Properties

Label 4010.2.a.k.1.8
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.81559\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.876107 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.876107 q^{6} +4.75824 q^{7} -1.00000 q^{8} -2.23244 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.876107 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.876107 q^{6} +4.75824 q^{7} -1.00000 q^{8} -2.23244 q^{9} +1.00000 q^{10} +0.395658 q^{11} -0.876107 q^{12} -1.38994 q^{13} -4.75824 q^{14} +0.876107 q^{15} +1.00000 q^{16} +1.97628 q^{17} +2.23244 q^{18} -4.95938 q^{19} -1.00000 q^{20} -4.16872 q^{21} -0.395658 q^{22} +7.99038 q^{23} +0.876107 q^{24} +1.00000 q^{25} +1.38994 q^{26} +4.58417 q^{27} +4.75824 q^{28} -5.94547 q^{29} -0.876107 q^{30} -7.55920 q^{31} -1.00000 q^{32} -0.346639 q^{33} -1.97628 q^{34} -4.75824 q^{35} -2.23244 q^{36} -7.50357 q^{37} +4.95938 q^{38} +1.21774 q^{39} +1.00000 q^{40} -3.64477 q^{41} +4.16872 q^{42} -1.96929 q^{43} +0.395658 q^{44} +2.23244 q^{45} -7.99038 q^{46} +10.0246 q^{47} -0.876107 q^{48} +15.6408 q^{49} -1.00000 q^{50} -1.73143 q^{51} -1.38994 q^{52} -9.91023 q^{53} -4.58417 q^{54} -0.395658 q^{55} -4.75824 q^{56} +4.34494 q^{57} +5.94547 q^{58} +9.82894 q^{59} +0.876107 q^{60} -5.61187 q^{61} +7.55920 q^{62} -10.6225 q^{63} +1.00000 q^{64} +1.38994 q^{65} +0.346639 q^{66} -12.8370 q^{67} +1.97628 q^{68} -7.00043 q^{69} +4.75824 q^{70} +2.66068 q^{71} +2.23244 q^{72} -4.87744 q^{73} +7.50357 q^{74} -0.876107 q^{75} -4.95938 q^{76} +1.88263 q^{77} -1.21774 q^{78} +9.52194 q^{79} -1.00000 q^{80} +2.68108 q^{81} +3.64477 q^{82} -11.3659 q^{83} -4.16872 q^{84} -1.97628 q^{85} +1.96929 q^{86} +5.20887 q^{87} -0.395658 q^{88} +7.21172 q^{89} -2.23244 q^{90} -6.61366 q^{91} +7.99038 q^{92} +6.62267 q^{93} -10.0246 q^{94} +4.95938 q^{95} +0.876107 q^{96} -10.6902 q^{97} -15.6408 q^{98} -0.883281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −0.876107 −0.505821 −0.252910 0.967490i \(-0.581388\pi\)
−0.252910 + 0.967490i \(0.581388\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.876107 0.357669
\(7\) 4.75824 1.79844 0.899222 0.437493i \(-0.144133\pi\)
0.899222 + 0.437493i \(0.144133\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.23244 −0.744146
\(10\) 1.00000 0.316228
\(11\) 0.395658 0.119295 0.0596477 0.998219i \(-0.481002\pi\)
0.0596477 + 0.998219i \(0.481002\pi\)
\(12\) −0.876107 −0.252910
\(13\) −1.38994 −0.385500 −0.192750 0.981248i \(-0.561741\pi\)
−0.192750 + 0.981248i \(0.561741\pi\)
\(14\) −4.75824 −1.27169
\(15\) 0.876107 0.226210
\(16\) 1.00000 0.250000
\(17\) 1.97628 0.479319 0.239659 0.970857i \(-0.422964\pi\)
0.239659 + 0.970857i \(0.422964\pi\)
\(18\) 2.23244 0.526190
\(19\) −4.95938 −1.13776 −0.568879 0.822421i \(-0.692623\pi\)
−0.568879 + 0.822421i \(0.692623\pi\)
\(20\) −1.00000 −0.223607
\(21\) −4.16872 −0.909690
\(22\) −0.395658 −0.0843546
\(23\) 7.99038 1.66611 0.833055 0.553191i \(-0.186590\pi\)
0.833055 + 0.553191i \(0.186590\pi\)
\(24\) 0.876107 0.178835
\(25\) 1.00000 0.200000
\(26\) 1.38994 0.272590
\(27\) 4.58417 0.882225
\(28\) 4.75824 0.899222
\(29\) −5.94547 −1.10405 −0.552023 0.833829i \(-0.686144\pi\)
−0.552023 + 0.833829i \(0.686144\pi\)
\(30\) −0.876107 −0.159955
\(31\) −7.55920 −1.35767 −0.678836 0.734290i \(-0.737515\pi\)
−0.678836 + 0.734290i \(0.737515\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.346639 −0.0603420
\(34\) −1.97628 −0.338929
\(35\) −4.75824 −0.804289
\(36\) −2.23244 −0.372073
\(37\) −7.50357 −1.23358 −0.616790 0.787128i \(-0.711567\pi\)
−0.616790 + 0.787128i \(0.711567\pi\)
\(38\) 4.95938 0.804517
\(39\) 1.21774 0.194994
\(40\) 1.00000 0.158114
\(41\) −3.64477 −0.569218 −0.284609 0.958644i \(-0.591864\pi\)
−0.284609 + 0.958644i \(0.591864\pi\)
\(42\) 4.16872 0.643248
\(43\) −1.96929 −0.300314 −0.150157 0.988662i \(-0.547978\pi\)
−0.150157 + 0.988662i \(0.547978\pi\)
\(44\) 0.395658 0.0596477
\(45\) 2.23244 0.332792
\(46\) −7.99038 −1.17812
\(47\) 10.0246 1.46224 0.731121 0.682248i \(-0.238997\pi\)
0.731121 + 0.682248i \(0.238997\pi\)
\(48\) −0.876107 −0.126455
\(49\) 15.6408 2.23440
\(50\) −1.00000 −0.141421
\(51\) −1.73143 −0.242449
\(52\) −1.38994 −0.192750
\(53\) −9.91023 −1.36127 −0.680637 0.732620i \(-0.738297\pi\)
−0.680637 + 0.732620i \(0.738297\pi\)
\(54\) −4.58417 −0.623827
\(55\) −0.395658 −0.0533505
\(56\) −4.75824 −0.635846
\(57\) 4.34494 0.575502
\(58\) 5.94547 0.780678
\(59\) 9.82894 1.27962 0.639810 0.768533i \(-0.279013\pi\)
0.639810 + 0.768533i \(0.279013\pi\)
\(60\) 0.876107 0.113105
\(61\) −5.61187 −0.718527 −0.359263 0.933236i \(-0.616972\pi\)
−0.359263 + 0.933236i \(0.616972\pi\)
\(62\) 7.55920 0.960019
\(63\) −10.6225 −1.33830
\(64\) 1.00000 0.125000
\(65\) 1.38994 0.172401
\(66\) 0.346639 0.0426683
\(67\) −12.8370 −1.56829 −0.784144 0.620578i \(-0.786898\pi\)
−0.784144 + 0.620578i \(0.786898\pi\)
\(68\) 1.97628 0.239659
\(69\) −7.00043 −0.842752
\(70\) 4.75824 0.568718
\(71\) 2.66068 0.315764 0.157882 0.987458i \(-0.449533\pi\)
0.157882 + 0.987458i \(0.449533\pi\)
\(72\) 2.23244 0.263095
\(73\) −4.87744 −0.570861 −0.285430 0.958399i \(-0.592137\pi\)
−0.285430 + 0.958399i \(0.592137\pi\)
\(74\) 7.50357 0.872273
\(75\) −0.876107 −0.101164
\(76\) −4.95938 −0.568879
\(77\) 1.88263 0.214546
\(78\) −1.21774 −0.137881
\(79\) 9.52194 1.07130 0.535651 0.844439i \(-0.320066\pi\)
0.535651 + 0.844439i \(0.320066\pi\)
\(80\) −1.00000 −0.111803
\(81\) 2.68108 0.297898
\(82\) 3.64477 0.402498
\(83\) −11.3659 −1.24757 −0.623787 0.781594i \(-0.714407\pi\)
−0.623787 + 0.781594i \(0.714407\pi\)
\(84\) −4.16872 −0.454845
\(85\) −1.97628 −0.214358
\(86\) 1.96929 0.212354
\(87\) 5.20887 0.558449
\(88\) −0.395658 −0.0421773
\(89\) 7.21172 0.764441 0.382221 0.924071i \(-0.375159\pi\)
0.382221 + 0.924071i \(0.375159\pi\)
\(90\) −2.23244 −0.235319
\(91\) −6.61366 −0.693300
\(92\) 7.99038 0.833055
\(93\) 6.62267 0.686738
\(94\) −10.0246 −1.03396
\(95\) 4.95938 0.508821
\(96\) 0.876107 0.0894173
\(97\) −10.6902 −1.08542 −0.542710 0.839920i \(-0.682602\pi\)
−0.542710 + 0.839920i \(0.682602\pi\)
\(98\) −15.6408 −1.57996
\(99\) −0.883281 −0.0887731
\(100\) 1.00000 0.100000
\(101\) −15.0071 −1.49327 −0.746633 0.665236i \(-0.768331\pi\)
−0.746633 + 0.665236i \(0.768331\pi\)
\(102\) 1.73143 0.171437
\(103\) 12.5325 1.23487 0.617433 0.786623i \(-0.288173\pi\)
0.617433 + 0.786623i \(0.288173\pi\)
\(104\) 1.38994 0.136295
\(105\) 4.16872 0.406826
\(106\) 9.91023 0.962567
\(107\) −8.92000 −0.862329 −0.431164 0.902273i \(-0.641897\pi\)
−0.431164 + 0.902273i \(0.641897\pi\)
\(108\) 4.58417 0.441112
\(109\) 0.0344053 0.00329543 0.00164771 0.999999i \(-0.499476\pi\)
0.00164771 + 0.999999i \(0.499476\pi\)
\(110\) 0.395658 0.0377245
\(111\) 6.57393 0.623970
\(112\) 4.75824 0.449611
\(113\) −9.62394 −0.905344 −0.452672 0.891677i \(-0.649529\pi\)
−0.452672 + 0.891677i \(0.649529\pi\)
\(114\) −4.34494 −0.406941
\(115\) −7.99038 −0.745107
\(116\) −5.94547 −0.552023
\(117\) 3.10295 0.286868
\(118\) −9.82894 −0.904828
\(119\) 9.40361 0.862027
\(120\) −0.876107 −0.0799773
\(121\) −10.8435 −0.985769
\(122\) 5.61187 0.508075
\(123\) 3.19321 0.287922
\(124\) −7.55920 −0.678836
\(125\) −1.00000 −0.0894427
\(126\) 10.6225 0.946324
\(127\) 22.1935 1.96936 0.984678 0.174380i \(-0.0557920\pi\)
0.984678 + 0.174380i \(0.0557920\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.72531 0.151905
\(130\) −1.38994 −0.121906
\(131\) 12.4596 1.08860 0.544299 0.838891i \(-0.316796\pi\)
0.544299 + 0.838891i \(0.316796\pi\)
\(132\) −0.346639 −0.0301710
\(133\) −23.5979 −2.04620
\(134\) 12.8370 1.10895
\(135\) −4.58417 −0.394543
\(136\) −1.97628 −0.169465
\(137\) 14.0918 1.20395 0.601973 0.798516i \(-0.294381\pi\)
0.601973 + 0.798516i \(0.294381\pi\)
\(138\) 7.00043 0.595916
\(139\) 9.24434 0.784095 0.392047 0.919945i \(-0.371767\pi\)
0.392047 + 0.919945i \(0.371767\pi\)
\(140\) −4.75824 −0.402144
\(141\) −8.78264 −0.739632
\(142\) −2.66068 −0.223279
\(143\) −0.549941 −0.0459884
\(144\) −2.23244 −0.186036
\(145\) 5.94547 0.493744
\(146\) 4.87744 0.403659
\(147\) −13.7030 −1.13021
\(148\) −7.50357 −0.616790
\(149\) 5.05203 0.413878 0.206939 0.978354i \(-0.433650\pi\)
0.206939 + 0.978354i \(0.433650\pi\)
\(150\) 0.876107 0.0715338
\(151\) 5.58234 0.454284 0.227142 0.973862i \(-0.427062\pi\)
0.227142 + 0.973862i \(0.427062\pi\)
\(152\) 4.95938 0.402259
\(153\) −4.41192 −0.356683
\(154\) −1.88263 −0.151707
\(155\) 7.55920 0.607169
\(156\) 1.21774 0.0974969
\(157\) −19.9358 −1.59105 −0.795526 0.605919i \(-0.792806\pi\)
−0.795526 + 0.605919i \(0.792806\pi\)
\(158\) −9.52194 −0.757525
\(159\) 8.68242 0.688561
\(160\) 1.00000 0.0790569
\(161\) 38.0201 2.99640
\(162\) −2.68108 −0.210646
\(163\) −9.29534 −0.728067 −0.364033 0.931386i \(-0.618601\pi\)
−0.364033 + 0.931386i \(0.618601\pi\)
\(164\) −3.64477 −0.284609
\(165\) 0.346639 0.0269858
\(166\) 11.3659 0.882168
\(167\) −10.5835 −0.818973 −0.409487 0.912316i \(-0.634292\pi\)
−0.409487 + 0.912316i \(0.634292\pi\)
\(168\) 4.16872 0.321624
\(169\) −11.0681 −0.851390
\(170\) 1.97628 0.151574
\(171\) 11.0715 0.846658
\(172\) −1.96929 −0.150157
\(173\) −8.23238 −0.625897 −0.312948 0.949770i \(-0.601317\pi\)
−0.312948 + 0.949770i \(0.601317\pi\)
\(174\) −5.20887 −0.394883
\(175\) 4.75824 0.359689
\(176\) 0.395658 0.0298238
\(177\) −8.61120 −0.647258
\(178\) −7.21172 −0.540542
\(179\) 13.4926 1.00848 0.504240 0.863563i \(-0.331773\pi\)
0.504240 + 0.863563i \(0.331773\pi\)
\(180\) 2.23244 0.166396
\(181\) 19.8239 1.47350 0.736749 0.676166i \(-0.236360\pi\)
0.736749 + 0.676166i \(0.236360\pi\)
\(182\) 6.61366 0.490237
\(183\) 4.91660 0.363445
\(184\) −7.99038 −0.589059
\(185\) 7.50357 0.551674
\(186\) −6.62267 −0.485597
\(187\) 0.781931 0.0571805
\(188\) 10.0246 0.731121
\(189\) 21.8126 1.58663
\(190\) −4.95938 −0.359791
\(191\) 4.39707 0.318161 0.159080 0.987266i \(-0.449147\pi\)
0.159080 + 0.987266i \(0.449147\pi\)
\(192\) −0.876107 −0.0632276
\(193\) −18.8033 −1.35349 −0.676745 0.736218i \(-0.736610\pi\)
−0.676745 + 0.736218i \(0.736610\pi\)
\(194\) 10.6902 0.767508
\(195\) −1.21774 −0.0872039
\(196\) 15.6408 1.11720
\(197\) 15.7824 1.12445 0.562223 0.826986i \(-0.309946\pi\)
0.562223 + 0.826986i \(0.309946\pi\)
\(198\) 0.883281 0.0627721
\(199\) −6.39499 −0.453329 −0.226664 0.973973i \(-0.572782\pi\)
−0.226664 + 0.973973i \(0.572782\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 11.2466 0.793273
\(202\) 15.0071 1.05590
\(203\) −28.2899 −1.98556
\(204\) −1.73143 −0.121225
\(205\) 3.64477 0.254562
\(206\) −12.5325 −0.873183
\(207\) −17.8380 −1.23983
\(208\) −1.38994 −0.0963750
\(209\) −1.96222 −0.135729
\(210\) −4.16872 −0.287669
\(211\) −21.5689 −1.48487 −0.742433 0.669921i \(-0.766328\pi\)
−0.742433 + 0.669921i \(0.766328\pi\)
\(212\) −9.91023 −0.680637
\(213\) −2.33104 −0.159720
\(214\) 8.92000 0.609758
\(215\) 1.96929 0.134305
\(216\) −4.58417 −0.311914
\(217\) −35.9684 −2.44170
\(218\) −0.0344053 −0.00233022
\(219\) 4.27315 0.288753
\(220\) −0.395658 −0.0266753
\(221\) −2.74691 −0.184777
\(222\) −6.57393 −0.441213
\(223\) −8.59690 −0.575691 −0.287845 0.957677i \(-0.592939\pi\)
−0.287845 + 0.957677i \(0.592939\pi\)
\(224\) −4.75824 −0.317923
\(225\) −2.23244 −0.148829
\(226\) 9.62394 0.640175
\(227\) 15.3902 1.02148 0.510742 0.859734i \(-0.329371\pi\)
0.510742 + 0.859734i \(0.329371\pi\)
\(228\) 4.34494 0.287751
\(229\) −27.3915 −1.81008 −0.905041 0.425324i \(-0.860160\pi\)
−0.905041 + 0.425324i \(0.860160\pi\)
\(230\) 7.99038 0.526870
\(231\) −1.64939 −0.108522
\(232\) 5.94547 0.390339
\(233\) 7.72662 0.506188 0.253094 0.967442i \(-0.418552\pi\)
0.253094 + 0.967442i \(0.418552\pi\)
\(234\) −3.10295 −0.202846
\(235\) −10.0246 −0.653935
\(236\) 9.82894 0.639810
\(237\) −8.34224 −0.541887
\(238\) −9.40361 −0.609545
\(239\) −21.0286 −1.36023 −0.680113 0.733107i \(-0.738069\pi\)
−0.680113 + 0.733107i \(0.738069\pi\)
\(240\) 0.876107 0.0565525
\(241\) −11.6531 −0.750645 −0.375322 0.926894i \(-0.622468\pi\)
−0.375322 + 0.926894i \(0.622468\pi\)
\(242\) 10.8435 0.697044
\(243\) −16.1014 −1.03291
\(244\) −5.61187 −0.359263
\(245\) −15.6408 −0.999254
\(246\) −3.19321 −0.203592
\(247\) 6.89323 0.438606
\(248\) 7.55920 0.480010
\(249\) 9.95778 0.631049
\(250\) 1.00000 0.0632456
\(251\) −10.6941 −0.675005 −0.337503 0.941325i \(-0.609582\pi\)
−0.337503 + 0.941325i \(0.609582\pi\)
\(252\) −10.6225 −0.669152
\(253\) 3.16146 0.198759
\(254\) −22.1935 −1.39255
\(255\) 1.73143 0.108427
\(256\) 1.00000 0.0625000
\(257\) −11.0713 −0.690611 −0.345305 0.938490i \(-0.612225\pi\)
−0.345305 + 0.938490i \(0.612225\pi\)
\(258\) −1.72531 −0.107413
\(259\) −35.7038 −2.21852
\(260\) 1.38994 0.0862004
\(261\) 13.2729 0.821571
\(262\) −12.4596 −0.769755
\(263\) −10.8041 −0.666208 −0.333104 0.942890i \(-0.608096\pi\)
−0.333104 + 0.942890i \(0.608096\pi\)
\(264\) 0.346639 0.0213341
\(265\) 9.91023 0.608781
\(266\) 23.5979 1.44688
\(267\) −6.31824 −0.386670
\(268\) −12.8370 −0.784144
\(269\) 12.3033 0.750143 0.375072 0.926996i \(-0.377618\pi\)
0.375072 + 0.926996i \(0.377618\pi\)
\(270\) 4.58417 0.278984
\(271\) −31.0283 −1.88484 −0.942418 0.334438i \(-0.891453\pi\)
−0.942418 + 0.334438i \(0.891453\pi\)
\(272\) 1.97628 0.119830
\(273\) 5.79427 0.350685
\(274\) −14.0918 −0.851319
\(275\) 0.395658 0.0238591
\(276\) −7.00043 −0.421376
\(277\) −3.37527 −0.202801 −0.101400 0.994846i \(-0.532332\pi\)
−0.101400 + 0.994846i \(0.532332\pi\)
\(278\) −9.24434 −0.554439
\(279\) 16.8754 1.01031
\(280\) 4.75824 0.284359
\(281\) −12.5542 −0.748918 −0.374459 0.927243i \(-0.622172\pi\)
−0.374459 + 0.927243i \(0.622172\pi\)
\(282\) 8.78264 0.522999
\(283\) 27.0370 1.60718 0.803592 0.595180i \(-0.202919\pi\)
0.803592 + 0.595180i \(0.202919\pi\)
\(284\) 2.66068 0.157882
\(285\) −4.34494 −0.257372
\(286\) 0.549941 0.0325187
\(287\) −17.3427 −1.02371
\(288\) 2.23244 0.131548
\(289\) −13.0943 −0.770254
\(290\) −5.94547 −0.349130
\(291\) 9.36572 0.549028
\(292\) −4.87744 −0.285430
\(293\) 6.48231 0.378700 0.189350 0.981910i \(-0.439362\pi\)
0.189350 + 0.981910i \(0.439362\pi\)
\(294\) 13.7030 0.799176
\(295\) −9.82894 −0.572263
\(296\) 7.50357 0.436136
\(297\) 1.81376 0.105245
\(298\) −5.05203 −0.292656
\(299\) −11.1061 −0.642285
\(300\) −0.876107 −0.0505821
\(301\) −9.37035 −0.540098
\(302\) −5.58234 −0.321228
\(303\) 13.1479 0.755324
\(304\) −4.95938 −0.284440
\(305\) 5.61187 0.321335
\(306\) 4.41192 0.252213
\(307\) 7.54205 0.430448 0.215224 0.976565i \(-0.430952\pi\)
0.215224 + 0.976565i \(0.430952\pi\)
\(308\) 1.88263 0.107273
\(309\) −10.9798 −0.624621
\(310\) −7.55920 −0.429334
\(311\) −20.5320 −1.16427 −0.582133 0.813094i \(-0.697782\pi\)
−0.582133 + 0.813094i \(0.697782\pi\)
\(312\) −1.21774 −0.0689407
\(313\) −33.5343 −1.89547 −0.947735 0.319059i \(-0.896633\pi\)
−0.947735 + 0.319059i \(0.896633\pi\)
\(314\) 19.9358 1.12504
\(315\) 10.6225 0.598508
\(316\) 9.52194 0.535651
\(317\) −25.7170 −1.44441 −0.722204 0.691680i \(-0.756871\pi\)
−0.722204 + 0.691680i \(0.756871\pi\)
\(318\) −8.68242 −0.486886
\(319\) −2.35237 −0.131708
\(320\) −1.00000 −0.0559017
\(321\) 7.81487 0.436183
\(322\) −38.0201 −2.11878
\(323\) −9.80112 −0.545349
\(324\) 2.68108 0.148949
\(325\) −1.38994 −0.0771000
\(326\) 9.29534 0.514821
\(327\) −0.0301427 −0.00166690
\(328\) 3.64477 0.201249
\(329\) 47.6995 2.62976
\(330\) −0.346639 −0.0190818
\(331\) −23.4317 −1.28792 −0.643960 0.765059i \(-0.722710\pi\)
−0.643960 + 0.765059i \(0.722710\pi\)
\(332\) −11.3659 −0.623787
\(333\) 16.7513 0.917963
\(334\) 10.5835 0.579102
\(335\) 12.8370 0.701360
\(336\) −4.16872 −0.227422
\(337\) −14.8968 −0.811482 −0.405741 0.913988i \(-0.632986\pi\)
−0.405741 + 0.913988i \(0.632986\pi\)
\(338\) 11.0681 0.602024
\(339\) 8.43160 0.457942
\(340\) −1.97628 −0.107179
\(341\) −2.99086 −0.161964
\(342\) −11.0715 −0.598678
\(343\) 41.1150 2.22000
\(344\) 1.96929 0.106177
\(345\) 7.00043 0.376890
\(346\) 8.23238 0.442576
\(347\) 22.8362 1.22591 0.612957 0.790116i \(-0.289980\pi\)
0.612957 + 0.790116i \(0.289980\pi\)
\(348\) 5.20887 0.279225
\(349\) 18.2849 0.978766 0.489383 0.872069i \(-0.337222\pi\)
0.489383 + 0.872069i \(0.337222\pi\)
\(350\) −4.75824 −0.254338
\(351\) −6.37172 −0.340098
\(352\) −0.395658 −0.0210886
\(353\) 2.13029 0.113384 0.0566920 0.998392i \(-0.481945\pi\)
0.0566920 + 0.998392i \(0.481945\pi\)
\(354\) 8.61120 0.457680
\(355\) −2.66068 −0.141214
\(356\) 7.21172 0.382221
\(357\) −8.23857 −0.436031
\(358\) −13.4926 −0.713104
\(359\) −3.43071 −0.181066 −0.0905330 0.995893i \(-0.528857\pi\)
−0.0905330 + 0.995893i \(0.528857\pi\)
\(360\) −2.23244 −0.117660
\(361\) 5.59541 0.294495
\(362\) −19.8239 −1.04192
\(363\) 9.50003 0.498622
\(364\) −6.61366 −0.346650
\(365\) 4.87744 0.255297
\(366\) −4.91660 −0.256995
\(367\) 20.1607 1.05238 0.526191 0.850366i \(-0.323620\pi\)
0.526191 + 0.850366i \(0.323620\pi\)
\(368\) 7.99038 0.416527
\(369\) 8.13673 0.423581
\(370\) −7.50357 −0.390092
\(371\) −47.1552 −2.44818
\(372\) 6.62267 0.343369
\(373\) −7.92957 −0.410578 −0.205289 0.978701i \(-0.565813\pi\)
−0.205289 + 0.978701i \(0.565813\pi\)
\(374\) −0.781931 −0.0404327
\(375\) 0.876107 0.0452420
\(376\) −10.0246 −0.516981
\(377\) 8.26384 0.425610
\(378\) −21.8126 −1.12192
\(379\) 7.50938 0.385731 0.192865 0.981225i \(-0.438222\pi\)
0.192865 + 0.981225i \(0.438222\pi\)
\(380\) 4.95938 0.254411
\(381\) −19.4439 −0.996141
\(382\) −4.39707 −0.224974
\(383\) −33.5814 −1.71593 −0.857964 0.513711i \(-0.828271\pi\)
−0.857964 + 0.513711i \(0.828271\pi\)
\(384\) 0.876107 0.0447086
\(385\) −1.88263 −0.0959479
\(386\) 18.8033 0.957061
\(387\) 4.39632 0.223477
\(388\) −10.6902 −0.542710
\(389\) −21.7398 −1.10225 −0.551125 0.834423i \(-0.685801\pi\)
−0.551125 + 0.834423i \(0.685801\pi\)
\(390\) 1.21774 0.0616624
\(391\) 15.7912 0.798597
\(392\) −15.6408 −0.789980
\(393\) −10.9159 −0.550635
\(394\) −15.7824 −0.795103
\(395\) −9.52194 −0.479101
\(396\) −0.883281 −0.0443866
\(397\) 4.08329 0.204935 0.102467 0.994736i \(-0.467326\pi\)
0.102467 + 0.994736i \(0.467326\pi\)
\(398\) 6.39499 0.320552
\(399\) 20.6743 1.03501
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −11.2466 −0.560929
\(403\) 10.5068 0.523382
\(404\) −15.0071 −0.746633
\(405\) −2.68108 −0.133224
\(406\) 28.2899 1.40401
\(407\) −2.96885 −0.147160
\(408\) 1.73143 0.0857187
\(409\) 3.59578 0.177800 0.0888999 0.996041i \(-0.471665\pi\)
0.0888999 + 0.996041i \(0.471665\pi\)
\(410\) −3.64477 −0.180003
\(411\) −12.3460 −0.608981
\(412\) 12.5325 0.617433
\(413\) 46.7684 2.30132
\(414\) 17.8380 0.876691
\(415\) 11.3659 0.557932
\(416\) 1.38994 0.0681474
\(417\) −8.09903 −0.396611
\(418\) 1.96222 0.0959752
\(419\) 26.1714 1.27855 0.639277 0.768976i \(-0.279234\pi\)
0.639277 + 0.768976i \(0.279234\pi\)
\(420\) 4.16872 0.203413
\(421\) −5.98077 −0.291485 −0.145742 0.989323i \(-0.546557\pi\)
−0.145742 + 0.989323i \(0.546557\pi\)
\(422\) 21.5689 1.04996
\(423\) −22.3793 −1.08812
\(424\) 9.91023 0.481283
\(425\) 1.97628 0.0958637
\(426\) 2.33104 0.112939
\(427\) −26.7026 −1.29223
\(428\) −8.92000 −0.431164
\(429\) 0.481807 0.0232619
\(430\) −1.96929 −0.0949677
\(431\) −36.2323 −1.74525 −0.872624 0.488393i \(-0.837583\pi\)
−0.872624 + 0.488393i \(0.837583\pi\)
\(432\) 4.58417 0.220556
\(433\) −27.4578 −1.31954 −0.659770 0.751468i \(-0.729346\pi\)
−0.659770 + 0.751468i \(0.729346\pi\)
\(434\) 35.9684 1.72654
\(435\) −5.20887 −0.249746
\(436\) 0.0344053 0.00164771
\(437\) −39.6273 −1.89563
\(438\) −4.27315 −0.204179
\(439\) −29.0886 −1.38833 −0.694163 0.719818i \(-0.744225\pi\)
−0.694163 + 0.719818i \(0.744225\pi\)
\(440\) 0.395658 0.0188623
\(441\) −34.9171 −1.66272
\(442\) 2.74691 0.130657
\(443\) 35.2356 1.67409 0.837047 0.547131i \(-0.184280\pi\)
0.837047 + 0.547131i \(0.184280\pi\)
\(444\) 6.57393 0.311985
\(445\) −7.21172 −0.341869
\(446\) 8.59690 0.407075
\(447\) −4.42612 −0.209348
\(448\) 4.75824 0.224805
\(449\) 16.6369 0.785144 0.392572 0.919721i \(-0.371585\pi\)
0.392572 + 0.919721i \(0.371585\pi\)
\(450\) 2.23244 0.105238
\(451\) −1.44208 −0.0679051
\(452\) −9.62394 −0.452672
\(453\) −4.89073 −0.229786
\(454\) −15.3902 −0.722298
\(455\) 6.61366 0.310053
\(456\) −4.34494 −0.203471
\(457\) −4.95999 −0.232018 −0.116009 0.993248i \(-0.537010\pi\)
−0.116009 + 0.993248i \(0.537010\pi\)
\(458\) 27.3915 1.27992
\(459\) 9.05962 0.422867
\(460\) −7.99038 −0.372553
\(461\) 14.9403 0.695840 0.347920 0.937524i \(-0.386888\pi\)
0.347920 + 0.937524i \(0.386888\pi\)
\(462\) 1.64939 0.0767365
\(463\) −21.7295 −1.00985 −0.504927 0.863162i \(-0.668481\pi\)
−0.504927 + 0.863162i \(0.668481\pi\)
\(464\) −5.94547 −0.276012
\(465\) −6.62267 −0.307119
\(466\) −7.72662 −0.357929
\(467\) −30.1884 −1.39695 −0.698475 0.715634i \(-0.746138\pi\)
−0.698475 + 0.715634i \(0.746138\pi\)
\(468\) 3.10295 0.143434
\(469\) −61.0815 −2.82048
\(470\) 10.0246 0.462402
\(471\) 17.4659 0.804787
\(472\) −9.82894 −0.452414
\(473\) −0.779166 −0.0358261
\(474\) 8.34224 0.383172
\(475\) −4.95938 −0.227552
\(476\) 9.40361 0.431014
\(477\) 22.1240 1.01299
\(478\) 21.0286 0.961825
\(479\) 3.17305 0.144981 0.0724903 0.997369i \(-0.476905\pi\)
0.0724903 + 0.997369i \(0.476905\pi\)
\(480\) −0.876107 −0.0399886
\(481\) 10.4295 0.475545
\(482\) 11.6531 0.530786
\(483\) −33.3097 −1.51564
\(484\) −10.8435 −0.492884
\(485\) 10.6902 0.485415
\(486\) 16.1014 0.730376
\(487\) −27.7483 −1.25739 −0.628697 0.777650i \(-0.716411\pi\)
−0.628697 + 0.777650i \(0.716411\pi\)
\(488\) 5.61187 0.254037
\(489\) 8.14371 0.368271
\(490\) 15.6408 0.706579
\(491\) 29.5110 1.33181 0.665907 0.746035i \(-0.268045\pi\)
0.665907 + 0.746035i \(0.268045\pi\)
\(492\) 3.19321 0.143961
\(493\) −11.7499 −0.529190
\(494\) −6.89323 −0.310141
\(495\) 0.883281 0.0397005
\(496\) −7.55920 −0.339418
\(497\) 12.6601 0.567884
\(498\) −9.95778 −0.446219
\(499\) −38.3533 −1.71693 −0.858464 0.512874i \(-0.828581\pi\)
−0.858464 + 0.512874i \(0.828581\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 9.27225 0.414254
\(502\) 10.6941 0.477301
\(503\) 1.67540 0.0747024 0.0373512 0.999302i \(-0.488108\pi\)
0.0373512 + 0.999302i \(0.488108\pi\)
\(504\) 10.6225 0.473162
\(505\) 15.0071 0.667809
\(506\) −3.16146 −0.140544
\(507\) 9.69681 0.430650
\(508\) 22.1935 0.984678
\(509\) 6.72849 0.298235 0.149118 0.988819i \(-0.452357\pi\)
0.149118 + 0.988819i \(0.452357\pi\)
\(510\) −1.73143 −0.0766692
\(511\) −23.2080 −1.02666
\(512\) −1.00000 −0.0441942
\(513\) −22.7346 −1.00376
\(514\) 11.0713 0.488336
\(515\) −12.5325 −0.552249
\(516\) 1.72531 0.0759525
\(517\) 3.96632 0.174439
\(518\) 35.7038 1.56873
\(519\) 7.21245 0.316591
\(520\) −1.38994 −0.0609529
\(521\) 17.0764 0.748129 0.374064 0.927403i \(-0.377964\pi\)
0.374064 + 0.927403i \(0.377964\pi\)
\(522\) −13.2729 −0.580938
\(523\) −8.47342 −0.370517 −0.185258 0.982690i \(-0.559312\pi\)
−0.185258 + 0.982690i \(0.559312\pi\)
\(524\) 12.4596 0.544299
\(525\) −4.16872 −0.181938
\(526\) 10.8041 0.471080
\(527\) −14.9391 −0.650757
\(528\) −0.346639 −0.0150855
\(529\) 40.8462 1.77592
\(530\) −9.91023 −0.430473
\(531\) −21.9425 −0.952223
\(532\) −23.5979 −1.02310
\(533\) 5.06602 0.219434
\(534\) 6.31824 0.273417
\(535\) 8.92000 0.385645
\(536\) 12.8370 0.554474
\(537\) −11.8209 −0.510110
\(538\) −12.3033 −0.530431
\(539\) 6.18841 0.266554
\(540\) −4.58417 −0.197271
\(541\) −40.1909 −1.72794 −0.863970 0.503543i \(-0.832029\pi\)
−0.863970 + 0.503543i \(0.832029\pi\)
\(542\) 31.0283 1.33278
\(543\) −17.3678 −0.745325
\(544\) −1.97628 −0.0847323
\(545\) −0.0344053 −0.00147376
\(546\) −5.79427 −0.247972
\(547\) 39.5768 1.69218 0.846090 0.533040i \(-0.178950\pi\)
0.846090 + 0.533040i \(0.178950\pi\)
\(548\) 14.0918 0.601973
\(549\) 12.5281 0.534688
\(550\) −0.395658 −0.0168709
\(551\) 29.4858 1.25614
\(552\) 7.00043 0.297958
\(553\) 45.3077 1.92668
\(554\) 3.37527 0.143402
\(555\) −6.57393 −0.279048
\(556\) 9.24434 0.392047
\(557\) −15.7255 −0.666309 −0.333155 0.942872i \(-0.608113\pi\)
−0.333155 + 0.942872i \(0.608113\pi\)
\(558\) −16.8754 −0.714394
\(559\) 2.73720 0.115771
\(560\) −4.75824 −0.201072
\(561\) −0.685055 −0.0289231
\(562\) 12.5542 0.529565
\(563\) −30.4925 −1.28510 −0.642552 0.766242i \(-0.722124\pi\)
−0.642552 + 0.766242i \(0.722124\pi\)
\(564\) −8.78264 −0.369816
\(565\) 9.62394 0.404882
\(566\) −27.0370 −1.13645
\(567\) 12.7572 0.535753
\(568\) −2.66068 −0.111639
\(569\) 21.6186 0.906300 0.453150 0.891434i \(-0.350300\pi\)
0.453150 + 0.891434i \(0.350300\pi\)
\(570\) 4.34494 0.181990
\(571\) 38.3294 1.60404 0.802018 0.597300i \(-0.203760\pi\)
0.802018 + 0.597300i \(0.203760\pi\)
\(572\) −0.549941 −0.0229942
\(573\) −3.85230 −0.160932
\(574\) 17.3427 0.723870
\(575\) 7.99038 0.333222
\(576\) −2.23244 −0.0930182
\(577\) 19.4816 0.811028 0.405514 0.914089i \(-0.367093\pi\)
0.405514 + 0.914089i \(0.367093\pi\)
\(578\) 13.0943 0.544652
\(579\) 16.4737 0.684623
\(580\) 5.94547 0.246872
\(581\) −54.0818 −2.24369
\(582\) −9.36572 −0.388222
\(583\) −3.92106 −0.162394
\(584\) 4.87744 0.201830
\(585\) −3.10295 −0.128291
\(586\) −6.48231 −0.267782
\(587\) −21.2556 −0.877313 −0.438656 0.898655i \(-0.644545\pi\)
−0.438656 + 0.898655i \(0.644545\pi\)
\(588\) −13.7030 −0.565103
\(589\) 37.4889 1.54470
\(590\) 9.82894 0.404651
\(591\) −13.8270 −0.568768
\(592\) −7.50357 −0.308395
\(593\) 43.6717 1.79338 0.896691 0.442657i \(-0.145964\pi\)
0.896691 + 0.442657i \(0.145964\pi\)
\(594\) −1.81376 −0.0744197
\(595\) −9.40361 −0.385510
\(596\) 5.05203 0.206939
\(597\) 5.60269 0.229303
\(598\) 11.1061 0.454164
\(599\) 7.61091 0.310973 0.155487 0.987838i \(-0.450305\pi\)
0.155487 + 0.987838i \(0.450305\pi\)
\(600\) 0.876107 0.0357669
\(601\) 29.9971 1.22361 0.611804 0.791010i \(-0.290444\pi\)
0.611804 + 0.791010i \(0.290444\pi\)
\(602\) 9.37035 0.381907
\(603\) 28.6578 1.16704
\(604\) 5.58234 0.227142
\(605\) 10.8435 0.440849
\(606\) −13.1479 −0.534095
\(607\) 24.4068 0.990643 0.495321 0.868710i \(-0.335050\pi\)
0.495321 + 0.868710i \(0.335050\pi\)
\(608\) 4.95938 0.201129
\(609\) 24.7850 1.00434
\(610\) −5.61187 −0.227218
\(611\) −13.9336 −0.563694
\(612\) −4.41192 −0.178341
\(613\) −10.3544 −0.418209 −0.209105 0.977893i \(-0.567055\pi\)
−0.209105 + 0.977893i \(0.567055\pi\)
\(614\) −7.54205 −0.304372
\(615\) −3.19321 −0.128763
\(616\) −1.88263 −0.0758535
\(617\) −18.9377 −0.762404 −0.381202 0.924492i \(-0.624490\pi\)
−0.381202 + 0.924492i \(0.624490\pi\)
\(618\) 10.9798 0.441674
\(619\) 28.8582 1.15991 0.579954 0.814649i \(-0.303070\pi\)
0.579954 + 0.814649i \(0.303070\pi\)
\(620\) 7.55920 0.303585
\(621\) 36.6293 1.46988
\(622\) 20.5320 0.823260
\(623\) 34.3151 1.37480
\(624\) 1.21774 0.0487484
\(625\) 1.00000 0.0400000
\(626\) 33.5343 1.34030
\(627\) 1.71911 0.0686547
\(628\) −19.9358 −0.795526
\(629\) −14.8292 −0.591278
\(630\) −10.6225 −0.423209
\(631\) −20.1714 −0.803010 −0.401505 0.915857i \(-0.631513\pi\)
−0.401505 + 0.915857i \(0.631513\pi\)
\(632\) −9.52194 −0.378763
\(633\) 18.8967 0.751075
\(634\) 25.7170 1.02135
\(635\) −22.1935 −0.880723
\(636\) 8.68242 0.344280
\(637\) −21.7398 −0.861361
\(638\) 2.35237 0.0931313
\(639\) −5.93979 −0.234974
\(640\) 1.00000 0.0395285
\(641\) 40.6758 1.60660 0.803300 0.595575i \(-0.203076\pi\)
0.803300 + 0.595575i \(0.203076\pi\)
\(642\) −7.81487 −0.308428
\(643\) −12.3398 −0.486636 −0.243318 0.969947i \(-0.578236\pi\)
−0.243318 + 0.969947i \(0.578236\pi\)
\(644\) 38.0201 1.49820
\(645\) −1.72531 −0.0679340
\(646\) 9.80112 0.385620
\(647\) −25.7692 −1.01309 −0.506545 0.862214i \(-0.669078\pi\)
−0.506545 + 0.862214i \(0.669078\pi\)
\(648\) −2.68108 −0.105323
\(649\) 3.88890 0.152653
\(650\) 1.38994 0.0545179
\(651\) 31.5122 1.23506
\(652\) −9.29534 −0.364033
\(653\) 31.4621 1.23121 0.615603 0.788057i \(-0.288913\pi\)
0.615603 + 0.788057i \(0.288913\pi\)
\(654\) 0.0301427 0.00117867
\(655\) −12.4596 −0.486836
\(656\) −3.64477 −0.142305
\(657\) 10.8886 0.424803
\(658\) −47.6995 −1.85952
\(659\) −26.1508 −1.01869 −0.509345 0.860562i \(-0.670112\pi\)
−0.509345 + 0.860562i \(0.670112\pi\)
\(660\) 0.346639 0.0134929
\(661\) −7.68461 −0.298897 −0.149448 0.988770i \(-0.547750\pi\)
−0.149448 + 0.988770i \(0.547750\pi\)
\(662\) 23.4317 0.910698
\(663\) 2.40659 0.0934641
\(664\) 11.3659 0.441084
\(665\) 23.5979 0.915086
\(666\) −16.7513 −0.649098
\(667\) −47.5066 −1.83946
\(668\) −10.5835 −0.409487
\(669\) 7.53180 0.291196
\(670\) −12.8370 −0.495937
\(671\) −2.22038 −0.0857169
\(672\) 4.16872 0.160812
\(673\) −29.5730 −1.13995 −0.569977 0.821660i \(-0.693048\pi\)
−0.569977 + 0.821660i \(0.693048\pi\)
\(674\) 14.8968 0.573804
\(675\) 4.58417 0.176445
\(676\) −11.0681 −0.425695
\(677\) −11.6055 −0.446036 −0.223018 0.974814i \(-0.571591\pi\)
−0.223018 + 0.974814i \(0.571591\pi\)
\(678\) −8.43160 −0.323814
\(679\) −50.8663 −1.95207
\(680\) 1.97628 0.0757869
\(681\) −13.4835 −0.516687
\(682\) 2.99086 0.114526
\(683\) 36.7503 1.40621 0.703105 0.711086i \(-0.251796\pi\)
0.703105 + 0.711086i \(0.251796\pi\)
\(684\) 11.0715 0.423329
\(685\) −14.0918 −0.538421
\(686\) −41.1150 −1.56978
\(687\) 23.9979 0.915577
\(688\) −1.96929 −0.0750785
\(689\) 13.7746 0.524771
\(690\) −7.00043 −0.266502
\(691\) 24.4972 0.931917 0.465959 0.884806i \(-0.345710\pi\)
0.465959 + 0.884806i \(0.345710\pi\)
\(692\) −8.23238 −0.312948
\(693\) −4.20286 −0.159653
\(694\) −22.8362 −0.866852
\(695\) −9.24434 −0.350658
\(696\) −5.20887 −0.197442
\(697\) −7.20310 −0.272837
\(698\) −18.2849 −0.692092
\(699\) −6.76934 −0.256040
\(700\) 4.75824 0.179844
\(701\) 15.2021 0.574174 0.287087 0.957905i \(-0.407313\pi\)
0.287087 + 0.957905i \(0.407313\pi\)
\(702\) 6.37172 0.240485
\(703\) 37.2130 1.40352
\(704\) 0.395658 0.0149119
\(705\) 8.78264 0.330774
\(706\) −2.13029 −0.0801746
\(707\) −71.4075 −2.68555
\(708\) −8.61120 −0.323629
\(709\) 25.5679 0.960224 0.480112 0.877207i \(-0.340596\pi\)
0.480112 + 0.877207i \(0.340596\pi\)
\(710\) 2.66068 0.0998534
\(711\) −21.2571 −0.797205
\(712\) −7.21172 −0.270271
\(713\) −60.4009 −2.26203
\(714\) 8.23857 0.308321
\(715\) 0.549941 0.0205666
\(716\) 13.4926 0.504240
\(717\) 18.4233 0.688030
\(718\) 3.43071 0.128033
\(719\) 19.1720 0.714997 0.357498 0.933914i \(-0.383630\pi\)
0.357498 + 0.933914i \(0.383630\pi\)
\(720\) 2.23244 0.0831980
\(721\) 59.6327 2.22084
\(722\) −5.59541 −0.208240
\(723\) 10.2094 0.379691
\(724\) 19.8239 0.736749
\(725\) −5.94547 −0.220809
\(726\) −9.50003 −0.352579
\(727\) 47.0498 1.74498 0.872491 0.488630i \(-0.162503\pi\)
0.872491 + 0.488630i \(0.162503\pi\)
\(728\) 6.61366 0.245119
\(729\) 6.06333 0.224568
\(730\) −4.87744 −0.180522
\(731\) −3.89187 −0.143946
\(732\) 4.91660 0.181723
\(733\) −39.6927 −1.46608 −0.733041 0.680185i \(-0.761900\pi\)
−0.733041 + 0.680185i \(0.761900\pi\)
\(734\) −20.1607 −0.744146
\(735\) 13.7030 0.505443
\(736\) −7.99038 −0.294529
\(737\) −5.07906 −0.187090
\(738\) −8.13673 −0.299517
\(739\) 20.5005 0.754122 0.377061 0.926188i \(-0.376935\pi\)
0.377061 + 0.926188i \(0.376935\pi\)
\(740\) 7.50357 0.275837
\(741\) −6.03921 −0.221856
\(742\) 47.1552 1.73112
\(743\) −25.8088 −0.946833 −0.473417 0.880839i \(-0.656980\pi\)
−0.473417 + 0.880839i \(0.656980\pi\)
\(744\) −6.62267 −0.242799
\(745\) −5.05203 −0.185092
\(746\) 7.92957 0.290322
\(747\) 25.3737 0.928377
\(748\) 0.781931 0.0285902
\(749\) −42.4434 −1.55085
\(750\) −0.876107 −0.0319909
\(751\) −7.09348 −0.258845 −0.129422 0.991590i \(-0.541312\pi\)
−0.129422 + 0.991590i \(0.541312\pi\)
\(752\) 10.0246 0.365561
\(753\) 9.36917 0.341432
\(754\) −8.26384 −0.300951
\(755\) −5.58234 −0.203162
\(756\) 21.8126 0.793316
\(757\) 20.5508 0.746933 0.373466 0.927644i \(-0.378169\pi\)
0.373466 + 0.927644i \(0.378169\pi\)
\(758\) −7.50938 −0.272753
\(759\) −2.76977 −0.100536
\(760\) −4.95938 −0.179895
\(761\) −40.4347 −1.46576 −0.732878 0.680360i \(-0.761824\pi\)
−0.732878 + 0.680360i \(0.761824\pi\)
\(762\) 19.4439 0.704378
\(763\) 0.163708 0.00592664
\(764\) 4.39707 0.159080
\(765\) 4.41192 0.159513
\(766\) 33.5814 1.21334
\(767\) −13.6616 −0.493293
\(768\) −0.876107 −0.0316138
\(769\) −6.15961 −0.222121 −0.111061 0.993814i \(-0.535425\pi\)
−0.111061 + 0.993814i \(0.535425\pi\)
\(770\) 1.88263 0.0678454
\(771\) 9.69967 0.349325
\(772\) −18.8033 −0.676745
\(773\) 22.1383 0.796259 0.398129 0.917329i \(-0.369659\pi\)
0.398129 + 0.917329i \(0.369659\pi\)
\(774\) −4.39632 −0.158022
\(775\) −7.55920 −0.271534
\(776\) 10.6902 0.383754
\(777\) 31.2803 1.12218
\(778\) 21.7398 0.779408
\(779\) 18.0758 0.647633
\(780\) −1.21774 −0.0436019
\(781\) 1.05272 0.0376692
\(782\) −15.7912 −0.564693
\(783\) −27.2551 −0.974017
\(784\) 15.6408 0.558600
\(785\) 19.9358 0.711540
\(786\) 10.9159 0.389358
\(787\) −14.8875 −0.530682 −0.265341 0.964155i \(-0.585484\pi\)
−0.265341 + 0.964155i \(0.585484\pi\)
\(788\) 15.7824 0.562223
\(789\) 9.46553 0.336982
\(790\) 9.52194 0.338776
\(791\) −45.7930 −1.62821
\(792\) 0.883281 0.0313860
\(793\) 7.80016 0.276992
\(794\) −4.08329 −0.144911
\(795\) −8.68242 −0.307934
\(796\) −6.39499 −0.226664
\(797\) −43.5372 −1.54217 −0.771083 0.636734i \(-0.780285\pi\)
−0.771083 + 0.636734i \(0.780285\pi\)
\(798\) −20.6743 −0.731861
\(799\) 19.8115 0.700880
\(800\) −1.00000 −0.0353553
\(801\) −16.0997 −0.568856
\(802\) 1.00000 0.0353112
\(803\) −1.92980 −0.0681010
\(804\) 11.2466 0.396636
\(805\) −38.0201 −1.34003
\(806\) −10.5068 −0.370087
\(807\) −10.7790 −0.379438
\(808\) 15.0071 0.527949
\(809\) 0.564011 0.0198296 0.00991479 0.999951i \(-0.496844\pi\)
0.00991479 + 0.999951i \(0.496844\pi\)
\(810\) 2.68108 0.0942037
\(811\) 26.4569 0.929027 0.464514 0.885566i \(-0.346229\pi\)
0.464514 + 0.885566i \(0.346229\pi\)
\(812\) −28.2899 −0.992782
\(813\) 27.1841 0.953388
\(814\) 2.96885 0.104058
\(815\) 9.29534 0.325601
\(816\) −1.73143 −0.0606123
\(817\) 9.76646 0.341685
\(818\) −3.59578 −0.125723
\(819\) 14.7646 0.515916
\(820\) 3.64477 0.127281
\(821\) 6.42811 0.224342 0.112171 0.993689i \(-0.464219\pi\)
0.112171 + 0.993689i \(0.464219\pi\)
\(822\) 12.3460 0.430615
\(823\) −44.0461 −1.53535 −0.767676 0.640838i \(-0.778587\pi\)
−0.767676 + 0.640838i \(0.778587\pi\)
\(824\) −12.5325 −0.436591
\(825\) −0.346639 −0.0120684
\(826\) −46.7684 −1.62728
\(827\) 10.6766 0.371263 0.185632 0.982619i \(-0.440567\pi\)
0.185632 + 0.982619i \(0.440567\pi\)
\(828\) −17.8380 −0.619914
\(829\) 45.6828 1.58663 0.793314 0.608813i \(-0.208354\pi\)
0.793314 + 0.608813i \(0.208354\pi\)
\(830\) −11.3659 −0.394518
\(831\) 2.95710 0.102581
\(832\) −1.38994 −0.0481875
\(833\) 30.9106 1.07099
\(834\) 8.09903 0.280446
\(835\) 10.5835 0.366256
\(836\) −1.96222 −0.0678647
\(837\) −34.6527 −1.19777
\(838\) −26.1714 −0.904075
\(839\) 14.4341 0.498319 0.249159 0.968462i \(-0.419846\pi\)
0.249159 + 0.968462i \(0.419846\pi\)
\(840\) −4.16872 −0.143835
\(841\) 6.34861 0.218918
\(842\) 5.98077 0.206111
\(843\) 10.9988 0.378818
\(844\) −21.5689 −0.742433
\(845\) 11.0681 0.380753
\(846\) 22.3793 0.769418
\(847\) −51.5957 −1.77285
\(848\) −9.91023 −0.340319
\(849\) −23.6873 −0.812947
\(850\) −1.97628 −0.0677859
\(851\) −59.9564 −2.05528
\(852\) −2.33104 −0.0798600
\(853\) 33.8632 1.15945 0.579726 0.814811i \(-0.303159\pi\)
0.579726 + 0.814811i \(0.303159\pi\)
\(854\) 26.7026 0.913744
\(855\) −11.0715 −0.378637
\(856\) 8.92000 0.304879
\(857\) 27.9423 0.954492 0.477246 0.878770i \(-0.341635\pi\)
0.477246 + 0.878770i \(0.341635\pi\)
\(858\) −0.481807 −0.0164486
\(859\) 35.0800 1.19692 0.598458 0.801154i \(-0.295780\pi\)
0.598458 + 0.801154i \(0.295780\pi\)
\(860\) 1.96929 0.0671523
\(861\) 15.1941 0.517812
\(862\) 36.2323 1.23408
\(863\) 1.82264 0.0620434 0.0310217 0.999519i \(-0.490124\pi\)
0.0310217 + 0.999519i \(0.490124\pi\)
\(864\) −4.58417 −0.155957
\(865\) 8.23238 0.279909
\(866\) 27.4578 0.933055
\(867\) 11.4720 0.389610
\(868\) −35.9684 −1.22085
\(869\) 3.76743 0.127801
\(870\) 5.20887 0.176597
\(871\) 17.8427 0.604575
\(872\) −0.0344053 −0.00116511
\(873\) 23.8651 0.807711
\(874\) 39.6273 1.34041
\(875\) −4.75824 −0.160858
\(876\) 4.27315 0.144377
\(877\) −31.9023 −1.07727 −0.538633 0.842541i \(-0.681059\pi\)
−0.538633 + 0.842541i \(0.681059\pi\)
\(878\) 29.0886 0.981694
\(879\) −5.67919 −0.191554
\(880\) −0.395658 −0.0133376
\(881\) −7.37640 −0.248517 −0.124259 0.992250i \(-0.539655\pi\)
−0.124259 + 0.992250i \(0.539655\pi\)
\(882\) 34.9171 1.17572
\(883\) 2.59396 0.0872937 0.0436469 0.999047i \(-0.486102\pi\)
0.0436469 + 0.999047i \(0.486102\pi\)
\(884\) −2.74691 −0.0923886
\(885\) 8.61120 0.289462
\(886\) −35.2356 −1.18376
\(887\) −8.88122 −0.298202 −0.149101 0.988822i \(-0.547638\pi\)
−0.149101 + 0.988822i \(0.547638\pi\)
\(888\) −6.57393 −0.220607
\(889\) 105.602 3.54178
\(890\) 7.21172 0.241738
\(891\) 1.06079 0.0355379
\(892\) −8.59690 −0.287845
\(893\) −49.7159 −1.66368
\(894\) 4.42612 0.148032
\(895\) −13.4926 −0.451006
\(896\) −4.75824 −0.158961
\(897\) 9.73017 0.324881
\(898\) −16.6369 −0.555181
\(899\) 44.9430 1.49893
\(900\) −2.23244 −0.0744146
\(901\) −19.5854 −0.652484
\(902\) 1.44208 0.0480161
\(903\) 8.20943 0.273193
\(904\) 9.62394 0.320088
\(905\) −19.8239 −0.658968
\(906\) 4.89073 0.162483
\(907\) 7.35532 0.244229 0.122115 0.992516i \(-0.461032\pi\)
0.122115 + 0.992516i \(0.461032\pi\)
\(908\) 15.3902 0.510742
\(909\) 33.5025 1.11121
\(910\) −6.61366 −0.219241
\(911\) −44.0558 −1.45963 −0.729817 0.683643i \(-0.760395\pi\)
−0.729817 + 0.683643i \(0.760395\pi\)
\(912\) 4.34494 0.143875
\(913\) −4.49702 −0.148830
\(914\) 4.95999 0.164062
\(915\) −4.91660 −0.162538
\(916\) −27.3915 −0.905041
\(917\) 59.2856 1.95778
\(918\) −9.05962 −0.299012
\(919\) −25.1336 −0.829082 −0.414541 0.910031i \(-0.636058\pi\)
−0.414541 + 0.910031i \(0.636058\pi\)
\(920\) 7.99038 0.263435
\(921\) −6.60764 −0.217729
\(922\) −14.9403 −0.492034
\(923\) −3.69818 −0.121727
\(924\) −1.64939 −0.0542609
\(925\) −7.50357 −0.246716
\(926\) 21.7295 0.714075
\(927\) −27.9781 −0.918920
\(928\) 5.94547 0.195170
\(929\) −7.27655 −0.238736 −0.119368 0.992850i \(-0.538087\pi\)
−0.119368 + 0.992850i \(0.538087\pi\)
\(930\) 6.62267 0.217166
\(931\) −77.5686 −2.54221
\(932\) 7.72662 0.253094
\(933\) 17.9883 0.588910
\(934\) 30.1884 0.987793
\(935\) −0.781931 −0.0255719
\(936\) −3.10295 −0.101423
\(937\) 45.4287 1.48409 0.742046 0.670349i \(-0.233856\pi\)
0.742046 + 0.670349i \(0.233856\pi\)
\(938\) 61.0815 1.99438
\(939\) 29.3796 0.958767
\(940\) −10.0246 −0.326967
\(941\) 41.6926 1.35914 0.679570 0.733611i \(-0.262167\pi\)
0.679570 + 0.733611i \(0.262167\pi\)
\(942\) −17.4659 −0.569070
\(943\) −29.1231 −0.948380
\(944\) 9.82894 0.319905
\(945\) −21.8126 −0.709563
\(946\) 0.779166 0.0253329
\(947\) −4.07217 −0.132328 −0.0661639 0.997809i \(-0.521076\pi\)
−0.0661639 + 0.997809i \(0.521076\pi\)
\(948\) −8.34224 −0.270943
\(949\) 6.77934 0.220067
\(950\) 4.95938 0.160903
\(951\) 22.5308 0.730611
\(952\) −9.40361 −0.304773
\(953\) 25.7356 0.833656 0.416828 0.908985i \(-0.363142\pi\)
0.416828 + 0.908985i \(0.363142\pi\)
\(954\) −22.1240 −0.716290
\(955\) −4.39707 −0.142286
\(956\) −21.0286 −0.680113
\(957\) 2.06093 0.0666204
\(958\) −3.17305 −0.102517
\(959\) 67.0523 2.16523
\(960\) 0.876107 0.0282762
\(961\) 26.1415 0.843273
\(962\) −10.4295 −0.336261
\(963\) 19.9133 0.641698
\(964\) −11.6531 −0.375322
\(965\) 18.8033 0.605299
\(966\) 33.3097 1.07172
\(967\) 42.7571 1.37498 0.687488 0.726196i \(-0.258713\pi\)
0.687488 + 0.726196i \(0.258713\pi\)
\(968\) 10.8435 0.348522
\(969\) 8.58683 0.275849
\(970\) −10.6902 −0.343240
\(971\) −27.5600 −0.884443 −0.442222 0.896906i \(-0.645810\pi\)
−0.442222 + 0.896906i \(0.645810\pi\)
\(972\) −16.1014 −0.516454
\(973\) 43.9867 1.41015
\(974\) 27.7483 0.889112
\(975\) 1.21774 0.0389988
\(976\) −5.61187 −0.179632
\(977\) −4.71904 −0.150975 −0.0754877 0.997147i \(-0.524051\pi\)
−0.0754877 + 0.997147i \(0.524051\pi\)
\(978\) −8.14371 −0.260407
\(979\) 2.85338 0.0911943
\(980\) −15.6408 −0.499627
\(981\) −0.0768076 −0.00245228
\(982\) −29.5110 −0.941735
\(983\) −39.5987 −1.26300 −0.631502 0.775374i \(-0.717561\pi\)
−0.631502 + 0.775374i \(0.717561\pi\)
\(984\) −3.19321 −0.101796
\(985\) −15.7824 −0.502868
\(986\) 11.7499 0.374194
\(987\) −41.7899 −1.33019
\(988\) 6.89323 0.219303
\(989\) −15.7354 −0.500356
\(990\) −0.883281 −0.0280725
\(991\) 27.7183 0.880499 0.440250 0.897875i \(-0.354890\pi\)
0.440250 + 0.897875i \(0.354890\pi\)
\(992\) 7.55920 0.240005
\(993\) 20.5286 0.651457
\(994\) −12.6601 −0.401555
\(995\) 6.39499 0.202735
\(996\) 9.95778 0.315524
\(997\) 8.22414 0.260461 0.130231 0.991484i \(-0.458428\pi\)
0.130231 + 0.991484i \(0.458428\pi\)
\(998\) 38.3533 1.21405
\(999\) −34.3977 −1.08829
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 \(a_p\))