Properties

Label 8041.2.a.i.1.6
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53120 q^{2} -2.76336 q^{3} +4.40698 q^{4} +3.58460 q^{5} +6.99462 q^{6} -0.727911 q^{7} -6.09254 q^{8} +4.63616 q^{9} +O(q^{10})\) \(q-2.53120 q^{2} -2.76336 q^{3} +4.40698 q^{4} +3.58460 q^{5} +6.99462 q^{6} -0.727911 q^{7} -6.09254 q^{8} +4.63616 q^{9} -9.07334 q^{10} +1.00000 q^{11} -12.1781 q^{12} -1.11146 q^{13} +1.84249 q^{14} -9.90554 q^{15} +6.60750 q^{16} -1.00000 q^{17} -11.7351 q^{18} +3.30470 q^{19} +15.7973 q^{20} +2.01148 q^{21} -2.53120 q^{22} -5.19699 q^{23} +16.8359 q^{24} +7.84935 q^{25} +2.81333 q^{26} -4.52131 q^{27} -3.20789 q^{28} -1.68648 q^{29} +25.0729 q^{30} +3.36917 q^{31} -4.53982 q^{32} -2.76336 q^{33} +2.53120 q^{34} -2.60927 q^{35} +20.4315 q^{36} -8.94366 q^{37} -8.36487 q^{38} +3.07136 q^{39} -21.8393 q^{40} -5.08833 q^{41} -5.09146 q^{42} -1.00000 q^{43} +4.40698 q^{44} +16.6188 q^{45} +13.1546 q^{46} +2.08535 q^{47} -18.2589 q^{48} -6.47015 q^{49} -19.8683 q^{50} +2.76336 q^{51} -4.89818 q^{52} -0.317816 q^{53} +11.4443 q^{54} +3.58460 q^{55} +4.43483 q^{56} -9.13209 q^{57} +4.26882 q^{58} +5.62610 q^{59} -43.6535 q^{60} -11.2332 q^{61} -8.52804 q^{62} -3.37471 q^{63} -1.72381 q^{64} -3.98414 q^{65} +6.99462 q^{66} -7.90842 q^{67} -4.40698 q^{68} +14.3612 q^{69} +6.60459 q^{70} +9.16197 q^{71} -28.2460 q^{72} -10.6186 q^{73} +22.6382 q^{74} -21.6906 q^{75} +14.5638 q^{76} -0.727911 q^{77} -7.77424 q^{78} +13.4281 q^{79} +23.6852 q^{80} -1.41449 q^{81} +12.8796 q^{82} -8.85038 q^{83} +8.86455 q^{84} -3.58460 q^{85} +2.53120 q^{86} +4.66035 q^{87} -6.09254 q^{88} +7.04878 q^{89} -42.0655 q^{90} +0.809044 q^{91} -22.9030 q^{92} -9.31022 q^{93} -5.27845 q^{94} +11.8460 q^{95} +12.5452 q^{96} +12.3075 q^{97} +16.3772 q^{98} +4.63616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53120 −1.78983 −0.894915 0.446237i \(-0.852764\pi\)
−0.894915 + 0.446237i \(0.852764\pi\)
\(3\) −2.76336 −1.59543 −0.797714 0.603037i \(-0.793957\pi\)
−0.797714 + 0.603037i \(0.793957\pi\)
\(4\) 4.40698 2.20349
\(5\) 3.58460 1.60308 0.801541 0.597940i \(-0.204014\pi\)
0.801541 + 0.597940i \(0.204014\pi\)
\(6\) 6.99462 2.85554
\(7\) −0.727911 −0.275125 −0.137562 0.990493i \(-0.543927\pi\)
−0.137562 + 0.990493i \(0.543927\pi\)
\(8\) −6.09254 −2.15404
\(9\) 4.63616 1.54539
\(10\) −9.07334 −2.86924
\(11\) 1.00000 0.301511
\(12\) −12.1781 −3.51551
\(13\) −1.11146 −0.308263 −0.154132 0.988050i \(-0.549258\pi\)
−0.154132 + 0.988050i \(0.549258\pi\)
\(14\) 1.84249 0.492426
\(15\) −9.90554 −2.55760
\(16\) 6.60750 1.65187
\(17\) −1.00000 −0.242536
\(18\) −11.7351 −2.76598
\(19\) 3.30470 0.758151 0.379075 0.925366i \(-0.376242\pi\)
0.379075 + 0.925366i \(0.376242\pi\)
\(20\) 15.7973 3.53237
\(21\) 2.01148 0.438941
\(22\) −2.53120 −0.539654
\(23\) −5.19699 −1.08365 −0.541824 0.840492i \(-0.682266\pi\)
−0.541824 + 0.840492i \(0.682266\pi\)
\(24\) 16.8359 3.43661
\(25\) 7.84935 1.56987
\(26\) 2.81333 0.551739
\(27\) −4.52131 −0.870126
\(28\) −3.20789 −0.606234
\(29\) −1.68648 −0.313172 −0.156586 0.987664i \(-0.550049\pi\)
−0.156586 + 0.987664i \(0.550049\pi\)
\(30\) 25.0729 4.57767
\(31\) 3.36917 0.605120 0.302560 0.953130i \(-0.402159\pi\)
0.302560 + 0.953130i \(0.402159\pi\)
\(32\) −4.53982 −0.802534
\(33\) −2.76336 −0.481039
\(34\) 2.53120 0.434097
\(35\) −2.60927 −0.441047
\(36\) 20.4315 3.40524
\(37\) −8.94366 −1.47033 −0.735164 0.677889i \(-0.762895\pi\)
−0.735164 + 0.677889i \(0.762895\pi\)
\(38\) −8.36487 −1.35696
\(39\) 3.07136 0.491812
\(40\) −21.8393 −3.45310
\(41\) −5.08833 −0.794663 −0.397331 0.917675i \(-0.630064\pi\)
−0.397331 + 0.917675i \(0.630064\pi\)
\(42\) −5.09146 −0.785630
\(43\) −1.00000 −0.152499
\(44\) 4.40698 0.664377
\(45\) 16.6188 2.47738
\(46\) 13.1546 1.93954
\(47\) 2.08535 0.304180 0.152090 0.988367i \(-0.451400\pi\)
0.152090 + 0.988367i \(0.451400\pi\)
\(48\) −18.2589 −2.63545
\(49\) −6.47015 −0.924306
\(50\) −19.8683 −2.80980
\(51\) 2.76336 0.386948
\(52\) −4.89818 −0.679255
\(53\) −0.317816 −0.0436554 −0.0218277 0.999762i \(-0.506949\pi\)
−0.0218277 + 0.999762i \(0.506949\pi\)
\(54\) 11.4443 1.55738
\(55\) 3.58460 0.483347
\(56\) 4.43483 0.592629
\(57\) −9.13209 −1.20957
\(58\) 4.26882 0.560524
\(59\) 5.62610 0.732455 0.366228 0.930525i \(-0.380649\pi\)
0.366228 + 0.930525i \(0.380649\pi\)
\(60\) −43.6535 −5.63564
\(61\) −11.2332 −1.43826 −0.719130 0.694875i \(-0.755459\pi\)
−0.719130 + 0.694875i \(0.755459\pi\)
\(62\) −8.52804 −1.08306
\(63\) −3.37471 −0.425174
\(64\) −1.72381 −0.215476
\(65\) −3.98414 −0.494171
\(66\) 6.99462 0.860978
\(67\) −7.90842 −0.966167 −0.483084 0.875574i \(-0.660483\pi\)
−0.483084 + 0.875574i \(0.660483\pi\)
\(68\) −4.40698 −0.534425
\(69\) 14.3612 1.72888
\(70\) 6.60459 0.789399
\(71\) 9.16197 1.08733 0.543663 0.839304i \(-0.317037\pi\)
0.543663 + 0.839304i \(0.317037\pi\)
\(72\) −28.2460 −3.32883
\(73\) −10.6186 −1.24282 −0.621408 0.783488i \(-0.713439\pi\)
−0.621408 + 0.783488i \(0.713439\pi\)
\(74\) 22.6382 2.63164
\(75\) −21.6906 −2.50461
\(76\) 14.5638 1.67058
\(77\) −0.727911 −0.0829532
\(78\) −7.77424 −0.880259
\(79\) 13.4281 1.51078 0.755389 0.655277i \(-0.227448\pi\)
0.755389 + 0.655277i \(0.227448\pi\)
\(80\) 23.6852 2.64809
\(81\) −1.41449 −0.157165
\(82\) 12.8796 1.42231
\(83\) −8.85038 −0.971455 −0.485728 0.874110i \(-0.661445\pi\)
−0.485728 + 0.874110i \(0.661445\pi\)
\(84\) 8.86455 0.967202
\(85\) −3.58460 −0.388804
\(86\) 2.53120 0.272946
\(87\) 4.66035 0.499642
\(88\) −6.09254 −0.649467
\(89\) 7.04878 0.747169 0.373584 0.927596i \(-0.378129\pi\)
0.373584 + 0.927596i \(0.378129\pi\)
\(90\) −42.0655 −4.43409
\(91\) 0.809044 0.0848109
\(92\) −22.9030 −2.38781
\(93\) −9.31022 −0.965425
\(94\) −5.27845 −0.544431
\(95\) 11.8460 1.21538
\(96\) 12.5452 1.28038
\(97\) 12.3075 1.24964 0.624819 0.780769i \(-0.285173\pi\)
0.624819 + 0.780769i \(0.285173\pi\)
\(98\) 16.3772 1.65435
\(99\) 4.63616 0.465952
\(100\) 34.5919 3.45919
\(101\) −15.5117 −1.54347 −0.771736 0.635943i \(-0.780611\pi\)
−0.771736 + 0.635943i \(0.780611\pi\)
\(102\) −6.99462 −0.692571
\(103\) 1.85325 0.182606 0.0913032 0.995823i \(-0.470897\pi\)
0.0913032 + 0.995823i \(0.470897\pi\)
\(104\) 6.77162 0.664012
\(105\) 7.21035 0.703659
\(106\) 0.804456 0.0781357
\(107\) −9.02054 −0.872049 −0.436024 0.899935i \(-0.643614\pi\)
−0.436024 + 0.899935i \(0.643614\pi\)
\(108\) −19.9253 −1.91731
\(109\) 17.7576 1.70087 0.850435 0.526080i \(-0.176339\pi\)
0.850435 + 0.526080i \(0.176339\pi\)
\(110\) −9.07334 −0.865109
\(111\) 24.7146 2.34580
\(112\) −4.80967 −0.454471
\(113\) −2.02453 −0.190452 −0.0952259 0.995456i \(-0.530357\pi\)
−0.0952259 + 0.995456i \(0.530357\pi\)
\(114\) 23.1151 2.16493
\(115\) −18.6291 −1.73718
\(116\) −7.43228 −0.690070
\(117\) −5.15291 −0.476386
\(118\) −14.2408 −1.31097
\(119\) 0.727911 0.0667275
\(120\) 60.3500 5.50917
\(121\) 1.00000 0.0909091
\(122\) 28.4334 2.57424
\(123\) 14.0609 1.26783
\(124\) 14.8478 1.33338
\(125\) 10.2138 0.913549
\(126\) 8.54208 0.760989
\(127\) 13.3695 1.18635 0.593174 0.805074i \(-0.297875\pi\)
0.593174 + 0.805074i \(0.297875\pi\)
\(128\) 13.4429 1.18820
\(129\) 2.76336 0.243300
\(130\) 10.0847 0.884483
\(131\) 6.46156 0.564549 0.282275 0.959334i \(-0.408911\pi\)
0.282275 + 0.959334i \(0.408911\pi\)
\(132\) −12.1781 −1.05996
\(133\) −2.40553 −0.208586
\(134\) 20.0178 1.72927
\(135\) −16.2071 −1.39488
\(136\) 6.09254 0.522431
\(137\) 19.0000 1.62328 0.811639 0.584160i \(-0.198576\pi\)
0.811639 + 0.584160i \(0.198576\pi\)
\(138\) −36.3510 −3.09440
\(139\) 7.35355 0.623720 0.311860 0.950128i \(-0.399048\pi\)
0.311860 + 0.950128i \(0.399048\pi\)
\(140\) −11.4990 −0.971843
\(141\) −5.76259 −0.485297
\(142\) −23.1908 −1.94613
\(143\) −1.11146 −0.0929449
\(144\) 30.6334 2.55279
\(145\) −6.04536 −0.502040
\(146\) 26.8779 2.22443
\(147\) 17.8793 1.47466
\(148\) −39.4145 −3.23985
\(149\) 0.0875898 0.00717564 0.00358782 0.999994i \(-0.498858\pi\)
0.00358782 + 0.999994i \(0.498858\pi\)
\(150\) 54.9033 4.48283
\(151\) −0.931349 −0.0757921 −0.0378961 0.999282i \(-0.512066\pi\)
−0.0378961 + 0.999282i \(0.512066\pi\)
\(152\) −20.1340 −1.63309
\(153\) −4.63616 −0.374811
\(154\) 1.84249 0.148472
\(155\) 12.0771 0.970057
\(156\) 13.5354 1.08370
\(157\) 12.4048 0.990009 0.495005 0.868890i \(-0.335166\pi\)
0.495005 + 0.868890i \(0.335166\pi\)
\(158\) −33.9892 −2.70403
\(159\) 0.878240 0.0696490
\(160\) −16.2734 −1.28653
\(161\) 3.78295 0.298138
\(162\) 3.58035 0.281299
\(163\) 13.3465 1.04538 0.522688 0.852524i \(-0.324929\pi\)
0.522688 + 0.852524i \(0.324929\pi\)
\(164\) −22.4241 −1.75103
\(165\) −9.90554 −0.771145
\(166\) 22.4021 1.73874
\(167\) 6.43560 0.498002 0.249001 0.968503i \(-0.419898\pi\)
0.249001 + 0.968503i \(0.419898\pi\)
\(168\) −12.2550 −0.945497
\(169\) −11.7647 −0.904974
\(170\) 9.07334 0.695894
\(171\) 15.3211 1.17164
\(172\) −4.40698 −0.336029
\(173\) −1.68221 −0.127896 −0.0639479 0.997953i \(-0.520369\pi\)
−0.0639479 + 0.997953i \(0.520369\pi\)
\(174\) −11.7963 −0.894275
\(175\) −5.71363 −0.431910
\(176\) 6.60750 0.498059
\(177\) −15.5469 −1.16858
\(178\) −17.8419 −1.33730
\(179\) 9.36711 0.700131 0.350065 0.936725i \(-0.386159\pi\)
0.350065 + 0.936725i \(0.386159\pi\)
\(180\) 73.2386 5.45888
\(181\) 10.7297 0.797533 0.398766 0.917053i \(-0.369438\pi\)
0.398766 + 0.917053i \(0.369438\pi\)
\(182\) −2.04785 −0.151797
\(183\) 31.0413 2.29464
\(184\) 31.6629 2.33422
\(185\) −32.0594 −2.35706
\(186\) 23.5660 1.72795
\(187\) −1.00000 −0.0731272
\(188\) 9.19011 0.670258
\(189\) 3.29111 0.239393
\(190\) −29.9847 −2.17532
\(191\) 13.4288 0.971674 0.485837 0.874049i \(-0.338515\pi\)
0.485837 + 0.874049i \(0.338515\pi\)
\(192\) 4.76351 0.343776
\(193\) 10.6725 0.768225 0.384112 0.923286i \(-0.374508\pi\)
0.384112 + 0.923286i \(0.374508\pi\)
\(194\) −31.1528 −2.23664
\(195\) 11.0096 0.788415
\(196\) −28.5138 −2.03670
\(197\) 15.7843 1.12458 0.562292 0.826938i \(-0.309920\pi\)
0.562292 + 0.826938i \(0.309920\pi\)
\(198\) −11.7351 −0.833974
\(199\) 8.05060 0.570692 0.285346 0.958425i \(-0.407892\pi\)
0.285346 + 0.958425i \(0.407892\pi\)
\(200\) −47.8225 −3.38156
\(201\) 21.8538 1.54145
\(202\) 39.2632 2.76255
\(203\) 1.22761 0.0861612
\(204\) 12.1781 0.852635
\(205\) −18.2396 −1.27391
\(206\) −4.69096 −0.326834
\(207\) −24.0941 −1.67466
\(208\) −7.34397 −0.509213
\(209\) 3.30470 0.228591
\(210\) −18.2509 −1.25943
\(211\) 9.21320 0.634263 0.317131 0.948382i \(-0.397280\pi\)
0.317131 + 0.948382i \(0.397280\pi\)
\(212\) −1.40061 −0.0961941
\(213\) −25.3178 −1.73475
\(214\) 22.8328 1.56082
\(215\) −3.58460 −0.244468
\(216\) 27.5463 1.87429
\(217\) −2.45245 −0.166483
\(218\) −44.9481 −3.04427
\(219\) 29.3431 1.98282
\(220\) 15.7973 1.06505
\(221\) 1.11146 0.0747649
\(222\) −62.5575 −4.19859
\(223\) 11.3001 0.756710 0.378355 0.925661i \(-0.376490\pi\)
0.378355 + 0.925661i \(0.376490\pi\)
\(224\) 3.30458 0.220797
\(225\) 36.3909 2.42606
\(226\) 5.12449 0.340876
\(227\) −12.4027 −0.823198 −0.411599 0.911365i \(-0.635030\pi\)
−0.411599 + 0.911365i \(0.635030\pi\)
\(228\) −40.2449 −2.66528
\(229\) −16.7062 −1.10397 −0.551987 0.833853i \(-0.686130\pi\)
−0.551987 + 0.833853i \(0.686130\pi\)
\(230\) 47.1541 3.10925
\(231\) 2.01148 0.132346
\(232\) 10.2750 0.674584
\(233\) 0.928042 0.0607981 0.0303990 0.999538i \(-0.490322\pi\)
0.0303990 + 0.999538i \(0.490322\pi\)
\(234\) 13.0430 0.852650
\(235\) 7.47516 0.487626
\(236\) 24.7941 1.61396
\(237\) −37.1066 −2.41033
\(238\) −1.84249 −0.119431
\(239\) −10.7737 −0.696891 −0.348445 0.937329i \(-0.613290\pi\)
−0.348445 + 0.937329i \(0.613290\pi\)
\(240\) −65.4508 −4.22483
\(241\) −16.2593 −1.04735 −0.523675 0.851918i \(-0.675439\pi\)
−0.523675 + 0.851918i \(0.675439\pi\)
\(242\) −2.53120 −0.162712
\(243\) 17.4727 1.12087
\(244\) −49.5043 −3.16919
\(245\) −23.1929 −1.48174
\(246\) −35.5909 −2.26919
\(247\) −3.67304 −0.233710
\(248\) −20.5268 −1.30345
\(249\) 24.4568 1.54989
\(250\) −25.8532 −1.63510
\(251\) −4.98582 −0.314702 −0.157351 0.987543i \(-0.550295\pi\)
−0.157351 + 0.987543i \(0.550295\pi\)
\(252\) −14.8723 −0.936866
\(253\) −5.19699 −0.326732
\(254\) −33.8408 −2.12336
\(255\) 9.90554 0.620309
\(256\) −30.5792 −1.91120
\(257\) 16.3442 1.01953 0.509763 0.860315i \(-0.329733\pi\)
0.509763 + 0.860315i \(0.329733\pi\)
\(258\) −6.99462 −0.435466
\(259\) 6.51019 0.404524
\(260\) −17.5580 −1.08890
\(261\) −7.81880 −0.483971
\(262\) −16.3555 −1.01045
\(263\) 9.81069 0.604953 0.302476 0.953157i \(-0.402187\pi\)
0.302476 + 0.953157i \(0.402187\pi\)
\(264\) 16.8359 1.03618
\(265\) −1.13924 −0.0699831
\(266\) 6.08888 0.373333
\(267\) −19.4783 −1.19205
\(268\) −34.8522 −2.12894
\(269\) 1.48875 0.0907706 0.0453853 0.998970i \(-0.485548\pi\)
0.0453853 + 0.998970i \(0.485548\pi\)
\(270\) 41.0234 2.49660
\(271\) −27.7376 −1.68494 −0.842468 0.538746i \(-0.818898\pi\)
−0.842468 + 0.538746i \(0.818898\pi\)
\(272\) −6.60750 −0.400638
\(273\) −2.23568 −0.135310
\(274\) −48.0928 −2.90539
\(275\) 7.84935 0.473334
\(276\) 63.2893 3.80957
\(277\) −24.6505 −1.48110 −0.740552 0.671999i \(-0.765436\pi\)
−0.740552 + 0.671999i \(0.765436\pi\)
\(278\) −18.6133 −1.11635
\(279\) 15.6200 0.935145
\(280\) 15.8971 0.950033
\(281\) 2.76881 0.165173 0.0825867 0.996584i \(-0.473682\pi\)
0.0825867 + 0.996584i \(0.473682\pi\)
\(282\) 14.5863 0.868599
\(283\) −14.7986 −0.879685 −0.439843 0.898075i \(-0.644966\pi\)
−0.439843 + 0.898075i \(0.644966\pi\)
\(284\) 40.3766 2.39591
\(285\) −32.7349 −1.93905
\(286\) 2.81333 0.166356
\(287\) 3.70385 0.218631
\(288\) −21.0473 −1.24023
\(289\) 1.00000 0.0588235
\(290\) 15.3020 0.898565
\(291\) −34.0101 −1.99371
\(292\) −46.7960 −2.73853
\(293\) 28.3688 1.65732 0.828662 0.559749i \(-0.189103\pi\)
0.828662 + 0.559749i \(0.189103\pi\)
\(294\) −45.2562 −2.63940
\(295\) 20.1673 1.17419
\(296\) 54.4897 3.16715
\(297\) −4.52131 −0.262353
\(298\) −0.221707 −0.0128432
\(299\) 5.77625 0.334049
\(300\) −95.5900 −5.51889
\(301\) 0.727911 0.0419561
\(302\) 2.35743 0.135655
\(303\) 42.8644 2.46250
\(304\) 21.8358 1.25237
\(305\) −40.2664 −2.30565
\(306\) 11.7351 0.670849
\(307\) −9.77116 −0.557670 −0.278835 0.960339i \(-0.589948\pi\)
−0.278835 + 0.960339i \(0.589948\pi\)
\(308\) −3.20789 −0.182786
\(309\) −5.12121 −0.291335
\(310\) −30.5696 −1.73624
\(311\) −9.98449 −0.566168 −0.283084 0.959095i \(-0.591358\pi\)
−0.283084 + 0.959095i \(0.591358\pi\)
\(312\) −18.7124 −1.05938
\(313\) 31.9647 1.80675 0.903376 0.428849i \(-0.141081\pi\)
0.903376 + 0.428849i \(0.141081\pi\)
\(314\) −31.3990 −1.77195
\(315\) −12.0970 −0.681589
\(316\) 59.1773 3.32898
\(317\) −17.1474 −0.963092 −0.481546 0.876421i \(-0.659925\pi\)
−0.481546 + 0.876421i \(0.659925\pi\)
\(318\) −2.22300 −0.124660
\(319\) −1.68648 −0.0944248
\(320\) −6.17916 −0.345426
\(321\) 24.9270 1.39129
\(322\) −9.57541 −0.533616
\(323\) −3.30470 −0.183879
\(324\) −6.23362 −0.346312
\(325\) −8.72424 −0.483934
\(326\) −33.7826 −1.87105
\(327\) −49.0707 −2.71361
\(328\) 31.0009 1.71174
\(329\) −1.51795 −0.0836874
\(330\) 25.0729 1.38022
\(331\) 10.9993 0.604578 0.302289 0.953216i \(-0.402249\pi\)
0.302289 + 0.953216i \(0.402249\pi\)
\(332\) −39.0034 −2.14059
\(333\) −41.4643 −2.27223
\(334\) −16.2898 −0.891338
\(335\) −28.3485 −1.54884
\(336\) 13.2909 0.725076
\(337\) −8.51147 −0.463649 −0.231825 0.972758i \(-0.574470\pi\)
−0.231825 + 0.972758i \(0.574470\pi\)
\(338\) 29.7787 1.61975
\(339\) 5.59451 0.303852
\(340\) −15.7973 −0.856726
\(341\) 3.36917 0.182451
\(342\) −38.7809 −2.09703
\(343\) 9.80507 0.529424
\(344\) 6.09254 0.328488
\(345\) 51.4790 2.77154
\(346\) 4.25800 0.228912
\(347\) 16.1557 0.867282 0.433641 0.901086i \(-0.357229\pi\)
0.433641 + 0.901086i \(0.357229\pi\)
\(348\) 20.5381 1.10096
\(349\) 17.5613 0.940034 0.470017 0.882657i \(-0.344248\pi\)
0.470017 + 0.882657i \(0.344248\pi\)
\(350\) 14.4624 0.773045
\(351\) 5.02525 0.268228
\(352\) −4.53982 −0.241973
\(353\) 8.61383 0.458468 0.229234 0.973371i \(-0.426378\pi\)
0.229234 + 0.973371i \(0.426378\pi\)
\(354\) 39.3524 2.09156
\(355\) 32.8420 1.74307
\(356\) 31.0638 1.64638
\(357\) −2.01148 −0.106459
\(358\) −23.7100 −1.25311
\(359\) 8.45971 0.446486 0.223243 0.974763i \(-0.428336\pi\)
0.223243 + 0.974763i \(0.428336\pi\)
\(360\) −101.251 −5.33638
\(361\) −8.07894 −0.425207
\(362\) −27.1590 −1.42745
\(363\) −2.76336 −0.145039
\(364\) 3.56544 0.186880
\(365\) −38.0635 −1.99233
\(366\) −78.5718 −4.10701
\(367\) −17.2297 −0.899385 −0.449692 0.893184i \(-0.648466\pi\)
−0.449692 + 0.893184i \(0.648466\pi\)
\(368\) −34.3391 −1.79005
\(369\) −23.5903 −1.22806
\(370\) 81.1489 4.21873
\(371\) 0.231342 0.0120107
\(372\) −41.0299 −2.12730
\(373\) −32.2724 −1.67100 −0.835500 0.549490i \(-0.814822\pi\)
−0.835500 + 0.549490i \(0.814822\pi\)
\(374\) 2.53120 0.130885
\(375\) −28.2244 −1.45750
\(376\) −12.7051 −0.655216
\(377\) 1.87446 0.0965393
\(378\) −8.33046 −0.428473
\(379\) −8.33140 −0.427955 −0.213978 0.976839i \(-0.568642\pi\)
−0.213978 + 0.976839i \(0.568642\pi\)
\(380\) 52.2052 2.67807
\(381\) −36.9446 −1.89273
\(382\) −33.9910 −1.73913
\(383\) −19.9560 −1.01970 −0.509852 0.860262i \(-0.670300\pi\)
−0.509852 + 0.860262i \(0.670300\pi\)
\(384\) −37.1477 −1.89569
\(385\) −2.60927 −0.132981
\(386\) −27.0143 −1.37499
\(387\) −4.63616 −0.235669
\(388\) 54.2389 2.75356
\(389\) 12.2884 0.623048 0.311524 0.950238i \(-0.399161\pi\)
0.311524 + 0.950238i \(0.399161\pi\)
\(390\) −27.8675 −1.41113
\(391\) 5.19699 0.262823
\(392\) 39.4196 1.99099
\(393\) −17.8556 −0.900697
\(394\) −39.9532 −2.01282
\(395\) 48.1343 2.42190
\(396\) 20.4315 1.02672
\(397\) 30.2991 1.52067 0.760334 0.649532i \(-0.225035\pi\)
0.760334 + 0.649532i \(0.225035\pi\)
\(398\) −20.3777 −1.02144
\(399\) 6.64735 0.332784
\(400\) 51.8646 2.59323
\(401\) 26.1087 1.30381 0.651903 0.758302i \(-0.273971\pi\)
0.651903 + 0.758302i \(0.273971\pi\)
\(402\) −55.3164 −2.75893
\(403\) −3.74469 −0.186536
\(404\) −68.3597 −3.40102
\(405\) −5.07037 −0.251949
\(406\) −3.10732 −0.154214
\(407\) −8.94366 −0.443321
\(408\) −16.8359 −0.833501
\(409\) −19.0915 −0.944014 −0.472007 0.881595i \(-0.656470\pi\)
−0.472007 + 0.881595i \(0.656470\pi\)
\(410\) 46.1681 2.28008
\(411\) −52.5038 −2.58982
\(412\) 8.16724 0.402371
\(413\) −4.09530 −0.201516
\(414\) 60.9870 2.99735
\(415\) −31.7251 −1.55732
\(416\) 5.04582 0.247392
\(417\) −20.3205 −0.995100
\(418\) −8.36487 −0.409139
\(419\) 25.7764 1.25926 0.629631 0.776894i \(-0.283206\pi\)
0.629631 + 0.776894i \(0.283206\pi\)
\(420\) 31.7759 1.55050
\(421\) 16.7687 0.817256 0.408628 0.912701i \(-0.366007\pi\)
0.408628 + 0.912701i \(0.366007\pi\)
\(422\) −23.3205 −1.13522
\(423\) 9.66804 0.470076
\(424\) 1.93631 0.0940354
\(425\) −7.84935 −0.380750
\(426\) 64.0845 3.10490
\(427\) 8.17675 0.395701
\(428\) −39.7533 −1.92155
\(429\) 3.07136 0.148287
\(430\) 9.07334 0.437555
\(431\) 17.0944 0.823410 0.411705 0.911317i \(-0.364933\pi\)
0.411705 + 0.911317i \(0.364933\pi\)
\(432\) −29.8745 −1.43734
\(433\) −8.46890 −0.406989 −0.203495 0.979076i \(-0.565230\pi\)
−0.203495 + 0.979076i \(0.565230\pi\)
\(434\) 6.20765 0.297977
\(435\) 16.7055 0.800968
\(436\) 78.2574 3.74785
\(437\) −17.1745 −0.821569
\(438\) −74.2732 −3.54891
\(439\) −2.76905 −0.132159 −0.0660797 0.997814i \(-0.521049\pi\)
−0.0660797 + 0.997814i \(0.521049\pi\)
\(440\) −21.8393 −1.04115
\(441\) −29.9966 −1.42841
\(442\) −2.81333 −0.133816
\(443\) 29.2479 1.38961 0.694804 0.719199i \(-0.255491\pi\)
0.694804 + 0.719199i \(0.255491\pi\)
\(444\) 108.917 5.16895
\(445\) 25.2670 1.19777
\(446\) −28.6028 −1.35438
\(447\) −0.242042 −0.0114482
\(448\) 1.25478 0.0592828
\(449\) −4.22147 −0.199224 −0.0996118 0.995026i \(-0.531760\pi\)
−0.0996118 + 0.995026i \(0.531760\pi\)
\(450\) −92.1126 −4.34223
\(451\) −5.08833 −0.239600
\(452\) −8.92206 −0.419658
\(453\) 2.57365 0.120921
\(454\) 31.3938 1.47338
\(455\) 2.90010 0.135959
\(456\) 55.6376 2.60547
\(457\) 5.45810 0.255319 0.127659 0.991818i \(-0.459254\pi\)
0.127659 + 0.991818i \(0.459254\pi\)
\(458\) 42.2867 1.97593
\(459\) 4.52131 0.211036
\(460\) −82.0982 −3.82785
\(461\) −23.6125 −1.09974 −0.549872 0.835249i \(-0.685324\pi\)
−0.549872 + 0.835249i \(0.685324\pi\)
\(462\) −5.09146 −0.236876
\(463\) −9.62190 −0.447168 −0.223584 0.974685i \(-0.571776\pi\)
−0.223584 + 0.974685i \(0.571776\pi\)
\(464\) −11.1434 −0.517320
\(465\) −33.3734 −1.54766
\(466\) −2.34906 −0.108818
\(467\) 28.5389 1.32062 0.660312 0.750992i \(-0.270424\pi\)
0.660312 + 0.750992i \(0.270424\pi\)
\(468\) −22.7087 −1.04971
\(469\) 5.75663 0.265816
\(470\) −18.9211 −0.872767
\(471\) −34.2789 −1.57949
\(472\) −34.2772 −1.57774
\(473\) −1.00000 −0.0459800
\(474\) 93.9243 4.31409
\(475\) 25.9398 1.19020
\(476\) 3.20789 0.147033
\(477\) −1.47345 −0.0674645
\(478\) 27.2703 1.24732
\(479\) 38.0948 1.74060 0.870298 0.492525i \(-0.163926\pi\)
0.870298 + 0.492525i \(0.163926\pi\)
\(480\) 44.9693 2.05256
\(481\) 9.94052 0.453249
\(482\) 41.1554 1.87458
\(483\) −10.4537 −0.475658
\(484\) 4.40698 0.200317
\(485\) 44.1175 2.00327
\(486\) −44.2268 −2.00617
\(487\) 21.4050 0.969955 0.484978 0.874527i \(-0.338828\pi\)
0.484978 + 0.874527i \(0.338828\pi\)
\(488\) 68.4386 3.09807
\(489\) −36.8811 −1.66782
\(490\) 58.7058 2.65206
\(491\) 7.63187 0.344421 0.172211 0.985060i \(-0.444909\pi\)
0.172211 + 0.985060i \(0.444909\pi\)
\(492\) 61.9660 2.79364
\(493\) 1.68648 0.0759553
\(494\) 9.29721 0.418301
\(495\) 16.6188 0.746959
\(496\) 22.2618 0.999583
\(497\) −6.66910 −0.299150
\(498\) −61.9050 −2.77403
\(499\) −1.11221 −0.0497895 −0.0248948 0.999690i \(-0.507925\pi\)
−0.0248948 + 0.999690i \(0.507925\pi\)
\(500\) 45.0119 2.01300
\(501\) −17.7839 −0.794526
\(502\) 12.6201 0.563263
\(503\) −13.8676 −0.618325 −0.309163 0.951009i \(-0.600049\pi\)
−0.309163 + 0.951009i \(0.600049\pi\)
\(504\) 20.5606 0.915842
\(505\) −55.6033 −2.47431
\(506\) 13.1546 0.584795
\(507\) 32.5100 1.44382
\(508\) 58.9189 2.61410
\(509\) −15.0736 −0.668125 −0.334063 0.942551i \(-0.608420\pi\)
−0.334063 + 0.942551i \(0.608420\pi\)
\(510\) −25.0729 −1.11025
\(511\) 7.72941 0.341929
\(512\) 50.5161 2.23252
\(513\) −14.9416 −0.659687
\(514\) −41.3706 −1.82478
\(515\) 6.64317 0.292733
\(516\) 12.1781 0.536110
\(517\) 2.08535 0.0917138
\(518\) −16.4786 −0.724028
\(519\) 4.64854 0.204048
\(520\) 24.2735 1.06447
\(521\) 36.0203 1.57808 0.789040 0.614342i \(-0.210579\pi\)
0.789040 + 0.614342i \(0.210579\pi\)
\(522\) 19.7909 0.866226
\(523\) 3.39338 0.148382 0.0741910 0.997244i \(-0.476363\pi\)
0.0741910 + 0.997244i \(0.476363\pi\)
\(524\) 28.4760 1.24398
\(525\) 15.7888 0.689081
\(526\) −24.8328 −1.08276
\(527\) −3.36917 −0.146763
\(528\) −18.2589 −0.794617
\(529\) 4.00874 0.174293
\(530\) 2.88365 0.125258
\(531\) 26.0835 1.13193
\(532\) −10.6011 −0.459617
\(533\) 5.65547 0.244966
\(534\) 49.3035 2.13357
\(535\) −32.3350 −1.39797
\(536\) 48.1824 2.08116
\(537\) −25.8847 −1.11701
\(538\) −3.76832 −0.162464
\(539\) −6.47015 −0.278689
\(540\) −71.4242 −3.07361
\(541\) 28.0282 1.20502 0.602512 0.798110i \(-0.294166\pi\)
0.602512 + 0.798110i \(0.294166\pi\)
\(542\) 70.2093 3.01575
\(543\) −29.6500 −1.27240
\(544\) 4.53982 0.194643
\(545\) 63.6539 2.72663
\(546\) 5.65896 0.242181
\(547\) −1.08127 −0.0462317 −0.0231159 0.999733i \(-0.507359\pi\)
−0.0231159 + 0.999733i \(0.507359\pi\)
\(548\) 83.7325 3.57687
\(549\) −52.0788 −2.22267
\(550\) −19.8683 −0.847187
\(551\) −5.57332 −0.237431
\(552\) −87.4960 −3.72408
\(553\) −9.77445 −0.415652
\(554\) 62.3953 2.65092
\(555\) 88.5918 3.76051
\(556\) 32.4070 1.37436
\(557\) −28.3971 −1.20322 −0.601612 0.798788i \(-0.705475\pi\)
−0.601612 + 0.798788i \(0.705475\pi\)
\(558\) −39.5374 −1.67375
\(559\) 1.11146 0.0470097
\(560\) −17.2407 −0.728555
\(561\) 2.76336 0.116669
\(562\) −7.00841 −0.295632
\(563\) 23.4617 0.988793 0.494396 0.869237i \(-0.335389\pi\)
0.494396 + 0.869237i \(0.335389\pi\)
\(564\) −25.3956 −1.06935
\(565\) −7.25713 −0.305310
\(566\) 37.4582 1.57449
\(567\) 1.02962 0.0432400
\(568\) −55.8197 −2.34214
\(569\) −28.0592 −1.17630 −0.588152 0.808750i \(-0.700144\pi\)
−0.588152 + 0.808750i \(0.700144\pi\)
\(570\) 82.8585 3.47056
\(571\) 29.8020 1.24718 0.623588 0.781753i \(-0.285674\pi\)
0.623588 + 0.781753i \(0.285674\pi\)
\(572\) −4.89818 −0.204803
\(573\) −37.1086 −1.55024
\(574\) −9.37519 −0.391313
\(575\) −40.7930 −1.70119
\(576\) −7.99186 −0.332994
\(577\) −36.2189 −1.50781 −0.753906 0.656982i \(-0.771833\pi\)
−0.753906 + 0.656982i \(0.771833\pi\)
\(578\) −2.53120 −0.105284
\(579\) −29.4920 −1.22565
\(580\) −26.6418 −1.10624
\(581\) 6.44229 0.267271
\(582\) 86.0864 3.56840
\(583\) −0.317816 −0.0131626
\(584\) 64.6944 2.67707
\(585\) −18.4711 −0.763686
\(586\) −71.8072 −2.96633
\(587\) 10.5470 0.435321 0.217660 0.976025i \(-0.430157\pi\)
0.217660 + 0.976025i \(0.430157\pi\)
\(588\) 78.7939 3.24940
\(589\) 11.1341 0.458772
\(590\) −51.0475 −2.10159
\(591\) −43.6177 −1.79419
\(592\) −59.0952 −2.42880
\(593\) −17.3195 −0.711228 −0.355614 0.934633i \(-0.615728\pi\)
−0.355614 + 0.934633i \(0.615728\pi\)
\(594\) 11.4443 0.469567
\(595\) 2.60927 0.106970
\(596\) 0.386006 0.0158114
\(597\) −22.2467 −0.910497
\(598\) −14.6208 −0.597891
\(599\) 14.3361 0.585756 0.292878 0.956150i \(-0.405387\pi\)
0.292878 + 0.956150i \(0.405387\pi\)
\(600\) 132.151 5.39504
\(601\) −25.2401 −1.02957 −0.514783 0.857320i \(-0.672128\pi\)
−0.514783 + 0.857320i \(0.672128\pi\)
\(602\) −1.84249 −0.0750943
\(603\) −36.6647 −1.49310
\(604\) −4.10443 −0.167007
\(605\) 3.58460 0.145735
\(606\) −108.499 −4.40745
\(607\) 31.2892 1.26999 0.634994 0.772517i \(-0.281003\pi\)
0.634994 + 0.772517i \(0.281003\pi\)
\(608\) −15.0027 −0.608442
\(609\) −3.39232 −0.137464
\(610\) 101.922 4.12672
\(611\) −2.31779 −0.0937676
\(612\) −20.4315 −0.825893
\(613\) −37.0168 −1.49509 −0.747547 0.664209i \(-0.768768\pi\)
−0.747547 + 0.664209i \(0.768768\pi\)
\(614\) 24.7328 0.998134
\(615\) 50.4026 2.03243
\(616\) 4.43483 0.178684
\(617\) 5.36868 0.216135 0.108067 0.994144i \(-0.465534\pi\)
0.108067 + 0.994144i \(0.465534\pi\)
\(618\) 12.9628 0.521440
\(619\) 24.3846 0.980100 0.490050 0.871694i \(-0.336979\pi\)
0.490050 + 0.871694i \(0.336979\pi\)
\(620\) 53.2236 2.13751
\(621\) 23.4972 0.942910
\(622\) 25.2727 1.01334
\(623\) −5.13088 −0.205564
\(624\) 20.2940 0.812412
\(625\) −2.63442 −0.105377
\(626\) −80.9091 −3.23378
\(627\) −9.13209 −0.364700
\(628\) 54.6676 2.18147
\(629\) 8.94366 0.356607
\(630\) 30.6199 1.21993
\(631\) −21.7848 −0.867239 −0.433620 0.901096i \(-0.642764\pi\)
−0.433620 + 0.901096i \(0.642764\pi\)
\(632\) −81.8112 −3.25427
\(633\) −25.4594 −1.01192
\(634\) 43.4034 1.72377
\(635\) 47.9242 1.90181
\(636\) 3.87038 0.153471
\(637\) 7.19131 0.284930
\(638\) 4.26882 0.169004
\(639\) 42.4764 1.68034
\(640\) 48.1876 1.90478
\(641\) 28.1880 1.11336 0.556680 0.830727i \(-0.312075\pi\)
0.556680 + 0.830727i \(0.312075\pi\)
\(642\) −63.0953 −2.49017
\(643\) −0.986771 −0.0389144 −0.0194572 0.999811i \(-0.506194\pi\)
−0.0194572 + 0.999811i \(0.506194\pi\)
\(644\) 16.6714 0.656944
\(645\) 9.90554 0.390030
\(646\) 8.36487 0.329111
\(647\) 12.6065 0.495614 0.247807 0.968809i \(-0.420290\pi\)
0.247807 + 0.968809i \(0.420290\pi\)
\(648\) 8.61783 0.338540
\(649\) 5.62610 0.220844
\(650\) 22.0828 0.866159
\(651\) 6.77702 0.265612
\(652\) 58.8176 2.30348
\(653\) 39.5312 1.54698 0.773488 0.633811i \(-0.218510\pi\)
0.773488 + 0.633811i \(0.218510\pi\)
\(654\) 124.208 4.85691
\(655\) 23.1621 0.905019
\(656\) −33.6211 −1.31268
\(657\) −49.2296 −1.92063
\(658\) 3.84224 0.149786
\(659\) 4.72138 0.183919 0.0919594 0.995763i \(-0.470687\pi\)
0.0919594 + 0.995763i \(0.470687\pi\)
\(660\) −43.6535 −1.69921
\(661\) −13.5522 −0.527121 −0.263561 0.964643i \(-0.584897\pi\)
−0.263561 + 0.964643i \(0.584897\pi\)
\(662\) −27.8415 −1.08209
\(663\) −3.07136 −0.119282
\(664\) 53.9213 2.09255
\(665\) −8.62286 −0.334380
\(666\) 104.954 4.06690
\(667\) 8.76463 0.339368
\(668\) 28.3616 1.09734
\(669\) −31.2262 −1.20728
\(670\) 71.7558 2.77217
\(671\) −11.2332 −0.433652
\(672\) −9.13176 −0.352265
\(673\) −43.0031 −1.65765 −0.828823 0.559511i \(-0.810989\pi\)
−0.828823 + 0.559511i \(0.810989\pi\)
\(674\) 21.5442 0.829853
\(675\) −35.4893 −1.36598
\(676\) −51.8466 −1.99410
\(677\) −5.30738 −0.203979 −0.101990 0.994785i \(-0.532521\pi\)
−0.101990 + 0.994785i \(0.532521\pi\)
\(678\) −14.1608 −0.543843
\(679\) −8.95878 −0.343806
\(680\) 21.8393 0.837500
\(681\) 34.2732 1.31335
\(682\) −8.52804 −0.326555
\(683\) −19.4323 −0.743555 −0.371777 0.928322i \(-0.621252\pi\)
−0.371777 + 0.928322i \(0.621252\pi\)
\(684\) 67.5199 2.58169
\(685\) 68.1073 2.60225
\(686\) −24.8186 −0.947579
\(687\) 46.1652 1.76131
\(688\) −6.60750 −0.251909
\(689\) 0.353240 0.0134574
\(690\) −130.304 −4.96058
\(691\) −19.1445 −0.728290 −0.364145 0.931342i \(-0.618639\pi\)
−0.364145 + 0.931342i \(0.618639\pi\)
\(692\) −7.41344 −0.281817
\(693\) −3.37471 −0.128195
\(694\) −40.8933 −1.55229
\(695\) 26.3595 0.999875
\(696\) −28.3934 −1.07625
\(697\) 5.08833 0.192734
\(698\) −44.4511 −1.68250
\(699\) −2.56452 −0.0969989
\(700\) −25.1799 −0.951709
\(701\) −17.8388 −0.673764 −0.336882 0.941547i \(-0.609372\pi\)
−0.336882 + 0.941547i \(0.609372\pi\)
\(702\) −12.7199 −0.480082
\(703\) −29.5561 −1.11473
\(704\) −1.72381 −0.0649685
\(705\) −20.6566 −0.777971
\(706\) −21.8033 −0.820579
\(707\) 11.2911 0.424647
\(708\) −68.5150 −2.57495
\(709\) −43.9451 −1.65039 −0.825196 0.564847i \(-0.808935\pi\)
−0.825196 + 0.564847i \(0.808935\pi\)
\(710\) −83.1297 −3.11980
\(711\) 62.2548 2.33474
\(712\) −42.9450 −1.60943
\(713\) −17.5095 −0.655737
\(714\) 5.09146 0.190543
\(715\) −3.98414 −0.148998
\(716\) 41.2806 1.54273
\(717\) 29.7715 1.11184
\(718\) −21.4132 −0.799135
\(719\) −21.3436 −0.795983 −0.397991 0.917389i \(-0.630293\pi\)
−0.397991 + 0.917389i \(0.630293\pi\)
\(720\) 109.809 4.09232
\(721\) −1.34900 −0.0502395
\(722\) 20.4494 0.761049
\(723\) 44.9302 1.67097
\(724\) 47.2856 1.75735
\(725\) −13.2378 −0.491639
\(726\) 6.99462 0.259595
\(727\) 22.3115 0.827487 0.413743 0.910394i \(-0.364221\pi\)
0.413743 + 0.910394i \(0.364221\pi\)
\(728\) −4.92914 −0.182686
\(729\) −44.0398 −1.63110
\(730\) 96.3463 3.56594
\(731\) 1.00000 0.0369863
\(732\) 136.798 5.05621
\(733\) 13.4155 0.495512 0.247756 0.968823i \(-0.420307\pi\)
0.247756 + 0.968823i \(0.420307\pi\)
\(734\) 43.6119 1.60974
\(735\) 64.0903 2.36401
\(736\) 23.5934 0.869664
\(737\) −7.90842 −0.291310
\(738\) 59.7118 2.19802
\(739\) 26.7037 0.982310 0.491155 0.871072i \(-0.336575\pi\)
0.491155 + 0.871072i \(0.336575\pi\)
\(740\) −141.285 −5.19375
\(741\) 10.1499 0.372868
\(742\) −0.585572 −0.0214970
\(743\) −46.4708 −1.70485 −0.852425 0.522849i \(-0.824869\pi\)
−0.852425 + 0.522849i \(0.824869\pi\)
\(744\) 56.7229 2.07956
\(745\) 0.313974 0.0115031
\(746\) 81.6879 2.99081
\(747\) −41.0318 −1.50127
\(748\) −4.40698 −0.161135
\(749\) 6.56615 0.239922
\(750\) 71.4416 2.60868
\(751\) 29.2481 1.06728 0.533639 0.845712i \(-0.320824\pi\)
0.533639 + 0.845712i \(0.320824\pi\)
\(752\) 13.7790 0.502467
\(753\) 13.7776 0.502084
\(754\) −4.74462 −0.172789
\(755\) −3.33851 −0.121501
\(756\) 14.5038 0.527500
\(757\) −47.5353 −1.72770 −0.863850 0.503748i \(-0.831954\pi\)
−0.863850 + 0.503748i \(0.831954\pi\)
\(758\) 21.0885 0.765967
\(759\) 14.3612 0.521277
\(760\) −72.1725 −2.61797
\(761\) 8.45911 0.306642 0.153321 0.988176i \(-0.451003\pi\)
0.153321 + 0.988176i \(0.451003\pi\)
\(762\) 93.5143 3.38767
\(763\) −12.9260 −0.467951
\(764\) 59.1804 2.14107
\(765\) −16.6188 −0.600853
\(766\) 50.5127 1.82510
\(767\) −6.25318 −0.225789
\(768\) 84.5013 3.04918
\(769\) 27.4662 0.990458 0.495229 0.868763i \(-0.335084\pi\)
0.495229 + 0.868763i \(0.335084\pi\)
\(770\) 6.60459 0.238013
\(771\) −45.1650 −1.62658
\(772\) 47.0336 1.69277
\(773\) 33.8368 1.21702 0.608512 0.793544i \(-0.291767\pi\)
0.608512 + 0.793544i \(0.291767\pi\)
\(774\) 11.7351 0.421808
\(775\) 26.4458 0.949960
\(776\) −74.9841 −2.69177
\(777\) −17.9900 −0.645388
\(778\) −31.1045 −1.11515
\(779\) −16.8154 −0.602474
\(780\) 48.5191 1.73726
\(781\) 9.16197 0.327841
\(782\) −13.1546 −0.470409
\(783\) 7.62509 0.272499
\(784\) −42.7515 −1.52684
\(785\) 44.4662 1.58707
\(786\) 45.1962 1.61209
\(787\) 7.45921 0.265892 0.132946 0.991123i \(-0.457556\pi\)
0.132946 + 0.991123i \(0.457556\pi\)
\(788\) 69.5611 2.47801
\(789\) −27.1105 −0.965158
\(790\) −121.838 −4.33479
\(791\) 1.47368 0.0523980
\(792\) −28.2460 −1.00368
\(793\) 12.4852 0.443363
\(794\) −76.6931 −2.72174
\(795\) 3.14814 0.111653
\(796\) 35.4788 1.25751
\(797\) 49.1949 1.74257 0.871286 0.490775i \(-0.163286\pi\)
0.871286 + 0.490775i \(0.163286\pi\)
\(798\) −16.8258 −0.595626
\(799\) −2.08535 −0.0737745
\(800\) −35.6346 −1.25987
\(801\) 32.6793 1.15467
\(802\) −66.0863 −2.33359
\(803\) −10.6186 −0.374723
\(804\) 96.3093 3.39657
\(805\) 13.5604 0.477940
\(806\) 9.47857 0.333868
\(807\) −4.11395 −0.144818
\(808\) 94.5058 3.32470
\(809\) −24.9932 −0.878713 −0.439356 0.898313i \(-0.644793\pi\)
−0.439356 + 0.898313i \(0.644793\pi\)
\(810\) 12.8341 0.450945
\(811\) 16.9689 0.595859 0.297929 0.954588i \(-0.403704\pi\)
0.297929 + 0.954588i \(0.403704\pi\)
\(812\) 5.41004 0.189855
\(813\) 76.6489 2.68819
\(814\) 22.6382 0.793469
\(815\) 47.8418 1.67582
\(816\) 18.2589 0.639189
\(817\) −3.30470 −0.115617
\(818\) 48.3244 1.68962
\(819\) 3.75086 0.131066
\(820\) −80.3816 −2.80705
\(821\) 21.2283 0.740874 0.370437 0.928858i \(-0.379208\pi\)
0.370437 + 0.928858i \(0.379208\pi\)
\(822\) 132.898 4.63534
\(823\) −21.6128 −0.753375 −0.376687 0.926340i \(-0.622937\pi\)
−0.376687 + 0.926340i \(0.622937\pi\)
\(824\) −11.2910 −0.393342
\(825\) −21.6906 −0.755170
\(826\) 10.3660 0.360680
\(827\) −34.6050 −1.20333 −0.601666 0.798747i \(-0.705496\pi\)
−0.601666 + 0.798747i \(0.705496\pi\)
\(828\) −106.182 −3.69009
\(829\) −16.8068 −0.583726 −0.291863 0.956460i \(-0.594275\pi\)
−0.291863 + 0.956460i \(0.594275\pi\)
\(830\) 80.3025 2.78734
\(831\) 68.1181 2.36299
\(832\) 1.91594 0.0664234
\(833\) 6.47015 0.224177
\(834\) 51.4353 1.78106
\(835\) 23.0691 0.798338
\(836\) 14.5638 0.503698
\(837\) −15.2330 −0.526531
\(838\) −65.2454 −2.25386
\(839\) 46.9449 1.62072 0.810358 0.585935i \(-0.199273\pi\)
0.810358 + 0.585935i \(0.199273\pi\)
\(840\) −43.9294 −1.51571
\(841\) −26.1558 −0.901924
\(842\) −42.4449 −1.46275
\(843\) −7.65122 −0.263522
\(844\) 40.6024 1.39759
\(845\) −42.1716 −1.45075
\(846\) −24.4717 −0.841356
\(847\) −0.727911 −0.0250113
\(848\) −2.09997 −0.0721132
\(849\) 40.8939 1.40347
\(850\) 19.8683 0.681477
\(851\) 46.4801 1.59332
\(852\) −111.575 −3.82250
\(853\) 22.0380 0.754566 0.377283 0.926098i \(-0.376858\pi\)
0.377283 + 0.926098i \(0.376858\pi\)
\(854\) −20.6970 −0.708237
\(855\) 54.9201 1.87823
\(856\) 54.9581 1.87843
\(857\) 49.2367 1.68189 0.840946 0.541119i \(-0.181999\pi\)
0.840946 + 0.541119i \(0.181999\pi\)
\(858\) −7.77424 −0.265408
\(859\) 11.4770 0.391590 0.195795 0.980645i \(-0.437271\pi\)
0.195795 + 0.980645i \(0.437271\pi\)
\(860\) −15.7973 −0.538682
\(861\) −10.2351 −0.348810
\(862\) −43.2695 −1.47376
\(863\) −25.2768 −0.860434 −0.430217 0.902726i \(-0.641563\pi\)
−0.430217 + 0.902726i \(0.641563\pi\)
\(864\) 20.5259 0.698305
\(865\) −6.03003 −0.205027
\(866\) 21.4365 0.728441
\(867\) −2.76336 −0.0938486
\(868\) −10.8079 −0.366844
\(869\) 13.4281 0.455516
\(870\) −42.2850 −1.43360
\(871\) 8.78989 0.297834
\(872\) −108.189 −3.66374
\(873\) 57.0596 1.93118
\(874\) 43.4722 1.47047
\(875\) −7.43473 −0.251340
\(876\) 129.314 4.36912
\(877\) −16.0833 −0.543093 −0.271546 0.962425i \(-0.587535\pi\)
−0.271546 + 0.962425i \(0.587535\pi\)
\(878\) 7.00902 0.236543
\(879\) −78.3933 −2.64414
\(880\) 23.6852 0.798429
\(881\) −39.9404 −1.34563 −0.672813 0.739812i \(-0.734914\pi\)
−0.672813 + 0.739812i \(0.734914\pi\)
\(882\) 75.9275 2.55661
\(883\) −23.3355 −0.785303 −0.392651 0.919687i \(-0.628442\pi\)
−0.392651 + 0.919687i \(0.628442\pi\)
\(884\) 4.89818 0.164744
\(885\) −55.7295 −1.87333
\(886\) −74.0322 −2.48716
\(887\) 19.0914 0.641028 0.320514 0.947244i \(-0.396144\pi\)
0.320514 + 0.947244i \(0.396144\pi\)
\(888\) −150.575 −5.05295
\(889\) −9.73178 −0.326393
\(890\) −63.9559 −2.14381
\(891\) −1.41449 −0.0473871
\(892\) 49.7992 1.66740
\(893\) 6.89148 0.230614
\(894\) 0.612658 0.0204903
\(895\) 33.5773 1.12237
\(896\) −9.78527 −0.326903
\(897\) −15.9619 −0.532951
\(898\) 10.6854 0.356576
\(899\) −5.68203 −0.189506
\(900\) 160.374 5.34579
\(901\) 0.317816 0.0105880
\(902\) 12.8796 0.428843
\(903\) −2.01148 −0.0669379
\(904\) 12.3345 0.410241
\(905\) 38.4617 1.27851
\(906\) −6.51443 −0.216428
\(907\) 6.32800 0.210118 0.105059 0.994466i \(-0.466497\pi\)
0.105059 + 0.994466i \(0.466497\pi\)
\(908\) −54.6585 −1.81391
\(909\) −71.9148 −2.38526
\(910\) −7.34073 −0.243343
\(911\) 39.9389 1.32324 0.661618 0.749841i \(-0.269870\pi\)
0.661618 + 0.749841i \(0.269870\pi\)
\(912\) −60.3402 −1.99807
\(913\) −8.85038 −0.292905
\(914\) −13.8155 −0.456977
\(915\) 111.271 3.67849
\(916\) −73.6237 −2.43260
\(917\) −4.70344 −0.155321
\(918\) −11.4443 −0.377719
\(919\) −11.2318 −0.370503 −0.185252 0.982691i \(-0.559310\pi\)
−0.185252 + 0.982691i \(0.559310\pi\)
\(920\) 113.499 3.74195
\(921\) 27.0013 0.889721
\(922\) 59.7680 1.96835
\(923\) −10.1832 −0.335183
\(924\) 8.86455 0.291622
\(925\) −70.2020 −2.30823
\(926\) 24.3550 0.800354
\(927\) 8.59198 0.282198
\(928\) 7.65631 0.251331
\(929\) 56.6387 1.85826 0.929128 0.369759i \(-0.120560\pi\)
0.929128 + 0.369759i \(0.120560\pi\)
\(930\) 84.4748 2.77004
\(931\) −21.3819 −0.700764
\(932\) 4.08986 0.133968
\(933\) 27.5907 0.903280
\(934\) −72.2377 −2.36369
\(935\) −3.58460 −0.117229
\(936\) 31.3943 1.02616
\(937\) −30.9539 −1.01122 −0.505610 0.862762i \(-0.668732\pi\)
−0.505610 + 0.862762i \(0.668732\pi\)
\(938\) −14.5712 −0.475766
\(939\) −88.3300 −2.88254
\(940\) 32.9429 1.07448
\(941\) −9.45627 −0.308266 −0.154133 0.988050i \(-0.549258\pi\)
−0.154133 + 0.988050i \(0.549258\pi\)
\(942\) 86.7667 2.82701
\(943\) 26.4440 0.861135
\(944\) 37.1744 1.20992
\(945\) 11.7973 0.383766
\(946\) 2.53120 0.0822964
\(947\) 22.4456 0.729383 0.364692 0.931128i \(-0.381174\pi\)
0.364692 + 0.931128i \(0.381174\pi\)
\(948\) −163.528 −5.31115
\(949\) 11.8022 0.383114
\(950\) −65.6588 −2.13025
\(951\) 47.3844 1.53654
\(952\) −4.43483 −0.143734
\(953\) 53.3749 1.72898 0.864492 0.502647i \(-0.167640\pi\)
0.864492 + 0.502647i \(0.167640\pi\)
\(954\) 3.72959 0.120750
\(955\) 48.1369 1.55767
\(956\) −47.4793 −1.53559
\(957\) 4.66035 0.150648
\(958\) −96.4256 −3.11537
\(959\) −13.8303 −0.446604
\(960\) 17.0753 0.551102
\(961\) −19.6487 −0.633830
\(962\) −25.1615 −0.811238
\(963\) −41.8207 −1.34765
\(964\) −71.6542 −2.30783
\(965\) 38.2567 1.23153
\(966\) 26.4603 0.851346
\(967\) 46.7318 1.50279 0.751397 0.659851i \(-0.229381\pi\)
0.751397 + 0.659851i \(0.229381\pi\)
\(968\) −6.09254 −0.195822
\(969\) 9.13209 0.293365
\(970\) −111.670 −3.58552
\(971\) 18.9699 0.608775 0.304387 0.952548i \(-0.401548\pi\)
0.304387 + 0.952548i \(0.401548\pi\)
\(972\) 77.0016 2.46983
\(973\) −5.35274 −0.171601
\(974\) −54.1805 −1.73605
\(975\) 24.1082 0.772081
\(976\) −74.2232 −2.37583
\(977\) −12.6718 −0.405407 −0.202703 0.979240i \(-0.564973\pi\)
−0.202703 + 0.979240i \(0.564973\pi\)
\(978\) 93.3535 2.98512
\(979\) 7.04878 0.225280
\(980\) −102.211 −3.26499
\(981\) 82.3271 2.62850
\(982\) −19.3178 −0.616456
\(983\) −42.1953 −1.34582 −0.672911 0.739723i \(-0.734956\pi\)
−0.672911 + 0.739723i \(0.734956\pi\)
\(984\) −85.6665 −2.73095
\(985\) 56.5804 1.80280
\(986\) −4.26882 −0.135947
\(987\) 4.19465 0.133517
\(988\) −16.1870 −0.514978
\(989\) 5.19699 0.165255
\(990\) −42.0655 −1.33693
\(991\) −46.4445 −1.47536 −0.737679 0.675151i \(-0.764078\pi\)
−0.737679 + 0.675151i \(0.764078\pi\)
\(992\) −15.2954 −0.485629
\(993\) −30.3951 −0.964560
\(994\) 16.8808 0.535427
\(995\) 28.8582 0.914865
\(996\) 107.781 3.41516
\(997\) 0.465258 0.0147349 0.00736743 0.999973i \(-0.497655\pi\)
0.00736743 + 0.999973i \(0.497655\pi\)
\(998\) 2.81524 0.0891147
\(999\) 40.4370 1.27937
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 \(a_p\))