Properties

Label 8007.2.a.j.1.17
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
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: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.58531 q^{2} -1.00000 q^{3} +0.513198 q^{4} -0.0940015 q^{5} +1.58531 q^{6} -1.19806 q^{7} +2.35704 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.58531 q^{2} -1.00000 q^{3} +0.513198 q^{4} -0.0940015 q^{5} +1.58531 q^{6} -1.19806 q^{7} +2.35704 q^{8} +1.00000 q^{9} +0.149021 q^{10} -1.17843 q^{11} -0.513198 q^{12} +4.14850 q^{13} +1.89929 q^{14} +0.0940015 q^{15} -4.76302 q^{16} +1.00000 q^{17} -1.58531 q^{18} -1.35404 q^{19} -0.0482414 q^{20} +1.19806 q^{21} +1.86818 q^{22} -6.52401 q^{23} -2.35704 q^{24} -4.99116 q^{25} -6.57665 q^{26} -1.00000 q^{27} -0.614842 q^{28} -0.853755 q^{29} -0.149021 q^{30} -3.39872 q^{31} +2.83678 q^{32} +1.17843 q^{33} -1.58531 q^{34} +0.112619 q^{35} +0.513198 q^{36} +5.55666 q^{37} +2.14657 q^{38} -4.14850 q^{39} -0.221565 q^{40} -2.58240 q^{41} -1.89929 q^{42} +3.96282 q^{43} -0.604769 q^{44} -0.0940015 q^{45} +10.3426 q^{46} +5.07300 q^{47} +4.76302 q^{48} -5.56465 q^{49} +7.91253 q^{50} -1.00000 q^{51} +2.12900 q^{52} -4.08553 q^{53} +1.58531 q^{54} +0.110774 q^{55} -2.82387 q^{56} +1.35404 q^{57} +1.35346 q^{58} +12.4715 q^{59} +0.0482414 q^{60} +4.03768 q^{61} +5.38802 q^{62} -1.19806 q^{63} +5.02888 q^{64} -0.389965 q^{65} -1.86818 q^{66} -7.06226 q^{67} +0.513198 q^{68} +6.52401 q^{69} -0.178536 q^{70} -3.45598 q^{71} +2.35704 q^{72} +4.62811 q^{73} -8.80901 q^{74} +4.99116 q^{75} -0.694890 q^{76} +1.41183 q^{77} +6.57665 q^{78} +10.1038 q^{79} +0.447732 q^{80} +1.00000 q^{81} +4.09390 q^{82} +2.57295 q^{83} +0.614842 q^{84} -0.0940015 q^{85} -6.28228 q^{86} +0.853755 q^{87} -2.77761 q^{88} +8.07859 q^{89} +0.149021 q^{90} -4.97015 q^{91} -3.34811 q^{92} +3.39872 q^{93} -8.04227 q^{94} +0.127282 q^{95} -2.83678 q^{96} -4.60570 q^{97} +8.82168 q^{98} -1.17843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q + 5q^{2} - 64q^{3} + 77q^{4} - 3q^{5} - 5q^{6} + 5q^{7} + 18q^{8} + 64q^{9} + O(q^{10}) \) \( 64q + 5q^{2} - 64q^{3} + 77q^{4} - 3q^{5} - 5q^{6} + 5q^{7} + 18q^{8} + 64q^{9} + 12q^{10} - 7q^{11} - 77q^{12} + 24q^{13} - 14q^{14} + 3q^{15} + 103q^{16} + 64q^{17} + 5q^{18} + 26q^{19} - 24q^{20} - 5q^{21} + 25q^{22} + 20q^{23} - 18q^{24} + 141q^{25} + 9q^{26} - 64q^{27} + 14q^{28} + 5q^{29} - 12q^{30} + 11q^{31} + 31q^{32} + 7q^{33} + 5q^{34} - 3q^{35} + 77q^{36} + 50q^{37} + 8q^{38} - 24q^{39} + 28q^{40} - 9q^{41} + 14q^{42} + 59q^{43} - 6q^{44} - 3q^{45} + 11q^{47} - 103q^{48} + 163q^{49} + 20q^{50} - 64q^{51} + 65q^{52} + 39q^{53} - 5q^{54} + 35q^{55} - 34q^{56} - 26q^{57} - 27q^{58} - 65q^{59} + 24q^{60} + 15q^{61} + 18q^{62} + 5q^{63} + 152q^{64} + 49q^{65} - 25q^{66} + 56q^{67} + 77q^{68} - 20q^{69} + 28q^{70} - 18q^{71} + 18q^{72} + 37q^{73} - 76q^{74} - 141q^{75} + 30q^{76} + 80q^{77} - 9q^{78} + 20q^{79} - 144q^{80} + 64q^{81} + 27q^{82} + 3q^{83} - 14q^{84} - 3q^{85} + 12q^{86} - 5q^{87} + 108q^{88} + 42q^{89} + 12q^{90} + 25q^{91} + 18q^{92} - 11q^{93} + 60q^{94} + 42q^{95} - 31q^{96} + 72q^{97} + 18q^{98} - 7q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58531 −1.12098 −0.560491 0.828161i \(-0.689387\pi\)
−0.560491 + 0.828161i \(0.689387\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.513198 0.256599
\(5\) −0.0940015 −0.0420388 −0.0210194 0.999779i \(-0.506691\pi\)
−0.0210194 + 0.999779i \(0.506691\pi\)
\(6\) 1.58531 0.647199
\(7\) −1.19806 −0.452824 −0.226412 0.974032i \(-0.572700\pi\)
−0.226412 + 0.974032i \(0.572700\pi\)
\(8\) 2.35704 0.833339
\(9\) 1.00000 0.333333
\(10\) 0.149021 0.0471247
\(11\) −1.17843 −0.355310 −0.177655 0.984093i \(-0.556851\pi\)
−0.177655 + 0.984093i \(0.556851\pi\)
\(12\) −0.513198 −0.148148
\(13\) 4.14850 1.15059 0.575293 0.817947i \(-0.304888\pi\)
0.575293 + 0.817947i \(0.304888\pi\)
\(14\) 1.89929 0.507607
\(15\) 0.0940015 0.0242711
\(16\) −4.76302 −1.19076
\(17\) 1.00000 0.242536
\(18\) −1.58531 −0.373660
\(19\) −1.35404 −0.310638 −0.155319 0.987864i \(-0.549641\pi\)
−0.155319 + 0.987864i \(0.549641\pi\)
\(20\) −0.0482414 −0.0107871
\(21\) 1.19806 0.261438
\(22\) 1.86818 0.398296
\(23\) −6.52401 −1.36035 −0.680175 0.733050i \(-0.738096\pi\)
−0.680175 + 0.733050i \(0.738096\pi\)
\(24\) −2.35704 −0.481128
\(25\) −4.99116 −0.998233
\(26\) −6.57665 −1.28979
\(27\) −1.00000 −0.192450
\(28\) −0.614842 −0.116194
\(29\) −0.853755 −0.158538 −0.0792692 0.996853i \(-0.525259\pi\)
−0.0792692 + 0.996853i \(0.525259\pi\)
\(30\) −0.149021 −0.0272074
\(31\) −3.39872 −0.610429 −0.305214 0.952284i \(-0.598728\pi\)
−0.305214 + 0.952284i \(0.598728\pi\)
\(32\) 2.83678 0.501477
\(33\) 1.17843 0.205139
\(34\) −1.58531 −0.271878
\(35\) 0.112619 0.0190362
\(36\) 0.513198 0.0855330
\(37\) 5.55666 0.913509 0.456754 0.889593i \(-0.349012\pi\)
0.456754 + 0.889593i \(0.349012\pi\)
\(38\) 2.14657 0.348219
\(39\) −4.14850 −0.664292
\(40\) −0.221565 −0.0350325
\(41\) −2.58240 −0.403303 −0.201652 0.979457i \(-0.564631\pi\)
−0.201652 + 0.979457i \(0.564631\pi\)
\(42\) −1.89929 −0.293067
\(43\) 3.96282 0.604324 0.302162 0.953257i \(-0.402292\pi\)
0.302162 + 0.953257i \(0.402292\pi\)
\(44\) −0.604769 −0.0911723
\(45\) −0.0940015 −0.0140129
\(46\) 10.3426 1.52493
\(47\) 5.07300 0.739974 0.369987 0.929037i \(-0.379362\pi\)
0.369987 + 0.929037i \(0.379362\pi\)
\(48\) 4.76302 0.687483
\(49\) −5.56465 −0.794950
\(50\) 7.91253 1.11900
\(51\) −1.00000 −0.140028
\(52\) 2.12900 0.295240
\(53\) −4.08553 −0.561191 −0.280596 0.959826i \(-0.590532\pi\)
−0.280596 + 0.959826i \(0.590532\pi\)
\(54\) 1.58531 0.215733
\(55\) 0.110774 0.0149368
\(56\) −2.82387 −0.377356
\(57\) 1.35404 0.179347
\(58\) 1.35346 0.177719
\(59\) 12.4715 1.62365 0.811823 0.583903i \(-0.198475\pi\)
0.811823 + 0.583903i \(0.198475\pi\)
\(60\) 0.0482414 0.00622794
\(61\) 4.03768 0.516972 0.258486 0.966015i \(-0.416776\pi\)
0.258486 + 0.966015i \(0.416776\pi\)
\(62\) 5.38802 0.684279
\(63\) −1.19806 −0.150941
\(64\) 5.02888 0.628610
\(65\) −0.389965 −0.0483693
\(66\) −1.86818 −0.229957
\(67\) −7.06226 −0.862792 −0.431396 0.902163i \(-0.641979\pi\)
−0.431396 + 0.902163i \(0.641979\pi\)
\(68\) 0.513198 0.0622344
\(69\) 6.52401 0.785398
\(70\) −0.178536 −0.0213392
\(71\) −3.45598 −0.410149 −0.205074 0.978746i \(-0.565744\pi\)
−0.205074 + 0.978746i \(0.565744\pi\)
\(72\) 2.35704 0.277780
\(73\) 4.62811 0.541680 0.270840 0.962624i \(-0.412699\pi\)
0.270840 + 0.962624i \(0.412699\pi\)
\(74\) −8.80901 −1.02403
\(75\) 4.99116 0.576330
\(76\) −0.694890 −0.0797094
\(77\) 1.41183 0.160893
\(78\) 6.57665 0.744659
\(79\) 10.1038 1.13676 0.568382 0.822765i \(-0.307570\pi\)
0.568382 + 0.822765i \(0.307570\pi\)
\(80\) 0.447732 0.0500579
\(81\) 1.00000 0.111111
\(82\) 4.09390 0.452096
\(83\) 2.57295 0.282418 0.141209 0.989980i \(-0.454901\pi\)
0.141209 + 0.989980i \(0.454901\pi\)
\(84\) 0.614842 0.0670848
\(85\) −0.0940015 −0.0101959
\(86\) −6.28228 −0.677436
\(87\) 0.853755 0.0915322
\(88\) −2.77761 −0.296094
\(89\) 8.07859 0.856329 0.428165 0.903701i \(-0.359160\pi\)
0.428165 + 0.903701i \(0.359160\pi\)
\(90\) 0.149021 0.0157082
\(91\) −4.97015 −0.521014
\(92\) −3.34811 −0.349064
\(93\) 3.39872 0.352431
\(94\) −8.04227 −0.829497
\(95\) 0.127282 0.0130588
\(96\) −2.83678 −0.289528
\(97\) −4.60570 −0.467638 −0.233819 0.972280i \(-0.575122\pi\)
−0.233819 + 0.972280i \(0.575122\pi\)
\(98\) 8.82168 0.891124
\(99\) −1.17843 −0.118437
\(100\) −2.56146 −0.256146
\(101\) 0.944097 0.0939412 0.0469706 0.998896i \(-0.485043\pi\)
0.0469706 + 0.998896i \(0.485043\pi\)
\(102\) 1.58531 0.156969
\(103\) 1.99061 0.196141 0.0980704 0.995179i \(-0.468733\pi\)
0.0980704 + 0.995179i \(0.468733\pi\)
\(104\) 9.77817 0.958828
\(105\) −0.112619 −0.0109905
\(106\) 6.47682 0.629085
\(107\) −13.6235 −1.31703 −0.658516 0.752567i \(-0.728815\pi\)
−0.658516 + 0.752567i \(0.728815\pi\)
\(108\) −0.513198 −0.0493825
\(109\) 9.68033 0.927207 0.463604 0.886043i \(-0.346556\pi\)
0.463604 + 0.886043i \(0.346556\pi\)
\(110\) −0.175611 −0.0167439
\(111\) −5.55666 −0.527414
\(112\) 5.70639 0.539203
\(113\) −18.8489 −1.77315 −0.886576 0.462583i \(-0.846923\pi\)
−0.886576 + 0.462583i \(0.846923\pi\)
\(114\) −2.14657 −0.201044
\(115\) 0.613267 0.0571874
\(116\) −0.438146 −0.0406808
\(117\) 4.14850 0.383529
\(118\) −19.7711 −1.82008
\(119\) −1.19806 −0.109826
\(120\) 0.221565 0.0202260
\(121\) −9.61130 −0.873754
\(122\) −6.40096 −0.579516
\(123\) 2.58240 0.232847
\(124\) −1.74422 −0.156635
\(125\) 0.939185 0.0840032
\(126\) 1.89929 0.169202
\(127\) −15.5826 −1.38273 −0.691365 0.722506i \(-0.742990\pi\)
−0.691365 + 0.722506i \(0.742990\pi\)
\(128\) −13.6459 −1.20614
\(129\) −3.96282 −0.348907
\(130\) 0.618215 0.0542210
\(131\) −5.08877 −0.444608 −0.222304 0.974977i \(-0.571358\pi\)
−0.222304 + 0.974977i \(0.571358\pi\)
\(132\) 0.604769 0.0526384
\(133\) 1.62222 0.140664
\(134\) 11.1958 0.967174
\(135\) 0.0940015 0.00809036
\(136\) 2.35704 0.202114
\(137\) 2.45837 0.210032 0.105016 0.994471i \(-0.466511\pi\)
0.105016 + 0.994471i \(0.466511\pi\)
\(138\) −10.3426 −0.880417
\(139\) 18.7419 1.58966 0.794832 0.606830i \(-0.207559\pi\)
0.794832 + 0.606830i \(0.207559\pi\)
\(140\) 0.0577961 0.00488466
\(141\) −5.07300 −0.427224
\(142\) 5.47878 0.459769
\(143\) −4.88872 −0.408816
\(144\) −4.76302 −0.396919
\(145\) 0.0802543 0.00666476
\(146\) −7.33698 −0.607213
\(147\) 5.56465 0.458965
\(148\) 2.85167 0.234405
\(149\) 12.2393 1.00269 0.501343 0.865249i \(-0.332840\pi\)
0.501343 + 0.865249i \(0.332840\pi\)
\(150\) −7.91253 −0.646055
\(151\) −14.7731 −1.20222 −0.601109 0.799167i \(-0.705274\pi\)
−0.601109 + 0.799167i \(0.705274\pi\)
\(152\) −3.19152 −0.258866
\(153\) 1.00000 0.0808452
\(154\) −2.23819 −0.180358
\(155\) 0.319485 0.0256617
\(156\) −2.12900 −0.170457
\(157\) −1.00000 −0.0798087
\(158\) −16.0176 −1.27429
\(159\) 4.08553 0.324004
\(160\) −0.266662 −0.0210815
\(161\) 7.81615 0.615999
\(162\) −1.58531 −0.124553
\(163\) 14.0288 1.09882 0.549412 0.835552i \(-0.314852\pi\)
0.549412 + 0.835552i \(0.314852\pi\)
\(164\) −1.32528 −0.103487
\(165\) −0.110774 −0.00862377
\(166\) −4.07892 −0.316585
\(167\) −8.24775 −0.638230 −0.319115 0.947716i \(-0.603386\pi\)
−0.319115 + 0.947716i \(0.603386\pi\)
\(168\) 2.82387 0.217866
\(169\) 4.21005 0.323850
\(170\) 0.149021 0.0114294
\(171\) −1.35404 −0.103546
\(172\) 2.03371 0.155069
\(173\) −15.5558 −1.18268 −0.591341 0.806421i \(-0.701401\pi\)
−0.591341 + 0.806421i \(0.701401\pi\)
\(174\) −1.35346 −0.102606
\(175\) 5.97971 0.452024
\(176\) 5.61290 0.423088
\(177\) −12.4715 −0.937413
\(178\) −12.8071 −0.959929
\(179\) −3.00889 −0.224895 −0.112448 0.993658i \(-0.535869\pi\)
−0.112448 + 0.993658i \(0.535869\pi\)
\(180\) −0.0482414 −0.00359570
\(181\) −0.214120 −0.0159155 −0.00795773 0.999968i \(-0.502533\pi\)
−0.00795773 + 0.999968i \(0.502533\pi\)
\(182\) 7.87922 0.584046
\(183\) −4.03768 −0.298474
\(184\) −15.3773 −1.13363
\(185\) −0.522334 −0.0384028
\(186\) −5.38802 −0.395069
\(187\) −1.17843 −0.0861754
\(188\) 2.60346 0.189877
\(189\) 1.19806 0.0871461
\(190\) −0.201781 −0.0146387
\(191\) −3.63746 −0.263197 −0.131599 0.991303i \(-0.542011\pi\)
−0.131599 + 0.991303i \(0.542011\pi\)
\(192\) −5.02888 −0.362928
\(193\) −3.88554 −0.279687 −0.139844 0.990174i \(-0.544660\pi\)
−0.139844 + 0.990174i \(0.544660\pi\)
\(194\) 7.30144 0.524213
\(195\) 0.389965 0.0279260
\(196\) −2.85577 −0.203984
\(197\) 4.76514 0.339502 0.169751 0.985487i \(-0.445704\pi\)
0.169751 + 0.985487i \(0.445704\pi\)
\(198\) 1.86818 0.132765
\(199\) −20.2641 −1.43648 −0.718242 0.695794i \(-0.755053\pi\)
−0.718242 + 0.695794i \(0.755053\pi\)
\(200\) −11.7644 −0.831866
\(201\) 7.06226 0.498133
\(202\) −1.49668 −0.105306
\(203\) 1.02285 0.0717900
\(204\) −0.513198 −0.0359311
\(205\) 0.242750 0.0169544
\(206\) −3.15573 −0.219870
\(207\) −6.52401 −0.453450
\(208\) −19.7594 −1.37007
\(209\) 1.59564 0.110373
\(210\) 0.178536 0.0123202
\(211\) −21.5453 −1.48324 −0.741618 0.670822i \(-0.765941\pi\)
−0.741618 + 0.670822i \(0.765941\pi\)
\(212\) −2.09669 −0.144001
\(213\) 3.45598 0.236800
\(214\) 21.5974 1.47637
\(215\) −0.372511 −0.0254050
\(216\) −2.35704 −0.160376
\(217\) 4.07187 0.276417
\(218\) −15.3463 −1.03938
\(219\) −4.62811 −0.312739
\(220\) 0.0568492 0.00383277
\(221\) 4.14850 0.279058
\(222\) 8.80901 0.591222
\(223\) 24.5380 1.64318 0.821592 0.570077i \(-0.193086\pi\)
0.821592 + 0.570077i \(0.193086\pi\)
\(224\) −3.39863 −0.227081
\(225\) −4.99116 −0.332744
\(226\) 29.8812 1.98767
\(227\) −5.47778 −0.363573 −0.181786 0.983338i \(-0.558188\pi\)
−0.181786 + 0.983338i \(0.558188\pi\)
\(228\) 0.694890 0.0460202
\(229\) 17.0915 1.12944 0.564718 0.825284i \(-0.308985\pi\)
0.564718 + 0.825284i \(0.308985\pi\)
\(230\) −0.972216 −0.0641060
\(231\) −1.41183 −0.0928917
\(232\) −2.01233 −0.132116
\(233\) 13.3891 0.877149 0.438574 0.898695i \(-0.355484\pi\)
0.438574 + 0.898695i \(0.355484\pi\)
\(234\) −6.57665 −0.429929
\(235\) −0.476870 −0.0311076
\(236\) 6.40033 0.416626
\(237\) −10.1038 −0.656311
\(238\) 1.89929 0.123113
\(239\) −20.8431 −1.34823 −0.674115 0.738627i \(-0.735475\pi\)
−0.674115 + 0.738627i \(0.735475\pi\)
\(240\) −0.447732 −0.0289009
\(241\) 4.56953 0.294349 0.147175 0.989111i \(-0.452982\pi\)
0.147175 + 0.989111i \(0.452982\pi\)
\(242\) 15.2369 0.979462
\(243\) −1.00000 −0.0641500
\(244\) 2.07213 0.132655
\(245\) 0.523086 0.0334187
\(246\) −4.09390 −0.261017
\(247\) −5.61723 −0.357416
\(248\) −8.01092 −0.508694
\(249\) −2.57295 −0.163054
\(250\) −1.48890 −0.0941661
\(251\) 19.4588 1.22823 0.614114 0.789218i \(-0.289514\pi\)
0.614114 + 0.789218i \(0.289514\pi\)
\(252\) −0.614842 −0.0387314
\(253\) 7.68810 0.483346
\(254\) 24.7031 1.55001
\(255\) 0.0940015 0.00588660
\(256\) 11.5751 0.723447
\(257\) −20.2944 −1.26593 −0.632964 0.774181i \(-0.718162\pi\)
−0.632964 + 0.774181i \(0.718162\pi\)
\(258\) 6.28228 0.391118
\(259\) −6.65721 −0.413659
\(260\) −0.200130 −0.0124115
\(261\) −0.853755 −0.0528461
\(262\) 8.06727 0.498398
\(263\) −19.0181 −1.17271 −0.586353 0.810055i \(-0.699437\pi\)
−0.586353 + 0.810055i \(0.699437\pi\)
\(264\) 2.77761 0.170950
\(265\) 0.384046 0.0235918
\(266\) −2.57172 −0.157682
\(267\) −8.07859 −0.494402
\(268\) −3.62434 −0.221392
\(269\) 7.11300 0.433687 0.216844 0.976206i \(-0.430424\pi\)
0.216844 + 0.976206i \(0.430424\pi\)
\(270\) −0.149021 −0.00906915
\(271\) 29.2547 1.77710 0.888548 0.458784i \(-0.151715\pi\)
0.888548 + 0.458784i \(0.151715\pi\)
\(272\) −4.76302 −0.288801
\(273\) 4.97015 0.300807
\(274\) −3.89727 −0.235442
\(275\) 5.88174 0.354683
\(276\) 3.34811 0.201532
\(277\) 18.3881 1.10483 0.552416 0.833569i \(-0.313706\pi\)
0.552416 + 0.833569i \(0.313706\pi\)
\(278\) −29.7116 −1.78198
\(279\) −3.39872 −0.203476
\(280\) 0.265448 0.0158636
\(281\) 31.2096 1.86181 0.930904 0.365264i \(-0.119021\pi\)
0.930904 + 0.365264i \(0.119021\pi\)
\(282\) 8.04227 0.478910
\(283\) 13.6719 0.812710 0.406355 0.913715i \(-0.366800\pi\)
0.406355 + 0.913715i \(0.366800\pi\)
\(284\) −1.77360 −0.105244
\(285\) −0.127282 −0.00753952
\(286\) 7.75013 0.458275
\(287\) 3.09387 0.182626
\(288\) 2.83678 0.167159
\(289\) 1.00000 0.0588235
\(290\) −0.127228 −0.00747107
\(291\) 4.60570 0.269991
\(292\) 2.37514 0.138995
\(293\) 16.5597 0.967431 0.483715 0.875225i \(-0.339287\pi\)
0.483715 + 0.875225i \(0.339287\pi\)
\(294\) −8.82168 −0.514491
\(295\) −1.17234 −0.0682561
\(296\) 13.0972 0.761262
\(297\) 1.17843 0.0683795
\(298\) −19.4031 −1.12399
\(299\) −27.0648 −1.56520
\(300\) 2.56146 0.147886
\(301\) −4.74769 −0.273652
\(302\) 23.4199 1.34766
\(303\) −0.944097 −0.0542370
\(304\) 6.44932 0.369894
\(305\) −0.379548 −0.0217329
\(306\) −1.58531 −0.0906260
\(307\) 13.0778 0.746391 0.373195 0.927753i \(-0.378262\pi\)
0.373195 + 0.927753i \(0.378262\pi\)
\(308\) 0.724550 0.0412850
\(309\) −1.99061 −0.113242
\(310\) −0.506482 −0.0287662
\(311\) −11.7915 −0.668632 −0.334316 0.942461i \(-0.608505\pi\)
−0.334316 + 0.942461i \(0.608505\pi\)
\(312\) −9.77817 −0.553580
\(313\) 27.2101 1.53800 0.769002 0.639247i \(-0.220754\pi\)
0.769002 + 0.639247i \(0.220754\pi\)
\(314\) 1.58531 0.0894640
\(315\) 0.112619 0.00634539
\(316\) 5.18524 0.291693
\(317\) 0.703267 0.0394994 0.0197497 0.999805i \(-0.493713\pi\)
0.0197497 + 0.999805i \(0.493713\pi\)
\(318\) −6.47682 −0.363202
\(319\) 1.00609 0.0563303
\(320\) −0.472722 −0.0264260
\(321\) 13.6235 0.760389
\(322\) −12.3910 −0.690524
\(323\) −1.35404 −0.0753407
\(324\) 0.513198 0.0285110
\(325\) −20.7058 −1.14855
\(326\) −22.2400 −1.23176
\(327\) −9.68033 −0.535323
\(328\) −6.08682 −0.336088
\(329\) −6.07776 −0.335078
\(330\) 0.175611 0.00966709
\(331\) 1.49559 0.0822052 0.0411026 0.999155i \(-0.486913\pi\)
0.0411026 + 0.999155i \(0.486913\pi\)
\(332\) 1.32043 0.0724682
\(333\) 5.55666 0.304503
\(334\) 13.0752 0.715444
\(335\) 0.663863 0.0362707
\(336\) −5.70639 −0.311309
\(337\) −21.5165 −1.17208 −0.586038 0.810284i \(-0.699313\pi\)
−0.586038 + 0.810284i \(0.699313\pi\)
\(338\) −6.67423 −0.363030
\(339\) 18.8489 1.02373
\(340\) −0.0482414 −0.00261626
\(341\) 4.00516 0.216892
\(342\) 2.14657 0.116073
\(343\) 15.0532 0.812797
\(344\) 9.34051 0.503606
\(345\) −0.613267 −0.0330172
\(346\) 24.6607 1.32577
\(347\) −4.01777 −0.215685 −0.107843 0.994168i \(-0.534394\pi\)
−0.107843 + 0.994168i \(0.534394\pi\)
\(348\) 0.438146 0.0234871
\(349\) 0.308071 0.0164907 0.00824533 0.999966i \(-0.497375\pi\)
0.00824533 + 0.999966i \(0.497375\pi\)
\(350\) −9.47968 −0.506710
\(351\) −4.14850 −0.221431
\(352\) −3.34295 −0.178180
\(353\) −16.4984 −0.878122 −0.439061 0.898457i \(-0.644689\pi\)
−0.439061 + 0.898457i \(0.644689\pi\)
\(354\) 19.7711 1.05082
\(355\) 0.324867 0.0172421
\(356\) 4.14592 0.219733
\(357\) 1.19806 0.0634081
\(358\) 4.77002 0.252103
\(359\) −10.1539 −0.535902 −0.267951 0.963433i \(-0.586347\pi\)
−0.267951 + 0.963433i \(0.586347\pi\)
\(360\) −0.221565 −0.0116775
\(361\) −17.1666 −0.903504
\(362\) 0.339447 0.0178409
\(363\) 9.61130 0.504462
\(364\) −2.55067 −0.133692
\(365\) −0.435050 −0.0227716
\(366\) 6.40096 0.334584
\(367\) 13.0341 0.680375 0.340188 0.940358i \(-0.389509\pi\)
0.340188 + 0.940358i \(0.389509\pi\)
\(368\) 31.0740 1.61984
\(369\) −2.58240 −0.134434
\(370\) 0.828060 0.0430488
\(371\) 4.89471 0.254121
\(372\) 1.74422 0.0904335
\(373\) 32.2015 1.66733 0.833666 0.552269i \(-0.186238\pi\)
0.833666 + 0.552269i \(0.186238\pi\)
\(374\) 1.86818 0.0966011
\(375\) −0.939185 −0.0484993
\(376\) 11.9573 0.616649
\(377\) −3.54180 −0.182412
\(378\) −1.89929 −0.0976891
\(379\) −24.5671 −1.26193 −0.630963 0.775813i \(-0.717340\pi\)
−0.630963 + 0.775813i \(0.717340\pi\)
\(380\) 0.0653207 0.00335088
\(381\) 15.5826 0.798319
\(382\) 5.76649 0.295039
\(383\) −12.8825 −0.658267 −0.329134 0.944283i \(-0.606757\pi\)
−0.329134 + 0.944283i \(0.606757\pi\)
\(384\) 13.6459 0.696363
\(385\) −0.132714 −0.00676375
\(386\) 6.15977 0.313524
\(387\) 3.96282 0.201441
\(388\) −2.36364 −0.119995
\(389\) −22.0471 −1.11783 −0.558915 0.829225i \(-0.688782\pi\)
−0.558915 + 0.829225i \(0.688782\pi\)
\(390\) −0.618215 −0.0313045
\(391\) −6.52401 −0.329933
\(392\) −13.1161 −0.662463
\(393\) 5.08877 0.256695
\(394\) −7.55421 −0.380575
\(395\) −0.949771 −0.0477881
\(396\) −0.604769 −0.0303908
\(397\) 7.25640 0.364188 0.182094 0.983281i \(-0.441712\pi\)
0.182094 + 0.983281i \(0.441712\pi\)
\(398\) 32.1248 1.61027
\(399\) −1.62222 −0.0812126
\(400\) 23.7730 1.18865
\(401\) 29.2533 1.46084 0.730420 0.682998i \(-0.239324\pi\)
0.730420 + 0.682998i \(0.239324\pi\)
\(402\) −11.1958 −0.558398
\(403\) −14.0996 −0.702351
\(404\) 0.484509 0.0241052
\(405\) −0.0940015 −0.00467097
\(406\) −1.62153 −0.0804753
\(407\) −6.54814 −0.324579
\(408\) −2.35704 −0.116691
\(409\) −2.46448 −0.121861 −0.0609303 0.998142i \(-0.519407\pi\)
−0.0609303 + 0.998142i \(0.519407\pi\)
\(410\) −0.384833 −0.0190055
\(411\) −2.45837 −0.121262
\(412\) 1.02158 0.0503295
\(413\) −14.9416 −0.735226
\(414\) 10.3426 0.508309
\(415\) −0.241861 −0.0118725
\(416\) 11.7684 0.576993
\(417\) −18.7419 −0.917793
\(418\) −2.52958 −0.123726
\(419\) −22.7859 −1.11316 −0.556582 0.830793i \(-0.687888\pi\)
−0.556582 + 0.830793i \(0.687888\pi\)
\(420\) −0.0577961 −0.00282016
\(421\) 18.3479 0.894222 0.447111 0.894479i \(-0.352453\pi\)
0.447111 + 0.894479i \(0.352453\pi\)
\(422\) 34.1558 1.66268
\(423\) 5.07300 0.246658
\(424\) −9.62975 −0.467662
\(425\) −4.99116 −0.242107
\(426\) −5.47878 −0.265448
\(427\) −4.83738 −0.234097
\(428\) −6.99155 −0.337949
\(429\) 4.88872 0.236030
\(430\) 0.590544 0.0284786
\(431\) −10.7821 −0.519356 −0.259678 0.965695i \(-0.583617\pi\)
−0.259678 + 0.965695i \(0.583617\pi\)
\(432\) 4.76302 0.229161
\(433\) 21.1233 1.01512 0.507560 0.861617i \(-0.330548\pi\)
0.507560 + 0.861617i \(0.330548\pi\)
\(434\) −6.45517 −0.309858
\(435\) −0.0802543 −0.00384790
\(436\) 4.96793 0.237921
\(437\) 8.83376 0.422576
\(438\) 7.33698 0.350575
\(439\) 31.4087 1.49905 0.749527 0.661974i \(-0.230281\pi\)
0.749527 + 0.661974i \(0.230281\pi\)
\(440\) 0.261099 0.0124474
\(441\) −5.56465 −0.264983
\(442\) −6.57665 −0.312819
\(443\) −32.7680 −1.55685 −0.778426 0.627736i \(-0.783982\pi\)
−0.778426 + 0.627736i \(0.783982\pi\)
\(444\) −2.85167 −0.135334
\(445\) −0.759400 −0.0359990
\(446\) −38.9002 −1.84198
\(447\) −12.2393 −0.578901
\(448\) −6.02490 −0.284650
\(449\) −17.6554 −0.833209 −0.416604 0.909088i \(-0.636780\pi\)
−0.416604 + 0.909088i \(0.636780\pi\)
\(450\) 7.91253 0.373000
\(451\) 3.04318 0.143298
\(452\) −9.67320 −0.454989
\(453\) 14.7731 0.694101
\(454\) 8.68396 0.407558
\(455\) 0.467202 0.0219028
\(456\) 3.19152 0.149457
\(457\) 9.67664 0.452654 0.226327 0.974051i \(-0.427328\pi\)
0.226327 + 0.974051i \(0.427328\pi\)
\(458\) −27.0952 −1.26608
\(459\) −1.00000 −0.0466760
\(460\) 0.314727 0.0146742
\(461\) 36.3672 1.69379 0.846894 0.531762i \(-0.178470\pi\)
0.846894 + 0.531762i \(0.178470\pi\)
\(462\) 2.23819 0.104130
\(463\) −27.7149 −1.28802 −0.644011 0.765016i \(-0.722731\pi\)
−0.644011 + 0.765016i \(0.722731\pi\)
\(464\) 4.06646 0.188781
\(465\) −0.319485 −0.0148158
\(466\) −21.2258 −0.983267
\(467\) 11.4205 0.528478 0.264239 0.964457i \(-0.414879\pi\)
0.264239 + 0.964457i \(0.414879\pi\)
\(468\) 2.12900 0.0984132
\(469\) 8.46101 0.390693
\(470\) 0.755986 0.0348710
\(471\) 1.00000 0.0460776
\(472\) 29.3957 1.35305
\(473\) −4.66991 −0.214723
\(474\) 16.0176 0.735712
\(475\) 6.75823 0.310089
\(476\) −0.614842 −0.0281813
\(477\) −4.08553 −0.187064
\(478\) 33.0427 1.51134
\(479\) 5.96685 0.272632 0.136316 0.990665i \(-0.456474\pi\)
0.136316 + 0.990665i \(0.456474\pi\)
\(480\) 0.266662 0.0121714
\(481\) 23.0518 1.05107
\(482\) −7.24411 −0.329960
\(483\) −7.81615 −0.355647
\(484\) −4.93250 −0.224205
\(485\) 0.432943 0.0196589
\(486\) 1.58531 0.0719110
\(487\) −7.19615 −0.326089 −0.163044 0.986619i \(-0.552131\pi\)
−0.163044 + 0.986619i \(0.552131\pi\)
\(488\) 9.51696 0.430813
\(489\) −14.0288 −0.634406
\(490\) −0.829252 −0.0374618
\(491\) −18.7626 −0.846743 −0.423371 0.905956i \(-0.639153\pi\)
−0.423371 + 0.905956i \(0.639153\pi\)
\(492\) 1.32528 0.0597484
\(493\) −0.853755 −0.0384512
\(494\) 8.90503 0.400656
\(495\) 0.110774 0.00497894
\(496\) 16.1882 0.726872
\(497\) 4.14047 0.185725
\(498\) 4.07892 0.182781
\(499\) −0.0189266 −0.000847271 0 −0.000423635 1.00000i \(-0.500135\pi\)
−0.000423635 1.00000i \(0.500135\pi\)
\(500\) 0.481988 0.0215552
\(501\) 8.24775 0.368483
\(502\) −30.8481 −1.37682
\(503\) −13.4502 −0.599715 −0.299857 0.953984i \(-0.596939\pi\)
−0.299857 + 0.953984i \(0.596939\pi\)
\(504\) −2.82387 −0.125785
\(505\) −0.0887466 −0.00394917
\(506\) −12.1880 −0.541822
\(507\) −4.21005 −0.186975
\(508\) −7.99694 −0.354807
\(509\) −8.21896 −0.364299 −0.182149 0.983271i \(-0.558305\pi\)
−0.182149 + 0.983271i \(0.558305\pi\)
\(510\) −0.149021 −0.00659877
\(511\) −5.54476 −0.245286
\(512\) 8.94160 0.395166
\(513\) 1.35404 0.0597823
\(514\) 32.1728 1.41908
\(515\) −0.187120 −0.00824551
\(516\) −2.03371 −0.0895291
\(517\) −5.97819 −0.262920
\(518\) 10.5537 0.463704
\(519\) 15.5558 0.682822
\(520\) −0.919163 −0.0403080
\(521\) −6.46434 −0.283208 −0.141604 0.989923i \(-0.545226\pi\)
−0.141604 + 0.989923i \(0.545226\pi\)
\(522\) 1.35346 0.0592395
\(523\) 21.0407 0.920046 0.460023 0.887907i \(-0.347841\pi\)
0.460023 + 0.887907i \(0.347841\pi\)
\(524\) −2.61155 −0.114086
\(525\) −5.97971 −0.260976
\(526\) 30.1495 1.31458
\(527\) −3.39872 −0.148051
\(528\) −5.61290 −0.244270
\(529\) 19.5627 0.850551
\(530\) −0.608831 −0.0264459
\(531\) 12.4715 0.541216
\(532\) 0.832520 0.0360943
\(533\) −10.7131 −0.464036
\(534\) 12.8071 0.554215
\(535\) 1.28063 0.0553664
\(536\) −16.6460 −0.718998
\(537\) 3.00889 0.129843
\(538\) −11.2763 −0.486155
\(539\) 6.55756 0.282454
\(540\) 0.0482414 0.00207598
\(541\) 5.74195 0.246866 0.123433 0.992353i \(-0.460610\pi\)
0.123433 + 0.992353i \(0.460610\pi\)
\(542\) −46.3777 −1.99209
\(543\) 0.214120 0.00918879
\(544\) 2.83678 0.121626
\(545\) −0.909966 −0.0389787
\(546\) −7.87922 −0.337199
\(547\) 37.9788 1.62385 0.811927 0.583759i \(-0.198419\pi\)
0.811927 + 0.583759i \(0.198419\pi\)
\(548\) 1.26163 0.0538941
\(549\) 4.03768 0.172324
\(550\) −9.32437 −0.397592
\(551\) 1.15602 0.0492480
\(552\) 15.3773 0.654503
\(553\) −12.1049 −0.514754
\(554\) −29.1507 −1.23850
\(555\) 0.522334 0.0221719
\(556\) 9.61829 0.407906
\(557\) 45.6129 1.93268 0.966341 0.257266i \(-0.0828216\pi\)
0.966341 + 0.257266i \(0.0828216\pi\)
\(558\) 5.38802 0.228093
\(559\) 16.4397 0.695327
\(560\) −0.536409 −0.0226674
\(561\) 1.17843 0.0497534
\(562\) −49.4768 −2.08705
\(563\) 1.55663 0.0656043 0.0328022 0.999462i \(-0.489557\pi\)
0.0328022 + 0.999462i \(0.489557\pi\)
\(564\) −2.60346 −0.109625
\(565\) 1.77182 0.0745411
\(566\) −21.6742 −0.911033
\(567\) −1.19806 −0.0503138
\(568\) −8.14586 −0.341793
\(569\) −24.6347 −1.03274 −0.516371 0.856365i \(-0.672717\pi\)
−0.516371 + 0.856365i \(0.672717\pi\)
\(570\) 0.201781 0.00845166
\(571\) −13.0800 −0.547382 −0.273691 0.961818i \(-0.588245\pi\)
−0.273691 + 0.961818i \(0.588245\pi\)
\(572\) −2.50888 −0.104902
\(573\) 3.63746 0.151957
\(574\) −4.90474 −0.204720
\(575\) 32.5624 1.35795
\(576\) 5.02888 0.209537
\(577\) 23.9952 0.998932 0.499466 0.866333i \(-0.333529\pi\)
0.499466 + 0.866333i \(0.333529\pi\)
\(578\) −1.58531 −0.0659401
\(579\) 3.88554 0.161477
\(580\) 0.0411864 0.00171017
\(581\) −3.08255 −0.127886
\(582\) −7.30144 −0.302655
\(583\) 4.81452 0.199397
\(584\) 10.9086 0.451403
\(585\) −0.389965 −0.0161231
\(586\) −26.2523 −1.08447
\(587\) 16.7954 0.693218 0.346609 0.938010i \(-0.387333\pi\)
0.346609 + 0.938010i \(0.387333\pi\)
\(588\) 2.85577 0.117770
\(589\) 4.60200 0.189622
\(590\) 1.85851 0.0765138
\(591\) −4.76514 −0.196012
\(592\) −26.4665 −1.08777
\(593\) 45.7288 1.87786 0.938929 0.344110i \(-0.111819\pi\)
0.938929 + 0.344110i \(0.111819\pi\)
\(594\) −1.86818 −0.0766522
\(595\) 0.112619 0.00461695
\(596\) 6.28121 0.257288
\(597\) 20.2641 0.829354
\(598\) 42.9061 1.75456
\(599\) 2.07274 0.0846897 0.0423449 0.999103i \(-0.486517\pi\)
0.0423449 + 0.999103i \(0.486517\pi\)
\(600\) 11.7644 0.480278
\(601\) −13.3066 −0.542787 −0.271393 0.962468i \(-0.587484\pi\)
−0.271393 + 0.962468i \(0.587484\pi\)
\(602\) 7.52655 0.306759
\(603\) −7.06226 −0.287597
\(604\) −7.58153 −0.308488
\(605\) 0.903477 0.0367316
\(606\) 1.49668 0.0607986
\(607\) 47.8341 1.94153 0.970763 0.240040i \(-0.0771607\pi\)
0.970763 + 0.240040i \(0.0771607\pi\)
\(608\) −3.84111 −0.155778
\(609\) −1.02285 −0.0414480
\(610\) 0.601700 0.0243621
\(611\) 21.0454 0.851404
\(612\) 0.513198 0.0207448
\(613\) 30.6114 1.23638 0.618191 0.786028i \(-0.287866\pi\)
0.618191 + 0.786028i \(0.287866\pi\)
\(614\) −20.7324 −0.836690
\(615\) −0.242750 −0.00978861
\(616\) 3.32774 0.134078
\(617\) 2.25525 0.0907928 0.0453964 0.998969i \(-0.485545\pi\)
0.0453964 + 0.998969i \(0.485545\pi\)
\(618\) 3.15573 0.126942
\(619\) −14.0837 −0.566071 −0.283035 0.959109i \(-0.591341\pi\)
−0.283035 + 0.959109i \(0.591341\pi\)
\(620\) 0.163959 0.00658476
\(621\) 6.52401 0.261799
\(622\) 18.6931 0.749524
\(623\) −9.67864 −0.387767
\(624\) 19.7594 0.791009
\(625\) 24.8675 0.994701
\(626\) −43.1363 −1.72407
\(627\) −1.59564 −0.0637238
\(628\) −0.513198 −0.0204788
\(629\) 5.55666 0.221558
\(630\) −0.178536 −0.00711306
\(631\) 10.2104 0.406471 0.203236 0.979130i \(-0.434854\pi\)
0.203236 + 0.979130i \(0.434854\pi\)
\(632\) 23.8150 0.947309
\(633\) 21.5453 0.856347
\(634\) −1.11489 −0.0442781
\(635\) 1.46479 0.0581282
\(636\) 2.09669 0.0831391
\(637\) −23.0850 −0.914659
\(638\) −1.59496 −0.0631453
\(639\) −3.45598 −0.136716
\(640\) 1.28273 0.0507045
\(641\) −15.1851 −0.599774 −0.299887 0.953975i \(-0.596949\pi\)
−0.299887 + 0.953975i \(0.596949\pi\)
\(642\) −21.5974 −0.852381
\(643\) −31.7845 −1.25346 −0.626728 0.779238i \(-0.715606\pi\)
−0.626728 + 0.779238i \(0.715606\pi\)
\(644\) 4.01124 0.158065
\(645\) 0.372511 0.0146676
\(646\) 2.14657 0.0844555
\(647\) −39.6248 −1.55781 −0.778906 0.627141i \(-0.784225\pi\)
−0.778906 + 0.627141i \(0.784225\pi\)
\(648\) 2.35704 0.0925932
\(649\) −14.6968 −0.576899
\(650\) 32.8251 1.28751
\(651\) −4.07187 −0.159589
\(652\) 7.19957 0.281957
\(653\) −5.10534 −0.199787 −0.0998937 0.994998i \(-0.531850\pi\)
−0.0998937 + 0.994998i \(0.531850\pi\)
\(654\) 15.3463 0.600088
\(655\) 0.478353 0.0186908
\(656\) 12.3000 0.480236
\(657\) 4.62811 0.180560
\(658\) 9.63512 0.375616
\(659\) 23.2663 0.906326 0.453163 0.891428i \(-0.350296\pi\)
0.453163 + 0.891428i \(0.350296\pi\)
\(660\) −0.0568492 −0.00221285
\(661\) 1.49758 0.0582491 0.0291246 0.999576i \(-0.490728\pi\)
0.0291246 + 0.999576i \(0.490728\pi\)
\(662\) −2.37097 −0.0921505
\(663\) −4.14850 −0.161114
\(664\) 6.06454 0.235350
\(665\) −0.152491 −0.00591335
\(666\) −8.80901 −0.341342
\(667\) 5.56991 0.215668
\(668\) −4.23273 −0.163769
\(669\) −24.5380 −0.948692
\(670\) −1.05243 −0.0406588
\(671\) −4.75813 −0.183686
\(672\) 3.39863 0.131105
\(673\) 29.8941 1.15233 0.576167 0.817332i \(-0.304548\pi\)
0.576167 + 0.817332i \(0.304548\pi\)
\(674\) 34.1102 1.31388
\(675\) 4.99116 0.192110
\(676\) 2.16059 0.0830997
\(677\) 47.9436 1.84262 0.921311 0.388827i \(-0.127120\pi\)
0.921311 + 0.388827i \(0.127120\pi\)
\(678\) −29.8812 −1.14758
\(679\) 5.51790 0.211758
\(680\) −0.221565 −0.00849663
\(681\) 5.47778 0.209909
\(682\) −6.34941 −0.243131
\(683\) 11.4373 0.437636 0.218818 0.975766i \(-0.429780\pi\)
0.218818 + 0.975766i \(0.429780\pi\)
\(684\) −0.694890 −0.0265698
\(685\) −0.231090 −0.00882950
\(686\) −23.8640 −0.911130
\(687\) −17.0915 −0.652080
\(688\) −18.8750 −0.719602
\(689\) −16.9488 −0.645699
\(690\) 0.972216 0.0370116
\(691\) −5.89264 −0.224166 −0.112083 0.993699i \(-0.535752\pi\)
−0.112083 + 0.993699i \(0.535752\pi\)
\(692\) −7.98319 −0.303475
\(693\) 1.41183 0.0536311
\(694\) 6.36940 0.241779
\(695\) −1.76176 −0.0668275
\(696\) 2.01233 0.0762773
\(697\) −2.58240 −0.0978154
\(698\) −0.488387 −0.0184857
\(699\) −13.3891 −0.506422
\(700\) 3.06878 0.115989
\(701\) −13.1328 −0.496019 −0.248009 0.968758i \(-0.579776\pi\)
−0.248009 + 0.968758i \(0.579776\pi\)
\(702\) 6.57665 0.248220
\(703\) −7.52393 −0.283770
\(704\) −5.92619 −0.223352
\(705\) 0.476870 0.0179600
\(706\) 26.1551 0.984359
\(707\) −1.13109 −0.0425388
\(708\) −6.40033 −0.240539
\(709\) −5.19511 −0.195106 −0.0975532 0.995230i \(-0.531102\pi\)
−0.0975532 + 0.995230i \(0.531102\pi\)
\(710\) −0.515014 −0.0193281
\(711\) 10.1038 0.378921
\(712\) 19.0415 0.713612
\(713\) 22.1733 0.830396
\(714\) −1.89929 −0.0710793
\(715\) 0.459547 0.0171861
\(716\) −1.54416 −0.0577079
\(717\) 20.8431 0.778401
\(718\) 16.0970 0.600736
\(719\) −19.0009 −0.708614 −0.354307 0.935129i \(-0.615283\pi\)
−0.354307 + 0.935129i \(0.615283\pi\)
\(720\) 0.447732 0.0166860
\(721\) −2.38487 −0.0888173
\(722\) 27.2143 1.01281
\(723\) −4.56953 −0.169943
\(724\) −0.109886 −0.00408389
\(725\) 4.26123 0.158258
\(726\) −15.2369 −0.565493
\(727\) 34.0186 1.26168 0.630841 0.775912i \(-0.282710\pi\)
0.630841 + 0.775912i \(0.282710\pi\)
\(728\) −11.7148 −0.434181
\(729\) 1.00000 0.0370370
\(730\) 0.689688 0.0255265
\(731\) 3.96282 0.146570
\(732\) −2.07213 −0.0765881
\(733\) 15.1993 0.561398 0.280699 0.959796i \(-0.409434\pi\)
0.280699 + 0.959796i \(0.409434\pi\)
\(734\) −20.6631 −0.762688
\(735\) −0.523086 −0.0192943
\(736\) −18.5072 −0.682184
\(737\) 8.32239 0.306559
\(738\) 4.09390 0.150699
\(739\) 22.5626 0.829980 0.414990 0.909826i \(-0.363785\pi\)
0.414990 + 0.909826i \(0.363785\pi\)
\(740\) −0.268061 −0.00985412
\(741\) 5.61723 0.206354
\(742\) −7.75962 −0.284865
\(743\) −17.1847 −0.630445 −0.315223 0.949018i \(-0.602079\pi\)
−0.315223 + 0.949018i \(0.602079\pi\)
\(744\) 8.01092 0.293694
\(745\) −1.15052 −0.0421517
\(746\) −51.0493 −1.86905
\(747\) 2.57295 0.0941393
\(748\) −0.604769 −0.0221125
\(749\) 16.3218 0.596384
\(750\) 1.48890 0.0543668
\(751\) 9.63721 0.351667 0.175833 0.984420i \(-0.443738\pi\)
0.175833 + 0.984420i \(0.443738\pi\)
\(752\) −24.1628 −0.881128
\(753\) −19.4588 −0.709117
\(754\) 5.61485 0.204481
\(755\) 1.38869 0.0505398
\(756\) 0.614842 0.0223616
\(757\) 52.4796 1.90740 0.953702 0.300754i \(-0.0972382\pi\)
0.953702 + 0.300754i \(0.0972382\pi\)
\(758\) 38.9463 1.41459
\(759\) −7.68810 −0.279060
\(760\) 0.300008 0.0108824
\(761\) 12.8888 0.467217 0.233609 0.972331i \(-0.424947\pi\)
0.233609 + 0.972331i \(0.424947\pi\)
\(762\) −24.7031 −0.894901
\(763\) −11.5976 −0.419862
\(764\) −1.86674 −0.0675362
\(765\) −0.0940015 −0.00339863
\(766\) 20.4228 0.737905
\(767\) 51.7379 1.86815
\(768\) −11.5751 −0.417682
\(769\) 44.8067 1.61577 0.807886 0.589339i \(-0.200612\pi\)
0.807886 + 0.589339i \(0.200612\pi\)
\(770\) 0.210393 0.00758204
\(771\) 20.2944 0.730884
\(772\) −1.99405 −0.0717675
\(773\) −9.47075 −0.340639 −0.170320 0.985389i \(-0.554480\pi\)
−0.170320 + 0.985389i \(0.554480\pi\)
\(774\) −6.28228 −0.225812
\(775\) 16.9636 0.609350
\(776\) −10.8558 −0.389701
\(777\) 6.65721 0.238826
\(778\) 34.9514 1.25307
\(779\) 3.49667 0.125281
\(780\) 0.200130 0.00716579
\(781\) 4.07263 0.145730
\(782\) 10.3426 0.369849
\(783\) 0.853755 0.0305107
\(784\) 26.5046 0.946592
\(785\) 0.0940015 0.00335506
\(786\) −8.06727 −0.287750
\(787\) 10.9358 0.389820 0.194910 0.980821i \(-0.437559\pi\)
0.194910 + 0.980821i \(0.437559\pi\)
\(788\) 2.44546 0.0871159
\(789\) 19.0181 0.677063
\(790\) 1.50568 0.0535696
\(791\) 22.5821 0.802926
\(792\) −2.77761 −0.0986980
\(793\) 16.7503 0.594821
\(794\) −11.5036 −0.408248
\(795\) −0.384046 −0.0136207
\(796\) −10.3995 −0.368600
\(797\) −0.490880 −0.0173879 −0.00869393 0.999962i \(-0.502767\pi\)
−0.00869393 + 0.999962i \(0.502767\pi\)
\(798\) 2.57172 0.0910378
\(799\) 5.07300 0.179470
\(800\) −14.1588 −0.500590
\(801\) 8.07859 0.285443
\(802\) −46.3755 −1.63757
\(803\) −5.45392 −0.192465
\(804\) 3.62434 0.127821
\(805\) −0.734730 −0.0258958
\(806\) 22.3522 0.787323
\(807\) −7.11300 −0.250389
\(808\) 2.22527 0.0782848
\(809\) 8.86525 0.311686 0.155843 0.987782i \(-0.450191\pi\)
0.155843 + 0.987782i \(0.450191\pi\)
\(810\) 0.149021 0.00523607
\(811\) −14.8785 −0.522456 −0.261228 0.965277i \(-0.584127\pi\)
−0.261228 + 0.965277i \(0.584127\pi\)
\(812\) 0.524925 0.0184213
\(813\) −29.2547 −1.02601
\(814\) 10.3808 0.363847
\(815\) −1.31873 −0.0461932
\(816\) 4.76302 0.166739
\(817\) −5.36581 −0.187726
\(818\) 3.90696 0.136604
\(819\) −4.97015 −0.173671
\(820\) 0.124579 0.00435048
\(821\) 35.2954 1.23182 0.615909 0.787817i \(-0.288789\pi\)
0.615909 + 0.787817i \(0.288789\pi\)
\(822\) 3.89727 0.135933
\(823\) −26.2260 −0.914181 −0.457091 0.889420i \(-0.651108\pi\)
−0.457091 + 0.889420i \(0.651108\pi\)
\(824\) 4.69194 0.163452
\(825\) −5.88174 −0.204776
\(826\) 23.6870 0.824175
\(827\) 12.8288 0.446100 0.223050 0.974807i \(-0.428399\pi\)
0.223050 + 0.974807i \(0.428399\pi\)
\(828\) −3.34811 −0.116355
\(829\) −38.9339 −1.35223 −0.676116 0.736795i \(-0.736338\pi\)
−0.676116 + 0.736795i \(0.736338\pi\)
\(830\) 0.383424 0.0133089
\(831\) −18.3881 −0.637875
\(832\) 20.8623 0.723270
\(833\) −5.56465 −0.192804
\(834\) 29.7116 1.02883
\(835\) 0.775302 0.0268304
\(836\) 0.818880 0.0283216
\(837\) 3.39872 0.117477
\(838\) 36.1227 1.24784
\(839\) −4.52967 −0.156382 −0.0781908 0.996938i \(-0.524914\pi\)
−0.0781908 + 0.996938i \(0.524914\pi\)
\(840\) −0.265448 −0.00915884
\(841\) −28.2711 −0.974866
\(842\) −29.0870 −1.00241
\(843\) −31.2096 −1.07492
\(844\) −11.0570 −0.380597
\(845\) −0.395751 −0.0136143
\(846\) −8.04227 −0.276499
\(847\) 11.5149 0.395657
\(848\) 19.4595 0.668242
\(849\) −13.6719 −0.469219
\(850\) 7.91253 0.271397
\(851\) −36.2517 −1.24269
\(852\) 1.77360 0.0607625
\(853\) 33.1425 1.13478 0.567388 0.823451i \(-0.307954\pi\)
0.567388 + 0.823451i \(0.307954\pi\)
\(854\) 7.66874 0.262419
\(855\) 0.127282 0.00435294
\(856\) −32.1111 −1.09753
\(857\) 30.3101 1.03537 0.517687 0.855570i \(-0.326793\pi\)
0.517687 + 0.855570i \(0.326793\pi\)
\(858\) −7.75013 −0.264585
\(859\) 13.9450 0.475799 0.237899 0.971290i \(-0.423541\pi\)
0.237899 + 0.971290i \(0.423541\pi\)
\(860\) −0.191172 −0.00651891
\(861\) −3.09387 −0.105439
\(862\) 17.0930 0.582189
\(863\) −7.77055 −0.264512 −0.132256 0.991216i \(-0.542222\pi\)
−0.132256 + 0.991216i \(0.542222\pi\)
\(864\) −2.83678 −0.0965092
\(865\) 1.46227 0.0497185
\(866\) −33.4868 −1.13793
\(867\) −1.00000 −0.0339618
\(868\) 2.08968 0.0709283
\(869\) −11.9066 −0.403904
\(870\) 0.127228 0.00431342
\(871\) −29.2978 −0.992717
\(872\) 22.8169 0.772678
\(873\) −4.60570 −0.155879
\(874\) −14.0042 −0.473700
\(875\) −1.12520 −0.0380387
\(876\) −2.37514 −0.0802485
\(877\) 24.2895 0.820198 0.410099 0.912041i \(-0.365494\pi\)
0.410099 + 0.912041i \(0.365494\pi\)
\(878\) −49.7924 −1.68041
\(879\) −16.5597 −0.558546
\(880\) −0.527621 −0.0177861
\(881\) −12.0254 −0.405146 −0.202573 0.979267i \(-0.564930\pi\)
−0.202573 + 0.979267i \(0.564930\pi\)
\(882\) 8.82168 0.297041
\(883\) −6.17274 −0.207729 −0.103865 0.994591i \(-0.533121\pi\)
−0.103865 + 0.994591i \(0.533121\pi\)
\(884\) 2.12900 0.0716061
\(885\) 1.17234 0.0394077
\(886\) 51.9473 1.74520
\(887\) −27.6016 −0.926772 −0.463386 0.886157i \(-0.653366\pi\)
−0.463386 + 0.886157i \(0.653366\pi\)
\(888\) −13.0972 −0.439515
\(889\) 18.6688 0.626133
\(890\) 1.20388 0.0403542
\(891\) −1.17843 −0.0394789
\(892\) 12.5928 0.421639
\(893\) −6.86904 −0.229864
\(894\) 19.4031 0.648937
\(895\) 0.282841 0.00945432
\(896\) 16.3486 0.546168
\(897\) 27.0648 0.903669
\(898\) 27.9892 0.934012
\(899\) 2.90168 0.0967764
\(900\) −2.56146 −0.0853819
\(901\) −4.08553 −0.136109
\(902\) −4.82438 −0.160634
\(903\) 4.74769 0.157993
\(904\) −44.4275 −1.47764
\(905\) 0.0201277 0.000669066 0
\(906\) −23.4199 −0.778074
\(907\) −35.2935 −1.17190 −0.585951 0.810346i \(-0.699279\pi\)
−0.585951 + 0.810346i \(0.699279\pi\)
\(908\) −2.81118 −0.0932924
\(909\) 0.944097 0.0313137
\(910\) −0.740659 −0.0245526
\(911\) 22.4896 0.745113 0.372557 0.928009i \(-0.378481\pi\)
0.372557 + 0.928009i \(0.378481\pi\)
\(912\) −6.44932 −0.213558
\(913\) −3.03204 −0.100346
\(914\) −15.3404 −0.507417
\(915\) 0.379548 0.0125475
\(916\) 8.77131 0.289812
\(917\) 6.09666 0.201329
\(918\) 1.58531 0.0523229
\(919\) −7.59835 −0.250646 −0.125323 0.992116i \(-0.539997\pi\)
−0.125323 + 0.992116i \(0.539997\pi\)
\(920\) 1.44549 0.0476565
\(921\) −13.0778 −0.430929
\(922\) −57.6531 −1.89870
\(923\) −14.3371 −0.471912
\(924\) −0.724550 −0.0238359
\(925\) −27.7342 −0.911894
\(926\) 43.9367 1.44385
\(927\) 1.99061 0.0653802
\(928\) −2.42192 −0.0795033
\(929\) 8.66415 0.284261 0.142131 0.989848i \(-0.454605\pi\)
0.142131 + 0.989848i \(0.454605\pi\)
\(930\) 0.506482 0.0166082
\(931\) 7.53475 0.246942
\(932\) 6.87126 0.225076
\(933\) 11.7915 0.386035
\(934\) −18.1050 −0.592414
\(935\) 0.110774 0.00362271
\(936\) 9.77817 0.319609
\(937\) 31.5936 1.03212 0.516059 0.856553i \(-0.327399\pi\)
0.516059 + 0.856553i \(0.327399\pi\)
\(938\) −13.4133 −0.437960
\(939\) −27.2101 −0.887967
\(940\) −0.244729 −0.00798218
\(941\) −46.0415 −1.50091 −0.750455 0.660921i \(-0.770166\pi\)
−0.750455 + 0.660921i \(0.770166\pi\)
\(942\) −1.58531 −0.0516521
\(943\) 16.8476 0.548634
\(944\) −59.4019 −1.93337
\(945\) −0.112619 −0.00366351
\(946\) 7.40324 0.240700
\(947\) 30.4961 0.990990 0.495495 0.868611i \(-0.334987\pi\)
0.495495 + 0.868611i \(0.334987\pi\)
\(948\) −5.18524 −0.168409
\(949\) 19.1997 0.623250
\(950\) −10.7139 −0.347604
\(951\) −0.703267 −0.0228050
\(952\) −2.82387 −0.0915222
\(953\) 34.4385 1.11557 0.557786 0.829985i \(-0.311651\pi\)
0.557786 + 0.829985i \(0.311651\pi\)
\(954\) 6.47682 0.209695
\(955\) 0.341927 0.0110645
\(956\) −10.6967 −0.345954
\(957\) −1.00609 −0.0325223
\(958\) −9.45929 −0.305616
\(959\) −2.94527 −0.0951078
\(960\) 0.472722 0.0152571
\(961\) −19.4487 −0.627377
\(962\) −36.5442 −1.17823
\(963\) −13.6235 −0.439011
\(964\) 2.34507 0.0755298
\(965\) 0.365247 0.0117577
\(966\) 12.3910 0.398674
\(967\) −16.7249 −0.537837 −0.268918 0.963163i \(-0.586666\pi\)
−0.268918 + 0.963163i \(0.586666\pi\)
\(968\) −22.6542 −0.728133
\(969\) 1.35404 0.0434980
\(970\) −0.686347 −0.0220373
\(971\) 13.5678 0.435411 0.217706 0.976014i \(-0.430143\pi\)
0.217706 + 0.976014i \(0.430143\pi\)
\(972\) −0.513198 −0.0164608
\(973\) −22.4539 −0.719838
\(974\) 11.4081 0.365539
\(975\) 20.7058 0.663118
\(976\) −19.2316 −0.615587
\(977\) −2.41584 −0.0772895 −0.0386448 0.999253i \(-0.512304\pi\)
−0.0386448 + 0.999253i \(0.512304\pi\)
\(978\) 22.2400 0.711157
\(979\) −9.52007 −0.304263
\(980\) 0.268447 0.00857522
\(981\) 9.68033 0.309069
\(982\) 29.7444 0.949183
\(983\) −3.62934 −0.115758 −0.0578790 0.998324i \(-0.518434\pi\)
−0.0578790 + 0.998324i \(0.518434\pi\)
\(984\) 6.08682 0.194041
\(985\) −0.447930 −0.0142722
\(986\) 1.35346 0.0431031
\(987\) 6.07776 0.193457
\(988\) −2.88275 −0.0917126
\(989\) −25.8534 −0.822092
\(990\) −0.175611 −0.00558130
\(991\) 53.7197 1.70646 0.853231 0.521533i \(-0.174640\pi\)
0.853231 + 0.521533i \(0.174640\pi\)
\(992\) −9.64143 −0.306116
\(993\) −1.49559 −0.0474612
\(994\) −6.56391 −0.208195
\(995\) 1.90486 0.0603880
\(996\) −1.32043 −0.0418395
\(997\) 28.0904 0.889633 0.444816 0.895622i \(-0.353269\pi\)
0.444816 + 0.895622i \(0.353269\pi\)
\(998\) 0.0300045 0.000949775 0
\(999\) −5.55666 −0.175805
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 \(a_p\))