Properties

Label 4017.2.a.j.1.25
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.73802 q^{2} -1.00000 q^{3} +5.49677 q^{4} +2.25213 q^{5} -2.73802 q^{6} -2.23039 q^{7} +9.57422 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.73802 q^{2} -1.00000 q^{3} +5.49677 q^{4} +2.25213 q^{5} -2.73802 q^{6} -2.23039 q^{7} +9.57422 q^{8} +1.00000 q^{9} +6.16638 q^{10} +4.01232 q^{11} -5.49677 q^{12} +1.00000 q^{13} -6.10685 q^{14} -2.25213 q^{15} +15.2209 q^{16} +1.93575 q^{17} +2.73802 q^{18} -3.89952 q^{19} +12.3794 q^{20} +2.23039 q^{21} +10.9858 q^{22} +1.46506 q^{23} -9.57422 q^{24} +0.0720843 q^{25} +2.73802 q^{26} -1.00000 q^{27} -12.2599 q^{28} -0.0392005 q^{29} -6.16638 q^{30} -0.286582 q^{31} +22.5267 q^{32} -4.01232 q^{33} +5.30011 q^{34} -5.02312 q^{35} +5.49677 q^{36} +0.862130 q^{37} -10.6770 q^{38} -1.00000 q^{39} +21.5624 q^{40} -6.36427 q^{41} +6.10685 q^{42} +2.68261 q^{43} +22.0548 q^{44} +2.25213 q^{45} +4.01136 q^{46} +3.27883 q^{47} -15.2209 q^{48} -2.02537 q^{49} +0.197368 q^{50} -1.93575 q^{51} +5.49677 q^{52} -11.3322 q^{53} -2.73802 q^{54} +9.03626 q^{55} -21.3542 q^{56} +3.89952 q^{57} -0.107332 q^{58} +12.5156 q^{59} -12.3794 q^{60} +1.47526 q^{61} -0.784668 q^{62} -2.23039 q^{63} +31.2369 q^{64} +2.25213 q^{65} -10.9858 q^{66} +3.33628 q^{67} +10.6403 q^{68} -1.46506 q^{69} -13.7534 q^{70} -4.53598 q^{71} +9.57422 q^{72} +7.69775 q^{73} +2.36053 q^{74} -0.0720843 q^{75} -21.4347 q^{76} -8.94903 q^{77} -2.73802 q^{78} +3.50200 q^{79} +34.2794 q^{80} +1.00000 q^{81} -17.4255 q^{82} -6.37677 q^{83} +12.2599 q^{84} +4.35955 q^{85} +7.34504 q^{86} +0.0392005 q^{87} +38.4148 q^{88} -9.23478 q^{89} +6.16638 q^{90} -2.23039 q^{91} +8.05309 q^{92} +0.286582 q^{93} +8.97752 q^{94} -8.78222 q^{95} -22.5267 q^{96} -17.3424 q^{97} -5.54550 q^{98} +4.01232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.73802 1.93607 0.968037 0.250807i \(-0.0806960\pi\)
0.968037 + 0.250807i \(0.0806960\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.49677 2.74838
\(5\) 2.25213 1.00718 0.503591 0.863942i \(-0.332012\pi\)
0.503591 + 0.863942i \(0.332012\pi\)
\(6\) −2.73802 −1.11779
\(7\) −2.23039 −0.843008 −0.421504 0.906827i \(-0.638498\pi\)
−0.421504 + 0.906827i \(0.638498\pi\)
\(8\) 9.57422 3.38500
\(9\) 1.00000 0.333333
\(10\) 6.16638 1.94998
\(11\) 4.01232 1.20976 0.604880 0.796317i \(-0.293221\pi\)
0.604880 + 0.796317i \(0.293221\pi\)
\(12\) −5.49677 −1.58678
\(13\) 1.00000 0.277350
\(14\) −6.10685 −1.63213
\(15\) −2.25213 −0.581497
\(16\) 15.2209 3.80523
\(17\) 1.93575 0.469487 0.234744 0.972057i \(-0.424575\pi\)
0.234744 + 0.972057i \(0.424575\pi\)
\(18\) 2.73802 0.645358
\(19\) −3.89952 −0.894611 −0.447306 0.894381i \(-0.647616\pi\)
−0.447306 + 0.894381i \(0.647616\pi\)
\(20\) 12.3794 2.76812
\(21\) 2.23039 0.486711
\(22\) 10.9858 2.34218
\(23\) 1.46506 0.305486 0.152743 0.988266i \(-0.451189\pi\)
0.152743 + 0.988266i \(0.451189\pi\)
\(24\) −9.57422 −1.95433
\(25\) 0.0720843 0.0144169
\(26\) 2.73802 0.536970
\(27\) −1.00000 −0.192450
\(28\) −12.2599 −2.31691
\(29\) −0.0392005 −0.00727935 −0.00363968 0.999993i \(-0.501159\pi\)
−0.00363968 + 0.999993i \(0.501159\pi\)
\(30\) −6.16638 −1.12582
\(31\) −0.286582 −0.0514716 −0.0257358 0.999669i \(-0.508193\pi\)
−0.0257358 + 0.999669i \(0.508193\pi\)
\(32\) 22.5267 3.98220
\(33\) −4.01232 −0.698455
\(34\) 5.30011 0.908962
\(35\) −5.02312 −0.849063
\(36\) 5.49677 0.916128
\(37\) 0.862130 0.141733 0.0708667 0.997486i \(-0.477424\pi\)
0.0708667 + 0.997486i \(0.477424\pi\)
\(38\) −10.6770 −1.73203
\(39\) −1.00000 −0.160128
\(40\) 21.5624 3.40931
\(41\) −6.36427 −0.993932 −0.496966 0.867770i \(-0.665553\pi\)
−0.496966 + 0.867770i \(0.665553\pi\)
\(42\) 6.10685 0.942308
\(43\) 2.68261 0.409094 0.204547 0.978857i \(-0.434428\pi\)
0.204547 + 0.978857i \(0.434428\pi\)
\(44\) 22.0548 3.32488
\(45\) 2.25213 0.335728
\(46\) 4.01136 0.591443
\(47\) 3.27883 0.478267 0.239133 0.970987i \(-0.423137\pi\)
0.239133 + 0.970987i \(0.423137\pi\)
\(48\) −15.2209 −2.19695
\(49\) −2.02537 −0.289338
\(50\) 0.197368 0.0279121
\(51\) −1.93575 −0.271059
\(52\) 5.49677 0.762264
\(53\) −11.3322 −1.55660 −0.778298 0.627895i \(-0.783917\pi\)
−0.778298 + 0.627895i \(0.783917\pi\)
\(54\) −2.73802 −0.372598
\(55\) 9.03626 1.21845
\(56\) −21.3542 −2.85358
\(57\) 3.89952 0.516504
\(58\) −0.107332 −0.0140934
\(59\) 12.5156 1.62940 0.814698 0.579886i \(-0.196903\pi\)
0.814698 + 0.579886i \(0.196903\pi\)
\(60\) −12.3794 −1.59818
\(61\) 1.47526 0.188888 0.0944439 0.995530i \(-0.469893\pi\)
0.0944439 + 0.995530i \(0.469893\pi\)
\(62\) −0.784668 −0.0996529
\(63\) −2.23039 −0.281003
\(64\) 31.2369 3.90461
\(65\) 2.25213 0.279342
\(66\) −10.9858 −1.35226
\(67\) 3.33628 0.407591 0.203796 0.979013i \(-0.434672\pi\)
0.203796 + 0.979013i \(0.434672\pi\)
\(68\) 10.6403 1.29033
\(69\) −1.46506 −0.176372
\(70\) −13.7534 −1.64385
\(71\) −4.53598 −0.538321 −0.269161 0.963095i \(-0.586746\pi\)
−0.269161 + 0.963095i \(0.586746\pi\)
\(72\) 9.57422 1.12833
\(73\) 7.69775 0.900954 0.450477 0.892788i \(-0.351254\pi\)
0.450477 + 0.892788i \(0.351254\pi\)
\(74\) 2.36053 0.274406
\(75\) −0.0720843 −0.00832358
\(76\) −21.4347 −2.45873
\(77\) −8.94903 −1.01984
\(78\) −2.73802 −0.310020
\(79\) 3.50200 0.394005 0.197003 0.980403i \(-0.436879\pi\)
0.197003 + 0.980403i \(0.436879\pi\)
\(80\) 34.2794 3.83256
\(81\) 1.00000 0.111111
\(82\) −17.4255 −1.92433
\(83\) −6.37677 −0.699941 −0.349970 0.936761i \(-0.613808\pi\)
−0.349970 + 0.936761i \(0.613808\pi\)
\(84\) 12.2599 1.33767
\(85\) 4.35955 0.472859
\(86\) 7.34504 0.792036
\(87\) 0.0392005 0.00420274
\(88\) 38.4148 4.09503
\(89\) −9.23478 −0.978885 −0.489442 0.872036i \(-0.662800\pi\)
−0.489442 + 0.872036i \(0.662800\pi\)
\(90\) 6.16638 0.649993
\(91\) −2.23039 −0.233808
\(92\) 8.05309 0.839592
\(93\) 0.286582 0.0297172
\(94\) 8.97752 0.925960
\(95\) −8.78222 −0.901037
\(96\) −22.5267 −2.29912
\(97\) −17.3424 −1.76086 −0.880428 0.474180i \(-0.842744\pi\)
−0.880428 + 0.474180i \(0.842744\pi\)
\(98\) −5.54550 −0.560180
\(99\) 4.01232 0.403253
\(100\) 0.396230 0.0396230
\(101\) −2.92744 −0.291291 −0.145646 0.989337i \(-0.546526\pi\)
−0.145646 + 0.989337i \(0.546526\pi\)
\(102\) −5.30011 −0.524789
\(103\) −1.00000 −0.0985329
\(104\) 9.57422 0.938830
\(105\) 5.02312 0.490207
\(106\) −31.0278 −3.01369
\(107\) −6.90978 −0.667994 −0.333997 0.942574i \(-0.608398\pi\)
−0.333997 + 0.942574i \(0.608398\pi\)
\(108\) −5.49677 −0.528927
\(109\) 1.29481 0.124020 0.0620100 0.998076i \(-0.480249\pi\)
0.0620100 + 0.998076i \(0.480249\pi\)
\(110\) 24.7415 2.35901
\(111\) −0.862130 −0.0818298
\(112\) −33.9485 −3.20783
\(113\) 13.8148 1.29959 0.649795 0.760109i \(-0.274855\pi\)
0.649795 + 0.760109i \(0.274855\pi\)
\(114\) 10.6770 0.999990
\(115\) 3.29950 0.307680
\(116\) −0.215476 −0.0200064
\(117\) 1.00000 0.0924500
\(118\) 34.2681 3.15463
\(119\) −4.31746 −0.395781
\(120\) −21.5624 −1.96837
\(121\) 5.09870 0.463518
\(122\) 4.03930 0.365701
\(123\) 6.36427 0.573847
\(124\) −1.57527 −0.141464
\(125\) −11.0983 −0.992662
\(126\) −6.10685 −0.544042
\(127\) 18.7055 1.65984 0.829922 0.557879i \(-0.188385\pi\)
0.829922 + 0.557879i \(0.188385\pi\)
\(128\) 40.4738 3.57741
\(129\) −2.68261 −0.236190
\(130\) 6.16638 0.540827
\(131\) 16.8203 1.46959 0.734797 0.678287i \(-0.237277\pi\)
0.734797 + 0.678287i \(0.237277\pi\)
\(132\) −22.0548 −1.91962
\(133\) 8.69744 0.754164
\(134\) 9.13481 0.789127
\(135\) −2.25213 −0.193832
\(136\) 18.5333 1.58921
\(137\) −5.88521 −0.502808 −0.251404 0.967882i \(-0.580892\pi\)
−0.251404 + 0.967882i \(0.580892\pi\)
\(138\) −4.01136 −0.341470
\(139\) −4.02739 −0.341599 −0.170799 0.985306i \(-0.554635\pi\)
−0.170799 + 0.985306i \(0.554635\pi\)
\(140\) −27.6109 −2.33355
\(141\) −3.27883 −0.276127
\(142\) −12.4196 −1.04223
\(143\) 4.01232 0.335527
\(144\) 15.2209 1.26841
\(145\) −0.0882846 −0.00733164
\(146\) 21.0766 1.74431
\(147\) 2.02537 0.167050
\(148\) 4.73893 0.389537
\(149\) 19.3486 1.58510 0.792549 0.609809i \(-0.208754\pi\)
0.792549 + 0.609809i \(0.208754\pi\)
\(150\) −0.197368 −0.0161151
\(151\) 7.51787 0.611796 0.305898 0.952064i \(-0.401043\pi\)
0.305898 + 0.952064i \(0.401043\pi\)
\(152\) −37.3349 −3.02826
\(153\) 1.93575 0.156496
\(154\) −24.5026 −1.97448
\(155\) −0.645420 −0.0518414
\(156\) −5.49677 −0.440093
\(157\) 6.80666 0.543231 0.271615 0.962406i \(-0.412442\pi\)
0.271615 + 0.962406i \(0.412442\pi\)
\(158\) 9.58854 0.762823
\(159\) 11.3322 0.898701
\(160\) 50.7331 4.01080
\(161\) −3.26765 −0.257527
\(162\) 2.73802 0.215119
\(163\) 25.0489 1.96198 0.980989 0.194064i \(-0.0621671\pi\)
0.980989 + 0.194064i \(0.0621671\pi\)
\(164\) −34.9829 −2.73171
\(165\) −9.03626 −0.703472
\(166\) −17.4597 −1.35514
\(167\) −12.1377 −0.939241 −0.469620 0.882868i \(-0.655609\pi\)
−0.469620 + 0.882868i \(0.655609\pi\)
\(168\) 21.3542 1.64751
\(169\) 1.00000 0.0769231
\(170\) 11.9365 0.915491
\(171\) −3.89952 −0.298204
\(172\) 14.7457 1.12435
\(173\) −10.3059 −0.783545 −0.391773 0.920062i \(-0.628138\pi\)
−0.391773 + 0.920062i \(0.628138\pi\)
\(174\) 0.107332 0.00813681
\(175\) −0.160776 −0.0121535
\(176\) 61.0711 4.60341
\(177\) −12.5156 −0.940732
\(178\) −25.2850 −1.89519
\(179\) −24.9691 −1.86628 −0.933140 0.359514i \(-0.882943\pi\)
−0.933140 + 0.359514i \(0.882943\pi\)
\(180\) 12.3794 0.922708
\(181\) −19.6972 −1.46408 −0.732042 0.681260i \(-0.761433\pi\)
−0.732042 + 0.681260i \(0.761433\pi\)
\(182\) −6.10685 −0.452670
\(183\) −1.47526 −0.109054
\(184\) 14.0268 1.03407
\(185\) 1.94163 0.142751
\(186\) 0.784668 0.0575346
\(187\) 7.76683 0.567967
\(188\) 18.0230 1.31446
\(189\) 2.23039 0.162237
\(190\) −24.0459 −1.74447
\(191\) −16.8097 −1.21631 −0.608153 0.793820i \(-0.708089\pi\)
−0.608153 + 0.793820i \(0.708089\pi\)
\(192\) −31.2369 −2.25433
\(193\) −13.7159 −0.987292 −0.493646 0.869663i \(-0.664336\pi\)
−0.493646 + 0.869663i \(0.664336\pi\)
\(194\) −47.4839 −3.40915
\(195\) −2.25213 −0.161278
\(196\) −11.1330 −0.795212
\(197\) −3.72352 −0.265290 −0.132645 0.991164i \(-0.542347\pi\)
−0.132645 + 0.991164i \(0.542347\pi\)
\(198\) 10.9858 0.780728
\(199\) 21.3145 1.51094 0.755472 0.655181i \(-0.227408\pi\)
0.755472 + 0.655181i \(0.227408\pi\)
\(200\) 0.690151 0.0488010
\(201\) −3.33628 −0.235323
\(202\) −8.01540 −0.563961
\(203\) 0.0874324 0.00613655
\(204\) −10.6403 −0.744973
\(205\) −14.3332 −1.00107
\(206\) −2.73802 −0.190767
\(207\) 1.46506 0.101829
\(208\) 15.2209 1.05538
\(209\) −15.6461 −1.08226
\(210\) 13.7534 0.949076
\(211\) −0.347438 −0.0239186 −0.0119593 0.999928i \(-0.503807\pi\)
−0.0119593 + 0.999928i \(0.503807\pi\)
\(212\) −62.2904 −4.27812
\(213\) 4.53598 0.310800
\(214\) −18.9191 −1.29329
\(215\) 6.04158 0.412032
\(216\) −9.57422 −0.651443
\(217\) 0.639189 0.0433910
\(218\) 3.54521 0.240112
\(219\) −7.69775 −0.520166
\(220\) 49.6702 3.34876
\(221\) 1.93575 0.130212
\(222\) −2.36053 −0.158429
\(223\) −8.88346 −0.594880 −0.297440 0.954740i \(-0.596133\pi\)
−0.297440 + 0.954740i \(0.596133\pi\)
\(224\) −50.2433 −3.35702
\(225\) 0.0720843 0.00480562
\(226\) 37.8253 2.51610
\(227\) −15.3482 −1.01870 −0.509349 0.860560i \(-0.670114\pi\)
−0.509349 + 0.860560i \(0.670114\pi\)
\(228\) 21.4347 1.41955
\(229\) −11.4562 −0.757044 −0.378522 0.925592i \(-0.623568\pi\)
−0.378522 + 0.925592i \(0.623568\pi\)
\(230\) 9.03411 0.595692
\(231\) 8.94903 0.588803
\(232\) −0.375314 −0.0246406
\(233\) 10.4366 0.683724 0.341862 0.939750i \(-0.388942\pi\)
0.341862 + 0.939750i \(0.388942\pi\)
\(234\) 2.73802 0.178990
\(235\) 7.38435 0.481702
\(236\) 68.7955 4.47820
\(237\) −3.50200 −0.227479
\(238\) −11.8213 −0.766262
\(239\) 4.27431 0.276482 0.138241 0.990399i \(-0.455855\pi\)
0.138241 + 0.990399i \(0.455855\pi\)
\(240\) −34.2794 −2.21273
\(241\) −15.5365 −1.00080 −0.500398 0.865796i \(-0.666813\pi\)
−0.500398 + 0.865796i \(0.666813\pi\)
\(242\) 13.9603 0.897405
\(243\) −1.00000 −0.0641500
\(244\) 8.10916 0.519136
\(245\) −4.56139 −0.291416
\(246\) 17.4255 1.11101
\(247\) −3.89952 −0.248121
\(248\) −2.74380 −0.174231
\(249\) 6.37677 0.404111
\(250\) −30.3874 −1.92187
\(251\) −3.10336 −0.195882 −0.0979412 0.995192i \(-0.531226\pi\)
−0.0979412 + 0.995192i \(0.531226\pi\)
\(252\) −12.2599 −0.772303
\(253\) 5.87828 0.369565
\(254\) 51.2161 3.21358
\(255\) −4.35955 −0.273005
\(256\) 48.3444 3.02152
\(257\) −17.7908 −1.10976 −0.554879 0.831931i \(-0.687236\pi\)
−0.554879 + 0.831931i \(0.687236\pi\)
\(258\) −7.34504 −0.457282
\(259\) −1.92289 −0.119482
\(260\) 12.3794 0.767739
\(261\) −0.0392005 −0.00242645
\(262\) 46.0543 2.84524
\(263\) −6.04045 −0.372470 −0.186235 0.982505i \(-0.559629\pi\)
−0.186235 + 0.982505i \(0.559629\pi\)
\(264\) −38.4148 −2.36427
\(265\) −25.5216 −1.56778
\(266\) 23.8138 1.46012
\(267\) 9.23478 0.565159
\(268\) 18.3387 1.12022
\(269\) −16.9184 −1.03153 −0.515766 0.856729i \(-0.672493\pi\)
−0.515766 + 0.856729i \(0.672493\pi\)
\(270\) −6.16638 −0.375274
\(271\) −16.4202 −0.997456 −0.498728 0.866758i \(-0.666199\pi\)
−0.498728 + 0.866758i \(0.666199\pi\)
\(272\) 29.4638 1.78650
\(273\) 2.23039 0.134989
\(274\) −16.1138 −0.973473
\(275\) 0.289225 0.0174409
\(276\) −8.05309 −0.484739
\(277\) −7.13667 −0.428801 −0.214401 0.976746i \(-0.568780\pi\)
−0.214401 + 0.976746i \(0.568780\pi\)
\(278\) −11.0271 −0.661360
\(279\) −0.286582 −0.0171572
\(280\) −48.0925 −2.87408
\(281\) −8.08608 −0.482375 −0.241188 0.970479i \(-0.577537\pi\)
−0.241188 + 0.970479i \(0.577537\pi\)
\(282\) −8.97752 −0.534603
\(283\) 1.86933 0.111120 0.0555600 0.998455i \(-0.482306\pi\)
0.0555600 + 0.998455i \(0.482306\pi\)
\(284\) −24.9332 −1.47951
\(285\) 8.78222 0.520214
\(286\) 10.9858 0.649605
\(287\) 14.1948 0.837893
\(288\) 22.5267 1.32740
\(289\) −13.2529 −0.779582
\(290\) −0.241725 −0.0141946
\(291\) 17.3424 1.01663
\(292\) 42.3127 2.47617
\(293\) −2.61365 −0.152691 −0.0763455 0.997081i \(-0.524325\pi\)
−0.0763455 + 0.997081i \(0.524325\pi\)
\(294\) 5.54550 0.323420
\(295\) 28.1868 1.64110
\(296\) 8.25423 0.479767
\(297\) −4.01232 −0.232818
\(298\) 52.9768 3.06887
\(299\) 1.46506 0.0847266
\(300\) −0.396230 −0.0228764
\(301\) −5.98325 −0.344869
\(302\) 20.5841 1.18448
\(303\) 2.92744 0.168177
\(304\) −59.3542 −3.40420
\(305\) 3.32248 0.190244
\(306\) 5.30011 0.302987
\(307\) 13.8308 0.789366 0.394683 0.918817i \(-0.370854\pi\)
0.394683 + 0.918817i \(0.370854\pi\)
\(308\) −49.1907 −2.80290
\(309\) 1.00000 0.0568880
\(310\) −1.76717 −0.100369
\(311\) 1.27395 0.0722389 0.0361195 0.999347i \(-0.488500\pi\)
0.0361195 + 0.999347i \(0.488500\pi\)
\(312\) −9.57422 −0.542034
\(313\) 2.55357 0.144336 0.0721681 0.997392i \(-0.477008\pi\)
0.0721681 + 0.997392i \(0.477008\pi\)
\(314\) 18.6368 1.05173
\(315\) −5.02312 −0.283021
\(316\) 19.2496 1.08288
\(317\) 17.1973 0.965894 0.482947 0.875649i \(-0.339566\pi\)
0.482947 + 0.875649i \(0.339566\pi\)
\(318\) 31.0278 1.73995
\(319\) −0.157285 −0.00880627
\(320\) 70.3494 3.93265
\(321\) 6.90978 0.385666
\(322\) −8.94690 −0.498591
\(323\) −7.54848 −0.420009
\(324\) 5.49677 0.305376
\(325\) 0.0720843 0.00399852
\(326\) 68.5843 3.79853
\(327\) −1.29481 −0.0716029
\(328\) −60.9330 −3.36446
\(329\) −7.31307 −0.403183
\(330\) −24.7415 −1.36197
\(331\) 6.63238 0.364548 0.182274 0.983248i \(-0.441654\pi\)
0.182274 + 0.983248i \(0.441654\pi\)
\(332\) −35.0516 −1.92371
\(333\) 0.862130 0.0472444
\(334\) −33.2332 −1.81844
\(335\) 7.51373 0.410519
\(336\) 33.9485 1.85204
\(337\) 8.19212 0.446253 0.223127 0.974789i \(-0.428374\pi\)
0.223127 + 0.974789i \(0.428374\pi\)
\(338\) 2.73802 0.148929
\(339\) −13.8148 −0.750319
\(340\) 23.9634 1.29960
\(341\) −1.14986 −0.0622683
\(342\) −10.6770 −0.577345
\(343\) 20.1301 1.08692
\(344\) 25.6839 1.38478
\(345\) −3.29950 −0.177639
\(346\) −28.2179 −1.51700
\(347\) 14.9052 0.800153 0.400076 0.916482i \(-0.368984\pi\)
0.400076 + 0.916482i \(0.368984\pi\)
\(348\) 0.215476 0.0115507
\(349\) −0.206241 −0.0110398 −0.00551990 0.999985i \(-0.501757\pi\)
−0.00551990 + 0.999985i \(0.501757\pi\)
\(350\) −0.440208 −0.0235301
\(351\) −1.00000 −0.0533761
\(352\) 90.3844 4.81750
\(353\) 15.8088 0.841416 0.420708 0.907196i \(-0.361782\pi\)
0.420708 + 0.907196i \(0.361782\pi\)
\(354\) −34.2681 −1.82133
\(355\) −10.2156 −0.542188
\(356\) −50.7614 −2.69035
\(357\) 4.31746 0.228504
\(358\) −68.3660 −3.61326
\(359\) 22.9336 1.21039 0.605195 0.796077i \(-0.293095\pi\)
0.605195 + 0.796077i \(0.293095\pi\)
\(360\) 21.5624 1.13644
\(361\) −3.79375 −0.199671
\(362\) −53.9315 −2.83457
\(363\) −5.09870 −0.267612
\(364\) −12.2599 −0.642595
\(365\) 17.3363 0.907425
\(366\) −4.03930 −0.211137
\(367\) −21.8950 −1.14291 −0.571455 0.820633i \(-0.693621\pi\)
−0.571455 + 0.820633i \(0.693621\pi\)
\(368\) 22.2995 1.16244
\(369\) −6.36427 −0.331311
\(370\) 5.31622 0.276377
\(371\) 25.2752 1.31222
\(372\) 1.57527 0.0816742
\(373\) −28.3129 −1.46599 −0.732994 0.680235i \(-0.761878\pi\)
−0.732994 + 0.680235i \(0.761878\pi\)
\(374\) 21.2657 1.09963
\(375\) 11.0983 0.573114
\(376\) 31.3923 1.61893
\(377\) −0.0392005 −0.00201893
\(378\) 6.10685 0.314103
\(379\) −4.66157 −0.239449 −0.119724 0.992807i \(-0.538201\pi\)
−0.119724 + 0.992807i \(0.538201\pi\)
\(380\) −48.2738 −2.47639
\(381\) −18.7055 −0.958312
\(382\) −46.0253 −2.35486
\(383\) −25.4152 −1.29866 −0.649328 0.760509i \(-0.724950\pi\)
−0.649328 + 0.760509i \(0.724950\pi\)
\(384\) −40.4738 −2.06542
\(385\) −20.1544 −1.02716
\(386\) −37.5544 −1.91147
\(387\) 2.68261 0.136365
\(388\) −95.3272 −4.83950
\(389\) 22.8812 1.16012 0.580060 0.814573i \(-0.303029\pi\)
0.580060 + 0.814573i \(0.303029\pi\)
\(390\) −6.16638 −0.312247
\(391\) 2.83598 0.143422
\(392\) −19.3913 −0.979410
\(393\) −16.8203 −0.848471
\(394\) −10.1951 −0.513621
\(395\) 7.88694 0.396835
\(396\) 22.0548 1.10829
\(397\) 8.76949 0.440128 0.220064 0.975485i \(-0.429373\pi\)
0.220064 + 0.975485i \(0.429373\pi\)
\(398\) 58.3596 2.92530
\(399\) −8.69744 −0.435417
\(400\) 1.09719 0.0548594
\(401\) −10.3080 −0.514757 −0.257379 0.966311i \(-0.582859\pi\)
−0.257379 + 0.966311i \(0.582859\pi\)
\(402\) −9.13481 −0.455603
\(403\) −0.286582 −0.0142757
\(404\) −16.0915 −0.800580
\(405\) 2.25213 0.111909
\(406\) 0.239392 0.0118808
\(407\) 3.45914 0.171463
\(408\) −18.5333 −0.917533
\(409\) −30.9929 −1.53250 −0.766250 0.642543i \(-0.777879\pi\)
−0.766250 + 0.642543i \(0.777879\pi\)
\(410\) −39.2445 −1.93815
\(411\) 5.88521 0.290296
\(412\) −5.49677 −0.270806
\(413\) −27.9147 −1.37359
\(414\) 4.01136 0.197148
\(415\) −14.3613 −0.704968
\(416\) 22.5267 1.10446
\(417\) 4.02739 0.197222
\(418\) −42.8394 −2.09534
\(419\) 26.0310 1.27170 0.635850 0.771813i \(-0.280650\pi\)
0.635850 + 0.771813i \(0.280650\pi\)
\(420\) 27.6109 1.34728
\(421\) 5.86010 0.285604 0.142802 0.989751i \(-0.454389\pi\)
0.142802 + 0.989751i \(0.454389\pi\)
\(422\) −0.951293 −0.0463082
\(423\) 3.27883 0.159422
\(424\) −108.497 −5.26908
\(425\) 0.139537 0.00676853
\(426\) 12.4196 0.601732
\(427\) −3.29040 −0.159234
\(428\) −37.9815 −1.83590
\(429\) −4.01232 −0.193717
\(430\) 16.5420 0.797725
\(431\) 22.3070 1.07449 0.537244 0.843427i \(-0.319465\pi\)
0.537244 + 0.843427i \(0.319465\pi\)
\(432\) −15.2209 −0.732316
\(433\) 12.5592 0.603559 0.301779 0.953378i \(-0.402419\pi\)
0.301779 + 0.953378i \(0.402419\pi\)
\(434\) 1.75011 0.0840082
\(435\) 0.0882846 0.00423292
\(436\) 7.11724 0.340854
\(437\) −5.71303 −0.273291
\(438\) −21.0766 −1.00708
\(439\) 20.4122 0.974223 0.487112 0.873340i \(-0.338050\pi\)
0.487112 + 0.873340i \(0.338050\pi\)
\(440\) 86.5151 4.12445
\(441\) −2.02537 −0.0964461
\(442\) 5.30011 0.252101
\(443\) −6.84950 −0.325430 −0.162715 0.986673i \(-0.552025\pi\)
−0.162715 + 0.986673i \(0.552025\pi\)
\(444\) −4.73893 −0.224900
\(445\) −20.7979 −0.985916
\(446\) −24.3231 −1.15173
\(447\) −19.3486 −0.915156
\(448\) −69.6703 −3.29161
\(449\) 19.0147 0.897359 0.448679 0.893693i \(-0.351894\pi\)
0.448679 + 0.893693i \(0.351894\pi\)
\(450\) 0.197368 0.00930403
\(451\) −25.5355 −1.20242
\(452\) 75.9369 3.57177
\(453\) −7.51787 −0.353220
\(454\) −42.0238 −1.97227
\(455\) −5.02312 −0.235488
\(456\) 37.3349 1.74837
\(457\) 29.2712 1.36925 0.684624 0.728897i \(-0.259967\pi\)
0.684624 + 0.728897i \(0.259967\pi\)
\(458\) −31.3672 −1.46569
\(459\) −1.93575 −0.0903529
\(460\) 18.1366 0.845623
\(461\) −31.9394 −1.48757 −0.743784 0.668420i \(-0.766971\pi\)
−0.743784 + 0.668420i \(0.766971\pi\)
\(462\) 24.5026 1.13997
\(463\) 7.27286 0.337998 0.168999 0.985616i \(-0.445946\pi\)
0.168999 + 0.985616i \(0.445946\pi\)
\(464\) −0.596667 −0.0276996
\(465\) 0.645420 0.0299306
\(466\) 28.5756 1.32374
\(467\) 19.9052 0.921101 0.460551 0.887633i \(-0.347652\pi\)
0.460551 + 0.887633i \(0.347652\pi\)
\(468\) 5.49677 0.254088
\(469\) −7.44120 −0.343603
\(470\) 20.2185 0.932611
\(471\) −6.80666 −0.313634
\(472\) 119.827 5.51550
\(473\) 10.7635 0.494905
\(474\) −9.58854 −0.440416
\(475\) −0.281094 −0.0128975
\(476\) −23.7321 −1.08776
\(477\) −11.3322 −0.518866
\(478\) 11.7032 0.535290
\(479\) −42.0670 −1.92209 −0.961046 0.276389i \(-0.910862\pi\)
−0.961046 + 0.276389i \(0.910862\pi\)
\(480\) −50.7331 −2.31564
\(481\) 0.862130 0.0393098
\(482\) −42.5394 −1.93761
\(483\) 3.26765 0.148683
\(484\) 28.0263 1.27392
\(485\) −39.0574 −1.77350
\(486\) −2.73802 −0.124199
\(487\) −31.9367 −1.44719 −0.723596 0.690224i \(-0.757512\pi\)
−0.723596 + 0.690224i \(0.757512\pi\)
\(488\) 14.1245 0.639385
\(489\) −25.0489 −1.13275
\(490\) −12.4892 −0.564204
\(491\) −12.9039 −0.582347 −0.291173 0.956670i \(-0.594046\pi\)
−0.291173 + 0.956670i \(0.594046\pi\)
\(492\) 34.9829 1.57715
\(493\) −0.0758822 −0.00341756
\(494\) −10.6770 −0.480380
\(495\) 9.03626 0.406150
\(496\) −4.36204 −0.195861
\(497\) 10.1170 0.453809
\(498\) 17.4597 0.782389
\(499\) 34.8983 1.56226 0.781130 0.624368i \(-0.214643\pi\)
0.781130 + 0.624368i \(0.214643\pi\)
\(500\) −61.0048 −2.72822
\(501\) 12.1377 0.542271
\(502\) −8.49707 −0.379243
\(503\) −23.7413 −1.05857 −0.529287 0.848443i \(-0.677540\pi\)
−0.529287 + 0.848443i \(0.677540\pi\)
\(504\) −21.3542 −0.951193
\(505\) −6.59297 −0.293383
\(506\) 16.0949 0.715504
\(507\) −1.00000 −0.0444116
\(508\) 102.820 4.56189
\(509\) 20.9102 0.926828 0.463414 0.886142i \(-0.346624\pi\)
0.463414 + 0.886142i \(0.346624\pi\)
\(510\) −11.9365 −0.528559
\(511\) −17.1690 −0.759511
\(512\) 51.4204 2.27248
\(513\) 3.89952 0.172168
\(514\) −48.7116 −2.14857
\(515\) −2.25213 −0.0992407
\(516\) −14.7457 −0.649141
\(517\) 13.1557 0.578588
\(518\) −5.26490 −0.231327
\(519\) 10.3059 0.452380
\(520\) 21.5624 0.945573
\(521\) 11.4309 0.500799 0.250399 0.968143i \(-0.419438\pi\)
0.250399 + 0.968143i \(0.419438\pi\)
\(522\) −0.107332 −0.00469779
\(523\) −26.2467 −1.14769 −0.573844 0.818965i \(-0.694548\pi\)
−0.573844 + 0.818965i \(0.694548\pi\)
\(524\) 92.4571 4.03901
\(525\) 0.160776 0.00701684
\(526\) −16.5389 −0.721130
\(527\) −0.554750 −0.0241653
\(528\) −61.0711 −2.65778
\(529\) −20.8536 −0.906678
\(530\) −69.8786 −3.03533
\(531\) 12.5156 0.543132
\(532\) 47.8078 2.07273
\(533\) −6.36427 −0.275667
\(534\) 25.2850 1.09419
\(535\) −15.5617 −0.672792
\(536\) 31.9423 1.37970
\(537\) 24.9691 1.07750
\(538\) −46.3229 −1.99712
\(539\) −8.12642 −0.350030
\(540\) −12.3794 −0.532726
\(541\) −6.81108 −0.292831 −0.146416 0.989223i \(-0.546774\pi\)
−0.146416 + 0.989223i \(0.546774\pi\)
\(542\) −44.9589 −1.93115
\(543\) 19.6972 0.845289
\(544\) 43.6060 1.86959
\(545\) 2.91607 0.124911
\(546\) 6.10685 0.261349
\(547\) 14.1543 0.605193 0.302597 0.953119i \(-0.402146\pi\)
0.302597 + 0.953119i \(0.402146\pi\)
\(548\) −32.3496 −1.38191
\(549\) 1.47526 0.0629626
\(550\) 0.791905 0.0337669
\(551\) 0.152863 0.00651219
\(552\) −14.0268 −0.597020
\(553\) −7.81081 −0.332149
\(554\) −19.5404 −0.830191
\(555\) −1.94163 −0.0824175
\(556\) −22.1376 −0.938843
\(557\) −23.5680 −0.998608 −0.499304 0.866427i \(-0.666411\pi\)
−0.499304 + 0.866427i \(0.666411\pi\)
\(558\) −0.784668 −0.0332176
\(559\) 2.68261 0.113462
\(560\) −76.4564 −3.23087
\(561\) −7.76683 −0.327916
\(562\) −22.1399 −0.933914
\(563\) −2.79150 −0.117648 −0.0588239 0.998268i \(-0.518735\pi\)
−0.0588239 + 0.998268i \(0.518735\pi\)
\(564\) −18.0230 −0.758904
\(565\) 31.1128 1.30893
\(566\) 5.11826 0.215137
\(567\) −2.23039 −0.0936675
\(568\) −43.4284 −1.82222
\(569\) −0.812193 −0.0340489 −0.0170245 0.999855i \(-0.505419\pi\)
−0.0170245 + 0.999855i \(0.505419\pi\)
\(570\) 24.0459 1.00717
\(571\) −12.4909 −0.522729 −0.261365 0.965240i \(-0.584172\pi\)
−0.261365 + 0.965240i \(0.584172\pi\)
\(572\) 22.0548 0.922156
\(573\) 16.8097 0.702235
\(574\) 38.8657 1.62222
\(575\) 0.105608 0.00440415
\(576\) 31.2369 1.30154
\(577\) −12.8212 −0.533756 −0.266878 0.963730i \(-0.585992\pi\)
−0.266878 + 0.963730i \(0.585992\pi\)
\(578\) −36.2867 −1.50933
\(579\) 13.7159 0.570013
\(580\) −0.485280 −0.0201501
\(581\) 14.2227 0.590056
\(582\) 47.4839 1.96827
\(583\) −45.4684 −1.88311
\(584\) 73.7000 3.04973
\(585\) 2.25213 0.0931141
\(586\) −7.15623 −0.295621
\(587\) 27.6397 1.14081 0.570405 0.821363i \(-0.306786\pi\)
0.570405 + 0.821363i \(0.306786\pi\)
\(588\) 11.1330 0.459116
\(589\) 1.11753 0.0460471
\(590\) 77.1761 3.17729
\(591\) 3.72352 0.153165
\(592\) 13.1224 0.539327
\(593\) 29.5963 1.21538 0.607688 0.794176i \(-0.292097\pi\)
0.607688 + 0.794176i \(0.292097\pi\)
\(594\) −10.9858 −0.450753
\(595\) −9.72349 −0.398624
\(596\) 106.355 4.35645
\(597\) −21.3145 −0.872344
\(598\) 4.01136 0.164037
\(599\) −30.6489 −1.25228 −0.626141 0.779710i \(-0.715367\pi\)
−0.626141 + 0.779710i \(0.715367\pi\)
\(600\) −0.690151 −0.0281753
\(601\) 12.0523 0.491623 0.245811 0.969318i \(-0.420946\pi\)
0.245811 + 0.969318i \(0.420946\pi\)
\(602\) −16.3823 −0.667692
\(603\) 3.33628 0.135864
\(604\) 41.3240 1.68145
\(605\) 11.4829 0.466847
\(606\) 8.01540 0.325603
\(607\) 33.6940 1.36760 0.683799 0.729671i \(-0.260327\pi\)
0.683799 + 0.729671i \(0.260327\pi\)
\(608\) −87.8434 −3.56252
\(609\) −0.0874324 −0.00354294
\(610\) 9.09702 0.368327
\(611\) 3.27883 0.132647
\(612\) 10.6403 0.430110
\(613\) −1.33551 −0.0539407 −0.0269704 0.999636i \(-0.508586\pi\)
−0.0269704 + 0.999636i \(0.508586\pi\)
\(614\) 37.8691 1.52827
\(615\) 14.3332 0.577969
\(616\) −85.6800 −3.45214
\(617\) −32.8870 −1.32398 −0.661991 0.749512i \(-0.730288\pi\)
−0.661991 + 0.749512i \(0.730288\pi\)
\(618\) 2.73802 0.110139
\(619\) −20.5063 −0.824217 −0.412108 0.911135i \(-0.635208\pi\)
−0.412108 + 0.911135i \(0.635208\pi\)
\(620\) −3.54772 −0.142480
\(621\) −1.46506 −0.0587908
\(622\) 3.48810 0.139860
\(623\) 20.5971 0.825207
\(624\) −15.2209 −0.609324
\(625\) −25.3552 −1.01421
\(626\) 6.99173 0.279446
\(627\) 15.6461 0.624846
\(628\) 37.4146 1.49301
\(629\) 1.66886 0.0665420
\(630\) −13.7534 −0.547949
\(631\) 39.4988 1.57242 0.786211 0.617958i \(-0.212040\pi\)
0.786211 + 0.617958i \(0.212040\pi\)
\(632\) 33.5289 1.33371
\(633\) 0.347438 0.0138094
\(634\) 47.0865 1.87004
\(635\) 42.1272 1.67177
\(636\) 62.2904 2.46998
\(637\) −2.02537 −0.0802480
\(638\) −0.430650 −0.0170496
\(639\) −4.53598 −0.179440
\(640\) 91.1522 3.60311
\(641\) −42.0904 −1.66247 −0.831236 0.555919i \(-0.812366\pi\)
−0.831236 + 0.555919i \(0.812366\pi\)
\(642\) 18.9191 0.746679
\(643\) 36.5921 1.44305 0.721525 0.692388i \(-0.243441\pi\)
0.721525 + 0.692388i \(0.243441\pi\)
\(644\) −17.9615 −0.707783
\(645\) −6.04158 −0.237887
\(646\) −20.6679 −0.813168
\(647\) 0.150619 0.00592144 0.00296072 0.999996i \(-0.499058\pi\)
0.00296072 + 0.999996i \(0.499058\pi\)
\(648\) 9.57422 0.376111
\(649\) 50.2167 1.97118
\(650\) 0.197368 0.00774142
\(651\) −0.639189 −0.0250518
\(652\) 137.688 5.39227
\(653\) 7.77619 0.304306 0.152153 0.988357i \(-0.451379\pi\)
0.152153 + 0.988357i \(0.451379\pi\)
\(654\) −3.54521 −0.138629
\(655\) 37.8814 1.48015
\(656\) −96.8700 −3.78214
\(657\) 7.69775 0.300318
\(658\) −20.0233 −0.780591
\(659\) −10.7563 −0.419004 −0.209502 0.977808i \(-0.567184\pi\)
−0.209502 + 0.977808i \(0.567184\pi\)
\(660\) −49.6702 −1.93341
\(661\) 32.8404 1.27734 0.638671 0.769480i \(-0.279485\pi\)
0.638671 + 0.769480i \(0.279485\pi\)
\(662\) 18.1596 0.705793
\(663\) −1.93575 −0.0751781
\(664\) −61.0526 −2.36930
\(665\) 19.5878 0.759581
\(666\) 2.36053 0.0914687
\(667\) −0.0574311 −0.00222374
\(668\) −66.7179 −2.58139
\(669\) 8.88346 0.343454
\(670\) 20.5728 0.794795
\(671\) 5.91921 0.228509
\(672\) 50.2433 1.93818
\(673\) 14.0879 0.543047 0.271523 0.962432i \(-0.412473\pi\)
0.271523 + 0.962432i \(0.412473\pi\)
\(674\) 22.4302 0.863979
\(675\) −0.0720843 −0.00277453
\(676\) 5.49677 0.211414
\(677\) 31.2527 1.20114 0.600569 0.799573i \(-0.294941\pi\)
0.600569 + 0.799573i \(0.294941\pi\)
\(678\) −37.8253 −1.45267
\(679\) 38.6803 1.48441
\(680\) 41.7393 1.60063
\(681\) 15.3482 0.588145
\(682\) −3.14834 −0.120556
\(683\) −45.8345 −1.75381 −0.876904 0.480665i \(-0.840395\pi\)
−0.876904 + 0.480665i \(0.840395\pi\)
\(684\) −21.4347 −0.819578
\(685\) −13.2543 −0.506419
\(686\) 55.1166 2.10436
\(687\) 11.4562 0.437080
\(688\) 40.8317 1.55669
\(689\) −11.3322 −0.431722
\(690\) −9.03411 −0.343923
\(691\) −43.0759 −1.63869 −0.819343 0.573304i \(-0.805661\pi\)
−0.819343 + 0.573304i \(0.805661\pi\)
\(692\) −56.6493 −2.15348
\(693\) −8.94903 −0.339945
\(694\) 40.8107 1.54915
\(695\) −9.07019 −0.344052
\(696\) 0.375314 0.0142263
\(697\) −12.3196 −0.466639
\(698\) −0.564691 −0.0213739
\(699\) −10.4366 −0.394748
\(700\) −0.883748 −0.0334025
\(701\) 30.4099 1.14857 0.574283 0.818657i \(-0.305281\pi\)
0.574283 + 0.818657i \(0.305281\pi\)
\(702\) −2.73802 −0.103340
\(703\) −3.36189 −0.126796
\(704\) 125.332 4.72364
\(705\) −7.38435 −0.278111
\(706\) 43.2848 1.62904
\(707\) 6.52933 0.245561
\(708\) −68.7955 −2.58549
\(709\) 8.91063 0.334646 0.167323 0.985902i \(-0.446488\pi\)
0.167323 + 0.985902i \(0.446488\pi\)
\(710\) −27.9705 −1.04972
\(711\) 3.50200 0.131335
\(712\) −88.4158 −3.31352
\(713\) −0.419860 −0.0157239
\(714\) 11.8213 0.442401
\(715\) 9.03626 0.337937
\(716\) −137.249 −5.12925
\(717\) −4.27431 −0.159627
\(718\) 62.7928 2.34341
\(719\) 4.70263 0.175379 0.0876893 0.996148i \(-0.472052\pi\)
0.0876893 + 0.996148i \(0.472052\pi\)
\(720\) 34.2794 1.27752
\(721\) 2.23039 0.0830640
\(722\) −10.3874 −0.386577
\(723\) 15.5365 0.577810
\(724\) −108.271 −4.02386
\(725\) −0.00282574 −0.000104945 0
\(726\) −13.9603 −0.518117
\(727\) −41.4810 −1.53844 −0.769222 0.638981i \(-0.779356\pi\)
−0.769222 + 0.638981i \(0.779356\pi\)
\(728\) −21.3542 −0.791441
\(729\) 1.00000 0.0370370
\(730\) 47.4673 1.75684
\(731\) 5.19284 0.192064
\(732\) −8.10916 −0.299723
\(733\) −24.8936 −0.919465 −0.459733 0.888057i \(-0.652055\pi\)
−0.459733 + 0.888057i \(0.652055\pi\)
\(734\) −59.9491 −2.21276
\(735\) 4.56139 0.168249
\(736\) 33.0030 1.21651
\(737\) 13.3862 0.493088
\(738\) −17.4255 −0.641442
\(739\) −11.6467 −0.428431 −0.214216 0.976786i \(-0.568720\pi\)
−0.214216 + 0.976786i \(0.568720\pi\)
\(740\) 10.6727 0.392335
\(741\) 3.89952 0.143252
\(742\) 69.2040 2.54056
\(743\) −30.6055 −1.12281 −0.561403 0.827543i \(-0.689738\pi\)
−0.561403 + 0.827543i \(0.689738\pi\)
\(744\) 2.74380 0.100593
\(745\) 43.5755 1.59648
\(746\) −77.5214 −2.83826
\(747\) −6.37677 −0.233314
\(748\) 42.6924 1.56099
\(749\) 15.4115 0.563124
\(750\) 30.3874 1.10959
\(751\) −29.1830 −1.06490 −0.532451 0.846461i \(-0.678729\pi\)
−0.532451 + 0.846461i \(0.678729\pi\)
\(752\) 49.9068 1.81991
\(753\) 3.10336 0.113093
\(754\) −0.107332 −0.00390880
\(755\) 16.9312 0.616190
\(756\) 12.2599 0.445889
\(757\) 15.0268 0.546158 0.273079 0.961992i \(-0.411958\pi\)
0.273079 + 0.961992i \(0.411958\pi\)
\(758\) −12.7635 −0.463590
\(759\) −5.87828 −0.213368
\(760\) −84.0829 −3.05001
\(761\) 12.0306 0.436111 0.218055 0.975936i \(-0.430029\pi\)
0.218055 + 0.975936i \(0.430029\pi\)
\(762\) −51.2161 −1.85536
\(763\) −2.88792 −0.104550
\(764\) −92.3989 −3.34287
\(765\) 4.35955 0.157620
\(766\) −69.5873 −2.51429
\(767\) 12.5156 0.451913
\(768\) −48.3444 −1.74448
\(769\) −3.09469 −0.111598 −0.0557988 0.998442i \(-0.517771\pi\)
−0.0557988 + 0.998442i \(0.517771\pi\)
\(770\) −55.1831 −1.98866
\(771\) 17.7908 0.640719
\(772\) −75.3931 −2.71346
\(773\) −34.2136 −1.23058 −0.615289 0.788301i \(-0.710961\pi\)
−0.615289 + 0.788301i \(0.710961\pi\)
\(774\) 7.34504 0.264012
\(775\) −0.0206581 −0.000742059 0
\(776\) −166.040 −5.96049
\(777\) 1.92289 0.0689831
\(778\) 62.6491 2.24608
\(779\) 24.8176 0.889183
\(780\) −12.3794 −0.443254
\(781\) −18.1998 −0.651239
\(782\) 7.76498 0.277675
\(783\) 0.0392005 0.00140091
\(784\) −30.8279 −1.10100
\(785\) 15.3295 0.547132
\(786\) −46.0543 −1.64270
\(787\) 37.0412 1.32038 0.660188 0.751101i \(-0.270477\pi\)
0.660188 + 0.751101i \(0.270477\pi\)
\(788\) −20.4673 −0.729118
\(789\) 6.04045 0.215046
\(790\) 21.5946 0.768302
\(791\) −30.8125 −1.09556
\(792\) 38.4148 1.36501
\(793\) 1.47526 0.0523880
\(794\) 24.0111 0.852120
\(795\) 25.5216 0.905157
\(796\) 117.161 4.15265
\(797\) 35.2454 1.24846 0.624228 0.781242i \(-0.285414\pi\)
0.624228 + 0.781242i \(0.285414\pi\)
\(798\) −23.8138 −0.842999
\(799\) 6.34698 0.224540
\(800\) 1.62382 0.0574108
\(801\) −9.23478 −0.326295
\(802\) −28.2235 −0.996608
\(803\) 30.8858 1.08994
\(804\) −18.3387 −0.646758
\(805\) −7.35917 −0.259377
\(806\) −0.784668 −0.0276387
\(807\) 16.9184 0.595556
\(808\) −28.0280 −0.986020
\(809\) 27.9356 0.982163 0.491082 0.871114i \(-0.336602\pi\)
0.491082 + 0.871114i \(0.336602\pi\)
\(810\) 6.16638 0.216664
\(811\) −15.2507 −0.535524 −0.267762 0.963485i \(-0.586284\pi\)
−0.267762 + 0.963485i \(0.586284\pi\)
\(812\) 0.480595 0.0168656
\(813\) 16.4202 0.575882
\(814\) 9.47120 0.331966
\(815\) 56.4132 1.97607
\(816\) −29.4638 −1.03144
\(817\) −10.4609 −0.365980
\(818\) −84.8592 −2.96703
\(819\) −2.23039 −0.0779361
\(820\) −78.7860 −2.75133
\(821\) 5.78489 0.201894 0.100947 0.994892i \(-0.467813\pi\)
0.100947 + 0.994892i \(0.467813\pi\)
\(822\) 16.1138 0.562035
\(823\) 49.3605 1.72060 0.860299 0.509790i \(-0.170277\pi\)
0.860299 + 0.509790i \(0.170277\pi\)
\(824\) −9.57422 −0.333534
\(825\) −0.289225 −0.0100695
\(826\) −76.4311 −2.65938
\(827\) −29.1946 −1.01519 −0.507597 0.861594i \(-0.669466\pi\)
−0.507597 + 0.861594i \(0.669466\pi\)
\(828\) 8.05309 0.279864
\(829\) 7.10218 0.246669 0.123335 0.992365i \(-0.460641\pi\)
0.123335 + 0.992365i \(0.460641\pi\)
\(830\) −39.3216 −1.36487
\(831\) 7.13667 0.247568
\(832\) 31.2369 1.08294
\(833\) −3.92060 −0.135841
\(834\) 11.0271 0.381836
\(835\) −27.3356 −0.945987
\(836\) −86.0030 −2.97448
\(837\) 0.286582 0.00990572
\(838\) 71.2736 2.46211
\(839\) −13.2473 −0.457346 −0.228673 0.973503i \(-0.573439\pi\)
−0.228673 + 0.973503i \(0.573439\pi\)
\(840\) 48.0925 1.65935
\(841\) −28.9985 −0.999947
\(842\) 16.0451 0.552950
\(843\) 8.08608 0.278499
\(844\) −1.90978 −0.0657375
\(845\) 2.25213 0.0774756
\(846\) 8.97752 0.308653
\(847\) −11.3721 −0.390749
\(848\) −172.486 −5.92320
\(849\) −1.86933 −0.0641552
\(850\) 0.382055 0.0131044
\(851\) 1.26307 0.0432975
\(852\) 24.9332 0.854197
\(853\) 33.7902 1.15695 0.578477 0.815698i \(-0.303647\pi\)
0.578477 + 0.815698i \(0.303647\pi\)
\(854\) −9.00920 −0.308288
\(855\) −8.78222 −0.300346
\(856\) −66.1558 −2.26116
\(857\) 0.434238 0.0148333 0.00741664 0.999972i \(-0.497639\pi\)
0.00741664 + 0.999972i \(0.497639\pi\)
\(858\) −10.9858 −0.375050
\(859\) −28.5717 −0.974855 −0.487427 0.873164i \(-0.662065\pi\)
−0.487427 + 0.873164i \(0.662065\pi\)
\(860\) 33.2091 1.13242
\(861\) −14.1948 −0.483757
\(862\) 61.0770 2.08029
\(863\) 48.2336 1.64189 0.820946 0.571007i \(-0.193447\pi\)
0.820946 + 0.571007i \(0.193447\pi\)
\(864\) −22.5267 −0.766375
\(865\) −23.2103 −0.789173
\(866\) 34.3875 1.16853
\(867\) 13.2529 0.450092
\(868\) 3.51347 0.119255
\(869\) 14.0511 0.476652
\(870\) 0.241725 0.00819525
\(871\) 3.33628 0.113046
\(872\) 12.3968 0.419807
\(873\) −17.3424 −0.586952
\(874\) −15.6424 −0.529112
\(875\) 24.7535 0.836822
\(876\) −42.3127 −1.42962
\(877\) −3.21501 −0.108563 −0.0542817 0.998526i \(-0.517287\pi\)
−0.0542817 + 0.998526i \(0.517287\pi\)
\(878\) 55.8892 1.88617
\(879\) 2.61365 0.0881562
\(880\) 137.540 4.63647
\(881\) 36.9025 1.24328 0.621639 0.783304i \(-0.286467\pi\)
0.621639 + 0.783304i \(0.286467\pi\)
\(882\) −5.54550 −0.186727
\(883\) 22.2626 0.749196 0.374598 0.927187i \(-0.377781\pi\)
0.374598 + 0.927187i \(0.377781\pi\)
\(884\) 10.6403 0.357873
\(885\) −28.1868 −0.947489
\(886\) −18.7541 −0.630056
\(887\) −18.7149 −0.628383 −0.314192 0.949360i \(-0.601733\pi\)
−0.314192 + 0.949360i \(0.601733\pi\)
\(888\) −8.25423 −0.276994
\(889\) −41.7205 −1.39926
\(890\) −56.9451 −1.90881
\(891\) 4.01232 0.134418
\(892\) −48.8303 −1.63496
\(893\) −12.7859 −0.427863
\(894\) −52.9768 −1.77181
\(895\) −56.2337 −1.87968
\(896\) −90.2722 −3.01578
\(897\) −1.46506 −0.0489169
\(898\) 52.0627 1.73735
\(899\) 0.0112342 0.000374680 0
\(900\) 0.396230 0.0132077
\(901\) −21.9362 −0.730802
\(902\) −69.9167 −2.32797
\(903\) 5.98325 0.199110
\(904\) 132.266 4.39911
\(905\) −44.3607 −1.47460
\(906\) −20.5841 −0.683861
\(907\) 27.6472 0.918009 0.459005 0.888434i \(-0.348206\pi\)
0.459005 + 0.888434i \(0.348206\pi\)
\(908\) −84.3656 −2.79977
\(909\) −2.92744 −0.0970971
\(910\) −13.7534 −0.455921
\(911\) −56.2268 −1.86288 −0.931438 0.363899i \(-0.881445\pi\)
−0.931438 + 0.363899i \(0.881445\pi\)
\(912\) 59.3542 1.96541
\(913\) −25.5856 −0.846760
\(914\) 80.1451 2.65096
\(915\) −3.32248 −0.109838
\(916\) −62.9718 −2.08065
\(917\) −37.5157 −1.23888
\(918\) −5.30011 −0.174930
\(919\) 49.4192 1.63019 0.815095 0.579327i \(-0.196685\pi\)
0.815095 + 0.579327i \(0.196685\pi\)
\(920\) 31.5902 1.04150
\(921\) −13.8308 −0.455741
\(922\) −87.4509 −2.88004
\(923\) −4.53598 −0.149303
\(924\) 49.1907 1.61826
\(925\) 0.0621460 0.00204335
\(926\) 19.9132 0.654390
\(927\) −1.00000 −0.0328443
\(928\) −0.883059 −0.0289878
\(929\) −6.98607 −0.229206 −0.114603 0.993411i \(-0.536560\pi\)
−0.114603 + 0.993411i \(0.536560\pi\)
\(930\) 1.76717 0.0579479
\(931\) 7.89796 0.258845
\(932\) 57.3675 1.87914
\(933\) −1.27395 −0.0417072
\(934\) 54.5008 1.78332
\(935\) 17.4919 0.572046
\(936\) 9.57422 0.312943
\(937\) −53.0486 −1.73302 −0.866511 0.499158i \(-0.833643\pi\)
−0.866511 + 0.499158i \(0.833643\pi\)
\(938\) −20.3742 −0.665240
\(939\) −2.55357 −0.0833326
\(940\) 40.5901 1.32390
\(941\) 60.1422 1.96058 0.980290 0.197563i \(-0.0633028\pi\)
0.980290 + 0.197563i \(0.0633028\pi\)
\(942\) −18.6368 −0.607219
\(943\) −9.32404 −0.303632
\(944\) 190.499 6.20022
\(945\) 5.02312 0.163402
\(946\) 29.4706 0.958173
\(947\) 43.9056 1.42674 0.713370 0.700787i \(-0.247168\pi\)
0.713370 + 0.700787i \(0.247168\pi\)
\(948\) −19.2496 −0.625199
\(949\) 7.69775 0.249880
\(950\) −0.769642 −0.0249705
\(951\) −17.1973 −0.557659
\(952\) −41.3364 −1.33972
\(953\) −19.5581 −0.633548 −0.316774 0.948501i \(-0.602600\pi\)
−0.316774 + 0.948501i \(0.602600\pi\)
\(954\) −31.0278 −1.00456
\(955\) −37.8576 −1.22504
\(956\) 23.4949 0.759879
\(957\) 0.157285 0.00508430
\(958\) −115.180 −3.72131
\(959\) 13.1263 0.423871
\(960\) −70.3494 −2.27052
\(961\) −30.9179 −0.997351
\(962\) 2.36053 0.0761066
\(963\) −6.90978 −0.222665
\(964\) −85.4006 −2.75057
\(965\) −30.8900 −0.994383
\(966\) 8.94690 0.287862
\(967\) −8.97958 −0.288764 −0.144382 0.989522i \(-0.546119\pi\)
−0.144382 + 0.989522i \(0.546119\pi\)
\(968\) 48.8160 1.56901
\(969\) 7.54848 0.242492
\(970\) −106.940 −3.43363
\(971\) −42.9997 −1.37992 −0.689962 0.723845i \(-0.742373\pi\)
−0.689962 + 0.723845i \(0.742373\pi\)
\(972\) −5.49677 −0.176309
\(973\) 8.98264 0.287970
\(974\) −87.4435 −2.80187
\(975\) −0.0720843 −0.00230854
\(976\) 22.4548 0.718760
\(977\) 45.3026 1.44936 0.724680 0.689086i \(-0.241988\pi\)
0.724680 + 0.689086i \(0.241988\pi\)
\(978\) −68.5843 −2.19308
\(979\) −37.0529 −1.18421
\(980\) −25.0729 −0.800924
\(981\) 1.29481 0.0413400
\(982\) −35.3313 −1.12747
\(983\) 36.6821 1.16998 0.584988 0.811042i \(-0.301099\pi\)
0.584988 + 0.811042i \(0.301099\pi\)
\(984\) 60.9330 1.94247
\(985\) −8.38585 −0.267195
\(986\) −0.207767 −0.00661666
\(987\) 7.31307 0.232778
\(988\) −21.4347 −0.681930
\(989\) 3.93018 0.124972
\(990\) 24.7415 0.786336
\(991\) −8.80711 −0.279767 −0.139884 0.990168i \(-0.544673\pi\)
−0.139884 + 0.990168i \(0.544673\pi\)
\(992\) −6.45575 −0.204970
\(993\) −6.63238 −0.210472
\(994\) 27.7005 0.878608
\(995\) 48.0030 1.52180
\(996\) 35.0516 1.11065
\(997\) −16.2359 −0.514195 −0.257098 0.966385i \(-0.582766\pi\)
−0.257098 + 0.966385i \(0.582766\pi\)
\(998\) 95.5522 3.02465
\(999\) −0.862130 −0.0272766
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 \(a_p\))