Properties

Label 8027.2.a.f.1.11
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57713 q^{2} -1.48333 q^{3} +4.64158 q^{4} -1.39440 q^{5} +3.82274 q^{6} -5.10805 q^{7} -6.80769 q^{8} -0.799719 q^{9} +O(q^{10})\) \(q-2.57713 q^{2} -1.48333 q^{3} +4.64158 q^{4} -1.39440 q^{5} +3.82274 q^{6} -5.10805 q^{7} -6.80769 q^{8} -0.799719 q^{9} +3.59355 q^{10} -1.30714 q^{11} -6.88502 q^{12} +0.398449 q^{13} +13.1641 q^{14} +2.06836 q^{15} +8.26112 q^{16} +2.72438 q^{17} +2.06098 q^{18} +0.445059 q^{19} -6.47223 q^{20} +7.57695 q^{21} +3.36868 q^{22} +1.00000 q^{23} +10.0981 q^{24} -3.05565 q^{25} -1.02685 q^{26} +5.63625 q^{27} -23.7094 q^{28} -7.89244 q^{29} -5.33043 q^{30} -1.20169 q^{31} -7.67456 q^{32} +1.93893 q^{33} -7.02107 q^{34} +7.12267 q^{35} -3.71196 q^{36} +1.57974 q^{37} -1.14697 q^{38} -0.591032 q^{39} +9.49265 q^{40} +0.346533 q^{41} -19.5268 q^{42} +1.60026 q^{43} -6.06722 q^{44} +1.11513 q^{45} -2.57713 q^{46} +10.7518 q^{47} -12.2540 q^{48} +19.0922 q^{49} +7.87479 q^{50} -4.04116 q^{51} +1.84943 q^{52} -1.77650 q^{53} -14.5253 q^{54} +1.82268 q^{55} +34.7740 q^{56} -0.660172 q^{57} +20.3398 q^{58} -3.20814 q^{59} +9.60048 q^{60} -11.0073 q^{61} +3.09690 q^{62} +4.08500 q^{63} +3.25609 q^{64} -0.555597 q^{65} -4.99687 q^{66} -9.27987 q^{67} +12.6454 q^{68} -1.48333 q^{69} -18.3560 q^{70} -6.33448 q^{71} +5.44424 q^{72} +2.18771 q^{73} -4.07118 q^{74} +4.53255 q^{75} +2.06578 q^{76} +6.67696 q^{77} +1.52317 q^{78} -16.0251 q^{79} -11.5193 q^{80} -5.96129 q^{81} -0.893059 q^{82} -8.96465 q^{83} +35.1690 q^{84} -3.79888 q^{85} -4.12407 q^{86} +11.7071 q^{87} +8.89864 q^{88} -14.8082 q^{89} -2.87383 q^{90} -2.03530 q^{91} +4.64158 q^{92} +1.78250 q^{93} -27.7089 q^{94} -0.620591 q^{95} +11.3839 q^{96} +4.83280 q^{97} -49.2030 q^{98} +1.04535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57713 −1.82230 −0.911152 0.412071i \(-0.864806\pi\)
−0.911152 + 0.412071i \(0.864806\pi\)
\(3\) −1.48333 −0.856404 −0.428202 0.903683i \(-0.640853\pi\)
−0.428202 + 0.903683i \(0.640853\pi\)
\(4\) 4.64158 2.32079
\(5\) −1.39440 −0.623595 −0.311798 0.950149i \(-0.600931\pi\)
−0.311798 + 0.950149i \(0.600931\pi\)
\(6\) 3.82274 1.56063
\(7\) −5.10805 −1.93066 −0.965331 0.261029i \(-0.915938\pi\)
−0.965331 + 0.261029i \(0.915938\pi\)
\(8\) −6.80769 −2.40688
\(9\) −0.799719 −0.266573
\(10\) 3.59355 1.13638
\(11\) −1.30714 −0.394119 −0.197059 0.980392i \(-0.563139\pi\)
−0.197059 + 0.980392i \(0.563139\pi\)
\(12\) −6.88502 −1.98753
\(13\) 0.398449 0.110510 0.0552549 0.998472i \(-0.482403\pi\)
0.0552549 + 0.998472i \(0.482403\pi\)
\(14\) 13.1641 3.51825
\(15\) 2.06836 0.534049
\(16\) 8.26112 2.06528
\(17\) 2.72438 0.660759 0.330379 0.943848i \(-0.392823\pi\)
0.330379 + 0.943848i \(0.392823\pi\)
\(18\) 2.06098 0.485777
\(19\) 0.445059 0.102104 0.0510518 0.998696i \(-0.483743\pi\)
0.0510518 + 0.998696i \(0.483743\pi\)
\(20\) −6.47223 −1.44723
\(21\) 7.57695 1.65343
\(22\) 3.36868 0.718204
\(23\) 1.00000 0.208514
\(24\) 10.0981 2.06126
\(25\) −3.05565 −0.611129
\(26\) −1.02685 −0.201382
\(27\) 5.63625 1.08470
\(28\) −23.7094 −4.48066
\(29\) −7.89244 −1.46559 −0.732794 0.680450i \(-0.761784\pi\)
−0.732794 + 0.680450i \(0.761784\pi\)
\(30\) −5.33043 −0.973200
\(31\) −1.20169 −0.215829 −0.107915 0.994160i \(-0.534417\pi\)
−0.107915 + 0.994160i \(0.534417\pi\)
\(32\) −7.67456 −1.35668
\(33\) 1.93893 0.337525
\(34\) −7.02107 −1.20410
\(35\) 7.12267 1.20395
\(36\) −3.71196 −0.618660
\(37\) 1.57974 0.259707 0.129854 0.991533i \(-0.458549\pi\)
0.129854 + 0.991533i \(0.458549\pi\)
\(38\) −1.14697 −0.186064
\(39\) −0.591032 −0.0946409
\(40\) 9.49265 1.50092
\(41\) 0.346533 0.0541193 0.0270597 0.999634i \(-0.491386\pi\)
0.0270597 + 0.999634i \(0.491386\pi\)
\(42\) −19.5268 −3.01304
\(43\) 1.60026 0.244037 0.122018 0.992528i \(-0.461063\pi\)
0.122018 + 0.992528i \(0.461063\pi\)
\(44\) −6.06722 −0.914668
\(45\) 1.11513 0.166234
\(46\) −2.57713 −0.379977
\(47\) 10.7518 1.56832 0.784159 0.620560i \(-0.213095\pi\)
0.784159 + 0.620560i \(0.213095\pi\)
\(48\) −12.2540 −1.76871
\(49\) 19.0922 2.72745
\(50\) 7.87479 1.11366
\(51\) −4.04116 −0.565876
\(52\) 1.84943 0.256470
\(53\) −1.77650 −0.244020 −0.122010 0.992529i \(-0.538934\pi\)
−0.122010 + 0.992529i \(0.538934\pi\)
\(54\) −14.5253 −1.97665
\(55\) 1.82268 0.245771
\(56\) 34.7740 4.64688
\(57\) −0.660172 −0.0874419
\(58\) 20.3398 2.67075
\(59\) −3.20814 −0.417665 −0.208832 0.977951i \(-0.566966\pi\)
−0.208832 + 0.977951i \(0.566966\pi\)
\(60\) 9.60048 1.23942
\(61\) −11.0073 −1.40935 −0.704673 0.709533i \(-0.748906\pi\)
−0.704673 + 0.709533i \(0.748906\pi\)
\(62\) 3.09690 0.393307
\(63\) 4.08500 0.514662
\(64\) 3.25609 0.407011
\(65\) −0.555597 −0.0689133
\(66\) −4.99687 −0.615073
\(67\) −9.27987 −1.13372 −0.566859 0.823815i \(-0.691841\pi\)
−0.566859 + 0.823815i \(0.691841\pi\)
\(68\) 12.6454 1.53348
\(69\) −1.48333 −0.178572
\(70\) −18.3560 −2.19396
\(71\) −6.33448 −0.751765 −0.375882 0.926667i \(-0.622660\pi\)
−0.375882 + 0.926667i \(0.622660\pi\)
\(72\) 5.44424 0.641610
\(73\) 2.18771 0.256052 0.128026 0.991771i \(-0.459136\pi\)
0.128026 + 0.991771i \(0.459136\pi\)
\(74\) −4.07118 −0.473265
\(75\) 4.53255 0.523373
\(76\) 2.06578 0.236961
\(77\) 6.67696 0.760910
\(78\) 1.52317 0.172465
\(79\) −16.0251 −1.80297 −0.901485 0.432811i \(-0.857522\pi\)
−0.901485 + 0.432811i \(0.857522\pi\)
\(80\) −11.5193 −1.28790
\(81\) −5.96129 −0.662366
\(82\) −0.893059 −0.0986218
\(83\) −8.96465 −0.983998 −0.491999 0.870596i \(-0.663734\pi\)
−0.491999 + 0.870596i \(0.663734\pi\)
\(84\) 35.1690 3.83726
\(85\) −3.79888 −0.412046
\(86\) −4.12407 −0.444710
\(87\) 11.7071 1.25514
\(88\) 8.89864 0.948598
\(89\) −14.8082 −1.56967 −0.784833 0.619708i \(-0.787251\pi\)
−0.784833 + 0.619708i \(0.787251\pi\)
\(90\) −2.87383 −0.302928
\(91\) −2.03530 −0.213357
\(92\) 4.64158 0.483918
\(93\) 1.78250 0.184837
\(94\) −27.7089 −2.85795
\(95\) −0.620591 −0.0636713
\(96\) 11.3839 1.16187
\(97\) 4.83280 0.490696 0.245348 0.969435i \(-0.421098\pi\)
0.245348 + 0.969435i \(0.421098\pi\)
\(98\) −49.2030 −4.97025
\(99\) 1.04535 0.105061
\(100\) −14.1830 −1.41830
\(101\) −3.37474 −0.335799 −0.167900 0.985804i \(-0.553698\pi\)
−0.167900 + 0.985804i \(0.553698\pi\)
\(102\) 10.4146 1.03120
\(103\) 3.48034 0.342928 0.171464 0.985190i \(-0.445150\pi\)
0.171464 + 0.985190i \(0.445150\pi\)
\(104\) −2.71251 −0.265984
\(105\) −10.5653 −1.03107
\(106\) 4.57825 0.444679
\(107\) −15.2318 −1.47251 −0.736256 0.676703i \(-0.763408\pi\)
−0.736256 + 0.676703i \(0.763408\pi\)
\(108\) 26.1611 2.51736
\(109\) 19.7275 1.88955 0.944774 0.327723i \(-0.106281\pi\)
0.944774 + 0.327723i \(0.106281\pi\)
\(110\) −4.69729 −0.447869
\(111\) −2.34328 −0.222414
\(112\) −42.1982 −3.98736
\(113\) −14.4365 −1.35808 −0.679038 0.734103i \(-0.737603\pi\)
−0.679038 + 0.734103i \(0.737603\pi\)
\(114\) 1.70135 0.159346
\(115\) −1.39440 −0.130029
\(116\) −36.6334 −3.40132
\(117\) −0.318647 −0.0294589
\(118\) 8.26779 0.761112
\(119\) −13.9163 −1.27570
\(120\) −14.0808 −1.28539
\(121\) −9.29137 −0.844670
\(122\) 28.3673 2.56825
\(123\) −0.514024 −0.0463480
\(124\) −5.57773 −0.500895
\(125\) 11.2328 1.00469
\(126\) −10.5276 −0.937871
\(127\) 0.742296 0.0658681 0.0329341 0.999458i \(-0.489515\pi\)
0.0329341 + 0.999458i \(0.489515\pi\)
\(128\) 6.95777 0.614986
\(129\) −2.37372 −0.208994
\(130\) 1.43184 0.125581
\(131\) −21.1656 −1.84924 −0.924622 0.380885i \(-0.875619\pi\)
−0.924622 + 0.380885i \(0.875619\pi\)
\(132\) 8.99971 0.783325
\(133\) −2.27338 −0.197127
\(134\) 23.9154 2.06598
\(135\) −7.85920 −0.676412
\(136\) −18.5467 −1.59037
\(137\) −18.4154 −1.57333 −0.786666 0.617378i \(-0.788195\pi\)
−0.786666 + 0.617378i \(0.788195\pi\)
\(138\) 3.82274 0.325413
\(139\) 1.46667 0.124402 0.0622008 0.998064i \(-0.480188\pi\)
0.0622008 + 0.998064i \(0.480188\pi\)
\(140\) 33.0605 2.79412
\(141\) −15.9486 −1.34311
\(142\) 16.3248 1.36994
\(143\) −0.520830 −0.0435540
\(144\) −6.60657 −0.550548
\(145\) 11.0052 0.913934
\(146\) −5.63801 −0.466605
\(147\) −28.3201 −2.33580
\(148\) 7.33248 0.602726
\(149\) −10.0619 −0.824303 −0.412152 0.911115i \(-0.635223\pi\)
−0.412152 + 0.911115i \(0.635223\pi\)
\(150\) −11.6809 −0.953745
\(151\) −18.4316 −1.49994 −0.749972 0.661469i \(-0.769933\pi\)
−0.749972 + 0.661469i \(0.769933\pi\)
\(152\) −3.02983 −0.245751
\(153\) −2.17874 −0.176140
\(154\) −17.2074 −1.38661
\(155\) 1.67563 0.134590
\(156\) −2.74333 −0.219642
\(157\) −1.37048 −0.109377 −0.0546883 0.998503i \(-0.517417\pi\)
−0.0546883 + 0.998503i \(0.517417\pi\)
\(158\) 41.2988 3.28556
\(159\) 2.63514 0.208980
\(160\) 10.7014 0.846022
\(161\) −5.10805 −0.402571
\(162\) 15.3630 1.20703
\(163\) 2.11634 0.165765 0.0828823 0.996559i \(-0.473587\pi\)
0.0828823 + 0.996559i \(0.473587\pi\)
\(164\) 1.60846 0.125600
\(165\) −2.70365 −0.210479
\(166\) 23.1030 1.79314
\(167\) 14.0825 1.08974 0.544870 0.838521i \(-0.316579\pi\)
0.544870 + 0.838521i \(0.316579\pi\)
\(168\) −51.5815 −3.97960
\(169\) −12.8412 −0.987788
\(170\) 9.79018 0.750873
\(171\) −0.355922 −0.0272181
\(172\) 7.42773 0.566359
\(173\) 8.39769 0.638464 0.319232 0.947677i \(-0.396575\pi\)
0.319232 + 0.947677i \(0.396575\pi\)
\(174\) −30.1707 −2.28724
\(175\) 15.6084 1.17988
\(176\) −10.7985 −0.813966
\(177\) 4.75875 0.357690
\(178\) 38.1626 2.86041
\(179\) 2.18758 0.163507 0.0817535 0.996653i \(-0.473948\pi\)
0.0817535 + 0.996653i \(0.473948\pi\)
\(180\) 5.17596 0.385793
\(181\) 4.16691 0.309724 0.154862 0.987936i \(-0.450507\pi\)
0.154862 + 0.987936i \(0.450507\pi\)
\(182\) 5.24521 0.388801
\(183\) 16.3276 1.20697
\(184\) −6.80769 −0.501870
\(185\) −2.20279 −0.161952
\(186\) −4.59374 −0.336829
\(187\) −3.56116 −0.260418
\(188\) 49.9056 3.63974
\(189\) −28.7903 −2.09418
\(190\) 1.59934 0.116028
\(191\) −12.8424 −0.929246 −0.464623 0.885509i \(-0.653810\pi\)
−0.464623 + 0.885509i \(0.653810\pi\)
\(192\) −4.82987 −0.348566
\(193\) 9.13829 0.657788 0.328894 0.944367i \(-0.393324\pi\)
0.328894 + 0.944367i \(0.393324\pi\)
\(194\) −12.4547 −0.894198
\(195\) 0.824136 0.0590176
\(196\) 88.6179 6.32985
\(197\) −12.3586 −0.880512 −0.440256 0.897872i \(-0.645112\pi\)
−0.440256 + 0.897872i \(0.645112\pi\)
\(198\) −2.69399 −0.191454
\(199\) −17.1797 −1.21784 −0.608918 0.793233i \(-0.708396\pi\)
−0.608918 + 0.793233i \(0.708396\pi\)
\(200\) 20.8019 1.47092
\(201\) 13.7652 0.970919
\(202\) 8.69713 0.611928
\(203\) 40.3150 2.82956
\(204\) −18.7574 −1.31328
\(205\) −0.483205 −0.0337485
\(206\) −8.96928 −0.624919
\(207\) −0.799719 −0.0555843
\(208\) 3.29163 0.228233
\(209\) −0.581757 −0.0402409
\(210\) 27.2281 1.87892
\(211\) 24.5039 1.68692 0.843458 0.537196i \(-0.180516\pi\)
0.843458 + 0.537196i \(0.180516\pi\)
\(212\) −8.24575 −0.566320
\(213\) 9.39615 0.643814
\(214\) 39.2543 2.68337
\(215\) −2.23140 −0.152180
\(216\) −38.3699 −2.61074
\(217\) 6.13828 0.416694
\(218\) −50.8402 −3.44333
\(219\) −3.24511 −0.219284
\(220\) 8.46013 0.570382
\(221\) 1.08552 0.0730203
\(222\) 6.03893 0.405306
\(223\) 8.19877 0.549030 0.274515 0.961583i \(-0.411483\pi\)
0.274515 + 0.961583i \(0.411483\pi\)
\(224\) 39.2021 2.61930
\(225\) 2.44366 0.162911
\(226\) 37.2048 2.47483
\(227\) −21.0455 −1.39684 −0.698419 0.715690i \(-0.746113\pi\)
−0.698419 + 0.715690i \(0.746113\pi\)
\(228\) −3.06424 −0.202934
\(229\) 20.9003 1.38113 0.690564 0.723271i \(-0.257362\pi\)
0.690564 + 0.723271i \(0.257362\pi\)
\(230\) 3.59355 0.236952
\(231\) −9.90417 −0.651646
\(232\) 53.7293 3.52750
\(233\) −4.17523 −0.273528 −0.136764 0.990604i \(-0.543670\pi\)
−0.136764 + 0.990604i \(0.543670\pi\)
\(234\) 0.821193 0.0536831
\(235\) −14.9924 −0.977995
\(236\) −14.8909 −0.969313
\(237\) 23.7706 1.54407
\(238\) 35.8640 2.32472
\(239\) −24.4798 −1.58347 −0.791733 0.610867i \(-0.790821\pi\)
−0.791733 + 0.610867i \(0.790821\pi\)
\(240\) 17.0870 1.10296
\(241\) 10.7187 0.690450 0.345225 0.938520i \(-0.387803\pi\)
0.345225 + 0.938520i \(0.387803\pi\)
\(242\) 23.9450 1.53925
\(243\) −8.06617 −0.517445
\(244\) −51.0915 −3.27080
\(245\) −26.6222 −1.70083
\(246\) 1.32470 0.0844601
\(247\) 0.177333 0.0112834
\(248\) 8.18072 0.519476
\(249\) 13.2976 0.842700
\(250\) −28.9483 −1.83085
\(251\) 19.6196 1.23838 0.619188 0.785243i \(-0.287462\pi\)
0.619188 + 0.785243i \(0.287462\pi\)
\(252\) 18.9609 1.19442
\(253\) −1.30714 −0.0821795
\(254\) −1.91299 −0.120032
\(255\) 5.63500 0.352878
\(256\) −24.4432 −1.52770
\(257\) 11.1300 0.694270 0.347135 0.937815i \(-0.387155\pi\)
0.347135 + 0.937815i \(0.387155\pi\)
\(258\) 6.11737 0.380851
\(259\) −8.06938 −0.501407
\(260\) −2.57885 −0.159933
\(261\) 6.31173 0.390686
\(262\) 54.5464 3.36989
\(263\) −10.9676 −0.676293 −0.338147 0.941093i \(-0.609800\pi\)
−0.338147 + 0.941093i \(0.609800\pi\)
\(264\) −13.1997 −0.812382
\(265\) 2.47715 0.152170
\(266\) 5.85880 0.359226
\(267\) 21.9655 1.34427
\(268\) −43.0733 −2.63112
\(269\) 11.9210 0.726833 0.363417 0.931627i \(-0.381610\pi\)
0.363417 + 0.931627i \(0.381610\pi\)
\(270\) 20.2541 1.23263
\(271\) 10.8169 0.657080 0.328540 0.944490i \(-0.393443\pi\)
0.328540 + 0.944490i \(0.393443\pi\)
\(272\) 22.5064 1.36465
\(273\) 3.01902 0.182720
\(274\) 47.4588 2.86709
\(275\) 3.99417 0.240858
\(276\) −6.88502 −0.414429
\(277\) −13.9071 −0.835594 −0.417797 0.908540i \(-0.637198\pi\)
−0.417797 + 0.908540i \(0.637198\pi\)
\(278\) −3.77980 −0.226698
\(279\) 0.961012 0.0575343
\(280\) −48.4889 −2.89777
\(281\) −25.9454 −1.54777 −0.773886 0.633325i \(-0.781690\pi\)
−0.773886 + 0.633325i \(0.781690\pi\)
\(282\) 41.1015 2.44756
\(283\) 0.100939 0.00600020 0.00300010 0.999995i \(-0.499045\pi\)
0.00300010 + 0.999995i \(0.499045\pi\)
\(284\) −29.4020 −1.74469
\(285\) 0.920544 0.0545283
\(286\) 1.34224 0.0793686
\(287\) −1.77011 −0.104486
\(288\) 6.13749 0.361655
\(289\) −9.57776 −0.563398
\(290\) −28.3618 −1.66546
\(291\) −7.16866 −0.420234
\(292\) 10.1544 0.594244
\(293\) −23.3528 −1.36429 −0.682143 0.731218i \(-0.738952\pi\)
−0.682143 + 0.731218i \(0.738952\pi\)
\(294\) 72.9845 4.25654
\(295\) 4.47344 0.260454
\(296\) −10.7544 −0.625085
\(297\) −7.36740 −0.427500
\(298\) 25.9308 1.50213
\(299\) 0.398449 0.0230429
\(300\) 21.0382 1.21464
\(301\) −8.17420 −0.471153
\(302\) 47.5006 2.73336
\(303\) 5.00587 0.287580
\(304\) 3.67669 0.210872
\(305\) 15.3486 0.878861
\(306\) 5.61488 0.320981
\(307\) −10.2083 −0.582618 −0.291309 0.956629i \(-0.594091\pi\)
−0.291309 + 0.956629i \(0.594091\pi\)
\(308\) 30.9917 1.76591
\(309\) −5.16251 −0.293685
\(310\) −4.31832 −0.245264
\(311\) −29.5659 −1.67653 −0.838265 0.545263i \(-0.816430\pi\)
−0.838265 + 0.545263i \(0.816430\pi\)
\(312\) 4.02357 0.227790
\(313\) −1.11389 −0.0629605 −0.0314803 0.999504i \(-0.510022\pi\)
−0.0314803 + 0.999504i \(0.510022\pi\)
\(314\) 3.53191 0.199317
\(315\) −5.69613 −0.320941
\(316\) −74.3820 −4.18431
\(317\) −26.8444 −1.50773 −0.753867 0.657027i \(-0.771814\pi\)
−0.753867 + 0.657027i \(0.771814\pi\)
\(318\) −6.79108 −0.380825
\(319\) 10.3166 0.577616
\(320\) −4.54030 −0.253810
\(321\) 22.5938 1.26107
\(322\) 13.1641 0.733606
\(323\) 1.21251 0.0674658
\(324\) −27.6698 −1.53721
\(325\) −1.21752 −0.0675357
\(326\) −5.45408 −0.302074
\(327\) −29.2624 −1.61822
\(328\) −2.35909 −0.130259
\(329\) −54.9210 −3.02789
\(330\) 6.96765 0.383556
\(331\) −19.1758 −1.05400 −0.526999 0.849866i \(-0.676683\pi\)
−0.526999 + 0.849866i \(0.676683\pi\)
\(332\) −41.6102 −2.28365
\(333\) −1.26335 −0.0692309
\(334\) −36.2925 −1.98584
\(335\) 12.9399 0.706980
\(336\) 62.5941 3.41479
\(337\) 6.91681 0.376783 0.188391 0.982094i \(-0.439673\pi\)
0.188391 + 0.982094i \(0.439673\pi\)
\(338\) 33.0935 1.80005
\(339\) 21.4142 1.16306
\(340\) −17.6328 −0.956272
\(341\) 1.57078 0.0850624
\(342\) 0.917257 0.0495996
\(343\) −61.7675 −3.33513
\(344\) −10.8941 −0.587368
\(345\) 2.06836 0.111357
\(346\) −21.6419 −1.16348
\(347\) 8.49468 0.456019 0.228009 0.973659i \(-0.426778\pi\)
0.228009 + 0.973659i \(0.426778\pi\)
\(348\) 54.3396 2.91291
\(349\) −1.00000 −0.0535288
\(350\) −40.2248 −2.15011
\(351\) 2.24576 0.119870
\(352\) 10.0318 0.534695
\(353\) 13.2769 0.706657 0.353328 0.935499i \(-0.385050\pi\)
0.353328 + 0.935499i \(0.385050\pi\)
\(354\) −12.2639 −0.651819
\(355\) 8.83281 0.468797
\(356\) −68.7335 −3.64287
\(357\) 20.6425 1.09252
\(358\) −5.63766 −0.297960
\(359\) 10.6397 0.561539 0.280770 0.959775i \(-0.409410\pi\)
0.280770 + 0.959775i \(0.409410\pi\)
\(360\) −7.59145 −0.400105
\(361\) −18.8019 −0.989575
\(362\) −10.7386 −0.564411
\(363\) 13.7822 0.723379
\(364\) −9.44699 −0.495157
\(365\) −3.05055 −0.159673
\(366\) −42.0782 −2.19946
\(367\) −21.0542 −1.09902 −0.549511 0.835487i \(-0.685186\pi\)
−0.549511 + 0.835487i \(0.685186\pi\)
\(368\) 8.26112 0.430641
\(369\) −0.277129 −0.0144267
\(370\) 5.67686 0.295126
\(371\) 9.07443 0.471121
\(372\) 8.27364 0.428968
\(373\) −4.43210 −0.229485 −0.114743 0.993395i \(-0.536604\pi\)
−0.114743 + 0.993395i \(0.536604\pi\)
\(374\) 9.17755 0.474560
\(375\) −16.6620 −0.860422
\(376\) −73.1952 −3.77475
\(377\) −3.14473 −0.161962
\(378\) 74.1962 3.81624
\(379\) −7.85223 −0.403342 −0.201671 0.979453i \(-0.564637\pi\)
−0.201671 + 0.979453i \(0.564637\pi\)
\(380\) −2.88052 −0.147768
\(381\) −1.10107 −0.0564097
\(382\) 33.0966 1.69337
\(383\) −0.669281 −0.0341987 −0.0170993 0.999854i \(-0.505443\pi\)
−0.0170993 + 0.999854i \(0.505443\pi\)
\(384\) −10.3207 −0.526676
\(385\) −9.31036 −0.474500
\(386\) −23.5505 −1.19869
\(387\) −1.27976 −0.0650537
\(388\) 22.4318 1.13880
\(389\) −27.3821 −1.38833 −0.694164 0.719817i \(-0.744226\pi\)
−0.694164 + 0.719817i \(0.744226\pi\)
\(390\) −2.12390 −0.107548
\(391\) 2.72438 0.137778
\(392\) −129.974 −6.56466
\(393\) 31.3956 1.58370
\(394\) 31.8496 1.60456
\(395\) 22.3455 1.12432
\(396\) 4.85207 0.243826
\(397\) 30.8072 1.54617 0.773085 0.634302i \(-0.218713\pi\)
0.773085 + 0.634302i \(0.218713\pi\)
\(398\) 44.2742 2.21927
\(399\) 3.37219 0.168821
\(400\) −25.2431 −1.26215
\(401\) 25.2006 1.25846 0.629230 0.777220i \(-0.283371\pi\)
0.629230 + 0.777220i \(0.283371\pi\)
\(402\) −35.4746 −1.76931
\(403\) −0.478810 −0.0238512
\(404\) −15.6641 −0.779320
\(405\) 8.31243 0.413048
\(406\) −103.897 −5.15631
\(407\) −2.06495 −0.102356
\(408\) 27.5110 1.36200
\(409\) 1.69505 0.0838150 0.0419075 0.999121i \(-0.486657\pi\)
0.0419075 + 0.999121i \(0.486657\pi\)
\(410\) 1.24528 0.0615001
\(411\) 27.3162 1.34741
\(412\) 16.1543 0.795865
\(413\) 16.3874 0.806369
\(414\) 2.06098 0.101291
\(415\) 12.5003 0.613617
\(416\) −3.05792 −0.149927
\(417\) −2.17557 −0.106538
\(418\) 1.49926 0.0733312
\(419\) 11.6073 0.567053 0.283527 0.958964i \(-0.408496\pi\)
0.283527 + 0.958964i \(0.408496\pi\)
\(420\) −49.0397 −2.39289
\(421\) −19.5786 −0.954203 −0.477102 0.878848i \(-0.658313\pi\)
−0.477102 + 0.878848i \(0.658313\pi\)
\(422\) −63.1496 −3.07407
\(423\) −8.59845 −0.418071
\(424\) 12.0938 0.587328
\(425\) −8.32474 −0.403809
\(426\) −24.2151 −1.17322
\(427\) 56.2260 2.72097
\(428\) −70.6996 −3.41739
\(429\) 0.772565 0.0372998
\(430\) 5.75060 0.277319
\(431\) −35.9552 −1.73190 −0.865951 0.500129i \(-0.833286\pi\)
−0.865951 + 0.500129i \(0.833286\pi\)
\(432\) 46.5618 2.24020
\(433\) 35.0490 1.68435 0.842173 0.539207i \(-0.181276\pi\)
0.842173 + 0.539207i \(0.181276\pi\)
\(434\) −15.8191 −0.759342
\(435\) −16.3244 −0.782696
\(436\) 91.5666 4.38525
\(437\) 0.445059 0.0212901
\(438\) 8.36306 0.399602
\(439\) −5.50875 −0.262918 −0.131459 0.991322i \(-0.541966\pi\)
−0.131459 + 0.991322i \(0.541966\pi\)
\(440\) −12.4083 −0.591541
\(441\) −15.2684 −0.727066
\(442\) −2.79753 −0.133065
\(443\) −11.5802 −0.550194 −0.275097 0.961416i \(-0.588710\pi\)
−0.275097 + 0.961416i \(0.588710\pi\)
\(444\) −10.8765 −0.516177
\(445\) 20.6486 0.978836
\(446\) −21.1293 −1.00050
\(447\) 14.9252 0.705936
\(448\) −16.6323 −0.785801
\(449\) 22.1291 1.04434 0.522168 0.852843i \(-0.325123\pi\)
0.522168 + 0.852843i \(0.325123\pi\)
\(450\) −6.29762 −0.296872
\(451\) −0.452968 −0.0213294
\(452\) −67.0084 −3.15181
\(453\) 27.3403 1.28456
\(454\) 54.2368 2.54546
\(455\) 2.83802 0.133048
\(456\) 4.49424 0.210462
\(457\) −19.7964 −0.926035 −0.463018 0.886349i \(-0.653233\pi\)
−0.463018 + 0.886349i \(0.653233\pi\)
\(458\) −53.8626 −2.51683
\(459\) 15.3553 0.716723
\(460\) −6.47223 −0.301769
\(461\) 23.6559 1.10176 0.550882 0.834583i \(-0.314292\pi\)
0.550882 + 0.834583i \(0.314292\pi\)
\(462\) 25.5243 1.18750
\(463\) 4.52171 0.210141 0.105071 0.994465i \(-0.466493\pi\)
0.105071 + 0.994465i \(0.466493\pi\)
\(464\) −65.2003 −3.02685
\(465\) −2.48553 −0.115263
\(466\) 10.7601 0.498451
\(467\) −23.2913 −1.07779 −0.538896 0.842373i \(-0.681158\pi\)
−0.538896 + 0.842373i \(0.681158\pi\)
\(468\) −1.47903 −0.0683680
\(469\) 47.4021 2.18882
\(470\) 38.6373 1.78220
\(471\) 2.03289 0.0936705
\(472\) 21.8401 1.00527
\(473\) −2.09177 −0.0961796
\(474\) −61.2600 −2.81376
\(475\) −1.35994 −0.0623985
\(476\) −64.5935 −2.96064
\(477\) 1.42070 0.0650493
\(478\) 63.0875 2.88556
\(479\) −17.0813 −0.780463 −0.390232 0.920717i \(-0.627605\pi\)
−0.390232 + 0.920717i \(0.627605\pi\)
\(480\) −15.8738 −0.724536
\(481\) 0.629444 0.0287002
\(482\) −27.6234 −1.25821
\(483\) 7.57695 0.344763
\(484\) −43.1267 −1.96030
\(485\) −6.73886 −0.305996
\(486\) 20.7875 0.942942
\(487\) −9.66394 −0.437915 −0.218957 0.975734i \(-0.570266\pi\)
−0.218957 + 0.975734i \(0.570266\pi\)
\(488\) 74.9345 3.39213
\(489\) −3.13924 −0.141961
\(490\) 68.6087 3.09942
\(491\) 19.9216 0.899051 0.449526 0.893267i \(-0.351593\pi\)
0.449526 + 0.893267i \(0.351593\pi\)
\(492\) −2.38588 −0.107564
\(493\) −21.5020 −0.968401
\(494\) −0.457010 −0.0205619
\(495\) −1.45763 −0.0655158
\(496\) −9.92728 −0.445748
\(497\) 32.3568 1.45140
\(498\) −34.2695 −1.53565
\(499\) −29.1900 −1.30672 −0.653361 0.757046i \(-0.726642\pi\)
−0.653361 + 0.757046i \(0.726642\pi\)
\(500\) 52.1380 2.33168
\(501\) −20.8891 −0.933257
\(502\) −50.5621 −2.25670
\(503\) 30.0883 1.34157 0.670785 0.741652i \(-0.265957\pi\)
0.670785 + 0.741652i \(0.265957\pi\)
\(504\) −27.8094 −1.23873
\(505\) 4.70574 0.209403
\(506\) 3.36868 0.149756
\(507\) 19.0479 0.845945
\(508\) 3.44543 0.152866
\(509\) −11.7322 −0.520022 −0.260011 0.965606i \(-0.583726\pi\)
−0.260011 + 0.965606i \(0.583726\pi\)
\(510\) −14.5221 −0.643050
\(511\) −11.1749 −0.494350
\(512\) 49.0778 2.16895
\(513\) 2.50847 0.110751
\(514\) −28.6834 −1.26517
\(515\) −4.85299 −0.213848
\(516\) −11.0178 −0.485032
\(517\) −14.0542 −0.618103
\(518\) 20.7958 0.913716
\(519\) −12.4566 −0.546783
\(520\) 3.78233 0.165866
\(521\) 14.8599 0.651026 0.325513 0.945538i \(-0.394463\pi\)
0.325513 + 0.945538i \(0.394463\pi\)
\(522\) −16.2661 −0.711949
\(523\) 12.4343 0.543714 0.271857 0.962338i \(-0.412362\pi\)
0.271857 + 0.962338i \(0.412362\pi\)
\(524\) −98.2417 −4.29171
\(525\) −23.1525 −1.01046
\(526\) 28.2650 1.23241
\(527\) −3.27385 −0.142611
\(528\) 16.0177 0.697083
\(529\) 1.00000 0.0434783
\(530\) −6.38392 −0.277300
\(531\) 2.56561 0.111338
\(532\) −10.5521 −0.457492
\(533\) 0.138075 0.00598071
\(534\) −56.6079 −2.44966
\(535\) 21.2392 0.918252
\(536\) 63.1745 2.72872
\(537\) −3.24491 −0.140028
\(538\) −30.7218 −1.32451
\(539\) −24.9562 −1.07494
\(540\) −36.4791 −1.56981
\(541\) 23.1728 0.996277 0.498138 0.867098i \(-0.334017\pi\)
0.498138 + 0.867098i \(0.334017\pi\)
\(542\) −27.8765 −1.19740
\(543\) −6.18092 −0.265248
\(544\) −20.9084 −0.896441
\(545\) −27.5080 −1.17831
\(546\) −7.78041 −0.332971
\(547\) −10.3513 −0.442591 −0.221295 0.975207i \(-0.571029\pi\)
−0.221295 + 0.975207i \(0.571029\pi\)
\(548\) −85.4765 −3.65138
\(549\) 8.80278 0.375693
\(550\) −10.2935 −0.438916
\(551\) −3.51260 −0.149642
\(552\) 10.0981 0.429803
\(553\) 81.8572 3.48092
\(554\) 35.8402 1.52271
\(555\) 3.26747 0.138696
\(556\) 6.80769 0.288710
\(557\) 12.8719 0.545401 0.272700 0.962099i \(-0.412083\pi\)
0.272700 + 0.962099i \(0.412083\pi\)
\(558\) −2.47665 −0.104845
\(559\) 0.637620 0.0269685
\(560\) 58.8412 2.48650
\(561\) 5.28239 0.223023
\(562\) 66.8645 2.82051
\(563\) −39.0661 −1.64644 −0.823219 0.567724i \(-0.807824\pi\)
−0.823219 + 0.567724i \(0.807824\pi\)
\(564\) −74.0266 −3.11708
\(565\) 20.1303 0.846889
\(566\) −0.260133 −0.0109342
\(567\) 30.4506 1.27880
\(568\) 43.1232 1.80941
\(569\) 6.17098 0.258701 0.129350 0.991599i \(-0.458711\pi\)
0.129350 + 0.991599i \(0.458711\pi\)
\(570\) −2.37236 −0.0993671
\(571\) −26.1851 −1.09581 −0.547906 0.836540i \(-0.684575\pi\)
−0.547906 + 0.836540i \(0.684575\pi\)
\(572\) −2.41747 −0.101080
\(573\) 19.0496 0.795810
\(574\) 4.56179 0.190405
\(575\) −3.05565 −0.127429
\(576\) −2.60396 −0.108498
\(577\) −36.2820 −1.51044 −0.755221 0.655471i \(-0.772470\pi\)
−0.755221 + 0.655471i \(0.772470\pi\)
\(578\) 24.6831 1.02668
\(579\) −13.5551 −0.563332
\(580\) 51.0816 2.12105
\(581\) 45.7919 1.89977
\(582\) 18.4745 0.765794
\(583\) 2.32214 0.0961731
\(584\) −14.8933 −0.616288
\(585\) 0.444321 0.0183704
\(586\) 60.1832 2.48614
\(587\) 4.99302 0.206084 0.103042 0.994677i \(-0.467142\pi\)
0.103042 + 0.994677i \(0.467142\pi\)
\(588\) −131.450 −5.42091
\(589\) −0.534822 −0.0220370
\(590\) −11.5286 −0.474626
\(591\) 18.3319 0.754074
\(592\) 13.0504 0.536368
\(593\) −19.3131 −0.793094 −0.396547 0.918014i \(-0.629792\pi\)
−0.396547 + 0.918014i \(0.629792\pi\)
\(594\) 18.9867 0.779034
\(595\) 19.4049 0.795521
\(596\) −46.7031 −1.91304
\(597\) 25.4832 1.04296
\(598\) −1.02685 −0.0419911
\(599\) 2.19955 0.0898710 0.0449355 0.998990i \(-0.485692\pi\)
0.0449355 + 0.998990i \(0.485692\pi\)
\(600\) −30.8562 −1.25970
\(601\) −16.2205 −0.661647 −0.330823 0.943693i \(-0.607326\pi\)
−0.330823 + 0.943693i \(0.607326\pi\)
\(602\) 21.0659 0.858584
\(603\) 7.42129 0.302218
\(604\) −85.5519 −3.48106
\(605\) 12.9559 0.526732
\(606\) −12.9008 −0.524058
\(607\) 1.14499 0.0464736 0.0232368 0.999730i \(-0.492603\pi\)
0.0232368 + 0.999730i \(0.492603\pi\)
\(608\) −3.41564 −0.138522
\(609\) −59.8006 −2.42324
\(610\) −39.5554 −1.60155
\(611\) 4.28406 0.173314
\(612\) −10.1128 −0.408785
\(613\) 33.0046 1.33304 0.666521 0.745486i \(-0.267782\pi\)
0.666521 + 0.745486i \(0.267782\pi\)
\(614\) 26.3081 1.06171
\(615\) 0.716755 0.0289024
\(616\) −45.4547 −1.83142
\(617\) 33.8515 1.36281 0.681405 0.731907i \(-0.261369\pi\)
0.681405 + 0.731907i \(0.261369\pi\)
\(618\) 13.3044 0.535183
\(619\) 18.4249 0.740559 0.370279 0.928920i \(-0.379262\pi\)
0.370279 + 0.928920i \(0.379262\pi\)
\(620\) 7.77759 0.312356
\(621\) 5.63625 0.226175
\(622\) 76.1952 3.05515
\(623\) 75.6410 3.03049
\(624\) −4.88259 −0.195460
\(625\) −0.384797 −0.0153919
\(626\) 2.87062 0.114733
\(627\) 0.862940 0.0344625
\(628\) −6.36122 −0.253840
\(629\) 4.30380 0.171604
\(630\) 14.6797 0.584852
\(631\) 24.6723 0.982190 0.491095 0.871106i \(-0.336597\pi\)
0.491095 + 0.871106i \(0.336597\pi\)
\(632\) 109.094 4.33953
\(633\) −36.3474 −1.44468
\(634\) 69.1815 2.74755
\(635\) −1.03506 −0.0410751
\(636\) 12.2312 0.484999
\(637\) 7.60725 0.301410
\(638\) −26.5871 −1.05259
\(639\) 5.06580 0.200400
\(640\) −9.70192 −0.383502
\(641\) 33.2574 1.31359 0.656795 0.754069i \(-0.271912\pi\)
0.656795 + 0.754069i \(0.271912\pi\)
\(642\) −58.2272 −2.29804
\(643\) −37.3997 −1.47490 −0.737450 0.675402i \(-0.763970\pi\)
−0.737450 + 0.675402i \(0.763970\pi\)
\(644\) −23.7094 −0.934283
\(645\) 3.30991 0.130328
\(646\) −3.12479 −0.122943
\(647\) 34.1333 1.34192 0.670960 0.741493i \(-0.265882\pi\)
0.670960 + 0.741493i \(0.265882\pi\)
\(648\) 40.5826 1.59424
\(649\) 4.19351 0.164610
\(650\) 3.13770 0.123071
\(651\) −9.10512 −0.356858
\(652\) 9.82317 0.384705
\(653\) −9.37924 −0.367038 −0.183519 0.983016i \(-0.558749\pi\)
−0.183519 + 0.983016i \(0.558749\pi\)
\(654\) 75.4130 2.94888
\(655\) 29.5133 1.15318
\(656\) 2.86275 0.111771
\(657\) −1.74955 −0.0682566
\(658\) 141.538 5.51774
\(659\) −40.8007 −1.58937 −0.794685 0.607022i \(-0.792364\pi\)
−0.794685 + 0.607022i \(0.792364\pi\)
\(660\) −12.5492 −0.488477
\(661\) −32.2817 −1.25561 −0.627807 0.778369i \(-0.716047\pi\)
−0.627807 + 0.778369i \(0.716047\pi\)
\(662\) 49.4185 1.92071
\(663\) −1.61020 −0.0625348
\(664\) 61.0286 2.36837
\(665\) 3.17001 0.122928
\(666\) 3.25580 0.126160
\(667\) −7.89244 −0.305596
\(668\) 65.3653 2.52906
\(669\) −12.1615 −0.470191
\(670\) −33.3477 −1.28833
\(671\) 14.3882 0.555450
\(672\) −58.1498 −2.24318
\(673\) 13.9329 0.537075 0.268538 0.963269i \(-0.413460\pi\)
0.268538 + 0.963269i \(0.413460\pi\)
\(674\) −17.8255 −0.686613
\(675\) −17.2224 −0.662890
\(676\) −59.6037 −2.29245
\(677\) −46.5802 −1.79022 −0.895112 0.445842i \(-0.852904\pi\)
−0.895112 + 0.445842i \(0.852904\pi\)
\(678\) −55.1872 −2.11945
\(679\) −24.6862 −0.947369
\(680\) 25.8616 0.991746
\(681\) 31.2175 1.19626
\(682\) −4.04810 −0.155010
\(683\) −21.7737 −0.833146 −0.416573 0.909102i \(-0.636769\pi\)
−0.416573 + 0.909102i \(0.636769\pi\)
\(684\) −1.65204 −0.0631674
\(685\) 25.6784 0.981123
\(686\) 159.183 6.07762
\(687\) −31.0021 −1.18280
\(688\) 13.2199 0.504005
\(689\) −0.707842 −0.0269666
\(690\) −5.33043 −0.202926
\(691\) −25.6002 −0.973877 −0.486938 0.873436i \(-0.661886\pi\)
−0.486938 + 0.873436i \(0.661886\pi\)
\(692\) 38.9785 1.48174
\(693\) −5.33969 −0.202838
\(694\) −21.8919 −0.831004
\(695\) −2.04513 −0.0775762
\(696\) −79.6985 −3.02096
\(697\) 0.944086 0.0357598
\(698\) 2.57713 0.0975457
\(699\) 6.19326 0.234250
\(700\) 72.4476 2.73826
\(701\) −51.0469 −1.92801 −0.964007 0.265875i \(-0.914339\pi\)
−0.964007 + 0.265875i \(0.914339\pi\)
\(702\) −5.78760 −0.218439
\(703\) 0.703077 0.0265170
\(704\) −4.25618 −0.160411
\(705\) 22.2387 0.837558
\(706\) −34.2162 −1.28774
\(707\) 17.2383 0.648315
\(708\) 22.0881 0.830123
\(709\) 38.1066 1.43112 0.715561 0.698550i \(-0.246171\pi\)
0.715561 + 0.698550i \(0.246171\pi\)
\(710\) −22.7633 −0.854290
\(711\) 12.8156 0.480623
\(712\) 100.810 3.77800
\(713\) −1.20169 −0.0450035
\(714\) −53.1983 −1.99090
\(715\) 0.726246 0.0271600
\(716\) 10.1538 0.379466
\(717\) 36.3117 1.35609
\(718\) −27.4197 −1.02330
\(719\) 1.47212 0.0549009 0.0274504 0.999623i \(-0.491261\pi\)
0.0274504 + 0.999623i \(0.491261\pi\)
\(720\) 9.21221 0.343319
\(721\) −17.7778 −0.662078
\(722\) 48.4549 1.80331
\(723\) −15.8994 −0.591304
\(724\) 19.3410 0.718804
\(725\) 24.1165 0.895664
\(726\) −35.5185 −1.31822
\(727\) −6.01668 −0.223146 −0.111573 0.993756i \(-0.535589\pi\)
−0.111573 + 0.993756i \(0.535589\pi\)
\(728\) 13.8557 0.513525
\(729\) 29.8487 1.10551
\(730\) 7.86165 0.290973
\(731\) 4.35971 0.161250
\(732\) 75.7857 2.80112
\(733\) 31.9758 1.18105 0.590527 0.807018i \(-0.298920\pi\)
0.590527 + 0.807018i \(0.298920\pi\)
\(734\) 54.2594 2.00275
\(735\) 39.4896 1.45659
\(736\) −7.67456 −0.282888
\(737\) 12.1301 0.446819
\(738\) 0.714196 0.0262899
\(739\) 18.6155 0.684783 0.342391 0.939557i \(-0.388763\pi\)
0.342391 + 0.939557i \(0.388763\pi\)
\(740\) −10.2244 −0.375857
\(741\) −0.263044 −0.00966318
\(742\) −23.3860 −0.858525
\(743\) −46.4828 −1.70529 −0.852645 0.522491i \(-0.825003\pi\)
−0.852645 + 0.522491i \(0.825003\pi\)
\(744\) −12.1347 −0.444881
\(745\) 14.0303 0.514031
\(746\) 11.4221 0.418192
\(747\) 7.16920 0.262307
\(748\) −16.5294 −0.604375
\(749\) 77.8048 2.84292
\(750\) 42.9401 1.56795
\(751\) −22.4885 −0.820615 −0.410308 0.911947i \(-0.634579\pi\)
−0.410308 + 0.911947i \(0.634579\pi\)
\(752\) 88.8222 3.23901
\(753\) −29.1024 −1.06055
\(754\) 8.10437 0.295144
\(755\) 25.7011 0.935358
\(756\) −133.632 −4.86016
\(757\) 12.6799 0.460859 0.230430 0.973089i \(-0.425987\pi\)
0.230430 + 0.973089i \(0.425987\pi\)
\(758\) 20.2362 0.735011
\(759\) 1.93893 0.0703788
\(760\) 4.22479 0.153249
\(761\) 1.85880 0.0673813 0.0336907 0.999432i \(-0.489274\pi\)
0.0336907 + 0.999432i \(0.489274\pi\)
\(762\) 2.83761 0.102796
\(763\) −100.769 −3.64808
\(764\) −59.6092 −2.15659
\(765\) 3.03803 0.109840
\(766\) 1.72482 0.0623204
\(767\) −1.27828 −0.0461560
\(768\) 36.2575 1.30833
\(769\) 9.94177 0.358509 0.179255 0.983803i \(-0.442631\pi\)
0.179255 + 0.983803i \(0.442631\pi\)
\(770\) 23.9940 0.864683
\(771\) −16.5095 −0.594575
\(772\) 42.4161 1.52659
\(773\) −29.4283 −1.05846 −0.529232 0.848477i \(-0.677520\pi\)
−0.529232 + 0.848477i \(0.677520\pi\)
\(774\) 3.29809 0.118548
\(775\) 3.67193 0.131900
\(776\) −32.9002 −1.18105
\(777\) 11.9696 0.429407
\(778\) 70.5671 2.52995
\(779\) 0.154228 0.00552577
\(780\) 3.82530 0.136968
\(781\) 8.28008 0.296285
\(782\) −7.02107 −0.251073
\(783\) −44.4838 −1.58972
\(784\) 157.723 5.63296
\(785\) 1.91100 0.0682067
\(786\) −80.9105 −2.88598
\(787\) −2.99186 −0.106648 −0.0533241 0.998577i \(-0.516982\pi\)
−0.0533241 + 0.998577i \(0.516982\pi\)
\(788\) −57.3633 −2.04348
\(789\) 16.2687 0.579180
\(790\) −57.5871 −2.04886
\(791\) 73.7426 2.62198
\(792\) −7.11641 −0.252870
\(793\) −4.38586 −0.155746
\(794\) −79.3941 −2.81759
\(795\) −3.67444 −0.130319
\(796\) −79.7409 −2.82634
\(797\) 9.36981 0.331896 0.165948 0.986135i \(-0.446932\pi\)
0.165948 + 0.986135i \(0.446932\pi\)
\(798\) −8.69056 −0.307643
\(799\) 29.2921 1.03628
\(800\) 23.4508 0.829109
\(801\) 11.8424 0.418430
\(802\) −64.9452 −2.29329
\(803\) −2.85966 −0.100915
\(804\) 63.8921 2.25330
\(805\) 7.12267 0.251041
\(806\) 1.23396 0.0434642
\(807\) −17.6828 −0.622463
\(808\) 22.9742 0.808229
\(809\) −40.8294 −1.43549 −0.717743 0.696308i \(-0.754825\pi\)
−0.717743 + 0.696308i \(0.754825\pi\)
\(810\) −21.4222 −0.752699
\(811\) −30.5752 −1.07364 −0.536820 0.843697i \(-0.680375\pi\)
−0.536820 + 0.843697i \(0.680375\pi\)
\(812\) 187.125 6.56681
\(813\) −16.0451 −0.562726
\(814\) 5.32163 0.186523
\(815\) −2.95103 −0.103370
\(816\) −33.3845 −1.16869
\(817\) 0.712209 0.0249170
\(818\) −4.36837 −0.152736
\(819\) 1.62766 0.0568752
\(820\) −2.24284 −0.0783233
\(821\) 8.68466 0.303097 0.151548 0.988450i \(-0.451574\pi\)
0.151548 + 0.988450i \(0.451574\pi\)
\(822\) −70.3973 −2.45539
\(823\) 20.8804 0.727843 0.363922 0.931430i \(-0.381438\pi\)
0.363922 + 0.931430i \(0.381438\pi\)
\(824\) −23.6931 −0.825388
\(825\) −5.92469 −0.206271
\(826\) −42.2323 −1.46945
\(827\) −38.3866 −1.33483 −0.667416 0.744685i \(-0.732600\pi\)
−0.667416 + 0.744685i \(0.732600\pi\)
\(828\) −3.71196 −0.129000
\(829\) 18.8152 0.653478 0.326739 0.945115i \(-0.394050\pi\)
0.326739 + 0.945115i \(0.394050\pi\)
\(830\) −32.2149 −1.11820
\(831\) 20.6288 0.715606
\(832\) 1.29738 0.0449787
\(833\) 52.0143 1.80219
\(834\) 5.60671 0.194145
\(835\) −19.6367 −0.679556
\(836\) −2.70027 −0.0933908
\(837\) −6.77301 −0.234110
\(838\) −29.9135 −1.03334
\(839\) −16.0948 −0.555653 −0.277827 0.960631i \(-0.589614\pi\)
−0.277827 + 0.960631i \(0.589614\pi\)
\(840\) 71.9253 2.48166
\(841\) 33.2905 1.14795
\(842\) 50.4566 1.73885
\(843\) 38.4857 1.32552
\(844\) 113.737 3.91498
\(845\) 17.9058 0.615979
\(846\) 22.1593 0.761852
\(847\) 47.4608 1.63077
\(848\) −14.6758 −0.503970
\(849\) −0.149726 −0.00513860
\(850\) 21.4539 0.735863
\(851\) 1.57974 0.0541527
\(852\) 43.6130 1.49416
\(853\) 3.31300 0.113435 0.0567175 0.998390i \(-0.481937\pi\)
0.0567175 + 0.998390i \(0.481937\pi\)
\(854\) −144.902 −4.95843
\(855\) 0.496298 0.0169730
\(856\) 103.693 3.54417
\(857\) −13.4082 −0.458017 −0.229008 0.973424i \(-0.573548\pi\)
−0.229008 + 0.973424i \(0.573548\pi\)
\(858\) −1.99100 −0.0679715
\(859\) 7.28956 0.248717 0.124358 0.992237i \(-0.460313\pi\)
0.124358 + 0.992237i \(0.460313\pi\)
\(860\) −10.3572 −0.353179
\(861\) 2.62566 0.0894823
\(862\) 92.6612 3.15605
\(863\) −30.7582 −1.04702 −0.523511 0.852019i \(-0.675378\pi\)
−0.523511 + 0.852019i \(0.675378\pi\)
\(864\) −43.2558 −1.47159
\(865\) −11.7097 −0.398143
\(866\) −90.3257 −3.06939
\(867\) 14.2070 0.482496
\(868\) 28.4913 0.967059
\(869\) 20.9472 0.710584
\(870\) 42.0701 1.42631
\(871\) −3.69755 −0.125287
\(872\) −134.298 −4.54792
\(873\) −3.86488 −0.130806
\(874\) −1.14697 −0.0387970
\(875\) −57.3777 −1.93972
\(876\) −15.0624 −0.508913
\(877\) 22.2242 0.750458 0.375229 0.926932i \(-0.377564\pi\)
0.375229 + 0.926932i \(0.377564\pi\)
\(878\) 14.1967 0.479117
\(879\) 34.6401 1.16838
\(880\) 15.0574 0.507585
\(881\) 22.2191 0.748581 0.374290 0.927312i \(-0.377886\pi\)
0.374290 + 0.927312i \(0.377886\pi\)
\(882\) 39.3485 1.32493
\(883\) −30.7186 −1.03376 −0.516882 0.856057i \(-0.672907\pi\)
−0.516882 + 0.856057i \(0.672907\pi\)
\(884\) 5.03855 0.169465
\(885\) −6.63561 −0.223053
\(886\) 29.8438 1.00262
\(887\) −44.0256 −1.47823 −0.739117 0.673577i \(-0.764757\pi\)
−0.739117 + 0.673577i \(0.764757\pi\)
\(888\) 15.9523 0.535325
\(889\) −3.79169 −0.127169
\(890\) −53.2140 −1.78374
\(891\) 7.79227 0.261051
\(892\) 38.0552 1.27418
\(893\) 4.78521 0.160131
\(894\) −38.4640 −1.28643
\(895\) −3.05036 −0.101962
\(896\) −35.5407 −1.18733
\(897\) −0.591032 −0.0197340
\(898\) −57.0295 −1.90310
\(899\) 9.48424 0.316317
\(900\) 11.3424 0.378081
\(901\) −4.83985 −0.161239
\(902\) 1.16736 0.0388687
\(903\) 12.1251 0.403497
\(904\) 98.2795 3.26873
\(905\) −5.81034 −0.193142
\(906\) −70.4593 −2.34086
\(907\) 56.6376 1.88062 0.940310 0.340320i \(-0.110536\pi\)
0.940310 + 0.340320i \(0.110536\pi\)
\(908\) −97.6843 −3.24177
\(909\) 2.69884 0.0895150
\(910\) −7.31393 −0.242454
\(911\) 52.0959 1.72601 0.863006 0.505193i \(-0.168579\pi\)
0.863006 + 0.505193i \(0.168579\pi\)
\(912\) −5.45376 −0.180592
\(913\) 11.7181 0.387812
\(914\) 51.0178 1.68752
\(915\) −22.7672 −0.752659
\(916\) 97.0103 3.20531
\(917\) 108.115 3.57027
\(918\) −39.5725 −1.30609
\(919\) −48.5347 −1.60101 −0.800506 0.599325i \(-0.795436\pi\)
−0.800506 + 0.599325i \(0.795436\pi\)
\(920\) 9.49265 0.312963
\(921\) 15.1423 0.498956
\(922\) −60.9642 −2.00775
\(923\) −2.52396 −0.0830773
\(924\) −45.9710 −1.51233
\(925\) −4.82712 −0.158715
\(926\) −11.6530 −0.382942
\(927\) −2.78329 −0.0914154
\(928\) 60.5710 1.98834
\(929\) 19.4642 0.638601 0.319300 0.947654i \(-0.396552\pi\)
0.319300 + 0.947654i \(0.396552\pi\)
\(930\) 6.40551 0.210045
\(931\) 8.49715 0.278483
\(932\) −19.3797 −0.634802
\(933\) 43.8562 1.43579
\(934\) 60.0245 1.96406
\(935\) 4.96568 0.162395
\(936\) 2.16925 0.0709041
\(937\) −12.2487 −0.400149 −0.200074 0.979781i \(-0.564118\pi\)
−0.200074 + 0.979781i \(0.564118\pi\)
\(938\) −122.161 −3.98870
\(939\) 1.65226 0.0539196
\(940\) −69.5883 −2.26972
\(941\) 41.7106 1.35973 0.679863 0.733339i \(-0.262039\pi\)
0.679863 + 0.733339i \(0.262039\pi\)
\(942\) −5.23901 −0.170696
\(943\) 0.346533 0.0112847
\(944\) −26.5029 −0.862594
\(945\) 40.1452 1.30592
\(946\) 5.39075 0.175268
\(947\) 14.4171 0.468494 0.234247 0.972177i \(-0.424737\pi\)
0.234247 + 0.972177i \(0.424737\pi\)
\(948\) 110.333 3.58346
\(949\) 0.871691 0.0282963
\(950\) 3.50475 0.113709
\(951\) 39.8193 1.29123
\(952\) 94.7376 3.07046
\(953\) −53.0174 −1.71740 −0.858701 0.512476i \(-0.828728\pi\)
−0.858701 + 0.512476i \(0.828728\pi\)
\(954\) −3.66132 −0.118539
\(955\) 17.9075 0.579473
\(956\) −113.625 −3.67489
\(957\) −15.3029 −0.494672
\(958\) 44.0206 1.42224
\(959\) 94.0667 3.03757
\(960\) 6.73478 0.217364
\(961\) −29.5559 −0.953418
\(962\) −1.62216 −0.0523004
\(963\) 12.1812 0.392532
\(964\) 49.7515 1.60239
\(965\) −12.7424 −0.410193
\(966\) −19.5268 −0.628263
\(967\) 57.6772 1.85477 0.927386 0.374106i \(-0.122050\pi\)
0.927386 + 0.374106i \(0.122050\pi\)
\(968\) 63.2528 2.03302
\(969\) −1.79856 −0.0577780
\(970\) 17.3669 0.557617
\(971\) 2.69869 0.0866050 0.0433025 0.999062i \(-0.486212\pi\)
0.0433025 + 0.999062i \(0.486212\pi\)
\(972\) −37.4398 −1.20088
\(973\) −7.49184 −0.240177
\(974\) 24.9052 0.798014
\(975\) 1.80599 0.0578378
\(976\) −90.9329 −2.91069
\(977\) −16.1484 −0.516633 −0.258317 0.966060i \(-0.583168\pi\)
−0.258317 + 0.966060i \(0.583168\pi\)
\(978\) 8.09023 0.258697
\(979\) 19.3565 0.618635
\(980\) −123.569 −3.94726
\(981\) −15.7764 −0.503702
\(982\) −51.3406 −1.63834
\(983\) 41.5219 1.32434 0.662172 0.749352i \(-0.269635\pi\)
0.662172 + 0.749352i \(0.269635\pi\)
\(984\) 3.49932 0.111554
\(985\) 17.2328 0.549083
\(986\) 55.4133 1.76472
\(987\) 81.4661 2.59310
\(988\) 0.823106 0.0261865
\(989\) 1.60026 0.0508852
\(990\) 3.75651 0.119390
\(991\) −4.85513 −0.154228 −0.0771142 0.997022i \(-0.524571\pi\)
−0.0771142 + 0.997022i \(0.524571\pi\)
\(992\) 9.22243 0.292812
\(993\) 28.4442 0.902648
\(994\) −83.3877 −2.64490
\(995\) 23.9554 0.759436
\(996\) 61.7218 1.95573
\(997\) 42.4359 1.34396 0.671980 0.740570i \(-0.265444\pi\)
0.671980 + 0.740570i \(0.265444\pi\)
\(998\) 75.2263 2.38125
\(999\) 8.90380 0.281704
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 \(a_p\))