Properties

Label 6027.2.a.bo.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 \(-0.406848\pi\)
0.288487 + 0.957484i \(0.406848\pi\)
\(6\) 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 \(-0.776694\pi\)
−0.763851 + 0.645393i \(0.776694\pi\)
\(14\) 0 0
\(15\) 1.29015 0.333116
\(16\) 3.85803 0.964507
\(17\) −0.121569 −0.0294848 −0.0147424 0.999891i \(-0.504693\pi\)
−0.0147424 + 0.999891i \(0.504693\pi\)
\(18\) 0.154130 0.0363289
\(19\) 6.50386 1.49209 0.746044 0.665897i \(-0.231951\pi\)
0.746044 + 0.665897i \(0.231951\pi\)
\(20\) −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 \(-0.496760\pi\)
0.0101771 + 0.999948i \(0.496760\pi\)
\(32\) 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 \(-0.424709\pi\)
0.234334 + 0.972156i \(0.424709\pi\)
\(48\) 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 \(-0.118876\pi\)
0.931071 + 0.364838i \(0.118876\pi\)
\(60\) −2.54966 −0.329159
\(61\) 2.67949 0.343073 0.171537 0.985178i \(-0.445127\pi\)
0.171537 + 0.985178i \(0.445127\pi\)
\(62\) 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 \(-0.486362\pi\)
0.0428311 + 0.999082i \(0.486362\pi\)
\(74\) −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 \(-0.382845\pi\)
0.359800 + 0.933029i \(0.382845\pi\)
\(84\) 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 \(-0.442861\pi\)
0.178546 + 0.983932i \(0.442861\pi\)
\(90\) 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 \(-0.392600\pi\)
0.331042 + 0.943616i \(0.392600\pi\)
\(98\) 0 0
\(99\) −3.77802 −0.379705
\(100\) 6.59177 0.659177
\(101\) 3.97834 0.395860 0.197930 0.980216i \(-0.436578\pi\)
0.197930 + 0.980216i \(0.436578\pi\)
\(102\) −0.0187375 −0.00185529
\(103\) 2.95010 0.290682 0.145341 0.989382i \(-0.453572\pi\)
0.145341 + 0.989382i \(0.453572\pi\)
\(104\) 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 \(-0.601101\pi\)
−0.312306 + 0.949982i \(0.601101\pi\)
\(132\) 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 \(-0.446359\pi\)
0.167722 + 0.985834i \(0.446359\pi\)
\(140\) 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 \(-0.551907\pi\)
−0.162348 + 0.986734i \(0.551907\pi\)
\(158\) −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 \(-0.309906\pi\)
0.562328 + 0.826914i \(0.309906\pi\)
\(168\) 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 \(-0.308648\pi\)
0.565590 + 0.824686i \(0.308648\pi\)
\(174\) −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 \(-0.596323\pi\)
−0.298011 + 0.954562i \(0.596323\pi\)
\(182\) 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 \(-0.133113\pi\)
0.913827 + 0.406104i \(0.133113\pi\)
\(200\) 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 \(-0.412605\pi\)
0.271122 + 0.962545i \(0.412605\pi\)
\(224\) 0 0
\(225\) −3.33550 −0.222367
\(226\) −0.694074 −0.0461691
\(227\) −11.4711 −0.761361 −0.380680 0.924707i \(-0.624310\pi\)
−0.380680 + 0.924707i \(0.624310\pi\)
\(228\) −12.8532 −0.851225
\(229\) −24.3289 −1.60770 −0.803850 0.594831i \(-0.797219\pi\)
−0.803850 + 0.594831i \(0.797219\pi\)
\(230\) 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 \(-0.653829\pi\)
−0.464677 + 0.885480i \(0.653829\pi\)
\(242\) 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 \(-0.811895\pi\)
−0.830412 + 0.557151i \(0.811895\pi\)
\(252\) 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 \(-0.694167\pi\)
−0.572862 + 0.819652i \(0.694167\pi\)
\(258\) 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 \(-0.482739\pi\)
0.0541992 + 0.998530i \(0.482739\pi\)
\(270\) 0.198852 0.0121017
\(271\) −8.39209 −0.509783 −0.254892 0.966970i \(-0.582040\pi\)
−0.254892 + 0.966970i \(0.582040\pi\)
\(272\) −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 \(-0.528276\pi\)
−0.0887136 + 0.996057i \(0.528276\pi\)
\(284\) −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 \(-0.504329\pi\)
−0.0135991 + 0.999908i \(0.504329\pi\)
\(294\) 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 \(-0.541786\pi\)
−0.130898 + 0.991396i \(0.541786\pi\)
\(308\) 0 0
\(309\) 2.95010 0.167825
\(310\) 0.0225354 0.00127993
\(311\) 6.72674 0.381439 0.190719 0.981645i \(-0.438918\pi\)
0.190719 + 0.981645i \(0.438918\pi\)
\(312\) 3.37576 0.191115
\(313\) −7.56580 −0.427644 −0.213822 0.976873i \(-0.568591\pi\)
−0.213822 + 0.976873i \(0.568591\pi\)
\(314\) −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 \(-0.787017\pi\)
−0.784377 + 0.620284i \(0.787017\pi\)
\(350\) 0 0
\(351\) −5.50821 −0.294006
\(352\) −6.87735 −0.366564
\(353\) −10.7354 −0.571387 −0.285693 0.958321i \(-0.592224\pi\)
−0.285693 + 0.958321i \(0.592224\pi\)
\(354\) 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 \(-0.220618\pi\)
0.769275 + 0.638918i \(0.220618\pi\)
\(368\) 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 \(-0.289373\pi\)
0.614463 + 0.788945i \(0.289373\pi\)
\(384\) −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 \(-0.437485\pi\)
0.195136 + 0.980776i \(0.437485\pi\)
\(398\) 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 \(-0.702680\pi\)
−0.594576 + 0.804040i \(0.702680\pi\)
\(410\) −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 \(-0.371243\pi\)
0.393560 + 0.919299i \(0.371243\pi\)
\(420\) 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 \(-0.309889\pi\)
0.562371 + 0.826885i \(0.309889\pi\)
\(434\) 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 \(-0.503928\pi\)
−0.0123399 + 0.999924i \(0.503928\pi\)
\(440\) 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 \(-0.465501\pi\)
0.108170 + 0.994132i \(0.465501\pi\)
\(462\) 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 \(-0.396228\pi\)
0.320265 + 0.947328i \(0.396228\pi\)
\(468\) 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 \(-0.679404\pi\)
−0.534245 + 0.845330i \(0.679404\pi\)
\(480\) 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 \(-0.197604\pi\)
0.813418 + 0.581680i \(0.197604\pi\)
\(504\) 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 \(-0.510411\pi\)
−0.0327014 + 0.999465i \(0.510411\pi\)
\(510\) −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 \(-0.196367\pi\)
0.815672 + 0.578515i \(0.196367\pi\)
\(522\) −0.174649 −0.00764416
\(523\) −28.3629 −1.24022 −0.620111 0.784514i \(-0.712913\pi\)
−0.620111 + 0.784514i \(0.712913\pi\)
\(524\) 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 \(-0.922339\pi\)
−0.970384 + 0.241567i \(0.922339\pi\)
\(564\) −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 \(-0.510289\pi\)
−0.0323167 + 0.999478i \(0.510289\pi\)
\(578\) −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 \(-0.657415\pi\)
−0.474620 + 0.880191i \(0.657415\pi\)
\(588\) 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 \(-0.163549\pi\)
0.870882 + 0.491493i \(0.163549\pi\)
\(594\) −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 \(-0.611396\pi\)
−0.342861 + 0.939386i \(0.611396\pi\)
\(602\) 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 \(-0.458886\pi\)
0.128804 + 0.991670i \(0.458886\pi\)
\(608\) 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 \(-0.429763\pi\)
0.218870 + 0.975754i \(0.429763\pi\)
\(620\) −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 \(-0.749239\pi\)
−0.705415 + 0.708795i \(0.749239\pi\)
\(644\) 0 0
\(645\) 5.94986 0.234276
\(646\) −0.121866 −0.00479475
\(647\) 45.1241 1.77401 0.887006 0.461758i \(-0.152781\pi\)
0.887006 + 0.461758i \(0.152781\pi\)
\(648\) −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 \(-0.855589\pi\)
−0.898840 + 0.438277i \(0.855589\pi\)
\(662\) −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 \(-0.304605\pi\)
0.576019 + 0.817436i \(0.304605\pi\)
\(678\) −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 \(-0.345200\pi\)
0.467375 + 0.884059i \(0.345200\pi\)
\(692\) −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 \(-0.573018\pi\)
−0.227386 + 0.973805i \(0.573018\pi\)
\(720\) 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 \(-0.604971\pi\)
−0.323831 + 0.946115i \(0.604971\pi\)
\(728\) 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 \(-0.508010\pi\)
−0.0251627 + 0.999683i \(0.508010\pi\)
\(734\) 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 \(-0.610904\pi\)
−0.341408 + 0.939915i \(0.610904\pi\)
\(762\) 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 \(-0.842162\pi\)
−0.879558 + 0.475791i \(0.842162\pi\)
\(770\) 0 0
\(771\) −18.3673 −0.661484
\(772\) −36.5163 −1.31425
\(773\) 32.9107 1.18371 0.591857 0.806043i \(-0.298395\pi\)
0.591857 + 0.806043i \(0.298395\pi\)
\(774\) 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 \(-0.404072\pi\)
0.296825 + 0.954932i \(0.404072\pi\)
\(788\) −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 \(-0.330204\pi\)
0.508490 + 0.861068i \(0.330204\pi\)
\(798\) 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 \(-0.713522\pi\)
−0.621613 + 0.783325i \(0.713522\pi\)
\(812\) 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 \(-0.585173\pi\)
−0.264398 + 0.964414i \(0.585173\pi\)
\(830\) 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 \(-0.450353\pi\)
0.155339 + 0.987861i \(0.450353\pi\)
\(840\) 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 \(-0.757629\pi\)
−0.723848 + 0.689959i \(0.757629\pi\)
\(854\) 0 0
\(855\) 8.39098 0.286965
\(856\) 0.799074 0.0273118
\(857\) −54.4644 −1.86047 −0.930235 0.366965i \(-0.880397\pi\)
−0.930235 + 0.366965i \(0.880397\pi\)
\(858\) 3.20747 0.109501
\(859\) −33.0384 −1.12725 −0.563627 0.826029i \(-0.690595\pi\)
−0.563627 + 0.826029i \(0.690595\pi\)
\(860\) −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 \(-0.274962\pi\)
0.649538 + 0.760329i \(0.274962\pi\)
\(882\) 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 \(-0.357642\pi\)
0.432472 + 0.901648i \(0.357642\pi\)
\(888\) 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 \(-0.387225\pi\)
0.346928 + 0.937892i \(0.387225\pi\)
\(930\) 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 \(-0.261391\pi\)
0.681355 + 0.731953i \(0.261391\pi\)
\(938\) 0 0
\(939\) −7.56580 −0.246901
\(940\) −8.19213 −0.267198
\(941\) −27.3925 −0.892969 −0.446484 0.894791i \(-0.647324\pi\)
−0.446484 + 0.894791i \(0.647324\pi\)
\(942\) −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 \(-0.265435\pi\)
0.672001 + 0.740550i \(0.265435\pi\)
\(972\) −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 \(-0.700873\pi\)
−0.590001 + 0.807402i \(0.700873\pi\)
\(984\) 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 \(-0.529323\pi\)
−0.0919905 + 0.995760i \(0.529323\pi\)
\(998\) 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 \(a_p\))