Properties

Label 8043.2.a.t.1.1
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.75477 q^{2} -1.00000 q^{3} +5.58878 q^{4} -0.0622071 q^{5} +2.75477 q^{6} +1.00000 q^{7} -9.88627 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.75477 q^{2} -1.00000 q^{3} +5.58878 q^{4} -0.0622071 q^{5} +2.75477 q^{6} +1.00000 q^{7} -9.88627 q^{8} +1.00000 q^{9} +0.171367 q^{10} +1.07439 q^{11} -5.58878 q^{12} +6.04155 q^{13} -2.75477 q^{14} +0.0622071 q^{15} +16.0569 q^{16} -0.508785 q^{17} -2.75477 q^{18} -4.80180 q^{19} -0.347662 q^{20} -1.00000 q^{21} -2.95970 q^{22} -4.88480 q^{23} +9.88627 q^{24} -4.99613 q^{25} -16.6431 q^{26} -1.00000 q^{27} +5.58878 q^{28} +1.19489 q^{29} -0.171367 q^{30} -8.60831 q^{31} -24.4605 q^{32} -1.07439 q^{33} +1.40159 q^{34} -0.0622071 q^{35} +5.58878 q^{36} -1.69413 q^{37} +13.2279 q^{38} -6.04155 q^{39} +0.614996 q^{40} -7.00680 q^{41} +2.75477 q^{42} +1.99737 q^{43} +6.00452 q^{44} -0.0622071 q^{45} +13.4565 q^{46} -5.71846 q^{47} -16.0569 q^{48} +1.00000 q^{49} +13.7632 q^{50} +0.508785 q^{51} +33.7649 q^{52} +1.01255 q^{53} +2.75477 q^{54} -0.0668347 q^{55} -9.88627 q^{56} +4.80180 q^{57} -3.29164 q^{58} -4.82268 q^{59} +0.347662 q^{60} +6.50953 q^{61} +23.7139 q^{62} +1.00000 q^{63} +35.2694 q^{64} -0.375827 q^{65} +2.95970 q^{66} -9.27574 q^{67} -2.84349 q^{68} +4.88480 q^{69} +0.171367 q^{70} -4.83756 q^{71} -9.88627 q^{72} +10.1283 q^{73} +4.66695 q^{74} +4.99613 q^{75} -26.8362 q^{76} +1.07439 q^{77} +16.6431 q^{78} +14.9495 q^{79} -0.998852 q^{80} +1.00000 q^{81} +19.3021 q^{82} -7.77734 q^{83} -5.58878 q^{84} +0.0316501 q^{85} -5.50229 q^{86} -1.19489 q^{87} -10.6217 q^{88} -11.8515 q^{89} +0.171367 q^{90} +6.04155 q^{91} -27.3000 q^{92} +8.60831 q^{93} +15.7531 q^{94} +0.298707 q^{95} +24.4605 q^{96} +18.5781 q^{97} -2.75477 q^{98} +1.07439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75477 −1.94792 −0.973959 0.226722i \(-0.927199\pi\)
−0.973959 + 0.226722i \(0.927199\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.58878 2.79439
\(5\) −0.0622071 −0.0278199 −0.0139099 0.999903i \(-0.504428\pi\)
−0.0139099 + 0.999903i \(0.504428\pi\)
\(6\) 2.75477 1.12463
\(7\) 1.00000 0.377964
\(8\) −9.88627 −3.49532
\(9\) 1.00000 0.333333
\(10\) 0.171367 0.0541909
\(11\) 1.07439 0.323941 0.161970 0.986796i \(-0.448215\pi\)
0.161970 + 0.986796i \(0.448215\pi\)
\(12\) −5.58878 −1.61334
\(13\) 6.04155 1.67562 0.837812 0.545959i \(-0.183835\pi\)
0.837812 + 0.545959i \(0.183835\pi\)
\(14\) −2.75477 −0.736244
\(15\) 0.0622071 0.0160618
\(16\) 16.0569 4.01422
\(17\) −0.508785 −0.123399 −0.0616993 0.998095i \(-0.519652\pi\)
−0.0616993 + 0.998095i \(0.519652\pi\)
\(18\) −2.75477 −0.649306
\(19\) −4.80180 −1.10161 −0.550805 0.834634i \(-0.685679\pi\)
−0.550805 + 0.834634i \(0.685679\pi\)
\(20\) −0.347662 −0.0777396
\(21\) −1.00000 −0.218218
\(22\) −2.95970 −0.631010
\(23\) −4.88480 −1.01855 −0.509275 0.860604i \(-0.670086\pi\)
−0.509275 + 0.860604i \(0.670086\pi\)
\(24\) 9.88627 2.01803
\(25\) −4.99613 −0.999226
\(26\) −16.6431 −3.26398
\(27\) −1.00000 −0.192450
\(28\) 5.58878 1.05618
\(29\) 1.19489 0.221885 0.110942 0.993827i \(-0.464613\pi\)
0.110942 + 0.993827i \(0.464613\pi\)
\(30\) −0.171367 −0.0312871
\(31\) −8.60831 −1.54610 −0.773049 0.634347i \(-0.781269\pi\)
−0.773049 + 0.634347i \(0.781269\pi\)
\(32\) −24.4605 −4.32405
\(33\) −1.07439 −0.187027
\(34\) 1.40159 0.240370
\(35\) −0.0622071 −0.0105149
\(36\) 5.58878 0.931463
\(37\) −1.69413 −0.278514 −0.139257 0.990256i \(-0.544471\pi\)
−0.139257 + 0.990256i \(0.544471\pi\)
\(38\) 13.2279 2.14585
\(39\) −6.04155 −0.967422
\(40\) 0.614996 0.0972395
\(41\) −7.00680 −1.09428 −0.547139 0.837042i \(-0.684283\pi\)
−0.547139 + 0.837042i \(0.684283\pi\)
\(42\) 2.75477 0.425071
\(43\) 1.99737 0.304595 0.152298 0.988335i \(-0.451333\pi\)
0.152298 + 0.988335i \(0.451333\pi\)
\(44\) 6.00452 0.905216
\(45\) −0.0622071 −0.00927329
\(46\) 13.4565 1.98405
\(47\) −5.71846 −0.834123 −0.417061 0.908878i \(-0.636940\pi\)
−0.417061 + 0.908878i \(0.636940\pi\)
\(48\) −16.0569 −2.31761
\(49\) 1.00000 0.142857
\(50\) 13.7632 1.94641
\(51\) 0.508785 0.0712442
\(52\) 33.7649 4.68234
\(53\) 1.01255 0.139085 0.0695424 0.997579i \(-0.477846\pi\)
0.0695424 + 0.997579i \(0.477846\pi\)
\(54\) 2.75477 0.374877
\(55\) −0.0668347 −0.00901199
\(56\) −9.88627 −1.32111
\(57\) 4.80180 0.636015
\(58\) −3.29164 −0.432213
\(59\) −4.82268 −0.627860 −0.313930 0.949446i \(-0.601646\pi\)
−0.313930 + 0.949446i \(0.601646\pi\)
\(60\) 0.347662 0.0448830
\(61\) 6.50953 0.833459 0.416730 0.909030i \(-0.363176\pi\)
0.416730 + 0.909030i \(0.363176\pi\)
\(62\) 23.7139 3.01167
\(63\) 1.00000 0.125988
\(64\) 35.2694 4.40867
\(65\) −0.375827 −0.0466157
\(66\) 2.95970 0.364314
\(67\) −9.27574 −1.13321 −0.566606 0.823989i \(-0.691744\pi\)
−0.566606 + 0.823989i \(0.691744\pi\)
\(68\) −2.84349 −0.344824
\(69\) 4.88480 0.588060
\(70\) 0.171367 0.0204822
\(71\) −4.83756 −0.574113 −0.287056 0.957914i \(-0.592677\pi\)
−0.287056 + 0.957914i \(0.592677\pi\)
\(72\) −9.88627 −1.16511
\(73\) 10.1283 1.18542 0.592712 0.805414i \(-0.298057\pi\)
0.592712 + 0.805414i \(0.298057\pi\)
\(74\) 4.66695 0.542522
\(75\) 4.99613 0.576903
\(76\) −26.8362 −3.07832
\(77\) 1.07439 0.122438
\(78\) 16.6431 1.88446
\(79\) 14.9495 1.68195 0.840975 0.541074i \(-0.181982\pi\)
0.840975 + 0.541074i \(0.181982\pi\)
\(80\) −0.998852 −0.111675
\(81\) 1.00000 0.111111
\(82\) 19.3021 2.13156
\(83\) −7.77734 −0.853673 −0.426837 0.904329i \(-0.640372\pi\)
−0.426837 + 0.904329i \(0.640372\pi\)
\(84\) −5.58878 −0.609785
\(85\) 0.0316501 0.00343293
\(86\) −5.50229 −0.593327
\(87\) −1.19489 −0.128105
\(88\) −10.6217 −1.13228
\(89\) −11.8515 −1.25625 −0.628126 0.778112i \(-0.716178\pi\)
−0.628126 + 0.778112i \(0.716178\pi\)
\(90\) 0.171367 0.0180636
\(91\) 6.04155 0.633326
\(92\) −27.3000 −2.84623
\(93\) 8.60831 0.892640
\(94\) 15.7531 1.62480
\(95\) 0.298707 0.0306466
\(96\) 24.4605 2.49649
\(97\) 18.5781 1.88632 0.943162 0.332334i \(-0.107836\pi\)
0.943162 + 0.332334i \(0.107836\pi\)
\(98\) −2.75477 −0.278274
\(99\) 1.07439 0.107980
\(100\) −27.9223 −2.79223
\(101\) 9.37959 0.933304 0.466652 0.884441i \(-0.345460\pi\)
0.466652 + 0.884441i \(0.345460\pi\)
\(102\) −1.40159 −0.138778
\(103\) 2.58365 0.254574 0.127287 0.991866i \(-0.459373\pi\)
0.127287 + 0.991866i \(0.459373\pi\)
\(104\) −59.7283 −5.85685
\(105\) 0.0622071 0.00607080
\(106\) −2.78935 −0.270926
\(107\) 4.00965 0.387627 0.193814 0.981038i \(-0.437914\pi\)
0.193814 + 0.981038i \(0.437914\pi\)
\(108\) −5.58878 −0.537780
\(109\) −6.55630 −0.627980 −0.313990 0.949426i \(-0.601666\pi\)
−0.313990 + 0.949426i \(0.601666\pi\)
\(110\) 0.184114 0.0175546
\(111\) 1.69413 0.160800
\(112\) 16.0569 1.51723
\(113\) 16.4661 1.54900 0.774502 0.632572i \(-0.218001\pi\)
0.774502 + 0.632572i \(0.218001\pi\)
\(114\) −13.2279 −1.23890
\(115\) 0.303869 0.0283360
\(116\) 6.67795 0.620032
\(117\) 6.04155 0.558541
\(118\) 13.2854 1.22302
\(119\) −0.508785 −0.0466403
\(120\) −0.614996 −0.0561412
\(121\) −9.84569 −0.895062
\(122\) −17.9323 −1.62351
\(123\) 7.00680 0.631782
\(124\) −48.1099 −4.32040
\(125\) 0.621831 0.0556182
\(126\) −2.75477 −0.245415
\(127\) 12.8824 1.14313 0.571563 0.820558i \(-0.306337\pi\)
0.571563 + 0.820558i \(0.306337\pi\)
\(128\) −48.2382 −4.26369
\(129\) −1.99737 −0.175858
\(130\) 1.03532 0.0908035
\(131\) 11.8402 1.03448 0.517242 0.855839i \(-0.326959\pi\)
0.517242 + 0.855839i \(0.326959\pi\)
\(132\) −6.00452 −0.522627
\(133\) −4.80180 −0.416369
\(134\) 25.5526 2.20741
\(135\) 0.0622071 0.00535394
\(136\) 5.02999 0.431318
\(137\) −2.48600 −0.212393 −0.106197 0.994345i \(-0.533867\pi\)
−0.106197 + 0.994345i \(0.533867\pi\)
\(138\) −13.4565 −1.14549
\(139\) −7.31586 −0.620523 −0.310262 0.950651i \(-0.600417\pi\)
−0.310262 + 0.950651i \(0.600417\pi\)
\(140\) −0.347662 −0.0293828
\(141\) 5.71846 0.481581
\(142\) 13.3264 1.11832
\(143\) 6.49098 0.542803
\(144\) 16.0569 1.33807
\(145\) −0.0743304 −0.00617281
\(146\) −27.9011 −2.30911
\(147\) −1.00000 −0.0824786
\(148\) −9.46812 −0.778275
\(149\) −1.48707 −0.121825 −0.0609126 0.998143i \(-0.519401\pi\)
−0.0609126 + 0.998143i \(0.519401\pi\)
\(150\) −13.7632 −1.12376
\(151\) −2.24879 −0.183004 −0.0915021 0.995805i \(-0.529167\pi\)
−0.0915021 + 0.995805i \(0.529167\pi\)
\(152\) 47.4719 3.85048
\(153\) −0.508785 −0.0411329
\(154\) −2.95970 −0.238499
\(155\) 0.535498 0.0430123
\(156\) −33.7649 −2.70335
\(157\) −8.58340 −0.685030 −0.342515 0.939512i \(-0.611279\pi\)
−0.342515 + 0.939512i \(0.611279\pi\)
\(158\) −41.1825 −3.27630
\(159\) −1.01255 −0.0803007
\(160\) 1.52162 0.120294
\(161\) −4.88480 −0.384976
\(162\) −2.75477 −0.216435
\(163\) −4.26636 −0.334167 −0.167084 0.985943i \(-0.553435\pi\)
−0.167084 + 0.985943i \(0.553435\pi\)
\(164\) −39.1594 −3.05784
\(165\) 0.0668347 0.00520308
\(166\) 21.4248 1.66289
\(167\) −1.84955 −0.143123 −0.0715613 0.997436i \(-0.522798\pi\)
−0.0715613 + 0.997436i \(0.522798\pi\)
\(168\) 9.88627 0.762742
\(169\) 23.5003 1.80771
\(170\) −0.0871888 −0.00668708
\(171\) −4.80180 −0.367203
\(172\) 11.1628 0.851158
\(173\) 19.9150 1.51411 0.757056 0.653350i \(-0.226637\pi\)
0.757056 + 0.653350i \(0.226637\pi\)
\(174\) 3.29164 0.249539
\(175\) −4.99613 −0.377672
\(176\) 17.2513 1.30037
\(177\) 4.82268 0.362495
\(178\) 32.6481 2.44708
\(179\) −7.55740 −0.564866 −0.282433 0.959287i \(-0.591142\pi\)
−0.282433 + 0.959287i \(0.591142\pi\)
\(180\) −0.347662 −0.0259132
\(181\) 12.6026 0.936742 0.468371 0.883532i \(-0.344841\pi\)
0.468371 + 0.883532i \(0.344841\pi\)
\(182\) −16.6431 −1.23367
\(183\) −6.50953 −0.481198
\(184\) 48.2924 3.56016
\(185\) 0.105387 0.00774821
\(186\) −23.7139 −1.73879
\(187\) −0.546634 −0.0399738
\(188\) −31.9592 −2.33086
\(189\) −1.00000 −0.0727393
\(190\) −0.822869 −0.0596972
\(191\) 9.86937 0.714123 0.357061 0.934081i \(-0.383779\pi\)
0.357061 + 0.934081i \(0.383779\pi\)
\(192\) −35.2694 −2.54535
\(193\) 22.3252 1.60700 0.803502 0.595302i \(-0.202968\pi\)
0.803502 + 0.595302i \(0.202968\pi\)
\(194\) −51.1785 −3.67441
\(195\) 0.375827 0.0269136
\(196\) 5.58878 0.399198
\(197\) 13.1973 0.940270 0.470135 0.882595i \(-0.344205\pi\)
0.470135 + 0.882595i \(0.344205\pi\)
\(198\) −2.95970 −0.210337
\(199\) −0.635396 −0.0450421 −0.0225210 0.999746i \(-0.507169\pi\)
−0.0225210 + 0.999746i \(0.507169\pi\)
\(200\) 49.3931 3.49262
\(201\) 9.27574 0.654260
\(202\) −25.8386 −1.81800
\(203\) 1.19489 0.0838645
\(204\) 2.84349 0.199084
\(205\) 0.435873 0.0304427
\(206\) −7.11737 −0.495890
\(207\) −4.88480 −0.339517
\(208\) 97.0083 6.72632
\(209\) −5.15901 −0.356856
\(210\) −0.171367 −0.0118254
\(211\) 25.7898 1.77545 0.887723 0.460379i \(-0.152286\pi\)
0.887723 + 0.460379i \(0.152286\pi\)
\(212\) 5.65893 0.388657
\(213\) 4.83756 0.331464
\(214\) −11.0457 −0.755067
\(215\) −0.124250 −0.00847381
\(216\) 9.88627 0.672675
\(217\) −8.60831 −0.584370
\(218\) 18.0611 1.22325
\(219\) −10.1283 −0.684405
\(220\) −0.373524 −0.0251830
\(221\) −3.07385 −0.206770
\(222\) −4.66695 −0.313225
\(223\) 15.7070 1.05182 0.525911 0.850540i \(-0.323725\pi\)
0.525911 + 0.850540i \(0.323725\pi\)
\(224\) −24.4605 −1.63434
\(225\) −4.99613 −0.333075
\(226\) −45.3605 −3.01733
\(227\) −2.90291 −0.192673 −0.0963363 0.995349i \(-0.530712\pi\)
−0.0963363 + 0.995349i \(0.530712\pi\)
\(228\) 26.8362 1.77727
\(229\) 0.832421 0.0550079 0.0275040 0.999622i \(-0.491244\pi\)
0.0275040 + 0.999622i \(0.491244\pi\)
\(230\) −0.837091 −0.0551961
\(231\) −1.07439 −0.0706896
\(232\) −11.8130 −0.775559
\(233\) 23.8340 1.56142 0.780709 0.624894i \(-0.214858\pi\)
0.780709 + 0.624894i \(0.214858\pi\)
\(234\) −16.6431 −1.08799
\(235\) 0.355729 0.0232052
\(236\) −26.9529 −1.75448
\(237\) −14.9495 −0.971075
\(238\) 1.40159 0.0908515
\(239\) 0.0398658 0.00257871 0.00128935 0.999999i \(-0.499590\pi\)
0.00128935 + 0.999999i \(0.499590\pi\)
\(240\) 0.998852 0.0644756
\(241\) 17.5074 1.12775 0.563877 0.825859i \(-0.309309\pi\)
0.563877 + 0.825859i \(0.309309\pi\)
\(242\) 27.1226 1.74351
\(243\) −1.00000 −0.0641500
\(244\) 36.3803 2.32901
\(245\) −0.0622071 −0.00397427
\(246\) −19.3021 −1.23066
\(247\) −29.0103 −1.84588
\(248\) 85.1040 5.40411
\(249\) 7.77734 0.492869
\(250\) −1.71300 −0.108340
\(251\) 29.0199 1.83172 0.915860 0.401498i \(-0.131510\pi\)
0.915860 + 0.401498i \(0.131510\pi\)
\(252\) 5.58878 0.352060
\(253\) −5.24817 −0.329950
\(254\) −35.4881 −2.22672
\(255\) −0.0316501 −0.00198201
\(256\) 62.3465 3.89666
\(257\) 25.5866 1.59605 0.798023 0.602626i \(-0.205879\pi\)
0.798023 + 0.602626i \(0.205879\pi\)
\(258\) 5.50229 0.342558
\(259\) −1.69413 −0.105268
\(260\) −2.10042 −0.130262
\(261\) 1.19489 0.0739616
\(262\) −32.6171 −2.01509
\(263\) −2.33319 −0.143871 −0.0719353 0.997409i \(-0.522918\pi\)
−0.0719353 + 0.997409i \(0.522918\pi\)
\(264\) 10.6217 0.653720
\(265\) −0.0629880 −0.00386932
\(266\) 13.2279 0.811054
\(267\) 11.8515 0.725297
\(268\) −51.8400 −3.16664
\(269\) −18.4044 −1.12213 −0.561067 0.827770i \(-0.689609\pi\)
−0.561067 + 0.827770i \(0.689609\pi\)
\(270\) −0.171367 −0.0104290
\(271\) 25.4471 1.54580 0.772901 0.634526i \(-0.218805\pi\)
0.772901 + 0.634526i \(0.218805\pi\)
\(272\) −8.16950 −0.495349
\(273\) −6.04155 −0.365651
\(274\) 6.84836 0.413724
\(275\) −5.36779 −0.323690
\(276\) 27.3000 1.64327
\(277\) −14.0025 −0.841329 −0.420664 0.907216i \(-0.638203\pi\)
−0.420664 + 0.907216i \(0.638203\pi\)
\(278\) 20.1535 1.20873
\(279\) −8.60831 −0.515366
\(280\) 0.614996 0.0367531
\(281\) −8.32382 −0.496557 −0.248279 0.968689i \(-0.579865\pi\)
−0.248279 + 0.968689i \(0.579865\pi\)
\(282\) −15.7531 −0.938081
\(283\) −20.0741 −1.19328 −0.596640 0.802509i \(-0.703498\pi\)
−0.596640 + 0.802509i \(0.703498\pi\)
\(284\) −27.0360 −1.60429
\(285\) −0.298707 −0.0176938
\(286\) −17.8812 −1.05734
\(287\) −7.00680 −0.413598
\(288\) −24.4605 −1.44135
\(289\) −16.7411 −0.984773
\(290\) 0.204764 0.0120241
\(291\) −18.5781 −1.08907
\(292\) 56.6046 3.31254
\(293\) 9.30777 0.543766 0.271883 0.962330i \(-0.412354\pi\)
0.271883 + 0.962330i \(0.412354\pi\)
\(294\) 2.75477 0.160662
\(295\) 0.300005 0.0174670
\(296\) 16.7486 0.973495
\(297\) −1.07439 −0.0623424
\(298\) 4.09653 0.237306
\(299\) −29.5117 −1.70671
\(300\) 27.9223 1.61209
\(301\) 1.99737 0.115126
\(302\) 6.19491 0.356477
\(303\) −9.37959 −0.538843
\(304\) −77.1019 −4.42210
\(305\) −0.404939 −0.0231867
\(306\) 1.40159 0.0801235
\(307\) −0.0661153 −0.00377340 −0.00188670 0.999998i \(-0.500601\pi\)
−0.00188670 + 0.999998i \(0.500601\pi\)
\(308\) 6.00452 0.342139
\(309\) −2.58365 −0.146979
\(310\) −1.47518 −0.0837844
\(311\) −25.7491 −1.46010 −0.730049 0.683395i \(-0.760503\pi\)
−0.730049 + 0.683395i \(0.760503\pi\)
\(312\) 59.7283 3.38145
\(313\) −24.2429 −1.37029 −0.685144 0.728408i \(-0.740261\pi\)
−0.685144 + 0.728408i \(0.740261\pi\)
\(314\) 23.6453 1.33438
\(315\) −0.0622071 −0.00350498
\(316\) 83.5494 4.70002
\(317\) 31.7699 1.78437 0.892187 0.451666i \(-0.149170\pi\)
0.892187 + 0.451666i \(0.149170\pi\)
\(318\) 2.78935 0.156419
\(319\) 1.28377 0.0718775
\(320\) −2.19401 −0.122649
\(321\) −4.00965 −0.223797
\(322\) 13.4565 0.749902
\(323\) 2.44309 0.135937
\(324\) 5.58878 0.310488
\(325\) −30.1844 −1.67433
\(326\) 11.7529 0.650931
\(327\) 6.55630 0.362564
\(328\) 69.2711 3.82485
\(329\) −5.71846 −0.315269
\(330\) −0.184114 −0.0101352
\(331\) −34.8179 −1.91377 −0.956883 0.290473i \(-0.906187\pi\)
−0.956883 + 0.290473i \(0.906187\pi\)
\(332\) −43.4658 −2.38550
\(333\) −1.69413 −0.0928378
\(334\) 5.09509 0.278791
\(335\) 0.577018 0.0315258
\(336\) −16.0569 −0.875974
\(337\) 23.4163 1.27557 0.637784 0.770215i \(-0.279851\pi\)
0.637784 + 0.770215i \(0.279851\pi\)
\(338\) −64.7380 −3.52128
\(339\) −16.4661 −0.894318
\(340\) 0.176885 0.00959295
\(341\) −9.24868 −0.500844
\(342\) 13.2279 0.715282
\(343\) 1.00000 0.0539949
\(344\) −19.7465 −1.06466
\(345\) −0.303869 −0.0163598
\(346\) −54.8614 −2.94937
\(347\) 24.2861 1.30375 0.651874 0.758327i \(-0.273983\pi\)
0.651874 + 0.758327i \(0.273983\pi\)
\(348\) −6.67795 −0.357976
\(349\) −17.1955 −0.920454 −0.460227 0.887801i \(-0.652232\pi\)
−0.460227 + 0.887801i \(0.652232\pi\)
\(350\) 13.7632 0.735674
\(351\) −6.04155 −0.322474
\(352\) −26.2801 −1.40073
\(353\) −4.36982 −0.232582 −0.116291 0.993215i \(-0.537101\pi\)
−0.116291 + 0.993215i \(0.537101\pi\)
\(354\) −13.2854 −0.706111
\(355\) 0.300931 0.0159717
\(356\) −66.2351 −3.51045
\(357\) 0.508785 0.0269278
\(358\) 20.8189 1.10031
\(359\) 25.6589 1.35422 0.677112 0.735880i \(-0.263231\pi\)
0.677112 + 0.735880i \(0.263231\pi\)
\(360\) 0.614996 0.0324132
\(361\) 4.05732 0.213543
\(362\) −34.7172 −1.82470
\(363\) 9.84569 0.516765
\(364\) 33.7649 1.76976
\(365\) −0.630051 −0.0329784
\(366\) 17.9323 0.937335
\(367\) 13.3943 0.699177 0.349589 0.936903i \(-0.386321\pi\)
0.349589 + 0.936903i \(0.386321\pi\)
\(368\) −78.4345 −4.08868
\(369\) −7.00680 −0.364759
\(370\) −0.290318 −0.0150929
\(371\) 1.01255 0.0525691
\(372\) 48.1099 2.49438
\(373\) −27.9726 −1.44837 −0.724184 0.689606i \(-0.757784\pi\)
−0.724184 + 0.689606i \(0.757784\pi\)
\(374\) 1.50585 0.0778658
\(375\) −0.621831 −0.0321112
\(376\) 56.5342 2.91553
\(377\) 7.21896 0.371795
\(378\) 2.75477 0.141690
\(379\) −17.3497 −0.891195 −0.445598 0.895233i \(-0.647009\pi\)
−0.445598 + 0.895233i \(0.647009\pi\)
\(380\) 1.66940 0.0856386
\(381\) −12.8824 −0.659985
\(382\) −27.1879 −1.39105
\(383\) −1.00000 −0.0510976
\(384\) 48.2382 2.46165
\(385\) −0.0668347 −0.00340621
\(386\) −61.5009 −3.13031
\(387\) 1.99737 0.101532
\(388\) 103.829 5.27112
\(389\) 25.7331 1.30472 0.652360 0.757909i \(-0.273779\pi\)
0.652360 + 0.757909i \(0.273779\pi\)
\(390\) −1.03532 −0.0524254
\(391\) 2.48531 0.125688
\(392\) −9.88627 −0.499332
\(393\) −11.8402 −0.597260
\(394\) −36.3556 −1.83157
\(395\) −0.929966 −0.0467917
\(396\) 6.00452 0.301739
\(397\) −24.5190 −1.23057 −0.615286 0.788304i \(-0.710960\pi\)
−0.615286 + 0.788304i \(0.710960\pi\)
\(398\) 1.75037 0.0877383
\(399\) 4.80180 0.240391
\(400\) −80.2222 −4.01111
\(401\) 22.3210 1.11466 0.557329 0.830291i \(-0.311826\pi\)
0.557329 + 0.830291i \(0.311826\pi\)
\(402\) −25.5526 −1.27445
\(403\) −52.0075 −2.59068
\(404\) 52.4204 2.60801
\(405\) −0.0622071 −0.00309110
\(406\) −3.29164 −0.163361
\(407\) −1.82016 −0.0902218
\(408\) −5.02999 −0.249022
\(409\) −7.39770 −0.365793 −0.182896 0.983132i \(-0.558547\pi\)
−0.182896 + 0.983132i \(0.558547\pi\)
\(410\) −1.20073 −0.0592999
\(411\) 2.48600 0.122625
\(412\) 14.4394 0.711380
\(413\) −4.82268 −0.237309
\(414\) 13.4565 0.661351
\(415\) 0.483806 0.0237491
\(416\) −147.779 −7.24547
\(417\) 7.31586 0.358259
\(418\) 14.2119 0.695127
\(419\) −14.3909 −0.703040 −0.351520 0.936180i \(-0.614335\pi\)
−0.351520 + 0.936180i \(0.614335\pi\)
\(420\) 0.347662 0.0169642
\(421\) 14.7365 0.718212 0.359106 0.933297i \(-0.383082\pi\)
0.359106 + 0.933297i \(0.383082\pi\)
\(422\) −71.0451 −3.45842
\(423\) −5.71846 −0.278041
\(424\) −10.0104 −0.486146
\(425\) 2.54196 0.123303
\(426\) −13.3264 −0.645665
\(427\) 6.50953 0.315018
\(428\) 22.4090 1.08318
\(429\) −6.49098 −0.313387
\(430\) 0.342282 0.0165063
\(431\) −33.1881 −1.59861 −0.799307 0.600924i \(-0.794800\pi\)
−0.799307 + 0.600924i \(0.794800\pi\)
\(432\) −16.0569 −0.772536
\(433\) 35.3732 1.69993 0.849963 0.526842i \(-0.176624\pi\)
0.849963 + 0.526842i \(0.176624\pi\)
\(434\) 23.7139 1.13831
\(435\) 0.0743304 0.00356387
\(436\) −36.6417 −1.75482
\(437\) 23.4558 1.12204
\(438\) 27.9011 1.33317
\(439\) −13.2140 −0.630672 −0.315336 0.948980i \(-0.602117\pi\)
−0.315336 + 0.948980i \(0.602117\pi\)
\(440\) 0.660746 0.0314998
\(441\) 1.00000 0.0476190
\(442\) 8.46776 0.402770
\(443\) 17.3294 0.823345 0.411672 0.911332i \(-0.364945\pi\)
0.411672 + 0.911332i \(0.364945\pi\)
\(444\) 9.46812 0.449337
\(445\) 0.737245 0.0349488
\(446\) −43.2694 −2.04886
\(447\) 1.48707 0.0703358
\(448\) 35.2694 1.66632
\(449\) 19.7160 0.930458 0.465229 0.885190i \(-0.345972\pi\)
0.465229 + 0.885190i \(0.345972\pi\)
\(450\) 13.7632 0.648804
\(451\) −7.52803 −0.354481
\(452\) 92.0256 4.32852
\(453\) 2.24879 0.105657
\(454\) 7.99685 0.375311
\(455\) −0.375827 −0.0176191
\(456\) −47.4719 −2.22308
\(457\) −13.0019 −0.608203 −0.304101 0.952640i \(-0.598356\pi\)
−0.304101 + 0.952640i \(0.598356\pi\)
\(458\) −2.29313 −0.107151
\(459\) 0.508785 0.0237481
\(460\) 1.69826 0.0791817
\(461\) −33.8132 −1.57484 −0.787420 0.616417i \(-0.788584\pi\)
−0.787420 + 0.616417i \(0.788584\pi\)
\(462\) 2.95970 0.137698
\(463\) 11.4436 0.531830 0.265915 0.963996i \(-0.414326\pi\)
0.265915 + 0.963996i \(0.414326\pi\)
\(464\) 19.1861 0.890693
\(465\) −0.535498 −0.0248331
\(466\) −65.6573 −3.04152
\(467\) −1.63772 −0.0757848 −0.0378924 0.999282i \(-0.512064\pi\)
−0.0378924 + 0.999282i \(0.512064\pi\)
\(468\) 33.7649 1.56078
\(469\) −9.27574 −0.428314
\(470\) −0.979953 −0.0452018
\(471\) 8.58340 0.395502
\(472\) 47.6783 2.19457
\(473\) 2.14595 0.0986709
\(474\) 41.1825 1.89157
\(475\) 23.9904 1.10076
\(476\) −2.84349 −0.130331
\(477\) 1.01255 0.0463616
\(478\) −0.109821 −0.00502311
\(479\) −17.0378 −0.778476 −0.389238 0.921137i \(-0.627262\pi\)
−0.389238 + 0.921137i \(0.627262\pi\)
\(480\) −1.52162 −0.0694520
\(481\) −10.2352 −0.466684
\(482\) −48.2290 −2.19677
\(483\) 4.88480 0.222266
\(484\) −55.0253 −2.50115
\(485\) −1.15569 −0.0524773
\(486\) 2.75477 0.124959
\(487\) 10.1822 0.461398 0.230699 0.973025i \(-0.425899\pi\)
0.230699 + 0.973025i \(0.425899\pi\)
\(488\) −64.3549 −2.91321
\(489\) 4.26636 0.192932
\(490\) 0.171367 0.00774155
\(491\) −9.69862 −0.437693 −0.218846 0.975759i \(-0.570229\pi\)
−0.218846 + 0.975759i \(0.570229\pi\)
\(492\) 39.1594 1.76544
\(493\) −0.607941 −0.0273803
\(494\) 79.9169 3.59563
\(495\) −0.0668347 −0.00300400
\(496\) −138.222 −6.20637
\(497\) −4.83756 −0.216994
\(498\) −21.4248 −0.960068
\(499\) 14.2515 0.637984 0.318992 0.947757i \(-0.396656\pi\)
0.318992 + 0.947757i \(0.396656\pi\)
\(500\) 3.47527 0.155419
\(501\) 1.84955 0.0826319
\(502\) −79.9433 −3.56804
\(503\) 0.233948 0.0104312 0.00521562 0.999986i \(-0.498340\pi\)
0.00521562 + 0.999986i \(0.498340\pi\)
\(504\) −9.88627 −0.440369
\(505\) −0.583477 −0.0259644
\(506\) 14.4575 0.642716
\(507\) −23.5003 −1.04368
\(508\) 71.9968 3.19434
\(509\) 24.2402 1.07443 0.537213 0.843446i \(-0.319477\pi\)
0.537213 + 0.843446i \(0.319477\pi\)
\(510\) 0.0871888 0.00386079
\(511\) 10.1283 0.448048
\(512\) −75.2741 −3.32668
\(513\) 4.80180 0.212005
\(514\) −70.4852 −3.10897
\(515\) −0.160721 −0.00708223
\(516\) −11.1628 −0.491416
\(517\) −6.14385 −0.270206
\(518\) 4.66695 0.205054
\(519\) −19.9150 −0.874173
\(520\) 3.71553 0.162937
\(521\) −12.9339 −0.566643 −0.283322 0.959025i \(-0.591436\pi\)
−0.283322 + 0.959025i \(0.591436\pi\)
\(522\) −3.29164 −0.144071
\(523\) −5.15784 −0.225537 −0.112768 0.993621i \(-0.535972\pi\)
−0.112768 + 0.993621i \(0.535972\pi\)
\(524\) 66.1723 2.89075
\(525\) 4.99613 0.218049
\(526\) 6.42741 0.280248
\(527\) 4.37978 0.190786
\(528\) −17.2513 −0.750768
\(529\) 0.861235 0.0374450
\(530\) 0.173518 0.00753713
\(531\) −4.82268 −0.209287
\(532\) −26.8362 −1.16350
\(533\) −42.3319 −1.83360
\(534\) −32.6481 −1.41282
\(535\) −0.249429 −0.0107837
\(536\) 91.7024 3.96094
\(537\) 7.55740 0.326126
\(538\) 50.6998 2.18583
\(539\) 1.07439 0.0462772
\(540\) 0.347662 0.0149610
\(541\) −4.79752 −0.206261 −0.103131 0.994668i \(-0.532886\pi\)
−0.103131 + 0.994668i \(0.532886\pi\)
\(542\) −70.1011 −3.01110
\(543\) −12.6026 −0.540828
\(544\) 12.4451 0.533581
\(545\) 0.407849 0.0174703
\(546\) 16.6431 0.712259
\(547\) 4.32095 0.184750 0.0923752 0.995724i \(-0.470554\pi\)
0.0923752 + 0.995724i \(0.470554\pi\)
\(548\) −13.8937 −0.593509
\(549\) 6.50953 0.277820
\(550\) 14.7870 0.630522
\(551\) −5.73761 −0.244430
\(552\) −48.2924 −2.05546
\(553\) 14.9495 0.635718
\(554\) 38.5737 1.63884
\(555\) −0.105387 −0.00447343
\(556\) −40.8867 −1.73398
\(557\) −43.3862 −1.83833 −0.919167 0.393869i \(-0.871137\pi\)
−0.919167 + 0.393869i \(0.871137\pi\)
\(558\) 23.7139 1.00389
\(559\) 12.0672 0.510387
\(560\) −0.998852 −0.0422092
\(561\) 0.546634 0.0230789
\(562\) 22.9302 0.967254
\(563\) 37.4142 1.57682 0.788411 0.615149i \(-0.210904\pi\)
0.788411 + 0.615149i \(0.210904\pi\)
\(564\) 31.9592 1.34572
\(565\) −1.02431 −0.0430931
\(566\) 55.2995 2.32441
\(567\) 1.00000 0.0419961
\(568\) 47.8254 2.00671
\(569\) −22.8628 −0.958459 −0.479229 0.877690i \(-0.659084\pi\)
−0.479229 + 0.877690i \(0.659084\pi\)
\(570\) 0.822869 0.0344662
\(571\) 8.08011 0.338142 0.169071 0.985604i \(-0.445923\pi\)
0.169071 + 0.985604i \(0.445923\pi\)
\(572\) 36.2766 1.51680
\(573\) −9.86937 −0.412299
\(574\) 19.3021 0.805656
\(575\) 24.4051 1.01776
\(576\) 35.2694 1.46956
\(577\) 30.7327 1.27942 0.639710 0.768616i \(-0.279054\pi\)
0.639710 + 0.768616i \(0.279054\pi\)
\(578\) 46.1180 1.91826
\(579\) −22.3252 −0.927804
\(580\) −0.415416 −0.0172492
\(581\) −7.77734 −0.322658
\(582\) 51.1785 2.12142
\(583\) 1.08788 0.0450552
\(584\) −100.131 −4.14344
\(585\) −0.375827 −0.0155386
\(586\) −25.6408 −1.05921
\(587\) 30.8287 1.27243 0.636217 0.771510i \(-0.280498\pi\)
0.636217 + 0.771510i \(0.280498\pi\)
\(588\) −5.58878 −0.230477
\(589\) 41.3354 1.70320
\(590\) −0.826446 −0.0340243
\(591\) −13.1973 −0.542865
\(592\) −27.2024 −1.11801
\(593\) −8.50164 −0.349120 −0.174560 0.984647i \(-0.555850\pi\)
−0.174560 + 0.984647i \(0.555850\pi\)
\(594\) 2.95970 0.121438
\(595\) 0.0316501 0.00129753
\(596\) −8.31088 −0.340427
\(597\) 0.635396 0.0260050
\(598\) 81.2981 3.32453
\(599\) −12.3139 −0.503131 −0.251565 0.967840i \(-0.580945\pi\)
−0.251565 + 0.967840i \(0.580945\pi\)
\(600\) −49.3931 −2.01646
\(601\) −34.8192 −1.42030 −0.710152 0.704048i \(-0.751374\pi\)
−0.710152 + 0.704048i \(0.751374\pi\)
\(602\) −5.50229 −0.224257
\(603\) −9.27574 −0.377737
\(604\) −12.5680 −0.511385
\(605\) 0.612472 0.0249005
\(606\) 25.8386 1.04962
\(607\) 44.2362 1.79549 0.897746 0.440513i \(-0.145204\pi\)
0.897746 + 0.440513i \(0.145204\pi\)
\(608\) 117.455 4.76341
\(609\) −1.19489 −0.0484192
\(610\) 1.11552 0.0451659
\(611\) −34.5483 −1.39768
\(612\) −2.84349 −0.114941
\(613\) 0.0580635 0.00234516 0.00117258 0.999999i \(-0.499627\pi\)
0.00117258 + 0.999999i \(0.499627\pi\)
\(614\) 0.182133 0.00735027
\(615\) −0.435873 −0.0175761
\(616\) −10.6217 −0.427960
\(617\) −15.9111 −0.640555 −0.320278 0.947324i \(-0.603776\pi\)
−0.320278 + 0.947324i \(0.603776\pi\)
\(618\) 7.11737 0.286302
\(619\) 39.8889 1.60327 0.801636 0.597813i \(-0.203963\pi\)
0.801636 + 0.597813i \(0.203963\pi\)
\(620\) 2.99278 0.120193
\(621\) 4.88480 0.196020
\(622\) 70.9329 2.84415
\(623\) −11.8515 −0.474818
\(624\) −97.0083 −3.88344
\(625\) 24.9420 0.997679
\(626\) 66.7836 2.66921
\(627\) 5.15901 0.206031
\(628\) −47.9707 −1.91424
\(629\) 0.861949 0.0343682
\(630\) 0.171367 0.00682741
\(631\) −5.43344 −0.216302 −0.108151 0.994134i \(-0.534493\pi\)
−0.108151 + 0.994134i \(0.534493\pi\)
\(632\) −147.795 −5.87896
\(633\) −25.7898 −1.02505
\(634\) −87.5188 −3.47582
\(635\) −0.801376 −0.0318017
\(636\) −5.65893 −0.224391
\(637\) 6.04155 0.239375
\(638\) −3.53650 −0.140012
\(639\) −4.83756 −0.191371
\(640\) 3.00076 0.118615
\(641\) 28.7454 1.13537 0.567687 0.823245i \(-0.307839\pi\)
0.567687 + 0.823245i \(0.307839\pi\)
\(642\) 11.0457 0.435938
\(643\) 13.5003 0.532402 0.266201 0.963918i \(-0.414232\pi\)
0.266201 + 0.963918i \(0.414232\pi\)
\(644\) −27.3000 −1.07577
\(645\) 0.124250 0.00489236
\(646\) −6.73015 −0.264794
\(647\) 16.6769 0.655635 0.327817 0.944741i \(-0.393687\pi\)
0.327817 + 0.944741i \(0.393687\pi\)
\(648\) −9.88627 −0.388369
\(649\) −5.18144 −0.203389
\(650\) 83.1511 3.26145
\(651\) 8.60831 0.337386
\(652\) −23.8438 −0.933793
\(653\) 10.1477 0.397111 0.198556 0.980090i \(-0.436375\pi\)
0.198556 + 0.980090i \(0.436375\pi\)
\(654\) −18.0611 −0.706246
\(655\) −0.736546 −0.0287792
\(656\) −112.507 −4.39267
\(657\) 10.1283 0.395142
\(658\) 15.7531 0.614118
\(659\) 24.5050 0.954578 0.477289 0.878746i \(-0.341619\pi\)
0.477289 + 0.878746i \(0.341619\pi\)
\(660\) 0.373524 0.0145394
\(661\) 46.8349 1.82167 0.910834 0.412773i \(-0.135440\pi\)
0.910834 + 0.412773i \(0.135440\pi\)
\(662\) 95.9155 3.72786
\(663\) 3.07385 0.119378
\(664\) 76.8888 2.98386
\(665\) 0.298707 0.0115833
\(666\) 4.66695 0.180841
\(667\) −5.83677 −0.226001
\(668\) −10.3367 −0.399940
\(669\) −15.7070 −0.607269
\(670\) −1.58955 −0.0614098
\(671\) 6.99377 0.269991
\(672\) 24.4605 0.943584
\(673\) 12.2569 0.472468 0.236234 0.971696i \(-0.424087\pi\)
0.236234 + 0.971696i \(0.424087\pi\)
\(674\) −64.5067 −2.48470
\(675\) 4.99613 0.192301
\(676\) 131.338 5.05146
\(677\) −18.4420 −0.708784 −0.354392 0.935097i \(-0.615312\pi\)
−0.354392 + 0.935097i \(0.615312\pi\)
\(678\) 45.3605 1.74206
\(679\) 18.5781 0.712963
\(680\) −0.312901 −0.0119992
\(681\) 2.90291 0.111240
\(682\) 25.4780 0.975603
\(683\) 25.2948 0.967878 0.483939 0.875102i \(-0.339206\pi\)
0.483939 + 0.875102i \(0.339206\pi\)
\(684\) −26.8362 −1.02611
\(685\) 0.154647 0.00590875
\(686\) −2.75477 −0.105178
\(687\) −0.832421 −0.0317588
\(688\) 32.0714 1.22271
\(689\) 6.11739 0.233054
\(690\) 0.837091 0.0318675
\(691\) −35.2927 −1.34260 −0.671298 0.741188i \(-0.734263\pi\)
−0.671298 + 0.741188i \(0.734263\pi\)
\(692\) 111.301 4.23102
\(693\) 1.07439 0.0408127
\(694\) −66.9028 −2.53960
\(695\) 0.455099 0.0172629
\(696\) 11.8130 0.447769
\(697\) 3.56496 0.135032
\(698\) 47.3697 1.79297
\(699\) −23.8340 −0.901485
\(700\) −27.9223 −1.05536
\(701\) 24.9776 0.943390 0.471695 0.881762i \(-0.343642\pi\)
0.471695 + 0.881762i \(0.343642\pi\)
\(702\) 16.6431 0.628153
\(703\) 8.13489 0.306813
\(704\) 37.8931 1.42815
\(705\) −0.355729 −0.0133975
\(706\) 12.0379 0.453051
\(707\) 9.37959 0.352756
\(708\) 26.9529 1.01295
\(709\) 17.0802 0.641461 0.320731 0.947170i \(-0.396072\pi\)
0.320731 + 0.947170i \(0.396072\pi\)
\(710\) −0.828996 −0.0311117
\(711\) 14.9495 0.560650
\(712\) 117.167 4.39100
\(713\) 42.0498 1.57478
\(714\) −1.40159 −0.0524531
\(715\) −0.403785 −0.0151007
\(716\) −42.2366 −1.57846
\(717\) −0.0398658 −0.00148882
\(718\) −70.6844 −2.63792
\(719\) −8.53982 −0.318481 −0.159241 0.987240i \(-0.550905\pi\)
−0.159241 + 0.987240i \(0.550905\pi\)
\(720\) −0.998852 −0.0372250
\(721\) 2.58365 0.0962201
\(722\) −11.1770 −0.415965
\(723\) −17.5074 −0.651109
\(724\) 70.4330 2.61762
\(725\) −5.96981 −0.221713
\(726\) −27.1226 −1.00662
\(727\) 40.2408 1.49245 0.746225 0.665694i \(-0.231865\pi\)
0.746225 + 0.665694i \(0.231865\pi\)
\(728\) −59.7283 −2.21368
\(729\) 1.00000 0.0370370
\(730\) 1.73565 0.0642392
\(731\) −1.01623 −0.0375867
\(732\) −36.3803 −1.34465
\(733\) 4.90667 0.181232 0.0906160 0.995886i \(-0.471116\pi\)
0.0906160 + 0.995886i \(0.471116\pi\)
\(734\) −36.8983 −1.36194
\(735\) 0.0622071 0.00229455
\(736\) 119.485 4.40426
\(737\) −9.96576 −0.367094
\(738\) 19.3021 0.710522
\(739\) −12.7916 −0.470548 −0.235274 0.971929i \(-0.575599\pi\)
−0.235274 + 0.971929i \(0.575599\pi\)
\(740\) 0.588985 0.0216515
\(741\) 29.0103 1.06572
\(742\) −2.78935 −0.102400
\(743\) −18.3697 −0.673919 −0.336960 0.941519i \(-0.609399\pi\)
−0.336960 + 0.941519i \(0.609399\pi\)
\(744\) −85.1040 −3.12006
\(745\) 0.0925061 0.00338916
\(746\) 77.0583 2.82130
\(747\) −7.77734 −0.284558
\(748\) −3.05501 −0.111702
\(749\) 4.00965 0.146509
\(750\) 1.71300 0.0625500
\(751\) −32.8771 −1.19970 −0.599851 0.800112i \(-0.704774\pi\)
−0.599851 + 0.800112i \(0.704774\pi\)
\(752\) −91.8205 −3.34835
\(753\) −29.0199 −1.05754
\(754\) −19.8866 −0.724227
\(755\) 0.139891 0.00509115
\(756\) −5.58878 −0.203262
\(757\) −10.0269 −0.364435 −0.182218 0.983258i \(-0.558328\pi\)
−0.182218 + 0.983258i \(0.558328\pi\)
\(758\) 47.7946 1.73598
\(759\) 5.24817 0.190497
\(760\) −2.95309 −0.107120
\(761\) 7.45689 0.270312 0.135156 0.990824i \(-0.456846\pi\)
0.135156 + 0.990824i \(0.456846\pi\)
\(762\) 35.4881 1.28560
\(763\) −6.55630 −0.237354
\(764\) 55.1577 1.99554
\(765\) 0.0316501 0.00114431
\(766\) 2.75477 0.0995340
\(767\) −29.1365 −1.05206
\(768\) −62.3465 −2.24974
\(769\) −32.4343 −1.16961 −0.584805 0.811174i \(-0.698829\pi\)
−0.584805 + 0.811174i \(0.698829\pi\)
\(770\) 0.184114 0.00663503
\(771\) −25.5866 −0.921478
\(772\) 124.771 4.49059
\(773\) −38.4735 −1.38380 −0.691898 0.721995i \(-0.743225\pi\)
−0.691898 + 0.721995i \(0.743225\pi\)
\(774\) −5.50229 −0.197776
\(775\) 43.0082 1.54490
\(776\) −183.668 −6.59331
\(777\) 1.69413 0.0607766
\(778\) −70.8889 −2.54149
\(779\) 33.6453 1.20547
\(780\) 2.10042 0.0752069
\(781\) −5.19742 −0.185978
\(782\) −6.84647 −0.244829
\(783\) −1.19489 −0.0427017
\(784\) 16.0569 0.573460
\(785\) 0.533949 0.0190574
\(786\) 32.6171 1.16341
\(787\) 10.3070 0.367404 0.183702 0.982982i \(-0.441192\pi\)
0.183702 + 0.982982i \(0.441192\pi\)
\(788\) 73.7568 2.62748
\(789\) 2.33319 0.0830638
\(790\) 2.56185 0.0911464
\(791\) 16.4661 0.585468
\(792\) −10.6217 −0.377426
\(793\) 39.3276 1.39656
\(794\) 67.5442 2.39706
\(795\) 0.0629880 0.00223396
\(796\) −3.55109 −0.125865
\(797\) −3.25265 −0.115215 −0.0576074 0.998339i \(-0.518347\pi\)
−0.0576074 + 0.998339i \(0.518347\pi\)
\(798\) −13.2279 −0.468262
\(799\) 2.90947 0.102930
\(800\) 122.208 4.32070
\(801\) −11.8515 −0.418751
\(802\) −61.4894 −2.17127
\(803\) 10.8817 0.384007
\(804\) 51.8400 1.82826
\(805\) 0.303869 0.0107100
\(806\) 143.269 5.04643
\(807\) 18.4044 0.647864
\(808\) −92.7291 −3.26220
\(809\) 52.7845 1.85580 0.927902 0.372825i \(-0.121611\pi\)
0.927902 + 0.372825i \(0.121611\pi\)
\(810\) 0.171367 0.00602121
\(811\) 28.6113 1.00468 0.502340 0.864670i \(-0.332473\pi\)
0.502340 + 0.864670i \(0.332473\pi\)
\(812\) 6.67795 0.234350
\(813\) −25.4471 −0.892470
\(814\) 5.01412 0.175745
\(815\) 0.265398 0.00929650
\(816\) 8.16950 0.285990
\(817\) −9.59096 −0.335545
\(818\) 20.3790 0.712534
\(819\) 6.04155 0.211109
\(820\) 2.43600 0.0850687
\(821\) 41.7489 1.45705 0.728523 0.685021i \(-0.240207\pi\)
0.728523 + 0.685021i \(0.240207\pi\)
\(822\) −6.84836 −0.238864
\(823\) −17.7142 −0.617478 −0.308739 0.951147i \(-0.599907\pi\)
−0.308739 + 0.951147i \(0.599907\pi\)
\(824\) −25.5426 −0.889820
\(825\) 5.36779 0.186882
\(826\) 13.2854 0.462258
\(827\) −36.6496 −1.27443 −0.637216 0.770685i \(-0.719914\pi\)
−0.637216 + 0.770685i \(0.719914\pi\)
\(828\) −27.3000 −0.948742
\(829\) −16.8926 −0.586704 −0.293352 0.956005i \(-0.594771\pi\)
−0.293352 + 0.956005i \(0.594771\pi\)
\(830\) −1.33278 −0.0462613
\(831\) 14.0025 0.485741
\(832\) 213.082 7.38728
\(833\) −0.508785 −0.0176284
\(834\) −20.1535 −0.697860
\(835\) 0.115055 0.00398165
\(836\) −28.8325 −0.997194
\(837\) 8.60831 0.297547
\(838\) 39.6436 1.36947
\(839\) 32.4506 1.12032 0.560159 0.828385i \(-0.310740\pi\)
0.560159 + 0.828385i \(0.310740\pi\)
\(840\) −0.614996 −0.0212194
\(841\) −27.5722 −0.950767
\(842\) −40.5957 −1.39902
\(843\) 8.32382 0.286688
\(844\) 144.134 4.96128
\(845\) −1.46189 −0.0502904
\(846\) 15.7531 0.541601
\(847\) −9.84569 −0.338302
\(848\) 16.2584 0.558317
\(849\) 20.0741 0.688941
\(850\) −7.00252 −0.240184
\(851\) 8.27549 0.283680
\(852\) 27.0360 0.926239
\(853\) −4.83915 −0.165689 −0.0828446 0.996562i \(-0.526401\pi\)
−0.0828446 + 0.996562i \(0.526401\pi\)
\(854\) −17.9323 −0.613630
\(855\) 0.298707 0.0102155
\(856\) −39.6404 −1.35488
\(857\) 49.5352 1.69209 0.846045 0.533112i \(-0.178978\pi\)
0.846045 + 0.533112i \(0.178978\pi\)
\(858\) 17.8812 0.610453
\(859\) −7.46891 −0.254836 −0.127418 0.991849i \(-0.540669\pi\)
−0.127418 + 0.991849i \(0.540669\pi\)
\(860\) −0.694408 −0.0236791
\(861\) 7.00680 0.238791
\(862\) 91.4256 3.11397
\(863\) 29.2130 0.994421 0.497211 0.867630i \(-0.334358\pi\)
0.497211 + 0.867630i \(0.334358\pi\)
\(864\) 24.4605 0.832163
\(865\) −1.23886 −0.0421224
\(866\) −97.4451 −3.31132
\(867\) 16.7411 0.568559
\(868\) −48.1099 −1.63296
\(869\) 16.0616 0.544852
\(870\) −0.204764 −0.00694213
\(871\) −56.0398 −1.89884
\(872\) 64.8174 2.19499
\(873\) 18.5781 0.628774
\(874\) −64.6155 −2.18565
\(875\) 0.621831 0.0210217
\(876\) −56.6046 −1.91249
\(877\) 4.74247 0.160142 0.0800709 0.996789i \(-0.474485\pi\)
0.0800709 + 0.996789i \(0.474485\pi\)
\(878\) 36.4017 1.22850
\(879\) −9.30777 −0.313943
\(880\) −1.07316 −0.0361761
\(881\) 7.63329 0.257172 0.128586 0.991698i \(-0.458956\pi\)
0.128586 + 0.991698i \(0.458956\pi\)
\(882\) −2.75477 −0.0927580
\(883\) 52.4049 1.76356 0.881782 0.471657i \(-0.156344\pi\)
0.881782 + 0.471657i \(0.156344\pi\)
\(884\) −17.1791 −0.577795
\(885\) −0.300005 −0.0100846
\(886\) −47.7386 −1.60381
\(887\) 7.01764 0.235629 0.117815 0.993036i \(-0.462411\pi\)
0.117815 + 0.993036i \(0.462411\pi\)
\(888\) −16.7486 −0.562047
\(889\) 12.8824 0.432061
\(890\) −2.03094 −0.0680774
\(891\) 1.07439 0.0359934
\(892\) 87.7832 2.93920
\(893\) 27.4589 0.918877
\(894\) −4.09653 −0.137008
\(895\) 0.470124 0.0157145
\(896\) −48.2382 −1.61153
\(897\) 29.5117 0.985368
\(898\) −54.3132 −1.81246
\(899\) −10.2859 −0.343055
\(900\) −27.9223 −0.930742
\(901\) −0.515172 −0.0171629
\(902\) 20.7380 0.690500
\(903\) −1.99737 −0.0664682
\(904\) −162.789 −5.41427
\(905\) −0.783970 −0.0260601
\(906\) −6.19491 −0.205812
\(907\) 17.5487 0.582696 0.291348 0.956617i \(-0.405896\pi\)
0.291348 + 0.956617i \(0.405896\pi\)
\(908\) −16.2237 −0.538402
\(909\) 9.37959 0.311101
\(910\) 1.03532 0.0343205
\(911\) −21.6509 −0.717327 −0.358664 0.933467i \(-0.616768\pi\)
−0.358664 + 0.933467i \(0.616768\pi\)
\(912\) 77.1019 2.55310
\(913\) −8.35589 −0.276540
\(914\) 35.8173 1.18473
\(915\) 0.404939 0.0133869
\(916\) 4.65222 0.153714
\(917\) 11.8402 0.390999
\(918\) −1.40159 −0.0462593
\(919\) −8.50116 −0.280427 −0.140214 0.990121i \(-0.544779\pi\)
−0.140214 + 0.990121i \(0.544779\pi\)
\(920\) −3.00413 −0.0990433
\(921\) 0.0661153 0.00217857
\(922\) 93.1478 3.06766
\(923\) −29.2263 −0.961997
\(924\) −6.00452 −0.197534
\(925\) 8.46410 0.278298
\(926\) −31.5246 −1.03596
\(927\) 2.58365 0.0848581
\(928\) −29.2275 −0.959440
\(929\) 50.4287 1.65451 0.827256 0.561825i \(-0.189900\pi\)
0.827256 + 0.561825i \(0.189900\pi\)
\(930\) 1.47518 0.0483729
\(931\) −4.80180 −0.157373
\(932\) 133.203 4.36321
\(933\) 25.7491 0.842988
\(934\) 4.51156 0.147623
\(935\) 0.0340045 0.00111207
\(936\) −59.7283 −1.95228
\(937\) −24.3609 −0.795836 −0.397918 0.917421i \(-0.630267\pi\)
−0.397918 + 0.917421i \(0.630267\pi\)
\(938\) 25.5526 0.834321
\(939\) 24.2429 0.791136
\(940\) 1.98809 0.0648443
\(941\) 55.4566 1.80783 0.903917 0.427708i \(-0.140679\pi\)
0.903917 + 0.427708i \(0.140679\pi\)
\(942\) −23.6453 −0.770406
\(943\) 34.2268 1.11458
\(944\) −77.4371 −2.52036
\(945\) 0.0622071 0.00202360
\(946\) −5.91160 −0.192203
\(947\) −53.8777 −1.75079 −0.875394 0.483409i \(-0.839398\pi\)
−0.875394 + 0.483409i \(0.839398\pi\)
\(948\) −83.5494 −2.71356
\(949\) 61.1904 1.98633
\(950\) −66.0882 −2.14419
\(951\) −31.7699 −1.03021
\(952\) 5.02999 0.163023
\(953\) −37.0182 −1.19914 −0.599568 0.800324i \(-0.704661\pi\)
−0.599568 + 0.800324i \(0.704661\pi\)
\(954\) −2.78935 −0.0903087
\(955\) −0.613945 −0.0198668
\(956\) 0.222801 0.00720590
\(957\) −1.28377 −0.0414985
\(958\) 46.9352 1.51641
\(959\) −2.48600 −0.0802770
\(960\) 2.19401 0.0708113
\(961\) 43.1030 1.39042
\(962\) 28.1956 0.909062
\(963\) 4.00965 0.129209
\(964\) 97.8452 3.15138
\(965\) −1.38879 −0.0447067
\(966\) −13.4565 −0.432956
\(967\) 14.8126 0.476341 0.238171 0.971223i \(-0.423452\pi\)
0.238171 + 0.971223i \(0.423452\pi\)
\(968\) 97.3371 3.12853
\(969\) −2.44309 −0.0784833
\(970\) 3.18367 0.102222
\(971\) −57.8696 −1.85713 −0.928563 0.371176i \(-0.878955\pi\)
−0.928563 + 0.371176i \(0.878955\pi\)
\(972\) −5.58878 −0.179260
\(973\) −7.31586 −0.234536
\(974\) −28.0495 −0.898765
\(975\) 30.1844 0.966673
\(976\) 104.523 3.34569
\(977\) −8.59063 −0.274839 −0.137419 0.990513i \(-0.543881\pi\)
−0.137419 + 0.990513i \(0.543881\pi\)
\(978\) −11.7529 −0.375815
\(979\) −12.7331 −0.406951
\(980\) −0.347662 −0.0111057
\(981\) −6.55630 −0.209327
\(982\) 26.7175 0.852590
\(983\) 9.43567 0.300951 0.150476 0.988614i \(-0.451919\pi\)
0.150476 + 0.988614i \(0.451919\pi\)
\(984\) −69.2711 −2.20828
\(985\) −0.820967 −0.0261582
\(986\) 1.67474 0.0533345
\(987\) 5.71846 0.182020
\(988\) −162.132 −5.15811
\(989\) −9.75673 −0.310246
\(990\) 0.184114 0.00585154
\(991\) 37.9315 1.20493 0.602467 0.798144i \(-0.294185\pi\)
0.602467 + 0.798144i \(0.294185\pi\)
\(992\) 210.563 6.68540
\(993\) 34.8179 1.10491
\(994\) 13.3264 0.422687
\(995\) 0.0395262 0.00125306
\(996\) 43.4658 1.37727
\(997\) −43.8717 −1.38943 −0.694716 0.719284i \(-0.744470\pi\)
−0.694716 + 0.719284i \(0.744470\pi\)
\(998\) −39.2596 −1.24274
\(999\) 1.69413 0.0535999
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 \(a_p\))