Properties

Label 8041.2.a.i.1.7
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 1.7
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36526 q^{2} -1.70691 q^{3} +3.59444 q^{4} -0.509718 q^{5} +4.03728 q^{6} +0.312769 q^{7} -3.77127 q^{8} -0.0864584 q^{9} +O(q^{10})\) \(q-2.36526 q^{2} -1.70691 q^{3} +3.59444 q^{4} -0.509718 q^{5} +4.03728 q^{6} +0.312769 q^{7} -3.77127 q^{8} -0.0864584 q^{9} +1.20561 q^{10} +1.00000 q^{11} -6.13539 q^{12} +3.76096 q^{13} -0.739780 q^{14} +0.870043 q^{15} +1.73114 q^{16} -1.00000 q^{17} +0.204496 q^{18} -3.37007 q^{19} -1.83215 q^{20} -0.533869 q^{21} -2.36526 q^{22} +0.611649 q^{23} +6.43722 q^{24} -4.74019 q^{25} -8.89564 q^{26} +5.26831 q^{27} +1.12423 q^{28} -7.27340 q^{29} -2.05788 q^{30} -7.89935 q^{31} +3.44795 q^{32} -1.70691 q^{33} +2.36526 q^{34} -0.159424 q^{35} -0.310770 q^{36} -6.00809 q^{37} +7.97109 q^{38} -6.41962 q^{39} +1.92229 q^{40} +6.21231 q^{41} +1.26274 q^{42} -1.00000 q^{43} +3.59444 q^{44} +0.0440694 q^{45} -1.44671 q^{46} -7.02890 q^{47} -2.95490 q^{48} -6.90218 q^{49} +11.2118 q^{50} +1.70691 q^{51} +13.5186 q^{52} -4.25497 q^{53} -12.4609 q^{54} -0.509718 q^{55} -1.17954 q^{56} +5.75241 q^{57} +17.2035 q^{58} +9.41026 q^{59} +3.12732 q^{60} +14.0984 q^{61} +18.6840 q^{62} -0.0270415 q^{63} -11.6176 q^{64} -1.91703 q^{65} +4.03728 q^{66} +9.83006 q^{67} -3.59444 q^{68} -1.04403 q^{69} +0.377079 q^{70} -3.92911 q^{71} +0.326058 q^{72} +1.30459 q^{73} +14.2107 q^{74} +8.09107 q^{75} -12.1135 q^{76} +0.312769 q^{77} +15.1841 q^{78} -13.1289 q^{79} -0.882393 q^{80} -8.73315 q^{81} -14.6937 q^{82} +4.52049 q^{83} -1.91896 q^{84} +0.509718 q^{85} +2.36526 q^{86} +12.4150 q^{87} -3.77127 q^{88} -7.93708 q^{89} -0.104235 q^{90} +1.17631 q^{91} +2.19854 q^{92} +13.4835 q^{93} +16.6252 q^{94} +1.71779 q^{95} -5.88534 q^{96} +1.17482 q^{97} +16.3254 q^{98} -0.0864584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36526 −1.67249 −0.836245 0.548356i \(-0.815254\pi\)
−0.836245 + 0.548356i \(0.815254\pi\)
\(3\) −1.70691 −0.985485 −0.492742 0.870175i \(-0.664006\pi\)
−0.492742 + 0.870175i \(0.664006\pi\)
\(4\) 3.59444 1.79722
\(5\) −0.509718 −0.227953 −0.113976 0.993483i \(-0.536359\pi\)
−0.113976 + 0.993483i \(0.536359\pi\)
\(6\) 4.03728 1.64821
\(7\) 0.312769 0.118216 0.0591079 0.998252i \(-0.481174\pi\)
0.0591079 + 0.998252i \(0.481174\pi\)
\(8\) −3.77127 −1.33335
\(9\) −0.0864584 −0.0288195
\(10\) 1.20561 0.381249
\(11\) 1.00000 0.301511
\(12\) −6.13539 −1.77114
\(13\) 3.76096 1.04310 0.521552 0.853220i \(-0.325353\pi\)
0.521552 + 0.853220i \(0.325353\pi\)
\(14\) −0.739780 −0.197715
\(15\) 0.870043 0.224644
\(16\) 1.73114 0.432785
\(17\) −1.00000 −0.242536
\(18\) 0.204496 0.0482002
\(19\) −3.37007 −0.773148 −0.386574 0.922258i \(-0.626342\pi\)
−0.386574 + 0.922258i \(0.626342\pi\)
\(20\) −1.83215 −0.409682
\(21\) −0.533869 −0.116500
\(22\) −2.36526 −0.504275
\(23\) 0.611649 0.127538 0.0637688 0.997965i \(-0.479688\pi\)
0.0637688 + 0.997965i \(0.479688\pi\)
\(24\) 6.43722 1.31399
\(25\) −4.74019 −0.948037
\(26\) −8.89564 −1.74458
\(27\) 5.26831 1.01389
\(28\) 1.12423 0.212460
\(29\) −7.27340 −1.35064 −0.675318 0.737527i \(-0.735994\pi\)
−0.675318 + 0.737527i \(0.735994\pi\)
\(30\) −2.05788 −0.375715
\(31\) −7.89935 −1.41876 −0.709382 0.704824i \(-0.751026\pi\)
−0.709382 + 0.704824i \(0.751026\pi\)
\(32\) 3.44795 0.609517
\(33\) −1.70691 −0.297135
\(34\) 2.36526 0.405638
\(35\) −0.159424 −0.0269476
\(36\) −0.310770 −0.0517950
\(37\) −6.00809 −0.987724 −0.493862 0.869540i \(-0.664415\pi\)
−0.493862 + 0.869540i \(0.664415\pi\)
\(38\) 7.97109 1.29308
\(39\) −6.41962 −1.02796
\(40\) 1.92229 0.303940
\(41\) 6.21231 0.970200 0.485100 0.874459i \(-0.338783\pi\)
0.485100 + 0.874459i \(0.338783\pi\)
\(42\) 1.26274 0.194845
\(43\) −1.00000 −0.152499
\(44\) 3.59444 0.541883
\(45\) 0.0440694 0.00656948
\(46\) −1.44671 −0.213305
\(47\) −7.02890 −1.02527 −0.512635 0.858607i \(-0.671331\pi\)
−0.512635 + 0.858607i \(0.671331\pi\)
\(48\) −2.95490 −0.426503
\(49\) −6.90218 −0.986025
\(50\) 11.2118 1.58558
\(51\) 1.70691 0.239015
\(52\) 13.5186 1.87469
\(53\) −4.25497 −0.584465 −0.292233 0.956347i \(-0.594398\pi\)
−0.292233 + 0.956347i \(0.594398\pi\)
\(54\) −12.4609 −1.69571
\(55\) −0.509718 −0.0687304
\(56\) −1.17954 −0.157622
\(57\) 5.75241 0.761926
\(58\) 17.2035 2.25892
\(59\) 9.41026 1.22511 0.612556 0.790427i \(-0.290142\pi\)
0.612556 + 0.790427i \(0.290142\pi\)
\(60\) 3.12732 0.403735
\(61\) 14.0984 1.80511 0.902555 0.430574i \(-0.141689\pi\)
0.902555 + 0.430574i \(0.141689\pi\)
\(62\) 18.6840 2.37287
\(63\) −0.0270415 −0.00340691
\(64\) −11.6176 −1.45220
\(65\) −1.91703 −0.237778
\(66\) 4.03728 0.496955
\(67\) 9.83006 1.20093 0.600467 0.799650i \(-0.294982\pi\)
0.600467 + 0.799650i \(0.294982\pi\)
\(68\) −3.59444 −0.435890
\(69\) −1.04403 −0.125686
\(70\) 0.377079 0.0450696
\(71\) −3.92911 −0.466299 −0.233150 0.972441i \(-0.574903\pi\)
−0.233150 + 0.972441i \(0.574903\pi\)
\(72\) 0.326058 0.0384263
\(73\) 1.30459 0.152690 0.0763451 0.997081i \(-0.475675\pi\)
0.0763451 + 0.997081i \(0.475675\pi\)
\(74\) 14.2107 1.65196
\(75\) 8.09107 0.934277
\(76\) −12.1135 −1.38952
\(77\) 0.312769 0.0356434
\(78\) 15.1841 1.71926
\(79\) −13.1289 −1.47711 −0.738557 0.674191i \(-0.764492\pi\)
−0.738557 + 0.674191i \(0.764492\pi\)
\(80\) −0.882393 −0.0986546
\(81\) −8.73315 −0.970350
\(82\) −14.6937 −1.62265
\(83\) 4.52049 0.496188 0.248094 0.968736i \(-0.420196\pi\)
0.248094 + 0.968736i \(0.420196\pi\)
\(84\) −1.91896 −0.209376
\(85\) 0.509718 0.0552867
\(86\) 2.36526 0.255052
\(87\) 12.4150 1.33103
\(88\) −3.77127 −0.402019
\(89\) −7.93708 −0.841329 −0.420665 0.907216i \(-0.638203\pi\)
−0.420665 + 0.907216i \(0.638203\pi\)
\(90\) −0.104235 −0.0109874
\(91\) 1.17631 0.123311
\(92\) 2.19854 0.229213
\(93\) 13.4835 1.39817
\(94\) 16.6252 1.71475
\(95\) 1.71779 0.176241
\(96\) −5.88534 −0.600670
\(97\) 1.17482 0.119285 0.0596426 0.998220i \(-0.481004\pi\)
0.0596426 + 0.998220i \(0.481004\pi\)
\(98\) 16.3254 1.64912
\(99\) −0.0864584 −0.00868939
\(100\) −17.0383 −1.70383
\(101\) −11.4548 −1.13979 −0.569896 0.821717i \(-0.693016\pi\)
−0.569896 + 0.821717i \(0.693016\pi\)
\(102\) −4.03728 −0.399750
\(103\) −3.30647 −0.325796 −0.162898 0.986643i \(-0.552084\pi\)
−0.162898 + 0.986643i \(0.552084\pi\)
\(104\) −14.1836 −1.39082
\(105\) 0.272123 0.0265565
\(106\) 10.0641 0.977512
\(107\) −13.3175 −1.28745 −0.643727 0.765255i \(-0.722613\pi\)
−0.643727 + 0.765255i \(0.722613\pi\)
\(108\) 18.9366 1.82218
\(109\) 7.19879 0.689519 0.344760 0.938691i \(-0.387960\pi\)
0.344760 + 0.938691i \(0.387960\pi\)
\(110\) 1.20561 0.114951
\(111\) 10.2553 0.973387
\(112\) 0.541448 0.0511620
\(113\) 3.29147 0.309635 0.154818 0.987943i \(-0.450521\pi\)
0.154818 + 0.987943i \(0.450521\pi\)
\(114\) −13.6059 −1.27431
\(115\) −0.311768 −0.0290726
\(116\) −26.1438 −2.42739
\(117\) −0.325167 −0.0300617
\(118\) −22.2577 −2.04899
\(119\) −0.312769 −0.0286715
\(120\) −3.28117 −0.299528
\(121\) 1.00000 0.0909091
\(122\) −33.3463 −3.01903
\(123\) −10.6039 −0.956118
\(124\) −28.3938 −2.54983
\(125\) 4.96475 0.444061
\(126\) 0.0639602 0.00569803
\(127\) −18.4845 −1.64023 −0.820116 0.572198i \(-0.806091\pi\)
−0.820116 + 0.572198i \(0.806091\pi\)
\(128\) 20.5826 1.81927
\(129\) 1.70691 0.150285
\(130\) 4.53427 0.397682
\(131\) 18.7532 1.63848 0.819239 0.573452i \(-0.194396\pi\)
0.819239 + 0.573452i \(0.194396\pi\)
\(132\) −6.13539 −0.534017
\(133\) −1.05406 −0.0913983
\(134\) −23.2506 −2.00855
\(135\) −2.68535 −0.231118
\(136\) 3.77127 0.323384
\(137\) 7.06003 0.603179 0.301590 0.953438i \(-0.402483\pi\)
0.301590 + 0.953438i \(0.402483\pi\)
\(138\) 2.46940 0.210209
\(139\) 10.3144 0.874853 0.437427 0.899254i \(-0.355890\pi\)
0.437427 + 0.899254i \(0.355890\pi\)
\(140\) −0.573042 −0.0484309
\(141\) 11.9977 1.01039
\(142\) 9.29335 0.779881
\(143\) 3.76096 0.314507
\(144\) −0.149671 −0.0124726
\(145\) 3.70738 0.307881
\(146\) −3.08568 −0.255373
\(147\) 11.7814 0.971713
\(148\) −21.5958 −1.77516
\(149\) 9.73609 0.797611 0.398806 0.917035i \(-0.369425\pi\)
0.398806 + 0.917035i \(0.369425\pi\)
\(150\) −19.1375 −1.56257
\(151\) 16.8568 1.37179 0.685893 0.727702i \(-0.259412\pi\)
0.685893 + 0.727702i \(0.259412\pi\)
\(152\) 12.7095 1.03087
\(153\) 0.0864584 0.00698974
\(154\) −0.739780 −0.0596132
\(155\) 4.02644 0.323411
\(156\) −23.0750 −1.84748
\(157\) 12.5896 1.00476 0.502379 0.864647i \(-0.332458\pi\)
0.502379 + 0.864647i \(0.332458\pi\)
\(158\) 31.0532 2.47046
\(159\) 7.26285 0.575982
\(160\) −1.75748 −0.138941
\(161\) 0.191305 0.0150769
\(162\) 20.6561 1.62290
\(163\) −24.8782 −1.94861 −0.974304 0.225236i \(-0.927685\pi\)
−0.974304 + 0.225236i \(0.927685\pi\)
\(164\) 22.3298 1.74367
\(165\) 0.870043 0.0677328
\(166\) −10.6921 −0.829870
\(167\) 2.02938 0.157038 0.0785192 0.996913i \(-0.474981\pi\)
0.0785192 + 0.996913i \(0.474981\pi\)
\(168\) 2.01337 0.155335
\(169\) 1.14484 0.0880643
\(170\) −1.20561 −0.0924664
\(171\) 0.291371 0.0222817
\(172\) −3.59444 −0.274074
\(173\) 17.4523 1.32687 0.663436 0.748233i \(-0.269097\pi\)
0.663436 + 0.748233i \(0.269097\pi\)
\(174\) −29.3647 −2.22614
\(175\) −1.48259 −0.112073
\(176\) 1.73114 0.130490
\(177\) −16.0625 −1.20733
\(178\) 18.7732 1.40711
\(179\) 16.3632 1.22304 0.611520 0.791229i \(-0.290558\pi\)
0.611520 + 0.791229i \(0.290558\pi\)
\(180\) 0.158405 0.0118068
\(181\) 11.9105 0.885303 0.442652 0.896694i \(-0.354038\pi\)
0.442652 + 0.896694i \(0.354038\pi\)
\(182\) −2.78229 −0.206237
\(183\) −24.0646 −1.77891
\(184\) −2.30669 −0.170052
\(185\) 3.06243 0.225155
\(186\) −31.8919 −2.33843
\(187\) −1.00000 −0.0731272
\(188\) −25.2650 −1.84264
\(189\) 1.64777 0.119857
\(190\) −4.06301 −0.294762
\(191\) 14.2196 1.02890 0.514449 0.857521i \(-0.327997\pi\)
0.514449 + 0.857521i \(0.327997\pi\)
\(192\) 19.8301 1.43112
\(193\) −7.28892 −0.524668 −0.262334 0.964977i \(-0.584492\pi\)
−0.262334 + 0.964977i \(0.584492\pi\)
\(194\) −2.77876 −0.199503
\(195\) 3.27220 0.234327
\(196\) −24.8095 −1.77211
\(197\) −21.6754 −1.54431 −0.772156 0.635434i \(-0.780821\pi\)
−0.772156 + 0.635434i \(0.780821\pi\)
\(198\) 0.204496 0.0145329
\(199\) −22.8038 −1.61652 −0.808259 0.588827i \(-0.799590\pi\)
−0.808259 + 0.588827i \(0.799590\pi\)
\(200\) 17.8765 1.26406
\(201\) −16.7790 −1.18350
\(202\) 27.0935 1.90629
\(203\) −2.27490 −0.159666
\(204\) 6.13539 0.429563
\(205\) −3.16653 −0.221160
\(206\) 7.82066 0.544891
\(207\) −0.0528821 −0.00367556
\(208\) 6.51075 0.451439
\(209\) −3.37007 −0.233113
\(210\) −0.643641 −0.0444154
\(211\) −10.6408 −0.732540 −0.366270 0.930509i \(-0.619365\pi\)
−0.366270 + 0.930509i \(0.619365\pi\)
\(212\) −15.2943 −1.05041
\(213\) 6.70663 0.459531
\(214\) 31.4994 2.15325
\(215\) 0.509718 0.0347625
\(216\) −19.8682 −1.35186
\(217\) −2.47067 −0.167720
\(218\) −17.0270 −1.15321
\(219\) −2.22681 −0.150474
\(220\) −1.83215 −0.123524
\(221\) −3.76096 −0.252990
\(222\) −24.2564 −1.62798
\(223\) −15.2857 −1.02361 −0.511805 0.859102i \(-0.671023\pi\)
−0.511805 + 0.859102i \(0.671023\pi\)
\(224\) 1.07841 0.0720545
\(225\) 0.409829 0.0273219
\(226\) −7.78517 −0.517862
\(227\) −0.255235 −0.0169406 −0.00847028 0.999964i \(-0.502696\pi\)
−0.00847028 + 0.999964i \(0.502696\pi\)
\(228\) 20.6767 1.36935
\(229\) −12.5246 −0.827648 −0.413824 0.910357i \(-0.635807\pi\)
−0.413824 + 0.910357i \(0.635807\pi\)
\(230\) 0.737413 0.0486235
\(231\) −0.533869 −0.0351260
\(232\) 27.4299 1.80086
\(233\) −9.08675 −0.595293 −0.297646 0.954676i \(-0.596202\pi\)
−0.297646 + 0.954676i \(0.596202\pi\)
\(234\) 0.769103 0.0502778
\(235\) 3.58276 0.233713
\(236\) 33.8246 2.20180
\(237\) 22.4098 1.45567
\(238\) 0.739780 0.0479528
\(239\) −13.3197 −0.861578 −0.430789 0.902453i \(-0.641765\pi\)
−0.430789 + 0.902453i \(0.641765\pi\)
\(240\) 1.50617 0.0972226
\(241\) 0.314487 0.0202579 0.0101290 0.999949i \(-0.496776\pi\)
0.0101290 + 0.999949i \(0.496776\pi\)
\(242\) −2.36526 −0.152045
\(243\) −0.898219 −0.0576208
\(244\) 50.6758 3.24418
\(245\) 3.51816 0.224767
\(246\) 25.0809 1.59910
\(247\) −12.6747 −0.806473
\(248\) 29.7906 1.89170
\(249\) −7.71607 −0.488986
\(250\) −11.7429 −0.742687
\(251\) 23.1569 1.46165 0.730827 0.682563i \(-0.239135\pi\)
0.730827 + 0.682563i \(0.239135\pi\)
\(252\) −0.0971993 −0.00612298
\(253\) 0.611649 0.0384540
\(254\) 43.7205 2.74327
\(255\) −0.870043 −0.0544842
\(256\) −25.4481 −1.59051
\(257\) −18.8193 −1.17392 −0.586959 0.809616i \(-0.699675\pi\)
−0.586959 + 0.809616i \(0.699675\pi\)
\(258\) −4.03728 −0.251350
\(259\) −1.87915 −0.116765
\(260\) −6.89066 −0.427341
\(261\) 0.628846 0.0389246
\(262\) −44.3563 −2.74034
\(263\) 28.5766 1.76211 0.881054 0.473016i \(-0.156835\pi\)
0.881054 + 0.473016i \(0.156835\pi\)
\(264\) 6.43722 0.396183
\(265\) 2.16884 0.133231
\(266\) 2.49311 0.152863
\(267\) 13.5479 0.829117
\(268\) 35.3336 2.15834
\(269\) 27.8727 1.69943 0.849716 0.527241i \(-0.176774\pi\)
0.849716 + 0.527241i \(0.176774\pi\)
\(270\) 6.35155 0.386543
\(271\) −15.3922 −0.935012 −0.467506 0.883990i \(-0.654847\pi\)
−0.467506 + 0.883990i \(0.654847\pi\)
\(272\) −1.73114 −0.104966
\(273\) −2.00786 −0.121521
\(274\) −16.6988 −1.00881
\(275\) −4.74019 −0.285844
\(276\) −3.75270 −0.225886
\(277\) −11.8593 −0.712554 −0.356277 0.934380i \(-0.615954\pi\)
−0.356277 + 0.934380i \(0.615954\pi\)
\(278\) −24.3961 −1.46318
\(279\) 0.682965 0.0408880
\(280\) 0.601232 0.0359305
\(281\) −26.2640 −1.56678 −0.783390 0.621531i \(-0.786511\pi\)
−0.783390 + 0.621531i \(0.786511\pi\)
\(282\) −28.3777 −1.68986
\(283\) −33.1837 −1.97257 −0.986284 0.165054i \(-0.947220\pi\)
−0.986284 + 0.165054i \(0.947220\pi\)
\(284\) −14.1230 −0.838044
\(285\) −2.93211 −0.173683
\(286\) −8.89564 −0.526010
\(287\) 1.94302 0.114693
\(288\) −0.298104 −0.0175660
\(289\) 1.00000 0.0588235
\(290\) −8.76891 −0.514928
\(291\) −2.00532 −0.117554
\(292\) 4.68926 0.274418
\(293\) 25.0005 1.46055 0.730273 0.683155i \(-0.239393\pi\)
0.730273 + 0.683155i \(0.239393\pi\)
\(294\) −27.8660 −1.62518
\(295\) −4.79658 −0.279268
\(296\) 22.6581 1.31698
\(297\) 5.26831 0.305698
\(298\) −23.0284 −1.33400
\(299\) 2.30039 0.133035
\(300\) 29.0829 1.67910
\(301\) −0.312769 −0.0180277
\(302\) −39.8707 −2.29430
\(303\) 19.5522 1.12325
\(304\) −5.83407 −0.334607
\(305\) −7.18619 −0.411480
\(306\) −0.204496 −0.0116903
\(307\) 0.0193220 0.00110276 0.000551381 1.00000i \(-0.499824\pi\)
0.000551381 1.00000i \(0.499824\pi\)
\(308\) 1.12423 0.0640591
\(309\) 5.64385 0.321068
\(310\) −9.52357 −0.540902
\(311\) 22.7414 1.28955 0.644773 0.764374i \(-0.276952\pi\)
0.644773 + 0.764374i \(0.276952\pi\)
\(312\) 24.2101 1.37063
\(313\) 9.55587 0.540130 0.270065 0.962842i \(-0.412955\pi\)
0.270065 + 0.962842i \(0.412955\pi\)
\(314\) −29.7776 −1.68045
\(315\) 0.0137836 0.000776616 0
\(316\) −47.1910 −2.65470
\(317\) −23.0615 −1.29526 −0.647632 0.761953i \(-0.724240\pi\)
−0.647632 + 0.761953i \(0.724240\pi\)
\(318\) −17.1785 −0.963324
\(319\) −7.27340 −0.407232
\(320\) 5.92169 0.331032
\(321\) 22.7318 1.26877
\(322\) −0.452486 −0.0252160
\(323\) 3.37007 0.187516
\(324\) −31.3908 −1.74393
\(325\) −17.8277 −0.988901
\(326\) 58.8433 3.25903
\(327\) −12.2877 −0.679511
\(328\) −23.4283 −1.29361
\(329\) −2.19843 −0.121203
\(330\) −2.05788 −0.113282
\(331\) −0.123516 −0.00678905 −0.00339453 0.999994i \(-0.501081\pi\)
−0.00339453 + 0.999994i \(0.501081\pi\)
\(332\) 16.2487 0.891761
\(333\) 0.519450 0.0284657
\(334\) −4.80001 −0.262645
\(335\) −5.01056 −0.273756
\(336\) −0.924202 −0.0504194
\(337\) 6.63459 0.361409 0.180705 0.983537i \(-0.442162\pi\)
0.180705 + 0.983537i \(0.442162\pi\)
\(338\) −2.70783 −0.147287
\(339\) −5.61824 −0.305141
\(340\) 1.83215 0.0993625
\(341\) −7.89935 −0.427774
\(342\) −0.689168 −0.0372659
\(343\) −4.34818 −0.234779
\(344\) 3.77127 0.203333
\(345\) 0.532161 0.0286506
\(346\) −41.2791 −2.21918
\(347\) −10.9413 −0.587357 −0.293679 0.955904i \(-0.594880\pi\)
−0.293679 + 0.955904i \(0.594880\pi\)
\(348\) 44.6251 2.39216
\(349\) 19.7751 1.05854 0.529268 0.848455i \(-0.322467\pi\)
0.529268 + 0.848455i \(0.322467\pi\)
\(350\) 3.50670 0.187441
\(351\) 19.8139 1.05759
\(352\) 3.44795 0.183776
\(353\) −29.5473 −1.57264 −0.786322 0.617816i \(-0.788018\pi\)
−0.786322 + 0.617816i \(0.788018\pi\)
\(354\) 37.9919 2.01924
\(355\) 2.00274 0.106294
\(356\) −28.5294 −1.51205
\(357\) 0.533869 0.0282554
\(358\) −38.7031 −2.04552
\(359\) 6.66030 0.351517 0.175758 0.984433i \(-0.443762\pi\)
0.175758 + 0.984433i \(0.443762\pi\)
\(360\) −0.166198 −0.00875938
\(361\) −7.64260 −0.402242
\(362\) −28.1715 −1.48066
\(363\) −1.70691 −0.0895895
\(364\) 4.22820 0.221618
\(365\) −0.664971 −0.0348062
\(366\) 56.9191 2.97521
\(367\) 32.3388 1.68807 0.844036 0.536286i \(-0.180173\pi\)
0.844036 + 0.536286i \(0.180173\pi\)
\(368\) 1.05885 0.0551963
\(369\) −0.537107 −0.0279606
\(370\) −7.24344 −0.376569
\(371\) −1.33083 −0.0690930
\(372\) 48.4656 2.51282
\(373\) −7.23152 −0.374434 −0.187217 0.982319i \(-0.559947\pi\)
−0.187217 + 0.982319i \(0.559947\pi\)
\(374\) 2.36526 0.122305
\(375\) −8.47438 −0.437615
\(376\) 26.5079 1.36704
\(377\) −27.3550 −1.40885
\(378\) −3.89739 −0.200460
\(379\) −13.0354 −0.669582 −0.334791 0.942292i \(-0.608666\pi\)
−0.334791 + 0.942292i \(0.608666\pi\)
\(380\) 6.17449 0.316745
\(381\) 31.5513 1.61642
\(382\) −33.6331 −1.72082
\(383\) 28.1019 1.43594 0.717970 0.696074i \(-0.245072\pi\)
0.717970 + 0.696074i \(0.245072\pi\)
\(384\) −35.1327 −1.79286
\(385\) −0.159424 −0.00812501
\(386\) 17.2402 0.877501
\(387\) 0.0864584 0.00439493
\(388\) 4.22284 0.214382
\(389\) −3.32203 −0.168434 −0.0842169 0.996447i \(-0.526839\pi\)
−0.0842169 + 0.996447i \(0.526839\pi\)
\(390\) −7.73959 −0.391910
\(391\) −0.611649 −0.0309324
\(392\) 26.0300 1.31471
\(393\) −32.0101 −1.61470
\(394\) 51.2680 2.58284
\(395\) 6.69202 0.336712
\(396\) −0.310770 −0.0156168
\(397\) −30.6687 −1.53922 −0.769609 0.638515i \(-0.779549\pi\)
−0.769609 + 0.638515i \(0.779549\pi\)
\(398\) 53.9369 2.70361
\(399\) 1.79918 0.0900716
\(400\) −8.20593 −0.410296
\(401\) 12.5440 0.626418 0.313209 0.949684i \(-0.398596\pi\)
0.313209 + 0.949684i \(0.398596\pi\)
\(402\) 39.6867 1.97939
\(403\) −29.7091 −1.47992
\(404\) −41.1735 −2.04846
\(405\) 4.45144 0.221194
\(406\) 5.38072 0.267040
\(407\) −6.00809 −0.297810
\(408\) −6.43722 −0.318690
\(409\) 18.1340 0.896670 0.448335 0.893866i \(-0.352017\pi\)
0.448335 + 0.893866i \(0.352017\pi\)
\(410\) 7.48966 0.369888
\(411\) −12.0508 −0.594424
\(412\) −11.8849 −0.585529
\(413\) 2.94324 0.144827
\(414\) 0.125080 0.00614734
\(415\) −2.30418 −0.113108
\(416\) 12.9676 0.635789
\(417\) −17.6057 −0.862155
\(418\) 7.97109 0.389879
\(419\) 2.68353 0.131099 0.0655496 0.997849i \(-0.479120\pi\)
0.0655496 + 0.997849i \(0.479120\pi\)
\(420\) 0.978130 0.0477279
\(421\) −21.5187 −1.04876 −0.524379 0.851485i \(-0.675702\pi\)
−0.524379 + 0.851485i \(0.675702\pi\)
\(422\) 25.1681 1.22517
\(423\) 0.607707 0.0295477
\(424\) 16.0467 0.779294
\(425\) 4.74019 0.229933
\(426\) −15.8629 −0.768561
\(427\) 4.40954 0.213392
\(428\) −47.8691 −2.31384
\(429\) −6.41962 −0.309942
\(430\) −1.20561 −0.0581399
\(431\) 30.9665 1.49160 0.745802 0.666168i \(-0.232067\pi\)
0.745802 + 0.666168i \(0.232067\pi\)
\(432\) 9.12017 0.438795
\(433\) −31.4210 −1.51000 −0.754999 0.655726i \(-0.772363\pi\)
−0.754999 + 0.655726i \(0.772363\pi\)
\(434\) 5.84378 0.280510
\(435\) −6.32817 −0.303412
\(436\) 25.8757 1.23922
\(437\) −2.06130 −0.0986054
\(438\) 5.26698 0.251666
\(439\) −12.7913 −0.610497 −0.305249 0.952273i \(-0.598740\pi\)
−0.305249 + 0.952273i \(0.598740\pi\)
\(440\) 1.92229 0.0916413
\(441\) 0.596751 0.0284167
\(442\) 8.89564 0.423123
\(443\) 8.83739 0.419877 0.209938 0.977715i \(-0.432674\pi\)
0.209938 + 0.977715i \(0.432674\pi\)
\(444\) 36.8620 1.74939
\(445\) 4.04567 0.191783
\(446\) 36.1547 1.71198
\(447\) −16.6186 −0.786034
\(448\) −3.63362 −0.171672
\(449\) −4.73996 −0.223693 −0.111846 0.993726i \(-0.535676\pi\)
−0.111846 + 0.993726i \(0.535676\pi\)
\(450\) −0.969351 −0.0456956
\(451\) 6.21231 0.292526
\(452\) 11.8310 0.556483
\(453\) −28.7730 −1.35187
\(454\) 0.603697 0.0283329
\(455\) −0.599589 −0.0281091
\(456\) −21.6939 −1.01591
\(457\) 20.2014 0.944980 0.472490 0.881336i \(-0.343355\pi\)
0.472490 + 0.881336i \(0.343355\pi\)
\(458\) 29.6239 1.38423
\(459\) −5.26831 −0.245903
\(460\) −1.12063 −0.0522498
\(461\) −14.2053 −0.661605 −0.330802 0.943700i \(-0.607319\pi\)
−0.330802 + 0.943700i \(0.607319\pi\)
\(462\) 1.26274 0.0587479
\(463\) −16.3574 −0.760191 −0.380095 0.924947i \(-0.624109\pi\)
−0.380095 + 0.924947i \(0.624109\pi\)
\(464\) −12.5913 −0.584535
\(465\) −6.87277 −0.318717
\(466\) 21.4925 0.995621
\(467\) 12.0886 0.559395 0.279698 0.960088i \(-0.409766\pi\)
0.279698 + 0.960088i \(0.409766\pi\)
\(468\) −1.16879 −0.0540275
\(469\) 3.07454 0.141969
\(470\) −8.47414 −0.390883
\(471\) −21.4893 −0.990175
\(472\) −35.4886 −1.63350
\(473\) −1.00000 −0.0459800
\(474\) −53.0050 −2.43460
\(475\) 15.9748 0.732973
\(476\) −1.12423 −0.0515291
\(477\) 0.367878 0.0168440
\(478\) 31.5045 1.44098
\(479\) −28.5546 −1.30469 −0.652347 0.757921i \(-0.726215\pi\)
−0.652347 + 0.757921i \(0.726215\pi\)
\(480\) 2.99987 0.136924
\(481\) −22.5962 −1.03030
\(482\) −0.743843 −0.0338811
\(483\) −0.326540 −0.0148581
\(484\) 3.59444 0.163384
\(485\) −0.598829 −0.0271914
\(486\) 2.12452 0.0963702
\(487\) −0.719499 −0.0326036 −0.0163018 0.999867i \(-0.505189\pi\)
−0.0163018 + 0.999867i \(0.505189\pi\)
\(488\) −53.1688 −2.40684
\(489\) 42.4648 1.92032
\(490\) −8.32136 −0.375921
\(491\) 16.7778 0.757170 0.378585 0.925566i \(-0.376411\pi\)
0.378585 + 0.925566i \(0.376411\pi\)
\(492\) −38.1150 −1.71836
\(493\) 7.27340 0.327577
\(494\) 29.9790 1.34882
\(495\) 0.0440694 0.00198077
\(496\) −13.6749 −0.614020
\(497\) −1.22891 −0.0551239
\(498\) 18.2505 0.817824
\(499\) −25.1626 −1.12643 −0.563216 0.826309i \(-0.690436\pi\)
−0.563216 + 0.826309i \(0.690436\pi\)
\(500\) 17.8455 0.798076
\(501\) −3.46397 −0.154759
\(502\) −54.7721 −2.44460
\(503\) 1.50296 0.0670138 0.0335069 0.999438i \(-0.489332\pi\)
0.0335069 + 0.999438i \(0.489332\pi\)
\(504\) 0.101981 0.00454259
\(505\) 5.83870 0.259819
\(506\) −1.44671 −0.0643140
\(507\) −1.95413 −0.0867860
\(508\) −66.4414 −2.94786
\(509\) 10.1558 0.450146 0.225073 0.974342i \(-0.427738\pi\)
0.225073 + 0.974342i \(0.427738\pi\)
\(510\) 2.05788 0.0911243
\(511\) 0.408034 0.0180504
\(512\) 19.0261 0.840842
\(513\) −17.7546 −0.783884
\(514\) 44.5126 1.96337
\(515\) 1.68537 0.0742662
\(516\) 6.13539 0.270096
\(517\) −7.02890 −0.309131
\(518\) 4.44467 0.195288
\(519\) −29.7895 −1.30761
\(520\) 7.22964 0.317041
\(521\) 15.9561 0.699051 0.349526 0.936927i \(-0.386343\pi\)
0.349526 + 0.936927i \(0.386343\pi\)
\(522\) −1.48738 −0.0651010
\(523\) −8.59964 −0.376036 −0.188018 0.982166i \(-0.560206\pi\)
−0.188018 + 0.982166i \(0.560206\pi\)
\(524\) 67.4075 2.94471
\(525\) 2.53064 0.110446
\(526\) −67.5910 −2.94711
\(527\) 7.89935 0.344101
\(528\) −2.95490 −0.128595
\(529\) −22.6259 −0.983734
\(530\) −5.12986 −0.222827
\(531\) −0.813596 −0.0353070
\(532\) −3.78875 −0.164263
\(533\) 23.3643 1.01202
\(534\) −32.0442 −1.38669
\(535\) 6.78819 0.293479
\(536\) −37.0718 −1.60126
\(537\) −27.9305 −1.20529
\(538\) −65.9262 −2.84228
\(539\) −6.90218 −0.297298
\(540\) −9.65234 −0.415371
\(541\) 29.5944 1.27236 0.636181 0.771540i \(-0.280513\pi\)
0.636181 + 0.771540i \(0.280513\pi\)
\(542\) 36.4066 1.56380
\(543\) −20.3302 −0.872453
\(544\) −3.44795 −0.147830
\(545\) −3.66936 −0.157178
\(546\) 4.74911 0.203243
\(547\) 22.9565 0.981551 0.490776 0.871286i \(-0.336714\pi\)
0.490776 + 0.871286i \(0.336714\pi\)
\(548\) 25.3769 1.08405
\(549\) −1.21892 −0.0520223
\(550\) 11.2118 0.478071
\(551\) 24.5119 1.04424
\(552\) 3.93732 0.167583
\(553\) −4.10631 −0.174618
\(554\) 28.0502 1.19174
\(555\) −5.22730 −0.221886
\(556\) 37.0744 1.57231
\(557\) −10.2043 −0.432372 −0.216186 0.976352i \(-0.569362\pi\)
−0.216186 + 0.976352i \(0.569362\pi\)
\(558\) −1.61539 −0.0683848
\(559\) −3.76096 −0.159072
\(560\) −0.275986 −0.0116625
\(561\) 1.70691 0.0720658
\(562\) 62.1212 2.62042
\(563\) −22.8913 −0.964752 −0.482376 0.875964i \(-0.660226\pi\)
−0.482376 + 0.875964i \(0.660226\pi\)
\(564\) 43.1251 1.81589
\(565\) −1.67772 −0.0705822
\(566\) 78.4881 3.29910
\(567\) −2.73146 −0.114711
\(568\) 14.8177 0.621738
\(569\) −17.4438 −0.731282 −0.365641 0.930756i \(-0.619150\pi\)
−0.365641 + 0.930756i \(0.619150\pi\)
\(570\) 6.93519 0.290483
\(571\) 35.6348 1.49127 0.745635 0.666355i \(-0.232146\pi\)
0.745635 + 0.666355i \(0.232146\pi\)
\(572\) 13.5186 0.565240
\(573\) −24.2717 −1.01396
\(574\) −4.59575 −0.191823
\(575\) −2.89933 −0.120910
\(576\) 1.00444 0.0418515
\(577\) 25.8987 1.07818 0.539089 0.842249i \(-0.318769\pi\)
0.539089 + 0.842249i \(0.318769\pi\)
\(578\) −2.36526 −0.0983818
\(579\) 12.4415 0.517052
\(580\) 13.3260 0.553331
\(581\) 1.41387 0.0586573
\(582\) 4.74309 0.196608
\(583\) −4.25497 −0.176223
\(584\) −4.91994 −0.203589
\(585\) 0.165743 0.00685264
\(586\) −59.1327 −2.44275
\(587\) −17.2978 −0.713957 −0.356978 0.934113i \(-0.616193\pi\)
−0.356978 + 0.934113i \(0.616193\pi\)
\(588\) 42.3476 1.74638
\(589\) 26.6214 1.09691
\(590\) 11.3451 0.467072
\(591\) 36.9980 1.52190
\(592\) −10.4008 −0.427472
\(593\) 3.05149 0.125310 0.0626549 0.998035i \(-0.480043\pi\)
0.0626549 + 0.998035i \(0.480043\pi\)
\(594\) −12.4609 −0.511277
\(595\) 0.159424 0.00653576
\(596\) 34.9958 1.43348
\(597\) 38.9240 1.59305
\(598\) −5.44101 −0.222499
\(599\) 41.6329 1.70107 0.850537 0.525915i \(-0.176277\pi\)
0.850537 + 0.525915i \(0.176277\pi\)
\(600\) −30.5136 −1.24571
\(601\) 43.9680 1.79349 0.896746 0.442545i \(-0.145924\pi\)
0.896746 + 0.442545i \(0.145924\pi\)
\(602\) 0.739780 0.0301512
\(603\) −0.849891 −0.0346102
\(604\) 60.5908 2.46540
\(605\) −0.509718 −0.0207230
\(606\) −46.2461 −1.87862
\(607\) 16.5287 0.670881 0.335441 0.942061i \(-0.391115\pi\)
0.335441 + 0.942061i \(0.391115\pi\)
\(608\) −11.6198 −0.471247
\(609\) 3.88304 0.157349
\(610\) 16.9972 0.688196
\(611\) −26.4354 −1.06946
\(612\) 0.310770 0.0125621
\(613\) −25.6612 −1.03644 −0.518222 0.855246i \(-0.673406\pi\)
−0.518222 + 0.855246i \(0.673406\pi\)
\(614\) −0.0457014 −0.00184436
\(615\) 5.40498 0.217950
\(616\) −1.17954 −0.0475250
\(617\) 7.89400 0.317800 0.158900 0.987295i \(-0.449205\pi\)
0.158900 + 0.987295i \(0.449205\pi\)
\(618\) −13.3492 −0.536982
\(619\) −12.7922 −0.514163 −0.257081 0.966390i \(-0.582761\pi\)
−0.257081 + 0.966390i \(0.582761\pi\)
\(620\) 14.4728 0.581242
\(621\) 3.22235 0.129309
\(622\) −53.7893 −2.15675
\(623\) −2.48248 −0.0994583
\(624\) −11.1133 −0.444887
\(625\) 21.1703 0.846813
\(626\) −22.6021 −0.903361
\(627\) 5.75241 0.229729
\(628\) 45.2526 1.80577
\(629\) 6.00809 0.239558
\(630\) −0.0326017 −0.00129888
\(631\) 49.4310 1.96782 0.983908 0.178677i \(-0.0571818\pi\)
0.983908 + 0.178677i \(0.0571818\pi\)
\(632\) 49.5125 1.96950
\(633\) 18.1628 0.721907
\(634\) 54.5464 2.16631
\(635\) 9.42187 0.373896
\(636\) 26.1059 1.03517
\(637\) −25.9588 −1.02853
\(638\) 17.2035 0.681091
\(639\) 0.339704 0.0134385
\(640\) −10.4913 −0.414707
\(641\) −38.3754 −1.51574 −0.757868 0.652408i \(-0.773759\pi\)
−0.757868 + 0.652408i \(0.773759\pi\)
\(642\) −53.7666 −2.12200
\(643\) 30.5589 1.20513 0.602563 0.798071i \(-0.294146\pi\)
0.602563 + 0.798071i \(0.294146\pi\)
\(644\) 0.687635 0.0270966
\(645\) −0.870043 −0.0342579
\(646\) −7.97109 −0.313618
\(647\) 7.59646 0.298648 0.149324 0.988788i \(-0.452290\pi\)
0.149324 + 0.988788i \(0.452290\pi\)
\(648\) 32.9351 1.29381
\(649\) 9.41026 0.369385
\(650\) 42.1670 1.65393
\(651\) 4.21722 0.165286
\(652\) −89.4232 −3.50208
\(653\) −2.12704 −0.0832375 −0.0416188 0.999134i \(-0.513251\pi\)
−0.0416188 + 0.999134i \(0.513251\pi\)
\(654\) 29.0636 1.13648
\(655\) −9.55887 −0.373496
\(656\) 10.7544 0.419888
\(657\) −0.112792 −0.00440045
\(658\) 5.19984 0.202711
\(659\) −25.9194 −1.00968 −0.504839 0.863214i \(-0.668448\pi\)
−0.504839 + 0.863214i \(0.668448\pi\)
\(660\) 3.12732 0.121731
\(661\) −34.0472 −1.32428 −0.662142 0.749379i \(-0.730352\pi\)
−0.662142 + 0.749379i \(0.730352\pi\)
\(662\) 0.292147 0.0113546
\(663\) 6.41962 0.249318
\(664\) −17.0480 −0.661591
\(665\) 0.537272 0.0208345
\(666\) −1.22863 −0.0476086
\(667\) −4.44876 −0.172257
\(668\) 7.29450 0.282233
\(669\) 26.0914 1.00875
\(670\) 11.8513 0.457854
\(671\) 14.0984 0.544261
\(672\) −1.84076 −0.0710087
\(673\) −40.8975 −1.57648 −0.788241 0.615367i \(-0.789008\pi\)
−0.788241 + 0.615367i \(0.789008\pi\)
\(674\) −15.6925 −0.604453
\(675\) −24.9728 −0.961202
\(676\) 4.11505 0.158271
\(677\) 35.8741 1.37875 0.689376 0.724403i \(-0.257885\pi\)
0.689376 + 0.724403i \(0.257885\pi\)
\(678\) 13.2886 0.510345
\(679\) 0.367449 0.0141014
\(680\) −1.92229 −0.0737163
\(681\) 0.435664 0.0166947
\(682\) 18.6840 0.715447
\(683\) 28.5667 1.09307 0.546537 0.837435i \(-0.315946\pi\)
0.546537 + 0.837435i \(0.315946\pi\)
\(684\) 1.04732 0.0400452
\(685\) −3.59862 −0.137496
\(686\) 10.2846 0.392666
\(687\) 21.3783 0.815635
\(688\) −1.73114 −0.0659991
\(689\) −16.0028 −0.609658
\(690\) −1.25870 −0.0479178
\(691\) 37.5901 1.42999 0.714997 0.699128i \(-0.246428\pi\)
0.714997 + 0.699128i \(0.246428\pi\)
\(692\) 62.7313 2.38468
\(693\) −0.0270415 −0.00102722
\(694\) 25.8789 0.982349
\(695\) −5.25742 −0.199425
\(696\) −46.8204 −1.77472
\(697\) −6.21231 −0.235308
\(698\) −46.7732 −1.77039
\(699\) 15.5103 0.586652
\(700\) −5.32907 −0.201420
\(701\) 26.6006 1.00469 0.502345 0.864667i \(-0.332471\pi\)
0.502345 + 0.864667i \(0.332471\pi\)
\(702\) −46.8650 −1.76880
\(703\) 20.2477 0.763657
\(704\) −11.6176 −0.437854
\(705\) −6.11544 −0.230321
\(706\) 69.8870 2.63023
\(707\) −3.58270 −0.134741
\(708\) −57.7356 −2.16984
\(709\) 22.4671 0.843768 0.421884 0.906650i \(-0.361369\pi\)
0.421884 + 0.906650i \(0.361369\pi\)
\(710\) −4.73699 −0.177776
\(711\) 1.13510 0.0425696
\(712\) 29.9329 1.12178
\(713\) −4.83162 −0.180946
\(714\) −1.26274 −0.0472568
\(715\) −1.91703 −0.0716929
\(716\) 58.8165 2.19808
\(717\) 22.7355 0.849072
\(718\) −15.7533 −0.587909
\(719\) 14.5171 0.541397 0.270699 0.962664i \(-0.412745\pi\)
0.270699 + 0.962664i \(0.412745\pi\)
\(720\) 0.0762903 0.00284317
\(721\) −1.03416 −0.0385143
\(722\) 18.0767 0.672746
\(723\) −0.536801 −0.0199639
\(724\) 42.8118 1.59109
\(725\) 34.4773 1.28045
\(726\) 4.03728 0.149838
\(727\) 21.5607 0.799642 0.399821 0.916593i \(-0.369072\pi\)
0.399821 + 0.916593i \(0.369072\pi\)
\(728\) −4.43620 −0.164416
\(729\) 27.7326 1.02713
\(730\) 1.57283 0.0582129
\(731\) 1.00000 0.0369863
\(732\) −86.4990 −3.19709
\(733\) 49.1129 1.81403 0.907013 0.421103i \(-0.138357\pi\)
0.907013 + 0.421103i \(0.138357\pi\)
\(734\) −76.4896 −2.82328
\(735\) −6.00519 −0.221505
\(736\) 2.10893 0.0777364
\(737\) 9.83006 0.362095
\(738\) 1.27040 0.0467639
\(739\) 34.3454 1.26342 0.631709 0.775206i \(-0.282354\pi\)
0.631709 + 0.775206i \(0.282354\pi\)
\(740\) 11.0077 0.404653
\(741\) 21.6346 0.794767
\(742\) 3.14774 0.115557
\(743\) −24.7269 −0.907141 −0.453571 0.891220i \(-0.649850\pi\)
−0.453571 + 0.891220i \(0.649850\pi\)
\(744\) −50.8498 −1.86425
\(745\) −4.96266 −0.181818
\(746\) 17.1044 0.626237
\(747\) −0.390834 −0.0142999
\(748\) −3.59444 −0.131426
\(749\) −4.16532 −0.152197
\(750\) 20.0441 0.731907
\(751\) 8.68683 0.316987 0.158493 0.987360i \(-0.449336\pi\)
0.158493 + 0.987360i \(0.449336\pi\)
\(752\) −12.1680 −0.443722
\(753\) −39.5268 −1.44044
\(754\) 64.7015 2.35629
\(755\) −8.59221 −0.312703
\(756\) 5.92280 0.215410
\(757\) −36.4264 −1.32394 −0.661970 0.749530i \(-0.730279\pi\)
−0.661970 + 0.749530i \(0.730279\pi\)
\(758\) 30.8320 1.11987
\(759\) −1.04403 −0.0378959
\(760\) −6.47824 −0.234991
\(761\) −27.3623 −0.991884 −0.495942 0.868356i \(-0.665177\pi\)
−0.495942 + 0.868356i \(0.665177\pi\)
\(762\) −74.6270 −2.70345
\(763\) 2.25156 0.0815120
\(764\) 51.1117 1.84916
\(765\) −0.0440694 −0.00159333
\(766\) −66.4682 −2.40159
\(767\) 35.3916 1.27792
\(768\) 43.4377 1.56742
\(769\) 1.11155 0.0400836 0.0200418 0.999799i \(-0.493620\pi\)
0.0200418 + 0.999799i \(0.493620\pi\)
\(770\) 0.377079 0.0135890
\(771\) 32.1229 1.15688
\(772\) −26.1996 −0.942944
\(773\) 24.6661 0.887179 0.443589 0.896230i \(-0.353705\pi\)
0.443589 + 0.896230i \(0.353705\pi\)
\(774\) −0.204496 −0.00735047
\(775\) 37.4444 1.34504
\(776\) −4.43058 −0.159048
\(777\) 3.20754 0.115070
\(778\) 7.85747 0.281704
\(779\) −20.9360 −0.750109
\(780\) 11.7617 0.421138
\(781\) −3.92911 −0.140595
\(782\) 1.44671 0.0517341
\(783\) −38.3185 −1.36939
\(784\) −11.9486 −0.426737
\(785\) −6.41714 −0.229038
\(786\) 75.7122 2.70056
\(787\) 27.8373 0.992293 0.496146 0.868239i \(-0.334748\pi\)
0.496146 + 0.868239i \(0.334748\pi\)
\(788\) −77.9111 −2.77547
\(789\) −48.7777 −1.73653
\(790\) −15.8284 −0.563148
\(791\) 1.02947 0.0366038
\(792\) 0.326058 0.0115860
\(793\) 53.0234 1.88292
\(794\) 72.5394 2.57433
\(795\) −3.70201 −0.131297
\(796\) −81.9670 −2.90524
\(797\) −11.2323 −0.397868 −0.198934 0.980013i \(-0.563748\pi\)
−0.198934 + 0.980013i \(0.563748\pi\)
\(798\) −4.25552 −0.150644
\(799\) 7.02890 0.248665
\(800\) −16.3439 −0.577845
\(801\) 0.686227 0.0242466
\(802\) −29.6698 −1.04768
\(803\) 1.30459 0.0460378
\(804\) −60.3113 −2.12702
\(805\) −0.0975116 −0.00343683
\(806\) 70.2698 2.47515
\(807\) −47.5763 −1.67476
\(808\) 43.1990 1.51974
\(809\) 35.6915 1.25485 0.627424 0.778678i \(-0.284109\pi\)
0.627424 + 0.778678i \(0.284109\pi\)
\(810\) −10.5288 −0.369945
\(811\) −29.3774 −1.03158 −0.515789 0.856715i \(-0.672501\pi\)
−0.515789 + 0.856715i \(0.672501\pi\)
\(812\) −8.17699 −0.286956
\(813\) 26.2732 0.921440
\(814\) 14.2107 0.498084
\(815\) 12.6809 0.444191
\(816\) 2.95490 0.103442
\(817\) 3.37007 0.117904
\(818\) −42.8916 −1.49967
\(819\) −0.101702 −0.00355376
\(820\) −11.3819 −0.397474
\(821\) −2.55006 −0.0889978 −0.0444989 0.999009i \(-0.514169\pi\)
−0.0444989 + 0.999009i \(0.514169\pi\)
\(822\) 28.5033 0.994168
\(823\) 37.1014 1.29327 0.646637 0.762798i \(-0.276175\pi\)
0.646637 + 0.762798i \(0.276175\pi\)
\(824\) 12.4696 0.434399
\(825\) 8.09107 0.281695
\(826\) −6.96152 −0.242222
\(827\) −25.2824 −0.879157 −0.439578 0.898204i \(-0.644872\pi\)
−0.439578 + 0.898204i \(0.644872\pi\)
\(828\) −0.190082 −0.00660580
\(829\) 4.68508 0.162720 0.0813598 0.996685i \(-0.474074\pi\)
0.0813598 + 0.996685i \(0.474074\pi\)
\(830\) 5.44997 0.189171
\(831\) 20.2427 0.702211
\(832\) −43.6932 −1.51479
\(833\) 6.90218 0.239146
\(834\) 41.6420 1.44195
\(835\) −1.03441 −0.0357973
\(836\) −12.1135 −0.418956
\(837\) −41.6162 −1.43847
\(838\) −6.34725 −0.219262
\(839\) 41.7286 1.44063 0.720315 0.693647i \(-0.243997\pi\)
0.720315 + 0.693647i \(0.243997\pi\)
\(840\) −1.02625 −0.0354090
\(841\) 23.9023 0.824217
\(842\) 50.8973 1.75404
\(843\) 44.8303 1.54404
\(844\) −38.2476 −1.31654
\(845\) −0.583543 −0.0200745
\(846\) −1.43738 −0.0494183
\(847\) 0.312769 0.0107469
\(848\) −7.36595 −0.252948
\(849\) 56.6417 1.94394
\(850\) −11.2118 −0.384560
\(851\) −3.67484 −0.125972
\(852\) 24.1066 0.825879
\(853\) −2.82726 −0.0968035 −0.0484017 0.998828i \(-0.515413\pi\)
−0.0484017 + 0.998828i \(0.515413\pi\)
\(854\) −10.4297 −0.356897
\(855\) −0.148517 −0.00507918
\(856\) 50.2240 1.71662
\(857\) 34.6563 1.18384 0.591919 0.805998i \(-0.298371\pi\)
0.591919 + 0.805998i \(0.298371\pi\)
\(858\) 15.1841 0.518375
\(859\) −20.5264 −0.700350 −0.350175 0.936684i \(-0.613878\pi\)
−0.350175 + 0.936684i \(0.613878\pi\)
\(860\) 1.83215 0.0624759
\(861\) −3.31656 −0.113028
\(862\) −73.2437 −2.49469
\(863\) 34.2767 1.16679 0.583396 0.812188i \(-0.301724\pi\)
0.583396 + 0.812188i \(0.301724\pi\)
\(864\) 18.1649 0.617981
\(865\) −8.89574 −0.302464
\(866\) 74.3188 2.52546
\(867\) −1.70691 −0.0579697
\(868\) −8.88070 −0.301431
\(869\) −13.1289 −0.445367
\(870\) 14.9677 0.507454
\(871\) 36.9705 1.25270
\(872\) −27.1486 −0.919368
\(873\) −0.101573 −0.00343774
\(874\) 4.87551 0.164917
\(875\) 1.55282 0.0524950
\(876\) −8.00414 −0.270435
\(877\) −27.4380 −0.926516 −0.463258 0.886223i \(-0.653320\pi\)
−0.463258 + 0.886223i \(0.653320\pi\)
\(878\) 30.2548 1.02105
\(879\) −42.6737 −1.43935
\(880\) −0.882393 −0.0297455
\(881\) 47.7276 1.60798 0.803991 0.594641i \(-0.202706\pi\)
0.803991 + 0.594641i \(0.202706\pi\)
\(882\) −1.41147 −0.0475266
\(883\) 30.4132 1.02349 0.511743 0.859139i \(-0.329000\pi\)
0.511743 + 0.859139i \(0.329000\pi\)
\(884\) −13.5186 −0.454679
\(885\) 8.18733 0.275214
\(886\) −20.9027 −0.702240
\(887\) −4.22268 −0.141784 −0.0708918 0.997484i \(-0.522585\pi\)
−0.0708918 + 0.997484i \(0.522585\pi\)
\(888\) −38.6754 −1.29786
\(889\) −5.78138 −0.193901
\(890\) −9.56906 −0.320756
\(891\) −8.73315 −0.292572
\(892\) −54.9438 −1.83965
\(893\) 23.6879 0.792686
\(894\) 39.3073 1.31463
\(895\) −8.34060 −0.278796
\(896\) 6.43762 0.215066
\(897\) −3.92655 −0.131104
\(898\) 11.2112 0.374124
\(899\) 57.4551 1.91623
\(900\) 1.47311 0.0491036
\(901\) 4.25497 0.141754
\(902\) −14.6937 −0.489247
\(903\) 0.533869 0.0177661
\(904\) −12.4130 −0.412851
\(905\) −6.07102 −0.201807
\(906\) 68.0556 2.26100
\(907\) 15.3236 0.508813 0.254407 0.967097i \(-0.418120\pi\)
0.254407 + 0.967097i \(0.418120\pi\)
\(908\) −0.917429 −0.0304460
\(909\) 0.990360 0.0328482
\(910\) 1.41818 0.0470123
\(911\) 12.3571 0.409409 0.204705 0.978824i \(-0.434377\pi\)
0.204705 + 0.978824i \(0.434377\pi\)
\(912\) 9.95823 0.329750
\(913\) 4.52049 0.149606
\(914\) −47.7815 −1.58047
\(915\) 12.2662 0.405507
\(916\) −45.0189 −1.48747
\(917\) 5.86544 0.193694
\(918\) 12.4609 0.411271
\(919\) −32.9133 −1.08571 −0.542854 0.839827i \(-0.682656\pi\)
−0.542854 + 0.839827i \(0.682656\pi\)
\(920\) 1.17576 0.0387638
\(921\) −0.0329809 −0.00108676
\(922\) 33.5991 1.10653
\(923\) −14.7772 −0.486398
\(924\) −1.91896 −0.0631293
\(925\) 28.4795 0.936400
\(926\) 38.6894 1.27141
\(927\) 0.285872 0.00938928
\(928\) −25.0783 −0.823236
\(929\) 9.54867 0.313282 0.156641 0.987656i \(-0.449933\pi\)
0.156641 + 0.987656i \(0.449933\pi\)
\(930\) 16.2559 0.533051
\(931\) 23.2608 0.762343
\(932\) −32.6618 −1.06987
\(933\) −38.8175 −1.27083
\(934\) −28.5927 −0.935583
\(935\) 0.509718 0.0166696
\(936\) 1.22629 0.0400826
\(937\) −7.39221 −0.241493 −0.120746 0.992683i \(-0.538529\pi\)
−0.120746 + 0.992683i \(0.538529\pi\)
\(938\) −7.27209 −0.237442
\(939\) −16.3110 −0.532290
\(940\) 12.8780 0.420035
\(941\) −10.3752 −0.338223 −0.169112 0.985597i \(-0.554090\pi\)
−0.169112 + 0.985597i \(0.554090\pi\)
\(942\) 50.8277 1.65606
\(943\) 3.79975 0.123737
\(944\) 16.2905 0.530210
\(945\) −0.839896 −0.0273218
\(946\) 2.36526 0.0769012
\(947\) −33.4153 −1.08585 −0.542925 0.839781i \(-0.682683\pi\)
−0.542925 + 0.839781i \(0.682683\pi\)
\(948\) 80.5508 2.61617
\(949\) 4.90650 0.159272
\(950\) −37.7845 −1.22589
\(951\) 39.3639 1.27646
\(952\) 1.17954 0.0382291
\(953\) −26.0232 −0.842974 −0.421487 0.906834i \(-0.638492\pi\)
−0.421487 + 0.906834i \(0.638492\pi\)
\(954\) −0.870126 −0.0281714
\(955\) −7.24801 −0.234540
\(956\) −47.8768 −1.54845
\(957\) 12.4150 0.401321
\(958\) 67.5390 2.18209
\(959\) 2.20816 0.0713053
\(960\) −10.1078 −0.326227
\(961\) 31.3997 1.01289
\(962\) 53.4459 1.72316
\(963\) 1.15141 0.0371037
\(964\) 1.13041 0.0364080
\(965\) 3.71529 0.119600
\(966\) 0.772352 0.0248500
\(967\) −21.6294 −0.695555 −0.347778 0.937577i \(-0.613064\pi\)
−0.347778 + 0.937577i \(0.613064\pi\)
\(968\) −3.77127 −0.121213
\(969\) −5.75241 −0.184794
\(970\) 1.41638 0.0454774
\(971\) −26.7593 −0.858746 −0.429373 0.903127i \(-0.641265\pi\)
−0.429373 + 0.903127i \(0.641265\pi\)
\(972\) −3.22860 −0.103557
\(973\) 3.22602 0.103421
\(974\) 1.70180 0.0545292
\(975\) 30.4302 0.974547
\(976\) 24.4062 0.781225
\(977\) 41.8826 1.33994 0.669971 0.742387i \(-0.266306\pi\)
0.669971 + 0.742387i \(0.266306\pi\)
\(978\) −100.440 −3.21172
\(979\) −7.93708 −0.253670
\(980\) 12.6458 0.403957
\(981\) −0.622396 −0.0198716
\(982\) −39.6838 −1.26636
\(983\) 30.0906 0.959743 0.479871 0.877339i \(-0.340683\pi\)
0.479871 + 0.877339i \(0.340683\pi\)
\(984\) 39.9900 1.27484
\(985\) 11.0484 0.352030
\(986\) −17.2035 −0.547870
\(987\) 3.75251 0.119444
\(988\) −45.5586 −1.44941
\(989\) −0.611649 −0.0194493
\(990\) −0.104235 −0.00331282
\(991\) 28.9251 0.918837 0.459419 0.888220i \(-0.348058\pi\)
0.459419 + 0.888220i \(0.348058\pi\)
\(992\) −27.2366 −0.864762
\(993\) 0.210831 0.00669051
\(994\) 2.90668 0.0921942
\(995\) 11.6235 0.368490
\(996\) −27.7350 −0.878817
\(997\) 39.2762 1.24389 0.621945 0.783061i \(-0.286343\pi\)
0.621945 + 0.783061i \(0.286343\pi\)
\(998\) 59.5160 1.88395
\(999\) −31.6525 −1.00144
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 \(a_p\))