Properties

Label 8018.2.a.j.1.5
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.83191 q^{3} +1.00000 q^{4} +1.28371 q^{5} -2.83191 q^{6} -4.11947 q^{7} +1.00000 q^{8} +5.01973 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.83191 q^{3} +1.00000 q^{4} +1.28371 q^{5} -2.83191 q^{6} -4.11947 q^{7} +1.00000 q^{8} +5.01973 q^{9} +1.28371 q^{10} -5.23374 q^{11} -2.83191 q^{12} +5.59050 q^{13} -4.11947 q^{14} -3.63535 q^{15} +1.00000 q^{16} +0.524964 q^{17} +5.01973 q^{18} -1.00000 q^{19} +1.28371 q^{20} +11.6660 q^{21} -5.23374 q^{22} +5.73168 q^{23} -2.83191 q^{24} -3.35209 q^{25} +5.59050 q^{26} -5.71969 q^{27} -4.11947 q^{28} -6.04256 q^{29} -3.63535 q^{30} +3.63067 q^{31} +1.00000 q^{32} +14.8215 q^{33} +0.524964 q^{34} -5.28820 q^{35} +5.01973 q^{36} +0.704536 q^{37} -1.00000 q^{38} -15.8318 q^{39} +1.28371 q^{40} +8.38098 q^{41} +11.6660 q^{42} -7.73214 q^{43} -5.23374 q^{44} +6.44387 q^{45} +5.73168 q^{46} -9.79446 q^{47} -2.83191 q^{48} +9.97004 q^{49} -3.35209 q^{50} -1.48665 q^{51} +5.59050 q^{52} -14.1758 q^{53} -5.71969 q^{54} -6.71860 q^{55} -4.11947 q^{56} +2.83191 q^{57} -6.04256 q^{58} -5.63431 q^{59} -3.63535 q^{60} +6.12935 q^{61} +3.63067 q^{62} -20.6786 q^{63} +1.00000 q^{64} +7.17658 q^{65} +14.8215 q^{66} +6.03732 q^{67} +0.524964 q^{68} -16.2316 q^{69} -5.28820 q^{70} -3.00259 q^{71} +5.01973 q^{72} -0.00181745 q^{73} +0.704536 q^{74} +9.49283 q^{75} -1.00000 q^{76} +21.5602 q^{77} -15.8318 q^{78} -10.9043 q^{79} +1.28371 q^{80} +1.13848 q^{81} +8.38098 q^{82} +7.23923 q^{83} +11.6660 q^{84} +0.673900 q^{85} -7.73214 q^{86} +17.1120 q^{87} -5.23374 q^{88} -7.41940 q^{89} +6.44387 q^{90} -23.0299 q^{91} +5.73168 q^{92} -10.2817 q^{93} -9.79446 q^{94} -1.28371 q^{95} -2.83191 q^{96} +4.32411 q^{97} +9.97004 q^{98} -26.2720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + O(q^{10}) \) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + 15q^{10} + 17q^{11} + 10q^{12} + 27q^{13} + 10q^{15} + 47q^{16} + 16q^{17} + 69q^{18} - 47q^{19} + 15q^{20} + 26q^{21} + 17q^{22} + 24q^{23} + 10q^{24} + 86q^{25} + 27q^{26} + 43q^{27} + 58q^{29} + 10q^{30} + 21q^{31} + 47q^{32} + 18q^{33} + 16q^{34} + 24q^{35} + 69q^{36} + 78q^{37} - 47q^{38} - 4q^{39} + 15q^{40} + 53q^{41} + 26q^{42} + 47q^{43} + 17q^{44} + 23q^{45} + 24q^{46} + 16q^{47} + 10q^{48} + 93q^{49} + 86q^{50} + 28q^{51} + 27q^{52} + 43q^{53} + 43q^{54} + 23q^{55} - 10q^{57} + 58q^{58} + 3q^{59} + 10q^{60} + 12q^{61} + 21q^{62} - 5q^{63} + 47q^{64} + 62q^{65} + 18q^{66} + 68q^{67} + 16q^{68} + 12q^{69} + 24q^{70} - 13q^{71} + 69q^{72} + 35q^{73} + 78q^{74} + 22q^{75} - 47q^{76} + 26q^{77} - 4q^{78} + 21q^{79} + 15q^{80} + 123q^{81} + 53q^{82} + 23q^{83} + 26q^{84} + 38q^{85} + 47q^{86} + 39q^{87} + 17q^{88} + 24q^{89} + 23q^{90} + 49q^{91} + 24q^{92} + 91q^{93} + 16q^{94} - 15q^{95} + 10q^{96} + 88q^{97} + 93q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.83191 −1.63501 −0.817503 0.575925i \(-0.804642\pi\)
−0.817503 + 0.575925i \(0.804642\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.28371 0.574092 0.287046 0.957917i \(-0.407327\pi\)
0.287046 + 0.957917i \(0.407327\pi\)
\(6\) −2.83191 −1.15612
\(7\) −4.11947 −1.55701 −0.778507 0.627636i \(-0.784023\pi\)
−0.778507 + 0.627636i \(0.784023\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.01973 1.67324
\(10\) 1.28371 0.405944
\(11\) −5.23374 −1.57803 −0.789016 0.614372i \(-0.789409\pi\)
−0.789016 + 0.614372i \(0.789409\pi\)
\(12\) −2.83191 −0.817503
\(13\) 5.59050 1.55053 0.775264 0.631638i \(-0.217617\pi\)
0.775264 + 0.631638i \(0.217617\pi\)
\(14\) −4.11947 −1.10097
\(15\) −3.63535 −0.938643
\(16\) 1.00000 0.250000
\(17\) 0.524964 0.127322 0.0636612 0.997972i \(-0.479722\pi\)
0.0636612 + 0.997972i \(0.479722\pi\)
\(18\) 5.01973 1.18316
\(19\) −1.00000 −0.229416
\(20\) 1.28371 0.287046
\(21\) 11.6660 2.54573
\(22\) −5.23374 −1.11584
\(23\) 5.73168 1.19514 0.597569 0.801817i \(-0.296133\pi\)
0.597569 + 0.801817i \(0.296133\pi\)
\(24\) −2.83191 −0.578062
\(25\) −3.35209 −0.670418
\(26\) 5.59050 1.09639
\(27\) −5.71969 −1.10075
\(28\) −4.11947 −0.778507
\(29\) −6.04256 −1.12208 −0.561038 0.827790i \(-0.689598\pi\)
−0.561038 + 0.827790i \(0.689598\pi\)
\(30\) −3.63535 −0.663721
\(31\) 3.63067 0.652087 0.326043 0.945355i \(-0.394284\pi\)
0.326043 + 0.945355i \(0.394284\pi\)
\(32\) 1.00000 0.176777
\(33\) 14.8215 2.58009
\(34\) 0.524964 0.0900305
\(35\) −5.28820 −0.893869
\(36\) 5.01973 0.836621
\(37\) 0.704536 0.115825 0.0579125 0.998322i \(-0.481556\pi\)
0.0579125 + 0.998322i \(0.481556\pi\)
\(38\) −1.00000 −0.162221
\(39\) −15.8318 −2.53512
\(40\) 1.28371 0.202972
\(41\) 8.38098 1.30889 0.654445 0.756110i \(-0.272902\pi\)
0.654445 + 0.756110i \(0.272902\pi\)
\(42\) 11.6660 1.80010
\(43\) −7.73214 −1.17914 −0.589570 0.807717i \(-0.700703\pi\)
−0.589570 + 0.807717i \(0.700703\pi\)
\(44\) −5.23374 −0.789016
\(45\) 6.44387 0.960595
\(46\) 5.73168 0.845091
\(47\) −9.79446 −1.42867 −0.714335 0.699804i \(-0.753271\pi\)
−0.714335 + 0.699804i \(0.753271\pi\)
\(48\) −2.83191 −0.408751
\(49\) 9.97004 1.42429
\(50\) −3.35209 −0.474057
\(51\) −1.48665 −0.208173
\(52\) 5.59050 0.775264
\(53\) −14.1758 −1.94719 −0.973595 0.228281i \(-0.926690\pi\)
−0.973595 + 0.228281i \(0.926690\pi\)
\(54\) −5.71969 −0.778351
\(55\) −6.71860 −0.905936
\(56\) −4.11947 −0.550487
\(57\) 2.83191 0.375096
\(58\) −6.04256 −0.793427
\(59\) −5.63431 −0.733524 −0.366762 0.930315i \(-0.619534\pi\)
−0.366762 + 0.930315i \(0.619534\pi\)
\(60\) −3.63535 −0.469322
\(61\) 6.12935 0.784783 0.392391 0.919798i \(-0.371648\pi\)
0.392391 + 0.919798i \(0.371648\pi\)
\(62\) 3.63067 0.461095
\(63\) −20.6786 −2.60526
\(64\) 1.00000 0.125000
\(65\) 7.17658 0.890145
\(66\) 14.8215 1.82440
\(67\) 6.03732 0.737576 0.368788 0.929514i \(-0.379773\pi\)
0.368788 + 0.929514i \(0.379773\pi\)
\(68\) 0.524964 0.0636612
\(69\) −16.2316 −1.95406
\(70\) −5.28820 −0.632061
\(71\) −3.00259 −0.356342 −0.178171 0.984000i \(-0.557018\pi\)
−0.178171 + 0.984000i \(0.557018\pi\)
\(72\) 5.01973 0.591581
\(73\) −0.00181745 −0.000212717 0 −0.000106358 1.00000i \(-0.500034\pi\)
−0.000106358 1.00000i \(0.500034\pi\)
\(74\) 0.704536 0.0819006
\(75\) 9.49283 1.09614
\(76\) −1.00000 −0.114708
\(77\) 21.5602 2.45702
\(78\) −15.8318 −1.79260
\(79\) −10.9043 −1.22683 −0.613413 0.789762i \(-0.710204\pi\)
−0.613413 + 0.789762i \(0.710204\pi\)
\(80\) 1.28371 0.143523
\(81\) 1.13848 0.126498
\(82\) 8.38098 0.925524
\(83\) 7.23923 0.794609 0.397304 0.917687i \(-0.369946\pi\)
0.397304 + 0.917687i \(0.369946\pi\)
\(84\) 11.6660 1.27286
\(85\) 0.673900 0.0730947
\(86\) −7.73214 −0.833779
\(87\) 17.1120 1.83460
\(88\) −5.23374 −0.557919
\(89\) −7.41940 −0.786455 −0.393227 0.919441i \(-0.628641\pi\)
−0.393227 + 0.919441i \(0.628641\pi\)
\(90\) 6.44387 0.679243
\(91\) −23.0299 −2.41419
\(92\) 5.73168 0.597569
\(93\) −10.2817 −1.06617
\(94\) −9.79446 −1.01022
\(95\) −1.28371 −0.131706
\(96\) −2.83191 −0.289031
\(97\) 4.32411 0.439047 0.219523 0.975607i \(-0.429550\pi\)
0.219523 + 0.975607i \(0.429550\pi\)
\(98\) 9.97004 1.00713
\(99\) −26.2720 −2.64043
\(100\) −3.35209 −0.335209
\(101\) 12.5630 1.25006 0.625031 0.780600i \(-0.285086\pi\)
0.625031 + 0.780600i \(0.285086\pi\)
\(102\) −1.48665 −0.147200
\(103\) −2.38747 −0.235244 −0.117622 0.993058i \(-0.537527\pi\)
−0.117622 + 0.993058i \(0.537527\pi\)
\(104\) 5.59050 0.548194
\(105\) 14.9757 1.46148
\(106\) −14.1758 −1.37687
\(107\) 12.6099 1.21905 0.609525 0.792767i \(-0.291360\pi\)
0.609525 + 0.792767i \(0.291360\pi\)
\(108\) −5.71969 −0.550377
\(109\) 0.357316 0.0342247 0.0171123 0.999854i \(-0.494553\pi\)
0.0171123 + 0.999854i \(0.494553\pi\)
\(110\) −6.71860 −0.640593
\(111\) −1.99518 −0.189374
\(112\) −4.11947 −0.389253
\(113\) −14.6762 −1.38062 −0.690312 0.723512i \(-0.742527\pi\)
−0.690312 + 0.723512i \(0.742527\pi\)
\(114\) 2.83191 0.265233
\(115\) 7.35781 0.686119
\(116\) −6.04256 −0.561038
\(117\) 28.0628 2.59441
\(118\) −5.63431 −0.518680
\(119\) −2.16257 −0.198243
\(120\) −3.63535 −0.331861
\(121\) 16.3921 1.49019
\(122\) 6.12935 0.554925
\(123\) −23.7342 −2.14004
\(124\) 3.63067 0.326043
\(125\) −10.7217 −0.958974
\(126\) −20.6786 −1.84220
\(127\) 11.8181 1.04868 0.524342 0.851508i \(-0.324311\pi\)
0.524342 + 0.851508i \(0.324311\pi\)
\(128\) 1.00000 0.0883883
\(129\) 21.8968 1.92790
\(130\) 7.17658 0.629428
\(131\) 19.5959 1.71210 0.856049 0.516894i \(-0.172912\pi\)
0.856049 + 0.516894i \(0.172912\pi\)
\(132\) 14.8215 1.29005
\(133\) 4.11947 0.357203
\(134\) 6.03732 0.521545
\(135\) −7.34241 −0.631934
\(136\) 0.524964 0.0450153
\(137\) 11.2612 0.962109 0.481054 0.876691i \(-0.340254\pi\)
0.481054 + 0.876691i \(0.340254\pi\)
\(138\) −16.2316 −1.38173
\(139\) 22.9412 1.94585 0.972925 0.231121i \(-0.0742392\pi\)
0.972925 + 0.231121i \(0.0742392\pi\)
\(140\) −5.28820 −0.446934
\(141\) 27.7371 2.33588
\(142\) −3.00259 −0.251972
\(143\) −29.2593 −2.44678
\(144\) 5.01973 0.418311
\(145\) −7.75689 −0.644174
\(146\) −0.00181745 −0.000150413 0
\(147\) −28.2343 −2.32872
\(148\) 0.704536 0.0579125
\(149\) 5.79470 0.474720 0.237360 0.971422i \(-0.423718\pi\)
0.237360 + 0.971422i \(0.423718\pi\)
\(150\) 9.49283 0.775086
\(151\) −12.6055 −1.02582 −0.512912 0.858441i \(-0.671433\pi\)
−0.512912 + 0.858441i \(0.671433\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 2.63517 0.213041
\(154\) 21.5602 1.73737
\(155\) 4.66072 0.374358
\(156\) −15.8318 −1.26756
\(157\) −16.4178 −1.31028 −0.655142 0.755506i \(-0.727391\pi\)
−0.655142 + 0.755506i \(0.727391\pi\)
\(158\) −10.9043 −0.867497
\(159\) 40.1445 3.18367
\(160\) 1.28371 0.101486
\(161\) −23.6115 −1.86085
\(162\) 1.13848 0.0894473
\(163\) 13.8959 1.08841 0.544207 0.838951i \(-0.316831\pi\)
0.544207 + 0.838951i \(0.316831\pi\)
\(164\) 8.38098 0.654445
\(165\) 19.0265 1.48121
\(166\) 7.23923 0.561873
\(167\) −10.0983 −0.781426 −0.390713 0.920512i \(-0.627772\pi\)
−0.390713 + 0.920512i \(0.627772\pi\)
\(168\) 11.6660 0.900050
\(169\) 18.2537 1.40413
\(170\) 0.673900 0.0516858
\(171\) −5.01973 −0.383868
\(172\) −7.73214 −0.589570
\(173\) 6.86873 0.522220 0.261110 0.965309i \(-0.415911\pi\)
0.261110 + 0.965309i \(0.415911\pi\)
\(174\) 17.1120 1.29726
\(175\) 13.8088 1.04385
\(176\) −5.23374 −0.394508
\(177\) 15.9559 1.19932
\(178\) −7.41940 −0.556107
\(179\) 2.65665 0.198567 0.0992836 0.995059i \(-0.468345\pi\)
0.0992836 + 0.995059i \(0.468345\pi\)
\(180\) 6.44387 0.480297
\(181\) −20.9411 −1.55654 −0.778271 0.627929i \(-0.783903\pi\)
−0.778271 + 0.627929i \(0.783903\pi\)
\(182\) −23.0299 −1.70709
\(183\) −17.3578 −1.28312
\(184\) 5.73168 0.422545
\(185\) 0.904419 0.0664942
\(186\) −10.2817 −0.753893
\(187\) −2.74752 −0.200919
\(188\) −9.79446 −0.714335
\(189\) 23.5621 1.71389
\(190\) −1.28371 −0.0931300
\(191\) −8.92459 −0.645761 −0.322880 0.946440i \(-0.604651\pi\)
−0.322880 + 0.946440i \(0.604651\pi\)
\(192\) −2.83191 −0.204376
\(193\) 21.0325 1.51395 0.756976 0.653442i \(-0.226676\pi\)
0.756976 + 0.653442i \(0.226676\pi\)
\(194\) 4.32411 0.310453
\(195\) −20.3234 −1.45539
\(196\) 9.97004 0.712146
\(197\) 16.0309 1.14215 0.571077 0.820896i \(-0.306526\pi\)
0.571077 + 0.820896i \(0.306526\pi\)
\(198\) −26.2720 −1.86707
\(199\) 10.3290 0.732201 0.366100 0.930575i \(-0.380693\pi\)
0.366100 + 0.930575i \(0.380693\pi\)
\(200\) −3.35209 −0.237029
\(201\) −17.0972 −1.20594
\(202\) 12.5630 0.883927
\(203\) 24.8921 1.74709
\(204\) −1.48665 −0.104086
\(205\) 10.7587 0.751423
\(206\) −2.38747 −0.166343
\(207\) 28.7715 1.99976
\(208\) 5.59050 0.387632
\(209\) 5.23374 0.362026
\(210\) 14.9757 1.03342
\(211\) −1.00000 −0.0688428
\(212\) −14.1758 −0.973595
\(213\) 8.50307 0.582621
\(214\) 12.6099 0.861998
\(215\) −9.92582 −0.676935
\(216\) −5.71969 −0.389176
\(217\) −14.9564 −1.01531
\(218\) 0.357316 0.0242005
\(219\) 0.00514686 0.000347793 0
\(220\) −6.71860 −0.452968
\(221\) 2.93481 0.197417
\(222\) −1.99518 −0.133908
\(223\) 13.6581 0.914616 0.457308 0.889308i \(-0.348814\pi\)
0.457308 + 0.889308i \(0.348814\pi\)
\(224\) −4.11947 −0.275244
\(225\) −16.8266 −1.12177
\(226\) −14.6762 −0.976248
\(227\) −25.6786 −1.70435 −0.852175 0.523256i \(-0.824717\pi\)
−0.852175 + 0.523256i \(0.824717\pi\)
\(228\) 2.83191 0.187548
\(229\) 23.4863 1.55202 0.776009 0.630721i \(-0.217241\pi\)
0.776009 + 0.630721i \(0.217241\pi\)
\(230\) 7.35781 0.485160
\(231\) −61.0567 −4.01724
\(232\) −6.04256 −0.396713
\(233\) −19.0914 −1.25072 −0.625361 0.780335i \(-0.715048\pi\)
−0.625361 + 0.780335i \(0.715048\pi\)
\(234\) 28.0628 1.83452
\(235\) −12.5732 −0.820187
\(236\) −5.63431 −0.366762
\(237\) 30.8799 2.00587
\(238\) −2.16257 −0.140179
\(239\) 2.78325 0.180034 0.0900168 0.995940i \(-0.471308\pi\)
0.0900168 + 0.995940i \(0.471308\pi\)
\(240\) −3.63535 −0.234661
\(241\) 27.2314 1.75413 0.877064 0.480374i \(-0.159499\pi\)
0.877064 + 0.480374i \(0.159499\pi\)
\(242\) 16.3921 1.05372
\(243\) 13.9350 0.893931
\(244\) 6.12935 0.392391
\(245\) 12.7986 0.817674
\(246\) −23.7342 −1.51324
\(247\) −5.59050 −0.355715
\(248\) 3.63067 0.230547
\(249\) −20.5009 −1.29919
\(250\) −10.7217 −0.678097
\(251\) 18.2310 1.15073 0.575367 0.817895i \(-0.304859\pi\)
0.575367 + 0.817895i \(0.304859\pi\)
\(252\) −20.6786 −1.30263
\(253\) −29.9982 −1.88597
\(254\) 11.8181 0.741531
\(255\) −1.90843 −0.119510
\(256\) 1.00000 0.0625000
\(257\) 20.9695 1.30804 0.654019 0.756478i \(-0.273082\pi\)
0.654019 + 0.756478i \(0.273082\pi\)
\(258\) 21.8968 1.36323
\(259\) −2.90231 −0.180341
\(260\) 7.17658 0.445072
\(261\) −30.3320 −1.87750
\(262\) 19.5959 1.21064
\(263\) −12.9974 −0.801452 −0.400726 0.916198i \(-0.631242\pi\)
−0.400726 + 0.916198i \(0.631242\pi\)
\(264\) 14.8215 0.912200
\(265\) −18.1975 −1.11787
\(266\) 4.11947 0.252581
\(267\) 21.0111 1.28586
\(268\) 6.03732 0.368788
\(269\) −12.3036 −0.750162 −0.375081 0.926992i \(-0.622385\pi\)
−0.375081 + 0.926992i \(0.622385\pi\)
\(270\) −7.34241 −0.446845
\(271\) 20.9145 1.27046 0.635231 0.772322i \(-0.280905\pi\)
0.635231 + 0.772322i \(0.280905\pi\)
\(272\) 0.524964 0.0318306
\(273\) 65.2187 3.94722
\(274\) 11.2612 0.680314
\(275\) 17.5440 1.05794
\(276\) −16.2316 −0.977029
\(277\) −8.96764 −0.538814 −0.269407 0.963026i \(-0.586828\pi\)
−0.269407 + 0.963026i \(0.586828\pi\)
\(278\) 22.9412 1.37592
\(279\) 18.2250 1.09110
\(280\) −5.28820 −0.316030
\(281\) −2.55717 −0.152548 −0.0762740 0.997087i \(-0.524302\pi\)
−0.0762740 + 0.997087i \(0.524302\pi\)
\(282\) 27.7371 1.65172
\(283\) −9.75811 −0.580060 −0.290030 0.957018i \(-0.593665\pi\)
−0.290030 + 0.957018i \(0.593665\pi\)
\(284\) −3.00259 −0.178171
\(285\) 3.63535 0.215340
\(286\) −29.2593 −1.73014
\(287\) −34.5252 −2.03796
\(288\) 5.01973 0.295790
\(289\) −16.7244 −0.983789
\(290\) −7.75689 −0.455500
\(291\) −12.2455 −0.717844
\(292\) −0.00181745 −0.000106358 0
\(293\) 22.1512 1.29409 0.647044 0.762453i \(-0.276005\pi\)
0.647044 + 0.762453i \(0.276005\pi\)
\(294\) −28.2343 −1.64666
\(295\) −7.23281 −0.421110
\(296\) 0.704536 0.0409503
\(297\) 29.9354 1.73703
\(298\) 5.79470 0.335678
\(299\) 32.0430 1.85309
\(300\) 9.49283 0.548069
\(301\) 31.8523 1.83594
\(302\) −12.6055 −0.725368
\(303\) −35.5772 −2.04386
\(304\) −1.00000 −0.0573539
\(305\) 7.86830 0.450537
\(306\) 2.63517 0.150643
\(307\) 18.8790 1.07748 0.538741 0.842471i \(-0.318900\pi\)
0.538741 + 0.842471i \(0.318900\pi\)
\(308\) 21.5602 1.22851
\(309\) 6.76109 0.384625
\(310\) 4.66072 0.264711
\(311\) −5.03635 −0.285585 −0.142793 0.989753i \(-0.545608\pi\)
−0.142793 + 0.989753i \(0.545608\pi\)
\(312\) −15.8318 −0.896300
\(313\) 25.5334 1.44323 0.721617 0.692292i \(-0.243399\pi\)
0.721617 + 0.692292i \(0.243399\pi\)
\(314\) −16.4178 −0.926510
\(315\) −26.5453 −1.49566
\(316\) −10.9043 −0.613413
\(317\) 31.3517 1.76089 0.880443 0.474152i \(-0.157245\pi\)
0.880443 + 0.474152i \(0.157245\pi\)
\(318\) 40.1445 2.25119
\(319\) 31.6252 1.77067
\(320\) 1.28371 0.0717615
\(321\) −35.7103 −1.99315
\(322\) −23.6115 −1.31582
\(323\) −0.524964 −0.0292098
\(324\) 1.13848 0.0632488
\(325\) −18.7399 −1.03950
\(326\) 13.8959 0.769624
\(327\) −1.01189 −0.0559575
\(328\) 8.38098 0.462762
\(329\) 40.3480 2.22446
\(330\) 19.0265 1.04737
\(331\) 16.7295 0.919538 0.459769 0.888039i \(-0.347932\pi\)
0.459769 + 0.888039i \(0.347932\pi\)
\(332\) 7.23923 0.397304
\(333\) 3.53658 0.193803
\(334\) −10.0983 −0.552552
\(335\) 7.75016 0.423436
\(336\) 11.6660 0.636431
\(337\) 26.3620 1.43603 0.718014 0.696028i \(-0.245051\pi\)
0.718014 + 0.696028i \(0.245051\pi\)
\(338\) 18.2537 0.992873
\(339\) 41.5618 2.25733
\(340\) 0.673900 0.0365474
\(341\) −19.0020 −1.02901
\(342\) −5.01973 −0.271436
\(343\) −12.2350 −0.660627
\(344\) −7.73214 −0.416889
\(345\) −20.8367 −1.12181
\(346\) 6.86873 0.369265
\(347\) −15.9815 −0.857932 −0.428966 0.903321i \(-0.641122\pi\)
−0.428966 + 0.903321i \(0.641122\pi\)
\(348\) 17.1120 0.917299
\(349\) −12.5484 −0.671701 −0.335851 0.941915i \(-0.609024\pi\)
−0.335851 + 0.941915i \(0.609024\pi\)
\(350\) 13.8088 0.738114
\(351\) −31.9760 −1.70675
\(352\) −5.23374 −0.278959
\(353\) −22.5524 −1.20034 −0.600171 0.799872i \(-0.704901\pi\)
−0.600171 + 0.799872i \(0.704901\pi\)
\(354\) 15.9559 0.848044
\(355\) −3.85445 −0.204573
\(356\) −7.41940 −0.393227
\(357\) 6.12421 0.324128
\(358\) 2.65665 0.140408
\(359\) −10.6303 −0.561046 −0.280523 0.959847i \(-0.590508\pi\)
−0.280523 + 0.959847i \(0.590508\pi\)
\(360\) 6.44387 0.339622
\(361\) 1.00000 0.0526316
\(362\) −20.9411 −1.10064
\(363\) −46.4209 −2.43646
\(364\) −23.0299 −1.20710
\(365\) −0.00233308 −0.000122119 0
\(366\) −17.3578 −0.907305
\(367\) −9.82680 −0.512955 −0.256477 0.966550i \(-0.582562\pi\)
−0.256477 + 0.966550i \(0.582562\pi\)
\(368\) 5.73168 0.298785
\(369\) 42.0702 2.19009
\(370\) 0.904419 0.0470185
\(371\) 58.3966 3.03180
\(372\) −10.2817 −0.533083
\(373\) −33.3362 −1.72608 −0.863042 0.505133i \(-0.831443\pi\)
−0.863042 + 0.505133i \(0.831443\pi\)
\(374\) −2.74752 −0.142071
\(375\) 30.3628 1.56793
\(376\) −9.79446 −0.505111
\(377\) −33.7810 −1.73981
\(378\) 23.5621 1.21190
\(379\) 5.11277 0.262625 0.131313 0.991341i \(-0.458081\pi\)
0.131313 + 0.991341i \(0.458081\pi\)
\(380\) −1.28371 −0.0658529
\(381\) −33.4677 −1.71460
\(382\) −8.92459 −0.456622
\(383\) −21.3710 −1.09201 −0.546003 0.837783i \(-0.683851\pi\)
−0.546003 + 0.837783i \(0.683851\pi\)
\(384\) −2.83191 −0.144515
\(385\) 27.6771 1.41055
\(386\) 21.0325 1.07053
\(387\) −38.8133 −1.97299
\(388\) 4.32411 0.219523
\(389\) 11.0314 0.559314 0.279657 0.960100i \(-0.409779\pi\)
0.279657 + 0.960100i \(0.409779\pi\)
\(390\) −20.3234 −1.02912
\(391\) 3.00892 0.152168
\(392\) 9.97004 0.503563
\(393\) −55.4938 −2.79929
\(394\) 16.0309 0.807626
\(395\) −13.9979 −0.704311
\(396\) −26.2720 −1.32022
\(397\) 26.1916 1.31452 0.657259 0.753664i \(-0.271716\pi\)
0.657259 + 0.753664i \(0.271716\pi\)
\(398\) 10.3290 0.517744
\(399\) −11.6660 −0.584029
\(400\) −3.35209 −0.167605
\(401\) 34.2743 1.71157 0.855787 0.517328i \(-0.173073\pi\)
0.855787 + 0.517328i \(0.173073\pi\)
\(402\) −17.0972 −0.852728
\(403\) 20.2973 1.01108
\(404\) 12.5630 0.625031
\(405\) 1.46147 0.0726212
\(406\) 24.8921 1.23538
\(407\) −3.68736 −0.182776
\(408\) −1.48665 −0.0736002
\(409\) −37.4081 −1.84971 −0.924855 0.380319i \(-0.875814\pi\)
−0.924855 + 0.380319i \(0.875814\pi\)
\(410\) 10.7587 0.531336
\(411\) −31.8907 −1.57305
\(412\) −2.38747 −0.117622
\(413\) 23.2104 1.14211
\(414\) 28.7715 1.41404
\(415\) 9.29306 0.456179
\(416\) 5.59050 0.274097
\(417\) −64.9676 −3.18148
\(418\) 5.23374 0.255991
\(419\) −11.4922 −0.561429 −0.280714 0.959791i \(-0.590571\pi\)
−0.280714 + 0.959791i \(0.590571\pi\)
\(420\) 14.9757 0.730740
\(421\) −27.6770 −1.34889 −0.674447 0.738323i \(-0.735618\pi\)
−0.674447 + 0.738323i \(0.735618\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −49.1655 −2.39051
\(424\) −14.1758 −0.688436
\(425\) −1.75973 −0.0853593
\(426\) 8.50307 0.411975
\(427\) −25.2497 −1.22192
\(428\) 12.6099 0.609525
\(429\) 82.8597 4.00050
\(430\) −9.92582 −0.478666
\(431\) 27.9087 1.34432 0.672158 0.740408i \(-0.265368\pi\)
0.672158 + 0.740408i \(0.265368\pi\)
\(432\) −5.71969 −0.275189
\(433\) 19.8795 0.955347 0.477673 0.878538i \(-0.341480\pi\)
0.477673 + 0.878538i \(0.341480\pi\)
\(434\) −14.9564 −0.717931
\(435\) 21.9668 1.05323
\(436\) 0.357316 0.0171123
\(437\) −5.73168 −0.274184
\(438\) 0.00514686 0.000245927 0
\(439\) −18.4375 −0.879972 −0.439986 0.898005i \(-0.645017\pi\)
−0.439986 + 0.898005i \(0.645017\pi\)
\(440\) −6.71860 −0.320297
\(441\) 50.0469 2.38318
\(442\) 2.93481 0.139595
\(443\) 33.8701 1.60922 0.804610 0.593804i \(-0.202375\pi\)
0.804610 + 0.593804i \(0.202375\pi\)
\(444\) −1.99518 −0.0946872
\(445\) −9.52435 −0.451497
\(446\) 13.6581 0.646731
\(447\) −16.4101 −0.776170
\(448\) −4.11947 −0.194627
\(449\) 19.6729 0.928422 0.464211 0.885725i \(-0.346338\pi\)
0.464211 + 0.885725i \(0.346338\pi\)
\(450\) −16.8266 −0.793213
\(451\) −43.8639 −2.06547
\(452\) −14.6762 −0.690312
\(453\) 35.6978 1.67723
\(454\) −25.6786 −1.20516
\(455\) −29.5637 −1.38597
\(456\) 2.83191 0.132616
\(457\) −2.54516 −0.119058 −0.0595288 0.998227i \(-0.518960\pi\)
−0.0595288 + 0.998227i \(0.518960\pi\)
\(458\) 23.4863 1.09744
\(459\) −3.00263 −0.140151
\(460\) 7.35781 0.343060
\(461\) −11.6962 −0.544745 −0.272373 0.962192i \(-0.587808\pi\)
−0.272373 + 0.962192i \(0.587808\pi\)
\(462\) −61.0567 −2.84062
\(463\) 7.72399 0.358964 0.179482 0.983761i \(-0.442558\pi\)
0.179482 + 0.983761i \(0.442558\pi\)
\(464\) −6.04256 −0.280519
\(465\) −13.1987 −0.612077
\(466\) −19.0914 −0.884394
\(467\) 10.9455 0.506498 0.253249 0.967401i \(-0.418501\pi\)
0.253249 + 0.967401i \(0.418501\pi\)
\(468\) 28.0628 1.29720
\(469\) −24.8705 −1.14842
\(470\) −12.5732 −0.579960
\(471\) 46.4938 2.14232
\(472\) −5.63431 −0.259340
\(473\) 40.4680 1.86072
\(474\) 30.8799 1.41836
\(475\) 3.35209 0.153805
\(476\) −2.16257 −0.0991213
\(477\) −71.1585 −3.25812
\(478\) 2.78325 0.127303
\(479\) 22.7293 1.03853 0.519264 0.854614i \(-0.326206\pi\)
0.519264 + 0.854614i \(0.326206\pi\)
\(480\) −3.63535 −0.165930
\(481\) 3.93871 0.179590
\(482\) 27.2314 1.24036
\(483\) 66.8657 3.04249
\(484\) 16.3921 0.745093
\(485\) 5.55089 0.252053
\(486\) 13.9350 0.632104
\(487\) 30.0182 1.36026 0.680128 0.733094i \(-0.261924\pi\)
0.680128 + 0.733094i \(0.261924\pi\)
\(488\) 6.12935 0.277463
\(489\) −39.3521 −1.77956
\(490\) 12.7986 0.578183
\(491\) −13.5501 −0.611506 −0.305753 0.952111i \(-0.598908\pi\)
−0.305753 + 0.952111i \(0.598908\pi\)
\(492\) −23.7342 −1.07002
\(493\) −3.17212 −0.142865
\(494\) −5.59050 −0.251529
\(495\) −33.7255 −1.51585
\(496\) 3.63067 0.163022
\(497\) 12.3691 0.554829
\(498\) −20.5009 −0.918666
\(499\) 8.09968 0.362592 0.181296 0.983429i \(-0.441971\pi\)
0.181296 + 0.983429i \(0.441971\pi\)
\(500\) −10.7217 −0.479487
\(501\) 28.5974 1.27764
\(502\) 18.2310 0.813692
\(503\) 25.9382 1.15653 0.578263 0.815851i \(-0.303731\pi\)
0.578263 + 0.815851i \(0.303731\pi\)
\(504\) −20.6786 −0.921099
\(505\) 16.1272 0.717650
\(506\) −29.9982 −1.33358
\(507\) −51.6930 −2.29577
\(508\) 11.8181 0.524342
\(509\) 16.6393 0.737523 0.368761 0.929524i \(-0.379782\pi\)
0.368761 + 0.929524i \(0.379782\pi\)
\(510\) −1.90843 −0.0845065
\(511\) 0.00748694 0.000331203 0
\(512\) 1.00000 0.0441942
\(513\) 5.71969 0.252530
\(514\) 20.9695 0.924923
\(515\) −3.06481 −0.135052
\(516\) 21.8968 0.963951
\(517\) 51.2617 2.25449
\(518\) −2.90231 −0.127520
\(519\) −19.4516 −0.853832
\(520\) 7.17658 0.314714
\(521\) 34.3543 1.50509 0.752545 0.658540i \(-0.228826\pi\)
0.752545 + 0.658540i \(0.228826\pi\)
\(522\) −30.3320 −1.32760
\(523\) 20.3256 0.888778 0.444389 0.895834i \(-0.353421\pi\)
0.444389 + 0.895834i \(0.353421\pi\)
\(524\) 19.5959 0.856049
\(525\) −39.1054 −1.70670
\(526\) −12.9974 −0.566712
\(527\) 1.90597 0.0830252
\(528\) 14.8215 0.645023
\(529\) 9.85219 0.428356
\(530\) −18.1975 −0.790451
\(531\) −28.2827 −1.22736
\(532\) 4.11947 0.178602
\(533\) 46.8539 2.02947
\(534\) 21.0111 0.909239
\(535\) 16.1875 0.699846
\(536\) 6.03732 0.260772
\(537\) −7.52339 −0.324658
\(538\) −12.3036 −0.530444
\(539\) −52.1806 −2.24758
\(540\) −7.34241 −0.315967
\(541\) −16.8219 −0.723230 −0.361615 0.932328i \(-0.617774\pi\)
−0.361615 + 0.932328i \(0.617774\pi\)
\(542\) 20.9145 0.898353
\(543\) 59.3034 2.54495
\(544\) 0.524964 0.0225076
\(545\) 0.458690 0.0196481
\(546\) 65.2187 2.79110
\(547\) 35.4720 1.51668 0.758338 0.651862i \(-0.226012\pi\)
0.758338 + 0.651862i \(0.226012\pi\)
\(548\) 11.2612 0.481054
\(549\) 30.7677 1.31313
\(550\) 17.5440 0.748078
\(551\) 6.04256 0.257422
\(552\) −16.2316 −0.690864
\(553\) 44.9198 1.91018
\(554\) −8.96764 −0.380999
\(555\) −2.56123 −0.108718
\(556\) 22.9412 0.972925
\(557\) 8.67246 0.367464 0.183732 0.982976i \(-0.441182\pi\)
0.183732 + 0.982976i \(0.441182\pi\)
\(558\) 18.2250 0.771524
\(559\) −43.2266 −1.82829
\(560\) −5.28820 −0.223467
\(561\) 7.78075 0.328503
\(562\) −2.55717 −0.107868
\(563\) 7.94154 0.334696 0.167348 0.985898i \(-0.446480\pi\)
0.167348 + 0.985898i \(0.446480\pi\)
\(564\) 27.7371 1.16794
\(565\) −18.8400 −0.792605
\(566\) −9.75811 −0.410164
\(567\) −4.68993 −0.196958
\(568\) −3.00259 −0.125986
\(569\) −11.9295 −0.500109 −0.250054 0.968232i \(-0.580449\pi\)
−0.250054 + 0.968232i \(0.580449\pi\)
\(570\) 3.63535 0.152268
\(571\) 2.24578 0.0939830 0.0469915 0.998895i \(-0.485037\pi\)
0.0469915 + 0.998895i \(0.485037\pi\)
\(572\) −29.2593 −1.22339
\(573\) 25.2737 1.05582
\(574\) −34.5252 −1.44105
\(575\) −19.2131 −0.801243
\(576\) 5.01973 0.209155
\(577\) 17.6498 0.734771 0.367385 0.930069i \(-0.380253\pi\)
0.367385 + 0.930069i \(0.380253\pi\)
\(578\) −16.7244 −0.695644
\(579\) −59.5622 −2.47532
\(580\) −7.75689 −0.322087
\(581\) −29.8218 −1.23722
\(582\) −12.2455 −0.507592
\(583\) 74.1923 3.07273
\(584\) −0.00181745 −7.52067e−5 0
\(585\) 36.0245 1.48943
\(586\) 22.1512 0.915059
\(587\) −24.3389 −1.00457 −0.502287 0.864701i \(-0.667508\pi\)
−0.502287 + 0.864701i \(0.667508\pi\)
\(588\) −28.2343 −1.16436
\(589\) −3.63067 −0.149599
\(590\) −7.23281 −0.297770
\(591\) −45.3981 −1.86743
\(592\) 0.704536 0.0289562
\(593\) −1.29881 −0.0533358 −0.0266679 0.999644i \(-0.508490\pi\)
−0.0266679 + 0.999644i \(0.508490\pi\)
\(594\) 29.9354 1.22826
\(595\) −2.77611 −0.113809
\(596\) 5.79470 0.237360
\(597\) −29.2507 −1.19715
\(598\) 32.0430 1.31034
\(599\) 20.2483 0.827324 0.413662 0.910431i \(-0.364250\pi\)
0.413662 + 0.910431i \(0.364250\pi\)
\(600\) 9.49283 0.387543
\(601\) −33.3441 −1.36013 −0.680067 0.733150i \(-0.738049\pi\)
−0.680067 + 0.733150i \(0.738049\pi\)
\(602\) 31.8523 1.29820
\(603\) 30.3057 1.23414
\(604\) −12.6055 −0.512912
\(605\) 21.0426 0.855504
\(606\) −35.5772 −1.44523
\(607\) 38.9819 1.58223 0.791113 0.611670i \(-0.209502\pi\)
0.791113 + 0.611670i \(0.209502\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −70.4924 −2.85650
\(610\) 7.86830 0.318578
\(611\) −54.7560 −2.21519
\(612\) 2.63517 0.106521
\(613\) 21.3296 0.861495 0.430748 0.902472i \(-0.358250\pi\)
0.430748 + 0.902472i \(0.358250\pi\)
\(614\) 18.8790 0.761895
\(615\) −30.4678 −1.22858
\(616\) 21.5602 0.868687
\(617\) −20.2404 −0.814847 −0.407424 0.913239i \(-0.633573\pi\)
−0.407424 + 0.913239i \(0.633573\pi\)
\(618\) 6.76109 0.271971
\(619\) 43.2649 1.73896 0.869482 0.493965i \(-0.164453\pi\)
0.869482 + 0.493965i \(0.164453\pi\)
\(620\) 4.66072 0.187179
\(621\) −32.7835 −1.31555
\(622\) −5.03635 −0.201939
\(623\) 30.5640 1.22452
\(624\) −15.8318 −0.633780
\(625\) 2.99699 0.119879
\(626\) 25.5334 1.02052
\(627\) −14.8215 −0.591914
\(628\) −16.4178 −0.655142
\(629\) 0.369856 0.0147471
\(630\) −26.5453 −1.05759
\(631\) −39.4632 −1.57101 −0.785503 0.618858i \(-0.787596\pi\)
−0.785503 + 0.618858i \(0.787596\pi\)
\(632\) −10.9043 −0.433748
\(633\) 2.83191 0.112558
\(634\) 31.3517 1.24513
\(635\) 15.1710 0.602041
\(636\) 40.1445 1.59183
\(637\) 55.7375 2.20840
\(638\) 31.6252 1.25205
\(639\) −15.0722 −0.596246
\(640\) 1.28371 0.0507430
\(641\) −26.9674 −1.06515 −0.532574 0.846383i \(-0.678775\pi\)
−0.532574 + 0.846383i \(0.678775\pi\)
\(642\) −35.7103 −1.40937
\(643\) −1.14849 −0.0452922 −0.0226461 0.999744i \(-0.507209\pi\)
−0.0226461 + 0.999744i \(0.507209\pi\)
\(644\) −23.6115 −0.930423
\(645\) 28.1090 1.10679
\(646\) −0.524964 −0.0206544
\(647\) −23.6049 −0.928003 −0.464002 0.885834i \(-0.653587\pi\)
−0.464002 + 0.885834i \(0.653587\pi\)
\(648\) 1.13848 0.0447237
\(649\) 29.4885 1.15752
\(650\) −18.7399 −0.735039
\(651\) 42.3553 1.66003
\(652\) 13.8959 0.544207
\(653\) −5.96224 −0.233320 −0.116660 0.993172i \(-0.537219\pi\)
−0.116660 + 0.993172i \(0.537219\pi\)
\(654\) −1.01189 −0.0395679
\(655\) 25.1554 0.982902
\(656\) 8.38098 0.327222
\(657\) −0.00912311 −0.000355926 0
\(658\) 40.3480 1.57293
\(659\) −5.28961 −0.206054 −0.103027 0.994679i \(-0.532853\pi\)
−0.103027 + 0.994679i \(0.532853\pi\)
\(660\) 19.0265 0.740605
\(661\) −35.1871 −1.36862 −0.684310 0.729191i \(-0.739897\pi\)
−0.684310 + 0.729191i \(0.739897\pi\)
\(662\) 16.7295 0.650211
\(663\) −8.31113 −0.322777
\(664\) 7.23923 0.280937
\(665\) 5.28820 0.205068
\(666\) 3.53658 0.137040
\(667\) −34.6340 −1.34104
\(668\) −10.0983 −0.390713
\(669\) −38.6786 −1.49540
\(670\) 7.75016 0.299415
\(671\) −32.0794 −1.23841
\(672\) 11.6660 0.450025
\(673\) 23.4092 0.902357 0.451178 0.892434i \(-0.351004\pi\)
0.451178 + 0.892434i \(0.351004\pi\)
\(674\) 26.3620 1.01543
\(675\) 19.1729 0.737966
\(676\) 18.2537 0.702067
\(677\) 37.0478 1.42386 0.711931 0.702249i \(-0.247821\pi\)
0.711931 + 0.702249i \(0.247821\pi\)
\(678\) 41.5618 1.59617
\(679\) −17.8130 −0.683602
\(680\) 0.673900 0.0258429
\(681\) 72.7196 2.78662
\(682\) −19.0020 −0.727623
\(683\) −19.2393 −0.736171 −0.368086 0.929792i \(-0.619987\pi\)
−0.368086 + 0.929792i \(0.619987\pi\)
\(684\) −5.01973 −0.191934
\(685\) 14.4561 0.552339
\(686\) −12.2350 −0.467134
\(687\) −66.5112 −2.53756
\(688\) −7.73214 −0.294785
\(689\) −79.2497 −3.01917
\(690\) −20.8367 −0.793239
\(691\) −2.61908 −0.0996344 −0.0498172 0.998758i \(-0.515864\pi\)
−0.0498172 + 0.998758i \(0.515864\pi\)
\(692\) 6.86873 0.261110
\(693\) 108.227 4.11119
\(694\) −15.9815 −0.606650
\(695\) 29.4499 1.11710
\(696\) 17.1120 0.648629
\(697\) 4.39971 0.166651
\(698\) −12.5484 −0.474964
\(699\) 54.0653 2.04494
\(700\) 13.8088 0.521925
\(701\) 40.8641 1.54342 0.771709 0.635976i \(-0.219402\pi\)
0.771709 + 0.635976i \(0.219402\pi\)
\(702\) −31.9760 −1.20685
\(703\) −0.704536 −0.0265721
\(704\) −5.23374 −0.197254
\(705\) 35.6063 1.34101
\(706\) −22.5524 −0.848770
\(707\) −51.7528 −1.94636
\(708\) 15.9559 0.599658
\(709\) 50.5698 1.89919 0.949593 0.313484i \(-0.101496\pi\)
0.949593 + 0.313484i \(0.101496\pi\)
\(710\) −3.85445 −0.144655
\(711\) −54.7364 −2.05278
\(712\) −7.41940 −0.278054
\(713\) 20.8098 0.779334
\(714\) 6.12421 0.229193
\(715\) −37.5604 −1.40468
\(716\) 2.65665 0.0992836
\(717\) −7.88192 −0.294356
\(718\) −10.6303 −0.396719
\(719\) −11.9160 −0.444393 −0.222197 0.975002i \(-0.571323\pi\)
−0.222197 + 0.975002i \(0.571323\pi\)
\(720\) 6.44387 0.240149
\(721\) 9.83510 0.366278
\(722\) 1.00000 0.0372161
\(723\) −77.1169 −2.86801
\(724\) −20.9411 −0.778271
\(725\) 20.2552 0.752260
\(726\) −46.4209 −1.72284
\(727\) 51.0029 1.89159 0.945797 0.324758i \(-0.105283\pi\)
0.945797 + 0.324758i \(0.105283\pi\)
\(728\) −23.0299 −0.853546
\(729\) −42.8781 −1.58808
\(730\) −0.00233308 −8.63511e−5 0
\(731\) −4.05909 −0.150131
\(732\) −17.3578 −0.641562
\(733\) −12.2799 −0.453568 −0.226784 0.973945i \(-0.572821\pi\)
−0.226784 + 0.973945i \(0.572821\pi\)
\(734\) −9.82680 −0.362714
\(735\) −36.2446 −1.33690
\(736\) 5.73168 0.211273
\(737\) −31.5978 −1.16392
\(738\) 42.0702 1.54863
\(739\) −20.6690 −0.760322 −0.380161 0.924920i \(-0.624131\pi\)
−0.380161 + 0.924920i \(0.624131\pi\)
\(740\) 0.904419 0.0332471
\(741\) 15.8318 0.581596
\(742\) 58.3966 2.14381
\(743\) 2.61303 0.0958629 0.0479315 0.998851i \(-0.484737\pi\)
0.0479315 + 0.998851i \(0.484737\pi\)
\(744\) −10.2817 −0.376946
\(745\) 7.43871 0.272533
\(746\) −33.3362 −1.22053
\(747\) 36.3390 1.32957
\(748\) −2.74752 −0.100459
\(749\) −51.9463 −1.89808
\(750\) 30.3628 1.10869
\(751\) −39.7386 −1.45008 −0.725041 0.688705i \(-0.758179\pi\)
−0.725041 + 0.688705i \(0.758179\pi\)
\(752\) −9.79446 −0.357167
\(753\) −51.6287 −1.88146
\(754\) −33.7810 −1.23023
\(755\) −16.1818 −0.588918
\(756\) 23.5621 0.856945
\(757\) −1.80296 −0.0655298 −0.0327649 0.999463i \(-0.510431\pi\)
−0.0327649 + 0.999463i \(0.510431\pi\)
\(758\) 5.11277 0.185704
\(759\) 84.9521 3.08357
\(760\) −1.28371 −0.0465650
\(761\) −7.51392 −0.272380 −0.136190 0.990683i \(-0.543486\pi\)
−0.136190 + 0.990683i \(0.543486\pi\)
\(762\) −33.4677 −1.21241
\(763\) −1.47195 −0.0532883
\(764\) −8.92459 −0.322880
\(765\) 3.38279 0.122305
\(766\) −21.3710 −0.772165
\(767\) −31.4986 −1.13735
\(768\) −2.83191 −0.102188
\(769\) −15.6871 −0.565691 −0.282845 0.959165i \(-0.591278\pi\)
−0.282845 + 0.959165i \(0.591278\pi\)
\(770\) 27.6771 0.997412
\(771\) −59.3836 −2.13865
\(772\) 21.0325 0.756976
\(773\) −16.5299 −0.594540 −0.297270 0.954793i \(-0.596076\pi\)
−0.297270 + 0.954793i \(0.596076\pi\)
\(774\) −38.8133 −1.39511
\(775\) −12.1703 −0.437171
\(776\) 4.32411 0.155226
\(777\) 8.21910 0.294859
\(778\) 11.0314 0.395495
\(779\) −8.38098 −0.300280
\(780\) −20.3234 −0.727696
\(781\) 15.7148 0.562319
\(782\) 3.00892 0.107599
\(783\) 34.5616 1.23513
\(784\) 9.97004 0.356073
\(785\) −21.0757 −0.752223
\(786\) −55.4938 −1.97940
\(787\) −14.3823 −0.512675 −0.256338 0.966587i \(-0.582516\pi\)
−0.256338 + 0.966587i \(0.582516\pi\)
\(788\) 16.0309 0.571077
\(789\) 36.8074 1.31038
\(790\) −13.9979 −0.498023
\(791\) 60.4583 2.14965
\(792\) −26.2720 −0.933533
\(793\) 34.2661 1.21683
\(794\) 26.1916 0.929505
\(795\) 51.5339 1.82772
\(796\) 10.3290 0.366100
\(797\) 29.9228 1.05992 0.529959 0.848023i \(-0.322207\pi\)
0.529959 + 0.848023i \(0.322207\pi\)
\(798\) −11.6660 −0.412971
\(799\) −5.14174 −0.181902
\(800\) −3.35209 −0.118514
\(801\) −37.2434 −1.31593
\(802\) 34.2743 1.21027
\(803\) 0.00951207 0.000335674 0
\(804\) −17.0972 −0.602970
\(805\) −30.3103 −1.06830
\(806\) 20.2973 0.714940
\(807\) 34.8426 1.22652
\(808\) 12.5630 0.441964
\(809\) 8.99588 0.316278 0.158139 0.987417i \(-0.449451\pi\)
0.158139 + 0.987417i \(0.449451\pi\)
\(810\) 1.46147 0.0513510
\(811\) 8.61968 0.302678 0.151339 0.988482i \(-0.451641\pi\)
0.151339 + 0.988482i \(0.451641\pi\)
\(812\) 24.8921 0.873543
\(813\) −59.2279 −2.07721
\(814\) −3.68736 −0.129242
\(815\) 17.8383 0.624849
\(816\) −1.48665 −0.0520432
\(817\) 7.73214 0.270513
\(818\) −37.4081 −1.30794
\(819\) −115.604 −4.03953
\(820\) 10.7587 0.375711
\(821\) −13.2047 −0.460847 −0.230423 0.973090i \(-0.574011\pi\)
−0.230423 + 0.973090i \(0.574011\pi\)
\(822\) −31.8907 −1.11232
\(823\) 0.0138661 0.000483342 0 0.000241671 1.00000i \(-0.499923\pi\)
0.000241671 1.00000i \(0.499923\pi\)
\(824\) −2.38747 −0.0831713
\(825\) −49.6830 −1.72974
\(826\) 23.2104 0.807592
\(827\) 38.0651 1.32365 0.661827 0.749656i \(-0.269781\pi\)
0.661827 + 0.749656i \(0.269781\pi\)
\(828\) 28.7715 0.999878
\(829\) 8.32910 0.289282 0.144641 0.989484i \(-0.453797\pi\)
0.144641 + 0.989484i \(0.453797\pi\)
\(830\) 9.29306 0.322567
\(831\) 25.3956 0.880963
\(832\) 5.59050 0.193816
\(833\) 5.23391 0.181344
\(834\) −64.9676 −2.24964
\(835\) −12.9632 −0.448611
\(836\) 5.23374 0.181013
\(837\) −20.7663 −0.717788
\(838\) −11.4922 −0.396990
\(839\) −26.5057 −0.915078 −0.457539 0.889189i \(-0.651269\pi\)
−0.457539 + 0.889189i \(0.651269\pi\)
\(840\) 14.9757 0.516711
\(841\) 7.51252 0.259053
\(842\) −27.6770 −0.953812
\(843\) 7.24169 0.249417
\(844\) −1.00000 −0.0344214
\(845\) 23.4325 0.806102
\(846\) −49.1655 −1.69035
\(847\) −67.5266 −2.32024
\(848\) −14.1758 −0.486798
\(849\) 27.6341 0.948401
\(850\) −1.75973 −0.0603581
\(851\) 4.03818 0.138427
\(852\) 8.50307 0.291310
\(853\) −33.2364 −1.13799 −0.568996 0.822340i \(-0.692668\pi\)
−0.568996 + 0.822340i \(0.692668\pi\)
\(854\) −25.2497 −0.864026
\(855\) −6.44387 −0.220376
\(856\) 12.6099 0.430999
\(857\) 22.0699 0.753895 0.376948 0.926235i \(-0.376974\pi\)
0.376948 + 0.926235i \(0.376974\pi\)
\(858\) 82.8597 2.82878
\(859\) −52.1401 −1.77900 −0.889498 0.456939i \(-0.848946\pi\)
−0.889498 + 0.456939i \(0.848946\pi\)
\(860\) −9.92582 −0.338468
\(861\) 97.7723 3.33207
\(862\) 27.9087 0.950575
\(863\) −18.5005 −0.629764 −0.314882 0.949131i \(-0.601965\pi\)
−0.314882 + 0.949131i \(0.601965\pi\)
\(864\) −5.71969 −0.194588
\(865\) 8.81745 0.299802
\(866\) 19.8795 0.675532
\(867\) 47.3621 1.60850
\(868\) −14.9564 −0.507654
\(869\) 57.0701 1.93597
\(870\) 21.9668 0.744745
\(871\) 33.7516 1.14363
\(872\) 0.357316 0.0121002
\(873\) 21.7058 0.734631
\(874\) −5.73168 −0.193877
\(875\) 44.1675 1.49314
\(876\) 0.00514686 0.000173896 0
\(877\) 44.6124 1.50645 0.753227 0.657761i \(-0.228496\pi\)
0.753227 + 0.657761i \(0.228496\pi\)
\(878\) −18.4375 −0.622234
\(879\) −62.7303 −2.11584
\(880\) −6.71860 −0.226484
\(881\) −51.9611 −1.75061 −0.875307 0.483567i \(-0.839341\pi\)
−0.875307 + 0.483567i \(0.839341\pi\)
\(882\) 50.0469 1.68517
\(883\) 2.67045 0.0898677 0.0449339 0.998990i \(-0.485692\pi\)
0.0449339 + 0.998990i \(0.485692\pi\)
\(884\) 2.93481 0.0987084
\(885\) 20.4827 0.688517
\(886\) 33.8701 1.13789
\(887\) 41.5772 1.39603 0.698014 0.716084i \(-0.254067\pi\)
0.698014 + 0.716084i \(0.254067\pi\)
\(888\) −1.99518 −0.0669540
\(889\) −48.6842 −1.63281
\(890\) −9.52435 −0.319257
\(891\) −5.95850 −0.199617
\(892\) 13.6581 0.457308
\(893\) 9.79446 0.327759
\(894\) −16.4101 −0.548835
\(895\) 3.41036 0.113996
\(896\) −4.11947 −0.137622
\(897\) −90.7430 −3.02982
\(898\) 19.6729 0.656494
\(899\) −21.9385 −0.731690
\(900\) −16.8266 −0.560886
\(901\) −7.44176 −0.247921
\(902\) −43.8639 −1.46051
\(903\) −90.2030 −3.00177
\(904\) −14.6762 −0.488124
\(905\) −26.8823 −0.893598
\(906\) 35.6978 1.18598
\(907\) −38.7421 −1.28641 −0.643205 0.765694i \(-0.722396\pi\)
−0.643205 + 0.765694i \(0.722396\pi\)
\(908\) −25.6786 −0.852175
\(909\) 63.0627 2.09166
\(910\) −29.5637 −0.980027
\(911\) −11.9422 −0.395663 −0.197832 0.980236i \(-0.563390\pi\)
−0.197832 + 0.980236i \(0.563390\pi\)
\(912\) 2.83191 0.0937740
\(913\) −37.8883 −1.25392
\(914\) −2.54516 −0.0841864
\(915\) −22.2823 −0.736631
\(916\) 23.4863 0.776009
\(917\) −80.7246 −2.66576
\(918\) −3.00263 −0.0991015
\(919\) 6.08053 0.200578 0.100289 0.994958i \(-0.468023\pi\)
0.100289 + 0.994958i \(0.468023\pi\)
\(920\) 7.35781 0.242580
\(921\) −53.4637 −1.76169
\(922\) −11.6962 −0.385193
\(923\) −16.7860 −0.552517
\(924\) −61.0567 −2.00862
\(925\) −2.36167 −0.0776512
\(926\) 7.72399 0.253826
\(927\) −11.9844 −0.393620
\(928\) −6.04256 −0.198357
\(929\) 31.7492 1.04166 0.520828 0.853661i \(-0.325623\pi\)
0.520828 + 0.853661i \(0.325623\pi\)
\(930\) −13.1987 −0.432804
\(931\) −9.97004 −0.326755
\(932\) −19.0914 −0.625361
\(933\) 14.2625 0.466933
\(934\) 10.9455 0.358148
\(935\) −3.52702 −0.115346
\(936\) 28.0628 0.917262
\(937\) 7.04364 0.230106 0.115053 0.993359i \(-0.463296\pi\)
0.115053 + 0.993359i \(0.463296\pi\)
\(938\) −24.8705 −0.812052
\(939\) −72.3084 −2.35970
\(940\) −12.5732 −0.410094
\(941\) 55.6064 1.81272 0.906359 0.422509i \(-0.138851\pi\)
0.906359 + 0.422509i \(0.138851\pi\)
\(942\) 46.4938 1.51485
\(943\) 48.0371 1.56430
\(944\) −5.63431 −0.183381
\(945\) 30.2469 0.983930
\(946\) 40.4680 1.31573
\(947\) 3.42796 0.111394 0.0556969 0.998448i \(-0.482262\pi\)
0.0556969 + 0.998448i \(0.482262\pi\)
\(948\) 30.8799 1.00293
\(949\) −0.0101605 −0.000329823 0
\(950\) 3.35209 0.108756
\(951\) −88.7852 −2.87906
\(952\) −2.16257 −0.0700894
\(953\) 29.8183 0.965910 0.482955 0.875645i \(-0.339563\pi\)
0.482955 + 0.875645i \(0.339563\pi\)
\(954\) −71.1585 −2.30384
\(955\) −11.4566 −0.370726
\(956\) 2.78325 0.0900168
\(957\) −89.5598 −2.89506
\(958\) 22.7293 0.734350
\(959\) −46.3902 −1.49802
\(960\) −3.63535 −0.117330
\(961\) −17.8183 −0.574783
\(962\) 3.93871 0.126989
\(963\) 63.2985 2.03977
\(964\) 27.2314 0.877064
\(965\) 26.9996 0.869148
\(966\) 66.8657 2.15137
\(967\) 30.8109 0.990811 0.495405 0.868662i \(-0.335020\pi\)
0.495405 + 0.868662i \(0.335020\pi\)
\(968\) 16.3921 0.526861
\(969\) 1.48665 0.0477581
\(970\) 5.55089 0.178228
\(971\) −46.9490 −1.50667 −0.753333 0.657640i \(-0.771555\pi\)
−0.753333 + 0.657640i \(0.771555\pi\)
\(972\) 13.9350 0.446965
\(973\) −94.5057 −3.02972
\(974\) 30.0182 0.961846
\(975\) 53.0697 1.69959
\(976\) 6.12935 0.196196
\(977\) 18.1762 0.581509 0.290754 0.956798i \(-0.406094\pi\)
0.290754 + 0.956798i \(0.406094\pi\)
\(978\) −39.3521 −1.25834
\(979\) 38.8312 1.24105
\(980\) 12.7986 0.408837
\(981\) 1.79363 0.0572662
\(982\) −13.5501 −0.432400
\(983\) −1.29361 −0.0412597 −0.0206298 0.999787i \(-0.506567\pi\)
−0.0206298 + 0.999787i \(0.506567\pi\)
\(984\) −23.7342 −0.756619
\(985\) 20.5790 0.655702
\(986\) −3.17212 −0.101021
\(987\) −114.262 −3.63700
\(988\) −5.59050 −0.177858
\(989\) −44.3182 −1.40924
\(990\) −33.7255 −1.07187
\(991\) 36.4309 1.15727 0.578633 0.815588i \(-0.303586\pi\)
0.578633 + 0.815588i \(0.303586\pi\)
\(992\) 3.63067 0.115274
\(993\) −47.3765 −1.50345
\(994\) 12.3691 0.392323
\(995\) 13.2594 0.420351
\(996\) −20.5009 −0.649595
\(997\) −32.6614 −1.03440 −0.517198 0.855866i \(-0.673025\pi\)
−0.517198 + 0.855866i \(0.673025\pi\)
\(998\) 8.09968 0.256391
\(999\) −4.02973 −0.127495
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 \(a_p\))