Properties

Label 6027.2.a.bk.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.13215\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.13215 q^{2} +1.00000 q^{3} +2.54608 q^{4} +2.91322 q^{5} -2.13215 q^{6} -1.16433 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.13215 q^{2} +1.00000 q^{3} +2.54608 q^{4} +2.91322 q^{5} -2.13215 q^{6} -1.16433 q^{8} +1.00000 q^{9} -6.21144 q^{10} -1.50055 q^{11} +2.54608 q^{12} -2.14723 q^{13} +2.91322 q^{15} -2.60963 q^{16} +2.46605 q^{17} -2.13215 q^{18} -7.23455 q^{19} +7.41731 q^{20} +3.19941 q^{22} +4.49416 q^{23} -1.16433 q^{24} +3.48687 q^{25} +4.57823 q^{26} +1.00000 q^{27} -9.11879 q^{29} -6.21144 q^{30} -7.76497 q^{31} +7.89280 q^{32} -1.50055 q^{33} -5.25800 q^{34} +2.54608 q^{36} +1.76746 q^{37} +15.4252 q^{38} -2.14723 q^{39} -3.39196 q^{40} -1.00000 q^{41} +6.47180 q^{43} -3.82053 q^{44} +2.91322 q^{45} -9.58224 q^{46} -1.43939 q^{47} -2.60963 q^{48} -7.43455 q^{50} +2.46605 q^{51} -5.46703 q^{52} +3.74917 q^{53} -2.13215 q^{54} -4.37145 q^{55} -7.23455 q^{57} +19.4427 q^{58} -7.69935 q^{59} +7.41731 q^{60} +5.74045 q^{61} +16.5561 q^{62} -11.6094 q^{64} -6.25537 q^{65} +3.19941 q^{66} -13.0781 q^{67} +6.27877 q^{68} +4.49416 q^{69} -4.11377 q^{71} -1.16433 q^{72} +2.78408 q^{73} -3.76851 q^{74} +3.48687 q^{75} -18.4198 q^{76} +4.57823 q^{78} +15.6156 q^{79} -7.60243 q^{80} +1.00000 q^{81} +2.13215 q^{82} -1.23966 q^{83} +7.18416 q^{85} -13.7989 q^{86} -9.11879 q^{87} +1.74714 q^{88} -10.2933 q^{89} -6.21144 q^{90} +11.4425 q^{92} -7.76497 q^{93} +3.06901 q^{94} -21.0759 q^{95} +7.89280 q^{96} +2.93804 q^{97} -1.50055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13215 −1.50766 −0.753830 0.657069i \(-0.771796\pi\)
−0.753830 + 0.657069i \(0.771796\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.54608 1.27304
\(5\) 2.91322 1.30283 0.651417 0.758720i \(-0.274175\pi\)
0.651417 + 0.758720i \(0.274175\pi\)
\(6\) −2.13215 −0.870448
\(7\) 0 0
\(8\) −1.16433 −0.411654
\(9\) 1.00000 0.333333
\(10\) −6.21144 −1.96423
\(11\) −1.50055 −0.452434 −0.226217 0.974077i \(-0.572636\pi\)
−0.226217 + 0.974077i \(0.572636\pi\)
\(12\) 2.54608 0.734991
\(13\) −2.14723 −0.595535 −0.297768 0.954638i \(-0.596242\pi\)
−0.297768 + 0.954638i \(0.596242\pi\)
\(14\) 0 0
\(15\) 2.91322 0.752191
\(16\) −2.60963 −0.652407
\(17\) 2.46605 0.598105 0.299053 0.954237i \(-0.403329\pi\)
0.299053 + 0.954237i \(0.403329\pi\)
\(18\) −2.13215 −0.502554
\(19\) −7.23455 −1.65972 −0.829860 0.557972i \(-0.811580\pi\)
−0.829860 + 0.557972i \(0.811580\pi\)
\(20\) 7.41731 1.65856
\(21\) 0 0
\(22\) 3.19941 0.682117
\(23\) 4.49416 0.937097 0.468548 0.883438i \(-0.344777\pi\)
0.468548 + 0.883438i \(0.344777\pi\)
\(24\) −1.16433 −0.237668
\(25\) 3.48687 0.697374
\(26\) 4.57823 0.897866
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −9.11879 −1.69332 −0.846659 0.532136i \(-0.821389\pi\)
−0.846659 + 0.532136i \(0.821389\pi\)
\(30\) −6.21144 −1.13405
\(31\) −7.76497 −1.39463 −0.697315 0.716765i \(-0.745622\pi\)
−0.697315 + 0.716765i \(0.745622\pi\)
\(32\) 7.89280 1.39526
\(33\) −1.50055 −0.261213
\(34\) −5.25800 −0.901740
\(35\) 0 0
\(36\) 2.54608 0.424347
\(37\) 1.76746 0.290569 0.145285 0.989390i \(-0.453590\pi\)
0.145285 + 0.989390i \(0.453590\pi\)
\(38\) 15.4252 2.50229
\(39\) −2.14723 −0.343833
\(40\) −3.39196 −0.536316
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 6.47180 0.986941 0.493470 0.869763i \(-0.335728\pi\)
0.493470 + 0.869763i \(0.335728\pi\)
\(44\) −3.82053 −0.575967
\(45\) 2.91322 0.434278
\(46\) −9.58224 −1.41282
\(47\) −1.43939 −0.209957 −0.104979 0.994474i \(-0.533477\pi\)
−0.104979 + 0.994474i \(0.533477\pi\)
\(48\) −2.60963 −0.376667
\(49\) 0 0
\(50\) −7.43455 −1.05140
\(51\) 2.46605 0.345316
\(52\) −5.46703 −0.758141
\(53\) 3.74917 0.514988 0.257494 0.966280i \(-0.417103\pi\)
0.257494 + 0.966280i \(0.417103\pi\)
\(54\) −2.13215 −0.290149
\(55\) −4.37145 −0.589446
\(56\) 0 0
\(57\) −7.23455 −0.958240
\(58\) 19.4427 2.55295
\(59\) −7.69935 −1.00237 −0.501185 0.865340i \(-0.667102\pi\)
−0.501185 + 0.865340i \(0.667102\pi\)
\(60\) 7.41731 0.957570
\(61\) 5.74045 0.734990 0.367495 0.930026i \(-0.380216\pi\)
0.367495 + 0.930026i \(0.380216\pi\)
\(62\) 16.5561 2.10263
\(63\) 0 0
\(64\) −11.6094 −1.45118
\(65\) −6.25537 −0.775883
\(66\) 3.19941 0.393821
\(67\) −13.0781 −1.59775 −0.798874 0.601499i \(-0.794571\pi\)
−0.798874 + 0.601499i \(0.794571\pi\)
\(68\) 6.27877 0.761413
\(69\) 4.49416 0.541033
\(70\) 0 0
\(71\) −4.11377 −0.488215 −0.244107 0.969748i \(-0.578495\pi\)
−0.244107 + 0.969748i \(0.578495\pi\)
\(72\) −1.16433 −0.137218
\(73\) 2.78408 0.325852 0.162926 0.986638i \(-0.447907\pi\)
0.162926 + 0.986638i \(0.447907\pi\)
\(74\) −3.76851 −0.438080
\(75\) 3.48687 0.402629
\(76\) −18.4198 −2.11289
\(77\) 0 0
\(78\) 4.57823 0.518383
\(79\) 15.6156 1.75690 0.878448 0.477838i \(-0.158580\pi\)
0.878448 + 0.477838i \(0.158580\pi\)
\(80\) −7.60243 −0.849977
\(81\) 1.00000 0.111111
\(82\) 2.13215 0.235457
\(83\) −1.23966 −0.136071 −0.0680353 0.997683i \(-0.521673\pi\)
−0.0680353 + 0.997683i \(0.521673\pi\)
\(84\) 0 0
\(85\) 7.18416 0.779232
\(86\) −13.7989 −1.48797
\(87\) −9.11879 −0.977637
\(88\) 1.74714 0.186246
\(89\) −10.2933 −1.09109 −0.545546 0.838081i \(-0.683678\pi\)
−0.545546 + 0.838081i \(0.683678\pi\)
\(90\) −6.21144 −0.654744
\(91\) 0 0
\(92\) 11.4425 1.19296
\(93\) −7.76497 −0.805190
\(94\) 3.06901 0.316544
\(95\) −21.0759 −2.16234
\(96\) 7.89280 0.805555
\(97\) 2.93804 0.298312 0.149156 0.988814i \(-0.452344\pi\)
0.149156 + 0.988814i \(0.452344\pi\)
\(98\) 0 0
\(99\) −1.50055 −0.150811
\(100\) 8.87786 0.887786
\(101\) −9.85932 −0.981039 −0.490520 0.871430i \(-0.663193\pi\)
−0.490520 + 0.871430i \(0.663193\pi\)
\(102\) −5.25800 −0.520620
\(103\) 5.59038 0.550836 0.275418 0.961325i \(-0.411184\pi\)
0.275418 + 0.961325i \(0.411184\pi\)
\(104\) 2.50010 0.245155
\(105\) 0 0
\(106\) −7.99380 −0.776427
\(107\) 13.7382 1.32812 0.664062 0.747678i \(-0.268831\pi\)
0.664062 + 0.747678i \(0.268831\pi\)
\(108\) 2.54608 0.244997
\(109\) −16.8992 −1.61865 −0.809323 0.587364i \(-0.800166\pi\)
−0.809323 + 0.587364i \(0.800166\pi\)
\(110\) 9.32061 0.888685
\(111\) 1.76746 0.167760
\(112\) 0 0
\(113\) −12.2739 −1.15463 −0.577315 0.816522i \(-0.695899\pi\)
−0.577315 + 0.816522i \(0.695899\pi\)
\(114\) 15.4252 1.44470
\(115\) 13.0925 1.22088
\(116\) −23.2172 −2.15566
\(117\) −2.14723 −0.198512
\(118\) 16.4162 1.51123
\(119\) 0 0
\(120\) −3.39196 −0.309642
\(121\) −8.74834 −0.795303
\(122\) −12.2395 −1.10811
\(123\) −1.00000 −0.0901670
\(124\) −19.7703 −1.77542
\(125\) −4.40808 −0.394271
\(126\) 0 0
\(127\) 9.83504 0.872719 0.436359 0.899773i \(-0.356268\pi\)
0.436359 + 0.899773i \(0.356268\pi\)
\(128\) 8.96745 0.792618
\(129\) 6.47180 0.569811
\(130\) 13.3374 1.16977
\(131\) −1.68941 −0.147605 −0.0738024 0.997273i \(-0.523513\pi\)
−0.0738024 + 0.997273i \(0.523513\pi\)
\(132\) −3.82053 −0.332535
\(133\) 0 0
\(134\) 27.8846 2.40886
\(135\) 2.91322 0.250730
\(136\) −2.87131 −0.246212
\(137\) −18.7959 −1.60584 −0.802921 0.596085i \(-0.796722\pi\)
−0.802921 + 0.596085i \(0.796722\pi\)
\(138\) −9.58224 −0.815695
\(139\) 3.46444 0.293850 0.146925 0.989148i \(-0.453062\pi\)
0.146925 + 0.989148i \(0.453062\pi\)
\(140\) 0 0
\(141\) −1.43939 −0.121219
\(142\) 8.77120 0.736062
\(143\) 3.22204 0.269441
\(144\) −2.60963 −0.217469
\(145\) −26.5651 −2.20611
\(146\) −5.93610 −0.491275
\(147\) 0 0
\(148\) 4.50011 0.369907
\(149\) −22.5119 −1.84424 −0.922121 0.386901i \(-0.873546\pi\)
−0.922121 + 0.386901i \(0.873546\pi\)
\(150\) −7.43455 −0.607028
\(151\) −15.5398 −1.26461 −0.632307 0.774718i \(-0.717892\pi\)
−0.632307 + 0.774718i \(0.717892\pi\)
\(152\) 8.42343 0.683230
\(153\) 2.46605 0.199368
\(154\) 0 0
\(155\) −22.6211 −1.81697
\(156\) −5.46703 −0.437713
\(157\) −20.4910 −1.63536 −0.817680 0.575674i \(-0.804740\pi\)
−0.817680 + 0.575674i \(0.804740\pi\)
\(158\) −33.2949 −2.64880
\(159\) 3.74917 0.297328
\(160\) 22.9935 1.81779
\(161\) 0 0
\(162\) −2.13215 −0.167518
\(163\) 11.4712 0.898495 0.449247 0.893407i \(-0.351692\pi\)
0.449247 + 0.893407i \(0.351692\pi\)
\(164\) −2.54608 −0.198816
\(165\) −4.37145 −0.340317
\(166\) 2.64315 0.205148
\(167\) 1.21433 0.0939673 0.0469837 0.998896i \(-0.485039\pi\)
0.0469837 + 0.998896i \(0.485039\pi\)
\(168\) 0 0
\(169\) −8.38939 −0.645338
\(170\) −15.3177 −1.17482
\(171\) −7.23455 −0.553240
\(172\) 16.4778 1.25642
\(173\) 18.3164 1.39257 0.696285 0.717765i \(-0.254835\pi\)
0.696285 + 0.717765i \(0.254835\pi\)
\(174\) 19.4427 1.47395
\(175\) 0 0
\(176\) 3.91589 0.295171
\(177\) −7.69935 −0.578719
\(178\) 21.9470 1.64500
\(179\) 7.80070 0.583052 0.291526 0.956563i \(-0.405837\pi\)
0.291526 + 0.956563i \(0.405837\pi\)
\(180\) 7.41731 0.552854
\(181\) 2.11732 0.157379 0.0786894 0.996899i \(-0.474926\pi\)
0.0786894 + 0.996899i \(0.474926\pi\)
\(182\) 0 0
\(183\) 5.74045 0.424346
\(184\) −5.23270 −0.385760
\(185\) 5.14902 0.378563
\(186\) 16.5561 1.21395
\(187\) −3.70044 −0.270603
\(188\) −3.66481 −0.267284
\(189\) 0 0
\(190\) 44.9370 3.26007
\(191\) −20.0465 −1.45051 −0.725256 0.688479i \(-0.758279\pi\)
−0.725256 + 0.688479i \(0.758279\pi\)
\(192\) −11.6094 −0.837837
\(193\) −8.66357 −0.623618 −0.311809 0.950145i \(-0.600935\pi\)
−0.311809 + 0.950145i \(0.600935\pi\)
\(194\) −6.26435 −0.449754
\(195\) −6.25537 −0.447956
\(196\) 0 0
\(197\) 10.9064 0.777051 0.388525 0.921438i \(-0.372985\pi\)
0.388525 + 0.921438i \(0.372985\pi\)
\(198\) 3.19941 0.227372
\(199\) −18.3904 −1.30366 −0.651829 0.758366i \(-0.725998\pi\)
−0.651829 + 0.758366i \(0.725998\pi\)
\(200\) −4.05988 −0.287077
\(201\) −13.0781 −0.922460
\(202\) 21.0216 1.47907
\(203\) 0 0
\(204\) 6.27877 0.439602
\(205\) −2.91322 −0.203468
\(206\) −11.9195 −0.830474
\(207\) 4.49416 0.312366
\(208\) 5.60348 0.388531
\(209\) 10.8558 0.750914
\(210\) 0 0
\(211\) 24.2561 1.66986 0.834928 0.550358i \(-0.185509\pi\)
0.834928 + 0.550358i \(0.185509\pi\)
\(212\) 9.54569 0.655601
\(213\) −4.11377 −0.281871
\(214\) −29.2920 −2.00236
\(215\) 18.8538 1.28582
\(216\) −1.16433 −0.0792228
\(217\) 0 0
\(218\) 36.0316 2.44037
\(219\) 2.78408 0.188131
\(220\) −11.1301 −0.750389
\(221\) −5.29519 −0.356193
\(222\) −3.76851 −0.252926
\(223\) −10.0523 −0.673149 −0.336574 0.941657i \(-0.609268\pi\)
−0.336574 + 0.941657i \(0.609268\pi\)
\(224\) 0 0
\(225\) 3.48687 0.232458
\(226\) 26.1698 1.74079
\(227\) −3.70831 −0.246129 −0.123065 0.992399i \(-0.539272\pi\)
−0.123065 + 0.992399i \(0.539272\pi\)
\(228\) −18.4198 −1.21988
\(229\) −0.627708 −0.0414801 −0.0207401 0.999785i \(-0.506602\pi\)
−0.0207401 + 0.999785i \(0.506602\pi\)
\(230\) −27.9152 −1.84067
\(231\) 0 0
\(232\) 10.6173 0.697061
\(233\) −5.69247 −0.372926 −0.186463 0.982462i \(-0.559702\pi\)
−0.186463 + 0.982462i \(0.559702\pi\)
\(234\) 4.57823 0.299289
\(235\) −4.19327 −0.273539
\(236\) −19.6032 −1.27606
\(237\) 15.6156 1.01434
\(238\) 0 0
\(239\) −2.28786 −0.147989 −0.0739947 0.997259i \(-0.523575\pi\)
−0.0739947 + 0.997259i \(0.523575\pi\)
\(240\) −7.60243 −0.490735
\(241\) 9.22536 0.594258 0.297129 0.954837i \(-0.403971\pi\)
0.297129 + 0.954837i \(0.403971\pi\)
\(242\) 18.6528 1.19905
\(243\) 1.00000 0.0641500
\(244\) 14.6157 0.935672
\(245\) 0 0
\(246\) 2.13215 0.135941
\(247\) 15.5343 0.988422
\(248\) 9.04101 0.574105
\(249\) −1.23966 −0.0785604
\(250\) 9.39871 0.594427
\(251\) −3.04049 −0.191914 −0.0959569 0.995385i \(-0.530591\pi\)
−0.0959569 + 0.995385i \(0.530591\pi\)
\(252\) 0 0
\(253\) −6.74373 −0.423975
\(254\) −20.9698 −1.31576
\(255\) 7.18416 0.449890
\(256\) 4.09881 0.256176
\(257\) 21.7197 1.35484 0.677418 0.735599i \(-0.263099\pi\)
0.677418 + 0.735599i \(0.263099\pi\)
\(258\) −13.7989 −0.859081
\(259\) 0 0
\(260\) −15.9267 −0.987732
\(261\) −9.11879 −0.564439
\(262\) 3.60209 0.222538
\(263\) −0.758785 −0.0467887 −0.0233944 0.999726i \(-0.507447\pi\)
−0.0233944 + 0.999726i \(0.507447\pi\)
\(264\) 1.74714 0.107529
\(265\) 10.9222 0.670943
\(266\) 0 0
\(267\) −10.2933 −0.629942
\(268\) −33.2980 −2.03400
\(269\) −9.21857 −0.562066 −0.281033 0.959698i \(-0.590677\pi\)
−0.281033 + 0.959698i \(0.590677\pi\)
\(270\) −6.21144 −0.378016
\(271\) 21.9651 1.33429 0.667143 0.744930i \(-0.267517\pi\)
0.667143 + 0.744930i \(0.267517\pi\)
\(272\) −6.43548 −0.390208
\(273\) 0 0
\(274\) 40.0758 2.42107
\(275\) −5.23224 −0.315516
\(276\) 11.4425 0.688758
\(277\) 17.9529 1.07869 0.539343 0.842086i \(-0.318673\pi\)
0.539343 + 0.842086i \(0.318673\pi\)
\(278\) −7.38672 −0.443026
\(279\) −7.76497 −0.464877
\(280\) 0 0
\(281\) −22.5886 −1.34752 −0.673761 0.738949i \(-0.735322\pi\)
−0.673761 + 0.738949i \(0.735322\pi\)
\(282\) 3.06901 0.182757
\(283\) 13.7918 0.819835 0.409917 0.912123i \(-0.365558\pi\)
0.409917 + 0.912123i \(0.365558\pi\)
\(284\) −10.4740 −0.621518
\(285\) −21.0759 −1.24843
\(286\) −6.86989 −0.406225
\(287\) 0 0
\(288\) 7.89280 0.465087
\(289\) −10.9186 −0.642270
\(290\) 56.6409 3.32607
\(291\) 2.93804 0.172231
\(292\) 7.08851 0.414824
\(293\) −7.85590 −0.458947 −0.229473 0.973315i \(-0.573700\pi\)
−0.229473 + 0.973315i \(0.573700\pi\)
\(294\) 0 0
\(295\) −22.4299 −1.30592
\(296\) −2.05792 −0.119614
\(297\) −1.50055 −0.0870710
\(298\) 47.9988 2.78049
\(299\) −9.65001 −0.558074
\(300\) 8.87786 0.512564
\(301\) 0 0
\(302\) 33.1333 1.90661
\(303\) −9.85932 −0.566403
\(304\) 18.8795 1.08281
\(305\) 16.7232 0.957569
\(306\) −5.25800 −0.300580
\(307\) −12.8613 −0.734035 −0.367018 0.930214i \(-0.619621\pi\)
−0.367018 + 0.930214i \(0.619621\pi\)
\(308\) 0 0
\(309\) 5.59038 0.318025
\(310\) 48.2317 2.73937
\(311\) 15.5497 0.881742 0.440871 0.897570i \(-0.354670\pi\)
0.440871 + 0.897570i \(0.354670\pi\)
\(312\) 2.50010 0.141540
\(313\) −27.1677 −1.53561 −0.767804 0.640685i \(-0.778651\pi\)
−0.767804 + 0.640685i \(0.778651\pi\)
\(314\) 43.6900 2.46557
\(315\) 0 0
\(316\) 39.7587 2.23660
\(317\) 2.98972 0.167920 0.0839598 0.996469i \(-0.473243\pi\)
0.0839598 + 0.996469i \(0.473243\pi\)
\(318\) −7.99380 −0.448270
\(319\) 13.6832 0.766114
\(320\) −33.8208 −1.89064
\(321\) 13.7382 0.766792
\(322\) 0 0
\(323\) −17.8408 −0.992687
\(324\) 2.54608 0.141449
\(325\) −7.48713 −0.415311
\(326\) −24.4584 −1.35463
\(327\) −16.8992 −0.934526
\(328\) 1.16433 0.0642895
\(329\) 0 0
\(330\) 9.32061 0.513082
\(331\) 11.4220 0.627809 0.313904 0.949455i \(-0.398363\pi\)
0.313904 + 0.949455i \(0.398363\pi\)
\(332\) −3.15628 −0.173224
\(333\) 1.76746 0.0968564
\(334\) −2.58913 −0.141671
\(335\) −38.0995 −2.08160
\(336\) 0 0
\(337\) 5.89417 0.321076 0.160538 0.987030i \(-0.448677\pi\)
0.160538 + 0.987030i \(0.448677\pi\)
\(338\) 17.8875 0.972950
\(339\) −12.2739 −0.666626
\(340\) 18.2915 0.991994
\(341\) 11.6518 0.630978
\(342\) 15.4252 0.834098
\(343\) 0 0
\(344\) −7.53534 −0.406278
\(345\) 13.0925 0.704876
\(346\) −39.0534 −2.09952
\(347\) −4.45569 −0.239194 −0.119597 0.992823i \(-0.538160\pi\)
−0.119597 + 0.992823i \(0.538160\pi\)
\(348\) −23.2172 −1.24457
\(349\) 12.0671 0.645940 0.322970 0.946409i \(-0.395319\pi\)
0.322970 + 0.946409i \(0.395319\pi\)
\(350\) 0 0
\(351\) −2.14723 −0.114611
\(352\) −11.8436 −0.631264
\(353\) −28.3315 −1.50793 −0.753966 0.656913i \(-0.771862\pi\)
−0.753966 + 0.656913i \(0.771862\pi\)
\(354\) 16.4162 0.872512
\(355\) −11.9843 −0.636063
\(356\) −26.2077 −1.38901
\(357\) 0 0
\(358\) −16.6323 −0.879044
\(359\) 15.1427 0.799203 0.399601 0.916689i \(-0.369149\pi\)
0.399601 + 0.916689i \(0.369149\pi\)
\(360\) −3.39196 −0.178772
\(361\) 33.3387 1.75467
\(362\) −4.51444 −0.237274
\(363\) −8.74834 −0.459169
\(364\) 0 0
\(365\) 8.11066 0.424531
\(366\) −12.2395 −0.639770
\(367\) 15.8017 0.824844 0.412422 0.910993i \(-0.364683\pi\)
0.412422 + 0.910993i \(0.364683\pi\)
\(368\) −11.7281 −0.611369
\(369\) −1.00000 −0.0520579
\(370\) −10.9785 −0.570745
\(371\) 0 0
\(372\) −19.7703 −1.02504
\(373\) 12.4879 0.646601 0.323301 0.946296i \(-0.395207\pi\)
0.323301 + 0.946296i \(0.395207\pi\)
\(374\) 7.88992 0.407978
\(375\) −4.40808 −0.227632
\(376\) 1.67593 0.0864296
\(377\) 19.5802 1.00843
\(378\) 0 0
\(379\) 3.92589 0.201659 0.100830 0.994904i \(-0.467850\pi\)
0.100830 + 0.994904i \(0.467850\pi\)
\(380\) −53.6609 −2.75275
\(381\) 9.83504 0.503864
\(382\) 42.7422 2.18688
\(383\) −12.8664 −0.657443 −0.328721 0.944427i \(-0.606618\pi\)
−0.328721 + 0.944427i \(0.606618\pi\)
\(384\) 8.96745 0.457618
\(385\) 0 0
\(386\) 18.4721 0.940204
\(387\) 6.47180 0.328980
\(388\) 7.48049 0.379764
\(389\) 24.1359 1.22374 0.611868 0.790960i \(-0.290418\pi\)
0.611868 + 0.790960i \(0.290418\pi\)
\(390\) 13.3374 0.675366
\(391\) 11.0828 0.560483
\(392\) 0 0
\(393\) −1.68941 −0.0852197
\(394\) −23.2542 −1.17153
\(395\) 45.4918 2.28894
\(396\) −3.82053 −0.191989
\(397\) 16.9939 0.852902 0.426451 0.904511i \(-0.359764\pi\)
0.426451 + 0.904511i \(0.359764\pi\)
\(398\) 39.2111 1.96547
\(399\) 0 0
\(400\) −9.09944 −0.454972
\(401\) 16.8777 0.842830 0.421415 0.906868i \(-0.361534\pi\)
0.421415 + 0.906868i \(0.361534\pi\)
\(402\) 27.8846 1.39076
\(403\) 16.6732 0.830551
\(404\) −25.1026 −1.24890
\(405\) 2.91322 0.144759
\(406\) 0 0
\(407\) −2.65217 −0.131463
\(408\) −2.87131 −0.142151
\(409\) −23.3733 −1.15573 −0.577867 0.816131i \(-0.696115\pi\)
−0.577867 + 0.816131i \(0.696115\pi\)
\(410\) 6.21144 0.306761
\(411\) −18.7959 −0.927133
\(412\) 14.2336 0.701237
\(413\) 0 0
\(414\) −9.58224 −0.470941
\(415\) −3.61141 −0.177277
\(416\) −16.9477 −0.830928
\(417\) 3.46444 0.169654
\(418\) −23.1463 −1.13212
\(419\) 0.638417 0.0311887 0.0155944 0.999878i \(-0.495036\pi\)
0.0155944 + 0.999878i \(0.495036\pi\)
\(420\) 0 0
\(421\) −34.1543 −1.66458 −0.832290 0.554340i \(-0.812971\pi\)
−0.832290 + 0.554340i \(0.812971\pi\)
\(422\) −51.7177 −2.51758
\(423\) −1.43939 −0.0699857
\(424\) −4.36528 −0.211997
\(425\) 8.59881 0.417103
\(426\) 8.77120 0.424966
\(427\) 0 0
\(428\) 34.9786 1.69076
\(429\) 3.22204 0.155562
\(430\) −40.1992 −1.93858
\(431\) −17.8141 −0.858073 −0.429036 0.903287i \(-0.641147\pi\)
−0.429036 + 0.903287i \(0.641147\pi\)
\(432\) −2.60963 −0.125556
\(433\) −18.6108 −0.894379 −0.447189 0.894439i \(-0.647575\pi\)
−0.447189 + 0.894439i \(0.647575\pi\)
\(434\) 0 0
\(435\) −26.5651 −1.27370
\(436\) −43.0267 −2.06060
\(437\) −32.5132 −1.55532
\(438\) −5.93610 −0.283638
\(439\) 30.0312 1.43331 0.716654 0.697428i \(-0.245673\pi\)
0.716654 + 0.697428i \(0.245673\pi\)
\(440\) 5.08982 0.242648
\(441\) 0 0
\(442\) 11.2902 0.537018
\(443\) 10.6865 0.507730 0.253865 0.967240i \(-0.418298\pi\)
0.253865 + 0.967240i \(0.418298\pi\)
\(444\) 4.50011 0.213566
\(445\) −29.9868 −1.42151
\(446\) 21.4330 1.01488
\(447\) −22.5119 −1.06477
\(448\) 0 0
\(449\) −10.0579 −0.474660 −0.237330 0.971429i \(-0.576272\pi\)
−0.237330 + 0.971429i \(0.576272\pi\)
\(450\) −7.43455 −0.350468
\(451\) 1.50055 0.0706583
\(452\) −31.2503 −1.46989
\(453\) −15.5398 −0.730125
\(454\) 7.90670 0.371080
\(455\) 0 0
\(456\) 8.42343 0.394463
\(457\) 28.5745 1.33666 0.668330 0.743865i \(-0.267010\pi\)
0.668330 + 0.743865i \(0.267010\pi\)
\(458\) 1.33837 0.0625380
\(459\) 2.46605 0.115105
\(460\) 33.3346 1.55423
\(461\) −9.51845 −0.443318 −0.221659 0.975124i \(-0.571147\pi\)
−0.221659 + 0.975124i \(0.571147\pi\)
\(462\) 0 0
\(463\) 31.0602 1.44349 0.721745 0.692159i \(-0.243340\pi\)
0.721745 + 0.692159i \(0.243340\pi\)
\(464\) 23.7967 1.10473
\(465\) −22.6211 −1.04903
\(466\) 12.1372 0.562246
\(467\) −22.7912 −1.05465 −0.527325 0.849663i \(-0.676805\pi\)
−0.527325 + 0.849663i \(0.676805\pi\)
\(468\) −5.46703 −0.252714
\(469\) 0 0
\(470\) 8.94071 0.412404
\(471\) −20.4910 −0.944175
\(472\) 8.96461 0.412630
\(473\) −9.71129 −0.446526
\(474\) −33.2949 −1.52929
\(475\) −25.2260 −1.15745
\(476\) 0 0
\(477\) 3.74917 0.171663
\(478\) 4.87807 0.223118
\(479\) −34.2503 −1.56493 −0.782467 0.622692i \(-0.786039\pi\)
−0.782467 + 0.622692i \(0.786039\pi\)
\(480\) 22.9935 1.04950
\(481\) −3.79516 −0.173044
\(482\) −19.6699 −0.895939
\(483\) 0 0
\(484\) −22.2740 −1.01245
\(485\) 8.55916 0.388651
\(486\) −2.13215 −0.0967165
\(487\) −9.18232 −0.416091 −0.208045 0.978119i \(-0.566710\pi\)
−0.208045 + 0.978119i \(0.566710\pi\)
\(488\) −6.68380 −0.302561
\(489\) 11.4712 0.518746
\(490\) 0 0
\(491\) −17.8804 −0.806931 −0.403465 0.914995i \(-0.632194\pi\)
−0.403465 + 0.914995i \(0.632194\pi\)
\(492\) −2.54608 −0.114786
\(493\) −22.4874 −1.01278
\(494\) −33.1215 −1.49021
\(495\) −4.37145 −0.196482
\(496\) 20.2637 0.909866
\(497\) 0 0
\(498\) 2.64315 0.118442
\(499\) −23.6303 −1.05784 −0.528919 0.848672i \(-0.677402\pi\)
−0.528919 + 0.848672i \(0.677402\pi\)
\(500\) −11.2233 −0.501923
\(501\) 1.21433 0.0542521
\(502\) 6.48278 0.289341
\(503\) 37.0939 1.65394 0.826968 0.562249i \(-0.190064\pi\)
0.826968 + 0.562249i \(0.190064\pi\)
\(504\) 0 0
\(505\) −28.7224 −1.27813
\(506\) 14.3787 0.639210
\(507\) −8.38939 −0.372586
\(508\) 25.0408 1.11101
\(509\) −35.2024 −1.56032 −0.780158 0.625582i \(-0.784862\pi\)
−0.780158 + 0.625582i \(0.784862\pi\)
\(510\) −15.3177 −0.678281
\(511\) 0 0
\(512\) −26.6742 −1.17884
\(513\) −7.23455 −0.319413
\(514\) −46.3097 −2.04263
\(515\) 16.2860 0.717648
\(516\) 16.4778 0.725393
\(517\) 2.15989 0.0949917
\(518\) 0 0
\(519\) 18.3164 0.804001
\(520\) 7.28334 0.319395
\(521\) 24.0907 1.05543 0.527715 0.849421i \(-0.323049\pi\)
0.527715 + 0.849421i \(0.323049\pi\)
\(522\) 19.4427 0.850983
\(523\) 10.2611 0.448687 0.224343 0.974510i \(-0.427976\pi\)
0.224343 + 0.974510i \(0.427976\pi\)
\(524\) −4.30139 −0.187907
\(525\) 0 0
\(526\) 1.61785 0.0705415
\(527\) −19.1488 −0.834136
\(528\) 3.91589 0.170417
\(529\) −2.80253 −0.121849
\(530\) −23.2877 −1.01155
\(531\) −7.69935 −0.334123
\(532\) 0 0
\(533\) 2.14723 0.0930070
\(534\) 21.9470 0.949739
\(535\) 40.0225 1.73032
\(536\) 15.2273 0.657719
\(537\) 7.80070 0.336625
\(538\) 19.6554 0.847406
\(539\) 0 0
\(540\) 7.41731 0.319190
\(541\) 34.4179 1.47974 0.739870 0.672750i \(-0.234887\pi\)
0.739870 + 0.672750i \(0.234887\pi\)
\(542\) −46.8330 −2.01165
\(543\) 2.11732 0.0908627
\(544\) 19.4640 0.834514
\(545\) −49.2310 −2.10883
\(546\) 0 0
\(547\) 29.2749 1.25171 0.625853 0.779941i \(-0.284751\pi\)
0.625853 + 0.779941i \(0.284751\pi\)
\(548\) −47.8559 −2.04430
\(549\) 5.74045 0.244997
\(550\) 11.1559 0.475691
\(551\) 65.9704 2.81043
\(552\) −5.23270 −0.222718
\(553\) 0 0
\(554\) −38.2784 −1.62629
\(555\) 5.14902 0.218564
\(556\) 8.82075 0.374083
\(557\) 33.6058 1.42392 0.711961 0.702219i \(-0.247807\pi\)
0.711961 + 0.702219i \(0.247807\pi\)
\(558\) 16.5561 0.700876
\(559\) −13.8965 −0.587758
\(560\) 0 0
\(561\) −3.70044 −0.156233
\(562\) 48.1623 2.03161
\(563\) −37.6392 −1.58630 −0.793152 0.609024i \(-0.791561\pi\)
−0.793152 + 0.609024i \(0.791561\pi\)
\(564\) −3.66481 −0.154316
\(565\) −35.7566 −1.50429
\(566\) −29.4062 −1.23603
\(567\) 0 0
\(568\) 4.78980 0.200976
\(569\) 16.5430 0.693520 0.346760 0.937954i \(-0.387282\pi\)
0.346760 + 0.937954i \(0.387282\pi\)
\(570\) 44.9370 1.88220
\(571\) −8.67402 −0.362997 −0.181498 0.983391i \(-0.558095\pi\)
−0.181498 + 0.983391i \(0.558095\pi\)
\(572\) 8.20358 0.343009
\(573\) −20.0465 −0.837454
\(574\) 0 0
\(575\) 15.6706 0.653507
\(576\) −11.6094 −0.483725
\(577\) 13.6404 0.567857 0.283929 0.958845i \(-0.408362\pi\)
0.283929 + 0.958845i \(0.408362\pi\)
\(578\) 23.2801 0.968325
\(579\) −8.66357 −0.360046
\(580\) −67.6369 −2.80847
\(581\) 0 0
\(582\) −6.26435 −0.259666
\(583\) −5.62583 −0.232998
\(584\) −3.24160 −0.134138
\(585\) −6.25537 −0.258628
\(586\) 16.7500 0.691936
\(587\) −8.81891 −0.363996 −0.181998 0.983299i \(-0.558256\pi\)
−0.181998 + 0.983299i \(0.558256\pi\)
\(588\) 0 0
\(589\) 56.1761 2.31469
\(590\) 47.8241 1.96889
\(591\) 10.9064 0.448631
\(592\) −4.61242 −0.189569
\(593\) 39.9050 1.63870 0.819351 0.573292i \(-0.194334\pi\)
0.819351 + 0.573292i \(0.194334\pi\)
\(594\) 3.19941 0.131274
\(595\) 0 0
\(596\) −57.3170 −2.34780
\(597\) −18.3904 −0.752667
\(598\) 20.5753 0.841387
\(599\) 10.0955 0.412493 0.206246 0.978500i \(-0.433875\pi\)
0.206246 + 0.978500i \(0.433875\pi\)
\(600\) −4.05988 −0.165744
\(601\) 9.21459 0.375871 0.187935 0.982181i \(-0.439820\pi\)
0.187935 + 0.982181i \(0.439820\pi\)
\(602\) 0 0
\(603\) −13.0781 −0.532583
\(604\) −39.5657 −1.60991
\(605\) −25.4859 −1.03615
\(606\) 21.0216 0.853944
\(607\) −39.5129 −1.60378 −0.801890 0.597471i \(-0.796172\pi\)
−0.801890 + 0.597471i \(0.796172\pi\)
\(608\) −57.1008 −2.31574
\(609\) 0 0
\(610\) −35.6565 −1.44369
\(611\) 3.09071 0.125037
\(612\) 6.27877 0.253804
\(613\) −19.9530 −0.805895 −0.402947 0.915223i \(-0.632014\pi\)
−0.402947 + 0.915223i \(0.632014\pi\)
\(614\) 27.4224 1.10668
\(615\) −2.91322 −0.117473
\(616\) 0 0
\(617\) 5.18441 0.208716 0.104358 0.994540i \(-0.466721\pi\)
0.104358 + 0.994540i \(0.466721\pi\)
\(618\) −11.9195 −0.479475
\(619\) 13.6896 0.550233 0.275117 0.961411i \(-0.411284\pi\)
0.275117 + 0.961411i \(0.411284\pi\)
\(620\) −57.5952 −2.31308
\(621\) 4.49416 0.180344
\(622\) −33.1543 −1.32937
\(623\) 0 0
\(624\) 5.60348 0.224319
\(625\) −30.2761 −1.21104
\(626\) 57.9257 2.31518
\(627\) 10.8558 0.433540
\(628\) −52.1718 −2.08188
\(629\) 4.35866 0.173791
\(630\) 0 0
\(631\) 42.1111 1.67642 0.838209 0.545350i \(-0.183603\pi\)
0.838209 + 0.545350i \(0.183603\pi\)
\(632\) −18.1818 −0.723233
\(633\) 24.2561 0.964092
\(634\) −6.37455 −0.253166
\(635\) 28.6517 1.13701
\(636\) 9.54569 0.378511
\(637\) 0 0
\(638\) −29.1748 −1.15504
\(639\) −4.11377 −0.162738
\(640\) 26.1242 1.03265
\(641\) −3.51098 −0.138676 −0.0693378 0.997593i \(-0.522089\pi\)
−0.0693378 + 0.997593i \(0.522089\pi\)
\(642\) −29.2920 −1.15606
\(643\) −36.4566 −1.43771 −0.718854 0.695161i \(-0.755333\pi\)
−0.718854 + 0.695161i \(0.755333\pi\)
\(644\) 0 0
\(645\) 18.8538 0.742368
\(646\) 38.0393 1.49664
\(647\) −14.4875 −0.569564 −0.284782 0.958592i \(-0.591921\pi\)
−0.284782 + 0.958592i \(0.591921\pi\)
\(648\) −1.16433 −0.0457393
\(649\) 11.5533 0.453507
\(650\) 15.9637 0.626148
\(651\) 0 0
\(652\) 29.2067 1.14382
\(653\) 26.6506 1.04292 0.521458 0.853277i \(-0.325388\pi\)
0.521458 + 0.853277i \(0.325388\pi\)
\(654\) 36.0316 1.40895
\(655\) −4.92164 −0.192304
\(656\) 2.60963 0.101889
\(657\) 2.78408 0.108617
\(658\) 0 0
\(659\) −36.9262 −1.43844 −0.719220 0.694782i \(-0.755501\pi\)
−0.719220 + 0.694782i \(0.755501\pi\)
\(660\) −11.1301 −0.433237
\(661\) −22.7844 −0.886210 −0.443105 0.896470i \(-0.646123\pi\)
−0.443105 + 0.896470i \(0.646123\pi\)
\(662\) −24.3534 −0.946523
\(663\) −5.29519 −0.205648
\(664\) 1.44338 0.0560140
\(665\) 0 0
\(666\) −3.76851 −0.146027
\(667\) −40.9813 −1.58680
\(668\) 3.09177 0.119624
\(669\) −10.0523 −0.388642
\(670\) 81.2340 3.13834
\(671\) −8.61386 −0.332534
\(672\) 0 0
\(673\) −22.6835 −0.874384 −0.437192 0.899368i \(-0.644027\pi\)
−0.437192 + 0.899368i \(0.644027\pi\)
\(674\) −12.5673 −0.484074
\(675\) 3.48687 0.134210
\(676\) −21.3601 −0.821541
\(677\) −47.1910 −1.81370 −0.906848 0.421457i \(-0.861519\pi\)
−0.906848 + 0.421457i \(0.861519\pi\)
\(678\) 26.1698 1.00505
\(679\) 0 0
\(680\) −8.36476 −0.320774
\(681\) −3.70831 −0.142103
\(682\) −24.8433 −0.951301
\(683\) 45.3118 1.73381 0.866904 0.498476i \(-0.166107\pi\)
0.866904 + 0.498476i \(0.166107\pi\)
\(684\) −18.4198 −0.704297
\(685\) −54.7567 −2.09214
\(686\) 0 0
\(687\) −0.627708 −0.0239486
\(688\) −16.8890 −0.643887
\(689\) −8.05034 −0.306693
\(690\) −27.9152 −1.06271
\(691\) 23.4256 0.891151 0.445576 0.895244i \(-0.352999\pi\)
0.445576 + 0.895244i \(0.352999\pi\)
\(692\) 46.6351 1.77280
\(693\) 0 0
\(694\) 9.50022 0.360623
\(695\) 10.0927 0.382838
\(696\) 10.6173 0.402448
\(697\) −2.46605 −0.0934084
\(698\) −25.7290 −0.973858
\(699\) −5.69247 −0.215309
\(700\) 0 0
\(701\) 3.95291 0.149299 0.0746496 0.997210i \(-0.476216\pi\)
0.0746496 + 0.997210i \(0.476216\pi\)
\(702\) 4.57823 0.172794
\(703\) −12.7868 −0.482264
\(704\) 17.4205 0.656561
\(705\) −4.19327 −0.157928
\(706\) 60.4071 2.27345
\(707\) 0 0
\(708\) −19.6032 −0.736733
\(709\) −43.7509 −1.64310 −0.821549 0.570137i \(-0.806890\pi\)
−0.821549 + 0.570137i \(0.806890\pi\)
\(710\) 25.5525 0.958967
\(711\) 15.6156 0.585632
\(712\) 11.9849 0.449152
\(713\) −34.8970 −1.30690
\(714\) 0 0
\(715\) 9.38652 0.351036
\(716\) 19.8612 0.742249
\(717\) −2.28786 −0.0854417
\(718\) −32.2867 −1.20493
\(719\) −39.2991 −1.46561 −0.732805 0.680439i \(-0.761789\pi\)
−0.732805 + 0.680439i \(0.761789\pi\)
\(720\) −7.60243 −0.283326
\(721\) 0 0
\(722\) −71.0833 −2.64545
\(723\) 9.22536 0.343095
\(724\) 5.39086 0.200350
\(725\) −31.7961 −1.18088
\(726\) 18.6528 0.692271
\(727\) 6.63007 0.245896 0.122948 0.992413i \(-0.460765\pi\)
0.122948 + 0.992413i \(0.460765\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −17.2932 −0.640049
\(731\) 15.9598 0.590295
\(732\) 14.6157 0.540211
\(733\) −18.4143 −0.680149 −0.340074 0.940399i \(-0.610452\pi\)
−0.340074 + 0.940399i \(0.610452\pi\)
\(734\) −33.6918 −1.24359
\(735\) 0 0
\(736\) 35.4715 1.30750
\(737\) 19.6244 0.722875
\(738\) 2.13215 0.0784857
\(739\) 45.5824 1.67678 0.838388 0.545073i \(-0.183498\pi\)
0.838388 + 0.545073i \(0.183498\pi\)
\(740\) 13.1098 0.481927
\(741\) 15.5343 0.570666
\(742\) 0 0
\(743\) 3.83501 0.140693 0.0703465 0.997523i \(-0.477590\pi\)
0.0703465 + 0.997523i \(0.477590\pi\)
\(744\) 9.04101 0.331460
\(745\) −65.5821 −2.40274
\(746\) −26.6262 −0.974855
\(747\) −1.23966 −0.0453569
\(748\) −9.42164 −0.344489
\(749\) 0 0
\(750\) 9.39871 0.343192
\(751\) −15.3335 −0.559528 −0.279764 0.960069i \(-0.590256\pi\)
−0.279764 + 0.960069i \(0.590256\pi\)
\(752\) 3.75628 0.136977
\(753\) −3.04049 −0.110801
\(754\) −41.7480 −1.52037
\(755\) −45.2710 −1.64758
\(756\) 0 0
\(757\) −40.5275 −1.47300 −0.736499 0.676439i \(-0.763522\pi\)
−0.736499 + 0.676439i \(0.763522\pi\)
\(758\) −8.37060 −0.304034
\(759\) −6.74373 −0.244782
\(760\) 24.5393 0.890135
\(761\) −49.4612 −1.79297 −0.896483 0.443077i \(-0.853887\pi\)
−0.896483 + 0.443077i \(0.853887\pi\)
\(762\) −20.9698 −0.759656
\(763\) 0 0
\(764\) −51.0400 −1.84656
\(765\) 7.18416 0.259744
\(766\) 27.4332 0.991201
\(767\) 16.5323 0.596947
\(768\) 4.09881 0.147903
\(769\) −30.7710 −1.10963 −0.554815 0.831974i \(-0.687211\pi\)
−0.554815 + 0.831974i \(0.687211\pi\)
\(770\) 0 0
\(771\) 21.7197 0.782215
\(772\) −22.0582 −0.793891
\(773\) −31.6733 −1.13921 −0.569605 0.821919i \(-0.692904\pi\)
−0.569605 + 0.821919i \(0.692904\pi\)
\(774\) −13.7989 −0.495991
\(775\) −27.0755 −0.972579
\(776\) −3.42085 −0.122801
\(777\) 0 0
\(778\) −51.4614 −1.84498
\(779\) 7.23455 0.259205
\(780\) −15.9267 −0.570267
\(781\) 6.17294 0.220885
\(782\) −23.6303 −0.845018
\(783\) −9.11879 −0.325879
\(784\) 0 0
\(785\) −59.6948 −2.13060
\(786\) 3.60209 0.128482
\(787\) −21.1978 −0.755621 −0.377810 0.925883i \(-0.623323\pi\)
−0.377810 + 0.925883i \(0.623323\pi\)
\(788\) 27.7687 0.989218
\(789\) −0.758785 −0.0270135
\(790\) −96.9956 −3.45095
\(791\) 0 0
\(792\) 1.74714 0.0620821
\(793\) −12.3261 −0.437712
\(794\) −36.2337 −1.28589
\(795\) 10.9222 0.387369
\(796\) −46.8234 −1.65961
\(797\) −39.5421 −1.40065 −0.700326 0.713823i \(-0.746962\pi\)
−0.700326 + 0.713823i \(0.746962\pi\)
\(798\) 0 0
\(799\) −3.54962 −0.125576
\(800\) 27.5212 0.973020
\(801\) −10.2933 −0.363697
\(802\) −35.9858 −1.27070
\(803\) −4.17767 −0.147427
\(804\) −33.2980 −1.17433
\(805\) 0 0
\(806\) −35.5498 −1.25219
\(807\) −9.21857 −0.324509
\(808\) 11.4795 0.403849
\(809\) 19.2888 0.678159 0.339080 0.940758i \(-0.389884\pi\)
0.339080 + 0.940758i \(0.389884\pi\)
\(810\) −6.21144 −0.218248
\(811\) 29.6499 1.04115 0.520574 0.853817i \(-0.325718\pi\)
0.520574 + 0.853817i \(0.325718\pi\)
\(812\) 0 0
\(813\) 21.9651 0.770350
\(814\) 5.65485 0.198202
\(815\) 33.4182 1.17059
\(816\) −6.43548 −0.225287
\(817\) −46.8206 −1.63805
\(818\) 49.8354 1.74245
\(819\) 0 0
\(820\) −7.41731 −0.259024
\(821\) 8.05452 0.281105 0.140552 0.990073i \(-0.455112\pi\)
0.140552 + 0.990073i \(0.455112\pi\)
\(822\) 40.0758 1.39780
\(823\) −5.13488 −0.178991 −0.0894953 0.995987i \(-0.528525\pi\)
−0.0894953 + 0.995987i \(0.528525\pi\)
\(824\) −6.50906 −0.226754
\(825\) −5.23224 −0.182163
\(826\) 0 0
\(827\) 38.1238 1.32570 0.662848 0.748754i \(-0.269348\pi\)
0.662848 + 0.748754i \(0.269348\pi\)
\(828\) 11.4425 0.397654
\(829\) 1.89733 0.0658970 0.0329485 0.999457i \(-0.489510\pi\)
0.0329485 + 0.999457i \(0.489510\pi\)
\(830\) 7.70009 0.267274
\(831\) 17.9529 0.622779
\(832\) 24.9281 0.864227
\(833\) 0 0
\(834\) −7.38672 −0.255781
\(835\) 3.53760 0.122424
\(836\) 27.6399 0.955944
\(837\) −7.76497 −0.268397
\(838\) −1.36120 −0.0470220
\(839\) −42.5450 −1.46882 −0.734408 0.678708i \(-0.762540\pi\)
−0.734408 + 0.678708i \(0.762540\pi\)
\(840\) 0 0
\(841\) 54.1524 1.86732
\(842\) 72.8223 2.50962
\(843\) −22.5886 −0.777992
\(844\) 61.7580 2.12580
\(845\) −24.4402 −0.840767
\(846\) 3.06901 0.105515
\(847\) 0 0
\(848\) −9.78393 −0.335981
\(849\) 13.7918 0.473332
\(850\) −18.3340 −0.628850
\(851\) 7.94326 0.272292
\(852\) −10.4740 −0.358833
\(853\) 17.4335 0.596913 0.298457 0.954423i \(-0.403528\pi\)
0.298457 + 0.954423i \(0.403528\pi\)
\(854\) 0 0
\(855\) −21.0759 −0.720779
\(856\) −15.9959 −0.546727
\(857\) −26.1027 −0.891653 −0.445826 0.895119i \(-0.647090\pi\)
−0.445826 + 0.895119i \(0.647090\pi\)
\(858\) −6.86989 −0.234534
\(859\) −36.5305 −1.24641 −0.623203 0.782060i \(-0.714169\pi\)
−0.623203 + 0.782060i \(0.714169\pi\)
\(860\) 48.0034 1.63690
\(861\) 0 0
\(862\) 37.9823 1.29368
\(863\) −9.24397 −0.314669 −0.157334 0.987545i \(-0.550290\pi\)
−0.157334 + 0.987545i \(0.550290\pi\)
\(864\) 7.89280 0.268518
\(865\) 53.3598 1.81429
\(866\) 39.6811 1.34842
\(867\) −10.9186 −0.370815
\(868\) 0 0
\(869\) −23.4321 −0.794879
\(870\) 56.6409 1.92031
\(871\) 28.0818 0.951515
\(872\) 19.6763 0.666322
\(873\) 2.93804 0.0994375
\(874\) 69.3232 2.34489
\(875\) 0 0
\(876\) 7.08851 0.239499
\(877\) −46.5927 −1.57332 −0.786662 0.617384i \(-0.788193\pi\)
−0.786662 + 0.617384i \(0.788193\pi\)
\(878\) −64.0311 −2.16094
\(879\) −7.85590 −0.264973
\(880\) 11.4079 0.384559
\(881\) −17.0942 −0.575918 −0.287959 0.957643i \(-0.592977\pi\)
−0.287959 + 0.957643i \(0.592977\pi\)
\(882\) 0 0
\(883\) −7.33116 −0.246713 −0.123357 0.992362i \(-0.539366\pi\)
−0.123357 + 0.992362i \(0.539366\pi\)
\(884\) −13.4820 −0.453448
\(885\) −22.4299 −0.753974
\(886\) −22.7852 −0.765485
\(887\) 9.21041 0.309255 0.154628 0.987973i \(-0.450582\pi\)
0.154628 + 0.987973i \(0.450582\pi\)
\(888\) −2.05792 −0.0690592
\(889\) 0 0
\(890\) 63.9365 2.14316
\(891\) −1.50055 −0.0502704
\(892\) −25.5939 −0.856946
\(893\) 10.4134 0.348470
\(894\) 47.9988 1.60532
\(895\) 22.7252 0.759619
\(896\) 0 0
\(897\) −9.65001 −0.322204
\(898\) 21.4449 0.715626
\(899\) 70.8071 2.36155
\(900\) 8.87786 0.295929
\(901\) 9.24564 0.308017
\(902\) −3.19941 −0.106529
\(903\) 0 0
\(904\) 14.2909 0.475308
\(905\) 6.16821 0.205038
\(906\) 33.1333 1.10078
\(907\) −1.42495 −0.0473147 −0.0236574 0.999720i \(-0.507531\pi\)
−0.0236574 + 0.999720i \(0.507531\pi\)
\(908\) −9.44167 −0.313333
\(909\) −9.85932 −0.327013
\(910\) 0 0
\(911\) 0.0834139 0.00276362 0.00138181 0.999999i \(-0.499560\pi\)
0.00138181 + 0.999999i \(0.499560\pi\)
\(912\) 18.8795 0.625162
\(913\) 1.86018 0.0615630
\(914\) −60.9253 −2.01523
\(915\) 16.7232 0.552853
\(916\) −1.59820 −0.0528059
\(917\) 0 0
\(918\) −5.25800 −0.173540
\(919\) 17.4891 0.576911 0.288456 0.957493i \(-0.406858\pi\)
0.288456 + 0.957493i \(0.406858\pi\)
\(920\) −15.2440 −0.502580
\(921\) −12.8613 −0.423795
\(922\) 20.2948 0.668374
\(923\) 8.83323 0.290749
\(924\) 0 0
\(925\) 6.16292 0.202636
\(926\) −66.2252 −2.17629
\(927\) 5.59038 0.183612
\(928\) −71.9728 −2.36262
\(929\) 37.0853 1.21673 0.608364 0.793658i \(-0.291826\pi\)
0.608364 + 0.793658i \(0.291826\pi\)
\(930\) 48.2317 1.58158
\(931\) 0 0
\(932\) −14.4935 −0.474751
\(933\) 15.5497 0.509074
\(934\) 48.5944 1.59006
\(935\) −10.7802 −0.352551
\(936\) 2.50010 0.0817182
\(937\) 51.2474 1.67418 0.837090 0.547065i \(-0.184255\pi\)
0.837090 + 0.547065i \(0.184255\pi\)
\(938\) 0 0
\(939\) −27.1677 −0.886584
\(940\) −10.6764 −0.348226
\(941\) 9.65205 0.314648 0.157324 0.987547i \(-0.449713\pi\)
0.157324 + 0.987547i \(0.449713\pi\)
\(942\) 43.6900 1.42350
\(943\) −4.49416 −0.146350
\(944\) 20.0924 0.653953
\(945\) 0 0
\(946\) 20.7060 0.673209
\(947\) −16.2966 −0.529570 −0.264785 0.964307i \(-0.585301\pi\)
−0.264785 + 0.964307i \(0.585301\pi\)
\(948\) 39.7587 1.29130
\(949\) −5.97808 −0.194057
\(950\) 53.7856 1.74504
\(951\) 2.98972 0.0969484
\(952\) 0 0
\(953\) 13.4806 0.436680 0.218340 0.975873i \(-0.429936\pi\)
0.218340 + 0.975873i \(0.429936\pi\)
\(954\) −7.99380 −0.258809
\(955\) −58.3999 −1.88978
\(956\) −5.82508 −0.188397
\(957\) 13.6832 0.442316
\(958\) 73.0268 2.35939
\(959\) 0 0
\(960\) −33.8208 −1.09156
\(961\) 29.2947 0.944992
\(962\) 8.09186 0.260892
\(963\) 13.7382 0.442708
\(964\) 23.4885 0.756515
\(965\) −25.2389 −0.812470
\(966\) 0 0
\(967\) 48.2230 1.55075 0.775373 0.631503i \(-0.217562\pi\)
0.775373 + 0.631503i \(0.217562\pi\)
\(968\) 10.1860 0.327390
\(969\) −17.8408 −0.573128
\(970\) −18.2494 −0.585954
\(971\) 0.494306 0.0158630 0.00793152 0.999969i \(-0.497475\pi\)
0.00793152 + 0.999969i \(0.497475\pi\)
\(972\) 2.54608 0.0816656
\(973\) 0 0
\(974\) 19.5781 0.627324
\(975\) −7.48713 −0.239780
\(976\) −14.9804 −0.479512
\(977\) 4.09452 0.130995 0.0654976 0.997853i \(-0.479137\pi\)
0.0654976 + 0.997853i \(0.479137\pi\)
\(978\) −24.4584 −0.782093
\(979\) 15.4457 0.493647
\(980\) 0 0
\(981\) −16.8992 −0.539549
\(982\) 38.1238 1.21658
\(983\) −20.4954 −0.653703 −0.326851 0.945076i \(-0.605988\pi\)
−0.326851 + 0.945076i \(0.605988\pi\)
\(984\) 1.16433 0.0371176
\(985\) 31.7729 1.01237
\(986\) 47.9466 1.52693
\(987\) 0 0
\(988\) 39.5515 1.25830
\(989\) 29.0853 0.924859
\(990\) 9.32061 0.296228
\(991\) 0.869374 0.0276166 0.0138083 0.999905i \(-0.495605\pi\)
0.0138083 + 0.999905i \(0.495605\pi\)
\(992\) −61.2873 −1.94587
\(993\) 11.4220 0.362466
\(994\) 0 0
\(995\) −53.5752 −1.69845
\(996\) −3.15628 −0.100011
\(997\) −36.6918 −1.16204 −0.581020 0.813889i \(-0.697346\pi\)
−0.581020 + 0.813889i \(0.697346\pi\)
\(998\) 50.3835 1.59486
\(999\) 1.76746 0.0559201
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 \(a_p\))