Properties

Label 8047.2.a.b.1.4
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73051 q^{2} +1.50429 q^{3} +5.45570 q^{4} -3.60561 q^{5} -4.10747 q^{6} +2.19221 q^{7} -9.43585 q^{8} -0.737125 q^{9} +O(q^{10})\) \(q-2.73051 q^{2} +1.50429 q^{3} +5.45570 q^{4} -3.60561 q^{5} -4.10747 q^{6} +2.19221 q^{7} -9.43585 q^{8} -0.737125 q^{9} +9.84515 q^{10} +3.45904 q^{11} +8.20694 q^{12} +1.00000 q^{13} -5.98585 q^{14} -5.42386 q^{15} +14.8533 q^{16} +0.177317 q^{17} +2.01273 q^{18} +2.34233 q^{19} -19.6711 q^{20} +3.29770 q^{21} -9.44496 q^{22} -6.25076 q^{23} -14.1942 q^{24} +8.00039 q^{25} -2.73051 q^{26} -5.62170 q^{27} +11.9600 q^{28} -6.36962 q^{29} +14.8099 q^{30} -0.718381 q^{31} -21.6854 q^{32} +5.20339 q^{33} -0.484166 q^{34} -7.90423 q^{35} -4.02154 q^{36} +7.99296 q^{37} -6.39577 q^{38} +1.50429 q^{39} +34.0219 q^{40} +9.73260 q^{41} -9.00443 q^{42} +4.13139 q^{43} +18.8715 q^{44} +2.65778 q^{45} +17.0678 q^{46} -2.61233 q^{47} +22.3436 q^{48} -2.19423 q^{49} -21.8452 q^{50} +0.266735 q^{51} +5.45570 q^{52} -9.07443 q^{53} +15.3501 q^{54} -12.4719 q^{55} -20.6853 q^{56} +3.52353 q^{57} +17.3923 q^{58} +4.03636 q^{59} -29.5910 q^{60} -0.809959 q^{61} +1.96155 q^{62} -1.61593 q^{63} +29.5058 q^{64} -3.60561 q^{65} -14.2079 q^{66} -13.0123 q^{67} +0.967388 q^{68} -9.40293 q^{69} +21.5826 q^{70} +10.3060 q^{71} +6.95540 q^{72} -14.3226 q^{73} -21.8249 q^{74} +12.0349 q^{75} +12.7791 q^{76} +7.58293 q^{77} -4.10747 q^{78} -6.47622 q^{79} -53.5552 q^{80} -6.24527 q^{81} -26.5750 q^{82} +5.29002 q^{83} +17.9913 q^{84} -0.639335 q^{85} -11.2808 q^{86} -9.58173 q^{87} -32.6390 q^{88} +8.97009 q^{89} -7.25711 q^{90} +2.19221 q^{91} -34.1023 q^{92} -1.08065 q^{93} +7.13300 q^{94} -8.44552 q^{95} -32.6211 q^{96} -5.00537 q^{97} +5.99138 q^{98} -2.54975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73051 −1.93076 −0.965382 0.260839i \(-0.916001\pi\)
−0.965382 + 0.260839i \(0.916001\pi\)
\(3\) 1.50429 0.868500 0.434250 0.900792i \(-0.357014\pi\)
0.434250 + 0.900792i \(0.357014\pi\)
\(4\) 5.45570 2.72785
\(5\) −3.60561 −1.61248 −0.806238 0.591591i \(-0.798500\pi\)
−0.806238 + 0.591591i \(0.798500\pi\)
\(6\) −4.10747 −1.67687
\(7\) 2.19221 0.828576 0.414288 0.910146i \(-0.364031\pi\)
0.414288 + 0.910146i \(0.364031\pi\)
\(8\) −9.43585 −3.33608
\(9\) −0.737125 −0.245708
\(10\) 9.84515 3.11331
\(11\) 3.45904 1.04294 0.521470 0.853270i \(-0.325384\pi\)
0.521470 + 0.853270i \(0.325384\pi\)
\(12\) 8.20694 2.36914
\(13\) 1.00000 0.277350
\(14\) −5.98585 −1.59979
\(15\) −5.42386 −1.40043
\(16\) 14.8533 3.71333
\(17\) 0.177317 0.0430057 0.0215028 0.999769i \(-0.493155\pi\)
0.0215028 + 0.999769i \(0.493155\pi\)
\(18\) 2.01273 0.474405
\(19\) 2.34233 0.537367 0.268684 0.963228i \(-0.413411\pi\)
0.268684 + 0.963228i \(0.413411\pi\)
\(20\) −19.6711 −4.39860
\(21\) 3.29770 0.719618
\(22\) −9.44496 −2.01367
\(23\) −6.25076 −1.30337 −0.651687 0.758488i \(-0.725939\pi\)
−0.651687 + 0.758488i \(0.725939\pi\)
\(24\) −14.1942 −2.89738
\(25\) 8.00039 1.60008
\(26\) −2.73051 −0.535498
\(27\) −5.62170 −1.08190
\(28\) 11.9600 2.26023
\(29\) −6.36962 −1.18281 −0.591405 0.806375i \(-0.701426\pi\)
−0.591405 + 0.806375i \(0.701426\pi\)
\(30\) 14.8099 2.70391
\(31\) −0.718381 −0.129025 −0.0645125 0.997917i \(-0.520549\pi\)
−0.0645125 + 0.997917i \(0.520549\pi\)
\(32\) −21.6854 −3.83348
\(33\) 5.20339 0.905793
\(34\) −0.484166 −0.0830338
\(35\) −7.90423 −1.33606
\(36\) −4.02154 −0.670256
\(37\) 7.99296 1.31403 0.657017 0.753875i \(-0.271818\pi\)
0.657017 + 0.753875i \(0.271818\pi\)
\(38\) −6.39577 −1.03753
\(39\) 1.50429 0.240878
\(40\) 34.0219 5.37934
\(41\) 9.73260 1.51998 0.759989 0.649936i \(-0.225204\pi\)
0.759989 + 0.649936i \(0.225204\pi\)
\(42\) −9.00443 −1.38941
\(43\) 4.13139 0.630031 0.315016 0.949086i \(-0.397990\pi\)
0.315016 + 0.949086i \(0.397990\pi\)
\(44\) 18.8715 2.84499
\(45\) 2.65778 0.396199
\(46\) 17.0678 2.51651
\(47\) −2.61233 −0.381047 −0.190524 0.981683i \(-0.561019\pi\)
−0.190524 + 0.981683i \(0.561019\pi\)
\(48\) 22.3436 3.22502
\(49\) −2.19423 −0.313462
\(50\) −21.8452 −3.08937
\(51\) 0.266735 0.0373504
\(52\) 5.45570 0.756570
\(53\) −9.07443 −1.24647 −0.623235 0.782035i \(-0.714182\pi\)
−0.623235 + 0.782035i \(0.714182\pi\)
\(54\) 15.3501 2.08889
\(55\) −12.4719 −1.68172
\(56\) −20.6853 −2.76419
\(57\) 3.52353 0.466703
\(58\) 17.3923 2.28373
\(59\) 4.03636 0.525489 0.262744 0.964865i \(-0.415372\pi\)
0.262744 + 0.964865i \(0.415372\pi\)
\(60\) −29.5910 −3.82018
\(61\) −0.809959 −0.103705 −0.0518523 0.998655i \(-0.516513\pi\)
−0.0518523 + 0.998655i \(0.516513\pi\)
\(62\) 1.96155 0.249117
\(63\) −1.61593 −0.203588
\(64\) 29.5058 3.68823
\(65\) −3.60561 −0.447220
\(66\) −14.2079 −1.74887
\(67\) −13.0123 −1.58970 −0.794852 0.606804i \(-0.792451\pi\)
−0.794852 + 0.606804i \(0.792451\pi\)
\(68\) 0.967388 0.117313
\(69\) −9.40293 −1.13198
\(70\) 21.5826 2.57962
\(71\) 10.3060 1.22310 0.611550 0.791206i \(-0.290547\pi\)
0.611550 + 0.791206i \(0.290547\pi\)
\(72\) 6.95540 0.819702
\(73\) −14.3226 −1.67634 −0.838169 0.545410i \(-0.816374\pi\)
−0.838169 + 0.545410i \(0.816374\pi\)
\(74\) −21.8249 −2.53709
\(75\) 12.0349 1.38967
\(76\) 12.7791 1.46586
\(77\) 7.58293 0.864155
\(78\) −4.10747 −0.465080
\(79\) −6.47622 −0.728632 −0.364316 0.931275i \(-0.618697\pi\)
−0.364316 + 0.931275i \(0.618697\pi\)
\(80\) −53.5552 −5.98765
\(81\) −6.24527 −0.693919
\(82\) −26.5750 −2.93472
\(83\) 5.29002 0.580656 0.290328 0.956927i \(-0.406236\pi\)
0.290328 + 0.956927i \(0.406236\pi\)
\(84\) 17.9913 1.96301
\(85\) −0.639335 −0.0693456
\(86\) −11.2808 −1.21644
\(87\) −9.58173 −1.02727
\(88\) −32.6390 −3.47933
\(89\) 8.97009 0.950827 0.475414 0.879762i \(-0.342298\pi\)
0.475414 + 0.879762i \(0.342298\pi\)
\(90\) −7.25711 −0.764967
\(91\) 2.19221 0.229806
\(92\) −34.1023 −3.55541
\(93\) −1.08065 −0.112058
\(94\) 7.13300 0.735713
\(95\) −8.44552 −0.866492
\(96\) −32.6211 −3.32938
\(97\) −5.00537 −0.508219 −0.254109 0.967176i \(-0.581782\pi\)
−0.254109 + 0.967176i \(0.581782\pi\)
\(98\) 5.99138 0.605221
\(99\) −2.54975 −0.256259
\(100\) 43.6478 4.36478
\(101\) 5.68847 0.566023 0.283012 0.959116i \(-0.408666\pi\)
0.283012 + 0.959116i \(0.408666\pi\)
\(102\) −0.728324 −0.0721148
\(103\) 18.8027 1.85268 0.926342 0.376683i \(-0.122935\pi\)
0.926342 + 0.376683i \(0.122935\pi\)
\(104\) −9.43585 −0.925261
\(105\) −11.8902 −1.16037
\(106\) 24.7779 2.40664
\(107\) −0.517006 −0.0499809 −0.0249905 0.999688i \(-0.507956\pi\)
−0.0249905 + 0.999688i \(0.507956\pi\)
\(108\) −30.6704 −2.95126
\(109\) −14.8345 −1.42089 −0.710445 0.703753i \(-0.751506\pi\)
−0.710445 + 0.703753i \(0.751506\pi\)
\(110\) 34.0548 3.24700
\(111\) 12.0237 1.14124
\(112\) 32.5615 3.07677
\(113\) −13.7771 −1.29604 −0.648022 0.761621i \(-0.724404\pi\)
−0.648022 + 0.761621i \(0.724404\pi\)
\(114\) −9.62106 −0.901095
\(115\) 22.5378 2.10166
\(116\) −34.7508 −3.22653
\(117\) −0.737125 −0.0681472
\(118\) −11.0213 −1.01460
\(119\) 0.388715 0.0356335
\(120\) 51.1787 4.67196
\(121\) 0.964964 0.0877240
\(122\) 2.21160 0.200229
\(123\) 14.6406 1.32010
\(124\) −3.91927 −0.351961
\(125\) −10.8182 −0.967612
\(126\) 4.41232 0.393081
\(127\) 12.8063 1.13637 0.568186 0.822900i \(-0.307646\pi\)
0.568186 + 0.822900i \(0.307646\pi\)
\(128\) −37.1951 −3.28761
\(129\) 6.21479 0.547182
\(130\) 9.84515 0.863477
\(131\) −17.8791 −1.56211 −0.781054 0.624463i \(-0.785318\pi\)
−0.781054 + 0.624463i \(0.785318\pi\)
\(132\) 28.3881 2.47087
\(133\) 5.13487 0.445250
\(134\) 35.5302 3.06934
\(135\) 20.2696 1.74453
\(136\) −1.67314 −0.143470
\(137\) −6.40781 −0.547456 −0.273728 0.961807i \(-0.588257\pi\)
−0.273728 + 0.961807i \(0.588257\pi\)
\(138\) 25.6748 2.18559
\(139\) −16.4046 −1.39142 −0.695712 0.718321i \(-0.744911\pi\)
−0.695712 + 0.718321i \(0.744911\pi\)
\(140\) −43.1231 −3.64457
\(141\) −3.92969 −0.330940
\(142\) −28.1407 −2.36152
\(143\) 3.45904 0.289260
\(144\) −10.9487 −0.912395
\(145\) 22.9663 1.90725
\(146\) 39.1082 3.23662
\(147\) −3.30075 −0.272241
\(148\) 43.6072 3.58449
\(149\) 7.34029 0.601340 0.300670 0.953728i \(-0.402790\pi\)
0.300670 + 0.953728i \(0.402790\pi\)
\(150\) −32.8614 −2.68312
\(151\) 0.130754 0.0106406 0.00532032 0.999986i \(-0.498306\pi\)
0.00532032 + 0.999986i \(0.498306\pi\)
\(152\) −22.1019 −1.79270
\(153\) −0.130705 −0.0105668
\(154\) −20.7053 −1.66848
\(155\) 2.59020 0.208050
\(156\) 8.20694 0.657081
\(157\) 0.163004 0.0130091 0.00650457 0.999979i \(-0.497930\pi\)
0.00650457 + 0.999979i \(0.497930\pi\)
\(158\) 17.6834 1.40682
\(159\) −13.6505 −1.08256
\(160\) 78.1892 6.18140
\(161\) −13.7030 −1.07994
\(162\) 17.0528 1.33979
\(163\) 6.00292 0.470185 0.235093 0.971973i \(-0.424461\pi\)
0.235093 + 0.971973i \(0.424461\pi\)
\(164\) 53.0982 4.14627
\(165\) −18.7614 −1.46057
\(166\) −14.4445 −1.12111
\(167\) −1.03941 −0.0804318 −0.0402159 0.999191i \(-0.512805\pi\)
−0.0402159 + 0.999191i \(0.512805\pi\)
\(168\) −31.1166 −2.40070
\(169\) 1.00000 0.0769231
\(170\) 1.74571 0.133890
\(171\) −1.72659 −0.132036
\(172\) 22.5397 1.71863
\(173\) −2.31995 −0.176383 −0.0881914 0.996104i \(-0.528109\pi\)
−0.0881914 + 0.996104i \(0.528109\pi\)
\(174\) 26.1630 1.98342
\(175\) 17.5385 1.32579
\(176\) 51.3782 3.87278
\(177\) 6.07183 0.456387
\(178\) −24.4929 −1.83582
\(179\) 12.6170 0.943037 0.471519 0.881856i \(-0.343706\pi\)
0.471519 + 0.881856i \(0.343706\pi\)
\(180\) 14.5001 1.08077
\(181\) 24.9892 1.85743 0.928716 0.370793i \(-0.120914\pi\)
0.928716 + 0.370793i \(0.120914\pi\)
\(182\) −5.98585 −0.443701
\(183\) −1.21841 −0.0900675
\(184\) 58.9813 4.34816
\(185\) −28.8195 −2.11885
\(186\) 2.95073 0.216358
\(187\) 0.613346 0.0448523
\(188\) −14.2521 −1.03944
\(189\) −12.3239 −0.896434
\(190\) 23.0606 1.67299
\(191\) −3.35168 −0.242519 −0.121259 0.992621i \(-0.538693\pi\)
−0.121259 + 0.992621i \(0.538693\pi\)
\(192\) 44.3852 3.20322
\(193\) 10.8865 0.783625 0.391813 0.920045i \(-0.371848\pi\)
0.391813 + 0.920045i \(0.371848\pi\)
\(194\) 13.6672 0.981250
\(195\) −5.42386 −0.388411
\(196\) −11.9711 −0.855077
\(197\) −10.7451 −0.765556 −0.382778 0.923840i \(-0.625033\pi\)
−0.382778 + 0.923840i \(0.625033\pi\)
\(198\) 6.96212 0.494776
\(199\) −17.1247 −1.21394 −0.606970 0.794725i \(-0.707615\pi\)
−0.606970 + 0.794725i \(0.707615\pi\)
\(200\) −75.4905 −5.33798
\(201\) −19.5742 −1.38066
\(202\) −15.5324 −1.09286
\(203\) −13.9635 −0.980047
\(204\) 1.45523 0.101886
\(205\) −35.0919 −2.45093
\(206\) −51.3410 −3.57710
\(207\) 4.60759 0.320250
\(208\) 14.8533 1.02989
\(209\) 8.10222 0.560442
\(210\) 32.4664 2.24039
\(211\) 7.75204 0.533673 0.266836 0.963742i \(-0.414022\pi\)
0.266836 + 0.963742i \(0.414022\pi\)
\(212\) −49.5074 −3.40018
\(213\) 15.5032 1.06226
\(214\) 1.41169 0.0965014
\(215\) −14.8962 −1.01591
\(216\) 53.0455 3.60929
\(217\) −1.57484 −0.106907
\(218\) 40.5059 2.74340
\(219\) −21.5453 −1.45590
\(220\) −68.0432 −4.58747
\(221\) 0.177317 0.0119276
\(222\) −32.8309 −2.20346
\(223\) 6.86594 0.459778 0.229889 0.973217i \(-0.426164\pi\)
0.229889 + 0.973217i \(0.426164\pi\)
\(224\) −47.5390 −3.17633
\(225\) −5.89729 −0.393153
\(226\) 37.6187 2.50236
\(227\) −18.3671 −1.21906 −0.609532 0.792761i \(-0.708643\pi\)
−0.609532 + 0.792761i \(0.708643\pi\)
\(228\) 19.2234 1.27310
\(229\) 22.0981 1.46029 0.730143 0.683295i \(-0.239454\pi\)
0.730143 + 0.683295i \(0.239454\pi\)
\(230\) −61.5397 −4.05781
\(231\) 11.4069 0.750518
\(232\) 60.1028 3.94594
\(233\) 0.429269 0.0281223 0.0140612 0.999901i \(-0.495524\pi\)
0.0140612 + 0.999901i \(0.495524\pi\)
\(234\) 2.01273 0.131576
\(235\) 9.41903 0.614430
\(236\) 22.0212 1.43346
\(237\) −9.74209 −0.632817
\(238\) −1.06139 −0.0687998
\(239\) 27.2498 1.76265 0.881323 0.472515i \(-0.156654\pi\)
0.881323 + 0.472515i \(0.156654\pi\)
\(240\) −80.5622 −5.20027
\(241\) −25.1285 −1.61867 −0.809335 0.587347i \(-0.800172\pi\)
−0.809335 + 0.587347i \(0.800172\pi\)
\(242\) −2.63485 −0.169374
\(243\) 7.47044 0.479229
\(244\) −4.41890 −0.282891
\(245\) 7.91153 0.505449
\(246\) −39.9764 −2.54880
\(247\) 2.34233 0.149039
\(248\) 6.77853 0.430437
\(249\) 7.95771 0.504299
\(250\) 29.5393 1.86823
\(251\) 5.41024 0.341491 0.170746 0.985315i \(-0.445382\pi\)
0.170746 + 0.985315i \(0.445382\pi\)
\(252\) −8.81604 −0.555358
\(253\) −21.6216 −1.35934
\(254\) −34.9677 −2.19407
\(255\) −0.961742 −0.0602266
\(256\) 42.5501 2.65938
\(257\) −28.3502 −1.76844 −0.884218 0.467075i \(-0.845308\pi\)
−0.884218 + 0.467075i \(0.845308\pi\)
\(258\) −16.9696 −1.05648
\(259\) 17.5222 1.08878
\(260\) −19.6711 −1.21995
\(261\) 4.69521 0.290626
\(262\) 48.8193 3.01606
\(263\) 14.8441 0.915325 0.457663 0.889126i \(-0.348687\pi\)
0.457663 + 0.889126i \(0.348687\pi\)
\(264\) −49.0984 −3.02179
\(265\) 32.7188 2.00990
\(266\) −14.0208 −0.859673
\(267\) 13.4936 0.825793
\(268\) −70.9912 −4.33648
\(269\) 11.2264 0.684484 0.342242 0.939612i \(-0.388814\pi\)
0.342242 + 0.939612i \(0.388814\pi\)
\(270\) −55.3465 −3.36828
\(271\) −4.31255 −0.261969 −0.130984 0.991384i \(-0.541814\pi\)
−0.130984 + 0.991384i \(0.541814\pi\)
\(272\) 2.63374 0.159694
\(273\) 3.29770 0.199586
\(274\) 17.4966 1.05701
\(275\) 27.6737 1.66879
\(276\) −51.2996 −3.08787
\(277\) −12.7004 −0.763095 −0.381547 0.924349i \(-0.624609\pi\)
−0.381547 + 0.924349i \(0.624609\pi\)
\(278\) 44.7931 2.68651
\(279\) 0.529537 0.0317025
\(280\) 74.5831 4.45719
\(281\) −22.8079 −1.36060 −0.680302 0.732932i \(-0.738151\pi\)
−0.680302 + 0.732932i \(0.738151\pi\)
\(282\) 10.7301 0.638966
\(283\) −11.7465 −0.698258 −0.349129 0.937075i \(-0.613522\pi\)
−0.349129 + 0.937075i \(0.613522\pi\)
\(284\) 56.2266 3.33643
\(285\) −12.7045 −0.752548
\(286\) −9.44496 −0.558492
\(287\) 21.3359 1.25942
\(288\) 15.9849 0.941919
\(289\) −16.9686 −0.998151
\(290\) −62.7099 −3.68245
\(291\) −7.52951 −0.441388
\(292\) −78.1401 −4.57280
\(293\) 4.23620 0.247481 0.123741 0.992315i \(-0.460511\pi\)
0.123741 + 0.992315i \(0.460511\pi\)
\(294\) 9.01275 0.525634
\(295\) −14.5535 −0.847338
\(296\) −75.4204 −4.38372
\(297\) −19.4457 −1.12835
\(298\) −20.0428 −1.16105
\(299\) −6.25076 −0.361491
\(300\) 65.6587 3.79081
\(301\) 9.05686 0.522029
\(302\) −0.357027 −0.0205446
\(303\) 8.55708 0.491591
\(304\) 34.7913 1.99542
\(305\) 2.92039 0.167221
\(306\) 0.356891 0.0204021
\(307\) −13.7975 −0.787463 −0.393731 0.919226i \(-0.628816\pi\)
−0.393731 + 0.919226i \(0.628816\pi\)
\(308\) 41.3702 2.35729
\(309\) 28.2846 1.60906
\(310\) −7.07257 −0.401695
\(311\) 2.50210 0.141881 0.0709404 0.997481i \(-0.477400\pi\)
0.0709404 + 0.997481i \(0.477400\pi\)
\(312\) −14.1942 −0.803589
\(313\) 4.99839 0.282526 0.141263 0.989972i \(-0.454884\pi\)
0.141263 + 0.989972i \(0.454884\pi\)
\(314\) −0.445085 −0.0251176
\(315\) 5.82641 0.328281
\(316\) −35.3324 −1.98760
\(317\) −17.6102 −0.989087 −0.494543 0.869153i \(-0.664665\pi\)
−0.494543 + 0.869153i \(0.664665\pi\)
\(318\) 37.2730 2.09017
\(319\) −22.0328 −1.23360
\(320\) −106.386 −5.94718
\(321\) −0.777725 −0.0434084
\(322\) 37.4161 2.08512
\(323\) 0.415335 0.0231098
\(324\) −34.0724 −1.89291
\(325\) 8.00039 0.443782
\(326\) −16.3911 −0.907817
\(327\) −22.3154 −1.23404
\(328\) −91.8354 −5.07076
\(329\) −5.72676 −0.315727
\(330\) 51.2281 2.82002
\(331\) −33.4265 −1.83729 −0.918644 0.395086i \(-0.870715\pi\)
−0.918644 + 0.395086i \(0.870715\pi\)
\(332\) 28.8608 1.58394
\(333\) −5.89181 −0.322869
\(334\) 2.83812 0.155295
\(335\) 46.9171 2.56336
\(336\) 48.9818 2.67218
\(337\) −27.3565 −1.49020 −0.745102 0.666951i \(-0.767599\pi\)
−0.745102 + 0.666951i \(0.767599\pi\)
\(338\) −2.73051 −0.148520
\(339\) −20.7248 −1.12561
\(340\) −3.48802 −0.189165
\(341\) −2.48491 −0.134565
\(342\) 4.71448 0.254930
\(343\) −20.1557 −1.08830
\(344\) −38.9832 −2.10183
\(345\) 33.9033 1.82529
\(346\) 6.33467 0.340554
\(347\) −3.23651 −0.173745 −0.0868725 0.996219i \(-0.527687\pi\)
−0.0868725 + 0.996219i \(0.527687\pi\)
\(348\) −52.2751 −2.80224
\(349\) −5.88567 −0.315052 −0.157526 0.987515i \(-0.550352\pi\)
−0.157526 + 0.987515i \(0.550352\pi\)
\(350\) −47.8891 −2.55978
\(351\) −5.62170 −0.300064
\(352\) −75.0109 −3.99809
\(353\) −5.87941 −0.312930 −0.156465 0.987684i \(-0.550010\pi\)
−0.156465 + 0.987684i \(0.550010\pi\)
\(354\) −16.5792 −0.881176
\(355\) −37.1594 −1.97222
\(356\) 48.9381 2.59372
\(357\) 0.584739 0.0309476
\(358\) −34.4508 −1.82078
\(359\) 20.2716 1.06989 0.534946 0.844886i \(-0.320332\pi\)
0.534946 + 0.844886i \(0.320332\pi\)
\(360\) −25.0784 −1.32175
\(361\) −13.5135 −0.711236
\(362\) −68.2333 −3.58626
\(363\) 1.45158 0.0761883
\(364\) 11.9600 0.626876
\(365\) 51.6418 2.70306
\(366\) 3.32689 0.173899
\(367\) −7.08194 −0.369674 −0.184837 0.982769i \(-0.559176\pi\)
−0.184837 + 0.982769i \(0.559176\pi\)
\(368\) −92.8445 −4.83985
\(369\) −7.17415 −0.373471
\(370\) 78.6919 4.09100
\(371\) −19.8930 −1.03279
\(372\) −5.89571 −0.305678
\(373\) 3.30909 0.171338 0.0856691 0.996324i \(-0.472697\pi\)
0.0856691 + 0.996324i \(0.472697\pi\)
\(374\) −1.67475 −0.0865993
\(375\) −16.2737 −0.840370
\(376\) 24.6495 1.27120
\(377\) −6.36962 −0.328052
\(378\) 33.6507 1.73080
\(379\) 31.5820 1.62226 0.811129 0.584868i \(-0.198854\pi\)
0.811129 + 0.584868i \(0.198854\pi\)
\(380\) −46.0763 −2.36366
\(381\) 19.2643 0.986938
\(382\) 9.15180 0.468247
\(383\) 12.0317 0.614792 0.307396 0.951582i \(-0.400542\pi\)
0.307396 + 0.951582i \(0.400542\pi\)
\(384\) −55.9521 −2.85529
\(385\) −27.3411 −1.39343
\(386\) −29.7256 −1.51300
\(387\) −3.04535 −0.154804
\(388\) −27.3078 −1.38635
\(389\) 25.1996 1.27767 0.638834 0.769344i \(-0.279417\pi\)
0.638834 + 0.769344i \(0.279417\pi\)
\(390\) 14.8099 0.749930
\(391\) −1.10837 −0.0560525
\(392\) 20.7044 1.04573
\(393\) −26.8953 −1.35669
\(394\) 29.3396 1.47811
\(395\) 23.3507 1.17490
\(396\) −13.9107 −0.699037
\(397\) 21.2739 1.06771 0.533854 0.845576i \(-0.320743\pi\)
0.533854 + 0.845576i \(0.320743\pi\)
\(398\) 46.7593 2.34383
\(399\) 7.72431 0.386699
\(400\) 118.832 5.94161
\(401\) 18.1041 0.904076 0.452038 0.891999i \(-0.350697\pi\)
0.452038 + 0.891999i \(0.350697\pi\)
\(402\) 53.4476 2.66572
\(403\) −0.718381 −0.0357851
\(404\) 31.0346 1.54403
\(405\) 22.5180 1.11893
\(406\) 38.1276 1.89224
\(407\) 27.6480 1.37046
\(408\) −2.51687 −0.124604
\(409\) −11.1956 −0.553586 −0.276793 0.960930i \(-0.589272\pi\)
−0.276793 + 0.960930i \(0.589272\pi\)
\(410\) 95.8190 4.73216
\(411\) −9.63917 −0.475465
\(412\) 102.582 5.05385
\(413\) 8.84853 0.435408
\(414\) −12.5811 −0.618327
\(415\) −19.0737 −0.936293
\(416\) −21.6854 −1.06322
\(417\) −24.6773 −1.20845
\(418\) −22.1232 −1.08208
\(419\) −21.3250 −1.04179 −0.520897 0.853619i \(-0.674403\pi\)
−0.520897 + 0.853619i \(0.674403\pi\)
\(420\) −64.8695 −3.16531
\(421\) −22.5343 −1.09825 −0.549126 0.835739i \(-0.685039\pi\)
−0.549126 + 0.835739i \(0.685039\pi\)
\(422\) −21.1671 −1.03040
\(423\) 1.92561 0.0936265
\(424\) 85.6250 4.15832
\(425\) 1.41860 0.0688124
\(426\) −42.3317 −2.05098
\(427\) −1.77560 −0.0859272
\(428\) −2.82063 −0.136341
\(429\) 5.20339 0.251222
\(430\) 40.6742 1.96148
\(431\) −18.0048 −0.867261 −0.433630 0.901091i \(-0.642768\pi\)
−0.433630 + 0.901091i \(0.642768\pi\)
\(432\) −83.5009 −4.01744
\(433\) 19.3407 0.929456 0.464728 0.885453i \(-0.346152\pi\)
0.464728 + 0.885453i \(0.346152\pi\)
\(434\) 4.30012 0.206412
\(435\) 34.5479 1.65645
\(436\) −80.9328 −3.87598
\(437\) −14.6414 −0.700391
\(438\) 58.8299 2.81100
\(439\) −33.9153 −1.61869 −0.809344 0.587335i \(-0.800177\pi\)
−0.809344 + 0.587335i \(0.800177\pi\)
\(440\) 117.683 5.61033
\(441\) 1.61742 0.0770202
\(442\) −0.484166 −0.0230294
\(443\) 3.94013 0.187201 0.0936005 0.995610i \(-0.470162\pi\)
0.0936005 + 0.995610i \(0.470162\pi\)
\(444\) 65.5977 3.11313
\(445\) −32.3426 −1.53319
\(446\) −18.7476 −0.887722
\(447\) 11.0419 0.522264
\(448\) 64.6828 3.05598
\(449\) 5.74186 0.270975 0.135488 0.990779i \(-0.456740\pi\)
0.135488 + 0.990779i \(0.456740\pi\)
\(450\) 16.1026 0.759085
\(451\) 33.6655 1.58525
\(452\) −75.1640 −3.53542
\(453\) 0.196692 0.00924140
\(454\) 50.1515 2.35373
\(455\) −7.90423 −0.370556
\(456\) −33.2475 −1.55696
\(457\) 10.9875 0.513972 0.256986 0.966415i \(-0.417271\pi\)
0.256986 + 0.966415i \(0.417271\pi\)
\(458\) −60.3392 −2.81947
\(459\) −0.996823 −0.0465277
\(460\) 122.960 5.73302
\(461\) 8.55511 0.398451 0.199226 0.979954i \(-0.436157\pi\)
0.199226 + 0.979954i \(0.436157\pi\)
\(462\) −31.1467 −1.44907
\(463\) 3.42436 0.159143 0.0795717 0.996829i \(-0.474645\pi\)
0.0795717 + 0.996829i \(0.474645\pi\)
\(464\) −94.6099 −4.39216
\(465\) 3.89640 0.180691
\(466\) −1.17212 −0.0542976
\(467\) −21.3397 −0.987483 −0.493742 0.869609i \(-0.664371\pi\)
−0.493742 + 0.869609i \(0.664371\pi\)
\(468\) −4.02154 −0.185896
\(469\) −28.5256 −1.31719
\(470\) −25.7188 −1.18632
\(471\) 0.245205 0.0112984
\(472\) −38.0865 −1.75307
\(473\) 14.2907 0.657085
\(474\) 26.6009 1.22182
\(475\) 18.7396 0.859830
\(476\) 2.12071 0.0972028
\(477\) 6.68899 0.306268
\(478\) −74.4060 −3.40325
\(479\) 6.83265 0.312192 0.156096 0.987742i \(-0.450109\pi\)
0.156096 + 0.987742i \(0.450109\pi\)
\(480\) 117.619 5.36854
\(481\) 7.99296 0.364448
\(482\) 68.6138 3.12527
\(483\) −20.6132 −0.937932
\(484\) 5.26456 0.239298
\(485\) 18.0474 0.819490
\(486\) −20.3981 −0.925278
\(487\) −5.38172 −0.243869 −0.121935 0.992538i \(-0.538910\pi\)
−0.121935 + 0.992538i \(0.538910\pi\)
\(488\) 7.64265 0.345967
\(489\) 9.03011 0.408356
\(490\) −21.6026 −0.975904
\(491\) 21.4758 0.969189 0.484595 0.874739i \(-0.338967\pi\)
0.484595 + 0.874739i \(0.338967\pi\)
\(492\) 79.8749 3.60104
\(493\) −1.12944 −0.0508675
\(494\) −6.39577 −0.287759
\(495\) 9.19338 0.413212
\(496\) −10.6703 −0.479112
\(497\) 22.5929 1.01343
\(498\) −21.7286 −0.973683
\(499\) 24.0262 1.07556 0.537781 0.843085i \(-0.319263\pi\)
0.537781 + 0.843085i \(0.319263\pi\)
\(500\) −59.0210 −2.63950
\(501\) −1.56357 −0.0698550
\(502\) −14.7727 −0.659339
\(503\) 36.0506 1.60742 0.803709 0.595023i \(-0.202857\pi\)
0.803709 + 0.595023i \(0.202857\pi\)
\(504\) 15.2477 0.679185
\(505\) −20.5104 −0.912699
\(506\) 59.0382 2.62457
\(507\) 1.50429 0.0668077
\(508\) 69.8671 3.09985
\(509\) −36.5216 −1.61879 −0.809395 0.587264i \(-0.800205\pi\)
−0.809395 + 0.587264i \(0.800205\pi\)
\(510\) 2.62605 0.116283
\(511\) −31.3982 −1.38897
\(512\) −41.7935 −1.84703
\(513\) −13.1679 −0.581376
\(514\) 77.4106 3.41443
\(515\) −67.7951 −2.98741
\(516\) 33.9061 1.49263
\(517\) −9.03615 −0.397410
\(518\) −47.8447 −2.10217
\(519\) −3.48987 −0.153188
\(520\) 34.0219 1.49196
\(521\) −32.1039 −1.40650 −0.703250 0.710943i \(-0.748268\pi\)
−0.703250 + 0.710943i \(0.748268\pi\)
\(522\) −12.8203 −0.561131
\(523\) 11.1476 0.487451 0.243726 0.969844i \(-0.421630\pi\)
0.243726 + 0.969844i \(0.421630\pi\)
\(524\) −97.5434 −4.26120
\(525\) 26.3829 1.15145
\(526\) −40.5320 −1.76728
\(527\) −0.127381 −0.00554881
\(528\) 77.2875 3.36350
\(529\) 16.0721 0.698785
\(530\) −89.3392 −3.88065
\(531\) −2.97530 −0.129117
\(532\) 28.0143 1.21458
\(533\) 9.73260 0.421566
\(534\) −36.8444 −1.59441
\(535\) 1.86412 0.0805930
\(536\) 122.782 5.30337
\(537\) 18.9795 0.819027
\(538\) −30.6538 −1.32158
\(539\) −7.58994 −0.326922
\(540\) 110.585 4.75883
\(541\) 1.14779 0.0493475 0.0246738 0.999696i \(-0.492145\pi\)
0.0246738 + 0.999696i \(0.492145\pi\)
\(542\) 11.7755 0.505800
\(543\) 37.5909 1.61318
\(544\) −3.84520 −0.164861
\(545\) 53.4874 2.29115
\(546\) −9.00443 −0.385354
\(547\) −41.5609 −1.77702 −0.888508 0.458862i \(-0.848257\pi\)
−0.888508 + 0.458862i \(0.848257\pi\)
\(548\) −34.9591 −1.49338
\(549\) 0.597041 0.0254811
\(550\) −75.5634 −3.22203
\(551\) −14.9198 −0.635603
\(552\) 88.7247 3.77637
\(553\) −14.1972 −0.603727
\(554\) 34.6787 1.47336
\(555\) −43.3527 −1.84022
\(556\) −89.4989 −3.79560
\(557\) 19.7512 0.836883 0.418442 0.908244i \(-0.362576\pi\)
0.418442 + 0.908244i \(0.362576\pi\)
\(558\) −1.44591 −0.0612101
\(559\) 4.13139 0.174739
\(560\) −117.404 −4.96122
\(561\) 0.922648 0.0389542
\(562\) 62.2772 2.62701
\(563\) −34.4356 −1.45129 −0.725644 0.688070i \(-0.758458\pi\)
−0.725644 + 0.688070i \(0.758458\pi\)
\(564\) −21.4392 −0.902754
\(565\) 49.6749 2.08984
\(566\) 32.0740 1.34817
\(567\) −13.6909 −0.574965
\(568\) −97.2460 −4.08035
\(569\) −33.5770 −1.40762 −0.703811 0.710387i \(-0.748520\pi\)
−0.703811 + 0.710387i \(0.748520\pi\)
\(570\) 34.6897 1.45299
\(571\) −19.1520 −0.801486 −0.400743 0.916191i \(-0.631248\pi\)
−0.400743 + 0.916191i \(0.631248\pi\)
\(572\) 18.8715 0.789057
\(573\) −5.04188 −0.210627
\(574\) −58.2579 −2.43164
\(575\) −50.0086 −2.08550
\(576\) −21.7495 −0.906228
\(577\) −27.1311 −1.12948 −0.564741 0.825268i \(-0.691024\pi\)
−0.564741 + 0.825268i \(0.691024\pi\)
\(578\) 46.3329 1.92719
\(579\) 16.3764 0.680578
\(580\) 125.298 5.20270
\(581\) 11.5968 0.481117
\(582\) 20.5594 0.852216
\(583\) −31.3888 −1.29999
\(584\) 135.146 5.59239
\(585\) 2.65778 0.109886
\(586\) −11.5670 −0.477828
\(587\) −35.7984 −1.47756 −0.738780 0.673947i \(-0.764598\pi\)
−0.738780 + 0.673947i \(0.764598\pi\)
\(588\) −18.0079 −0.742634
\(589\) −1.68269 −0.0693338
\(590\) 39.7386 1.63601
\(591\) −16.1637 −0.664885
\(592\) 118.722 4.87944
\(593\) 25.4766 1.04620 0.523100 0.852271i \(-0.324775\pi\)
0.523100 + 0.852271i \(0.324775\pi\)
\(594\) 53.0968 2.17859
\(595\) −1.40155 −0.0574581
\(596\) 40.0465 1.64037
\(597\) −25.7605 −1.05431
\(598\) 17.0678 0.697954
\(599\) 40.4181 1.65144 0.825720 0.564080i \(-0.190769\pi\)
0.825720 + 0.564080i \(0.190769\pi\)
\(600\) −113.559 −4.63604
\(601\) 40.4371 1.64946 0.824732 0.565524i \(-0.191326\pi\)
0.824732 + 0.565524i \(0.191326\pi\)
\(602\) −24.7299 −1.00792
\(603\) 9.59168 0.390603
\(604\) 0.713358 0.0290261
\(605\) −3.47928 −0.141453
\(606\) −23.3652 −0.949147
\(607\) 4.20442 0.170652 0.0853262 0.996353i \(-0.472807\pi\)
0.0853262 + 0.996353i \(0.472807\pi\)
\(608\) −50.7945 −2.05999
\(609\) −21.0051 −0.851171
\(610\) −7.97418 −0.322865
\(611\) −2.61233 −0.105684
\(612\) −0.713086 −0.0288248
\(613\) 1.09015 0.0440309 0.0220155 0.999758i \(-0.492992\pi\)
0.0220155 + 0.999758i \(0.492992\pi\)
\(614\) 37.6742 1.52041
\(615\) −52.7883 −2.12863
\(616\) −71.5514 −2.88289
\(617\) 4.16647 0.167736 0.0838679 0.996477i \(-0.473273\pi\)
0.0838679 + 0.996477i \(0.473273\pi\)
\(618\) −77.2315 −3.10671
\(619\) 1.00000 0.0401934
\(620\) 14.1314 0.567529
\(621\) 35.1399 1.41012
\(622\) −6.83201 −0.273939
\(623\) 19.6643 0.787833
\(624\) 22.3436 0.894460
\(625\) −0.995698 −0.0398279
\(626\) −13.6482 −0.545490
\(627\) 12.1880 0.486744
\(628\) 0.889303 0.0354870
\(629\) 1.41729 0.0565109
\(630\) −15.9091 −0.633833
\(631\) −28.2352 −1.12403 −0.562014 0.827128i \(-0.689973\pi\)
−0.562014 + 0.827128i \(0.689973\pi\)
\(632\) 61.1087 2.43077
\(633\) 11.6613 0.463494
\(634\) 48.0849 1.90969
\(635\) −46.1743 −1.83237
\(636\) −74.4733 −2.95306
\(637\) −2.19423 −0.0869386
\(638\) 60.1608 2.38179
\(639\) −7.59682 −0.300526
\(640\) 134.111 5.30120
\(641\) −36.2825 −1.43307 −0.716537 0.697549i \(-0.754274\pi\)
−0.716537 + 0.697549i \(0.754274\pi\)
\(642\) 2.12359 0.0838114
\(643\) −11.6968 −0.461278 −0.230639 0.973039i \(-0.574082\pi\)
−0.230639 + 0.973039i \(0.574082\pi\)
\(644\) −74.7593 −2.94593
\(645\) −22.4081 −0.882318
\(646\) −1.13408 −0.0446197
\(647\) −33.9983 −1.33661 −0.668305 0.743887i \(-0.732980\pi\)
−0.668305 + 0.743887i \(0.732980\pi\)
\(648\) 58.9294 2.31497
\(649\) 13.9619 0.548054
\(650\) −21.8452 −0.856838
\(651\) −2.36901 −0.0928487
\(652\) 32.7502 1.28260
\(653\) 25.4578 0.996240 0.498120 0.867108i \(-0.334024\pi\)
0.498120 + 0.867108i \(0.334024\pi\)
\(654\) 60.9324 2.38264
\(655\) 64.4652 2.51886
\(656\) 144.561 5.64417
\(657\) 10.5576 0.411890
\(658\) 15.6370 0.609594
\(659\) −49.2889 −1.92002 −0.960012 0.279959i \(-0.909679\pi\)
−0.960012 + 0.279959i \(0.909679\pi\)
\(660\) −102.356 −3.98422
\(661\) −11.1707 −0.434491 −0.217246 0.976117i \(-0.569707\pi\)
−0.217246 + 0.976117i \(0.569707\pi\)
\(662\) 91.2716 3.54737
\(663\) 0.266735 0.0103591
\(664\) −49.9159 −1.93711
\(665\) −18.5143 −0.717955
\(666\) 16.0877 0.623385
\(667\) 39.8150 1.54164
\(668\) −5.67070 −0.219406
\(669\) 10.3283 0.399317
\(670\) −128.108 −4.94924
\(671\) −2.80168 −0.108158
\(672\) −71.5122 −2.75864
\(673\) 1.64252 0.0633145 0.0316573 0.999499i \(-0.489921\pi\)
0.0316573 + 0.999499i \(0.489921\pi\)
\(674\) 74.6973 2.87723
\(675\) −44.9758 −1.73112
\(676\) 5.45570 0.209835
\(677\) 4.72021 0.181413 0.0907063 0.995878i \(-0.471088\pi\)
0.0907063 + 0.995878i \(0.471088\pi\)
\(678\) 56.5892 2.17330
\(679\) −10.9728 −0.421098
\(680\) 6.03267 0.231342
\(681\) −27.6293 −1.05876
\(682\) 6.78508 0.259814
\(683\) −23.0772 −0.883026 −0.441513 0.897255i \(-0.645558\pi\)
−0.441513 + 0.897255i \(0.645558\pi\)
\(684\) −9.41977 −0.360174
\(685\) 23.1040 0.882759
\(686\) 55.0353 2.10126
\(687\) 33.2419 1.26826
\(688\) 61.3648 2.33951
\(689\) −9.07443 −0.345708
\(690\) −92.5733 −3.52421
\(691\) 6.34271 0.241288 0.120644 0.992696i \(-0.461504\pi\)
0.120644 + 0.992696i \(0.461504\pi\)
\(692\) −12.6570 −0.481146
\(693\) −5.58957 −0.212330
\(694\) 8.83733 0.335461
\(695\) 59.1487 2.24364
\(696\) 90.4117 3.42705
\(697\) 1.72575 0.0653676
\(698\) 16.0709 0.608292
\(699\) 0.645743 0.0244242
\(700\) 95.6849 3.61655
\(701\) −6.86129 −0.259147 −0.129574 0.991570i \(-0.541361\pi\)
−0.129574 + 0.991570i \(0.541361\pi\)
\(702\) 15.3501 0.579354
\(703\) 18.7222 0.706119
\(704\) 102.062 3.84660
\(705\) 14.1689 0.533632
\(706\) 16.0538 0.604193
\(707\) 12.4703 0.468993
\(708\) 33.1261 1.24496
\(709\) −34.8672 −1.30946 −0.654732 0.755861i \(-0.727218\pi\)
−0.654732 + 0.755861i \(0.727218\pi\)
\(710\) 101.464 3.80789
\(711\) 4.77379 0.179031
\(712\) −84.6404 −3.17203
\(713\) 4.49043 0.168168
\(714\) −1.59664 −0.0597526
\(715\) −12.4719 −0.466424
\(716\) 68.8345 2.57247
\(717\) 40.9915 1.53086
\(718\) −55.3518 −2.06571
\(719\) −18.9910 −0.708246 −0.354123 0.935199i \(-0.615221\pi\)
−0.354123 + 0.935199i \(0.615221\pi\)
\(720\) 39.4768 1.47122
\(721\) 41.2194 1.53509
\(722\) 36.8988 1.37323
\(723\) −37.8005 −1.40581
\(724\) 136.334 5.06680
\(725\) −50.9595 −1.89259
\(726\) −3.96356 −0.147102
\(727\) −17.4529 −0.647294 −0.323647 0.946178i \(-0.604909\pi\)
−0.323647 + 0.946178i \(0.604909\pi\)
\(728\) −20.6853 −0.766649
\(729\) 29.9735 1.11013
\(730\) −141.009 −5.21896
\(731\) 0.732566 0.0270949
\(732\) −6.64729 −0.245691
\(733\) 14.3534 0.530154 0.265077 0.964227i \(-0.414603\pi\)
0.265077 + 0.964227i \(0.414603\pi\)
\(734\) 19.3373 0.713754
\(735\) 11.9012 0.438983
\(736\) 135.551 4.99646
\(737\) −45.0100 −1.65797
\(738\) 19.5891 0.721085
\(739\) −43.0377 −1.58317 −0.791585 0.611060i \(-0.790744\pi\)
−0.791585 + 0.611060i \(0.790744\pi\)
\(740\) −157.230 −5.77991
\(741\) 3.52353 0.129440
\(742\) 54.3182 1.99408
\(743\) −34.4552 −1.26404 −0.632019 0.774953i \(-0.717774\pi\)
−0.632019 + 0.774953i \(0.717774\pi\)
\(744\) 10.1968 0.373835
\(745\) −26.4662 −0.969647
\(746\) −9.03551 −0.330814
\(747\) −3.89941 −0.142672
\(748\) 3.34624 0.122351
\(749\) −1.13338 −0.0414130
\(750\) 44.4356 1.62256
\(751\) 20.4139 0.744913 0.372456 0.928050i \(-0.378516\pi\)
0.372456 + 0.928050i \(0.378516\pi\)
\(752\) −38.8017 −1.41495
\(753\) 8.13855 0.296585
\(754\) 17.3923 0.633392
\(755\) −0.471449 −0.0171578
\(756\) −67.2357 −2.44534
\(757\) 11.2119 0.407503 0.203752 0.979023i \(-0.434687\pi\)
0.203752 + 0.979023i \(0.434687\pi\)
\(758\) −86.2350 −3.13220
\(759\) −32.5251 −1.18059
\(760\) 79.6906 2.89068
\(761\) 51.0964 1.85224 0.926122 0.377223i \(-0.123121\pi\)
0.926122 + 0.377223i \(0.123121\pi\)
\(762\) −52.6013 −1.90555
\(763\) −32.5203 −1.17731
\(764\) −18.2858 −0.661555
\(765\) 0.471270 0.0170388
\(766\) −32.8528 −1.18702
\(767\) 4.03636 0.145744
\(768\) 64.0076 2.30967
\(769\) 40.1807 1.44895 0.724476 0.689300i \(-0.242082\pi\)
0.724476 + 0.689300i \(0.242082\pi\)
\(770\) 74.6551 2.69038
\(771\) −42.6468 −1.53589
\(772\) 59.3933 2.13761
\(773\) −21.6166 −0.777497 −0.388748 0.921344i \(-0.627092\pi\)
−0.388748 + 0.921344i \(0.627092\pi\)
\(774\) 8.31538 0.298890
\(775\) −5.74733 −0.206450
\(776\) 47.2299 1.69546
\(777\) 26.3584 0.945603
\(778\) −68.8077 −2.46688
\(779\) 22.7970 0.816786
\(780\) −29.5910 −1.05953
\(781\) 35.6489 1.27562
\(782\) 3.02641 0.108224
\(783\) 35.8081 1.27968
\(784\) −32.5916 −1.16399
\(785\) −0.587729 −0.0209769
\(786\) 73.4381 2.61945
\(787\) 5.33104 0.190031 0.0950156 0.995476i \(-0.469710\pi\)
0.0950156 + 0.995476i \(0.469710\pi\)
\(788\) −58.6220 −2.08832
\(789\) 22.3297 0.794960
\(790\) −63.7594 −2.26846
\(791\) −30.2023 −1.07387
\(792\) 24.0590 0.854900
\(793\) −0.809959 −0.0287625
\(794\) −58.0888 −2.06149
\(795\) 49.2185 1.74560
\(796\) −93.4275 −3.31145
\(797\) −5.94980 −0.210753 −0.105376 0.994432i \(-0.533605\pi\)
−0.105376 + 0.994432i \(0.533605\pi\)
\(798\) −21.0913 −0.746625
\(799\) −0.463210 −0.0163872
\(800\) −173.492 −6.13387
\(801\) −6.61208 −0.233626
\(802\) −49.4335 −1.74556
\(803\) −49.5426 −1.74832
\(804\) −106.791 −3.76623
\(805\) 49.4075 1.74138
\(806\) 1.96155 0.0690926
\(807\) 16.8877 0.594474
\(808\) −53.6755 −1.88830
\(809\) −19.2018 −0.675100 −0.337550 0.941308i \(-0.609598\pi\)
−0.337550 + 0.941308i \(0.609598\pi\)
\(810\) −61.4857 −2.16039
\(811\) −12.5498 −0.440683 −0.220341 0.975423i \(-0.570717\pi\)
−0.220341 + 0.975423i \(0.570717\pi\)
\(812\) −76.1809 −2.67342
\(813\) −6.48730 −0.227520
\(814\) −75.4932 −2.64603
\(815\) −21.6442 −0.758162
\(816\) 3.96190 0.138694
\(817\) 9.67709 0.338558
\(818\) 30.5697 1.06884
\(819\) −1.61593 −0.0564652
\(820\) −191.451 −6.68577
\(821\) 49.8121 1.73846 0.869228 0.494412i \(-0.164616\pi\)
0.869228 + 0.494412i \(0.164616\pi\)
\(822\) 26.3199 0.918011
\(823\) −32.6883 −1.13944 −0.569722 0.821838i \(-0.692949\pi\)
−0.569722 + 0.821838i \(0.692949\pi\)
\(824\) −177.419 −6.18070
\(825\) 41.6291 1.44934
\(826\) −24.1610 −0.840670
\(827\) 8.17642 0.284322 0.142161 0.989844i \(-0.454595\pi\)
0.142161 + 0.989844i \(0.454595\pi\)
\(828\) 25.1377 0.873595
\(829\) 37.1214 1.28928 0.644640 0.764487i \(-0.277007\pi\)
0.644640 + 0.764487i \(0.277007\pi\)
\(830\) 52.0811 1.80776
\(831\) −19.1051 −0.662747
\(832\) 29.5058 1.02293
\(833\) −0.389074 −0.0134806
\(834\) 67.3816 2.33323
\(835\) 3.74770 0.129694
\(836\) 44.2033 1.52880
\(837\) 4.03852 0.139592
\(838\) 58.2282 2.01146
\(839\) −51.3616 −1.77320 −0.886599 0.462538i \(-0.846939\pi\)
−0.886599 + 0.462538i \(0.846939\pi\)
\(840\) 112.194 3.87107
\(841\) 11.5721 0.399037
\(842\) 61.5301 2.12047
\(843\) −34.3096 −1.18168
\(844\) 42.2928 1.45578
\(845\) −3.60561 −0.124037
\(846\) −5.25791 −0.180771
\(847\) 2.11540 0.0726860
\(848\) −134.785 −4.62855
\(849\) −17.6701 −0.606437
\(850\) −3.87352 −0.132861
\(851\) −49.9621 −1.71268
\(852\) 84.5808 2.89769
\(853\) −49.8969 −1.70844 −0.854219 0.519914i \(-0.825964\pi\)
−0.854219 + 0.519914i \(0.825964\pi\)
\(854\) 4.84829 0.165905
\(855\) 6.22540 0.212904
\(856\) 4.87839 0.166740
\(857\) 37.5103 1.28133 0.640664 0.767821i \(-0.278659\pi\)
0.640664 + 0.767821i \(0.278659\pi\)
\(858\) −14.2079 −0.485050
\(859\) 34.7413 1.18536 0.592679 0.805439i \(-0.298070\pi\)
0.592679 + 0.805439i \(0.298070\pi\)
\(860\) −81.2691 −2.77125
\(861\) 32.0952 1.09380
\(862\) 49.1623 1.67448
\(863\) −0.427901 −0.0145659 −0.00728296 0.999973i \(-0.502318\pi\)
−0.00728296 + 0.999973i \(0.502318\pi\)
\(864\) 121.909 4.14743
\(865\) 8.36484 0.284413
\(866\) −52.8101 −1.79456
\(867\) −25.5256 −0.866893
\(868\) −8.59186 −0.291627
\(869\) −22.4015 −0.759919
\(870\) −94.3336 −3.19821
\(871\) −13.0123 −0.440904
\(872\) 139.976 4.74020
\(873\) 3.68958 0.124874
\(874\) 39.9784 1.35229
\(875\) −23.7158 −0.801740
\(876\) −117.545 −3.97148
\(877\) −47.1146 −1.59095 −0.795473 0.605989i \(-0.792778\pi\)
−0.795473 + 0.605989i \(0.792778\pi\)
\(878\) 92.6061 3.12531
\(879\) 6.37245 0.214937
\(880\) −185.249 −6.24476
\(881\) −33.0147 −1.11229 −0.556147 0.831084i \(-0.687721\pi\)
−0.556147 + 0.831084i \(0.687721\pi\)
\(882\) −4.41640 −0.148708
\(883\) −27.4187 −0.922714 −0.461357 0.887215i \(-0.652637\pi\)
−0.461357 + 0.887215i \(0.652637\pi\)
\(884\) 0.967388 0.0325368
\(885\) −21.8926 −0.735913
\(886\) −10.7586 −0.361441
\(887\) −28.6524 −0.962055 −0.481027 0.876706i \(-0.659736\pi\)
−0.481027 + 0.876706i \(0.659736\pi\)
\(888\) −113.454 −3.80726
\(889\) 28.0739 0.941570
\(890\) 88.3119 2.96022
\(891\) −21.6027 −0.723716
\(892\) 37.4586 1.25421
\(893\) −6.11894 −0.204762
\(894\) −30.1500 −1.00837
\(895\) −45.4918 −1.52062
\(896\) −81.5394 −2.72404
\(897\) −9.40293 −0.313955
\(898\) −15.6782 −0.523189
\(899\) 4.57581 0.152612
\(900\) −32.1739 −1.07246
\(901\) −1.60905 −0.0536052
\(902\) −91.9240 −3.06074
\(903\) 13.6241 0.453382
\(904\) 129.999 4.32370
\(905\) −90.1011 −2.99506
\(906\) −0.537070 −0.0178430
\(907\) −50.3220 −1.67091 −0.835457 0.549555i \(-0.814797\pi\)
−0.835457 + 0.549555i \(0.814797\pi\)
\(908\) −100.205 −3.32543
\(909\) −4.19311 −0.139077
\(910\) 21.5826 0.715457
\(911\) −30.9739 −1.02621 −0.513106 0.858326i \(-0.671505\pi\)
−0.513106 + 0.858326i \(0.671505\pi\)
\(912\) 52.3361 1.73302
\(913\) 18.2984 0.605589
\(914\) −30.0014 −0.992358
\(915\) 4.39311 0.145232
\(916\) 120.561 3.98344
\(917\) −39.1948 −1.29433
\(918\) 2.72184 0.0898340
\(919\) −16.4893 −0.543933 −0.271966 0.962307i \(-0.587674\pi\)
−0.271966 + 0.962307i \(0.587674\pi\)
\(920\) −212.663 −7.01130
\(921\) −20.7553 −0.683911
\(922\) −23.3598 −0.769315
\(923\) 10.3060 0.339227
\(924\) 62.2326 2.04730
\(925\) 63.9468 2.10256
\(926\) −9.35025 −0.307268
\(927\) −13.8599 −0.455220
\(928\) 138.128 4.53428
\(929\) −18.9491 −0.621701 −0.310851 0.950459i \(-0.600614\pi\)
−0.310851 + 0.950459i \(0.600614\pi\)
\(930\) −10.6392 −0.348872
\(931\) −5.13962 −0.168444
\(932\) 2.34196 0.0767135
\(933\) 3.76387 0.123223
\(934\) 58.2683 1.90660
\(935\) −2.21148 −0.0723233
\(936\) 6.95540 0.227344
\(937\) 22.5115 0.735420 0.367710 0.929941i \(-0.380142\pi\)
0.367710 + 0.929941i \(0.380142\pi\)
\(938\) 77.8895 2.54318
\(939\) 7.51900 0.245373
\(940\) 51.3874 1.67607
\(941\) 39.3552 1.28294 0.641471 0.767147i \(-0.278324\pi\)
0.641471 + 0.767147i \(0.278324\pi\)
\(942\) −0.669535 −0.0218146
\(943\) −60.8362 −1.98110
\(944\) 59.9532 1.95131
\(945\) 44.4352 1.44548
\(946\) −39.0208 −1.26868
\(947\) −35.1050 −1.14076 −0.570380 0.821381i \(-0.693204\pi\)
−0.570380 + 0.821381i \(0.693204\pi\)
\(948\) −53.1500 −1.72623
\(949\) −14.3226 −0.464933
\(950\) −51.1686 −1.66013
\(951\) −26.4907 −0.859021
\(952\) −3.66786 −0.118876
\(953\) −32.8639 −1.06457 −0.532283 0.846567i \(-0.678666\pi\)
−0.532283 + 0.846567i \(0.678666\pi\)
\(954\) −18.2644 −0.591331
\(955\) 12.0848 0.391056
\(956\) 148.667 4.80824
\(957\) −33.1436 −1.07138
\(958\) −18.6566 −0.602768
\(959\) −14.0472 −0.453609
\(960\) −160.035 −5.16512
\(961\) −30.4839 −0.983353
\(962\) −21.8249 −0.703663
\(963\) 0.381098 0.0122807
\(964\) −137.094 −4.41549
\(965\) −39.2523 −1.26358
\(966\) 56.2845 1.81093
\(967\) 1.94298 0.0624822 0.0312411 0.999512i \(-0.490054\pi\)
0.0312411 + 0.999512i \(0.490054\pi\)
\(968\) −9.10526 −0.292654
\(969\) 0.624782 0.0200709
\(970\) −49.2787 −1.58224
\(971\) 40.7934 1.30912 0.654561 0.756009i \(-0.272853\pi\)
0.654561 + 0.756009i \(0.272853\pi\)
\(972\) 40.7565 1.30727
\(973\) −35.9624 −1.15290
\(974\) 14.6949 0.470854
\(975\) 12.0349 0.385424
\(976\) −12.0306 −0.385089
\(977\) 46.6703 1.49312 0.746558 0.665321i \(-0.231705\pi\)
0.746558 + 0.665321i \(0.231705\pi\)
\(978\) −24.6568 −0.788439
\(979\) 31.0279 0.991656
\(980\) 43.1630 1.37879
\(981\) 10.9349 0.349124
\(982\) −58.6399 −1.87128
\(983\) 24.3825 0.777681 0.388841 0.921305i \(-0.372876\pi\)
0.388841 + 0.921305i \(0.372876\pi\)
\(984\) −138.147 −4.40395
\(985\) 38.7425 1.23444
\(986\) 3.08396 0.0982131
\(987\) −8.61469 −0.274209
\(988\) 12.7791 0.406556
\(989\) −25.8244 −0.821167
\(990\) −25.1026 −0.797814
\(991\) 13.5031 0.428941 0.214471 0.976730i \(-0.431197\pi\)
0.214471 + 0.976730i \(0.431197\pi\)
\(992\) 15.5784 0.494615
\(993\) −50.2831 −1.59568
\(994\) −61.6903 −1.95670
\(995\) 61.7450 1.95745
\(996\) 43.4149 1.37565
\(997\) 23.3919 0.740828 0.370414 0.928867i \(-0.379216\pi\)
0.370414 + 0.928867i \(0.379216\pi\)
\(998\) −65.6039 −2.07666
\(999\) −44.9341 −1.42165
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 \(a_p\))