Properties

Label 8007.2.a.e.1.8
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.12891 q^{2}\) \(+1.00000 q^{3}\) \(+2.53226 q^{4}\) \(-4.00748 q^{5}\) \(-2.12891 q^{6}\) \(+2.85209 q^{7}\) \(-1.13314 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.12891 q^{2}\) \(+1.00000 q^{3}\) \(+2.53226 q^{4}\) \(-4.00748 q^{5}\) \(-2.12891 q^{6}\) \(+2.85209 q^{7}\) \(-1.13314 q^{8}\) \(+1.00000 q^{9}\) \(+8.53157 q^{10}\) \(+0.813194 q^{11}\) \(+2.53226 q^{12}\) \(-0.802739 q^{13}\) \(-6.07185 q^{14}\) \(-4.00748 q^{15}\) \(-2.65217 q^{16}\) \(-1.00000 q^{17}\) \(-2.12891 q^{18}\) \(+1.48404 q^{19}\) \(-10.1480 q^{20}\) \(+2.85209 q^{21}\) \(-1.73122 q^{22}\) \(+0.00429005 q^{23}\) \(-1.13314 q^{24}\) \(+11.0599 q^{25}\) \(+1.70896 q^{26}\) \(+1.00000 q^{27}\) \(+7.22225 q^{28}\) \(-4.50932 q^{29}\) \(+8.53157 q^{30}\) \(+1.77596 q^{31}\) \(+7.91251 q^{32}\) \(+0.813194 q^{33}\) \(+2.12891 q^{34}\) \(-11.4297 q^{35}\) \(+2.53226 q^{36}\) \(+5.09542 q^{37}\) \(-3.15940 q^{38}\) \(-0.802739 q^{39}\) \(+4.54105 q^{40}\) \(-10.8653 q^{41}\) \(-6.07185 q^{42}\) \(-2.58810 q^{43}\) \(+2.05922 q^{44}\) \(-4.00748 q^{45}\) \(-0.00913315 q^{46}\) \(-3.09960 q^{47}\) \(-2.65217 q^{48}\) \(+1.13443 q^{49}\) \(-23.5456 q^{50}\) \(-1.00000 q^{51}\) \(-2.03275 q^{52}\) \(+0.598271 q^{53}\) \(-2.12891 q^{54}\) \(-3.25886 q^{55}\) \(-3.23183 q^{56}\) \(+1.48404 q^{57}\) \(+9.59994 q^{58}\) \(+4.12232 q^{59}\) \(-10.1480 q^{60}\) \(+5.03103 q^{61}\) \(-3.78085 q^{62}\) \(+2.85209 q^{63}\) \(-11.5407 q^{64}\) \(+3.21696 q^{65}\) \(-1.73122 q^{66}\) \(-1.96620 q^{67}\) \(-2.53226 q^{68}\) \(+0.00429005 q^{69}\) \(+24.3328 q^{70}\) \(+8.01047 q^{71}\) \(-1.13314 q^{72}\) \(+3.22375 q^{73}\) \(-10.8477 q^{74}\) \(+11.0599 q^{75}\) \(+3.75799 q^{76}\) \(+2.31930 q^{77}\) \(+1.70896 q^{78}\) \(+1.07267 q^{79}\) \(+10.6285 q^{80}\) \(+1.00000 q^{81}\) \(+23.1313 q^{82}\) \(-10.1842 q^{83}\) \(+7.22225 q^{84}\) \(+4.00748 q^{85}\) \(+5.50984 q^{86}\) \(-4.50932 q^{87}\) \(-0.921465 q^{88}\) \(+5.84226 q^{89}\) \(+8.53157 q^{90}\) \(-2.28948 q^{91}\) \(+0.0108636 q^{92}\) \(+1.77596 q^{93}\) \(+6.59878 q^{94}\) \(-5.94727 q^{95}\) \(+7.91251 q^{96}\) \(-17.9365 q^{97}\) \(-2.41509 q^{98}\) \(+0.813194 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12891 −1.50537 −0.752684 0.658382i \(-0.771241\pi\)
−0.752684 + 0.658382i \(0.771241\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.53226 1.26613
\(5\) −4.00748 −1.79220 −0.896100 0.443852i \(-0.853612\pi\)
−0.896100 + 0.443852i \(0.853612\pi\)
\(6\) −2.12891 −0.869124
\(7\) 2.85209 1.07799 0.538995 0.842309i \(-0.318804\pi\)
0.538995 + 0.842309i \(0.318804\pi\)
\(8\) −1.13314 −0.400627
\(9\) 1.00000 0.333333
\(10\) 8.53157 2.69792
\(11\) 0.813194 0.245187 0.122594 0.992457i \(-0.460879\pi\)
0.122594 + 0.992457i \(0.460879\pi\)
\(12\) 2.53226 0.731002
\(13\) −0.802739 −0.222640 −0.111320 0.993785i \(-0.535508\pi\)
−0.111320 + 0.993785i \(0.535508\pi\)
\(14\) −6.07185 −1.62277
\(15\) −4.00748 −1.03473
\(16\) −2.65217 −0.663042
\(17\) −1.00000 −0.242536
\(18\) −2.12891 −0.501789
\(19\) 1.48404 0.340463 0.170231 0.985404i \(-0.445548\pi\)
0.170231 + 0.985404i \(0.445548\pi\)
\(20\) −10.1480 −2.26916
\(21\) 2.85209 0.622377
\(22\) −1.73122 −0.369097
\(23\) 0.00429005 0.000894538 0 0.000447269 1.00000i \(-0.499858\pi\)
0.000447269 1.00000i \(0.499858\pi\)
\(24\) −1.13314 −0.231302
\(25\) 11.0599 2.21198
\(26\) 1.70896 0.335155
\(27\) 1.00000 0.192450
\(28\) 7.22225 1.36488
\(29\) −4.50932 −0.837360 −0.418680 0.908134i \(-0.637507\pi\)
−0.418680 + 0.908134i \(0.637507\pi\)
\(30\) 8.53157 1.55765
\(31\) 1.77596 0.318971 0.159486 0.987200i \(-0.449016\pi\)
0.159486 + 0.987200i \(0.449016\pi\)
\(32\) 7.91251 1.39875
\(33\) 0.813194 0.141559
\(34\) 2.12891 0.365105
\(35\) −11.4297 −1.93197
\(36\) 2.53226 0.422044
\(37\) 5.09542 0.837681 0.418841 0.908060i \(-0.362437\pi\)
0.418841 + 0.908060i \(0.362437\pi\)
\(38\) −3.15940 −0.512522
\(39\) −0.802739 −0.128541
\(40\) 4.54105 0.718003
\(41\) −10.8653 −1.69688 −0.848438 0.529295i \(-0.822456\pi\)
−0.848438 + 0.529295i \(0.822456\pi\)
\(42\) −6.07185 −0.936907
\(43\) −2.58810 −0.394682 −0.197341 0.980335i \(-0.563231\pi\)
−0.197341 + 0.980335i \(0.563231\pi\)
\(44\) 2.05922 0.310439
\(45\) −4.00748 −0.597400
\(46\) −0.00913315 −0.00134661
\(47\) −3.09960 −0.452124 −0.226062 0.974113i \(-0.572585\pi\)
−0.226062 + 0.974113i \(0.572585\pi\)
\(48\) −2.65217 −0.382807
\(49\) 1.13443 0.162061
\(50\) −23.5456 −3.32985
\(51\) −1.00000 −0.140028
\(52\) −2.03275 −0.281891
\(53\) 0.598271 0.0821788 0.0410894 0.999155i \(-0.486917\pi\)
0.0410894 + 0.999155i \(0.486917\pi\)
\(54\) −2.12891 −0.289708
\(55\) −3.25886 −0.439425
\(56\) −3.23183 −0.431871
\(57\) 1.48404 0.196566
\(58\) 9.59994 1.26053
\(59\) 4.12232 0.536680 0.268340 0.963324i \(-0.413525\pi\)
0.268340 + 0.963324i \(0.413525\pi\)
\(60\) −10.1480 −1.31010
\(61\) 5.03103 0.644158 0.322079 0.946713i \(-0.395618\pi\)
0.322079 + 0.946713i \(0.395618\pi\)
\(62\) −3.78085 −0.480169
\(63\) 2.85209 0.359330
\(64\) −11.5407 −1.44259
\(65\) 3.21696 0.399015
\(66\) −1.73122 −0.213098
\(67\) −1.96620 −0.240209 −0.120105 0.992761i \(-0.538323\pi\)
−0.120105 + 0.992761i \(0.538323\pi\)
\(68\) −2.53226 −0.307082
\(69\) 0.00429005 0.000516462 0
\(70\) 24.3328 2.90833
\(71\) 8.01047 0.950668 0.475334 0.879806i \(-0.342327\pi\)
0.475334 + 0.879806i \(0.342327\pi\)
\(72\) −1.13314 −0.133542
\(73\) 3.22375 0.377312 0.188656 0.982043i \(-0.439587\pi\)
0.188656 + 0.982043i \(0.439587\pi\)
\(74\) −10.8477 −1.26102
\(75\) 11.0599 1.27709
\(76\) 3.75799 0.431071
\(77\) 2.31930 0.264309
\(78\) 1.70896 0.193502
\(79\) 1.07267 0.120685 0.0603426 0.998178i \(-0.480781\pi\)
0.0603426 + 0.998178i \(0.480781\pi\)
\(80\) 10.6285 1.18830
\(81\) 1.00000 0.111111
\(82\) 23.1313 2.55442
\(83\) −10.1842 −1.11786 −0.558931 0.829214i \(-0.688788\pi\)
−0.558931 + 0.829214i \(0.688788\pi\)
\(84\) 7.22225 0.788012
\(85\) 4.00748 0.434672
\(86\) 5.50984 0.594142
\(87\) −4.50932 −0.483450
\(88\) −0.921465 −0.0982286
\(89\) 5.84226 0.619279 0.309639 0.950854i \(-0.399792\pi\)
0.309639 + 0.950854i \(0.399792\pi\)
\(90\) 8.53157 0.899307
\(91\) −2.28948 −0.240003
\(92\) 0.0108636 0.00113260
\(93\) 1.77596 0.184158
\(94\) 6.59878 0.680612
\(95\) −5.94727 −0.610177
\(96\) 7.91251 0.807568
\(97\) −17.9365 −1.82117 −0.910587 0.413319i \(-0.864370\pi\)
−0.910587 + 0.413319i \(0.864370\pi\)
\(98\) −2.41509 −0.243961
\(99\) 0.813194 0.0817291
\(100\) 28.0066 2.80066
\(101\) −12.9844 −1.29200 −0.645998 0.763339i \(-0.723559\pi\)
−0.645998 + 0.763339i \(0.723559\pi\)
\(102\) 2.12891 0.210794
\(103\) −9.54145 −0.940147 −0.470073 0.882627i \(-0.655773\pi\)
−0.470073 + 0.882627i \(0.655773\pi\)
\(104\) 0.909618 0.0891954
\(105\) −11.4297 −1.11542
\(106\) −1.27367 −0.123709
\(107\) −0.584447 −0.0565006 −0.0282503 0.999601i \(-0.508994\pi\)
−0.0282503 + 0.999601i \(0.508994\pi\)
\(108\) 2.53226 0.243667
\(109\) −9.66169 −0.925422 −0.462711 0.886509i \(-0.653123\pi\)
−0.462711 + 0.886509i \(0.653123\pi\)
\(110\) 6.93782 0.661496
\(111\) 5.09542 0.483636
\(112\) −7.56422 −0.714752
\(113\) 2.48201 0.233488 0.116744 0.993162i \(-0.462754\pi\)
0.116744 + 0.993162i \(0.462754\pi\)
\(114\) −3.15940 −0.295904
\(115\) −0.0171923 −0.00160319
\(116\) −11.4188 −1.06021
\(117\) −0.802739 −0.0742132
\(118\) −8.77605 −0.807901
\(119\) −2.85209 −0.261451
\(120\) 4.54105 0.414539
\(121\) −10.3387 −0.939883
\(122\) −10.7106 −0.969695
\(123\) −10.8653 −0.979692
\(124\) 4.49719 0.403860
\(125\) −24.2850 −2.17211
\(126\) −6.07185 −0.540923
\(127\) 22.1015 1.96119 0.980596 0.196040i \(-0.0628082\pi\)
0.980596 + 0.196040i \(0.0628082\pi\)
\(128\) 8.74412 0.772879
\(129\) −2.58810 −0.227870
\(130\) −6.84862 −0.600664
\(131\) 0.556990 0.0486644 0.0243322 0.999704i \(-0.492254\pi\)
0.0243322 + 0.999704i \(0.492254\pi\)
\(132\) 2.05922 0.179232
\(133\) 4.23263 0.367015
\(134\) 4.18586 0.361603
\(135\) −4.00748 −0.344909
\(136\) 1.13314 0.0971663
\(137\) 6.21709 0.531162 0.265581 0.964089i \(-0.414436\pi\)
0.265581 + 0.964089i \(0.414436\pi\)
\(138\) −0.00913315 −0.000777465 0
\(139\) 19.1812 1.62693 0.813466 0.581613i \(-0.197578\pi\)
0.813466 + 0.581613i \(0.197578\pi\)
\(140\) −28.9430 −2.44613
\(141\) −3.09960 −0.261034
\(142\) −17.0536 −1.43110
\(143\) −0.652782 −0.0545884
\(144\) −2.65217 −0.221014
\(145\) 18.0710 1.50072
\(146\) −6.86309 −0.567993
\(147\) 1.13443 0.0935659
\(148\) 12.9029 1.06062
\(149\) 5.65926 0.463624 0.231812 0.972761i \(-0.425535\pi\)
0.231812 + 0.972761i \(0.425535\pi\)
\(150\) −23.5456 −1.92249
\(151\) −17.1460 −1.39532 −0.697661 0.716428i \(-0.745776\pi\)
−0.697661 + 0.716428i \(0.745776\pi\)
\(152\) −1.68163 −0.136398
\(153\) −1.00000 −0.0808452
\(154\) −4.93759 −0.397883
\(155\) −7.11711 −0.571660
\(156\) −2.03275 −0.162750
\(157\) 1.00000 0.0798087
\(158\) −2.28363 −0.181676
\(159\) 0.598271 0.0474460
\(160\) −31.7093 −2.50684
\(161\) 0.0122356 0.000964303 0
\(162\) −2.12891 −0.167263
\(163\) 6.17232 0.483453 0.241727 0.970344i \(-0.422286\pi\)
0.241727 + 0.970344i \(0.422286\pi\)
\(164\) −27.5138 −2.14847
\(165\) −3.25886 −0.253702
\(166\) 21.6813 1.68279
\(167\) 16.8847 1.30658 0.653288 0.757109i \(-0.273389\pi\)
0.653288 + 0.757109i \(0.273389\pi\)
\(168\) −3.23183 −0.249341
\(169\) −12.3556 −0.950432
\(170\) −8.53157 −0.654342
\(171\) 1.48404 0.113488
\(172\) −6.55376 −0.499720
\(173\) 18.2355 1.38642 0.693209 0.720737i \(-0.256196\pi\)
0.693209 + 0.720737i \(0.256196\pi\)
\(174\) 9.59994 0.727770
\(175\) 31.5439 2.38449
\(176\) −2.15673 −0.162569
\(177\) 4.12232 0.309852
\(178\) −12.4377 −0.932242
\(179\) −14.0904 −1.05317 −0.526583 0.850124i \(-0.676527\pi\)
−0.526583 + 0.850124i \(0.676527\pi\)
\(180\) −10.1480 −0.756387
\(181\) −11.4708 −0.852618 −0.426309 0.904578i \(-0.640186\pi\)
−0.426309 + 0.904578i \(0.640186\pi\)
\(182\) 4.87411 0.361293
\(183\) 5.03103 0.371905
\(184\) −0.00486125 −0.000358376 0
\(185\) −20.4198 −1.50129
\(186\) −3.78085 −0.277226
\(187\) −0.813194 −0.0594666
\(188\) −7.84901 −0.572448
\(189\) 2.85209 0.207459
\(190\) 12.6612 0.918541
\(191\) −0.0781279 −0.00565314 −0.00282657 0.999996i \(-0.500900\pi\)
−0.00282657 + 0.999996i \(0.500900\pi\)
\(192\) −11.5407 −0.832879
\(193\) 7.50763 0.540411 0.270206 0.962803i \(-0.412908\pi\)
0.270206 + 0.962803i \(0.412908\pi\)
\(194\) 38.1852 2.74154
\(195\) 3.21696 0.230371
\(196\) 2.87267 0.205191
\(197\) −5.57024 −0.396863 −0.198432 0.980115i \(-0.563585\pi\)
−0.198432 + 0.980115i \(0.563585\pi\)
\(198\) −1.73122 −0.123032
\(199\) 3.99647 0.283302 0.141651 0.989917i \(-0.454759\pi\)
0.141651 + 0.989917i \(0.454759\pi\)
\(200\) −12.5325 −0.886179
\(201\) −1.96620 −0.138685
\(202\) 27.6426 1.94493
\(203\) −12.8610 −0.902665
\(204\) −2.53226 −0.177294
\(205\) 43.5425 3.04114
\(206\) 20.3129 1.41527
\(207\) 0.00429005 0.000298179 0
\(208\) 2.12900 0.147619
\(209\) 1.20681 0.0834771
\(210\) 24.3328 1.67912
\(211\) 13.2966 0.915377 0.457689 0.889113i \(-0.348677\pi\)
0.457689 + 0.889113i \(0.348677\pi\)
\(212\) 1.51498 0.104049
\(213\) 8.01047 0.548868
\(214\) 1.24424 0.0850542
\(215\) 10.3718 0.707349
\(216\) −1.13314 −0.0771007
\(217\) 5.06519 0.343847
\(218\) 20.5689 1.39310
\(219\) 3.22375 0.217841
\(220\) −8.25229 −0.556370
\(221\) 0.802739 0.0539980
\(222\) −10.8477 −0.728049
\(223\) −4.93797 −0.330671 −0.165335 0.986237i \(-0.552871\pi\)
−0.165335 + 0.986237i \(0.552871\pi\)
\(224\) 22.5672 1.50784
\(225\) 11.0599 0.737327
\(226\) −5.28399 −0.351486
\(227\) −9.93583 −0.659464 −0.329732 0.944075i \(-0.606958\pi\)
−0.329732 + 0.944075i \(0.606958\pi\)
\(228\) 3.75799 0.248879
\(229\) −5.59798 −0.369925 −0.184962 0.982746i \(-0.559216\pi\)
−0.184962 + 0.982746i \(0.559216\pi\)
\(230\) 0.0366009 0.00241339
\(231\) 2.31930 0.152599
\(232\) 5.10971 0.335469
\(233\) 7.52621 0.493058 0.246529 0.969135i \(-0.420710\pi\)
0.246529 + 0.969135i \(0.420710\pi\)
\(234\) 1.70896 0.111718
\(235\) 12.4216 0.810296
\(236\) 10.4388 0.679508
\(237\) 1.07267 0.0696776
\(238\) 6.07185 0.393580
\(239\) −7.95335 −0.514460 −0.257230 0.966350i \(-0.582810\pi\)
−0.257230 + 0.966350i \(0.582810\pi\)
\(240\) 10.6285 0.686067
\(241\) 3.53315 0.227590 0.113795 0.993504i \(-0.463699\pi\)
0.113795 + 0.993504i \(0.463699\pi\)
\(242\) 22.0102 1.41487
\(243\) 1.00000 0.0641500
\(244\) 12.7399 0.815589
\(245\) −4.54619 −0.290446
\(246\) 23.1313 1.47480
\(247\) −1.19130 −0.0758005
\(248\) −2.01241 −0.127788
\(249\) −10.1842 −0.645398
\(250\) 51.7005 3.26983
\(251\) 13.5091 0.852685 0.426342 0.904562i \(-0.359802\pi\)
0.426342 + 0.904562i \(0.359802\pi\)
\(252\) 7.22225 0.454959
\(253\) 0.00348865 0.000219329 0
\(254\) −47.0522 −2.95231
\(255\) 4.00748 0.250958
\(256\) 4.46596 0.279122
\(257\) −2.38848 −0.148990 −0.0744948 0.997221i \(-0.523734\pi\)
−0.0744948 + 0.997221i \(0.523734\pi\)
\(258\) 5.50984 0.343028
\(259\) 14.5326 0.903012
\(260\) 8.14619 0.505205
\(261\) −4.50932 −0.279120
\(262\) −1.18578 −0.0732579
\(263\) −19.3669 −1.19421 −0.597106 0.802163i \(-0.703683\pi\)
−0.597106 + 0.802163i \(0.703683\pi\)
\(264\) −0.921465 −0.0567123
\(265\) −2.39756 −0.147281
\(266\) −9.01088 −0.552493
\(267\) 5.84226 0.357541
\(268\) −4.97893 −0.304137
\(269\) 13.2705 0.809116 0.404558 0.914512i \(-0.367425\pi\)
0.404558 + 0.914512i \(0.367425\pi\)
\(270\) 8.53157 0.519215
\(271\) 13.5635 0.823925 0.411963 0.911201i \(-0.364843\pi\)
0.411963 + 0.911201i \(0.364843\pi\)
\(272\) 2.65217 0.160811
\(273\) −2.28948 −0.138566
\(274\) −13.2356 −0.799594
\(275\) 8.99385 0.542350
\(276\) 0.0108636 0.000653909 0
\(277\) −2.48199 −0.149129 −0.0745643 0.997216i \(-0.523757\pi\)
−0.0745643 + 0.997216i \(0.523757\pi\)
\(278\) −40.8352 −2.44913
\(279\) 1.77596 0.106324
\(280\) 12.9515 0.774000
\(281\) −14.5413 −0.867463 −0.433731 0.901042i \(-0.642803\pi\)
−0.433731 + 0.901042i \(0.642803\pi\)
\(282\) 6.59878 0.392952
\(283\) 3.02763 0.179974 0.0899868 0.995943i \(-0.471318\pi\)
0.0899868 + 0.995943i \(0.471318\pi\)
\(284\) 20.2846 1.20367
\(285\) −5.94727 −0.352286
\(286\) 1.38972 0.0821756
\(287\) −30.9888 −1.82921
\(288\) 7.91251 0.466249
\(289\) 1.00000 0.0588235
\(290\) −38.4716 −2.25913
\(291\) −17.9365 −1.05145
\(292\) 8.16340 0.477727
\(293\) 11.9770 0.699706 0.349853 0.936805i \(-0.386232\pi\)
0.349853 + 0.936805i \(0.386232\pi\)
\(294\) −2.41509 −0.140851
\(295\) −16.5201 −0.961838
\(296\) −5.77384 −0.335598
\(297\) 0.813194 0.0471863
\(298\) −12.0481 −0.697925
\(299\) −0.00344379 −0.000199160 0
\(300\) 28.0066 1.61696
\(301\) −7.38151 −0.425463
\(302\) 36.5023 2.10047
\(303\) −12.9844 −0.745934
\(304\) −3.93593 −0.225741
\(305\) −20.1618 −1.15446
\(306\) 2.12891 0.121702
\(307\) 19.6453 1.12122 0.560609 0.828081i \(-0.310567\pi\)
0.560609 + 0.828081i \(0.310567\pi\)
\(308\) 5.87309 0.334650
\(309\) −9.54145 −0.542794
\(310\) 15.1517 0.860559
\(311\) −31.9495 −1.81169 −0.905844 0.423612i \(-0.860762\pi\)
−0.905844 + 0.423612i \(0.860762\pi\)
\(312\) 0.909618 0.0514970
\(313\) −0.0391080 −0.00221051 −0.00110526 0.999999i \(-0.500352\pi\)
−0.00110526 + 0.999999i \(0.500352\pi\)
\(314\) −2.12891 −0.120141
\(315\) −11.4297 −0.643991
\(316\) 2.71629 0.152803
\(317\) −26.6746 −1.49819 −0.749097 0.662460i \(-0.769512\pi\)
−0.749097 + 0.662460i \(0.769512\pi\)
\(318\) −1.27367 −0.0714236
\(319\) −3.66695 −0.205310
\(320\) 46.2492 2.58541
\(321\) −0.584447 −0.0326206
\(322\) −0.0260486 −0.00145163
\(323\) −1.48404 −0.0825743
\(324\) 2.53226 0.140681
\(325\) −8.87822 −0.492475
\(326\) −13.1403 −0.727775
\(327\) −9.66169 −0.534293
\(328\) 12.3119 0.679814
\(329\) −8.84035 −0.487384
\(330\) 6.93782 0.381915
\(331\) 25.4564 1.39921 0.699604 0.714531i \(-0.253360\pi\)
0.699604 + 0.714531i \(0.253360\pi\)
\(332\) −25.7891 −1.41536
\(333\) 5.09542 0.279227
\(334\) −35.9460 −1.96688
\(335\) 7.87950 0.430503
\(336\) −7.56422 −0.412662
\(337\) −22.4887 −1.22504 −0.612518 0.790457i \(-0.709843\pi\)
−0.612518 + 0.790457i \(0.709843\pi\)
\(338\) 26.3040 1.43075
\(339\) 2.48201 0.134804
\(340\) 10.1480 0.550353
\(341\) 1.44420 0.0782076
\(342\) −3.15940 −0.170841
\(343\) −16.7292 −0.903289
\(344\) 2.93269 0.158120
\(345\) −0.0171923 −0.000925603 0
\(346\) −38.8217 −2.08707
\(347\) 16.1742 0.868276 0.434138 0.900846i \(-0.357053\pi\)
0.434138 + 0.900846i \(0.357053\pi\)
\(348\) −11.4188 −0.612111
\(349\) 1.97956 0.105963 0.0529817 0.998595i \(-0.483128\pi\)
0.0529817 + 0.998595i \(0.483128\pi\)
\(350\) −67.1541 −3.58954
\(351\) −0.802739 −0.0428470
\(352\) 6.43441 0.342955
\(353\) 4.39988 0.234182 0.117091 0.993121i \(-0.462643\pi\)
0.117091 + 0.993121i \(0.462643\pi\)
\(354\) −8.77605 −0.466442
\(355\) −32.1018 −1.70379
\(356\) 14.7942 0.784089
\(357\) −2.85209 −0.150949
\(358\) 29.9972 1.58540
\(359\) −6.36032 −0.335685 −0.167842 0.985814i \(-0.553680\pi\)
−0.167842 + 0.985814i \(0.553680\pi\)
\(360\) 4.54105 0.239334
\(361\) −16.7976 −0.884085
\(362\) 24.4203 1.28350
\(363\) −10.3387 −0.542642
\(364\) −5.79758 −0.303876
\(365\) −12.9191 −0.676218
\(366\) −10.7106 −0.559853
\(367\) −19.8848 −1.03798 −0.518989 0.854781i \(-0.673692\pi\)
−0.518989 + 0.854781i \(0.673692\pi\)
\(368\) −0.0113779 −0.000593116 0
\(369\) −10.8653 −0.565625
\(370\) 43.4719 2.26000
\(371\) 1.70632 0.0885879
\(372\) 4.49719 0.233168
\(373\) −9.40158 −0.486795 −0.243398 0.969927i \(-0.578262\pi\)
−0.243398 + 0.969927i \(0.578262\pi\)
\(374\) 1.73122 0.0895192
\(375\) −24.2850 −1.25407
\(376\) 3.51230 0.181133
\(377\) 3.61981 0.186429
\(378\) −6.07185 −0.312302
\(379\) −0.205156 −0.0105382 −0.00526909 0.999986i \(-0.501677\pi\)
−0.00526909 + 0.999986i \(0.501677\pi\)
\(380\) −15.0601 −0.772565
\(381\) 22.1015 1.13229
\(382\) 0.166327 0.00851005
\(383\) −15.2014 −0.776754 −0.388377 0.921501i \(-0.626964\pi\)
−0.388377 + 0.921501i \(0.626964\pi\)
\(384\) 8.74412 0.446222
\(385\) −9.29457 −0.473695
\(386\) −15.9831 −0.813518
\(387\) −2.58810 −0.131561
\(388\) −45.4199 −2.30585
\(389\) 11.2965 0.572757 0.286379 0.958117i \(-0.407549\pi\)
0.286379 + 0.958117i \(0.407549\pi\)
\(390\) −6.84862 −0.346794
\(391\) −0.00429005 −0.000216957 0
\(392\) −1.28547 −0.0649259
\(393\) 0.556990 0.0280964
\(394\) 11.8586 0.597425
\(395\) −4.29872 −0.216292
\(396\) 2.05922 0.103480
\(397\) 25.6761 1.28865 0.644324 0.764753i \(-0.277139\pi\)
0.644324 + 0.764753i \(0.277139\pi\)
\(398\) −8.50813 −0.426474
\(399\) 4.23263 0.211896
\(400\) −29.3327 −1.46664
\(401\) −23.4193 −1.16951 −0.584753 0.811211i \(-0.698809\pi\)
−0.584753 + 0.811211i \(0.698809\pi\)
\(402\) 4.18586 0.208772
\(403\) −1.42563 −0.0710156
\(404\) −32.8799 −1.63584
\(405\) −4.00748 −0.199133
\(406\) 27.3799 1.35884
\(407\) 4.14356 0.205389
\(408\) 1.13314 0.0560990
\(409\) 17.5648 0.868525 0.434262 0.900786i \(-0.357009\pi\)
0.434262 + 0.900786i \(0.357009\pi\)
\(410\) −92.6981 −4.57803
\(411\) 6.21709 0.306666
\(412\) −24.1615 −1.19035
\(413\) 11.7572 0.578535
\(414\) −0.00913315 −0.000448870 0
\(415\) 40.8130 2.00343
\(416\) −6.35168 −0.311417
\(417\) 19.1812 0.939310
\(418\) −2.56920 −0.125664
\(419\) 25.0494 1.22374 0.611871 0.790958i \(-0.290417\pi\)
0.611871 + 0.790958i \(0.290417\pi\)
\(420\) −28.9430 −1.41228
\(421\) −23.8720 −1.16345 −0.581725 0.813385i \(-0.697622\pi\)
−0.581725 + 0.813385i \(0.697622\pi\)
\(422\) −28.3073 −1.37798
\(423\) −3.09960 −0.150708
\(424\) −0.677927 −0.0329230
\(425\) −11.0599 −0.536484
\(426\) −17.0536 −0.826248
\(427\) 14.3490 0.694395
\(428\) −1.47997 −0.0715373
\(429\) −0.652782 −0.0315166
\(430\) −22.0806 −1.06482
\(431\) −38.8204 −1.86991 −0.934957 0.354761i \(-0.884562\pi\)
−0.934957 + 0.354761i \(0.884562\pi\)
\(432\) −2.65217 −0.127602
\(433\) 25.1126 1.20684 0.603418 0.797425i \(-0.293805\pi\)
0.603418 + 0.797425i \(0.293805\pi\)
\(434\) −10.7833 −0.517617
\(435\) 18.0710 0.866439
\(436\) −24.4660 −1.17171
\(437\) 0.00636662 0.000304557 0
\(438\) −6.86309 −0.327931
\(439\) −9.49343 −0.453097 −0.226548 0.974000i \(-0.572744\pi\)
−0.226548 + 0.974000i \(0.572744\pi\)
\(440\) 3.69276 0.176045
\(441\) 1.13443 0.0540203
\(442\) −1.70896 −0.0812869
\(443\) −39.2897 −1.86671 −0.933354 0.358958i \(-0.883132\pi\)
−0.933354 + 0.358958i \(0.883132\pi\)
\(444\) 12.9029 0.612347
\(445\) −23.4128 −1.10987
\(446\) 10.5125 0.497781
\(447\) 5.65926 0.267674
\(448\) −32.9152 −1.55510
\(449\) −18.8579 −0.889959 −0.444979 0.895541i \(-0.646789\pi\)
−0.444979 + 0.895541i \(0.646789\pi\)
\(450\) −23.5456 −1.10995
\(451\) −8.83560 −0.416052
\(452\) 6.28511 0.295627
\(453\) −17.1460 −0.805589
\(454\) 21.1525 0.992736
\(455\) 9.17507 0.430134
\(456\) −1.68163 −0.0787497
\(457\) −3.59660 −0.168242 −0.0841208 0.996456i \(-0.526808\pi\)
−0.0841208 + 0.996456i \(0.526808\pi\)
\(458\) 11.9176 0.556873
\(459\) −1.00000 −0.0466760
\(460\) −0.0435355 −0.00202985
\(461\) 10.4668 0.487488 0.243744 0.969840i \(-0.421624\pi\)
0.243744 + 0.969840i \(0.421624\pi\)
\(462\) −4.93759 −0.229718
\(463\) 7.43143 0.345368 0.172684 0.984977i \(-0.444756\pi\)
0.172684 + 0.984977i \(0.444756\pi\)
\(464\) 11.9595 0.555204
\(465\) −7.11711 −0.330048
\(466\) −16.0226 −0.742234
\(467\) 9.46868 0.438158 0.219079 0.975707i \(-0.429695\pi\)
0.219079 + 0.975707i \(0.429695\pi\)
\(468\) −2.03275 −0.0939637
\(469\) −5.60777 −0.258943
\(470\) −26.4445 −1.21979
\(471\) 1.00000 0.0460776
\(472\) −4.67118 −0.215008
\(473\) −2.10463 −0.0967710
\(474\) −2.28363 −0.104890
\(475\) 16.4134 0.753097
\(476\) −7.22225 −0.331031
\(477\) 0.598271 0.0273929
\(478\) 16.9320 0.774451
\(479\) −36.9612 −1.68880 −0.844401 0.535712i \(-0.820043\pi\)
−0.844401 + 0.535712i \(0.820043\pi\)
\(480\) −31.7093 −1.44732
\(481\) −4.09029 −0.186501
\(482\) −7.52175 −0.342606
\(483\) 0.0122356 0.000556740 0
\(484\) −26.1804 −1.19002
\(485\) 71.8801 3.26391
\(486\) −2.12891 −0.0965694
\(487\) 1.34006 0.0607240 0.0303620 0.999539i \(-0.490334\pi\)
0.0303620 + 0.999539i \(0.490334\pi\)
\(488\) −5.70088 −0.258067
\(489\) 6.17232 0.279122
\(490\) 9.67844 0.437227
\(491\) 12.5707 0.567307 0.283653 0.958927i \(-0.408454\pi\)
0.283653 + 0.958927i \(0.408454\pi\)
\(492\) −27.5138 −1.24042
\(493\) 4.50932 0.203090
\(494\) 2.53617 0.114108
\(495\) −3.25886 −0.146475
\(496\) −4.71013 −0.211491
\(497\) 22.8466 1.02481
\(498\) 21.6813 0.971562
\(499\) −33.1031 −1.48190 −0.740948 0.671562i \(-0.765624\pi\)
−0.740948 + 0.671562i \(0.765624\pi\)
\(500\) −61.4959 −2.75018
\(501\) 16.8847 0.754352
\(502\) −28.7596 −1.28360
\(503\) −7.14237 −0.318463 −0.159231 0.987241i \(-0.550902\pi\)
−0.159231 + 0.987241i \(0.550902\pi\)
\(504\) −3.23183 −0.143957
\(505\) 52.0347 2.31552
\(506\) −0.00742702 −0.000330171 0
\(507\) −12.3556 −0.548732
\(508\) 55.9669 2.48313
\(509\) 21.6001 0.957409 0.478704 0.877976i \(-0.341107\pi\)
0.478704 + 0.877976i \(0.341107\pi\)
\(510\) −8.53157 −0.377784
\(511\) 9.19444 0.406738
\(512\) −26.9959 −1.19306
\(513\) 1.48404 0.0655221
\(514\) 5.08487 0.224284
\(515\) 38.2372 1.68493
\(516\) −6.55376 −0.288513
\(517\) −2.52058 −0.110855
\(518\) −30.9386 −1.35936
\(519\) 18.2355 0.800448
\(520\) −3.64528 −0.159856
\(521\) 21.3291 0.934445 0.467223 0.884140i \(-0.345255\pi\)
0.467223 + 0.884140i \(0.345255\pi\)
\(522\) 9.59994 0.420178
\(523\) −25.7677 −1.12674 −0.563371 0.826204i \(-0.690496\pi\)
−0.563371 + 0.826204i \(0.690496\pi\)
\(524\) 1.41045 0.0616156
\(525\) 31.5439 1.37669
\(526\) 41.2303 1.79773
\(527\) −1.77596 −0.0773619
\(528\) −2.15673 −0.0938594
\(529\) −23.0000 −0.999999
\(530\) 5.10419 0.221712
\(531\) 4.12232 0.178893
\(532\) 10.7181 0.464690
\(533\) 8.72200 0.377792
\(534\) −12.4377 −0.538230
\(535\) 2.34216 0.101260
\(536\) 2.22798 0.0962342
\(537\) −14.0904 −0.608046
\(538\) −28.2517 −1.21802
\(539\) 0.922509 0.0397353
\(540\) −10.1480 −0.436700
\(541\) −14.0882 −0.605698 −0.302849 0.953039i \(-0.597938\pi\)
−0.302849 + 0.953039i \(0.597938\pi\)
\(542\) −28.8755 −1.24031
\(543\) −11.4708 −0.492259
\(544\) −7.91251 −0.339246
\(545\) 38.7191 1.65854
\(546\) 4.87411 0.208593
\(547\) −19.9739 −0.854024 −0.427012 0.904246i \(-0.640434\pi\)
−0.427012 + 0.904246i \(0.640434\pi\)
\(548\) 15.7433 0.672521
\(549\) 5.03103 0.214719
\(550\) −19.1471 −0.816436
\(551\) −6.69202 −0.285090
\(552\) −0.00486125 −0.000206908 0
\(553\) 3.05936 0.130097
\(554\) 5.28395 0.224493
\(555\) −20.4198 −0.866772
\(556\) 48.5720 2.05991
\(557\) 7.77900 0.329607 0.164803 0.986326i \(-0.447301\pi\)
0.164803 + 0.986326i \(0.447301\pi\)
\(558\) −3.78085 −0.160056
\(559\) 2.07757 0.0878719
\(560\) 30.3135 1.28098
\(561\) −0.813194 −0.0343331
\(562\) 30.9572 1.30585
\(563\) −15.9953 −0.674122 −0.337061 0.941483i \(-0.609433\pi\)
−0.337061 + 0.941483i \(0.609433\pi\)
\(564\) −7.84901 −0.330503
\(565\) −9.94662 −0.418457
\(566\) −6.44555 −0.270926
\(567\) 2.85209 0.119777
\(568\) −9.07701 −0.380863
\(569\) 2.36336 0.0990772 0.0495386 0.998772i \(-0.484225\pi\)
0.0495386 + 0.998772i \(0.484225\pi\)
\(570\) 12.6612 0.530320
\(571\) −43.0321 −1.80084 −0.900419 0.435024i \(-0.856740\pi\)
−0.900419 + 0.435024i \(0.856740\pi\)
\(572\) −1.65302 −0.0691161
\(573\) −0.0781279 −0.00326384
\(574\) 65.9725 2.75364
\(575\) 0.0474476 0.00197870
\(576\) −11.5407 −0.480863
\(577\) −24.7015 −1.02834 −0.514168 0.857689i \(-0.671899\pi\)
−0.514168 + 0.857689i \(0.671899\pi\)
\(578\) −2.12891 −0.0885510
\(579\) 7.50763 0.312007
\(580\) 45.7606 1.90011
\(581\) −29.0463 −1.20504
\(582\) 38.1852 1.58283
\(583\) 0.486510 0.0201492
\(584\) −3.65298 −0.151161
\(585\) 3.21696 0.133005
\(586\) −25.4980 −1.05331
\(587\) −16.0915 −0.664169 −0.332085 0.943250i \(-0.607752\pi\)
−0.332085 + 0.943250i \(0.607752\pi\)
\(588\) 2.87267 0.118467
\(589\) 2.63559 0.108598
\(590\) 35.1699 1.44792
\(591\) −5.57024 −0.229129
\(592\) −13.5139 −0.555418
\(593\) 3.49542 0.143540 0.0717699 0.997421i \(-0.477135\pi\)
0.0717699 + 0.997421i \(0.477135\pi\)
\(594\) −1.73122 −0.0710327
\(595\) 11.4297 0.468572
\(596\) 14.3307 0.587010
\(597\) 3.99647 0.163565
\(598\) 0.00733153 0.000299809 0
\(599\) 6.85180 0.279957 0.139978 0.990155i \(-0.455297\pi\)
0.139978 + 0.990155i \(0.455297\pi\)
\(600\) −12.5325 −0.511636
\(601\) −25.5562 −1.04246 −0.521229 0.853417i \(-0.674526\pi\)
−0.521229 + 0.853417i \(0.674526\pi\)
\(602\) 15.7146 0.640479
\(603\) −1.96620 −0.0800697
\(604\) −43.4182 −1.76666
\(605\) 41.4322 1.68446
\(606\) 27.6426 1.12291
\(607\) −17.2478 −0.700067 −0.350033 0.936737i \(-0.613830\pi\)
−0.350033 + 0.936737i \(0.613830\pi\)
\(608\) 11.7425 0.476222
\(609\) −12.8610 −0.521154
\(610\) 42.9226 1.73789
\(611\) 2.48817 0.100661
\(612\) −2.53226 −0.102361
\(613\) −10.9666 −0.442936 −0.221468 0.975168i \(-0.571085\pi\)
−0.221468 + 0.975168i \(0.571085\pi\)
\(614\) −41.8231 −1.68784
\(615\) 43.5425 1.75580
\(616\) −2.62810 −0.105889
\(617\) −18.4491 −0.742733 −0.371366 0.928486i \(-0.621111\pi\)
−0.371366 + 0.928486i \(0.621111\pi\)
\(618\) 20.3129 0.817105
\(619\) −27.1458 −1.09108 −0.545541 0.838084i \(-0.683676\pi\)
−0.545541 + 0.838084i \(0.683676\pi\)
\(620\) −18.0224 −0.723797
\(621\) 0.00429005 0.000172154 0
\(622\) 68.0176 2.72726
\(623\) 16.6627 0.667576
\(624\) 2.12900 0.0852281
\(625\) 42.0220 1.68088
\(626\) 0.0832574 0.00332763
\(627\) 1.20681 0.0481955
\(628\) 2.53226 0.101048
\(629\) −5.09542 −0.203168
\(630\) 24.3328 0.969443
\(631\) 31.1086 1.23841 0.619207 0.785228i \(-0.287454\pi\)
0.619207 + 0.785228i \(0.287454\pi\)
\(632\) −1.21549 −0.0483497
\(633\) 13.2966 0.528493
\(634\) 56.7878 2.25533
\(635\) −88.5714 −3.51485
\(636\) 1.51498 0.0600728
\(637\) −0.910648 −0.0360812
\(638\) 7.80662 0.309067
\(639\) 8.01047 0.316889
\(640\) −35.0419 −1.38515
\(641\) −12.5988 −0.497622 −0.248811 0.968552i \(-0.580040\pi\)
−0.248811 + 0.968552i \(0.580040\pi\)
\(642\) 1.24424 0.0491061
\(643\) −29.0697 −1.14640 −0.573199 0.819416i \(-0.694298\pi\)
−0.573199 + 0.819416i \(0.694298\pi\)
\(644\) 0.0309838 0.00122093
\(645\) 10.3718 0.408388
\(646\) 3.15940 0.124305
\(647\) 10.6663 0.419335 0.209667 0.977773i \(-0.432762\pi\)
0.209667 + 0.977773i \(0.432762\pi\)
\(648\) −1.13314 −0.0445141
\(649\) 3.35224 0.131587
\(650\) 18.9009 0.741356
\(651\) 5.06519 0.198520
\(652\) 15.6299 0.612116
\(653\) 44.9547 1.75921 0.879607 0.475700i \(-0.157805\pi\)
0.879607 + 0.475700i \(0.157805\pi\)
\(654\) 20.5689 0.804307
\(655\) −2.23213 −0.0872164
\(656\) 28.8166 1.12510
\(657\) 3.22375 0.125771
\(658\) 18.8203 0.733693
\(659\) −9.10096 −0.354523 −0.177262 0.984164i \(-0.556724\pi\)
−0.177262 + 0.984164i \(0.556724\pi\)
\(660\) −8.25229 −0.321220
\(661\) 24.7809 0.963864 0.481932 0.876209i \(-0.339935\pi\)
0.481932 + 0.876209i \(0.339935\pi\)
\(662\) −54.1943 −2.10632
\(663\) 0.802739 0.0311758
\(664\) 11.5402 0.447846
\(665\) −16.9622 −0.657765
\(666\) −10.8477 −0.420340
\(667\) −0.0193452 −0.000749050 0
\(668\) 42.7565 1.65430
\(669\) −4.93797 −0.190913
\(670\) −16.7747 −0.648065
\(671\) 4.09121 0.157939
\(672\) 22.5672 0.870549
\(673\) −41.7041 −1.60758 −0.803788 0.594916i \(-0.797185\pi\)
−0.803788 + 0.594916i \(0.797185\pi\)
\(674\) 47.8764 1.84413
\(675\) 11.0599 0.425696
\(676\) −31.2877 −1.20337
\(677\) 5.67429 0.218081 0.109040 0.994037i \(-0.465222\pi\)
0.109040 + 0.994037i \(0.465222\pi\)
\(678\) −5.28399 −0.202930
\(679\) −51.1565 −1.96321
\(680\) −4.54105 −0.174141
\(681\) −9.93583 −0.380742
\(682\) −3.07457 −0.117731
\(683\) −3.21416 −0.122987 −0.0614933 0.998107i \(-0.519586\pi\)
−0.0614933 + 0.998107i \(0.519586\pi\)
\(684\) 3.75799 0.143690
\(685\) −24.9149 −0.951948
\(686\) 35.6149 1.35978
\(687\) −5.59798 −0.213576
\(688\) 6.86408 0.261691
\(689\) −0.480255 −0.0182963
\(690\) 0.0366009 0.00139337
\(691\) 29.8338 1.13493 0.567466 0.823397i \(-0.307924\pi\)
0.567466 + 0.823397i \(0.307924\pi\)
\(692\) 46.1770 1.75539
\(693\) 2.31930 0.0881031
\(694\) −34.4334 −1.30707
\(695\) −76.8685 −2.91579
\(696\) 5.10971 0.193683
\(697\) 10.8653 0.411553
\(698\) −4.21430 −0.159514
\(699\) 7.52621 0.284667
\(700\) 79.8774 3.01908
\(701\) 11.8409 0.447225 0.223612 0.974678i \(-0.428215\pi\)
0.223612 + 0.974678i \(0.428215\pi\)
\(702\) 1.70896 0.0645005
\(703\) 7.56182 0.285199
\(704\) −9.38484 −0.353704
\(705\) 12.4216 0.467825
\(706\) −9.36695 −0.352530
\(707\) −37.0327 −1.39276
\(708\) 10.4388 0.392314
\(709\) −41.8994 −1.57357 −0.786783 0.617230i \(-0.788255\pi\)
−0.786783 + 0.617230i \(0.788255\pi\)
\(710\) 68.3419 2.56483
\(711\) 1.07267 0.0402284
\(712\) −6.62012 −0.248100
\(713\) 0.00761895 0.000285332 0
\(714\) 6.07185 0.227233
\(715\) 2.61601 0.0978333
\(716\) −35.6806 −1.33345
\(717\) −7.95335 −0.297023
\(718\) 13.5406 0.505329
\(719\) 44.8695 1.67335 0.836674 0.547701i \(-0.184497\pi\)
0.836674 + 0.547701i \(0.184497\pi\)
\(720\) 10.6285 0.396101
\(721\) −27.2131 −1.01347
\(722\) 35.7606 1.33087
\(723\) 3.53315 0.131399
\(724\) −29.0471 −1.07953
\(725\) −49.8727 −1.85222
\(726\) 22.0102 0.816876
\(727\) −12.5972 −0.467204 −0.233602 0.972332i \(-0.575051\pi\)
−0.233602 + 0.972332i \(0.575051\pi\)
\(728\) 2.59431 0.0961517
\(729\) 1.00000 0.0370370
\(730\) 27.5037 1.01796
\(731\) 2.58810 0.0957245
\(732\) 12.7399 0.470881
\(733\) 22.1920 0.819680 0.409840 0.912157i \(-0.365584\pi\)
0.409840 + 0.912157i \(0.365584\pi\)
\(734\) 42.3330 1.56254
\(735\) −4.54619 −0.167689
\(736\) 0.0339451 0.00125123
\(737\) −1.59890 −0.0588962
\(738\) 23.1313 0.851474
\(739\) 13.6000 0.500283 0.250142 0.968209i \(-0.419523\pi\)
0.250142 + 0.968209i \(0.419523\pi\)
\(740\) −51.7083 −1.90083
\(741\) −1.19130 −0.0437634
\(742\) −3.63261 −0.133357
\(743\) −7.79534 −0.285983 −0.142992 0.989724i \(-0.545672\pi\)
−0.142992 + 0.989724i \(0.545672\pi\)
\(744\) −2.01241 −0.0737786
\(745\) −22.6794 −0.830908
\(746\) 20.0151 0.732806
\(747\) −10.1842 −0.372621
\(748\) −2.05922 −0.0752926
\(749\) −1.66690 −0.0609071
\(750\) 51.7005 1.88784
\(751\) −4.17834 −0.152470 −0.0762348 0.997090i \(-0.524290\pi\)
−0.0762348 + 0.997090i \(0.524290\pi\)
\(752\) 8.22066 0.299777
\(753\) 13.5091 0.492298
\(754\) −7.70625 −0.280645
\(755\) 68.7123 2.50069
\(756\) 7.22225 0.262671
\(757\) −38.4381 −1.39706 −0.698528 0.715583i \(-0.746161\pi\)
−0.698528 + 0.715583i \(0.746161\pi\)
\(758\) 0.436760 0.0158638
\(759\) 0.00348865 0.000126630 0
\(760\) 6.73911 0.244453
\(761\) 11.1499 0.404185 0.202092 0.979366i \(-0.435226\pi\)
0.202092 + 0.979366i \(0.435226\pi\)
\(762\) −47.0522 −1.70452
\(763\) −27.5560 −0.997595
\(764\) −0.197840 −0.00715762
\(765\) 4.00748 0.144891
\(766\) 32.3624 1.16930
\(767\) −3.30914 −0.119486
\(768\) 4.46596 0.161151
\(769\) 8.17689 0.294866 0.147433 0.989072i \(-0.452899\pi\)
0.147433 + 0.989072i \(0.452899\pi\)
\(770\) 19.7873 0.713085
\(771\) −2.38848 −0.0860191
\(772\) 19.0113 0.684232
\(773\) −0.970111 −0.0348925 −0.0174462 0.999848i \(-0.505554\pi\)
−0.0174462 + 0.999848i \(0.505554\pi\)
\(774\) 5.50984 0.198047
\(775\) 19.6419 0.705558
\(776\) 20.3246 0.729611
\(777\) 14.5326 0.521354
\(778\) −24.0493 −0.862210
\(779\) −16.1246 −0.577723
\(780\) 8.14619 0.291681
\(781\) 6.51406 0.233092
\(782\) 0.00913315 0.000326601 0
\(783\) −4.50932 −0.161150
\(784\) −3.00869 −0.107453
\(785\) −4.00748 −0.143033
\(786\) −1.18578 −0.0422955
\(787\) −34.0222 −1.21276 −0.606380 0.795175i \(-0.707379\pi\)
−0.606380 + 0.795175i \(0.707379\pi\)
\(788\) −14.1053 −0.502482
\(789\) −19.3669 −0.689478
\(790\) 9.15159 0.325599
\(791\) 7.07893 0.251698
\(792\) −0.921465 −0.0327429
\(793\) −4.03861 −0.143415
\(794\) −54.6622 −1.93989
\(795\) −2.39756 −0.0850326
\(796\) 10.1201 0.358698
\(797\) 15.1803 0.537714 0.268857 0.963180i \(-0.413354\pi\)
0.268857 + 0.963180i \(0.413354\pi\)
\(798\) −9.01088 −0.318982
\(799\) 3.09960 0.109656
\(800\) 87.5117 3.09400
\(801\) 5.84226 0.206426
\(802\) 49.8577 1.76054
\(803\) 2.62154 0.0925120
\(804\) −4.97893 −0.175593
\(805\) −0.0490341 −0.00172822
\(806\) 3.03504 0.106905
\(807\) 13.2705 0.467143
\(808\) 14.7132 0.517608
\(809\) −44.3717 −1.56003 −0.780013 0.625764i \(-0.784787\pi\)
−0.780013 + 0.625764i \(0.784787\pi\)
\(810\) 8.53157 0.299769
\(811\) 6.16017 0.216313 0.108156 0.994134i \(-0.465505\pi\)
0.108156 + 0.994134i \(0.465505\pi\)
\(812\) −32.5674 −1.14289
\(813\) 13.5635 0.475694
\(814\) −8.82128 −0.309186
\(815\) −24.7354 −0.866445
\(816\) 2.65217 0.0928444
\(817\) −3.84086 −0.134375
\(818\) −37.3940 −1.30745
\(819\) −2.28948 −0.0800011
\(820\) 110.261 3.85049
\(821\) −7.48370 −0.261183 −0.130591 0.991436i \(-0.541688\pi\)
−0.130591 + 0.991436i \(0.541688\pi\)
\(822\) −13.2356 −0.461646
\(823\) −16.6712 −0.581121 −0.290560 0.956857i \(-0.593842\pi\)
−0.290560 + 0.956857i \(0.593842\pi\)
\(824\) 10.8118 0.376648
\(825\) 8.99385 0.313126
\(826\) −25.0301 −0.870908
\(827\) 7.85898 0.273284 0.136642 0.990621i \(-0.456369\pi\)
0.136642 + 0.990621i \(0.456369\pi\)
\(828\) 0.0108636 0.000377535 0
\(829\) −21.1657 −0.735114 −0.367557 0.930001i \(-0.619806\pi\)
−0.367557 + 0.930001i \(0.619806\pi\)
\(830\) −86.8873 −3.01590
\(831\) −2.48199 −0.0860994
\(832\) 9.26417 0.321177
\(833\) −1.13443 −0.0393055
\(834\) −40.8352 −1.41401
\(835\) −67.6651 −2.34165
\(836\) 3.05597 0.105693
\(837\) 1.77596 0.0613860
\(838\) −53.3279 −1.84218
\(839\) −11.3070 −0.390361 −0.195180 0.980767i \(-0.562529\pi\)
−0.195180 + 0.980767i \(0.562529\pi\)
\(840\) 12.9515 0.446869
\(841\) −8.66603 −0.298829
\(842\) 50.8214 1.75142
\(843\) −14.5413 −0.500830
\(844\) 33.6706 1.15899
\(845\) 49.5149 1.70336
\(846\) 6.59878 0.226871
\(847\) −29.4870 −1.01318
\(848\) −1.58671 −0.0544880
\(849\) 3.02763 0.103908
\(850\) 23.5456 0.807606
\(851\) 0.0218596 0.000749338 0
\(852\) 20.2846 0.694940
\(853\) 37.3825 1.27995 0.639976 0.768395i \(-0.278944\pi\)
0.639976 + 0.768395i \(0.278944\pi\)
\(854\) −30.5477 −1.04532
\(855\) −5.94727 −0.203392
\(856\) 0.662262 0.0226357
\(857\) −8.18965 −0.279753 −0.139877 0.990169i \(-0.544671\pi\)
−0.139877 + 0.990169i \(0.544671\pi\)
\(858\) 1.38972 0.0474441
\(859\) −12.7004 −0.433333 −0.216667 0.976246i \(-0.569518\pi\)
−0.216667 + 0.976246i \(0.569518\pi\)
\(860\) 26.2641 0.895598
\(861\) −30.9888 −1.05610
\(862\) 82.6452 2.81491
\(863\) −25.0741 −0.853531 −0.426766 0.904362i \(-0.640347\pi\)
−0.426766 + 0.904362i \(0.640347\pi\)
\(864\) 7.91251 0.269189
\(865\) −73.0783 −2.48474
\(866\) −53.4626 −1.81673
\(867\) 1.00000 0.0339618
\(868\) 12.8264 0.435356
\(869\) 0.872292 0.0295905
\(870\) −38.4716 −1.30431
\(871\) 1.57834 0.0534801
\(872\) 10.9481 0.370749
\(873\) −17.9365 −0.607058
\(874\) −0.0135540 −0.000458470 0
\(875\) −69.2629 −2.34151
\(876\) 8.16340 0.275816
\(877\) −37.2379 −1.25744 −0.628718 0.777633i \(-0.716420\pi\)
−0.628718 + 0.777633i \(0.716420\pi\)
\(878\) 20.2107 0.682077
\(879\) 11.9770 0.403975
\(880\) 8.64304 0.291357
\(881\) −28.0328 −0.944449 −0.472224 0.881478i \(-0.656549\pi\)
−0.472224 + 0.881478i \(0.656549\pi\)
\(882\) −2.41509 −0.0813204
\(883\) −14.3024 −0.481316 −0.240658 0.970610i \(-0.577363\pi\)
−0.240658 + 0.970610i \(0.577363\pi\)
\(884\) 2.03275 0.0683687
\(885\) −16.5201 −0.555317
\(886\) 83.6442 2.81008
\(887\) −27.2040 −0.913422 −0.456711 0.889615i \(-0.650973\pi\)
−0.456711 + 0.889615i \(0.650973\pi\)
\(888\) −5.77384 −0.193757
\(889\) 63.0355 2.11414
\(890\) 49.8437 1.67077
\(891\) 0.813194 0.0272430
\(892\) −12.5042 −0.418673
\(893\) −4.59994 −0.153931
\(894\) −12.0481 −0.402947
\(895\) 56.4670 1.88748
\(896\) 24.9390 0.833155
\(897\) −0.00344379 −0.000114985 0
\(898\) 40.1468 1.33972
\(899\) −8.00835 −0.267094
\(900\) 28.0066 0.933554
\(901\) −0.598271 −0.0199313
\(902\) 18.8102 0.626312
\(903\) −7.38151 −0.245641
\(904\) −2.81248 −0.0935416
\(905\) 45.9690 1.52806
\(906\) 36.5023 1.21271
\(907\) −38.4472 −1.27662 −0.638309 0.769780i \(-0.720366\pi\)
−0.638309 + 0.769780i \(0.720366\pi\)
\(908\) −25.1601 −0.834969
\(909\) −12.9844 −0.430665
\(910\) −19.5329 −0.647509
\(911\) −28.2072 −0.934548 −0.467274 0.884113i \(-0.654764\pi\)
−0.467274 + 0.884113i \(0.654764\pi\)
\(912\) −3.93593 −0.130332
\(913\) −8.28174 −0.274086
\(914\) 7.65683 0.253266
\(915\) −20.1618 −0.666528
\(916\) −14.1756 −0.468374
\(917\) 1.58859 0.0524597
\(918\) 2.12891 0.0702646
\(919\) −46.0460 −1.51892 −0.759459 0.650556i \(-0.774536\pi\)
−0.759459 + 0.650556i \(0.774536\pi\)
\(920\) 0.0194814 0.000642281 0
\(921\) 19.6453 0.647335
\(922\) −22.2829 −0.733849
\(923\) −6.43031 −0.211656
\(924\) 5.87309 0.193210
\(925\) 56.3548 1.85294
\(926\) −15.8209 −0.519906
\(927\) −9.54145 −0.313382
\(928\) −35.6801 −1.17126
\(929\) 50.7773 1.66595 0.832975 0.553310i \(-0.186636\pi\)
0.832975 + 0.553310i \(0.186636\pi\)
\(930\) 15.1517 0.496844
\(931\) 1.68354 0.0551757
\(932\) 19.0584 0.624277
\(933\) −31.9495 −1.04598
\(934\) −20.1580 −0.659590
\(935\) 3.25886 0.106576
\(936\) 0.909618 0.0297318
\(937\) −12.4592 −0.407024 −0.203512 0.979072i \(-0.565236\pi\)
−0.203512 + 0.979072i \(0.565236\pi\)
\(938\) 11.9385 0.389804
\(939\) −0.0391080 −0.00127624
\(940\) 31.4548 1.02594
\(941\) 16.4536 0.536373 0.268187 0.963367i \(-0.413576\pi\)
0.268187 + 0.963367i \(0.413576\pi\)
\(942\) −2.12891 −0.0693637
\(943\) −0.0466127 −0.00151792
\(944\) −10.9331 −0.355841
\(945\) −11.4297 −0.371808
\(946\) 4.48057 0.145676
\(947\) 6.70863 0.218001 0.109001 0.994042i \(-0.465235\pi\)
0.109001 + 0.994042i \(0.465235\pi\)
\(948\) 2.71629 0.0882211
\(949\) −2.58783 −0.0840046
\(950\) −34.9426 −1.13369
\(951\) −26.6746 −0.864983
\(952\) 3.23183 0.104744
\(953\) −16.9559 −0.549255 −0.274628 0.961551i \(-0.588555\pi\)
−0.274628 + 0.961551i \(0.588555\pi\)
\(954\) −1.27367 −0.0412364
\(955\) 0.313096 0.0101316
\(956\) −20.1400 −0.651374
\(957\) −3.66695 −0.118536
\(958\) 78.6872 2.54227
\(959\) 17.7317 0.572587
\(960\) 46.2492 1.49269
\(961\) −27.8460 −0.898257
\(962\) 8.70786 0.280753
\(963\) −0.584447 −0.0188335
\(964\) 8.94686 0.288159
\(965\) −30.0867 −0.968525
\(966\) −0.0260486 −0.000838099 0
\(967\) 39.3501 1.26541 0.632707 0.774392i \(-0.281944\pi\)
0.632707 + 0.774392i \(0.281944\pi\)
\(968\) 11.7152 0.376542
\(969\) −1.48404 −0.0476743
\(970\) −153.026 −4.91338
\(971\) 19.0567 0.611558 0.305779 0.952103i \(-0.401083\pi\)
0.305779 + 0.952103i \(0.401083\pi\)
\(972\) 2.53226 0.0812224
\(973\) 54.7067 1.75382
\(974\) −2.85287 −0.0914120
\(975\) −8.87822 −0.284330
\(976\) −13.3431 −0.427103
\(977\) −14.3622 −0.459489 −0.229744 0.973251i \(-0.573789\pi\)
−0.229744 + 0.973251i \(0.573789\pi\)
\(978\) −13.1403 −0.420181
\(979\) 4.75089 0.151839
\(980\) −11.5122 −0.367742
\(981\) −9.66169 −0.308474
\(982\) −26.7619 −0.854005
\(983\) 54.5242 1.73905 0.869526 0.493886i \(-0.164424\pi\)
0.869526 + 0.493886i \(0.164424\pi\)
\(984\) 12.3119 0.392491
\(985\) 22.3226 0.711259
\(986\) −9.59994 −0.305725
\(987\) −8.84035 −0.281392
\(988\) −3.01668 −0.0959734
\(989\) −0.0111031 −0.000353058 0
\(990\) 6.93782 0.220499
\(991\) 19.3655 0.615167 0.307583 0.951521i \(-0.400480\pi\)
0.307583 + 0.951521i \(0.400480\pi\)
\(992\) 14.0523 0.446160
\(993\) 25.4564 0.807833
\(994\) −48.6384 −1.54272
\(995\) −16.0158 −0.507734
\(996\) −25.7891 −0.817159
\(997\) −20.2359 −0.640877 −0.320439 0.947269i \(-0.603830\pi\)
−0.320439 + 0.947269i \(0.603830\pi\)
\(998\) 70.4735 2.23080
\(999\) 5.09542 0.161212
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 \(a_p\))