Properties

Label 8047.2.a.b.1.13
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.50524 q^{2} -0.199696 q^{3} +4.27622 q^{4} -1.81098 q^{5} +0.500286 q^{6} -1.67033 q^{7} -5.70247 q^{8} -2.96012 q^{9} +O(q^{10})\) \(q-2.50524 q^{2} -0.199696 q^{3} +4.27622 q^{4} -1.81098 q^{5} +0.500286 q^{6} -1.67033 q^{7} -5.70247 q^{8} -2.96012 q^{9} +4.53694 q^{10} -2.18034 q^{11} -0.853944 q^{12} +1.00000 q^{13} +4.18458 q^{14} +0.361646 q^{15} +5.73360 q^{16} -5.47406 q^{17} +7.41581 q^{18} -5.01728 q^{19} -7.74415 q^{20} +0.333558 q^{21} +5.46227 q^{22} -7.67508 q^{23} +1.13876 q^{24} -1.72035 q^{25} -2.50524 q^{26} +1.19021 q^{27} -7.14270 q^{28} +6.13521 q^{29} -0.906008 q^{30} +6.78991 q^{31} -2.95911 q^{32} +0.435405 q^{33} +13.7138 q^{34} +3.02494 q^{35} -12.6581 q^{36} +2.77921 q^{37} +12.5695 q^{38} -0.199696 q^{39} +10.3271 q^{40} +9.42791 q^{41} -0.835643 q^{42} +9.65573 q^{43} -9.32361 q^{44} +5.36072 q^{45} +19.2279 q^{46} -10.9626 q^{47} -1.14498 q^{48} -4.21000 q^{49} +4.30989 q^{50} +1.09315 q^{51} +4.27622 q^{52} +5.00152 q^{53} -2.98177 q^{54} +3.94855 q^{55} +9.52500 q^{56} +1.00193 q^{57} -15.3702 q^{58} +9.88717 q^{59} +1.54648 q^{60} +4.28862 q^{61} -17.0103 q^{62} +4.94438 q^{63} -4.05394 q^{64} -1.81098 q^{65} -1.09079 q^{66} +8.87803 q^{67} -23.4083 q^{68} +1.53268 q^{69} -7.57818 q^{70} +10.8445 q^{71} +16.8800 q^{72} +13.1005 q^{73} -6.96258 q^{74} +0.343547 q^{75} -21.4550 q^{76} +3.64189 q^{77} +0.500286 q^{78} +1.61729 q^{79} -10.3834 q^{80} +8.64268 q^{81} -23.6192 q^{82} -7.95866 q^{83} +1.42637 q^{84} +9.91342 q^{85} -24.1899 q^{86} -1.22518 q^{87} +12.4333 q^{88} -6.16302 q^{89} -13.4299 q^{90} -1.67033 q^{91} -32.8203 q^{92} -1.35592 q^{93} +27.4640 q^{94} +9.08619 q^{95} +0.590922 q^{96} -2.74166 q^{97} +10.5470 q^{98} +6.45407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50524 −1.77147 −0.885735 0.464190i \(-0.846345\pi\)
−0.885735 + 0.464190i \(0.846345\pi\)
\(3\) −0.199696 −0.115295 −0.0576473 0.998337i \(-0.518360\pi\)
−0.0576473 + 0.998337i \(0.518360\pi\)
\(4\) 4.27622 2.13811
\(5\) −1.81098 −0.809895 −0.404947 0.914340i \(-0.632710\pi\)
−0.404947 + 0.914340i \(0.632710\pi\)
\(6\) 0.500286 0.204241
\(7\) −1.67033 −0.631326 −0.315663 0.948871i \(-0.602227\pi\)
−0.315663 + 0.948871i \(0.602227\pi\)
\(8\) −5.70247 −2.01613
\(9\) −2.96012 −0.986707
\(10\) 4.53694 1.43471
\(11\) −2.18034 −0.657397 −0.328699 0.944435i \(-0.606610\pi\)
−0.328699 + 0.944435i \(0.606610\pi\)
\(12\) −0.853944 −0.246512
\(13\) 1.00000 0.277350
\(14\) 4.18458 1.11837
\(15\) 0.361646 0.0933765
\(16\) 5.73360 1.43340
\(17\) −5.47406 −1.32765 −0.663827 0.747886i \(-0.731069\pi\)
−0.663827 + 0.747886i \(0.731069\pi\)
\(18\) 7.41581 1.74792
\(19\) −5.01728 −1.15104 −0.575521 0.817787i \(-0.695201\pi\)
−0.575521 + 0.817787i \(0.695201\pi\)
\(20\) −7.74415 −1.73164
\(21\) 0.333558 0.0727884
\(22\) 5.46227 1.16456
\(23\) −7.67508 −1.60036 −0.800182 0.599757i \(-0.795264\pi\)
−0.800182 + 0.599757i \(0.795264\pi\)
\(24\) 1.13876 0.232448
\(25\) −1.72035 −0.344070
\(26\) −2.50524 −0.491318
\(27\) 1.19021 0.229057
\(28\) −7.14270 −1.34984
\(29\) 6.13521 1.13928 0.569640 0.821895i \(-0.307083\pi\)
0.569640 + 0.821895i \(0.307083\pi\)
\(30\) −0.906008 −0.165414
\(31\) 6.78991 1.21950 0.609752 0.792592i \(-0.291269\pi\)
0.609752 + 0.792592i \(0.291269\pi\)
\(32\) −2.95911 −0.523101
\(33\) 0.435405 0.0757943
\(34\) 13.7138 2.35190
\(35\) 3.02494 0.511307
\(36\) −12.6581 −2.10969
\(37\) 2.77921 0.456899 0.228450 0.973556i \(-0.426634\pi\)
0.228450 + 0.973556i \(0.426634\pi\)
\(38\) 12.5695 2.03904
\(39\) −0.199696 −0.0319770
\(40\) 10.3271 1.63285
\(41\) 9.42791 1.47239 0.736196 0.676768i \(-0.236620\pi\)
0.736196 + 0.676768i \(0.236620\pi\)
\(42\) −0.835643 −0.128943
\(43\) 9.65573 1.47249 0.736243 0.676718i \(-0.236598\pi\)
0.736243 + 0.676718i \(0.236598\pi\)
\(44\) −9.32361 −1.40559
\(45\) 5.36072 0.799129
\(46\) 19.2279 2.83500
\(47\) −10.9626 −1.59906 −0.799532 0.600623i \(-0.794919\pi\)
−0.799532 + 0.600623i \(0.794919\pi\)
\(48\) −1.14498 −0.165263
\(49\) −4.21000 −0.601428
\(50\) 4.30989 0.609510
\(51\) 1.09315 0.153071
\(52\) 4.27622 0.593005
\(53\) 5.00152 0.687012 0.343506 0.939151i \(-0.388385\pi\)
0.343506 + 0.939151i \(0.388385\pi\)
\(54\) −2.98177 −0.405767
\(55\) 3.94855 0.532423
\(56\) 9.52500 1.27283
\(57\) 1.00193 0.132709
\(58\) −15.3702 −2.01820
\(59\) 9.88717 1.28720 0.643600 0.765362i \(-0.277440\pi\)
0.643600 + 0.765362i \(0.277440\pi\)
\(60\) 1.54648 0.199649
\(61\) 4.28862 0.549102 0.274551 0.961573i \(-0.411471\pi\)
0.274551 + 0.961573i \(0.411471\pi\)
\(62\) −17.0103 −2.16032
\(63\) 4.94438 0.622933
\(64\) −4.05394 −0.506743
\(65\) −1.81098 −0.224624
\(66\) −1.09079 −0.134267
\(67\) 8.87803 1.08462 0.542312 0.840177i \(-0.317549\pi\)
0.542312 + 0.840177i \(0.317549\pi\)
\(68\) −23.4083 −2.83867
\(69\) 1.53268 0.184513
\(70\) −7.57818 −0.905766
\(71\) 10.8445 1.28701 0.643504 0.765442i \(-0.277480\pi\)
0.643504 + 0.765442i \(0.277480\pi\)
\(72\) 16.8800 1.98933
\(73\) 13.1005 1.53330 0.766651 0.642064i \(-0.221921\pi\)
0.766651 + 0.642064i \(0.221921\pi\)
\(74\) −6.96258 −0.809384
\(75\) 0.343547 0.0396694
\(76\) −21.4550 −2.46105
\(77\) 3.64189 0.415032
\(78\) 0.500286 0.0566463
\(79\) 1.61729 0.181960 0.0909798 0.995853i \(-0.471000\pi\)
0.0909798 + 0.995853i \(0.471000\pi\)
\(80\) −10.3834 −1.16090
\(81\) 8.64268 0.960298
\(82\) −23.6192 −2.60830
\(83\) −7.95866 −0.873576 −0.436788 0.899564i \(-0.643884\pi\)
−0.436788 + 0.899564i \(0.643884\pi\)
\(84\) 1.42637 0.155630
\(85\) 9.91342 1.07526
\(86\) −24.1899 −2.60846
\(87\) −1.22518 −0.131353
\(88\) 12.4333 1.32540
\(89\) −6.16302 −0.653279 −0.326639 0.945149i \(-0.605916\pi\)
−0.326639 + 0.945149i \(0.605916\pi\)
\(90\) −13.4299 −1.41563
\(91\) −1.67033 −0.175098
\(92\) −32.8203 −3.42175
\(93\) −1.35592 −0.140602
\(94\) 27.4640 2.83270
\(95\) 9.08619 0.932223
\(96\) 0.590922 0.0603107
\(97\) −2.74166 −0.278373 −0.139187 0.990266i \(-0.544449\pi\)
−0.139187 + 0.990266i \(0.544449\pi\)
\(98\) 10.5470 1.06541
\(99\) 6.45407 0.648658
\(100\) −7.35659 −0.735659
\(101\) 5.41761 0.539073 0.269536 0.962990i \(-0.413130\pi\)
0.269536 + 0.962990i \(0.413130\pi\)
\(102\) −2.73860 −0.271162
\(103\) −3.68710 −0.363300 −0.181650 0.983363i \(-0.558144\pi\)
−0.181650 + 0.983363i \(0.558144\pi\)
\(104\) −5.70247 −0.559173
\(105\) −0.604068 −0.0589510
\(106\) −12.5300 −1.21702
\(107\) −7.66909 −0.741398 −0.370699 0.928753i \(-0.620882\pi\)
−0.370699 + 0.928753i \(0.620882\pi\)
\(108\) 5.08961 0.489748
\(109\) −8.41150 −0.805676 −0.402838 0.915271i \(-0.631976\pi\)
−0.402838 + 0.915271i \(0.631976\pi\)
\(110\) −9.89206 −0.943171
\(111\) −0.554997 −0.0526780
\(112\) −9.57701 −0.904942
\(113\) 5.77055 0.542848 0.271424 0.962460i \(-0.412505\pi\)
0.271424 + 0.962460i \(0.412505\pi\)
\(114\) −2.51007 −0.235090
\(115\) 13.8994 1.29613
\(116\) 26.2355 2.43590
\(117\) −2.96012 −0.273663
\(118\) −24.7697 −2.28024
\(119\) 9.14349 0.838182
\(120\) −2.06227 −0.188259
\(121\) −6.24612 −0.567829
\(122\) −10.7440 −0.972718
\(123\) −1.88272 −0.169759
\(124\) 29.0351 2.60743
\(125\) 12.1704 1.08856
\(126\) −12.3869 −1.10351
\(127\) 17.1758 1.52411 0.762055 0.647513i \(-0.224191\pi\)
0.762055 + 0.647513i \(0.224191\pi\)
\(128\) 16.0743 1.42078
\(129\) −1.92821 −0.169770
\(130\) 4.53694 0.397916
\(131\) −15.2987 −1.33665 −0.668326 0.743869i \(-0.732989\pi\)
−0.668326 + 0.743869i \(0.732989\pi\)
\(132\) 1.86189 0.162057
\(133\) 8.38051 0.726682
\(134\) −22.2416 −1.92138
\(135\) −2.15545 −0.185512
\(136\) 31.2157 2.67672
\(137\) −5.98203 −0.511079 −0.255540 0.966799i \(-0.582253\pi\)
−0.255540 + 0.966799i \(0.582253\pi\)
\(138\) −3.83973 −0.326860
\(139\) 8.03303 0.681353 0.340676 0.940181i \(-0.389344\pi\)
0.340676 + 0.940181i \(0.389344\pi\)
\(140\) 12.9353 1.09323
\(141\) 2.18920 0.184363
\(142\) −27.1681 −2.27990
\(143\) −2.18034 −0.182329
\(144\) −16.9722 −1.41435
\(145\) −11.1107 −0.922697
\(146\) −32.8200 −2.71620
\(147\) 0.840720 0.0693414
\(148\) 11.8845 0.976900
\(149\) −6.08884 −0.498817 −0.249408 0.968398i \(-0.580236\pi\)
−0.249408 + 0.968398i \(0.580236\pi\)
\(150\) −0.860668 −0.0702732
\(151\) 20.2753 1.64998 0.824989 0.565149i \(-0.191181\pi\)
0.824989 + 0.565149i \(0.191181\pi\)
\(152\) 28.6109 2.32065
\(153\) 16.2039 1.31001
\(154\) −9.12380 −0.735216
\(155\) −12.2964 −0.987670
\(156\) −0.853944 −0.0683702
\(157\) −1.45238 −0.115913 −0.0579564 0.998319i \(-0.518458\pi\)
−0.0579564 + 0.998319i \(0.518458\pi\)
\(158\) −4.05170 −0.322336
\(159\) −0.998784 −0.0792087
\(160\) 5.35888 0.423657
\(161\) 12.8199 1.01035
\(162\) −21.6520 −1.70114
\(163\) 19.2277 1.50603 0.753014 0.658005i \(-0.228599\pi\)
0.753014 + 0.658005i \(0.228599\pi\)
\(164\) 40.3158 3.14813
\(165\) −0.788510 −0.0613854
\(166\) 19.9383 1.54752
\(167\) −10.4563 −0.809131 −0.404566 0.914509i \(-0.632577\pi\)
−0.404566 + 0.914509i \(0.632577\pi\)
\(168\) −1.90211 −0.146751
\(169\) 1.00000 0.0769231
\(170\) −24.8355 −1.90479
\(171\) 14.8517 1.13574
\(172\) 41.2900 3.14833
\(173\) −16.8874 −1.28393 −0.641964 0.766735i \(-0.721880\pi\)
−0.641964 + 0.766735i \(0.721880\pi\)
\(174\) 3.06936 0.232687
\(175\) 2.87355 0.217220
\(176\) −12.5012 −0.942314
\(177\) −1.97443 −0.148407
\(178\) 15.4398 1.15726
\(179\) −5.00340 −0.373972 −0.186986 0.982363i \(-0.559872\pi\)
−0.186986 + 0.982363i \(0.559872\pi\)
\(180\) 22.9236 1.70863
\(181\) −24.3098 −1.80693 −0.903467 0.428658i \(-0.858987\pi\)
−0.903467 + 0.428658i \(0.858987\pi\)
\(182\) 4.18458 0.310181
\(183\) −0.856421 −0.0633085
\(184\) 43.7669 3.22654
\(185\) −5.03309 −0.370040
\(186\) 3.39690 0.249073
\(187\) 11.9353 0.872797
\(188\) −46.8786 −3.41897
\(189\) −1.98805 −0.144609
\(190\) −22.7631 −1.65141
\(191\) 17.1577 1.24149 0.620745 0.784013i \(-0.286830\pi\)
0.620745 + 0.784013i \(0.286830\pi\)
\(192\) 0.809556 0.0584247
\(193\) −17.4734 −1.25776 −0.628880 0.777502i \(-0.716486\pi\)
−0.628880 + 0.777502i \(0.716486\pi\)
\(194\) 6.86851 0.493130
\(195\) 0.361646 0.0258980
\(196\) −18.0029 −1.28592
\(197\) −19.8044 −1.41100 −0.705502 0.708708i \(-0.749278\pi\)
−0.705502 + 0.708708i \(0.749278\pi\)
\(198\) −16.1690 −1.14908
\(199\) 5.54259 0.392904 0.196452 0.980513i \(-0.437058\pi\)
0.196452 + 0.980513i \(0.437058\pi\)
\(200\) 9.81024 0.693689
\(201\) −1.77291 −0.125051
\(202\) −13.5724 −0.954952
\(203\) −10.2478 −0.719256
\(204\) 4.67454 0.327283
\(205\) −17.0738 −1.19248
\(206\) 9.23705 0.643576
\(207\) 22.7192 1.57909
\(208\) 5.73360 0.397554
\(209\) 10.9394 0.756692
\(210\) 1.51333 0.104430
\(211\) −8.92280 −0.614271 −0.307135 0.951666i \(-0.599370\pi\)
−0.307135 + 0.951666i \(0.599370\pi\)
\(212\) 21.3876 1.46891
\(213\) −2.16561 −0.148385
\(214\) 19.2129 1.31337
\(215\) −17.4863 −1.19256
\(216\) −6.78715 −0.461807
\(217\) −11.3414 −0.769904
\(218\) 21.0728 1.42723
\(219\) −2.61613 −0.176781
\(220\) 16.8849 1.13838
\(221\) −5.47406 −0.368225
\(222\) 1.39040 0.0933175
\(223\) 8.38021 0.561181 0.280590 0.959828i \(-0.409470\pi\)
0.280590 + 0.959828i \(0.409470\pi\)
\(224\) 4.94268 0.330247
\(225\) 5.09245 0.339496
\(226\) −14.4566 −0.961639
\(227\) −13.3752 −0.887741 −0.443871 0.896091i \(-0.646395\pi\)
−0.443871 + 0.896091i \(0.646395\pi\)
\(228\) 4.28447 0.283746
\(229\) 1.90637 0.125976 0.0629882 0.998014i \(-0.479937\pi\)
0.0629882 + 0.998014i \(0.479937\pi\)
\(230\) −34.8213 −2.29605
\(231\) −0.727271 −0.0478509
\(232\) −34.9858 −2.29693
\(233\) −26.1365 −1.71226 −0.856129 0.516763i \(-0.827137\pi\)
−0.856129 + 0.516763i \(0.827137\pi\)
\(234\) 7.41581 0.484787
\(235\) 19.8531 1.29507
\(236\) 42.2797 2.75217
\(237\) −0.322967 −0.0209790
\(238\) −22.9066 −1.48482
\(239\) −17.2966 −1.11883 −0.559413 0.828889i \(-0.688973\pi\)
−0.559413 + 0.828889i \(0.688973\pi\)
\(240\) 2.07353 0.133846
\(241\) 24.0170 1.54707 0.773536 0.633753i \(-0.218486\pi\)
0.773536 + 0.633753i \(0.218486\pi\)
\(242\) 15.6480 1.00589
\(243\) −5.29655 −0.339774
\(244\) 18.3391 1.17404
\(245\) 7.62422 0.487094
\(246\) 4.71665 0.300723
\(247\) −5.01728 −0.319242
\(248\) −38.7192 −2.45867
\(249\) 1.58931 0.100719
\(250\) −30.4898 −1.92834
\(251\) −4.70182 −0.296776 −0.148388 0.988929i \(-0.547408\pi\)
−0.148388 + 0.988929i \(0.547408\pi\)
\(252\) 21.1432 1.33190
\(253\) 16.7343 1.05207
\(254\) −43.0296 −2.69992
\(255\) −1.97967 −0.123972
\(256\) −32.1621 −2.01013
\(257\) 25.4987 1.59057 0.795284 0.606238i \(-0.207322\pi\)
0.795284 + 0.606238i \(0.207322\pi\)
\(258\) 4.83063 0.300742
\(259\) −4.64220 −0.288452
\(260\) −7.74415 −0.480272
\(261\) −18.1610 −1.12413
\(262\) 38.3268 2.36784
\(263\) −8.65026 −0.533398 −0.266699 0.963780i \(-0.585933\pi\)
−0.266699 + 0.963780i \(0.585933\pi\)
\(264\) −2.48288 −0.152811
\(265\) −9.05765 −0.556407
\(266\) −20.9952 −1.28730
\(267\) 1.23073 0.0753195
\(268\) 37.9644 2.31904
\(269\) −17.3019 −1.05492 −0.527458 0.849581i \(-0.676855\pi\)
−0.527458 + 0.849581i \(0.676855\pi\)
\(270\) 5.39992 0.328629
\(271\) −9.79266 −0.594862 −0.297431 0.954743i \(-0.596130\pi\)
−0.297431 + 0.954743i \(0.596130\pi\)
\(272\) −31.3861 −1.90306
\(273\) 0.333558 0.0201879
\(274\) 14.9864 0.905362
\(275\) 3.75095 0.226191
\(276\) 6.55408 0.394509
\(277\) −25.6167 −1.53916 −0.769578 0.638552i \(-0.779534\pi\)
−0.769578 + 0.638552i \(0.779534\pi\)
\(278\) −20.1247 −1.20700
\(279\) −20.0990 −1.20329
\(280\) −17.2496 −1.03086
\(281\) −11.7051 −0.698266 −0.349133 0.937073i \(-0.613524\pi\)
−0.349133 + 0.937073i \(0.613524\pi\)
\(282\) −5.48446 −0.326595
\(283\) −9.34959 −0.555775 −0.277888 0.960614i \(-0.589634\pi\)
−0.277888 + 0.960614i \(0.589634\pi\)
\(284\) 46.3736 2.75177
\(285\) −1.81448 −0.107480
\(286\) 5.46227 0.322991
\(287\) −15.7477 −0.929559
\(288\) 8.75931 0.516147
\(289\) 12.9653 0.762667
\(290\) 27.8350 1.63453
\(291\) 0.547499 0.0320949
\(292\) 56.0208 3.27837
\(293\) 28.0922 1.64116 0.820582 0.571529i \(-0.193650\pi\)
0.820582 + 0.571529i \(0.193650\pi\)
\(294\) −2.10620 −0.122836
\(295\) −17.9055 −1.04250
\(296\) −15.8483 −0.921167
\(297\) −2.59507 −0.150581
\(298\) 15.2540 0.883640
\(299\) −7.67508 −0.443861
\(300\) 1.46908 0.0848175
\(301\) −16.1283 −0.929618
\(302\) −50.7944 −2.92289
\(303\) −1.08188 −0.0621522
\(304\) −28.7671 −1.64990
\(305\) −7.76661 −0.444715
\(306\) −40.5946 −2.32064
\(307\) −8.69391 −0.496187 −0.248094 0.968736i \(-0.579804\pi\)
−0.248094 + 0.968736i \(0.579804\pi\)
\(308\) 15.5735 0.887383
\(309\) 0.736298 0.0418866
\(310\) 30.8054 1.74963
\(311\) −1.47728 −0.0837688 −0.0418844 0.999122i \(-0.513336\pi\)
−0.0418844 + 0.999122i \(0.513336\pi\)
\(312\) 1.13876 0.0644696
\(313\) −0.326946 −0.0184801 −0.00924005 0.999957i \(-0.502941\pi\)
−0.00924005 + 0.999957i \(0.502941\pi\)
\(314\) 3.63856 0.205336
\(315\) −8.95418 −0.504511
\(316\) 6.91590 0.389050
\(317\) 31.5000 1.76922 0.884609 0.466334i \(-0.154426\pi\)
0.884609 + 0.466334i \(0.154426\pi\)
\(318\) 2.50219 0.140316
\(319\) −13.3768 −0.748959
\(320\) 7.34161 0.410408
\(321\) 1.53149 0.0854792
\(322\) −32.1169 −1.78981
\(323\) 27.4649 1.52819
\(324\) 36.9580 2.05322
\(325\) −1.72035 −0.0954279
\(326\) −48.1699 −2.66788
\(327\) 1.67974 0.0928900
\(328\) −53.7623 −2.96853
\(329\) 18.3112 1.00953
\(330\) 1.97541 0.108743
\(331\) 21.4205 1.17738 0.588689 0.808360i \(-0.299644\pi\)
0.588689 + 0.808360i \(0.299644\pi\)
\(332\) −34.0330 −1.86780
\(333\) −8.22680 −0.450826
\(334\) 26.1955 1.43335
\(335\) −16.0779 −0.878432
\(336\) 1.91249 0.104335
\(337\) 8.42630 0.459010 0.229505 0.973308i \(-0.426289\pi\)
0.229505 + 0.973308i \(0.426289\pi\)
\(338\) −2.50524 −0.136267
\(339\) −1.15236 −0.0625874
\(340\) 42.3919 2.29903
\(341\) −14.8043 −0.801699
\(342\) −37.2072 −2.01193
\(343\) 18.7244 1.01102
\(344\) −55.0615 −2.96872
\(345\) −2.77566 −0.149436
\(346\) 42.3071 2.27444
\(347\) −4.41119 −0.236805 −0.118403 0.992966i \(-0.537777\pi\)
−0.118403 + 0.992966i \(0.537777\pi\)
\(348\) −5.23912 −0.280846
\(349\) 2.18734 0.117085 0.0585427 0.998285i \(-0.481355\pi\)
0.0585427 + 0.998285i \(0.481355\pi\)
\(350\) −7.19894 −0.384799
\(351\) 1.19021 0.0635289
\(352\) 6.45186 0.343885
\(353\) −2.53760 −0.135063 −0.0675315 0.997717i \(-0.521512\pi\)
−0.0675315 + 0.997717i \(0.521512\pi\)
\(354\) 4.94642 0.262899
\(355\) −19.6392 −1.04234
\(356\) −26.3544 −1.39678
\(357\) −1.82592 −0.0966379
\(358\) 12.5347 0.662480
\(359\) 13.5734 0.716378 0.358189 0.933649i \(-0.383394\pi\)
0.358189 + 0.933649i \(0.383394\pi\)
\(360\) −30.5693 −1.61115
\(361\) 6.17306 0.324898
\(362\) 60.9019 3.20093
\(363\) 1.24733 0.0654676
\(364\) −7.14270 −0.374379
\(365\) −23.7248 −1.24181
\(366\) 2.14554 0.112149
\(367\) −29.6207 −1.54619 −0.773094 0.634291i \(-0.781292\pi\)
−0.773094 + 0.634291i \(0.781292\pi\)
\(368\) −44.0058 −2.29396
\(369\) −27.9078 −1.45282
\(370\) 12.6091 0.655516
\(371\) −8.35419 −0.433728
\(372\) −5.79820 −0.300623
\(373\) −23.3609 −1.20958 −0.604792 0.796383i \(-0.706744\pi\)
−0.604792 + 0.796383i \(0.706744\pi\)
\(374\) −29.9008 −1.54613
\(375\) −2.43039 −0.125505
\(376\) 62.5141 3.22392
\(377\) 6.13521 0.315979
\(378\) 4.98053 0.256171
\(379\) 2.29228 0.117747 0.0588733 0.998265i \(-0.481249\pi\)
0.0588733 + 0.998265i \(0.481249\pi\)
\(380\) 38.8545 1.99319
\(381\) −3.42995 −0.175722
\(382\) −42.9842 −2.19926
\(383\) 5.12776 0.262016 0.131008 0.991381i \(-0.458179\pi\)
0.131008 + 0.991381i \(0.458179\pi\)
\(384\) −3.20997 −0.163808
\(385\) −6.59539 −0.336132
\(386\) 43.7750 2.22809
\(387\) −28.5821 −1.45291
\(388\) −11.7239 −0.595193
\(389\) 6.32423 0.320651 0.160326 0.987064i \(-0.448746\pi\)
0.160326 + 0.987064i \(0.448746\pi\)
\(390\) −0.906008 −0.0458775
\(391\) 42.0138 2.12473
\(392\) 24.0074 1.21256
\(393\) 3.05509 0.154109
\(394\) 49.6147 2.49955
\(395\) −2.92889 −0.147368
\(396\) 27.5990 1.38690
\(397\) −8.25134 −0.414123 −0.207061 0.978328i \(-0.566390\pi\)
−0.207061 + 0.978328i \(0.566390\pi\)
\(398\) −13.8855 −0.696017
\(399\) −1.67355 −0.0837825
\(400\) −9.86381 −0.493190
\(401\) 17.6036 0.879082 0.439541 0.898222i \(-0.355141\pi\)
0.439541 + 0.898222i \(0.355141\pi\)
\(402\) 4.44156 0.221525
\(403\) 6.78991 0.338230
\(404\) 23.1669 1.15260
\(405\) −15.6517 −0.777741
\(406\) 25.6732 1.27414
\(407\) −6.05962 −0.300364
\(408\) −6.23364 −0.308611
\(409\) 29.1750 1.44261 0.721304 0.692618i \(-0.243543\pi\)
0.721304 + 0.692618i \(0.243543\pi\)
\(410\) 42.7738 2.11245
\(411\) 1.19459 0.0589246
\(412\) −15.7668 −0.776776
\(413\) −16.5148 −0.812642
\(414\) −56.9169 −2.79731
\(415\) 14.4130 0.707505
\(416\) −2.95911 −0.145082
\(417\) −1.60416 −0.0785563
\(418\) −27.4057 −1.34046
\(419\) 13.6855 0.668579 0.334289 0.942470i \(-0.391504\pi\)
0.334289 + 0.942470i \(0.391504\pi\)
\(420\) −2.58312 −0.126044
\(421\) 17.8598 0.870432 0.435216 0.900326i \(-0.356672\pi\)
0.435216 + 0.900326i \(0.356672\pi\)
\(422\) 22.3537 1.08816
\(423\) 32.4507 1.57781
\(424\) −28.5210 −1.38510
\(425\) 9.41730 0.456806
\(426\) 5.42537 0.262860
\(427\) −7.16342 −0.346662
\(428\) −32.7947 −1.58519
\(429\) 0.435405 0.0210216
\(430\) 43.8074 2.11258
\(431\) 7.48144 0.360368 0.180184 0.983633i \(-0.442331\pi\)
0.180184 + 0.983633i \(0.442331\pi\)
\(432\) 6.82421 0.328330
\(433\) 15.7749 0.758095 0.379048 0.925377i \(-0.376252\pi\)
0.379048 + 0.925377i \(0.376252\pi\)
\(434\) 28.4129 1.36386
\(435\) 2.21877 0.106382
\(436\) −35.9694 −1.72262
\(437\) 38.5080 1.84209
\(438\) 6.55402 0.313163
\(439\) −19.0397 −0.908716 −0.454358 0.890819i \(-0.650131\pi\)
−0.454358 + 0.890819i \(0.650131\pi\)
\(440\) −22.5165 −1.07343
\(441\) 12.4621 0.593433
\(442\) 13.7138 0.652300
\(443\) 10.6043 0.503826 0.251913 0.967750i \(-0.418940\pi\)
0.251913 + 0.967750i \(0.418940\pi\)
\(444\) −2.37329 −0.112631
\(445\) 11.1611 0.529087
\(446\) −20.9944 −0.994115
\(447\) 1.21592 0.0575109
\(448\) 6.77142 0.319920
\(449\) 31.2631 1.47540 0.737699 0.675130i \(-0.235912\pi\)
0.737699 + 0.675130i \(0.235912\pi\)
\(450\) −12.7578 −0.601408
\(451\) −20.5560 −0.967946
\(452\) 24.6761 1.16067
\(453\) −4.04889 −0.190234
\(454\) 33.5080 1.57261
\(455\) 3.02494 0.141811
\(456\) −5.71348 −0.267558
\(457\) 39.2077 1.83406 0.917030 0.398819i \(-0.130580\pi\)
0.917030 + 0.398819i \(0.130580\pi\)
\(458\) −4.77591 −0.223164
\(459\) −6.51530 −0.304108
\(460\) 59.4369 2.77126
\(461\) 8.61472 0.401227 0.200614 0.979670i \(-0.435706\pi\)
0.200614 + 0.979670i \(0.435706\pi\)
\(462\) 1.82199 0.0847665
\(463\) −11.9212 −0.554023 −0.277012 0.960867i \(-0.589344\pi\)
−0.277012 + 0.960867i \(0.589344\pi\)
\(464\) 35.1768 1.63304
\(465\) 2.45554 0.113873
\(466\) 65.4781 3.03321
\(467\) 22.9991 1.06427 0.532135 0.846660i \(-0.321390\pi\)
0.532135 + 0.846660i \(0.321390\pi\)
\(468\) −12.6581 −0.585122
\(469\) −14.8292 −0.684751
\(470\) −49.7368 −2.29419
\(471\) 0.290035 0.0133641
\(472\) −56.3813 −2.59516
\(473\) −21.0528 −0.968008
\(474\) 0.809109 0.0371636
\(475\) 8.63148 0.396039
\(476\) 39.0996 1.79213
\(477\) −14.8051 −0.677879
\(478\) 43.3322 1.98197
\(479\) −24.7332 −1.13009 −0.565044 0.825061i \(-0.691141\pi\)
−0.565044 + 0.825061i \(0.691141\pi\)
\(480\) −1.07015 −0.0488453
\(481\) 2.77921 0.126721
\(482\) −60.1683 −2.74059
\(483\) −2.56009 −0.116488
\(484\) −26.7098 −1.21408
\(485\) 4.96509 0.225453
\(486\) 13.2691 0.601899
\(487\) 15.8497 0.718217 0.359109 0.933296i \(-0.383081\pi\)
0.359109 + 0.933296i \(0.383081\pi\)
\(488\) −24.4557 −1.10706
\(489\) −3.83969 −0.173637
\(490\) −19.1005 −0.862872
\(491\) −0.602420 −0.0271868 −0.0135934 0.999908i \(-0.504327\pi\)
−0.0135934 + 0.999908i \(0.504327\pi\)
\(492\) −8.05090 −0.362963
\(493\) −33.5845 −1.51257
\(494\) 12.5695 0.565527
\(495\) −11.6882 −0.525345
\(496\) 38.9307 1.74804
\(497\) −18.1139 −0.812522
\(498\) −3.98161 −0.178420
\(499\) −22.1344 −0.990870 −0.495435 0.868645i \(-0.664991\pi\)
−0.495435 + 0.868645i \(0.664991\pi\)
\(500\) 52.0434 2.32745
\(501\) 2.08808 0.0932885
\(502\) 11.7792 0.525730
\(503\) 34.3426 1.53126 0.765630 0.643281i \(-0.222427\pi\)
0.765630 + 0.643281i \(0.222427\pi\)
\(504\) −28.1952 −1.25591
\(505\) −9.81119 −0.436592
\(506\) −41.9233 −1.86372
\(507\) −0.199696 −0.00886881
\(508\) 73.4476 3.25871
\(509\) −37.0427 −1.64189 −0.820945 0.571007i \(-0.806553\pi\)
−0.820945 + 0.571007i \(0.806553\pi\)
\(510\) 4.95954 0.219612
\(511\) −21.8822 −0.968013
\(512\) 48.4250 2.14010
\(513\) −5.97163 −0.263654
\(514\) −63.8804 −2.81764
\(515\) 6.67726 0.294235
\(516\) −8.24545 −0.362986
\(517\) 23.9023 1.05122
\(518\) 11.6298 0.510984
\(519\) 3.37235 0.148030
\(520\) 10.3271 0.452871
\(521\) 40.2968 1.76544 0.882718 0.469904i \(-0.155711\pi\)
0.882718 + 0.469904i \(0.155711\pi\)
\(522\) 45.4975 1.99137
\(523\) −26.1770 −1.14464 −0.572320 0.820030i \(-0.693956\pi\)
−0.572320 + 0.820030i \(0.693956\pi\)
\(524\) −65.4205 −2.85791
\(525\) −0.573837 −0.0250443
\(526\) 21.6710 0.944898
\(527\) −37.1684 −1.61908
\(528\) 2.49644 0.108644
\(529\) 35.9068 1.56116
\(530\) 22.6916 0.985659
\(531\) −29.2672 −1.27009
\(532\) 35.8369 1.55373
\(533\) 9.42791 0.408368
\(534\) −3.08327 −0.133426
\(535\) 13.8886 0.600455
\(536\) −50.6267 −2.18674
\(537\) 0.999159 0.0431169
\(538\) 43.3454 1.86875
\(539\) 9.17922 0.395377
\(540\) −9.21718 −0.396644
\(541\) 15.7254 0.676086 0.338043 0.941131i \(-0.390235\pi\)
0.338043 + 0.941131i \(0.390235\pi\)
\(542\) 24.5329 1.05378
\(543\) 4.85457 0.208330
\(544\) 16.1983 0.694497
\(545\) 15.2331 0.652513
\(546\) −0.835643 −0.0357622
\(547\) 18.5417 0.792788 0.396394 0.918081i \(-0.370261\pi\)
0.396394 + 0.918081i \(0.370261\pi\)
\(548\) −25.5805 −1.09274
\(549\) −12.6948 −0.541803
\(550\) −9.39702 −0.400690
\(551\) −30.7820 −1.31136
\(552\) −8.74007 −0.372002
\(553\) −2.70141 −0.114876
\(554\) 64.1759 2.72657
\(555\) 1.00509 0.0426636
\(556\) 34.3510 1.45681
\(557\) −18.3607 −0.777969 −0.388985 0.921244i \(-0.627174\pi\)
−0.388985 + 0.921244i \(0.627174\pi\)
\(558\) 50.3527 2.13160
\(559\) 9.65573 0.408394
\(560\) 17.3438 0.732908
\(561\) −2.38343 −0.100629
\(562\) 29.3240 1.23696
\(563\) −8.23909 −0.347236 −0.173618 0.984813i \(-0.555546\pi\)
−0.173618 + 0.984813i \(0.555546\pi\)
\(564\) 9.36148 0.394189
\(565\) −10.4504 −0.439650
\(566\) 23.4230 0.984540
\(567\) −14.4361 −0.606261
\(568\) −61.8406 −2.59477
\(569\) −20.3979 −0.855125 −0.427563 0.903986i \(-0.640628\pi\)
−0.427563 + 0.903986i \(0.640628\pi\)
\(570\) 4.54569 0.190398
\(571\) 36.7042 1.53602 0.768011 0.640437i \(-0.221247\pi\)
0.768011 + 0.640437i \(0.221247\pi\)
\(572\) −9.32361 −0.389840
\(573\) −3.42633 −0.143137
\(574\) 39.4518 1.64669
\(575\) 13.2038 0.550637
\(576\) 12.0002 0.500007
\(577\) −37.8458 −1.57554 −0.787770 0.615970i \(-0.788764\pi\)
−0.787770 + 0.615970i \(0.788764\pi\)
\(578\) −32.4813 −1.35104
\(579\) 3.48936 0.145013
\(580\) −47.5119 −1.97283
\(581\) 13.2936 0.551511
\(582\) −1.37161 −0.0568553
\(583\) −10.9050 −0.451640
\(584\) −74.7054 −3.09133
\(585\) 5.36072 0.221639
\(586\) −70.3776 −2.90727
\(587\) 5.02106 0.207241 0.103621 0.994617i \(-0.466957\pi\)
0.103621 + 0.994617i \(0.466957\pi\)
\(588\) 3.59510 0.148259
\(589\) −34.0669 −1.40370
\(590\) 44.8575 1.84675
\(591\) 3.95486 0.162681
\(592\) 15.9349 0.654920
\(593\) −15.2200 −0.625012 −0.312506 0.949916i \(-0.601168\pi\)
−0.312506 + 0.949916i \(0.601168\pi\)
\(594\) 6.50126 0.266750
\(595\) −16.5587 −0.678840
\(596\) −26.0372 −1.06652
\(597\) −1.10683 −0.0452997
\(598\) 19.2279 0.786287
\(599\) 28.8366 1.17823 0.589115 0.808049i \(-0.299476\pi\)
0.589115 + 0.808049i \(0.299476\pi\)
\(600\) −1.95907 −0.0799786
\(601\) 17.2014 0.701658 0.350829 0.936439i \(-0.385900\pi\)
0.350829 + 0.936439i \(0.385900\pi\)
\(602\) 40.4051 1.64679
\(603\) −26.2801 −1.07021
\(604\) 86.7015 3.52783
\(605\) 11.3116 0.459882
\(606\) 2.71036 0.110101
\(607\) 17.8409 0.724140 0.362070 0.932151i \(-0.382070\pi\)
0.362070 + 0.932151i \(0.382070\pi\)
\(608\) 14.8467 0.602111
\(609\) 2.04645 0.0829263
\(610\) 19.4572 0.787800
\(611\) −10.9626 −0.443501
\(612\) 69.2913 2.80094
\(613\) 23.8354 0.962702 0.481351 0.876528i \(-0.340146\pi\)
0.481351 + 0.876528i \(0.340146\pi\)
\(614\) 21.7803 0.878981
\(615\) 3.40956 0.137487
\(616\) −20.7677 −0.836756
\(617\) −26.0279 −1.04784 −0.523921 0.851767i \(-0.675531\pi\)
−0.523921 + 0.851767i \(0.675531\pi\)
\(618\) −1.84460 −0.0742008
\(619\) 1.00000 0.0401934
\(620\) −52.5821 −2.11175
\(621\) −9.13497 −0.366574
\(622\) 3.70094 0.148394
\(623\) 10.2943 0.412432
\(624\) −1.14498 −0.0458358
\(625\) −13.4386 −0.537546
\(626\) 0.819079 0.0327370
\(627\) −2.18455 −0.0872425
\(628\) −6.21071 −0.247834
\(629\) −15.2136 −0.606604
\(630\) 22.4323 0.893726
\(631\) 0.213627 0.00850434 0.00425217 0.999991i \(-0.498646\pi\)
0.00425217 + 0.999991i \(0.498646\pi\)
\(632\) −9.22256 −0.366854
\(633\) 1.78185 0.0708221
\(634\) −78.9151 −3.13412
\(635\) −31.1051 −1.23437
\(636\) −4.27102 −0.169357
\(637\) −4.21000 −0.166806
\(638\) 33.5122 1.32676
\(639\) −32.1011 −1.26990
\(640\) −29.1102 −1.15068
\(641\) 23.5677 0.930870 0.465435 0.885082i \(-0.345898\pi\)
0.465435 + 0.885082i \(0.345898\pi\)
\(642\) −3.83674 −0.151424
\(643\) 11.3833 0.448913 0.224456 0.974484i \(-0.427939\pi\)
0.224456 + 0.974484i \(0.427939\pi\)
\(644\) 54.8207 2.16024
\(645\) 3.49195 0.137496
\(646\) −68.8061 −2.70714
\(647\) −40.4963 −1.59207 −0.796036 0.605249i \(-0.793074\pi\)
−0.796036 + 0.605249i \(0.793074\pi\)
\(648\) −49.2846 −1.93608
\(649\) −21.5574 −0.846202
\(650\) 4.30989 0.169048
\(651\) 2.26483 0.0887658
\(652\) 82.2217 3.22005
\(653\) −32.9583 −1.28976 −0.644879 0.764284i \(-0.723092\pi\)
−0.644879 + 0.764284i \(0.723092\pi\)
\(654\) −4.20816 −0.164552
\(655\) 27.7056 1.08255
\(656\) 54.0559 2.11053
\(657\) −38.7792 −1.51292
\(658\) −45.8740 −1.78835
\(659\) 1.01809 0.0396592 0.0198296 0.999803i \(-0.493688\pi\)
0.0198296 + 0.999803i \(0.493688\pi\)
\(660\) −3.37184 −0.131249
\(661\) −41.5968 −1.61793 −0.808963 0.587859i \(-0.799971\pi\)
−0.808963 + 0.587859i \(0.799971\pi\)
\(662\) −53.6635 −2.08569
\(663\) 1.09315 0.0424544
\(664\) 45.3840 1.76124
\(665\) −15.1769 −0.588536
\(666\) 20.6101 0.798625
\(667\) −47.0882 −1.82326
\(668\) −44.7133 −1.73001
\(669\) −1.67350 −0.0647011
\(670\) 40.2791 1.55612
\(671\) −9.35066 −0.360978
\(672\) −0.987034 −0.0380757
\(673\) −40.3372 −1.55488 −0.777442 0.628954i \(-0.783483\pi\)
−0.777442 + 0.628954i \(0.783483\pi\)
\(674\) −21.1099 −0.813122
\(675\) −2.04758 −0.0788115
\(676\) 4.27622 0.164470
\(677\) −14.3476 −0.551421 −0.275711 0.961241i \(-0.588913\pi\)
−0.275711 + 0.961241i \(0.588913\pi\)
\(678\) 2.88693 0.110872
\(679\) 4.57948 0.175744
\(680\) −56.5309 −2.16786
\(681\) 2.67097 0.102352
\(682\) 37.0883 1.42019
\(683\) −26.7994 −1.02545 −0.512725 0.858553i \(-0.671364\pi\)
−0.512725 + 0.858553i \(0.671364\pi\)
\(684\) 63.5093 2.42834
\(685\) 10.8333 0.413920
\(686\) −46.9091 −1.79100
\(687\) −0.380694 −0.0145244
\(688\) 55.3621 2.11066
\(689\) 5.00152 0.190543
\(690\) 6.95368 0.264722
\(691\) 51.1814 1.94703 0.973515 0.228622i \(-0.0734218\pi\)
0.973515 + 0.228622i \(0.0734218\pi\)
\(692\) −72.2144 −2.74518
\(693\) −10.7804 −0.409515
\(694\) 11.0511 0.419493
\(695\) −14.5477 −0.551824
\(696\) 6.98653 0.264824
\(697\) −51.6089 −1.95483
\(698\) −5.47980 −0.207413
\(699\) 5.21935 0.197414
\(700\) 12.2879 0.464441
\(701\) −13.1856 −0.498012 −0.249006 0.968502i \(-0.580104\pi\)
−0.249006 + 0.968502i \(0.580104\pi\)
\(702\) −2.98177 −0.112540
\(703\) −13.9441 −0.525910
\(704\) 8.83897 0.333131
\(705\) −3.96459 −0.149315
\(706\) 6.35730 0.239260
\(707\) −9.04920 −0.340330
\(708\) −8.44309 −0.317311
\(709\) 42.3122 1.58907 0.794533 0.607221i \(-0.207716\pi\)
0.794533 + 0.607221i \(0.207716\pi\)
\(710\) 49.2009 1.84648
\(711\) −4.78738 −0.179541
\(712\) 35.1444 1.31709
\(713\) −52.1131 −1.95165
\(714\) 4.57436 0.171191
\(715\) 3.94855 0.147667
\(716\) −21.3956 −0.799592
\(717\) 3.45407 0.128995
\(718\) −34.0047 −1.26904
\(719\) −26.5241 −0.989182 −0.494591 0.869126i \(-0.664682\pi\)
−0.494591 + 0.869126i \(0.664682\pi\)
\(720\) 30.7362 1.14547
\(721\) 6.15867 0.229361
\(722\) −15.4650 −0.575548
\(723\) −4.79610 −0.178369
\(724\) −103.954 −3.86342
\(725\) −10.5547 −0.391992
\(726\) −3.12485 −0.115974
\(727\) 24.4085 0.905262 0.452631 0.891698i \(-0.350486\pi\)
0.452631 + 0.891698i \(0.350486\pi\)
\(728\) 9.52500 0.353020
\(729\) −24.8704 −0.921124
\(730\) 59.4363 2.19984
\(731\) −52.8561 −1.95495
\(732\) −3.66224 −0.135360
\(733\) 16.4822 0.608782 0.304391 0.952547i \(-0.401547\pi\)
0.304391 + 0.952547i \(0.401547\pi\)
\(734\) 74.2070 2.73903
\(735\) −1.52253 −0.0561592
\(736\) 22.7114 0.837152
\(737\) −19.3571 −0.713029
\(738\) 69.9156 2.57363
\(739\) 3.85289 0.141731 0.0708654 0.997486i \(-0.477424\pi\)
0.0708654 + 0.997486i \(0.477424\pi\)
\(740\) −21.5226 −0.791187
\(741\) 1.00193 0.0368068
\(742\) 20.9292 0.768336
\(743\) 28.3467 1.03994 0.519970 0.854184i \(-0.325943\pi\)
0.519970 + 0.854184i \(0.325943\pi\)
\(744\) 7.73208 0.283472
\(745\) 11.0268 0.403989
\(746\) 58.5247 2.14274
\(747\) 23.5586 0.861964
\(748\) 51.0380 1.86613
\(749\) 12.8099 0.468064
\(750\) 6.08869 0.222328
\(751\) 47.2765 1.72515 0.862573 0.505933i \(-0.168852\pi\)
0.862573 + 0.505933i \(0.168852\pi\)
\(752\) −62.8554 −2.29210
\(753\) 0.938934 0.0342167
\(754\) −15.3702 −0.559748
\(755\) −36.7181 −1.33631
\(756\) −8.50133 −0.309190
\(757\) −25.9581 −0.943464 −0.471732 0.881742i \(-0.656371\pi\)
−0.471732 + 0.881742i \(0.656371\pi\)
\(758\) −5.74271 −0.208585
\(759\) −3.34177 −0.121298
\(760\) −51.8137 −1.87948
\(761\) 29.6907 1.07629 0.538143 0.842853i \(-0.319126\pi\)
0.538143 + 0.842853i \(0.319126\pi\)
\(762\) 8.59284 0.311286
\(763\) 14.0500 0.508644
\(764\) 73.3702 2.65444
\(765\) −29.3449 −1.06097
\(766\) −12.8463 −0.464154
\(767\) 9.88717 0.357005
\(768\) 6.42264 0.231757
\(769\) −12.3306 −0.444652 −0.222326 0.974972i \(-0.571365\pi\)
−0.222326 + 0.974972i \(0.571365\pi\)
\(770\) 16.5230 0.595448
\(771\) −5.09200 −0.183384
\(772\) −74.7199 −2.68923
\(773\) −35.0532 −1.26078 −0.630388 0.776280i \(-0.717104\pi\)
−0.630388 + 0.776280i \(0.717104\pi\)
\(774\) 71.6051 2.57379
\(775\) −11.6810 −0.419595
\(776\) 15.6342 0.561236
\(777\) 0.927029 0.0332570
\(778\) −15.8437 −0.568024
\(779\) −47.3024 −1.69479
\(780\) 1.54648 0.0553727
\(781\) −23.6448 −0.846076
\(782\) −105.255 −3.76390
\(783\) 7.30220 0.260959
\(784\) −24.1384 −0.862087
\(785\) 2.63024 0.0938772
\(786\) −7.65372 −0.272999
\(787\) −23.3001 −0.830558 −0.415279 0.909694i \(-0.636316\pi\)
−0.415279 + 0.909694i \(0.636316\pi\)
\(788\) −84.6878 −3.01688
\(789\) 1.72742 0.0614979
\(790\) 7.33756 0.261059
\(791\) −9.63872 −0.342714
\(792\) −36.8041 −1.30778
\(793\) 4.28862 0.152294
\(794\) 20.6716 0.733606
\(795\) 1.80878 0.0641507
\(796\) 23.7013 0.840071
\(797\) 38.2905 1.35632 0.678159 0.734915i \(-0.262778\pi\)
0.678159 + 0.734915i \(0.262778\pi\)
\(798\) 4.19265 0.148418
\(799\) 60.0101 2.12301
\(800\) 5.09070 0.179983
\(801\) 18.2433 0.644595
\(802\) −44.1012 −1.55727
\(803\) −28.5636 −1.00799
\(804\) −7.58134 −0.267373
\(805\) −23.2166 −0.818278
\(806\) −17.0103 −0.599164
\(807\) 3.45512 0.121626
\(808\) −30.8938 −1.08684
\(809\) −12.9823 −0.456434 −0.228217 0.973610i \(-0.573290\pi\)
−0.228217 + 0.973610i \(0.573290\pi\)
\(810\) 39.2113 1.37774
\(811\) 0.891683 0.0313112 0.0156556 0.999877i \(-0.495016\pi\)
0.0156556 + 0.999877i \(0.495016\pi\)
\(812\) −43.8219 −1.53785
\(813\) 1.95556 0.0685843
\(814\) 15.1808 0.532086
\(815\) −34.8209 −1.21972
\(816\) 6.26768 0.219413
\(817\) −48.4455 −1.69489
\(818\) −73.0902 −2.55554
\(819\) 4.94438 0.172771
\(820\) −73.0111 −2.54966
\(821\) 7.76982 0.271169 0.135584 0.990766i \(-0.456709\pi\)
0.135584 + 0.990766i \(0.456709\pi\)
\(822\) −2.99273 −0.104383
\(823\) −30.8395 −1.07500 −0.537500 0.843264i \(-0.680631\pi\)
−0.537500 + 0.843264i \(0.680631\pi\)
\(824\) 21.0255 0.732459
\(825\) −0.749050 −0.0260786
\(826\) 41.3736 1.43957
\(827\) 26.2937 0.914322 0.457161 0.889384i \(-0.348866\pi\)
0.457161 + 0.889384i \(0.348866\pi\)
\(828\) 97.1521 3.37627
\(829\) −44.8084 −1.55626 −0.778129 0.628104i \(-0.783831\pi\)
−0.778129 + 0.628104i \(0.783831\pi\)
\(830\) −36.1079 −1.25332
\(831\) 5.11555 0.177456
\(832\) −4.05394 −0.140545
\(833\) 23.0458 0.798489
\(834\) 4.01881 0.139160
\(835\) 18.9361 0.655311
\(836\) 46.7791 1.61789
\(837\) 8.08144 0.279335
\(838\) −34.2854 −1.18437
\(839\) 34.8353 1.20265 0.601323 0.799006i \(-0.294640\pi\)
0.601323 + 0.799006i \(0.294640\pi\)
\(840\) 3.44468 0.118853
\(841\) 8.64076 0.297957
\(842\) −44.7430 −1.54195
\(843\) 2.33746 0.0805063
\(844\) −38.1558 −1.31338
\(845\) −1.81098 −0.0622996
\(846\) −81.2968 −2.79504
\(847\) 10.4331 0.358485
\(848\) 28.6767 0.984763
\(849\) 1.86708 0.0640779
\(850\) −23.5926 −0.809219
\(851\) −21.3306 −0.731205
\(852\) −9.26062 −0.317264
\(853\) 7.73941 0.264992 0.132496 0.991184i \(-0.457701\pi\)
0.132496 + 0.991184i \(0.457701\pi\)
\(854\) 17.9461 0.614102
\(855\) −26.8962 −0.919831
\(856\) 43.7327 1.49475
\(857\) 37.5440 1.28248 0.641240 0.767340i \(-0.278420\pi\)
0.641240 + 0.767340i \(0.278420\pi\)
\(858\) −1.09079 −0.0372391
\(859\) −12.7009 −0.433350 −0.216675 0.976244i \(-0.569521\pi\)
−0.216675 + 0.976244i \(0.569521\pi\)
\(860\) −74.7754 −2.54982
\(861\) 3.14476 0.107173
\(862\) −18.7428 −0.638382
\(863\) 20.4656 0.696657 0.348329 0.937372i \(-0.386749\pi\)
0.348329 + 0.937372i \(0.386749\pi\)
\(864\) −3.52197 −0.119820
\(865\) 30.5828 1.03985
\(866\) −39.5200 −1.34294
\(867\) −2.58913 −0.0879314
\(868\) −48.4983 −1.64614
\(869\) −3.52625 −0.119620
\(870\) −5.55855 −0.188452
\(871\) 8.87803 0.300821
\(872\) 47.9663 1.62434
\(873\) 8.11565 0.274673
\(874\) −96.4716 −3.26320
\(875\) −20.3286 −0.687233
\(876\) −11.1871 −0.377978
\(877\) −18.1890 −0.614198 −0.307099 0.951678i \(-0.599358\pi\)
−0.307099 + 0.951678i \(0.599358\pi\)
\(878\) 47.6990 1.60976
\(879\) −5.60990 −0.189217
\(880\) 22.6394 0.763175
\(881\) −43.5593 −1.46755 −0.733775 0.679392i \(-0.762243\pi\)
−0.733775 + 0.679392i \(0.762243\pi\)
\(882\) −31.2205 −1.05125
\(883\) −25.1561 −0.846569 −0.423285 0.905997i \(-0.639123\pi\)
−0.423285 + 0.905997i \(0.639123\pi\)
\(884\) −23.4083 −0.787306
\(885\) 3.57565 0.120194
\(886\) −26.5663 −0.892513
\(887\) −34.8592 −1.17046 −0.585229 0.810868i \(-0.698995\pi\)
−0.585229 + 0.810868i \(0.698995\pi\)
\(888\) 3.16485 0.106206
\(889\) −28.6893 −0.962209
\(890\) −27.9612 −0.937262
\(891\) −18.8440 −0.631297
\(892\) 35.8356 1.19987
\(893\) 55.0026 1.84059
\(894\) −3.04616 −0.101879
\(895\) 9.06106 0.302878
\(896\) −26.8494 −0.896975
\(897\) 1.53268 0.0511748
\(898\) −78.3216 −2.61362
\(899\) 41.6575 1.38936
\(900\) 21.7764 0.725880
\(901\) −27.3786 −0.912114
\(902\) 51.4978 1.71469
\(903\) 3.22075 0.107180
\(904\) −32.9064 −1.09445
\(905\) 44.0246 1.46343
\(906\) 10.1434 0.336993
\(907\) −32.8978 −1.09235 −0.546177 0.837670i \(-0.683917\pi\)
−0.546177 + 0.837670i \(0.683917\pi\)
\(908\) −57.1951 −1.89809
\(909\) −16.0368 −0.531907
\(910\) −7.57818 −0.251214
\(911\) −2.27484 −0.0753687 −0.0376843 0.999290i \(-0.511998\pi\)
−0.0376843 + 0.999290i \(0.511998\pi\)
\(912\) 5.74467 0.190225
\(913\) 17.3526 0.574287
\(914\) −98.2246 −3.24898
\(915\) 1.55096 0.0512732
\(916\) 8.15205 0.269351
\(917\) 25.5538 0.843862
\(918\) 16.3224 0.538719
\(919\) 30.4370 1.00402 0.502012 0.864861i \(-0.332593\pi\)
0.502012 + 0.864861i \(0.332593\pi\)
\(920\) −79.2609 −2.61316
\(921\) 1.73614 0.0572077
\(922\) −21.5819 −0.710762
\(923\) 10.8445 0.356952
\(924\) −3.10997 −0.102310
\(925\) −4.78121 −0.157205
\(926\) 29.8653 0.981436
\(927\) 10.9143 0.358471
\(928\) −18.1547 −0.595958
\(929\) 12.7484 0.418263 0.209131 0.977888i \(-0.432936\pi\)
0.209131 + 0.977888i \(0.432936\pi\)
\(930\) −6.15172 −0.201723
\(931\) 21.1227 0.692269
\(932\) −111.765 −3.66099
\(933\) 0.295007 0.00965809
\(934\) −57.6181 −1.88532
\(935\) −21.6146 −0.706874
\(936\) 16.8800 0.551740
\(937\) −1.91330 −0.0625047 −0.0312524 0.999512i \(-0.509950\pi\)
−0.0312524 + 0.999512i \(0.509950\pi\)
\(938\) 37.1508 1.21302
\(939\) 0.0652899 0.00213066
\(940\) 84.8963 2.76901
\(941\) −6.83999 −0.222977 −0.111489 0.993766i \(-0.535562\pi\)
−0.111489 + 0.993766i \(0.535562\pi\)
\(942\) −0.726607 −0.0236741
\(943\) −72.3599 −2.35636
\(944\) 56.6891 1.84507
\(945\) 3.60032 0.117118
\(946\) 52.7422 1.71480
\(947\) 1.43457 0.0466173 0.0233086 0.999728i \(-0.492580\pi\)
0.0233086 + 0.999728i \(0.492580\pi\)
\(948\) −1.38108 −0.0448553
\(949\) 13.1005 0.425262
\(950\) −21.6239 −0.701572
\(951\) −6.29043 −0.203981
\(952\) −52.1405 −1.68988
\(953\) 52.6773 1.70638 0.853192 0.521597i \(-0.174664\pi\)
0.853192 + 0.521597i \(0.174664\pi\)
\(954\) 37.0903 1.20084
\(955\) −31.0723 −1.00548
\(956\) −73.9641 −2.39217
\(957\) 2.67130 0.0863509
\(958\) 61.9625 2.00192
\(959\) 9.99196 0.322657
\(960\) −1.46609 −0.0473179
\(961\) 15.1029 0.487190
\(962\) −6.96258 −0.224483
\(963\) 22.7014 0.731543
\(964\) 102.702 3.30781
\(965\) 31.6439 1.01865
\(966\) 6.41362 0.206355
\(967\) −8.06123 −0.259232 −0.129616 0.991564i \(-0.541374\pi\)
−0.129616 + 0.991564i \(0.541374\pi\)
\(968\) 35.6183 1.14482
\(969\) −5.48463 −0.176192
\(970\) −12.4387 −0.399384
\(971\) 13.2340 0.424701 0.212350 0.977194i \(-0.431888\pi\)
0.212350 + 0.977194i \(0.431888\pi\)
\(972\) −22.6492 −0.726473
\(973\) −13.4178 −0.430155
\(974\) −39.7072 −1.27230
\(975\) 0.343547 0.0110023
\(976\) 24.5893 0.787083
\(977\) −30.5092 −0.976075 −0.488037 0.872823i \(-0.662287\pi\)
−0.488037 + 0.872823i \(0.662287\pi\)
\(978\) 9.61934 0.307592
\(979\) 13.4375 0.429464
\(980\) 32.6028 1.04146
\(981\) 24.8991 0.794966
\(982\) 1.50920 0.0481607
\(983\) −19.2281 −0.613282 −0.306641 0.951825i \(-0.599205\pi\)
−0.306641 + 0.951825i \(0.599205\pi\)
\(984\) 10.7361 0.342255
\(985\) 35.8653 1.14276
\(986\) 84.1372 2.67947
\(987\) −3.65668 −0.116393
\(988\) −21.4550 −0.682573
\(989\) −74.1085 −2.35651
\(990\) 29.2817 0.930634
\(991\) 22.4644 0.713607 0.356803 0.934180i \(-0.383867\pi\)
0.356803 + 0.934180i \(0.383867\pi\)
\(992\) −20.0921 −0.637924
\(993\) −4.27759 −0.135745
\(994\) 45.3797 1.43936
\(995\) −10.0375 −0.318211
\(996\) 6.79625 0.215347
\(997\) 44.8710 1.42108 0.710540 0.703657i \(-0.248451\pi\)
0.710540 + 0.703657i \(0.248451\pi\)
\(998\) 55.4518 1.75530
\(999\) 3.30785 0.104656
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 \(a_p\))