Properties

Label 5077.2.a.c.1.19
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42574 q^{2} -1.56213 q^{3} +3.88424 q^{4} +2.05918 q^{5} +3.78933 q^{6} -2.28895 q^{7} -4.57068 q^{8} -0.559747 q^{9} +O(q^{10})\) \(q-2.42574 q^{2} -1.56213 q^{3} +3.88424 q^{4} +2.05918 q^{5} +3.78933 q^{6} -2.28895 q^{7} -4.57068 q^{8} -0.559747 q^{9} -4.99504 q^{10} -5.80011 q^{11} -6.06769 q^{12} -4.60944 q^{13} +5.55240 q^{14} -3.21671 q^{15} +3.31883 q^{16} +6.41164 q^{17} +1.35780 q^{18} +6.83128 q^{19} +7.99834 q^{20} +3.57564 q^{21} +14.0696 q^{22} -2.96482 q^{23} +7.14000 q^{24} -0.759787 q^{25} +11.1813 q^{26} +5.56079 q^{27} -8.89082 q^{28} -8.95853 q^{29} +7.80291 q^{30} -0.0443456 q^{31} +1.09073 q^{32} +9.06053 q^{33} -15.5530 q^{34} -4.71335 q^{35} -2.17419 q^{36} -3.78168 q^{37} -16.5709 q^{38} +7.20055 q^{39} -9.41184 q^{40} -2.12203 q^{41} -8.67358 q^{42} +0.112527 q^{43} -22.5290 q^{44} -1.15262 q^{45} +7.19190 q^{46} -0.270503 q^{47} -5.18444 q^{48} -1.76071 q^{49} +1.84305 q^{50} -10.0158 q^{51} -17.9042 q^{52} -3.37618 q^{53} -13.4891 q^{54} -11.9435 q^{55} +10.4620 q^{56} -10.6714 q^{57} +21.7311 q^{58} +1.96851 q^{59} -12.4944 q^{60} +3.04149 q^{61} +0.107571 q^{62} +1.28123 q^{63} -9.28349 q^{64} -9.49166 q^{65} -21.9785 q^{66} -8.25273 q^{67} +24.9043 q^{68} +4.63144 q^{69} +11.4334 q^{70} -3.54466 q^{71} +2.55842 q^{72} -9.18737 q^{73} +9.17340 q^{74} +1.18689 q^{75} +26.5343 q^{76} +13.2762 q^{77} -17.4667 q^{78} -13.7295 q^{79} +6.83405 q^{80} -7.00744 q^{81} +5.14750 q^{82} +9.68690 q^{83} +13.8886 q^{84} +13.2027 q^{85} -0.272962 q^{86} +13.9944 q^{87} +26.5104 q^{88} -2.01602 q^{89} +2.79596 q^{90} +10.5508 q^{91} -11.5161 q^{92} +0.0692736 q^{93} +0.656171 q^{94} +14.0668 q^{95} -1.70387 q^{96} -5.72428 q^{97} +4.27104 q^{98} +3.24660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42574 −1.71526 −0.857630 0.514267i \(-0.828064\pi\)
−0.857630 + 0.514267i \(0.828064\pi\)
\(3\) −1.56213 −0.901897 −0.450948 0.892550i \(-0.648914\pi\)
−0.450948 + 0.892550i \(0.648914\pi\)
\(4\) 3.88424 1.94212
\(5\) 2.05918 0.920892 0.460446 0.887688i \(-0.347689\pi\)
0.460446 + 0.887688i \(0.347689\pi\)
\(6\) 3.78933 1.54699
\(7\) −2.28895 −0.865141 −0.432571 0.901600i \(-0.642393\pi\)
−0.432571 + 0.901600i \(0.642393\pi\)
\(8\) −4.57068 −1.61598
\(9\) −0.559747 −0.186582
\(10\) −4.99504 −1.57957
\(11\) −5.80011 −1.74880 −0.874400 0.485206i \(-0.838745\pi\)
−0.874400 + 0.485206i \(0.838745\pi\)
\(12\) −6.06769 −1.75159
\(13\) −4.60944 −1.27843 −0.639215 0.769028i \(-0.720740\pi\)
−0.639215 + 0.769028i \(0.720740\pi\)
\(14\) 5.55240 1.48394
\(15\) −3.21671 −0.830550
\(16\) 3.31883 0.829706
\(17\) 6.41164 1.55505 0.777526 0.628851i \(-0.216475\pi\)
0.777526 + 0.628851i \(0.216475\pi\)
\(18\) 1.35780 0.320037
\(19\) 6.83128 1.56720 0.783601 0.621264i \(-0.213380\pi\)
0.783601 + 0.621264i \(0.213380\pi\)
\(20\) 7.99834 1.78848
\(21\) 3.57564 0.780268
\(22\) 14.0696 2.99965
\(23\) −2.96482 −0.618208 −0.309104 0.951028i \(-0.600029\pi\)
−0.309104 + 0.951028i \(0.600029\pi\)
\(24\) 7.14000 1.45745
\(25\) −0.759787 −0.151957
\(26\) 11.1813 2.19284
\(27\) 5.56079 1.07017
\(28\) −8.89082 −1.68021
\(29\) −8.95853 −1.66356 −0.831778 0.555108i \(-0.812677\pi\)
−0.831778 + 0.555108i \(0.812677\pi\)
\(30\) 7.80291 1.42461
\(31\) −0.0443456 −0.00796470 −0.00398235 0.999992i \(-0.501268\pi\)
−0.00398235 + 0.999992i \(0.501268\pi\)
\(32\) 1.09073 0.192816
\(33\) 9.06053 1.57724
\(34\) −15.5530 −2.66732
\(35\) −4.71335 −0.796702
\(36\) −2.17419 −0.362365
\(37\) −3.78168 −0.621705 −0.310852 0.950458i \(-0.600614\pi\)
−0.310852 + 0.950458i \(0.600614\pi\)
\(38\) −16.5709 −2.68816
\(39\) 7.20055 1.15301
\(40\) −9.41184 −1.48814
\(41\) −2.12203 −0.331405 −0.165702 0.986176i \(-0.552989\pi\)
−0.165702 + 0.986176i \(0.552989\pi\)
\(42\) −8.67358 −1.33836
\(43\) 0.112527 0.0171602 0.00858012 0.999963i \(-0.497269\pi\)
0.00858012 + 0.999963i \(0.497269\pi\)
\(44\) −22.5290 −3.39638
\(45\) −1.15262 −0.171822
\(46\) 7.19190 1.06039
\(47\) −0.270503 −0.0394569 −0.0197285 0.999805i \(-0.506280\pi\)
−0.0197285 + 0.999805i \(0.506280\pi\)
\(48\) −5.18444 −0.748309
\(49\) −1.76071 −0.251531
\(50\) 1.84305 0.260647
\(51\) −10.0158 −1.40250
\(52\) −17.9042 −2.48286
\(53\) −3.37618 −0.463754 −0.231877 0.972745i \(-0.574487\pi\)
−0.231877 + 0.972745i \(0.574487\pi\)
\(54\) −13.4891 −1.83563
\(55\) −11.9435 −1.61046
\(56\) 10.4620 1.39805
\(57\) −10.6714 −1.41346
\(58\) 21.7311 2.85343
\(59\) 1.96851 0.256278 0.128139 0.991756i \(-0.459100\pi\)
0.128139 + 0.991756i \(0.459100\pi\)
\(60\) −12.4944 −1.61303
\(61\) 3.04149 0.389423 0.194712 0.980861i \(-0.437623\pi\)
0.194712 + 0.980861i \(0.437623\pi\)
\(62\) 0.107571 0.0136615
\(63\) 1.28123 0.161420
\(64\) −9.28349 −1.16044
\(65\) −9.49166 −1.17730
\(66\) −21.9785 −2.70537
\(67\) −8.25273 −1.00823 −0.504115 0.863636i \(-0.668181\pi\)
−0.504115 + 0.863636i \(0.668181\pi\)
\(68\) 24.9043 3.02009
\(69\) 4.63144 0.557560
\(70\) 11.4334 1.36655
\(71\) −3.54466 −0.420674 −0.210337 0.977629i \(-0.567456\pi\)
−0.210337 + 0.977629i \(0.567456\pi\)
\(72\) 2.55842 0.301513
\(73\) −9.18737 −1.07530 −0.537650 0.843168i \(-0.680688\pi\)
−0.537650 + 0.843168i \(0.680688\pi\)
\(74\) 9.17340 1.06639
\(75\) 1.18689 0.137050
\(76\) 26.5343 3.04369
\(77\) 13.2762 1.51296
\(78\) −17.4667 −1.97771
\(79\) −13.7295 −1.54469 −0.772347 0.635201i \(-0.780917\pi\)
−0.772347 + 0.635201i \(0.780917\pi\)
\(80\) 6.83405 0.764070
\(81\) −7.00744 −0.778605
\(82\) 5.14750 0.568446
\(83\) 9.68690 1.06327 0.531637 0.846972i \(-0.321577\pi\)
0.531637 + 0.846972i \(0.321577\pi\)
\(84\) 13.8886 1.51537
\(85\) 13.2027 1.43203
\(86\) −0.272962 −0.0294343
\(87\) 13.9944 1.50036
\(88\) 26.5104 2.82602
\(89\) −2.01602 −0.213698 −0.106849 0.994275i \(-0.534076\pi\)
−0.106849 + 0.994275i \(0.534076\pi\)
\(90\) 2.79596 0.294720
\(91\) 10.5508 1.10602
\(92\) −11.5161 −1.20063
\(93\) 0.0692736 0.00718334
\(94\) 0.656171 0.0676789
\(95\) 14.0668 1.44323
\(96\) −1.70387 −0.173901
\(97\) −5.72428 −0.581213 −0.290606 0.956843i \(-0.593857\pi\)
−0.290606 + 0.956843i \(0.593857\pi\)
\(98\) 4.27104 0.431441
\(99\) 3.24660 0.326295
\(100\) −2.95119 −0.295119
\(101\) −20.0427 −1.99432 −0.997162 0.0752845i \(-0.976013\pi\)
−0.997162 + 0.0752845i \(0.976013\pi\)
\(102\) 24.2958 2.40565
\(103\) 11.9064 1.17318 0.586588 0.809886i \(-0.300471\pi\)
0.586588 + 0.809886i \(0.300471\pi\)
\(104\) 21.0683 2.06592
\(105\) 7.36287 0.718543
\(106\) 8.18976 0.795459
\(107\) 4.58073 0.442836 0.221418 0.975179i \(-0.428931\pi\)
0.221418 + 0.975179i \(0.428931\pi\)
\(108\) 21.5994 2.07841
\(109\) 8.04979 0.771030 0.385515 0.922702i \(-0.374024\pi\)
0.385515 + 0.922702i \(0.374024\pi\)
\(110\) 28.9718 2.76235
\(111\) 5.90748 0.560713
\(112\) −7.59662 −0.717813
\(113\) −4.43589 −0.417294 −0.208647 0.977991i \(-0.566906\pi\)
−0.208647 + 0.977991i \(0.566906\pi\)
\(114\) 25.8860 2.42444
\(115\) −6.10510 −0.569303
\(116\) −34.7970 −3.23082
\(117\) 2.58012 0.238532
\(118\) −4.77510 −0.439583
\(119\) −14.6759 −1.34534
\(120\) 14.7025 1.34215
\(121\) 22.6413 2.05830
\(122\) −7.37789 −0.667963
\(123\) 3.31488 0.298893
\(124\) −0.172249 −0.0154684
\(125\) −11.8604 −1.06083
\(126\) −3.10794 −0.276878
\(127\) −1.41651 −0.125695 −0.0628476 0.998023i \(-0.520018\pi\)
−0.0628476 + 0.998023i \(0.520018\pi\)
\(128\) 20.3379 1.79764
\(129\) −0.175782 −0.0154768
\(130\) 23.0243 2.01937
\(131\) 4.69318 0.410045 0.205023 0.978757i \(-0.434273\pi\)
0.205023 + 0.978757i \(0.434273\pi\)
\(132\) 35.1933 3.06318
\(133\) −15.6364 −1.35585
\(134\) 20.0190 1.72938
\(135\) 11.4507 0.985516
\(136\) −29.3056 −2.51293
\(137\) −9.23756 −0.789218 −0.394609 0.918849i \(-0.629120\pi\)
−0.394609 + 0.918849i \(0.629120\pi\)
\(138\) −11.2347 −0.956360
\(139\) −2.92337 −0.247957 −0.123978 0.992285i \(-0.539565\pi\)
−0.123978 + 0.992285i \(0.539565\pi\)
\(140\) −18.3078 −1.54729
\(141\) 0.422561 0.0355861
\(142\) 8.59845 0.721566
\(143\) 26.7353 2.23572
\(144\) −1.85770 −0.154809
\(145\) −18.4472 −1.53196
\(146\) 22.2862 1.84442
\(147\) 2.75047 0.226855
\(148\) −14.6890 −1.20742
\(149\) 7.39579 0.605886 0.302943 0.953009i \(-0.402031\pi\)
0.302943 + 0.953009i \(0.402031\pi\)
\(150\) −2.87908 −0.235076
\(151\) −0.0268784 −0.00218733 −0.00109367 0.999999i \(-0.500348\pi\)
−0.00109367 + 0.999999i \(0.500348\pi\)
\(152\) −31.2236 −2.53257
\(153\) −3.58890 −0.290145
\(154\) −32.2046 −2.59512
\(155\) −0.0913154 −0.00733463
\(156\) 27.9687 2.23928
\(157\) −5.07212 −0.404799 −0.202399 0.979303i \(-0.564874\pi\)
−0.202399 + 0.979303i \(0.564874\pi\)
\(158\) 33.3044 2.64955
\(159\) 5.27404 0.418258
\(160\) 2.24602 0.177563
\(161\) 6.78632 0.534837
\(162\) 16.9983 1.33551
\(163\) −11.8124 −0.925217 −0.462609 0.886563i \(-0.653086\pi\)
−0.462609 + 0.886563i \(0.653086\pi\)
\(164\) −8.24246 −0.643628
\(165\) 18.6572 1.45246
\(166\) −23.4979 −1.82379
\(167\) 18.5164 1.43284 0.716421 0.697668i \(-0.245779\pi\)
0.716421 + 0.697668i \(0.245779\pi\)
\(168\) −16.3431 −1.26090
\(169\) 8.24696 0.634382
\(170\) −32.0264 −2.45631
\(171\) −3.82379 −0.292412
\(172\) 0.437082 0.0333272
\(173\) 3.96285 0.301290 0.150645 0.988588i \(-0.451865\pi\)
0.150645 + 0.988588i \(0.451865\pi\)
\(174\) −33.9468 −2.57350
\(175\) 1.73911 0.131465
\(176\) −19.2496 −1.45099
\(177\) −3.07507 −0.231136
\(178\) 4.89035 0.366547
\(179\) −20.9482 −1.56574 −0.782872 0.622183i \(-0.786246\pi\)
−0.782872 + 0.622183i \(0.786246\pi\)
\(180\) −4.47705 −0.333699
\(181\) 2.23679 0.166259 0.0831296 0.996539i \(-0.473508\pi\)
0.0831296 + 0.996539i \(0.473508\pi\)
\(182\) −25.5935 −1.89712
\(183\) −4.75121 −0.351220
\(184\) 13.5512 0.999011
\(185\) −7.78716 −0.572523
\(186\) −0.168040 −0.0123213
\(187\) −37.1882 −2.71947
\(188\) −1.05070 −0.0766300
\(189\) −12.7284 −0.925852
\(190\) −34.1225 −2.47551
\(191\) 10.4705 0.757620 0.378810 0.925475i \(-0.376333\pi\)
0.378810 + 0.925475i \(0.376333\pi\)
\(192\) 14.5020 1.04659
\(193\) 16.2046 1.16643 0.583217 0.812317i \(-0.301794\pi\)
0.583217 + 0.812317i \(0.301794\pi\)
\(194\) 13.8856 0.996931
\(195\) 14.8272 1.06180
\(196\) −6.83903 −0.488502
\(197\) −10.9169 −0.777798 −0.388899 0.921280i \(-0.627144\pi\)
−0.388899 + 0.921280i \(0.627144\pi\)
\(198\) −7.87541 −0.559681
\(199\) −11.3412 −0.803959 −0.401979 0.915649i \(-0.631678\pi\)
−0.401979 + 0.915649i \(0.631678\pi\)
\(200\) 3.47274 0.245560
\(201\) 12.8918 0.909320
\(202\) 48.6185 3.42079
\(203\) 20.5056 1.43921
\(204\) −38.9038 −2.72381
\(205\) −4.36963 −0.305188
\(206\) −28.8820 −2.01230
\(207\) 1.65955 0.115347
\(208\) −15.2979 −1.06072
\(209\) −39.6222 −2.74072
\(210\) −17.8604 −1.23249
\(211\) 7.13087 0.490910 0.245455 0.969408i \(-0.421063\pi\)
0.245455 + 0.969408i \(0.421063\pi\)
\(212\) −13.1139 −0.900666
\(213\) 5.53723 0.379405
\(214\) −11.1117 −0.759580
\(215\) 0.231713 0.0158027
\(216\) −25.4166 −1.72938
\(217\) 0.101505 0.00689059
\(218\) −19.5267 −1.32252
\(219\) 14.3519 0.969809
\(220\) −46.3912 −3.12770
\(221\) −29.5541 −1.98802
\(222\) −14.3300 −0.961770
\(223\) 14.6473 0.980853 0.490427 0.871482i \(-0.336841\pi\)
0.490427 + 0.871482i \(0.336841\pi\)
\(224\) −2.49664 −0.166813
\(225\) 0.425289 0.0283526
\(226\) 10.7603 0.715767
\(227\) 2.60750 0.173066 0.0865330 0.996249i \(-0.472421\pi\)
0.0865330 + 0.996249i \(0.472421\pi\)
\(228\) −41.4501 −2.74510
\(229\) −27.6328 −1.82603 −0.913013 0.407930i \(-0.866251\pi\)
−0.913013 + 0.407930i \(0.866251\pi\)
\(230\) 14.8094 0.976503
\(231\) −20.7391 −1.36453
\(232\) 40.9465 2.68827
\(233\) 4.36316 0.285840 0.142920 0.989734i \(-0.454351\pi\)
0.142920 + 0.989734i \(0.454351\pi\)
\(234\) −6.25872 −0.409145
\(235\) −0.557014 −0.0363356
\(236\) 7.64615 0.497722
\(237\) 21.4473 1.39315
\(238\) 35.6000 2.30761
\(239\) −13.9622 −0.903137 −0.451568 0.892236i \(-0.649135\pi\)
−0.451568 + 0.892236i \(0.649135\pi\)
\(240\) −10.6757 −0.689112
\(241\) −18.1453 −1.16884 −0.584420 0.811452i \(-0.698678\pi\)
−0.584420 + 0.811452i \(0.698678\pi\)
\(242\) −54.9220 −3.53052
\(243\) −5.73583 −0.367954
\(244\) 11.8139 0.756306
\(245\) −3.62562 −0.231633
\(246\) −8.04106 −0.512679
\(247\) −31.4884 −2.00356
\(248\) 0.202689 0.0128708
\(249\) −15.1322 −0.958964
\(250\) 28.7704 1.81960
\(251\) 13.5816 0.857264 0.428632 0.903479i \(-0.358996\pi\)
0.428632 + 0.903479i \(0.358996\pi\)
\(252\) 4.97661 0.313497
\(253\) 17.1963 1.08112
\(254\) 3.43610 0.215600
\(255\) −20.6244 −1.29155
\(256\) −30.7676 −1.92298
\(257\) 27.0662 1.68834 0.844171 0.536075i \(-0.180093\pi\)
0.844171 + 0.536075i \(0.180093\pi\)
\(258\) 0.426403 0.0265467
\(259\) 8.65608 0.537862
\(260\) −36.8679 −2.28645
\(261\) 5.01451 0.310390
\(262\) −11.3845 −0.703334
\(263\) 21.0277 1.29662 0.648312 0.761374i \(-0.275475\pi\)
0.648312 + 0.761374i \(0.275475\pi\)
\(264\) −41.4128 −2.54878
\(265\) −6.95216 −0.427068
\(266\) 37.9300 2.32564
\(267\) 3.14929 0.192733
\(268\) −32.0555 −1.95810
\(269\) 14.3612 0.875616 0.437808 0.899068i \(-0.355755\pi\)
0.437808 + 0.899068i \(0.355755\pi\)
\(270\) −27.7764 −1.69042
\(271\) −16.5621 −1.00607 −0.503037 0.864265i \(-0.667784\pi\)
−0.503037 + 0.864265i \(0.667784\pi\)
\(272\) 21.2791 1.29024
\(273\) −16.4817 −0.997518
\(274\) 22.4080 1.35371
\(275\) 4.40685 0.265743
\(276\) 17.9896 1.08285
\(277\) −28.9776 −1.74109 −0.870547 0.492086i \(-0.836235\pi\)
−0.870547 + 0.492086i \(0.836235\pi\)
\(278\) 7.09135 0.425311
\(279\) 0.0248223 0.00148607
\(280\) 21.5432 1.28745
\(281\) −15.6451 −0.933307 −0.466653 0.884440i \(-0.654540\pi\)
−0.466653 + 0.884440i \(0.654540\pi\)
\(282\) −1.02503 −0.0610394
\(283\) 25.8810 1.53847 0.769233 0.638969i \(-0.220639\pi\)
0.769233 + 0.638969i \(0.220639\pi\)
\(284\) −13.7683 −0.816999
\(285\) −21.9742 −1.30164
\(286\) −64.8530 −3.83484
\(287\) 4.85721 0.286712
\(288\) −0.610536 −0.0359762
\(289\) 24.1091 1.41818
\(290\) 44.7482 2.62770
\(291\) 8.94208 0.524194
\(292\) −35.6859 −2.08836
\(293\) 8.89669 0.519750 0.259875 0.965642i \(-0.416319\pi\)
0.259875 + 0.965642i \(0.416319\pi\)
\(294\) −6.67193 −0.389115
\(295\) 4.05351 0.236004
\(296\) 17.2849 1.00466
\(297\) −32.2532 −1.87152
\(298\) −17.9403 −1.03925
\(299\) 13.6662 0.790335
\(300\) 4.61015 0.266167
\(301\) −0.257569 −0.0148460
\(302\) 0.0652001 0.00375184
\(303\) 31.3093 1.79867
\(304\) 22.6718 1.30032
\(305\) 6.26298 0.358617
\(306\) 8.70575 0.497675
\(307\) −16.2746 −0.928840 −0.464420 0.885615i \(-0.653737\pi\)
−0.464420 + 0.885615i \(0.653737\pi\)
\(308\) 51.5677 2.93835
\(309\) −18.5994 −1.05808
\(310\) 0.221508 0.0125808
\(311\) 28.8159 1.63400 0.816999 0.576639i \(-0.195636\pi\)
0.816999 + 0.576639i \(0.195636\pi\)
\(312\) −32.9114 −1.86324
\(313\) 16.3485 0.924074 0.462037 0.886861i \(-0.347119\pi\)
0.462037 + 0.886861i \(0.347119\pi\)
\(314\) 12.3037 0.694336
\(315\) 2.63829 0.148651
\(316\) −53.3288 −2.99998
\(317\) 29.2646 1.64366 0.821832 0.569730i \(-0.192952\pi\)
0.821832 + 0.569730i \(0.192952\pi\)
\(318\) −12.7935 −0.717422
\(319\) 51.9605 2.90923
\(320\) −19.1164 −1.06864
\(321\) −7.15571 −0.399393
\(322\) −16.4619 −0.917385
\(323\) 43.7997 2.43708
\(324\) −27.2186 −1.51214
\(325\) 3.50219 0.194267
\(326\) 28.6538 1.58699
\(327\) −12.5748 −0.695389
\(328\) 9.69911 0.535544
\(329\) 0.619167 0.0341358
\(330\) −45.2577 −2.49136
\(331\) 11.5934 0.637229 0.318615 0.947884i \(-0.396782\pi\)
0.318615 + 0.947884i \(0.396782\pi\)
\(332\) 37.6262 2.06501
\(333\) 2.11679 0.115999
\(334\) −44.9161 −2.45770
\(335\) −16.9938 −0.928472
\(336\) 11.8669 0.647393
\(337\) 0.140612 0.00765963 0.00382981 0.999993i \(-0.498781\pi\)
0.00382981 + 0.999993i \(0.498781\pi\)
\(338\) −20.0050 −1.08813
\(339\) 6.92944 0.376356
\(340\) 51.2825 2.78118
\(341\) 0.257209 0.0139287
\(342\) 9.27554 0.501564
\(343\) 20.0528 1.08275
\(344\) −0.514326 −0.0277306
\(345\) 9.53696 0.513453
\(346\) −9.61287 −0.516791
\(347\) 19.5651 1.05031 0.525154 0.851007i \(-0.324008\pi\)
0.525154 + 0.851007i \(0.324008\pi\)
\(348\) 54.3575 2.91387
\(349\) 9.75644 0.522250 0.261125 0.965305i \(-0.415906\pi\)
0.261125 + 0.965305i \(0.415906\pi\)
\(350\) −4.21864 −0.225496
\(351\) −25.6321 −1.36814
\(352\) −6.32638 −0.337197
\(353\) 7.66210 0.407812 0.203906 0.978990i \(-0.434636\pi\)
0.203906 + 0.978990i \(0.434636\pi\)
\(354\) 7.45933 0.396459
\(355\) −7.29909 −0.387396
\(356\) −7.83071 −0.415027
\(357\) 22.9257 1.21336
\(358\) 50.8151 2.68566
\(359\) −28.9320 −1.52698 −0.763488 0.645823i \(-0.776515\pi\)
−0.763488 + 0.645823i \(0.776515\pi\)
\(360\) 5.26825 0.277661
\(361\) 27.6664 1.45612
\(362\) −5.42588 −0.285178
\(363\) −35.3687 −1.85637
\(364\) 40.9817 2.14803
\(365\) −18.9184 −0.990235
\(366\) 11.5252 0.602433
\(367\) −26.9298 −1.40572 −0.702861 0.711327i \(-0.748094\pi\)
−0.702861 + 0.711327i \(0.748094\pi\)
\(368\) −9.83973 −0.512931
\(369\) 1.18780 0.0618343
\(370\) 18.8897 0.982026
\(371\) 7.72791 0.401213
\(372\) 0.269075 0.0139509
\(373\) 2.12880 0.110225 0.0551125 0.998480i \(-0.482448\pi\)
0.0551125 + 0.998480i \(0.482448\pi\)
\(374\) 90.2092 4.66460
\(375\) 18.5275 0.956758
\(376\) 1.23638 0.0637615
\(377\) 41.2938 2.12674
\(378\) 30.8758 1.58808
\(379\) 12.8192 0.658477 0.329238 0.944247i \(-0.393208\pi\)
0.329238 + 0.944247i \(0.393208\pi\)
\(380\) 54.6389 2.80291
\(381\) 2.21278 0.113364
\(382\) −25.3988 −1.29951
\(383\) −0.850467 −0.0434569 −0.0217284 0.999764i \(-0.506917\pi\)
−0.0217284 + 0.999764i \(0.506917\pi\)
\(384\) −31.7705 −1.62128
\(385\) 27.3380 1.39327
\(386\) −39.3083 −2.00074
\(387\) −0.0629868 −0.00320180
\(388\) −22.2345 −1.12878
\(389\) 38.4592 1.94996 0.974979 0.222297i \(-0.0713554\pi\)
0.974979 + 0.222297i \(0.0713554\pi\)
\(390\) −35.9670 −1.82126
\(391\) −19.0094 −0.961345
\(392\) 8.04766 0.406468
\(393\) −7.33136 −0.369818
\(394\) 26.4816 1.33413
\(395\) −28.2716 −1.42250
\(396\) 12.6106 0.633704
\(397\) 13.9730 0.701286 0.350643 0.936509i \(-0.385963\pi\)
0.350643 + 0.936509i \(0.385963\pi\)
\(398\) 27.5109 1.37900
\(399\) 24.4262 1.22284
\(400\) −2.52160 −0.126080
\(401\) −36.5357 −1.82451 −0.912254 0.409626i \(-0.865659\pi\)
−0.912254 + 0.409626i \(0.865659\pi\)
\(402\) −31.2723 −1.55972
\(403\) 0.204408 0.0101823
\(404\) −77.8506 −3.87321
\(405\) −14.4296 −0.717011
\(406\) −49.7414 −2.46862
\(407\) 21.9342 1.08724
\(408\) 45.7791 2.26640
\(409\) −12.8893 −0.637337 −0.318668 0.947866i \(-0.603236\pi\)
−0.318668 + 0.947866i \(0.603236\pi\)
\(410\) 10.5996 0.523477
\(411\) 14.4303 0.711793
\(412\) 46.2474 2.27845
\(413\) −4.50581 −0.221717
\(414\) −4.02565 −0.197850
\(415\) 19.9470 0.979162
\(416\) −5.02768 −0.246502
\(417\) 4.56668 0.223631
\(418\) 96.1133 4.70106
\(419\) −12.4117 −0.606350 −0.303175 0.952935i \(-0.598047\pi\)
−0.303175 + 0.952935i \(0.598047\pi\)
\(420\) 28.5991 1.39550
\(421\) −0.317345 −0.0154664 −0.00773322 0.999970i \(-0.502462\pi\)
−0.00773322 + 0.999970i \(0.502462\pi\)
\(422\) −17.2977 −0.842038
\(423\) 0.151413 0.00736196
\(424\) 15.4314 0.749417
\(425\) −4.87148 −0.236302
\(426\) −13.4319 −0.650778
\(427\) −6.96182 −0.336906
\(428\) 17.7927 0.860041
\(429\) −41.7640 −2.01639
\(430\) −0.562078 −0.0271058
\(431\) 37.8615 1.82372 0.911861 0.410499i \(-0.134645\pi\)
0.911861 + 0.410499i \(0.134645\pi\)
\(432\) 18.4553 0.887931
\(433\) −32.8172 −1.57709 −0.788547 0.614974i \(-0.789166\pi\)
−0.788547 + 0.614974i \(0.789166\pi\)
\(434\) −0.246225 −0.0118192
\(435\) 28.8169 1.38167
\(436\) 31.2673 1.49743
\(437\) −20.2535 −0.968858
\(438\) −34.8140 −1.66348
\(439\) −37.5346 −1.79143 −0.895715 0.444628i \(-0.853336\pi\)
−0.895715 + 0.444628i \(0.853336\pi\)
\(440\) 54.5897 2.60246
\(441\) 0.985555 0.0469312
\(442\) 71.6907 3.40998
\(443\) −2.54505 −0.120919 −0.0604594 0.998171i \(-0.519257\pi\)
−0.0604594 + 0.998171i \(0.519257\pi\)
\(444\) 22.9461 1.08897
\(445\) −4.15135 −0.196793
\(446\) −35.5305 −1.68242
\(447\) −11.5532 −0.546447
\(448\) 21.2494 1.00394
\(449\) 30.7052 1.44907 0.724534 0.689239i \(-0.242055\pi\)
0.724534 + 0.689239i \(0.242055\pi\)
\(450\) −1.03164 −0.0486320
\(451\) 12.3080 0.579561
\(452\) −17.2301 −0.810434
\(453\) 0.0419875 0.00197275
\(454\) −6.32513 −0.296853
\(455\) 21.7259 1.01853
\(456\) 48.7753 2.28411
\(457\) −5.09754 −0.238453 −0.119226 0.992867i \(-0.538041\pi\)
−0.119226 + 0.992867i \(0.538041\pi\)
\(458\) 67.0301 3.13211
\(459\) 35.6538 1.66418
\(460\) −23.7136 −1.10565
\(461\) 18.1124 0.843581 0.421790 0.906693i \(-0.361402\pi\)
0.421790 + 0.906693i \(0.361402\pi\)
\(462\) 50.3078 2.34053
\(463\) 3.83657 0.178300 0.0891502 0.996018i \(-0.471585\pi\)
0.0891502 + 0.996018i \(0.471585\pi\)
\(464\) −29.7318 −1.38026
\(465\) 0.142647 0.00661508
\(466\) −10.5839 −0.490290
\(467\) 35.4850 1.64205 0.821026 0.570891i \(-0.193402\pi\)
0.821026 + 0.570891i \(0.193402\pi\)
\(468\) 10.0218 0.463258
\(469\) 18.8901 0.872262
\(470\) 1.35117 0.0623250
\(471\) 7.92331 0.365087
\(472\) −8.99742 −0.414140
\(473\) −0.652670 −0.0300098
\(474\) −52.0258 −2.38962
\(475\) −5.19032 −0.238148
\(476\) −57.0047 −2.61281
\(477\) 1.88981 0.0865284
\(478\) 33.8686 1.54912
\(479\) −24.2725 −1.10904 −0.554519 0.832171i \(-0.687098\pi\)
−0.554519 + 0.832171i \(0.687098\pi\)
\(480\) −3.50857 −0.160144
\(481\) 17.4314 0.794806
\(482\) 44.0158 2.00486
\(483\) −10.6011 −0.482368
\(484\) 87.9442 3.99746
\(485\) −11.7873 −0.535234
\(486\) 13.9137 0.631137
\(487\) 14.9614 0.677968 0.338984 0.940792i \(-0.389917\pi\)
0.338984 + 0.940792i \(0.389917\pi\)
\(488\) −13.9017 −0.629300
\(489\) 18.4525 0.834450
\(490\) 8.79484 0.397310
\(491\) −28.6489 −1.29291 −0.646454 0.762953i \(-0.723749\pi\)
−0.646454 + 0.762953i \(0.723749\pi\)
\(492\) 12.8758 0.580486
\(493\) −57.4389 −2.58692
\(494\) 76.3828 3.43662
\(495\) 6.68532 0.300483
\(496\) −0.147175 −0.00660836
\(497\) 8.11356 0.363943
\(498\) 36.7069 1.64487
\(499\) 31.2043 1.39690 0.698448 0.715661i \(-0.253874\pi\)
0.698448 + 0.715661i \(0.253874\pi\)
\(500\) −46.0687 −2.06026
\(501\) −28.9251 −1.29228
\(502\) −32.9455 −1.47043
\(503\) −27.4422 −1.22359 −0.611794 0.791017i \(-0.709552\pi\)
−0.611794 + 0.791017i \(0.709552\pi\)
\(504\) −5.85610 −0.260852
\(505\) −41.2715 −1.83656
\(506\) −41.7138 −1.85441
\(507\) −12.8828 −0.572147
\(508\) −5.50207 −0.244115
\(509\) 5.56861 0.246824 0.123412 0.992355i \(-0.460616\pi\)
0.123412 + 0.992355i \(0.460616\pi\)
\(510\) 50.0294 2.21534
\(511\) 21.0294 0.930286
\(512\) 33.9585 1.50077
\(513\) 37.9873 1.67718
\(514\) −65.6556 −2.89594
\(515\) 24.5175 1.08037
\(516\) −0.682780 −0.0300577
\(517\) 1.56895 0.0690022
\(518\) −20.9974 −0.922574
\(519\) −6.19049 −0.271733
\(520\) 43.3833 1.90249
\(521\) −13.3389 −0.584389 −0.292195 0.956359i \(-0.594385\pi\)
−0.292195 + 0.956359i \(0.594385\pi\)
\(522\) −12.1639 −0.532400
\(523\) 25.2134 1.10250 0.551251 0.834339i \(-0.314150\pi\)
0.551251 + 0.834339i \(0.314150\pi\)
\(524\) 18.2294 0.796356
\(525\) −2.71672 −0.118567
\(526\) −51.0079 −2.22405
\(527\) −0.284328 −0.0123855
\(528\) 30.0703 1.30864
\(529\) −14.2098 −0.617819
\(530\) 16.8642 0.732533
\(531\) −1.10187 −0.0478170
\(532\) −60.7357 −2.63323
\(533\) 9.78136 0.423678
\(534\) −7.63937 −0.330588
\(535\) 9.43255 0.407805
\(536\) 37.7206 1.62928
\(537\) 32.7239 1.41214
\(538\) −34.8365 −1.50191
\(539\) 10.2123 0.439877
\(540\) 44.4771 1.91399
\(541\) 5.94819 0.255733 0.127866 0.991791i \(-0.459187\pi\)
0.127866 + 0.991791i \(0.459187\pi\)
\(542\) 40.1754 1.72568
\(543\) −3.49416 −0.149949
\(544\) 6.99340 0.299839
\(545\) 16.5759 0.710036
\(546\) 39.9804 1.71100
\(547\) 3.05965 0.130821 0.0654106 0.997858i \(-0.479164\pi\)
0.0654106 + 0.997858i \(0.479164\pi\)
\(548\) −35.8809 −1.53275
\(549\) −1.70247 −0.0726595
\(550\) −10.6899 −0.455819
\(551\) −61.1982 −2.60713
\(552\) −21.1688 −0.901005
\(553\) 31.4262 1.33638
\(554\) 70.2922 2.98643
\(555\) 12.1646 0.516357
\(556\) −11.3551 −0.481562
\(557\) −28.8557 −1.22266 −0.611329 0.791377i \(-0.709365\pi\)
−0.611329 + 0.791377i \(0.709365\pi\)
\(558\) −0.0602126 −0.00254900
\(559\) −0.518688 −0.0219381
\(560\) −15.6428 −0.661029
\(561\) 58.0929 2.45268
\(562\) 37.9510 1.60086
\(563\) 17.2038 0.725055 0.362527 0.931973i \(-0.381914\pi\)
0.362527 + 0.931973i \(0.381914\pi\)
\(564\) 1.64133 0.0691123
\(565\) −9.13429 −0.384282
\(566\) −62.7807 −2.63887
\(567\) 16.0397 0.673603
\(568\) 16.2015 0.679801
\(569\) −44.1835 −1.85227 −0.926134 0.377195i \(-0.876889\pi\)
−0.926134 + 0.377195i \(0.876889\pi\)
\(570\) 53.3038 2.23265
\(571\) −40.4540 −1.69295 −0.846473 0.532431i \(-0.821279\pi\)
−0.846473 + 0.532431i \(0.821279\pi\)
\(572\) 103.846 4.34203
\(573\) −16.3563 −0.683295
\(574\) −11.7824 −0.491786
\(575\) 2.25263 0.0939413
\(576\) 5.19641 0.216517
\(577\) −25.5282 −1.06275 −0.531377 0.847136i \(-0.678325\pi\)
−0.531377 + 0.847136i \(0.678325\pi\)
\(578\) −58.4826 −2.43256
\(579\) −25.3137 −1.05200
\(580\) −71.6533 −2.97524
\(581\) −22.1728 −0.919883
\(582\) −21.6912 −0.899129
\(583\) 19.5822 0.811013
\(584\) 41.9925 1.73766
\(585\) 5.31293 0.219663
\(586\) −21.5811 −0.891507
\(587\) 35.8989 1.48171 0.740853 0.671667i \(-0.234421\pi\)
0.740853 + 0.671667i \(0.234421\pi\)
\(588\) 10.6835 0.440579
\(589\) −0.302937 −0.0124823
\(590\) −9.83278 −0.404809
\(591\) 17.0536 0.701493
\(592\) −12.5507 −0.515832
\(593\) 42.7221 1.75439 0.877194 0.480137i \(-0.159413\pi\)
0.877194 + 0.480137i \(0.159413\pi\)
\(594\) 78.2381 3.21015
\(595\) −30.2203 −1.23891
\(596\) 28.7270 1.17670
\(597\) 17.7165 0.725088
\(598\) −33.1507 −1.35563
\(599\) 13.4305 0.548755 0.274378 0.961622i \(-0.411528\pi\)
0.274378 + 0.961622i \(0.411528\pi\)
\(600\) −5.42488 −0.221470
\(601\) −2.26638 −0.0924474 −0.0462237 0.998931i \(-0.514719\pi\)
−0.0462237 + 0.998931i \(0.514719\pi\)
\(602\) 0.624797 0.0254648
\(603\) 4.61944 0.188118
\(604\) −0.104402 −0.00424806
\(605\) 46.6225 1.89547
\(606\) −75.9485 −3.08520
\(607\) 34.4150 1.39686 0.698430 0.715678i \(-0.253882\pi\)
0.698430 + 0.715678i \(0.253882\pi\)
\(608\) 7.45111 0.302182
\(609\) −32.0324 −1.29802
\(610\) −15.1924 −0.615122
\(611\) 1.24687 0.0504429
\(612\) −13.9401 −0.563496
\(613\) −24.0650 −0.971977 −0.485989 0.873965i \(-0.661540\pi\)
−0.485989 + 0.873965i \(0.661540\pi\)
\(614\) 39.4780 1.59320
\(615\) 6.82594 0.275248
\(616\) −60.6811 −2.44491
\(617\) 23.6360 0.951552 0.475776 0.879567i \(-0.342167\pi\)
0.475776 + 0.879567i \(0.342167\pi\)
\(618\) 45.1174 1.81489
\(619\) −17.1471 −0.689202 −0.344601 0.938749i \(-0.611986\pi\)
−0.344601 + 0.938749i \(0.611986\pi\)
\(620\) −0.354691 −0.0142447
\(621\) −16.4868 −0.661591
\(622\) −69.9000 −2.80273
\(623\) 4.61457 0.184879
\(624\) 23.8974 0.956661
\(625\) −20.6238 −0.824952
\(626\) −39.6574 −1.58503
\(627\) 61.8950 2.47185
\(628\) −19.7013 −0.786168
\(629\) −24.2468 −0.966783
\(630\) −6.39981 −0.254974
\(631\) −9.06466 −0.360859 −0.180429 0.983588i \(-0.557749\pi\)
−0.180429 + 0.983588i \(0.557749\pi\)
\(632\) 62.7533 2.49619
\(633\) −11.1394 −0.442750
\(634\) −70.9885 −2.81931
\(635\) −2.91685 −0.115752
\(636\) 20.4856 0.812308
\(637\) 8.11591 0.321564
\(638\) −126.043 −4.99008
\(639\) 1.98412 0.0784904
\(640\) 41.8794 1.65543
\(641\) 40.4480 1.59760 0.798801 0.601596i \(-0.205468\pi\)
0.798801 + 0.601596i \(0.205468\pi\)
\(642\) 17.3579 0.685062
\(643\) 7.64870 0.301635 0.150818 0.988562i \(-0.451809\pi\)
0.150818 + 0.988562i \(0.451809\pi\)
\(644\) 26.3597 1.03872
\(645\) −0.361967 −0.0142524
\(646\) −106.247 −4.18023
\(647\) 41.7733 1.64228 0.821139 0.570728i \(-0.193339\pi\)
0.821139 + 0.570728i \(0.193339\pi\)
\(648\) 32.0288 1.25821
\(649\) −11.4176 −0.448179
\(650\) −8.49543 −0.333218
\(651\) −0.158564 −0.00621460
\(652\) −45.8821 −1.79688
\(653\) 18.7320 0.733039 0.366520 0.930410i \(-0.380549\pi\)
0.366520 + 0.930410i \(0.380549\pi\)
\(654\) 30.5033 1.19277
\(655\) 9.66409 0.377607
\(656\) −7.04264 −0.274969
\(657\) 5.14260 0.200632
\(658\) −1.50194 −0.0585518
\(659\) 38.2256 1.48906 0.744529 0.667590i \(-0.232674\pi\)
0.744529 + 0.667590i \(0.232674\pi\)
\(660\) 72.4692 2.82086
\(661\) −13.4050 −0.521393 −0.260697 0.965421i \(-0.583952\pi\)
−0.260697 + 0.965421i \(0.583952\pi\)
\(662\) −28.1225 −1.09301
\(663\) 46.1674 1.79299
\(664\) −44.2757 −1.71823
\(665\) −32.1982 −1.24859
\(666\) −5.13478 −0.198969
\(667\) 26.5604 1.02842
\(668\) 71.9221 2.78275
\(669\) −22.8809 −0.884628
\(670\) 41.2227 1.59257
\(671\) −17.6410 −0.681023
\(672\) 3.90007 0.150449
\(673\) −8.36526 −0.322457 −0.161229 0.986917i \(-0.551546\pi\)
−0.161229 + 0.986917i \(0.551546\pi\)
\(674\) −0.341089 −0.0131383
\(675\) −4.22502 −0.162621
\(676\) 32.0332 1.23204
\(677\) −4.25412 −0.163499 −0.0817496 0.996653i \(-0.526051\pi\)
−0.0817496 + 0.996653i \(0.526051\pi\)
\(678\) −16.8091 −0.645548
\(679\) 13.1026 0.502831
\(680\) −60.3453 −2.31414
\(681\) −4.07326 −0.156088
\(682\) −0.623924 −0.0238913
\(683\) 36.0456 1.37925 0.689624 0.724168i \(-0.257776\pi\)
0.689624 + 0.724168i \(0.257776\pi\)
\(684\) −14.8525 −0.567900
\(685\) −19.0218 −0.726784
\(686\) −48.6430 −1.85720
\(687\) 43.1660 1.64689
\(688\) 0.373458 0.0142380
\(689\) 15.5623 0.592877
\(690\) −23.1342 −0.880705
\(691\) 51.1452 1.94565 0.972827 0.231532i \(-0.0743738\pi\)
0.972827 + 0.231532i \(0.0743738\pi\)
\(692\) 15.3927 0.585141
\(693\) −7.43129 −0.282291
\(694\) −47.4599 −1.80155
\(695\) −6.01974 −0.228342
\(696\) −63.9639 −2.42454
\(697\) −13.6057 −0.515352
\(698\) −23.6666 −0.895796
\(699\) −6.81582 −0.257798
\(700\) 6.75513 0.255320
\(701\) 24.3917 0.921262 0.460631 0.887592i \(-0.347623\pi\)
0.460631 + 0.887592i \(0.347623\pi\)
\(702\) 62.1770 2.34672
\(703\) −25.8337 −0.974337
\(704\) 53.8453 2.02937
\(705\) 0.870128 0.0327709
\(706\) −18.5863 −0.699504
\(707\) 45.8767 1.72537
\(708\) −11.9443 −0.448894
\(709\) −33.6884 −1.26519 −0.632597 0.774481i \(-0.718011\pi\)
−0.632597 + 0.774481i \(0.718011\pi\)
\(710\) 17.7057 0.664485
\(711\) 7.68507 0.288213
\(712\) 9.21459 0.345331
\(713\) 0.131477 0.00492384
\(714\) −55.6119 −2.08122
\(715\) 55.0527 2.05885
\(716\) −81.3679 −3.04086
\(717\) 21.8107 0.814536
\(718\) 70.1818 2.61916
\(719\) 48.9834 1.82677 0.913385 0.407096i \(-0.133459\pi\)
0.913385 + 0.407096i \(0.133459\pi\)
\(720\) −3.82534 −0.142562
\(721\) −27.2532 −1.01496
\(722\) −67.1116 −2.49763
\(723\) 28.3453 1.05417
\(724\) 8.68822 0.322895
\(725\) 6.80657 0.252790
\(726\) 85.7954 3.18416
\(727\) −3.58508 −0.132963 −0.0664816 0.997788i \(-0.521177\pi\)
−0.0664816 + 0.997788i \(0.521177\pi\)
\(728\) −48.2242 −1.78731
\(729\) 29.9824 1.11046
\(730\) 45.8913 1.69851
\(731\) 0.721484 0.0266850
\(732\) −18.4548 −0.682110
\(733\) −15.5288 −0.573569 −0.286784 0.957995i \(-0.592586\pi\)
−0.286784 + 0.957995i \(0.592586\pi\)
\(734\) 65.3247 2.41118
\(735\) 5.66370 0.208909
\(736\) −3.23383 −0.119201
\(737\) 47.8667 1.76319
\(738\) −2.88130 −0.106062
\(739\) 25.0152 0.920198 0.460099 0.887868i \(-0.347814\pi\)
0.460099 + 0.887868i \(0.347814\pi\)
\(740\) −30.2472 −1.11191
\(741\) 49.1890 1.80700
\(742\) −18.7459 −0.688185
\(743\) −22.4347 −0.823051 −0.411526 0.911398i \(-0.635004\pi\)
−0.411526 + 0.911398i \(0.635004\pi\)
\(744\) −0.316627 −0.0116081
\(745\) 15.2292 0.557956
\(746\) −5.16392 −0.189065
\(747\) −5.42221 −0.198388
\(748\) −144.448 −5.28154
\(749\) −10.4851 −0.383116
\(750\) −44.9431 −1.64109
\(751\) 1.74911 0.0638259 0.0319130 0.999491i \(-0.489840\pi\)
0.0319130 + 0.999491i \(0.489840\pi\)
\(752\) −0.897752 −0.0327376
\(753\) −21.2163 −0.773164
\(754\) −100.168 −3.64791
\(755\) −0.0553473 −0.00201430
\(756\) −49.4400 −1.79811
\(757\) −15.7128 −0.571090 −0.285545 0.958365i \(-0.592175\pi\)
−0.285545 + 0.958365i \(0.592175\pi\)
\(758\) −31.0961 −1.12946
\(759\) −26.8629 −0.975060
\(760\) −64.2949 −2.33222
\(761\) −25.3025 −0.917216 −0.458608 0.888639i \(-0.651652\pi\)
−0.458608 + 0.888639i \(0.651652\pi\)
\(762\) −5.36764 −0.194449
\(763\) −18.4256 −0.667050
\(764\) 40.6699 1.47139
\(765\) −7.39018 −0.267192
\(766\) 2.06302 0.0745398
\(767\) −9.07373 −0.327633
\(768\) 48.0630 1.73433
\(769\) −50.2908 −1.81353 −0.906766 0.421634i \(-0.861457\pi\)
−0.906766 + 0.421634i \(0.861457\pi\)
\(770\) −66.3149 −2.38982
\(771\) −42.2809 −1.52271
\(772\) 62.9426 2.26535
\(773\) −2.41580 −0.0868903 −0.0434451 0.999056i \(-0.513833\pi\)
−0.0434451 + 0.999056i \(0.513833\pi\)
\(774\) 0.152790 0.00549192
\(775\) 0.0336932 0.00121030
\(776\) 26.1639 0.939228
\(777\) −13.5219 −0.485096
\(778\) −93.2922 −3.34469
\(779\) −14.4962 −0.519379
\(780\) 57.5924 2.06214
\(781\) 20.5595 0.735675
\(782\) 46.1119 1.64896
\(783\) −49.8165 −1.78030
\(784\) −5.84350 −0.208697
\(785\) −10.4444 −0.372776
\(786\) 17.7840 0.634335
\(787\) −18.1082 −0.645489 −0.322744 0.946486i \(-0.604605\pi\)
−0.322744 + 0.946486i \(0.604605\pi\)
\(788\) −42.4039 −1.51058
\(789\) −32.8481 −1.16942
\(790\) 68.5796 2.43995
\(791\) 10.1535 0.361018
\(792\) −14.8391 −0.527286
\(793\) −14.0196 −0.497850
\(794\) −33.8950 −1.20289
\(795\) 10.8602 0.385171
\(796\) −44.0520 −1.56138
\(797\) −34.3957 −1.21836 −0.609178 0.793033i \(-0.708501\pi\)
−0.609178 + 0.793033i \(0.708501\pi\)
\(798\) −59.2517 −2.09749
\(799\) −1.73437 −0.0613575
\(800\) −0.828726 −0.0292999
\(801\) 1.12846 0.0398723
\(802\) 88.6264 3.12951
\(803\) 53.2878 1.88048
\(804\) 50.0750 1.76601
\(805\) 13.9742 0.492528
\(806\) −0.495843 −0.0174653
\(807\) −22.4340 −0.789715
\(808\) 91.6088 3.22279
\(809\) 47.5598 1.67211 0.836056 0.548644i \(-0.184856\pi\)
0.836056 + 0.548644i \(0.184856\pi\)
\(810\) 35.0024 1.22986
\(811\) 31.9953 1.12351 0.561754 0.827305i \(-0.310127\pi\)
0.561754 + 0.827305i \(0.310127\pi\)
\(812\) 79.6486 2.79512
\(813\) 25.8721 0.907376
\(814\) −53.2067 −1.86489
\(815\) −24.3238 −0.852026
\(816\) −33.2408 −1.16366
\(817\) 0.768705 0.0268936
\(818\) 31.2662 1.09320
\(819\) −5.90577 −0.206364
\(820\) −16.9727 −0.592712
\(821\) −6.66881 −0.232743 −0.116372 0.993206i \(-0.537126\pi\)
−0.116372 + 0.993206i \(0.537126\pi\)
\(822\) −35.0042 −1.22091
\(823\) 34.1861 1.19165 0.595827 0.803113i \(-0.296824\pi\)
0.595827 + 0.803113i \(0.296824\pi\)
\(824\) −54.4205 −1.89583
\(825\) −6.88408 −0.239673
\(826\) 10.9300 0.380302
\(827\) −29.0965 −1.01178 −0.505892 0.862597i \(-0.668837\pi\)
−0.505892 + 0.862597i \(0.668837\pi\)
\(828\) 6.44609 0.224017
\(829\) 39.7742 1.38141 0.690707 0.723135i \(-0.257300\pi\)
0.690707 + 0.723135i \(0.257300\pi\)
\(830\) −48.3864 −1.67952
\(831\) 45.2668 1.57029
\(832\) 42.7917 1.48354
\(833\) −11.2891 −0.391143
\(834\) −11.0776 −0.383586
\(835\) 38.1286 1.31949
\(836\) −153.902 −5.32281
\(837\) −0.246596 −0.00852362
\(838\) 30.1075 1.04005
\(839\) −36.0138 −1.24333 −0.621667 0.783281i \(-0.713544\pi\)
−0.621667 + 0.783281i \(0.713544\pi\)
\(840\) −33.6533 −1.16115
\(841\) 51.2552 1.76742
\(842\) 0.769798 0.0265290
\(843\) 24.4397 0.841746
\(844\) 27.6980 0.953405
\(845\) 16.9820 0.584197
\(846\) −0.367290 −0.0126277
\(847\) −51.8248 −1.78072
\(848\) −11.2050 −0.384780
\(849\) −40.4295 −1.38754
\(850\) 11.8170 0.405319
\(851\) 11.2120 0.384343
\(852\) 21.5079 0.736849
\(853\) 48.1008 1.64694 0.823469 0.567361i \(-0.192036\pi\)
0.823469 + 0.567361i \(0.192036\pi\)
\(854\) 16.8876 0.577882
\(855\) −7.87386 −0.269280
\(856\) −20.9371 −0.715614
\(857\) 12.0261 0.410805 0.205402 0.978678i \(-0.434150\pi\)
0.205402 + 0.978678i \(0.434150\pi\)
\(858\) 101.309 3.45863
\(859\) 8.89951 0.303647 0.151824 0.988408i \(-0.451485\pi\)
0.151824 + 0.988408i \(0.451485\pi\)
\(860\) 0.900030 0.0306908
\(861\) −7.58760 −0.258585
\(862\) −91.8422 −3.12816
\(863\) 7.65175 0.260469 0.130234 0.991483i \(-0.458427\pi\)
0.130234 + 0.991483i \(0.458427\pi\)
\(864\) 6.06535 0.206347
\(865\) 8.16022 0.277456
\(866\) 79.6062 2.70513
\(867\) −37.6616 −1.27906
\(868\) 0.394269 0.0133823
\(869\) 79.6328 2.70136
\(870\) −69.9025 −2.36992
\(871\) 38.0405 1.28895
\(872\) −36.7930 −1.24597
\(873\) 3.20415 0.108444
\(874\) 49.1299 1.66184
\(875\) 27.1479 0.917767
\(876\) 55.7461 1.88348
\(877\) 0.0219545 0.000741352 0 0.000370676 1.00000i \(-0.499882\pi\)
0.000370676 1.00000i \(0.499882\pi\)
\(878\) 91.0495 3.07277
\(879\) −13.8978 −0.468761
\(880\) −39.6383 −1.33621
\(881\) 31.8051 1.07154 0.535771 0.844363i \(-0.320021\pi\)
0.535771 + 0.844363i \(0.320021\pi\)
\(882\) −2.39070 −0.0804992
\(883\) −24.8895 −0.837599 −0.418800 0.908079i \(-0.637549\pi\)
−0.418800 + 0.908079i \(0.637549\pi\)
\(884\) −114.795 −3.86098
\(885\) −6.33211 −0.212852
\(886\) 6.17364 0.207407
\(887\) 9.02867 0.303153 0.151577 0.988446i \(-0.451565\pi\)
0.151577 + 0.988446i \(0.451565\pi\)
\(888\) −27.0012 −0.906101
\(889\) 3.24233 0.108744
\(890\) 10.0701 0.337551
\(891\) 40.6439 1.36162
\(892\) 56.8935 1.90493
\(893\) −1.84788 −0.0618370
\(894\) 28.0251 0.937299
\(895\) −43.1361 −1.44188
\(896\) −46.5524 −1.55521
\(897\) −21.3484 −0.712801
\(898\) −74.4830 −2.48553
\(899\) 0.397271 0.0132497
\(900\) 1.65192 0.0550641
\(901\) −21.6469 −0.721162
\(902\) −29.8561 −0.994098
\(903\) 0.402356 0.0133896
\(904\) 20.2750 0.674338
\(905\) 4.60595 0.153107
\(906\) −0.101851 −0.00338377
\(907\) 1.00343 0.0333185 0.0166592 0.999861i \(-0.494697\pi\)
0.0166592 + 0.999861i \(0.494697\pi\)
\(908\) 10.1282 0.336115
\(909\) 11.2188 0.372106
\(910\) −52.7015 −1.74704
\(911\) 3.10353 0.102825 0.0514123 0.998678i \(-0.483628\pi\)
0.0514123 + 0.998678i \(0.483628\pi\)
\(912\) −35.4164 −1.17275
\(913\) −56.1851 −1.85945
\(914\) 12.3653 0.409009
\(915\) −9.78359 −0.323435
\(916\) −107.332 −3.54636
\(917\) −10.7424 −0.354747
\(918\) −86.4870 −2.85450
\(919\) −33.0360 −1.08976 −0.544878 0.838515i \(-0.683424\pi\)
−0.544878 + 0.838515i \(0.683424\pi\)
\(920\) 27.9044 0.919982
\(921\) 25.4230 0.837718
\(922\) −43.9362 −1.44696
\(923\) 16.3389 0.537802
\(924\) −80.5556 −2.65008
\(925\) 2.87327 0.0944726
\(926\) −9.30653 −0.305832
\(927\) −6.66459 −0.218894
\(928\) −9.77137 −0.320761
\(929\) 25.3858 0.832880 0.416440 0.909163i \(-0.363278\pi\)
0.416440 + 0.909163i \(0.363278\pi\)
\(930\) −0.346024 −0.0113466
\(931\) −12.0279 −0.394200
\(932\) 16.9475 0.555135
\(933\) −45.0142 −1.47370
\(934\) −86.0777 −2.81655
\(935\) −76.5772 −2.50434
\(936\) −11.7929 −0.385463
\(937\) 32.1424 1.05005 0.525024 0.851088i \(-0.324057\pi\)
0.525024 + 0.851088i \(0.324057\pi\)
\(938\) −45.8225 −1.49616
\(939\) −25.5385 −0.833419
\(940\) −2.16357 −0.0705680
\(941\) −13.9674 −0.455325 −0.227662 0.973740i \(-0.573108\pi\)
−0.227662 + 0.973740i \(0.573108\pi\)
\(942\) −19.2199 −0.626219
\(943\) 6.29143 0.204877
\(944\) 6.53314 0.212635
\(945\) −26.2100 −0.852610
\(946\) 1.58321 0.0514746
\(947\) 48.8909 1.58874 0.794370 0.607434i \(-0.207801\pi\)
0.794370 + 0.607434i \(0.207801\pi\)
\(948\) 83.3065 2.70567
\(949\) 42.3486 1.37469
\(950\) 12.5904 0.408486
\(951\) −45.7151 −1.48241
\(952\) 67.0789 2.17404
\(953\) 52.2428 1.69231 0.846155 0.532937i \(-0.178912\pi\)
0.846155 + 0.532937i \(0.178912\pi\)
\(954\) −4.58419 −0.148419
\(955\) 21.5606 0.697686
\(956\) −54.2323 −1.75400
\(957\) −81.1690 −2.62382
\(958\) 58.8788 1.90229
\(959\) 21.1443 0.682785
\(960\) 29.8623 0.963800
\(961\) −30.9980 −0.999937
\(962\) −42.2842 −1.36330
\(963\) −2.56405 −0.0826255
\(964\) −70.4805 −2.27002
\(965\) 33.3682 1.07416
\(966\) 25.7156 0.827387
\(967\) −29.1713 −0.938087 −0.469043 0.883175i \(-0.655401\pi\)
−0.469043 + 0.883175i \(0.655401\pi\)
\(968\) −103.486 −3.32617
\(969\) −68.4209 −2.19800
\(970\) 28.5930 0.918066
\(971\) −20.8016 −0.667557 −0.333778 0.942652i \(-0.608324\pi\)
−0.333778 + 0.942652i \(0.608324\pi\)
\(972\) −22.2793 −0.714610
\(973\) 6.69144 0.214518
\(974\) −36.2926 −1.16289
\(975\) −5.47089 −0.175209
\(976\) 10.0942 0.323107
\(977\) 33.6083 1.07523 0.537613 0.843192i \(-0.319326\pi\)
0.537613 + 0.843192i \(0.319326\pi\)
\(978\) −44.7610 −1.43130
\(979\) 11.6932 0.373715
\(980\) −14.0828 −0.449858
\(981\) −4.50585 −0.143861
\(982\) 69.4950 2.21768
\(983\) −24.6901 −0.787492 −0.393746 0.919219i \(-0.628821\pi\)
−0.393746 + 0.919219i \(0.628821\pi\)
\(984\) −15.1513 −0.483005
\(985\) −22.4799 −0.716268
\(986\) 139.332 4.43723
\(987\) −0.967220 −0.0307870
\(988\) −122.308 −3.89115
\(989\) −0.333623 −0.0106086
\(990\) −16.2169 −0.515406
\(991\) 46.5567 1.47892 0.739461 0.673199i \(-0.235080\pi\)
0.739461 + 0.673199i \(0.235080\pi\)
\(992\) −0.0483693 −0.00153573
\(993\) −18.1104 −0.574715
\(994\) −19.6814 −0.624257
\(995\) −23.3536 −0.740359
\(996\) −58.7771 −1.86242
\(997\) −55.2891 −1.75102 −0.875511 0.483198i \(-0.839475\pi\)
−0.875511 + 0.483198i \(0.839475\pi\)
\(998\) −75.6937 −2.39604
\(999\) −21.0291 −0.665333
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 \(a_p\))