Properties

Label 8047.2.a.b.1.1
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 1.1
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78532 q^{2} -0.218444 q^{3} +5.75799 q^{4} +3.30077 q^{5} +0.608437 q^{6} -0.196953 q^{7} -10.4672 q^{8} -2.95228 q^{9} +O(q^{10})\) \(q-2.78532 q^{2} -0.218444 q^{3} +5.75799 q^{4} +3.30077 q^{5} +0.608437 q^{6} -0.196953 q^{7} -10.4672 q^{8} -2.95228 q^{9} -9.19368 q^{10} -0.112785 q^{11} -1.25780 q^{12} +1.00000 q^{13} +0.548577 q^{14} -0.721034 q^{15} +17.6384 q^{16} +1.07399 q^{17} +8.22304 q^{18} +2.45645 q^{19} +19.0058 q^{20} +0.0430233 q^{21} +0.314141 q^{22} -2.79072 q^{23} +2.28650 q^{24} +5.89507 q^{25} -2.78532 q^{26} +1.30024 q^{27} -1.13405 q^{28} -4.40077 q^{29} +2.00831 q^{30} +9.82701 q^{31} -28.1943 q^{32} +0.0246372 q^{33} -2.99139 q^{34} -0.650097 q^{35} -16.9992 q^{36} -1.84834 q^{37} -6.84199 q^{38} -0.218444 q^{39} -34.5497 q^{40} -7.55605 q^{41} -0.119833 q^{42} +0.395497 q^{43} -0.649414 q^{44} -9.74480 q^{45} +7.77305 q^{46} -7.12697 q^{47} -3.85302 q^{48} -6.96121 q^{49} -16.4196 q^{50} -0.234606 q^{51} +5.75799 q^{52} +3.72379 q^{53} -3.62159 q^{54} -0.372277 q^{55} +2.06154 q^{56} -0.536597 q^{57} +12.2575 q^{58} -8.99756 q^{59} -4.15171 q^{60} +4.26565 q^{61} -27.3713 q^{62} +0.581461 q^{63} +43.2531 q^{64} +3.30077 q^{65} -0.0686224 q^{66} -9.82507 q^{67} +6.18400 q^{68} +0.609618 q^{69} +1.81072 q^{70} +2.31105 q^{71} +30.9021 q^{72} -0.109087 q^{73} +5.14820 q^{74} -1.28775 q^{75} +14.1442 q^{76} +0.0222133 q^{77} +0.608437 q^{78} -12.1736 q^{79} +58.2204 q^{80} +8.57282 q^{81} +21.0460 q^{82} -2.73580 q^{83} +0.247728 q^{84} +3.54498 q^{85} -1.10158 q^{86} +0.961323 q^{87} +1.18054 q^{88} -3.45780 q^{89} +27.1423 q^{90} -0.196953 q^{91} -16.0690 q^{92} -2.14666 q^{93} +19.8509 q^{94} +8.10817 q^{95} +6.15888 q^{96} -7.59364 q^{97} +19.3892 q^{98} +0.332973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78532 −1.96952 −0.984758 0.173930i \(-0.944353\pi\)
−0.984758 + 0.173930i \(0.944353\pi\)
\(3\) −0.218444 −0.126119 −0.0630595 0.998010i \(-0.520086\pi\)
−0.0630595 + 0.998010i \(0.520086\pi\)
\(4\) 5.75799 2.87899
\(5\) 3.30077 1.47615 0.738074 0.674719i \(-0.235735\pi\)
0.738074 + 0.674719i \(0.235735\pi\)
\(6\) 0.608437 0.248393
\(7\) −0.196953 −0.0744413 −0.0372206 0.999307i \(-0.511850\pi\)
−0.0372206 + 0.999307i \(0.511850\pi\)
\(8\) −10.4672 −3.70071
\(9\) −2.95228 −0.984094
\(10\) −9.19368 −2.90730
\(11\) −0.112785 −0.0340059 −0.0170030 0.999855i \(-0.505412\pi\)
−0.0170030 + 0.999855i \(0.505412\pi\)
\(12\) −1.25780 −0.363096
\(13\) 1.00000 0.277350
\(14\) 0.548577 0.146613
\(15\) −0.721034 −0.186170
\(16\) 17.6384 4.40961
\(17\) 1.07399 0.260480 0.130240 0.991483i \(-0.458425\pi\)
0.130240 + 0.991483i \(0.458425\pi\)
\(18\) 8.22304 1.93819
\(19\) 2.45645 0.563548 0.281774 0.959481i \(-0.409077\pi\)
0.281774 + 0.959481i \(0.409077\pi\)
\(20\) 19.0058 4.24982
\(21\) 0.0430233 0.00938845
\(22\) 0.314141 0.0669752
\(23\) −2.79072 −0.581906 −0.290953 0.956737i \(-0.593972\pi\)
−0.290953 + 0.956737i \(0.593972\pi\)
\(24\) 2.28650 0.466729
\(25\) 5.89507 1.17901
\(26\) −2.78532 −0.546245
\(27\) 1.30024 0.250232
\(28\) −1.13405 −0.214316
\(29\) −4.40077 −0.817203 −0.408601 0.912713i \(-0.633983\pi\)
−0.408601 + 0.912713i \(0.633983\pi\)
\(30\) 2.00831 0.366665
\(31\) 9.82701 1.76498 0.882492 0.470328i \(-0.155864\pi\)
0.882492 + 0.470328i \(0.155864\pi\)
\(32\) −28.1943 −4.98409
\(33\) 0.0246372 0.00428879
\(34\) −2.99139 −0.513019
\(35\) −0.650097 −0.109886
\(36\) −16.9992 −2.83320
\(37\) −1.84834 −0.303865 −0.151932 0.988391i \(-0.548550\pi\)
−0.151932 + 0.988391i \(0.548550\pi\)
\(38\) −6.84199 −1.10992
\(39\) −0.218444 −0.0349791
\(40\) −34.5497 −5.46279
\(41\) −7.55605 −1.18006 −0.590028 0.807383i \(-0.700883\pi\)
−0.590028 + 0.807383i \(0.700883\pi\)
\(42\) −0.119833 −0.0184907
\(43\) 0.395497 0.0603128 0.0301564 0.999545i \(-0.490399\pi\)
0.0301564 + 0.999545i \(0.490399\pi\)
\(44\) −0.649414 −0.0979028
\(45\) −9.74480 −1.45267
\(46\) 7.77305 1.14607
\(47\) −7.12697 −1.03958 −0.519788 0.854295i \(-0.673989\pi\)
−0.519788 + 0.854295i \(0.673989\pi\)
\(48\) −3.85302 −0.556135
\(49\) −6.96121 −0.994458
\(50\) −16.4196 −2.32209
\(51\) −0.234606 −0.0328514
\(52\) 5.75799 0.798489
\(53\) 3.72379 0.511503 0.255751 0.966743i \(-0.417677\pi\)
0.255751 + 0.966743i \(0.417677\pi\)
\(54\) −3.62159 −0.492836
\(55\) −0.372277 −0.0501978
\(56\) 2.06154 0.275485
\(57\) −0.536597 −0.0710741
\(58\) 12.2575 1.60949
\(59\) −8.99756 −1.17138 −0.585691 0.810534i \(-0.699177\pi\)
−0.585691 + 0.810534i \(0.699177\pi\)
\(60\) −4.15171 −0.535983
\(61\) 4.26565 0.546160 0.273080 0.961991i \(-0.411958\pi\)
0.273080 + 0.961991i \(0.411958\pi\)
\(62\) −27.3713 −3.47616
\(63\) 0.581461 0.0732572
\(64\) 43.2531 5.40663
\(65\) 3.30077 0.409410
\(66\) −0.0686224 −0.00844684
\(67\) −9.82507 −1.20032 −0.600162 0.799879i \(-0.704897\pi\)
−0.600162 + 0.799879i \(0.704897\pi\)
\(68\) 6.18400 0.749920
\(69\) 0.609618 0.0733894
\(70\) 1.81072 0.216423
\(71\) 2.31105 0.274271 0.137136 0.990552i \(-0.456210\pi\)
0.137136 + 0.990552i \(0.456210\pi\)
\(72\) 30.9021 3.64184
\(73\) −0.109087 −0.0127677 −0.00638384 0.999980i \(-0.502032\pi\)
−0.00638384 + 0.999980i \(0.502032\pi\)
\(74\) 5.14820 0.598466
\(75\) −1.28775 −0.148696
\(76\) 14.1442 1.62245
\(77\) 0.0222133 0.00253144
\(78\) 0.608437 0.0688919
\(79\) −12.1736 −1.36963 −0.684816 0.728716i \(-0.740118\pi\)
−0.684816 + 0.728716i \(0.740118\pi\)
\(80\) 58.2204 6.50924
\(81\) 8.57282 0.952535
\(82\) 21.0460 2.32414
\(83\) −2.73580 −0.300293 −0.150146 0.988664i \(-0.547975\pi\)
−0.150146 + 0.988664i \(0.547975\pi\)
\(84\) 0.247728 0.0270293
\(85\) 3.54498 0.384507
\(86\) −1.10158 −0.118787
\(87\) 0.961323 0.103065
\(88\) 1.18054 0.125846
\(89\) −3.45780 −0.366526 −0.183263 0.983064i \(-0.558666\pi\)
−0.183263 + 0.983064i \(0.558666\pi\)
\(90\) 27.1423 2.86105
\(91\) −0.196953 −0.0206463
\(92\) −16.0690 −1.67530
\(93\) −2.14666 −0.222598
\(94\) 19.8509 2.04746
\(95\) 8.10817 0.831881
\(96\) 6.15888 0.628588
\(97\) −7.59364 −0.771017 −0.385509 0.922704i \(-0.625974\pi\)
−0.385509 + 0.922704i \(0.625974\pi\)
\(98\) 19.3892 1.95860
\(99\) 0.332973 0.0334650
\(100\) 33.9438 3.39438
\(101\) 10.1958 1.01452 0.507259 0.861794i \(-0.330659\pi\)
0.507259 + 0.861794i \(0.330659\pi\)
\(102\) 0.653453 0.0647014
\(103\) −6.55370 −0.645755 −0.322878 0.946441i \(-0.604650\pi\)
−0.322878 + 0.946441i \(0.604650\pi\)
\(104\) −10.4672 −1.02639
\(105\) 0.142010 0.0138588
\(106\) −10.3719 −1.00741
\(107\) −1.31620 −0.127242 −0.0636210 0.997974i \(-0.520265\pi\)
−0.0636210 + 0.997974i \(0.520265\pi\)
\(108\) 7.48678 0.720416
\(109\) 15.6413 1.49816 0.749082 0.662477i \(-0.230495\pi\)
0.749082 + 0.662477i \(0.230495\pi\)
\(110\) 1.03691 0.0988653
\(111\) 0.403759 0.0383231
\(112\) −3.47394 −0.328257
\(113\) 11.4392 1.07611 0.538055 0.842910i \(-0.319159\pi\)
0.538055 + 0.842910i \(0.319159\pi\)
\(114\) 1.49459 0.139981
\(115\) −9.21153 −0.858980
\(116\) −25.3396 −2.35272
\(117\) −2.95228 −0.272939
\(118\) 25.0610 2.30706
\(119\) −0.211525 −0.0193905
\(120\) 7.54720 0.688962
\(121\) −10.9873 −0.998844
\(122\) −11.8812 −1.07567
\(123\) 1.65058 0.148827
\(124\) 56.5838 5.08137
\(125\) 2.95443 0.264252
\(126\) −1.61955 −0.144281
\(127\) −1.82365 −0.161822 −0.0809112 0.996721i \(-0.525783\pi\)
−0.0809112 + 0.996721i \(0.525783\pi\)
\(128\) −64.0849 −5.66436
\(129\) −0.0863941 −0.00760658
\(130\) −9.19368 −0.806339
\(131\) 13.8527 1.21032 0.605158 0.796106i \(-0.293110\pi\)
0.605158 + 0.796106i \(0.293110\pi\)
\(132\) 0.141861 0.0123474
\(133\) −0.483805 −0.0419512
\(134\) 27.3659 2.36406
\(135\) 4.29180 0.369379
\(136\) −11.2416 −0.963960
\(137\) −10.8697 −0.928658 −0.464329 0.885663i \(-0.653704\pi\)
−0.464329 + 0.885663i \(0.653704\pi\)
\(138\) −1.69798 −0.144542
\(139\) 9.04896 0.767523 0.383761 0.923432i \(-0.374629\pi\)
0.383761 + 0.923432i \(0.374629\pi\)
\(140\) −3.74325 −0.316362
\(141\) 1.55685 0.131110
\(142\) −6.43701 −0.540182
\(143\) −0.112785 −0.00943154
\(144\) −52.0736 −4.33947
\(145\) −14.5259 −1.20631
\(146\) 0.303842 0.0251462
\(147\) 1.52064 0.125420
\(148\) −10.6427 −0.874824
\(149\) −21.4379 −1.75626 −0.878129 0.478425i \(-0.841208\pi\)
−0.878129 + 0.478425i \(0.841208\pi\)
\(150\) 3.58678 0.292859
\(151\) 12.0105 0.977398 0.488699 0.872453i \(-0.337472\pi\)
0.488699 + 0.872453i \(0.337472\pi\)
\(152\) −25.7121 −2.08553
\(153\) −3.17071 −0.256337
\(154\) −0.0618711 −0.00498572
\(155\) 32.4367 2.60538
\(156\) −1.25780 −0.100705
\(157\) −22.2264 −1.77386 −0.886929 0.461906i \(-0.847166\pi\)
−0.886929 + 0.461906i \(0.847166\pi\)
\(158\) 33.9072 2.69751
\(159\) −0.813442 −0.0645101
\(160\) −93.0627 −7.35725
\(161\) 0.549642 0.0433178
\(162\) −23.8780 −1.87603
\(163\) −17.3689 −1.36044 −0.680218 0.733010i \(-0.738115\pi\)
−0.680218 + 0.733010i \(0.738115\pi\)
\(164\) −43.5076 −3.39737
\(165\) 0.0813217 0.00633089
\(166\) 7.62007 0.591432
\(167\) 18.9693 1.46789 0.733943 0.679211i \(-0.237678\pi\)
0.733943 + 0.679211i \(0.237678\pi\)
\(168\) −0.450333 −0.0347439
\(169\) 1.00000 0.0769231
\(170\) −9.87389 −0.757293
\(171\) −7.25213 −0.554584
\(172\) 2.27727 0.173640
\(173\) 4.92266 0.374263 0.187131 0.982335i \(-0.440081\pi\)
0.187131 + 0.982335i \(0.440081\pi\)
\(174\) −2.67759 −0.202988
\(175\) −1.16105 −0.0877673
\(176\) −1.98935 −0.149953
\(177\) 1.96547 0.147733
\(178\) 9.63106 0.721878
\(179\) −7.75093 −0.579332 −0.289666 0.957128i \(-0.593544\pi\)
−0.289666 + 0.957128i \(0.593544\pi\)
\(180\) −56.1104 −4.18222
\(181\) −2.32461 −0.172787 −0.0863933 0.996261i \(-0.527534\pi\)
−0.0863933 + 0.996261i \(0.527534\pi\)
\(182\) 0.548577 0.0406632
\(183\) −0.931807 −0.0688811
\(184\) 29.2110 2.15346
\(185\) −6.10093 −0.448549
\(186\) 5.97911 0.438410
\(187\) −0.121129 −0.00885786
\(188\) −41.0370 −2.99293
\(189\) −0.256087 −0.0186276
\(190\) −22.5838 −1.63840
\(191\) −21.6777 −1.56854 −0.784271 0.620419i \(-0.786963\pi\)
−0.784271 + 0.620419i \(0.786963\pi\)
\(192\) −9.44839 −0.681879
\(193\) 16.4639 1.18510 0.592549 0.805534i \(-0.298121\pi\)
0.592549 + 0.805534i \(0.298121\pi\)
\(194\) 21.1507 1.51853
\(195\) −0.721034 −0.0516343
\(196\) −40.0826 −2.86304
\(197\) −25.2251 −1.79721 −0.898607 0.438754i \(-0.855420\pi\)
−0.898607 + 0.438754i \(0.855420\pi\)
\(198\) −0.927434 −0.0659099
\(199\) −18.8149 −1.33376 −0.666878 0.745167i \(-0.732370\pi\)
−0.666878 + 0.745167i \(0.732370\pi\)
\(200\) −61.7048 −4.36319
\(201\) 2.14623 0.151384
\(202\) −28.3985 −1.99811
\(203\) 0.866745 0.0608336
\(204\) −1.35086 −0.0945791
\(205\) −24.9408 −1.74194
\(206\) 18.2541 1.27183
\(207\) 8.23901 0.572650
\(208\) 17.6384 1.22301
\(209\) −0.277050 −0.0191640
\(210\) −0.395543 −0.0272950
\(211\) −10.6244 −0.731412 −0.365706 0.930730i \(-0.619172\pi\)
−0.365706 + 0.930730i \(0.619172\pi\)
\(212\) 21.4416 1.47261
\(213\) −0.504836 −0.0345908
\(214\) 3.66604 0.250605
\(215\) 1.30544 0.0890306
\(216\) −13.6099 −0.926035
\(217\) −1.93546 −0.131388
\(218\) −43.5659 −2.95066
\(219\) 0.0238295 0.00161025
\(220\) −2.14356 −0.144519
\(221\) 1.07399 0.0722441
\(222\) −1.12460 −0.0754779
\(223\) 9.63034 0.644895 0.322448 0.946587i \(-0.395494\pi\)
0.322448 + 0.946587i \(0.395494\pi\)
\(224\) 5.55295 0.371022
\(225\) −17.4039 −1.16026
\(226\) −31.8618 −2.11942
\(227\) 10.8519 0.720264 0.360132 0.932901i \(-0.382732\pi\)
0.360132 + 0.932901i \(0.382732\pi\)
\(228\) −3.08972 −0.204622
\(229\) 25.6843 1.69727 0.848635 0.528980i \(-0.177425\pi\)
0.848635 + 0.528980i \(0.177425\pi\)
\(230\) 25.6570 1.69177
\(231\) −0.00485238 −0.000319263 0
\(232\) 46.0637 3.02423
\(233\) −13.7275 −0.899321 −0.449660 0.893200i \(-0.648455\pi\)
−0.449660 + 0.893200i \(0.648455\pi\)
\(234\) 8.22304 0.537557
\(235\) −23.5245 −1.53457
\(236\) −51.8078 −3.37240
\(237\) 2.65925 0.172737
\(238\) 0.589164 0.0381898
\(239\) 21.3946 1.38390 0.691950 0.721946i \(-0.256752\pi\)
0.691950 + 0.721946i \(0.256752\pi\)
\(240\) −12.7179 −0.820938
\(241\) 20.1886 1.30046 0.650232 0.759736i \(-0.274672\pi\)
0.650232 + 0.759736i \(0.274672\pi\)
\(242\) 30.6030 1.96724
\(243\) −5.77341 −0.370364
\(244\) 24.5615 1.57239
\(245\) −22.9773 −1.46797
\(246\) −4.59738 −0.293118
\(247\) 2.45645 0.156300
\(248\) −102.861 −6.53169
\(249\) 0.597620 0.0378726
\(250\) −8.22902 −0.520449
\(251\) 3.32965 0.210166 0.105083 0.994463i \(-0.466489\pi\)
0.105083 + 0.994463i \(0.466489\pi\)
\(252\) 3.34805 0.210907
\(253\) 0.314751 0.0197882
\(254\) 5.07943 0.318712
\(255\) −0.774381 −0.0484936
\(256\) 91.9907 5.74942
\(257\) −15.4478 −0.963605 −0.481802 0.876280i \(-0.660018\pi\)
−0.481802 + 0.876280i \(0.660018\pi\)
\(258\) 0.240635 0.0149813
\(259\) 0.364036 0.0226201
\(260\) 19.0058 1.17869
\(261\) 12.9923 0.804204
\(262\) −38.5841 −2.38374
\(263\) −0.409596 −0.0252568 −0.0126284 0.999920i \(-0.504020\pi\)
−0.0126284 + 0.999920i \(0.504020\pi\)
\(264\) −0.257882 −0.0158715
\(265\) 12.2914 0.755054
\(266\) 1.34755 0.0826236
\(267\) 0.755336 0.0462258
\(268\) −56.5726 −3.45572
\(269\) −9.23392 −0.563002 −0.281501 0.959561i \(-0.590832\pi\)
−0.281501 + 0.959561i \(0.590832\pi\)
\(270\) −11.9540 −0.727498
\(271\) −21.0588 −1.27923 −0.639616 0.768694i \(-0.720907\pi\)
−0.639616 + 0.768694i \(0.720907\pi\)
\(272\) 18.9434 1.14861
\(273\) 0.0430233 0.00260389
\(274\) 30.2754 1.82901
\(275\) −0.664875 −0.0400935
\(276\) 3.51017 0.211288
\(277\) −15.3968 −0.925105 −0.462552 0.886592i \(-0.653066\pi\)
−0.462552 + 0.886592i \(0.653066\pi\)
\(278\) −25.2042 −1.51165
\(279\) −29.0121 −1.73691
\(280\) 6.80468 0.406657
\(281\) 20.3336 1.21300 0.606499 0.795084i \(-0.292573\pi\)
0.606499 + 0.795084i \(0.292573\pi\)
\(282\) −4.33631 −0.258224
\(283\) 7.80832 0.464157 0.232078 0.972697i \(-0.425447\pi\)
0.232078 + 0.972697i \(0.425447\pi\)
\(284\) 13.3070 0.789626
\(285\) −1.77118 −0.104916
\(286\) 0.314141 0.0185756
\(287\) 1.48819 0.0878449
\(288\) 83.2374 4.90481
\(289\) −15.8466 −0.932150
\(290\) 40.4593 2.37585
\(291\) 1.65879 0.0972399
\(292\) −0.628122 −0.0367581
\(293\) 15.5609 0.909077 0.454539 0.890727i \(-0.349804\pi\)
0.454539 + 0.890727i \(0.349804\pi\)
\(294\) −4.23546 −0.247017
\(295\) −29.6989 −1.72913
\(296\) 19.3469 1.12451
\(297\) −0.146648 −0.00850936
\(298\) 59.7112 3.45898
\(299\) −2.79072 −0.161392
\(300\) −7.41482 −0.428095
\(301\) −0.0778944 −0.00448976
\(302\) −33.4529 −1.92500
\(303\) −2.22721 −0.127950
\(304\) 43.3279 2.48503
\(305\) 14.0799 0.806214
\(306\) 8.83143 0.504859
\(307\) −8.34124 −0.476060 −0.238030 0.971258i \(-0.576502\pi\)
−0.238030 + 0.971258i \(0.576502\pi\)
\(308\) 0.127904 0.00728801
\(309\) 1.43162 0.0814420
\(310\) −90.3464 −5.13133
\(311\) −8.32549 −0.472095 −0.236047 0.971742i \(-0.575852\pi\)
−0.236047 + 0.971742i \(0.575852\pi\)
\(312\) 2.28650 0.129447
\(313\) 22.8449 1.29127 0.645636 0.763645i \(-0.276592\pi\)
0.645636 + 0.763645i \(0.276592\pi\)
\(314\) 61.9075 3.49364
\(315\) 1.91927 0.108139
\(316\) −70.0952 −3.94316
\(317\) −31.3137 −1.75875 −0.879376 0.476127i \(-0.842040\pi\)
−0.879376 + 0.476127i \(0.842040\pi\)
\(318\) 2.26569 0.127054
\(319\) 0.496340 0.0277897
\(320\) 142.768 7.98099
\(321\) 0.287517 0.0160476
\(322\) −1.53093 −0.0853152
\(323\) 2.63819 0.146793
\(324\) 49.3622 2.74234
\(325\) 5.89507 0.327000
\(326\) 48.3778 2.67940
\(327\) −3.41675 −0.188947
\(328\) 79.0905 4.36704
\(329\) 1.40368 0.0773874
\(330\) −0.226507 −0.0124688
\(331\) 21.2173 1.16621 0.583104 0.812398i \(-0.301838\pi\)
0.583104 + 0.812398i \(0.301838\pi\)
\(332\) −15.7527 −0.864541
\(333\) 5.45681 0.299031
\(334\) −52.8354 −2.89103
\(335\) −32.4303 −1.77186
\(336\) 0.758864 0.0413994
\(337\) 3.17707 0.173066 0.0865330 0.996249i \(-0.472421\pi\)
0.0865330 + 0.996249i \(0.472421\pi\)
\(338\) −2.78532 −0.151501
\(339\) −2.49883 −0.135718
\(340\) 20.4119 1.10699
\(341\) −1.10834 −0.0600198
\(342\) 20.1995 1.09226
\(343\) 2.74970 0.148470
\(344\) −4.13974 −0.223200
\(345\) 2.01221 0.108334
\(346\) −13.7112 −0.737116
\(347\) 1.16585 0.0625862 0.0312931 0.999510i \(-0.490037\pi\)
0.0312931 + 0.999510i \(0.490037\pi\)
\(348\) 5.53529 0.296723
\(349\) 25.1005 1.34360 0.671798 0.740734i \(-0.265522\pi\)
0.671798 + 0.740734i \(0.265522\pi\)
\(350\) 3.23390 0.172859
\(351\) 1.30024 0.0694018
\(352\) 3.17988 0.169488
\(353\) −29.0400 −1.54564 −0.772822 0.634622i \(-0.781156\pi\)
−0.772822 + 0.634622i \(0.781156\pi\)
\(354\) −5.47444 −0.290963
\(355\) 7.62825 0.404865
\(356\) −19.9099 −1.05523
\(357\) 0.0462064 0.00244550
\(358\) 21.5888 1.14100
\(359\) 0.382166 0.0201700 0.0100850 0.999949i \(-0.496790\pi\)
0.0100850 + 0.999949i \(0.496790\pi\)
\(360\) 102.001 5.37590
\(361\) −12.9659 −0.682414
\(362\) 6.47477 0.340306
\(363\) 2.40011 0.125973
\(364\) −1.13405 −0.0594405
\(365\) −0.360071 −0.0188470
\(366\) 2.59538 0.135662
\(367\) −24.6922 −1.28892 −0.644461 0.764637i \(-0.722918\pi\)
−0.644461 + 0.764637i \(0.722918\pi\)
\(368\) −49.2240 −2.56598
\(369\) 22.3076 1.16129
\(370\) 16.9930 0.883425
\(371\) −0.733413 −0.0380769
\(372\) −12.3604 −0.640857
\(373\) −2.33779 −0.121046 −0.0605231 0.998167i \(-0.519277\pi\)
−0.0605231 + 0.998167i \(0.519277\pi\)
\(374\) 0.337384 0.0174457
\(375\) −0.645378 −0.0333272
\(376\) 74.5993 3.84717
\(377\) −4.40077 −0.226651
\(378\) 0.713283 0.0366873
\(379\) 9.20946 0.473058 0.236529 0.971624i \(-0.423990\pi\)
0.236529 + 0.971624i \(0.423990\pi\)
\(380\) 46.6867 2.39498
\(381\) 0.398365 0.0204089
\(382\) 60.3792 3.08927
\(383\) −18.3727 −0.938802 −0.469401 0.882985i \(-0.655530\pi\)
−0.469401 + 0.882985i \(0.655530\pi\)
\(384\) 13.9990 0.714383
\(385\) 0.0733210 0.00373679
\(386\) −45.8572 −2.33407
\(387\) −1.16762 −0.0593534
\(388\) −43.7241 −2.21975
\(389\) −2.39605 −0.121484 −0.0607422 0.998153i \(-0.519347\pi\)
−0.0607422 + 0.998153i \(0.519347\pi\)
\(390\) 2.00831 0.101695
\(391\) −2.99720 −0.151575
\(392\) 72.8642 3.68020
\(393\) −3.02604 −0.152644
\(394\) 70.2599 3.53964
\(395\) −40.1821 −2.02178
\(396\) 1.91725 0.0963455
\(397\) 29.8137 1.49630 0.748152 0.663527i \(-0.230941\pi\)
0.748152 + 0.663527i \(0.230941\pi\)
\(398\) 52.4056 2.62685
\(399\) 0.105685 0.00529084
\(400\) 103.980 5.19899
\(401\) 11.0203 0.550328 0.275164 0.961397i \(-0.411268\pi\)
0.275164 + 0.961397i \(0.411268\pi\)
\(402\) −5.97793 −0.298152
\(403\) 9.82701 0.489518
\(404\) 58.7072 2.92079
\(405\) 28.2969 1.40608
\(406\) −2.41416 −0.119813
\(407\) 0.208464 0.0103332
\(408\) 2.45567 0.121574
\(409\) 2.40843 0.119089 0.0595446 0.998226i \(-0.481035\pi\)
0.0595446 + 0.998226i \(0.481035\pi\)
\(410\) 69.4679 3.43078
\(411\) 2.37442 0.117121
\(412\) −37.7361 −1.85913
\(413\) 1.77210 0.0871992
\(414\) −22.9482 −1.12784
\(415\) −9.03024 −0.443277
\(416\) −28.1943 −1.38234
\(417\) −1.97669 −0.0967991
\(418\) 0.771672 0.0377437
\(419\) −9.91740 −0.484497 −0.242248 0.970214i \(-0.577885\pi\)
−0.242248 + 0.970214i \(0.577885\pi\)
\(420\) 0.817691 0.0398993
\(421\) −32.5450 −1.58615 −0.793073 0.609126i \(-0.791520\pi\)
−0.793073 + 0.609126i \(0.791520\pi\)
\(422\) 29.5922 1.44053
\(423\) 21.0408 1.02304
\(424\) −38.9776 −1.89292
\(425\) 6.33123 0.307110
\(426\) 1.40613 0.0681272
\(427\) −0.840132 −0.0406569
\(428\) −7.57867 −0.366329
\(429\) 0.0246372 0.00118950
\(430\) −3.63608 −0.175347
\(431\) 6.13703 0.295610 0.147805 0.989016i \(-0.452779\pi\)
0.147805 + 0.989016i \(0.452779\pi\)
\(432\) 22.9342 1.10342
\(433\) 14.5672 0.700054 0.350027 0.936740i \(-0.386172\pi\)
0.350027 + 0.936740i \(0.386172\pi\)
\(434\) 5.39087 0.258770
\(435\) 3.17311 0.152139
\(436\) 90.0623 4.31320
\(437\) −6.85527 −0.327932
\(438\) −0.0663726 −0.00317141
\(439\) 11.4353 0.545779 0.272890 0.962045i \(-0.412021\pi\)
0.272890 + 0.962045i \(0.412021\pi\)
\(440\) 3.89669 0.185767
\(441\) 20.5515 0.978641
\(442\) −2.99139 −0.142286
\(443\) −0.389132 −0.0184882 −0.00924411 0.999957i \(-0.502943\pi\)
−0.00924411 + 0.999957i \(0.502943\pi\)
\(444\) 2.32484 0.110332
\(445\) −11.4134 −0.541046
\(446\) −26.8235 −1.27013
\(447\) 4.68298 0.221497
\(448\) −8.51882 −0.402477
\(449\) 17.1628 0.809963 0.404982 0.914325i \(-0.367278\pi\)
0.404982 + 0.914325i \(0.367278\pi\)
\(450\) 48.4754 2.28515
\(451\) 0.852207 0.0401289
\(452\) 65.8668 3.09811
\(453\) −2.62362 −0.123268
\(454\) −30.2259 −1.41857
\(455\) −0.650097 −0.0304770
\(456\) 5.61666 0.263024
\(457\) −35.6845 −1.66925 −0.834626 0.550818i \(-0.814316\pi\)
−0.834626 + 0.550818i \(0.814316\pi\)
\(458\) −71.5390 −3.34280
\(459\) 1.39644 0.0651804
\(460\) −53.0399 −2.47300
\(461\) 20.7104 0.964580 0.482290 0.876012i \(-0.339805\pi\)
0.482290 + 0.876012i \(0.339805\pi\)
\(462\) 0.0135154 0.000628793 0
\(463\) 24.5900 1.14279 0.571397 0.820674i \(-0.306402\pi\)
0.571397 + 0.820674i \(0.306402\pi\)
\(464\) −77.6227 −3.60354
\(465\) −7.08561 −0.328587
\(466\) 38.2355 1.77123
\(467\) −15.5851 −0.721191 −0.360596 0.932722i \(-0.617427\pi\)
−0.360596 + 0.932722i \(0.617427\pi\)
\(468\) −16.9992 −0.785788
\(469\) 1.93508 0.0893536
\(470\) 65.5231 3.02236
\(471\) 4.85523 0.223717
\(472\) 94.1791 4.33494
\(473\) −0.0446061 −0.00205099
\(474\) −7.40684 −0.340207
\(475\) 14.4809 0.664431
\(476\) −1.21796 −0.0558250
\(477\) −10.9937 −0.503367
\(478\) −59.5906 −2.72561
\(479\) −33.7281 −1.54108 −0.770538 0.637394i \(-0.780012\pi\)
−0.770538 + 0.637394i \(0.780012\pi\)
\(480\) 20.3290 0.927889
\(481\) −1.84834 −0.0842769
\(482\) −56.2317 −2.56128
\(483\) −0.120066 −0.00546320
\(484\) −63.2646 −2.87566
\(485\) −25.0648 −1.13814
\(486\) 16.0808 0.729439
\(487\) 23.5252 1.06603 0.533015 0.846106i \(-0.321059\pi\)
0.533015 + 0.846106i \(0.321059\pi\)
\(488\) −44.6493 −2.02118
\(489\) 3.79413 0.171577
\(490\) 63.9992 2.89119
\(491\) 15.2704 0.689143 0.344572 0.938760i \(-0.388024\pi\)
0.344572 + 0.938760i \(0.388024\pi\)
\(492\) 9.50399 0.428473
\(493\) −4.72637 −0.212865
\(494\) −6.84199 −0.307836
\(495\) 1.09907 0.0493993
\(496\) 173.333 7.78289
\(497\) −0.455169 −0.0204171
\(498\) −1.66456 −0.0745907
\(499\) 24.3679 1.09086 0.545429 0.838157i \(-0.316367\pi\)
0.545429 + 0.838157i \(0.316367\pi\)
\(500\) 17.0116 0.760780
\(501\) −4.14373 −0.185128
\(502\) −9.27412 −0.413924
\(503\) −32.2446 −1.43772 −0.718858 0.695156i \(-0.755335\pi\)
−0.718858 + 0.695156i \(0.755335\pi\)
\(504\) −6.08626 −0.271104
\(505\) 33.6539 1.49758
\(506\) −0.876682 −0.0389733
\(507\) −0.218444 −0.00970146
\(508\) −10.5005 −0.465886
\(509\) −33.3970 −1.48030 −0.740148 0.672444i \(-0.765245\pi\)
−0.740148 + 0.672444i \(0.765245\pi\)
\(510\) 2.15690 0.0955089
\(511\) 0.0214850 0.000950443 0
\(512\) −128.053 −5.65921
\(513\) 3.19398 0.141018
\(514\) 43.0269 1.89783
\(515\) −21.6323 −0.953231
\(516\) −0.497456 −0.0218993
\(517\) 0.803814 0.0353517
\(518\) −1.01395 −0.0445506
\(519\) −1.07533 −0.0472016
\(520\) −34.5497 −1.51511
\(521\) −34.9871 −1.53281 −0.766405 0.642357i \(-0.777957\pi\)
−0.766405 + 0.642357i \(0.777957\pi\)
\(522\) −36.1877 −1.58389
\(523\) −17.9117 −0.783225 −0.391612 0.920130i \(-0.628083\pi\)
−0.391612 + 0.920130i \(0.628083\pi\)
\(524\) 79.7636 3.48449
\(525\) 0.253625 0.0110691
\(526\) 1.14085 0.0497436
\(527\) 10.5541 0.459743
\(528\) 0.434562 0.0189119
\(529\) −15.2119 −0.661385
\(530\) −34.2354 −1.48709
\(531\) 26.5633 1.15275
\(532\) −2.78574 −0.120777
\(533\) −7.55605 −0.327289
\(534\) −2.10385 −0.0910425
\(535\) −4.34448 −0.187828
\(536\) 102.841 4.44205
\(537\) 1.69315 0.0730647
\(538\) 25.7194 1.10884
\(539\) 0.785119 0.0338175
\(540\) 24.7121 1.06344
\(541\) 15.5408 0.668151 0.334076 0.942546i \(-0.391576\pi\)
0.334076 + 0.942546i \(0.391576\pi\)
\(542\) 58.6555 2.51947
\(543\) 0.507797 0.0217917
\(544\) −30.2802 −1.29825
\(545\) 51.6283 2.21151
\(546\) −0.119833 −0.00512840
\(547\) −33.0512 −1.41317 −0.706583 0.707631i \(-0.749764\pi\)
−0.706583 + 0.707631i \(0.749764\pi\)
\(548\) −62.5874 −2.67360
\(549\) −12.5934 −0.537473
\(550\) 1.85189 0.0789647
\(551\) −10.8103 −0.460533
\(552\) −6.38098 −0.271593
\(553\) 2.39762 0.101957
\(554\) 42.8850 1.82201
\(555\) 1.33271 0.0565706
\(556\) 52.1038 2.20969
\(557\) −24.7518 −1.04877 −0.524383 0.851483i \(-0.675704\pi\)
−0.524383 + 0.851483i \(0.675704\pi\)
\(558\) 80.8079 3.42087
\(559\) 0.395497 0.0167277
\(560\) −11.4667 −0.484556
\(561\) 0.0264600 0.00111714
\(562\) −56.6354 −2.38902
\(563\) 15.4964 0.653093 0.326547 0.945181i \(-0.394115\pi\)
0.326547 + 0.945181i \(0.394115\pi\)
\(564\) 8.96431 0.377465
\(565\) 37.7582 1.58850
\(566\) −21.7486 −0.914164
\(567\) −1.68844 −0.0709079
\(568\) −24.1902 −1.01500
\(569\) −3.24444 −0.136014 −0.0680070 0.997685i \(-0.521664\pi\)
−0.0680070 + 0.997685i \(0.521664\pi\)
\(570\) 4.93331 0.206633
\(571\) −7.80474 −0.326618 −0.163309 0.986575i \(-0.552217\pi\)
−0.163309 + 0.986575i \(0.552217\pi\)
\(572\) −0.649414 −0.0271533
\(573\) 4.73536 0.197823
\(574\) −4.14507 −0.173012
\(575\) −16.4515 −0.686076
\(576\) −127.695 −5.32063
\(577\) −5.80806 −0.241793 −0.120896 0.992665i \(-0.538577\pi\)
−0.120896 + 0.992665i \(0.538577\pi\)
\(578\) 44.1377 1.83588
\(579\) −3.59645 −0.149463
\(580\) −83.6401 −3.47297
\(581\) 0.538824 0.0223542
\(582\) −4.62025 −0.191515
\(583\) −0.419988 −0.0173941
\(584\) 1.14183 0.0472495
\(585\) −9.74480 −0.402898
\(586\) −43.3420 −1.79044
\(587\) 12.4736 0.514841 0.257421 0.966299i \(-0.417127\pi\)
0.257421 + 0.966299i \(0.417127\pi\)
\(588\) 8.75581 0.361083
\(589\) 24.1395 0.994653
\(590\) 82.7207 3.40556
\(591\) 5.51028 0.226663
\(592\) −32.6018 −1.33992
\(593\) 3.99777 0.164169 0.0820843 0.996625i \(-0.473842\pi\)
0.0820843 + 0.996625i \(0.473842\pi\)
\(594\) 0.408460 0.0167593
\(595\) −0.698195 −0.0286232
\(596\) −123.439 −5.05625
\(597\) 4.11002 0.168212
\(598\) 7.77305 0.317864
\(599\) 15.6207 0.638246 0.319123 0.947713i \(-0.396612\pi\)
0.319123 + 0.947713i \(0.396612\pi\)
\(600\) 13.4791 0.550281
\(601\) −23.5181 −0.959324 −0.479662 0.877453i \(-0.659241\pi\)
−0.479662 + 0.877453i \(0.659241\pi\)
\(602\) 0.216961 0.00884265
\(603\) 29.0064 1.18123
\(604\) 69.1561 2.81392
\(605\) −36.2665 −1.47444
\(606\) 6.20349 0.251999
\(607\) 41.4881 1.68395 0.841974 0.539518i \(-0.181394\pi\)
0.841974 + 0.539518i \(0.181394\pi\)
\(608\) −69.2578 −2.80877
\(609\) −0.189336 −0.00767227
\(610\) −39.2170 −1.58785
\(611\) −7.12697 −0.288326
\(612\) −18.2569 −0.737992
\(613\) 6.75731 0.272925 0.136463 0.990645i \(-0.456427\pi\)
0.136463 + 0.990645i \(0.456427\pi\)
\(614\) 23.2330 0.937607
\(615\) 5.44817 0.219691
\(616\) −0.232511 −0.00936813
\(617\) 0.0751672 0.00302612 0.00151306 0.999999i \(-0.499518\pi\)
0.00151306 + 0.999999i \(0.499518\pi\)
\(618\) −3.98751 −0.160401
\(619\) 1.00000 0.0401934
\(620\) 186.770 7.50086
\(621\) −3.62862 −0.145611
\(622\) 23.1891 0.929799
\(623\) 0.681024 0.0272846
\(624\) −3.85302 −0.154244
\(625\) −19.7235 −0.788939
\(626\) −63.6303 −2.54318
\(627\) 0.0605200 0.00241694
\(628\) −127.979 −5.10692
\(629\) −1.98509 −0.0791506
\(630\) −5.34577 −0.212981
\(631\) 6.82304 0.271621 0.135811 0.990735i \(-0.456636\pi\)
0.135811 + 0.990735i \(0.456636\pi\)
\(632\) 127.423 5.06861
\(633\) 2.32083 0.0922449
\(634\) 87.2186 3.46389
\(635\) −6.01944 −0.238874
\(636\) −4.68379 −0.185724
\(637\) −6.96121 −0.275813
\(638\) −1.38246 −0.0547323
\(639\) −6.82288 −0.269909
\(640\) −211.530 −8.36144
\(641\) −20.6467 −0.815494 −0.407747 0.913095i \(-0.633685\pi\)
−0.407747 + 0.913095i \(0.633685\pi\)
\(642\) −0.800826 −0.0316061
\(643\) −15.9420 −0.628693 −0.314347 0.949308i \(-0.601785\pi\)
−0.314347 + 0.949308i \(0.601785\pi\)
\(644\) 3.16483 0.124712
\(645\) −0.285167 −0.0112284
\(646\) −7.34820 −0.289111
\(647\) −17.8798 −0.702926 −0.351463 0.936202i \(-0.614316\pi\)
−0.351463 + 0.936202i \(0.614316\pi\)
\(648\) −89.7332 −3.52505
\(649\) 1.01479 0.0398339
\(650\) −16.4196 −0.644031
\(651\) 0.422790 0.0165705
\(652\) −100.010 −3.91669
\(653\) −15.6763 −0.613459 −0.306730 0.951797i \(-0.599235\pi\)
−0.306730 + 0.951797i \(0.599235\pi\)
\(654\) 9.51673 0.372134
\(655\) 45.7245 1.78661
\(656\) −133.277 −5.20359
\(657\) 0.322056 0.0125646
\(658\) −3.90969 −0.152416
\(659\) 24.7991 0.966037 0.483018 0.875610i \(-0.339540\pi\)
0.483018 + 0.875610i \(0.339540\pi\)
\(660\) 0.468249 0.0182266
\(661\) −8.16894 −0.317735 −0.158867 0.987300i \(-0.550784\pi\)
−0.158867 + 0.987300i \(0.550784\pi\)
\(662\) −59.0969 −2.29686
\(663\) −0.234606 −0.00911135
\(664\) 28.6361 1.11130
\(665\) −1.59693 −0.0619262
\(666\) −15.1989 −0.588947
\(667\) 12.2813 0.475535
\(668\) 109.225 4.22604
\(669\) −2.10369 −0.0813335
\(670\) 90.3286 3.48970
\(671\) −0.481100 −0.0185727
\(672\) −1.21301 −0.0467929
\(673\) −24.2244 −0.933781 −0.466890 0.884315i \(-0.654626\pi\)
−0.466890 + 0.884315i \(0.654626\pi\)
\(674\) −8.84915 −0.340856
\(675\) 7.66502 0.295027
\(676\) 5.75799 0.221461
\(677\) −36.5211 −1.40362 −0.701810 0.712364i \(-0.747624\pi\)
−0.701810 + 0.712364i \(0.747624\pi\)
\(678\) 6.96003 0.267298
\(679\) 1.49559 0.0573955
\(680\) −37.1059 −1.42295
\(681\) −2.37053 −0.0908389
\(682\) 3.08707 0.118210
\(683\) −48.2973 −1.84804 −0.924022 0.382339i \(-0.875119\pi\)
−0.924022 + 0.382339i \(0.875119\pi\)
\(684\) −41.7577 −1.59664
\(685\) −35.8782 −1.37084
\(686\) −7.65879 −0.292414
\(687\) −5.61060 −0.214058
\(688\) 6.97595 0.265956
\(689\) 3.72379 0.141865
\(690\) −5.60464 −0.213365
\(691\) 7.55277 0.287321 0.143660 0.989627i \(-0.454113\pi\)
0.143660 + 0.989627i \(0.454113\pi\)
\(692\) 28.3446 1.07750
\(693\) −0.0655800 −0.00249118
\(694\) −3.24726 −0.123264
\(695\) 29.8685 1.13298
\(696\) −10.0623 −0.381412
\(697\) −8.11509 −0.307381
\(698\) −69.9127 −2.64624
\(699\) 2.99870 0.113421
\(700\) −6.68533 −0.252682
\(701\) −14.6796 −0.554441 −0.277221 0.960806i \(-0.589413\pi\)
−0.277221 + 0.960806i \(0.589413\pi\)
\(702\) −3.62159 −0.136688
\(703\) −4.54034 −0.171242
\(704\) −4.87829 −0.183857
\(705\) 5.13879 0.193538
\(706\) 80.8857 3.04417
\(707\) −2.00809 −0.0755220
\(708\) 11.3171 0.425324
\(709\) 22.9673 0.862553 0.431277 0.902220i \(-0.358063\pi\)
0.431277 + 0.902220i \(0.358063\pi\)
\(710\) −21.2471 −0.797389
\(711\) 35.9398 1.34785
\(712\) 36.1934 1.35640
\(713\) −27.4245 −1.02705
\(714\) −0.128700 −0.00481646
\(715\) −0.372277 −0.0139224
\(716\) −44.6298 −1.66789
\(717\) −4.67352 −0.174536
\(718\) −1.06445 −0.0397251
\(719\) 19.2914 0.719446 0.359723 0.933059i \(-0.382871\pi\)
0.359723 + 0.933059i \(0.382871\pi\)
\(720\) −171.883 −6.40570
\(721\) 1.29077 0.0480709
\(722\) 36.1140 1.34402
\(723\) −4.41009 −0.164013
\(724\) −13.3851 −0.497452
\(725\) −25.9429 −0.963494
\(726\) −6.68506 −0.248106
\(727\) −20.7186 −0.768409 −0.384204 0.923248i \(-0.625524\pi\)
−0.384204 + 0.923248i \(0.625524\pi\)
\(728\) 2.06154 0.0764059
\(729\) −24.4573 −0.905825
\(730\) 1.00291 0.0371195
\(731\) 0.424759 0.0157103
\(732\) −5.36533 −0.198308
\(733\) −2.60035 −0.0960462 −0.0480231 0.998846i \(-0.515292\pi\)
−0.0480231 + 0.998846i \(0.515292\pi\)
\(734\) 68.7756 2.53855
\(735\) 5.01927 0.185139
\(736\) 78.6824 2.90027
\(737\) 1.10812 0.0408181
\(738\) −62.1337 −2.28717
\(739\) −36.4001 −1.33900 −0.669499 0.742813i \(-0.733491\pi\)
−0.669499 + 0.742813i \(0.733491\pi\)
\(740\) −35.1291 −1.29137
\(741\) −0.536597 −0.0197124
\(742\) 2.04279 0.0749931
\(743\) 40.7197 1.49386 0.746930 0.664903i \(-0.231527\pi\)
0.746930 + 0.664903i \(0.231527\pi\)
\(744\) 22.4694 0.823769
\(745\) −70.7614 −2.59250
\(746\) 6.51148 0.238402
\(747\) 8.07685 0.295517
\(748\) −0.697461 −0.0255017
\(749\) 0.259230 0.00947206
\(750\) 1.79758 0.0656384
\(751\) 10.7050 0.390630 0.195315 0.980741i \(-0.437427\pi\)
0.195315 + 0.980741i \(0.437427\pi\)
\(752\) −125.709 −4.58412
\(753\) −0.727343 −0.0265059
\(754\) 12.2575 0.446393
\(755\) 39.6438 1.44278
\(756\) −1.47454 −0.0536287
\(757\) 2.57150 0.0934627 0.0467314 0.998907i \(-0.485120\pi\)
0.0467314 + 0.998907i \(0.485120\pi\)
\(758\) −25.6513 −0.931696
\(759\) −0.0687557 −0.00249567
\(760\) −84.8697 −3.07855
\(761\) −38.7869 −1.40602 −0.703011 0.711179i \(-0.748162\pi\)
−0.703011 + 0.711179i \(0.748162\pi\)
\(762\) −1.10957 −0.0401956
\(763\) −3.08060 −0.111525
\(764\) −124.820 −4.51582
\(765\) −10.4658 −0.378391
\(766\) 51.1738 1.84899
\(767\) −8.99756 −0.324883
\(768\) −20.0948 −0.725110
\(769\) −12.9522 −0.467070 −0.233535 0.972348i \(-0.575029\pi\)
−0.233535 + 0.972348i \(0.575029\pi\)
\(770\) −0.204222 −0.00735966
\(771\) 3.37448 0.121529
\(772\) 94.7990 3.41189
\(773\) 13.1192 0.471866 0.235933 0.971769i \(-0.424185\pi\)
0.235933 + 0.971769i \(0.424185\pi\)
\(774\) 3.25219 0.116898
\(775\) 57.9309 2.08094
\(776\) 79.4840 2.85331
\(777\) −0.0795215 −0.00285282
\(778\) 6.67375 0.239266
\(779\) −18.5610 −0.665018
\(780\) −4.15171 −0.148655
\(781\) −0.260652 −0.00932685
\(782\) 8.34815 0.298529
\(783\) −5.72207 −0.204490
\(784\) −122.785 −4.38517
\(785\) −73.3641 −2.61848
\(786\) 8.42849 0.300634
\(787\) 19.5051 0.695282 0.347641 0.937628i \(-0.386983\pi\)
0.347641 + 0.937628i \(0.386983\pi\)
\(788\) −145.246 −5.17417
\(789\) 0.0894740 0.00318536
\(790\) 111.920 3.98193
\(791\) −2.25299 −0.0801070
\(792\) −3.48528 −0.123844
\(793\) 4.26565 0.151478
\(794\) −83.0405 −2.94700
\(795\) −2.68498 −0.0952266
\(796\) −108.336 −3.83987
\(797\) −22.2545 −0.788294 −0.394147 0.919047i \(-0.628960\pi\)
−0.394147 + 0.919047i \(0.628960\pi\)
\(798\) −0.294365 −0.0104204
\(799\) −7.65427 −0.270789
\(800\) −166.207 −5.87631
\(801\) 10.2084 0.360696
\(802\) −30.6951 −1.08388
\(803\) 0.0123034 0.000434177 0
\(804\) 12.3580 0.435832
\(805\) 1.81424 0.0639436
\(806\) −27.3713 −0.964114
\(807\) 2.01710 0.0710052
\(808\) −106.721 −3.75443
\(809\) 11.0616 0.388906 0.194453 0.980912i \(-0.437707\pi\)
0.194453 + 0.980912i \(0.437707\pi\)
\(810\) −78.8158 −2.76930
\(811\) −7.94801 −0.279092 −0.139546 0.990216i \(-0.544564\pi\)
−0.139546 + 0.990216i \(0.544564\pi\)
\(812\) 4.99071 0.175140
\(813\) 4.60018 0.161335
\(814\) −0.580639 −0.0203514
\(815\) −57.3307 −2.00821
\(816\) −4.13809 −0.144862
\(817\) 0.971519 0.0339891
\(818\) −6.70824 −0.234548
\(819\) 0.581461 0.0203179
\(820\) −143.609 −5.01503
\(821\) −6.66062 −0.232457 −0.116229 0.993222i \(-0.537081\pi\)
−0.116229 + 0.993222i \(0.537081\pi\)
\(822\) −6.61350 −0.230672
\(823\) 18.8733 0.657882 0.328941 0.944350i \(-0.393308\pi\)
0.328941 + 0.944350i \(0.393308\pi\)
\(824\) 68.5988 2.38975
\(825\) 0.145238 0.00505654
\(826\) −4.93585 −0.171740
\(827\) −16.8673 −0.586532 −0.293266 0.956031i \(-0.594742\pi\)
−0.293266 + 0.956031i \(0.594742\pi\)
\(828\) 47.4401 1.64866
\(829\) 29.9562 1.04042 0.520211 0.854038i \(-0.325853\pi\)
0.520211 + 0.854038i \(0.325853\pi\)
\(830\) 25.1521 0.873041
\(831\) 3.36335 0.116673
\(832\) 43.2531 1.49953
\(833\) −7.47624 −0.259036
\(834\) 5.50572 0.190647
\(835\) 62.6132 2.16682
\(836\) −1.59525 −0.0551729
\(837\) 12.7775 0.441655
\(838\) 27.6231 0.954224
\(839\) −0.370000 −0.0127738 −0.00638691 0.999980i \(-0.502033\pi\)
−0.00638691 + 0.999980i \(0.502033\pi\)
\(840\) −1.48644 −0.0512872
\(841\) −9.63322 −0.332180
\(842\) 90.6481 3.12394
\(843\) −4.44175 −0.152982
\(844\) −61.1750 −2.10573
\(845\) 3.30077 0.113550
\(846\) −58.6054 −2.01489
\(847\) 2.16398 0.0743552
\(848\) 65.6819 2.25553
\(849\) −1.70568 −0.0585389
\(850\) −17.6345 −0.604857
\(851\) 5.15820 0.176821
\(852\) −2.90684 −0.0995867
\(853\) −39.2122 −1.34260 −0.671300 0.741186i \(-0.734264\pi\)
−0.671300 + 0.741186i \(0.734264\pi\)
\(854\) 2.34003 0.0800743
\(855\) −23.9376 −0.818649
\(856\) 13.7769 0.470886
\(857\) 24.7901 0.846814 0.423407 0.905940i \(-0.360834\pi\)
0.423407 + 0.905940i \(0.360834\pi\)
\(858\) −0.0686224 −0.00234273
\(859\) 31.9652 1.09064 0.545319 0.838228i \(-0.316408\pi\)
0.545319 + 0.838228i \(0.316408\pi\)
\(860\) 7.51673 0.256318
\(861\) −0.325086 −0.0110789
\(862\) −17.0936 −0.582209
\(863\) −6.90151 −0.234930 −0.117465 0.993077i \(-0.537477\pi\)
−0.117465 + 0.993077i \(0.537477\pi\)
\(864\) −36.6594 −1.24718
\(865\) 16.2485 0.552467
\(866\) −40.5742 −1.37877
\(867\) 3.46159 0.117562
\(868\) −11.1444 −0.378264
\(869\) 1.37299 0.0465756
\(870\) −8.83810 −0.299640
\(871\) −9.82507 −0.332910
\(872\) −163.720 −5.54427
\(873\) 22.4186 0.758753
\(874\) 19.0941 0.645867
\(875\) −0.581884 −0.0196713
\(876\) 0.137210 0.00463589
\(877\) −7.53594 −0.254471 −0.127235 0.991873i \(-0.540610\pi\)
−0.127235 + 0.991873i \(0.540610\pi\)
\(878\) −31.8510 −1.07492
\(879\) −3.39919 −0.114652
\(880\) −6.56638 −0.221353
\(881\) 21.9387 0.739133 0.369566 0.929204i \(-0.379506\pi\)
0.369566 + 0.929204i \(0.379506\pi\)
\(882\) −57.2423 −1.92745
\(883\) 0.345527 0.0116279 0.00581395 0.999983i \(-0.498149\pi\)
0.00581395 + 0.999983i \(0.498149\pi\)
\(884\) 6.18400 0.207990
\(885\) 6.48755 0.218077
\(886\) 1.08386 0.0364128
\(887\) −38.9942 −1.30930 −0.654649 0.755933i \(-0.727184\pi\)
−0.654649 + 0.755933i \(0.727184\pi\)
\(888\) −4.22622 −0.141823
\(889\) 0.359173 0.0120463
\(890\) 31.7899 1.06560
\(891\) −0.966884 −0.0323918
\(892\) 55.4514 1.85665
\(893\) −17.5070 −0.585851
\(894\) −13.0436 −0.436242
\(895\) −25.5840 −0.855180
\(896\) 12.6217 0.421662
\(897\) 0.609618 0.0203546
\(898\) −47.8039 −1.59524
\(899\) −43.2464 −1.44235
\(900\) −100.212 −3.34038
\(901\) 3.99930 0.133236
\(902\) −2.37367 −0.0790345
\(903\) 0.0170156 0.000566244 0
\(904\) −119.736 −3.98237
\(905\) −7.67299 −0.255059
\(906\) 7.30761 0.242779
\(907\) 56.2085 1.86637 0.933186 0.359393i \(-0.117016\pi\)
0.933186 + 0.359393i \(0.117016\pi\)
\(908\) 62.4849 2.07364
\(909\) −30.1008 −0.998381
\(910\) 1.81072 0.0600249
\(911\) 52.8425 1.75075 0.875376 0.483443i \(-0.160614\pi\)
0.875376 + 0.483443i \(0.160614\pi\)
\(912\) −9.46474 −0.313409
\(913\) 0.308557 0.0102117
\(914\) 99.3926 3.28762
\(915\) −3.07568 −0.101679
\(916\) 147.890 4.88643
\(917\) −2.72833 −0.0900974
\(918\) −3.88953 −0.128374
\(919\) −5.50777 −0.181685 −0.0908423 0.995865i \(-0.528956\pi\)
−0.0908423 + 0.995865i \(0.528956\pi\)
\(920\) 96.4188 3.17883
\(921\) 1.82210 0.0600401
\(922\) −57.6850 −1.89975
\(923\) 2.31105 0.0760692
\(924\) −0.0279399 −0.000919156 0
\(925\) −10.8961 −0.358261
\(926\) −68.4909 −2.25075
\(927\) 19.3484 0.635484
\(928\) 124.076 4.07301
\(929\) −31.1379 −1.02160 −0.510801 0.859699i \(-0.670651\pi\)
−0.510801 + 0.859699i \(0.670651\pi\)
\(930\) 19.7357 0.647158
\(931\) −17.0999 −0.560425
\(932\) −79.0430 −2.58914
\(933\) 1.81866 0.0595401
\(934\) 43.4094 1.42040
\(935\) −0.399820 −0.0130755
\(936\) 30.9021 1.01007
\(937\) −29.3654 −0.959325 −0.479663 0.877453i \(-0.659241\pi\)
−0.479663 + 0.877453i \(0.659241\pi\)
\(938\) −5.38981 −0.175983
\(939\) −4.99035 −0.162854
\(940\) −135.454 −4.41801
\(941\) −21.4960 −0.700751 −0.350376 0.936609i \(-0.613946\pi\)
−0.350376 + 0.936609i \(0.613946\pi\)
\(942\) −13.5233 −0.440614
\(943\) 21.0868 0.686682
\(944\) −158.703 −5.16534
\(945\) −0.845283 −0.0274971
\(946\) 0.124242 0.00403946
\(947\) 34.1868 1.11092 0.555461 0.831543i \(-0.312542\pi\)
0.555461 + 0.831543i \(0.312542\pi\)
\(948\) 15.3119 0.497307
\(949\) −0.109087 −0.00354112
\(950\) −40.3340 −1.30861
\(951\) 6.84030 0.221812
\(952\) 2.21407 0.0717584
\(953\) 12.0807 0.391333 0.195667 0.980670i \(-0.437313\pi\)
0.195667 + 0.980670i \(0.437313\pi\)
\(954\) 30.6209 0.991389
\(955\) −71.5530 −2.31540
\(956\) 123.190 3.98424
\(957\) −0.108423 −0.00350481
\(958\) 93.9434 3.03517
\(959\) 2.14081 0.0691305
\(960\) −31.1869 −1.00655
\(961\) 65.5701 2.11517
\(962\) 5.14820 0.165985
\(963\) 3.88580 0.125218
\(964\) 116.246 3.74403
\(965\) 54.3436 1.74938
\(966\) 0.334422 0.0107599
\(967\) 31.1851 1.00284 0.501422 0.865203i \(-0.332810\pi\)
0.501422 + 0.865203i \(0.332810\pi\)
\(968\) 115.006 3.69643
\(969\) −0.576298 −0.0185134
\(970\) 69.8135 2.24158
\(971\) 3.92415 0.125932 0.0629660 0.998016i \(-0.479944\pi\)
0.0629660 + 0.998016i \(0.479944\pi\)
\(972\) −33.2432 −1.06628
\(973\) −1.78222 −0.0571354
\(974\) −65.5252 −2.09956
\(975\) −1.28775 −0.0412409
\(976\) 75.2393 2.40835
\(977\) −27.9425 −0.893959 −0.446979 0.894544i \(-0.647500\pi\)
−0.446979 + 0.894544i \(0.647500\pi\)
\(978\) −10.5679 −0.337923
\(979\) 0.389987 0.0124640
\(980\) −132.303 −4.22627
\(981\) −46.1775 −1.47433
\(982\) −42.5329 −1.35728
\(983\) −16.7077 −0.532892 −0.266446 0.963850i \(-0.585849\pi\)
−0.266446 + 0.963850i \(0.585849\pi\)
\(984\) −17.2769 −0.550767
\(985\) −83.2622 −2.65295
\(986\) 13.1644 0.419241
\(987\) −0.306626 −0.00976001
\(988\) 14.1442 0.449987
\(989\) −1.10372 −0.0350964
\(990\) −3.06125 −0.0972928
\(991\) 22.9017 0.727496 0.363748 0.931497i \(-0.381497\pi\)
0.363748 + 0.931497i \(0.381497\pi\)
\(992\) −277.065 −8.79683
\(993\) −4.63480 −0.147081
\(994\) 1.26779 0.0402118
\(995\) −62.1038 −1.96882
\(996\) 3.44109 0.109035
\(997\) 26.0098 0.823737 0.411869 0.911243i \(-0.364876\pi\)
0.411869 + 0.911243i \(0.364876\pi\)
\(998\) −67.8724 −2.14846
\(999\) −2.40329 −0.0760366
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 \(a_p\))