Properties

Label 8002.2.a.e.1.10
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.45617 q^{3} +1.00000 q^{4} +0.358646 q^{5} +2.45617 q^{6} -1.91182 q^{7} -1.00000 q^{8} +3.03279 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.45617 q^{3} +1.00000 q^{4} +0.358646 q^{5} +2.45617 q^{6} -1.91182 q^{7} -1.00000 q^{8} +3.03279 q^{9} -0.358646 q^{10} +5.12829 q^{11} -2.45617 q^{12} +3.67709 q^{13} +1.91182 q^{14} -0.880897 q^{15} +1.00000 q^{16} +3.57578 q^{17} -3.03279 q^{18} -7.77991 q^{19} +0.358646 q^{20} +4.69577 q^{21} -5.12829 q^{22} -0.723070 q^{23} +2.45617 q^{24} -4.87137 q^{25} -3.67709 q^{26} -0.0805476 q^{27} -1.91182 q^{28} +0.330291 q^{29} +0.880897 q^{30} +7.74033 q^{31} -1.00000 q^{32} -12.5960 q^{33} -3.57578 q^{34} -0.685668 q^{35} +3.03279 q^{36} +6.25420 q^{37} +7.77991 q^{38} -9.03159 q^{39} -0.358646 q^{40} -2.75424 q^{41} -4.69577 q^{42} +10.5331 q^{43} +5.12829 q^{44} +1.08770 q^{45} +0.723070 q^{46} +1.93642 q^{47} -2.45617 q^{48} -3.34493 q^{49} +4.87137 q^{50} -8.78273 q^{51} +3.67709 q^{52} -8.76896 q^{53} +0.0805476 q^{54} +1.83924 q^{55} +1.91182 q^{56} +19.1088 q^{57} -0.330291 q^{58} +4.14217 q^{59} -0.880897 q^{60} +13.8353 q^{61} -7.74033 q^{62} -5.79817 q^{63} +1.00000 q^{64} +1.31877 q^{65} +12.5960 q^{66} +10.2792 q^{67} +3.57578 q^{68} +1.77599 q^{69} +0.685668 q^{70} +11.3216 q^{71} -3.03279 q^{72} +2.13860 q^{73} -6.25420 q^{74} +11.9649 q^{75} -7.77991 q^{76} -9.80438 q^{77} +9.03159 q^{78} +2.66262 q^{79} +0.358646 q^{80} -8.90054 q^{81} +2.75424 q^{82} +16.1458 q^{83} +4.69577 q^{84} +1.28244 q^{85} -10.5331 q^{86} -0.811252 q^{87} -5.12829 q^{88} +6.65673 q^{89} -1.08770 q^{90} -7.02996 q^{91} -0.723070 q^{92} -19.0116 q^{93} -1.93642 q^{94} -2.79023 q^{95} +2.45617 q^{96} -15.5223 q^{97} +3.34493 q^{98} +15.5530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.45617 −1.41807 −0.709037 0.705172i \(-0.750870\pi\)
−0.709037 + 0.705172i \(0.750870\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.358646 0.160391 0.0801957 0.996779i \(-0.474445\pi\)
0.0801957 + 0.996779i \(0.474445\pi\)
\(6\) 2.45617 1.00273
\(7\) −1.91182 −0.722602 −0.361301 0.932449i \(-0.617667\pi\)
−0.361301 + 0.932449i \(0.617667\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.03279 1.01093
\(10\) −0.358646 −0.113414
\(11\) 5.12829 1.54624 0.773118 0.634262i \(-0.218696\pi\)
0.773118 + 0.634262i \(0.218696\pi\)
\(12\) −2.45617 −0.709037
\(13\) 3.67709 1.01984 0.509921 0.860221i \(-0.329675\pi\)
0.509921 + 0.860221i \(0.329675\pi\)
\(14\) 1.91182 0.510957
\(15\) −0.880897 −0.227447
\(16\) 1.00000 0.250000
\(17\) 3.57578 0.867254 0.433627 0.901093i \(-0.357234\pi\)
0.433627 + 0.901093i \(0.357234\pi\)
\(18\) −3.03279 −0.714836
\(19\) −7.77991 −1.78483 −0.892417 0.451211i \(-0.850992\pi\)
−0.892417 + 0.451211i \(0.850992\pi\)
\(20\) 0.358646 0.0801957
\(21\) 4.69577 1.02470
\(22\) −5.12829 −1.09335
\(23\) −0.723070 −0.150771 −0.0753853 0.997154i \(-0.524019\pi\)
−0.0753853 + 0.997154i \(0.524019\pi\)
\(24\) 2.45617 0.501365
\(25\) −4.87137 −0.974275
\(26\) −3.67709 −0.721138
\(27\) −0.0805476 −0.0155014
\(28\) −1.91182 −0.361301
\(29\) 0.330291 0.0613335 0.0306667 0.999530i \(-0.490237\pi\)
0.0306667 + 0.999530i \(0.490237\pi\)
\(30\) 0.880897 0.160829
\(31\) 7.74033 1.39021 0.695103 0.718911i \(-0.255359\pi\)
0.695103 + 0.718911i \(0.255359\pi\)
\(32\) −1.00000 −0.176777
\(33\) −12.5960 −2.19268
\(34\) −3.57578 −0.613241
\(35\) −0.685668 −0.115899
\(36\) 3.03279 0.505466
\(37\) 6.25420 1.02818 0.514092 0.857735i \(-0.328129\pi\)
0.514092 + 0.857735i \(0.328129\pi\)
\(38\) 7.77991 1.26207
\(39\) −9.03159 −1.44621
\(40\) −0.358646 −0.0567069
\(41\) −2.75424 −0.430140 −0.215070 0.976599i \(-0.568998\pi\)
−0.215070 + 0.976599i \(0.568998\pi\)
\(42\) −4.69577 −0.724574
\(43\) 10.5331 1.60628 0.803142 0.595788i \(-0.203160\pi\)
0.803142 + 0.595788i \(0.203160\pi\)
\(44\) 5.12829 0.773118
\(45\) 1.08770 0.162145
\(46\) 0.723070 0.106611
\(47\) 1.93642 0.282456 0.141228 0.989977i \(-0.454895\pi\)
0.141228 + 0.989977i \(0.454895\pi\)
\(48\) −2.45617 −0.354518
\(49\) −3.34493 −0.477847
\(50\) 4.87137 0.688916
\(51\) −8.78273 −1.22983
\(52\) 3.67709 0.509921
\(53\) −8.76896 −1.20451 −0.602255 0.798304i \(-0.705731\pi\)
−0.602255 + 0.798304i \(0.705731\pi\)
\(54\) 0.0805476 0.0109611
\(55\) 1.83924 0.248003
\(56\) 1.91182 0.255478
\(57\) 19.1088 2.53103
\(58\) −0.330291 −0.0433693
\(59\) 4.14217 0.539265 0.269632 0.962963i \(-0.413098\pi\)
0.269632 + 0.962963i \(0.413098\pi\)
\(60\) −0.880897 −0.113723
\(61\) 13.8353 1.77142 0.885712 0.464235i \(-0.153671\pi\)
0.885712 + 0.464235i \(0.153671\pi\)
\(62\) −7.74033 −0.983023
\(63\) −5.79817 −0.730501
\(64\) 1.00000 0.125000
\(65\) 1.31877 0.163574
\(66\) 12.5960 1.55046
\(67\) 10.2792 1.25580 0.627901 0.778293i \(-0.283914\pi\)
0.627901 + 0.778293i \(0.283914\pi\)
\(68\) 3.57578 0.433627
\(69\) 1.77599 0.213804
\(70\) 0.685668 0.0819530
\(71\) 11.3216 1.34363 0.671815 0.740719i \(-0.265515\pi\)
0.671815 + 0.740719i \(0.265515\pi\)
\(72\) −3.03279 −0.357418
\(73\) 2.13860 0.250304 0.125152 0.992138i \(-0.460058\pi\)
0.125152 + 0.992138i \(0.460058\pi\)
\(74\) −6.25420 −0.727035
\(75\) 11.9649 1.38159
\(76\) −7.77991 −0.892417
\(77\) −9.80438 −1.11731
\(78\) 9.03159 1.02263
\(79\) 2.66262 0.299569 0.149784 0.988719i \(-0.452142\pi\)
0.149784 + 0.988719i \(0.452142\pi\)
\(80\) 0.358646 0.0400978
\(81\) −8.90054 −0.988949
\(82\) 2.75424 0.304155
\(83\) 16.1458 1.77223 0.886115 0.463466i \(-0.153395\pi\)
0.886115 + 0.463466i \(0.153395\pi\)
\(84\) 4.69577 0.512351
\(85\) 1.28244 0.139100
\(86\) −10.5331 −1.13581
\(87\) −0.811252 −0.0869753
\(88\) −5.12829 −0.546677
\(89\) 6.65673 0.705612 0.352806 0.935697i \(-0.385228\pi\)
0.352806 + 0.935697i \(0.385228\pi\)
\(90\) −1.08770 −0.114654
\(91\) −7.02996 −0.736940
\(92\) −0.723070 −0.0753853
\(93\) −19.0116 −1.97141
\(94\) −1.93642 −0.199726
\(95\) −2.79023 −0.286272
\(96\) 2.45617 0.250682
\(97\) −15.5223 −1.57605 −0.788025 0.615644i \(-0.788896\pi\)
−0.788025 + 0.615644i \(0.788896\pi\)
\(98\) 3.34493 0.337889
\(99\) 15.5530 1.56314
\(100\) −4.87137 −0.487137
\(101\) −17.1278 −1.70428 −0.852142 0.523310i \(-0.824697\pi\)
−0.852142 + 0.523310i \(0.824697\pi\)
\(102\) 8.78273 0.869620
\(103\) 0.0678555 0.00668600 0.00334300 0.999994i \(-0.498936\pi\)
0.00334300 + 0.999994i \(0.498936\pi\)
\(104\) −3.67709 −0.360569
\(105\) 1.68412 0.164353
\(106\) 8.76896 0.851717
\(107\) −9.95374 −0.962264 −0.481132 0.876648i \(-0.659774\pi\)
−0.481132 + 0.876648i \(0.659774\pi\)
\(108\) −0.0805476 −0.00775069
\(109\) −12.1877 −1.16737 −0.583685 0.811980i \(-0.698390\pi\)
−0.583685 + 0.811980i \(0.698390\pi\)
\(110\) −1.83924 −0.175365
\(111\) −15.3614 −1.45804
\(112\) −1.91182 −0.180650
\(113\) 0.0565757 0.00532220 0.00266110 0.999996i \(-0.499153\pi\)
0.00266110 + 0.999996i \(0.499153\pi\)
\(114\) −19.1088 −1.78971
\(115\) −0.259326 −0.0241823
\(116\) 0.330291 0.0306667
\(117\) 11.1519 1.03099
\(118\) −4.14217 −0.381318
\(119\) −6.83626 −0.626679
\(120\) 0.880897 0.0804145
\(121\) 15.2993 1.39085
\(122\) −13.8353 −1.25259
\(123\) 6.76490 0.609971
\(124\) 7.74033 0.695103
\(125\) −3.54033 −0.316656
\(126\) 5.79817 0.516542
\(127\) 1.91398 0.169838 0.0849190 0.996388i \(-0.472937\pi\)
0.0849190 + 0.996388i \(0.472937\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −25.8712 −2.27783
\(130\) −1.31877 −0.115664
\(131\) −5.97806 −0.522305 −0.261153 0.965297i \(-0.584103\pi\)
−0.261153 + 0.965297i \(0.584103\pi\)
\(132\) −12.5960 −1.09634
\(133\) 14.8738 1.28972
\(134\) −10.2792 −0.887986
\(135\) −0.0288880 −0.00248629
\(136\) −3.57578 −0.306620
\(137\) −8.64368 −0.738480 −0.369240 0.929334i \(-0.620382\pi\)
−0.369240 + 0.929334i \(0.620382\pi\)
\(138\) −1.77599 −0.151182
\(139\) −6.52529 −0.553468 −0.276734 0.960947i \(-0.589252\pi\)
−0.276734 + 0.960947i \(0.589252\pi\)
\(140\) −0.685668 −0.0579495
\(141\) −4.75618 −0.400543
\(142\) −11.3216 −0.950090
\(143\) 18.8572 1.57692
\(144\) 3.03279 0.252733
\(145\) 0.118457 0.00983735
\(146\) −2.13860 −0.176992
\(147\) 8.21573 0.677622
\(148\) 6.25420 0.514092
\(149\) −8.17522 −0.669740 −0.334870 0.942264i \(-0.608692\pi\)
−0.334870 + 0.942264i \(0.608692\pi\)
\(150\) −11.9649 −0.976934
\(151\) −8.63009 −0.702307 −0.351153 0.936318i \(-0.614210\pi\)
−0.351153 + 0.936318i \(0.614210\pi\)
\(152\) 7.77991 0.631034
\(153\) 10.8446 0.876734
\(154\) 9.80438 0.790060
\(155\) 2.77604 0.222977
\(156\) −9.03159 −0.723106
\(157\) −0.895203 −0.0714450 −0.0357225 0.999362i \(-0.511373\pi\)
−0.0357225 + 0.999362i \(0.511373\pi\)
\(158\) −2.66262 −0.211827
\(159\) 21.5381 1.70808
\(160\) −0.358646 −0.0283534
\(161\) 1.38238 0.108947
\(162\) 8.90054 0.699293
\(163\) 12.6311 0.989341 0.494671 0.869081i \(-0.335289\pi\)
0.494671 + 0.869081i \(0.335289\pi\)
\(164\) −2.75424 −0.215070
\(165\) −4.51749 −0.351686
\(166\) −16.1458 −1.25316
\(167\) −8.71988 −0.674764 −0.337382 0.941368i \(-0.609541\pi\)
−0.337382 + 0.941368i \(0.609541\pi\)
\(168\) −4.69577 −0.362287
\(169\) 0.521025 0.0400789
\(170\) −1.28244 −0.0983585
\(171\) −23.5949 −1.80435
\(172\) 10.5331 0.803142
\(173\) 4.33803 0.329815 0.164907 0.986309i \(-0.447268\pi\)
0.164907 + 0.986309i \(0.447268\pi\)
\(174\) 0.811252 0.0615008
\(175\) 9.31321 0.704013
\(176\) 5.12829 0.386559
\(177\) −10.1739 −0.764717
\(178\) −6.65673 −0.498943
\(179\) −1.50661 −0.112609 −0.0563047 0.998414i \(-0.517932\pi\)
−0.0563047 + 0.998414i \(0.517932\pi\)
\(180\) 1.08770 0.0810723
\(181\) 8.54956 0.635484 0.317742 0.948177i \(-0.397075\pi\)
0.317742 + 0.948177i \(0.397075\pi\)
\(182\) 7.02996 0.521095
\(183\) −33.9818 −2.51201
\(184\) 0.723070 0.0533055
\(185\) 2.24304 0.164912
\(186\) 19.0116 1.39400
\(187\) 18.3376 1.34098
\(188\) 1.93642 0.141228
\(189\) 0.153993 0.0112013
\(190\) 2.79023 0.202425
\(191\) −3.47248 −0.251260 −0.125630 0.992077i \(-0.540095\pi\)
−0.125630 + 0.992077i \(0.540095\pi\)
\(192\) −2.45617 −0.177259
\(193\) −25.1942 −1.81352 −0.906758 0.421652i \(-0.861450\pi\)
−0.906758 + 0.421652i \(0.861450\pi\)
\(194\) 15.5223 1.11444
\(195\) −3.23914 −0.231960
\(196\) −3.34493 −0.238923
\(197\) 19.7918 1.41011 0.705055 0.709152i \(-0.250922\pi\)
0.705055 + 0.709152i \(0.250922\pi\)
\(198\) −15.5530 −1.10531
\(199\) 0.695954 0.0493349 0.0246674 0.999696i \(-0.492147\pi\)
0.0246674 + 0.999696i \(0.492147\pi\)
\(200\) 4.87137 0.344458
\(201\) −25.2475 −1.78082
\(202\) 17.1278 1.20511
\(203\) −0.631458 −0.0443197
\(204\) −8.78273 −0.614914
\(205\) −0.987798 −0.0689908
\(206\) −0.0678555 −0.00472772
\(207\) −2.19292 −0.152419
\(208\) 3.67709 0.254961
\(209\) −39.8976 −2.75978
\(210\) −1.68412 −0.116215
\(211\) 12.5891 0.866671 0.433336 0.901233i \(-0.357336\pi\)
0.433336 + 0.901233i \(0.357336\pi\)
\(212\) −8.76896 −0.602255
\(213\) −27.8079 −1.90537
\(214\) 9.95374 0.680423
\(215\) 3.77766 0.257634
\(216\) 0.0805476 0.00548057
\(217\) −14.7982 −1.00456
\(218\) 12.1877 0.825455
\(219\) −5.25277 −0.354949
\(220\) 1.83924 0.124001
\(221\) 13.1485 0.884462
\(222\) 15.3614 1.03099
\(223\) 18.6690 1.25017 0.625083 0.780558i \(-0.285065\pi\)
0.625083 + 0.780558i \(0.285065\pi\)
\(224\) 1.91182 0.127739
\(225\) −14.7739 −0.984925
\(226\) −0.0565757 −0.00376336
\(227\) −6.28244 −0.416980 −0.208490 0.978024i \(-0.566855\pi\)
−0.208490 + 0.978024i \(0.566855\pi\)
\(228\) 19.1088 1.26551
\(229\) 11.4404 0.756003 0.378001 0.925805i \(-0.376611\pi\)
0.378001 + 0.925805i \(0.376611\pi\)
\(230\) 0.259326 0.0170995
\(231\) 24.0813 1.58443
\(232\) −0.330291 −0.0216847
\(233\) 24.7109 1.61886 0.809432 0.587214i \(-0.199775\pi\)
0.809432 + 0.587214i \(0.199775\pi\)
\(234\) −11.1519 −0.729021
\(235\) 0.694489 0.0453035
\(236\) 4.14217 0.269632
\(237\) −6.53987 −0.424810
\(238\) 6.83626 0.443129
\(239\) −11.3472 −0.733988 −0.366994 0.930223i \(-0.619613\pi\)
−0.366994 + 0.930223i \(0.619613\pi\)
\(240\) −0.880897 −0.0568616
\(241\) −20.3946 −1.31373 −0.656866 0.754007i \(-0.728118\pi\)
−0.656866 + 0.754007i \(0.728118\pi\)
\(242\) −15.2993 −0.983477
\(243\) 22.1029 1.41790
\(244\) 13.8353 0.885712
\(245\) −1.19964 −0.0766425
\(246\) −6.76490 −0.431314
\(247\) −28.6075 −1.82025
\(248\) −7.74033 −0.491512
\(249\) −39.6568 −2.51315
\(250\) 3.54033 0.223910
\(251\) −3.23769 −0.204361 −0.102180 0.994766i \(-0.532582\pi\)
−0.102180 + 0.994766i \(0.532582\pi\)
\(252\) −5.79817 −0.365250
\(253\) −3.70811 −0.233127
\(254\) −1.91398 −0.120094
\(255\) −3.14989 −0.197254
\(256\) 1.00000 0.0625000
\(257\) −23.2428 −1.44985 −0.724924 0.688829i \(-0.758125\pi\)
−0.724924 + 0.688829i \(0.758125\pi\)
\(258\) 25.8712 1.61067
\(259\) −11.9569 −0.742967
\(260\) 1.31877 0.0817869
\(261\) 1.00170 0.0620039
\(262\) 5.97806 0.369326
\(263\) 15.4903 0.955174 0.477587 0.878584i \(-0.341511\pi\)
0.477587 + 0.878584i \(0.341511\pi\)
\(264\) 12.5960 0.775228
\(265\) −3.14495 −0.193193
\(266\) −14.8738 −0.911973
\(267\) −16.3501 −1.00061
\(268\) 10.2792 0.627901
\(269\) −2.11017 −0.128659 −0.0643297 0.997929i \(-0.520491\pi\)
−0.0643297 + 0.997929i \(0.520491\pi\)
\(270\) 0.0288880 0.00175807
\(271\) 26.5888 1.61515 0.807577 0.589762i \(-0.200778\pi\)
0.807577 + 0.589762i \(0.200778\pi\)
\(272\) 3.57578 0.216813
\(273\) 17.2668 1.04503
\(274\) 8.64368 0.522184
\(275\) −24.9818 −1.50646
\(276\) 1.77599 0.106902
\(277\) −13.0767 −0.785704 −0.392852 0.919602i \(-0.628512\pi\)
−0.392852 + 0.919602i \(0.628512\pi\)
\(278\) 6.52529 0.391361
\(279\) 23.4748 1.40540
\(280\) 0.685668 0.0409765
\(281\) 16.5235 0.985707 0.492854 0.870112i \(-0.335954\pi\)
0.492854 + 0.870112i \(0.335954\pi\)
\(282\) 4.75618 0.283227
\(283\) 23.5299 1.39871 0.699353 0.714777i \(-0.253472\pi\)
0.699353 + 0.714777i \(0.253472\pi\)
\(284\) 11.3216 0.671815
\(285\) 6.85330 0.405955
\(286\) −18.8572 −1.11505
\(287\) 5.26563 0.310820
\(288\) −3.03279 −0.178709
\(289\) −4.21381 −0.247871
\(290\) −0.118457 −0.00695606
\(291\) 38.1254 2.23495
\(292\) 2.13860 0.125152
\(293\) 10.6440 0.621828 0.310914 0.950438i \(-0.399365\pi\)
0.310914 + 0.950438i \(0.399365\pi\)
\(294\) −8.21573 −0.479151
\(295\) 1.48557 0.0864934
\(296\) −6.25420 −0.363518
\(297\) −0.413071 −0.0239688
\(298\) 8.17522 0.473578
\(299\) −2.65880 −0.153762
\(300\) 11.9649 0.690796
\(301\) −20.1375 −1.16070
\(302\) 8.63009 0.496606
\(303\) 42.0690 2.41680
\(304\) −7.77991 −0.446209
\(305\) 4.96196 0.284121
\(306\) −10.8446 −0.619944
\(307\) −22.2739 −1.27124 −0.635619 0.772003i \(-0.719255\pi\)
−0.635619 + 0.772003i \(0.719255\pi\)
\(308\) −9.80438 −0.558657
\(309\) −0.166665 −0.00948124
\(310\) −2.77604 −0.157668
\(311\) −34.2323 −1.94114 −0.970568 0.240828i \(-0.922581\pi\)
−0.970568 + 0.240828i \(0.922581\pi\)
\(312\) 9.03159 0.511313
\(313\) −10.5955 −0.598896 −0.299448 0.954113i \(-0.596802\pi\)
−0.299448 + 0.954113i \(0.596802\pi\)
\(314\) 0.895203 0.0505192
\(315\) −2.07949 −0.117166
\(316\) 2.66262 0.149784
\(317\) −3.74670 −0.210436 −0.105218 0.994449i \(-0.533554\pi\)
−0.105218 + 0.994449i \(0.533554\pi\)
\(318\) −21.5381 −1.20780
\(319\) 1.69383 0.0948360
\(320\) 0.358646 0.0200489
\(321\) 24.4481 1.36456
\(322\) −1.38238 −0.0770372
\(323\) −27.8192 −1.54790
\(324\) −8.90054 −0.494475
\(325\) −17.9125 −0.993607
\(326\) −12.6311 −0.699570
\(327\) 29.9351 1.65542
\(328\) 2.75424 0.152078
\(329\) −3.70209 −0.204103
\(330\) 4.51749 0.248680
\(331\) 28.1086 1.54499 0.772494 0.635023i \(-0.219009\pi\)
0.772494 + 0.635023i \(0.219009\pi\)
\(332\) 16.1458 0.886115
\(333\) 18.9677 1.03942
\(334\) 8.71988 0.477130
\(335\) 3.68658 0.201420
\(336\) 4.69577 0.256176
\(337\) 27.0540 1.47373 0.736863 0.676042i \(-0.236306\pi\)
0.736863 + 0.676042i \(0.236306\pi\)
\(338\) −0.521025 −0.0283400
\(339\) −0.138960 −0.00754726
\(340\) 1.28244 0.0695500
\(341\) 39.6946 2.14959
\(342\) 23.5949 1.27586
\(343\) 19.7777 1.06789
\(344\) −10.5331 −0.567907
\(345\) 0.636950 0.0342923
\(346\) −4.33803 −0.233214
\(347\) 14.3269 0.769109 0.384555 0.923102i \(-0.374355\pi\)
0.384555 + 0.923102i \(0.374355\pi\)
\(348\) −0.811252 −0.0434877
\(349\) −28.2450 −1.51192 −0.755959 0.654618i \(-0.772829\pi\)
−0.755959 + 0.654618i \(0.772829\pi\)
\(350\) −9.31321 −0.497812
\(351\) −0.296181 −0.0158090
\(352\) −5.12829 −0.273339
\(353\) 29.7589 1.58391 0.791954 0.610581i \(-0.209064\pi\)
0.791954 + 0.610581i \(0.209064\pi\)
\(354\) 10.1739 0.540736
\(355\) 4.06046 0.215507
\(356\) 6.65673 0.352806
\(357\) 16.7910 0.888676
\(358\) 1.50661 0.0796269
\(359\) −7.83656 −0.413598 −0.206799 0.978383i \(-0.566305\pi\)
−0.206799 + 0.978383i \(0.566305\pi\)
\(360\) −1.08770 −0.0573268
\(361\) 41.5271 2.18563
\(362\) −8.54956 −0.449355
\(363\) −37.5778 −1.97232
\(364\) −7.02996 −0.368470
\(365\) 0.767000 0.0401466
\(366\) 33.9818 1.77626
\(367\) −11.8807 −0.620170 −0.310085 0.950709i \(-0.600357\pi\)
−0.310085 + 0.950709i \(0.600357\pi\)
\(368\) −0.723070 −0.0376926
\(369\) −8.35305 −0.434842
\(370\) −2.24304 −0.116610
\(371\) 16.7647 0.870381
\(372\) −19.0116 −0.985706
\(373\) 16.2587 0.841845 0.420923 0.907097i \(-0.361706\pi\)
0.420923 + 0.907097i \(0.361706\pi\)
\(374\) −18.3376 −0.948215
\(375\) 8.69566 0.449042
\(376\) −1.93642 −0.0998632
\(377\) 1.21451 0.0625505
\(378\) −0.153993 −0.00792053
\(379\) −30.0310 −1.54259 −0.771294 0.636479i \(-0.780390\pi\)
−0.771294 + 0.636479i \(0.780390\pi\)
\(380\) −2.79023 −0.143136
\(381\) −4.70106 −0.240843
\(382\) 3.47248 0.177667
\(383\) 6.22357 0.318010 0.159005 0.987278i \(-0.449171\pi\)
0.159005 + 0.987278i \(0.449171\pi\)
\(384\) 2.45617 0.125341
\(385\) −3.51630 −0.179207
\(386\) 25.1942 1.28235
\(387\) 31.9447 1.62384
\(388\) −15.5223 −0.788025
\(389\) −27.8418 −1.41164 −0.705818 0.708393i \(-0.749420\pi\)
−0.705818 + 0.708393i \(0.749420\pi\)
\(390\) 3.23914 0.164020
\(391\) −2.58554 −0.130756
\(392\) 3.34493 0.168944
\(393\) 14.6832 0.740667
\(394\) −19.7918 −0.997099
\(395\) 0.954939 0.0480482
\(396\) 15.5530 0.781569
\(397\) −5.78872 −0.290527 −0.145264 0.989393i \(-0.546403\pi\)
−0.145264 + 0.989393i \(0.546403\pi\)
\(398\) −0.695954 −0.0348850
\(399\) −36.5327 −1.82892
\(400\) −4.87137 −0.243569
\(401\) 17.4983 0.873821 0.436911 0.899505i \(-0.356073\pi\)
0.436911 + 0.899505i \(0.356073\pi\)
\(402\) 25.2475 1.25923
\(403\) 28.4619 1.41779
\(404\) −17.1278 −0.852142
\(405\) −3.19214 −0.158619
\(406\) 0.631458 0.0313387
\(407\) 32.0733 1.58981
\(408\) 8.78273 0.434810
\(409\) 29.7803 1.47254 0.736270 0.676687i \(-0.236585\pi\)
0.736270 + 0.676687i \(0.236585\pi\)
\(410\) 0.987798 0.0487839
\(411\) 21.2304 1.04722
\(412\) 0.0678555 0.00334300
\(413\) −7.91910 −0.389674
\(414\) 2.19292 0.107776
\(415\) 5.79062 0.284250
\(416\) −3.67709 −0.180284
\(417\) 16.0273 0.784858
\(418\) 39.8976 1.95146
\(419\) 20.3335 0.993356 0.496678 0.867935i \(-0.334553\pi\)
0.496678 + 0.867935i \(0.334553\pi\)
\(420\) 1.68412 0.0821767
\(421\) −22.2050 −1.08220 −0.541102 0.840957i \(-0.681993\pi\)
−0.541102 + 0.840957i \(0.681993\pi\)
\(422\) −12.5891 −0.612829
\(423\) 5.87276 0.285543
\(424\) 8.76896 0.425859
\(425\) −17.4189 −0.844943
\(426\) 27.8079 1.34730
\(427\) −26.4506 −1.28003
\(428\) −9.95374 −0.481132
\(429\) −46.3166 −2.23618
\(430\) −3.77766 −0.182175
\(431\) −30.6666 −1.47716 −0.738579 0.674167i \(-0.764503\pi\)
−0.738579 + 0.674167i \(0.764503\pi\)
\(432\) −0.0805476 −0.00387535
\(433\) −21.6081 −1.03842 −0.519210 0.854646i \(-0.673774\pi\)
−0.519210 + 0.854646i \(0.673774\pi\)
\(434\) 14.7982 0.710334
\(435\) −0.290952 −0.0139501
\(436\) −12.1877 −0.583685
\(437\) 5.62542 0.269101
\(438\) 5.25277 0.250987
\(439\) 0.409379 0.0195386 0.00976930 0.999952i \(-0.496890\pi\)
0.00976930 + 0.999952i \(0.496890\pi\)
\(440\) −1.83924 −0.0876823
\(441\) −10.1445 −0.483070
\(442\) −13.1485 −0.625409
\(443\) −13.5597 −0.644241 −0.322121 0.946699i \(-0.604396\pi\)
−0.322121 + 0.946699i \(0.604396\pi\)
\(444\) −15.3614 −0.729020
\(445\) 2.38741 0.113174
\(446\) −18.6690 −0.884001
\(447\) 20.0798 0.949740
\(448\) −1.91182 −0.0903252
\(449\) 3.71919 0.175519 0.0877597 0.996142i \(-0.472029\pi\)
0.0877597 + 0.996142i \(0.472029\pi\)
\(450\) 14.7739 0.696447
\(451\) −14.1245 −0.665099
\(452\) 0.0565757 0.00266110
\(453\) 21.1970 0.995923
\(454\) 6.28244 0.294849
\(455\) −2.52127 −0.118199
\(456\) −19.1088 −0.894853
\(457\) 20.8371 0.974720 0.487360 0.873201i \(-0.337960\pi\)
0.487360 + 0.873201i \(0.337960\pi\)
\(458\) −11.4404 −0.534575
\(459\) −0.288020 −0.0134436
\(460\) −0.259326 −0.0120911
\(461\) −22.4406 −1.04516 −0.522582 0.852589i \(-0.675031\pi\)
−0.522582 + 0.852589i \(0.675031\pi\)
\(462\) −24.0813 −1.12036
\(463\) −18.5063 −0.860062 −0.430031 0.902814i \(-0.641497\pi\)
−0.430031 + 0.902814i \(0.641497\pi\)
\(464\) 0.330291 0.0153334
\(465\) −6.81844 −0.316197
\(466\) −24.7109 −1.14471
\(467\) 29.4384 1.36225 0.681124 0.732168i \(-0.261492\pi\)
0.681124 + 0.732168i \(0.261492\pi\)
\(468\) 11.1519 0.515495
\(469\) −19.6520 −0.907444
\(470\) −0.694489 −0.0320344
\(471\) 2.19877 0.101314
\(472\) −4.14217 −0.190659
\(473\) 54.0168 2.48369
\(474\) 6.53987 0.300386
\(475\) 37.8989 1.73892
\(476\) −6.83626 −0.313339
\(477\) −26.5945 −1.21768
\(478\) 11.3472 0.519008
\(479\) −15.8363 −0.723581 −0.361790 0.932259i \(-0.617834\pi\)
−0.361790 + 0.932259i \(0.617834\pi\)
\(480\) 0.880897 0.0402073
\(481\) 22.9973 1.04859
\(482\) 20.3946 0.928949
\(483\) −3.39538 −0.154495
\(484\) 15.2993 0.695423
\(485\) −5.56700 −0.252785
\(486\) −22.1029 −1.00261
\(487\) −22.4529 −1.01744 −0.508719 0.860933i \(-0.669881\pi\)
−0.508719 + 0.860933i \(0.669881\pi\)
\(488\) −13.8353 −0.626293
\(489\) −31.0241 −1.40296
\(490\) 1.19964 0.0541944
\(491\) −0.215708 −0.00973478 −0.00486739 0.999988i \(-0.501549\pi\)
−0.00486739 + 0.999988i \(0.501549\pi\)
\(492\) 6.76490 0.304985
\(493\) 1.18105 0.0531917
\(494\) 28.6075 1.28711
\(495\) 5.57803 0.250714
\(496\) 7.74033 0.347551
\(497\) −21.6450 −0.970910
\(498\) 39.6568 1.77707
\(499\) 15.1384 0.677687 0.338843 0.940843i \(-0.389964\pi\)
0.338843 + 0.940843i \(0.389964\pi\)
\(500\) −3.54033 −0.158328
\(501\) 21.4175 0.956865
\(502\) 3.23769 0.144505
\(503\) 16.6980 0.744528 0.372264 0.928127i \(-0.378582\pi\)
0.372264 + 0.928127i \(0.378582\pi\)
\(504\) 5.79817 0.258271
\(505\) −6.14283 −0.273352
\(506\) 3.70811 0.164846
\(507\) −1.27973 −0.0568348
\(508\) 1.91398 0.0849190
\(509\) 33.9377 1.50426 0.752132 0.659013i \(-0.229026\pi\)
0.752132 + 0.659013i \(0.229026\pi\)
\(510\) 3.14989 0.139480
\(511\) −4.08863 −0.180870
\(512\) −1.00000 −0.0441942
\(513\) 0.626653 0.0276674
\(514\) 23.2428 1.02520
\(515\) 0.0243361 0.00107238
\(516\) −25.8712 −1.13891
\(517\) 9.93051 0.436743
\(518\) 11.9569 0.525357
\(519\) −10.6550 −0.467701
\(520\) −1.31877 −0.0578321
\(521\) 29.4692 1.29107 0.645534 0.763731i \(-0.276635\pi\)
0.645534 + 0.763731i \(0.276635\pi\)
\(522\) −1.00170 −0.0438434
\(523\) 35.0301 1.53176 0.765881 0.642983i \(-0.222303\pi\)
0.765881 + 0.642983i \(0.222303\pi\)
\(524\) −5.97806 −0.261153
\(525\) −22.8749 −0.998341
\(526\) −15.4903 −0.675410
\(527\) 27.6777 1.20566
\(528\) −12.5960 −0.548169
\(529\) −22.4772 −0.977268
\(530\) 3.14495 0.136608
\(531\) 12.5624 0.545160
\(532\) 14.8738 0.644862
\(533\) −10.1276 −0.438676
\(534\) 16.3501 0.707537
\(535\) −3.56987 −0.154339
\(536\) −10.2792 −0.443993
\(537\) 3.70050 0.159688
\(538\) 2.11017 0.0909759
\(539\) −17.1537 −0.738864
\(540\) −0.0288880 −0.00124314
\(541\) −21.7312 −0.934297 −0.467149 0.884179i \(-0.654719\pi\)
−0.467149 + 0.884179i \(0.654719\pi\)
\(542\) −26.5888 −1.14209
\(543\) −20.9992 −0.901162
\(544\) −3.57578 −0.153310
\(545\) −4.37107 −0.187236
\(546\) −17.2668 −0.738951
\(547\) 10.9312 0.467383 0.233692 0.972311i \(-0.424919\pi\)
0.233692 + 0.972311i \(0.424919\pi\)
\(548\) −8.64368 −0.369240
\(549\) 41.9595 1.79079
\(550\) 24.9818 1.06523
\(551\) −2.56963 −0.109470
\(552\) −1.77599 −0.0755910
\(553\) −5.09047 −0.216469
\(554\) 13.0767 0.555577
\(555\) −5.50930 −0.233857
\(556\) −6.52529 −0.276734
\(557\) 41.0887 1.74098 0.870492 0.492183i \(-0.163801\pi\)
0.870492 + 0.492183i \(0.163801\pi\)
\(558\) −23.4748 −0.993769
\(559\) 38.7312 1.63816
\(560\) −0.685668 −0.0289748
\(561\) −45.0404 −1.90161
\(562\) −16.5235 −0.697000
\(563\) 30.3308 1.27829 0.639145 0.769086i \(-0.279288\pi\)
0.639145 + 0.769086i \(0.279288\pi\)
\(564\) −4.75618 −0.200271
\(565\) 0.0202906 0.000853634 0
\(566\) −23.5299 −0.989034
\(567\) 17.0163 0.714616
\(568\) −11.3216 −0.475045
\(569\) 35.7618 1.49921 0.749605 0.661885i \(-0.230243\pi\)
0.749605 + 0.661885i \(0.230243\pi\)
\(570\) −6.85330 −0.287053
\(571\) 33.2767 1.39259 0.696293 0.717757i \(-0.254831\pi\)
0.696293 + 0.717757i \(0.254831\pi\)
\(572\) 18.8572 0.788459
\(573\) 8.52901 0.356304
\(574\) −5.26563 −0.219783
\(575\) 3.52235 0.146892
\(576\) 3.03279 0.126366
\(577\) −12.5284 −0.521563 −0.260782 0.965398i \(-0.583980\pi\)
−0.260782 + 0.965398i \(0.583980\pi\)
\(578\) 4.21381 0.175272
\(579\) 61.8813 2.57170
\(580\) 0.118457 0.00491868
\(581\) −30.8679 −1.28062
\(582\) −38.1254 −1.58035
\(583\) −44.9698 −1.86246
\(584\) −2.13860 −0.0884958
\(585\) 3.99957 0.165362
\(586\) −10.6440 −0.439699
\(587\) 1.98145 0.0817833 0.0408917 0.999164i \(-0.486980\pi\)
0.0408917 + 0.999164i \(0.486980\pi\)
\(588\) 8.21573 0.338811
\(589\) −60.2191 −2.48129
\(590\) −1.48557 −0.0611601
\(591\) −48.6122 −1.99964
\(592\) 6.25420 0.257046
\(593\) 3.55257 0.145886 0.0729432 0.997336i \(-0.476761\pi\)
0.0729432 + 0.997336i \(0.476761\pi\)
\(594\) 0.413071 0.0169485
\(595\) −2.45180 −0.100514
\(596\) −8.17522 −0.334870
\(597\) −1.70939 −0.0699605
\(598\) 2.65880 0.108726
\(599\) −7.42041 −0.303190 −0.151595 0.988443i \(-0.548441\pi\)
−0.151595 + 0.988443i \(0.548441\pi\)
\(600\) −11.9649 −0.488467
\(601\) −38.9084 −1.58711 −0.793553 0.608501i \(-0.791771\pi\)
−0.793553 + 0.608501i \(0.791771\pi\)
\(602\) 20.1375 0.820741
\(603\) 31.1746 1.26953
\(604\) −8.63009 −0.351153
\(605\) 5.48704 0.223080
\(606\) −42.0690 −1.70894
\(607\) −23.2176 −0.942373 −0.471187 0.882033i \(-0.656174\pi\)
−0.471187 + 0.882033i \(0.656174\pi\)
\(608\) 7.77991 0.315517
\(609\) 1.55097 0.0628485
\(610\) −4.96196 −0.200904
\(611\) 7.12040 0.288060
\(612\) 10.8446 0.438367
\(613\) 8.72008 0.352201 0.176100 0.984372i \(-0.443652\pi\)
0.176100 + 0.984372i \(0.443652\pi\)
\(614\) 22.2739 0.898901
\(615\) 2.42620 0.0978340
\(616\) 9.80438 0.395030
\(617\) −3.00235 −0.120870 −0.0604351 0.998172i \(-0.519249\pi\)
−0.0604351 + 0.998172i \(0.519249\pi\)
\(618\) 0.166665 0.00670425
\(619\) 38.8483 1.56145 0.780723 0.624877i \(-0.214851\pi\)
0.780723 + 0.624877i \(0.214851\pi\)
\(620\) 2.77604 0.111488
\(621\) 0.0582415 0.00233715
\(622\) 34.2323 1.37259
\(623\) −12.7265 −0.509876
\(624\) −9.03159 −0.361553
\(625\) 23.0871 0.923486
\(626\) 10.5955 0.423483
\(627\) 97.9955 3.91356
\(628\) −0.895203 −0.0357225
\(629\) 22.3636 0.891696
\(630\) 2.07949 0.0828488
\(631\) 16.8132 0.669321 0.334661 0.942339i \(-0.391378\pi\)
0.334661 + 0.942339i \(0.391378\pi\)
\(632\) −2.66262 −0.105914
\(633\) −30.9211 −1.22900
\(634\) 3.74670 0.148801
\(635\) 0.686440 0.0272406
\(636\) 21.5381 0.854041
\(637\) −12.2996 −0.487328
\(638\) −1.69383 −0.0670592
\(639\) 34.3362 1.35832
\(640\) −0.358646 −0.0141767
\(641\) 24.6632 0.974137 0.487068 0.873364i \(-0.338066\pi\)
0.487068 + 0.873364i \(0.338066\pi\)
\(642\) −24.4481 −0.964890
\(643\) 31.4955 1.24206 0.621030 0.783787i \(-0.286714\pi\)
0.621030 + 0.783787i \(0.286714\pi\)
\(644\) 1.38238 0.0544735
\(645\) −9.27858 −0.365344
\(646\) 27.8192 1.09453
\(647\) 3.61562 0.142144 0.0710722 0.997471i \(-0.477358\pi\)
0.0710722 + 0.997471i \(0.477358\pi\)
\(648\) 8.90054 0.349646
\(649\) 21.2422 0.833831
\(650\) 17.9125 0.702586
\(651\) 36.3469 1.42455
\(652\) 12.6311 0.494671
\(653\) 32.6830 1.27898 0.639492 0.768797i \(-0.279145\pi\)
0.639492 + 0.768797i \(0.279145\pi\)
\(654\) −29.9351 −1.17056
\(655\) −2.14401 −0.0837733
\(656\) −2.75424 −0.107535
\(657\) 6.48593 0.253040
\(658\) 3.70209 0.144323
\(659\) −6.75197 −0.263020 −0.131510 0.991315i \(-0.541982\pi\)
−0.131510 + 0.991315i \(0.541982\pi\)
\(660\) −4.51749 −0.175843
\(661\) 26.3807 1.02609 0.513044 0.858362i \(-0.328518\pi\)
0.513044 + 0.858362i \(0.328518\pi\)
\(662\) −28.1086 −1.09247
\(663\) −32.2949 −1.25423
\(664\) −16.1458 −0.626578
\(665\) 5.33444 0.206861
\(666\) −18.9677 −0.734983
\(667\) −0.238823 −0.00924728
\(668\) −8.71988 −0.337382
\(669\) −45.8542 −1.77283
\(670\) −3.68658 −0.142425
\(671\) 70.9512 2.73904
\(672\) −4.69577 −0.181143
\(673\) 11.5529 0.445330 0.222665 0.974895i \(-0.428524\pi\)
0.222665 + 0.974895i \(0.428524\pi\)
\(674\) −27.0540 −1.04208
\(675\) 0.392377 0.0151026
\(676\) 0.521025 0.0200394
\(677\) 26.6911 1.02582 0.512910 0.858442i \(-0.328567\pi\)
0.512910 + 0.858442i \(0.328567\pi\)
\(678\) 0.138960 0.00533672
\(679\) 29.6759 1.13886
\(680\) −1.28244 −0.0491793
\(681\) 15.4308 0.591308
\(682\) −39.6946 −1.51999
\(683\) −35.6474 −1.36401 −0.682005 0.731347i \(-0.738892\pi\)
−0.682005 + 0.731347i \(0.738892\pi\)
\(684\) −23.5949 −0.902173
\(685\) −3.10002 −0.118446
\(686\) −19.7777 −0.755116
\(687\) −28.0996 −1.07207
\(688\) 10.5331 0.401571
\(689\) −32.2443 −1.22841
\(690\) −0.636950 −0.0242483
\(691\) −38.6427 −1.47004 −0.735018 0.678048i \(-0.762826\pi\)
−0.735018 + 0.678048i \(0.762826\pi\)
\(692\) 4.33803 0.164907
\(693\) −29.7347 −1.12953
\(694\) −14.3269 −0.543843
\(695\) −2.34027 −0.0887715
\(696\) 0.811252 0.0307504
\(697\) −9.84856 −0.373041
\(698\) 28.2450 1.06909
\(699\) −60.6942 −2.29567
\(700\) 9.31321 0.352006
\(701\) −11.9512 −0.451392 −0.225696 0.974198i \(-0.572466\pi\)
−0.225696 + 0.974198i \(0.572466\pi\)
\(702\) 0.296181 0.0111786
\(703\) −48.6571 −1.83514
\(704\) 5.12829 0.193280
\(705\) −1.70579 −0.0642436
\(706\) −29.7589 −1.11999
\(707\) 32.7454 1.23152
\(708\) −10.1739 −0.382358
\(709\) −3.26106 −0.122472 −0.0612358 0.998123i \(-0.519504\pi\)
−0.0612358 + 0.998123i \(0.519504\pi\)
\(710\) −4.06046 −0.152386
\(711\) 8.07519 0.302843
\(712\) −6.65673 −0.249471
\(713\) −5.59681 −0.209602
\(714\) −16.7910 −0.628389
\(715\) 6.76305 0.252924
\(716\) −1.50661 −0.0563047
\(717\) 27.8706 1.04085
\(718\) 7.83656 0.292458
\(719\) 8.47916 0.316219 0.158110 0.987422i \(-0.449460\pi\)
0.158110 + 0.987422i \(0.449460\pi\)
\(720\) 1.08770 0.0405361
\(721\) −0.129728 −0.00483132
\(722\) −41.5271 −1.54548
\(723\) 50.0927 1.86297
\(724\) 8.54956 0.317742
\(725\) −1.60897 −0.0597556
\(726\) 37.5778 1.39464
\(727\) 34.0631 1.26333 0.631665 0.775242i \(-0.282372\pi\)
0.631665 + 0.775242i \(0.282372\pi\)
\(728\) 7.02996 0.260548
\(729\) −27.5870 −1.02174
\(730\) −0.767000 −0.0283879
\(731\) 37.6641 1.39306
\(732\) −33.9818 −1.25600
\(733\) −6.23377 −0.230250 −0.115125 0.993351i \(-0.536727\pi\)
−0.115125 + 0.993351i \(0.536727\pi\)
\(734\) 11.8807 0.438526
\(735\) 2.94654 0.108685
\(736\) 0.723070 0.0266527
\(737\) 52.7146 1.94177
\(738\) 8.35305 0.307480
\(739\) −23.9882 −0.882418 −0.441209 0.897404i \(-0.645450\pi\)
−0.441209 + 0.897404i \(0.645450\pi\)
\(740\) 2.24304 0.0824558
\(741\) 70.2650 2.58125
\(742\) −16.7647 −0.615452
\(743\) −21.4444 −0.786717 −0.393359 0.919385i \(-0.628687\pi\)
−0.393359 + 0.919385i \(0.628687\pi\)
\(744\) 19.0116 0.697000
\(745\) −2.93201 −0.107420
\(746\) −16.2587 −0.595274
\(747\) 48.9668 1.79160
\(748\) 18.3376 0.670489
\(749\) 19.0298 0.695334
\(750\) −8.69566 −0.317521
\(751\) −32.9586 −1.20268 −0.601338 0.798995i \(-0.705365\pi\)
−0.601338 + 0.798995i \(0.705365\pi\)
\(752\) 1.93642 0.0706140
\(753\) 7.95232 0.289799
\(754\) −1.21451 −0.0442299
\(755\) −3.09515 −0.112644
\(756\) 0.153993 0.00560066
\(757\) 5.29760 0.192544 0.0962722 0.995355i \(-0.469308\pi\)
0.0962722 + 0.995355i \(0.469308\pi\)
\(758\) 30.0310 1.09077
\(759\) 9.10777 0.330591
\(760\) 2.79023 0.101212
\(761\) 38.7255 1.40380 0.701900 0.712276i \(-0.252335\pi\)
0.701900 + 0.712276i \(0.252335\pi\)
\(762\) 4.70106 0.170302
\(763\) 23.3007 0.843543
\(764\) −3.47248 −0.125630
\(765\) 3.88937 0.140620
\(766\) −6.22357 −0.224867
\(767\) 15.2312 0.549965
\(768\) −2.45617 −0.0886296
\(769\) −46.1948 −1.66583 −0.832913 0.553404i \(-0.813329\pi\)
−0.832913 + 0.553404i \(0.813329\pi\)
\(770\) 3.51630 0.126719
\(771\) 57.0884 2.05599
\(772\) −25.1942 −0.906758
\(773\) −0.152902 −0.00549949 −0.00274975 0.999996i \(-0.500875\pi\)
−0.00274975 + 0.999996i \(0.500875\pi\)
\(774\) −31.9447 −1.14823
\(775\) −37.7061 −1.35444
\(776\) 15.5223 0.557218
\(777\) 29.3683 1.05358
\(778\) 27.8418 0.998177
\(779\) 21.4278 0.767729
\(780\) −3.23914 −0.115980
\(781\) 58.0606 2.07757
\(782\) 2.58554 0.0924587
\(783\) −0.0266041 −0.000950753 0
\(784\) −3.34493 −0.119462
\(785\) −0.321061 −0.0114592
\(786\) −14.6832 −0.523731
\(787\) −49.4510 −1.76274 −0.881369 0.472429i \(-0.843377\pi\)
−0.881369 + 0.472429i \(0.843377\pi\)
\(788\) 19.7918 0.705055
\(789\) −38.0469 −1.35451
\(790\) −0.954939 −0.0339752
\(791\) −0.108163 −0.00384583
\(792\) −15.5530 −0.552653
\(793\) 50.8736 1.80657
\(794\) 5.78872 0.205434
\(795\) 7.72455 0.273962
\(796\) 0.695954 0.0246674
\(797\) 41.4911 1.46969 0.734845 0.678235i \(-0.237255\pi\)
0.734845 + 0.678235i \(0.237255\pi\)
\(798\) 36.5327 1.29324
\(799\) 6.92421 0.244961
\(800\) 4.87137 0.172229
\(801\) 20.1885 0.713325
\(802\) −17.4983 −0.617885
\(803\) 10.9673 0.387029
\(804\) −25.2475 −0.890409
\(805\) 0.495786 0.0174742
\(806\) −28.4619 −1.00253
\(807\) 5.18295 0.182448
\(808\) 17.1278 0.602555
\(809\) 19.0841 0.670961 0.335480 0.942047i \(-0.391101\pi\)
0.335480 + 0.942047i \(0.391101\pi\)
\(810\) 3.19214 0.112160
\(811\) −47.1843 −1.65687 −0.828433 0.560088i \(-0.810767\pi\)
−0.828433 + 0.560088i \(0.810767\pi\)
\(812\) −0.631458 −0.0221598
\(813\) −65.3067 −2.29041
\(814\) −32.0733 −1.12417
\(815\) 4.53008 0.158682
\(816\) −8.78273 −0.307457
\(817\) −81.9467 −2.86695
\(818\) −29.7803 −1.04124
\(819\) −21.3204 −0.744996
\(820\) −0.987798 −0.0344954
\(821\) 25.2469 0.881123 0.440562 0.897722i \(-0.354779\pi\)
0.440562 + 0.897722i \(0.354779\pi\)
\(822\) −21.2304 −0.740495
\(823\) 25.6178 0.892980 0.446490 0.894789i \(-0.352674\pi\)
0.446490 + 0.894789i \(0.352674\pi\)
\(824\) −0.0678555 −0.00236386
\(825\) 61.3596 2.13627
\(826\) 7.91910 0.275541
\(827\) −0.457860 −0.0159213 −0.00796067 0.999968i \(-0.502534\pi\)
−0.00796067 + 0.999968i \(0.502534\pi\)
\(828\) −2.19292 −0.0762094
\(829\) −2.95124 −0.102501 −0.0512504 0.998686i \(-0.516321\pi\)
−0.0512504 + 0.998686i \(0.516321\pi\)
\(830\) −5.79062 −0.200995
\(831\) 32.1187 1.11419
\(832\) 3.67709 0.127480
\(833\) −11.9607 −0.414414
\(834\) −16.0273 −0.554979
\(835\) −3.12735 −0.108226
\(836\) −39.8976 −1.37989
\(837\) −0.623465 −0.0215501
\(838\) −20.3335 −0.702409
\(839\) 53.5531 1.84886 0.924428 0.381356i \(-0.124543\pi\)
0.924428 + 0.381356i \(0.124543\pi\)
\(840\) −1.68412 −0.0581077
\(841\) −28.8909 −0.996238
\(842\) 22.2050 0.765234
\(843\) −40.5845 −1.39780
\(844\) 12.5891 0.433336
\(845\) 0.186864 0.00642830
\(846\) −5.87276 −0.201910
\(847\) −29.2496 −1.00503
\(848\) −8.76896 −0.301127
\(849\) −57.7935 −1.98347
\(850\) 17.4189 0.597465
\(851\) −4.52222 −0.155020
\(852\) −27.8079 −0.952683
\(853\) −4.09284 −0.140136 −0.0700680 0.997542i \(-0.522322\pi\)
−0.0700680 + 0.997542i \(0.522322\pi\)
\(854\) 26.4506 0.905121
\(855\) −8.46220 −0.289401
\(856\) 9.95374 0.340212
\(857\) 5.08447 0.173682 0.0868411 0.996222i \(-0.472323\pi\)
0.0868411 + 0.996222i \(0.472323\pi\)
\(858\) 46.3166 1.58122
\(859\) −16.9189 −0.577265 −0.288632 0.957440i \(-0.593201\pi\)
−0.288632 + 0.957440i \(0.593201\pi\)
\(860\) 3.77766 0.128817
\(861\) −12.9333 −0.440766
\(862\) 30.6666 1.04451
\(863\) 41.0261 1.39654 0.698272 0.715832i \(-0.253952\pi\)
0.698272 + 0.715832i \(0.253952\pi\)
\(864\) 0.0805476 0.00274028
\(865\) 1.55582 0.0528994
\(866\) 21.6081 0.734274
\(867\) 10.3499 0.351500
\(868\) −14.7982 −0.502282
\(869\) 13.6547 0.463204
\(870\) 0.290952 0.00986420
\(871\) 37.7975 1.28072
\(872\) 12.1877 0.412727
\(873\) −47.0759 −1.59328
\(874\) −5.62542 −0.190283
\(875\) 6.76848 0.228817
\(876\) −5.25277 −0.177475
\(877\) 16.3670 0.552673 0.276337 0.961061i \(-0.410880\pi\)
0.276337 + 0.961061i \(0.410880\pi\)
\(878\) −0.409379 −0.0138159
\(879\) −26.1435 −0.881797
\(880\) 1.83924 0.0620007
\(881\) 30.8066 1.03790 0.518951 0.854804i \(-0.326323\pi\)
0.518951 + 0.854804i \(0.326323\pi\)
\(882\) 10.1445 0.341582
\(883\) 18.4888 0.622197 0.311098 0.950378i \(-0.399303\pi\)
0.311098 + 0.950378i \(0.399303\pi\)
\(884\) 13.1485 0.442231
\(885\) −3.64883 −0.122654
\(886\) 13.5597 0.455547
\(887\) −0.118637 −0.00398344 −0.00199172 0.999998i \(-0.500634\pi\)
−0.00199172 + 0.999998i \(0.500634\pi\)
\(888\) 15.3614 0.515495
\(889\) −3.65919 −0.122725
\(890\) −2.38741 −0.0800261
\(891\) −45.6445 −1.52915
\(892\) 18.6690 0.625083
\(893\) −15.0652 −0.504137
\(894\) −20.0798 −0.671568
\(895\) −0.540340 −0.0180616
\(896\) 1.91182 0.0638696
\(897\) 6.53047 0.218046
\(898\) −3.71919 −0.124111
\(899\) 2.55656 0.0852661
\(900\) −14.7739 −0.492462
\(901\) −31.3559 −1.04462
\(902\) 14.1245 0.470296
\(903\) 49.4611 1.64596
\(904\) −0.0565757 −0.00188168
\(905\) 3.06626 0.101926
\(906\) −21.1970 −0.704224
\(907\) 12.8960 0.428203 0.214102 0.976811i \(-0.431318\pi\)
0.214102 + 0.976811i \(0.431318\pi\)
\(908\) −6.28244 −0.208490
\(909\) −51.9452 −1.72291
\(910\) 2.52127 0.0835792
\(911\) −6.76255 −0.224053 −0.112027 0.993705i \(-0.535734\pi\)
−0.112027 + 0.993705i \(0.535734\pi\)
\(912\) 19.1088 0.632756
\(913\) 82.8001 2.74029
\(914\) −20.8371 −0.689231
\(915\) −12.1874 −0.402904
\(916\) 11.4404 0.378001
\(917\) 11.4290 0.377419
\(918\) 0.288020 0.00950608
\(919\) −15.3379 −0.505952 −0.252976 0.967473i \(-0.581409\pi\)
−0.252976 + 0.967473i \(0.581409\pi\)
\(920\) 0.259326 0.00854973
\(921\) 54.7086 1.80271
\(922\) 22.4406 0.739042
\(923\) 41.6307 1.37029
\(924\) 24.0813 0.792216
\(925\) −30.4665 −1.00173
\(926\) 18.5063 0.608156
\(927\) 0.205792 0.00675909
\(928\) −0.330291 −0.0108423
\(929\) 8.29140 0.272032 0.136016 0.990707i \(-0.456570\pi\)
0.136016 + 0.990707i \(0.456570\pi\)
\(930\) 6.81844 0.223585
\(931\) 26.0232 0.852877
\(932\) 24.7109 0.809432
\(933\) 84.0805 2.75267
\(934\) −29.4384 −0.963254
\(935\) 6.57671 0.215081
\(936\) −11.1519 −0.364510
\(937\) 28.3171 0.925078 0.462539 0.886599i \(-0.346939\pi\)
0.462539 + 0.886599i \(0.346939\pi\)
\(938\) 19.6520 0.641660
\(939\) 26.0245 0.849278
\(940\) 0.694489 0.0226517
\(941\) 52.5776 1.71398 0.856990 0.515334i \(-0.172332\pi\)
0.856990 + 0.515334i \(0.172332\pi\)
\(942\) −2.19877 −0.0716400
\(943\) 1.99151 0.0648525
\(944\) 4.14217 0.134816
\(945\) 0.0552289 0.00179660
\(946\) −54.0168 −1.75624
\(947\) −31.0785 −1.00992 −0.504958 0.863144i \(-0.668492\pi\)
−0.504958 + 0.863144i \(0.668492\pi\)
\(948\) −6.53987 −0.212405
\(949\) 7.86383 0.255271
\(950\) −37.8989 −1.22960
\(951\) 9.20255 0.298413
\(952\) 6.83626 0.221564
\(953\) 30.1400 0.976329 0.488165 0.872752i \(-0.337667\pi\)
0.488165 + 0.872752i \(0.337667\pi\)
\(954\) 26.5945 0.861027
\(955\) −1.24539 −0.0402998
\(956\) −11.3472 −0.366994
\(957\) −4.16033 −0.134484
\(958\) 15.8363 0.511649
\(959\) 16.5252 0.533627
\(960\) −0.880897 −0.0284308
\(961\) 28.9128 0.932670
\(962\) −22.9973 −0.741462
\(963\) −30.1876 −0.972783
\(964\) −20.3946 −0.656866
\(965\) −9.03578 −0.290872
\(966\) 3.39538 0.109244
\(967\) 15.9836 0.513999 0.257000 0.966412i \(-0.417266\pi\)
0.257000 + 0.966412i \(0.417266\pi\)
\(968\) −15.2993 −0.491739
\(969\) 68.3289 2.19504
\(970\) 5.56700 0.178746
\(971\) −8.63180 −0.277008 −0.138504 0.990362i \(-0.544229\pi\)
−0.138504 + 0.990362i \(0.544229\pi\)
\(972\) 22.1029 0.708952
\(973\) 12.4752 0.399937
\(974\) 22.4529 0.719437
\(975\) 43.9962 1.40901
\(976\) 13.8353 0.442856
\(977\) 11.0749 0.354317 0.177159 0.984182i \(-0.443309\pi\)
0.177159 + 0.984182i \(0.443309\pi\)
\(978\) 31.0241 0.992041
\(979\) 34.1376 1.09104
\(980\) −1.19964 −0.0383212
\(981\) −36.9628 −1.18013
\(982\) 0.215708 0.00688353
\(983\) 3.07802 0.0981737 0.0490868 0.998795i \(-0.484369\pi\)
0.0490868 + 0.998795i \(0.484369\pi\)
\(984\) −6.76490 −0.215657
\(985\) 7.09826 0.226169
\(986\) −1.18105 −0.0376122
\(987\) 9.09299 0.289433
\(988\) −28.6075 −0.910125
\(989\) −7.61618 −0.242180
\(990\) −5.57803 −0.177281
\(991\) −57.9932 −1.84221 −0.921107 0.389310i \(-0.872714\pi\)
−0.921107 + 0.389310i \(0.872714\pi\)
\(992\) −7.74033 −0.245756
\(993\) −69.0396 −2.19090
\(994\) 21.6450 0.686537
\(995\) 0.249601 0.00791289
\(996\) −39.6568 −1.25658
\(997\) −26.2100 −0.830080 −0.415040 0.909803i \(-0.636232\pi\)
−0.415040 + 0.909803i \(0.636232\pi\)
\(998\) −15.1384 −0.479197
\(999\) −0.503760 −0.0159383
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 \(a_p\))