Properties

Label 5077.2.a.c.1.16
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45990 q^{2} +1.58815 q^{3} +4.05112 q^{4} -3.55113 q^{5} -3.90668 q^{6} -1.72696 q^{7} -5.04554 q^{8} -0.477790 q^{9} +O(q^{10})\) \(q-2.45990 q^{2} +1.58815 q^{3} +4.05112 q^{4} -3.55113 q^{5} -3.90668 q^{6} -1.72696 q^{7} -5.04554 q^{8} -0.477790 q^{9} +8.73542 q^{10} +0.521731 q^{11} +6.43377 q^{12} -6.48917 q^{13} +4.24815 q^{14} -5.63971 q^{15} +4.30930 q^{16} -0.0823109 q^{17} +1.17532 q^{18} -1.33145 q^{19} -14.3860 q^{20} -2.74267 q^{21} -1.28341 q^{22} +1.60664 q^{23} -8.01306 q^{24} +7.61050 q^{25} +15.9627 q^{26} -5.52324 q^{27} -6.99612 q^{28} -5.29778 q^{29} +13.8731 q^{30} -3.36137 q^{31} -0.509382 q^{32} +0.828585 q^{33} +0.202477 q^{34} +6.13265 q^{35} -1.93558 q^{36} +1.70361 q^{37} +3.27523 q^{38} -10.3058 q^{39} +17.9174 q^{40} -6.24946 q^{41} +6.74669 q^{42} -11.5125 q^{43} +2.11359 q^{44} +1.69669 q^{45} -3.95218 q^{46} +0.681014 q^{47} +6.84381 q^{48} -4.01761 q^{49} -18.7211 q^{50} -0.130722 q^{51} -26.2884 q^{52} -5.03721 q^{53} +13.5866 q^{54} -1.85273 q^{55} +8.71345 q^{56} -2.11454 q^{57} +13.0320 q^{58} +3.94334 q^{59} -22.8471 q^{60} +4.73428 q^{61} +8.26863 q^{62} +0.825124 q^{63} -7.36558 q^{64} +23.0439 q^{65} -2.03824 q^{66} +11.5204 q^{67} -0.333451 q^{68} +2.55158 q^{69} -15.0857 q^{70} -3.21876 q^{71} +2.41071 q^{72} -13.0677 q^{73} -4.19071 q^{74} +12.0866 q^{75} -5.39385 q^{76} -0.901009 q^{77} +25.3511 q^{78} -15.5574 q^{79} -15.3029 q^{80} -7.33835 q^{81} +15.3730 q^{82} +8.37536 q^{83} -11.1109 q^{84} +0.292296 q^{85} +28.3196 q^{86} -8.41365 q^{87} -2.63242 q^{88} +5.06939 q^{89} -4.17370 q^{90} +11.2065 q^{91} +6.50869 q^{92} -5.33835 q^{93} -1.67523 q^{94} +4.72814 q^{95} -0.808973 q^{96} -9.06329 q^{97} +9.88292 q^{98} -0.249278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45990 −1.73941 −0.869707 0.493569i \(-0.835692\pi\)
−0.869707 + 0.493569i \(0.835692\pi\)
\(3\) 1.58815 0.916917 0.458458 0.888716i \(-0.348402\pi\)
0.458458 + 0.888716i \(0.348402\pi\)
\(4\) 4.05112 2.02556
\(5\) −3.55113 −1.58811 −0.794056 0.607845i \(-0.792034\pi\)
−0.794056 + 0.607845i \(0.792034\pi\)
\(6\) −3.90668 −1.59490
\(7\) −1.72696 −0.652730 −0.326365 0.945244i \(-0.605824\pi\)
−0.326365 + 0.945244i \(0.605824\pi\)
\(8\) −5.04554 −1.78387
\(9\) −0.477790 −0.159263
\(10\) 8.73542 2.76238
\(11\) 0.521731 0.157308 0.0786539 0.996902i \(-0.474938\pi\)
0.0786539 + 0.996902i \(0.474938\pi\)
\(12\) 6.43377 1.85727
\(13\) −6.48917 −1.79977 −0.899886 0.436126i \(-0.856350\pi\)
−0.899886 + 0.436126i \(0.856350\pi\)
\(14\) 4.24815 1.13537
\(15\) −5.63971 −1.45617
\(16\) 4.30930 1.07733
\(17\) −0.0823109 −0.0199633 −0.00998166 0.999950i \(-0.503177\pi\)
−0.00998166 + 0.999950i \(0.503177\pi\)
\(18\) 1.17532 0.277025
\(19\) −1.33145 −0.305455 −0.152728 0.988268i \(-0.548806\pi\)
−0.152728 + 0.988268i \(0.548806\pi\)
\(20\) −14.3860 −3.21681
\(21\) −2.74267 −0.598499
\(22\) −1.28341 −0.273623
\(23\) 1.60664 0.335008 0.167504 0.985871i \(-0.446429\pi\)
0.167504 + 0.985871i \(0.446429\pi\)
\(24\) −8.01306 −1.63566
\(25\) 7.61050 1.52210
\(26\) 15.9627 3.13055
\(27\) −5.52324 −1.06295
\(28\) −6.99612 −1.32214
\(29\) −5.29778 −0.983773 −0.491886 0.870659i \(-0.663692\pi\)
−0.491886 + 0.870659i \(0.663692\pi\)
\(30\) 13.8731 2.53288
\(31\) −3.36137 −0.603720 −0.301860 0.953352i \(-0.597607\pi\)
−0.301860 + 0.953352i \(0.597607\pi\)
\(32\) −0.509382 −0.0900469
\(33\) 0.828585 0.144238
\(34\) 0.202477 0.0347245
\(35\) 6.13265 1.03661
\(36\) −1.93558 −0.322597
\(37\) 1.70361 0.280072 0.140036 0.990146i \(-0.455278\pi\)
0.140036 + 0.990146i \(0.455278\pi\)
\(38\) 3.27523 0.531313
\(39\) −10.3058 −1.65024
\(40\) 17.9174 2.83298
\(41\) −6.24946 −0.976001 −0.488001 0.872843i \(-0.662274\pi\)
−0.488001 + 0.872843i \(0.662274\pi\)
\(42\) 6.74669 1.04104
\(43\) −11.5125 −1.75564 −0.877819 0.478992i \(-0.841002\pi\)
−0.877819 + 0.478992i \(0.841002\pi\)
\(44\) 2.11359 0.318636
\(45\) 1.69669 0.252928
\(46\) −3.95218 −0.582717
\(47\) 0.681014 0.0993362 0.0496681 0.998766i \(-0.484184\pi\)
0.0496681 + 0.998766i \(0.484184\pi\)
\(48\) 6.84381 0.987819
\(49\) −4.01761 −0.573944
\(50\) −18.7211 −2.64756
\(51\) −0.130722 −0.0183047
\(52\) −26.2884 −3.64554
\(53\) −5.03721 −0.691914 −0.345957 0.938250i \(-0.612446\pi\)
−0.345957 + 0.938250i \(0.612446\pi\)
\(54\) 13.5866 1.84891
\(55\) −1.85273 −0.249822
\(56\) 8.71345 1.16438
\(57\) −2.11454 −0.280077
\(58\) 13.0320 1.71119
\(59\) 3.94334 0.513379 0.256690 0.966494i \(-0.417368\pi\)
0.256690 + 0.966494i \(0.417368\pi\)
\(60\) −22.8471 −2.94955
\(61\) 4.73428 0.606162 0.303081 0.952965i \(-0.401985\pi\)
0.303081 + 0.952965i \(0.401985\pi\)
\(62\) 8.26863 1.05012
\(63\) 0.825124 0.103956
\(64\) −7.36558 −0.920698
\(65\) 23.0439 2.85824
\(66\) −2.03824 −0.250890
\(67\) 11.5204 1.40744 0.703722 0.710475i \(-0.251520\pi\)
0.703722 + 0.710475i \(0.251520\pi\)
\(68\) −0.333451 −0.0404369
\(69\) 2.55158 0.307174
\(70\) −15.0857 −1.80309
\(71\) −3.21876 −0.381996 −0.190998 0.981590i \(-0.561172\pi\)
−0.190998 + 0.981590i \(0.561172\pi\)
\(72\) 2.41071 0.284105
\(73\) −13.0677 −1.52946 −0.764729 0.644352i \(-0.777127\pi\)
−0.764729 + 0.644352i \(0.777127\pi\)
\(74\) −4.19071 −0.487161
\(75\) 12.0866 1.39564
\(76\) −5.39385 −0.618718
\(77\) −0.901009 −0.102679
\(78\) 25.3511 2.87045
\(79\) −15.5574 −1.75034 −0.875171 0.483814i \(-0.839251\pi\)
−0.875171 + 0.483814i \(0.839251\pi\)
\(80\) −15.3029 −1.71091
\(81\) −7.33835 −0.815372
\(82\) 15.3730 1.69767
\(83\) 8.37536 0.919315 0.459658 0.888096i \(-0.347972\pi\)
0.459658 + 0.888096i \(0.347972\pi\)
\(84\) −11.1109 −1.21229
\(85\) 0.292296 0.0317040
\(86\) 28.3196 3.05378
\(87\) −8.41365 −0.902038
\(88\) −2.63242 −0.280616
\(89\) 5.06939 0.537354 0.268677 0.963230i \(-0.413414\pi\)
0.268677 + 0.963230i \(0.413414\pi\)
\(90\) −4.17370 −0.439946
\(91\) 11.2065 1.17476
\(92\) 6.50869 0.678577
\(93\) −5.33835 −0.553561
\(94\) −1.67523 −0.172787
\(95\) 4.72814 0.485097
\(96\) −0.808973 −0.0825655
\(97\) −9.06329 −0.920238 −0.460119 0.887857i \(-0.652193\pi\)
−0.460119 + 0.887857i \(0.652193\pi\)
\(98\) 9.88292 0.998326
\(99\) −0.249278 −0.0250534
\(100\) 30.8310 3.08310
\(101\) −19.1942 −1.90990 −0.954948 0.296772i \(-0.904090\pi\)
−0.954948 + 0.296772i \(0.904090\pi\)
\(102\) 0.321563 0.0318395
\(103\) −12.6345 −1.24491 −0.622456 0.782655i \(-0.713865\pi\)
−0.622456 + 0.782655i \(0.713865\pi\)
\(104\) 32.7414 3.21056
\(105\) 9.73955 0.950483
\(106\) 12.3910 1.20352
\(107\) −8.24556 −0.797128 −0.398564 0.917140i \(-0.630491\pi\)
−0.398564 + 0.917140i \(0.630491\pi\)
\(108\) −22.3753 −2.15306
\(109\) −16.8635 −1.61523 −0.807617 0.589707i \(-0.799243\pi\)
−0.807617 + 0.589707i \(0.799243\pi\)
\(110\) 4.55754 0.434544
\(111\) 2.70558 0.256803
\(112\) −7.44200 −0.703203
\(113\) 15.7677 1.48330 0.741648 0.670789i \(-0.234044\pi\)
0.741648 + 0.670789i \(0.234044\pi\)
\(114\) 5.20155 0.487170
\(115\) −5.70538 −0.532030
\(116\) −21.4619 −1.99269
\(117\) 3.10046 0.286638
\(118\) −9.70023 −0.892978
\(119\) 0.142148 0.0130307
\(120\) 28.4554 2.59761
\(121\) −10.7278 −0.975254
\(122\) −11.6459 −1.05437
\(123\) −9.92505 −0.894912
\(124\) −13.6173 −1.22287
\(125\) −9.27020 −0.829152
\(126\) −2.02972 −0.180822
\(127\) 1.11937 0.0993276 0.0496638 0.998766i \(-0.484185\pi\)
0.0496638 + 0.998766i \(0.484185\pi\)
\(128\) 19.1374 1.69152
\(129\) −18.2835 −1.60977
\(130\) −56.6856 −4.97166
\(131\) −2.29123 −0.200186 −0.100093 0.994978i \(-0.531914\pi\)
−0.100093 + 0.994978i \(0.531914\pi\)
\(132\) 3.35669 0.292163
\(133\) 2.29936 0.199380
\(134\) −28.3391 −2.44813
\(135\) 19.6137 1.68808
\(136\) 0.415303 0.0356120
\(137\) 5.67546 0.484887 0.242444 0.970166i \(-0.422051\pi\)
0.242444 + 0.970166i \(0.422051\pi\)
\(138\) −6.27664 −0.534303
\(139\) 16.5980 1.40782 0.703912 0.710287i \(-0.251435\pi\)
0.703912 + 0.710287i \(0.251435\pi\)
\(140\) 24.8441 2.09971
\(141\) 1.08155 0.0910830
\(142\) 7.91783 0.664449
\(143\) −3.38560 −0.283118
\(144\) −2.05894 −0.171579
\(145\) 18.8131 1.56234
\(146\) 32.1452 2.66036
\(147\) −6.38055 −0.526259
\(148\) 6.90152 0.567302
\(149\) 13.8639 1.13577 0.567887 0.823106i \(-0.307761\pi\)
0.567887 + 0.823106i \(0.307761\pi\)
\(150\) −29.7318 −2.42759
\(151\) −3.97982 −0.323873 −0.161937 0.986801i \(-0.551774\pi\)
−0.161937 + 0.986801i \(0.551774\pi\)
\(152\) 6.71788 0.544892
\(153\) 0.0393273 0.00317943
\(154\) 2.21639 0.178602
\(155\) 11.9366 0.958774
\(156\) −41.7498 −3.34266
\(157\) −2.80504 −0.223867 −0.111933 0.993716i \(-0.535704\pi\)
−0.111933 + 0.993716i \(0.535704\pi\)
\(158\) 38.2696 3.04457
\(159\) −7.99983 −0.634428
\(160\) 1.80888 0.143005
\(161\) −2.77460 −0.218669
\(162\) 18.0516 1.41827
\(163\) 18.0445 1.41335 0.706677 0.707536i \(-0.250193\pi\)
0.706677 + 0.707536i \(0.250193\pi\)
\(164\) −25.3173 −1.97695
\(165\) −2.94241 −0.229066
\(166\) −20.6026 −1.59907
\(167\) 11.0705 0.856660 0.428330 0.903622i \(-0.359102\pi\)
0.428330 + 0.903622i \(0.359102\pi\)
\(168\) 13.8382 1.06764
\(169\) 29.1093 2.23918
\(170\) −0.719020 −0.0551464
\(171\) 0.636153 0.0486478
\(172\) −46.6384 −3.55615
\(173\) 22.7368 1.72865 0.864324 0.502936i \(-0.167747\pi\)
0.864324 + 0.502936i \(0.167747\pi\)
\(174\) 20.6968 1.56902
\(175\) −13.1430 −0.993519
\(176\) 2.24830 0.169472
\(177\) 6.26260 0.470726
\(178\) −12.4702 −0.934681
\(179\) −10.2359 −0.765066 −0.382533 0.923942i \(-0.624948\pi\)
−0.382533 + 0.923942i \(0.624948\pi\)
\(180\) 6.87350 0.512320
\(181\) 6.64223 0.493713 0.246857 0.969052i \(-0.420602\pi\)
0.246857 + 0.969052i \(0.420602\pi\)
\(182\) −27.5670 −2.04340
\(183\) 7.51873 0.555801
\(184\) −8.10637 −0.597610
\(185\) −6.04974 −0.444786
\(186\) 13.1318 0.962871
\(187\) −0.0429441 −0.00314039
\(188\) 2.75887 0.201211
\(189\) 9.53842 0.693818
\(190\) −11.6308 −0.843785
\(191\) 11.2867 0.816678 0.408339 0.912830i \(-0.366108\pi\)
0.408339 + 0.912830i \(0.366108\pi\)
\(192\) −11.6976 −0.844203
\(193\) 3.74238 0.269383 0.134691 0.990888i \(-0.456996\pi\)
0.134691 + 0.990888i \(0.456996\pi\)
\(194\) 22.2948 1.60067
\(195\) 36.5970 2.62077
\(196\) −16.2758 −1.16256
\(197\) −10.3683 −0.738713 −0.369356 0.929288i \(-0.620422\pi\)
−0.369356 + 0.929288i \(0.620422\pi\)
\(198\) 0.613199 0.0435781
\(199\) 24.8886 1.76431 0.882154 0.470961i \(-0.156093\pi\)
0.882154 + 0.470961i \(0.156093\pi\)
\(200\) −38.3991 −2.71522
\(201\) 18.2961 1.29051
\(202\) 47.2159 3.32210
\(203\) 9.14906 0.642138
\(204\) −0.529569 −0.0370773
\(205\) 22.1926 1.55000
\(206\) 31.0795 2.16541
\(207\) −0.767637 −0.0533544
\(208\) −27.9638 −1.93894
\(209\) −0.694658 −0.0480505
\(210\) −23.9583 −1.65328
\(211\) −28.0208 −1.92903 −0.964516 0.264024i \(-0.914950\pi\)
−0.964516 + 0.264024i \(0.914950\pi\)
\(212\) −20.4063 −1.40151
\(213\) −5.11186 −0.350259
\(214\) 20.2833 1.38654
\(215\) 40.8823 2.78815
\(216\) 27.8677 1.89616
\(217\) 5.80495 0.394066
\(218\) 41.4827 2.80956
\(219\) −20.7534 −1.40239
\(220\) −7.50563 −0.506030
\(221\) 0.534129 0.0359294
\(222\) −6.65547 −0.446686
\(223\) −3.74555 −0.250820 −0.125410 0.992105i \(-0.540025\pi\)
−0.125410 + 0.992105i \(0.540025\pi\)
\(224\) 0.879683 0.0587763
\(225\) −3.63622 −0.242415
\(226\) −38.7869 −2.58007
\(227\) 17.0030 1.12853 0.564264 0.825595i \(-0.309160\pi\)
0.564264 + 0.825595i \(0.309160\pi\)
\(228\) −8.56623 −0.567313
\(229\) −10.2817 −0.679434 −0.339717 0.940528i \(-0.610331\pi\)
−0.339717 + 0.940528i \(0.610331\pi\)
\(230\) 14.0347 0.925419
\(231\) −1.43093 −0.0941485
\(232\) 26.7302 1.75492
\(233\) −20.4752 −1.34138 −0.670688 0.741739i \(-0.734001\pi\)
−0.670688 + 0.741739i \(0.734001\pi\)
\(234\) −7.62682 −0.498581
\(235\) −2.41837 −0.157757
\(236\) 15.9749 1.03988
\(237\) −24.7074 −1.60492
\(238\) −0.349669 −0.0226657
\(239\) −9.55740 −0.618217 −0.309109 0.951027i \(-0.600031\pi\)
−0.309109 + 0.951027i \(0.600031\pi\)
\(240\) −24.3032 −1.56877
\(241\) 24.5206 1.57951 0.789755 0.613423i \(-0.210208\pi\)
0.789755 + 0.613423i \(0.210208\pi\)
\(242\) 26.3893 1.69637
\(243\) 4.91535 0.315320
\(244\) 19.1791 1.22782
\(245\) 14.2670 0.911487
\(246\) 24.4147 1.55662
\(247\) 8.64000 0.549750
\(248\) 16.9599 1.07696
\(249\) 13.3013 0.842936
\(250\) 22.8038 1.44224
\(251\) 5.98919 0.378034 0.189017 0.981974i \(-0.439470\pi\)
0.189017 + 0.981974i \(0.439470\pi\)
\(252\) 3.34267 0.210569
\(253\) 0.838234 0.0526993
\(254\) −2.75353 −0.172772
\(255\) 0.464210 0.0290699
\(256\) −32.3449 −2.02155
\(257\) −6.32166 −0.394334 −0.197167 0.980370i \(-0.563174\pi\)
−0.197167 + 0.980370i \(0.563174\pi\)
\(258\) 44.9757 2.80006
\(259\) −2.94207 −0.182811
\(260\) 93.3533 5.78953
\(261\) 2.53123 0.156679
\(262\) 5.63621 0.348206
\(263\) 3.38587 0.208782 0.104391 0.994536i \(-0.466711\pi\)
0.104391 + 0.994536i \(0.466711\pi\)
\(264\) −4.18066 −0.257302
\(265\) 17.8878 1.09884
\(266\) −5.65620 −0.346804
\(267\) 8.05093 0.492709
\(268\) 46.6706 2.85086
\(269\) −30.8170 −1.87895 −0.939473 0.342623i \(-0.888685\pi\)
−0.939473 + 0.342623i \(0.888685\pi\)
\(270\) −48.2478 −2.93627
\(271\) −24.7506 −1.50349 −0.751745 0.659454i \(-0.770788\pi\)
−0.751745 + 0.659454i \(0.770788\pi\)
\(272\) −0.354703 −0.0215070
\(273\) 17.7976 1.07716
\(274\) −13.9611 −0.843419
\(275\) 3.97063 0.239438
\(276\) 10.3367 0.622199
\(277\) 15.2327 0.915243 0.457621 0.889147i \(-0.348702\pi\)
0.457621 + 0.889147i \(0.348702\pi\)
\(278\) −40.8294 −2.44879
\(279\) 1.60603 0.0961504
\(280\) −30.9426 −1.84917
\(281\) 18.4994 1.10358 0.551792 0.833982i \(-0.313944\pi\)
0.551792 + 0.833982i \(0.313944\pi\)
\(282\) −2.66051 −0.158431
\(283\) −4.00257 −0.237928 −0.118964 0.992899i \(-0.537957\pi\)
−0.118964 + 0.992899i \(0.537957\pi\)
\(284\) −13.0396 −0.773755
\(285\) 7.50899 0.444794
\(286\) 8.32824 0.492459
\(287\) 10.7926 0.637065
\(288\) 0.243378 0.0143412
\(289\) −16.9932 −0.999601
\(290\) −46.2783 −2.71756
\(291\) −14.3938 −0.843782
\(292\) −52.9387 −3.09800
\(293\) 19.9352 1.16462 0.582312 0.812965i \(-0.302148\pi\)
0.582312 + 0.812965i \(0.302148\pi\)
\(294\) 15.6955 0.915382
\(295\) −14.0033 −0.815303
\(296\) −8.59564 −0.499611
\(297\) −2.88165 −0.167210
\(298\) −34.1038 −1.97558
\(299\) −10.4258 −0.602937
\(300\) 48.9642 2.82695
\(301\) 19.8816 1.14596
\(302\) 9.78997 0.563350
\(303\) −30.4832 −1.75122
\(304\) −5.73762 −0.329075
\(305\) −16.8120 −0.962654
\(306\) −0.0967414 −0.00553034
\(307\) −23.8579 −1.36164 −0.680822 0.732449i \(-0.738377\pi\)
−0.680822 + 0.732449i \(0.738377\pi\)
\(308\) −3.65009 −0.207983
\(309\) −20.0654 −1.14148
\(310\) −29.3630 −1.66770
\(311\) 5.55638 0.315073 0.157537 0.987513i \(-0.449645\pi\)
0.157537 + 0.987513i \(0.449645\pi\)
\(312\) 51.9981 2.94381
\(313\) −4.89132 −0.276474 −0.138237 0.990399i \(-0.544144\pi\)
−0.138237 + 0.990399i \(0.544144\pi\)
\(314\) 6.90013 0.389397
\(315\) −2.93012 −0.165094
\(316\) −63.0247 −3.54542
\(317\) −25.7739 −1.44761 −0.723803 0.690007i \(-0.757608\pi\)
−0.723803 + 0.690007i \(0.757608\pi\)
\(318\) 19.6788 1.10353
\(319\) −2.76402 −0.154755
\(320\) 26.1561 1.46217
\(321\) −13.0952 −0.730901
\(322\) 6.82525 0.380357
\(323\) 0.109593 0.00609791
\(324\) −29.7285 −1.65158
\(325\) −49.3858 −2.73943
\(326\) −44.3877 −2.45841
\(327\) −26.7818 −1.48104
\(328\) 31.5319 1.74106
\(329\) −1.17608 −0.0648397
\(330\) 7.23804 0.398441
\(331\) 21.8664 1.20189 0.600944 0.799291i \(-0.294792\pi\)
0.600944 + 0.799291i \(0.294792\pi\)
\(332\) 33.9296 1.86213
\(333\) −0.813968 −0.0446052
\(334\) −27.2323 −1.49009
\(335\) −40.9105 −2.23518
\(336\) −11.8190 −0.644779
\(337\) 13.8352 0.753651 0.376826 0.926284i \(-0.377016\pi\)
0.376826 + 0.926284i \(0.377016\pi\)
\(338\) −71.6060 −3.89485
\(339\) 25.0414 1.36006
\(340\) 1.18413 0.0642183
\(341\) −1.75373 −0.0949698
\(342\) −1.56487 −0.0846187
\(343\) 19.0270 1.02736
\(344\) 58.0867 3.13183
\(345\) −9.06099 −0.487827
\(346\) −55.9303 −3.00683
\(347\) 16.5307 0.887415 0.443707 0.896172i \(-0.353663\pi\)
0.443707 + 0.896172i \(0.353663\pi\)
\(348\) −34.0847 −1.82713
\(349\) 3.96726 0.212362 0.106181 0.994347i \(-0.466138\pi\)
0.106181 + 0.994347i \(0.466138\pi\)
\(350\) 32.3306 1.72814
\(351\) 35.8412 1.91306
\(352\) −0.265760 −0.0141651
\(353\) 23.0752 1.22817 0.614085 0.789240i \(-0.289525\pi\)
0.614085 + 0.789240i \(0.289525\pi\)
\(354\) −15.4054 −0.818787
\(355\) 11.4302 0.606653
\(356\) 20.5367 1.08844
\(357\) 0.225751 0.0119480
\(358\) 25.1793 1.33077
\(359\) −17.8603 −0.942632 −0.471316 0.881965i \(-0.656221\pi\)
−0.471316 + 0.881965i \(0.656221\pi\)
\(360\) −8.56073 −0.451190
\(361\) −17.2272 −0.906697
\(362\) −16.3392 −0.858772
\(363\) −17.0373 −0.894227
\(364\) 45.3990 2.37955
\(365\) 46.4050 2.42895
\(366\) −18.4953 −0.966767
\(367\) −6.24911 −0.326201 −0.163100 0.986609i \(-0.552149\pi\)
−0.163100 + 0.986609i \(0.552149\pi\)
\(368\) 6.92350 0.360913
\(369\) 2.98593 0.155441
\(370\) 14.8818 0.773666
\(371\) 8.69907 0.451633
\(372\) −21.6263 −1.12127
\(373\) 5.43820 0.281579 0.140790 0.990040i \(-0.455036\pi\)
0.140790 + 0.990040i \(0.455036\pi\)
\(374\) 0.105638 0.00546243
\(375\) −14.7224 −0.760264
\(376\) −3.43609 −0.177203
\(377\) 34.3782 1.77057
\(378\) −23.4636 −1.20684
\(379\) −30.0170 −1.54187 −0.770936 0.636913i \(-0.780211\pi\)
−0.770936 + 0.636913i \(0.780211\pi\)
\(380\) 19.1543 0.982593
\(381\) 1.77772 0.0910752
\(382\) −27.7642 −1.42054
\(383\) −7.03107 −0.359271 −0.179635 0.983733i \(-0.557492\pi\)
−0.179635 + 0.983733i \(0.557492\pi\)
\(384\) 30.3929 1.55098
\(385\) 3.19960 0.163066
\(386\) −9.20589 −0.468568
\(387\) 5.50055 0.279609
\(388\) −36.7164 −1.86399
\(389\) −4.50037 −0.228178 −0.114089 0.993471i \(-0.536395\pi\)
−0.114089 + 0.993471i \(0.536395\pi\)
\(390\) −90.0251 −4.55860
\(391\) −0.132244 −0.00668787
\(392\) 20.2710 1.02384
\(393\) −3.63882 −0.183554
\(394\) 25.5051 1.28493
\(395\) 55.2462 2.77974
\(396\) −1.00985 −0.0507470
\(397\) −9.45105 −0.474335 −0.237167 0.971469i \(-0.576219\pi\)
−0.237167 + 0.971469i \(0.576219\pi\)
\(398\) −61.2236 −3.06886
\(399\) 3.65172 0.182815
\(400\) 32.7959 1.63980
\(401\) 13.2693 0.662638 0.331319 0.943519i \(-0.392506\pi\)
0.331319 + 0.943519i \(0.392506\pi\)
\(402\) −45.0067 −2.24473
\(403\) 21.8125 1.08656
\(404\) −77.7580 −3.86861
\(405\) 26.0594 1.29490
\(406\) −22.5058 −1.11694
\(407\) 0.888826 0.0440575
\(408\) 0.659562 0.0326532
\(409\) 31.4287 1.55405 0.777025 0.629470i \(-0.216728\pi\)
0.777025 + 0.629470i \(0.216728\pi\)
\(410\) −54.5916 −2.69609
\(411\) 9.01346 0.444601
\(412\) −51.1837 −2.52164
\(413\) −6.80999 −0.335098
\(414\) 1.88831 0.0928054
\(415\) −29.7420 −1.45998
\(416\) 3.30547 0.162064
\(417\) 26.3601 1.29086
\(418\) 1.70879 0.0835797
\(419\) −16.4010 −0.801240 −0.400620 0.916244i \(-0.631205\pi\)
−0.400620 + 0.916244i \(0.631205\pi\)
\(420\) 39.4561 1.92526
\(421\) −0.00764314 −0.000372504 0 −0.000186252 1.00000i \(-0.500059\pi\)
−0.000186252 1.00000i \(0.500059\pi\)
\(422\) 68.9284 3.35538
\(423\) −0.325382 −0.0158206
\(424\) 25.4155 1.23428
\(425\) −0.626427 −0.0303862
\(426\) 12.5747 0.609245
\(427\) −8.17591 −0.395660
\(428\) −33.4037 −1.61463
\(429\) −5.37683 −0.259596
\(430\) −100.566 −4.84974
\(431\) −27.0587 −1.30337 −0.651685 0.758489i \(-0.725938\pi\)
−0.651685 + 0.758489i \(0.725938\pi\)
\(432\) −23.8013 −1.14514
\(433\) 35.6967 1.71547 0.857737 0.514088i \(-0.171870\pi\)
0.857737 + 0.514088i \(0.171870\pi\)
\(434\) −14.2796 −0.685443
\(435\) 29.8779 1.43254
\(436\) −68.3162 −3.27175
\(437\) −2.13916 −0.102330
\(438\) 51.0513 2.43933
\(439\) −0.366379 −0.0174863 −0.00874315 0.999962i \(-0.502783\pi\)
−0.00874315 + 0.999962i \(0.502783\pi\)
\(440\) 9.34804 0.445650
\(441\) 1.91957 0.0914082
\(442\) −1.31391 −0.0624961
\(443\) 15.4416 0.733651 0.366826 0.930290i \(-0.380445\pi\)
0.366826 + 0.930290i \(0.380445\pi\)
\(444\) 10.9606 0.520169
\(445\) −18.0020 −0.853379
\(446\) 9.21367 0.436280
\(447\) 22.0179 1.04141
\(448\) 12.7201 0.600967
\(449\) 5.18194 0.244551 0.122276 0.992496i \(-0.460981\pi\)
0.122276 + 0.992496i \(0.460981\pi\)
\(450\) 8.94474 0.421659
\(451\) −3.26053 −0.153533
\(452\) 63.8766 3.00450
\(453\) −6.32054 −0.296965
\(454\) −41.8257 −1.96298
\(455\) −39.7958 −1.86566
\(456\) 10.6690 0.499621
\(457\) 32.5937 1.52467 0.762335 0.647183i \(-0.224053\pi\)
0.762335 + 0.647183i \(0.224053\pi\)
\(458\) 25.2920 1.18182
\(459\) 0.454623 0.0212200
\(460\) −23.1132 −1.07766
\(461\) −7.23003 −0.336736 −0.168368 0.985724i \(-0.553850\pi\)
−0.168368 + 0.985724i \(0.553850\pi\)
\(462\) 3.51996 0.163763
\(463\) −33.7004 −1.56619 −0.783094 0.621903i \(-0.786360\pi\)
−0.783094 + 0.621903i \(0.786360\pi\)
\(464\) −22.8297 −1.05984
\(465\) 18.9571 0.879116
\(466\) 50.3670 2.33321
\(467\) 10.0468 0.464911 0.232456 0.972607i \(-0.425324\pi\)
0.232456 + 0.972607i \(0.425324\pi\)
\(468\) 12.5603 0.580601
\(469\) −19.8953 −0.918681
\(470\) 5.94895 0.274404
\(471\) −4.45482 −0.205267
\(472\) −19.8963 −0.915801
\(473\) −6.00642 −0.276176
\(474\) 60.7778 2.79162
\(475\) −10.1330 −0.464933
\(476\) 0.575857 0.0263943
\(477\) 2.40673 0.110197
\(478\) 23.5103 1.07533
\(479\) −6.20194 −0.283374 −0.141687 0.989912i \(-0.545253\pi\)
−0.141687 + 0.989912i \(0.545253\pi\)
\(480\) 2.87277 0.131123
\(481\) −11.0550 −0.504065
\(482\) −60.3182 −2.74742
\(483\) −4.40648 −0.200502
\(484\) −43.4595 −1.97543
\(485\) 32.1849 1.46144
\(486\) −12.0913 −0.548472
\(487\) −21.8945 −0.992135 −0.496067 0.868284i \(-0.665223\pi\)
−0.496067 + 0.868284i \(0.665223\pi\)
\(488\) −23.8870 −1.08131
\(489\) 28.6573 1.29593
\(490\) −35.0955 −1.58545
\(491\) −9.16110 −0.413435 −0.206717 0.978401i \(-0.566278\pi\)
−0.206717 + 0.978401i \(0.566278\pi\)
\(492\) −40.2075 −1.81270
\(493\) 0.436065 0.0196394
\(494\) −21.2535 −0.956242
\(495\) 0.885217 0.0397875
\(496\) −14.4852 −0.650403
\(497\) 5.55867 0.249340
\(498\) −32.7199 −1.46621
\(499\) 8.39825 0.375957 0.187979 0.982173i \(-0.439806\pi\)
0.187979 + 0.982173i \(0.439806\pi\)
\(500\) −37.5547 −1.67950
\(501\) 17.5816 0.785486
\(502\) −14.7328 −0.657558
\(503\) 6.13750 0.273658 0.136829 0.990595i \(-0.456309\pi\)
0.136829 + 0.990595i \(0.456309\pi\)
\(504\) −4.16320 −0.185444
\(505\) 68.1611 3.03313
\(506\) −2.06197 −0.0916659
\(507\) 46.2298 2.05314
\(508\) 4.53468 0.201194
\(509\) 27.4079 1.21483 0.607416 0.794384i \(-0.292206\pi\)
0.607416 + 0.794384i \(0.292206\pi\)
\(510\) −1.14191 −0.0505646
\(511\) 22.5674 0.998322
\(512\) 41.2905 1.82480
\(513\) 7.35391 0.324683
\(514\) 15.5506 0.685910
\(515\) 44.8666 1.97706
\(516\) −74.0687 −3.26069
\(517\) 0.355306 0.0156264
\(518\) 7.23720 0.317984
\(519\) 36.1094 1.58503
\(520\) −116.269 −5.09872
\(521\) 8.25760 0.361772 0.180886 0.983504i \(-0.442104\pi\)
0.180886 + 0.983504i \(0.442104\pi\)
\(522\) −6.22657 −0.272529
\(523\) −10.1348 −0.443164 −0.221582 0.975142i \(-0.571122\pi\)
−0.221582 + 0.975142i \(0.571122\pi\)
\(524\) −9.28205 −0.405488
\(525\) −20.8731 −0.910975
\(526\) −8.32890 −0.363157
\(527\) 0.276677 0.0120523
\(528\) 3.57063 0.155392
\(529\) −20.4187 −0.887770
\(530\) −44.0022 −1.91133
\(531\) −1.88409 −0.0817625
\(532\) 9.31497 0.403855
\(533\) 40.5538 1.75658
\(534\) −19.8045 −0.857025
\(535\) 29.2810 1.26593
\(536\) −58.1268 −2.51070
\(537\) −16.2561 −0.701502
\(538\) 75.8068 3.26826
\(539\) −2.09611 −0.0902859
\(540\) 79.4575 3.41930
\(541\) 24.8963 1.07037 0.535187 0.844734i \(-0.320241\pi\)
0.535187 + 0.844734i \(0.320241\pi\)
\(542\) 60.8840 2.61519
\(543\) 10.5488 0.452694
\(544\) 0.0419277 0.00179764
\(545\) 59.8846 2.56517
\(546\) −43.7804 −1.87363
\(547\) 9.35363 0.399933 0.199966 0.979803i \(-0.435917\pi\)
0.199966 + 0.979803i \(0.435917\pi\)
\(548\) 22.9919 0.982167
\(549\) −2.26199 −0.0965394
\(550\) −9.76736 −0.416482
\(551\) 7.05372 0.300499
\(552\) −12.8741 −0.547958
\(553\) 26.8670 1.14250
\(554\) −37.4709 −1.59199
\(555\) −9.60787 −0.407831
\(556\) 67.2404 2.85163
\(557\) −14.8190 −0.627900 −0.313950 0.949439i \(-0.601652\pi\)
−0.313950 + 0.949439i \(0.601652\pi\)
\(558\) −3.95067 −0.167245
\(559\) 74.7065 3.15975
\(560\) 26.4275 1.11676
\(561\) −0.0682016 −0.00287947
\(562\) −45.5068 −1.91959
\(563\) −28.3788 −1.19603 −0.598013 0.801487i \(-0.704043\pi\)
−0.598013 + 0.801487i \(0.704043\pi\)
\(564\) 4.38149 0.184494
\(565\) −55.9929 −2.35564
\(566\) 9.84592 0.413855
\(567\) 12.6730 0.532217
\(568\) 16.2404 0.681431
\(569\) 22.1033 0.926617 0.463309 0.886197i \(-0.346662\pi\)
0.463309 + 0.886197i \(0.346662\pi\)
\(570\) −18.4714 −0.773680
\(571\) −17.1566 −0.717980 −0.358990 0.933341i \(-0.616879\pi\)
−0.358990 + 0.933341i \(0.616879\pi\)
\(572\) −13.7155 −0.573472
\(573\) 17.9250 0.748826
\(574\) −26.5486 −1.10812
\(575\) 12.2273 0.509915
\(576\) 3.51920 0.146633
\(577\) −0.0330496 −0.00137587 −0.000687936 1.00000i \(-0.500219\pi\)
−0.000687936 1.00000i \(0.500219\pi\)
\(578\) 41.8017 1.73872
\(579\) 5.94345 0.247001
\(580\) 76.2140 3.16461
\(581\) −14.4639 −0.600064
\(582\) 35.4074 1.46768
\(583\) −2.62807 −0.108844
\(584\) 65.9336 2.72835
\(585\) −11.0101 −0.455213
\(586\) −49.0385 −2.02576
\(587\) 3.65229 0.150746 0.0753731 0.997155i \(-0.475985\pi\)
0.0753731 + 0.997155i \(0.475985\pi\)
\(588\) −25.8483 −1.06597
\(589\) 4.47549 0.184409
\(590\) 34.4467 1.41815
\(591\) −16.4664 −0.677338
\(592\) 7.34138 0.301729
\(593\) −36.3894 −1.49433 −0.747167 0.664637i \(-0.768586\pi\)
−0.747167 + 0.664637i \(0.768586\pi\)
\(594\) 7.08856 0.290847
\(595\) −0.504784 −0.0206941
\(596\) 56.1642 2.30058
\(597\) 39.5268 1.61772
\(598\) 25.6463 1.04876
\(599\) 0.140841 0.00575460 0.00287730 0.999996i \(-0.499084\pi\)
0.00287730 + 0.999996i \(0.499084\pi\)
\(600\) −60.9834 −2.48964
\(601\) −45.5881 −1.85958 −0.929789 0.368093i \(-0.880011\pi\)
−0.929789 + 0.368093i \(0.880011\pi\)
\(602\) −48.9068 −1.99329
\(603\) −5.50435 −0.224154
\(604\) −16.1227 −0.656024
\(605\) 38.0958 1.54881
\(606\) 74.9858 3.04609
\(607\) −31.2698 −1.26920 −0.634600 0.772841i \(-0.718835\pi\)
−0.634600 + 0.772841i \(0.718835\pi\)
\(608\) 0.678216 0.0275053
\(609\) 14.5300 0.588787
\(610\) 41.3559 1.67445
\(611\) −4.41922 −0.178782
\(612\) 0.159320 0.00644011
\(613\) 14.1771 0.572609 0.286304 0.958139i \(-0.407573\pi\)
0.286304 + 0.958139i \(0.407573\pi\)
\(614\) 58.6881 2.36846
\(615\) 35.2451 1.42122
\(616\) 4.54608 0.183167
\(617\) −14.4874 −0.583243 −0.291621 0.956534i \(-0.594195\pi\)
−0.291621 + 0.956534i \(0.594195\pi\)
\(618\) 49.3589 1.98551
\(619\) 11.1855 0.449583 0.224791 0.974407i \(-0.427830\pi\)
0.224791 + 0.974407i \(0.427830\pi\)
\(620\) 48.3567 1.94205
\(621\) −8.87386 −0.356096
\(622\) −13.6681 −0.548043
\(623\) −8.75464 −0.350747
\(624\) −44.4106 −1.77785
\(625\) −5.13283 −0.205313
\(626\) 12.0322 0.480902
\(627\) −1.10322 −0.0440583
\(628\) −11.3636 −0.453455
\(629\) −0.140226 −0.00559117
\(630\) 7.20781 0.287166
\(631\) −47.8932 −1.90660 −0.953299 0.302028i \(-0.902337\pi\)
−0.953299 + 0.302028i \(0.902337\pi\)
\(632\) 78.4954 3.12238
\(633\) −44.5012 −1.76876
\(634\) 63.4012 2.51798
\(635\) −3.97501 −0.157743
\(636\) −32.4082 −1.28507
\(637\) 26.0709 1.03297
\(638\) 6.79920 0.269183
\(639\) 1.53789 0.0608380
\(640\) −67.9592 −2.68632
\(641\) 14.6770 0.579705 0.289853 0.957071i \(-0.406394\pi\)
0.289853 + 0.957071i \(0.406394\pi\)
\(642\) 32.2128 1.27134
\(643\) −11.8705 −0.468128 −0.234064 0.972221i \(-0.575203\pi\)
−0.234064 + 0.972221i \(0.575203\pi\)
\(644\) −11.2402 −0.442928
\(645\) 64.9271 2.55650
\(646\) −0.269588 −0.0106068
\(647\) 26.1304 1.02729 0.513645 0.858003i \(-0.328295\pi\)
0.513645 + 0.858003i \(0.328295\pi\)
\(648\) 37.0259 1.45452
\(649\) 2.05736 0.0807585
\(650\) 121.484 4.76500
\(651\) 9.21911 0.361325
\(652\) 73.1004 2.86283
\(653\) 38.5577 1.50888 0.754440 0.656369i \(-0.227909\pi\)
0.754440 + 0.656369i \(0.227909\pi\)
\(654\) 65.8805 2.57613
\(655\) 8.13646 0.317918
\(656\) −26.9308 −1.05147
\(657\) 6.24361 0.243586
\(658\) 2.89305 0.112783
\(659\) 10.0132 0.390059 0.195029 0.980797i \(-0.437520\pi\)
0.195029 + 0.980797i \(0.437520\pi\)
\(660\) −11.9200 −0.463987
\(661\) −12.0432 −0.468425 −0.234212 0.972185i \(-0.575251\pi\)
−0.234212 + 0.972185i \(0.575251\pi\)
\(662\) −53.7893 −2.09058
\(663\) 0.848276 0.0329443
\(664\) −42.2582 −1.63994
\(665\) −8.16532 −0.316637
\(666\) 2.00228 0.0775868
\(667\) −8.51163 −0.329572
\(668\) 44.8478 1.73521
\(669\) −5.94848 −0.229981
\(670\) 100.636 3.88790
\(671\) 2.47002 0.0953541
\(672\) 1.39707 0.0538930
\(673\) −28.2075 −1.08732 −0.543659 0.839306i \(-0.682961\pi\)
−0.543659 + 0.839306i \(0.682961\pi\)
\(674\) −34.0332 −1.31091
\(675\) −42.0346 −1.61791
\(676\) 117.925 4.53558
\(677\) −23.8767 −0.917657 −0.458829 0.888525i \(-0.651731\pi\)
−0.458829 + 0.888525i \(0.651731\pi\)
\(678\) −61.5993 −2.36571
\(679\) 15.6519 0.600667
\(680\) −1.47479 −0.0565558
\(681\) 27.0032 1.03477
\(682\) 4.31400 0.165192
\(683\) −20.7517 −0.794043 −0.397022 0.917809i \(-0.629956\pi\)
−0.397022 + 0.917809i \(0.629956\pi\)
\(684\) 2.57713 0.0985390
\(685\) −20.1543 −0.770055
\(686\) −46.8045 −1.78700
\(687\) −16.3289 −0.622985
\(688\) −49.6108 −1.89140
\(689\) 32.6873 1.24529
\(690\) 22.2891 0.848533
\(691\) 34.4125 1.30911 0.654556 0.756014i \(-0.272856\pi\)
0.654556 + 0.756014i \(0.272856\pi\)
\(692\) 92.1094 3.50147
\(693\) 0.430493 0.0163531
\(694\) −40.6639 −1.54358
\(695\) −58.9416 −2.23578
\(696\) 42.4514 1.60912
\(697\) 0.514398 0.0194842
\(698\) −9.75907 −0.369386
\(699\) −32.5177 −1.22993
\(700\) −53.2439 −2.01243
\(701\) −19.9660 −0.754106 −0.377053 0.926192i \(-0.623063\pi\)
−0.377053 + 0.926192i \(0.623063\pi\)
\(702\) −88.1659 −3.32761
\(703\) −2.26827 −0.0855495
\(704\) −3.84285 −0.144833
\(705\) −3.84072 −0.144650
\(706\) −56.7628 −2.13630
\(707\) 33.1477 1.24665
\(708\) 25.3705 0.953483
\(709\) 34.9806 1.31372 0.656862 0.754011i \(-0.271883\pi\)
0.656862 + 0.754011i \(0.271883\pi\)
\(710\) −28.1172 −1.05522
\(711\) 7.43316 0.278765
\(712\) −25.5778 −0.958569
\(713\) −5.40051 −0.202251
\(714\) −0.555326 −0.0207826
\(715\) 12.0227 0.449623
\(716\) −41.4668 −1.54969
\(717\) −15.1786 −0.566854
\(718\) 43.9346 1.63963
\(719\) 10.4400 0.389347 0.194674 0.980868i \(-0.437635\pi\)
0.194674 + 0.980868i \(0.437635\pi\)
\(720\) 7.31156 0.272486
\(721\) 21.8192 0.812591
\(722\) 42.3773 1.57712
\(723\) 38.9423 1.44828
\(724\) 26.9085 1.00005
\(725\) −40.3187 −1.49740
\(726\) 41.9101 1.55543
\(727\) −34.0466 −1.26272 −0.631360 0.775490i \(-0.717503\pi\)
−0.631360 + 0.775490i \(0.717503\pi\)
\(728\) −56.5430 −2.09562
\(729\) 29.8213 1.10449
\(730\) −114.152 −4.22495
\(731\) 0.947604 0.0350484
\(732\) 30.4592 1.12581
\(733\) 46.3189 1.71083 0.855413 0.517947i \(-0.173303\pi\)
0.855413 + 0.517947i \(0.173303\pi\)
\(734\) 15.3722 0.567398
\(735\) 22.6581 0.835758
\(736\) −0.818394 −0.0301664
\(737\) 6.01057 0.221402
\(738\) −7.34509 −0.270376
\(739\) −32.5051 −1.19572 −0.597859 0.801601i \(-0.703982\pi\)
−0.597859 + 0.801601i \(0.703982\pi\)
\(740\) −24.5082 −0.900939
\(741\) 13.7216 0.504075
\(742\) −21.3989 −0.785577
\(743\) 10.9235 0.400743 0.200372 0.979720i \(-0.435785\pi\)
0.200372 + 0.979720i \(0.435785\pi\)
\(744\) 26.9348 0.987479
\(745\) −49.2324 −1.80374
\(746\) −13.3774 −0.489783
\(747\) −4.00166 −0.146413
\(748\) −0.173972 −0.00636104
\(749\) 14.2398 0.520309
\(750\) 36.2158 1.32241
\(751\) −20.4686 −0.746909 −0.373454 0.927649i \(-0.621827\pi\)
−0.373454 + 0.927649i \(0.621827\pi\)
\(752\) 2.93470 0.107017
\(753\) 9.51171 0.346626
\(754\) −84.5669 −3.07975
\(755\) 14.1329 0.514347
\(756\) 38.6412 1.40537
\(757\) 14.1329 0.513668 0.256834 0.966456i \(-0.417321\pi\)
0.256834 + 0.966456i \(0.417321\pi\)
\(758\) 73.8389 2.68195
\(759\) 1.33124 0.0483209
\(760\) −23.8560 −0.865350
\(761\) −33.6811 −1.22094 −0.610470 0.792039i \(-0.709019\pi\)
−0.610470 + 0.792039i \(0.709019\pi\)
\(762\) −4.37301 −0.158417
\(763\) 29.1227 1.05431
\(764\) 45.7238 1.65423
\(765\) −0.139656 −0.00504928
\(766\) 17.2957 0.624921
\(767\) −25.5890 −0.923965
\(768\) −51.3684 −1.85360
\(769\) 9.33897 0.336772 0.168386 0.985721i \(-0.446145\pi\)
0.168386 + 0.985721i \(0.446145\pi\)
\(770\) −7.87069 −0.283640
\(771\) −10.0397 −0.361572
\(772\) 15.1608 0.545650
\(773\) 20.3730 0.732764 0.366382 0.930464i \(-0.380596\pi\)
0.366382 + 0.930464i \(0.380596\pi\)
\(774\) −13.5308 −0.486355
\(775\) −25.5817 −0.918921
\(776\) 45.7292 1.64158
\(777\) −4.67244 −0.167623
\(778\) 11.0705 0.396895
\(779\) 8.32083 0.298125
\(780\) 148.259 5.30851
\(781\) −1.67933 −0.0600910
\(782\) 0.325307 0.0116330
\(783\) 29.2609 1.04570
\(784\) −17.3131 −0.618325
\(785\) 9.96106 0.355526
\(786\) 8.95113 0.319276
\(787\) −3.99657 −0.142462 −0.0712312 0.997460i \(-0.522693\pi\)
−0.0712312 + 0.997460i \(0.522693\pi\)
\(788\) −42.0033 −1.49631
\(789\) 5.37726 0.191435
\(790\) −135.900 −4.83511
\(791\) −27.2301 −0.968192
\(792\) 1.25774 0.0446919
\(793\) −30.7215 −1.09095
\(794\) 23.2487 0.825064
\(795\) 28.4084 1.00754
\(796\) 100.827 3.57371
\(797\) 43.2861 1.53327 0.766636 0.642082i \(-0.221929\pi\)
0.766636 + 0.642082i \(0.221929\pi\)
\(798\) −8.98287 −0.317990
\(799\) −0.0560549 −0.00198308
\(800\) −3.87665 −0.137060
\(801\) −2.42210 −0.0855808
\(802\) −32.6412 −1.15260
\(803\) −6.81782 −0.240596
\(804\) 74.1198 2.61400
\(805\) 9.85297 0.347272
\(806\) −53.6566 −1.88997
\(807\) −48.9419 −1.72284
\(808\) 96.8453 3.40700
\(809\) −46.5763 −1.63753 −0.818767 0.574126i \(-0.805342\pi\)
−0.818767 + 0.574126i \(0.805342\pi\)
\(810\) −64.1035 −2.25237
\(811\) 44.4191 1.55977 0.779883 0.625926i \(-0.215279\pi\)
0.779883 + 0.625926i \(0.215279\pi\)
\(812\) 37.0639 1.30069
\(813\) −39.3075 −1.37858
\(814\) −2.18643 −0.0766342
\(815\) −64.0783 −2.24457
\(816\) −0.563320 −0.0197201
\(817\) 15.3283 0.536269
\(818\) −77.3115 −2.70313
\(819\) −5.35437 −0.187097
\(820\) 89.9048 3.13961
\(821\) 16.0131 0.558860 0.279430 0.960166i \(-0.409854\pi\)
0.279430 + 0.960166i \(0.409854\pi\)
\(822\) −22.1722 −0.773345
\(823\) 26.1091 0.910105 0.455052 0.890465i \(-0.349621\pi\)
0.455052 + 0.890465i \(0.349621\pi\)
\(824\) 63.7477 2.22076
\(825\) 6.30595 0.219545
\(826\) 16.7519 0.582873
\(827\) 42.5792 1.48062 0.740312 0.672263i \(-0.234678\pi\)
0.740312 + 0.672263i \(0.234678\pi\)
\(828\) −3.10979 −0.108073
\(829\) 2.34632 0.0814909 0.0407455 0.999170i \(-0.487027\pi\)
0.0407455 + 0.999170i \(0.487027\pi\)
\(830\) 73.1623 2.53950
\(831\) 24.1917 0.839202
\(832\) 47.7965 1.65704
\(833\) 0.330693 0.0114578
\(834\) −64.8431 −2.24533
\(835\) −39.3127 −1.36047
\(836\) −2.81414 −0.0973291
\(837\) 18.5656 0.641723
\(838\) 40.3448 1.39369
\(839\) 48.0298 1.65817 0.829087 0.559120i \(-0.188861\pi\)
0.829087 + 0.559120i \(0.188861\pi\)
\(840\) −49.1413 −1.69554
\(841\) −0.933537 −0.0321909
\(842\) 0.0188014 0.000647938 0
\(843\) 29.3798 1.01190
\(844\) −113.516 −3.90737
\(845\) −103.371 −3.55606
\(846\) 0.800407 0.0275186
\(847\) 18.5265 0.636577
\(848\) −21.7069 −0.745418
\(849\) −6.35667 −0.218160
\(850\) 1.54095 0.0528541
\(851\) 2.73709 0.0938263
\(852\) −20.7087 −0.709469
\(853\) 1.17879 0.0403609 0.0201805 0.999796i \(-0.493576\pi\)
0.0201805 + 0.999796i \(0.493576\pi\)
\(854\) 20.1119 0.688217
\(855\) −2.25906 −0.0772582
\(856\) 41.6033 1.42197
\(857\) 12.6071 0.430651 0.215326 0.976542i \(-0.430919\pi\)
0.215326 + 0.976542i \(0.430919\pi\)
\(858\) 13.2265 0.451544
\(859\) 42.5968 1.45338 0.726692 0.686964i \(-0.241057\pi\)
0.726692 + 0.686964i \(0.241057\pi\)
\(860\) 165.619 5.64756
\(861\) 17.1402 0.584136
\(862\) 66.5617 2.26710
\(863\) 23.0189 0.783573 0.391787 0.920056i \(-0.371857\pi\)
0.391787 + 0.920056i \(0.371857\pi\)
\(864\) 2.81344 0.0957152
\(865\) −80.7413 −2.74529
\(866\) −87.8104 −2.98392
\(867\) −26.9877 −0.916552
\(868\) 23.5165 0.798203
\(869\) −8.11677 −0.275342
\(870\) −73.4968 −2.49177
\(871\) −74.7580 −2.53308
\(872\) 85.0857 2.88137
\(873\) 4.33035 0.146560
\(874\) 5.26212 0.177994
\(875\) 16.0093 0.541212
\(876\) −84.0745 −2.84061
\(877\) 37.2894 1.25917 0.629587 0.776930i \(-0.283224\pi\)
0.629587 + 0.776930i \(0.283224\pi\)
\(878\) 0.901255 0.0304159
\(879\) 31.6600 1.06786
\(880\) −7.98399 −0.269140
\(881\) 11.2948 0.380531 0.190266 0.981733i \(-0.439065\pi\)
0.190266 + 0.981733i \(0.439065\pi\)
\(882\) −4.72196 −0.158997
\(883\) −11.1627 −0.375655 −0.187827 0.982202i \(-0.560145\pi\)
−0.187827 + 0.982202i \(0.560145\pi\)
\(884\) 2.16382 0.0727771
\(885\) −22.2393 −0.747565
\(886\) −37.9847 −1.27612
\(887\) 26.6576 0.895076 0.447538 0.894265i \(-0.352301\pi\)
0.447538 + 0.894265i \(0.352301\pi\)
\(888\) −13.6511 −0.458102
\(889\) −1.93310 −0.0648341
\(890\) 44.2832 1.48438
\(891\) −3.82864 −0.128264
\(892\) −15.1736 −0.508051
\(893\) −0.906736 −0.0303428
\(894\) −54.1619 −1.81144
\(895\) 36.3489 1.21501
\(896\) −33.0495 −1.10411
\(897\) −16.5576 −0.552843
\(898\) −12.7471 −0.425375
\(899\) 17.8078 0.593923
\(900\) −14.7307 −0.491025
\(901\) 0.414618 0.0138129
\(902\) 8.02059 0.267057
\(903\) 31.5749 1.05075
\(904\) −79.5564 −2.64601
\(905\) −23.5874 −0.784072
\(906\) 15.5479 0.516545
\(907\) 39.3531 1.30670 0.653349 0.757057i \(-0.273363\pi\)
0.653349 + 0.757057i \(0.273363\pi\)
\(908\) 68.8810 2.28590
\(909\) 9.17081 0.304177
\(910\) 97.8938 3.24515
\(911\) −37.8619 −1.25442 −0.627210 0.778850i \(-0.715803\pi\)
−0.627210 + 0.778850i \(0.715803\pi\)
\(912\) −9.11218 −0.301735
\(913\) 4.36968 0.144615
\(914\) −80.1773 −2.65203
\(915\) −26.7000 −0.882674
\(916\) −41.6524 −1.37623
\(917\) 3.95687 0.130667
\(918\) −1.11833 −0.0369103
\(919\) 40.0561 1.32133 0.660665 0.750681i \(-0.270275\pi\)
0.660665 + 0.750681i \(0.270275\pi\)
\(920\) 28.7867 0.949071
\(921\) −37.8899 −1.24851
\(922\) 17.7852 0.585723
\(923\) 20.8871 0.687506
\(924\) −5.79688 −0.190703
\(925\) 12.9653 0.426297
\(926\) 82.8996 2.72425
\(927\) 6.03662 0.198269
\(928\) 2.69859 0.0885857
\(929\) −12.0221 −0.394432 −0.197216 0.980360i \(-0.563190\pi\)
−0.197216 + 0.980360i \(0.563190\pi\)
\(930\) −46.6327 −1.52915
\(931\) 5.34924 0.175314
\(932\) −82.9475 −2.71704
\(933\) 8.82434 0.288896
\(934\) −24.7142 −0.808673
\(935\) 0.152500 0.00498729
\(936\) −15.6435 −0.511324
\(937\) −23.3096 −0.761490 −0.380745 0.924680i \(-0.624332\pi\)
−0.380745 + 0.924680i \(0.624332\pi\)
\(938\) 48.9406 1.59797
\(939\) −7.76813 −0.253503
\(940\) −9.79709 −0.319546
\(941\) 7.61178 0.248137 0.124068 0.992274i \(-0.460406\pi\)
0.124068 + 0.992274i \(0.460406\pi\)
\(942\) 10.9584 0.357045
\(943\) −10.0406 −0.326968
\(944\) 16.9931 0.553077
\(945\) −33.8721 −1.10186
\(946\) 14.7752 0.480383
\(947\) −12.5574 −0.408062 −0.204031 0.978964i \(-0.565404\pi\)
−0.204031 + 0.978964i \(0.565404\pi\)
\(948\) −100.093 −3.25085
\(949\) 84.7984 2.75267
\(950\) 24.9262 0.808711
\(951\) −40.9327 −1.32733
\(952\) −0.717212 −0.0232450
\(953\) 3.08729 0.100007 0.0500036 0.998749i \(-0.484077\pi\)
0.0500036 + 0.998749i \(0.484077\pi\)
\(954\) −5.92032 −0.191677
\(955\) −40.0806 −1.29698
\(956\) −38.7181 −1.25223
\(957\) −4.38966 −0.141898
\(958\) 15.2562 0.492904
\(959\) −9.80129 −0.316500
\(960\) 41.5397 1.34069
\(961\) −19.7012 −0.635523
\(962\) 27.1943 0.876778
\(963\) 3.93965 0.126953
\(964\) 99.3357 3.19939
\(965\) −13.2897 −0.427810
\(966\) 10.8395 0.348755
\(967\) 11.6797 0.375592 0.187796 0.982208i \(-0.439866\pi\)
0.187796 + 0.982208i \(0.439866\pi\)
\(968\) 54.1275 1.73973
\(969\) 0.174049 0.00559127
\(970\) −79.1717 −2.54205
\(971\) −29.6158 −0.950416 −0.475208 0.879874i \(-0.657627\pi\)
−0.475208 + 0.879874i \(0.657627\pi\)
\(972\) 19.9127 0.638699
\(973\) −28.6641 −0.918928
\(974\) 53.8583 1.72573
\(975\) −78.4319 −2.51183
\(976\) 20.4015 0.653035
\(977\) 19.9372 0.637848 0.318924 0.947780i \(-0.396679\pi\)
0.318924 + 0.947780i \(0.396679\pi\)
\(978\) −70.4942 −2.25416
\(979\) 2.64486 0.0845300
\(980\) 57.7974 1.84627
\(981\) 8.05723 0.257248
\(982\) 22.5354 0.719134
\(983\) −19.2335 −0.613452 −0.306726 0.951798i \(-0.599234\pi\)
−0.306726 + 0.951798i \(0.599234\pi\)
\(984\) 50.0773 1.59641
\(985\) 36.8192 1.17316
\(986\) −1.07268 −0.0341610
\(987\) −1.86780 −0.0594526
\(988\) 35.0016 1.11355
\(989\) −18.4964 −0.588152
\(990\) −2.17755 −0.0692070
\(991\) −13.4861 −0.428399 −0.214199 0.976790i \(-0.568714\pi\)
−0.214199 + 0.976790i \(0.568714\pi\)
\(992\) 1.71222 0.0543631
\(993\) 34.7271 1.10203
\(994\) −13.6738 −0.433706
\(995\) −88.3827 −2.80192
\(996\) 53.8851 1.70742
\(997\) 42.8373 1.35667 0.678336 0.734752i \(-0.262702\pi\)
0.678336 + 0.734752i \(0.262702\pi\)
\(998\) −20.6589 −0.653945
\(999\) −9.40945 −0.297702
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 \(a_p\))