Properties

Label 6027.2.a.bo.1.5
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 1.5
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.80081 q^{2} +1.00000 q^{3} +1.24292 q^{4} -2.17778 q^{5} -1.80081 q^{6} +1.36336 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.80081 q^{2} +1.00000 q^{3} +1.24292 q^{4} -2.17778 q^{5} -1.80081 q^{6} +1.36336 q^{8} +1.00000 q^{9} +3.92176 q^{10} -0.798673 q^{11} +1.24292 q^{12} +1.19276 q^{13} -2.17778 q^{15} -4.94099 q^{16} -5.17880 q^{17} -1.80081 q^{18} -4.47213 q^{19} -2.70680 q^{20} +1.43826 q^{22} +6.71919 q^{23} +1.36336 q^{24} -0.257287 q^{25} -2.14794 q^{26} +1.00000 q^{27} +4.22854 q^{29} +3.92176 q^{30} +0.168434 q^{31} +6.17106 q^{32} -0.798673 q^{33} +9.32603 q^{34} +1.24292 q^{36} -5.83538 q^{37} +8.05346 q^{38} +1.19276 q^{39} -2.96910 q^{40} -1.00000 q^{41} +1.82010 q^{43} -0.992684 q^{44} -2.17778 q^{45} -12.1000 q^{46} -5.26975 q^{47} -4.94099 q^{48} +0.463325 q^{50} -5.17880 q^{51} +1.48251 q^{52} -1.21884 q^{53} -1.80081 q^{54} +1.73933 q^{55} -4.47213 q^{57} -7.61479 q^{58} +11.7353 q^{59} -2.70680 q^{60} -12.5796 q^{61} -0.303318 q^{62} -1.23093 q^{64} -2.59757 q^{65} +1.43826 q^{66} -2.41092 q^{67} -6.43681 q^{68} +6.71919 q^{69} +0.255861 q^{71} +1.36336 q^{72} -5.27880 q^{73} +10.5084 q^{74} -0.257287 q^{75} -5.55849 q^{76} -2.14794 q^{78} +13.1519 q^{79} +10.7604 q^{80} +1.00000 q^{81} +1.80081 q^{82} +10.9425 q^{83} +11.2783 q^{85} -3.27766 q^{86} +4.22854 q^{87} -1.08888 q^{88} -9.74201 q^{89} +3.92176 q^{90} +8.35140 q^{92} +0.168434 q^{93} +9.48982 q^{94} +9.73931 q^{95} +6.17106 q^{96} +4.79462 q^{97} -0.798673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80081 −1.27337 −0.636683 0.771126i \(-0.719694\pi\)
−0.636683 + 0.771126i \(0.719694\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.24292 0.621458
\(5\) −2.17778 −0.973932 −0.486966 0.873421i \(-0.661896\pi\)
−0.486966 + 0.873421i \(0.661896\pi\)
\(6\) −1.80081 −0.735178
\(7\) 0 0
\(8\) 1.36336 0.482022
\(9\) 1.00000 0.333333
\(10\) 3.92176 1.24017
\(11\) −0.798673 −0.240809 −0.120404 0.992725i \(-0.538419\pi\)
−0.120404 + 0.992725i \(0.538419\pi\)
\(12\) 1.24292 0.358799
\(13\) 1.19276 0.330813 0.165406 0.986225i \(-0.447106\pi\)
0.165406 + 0.986225i \(0.447106\pi\)
\(14\) 0 0
\(15\) −2.17778 −0.562300
\(16\) −4.94099 −1.23525
\(17\) −5.17880 −1.25604 −0.628021 0.778196i \(-0.716135\pi\)
−0.628021 + 0.778196i \(0.716135\pi\)
\(18\) −1.80081 −0.424455
\(19\) −4.47213 −1.02598 −0.512989 0.858395i \(-0.671462\pi\)
−0.512989 + 0.858395i \(0.671462\pi\)
\(20\) −2.70680 −0.605258
\(21\) 0 0
\(22\) 1.43826 0.306638
\(23\) 6.71919 1.40105 0.700524 0.713629i \(-0.252950\pi\)
0.700524 + 0.713629i \(0.252950\pi\)
\(24\) 1.36336 0.278295
\(25\) −0.257287 −0.0514574
\(26\) −2.14794 −0.421246
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.22854 0.785220 0.392610 0.919705i \(-0.371572\pi\)
0.392610 + 0.919705i \(0.371572\pi\)
\(30\) 3.92176 0.716013
\(31\) 0.168434 0.0302517 0.0151258 0.999886i \(-0.495185\pi\)
0.0151258 + 0.999886i \(0.495185\pi\)
\(32\) 6.17106 1.09090
\(33\) −0.798673 −0.139031
\(34\) 9.32603 1.59940
\(35\) 0 0
\(36\) 1.24292 0.207153
\(37\) −5.83538 −0.959330 −0.479665 0.877452i \(-0.659242\pi\)
−0.479665 + 0.877452i \(0.659242\pi\)
\(38\) 8.05346 1.30644
\(39\) 1.19276 0.190995
\(40\) −2.96910 −0.469456
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 1.82010 0.277563 0.138782 0.990323i \(-0.455681\pi\)
0.138782 + 0.990323i \(0.455681\pi\)
\(44\) −0.992684 −0.149653
\(45\) −2.17778 −0.324644
\(46\) −12.1000 −1.78405
\(47\) −5.26975 −0.768672 −0.384336 0.923193i \(-0.625570\pi\)
−0.384336 + 0.923193i \(0.625570\pi\)
\(48\) −4.94099 −0.713171
\(49\) 0 0
\(50\) 0.463325 0.0655241
\(51\) −5.17880 −0.725177
\(52\) 1.48251 0.205587
\(53\) −1.21884 −0.167421 −0.0837103 0.996490i \(-0.526677\pi\)
−0.0837103 + 0.996490i \(0.526677\pi\)
\(54\) −1.80081 −0.245059
\(55\) 1.73933 0.234531
\(56\) 0 0
\(57\) −4.47213 −0.592348
\(58\) −7.61479 −0.999871
\(59\) 11.7353 1.52780 0.763900 0.645334i \(-0.223282\pi\)
0.763900 + 0.645334i \(0.223282\pi\)
\(60\) −2.70680 −0.349446
\(61\) −12.5796 −1.61065 −0.805325 0.592833i \(-0.798009\pi\)
−0.805325 + 0.592833i \(0.798009\pi\)
\(62\) −0.303318 −0.0385214
\(63\) 0 0
\(64\) −1.23093 −0.153866
\(65\) −2.59757 −0.322189
\(66\) 1.43826 0.177037
\(67\) −2.41092 −0.294541 −0.147271 0.989096i \(-0.547049\pi\)
−0.147271 + 0.989096i \(0.547049\pi\)
\(68\) −6.43681 −0.780578
\(69\) 6.71919 0.808895
\(70\) 0 0
\(71\) 0.255861 0.0303651 0.0151826 0.999885i \(-0.495167\pi\)
0.0151826 + 0.999885i \(0.495167\pi\)
\(72\) 1.36336 0.160674
\(73\) −5.27880 −0.617837 −0.308918 0.951089i \(-0.599967\pi\)
−0.308918 + 0.951089i \(0.599967\pi\)
\(74\) 10.5084 1.22158
\(75\) −0.257287 −0.0297089
\(76\) −5.55849 −0.637602
\(77\) 0 0
\(78\) −2.14794 −0.243206
\(79\) 13.1519 1.47970 0.739851 0.672771i \(-0.234896\pi\)
0.739851 + 0.672771i \(0.234896\pi\)
\(80\) 10.7604 1.20305
\(81\) 1.00000 0.111111
\(82\) 1.80081 0.198866
\(83\) 10.9425 1.20109 0.600546 0.799590i \(-0.294950\pi\)
0.600546 + 0.799590i \(0.294950\pi\)
\(84\) 0 0
\(85\) 11.2783 1.22330
\(86\) −3.27766 −0.353439
\(87\) 4.22854 0.453347
\(88\) −1.08888 −0.116075
\(89\) −9.74201 −1.03265 −0.516325 0.856392i \(-0.672700\pi\)
−0.516325 + 0.856392i \(0.672700\pi\)
\(90\) 3.92176 0.413390
\(91\) 0 0
\(92\) 8.35140 0.870693
\(93\) 0.168434 0.0174658
\(94\) 9.48982 0.978800
\(95\) 9.73931 0.999232
\(96\) 6.17106 0.629831
\(97\) 4.79462 0.486820 0.243410 0.969923i \(-0.421734\pi\)
0.243410 + 0.969923i \(0.421734\pi\)
\(98\) 0 0
\(99\) −0.798673 −0.0802696
\(100\) −0.319786 −0.0319786
\(101\) −2.54061 −0.252800 −0.126400 0.991979i \(-0.540342\pi\)
−0.126400 + 0.991979i \(0.540342\pi\)
\(102\) 9.32603 0.923415
\(103\) −5.43950 −0.535970 −0.267985 0.963423i \(-0.586358\pi\)
−0.267985 + 0.963423i \(0.586358\pi\)
\(104\) 1.62617 0.159459
\(105\) 0 0
\(106\) 2.19490 0.213188
\(107\) 16.2891 1.57473 0.787364 0.616489i \(-0.211445\pi\)
0.787364 + 0.616489i \(0.211445\pi\)
\(108\) 1.24292 0.119600
\(109\) 10.3602 0.992326 0.496163 0.868229i \(-0.334742\pi\)
0.496163 + 0.868229i \(0.334742\pi\)
\(110\) −3.13221 −0.298644
\(111\) −5.83538 −0.553869
\(112\) 0 0
\(113\) 2.79770 0.263185 0.131593 0.991304i \(-0.457991\pi\)
0.131593 + 0.991304i \(0.457991\pi\)
\(114\) 8.05346 0.754276
\(115\) −14.6329 −1.36452
\(116\) 5.25572 0.487981
\(117\) 1.19276 0.110271
\(118\) −21.1330 −1.94545
\(119\) 0 0
\(120\) −2.96910 −0.271041
\(121\) −10.3621 −0.942011
\(122\) 22.6534 2.05095
\(123\) −1.00000 −0.0901670
\(124\) 0.209350 0.0188001
\(125\) 11.4492 1.02405
\(126\) 0 0
\(127\) −14.5164 −1.28812 −0.644062 0.764973i \(-0.722752\pi\)
−0.644062 + 0.764973i \(0.722752\pi\)
\(128\) −10.1255 −0.894972
\(129\) 1.82010 0.160251
\(130\) 4.67773 0.410264
\(131\) 0.770663 0.0673331 0.0336666 0.999433i \(-0.489282\pi\)
0.0336666 + 0.999433i \(0.489282\pi\)
\(132\) −0.992684 −0.0864020
\(133\) 0 0
\(134\) 4.34161 0.375058
\(135\) −2.17778 −0.187433
\(136\) −7.06058 −0.605440
\(137\) 4.75720 0.406435 0.203218 0.979134i \(-0.434860\pi\)
0.203218 + 0.979134i \(0.434860\pi\)
\(138\) −12.1000 −1.03002
\(139\) 0.628119 0.0532764 0.0266382 0.999645i \(-0.491520\pi\)
0.0266382 + 0.999645i \(0.491520\pi\)
\(140\) 0 0
\(141\) −5.26975 −0.443793
\(142\) −0.460758 −0.0386659
\(143\) −0.952627 −0.0796627
\(144\) −4.94099 −0.411749
\(145\) −9.20881 −0.764750
\(146\) 9.50612 0.786732
\(147\) 0 0
\(148\) −7.25289 −0.596184
\(149\) −0.960953 −0.0787243 −0.0393622 0.999225i \(-0.512533\pi\)
−0.0393622 + 0.999225i \(0.512533\pi\)
\(150\) 0.463325 0.0378303
\(151\) −5.66573 −0.461071 −0.230535 0.973064i \(-0.574048\pi\)
−0.230535 + 0.973064i \(0.574048\pi\)
\(152\) −6.09714 −0.494543
\(153\) −5.17880 −0.418681
\(154\) 0 0
\(155\) −0.366812 −0.0294630
\(156\) 1.48251 0.118695
\(157\) −14.1792 −1.13162 −0.565812 0.824534i \(-0.691437\pi\)
−0.565812 + 0.824534i \(0.691437\pi\)
\(158\) −23.6840 −1.88420
\(159\) −1.21884 −0.0966603
\(160\) −13.4392 −1.06246
\(161\) 0 0
\(162\) −1.80081 −0.141485
\(163\) 10.5373 0.825346 0.412673 0.910879i \(-0.364595\pi\)
0.412673 + 0.910879i \(0.364595\pi\)
\(164\) −1.24292 −0.0970555
\(165\) 1.73933 0.135407
\(166\) −19.7053 −1.52943
\(167\) 13.9834 1.08207 0.541034 0.841001i \(-0.318033\pi\)
0.541034 + 0.841001i \(0.318033\pi\)
\(168\) 0 0
\(169\) −11.5773 −0.890563
\(170\) −20.3100 −1.55771
\(171\) −4.47213 −0.341992
\(172\) 2.26224 0.172494
\(173\) 5.17342 0.393328 0.196664 0.980471i \(-0.436989\pi\)
0.196664 + 0.980471i \(0.436989\pi\)
\(174\) −7.61479 −0.577276
\(175\) 0 0
\(176\) 3.94624 0.297459
\(177\) 11.7353 0.882076
\(178\) 17.5435 1.31494
\(179\) −0.884735 −0.0661282 −0.0330641 0.999453i \(-0.510527\pi\)
−0.0330641 + 0.999453i \(0.510527\pi\)
\(180\) −2.70680 −0.201753
\(181\) −10.6540 −0.791905 −0.395952 0.918271i \(-0.629586\pi\)
−0.395952 + 0.918271i \(0.629586\pi\)
\(182\) 0 0
\(183\) −12.5796 −0.929910
\(184\) 9.16069 0.675335
\(185\) 12.7081 0.934321
\(186\) −0.303318 −0.0222403
\(187\) 4.13616 0.302466
\(188\) −6.54986 −0.477698
\(189\) 0 0
\(190\) −17.5386 −1.27239
\(191\) −5.78471 −0.418567 −0.209283 0.977855i \(-0.567113\pi\)
−0.209283 + 0.977855i \(0.567113\pi\)
\(192\) −1.23093 −0.0888345
\(193\) 16.6099 1.19561 0.597803 0.801643i \(-0.296040\pi\)
0.597803 + 0.801643i \(0.296040\pi\)
\(194\) −8.63420 −0.619900
\(195\) −2.59757 −0.186016
\(196\) 0 0
\(197\) −16.2889 −1.16054 −0.580268 0.814426i \(-0.697052\pi\)
−0.580268 + 0.814426i \(0.697052\pi\)
\(198\) 1.43826 0.102213
\(199\) 21.9239 1.55414 0.777070 0.629414i \(-0.216705\pi\)
0.777070 + 0.629414i \(0.216705\pi\)
\(200\) −0.350776 −0.0248036
\(201\) −2.41092 −0.170053
\(202\) 4.57515 0.321907
\(203\) 0 0
\(204\) −6.43681 −0.450667
\(205\) 2.17778 0.152103
\(206\) 9.79550 0.682485
\(207\) 6.71919 0.467016
\(208\) −5.89343 −0.408636
\(209\) 3.57177 0.247064
\(210\) 0 0
\(211\) −9.48428 −0.652925 −0.326462 0.945210i \(-0.605857\pi\)
−0.326462 + 0.945210i \(0.605857\pi\)
\(212\) −1.51492 −0.104045
\(213\) 0.255861 0.0175313
\(214\) −29.3336 −2.00520
\(215\) −3.96378 −0.270327
\(216\) 1.36336 0.0927651
\(217\) 0 0
\(218\) −18.6567 −1.26359
\(219\) −5.27880 −0.356708
\(220\) 2.16184 0.145752
\(221\) −6.17708 −0.415515
\(222\) 10.5084 0.705278
\(223\) 5.77091 0.386449 0.193224 0.981155i \(-0.438105\pi\)
0.193224 + 0.981155i \(0.438105\pi\)
\(224\) 0 0
\(225\) −0.257287 −0.0171525
\(226\) −5.03813 −0.335131
\(227\) −0.172461 −0.0114466 −0.00572332 0.999984i \(-0.501822\pi\)
−0.00572332 + 0.999984i \(0.501822\pi\)
\(228\) −5.55849 −0.368120
\(229\) 2.34851 0.155194 0.0775970 0.996985i \(-0.475275\pi\)
0.0775970 + 0.996985i \(0.475275\pi\)
\(230\) 26.3511 1.73754
\(231\) 0 0
\(232\) 5.76503 0.378493
\(233\) −2.17060 −0.142201 −0.0711004 0.997469i \(-0.522651\pi\)
−0.0711004 + 0.997469i \(0.522651\pi\)
\(234\) −2.14794 −0.140415
\(235\) 11.4763 0.748634
\(236\) 14.5860 0.949465
\(237\) 13.1519 0.854306
\(238\) 0 0
\(239\) 16.2909 1.05377 0.526886 0.849936i \(-0.323359\pi\)
0.526886 + 0.849936i \(0.323359\pi\)
\(240\) 10.7604 0.694579
\(241\) 22.5603 1.45324 0.726619 0.687041i \(-0.241091\pi\)
0.726619 + 0.687041i \(0.241091\pi\)
\(242\) 18.6602 1.19952
\(243\) 1.00000 0.0641500
\(244\) −15.6354 −1.00095
\(245\) 0 0
\(246\) 1.80081 0.114815
\(247\) −5.33419 −0.339407
\(248\) 0.229637 0.0145819
\(249\) 10.9425 0.693451
\(250\) −20.6178 −1.30399
\(251\) 15.9372 1.00594 0.502972 0.864303i \(-0.332240\pi\)
0.502972 + 0.864303i \(0.332240\pi\)
\(252\) 0 0
\(253\) −5.36643 −0.337385
\(254\) 26.1413 1.64025
\(255\) 11.2783 0.706272
\(256\) 20.6959 1.29349
\(257\) 4.67166 0.291410 0.145705 0.989328i \(-0.453455\pi\)
0.145705 + 0.989328i \(0.453455\pi\)
\(258\) −3.27766 −0.204058
\(259\) 0 0
\(260\) −3.22857 −0.200227
\(261\) 4.22854 0.261740
\(262\) −1.38782 −0.0857397
\(263\) −27.7645 −1.71203 −0.856017 0.516948i \(-0.827068\pi\)
−0.856017 + 0.516948i \(0.827068\pi\)
\(264\) −1.08888 −0.0670160
\(265\) 2.65436 0.163056
\(266\) 0 0
\(267\) −9.74201 −0.596201
\(268\) −2.99658 −0.183045
\(269\) 0.216531 0.0132021 0.00660106 0.999978i \(-0.497899\pi\)
0.00660106 + 0.999978i \(0.497899\pi\)
\(270\) 3.92176 0.238671
\(271\) 15.4909 0.941007 0.470504 0.882398i \(-0.344072\pi\)
0.470504 + 0.882398i \(0.344072\pi\)
\(272\) 25.5884 1.55152
\(273\) 0 0
\(274\) −8.56682 −0.517540
\(275\) 0.205488 0.0123914
\(276\) 8.35140 0.502695
\(277\) 2.35151 0.141289 0.0706443 0.997502i \(-0.477494\pi\)
0.0706443 + 0.997502i \(0.477494\pi\)
\(278\) −1.13112 −0.0678403
\(279\) 0.168434 0.0100839
\(280\) 0 0
\(281\) 23.8868 1.42497 0.712483 0.701690i \(-0.247571\pi\)
0.712483 + 0.701690i \(0.247571\pi\)
\(282\) 9.48982 0.565111
\(283\) −7.09006 −0.421461 −0.210730 0.977544i \(-0.567584\pi\)
−0.210730 + 0.977544i \(0.567584\pi\)
\(284\) 0.318014 0.0188707
\(285\) 9.73931 0.576907
\(286\) 1.71550 0.101440
\(287\) 0 0
\(288\) 6.17106 0.363633
\(289\) 9.81994 0.577644
\(290\) 16.5833 0.973806
\(291\) 4.79462 0.281066
\(292\) −6.56111 −0.383960
\(293\) −29.3669 −1.71563 −0.857815 0.513958i \(-0.828179\pi\)
−0.857815 + 0.513958i \(0.828179\pi\)
\(294\) 0 0
\(295\) −25.5568 −1.48797
\(296\) −7.95573 −0.462418
\(297\) −0.798673 −0.0463437
\(298\) 1.73049 0.100245
\(299\) 8.01440 0.463485
\(300\) −0.319786 −0.0184629
\(301\) 0 0
\(302\) 10.2029 0.587111
\(303\) −2.54061 −0.145954
\(304\) 22.0968 1.26734
\(305\) 27.3955 1.56866
\(306\) 9.32603 0.533134
\(307\) −30.7496 −1.75497 −0.877485 0.479604i \(-0.840780\pi\)
−0.877485 + 0.479604i \(0.840780\pi\)
\(308\) 0 0
\(309\) −5.43950 −0.309442
\(310\) 0.660558 0.0375172
\(311\) 17.9250 1.01644 0.508218 0.861228i \(-0.330304\pi\)
0.508218 + 0.861228i \(0.330304\pi\)
\(312\) 1.62617 0.0920637
\(313\) 15.7109 0.888035 0.444018 0.896018i \(-0.353553\pi\)
0.444018 + 0.896018i \(0.353553\pi\)
\(314\) 25.5340 1.44097
\(315\) 0 0
\(316\) 16.3467 0.919573
\(317\) −3.37598 −0.189614 −0.0948070 0.995496i \(-0.530223\pi\)
−0.0948070 + 0.995496i \(0.530223\pi\)
\(318\) 2.19490 0.123084
\(319\) −3.37722 −0.189088
\(320\) 2.68069 0.149855
\(321\) 16.2891 0.909169
\(322\) 0 0
\(323\) 23.1603 1.28867
\(324\) 1.24292 0.0690509
\(325\) −0.306882 −0.0170228
\(326\) −18.9757 −1.05097
\(327\) 10.3602 0.572920
\(328\) −1.36336 −0.0752791
\(329\) 0 0
\(330\) −3.13221 −0.172422
\(331\) 22.9215 1.25988 0.629940 0.776644i \(-0.283079\pi\)
0.629940 + 0.776644i \(0.283079\pi\)
\(332\) 13.6006 0.746429
\(333\) −5.83538 −0.319777
\(334\) −25.1815 −1.37787
\(335\) 5.25045 0.286863
\(336\) 0 0
\(337\) 18.3916 1.00185 0.500927 0.865489i \(-0.332992\pi\)
0.500927 + 0.865489i \(0.332992\pi\)
\(338\) 20.8485 1.13401
\(339\) 2.79770 0.151950
\(340\) 14.0179 0.760230
\(341\) −0.134524 −0.00728487
\(342\) 8.05346 0.435481
\(343\) 0 0
\(344\) 2.48146 0.133791
\(345\) −14.6329 −0.787809
\(346\) −9.31635 −0.500850
\(347\) 8.01891 0.430477 0.215239 0.976561i \(-0.430947\pi\)
0.215239 + 0.976561i \(0.430947\pi\)
\(348\) 5.25572 0.281736
\(349\) −14.8361 −0.794159 −0.397079 0.917784i \(-0.629976\pi\)
−0.397079 + 0.917784i \(0.629976\pi\)
\(350\) 0 0
\(351\) 1.19276 0.0636650
\(352\) −4.92866 −0.262698
\(353\) 31.7462 1.68968 0.844840 0.535020i \(-0.179696\pi\)
0.844840 + 0.535020i \(0.179696\pi\)
\(354\) −21.1330 −1.12320
\(355\) −0.557209 −0.0295736
\(356\) −12.1085 −0.641750
\(357\) 0 0
\(358\) 1.59324 0.0842054
\(359\) 20.9734 1.10693 0.553466 0.832872i \(-0.313305\pi\)
0.553466 + 0.832872i \(0.313305\pi\)
\(360\) −2.96910 −0.156485
\(361\) 0.999965 0.0526297
\(362\) 19.1858 1.00838
\(363\) −10.3621 −0.543870
\(364\) 0 0
\(365\) 11.4961 0.601731
\(366\) 22.6534 1.18411
\(367\) 9.23972 0.482309 0.241155 0.970487i \(-0.422474\pi\)
0.241155 + 0.970487i \(0.422474\pi\)
\(368\) −33.1995 −1.73064
\(369\) −1.00000 −0.0520579
\(370\) −22.8850 −1.18973
\(371\) 0 0
\(372\) 0.209350 0.0108543
\(373\) 35.1745 1.82127 0.910634 0.413214i \(-0.135594\pi\)
0.910634 + 0.413214i \(0.135594\pi\)
\(374\) −7.44845 −0.385150
\(375\) 11.4492 0.591234
\(376\) −7.18458 −0.370517
\(377\) 5.04364 0.259761
\(378\) 0 0
\(379\) 28.1280 1.44484 0.722419 0.691456i \(-0.243030\pi\)
0.722419 + 0.691456i \(0.243030\pi\)
\(380\) 12.1051 0.620981
\(381\) −14.5164 −0.743699
\(382\) 10.4172 0.532988
\(383\) 1.11304 0.0568738 0.0284369 0.999596i \(-0.490947\pi\)
0.0284369 + 0.999596i \(0.490947\pi\)
\(384\) −10.1255 −0.516713
\(385\) 0 0
\(386\) −29.9113 −1.52244
\(387\) 1.82010 0.0925210
\(388\) 5.95932 0.302538
\(389\) −24.4665 −1.24050 −0.620251 0.784404i \(-0.712969\pi\)
−0.620251 + 0.784404i \(0.712969\pi\)
\(390\) 4.67773 0.236866
\(391\) −34.7973 −1.75978
\(392\) 0 0
\(393\) 0.770663 0.0388748
\(394\) 29.3332 1.47779
\(395\) −28.6419 −1.44113
\(396\) −0.992684 −0.0498842
\(397\) 4.87136 0.244487 0.122243 0.992500i \(-0.460991\pi\)
0.122243 + 0.992500i \(0.460991\pi\)
\(398\) −39.4807 −1.97899
\(399\) 0 0
\(400\) 1.27125 0.0635626
\(401\) −8.56547 −0.427739 −0.213869 0.976862i \(-0.568607\pi\)
−0.213869 + 0.976862i \(0.568607\pi\)
\(402\) 4.34161 0.216540
\(403\) 0.200902 0.0100076
\(404\) −3.15777 −0.157105
\(405\) −2.17778 −0.108215
\(406\) 0 0
\(407\) 4.66056 0.231015
\(408\) −7.06058 −0.349551
\(409\) −30.9507 −1.53041 −0.765207 0.643784i \(-0.777363\pi\)
−0.765207 + 0.643784i \(0.777363\pi\)
\(410\) −3.92176 −0.193682
\(411\) 4.75720 0.234655
\(412\) −6.76085 −0.333083
\(413\) 0 0
\(414\) −12.1000 −0.594682
\(415\) −23.8303 −1.16978
\(416\) 7.36061 0.360884
\(417\) 0.628119 0.0307591
\(418\) −6.43208 −0.314603
\(419\) −21.7112 −1.06066 −0.530331 0.847791i \(-0.677932\pi\)
−0.530331 + 0.847791i \(0.677932\pi\)
\(420\) 0 0
\(421\) 27.4470 1.33768 0.668841 0.743405i \(-0.266791\pi\)
0.668841 + 0.743405i \(0.266791\pi\)
\(422\) 17.0794 0.831412
\(423\) −5.26975 −0.256224
\(424\) −1.66172 −0.0807003
\(425\) 1.33244 0.0646327
\(426\) −0.460758 −0.0223238
\(427\) 0 0
\(428\) 20.2460 0.978628
\(429\) −0.952627 −0.0459933
\(430\) 7.13801 0.344226
\(431\) 17.8045 0.857611 0.428806 0.903397i \(-0.358934\pi\)
0.428806 + 0.903397i \(0.358934\pi\)
\(432\) −4.94099 −0.237724
\(433\) −13.7451 −0.660549 −0.330274 0.943885i \(-0.607141\pi\)
−0.330274 + 0.943885i \(0.607141\pi\)
\(434\) 0 0
\(435\) −9.20881 −0.441529
\(436\) 12.8769 0.616690
\(437\) −30.0491 −1.43744
\(438\) 9.50612 0.454220
\(439\) −4.70167 −0.224398 −0.112199 0.993686i \(-0.535789\pi\)
−0.112199 + 0.993686i \(0.535789\pi\)
\(440\) 2.37134 0.113049
\(441\) 0 0
\(442\) 11.1237 0.529103
\(443\) 31.8616 1.51379 0.756894 0.653537i \(-0.226716\pi\)
0.756894 + 0.653537i \(0.226716\pi\)
\(444\) −7.25289 −0.344207
\(445\) 21.2159 1.00573
\(446\) −10.3923 −0.492091
\(447\) −0.960953 −0.0454515
\(448\) 0 0
\(449\) 30.7586 1.45159 0.725795 0.687911i \(-0.241472\pi\)
0.725795 + 0.687911i \(0.241472\pi\)
\(450\) 0.463325 0.0218414
\(451\) 0.798673 0.0376080
\(452\) 3.47731 0.163559
\(453\) −5.66573 −0.266199
\(454\) 0.310569 0.0145757
\(455\) 0 0
\(456\) −6.09714 −0.285525
\(457\) 4.85756 0.227227 0.113614 0.993525i \(-0.463757\pi\)
0.113614 + 0.993525i \(0.463757\pi\)
\(458\) −4.22922 −0.197619
\(459\) −5.17880 −0.241726
\(460\) −18.1875 −0.847995
\(461\) 34.9988 1.63006 0.815028 0.579422i \(-0.196722\pi\)
0.815028 + 0.579422i \(0.196722\pi\)
\(462\) 0 0
\(463\) −0.712122 −0.0330951 −0.0165476 0.999863i \(-0.505267\pi\)
−0.0165476 + 0.999863i \(0.505267\pi\)
\(464\) −20.8932 −0.969941
\(465\) −0.366812 −0.0170105
\(466\) 3.90884 0.181073
\(467\) 20.5280 0.949922 0.474961 0.880007i \(-0.342462\pi\)
0.474961 + 0.880007i \(0.342462\pi\)
\(468\) 1.48251 0.0685288
\(469\) 0 0
\(470\) −20.6667 −0.953284
\(471\) −14.1792 −0.653343
\(472\) 15.9994 0.736433
\(473\) −1.45367 −0.0668397
\(474\) −23.6840 −1.08784
\(475\) 1.15062 0.0527941
\(476\) 0 0
\(477\) −1.21884 −0.0558069
\(478\) −29.3369 −1.34184
\(479\) 41.3853 1.89094 0.945471 0.325705i \(-0.105602\pi\)
0.945471 + 0.325705i \(0.105602\pi\)
\(480\) −13.4392 −0.613413
\(481\) −6.96022 −0.317359
\(482\) −40.6268 −1.85050
\(483\) 0 0
\(484\) −12.8793 −0.585421
\(485\) −10.4416 −0.474129
\(486\) −1.80081 −0.0816864
\(487\) 9.90202 0.448703 0.224352 0.974508i \(-0.427974\pi\)
0.224352 + 0.974508i \(0.427974\pi\)
\(488\) −17.1505 −0.776368
\(489\) 10.5373 0.476513
\(490\) 0 0
\(491\) −29.9292 −1.35069 −0.675343 0.737504i \(-0.736004\pi\)
−0.675343 + 0.737504i \(0.736004\pi\)
\(492\) −1.24292 −0.0560350
\(493\) −21.8987 −0.986269
\(494\) 9.60587 0.432189
\(495\) 1.73933 0.0781771
\(496\) −0.832231 −0.0373683
\(497\) 0 0
\(498\) −19.7053 −0.883017
\(499\) −26.4456 −1.18387 −0.591934 0.805986i \(-0.701635\pi\)
−0.591934 + 0.805986i \(0.701635\pi\)
\(500\) 14.2304 0.636403
\(501\) 13.9834 0.624733
\(502\) −28.6998 −1.28093
\(503\) 0.150863 0.00672665 0.00336333 0.999994i \(-0.498929\pi\)
0.00336333 + 0.999994i \(0.498929\pi\)
\(504\) 0 0
\(505\) 5.53288 0.246210
\(506\) 9.66393 0.429614
\(507\) −11.5773 −0.514167
\(508\) −18.0427 −0.800516
\(509\) 36.0422 1.59754 0.798771 0.601635i \(-0.205484\pi\)
0.798771 + 0.601635i \(0.205484\pi\)
\(510\) −20.3100 −0.899343
\(511\) 0 0
\(512\) −17.0184 −0.752116
\(513\) −4.47213 −0.197449
\(514\) −8.41276 −0.371071
\(515\) 11.8460 0.521998
\(516\) 2.26224 0.0995894
\(517\) 4.20881 0.185103
\(518\) 0 0
\(519\) 5.17342 0.227088
\(520\) −3.54143 −0.155302
\(521\) 20.8532 0.913594 0.456797 0.889571i \(-0.348996\pi\)
0.456797 + 0.889571i \(0.348996\pi\)
\(522\) −7.61479 −0.333290
\(523\) 14.0673 0.615122 0.307561 0.951528i \(-0.400487\pi\)
0.307561 + 0.951528i \(0.400487\pi\)
\(524\) 0.957870 0.0418448
\(525\) 0 0
\(526\) 49.9986 2.18004
\(527\) −0.872286 −0.0379974
\(528\) 3.94624 0.171738
\(529\) 22.1475 0.962935
\(530\) −4.78000 −0.207630
\(531\) 11.7353 0.509267
\(532\) 0 0
\(533\) −1.19276 −0.0516643
\(534\) 17.5435 0.759182
\(535\) −35.4741 −1.53368
\(536\) −3.28696 −0.141975
\(537\) −0.884735 −0.0381791
\(538\) −0.389931 −0.0168111
\(539\) 0 0
\(540\) −2.70680 −0.116482
\(541\) 16.8592 0.724835 0.362417 0.932016i \(-0.381952\pi\)
0.362417 + 0.932016i \(0.381952\pi\)
\(542\) −27.8962 −1.19825
\(543\) −10.6540 −0.457207
\(544\) −31.9587 −1.37022
\(545\) −22.5622 −0.966458
\(546\) 0 0
\(547\) −0.789938 −0.0337753 −0.0168877 0.999857i \(-0.505376\pi\)
−0.0168877 + 0.999857i \(0.505376\pi\)
\(548\) 5.91281 0.252583
\(549\) −12.5796 −0.536884
\(550\) −0.370045 −0.0157788
\(551\) −18.9106 −0.805618
\(552\) 9.16069 0.389905
\(553\) 0 0
\(554\) −4.23463 −0.179912
\(555\) 12.7081 0.539431
\(556\) 0.780700 0.0331091
\(557\) 22.2700 0.943610 0.471805 0.881703i \(-0.343603\pi\)
0.471805 + 0.881703i \(0.343603\pi\)
\(558\) −0.303318 −0.0128405
\(559\) 2.17095 0.0918215
\(560\) 0 0
\(561\) 4.13616 0.174629
\(562\) −43.0155 −1.81450
\(563\) 0.488170 0.0205739 0.0102870 0.999947i \(-0.496726\pi\)
0.0102870 + 0.999947i \(0.496726\pi\)
\(564\) −6.54986 −0.275799
\(565\) −6.09277 −0.256325
\(566\) 12.7679 0.536673
\(567\) 0 0
\(568\) 0.348832 0.0146367
\(569\) 20.2741 0.849936 0.424968 0.905208i \(-0.360285\pi\)
0.424968 + 0.905208i \(0.360285\pi\)
\(570\) −17.5386 −0.734613
\(571\) 29.6973 1.24279 0.621397 0.783496i \(-0.286566\pi\)
0.621397 + 0.783496i \(0.286566\pi\)
\(572\) −1.18404 −0.0495071
\(573\) −5.78471 −0.241660
\(574\) 0 0
\(575\) −1.72876 −0.0720943
\(576\) −1.23093 −0.0512886
\(577\) −38.6879 −1.61060 −0.805300 0.592868i \(-0.797996\pi\)
−0.805300 + 0.592868i \(0.797996\pi\)
\(578\) −17.6838 −0.735551
\(579\) 16.6099 0.690284
\(580\) −11.4458 −0.475260
\(581\) 0 0
\(582\) −8.63420 −0.357899
\(583\) 0.973455 0.0403164
\(584\) −7.19692 −0.297811
\(585\) −2.59757 −0.107396
\(586\) 52.8841 2.18462
\(587\) 9.27772 0.382932 0.191466 0.981499i \(-0.438676\pi\)
0.191466 + 0.981499i \(0.438676\pi\)
\(588\) 0 0
\(589\) −0.753259 −0.0310375
\(590\) 46.0229 1.89473
\(591\) −16.2889 −0.670036
\(592\) 28.8325 1.18501
\(593\) −42.3599 −1.73951 −0.869756 0.493482i \(-0.835724\pi\)
−0.869756 + 0.493482i \(0.835724\pi\)
\(594\) 1.43826 0.0590124
\(595\) 0 0
\(596\) −1.19438 −0.0489239
\(597\) 21.9239 0.897284
\(598\) −14.4324 −0.590185
\(599\) 12.3390 0.504159 0.252080 0.967706i \(-0.418886\pi\)
0.252080 + 0.967706i \(0.418886\pi\)
\(600\) −0.350776 −0.0143204
\(601\) −16.6041 −0.677297 −0.338648 0.940913i \(-0.609970\pi\)
−0.338648 + 0.940913i \(0.609970\pi\)
\(602\) 0 0
\(603\) −2.41092 −0.0981803
\(604\) −7.04203 −0.286536
\(605\) 22.5664 0.917454
\(606\) 4.57515 0.185853
\(607\) 3.93533 0.159730 0.0798652 0.996806i \(-0.474551\pi\)
0.0798652 + 0.996806i \(0.474551\pi\)
\(608\) −27.5978 −1.11924
\(609\) 0 0
\(610\) −49.3342 −1.99748
\(611\) −6.28556 −0.254287
\(612\) −6.43681 −0.260193
\(613\) 31.1638 1.25870 0.629348 0.777124i \(-0.283322\pi\)
0.629348 + 0.777124i \(0.283322\pi\)
\(614\) 55.3741 2.23472
\(615\) 2.17778 0.0878164
\(616\) 0 0
\(617\) 21.9486 0.883615 0.441808 0.897110i \(-0.354337\pi\)
0.441808 + 0.897110i \(0.354337\pi\)
\(618\) 9.79550 0.394033
\(619\) −17.1921 −0.691010 −0.345505 0.938417i \(-0.612292\pi\)
−0.345505 + 0.938417i \(0.612292\pi\)
\(620\) −0.455917 −0.0183101
\(621\) 6.71919 0.269632
\(622\) −32.2796 −1.29429
\(623\) 0 0
\(624\) −5.89343 −0.235926
\(625\) −23.6474 −0.945895
\(626\) −28.2924 −1.13079
\(627\) 3.57177 0.142643
\(628\) −17.6236 −0.703257
\(629\) 30.2202 1.20496
\(630\) 0 0
\(631\) −12.5560 −0.499847 −0.249923 0.968266i \(-0.580405\pi\)
−0.249923 + 0.968266i \(0.580405\pi\)
\(632\) 17.9308 0.713248
\(633\) −9.48428 −0.376966
\(634\) 6.07950 0.241448
\(635\) 31.6135 1.25454
\(636\) −1.51492 −0.0600704
\(637\) 0 0
\(638\) 6.08173 0.240778
\(639\) 0.255861 0.0101217
\(640\) 22.0510 0.871642
\(641\) −28.6102 −1.13003 −0.565017 0.825079i \(-0.691130\pi\)
−0.565017 + 0.825079i \(0.691130\pi\)
\(642\) −29.3336 −1.15770
\(643\) −0.325302 −0.0128287 −0.00641434 0.999979i \(-0.502042\pi\)
−0.00641434 + 0.999979i \(0.502042\pi\)
\(644\) 0 0
\(645\) −3.96378 −0.156074
\(646\) −41.7072 −1.64095
\(647\) −2.72658 −0.107193 −0.0535965 0.998563i \(-0.517068\pi\)
−0.0535965 + 0.998563i \(0.517068\pi\)
\(648\) 1.36336 0.0535579
\(649\) −9.37263 −0.367908
\(650\) 0.552637 0.0216762
\(651\) 0 0
\(652\) 13.0970 0.512918
\(653\) −3.40058 −0.133075 −0.0665375 0.997784i \(-0.521195\pi\)
−0.0665375 + 0.997784i \(0.521195\pi\)
\(654\) −18.6567 −0.729536
\(655\) −1.67833 −0.0655779
\(656\) 4.94099 0.192913
\(657\) −5.27880 −0.205946
\(658\) 0 0
\(659\) 6.29196 0.245100 0.122550 0.992462i \(-0.460893\pi\)
0.122550 + 0.992462i \(0.460893\pi\)
\(660\) 2.16184 0.0841497
\(661\) −16.2199 −0.630880 −0.315440 0.948945i \(-0.602152\pi\)
−0.315440 + 0.948945i \(0.602152\pi\)
\(662\) −41.2773 −1.60429
\(663\) −6.17708 −0.239898
\(664\) 14.9186 0.578953
\(665\) 0 0
\(666\) 10.5084 0.407192
\(667\) 28.4123 1.10013
\(668\) 17.3802 0.672461
\(669\) 5.77091 0.223116
\(670\) −9.45507 −0.365281
\(671\) 10.0470 0.387859
\(672\) 0 0
\(673\) 16.2265 0.625486 0.312743 0.949838i \(-0.398752\pi\)
0.312743 + 0.949838i \(0.398752\pi\)
\(674\) −33.1198 −1.27573
\(675\) −0.257287 −0.00990298
\(676\) −14.3896 −0.553448
\(677\) −34.2117 −1.31486 −0.657432 0.753514i \(-0.728357\pi\)
−0.657432 + 0.753514i \(0.728357\pi\)
\(678\) −5.03813 −0.193488
\(679\) 0 0
\(680\) 15.3764 0.589657
\(681\) −0.172461 −0.00660872
\(682\) 0.242252 0.00927629
\(683\) 3.88638 0.148708 0.0743540 0.997232i \(-0.476311\pi\)
0.0743540 + 0.997232i \(0.476311\pi\)
\(684\) −5.55849 −0.212534
\(685\) −10.3601 −0.395840
\(686\) 0 0
\(687\) 2.34851 0.0896013
\(688\) −8.99311 −0.342859
\(689\) −1.45379 −0.0553849
\(690\) 26.3511 1.00317
\(691\) 47.1900 1.79519 0.897595 0.440821i \(-0.145313\pi\)
0.897595 + 0.440821i \(0.145313\pi\)
\(692\) 6.43013 0.244437
\(693\) 0 0
\(694\) −14.4405 −0.548155
\(695\) −1.36790 −0.0518876
\(696\) 5.76503 0.218523
\(697\) 5.17880 0.196161
\(698\) 26.7170 1.01125
\(699\) −2.17060 −0.0820997
\(700\) 0 0
\(701\) 17.0103 0.642469 0.321234 0.947000i \(-0.395902\pi\)
0.321234 + 0.947000i \(0.395902\pi\)
\(702\) −2.14794 −0.0810688
\(703\) 26.0966 0.984251
\(704\) 0.983108 0.0370523
\(705\) 11.4763 0.432224
\(706\) −57.1689 −2.15158
\(707\) 0 0
\(708\) 14.5860 0.548174
\(709\) 24.8723 0.934100 0.467050 0.884231i \(-0.345317\pi\)
0.467050 + 0.884231i \(0.345317\pi\)
\(710\) 1.00343 0.0376580
\(711\) 13.1519 0.493234
\(712\) −13.2819 −0.497760
\(713\) 1.13174 0.0423840
\(714\) 0 0
\(715\) 2.07461 0.0775860
\(716\) −1.09965 −0.0410959
\(717\) 16.2909 0.608396
\(718\) −37.7690 −1.40953
\(719\) 24.7701 0.923768 0.461884 0.886940i \(-0.347174\pi\)
0.461884 + 0.886940i \(0.347174\pi\)
\(720\) 10.7604 0.401016
\(721\) 0 0
\(722\) −1.80075 −0.0670169
\(723\) 22.5603 0.839027
\(724\) −13.2420 −0.492136
\(725\) −1.08795 −0.0404054
\(726\) 18.6602 0.692545
\(727\) 29.1958 1.08281 0.541406 0.840761i \(-0.317892\pi\)
0.541406 + 0.840761i \(0.317892\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −20.7022 −0.766223
\(731\) −9.42595 −0.348631
\(732\) −15.6354 −0.577900
\(733\) 17.8678 0.659961 0.329981 0.943988i \(-0.392958\pi\)
0.329981 + 0.943988i \(0.392958\pi\)
\(734\) −16.6390 −0.614156
\(735\) 0 0
\(736\) 41.4645 1.52840
\(737\) 1.92554 0.0709281
\(738\) 1.80081 0.0662887
\(739\) 14.4976 0.533303 0.266651 0.963793i \(-0.414083\pi\)
0.266651 + 0.963793i \(0.414083\pi\)
\(740\) 15.7952 0.580642
\(741\) −5.33419 −0.195956
\(742\) 0 0
\(743\) 28.9665 1.06268 0.531339 0.847160i \(-0.321689\pi\)
0.531339 + 0.847160i \(0.321689\pi\)
\(744\) 0.229637 0.00841889
\(745\) 2.09274 0.0766721
\(746\) −63.3426 −2.31914
\(747\) 10.9425 0.400364
\(748\) 5.14091 0.187970
\(749\) 0 0
\(750\) −20.6178 −0.752857
\(751\) −22.0943 −0.806234 −0.403117 0.915148i \(-0.632073\pi\)
−0.403117 + 0.915148i \(0.632073\pi\)
\(752\) 26.0378 0.949501
\(753\) 15.9372 0.580782
\(754\) −9.08264 −0.330770
\(755\) 12.3387 0.449051
\(756\) 0 0
\(757\) 41.0884 1.49338 0.746692 0.665170i \(-0.231641\pi\)
0.746692 + 0.665170i \(0.231641\pi\)
\(758\) −50.6532 −1.83981
\(759\) −5.36643 −0.194789
\(760\) 13.2782 0.481651
\(761\) −23.2864 −0.844132 −0.422066 0.906565i \(-0.638695\pi\)
−0.422066 + 0.906565i \(0.638695\pi\)
\(762\) 26.1413 0.947000
\(763\) 0 0
\(764\) −7.18991 −0.260122
\(765\) 11.2783 0.407767
\(766\) −2.00438 −0.0724212
\(767\) 13.9974 0.505416
\(768\) 20.6959 0.746798
\(769\) −15.2750 −0.550832 −0.275416 0.961325i \(-0.588816\pi\)
−0.275416 + 0.961325i \(0.588816\pi\)
\(770\) 0 0
\(771\) 4.67166 0.168246
\(772\) 20.6447 0.743020
\(773\) 9.69680 0.348770 0.174385 0.984678i \(-0.444206\pi\)
0.174385 + 0.984678i \(0.444206\pi\)
\(774\) −3.27766 −0.117813
\(775\) −0.0433359 −0.00155667
\(776\) 6.53681 0.234658
\(777\) 0 0
\(778\) 44.0595 1.57961
\(779\) 4.47213 0.160231
\(780\) −3.22857 −0.115601
\(781\) −0.204349 −0.00731220
\(782\) 62.6634 2.24084
\(783\) 4.22854 0.151116
\(784\) 0 0
\(785\) 30.8791 1.10212
\(786\) −1.38782 −0.0495018
\(787\) −18.3462 −0.653972 −0.326986 0.945029i \(-0.606033\pi\)
−0.326986 + 0.945029i \(0.606033\pi\)
\(788\) −20.2458 −0.721225
\(789\) −27.7645 −0.988443
\(790\) 51.5786 1.83508
\(791\) 0 0
\(792\) −1.08888 −0.0386917
\(793\) −15.0045 −0.532824
\(794\) −8.77240 −0.311321
\(795\) 2.65436 0.0941406
\(796\) 27.2495 0.965834
\(797\) −29.5627 −1.04717 −0.523583 0.851975i \(-0.675405\pi\)
−0.523583 + 0.851975i \(0.675405\pi\)
\(798\) 0 0
\(799\) 27.2910 0.965485
\(800\) −1.58773 −0.0561349
\(801\) −9.74201 −0.344217
\(802\) 15.4248 0.544668
\(803\) 4.21603 0.148781
\(804\) −2.99658 −0.105681
\(805\) 0 0
\(806\) −0.361786 −0.0127434
\(807\) 0.216531 0.00762224
\(808\) −3.46377 −0.121855
\(809\) −18.4302 −0.647970 −0.323985 0.946062i \(-0.605023\pi\)
−0.323985 + 0.946062i \(0.605023\pi\)
\(810\) 3.92176 0.137797
\(811\) 19.9706 0.701264 0.350632 0.936513i \(-0.385967\pi\)
0.350632 + 0.936513i \(0.385967\pi\)
\(812\) 0 0
\(813\) 15.4909 0.543291
\(814\) −8.39277 −0.294167
\(815\) −22.9479 −0.803830
\(816\) 25.5884 0.895773
\(817\) −8.13974 −0.284774
\(818\) 55.7364 1.94878
\(819\) 0 0
\(820\) 2.70680 0.0945254
\(821\) 37.2773 1.30099 0.650493 0.759512i \(-0.274562\pi\)
0.650493 + 0.759512i \(0.274562\pi\)
\(822\) −8.56682 −0.298802
\(823\) 42.9513 1.49719 0.748593 0.663029i \(-0.230730\pi\)
0.748593 + 0.663029i \(0.230730\pi\)
\(824\) −7.41601 −0.258349
\(825\) 0.205488 0.00715418
\(826\) 0 0
\(827\) 41.0895 1.42882 0.714411 0.699726i \(-0.246695\pi\)
0.714411 + 0.699726i \(0.246695\pi\)
\(828\) 8.35140 0.290231
\(829\) 9.71580 0.337444 0.168722 0.985664i \(-0.446036\pi\)
0.168722 + 0.985664i \(0.446036\pi\)
\(830\) 42.9138 1.48956
\(831\) 2.35151 0.0815730
\(832\) −1.46820 −0.0509008
\(833\) 0 0
\(834\) −1.13112 −0.0391676
\(835\) −30.4527 −1.05386
\(836\) 4.43941 0.153540
\(837\) 0.168434 0.00582193
\(838\) 39.0978 1.35061
\(839\) 18.1433 0.626378 0.313189 0.949691i \(-0.398603\pi\)
0.313189 + 0.949691i \(0.398603\pi\)
\(840\) 0 0
\(841\) −11.1195 −0.383430
\(842\) −49.4268 −1.70336
\(843\) 23.8868 0.822704
\(844\) −11.7882 −0.405766
\(845\) 25.2128 0.867347
\(846\) 9.48982 0.326267
\(847\) 0 0
\(848\) 6.02228 0.206806
\(849\) −7.09006 −0.243330
\(850\) −2.39947 −0.0823010
\(851\) −39.2090 −1.34407
\(852\) 0.318014 0.0108950
\(853\) −3.18526 −0.109061 −0.0545306 0.998512i \(-0.517366\pi\)
−0.0545306 + 0.998512i \(0.517366\pi\)
\(854\) 0 0
\(855\) 9.73931 0.333077
\(856\) 22.2080 0.759053
\(857\) 23.0555 0.787562 0.393781 0.919204i \(-0.371167\pi\)
0.393781 + 0.919204i \(0.371167\pi\)
\(858\) 1.71550 0.0585662
\(859\) 7.33171 0.250155 0.125077 0.992147i \(-0.460082\pi\)
0.125077 + 0.992147i \(0.460082\pi\)
\(860\) −4.92665 −0.167997
\(861\) 0 0
\(862\) −32.0625 −1.09205
\(863\) 27.6924 0.942660 0.471330 0.881957i \(-0.343774\pi\)
0.471330 + 0.881957i \(0.343774\pi\)
\(864\) 6.17106 0.209944
\(865\) −11.2666 −0.383074
\(866\) 24.7524 0.841120
\(867\) 9.81994 0.333503
\(868\) 0 0
\(869\) −10.5040 −0.356325
\(870\) 16.5833 0.562227
\(871\) −2.87566 −0.0974380
\(872\) 14.1247 0.478323
\(873\) 4.79462 0.162273
\(874\) 54.1127 1.83039
\(875\) 0 0
\(876\) −6.56111 −0.221679
\(877\) 3.66484 0.123753 0.0618764 0.998084i \(-0.480292\pi\)
0.0618764 + 0.998084i \(0.480292\pi\)
\(878\) 8.46681 0.285741
\(879\) −29.3669 −0.990520
\(880\) −8.59402 −0.289704
\(881\) −15.2030 −0.512203 −0.256101 0.966650i \(-0.582438\pi\)
−0.256101 + 0.966650i \(0.582438\pi\)
\(882\) 0 0
\(883\) −0.478768 −0.0161118 −0.00805591 0.999968i \(-0.502564\pi\)
−0.00805591 + 0.999968i \(0.502564\pi\)
\(884\) −7.67759 −0.258225
\(885\) −25.5568 −0.859082
\(886\) −57.3766 −1.92761
\(887\) 2.63212 0.0883781 0.0441890 0.999023i \(-0.485930\pi\)
0.0441890 + 0.999023i \(0.485930\pi\)
\(888\) −7.95573 −0.266977
\(889\) 0 0
\(890\) −38.2058 −1.28066
\(891\) −0.798673 −0.0267565
\(892\) 7.17277 0.240162
\(893\) 23.5670 0.788640
\(894\) 1.73049 0.0578764
\(895\) 1.92676 0.0644044
\(896\) 0 0
\(897\) 8.01440 0.267593
\(898\) −55.3905 −1.84840
\(899\) 0.712230 0.0237542
\(900\) −0.319786 −0.0106595
\(901\) 6.31213 0.210287
\(902\) −1.43826 −0.0478888
\(903\) 0 0
\(904\) 3.81428 0.126861
\(905\) 23.2020 0.771261
\(906\) 10.2029 0.338969
\(907\) 11.6650 0.387329 0.193664 0.981068i \(-0.437963\pi\)
0.193664 + 0.981068i \(0.437963\pi\)
\(908\) −0.214355 −0.00711361
\(909\) −2.54061 −0.0842667
\(910\) 0 0
\(911\) 20.4241 0.676680 0.338340 0.941024i \(-0.390135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(912\) 22.0968 0.731697
\(913\) −8.73946 −0.289234
\(914\) −8.74755 −0.289343
\(915\) 27.3955 0.905668
\(916\) 2.91900 0.0964466
\(917\) 0 0
\(918\) 9.32603 0.307805
\(919\) −46.0665 −1.51959 −0.759797 0.650161i \(-0.774702\pi\)
−0.759797 + 0.650161i \(0.774702\pi\)
\(920\) −19.9499 −0.657730
\(921\) −30.7496 −1.01323
\(922\) −63.0261 −2.07566
\(923\) 0.305182 0.0100452
\(924\) 0 0
\(925\) 1.50137 0.0493646
\(926\) 1.28240 0.0421422
\(927\) −5.43950 −0.178657
\(928\) 26.0946 0.856596
\(929\) −9.23449 −0.302974 −0.151487 0.988459i \(-0.548406\pi\)
−0.151487 + 0.988459i \(0.548406\pi\)
\(930\) 0.660558 0.0216606
\(931\) 0 0
\(932\) −2.69788 −0.0883719
\(933\) 17.9250 0.586840
\(934\) −36.9670 −1.20960
\(935\) −9.00764 −0.294581
\(936\) 1.62617 0.0531530
\(937\) 5.01754 0.163916 0.0819580 0.996636i \(-0.473883\pi\)
0.0819580 + 0.996636i \(0.473883\pi\)
\(938\) 0 0
\(939\) 15.7109 0.512707
\(940\) 14.2641 0.465245
\(941\) −34.8594 −1.13638 −0.568191 0.822897i \(-0.692357\pi\)
−0.568191 + 0.822897i \(0.692357\pi\)
\(942\) 25.5340 0.831944
\(943\) −6.71919 −0.218807
\(944\) −57.9838 −1.88721
\(945\) 0 0
\(946\) 2.61778 0.0851113
\(947\) 0.0282576 0.000918248 0 0.000459124 1.00000i \(-0.499854\pi\)
0.000459124 1.00000i \(0.499854\pi\)
\(948\) 16.3467 0.530916
\(949\) −6.29636 −0.204388
\(950\) −2.07205 −0.0672262
\(951\) −3.37598 −0.109474
\(952\) 0 0
\(953\) 46.0320 1.49112 0.745562 0.666436i \(-0.232181\pi\)
0.745562 + 0.666436i \(0.232181\pi\)
\(954\) 2.19490 0.0710625
\(955\) 12.5978 0.407655
\(956\) 20.2483 0.654876
\(957\) −3.37722 −0.109170
\(958\) −74.5271 −2.40786
\(959\) 0 0
\(960\) 2.68069 0.0865187
\(961\) −30.9716 −0.999085
\(962\) 12.5340 0.404113
\(963\) 16.2891 0.524909
\(964\) 28.0406 0.903127
\(965\) −36.1726 −1.16444
\(966\) 0 0
\(967\) −19.8768 −0.639196 −0.319598 0.947553i \(-0.603548\pi\)
−0.319598 + 0.947553i \(0.603548\pi\)
\(968\) −14.1273 −0.454070
\(969\) 23.1603 0.744015
\(970\) 18.8034 0.603740
\(971\) 11.5108 0.369400 0.184700 0.982795i \(-0.440869\pi\)
0.184700 + 0.982795i \(0.440869\pi\)
\(972\) 1.24292 0.0398666
\(973\) 0 0
\(974\) −17.8317 −0.571363
\(975\) −0.306882 −0.00982810
\(976\) 62.1556 1.98955
\(977\) 8.68854 0.277971 0.138985 0.990294i \(-0.455616\pi\)
0.138985 + 0.990294i \(0.455616\pi\)
\(978\) −18.9757 −0.606776
\(979\) 7.78068 0.248671
\(980\) 0 0
\(981\) 10.3602 0.330775
\(982\) 53.8968 1.71992
\(983\) 7.47496 0.238414 0.119207 0.992869i \(-0.461965\pi\)
0.119207 + 0.992869i \(0.461965\pi\)
\(984\) −1.36336 −0.0434624
\(985\) 35.4736 1.13028
\(986\) 39.4355 1.25588
\(987\) 0 0
\(988\) −6.62996 −0.210927
\(989\) 12.2296 0.388879
\(990\) −3.13221 −0.0995480
\(991\) −27.3575 −0.869040 −0.434520 0.900662i \(-0.643082\pi\)
−0.434520 + 0.900662i \(0.643082\pi\)
\(992\) 1.03942 0.0330015
\(993\) 22.9215 0.727392
\(994\) 0 0
\(995\) −47.7453 −1.51363
\(996\) 13.6006 0.430951
\(997\) −28.2187 −0.893695 −0.446848 0.894610i \(-0.647453\pi\)
−0.446848 + 0.894610i \(0.647453\pi\)
\(998\) 47.6235 1.50750
\(999\) −5.83538 −0.184623
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 \(a_p\))