Properties

Label 6027.2.a.bm.1.9
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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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: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.304034\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.304034 q^{2} +1.00000 q^{3} -1.90756 q^{4} -0.824488 q^{5} -0.304034 q^{6} +1.18803 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.304034 q^{2} +1.00000 q^{3} -1.90756 q^{4} -0.824488 q^{5} -0.304034 q^{6} +1.18803 q^{8} +1.00000 q^{9} +0.250672 q^{10} +1.95390 q^{11} -1.90756 q^{12} +3.83923 q^{13} -0.824488 q^{15} +3.45392 q^{16} -6.15541 q^{17} -0.304034 q^{18} +0.304128 q^{19} +1.57276 q^{20} -0.594052 q^{22} -2.69849 q^{23} +1.18803 q^{24} -4.32022 q^{25} -1.16726 q^{26} +1.00000 q^{27} -8.02434 q^{29} +0.250672 q^{30} +0.213848 q^{31} -3.42617 q^{32} +1.95390 q^{33} +1.87145 q^{34} -1.90756 q^{36} +1.79812 q^{37} -0.0924652 q^{38} +3.83923 q^{39} -0.979519 q^{40} +1.00000 q^{41} +9.13470 q^{43} -3.72719 q^{44} -0.824488 q^{45} +0.820432 q^{46} +5.90710 q^{47} +3.45392 q^{48} +1.31349 q^{50} -6.15541 q^{51} -7.32357 q^{52} +3.40809 q^{53} -0.304034 q^{54} -1.61097 q^{55} +0.304128 q^{57} +2.43967 q^{58} -6.19218 q^{59} +1.57276 q^{60} +2.00046 q^{61} -0.0650170 q^{62} -5.86618 q^{64} -3.16540 q^{65} -0.594052 q^{66} -0.370824 q^{67} +11.7418 q^{68} -2.69849 q^{69} -14.2671 q^{71} +1.18803 q^{72} -11.4202 q^{73} -0.546689 q^{74} -4.32022 q^{75} -0.580143 q^{76} -1.16726 q^{78} -0.0753488 q^{79} -2.84772 q^{80} +1.00000 q^{81} -0.304034 q^{82} +0.111368 q^{83} +5.07506 q^{85} -2.77726 q^{86} -8.02434 q^{87} +2.32130 q^{88} +4.92634 q^{89} +0.250672 q^{90} +5.14754 q^{92} +0.213848 q^{93} -1.79596 q^{94} -0.250750 q^{95} -3.42617 q^{96} +5.06400 q^{97} +1.95390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.304034 −0.214985 −0.107492 0.994206i \(-0.534282\pi\)
−0.107492 + 0.994206i \(0.534282\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.90756 −0.953782
\(5\) −0.824488 −0.368722 −0.184361 0.982859i \(-0.559022\pi\)
−0.184361 + 0.982859i \(0.559022\pi\)
\(6\) −0.304034 −0.124121
\(7\) 0 0
\(8\) 1.18803 0.420033
\(9\) 1.00000 0.333333
\(10\) 0.250672 0.0792696
\(11\) 1.95390 0.589123 0.294562 0.955632i \(-0.404826\pi\)
0.294562 + 0.955632i \(0.404826\pi\)
\(12\) −1.90756 −0.550666
\(13\) 3.83923 1.06481 0.532405 0.846490i \(-0.321288\pi\)
0.532405 + 0.846490i \(0.321288\pi\)
\(14\) 0 0
\(15\) −0.824488 −0.212882
\(16\) 3.45392 0.863481
\(17\) −6.15541 −1.49291 −0.746453 0.665439i \(-0.768245\pi\)
−0.746453 + 0.665439i \(0.768245\pi\)
\(18\) −0.304034 −0.0716615
\(19\) 0.304128 0.0697717 0.0348858 0.999391i \(-0.488893\pi\)
0.0348858 + 0.999391i \(0.488893\pi\)
\(20\) 1.57276 0.351681
\(21\) 0 0
\(22\) −0.594052 −0.126652
\(23\) −2.69849 −0.562674 −0.281337 0.959609i \(-0.590778\pi\)
−0.281337 + 0.959609i \(0.590778\pi\)
\(24\) 1.18803 0.242506
\(25\) −4.32022 −0.864044
\(26\) −1.16726 −0.228918
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.02434 −1.49008 −0.745041 0.667019i \(-0.767570\pi\)
−0.745041 + 0.667019i \(0.767570\pi\)
\(30\) 0.250672 0.0457663
\(31\) 0.213848 0.0384082 0.0192041 0.999816i \(-0.493887\pi\)
0.0192041 + 0.999816i \(0.493887\pi\)
\(32\) −3.42617 −0.605668
\(33\) 1.95390 0.340131
\(34\) 1.87145 0.320952
\(35\) 0 0
\(36\) −1.90756 −0.317927
\(37\) 1.79812 0.295609 0.147804 0.989017i \(-0.452779\pi\)
0.147804 + 0.989017i \(0.452779\pi\)
\(38\) −0.0924652 −0.0149998
\(39\) 3.83923 0.614769
\(40\) −0.979519 −0.154875
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 9.13470 1.39303 0.696515 0.717543i \(-0.254733\pi\)
0.696515 + 0.717543i \(0.254733\pi\)
\(44\) −3.72719 −0.561895
\(45\) −0.824488 −0.122907
\(46\) 0.820432 0.120966
\(47\) 5.90710 0.861639 0.430819 0.902438i \(-0.358225\pi\)
0.430819 + 0.902438i \(0.358225\pi\)
\(48\) 3.45392 0.498531
\(49\) 0 0
\(50\) 1.31349 0.185756
\(51\) −6.15541 −0.861929
\(52\) −7.32357 −1.01560
\(53\) 3.40809 0.468138 0.234069 0.972220i \(-0.424796\pi\)
0.234069 + 0.972220i \(0.424796\pi\)
\(54\) −0.304034 −0.0413738
\(55\) −1.61097 −0.217223
\(56\) 0 0
\(57\) 0.304128 0.0402827
\(58\) 2.43967 0.320345
\(59\) −6.19218 −0.806153 −0.403076 0.915166i \(-0.632059\pi\)
−0.403076 + 0.915166i \(0.632059\pi\)
\(60\) 1.57276 0.203043
\(61\) 2.00046 0.256132 0.128066 0.991766i \(-0.459123\pi\)
0.128066 + 0.991766i \(0.459123\pi\)
\(62\) −0.0650170 −0.00825716
\(63\) 0 0
\(64\) −5.86618 −0.733272
\(65\) −3.16540 −0.392620
\(66\) −0.594052 −0.0731228
\(67\) −0.370824 −0.0453034 −0.0226517 0.999743i \(-0.507211\pi\)
−0.0226517 + 0.999743i \(0.507211\pi\)
\(68\) 11.7418 1.42391
\(69\) −2.69849 −0.324860
\(70\) 0 0
\(71\) −14.2671 −1.69319 −0.846595 0.532238i \(-0.821351\pi\)
−0.846595 + 0.532238i \(0.821351\pi\)
\(72\) 1.18803 0.140011
\(73\) −11.4202 −1.33664 −0.668318 0.743876i \(-0.732986\pi\)
−0.668318 + 0.743876i \(0.732986\pi\)
\(74\) −0.546689 −0.0635513
\(75\) −4.32022 −0.498856
\(76\) −0.580143 −0.0665470
\(77\) 0 0
\(78\) −1.16726 −0.132166
\(79\) −0.0753488 −0.00847740 −0.00423870 0.999991i \(-0.501349\pi\)
−0.00423870 + 0.999991i \(0.501349\pi\)
\(80\) −2.84772 −0.318385
\(81\) 1.00000 0.111111
\(82\) −0.304034 −0.0335749
\(83\) 0.111368 0.0122242 0.00611209 0.999981i \(-0.498054\pi\)
0.00611209 + 0.999981i \(0.498054\pi\)
\(84\) 0 0
\(85\) 5.07506 0.550468
\(86\) −2.77726 −0.299480
\(87\) −8.02434 −0.860299
\(88\) 2.32130 0.247451
\(89\) 4.92634 0.522191 0.261096 0.965313i \(-0.415916\pi\)
0.261096 + 0.965313i \(0.415916\pi\)
\(90\) 0.250672 0.0264232
\(91\) 0 0
\(92\) 5.14754 0.536668
\(93\) 0.213848 0.0221750
\(94\) −1.79596 −0.185239
\(95\) −0.250750 −0.0257264
\(96\) −3.42617 −0.349683
\(97\) 5.06400 0.514172 0.257086 0.966389i \(-0.417238\pi\)
0.257086 + 0.966389i \(0.417238\pi\)
\(98\) 0 0
\(99\) 1.95390 0.196374
\(100\) 8.24109 0.824109
\(101\) −8.17374 −0.813317 −0.406659 0.913580i \(-0.633306\pi\)
−0.406659 + 0.913580i \(0.633306\pi\)
\(102\) 1.87145 0.185301
\(103\) −0.577334 −0.0568864 −0.0284432 0.999595i \(-0.509055\pi\)
−0.0284432 + 0.999595i \(0.509055\pi\)
\(104\) 4.56113 0.447255
\(105\) 0 0
\(106\) −1.03618 −0.100642
\(107\) 0.174403 0.0168602 0.00843010 0.999964i \(-0.497317\pi\)
0.00843010 + 0.999964i \(0.497317\pi\)
\(108\) −1.90756 −0.183555
\(109\) 16.0556 1.53785 0.768923 0.639341i \(-0.220793\pi\)
0.768923 + 0.639341i \(0.220793\pi\)
\(110\) 0.489789 0.0466996
\(111\) 1.79812 0.170670
\(112\) 0 0
\(113\) −1.20756 −0.113597 −0.0567987 0.998386i \(-0.518089\pi\)
−0.0567987 + 0.998386i \(0.518089\pi\)
\(114\) −0.0924652 −0.00866016
\(115\) 2.22487 0.207470
\(116\) 15.3069 1.42121
\(117\) 3.83923 0.354937
\(118\) 1.88263 0.173310
\(119\) 0 0
\(120\) −0.979519 −0.0894174
\(121\) −7.18227 −0.652934
\(122\) −0.608207 −0.0550645
\(123\) 1.00000 0.0901670
\(124\) −0.407928 −0.0366330
\(125\) 7.68441 0.687315
\(126\) 0 0
\(127\) 9.78876 0.868612 0.434306 0.900765i \(-0.356994\pi\)
0.434306 + 0.900765i \(0.356994\pi\)
\(128\) 8.63587 0.763310
\(129\) 9.13470 0.804266
\(130\) 0.962389 0.0844071
\(131\) −11.1182 −0.971400 −0.485700 0.874126i \(-0.661435\pi\)
−0.485700 + 0.874126i \(0.661435\pi\)
\(132\) −3.72719 −0.324410
\(133\) 0 0
\(134\) 0.112743 0.00973953
\(135\) −0.824488 −0.0709607
\(136\) −7.31282 −0.627069
\(137\) 4.17858 0.357000 0.178500 0.983940i \(-0.442876\pi\)
0.178500 + 0.983940i \(0.442876\pi\)
\(138\) 0.820432 0.0698398
\(139\) −7.95306 −0.674570 −0.337285 0.941403i \(-0.609509\pi\)
−0.337285 + 0.941403i \(0.609509\pi\)
\(140\) 0 0
\(141\) 5.90710 0.497467
\(142\) 4.33767 0.364010
\(143\) 7.50147 0.627305
\(144\) 3.45392 0.287827
\(145\) 6.61597 0.549427
\(146\) 3.47214 0.287356
\(147\) 0 0
\(148\) −3.43002 −0.281946
\(149\) −2.08376 −0.170709 −0.0853543 0.996351i \(-0.527202\pi\)
−0.0853543 + 0.996351i \(0.527202\pi\)
\(150\) 1.31349 0.107246
\(151\) −20.1606 −1.64064 −0.820321 0.571903i \(-0.806205\pi\)
−0.820321 + 0.571903i \(0.806205\pi\)
\(152\) 0.361314 0.0293064
\(153\) −6.15541 −0.497635
\(154\) 0 0
\(155\) −0.176315 −0.0141620
\(156\) −7.32357 −0.586355
\(157\) −17.5517 −1.40078 −0.700390 0.713761i \(-0.746990\pi\)
−0.700390 + 0.713761i \(0.746990\pi\)
\(158\) 0.0229086 0.00182251
\(159\) 3.40809 0.270279
\(160\) 2.82484 0.223323
\(161\) 0 0
\(162\) −0.304034 −0.0238872
\(163\) −6.81077 −0.533461 −0.266730 0.963771i \(-0.585943\pi\)
−0.266730 + 0.963771i \(0.585943\pi\)
\(164\) −1.90756 −0.148956
\(165\) −1.61097 −0.125414
\(166\) −0.0338595 −0.00262801
\(167\) −1.20396 −0.0931656 −0.0465828 0.998914i \(-0.514833\pi\)
−0.0465828 + 0.998914i \(0.514833\pi\)
\(168\) 0 0
\(169\) 1.73968 0.133822
\(170\) −1.54299 −0.118342
\(171\) 0.304128 0.0232572
\(172\) −17.4250 −1.32865
\(173\) 21.1160 1.60542 0.802710 0.596370i \(-0.203391\pi\)
0.802710 + 0.596370i \(0.203391\pi\)
\(174\) 2.43967 0.184951
\(175\) 0 0
\(176\) 6.74863 0.508697
\(177\) −6.19218 −0.465432
\(178\) −1.49778 −0.112263
\(179\) −5.39627 −0.403336 −0.201668 0.979454i \(-0.564636\pi\)
−0.201668 + 0.979454i \(0.564636\pi\)
\(180\) 1.57276 0.117227
\(181\) 17.6205 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(182\) 0 0
\(183\) 2.00046 0.147878
\(184\) −3.20589 −0.236341
\(185\) −1.48253 −0.108998
\(186\) −0.0650170 −0.00476728
\(187\) −12.0271 −0.879505
\(188\) −11.2682 −0.821815
\(189\) 0 0
\(190\) 0.0762365 0.00553077
\(191\) −22.1613 −1.60354 −0.801769 0.597634i \(-0.796108\pi\)
−0.801769 + 0.597634i \(0.796108\pi\)
\(192\) −5.86618 −0.423355
\(193\) −20.1634 −1.45139 −0.725695 0.688016i \(-0.758482\pi\)
−0.725695 + 0.688016i \(0.758482\pi\)
\(194\) −1.53963 −0.110539
\(195\) −3.16540 −0.226679
\(196\) 0 0
\(197\) 5.91038 0.421097 0.210549 0.977583i \(-0.432475\pi\)
0.210549 + 0.977583i \(0.432475\pi\)
\(198\) −0.594052 −0.0422175
\(199\) −7.37667 −0.522918 −0.261459 0.965215i \(-0.584204\pi\)
−0.261459 + 0.965215i \(0.584204\pi\)
\(200\) −5.13256 −0.362927
\(201\) −0.370824 −0.0261559
\(202\) 2.48509 0.174851
\(203\) 0 0
\(204\) 11.7418 0.822092
\(205\) −0.824488 −0.0575848
\(206\) 0.175529 0.0122297
\(207\) −2.69849 −0.187558
\(208\) 13.2604 0.919444
\(209\) 0.594235 0.0411041
\(210\) 0 0
\(211\) −21.9328 −1.50992 −0.754958 0.655773i \(-0.772343\pi\)
−0.754958 + 0.655773i \(0.772343\pi\)
\(212\) −6.50116 −0.446501
\(213\) −14.2671 −0.977563
\(214\) −0.0530245 −0.00362468
\(215\) −7.53146 −0.513641
\(216\) 1.18803 0.0808353
\(217\) 0 0
\(218\) −4.88144 −0.330613
\(219\) −11.4202 −0.771707
\(220\) 3.07302 0.207183
\(221\) −23.6320 −1.58966
\(222\) −0.546689 −0.0366913
\(223\) 9.87045 0.660974 0.330487 0.943811i \(-0.392787\pi\)
0.330487 + 0.943811i \(0.392787\pi\)
\(224\) 0 0
\(225\) −4.32022 −0.288015
\(226\) 0.367139 0.0244217
\(227\) 8.90214 0.590856 0.295428 0.955365i \(-0.404538\pi\)
0.295428 + 0.955365i \(0.404538\pi\)
\(228\) −0.580143 −0.0384209
\(229\) 14.3058 0.945357 0.472678 0.881235i \(-0.343287\pi\)
0.472678 + 0.881235i \(0.343287\pi\)
\(230\) −0.676437 −0.0446029
\(231\) 0 0
\(232\) −9.53317 −0.625883
\(233\) 13.9817 0.915973 0.457986 0.888959i \(-0.348571\pi\)
0.457986 + 0.888959i \(0.348571\pi\)
\(234\) −1.16726 −0.0763059
\(235\) −4.87033 −0.317705
\(236\) 11.8120 0.768894
\(237\) −0.0753488 −0.00489443
\(238\) 0 0
\(239\) −0.233591 −0.0151098 −0.00755488 0.999971i \(-0.502405\pi\)
−0.00755488 + 0.999971i \(0.502405\pi\)
\(240\) −2.84772 −0.183820
\(241\) −6.04709 −0.389527 −0.194764 0.980850i \(-0.562394\pi\)
−0.194764 + 0.980850i \(0.562394\pi\)
\(242\) 2.18365 0.140371
\(243\) 1.00000 0.0641500
\(244\) −3.81600 −0.244294
\(245\) 0 0
\(246\) −0.304034 −0.0193845
\(247\) 1.16762 0.0742936
\(248\) 0.254058 0.0161327
\(249\) 0.111368 0.00705763
\(250\) −2.33632 −0.147762
\(251\) −15.0025 −0.946951 −0.473475 0.880807i \(-0.657001\pi\)
−0.473475 + 0.880807i \(0.657001\pi\)
\(252\) 0 0
\(253\) −5.27258 −0.331484
\(254\) −2.97612 −0.186738
\(255\) 5.07506 0.317813
\(256\) 9.10675 0.569172
\(257\) −20.7251 −1.29279 −0.646397 0.763001i \(-0.723725\pi\)
−0.646397 + 0.763001i \(0.723725\pi\)
\(258\) −2.77726 −0.172905
\(259\) 0 0
\(260\) 6.03820 0.374473
\(261\) −8.02434 −0.496694
\(262\) 3.38031 0.208836
\(263\) −23.0605 −1.42197 −0.710986 0.703206i \(-0.751751\pi\)
−0.710986 + 0.703206i \(0.751751\pi\)
\(264\) 2.32130 0.142866
\(265\) −2.80993 −0.172613
\(266\) 0 0
\(267\) 4.92634 0.301487
\(268\) 0.707371 0.0432096
\(269\) −2.46864 −0.150516 −0.0752578 0.997164i \(-0.523978\pi\)
−0.0752578 + 0.997164i \(0.523978\pi\)
\(270\) 0.250672 0.0152554
\(271\) −28.8712 −1.75380 −0.876899 0.480674i \(-0.840392\pi\)
−0.876899 + 0.480674i \(0.840392\pi\)
\(272\) −21.2603 −1.28910
\(273\) 0 0
\(274\) −1.27043 −0.0767495
\(275\) −8.44128 −0.509028
\(276\) 5.14754 0.309845
\(277\) −27.1493 −1.63124 −0.815621 0.578587i \(-0.803604\pi\)
−0.815621 + 0.578587i \(0.803604\pi\)
\(278\) 2.41800 0.145022
\(279\) 0.213848 0.0128027
\(280\) 0 0
\(281\) −20.3227 −1.21235 −0.606174 0.795332i \(-0.707297\pi\)
−0.606174 + 0.795332i \(0.707297\pi\)
\(282\) −1.79596 −0.106948
\(283\) 17.4332 1.03630 0.518148 0.855291i \(-0.326622\pi\)
0.518148 + 0.855291i \(0.326622\pi\)
\(284\) 27.2153 1.61493
\(285\) −0.250750 −0.0148531
\(286\) −2.28070 −0.134861
\(287\) 0 0
\(288\) −3.42617 −0.201889
\(289\) 20.8890 1.22877
\(290\) −2.01148 −0.118118
\(291\) 5.06400 0.296857
\(292\) 21.7848 1.27486
\(293\) −3.43534 −0.200694 −0.100347 0.994952i \(-0.531995\pi\)
−0.100347 + 0.994952i \(0.531995\pi\)
\(294\) 0 0
\(295\) 5.10538 0.297247
\(296\) 2.13622 0.124165
\(297\) 1.95390 0.113377
\(298\) 0.633535 0.0366997
\(299\) −10.3601 −0.599141
\(300\) 8.24109 0.475800
\(301\) 0 0
\(302\) 6.12950 0.352713
\(303\) −8.17374 −0.469569
\(304\) 1.05043 0.0602465
\(305\) −1.64935 −0.0944417
\(306\) 1.87145 0.106984
\(307\) 13.8857 0.792500 0.396250 0.918143i \(-0.370311\pi\)
0.396250 + 0.918143i \(0.370311\pi\)
\(308\) 0 0
\(309\) −0.577334 −0.0328434
\(310\) 0.0536057 0.00304460
\(311\) −15.9730 −0.905744 −0.452872 0.891575i \(-0.649601\pi\)
−0.452872 + 0.891575i \(0.649601\pi\)
\(312\) 4.56113 0.258223
\(313\) 11.0452 0.624309 0.312155 0.950031i \(-0.398949\pi\)
0.312155 + 0.950031i \(0.398949\pi\)
\(314\) 5.33632 0.301146
\(315\) 0 0
\(316\) 0.143733 0.00808559
\(317\) −17.6341 −0.990431 −0.495215 0.868770i \(-0.664911\pi\)
−0.495215 + 0.868770i \(0.664911\pi\)
\(318\) −1.03618 −0.0581059
\(319\) −15.6788 −0.877842
\(320\) 4.83659 0.270374
\(321\) 0.174403 0.00973424
\(322\) 0 0
\(323\) −1.87203 −0.104163
\(324\) −1.90756 −0.105976
\(325\) −16.5863 −0.920043
\(326\) 2.07071 0.114686
\(327\) 16.0556 0.887876
\(328\) 1.18803 0.0655981
\(329\) 0 0
\(330\) 0.489789 0.0269620
\(331\) 6.98035 0.383675 0.191837 0.981427i \(-0.438555\pi\)
0.191837 + 0.981427i \(0.438555\pi\)
\(332\) −0.212441 −0.0116592
\(333\) 1.79812 0.0985362
\(334\) 0.366046 0.0200292
\(335\) 0.305740 0.0167044
\(336\) 0 0
\(337\) −35.1650 −1.91556 −0.957779 0.287505i \(-0.907174\pi\)
−0.957779 + 0.287505i \(0.907174\pi\)
\(338\) −0.528923 −0.0287696
\(339\) −1.20756 −0.0655855
\(340\) −9.68100 −0.525026
\(341\) 0.417837 0.0226272
\(342\) −0.0924652 −0.00499994
\(343\) 0 0
\(344\) 10.8523 0.585118
\(345\) 2.22487 0.119783
\(346\) −6.41998 −0.345140
\(347\) −4.60835 −0.247389 −0.123695 0.992320i \(-0.539474\pi\)
−0.123695 + 0.992320i \(0.539474\pi\)
\(348\) 15.3069 0.820538
\(349\) 6.65142 0.356042 0.178021 0.984027i \(-0.443030\pi\)
0.178021 + 0.984027i \(0.443030\pi\)
\(350\) 0 0
\(351\) 3.83923 0.204923
\(352\) −6.69441 −0.356813
\(353\) −12.6753 −0.674636 −0.337318 0.941391i \(-0.609520\pi\)
−0.337318 + 0.941391i \(0.609520\pi\)
\(354\) 1.88263 0.100061
\(355\) 11.7630 0.624317
\(356\) −9.39731 −0.498057
\(357\) 0 0
\(358\) 1.64065 0.0867111
\(359\) −17.9318 −0.946405 −0.473203 0.880954i \(-0.656902\pi\)
−0.473203 + 0.880954i \(0.656902\pi\)
\(360\) −0.979519 −0.0516252
\(361\) −18.9075 −0.995132
\(362\) −5.35723 −0.281570
\(363\) −7.18227 −0.376971
\(364\) 0 0
\(365\) 9.41584 0.492848
\(366\) −0.608207 −0.0317915
\(367\) −25.4224 −1.32704 −0.663520 0.748159i \(-0.730938\pi\)
−0.663520 + 0.748159i \(0.730938\pi\)
\(368\) −9.32037 −0.485858
\(369\) 1.00000 0.0520579
\(370\) 0.450738 0.0234328
\(371\) 0 0
\(372\) −0.407928 −0.0211501
\(373\) −11.5361 −0.597317 −0.298658 0.954360i \(-0.596539\pi\)
−0.298658 + 0.954360i \(0.596539\pi\)
\(374\) 3.65663 0.189080
\(375\) 7.68441 0.396821
\(376\) 7.01782 0.361916
\(377\) −30.8073 −1.58666
\(378\) 0 0
\(379\) 15.5730 0.799931 0.399965 0.916530i \(-0.369022\pi\)
0.399965 + 0.916530i \(0.369022\pi\)
\(380\) 0.478321 0.0245374
\(381\) 9.78876 0.501493
\(382\) 6.73780 0.344736
\(383\) 17.7212 0.905510 0.452755 0.891635i \(-0.350441\pi\)
0.452755 + 0.891635i \(0.350441\pi\)
\(384\) 8.63587 0.440697
\(385\) 0 0
\(386\) 6.13035 0.312026
\(387\) 9.13470 0.464343
\(388\) −9.65991 −0.490408
\(389\) 8.26395 0.418999 0.209499 0.977809i \(-0.432817\pi\)
0.209499 + 0.977809i \(0.432817\pi\)
\(390\) 0.962389 0.0487325
\(391\) 16.6103 0.840018
\(392\) 0 0
\(393\) −11.1182 −0.560838
\(394\) −1.79696 −0.0905293
\(395\) 0.0621242 0.00312581
\(396\) −3.72719 −0.187298
\(397\) −16.3883 −0.822508 −0.411254 0.911521i \(-0.634909\pi\)
−0.411254 + 0.911521i \(0.634909\pi\)
\(398\) 2.24276 0.112419
\(399\) 0 0
\(400\) −14.9217 −0.746086
\(401\) −11.4693 −0.572751 −0.286376 0.958117i \(-0.592451\pi\)
−0.286376 + 0.958117i \(0.592451\pi\)
\(402\) 0.112743 0.00562312
\(403\) 0.821010 0.0408974
\(404\) 15.5919 0.775727
\(405\) −0.824488 −0.0409692
\(406\) 0 0
\(407\) 3.51334 0.174150
\(408\) −7.31282 −0.362039
\(409\) 22.7878 1.12678 0.563392 0.826190i \(-0.309496\pi\)
0.563392 + 0.826190i \(0.309496\pi\)
\(410\) 0.250672 0.0123798
\(411\) 4.17858 0.206114
\(412\) 1.10130 0.0542572
\(413\) 0 0
\(414\) 0.820432 0.0403220
\(415\) −0.0918213 −0.00450733
\(416\) −13.1539 −0.644922
\(417\) −7.95306 −0.389463
\(418\) −0.180668 −0.00883675
\(419\) −17.0874 −0.834774 −0.417387 0.908729i \(-0.637054\pi\)
−0.417387 + 0.908729i \(0.637054\pi\)
\(420\) 0 0
\(421\) 12.3189 0.600386 0.300193 0.953878i \(-0.402949\pi\)
0.300193 + 0.953878i \(0.402949\pi\)
\(422\) 6.66832 0.324609
\(423\) 5.90710 0.287213
\(424\) 4.04893 0.196633
\(425\) 26.5927 1.28994
\(426\) 4.33767 0.210161
\(427\) 0 0
\(428\) −0.332685 −0.0160809
\(429\) 7.50147 0.362175
\(430\) 2.28982 0.110425
\(431\) −17.7542 −0.855191 −0.427595 0.903970i \(-0.640639\pi\)
−0.427595 + 0.903970i \(0.640639\pi\)
\(432\) 3.45392 0.166177
\(433\) 22.6127 1.08669 0.543347 0.839508i \(-0.317157\pi\)
0.543347 + 0.839508i \(0.317157\pi\)
\(434\) 0 0
\(435\) 6.61597 0.317212
\(436\) −30.6270 −1.46677
\(437\) −0.820685 −0.0392587
\(438\) 3.47214 0.165905
\(439\) 14.7274 0.702900 0.351450 0.936207i \(-0.385689\pi\)
0.351450 + 0.936207i \(0.385689\pi\)
\(440\) −1.91388 −0.0912408
\(441\) 0 0
\(442\) 7.18494 0.341753
\(443\) −37.1985 −1.76735 −0.883677 0.468097i \(-0.844940\pi\)
−0.883677 + 0.468097i \(0.844940\pi\)
\(444\) −3.43002 −0.162782
\(445\) −4.06171 −0.192544
\(446\) −3.00095 −0.142099
\(447\) −2.08376 −0.0985586
\(448\) 0 0
\(449\) −19.3799 −0.914594 −0.457297 0.889314i \(-0.651182\pi\)
−0.457297 + 0.889314i \(0.651182\pi\)
\(450\) 1.31349 0.0619187
\(451\) 1.95390 0.0920056
\(452\) 2.30349 0.108347
\(453\) −20.1606 −0.947226
\(454\) −2.70655 −0.127025
\(455\) 0 0
\(456\) 0.361314 0.0169201
\(457\) 22.6263 1.05841 0.529207 0.848493i \(-0.322490\pi\)
0.529207 + 0.848493i \(0.322490\pi\)
\(458\) −4.34946 −0.203237
\(459\) −6.15541 −0.287310
\(460\) −4.24408 −0.197881
\(461\) 29.9890 1.39673 0.698363 0.715744i \(-0.253912\pi\)
0.698363 + 0.715744i \(0.253912\pi\)
\(462\) 0 0
\(463\) −29.5330 −1.37251 −0.686257 0.727359i \(-0.740748\pi\)
−0.686257 + 0.727359i \(0.740748\pi\)
\(464\) −27.7155 −1.28666
\(465\) −0.176315 −0.00817641
\(466\) −4.25092 −0.196920
\(467\) −33.0511 −1.52942 −0.764710 0.644374i \(-0.777118\pi\)
−0.764710 + 0.644374i \(0.777118\pi\)
\(468\) −7.32357 −0.338532
\(469\) 0 0
\(470\) 1.48075 0.0683017
\(471\) −17.5517 −0.808741
\(472\) −7.35650 −0.338611
\(473\) 17.8483 0.820666
\(474\) 0.0229086 0.00105223
\(475\) −1.31390 −0.0602858
\(476\) 0 0
\(477\) 3.40809 0.156046
\(478\) 0.0710197 0.00324836
\(479\) −12.3823 −0.565760 −0.282880 0.959155i \(-0.591290\pi\)
−0.282880 + 0.959155i \(0.591290\pi\)
\(480\) 2.82484 0.128936
\(481\) 6.90338 0.314767
\(482\) 1.83852 0.0837423
\(483\) 0 0
\(484\) 13.7006 0.622756
\(485\) −4.17521 −0.189587
\(486\) −0.304034 −0.0137913
\(487\) −4.33875 −0.196607 −0.0983037 0.995156i \(-0.531342\pi\)
−0.0983037 + 0.995156i \(0.531342\pi\)
\(488\) 2.37661 0.107584
\(489\) −6.81077 −0.307994
\(490\) 0 0
\(491\) 6.72949 0.303698 0.151849 0.988404i \(-0.451477\pi\)
0.151849 + 0.988404i \(0.451477\pi\)
\(492\) −1.90756 −0.0859996
\(493\) 49.3931 2.22455
\(494\) −0.354995 −0.0159720
\(495\) −1.61097 −0.0724077
\(496\) 0.738614 0.0331647
\(497\) 0 0
\(498\) −0.0338595 −0.00151728
\(499\) 11.7896 0.527774 0.263887 0.964554i \(-0.414995\pi\)
0.263887 + 0.964554i \(0.414995\pi\)
\(500\) −14.6585 −0.655548
\(501\) −1.20396 −0.0537892
\(502\) 4.56128 0.203580
\(503\) 31.5446 1.40650 0.703252 0.710940i \(-0.251730\pi\)
0.703252 + 0.710940i \(0.251730\pi\)
\(504\) 0 0
\(505\) 6.73915 0.299888
\(506\) 1.60304 0.0712640
\(507\) 1.73968 0.0772620
\(508\) −18.6727 −0.828466
\(509\) 26.0248 1.15353 0.576764 0.816911i \(-0.304315\pi\)
0.576764 + 0.816911i \(0.304315\pi\)
\(510\) −1.54299 −0.0683248
\(511\) 0 0
\(512\) −20.0405 −0.885673
\(513\) 0.304128 0.0134276
\(514\) 6.30112 0.277931
\(515\) 0.476005 0.0209753
\(516\) −17.4250 −0.767094
\(517\) 11.5419 0.507611
\(518\) 0 0
\(519\) 21.1160 0.926889
\(520\) −3.76060 −0.164913
\(521\) −3.46419 −0.151769 −0.0758844 0.997117i \(-0.524178\pi\)
−0.0758844 + 0.997117i \(0.524178\pi\)
\(522\) 2.43967 0.106782
\(523\) −3.05544 −0.133605 −0.0668024 0.997766i \(-0.521280\pi\)
−0.0668024 + 0.997766i \(0.521280\pi\)
\(524\) 21.2086 0.926503
\(525\) 0 0
\(526\) 7.01118 0.305702
\(527\) −1.31632 −0.0573398
\(528\) 6.74863 0.293696
\(529\) −15.7182 −0.683398
\(530\) 0.854316 0.0371091
\(531\) −6.19218 −0.268718
\(532\) 0 0
\(533\) 3.83923 0.166295
\(534\) −1.49778 −0.0648151
\(535\) −0.143793 −0.00621673
\(536\) −0.440551 −0.0190289
\(537\) −5.39627 −0.232866
\(538\) 0.750550 0.0323585
\(539\) 0 0
\(540\) 1.57276 0.0676810
\(541\) −24.4632 −1.05175 −0.525877 0.850560i \(-0.676263\pi\)
−0.525877 + 0.850560i \(0.676263\pi\)
\(542\) 8.77782 0.377039
\(543\) 17.6205 0.756168
\(544\) 21.0895 0.904205
\(545\) −13.2376 −0.567038
\(546\) 0 0
\(547\) 20.1482 0.861476 0.430738 0.902477i \(-0.358253\pi\)
0.430738 + 0.902477i \(0.358253\pi\)
\(548\) −7.97090 −0.340500
\(549\) 2.00046 0.0853774
\(550\) 2.56644 0.109433
\(551\) −2.44042 −0.103966
\(552\) −3.20589 −0.136452
\(553\) 0 0
\(554\) 8.25430 0.350692
\(555\) −1.48253 −0.0629297
\(556\) 15.1710 0.643392
\(557\) −24.8249 −1.05186 −0.525932 0.850527i \(-0.676283\pi\)
−0.525932 + 0.850527i \(0.676283\pi\)
\(558\) −0.0650170 −0.00275239
\(559\) 35.0702 1.48331
\(560\) 0 0
\(561\) −12.0271 −0.507783
\(562\) 6.17878 0.260636
\(563\) 26.4710 1.11562 0.557810 0.829969i \(-0.311642\pi\)
0.557810 + 0.829969i \(0.311642\pi\)
\(564\) −11.2682 −0.474475
\(565\) 0.995617 0.0418859
\(566\) −5.30028 −0.222787
\(567\) 0 0
\(568\) −16.9497 −0.711195
\(569\) 26.6313 1.11644 0.558222 0.829692i \(-0.311484\pi\)
0.558222 + 0.829692i \(0.311484\pi\)
\(570\) 0.0762365 0.00319319
\(571\) 33.2752 1.39253 0.696263 0.717787i \(-0.254845\pi\)
0.696263 + 0.717787i \(0.254845\pi\)
\(572\) −14.3095 −0.598312
\(573\) −22.1613 −0.925803
\(574\) 0 0
\(575\) 11.6581 0.486175
\(576\) −5.86618 −0.244424
\(577\) 15.7796 0.656913 0.328456 0.944519i \(-0.393472\pi\)
0.328456 + 0.944519i \(0.393472\pi\)
\(578\) −6.35097 −0.264166
\(579\) −20.1634 −0.837961
\(580\) −12.6204 −0.524033
\(581\) 0 0
\(582\) −1.53963 −0.0638197
\(583\) 6.65908 0.275791
\(584\) −13.5676 −0.561431
\(585\) −3.16540 −0.130873
\(586\) 1.04446 0.0431462
\(587\) 29.1620 1.20365 0.601823 0.798630i \(-0.294441\pi\)
0.601823 + 0.798630i \(0.294441\pi\)
\(588\) 0 0
\(589\) 0.0650370 0.00267980
\(590\) −1.55221 −0.0639034
\(591\) 5.91038 0.243121
\(592\) 6.21056 0.255252
\(593\) −27.2506 −1.11905 −0.559523 0.828815i \(-0.689016\pi\)
−0.559523 + 0.828815i \(0.689016\pi\)
\(594\) −0.594052 −0.0243743
\(595\) 0 0
\(596\) 3.97491 0.162819
\(597\) −7.37667 −0.301907
\(598\) 3.14983 0.128806
\(599\) 32.7059 1.33633 0.668164 0.744014i \(-0.267081\pi\)
0.668164 + 0.744014i \(0.267081\pi\)
\(600\) −5.13256 −0.209536
\(601\) 26.4132 1.07741 0.538707 0.842493i \(-0.318913\pi\)
0.538707 + 0.842493i \(0.318913\pi\)
\(602\) 0 0
\(603\) −0.370824 −0.0151011
\(604\) 38.4575 1.56482
\(605\) 5.92170 0.240751
\(606\) 2.48509 0.100950
\(607\) −21.9836 −0.892285 −0.446143 0.894962i \(-0.647203\pi\)
−0.446143 + 0.894962i \(0.647203\pi\)
\(608\) −1.04199 −0.0422585
\(609\) 0 0
\(610\) 0.501459 0.0203035
\(611\) 22.6787 0.917482
\(612\) 11.7418 0.474635
\(613\) −22.5556 −0.911012 −0.455506 0.890233i \(-0.650542\pi\)
−0.455506 + 0.890233i \(0.650542\pi\)
\(614\) −4.22173 −0.170375
\(615\) −0.824488 −0.0332466
\(616\) 0 0
\(617\) 1.67765 0.0675396 0.0337698 0.999430i \(-0.489249\pi\)
0.0337698 + 0.999430i \(0.489249\pi\)
\(618\) 0.175529 0.00706082
\(619\) 10.8832 0.437431 0.218716 0.975789i \(-0.429813\pi\)
0.218716 + 0.975789i \(0.429813\pi\)
\(620\) 0.336332 0.0135074
\(621\) −2.69849 −0.108287
\(622\) 4.85633 0.194721
\(623\) 0 0
\(624\) 13.2604 0.530841
\(625\) 15.2654 0.610615
\(626\) −3.35810 −0.134217
\(627\) 0.594235 0.0237315
\(628\) 33.4810 1.33604
\(629\) −11.0681 −0.441316
\(630\) 0 0
\(631\) 20.5955 0.819894 0.409947 0.912109i \(-0.365547\pi\)
0.409947 + 0.912109i \(0.365547\pi\)
\(632\) −0.0895168 −0.00356079
\(633\) −21.9328 −0.871751
\(634\) 5.36137 0.212927
\(635\) −8.07072 −0.320277
\(636\) −6.50116 −0.257788
\(637\) 0 0
\(638\) 4.76688 0.188722
\(639\) −14.2671 −0.564397
\(640\) −7.12017 −0.281449
\(641\) 9.57358 0.378134 0.189067 0.981964i \(-0.439454\pi\)
0.189067 + 0.981964i \(0.439454\pi\)
\(642\) −0.0530245 −0.00209271
\(643\) 39.7169 1.56628 0.783141 0.621844i \(-0.213616\pi\)
0.783141 + 0.621844i \(0.213616\pi\)
\(644\) 0 0
\(645\) −7.53146 −0.296551
\(646\) 0.569161 0.0223933
\(647\) −25.7976 −1.01421 −0.507105 0.861885i \(-0.669284\pi\)
−0.507105 + 0.861885i \(0.669284\pi\)
\(648\) 1.18803 0.0466703
\(649\) −12.0989 −0.474923
\(650\) 5.04280 0.197795
\(651\) 0 0
\(652\) 12.9920 0.508805
\(653\) −30.6204 −1.19827 −0.599134 0.800649i \(-0.704488\pi\)
−0.599134 + 0.800649i \(0.704488\pi\)
\(654\) −4.88144 −0.190880
\(655\) 9.16681 0.358177
\(656\) 3.45392 0.134853
\(657\) −11.4202 −0.445545
\(658\) 0 0
\(659\) 3.87029 0.150765 0.0753826 0.997155i \(-0.475982\pi\)
0.0753826 + 0.997155i \(0.475982\pi\)
\(660\) 3.07302 0.119617
\(661\) 5.42483 0.211001 0.105501 0.994419i \(-0.466355\pi\)
0.105501 + 0.994419i \(0.466355\pi\)
\(662\) −2.12226 −0.0824841
\(663\) −23.6320 −0.917791
\(664\) 0.132308 0.00513456
\(665\) 0 0
\(666\) −0.546689 −0.0211838
\(667\) 21.6536 0.838430
\(668\) 2.29664 0.0888596
\(669\) 9.87045 0.381613
\(670\) −0.0929555 −0.00359118
\(671\) 3.90869 0.150893
\(672\) 0 0
\(673\) −44.2892 −1.70722 −0.853611 0.520910i \(-0.825593\pi\)
−0.853611 + 0.520910i \(0.825593\pi\)
\(674\) 10.6913 0.411815
\(675\) −4.32022 −0.166285
\(676\) −3.31856 −0.127637
\(677\) −5.66224 −0.217617 −0.108809 0.994063i \(-0.534704\pi\)
−0.108809 + 0.994063i \(0.534704\pi\)
\(678\) 0.367139 0.0140999
\(679\) 0 0
\(680\) 6.02934 0.231214
\(681\) 8.90214 0.341131
\(682\) −0.127037 −0.00486449
\(683\) 12.2367 0.468224 0.234112 0.972210i \(-0.424782\pi\)
0.234112 + 0.972210i \(0.424782\pi\)
\(684\) −0.580143 −0.0221823
\(685\) −3.44519 −0.131634
\(686\) 0 0
\(687\) 14.3058 0.545802
\(688\) 31.5506 1.20285
\(689\) 13.0845 0.498478
\(690\) −0.676437 −0.0257515
\(691\) 27.8737 1.06037 0.530183 0.847883i \(-0.322123\pi\)
0.530183 + 0.847883i \(0.322123\pi\)
\(692\) −40.2801 −1.53122
\(693\) 0 0
\(694\) 1.40109 0.0531848
\(695\) 6.55721 0.248729
\(696\) −9.53317 −0.361354
\(697\) −6.15541 −0.233153
\(698\) −2.02226 −0.0765436
\(699\) 13.9817 0.528837
\(700\) 0 0
\(701\) −15.7568 −0.595128 −0.297564 0.954702i \(-0.596174\pi\)
−0.297564 + 0.954702i \(0.596174\pi\)
\(702\) −1.16726 −0.0440553
\(703\) 0.546857 0.0206251
\(704\) −11.4619 −0.431988
\(705\) −4.87033 −0.183427
\(706\) 3.85371 0.145036
\(707\) 0 0
\(708\) 11.8120 0.443921
\(709\) 6.33725 0.238001 0.119000 0.992894i \(-0.462031\pi\)
0.119000 + 0.992894i \(0.462031\pi\)
\(710\) −3.57636 −0.134218
\(711\) −0.0753488 −0.00282580
\(712\) 5.85265 0.219337
\(713\) −0.577065 −0.0216113
\(714\) 0 0
\(715\) −6.18488 −0.231301
\(716\) 10.2937 0.384695
\(717\) −0.233591 −0.00872362
\(718\) 5.45188 0.203462
\(719\) −52.7723 −1.96808 −0.984038 0.177960i \(-0.943050\pi\)
−0.984038 + 0.177960i \(0.943050\pi\)
\(720\) −2.84772 −0.106128
\(721\) 0 0
\(722\) 5.74852 0.213938
\(723\) −6.04709 −0.224894
\(724\) −33.6122 −1.24919
\(725\) 34.6669 1.28750
\(726\) 2.18365 0.0810430
\(727\) −22.6883 −0.841463 −0.420731 0.907185i \(-0.638226\pi\)
−0.420731 + 0.907185i \(0.638226\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.86274 −0.105955
\(731\) −56.2278 −2.07966
\(732\) −3.81600 −0.141043
\(733\) 50.5473 1.86701 0.933503 0.358569i \(-0.116735\pi\)
0.933503 + 0.358569i \(0.116735\pi\)
\(734\) 7.72928 0.285293
\(735\) 0 0
\(736\) 9.24549 0.340793
\(737\) −0.724554 −0.0266893
\(738\) −0.304034 −0.0111916
\(739\) 25.4396 0.935811 0.467905 0.883779i \(-0.345009\pi\)
0.467905 + 0.883779i \(0.345009\pi\)
\(740\) 2.82801 0.103960
\(741\) 1.16762 0.0428934
\(742\) 0 0
\(743\) −31.7789 −1.16585 −0.582927 0.812524i \(-0.698093\pi\)
−0.582927 + 0.812524i \(0.698093\pi\)
\(744\) 0.254058 0.00931422
\(745\) 1.71804 0.0629441
\(746\) 3.50737 0.128414
\(747\) 0.111368 0.00407473
\(748\) 22.9424 0.838856
\(749\) 0 0
\(750\) −2.33632 −0.0853104
\(751\) 19.8867 0.725676 0.362838 0.931852i \(-0.381808\pi\)
0.362838 + 0.931852i \(0.381808\pi\)
\(752\) 20.4027 0.744009
\(753\) −15.0025 −0.546722
\(754\) 9.36646 0.341106
\(755\) 16.6221 0.604942
\(756\) 0 0
\(757\) −48.2331 −1.75306 −0.876531 0.481345i \(-0.840148\pi\)
−0.876531 + 0.481345i \(0.840148\pi\)
\(758\) −4.73472 −0.171973
\(759\) −5.27258 −0.191382
\(760\) −0.297899 −0.0108059
\(761\) 7.14668 0.259067 0.129533 0.991575i \(-0.458652\pi\)
0.129533 + 0.991575i \(0.458652\pi\)
\(762\) −2.97612 −0.107813
\(763\) 0 0
\(764\) 42.2742 1.52943
\(765\) 5.07506 0.183489
\(766\) −5.38784 −0.194671
\(767\) −23.7732 −0.858400
\(768\) 9.10675 0.328612
\(769\) −45.7056 −1.64819 −0.824093 0.566454i \(-0.808315\pi\)
−0.824093 + 0.566454i \(0.808315\pi\)
\(770\) 0 0
\(771\) −20.7251 −0.746395
\(772\) 38.4629 1.38431
\(773\) −7.30178 −0.262627 −0.131313 0.991341i \(-0.541919\pi\)
−0.131313 + 0.991341i \(0.541919\pi\)
\(774\) −2.77726 −0.0998266
\(775\) −0.923869 −0.0331864
\(776\) 6.01620 0.215969
\(777\) 0 0
\(778\) −2.51252 −0.0900783
\(779\) 0.304128 0.0108965
\(780\) 6.03820 0.216202
\(781\) −27.8764 −0.997497
\(782\) −5.05009 −0.180591
\(783\) −8.02434 −0.286766
\(784\) 0 0
\(785\) 14.4712 0.516499
\(786\) 3.38031 0.120571
\(787\) 29.8623 1.06447 0.532237 0.846595i \(-0.321351\pi\)
0.532237 + 0.846595i \(0.321351\pi\)
\(788\) −11.2744 −0.401635
\(789\) −23.0605 −0.820976
\(790\) −0.0188879 −0.000672000 0
\(791\) 0 0
\(792\) 2.32130 0.0824837
\(793\) 7.68021 0.272732
\(794\) 4.98262 0.176826
\(795\) −2.80993 −0.0996581
\(796\) 14.0715 0.498750
\(797\) 14.7557 0.522672 0.261336 0.965248i \(-0.415837\pi\)
0.261336 + 0.965248i \(0.415837\pi\)
\(798\) 0 0
\(799\) −36.3606 −1.28634
\(800\) 14.8018 0.523324
\(801\) 4.92634 0.174064
\(802\) 3.48707 0.123133
\(803\) −22.3140 −0.787444
\(804\) 0.707371 0.0249471
\(805\) 0 0
\(806\) −0.249615 −0.00879232
\(807\) −2.46864 −0.0869002
\(808\) −9.71066 −0.341620
\(809\) 34.7471 1.22164 0.610822 0.791768i \(-0.290839\pi\)
0.610822 + 0.791768i \(0.290839\pi\)
\(810\) 0.250672 0.00880773
\(811\) 38.7222 1.35972 0.679861 0.733341i \(-0.262040\pi\)
0.679861 + 0.733341i \(0.262040\pi\)
\(812\) 0 0
\(813\) −28.8712 −1.01256
\(814\) −1.06818 −0.0374395
\(815\) 5.61540 0.196699
\(816\) −21.2603 −0.744260
\(817\) 2.77812 0.0971940
\(818\) −6.92827 −0.242241
\(819\) 0 0
\(820\) 1.57276 0.0549233
\(821\) −31.2028 −1.08899 −0.544493 0.838766i \(-0.683278\pi\)
−0.544493 + 0.838766i \(0.683278\pi\)
\(822\) −1.27043 −0.0443113
\(823\) 23.7638 0.828355 0.414178 0.910196i \(-0.364069\pi\)
0.414178 + 0.910196i \(0.364069\pi\)
\(824\) −0.685891 −0.0238942
\(825\) −8.44128 −0.293888
\(826\) 0 0
\(827\) −21.4012 −0.744192 −0.372096 0.928194i \(-0.621361\pi\)
−0.372096 + 0.928194i \(0.621361\pi\)
\(828\) 5.14754 0.178889
\(829\) 22.2690 0.773434 0.386717 0.922198i \(-0.373609\pi\)
0.386717 + 0.922198i \(0.373609\pi\)
\(830\) 0.0279168 0.000969006 0
\(831\) −27.1493 −0.941798
\(832\) −22.5216 −0.780796
\(833\) 0 0
\(834\) 2.41800 0.0837285
\(835\) 0.992655 0.0343522
\(836\) −1.13354 −0.0392044
\(837\) 0.213848 0.00739166
\(838\) 5.19515 0.179463
\(839\) −21.3337 −0.736522 −0.368261 0.929723i \(-0.620047\pi\)
−0.368261 + 0.929723i \(0.620047\pi\)
\(840\) 0 0
\(841\) 35.3900 1.22034
\(842\) −3.74536 −0.129074
\(843\) −20.3227 −0.699950
\(844\) 41.8382 1.44013
\(845\) −1.43435 −0.0493431
\(846\) −1.79596 −0.0617463
\(847\) 0 0
\(848\) 11.7713 0.404228
\(849\) 17.4332 0.598305
\(850\) −8.08509 −0.277316
\(851\) −4.85220 −0.166331
\(852\) 27.2153 0.932382
\(853\) 41.5413 1.42235 0.711174 0.703016i \(-0.248164\pi\)
0.711174 + 0.703016i \(0.248164\pi\)
\(854\) 0 0
\(855\) −0.250750 −0.00857546
\(856\) 0.207197 0.00708184
\(857\) 31.3775 1.07184 0.535918 0.844270i \(-0.319966\pi\)
0.535918 + 0.844270i \(0.319966\pi\)
\(858\) −2.28070 −0.0778619
\(859\) −2.99781 −0.102284 −0.0511420 0.998691i \(-0.516286\pi\)
−0.0511420 + 0.998691i \(0.516286\pi\)
\(860\) 14.3667 0.489901
\(861\) 0 0
\(862\) 5.39789 0.183853
\(863\) 21.3912 0.728166 0.364083 0.931367i \(-0.381382\pi\)
0.364083 + 0.931367i \(0.381382\pi\)
\(864\) −3.42617 −0.116561
\(865\) −17.4099 −0.591954
\(866\) −6.87502 −0.233623
\(867\) 20.8890 0.709429
\(868\) 0 0
\(869\) −0.147224 −0.00499424
\(870\) −2.01148 −0.0681956
\(871\) −1.42368 −0.0482396
\(872\) 19.0746 0.645946
\(873\) 5.06400 0.171391
\(874\) 0.249516 0.00844001
\(875\) 0 0
\(876\) 21.7848 0.736040
\(877\) 22.5441 0.761261 0.380630 0.924727i \(-0.375707\pi\)
0.380630 + 0.924727i \(0.375707\pi\)
\(878\) −4.47763 −0.151113
\(879\) −3.43534 −0.115871
\(880\) −5.56416 −0.187568
\(881\) −19.3535 −0.652037 −0.326018 0.945363i \(-0.605707\pi\)
−0.326018 + 0.945363i \(0.605707\pi\)
\(882\) 0 0
\(883\) 28.2584 0.950970 0.475485 0.879724i \(-0.342273\pi\)
0.475485 + 0.879724i \(0.342273\pi\)
\(884\) 45.0796 1.51619
\(885\) 5.10538 0.171615
\(886\) 11.3096 0.379954
\(887\) 2.76069 0.0926949 0.0463475 0.998925i \(-0.485242\pi\)
0.0463475 + 0.998925i \(0.485242\pi\)
\(888\) 2.13622 0.0716869
\(889\) 0 0
\(890\) 1.23490 0.0413939
\(891\) 1.95390 0.0654582
\(892\) −18.8285 −0.630425
\(893\) 1.79651 0.0601180
\(894\) 0.633535 0.0211886
\(895\) 4.44916 0.148719
\(896\) 0 0
\(897\) −10.3601 −0.345914
\(898\) 5.89215 0.196623
\(899\) −1.71599 −0.0572313
\(900\) 8.24109 0.274703
\(901\) −20.9782 −0.698885
\(902\) −0.594052 −0.0197798
\(903\) 0 0
\(904\) −1.43462 −0.0477147
\(905\) −14.5279 −0.482924
\(906\) 6.12950 0.203639
\(907\) 31.9728 1.06164 0.530820 0.847485i \(-0.321884\pi\)
0.530820 + 0.847485i \(0.321884\pi\)
\(908\) −16.9814 −0.563548
\(909\) −8.17374 −0.271106
\(910\) 0 0
\(911\) 27.0589 0.896500 0.448250 0.893908i \(-0.352047\pi\)
0.448250 + 0.893908i \(0.352047\pi\)
\(912\) 1.05043 0.0347834
\(913\) 0.217601 0.00720155
\(914\) −6.87916 −0.227542
\(915\) −1.64935 −0.0545259
\(916\) −27.2893 −0.901664
\(917\) 0 0
\(918\) 1.87145 0.0617671
\(919\) −33.9219 −1.11898 −0.559491 0.828836i \(-0.689003\pi\)
−0.559491 + 0.828836i \(0.689003\pi\)
\(920\) 2.64322 0.0871443
\(921\) 13.8857 0.457550
\(922\) −9.11767 −0.300275
\(923\) −54.7745 −1.80293
\(924\) 0 0
\(925\) −7.76826 −0.255419
\(926\) 8.97903 0.295069
\(927\) −0.577334 −0.0189621
\(928\) 27.4928 0.902495
\(929\) −51.4407 −1.68772 −0.843858 0.536567i \(-0.819721\pi\)
−0.843858 + 0.536567i \(0.819721\pi\)
\(930\) 0.0536057 0.00175780
\(931\) 0 0
\(932\) −26.6710 −0.873638
\(933\) −15.9730 −0.522932
\(934\) 10.0486 0.328802
\(935\) 9.91617 0.324293
\(936\) 4.56113 0.149085
\(937\) −47.7548 −1.56008 −0.780041 0.625728i \(-0.784802\pi\)
−0.780041 + 0.625728i \(0.784802\pi\)
\(938\) 0 0
\(939\) 11.0452 0.360445
\(940\) 9.29047 0.303022
\(941\) 3.86344 0.125944 0.0629722 0.998015i \(-0.479942\pi\)
0.0629722 + 0.998015i \(0.479942\pi\)
\(942\) 5.33632 0.173867
\(943\) −2.69849 −0.0878748
\(944\) −21.3873 −0.696098
\(945\) 0 0
\(946\) −5.42649 −0.176431
\(947\) −20.9977 −0.682332 −0.341166 0.940003i \(-0.610822\pi\)
−0.341166 + 0.940003i \(0.610822\pi\)
\(948\) 0.143733 0.00466822
\(949\) −43.8449 −1.42326
\(950\) 0.399470 0.0129605
\(951\) −17.6341 −0.571825
\(952\) 0 0
\(953\) −6.47314 −0.209685 −0.104843 0.994489i \(-0.533434\pi\)
−0.104843 + 0.994489i \(0.533434\pi\)
\(954\) −1.03618 −0.0335475
\(955\) 18.2718 0.591260
\(956\) 0.445590 0.0144114
\(957\) −15.6788 −0.506822
\(958\) 3.76463 0.121630
\(959\) 0 0
\(960\) 4.83659 0.156100
\(961\) −30.9543 −0.998525
\(962\) −2.09886 −0.0676701
\(963\) 0.174403 0.00562007
\(964\) 11.5352 0.371524
\(965\) 16.6245 0.535160
\(966\) 0 0
\(967\) −0.488375 −0.0157051 −0.00785253 0.999969i \(-0.502500\pi\)
−0.00785253 + 0.999969i \(0.502500\pi\)
\(968\) −8.53277 −0.274254
\(969\) −1.87203 −0.0601383
\(970\) 1.26941 0.0407582
\(971\) 34.4565 1.10576 0.552880 0.833261i \(-0.313529\pi\)
0.552880 + 0.833261i \(0.313529\pi\)
\(972\) −1.90756 −0.0611851
\(973\) 0 0
\(974\) 1.31913 0.0422675
\(975\) −16.5863 −0.531187
\(976\) 6.90943 0.221165
\(977\) 58.1836 1.86146 0.930729 0.365709i \(-0.119173\pi\)
0.930729 + 0.365709i \(0.119173\pi\)
\(978\) 2.07071 0.0662138
\(979\) 9.62559 0.307635
\(980\) 0 0
\(981\) 16.0556 0.512615
\(982\) −2.04599 −0.0652903
\(983\) 30.8254 0.983176 0.491588 0.870828i \(-0.336417\pi\)
0.491588 + 0.870828i \(0.336417\pi\)
\(984\) 1.18803 0.0378731
\(985\) −4.87304 −0.155268
\(986\) −15.0172 −0.478244
\(987\) 0 0
\(988\) −2.22730 −0.0708599
\(989\) −24.6499 −0.783821
\(990\) 0.489789 0.0155665
\(991\) 15.6915 0.498458 0.249229 0.968445i \(-0.419823\pi\)
0.249229 + 0.968445i \(0.419823\pi\)
\(992\) −0.732680 −0.0232626
\(993\) 6.98035 0.221515
\(994\) 0 0
\(995\) 6.08198 0.192812
\(996\) −0.212441 −0.00673144
\(997\) −2.61102 −0.0826918 −0.0413459 0.999145i \(-0.513165\pi\)
−0.0413459 + 0.999145i \(0.513165\pi\)
\(998\) −3.58444 −0.113463
\(999\) 1.79812 0.0568899
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 \(a_p\))