Properties

Label 6027.2.a.bk.1.11
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 1.11
Root \(-1.67187\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.67187 q^{2} +1.00000 q^{3} +0.795136 q^{4} +2.68319 q^{5} +1.67187 q^{6} -2.01437 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.67187 q^{2} +1.00000 q^{3} +0.795136 q^{4} +2.68319 q^{5} +1.67187 q^{6} -2.01437 q^{8} +1.00000 q^{9} +4.48594 q^{10} -5.74918 q^{11} +0.795136 q^{12} -4.92750 q^{13} +2.68319 q^{15} -4.95803 q^{16} -2.19332 q^{17} +1.67187 q^{18} +3.26234 q^{19} +2.13350 q^{20} -9.61186 q^{22} -6.02193 q^{23} -2.01437 q^{24} +2.19953 q^{25} -8.23812 q^{26} +1.00000 q^{27} -4.01001 q^{29} +4.48594 q^{30} +7.54177 q^{31} -4.26042 q^{32} -5.74918 q^{33} -3.66694 q^{34} +0.795136 q^{36} +7.78383 q^{37} +5.45419 q^{38} -4.92750 q^{39} -5.40495 q^{40} -1.00000 q^{41} -4.98774 q^{43} -4.57138 q^{44} +2.68319 q^{45} -10.0679 q^{46} -4.57188 q^{47} -4.95803 q^{48} +3.67731 q^{50} -2.19332 q^{51} -3.91803 q^{52} +1.25191 q^{53} +1.67187 q^{54} -15.4262 q^{55} +3.26234 q^{57} -6.70420 q^{58} -6.36958 q^{59} +2.13350 q^{60} -6.05423 q^{61} +12.6088 q^{62} +2.79321 q^{64} -13.2214 q^{65} -9.61186 q^{66} +1.90292 q^{67} -1.74399 q^{68} -6.02193 q^{69} -9.71759 q^{71} -2.01437 q^{72} +6.59874 q^{73} +13.0135 q^{74} +2.19953 q^{75} +2.59400 q^{76} -8.23812 q^{78} +3.22930 q^{79} -13.3034 q^{80} +1.00000 q^{81} -1.67187 q^{82} -9.82725 q^{83} -5.88510 q^{85} -8.33883 q^{86} -4.01001 q^{87} +11.5810 q^{88} -12.3768 q^{89} +4.48594 q^{90} -4.78825 q^{92} +7.54177 q^{93} -7.64357 q^{94} +8.75348 q^{95} -4.26042 q^{96} -7.28315 q^{97} -5.74918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67187 1.18219 0.591094 0.806603i \(-0.298696\pi\)
0.591094 + 0.806603i \(0.298696\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.795136 0.397568
\(5\) 2.68319 1.19996 0.599980 0.800015i \(-0.295175\pi\)
0.599980 + 0.800015i \(0.295175\pi\)
\(6\) 1.67187 0.682536
\(7\) 0 0
\(8\) −2.01437 −0.712188
\(9\) 1.00000 0.333333
\(10\) 4.48594 1.41858
\(11\) −5.74918 −1.73344 −0.866722 0.498791i \(-0.833777\pi\)
−0.866722 + 0.498791i \(0.833777\pi\)
\(12\) 0.795136 0.229536
\(13\) −4.92750 −1.36664 −0.683322 0.730118i \(-0.739465\pi\)
−0.683322 + 0.730118i \(0.739465\pi\)
\(14\) 0 0
\(15\) 2.68319 0.692798
\(16\) −4.95803 −1.23951
\(17\) −2.19332 −0.531958 −0.265979 0.963979i \(-0.585695\pi\)
−0.265979 + 0.963979i \(0.585695\pi\)
\(18\) 1.67187 0.394063
\(19\) 3.26234 0.748431 0.374216 0.927342i \(-0.377912\pi\)
0.374216 + 0.927342i \(0.377912\pi\)
\(20\) 2.13350 0.477066
\(21\) 0 0
\(22\) −9.61186 −2.04926
\(23\) −6.02193 −1.25566 −0.627830 0.778351i \(-0.716057\pi\)
−0.627830 + 0.778351i \(0.716057\pi\)
\(24\) −2.01437 −0.411182
\(25\) 2.19953 0.439905
\(26\) −8.23812 −1.61563
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.01001 −0.744641 −0.372320 0.928104i \(-0.621438\pi\)
−0.372320 + 0.928104i \(0.621438\pi\)
\(30\) 4.48594 0.819017
\(31\) 7.54177 1.35454 0.677271 0.735734i \(-0.263163\pi\)
0.677271 + 0.735734i \(0.263163\pi\)
\(32\) −4.26042 −0.753143
\(33\) −5.74918 −1.00080
\(34\) −3.66694 −0.628875
\(35\) 0 0
\(36\) 0.795136 0.132523
\(37\) 7.78383 1.27965 0.639827 0.768519i \(-0.279006\pi\)
0.639827 + 0.768519i \(0.279006\pi\)
\(38\) 5.45419 0.884786
\(39\) −4.92750 −0.789032
\(40\) −5.40495 −0.854597
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.98774 −0.760623 −0.380312 0.924858i \(-0.624183\pi\)
−0.380312 + 0.924858i \(0.624183\pi\)
\(44\) −4.57138 −0.689161
\(45\) 2.68319 0.399987
\(46\) −10.0679 −1.48443
\(47\) −4.57188 −0.666877 −0.333439 0.942772i \(-0.608209\pi\)
−0.333439 + 0.942772i \(0.608209\pi\)
\(48\) −4.95803 −0.715630
\(49\) 0 0
\(50\) 3.67731 0.520051
\(51\) −2.19332 −0.307126
\(52\) −3.91803 −0.543333
\(53\) 1.25191 0.171963 0.0859813 0.996297i \(-0.472597\pi\)
0.0859813 + 0.996297i \(0.472597\pi\)
\(54\) 1.67187 0.227512
\(55\) −15.4262 −2.08006
\(56\) 0 0
\(57\) 3.26234 0.432107
\(58\) −6.70420 −0.880305
\(59\) −6.36958 −0.829249 −0.414624 0.909993i \(-0.636087\pi\)
−0.414624 + 0.909993i \(0.636087\pi\)
\(60\) 2.13350 0.275434
\(61\) −6.05423 −0.775165 −0.387583 0.921835i \(-0.626690\pi\)
−0.387583 + 0.921835i \(0.626690\pi\)
\(62\) 12.6088 1.60132
\(63\) 0 0
\(64\) 2.79321 0.349152
\(65\) −13.2214 −1.63992
\(66\) −9.61186 −1.18314
\(67\) 1.90292 0.232479 0.116239 0.993221i \(-0.462916\pi\)
0.116239 + 0.993221i \(0.462916\pi\)
\(68\) −1.74399 −0.211490
\(69\) −6.02193 −0.724955
\(70\) 0 0
\(71\) −9.71759 −1.15327 −0.576633 0.817004i \(-0.695634\pi\)
−0.576633 + 0.817004i \(0.695634\pi\)
\(72\) −2.01437 −0.237396
\(73\) 6.59874 0.772324 0.386162 0.922431i \(-0.373801\pi\)
0.386162 + 0.922431i \(0.373801\pi\)
\(74\) 13.0135 1.51279
\(75\) 2.19953 0.253979
\(76\) 2.59400 0.297552
\(77\) 0 0
\(78\) −8.23812 −0.932784
\(79\) 3.22930 0.363324 0.181662 0.983361i \(-0.441852\pi\)
0.181662 + 0.983361i \(0.441852\pi\)
\(80\) −13.3034 −1.48736
\(81\) 1.00000 0.111111
\(82\) −1.67187 −0.184627
\(83\) −9.82725 −1.07868 −0.539341 0.842088i \(-0.681326\pi\)
−0.539341 + 0.842088i \(0.681326\pi\)
\(84\) 0 0
\(85\) −5.88510 −0.638329
\(86\) −8.33883 −0.899199
\(87\) −4.01001 −0.429918
\(88\) 11.5810 1.23454
\(89\) −12.3768 −1.31194 −0.655968 0.754789i \(-0.727739\pi\)
−0.655968 + 0.754789i \(0.727739\pi\)
\(90\) 4.48594 0.472860
\(91\) 0 0
\(92\) −4.78825 −0.499210
\(93\) 7.54177 0.782045
\(94\) −7.64357 −0.788374
\(95\) 8.75348 0.898088
\(96\) −4.26042 −0.434827
\(97\) −7.28315 −0.739492 −0.369746 0.929133i \(-0.620555\pi\)
−0.369746 + 0.929133i \(0.620555\pi\)
\(98\) 0 0
\(99\) −5.74918 −0.577815
\(100\) 1.74892 0.174892
\(101\) −10.6773 −1.06243 −0.531213 0.847238i \(-0.678264\pi\)
−0.531213 + 0.847238i \(0.678264\pi\)
\(102\) −3.66694 −0.363081
\(103\) 18.6226 1.83494 0.917471 0.397802i \(-0.130227\pi\)
0.917471 + 0.397802i \(0.130227\pi\)
\(104\) 9.92582 0.973307
\(105\) 0 0
\(106\) 2.09302 0.203292
\(107\) −16.2398 −1.56996 −0.784981 0.619519i \(-0.787328\pi\)
−0.784981 + 0.619519i \(0.787328\pi\)
\(108\) 0.795136 0.0765119
\(109\) −11.6467 −1.11556 −0.557778 0.829990i \(-0.688346\pi\)
−0.557778 + 0.829990i \(0.688346\pi\)
\(110\) −25.7905 −2.45903
\(111\) 7.78383 0.738808
\(112\) 0 0
\(113\) −6.93908 −0.652774 −0.326387 0.945236i \(-0.605831\pi\)
−0.326387 + 0.945236i \(0.605831\pi\)
\(114\) 5.45419 0.510832
\(115\) −16.1580 −1.50674
\(116\) −3.18850 −0.296045
\(117\) −4.92750 −0.455548
\(118\) −10.6491 −0.980328
\(119\) 0 0
\(120\) −5.40495 −0.493402
\(121\) 22.0531 2.00483
\(122\) −10.1219 −0.916391
\(123\) −1.00000 −0.0901670
\(124\) 5.99673 0.538522
\(125\) −7.51421 −0.672092
\(126\) 0 0
\(127\) 17.6247 1.56394 0.781969 0.623318i \(-0.214216\pi\)
0.781969 + 0.623318i \(0.214216\pi\)
\(128\) 13.1907 1.16591
\(129\) −4.98774 −0.439146
\(130\) −22.1045 −1.93869
\(131\) 12.4815 1.09051 0.545255 0.838270i \(-0.316433\pi\)
0.545255 + 0.838270i \(0.316433\pi\)
\(132\) −4.57138 −0.397888
\(133\) 0 0
\(134\) 3.18143 0.274833
\(135\) 2.68319 0.230933
\(136\) 4.41816 0.378854
\(137\) 17.9429 1.53296 0.766482 0.642266i \(-0.222006\pi\)
0.766482 + 0.642266i \(0.222006\pi\)
\(138\) −10.0679 −0.857033
\(139\) −12.5345 −1.06316 −0.531579 0.847009i \(-0.678401\pi\)
−0.531579 + 0.847009i \(0.678401\pi\)
\(140\) 0 0
\(141\) −4.57188 −0.385022
\(142\) −16.2465 −1.36338
\(143\) 28.3291 2.36900
\(144\) −4.95803 −0.413169
\(145\) −10.7596 −0.893539
\(146\) 11.0322 0.913032
\(147\) 0 0
\(148\) 6.18920 0.508749
\(149\) −11.5126 −0.943152 −0.471576 0.881825i \(-0.656315\pi\)
−0.471576 + 0.881825i \(0.656315\pi\)
\(150\) 3.67731 0.300251
\(151\) 16.8492 1.37116 0.685582 0.727995i \(-0.259548\pi\)
0.685582 + 0.727995i \(0.259548\pi\)
\(152\) −6.57156 −0.533024
\(153\) −2.19332 −0.177319
\(154\) 0 0
\(155\) 20.2360 1.62540
\(156\) −3.91803 −0.313694
\(157\) −22.5829 −1.80231 −0.901154 0.433498i \(-0.857279\pi\)
−0.901154 + 0.433498i \(0.857279\pi\)
\(158\) 5.39895 0.429518
\(159\) 1.25191 0.0992826
\(160\) −11.4315 −0.903741
\(161\) 0 0
\(162\) 1.67187 0.131354
\(163\) 1.83938 0.144071 0.0720356 0.997402i \(-0.477050\pi\)
0.0720356 + 0.997402i \(0.477050\pi\)
\(164\) −0.795136 −0.0620897
\(165\) −15.4262 −1.20093
\(166\) −16.4298 −1.27520
\(167\) 16.8266 1.30208 0.651041 0.759042i \(-0.274332\pi\)
0.651041 + 0.759042i \(0.274332\pi\)
\(168\) 0 0
\(169\) 11.2803 0.867714
\(170\) −9.83910 −0.754625
\(171\) 3.26234 0.249477
\(172\) −3.96593 −0.302399
\(173\) 3.10789 0.236288 0.118144 0.992996i \(-0.462306\pi\)
0.118144 + 0.992996i \(0.462306\pi\)
\(174\) −6.70420 −0.508244
\(175\) 0 0
\(176\) 28.5046 2.14862
\(177\) −6.36958 −0.478767
\(178\) −20.6923 −1.55095
\(179\) −12.2390 −0.914785 −0.457393 0.889265i \(-0.651217\pi\)
−0.457393 + 0.889265i \(0.651217\pi\)
\(180\) 2.13350 0.159022
\(181\) 4.57609 0.340138 0.170069 0.985432i \(-0.445601\pi\)
0.170069 + 0.985432i \(0.445601\pi\)
\(182\) 0 0
\(183\) −6.05423 −0.447542
\(184\) 12.1304 0.894265
\(185\) 20.8855 1.53553
\(186\) 12.6088 0.924524
\(187\) 12.6098 0.922120
\(188\) −3.63526 −0.265129
\(189\) 0 0
\(190\) 14.6346 1.06171
\(191\) 8.36063 0.604954 0.302477 0.953157i \(-0.402187\pi\)
0.302477 + 0.953157i \(0.402187\pi\)
\(192\) 2.79321 0.201583
\(193\) 20.0405 1.44255 0.721274 0.692650i \(-0.243557\pi\)
0.721274 + 0.692650i \(0.243557\pi\)
\(194\) −12.1765 −0.874218
\(195\) −13.2214 −0.946807
\(196\) 0 0
\(197\) 20.6431 1.47076 0.735380 0.677655i \(-0.237004\pi\)
0.735380 + 0.677655i \(0.237004\pi\)
\(198\) −9.61186 −0.683085
\(199\) −14.3279 −1.01568 −0.507838 0.861453i \(-0.669555\pi\)
−0.507838 + 0.861453i \(0.669555\pi\)
\(200\) −4.43066 −0.313295
\(201\) 1.90292 0.134222
\(202\) −17.8509 −1.25599
\(203\) 0 0
\(204\) −1.74399 −0.122104
\(205\) −2.68319 −0.187402
\(206\) 31.1345 2.16925
\(207\) −6.02193 −0.418553
\(208\) 24.4307 1.69396
\(209\) −18.7558 −1.29736
\(210\) 0 0
\(211\) 11.7553 0.809269 0.404634 0.914479i \(-0.367399\pi\)
0.404634 + 0.914479i \(0.367399\pi\)
\(212\) 0.995435 0.0683668
\(213\) −9.71759 −0.665838
\(214\) −27.1508 −1.85599
\(215\) −13.3831 −0.912718
\(216\) −2.01437 −0.137061
\(217\) 0 0
\(218\) −19.4718 −1.31880
\(219\) 6.59874 0.445901
\(220\) −12.2659 −0.826967
\(221\) 10.8076 0.726997
\(222\) 13.0135 0.873410
\(223\) 3.69604 0.247505 0.123753 0.992313i \(-0.460507\pi\)
0.123753 + 0.992313i \(0.460507\pi\)
\(224\) 0 0
\(225\) 2.19953 0.146635
\(226\) −11.6012 −0.771701
\(227\) 16.4981 1.09502 0.547509 0.836800i \(-0.315576\pi\)
0.547509 + 0.836800i \(0.315576\pi\)
\(228\) 2.59400 0.171792
\(229\) −25.3427 −1.67469 −0.837347 0.546672i \(-0.815894\pi\)
−0.837347 + 0.546672i \(0.815894\pi\)
\(230\) −27.0140 −1.78125
\(231\) 0 0
\(232\) 8.07766 0.530324
\(233\) −8.64005 −0.566029 −0.283014 0.959116i \(-0.591334\pi\)
−0.283014 + 0.959116i \(0.591334\pi\)
\(234\) −8.23812 −0.538543
\(235\) −12.2672 −0.800226
\(236\) −5.06468 −0.329683
\(237\) 3.22930 0.209765
\(238\) 0 0
\(239\) 3.03713 0.196455 0.0982277 0.995164i \(-0.468683\pi\)
0.0982277 + 0.995164i \(0.468683\pi\)
\(240\) −13.3034 −0.858728
\(241\) 6.48505 0.417739 0.208869 0.977944i \(-0.433022\pi\)
0.208869 + 0.977944i \(0.433022\pi\)
\(242\) 36.8698 2.37008
\(243\) 1.00000 0.0641500
\(244\) −4.81394 −0.308181
\(245\) 0 0
\(246\) −1.67187 −0.106594
\(247\) −16.0752 −1.02284
\(248\) −15.1919 −0.964688
\(249\) −9.82725 −0.622777
\(250\) −12.5628 −0.794538
\(251\) −9.10964 −0.574995 −0.287498 0.957781i \(-0.592823\pi\)
−0.287498 + 0.957781i \(0.592823\pi\)
\(252\) 0 0
\(253\) 34.6212 2.17662
\(254\) 29.4661 1.84887
\(255\) −5.88510 −0.368539
\(256\) 16.4667 1.02917
\(257\) −2.97249 −0.185419 −0.0927093 0.995693i \(-0.529553\pi\)
−0.0927093 + 0.995693i \(0.529553\pi\)
\(258\) −8.33883 −0.519153
\(259\) 0 0
\(260\) −10.5128 −0.651978
\(261\) −4.01001 −0.248214
\(262\) 20.8673 1.28919
\(263\) −11.0113 −0.678986 −0.339493 0.940609i \(-0.610255\pi\)
−0.339493 + 0.940609i \(0.610255\pi\)
\(264\) 11.5810 0.712761
\(265\) 3.35911 0.206348
\(266\) 0 0
\(267\) −12.3768 −0.757446
\(268\) 1.51308 0.0924260
\(269\) −11.8444 −0.722167 −0.361084 0.932533i \(-0.617593\pi\)
−0.361084 + 0.932533i \(0.617593\pi\)
\(270\) 4.48594 0.273006
\(271\) 5.03055 0.305584 0.152792 0.988258i \(-0.451174\pi\)
0.152792 + 0.988258i \(0.451174\pi\)
\(272\) 10.8746 0.659367
\(273\) 0 0
\(274\) 29.9981 1.81225
\(275\) −12.6455 −0.762551
\(276\) −4.78825 −0.288219
\(277\) 27.8013 1.67042 0.835210 0.549932i \(-0.185346\pi\)
0.835210 + 0.549932i \(0.185346\pi\)
\(278\) −20.9559 −1.25685
\(279\) 7.54177 0.451514
\(280\) 0 0
\(281\) 2.50306 0.149320 0.0746600 0.997209i \(-0.476213\pi\)
0.0746600 + 0.997209i \(0.476213\pi\)
\(282\) −7.64357 −0.455168
\(283\) −9.19192 −0.546403 −0.273201 0.961957i \(-0.588083\pi\)
−0.273201 + 0.961957i \(0.588083\pi\)
\(284\) −7.72680 −0.458501
\(285\) 8.75348 0.518511
\(286\) 47.3625 2.80060
\(287\) 0 0
\(288\) −4.26042 −0.251048
\(289\) −12.1893 −0.717020
\(290\) −17.9887 −1.05633
\(291\) −7.28315 −0.426946
\(292\) 5.24689 0.307051
\(293\) 11.9253 0.696685 0.348342 0.937367i \(-0.386745\pi\)
0.348342 + 0.937367i \(0.386745\pi\)
\(294\) 0 0
\(295\) −17.0908 −0.995066
\(296\) −15.6795 −0.911354
\(297\) −5.74918 −0.333601
\(298\) −19.2476 −1.11498
\(299\) 29.6731 1.71604
\(300\) 1.74892 0.100974
\(301\) 0 0
\(302\) 28.1695 1.62097
\(303\) −10.6773 −0.613392
\(304\) −16.1748 −0.927686
\(305\) −16.2447 −0.930168
\(306\) −3.66694 −0.209625
\(307\) −20.1527 −1.15017 −0.575086 0.818093i \(-0.695032\pi\)
−0.575086 + 0.818093i \(0.695032\pi\)
\(308\) 0 0
\(309\) 18.6226 1.05940
\(310\) 33.8319 1.92152
\(311\) 10.6834 0.605801 0.302901 0.953022i \(-0.402045\pi\)
0.302901 + 0.953022i \(0.402045\pi\)
\(312\) 9.92582 0.561939
\(313\) 3.63577 0.205506 0.102753 0.994707i \(-0.467235\pi\)
0.102753 + 0.994707i \(0.467235\pi\)
\(314\) −37.7555 −2.13067
\(315\) 0 0
\(316\) 2.56773 0.144446
\(317\) −10.0765 −0.565955 −0.282977 0.959127i \(-0.591322\pi\)
−0.282977 + 0.959127i \(0.591322\pi\)
\(318\) 2.09302 0.117371
\(319\) 23.0543 1.29079
\(320\) 7.49473 0.418968
\(321\) −16.2398 −0.906419
\(322\) 0 0
\(323\) −7.15535 −0.398134
\(324\) 0.795136 0.0441742
\(325\) −10.8382 −0.601194
\(326\) 3.07519 0.170319
\(327\) −11.6467 −0.644067
\(328\) 2.01437 0.111225
\(329\) 0 0
\(330\) −25.7905 −1.41972
\(331\) 23.6396 1.29935 0.649674 0.760213i \(-0.274906\pi\)
0.649674 + 0.760213i \(0.274906\pi\)
\(332\) −7.81400 −0.428849
\(333\) 7.78383 0.426551
\(334\) 28.1318 1.53931
\(335\) 5.10590 0.278965
\(336\) 0 0
\(337\) 0.762900 0.0415578 0.0207789 0.999784i \(-0.493385\pi\)
0.0207789 + 0.999784i \(0.493385\pi\)
\(338\) 18.8591 1.02580
\(339\) −6.93908 −0.376879
\(340\) −4.67945 −0.253779
\(341\) −43.3590 −2.34802
\(342\) 5.45419 0.294929
\(343\) 0 0
\(344\) 10.0472 0.541707
\(345\) −16.1580 −0.869918
\(346\) 5.19597 0.279337
\(347\) 9.76444 0.524183 0.262091 0.965043i \(-0.415588\pi\)
0.262091 + 0.965043i \(0.415588\pi\)
\(348\) −3.18850 −0.170922
\(349\) 5.55789 0.297507 0.148753 0.988874i \(-0.452474\pi\)
0.148753 + 0.988874i \(0.452474\pi\)
\(350\) 0 0
\(351\) −4.92750 −0.263011
\(352\) 24.4939 1.30553
\(353\) 33.2759 1.77110 0.885548 0.464549i \(-0.153783\pi\)
0.885548 + 0.464549i \(0.153783\pi\)
\(354\) −10.6491 −0.565992
\(355\) −26.0742 −1.38387
\(356\) −9.84121 −0.521583
\(357\) 0 0
\(358\) −20.4620 −1.08145
\(359\) 6.49396 0.342738 0.171369 0.985207i \(-0.445181\pi\)
0.171369 + 0.985207i \(0.445181\pi\)
\(360\) −5.40495 −0.284866
\(361\) −8.35716 −0.439850
\(362\) 7.65061 0.402107
\(363\) 22.0531 1.15749
\(364\) 0 0
\(365\) 17.7057 0.926758
\(366\) −10.1219 −0.529078
\(367\) −6.13150 −0.320062 −0.160031 0.987112i \(-0.551159\pi\)
−0.160031 + 0.987112i \(0.551159\pi\)
\(368\) 29.8569 1.55640
\(369\) −1.00000 −0.0520579
\(370\) 34.9178 1.81529
\(371\) 0 0
\(372\) 5.99673 0.310916
\(373\) −29.8839 −1.54733 −0.773664 0.633596i \(-0.781578\pi\)
−0.773664 + 0.633596i \(0.781578\pi\)
\(374\) 21.0819 1.09012
\(375\) −7.51421 −0.388032
\(376\) 9.20947 0.474942
\(377\) 19.7593 1.01766
\(378\) 0 0
\(379\) −25.2721 −1.29814 −0.649071 0.760728i \(-0.724842\pi\)
−0.649071 + 0.760728i \(0.724842\pi\)
\(380\) 6.96020 0.357051
\(381\) 17.6247 0.902940
\(382\) 13.9778 0.715169
\(383\) 16.1906 0.827299 0.413650 0.910436i \(-0.364254\pi\)
0.413650 + 0.910436i \(0.364254\pi\)
\(384\) 13.1907 0.673136
\(385\) 0 0
\(386\) 33.5051 1.70536
\(387\) −4.98774 −0.253541
\(388\) −5.79109 −0.293998
\(389\) −2.95610 −0.149880 −0.0749402 0.997188i \(-0.523877\pi\)
−0.0749402 + 0.997188i \(0.523877\pi\)
\(390\) −22.1045 −1.11930
\(391\) 13.2080 0.667959
\(392\) 0 0
\(393\) 12.4815 0.629606
\(394\) 34.5125 1.73872
\(395\) 8.66483 0.435975
\(396\) −4.57138 −0.229720
\(397\) 20.5747 1.03261 0.516306 0.856404i \(-0.327307\pi\)
0.516306 + 0.856404i \(0.327307\pi\)
\(398\) −23.9543 −1.20072
\(399\) 0 0
\(400\) −10.9053 −0.545266
\(401\) 10.2070 0.509713 0.254856 0.966979i \(-0.417972\pi\)
0.254856 + 0.966979i \(0.417972\pi\)
\(402\) 3.18143 0.158675
\(403\) −37.1621 −1.85117
\(404\) −8.48987 −0.422387
\(405\) 2.68319 0.133329
\(406\) 0 0
\(407\) −44.7507 −2.21821
\(408\) 4.41816 0.218732
\(409\) 12.1659 0.601564 0.300782 0.953693i \(-0.402752\pi\)
0.300782 + 0.953693i \(0.402752\pi\)
\(410\) −4.48594 −0.221545
\(411\) 17.9429 0.885057
\(412\) 14.8075 0.729514
\(413\) 0 0
\(414\) −10.0679 −0.494808
\(415\) −26.3684 −1.29437
\(416\) 20.9932 1.02928
\(417\) −12.5345 −0.613815
\(418\) −31.3571 −1.53373
\(419\) 21.2879 1.03998 0.519991 0.854172i \(-0.325935\pi\)
0.519991 + 0.854172i \(0.325935\pi\)
\(420\) 0 0
\(421\) 14.8072 0.721661 0.360830 0.932631i \(-0.382493\pi\)
0.360830 + 0.932631i \(0.382493\pi\)
\(422\) 19.6533 0.956707
\(423\) −4.57188 −0.222292
\(424\) −2.52181 −0.122470
\(425\) −4.82427 −0.234011
\(426\) −16.2465 −0.787146
\(427\) 0 0
\(428\) −12.9129 −0.624167
\(429\) 28.3291 1.36774
\(430\) −22.3747 −1.07900
\(431\) −30.3000 −1.45950 −0.729751 0.683713i \(-0.760364\pi\)
−0.729751 + 0.683713i \(0.760364\pi\)
\(432\) −4.95803 −0.238543
\(433\) 8.76123 0.421038 0.210519 0.977590i \(-0.432485\pi\)
0.210519 + 0.977590i \(0.432485\pi\)
\(434\) 0 0
\(435\) −10.7596 −0.515885
\(436\) −9.26074 −0.443509
\(437\) −19.6456 −0.939775
\(438\) 11.0322 0.527139
\(439\) 8.81222 0.420585 0.210292 0.977639i \(-0.432558\pi\)
0.210292 + 0.977639i \(0.432558\pi\)
\(440\) 31.0740 1.48140
\(441\) 0 0
\(442\) 18.0688 0.859447
\(443\) −14.9446 −0.710040 −0.355020 0.934859i \(-0.615526\pi\)
−0.355020 + 0.934859i \(0.615526\pi\)
\(444\) 6.18920 0.293726
\(445\) −33.2093 −1.57427
\(446\) 6.17928 0.292598
\(447\) −11.5126 −0.544529
\(448\) 0 0
\(449\) −22.7149 −1.07198 −0.535991 0.844224i \(-0.680062\pi\)
−0.535991 + 0.844224i \(0.680062\pi\)
\(450\) 3.67731 0.173350
\(451\) 5.74918 0.270718
\(452\) −5.51751 −0.259522
\(453\) 16.8492 0.791642
\(454\) 27.5826 1.29452
\(455\) 0 0
\(456\) −6.57156 −0.307741
\(457\) −24.4566 −1.14403 −0.572015 0.820243i \(-0.693838\pi\)
−0.572015 + 0.820243i \(0.693838\pi\)
\(458\) −42.3696 −1.97980
\(459\) −2.19332 −0.102375
\(460\) −12.8478 −0.599032
\(461\) 36.2868 1.69004 0.845022 0.534732i \(-0.179588\pi\)
0.845022 + 0.534732i \(0.179588\pi\)
\(462\) 0 0
\(463\) −14.1747 −0.658753 −0.329377 0.944199i \(-0.606839\pi\)
−0.329377 + 0.944199i \(0.606839\pi\)
\(464\) 19.8818 0.922988
\(465\) 20.2360 0.938423
\(466\) −14.4450 −0.669152
\(467\) −37.3073 −1.72637 −0.863187 0.504884i \(-0.831535\pi\)
−0.863187 + 0.504884i \(0.831535\pi\)
\(468\) −3.91803 −0.181111
\(469\) 0 0
\(470\) −20.5092 −0.946018
\(471\) −22.5829 −1.04056
\(472\) 12.8307 0.590581
\(473\) 28.6754 1.31850
\(474\) 5.39895 0.247982
\(475\) 7.17560 0.329239
\(476\) 0 0
\(477\) 1.25191 0.0573209
\(478\) 5.07767 0.232247
\(479\) −15.2424 −0.696445 −0.348223 0.937412i \(-0.613215\pi\)
−0.348223 + 0.937412i \(0.613215\pi\)
\(480\) −11.4315 −0.521775
\(481\) −38.3548 −1.74883
\(482\) 10.8421 0.493846
\(483\) 0 0
\(484\) 17.5352 0.797055
\(485\) −19.5421 −0.887361
\(486\) 1.67187 0.0758374
\(487\) 23.9126 1.08358 0.541791 0.840514i \(-0.317747\pi\)
0.541791 + 0.840514i \(0.317747\pi\)
\(488\) 12.1955 0.552063
\(489\) 1.83938 0.0831796
\(490\) 0 0
\(491\) 37.6434 1.69882 0.849412 0.527731i \(-0.176957\pi\)
0.849412 + 0.527731i \(0.176957\pi\)
\(492\) −0.795136 −0.0358475
\(493\) 8.79524 0.396118
\(494\) −26.8755 −1.20919
\(495\) −15.4262 −0.693355
\(496\) −37.3923 −1.67896
\(497\) 0 0
\(498\) −16.4298 −0.736239
\(499\) −21.5059 −0.962737 −0.481369 0.876518i \(-0.659860\pi\)
−0.481369 + 0.876518i \(0.659860\pi\)
\(500\) −5.97482 −0.267202
\(501\) 16.8266 0.751758
\(502\) −15.2301 −0.679752
\(503\) 19.3530 0.862908 0.431454 0.902135i \(-0.358001\pi\)
0.431454 + 0.902135i \(0.358001\pi\)
\(504\) 0 0
\(505\) −28.6491 −1.27487
\(506\) 57.8820 2.57317
\(507\) 11.2803 0.500975
\(508\) 14.0140 0.621771
\(509\) −35.6578 −1.58050 −0.790252 0.612782i \(-0.790050\pi\)
−0.790252 + 0.612782i \(0.790050\pi\)
\(510\) −9.83910 −0.435683
\(511\) 0 0
\(512\) 1.14865 0.0507637
\(513\) 3.26234 0.144036
\(514\) −4.96960 −0.219200
\(515\) 49.9681 2.20186
\(516\) −3.96593 −0.174590
\(517\) 26.2846 1.15599
\(518\) 0 0
\(519\) 3.10789 0.136421
\(520\) 26.6329 1.16793
\(521\) −35.9700 −1.57587 −0.787937 0.615756i \(-0.788851\pi\)
−0.787937 + 0.615756i \(0.788851\pi\)
\(522\) −6.70420 −0.293435
\(523\) −23.2164 −1.01518 −0.507591 0.861598i \(-0.669464\pi\)
−0.507591 + 0.861598i \(0.669464\pi\)
\(524\) 9.92445 0.433551
\(525\) 0 0
\(526\) −18.4094 −0.802689
\(527\) −16.5415 −0.720560
\(528\) 28.5046 1.24050
\(529\) 13.2636 0.576680
\(530\) 5.61598 0.243942
\(531\) −6.36958 −0.276416
\(532\) 0 0
\(533\) 4.92750 0.213434
\(534\) −20.6923 −0.895444
\(535\) −43.5746 −1.88389
\(536\) −3.83319 −0.165568
\(537\) −12.2390 −0.528152
\(538\) −19.8023 −0.853737
\(539\) 0 0
\(540\) 2.13350 0.0918113
\(541\) −18.9977 −0.816776 −0.408388 0.912808i \(-0.633909\pi\)
−0.408388 + 0.912808i \(0.633909\pi\)
\(542\) 8.41040 0.361258
\(543\) 4.57609 0.196379
\(544\) 9.34446 0.400641
\(545\) −31.2505 −1.33862
\(546\) 0 0
\(547\) −3.61372 −0.154511 −0.0772557 0.997011i \(-0.524616\pi\)
−0.0772557 + 0.997011i \(0.524616\pi\)
\(548\) 14.2670 0.609457
\(549\) −6.05423 −0.258388
\(550\) −21.1415 −0.901479
\(551\) −13.0820 −0.557312
\(552\) 12.1304 0.516304
\(553\) 0 0
\(554\) 46.4801 1.97475
\(555\) 20.8855 0.886541
\(556\) −9.96659 −0.422677
\(557\) −20.5061 −0.868871 −0.434435 0.900703i \(-0.643052\pi\)
−0.434435 + 0.900703i \(0.643052\pi\)
\(558\) 12.6088 0.533774
\(559\) 24.5771 1.03950
\(560\) 0 0
\(561\) 12.6098 0.532386
\(562\) 4.18478 0.176524
\(563\) 13.7174 0.578120 0.289060 0.957311i \(-0.406657\pi\)
0.289060 + 0.957311i \(0.406657\pi\)
\(564\) −3.63526 −0.153072
\(565\) −18.6189 −0.783303
\(566\) −15.3677 −0.645951
\(567\) 0 0
\(568\) 19.5748 0.821342
\(569\) 37.3091 1.56408 0.782040 0.623228i \(-0.214179\pi\)
0.782040 + 0.623228i \(0.214179\pi\)
\(570\) 14.6346 0.612978
\(571\) −4.51838 −0.189088 −0.0945442 0.995521i \(-0.530139\pi\)
−0.0945442 + 0.995521i \(0.530139\pi\)
\(572\) 22.5255 0.941838
\(573\) 8.36063 0.349270
\(574\) 0 0
\(575\) −13.2454 −0.552371
\(576\) 2.79321 0.116384
\(577\) −44.5018 −1.85264 −0.926318 0.376743i \(-0.877044\pi\)
−0.926318 + 0.376743i \(0.877044\pi\)
\(578\) −20.3789 −0.847653
\(579\) 20.0405 0.832855
\(580\) −8.55537 −0.355242
\(581\) 0 0
\(582\) −12.1765 −0.504730
\(583\) −7.19744 −0.298088
\(584\) −13.2923 −0.550040
\(585\) −13.2214 −0.546639
\(586\) 19.9375 0.823612
\(587\) 26.0044 1.07332 0.536658 0.843800i \(-0.319687\pi\)
0.536658 + 0.843800i \(0.319687\pi\)
\(588\) 0 0
\(589\) 24.6038 1.01378
\(590\) −28.5735 −1.17635
\(591\) 20.6431 0.849144
\(592\) −38.5925 −1.58614
\(593\) −11.0023 −0.451812 −0.225906 0.974149i \(-0.572534\pi\)
−0.225906 + 0.974149i \(0.572534\pi\)
\(594\) −9.61186 −0.394380
\(595\) 0 0
\(596\) −9.15411 −0.374967
\(597\) −14.3279 −0.586400
\(598\) 49.6094 2.02868
\(599\) 1.53047 0.0625333 0.0312667 0.999511i \(-0.490046\pi\)
0.0312667 + 0.999511i \(0.490046\pi\)
\(600\) −4.43066 −0.180881
\(601\) −25.9191 −1.05726 −0.528630 0.848852i \(-0.677294\pi\)
−0.528630 + 0.848852i \(0.677294\pi\)
\(602\) 0 0
\(603\) 1.90292 0.0774929
\(604\) 13.3974 0.545131
\(605\) 59.1728 2.40572
\(606\) −17.8509 −0.725145
\(607\) 2.93827 0.119261 0.0596304 0.998221i \(-0.481008\pi\)
0.0596304 + 0.998221i \(0.481008\pi\)
\(608\) −13.8989 −0.563676
\(609\) 0 0
\(610\) −27.1589 −1.09963
\(611\) 22.5280 0.911383
\(612\) −1.74399 −0.0704965
\(613\) −40.7457 −1.64570 −0.822851 0.568257i \(-0.807618\pi\)
−0.822851 + 0.568257i \(0.807618\pi\)
\(614\) −33.6925 −1.35972
\(615\) −2.68319 −0.108197
\(616\) 0 0
\(617\) −19.0384 −0.766458 −0.383229 0.923653i \(-0.625188\pi\)
−0.383229 + 0.923653i \(0.625188\pi\)
\(618\) 31.1345 1.25242
\(619\) −12.9180 −0.519216 −0.259608 0.965714i \(-0.583593\pi\)
−0.259608 + 0.965714i \(0.583593\pi\)
\(620\) 16.0904 0.646205
\(621\) −6.02193 −0.241652
\(622\) 17.8612 0.716171
\(623\) 0 0
\(624\) 24.4307 0.978011
\(625\) −31.1597 −1.24639
\(626\) 6.07852 0.242947
\(627\) −18.7558 −0.749033
\(628\) −17.9564 −0.716540
\(629\) −17.0724 −0.680722
\(630\) 0 0
\(631\) 36.4942 1.45281 0.726405 0.687267i \(-0.241190\pi\)
0.726405 + 0.687267i \(0.241190\pi\)
\(632\) −6.50501 −0.258755
\(633\) 11.7553 0.467231
\(634\) −16.8466 −0.669065
\(635\) 47.2904 1.87666
\(636\) 0.995435 0.0394716
\(637\) 0 0
\(638\) 38.5437 1.52596
\(639\) −9.71759 −0.384422
\(640\) 35.3932 1.39904
\(641\) 21.5726 0.852067 0.426034 0.904707i \(-0.359911\pi\)
0.426034 + 0.904707i \(0.359911\pi\)
\(642\) −27.1508 −1.07156
\(643\) −44.0381 −1.73669 −0.868347 0.495957i \(-0.834817\pi\)
−0.868347 + 0.495957i \(0.834817\pi\)
\(644\) 0 0
\(645\) −13.3831 −0.526958
\(646\) −11.9628 −0.470670
\(647\) −5.13575 −0.201907 −0.100954 0.994891i \(-0.532189\pi\)
−0.100954 + 0.994891i \(0.532189\pi\)
\(648\) −2.01437 −0.0791320
\(649\) 36.6199 1.43746
\(650\) −18.1200 −0.710724
\(651\) 0 0
\(652\) 1.46256 0.0572781
\(653\) −42.3884 −1.65879 −0.829394 0.558664i \(-0.811314\pi\)
−0.829394 + 0.558664i \(0.811314\pi\)
\(654\) −19.4718 −0.761408
\(655\) 33.4902 1.30857
\(656\) 4.95803 0.193579
\(657\) 6.59874 0.257441
\(658\) 0 0
\(659\) 33.0120 1.28596 0.642982 0.765881i \(-0.277697\pi\)
0.642982 + 0.765881i \(0.277697\pi\)
\(660\) −12.2659 −0.477449
\(661\) 5.30085 0.206179 0.103090 0.994672i \(-0.467127\pi\)
0.103090 + 0.994672i \(0.467127\pi\)
\(662\) 39.5222 1.53607
\(663\) 10.8076 0.419732
\(664\) 19.7957 0.768224
\(665\) 0 0
\(666\) 13.0135 0.504264
\(667\) 24.1480 0.935015
\(668\) 13.3794 0.517666
\(669\) 3.69604 0.142897
\(670\) 8.53638 0.329789
\(671\) 34.8069 1.34371
\(672\) 0 0
\(673\) −21.1001 −0.813350 −0.406675 0.913573i \(-0.633312\pi\)
−0.406675 + 0.913573i \(0.633312\pi\)
\(674\) 1.27547 0.0491291
\(675\) 2.19953 0.0846598
\(676\) 8.96935 0.344975
\(677\) −6.76567 −0.260026 −0.130013 0.991512i \(-0.541502\pi\)
−0.130013 + 0.991512i \(0.541502\pi\)
\(678\) −11.6012 −0.445542
\(679\) 0 0
\(680\) 11.8548 0.454610
\(681\) 16.4981 0.632209
\(682\) −72.4904 −2.77580
\(683\) 4.65406 0.178083 0.0890413 0.996028i \(-0.471620\pi\)
0.0890413 + 0.996028i \(0.471620\pi\)
\(684\) 2.59400 0.0991841
\(685\) 48.1442 1.83950
\(686\) 0 0
\(687\) −25.3427 −0.966885
\(688\) 24.7294 0.942798
\(689\) −6.16877 −0.235011
\(690\) −27.0140 −1.02841
\(691\) 23.2065 0.882817 0.441408 0.897306i \(-0.354479\pi\)
0.441408 + 0.897306i \(0.354479\pi\)
\(692\) 2.47119 0.0939405
\(693\) 0 0
\(694\) 16.3248 0.619682
\(695\) −33.6324 −1.27575
\(696\) 8.07766 0.306183
\(697\) 2.19332 0.0830779
\(698\) 9.29204 0.351709
\(699\) −8.64005 −0.326797
\(700\) 0 0
\(701\) 1.03773 0.0391944 0.0195972 0.999808i \(-0.493762\pi\)
0.0195972 + 0.999808i \(0.493762\pi\)
\(702\) −8.23812 −0.310928
\(703\) 25.3935 0.957733
\(704\) −16.0587 −0.605235
\(705\) −12.2672 −0.462011
\(706\) 55.6328 2.09377
\(707\) 0 0
\(708\) −5.06468 −0.190342
\(709\) 41.8920 1.57329 0.786644 0.617407i \(-0.211817\pi\)
0.786644 + 0.617407i \(0.211817\pi\)
\(710\) −43.5925 −1.63600
\(711\) 3.22930 0.121108
\(712\) 24.9314 0.934345
\(713\) −45.4160 −1.70084
\(714\) 0 0
\(715\) 76.0125 2.84271
\(716\) −9.73166 −0.363689
\(717\) 3.03713 0.113424
\(718\) 10.8570 0.405181
\(719\) −27.6871 −1.03256 −0.516278 0.856421i \(-0.672683\pi\)
−0.516278 + 0.856421i \(0.672683\pi\)
\(720\) −13.3034 −0.495787
\(721\) 0 0
\(722\) −13.9720 −0.519986
\(723\) 6.48505 0.241182
\(724\) 3.63861 0.135228
\(725\) −8.82013 −0.327571
\(726\) 36.8698 1.36837
\(727\) −35.7583 −1.32620 −0.663102 0.748529i \(-0.730760\pi\)
−0.663102 + 0.748529i \(0.730760\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 29.6015 1.09560
\(731\) 10.9397 0.404620
\(732\) −4.81394 −0.177928
\(733\) 39.1256 1.44514 0.722568 0.691300i \(-0.242962\pi\)
0.722568 + 0.691300i \(0.242962\pi\)
\(734\) −10.2510 −0.378373
\(735\) 0 0
\(736\) 25.6559 0.945691
\(737\) −10.9402 −0.402989
\(738\) −1.67187 −0.0615422
\(739\) 1.16161 0.0427304 0.0213652 0.999772i \(-0.493199\pi\)
0.0213652 + 0.999772i \(0.493199\pi\)
\(740\) 16.6068 0.610479
\(741\) −16.0752 −0.590536
\(742\) 0 0
\(743\) 47.1939 1.73138 0.865688 0.500584i \(-0.166882\pi\)
0.865688 + 0.500584i \(0.166882\pi\)
\(744\) −15.1919 −0.556963
\(745\) −30.8906 −1.13175
\(746\) −49.9618 −1.82923
\(747\) −9.82725 −0.359560
\(748\) 10.0265 0.366605
\(749\) 0 0
\(750\) −12.5628 −0.458727
\(751\) −8.04927 −0.293722 −0.146861 0.989157i \(-0.546917\pi\)
−0.146861 + 0.989157i \(0.546917\pi\)
\(752\) 22.6675 0.826599
\(753\) −9.10964 −0.331974
\(754\) 33.0350 1.20306
\(755\) 45.2095 1.64534
\(756\) 0 0
\(757\) −54.1130 −1.96677 −0.983384 0.181536i \(-0.941893\pi\)
−0.983384 + 0.181536i \(0.941893\pi\)
\(758\) −42.2516 −1.53465
\(759\) 34.6212 1.25667
\(760\) −17.6328 −0.639608
\(761\) 50.6064 1.83448 0.917240 0.398336i \(-0.130412\pi\)
0.917240 + 0.398336i \(0.130412\pi\)
\(762\) 29.4661 1.06744
\(763\) 0 0
\(764\) 6.64783 0.240510
\(765\) −5.88510 −0.212776
\(766\) 27.0685 0.978023
\(767\) 31.3861 1.13329
\(768\) 16.4667 0.594190
\(769\) 14.0679 0.507301 0.253651 0.967296i \(-0.418369\pi\)
0.253651 + 0.967296i \(0.418369\pi\)
\(770\) 0 0
\(771\) −2.97249 −0.107051
\(772\) 15.9349 0.573511
\(773\) 8.26697 0.297342 0.148671 0.988887i \(-0.452500\pi\)
0.148671 + 0.988887i \(0.452500\pi\)
\(774\) −8.33883 −0.299733
\(775\) 16.5883 0.595870
\(776\) 14.6710 0.526657
\(777\) 0 0
\(778\) −4.94221 −0.177187
\(779\) −3.26234 −0.116885
\(780\) −10.5128 −0.376420
\(781\) 55.8682 1.99912
\(782\) 22.0820 0.789652
\(783\) −4.01001 −0.143306
\(784\) 0 0
\(785\) −60.5942 −2.16270
\(786\) 20.8673 0.744313
\(787\) −20.5670 −0.733135 −0.366568 0.930391i \(-0.619467\pi\)
−0.366568 + 0.930391i \(0.619467\pi\)
\(788\) 16.4141 0.584727
\(789\) −11.0113 −0.392013
\(790\) 14.4864 0.515404
\(791\) 0 0
\(792\) 11.5810 0.411513
\(793\) 29.8323 1.05937
\(794\) 34.3981 1.22074
\(795\) 3.35911 0.119135
\(796\) −11.3926 −0.403800
\(797\) −19.5339 −0.691925 −0.345963 0.938248i \(-0.612448\pi\)
−0.345963 + 0.938248i \(0.612448\pi\)
\(798\) 0 0
\(799\) 10.0276 0.354751
\(800\) −9.37090 −0.331311
\(801\) −12.3768 −0.437312
\(802\) 17.0647 0.602576
\(803\) −37.9374 −1.33878
\(804\) 1.51308 0.0533622
\(805\) 0 0
\(806\) −62.1300 −2.18844
\(807\) −11.8444 −0.416943
\(808\) 21.5080 0.756648
\(809\) −42.4368 −1.49200 −0.745999 0.665947i \(-0.768028\pi\)
−0.745999 + 0.665947i \(0.768028\pi\)
\(810\) 4.48594 0.157620
\(811\) −10.7525 −0.377572 −0.188786 0.982018i \(-0.560455\pi\)
−0.188786 + 0.982018i \(0.560455\pi\)
\(812\) 0 0
\(813\) 5.03055 0.176429
\(814\) −74.8171 −2.62234
\(815\) 4.93541 0.172880
\(816\) 10.8746 0.380685
\(817\) −16.2717 −0.569274
\(818\) 20.3397 0.711162
\(819\) 0 0
\(820\) −2.13350 −0.0745051
\(821\) −13.1832 −0.460097 −0.230048 0.973179i \(-0.573888\pi\)
−0.230048 + 0.973179i \(0.573888\pi\)
\(822\) 29.9981 1.04630
\(823\) 25.9409 0.904242 0.452121 0.891957i \(-0.350668\pi\)
0.452121 + 0.891957i \(0.350668\pi\)
\(824\) −37.5129 −1.30682
\(825\) −12.6455 −0.440259
\(826\) 0 0
\(827\) 14.2607 0.495893 0.247947 0.968774i \(-0.420244\pi\)
0.247947 + 0.968774i \(0.420244\pi\)
\(828\) −4.78825 −0.166403
\(829\) 3.17209 0.110171 0.0550857 0.998482i \(-0.482457\pi\)
0.0550857 + 0.998482i \(0.482457\pi\)
\(830\) −44.0845 −1.53019
\(831\) 27.8013 0.964417
\(832\) −13.7636 −0.477166
\(833\) 0 0
\(834\) −20.9559 −0.725644
\(835\) 45.1491 1.56245
\(836\) −14.9134 −0.515790
\(837\) 7.54177 0.260682
\(838\) 35.5905 1.22945
\(839\) −47.4102 −1.63678 −0.818390 0.574663i \(-0.805133\pi\)
−0.818390 + 0.574663i \(0.805133\pi\)
\(840\) 0 0
\(841\) −12.9198 −0.445510
\(842\) 24.7557 0.853138
\(843\) 2.50306 0.0862099
\(844\) 9.34706 0.321739
\(845\) 30.2672 1.04122
\(846\) −7.64357 −0.262791
\(847\) 0 0
\(848\) −6.20699 −0.213149
\(849\) −9.19192 −0.315466
\(850\) −8.06553 −0.276645
\(851\) −46.8737 −1.60681
\(852\) −7.72680 −0.264716
\(853\) −19.0742 −0.653089 −0.326545 0.945182i \(-0.605884\pi\)
−0.326545 + 0.945182i \(0.605884\pi\)
\(854\) 0 0
\(855\) 8.75348 0.299363
\(856\) 32.7130 1.11811
\(857\) 31.1474 1.06397 0.531987 0.846752i \(-0.321445\pi\)
0.531987 + 0.846752i \(0.321445\pi\)
\(858\) 47.3625 1.61693
\(859\) −48.2879 −1.64756 −0.823782 0.566907i \(-0.808140\pi\)
−0.823782 + 0.566907i \(0.808140\pi\)
\(860\) −10.6414 −0.362867
\(861\) 0 0
\(862\) −50.6576 −1.72541
\(863\) 16.6007 0.565096 0.282548 0.959253i \(-0.408820\pi\)
0.282548 + 0.959253i \(0.408820\pi\)
\(864\) −4.26042 −0.144942
\(865\) 8.33906 0.283536
\(866\) 14.6476 0.497746
\(867\) −12.1893 −0.413972
\(868\) 0 0
\(869\) −18.5658 −0.629803
\(870\) −17.9887 −0.609873
\(871\) −9.37664 −0.317715
\(872\) 23.4609 0.794486
\(873\) −7.28315 −0.246497
\(874\) −32.8448 −1.11099
\(875\) 0 0
\(876\) 5.24689 0.177276
\(877\) 22.8845 0.772753 0.386377 0.922341i \(-0.373726\pi\)
0.386377 + 0.922341i \(0.373726\pi\)
\(878\) 14.7329 0.497210
\(879\) 11.9253 0.402231
\(880\) 76.4834 2.57826
\(881\) −9.00099 −0.303251 −0.151626 0.988438i \(-0.548451\pi\)
−0.151626 + 0.988438i \(0.548451\pi\)
\(882\) 0 0
\(883\) −16.3127 −0.548967 −0.274483 0.961592i \(-0.588507\pi\)
−0.274483 + 0.961592i \(0.588507\pi\)
\(884\) 8.59350 0.289031
\(885\) −17.0908 −0.574501
\(886\) −24.9854 −0.839401
\(887\) −18.1119 −0.608138 −0.304069 0.952650i \(-0.598345\pi\)
−0.304069 + 0.952650i \(0.598345\pi\)
\(888\) −15.6795 −0.526170
\(889\) 0 0
\(890\) −55.5215 −1.86108
\(891\) −5.74918 −0.192605
\(892\) 2.93885 0.0984001
\(893\) −14.9150 −0.499112
\(894\) −19.2476 −0.643736
\(895\) −32.8396 −1.09771
\(896\) 0 0
\(897\) 29.6731 0.990755
\(898\) −37.9763 −1.26728
\(899\) −30.2426 −1.00865
\(900\) 1.74892 0.0582974
\(901\) −2.74583 −0.0914769
\(902\) 9.61186 0.320040
\(903\) 0 0
\(904\) 13.9779 0.464898
\(905\) 12.2785 0.408152
\(906\) 28.1695 0.935870
\(907\) 48.6726 1.61615 0.808074 0.589081i \(-0.200510\pi\)
0.808074 + 0.589081i \(0.200510\pi\)
\(908\) 13.1182 0.435344
\(909\) −10.6773 −0.354142
\(910\) 0 0
\(911\) −48.5444 −1.60835 −0.804175 0.594393i \(-0.797392\pi\)
−0.804175 + 0.594393i \(0.797392\pi\)
\(912\) −16.1748 −0.535600
\(913\) 56.4987 1.86983
\(914\) −40.8881 −1.35246
\(915\) −16.2447 −0.537033
\(916\) −20.1509 −0.665804
\(917\) 0 0
\(918\) −3.66694 −0.121027
\(919\) −12.8856 −0.425058 −0.212529 0.977155i \(-0.568170\pi\)
−0.212529 + 0.977155i \(0.568170\pi\)
\(920\) 32.5482 1.07308
\(921\) −20.1527 −0.664052
\(922\) 60.6666 1.99795
\(923\) 47.8834 1.57610
\(924\) 0 0
\(925\) 17.1207 0.562926
\(926\) −23.6982 −0.778770
\(927\) 18.6226 0.611648
\(928\) 17.0843 0.560821
\(929\) −6.97988 −0.229003 −0.114501 0.993423i \(-0.536527\pi\)
−0.114501 + 0.993423i \(0.536527\pi\)
\(930\) 33.8319 1.10939
\(931\) 0 0
\(932\) −6.87001 −0.225035
\(933\) 10.6834 0.349759
\(934\) −62.3727 −2.04090
\(935\) 33.8345 1.10651
\(936\) 9.92582 0.324436
\(937\) 50.1075 1.63694 0.818471 0.574548i \(-0.194822\pi\)
0.818471 + 0.574548i \(0.194822\pi\)
\(938\) 0 0
\(939\) 3.63577 0.118649
\(940\) −9.75412 −0.318144
\(941\) −35.3645 −1.15285 −0.576425 0.817150i \(-0.695553\pi\)
−0.576425 + 0.817150i \(0.695553\pi\)
\(942\) −37.7555 −1.23014
\(943\) 6.02193 0.196101
\(944\) 31.5806 1.02786
\(945\) 0 0
\(946\) 47.9415 1.55871
\(947\) 49.0711 1.59460 0.797298 0.603586i \(-0.206262\pi\)
0.797298 + 0.603586i \(0.206262\pi\)
\(948\) 2.56773 0.0833960
\(949\) −32.5153 −1.05549
\(950\) 11.9966 0.389222
\(951\) −10.0765 −0.326754
\(952\) 0 0
\(953\) −29.3314 −0.950138 −0.475069 0.879948i \(-0.657577\pi\)
−0.475069 + 0.879948i \(0.657577\pi\)
\(954\) 2.09302 0.0677640
\(955\) 22.4332 0.725921
\(956\) 2.41493 0.0781043
\(957\) 23.0543 0.745240
\(958\) −25.4833 −0.823329
\(959\) 0 0
\(960\) 7.49473 0.241891
\(961\) 25.8783 0.834782
\(962\) −64.1241 −2.06745
\(963\) −16.2398 −0.523321
\(964\) 5.15650 0.166080
\(965\) 53.7726 1.73100
\(966\) 0 0
\(967\) −54.0060 −1.73672 −0.868358 0.495938i \(-0.834824\pi\)
−0.868358 + 0.495938i \(0.834824\pi\)
\(968\) −44.4232 −1.42781
\(969\) −7.15535 −0.229863
\(970\) −32.6718 −1.04903
\(971\) 16.2246 0.520672 0.260336 0.965518i \(-0.416167\pi\)
0.260336 + 0.965518i \(0.416167\pi\)
\(972\) 0.795136 0.0255040
\(973\) 0 0
\(974\) 39.9786 1.28100
\(975\) −10.8382 −0.347099
\(976\) 30.0171 0.960823
\(977\) −31.9276 −1.02145 −0.510727 0.859743i \(-0.670624\pi\)
−0.510727 + 0.859743i \(0.670624\pi\)
\(978\) 3.07519 0.0983339
\(979\) 71.1564 2.27417
\(980\) 0 0
\(981\) −11.6467 −0.371852
\(982\) 62.9347 2.00833
\(983\) −4.38826 −0.139964 −0.0699819 0.997548i \(-0.522294\pi\)
−0.0699819 + 0.997548i \(0.522294\pi\)
\(984\) 2.01437 0.0642158
\(985\) 55.3895 1.76485
\(986\) 14.7045 0.468286
\(987\) 0 0
\(988\) −12.7819 −0.406648
\(989\) 30.0358 0.955084
\(990\) −25.7905 −0.819676
\(991\) 34.7060 1.10247 0.551237 0.834349i \(-0.314156\pi\)
0.551237 + 0.834349i \(0.314156\pi\)
\(992\) −32.1311 −1.02016
\(993\) 23.6396 0.750179
\(994\) 0 0
\(995\) −38.4444 −1.21877
\(996\) −7.81400 −0.247596
\(997\) 2.73909 0.0867479 0.0433739 0.999059i \(-0.486189\pi\)
0.0433739 + 0.999059i \(0.486189\pi\)
\(998\) −35.9550 −1.13814
\(999\) 7.78383 0.246269
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 \(a_p\))