Properties

Label 6010.2.a.c.1.16
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(3.28691\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.28691 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.28691 q^{6} -3.46813 q^{7} +1.00000 q^{8} +2.22998 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.28691 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.28691 q^{6} -3.46813 q^{7} +1.00000 q^{8} +2.22998 q^{9} +1.00000 q^{10} -3.41913 q^{11} +2.28691 q^{12} -2.63900 q^{13} -3.46813 q^{14} +2.28691 q^{15} +1.00000 q^{16} -3.45967 q^{17} +2.22998 q^{18} +1.07603 q^{19} +1.00000 q^{20} -7.93132 q^{21} -3.41913 q^{22} -6.75440 q^{23} +2.28691 q^{24} +1.00000 q^{25} -2.63900 q^{26} -1.76098 q^{27} -3.46813 q^{28} -1.95342 q^{29} +2.28691 q^{30} +4.65022 q^{31} +1.00000 q^{32} -7.81926 q^{33} -3.45967 q^{34} -3.46813 q^{35} +2.22998 q^{36} -6.85159 q^{37} +1.07603 q^{38} -6.03517 q^{39} +1.00000 q^{40} +0.892755 q^{41} -7.93132 q^{42} +10.1922 q^{43} -3.41913 q^{44} +2.22998 q^{45} -6.75440 q^{46} +2.60823 q^{47} +2.28691 q^{48} +5.02795 q^{49} +1.00000 q^{50} -7.91196 q^{51} -2.63900 q^{52} -14.2976 q^{53} -1.76098 q^{54} -3.41913 q^{55} -3.46813 q^{56} +2.46079 q^{57} -1.95342 q^{58} -9.44473 q^{59} +2.28691 q^{60} +9.42299 q^{61} +4.65022 q^{62} -7.73385 q^{63} +1.00000 q^{64} -2.63900 q^{65} -7.81926 q^{66} +9.09482 q^{67} -3.45967 q^{68} -15.4467 q^{69} -3.46813 q^{70} -11.7865 q^{71} +2.22998 q^{72} +3.96524 q^{73} -6.85159 q^{74} +2.28691 q^{75} +1.07603 q^{76} +11.8580 q^{77} -6.03517 q^{78} -12.9753 q^{79} +1.00000 q^{80} -10.7171 q^{81} +0.892755 q^{82} -10.1444 q^{83} -7.93132 q^{84} -3.45967 q^{85} +10.1922 q^{86} -4.46731 q^{87} -3.41913 q^{88} +0.456762 q^{89} +2.22998 q^{90} +9.15240 q^{91} -6.75440 q^{92} +10.6347 q^{93} +2.60823 q^{94} +1.07603 q^{95} +2.28691 q^{96} +16.6254 q^{97} +5.02795 q^{98} -7.62458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + O(q^{10}) \) \( 16q + 16q^{2} - 8q^{3} + 16q^{4} + 16q^{5} - 8q^{6} - 10q^{7} + 16q^{8} - 2q^{9} + 16q^{10} - 14q^{11} - 8q^{12} - 20q^{13} - 10q^{14} - 8q^{15} + 16q^{16} - 27q^{17} - 2q^{18} - 17q^{19} + 16q^{20} - 12q^{21} - 14q^{22} - 9q^{23} - 8q^{24} + 16q^{25} - 20q^{26} - 11q^{27} - 10q^{28} - 23q^{29} - 8q^{30} - 21q^{31} + 16q^{32} - 9q^{33} - 27q^{34} - 10q^{35} - 2q^{36} - 16q^{37} - 17q^{38} - 6q^{39} + 16q^{40} - 35q^{41} - 12q^{42} + 3q^{43} - 14q^{44} - 2q^{45} - 9q^{46} - 25q^{47} - 8q^{48} - 24q^{49} + 16q^{50} - q^{51} - 20q^{52} - 39q^{53} - 11q^{54} - 14q^{55} - 10q^{56} - 6q^{57} - 23q^{58} - 32q^{59} - 8q^{60} - 38q^{61} - 21q^{62} + q^{63} + 16q^{64} - 20q^{65} - 9q^{66} + 5q^{67} - 27q^{68} - 25q^{69} - 10q^{70} - 16q^{71} - 2q^{72} - 17q^{73} - 16q^{74} - 8q^{75} - 17q^{76} - 34q^{77} - 6q^{78} - 40q^{79} + 16q^{80} - 28q^{81} - 35q^{82} - 22q^{83} - 12q^{84} - 27q^{85} + 3q^{86} + 10q^{87} - 14q^{88} - 46q^{89} - 2q^{90} - q^{91} - 9q^{92} + 14q^{93} - 25q^{94} - 17q^{95} - 8q^{96} - 21q^{97} - 24q^{98} + 15q^{99} + O(q^{100}) \)

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
\(3\) 2.28691 1.32035 0.660175 0.751112i \(-0.270482\pi\)
0.660175 + 0.751112i \(0.270482\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 2.28691 0.933629
\(7\) −3.46813 −1.31083 −0.655415 0.755269i \(-0.727506\pi\)
−0.655415 + 0.755269i \(0.727506\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.22998 0.743325
\(10\) 1.00000 0.316228
\(11\) −3.41913 −1.03091 −0.515453 0.856918i \(-0.672376\pi\)
−0.515453 + 0.856918i \(0.672376\pi\)
\(12\) 2.28691 0.660175
\(13\) −2.63900 −0.731927 −0.365964 0.930629i \(-0.619261\pi\)
−0.365964 + 0.930629i \(0.619261\pi\)
\(14\) −3.46813 −0.926897
\(15\) 2.28691 0.590479
\(16\) 1.00000 0.250000
\(17\) −3.45967 −0.839092 −0.419546 0.907734i \(-0.637811\pi\)
−0.419546 + 0.907734i \(0.637811\pi\)
\(18\) 2.22998 0.525610
\(19\) 1.07603 0.246859 0.123429 0.992353i \(-0.460611\pi\)
0.123429 + 0.992353i \(0.460611\pi\)
\(20\) 1.00000 0.223607
\(21\) −7.93132 −1.73076
\(22\) −3.41913 −0.728961
\(23\) −6.75440 −1.40839 −0.704195 0.710007i \(-0.748692\pi\)
−0.704195 + 0.710007i \(0.748692\pi\)
\(24\) 2.28691 0.466814
\(25\) 1.00000 0.200000
\(26\) −2.63900 −0.517551
\(27\) −1.76098 −0.338901
\(28\) −3.46813 −0.655415
\(29\) −1.95342 −0.362742 −0.181371 0.983415i \(-0.558053\pi\)
−0.181371 + 0.983415i \(0.558053\pi\)
\(30\) 2.28691 0.417531
\(31\) 4.65022 0.835204 0.417602 0.908630i \(-0.362871\pi\)
0.417602 + 0.908630i \(0.362871\pi\)
\(32\) 1.00000 0.176777
\(33\) −7.81926 −1.36116
\(34\) −3.45967 −0.593328
\(35\) −3.46813 −0.586221
\(36\) 2.22998 0.371663
\(37\) −6.85159 −1.12639 −0.563197 0.826322i \(-0.690429\pi\)
−0.563197 + 0.826322i \(0.690429\pi\)
\(38\) 1.07603 0.174555
\(39\) −6.03517 −0.966400
\(40\) 1.00000 0.158114
\(41\) 0.892755 0.139425 0.0697125 0.997567i \(-0.477792\pi\)
0.0697125 + 0.997567i \(0.477792\pi\)
\(42\) −7.93132 −1.22383
\(43\) 10.1922 1.55429 0.777145 0.629321i \(-0.216667\pi\)
0.777145 + 0.629321i \(0.216667\pi\)
\(44\) −3.41913 −0.515453
\(45\) 2.22998 0.332425
\(46\) −6.75440 −0.995882
\(47\) 2.60823 0.380449 0.190224 0.981741i \(-0.439078\pi\)
0.190224 + 0.981741i \(0.439078\pi\)
\(48\) 2.28691 0.330088
\(49\) 5.02795 0.718278
\(50\) 1.00000 0.141421
\(51\) −7.91196 −1.10790
\(52\) −2.63900 −0.365964
\(53\) −14.2976 −1.96393 −0.981964 0.189068i \(-0.939453\pi\)
−0.981964 + 0.189068i \(0.939453\pi\)
\(54\) −1.76098 −0.239639
\(55\) −3.41913 −0.461035
\(56\) −3.46813 −0.463449
\(57\) 2.46079 0.325940
\(58\) −1.95342 −0.256497
\(59\) −9.44473 −1.22960 −0.614800 0.788683i \(-0.710763\pi\)
−0.614800 + 0.788683i \(0.710763\pi\)
\(60\) 2.28691 0.295239
\(61\) 9.42299 1.20649 0.603245 0.797556i \(-0.293874\pi\)
0.603245 + 0.797556i \(0.293874\pi\)
\(62\) 4.65022 0.590579
\(63\) −7.73385 −0.974374
\(64\) 1.00000 0.125000
\(65\) −2.63900 −0.327328
\(66\) −7.81926 −0.962484
\(67\) 9.09482 1.11111 0.555554 0.831480i \(-0.312506\pi\)
0.555554 + 0.831480i \(0.312506\pi\)
\(68\) −3.45967 −0.419546
\(69\) −15.4467 −1.85957
\(70\) −3.46813 −0.414521
\(71\) −11.7865 −1.39880 −0.699398 0.714732i \(-0.746549\pi\)
−0.699398 + 0.714732i \(0.746549\pi\)
\(72\) 2.22998 0.262805
\(73\) 3.96524 0.464097 0.232048 0.972704i \(-0.425457\pi\)
0.232048 + 0.972704i \(0.425457\pi\)
\(74\) −6.85159 −0.796481
\(75\) 2.28691 0.264070
\(76\) 1.07603 0.123429
\(77\) 11.8580 1.35134
\(78\) −6.03517 −0.683348
\(79\) −12.9753 −1.45983 −0.729917 0.683536i \(-0.760441\pi\)
−0.729917 + 0.683536i \(0.760441\pi\)
\(80\) 1.00000 0.111803
\(81\) −10.7171 −1.19079
\(82\) 0.892755 0.0985883
\(83\) −10.1444 −1.11349 −0.556746 0.830683i \(-0.687950\pi\)
−0.556746 + 0.830683i \(0.687950\pi\)
\(84\) −7.93132 −0.865378
\(85\) −3.45967 −0.375253
\(86\) 10.1922 1.09905
\(87\) −4.46731 −0.478946
\(88\) −3.41913 −0.364480
\(89\) 0.456762 0.0484167 0.0242084 0.999707i \(-0.492293\pi\)
0.0242084 + 0.999707i \(0.492293\pi\)
\(90\) 2.22998 0.235060
\(91\) 9.15240 0.959433
\(92\) −6.75440 −0.704195
\(93\) 10.6347 1.10276
\(94\) 2.60823 0.269018
\(95\) 1.07603 0.110399
\(96\) 2.28691 0.233407
\(97\) 16.6254 1.68806 0.844029 0.536298i \(-0.180178\pi\)
0.844029 + 0.536298i \(0.180178\pi\)
\(98\) 5.02795 0.507899
\(99\) −7.62458 −0.766299
\(100\) 1.00000 0.100000
\(101\) −12.3402 −1.22790 −0.613949 0.789346i \(-0.710420\pi\)
−0.613949 + 0.789346i \(0.710420\pi\)
\(102\) −7.91196 −0.783401
\(103\) 8.99878 0.886677 0.443338 0.896354i \(-0.353794\pi\)
0.443338 + 0.896354i \(0.353794\pi\)
\(104\) −2.63900 −0.258775
\(105\) −7.93132 −0.774018
\(106\) −14.2976 −1.38871
\(107\) −3.18238 −0.307652 −0.153826 0.988098i \(-0.549160\pi\)
−0.153826 + 0.988098i \(0.549160\pi\)
\(108\) −1.76098 −0.169450
\(109\) 1.47514 0.141293 0.0706465 0.997501i \(-0.477494\pi\)
0.0706465 + 0.997501i \(0.477494\pi\)
\(110\) −3.41913 −0.326001
\(111\) −15.6690 −1.48724
\(112\) −3.46813 −0.327708
\(113\) −5.35901 −0.504133 −0.252067 0.967710i \(-0.581110\pi\)
−0.252067 + 0.967710i \(0.581110\pi\)
\(114\) 2.46079 0.230474
\(115\) −6.75440 −0.629851
\(116\) −1.95342 −0.181371
\(117\) −5.88491 −0.544060
\(118\) −9.44473 −0.869458
\(119\) 11.9986 1.09991
\(120\) 2.28691 0.208766
\(121\) 0.690448 0.0627680
\(122\) 9.42299 0.853118
\(123\) 2.04165 0.184090
\(124\) 4.65022 0.417602
\(125\) 1.00000 0.0894427
\(126\) −7.73385 −0.688986
\(127\) 13.4391 1.19253 0.596263 0.802789i \(-0.296651\pi\)
0.596263 + 0.802789i \(0.296651\pi\)
\(128\) 1.00000 0.0883883
\(129\) 23.3086 2.05221
\(130\) −2.63900 −0.231456
\(131\) 6.82635 0.596421 0.298211 0.954500i \(-0.403610\pi\)
0.298211 + 0.954500i \(0.403610\pi\)
\(132\) −7.81926 −0.680579
\(133\) −3.73182 −0.323590
\(134\) 9.09482 0.785672
\(135\) −1.76098 −0.151561
\(136\) −3.45967 −0.296664
\(137\) −1.49274 −0.127534 −0.0637668 0.997965i \(-0.520311\pi\)
−0.0637668 + 0.997965i \(0.520311\pi\)
\(138\) −15.4467 −1.31491
\(139\) 3.60693 0.305935 0.152968 0.988231i \(-0.451117\pi\)
0.152968 + 0.988231i \(0.451117\pi\)
\(140\) −3.46813 −0.293111
\(141\) 5.96479 0.502326
\(142\) −11.7865 −0.989098
\(143\) 9.02309 0.754548
\(144\) 2.22998 0.185831
\(145\) −1.95342 −0.162223
\(146\) 3.96524 0.328166
\(147\) 11.4985 0.948378
\(148\) −6.85159 −0.563197
\(149\) −2.87791 −0.235767 −0.117884 0.993027i \(-0.537611\pi\)
−0.117884 + 0.993027i \(0.537611\pi\)
\(150\) 2.28691 0.186726
\(151\) −16.4331 −1.33731 −0.668655 0.743573i \(-0.733130\pi\)
−0.668655 + 0.743573i \(0.733130\pi\)
\(152\) 1.07603 0.0872777
\(153\) −7.71497 −0.623718
\(154\) 11.8580 0.955545
\(155\) 4.65022 0.373515
\(156\) −6.03517 −0.483200
\(157\) 12.2295 0.976021 0.488011 0.872838i \(-0.337723\pi\)
0.488011 + 0.872838i \(0.337723\pi\)
\(158\) −12.9753 −1.03226
\(159\) −32.6974 −2.59307
\(160\) 1.00000 0.0790569
\(161\) 23.4252 1.84616
\(162\) −10.7171 −0.842018
\(163\) −1.53692 −0.120381 −0.0601906 0.998187i \(-0.519171\pi\)
−0.0601906 + 0.998187i \(0.519171\pi\)
\(164\) 0.892755 0.0697125
\(165\) −7.81926 −0.608728
\(166\) −10.1444 −0.787357
\(167\) 5.13478 0.397341 0.198671 0.980066i \(-0.436338\pi\)
0.198671 + 0.980066i \(0.436338\pi\)
\(168\) −7.93132 −0.611915
\(169\) −6.03568 −0.464283
\(170\) −3.45967 −0.265344
\(171\) 2.39952 0.183496
\(172\) 10.1922 0.777145
\(173\) −0.0718874 −0.00546550 −0.00273275 0.999996i \(-0.500870\pi\)
−0.00273275 + 0.999996i \(0.500870\pi\)
\(174\) −4.46731 −0.338666
\(175\) −3.46813 −0.262166
\(176\) −3.41913 −0.257727
\(177\) −21.5993 −1.62350
\(178\) 0.456762 0.0342358
\(179\) −5.16654 −0.386166 −0.193083 0.981182i \(-0.561849\pi\)
−0.193083 + 0.981182i \(0.561849\pi\)
\(180\) 2.22998 0.166213
\(181\) 1.51191 0.112380 0.0561898 0.998420i \(-0.482105\pi\)
0.0561898 + 0.998420i \(0.482105\pi\)
\(182\) 9.15240 0.678421
\(183\) 21.5496 1.59299
\(184\) −6.75440 −0.497941
\(185\) −6.85159 −0.503739
\(186\) 10.6347 0.779771
\(187\) 11.8290 0.865025
\(188\) 2.60823 0.190224
\(189\) 6.10731 0.444241
\(190\) 1.07603 0.0780635
\(191\) 13.0731 0.945936 0.472968 0.881080i \(-0.343183\pi\)
0.472968 + 0.881080i \(0.343183\pi\)
\(192\) 2.28691 0.165044
\(193\) −1.07841 −0.0776260 −0.0388130 0.999246i \(-0.512358\pi\)
−0.0388130 + 0.999246i \(0.512358\pi\)
\(194\) 16.6254 1.19364
\(195\) −6.03517 −0.432187
\(196\) 5.02795 0.359139
\(197\) 13.5161 0.962981 0.481490 0.876451i \(-0.340096\pi\)
0.481490 + 0.876451i \(0.340096\pi\)
\(198\) −7.62458 −0.541855
\(199\) −20.3859 −1.44512 −0.722558 0.691310i \(-0.757034\pi\)
−0.722558 + 0.691310i \(0.757034\pi\)
\(200\) 1.00000 0.0707107
\(201\) 20.7991 1.46705
\(202\) −12.3402 −0.868255
\(203\) 6.77473 0.475493
\(204\) −7.91196 −0.553948
\(205\) 0.892755 0.0623527
\(206\) 8.99878 0.626975
\(207\) −15.0621 −1.04689
\(208\) −2.63900 −0.182982
\(209\) −3.67909 −0.254488
\(210\) −7.93132 −0.547313
\(211\) −14.3190 −0.985761 −0.492880 0.870097i \(-0.664056\pi\)
−0.492880 + 0.870097i \(0.664056\pi\)
\(212\) −14.2976 −0.981964
\(213\) −26.9546 −1.84690
\(214\) −3.18238 −0.217543
\(215\) 10.1922 0.695100
\(216\) −1.76098 −0.119819
\(217\) −16.1276 −1.09481
\(218\) 1.47514 0.0999092
\(219\) 9.06817 0.612770
\(220\) −3.41913 −0.230518
\(221\) 9.13006 0.614154
\(222\) −15.6690 −1.05163
\(223\) 12.1093 0.810899 0.405450 0.914117i \(-0.367115\pi\)
0.405450 + 0.914117i \(0.367115\pi\)
\(224\) −3.46813 −0.231724
\(225\) 2.22998 0.148665
\(226\) −5.35901 −0.356476
\(227\) 0.00202746 0.000134567 0 6.72835e−5 1.00000i \(-0.499979\pi\)
6.72835e−5 1.00000i \(0.499979\pi\)
\(228\) 2.46079 0.162970
\(229\) −4.08309 −0.269818 −0.134909 0.990858i \(-0.543074\pi\)
−0.134909 + 0.990858i \(0.543074\pi\)
\(230\) −6.75440 −0.445372
\(231\) 27.1182 1.78425
\(232\) −1.95342 −0.128249
\(233\) −25.4843 −1.66953 −0.834764 0.550607i \(-0.814396\pi\)
−0.834764 + 0.550607i \(0.814396\pi\)
\(234\) −5.88491 −0.384708
\(235\) 2.60823 0.170142
\(236\) −9.44473 −0.614800
\(237\) −29.6734 −1.92749
\(238\) 11.9986 0.777752
\(239\) −11.3288 −0.732801 −0.366400 0.930457i \(-0.619410\pi\)
−0.366400 + 0.930457i \(0.619410\pi\)
\(240\) 2.28691 0.147620
\(241\) 17.6302 1.13566 0.567829 0.823146i \(-0.307783\pi\)
0.567829 + 0.823146i \(0.307783\pi\)
\(242\) 0.690448 0.0443837
\(243\) −19.2262 −1.23336
\(244\) 9.42299 0.603245
\(245\) 5.02795 0.321224
\(246\) 2.04165 0.130171
\(247\) −2.83965 −0.180682
\(248\) 4.65022 0.295289
\(249\) −23.1993 −1.47020
\(250\) 1.00000 0.0632456
\(251\) 20.1405 1.27126 0.635629 0.771995i \(-0.280741\pi\)
0.635629 + 0.771995i \(0.280741\pi\)
\(252\) −7.73385 −0.487187
\(253\) 23.0942 1.45192
\(254\) 13.4391 0.843244
\(255\) −7.91196 −0.495466
\(256\) 1.00000 0.0625000
\(257\) 22.8286 1.42401 0.712005 0.702175i \(-0.247787\pi\)
0.712005 + 0.702175i \(0.247787\pi\)
\(258\) 23.3086 1.45113
\(259\) 23.7622 1.47651
\(260\) −2.63900 −0.163664
\(261\) −4.35609 −0.269635
\(262\) 6.82635 0.421733
\(263\) −0.616108 −0.0379909 −0.0189954 0.999820i \(-0.506047\pi\)
−0.0189954 + 0.999820i \(0.506047\pi\)
\(264\) −7.81926 −0.481242
\(265\) −14.2976 −0.878295
\(266\) −3.73182 −0.228813
\(267\) 1.04458 0.0639270
\(268\) 9.09482 0.555554
\(269\) −12.1415 −0.740281 −0.370141 0.928976i \(-0.620691\pi\)
−0.370141 + 0.928976i \(0.620691\pi\)
\(270\) −1.76098 −0.107170
\(271\) −2.61919 −0.159104 −0.0795521 0.996831i \(-0.525349\pi\)
−0.0795521 + 0.996831i \(0.525349\pi\)
\(272\) −3.45967 −0.209773
\(273\) 20.9308 1.26679
\(274\) −1.49274 −0.0901798
\(275\) −3.41913 −0.206181
\(276\) −15.4467 −0.929784
\(277\) 12.2159 0.733985 0.366993 0.930224i \(-0.380387\pi\)
0.366993 + 0.930224i \(0.380387\pi\)
\(278\) 3.60693 0.216329
\(279\) 10.3699 0.620828
\(280\) −3.46813 −0.207261
\(281\) 10.2239 0.609904 0.304952 0.952368i \(-0.401360\pi\)
0.304952 + 0.952368i \(0.401360\pi\)
\(282\) 5.96479 0.355198
\(283\) 20.7073 1.23092 0.615462 0.788167i \(-0.288970\pi\)
0.615462 + 0.788167i \(0.288970\pi\)
\(284\) −11.7865 −0.699398
\(285\) 2.46079 0.145765
\(286\) 9.02309 0.533546
\(287\) −3.09619 −0.182763
\(288\) 2.22998 0.131403
\(289\) −5.03071 −0.295924
\(290\) −1.95342 −0.114709
\(291\) 38.0209 2.22883
\(292\) 3.96524 0.232048
\(293\) −24.4481 −1.42827 −0.714136 0.700007i \(-0.753180\pi\)
−0.714136 + 0.700007i \(0.753180\pi\)
\(294\) 11.4985 0.670605
\(295\) −9.44473 −0.549893
\(296\) −6.85159 −0.398241
\(297\) 6.02102 0.349375
\(298\) −2.87791 −0.166713
\(299\) 17.8249 1.03084
\(300\) 2.28691 0.132035
\(301\) −35.3478 −2.03741
\(302\) −16.4331 −0.945621
\(303\) −28.2210 −1.62126
\(304\) 1.07603 0.0617146
\(305\) 9.42299 0.539559
\(306\) −7.71497 −0.441035
\(307\) −0.655961 −0.0374376 −0.0187188 0.999825i \(-0.505959\pi\)
−0.0187188 + 0.999825i \(0.505959\pi\)
\(308\) 11.8580 0.675672
\(309\) 20.5794 1.17072
\(310\) 4.65022 0.264115
\(311\) −7.06795 −0.400787 −0.200393 0.979716i \(-0.564222\pi\)
−0.200393 + 0.979716i \(0.564222\pi\)
\(312\) −6.03517 −0.341674
\(313\) 22.6761 1.28173 0.640863 0.767655i \(-0.278577\pi\)
0.640863 + 0.767655i \(0.278577\pi\)
\(314\) 12.2295 0.690151
\(315\) −7.73385 −0.435753
\(316\) −12.9753 −0.729917
\(317\) 9.20507 0.517008 0.258504 0.966010i \(-0.416770\pi\)
0.258504 + 0.966010i \(0.416770\pi\)
\(318\) −32.6974 −1.83358
\(319\) 6.67901 0.373953
\(320\) 1.00000 0.0559017
\(321\) −7.27783 −0.406209
\(322\) 23.4252 1.30543
\(323\) −3.72271 −0.207137
\(324\) −10.7171 −0.595396
\(325\) −2.63900 −0.146385
\(326\) −1.53692 −0.0851223
\(327\) 3.37352 0.186556
\(328\) 0.892755 0.0492942
\(329\) −9.04567 −0.498704
\(330\) −7.81926 −0.430436
\(331\) 9.28864 0.510550 0.255275 0.966869i \(-0.417834\pi\)
0.255275 + 0.966869i \(0.417834\pi\)
\(332\) −10.1444 −0.556746
\(333\) −15.2789 −0.837278
\(334\) 5.13478 0.280963
\(335\) 9.09482 0.496903
\(336\) −7.93132 −0.432689
\(337\) 3.36720 0.183423 0.0917115 0.995786i \(-0.470766\pi\)
0.0917115 + 0.995786i \(0.470766\pi\)
\(338\) −6.03568 −0.328298
\(339\) −12.2556 −0.665633
\(340\) −3.45967 −0.187627
\(341\) −15.8997 −0.861017
\(342\) 2.39952 0.129751
\(343\) 6.83935 0.369290
\(344\) 10.1922 0.549525
\(345\) −15.4467 −0.831624
\(346\) −0.0718874 −0.00386469
\(347\) 7.07999 0.380074 0.190037 0.981777i \(-0.439139\pi\)
0.190037 + 0.981777i \(0.439139\pi\)
\(348\) −4.46731 −0.239473
\(349\) −30.8890 −1.65345 −0.826724 0.562607i \(-0.809798\pi\)
−0.826724 + 0.562607i \(0.809798\pi\)
\(350\) −3.46813 −0.185379
\(351\) 4.64722 0.248051
\(352\) −3.41913 −0.182240
\(353\) −10.2224 −0.544082 −0.272041 0.962286i \(-0.587699\pi\)
−0.272041 + 0.962286i \(0.587699\pi\)
\(354\) −21.5993 −1.14799
\(355\) −11.7865 −0.625561
\(356\) 0.456762 0.0242084
\(357\) 27.4397 1.45226
\(358\) −5.16654 −0.273060
\(359\) −7.35821 −0.388351 −0.194176 0.980967i \(-0.562203\pi\)
−0.194176 + 0.980967i \(0.562203\pi\)
\(360\) 2.22998 0.117530
\(361\) −17.8422 −0.939061
\(362\) 1.51191 0.0794644
\(363\) 1.57900 0.0828758
\(364\) 9.15240 0.479716
\(365\) 3.96524 0.207550
\(366\) 21.5496 1.12641
\(367\) 24.7672 1.29284 0.646420 0.762982i \(-0.276266\pi\)
0.646420 + 0.762982i \(0.276266\pi\)
\(368\) −6.75440 −0.352097
\(369\) 1.99082 0.103638
\(370\) −6.85159 −0.356197
\(371\) 49.5860 2.57438
\(372\) 10.6347 0.551381
\(373\) 0.888462 0.0460028 0.0230014 0.999735i \(-0.492678\pi\)
0.0230014 + 0.999735i \(0.492678\pi\)
\(374\) 11.8290 0.611665
\(375\) 2.28691 0.118096
\(376\) 2.60823 0.134509
\(377\) 5.15509 0.265500
\(378\) 6.10731 0.314126
\(379\) −7.54193 −0.387403 −0.193701 0.981061i \(-0.562049\pi\)
−0.193701 + 0.981061i \(0.562049\pi\)
\(380\) 1.07603 0.0551993
\(381\) 30.7340 1.57455
\(382\) 13.0731 0.668878
\(383\) 16.9073 0.863924 0.431962 0.901892i \(-0.357821\pi\)
0.431962 + 0.901892i \(0.357821\pi\)
\(384\) 2.28691 0.116704
\(385\) 11.8580 0.604339
\(386\) −1.07841 −0.0548898
\(387\) 22.7283 1.15534
\(388\) 16.6254 0.844029
\(389\) −10.4172 −0.528175 −0.264088 0.964499i \(-0.585071\pi\)
−0.264088 + 0.964499i \(0.585071\pi\)
\(390\) −6.03517 −0.305603
\(391\) 23.3680 1.18177
\(392\) 5.02795 0.253950
\(393\) 15.6113 0.787485
\(394\) 13.5161 0.680930
\(395\) −12.9753 −0.652857
\(396\) −7.62458 −0.383149
\(397\) 19.4309 0.975208 0.487604 0.873065i \(-0.337871\pi\)
0.487604 + 0.873065i \(0.337871\pi\)
\(398\) −20.3859 −1.02185
\(399\) −8.53435 −0.427252
\(400\) 1.00000 0.0500000
\(401\) −9.96824 −0.497790 −0.248895 0.968530i \(-0.580067\pi\)
−0.248895 + 0.968530i \(0.580067\pi\)
\(402\) 20.7991 1.03736
\(403\) −12.2719 −0.611309
\(404\) −12.3402 −0.613949
\(405\) −10.7171 −0.532539
\(406\) 6.77473 0.336224
\(407\) 23.4265 1.16121
\(408\) −7.91196 −0.391700
\(409\) −24.5937 −1.21608 −0.608039 0.793907i \(-0.708044\pi\)
−0.608039 + 0.793907i \(0.708044\pi\)
\(410\) 0.892755 0.0440900
\(411\) −3.41377 −0.168389
\(412\) 8.99878 0.443338
\(413\) 32.7556 1.61180
\(414\) −15.0621 −0.740264
\(415\) −10.1444 −0.497968
\(416\) −2.63900 −0.129388
\(417\) 8.24873 0.403942
\(418\) −3.67909 −0.179950
\(419\) 26.5545 1.29727 0.648636 0.761099i \(-0.275340\pi\)
0.648636 + 0.761099i \(0.275340\pi\)
\(420\) −7.93132 −0.387009
\(421\) −9.27013 −0.451798 −0.225899 0.974151i \(-0.572532\pi\)
−0.225899 + 0.974151i \(0.572532\pi\)
\(422\) −14.3190 −0.697038
\(423\) 5.81628 0.282797
\(424\) −14.2976 −0.694353
\(425\) −3.45967 −0.167818
\(426\) −26.9546 −1.30596
\(427\) −32.6802 −1.58151
\(428\) −3.18238 −0.153826
\(429\) 20.6350 0.996268
\(430\) 10.1922 0.491510
\(431\) 10.0647 0.484802 0.242401 0.970176i \(-0.422065\pi\)
0.242401 + 0.970176i \(0.422065\pi\)
\(432\) −1.76098 −0.0847251
\(433\) 17.6499 0.848198 0.424099 0.905616i \(-0.360591\pi\)
0.424099 + 0.905616i \(0.360591\pi\)
\(434\) −16.1276 −0.774149
\(435\) −4.46731 −0.214191
\(436\) 1.47514 0.0706465
\(437\) −7.26795 −0.347673
\(438\) 9.06817 0.433294
\(439\) 24.8537 1.18620 0.593102 0.805127i \(-0.297903\pi\)
0.593102 + 0.805127i \(0.297903\pi\)
\(440\) −3.41913 −0.163001
\(441\) 11.2122 0.533914
\(442\) 9.13006 0.434273
\(443\) 21.0429 0.999777 0.499888 0.866090i \(-0.333374\pi\)
0.499888 + 0.866090i \(0.333374\pi\)
\(444\) −15.6690 −0.743618
\(445\) 0.456762 0.0216526
\(446\) 12.1093 0.573392
\(447\) −6.58152 −0.311295
\(448\) −3.46813 −0.163854
\(449\) −6.39622 −0.301856 −0.150928 0.988545i \(-0.548226\pi\)
−0.150928 + 0.988545i \(0.548226\pi\)
\(450\) 2.22998 0.105122
\(451\) −3.05245 −0.143734
\(452\) −5.35901 −0.252067
\(453\) −37.5812 −1.76572
\(454\) 0.00202746 9.51532e−5 0
\(455\) 9.15240 0.429071
\(456\) 2.46079 0.115237
\(457\) −20.1485 −0.942508 −0.471254 0.881998i \(-0.656198\pi\)
−0.471254 + 0.881998i \(0.656198\pi\)
\(458\) −4.08309 −0.190790
\(459\) 6.09240 0.284369
\(460\) −6.75440 −0.314926
\(461\) −4.34495 −0.202365 −0.101182 0.994868i \(-0.532263\pi\)
−0.101182 + 0.994868i \(0.532263\pi\)
\(462\) 27.1182 1.26165
\(463\) 2.35773 0.109573 0.0547864 0.998498i \(-0.482552\pi\)
0.0547864 + 0.998498i \(0.482552\pi\)
\(464\) −1.95342 −0.0906854
\(465\) 10.6347 0.493170
\(466\) −25.4843 −1.18054
\(467\) −6.22229 −0.287933 −0.143967 0.989583i \(-0.545986\pi\)
−0.143967 + 0.989583i \(0.545986\pi\)
\(468\) −5.88491 −0.272030
\(469\) −31.5420 −1.45648
\(470\) 2.60823 0.120308
\(471\) 27.9678 1.28869
\(472\) −9.44473 −0.434729
\(473\) −34.8483 −1.60233
\(474\) −29.6734 −1.36294
\(475\) 1.07603 0.0493717
\(476\) 11.9986 0.549954
\(477\) −31.8833 −1.45984
\(478\) −11.3288 −0.518169
\(479\) −20.8295 −0.951725 −0.475862 0.879520i \(-0.657864\pi\)
−0.475862 + 0.879520i \(0.657864\pi\)
\(480\) 2.28691 0.104383
\(481\) 18.0814 0.824439
\(482\) 17.6302 0.803032
\(483\) 53.5713 2.43758
\(484\) 0.690448 0.0313840
\(485\) 16.6254 0.754922
\(486\) −19.2262 −0.872119
\(487\) −3.26784 −0.148080 −0.0740401 0.997255i \(-0.523589\pi\)
−0.0740401 + 0.997255i \(0.523589\pi\)
\(488\) 9.42299 0.426559
\(489\) −3.51481 −0.158945
\(490\) 5.02795 0.227139
\(491\) 24.0782 1.08663 0.543317 0.839528i \(-0.317168\pi\)
0.543317 + 0.839528i \(0.317168\pi\)
\(492\) 2.04165 0.0920449
\(493\) 6.75819 0.304374
\(494\) −2.83965 −0.127762
\(495\) −7.62458 −0.342699
\(496\) 4.65022 0.208801
\(497\) 40.8770 1.83359
\(498\) −23.1993 −1.03959
\(499\) 18.8538 0.844012 0.422006 0.906593i \(-0.361326\pi\)
0.422006 + 0.906593i \(0.361326\pi\)
\(500\) 1.00000 0.0447214
\(501\) 11.7428 0.524629
\(502\) 20.1405 0.898915
\(503\) −38.9095 −1.73489 −0.867444 0.497534i \(-0.834239\pi\)
−0.867444 + 0.497534i \(0.834239\pi\)
\(504\) −7.73385 −0.344493
\(505\) −12.3402 −0.549133
\(506\) 23.0942 1.02666
\(507\) −13.8031 −0.613016
\(508\) 13.4391 0.596263
\(509\) −3.71681 −0.164745 −0.0823724 0.996602i \(-0.526250\pi\)
−0.0823724 + 0.996602i \(0.526250\pi\)
\(510\) −7.91196 −0.350347
\(511\) −13.7520 −0.608352
\(512\) 1.00000 0.0441942
\(513\) −1.89487 −0.0836605
\(514\) 22.8286 1.00693
\(515\) 8.99878 0.396534
\(516\) 23.3086 1.02610
\(517\) −8.91786 −0.392207
\(518\) 23.7622 1.04405
\(519\) −0.164400 −0.00721637
\(520\) −2.63900 −0.115728
\(521\) −15.6307 −0.684793 −0.342396 0.939556i \(-0.611239\pi\)
−0.342396 + 0.939556i \(0.611239\pi\)
\(522\) −4.35609 −0.190661
\(523\) −15.6826 −0.685753 −0.342877 0.939380i \(-0.611401\pi\)
−0.342877 + 0.939380i \(0.611401\pi\)
\(524\) 6.82635 0.298211
\(525\) −7.93132 −0.346151
\(526\) −0.616108 −0.0268636
\(527\) −16.0882 −0.700813
\(528\) −7.81926 −0.340289
\(529\) 22.6219 0.983562
\(530\) −14.2976 −0.621049
\(531\) −21.0615 −0.913992
\(532\) −3.73182 −0.161795
\(533\) −2.35598 −0.102049
\(534\) 1.04458 0.0452032
\(535\) −3.18238 −0.137586
\(536\) 9.09482 0.392836
\(537\) −11.8154 −0.509874
\(538\) −12.1415 −0.523458
\(539\) −17.1912 −0.740477
\(540\) −1.76098 −0.0757805
\(541\) 31.4126 1.35053 0.675266 0.737575i \(-0.264029\pi\)
0.675266 + 0.737575i \(0.264029\pi\)
\(542\) −2.61919 −0.112504
\(543\) 3.45762 0.148381
\(544\) −3.45967 −0.148332
\(545\) 1.47514 0.0631881
\(546\) 20.9308 0.895754
\(547\) −36.9988 −1.58195 −0.790977 0.611846i \(-0.790427\pi\)
−0.790977 + 0.611846i \(0.790427\pi\)
\(548\) −1.49274 −0.0637668
\(549\) 21.0130 0.896815
\(550\) −3.41913 −0.145792
\(551\) −2.10195 −0.0895459
\(552\) −15.4467 −0.657457
\(553\) 45.0000 1.91360
\(554\) 12.2159 0.519006
\(555\) −15.6690 −0.665112
\(556\) 3.60693 0.152968
\(557\) −26.4800 −1.12199 −0.560996 0.827818i \(-0.689582\pi\)
−0.560996 + 0.827818i \(0.689582\pi\)
\(558\) 10.3699 0.438992
\(559\) −26.8971 −1.13763
\(560\) −3.46813 −0.146555
\(561\) 27.0520 1.14214
\(562\) 10.2239 0.431268
\(563\) 35.0804 1.47846 0.739230 0.673453i \(-0.235189\pi\)
0.739230 + 0.673453i \(0.235189\pi\)
\(564\) 5.96479 0.251163
\(565\) −5.35901 −0.225455
\(566\) 20.7073 0.870394
\(567\) 37.1684 1.56093
\(568\) −11.7865 −0.494549
\(569\) −10.0633 −0.421876 −0.210938 0.977499i \(-0.567652\pi\)
−0.210938 + 0.977499i \(0.567652\pi\)
\(570\) 2.46079 0.103071
\(571\) 4.19294 0.175469 0.0877346 0.996144i \(-0.472037\pi\)
0.0877346 + 0.996144i \(0.472037\pi\)
\(572\) 9.02309 0.377274
\(573\) 29.8970 1.24897
\(574\) −3.09619 −0.129233
\(575\) −6.75440 −0.281678
\(576\) 2.22998 0.0929157
\(577\) −12.6805 −0.527897 −0.263949 0.964537i \(-0.585025\pi\)
−0.263949 + 0.964537i \(0.585025\pi\)
\(578\) −5.03071 −0.209250
\(579\) −2.46624 −0.102493
\(580\) −1.95342 −0.0811115
\(581\) 35.1821 1.45960
\(582\) 38.0209 1.57602
\(583\) 48.8854 2.02463
\(584\) 3.96524 0.164083
\(585\) −5.88491 −0.243311
\(586\) −24.4481 −1.00994
\(587\) 14.4013 0.594404 0.297202 0.954815i \(-0.403947\pi\)
0.297202 + 0.954815i \(0.403947\pi\)
\(588\) 11.4985 0.474189
\(589\) 5.00378 0.206177
\(590\) −9.44473 −0.388833
\(591\) 30.9101 1.27147
\(592\) −6.85159 −0.281599
\(593\) −18.3748 −0.754563 −0.377282 0.926099i \(-0.623141\pi\)
−0.377282 + 0.926099i \(0.623141\pi\)
\(594\) 6.02102 0.247045
\(595\) 11.9986 0.491894
\(596\) −2.87791 −0.117884
\(597\) −46.6207 −1.90806
\(598\) 17.8249 0.728913
\(599\) −25.4849 −1.04129 −0.520643 0.853774i \(-0.674308\pi\)
−0.520643 + 0.853774i \(0.674308\pi\)
\(600\) 2.28691 0.0933629
\(601\) −1.00000 −0.0407909
\(602\) −35.3478 −1.44067
\(603\) 20.2812 0.825915
\(604\) −16.4331 −0.668655
\(605\) 0.690448 0.0280707
\(606\) −28.2210 −1.14640
\(607\) −12.5100 −0.507764 −0.253882 0.967235i \(-0.581708\pi\)
−0.253882 + 0.967235i \(0.581708\pi\)
\(608\) 1.07603 0.0436388
\(609\) 15.4932 0.627817
\(610\) 9.42299 0.381526
\(611\) −6.88311 −0.278461
\(612\) −7.71497 −0.311859
\(613\) −38.2008 −1.54292 −0.771458 0.636280i \(-0.780472\pi\)
−0.771458 + 0.636280i \(0.780472\pi\)
\(614\) −0.655961 −0.0264724
\(615\) 2.04165 0.0823275
\(616\) 11.8580 0.477772
\(617\) −40.2974 −1.62231 −0.811156 0.584829i \(-0.801161\pi\)
−0.811156 + 0.584829i \(0.801161\pi\)
\(618\) 20.5794 0.827827
\(619\) −22.1722 −0.891174 −0.445587 0.895239i \(-0.647005\pi\)
−0.445587 + 0.895239i \(0.647005\pi\)
\(620\) 4.65022 0.186757
\(621\) 11.8944 0.477304
\(622\) −7.06795 −0.283399
\(623\) −1.58411 −0.0634661
\(624\) −6.03517 −0.241600
\(625\) 1.00000 0.0400000
\(626\) 22.6761 0.906317
\(627\) −8.41377 −0.336013
\(628\) 12.2295 0.488011
\(629\) 23.7042 0.945149
\(630\) −7.73385 −0.308124
\(631\) −47.0690 −1.87379 −0.936893 0.349615i \(-0.886312\pi\)
−0.936893 + 0.349615i \(0.886312\pi\)
\(632\) −12.9753 −0.516129
\(633\) −32.7463 −1.30155
\(634\) 9.20507 0.365580
\(635\) 13.4391 0.533314
\(636\) −32.6974 −1.29654
\(637\) −13.2687 −0.525727
\(638\) 6.67901 0.264424
\(639\) −26.2835 −1.03976
\(640\) 1.00000 0.0395285
\(641\) −11.6058 −0.458402 −0.229201 0.973379i \(-0.573611\pi\)
−0.229201 + 0.973379i \(0.573611\pi\)
\(642\) −7.27783 −0.287233
\(643\) 16.3522 0.644867 0.322433 0.946592i \(-0.395499\pi\)
0.322433 + 0.946592i \(0.395499\pi\)
\(644\) 23.4252 0.923080
\(645\) 23.3086 0.917776
\(646\) −3.72271 −0.146468
\(647\) 43.5027 1.71027 0.855134 0.518407i \(-0.173475\pi\)
0.855134 + 0.518407i \(0.173475\pi\)
\(648\) −10.7171 −0.421009
\(649\) 32.2928 1.26760
\(650\) −2.63900 −0.103510
\(651\) −36.8824 −1.44553
\(652\) −1.53692 −0.0601906
\(653\) 18.4089 0.720397 0.360199 0.932876i \(-0.382709\pi\)
0.360199 + 0.932876i \(0.382709\pi\)
\(654\) 3.37352 0.131915
\(655\) 6.82635 0.266728
\(656\) 0.892755 0.0348562
\(657\) 8.84240 0.344975
\(658\) −9.04567 −0.352637
\(659\) −32.7240 −1.27475 −0.637373 0.770556i \(-0.719979\pi\)
−0.637373 + 0.770556i \(0.719979\pi\)
\(660\) −7.81926 −0.304364
\(661\) −19.1635 −0.745374 −0.372687 0.927957i \(-0.621563\pi\)
−0.372687 + 0.927957i \(0.621563\pi\)
\(662\) 9.28864 0.361013
\(663\) 20.8797 0.810899
\(664\) −10.1444 −0.393679
\(665\) −3.73182 −0.144714
\(666\) −15.2789 −0.592045
\(667\) 13.1942 0.510882
\(668\) 5.13478 0.198671
\(669\) 27.6929 1.07067
\(670\) 9.09482 0.351363
\(671\) −32.2184 −1.24378
\(672\) −7.93132 −0.305957
\(673\) 41.2479 1.58999 0.794995 0.606616i \(-0.207473\pi\)
0.794995 + 0.606616i \(0.207473\pi\)
\(674\) 3.36720 0.129700
\(675\) −1.76098 −0.0677801
\(676\) −6.03568 −0.232141
\(677\) −13.4359 −0.516382 −0.258191 0.966094i \(-0.583126\pi\)
−0.258191 + 0.966094i \(0.583126\pi\)
\(678\) −12.2556 −0.470673
\(679\) −57.6592 −2.21276
\(680\) −3.45967 −0.132672
\(681\) 0.00463662 0.000177676 0
\(682\) −15.8997 −0.608831
\(683\) −5.40108 −0.206667 −0.103333 0.994647i \(-0.532951\pi\)
−0.103333 + 0.994647i \(0.532951\pi\)
\(684\) 2.39952 0.0917481
\(685\) −1.49274 −0.0570347
\(686\) 6.83935 0.261128
\(687\) −9.33768 −0.356255
\(688\) 10.1922 0.388573
\(689\) 37.7314 1.43745
\(690\) −15.4467 −0.588047
\(691\) 6.15996 0.234336 0.117168 0.993112i \(-0.462618\pi\)
0.117168 + 0.993112i \(0.462618\pi\)
\(692\) −0.0718874 −0.00273275
\(693\) 26.4430 1.00449
\(694\) 7.07999 0.268753
\(695\) 3.60693 0.136819
\(696\) −4.46731 −0.169333
\(697\) −3.08863 −0.116990
\(698\) −30.8890 −1.16916
\(699\) −58.2803 −2.20436
\(700\) −3.46813 −0.131083
\(701\) 9.14301 0.345327 0.172663 0.984981i \(-0.444763\pi\)
0.172663 + 0.984981i \(0.444763\pi\)
\(702\) 4.64722 0.175398
\(703\) −7.37253 −0.278060
\(704\) −3.41913 −0.128863
\(705\) 5.96479 0.224647
\(706\) −10.2224 −0.384724
\(707\) 42.7975 1.60957
\(708\) −21.5993 −0.811751
\(709\) −14.8939 −0.559350 −0.279675 0.960095i \(-0.590227\pi\)
−0.279675 + 0.960095i \(0.590227\pi\)
\(710\) −11.7865 −0.442338
\(711\) −28.9346 −1.08513
\(712\) 0.456762 0.0171179
\(713\) −31.4094 −1.17629
\(714\) 27.4397 1.02691
\(715\) 9.02309 0.337444
\(716\) −5.16654 −0.193083
\(717\) −25.9081 −0.967554
\(718\) −7.35821 −0.274606
\(719\) 50.8962 1.89811 0.949053 0.315116i \(-0.102043\pi\)
0.949053 + 0.315116i \(0.102043\pi\)
\(720\) 2.22998 0.0831063
\(721\) −31.2090 −1.16228
\(722\) −17.8422 −0.664016
\(723\) 40.3187 1.49947
\(724\) 1.51191 0.0561898
\(725\) −1.95342 −0.0725483
\(726\) 1.57900 0.0586020
\(727\) −28.3480 −1.05137 −0.525684 0.850680i \(-0.676190\pi\)
−0.525684 + 0.850680i \(0.676190\pi\)
\(728\) 9.15240 0.339211
\(729\) −11.8173 −0.437679
\(730\) 3.96524 0.146760
\(731\) −35.2615 −1.30419
\(732\) 21.5496 0.796495
\(733\) −22.1043 −0.816442 −0.408221 0.912883i \(-0.633851\pi\)
−0.408221 + 0.912883i \(0.633851\pi\)
\(734\) 24.7672 0.914175
\(735\) 11.4985 0.424128
\(736\) −6.75440 −0.248970
\(737\) −31.0964 −1.14545
\(738\) 1.99082 0.0732832
\(739\) 43.4697 1.59906 0.799529 0.600627i \(-0.205082\pi\)
0.799529 + 0.600627i \(0.205082\pi\)
\(740\) −6.85159 −0.251870
\(741\) −6.49403 −0.238564
\(742\) 49.5860 1.82036
\(743\) −11.3533 −0.416514 −0.208257 0.978074i \(-0.566779\pi\)
−0.208257 + 0.978074i \(0.566779\pi\)
\(744\) 10.6347 0.389885
\(745\) −2.87791 −0.105438
\(746\) 0.888462 0.0325289
\(747\) −22.6217 −0.827686
\(748\) 11.8290 0.432513
\(749\) 11.0369 0.403280
\(750\) 2.28691 0.0835063
\(751\) 35.7866 1.30587 0.652935 0.757414i \(-0.273537\pi\)
0.652935 + 0.757414i \(0.273537\pi\)
\(752\) 2.60823 0.0951122
\(753\) 46.0596 1.67851
\(754\) 5.15509 0.187737
\(755\) −16.4331 −0.598063
\(756\) 6.10731 0.222121
\(757\) 28.1509 1.02316 0.511581 0.859235i \(-0.329060\pi\)
0.511581 + 0.859235i \(0.329060\pi\)
\(758\) −7.54193 −0.273935
\(759\) 52.8144 1.91704
\(760\) 1.07603 0.0390318
\(761\) −11.7505 −0.425956 −0.212978 0.977057i \(-0.568316\pi\)
−0.212978 + 0.977057i \(0.568316\pi\)
\(762\) 30.7340 1.11338
\(763\) −5.11599 −0.185211
\(764\) 13.0731 0.472968
\(765\) −7.71497 −0.278935
\(766\) 16.9073 0.610886
\(767\) 24.9246 0.899977
\(768\) 2.28691 0.0825219
\(769\) −31.9995 −1.15393 −0.576966 0.816768i \(-0.695764\pi\)
−0.576966 + 0.816768i \(0.695764\pi\)
\(770\) 11.8580 0.427333
\(771\) 52.2071 1.88019
\(772\) −1.07841 −0.0388130
\(773\) 42.9219 1.54379 0.771897 0.635747i \(-0.219308\pi\)
0.771897 + 0.635747i \(0.219308\pi\)
\(774\) 22.7283 0.816951
\(775\) 4.65022 0.167041
\(776\) 16.6254 0.596818
\(777\) 54.3422 1.94951
\(778\) −10.4172 −0.373476
\(779\) 0.960633 0.0344182
\(780\) −6.03517 −0.216094
\(781\) 40.2995 1.44203
\(782\) 23.3680 0.835637
\(783\) 3.43994 0.122933
\(784\) 5.02795 0.179569
\(785\) 12.2295 0.436490
\(786\) 15.6113 0.556836
\(787\) −30.2128 −1.07697 −0.538484 0.842636i \(-0.681003\pi\)
−0.538484 + 0.842636i \(0.681003\pi\)
\(788\) 13.5161 0.481490
\(789\) −1.40899 −0.0501612
\(790\) −12.9753 −0.461640
\(791\) 18.5858 0.660833
\(792\) −7.62458 −0.270928
\(793\) −24.8673 −0.883063
\(794\) 19.4309 0.689576
\(795\) −32.6974 −1.15966
\(796\) −20.3859 −0.722558
\(797\) 32.9373 1.16670 0.583349 0.812222i \(-0.301742\pi\)
0.583349 + 0.812222i \(0.301742\pi\)
\(798\) −8.53435 −0.302113
\(799\) −9.02359 −0.319232
\(800\) 1.00000 0.0353553
\(801\) 1.01857 0.0359894
\(802\) −9.96824 −0.351991
\(803\) −13.5577 −0.478440
\(804\) 20.7991 0.733526
\(805\) 23.4252 0.825628
\(806\) −12.2719 −0.432260
\(807\) −27.7666 −0.977431
\(808\) −12.3402 −0.434127
\(809\) 11.9501 0.420143 0.210071 0.977686i \(-0.432630\pi\)
0.210071 + 0.977686i \(0.432630\pi\)
\(810\) −10.7171 −0.376562
\(811\) −26.2408 −0.921439 −0.460719 0.887546i \(-0.652409\pi\)
−0.460719 + 0.887546i \(0.652409\pi\)
\(812\) 6.77473 0.237746
\(813\) −5.98985 −0.210073
\(814\) 23.4265 0.821098
\(815\) −1.53692 −0.0538361
\(816\) −7.91196 −0.276974
\(817\) 10.9671 0.383690
\(818\) −24.5937 −0.859897
\(819\) 20.4096 0.713171
\(820\) 0.892755 0.0311764
\(821\) −27.9055 −0.973909 −0.486954 0.873427i \(-0.661892\pi\)
−0.486954 + 0.873427i \(0.661892\pi\)
\(822\) −3.41377 −0.119069
\(823\) 16.9874 0.592144 0.296072 0.955166i \(-0.404323\pi\)
0.296072 + 0.955166i \(0.404323\pi\)
\(824\) 8.99878 0.313487
\(825\) −7.81926 −0.272232
\(826\) 32.7556 1.13971
\(827\) −36.8601 −1.28175 −0.640876 0.767645i \(-0.721429\pi\)
−0.640876 + 0.767645i \(0.721429\pi\)
\(828\) −15.0621 −0.523446
\(829\) −17.1133 −0.594369 −0.297184 0.954820i \(-0.596048\pi\)
−0.297184 + 0.954820i \(0.596048\pi\)
\(830\) −10.1444 −0.352117
\(831\) 27.9368 0.969118
\(832\) −2.63900 −0.0914909
\(833\) −17.3950 −0.602701
\(834\) 8.24873 0.285630
\(835\) 5.13478 0.177696
\(836\) −3.67909 −0.127244
\(837\) −8.18894 −0.283051
\(838\) 26.5545 0.917310
\(839\) 26.2070 0.904765 0.452383 0.891824i \(-0.350574\pi\)
0.452383 + 0.891824i \(0.350574\pi\)
\(840\) −7.93132 −0.273657
\(841\) −25.1841 −0.868419
\(842\) −9.27013 −0.319470
\(843\) 23.3811 0.805287
\(844\) −14.3190 −0.492880
\(845\) −6.03568 −0.207634
\(846\) 5.81628 0.199968
\(847\) −2.39457 −0.0822783
\(848\) −14.2976 −0.490982
\(849\) 47.3559 1.62525
\(850\) −3.45967 −0.118666
\(851\) 46.2784 1.58640
\(852\) −26.9546 −0.923451
\(853\) −46.6720 −1.59802 −0.799010 0.601318i \(-0.794642\pi\)
−0.799010 + 0.601318i \(0.794642\pi\)
\(854\) −32.6802 −1.11829
\(855\) 2.39952 0.0820620
\(856\) −3.18238 −0.108772
\(857\) −51.6221 −1.76338 −0.881689 0.471831i \(-0.843593\pi\)
−0.881689 + 0.471831i \(0.843593\pi\)
\(858\) 20.6350 0.704468
\(859\) −0.0411982 −0.00140567 −0.000702833 1.00000i \(-0.500224\pi\)
−0.000702833 1.00000i \(0.500224\pi\)
\(860\) 10.1922 0.347550
\(861\) −7.08073 −0.241311
\(862\) 10.0647 0.342806
\(863\) 10.3915 0.353731 0.176866 0.984235i \(-0.443404\pi\)
0.176866 + 0.984235i \(0.443404\pi\)
\(864\) −1.76098 −0.0599097
\(865\) −0.0718874 −0.00244424
\(866\) 17.6499 0.599766
\(867\) −11.5048 −0.390724
\(868\) −16.1276 −0.547406
\(869\) 44.3642 1.50495
\(870\) −4.46731 −0.151456
\(871\) −24.0012 −0.813250
\(872\) 1.47514 0.0499546
\(873\) 37.0743 1.25478
\(874\) −7.26795 −0.245842
\(875\) −3.46813 −0.117244
\(876\) 9.06817 0.306385
\(877\) −39.5376 −1.33509 −0.667544 0.744570i \(-0.732655\pi\)
−0.667544 + 0.744570i \(0.732655\pi\)
\(878\) 24.8537 0.838773
\(879\) −55.9106 −1.88582
\(880\) −3.41913 −0.115259
\(881\) 9.99559 0.336760 0.168380 0.985722i \(-0.446146\pi\)
0.168380 + 0.985722i \(0.446146\pi\)
\(882\) 11.2122 0.377534
\(883\) −28.9383 −0.973850 −0.486925 0.873444i \(-0.661882\pi\)
−0.486925 + 0.873444i \(0.661882\pi\)
\(884\) 9.13006 0.307077
\(885\) −21.5993 −0.726052
\(886\) 21.0429 0.706949
\(887\) −16.9411 −0.568827 −0.284413 0.958702i \(-0.591799\pi\)
−0.284413 + 0.958702i \(0.591799\pi\)
\(888\) −15.6690 −0.525817
\(889\) −46.6086 −1.56320
\(890\) 0.456762 0.0153107
\(891\) 36.6433 1.22760
\(892\) 12.1093 0.405450
\(893\) 2.80653 0.0939170
\(894\) −6.58152 −0.220119
\(895\) −5.16654 −0.172699
\(896\) −3.46813 −0.115862
\(897\) 40.7639 1.36107
\(898\) −6.39622 −0.213445
\(899\) −9.08385 −0.302963
\(900\) 2.22998 0.0743325
\(901\) 49.4650 1.64792
\(902\) −3.05245 −0.101635
\(903\) −80.8373 −2.69010
\(904\) −5.35901 −0.178238
\(905\) 1.51191 0.0502577
\(906\) −37.5812 −1.24855
\(907\) −35.1477 −1.16706 −0.583531 0.812091i \(-0.698329\pi\)
−0.583531 + 0.812091i \(0.698329\pi\)
\(908\) 0.00202746 6.72835e−5 0
\(909\) −27.5184 −0.912727
\(910\) 9.15240 0.303399
\(911\) 7.21548 0.239059 0.119530 0.992831i \(-0.461861\pi\)
0.119530 + 0.992831i \(0.461861\pi\)
\(912\) 2.46079 0.0814850
\(913\) 34.6850 1.14791
\(914\) −20.1485 −0.666454
\(915\) 21.5496 0.712407
\(916\) −4.08309 −0.134909
\(917\) −23.6747 −0.781807
\(918\) 6.09240 0.201079
\(919\) −36.6000 −1.20732 −0.603662 0.797241i \(-0.706292\pi\)
−0.603662 + 0.797241i \(0.706292\pi\)
\(920\) −6.75440 −0.222686
\(921\) −1.50013 −0.0494308
\(922\) −4.34495 −0.143093
\(923\) 31.1045 1.02382
\(924\) 27.1182 0.892124
\(925\) −6.85159 −0.225279
\(926\) 2.35773 0.0774797
\(927\) 20.0671 0.659089
\(928\) −1.95342 −0.0641243
\(929\) −7.88078 −0.258560 −0.129280 0.991608i \(-0.541267\pi\)
−0.129280 + 0.991608i \(0.541267\pi\)
\(930\) 10.6347 0.348724
\(931\) 5.41023 0.177313
\(932\) −25.4843 −0.834764
\(933\) −16.1638 −0.529179
\(934\) −6.22229 −0.203599
\(935\) 11.8290 0.386851
\(936\) −5.88491 −0.192354
\(937\) 46.9540 1.53392 0.766960 0.641695i \(-0.221768\pi\)
0.766960 + 0.641695i \(0.221768\pi\)
\(938\) −31.5420 −1.02988
\(939\) 51.8582 1.69233
\(940\) 2.60823 0.0850709
\(941\) 8.86863 0.289109 0.144555 0.989497i \(-0.453825\pi\)
0.144555 + 0.989497i \(0.453825\pi\)
\(942\) 27.9678 0.911241
\(943\) −6.03003 −0.196365
\(944\) −9.44473 −0.307400
\(945\) 6.10731 0.198671
\(946\) −34.8483 −1.13302
\(947\) −2.59018 −0.0841695 −0.0420848 0.999114i \(-0.513400\pi\)
−0.0420848 + 0.999114i \(0.513400\pi\)
\(948\) −29.6734 −0.963746
\(949\) −10.4643 −0.339685
\(950\) 1.07603 0.0349111
\(951\) 21.0512 0.682632
\(952\) 11.9986 0.388876
\(953\) −49.6993 −1.60992 −0.804959 0.593331i \(-0.797813\pi\)
−0.804959 + 0.593331i \(0.797813\pi\)
\(954\) −31.8833 −1.03226
\(955\) 13.0731 0.423035
\(956\) −11.3288 −0.366400
\(957\) 15.2743 0.493749
\(958\) −20.8295 −0.672971
\(959\) 5.17703 0.167175
\(960\) 2.28691 0.0738098
\(961\) −9.37545 −0.302434
\(962\) 18.0814 0.582966
\(963\) −7.09663 −0.228686
\(964\) 17.6302 0.567829
\(965\) −1.07841 −0.0347154
\(966\) 53.5713 1.72363
\(967\) 33.0048 1.06136 0.530682 0.847571i \(-0.321936\pi\)
0.530682 + 0.847571i \(0.321936\pi\)
\(968\) 0.690448 0.0221918
\(969\) −8.51352 −0.273494
\(970\) 16.6254 0.533810
\(971\) 16.3480 0.524633 0.262316 0.964982i \(-0.415514\pi\)
0.262316 + 0.964982i \(0.415514\pi\)
\(972\) −19.2262 −0.616682
\(973\) −12.5093 −0.401030
\(974\) −3.26784 −0.104708
\(975\) −6.03517 −0.193280
\(976\) 9.42299 0.301623
\(977\) −21.0197 −0.672481 −0.336241 0.941776i \(-0.609156\pi\)
−0.336241 + 0.941776i \(0.609156\pi\)
\(978\) −3.51481 −0.112391
\(979\) −1.56173 −0.0499131
\(980\) 5.02795 0.160612
\(981\) 3.28953 0.105027
\(982\) 24.0782 0.768366
\(983\) 23.8635 0.761127 0.380564 0.924755i \(-0.375730\pi\)
0.380564 + 0.924755i \(0.375730\pi\)
\(984\) 2.04165 0.0650856
\(985\) 13.5161 0.430658
\(986\) 6.75819 0.215225
\(987\) −20.6867 −0.658464
\(988\) −2.83965 −0.0903412
\(989\) −68.8420 −2.18905
\(990\) −7.62458 −0.242325
\(991\) −26.1375 −0.830285 −0.415142 0.909757i \(-0.636268\pi\)
−0.415142 + 0.909757i \(0.636268\pi\)
\(992\) 4.65022 0.147645
\(993\) 21.2423 0.674105
\(994\) 40.8770 1.29654
\(995\) −20.3859 −0.646275
\(996\) −23.1993 −0.735099
\(997\) −37.3032 −1.18140 −0.590702 0.806890i \(-0.701149\pi\)
−0.590702 + 0.806890i \(0.701149\pi\)
\(998\) 18.8538 0.596807
\(999\) 12.0655 0.381736
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 \(a_p\))