Properties

Label 8007.2.a.f.1.20
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.557584 q^{2} -1.00000 q^{3} -1.68910 q^{4} +2.57031 q^{5} +0.557584 q^{6} +2.28117 q^{7} +2.05698 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.557584 q^{2} -1.00000 q^{3} -1.68910 q^{4} +2.57031 q^{5} +0.557584 q^{6} +2.28117 q^{7} +2.05698 q^{8} +1.00000 q^{9} -1.43316 q^{10} -2.42518 q^{11} +1.68910 q^{12} +5.98863 q^{13} -1.27194 q^{14} -2.57031 q^{15} +2.23126 q^{16} -1.00000 q^{17} -0.557584 q^{18} +4.65582 q^{19} -4.34151 q^{20} -2.28117 q^{21} +1.35224 q^{22} +0.860875 q^{23} -2.05698 q^{24} +1.60649 q^{25} -3.33917 q^{26} -1.00000 q^{27} -3.85312 q^{28} -5.60357 q^{29} +1.43316 q^{30} -7.14237 q^{31} -5.35808 q^{32} +2.42518 q^{33} +0.557584 q^{34} +5.86331 q^{35} -1.68910 q^{36} -7.55997 q^{37} -2.59601 q^{38} -5.98863 q^{39} +5.28708 q^{40} +7.64575 q^{41} +1.27194 q^{42} -10.6920 q^{43} +4.09638 q^{44} +2.57031 q^{45} -0.480010 q^{46} -11.4803 q^{47} -2.23126 q^{48} -1.79626 q^{49} -0.895754 q^{50} +1.00000 q^{51} -10.1154 q^{52} -1.24871 q^{53} +0.557584 q^{54} -6.23347 q^{55} +4.69233 q^{56} -4.65582 q^{57} +3.12446 q^{58} +10.3301 q^{59} +4.34151 q^{60} -12.6616 q^{61} +3.98247 q^{62} +2.28117 q^{63} -1.47494 q^{64} +15.3926 q^{65} -1.35224 q^{66} +0.360054 q^{67} +1.68910 q^{68} -0.860875 q^{69} -3.26929 q^{70} -6.84154 q^{71} +2.05698 q^{72} -6.78327 q^{73} +4.21532 q^{74} -1.60649 q^{75} -7.86414 q^{76} -5.53226 q^{77} +3.33917 q^{78} -13.1176 q^{79} +5.73503 q^{80} +1.00000 q^{81} -4.26315 q^{82} -7.63054 q^{83} +3.85312 q^{84} -2.57031 q^{85} +5.96171 q^{86} +5.60357 q^{87} -4.98856 q^{88} -5.84324 q^{89} -1.43316 q^{90} +13.6611 q^{91} -1.45410 q^{92} +7.14237 q^{93} +6.40121 q^{94} +11.9669 q^{95} +5.35808 q^{96} -2.78593 q^{97} +1.00157 q^{98} -2.42518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.557584 −0.394271 −0.197136 0.980376i \(-0.563164\pi\)
−0.197136 + 0.980376i \(0.563164\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.68910 −0.844550
\(5\) 2.57031 1.14948 0.574739 0.818337i \(-0.305104\pi\)
0.574739 + 0.818337i \(0.305104\pi\)
\(6\) 0.557584 0.227633
\(7\) 2.28117 0.862201 0.431101 0.902304i \(-0.358125\pi\)
0.431101 + 0.902304i \(0.358125\pi\)
\(8\) 2.05698 0.727253
\(9\) 1.00000 0.333333
\(10\) −1.43316 −0.453206
\(11\) −2.42518 −0.731220 −0.365610 0.930768i \(-0.619140\pi\)
−0.365610 + 0.930768i \(0.619140\pi\)
\(12\) 1.68910 0.487601
\(13\) 5.98863 1.66095 0.830474 0.557058i \(-0.188070\pi\)
0.830474 + 0.557058i \(0.188070\pi\)
\(14\) −1.27194 −0.339941
\(15\) −2.57031 −0.663651
\(16\) 2.23126 0.557815
\(17\) −1.00000 −0.242536
\(18\) −0.557584 −0.131424
\(19\) 4.65582 1.06812 0.534059 0.845447i \(-0.320666\pi\)
0.534059 + 0.845447i \(0.320666\pi\)
\(20\) −4.34151 −0.970791
\(21\) −2.28117 −0.497792
\(22\) 1.35224 0.288299
\(23\) 0.860875 0.179505 0.0897524 0.995964i \(-0.471392\pi\)
0.0897524 + 0.995964i \(0.471392\pi\)
\(24\) −2.05698 −0.419880
\(25\) 1.60649 0.321298
\(26\) −3.33917 −0.654864
\(27\) −1.00000 −0.192450
\(28\) −3.85312 −0.728172
\(29\) −5.60357 −1.04056 −0.520279 0.853997i \(-0.674172\pi\)
−0.520279 + 0.853997i \(0.674172\pi\)
\(30\) 1.43316 0.261659
\(31\) −7.14237 −1.28281 −0.641404 0.767203i \(-0.721648\pi\)
−0.641404 + 0.767203i \(0.721648\pi\)
\(32\) −5.35808 −0.947184
\(33\) 2.42518 0.422170
\(34\) 0.557584 0.0956249
\(35\) 5.86331 0.991081
\(36\) −1.68910 −0.281517
\(37\) −7.55997 −1.24285 −0.621426 0.783473i \(-0.713446\pi\)
−0.621426 + 0.783473i \(0.713446\pi\)
\(38\) −2.59601 −0.421128
\(39\) −5.98863 −0.958948
\(40\) 5.28708 0.835961
\(41\) 7.64575 1.19406 0.597032 0.802217i \(-0.296346\pi\)
0.597032 + 0.802217i \(0.296346\pi\)
\(42\) 1.27194 0.196265
\(43\) −10.6920 −1.63052 −0.815260 0.579095i \(-0.803406\pi\)
−0.815260 + 0.579095i \(0.803406\pi\)
\(44\) 4.09638 0.617552
\(45\) 2.57031 0.383159
\(46\) −0.480010 −0.0707736
\(47\) −11.4803 −1.67457 −0.837284 0.546768i \(-0.815858\pi\)
−0.837284 + 0.546768i \(0.815858\pi\)
\(48\) −2.23126 −0.322054
\(49\) −1.79626 −0.256609
\(50\) −0.895754 −0.126679
\(51\) 1.00000 0.140028
\(52\) −10.1154 −1.40275
\(53\) −1.24871 −0.171524 −0.0857618 0.996316i \(-0.527332\pi\)
−0.0857618 + 0.996316i \(0.527332\pi\)
\(54\) 0.557584 0.0758776
\(55\) −6.23347 −0.840521
\(56\) 4.69233 0.627039
\(57\) −4.65582 −0.616678
\(58\) 3.12446 0.410262
\(59\) 10.3301 1.34487 0.672435 0.740156i \(-0.265249\pi\)
0.672435 + 0.740156i \(0.265249\pi\)
\(60\) 4.34151 0.560487
\(61\) −12.6616 −1.62115 −0.810576 0.585634i \(-0.800846\pi\)
−0.810576 + 0.585634i \(0.800846\pi\)
\(62\) 3.98247 0.505775
\(63\) 2.28117 0.287400
\(64\) −1.47494 −0.184367
\(65\) 15.3926 1.90922
\(66\) −1.35224 −0.166450
\(67\) 0.360054 0.0439875 0.0219938 0.999758i \(-0.492999\pi\)
0.0219938 + 0.999758i \(0.492999\pi\)
\(68\) 1.68910 0.204833
\(69\) −0.860875 −0.103637
\(70\) −3.26929 −0.390755
\(71\) −6.84154 −0.811941 −0.405970 0.913886i \(-0.633066\pi\)
−0.405970 + 0.913886i \(0.633066\pi\)
\(72\) 2.05698 0.242418
\(73\) −6.78327 −0.793922 −0.396961 0.917836i \(-0.629935\pi\)
−0.396961 + 0.917836i \(0.629935\pi\)
\(74\) 4.21532 0.490021
\(75\) −1.60649 −0.185502
\(76\) −7.86414 −0.902079
\(77\) −5.53226 −0.630459
\(78\) 3.33917 0.378086
\(79\) −13.1176 −1.47584 −0.737921 0.674887i \(-0.764192\pi\)
−0.737921 + 0.674887i \(0.764192\pi\)
\(80\) 5.73503 0.641195
\(81\) 1.00000 0.111111
\(82\) −4.26315 −0.470786
\(83\) −7.63054 −0.837560 −0.418780 0.908088i \(-0.637542\pi\)
−0.418780 + 0.908088i \(0.637542\pi\)
\(84\) 3.85312 0.420410
\(85\) −2.57031 −0.278789
\(86\) 5.96171 0.642868
\(87\) 5.60357 0.600766
\(88\) −4.98856 −0.531783
\(89\) −5.84324 −0.619382 −0.309691 0.950837i \(-0.600226\pi\)
−0.309691 + 0.950837i \(0.600226\pi\)
\(90\) −1.43316 −0.151069
\(91\) 13.6611 1.43207
\(92\) −1.45410 −0.151601
\(93\) 7.14237 0.740630
\(94\) 6.40121 0.660235
\(95\) 11.9669 1.22778
\(96\) 5.35808 0.546857
\(97\) −2.78593 −0.282868 −0.141434 0.989948i \(-0.545171\pi\)
−0.141434 + 0.989948i \(0.545171\pi\)
\(98\) 1.00157 0.101174
\(99\) −2.42518 −0.243740
\(100\) −2.71353 −0.271353
\(101\) −9.86245 −0.981350 −0.490675 0.871343i \(-0.663250\pi\)
−0.490675 + 0.871343i \(0.663250\pi\)
\(102\) −0.557584 −0.0552091
\(103\) 10.6391 1.04830 0.524150 0.851626i \(-0.324383\pi\)
0.524150 + 0.851626i \(0.324383\pi\)
\(104\) 12.3185 1.20793
\(105\) −5.86331 −0.572201
\(106\) 0.696261 0.0676268
\(107\) 4.70455 0.454806 0.227403 0.973801i \(-0.426977\pi\)
0.227403 + 0.973801i \(0.426977\pi\)
\(108\) 1.68910 0.162534
\(109\) −14.6987 −1.40788 −0.703939 0.710261i \(-0.748577\pi\)
−0.703939 + 0.710261i \(0.748577\pi\)
\(110\) 3.47569 0.331394
\(111\) 7.55997 0.717561
\(112\) 5.08988 0.480949
\(113\) −10.7705 −1.01320 −0.506599 0.862182i \(-0.669098\pi\)
−0.506599 + 0.862182i \(0.669098\pi\)
\(114\) 2.59601 0.243139
\(115\) 2.21271 0.206337
\(116\) 9.46499 0.878803
\(117\) 5.98863 0.553649
\(118\) −5.75992 −0.530244
\(119\) −2.28117 −0.209115
\(120\) −5.28708 −0.482643
\(121\) −5.11848 −0.465317
\(122\) 7.05990 0.639174
\(123\) −7.64575 −0.689394
\(124\) 12.0642 1.08340
\(125\) −8.72237 −0.780152
\(126\) −1.27194 −0.113314
\(127\) −18.7363 −1.66258 −0.831290 0.555839i \(-0.812397\pi\)
−0.831290 + 0.555839i \(0.812397\pi\)
\(128\) 11.5386 1.01987
\(129\) 10.6920 0.941381
\(130\) −8.58269 −0.752752
\(131\) 15.2673 1.33391 0.666954 0.745099i \(-0.267598\pi\)
0.666954 + 0.745099i \(0.267598\pi\)
\(132\) −4.09638 −0.356544
\(133\) 10.6207 0.920932
\(134\) −0.200760 −0.0173430
\(135\) −2.57031 −0.221217
\(136\) −2.05698 −0.176385
\(137\) −14.4760 −1.23677 −0.618383 0.785877i \(-0.712212\pi\)
−0.618383 + 0.785877i \(0.712212\pi\)
\(138\) 0.480010 0.0408612
\(139\) 20.2579 1.71825 0.859126 0.511764i \(-0.171008\pi\)
0.859126 + 0.511764i \(0.171008\pi\)
\(140\) −9.90372 −0.837017
\(141\) 11.4803 0.966813
\(142\) 3.81473 0.320125
\(143\) −14.5235 −1.21452
\(144\) 2.23126 0.185938
\(145\) −14.4029 −1.19610
\(146\) 3.78224 0.313021
\(147\) 1.79626 0.148153
\(148\) 12.7696 1.04965
\(149\) −0.913554 −0.0748413 −0.0374206 0.999300i \(-0.511914\pi\)
−0.0374206 + 0.999300i \(0.511914\pi\)
\(150\) 0.895754 0.0731380
\(151\) 11.5558 0.940398 0.470199 0.882561i \(-0.344182\pi\)
0.470199 + 0.882561i \(0.344182\pi\)
\(152\) 9.57694 0.776792
\(153\) −1.00000 −0.0808452
\(154\) 3.08470 0.248572
\(155\) −18.3581 −1.47456
\(156\) 10.1154 0.809880
\(157\) −1.00000 −0.0798087
\(158\) 7.31415 0.581882
\(159\) 1.24871 0.0990292
\(160\) −13.7719 −1.08877
\(161\) 1.96380 0.154769
\(162\) −0.557584 −0.0438079
\(163\) 7.21230 0.564911 0.282455 0.959280i \(-0.408851\pi\)
0.282455 + 0.959280i \(0.408851\pi\)
\(164\) −12.9144 −1.00845
\(165\) 6.23347 0.485275
\(166\) 4.25467 0.330226
\(167\) 22.2178 1.71926 0.859631 0.510916i \(-0.170694\pi\)
0.859631 + 0.510916i \(0.170694\pi\)
\(168\) −4.69233 −0.362021
\(169\) 22.8637 1.75875
\(170\) 1.43316 0.109919
\(171\) 4.65582 0.356039
\(172\) 18.0599 1.37706
\(173\) −5.66663 −0.430826 −0.215413 0.976523i \(-0.569110\pi\)
−0.215413 + 0.976523i \(0.569110\pi\)
\(174\) −3.12446 −0.236865
\(175\) 3.66468 0.277024
\(176\) −5.41121 −0.407885
\(177\) −10.3301 −0.776461
\(178\) 3.25810 0.244205
\(179\) −3.06701 −0.229239 −0.114619 0.993409i \(-0.536565\pi\)
−0.114619 + 0.993409i \(0.536565\pi\)
\(180\) −4.34151 −0.323597
\(181\) −23.2615 −1.72901 −0.864506 0.502623i \(-0.832368\pi\)
−0.864506 + 0.502623i \(0.832368\pi\)
\(182\) −7.61721 −0.564625
\(183\) 12.6616 0.935972
\(184\) 1.77080 0.130545
\(185\) −19.4315 −1.42863
\(186\) −3.98247 −0.292009
\(187\) 2.42518 0.177347
\(188\) 19.3913 1.41426
\(189\) −2.28117 −0.165931
\(190\) −6.67255 −0.484078
\(191\) 16.4607 1.19106 0.595528 0.803334i \(-0.296943\pi\)
0.595528 + 0.803334i \(0.296943\pi\)
\(192\) 1.47494 0.106444
\(193\) −10.7056 −0.770609 −0.385305 0.922789i \(-0.625904\pi\)
−0.385305 + 0.922789i \(0.625904\pi\)
\(194\) 1.55339 0.111527
\(195\) −15.3926 −1.10229
\(196\) 3.03407 0.216719
\(197\) 2.97115 0.211686 0.105843 0.994383i \(-0.466246\pi\)
0.105843 + 0.994383i \(0.466246\pi\)
\(198\) 1.35224 0.0960998
\(199\) 0.00311595 0.000220884 0 0.000110442 1.00000i \(-0.499965\pi\)
0.000110442 1.00000i \(0.499965\pi\)
\(200\) 3.30453 0.233665
\(201\) −0.360054 −0.0253962
\(202\) 5.49914 0.386918
\(203\) −12.7827 −0.897170
\(204\) −1.68910 −0.118261
\(205\) 19.6519 1.37255
\(206\) −5.93218 −0.413315
\(207\) 0.860875 0.0598349
\(208\) 13.3622 0.926501
\(209\) −11.2912 −0.781029
\(210\) 3.26929 0.225602
\(211\) 7.48494 0.515285 0.257642 0.966240i \(-0.417054\pi\)
0.257642 + 0.966240i \(0.417054\pi\)
\(212\) 2.10920 0.144860
\(213\) 6.84154 0.468774
\(214\) −2.62318 −0.179317
\(215\) −27.4818 −1.87425
\(216\) −2.05698 −0.139960
\(217\) −16.2930 −1.10604
\(218\) 8.19575 0.555086
\(219\) 6.78327 0.458371
\(220\) 10.5290 0.709862
\(221\) −5.98863 −0.402839
\(222\) −4.21532 −0.282914
\(223\) 21.5652 1.44411 0.722056 0.691835i \(-0.243197\pi\)
0.722056 + 0.691835i \(0.243197\pi\)
\(224\) −12.2227 −0.816663
\(225\) 1.60649 0.107099
\(226\) 6.00543 0.399475
\(227\) −2.09643 −0.139145 −0.0695726 0.997577i \(-0.522164\pi\)
−0.0695726 + 0.997577i \(0.522164\pi\)
\(228\) 7.86414 0.520815
\(229\) 7.93938 0.524649 0.262324 0.964980i \(-0.415511\pi\)
0.262324 + 0.964980i \(0.415511\pi\)
\(230\) −1.23377 −0.0813527
\(231\) 5.53226 0.363996
\(232\) −11.5265 −0.756749
\(233\) 10.4908 0.687276 0.343638 0.939102i \(-0.388341\pi\)
0.343638 + 0.939102i \(0.388341\pi\)
\(234\) −3.33917 −0.218288
\(235\) −29.5078 −1.92488
\(236\) −17.4486 −1.13581
\(237\) 13.1176 0.852078
\(238\) 1.27194 0.0824479
\(239\) −2.06358 −0.133482 −0.0667409 0.997770i \(-0.521260\pi\)
−0.0667409 + 0.997770i \(0.521260\pi\)
\(240\) −5.73503 −0.370194
\(241\) −17.6112 −1.13444 −0.567219 0.823567i \(-0.691981\pi\)
−0.567219 + 0.823567i \(0.691981\pi\)
\(242\) 2.85399 0.183461
\(243\) −1.00000 −0.0641500
\(244\) 21.3867 1.36914
\(245\) −4.61695 −0.294966
\(246\) 4.26315 0.271808
\(247\) 27.8820 1.77409
\(248\) −14.6917 −0.932927
\(249\) 7.63054 0.483566
\(250\) 4.86345 0.307592
\(251\) −24.4298 −1.54200 −0.770999 0.636837i \(-0.780242\pi\)
−0.770999 + 0.636837i \(0.780242\pi\)
\(252\) −3.85312 −0.242724
\(253\) −2.08778 −0.131258
\(254\) 10.4471 0.655508
\(255\) 2.57031 0.160959
\(256\) −3.48385 −0.217740
\(257\) 0.168260 0.0104957 0.00524787 0.999986i \(-0.498330\pi\)
0.00524787 + 0.999986i \(0.498330\pi\)
\(258\) −5.96171 −0.371160
\(259\) −17.2456 −1.07159
\(260\) −25.9997 −1.61243
\(261\) −5.60357 −0.346852
\(262\) −8.51279 −0.525922
\(263\) 13.4461 0.829124 0.414562 0.910021i \(-0.363935\pi\)
0.414562 + 0.910021i \(0.363935\pi\)
\(264\) 4.98856 0.307025
\(265\) −3.20957 −0.197162
\(266\) −5.92194 −0.363097
\(267\) 5.84324 0.357600
\(268\) −0.608166 −0.0371497
\(269\) −11.1882 −0.682156 −0.341078 0.940035i \(-0.610792\pi\)
−0.341078 + 0.940035i \(0.610792\pi\)
\(270\) 1.43316 0.0872196
\(271\) 12.8358 0.779720 0.389860 0.920874i \(-0.372523\pi\)
0.389860 + 0.920874i \(0.372523\pi\)
\(272\) −2.23126 −0.135290
\(273\) −13.6611 −0.826807
\(274\) 8.07157 0.487621
\(275\) −3.89604 −0.234940
\(276\) 1.45410 0.0875267
\(277\) −12.8645 −0.772952 −0.386476 0.922299i \(-0.626308\pi\)
−0.386476 + 0.922299i \(0.626308\pi\)
\(278\) −11.2955 −0.677458
\(279\) −7.14237 −0.427603
\(280\) 12.0607 0.720767
\(281\) 26.9236 1.60613 0.803064 0.595893i \(-0.203202\pi\)
0.803064 + 0.595893i \(0.203202\pi\)
\(282\) −6.40121 −0.381187
\(283\) −16.5871 −0.986001 −0.493000 0.870029i \(-0.664100\pi\)
−0.493000 + 0.870029i \(0.664100\pi\)
\(284\) 11.5560 0.685725
\(285\) −11.9669 −0.708857
\(286\) 8.09809 0.478850
\(287\) 17.4412 1.02952
\(288\) −5.35808 −0.315728
\(289\) 1.00000 0.0588235
\(290\) 8.03084 0.471587
\(291\) 2.78593 0.163314
\(292\) 11.4576 0.670507
\(293\) 32.8754 1.92060 0.960299 0.278972i \(-0.0899935\pi\)
0.960299 + 0.278972i \(0.0899935\pi\)
\(294\) −1.00157 −0.0584126
\(295\) 26.5517 1.54590
\(296\) −15.5507 −0.903868
\(297\) 2.42518 0.140723
\(298\) 0.509383 0.0295078
\(299\) 5.15546 0.298148
\(300\) 2.71353 0.156665
\(301\) −24.3904 −1.40584
\(302\) −6.44333 −0.370772
\(303\) 9.86245 0.566583
\(304\) 10.3883 0.595812
\(305\) −32.5442 −1.86348
\(306\) 0.557584 0.0318750
\(307\) −9.51912 −0.543285 −0.271643 0.962398i \(-0.587567\pi\)
−0.271643 + 0.962398i \(0.587567\pi\)
\(308\) 9.34454 0.532454
\(309\) −10.6391 −0.605236
\(310\) 10.2362 0.581377
\(311\) 5.96578 0.338288 0.169144 0.985591i \(-0.445900\pi\)
0.169144 + 0.985591i \(0.445900\pi\)
\(312\) −12.3185 −0.697399
\(313\) 5.60364 0.316736 0.158368 0.987380i \(-0.449377\pi\)
0.158368 + 0.987380i \(0.449377\pi\)
\(314\) 0.557584 0.0314663
\(315\) 5.86331 0.330360
\(316\) 22.1569 1.24642
\(317\) −17.3820 −0.976268 −0.488134 0.872769i \(-0.662322\pi\)
−0.488134 + 0.872769i \(0.662322\pi\)
\(318\) −0.696261 −0.0390444
\(319\) 13.5897 0.760877
\(320\) −3.79104 −0.211926
\(321\) −4.70455 −0.262582
\(322\) −1.09498 −0.0610211
\(323\) −4.65582 −0.259057
\(324\) −1.68910 −0.0938389
\(325\) 9.62069 0.533660
\(326\) −4.02146 −0.222728
\(327\) 14.6987 0.812839
\(328\) 15.7272 0.868388
\(329\) −26.1884 −1.44382
\(330\) −3.47569 −0.191330
\(331\) 7.45842 0.409952 0.204976 0.978767i \(-0.434288\pi\)
0.204976 + 0.978767i \(0.434288\pi\)
\(332\) 12.8887 0.707362
\(333\) −7.55997 −0.414284
\(334\) −12.3883 −0.677856
\(335\) 0.925449 0.0505627
\(336\) −5.08988 −0.277676
\(337\) −15.2165 −0.828893 −0.414447 0.910074i \(-0.636025\pi\)
−0.414447 + 0.910074i \(0.636025\pi\)
\(338\) −12.7484 −0.693424
\(339\) 10.7705 0.584971
\(340\) 4.34151 0.235451
\(341\) 17.3216 0.938015
\(342\) −2.59601 −0.140376
\(343\) −20.0658 −1.08345
\(344\) −21.9933 −1.18580
\(345\) −2.21271 −0.119129
\(346\) 3.15962 0.169862
\(347\) 16.3866 0.879680 0.439840 0.898076i \(-0.355035\pi\)
0.439840 + 0.898076i \(0.355035\pi\)
\(348\) −9.46499 −0.507377
\(349\) −24.0635 −1.28809 −0.644045 0.764988i \(-0.722745\pi\)
−0.644045 + 0.764988i \(0.722745\pi\)
\(350\) −2.04337 −0.109223
\(351\) −5.98863 −0.319649
\(352\) 12.9943 0.692600
\(353\) 19.1711 1.02038 0.510189 0.860063i \(-0.329576\pi\)
0.510189 + 0.860063i \(0.329576\pi\)
\(354\) 5.75992 0.306136
\(355\) −17.5849 −0.933308
\(356\) 9.86981 0.523099
\(357\) 2.28117 0.120732
\(358\) 1.71011 0.0903823
\(359\) 13.0198 0.687157 0.343578 0.939124i \(-0.388361\pi\)
0.343578 + 0.939124i \(0.388361\pi\)
\(360\) 5.28708 0.278654
\(361\) 2.67663 0.140875
\(362\) 12.9702 0.681700
\(363\) 5.11848 0.268651
\(364\) −23.0749 −1.20946
\(365\) −17.4351 −0.912595
\(366\) −7.05990 −0.369027
\(367\) −0.448480 −0.0234105 −0.0117052 0.999931i \(-0.503726\pi\)
−0.0117052 + 0.999931i \(0.503726\pi\)
\(368\) 1.92083 0.100130
\(369\) 7.64575 0.398022
\(370\) 10.8347 0.563268
\(371\) −2.84852 −0.147888
\(372\) −12.0642 −0.625499
\(373\) 25.1547 1.30246 0.651229 0.758881i \(-0.274254\pi\)
0.651229 + 0.758881i \(0.274254\pi\)
\(374\) −1.35224 −0.0699229
\(375\) 8.72237 0.450421
\(376\) −23.6147 −1.21784
\(377\) −33.5577 −1.72831
\(378\) 1.27194 0.0654218
\(379\) −8.21734 −0.422096 −0.211048 0.977476i \(-0.567688\pi\)
−0.211048 + 0.977476i \(0.567688\pi\)
\(380\) −20.2133 −1.03692
\(381\) 18.7363 0.959891
\(382\) −9.17824 −0.469600
\(383\) −18.4339 −0.941927 −0.470963 0.882153i \(-0.656094\pi\)
−0.470963 + 0.882153i \(0.656094\pi\)
\(384\) −11.5386 −0.588825
\(385\) −14.2196 −0.724699
\(386\) 5.96930 0.303829
\(387\) −10.6920 −0.543507
\(388\) 4.70571 0.238896
\(389\) 11.7237 0.594415 0.297207 0.954813i \(-0.403945\pi\)
0.297207 + 0.954813i \(0.403945\pi\)
\(390\) 8.58269 0.434601
\(391\) −0.860875 −0.0435363
\(392\) −3.69488 −0.186620
\(393\) −15.2673 −0.770132
\(394\) −1.65667 −0.0834616
\(395\) −33.7162 −1.69645
\(396\) 4.09638 0.205851
\(397\) −1.62892 −0.0817529 −0.0408765 0.999164i \(-0.513015\pi\)
−0.0408765 + 0.999164i \(0.513015\pi\)
\(398\) −0.00173740 −8.70882e−5 0
\(399\) −10.6207 −0.531701
\(400\) 3.58450 0.179225
\(401\) −7.92567 −0.395789 −0.197894 0.980223i \(-0.563410\pi\)
−0.197894 + 0.980223i \(0.563410\pi\)
\(402\) 0.200760 0.0100130
\(403\) −42.7730 −2.13068
\(404\) 16.6587 0.828799
\(405\) 2.57031 0.127720
\(406\) 7.12743 0.353728
\(407\) 18.3343 0.908799
\(408\) 2.05698 0.101836
\(409\) −7.49370 −0.370540 −0.185270 0.982688i \(-0.559316\pi\)
−0.185270 + 0.982688i \(0.559316\pi\)
\(410\) −10.9576 −0.541158
\(411\) 14.4760 0.714047
\(412\) −17.9705 −0.885342
\(413\) 23.5648 1.15955
\(414\) −0.480010 −0.0235912
\(415\) −19.6128 −0.962757
\(416\) −32.0876 −1.57322
\(417\) −20.2579 −0.992033
\(418\) 6.29580 0.307938
\(419\) 21.4723 1.04899 0.524496 0.851413i \(-0.324254\pi\)
0.524496 + 0.851413i \(0.324254\pi\)
\(420\) 9.90372 0.483252
\(421\) 15.7215 0.766221 0.383110 0.923703i \(-0.374853\pi\)
0.383110 + 0.923703i \(0.374853\pi\)
\(422\) −4.17348 −0.203162
\(423\) −11.4803 −0.558190
\(424\) −2.56858 −0.124741
\(425\) −1.60649 −0.0779263
\(426\) −3.81473 −0.184824
\(427\) −28.8833 −1.39776
\(428\) −7.94645 −0.384106
\(429\) 14.5235 0.701203
\(430\) 15.3234 0.738962
\(431\) 22.3477 1.07645 0.538226 0.842801i \(-0.319095\pi\)
0.538226 + 0.842801i \(0.319095\pi\)
\(432\) −2.23126 −0.107351
\(433\) 21.3451 1.02578 0.512890 0.858455i \(-0.328575\pi\)
0.512890 + 0.858455i \(0.328575\pi\)
\(434\) 9.08470 0.436080
\(435\) 14.4029 0.690567
\(436\) 24.8275 1.18902
\(437\) 4.00807 0.191732
\(438\) −3.78224 −0.180723
\(439\) 25.4189 1.21318 0.606589 0.795015i \(-0.292537\pi\)
0.606589 + 0.795015i \(0.292537\pi\)
\(440\) −12.8222 −0.611272
\(441\) −1.79626 −0.0855363
\(442\) 3.33917 0.158828
\(443\) 7.98059 0.379169 0.189585 0.981864i \(-0.439286\pi\)
0.189585 + 0.981864i \(0.439286\pi\)
\(444\) −12.7696 −0.606016
\(445\) −15.0189 −0.711965
\(446\) −12.0244 −0.569372
\(447\) 0.913554 0.0432096
\(448\) −3.36458 −0.158962
\(449\) −4.58022 −0.216154 −0.108077 0.994143i \(-0.534469\pi\)
−0.108077 + 0.994143i \(0.534469\pi\)
\(450\) −0.895754 −0.0422263
\(451\) −18.5423 −0.873125
\(452\) 18.1924 0.855697
\(453\) −11.5558 −0.542939
\(454\) 1.16894 0.0548610
\(455\) 35.1132 1.64613
\(456\) −9.57694 −0.448481
\(457\) 29.9508 1.40104 0.700520 0.713633i \(-0.252952\pi\)
0.700520 + 0.713633i \(0.252952\pi\)
\(458\) −4.42687 −0.206854
\(459\) 1.00000 0.0466760
\(460\) −3.73750 −0.174262
\(461\) −23.1577 −1.07856 −0.539281 0.842126i \(-0.681304\pi\)
−0.539281 + 0.842126i \(0.681304\pi\)
\(462\) −3.08470 −0.143513
\(463\) 1.97968 0.0920035 0.0460017 0.998941i \(-0.485352\pi\)
0.0460017 + 0.998941i \(0.485352\pi\)
\(464\) −12.5030 −0.580438
\(465\) 18.3581 0.851337
\(466\) −5.84951 −0.270973
\(467\) 31.0397 1.43635 0.718173 0.695864i \(-0.244978\pi\)
0.718173 + 0.695864i \(0.244978\pi\)
\(468\) −10.1154 −0.467584
\(469\) 0.821344 0.0379261
\(470\) 16.4531 0.758925
\(471\) 1.00000 0.0460776
\(472\) 21.2489 0.978061
\(473\) 25.9302 1.19227
\(474\) −7.31415 −0.335950
\(475\) 7.47953 0.343184
\(476\) 3.85312 0.176608
\(477\) −1.24871 −0.0571745
\(478\) 1.15062 0.0526280
\(479\) −11.0544 −0.505090 −0.252545 0.967585i \(-0.581268\pi\)
−0.252545 + 0.967585i \(0.581268\pi\)
\(480\) 13.7719 0.628600
\(481\) −45.2739 −2.06431
\(482\) 9.81973 0.447276
\(483\) −1.96380 −0.0893561
\(484\) 8.64563 0.392983
\(485\) −7.16069 −0.325150
\(486\) 0.557584 0.0252925
\(487\) −31.8709 −1.44421 −0.722105 0.691784i \(-0.756825\pi\)
−0.722105 + 0.691784i \(0.756825\pi\)
\(488\) −26.0447 −1.17899
\(489\) −7.21230 −0.326151
\(490\) 2.57434 0.116297
\(491\) −37.3317 −1.68476 −0.842379 0.538885i \(-0.818846\pi\)
−0.842379 + 0.538885i \(0.818846\pi\)
\(492\) 12.9144 0.582227
\(493\) 5.60357 0.252372
\(494\) −15.5465 −0.699472
\(495\) −6.23347 −0.280174
\(496\) −15.9365 −0.715569
\(497\) −15.6067 −0.700057
\(498\) −4.25467 −0.190656
\(499\) −27.8344 −1.24604 −0.623020 0.782206i \(-0.714095\pi\)
−0.623020 + 0.782206i \(0.714095\pi\)
\(500\) 14.7330 0.658878
\(501\) −22.2178 −0.992616
\(502\) 13.6217 0.607966
\(503\) 43.3557 1.93314 0.966569 0.256408i \(-0.0825392\pi\)
0.966569 + 0.256408i \(0.0825392\pi\)
\(504\) 4.69233 0.209013
\(505\) −25.3495 −1.12804
\(506\) 1.16411 0.0517511
\(507\) −22.8637 −1.01541
\(508\) 31.6475 1.40413
\(509\) 4.03475 0.178837 0.0894187 0.995994i \(-0.471499\pi\)
0.0894187 + 0.995994i \(0.471499\pi\)
\(510\) −1.43316 −0.0634616
\(511\) −15.4738 −0.684520
\(512\) −21.1346 −0.934026
\(513\) −4.65582 −0.205559
\(514\) −0.0938189 −0.00413817
\(515\) 27.3457 1.20500
\(516\) −18.0599 −0.795044
\(517\) 27.8417 1.22448
\(518\) 9.61587 0.422497
\(519\) 5.66663 0.248738
\(520\) 31.6624 1.38849
\(521\) 1.75526 0.0768994 0.0384497 0.999261i \(-0.487758\pi\)
0.0384497 + 0.999261i \(0.487758\pi\)
\(522\) 3.12446 0.136754
\(523\) −3.12261 −0.136542 −0.0682711 0.997667i \(-0.521748\pi\)
−0.0682711 + 0.997667i \(0.521748\pi\)
\(524\) −25.7880 −1.12655
\(525\) −3.66468 −0.159940
\(526\) −7.49735 −0.326900
\(527\) 7.14237 0.311127
\(528\) 5.41121 0.235493
\(529\) −22.2589 −0.967778
\(530\) 1.78961 0.0777355
\(531\) 10.3301 0.448290
\(532\) −17.9394 −0.777774
\(533\) 45.7876 1.98328
\(534\) −3.25810 −0.140992
\(535\) 12.0921 0.522789
\(536\) 0.740624 0.0319901
\(537\) 3.06701 0.132351
\(538\) 6.23836 0.268955
\(539\) 4.35626 0.187638
\(540\) 4.34151 0.186829
\(541\) 22.3133 0.959325 0.479663 0.877453i \(-0.340759\pi\)
0.479663 + 0.877453i \(0.340759\pi\)
\(542\) −7.15704 −0.307421
\(543\) 23.2615 0.998245
\(544\) 5.35808 0.229726
\(545\) −37.7801 −1.61832
\(546\) 7.61721 0.325986
\(547\) −6.96561 −0.297828 −0.148914 0.988850i \(-0.547578\pi\)
−0.148914 + 0.988850i \(0.547578\pi\)
\(548\) 24.4514 1.04451
\(549\) −12.6616 −0.540384
\(550\) 2.17237 0.0926301
\(551\) −26.0892 −1.11144
\(552\) −1.77080 −0.0753704
\(553\) −29.9234 −1.27247
\(554\) 7.17304 0.304753
\(555\) 19.4315 0.824820
\(556\) −34.2176 −1.45115
\(557\) 21.4567 0.909150 0.454575 0.890708i \(-0.349791\pi\)
0.454575 + 0.890708i \(0.349791\pi\)
\(558\) 3.98247 0.168592
\(559\) −64.0307 −2.70821
\(560\) 13.0826 0.552840
\(561\) −2.42518 −0.102391
\(562\) −15.0122 −0.633251
\(563\) −44.8900 −1.89189 −0.945944 0.324329i \(-0.894861\pi\)
−0.945944 + 0.324329i \(0.894861\pi\)
\(564\) −19.3913 −0.816522
\(565\) −27.6834 −1.16465
\(566\) 9.24870 0.388752
\(567\) 2.28117 0.0958002
\(568\) −14.0729 −0.590487
\(569\) 14.8993 0.624611 0.312305 0.949982i \(-0.398899\pi\)
0.312305 + 0.949982i \(0.398899\pi\)
\(570\) 6.67255 0.279482
\(571\) 20.4277 0.854872 0.427436 0.904046i \(-0.359417\pi\)
0.427436 + 0.904046i \(0.359417\pi\)
\(572\) 24.5317 1.02572
\(573\) −16.4607 −0.687657
\(574\) −9.72496 −0.405912
\(575\) 1.38299 0.0576746
\(576\) −1.47494 −0.0614557
\(577\) 28.7380 1.19638 0.598188 0.801356i \(-0.295887\pi\)
0.598188 + 0.801356i \(0.295887\pi\)
\(578\) −0.557584 −0.0231924
\(579\) 10.7056 0.444911
\(580\) 24.3280 1.01016
\(581\) −17.4066 −0.722146
\(582\) −1.55339 −0.0643900
\(583\) 3.02835 0.125422
\(584\) −13.9531 −0.577382
\(585\) 15.3926 0.636407
\(586\) −18.3308 −0.757237
\(587\) −21.1509 −0.872989 −0.436495 0.899707i \(-0.643780\pi\)
−0.436495 + 0.899707i \(0.643780\pi\)
\(588\) −3.03407 −0.125123
\(589\) −33.2536 −1.37019
\(590\) −14.8048 −0.609503
\(591\) −2.97115 −0.122217
\(592\) −16.8683 −0.693281
\(593\) 4.18862 0.172006 0.0860030 0.996295i \(-0.472591\pi\)
0.0860030 + 0.996295i \(0.472591\pi\)
\(594\) −1.35224 −0.0554832
\(595\) −5.86331 −0.240372
\(596\) 1.54308 0.0632072
\(597\) −0.00311595 −0.000127527 0
\(598\) −2.87460 −0.117551
\(599\) −31.5329 −1.28840 −0.644200 0.764857i \(-0.722810\pi\)
−0.644200 + 0.764857i \(0.722810\pi\)
\(600\) −3.30453 −0.134907
\(601\) −0.898549 −0.0366526 −0.0183263 0.999832i \(-0.505834\pi\)
−0.0183263 + 0.999832i \(0.505834\pi\)
\(602\) 13.5997 0.554281
\(603\) 0.360054 0.0146625
\(604\) −19.5189 −0.794213
\(605\) −13.1561 −0.534871
\(606\) −5.49914 −0.223387
\(607\) −2.27389 −0.0922943 −0.0461472 0.998935i \(-0.514694\pi\)
−0.0461472 + 0.998935i \(0.514694\pi\)
\(608\) −24.9462 −1.01170
\(609\) 12.7827 0.517981
\(610\) 18.1461 0.734716
\(611\) −68.7511 −2.78137
\(612\) 1.68910 0.0682778
\(613\) −17.4478 −0.704711 −0.352356 0.935866i \(-0.614619\pi\)
−0.352356 + 0.935866i \(0.614619\pi\)
\(614\) 5.30771 0.214202
\(615\) −19.6519 −0.792442
\(616\) −11.3798 −0.458504
\(617\) 11.7395 0.472616 0.236308 0.971678i \(-0.424063\pi\)
0.236308 + 0.971678i \(0.424063\pi\)
\(618\) 5.93218 0.238627
\(619\) 0.193779 0.00778865 0.00389433 0.999992i \(-0.498760\pi\)
0.00389433 + 0.999992i \(0.498760\pi\)
\(620\) 31.0087 1.24534
\(621\) −0.860875 −0.0345457
\(622\) −3.32642 −0.133377
\(623\) −13.3294 −0.534032
\(624\) −13.3622 −0.534916
\(625\) −30.4516 −1.21807
\(626\) −3.12450 −0.124880
\(627\) 11.2912 0.450928
\(628\) 1.68910 0.0674024
\(629\) 7.55997 0.301436
\(630\) −3.26929 −0.130252
\(631\) −7.13757 −0.284142 −0.142071 0.989856i \(-0.545376\pi\)
−0.142071 + 0.989856i \(0.545376\pi\)
\(632\) −26.9826 −1.07331
\(633\) −7.48494 −0.297500
\(634\) 9.69190 0.384915
\(635\) −48.1581 −1.91110
\(636\) −2.10920 −0.0836351
\(637\) −10.7571 −0.426214
\(638\) −7.57740 −0.299992
\(639\) −6.84154 −0.270647
\(640\) 29.6577 1.17232
\(641\) −37.3037 −1.47341 −0.736703 0.676216i \(-0.763619\pi\)
−0.736703 + 0.676216i \(0.763619\pi\)
\(642\) 2.62318 0.103529
\(643\) −15.5799 −0.614411 −0.307206 0.951643i \(-0.599394\pi\)
−0.307206 + 0.951643i \(0.599394\pi\)
\(644\) −3.31706 −0.130710
\(645\) 27.4818 1.08210
\(646\) 2.59601 0.102139
\(647\) 8.41034 0.330645 0.165322 0.986240i \(-0.447134\pi\)
0.165322 + 0.986240i \(0.447134\pi\)
\(648\) 2.05698 0.0808059
\(649\) −25.0525 −0.983396
\(650\) −5.36434 −0.210407
\(651\) 16.2930 0.638572
\(652\) −12.1823 −0.477095
\(653\) 1.19781 0.0468738 0.0234369 0.999725i \(-0.492539\pi\)
0.0234369 + 0.999725i \(0.492539\pi\)
\(654\) −8.19575 −0.320479
\(655\) 39.2416 1.53330
\(656\) 17.0596 0.666067
\(657\) −6.78327 −0.264641
\(658\) 14.6023 0.569255
\(659\) −12.0572 −0.469681 −0.234840 0.972034i \(-0.575457\pi\)
−0.234840 + 0.972034i \(0.575457\pi\)
\(660\) −10.5290 −0.409839
\(661\) 19.4807 0.757711 0.378856 0.925456i \(-0.376318\pi\)
0.378856 + 0.925456i \(0.376318\pi\)
\(662\) −4.15870 −0.161632
\(663\) 5.98863 0.232579
\(664\) −15.6959 −0.609119
\(665\) 27.2985 1.05859
\(666\) 4.21532 0.163340
\(667\) −4.82397 −0.186785
\(668\) −37.5280 −1.45200
\(669\) −21.5652 −0.833758
\(670\) −0.516016 −0.0199354
\(671\) 30.7067 1.18542
\(672\) 12.2227 0.471501
\(673\) −21.8095 −0.840693 −0.420346 0.907364i \(-0.638091\pi\)
−0.420346 + 0.907364i \(0.638091\pi\)
\(674\) 8.48446 0.326809
\(675\) −1.60649 −0.0618339
\(676\) −38.6191 −1.48535
\(677\) −25.6392 −0.985395 −0.492698 0.870201i \(-0.663989\pi\)
−0.492698 + 0.870201i \(0.663989\pi\)
\(678\) −6.00543 −0.230637
\(679\) −6.35517 −0.243889
\(680\) −5.28708 −0.202750
\(681\) 2.09643 0.0803355
\(682\) −9.65823 −0.369833
\(683\) 25.6713 0.982284 0.491142 0.871079i \(-0.336580\pi\)
0.491142 + 0.871079i \(0.336580\pi\)
\(684\) −7.86414 −0.300693
\(685\) −37.2077 −1.42163
\(686\) 11.1884 0.427173
\(687\) −7.93938 −0.302906
\(688\) −23.8567 −0.909528
\(689\) −7.47807 −0.284892
\(690\) 1.23377 0.0469690
\(691\) −34.8985 −1.32760 −0.663800 0.747910i \(-0.731057\pi\)
−0.663800 + 0.747910i \(0.731057\pi\)
\(692\) 9.57151 0.363854
\(693\) −5.53226 −0.210153
\(694\) −9.13692 −0.346833
\(695\) 52.0691 1.97509
\(696\) 11.5265 0.436909
\(697\) −7.64575 −0.289603
\(698\) 13.4174 0.507857
\(699\) −10.4908 −0.396799
\(700\) −6.19001 −0.233960
\(701\) 32.7128 1.23554 0.617772 0.786357i \(-0.288035\pi\)
0.617772 + 0.786357i \(0.288035\pi\)
\(702\) 3.33917 0.126029
\(703\) −35.1979 −1.32751
\(704\) 3.57699 0.134813
\(705\) 29.5078 1.11133
\(706\) −10.6895 −0.402306
\(707\) −22.4979 −0.846121
\(708\) 17.4486 0.655760
\(709\) 25.2635 0.948789 0.474394 0.880312i \(-0.342667\pi\)
0.474394 + 0.880312i \(0.342667\pi\)
\(710\) 9.80504 0.367977
\(711\) −13.1176 −0.491947
\(712\) −12.0194 −0.450448
\(713\) −6.14869 −0.230270
\(714\) −1.27194 −0.0476013
\(715\) −37.3300 −1.39606
\(716\) 5.18048 0.193604
\(717\) 2.06358 0.0770657
\(718\) −7.25961 −0.270926
\(719\) 25.0704 0.934967 0.467483 0.884002i \(-0.345161\pi\)
0.467483 + 0.884002i \(0.345161\pi\)
\(720\) 5.73503 0.213732
\(721\) 24.2696 0.903846
\(722\) −1.49245 −0.0555431
\(723\) 17.6112 0.654968
\(724\) 39.2910 1.46024
\(725\) −9.00209 −0.334329
\(726\) −2.85399 −0.105921
\(727\) −28.0600 −1.04069 −0.520344 0.853957i \(-0.674196\pi\)
−0.520344 + 0.853957i \(0.674196\pi\)
\(728\) 28.1006 1.04148
\(729\) 1.00000 0.0370370
\(730\) 9.72154 0.359810
\(731\) 10.6920 0.395459
\(732\) −21.3867 −0.790475
\(733\) 12.8857 0.475944 0.237972 0.971272i \(-0.423517\pi\)
0.237972 + 0.971272i \(0.423517\pi\)
\(734\) 0.250065 0.00923007
\(735\) 4.61695 0.170299
\(736\) −4.61264 −0.170024
\(737\) −0.873196 −0.0321646
\(738\) −4.26315 −0.156929
\(739\) −6.60328 −0.242906 −0.121453 0.992597i \(-0.538755\pi\)
−0.121453 + 0.992597i \(0.538755\pi\)
\(740\) 32.8217 1.20655
\(741\) −27.8820 −1.02427
\(742\) 1.58829 0.0583080
\(743\) −28.5658 −1.04798 −0.523990 0.851725i \(-0.675557\pi\)
−0.523990 + 0.851725i \(0.675557\pi\)
\(744\) 14.6917 0.538625
\(745\) −2.34812 −0.0860284
\(746\) −14.0258 −0.513522
\(747\) −7.63054 −0.279187
\(748\) −4.09638 −0.149778
\(749\) 10.7319 0.392134
\(750\) −4.86345 −0.177588
\(751\) 8.20013 0.299227 0.149613 0.988745i \(-0.452197\pi\)
0.149613 + 0.988745i \(0.452197\pi\)
\(752\) −25.6154 −0.934099
\(753\) 24.4298 0.890272
\(754\) 18.7113 0.681424
\(755\) 29.7020 1.08097
\(756\) 3.85312 0.140137
\(757\) −38.8721 −1.41283 −0.706416 0.707797i \(-0.749689\pi\)
−0.706416 + 0.707797i \(0.749689\pi\)
\(758\) 4.58186 0.166420
\(759\) 2.08778 0.0757816
\(760\) 24.6157 0.892905
\(761\) 11.0561 0.400782 0.200391 0.979716i \(-0.435779\pi\)
0.200391 + 0.979716i \(0.435779\pi\)
\(762\) −10.4471 −0.378458
\(763\) −33.5302 −1.21387
\(764\) −27.8038 −1.00591
\(765\) −2.57031 −0.0929297
\(766\) 10.2784 0.371375
\(767\) 61.8634 2.23376
\(768\) 3.48385 0.125712
\(769\) −1.74873 −0.0630609 −0.0315305 0.999503i \(-0.510038\pi\)
−0.0315305 + 0.999503i \(0.510038\pi\)
\(770\) 7.92863 0.285728
\(771\) −0.168260 −0.00605972
\(772\) 18.0829 0.650818
\(773\) 37.4020 1.34526 0.672628 0.739981i \(-0.265165\pi\)
0.672628 + 0.739981i \(0.265165\pi\)
\(774\) 5.96171 0.214289
\(775\) −11.4742 −0.412164
\(776\) −5.73060 −0.205717
\(777\) 17.2456 0.618682
\(778\) −6.53694 −0.234361
\(779\) 35.5972 1.27540
\(780\) 25.9997 0.930939
\(781\) 16.5920 0.593708
\(782\) 0.480010 0.0171651
\(783\) 5.60357 0.200255
\(784\) −4.00792 −0.143140
\(785\) −2.57031 −0.0917383
\(786\) 8.51279 0.303641
\(787\) 44.4020 1.58276 0.791380 0.611324i \(-0.209363\pi\)
0.791380 + 0.611324i \(0.209363\pi\)
\(788\) −5.01857 −0.178779
\(789\) −13.4461 −0.478695
\(790\) 18.7996 0.668861
\(791\) −24.5692 −0.873582
\(792\) −4.98856 −0.177261
\(793\) −75.8256 −2.69265
\(794\) 0.908257 0.0322328
\(795\) 3.20957 0.113832
\(796\) −0.00526315 −0.000186547 0
\(797\) 23.3214 0.826085 0.413042 0.910712i \(-0.364466\pi\)
0.413042 + 0.910712i \(0.364466\pi\)
\(798\) 5.92194 0.209634
\(799\) 11.4803 0.406143
\(800\) −8.60771 −0.304329
\(801\) −5.84324 −0.206461
\(802\) 4.41923 0.156048
\(803\) 16.4507 0.580532
\(804\) 0.608166 0.0214484
\(805\) 5.04758 0.177904
\(806\) 23.8496 0.840065
\(807\) 11.1882 0.393843
\(808\) −20.2869 −0.713690
\(809\) 36.3204 1.27696 0.638478 0.769640i \(-0.279564\pi\)
0.638478 + 0.769640i \(0.279564\pi\)
\(810\) −1.43316 −0.0503562
\(811\) −23.9469 −0.840891 −0.420445 0.907318i \(-0.638126\pi\)
−0.420445 + 0.907318i \(0.638126\pi\)
\(812\) 21.5913 0.757705
\(813\) −12.8358 −0.450172
\(814\) −10.2229 −0.358313
\(815\) 18.5378 0.649352
\(816\) 2.23126 0.0781097
\(817\) −49.7802 −1.74159
\(818\) 4.17837 0.146093
\(819\) 13.6611 0.477357
\(820\) −33.1941 −1.15919
\(821\) −15.4203 −0.538171 −0.269086 0.963116i \(-0.586721\pi\)
−0.269086 + 0.963116i \(0.586721\pi\)
\(822\) −8.07157 −0.281528
\(823\) −41.3441 −1.44116 −0.720582 0.693370i \(-0.756125\pi\)
−0.720582 + 0.693370i \(0.756125\pi\)
\(824\) 21.8844 0.762380
\(825\) 3.89604 0.135643
\(826\) −13.1394 −0.457177
\(827\) −4.02627 −0.140007 −0.0700035 0.997547i \(-0.522301\pi\)
−0.0700035 + 0.997547i \(0.522301\pi\)
\(828\) −1.45410 −0.0505336
\(829\) 13.2272 0.459401 0.229700 0.973261i \(-0.426225\pi\)
0.229700 + 0.973261i \(0.426225\pi\)
\(830\) 10.9358 0.379587
\(831\) 12.8645 0.446264
\(832\) −8.83285 −0.306224
\(833\) 1.79626 0.0622368
\(834\) 11.2955 0.391130
\(835\) 57.1065 1.97625
\(836\) 19.0720 0.659618
\(837\) 7.14237 0.246877
\(838\) −11.9726 −0.413587
\(839\) −22.7731 −0.786216 −0.393108 0.919492i \(-0.628600\pi\)
−0.393108 + 0.919492i \(0.628600\pi\)
\(840\) −12.0607 −0.416135
\(841\) 2.40002 0.0827592
\(842\) −8.76608 −0.302099
\(843\) −26.9236 −0.927299
\(844\) −12.6428 −0.435184
\(845\) 58.7668 2.02164
\(846\) 6.40121 0.220078
\(847\) −11.6761 −0.401197
\(848\) −2.78620 −0.0956784
\(849\) 16.5871 0.569268
\(850\) 0.895754 0.0307241
\(851\) −6.50819 −0.223098
\(852\) −11.5560 −0.395903
\(853\) −21.5422 −0.737592 −0.368796 0.929510i \(-0.620230\pi\)
−0.368796 + 0.929510i \(0.620230\pi\)
\(854\) 16.1048 0.551096
\(855\) 11.9669 0.409259
\(856\) 9.67717 0.330759
\(857\) 15.3627 0.524779 0.262389 0.964962i \(-0.415490\pi\)
0.262389 + 0.964962i \(0.415490\pi\)
\(858\) −8.09809 −0.276464
\(859\) 27.6812 0.944471 0.472235 0.881473i \(-0.343447\pi\)
0.472235 + 0.881473i \(0.343447\pi\)
\(860\) 46.4196 1.58289
\(861\) −17.4412 −0.594396
\(862\) −12.4607 −0.424414
\(863\) −1.19662 −0.0407335 −0.0203667 0.999793i \(-0.506483\pi\)
−0.0203667 + 0.999793i \(0.506483\pi\)
\(864\) 5.35808 0.182286
\(865\) −14.5650 −0.495225
\(866\) −11.9017 −0.404435
\(867\) −1.00000 −0.0339618
\(868\) 27.5205 0.934105
\(869\) 31.8125 1.07917
\(870\) −8.03084 −0.272271
\(871\) 2.15623 0.0730610
\(872\) −30.2349 −1.02388
\(873\) −2.78593 −0.0942893
\(874\) −2.23484 −0.0755945
\(875\) −19.8972 −0.672648
\(876\) −11.4576 −0.387117
\(877\) 3.50001 0.118187 0.0590935 0.998252i \(-0.481179\pi\)
0.0590935 + 0.998252i \(0.481179\pi\)
\(878\) −14.1732 −0.478322
\(879\) −32.8754 −1.10886
\(880\) −13.9085 −0.468855
\(881\) −56.9316 −1.91807 −0.959037 0.283282i \(-0.908577\pi\)
−0.959037 + 0.283282i \(0.908577\pi\)
\(882\) 1.00157 0.0337245
\(883\) 10.2254 0.344112 0.172056 0.985087i \(-0.444959\pi\)
0.172056 + 0.985087i \(0.444959\pi\)
\(884\) 10.1154 0.340218
\(885\) −26.5517 −0.892524
\(886\) −4.44985 −0.149496
\(887\) −5.02440 −0.168703 −0.0843514 0.996436i \(-0.526882\pi\)
−0.0843514 + 0.996436i \(0.526882\pi\)
\(888\) 15.5507 0.521849
\(889\) −42.7407 −1.43348
\(890\) 8.37431 0.280708
\(891\) −2.42518 −0.0812467
\(892\) −36.4258 −1.21962
\(893\) −53.4500 −1.78864
\(894\) −0.509383 −0.0170363
\(895\) −7.88316 −0.263505
\(896\) 26.3214 0.879337
\(897\) −5.15546 −0.172136
\(898\) 2.55386 0.0852233
\(899\) 40.0228 1.33484
\(900\) −2.71353 −0.0904508
\(901\) 1.24871 0.0416006
\(902\) 10.3389 0.344248
\(903\) 24.3904 0.811660
\(904\) −22.1546 −0.736852
\(905\) −59.7892 −1.98746
\(906\) 6.44333 0.214065
\(907\) 58.1444 1.93065 0.965326 0.261048i \(-0.0840681\pi\)
0.965326 + 0.261048i \(0.0840681\pi\)
\(908\) 3.54109 0.117515
\(909\) −9.86245 −0.327117
\(910\) −19.5786 −0.649023
\(911\) −13.1575 −0.435927 −0.217963 0.975957i \(-0.569941\pi\)
−0.217963 + 0.975957i \(0.569941\pi\)
\(912\) −10.3883 −0.343992
\(913\) 18.5055 0.612441
\(914\) −16.7001 −0.552390
\(915\) 32.5442 1.07588
\(916\) −13.4104 −0.443092
\(917\) 34.8273 1.15010
\(918\) −0.557584 −0.0184030
\(919\) −15.0798 −0.497436 −0.248718 0.968576i \(-0.580009\pi\)
−0.248718 + 0.968576i \(0.580009\pi\)
\(920\) 4.55152 0.150059
\(921\) 9.51912 0.313666
\(922\) 12.9124 0.425246
\(923\) −40.9714 −1.34859
\(924\) −9.34454 −0.307413
\(925\) −12.1450 −0.399326
\(926\) −1.10384 −0.0362744
\(927\) 10.6391 0.349433
\(928\) 30.0244 0.985599
\(929\) 8.61431 0.282626 0.141313 0.989965i \(-0.454868\pi\)
0.141313 + 0.989965i \(0.454868\pi\)
\(930\) −10.2362 −0.335658
\(931\) −8.36307 −0.274088
\(932\) −17.7200 −0.580439
\(933\) −5.96578 −0.195311
\(934\) −17.3073 −0.566311
\(935\) 6.23347 0.203856
\(936\) 12.3185 0.402643
\(937\) −2.26912 −0.0741288 −0.0370644 0.999313i \(-0.511801\pi\)
−0.0370644 + 0.999313i \(0.511801\pi\)
\(938\) −0.457968 −0.0149532
\(939\) −5.60364 −0.182868
\(940\) 49.8417 1.62566
\(941\) −45.7976 −1.49296 −0.746479 0.665409i \(-0.768257\pi\)
−0.746479 + 0.665409i \(0.768257\pi\)
\(942\) −0.557584 −0.0181671
\(943\) 6.58203 0.214340
\(944\) 23.0492 0.750188
\(945\) −5.86331 −0.190734
\(946\) −14.4582 −0.470078
\(947\) 44.2873 1.43914 0.719572 0.694418i \(-0.244338\pi\)
0.719572 + 0.694418i \(0.244338\pi\)
\(948\) −22.1569 −0.719622
\(949\) −40.6225 −1.31866
\(950\) −4.17047 −0.135308
\(951\) 17.3820 0.563648
\(952\) −4.69233 −0.152079
\(953\) 6.83616 0.221445 0.110722 0.993851i \(-0.464684\pi\)
0.110722 + 0.993851i \(0.464684\pi\)
\(954\) 0.696261 0.0225423
\(955\) 42.3092 1.36909
\(956\) 3.48559 0.112732
\(957\) −13.5897 −0.439292
\(958\) 6.16377 0.199142
\(959\) −33.0221 −1.06634
\(960\) 3.79104 0.122355
\(961\) 20.0135 0.645597
\(962\) 25.2440 0.813899
\(963\) 4.70455 0.151602
\(964\) 29.7471 0.958089
\(965\) −27.5168 −0.885798
\(966\) 1.09498 0.0352305
\(967\) 1.54153 0.0495722 0.0247861 0.999693i \(-0.492110\pi\)
0.0247861 + 0.999693i \(0.492110\pi\)
\(968\) −10.5286 −0.338403
\(969\) 4.65582 0.149566
\(970\) 3.99269 0.128197
\(971\) −56.6339 −1.81747 −0.908734 0.417375i \(-0.862950\pi\)
−0.908734 + 0.417375i \(0.862950\pi\)
\(972\) 1.68910 0.0541779
\(973\) 46.2117 1.48148
\(974\) 17.7707 0.569411
\(975\) −9.62069 −0.308109
\(976\) −28.2513 −0.904302
\(977\) −8.93841 −0.285965 −0.142982 0.989725i \(-0.545669\pi\)
−0.142982 + 0.989725i \(0.545669\pi\)
\(978\) 4.02146 0.128592
\(979\) 14.1709 0.452905
\(980\) 7.79849 0.249114
\(981\) −14.6987 −0.469293
\(982\) 20.8156 0.664252
\(983\) −12.5330 −0.399741 −0.199870 0.979822i \(-0.564052\pi\)
−0.199870 + 0.979822i \(0.564052\pi\)
\(984\) −15.7272 −0.501364
\(985\) 7.63678 0.243328
\(986\) −3.12446 −0.0995032
\(987\) 26.1884 0.833587
\(988\) −47.0954 −1.49831
\(989\) −9.20450 −0.292686
\(990\) 3.47569 0.110465
\(991\) 58.0655 1.84451 0.922256 0.386581i \(-0.126344\pi\)
0.922256 + 0.386581i \(0.126344\pi\)
\(992\) 38.2694 1.21506
\(993\) −7.45842 −0.236686
\(994\) 8.70205 0.276012
\(995\) 0.00800895 0.000253901 0
\(996\) −12.8887 −0.408395
\(997\) 39.9132 1.26406 0.632032 0.774942i \(-0.282221\pi\)
0.632032 + 0.774942i \(0.282221\pi\)
\(998\) 15.5200 0.491278
\(999\) 7.55997 0.239187
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 \(a_p\))