 0.605429i \(0.793002\pi\)
\(710\) 0 0
\(711\) 22.3657 0.838779
\(712\) 0 0
\(713\) −1.92893 −0.0722389
\(714\) 0 0
\(715\) 9.31580 0.348391
\(716\) 0 0
\(717\) 18.5921 0.694336
\(718\) 0 0
\(719\) 29.6547 1.10593 0.552967 0.833203i \(-0.313495\pi\)
0.552967 + 0.833203i \(0.313495\pi\)
\(720\) 0 0
\(721\) −59.3525 −2.21040
\(722\) 0 0
\(723\) 3.96460 0.147445
\(724\) 0 0
\(725\) −16.5176 −0.613449
\(726\) 0 0
\(727\) −9.18661 −0.340713 −0.170356 0.985383i \(-0.554492\pi\)
−0.170356 + 0.985383i \(0.554492\pi\)
\(728\) 0 0
\(729\) 7.07557 0.262058
\(730\) 0 0
\(731\) 35.9697 1.33039
\(732\) 0 0
\(733\) −3.92172 −0.144852 −0.0724260 0.997374i \(-0.523074\pi\)
−0.0724260 + 0.997374i \(0.523074\pi\)
\(734\) 0 0
\(735\) −25.0414 −0.923668
\(736\) 0 0
\(737\) −9.90809 −0.364969
\(738\) 0 0
\(739\) 40.3182 1.48313 0.741564 0.670882i \(-0.234084\pi\)
0.741564 + 0.670882i \(0.234084\pi\)
\(740\) 0 0
\(741\) 0.0318079 0.00116849
\(742\) 0 0
\(743\) −12.1172 −0.444535 −0.222268 0.974986i \(-0.571346\pi\)
−0.222268 + 0.974986i \(0.571346\pi\)
\(744\) 0 0
\(745\) −74.0641 −2.71350
\(746\) 0 0
\(747\) 25.8675 0.946442
\(748\) 0 0
\(749\) −29.4964 −1.07778
\(750\) 0 0
\(751\) 15.8609 0.578771 0.289386 0.957213i \(-0.406549\pi\)
0.289386 + 0.957213i \(0.406549\pi\)
\(752\) 0 0
\(753\) 20.0852 0.731947
\(754\) 0 0
\(755\) −28.3007 −1.02997
\(756\) 0 0
\(757\) 24.4267 0.887805 0.443902 0.896075i \(-0.353594\pi\)
0.443902 + 0.896075i \(0.353594\pi\)
\(758\) 0 0
\(759\) −21.9429 −0.796477
\(760\) 0 0
\(761\) 20.2267 0.733216 0.366608 0.930375i \(-0.380519\pi\)
0.366608 + 0.930375i \(0.380519\pi\)
\(762\) 0 0
\(763\) 5.57811 0.201941
\(764\) 0 0
\(765\) 47.8326 1.72939
\(766\) 0 0
\(767\) −6.66126 −0.240524
\(768\) 0 0
\(769\) −2.17563 −0.0784551 −0.0392275 0.999230i \(-0.512490\pi\)
−0.0392275 + 0.999230i \(0.512490\pi\)
\(770\) 0 0
\(771\) 0.330408 0.0118994
\(772\) 0 0
\(773\) 3.49777 0.125806 0.0629030 0.998020i \(-0.479964\pi\)
0.0629030 + 0.998020i \(0.479964\pi\)
\(774\) 0 0
\(775\) 3.66782 0.131752
\(776\) 0 0
\(777\) −3.14860 −0.112955
\(778\) 0 0
\(779\) −0.352339 −0.0126239
\(780\) 0 0
\(781\) −15.6174 −0.558834
\(782\) 0 0
\(783\) 7.76201 0.277392
\(784\) 0 0
\(785\) −78.7083 −2.80922
\(786\) 0 0
\(787\) 25.5395 0.910384 0.455192 0.890393i \(-0.349571\pi\)
0.455192 + 0.890393i \(0.349571\pi\)
\(788\) 0 0
\(789\) −2.18611 −0.0778275
\(790\) 0 0
\(791\) 18.6499 0.663115
\(792\) 0 0
\(793\) −5.32738 −0.189181
\(794\) 0 0
\(795\) −4.51910 −0.160276
\(796\) 0 0
\(797\) −31.0283 −1.09908 −0.549540 0.835467i \(-0.685197\pi\)
−0.549540 + 0.835467i \(0.685197\pi\)
\(798\) 0 0
\(799\) 23.6434 0.836442
\(800\) 0 0
\(801\) 36.3210 1.28334
\(802\) 0 0
\(803\) 5.07964 0.179257
\(804\) 0 0
\(805\) −75.8156 −2.67215
\(806\) 0 0
\(807\) −3.44169 −0.121153
\(808\) 0 0
\(809\) 33.7935 1.18812 0.594059 0.804422i \(-0.297525\pi\)
0.594059 + 0.804422i \(0.297525\pi\)
\(810\) 0 0
\(811\) 14.3158 0.502697 0.251348 0.967897i \(-0.419126\pi\)
0.251348 + 0.967897i \(0.419126\pi\)
\(812\) 0 0
\(813\) 26.5525 0.931237
\(814\) 0 0
\(815\) 5.89930 0.206643
\(816\) 0 0
\(817\) −0.444378 −0.0155468
\(818\) 0 0
\(819\) −4.25207 −0.148579
\(820\) 0 0
\(821\) −46.7093 −1.63017 −0.815083 0.579344i \(-0.803309\pi\)
−0.815083 + 0.579344i \(0.803309\pi\)
\(822\) 0 0
\(823\) −8.77876 −0.306008 −0.153004 0.988226i \(-0.548895\pi\)
−0.153004 + 0.988226i \(0.548895\pi\)
\(824\) 0 0
\(825\) 41.7241 1.45265
\(826\) 0 0
\(827\) 40.5870 1.41135 0.705674 0.708537i \(-0.250644\pi\)
0.705674 + 0.708537i \(0.250644\pi\)
\(828\) 0 0
\(829\) 36.2857 1.26025 0.630127 0.776492i \(-0.283003\pi\)
0.630127 + 0.776492i \(0.283003\pi\)
\(830\) 0 0
\(831\) 19.3806 0.672304
\(832\) 0 0
\(833\) 40.8820 1.41648
\(834\) 0 0
\(835\) 26.6073 0.920784
\(836\) 0 0
\(837\) −1.72360 −0.0595762
\(838\) 0 0
\(839\) 18.1603 0.626963 0.313481 0.949594i \(-0.398505\pi\)
0.313481 + 0.949594i \(0.398505\pi\)
\(840\) 0 0
\(841\) −26.2121 −0.903865
\(842\) 0 0
\(843\) −2.65245 −0.0913551
\(844\) 0 0
\(845\) 49.1582 1.69109
\(846\) 0 0
\(847\) −42.5524 −1.46212
\(848\) 0 0
\(849\) 0.483592 0.0165968
\(850\) 0 0
\(851\) −4.85329 −0.166369
\(852\) 0 0
\(853\) −42.2922 −1.44806 −0.724028 0.689771i \(-0.757711\pi\)
−0.724028 + 0.689771i \(0.757711\pi\)
\(854\) 0 0
\(855\) −0.590936 −0.0202096
\(856\) 0 0
\(857\) 39.9946 1.36619 0.683095 0.730330i \(-0.260633\pi\)
0.683095 + 0.730330i \(0.260633\pi\)
\(858\) 0 0
\(859\) −55.2653 −1.88563 −0.942813 0.333322i \(-0.891830\pi\)
−0.942813 + 0.333322i \(0.891830\pi\)
\(860\) 0 0
\(861\) −17.0942 −0.582569
\(862\) 0 0
\(863\) −14.9582 −0.509185 −0.254592 0.967048i \(-0.581941\pi\)
−0.254592 + 0.967048i \(0.581941\pi\)
\(864\) 0 0
\(865\) 93.4879 3.17868
\(866\) 0 0
\(867\) 13.1468 0.446490
\(868\) 0 0
\(869\) −47.9490 −1.62656
\(870\) 0 0
\(871\) 1.07408 0.0363938
\(872\) 0 0
\(873\) 27.7302 0.938526
\(874\) 0 0
\(875\) 71.2979 2.41031
\(876\) 0 0
\(877\) −33.7083 −1.13825 −0.569124 0.822252i \(-0.692717\pi\)
−0.569124 + 0.822252i \(0.692717\pi\)
\(878\) 0 0
\(879\) −10.1582 −0.342626
\(880\) 0 0
\(881\) 24.4774 0.824666 0.412333 0.911033i \(-0.364714\pi\)
0.412333 + 0.911033i \(0.364714\pi\)
\(882\) 0 0
\(883\) −22.1930 −0.746853 −0.373426 0.927660i \(-0.621817\pi\)
−0.373426 + 0.927660i \(0.621817\pi\)
\(884\) 0 0
\(885\) −44.9143 −1.50978
\(886\) 0 0
\(887\) −8.44417 −0.283528 −0.141764 0.989901i \(-0.545277\pi\)
−0.141764 + 0.989901i \(0.545277\pi\)
\(888\) 0 0
\(889\) −45.4777 −1.52527
\(890\) 0 0
\(891\) 11.5541 0.387076
\(892\) 0 0
\(893\) −0.292096 −0.00977462
\(894\) 0 0
\(895\) 67.5816 2.25900
\(896\) 0 0
\(897\) 2.37871 0.0794227
\(898\) 0 0
\(899\) −0.619073 −0.0206472
\(900\) 0 0
\(901\) 7.37776 0.245789
\(902\) 0 0
\(903\) −21.5596 −0.717458
\(904\) 0 0
\(905\) 54.3188 1.80562
\(906\) 0 0
\(907\) −16.7572 −0.556413 −0.278207 0.960521i \(-0.589740\pi\)
−0.278207 + 0.960521i \(0.589740\pi\)
\(908\) 0 0
\(909\) 37.4050 1.24065
\(910\) 0 0
\(911\) 48.2461 1.59847 0.799233 0.601021i \(-0.205239\pi\)
0.799233 + 0.601021i \(0.205239\pi\)
\(912\) 0 0
\(913\) −55.4564 −1.83534
\(914\) 0 0
\(915\) −35.9204 −1.18749
\(916\) 0 0
\(917\) 0.654782 0.0216228
\(918\) 0 0
\(919\) −18.0249 −0.594587 −0.297294 0.954786i \(-0.596084\pi\)
−0.297294 + 0.954786i \(0.596084\pi\)
\(920\) 0 0
\(921\) −8.00793 −0.263870
\(922\) 0 0
\(923\) 1.69299 0.0557256
\(924\) 0 0
\(925\) 9.22845 0.303430
\(926\) 0 0
\(927\) −34.5960 −1.13628
\(928\) 0 0
\(929\) 9.46901 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(930\) 0 0
\(931\) −0.505066 −0.0165529
\(932\) 0 0
\(933\) 20.5067 0.671358
\(934\) 0 0
\(935\) −102.546 −3.35363
\(936\) 0 0
\(937\) −29.3194 −0.957824 −0.478912 0.877863i \(-0.658969\pi\)
−0.478912 + 0.877863i \(0.658969\pi\)
\(938\) 0 0
\(939\) −25.9745 −0.847644
\(940\) 0 0
\(941\) 54.4765 1.77588 0.887942 0.459956i \(-0.152135\pi\)
0.887942 + 0.459956i \(0.152135\pi\)
\(942\) 0 0
\(943\) −26.3492 −0.858047
\(944\) 0 0
\(945\) −67.7452 −2.20375
\(946\) 0 0
\(947\) 0.898972 0.0292127 0.0146063 0.999893i \(-0.495350\pi\)
0.0146063 + 0.999893i \(0.495350\pi\)
\(948\) 0 0
\(949\) −0.550655 −0.0178750
\(950\) 0 0
\(951\) 19.9361 0.646472
\(952\) 0 0
\(953\) −47.1222 −1.52644 −0.763218 0.646141i \(-0.776382\pi\)
−0.763218 + 0.646141i \(0.776382\pi\)
\(954\) 0 0
\(955\) −69.7998 −2.25867
\(956\) 0 0
\(957\) −7.04239 −0.227648
\(958\) 0 0
\(959\) 39.2015 1.26588
\(960\) 0 0
\(961\) −30.8625 −0.995566
\(962\) 0 0
\(963\) −17.1932 −0.554043
\(964\) 0 0
\(965\) 16.0757 0.517496
\(966\) 0 0
\(967\) −24.3871 −0.784235 −0.392118 0.919915i \(-0.628257\pi\)
−0.392118 + 0.919915i \(0.628257\pi\)
\(968\) 0 0
\(969\) −0.350135 −0.0112480
\(970\) 0 0
\(971\) 36.8714 1.18326 0.591630 0.806209i \(-0.298485\pi\)
0.591630 + 0.806209i \(0.298485\pi\)
\(972\) 0 0
\(973\) 53.4404 1.71322
\(974\) 0 0
\(975\) −4.52307 −0.144854
\(976\) 0 0
\(977\) 10.0886 0.322763 0.161382 0.986892i \(-0.448405\pi\)
0.161382 + 0.986892i \(0.448405\pi\)
\(978\) 0 0
\(979\) −77.8673 −2.48865
\(980\) 0 0
\(981\) 3.25143 0.103810
\(982\) 0 0
\(983\) −29.7977 −0.950399 −0.475200 0.879878i \(-0.657624\pi\)
−0.475200 + 0.879878i \(0.657624\pi\)
\(984\) 0 0
\(985\) 69.0806 2.20109
\(986\) 0 0
\(987\) −14.1714 −0.451081
\(988\) 0 0
\(989\) −33.2322 −1.05672
\(990\) 0 0
\(991\) 14.3363 0.455408 0.227704 0.973730i \(-0.426878\pi\)
0.227704 + 0.973730i \(0.426878\pi\)
\(992\) 0 0
\(993\) −14.9939 −0.475818
\(994\) 0 0
\(995\) 72.8209 2.30858
\(996\) 0 0
\(997\) −5.98970 −0.189696 −0.0948478 0.995492i \(-0.530236\pi\)
−0.0948478 + 0.995492i \(0.530236\pi\)
\(998\) 0 0
\(999\) −4.33666 −0.137206
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 \(a_p\))