Properties

Label 6004.2.a.g.1.8
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.68125 q^{3} -3.32036 q^{5} +3.49635 q^{7} -0.173410 q^{9} +O(q^{10})\) \(q-1.68125 q^{3} -3.32036 q^{5} +3.49635 q^{7} -0.173410 q^{9} +1.26661 q^{11} -1.98312 q^{13} +5.58235 q^{15} -1.03307 q^{17} +1.00000 q^{19} -5.87823 q^{21} -6.45830 q^{23} +6.02481 q^{25} +5.33528 q^{27} +5.24328 q^{29} -0.427070 q^{31} -2.12948 q^{33} -11.6092 q^{35} +8.20179 q^{37} +3.33411 q^{39} -12.4681 q^{41} -4.70973 q^{43} +0.575785 q^{45} +9.04823 q^{47} +5.22450 q^{49} +1.73684 q^{51} +0.909060 q^{53} -4.20559 q^{55} -1.68125 q^{57} -10.3555 q^{59} +15.1296 q^{61} -0.606304 q^{63} +6.58467 q^{65} -3.76031 q^{67} +10.8580 q^{69} +5.33012 q^{71} +5.75154 q^{73} -10.1292 q^{75} +4.42851 q^{77} -1.00000 q^{79} -8.44970 q^{81} -8.11305 q^{83} +3.43016 q^{85} -8.81525 q^{87} -2.12521 q^{89} -6.93369 q^{91} +0.718010 q^{93} -3.32036 q^{95} +14.4726 q^{97} -0.219643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) −1.68125 −0.970668 −0.485334 0.874329i \(-0.661302\pi\)
−0.485334 + 0.874329i \(0.661302\pi\)
\(4\) 0 0
\(5\) −3.32036 −1.48491 −0.742456 0.669895i \(-0.766339\pi\)
−0.742456 + 0.669895i \(0.766339\pi\)
\(6\) 0 0
\(7\) 3.49635 1.32150 0.660749 0.750607i \(-0.270239\pi\)
0.660749 + 0.750607i \(0.270239\pi\)
\(8\) 0 0
\(9\) −0.173410 −0.0578034
\(10\) 0 0
\(11\) 1.26661 0.381896 0.190948 0.981600i \(-0.438844\pi\)
0.190948 + 0.981600i \(0.438844\pi\)
\(12\) 0 0
\(13\) −1.98312 −0.550018 −0.275009 0.961442i \(-0.588681\pi\)
−0.275009 + 0.961442i \(0.588681\pi\)
\(14\) 0 0
\(15\) 5.58235 1.44136
\(16\) 0 0
\(17\) −1.03307 −0.250556 −0.125278 0.992122i \(-0.539982\pi\)
−0.125278 + 0.992122i \(0.539982\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −5.87823 −1.28274
\(22\) 0 0
\(23\) −6.45830 −1.34665 −0.673325 0.739347i \(-0.735134\pi\)
−0.673325 + 0.739347i \(0.735134\pi\)
\(24\) 0 0
\(25\) 6.02481 1.20496
\(26\) 0 0
\(27\) 5.33528 1.02678
\(28\) 0 0
\(29\) 5.24328 0.973653 0.486826 0.873499i \(-0.338154\pi\)
0.486826 + 0.873499i \(0.338154\pi\)
\(30\) 0 0
\(31\) −0.427070 −0.0767041 −0.0383520 0.999264i \(-0.512211\pi\)
−0.0383520 + 0.999264i \(0.512211\pi\)
\(32\) 0 0
\(33\) −2.12948 −0.370694
\(34\) 0 0
\(35\) −11.6092 −1.96231
\(36\) 0 0
\(37\) 8.20179 1.34837 0.674183 0.738564i \(-0.264496\pi\)
0.674183 + 0.738564i \(0.264496\pi\)
\(38\) 0 0
\(39\) 3.33411 0.533885
\(40\) 0 0
\(41\) −12.4681 −1.94719 −0.973593 0.228289i \(-0.926687\pi\)
−0.973593 + 0.228289i \(0.926687\pi\)
\(42\) 0 0
\(43\) −4.70973 −0.718227 −0.359114 0.933294i \(-0.616921\pi\)
−0.359114 + 0.933294i \(0.616921\pi\)
\(44\) 0 0
\(45\) 0.575785 0.0858330
\(46\) 0 0
\(47\) 9.04823 1.31982 0.659910 0.751345i \(-0.270594\pi\)
0.659910 + 0.751345i \(0.270594\pi\)
\(48\) 0 0
\(49\) 5.22450 0.746357
\(50\) 0 0
\(51\) 1.73684 0.243206
\(52\) 0 0
\(53\) 0.909060 0.124869 0.0624345 0.998049i \(-0.480114\pi\)
0.0624345 + 0.998049i \(0.480114\pi\)
\(54\) 0 0
\(55\) −4.20559 −0.567082
\(56\) 0 0
\(57\) −1.68125 −0.222687
\(58\) 0 0
\(59\) −10.3555 −1.34818 −0.674088 0.738651i \(-0.735463\pi\)
−0.674088 + 0.738651i \(0.735463\pi\)
\(60\) 0 0
\(61\) 15.1296 1.93714 0.968572 0.248732i \(-0.0800139\pi\)
0.968572 + 0.248732i \(0.0800139\pi\)
\(62\) 0 0
\(63\) −0.606304 −0.0763871
\(64\) 0 0
\(65\) 6.58467 0.816728
\(66\) 0 0
\(67\) −3.76031 −0.459395 −0.229698 0.973262i \(-0.573774\pi\)
−0.229698 + 0.973262i \(0.573774\pi\)
\(68\) 0 0
\(69\) 10.8580 1.30715
\(70\) 0 0
\(71\) 5.33012 0.632569 0.316284 0.948664i \(-0.397565\pi\)
0.316284 + 0.948664i \(0.397565\pi\)
\(72\) 0 0
\(73\) 5.75154 0.673167 0.336584 0.941654i \(-0.390729\pi\)
0.336584 + 0.941654i \(0.390729\pi\)
\(74\) 0 0
\(75\) −10.1292 −1.16962
\(76\) 0 0
\(77\) 4.42851 0.504675
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −8.44970 −0.938855
\(82\) 0 0
\(83\) −8.11305 −0.890523 −0.445261 0.895401i \(-0.646889\pi\)
−0.445261 + 0.895401i \(0.646889\pi\)
\(84\) 0 0
\(85\) 3.43016 0.372053
\(86\) 0 0
\(87\) −8.81525 −0.945094
\(88\) 0 0
\(89\) −2.12521 −0.225271 −0.112636 0.993636i \(-0.535929\pi\)
−0.112636 + 0.993636i \(0.535929\pi\)
\(90\) 0 0
\(91\) −6.93369 −0.726848
\(92\) 0 0
\(93\) 0.718010 0.0744542
\(94\) 0 0
\(95\) −3.32036 −0.340662
\(96\) 0 0
\(97\) 14.4726 1.46947 0.734734 0.678355i \(-0.237307\pi\)
0.734734 + 0.678355i \(0.237307\pi\)
\(98\) 0 0
\(99\) −0.219643 −0.0220749
\(100\) 0 0
\(101\) 18.5493 1.84572 0.922861 0.385134i \(-0.125845\pi\)
0.922861 + 0.385134i \(0.125845\pi\)
\(102\) 0 0
\(103\) −0.132652 −0.0130706 −0.00653528 0.999979i \(-0.502080\pi\)
−0.00653528 + 0.999979i \(0.502080\pi\)
\(104\) 0 0
\(105\) 19.5179 1.90475
\(106\) 0 0
\(107\) −0.807610 −0.0780746 −0.0390373 0.999238i \(-0.512429\pi\)
−0.0390373 + 0.999238i \(0.512429\pi\)
\(108\) 0 0
\(109\) 4.29642 0.411522 0.205761 0.978602i \(-0.434033\pi\)
0.205761 + 0.978602i \(0.434033\pi\)
\(110\) 0 0
\(111\) −13.7892 −1.30882
\(112\) 0 0
\(113\) −15.2214 −1.43191 −0.715956 0.698145i \(-0.754009\pi\)
−0.715956 + 0.698145i \(0.754009\pi\)
\(114\) 0 0
\(115\) 21.4439 1.99965
\(116\) 0 0
\(117\) 0.343893 0.0317930
\(118\) 0 0
\(119\) −3.61197 −0.331109
\(120\) 0 0
\(121\) −9.39571 −0.854155
\(122\) 0 0
\(123\) 20.9619 1.89007
\(124\) 0 0
\(125\) −3.40273 −0.304350
\(126\) 0 0
\(127\) 0.371561 0.0329707 0.0164853 0.999864i \(-0.494752\pi\)
0.0164853 + 0.999864i \(0.494752\pi\)
\(128\) 0 0
\(129\) 7.91822 0.697160
\(130\) 0 0
\(131\) 4.99094 0.436060 0.218030 0.975942i \(-0.430037\pi\)
0.218030 + 0.975942i \(0.430037\pi\)
\(132\) 0 0
\(133\) 3.49635 0.303172
\(134\) 0 0
\(135\) −17.7151 −1.52467
\(136\) 0 0
\(137\) −12.2861 −1.04967 −0.524837 0.851203i \(-0.675874\pi\)
−0.524837 + 0.851203i \(0.675874\pi\)
\(138\) 0 0
\(139\) 10.3930 0.881520 0.440760 0.897625i \(-0.354709\pi\)
0.440760 + 0.897625i \(0.354709\pi\)
\(140\) 0 0
\(141\) −15.2123 −1.28111
\(142\) 0 0
\(143\) −2.51183 −0.210050
\(144\) 0 0
\(145\) −17.4096 −1.44579
\(146\) 0 0
\(147\) −8.78367 −0.724465
\(148\) 0 0
\(149\) 5.52981 0.453020 0.226510 0.974009i \(-0.427268\pi\)
0.226510 + 0.974009i \(0.427268\pi\)
\(150\) 0 0
\(151\) −2.05849 −0.167517 −0.0837586 0.996486i \(-0.526692\pi\)
−0.0837586 + 0.996486i \(0.526692\pi\)
\(152\) 0 0
\(153\) 0.179145 0.0144830
\(154\) 0 0
\(155\) 1.41803 0.113899
\(156\) 0 0
\(157\) −4.42056 −0.352799 −0.176400 0.984319i \(-0.556445\pi\)
−0.176400 + 0.984319i \(0.556445\pi\)
\(158\) 0 0
\(159\) −1.52835 −0.121206
\(160\) 0 0
\(161\) −22.5805 −1.77959
\(162\) 0 0
\(163\) −5.01264 −0.392620 −0.196310 0.980542i \(-0.562896\pi\)
−0.196310 + 0.980542i \(0.562896\pi\)
\(164\) 0 0
\(165\) 7.07064 0.550448
\(166\) 0 0
\(167\) 23.8475 1.84538 0.922689 0.385544i \(-0.125986\pi\)
0.922689 + 0.385544i \(0.125986\pi\)
\(168\) 0 0
\(169\) −9.06724 −0.697480
\(170\) 0 0
\(171\) −0.173410 −0.0132610
\(172\) 0 0
\(173\) −8.06203 −0.612945 −0.306472 0.951880i \(-0.599149\pi\)
−0.306472 + 0.951880i \(0.599149\pi\)
\(174\) 0 0
\(175\) 21.0649 1.59235
\(176\) 0 0
\(177\) 17.4102 1.30863
\(178\) 0 0
\(179\) −3.39075 −0.253436 −0.126718 0.991939i \(-0.540444\pi\)
−0.126718 + 0.991939i \(0.540444\pi\)
\(180\) 0 0
\(181\) 5.58804 0.415356 0.207678 0.978197i \(-0.433409\pi\)
0.207678 + 0.978197i \(0.433409\pi\)
\(182\) 0 0
\(183\) −25.4366 −1.88032
\(184\) 0 0
\(185\) −27.2329 −2.00220
\(186\) 0 0
\(187\) −1.30849 −0.0956863
\(188\) 0 0
\(189\) 18.6540 1.35688
\(190\) 0 0
\(191\) −14.7560 −1.06770 −0.533852 0.845578i \(-0.679256\pi\)
−0.533852 + 0.845578i \(0.679256\pi\)
\(192\) 0 0
\(193\) −7.77834 −0.559897 −0.279949 0.960015i \(-0.590317\pi\)
−0.279949 + 0.960015i \(0.590317\pi\)
\(194\) 0 0
\(195\) −11.0705 −0.792772
\(196\) 0 0
\(197\) −14.6711 −1.04527 −0.522636 0.852556i \(-0.675051\pi\)
−0.522636 + 0.852556i \(0.675051\pi\)
\(198\) 0 0
\(199\) 2.33881 0.165794 0.0828969 0.996558i \(-0.473583\pi\)
0.0828969 + 0.996558i \(0.473583\pi\)
\(200\) 0 0
\(201\) 6.32201 0.445920
\(202\) 0 0
\(203\) 18.3324 1.28668
\(204\) 0 0
\(205\) 41.3985 2.89140
\(206\) 0 0
\(207\) 1.11994 0.0778410
\(208\) 0 0
\(209\) 1.26661 0.0876130
\(210\) 0 0
\(211\) 19.5048 1.34277 0.671384 0.741110i \(-0.265700\pi\)
0.671384 + 0.741110i \(0.265700\pi\)
\(212\) 0 0
\(213\) −8.96125 −0.614014
\(214\) 0 0
\(215\) 15.6380 1.06650
\(216\) 0 0
\(217\) −1.49319 −0.101364
\(218\) 0 0
\(219\) −9.66976 −0.653422
\(220\) 0 0
\(221\) 2.04870 0.137810
\(222\) 0 0
\(223\) −23.8667 −1.59823 −0.799116 0.601177i \(-0.794699\pi\)
−0.799116 + 0.601177i \(0.794699\pi\)
\(224\) 0 0
\(225\) −1.04476 −0.0696509
\(226\) 0 0
\(227\) 19.8376 1.31666 0.658332 0.752727i \(-0.271262\pi\)
0.658332 + 0.752727i \(0.271262\pi\)
\(228\) 0 0
\(229\) −13.8457 −0.914949 −0.457474 0.889223i \(-0.651246\pi\)
−0.457474 + 0.889223i \(0.651246\pi\)
\(230\) 0 0
\(231\) −7.44541 −0.489872
\(232\) 0 0
\(233\) 20.6041 1.34982 0.674911 0.737899i \(-0.264182\pi\)
0.674911 + 0.737899i \(0.264182\pi\)
\(234\) 0 0
\(235\) −30.0434 −1.95982
\(236\) 0 0
\(237\) 1.68125 0.109209
\(238\) 0 0
\(239\) −23.1289 −1.49608 −0.748042 0.663651i \(-0.769006\pi\)
−0.748042 + 0.663651i \(0.769006\pi\)
\(240\) 0 0
\(241\) −19.9271 −1.28362 −0.641810 0.766863i \(-0.721816\pi\)
−0.641810 + 0.766863i \(0.721816\pi\)
\(242\) 0 0
\(243\) −1.79983 −0.115459
\(244\) 0 0
\(245\) −17.3472 −1.10827
\(246\) 0 0
\(247\) −1.98312 −0.126183
\(248\) 0 0
\(249\) 13.6400 0.864402
\(250\) 0 0
\(251\) −26.8450 −1.69444 −0.847220 0.531242i \(-0.821725\pi\)
−0.847220 + 0.531242i \(0.821725\pi\)
\(252\) 0 0
\(253\) −8.18013 −0.514280
\(254\) 0 0
\(255\) −5.76694 −0.361140
\(256\) 0 0
\(257\) 18.7548 1.16989 0.584946 0.811072i \(-0.301116\pi\)
0.584946 + 0.811072i \(0.301116\pi\)
\(258\) 0 0
\(259\) 28.6764 1.78186
\(260\) 0 0
\(261\) −0.909239 −0.0562805
\(262\) 0 0
\(263\) −21.4425 −1.32220 −0.661101 0.750297i \(-0.729910\pi\)
−0.661101 + 0.750297i \(0.729910\pi\)
\(264\) 0 0
\(265\) −3.01841 −0.185419
\(266\) 0 0
\(267\) 3.57299 0.218664
\(268\) 0 0
\(269\) −26.0706 −1.58955 −0.794776 0.606903i \(-0.792412\pi\)
−0.794776 + 0.606903i \(0.792412\pi\)
\(270\) 0 0
\(271\) −13.8688 −0.842470 −0.421235 0.906952i \(-0.638403\pi\)
−0.421235 + 0.906952i \(0.638403\pi\)
\(272\) 0 0
\(273\) 11.6572 0.705528
\(274\) 0 0
\(275\) 7.63106 0.460170
\(276\) 0 0
\(277\) −7.24715 −0.435439 −0.217719 0.976011i \(-0.569862\pi\)
−0.217719 + 0.976011i \(0.569862\pi\)
\(278\) 0 0
\(279\) 0.0740584 0.00443376
\(280\) 0 0
\(281\) −15.8410 −0.944993 −0.472496 0.881333i \(-0.656647\pi\)
−0.472496 + 0.881333i \(0.656647\pi\)
\(282\) 0 0
\(283\) −18.3513 −1.09087 −0.545436 0.838153i \(-0.683636\pi\)
−0.545436 + 0.838153i \(0.683636\pi\)
\(284\) 0 0
\(285\) 5.58235 0.330670
\(286\) 0 0
\(287\) −43.5928 −2.57320
\(288\) 0 0
\(289\) −15.9328 −0.937222
\(290\) 0 0
\(291\) −24.3320 −1.42637
\(292\) 0 0
\(293\) −11.0088 −0.643143 −0.321572 0.946885i \(-0.604211\pi\)
−0.321572 + 0.946885i \(0.604211\pi\)
\(294\) 0 0
\(295\) 34.3841 2.00192
\(296\) 0 0
\(297\) 6.75771 0.392122
\(298\) 0 0
\(299\) 12.8076 0.740682
\(300\) 0 0
\(301\) −16.4669 −0.949136
\(302\) 0 0
\(303\) −31.1859 −1.79158
\(304\) 0 0
\(305\) −50.2357 −2.87649
\(306\) 0 0
\(307\) 20.0621 1.14500 0.572502 0.819903i \(-0.305973\pi\)
0.572502 + 0.819903i \(0.305973\pi\)
\(308\) 0 0
\(309\) 0.223020 0.0126872
\(310\) 0 0
\(311\) 32.1654 1.82393 0.911965 0.410268i \(-0.134565\pi\)
0.911965 + 0.410268i \(0.134565\pi\)
\(312\) 0 0
\(313\) −25.4898 −1.44077 −0.720385 0.693574i \(-0.756035\pi\)
−0.720385 + 0.693574i \(0.756035\pi\)
\(314\) 0 0
\(315\) 2.01315 0.113428
\(316\) 0 0
\(317\) −18.3911 −1.03295 −0.516475 0.856302i \(-0.672756\pi\)
−0.516475 + 0.856302i \(0.672756\pi\)
\(318\) 0 0
\(319\) 6.64117 0.371834
\(320\) 0 0
\(321\) 1.35779 0.0757846
\(322\) 0 0
\(323\) −1.03307 −0.0574814
\(324\) 0 0
\(325\) −11.9479 −0.662751
\(326\) 0 0
\(327\) −7.22334 −0.399452
\(328\) 0 0
\(329\) 31.6358 1.74414
\(330\) 0 0
\(331\) −28.1213 −1.54569 −0.772844 0.634596i \(-0.781166\pi\)
−0.772844 + 0.634596i \(0.781166\pi\)
\(332\) 0 0
\(333\) −1.42228 −0.0779402
\(334\) 0 0
\(335\) 12.4856 0.682161
\(336\) 0 0
\(337\) 0.794119 0.0432584 0.0216292 0.999766i \(-0.493115\pi\)
0.0216292 + 0.999766i \(0.493115\pi\)
\(338\) 0 0
\(339\) 25.5910 1.38991
\(340\) 0 0
\(341\) −0.540930 −0.0292930
\(342\) 0 0
\(343\) −6.20779 −0.335189
\(344\) 0 0
\(345\) −36.0525 −1.94100
\(346\) 0 0
\(347\) 14.7652 0.792635 0.396317 0.918114i \(-0.370288\pi\)
0.396317 + 0.918114i \(0.370288\pi\)
\(348\) 0 0
\(349\) 7.21238 0.386070 0.193035 0.981192i \(-0.438167\pi\)
0.193035 + 0.981192i \(0.438167\pi\)
\(350\) 0 0
\(351\) −10.5805 −0.564746
\(352\) 0 0
\(353\) 24.3047 1.29361 0.646804 0.762656i \(-0.276105\pi\)
0.646804 + 0.762656i \(0.276105\pi\)
\(354\) 0 0
\(355\) −17.6979 −0.939309
\(356\) 0 0
\(357\) 6.07261 0.321397
\(358\) 0 0
\(359\) 1.46627 0.0773870 0.0386935 0.999251i \(-0.487680\pi\)
0.0386935 + 0.999251i \(0.487680\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 15.7965 0.829101
\(364\) 0 0
\(365\) −19.0972 −0.999593
\(366\) 0 0
\(367\) 0.999961 0.0521975 0.0260988 0.999659i \(-0.491692\pi\)
0.0260988 + 0.999659i \(0.491692\pi\)
\(368\) 0 0
\(369\) 2.16209 0.112554
\(370\) 0 0
\(371\) 3.17840 0.165014
\(372\) 0 0
\(373\) −9.61737 −0.497968 −0.248984 0.968508i \(-0.580097\pi\)
−0.248984 + 0.968508i \(0.580097\pi\)
\(374\) 0 0
\(375\) 5.72083 0.295422
\(376\) 0 0
\(377\) −10.3980 −0.535527
\(378\) 0 0
\(379\) −1.63781 −0.0841289 −0.0420645 0.999115i \(-0.513393\pi\)
−0.0420645 + 0.999115i \(0.513393\pi\)
\(380\) 0 0
\(381\) −0.624685 −0.0320036
\(382\) 0 0
\(383\) −31.0318 −1.58565 −0.792825 0.609449i \(-0.791391\pi\)
−0.792825 + 0.609449i \(0.791391\pi\)
\(384\) 0 0
\(385\) −14.7042 −0.749398
\(386\) 0 0
\(387\) 0.816716 0.0415160
\(388\) 0 0
\(389\) −24.5350 −1.24398 −0.621988 0.783027i \(-0.713675\pi\)
−0.621988 + 0.783027i \(0.713675\pi\)
\(390\) 0 0
\(391\) 6.67186 0.337411
\(392\) 0 0
\(393\) −8.39100 −0.423270
\(394\) 0 0
\(395\) 3.32036 0.167066
\(396\) 0 0
\(397\) −17.9648 −0.901627 −0.450813 0.892618i \(-0.648866\pi\)
−0.450813 + 0.892618i \(0.648866\pi\)
\(398\) 0 0
\(399\) −5.87823 −0.294280
\(400\) 0 0
\(401\) −33.2471 −1.66028 −0.830140 0.557555i \(-0.811740\pi\)
−0.830140 + 0.557555i \(0.811740\pi\)
\(402\) 0 0
\(403\) 0.846931 0.0421886
\(404\) 0 0
\(405\) 28.0561 1.39412
\(406\) 0 0
\(407\) 10.3884 0.514936
\(408\) 0 0
\(409\) −8.24436 −0.407657 −0.203829 0.979007i \(-0.565339\pi\)
−0.203829 + 0.979007i \(0.565339\pi\)
\(410\) 0 0
\(411\) 20.6560 1.01888
\(412\) 0 0
\(413\) −36.2066 −1.78161
\(414\) 0 0
\(415\) 26.9383 1.32235
\(416\) 0 0
\(417\) −17.4731 −0.855663
\(418\) 0 0
\(419\) −12.3445 −0.603068 −0.301534 0.953455i \(-0.597499\pi\)
−0.301534 + 0.953455i \(0.597499\pi\)
\(420\) 0 0
\(421\) −21.8527 −1.06504 −0.532518 0.846419i \(-0.678754\pi\)
−0.532518 + 0.846419i \(0.678754\pi\)
\(422\) 0 0
\(423\) −1.56906 −0.0762901
\(424\) 0 0
\(425\) −6.22403 −0.301910
\(426\) 0 0
\(427\) 52.8984 2.55993
\(428\) 0 0
\(429\) 4.22301 0.203889
\(430\) 0 0
\(431\) −29.0252 −1.39809 −0.699047 0.715076i \(-0.746392\pi\)
−0.699047 + 0.715076i \(0.746392\pi\)
\(432\) 0 0
\(433\) 27.2078 1.30753 0.653763 0.756700i \(-0.273190\pi\)
0.653763 + 0.756700i \(0.273190\pi\)
\(434\) 0 0
\(435\) 29.2698 1.40338
\(436\) 0 0
\(437\) −6.45830 −0.308943
\(438\) 0 0
\(439\) −26.5741 −1.26831 −0.634156 0.773206i \(-0.718652\pi\)
−0.634156 + 0.773206i \(0.718652\pi\)
\(440\) 0 0
\(441\) −0.905982 −0.0431420
\(442\) 0 0
\(443\) 30.8090 1.46378 0.731890 0.681423i \(-0.238638\pi\)
0.731890 + 0.681423i \(0.238638\pi\)
\(444\) 0 0
\(445\) 7.05645 0.334508
\(446\) 0 0
\(447\) −9.29698 −0.439732
\(448\) 0 0
\(449\) 10.9251 0.515587 0.257793 0.966200i \(-0.417005\pi\)
0.257793 + 0.966200i \(0.417005\pi\)
\(450\) 0 0
\(451\) −15.7922 −0.743623
\(452\) 0 0
\(453\) 3.46082 0.162604
\(454\) 0 0
\(455\) 23.0224 1.07930
\(456\) 0 0
\(457\) 14.3313 0.670388 0.335194 0.942149i \(-0.391198\pi\)
0.335194 + 0.942149i \(0.391198\pi\)
\(458\) 0 0
\(459\) −5.51171 −0.257265
\(460\) 0 0
\(461\) 24.6189 1.14661 0.573307 0.819340i \(-0.305660\pi\)
0.573307 + 0.819340i \(0.305660\pi\)
\(462\) 0 0
\(463\) −16.6334 −0.773020 −0.386510 0.922285i \(-0.626320\pi\)
−0.386510 + 0.922285i \(0.626320\pi\)
\(464\) 0 0
\(465\) −2.38405 −0.110558
\(466\) 0 0
\(467\) −31.8559 −1.47412 −0.737059 0.675829i \(-0.763786\pi\)
−0.737059 + 0.675829i \(0.763786\pi\)
\(468\) 0 0
\(469\) −13.1474 −0.607090
\(470\) 0 0
\(471\) 7.43206 0.342451
\(472\) 0 0
\(473\) −5.96538 −0.274288
\(474\) 0 0
\(475\) 6.02481 0.276437
\(476\) 0 0
\(477\) −0.157640 −0.00721786
\(478\) 0 0
\(479\) 10.7382 0.490643 0.245321 0.969442i \(-0.421106\pi\)
0.245321 + 0.969442i \(0.421106\pi\)
\(480\) 0 0
\(481\) −16.2651 −0.741626
\(482\) 0 0
\(483\) 37.9634 1.72740
\(484\) 0 0
\(485\) −48.0542 −2.18203
\(486\) 0 0
\(487\) 11.9175 0.540035 0.270018 0.962855i \(-0.412970\pi\)
0.270018 + 0.962855i \(0.412970\pi\)
\(488\) 0 0
\(489\) 8.42748 0.381104
\(490\) 0 0
\(491\) 31.7813 1.43427 0.717134 0.696935i \(-0.245454\pi\)
0.717134 + 0.696935i \(0.245454\pi\)
\(492\) 0 0
\(493\) −5.41666 −0.243954
\(494\) 0 0
\(495\) 0.729293 0.0327793
\(496\) 0 0
\(497\) 18.6360 0.835938
\(498\) 0 0
\(499\) 13.8203 0.618681 0.309341 0.950951i \(-0.399892\pi\)
0.309341 + 0.950951i \(0.399892\pi\)
\(500\) 0 0
\(501\) −40.0936 −1.79125
\(502\) 0 0
\(503\) −22.7226 −1.01315 −0.506575 0.862196i \(-0.669089\pi\)
−0.506575 + 0.862196i \(0.669089\pi\)
\(504\) 0 0
\(505\) −61.5903 −2.74073
\(506\) 0 0
\(507\) 15.2443 0.677021
\(508\) 0 0
\(509\) 18.6081 0.824789 0.412395 0.911005i \(-0.364692\pi\)
0.412395 + 0.911005i \(0.364692\pi\)
\(510\) 0 0
\(511\) 20.1094 0.889589
\(512\) 0 0
\(513\) 5.33528 0.235559
\(514\) 0 0
\(515\) 0.440452 0.0194086
\(516\) 0 0
\(517\) 11.4605 0.504034
\(518\) 0 0
\(519\) 13.5543 0.594966
\(520\) 0 0
\(521\) 5.63400 0.246830 0.123415 0.992355i \(-0.460615\pi\)
0.123415 + 0.992355i \(0.460615\pi\)
\(522\) 0 0
\(523\) −13.0347 −0.569969 −0.284985 0.958532i \(-0.591989\pi\)
−0.284985 + 0.958532i \(0.591989\pi\)
\(524\) 0 0
\(525\) −35.4152 −1.54565
\(526\) 0 0
\(527\) 0.441192 0.0192186
\(528\) 0 0
\(529\) 18.7097 0.813464
\(530\) 0 0
\(531\) 1.79576 0.0779292
\(532\) 0 0
\(533\) 24.7257 1.07099
\(534\) 0 0
\(535\) 2.68156 0.115934
\(536\) 0 0
\(537\) 5.70068 0.246003
\(538\) 0 0
\(539\) 6.61738 0.285031
\(540\) 0 0
\(541\) 14.0611 0.604535 0.302267 0.953223i \(-0.402256\pi\)
0.302267 + 0.953223i \(0.402256\pi\)
\(542\) 0 0
\(543\) −9.39487 −0.403173
\(544\) 0 0
\(545\) −14.2657 −0.611074
\(546\) 0 0
\(547\) −7.59072 −0.324556 −0.162278 0.986745i \(-0.551884\pi\)
−0.162278 + 0.986745i \(0.551884\pi\)
\(548\) 0 0
\(549\) −2.62363 −0.111974
\(550\) 0 0
\(551\) 5.24328 0.223371
\(552\) 0 0
\(553\) −3.49635 −0.148680
\(554\) 0 0
\(555\) 45.7853 1.94348
\(556\) 0 0
\(557\) −19.3102 −0.818201 −0.409100 0.912489i \(-0.634157\pi\)
−0.409100 + 0.912489i \(0.634157\pi\)
\(558\) 0 0
\(559\) 9.33996 0.395038
\(560\) 0 0
\(561\) 2.19989 0.0928796
\(562\) 0 0
\(563\) −11.2777 −0.475299 −0.237649 0.971351i \(-0.576377\pi\)
−0.237649 + 0.971351i \(0.576377\pi\)
\(564\) 0 0
\(565\) 50.5407 2.12626
\(566\) 0 0
\(567\) −29.5431 −1.24070
\(568\) 0 0
\(569\) 14.6778 0.615327 0.307663 0.951495i \(-0.400453\pi\)
0.307663 + 0.951495i \(0.400453\pi\)
\(570\) 0 0
\(571\) 23.2476 0.972883 0.486441 0.873713i \(-0.338295\pi\)
0.486441 + 0.873713i \(0.338295\pi\)
\(572\) 0 0
\(573\) 24.8084 1.03639
\(574\) 0 0
\(575\) −38.9100 −1.62266
\(576\) 0 0
\(577\) −2.79889 −0.116519 −0.0582596 0.998301i \(-0.518555\pi\)
−0.0582596 + 0.998301i \(0.518555\pi\)
\(578\) 0 0
\(579\) 13.0773 0.543475
\(580\) 0 0
\(581\) −28.3661 −1.17682
\(582\) 0 0
\(583\) 1.15142 0.0476870
\(584\) 0 0
\(585\) −1.14185 −0.0472097
\(586\) 0 0
\(587\) 44.4760 1.83572 0.917860 0.396905i \(-0.129916\pi\)
0.917860 + 0.396905i \(0.129916\pi\)
\(588\) 0 0
\(589\) −0.427070 −0.0175971
\(590\) 0 0
\(591\) 24.6657 1.01461
\(592\) 0 0
\(593\) −34.2530 −1.40660 −0.703300 0.710893i \(-0.748291\pi\)
−0.703300 + 0.710893i \(0.748291\pi\)
\(594\) 0 0
\(595\) 11.9931 0.491667
\(596\) 0 0
\(597\) −3.93211 −0.160931
\(598\) 0 0
\(599\) −40.6935 −1.66269 −0.831346 0.555755i \(-0.812429\pi\)
−0.831346 + 0.555755i \(0.812429\pi\)
\(600\) 0 0
\(601\) 28.4266 1.15954 0.579772 0.814778i \(-0.303141\pi\)
0.579772 + 0.814778i \(0.303141\pi\)
\(602\) 0 0
\(603\) 0.652077 0.0265546
\(604\) 0 0
\(605\) 31.1972 1.26834
\(606\) 0 0
\(607\) −13.1611 −0.534191 −0.267095 0.963670i \(-0.586064\pi\)
−0.267095 + 0.963670i \(0.586064\pi\)
\(608\) 0 0
\(609\) −30.8212 −1.24894
\(610\) 0 0
\(611\) −17.9437 −0.725925
\(612\) 0 0
\(613\) −16.6195 −0.671257 −0.335628 0.941995i \(-0.608949\pi\)
−0.335628 + 0.941995i \(0.608949\pi\)
\(614\) 0 0
\(615\) −69.6012 −2.80659
\(616\) 0 0
\(617\) −42.4142 −1.70753 −0.853765 0.520658i \(-0.825687\pi\)
−0.853765 + 0.520658i \(0.825687\pi\)
\(618\) 0 0
\(619\) −25.6570 −1.03124 −0.515622 0.856816i \(-0.672439\pi\)
−0.515622 + 0.856816i \(0.672439\pi\)
\(620\) 0 0
\(621\) −34.4569 −1.38271
\(622\) 0 0
\(623\) −7.43047 −0.297696
\(624\) 0 0
\(625\) −18.8257 −0.753029
\(626\) 0 0
\(627\) −2.12948 −0.0850431
\(628\) 0 0
\(629\) −8.47301 −0.337841
\(630\) 0 0
\(631\) 11.9840 0.477077 0.238538 0.971133i \(-0.423332\pi\)
0.238538 + 0.971133i \(0.423332\pi\)
\(632\) 0 0
\(633\) −32.7924 −1.30338
\(634\) 0 0
\(635\) −1.23372 −0.0489586
\(636\) 0 0
\(637\) −10.3608 −0.410510
\(638\) 0 0
\(639\) −0.924298 −0.0365647
\(640\) 0 0
\(641\) −37.7830 −1.49234 −0.746170 0.665756i \(-0.768109\pi\)
−0.746170 + 0.665756i \(0.768109\pi\)
\(642\) 0 0
\(643\) 18.0679 0.712528 0.356264 0.934385i \(-0.384050\pi\)
0.356264 + 0.934385i \(0.384050\pi\)
\(644\) 0 0
\(645\) −26.2914 −1.03522
\(646\) 0 0
\(647\) 14.8721 0.584681 0.292341 0.956314i \(-0.405566\pi\)
0.292341 + 0.956314i \(0.405566\pi\)
\(648\) 0 0
\(649\) −13.1164 −0.514863
\(650\) 0 0
\(651\) 2.51042 0.0983911
\(652\) 0 0
\(653\) 21.0504 0.823766 0.411883 0.911237i \(-0.364871\pi\)
0.411883 + 0.911237i \(0.364871\pi\)
\(654\) 0 0
\(655\) −16.5717 −0.647511
\(656\) 0 0
\(657\) −0.997377 −0.0389114
\(658\) 0 0
\(659\) −24.7380 −0.963657 −0.481829 0.876265i \(-0.660027\pi\)
−0.481829 + 0.876265i \(0.660027\pi\)
\(660\) 0 0
\(661\) 28.5182 1.10923 0.554615 0.832107i \(-0.312866\pi\)
0.554615 + 0.832107i \(0.312866\pi\)
\(662\) 0 0
\(663\) −3.44436 −0.133768
\(664\) 0 0
\(665\) −11.6092 −0.450184
\(666\) 0 0
\(667\) −33.8627 −1.31117
\(668\) 0 0
\(669\) 40.1258 1.55135
\(670\) 0 0
\(671\) 19.1632 0.739788
\(672\) 0 0
\(673\) 9.05670 0.349110 0.174555 0.984647i \(-0.444151\pi\)
0.174555 + 0.984647i \(0.444151\pi\)
\(674\) 0 0
\(675\) 32.1441 1.23723
\(676\) 0 0
\(677\) −4.32881 −0.166370 −0.0831848 0.996534i \(-0.526509\pi\)
−0.0831848 + 0.996534i \(0.526509\pi\)
\(678\) 0 0
\(679\) 50.6013 1.94190
\(680\) 0 0
\(681\) −33.3518 −1.27804
\(682\) 0 0
\(683\) −2.08891 −0.0799299 −0.0399650 0.999201i \(-0.512725\pi\)
−0.0399650 + 0.999201i \(0.512725\pi\)
\(684\) 0 0
\(685\) 40.7944 1.55867
\(686\) 0 0
\(687\) 23.2780 0.888111
\(688\) 0 0
\(689\) −1.80277 −0.0686802
\(690\) 0 0
\(691\) 17.9220 0.681785 0.340892 0.940102i \(-0.389271\pi\)
0.340892 + 0.940102i \(0.389271\pi\)
\(692\) 0 0
\(693\) −0.767949 −0.0291720
\(694\) 0 0
\(695\) −34.5084 −1.30898
\(696\) 0 0
\(697\) 12.8804 0.487879
\(698\) 0 0
\(699\) −34.6406 −1.31023
\(700\) 0 0
\(701\) −27.2178 −1.02800 −0.514002 0.857789i \(-0.671838\pi\)
−0.514002 + 0.857789i \(0.671838\pi\)
\(702\) 0 0
\(703\) 8.20179 0.309337
\(704\) 0 0
\(705\) 50.5104 1.90233
\(706\) 0 0
\(707\) 64.8548 2.43912
\(708\) 0 0
\(709\) −16.0913 −0.604321 −0.302160 0.953257i \(-0.597708\pi\)
−0.302160 + 0.953257i \(0.597708\pi\)
\(710\) 0 0
\(711\) 0.173410 0.00650340
\(712\) 0 0
\(713\) 2.75815 0.103294
\(714\) 0 0
\(715\) 8.34019 0.311905
\(716\) 0 0
\(717\) 38.8854 1.45220
\(718\) 0 0
\(719\) 9.17704 0.342246 0.171123 0.985250i \(-0.445260\pi\)
0.171123 + 0.985250i \(0.445260\pi\)
\(720\) 0 0
\(721\) −0.463797 −0.0172727
\(722\) 0 0
\(723\) 33.5024 1.24597
\(724\) 0 0
\(725\) 31.5898 1.17321
\(726\) 0 0
\(727\) 39.6531 1.47065 0.735326 0.677713i \(-0.237029\pi\)
0.735326 + 0.677713i \(0.237029\pi\)
\(728\) 0 0
\(729\) 28.3751 1.05093
\(730\) 0 0
\(731\) 4.86547 0.179956
\(732\) 0 0
\(733\) 22.2952 0.823493 0.411746 0.911298i \(-0.364919\pi\)
0.411746 + 0.911298i \(0.364919\pi\)
\(734\) 0 0
\(735\) 29.1650 1.07577
\(736\) 0 0
\(737\) −4.76284 −0.175441
\(738\) 0 0
\(739\) 13.5829 0.499656 0.249828 0.968290i \(-0.419626\pi\)
0.249828 + 0.968290i \(0.419626\pi\)
\(740\) 0 0
\(741\) 3.33411 0.122482
\(742\) 0 0
\(743\) 8.05890 0.295653 0.147826 0.989013i \(-0.452772\pi\)
0.147826 + 0.989013i \(0.452772\pi\)
\(744\) 0 0
\(745\) −18.3610 −0.672694
\(746\) 0 0
\(747\) 1.40689 0.0514753
\(748\) 0 0
\(749\) −2.82369 −0.103175
\(750\) 0 0
\(751\) 24.5015 0.894072 0.447036 0.894516i \(-0.352480\pi\)
0.447036 + 0.894516i \(0.352480\pi\)
\(752\) 0 0
\(753\) 45.1330 1.64474
\(754\) 0 0
\(755\) 6.83492 0.248748
\(756\) 0 0
\(757\) −9.28504 −0.337471 −0.168735 0.985661i \(-0.553968\pi\)
−0.168735 + 0.985661i \(0.553968\pi\)
\(758\) 0 0
\(759\) 13.7528 0.499195
\(760\) 0 0
\(761\) −1.08497 −0.0393303 −0.0196651 0.999807i \(-0.506260\pi\)
−0.0196651 + 0.999807i \(0.506260\pi\)
\(762\) 0 0
\(763\) 15.0218 0.543826
\(764\) 0 0
\(765\) −0.594825 −0.0215059
\(766\) 0 0
\(767\) 20.5363 0.741521
\(768\) 0 0
\(769\) −38.3327 −1.38231 −0.691156 0.722705i \(-0.742898\pi\)
−0.691156 + 0.722705i \(0.742898\pi\)
\(770\) 0 0
\(771\) −31.5314 −1.13558
\(772\) 0 0
\(773\) 20.9782 0.754532 0.377266 0.926105i \(-0.376864\pi\)
0.377266 + 0.926105i \(0.376864\pi\)
\(774\) 0 0
\(775\) −2.57302 −0.0924255
\(776\) 0 0
\(777\) −48.2121 −1.72960
\(778\) 0 0
\(779\) −12.4681 −0.446715
\(780\) 0 0
\(781\) 6.75117 0.241576
\(782\) 0 0
\(783\) 27.9744 0.999723
\(784\) 0 0
\(785\) 14.6779 0.523876
\(786\) 0 0
\(787\) 30.0647 1.07169 0.535846 0.844316i \(-0.319993\pi\)
0.535846 + 0.844316i \(0.319993\pi\)
\(788\) 0 0
\(789\) 36.0501 1.28342
\(790\) 0 0
\(791\) −53.2195 −1.89227
\(792\) 0 0
\(793\) −30.0038 −1.06546
\(794\) 0 0
\(795\) 5.07469 0.179981
\(796\) 0 0
\(797\) 18.5740 0.657925 0.328963 0.944343i \(-0.393301\pi\)
0.328963 + 0.944343i \(0.393301\pi\)
\(798\) 0 0
\(799\) −9.34743 −0.330688
\(800\) 0 0
\(801\) 0.368533 0.0130215
\(802\) 0 0
\(803\) 7.28494 0.257080
\(804\) 0 0
\(805\) 74.9755 2.64254
\(806\) 0 0
\(807\) 43.8311 1.54293
\(808\) 0 0
\(809\) 8.15637 0.286763 0.143381 0.989668i \(-0.454202\pi\)
0.143381 + 0.989668i \(0.454202\pi\)
\(810\) 0 0
\(811\) 20.4763 0.719022 0.359511 0.933141i \(-0.382944\pi\)
0.359511 + 0.933141i \(0.382944\pi\)
\(812\) 0 0
\(813\) 23.3169 0.817759
\(814\) 0 0
\(815\) 16.6438 0.583006
\(816\) 0 0
\(817\) −4.70973 −0.164773
\(818\) 0 0
\(819\) 1.20237 0.0420143
\(820\) 0 0
\(821\) 30.2547 1.05590 0.527949 0.849276i \(-0.322961\pi\)
0.527949 + 0.849276i \(0.322961\pi\)
\(822\) 0 0
\(823\) 44.4332 1.54884 0.774422 0.632669i \(-0.218041\pi\)
0.774422 + 0.632669i \(0.218041\pi\)
\(824\) 0 0
\(825\) −12.8297 −0.446673
\(826\) 0 0
\(827\) −15.4952 −0.538820 −0.269410 0.963026i \(-0.586829\pi\)
−0.269410 + 0.963026i \(0.586829\pi\)
\(828\) 0 0
\(829\) 21.5222 0.747499 0.373749 0.927530i \(-0.378072\pi\)
0.373749 + 0.927530i \(0.378072\pi\)
\(830\) 0 0
\(831\) 12.1842 0.422667
\(832\) 0 0
\(833\) −5.39726 −0.187004
\(834\) 0 0
\(835\) −79.1825 −2.74022
\(836\) 0 0
\(837\) −2.27854 −0.0787579
\(838\) 0 0
\(839\) −15.6891 −0.541649 −0.270825 0.962629i \(-0.587296\pi\)
−0.270825 + 0.962629i \(0.587296\pi\)
\(840\) 0 0
\(841\) −1.50801 −0.0520004
\(842\) 0 0
\(843\) 26.6326 0.917274
\(844\) 0 0
\(845\) 30.1065 1.03570
\(846\) 0 0
\(847\) −32.8507 −1.12876
\(848\) 0 0
\(849\) 30.8531 1.05887
\(850\) 0 0
\(851\) −52.9697 −1.81578
\(852\) 0 0
\(853\) 34.9636 1.19713 0.598565 0.801074i \(-0.295738\pi\)
0.598565 + 0.801074i \(0.295738\pi\)
\(854\) 0 0
\(855\) 0.575785 0.0196914
\(856\) 0 0
\(857\) −18.8079 −0.642466 −0.321233 0.947000i \(-0.604097\pi\)
−0.321233 + 0.947000i \(0.604097\pi\)
\(858\) 0 0
\(859\) −10.2523 −0.349803 −0.174901 0.984586i \(-0.555961\pi\)
−0.174901 + 0.984586i \(0.555961\pi\)
\(860\) 0 0
\(861\) 73.2903 2.49773
\(862\) 0 0
\(863\) −33.0872 −1.12630 −0.563151 0.826354i \(-0.690411\pi\)
−0.563151 + 0.826354i \(0.690411\pi\)
\(864\) 0 0
\(865\) 26.7689 0.910169
\(866\) 0 0
\(867\) 26.7869 0.909731
\(868\) 0 0
\(869\) −1.26661 −0.0429667
\(870\) 0 0
\(871\) 7.45715 0.252676
\(872\) 0 0
\(873\) −2.50970 −0.0849403
\(874\) 0 0
\(875\) −11.8972 −0.402197
\(876\) 0 0
\(877\) 12.9270 0.436514 0.218257 0.975891i \(-0.429963\pi\)
0.218257 + 0.975891i \(0.429963\pi\)
\(878\) 0 0
\(879\) 18.5086 0.624279
\(880\) 0 0
\(881\) 52.1846 1.75814 0.879072 0.476689i \(-0.158163\pi\)
0.879072 + 0.476689i \(0.158163\pi\)
\(882\) 0 0
\(883\) 39.5787 1.33193 0.665965 0.745983i \(-0.268020\pi\)
0.665965 + 0.745983i \(0.268020\pi\)
\(884\) 0 0
\(885\) −57.8082 −1.94320
\(886\) 0 0
\(887\) −32.1055 −1.07800 −0.538998 0.842307i \(-0.681197\pi\)
−0.538998 + 0.842307i \(0.681197\pi\)
\(888\) 0 0
\(889\) 1.29911 0.0435707
\(890\) 0 0
\(891\) −10.7024 −0.358545
\(892\) 0 0
\(893\) 9.04823 0.302787
\(894\) 0 0
\(895\) 11.2585 0.376331
\(896\) 0 0
\(897\) −21.5327 −0.718956
\(898\) 0 0
\(899\) −2.23925 −0.0746831
\(900\) 0 0
\(901\) −0.939120 −0.0312866
\(902\) 0 0
\(903\) 27.6849 0.921296
\(904\) 0 0
\(905\) −18.5543 −0.616766
\(906\) 0 0
\(907\) −40.4698 −1.34378 −0.671889 0.740651i \(-0.734517\pi\)
−0.671889 + 0.740651i \(0.734517\pi\)
\(908\) 0 0
\(909\) −3.21664 −0.106689
\(910\) 0 0
\(911\) 13.5309 0.448297 0.224149 0.974555i \(-0.428040\pi\)
0.224149 + 0.974555i \(0.428040\pi\)
\(912\) 0 0
\(913\) −10.2760 −0.340087
\(914\) 0 0
\(915\) 84.4586 2.79211
\(916\) 0 0
\(917\) 17.4501 0.576253
\(918\) 0 0
\(919\) 40.0076 1.31973 0.659864 0.751385i \(-0.270614\pi\)
0.659864 + 0.751385i \(0.270614\pi\)
\(920\) 0 0
\(921\) −33.7293 −1.11142
\(922\) 0 0
\(923\) −10.5703 −0.347924
\(924\) 0 0
\(925\) 49.4142 1.62473
\(926\) 0 0
\(927\) 0.0230032 0.000755523 0
\(928\) 0 0
\(929\) −14.3525 −0.470889 −0.235444 0.971888i \(-0.575655\pi\)
−0.235444 + 0.971888i \(0.575655\pi\)
\(930\) 0 0
\(931\) 5.22450 0.171226
\(932\) 0 0
\(933\) −54.0779 −1.77043
\(934\) 0 0
\(935\) 4.34466 0.142086
\(936\) 0 0
\(937\) −3.23488 −0.105679 −0.0528394 0.998603i \(-0.516827\pi\)
−0.0528394 + 0.998603i \(0.516827\pi\)
\(938\) 0 0
\(939\) 42.8547 1.39851
\(940\) 0 0
\(941\) −47.5835 −1.55118 −0.775589 0.631238i \(-0.782547\pi\)
−0.775589 + 0.631238i \(0.782547\pi\)
\(942\) 0 0
\(943\) 80.5226 2.62218
\(944\) 0 0
\(945\) −61.9382 −2.01485
\(946\) 0 0
\(947\) −12.9219 −0.419905 −0.209953 0.977712i \(-0.567331\pi\)
−0.209953 + 0.977712i \(0.567331\pi\)
\(948\) 0 0
\(949\) −11.4060 −0.370254
\(950\) 0 0
\(951\) 30.9200 1.00265
\(952\) 0 0
\(953\) −53.1361 −1.72125 −0.860624 0.509241i \(-0.829926\pi\)
−0.860624 + 0.509241i \(0.829926\pi\)
\(954\) 0 0
\(955\) 48.9951 1.58545
\(956\) 0 0
\(957\) −11.1654 −0.360928
\(958\) 0 0
\(959\) −42.9566 −1.38714
\(960\) 0 0
\(961\) −30.8176 −0.994116
\(962\) 0 0
\(963\) 0.140048 0.00451298
\(964\) 0 0
\(965\) 25.8269 0.831398
\(966\) 0 0
\(967\) −22.1088 −0.710972 −0.355486 0.934682i \(-0.615685\pi\)
−0.355486 + 0.934682i \(0.615685\pi\)
\(968\) 0 0
\(969\) 1.73684 0.0557954
\(970\) 0 0
\(971\) −0.955264 −0.0306559 −0.0153279 0.999883i \(-0.504879\pi\)
−0.0153279 + 0.999883i \(0.504879\pi\)
\(972\) 0 0
\(973\) 36.3375 1.16493
\(974\) 0 0
\(975\) 20.0874 0.643311
\(976\) 0 0
\(977\) 20.5005 0.655868 0.327934 0.944701i \(-0.393648\pi\)
0.327934 + 0.944701i \(0.393648\pi\)
\(978\) 0 0
\(979\) −2.69180 −0.0860303
\(980\) 0 0
\(981\) −0.745044 −0.0237874
\(982\) 0 0
\(983\) −38.5967 −1.23104 −0.615522 0.788120i \(-0.711055\pi\)
−0.615522 + 0.788120i \(0.711055\pi\)
\(984\) 0 0
\(985\) 48.7133 1.55213
\(986\) 0 0
\(987\) −53.1876 −1.69298
\(988\) 0 0
\(989\) 30.4169 0.967200
\(990\) 0 0
\(991\) −30.8674 −0.980535 −0.490267 0.871572i \(-0.663101\pi\)
−0.490267 + 0.871572i \(0.663101\pi\)
\(992\) 0 0
\(993\) 47.2789 1.50035
\(994\) 0 0
\(995\) −7.76569 −0.246189
\(996\) 0 0
\(997\) 5.75663 0.182314 0.0911571 0.995837i \(-0.470943\pi\)
0.0911571 + 0.995837i \(0.470943\pi\)
\(998\) 0 0
\(999\) 43.7589 1.38447
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 \(a_p\))