Properties

Label 8020.2.a.c.1.9
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.48695 q^{3}\) \(-1.00000 q^{5}\) \(-3.53428 q^{7}\) \(-0.788974 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.48695 q^{3}\) \(-1.00000 q^{5}\) \(-3.53428 q^{7}\) \(-0.788974 q^{9}\) \(-0.193476 q^{11}\) \(-1.78611 q^{13}\) \(+1.48695 q^{15}\) \(+0.112625 q^{17}\) \(-1.44633 q^{19}\) \(+5.25531 q^{21}\) \(+7.37160 q^{23}\) \(+1.00000 q^{25}\) \(+5.63402 q^{27}\) \(-1.99452 q^{29}\) \(-2.75759 q^{31}\) \(+0.287689 q^{33}\) \(+3.53428 q^{35}\) \(-5.38909 q^{37}\) \(+2.65587 q^{39}\) \(+9.08586 q^{41}\) \(+7.95947 q^{43}\) \(+0.788974 q^{45}\) \(-9.63499 q^{47}\) \(+5.49115 q^{49}\) \(-0.167468 q^{51}\) \(+1.21869 q^{53}\) \(+0.193476 q^{55}\) \(+2.15063 q^{57}\) \(-4.20935 q^{59}\) \(+6.14882 q^{61}\) \(+2.78846 q^{63}\) \(+1.78611 q^{65}\) \(+8.98383 q^{67}\) \(-10.9612 q^{69}\) \(-7.09651 q^{71}\) \(+11.1077 q^{73}\) \(-1.48695 q^{75}\) \(+0.683797 q^{77}\) \(+5.03284 q^{79}\) \(-6.01060 q^{81}\) \(+13.2788 q^{83}\) \(-0.112625 q^{85}\) \(+2.96575 q^{87}\) \(+16.2676 q^{89}\) \(+6.31263 q^{91}\) \(+4.10040 q^{93}\) \(+1.44633 q^{95}\) \(-6.48853 q^{97}\) \(+0.152647 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.48695 −0.858492 −0.429246 0.903188i \(-0.641221\pi\)
−0.429246 + 0.903188i \(0.641221\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.53428 −1.33583 −0.667916 0.744236i \(-0.732814\pi\)
−0.667916 + 0.744236i \(0.732814\pi\)
\(8\) 0 0
\(9\) −0.788974 −0.262991
\(10\) 0 0
\(11\) −0.193476 −0.0583351 −0.0291675 0.999575i \(-0.509286\pi\)
−0.0291675 + 0.999575i \(0.509286\pi\)
\(12\) 0 0
\(13\) −1.78611 −0.495379 −0.247689 0.968839i \(-0.579671\pi\)
−0.247689 + 0.968839i \(0.579671\pi\)
\(14\) 0 0
\(15\) 1.48695 0.383929
\(16\) 0 0
\(17\) 0.112625 0.0273156 0.0136578 0.999907i \(-0.495652\pi\)
0.0136578 + 0.999907i \(0.495652\pi\)
\(18\) 0 0
\(19\) −1.44633 −0.331812 −0.165906 0.986142i \(-0.553055\pi\)
−0.165906 + 0.986142i \(0.553055\pi\)
\(20\) 0 0
\(21\) 5.25531 1.14680
\(22\) 0 0
\(23\) 7.37160 1.53708 0.768542 0.639799i \(-0.220982\pi\)
0.768542 + 0.639799i \(0.220982\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.63402 1.08427
\(28\) 0 0
\(29\) −1.99452 −0.370372 −0.185186 0.982703i \(-0.559289\pi\)
−0.185186 + 0.982703i \(0.559289\pi\)
\(30\) 0 0
\(31\) −2.75759 −0.495277 −0.247639 0.968852i \(-0.579655\pi\)
−0.247639 + 0.968852i \(0.579655\pi\)
\(32\) 0 0
\(33\) 0.287689 0.0500802
\(34\) 0 0
\(35\) 3.53428 0.597403
\(36\) 0 0
\(37\) −5.38909 −0.885961 −0.442980 0.896531i \(-0.646079\pi\)
−0.442980 + 0.896531i \(0.646079\pi\)
\(38\) 0 0
\(39\) 2.65587 0.425279
\(40\) 0 0
\(41\) 9.08586 1.41897 0.709487 0.704719i \(-0.248927\pi\)
0.709487 + 0.704719i \(0.248927\pi\)
\(42\) 0 0
\(43\) 7.95947 1.21381 0.606904 0.794775i \(-0.292411\pi\)
0.606904 + 0.794775i \(0.292411\pi\)
\(44\) 0 0
\(45\) 0.788974 0.117613
\(46\) 0 0
\(47\) −9.63499 −1.40541 −0.702704 0.711483i \(-0.748024\pi\)
−0.702704 + 0.711483i \(0.748024\pi\)
\(48\) 0 0
\(49\) 5.49115 0.784449
\(50\) 0 0
\(51\) −0.167468 −0.0234502
\(52\) 0 0
\(53\) 1.21869 0.167400 0.0836999 0.996491i \(-0.473326\pi\)
0.0836999 + 0.996491i \(0.473326\pi\)
\(54\) 0 0
\(55\) 0.193476 0.0260882
\(56\) 0 0
\(57\) 2.15063 0.284858
\(58\) 0 0
\(59\) −4.20935 −0.548010 −0.274005 0.961728i \(-0.588348\pi\)
−0.274005 + 0.961728i \(0.588348\pi\)
\(60\) 0 0
\(61\) 6.14882 0.787276 0.393638 0.919266i \(-0.371216\pi\)
0.393638 + 0.919266i \(0.371216\pi\)
\(62\) 0 0
\(63\) 2.78846 0.351313
\(64\) 0 0
\(65\) 1.78611 0.221540
\(66\) 0 0
\(67\) 8.98383 1.09755 0.548775 0.835970i \(-0.315094\pi\)
0.548775 + 0.835970i \(0.315094\pi\)
\(68\) 0 0
\(69\) −10.9612 −1.31957
\(70\) 0 0
\(71\) −7.09651 −0.842201 −0.421100 0.907014i \(-0.638356\pi\)
−0.421100 + 0.907014i \(0.638356\pi\)
\(72\) 0 0
\(73\) 11.1077 1.30006 0.650029 0.759909i \(-0.274757\pi\)
0.650029 + 0.759909i \(0.274757\pi\)
\(74\) 0 0
\(75\) −1.48695 −0.171698
\(76\) 0 0
\(77\) 0.683797 0.0779259
\(78\) 0 0
\(79\) 5.03284 0.566239 0.283119 0.959085i \(-0.408631\pi\)
0.283119 + 0.959085i \(0.408631\pi\)
\(80\) 0 0
\(81\) −6.01060 −0.667844
\(82\) 0 0
\(83\) 13.2788 1.45753 0.728767 0.684762i \(-0.240094\pi\)
0.728767 + 0.684762i \(0.240094\pi\)
\(84\) 0 0
\(85\) −0.112625 −0.0122159
\(86\) 0 0
\(87\) 2.96575 0.317962
\(88\) 0 0
\(89\) 16.2676 1.72436 0.862179 0.506603i \(-0.169099\pi\)
0.862179 + 0.506603i \(0.169099\pi\)
\(90\) 0 0
\(91\) 6.31263 0.661743
\(92\) 0 0
\(93\) 4.10040 0.425192
\(94\) 0 0
\(95\) 1.44633 0.148391
\(96\) 0 0
\(97\) −6.48853 −0.658810 −0.329405 0.944189i \(-0.606848\pi\)
−0.329405 + 0.944189i \(0.606848\pi\)
\(98\) 0 0
\(99\) 0.152647 0.0153416
\(100\) 0 0
\(101\) −13.5189 −1.34518 −0.672590 0.740015i \(-0.734818\pi\)
−0.672590 + 0.740015i \(0.734818\pi\)
\(102\) 0 0
\(103\) 3.98880 0.393028 0.196514 0.980501i \(-0.437038\pi\)
0.196514 + 0.980501i \(0.437038\pi\)
\(104\) 0 0
\(105\) −5.25531 −0.512865
\(106\) 0 0
\(107\) 6.98727 0.675485 0.337742 0.941239i \(-0.390337\pi\)
0.337742 + 0.941239i \(0.390337\pi\)
\(108\) 0 0
\(109\) −4.01805 −0.384860 −0.192430 0.981311i \(-0.561637\pi\)
−0.192430 + 0.981311i \(0.561637\pi\)
\(110\) 0 0
\(111\) 8.01331 0.760590
\(112\) 0 0
\(113\) −4.47938 −0.421384 −0.210692 0.977552i \(-0.567572\pi\)
−0.210692 + 0.977552i \(0.567572\pi\)
\(114\) 0 0
\(115\) −7.37160 −0.687405
\(116\) 0 0
\(117\) 1.40920 0.130280
\(118\) 0 0
\(119\) −0.398049 −0.0364891
\(120\) 0 0
\(121\) −10.9626 −0.996597
\(122\) 0 0
\(123\) −13.5102 −1.21818
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −13.8211 −1.22643 −0.613213 0.789918i \(-0.710123\pi\)
−0.613213 + 0.789918i \(0.710123\pi\)
\(128\) 0 0
\(129\) −11.8353 −1.04204
\(130\) 0 0
\(131\) 1.38722 0.121202 0.0606012 0.998162i \(-0.480698\pi\)
0.0606012 + 0.998162i \(0.480698\pi\)
\(132\) 0 0
\(133\) 5.11175 0.443245
\(134\) 0 0
\(135\) −5.63402 −0.484899
\(136\) 0 0
\(137\) 19.4983 1.66585 0.832926 0.553385i \(-0.186664\pi\)
0.832926 + 0.553385i \(0.186664\pi\)
\(138\) 0 0
\(139\) 17.9114 1.51922 0.759611 0.650378i \(-0.225389\pi\)
0.759611 + 0.650378i \(0.225389\pi\)
\(140\) 0 0
\(141\) 14.3268 1.20653
\(142\) 0 0
\(143\) 0.345569 0.0288980
\(144\) 0 0
\(145\) 1.99452 0.165636
\(146\) 0 0
\(147\) −8.16507 −0.673444
\(148\) 0 0
\(149\) −14.3947 −1.17926 −0.589629 0.807674i \(-0.700726\pi\)
−0.589629 + 0.807674i \(0.700726\pi\)
\(150\) 0 0
\(151\) −17.5542 −1.42854 −0.714269 0.699872i \(-0.753241\pi\)
−0.714269 + 0.699872i \(0.753241\pi\)
\(152\) 0 0
\(153\) −0.0888583 −0.00718377
\(154\) 0 0
\(155\) 2.75759 0.221495
\(156\) 0 0
\(157\) −0.777288 −0.0620343 −0.0310172 0.999519i \(-0.509875\pi\)
−0.0310172 + 0.999519i \(0.509875\pi\)
\(158\) 0 0
\(159\) −1.81213 −0.143711
\(160\) 0 0
\(161\) −26.0533 −2.05329
\(162\) 0 0
\(163\) −15.1267 −1.18481 −0.592405 0.805640i \(-0.701822\pi\)
−0.592405 + 0.805640i \(0.701822\pi\)
\(164\) 0 0
\(165\) −0.287689 −0.0223966
\(166\) 0 0
\(167\) −17.0767 −1.32143 −0.660717 0.750635i \(-0.729748\pi\)
−0.660717 + 0.750635i \(0.729748\pi\)
\(168\) 0 0
\(169\) −9.80980 −0.754600
\(170\) 0 0
\(171\) 1.14112 0.0872637
\(172\) 0 0
\(173\) 5.50041 0.418189 0.209094 0.977895i \(-0.432948\pi\)
0.209094 + 0.977895i \(0.432948\pi\)
\(174\) 0 0
\(175\) −3.53428 −0.267167
\(176\) 0 0
\(177\) 6.25909 0.470462
\(178\) 0 0
\(179\) 23.0063 1.71957 0.859787 0.510652i \(-0.170596\pi\)
0.859787 + 0.510652i \(0.170596\pi\)
\(180\) 0 0
\(181\) −14.5892 −1.08441 −0.542204 0.840247i \(-0.682410\pi\)
−0.542204 + 0.840247i \(0.682410\pi\)
\(182\) 0 0
\(183\) −9.14300 −0.675870
\(184\) 0 0
\(185\) 5.38909 0.396214
\(186\) 0 0
\(187\) −0.0217902 −0.00159346
\(188\) 0 0
\(189\) −19.9122 −1.44840
\(190\) 0 0
\(191\) 18.7289 1.35518 0.677588 0.735442i \(-0.263025\pi\)
0.677588 + 0.735442i \(0.263025\pi\)
\(192\) 0 0
\(193\) 5.04939 0.363463 0.181731 0.983348i \(-0.441830\pi\)
0.181731 + 0.983348i \(0.441830\pi\)
\(194\) 0 0
\(195\) −2.65587 −0.190190
\(196\) 0 0
\(197\) 16.5642 1.18015 0.590075 0.807348i \(-0.299098\pi\)
0.590075 + 0.807348i \(0.299098\pi\)
\(198\) 0 0
\(199\) −3.77860 −0.267858 −0.133929 0.990991i \(-0.542759\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(200\) 0 0
\(201\) −13.3585 −0.942238
\(202\) 0 0
\(203\) 7.04918 0.494756
\(204\) 0 0
\(205\) −9.08586 −0.634584
\(206\) 0 0
\(207\) −5.81600 −0.404240
\(208\) 0 0
\(209\) 0.279830 0.0193563
\(210\) 0 0
\(211\) −25.0139 −1.72203 −0.861013 0.508583i \(-0.830169\pi\)
−0.861013 + 0.508583i \(0.830169\pi\)
\(212\) 0 0
\(213\) 10.5522 0.723022
\(214\) 0 0
\(215\) −7.95947 −0.542831
\(216\) 0 0
\(217\) 9.74609 0.661608
\(218\) 0 0
\(219\) −16.5166 −1.11609
\(220\) 0 0
\(221\) −0.201161 −0.0135316
\(222\) 0 0
\(223\) 4.64801 0.311254 0.155627 0.987816i \(-0.450260\pi\)
0.155627 + 0.987816i \(0.450260\pi\)
\(224\) 0 0
\(225\) −0.788974 −0.0525983
\(226\) 0 0
\(227\) 9.26965 0.615248 0.307624 0.951508i \(-0.400466\pi\)
0.307624 + 0.951508i \(0.400466\pi\)
\(228\) 0 0
\(229\) −18.5492 −1.22577 −0.612883 0.790174i \(-0.709990\pi\)
−0.612883 + 0.790174i \(0.709990\pi\)
\(230\) 0 0
\(231\) −1.01677 −0.0668988
\(232\) 0 0
\(233\) −18.0707 −1.18385 −0.591925 0.805993i \(-0.701632\pi\)
−0.591925 + 0.805993i \(0.701632\pi\)
\(234\) 0 0
\(235\) 9.63499 0.628517
\(236\) 0 0
\(237\) −7.48359 −0.486111
\(238\) 0 0
\(239\) 19.1329 1.23761 0.618804 0.785546i \(-0.287618\pi\)
0.618804 + 0.785546i \(0.287618\pi\)
\(240\) 0 0
\(241\) −11.6502 −0.750454 −0.375227 0.926933i \(-0.622435\pi\)
−0.375227 + 0.926933i \(0.622435\pi\)
\(242\) 0 0
\(243\) −7.96460 −0.510929
\(244\) 0 0
\(245\) −5.49115 −0.350816
\(246\) 0 0
\(247\) 2.58332 0.164373
\(248\) 0 0
\(249\) −19.7449 −1.25128
\(250\) 0 0
\(251\) 19.1082 1.20610 0.603050 0.797703i \(-0.293952\pi\)
0.603050 + 0.797703i \(0.293952\pi\)
\(252\) 0 0
\(253\) −1.42622 −0.0896660
\(254\) 0 0
\(255\) 0.167468 0.0104873
\(256\) 0 0
\(257\) −15.1419 −0.944527 −0.472263 0.881458i \(-0.656563\pi\)
−0.472263 + 0.881458i \(0.656563\pi\)
\(258\) 0 0
\(259\) 19.0466 1.18350
\(260\) 0 0
\(261\) 1.57362 0.0974048
\(262\) 0 0
\(263\) 6.07163 0.374393 0.187196 0.982323i \(-0.440060\pi\)
0.187196 + 0.982323i \(0.440060\pi\)
\(264\) 0 0
\(265\) −1.21869 −0.0748635
\(266\) 0 0
\(267\) −24.1891 −1.48035
\(268\) 0 0
\(269\) −8.96215 −0.546432 −0.273216 0.961953i \(-0.588087\pi\)
−0.273216 + 0.961953i \(0.588087\pi\)
\(270\) 0 0
\(271\) −7.54580 −0.458375 −0.229187 0.973382i \(-0.573607\pi\)
−0.229187 + 0.973382i \(0.573607\pi\)
\(272\) 0 0
\(273\) −9.38658 −0.568101
\(274\) 0 0
\(275\) −0.193476 −0.0116670
\(276\) 0 0
\(277\) −7.84641 −0.471445 −0.235722 0.971820i \(-0.575746\pi\)
−0.235722 + 0.971820i \(0.575746\pi\)
\(278\) 0 0
\(279\) 2.17567 0.130254
\(280\) 0 0
\(281\) 9.57281 0.571066 0.285533 0.958369i \(-0.407829\pi\)
0.285533 + 0.958369i \(0.407829\pi\)
\(282\) 0 0
\(283\) −14.3180 −0.851117 −0.425559 0.904931i \(-0.639922\pi\)
−0.425559 + 0.904931i \(0.639922\pi\)
\(284\) 0 0
\(285\) −2.15063 −0.127392
\(286\) 0 0
\(287\) −32.1120 −1.89551
\(288\) 0 0
\(289\) −16.9873 −0.999254
\(290\) 0 0
\(291\) 9.64812 0.565583
\(292\) 0 0
\(293\) −0.431624 −0.0252158 −0.0126079 0.999921i \(-0.504013\pi\)
−0.0126079 + 0.999921i \(0.504013\pi\)
\(294\) 0 0
\(295\) 4.20935 0.245078
\(296\) 0 0
\(297\) −1.09005 −0.0632509
\(298\) 0 0
\(299\) −13.1665 −0.761439
\(300\) 0 0
\(301\) −28.1310 −1.62144
\(302\) 0 0
\(303\) 20.1019 1.15483
\(304\) 0 0
\(305\) −6.14882 −0.352080
\(306\) 0 0
\(307\) 30.5282 1.74234 0.871169 0.490983i \(-0.163362\pi\)
0.871169 + 0.490983i \(0.163362\pi\)
\(308\) 0 0
\(309\) −5.93116 −0.337412
\(310\) 0 0
\(311\) 3.45876 0.196128 0.0980642 0.995180i \(-0.468735\pi\)
0.0980642 + 0.995180i \(0.468735\pi\)
\(312\) 0 0
\(313\) −2.74163 −0.154966 −0.0774829 0.996994i \(-0.524688\pi\)
−0.0774829 + 0.996994i \(0.524688\pi\)
\(314\) 0 0
\(315\) −2.78846 −0.157112
\(316\) 0 0
\(317\) −4.42548 −0.248560 −0.124280 0.992247i \(-0.539662\pi\)
−0.124280 + 0.992247i \(0.539662\pi\)
\(318\) 0 0
\(319\) 0.385890 0.0216057
\(320\) 0 0
\(321\) −10.3897 −0.579898
\(322\) 0 0
\(323\) −0.162894 −0.00906364
\(324\) 0 0
\(325\) −1.78611 −0.0990758
\(326\) 0 0
\(327\) 5.97465 0.330399
\(328\) 0 0
\(329\) 34.0528 1.87739
\(330\) 0 0
\(331\) −3.28540 −0.180582 −0.0902910 0.995915i \(-0.528780\pi\)
−0.0902910 + 0.995915i \(0.528780\pi\)
\(332\) 0 0
\(333\) 4.25185 0.233000
\(334\) 0 0
\(335\) −8.98383 −0.490839
\(336\) 0 0
\(337\) −1.70217 −0.0927231 −0.0463616 0.998925i \(-0.514763\pi\)
−0.0463616 + 0.998925i \(0.514763\pi\)
\(338\) 0 0
\(339\) 6.66062 0.361755
\(340\) 0 0
\(341\) 0.533526 0.0288921
\(342\) 0 0
\(343\) 5.33271 0.287939
\(344\) 0 0
\(345\) 10.9612 0.590132
\(346\) 0 0
\(347\) 20.1025 1.07916 0.539579 0.841935i \(-0.318583\pi\)
0.539579 + 0.841935i \(0.318583\pi\)
\(348\) 0 0
\(349\) −17.2275 −0.922165 −0.461082 0.887357i \(-0.652539\pi\)
−0.461082 + 0.887357i \(0.652539\pi\)
\(350\) 0 0
\(351\) −10.0630 −0.537123
\(352\) 0 0
\(353\) −25.0409 −1.33279 −0.666397 0.745597i \(-0.732164\pi\)
−0.666397 + 0.745597i \(0.732164\pi\)
\(354\) 0 0
\(355\) 7.09651 0.376644
\(356\) 0 0
\(357\) 0.591880 0.0313256
\(358\) 0 0
\(359\) 21.3525 1.12694 0.563471 0.826136i \(-0.309466\pi\)
0.563471 + 0.826136i \(0.309466\pi\)
\(360\) 0 0
\(361\) −16.9081 −0.889901
\(362\) 0 0
\(363\) 16.3008 0.855571
\(364\) 0 0
\(365\) −11.1077 −0.581404
\(366\) 0 0
\(367\) 29.3382 1.53144 0.765721 0.643173i \(-0.222382\pi\)
0.765721 + 0.643173i \(0.222382\pi\)
\(368\) 0 0
\(369\) −7.16851 −0.373178
\(370\) 0 0
\(371\) −4.30719 −0.223618
\(372\) 0 0
\(373\) −16.3750 −0.847866 −0.423933 0.905694i \(-0.639351\pi\)
−0.423933 + 0.905694i \(0.639351\pi\)
\(374\) 0 0
\(375\) 1.48695 0.0767859
\(376\) 0 0
\(377\) 3.56243 0.183475
\(378\) 0 0
\(379\) 12.1622 0.624729 0.312365 0.949962i \(-0.398879\pi\)
0.312365 + 0.949962i \(0.398879\pi\)
\(380\) 0 0
\(381\) 20.5513 1.05288
\(382\) 0 0
\(383\) 33.7095 1.72247 0.861237 0.508204i \(-0.169690\pi\)
0.861237 + 0.508204i \(0.169690\pi\)
\(384\) 0 0
\(385\) −0.683797 −0.0348495
\(386\) 0 0
\(387\) −6.27982 −0.319221
\(388\) 0 0
\(389\) −21.2394 −1.07688 −0.538441 0.842663i \(-0.680987\pi\)
−0.538441 + 0.842663i \(0.680987\pi\)
\(390\) 0 0
\(391\) 0.830227 0.0419864
\(392\) 0 0
\(393\) −2.06274 −0.104051
\(394\) 0 0
\(395\) −5.03284 −0.253230
\(396\) 0 0
\(397\) 32.7491 1.64363 0.821814 0.569756i \(-0.192962\pi\)
0.821814 + 0.569756i \(0.192962\pi\)
\(398\) 0 0
\(399\) −7.60093 −0.380522
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 4.92537 0.245350
\(404\) 0 0
\(405\) 6.01060 0.298669
\(406\) 0 0
\(407\) 1.04266 0.0516826
\(408\) 0 0
\(409\) −21.0172 −1.03924 −0.519618 0.854399i \(-0.673926\pi\)
−0.519618 + 0.854399i \(0.673926\pi\)
\(410\) 0 0
\(411\) −28.9930 −1.43012
\(412\) 0 0
\(413\) 14.8770 0.732050
\(414\) 0 0
\(415\) −13.2788 −0.651829
\(416\) 0 0
\(417\) −26.6333 −1.30424
\(418\) 0 0
\(419\) −38.3818 −1.87507 −0.937536 0.347889i \(-0.886899\pi\)
−0.937536 + 0.347889i \(0.886899\pi\)
\(420\) 0 0
\(421\) 28.3134 1.37991 0.689955 0.723853i \(-0.257631\pi\)
0.689955 + 0.723853i \(0.257631\pi\)
\(422\) 0 0
\(423\) 7.60176 0.369610
\(424\) 0 0
\(425\) 0.112625 0.00546312
\(426\) 0 0
\(427\) −21.7317 −1.05167
\(428\) 0 0
\(429\) −0.513845 −0.0248087
\(430\) 0 0
\(431\) −38.6760 −1.86296 −0.931480 0.363793i \(-0.881482\pi\)
−0.931480 + 0.363793i \(0.881482\pi\)
\(432\) 0 0
\(433\) 24.4278 1.17393 0.586963 0.809613i \(-0.300323\pi\)
0.586963 + 0.809613i \(0.300323\pi\)
\(434\) 0 0
\(435\) −2.96575 −0.142197
\(436\) 0 0
\(437\) −10.6618 −0.510023
\(438\) 0 0
\(439\) −18.8409 −0.899226 −0.449613 0.893223i \(-0.648438\pi\)
−0.449613 + 0.893223i \(0.648438\pi\)
\(440\) 0 0
\(441\) −4.33237 −0.206304
\(442\) 0 0
\(443\) −17.2871 −0.821333 −0.410666 0.911786i \(-0.634704\pi\)
−0.410666 + 0.911786i \(0.634704\pi\)
\(444\) 0 0
\(445\) −16.2676 −0.771157
\(446\) 0 0
\(447\) 21.4042 1.01238
\(448\) 0 0
\(449\) −18.9137 −0.892594 −0.446297 0.894885i \(-0.647258\pi\)
−0.446297 + 0.894885i \(0.647258\pi\)
\(450\) 0 0
\(451\) −1.75789 −0.0827760
\(452\) 0 0
\(453\) 26.1022 1.22639
\(454\) 0 0
\(455\) −6.31263 −0.295941
\(456\) 0 0
\(457\) −28.8322 −1.34871 −0.674357 0.738406i \(-0.735579\pi\)
−0.674357 + 0.738406i \(0.735579\pi\)
\(458\) 0 0
\(459\) 0.634533 0.0296174
\(460\) 0 0
\(461\) −39.8142 −1.85433 −0.927167 0.374649i \(-0.877763\pi\)
−0.927167 + 0.374649i \(0.877763\pi\)
\(462\) 0 0
\(463\) 4.38144 0.203623 0.101811 0.994804i \(-0.467536\pi\)
0.101811 + 0.994804i \(0.467536\pi\)
\(464\) 0 0
\(465\) −4.10040 −0.190151
\(466\) 0 0
\(467\) −11.6136 −0.537414 −0.268707 0.963222i \(-0.586596\pi\)
−0.268707 + 0.963222i \(0.586596\pi\)
\(468\) 0 0
\(469\) −31.7514 −1.46614
\(470\) 0 0
\(471\) 1.15579 0.0532560
\(472\) 0 0
\(473\) −1.53996 −0.0708076
\(474\) 0 0
\(475\) −1.44633 −0.0663623
\(476\) 0 0
\(477\) −0.961515 −0.0440247
\(478\) 0 0
\(479\) 10.6284 0.485624 0.242812 0.970073i \(-0.421930\pi\)
0.242812 + 0.970073i \(0.421930\pi\)
\(480\) 0 0
\(481\) 9.62552 0.438886
\(482\) 0 0
\(483\) 38.7400 1.76273
\(484\) 0 0
\(485\) 6.48853 0.294629
\(486\) 0 0
\(487\) 1.50656 0.0682686 0.0341343 0.999417i \(-0.489133\pi\)
0.0341343 + 0.999417i \(0.489133\pi\)
\(488\) 0 0
\(489\) 22.4926 1.01715
\(490\) 0 0
\(491\) −36.0549 −1.62714 −0.813568 0.581470i \(-0.802478\pi\)
−0.813568 + 0.581470i \(0.802478\pi\)
\(492\) 0 0
\(493\) −0.224633 −0.0101169
\(494\) 0 0
\(495\) −0.152647 −0.00686099
\(496\) 0 0
\(497\) 25.0811 1.12504
\(498\) 0 0
\(499\) 3.62024 0.162064 0.0810322 0.996711i \(-0.474178\pi\)
0.0810322 + 0.996711i \(0.474178\pi\)
\(500\) 0 0
\(501\) 25.3922 1.13444
\(502\) 0 0
\(503\) 14.4027 0.642183 0.321091 0.947048i \(-0.395950\pi\)
0.321091 + 0.947048i \(0.395950\pi\)
\(504\) 0 0
\(505\) 13.5189 0.601583
\(506\) 0 0
\(507\) 14.5867 0.647818
\(508\) 0 0
\(509\) 10.4384 0.462676 0.231338 0.972873i \(-0.425690\pi\)
0.231338 + 0.972873i \(0.425690\pi\)
\(510\) 0 0
\(511\) −39.2577 −1.73666
\(512\) 0 0
\(513\) −8.14868 −0.359773
\(514\) 0 0
\(515\) −3.98880 −0.175768
\(516\) 0 0
\(517\) 1.86414 0.0819846
\(518\) 0 0
\(519\) −8.17885 −0.359012
\(520\) 0 0
\(521\) −15.0504 −0.659371 −0.329686 0.944091i \(-0.606943\pi\)
−0.329686 + 0.944091i \(0.606943\pi\)
\(522\) 0 0
\(523\) 9.23145 0.403663 0.201832 0.979420i \(-0.435311\pi\)
0.201832 + 0.979420i \(0.435311\pi\)
\(524\) 0 0
\(525\) 5.25531 0.229360
\(526\) 0 0
\(527\) −0.310574 −0.0135288
\(528\) 0 0
\(529\) 31.3405 1.36263
\(530\) 0 0
\(531\) 3.32107 0.144122
\(532\) 0 0
\(533\) −16.2284 −0.702929
\(534\) 0 0
\(535\) −6.98727 −0.302086
\(536\) 0 0
\(537\) −34.2093 −1.47624
\(538\) 0 0
\(539\) −1.06240 −0.0457609
\(540\) 0 0
\(541\) −22.6894 −0.975493 −0.487747 0.872985i \(-0.662181\pi\)
−0.487747 + 0.872985i \(0.662181\pi\)
\(542\) 0 0
\(543\) 21.6935 0.930956
\(544\) 0 0
\(545\) 4.01805 0.172114
\(546\) 0 0
\(547\) 3.94368 0.168619 0.0843097 0.996440i \(-0.473131\pi\)
0.0843097 + 0.996440i \(0.473131\pi\)
\(548\) 0 0
\(549\) −4.85126 −0.207047
\(550\) 0 0
\(551\) 2.88474 0.122894
\(552\) 0 0
\(553\) −17.7875 −0.756400
\(554\) 0 0
\(555\) −8.01331 −0.340146
\(556\) 0 0
\(557\) 34.9761 1.48199 0.740993 0.671513i \(-0.234355\pi\)
0.740993 + 0.671513i \(0.234355\pi\)
\(558\) 0 0
\(559\) −14.2165 −0.601295
\(560\) 0 0
\(561\) 0.0324010 0.00136797
\(562\) 0 0
\(563\) −25.6779 −1.08219 −0.541096 0.840961i \(-0.681991\pi\)
−0.541096 + 0.840961i \(0.681991\pi\)
\(564\) 0 0
\(565\) 4.47938 0.188449
\(566\) 0 0
\(567\) 21.2431 0.892128
\(568\) 0 0
\(569\) −31.2230 −1.30893 −0.654467 0.756090i \(-0.727107\pi\)
−0.654467 + 0.756090i \(0.727107\pi\)
\(570\) 0 0
\(571\) 3.98990 0.166972 0.0834861 0.996509i \(-0.473395\pi\)
0.0834861 + 0.996509i \(0.473395\pi\)
\(572\) 0 0
\(573\) −27.8490 −1.16341
\(574\) 0 0
\(575\) 7.37160 0.307417
\(576\) 0 0
\(577\) 4.20979 0.175256 0.0876279 0.996153i \(-0.472071\pi\)
0.0876279 + 0.996153i \(0.472071\pi\)
\(578\) 0 0
\(579\) −7.50819 −0.312030
\(580\) 0 0
\(581\) −46.9309 −1.94702
\(582\) 0 0
\(583\) −0.235787 −0.00976529
\(584\) 0 0
\(585\) −1.40920 −0.0582632
\(586\) 0 0
\(587\) −21.3113 −0.879610 −0.439805 0.898093i \(-0.644952\pi\)
−0.439805 + 0.898093i \(0.644952\pi\)
\(588\) 0 0
\(589\) 3.98839 0.164339
\(590\) 0 0
\(591\) −24.6302 −1.01315
\(592\) 0 0
\(593\) −28.8757 −1.18578 −0.592892 0.805282i \(-0.702014\pi\)
−0.592892 + 0.805282i \(0.702014\pi\)
\(594\) 0 0
\(595\) 0.398049 0.0163184
\(596\) 0 0
\(597\) 5.61860 0.229954
\(598\) 0 0
\(599\) −3.18410 −0.130099 −0.0650494 0.997882i \(-0.520721\pi\)
−0.0650494 + 0.997882i \(0.520721\pi\)
\(600\) 0 0
\(601\) 29.4009 1.19929 0.599644 0.800267i \(-0.295309\pi\)
0.599644 + 0.800267i \(0.295309\pi\)
\(602\) 0 0
\(603\) −7.08802 −0.288646
\(604\) 0 0
\(605\) 10.9626 0.445692
\(606\) 0 0
\(607\) −15.0583 −0.611199 −0.305600 0.952160i \(-0.598857\pi\)
−0.305600 + 0.952160i \(0.598857\pi\)
\(608\) 0 0
\(609\) −10.4818 −0.424744
\(610\) 0 0
\(611\) 17.2092 0.696209
\(612\) 0 0
\(613\) −0.903071 −0.0364747 −0.0182374 0.999834i \(-0.505805\pi\)
−0.0182374 + 0.999834i \(0.505805\pi\)
\(614\) 0 0
\(615\) 13.5102 0.544786
\(616\) 0 0
\(617\) −17.3753 −0.699503 −0.349751 0.936843i \(-0.613734\pi\)
−0.349751 + 0.936843i \(0.613734\pi\)
\(618\) 0 0
\(619\) −26.6595 −1.07154 −0.535768 0.844366i \(-0.679978\pi\)
−0.535768 + 0.844366i \(0.679978\pi\)
\(620\) 0 0
\(621\) 41.5317 1.66661
\(622\) 0 0
\(623\) −57.4942 −2.30346
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.416094 −0.0166172
\(628\) 0 0
\(629\) −0.606947 −0.0242006
\(630\) 0 0
\(631\) 38.4043 1.52885 0.764425 0.644712i \(-0.223023\pi\)
0.764425 + 0.644712i \(0.223023\pi\)
\(632\) 0 0
\(633\) 37.1944 1.47835
\(634\) 0 0
\(635\) 13.8211 0.548474
\(636\) 0 0
\(637\) −9.80781 −0.388600
\(638\) 0 0
\(639\) 5.59896 0.221492
\(640\) 0 0
\(641\) −35.3895 −1.39780 −0.698901 0.715219i \(-0.746327\pi\)
−0.698901 + 0.715219i \(0.746327\pi\)
\(642\) 0 0
\(643\) 19.2717 0.760000 0.380000 0.924986i \(-0.375924\pi\)
0.380000 + 0.924986i \(0.375924\pi\)
\(644\) 0 0
\(645\) 11.8353 0.466016
\(646\) 0 0
\(647\) 0.813647 0.0319878 0.0159939 0.999872i \(-0.494909\pi\)
0.0159939 + 0.999872i \(0.494909\pi\)
\(648\) 0 0
\(649\) 0.814406 0.0319682
\(650\) 0 0
\(651\) −14.4920 −0.567985
\(652\) 0 0
\(653\) −17.9370 −0.701931 −0.350965 0.936388i \(-0.614147\pi\)
−0.350965 + 0.936388i \(0.614147\pi\)
\(654\) 0 0
\(655\) −1.38722 −0.0542034
\(656\) 0 0
\(657\) −8.76369 −0.341904
\(658\) 0 0
\(659\) −19.3867 −0.755198 −0.377599 0.925969i \(-0.623250\pi\)
−0.377599 + 0.925969i \(0.623250\pi\)
\(660\) 0 0
\(661\) 30.3116 1.17898 0.589491 0.807775i \(-0.299328\pi\)
0.589491 + 0.807775i \(0.299328\pi\)
\(662\) 0 0
\(663\) 0.299117 0.0116167
\(664\) 0 0
\(665\) −5.11175 −0.198225
\(666\) 0 0
\(667\) −14.7028 −0.569294
\(668\) 0 0
\(669\) −6.91137 −0.267209
\(670\) 0 0
\(671\) −1.18965 −0.0459258
\(672\) 0 0
\(673\) 39.9797 1.54110 0.770552 0.637377i \(-0.219981\pi\)
0.770552 + 0.637377i \(0.219981\pi\)
\(674\) 0 0
\(675\) 5.63402 0.216854
\(676\) 0 0
\(677\) 20.2058 0.776570 0.388285 0.921539i \(-0.373068\pi\)
0.388285 + 0.921539i \(0.373068\pi\)
\(678\) 0 0
\(679\) 22.9323 0.880060
\(680\) 0 0
\(681\) −13.7835 −0.528185
\(682\) 0 0
\(683\) 42.0610 1.60942 0.804709 0.593670i \(-0.202321\pi\)
0.804709 + 0.593670i \(0.202321\pi\)
\(684\) 0 0
\(685\) −19.4983 −0.744992
\(686\) 0 0
\(687\) 27.5818 1.05231
\(688\) 0 0
\(689\) −2.17672 −0.0829263
\(690\) 0 0
\(691\) −10.9484 −0.416496 −0.208248 0.978076i \(-0.566776\pi\)
−0.208248 + 0.978076i \(0.566776\pi\)
\(692\) 0 0
\(693\) −0.539499 −0.0204939
\(694\) 0 0
\(695\) −17.9114 −0.679417
\(696\) 0 0
\(697\) 1.02330 0.0387601
\(698\) 0 0
\(699\) 26.8702 1.01633
\(700\) 0 0
\(701\) 14.8360 0.560349 0.280175 0.959949i \(-0.409608\pi\)
0.280175 + 0.959949i \(0.409608\pi\)
\(702\) 0 0
\(703\) 7.79442 0.293972
\(704\) 0 0
\(705\) −14.3268 −0.539577
\(706\) 0 0
\(707\) 47.7796 1.79694
\(708\) 0 0
\(709\) 12.2554 0.460262 0.230131 0.973160i \(-0.426085\pi\)
0.230131 + 0.973160i \(0.426085\pi\)
\(710\) 0 0
\(711\) −3.97078 −0.148916
\(712\) 0 0
\(713\) −20.3278 −0.761283
\(714\) 0 0
\(715\) −0.345569 −0.0129236
\(716\) 0 0
\(717\) −28.4498 −1.06248
\(718\) 0 0
\(719\) 23.4270 0.873678 0.436839 0.899540i \(-0.356098\pi\)
0.436839 + 0.899540i \(0.356098\pi\)
\(720\) 0 0
\(721\) −14.0975 −0.525020
\(722\) 0 0
\(723\) 17.3232 0.644258
\(724\) 0 0
\(725\) −1.99452 −0.0740745
\(726\) 0 0
\(727\) −37.9929 −1.40908 −0.704540 0.709664i \(-0.748847\pi\)
−0.704540 + 0.709664i \(0.748847\pi\)
\(728\) 0 0
\(729\) 29.8748 1.10647
\(730\) 0 0
\(731\) 0.896436 0.0331559
\(732\) 0 0
\(733\) 33.5719 1.24001 0.620003 0.784600i \(-0.287131\pi\)
0.620003 + 0.784600i \(0.287131\pi\)
\(734\) 0 0
\(735\) 8.16507 0.301173
\(736\) 0 0
\(737\) −1.73815 −0.0640257
\(738\) 0 0
\(739\) −11.1897 −0.411620 −0.205810 0.978592i \(-0.565983\pi\)
−0.205810 + 0.978592i \(0.565983\pi\)
\(740\) 0 0
\(741\) −3.84127 −0.141112
\(742\) 0 0
\(743\) 27.5552 1.01090 0.505450 0.862856i \(-0.331326\pi\)
0.505450 + 0.862856i \(0.331326\pi\)
\(744\) 0 0
\(745\) 14.3947 0.527380
\(746\) 0 0
\(747\) −10.4766 −0.383319
\(748\) 0 0
\(749\) −24.6950 −0.902335
\(750\) 0 0
\(751\) −16.2253 −0.592068 −0.296034 0.955177i \(-0.595664\pi\)
−0.296034 + 0.955177i \(0.595664\pi\)
\(752\) 0 0
\(753\) −28.4130 −1.03543
\(754\) 0 0
\(755\) 17.5542 0.638861
\(756\) 0 0
\(757\) 4.51887 0.164241 0.0821206 0.996622i \(-0.473831\pi\)
0.0821206 + 0.996622i \(0.473831\pi\)
\(758\) 0 0
\(759\) 2.12073 0.0769775
\(760\) 0 0
\(761\) 17.0959 0.619727 0.309864 0.950781i \(-0.399717\pi\)
0.309864 + 0.950781i \(0.399717\pi\)
\(762\) 0 0
\(763\) 14.2009 0.514108
\(764\) 0 0
\(765\) 0.0888583 0.00321268
\(766\) 0 0
\(767\) 7.51837 0.271473
\(768\) 0 0
\(769\) 39.2230 1.41442 0.707209 0.707005i \(-0.249954\pi\)
0.707209 + 0.707005i \(0.249954\pi\)
\(770\) 0 0
\(771\) 22.5153 0.810869
\(772\) 0 0
\(773\) −28.9671 −1.04188 −0.520938 0.853595i \(-0.674418\pi\)
−0.520938 + 0.853595i \(0.674418\pi\)
\(774\) 0 0
\(775\) −2.75759 −0.0990555
\(776\) 0 0
\(777\) −28.3213 −1.01602
\(778\) 0 0
\(779\) −13.1412 −0.470832
\(780\) 0 0
\(781\) 1.37300 0.0491298
\(782\) 0 0
\(783\) −11.2371 −0.401583
\(784\) 0 0
\(785\) 0.777288 0.0277426
\(786\) 0 0
\(787\) 54.9282 1.95798 0.978990 0.203911i \(-0.0653652\pi\)
0.978990 + 0.203911i \(0.0653652\pi\)
\(788\) 0 0
\(789\) −9.02822 −0.321413
\(790\) 0 0
\(791\) 15.8314 0.562899
\(792\) 0 0
\(793\) −10.9825 −0.390000
\(794\) 0 0
\(795\) 1.81213 0.0642697
\(796\) 0 0
\(797\) −30.6568 −1.08592 −0.542959 0.839759i \(-0.682696\pi\)
−0.542959 + 0.839759i \(0.682696\pi\)
\(798\) 0 0
\(799\) −1.08514 −0.0383896
\(800\) 0 0
\(801\) −12.8347 −0.453492
\(802\) 0 0
\(803\) −2.14907 −0.0758390
\(804\) 0 0
\(805\) 26.0533 0.918258
\(806\) 0 0
\(807\) 13.3263 0.469108
\(808\) 0 0
\(809\) −37.4876 −1.31799 −0.658997 0.752146i \(-0.729019\pi\)
−0.658997 + 0.752146i \(0.729019\pi\)
\(810\) 0 0
\(811\) 26.9039 0.944723 0.472361 0.881405i \(-0.343402\pi\)
0.472361 + 0.881405i \(0.343402\pi\)
\(812\) 0 0
\(813\) 11.2202 0.393511
\(814\) 0 0
\(815\) 15.1267 0.529864
\(816\) 0 0
\(817\) −11.5121 −0.402756
\(818\) 0 0
\(819\) −4.98050 −0.174033
\(820\) 0 0
\(821\) −54.6042 −1.90570 −0.952849 0.303444i \(-0.901864\pi\)
−0.952849 + 0.303444i \(0.901864\pi\)
\(822\) 0 0
\(823\) −54.6787 −1.90598 −0.952990 0.303000i \(-0.902012\pi\)
−0.952990 + 0.303000i \(0.902012\pi\)
\(824\) 0 0
\(825\) 0.287689 0.0100160
\(826\) 0 0
\(827\) 7.35326 0.255698 0.127849 0.991794i \(-0.459193\pi\)
0.127849 + 0.991794i \(0.459193\pi\)
\(828\) 0 0
\(829\) 42.0723 1.46123 0.730616 0.682788i \(-0.239233\pi\)
0.730616 + 0.682788i \(0.239233\pi\)
\(830\) 0 0
\(831\) 11.6672 0.404732
\(832\) 0 0
\(833\) 0.618441 0.0214277
\(834\) 0 0
\(835\) 17.0767 0.590963
\(836\) 0 0
\(837\) −15.5363 −0.537013
\(838\) 0 0
\(839\) 51.5945 1.78124 0.890621 0.454747i \(-0.150270\pi\)
0.890621 + 0.454747i \(0.150270\pi\)
\(840\) 0 0
\(841\) −25.0219 −0.862824
\(842\) 0 0
\(843\) −14.2343 −0.490256
\(844\) 0 0
\(845\) 9.80980 0.337467
\(846\) 0 0
\(847\) 38.7448 1.33129
\(848\) 0 0
\(849\) 21.2902 0.730678
\(850\) 0 0
\(851\) −39.7262 −1.36180
\(852\) 0 0
\(853\) 48.5634 1.66278 0.831389 0.555691i \(-0.187546\pi\)
0.831389 + 0.555691i \(0.187546\pi\)
\(854\) 0 0
\(855\) −1.14112 −0.0390255
\(856\) 0 0
\(857\) −36.0291 −1.23073 −0.615365 0.788242i \(-0.710991\pi\)
−0.615365 + 0.788242i \(0.710991\pi\)
\(858\) 0 0
\(859\) 40.9646 1.39769 0.698846 0.715272i \(-0.253697\pi\)
0.698846 + 0.715272i \(0.253697\pi\)
\(860\) 0 0
\(861\) 47.7490 1.62728
\(862\) 0 0
\(863\) −29.6228 −1.00837 −0.504186 0.863595i \(-0.668207\pi\)
−0.504186 + 0.863595i \(0.668207\pi\)
\(864\) 0 0
\(865\) −5.50041 −0.187020
\(866\) 0 0
\(867\) 25.2593 0.857851
\(868\) 0 0
\(869\) −0.973732 −0.0330316
\(870\) 0 0
\(871\) −16.0462 −0.543703
\(872\) 0 0
\(873\) 5.11928 0.173261
\(874\) 0 0
\(875\) 3.53428 0.119481
\(876\) 0 0
\(877\) −15.8356 −0.534730 −0.267365 0.963595i \(-0.586153\pi\)
−0.267365 + 0.963595i \(0.586153\pi\)
\(878\) 0 0
\(879\) 0.641805 0.0216475
\(880\) 0 0
\(881\) 7.64366 0.257522 0.128761 0.991676i \(-0.458900\pi\)
0.128761 + 0.991676i \(0.458900\pi\)
\(882\) 0 0
\(883\) −55.2861 −1.86052 −0.930262 0.366896i \(-0.880421\pi\)
−0.930262 + 0.366896i \(0.880421\pi\)
\(884\) 0 0
\(885\) −6.25909 −0.210397
\(886\) 0 0
\(887\) −21.2402 −0.713176 −0.356588 0.934262i \(-0.616060\pi\)
−0.356588 + 0.934262i \(0.616060\pi\)
\(888\) 0 0
\(889\) 48.8477 1.63830
\(890\) 0 0
\(891\) 1.16290 0.0389587
\(892\) 0 0
\(893\) 13.9354 0.466331
\(894\) 0 0
\(895\) −23.0063 −0.769017
\(896\) 0 0
\(897\) 19.5780 0.653689
\(898\) 0 0
\(899\) 5.50005 0.183437
\(900\) 0 0
\(901\) 0.137255 0.00457263
\(902\) 0 0
\(903\) 41.8295 1.39200
\(904\) 0 0
\(905\) 14.5892 0.484962
\(906\) 0 0
\(907\) −34.3924 −1.14198 −0.570991 0.820957i \(-0.693441\pi\)
−0.570991 + 0.820957i \(0.693441\pi\)
\(908\) 0 0
\(909\) 10.6661 0.353771
\(910\) 0 0
\(911\) −31.0166 −1.02763 −0.513814 0.857902i \(-0.671768\pi\)
−0.513814 + 0.857902i \(0.671768\pi\)
\(912\) 0 0
\(913\) −2.56912 −0.0850253
\(914\) 0 0
\(915\) 9.14300 0.302258
\(916\) 0 0
\(917\) −4.90284 −0.161906
\(918\) 0 0
\(919\) 31.6511 1.04407 0.522037 0.852923i \(-0.325172\pi\)
0.522037 + 0.852923i \(0.325172\pi\)
\(920\) 0 0
\(921\) −45.3940 −1.49578
\(922\) 0 0
\(923\) 12.6752 0.417208
\(924\) 0 0
\(925\) −5.38909 −0.177192
\(926\) 0 0
\(927\) −3.14706 −0.103363
\(928\) 0 0
\(929\) 42.4108 1.39145 0.695726 0.718307i \(-0.255083\pi\)
0.695726 + 0.718307i \(0.255083\pi\)
\(930\) 0 0
\(931\) −7.94203 −0.260290
\(932\) 0 0
\(933\) −5.14301 −0.168375
\(934\) 0 0
\(935\) 0.0217902 0.000712616 0
\(936\) 0 0
\(937\) −13.0283 −0.425615 −0.212807 0.977094i \(-0.568261\pi\)
−0.212807 + 0.977094i \(0.568261\pi\)
\(938\) 0 0
\(939\) 4.07667 0.133037
\(940\) 0 0
\(941\) −31.8993 −1.03989 −0.519944 0.854201i \(-0.674047\pi\)
−0.519944 + 0.854201i \(0.674047\pi\)
\(942\) 0 0
\(943\) 66.9773 2.18108
\(944\) 0 0
\(945\) 19.9122 0.647745
\(946\) 0 0
\(947\) −37.1351 −1.20673 −0.603364 0.797466i \(-0.706174\pi\)
−0.603364 + 0.797466i \(0.706174\pi\)
\(948\) 0 0
\(949\) −19.8396 −0.644021
\(950\) 0 0
\(951\) 6.58048 0.213387
\(952\) 0 0
\(953\) 13.3835 0.433533 0.216767 0.976223i \(-0.430449\pi\)
0.216767 + 0.976223i \(0.430449\pi\)
\(954\) 0 0
\(955\) −18.7289 −0.606053
\(956\) 0 0
\(957\) −0.573800 −0.0185483
\(958\) 0 0
\(959\) −68.9125 −2.22530
\(960\) 0 0
\(961\) −23.3957 −0.754700
\(962\) 0 0
\(963\) −5.51278 −0.177647
\(964\) 0 0
\(965\) −5.04939 −0.162546
\(966\) 0 0
\(967\) −57.5577 −1.85093 −0.925466 0.378831i \(-0.876326\pi\)
−0.925466 + 0.378831i \(0.876326\pi\)
\(968\) 0 0
\(969\) 0.242215 0.00778106
\(970\) 0 0
\(971\) 40.4756 1.29892 0.649462 0.760394i \(-0.274994\pi\)
0.649462 + 0.760394i \(0.274994\pi\)
\(972\) 0 0
\(973\) −63.3038 −2.02943
\(974\) 0 0
\(975\) 2.65587 0.0850558
\(976\) 0 0
\(977\) −42.6625 −1.36489 −0.682447 0.730935i \(-0.739084\pi\)
−0.682447 + 0.730935i \(0.739084\pi\)
\(978\) 0 0
\(979\) −3.14738 −0.100591
\(980\) 0 0
\(981\) 3.17014 0.101215
\(982\) 0 0
\(983\) −37.5482 −1.19760 −0.598801 0.800898i \(-0.704356\pi\)
−0.598801 + 0.800898i \(0.704356\pi\)
\(984\) 0 0
\(985\) −16.5642 −0.527780
\(986\) 0 0
\(987\) −50.6348 −1.61172
\(988\) 0 0
\(989\) 58.6740 1.86573
\(990\) 0 0
\(991\) −47.7458 −1.51669 −0.758347 0.651851i \(-0.773993\pi\)
−0.758347 + 0.651851i \(0.773993\pi\)
\(992\) 0 0
\(993\) 4.88524 0.155028
\(994\) 0 0
\(995\) 3.77860 0.119790
\(996\) 0 0
\(997\) −19.8594 −0.628952 −0.314476 0.949265i \(-0.601829\pi\)
−0.314476 + 0.949265i \(0.601829\pi\)
\(998\) 0 0
\(999\) −30.3622 −0.960619
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 \(a_p\))