Properties

Label 6027.2.a.bn.1.9
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-0.423828 q^{2} -1.00000 q^{3} -1.82037 q^{4} -3.41632 q^{5} +0.423828 q^{6} +1.61918 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.423828 q^{2} -1.00000 q^{3} -1.82037 q^{4} -3.41632 q^{5} +0.423828 q^{6} +1.61918 q^{8} +1.00000 q^{9} +1.44793 q^{10} +1.20844 q^{11} +1.82037 q^{12} -1.26276 q^{13} +3.41632 q^{15} +2.95449 q^{16} -2.17395 q^{17} -0.423828 q^{18} +7.30164 q^{19} +6.21897 q^{20} -0.512171 q^{22} +4.90922 q^{23} -1.61918 q^{24} +6.67126 q^{25} +0.535192 q^{26} -1.00000 q^{27} +0.506374 q^{29} -1.44793 q^{30} -6.04329 q^{31} -4.49055 q^{32} -1.20844 q^{33} +0.921382 q^{34} -1.82037 q^{36} +6.73103 q^{37} -3.09464 q^{38} +1.26276 q^{39} -5.53164 q^{40} +1.00000 q^{41} -7.21084 q^{43} -2.19981 q^{44} -3.41632 q^{45} -2.08066 q^{46} -5.13896 q^{47} -2.95449 q^{48} -2.82746 q^{50} +2.17395 q^{51} +2.29869 q^{52} -7.67647 q^{53} +0.423828 q^{54} -4.12842 q^{55} -7.30164 q^{57} -0.214615 q^{58} -3.05287 q^{59} -6.21897 q^{60} -1.50585 q^{61} +2.56131 q^{62} -4.00576 q^{64} +4.31399 q^{65} +0.512171 q^{66} +2.66239 q^{67} +3.95740 q^{68} -4.90922 q^{69} -8.67388 q^{71} +1.61918 q^{72} -12.5013 q^{73} -2.85280 q^{74} -6.67126 q^{75} -13.2917 q^{76} -0.535192 q^{78} +7.94958 q^{79} -10.0935 q^{80} +1.00000 q^{81} -0.423828 q^{82} +5.53811 q^{83} +7.42693 q^{85} +3.05615 q^{86} -0.506374 q^{87} +1.95668 q^{88} -4.64437 q^{89} +1.44793 q^{90} -8.93659 q^{92} +6.04329 q^{93} +2.17803 q^{94} -24.9448 q^{95} +4.49055 q^{96} +1.13053 q^{97} +1.20844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.423828 −0.299691 −0.149846 0.988709i \(-0.547878\pi\)
−0.149846 + 0.988709i \(0.547878\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.82037 −0.910185
\(5\) −3.41632 −1.52783 −0.763913 0.645319i \(-0.776724\pi\)
−0.763913 + 0.645319i \(0.776724\pi\)
\(6\) 0.423828 0.173027
\(7\) 0 0
\(8\) 1.61918 0.572466
\(9\) 1.00000 0.333333
\(10\) 1.44793 0.457876
\(11\) 1.20844 0.364359 0.182179 0.983265i \(-0.441685\pi\)
0.182179 + 0.983265i \(0.441685\pi\)
\(12\) 1.82037 0.525496
\(13\) −1.26276 −0.350226 −0.175113 0.984548i \(-0.556029\pi\)
−0.175113 + 0.984548i \(0.556029\pi\)
\(14\) 0 0
\(15\) 3.41632 0.882091
\(16\) 2.95449 0.738622
\(17\) −2.17395 −0.527261 −0.263631 0.964624i \(-0.584920\pi\)
−0.263631 + 0.964624i \(0.584920\pi\)
\(18\) −0.423828 −0.0998971
\(19\) 7.30164 1.67511 0.837556 0.546352i \(-0.183984\pi\)
0.837556 + 0.546352i \(0.183984\pi\)
\(20\) 6.21897 1.39060
\(21\) 0 0
\(22\) −0.512171 −0.109195
\(23\) 4.90922 1.02364 0.511821 0.859092i \(-0.328971\pi\)
0.511821 + 0.859092i \(0.328971\pi\)
\(24\) −1.61918 −0.330513
\(25\) 6.67126 1.33425
\(26\) 0.535192 0.104960
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 0.506374 0.0940313 0.0470156 0.998894i \(-0.485029\pi\)
0.0470156 + 0.998894i \(0.485029\pi\)
\(30\) −1.44793 −0.264355
\(31\) −6.04329 −1.08541 −0.542703 0.839925i \(-0.682599\pi\)
−0.542703 + 0.839925i \(0.682599\pi\)
\(32\) −4.49055 −0.793825
\(33\) −1.20844 −0.210363
\(34\) 0.921382 0.158016
\(35\) 0 0
\(36\) −1.82037 −0.303395
\(37\) 6.73103 1.10658 0.553288 0.832990i \(-0.313373\pi\)
0.553288 + 0.832990i \(0.313373\pi\)
\(38\) −3.09464 −0.502017
\(39\) 1.26276 0.202203
\(40\) −5.53164 −0.874629
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −7.21084 −1.09964 −0.549821 0.835282i \(-0.685304\pi\)
−0.549821 + 0.835282i \(0.685304\pi\)
\(44\) −2.19981 −0.331634
\(45\) −3.41632 −0.509275
\(46\) −2.08066 −0.306777
\(47\) −5.13896 −0.749595 −0.374797 0.927107i \(-0.622288\pi\)
−0.374797 + 0.927107i \(0.622288\pi\)
\(48\) −2.95449 −0.426444
\(49\) 0 0
\(50\) −2.82746 −0.399864
\(51\) 2.17395 0.304414
\(52\) 2.29869 0.318771
\(53\) −7.67647 −1.05444 −0.527222 0.849727i \(-0.676766\pi\)
−0.527222 + 0.849727i \(0.676766\pi\)
\(54\) 0.423828 0.0576756
\(55\) −4.12842 −0.556677
\(56\) 0 0
\(57\) −7.30164 −0.967126
\(58\) −0.214615 −0.0281804
\(59\) −3.05287 −0.397450 −0.198725 0.980055i \(-0.563680\pi\)
−0.198725 + 0.980055i \(0.563680\pi\)
\(60\) −6.21897 −0.802866
\(61\) −1.50585 −0.192805 −0.0964024 0.995342i \(-0.530734\pi\)
−0.0964024 + 0.995342i \(0.530734\pi\)
\(62\) 2.56131 0.325287
\(63\) 0 0
\(64\) −4.00576 −0.500719
\(65\) 4.31399 0.535084
\(66\) 0.512171 0.0630438
\(67\) 2.66239 0.325263 0.162632 0.986687i \(-0.448002\pi\)
0.162632 + 0.986687i \(0.448002\pi\)
\(68\) 3.95740 0.479905
\(69\) −4.90922 −0.591000
\(70\) 0 0
\(71\) −8.67388 −1.02940 −0.514700 0.857370i \(-0.672097\pi\)
−0.514700 + 0.857370i \(0.672097\pi\)
\(72\) 1.61918 0.190822
\(73\) −12.5013 −1.46316 −0.731580 0.681755i \(-0.761217\pi\)
−0.731580 + 0.681755i \(0.761217\pi\)
\(74\) −2.85280 −0.331631
\(75\) −6.67126 −0.770331
\(76\) −13.2917 −1.52466
\(77\) 0 0
\(78\) −0.535192 −0.0605985
\(79\) 7.94958 0.894397 0.447199 0.894435i \(-0.352422\pi\)
0.447199 + 0.894435i \(0.352422\pi\)
\(80\) −10.0935 −1.12849
\(81\) 1.00000 0.111111
\(82\) −0.423828 −0.0468039
\(83\) 5.53811 0.607886 0.303943 0.952690i \(-0.401697\pi\)
0.303943 + 0.952690i \(0.401697\pi\)
\(84\) 0 0
\(85\) 7.42693 0.805563
\(86\) 3.05615 0.329553
\(87\) −0.506374 −0.0542890
\(88\) 1.95668 0.208583
\(89\) −4.64437 −0.492303 −0.246151 0.969231i \(-0.579166\pi\)
−0.246151 + 0.969231i \(0.579166\pi\)
\(90\) 1.44793 0.152625
\(91\) 0 0
\(92\) −8.93659 −0.931704
\(93\) 6.04329 0.626660
\(94\) 2.17803 0.224647
\(95\) −24.9448 −2.55928
\(96\) 4.49055 0.458315
\(97\) 1.13053 0.114788 0.0573940 0.998352i \(-0.481721\pi\)
0.0573940 + 0.998352i \(0.481721\pi\)
\(98\) 0 0
\(99\) 1.20844 0.121453
\(100\) −12.1442 −1.21442
\(101\) −5.31509 −0.528871 −0.264436 0.964403i \(-0.585186\pi\)
−0.264436 + 0.964403i \(0.585186\pi\)
\(102\) −0.921382 −0.0912304
\(103\) 5.38877 0.530972 0.265486 0.964115i \(-0.414468\pi\)
0.265486 + 0.964115i \(0.414468\pi\)
\(104\) −2.04463 −0.200493
\(105\) 0 0
\(106\) 3.25350 0.316008
\(107\) 2.77874 0.268631 0.134315 0.990939i \(-0.457116\pi\)
0.134315 + 0.990939i \(0.457116\pi\)
\(108\) 1.82037 0.175165
\(109\) 11.6577 1.11661 0.558304 0.829637i \(-0.311452\pi\)
0.558304 + 0.829637i \(0.311452\pi\)
\(110\) 1.74974 0.166831
\(111\) −6.73103 −0.638882
\(112\) 0 0
\(113\) 11.6261 1.09369 0.546844 0.837234i \(-0.315829\pi\)
0.546844 + 0.837234i \(0.315829\pi\)
\(114\) 3.09464 0.289839
\(115\) −16.7715 −1.56395
\(116\) −0.921788 −0.0855859
\(117\) −1.26276 −0.116742
\(118\) 1.29389 0.119112
\(119\) 0 0
\(120\) 5.53164 0.504967
\(121\) −9.53967 −0.867243
\(122\) 0.638222 0.0577819
\(123\) −1.00000 −0.0901670
\(124\) 11.0010 0.987921
\(125\) −5.70956 −0.510679
\(126\) 0 0
\(127\) 9.37534 0.831927 0.415964 0.909381i \(-0.363444\pi\)
0.415964 + 0.909381i \(0.363444\pi\)
\(128\) 10.6789 0.943886
\(129\) 7.21084 0.634879
\(130\) −1.82839 −0.160360
\(131\) −5.63692 −0.492500 −0.246250 0.969206i \(-0.579198\pi\)
−0.246250 + 0.969206i \(0.579198\pi\)
\(132\) 2.19981 0.191469
\(133\) 0 0
\(134\) −1.12840 −0.0974785
\(135\) 3.41632 0.294030
\(136\) −3.52002 −0.301839
\(137\) 6.59136 0.563138 0.281569 0.959541i \(-0.409145\pi\)
0.281569 + 0.959541i \(0.409145\pi\)
\(138\) 2.08066 0.177118
\(139\) 9.80432 0.831592 0.415796 0.909458i \(-0.363503\pi\)
0.415796 + 0.909458i \(0.363503\pi\)
\(140\) 0 0
\(141\) 5.13896 0.432779
\(142\) 3.67623 0.308502
\(143\) −1.52597 −0.127608
\(144\) 2.95449 0.246207
\(145\) −1.72994 −0.143663
\(146\) 5.29838 0.438497
\(147\) 0 0
\(148\) −12.2530 −1.00719
\(149\) −16.2225 −1.32900 −0.664501 0.747288i \(-0.731356\pi\)
−0.664501 + 0.747288i \(0.731356\pi\)
\(150\) 2.82746 0.230862
\(151\) 10.1199 0.823542 0.411771 0.911287i \(-0.364910\pi\)
0.411771 + 0.911287i \(0.364910\pi\)
\(152\) 11.8227 0.958944
\(153\) −2.17395 −0.175754
\(154\) 0 0
\(155\) 20.6458 1.65831
\(156\) −2.29869 −0.184042
\(157\) −9.73266 −0.776751 −0.388375 0.921501i \(-0.626964\pi\)
−0.388375 + 0.921501i \(0.626964\pi\)
\(158\) −3.36925 −0.268043
\(159\) 7.67647 0.608784
\(160\) 15.3412 1.21283
\(161\) 0 0
\(162\) −0.423828 −0.0332990
\(163\) −8.37276 −0.655805 −0.327902 0.944712i \(-0.606342\pi\)
−0.327902 + 0.944712i \(0.606342\pi\)
\(164\) −1.82037 −0.142147
\(165\) 4.12842 0.321397
\(166\) −2.34720 −0.182178
\(167\) 8.10166 0.626925 0.313463 0.949601i \(-0.398511\pi\)
0.313463 + 0.949601i \(0.398511\pi\)
\(168\) 0 0
\(169\) −11.4054 −0.877342
\(170\) −3.14774 −0.241420
\(171\) 7.30164 0.558370
\(172\) 13.1264 1.00088
\(173\) 20.1515 1.53209 0.766045 0.642787i \(-0.222222\pi\)
0.766045 + 0.642787i \(0.222222\pi\)
\(174\) 0.214615 0.0162699
\(175\) 0 0
\(176\) 3.57032 0.269123
\(177\) 3.05287 0.229468
\(178\) 1.96841 0.147539
\(179\) −22.8501 −1.70790 −0.853949 0.520356i \(-0.825799\pi\)
−0.853949 + 0.520356i \(0.825799\pi\)
\(180\) 6.21897 0.463535
\(181\) 4.04932 0.300984 0.150492 0.988611i \(-0.451914\pi\)
0.150492 + 0.988611i \(0.451914\pi\)
\(182\) 0 0
\(183\) 1.50585 0.111316
\(184\) 7.94890 0.586001
\(185\) −22.9954 −1.69065
\(186\) −2.56131 −0.187805
\(187\) −2.62709 −0.192112
\(188\) 9.35481 0.682270
\(189\) 0 0
\(190\) 10.5723 0.766994
\(191\) −7.32116 −0.529741 −0.264870 0.964284i \(-0.585329\pi\)
−0.264870 + 0.964284i \(0.585329\pi\)
\(192\) 4.00576 0.289090
\(193\) 7.86097 0.565845 0.282922 0.959143i \(-0.408696\pi\)
0.282922 + 0.959143i \(0.408696\pi\)
\(194\) −0.479150 −0.0344010
\(195\) −4.31399 −0.308931
\(196\) 0 0
\(197\) −15.2389 −1.08573 −0.542865 0.839820i \(-0.682660\pi\)
−0.542865 + 0.839820i \(0.682660\pi\)
\(198\) −0.512171 −0.0363984
\(199\) 0.755541 0.0535589 0.0267795 0.999641i \(-0.491475\pi\)
0.0267795 + 0.999641i \(0.491475\pi\)
\(200\) 10.8020 0.763814
\(201\) −2.66239 −0.187791
\(202\) 2.25268 0.158498
\(203\) 0 0
\(204\) −3.95740 −0.277073
\(205\) −3.41632 −0.238606
\(206\) −2.28391 −0.159128
\(207\) 4.90922 0.341214
\(208\) −3.73080 −0.258685
\(209\) 8.82360 0.610341
\(210\) 0 0
\(211\) 18.4932 1.27312 0.636562 0.771225i \(-0.280356\pi\)
0.636562 + 0.771225i \(0.280356\pi\)
\(212\) 13.9740 0.959739
\(213\) 8.67388 0.594324
\(214\) −1.17771 −0.0805063
\(215\) 24.6345 1.68006
\(216\) −1.61918 −0.110171
\(217\) 0 0
\(218\) −4.94087 −0.334638
\(219\) 12.5013 0.844756
\(220\) 7.51526 0.506679
\(221\) 2.74518 0.184661
\(222\) 2.85280 0.191467
\(223\) −0.388827 −0.0260378 −0.0130189 0.999915i \(-0.504144\pi\)
−0.0130189 + 0.999915i \(0.504144\pi\)
\(224\) 0 0
\(225\) 6.67126 0.444751
\(226\) −4.92745 −0.327769
\(227\) −3.86038 −0.256223 −0.128111 0.991760i \(-0.540891\pi\)
−0.128111 + 0.991760i \(0.540891\pi\)
\(228\) 13.2917 0.880264
\(229\) −20.9616 −1.38518 −0.692591 0.721331i \(-0.743531\pi\)
−0.692591 + 0.721331i \(0.743531\pi\)
\(230\) 7.10821 0.468702
\(231\) 0 0
\(232\) 0.819910 0.0538297
\(233\) −4.79767 −0.314306 −0.157153 0.987574i \(-0.550232\pi\)
−0.157153 + 0.987574i \(0.550232\pi\)
\(234\) 0.535192 0.0349866
\(235\) 17.5564 1.14525
\(236\) 5.55735 0.361753
\(237\) −7.94958 −0.516380
\(238\) 0 0
\(239\) 16.4100 1.06147 0.530737 0.847536i \(-0.321915\pi\)
0.530737 + 0.847536i \(0.321915\pi\)
\(240\) 10.0935 0.651532
\(241\) −29.2741 −1.88571 −0.942856 0.333199i \(-0.891872\pi\)
−0.942856 + 0.333199i \(0.891872\pi\)
\(242\) 4.04318 0.259905
\(243\) −1.00000 −0.0641500
\(244\) 2.74121 0.175488
\(245\) 0 0
\(246\) 0.423828 0.0270223
\(247\) −9.22021 −0.586668
\(248\) −9.78516 −0.621358
\(249\) −5.53811 −0.350963
\(250\) 2.41987 0.153046
\(251\) −16.9300 −1.06861 −0.534305 0.845292i \(-0.679427\pi\)
−0.534305 + 0.845292i \(0.679427\pi\)
\(252\) 0 0
\(253\) 5.93250 0.372973
\(254\) −3.97353 −0.249321
\(255\) −7.42693 −0.465092
\(256\) 3.48552 0.217845
\(257\) −17.2556 −1.07637 −0.538186 0.842826i \(-0.680890\pi\)
−0.538186 + 0.842826i \(0.680890\pi\)
\(258\) −3.05615 −0.190268
\(259\) 0 0
\(260\) −7.85306 −0.487026
\(261\) 0.506374 0.0313438
\(262\) 2.38908 0.147598
\(263\) 20.1756 1.24408 0.622041 0.782984i \(-0.286304\pi\)
0.622041 + 0.782984i \(0.286304\pi\)
\(264\) −1.95668 −0.120425
\(265\) 26.2253 1.61101
\(266\) 0 0
\(267\) 4.64437 0.284231
\(268\) −4.84654 −0.296050
\(269\) −19.9933 −1.21901 −0.609506 0.792781i \(-0.708632\pi\)
−0.609506 + 0.792781i \(0.708632\pi\)
\(270\) −1.44793 −0.0881183
\(271\) 30.7338 1.86694 0.933471 0.358652i \(-0.116764\pi\)
0.933471 + 0.358652i \(0.116764\pi\)
\(272\) −6.42292 −0.389447
\(273\) 0 0
\(274\) −2.79360 −0.168768
\(275\) 8.06182 0.486146
\(276\) 8.93659 0.537920
\(277\) 17.0956 1.02718 0.513588 0.858037i \(-0.328316\pi\)
0.513588 + 0.858037i \(0.328316\pi\)
\(278\) −4.15534 −0.249221
\(279\) −6.04329 −0.361802
\(280\) 0 0
\(281\) −6.90275 −0.411783 −0.205892 0.978575i \(-0.566009\pi\)
−0.205892 + 0.978575i \(0.566009\pi\)
\(282\) −2.17803 −0.129700
\(283\) 14.7476 0.876653 0.438326 0.898816i \(-0.355571\pi\)
0.438326 + 0.898816i \(0.355571\pi\)
\(284\) 15.7897 0.936944
\(285\) 24.9448 1.47760
\(286\) 0.646748 0.0382430
\(287\) 0 0
\(288\) −4.49055 −0.264608
\(289\) −12.2739 −0.721996
\(290\) 0.733195 0.0430547
\(291\) −1.13053 −0.0662729
\(292\) 22.7569 1.33175
\(293\) 4.27776 0.249910 0.124955 0.992162i \(-0.460121\pi\)
0.124955 + 0.992162i \(0.460121\pi\)
\(294\) 0 0
\(295\) 10.4296 0.607234
\(296\) 10.8987 0.633477
\(297\) −1.20844 −0.0701208
\(298\) 6.87556 0.398290
\(299\) −6.19915 −0.358506
\(300\) 12.1442 0.701144
\(301\) 0 0
\(302\) −4.28907 −0.246808
\(303\) 5.31509 0.305344
\(304\) 21.5726 1.23727
\(305\) 5.14448 0.294572
\(306\) 0.921382 0.0526719
\(307\) 13.5544 0.773593 0.386796 0.922165i \(-0.373582\pi\)
0.386796 + 0.922165i \(0.373582\pi\)
\(308\) 0 0
\(309\) −5.38877 −0.306557
\(310\) −8.75027 −0.496982
\(311\) 1.34293 0.0761505 0.0380753 0.999275i \(-0.487877\pi\)
0.0380753 + 0.999275i \(0.487877\pi\)
\(312\) 2.04463 0.115754
\(313\) −12.5685 −0.710415 −0.355208 0.934787i \(-0.615590\pi\)
−0.355208 + 0.934787i \(0.615590\pi\)
\(314\) 4.12497 0.232785
\(315\) 0 0
\(316\) −14.4712 −0.814067
\(317\) −8.59197 −0.482573 −0.241287 0.970454i \(-0.577569\pi\)
−0.241287 + 0.970454i \(0.577569\pi\)
\(318\) −3.25350 −0.182447
\(319\) 0.611923 0.0342611
\(320\) 13.6850 0.765012
\(321\) −2.77874 −0.155094
\(322\) 0 0
\(323\) −15.8734 −0.883221
\(324\) −1.82037 −0.101132
\(325\) −8.42419 −0.467290
\(326\) 3.54861 0.196539
\(327\) −11.6577 −0.644674
\(328\) 1.61918 0.0894042
\(329\) 0 0
\(330\) −1.74974 −0.0963200
\(331\) 35.0682 1.92752 0.963761 0.266766i \(-0.0859551\pi\)
0.963761 + 0.266766i \(0.0859551\pi\)
\(332\) −10.0814 −0.553289
\(333\) 6.73103 0.368858
\(334\) −3.43371 −0.187884
\(335\) −9.09559 −0.496945
\(336\) 0 0
\(337\) 14.8438 0.808594 0.404297 0.914628i \(-0.367516\pi\)
0.404297 + 0.914628i \(0.367516\pi\)
\(338\) 4.83394 0.262932
\(339\) −11.6261 −0.631441
\(340\) −13.5198 −0.733212
\(341\) −7.30296 −0.395477
\(342\) −3.09464 −0.167339
\(343\) 0 0
\(344\) −11.6756 −0.629508
\(345\) 16.7715 0.902946
\(346\) −8.54076 −0.459154
\(347\) −2.60346 −0.139761 −0.0698805 0.997555i \(-0.522262\pi\)
−0.0698805 + 0.997555i \(0.522262\pi\)
\(348\) 0.921788 0.0494130
\(349\) −10.8091 −0.578596 −0.289298 0.957239i \(-0.593422\pi\)
−0.289298 + 0.957239i \(0.593422\pi\)
\(350\) 0 0
\(351\) 1.26276 0.0674010
\(352\) −5.42656 −0.289237
\(353\) 28.5337 1.51869 0.759347 0.650686i \(-0.225518\pi\)
0.759347 + 0.650686i \(0.225518\pi\)
\(354\) −1.29389 −0.0687695
\(355\) 29.6328 1.57274
\(356\) 8.45448 0.448086
\(357\) 0 0
\(358\) 9.68452 0.511843
\(359\) 5.71023 0.301375 0.150687 0.988581i \(-0.451851\pi\)
0.150687 + 0.988581i \(0.451851\pi\)
\(360\) −5.53164 −0.291543
\(361\) 34.3140 1.80600
\(362\) −1.71622 −0.0902023
\(363\) 9.53967 0.500703
\(364\) 0 0
\(365\) 42.7083 2.23546
\(366\) −0.638222 −0.0333604
\(367\) 35.6658 1.86174 0.930869 0.365354i \(-0.119052\pi\)
0.930869 + 0.365354i \(0.119052\pi\)
\(368\) 14.5042 0.756085
\(369\) 1.00000 0.0520579
\(370\) 9.74608 0.506675
\(371\) 0 0
\(372\) −11.0010 −0.570376
\(373\) −30.0359 −1.55520 −0.777600 0.628760i \(-0.783563\pi\)
−0.777600 + 0.628760i \(0.783563\pi\)
\(374\) 1.11344 0.0575744
\(375\) 5.70956 0.294841
\(376\) −8.32090 −0.429118
\(377\) −0.639428 −0.0329322
\(378\) 0 0
\(379\) −31.5503 −1.62063 −0.810316 0.585994i \(-0.800704\pi\)
−0.810316 + 0.585994i \(0.800704\pi\)
\(380\) 45.4087 2.32942
\(381\) −9.37534 −0.480313
\(382\) 3.10291 0.158759
\(383\) 12.9828 0.663392 0.331696 0.943386i \(-0.392379\pi\)
0.331696 + 0.943386i \(0.392379\pi\)
\(384\) −10.6789 −0.544953
\(385\) 0 0
\(386\) −3.33169 −0.169579
\(387\) −7.21084 −0.366547
\(388\) −2.05798 −0.104478
\(389\) 27.2660 1.38244 0.691220 0.722644i \(-0.257073\pi\)
0.691220 + 0.722644i \(0.257073\pi\)
\(390\) 1.82839 0.0925840
\(391\) −10.6724 −0.539727
\(392\) 0 0
\(393\) 5.63692 0.284345
\(394\) 6.45868 0.325384
\(395\) −27.1583 −1.36648
\(396\) −2.19981 −0.110545
\(397\) 13.0527 0.655097 0.327548 0.944834i \(-0.393778\pi\)
0.327548 + 0.944834i \(0.393778\pi\)
\(398\) −0.320219 −0.0160511
\(399\) 0 0
\(400\) 19.7102 0.985508
\(401\) 21.1440 1.05588 0.527940 0.849282i \(-0.322965\pi\)
0.527940 + 0.849282i \(0.322965\pi\)
\(402\) 1.12840 0.0562793
\(403\) 7.63121 0.380138
\(404\) 9.67543 0.481371
\(405\) −3.41632 −0.169758
\(406\) 0 0
\(407\) 8.13406 0.403190
\(408\) 3.52002 0.174267
\(409\) 21.5539 1.06577 0.532887 0.846186i \(-0.321107\pi\)
0.532887 + 0.846186i \(0.321107\pi\)
\(410\) 1.44793 0.0715083
\(411\) −6.59136 −0.325128
\(412\) −9.80956 −0.483282
\(413\) 0 0
\(414\) −2.08066 −0.102259
\(415\) −18.9200 −0.928744
\(416\) 5.67048 0.278018
\(417\) −9.80432 −0.480120
\(418\) −3.73969 −0.182914
\(419\) −26.8639 −1.31239 −0.656194 0.754592i \(-0.727835\pi\)
−0.656194 + 0.754592i \(0.727835\pi\)
\(420\) 0 0
\(421\) 35.5557 1.73288 0.866440 0.499282i \(-0.166403\pi\)
0.866440 + 0.499282i \(0.166403\pi\)
\(422\) −7.83793 −0.381545
\(423\) −5.13896 −0.249865
\(424\) −12.4296 −0.603634
\(425\) −14.5030 −0.703499
\(426\) −3.67623 −0.178114
\(427\) 0 0
\(428\) −5.05833 −0.244504
\(429\) 1.52597 0.0736744
\(430\) −10.4408 −0.503500
\(431\) −17.9655 −0.865366 −0.432683 0.901546i \(-0.642433\pi\)
−0.432683 + 0.901546i \(0.642433\pi\)
\(432\) −2.95449 −0.142148
\(433\) 1.94081 0.0932692 0.0466346 0.998912i \(-0.485150\pi\)
0.0466346 + 0.998912i \(0.485150\pi\)
\(434\) 0 0
\(435\) 1.72994 0.0829441
\(436\) −21.2214 −1.01632
\(437\) 35.8453 1.71472
\(438\) −5.29838 −0.253166
\(439\) 19.9327 0.951334 0.475667 0.879626i \(-0.342207\pi\)
0.475667 + 0.879626i \(0.342207\pi\)
\(440\) −6.68466 −0.318678
\(441\) 0 0
\(442\) −1.16348 −0.0553412
\(443\) 41.5846 1.97575 0.987873 0.155263i \(-0.0496226\pi\)
0.987873 + 0.155263i \(0.0496226\pi\)
\(444\) 12.2530 0.581500
\(445\) 15.8667 0.752153
\(446\) 0.164796 0.00780330
\(447\) 16.2225 0.767299
\(448\) 0 0
\(449\) −25.2582 −1.19201 −0.596003 0.802982i \(-0.703245\pi\)
−0.596003 + 0.802982i \(0.703245\pi\)
\(450\) −2.82746 −0.133288
\(451\) 1.20844 0.0569033
\(452\) −21.1637 −0.995459
\(453\) −10.1199 −0.475472
\(454\) 1.63614 0.0767877
\(455\) 0 0
\(456\) −11.8227 −0.553647
\(457\) 24.9161 1.16552 0.582762 0.812643i \(-0.301972\pi\)
0.582762 + 0.812643i \(0.301972\pi\)
\(458\) 8.88411 0.415127
\(459\) 2.17395 0.101471
\(460\) 30.5303 1.42348
\(461\) 21.5407 1.00325 0.501626 0.865085i \(-0.332735\pi\)
0.501626 + 0.865085i \(0.332735\pi\)
\(462\) 0 0
\(463\) 4.53297 0.210665 0.105332 0.994437i \(-0.466409\pi\)
0.105332 + 0.994437i \(0.466409\pi\)
\(464\) 1.49608 0.0694536
\(465\) −20.6458 −0.957427
\(466\) 2.03338 0.0941947
\(467\) −15.2773 −0.706947 −0.353474 0.935445i \(-0.615000\pi\)
−0.353474 + 0.935445i \(0.615000\pi\)
\(468\) 2.29869 0.106257
\(469\) 0 0
\(470\) −7.44087 −0.343222
\(471\) 9.73266 0.448457
\(472\) −4.94314 −0.227526
\(473\) −8.71387 −0.400664
\(474\) 3.36925 0.154755
\(475\) 48.7112 2.23502
\(476\) 0 0
\(477\) −7.67647 −0.351481
\(478\) −6.95501 −0.318115
\(479\) 15.1805 0.693616 0.346808 0.937936i \(-0.387266\pi\)
0.346808 + 0.937936i \(0.387266\pi\)
\(480\) −15.3412 −0.700225
\(481\) −8.49967 −0.387551
\(482\) 12.4072 0.565132
\(483\) 0 0
\(484\) 17.3657 0.789351
\(485\) −3.86226 −0.175376
\(486\) 0.423828 0.0192252
\(487\) −6.13268 −0.277898 −0.138949 0.990300i \(-0.544372\pi\)
−0.138949 + 0.990300i \(0.544372\pi\)
\(488\) −2.43825 −0.110374
\(489\) 8.37276 0.378629
\(490\) 0 0
\(491\) 26.8565 1.21202 0.606009 0.795457i \(-0.292769\pi\)
0.606009 + 0.795457i \(0.292769\pi\)
\(492\) 1.82037 0.0820686
\(493\) −1.10083 −0.0495790
\(494\) 3.90778 0.175819
\(495\) −4.12842 −0.185559
\(496\) −17.8548 −0.801705
\(497\) 0 0
\(498\) 2.34720 0.105181
\(499\) 30.2368 1.35358 0.676792 0.736174i \(-0.263370\pi\)
0.676792 + 0.736174i \(0.263370\pi\)
\(500\) 10.3935 0.464812
\(501\) −8.10166 −0.361955
\(502\) 7.17539 0.320253
\(503\) 21.6645 0.965971 0.482985 0.875628i \(-0.339552\pi\)
0.482985 + 0.875628i \(0.339552\pi\)
\(504\) 0 0
\(505\) 18.1581 0.808023
\(506\) −2.51436 −0.111777
\(507\) 11.4054 0.506533
\(508\) −17.0666 −0.757208
\(509\) −18.6777 −0.827876 −0.413938 0.910305i \(-0.635847\pi\)
−0.413938 + 0.910305i \(0.635847\pi\)
\(510\) 3.14774 0.139384
\(511\) 0 0
\(512\) −22.8350 −1.00917
\(513\) −7.30164 −0.322375
\(514\) 7.31338 0.322580
\(515\) −18.4098 −0.811232
\(516\) −13.1264 −0.577857
\(517\) −6.21013 −0.273121
\(518\) 0 0
\(519\) −20.1515 −0.884552
\(520\) 6.98512 0.306318
\(521\) −39.8641 −1.74648 −0.873239 0.487291i \(-0.837985\pi\)
−0.873239 + 0.487291i \(0.837985\pi\)
\(522\) −0.214615 −0.00939346
\(523\) 16.5889 0.725381 0.362690 0.931910i \(-0.381858\pi\)
0.362690 + 0.931910i \(0.381858\pi\)
\(524\) 10.2613 0.448266
\(525\) 0 0
\(526\) −8.55099 −0.372841
\(527\) 13.1378 0.572293
\(528\) −3.57032 −0.155378
\(529\) 1.10041 0.0478441
\(530\) −11.1150 −0.482805
\(531\) −3.05287 −0.132483
\(532\) 0 0
\(533\) −1.26276 −0.0546961
\(534\) −1.96841 −0.0851816
\(535\) −9.49307 −0.410421
\(536\) 4.31089 0.186202
\(537\) 22.8501 0.986056
\(538\) 8.47371 0.365328
\(539\) 0 0
\(540\) −6.21897 −0.267622
\(541\) 22.9294 0.985813 0.492906 0.870082i \(-0.335935\pi\)
0.492906 + 0.870082i \(0.335935\pi\)
\(542\) −13.0258 −0.559507
\(543\) −4.04932 −0.173773
\(544\) 9.76225 0.418553
\(545\) −39.8266 −1.70598
\(546\) 0 0
\(547\) 9.12814 0.390291 0.195146 0.980774i \(-0.437482\pi\)
0.195146 + 0.980774i \(0.437482\pi\)
\(548\) −11.9987 −0.512560
\(549\) −1.50585 −0.0642682
\(550\) −3.41682 −0.145694
\(551\) 3.69736 0.157513
\(552\) −7.94890 −0.338328
\(553\) 0 0
\(554\) −7.24560 −0.307836
\(555\) 22.9954 0.976100
\(556\) −17.8475 −0.756902
\(557\) 18.9625 0.803465 0.401732 0.915757i \(-0.368408\pi\)
0.401732 + 0.915757i \(0.368408\pi\)
\(558\) 2.56131 0.108429
\(559\) 9.10554 0.385123
\(560\) 0 0
\(561\) 2.62709 0.110916
\(562\) 2.92558 0.123408
\(563\) −41.9549 −1.76819 −0.884093 0.467310i \(-0.845223\pi\)
−0.884093 + 0.467310i \(0.845223\pi\)
\(564\) −9.35481 −0.393909
\(565\) −39.7184 −1.67097
\(566\) −6.25043 −0.262725
\(567\) 0 0
\(568\) −14.0446 −0.589296
\(569\) 3.36971 0.141266 0.0706328 0.997502i \(-0.477498\pi\)
0.0706328 + 0.997502i \(0.477498\pi\)
\(570\) −10.5723 −0.442824
\(571\) −7.37068 −0.308454 −0.154227 0.988035i \(-0.549289\pi\)
−0.154227 + 0.988035i \(0.549289\pi\)
\(572\) 2.77783 0.116147
\(573\) 7.32116 0.305846
\(574\) 0 0
\(575\) 32.7507 1.36580
\(576\) −4.00576 −0.166906
\(577\) −32.5328 −1.35436 −0.677180 0.735818i \(-0.736798\pi\)
−0.677180 + 0.735818i \(0.736798\pi\)
\(578\) 5.20203 0.216376
\(579\) −7.86097 −0.326691
\(580\) 3.14913 0.130760
\(581\) 0 0
\(582\) 0.479150 0.0198614
\(583\) −9.27656 −0.384196
\(584\) −20.2418 −0.837610
\(585\) 4.31399 0.178361
\(586\) −1.81303 −0.0748957
\(587\) −29.8858 −1.23352 −0.616759 0.787152i \(-0.711555\pi\)
−0.616759 + 0.787152i \(0.711555\pi\)
\(588\) 0 0
\(589\) −44.1259 −1.81818
\(590\) −4.42035 −0.181983
\(591\) 15.2389 0.626846
\(592\) 19.8868 0.817341
\(593\) −35.3874 −1.45319 −0.726594 0.687068i \(-0.758898\pi\)
−0.726594 + 0.687068i \(0.758898\pi\)
\(594\) 0.512171 0.0210146
\(595\) 0 0
\(596\) 29.5310 1.20964
\(597\) −0.755541 −0.0309222
\(598\) 2.62737 0.107441
\(599\) −12.9486 −0.529064 −0.264532 0.964377i \(-0.585217\pi\)
−0.264532 + 0.964377i \(0.585217\pi\)
\(600\) −10.8020 −0.440988
\(601\) 31.0540 1.26672 0.633359 0.773858i \(-0.281676\pi\)
0.633359 + 0.773858i \(0.281676\pi\)
\(602\) 0 0
\(603\) 2.66239 0.108421
\(604\) −18.4219 −0.749575
\(605\) 32.5906 1.32500
\(606\) −2.25268 −0.0915090
\(607\) −6.57550 −0.266891 −0.133446 0.991056i \(-0.542604\pi\)
−0.133446 + 0.991056i \(0.542604\pi\)
\(608\) −32.7884 −1.32974
\(609\) 0 0
\(610\) −2.18037 −0.0882807
\(611\) 6.48927 0.262528
\(612\) 3.95740 0.159968
\(613\) 9.22564 0.372620 0.186310 0.982491i \(-0.440347\pi\)
0.186310 + 0.982491i \(0.440347\pi\)
\(614\) −5.74475 −0.231839
\(615\) 3.41632 0.137759
\(616\) 0 0
\(617\) −30.7333 −1.23727 −0.618637 0.785677i \(-0.712315\pi\)
−0.618637 + 0.785677i \(0.712315\pi\)
\(618\) 2.28391 0.0918724
\(619\) 10.0098 0.402328 0.201164 0.979558i \(-0.435528\pi\)
0.201164 + 0.979558i \(0.435528\pi\)
\(620\) −37.5830 −1.50937
\(621\) −4.90922 −0.197000
\(622\) −0.569171 −0.0228217
\(623\) 0 0
\(624\) 3.73080 0.149352
\(625\) −13.8506 −0.554023
\(626\) 5.32689 0.212905
\(627\) −8.82360 −0.352381
\(628\) 17.7170 0.706987
\(629\) −14.6330 −0.583454
\(630\) 0 0
\(631\) −36.9084 −1.46930 −0.734649 0.678447i \(-0.762653\pi\)
−0.734649 + 0.678447i \(0.762653\pi\)
\(632\) 12.8718 0.512012
\(633\) −18.4932 −0.735039
\(634\) 3.64152 0.144623
\(635\) −32.0292 −1.27104
\(636\) −13.9740 −0.554106
\(637\) 0 0
\(638\) −0.259350 −0.0102678
\(639\) −8.67388 −0.343133
\(640\) −36.4824 −1.44209
\(641\) 5.70866 0.225478 0.112739 0.993625i \(-0.464038\pi\)
0.112739 + 0.993625i \(0.464038\pi\)
\(642\) 1.17771 0.0464804
\(643\) 18.1855 0.717166 0.358583 0.933498i \(-0.383260\pi\)
0.358583 + 0.933498i \(0.383260\pi\)
\(644\) 0 0
\(645\) −24.6345 −0.969984
\(646\) 6.72760 0.264694
\(647\) 26.0068 1.02243 0.511217 0.859452i \(-0.329195\pi\)
0.511217 + 0.859452i \(0.329195\pi\)
\(648\) 1.61918 0.0636073
\(649\) −3.68921 −0.144814
\(650\) 3.57040 0.140043
\(651\) 0 0
\(652\) 15.2415 0.596904
\(653\) 35.2363 1.37890 0.689451 0.724332i \(-0.257852\pi\)
0.689451 + 0.724332i \(0.257852\pi\)
\(654\) 4.94087 0.193203
\(655\) 19.2575 0.752454
\(656\) 2.95449 0.115353
\(657\) −12.5013 −0.487720
\(658\) 0 0
\(659\) −44.6310 −1.73858 −0.869289 0.494304i \(-0.835423\pi\)
−0.869289 + 0.494304i \(0.835423\pi\)
\(660\) −7.51526 −0.292531
\(661\) 2.58592 0.100581 0.0502903 0.998735i \(-0.483985\pi\)
0.0502903 + 0.998735i \(0.483985\pi\)
\(662\) −14.8629 −0.577662
\(663\) −2.74518 −0.106614
\(664\) 8.96718 0.347994
\(665\) 0 0
\(666\) −2.85280 −0.110544
\(667\) 2.48590 0.0962544
\(668\) −14.7480 −0.570618
\(669\) 0.388827 0.0150329
\(670\) 3.85496 0.148930
\(671\) −1.81973 −0.0702501
\(672\) 0 0
\(673\) −28.3612 −1.09324 −0.546621 0.837380i \(-0.684086\pi\)
−0.546621 + 0.837380i \(0.684086\pi\)
\(674\) −6.29122 −0.242329
\(675\) −6.67126 −0.256777
\(676\) 20.7621 0.798543
\(677\) 27.6693 1.06342 0.531709 0.846927i \(-0.321550\pi\)
0.531709 + 0.846927i \(0.321550\pi\)
\(678\) 4.92745 0.189237
\(679\) 0 0
\(680\) 12.0255 0.461158
\(681\) 3.86038 0.147930
\(682\) 3.09519 0.118521
\(683\) −25.5819 −0.978863 −0.489432 0.872042i \(-0.662796\pi\)
−0.489432 + 0.872042i \(0.662796\pi\)
\(684\) −13.2917 −0.508220
\(685\) −22.5182 −0.860377
\(686\) 0 0
\(687\) 20.9616 0.799735
\(688\) −21.3043 −0.812220
\(689\) 9.69352 0.369294
\(690\) −7.10821 −0.270605
\(691\) −27.6456 −1.05169 −0.525845 0.850581i \(-0.676251\pi\)
−0.525845 + 0.850581i \(0.676251\pi\)
\(692\) −36.6832 −1.39448
\(693\) 0 0
\(694\) 1.10342 0.0418852
\(695\) −33.4947 −1.27053
\(696\) −0.819910 −0.0310786
\(697\) −2.17395 −0.0823444
\(698\) 4.58118 0.173400
\(699\) 4.79767 0.181464
\(700\) 0 0
\(701\) 46.2861 1.74820 0.874101 0.485745i \(-0.161452\pi\)
0.874101 + 0.485745i \(0.161452\pi\)
\(702\) −0.535192 −0.0201995
\(703\) 49.1476 1.85364
\(704\) −4.84072 −0.182441
\(705\) −17.5564 −0.661211
\(706\) −12.0934 −0.455140
\(707\) 0 0
\(708\) −5.55735 −0.208858
\(709\) 13.4057 0.503461 0.251730 0.967797i \(-0.419000\pi\)
0.251730 + 0.967797i \(0.419000\pi\)
\(710\) −12.5592 −0.471338
\(711\) 7.94958 0.298132
\(712\) −7.52007 −0.281827
\(713\) −29.6678 −1.11107
\(714\) 0 0
\(715\) 5.21320 0.194963
\(716\) 41.5957 1.55450
\(717\) −16.4100 −0.612843
\(718\) −2.42015 −0.0903194
\(719\) −42.4424 −1.58283 −0.791417 0.611276i \(-0.790656\pi\)
−0.791417 + 0.611276i \(0.790656\pi\)
\(720\) −10.0935 −0.376162
\(721\) 0 0
\(722\) −14.5432 −0.541242
\(723\) 29.2741 1.08872
\(724\) −7.37127 −0.273951
\(725\) 3.37815 0.125461
\(726\) −4.04318 −0.150056
\(727\) 20.6826 0.767077 0.383538 0.923525i \(-0.374705\pi\)
0.383538 + 0.923525i \(0.374705\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −18.1010 −0.669947
\(731\) 15.6760 0.579799
\(732\) −2.74121 −0.101318
\(733\) 26.2703 0.970314 0.485157 0.874427i \(-0.338762\pi\)
0.485157 + 0.874427i \(0.338762\pi\)
\(734\) −15.1161 −0.557947
\(735\) 0 0
\(736\) −22.0451 −0.812593
\(737\) 3.21734 0.118512
\(738\) −0.423828 −0.0156013
\(739\) −0.000930324 0 −3.42225e−5 0 −1.71113e−5 1.00000i \(-0.500005\pi\)
−1.71113e−5 1.00000i \(0.500005\pi\)
\(740\) 41.8601 1.53881
\(741\) 9.22021 0.338713
\(742\) 0 0
\(743\) −12.6652 −0.464641 −0.232321 0.972639i \(-0.574632\pi\)
−0.232321 + 0.972639i \(0.574632\pi\)
\(744\) 9.78516 0.358741
\(745\) 55.4214 2.03048
\(746\) 12.7300 0.466080
\(747\) 5.53811 0.202629
\(748\) 4.78228 0.174858
\(749\) 0 0
\(750\) −2.41987 −0.0883612
\(751\) −10.0869 −0.368075 −0.184038 0.982919i \(-0.558917\pi\)
−0.184038 + 0.982919i \(0.558917\pi\)
\(752\) −15.1830 −0.553667
\(753\) 16.9300 0.616963
\(754\) 0.271007 0.00986950
\(755\) −34.5727 −1.25823
\(756\) 0 0
\(757\) 15.8957 0.577739 0.288869 0.957369i \(-0.406721\pi\)
0.288869 + 0.957369i \(0.406721\pi\)
\(758\) 13.3719 0.485689
\(759\) −5.93250 −0.215336
\(760\) −40.3900 −1.46510
\(761\) −6.40153 −0.232055 −0.116028 0.993246i \(-0.537016\pi\)
−0.116028 + 0.993246i \(0.537016\pi\)
\(762\) 3.97353 0.143946
\(763\) 0 0
\(764\) 13.3272 0.482162
\(765\) 7.42693 0.268521
\(766\) −5.50249 −0.198813
\(767\) 3.85503 0.139197
\(768\) −3.48552 −0.125773
\(769\) 35.6888 1.28697 0.643485 0.765459i \(-0.277488\pi\)
0.643485 + 0.765459i \(0.277488\pi\)
\(770\) 0 0
\(771\) 17.2556 0.621444
\(772\) −14.3099 −0.515023
\(773\) 33.3248 1.19861 0.599305 0.800521i \(-0.295444\pi\)
0.599305 + 0.800521i \(0.295444\pi\)
\(774\) 3.05615 0.109851
\(775\) −40.3163 −1.44821
\(776\) 1.83053 0.0657122
\(777\) 0 0
\(778\) −11.5561 −0.414306
\(779\) 7.30164 0.261608
\(780\) 7.85306 0.281185
\(781\) −10.4819 −0.375071
\(782\) 4.52326 0.161752
\(783\) −0.506374 −0.0180963
\(784\) 0 0
\(785\) 33.2499 1.18674
\(786\) −2.38908 −0.0852157
\(787\) 41.0212 1.46225 0.731124 0.682244i \(-0.238996\pi\)
0.731124 + 0.682244i \(0.238996\pi\)
\(788\) 27.7405 0.988214
\(789\) −20.1756 −0.718271
\(790\) 11.5104 0.409523
\(791\) 0 0
\(792\) 1.95668 0.0695276
\(793\) 1.90153 0.0675252
\(794\) −5.53210 −0.196327
\(795\) −26.2253 −0.930116
\(796\) −1.37536 −0.0487485
\(797\) −20.9473 −0.741990 −0.370995 0.928635i \(-0.620983\pi\)
−0.370995 + 0.928635i \(0.620983\pi\)
\(798\) 0 0
\(799\) 11.1719 0.395232
\(800\) −29.9576 −1.05916
\(801\) −4.64437 −0.164101
\(802\) −8.96140 −0.316438
\(803\) −15.1070 −0.533115
\(804\) 4.84654 0.170924
\(805\) 0 0
\(806\) −3.23432 −0.113924
\(807\) 19.9933 0.703797
\(808\) −8.60608 −0.302761
\(809\) 23.3753 0.821832 0.410916 0.911673i \(-0.365209\pi\)
0.410916 + 0.911673i \(0.365209\pi\)
\(810\) 1.44793 0.0508751
\(811\) 9.25028 0.324821 0.162411 0.986723i \(-0.448073\pi\)
0.162411 + 0.986723i \(0.448073\pi\)
\(812\) 0 0
\(813\) −30.7338 −1.07788
\(814\) −3.44744 −0.120833
\(815\) 28.6040 1.00196
\(816\) 6.42292 0.224847
\(817\) −52.6509 −1.84202
\(818\) −9.13516 −0.319403
\(819\) 0 0
\(820\) 6.21897 0.217176
\(821\) −23.9584 −0.836154 −0.418077 0.908412i \(-0.637296\pi\)
−0.418077 + 0.908412i \(0.637296\pi\)
\(822\) 2.79360 0.0974380
\(823\) −39.7518 −1.38566 −0.692830 0.721101i \(-0.743636\pi\)
−0.692830 + 0.721101i \(0.743636\pi\)
\(824\) 8.72539 0.303963
\(825\) −8.06182 −0.280677
\(826\) 0 0
\(827\) 27.1064 0.942581 0.471291 0.881978i \(-0.343788\pi\)
0.471291 + 0.881978i \(0.343788\pi\)
\(828\) −8.93659 −0.310568
\(829\) −37.7500 −1.31111 −0.655556 0.755146i \(-0.727566\pi\)
−0.655556 + 0.755146i \(0.727566\pi\)
\(830\) 8.01880 0.278337
\(831\) −17.0956 −0.593041
\(832\) 5.05830 0.175365
\(833\) 0 0
\(834\) 4.15534 0.143888
\(835\) −27.6779 −0.957832
\(836\) −16.0622 −0.555524
\(837\) 6.04329 0.208887
\(838\) 11.3857 0.393311
\(839\) 42.9086 1.48137 0.740684 0.671853i \(-0.234502\pi\)
0.740684 + 0.671853i \(0.234502\pi\)
\(840\) 0 0
\(841\) −28.7436 −0.991158
\(842\) −15.0695 −0.519329
\(843\) 6.90275 0.237743
\(844\) −33.6645 −1.15878
\(845\) 38.9647 1.34043
\(846\) 2.17803 0.0748824
\(847\) 0 0
\(848\) −22.6800 −0.778836
\(849\) −14.7476 −0.506136
\(850\) 6.14678 0.210833
\(851\) 33.0441 1.13274
\(852\) −15.7897 −0.540945
\(853\) 23.4761 0.803806 0.401903 0.915682i \(-0.368349\pi\)
0.401903 + 0.915682i \(0.368349\pi\)
\(854\) 0 0
\(855\) −24.9448 −0.853093
\(856\) 4.49927 0.153782
\(857\) 43.1486 1.47393 0.736965 0.675931i \(-0.236258\pi\)
0.736965 + 0.675931i \(0.236258\pi\)
\(858\) −0.646748 −0.0220796
\(859\) 33.5419 1.14444 0.572218 0.820102i \(-0.306083\pi\)
0.572218 + 0.820102i \(0.306083\pi\)
\(860\) −44.8440 −1.52917
\(861\) 0 0
\(862\) 7.61426 0.259343
\(863\) −20.8609 −0.710112 −0.355056 0.934845i \(-0.615538\pi\)
−0.355056 + 0.934845i \(0.615538\pi\)
\(864\) 4.49055 0.152772
\(865\) −68.8440 −2.34077
\(866\) −0.822568 −0.0279520
\(867\) 12.2739 0.416844
\(868\) 0 0
\(869\) 9.60659 0.325881
\(870\) −0.733195 −0.0248576
\(871\) −3.36196 −0.113916
\(872\) 18.8759 0.639220
\(873\) 1.13053 0.0382627
\(874\) −15.1922 −0.513885
\(875\) 0 0
\(876\) −22.7569 −0.768885
\(877\) −12.2475 −0.413569 −0.206784 0.978387i \(-0.566300\pi\)
−0.206784 + 0.978387i \(0.566300\pi\)
\(878\) −8.44801 −0.285107
\(879\) −4.27776 −0.144285
\(880\) −12.1974 −0.411173
\(881\) 42.3355 1.42632 0.713160 0.701002i \(-0.247263\pi\)
0.713160 + 0.701002i \(0.247263\pi\)
\(882\) 0 0
\(883\) 33.7723 1.13653 0.568265 0.822846i \(-0.307615\pi\)
0.568265 + 0.822846i \(0.307615\pi\)
\(884\) −4.99724 −0.168075
\(885\) −10.4296 −0.350587
\(886\) −17.6247 −0.592114
\(887\) −18.4300 −0.618819 −0.309410 0.950929i \(-0.600131\pi\)
−0.309410 + 0.950929i \(0.600131\pi\)
\(888\) −10.8987 −0.365738
\(889\) 0 0
\(890\) −6.72474 −0.225414
\(891\) 1.20844 0.0404843
\(892\) 0.707809 0.0236992
\(893\) −37.5229 −1.25565
\(894\) −6.87556 −0.229953
\(895\) 78.0634 2.60937
\(896\) 0 0
\(897\) 6.19915 0.206984
\(898\) 10.7051 0.357234
\(899\) −3.06016 −0.102062
\(900\) −12.1442 −0.404805
\(901\) 16.6883 0.555968
\(902\) −0.512171 −0.0170534
\(903\) 0 0
\(904\) 18.8247 0.626099
\(905\) −13.8338 −0.459851
\(906\) 4.28907 0.142495
\(907\) 17.8679 0.593292 0.296646 0.954987i \(-0.404132\pi\)
0.296646 + 0.954987i \(0.404132\pi\)
\(908\) 7.02733 0.233210
\(909\) −5.31509 −0.176290
\(910\) 0 0
\(911\) −52.6939 −1.74583 −0.872913 0.487877i \(-0.837772\pi\)
−0.872913 + 0.487877i \(0.837772\pi\)
\(912\) −21.5726 −0.714340
\(913\) 6.69247 0.221489
\(914\) −10.5601 −0.349298
\(915\) −5.14448 −0.170071
\(916\) 38.1579 1.26077
\(917\) 0 0
\(918\) −0.921382 −0.0304101
\(919\) −53.7884 −1.77432 −0.887158 0.461466i \(-0.847323\pi\)
−0.887158 + 0.461466i \(0.847323\pi\)
\(920\) −27.1560 −0.895307
\(921\) −13.5544 −0.446634
\(922\) −9.12956 −0.300666
\(923\) 10.9530 0.360523
\(924\) 0 0
\(925\) 44.9045 1.47645
\(926\) −1.92120 −0.0631345
\(927\) 5.38877 0.176991
\(928\) −2.27390 −0.0746444
\(929\) 1.19669 0.0392621 0.0196310 0.999807i \(-0.493751\pi\)
0.0196310 + 0.999807i \(0.493751\pi\)
\(930\) 8.75027 0.286933
\(931\) 0 0
\(932\) 8.73353 0.286076
\(933\) −1.34293 −0.0439655
\(934\) 6.47492 0.211866
\(935\) 8.97500 0.293514
\(936\) −2.04463 −0.0668308
\(937\) 2.69258 0.0879626 0.0439813 0.999032i \(-0.485996\pi\)
0.0439813 + 0.999032i \(0.485996\pi\)
\(938\) 0 0
\(939\) 12.5685 0.410158
\(940\) −31.9591 −1.04239
\(941\) 7.77008 0.253297 0.126649 0.991948i \(-0.459578\pi\)
0.126649 + 0.991948i \(0.459578\pi\)
\(942\) −4.12497 −0.134399
\(943\) 4.90922 0.159866
\(944\) −9.01966 −0.293565
\(945\) 0 0
\(946\) 3.69318 0.120076
\(947\) 22.8040 0.741032 0.370516 0.928826i \(-0.379181\pi\)
0.370516 + 0.928826i \(0.379181\pi\)
\(948\) 14.4712 0.470002
\(949\) 15.7861 0.512437
\(950\) −20.6451 −0.669817
\(951\) 8.59197 0.278614
\(952\) 0 0
\(953\) −13.6387 −0.441801 −0.220901 0.975296i \(-0.570900\pi\)
−0.220901 + 0.975296i \(0.570900\pi\)
\(954\) 3.25350 0.105336
\(955\) 25.0114 0.809351
\(956\) −29.8723 −0.966138
\(957\) −0.611923 −0.0197807
\(958\) −6.43393 −0.207871
\(959\) 0 0
\(960\) −13.6850 −0.441680
\(961\) 5.52132 0.178107
\(962\) 3.60239 0.116146
\(963\) 2.77874 0.0895436
\(964\) 53.2898 1.71635
\(965\) −26.8556 −0.864512
\(966\) 0 0
\(967\) 28.6375 0.920920 0.460460 0.887680i \(-0.347684\pi\)
0.460460 + 0.887680i \(0.347684\pi\)
\(968\) −15.4464 −0.496467
\(969\) 15.8734 0.509928
\(970\) 1.63693 0.0525587
\(971\) −18.7450 −0.601555 −0.300778 0.953694i \(-0.597246\pi\)
−0.300778 + 0.953694i \(0.597246\pi\)
\(972\) 1.82037 0.0583884
\(973\) 0 0
\(974\) 2.59920 0.0832838
\(975\) 8.42419 0.269790
\(976\) −4.44902 −0.142410
\(977\) −0.0431378 −0.00138010 −0.000690050 1.00000i \(-0.500220\pi\)
−0.000690050 1.00000i \(0.500220\pi\)
\(978\) −3.54861 −0.113472
\(979\) −5.61245 −0.179375
\(980\) 0 0
\(981\) 11.6577 0.372203
\(982\) −11.3825 −0.363232
\(983\) −18.2855 −0.583217 −0.291608 0.956538i \(-0.594190\pi\)
−0.291608 + 0.956538i \(0.594190\pi\)
\(984\) −1.61918 −0.0516175
\(985\) 52.0611 1.65881
\(986\) 0.466564 0.0148584
\(987\) 0 0
\(988\) 16.7842 0.533976
\(989\) −35.3996 −1.12564
\(990\) 1.74974 0.0556104
\(991\) 0.164594 0.00522850 0.00261425 0.999997i \(-0.499168\pi\)
0.00261425 + 0.999997i \(0.499168\pi\)
\(992\) 27.1377 0.861622
\(993\) −35.0682 −1.11286
\(994\) 0 0
\(995\) −2.58117 −0.0818287
\(996\) 10.0814 0.319442
\(997\) −8.72804 −0.276420 −0.138210 0.990403i \(-0.544135\pi\)
−0.138210 + 0.990403i \(0.544135\pi\)
\(998\) −12.8152 −0.405658
\(999\) −6.73103 −0.212961
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 \(a_p\))