Properties

Label 6027.2.a.bn.1.12
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.154130 q^{2} -1.00000 q^{3} -1.97624 q^{4} -1.29015 q^{5} -0.154130 q^{6} -0.612860 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.154130 q^{2} -1.00000 q^{3} -1.97624 q^{4} -1.29015 q^{5} -0.154130 q^{6} -0.612860 q^{8} +1.00000 q^{9} -0.198852 q^{10} -3.77802 q^{11} +1.97624 q^{12} +5.50821 q^{13} +1.29015 q^{15} +3.85803 q^{16} +0.121569 q^{17} +0.154130 q^{18} -6.50386 q^{19} +2.54966 q^{20} -0.582308 q^{22} +2.09276 q^{23} +0.612860 q^{24} -3.33550 q^{25} +0.848983 q^{26} -1.00000 q^{27} -1.13312 q^{29} +0.198852 q^{30} -0.113328 q^{31} +1.82036 q^{32} +3.77802 q^{33} +0.0187375 q^{34} -1.97624 q^{36} -4.51508 q^{37} -1.00244 q^{38} -5.50821 q^{39} +0.790684 q^{40} +1.00000 q^{41} +4.61175 q^{43} +7.46629 q^{44} -1.29015 q^{45} +0.322558 q^{46} -3.21303 q^{47} -3.85803 q^{48} -0.514103 q^{50} -0.121569 q^{51} -10.8856 q^{52} -3.27698 q^{53} -0.154130 q^{54} +4.87422 q^{55} +6.50386 q^{57} -0.174649 q^{58} -14.3034 q^{59} -2.54966 q^{60} -2.67949 q^{61} -0.0174672 q^{62} -7.43548 q^{64} -7.10643 q^{65} +0.582308 q^{66} +7.34269 q^{67} -0.240250 q^{68} -2.09276 q^{69} +3.10604 q^{71} -0.612860 q^{72} -0.731899 q^{73} -0.695912 q^{74} +3.33550 q^{75} +12.8532 q^{76} -0.848983 q^{78} -2.88303 q^{79} -4.97745 q^{80} +1.00000 q^{81} +0.154130 q^{82} -6.55587 q^{83} -0.156842 q^{85} +0.710811 q^{86} +1.13312 q^{87} +2.31540 q^{88} -3.36880 q^{89} -0.198852 q^{90} -4.13580 q^{92} +0.113328 q^{93} -0.495226 q^{94} +8.39098 q^{95} -1.82036 q^{96} -6.52076 q^{97} -3.77802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.154130 0.108987 0.0544933 0.998514i \(-0.482646\pi\)
0.0544933 + 0.998514i \(0.482646\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.97624 −0.988122
\(5\) −1.29015 −0.576974 −0.288487 0.957484i \(-0.593152\pi\)
−0.288487 + 0.957484i \(0.593152\pi\)
\(6\) −0.154130 −0.0629235
\(7\) 0 0
\(8\) −0.612860 −0.216679
\(9\) 1.00000 0.333333
\(10\) −0.198852 −0.0628825
\(11\) −3.77802 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(12\) 1.97624 0.570492
\(13\) 5.50821 1.52770 0.763851 0.645393i \(-0.223306\pi\)
0.763851 + 0.645393i \(0.223306\pi\)
\(14\) 0 0
\(15\) 1.29015 0.333116
\(16\) 3.85803 0.964507
\(17\) 0.121569 0.0294848 0.0147424 0.999891i \(-0.495307\pi\)
0.0147424 + 0.999891i \(0.495307\pi\)
\(18\) 0.154130 0.0363289
\(19\) −6.50386 −1.49209 −0.746044 0.665897i \(-0.768049\pi\)
−0.746044 + 0.665897i \(0.768049\pi\)
\(20\) 2.54966 0.570121
\(21\) 0 0
\(22\) −0.582308 −0.124148
\(23\) 2.09276 0.436370 0.218185 0.975907i \(-0.429986\pi\)
0.218185 + 0.975907i \(0.429986\pi\)
\(24\) 0.612860 0.125100
\(25\) −3.33550 −0.667101
\(26\) 0.848983 0.166499
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.13312 −0.210416 −0.105208 0.994450i \(-0.533551\pi\)
−0.105208 + 0.994450i \(0.533551\pi\)
\(30\) 0.198852 0.0363052
\(31\) −0.113328 −0.0203543 −0.0101771 0.999948i \(-0.503240\pi\)
−0.0101771 + 0.999948i \(0.503240\pi\)
\(32\) 1.82036 0.321797
\(33\) 3.77802 0.657669
\(34\) 0.0187375 0.00321345
\(35\) 0 0
\(36\) −1.97624 −0.329374
\(37\) −4.51508 −0.742275 −0.371137 0.928578i \(-0.621032\pi\)
−0.371137 + 0.928578i \(0.621032\pi\)
\(38\) −1.00244 −0.162618
\(39\) −5.50821 −0.882019
\(40\) 0.790684 0.125018
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 4.61175 0.703285 0.351642 0.936134i \(-0.385623\pi\)
0.351642 + 0.936134i \(0.385623\pi\)
\(44\) 7.46629 1.12558
\(45\) −1.29015 −0.192325
\(46\) 0.322558 0.0475586
\(47\) −3.21303 −0.468669 −0.234334 0.972156i \(-0.575291\pi\)
−0.234334 + 0.972156i \(0.575291\pi\)
\(48\) −3.85803 −0.556858
\(49\) 0 0
\(50\) −0.514103 −0.0727051
\(51\) −0.121569 −0.0170230
\(52\) −10.8856 −1.50956
\(53\) −3.27698 −0.450128 −0.225064 0.974344i \(-0.572259\pi\)
−0.225064 + 0.974344i \(0.572259\pi\)
\(54\) −0.154130 −0.0209745
\(55\) 4.87422 0.657240
\(56\) 0 0
\(57\) 6.50386 0.861457
\(58\) −0.174649 −0.0229325
\(59\) −14.3034 −1.86214 −0.931071 0.364838i \(-0.881124\pi\)
−0.931071 + 0.364838i \(0.881124\pi\)
\(60\) −2.54966 −0.329159
\(61\) −2.67949 −0.343073 −0.171537 0.985178i \(-0.554873\pi\)
−0.171537 + 0.985178i \(0.554873\pi\)
\(62\) −0.0174672 −0.00221834
\(63\) 0 0
\(64\) −7.43548 −0.929435
\(65\) −7.10643 −0.881445
\(66\) 0.582308 0.0716771
\(67\) 7.34269 0.897052 0.448526 0.893770i \(-0.351949\pi\)
0.448526 + 0.893770i \(0.351949\pi\)
\(68\) −0.240250 −0.0291346
\(69\) −2.09276 −0.251939
\(70\) 0 0
\(71\) 3.10604 0.368619 0.184310 0.982868i \(-0.440995\pi\)
0.184310 + 0.982868i \(0.440995\pi\)
\(72\) −0.612860 −0.0722263
\(73\) −0.731899 −0.0856622 −0.0428311 0.999082i \(-0.513638\pi\)
−0.0428311 + 0.999082i \(0.513638\pi\)
\(74\) −0.695912 −0.0808981
\(75\) 3.33550 0.385151
\(76\) 12.8532 1.47436
\(77\) 0 0
\(78\) −0.848983 −0.0961284
\(79\) −2.88303 −0.324367 −0.162183 0.986761i \(-0.551854\pi\)
−0.162183 + 0.986761i \(0.551854\pi\)
\(80\) −4.97745 −0.556495
\(81\) 1.00000 0.111111
\(82\) 0.154130 0.0170209
\(83\) −6.55587 −0.719600 −0.359800 0.933029i \(-0.617155\pi\)
−0.359800 + 0.933029i \(0.617155\pi\)
\(84\) 0 0
\(85\) −0.156842 −0.0170120
\(86\) 0.710811 0.0766487
\(87\) 1.13312 0.121483
\(88\) 2.31540 0.246822
\(89\) −3.36880 −0.357092 −0.178546 0.983932i \(-0.557139\pi\)
−0.178546 + 0.983932i \(0.557139\pi\)
\(90\) −0.198852 −0.0209608
\(91\) 0 0
\(92\) −4.13580 −0.431187
\(93\) 0.113328 0.0117515
\(94\) −0.495226 −0.0510787
\(95\) 8.39098 0.860896
\(96\) −1.82036 −0.185790
\(97\) −6.52076 −0.662083 −0.331042 0.943616i \(-0.607400\pi\)
−0.331042 + 0.943616i \(0.607400\pi\)
\(98\) 0 0
\(99\) −3.77802 −0.379705
\(100\) 6.59177 0.659177
\(101\) −3.97834 −0.395860 −0.197930 0.980216i \(-0.563422\pi\)
−0.197930 + 0.980216i \(0.563422\pi\)
\(102\) −0.0187375 −0.00185529
\(103\) −2.95010 −0.290682 −0.145341 0.989382i \(-0.546428\pi\)
−0.145341 + 0.989382i \(0.546428\pi\)
\(104\) −3.37576 −0.331021
\(105\) 0 0
\(106\) −0.505083 −0.0490580
\(107\) −1.30384 −0.126047 −0.0630236 0.998012i \(-0.520074\pi\)
−0.0630236 + 0.998012i \(0.520074\pi\)
\(108\) 1.97624 0.190164
\(109\) 10.5669 1.01213 0.506064 0.862496i \(-0.331100\pi\)
0.506064 + 0.862496i \(0.331100\pi\)
\(110\) 0.751266 0.0716304
\(111\) 4.51508 0.428553
\(112\) 0 0
\(113\) −4.50316 −0.423622 −0.211811 0.977311i \(-0.567936\pi\)
−0.211811 + 0.977311i \(0.567936\pi\)
\(114\) 1.00244 0.0938874
\(115\) −2.69998 −0.251774
\(116\) 2.23933 0.207916
\(117\) 5.50821 0.509234
\(118\) −2.20459 −0.202949
\(119\) 0 0
\(120\) −0.790684 −0.0721792
\(121\) 3.27343 0.297584
\(122\) −0.412991 −0.0373904
\(123\) −1.00000 −0.0901670
\(124\) 0.223963 0.0201125
\(125\) 10.7541 0.961874
\(126\) 0 0
\(127\) 4.04765 0.359171 0.179586 0.983742i \(-0.442524\pi\)
0.179586 + 0.983742i \(0.442524\pi\)
\(128\) −4.78675 −0.423093
\(129\) −4.61175 −0.406042
\(130\) −1.09532 −0.0960657
\(131\) 7.14901 0.624611 0.312306 0.949982i \(-0.398899\pi\)
0.312306 + 0.949982i \(0.398899\pi\)
\(132\) −7.46629 −0.649857
\(133\) 0 0
\(134\) 1.13173 0.0977667
\(135\) 1.29015 0.111039
\(136\) −0.0745047 −0.00638873
\(137\) −17.5752 −1.50155 −0.750776 0.660557i \(-0.770320\pi\)
−0.750776 + 0.660557i \(0.770320\pi\)
\(138\) −0.322558 −0.0274579
\(139\) −3.95483 −0.335444 −0.167722 0.985834i \(-0.553641\pi\)
−0.167722 + 0.985834i \(0.553641\pi\)
\(140\) 0 0
\(141\) 3.21303 0.270586
\(142\) 0.478735 0.0401746
\(143\) −20.8101 −1.74023
\(144\) 3.85803 0.321502
\(145\) 1.46190 0.121404
\(146\) −0.112808 −0.00933604
\(147\) 0 0
\(148\) 8.92290 0.733458
\(149\) 16.2067 1.32770 0.663851 0.747865i \(-0.268921\pi\)
0.663851 + 0.747865i \(0.268921\pi\)
\(150\) 0.514103 0.0419763
\(151\) 14.5427 1.18347 0.591733 0.806134i \(-0.298444\pi\)
0.591733 + 0.806134i \(0.298444\pi\)
\(152\) 3.98596 0.323304
\(153\) 0.121569 0.00982826
\(154\) 0 0
\(155\) 0.146210 0.0117439
\(156\) 10.8856 0.871543
\(157\) 4.06842 0.324695 0.162348 0.986734i \(-0.448093\pi\)
0.162348 + 0.986734i \(0.448093\pi\)
\(158\) −0.444363 −0.0353516
\(159\) 3.27698 0.259881
\(160\) −2.34854 −0.185669
\(161\) 0 0
\(162\) 0.154130 0.0121096
\(163\) 7.98083 0.625107 0.312553 0.949900i \(-0.398816\pi\)
0.312553 + 0.949900i \(0.398816\pi\)
\(164\) −1.97624 −0.154319
\(165\) −4.87422 −0.379458
\(166\) −1.01046 −0.0784268
\(167\) −14.5338 −1.12466 −0.562328 0.826914i \(-0.690094\pi\)
−0.562328 + 0.826914i \(0.690094\pi\)
\(168\) 0 0
\(169\) 17.3404 1.33387
\(170\) −0.0241742 −0.00185408
\(171\) −6.50386 −0.497363
\(172\) −9.11394 −0.694931
\(173\) −14.8784 −1.13118 −0.565590 0.824686i \(-0.691352\pi\)
−0.565590 + 0.824686i \(0.691352\pi\)
\(174\) 0.174649 0.0132401
\(175\) 0 0
\(176\) −14.5757 −1.09868
\(177\) 14.3034 1.07511
\(178\) −0.519234 −0.0389182
\(179\) 4.68426 0.350118 0.175059 0.984558i \(-0.443988\pi\)
0.175059 + 0.984558i \(0.443988\pi\)
\(180\) 2.54966 0.190040
\(181\) 8.01866 0.596022 0.298011 0.954562i \(-0.403677\pi\)
0.298011 + 0.954562i \(0.403677\pi\)
\(182\) 0 0
\(183\) 2.67949 0.198074
\(184\) −1.28257 −0.0945522
\(185\) 5.82515 0.428273
\(186\) 0.0174672 0.00128076
\(187\) −0.459289 −0.0335866
\(188\) 6.34973 0.463102
\(189\) 0 0
\(190\) 1.29330 0.0938262
\(191\) 13.6428 0.987159 0.493580 0.869701i \(-0.335688\pi\)
0.493580 + 0.869701i \(0.335688\pi\)
\(192\) 7.43548 0.536610
\(193\) 18.4776 1.33005 0.665024 0.746822i \(-0.268422\pi\)
0.665024 + 0.746822i \(0.268422\pi\)
\(194\) −1.00505 −0.0721583
\(195\) 7.10643 0.508902
\(196\) 0 0
\(197\) 17.1601 1.22261 0.611305 0.791395i \(-0.290645\pi\)
0.611305 + 0.791395i \(0.290645\pi\)
\(198\) −0.582308 −0.0413828
\(199\) −25.7822 −1.82765 −0.913827 0.406104i \(-0.866887\pi\)
−0.913827 + 0.406104i \(0.866887\pi\)
\(200\) 2.04420 0.144547
\(201\) −7.34269 −0.517913
\(202\) −0.613184 −0.0431435
\(203\) 0 0
\(204\) 0.240250 0.0168208
\(205\) −1.29015 −0.0901082
\(206\) −0.454700 −0.0316805
\(207\) 2.09276 0.145457
\(208\) 21.2508 1.47348
\(209\) 24.5717 1.69966
\(210\) 0 0
\(211\) 12.0460 0.829278 0.414639 0.909986i \(-0.363908\pi\)
0.414639 + 0.909986i \(0.363908\pi\)
\(212\) 6.47611 0.444781
\(213\) −3.10604 −0.212822
\(214\) −0.200962 −0.0137375
\(215\) −5.94986 −0.405777
\(216\) 0.612860 0.0416999
\(217\) 0 0
\(218\) 1.62868 0.110308
\(219\) 0.731899 0.0494571
\(220\) −9.63265 −0.649433
\(221\) 0.669627 0.0450440
\(222\) 0.695912 0.0467065
\(223\) −8.09744 −0.542244 −0.271122 0.962545i \(-0.587395\pi\)
−0.271122 + 0.962545i \(0.587395\pi\)
\(224\) 0 0
\(225\) −3.33550 −0.222367
\(226\) −0.694074 −0.0461691
\(227\) 11.4711 0.761361 0.380680 0.924707i \(-0.375690\pi\)
0.380680 + 0.924707i \(0.375690\pi\)
\(228\) −12.8532 −0.851225
\(229\) 24.3289 1.60770 0.803850 0.594831i \(-0.202781\pi\)
0.803850 + 0.594831i \(0.202781\pi\)
\(230\) −0.416149 −0.0274401
\(231\) 0 0
\(232\) 0.694446 0.0455926
\(233\) 25.1806 1.64964 0.824818 0.565399i \(-0.191278\pi\)
0.824818 + 0.565399i \(0.191278\pi\)
\(234\) 0.848983 0.0554997
\(235\) 4.14530 0.270410
\(236\) 28.2670 1.84002
\(237\) 2.88303 0.187273
\(238\) 0 0
\(239\) −9.08432 −0.587616 −0.293808 0.955864i \(-0.594923\pi\)
−0.293808 + 0.955864i \(0.594923\pi\)
\(240\) 4.97745 0.321293
\(241\) 14.4274 0.929354 0.464677 0.885480i \(-0.346171\pi\)
0.464677 + 0.885480i \(0.346171\pi\)
\(242\) 0.504535 0.0324327
\(243\) −1.00000 −0.0641500
\(244\) 5.29532 0.338998
\(245\) 0 0
\(246\) −0.154130 −0.00982700
\(247\) −35.8246 −2.27947
\(248\) 0.0694540 0.00441034
\(249\) 6.55587 0.415461
\(250\) 1.65753 0.104831
\(251\) 26.3124 1.66082 0.830412 0.557151i \(-0.188105\pi\)
0.830412 + 0.557151i \(0.188105\pi\)
\(252\) 0 0
\(253\) −7.90648 −0.497076
\(254\) 0.623866 0.0391449
\(255\) 0.156842 0.00982186
\(256\) 14.1332 0.883324
\(257\) 18.3673 1.14572 0.572862 0.819652i \(-0.305833\pi\)
0.572862 + 0.819652i \(0.305833\pi\)
\(258\) −0.710811 −0.0442531
\(259\) 0 0
\(260\) 14.0440 0.870975
\(261\) −1.13312 −0.0701385
\(262\) 1.10188 0.0680743
\(263\) −13.5912 −0.838068 −0.419034 0.907971i \(-0.637631\pi\)
−0.419034 + 0.907971i \(0.637631\pi\)
\(264\) −2.31540 −0.142503
\(265\) 4.22781 0.259712
\(266\) 0 0
\(267\) 3.36880 0.206167
\(268\) −14.5109 −0.886397
\(269\) −1.77787 −0.108398 −0.0541992 0.998530i \(-0.517261\pi\)
−0.0541992 + 0.998530i \(0.517261\pi\)
\(270\) 0.198852 0.0121017
\(271\) 8.39209 0.509783 0.254892 0.966970i \(-0.417960\pi\)
0.254892 + 0.966970i \(0.417960\pi\)
\(272\) 0.469016 0.0284383
\(273\) 0 0
\(274\) −2.70888 −0.163649
\(275\) 12.6016 0.759905
\(276\) 4.13580 0.248946
\(277\) 29.7741 1.78895 0.894477 0.447113i \(-0.147548\pi\)
0.894477 + 0.447113i \(0.147548\pi\)
\(278\) −0.609560 −0.0365590
\(279\) −0.113328 −0.00678475
\(280\) 0 0
\(281\) −4.65730 −0.277831 −0.138915 0.990304i \(-0.544362\pi\)
−0.138915 + 0.990304i \(0.544362\pi\)
\(282\) 0.495226 0.0294903
\(283\) 2.98479 0.177427 0.0887136 0.996057i \(-0.471724\pi\)
0.0887136 + 0.996057i \(0.471724\pi\)
\(284\) −6.13829 −0.364241
\(285\) −8.39098 −0.497038
\(286\) −3.20747 −0.189662
\(287\) 0 0
\(288\) 1.82036 0.107266
\(289\) −16.9852 −0.999131
\(290\) 0.225324 0.0132315
\(291\) 6.52076 0.382254
\(292\) 1.44641 0.0846447
\(293\) 0.465557 0.0271982 0.0135991 0.999908i \(-0.495671\pi\)
0.0135991 + 0.999908i \(0.495671\pi\)
\(294\) 0 0
\(295\) 18.4536 1.07441
\(296\) 2.76711 0.160835
\(297\) 3.77802 0.219223
\(298\) 2.49794 0.144702
\(299\) 11.5274 0.666644
\(300\) −6.59177 −0.380576
\(301\) 0 0
\(302\) 2.24147 0.128982
\(303\) 3.97834 0.228550
\(304\) −25.0921 −1.43913
\(305\) 3.45695 0.197944
\(306\) 0.0187375 0.00107115
\(307\) 4.58705 0.261797 0.130898 0.991396i \(-0.458214\pi\)
0.130898 + 0.991396i \(0.458214\pi\)
\(308\) 0 0
\(309\) 2.95010 0.167825
\(310\) 0.0225354 0.00127993
\(311\) −6.72674 −0.381439 −0.190719 0.981645i \(-0.561082\pi\)
−0.190719 + 0.981645i \(0.561082\pi\)
\(312\) 3.37576 0.191115
\(313\) 7.56580 0.427644 0.213822 0.976873i \(-0.431409\pi\)
0.213822 + 0.976873i \(0.431409\pi\)
\(314\) 0.627067 0.0353874
\(315\) 0 0
\(316\) 5.69758 0.320514
\(317\) −6.60093 −0.370745 −0.185373 0.982668i \(-0.559349\pi\)
−0.185373 + 0.982668i \(0.559349\pi\)
\(318\) 0.505083 0.0283236
\(319\) 4.28096 0.239688
\(320\) 9.59291 0.536260
\(321\) 1.30384 0.0727734
\(322\) 0 0
\(323\) −0.790667 −0.0439939
\(324\) −1.97624 −0.109791
\(325\) −18.3727 −1.01913
\(326\) 1.23009 0.0681283
\(327\) −10.5669 −0.584352
\(328\) −0.612860 −0.0338395
\(329\) 0 0
\(330\) −0.751266 −0.0413558
\(331\) −1.51697 −0.0833804 −0.0416902 0.999131i \(-0.513274\pi\)
−0.0416902 + 0.999131i \(0.513274\pi\)
\(332\) 12.9560 0.711053
\(333\) −4.51508 −0.247425
\(334\) −2.24010 −0.122573
\(335\) −9.47319 −0.517576
\(336\) 0 0
\(337\) −9.49236 −0.517082 −0.258541 0.966000i \(-0.583242\pi\)
−0.258541 + 0.966000i \(0.583242\pi\)
\(338\) 2.67268 0.145374
\(339\) 4.50316 0.244578
\(340\) 0.309959 0.0168099
\(341\) 0.428154 0.0231858
\(342\) −1.00244 −0.0542059
\(343\) 0 0
\(344\) −2.82636 −0.152387
\(345\) 2.69998 0.145362
\(346\) −2.29321 −0.123284
\(347\) −8.34881 −0.448187 −0.224094 0.974568i \(-0.571942\pi\)
−0.224094 + 0.974568i \(0.571942\pi\)
\(348\) −2.23933 −0.120040
\(349\) 29.3068 1.56875 0.784377 0.620284i \(-0.212983\pi\)
0.784377 + 0.620284i \(0.212983\pi\)
\(350\) 0 0
\(351\) −5.50821 −0.294006
\(352\) −6.87735 −0.366564
\(353\) 10.7354 0.571387 0.285693 0.958321i \(-0.407776\pi\)
0.285693 + 0.958321i \(0.407776\pi\)
\(354\) 2.20459 0.117172
\(355\) −4.00727 −0.212684
\(356\) 6.65756 0.352850
\(357\) 0 0
\(358\) 0.721987 0.0381582
\(359\) 6.31700 0.333398 0.166699 0.986008i \(-0.446689\pi\)
0.166699 + 0.986008i \(0.446689\pi\)
\(360\) 0.790684 0.0416727
\(361\) 23.3002 1.22633
\(362\) 1.23592 0.0649585
\(363\) −3.27343 −0.171810
\(364\) 0 0
\(365\) 0.944261 0.0494249
\(366\) 0.412991 0.0215874
\(367\) −29.4744 −1.53855 −0.769275 0.638918i \(-0.779382\pi\)
−0.769275 + 0.638918i \(0.779382\pi\)
\(368\) 8.07392 0.420882
\(369\) 1.00000 0.0520579
\(370\) 0.897833 0.0466761
\(371\) 0 0
\(372\) −0.223963 −0.0116119
\(373\) 23.6804 1.22612 0.613062 0.790035i \(-0.289938\pi\)
0.613062 + 0.790035i \(0.289938\pi\)
\(374\) −0.0707905 −0.00366049
\(375\) −10.7541 −0.555338
\(376\) 1.96914 0.101551
\(377\) −6.24147 −0.321452
\(378\) 0 0
\(379\) −3.19736 −0.164238 −0.0821188 0.996623i \(-0.526169\pi\)
−0.0821188 + 0.996623i \(0.526169\pi\)
\(380\) −16.5826 −0.850670
\(381\) −4.04765 −0.207368
\(382\) 2.10277 0.107587
\(383\) −24.0506 −1.22893 −0.614463 0.788945i \(-0.710627\pi\)
−0.614463 + 0.788945i \(0.710627\pi\)
\(384\) 4.78675 0.244273
\(385\) 0 0
\(386\) 2.84796 0.144957
\(387\) 4.61175 0.234428
\(388\) 12.8866 0.654219
\(389\) 21.5294 1.09158 0.545792 0.837921i \(-0.316229\pi\)
0.545792 + 0.837921i \(0.316229\pi\)
\(390\) 1.09532 0.0554636
\(391\) 0.254414 0.0128663
\(392\) 0 0
\(393\) −7.14901 −0.360620
\(394\) 2.64490 0.133248
\(395\) 3.71956 0.187151
\(396\) 7.46629 0.375195
\(397\) −7.77612 −0.390272 −0.195136 0.980776i \(-0.562515\pi\)
−0.195136 + 0.980776i \(0.562515\pi\)
\(398\) −3.97383 −0.199190
\(399\) 0 0
\(400\) −12.8685 −0.643423
\(401\) 33.4974 1.67278 0.836391 0.548134i \(-0.184661\pi\)
0.836391 + 0.548134i \(0.184661\pi\)
\(402\) −1.13173 −0.0564456
\(403\) −0.624233 −0.0310952
\(404\) 7.86217 0.391158
\(405\) −1.29015 −0.0641082
\(406\) 0 0
\(407\) 17.0581 0.845537
\(408\) 0.0745047 0.00368853
\(409\) 24.0491 1.18915 0.594576 0.804040i \(-0.297320\pi\)
0.594576 + 0.804040i \(0.297320\pi\)
\(410\) −0.198852 −0.00982060
\(411\) 17.5752 0.866921
\(412\) 5.83011 0.287229
\(413\) 0 0
\(414\) 0.322558 0.0158529
\(415\) 8.45808 0.415191
\(416\) 10.0269 0.491610
\(417\) 3.95483 0.193669
\(418\) 3.78725 0.185240
\(419\) −16.1119 −0.787120 −0.393560 0.919299i \(-0.628757\pi\)
−0.393560 + 0.919299i \(0.628757\pi\)
\(420\) 0 0
\(421\) −19.6558 −0.957965 −0.478983 0.877824i \(-0.658994\pi\)
−0.478983 + 0.877824i \(0.658994\pi\)
\(422\) 1.85665 0.0903802
\(423\) −3.21303 −0.156223
\(424\) 2.00833 0.0975332
\(425\) −0.405494 −0.0196693
\(426\) −0.478735 −0.0231948
\(427\) 0 0
\(428\) 2.57671 0.124550
\(429\) 20.8101 1.00472
\(430\) −0.917055 −0.0442243
\(431\) 18.4967 0.890954 0.445477 0.895293i \(-0.353034\pi\)
0.445477 + 0.895293i \(0.353034\pi\)
\(432\) −3.85803 −0.185619
\(433\) −23.4044 −1.12474 −0.562371 0.826885i \(-0.690111\pi\)
−0.562371 + 0.826885i \(0.690111\pi\)
\(434\) 0 0
\(435\) −1.46190 −0.0700928
\(436\) −20.8828 −1.00011
\(437\) −13.6110 −0.651103
\(438\) 0.112808 0.00539017
\(439\) 0.517097 0.0246797 0.0123399 0.999924i \(-0.496072\pi\)
0.0123399 + 0.999924i \(0.496072\pi\)
\(440\) −2.98722 −0.142410
\(441\) 0 0
\(442\) 0.103210 0.00490919
\(443\) 17.2656 0.820315 0.410158 0.912015i \(-0.365474\pi\)
0.410158 + 0.912015i \(0.365474\pi\)
\(444\) −8.92290 −0.423462
\(445\) 4.34626 0.206033
\(446\) −1.24806 −0.0590974
\(447\) −16.2067 −0.766549
\(448\) 0 0
\(449\) 10.2397 0.483243 0.241621 0.970371i \(-0.422321\pi\)
0.241621 + 0.970371i \(0.422321\pi\)
\(450\) −0.514103 −0.0242350
\(451\) −3.77802 −0.177900
\(452\) 8.89934 0.418590
\(453\) −14.5427 −0.683274
\(454\) 1.76804 0.0829782
\(455\) 0 0
\(456\) −3.98596 −0.186660
\(457\) 6.07076 0.283978 0.141989 0.989868i \(-0.454650\pi\)
0.141989 + 0.989868i \(0.454650\pi\)
\(458\) 3.74983 0.175218
\(459\) −0.121569 −0.00567435
\(460\) 5.33582 0.248784
\(461\) −4.64500 −0.216339 −0.108170 0.994132i \(-0.534499\pi\)
−0.108170 + 0.994132i \(0.534499\pi\)
\(462\) 0 0
\(463\) −34.1752 −1.58826 −0.794128 0.607751i \(-0.792072\pi\)
−0.794128 + 0.607751i \(0.792072\pi\)
\(464\) −4.37162 −0.202947
\(465\) −0.146210 −0.00678033
\(466\) 3.88110 0.179788
\(467\) −13.8420 −0.640530 −0.320265 0.947328i \(-0.603772\pi\)
−0.320265 + 0.947328i \(0.603772\pi\)
\(468\) −10.8856 −0.503185
\(469\) 0 0
\(470\) 0.638917 0.0294711
\(471\) −4.06842 −0.187463
\(472\) 8.76598 0.403487
\(473\) −17.4233 −0.801123
\(474\) 0.444363 0.0204103
\(475\) 21.6936 0.995373
\(476\) 0 0
\(477\) −3.27698 −0.150043
\(478\) −1.40017 −0.0640423
\(479\) 23.3850 1.06849 0.534245 0.845330i \(-0.320596\pi\)
0.534245 + 0.845330i \(0.320596\pi\)
\(480\) 2.34854 0.107196
\(481\) −24.8700 −1.13397
\(482\) 2.22371 0.101287
\(483\) 0 0
\(484\) −6.46909 −0.294049
\(485\) 8.41279 0.382005
\(486\) −0.154130 −0.00699150
\(487\) 6.83886 0.309898 0.154949 0.987922i \(-0.450479\pi\)
0.154949 + 0.987922i \(0.450479\pi\)
\(488\) 1.64215 0.0743367
\(489\) −7.98083 −0.360905
\(490\) 0 0
\(491\) −39.3373 −1.77527 −0.887634 0.460550i \(-0.847652\pi\)
−0.887634 + 0.460550i \(0.847652\pi\)
\(492\) 1.97624 0.0890960
\(493\) −0.137752 −0.00620406
\(494\) −5.52166 −0.248431
\(495\) 4.87422 0.219080
\(496\) −0.437221 −0.0196318
\(497\) 0 0
\(498\) 1.01046 0.0452798
\(499\) 12.7479 0.570675 0.285338 0.958427i \(-0.407894\pi\)
0.285338 + 0.958427i \(0.407894\pi\)
\(500\) −21.2527 −0.950449
\(501\) 14.5338 0.649321
\(502\) 4.05554 0.181008
\(503\) −36.4861 −1.62684 −0.813418 0.581680i \(-0.802396\pi\)
−0.813418 + 0.581680i \(0.802396\pi\)
\(504\) 0 0
\(505\) 5.13267 0.228401
\(506\) −1.21863 −0.0541747
\(507\) −17.3404 −0.770112
\(508\) −7.99915 −0.354905
\(509\) 1.47556 0.0654028 0.0327014 0.999465i \(-0.489589\pi\)
0.0327014 + 0.999465i \(0.489589\pi\)
\(510\) 0.0241742 0.00107045
\(511\) 0 0
\(512\) 11.7519 0.519364
\(513\) 6.50386 0.287152
\(514\) 2.83097 0.124869
\(515\) 3.80608 0.167716
\(516\) 9.11394 0.401219
\(517\) 12.1389 0.533868
\(518\) 0 0
\(519\) 14.8784 0.653088
\(520\) 4.35525 0.190990
\(521\) −37.2361 −1.63134 −0.815672 0.578515i \(-0.803633\pi\)
−0.815672 + 0.578515i \(0.803633\pi\)
\(522\) −0.174649 −0.00764416
\(523\) 28.3629 1.24022 0.620111 0.784514i \(-0.287087\pi\)
0.620111 + 0.784514i \(0.287087\pi\)
\(524\) −14.1282 −0.617192
\(525\) 0 0
\(526\) −2.09481 −0.0913382
\(527\) −0.0137771 −0.000600141 0
\(528\) 14.5757 0.634326
\(529\) −18.6204 −0.809581
\(530\) 0.651634 0.0283052
\(531\) −14.3034 −0.620714
\(532\) 0 0
\(533\) 5.50821 0.238587
\(534\) 0.519234 0.0224695
\(535\) 1.68216 0.0727260
\(536\) −4.50004 −0.194372
\(537\) −4.68426 −0.202141
\(538\) −0.274023 −0.0118140
\(539\) 0 0
\(540\) −2.54966 −0.109720
\(541\) −25.2475 −1.08547 −0.542737 0.839903i \(-0.682612\pi\)
−0.542737 + 0.839903i \(0.682612\pi\)
\(542\) 1.29348 0.0555596
\(543\) −8.01866 −0.344113
\(544\) 0.221299 0.00948812
\(545\) −13.6330 −0.583971
\(546\) 0 0
\(547\) 40.2326 1.72022 0.860110 0.510108i \(-0.170395\pi\)
0.860110 + 0.510108i \(0.170395\pi\)
\(548\) 34.7329 1.48372
\(549\) −2.67949 −0.114358
\(550\) 1.94229 0.0828195
\(551\) 7.36967 0.313958
\(552\) 1.28257 0.0545897
\(553\) 0 0
\(554\) 4.58910 0.194972
\(555\) −5.82515 −0.247264
\(556\) 7.81571 0.331460
\(557\) 35.8092 1.51728 0.758641 0.651509i \(-0.225864\pi\)
0.758641 + 0.651509i \(0.225864\pi\)
\(558\) −0.0174672 −0.000739448 0
\(559\) 25.4025 1.07441
\(560\) 0 0
\(561\) 0.459289 0.0193912
\(562\) −0.717831 −0.0302799
\(563\) 46.0498 1.94077 0.970384 0.241567i \(-0.0776615\pi\)
0.970384 + 0.241567i \(0.0776615\pi\)
\(564\) −6.34973 −0.267372
\(565\) 5.80977 0.244419
\(566\) 0.460047 0.0193372
\(567\) 0 0
\(568\) −1.90357 −0.0798720
\(569\) 12.4998 0.524020 0.262010 0.965065i \(-0.415615\pi\)
0.262010 + 0.965065i \(0.415615\pi\)
\(570\) −1.29330 −0.0541706
\(571\) 23.9412 1.00191 0.500955 0.865473i \(-0.332982\pi\)
0.500955 + 0.865473i \(0.332982\pi\)
\(572\) 41.1259 1.71956
\(573\) −13.6428 −0.569937
\(574\) 0 0
\(575\) −6.98041 −0.291103
\(576\) −7.43548 −0.309812
\(577\) 1.55255 0.0646333 0.0323167 0.999478i \(-0.489711\pi\)
0.0323167 + 0.999478i \(0.489711\pi\)
\(578\) −2.61794 −0.108892
\(579\) −18.4776 −0.767903
\(580\) −2.88907 −0.119962
\(581\) 0 0
\(582\) 1.00505 0.0416606
\(583\) 12.3805 0.512748
\(584\) 0.448552 0.0185612
\(585\) −7.10643 −0.293815
\(586\) 0.0717566 0.00296424
\(587\) 22.9983 0.949241 0.474620 0.880191i \(-0.342585\pi\)
0.474620 + 0.880191i \(0.342585\pi\)
\(588\) 0 0
\(589\) 0.737067 0.0303703
\(590\) 2.84426 0.117096
\(591\) −17.1601 −0.705874
\(592\) −17.4193 −0.715929
\(593\) −42.4147 −1.74176 −0.870882 0.491493i \(-0.836451\pi\)
−0.870882 + 0.491493i \(0.836451\pi\)
\(594\) 0.582308 0.0238924
\(595\) 0 0
\(596\) −32.0283 −1.31193
\(597\) 25.7822 1.05520
\(598\) 1.77672 0.0726553
\(599\) −23.6434 −0.966044 −0.483022 0.875608i \(-0.660461\pi\)
−0.483022 + 0.875608i \(0.660461\pi\)
\(600\) −2.04420 −0.0834540
\(601\) 16.8107 0.685723 0.342861 0.939386i \(-0.388604\pi\)
0.342861 + 0.939386i \(0.388604\pi\)
\(602\) 0 0
\(603\) 7.34269 0.299017
\(604\) −28.7398 −1.16941
\(605\) −4.22322 −0.171698
\(606\) 0.613184 0.0249089
\(607\) −6.34679 −0.257608 −0.128804 0.991670i \(-0.541114\pi\)
−0.128804 + 0.991670i \(0.541114\pi\)
\(608\) −11.8394 −0.480150
\(609\) 0 0
\(610\) 0.532821 0.0215733
\(611\) −17.6980 −0.715986
\(612\) −0.240250 −0.00971152
\(613\) 24.9933 1.00947 0.504735 0.863274i \(-0.331590\pi\)
0.504735 + 0.863274i \(0.331590\pi\)
\(614\) 0.707004 0.0285324
\(615\) 1.29015 0.0520240
\(616\) 0 0
\(617\) 7.73786 0.311514 0.155757 0.987795i \(-0.450218\pi\)
0.155757 + 0.987795i \(0.450218\pi\)
\(618\) 0.454700 0.0182907
\(619\) −10.8909 −0.437740 −0.218870 0.975754i \(-0.570237\pi\)
−0.218870 + 0.975754i \(0.570237\pi\)
\(620\) −0.288947 −0.0116044
\(621\) −2.09276 −0.0839795
\(622\) −1.03680 −0.0415717
\(623\) 0 0
\(624\) −21.2508 −0.850714
\(625\) 2.80311 0.112124
\(626\) 1.16612 0.0466075
\(627\) −24.5717 −0.981299
\(628\) −8.04019 −0.320838
\(629\) −0.548893 −0.0218858
\(630\) 0 0
\(631\) 40.7070 1.62052 0.810260 0.586070i \(-0.199326\pi\)
0.810260 + 0.586070i \(0.199326\pi\)
\(632\) 1.76690 0.0702834
\(633\) −12.0460 −0.478784
\(634\) −1.01740 −0.0404063
\(635\) −5.22209 −0.207232
\(636\) −6.47611 −0.256795
\(637\) 0 0
\(638\) 0.659826 0.0261228
\(639\) 3.10604 0.122873
\(640\) 6.17565 0.244114
\(641\) 26.8036 1.05868 0.529339 0.848410i \(-0.322440\pi\)
0.529339 + 0.848410i \(0.322440\pi\)
\(642\) 0.200962 0.00793134
\(643\) 35.7750 1.41083 0.705415 0.708795i \(-0.250761\pi\)
0.705415 + 0.708795i \(0.250761\pi\)
\(644\) 0 0
\(645\) 5.94986 0.234276
\(646\) −0.121866 −0.00479475
\(647\) −45.1241 −1.77401 −0.887006 0.461758i \(-0.847219\pi\)
−0.887006 + 0.461758i \(0.847219\pi\)
\(648\) −0.612860 −0.0240754
\(649\) 54.0385 2.12119
\(650\) −2.83179 −0.111072
\(651\) 0 0
\(652\) −15.7721 −0.617681
\(653\) −2.37175 −0.0928136 −0.0464068 0.998923i \(-0.514777\pi\)
−0.0464068 + 0.998923i \(0.514777\pi\)
\(654\) −1.62868 −0.0636866
\(655\) −9.22331 −0.360385
\(656\) 3.85803 0.150631
\(657\) −0.731899 −0.0285541
\(658\) 0 0
\(659\) −50.6766 −1.97408 −0.987039 0.160478i \(-0.948696\pi\)
−0.987039 + 0.160478i \(0.948696\pi\)
\(660\) 9.63265 0.374951
\(661\) 46.2182 1.79768 0.898840 0.438277i \(-0.144411\pi\)
0.898840 + 0.438277i \(0.144411\pi\)
\(662\) −0.233812 −0.00908735
\(663\) −0.669627 −0.0260061
\(664\) 4.01783 0.155922
\(665\) 0 0
\(666\) −0.695912 −0.0269660
\(667\) −2.37135 −0.0918191
\(668\) 28.7223 1.11130
\(669\) 8.09744 0.313065
\(670\) −1.46011 −0.0564089
\(671\) 10.1232 0.390800
\(672\) 0 0
\(673\) 15.7924 0.608752 0.304376 0.952552i \(-0.401552\pi\)
0.304376 + 0.952552i \(0.401552\pi\)
\(674\) −1.46306 −0.0563550
\(675\) 3.33550 0.128384
\(676\) −34.2688 −1.31803
\(677\) −29.9752 −1.15204 −0.576019 0.817436i \(-0.695395\pi\)
−0.576019 + 0.817436i \(0.695395\pi\)
\(678\) 0.694074 0.0266557
\(679\) 0 0
\(680\) 0.0961225 0.00368613
\(681\) −11.4711 −0.439572
\(682\) 0.0659916 0.00252695
\(683\) −7.05810 −0.270071 −0.135035 0.990841i \(-0.543115\pi\)
−0.135035 + 0.990841i \(0.543115\pi\)
\(684\) 12.8532 0.491455
\(685\) 22.6747 0.866357
\(686\) 0 0
\(687\) −24.3289 −0.928207
\(688\) 17.7922 0.678323
\(689\) −18.0503 −0.687661
\(690\) 0.416149 0.0158425
\(691\) −24.5716 −0.934749 −0.467375 0.884059i \(-0.654800\pi\)
−0.467375 + 0.884059i \(0.654800\pi\)
\(692\) 29.4033 1.11774
\(693\) 0 0
\(694\) −1.28681 −0.0488465
\(695\) 5.10234 0.193543
\(696\) −0.694446 −0.0263229
\(697\) 0.121569 0.00460475
\(698\) 4.51706 0.170973
\(699\) −25.1806 −0.952417
\(700\) 0 0
\(701\) 28.8840 1.09093 0.545467 0.838132i \(-0.316352\pi\)
0.545467 + 0.838132i \(0.316352\pi\)
\(702\) −0.848983 −0.0320428
\(703\) 29.3655 1.10754
\(704\) 28.0914 1.05873
\(705\) −4.14530 −0.156121
\(706\) 1.65465 0.0622735
\(707\) 0 0
\(708\) −28.2670 −1.06234
\(709\) −17.6966 −0.664610 −0.332305 0.943172i \(-0.607826\pi\)
−0.332305 + 0.943172i \(0.607826\pi\)
\(710\) −0.617642 −0.0231797
\(711\) −2.88303 −0.108122
\(712\) 2.06460 0.0773742
\(713\) −0.237167 −0.00888199
\(714\) 0 0
\(715\) 26.8482 1.00407
\(716\) −9.25723 −0.345959
\(717\) 9.08432 0.339260
\(718\) 0.973642 0.0363360
\(719\) 12.1944 0.454773 0.227386 0.973805i \(-0.426982\pi\)
0.227386 + 0.973805i \(0.426982\pi\)
\(720\) −4.97745 −0.185498
\(721\) 0 0
\(722\) 3.59127 0.133653
\(723\) −14.4274 −0.536563
\(724\) −15.8468 −0.588942
\(725\) 3.77953 0.140368
\(726\) −0.504535 −0.0187250
\(727\) 17.4629 0.647662 0.323831 0.946115i \(-0.395029\pi\)
0.323831 + 0.946115i \(0.395029\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.145539 0.00538666
\(731\) 0.560645 0.0207362
\(732\) −5.29532 −0.195721
\(733\) 1.36251 0.0503254 0.0251627 0.999683i \(-0.491990\pi\)
0.0251627 + 0.999683i \(0.491990\pi\)
\(734\) −4.54290 −0.167681
\(735\) 0 0
\(736\) 3.80957 0.140423
\(737\) −27.7408 −1.02185
\(738\) 0.154130 0.00567362
\(739\) −50.2109 −1.84704 −0.923520 0.383551i \(-0.874701\pi\)
−0.923520 + 0.383551i \(0.874701\pi\)
\(740\) −11.5119 −0.423186
\(741\) 35.8246 1.31605
\(742\) 0 0
\(743\) −17.6408 −0.647177 −0.323588 0.946198i \(-0.604889\pi\)
−0.323588 + 0.946198i \(0.604889\pi\)
\(744\) −0.0694540 −0.00254631
\(745\) −20.9091 −0.766050
\(746\) 3.64987 0.133631
\(747\) −6.55587 −0.239867
\(748\) 0.907668 0.0331876
\(749\) 0 0
\(750\) −1.65753 −0.0605245
\(751\) 30.8991 1.12752 0.563762 0.825938i \(-0.309354\pi\)
0.563762 + 0.825938i \(0.309354\pi\)
\(752\) −12.3960 −0.452034
\(753\) −26.3124 −0.958877
\(754\) −0.962001 −0.0350340
\(755\) −18.7623 −0.682829
\(756\) 0 0
\(757\) 20.5550 0.747084 0.373542 0.927613i \(-0.378143\pi\)
0.373542 + 0.927613i \(0.378143\pi\)
\(758\) −0.492811 −0.0178997
\(759\) 7.90648 0.286987
\(760\) −5.14250 −0.186538
\(761\) 18.8363 0.682816 0.341408 0.939915i \(-0.389096\pi\)
0.341408 + 0.939915i \(0.389096\pi\)
\(762\) −0.623866 −0.0226003
\(763\) 0 0
\(764\) −26.9615 −0.975434
\(765\) −0.156842 −0.00567065
\(766\) −3.70693 −0.133937
\(767\) −78.7860 −2.84480
\(768\) −14.1332 −0.509987
\(769\) 48.7818 1.75912 0.879558 0.475791i \(-0.157838\pi\)
0.879558 + 0.475791i \(0.157838\pi\)
\(770\) 0 0
\(771\) −18.3673 −0.661484
\(772\) −36.5163 −1.31425
\(773\) −32.9107 −1.18371 −0.591857 0.806043i \(-0.701605\pi\)
−0.591857 + 0.806043i \(0.701605\pi\)
\(774\) 0.710811 0.0255496
\(775\) 0.378005 0.0135783
\(776\) 3.99632 0.143459
\(777\) 0 0
\(778\) 3.31834 0.118968
\(779\) −6.50386 −0.233025
\(780\) −14.0440 −0.502857
\(781\) −11.7347 −0.419900
\(782\) 0.0392130 0.00140225
\(783\) 1.13312 0.0404945
\(784\) 0 0
\(785\) −5.24888 −0.187341
\(786\) −1.10188 −0.0393027
\(787\) −16.6540 −0.593651 −0.296825 0.954932i \(-0.595928\pi\)
−0.296825 + 0.954932i \(0.595928\pi\)
\(788\) −33.9126 −1.20809
\(789\) 13.5912 0.483859
\(790\) 0.573297 0.0203970
\(791\) 0 0
\(792\) 2.31540 0.0822741
\(793\) −14.7592 −0.524114
\(794\) −1.19854 −0.0425345
\(795\) −4.22781 −0.149945
\(796\) 50.9520 1.80594
\(797\) −28.7105 −1.01698 −0.508490 0.861068i \(-0.669796\pi\)
−0.508490 + 0.861068i \(0.669796\pi\)
\(798\) 0 0
\(799\) −0.390605 −0.0138186
\(800\) −6.07182 −0.214671
\(801\) −3.36880 −0.119031
\(802\) 5.16297 0.182311
\(803\) 2.76513 0.0975792
\(804\) 14.5109 0.511761
\(805\) 0 0
\(806\) −0.0962132 −0.00338897
\(807\) 1.77787 0.0625838
\(808\) 2.43817 0.0857744
\(809\) −4.33830 −0.152527 −0.0762633 0.997088i \(-0.524299\pi\)
−0.0762633 + 0.997088i \(0.524299\pi\)
\(810\) −0.198852 −0.00698694
\(811\) 35.4046 1.24323 0.621613 0.783325i \(-0.286478\pi\)
0.621613 + 0.783325i \(0.286478\pi\)
\(812\) 0 0
\(813\) −8.39209 −0.294324
\(814\) 2.62917 0.0921523
\(815\) −10.2965 −0.360670
\(816\) −0.469016 −0.0164188
\(817\) −29.9942 −1.04936
\(818\) 3.70670 0.129602
\(819\) 0 0
\(820\) 2.54966 0.0890379
\(821\) −32.8474 −1.14638 −0.573192 0.819421i \(-0.694295\pi\)
−0.573192 + 0.819421i \(0.694295\pi\)
\(822\) 2.70888 0.0944829
\(823\) −22.3021 −0.777401 −0.388701 0.921364i \(-0.627076\pi\)
−0.388701 + 0.921364i \(0.627076\pi\)
\(824\) 1.80800 0.0629846
\(825\) −12.6016 −0.438731
\(826\) 0 0
\(827\) 5.75475 0.200112 0.100056 0.994982i \(-0.468098\pi\)
0.100056 + 0.994982i \(0.468098\pi\)
\(828\) −4.13580 −0.143729
\(829\) 15.2253 0.528797 0.264398 0.964414i \(-0.414827\pi\)
0.264398 + 0.964414i \(0.414827\pi\)
\(830\) 1.30365 0.0452503
\(831\) −29.7741 −1.03285
\(832\) −40.9562 −1.41990
\(833\) 0 0
\(834\) 0.609560 0.0211073
\(835\) 18.7508 0.648898
\(836\) −48.5597 −1.67947
\(837\) 0.113328 0.00391718
\(838\) −2.48334 −0.0857856
\(839\) −8.99897 −0.310679 −0.155339 0.987861i \(-0.549647\pi\)
−0.155339 + 0.987861i \(0.549647\pi\)
\(840\) 0 0
\(841\) −27.7160 −0.955725
\(842\) −3.02956 −0.104405
\(843\) 4.65730 0.160406
\(844\) −23.8057 −0.819427
\(845\) −22.3717 −0.769611
\(846\) −0.495226 −0.0170262
\(847\) 0 0
\(848\) −12.6427 −0.434151
\(849\) −2.98479 −0.102438
\(850\) −0.0624989 −0.00214369
\(851\) −9.44898 −0.323907
\(852\) 6.13829 0.210294
\(853\) 42.2817 1.44770 0.723848 0.689959i \(-0.242371\pi\)
0.723848 + 0.689959i \(0.242371\pi\)
\(854\) 0 0
\(855\) 8.39098 0.286965
\(856\) 0.799074 0.0273118
\(857\) 54.4644 1.86047 0.930235 0.366965i \(-0.119603\pi\)
0.930235 + 0.366965i \(0.119603\pi\)
\(858\) 3.20747 0.109501
\(859\) 33.0384 1.12725 0.563627 0.826029i \(-0.309405\pi\)
0.563627 + 0.826029i \(0.309405\pi\)
\(860\) 11.7584 0.400957
\(861\) 0 0
\(862\) 2.85090 0.0971021
\(863\) 0.592175 0.0201579 0.0100789 0.999949i \(-0.496792\pi\)
0.0100789 + 0.999949i \(0.496792\pi\)
\(864\) −1.82036 −0.0619299
\(865\) 19.1954 0.652662
\(866\) −3.60732 −0.122582
\(867\) 16.9852 0.576848
\(868\) 0 0
\(869\) 10.8922 0.369491
\(870\) −0.225324 −0.00763918
\(871\) 40.4450 1.37043
\(872\) −6.47605 −0.219307
\(873\) −6.52076 −0.220694
\(874\) −2.09787 −0.0709615
\(875\) 0 0
\(876\) −1.44641 −0.0488697
\(877\) −53.9735 −1.82256 −0.911278 0.411791i \(-0.864903\pi\)
−0.911278 + 0.411791i \(0.864903\pi\)
\(878\) 0.0797005 0.00268976
\(879\) −0.465557 −0.0157029
\(880\) 18.8049 0.633913
\(881\) −38.5587 −1.29908 −0.649538 0.760329i \(-0.725038\pi\)
−0.649538 + 0.760329i \(0.725038\pi\)
\(882\) 0 0
\(883\) 36.6057 1.23188 0.615941 0.787793i \(-0.288776\pi\)
0.615941 + 0.787793i \(0.288776\pi\)
\(884\) −1.32335 −0.0445089
\(885\) −18.4536 −0.620310
\(886\) 2.66116 0.0894035
\(887\) −25.7602 −0.864943 −0.432472 0.901648i \(-0.642358\pi\)
−0.432472 + 0.901648i \(0.642358\pi\)
\(888\) −2.76711 −0.0928583
\(889\) 0 0
\(890\) 0.669892 0.0224548
\(891\) −3.77802 −0.126568
\(892\) 16.0025 0.535804
\(893\) 20.8971 0.699295
\(894\) −2.49794 −0.0835436
\(895\) −6.04341 −0.202009
\(896\) 0 0
\(897\) −11.5274 −0.384887
\(898\) 1.57825 0.0526670
\(899\) 0.128414 0.00428285
\(900\) 6.59177 0.219726
\(901\) −0.398379 −0.0132719
\(902\) −0.582308 −0.0193887
\(903\) 0 0
\(904\) 2.75981 0.0917898
\(905\) −10.3453 −0.343889
\(906\) −2.24147 −0.0744678
\(907\) −21.8000 −0.723858 −0.361929 0.932206i \(-0.617882\pi\)
−0.361929 + 0.932206i \(0.617882\pi\)
\(908\) −22.6696 −0.752317
\(909\) −3.97834 −0.131953
\(910\) 0 0
\(911\) −0.945390 −0.0313222 −0.0156611 0.999877i \(-0.504985\pi\)
−0.0156611 + 0.999877i \(0.504985\pi\)
\(912\) 25.0921 0.830881
\(913\) 24.7682 0.819708
\(914\) 0.935689 0.0309498
\(915\) −3.45695 −0.114283
\(916\) −48.0799 −1.58860
\(917\) 0 0
\(918\) −0.0187375 −0.000618429 0
\(919\) 37.0061 1.22072 0.610359 0.792125i \(-0.291025\pi\)
0.610359 + 0.792125i \(0.291025\pi\)
\(920\) 1.65471 0.0545542
\(921\) −4.58705 −0.151148
\(922\) −0.715936 −0.0235781
\(923\) 17.1087 0.563140
\(924\) 0 0
\(925\) 15.0601 0.495172
\(926\) −5.26744 −0.173099
\(927\) −2.95010 −0.0968940
\(928\) −2.06269 −0.0677111
\(929\) −21.1484 −0.693856 −0.346928 0.937892i \(-0.612775\pi\)
−0.346928 + 0.937892i \(0.612775\pi\)
\(930\) −0.0225354 −0.000738966 0
\(931\) 0 0
\(932\) −49.7630 −1.63004
\(933\) 6.72674 0.220224
\(934\) −2.13347 −0.0698093
\(935\) 0.592554 0.0193786
\(936\) −3.37576 −0.110340
\(937\) −41.7132 −1.36271 −0.681355 0.731953i \(-0.738609\pi\)
−0.681355 + 0.731953i \(0.738609\pi\)
\(938\) 0 0
\(939\) −7.56580 −0.246901
\(940\) −8.19213 −0.267198
\(941\) 27.3925 0.892969 0.446484 0.894791i \(-0.352676\pi\)
0.446484 + 0.894791i \(0.352676\pi\)
\(942\) −0.627067 −0.0204309
\(943\) 2.09276 0.0681496
\(944\) −55.1828 −1.79605
\(945\) 0 0
\(946\) −2.68546 −0.0873117
\(947\) −54.1364 −1.75920 −0.879598 0.475718i \(-0.842188\pi\)
−0.879598 + 0.475718i \(0.842188\pi\)
\(948\) −5.69758 −0.185049
\(949\) −4.03145 −0.130866
\(950\) 3.34365 0.108482
\(951\) 6.60093 0.214050
\(952\) 0 0
\(953\) −1.05940 −0.0343173 −0.0171587 0.999853i \(-0.505462\pi\)
−0.0171587 + 0.999853i \(0.505462\pi\)
\(954\) −0.505083 −0.0163527
\(955\) −17.6013 −0.569565
\(956\) 17.9528 0.580636
\(957\) −4.28096 −0.138384
\(958\) 3.60435 0.116451
\(959\) 0 0
\(960\) −9.59291 −0.309610
\(961\) −30.9872 −0.999586
\(962\) −3.83323 −0.123588
\(963\) −1.30384 −0.0420158
\(964\) −28.5122 −0.918315
\(965\) −23.8389 −0.767403
\(966\) 0 0
\(967\) −50.6626 −1.62920 −0.814600 0.580023i \(-0.803043\pi\)
−0.814600 + 0.580023i \(0.803043\pi\)
\(968\) −2.00615 −0.0644802
\(969\) 0.790667 0.0253999
\(970\) 1.29667 0.0416334
\(971\) −41.8803 −1.34400 −0.672001 0.740550i \(-0.734565\pi\)
−0.672001 + 0.740550i \(0.734565\pi\)
\(972\) 1.97624 0.0633880
\(973\) 0 0
\(974\) 1.05408 0.0337748
\(975\) 18.3727 0.588396
\(976\) −10.3375 −0.330897
\(977\) 15.2242 0.487064 0.243532 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(978\) −1.23009 −0.0393339
\(979\) 12.7274 0.406769
\(980\) 0 0
\(981\) 10.5669 0.337376
\(982\) −6.06308 −0.193481
\(983\) 36.9964 1.18000 0.590001 0.807402i \(-0.299127\pi\)
0.590001 + 0.807402i \(0.299127\pi\)
\(984\) 0.612860 0.0195373
\(985\) −22.1392 −0.705414
\(986\) −0.0212318 −0.000676160 0
\(987\) 0 0
\(988\) 70.7982 2.25239
\(989\) 9.65128 0.306893
\(990\) 0.751266 0.0238768
\(991\) −18.9571 −0.602194 −0.301097 0.953594i \(-0.597353\pi\)
−0.301097 + 0.953594i \(0.597353\pi\)
\(992\) −0.206297 −0.00654994
\(993\) 1.51697 0.0481397
\(994\) 0 0
\(995\) 33.2630 1.05451
\(996\) −12.9560 −0.410526
\(997\) 5.80926 0.183981 0.0919905 0.995760i \(-0.470677\pi\)
0.0919905 + 0.995760i \(0.470677\pi\)
\(998\) 1.96484 0.0621960
\(999\) 4.51508 0.142851
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 \(a_p\))