Properties

Label 8008.2.a.i.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.86081\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.46260 q^{3} +3.86081 q^{5} -1.00000 q^{7} -0.860806 q^{9} +O(q^{10})\) \(q+1.46260 q^{3} +3.86081 q^{5} -1.00000 q^{7} -0.860806 q^{9} -1.00000 q^{11} +1.00000 q^{13} +5.64681 q^{15} -7.78600 q^{17} -4.18421 q^{19} -1.46260 q^{21} -9.11982 q^{23} +9.90582 q^{25} -5.64681 q^{27} +4.79641 q^{29} -8.32340 q^{31} -1.46260 q^{33} -3.86081 q^{35} -0.323404 q^{37} +1.46260 q^{39} +11.0152 q^{41} -2.58242 q^{43} -3.32340 q^{45} +8.36842 q^{47} +1.00000 q^{49} -11.3878 q^{51} -4.98959 q^{53} -3.86081 q^{55} -6.11982 q^{57} -4.97021 q^{59} +1.13919 q^{61} +0.860806 q^{63} +3.86081 q^{65} +1.18421 q^{67} -13.3386 q^{69} -10.7860 q^{71} +1.44322 q^{73} +14.4882 q^{75} +1.00000 q^{77} -2.33382 q^{79} -5.67660 q^{81} -6.98062 q^{83} -30.0602 q^{85} +7.01523 q^{87} -2.90582 q^{89} -1.00000 q^{91} -12.1738 q^{93} -16.1544 q^{95} -14.5422 q^{97} +0.860806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 2q^{3} + 6q^{5} - 3q^{7} + 3q^{9} + O(q^{10}) \) \( 3q + 2q^{3} + 6q^{5} - 3q^{7} + 3q^{9} - 3q^{11} + 3q^{13} + q^{15} - 13q^{17} + q^{19} - 2q^{21} - 13q^{23} + 5q^{25} - q^{27} + 8q^{29} - 17q^{31} - 2q^{33} - 6q^{35} + 7q^{37} + 2q^{39} - 10q^{41} + 9q^{43} - 2q^{45} - 2q^{47} + 3q^{49} - 27q^{51} - 11q^{53} - 6q^{55} - 4q^{57} + 9q^{59} + 9q^{61} - 3q^{63} + 6q^{65} - 10q^{67} + 11q^{69} - 22q^{71} - 18q^{73} + 2q^{75} + 3q^{77} - 3q^{79} - 25q^{81} - q^{83} - 28q^{85} - 22q^{87} + 16q^{89} - 3q^{91} - 19q^{93} - 11q^{95} + q^{97} - 3q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.46260 0.844432 0.422216 0.906495i \(-0.361252\pi\)
0.422216 + 0.906495i \(0.361252\pi\)
\(4\) 0 0
\(5\) 3.86081 1.72660 0.863302 0.504687i \(-0.168392\pi\)
0.863302 + 0.504687i \(0.168392\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.860806 −0.286935
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 5.64681 1.45800
\(16\) 0 0
\(17\) −7.78600 −1.88838 −0.944192 0.329397i \(-0.893155\pi\)
−0.944192 + 0.329397i \(0.893155\pi\)
\(18\) 0 0
\(19\) −4.18421 −0.959924 −0.479962 0.877289i \(-0.659349\pi\)
−0.479962 + 0.877289i \(0.659349\pi\)
\(20\) 0 0
\(21\) −1.46260 −0.319165
\(22\) 0 0
\(23\) −9.11982 −1.90161 −0.950807 0.309784i \(-0.899743\pi\)
−0.950807 + 0.309784i \(0.899743\pi\)
\(24\) 0 0
\(25\) 9.90582 1.98116
\(26\) 0 0
\(27\) −5.64681 −1.08673
\(28\) 0 0
\(29\) 4.79641 0.890672 0.445336 0.895364i \(-0.353084\pi\)
0.445336 + 0.895364i \(0.353084\pi\)
\(30\) 0 0
\(31\) −8.32340 −1.49493 −0.747464 0.664303i \(-0.768729\pi\)
−0.747464 + 0.664303i \(0.768729\pi\)
\(32\) 0 0
\(33\) −1.46260 −0.254606
\(34\) 0 0
\(35\) −3.86081 −0.652595
\(36\) 0 0
\(37\) −0.323404 −0.0531673 −0.0265837 0.999647i \(-0.508463\pi\)
−0.0265837 + 0.999647i \(0.508463\pi\)
\(38\) 0 0
\(39\) 1.46260 0.234203
\(40\) 0 0
\(41\) 11.0152 1.72029 0.860145 0.510050i \(-0.170373\pi\)
0.860145 + 0.510050i \(0.170373\pi\)
\(42\) 0 0
\(43\) −2.58242 −0.393815 −0.196907 0.980422i \(-0.563090\pi\)
−0.196907 + 0.980422i \(0.563090\pi\)
\(44\) 0 0
\(45\) −3.32340 −0.495424
\(46\) 0 0
\(47\) 8.36842 1.22066 0.610330 0.792147i \(-0.291037\pi\)
0.610330 + 0.792147i \(0.291037\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −11.3878 −1.59461
\(52\) 0 0
\(53\) −4.98959 −0.685373 −0.342686 0.939450i \(-0.611337\pi\)
−0.342686 + 0.939450i \(0.611337\pi\)
\(54\) 0 0
\(55\) −3.86081 −0.520591
\(56\) 0 0
\(57\) −6.11982 −0.810590
\(58\) 0 0
\(59\) −4.97021 −0.647067 −0.323533 0.946217i \(-0.604871\pi\)
−0.323533 + 0.946217i \(0.604871\pi\)
\(60\) 0 0
\(61\) 1.13919 0.145859 0.0729294 0.997337i \(-0.476765\pi\)
0.0729294 + 0.997337i \(0.476765\pi\)
\(62\) 0 0
\(63\) 0.860806 0.108451
\(64\) 0 0
\(65\) 3.86081 0.478874
\(66\) 0 0
\(67\) 1.18421 0.144674 0.0723371 0.997380i \(-0.476954\pi\)
0.0723371 + 0.997380i \(0.476954\pi\)
\(68\) 0 0
\(69\) −13.3386 −1.60578
\(70\) 0 0
\(71\) −10.7860 −1.28006 −0.640032 0.768349i \(-0.721079\pi\)
−0.640032 + 0.768349i \(0.721079\pi\)
\(72\) 0 0
\(73\) 1.44322 0.168917 0.0844583 0.996427i \(-0.473084\pi\)
0.0844583 + 0.996427i \(0.473084\pi\)
\(74\) 0 0
\(75\) 14.4882 1.67296
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −2.33382 −0.262575 −0.131287 0.991344i \(-0.541911\pi\)
−0.131287 + 0.991344i \(0.541911\pi\)
\(80\) 0 0
\(81\) −5.67660 −0.630733
\(82\) 0 0
\(83\) −6.98062 −0.766223 −0.383112 0.923702i \(-0.625148\pi\)
−0.383112 + 0.923702i \(0.625148\pi\)
\(84\) 0 0
\(85\) −30.0602 −3.26049
\(86\) 0 0
\(87\) 7.01523 0.752111
\(88\) 0 0
\(89\) −2.90582 −0.308016 −0.154008 0.988070i \(-0.549218\pi\)
−0.154008 + 0.988070i \(0.549218\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −12.1738 −1.26236
\(94\) 0 0
\(95\) −16.1544 −1.65741
\(96\) 0 0
\(97\) −14.5422 −1.47654 −0.738269 0.674506i \(-0.764357\pi\)
−0.738269 + 0.674506i \(0.764357\pi\)
\(98\) 0 0
\(99\) 0.860806 0.0865142
\(100\) 0 0
\(101\) −5.53740 −0.550992 −0.275496 0.961302i \(-0.588842\pi\)
−0.275496 + 0.961302i \(0.588842\pi\)
\(102\) 0 0
\(103\) 5.29362 0.521596 0.260798 0.965393i \(-0.416014\pi\)
0.260798 + 0.965393i \(0.416014\pi\)
\(104\) 0 0
\(105\) −5.64681 −0.551072
\(106\) 0 0
\(107\) 15.1004 1.45982 0.729908 0.683546i \(-0.239563\pi\)
0.729908 + 0.683546i \(0.239563\pi\)
\(108\) 0 0
\(109\) 0.0941782 0.00902063 0.00451032 0.999990i \(-0.498564\pi\)
0.00451032 + 0.999990i \(0.498564\pi\)
\(110\) 0 0
\(111\) −0.473011 −0.0448962
\(112\) 0 0
\(113\) −11.2140 −1.05492 −0.527462 0.849579i \(-0.676856\pi\)
−0.527462 + 0.849579i \(0.676856\pi\)
\(114\) 0 0
\(115\) −35.2099 −3.28334
\(116\) 0 0
\(117\) −0.860806 −0.0795815
\(118\) 0 0
\(119\) 7.78600 0.713742
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 16.1109 1.45267
\(124\) 0 0
\(125\) 18.9404 1.69408
\(126\) 0 0
\(127\) 9.13023 0.810177 0.405089 0.914277i \(-0.367241\pi\)
0.405089 + 0.914277i \(0.367241\pi\)
\(128\) 0 0
\(129\) −3.77704 −0.332550
\(130\) 0 0
\(131\) 10.4972 0.917145 0.458572 0.888657i \(-0.348361\pi\)
0.458572 + 0.888657i \(0.348361\pi\)
\(132\) 0 0
\(133\) 4.18421 0.362817
\(134\) 0 0
\(135\) −21.8012 −1.87635
\(136\) 0 0
\(137\) −19.6170 −1.67600 −0.837998 0.545674i \(-0.816274\pi\)
−0.837998 + 0.545674i \(0.816274\pi\)
\(138\) 0 0
\(139\) 8.64681 0.733413 0.366706 0.930337i \(-0.380485\pi\)
0.366706 + 0.930337i \(0.380485\pi\)
\(140\) 0 0
\(141\) 12.2396 1.03076
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 18.5180 1.53784
\(146\) 0 0
\(147\) 1.46260 0.120633
\(148\) 0 0
\(149\) −2.98062 −0.244182 −0.122091 0.992519i \(-0.538960\pi\)
−0.122091 + 0.992519i \(0.538960\pi\)
\(150\) 0 0
\(151\) 3.57201 0.290686 0.145343 0.989381i \(-0.453571\pi\)
0.145343 + 0.989381i \(0.453571\pi\)
\(152\) 0 0
\(153\) 6.70224 0.541844
\(154\) 0 0
\(155\) −32.1350 −2.58115
\(156\) 0 0
\(157\) 5.37738 0.429162 0.214581 0.976706i \(-0.431161\pi\)
0.214581 + 0.976706i \(0.431161\pi\)
\(158\) 0 0
\(159\) −7.29776 −0.578750
\(160\) 0 0
\(161\) 9.11982 0.718742
\(162\) 0 0
\(163\) −1.53740 −0.120419 −0.0602093 0.998186i \(-0.519177\pi\)
−0.0602093 + 0.998186i \(0.519177\pi\)
\(164\) 0 0
\(165\) −5.64681 −0.439603
\(166\) 0 0
\(167\) −18.5824 −1.43795 −0.718975 0.695036i \(-0.755389\pi\)
−0.718975 + 0.695036i \(0.755389\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 3.60179 0.275436
\(172\) 0 0
\(173\) 4.70224 0.357504 0.178752 0.983894i \(-0.442794\pi\)
0.178752 + 0.983894i \(0.442794\pi\)
\(174\) 0 0
\(175\) −9.90582 −0.748810
\(176\) 0 0
\(177\) −7.26943 −0.546403
\(178\) 0 0
\(179\) −8.73057 −0.652554 −0.326277 0.945274i \(-0.605794\pi\)
−0.326277 + 0.945274i \(0.605794\pi\)
\(180\) 0 0
\(181\) −9.48824 −0.705255 −0.352628 0.935764i \(-0.614712\pi\)
−0.352628 + 0.935764i \(0.614712\pi\)
\(182\) 0 0
\(183\) 1.66618 0.123168
\(184\) 0 0
\(185\) −1.24860 −0.0917990
\(186\) 0 0
\(187\) 7.78600 0.569369
\(188\) 0 0
\(189\) 5.64681 0.410745
\(190\) 0 0
\(191\) −13.7666 −0.996118 −0.498059 0.867143i \(-0.665954\pi\)
−0.498059 + 0.867143i \(0.665954\pi\)
\(192\) 0 0
\(193\) 12.8012 0.921453 0.460726 0.887542i \(-0.347589\pi\)
0.460726 + 0.887542i \(0.347589\pi\)
\(194\) 0 0
\(195\) 5.64681 0.404376
\(196\) 0 0
\(197\) −27.3193 −1.94642 −0.973208 0.229925i \(-0.926152\pi\)
−0.973208 + 0.229925i \(0.926152\pi\)
\(198\) 0 0
\(199\) −10.1634 −0.720463 −0.360232 0.932863i \(-0.617302\pi\)
−0.360232 + 0.932863i \(0.617302\pi\)
\(200\) 0 0
\(201\) 1.73202 0.122168
\(202\) 0 0
\(203\) −4.79641 −0.336642
\(204\) 0 0
\(205\) 42.5277 2.97026
\(206\) 0 0
\(207\) 7.85039 0.545640
\(208\) 0 0
\(209\) 4.18421 0.289428
\(210\) 0 0
\(211\) −4.30403 −0.296302 −0.148151 0.988965i \(-0.547332\pi\)
−0.148151 + 0.988965i \(0.547332\pi\)
\(212\) 0 0
\(213\) −15.7756 −1.08093
\(214\) 0 0
\(215\) −9.97021 −0.679963
\(216\) 0 0
\(217\) 8.32340 0.565029
\(218\) 0 0
\(219\) 2.11086 0.142638
\(220\) 0 0
\(221\) −7.78600 −0.523743
\(222\) 0 0
\(223\) −11.4674 −0.767915 −0.383957 0.923351i \(-0.625439\pi\)
−0.383957 + 0.923351i \(0.625439\pi\)
\(224\) 0 0
\(225\) −8.52699 −0.568466
\(226\) 0 0
\(227\) 13.4868 0.895150 0.447575 0.894246i \(-0.352288\pi\)
0.447575 + 0.894246i \(0.352288\pi\)
\(228\) 0 0
\(229\) 23.0256 1.52158 0.760789 0.649000i \(-0.224812\pi\)
0.760789 + 0.649000i \(0.224812\pi\)
\(230\) 0 0
\(231\) 1.46260 0.0962319
\(232\) 0 0
\(233\) 11.6620 0.764005 0.382003 0.924161i \(-0.375234\pi\)
0.382003 + 0.924161i \(0.375234\pi\)
\(234\) 0 0
\(235\) 32.3088 2.10760
\(236\) 0 0
\(237\) −3.41344 −0.221727
\(238\) 0 0
\(239\) 14.7756 0.955753 0.477877 0.878427i \(-0.341407\pi\)
0.477877 + 0.878427i \(0.341407\pi\)
\(240\) 0 0
\(241\) 2.36842 0.152563 0.0762817 0.997086i \(-0.475695\pi\)
0.0762817 + 0.997086i \(0.475695\pi\)
\(242\) 0 0
\(243\) 8.63785 0.554118
\(244\) 0 0
\(245\) 3.86081 0.246658
\(246\) 0 0
\(247\) −4.18421 −0.266235
\(248\) 0 0
\(249\) −10.2099 −0.647023
\(250\) 0 0
\(251\) 19.2445 1.21470 0.607350 0.794435i \(-0.292233\pi\)
0.607350 + 0.794435i \(0.292233\pi\)
\(252\) 0 0
\(253\) 9.11982 0.573358
\(254\) 0 0
\(255\) −43.9661 −2.75326
\(256\) 0 0
\(257\) 10.6676 0.665429 0.332714 0.943028i \(-0.392036\pi\)
0.332714 + 0.943028i \(0.392036\pi\)
\(258\) 0 0
\(259\) 0.323404 0.0200954
\(260\) 0 0
\(261\) −4.12878 −0.255565
\(262\) 0 0
\(263\) −18.4238 −1.13606 −0.568032 0.823007i \(-0.692295\pi\)
−0.568032 + 0.823007i \(0.692295\pi\)
\(264\) 0 0
\(265\) −19.2638 −1.18337
\(266\) 0 0
\(267\) −4.25005 −0.260099
\(268\) 0 0
\(269\) 8.70638 0.530838 0.265419 0.964133i \(-0.414490\pi\)
0.265419 + 0.964133i \(0.414490\pi\)
\(270\) 0 0
\(271\) −26.3732 −1.60206 −0.801030 0.598624i \(-0.795714\pi\)
−0.801030 + 0.598624i \(0.795714\pi\)
\(272\) 0 0
\(273\) −1.46260 −0.0885205
\(274\) 0 0
\(275\) −9.90582 −0.597344
\(276\) 0 0
\(277\) −5.48197 −0.329380 −0.164690 0.986345i \(-0.552662\pi\)
−0.164690 + 0.986345i \(0.552662\pi\)
\(278\) 0 0
\(279\) 7.16484 0.428947
\(280\) 0 0
\(281\) 15.8969 0.948327 0.474164 0.880437i \(-0.342751\pi\)
0.474164 + 0.880437i \(0.342751\pi\)
\(282\) 0 0
\(283\) −16.3892 −0.974239 −0.487120 0.873335i \(-0.661952\pi\)
−0.487120 + 0.873335i \(0.661952\pi\)
\(284\) 0 0
\(285\) −23.6274 −1.39957
\(286\) 0 0
\(287\) −11.0152 −0.650208
\(288\) 0 0
\(289\) 43.6218 2.56599
\(290\) 0 0
\(291\) −21.2694 −1.24684
\(292\) 0 0
\(293\) 14.5180 0.848152 0.424076 0.905627i \(-0.360599\pi\)
0.424076 + 0.905627i \(0.360599\pi\)
\(294\) 0 0
\(295\) −19.1890 −1.11723
\(296\) 0 0
\(297\) 5.64681 0.327661
\(298\) 0 0
\(299\) −9.11982 −0.527413
\(300\) 0 0
\(301\) 2.58242 0.148848
\(302\) 0 0
\(303\) −8.09899 −0.465275
\(304\) 0 0
\(305\) 4.39821 0.251841
\(306\) 0 0
\(307\) 17.8760 1.02024 0.510120 0.860103i \(-0.329601\pi\)
0.510120 + 0.860103i \(0.329601\pi\)
\(308\) 0 0
\(309\) 7.74244 0.440452
\(310\) 0 0
\(311\) −13.1690 −0.746744 −0.373372 0.927682i \(-0.621799\pi\)
−0.373372 + 0.927682i \(0.621799\pi\)
\(312\) 0 0
\(313\) −23.4674 −1.32646 −0.663228 0.748417i \(-0.730814\pi\)
−0.663228 + 0.748417i \(0.730814\pi\)
\(314\) 0 0
\(315\) 3.32340 0.187253
\(316\) 0 0
\(317\) −3.67660 −0.206498 −0.103249 0.994656i \(-0.532924\pi\)
−0.103249 + 0.994656i \(0.532924\pi\)
\(318\) 0 0
\(319\) −4.79641 −0.268548
\(320\) 0 0
\(321\) 22.0859 1.23271
\(322\) 0 0
\(323\) 32.5783 1.81270
\(324\) 0 0
\(325\) 9.90582 0.549476
\(326\) 0 0
\(327\) 0.137745 0.00761731
\(328\) 0 0
\(329\) −8.36842 −0.461366
\(330\) 0 0
\(331\) −7.86081 −0.432069 −0.216034 0.976386i \(-0.569312\pi\)
−0.216034 + 0.976386i \(0.569312\pi\)
\(332\) 0 0
\(333\) 0.278388 0.0152556
\(334\) 0 0
\(335\) 4.57201 0.249795
\(336\) 0 0
\(337\) −26.9557 −1.46837 −0.734184 0.678951i \(-0.762435\pi\)
−0.734184 + 0.678951i \(0.762435\pi\)
\(338\) 0 0
\(339\) −16.4016 −0.890811
\(340\) 0 0
\(341\) 8.32340 0.450738
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −51.4979 −2.77255
\(346\) 0 0
\(347\) 17.9058 0.961235 0.480617 0.876930i \(-0.340413\pi\)
0.480617 + 0.876930i \(0.340413\pi\)
\(348\) 0 0
\(349\) −13.2244 −0.707886 −0.353943 0.935267i \(-0.615159\pi\)
−0.353943 + 0.935267i \(0.615159\pi\)
\(350\) 0 0
\(351\) −5.64681 −0.301404
\(352\) 0 0
\(353\) −1.63785 −0.0871737 −0.0435869 0.999050i \(-0.513879\pi\)
−0.0435869 + 0.999050i \(0.513879\pi\)
\(354\) 0 0
\(355\) −41.6427 −2.21016
\(356\) 0 0
\(357\) 11.3878 0.602706
\(358\) 0 0
\(359\) −23.4045 −1.23524 −0.617620 0.786476i \(-0.711903\pi\)
−0.617620 + 0.786476i \(0.711903\pi\)
\(360\) 0 0
\(361\) −1.49239 −0.0785466
\(362\) 0 0
\(363\) 1.46260 0.0767665
\(364\) 0 0
\(365\) 5.57201 0.291652
\(366\) 0 0
\(367\) 11.6814 0.609765 0.304882 0.952390i \(-0.401383\pi\)
0.304882 + 0.952390i \(0.401383\pi\)
\(368\) 0 0
\(369\) −9.48197 −0.493612
\(370\) 0 0
\(371\) 4.98959 0.259046
\(372\) 0 0
\(373\) 30.8448 1.59708 0.798542 0.601940i \(-0.205605\pi\)
0.798542 + 0.601940i \(0.205605\pi\)
\(374\) 0 0
\(375\) 27.7022 1.43054
\(376\) 0 0
\(377\) 4.79641 0.247028
\(378\) 0 0
\(379\) −10.7354 −0.551440 −0.275720 0.961238i \(-0.588916\pi\)
−0.275720 + 0.961238i \(0.588916\pi\)
\(380\) 0 0
\(381\) 13.3539 0.684139
\(382\) 0 0
\(383\) −24.4343 −1.24853 −0.624266 0.781212i \(-0.714602\pi\)
−0.624266 + 0.781212i \(0.714602\pi\)
\(384\) 0 0
\(385\) 3.86081 0.196765
\(386\) 0 0
\(387\) 2.22296 0.112999
\(388\) 0 0
\(389\) 11.2445 0.570116 0.285058 0.958510i \(-0.407987\pi\)
0.285058 + 0.958510i \(0.407987\pi\)
\(390\) 0 0
\(391\) 71.0069 3.59098
\(392\) 0 0
\(393\) 15.3532 0.774466
\(394\) 0 0
\(395\) −9.01041 −0.453363
\(396\) 0 0
\(397\) 0.621168 0.0311755 0.0155878 0.999879i \(-0.495038\pi\)
0.0155878 + 0.999879i \(0.495038\pi\)
\(398\) 0 0
\(399\) 6.11982 0.306374
\(400\) 0 0
\(401\) 28.7577 1.43609 0.718045 0.695997i \(-0.245037\pi\)
0.718045 + 0.695997i \(0.245037\pi\)
\(402\) 0 0
\(403\) −8.32340 −0.414618
\(404\) 0 0
\(405\) −21.9162 −1.08903
\(406\) 0 0
\(407\) 0.323404 0.0160306
\(408\) 0 0
\(409\) 10.3088 0.509740 0.254870 0.966975i \(-0.417967\pi\)
0.254870 + 0.966975i \(0.417967\pi\)
\(410\) 0 0
\(411\) −28.6918 −1.41526
\(412\) 0 0
\(413\) 4.97021 0.244568
\(414\) 0 0
\(415\) −26.9508 −1.32296
\(416\) 0 0
\(417\) 12.6468 0.619317
\(418\) 0 0
\(419\) 26.1752 1.27874 0.639372 0.768897i \(-0.279194\pi\)
0.639372 + 0.768897i \(0.279194\pi\)
\(420\) 0 0
\(421\) 35.4737 1.72888 0.864441 0.502735i \(-0.167673\pi\)
0.864441 + 0.502735i \(0.167673\pi\)
\(422\) 0 0
\(423\) −7.20359 −0.350250
\(424\) 0 0
\(425\) −77.1268 −3.74120
\(426\) 0 0
\(427\) −1.13919 −0.0551295
\(428\) 0 0
\(429\) −1.46260 −0.0706149
\(430\) 0 0
\(431\) 32.5872 1.56967 0.784836 0.619704i \(-0.212747\pi\)
0.784836 + 0.619704i \(0.212747\pi\)
\(432\) 0 0
\(433\) −16.5839 −0.796970 −0.398485 0.917175i \(-0.630464\pi\)
−0.398485 + 0.917175i \(0.630464\pi\)
\(434\) 0 0
\(435\) 27.0844 1.29860
\(436\) 0 0
\(437\) 38.1592 1.82540
\(438\) 0 0
\(439\) −0.427995 −0.0204271 −0.0102135 0.999948i \(-0.503251\pi\)
−0.0102135 + 0.999948i \(0.503251\pi\)
\(440\) 0 0
\(441\) −0.860806 −0.0409908
\(442\) 0 0
\(443\) 37.9259 1.80191 0.900956 0.433910i \(-0.142866\pi\)
0.900956 + 0.433910i \(0.142866\pi\)
\(444\) 0 0
\(445\) −11.2188 −0.531823
\(446\) 0 0
\(447\) −4.35946 −0.206195
\(448\) 0 0
\(449\) 20.2251 0.954481 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(450\) 0 0
\(451\) −11.0152 −0.518687
\(452\) 0 0
\(453\) 5.22441 0.245464
\(454\) 0 0
\(455\) −3.86081 −0.180997
\(456\) 0 0
\(457\) 28.4931 1.33285 0.666424 0.745573i \(-0.267824\pi\)
0.666424 + 0.745573i \(0.267824\pi\)
\(458\) 0 0
\(459\) 43.9661 2.05216
\(460\) 0 0
\(461\) −2.45845 −0.114502 −0.0572508 0.998360i \(-0.518233\pi\)
−0.0572508 + 0.998360i \(0.518233\pi\)
\(462\) 0 0
\(463\) −42.0450 −1.95400 −0.976999 0.213245i \(-0.931597\pi\)
−0.976999 + 0.213245i \(0.931597\pi\)
\(464\) 0 0
\(465\) −47.0007 −2.17960
\(466\) 0 0
\(467\) −3.31299 −0.153307 −0.0766535 0.997058i \(-0.524424\pi\)
−0.0766535 + 0.997058i \(0.524424\pi\)
\(468\) 0 0
\(469\) −1.18421 −0.0546817
\(470\) 0 0
\(471\) 7.86495 0.362398
\(472\) 0 0
\(473\) 2.58242 0.118740
\(474\) 0 0
\(475\) −41.4480 −1.90177
\(476\) 0 0
\(477\) 4.29507 0.196658
\(478\) 0 0
\(479\) 23.7562 1.08545 0.542725 0.839911i \(-0.317393\pi\)
0.542725 + 0.839911i \(0.317393\pi\)
\(480\) 0 0
\(481\) −0.323404 −0.0147460
\(482\) 0 0
\(483\) 13.3386 0.606929
\(484\) 0 0
\(485\) −56.1447 −2.54940
\(486\) 0 0
\(487\) 7.33863 0.332545 0.166273 0.986080i \(-0.446827\pi\)
0.166273 + 0.986080i \(0.446827\pi\)
\(488\) 0 0
\(489\) −2.24860 −0.101685
\(490\) 0 0
\(491\) 28.6468 1.29281 0.646406 0.762993i \(-0.276271\pi\)
0.646406 + 0.762993i \(0.276271\pi\)
\(492\) 0 0
\(493\) −37.3449 −1.68193
\(494\) 0 0
\(495\) 3.32340 0.149376
\(496\) 0 0
\(497\) 10.7860 0.483818
\(498\) 0 0
\(499\) −14.9419 −0.668890 −0.334445 0.942415i \(-0.608549\pi\)
−0.334445 + 0.942415i \(0.608549\pi\)
\(500\) 0 0
\(501\) −27.1786 −1.21425
\(502\) 0 0
\(503\) 18.3892 0.819936 0.409968 0.912100i \(-0.365540\pi\)
0.409968 + 0.912100i \(0.365540\pi\)
\(504\) 0 0
\(505\) −21.3788 −0.951346
\(506\) 0 0
\(507\) 1.46260 0.0649563
\(508\) 0 0
\(509\) 8.39261 0.371996 0.185998 0.982550i \(-0.440448\pi\)
0.185998 + 0.982550i \(0.440448\pi\)
\(510\) 0 0
\(511\) −1.44322 −0.0638444
\(512\) 0 0
\(513\) 23.6274 1.04318
\(514\) 0 0
\(515\) 20.4376 0.900589
\(516\) 0 0
\(517\) −8.36842 −0.368043
\(518\) 0 0
\(519\) 6.87748 0.301888
\(520\) 0 0
\(521\) −40.5935 −1.77843 −0.889217 0.457486i \(-0.848750\pi\)
−0.889217 + 0.457486i \(0.848750\pi\)
\(522\) 0 0
\(523\) −12.8352 −0.561243 −0.280621 0.959819i \(-0.590540\pi\)
−0.280621 + 0.959819i \(0.590540\pi\)
\(524\) 0 0
\(525\) −14.4882 −0.632319
\(526\) 0 0
\(527\) 64.8060 2.82300
\(528\) 0 0
\(529\) 60.1711 2.61613
\(530\) 0 0
\(531\) 4.27839 0.185666
\(532\) 0 0
\(533\) 11.0152 0.477123
\(534\) 0 0
\(535\) 58.2999 2.52052
\(536\) 0 0
\(537\) −12.7693 −0.551037
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 29.7008 1.27694 0.638468 0.769648i \(-0.279568\pi\)
0.638468 + 0.769648i \(0.279568\pi\)
\(542\) 0 0
\(543\) −13.8775 −0.595540
\(544\) 0 0
\(545\) 0.363604 0.0155751
\(546\) 0 0
\(547\) 20.4376 0.873850 0.436925 0.899498i \(-0.356068\pi\)
0.436925 + 0.899498i \(0.356068\pi\)
\(548\) 0 0
\(549\) −0.980625 −0.0418521
\(550\) 0 0
\(551\) −20.0692 −0.854977
\(552\) 0 0
\(553\) 2.33382 0.0992440
\(554\) 0 0
\(555\) −1.82620 −0.0775180
\(556\) 0 0
\(557\) −13.7770 −0.583752 −0.291876 0.956456i \(-0.594279\pi\)
−0.291876 + 0.956456i \(0.594279\pi\)
\(558\) 0 0
\(559\) −2.58242 −0.109225
\(560\) 0 0
\(561\) 11.3878 0.480793
\(562\) 0 0
\(563\) −45.2132 −1.90551 −0.952755 0.303740i \(-0.901765\pi\)
−0.952755 + 0.303740i \(0.901765\pi\)
\(564\) 0 0
\(565\) −43.2951 −1.82144
\(566\) 0 0
\(567\) 5.67660 0.238395
\(568\) 0 0
\(569\) −24.5180 −1.02785 −0.513925 0.857835i \(-0.671809\pi\)
−0.513925 + 0.857835i \(0.671809\pi\)
\(570\) 0 0
\(571\) 11.9446 0.499865 0.249932 0.968263i \(-0.419592\pi\)
0.249932 + 0.968263i \(0.419592\pi\)
\(572\) 0 0
\(573\) −20.1350 −0.841154
\(574\) 0 0
\(575\) −90.3393 −3.76741
\(576\) 0 0
\(577\) −33.5735 −1.39768 −0.698841 0.715277i \(-0.746300\pi\)
−0.698841 + 0.715277i \(0.746300\pi\)
\(578\) 0 0
\(579\) 18.7231 0.778104
\(580\) 0 0
\(581\) 6.98062 0.289605
\(582\) 0 0
\(583\) 4.98959 0.206648
\(584\) 0 0
\(585\) −3.32340 −0.137406
\(586\) 0 0
\(587\) −7.87122 −0.324880 −0.162440 0.986718i \(-0.551936\pi\)
−0.162440 + 0.986718i \(0.551936\pi\)
\(588\) 0 0
\(589\) 34.8269 1.43502
\(590\) 0 0
\(591\) −39.9571 −1.64362
\(592\) 0 0
\(593\) −47.9196 −1.96782 −0.983911 0.178659i \(-0.942824\pi\)
−0.983911 + 0.178659i \(0.942824\pi\)
\(594\) 0 0
\(595\) 30.0602 1.23235
\(596\) 0 0
\(597\) −14.8650 −0.608382
\(598\) 0 0
\(599\) −11.6137 −0.474521 −0.237261 0.971446i \(-0.576250\pi\)
−0.237261 + 0.971446i \(0.576250\pi\)
\(600\) 0 0
\(601\) 7.52844 0.307091 0.153546 0.988142i \(-0.450931\pi\)
0.153546 + 0.988142i \(0.450931\pi\)
\(602\) 0 0
\(603\) −1.01938 −0.0415122
\(604\) 0 0
\(605\) 3.86081 0.156964
\(606\) 0 0
\(607\) 30.9765 1.25730 0.628648 0.777690i \(-0.283609\pi\)
0.628648 + 0.777690i \(0.283609\pi\)
\(608\) 0 0
\(609\) −7.01523 −0.284271
\(610\) 0 0
\(611\) 8.36842 0.338550
\(612\) 0 0
\(613\) −41.0665 −1.65866 −0.829330 0.558759i \(-0.811278\pi\)
−0.829330 + 0.558759i \(0.811278\pi\)
\(614\) 0 0
\(615\) 62.2009 2.50818
\(616\) 0 0
\(617\) 26.9765 1.08603 0.543016 0.839722i \(-0.317282\pi\)
0.543016 + 0.839722i \(0.317282\pi\)
\(618\) 0 0
\(619\) −5.43696 −0.218530 −0.109265 0.994013i \(-0.534850\pi\)
−0.109265 + 0.994013i \(0.534850\pi\)
\(620\) 0 0
\(621\) 51.4979 2.06654
\(622\) 0 0
\(623\) 2.90582 0.116419
\(624\) 0 0
\(625\) 23.5962 0.943848
\(626\) 0 0
\(627\) 6.11982 0.244402
\(628\) 0 0
\(629\) 2.51803 0.100400
\(630\) 0 0
\(631\) 46.5083 1.85147 0.925733 0.378178i \(-0.123449\pi\)
0.925733 + 0.378178i \(0.123449\pi\)
\(632\) 0 0
\(633\) −6.29507 −0.250206
\(634\) 0 0
\(635\) 35.2501 1.39886
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) 9.28465 0.367295
\(640\) 0 0
\(641\) −16.7383 −0.661123 −0.330561 0.943785i \(-0.607238\pi\)
−0.330561 + 0.943785i \(0.607238\pi\)
\(642\) 0 0
\(643\) −6.43426 −0.253742 −0.126871 0.991919i \(-0.540494\pi\)
−0.126871 + 0.991919i \(0.540494\pi\)
\(644\) 0 0
\(645\) −14.5824 −0.574182
\(646\) 0 0
\(647\) −24.7514 −0.973078 −0.486539 0.873659i \(-0.661741\pi\)
−0.486539 + 0.873659i \(0.661741\pi\)
\(648\) 0 0
\(649\) 4.97021 0.195098
\(650\) 0 0
\(651\) 12.1738 0.477129
\(652\) 0 0
\(653\) 44.8046 1.75334 0.876670 0.481093i \(-0.159760\pi\)
0.876670 + 0.481093i \(0.159760\pi\)
\(654\) 0 0
\(655\) 40.5277 1.58355
\(656\) 0 0
\(657\) −1.24234 −0.0484681
\(658\) 0 0
\(659\) −23.6156 −0.919932 −0.459966 0.887937i \(-0.652138\pi\)
−0.459966 + 0.887937i \(0.652138\pi\)
\(660\) 0 0
\(661\) 43.9300 1.70868 0.854340 0.519715i \(-0.173962\pi\)
0.854340 + 0.519715i \(0.173962\pi\)
\(662\) 0 0
\(663\) −11.3878 −0.442265
\(664\) 0 0
\(665\) 16.1544 0.626442
\(666\) 0 0
\(667\) −43.7424 −1.69371
\(668\) 0 0
\(669\) −16.7722 −0.648452
\(670\) 0 0
\(671\) −1.13919 −0.0439781
\(672\) 0 0
\(673\) −30.0096 −1.15679 −0.578393 0.815758i \(-0.696320\pi\)
−0.578393 + 0.815758i \(0.696320\pi\)
\(674\) 0 0
\(675\) −55.9363 −2.15299
\(676\) 0 0
\(677\) 9.17794 0.352737 0.176369 0.984324i \(-0.443565\pi\)
0.176369 + 0.984324i \(0.443565\pi\)
\(678\) 0 0
\(679\) 14.5422 0.558079
\(680\) 0 0
\(681\) 19.7258 0.755893
\(682\) 0 0
\(683\) 32.3941 1.23952 0.619762 0.784790i \(-0.287229\pi\)
0.619762 + 0.784790i \(0.287229\pi\)
\(684\) 0 0
\(685\) −75.7375 −2.89378
\(686\) 0 0
\(687\) 33.6773 1.28487
\(688\) 0 0
\(689\) −4.98959 −0.190088
\(690\) 0 0
\(691\) 20.9910 0.798537 0.399268 0.916834i \(-0.369264\pi\)
0.399268 + 0.916834i \(0.369264\pi\)
\(692\) 0 0
\(693\) −0.860806 −0.0326993
\(694\) 0 0
\(695\) 33.3836 1.26631
\(696\) 0 0
\(697\) −85.7646 −3.24857
\(698\) 0 0
\(699\) 17.0569 0.645150
\(700\) 0 0
\(701\) −11.5028 −0.434455 −0.217227 0.976121i \(-0.569701\pi\)
−0.217227 + 0.976121i \(0.569701\pi\)
\(702\) 0 0
\(703\) 1.35319 0.0510366
\(704\) 0 0
\(705\) 47.2549 1.77972
\(706\) 0 0
\(707\) 5.53740 0.208255
\(708\) 0 0
\(709\) −35.3207 −1.32650 −0.663249 0.748399i \(-0.730823\pi\)
−0.663249 + 0.748399i \(0.730823\pi\)
\(710\) 0 0
\(711\) 2.00896 0.0753420
\(712\) 0 0
\(713\) 75.9079 2.84277
\(714\) 0 0
\(715\) −3.86081 −0.144386
\(716\) 0 0
\(717\) 21.6108 0.807068
\(718\) 0 0
\(719\) −42.7867 −1.59567 −0.797837 0.602873i \(-0.794022\pi\)
−0.797837 + 0.602873i \(0.794022\pi\)
\(720\) 0 0
\(721\) −5.29362 −0.197145
\(722\) 0 0
\(723\) 3.46405 0.128829
\(724\) 0 0
\(725\) 47.5124 1.76457
\(726\) 0 0
\(727\) −40.1517 −1.48915 −0.744573 0.667542i \(-0.767347\pi\)
−0.744573 + 0.667542i \(0.767347\pi\)
\(728\) 0 0
\(729\) 29.6635 1.09865
\(730\) 0 0
\(731\) 20.1067 0.743674
\(732\) 0 0
\(733\) 34.1109 1.25991 0.629957 0.776630i \(-0.283073\pi\)
0.629957 + 0.776630i \(0.283073\pi\)
\(734\) 0 0
\(735\) 5.64681 0.208286
\(736\) 0 0
\(737\) −1.18421 −0.0436209
\(738\) 0 0
\(739\) −23.4045 −0.860947 −0.430474 0.902603i \(-0.641653\pi\)
−0.430474 + 0.902603i \(0.641653\pi\)
\(740\) 0 0
\(741\) −6.11982 −0.224817
\(742\) 0 0
\(743\) −16.8864 −0.619504 −0.309752 0.950817i \(-0.600246\pi\)
−0.309752 + 0.950817i \(0.600246\pi\)
\(744\) 0 0
\(745\) −11.5076 −0.421606
\(746\) 0 0
\(747\) 6.00896 0.219856
\(748\) 0 0
\(749\) −15.1004 −0.551758
\(750\) 0 0
\(751\) −49.0394 −1.78947 −0.894737 0.446594i \(-0.852637\pi\)
−0.894737 + 0.446594i \(0.852637\pi\)
\(752\) 0 0
\(753\) 28.1469 1.02573
\(754\) 0 0
\(755\) 13.7908 0.501899
\(756\) 0 0
\(757\) 24.3434 0.884778 0.442389 0.896823i \(-0.354131\pi\)
0.442389 + 0.896823i \(0.354131\pi\)
\(758\) 0 0
\(759\) 13.3386 0.484162
\(760\) 0 0
\(761\) 8.90437 0.322783 0.161392 0.986890i \(-0.448402\pi\)
0.161392 + 0.986890i \(0.448402\pi\)
\(762\) 0 0
\(763\) −0.0941782 −0.00340948
\(764\) 0 0
\(765\) 25.8760 0.935550
\(766\) 0 0
\(767\) −4.97021 −0.179464
\(768\) 0 0
\(769\) −40.5901 −1.46372 −0.731859 0.681456i \(-0.761347\pi\)
−0.731859 + 0.681456i \(0.761347\pi\)
\(770\) 0 0
\(771\) 15.6025 0.561909
\(772\) 0 0
\(773\) −33.1517 −1.19238 −0.596192 0.802842i \(-0.703320\pi\)
−0.596192 + 0.802842i \(0.703320\pi\)
\(774\) 0 0
\(775\) −82.4502 −2.96170
\(776\) 0 0
\(777\) 0.473011 0.0169692
\(778\) 0 0
\(779\) −46.0900 −1.65135
\(780\) 0 0
\(781\) 10.7860 0.385954
\(782\) 0 0
\(783\) −27.0844 −0.967919
\(784\) 0 0
\(785\) 20.7610 0.740993
\(786\) 0 0
\(787\) 15.2501 0.543606 0.271803 0.962353i \(-0.412380\pi\)
0.271803 + 0.962353i \(0.412380\pi\)
\(788\) 0 0
\(789\) −26.9467 −0.959328
\(790\) 0 0
\(791\) 11.2140 0.398724
\(792\) 0 0
\(793\) 1.13919 0.0404540
\(794\) 0 0
\(795\) −28.1752 −0.999273
\(796\) 0 0
\(797\) 46.5243 1.64797 0.823987 0.566608i \(-0.191745\pi\)
0.823987 + 0.566608i \(0.191745\pi\)
\(798\) 0 0
\(799\) −65.1565 −2.30507
\(800\) 0 0
\(801\) 2.50135 0.0883808
\(802\) 0 0
\(803\) −1.44322 −0.0509302
\(804\) 0 0
\(805\) 35.2099 1.24098
\(806\) 0 0
\(807\) 12.7339 0.448256
\(808\) 0 0
\(809\) −39.5845 −1.39172 −0.695859 0.718178i \(-0.744976\pi\)
−0.695859 + 0.718178i \(0.744976\pi\)
\(810\) 0 0
\(811\) −7.99585 −0.280772 −0.140386 0.990097i \(-0.544834\pi\)
−0.140386 + 0.990097i \(0.544834\pi\)
\(812\) 0 0
\(813\) −38.5735 −1.35283
\(814\) 0 0
\(815\) −5.93561 −0.207915
\(816\) 0 0
\(817\) 10.8054 0.378032
\(818\) 0 0
\(819\) 0.860806 0.0300790
\(820\) 0 0
\(821\) 27.6669 0.965580 0.482790 0.875736i \(-0.339623\pi\)
0.482790 + 0.875736i \(0.339623\pi\)
\(822\) 0 0
\(823\) −8.49383 −0.296076 −0.148038 0.988982i \(-0.547296\pi\)
−0.148038 + 0.988982i \(0.547296\pi\)
\(824\) 0 0
\(825\) −14.4882 −0.504416
\(826\) 0 0
\(827\) −11.1648 −0.388239 −0.194120 0.980978i \(-0.562185\pi\)
−0.194120 + 0.980978i \(0.562185\pi\)
\(828\) 0 0
\(829\) 0.382979 0.0133014 0.00665070 0.999978i \(-0.497883\pi\)
0.00665070 + 0.999978i \(0.497883\pi\)
\(830\) 0 0
\(831\) −8.01793 −0.278139
\(832\) 0 0
\(833\) −7.78600 −0.269769
\(834\) 0 0
\(835\) −71.7431 −2.48277
\(836\) 0 0
\(837\) 47.0007 1.62458
\(838\) 0 0
\(839\) −4.02419 −0.138931 −0.0694653 0.997584i \(-0.522129\pi\)
−0.0694653 + 0.997584i \(0.522129\pi\)
\(840\) 0 0
\(841\) −5.99440 −0.206704
\(842\) 0 0
\(843\) 23.2507 0.800797
\(844\) 0 0
\(845\) 3.86081 0.132816
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −23.9709 −0.822679
\(850\) 0 0
\(851\) 2.94939 0.101104
\(852\) 0 0
\(853\) −54.1205 −1.85305 −0.926525 0.376233i \(-0.877219\pi\)
−0.926525 + 0.376233i \(0.877219\pi\)
\(854\) 0 0
\(855\) 13.9058 0.475569
\(856\) 0 0
\(857\) −0.225859 −0.00771519 −0.00385759 0.999993i \(-0.501228\pi\)
−0.00385759 + 0.999993i \(0.501228\pi\)
\(858\) 0 0
\(859\) −19.1586 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(860\) 0 0
\(861\) −16.1109 −0.549057
\(862\) 0 0
\(863\) −3.70079 −0.125976 −0.0629881 0.998014i \(-0.520063\pi\)
−0.0629881 + 0.998014i \(0.520063\pi\)
\(864\) 0 0
\(865\) 18.1544 0.617269
\(866\) 0 0
\(867\) 63.8012 2.16680
\(868\) 0 0
\(869\) 2.33382 0.0791693
\(870\) 0 0
\(871\) 1.18421 0.0401254
\(872\) 0 0
\(873\) 12.5180 0.423671
\(874\) 0 0
\(875\) −18.9404 −0.640303
\(876\) 0 0
\(877\) −42.2445 −1.42649 −0.713247 0.700913i \(-0.752776\pi\)
−0.713247 + 0.700913i \(0.752776\pi\)
\(878\) 0 0
\(879\) 21.2340 0.716206
\(880\) 0 0
\(881\) 3.46742 0.116820 0.0584101 0.998293i \(-0.481397\pi\)
0.0584101 + 0.998293i \(0.481397\pi\)
\(882\) 0 0
\(883\) −3.68286 −0.123938 −0.0619691 0.998078i \(-0.519738\pi\)
−0.0619691 + 0.998078i \(0.519738\pi\)
\(884\) 0 0
\(885\) −28.0658 −0.943423
\(886\) 0 0
\(887\) −40.7368 −1.36781 −0.683905 0.729571i \(-0.739720\pi\)
−0.683905 + 0.729571i \(0.739720\pi\)
\(888\) 0 0
\(889\) −9.13023 −0.306218
\(890\) 0 0
\(891\) 5.67660 0.190173
\(892\) 0 0
\(893\) −35.0152 −1.17174
\(894\) 0 0
\(895\) −33.7071 −1.12670
\(896\) 0 0
\(897\) −13.3386 −0.445364
\(898\) 0 0
\(899\) −39.9225 −1.33149
\(900\) 0 0
\(901\) 38.8489 1.29425
\(902\) 0 0
\(903\) 3.77704 0.125692
\(904\) 0 0
\(905\) −36.6323 −1.21770
\(906\) 0 0
\(907\) −46.9140 −1.55775 −0.778877 0.627177i \(-0.784210\pi\)
−0.778877 + 0.627177i \(0.784210\pi\)
\(908\) 0 0
\(909\) 4.76663 0.158099
\(910\) 0 0
\(911\) −29.4640 −0.976187 −0.488094 0.872791i \(-0.662308\pi\)
−0.488094 + 0.872791i \(0.662308\pi\)
\(912\) 0 0
\(913\) 6.98062 0.231025
\(914\) 0 0
\(915\) 6.43281 0.212662
\(916\) 0 0
\(917\) −10.4972 −0.346648
\(918\) 0 0
\(919\) 41.5284 1.36990 0.684948 0.728592i \(-0.259825\pi\)
0.684948 + 0.728592i \(0.259825\pi\)
\(920\) 0 0
\(921\) 26.1455 0.861522
\(922\) 0 0
\(923\) −10.7860 −0.355026
\(924\) 0 0
\(925\) −3.20359 −0.105333
\(926\) 0 0
\(927\) −4.55678 −0.149664
\(928\) 0 0
\(929\) −39.6281 −1.30016 −0.650078 0.759868i \(-0.725264\pi\)
−0.650078 + 0.759868i \(0.725264\pi\)
\(930\) 0 0
\(931\) −4.18421 −0.137132
\(932\) 0 0
\(933\) −19.2609 −0.630575
\(934\) 0 0
\(935\) 30.0602 0.983075
\(936\) 0 0
\(937\) 3.92665 0.128278 0.0641390 0.997941i \(-0.479570\pi\)
0.0641390 + 0.997941i \(0.479570\pi\)
\(938\) 0 0
\(939\) −34.3234 −1.12010
\(940\) 0 0
\(941\) 10.5180 0.342878 0.171439 0.985195i \(-0.445158\pi\)
0.171439 + 0.985195i \(0.445158\pi\)
\(942\) 0 0
\(943\) −100.457 −3.27133
\(944\) 0 0
\(945\) 21.8012 0.709194
\(946\) 0 0
\(947\) −41.8407 −1.35964 −0.679819 0.733380i \(-0.737942\pi\)
−0.679819 + 0.733380i \(0.737942\pi\)
\(948\) 0 0
\(949\) 1.44322 0.0468490
\(950\) 0 0
\(951\) −5.37738 −0.174374
\(952\) 0 0
\(953\) −17.5415 −0.568226 −0.284113 0.958791i \(-0.591699\pi\)
−0.284113 + 0.958791i \(0.591699\pi\)
\(954\) 0 0
\(955\) −53.1503 −1.71990
\(956\) 0 0
\(957\) −7.01523 −0.226770
\(958\) 0 0
\(959\) 19.6170 0.633467
\(960\) 0 0
\(961\) 38.2791 1.23481
\(962\) 0 0
\(963\) −12.9986 −0.418872
\(964\) 0 0
\(965\) 49.4231 1.59098
\(966\) 0 0
\(967\) 29.1857 0.938548 0.469274 0.883053i \(-0.344516\pi\)
0.469274 + 0.883053i \(0.344516\pi\)
\(968\) 0 0
\(969\) 47.6489 1.53070
\(970\) 0 0
\(971\) −3.57952 −0.114872 −0.0574361 0.998349i \(-0.518293\pi\)
−0.0574361 + 0.998349i \(0.518293\pi\)
\(972\) 0 0
\(973\) −8.64681 −0.277204
\(974\) 0 0
\(975\) 14.4882 0.463995
\(976\) 0 0
\(977\) 0.709750 0.0227069 0.0113535 0.999936i \(-0.496386\pi\)
0.0113535 + 0.999936i \(0.496386\pi\)
\(978\) 0 0
\(979\) 2.90582 0.0928705
\(980\) 0 0
\(981\) −0.0810691 −0.00258834
\(982\) 0 0
\(983\) −5.60739 −0.178848 −0.0894240 0.995994i \(-0.528503\pi\)
−0.0894240 + 0.995994i \(0.528503\pi\)
\(984\) 0 0
\(985\) −105.474 −3.36069
\(986\) 0 0
\(987\) −12.2396 −0.389592
\(988\) 0 0
\(989\) 23.5512 0.748884
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 0 0
\(993\) −11.4972 −0.364853
\(994\) 0 0
\(995\) −39.2389 −1.24396
\(996\) 0 0
\(997\) 57.1190 1.80898 0.904489 0.426497i \(-0.140252\pi\)
0.904489 + 0.426497i \(0.140252\pi\)
\(998\) 0 0
\(999\) 1.82620 0.0577785
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 \(a_p\))