Properties

Label 6040.2.a.l.1.1
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
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 1.1
Root \(0.390645\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.96251 q^{3} +1.00000 q^{5} -2.16922 q^{7} +0.851433 q^{9} +O(q^{10})\) \(q-1.96251 q^{3} +1.00000 q^{5} -2.16922 q^{7} +0.851433 q^{9} +3.01214 q^{11} -2.71469 q^{13} -1.96251 q^{15} +0.748145 q^{17} -4.29171 q^{19} +4.25712 q^{21} +1.71882 q^{23} +1.00000 q^{25} +4.21658 q^{27} -1.74832 q^{29} +4.16689 q^{31} -5.91134 q^{33} -2.16922 q^{35} +4.69387 q^{37} +5.32759 q^{39} -9.89262 q^{41} +8.49792 q^{43} +0.851433 q^{45} +12.8181 q^{47} -2.29447 q^{49} -1.46824 q^{51} -7.88590 q^{53} +3.01214 q^{55} +8.42251 q^{57} +6.20478 q^{59} -9.79583 q^{61} -1.84695 q^{63} -2.71469 q^{65} +2.54968 q^{67} -3.37319 q^{69} -6.64355 q^{71} -6.53691 q^{73} -1.96251 q^{75} -6.53400 q^{77} -5.44102 q^{79} -10.8294 q^{81} +4.01722 q^{83} +0.748145 q^{85} +3.43108 q^{87} +15.0573 q^{89} +5.88877 q^{91} -8.17755 q^{93} -4.29171 q^{95} -2.91029 q^{97} +2.56463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{5} - 2q^{7} - 3q^{9} + O(q^{10}) \) \( 9q + 9q^{5} - 2q^{7} - 3q^{9} - 6q^{11} - 9q^{13} - 2q^{17} - 10q^{19} - 9q^{21} - 6q^{23} + 9q^{25} + 12q^{27} - 6q^{29} + 9q^{31} - 11q^{33} - 2q^{35} - 12q^{37} - 3q^{39} - 20q^{41} + q^{43} - 3q^{45} + 22q^{47} - 29q^{49} + 2q^{51} - 35q^{53} - 6q^{55} - 20q^{57} + 14q^{59} - 22q^{61} - 12q^{63} - 9q^{65} + 4q^{67} + 5q^{69} - 22q^{71} - 34q^{73} - 5q^{77} + 8q^{79} - 31q^{81} - 3q^{83} - 2q^{85} - 5q^{89} - 7q^{91} - 21q^{93} - 10q^{95} - 33q^{97} - 15q^{99} + O(q^{100}) \)

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
\(3\) −1.96251 −1.13305 −0.566527 0.824043i \(-0.691713\pi\)
−0.566527 + 0.824043i \(0.691713\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.16922 −0.819890 −0.409945 0.912110i \(-0.634452\pi\)
−0.409945 + 0.912110i \(0.634452\pi\)
\(8\) 0 0
\(9\) 0.851433 0.283811
\(10\) 0 0
\(11\) 3.01214 0.908193 0.454097 0.890952i \(-0.349962\pi\)
0.454097 + 0.890952i \(0.349962\pi\)
\(12\) 0 0
\(13\) −2.71469 −0.752919 −0.376460 0.926433i \(-0.622859\pi\)
−0.376460 + 0.926433i \(0.622859\pi\)
\(14\) 0 0
\(15\) −1.96251 −0.506717
\(16\) 0 0
\(17\) 0.748145 0.181452 0.0907259 0.995876i \(-0.471081\pi\)
0.0907259 + 0.995876i \(0.471081\pi\)
\(18\) 0 0
\(19\) −4.29171 −0.984585 −0.492293 0.870430i \(-0.663841\pi\)
−0.492293 + 0.870430i \(0.663841\pi\)
\(20\) 0 0
\(21\) 4.25712 0.928979
\(22\) 0 0
\(23\) 1.71882 0.358398 0.179199 0.983813i \(-0.442649\pi\)
0.179199 + 0.983813i \(0.442649\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 4.21658 0.811481
\(28\) 0 0
\(29\) −1.74832 −0.324654 −0.162327 0.986737i \(-0.551900\pi\)
−0.162327 + 0.986737i \(0.551900\pi\)
\(30\) 0 0
\(31\) 4.16689 0.748396 0.374198 0.927349i \(-0.377918\pi\)
0.374198 + 0.927349i \(0.377918\pi\)
\(32\) 0 0
\(33\) −5.91134 −1.02903
\(34\) 0 0
\(35\) −2.16922 −0.366666
\(36\) 0 0
\(37\) 4.69387 0.771668 0.385834 0.922568i \(-0.373914\pi\)
0.385834 + 0.922568i \(0.373914\pi\)
\(38\) 0 0
\(39\) 5.32759 0.853098
\(40\) 0 0
\(41\) −9.89262 −1.54497 −0.772484 0.635034i \(-0.780986\pi\)
−0.772484 + 0.635034i \(0.780986\pi\)
\(42\) 0 0
\(43\) 8.49792 1.29592 0.647960 0.761674i \(-0.275622\pi\)
0.647960 + 0.761674i \(0.275622\pi\)
\(44\) 0 0
\(45\) 0.851433 0.126924
\(46\) 0 0
\(47\) 12.8181 1.86971 0.934856 0.355028i \(-0.115529\pi\)
0.934856 + 0.355028i \(0.115529\pi\)
\(48\) 0 0
\(49\) −2.29447 −0.327781
\(50\) 0 0
\(51\) −1.46824 −0.205595
\(52\) 0 0
\(53\) −7.88590 −1.08321 −0.541606 0.840633i \(-0.682183\pi\)
−0.541606 + 0.840633i \(0.682183\pi\)
\(54\) 0 0
\(55\) 3.01214 0.406156
\(56\) 0 0
\(57\) 8.42251 1.11559
\(58\) 0 0
\(59\) 6.20478 0.807793 0.403897 0.914805i \(-0.367656\pi\)
0.403897 + 0.914805i \(0.367656\pi\)
\(60\) 0 0
\(61\) −9.79583 −1.25423 −0.627114 0.778927i \(-0.715764\pi\)
−0.627114 + 0.778927i \(0.715764\pi\)
\(62\) 0 0
\(63\) −1.84695 −0.232694
\(64\) 0 0
\(65\) −2.71469 −0.336716
\(66\) 0 0
\(67\) 2.54968 0.311493 0.155746 0.987797i \(-0.450222\pi\)
0.155746 + 0.987797i \(0.450222\pi\)
\(68\) 0 0
\(69\) −3.37319 −0.406084
\(70\) 0 0
\(71\) −6.64355 −0.788445 −0.394222 0.919015i \(-0.628986\pi\)
−0.394222 + 0.919015i \(0.628986\pi\)
\(72\) 0 0
\(73\) −6.53691 −0.765088 −0.382544 0.923937i \(-0.624952\pi\)
−0.382544 + 0.923937i \(0.624952\pi\)
\(74\) 0 0
\(75\) −1.96251 −0.226611
\(76\) 0 0
\(77\) −6.53400 −0.744618
\(78\) 0 0
\(79\) −5.44102 −0.612163 −0.306081 0.952005i \(-0.599018\pi\)
−0.306081 + 0.952005i \(0.599018\pi\)
\(80\) 0 0
\(81\) −10.8294 −1.20326
\(82\) 0 0
\(83\) 4.01722 0.440947 0.220473 0.975393i \(-0.429240\pi\)
0.220473 + 0.975393i \(0.429240\pi\)
\(84\) 0 0
\(85\) 0.748145 0.0811477
\(86\) 0 0
\(87\) 3.43108 0.367850
\(88\) 0 0
\(89\) 15.0573 1.59607 0.798036 0.602610i \(-0.205873\pi\)
0.798036 + 0.602610i \(0.205873\pi\)
\(90\) 0 0
\(91\) 5.88877 0.617311
\(92\) 0 0
\(93\) −8.17755 −0.847973
\(94\) 0 0
\(95\) −4.29171 −0.440320
\(96\) 0 0
\(97\) −2.91029 −0.295495 −0.147748 0.989025i \(-0.547202\pi\)
−0.147748 + 0.989025i \(0.547202\pi\)
\(98\) 0 0
\(99\) 2.56463 0.257755
\(100\) 0 0
\(101\) 2.73382 0.272025 0.136013 0.990707i \(-0.456571\pi\)
0.136013 + 0.990707i \(0.456571\pi\)
\(102\) 0 0
\(103\) 3.62541 0.357222 0.178611 0.983920i \(-0.442840\pi\)
0.178611 + 0.983920i \(0.442840\pi\)
\(104\) 0 0
\(105\) 4.25712 0.415452
\(106\) 0 0
\(107\) −3.20902 −0.310227 −0.155114 0.987897i \(-0.549574\pi\)
−0.155114 + 0.987897i \(0.549574\pi\)
\(108\) 0 0
\(109\) −4.88474 −0.467873 −0.233936 0.972252i \(-0.575161\pi\)
−0.233936 + 0.972252i \(0.575161\pi\)
\(110\) 0 0
\(111\) −9.21176 −0.874341
\(112\) 0 0
\(113\) 8.30803 0.781554 0.390777 0.920485i \(-0.372206\pi\)
0.390777 + 0.920485i \(0.372206\pi\)
\(114\) 0 0
\(115\) 1.71882 0.160281
\(116\) 0 0
\(117\) −2.31138 −0.213687
\(118\) 0 0
\(119\) −1.62289 −0.148770
\(120\) 0 0
\(121\) −1.92703 −0.175185
\(122\) 0 0
\(123\) 19.4143 1.75053
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.07348 0.183992 0.0919958 0.995759i \(-0.470675\pi\)
0.0919958 + 0.995759i \(0.470675\pi\)
\(128\) 0 0
\(129\) −16.6772 −1.46835
\(130\) 0 0
\(131\) −13.3055 −1.16251 −0.581253 0.813723i \(-0.697437\pi\)
−0.581253 + 0.813723i \(0.697437\pi\)
\(132\) 0 0
\(133\) 9.30968 0.807251
\(134\) 0 0
\(135\) 4.21658 0.362905
\(136\) 0 0
\(137\) 18.3490 1.56766 0.783832 0.620973i \(-0.213262\pi\)
0.783832 + 0.620973i \(0.213262\pi\)
\(138\) 0 0
\(139\) −0.0634977 −0.00538581 −0.00269290 0.999996i \(-0.500857\pi\)
−0.00269290 + 0.999996i \(0.500857\pi\)
\(140\) 0 0
\(141\) −25.1556 −2.11848
\(142\) 0 0
\(143\) −8.17701 −0.683796
\(144\) 0 0
\(145\) −1.74832 −0.145190
\(146\) 0 0
\(147\) 4.50291 0.371393
\(148\) 0 0
\(149\) 11.4828 0.940711 0.470356 0.882477i \(-0.344126\pi\)
0.470356 + 0.882477i \(0.344126\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) 0.636995 0.0514980
\(154\) 0 0
\(155\) 4.16689 0.334693
\(156\) 0 0
\(157\) 2.26410 0.180695 0.0903475 0.995910i \(-0.471202\pi\)
0.0903475 + 0.995910i \(0.471202\pi\)
\(158\) 0 0
\(159\) 15.4761 1.22734
\(160\) 0 0
\(161\) −3.72850 −0.293847
\(162\) 0 0
\(163\) −18.5884 −1.45595 −0.727976 0.685602i \(-0.759539\pi\)
−0.727976 + 0.685602i \(0.759539\pi\)
\(164\) 0 0
\(165\) −5.91134 −0.460197
\(166\) 0 0
\(167\) 1.75344 0.135685 0.0678426 0.997696i \(-0.478388\pi\)
0.0678426 + 0.997696i \(0.478388\pi\)
\(168\) 0 0
\(169\) −5.63047 −0.433113
\(170\) 0 0
\(171\) −3.65410 −0.279436
\(172\) 0 0
\(173\) 17.5676 1.33564 0.667819 0.744324i \(-0.267228\pi\)
0.667819 + 0.744324i \(0.267228\pi\)
\(174\) 0 0
\(175\) −2.16922 −0.163978
\(176\) 0 0
\(177\) −12.1769 −0.915273
\(178\) 0 0
\(179\) −16.1306 −1.20566 −0.602829 0.797870i \(-0.705960\pi\)
−0.602829 + 0.797870i \(0.705960\pi\)
\(180\) 0 0
\(181\) −16.9945 −1.26319 −0.631596 0.775298i \(-0.717600\pi\)
−0.631596 + 0.775298i \(0.717600\pi\)
\(182\) 0 0
\(183\) 19.2244 1.42111
\(184\) 0 0
\(185\) 4.69387 0.345100
\(186\) 0 0
\(187\) 2.25352 0.164793
\(188\) 0 0
\(189\) −9.14670 −0.665325
\(190\) 0 0
\(191\) −8.52383 −0.616763 −0.308381 0.951263i \(-0.599787\pi\)
−0.308381 + 0.951263i \(0.599787\pi\)
\(192\) 0 0
\(193\) −21.7917 −1.56860 −0.784300 0.620382i \(-0.786977\pi\)
−0.784300 + 0.620382i \(0.786977\pi\)
\(194\) 0 0
\(195\) 5.32759 0.381517
\(196\) 0 0
\(197\) 11.6273 0.828408 0.414204 0.910184i \(-0.364060\pi\)
0.414204 + 0.910184i \(0.364060\pi\)
\(198\) 0 0
\(199\) −20.9477 −1.48495 −0.742473 0.669876i \(-0.766347\pi\)
−0.742473 + 0.669876i \(0.766347\pi\)
\(200\) 0 0
\(201\) −5.00376 −0.352938
\(202\) 0 0
\(203\) 3.79249 0.266180
\(204\) 0 0
\(205\) −9.89262 −0.690931
\(206\) 0 0
\(207\) 1.46346 0.101717
\(208\) 0 0
\(209\) −12.9272 −0.894194
\(210\) 0 0
\(211\) −9.21057 −0.634082 −0.317041 0.948412i \(-0.602689\pi\)
−0.317041 + 0.948412i \(0.602689\pi\)
\(212\) 0 0
\(213\) 13.0380 0.893350
\(214\) 0 0
\(215\) 8.49792 0.579553
\(216\) 0 0
\(217\) −9.03892 −0.613602
\(218\) 0 0
\(219\) 12.8287 0.866886
\(220\) 0 0
\(221\) −2.03098 −0.136619
\(222\) 0 0
\(223\) 13.4874 0.903185 0.451592 0.892224i \(-0.350856\pi\)
0.451592 + 0.892224i \(0.350856\pi\)
\(224\) 0 0
\(225\) 0.851433 0.0567622
\(226\) 0 0
\(227\) 10.3020 0.683765 0.341882 0.939743i \(-0.388936\pi\)
0.341882 + 0.939743i \(0.388936\pi\)
\(228\) 0 0
\(229\) −14.3497 −0.948258 −0.474129 0.880455i \(-0.657237\pi\)
−0.474129 + 0.880455i \(0.657237\pi\)
\(230\) 0 0
\(231\) 12.8230 0.843693
\(232\) 0 0
\(233\) −20.7413 −1.35881 −0.679404 0.733764i \(-0.737762\pi\)
−0.679404 + 0.733764i \(0.737762\pi\)
\(234\) 0 0
\(235\) 12.8181 0.836160
\(236\) 0 0
\(237\) 10.6780 0.693613
\(238\) 0 0
\(239\) 6.25664 0.404708 0.202354 0.979312i \(-0.435141\pi\)
0.202354 + 0.979312i \(0.435141\pi\)
\(240\) 0 0
\(241\) 20.1542 1.29825 0.649125 0.760682i \(-0.275135\pi\)
0.649125 + 0.760682i \(0.275135\pi\)
\(242\) 0 0
\(243\) 8.60296 0.551880
\(244\) 0 0
\(245\) −2.29447 −0.146588
\(246\) 0 0
\(247\) 11.6506 0.741313
\(248\) 0 0
\(249\) −7.88381 −0.499616
\(250\) 0 0
\(251\) 4.67467 0.295063 0.147531 0.989057i \(-0.452867\pi\)
0.147531 + 0.989057i \(0.452867\pi\)
\(252\) 0 0
\(253\) 5.17731 0.325495
\(254\) 0 0
\(255\) −1.46824 −0.0919447
\(256\) 0 0
\(257\) −4.57646 −0.285472 −0.142736 0.989761i \(-0.545590\pi\)
−0.142736 + 0.989761i \(0.545590\pi\)
\(258\) 0 0
\(259\) −10.1821 −0.632683
\(260\) 0 0
\(261\) −1.48857 −0.0921404
\(262\) 0 0
\(263\) −16.0834 −0.991745 −0.495873 0.868395i \(-0.665152\pi\)
−0.495873 + 0.868395i \(0.665152\pi\)
\(264\) 0 0
\(265\) −7.88590 −0.484427
\(266\) 0 0
\(267\) −29.5501 −1.80843
\(268\) 0 0
\(269\) −1.32579 −0.0808347 −0.0404174 0.999183i \(-0.512869\pi\)
−0.0404174 + 0.999183i \(0.512869\pi\)
\(270\) 0 0
\(271\) 6.50832 0.395353 0.197676 0.980267i \(-0.436661\pi\)
0.197676 + 0.980267i \(0.436661\pi\)
\(272\) 0 0
\(273\) −11.5567 −0.699446
\(274\) 0 0
\(275\) 3.01214 0.181639
\(276\) 0 0
\(277\) −14.4607 −0.868859 −0.434430 0.900706i \(-0.643050\pi\)
−0.434430 + 0.900706i \(0.643050\pi\)
\(278\) 0 0
\(279\) 3.54783 0.212403
\(280\) 0 0
\(281\) −6.05087 −0.360964 −0.180482 0.983578i \(-0.557766\pi\)
−0.180482 + 0.983578i \(0.557766\pi\)
\(282\) 0 0
\(283\) −20.6207 −1.22577 −0.612887 0.790170i \(-0.709992\pi\)
−0.612887 + 0.790170i \(0.709992\pi\)
\(284\) 0 0
\(285\) 8.42251 0.498906
\(286\) 0 0
\(287\) 21.4593 1.26670
\(288\) 0 0
\(289\) −16.4403 −0.967075
\(290\) 0 0
\(291\) 5.71147 0.334812
\(292\) 0 0
\(293\) 16.7712 0.979786 0.489893 0.871783i \(-0.337036\pi\)
0.489893 + 0.871783i \(0.337036\pi\)
\(294\) 0 0
\(295\) 6.20478 0.361256
\(296\) 0 0
\(297\) 12.7009 0.736981
\(298\) 0 0
\(299\) −4.66605 −0.269845
\(300\) 0 0
\(301\) −18.4339 −1.06251
\(302\) 0 0
\(303\) −5.36514 −0.308219
\(304\) 0 0
\(305\) −9.79583 −0.560908
\(306\) 0 0
\(307\) 10.7421 0.613081 0.306541 0.951858i \(-0.400828\pi\)
0.306541 + 0.951858i \(0.400828\pi\)
\(308\) 0 0
\(309\) −7.11489 −0.404752
\(310\) 0 0
\(311\) 2.82492 0.160186 0.0800932 0.996787i \(-0.474478\pi\)
0.0800932 + 0.996787i \(0.474478\pi\)
\(312\) 0 0
\(313\) −28.7090 −1.62273 −0.811365 0.584540i \(-0.801275\pi\)
−0.811365 + 0.584540i \(0.801275\pi\)
\(314\) 0 0
\(315\) −1.84695 −0.104064
\(316\) 0 0
\(317\) −9.72265 −0.546078 −0.273039 0.962003i \(-0.588029\pi\)
−0.273039 + 0.962003i \(0.588029\pi\)
\(318\) 0 0
\(319\) −5.26616 −0.294849
\(320\) 0 0
\(321\) 6.29772 0.351504
\(322\) 0 0
\(323\) −3.21082 −0.178655
\(324\) 0 0
\(325\) −2.71469 −0.150584
\(326\) 0 0
\(327\) 9.58633 0.530125
\(328\) 0 0
\(329\) −27.8053 −1.53296
\(330\) 0 0
\(331\) 0.830070 0.0456248 0.0228124 0.999740i \(-0.492738\pi\)
0.0228124 + 0.999740i \(0.492738\pi\)
\(332\) 0 0
\(333\) 3.99652 0.219008
\(334\) 0 0
\(335\) 2.54968 0.139304
\(336\) 0 0
\(337\) −26.9322 −1.46709 −0.733544 0.679642i \(-0.762135\pi\)
−0.733544 + 0.679642i \(0.762135\pi\)
\(338\) 0 0
\(339\) −16.3046 −0.885542
\(340\) 0 0
\(341\) 12.5512 0.679688
\(342\) 0 0
\(343\) 20.1618 1.08863
\(344\) 0 0
\(345\) −3.37319 −0.181606
\(346\) 0 0
\(347\) −26.5136 −1.42332 −0.711662 0.702522i \(-0.752057\pi\)
−0.711662 + 0.702522i \(0.752057\pi\)
\(348\) 0 0
\(349\) −16.3698 −0.876254 −0.438127 0.898913i \(-0.644358\pi\)
−0.438127 + 0.898913i \(0.644358\pi\)
\(350\) 0 0
\(351\) −11.4467 −0.610979
\(352\) 0 0
\(353\) −8.02380 −0.427064 −0.213532 0.976936i \(-0.568497\pi\)
−0.213532 + 0.976936i \(0.568497\pi\)
\(354\) 0 0
\(355\) −6.64355 −0.352603
\(356\) 0 0
\(357\) 3.18494 0.168565
\(358\) 0 0
\(359\) 4.18033 0.220629 0.110315 0.993897i \(-0.464814\pi\)
0.110315 + 0.993897i \(0.464814\pi\)
\(360\) 0 0
\(361\) −0.581244 −0.0305918
\(362\) 0 0
\(363\) 3.78181 0.198494
\(364\) 0 0
\(365\) −6.53691 −0.342158
\(366\) 0 0
\(367\) −20.8757 −1.08970 −0.544851 0.838533i \(-0.683414\pi\)
−0.544851 + 0.838533i \(0.683414\pi\)
\(368\) 0 0
\(369\) −8.42290 −0.438479
\(370\) 0 0
\(371\) 17.1063 0.888114
\(372\) 0 0
\(373\) −31.6271 −1.63759 −0.818796 0.574085i \(-0.805358\pi\)
−0.818796 + 0.574085i \(0.805358\pi\)
\(374\) 0 0
\(375\) −1.96251 −0.101343
\(376\) 0 0
\(377\) 4.74613 0.244438
\(378\) 0 0
\(379\) −7.38975 −0.379586 −0.189793 0.981824i \(-0.560782\pi\)
−0.189793 + 0.981824i \(0.560782\pi\)
\(380\) 0 0
\(381\) −4.06922 −0.208472
\(382\) 0 0
\(383\) −30.4978 −1.55836 −0.779182 0.626798i \(-0.784365\pi\)
−0.779182 + 0.626798i \(0.784365\pi\)
\(384\) 0 0
\(385\) −6.53400 −0.333003
\(386\) 0 0
\(387\) 7.23541 0.367796
\(388\) 0 0
\(389\) 27.2328 1.38076 0.690379 0.723448i \(-0.257444\pi\)
0.690379 + 0.723448i \(0.257444\pi\)
\(390\) 0 0
\(391\) 1.28592 0.0650320
\(392\) 0 0
\(393\) 26.1121 1.31718
\(394\) 0 0
\(395\) −5.44102 −0.273768
\(396\) 0 0
\(397\) 13.2555 0.665273 0.332637 0.943055i \(-0.392062\pi\)
0.332637 + 0.943055i \(0.392062\pi\)
\(398\) 0 0
\(399\) −18.2703 −0.914659
\(400\) 0 0
\(401\) −20.4575 −1.02160 −0.510800 0.859699i \(-0.670651\pi\)
−0.510800 + 0.859699i \(0.670651\pi\)
\(402\) 0 0
\(403\) −11.3118 −0.563481
\(404\) 0 0
\(405\) −10.8294 −0.538115
\(406\) 0 0
\(407\) 14.1386 0.700824
\(408\) 0 0
\(409\) 21.9027 1.08302 0.541509 0.840695i \(-0.317853\pi\)
0.541509 + 0.840695i \(0.317853\pi\)
\(410\) 0 0
\(411\) −36.0101 −1.77625
\(412\) 0 0
\(413\) −13.4596 −0.662301
\(414\) 0 0
\(415\) 4.01722 0.197197
\(416\) 0 0
\(417\) 0.124615 0.00610241
\(418\) 0 0
\(419\) 33.9905 1.66055 0.830273 0.557357i \(-0.188185\pi\)
0.830273 + 0.557357i \(0.188185\pi\)
\(420\) 0 0
\(421\) 4.66631 0.227422 0.113711 0.993514i \(-0.463726\pi\)
0.113711 + 0.993514i \(0.463726\pi\)
\(422\) 0 0
\(423\) 10.9137 0.530645
\(424\) 0 0
\(425\) 0.748145 0.0362904
\(426\) 0 0
\(427\) 21.2494 1.02833
\(428\) 0 0
\(429\) 16.0474 0.774778
\(430\) 0 0
\(431\) −11.8922 −0.572829 −0.286414 0.958106i \(-0.592463\pi\)
−0.286414 + 0.958106i \(0.592463\pi\)
\(432\) 0 0
\(433\) 2.07028 0.0994911 0.0497455 0.998762i \(-0.484159\pi\)
0.0497455 + 0.998762i \(0.484159\pi\)
\(434\) 0 0
\(435\) 3.43108 0.164508
\(436\) 0 0
\(437\) −7.37666 −0.352874
\(438\) 0 0
\(439\) −19.5142 −0.931361 −0.465680 0.884953i \(-0.654190\pi\)
−0.465680 + 0.884953i \(0.654190\pi\)
\(440\) 0 0
\(441\) −1.95358 −0.0930278
\(442\) 0 0
\(443\) 26.5032 1.25920 0.629601 0.776918i \(-0.283218\pi\)
0.629601 + 0.776918i \(0.283218\pi\)
\(444\) 0 0
\(445\) 15.0573 0.713785
\(446\) 0 0
\(447\) −22.5352 −1.06588
\(448\) 0 0
\(449\) −37.4184 −1.76588 −0.882941 0.469484i \(-0.844440\pi\)
−0.882941 + 0.469484i \(0.844440\pi\)
\(450\) 0 0
\(451\) −29.7979 −1.40313
\(452\) 0 0
\(453\) 1.96251 0.0922066
\(454\) 0 0
\(455\) 5.88877 0.276070
\(456\) 0 0
\(457\) −5.56466 −0.260304 −0.130152 0.991494i \(-0.541547\pi\)
−0.130152 + 0.991494i \(0.541547\pi\)
\(458\) 0 0
\(459\) 3.15461 0.147245
\(460\) 0 0
\(461\) 0.103086 0.00480120 0.00240060 0.999997i \(-0.499236\pi\)
0.00240060 + 0.999997i \(0.499236\pi\)
\(462\) 0 0
\(463\) −25.5155 −1.18581 −0.592904 0.805273i \(-0.702019\pi\)
−0.592904 + 0.805273i \(0.702019\pi\)
\(464\) 0 0
\(465\) −8.17755 −0.379225
\(466\) 0 0
\(467\) 4.88782 0.226181 0.113091 0.993585i \(-0.463925\pi\)
0.113091 + 0.993585i \(0.463925\pi\)
\(468\) 0 0
\(469\) −5.53083 −0.255390
\(470\) 0 0
\(471\) −4.44331 −0.204737
\(472\) 0 0
\(473\) 25.5969 1.17695
\(474\) 0 0
\(475\) −4.29171 −0.196917
\(476\) 0 0
\(477\) −6.71432 −0.307427
\(478\) 0 0
\(479\) 7.80514 0.356626 0.178313 0.983974i \(-0.442936\pi\)
0.178313 + 0.983974i \(0.442936\pi\)
\(480\) 0 0
\(481\) −12.7424 −0.581004
\(482\) 0 0
\(483\) 7.31721 0.332944
\(484\) 0 0
\(485\) −2.91029 −0.132150
\(486\) 0 0
\(487\) −11.3311 −0.513462 −0.256731 0.966483i \(-0.582645\pi\)
−0.256731 + 0.966483i \(0.582645\pi\)
\(488\) 0 0
\(489\) 36.4798 1.64967
\(490\) 0 0
\(491\) −0.687619 −0.0310318 −0.0155159 0.999880i \(-0.504939\pi\)
−0.0155159 + 0.999880i \(0.504939\pi\)
\(492\) 0 0
\(493\) −1.30799 −0.0589091
\(494\) 0 0
\(495\) 2.56463 0.115272
\(496\) 0 0
\(497\) 14.4114 0.646438
\(498\) 0 0
\(499\) 18.6479 0.834793 0.417396 0.908725i \(-0.362943\pi\)
0.417396 + 0.908725i \(0.362943\pi\)
\(500\) 0 0
\(501\) −3.44114 −0.153739
\(502\) 0 0
\(503\) −24.8823 −1.10945 −0.554724 0.832035i \(-0.687176\pi\)
−0.554724 + 0.832035i \(0.687176\pi\)
\(504\) 0 0
\(505\) 2.73382 0.121653
\(506\) 0 0
\(507\) 11.0498 0.490740
\(508\) 0 0
\(509\) −18.0862 −0.801658 −0.400829 0.916153i \(-0.631278\pi\)
−0.400829 + 0.916153i \(0.631278\pi\)
\(510\) 0 0
\(511\) 14.1800 0.627288
\(512\) 0 0
\(513\) −18.0963 −0.798972
\(514\) 0 0
\(515\) 3.62541 0.159755
\(516\) 0 0
\(517\) 38.6099 1.69806
\(518\) 0 0
\(519\) −34.4765 −1.51335
\(520\) 0 0
\(521\) −3.52627 −0.154489 −0.0772444 0.997012i \(-0.524612\pi\)
−0.0772444 + 0.997012i \(0.524612\pi\)
\(522\) 0 0
\(523\) −1.83625 −0.0802934 −0.0401467 0.999194i \(-0.512783\pi\)
−0.0401467 + 0.999194i \(0.512783\pi\)
\(524\) 0 0
\(525\) 4.25712 0.185796
\(526\) 0 0
\(527\) 3.11744 0.135798
\(528\) 0 0
\(529\) −20.0457 −0.871551
\(530\) 0 0
\(531\) 5.28295 0.229261
\(532\) 0 0
\(533\) 26.8554 1.16324
\(534\) 0 0
\(535\) −3.20902 −0.138738
\(536\) 0 0
\(537\) 31.6564 1.36608
\(538\) 0 0
\(539\) −6.91125 −0.297688
\(540\) 0 0
\(541\) 5.43440 0.233643 0.116822 0.993153i \(-0.462729\pi\)
0.116822 + 0.993153i \(0.462729\pi\)
\(542\) 0 0
\(543\) 33.3518 1.43126
\(544\) 0 0
\(545\) −4.88474 −0.209239
\(546\) 0 0
\(547\) −13.7390 −0.587436 −0.293718 0.955892i \(-0.594893\pi\)
−0.293718 + 0.955892i \(0.594893\pi\)
\(548\) 0 0
\(549\) −8.34050 −0.355964
\(550\) 0 0
\(551\) 7.50326 0.319650
\(552\) 0 0
\(553\) 11.8028 0.501906
\(554\) 0 0
\(555\) −9.21176 −0.391017
\(556\) 0 0
\(557\) −30.8848 −1.30863 −0.654315 0.756222i \(-0.727043\pi\)
−0.654315 + 0.756222i \(0.727043\pi\)
\(558\) 0 0
\(559\) −23.0692 −0.975723
\(560\) 0 0
\(561\) −4.42254 −0.186720
\(562\) 0 0
\(563\) −34.0179 −1.43368 −0.716842 0.697235i \(-0.754413\pi\)
−0.716842 + 0.697235i \(0.754413\pi\)
\(564\) 0 0
\(565\) 8.30803 0.349521
\(566\) 0 0
\(567\) 23.4913 0.986542
\(568\) 0 0
\(569\) −16.6839 −0.699425 −0.349712 0.936857i \(-0.613721\pi\)
−0.349712 + 0.936857i \(0.613721\pi\)
\(570\) 0 0
\(571\) 13.6448 0.571016 0.285508 0.958376i \(-0.407838\pi\)
0.285508 + 0.958376i \(0.407838\pi\)
\(572\) 0 0
\(573\) 16.7281 0.698825
\(574\) 0 0
\(575\) 1.71882 0.0716796
\(576\) 0 0
\(577\) 34.1896 1.42333 0.711666 0.702518i \(-0.247941\pi\)
0.711666 + 0.702518i \(0.247941\pi\)
\(578\) 0 0
\(579\) 42.7663 1.77731
\(580\) 0 0
\(581\) −8.71424 −0.361528
\(582\) 0 0
\(583\) −23.7534 −0.983766
\(584\) 0 0
\(585\) −2.31138 −0.0955636
\(586\) 0 0
\(587\) 9.60515 0.396447 0.198223 0.980157i \(-0.436483\pi\)
0.198223 + 0.980157i \(0.436483\pi\)
\(588\) 0 0
\(589\) −17.8831 −0.736859
\(590\) 0 0
\(591\) −22.8186 −0.938631
\(592\) 0 0
\(593\) 11.4144 0.468733 0.234366 0.972148i \(-0.424698\pi\)
0.234366 + 0.972148i \(0.424698\pi\)
\(594\) 0 0
\(595\) −1.62289 −0.0665322
\(596\) 0 0
\(597\) 41.1101 1.68252
\(598\) 0 0
\(599\) 23.1359 0.945307 0.472653 0.881248i \(-0.343296\pi\)
0.472653 + 0.881248i \(0.343296\pi\)
\(600\) 0 0
\(601\) −31.2599 −1.27512 −0.637559 0.770402i \(-0.720056\pi\)
−0.637559 + 0.770402i \(0.720056\pi\)
\(602\) 0 0
\(603\) 2.17088 0.0884051
\(604\) 0 0
\(605\) −1.92703 −0.0783450
\(606\) 0 0
\(607\) 26.2273 1.06453 0.532267 0.846577i \(-0.321340\pi\)
0.532267 + 0.846577i \(0.321340\pi\)
\(608\) 0 0
\(609\) −7.44278 −0.301597
\(610\) 0 0
\(611\) −34.7971 −1.40774
\(612\) 0 0
\(613\) 24.3200 0.982275 0.491138 0.871082i \(-0.336581\pi\)
0.491138 + 0.871082i \(0.336581\pi\)
\(614\) 0 0
\(615\) 19.4143 0.782862
\(616\) 0 0
\(617\) 6.43402 0.259024 0.129512 0.991578i \(-0.458659\pi\)
0.129512 + 0.991578i \(0.458659\pi\)
\(618\) 0 0
\(619\) 42.7419 1.71794 0.858971 0.512024i \(-0.171104\pi\)
0.858971 + 0.512024i \(0.171104\pi\)
\(620\) 0 0
\(621\) 7.24753 0.290833
\(622\) 0 0
\(623\) −32.6627 −1.30860
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 25.3697 1.01317
\(628\) 0 0
\(629\) 3.51170 0.140021
\(630\) 0 0
\(631\) 23.1177 0.920303 0.460151 0.887840i \(-0.347795\pi\)
0.460151 + 0.887840i \(0.347795\pi\)
\(632\) 0 0
\(633\) 18.0758 0.718449
\(634\) 0 0
\(635\) 2.07348 0.0822836
\(636\) 0 0
\(637\) 6.22876 0.246793
\(638\) 0 0
\(639\) −5.65654 −0.223769
\(640\) 0 0
\(641\) 4.45325 0.175893 0.0879464 0.996125i \(-0.471970\pi\)
0.0879464 + 0.996125i \(0.471970\pi\)
\(642\) 0 0
\(643\) 0.00677368 0.000267128 0 0.000133564 1.00000i \(-0.499957\pi\)
0.000133564 1.00000i \(0.499957\pi\)
\(644\) 0 0
\(645\) −16.6772 −0.656665
\(646\) 0 0
\(647\) −45.8824 −1.80383 −0.901913 0.431919i \(-0.857837\pi\)
−0.901913 + 0.431919i \(0.857837\pi\)
\(648\) 0 0
\(649\) 18.6896 0.733632
\(650\) 0 0
\(651\) 17.7389 0.695244
\(652\) 0 0
\(653\) −43.3779 −1.69751 −0.848754 0.528788i \(-0.822647\pi\)
−0.848754 + 0.528788i \(0.822647\pi\)
\(654\) 0 0
\(655\) −13.3055 −0.519889
\(656\) 0 0
\(657\) −5.56574 −0.217140
\(658\) 0 0
\(659\) −30.8265 −1.20083 −0.600414 0.799689i \(-0.704998\pi\)
−0.600414 + 0.799689i \(0.704998\pi\)
\(660\) 0 0
\(661\) −3.59334 −0.139765 −0.0698824 0.997555i \(-0.522262\pi\)
−0.0698824 + 0.997555i \(0.522262\pi\)
\(662\) 0 0
\(663\) 3.98581 0.154796
\(664\) 0 0
\(665\) 9.30968 0.361014
\(666\) 0 0
\(667\) −3.00503 −0.116355
\(668\) 0 0
\(669\) −26.4692 −1.02336
\(670\) 0 0
\(671\) −29.5064 −1.13908
\(672\) 0 0
\(673\) 17.8727 0.688942 0.344471 0.938797i \(-0.388058\pi\)
0.344471 + 0.938797i \(0.388058\pi\)
\(674\) 0 0
\(675\) 4.21658 0.162296
\(676\) 0 0
\(677\) −50.1714 −1.92824 −0.964122 0.265460i \(-0.914476\pi\)
−0.964122 + 0.265460i \(0.914476\pi\)
\(678\) 0 0
\(679\) 6.31308 0.242274
\(680\) 0 0
\(681\) −20.2177 −0.774742
\(682\) 0 0
\(683\) −43.2419 −1.65461 −0.827303 0.561756i \(-0.810126\pi\)
−0.827303 + 0.561756i \(0.810126\pi\)
\(684\) 0 0
\(685\) 18.3490 0.701081
\(686\) 0 0
\(687\) 28.1615 1.07443
\(688\) 0 0
\(689\) 21.4078 0.815571
\(690\) 0 0
\(691\) −11.3083 −0.430188 −0.215094 0.976593i \(-0.569006\pi\)
−0.215094 + 0.976593i \(0.569006\pi\)
\(692\) 0 0
\(693\) −5.56326 −0.211331
\(694\) 0 0
\(695\) −0.0634977 −0.00240861
\(696\) 0 0
\(697\) −7.40112 −0.280337
\(698\) 0 0
\(699\) 40.7050 1.53960
\(700\) 0 0
\(701\) 16.5642 0.625620 0.312810 0.949816i \(-0.398730\pi\)
0.312810 + 0.949816i \(0.398730\pi\)
\(702\) 0 0
\(703\) −20.1447 −0.759773
\(704\) 0 0
\(705\) −25.1556 −0.947415
\(706\) 0 0
\(707\) −5.93027 −0.223031
\(708\) 0 0
\(709\) 46.7990 1.75757 0.878786 0.477216i \(-0.158354\pi\)
0.878786 + 0.477216i \(0.158354\pi\)
\(710\) 0 0
\(711\) −4.63267 −0.173739
\(712\) 0 0
\(713\) 7.16212 0.268224
\(714\) 0 0
\(715\) −8.17701 −0.305803
\(716\) 0 0
\(717\) −12.2787 −0.458556
\(718\) 0 0
\(719\) −31.6279 −1.17952 −0.589760 0.807578i \(-0.700778\pi\)
−0.589760 + 0.807578i \(0.700778\pi\)
\(720\) 0 0
\(721\) −7.86432 −0.292883
\(722\) 0 0
\(723\) −39.5528 −1.47099
\(724\) 0 0
\(725\) −1.74832 −0.0649308
\(726\) 0 0
\(727\) −16.5897 −0.615277 −0.307639 0.951503i \(-0.599539\pi\)
−0.307639 + 0.951503i \(0.599539\pi\)
\(728\) 0 0
\(729\) 15.6047 0.577952
\(730\) 0 0
\(731\) 6.35768 0.235147
\(732\) 0 0
\(733\) −29.1792 −1.07776 −0.538880 0.842383i \(-0.681152\pi\)
−0.538880 + 0.842383i \(0.681152\pi\)
\(734\) 0 0
\(735\) 4.50291 0.166092
\(736\) 0 0
\(737\) 7.67998 0.282896
\(738\) 0 0
\(739\) −0.503787 −0.0185321 −0.00926604 0.999957i \(-0.502950\pi\)
−0.00926604 + 0.999957i \(0.502950\pi\)
\(740\) 0 0
\(741\) −22.8645 −0.839948
\(742\) 0 0
\(743\) −26.4912 −0.971868 −0.485934 0.873995i \(-0.661521\pi\)
−0.485934 + 0.873995i \(0.661521\pi\)
\(744\) 0 0
\(745\) 11.4828 0.420699
\(746\) 0 0
\(747\) 3.42039 0.125146
\(748\) 0 0
\(749\) 6.96108 0.254352
\(750\) 0 0
\(751\) 48.4483 1.76790 0.883952 0.467577i \(-0.154873\pi\)
0.883952 + 0.467577i \(0.154873\pi\)
\(752\) 0 0
\(753\) −9.17408 −0.334322
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) 6.76709 0.245954 0.122977 0.992410i \(-0.460756\pi\)
0.122977 + 0.992410i \(0.460756\pi\)
\(758\) 0 0
\(759\) −10.1605 −0.368803
\(760\) 0 0
\(761\) 8.93154 0.323768 0.161884 0.986810i \(-0.448243\pi\)
0.161884 + 0.986810i \(0.448243\pi\)
\(762\) 0 0
\(763\) 10.5961 0.383604
\(764\) 0 0
\(765\) 0.636995 0.0230306
\(766\) 0 0
\(767\) −16.8440 −0.608203
\(768\) 0 0
\(769\) −15.1159 −0.545095 −0.272548 0.962142i \(-0.587866\pi\)
−0.272548 + 0.962142i \(0.587866\pi\)
\(770\) 0 0
\(771\) 8.98134 0.323455
\(772\) 0 0
\(773\) 0.404826 0.0145606 0.00728028 0.999973i \(-0.497683\pi\)
0.00728028 + 0.999973i \(0.497683\pi\)
\(774\) 0 0
\(775\) 4.16689 0.149679
\(776\) 0 0
\(777\) 19.9824 0.716863
\(778\) 0 0
\(779\) 42.4562 1.52115
\(780\) 0 0
\(781\) −20.0113 −0.716060
\(782\) 0 0
\(783\) −7.37191 −0.263450
\(784\) 0 0
\(785\) 2.26410 0.0808092
\(786\) 0 0
\(787\) 42.2257 1.50519 0.752593 0.658486i \(-0.228803\pi\)
0.752593 + 0.658486i \(0.228803\pi\)
\(788\) 0 0
\(789\) 31.5638 1.12370
\(790\) 0 0
\(791\) −18.0220 −0.640788
\(792\) 0 0
\(793\) 26.5926 0.944332
\(794\) 0 0
\(795\) 15.4761 0.548882
\(796\) 0 0
\(797\) −0.488145 −0.0172910 −0.00864549 0.999963i \(-0.502752\pi\)
−0.00864549 + 0.999963i \(0.502752\pi\)
\(798\) 0 0
\(799\) 9.58980 0.339263
\(800\) 0 0
\(801\) 12.8203 0.452983
\(802\) 0 0
\(803\) −19.6901 −0.694848
\(804\) 0 0
\(805\) −3.72850 −0.131412
\(806\) 0 0
\(807\) 2.60187 0.0915901
\(808\) 0 0
\(809\) −21.1286 −0.742843 −0.371422 0.928464i \(-0.621130\pi\)
−0.371422 + 0.928464i \(0.621130\pi\)
\(810\) 0 0
\(811\) −20.8571 −0.732392 −0.366196 0.930538i \(-0.619340\pi\)
−0.366196 + 0.930538i \(0.619340\pi\)
\(812\) 0 0
\(813\) −12.7726 −0.447956
\(814\) 0 0
\(815\) −18.5884 −0.651122
\(816\) 0 0
\(817\) −36.4706 −1.27594
\(818\) 0 0
\(819\) 5.01389 0.175200
\(820\) 0 0
\(821\) −30.9000 −1.07842 −0.539209 0.842172i \(-0.681277\pi\)
−0.539209 + 0.842172i \(0.681277\pi\)
\(822\) 0 0
\(823\) 3.04961 0.106303 0.0531513 0.998586i \(-0.483073\pi\)
0.0531513 + 0.998586i \(0.483073\pi\)
\(824\) 0 0
\(825\) −5.91134 −0.205806
\(826\) 0 0
\(827\) 41.4450 1.44118 0.720591 0.693360i \(-0.243870\pi\)
0.720591 + 0.693360i \(0.243870\pi\)
\(828\) 0 0
\(829\) −3.61104 −0.125417 −0.0627083 0.998032i \(-0.519974\pi\)
−0.0627083 + 0.998032i \(0.519974\pi\)
\(830\) 0 0
\(831\) 28.3792 0.984464
\(832\) 0 0
\(833\) −1.71659 −0.0594764
\(834\) 0 0
\(835\) 1.75344 0.0606803
\(836\) 0 0
\(837\) 17.5700 0.607309
\(838\) 0 0
\(839\) 7.85452 0.271168 0.135584 0.990766i \(-0.456709\pi\)
0.135584 + 0.990766i \(0.456709\pi\)
\(840\) 0 0
\(841\) −25.9434 −0.894600
\(842\) 0 0
\(843\) 11.8749 0.408992
\(844\) 0 0
\(845\) −5.63047 −0.193694
\(846\) 0 0
\(847\) 4.18017 0.143632
\(848\) 0 0
\(849\) 40.4683 1.38887
\(850\) 0 0
\(851\) 8.06791 0.276564
\(852\) 0 0
\(853\) 33.5124 1.14744 0.573721 0.819051i \(-0.305500\pi\)
0.573721 + 0.819051i \(0.305500\pi\)
\(854\) 0 0
\(855\) −3.65410 −0.124968
\(856\) 0 0
\(857\) −24.7458 −0.845299 −0.422649 0.906293i \(-0.638900\pi\)
−0.422649 + 0.906293i \(0.638900\pi\)
\(858\) 0 0
\(859\) 20.9899 0.716166 0.358083 0.933690i \(-0.383430\pi\)
0.358083 + 0.933690i \(0.383430\pi\)
\(860\) 0 0
\(861\) −42.1140 −1.43524
\(862\) 0 0
\(863\) 28.6868 0.976510 0.488255 0.872701i \(-0.337634\pi\)
0.488255 + 0.872701i \(0.337634\pi\)
\(864\) 0 0
\(865\) 17.5676 0.597315
\(866\) 0 0
\(867\) 32.2642 1.09575
\(868\) 0 0
\(869\) −16.3891 −0.555962
\(870\) 0 0
\(871\) −6.92159 −0.234529
\(872\) 0 0
\(873\) −2.47792 −0.0838649
\(874\) 0 0
\(875\) −2.16922 −0.0733332
\(876\) 0 0
\(877\) 38.5479 1.30167 0.650835 0.759219i \(-0.274419\pi\)
0.650835 + 0.759219i \(0.274419\pi\)
\(878\) 0 0
\(879\) −32.9137 −1.11015
\(880\) 0 0
\(881\) 53.0568 1.78753 0.893765 0.448535i \(-0.148054\pi\)
0.893765 + 0.448535i \(0.148054\pi\)
\(882\) 0 0
\(883\) 28.7759 0.968386 0.484193 0.874961i \(-0.339113\pi\)
0.484193 + 0.874961i \(0.339113\pi\)
\(884\) 0 0
\(885\) −12.1769 −0.409323
\(886\) 0 0
\(887\) 42.2665 1.41917 0.709586 0.704619i \(-0.248882\pi\)
0.709586 + 0.704619i \(0.248882\pi\)
\(888\) 0 0
\(889\) −4.49784 −0.150853
\(890\) 0 0
\(891\) −32.6195 −1.09279
\(892\) 0 0
\(893\) −55.0115 −1.84089
\(894\) 0 0
\(895\) −16.1306 −0.539187
\(896\) 0 0
\(897\) 9.15716 0.305749
\(898\) 0 0
\(899\) −7.28504 −0.242970
\(900\) 0 0
\(901\) −5.89980 −0.196551
\(902\) 0 0
\(903\) 36.1766 1.20388
\(904\) 0 0
\(905\) −16.9945 −0.564916
\(906\) 0 0
\(907\) 7.95833 0.264252 0.132126 0.991233i \(-0.457820\pi\)
0.132126 + 0.991233i \(0.457820\pi\)
\(908\) 0 0
\(909\) 2.32767 0.0772038
\(910\) 0 0
\(911\) −22.4319 −0.743201 −0.371600 0.928393i \(-0.621191\pi\)
−0.371600 + 0.928393i \(0.621191\pi\)
\(912\) 0 0
\(913\) 12.1004 0.400465
\(914\) 0 0
\(915\) 19.2244 0.635539
\(916\) 0 0
\(917\) 28.8626 0.953127
\(918\) 0 0
\(919\) −47.4862 −1.56642 −0.783212 0.621755i \(-0.786420\pi\)
−0.783212 + 0.621755i \(0.786420\pi\)
\(920\) 0 0
\(921\) −21.0813 −0.694654
\(922\) 0 0
\(923\) 18.0352 0.593635
\(924\) 0 0
\(925\) 4.69387 0.154334
\(926\) 0 0
\(927\) 3.08679 0.101384
\(928\) 0 0
\(929\) 13.1937 0.432871 0.216436 0.976297i \(-0.430557\pi\)
0.216436 + 0.976297i \(0.430557\pi\)
\(930\) 0 0
\(931\) 9.84718 0.322728
\(932\) 0 0
\(933\) −5.54392 −0.181500
\(934\) 0 0
\(935\) 2.25352 0.0736978
\(936\) 0 0
\(937\) −36.0411 −1.17741 −0.588706 0.808347i \(-0.700363\pi\)
−0.588706 + 0.808347i \(0.700363\pi\)
\(938\) 0 0
\(939\) 56.3416 1.83864
\(940\) 0 0
\(941\) 41.8765 1.36514 0.682568 0.730822i \(-0.260863\pi\)
0.682568 + 0.730822i \(0.260863\pi\)
\(942\) 0 0
\(943\) −17.0036 −0.553714
\(944\) 0 0
\(945\) −9.14670 −0.297542
\(946\) 0 0
\(947\) −27.3169 −0.887679 −0.443840 0.896106i \(-0.646384\pi\)
−0.443840 + 0.896106i \(0.646384\pi\)
\(948\) 0 0
\(949\) 17.7457 0.576049
\(950\) 0 0
\(951\) 19.0808 0.618736
\(952\) 0 0
\(953\) −14.3197 −0.463861 −0.231931 0.972732i \(-0.574504\pi\)
−0.231931 + 0.972732i \(0.574504\pi\)
\(954\) 0 0
\(955\) −8.52383 −0.275825
\(956\) 0 0
\(957\) 10.3349 0.334079
\(958\) 0 0
\(959\) −39.8032 −1.28531
\(960\) 0 0
\(961\) −13.6370 −0.439904
\(962\) 0 0
\(963\) −2.73226 −0.0880459
\(964\) 0 0
\(965\) −21.7917 −0.701499
\(966\) 0 0
\(967\) 40.2007 1.29277 0.646384 0.763013i \(-0.276281\pi\)
0.646384 + 0.763013i \(0.276281\pi\)
\(968\) 0 0
\(969\) 6.30126 0.202426
\(970\) 0 0
\(971\) −40.0498 −1.28526 −0.642630 0.766177i \(-0.722157\pi\)
−0.642630 + 0.766177i \(0.722157\pi\)
\(972\) 0 0
\(973\) 0.137741 0.00441577
\(974\) 0 0
\(975\) 5.32759 0.170620
\(976\) 0 0
\(977\) −48.8020 −1.56131 −0.780657 0.624959i \(-0.785116\pi\)
−0.780657 + 0.624959i \(0.785116\pi\)
\(978\) 0 0
\(979\) 45.3547 1.44954
\(980\) 0 0
\(981\) −4.15903 −0.132787
\(982\) 0 0
\(983\) 20.1288 0.642009 0.321004 0.947078i \(-0.395980\pi\)
0.321004 + 0.947078i \(0.395980\pi\)
\(984\) 0 0
\(985\) 11.6273 0.370475
\(986\) 0 0
\(987\) 54.5681 1.73692
\(988\) 0 0
\(989\) 14.6064 0.464456
\(990\) 0 0
\(991\) −21.8226 −0.693219 −0.346609 0.938010i \(-0.612667\pi\)
−0.346609 + 0.938010i \(0.612667\pi\)
\(992\) 0 0
\(993\) −1.62902 −0.0516953
\(994\) 0 0
\(995\) −20.9477 −0.664088
\(996\) 0 0
\(997\) 27.6835 0.876745 0.438373 0.898793i \(-0.355555\pi\)
0.438373 + 0.898793i \(0.355555\pi\)
\(998\) 0 0
\(999\) 19.7921 0.626194
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 \(a_p\))